LMFDB - Embedded newform 425.2.p.a.16.8

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			16.8
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.58733 - 1.15326i) q^{2} +(2.60850 - 0.847551i) q^{3} +(0.571562 + 1.75909i) q^{4} +(0.656872 + 2.13741i) q^{5} +(-5.11798 - 1.66293i) q^{6} +2.38074i q^{7} +(-0.0911795 + 0.280622i) q^{8} +(3.65885 - 2.65831i) q^{9} +(1.42232 - 4.15031i) q^{10} +(-2.86011 + 3.93660i) q^{11} +(2.98183 + 4.10414i) q^{12} +(1.71250 - 1.24420i) q^{13} +(2.74561 - 3.77901i) q^{14} +(3.52501 + 5.01869i) q^{15} +(3.46110 - 2.51464i) q^{16} +(4.10875 + 0.343741i) q^{17} -8.87352 q^{18} +(0.394408 - 1.21386i) q^{19} +(-3.38445 + 2.37716i) q^{20} +(2.01780 + 6.21015i) q^{21} +(9.07986 - 2.95022i) q^{22} +(-2.05007 + 2.82167i) q^{23} +0.809280i q^{24} +(-4.13704 + 2.80801i) q^{25} -4.15318 q^{26} +(2.45463 - 3.37850i) q^{27} +(-4.18793 + 1.36074i) q^{28} +(9.79249 - 3.18177i) q^{29} +(0.192508 - 12.0316i) q^{30} +(-1.13128 - 0.367576i) q^{31} -7.80380 q^{32} +(-4.12411 + 12.6927i) q^{33} +(-6.12551 - 5.28409i) q^{34} +(-5.08862 + 1.56384i) q^{35} +(6.76747 + 4.91685i) q^{36} +(-5.57451 - 7.67265i) q^{37} +(-2.02595 + 1.47194i) q^{38} +(3.41252 - 4.69692i) q^{39} +(-0.659697 - 0.0105553i) q^{40} +(2.55451 + 3.51598i) q^{41} +(3.95901 - 12.1846i) q^{42} -6.70123 q^{43} +(-8.55956 - 2.78117i) q^{44} +(8.08530 + 6.07429i) q^{45} +(6.50825 - 2.11466i) q^{46} +(0.401562 + 1.23588i) q^{47} +(6.89698 - 9.49288i) q^{48} +1.33208 q^{49} +(9.80520 + 0.313852i) q^{50} +(11.0090 - 2.58573i) q^{51} +(3.16746 + 2.30129i) q^{52} +(-2.53638 - 7.80616i) q^{53} +(-7.79259 + 2.53197i) q^{54} +(-10.2929 - 3.52738i) q^{55} +(-0.668087 - 0.217075i) q^{56} -3.50064i q^{57} +(-19.2133 - 6.24278i) q^{58} +(5.35824 - 3.89299i) q^{59} +(-6.81355 + 9.06930i) q^{60} +(7.63310 - 10.5061i) q^{61} +(1.37181 + 1.88813i) q^{62} +(6.32875 + 8.71078i) q^{63} +(5.46498 + 3.97054i) q^{64} +(3.78426 + 2.84303i) q^{65} +(21.1843 - 15.3913i) q^{66} +(2.26955 - 6.98497i) q^{67} +(1.74374 + 7.42412i) q^{68} +(-2.95607 + 9.09786i) q^{69} +(9.88081 + 3.38617i) q^{70} +(-8.07004 + 2.62211i) q^{71} +(0.412368 + 1.26914i) q^{72} +(0.863598 - 1.18864i) q^{73} +18.6079i q^{74} +(-8.41151 + 10.8310i) q^{75} +2.36072 q^{76} +(-9.37203 - 6.80918i) q^{77} +(-10.8336 + 3.52003i) q^{78} +(4.40451 - 1.43111i) q^{79} +(7.64831 + 5.74599i) q^{80} +(-0.653245 + 2.01048i) q^{81} -8.52703i q^{82} +(-2.47300 + 7.61111i) q^{83} +(-9.77090 + 7.09897i) q^{84} +(1.96421 + 9.00788i) q^{85} +(10.6370 + 7.72826i) q^{86} +(22.8469 - 16.5993i) q^{87} +(-0.843913 - 1.16155i) q^{88} +(-3.36173 - 2.44244i) q^{89} +(-5.82877 - 18.9663i) q^{90} +(2.96212 + 4.07701i) q^{91} +(-6.13531 - 1.99348i) q^{92} -3.26249 q^{93} +(0.787881 - 2.42485i) q^{94} +(2.85360 + 0.0456584i) q^{95} +(-20.3562 + 6.61412i) q^{96} +(-9.23012 + 2.99905i) q^{97} +(-2.11444 - 1.53623i) q^{98} +22.0065i 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 $

$2$	−1.58733	−	1.15326i	−1.12241	−	0.815478i	−0.137837	−	0.990455i	$-0.544015\pi$
$2$	−1.58733	−	1.15326i	−1.12241	−	0.815478i	−0.984573	+	0.174977i	$0.944015\pi$
$3$	2.60850	−	0.847551i	1.50602	−	0.489334i	0.564250	−	0.825604i	$-0.309165\pi$
$3$	2.60850	−	0.847551i	1.50602	−	0.489334i	0.941766	+	0.336270i	$0.109165\pi$
$4$	0.571562	+	1.75909i	0.285781	+	0.879544i
$5$	0.656872	+	2.13741i	0.293762	+	0.955879i
$5$	0.656872	+	2.13741i	0.293762	+	0.955879i
$6$	−5.11798	−	1.66293i	−2.08941	−	0.678889i
$7$			2.38074i			0.899835i	0.893070	+	0.449917i	$0.148547\pi$
$7$			2.38074i			0.899835i	−0.893070	+	0.449917i	$0.851453\pi$
$8$	−0.0911795	+	0.280622i	−0.0322368	+	0.0992147i
$9$	3.65885	−	2.65831i	1.21962	−	0.886104i
$10$	1.42232	−	4.15031i	0.449777	−	1.31244i
$11$	−2.86011	+	3.93660i	−0.862356	+	1.18693i	0.118647	+	0.992937i	$0.462144\pi$
$11$	−2.86011	+	3.93660i	−0.862356	+	1.18693i	−0.981003	+	0.193994i	$0.937856\pi$
$12$	2.98183	+	4.10414i	0.860782	+	1.18476i
$13$	1.71250	−	1.24420i	0.474961	−	0.345080i	−0.324410	−	0.945916i	$-0.605166\pi$
$13$	1.71250	−	1.24420i	0.474961	−	0.345080i	0.799372	+	0.600837i	$0.205166\pi$
$14$	2.74561	−	3.77901i	0.733796	−	1.00998i
$15$	3.52501	+	5.01869i	0.910154	+	1.29582i
$16$	3.46110	−	2.51464i	0.865275	−	0.628659i
$17$	4.10875	+	0.343741i	0.996519	+	0.0833694i
$17$	4.10875	+	0.343741i	0.996519	+	0.0833694i
$18$	−8.87352			−2.09151
$19$	0.394408	−	1.21386i	0.0904834	−	0.278479i	−0.895567	−	0.444927i	$-0.853230\pi$
$19$	0.394408	−	1.21386i	0.0904834	−	0.278479i	0.986050	+	0.166448i	$0.0532297\pi$
$20$	−3.38445	+	2.37716i	−0.756785	+	0.531549i
$21$	2.01780	+	6.21015i	0.440320	+	1.35517i
$22$	9.07986	−	2.95022i	1.93583	−	0.628990i
$23$	−2.05007	+	2.82167i	−0.427468	+	0.588360i	−0.967370	−	0.253368i	$-0.918462\pi$
$23$	−2.05007	+	2.82167i	−0.427468	+	0.588360i	0.539901	+	0.841728i	$0.318462\pi$
$24$			0.809280i			0.165194i
$25$	−4.13704	+	2.80801i	−0.827408	+	0.561602i
$26$	−4.15318			−0.814506
$27$	2.45463	−	3.37850i	0.472393	−	0.650194i
$28$	−4.18793	+	1.36074i	−0.791444	+	0.257156i
$29$	9.79249	−	3.18177i	1.81842	−	0.590840i	0.818554	−	0.574429i	$-0.194776\pi$
$29$	9.79249	−	3.18177i	1.81842	−	0.590840i	0.999865	−	0.0164111i	$-0.00522405\pi$
$30$	0.192508	−	12.0316i	0.0351471	−	2.19665i
$31$	−1.13128	−	0.367576i	−0.203184	−	0.0660186i	0.205657	−	0.978624i	$-0.434067\pi$
$31$	−1.13128	−	0.367576i	−0.203184	−	0.0660186i	−0.408841	+	0.912606i	$0.634067\pi$
$32$	−7.80380			−1.37953
$33$	−4.12411	+	12.6927i	−0.717915	+	2.20952i
$34$	−6.12551	−	5.28409i	−1.05052	−	0.906214i
$35$	−5.08862	+	1.56384i	−0.860133	+	0.264338i
$36$	6.76747	+	4.91685i	1.12791	+	0.819475i
$37$	−5.57451	−	7.67265i	−0.916443	−	1.26138i	−0.964918	−	0.262551i	$-0.915436\pi$
$37$	−5.57451	−	7.67265i	−0.916443	−	1.26138i	0.0484749	−	0.998824i	$-0.484564\pi$
$38$	−2.02595	+	1.47194i	−0.328653	+	0.238781i
$39$	3.41252	−	4.69692i	0.546440	−	0.752110i
$40$	−0.659697	−	0.0105553i	−0.104307	−	0.00166895i
$41$	2.55451	+	3.51598i	0.398948	+	0.549104i	0.960479	−	0.278351i	$-0.0897878\pi$
$41$	2.55451	+	3.51598i	0.398948	+	0.549104i	−0.561532	+	0.827455i	$0.689788\pi$
$42$	3.95901	−	12.1846i	0.610888	−	1.88012i
$43$	−6.70123			−1.02193			−0.510964	−	0.859602i	$-0.670711\pi$
$43$	−6.70123			−1.02193			−0.510964	+	0.859602i	$0.670711\pi$
$44$	−8.55956	−	2.78117i	−1.29040	−	0.419277i
$45$	8.08530	+	6.07429i	1.20529	+	0.905502i
$46$	6.50825	−	2.11466i	0.959589	−	0.311789i
$47$	0.401562	+	1.23588i	0.0585738	+	0.180272i	0.976062	−	0.217490i	$-0.0697870\pi$
$47$	0.401562	+	1.23588i	0.0585738	+	0.180272i	−0.917489	+	0.397762i	$0.869787\pi$
$48$	6.89698	−	9.49288i	0.995493	−	1.37018i
$49$	1.33208			0.190297
$50$	9.80520	+	0.313852i	1.38666	+	0.0443854i
$51$	11.0090	−	2.58573i	1.54157	−	0.362075i
$52$	3.16746	+	2.30129i	0.439248	+	0.319132i
$53$	−2.53638	−	7.80616i	−0.348398	−	1.07226i	−0.959739	−	0.280892i	$-0.909370\pi$
$53$	−2.53638	−	7.80616i	−0.348398	−	1.07226i	0.611341	−	0.791367i	$-0.290630\pi$
$54$	−7.79259	+	2.53197i	−1.06044	+	0.344557i
$55$	−10.2929	−	3.52738i	−1.38789	−	0.475632i
$56$	−0.668087	−	0.217075i	−0.0892769	−	0.0290078i
$57$		−	3.50064i		−	0.463671i
$58$	−19.2133	−	6.24278i	−2.52283	−	0.819717i
$59$	5.35824	−	3.89299i	0.697583	−	0.506824i	−0.181561	−	0.983380i	$-0.558115\pi$
$59$	5.35824	−	3.89299i	0.697583	−	0.506824i	0.879144	+	0.476556i	$0.158115\pi$
$60$	−6.81355	+	9.06930i	−0.879626	+	1.17084i
$61$	7.63310	−	10.5061i	0.977319	−	1.34516i	0.0390573	−	0.999237i	$-0.487565\pi$
$61$	7.63310	−	10.5061i	0.977319	−	1.34516i	0.938261	−	0.345927i	$-0.112435\pi$
$62$	1.37181	+	1.88813i	0.174219	+	0.239792i
$63$	6.32875	+	8.71078i	0.797347	+	1.09745i
$64$	5.46498	+	3.97054i	0.683122	+	0.496317i
$65$	3.78426	+	2.84303i	0.469380	+	0.352634i
$66$	21.1843	−	15.3913i	2.60761	−	1.89454i
$67$	2.26955	−	6.98497i	0.277270	−	0.853350i	−0.711340	−	0.702848i	$-0.751911\pi$
$67$	2.26955	−	6.98497i	0.277270	−	0.853350i	0.988610	−	0.150501i	$-0.0480888\pi$
$68$	1.74374	+	7.42412i	0.211459	+	0.900307i
$69$	−2.95607	+	9.09786i	−0.355870	+	1.09525i
$70$	9.88081	+	3.38617i	1.18098	+	0.404725i
$71$	−8.07004	+	2.62211i	−0.957738	+	0.311188i	−0.745856	−	0.666108i	$-0.767959\pi$
$71$	−8.07004	+	2.62211i	−0.957738	+	0.311188i	−0.211882	+	0.977295i	$0.567959\pi$
$72$	0.412368	+	1.26914i	0.0485980	+	0.149569i
$73$	0.863598	−	1.18864i	0.101076	−	0.139120i	−0.755483	−	0.655168i	$-0.772598\pi$
$73$	0.863598	−	1.18864i	0.101076	−	0.139120i	0.856559	+	0.516049i	$0.172598\pi$
$74$			18.6079i			2.16312i
$75$	−8.41151	+	10.8310i	−0.971278	+	1.25066i
$76$	2.36072			0.270793
$77$	−9.37203	−	6.80918i	−1.06804	−	0.775978i
$78$	−10.8336	+	3.52003i	−1.22666	+	0.398565i
$79$	4.40451	−	1.43111i	0.495547	−	0.161013i	−0.0505725	−	0.998720i	$-0.516105\pi$
$79$	4.40451	−	1.43111i	0.495547	−	0.161013i	0.546119	+	0.837708i	$0.316105\pi$
$80$	7.64831	+	5.74599i	0.855107	+	0.642422i
$81$	−0.653245	+	2.01048i	−0.0725828	+	0.223387i
$82$		−	8.52703i		−	0.941653i
$83$	−2.47300	+	7.61111i	−0.271447	+	0.835427i	0.718691	+	0.695330i	$0.244742\pi$
$83$	−2.47300	+	7.61111i	−0.271447	+	0.835427i	−0.990138	+	0.140098i	$0.955258\pi$
$84$	−9.77090	+	7.09897i	−1.06609	+	0.774561i
$85$	1.96421	+	9.00788i	0.213049	+	0.977042i
$86$	10.6370	+	7.72826i	1.14702	+	0.833360i
$87$	22.8469	−	16.5993i	2.44945	−	1.77963i
$88$	−0.843913	−	1.16155i	−0.0899614	−	0.123821i
$89$	−3.36173	−	2.44244i	−0.356343	−	0.258898i	0.395182	−	0.918603i	$-0.370681\pi$
$89$	−3.36173	−	2.44244i	−0.356343	−	0.258898i	−0.751525	+	0.659705i	$0.770681\pi$
$90$	−5.82877	−	18.9663i	−0.614406	−	1.99923i
$91$	2.96212	+	4.07701i	0.310515	+	0.427387i
$92$	−6.13531	−	1.99348i	−0.639651	−	0.207835i
$93$	−3.26249			−0.338304
$94$	0.787881	−	2.42485i	0.0812637	−	0.250104i
$95$	2.85360	+	0.0456584i	0.292773	+	0.00468446i
$96$	−20.3562	+	6.61412i	−2.07759	+	0.675051i
$97$	−9.23012	+	2.99905i	−0.937177	+	0.304507i	−0.737494	−	0.675354i	$-0.763991\pi$
$97$	−9.23012	+	2.99905i	−0.937177	+	0.304507i	−0.199682	+	0.979861i	$0.563991\pi$
$98$	−2.11444	−	1.53623i	−0.213591	−	0.155183i
$99$			22.0065i			2.21174i
$100$	−7.30411	−	5.67246i	−0.730411	−	0.567246i
$101$	−19.0997			−1.90049			−0.950246	−	0.311501i	$-0.899168\pi$
$101$	−19.0997			−1.90049			−0.950246	+	0.311501i	$0.899168\pi$
$102$	−20.4569	−	8.59184i	−2.02553	−	0.850719i
$103$	−2.68808	−	8.27305i	−0.264864	−	0.815167i	−0.991725	−	0.128383i	$-0.959021\pi$
$103$	−2.68808	−	8.27305i	−0.264864	−	0.815167i	0.726861	−	0.686785i	$-0.240979\pi$
$104$	0.193005	+	0.594010i	0.0189257	+	0.0582474i
$105$	−11.9482	+	8.39214i	−1.16602	+	0.818989i
$106$	−4.97648	+	15.3160i	−0.483359	+	1.48762i
$107$			5.62025i			0.543330i	0.962392	+	0.271665i	$0.0875743\pi$
$107$			5.62025i			0.543330i	−0.962392	+	0.271665i	$0.912426\pi$
$108$	7.34606	+	2.38688i	0.706875	+	0.229678i
$109$	−0.643086	−	0.885132i	−0.0615965	−	0.0847802i	0.777107	−	0.629368i	$-0.216686\pi$
$109$	−0.643086	−	0.885132i	−0.0615965	−	0.0847802i	−0.838704	+	0.544588i	$0.816686\pi$
$110$	12.2701	+	17.4695i	1.16991	+	1.66565i
$111$	−21.0440	−	15.2894i	−1.99741	−	1.45120i
$112$	5.98669	+	8.23998i	0.565689	+	0.778605i
$113$	−5.72080	−	7.87401i	−0.538168	−	0.740725i	0.450180	−	0.892938i	$-0.351360\pi$
$113$	−5.72080	−	7.87401i	−0.538168	−	0.740725i	−0.988348	+	0.152213i	$0.951360\pi$
$114$	−4.03715	+	5.55665i	−0.378113	+	0.520428i
$115$	−7.37771	−	2.52835i	−0.687975	−	0.235770i
$116$	11.1940	+	15.4073i	1.03934	+	1.43053i
$117$	2.95830	−	9.10470i	0.273495	−	0.841730i
$118$	−12.9949			−1.19628
$119$	−0.818357	+	9.78187i	−0.0750187	+	0.896702i
$120$	−1.72976	+	0.531593i	−0.157905	+	0.0485276i
$121$	−3.91744	−	12.0566i	−0.356130	−	1.09606i
$122$	−24.2325	+	7.87360i	−2.19390	+	0.712842i
$123$	9.64341	+	7.00634i	0.869517	+	0.631741i
$124$		−	2.20012i		−	0.197577i
$125$	−8.71937	−	6.99804i	−0.779884	−	0.625924i
$126$		−	21.1255i		−	1.88201i
$127$	15.3222	+	11.1323i	1.35963	+	0.987828i	0.998468	+	0.0553239i	$0.0176191\pi$
$127$	15.3222	+	11.1323i	1.35963	+	0.987828i	0.361160	+	0.932504i	$0.382381\pi$
$128$	0.727374	+	2.23863i	0.0642914	+	0.197869i
$129$	−17.4801	+	5.67964i	−1.53904	+	0.500064i
$130$	−2.72811	−	8.87705i	−0.239271	−	0.778569i
$131$	15.7549	+	5.11907i	1.37651	+	0.447255i	0.901521	−	0.432736i	$-0.142452\pi$
$131$	15.7549	+	5.11907i	1.37651	+	0.447255i	0.474990	+	0.879991i	$0.342452\pi$
$132$	−24.6848			−2.14853
$133$	2.88989	+	0.938983i	0.250585	+	0.0814201i
$134$	−11.6580	+	8.47004i	−1.00710	+	0.731700i
$135$	8.83362	+	3.02730i	0.760277	+	0.260548i
$136$	−0.471095	+	1.12166i	−0.0403961	+	0.0961818i
$137$	−4.08944	+	2.97116i	−0.349385	+	0.253843i	−0.748611	−	0.663010i	$-0.769279\pi$
$137$	−4.08944	+	2.97116i	−0.349385	+	0.253843i	0.399226	+	0.916853i	$0.369279\pi$
$138$	15.1845	−	11.0322i	1.29259	−	0.939119i
$139$	6.49705	−	8.94242i	0.551072	−	0.758486i	−0.439085	−	0.898446i	$-0.644697\pi$
$139$	6.49705	−	8.94242i	0.551072	−	0.758486i	0.990157	+	0.139960i	$0.0446973\pi$
$140$	−5.65940	−	8.05749i	−0.478306	−	0.680982i
$141$	2.09494	+	2.88344i	0.176426	+	0.242830i
$142$	15.8338	+	5.14470i	1.32874	+	0.431734i
$143$			10.3000i			0.861328i
$144$	5.97897	−	18.4014i	0.498247	−	1.53345i
$145$	13.2332	+	18.8405i	1.09895	+	1.56462i
$146$	−2.74162	+	0.890807i	−0.226898	+	0.0737237i
$147$	3.47472	−	1.12901i	0.286590	−	0.0931188i
$148$	10.3107	−	14.1914i	0.847533	−	1.16653i
$149$	18.4354			1.51029			0.755145	−	0.655558i	$-0.227567\pi$
$149$	18.4354			1.51029			0.755145	+	0.655558i	$0.227567\pi$
$150$	25.8428	−	7.49173i	2.11006	−	0.611697i
$151$	11.0367			0.898157			0.449078	−	0.893492i	$-0.351752\pi$
$151$	11.0367			0.898157			0.449078	+	0.893492i	$0.351752\pi$
$152$	0.304674	+	0.221359i	0.0247124	+	0.0179546i
$153$	15.9471	−	9.66465i	1.28925	−	0.781340i
$154$	7.02372	+	21.6168i	0.565987	+	1.74193i
$155$	0.0425523	−	2.65947i	0.00341788	−	0.213613i
$156$	10.2128	+	3.31833i	0.817676	+	0.265679i
$157$	−6.81519			−0.543911			−0.271956	−	0.962310i	$-0.587670\pi$
$157$	−6.81519			−0.543911			−0.271956	+	0.962310i	$0.587670\pi$
$158$	−8.64185	−	2.80791i	−0.687508	−	0.223385i
$159$	−13.2323	−	18.2126i	−1.04939	−	1.44436i
$160$	−5.12610	−	16.6799i	−0.405254	−	1.31866i
$161$	−6.71767	−	4.88068i	−0.529427	−	0.384651i
$162$	3.35552	−	2.43793i	0.263635	−	0.191542i
$163$	8.16977	+	11.2447i	0.639906	+	0.880755i	0.998611	−	0.0526961i	$-0.0167814\pi$
$163$	8.16977	+	11.2447i	0.639906	+	0.880755i	−0.358705	+	0.933451i	$0.616781\pi$
$164$	−4.72486	+	6.50321i	−0.368950	+	0.507816i
$165$	−29.8385	−	0.477425i	−2.32293	−	0.0371675i
$166$	12.7030	−	9.22930i	0.985947	−	0.716333i
$167$	−9.15782	−	2.97555i	−0.708653	−	0.230255i	−0.0675564	−	0.997715i	$-0.521520\pi$
$167$	−9.15782	−	2.97555i	−0.708653	−	0.230255i	−0.641097	+	0.767460i	$0.721520\pi$
$168$	−1.92668			−0.148647
$169$	−2.63261	+	8.10235i	−0.202509	+	0.623258i
$170$	7.27058	−	16.5637i	0.557628	−	1.27038i
$171$	−1.78375	−	5.48981i	−0.136406	−	0.419816i
$172$	−3.83017	−	11.7881i	−0.292048	−	0.898831i
$173$	9.28078	−	12.7739i	0.705605	−	0.971181i	−0.294276	−	0.955721i	$-0.595078\pi$
$173$	9.28078	−	12.7739i	0.705605	−	0.971181i	0.999880	−	0.0154609i	$-0.00492155\pi$
$174$	−55.4088			−4.20053
$175$	−6.68514	−	9.84921i	−0.505349	−	0.744530i
$176$			20.8171i			1.56915i
$177$	10.6774	−	14.6962i	0.802564	−	1.10464i
$178$	2.51939	+	7.75390i	0.188837	+	0.581179i
$179$	2.14980	+	6.61640i	0.160684	+	0.494533i	0.998692	−	0.0511237i	$-0.0162803\pi$
$179$	2.14980	+	6.61640i	0.160684	+	0.494533i	−0.838009	+	0.545657i	$0.816280\pi$
$180$	−6.06397	+	17.6946i	−0.451981	+	1.31888i
$181$	10.2759	+	3.33883i	0.763798	+	0.248173i	0.664908	−	0.746925i	$-0.268471\pi$
$181$	10.2759	+	3.33883i	0.763798	+	0.248173i	0.0988901	+	0.995098i	$0.468471\pi$
$182$		−	9.88764i		−	0.732921i
$183$	11.0065	−	33.8745i	0.813623	−	2.50407i
$184$	−0.604899	−	0.832572i	−0.0445938	−	0.0613780i
$185$	12.7379	−	16.9550i	0.936506	−	1.24655i
$186$	5.17863	+	3.76250i	0.379716	+	0.275880i
$187$	−13.1047	+	15.1914i	−0.958307	+	1.11090i
$188$	−1.94450	+	1.41276i	−0.141817	+	0.103036i
$189$	8.04334	+	5.84383i	0.585067	+	0.425076i
$190$	−4.47694	−	3.36342i	−0.324791	−	0.244008i
$191$	2.89436	−	2.10288i	0.209429	−	0.152159i	−0.478126	−	0.878291i	$-0.658684\pi$
$191$	2.89436	−	2.10288i	0.209429	−	0.152159i	0.687555	+	0.726132i	$0.258684\pi$
$192$	17.6206	+	5.72528i	1.27166	+	0.413187i
$193$		−	6.96428i		−	0.501300i	−0.968078	−	0.250650i	$-0.919356\pi$
$193$		−	6.96428i		−	0.501300i	0.968078	−	0.250650i	$-0.0806443\pi$
$194$	18.1099	+	5.88426i	1.30021	+	0.422465i
$195$	12.2808	+	4.20866i	0.879449	+	0.301389i
$196$	0.761366	+	2.34324i	0.0543833	+	0.167375i
$197$	−11.6645	+	3.79003i	−0.831061	+	0.270028i	−0.693492	−	0.720464i	$-0.743929\pi$
$197$	−11.6645	+	3.79003i	−0.831061	+	0.270028i	−0.137569	+	0.990492i	$0.543929\pi$
$198$	25.3792	−	34.9315i	1.80362	−	2.48248i
$199$		−	18.3192i		−	1.29862i	−0.760526	−	0.649308i	$-0.775059\pi$
$199$		−	18.3192i		−	1.29862i	0.760526	−	0.649308i	$-0.224941\pi$
$200$	−0.410775	−	1.41698i	−0.0290462	−	0.100195i
$201$		−	20.1438i		−	1.42084i
$202$	30.3175	+	22.0269i	2.13313	+	1.54981i
$203$	7.57497	+	23.3134i	0.531659	+	1.63628i
$204$	10.8409	+	17.8879i	0.759012	+	1.25240i
$205$	−5.83711	+	7.76959i	−0.407681	+	0.542652i
$206$	−5.27412	+	16.2321i	−0.367465	+	1.13094i
$207$			15.7738i			1.09636i
$208$	2.79841	−	8.61262i	0.194035	−	0.597178i
$209$	3.65045	+	5.02441i	0.252507	+	0.347546i
$210$	28.6440	+	0.458313i	1.97662	+	0.0316266i
$211$	−7.33283	+	10.0928i	−0.504813	+	0.694815i	−0.983034	−	0.183424i	$-0.941282\pi$
$211$	−7.33283	+	10.0928i	−0.504813	+	0.694815i	0.478221	+	0.878240i	$0.341282\pi$
$212$	12.2820	−	8.92342i	0.843533	−	0.612863i
$213$	−18.8283	+	13.6795i	−1.29009	+	0.937307i
$214$	6.48161	−	8.92117i	0.443074	−	0.609839i
$215$	−4.40185	−	14.3233i	−0.300204	−	0.976839i
$216$	0.724270	+	0.996872i	0.0492803	+	0.0678286i
$217$	0.875103	−	2.69329i	0.0594059	−	0.182833i
$218$			2.14664i			0.145389i
$219$	1.24526	−	3.83251i	0.0841466	−	0.258977i
$220$	0.321961	−	20.1222i	0.0217066	−	1.35664i
$221$	7.46391	−	4.52346i	0.502077	−	0.304281i
$222$	15.7711	+	48.5385i	1.05849	+	3.25769i
$223$	−1.61589	−	1.17401i	−0.108208	−	0.0786175i	0.532366	−	0.846515i	$-0.321303\pi$
$223$	−1.61589	−	1.17401i	−0.108208	−	0.0786175i	−0.640573	+	0.767897i	$0.721303\pi$
$224$		−	18.5788i		−	1.24135i
$225$	−7.67225	+	21.2716i	−0.511483	+	1.41811i
$226$			19.0962i			1.27026i
$227$	8.18898	−	11.2712i	0.543522	−	0.748094i	−0.445594	−	0.895235i	$-0.647007\pi$
$227$	8.18898	−	11.2712i	0.543522	−	0.748094i	0.989115	+	0.147142i	$0.0470073\pi$
$228$	6.15793	−	2.00083i	0.407819	−	0.132508i
$229$	−9.16139	−	28.1958i	−0.605401	−	1.86323i	−0.494008	−	0.869457i	$-0.664469\pi$
$229$	−9.16139	−	28.1958i	−0.605401	−	1.86323i	−0.111393	−	0.993776i	$-0.535531\pi$
$230$	8.79498	+	12.5217i	0.579924	+	0.825659i
$231$	−30.2180	−	9.81843i	−1.98820	−	0.646005i
$232$			3.03810i			0.199461i
$233$	−8.28164	−	2.69087i	−0.542549	−	0.176285i	0.0249054	−	0.999690i	$-0.492072\pi$
$233$	−8.28164	−	2.69087i	−0.542549	−	0.176285i	−0.567454	+	0.823405i	$0.692072\pi$
$234$	−15.1959	+	11.0405i	−0.993386	+	0.721737i
$235$	−2.37781	+	1.67012i	−0.155111	+	0.108946i
$236$	9.91067	+	7.20052i	0.645130	+	0.468714i
$237$	10.2762	−	7.46610i	0.667512	−	0.484976i
$238$	12.5800	−	14.5832i	0.815443	−	0.945291i
$239$	−12.6119	−	9.16306i	−0.815794	−	0.592709i	0.0997108	−	0.995016i	$-0.468208\pi$
$239$	−12.6119	−	9.16306i	−0.815794	−	0.592709i	−0.915505	+	0.402308i	$0.868208\pi$
$240$	24.8206	+	8.50606i	1.60216	+	0.549064i
$241$	10.9045	+	15.0087i	0.702419	+	0.966797i	0.999927	+	0.0120777i	$0.00384454\pi$
$241$	10.9045	+	15.0087i	0.702419	+	0.966797i	−0.297508	+	0.954719i	$0.596155\pi$
$242$	−7.68618	+	23.6556i	−0.494086	+	1.52064i
$243$			18.3262i			1.17562i
$244$	22.8439	+	7.42243i	1.46243	+	0.475172i
$245$	0.875006	+	2.84720i	0.0559021	+	0.181901i
$246$	−7.22710	−	22.2427i	−0.460783	−	1.41814i
$247$	−0.834868	−	2.56946i	−0.0531214	−	0.163491i
$248$	0.206300	−	0.283947i	0.0131000	−	0.0180307i
$249$			21.9495i			1.39099i
$250$	5.76993	+	21.1639i	0.364922	+	1.33852i
$251$	−7.76983			−0.490428			−0.245214	−	0.969469i	$-0.578858\pi$
$251$	−7.76983			−0.490428			−0.245214	+	0.969469i	$0.578858\pi$
$252$	−11.7057	+	16.1116i	−0.737393	+	1.01493i
$253$	−5.24440	−	16.1406i	−0.329713	−	1.01475i
$254$	−11.4830	−	35.3410i	−0.720508	−	2.21749i
$255$	12.7583	+	21.8322i	0.798954	+	1.36719i
$256$	5.60201	−	17.2412i	0.350126	−	1.07758i
$257$	−1.91894			−0.119700			−0.0598502	−	0.998207i	$-0.519062\pi$
$257$	−1.91894			−0.119700			−0.0598502	+	0.998207i	$0.519062\pi$
$258$	34.2968	+	11.1437i	2.13522	+	0.693776i
$259$	18.2666	−	13.2714i	1.13503	−	0.824648i
$260$	−2.83819	+	8.28181i	−0.176017	+	0.513616i
$261$	27.3711	−	37.6731i	1.69423	−	2.33191i
$262$	−19.1045	−	26.2951i	−1.18028	−	1.62452i
$263$	−6.55314	+	4.76113i	−0.404084	+	0.293584i	−0.771202	−	0.636590i	$-0.780344\pi$
$263$	−6.55314	+	4.76113i	−0.404084	+	0.293584i	0.367119	+	0.930174i	$0.380344\pi$
$264$	−3.18581	−	2.31463i	−0.196073	−	0.142456i
$265$	15.0189	−	10.5489i	0.922603	−	0.648015i
$266$	−3.50431	−	4.82327i	−0.214863	−	0.295734i
$267$	−10.8392	−	3.52185i	−0.663345	−	0.215534i
$268$	13.5844			0.829797
$269$	0.659782	+	0.214376i	0.0402276	+	0.0130707i	0.329062	−	0.944308i	$-0.393268\pi$
$269$	0.659782	+	0.214376i	0.0402276	+	0.0130707i	−0.288834	+	0.957379i	$0.593268\pi$
$270$	−10.5306	−	14.9928i	−0.640871	−	0.912431i
$271$	−8.30864	−	25.5714i	−0.504714	−	1.55335i	−0.801251	−	0.598329i	$-0.795832\pi$
$271$	−8.30864	−	25.5714i	−0.504714	−	1.55335i	0.296537	−	0.955021i	$-0.404168\pi$
$272$	15.0852	−	9.14230i	0.914674	−	0.554333i
$273$	11.1822	+	8.12431i	0.676775	+	0.491706i
$274$	9.91780			0.599156
$275$	0.778361	−	24.3171i	0.0469369	−	1.46638i
$276$	−17.6935			−1.06502
$277$	−18.2247	+	25.0841i	−1.09501	+	1.50716i	−0.253182	+	0.967419i	$0.581477\pi$
$277$	−18.2247	+	25.0841i	−1.09501	+	1.50716i	−0.841832	+	0.539739i	$0.818523\pi$
$278$	−20.6259	+	6.70175i	−1.23706	+	0.401944i
$279$	−5.11633	+	1.66240i	−0.306307	+	0.0995251i
$280$	0.0251295	−	1.57057i	0.00150178	−	0.0938593i
$281$	−1.77281	+	5.45615i	−0.105757	+	0.325487i	−0.989907	−	0.141716i	$-0.954738\pi$
$281$	−1.77281	+	5.45615i	−0.105757	+	0.325487i	0.884150	+	0.467202i	$0.154738\pi$
$282$		−	6.99298i		−	0.416426i
$283$	−4.19701	−	1.36369i	−0.249487	−	0.0810631i	0.181604	−	0.983372i	$-0.441871\pi$
$283$	−4.19701	−	1.36369i	−0.249487	−	0.0810631i	−0.431091	+	0.902309i	$0.641871\pi$
$284$	−9.22506	−	12.6972i	−0.547407	−	0.753441i
$285$	7.48230	−	2.29947i	0.443213	−	0.136209i
$286$	11.8786	−	16.3494i	0.702394	−	0.966762i
$287$	−8.37064	+	6.08163i	−0.494103	+	0.358987i
$288$	−28.5530	+	20.7449i	−1.68250	+	1.22241i
$289$	16.7637	+	2.82469i	0.986099	+	0.166158i
$290$	0.722691	−	45.1674i	0.0424379	−	2.65232i
$291$	−21.5349	+	15.6460i	−1.26240	+	0.917185i
$292$	2.58452	+	0.839762i	0.151248	+	0.0491434i
$293$	3.14557			0.183766			0.0918831	−	0.995770i	$-0.470711\pi$
$293$	3.14557			0.183766			0.0918831	+	0.995770i	$0.470711\pi$
$294$	−6.81756	−	2.21516i	−0.397608	−	0.129191i
$295$	11.8406	+	8.89555i	0.689385	+	0.517919i
$296$	2.66139	−	0.864739i	0.154690	−	0.0502619i
$297$	6.27933	+	19.3258i	0.364364	+	1.12140i
$298$	−29.2630	−	21.2608i	−1.69516	−	1.23161i
$299$			7.38281i			0.426959i
$300$	−23.8604	−	8.60598i	−1.37758	−	0.496866i
$301$		−	15.9539i		−	0.919567i
$302$	−17.5189	−	12.7282i	−1.00810	−	0.732427i
$303$	−49.8215	+	16.1880i	−2.86217	+	0.929975i
$304$	−1.68734	−	5.19310i	−0.0967755	−	0.297844i
$305$	27.4697	+	9.41392i	1.57291	+	0.539040i
$306$	−36.4591	−	3.05019i	−2.08423	−	0.174368i
$307$	−15.8606			−0.905210			−0.452605	−	0.891711i	$-0.649505\pi$
$307$	−15.8606			−0.905210			−0.452605	+	0.891711i	$0.649505\pi$
$308$	6.62124	−	20.3781i	0.377280	−	1.16115i
$309$	−14.0237	−	19.3019i	−0.797778	−	1.09805i
$310$	−3.13460	+	4.17237i	−0.178033	+	0.236975i
$311$	−13.1216	+	18.0603i	−0.744055	+	1.02410i	0.254320	+	0.967120i	$0.418148\pi$
$311$	−13.1216	+	18.0603i	−0.744055	+	1.02410i	−0.998375	+	0.0569836i	$0.981852\pi$
$312$	1.00691	+	1.38589i	0.0570049	+	0.0784605i
$313$	13.3456	+	18.3686i	0.754336	+	1.03825i	0.997664	+	0.0683107i	$0.0217609\pi$
$313$	13.3456	+	18.3686i	0.754336	+	1.03825i	−0.243328	+	0.969944i	$0.578239\pi$
$314$	10.8179	+	7.85969i	0.610491	+	0.443548i
$315$	−14.4613	+	19.2490i	−0.814803	+	1.08456i
$316$	5.03491	+	6.92996i	0.283236	+	0.389840i
$317$	14.7164	+	4.78166i	0.826557	+	0.268565i	0.691594	−	0.722286i	$-0.256909\pi$
$317$	14.7164	+	4.78166i	0.826557	+	0.268565i	0.134962	+	0.990851i	$0.456909\pi$
$318$			44.1696i			2.47691i
$319$	−15.4822	+	47.6494i	−0.866838	+	2.66785i
$320$	−4.89687	+	14.2890i	−0.273744	+	0.798781i
$321$	4.76345	+	14.6604i	0.265870	+	0.818264i
$322$	5.03445	+	15.4944i	0.280559	+	0.863472i
$323$	2.03778	−	4.85189i	0.113385	−	0.269966i
$324$	−3.90998			−0.217221
$325$	−3.59093	+	9.95602i	−0.199189	+	0.552261i
$326$		−	27.2709i		−	1.51040i
$327$	−2.42768	−	1.76381i	−0.134251	−	0.0975391i
$328$	−1.21958	+	0.396266i	−0.0673400	+	0.0218801i
$329$	−2.94231	+	0.956013i	−0.162215	+	0.0527067i
$330$	46.8129	+	35.1694i	2.57696	+	1.93601i
$331$	−0.173523	+	0.534049i	−0.00953768	+	0.0293540i	−0.955712	−	0.294303i	$-0.904912\pi$
$331$	−0.173523	+	0.534049i	−0.00953768	+	0.0293540i	0.946174	+	0.323657i	$0.104912\pi$
$332$	−14.8021			−0.812370
$333$	−40.7926	−	13.2543i	−2.23542	−	0.726332i
$334$	11.1049	+	15.2845i	0.607631	+	0.836332i
$335$	16.4205	+	0.262734i	0.897150	+	0.0143547i
$336$	22.6001	+	16.4199i	1.23293	+	0.895780i
$337$	−12.8908	−	17.7427i	−0.702207	−	0.966505i	−0.999930	−	0.0118529i	$-0.996227\pi$
$337$	−12.8908	−	17.7427i	−0.702207	−	0.966505i	0.297723	−	0.954652i	$-0.403773\pi$
$338$	13.5229	−	9.82499i	0.735551	−	0.534409i
$339$	−21.5963	−	15.6906i	−1.17295	−	0.852199i
$340$	−14.7230	+	8.60378i	−0.798466	+	0.466606i
$341$	4.68260	−	3.40211i	0.253577	−	0.184234i
$342$	−3.49979	+	10.7712i	−0.189247	+	0.582442i
$343$			19.8365i			1.07107i
$344$	0.611015	−	1.88051i	0.0329437	−	0.101390i
$345$	−21.3876	−	0.342208i	−1.15147	−	0.0184239i
$346$	−29.4633	+	9.57319i	−1.58395	+	0.514658i
$347$	6.62052	−	2.15114i	0.355408	−	0.115479i	−0.125871	−	0.992047i	$-0.540172\pi$
$347$	6.62052	−	2.15114i	0.355408	−	0.115479i	0.481279	+	0.876568i	$0.340172\pi$
$348$	42.2580	+	30.7023i	2.26527	+	1.64581i
$349$	0.897170			0.0480244			0.0240122	−	0.999712i	$-0.492356\pi$
$349$	0.897170			0.0480244			0.0240122	+	0.999712i	$0.492356\pi$
$350$	−0.747201	+	23.3436i	−0.0399396	+	1.24777i
$351$		−	8.83973i		−	0.471830i
$352$	22.3197	−	30.7205i	1.18965	−	1.63741i
$353$	−5.91870	−	18.2159i	−0.315021	−	0.969534i	−0.975746	−	0.218906i	$-0.929751\pi$
$353$	−5.91870	−	18.2159i	−0.315021	−	0.969534i	0.660725	−	0.750628i	$-0.270249\pi$
$354$	−33.8971	+	11.0138i	−1.80161	+	0.585379i
$355$	−10.9055	−	15.5266i	−0.578805	−	0.824066i
$356$	2.37503	−	7.30959i	0.125876	−	0.387407i
$357$	6.15596	+	26.2096i	0.325808	+	1.38716i
$358$	4.21800	−	12.9817i	0.222928	−	0.686102i
$359$	25.8053	−	18.7487i	1.36195	−	0.989517i	0.363636	−	0.931541i	$-0.381535\pi$
$359$	25.8053	−	18.7487i	1.36195	−	0.989517i	0.998318	−	0.0579760i	$-0.0184647\pi$
$360$	−2.44179	+	1.71506i	−0.128694	+	0.0903916i
$361$	14.0534	+	10.2104i	0.739654	+	0.537390i
$362$	−12.4606	−	17.1505i	−0.654914	−	0.901412i
$363$	−20.4372	−	28.1294i	−1.07268	−	1.47641i
$364$	−5.47878	+	7.54090i	−0.287166	+	0.395250i
$365$	3.10788	+	1.06508i	0.162674	+	0.0557487i
$366$	−56.5370	+	41.0765i	−2.95523	+	2.14710i
$367$	−6.94642	−	2.25703i	−0.362600	−	0.117816i	0.122050	−	0.992524i	$-0.461053\pi$
$367$	−6.94642	−	2.25703i	−0.362600	−	0.117816i	−0.484650	+	0.874708i	$0.661053\pi$
$368$			14.9213i			0.777825i
$369$	18.6932	+	6.07378i	0.973127	+	0.316188i
$370$	−39.7726	+	12.2230i	−2.06768	+	0.635443i
$371$	18.5844	−	6.03845i	0.964856	−	0.313501i
$372$	−1.86471	−	5.73900i	−0.0966809	−	0.297553i
$373$	−8.44856	−	6.13824i	−0.437450	−	0.317826i	0.347171	−	0.937802i	$-0.387142\pi$
$373$	−8.44856	−	6.13824i	−0.437450	−	0.317826i	−0.784621	+	0.619976i	$0.787142\pi$
$374$	38.3210	−	9.00062i	1.98153	−	0.465411i
$375$	−28.6756	−	10.8642i	−1.48080	−	0.561027i
$376$	−0.383429			−0.0197738
$377$	12.8108	−	17.6326i	0.659792	−	0.908126i
$378$	−6.02795	−	18.5521i	−0.310044	−	0.954218i
$379$	11.6687	−	3.79140i	0.599383	−	0.194751i	0.00641766	−	0.999979i	$-0.497957\pi$
$379$	11.6687	−	3.79140i	0.599383	−	0.194751i	0.592965	+	0.805228i	$0.297957\pi$
$380$	1.55069	+	5.04583i	0.0795488	+	0.258845i
$381$	49.4031	+	16.0521i	2.53100	+	0.822371i
$382$	−7.01947			−0.359147
$383$	3.38669	−	10.4232i	0.173052	−	0.532599i	−0.826487	−	0.562955i	$-0.809664\pi$
$383$	3.38669	−	10.4232i	0.173052	−	0.532599i	0.999539	+	0.0303566i	$0.00966430\pi$
$384$	3.79470	+	5.22296i	0.193648	+	0.266533i
$385$	8.39778	−	24.5046i	0.427990	−	1.24887i
$386$	−8.03163	+	11.0546i	−0.408799	+	0.562664i
$387$	−24.5188	+	17.8140i	−1.24636	+	0.905535i
$388$	−10.5512	−	14.5224i	−0.535655	−	0.737266i
$389$	−10.1935	−	7.40598i	−0.516829	−	0.375498i	0.298579	−	0.954385i	$-0.403487\pi$
$389$	−10.1935	−	7.40598i	−0.516829	−	0.375498i	−0.815408	+	0.578887i	$0.803487\pi$
$390$	−14.6400	−	20.8435i	−0.741326	−	1.05545i
$391$	−9.39314	+	10.8889i	−0.475032	+	0.550674i
$392$	−0.121458	+	0.373810i	−0.00613457	+	0.0188803i
$393$	45.4352			2.29190
$394$	22.8863	+	7.43620i	1.15299	+	0.374630i
$395$	5.95208	+	8.47419i	0.299482	+	0.426383i
$396$	−38.7114	+	12.5781i	−1.94532	+	0.632073i
$397$	−16.1225	+	5.23853i	−0.809167	+	0.262914i	−0.684245	−	0.729252i	$-0.739868\pi$
$397$	−16.1225	+	5.23853i	−0.809167	+	0.262914i	−0.124922	+	0.992167i	$0.539868\pi$
$398$	−21.1268	+	29.0786i	−1.05899	+	1.45758i
$399$	8.33411			0.417227
$400$	−7.25758	+	20.1220i	−0.362879	+	1.00610i
$401$		−	18.9063i		−	0.944138i	−0.881562	−	0.472069i	$-0.843507\pi$
$401$		−	18.9063i		−	0.944138i	0.881562	−	0.472069i	$-0.156493\pi$
$402$	−23.2311	+	31.9748i	−1.15866	+	1.59476i
$403$	−2.39466	+	0.778072i	−0.119286	+	0.0387585i
$404$	−10.9167	−	33.5981i	−0.543125	−	1.67157i
$405$	−4.72632	−	0.0756226i	−0.234853	−	0.00375771i
$406$	14.8624	−	45.7418i	0.737610	−	2.27013i
$407$	46.1479			2.28747
$408$	−0.278182	+	3.32513i	−0.0137721	+	0.164618i
$409$	13.6987	−	9.95266i	0.677355	−	0.492128i	−0.195124	−	0.980779i	$-0.562511\pi$
$409$	13.6987	−	9.95266i	0.677355	−	0.492128i	0.872479	+	0.488651i	$0.162511\pi$
$410$	18.2258	−	5.60117i	0.900106	−	0.276622i
$411$	−8.14909	+	11.2163i	−0.401965	+	0.553257i
$412$	13.0166	−	9.45712i	0.641282	−	0.465919i
$413$	9.26819	+	12.7566i	0.456058	+	0.627709i
$414$	18.1913	−	25.0382i	0.894054	−	1.23056i
$415$	−17.8925	−	0.286285i	−0.878308	−	0.0140532i
$416$	−13.3640	+	9.70950i	−0.655223	+	0.476048i
$417$	9.36836	−	28.8328i	0.458770	−	1.41195i
$418$		−	12.1853i		−	0.596002i
$419$	−32.7462	−	10.6399i	−1.59975	−	0.519792i	−0.632708	−	0.774391i	$-0.718056\pi$
$419$	−32.7462	−	10.6399i	−1.59975	−	0.519792i	−0.967047	+	0.254599i	$0.918056\pi$
$420$	−21.5916	−	16.2213i	−1.05356	−	0.791518i
$421$	−7.02796	−	21.6298i	−0.342522	−	1.05417i	−0.962897	−	0.269869i	$-0.913020\pi$
$421$	−7.02796	−	21.6298i	−0.342522	−	1.05417i	0.620375	−	0.784305i	$-0.286980\pi$
$422$	23.2792	−	7.56387i	1.13321	−	0.368203i
$423$	4.75461	+	3.45442i	0.231177	+	0.167960i
$424$	2.42184			0.117615
$425$	−17.9633	+	10.1153i	−0.871348	+	0.490666i
$426$	45.6627			2.21237
$427$	25.0122	+	18.1724i	1.21043	+	0.879426i
$428$	−9.88652	+	3.21232i	−0.477883	+	0.155274i
$429$	8.72976	+	26.8674i	0.421477	+	1.29717i
$430$	−9.53128	+	27.8122i	−0.459639	+	1.34122i
$431$	−32.2110	−	10.4660i	−1.55155	−	0.504129i	−0.597015	−	0.802230i	$-0.703647\pi$
$431$	−32.2110	−	10.4660i	−1.55155	−	0.504129i	−0.954534	+	0.298101i	$0.903647\pi$
$432$		−	17.8658i		−	0.859571i
$433$	1.07974	−	3.32308i	0.0518888	−	0.159697i	−0.921754	−	0.387775i	$-0.873244\pi$
$433$	1.07974	−	3.32308i	0.0518888	−	0.159697i	0.973643	+	0.228077i	$0.0732439\pi$
$434$	−4.49514	+	3.26591i	−0.215774	+	0.156769i
$435$	50.4870	+	37.9297i	2.42067	+	1.81859i
$436$	1.18946	−	1.63715i	0.0569648	−	0.0784054i
$437$	2.61656	+	3.60139i	0.125167	+	0.172278i
$438$	−6.39650	+	4.64733i	−0.305637	+	0.222058i
$439$	−19.1629	+	26.3755i	−0.914597	+	1.25883i	0.0509758	+	0.998700i	$0.483767\pi$
$439$	−19.1629	+	26.3755i	−0.914597	+	1.25883i	−0.965572	+	0.260134i	$0.916233\pi$
$440$	1.92836	−	2.56678i	0.0919308	−	0.122366i
$441$	4.87388	−	3.54108i	0.232090	−	0.168623i
$442$	−17.0644	−	1.42762i	−0.811670	−	0.0679048i
$443$	3.85312			0.183067			0.0915337	−	0.995802i	$-0.470823\pi$
$443$	3.85312			0.183067			0.0915337	+	0.995802i	$0.470823\pi$
$444$	14.8674	−	45.7571i	0.705576	−	2.17154i
$445$	3.01227	−	8.78976i	0.142795	−	0.416675i
$446$	1.21100	+	3.72707i	0.0573425	+	0.176482i
$447$	48.0887	−	15.6250i	2.27452	−	0.739036i
$448$	−9.45282	+	13.0107i	−0.446604	+	0.614697i
$449$		−	6.37894i		−	0.301041i	−0.988607	−	0.150520i	$-0.951905\pi$
$449$		−	6.37894i		−	0.301041i	0.988607	−	0.150520i	$-0.0480949\pi$
$450$	36.7101	−	24.9169i	1.73053	−	1.17460i
$451$	−21.1472			−0.995784
$452$	10.5813	−	14.5639i	0.497702	−	0.685028i
$453$	28.7893	−	9.35420i	1.35264	−	0.439499i
$454$	−25.9972	+	8.44700i	−1.22011	+	0.396437i
$455$	−6.76850	+	9.00934i	−0.317312	+	0.422364i
$456$	0.982355	+	0.319186i	0.0460030	+	0.0149473i
$457$	32.7184			1.53050			0.765252	−	0.643731i	$-0.222614\pi$
$457$	32.7184			1.53050			0.765252	+	0.643731i	$0.222614\pi$
$458$	−17.9750	+	55.3215i	−0.839918	+	2.58500i
$459$	11.2468	−	13.0377i	0.524955	−	0.608547i
$460$	0.230775	−	14.4231i	0.0107599	−	0.672483i
$461$	12.5047	+	9.08517i	0.582400	+	0.423139i	0.839589	−	0.543223i	$-0.182796\pi$
$461$	12.5047	+	9.08517i	0.582400	+	0.423139i	−0.257188	+	0.966361i	$0.582796\pi$
$462$	36.6427	+	50.4343i	1.70477	+	2.34642i
$463$	−15.3059	+	11.1204i	−0.711325	+	0.516808i	−0.883601	−	0.468241i	$-0.844888\pi$
$463$	−15.3059	+	11.1204i	−0.711325	+	0.516808i	0.172276	+	0.985049i	$0.444888\pi$
$464$	25.8918	−	35.6370i	1.20200	−	1.65441i
$465$	−2.14304	−	6.97327i	−0.0993810	−	0.323378i
$466$	10.0424	+	13.8222i	0.465205	+	0.640300i
$467$	8.11766	−	24.9836i	0.375640	−	1.15610i	−0.567405	−	0.823439i	$-0.692053\pi$
$467$	8.11766	−	24.9836i	0.375640	−	1.15610i	0.943046	−	0.332664i	$-0.107947\pi$
$468$	17.7068			0.818498
$469$	16.6294	+	5.40322i	0.767874	+	0.249497i
$470$	5.70043	+	0.0912086i	0.262941	+	0.00420714i
$471$	−17.7774	+	5.77622i	−0.819139	+	0.266154i
$472$	0.603895	+	1.85860i	0.0277965	+	0.0855489i
$473$	19.1663	−	26.3801i	0.881266	−	1.21296i
$474$	−24.9221			−1.14471
$475$	1.77686	+	6.12930i	0.0815279	+	0.281232i
$476$	−17.6749	+	4.15138i	−0.810128	+	0.190278i
$477$	−30.0314	−	21.8191i	−1.37505	−	0.999029i
$478$	9.45176	+	29.0895i	0.432313	+	1.33052i
$479$	3.34599	−	1.08718i	0.152882	−	0.0496744i	−0.231576	−	0.972817i	$-0.574388\pi$
$479$	3.34599	−	1.08718i	0.152882	−	0.0496744i	0.384458	+	0.923142i	$0.374388\pi$
$480$	−27.5085	−	39.1648i	−1.25559	−	1.78762i
$481$	−19.0927	−	6.20358i	−0.870550	−	0.282859i
$482$		−	36.3994i		−	1.65795i
$483$	−21.6596	−	7.03764i	−0.985548	−	0.320224i
$484$	18.9696	−	13.7822i	0.862255	−	0.626465i
$485$	−12.4732	−	17.7586i	−0.566379	−	0.806374i
$486$	21.1348	−	29.0896i	0.958696	−	1.31953i
$487$	24.8374	+	34.1857i	1.12549	+	1.54910i	0.796364	+	0.604817i	$0.206754\pi$
$487$	24.8374	+	34.1857i	1.12549	+	1.54910i	0.329125	+	0.944286i	$0.393246\pi$
$488$	2.25225	+	3.09995i	0.101954	+	0.140328i
$489$	30.8413	+	22.4075i	1.39469	+	1.01330i
$490$	1.89464	−	5.52854i	0.0855911	−	0.249754i
$491$	−24.2390	+	17.6106i	−1.09389	+	0.794757i	−0.980052	−	0.198743i	$-0.936314\pi$
$491$	−24.2390	+	17.6106i	−1.09389	+	0.794757i	−0.113837	+	0.993499i	$0.536314\pi$
$492$	−6.81297	+	20.9682i	−0.307152	+	0.945318i
$493$	41.3286	−	9.70704i	1.86135	−	0.437183i
$494$	−1.63805	+	5.04139i	−0.0736993	+	0.226823i
$495$	−47.0369	+	14.4555i	−2.11415	+	0.649725i
$496$	−4.83981	+	1.57255i	−0.217314	+	0.0706095i
$497$	−6.24257	−	19.2127i	−0.280018	−	0.861806i
$498$	25.3135	−	34.8411i	1.13433	−	1.56127i
$499$			1.37045i			0.0613498i	0.999529	+	0.0306749i	$0.00976565\pi$
$499$			1.37045i			0.0613498i	−0.999529	+	0.0306749i	$0.990234\pi$
$500$	7.32650	−	19.3380i	0.327651	−	0.864820i
$501$	−26.4101			−1.17991
$502$	12.3333	+	8.96064i	0.550460	+	0.399933i
$503$	12.1222	−	3.93873i	0.540500	−	0.175619i	−0.0260284	−	0.999661i	$-0.508286\pi$
$503$	12.1222	−	3.93873i	0.540500	−	0.175619i	0.566529	+	0.824042i	$0.308286\pi$
$504$	−3.02148	+	0.981740i	−0.134588	+	0.0437302i
$505$	−12.5461	−	40.8239i	−0.558293	−	1.81664i
$506$	−10.2897	+	31.6686i	−0.457435	+	1.40784i
$507$			23.3662i			1.03773i
$508$	−10.8250	+	33.3159i	−0.480282	+	1.47816i
$509$	−6.11839	+	4.44527i	−0.271193	+	0.197033i	−0.715067	−	0.699056i	$-0.753604\pi$
$509$	−6.11839	+	4.44527i	−0.271193	+	0.197033i	0.443874	+	0.896089i	$0.353604\pi$
$510$	4.92671	−	49.3685i	0.218158	−	2.18607i
$511$	2.82984	+	2.05600i	0.125185	+	0.0909521i
$512$	−24.9673	+	18.1398i	−1.10341	+	0.801672i
$513$	−3.13292	−	4.31209i	−0.138322	−	0.190383i
$514$	3.04599	+	2.21304i	0.134353	+	0.0976131i
$515$	15.9172	−	11.1799i	0.701394	−	0.492643i
$516$	−19.9820	−	27.5028i	−0.879657	−	1.21074i
$517$	−6.01368	−	1.95396i	−0.264481	−	0.0859352i
$518$	−44.3005			−1.94645
$519$	13.3823	−	41.1866i	0.587419	−	1.80789i
$520$	−1.14286	+	0.802720i	−0.0501178	+	0.0352016i
$521$	−23.5772	+	7.66069i	−1.03293	+	0.335621i	−0.775950	−	0.630795i	$-0.782729\pi$
$521$	−23.5772	+	7.66069i	−1.03293	+	0.335621i	−0.256985	+	0.966415i	$0.582729\pi$
$522$	−86.8938	+	28.2335i	−3.80324	+	1.23575i
$523$	6.33547	+	4.60299i	0.277031	+	0.201275i	0.717621	−	0.696434i	$-0.245231\pi$
$523$	6.33547	+	4.60299i	0.277031	+	0.201275i	−0.440590	+	0.897708i	$0.645231\pi$
$524$			30.6401i			1.33852i
$525$	−25.7859	−	20.0256i	−1.12539	−	0.873989i
$526$	15.8928			0.692959
$527$	−4.52181	−	1.89915i	−0.196973	−	0.0827282i
$528$	17.6436	+	54.3014i	0.767838	+	2.36316i
$529$	3.34832	+	10.3051i	0.145579	+	0.448046i
$530$	−36.0055	−	0.576099i	−1.56398	−	0.0250242i
$531$	9.25622	−	28.4877i	0.401686	−	1.23626i
$532$			5.62026i			0.243669i
$533$	8.74919	+	2.84278i	0.378969	+	0.123135i
$534$	13.1437	+	18.0907i	0.568782	+	0.782861i
$535$	−12.0128	+	3.69179i	−0.519358	+	0.159610i
$536$	1.75320	+	1.27377i	0.0757266	+	0.0550186i
$537$	11.2155	+	15.4368i	0.483984	+	0.666146i
$538$	−0.800057	−	1.10118i	−0.0344929	−	0.0474754i
$539$	−3.80989	+	5.24387i	−0.164104	+	0.225869i
$540$	−0.276316	+	17.2694i	−0.0118907	+	0.743157i
$541$	13.4409	+	18.4998i	0.577870	+	0.795370i	0.993460	−	0.114182i	$-0.0364247\pi$
$541$	13.4409	+	18.4998i	0.577870	+	0.795370i	−0.415589	+	0.909552i	$0.636425\pi$
$542$	−16.3019	+	50.1721i	−0.700227	+	2.15508i
$543$	29.6343			1.27173
$544$	−32.0639	−	2.68248i	−1.37473	−	0.115011i
$545$	1.46946	−	1.95596i	0.0629449	−	0.0837840i
$546$	−8.38029	−	25.7919i	−0.358643	−	1.10379i
$547$	30.3175	−	9.85074i	1.29628	−	0.421187i	0.421995	−	0.906598i	$-0.361330\pi$
$547$	30.3175	−	9.85074i	1.29628	−	0.421187i	0.874286	+	0.485411i	$0.161330\pi$
$548$	−7.56390	−	5.49549i	−0.323114	−	0.234756i
$549$		−	58.7313i		−	2.50659i
$550$	−29.2795	+	37.7015i	−1.24848	+	1.60760i
$551$		−	13.1417i		−	0.559854i
$552$	−2.28352	−	1.65908i	−0.0971932	−	0.0706150i
$553$	3.40711	+	10.4860i	0.144885	+	0.445910i
$554$	57.8570	−	18.7989i	2.45811	−	0.798688i
$555$	18.8564	−	55.0229i	0.800411	−	2.33559i
$556$	19.4440	+	6.31773i	0.824608	+	0.267931i
$557$	−27.9285			−1.18337			−0.591683	−	0.806171i	$-0.701536\pi$
$557$	−27.9285			−1.18337			−0.591683	+	0.806171i	$0.701536\pi$
$558$	10.0385	+	3.26169i	0.424962	+	0.138079i
$559$	−11.4758	+	8.33769i	−0.485376	+	0.352647i
$560$	−13.6797	+	18.2086i	−0.578073	+	0.769455i
$561$	−21.3079	+	50.7335i	−0.899622	+	2.14197i
$562$	9.10639	−	6.61618i	0.384130	−	0.279087i
$563$	−11.3814	+	8.26908i	−0.479669	+	0.348500i	−0.801198	−	0.598400i	$-0.795803\pi$
$563$	−11.3814	+	8.26908i	−0.479669	+	0.348500i	0.321528	+	0.946900i	$0.395803\pi$
$564$	−3.87484	+	5.33325i	−0.163160	+	0.224571i
$565$	13.0721	−	17.3999i	0.549949	−	0.732020i
$566$	5.08934	+	7.00487i	0.213921	+	0.294437i
$567$	−4.78643	−	1.55521i	−0.201011	−	0.0653125i
$568$		−	2.50371i		−	0.105053i
$569$	−13.3794	+	41.1774i	−0.560892	+	1.72625i	0.118961	+	0.992899i	$0.462044\pi$
$569$	−13.3794	+	41.1774i	−0.560892	+	1.72625i	−0.679852	+	0.733349i	$0.737956\pi$
$570$	−14.5287	−	4.97902i	−0.608542	−	0.208548i
$571$	−24.8142	+	8.06263i	−1.03844	+	0.337410i	−0.778123	−	0.628112i	$-0.783828\pi$
$571$	−24.8142	+	8.06263i	−1.03844	+	0.337410i	−0.260320	+	0.965523i	$0.583828\pi$
$572$	−18.1186	+	5.88708i	−0.757575	+	0.246151i
$573$	5.76764	−	7.93847i	0.240946	−	0.331634i
$574$	20.3006			0.847332
$575$	0.557913	−	17.4300i	0.0232666	−	0.726881i
$576$	30.5505			1.27294
$577$	−12.8946	−	9.36851i	−0.536811	−	0.390016i	0.286088	−	0.958203i	$-0.407645\pi$
$577$	−12.8946	−	9.36851i	−0.536811	−	0.390016i	−0.822899	+	0.568187i	$0.807645\pi$
$578$	−23.3518	−	23.8166i	−0.971308	−	0.990640i
$579$	−5.90259	−	18.1663i	−0.245303	−	0.754966i
$580$	−25.5786	+	34.0468i	−1.06209	+	1.41372i
$581$	−18.1201	−	5.88757i	−0.751747	−	0.244257i
$582$	52.2268			2.16487
$583$	37.9841	+	12.3418i	1.57314	+	0.511144i
$584$	0.254816	+	0.350724i	0.0105444	+	0.0145131i
$585$	21.4037	+	0.342466i	0.884934	+	0.0141592i
$586$	−4.99305	−	3.62766i	−0.206261	−	0.149857i
$587$	−16.3147	+	11.8533i	−0.673380	+	0.489239i	−0.871155	−	0.491008i	$-0.836629\pi$
$587$	−16.3147	+	11.8533i	−0.673380	+	0.489239i	0.197775	+	0.980247i	$0.436629\pi$
$588$	3.97204	+	5.46704i	0.163804	+	0.225457i
$589$	−0.892375	+	1.22825i	−0.0367697	+	0.0506091i
$590$	−8.53599	−	27.7754i	−0.351421	−	1.14350i
$591$	−27.2145	+	19.7725i	−1.11946	+	0.813333i
$592$	−38.5879	−	12.5380i	−1.58595	−	0.515307i
$593$	−13.0166			−0.534528			−0.267264	−	0.963623i	$-0.586120\pi$
$593$	−13.0166			−0.534528			−0.267264	+	0.963623i	$0.586120\pi$
$594$	12.3203	−	37.9180i	0.505509	−	1.55580i
$595$	−21.4454	+	4.67627i	−0.879176	+	0.191709i
$596$	10.5370	+	32.4295i	0.431612	+	1.32837i
$597$	−15.5265	−	47.7856i	−0.635457	−	1.95573i
$598$	8.51430	−	11.7189i	0.348176	−	0.479223i
$599$	5.51307			0.225258			0.112629	−	0.993637i	$-0.464073\pi$
$599$	5.51307			0.225258			0.112629	+	0.993637i	$0.464073\pi$
$600$	−2.27247	−	3.34802i	−0.0927730	−	0.136682i
$601$			26.2375i			1.07025i	0.844773	+	0.535125i	$0.179736\pi$
$601$			26.2375i			1.07025i	−0.844773	+	0.535125i	$0.820264\pi$
$602$	−18.3990	+	25.3240i	−0.749886	+	1.03213i
$603$	−10.2643	−	31.5902i	−0.417993	−	1.28645i
$604$	6.30818	+	19.4146i	0.256676	+	0.789968i
$605$	23.1967	−	16.2928i	0.943080	−	0.662398i
$606$	97.7519	+	31.7615i	3.97090	+	1.29022i
$607$		−	8.99883i		−	0.365251i	−0.983183	−	0.182626i	$-0.941540\pi$
$607$		−	8.99883i		−	0.365251i	0.983183	−	0.182626i	$-0.0584596\pi$
$608$	−3.07788	+	9.47275i	−0.124825	+	0.384171i
$609$	39.5186	+	54.3926i	1.60137	+	2.20410i
$610$	−32.7467	−	46.6227i	−1.32588	−	1.88770i
$611$	2.22536	+	1.61682i	0.0900283	+	0.0654094i
$612$	26.1157	+	22.5284i	1.05567	+	0.910656i
$613$	7.73363	−	5.61881i	0.312358	−	0.226942i	−0.420550	−	0.907270i	$-0.638163\pi$
$613$	7.73363	−	5.61881i	0.312358	−	0.226942i	0.732908	+	0.680328i	$0.238163\pi$
$614$	25.1759	+	18.2914i	1.01602	+	0.738179i
$615$	−8.64094	+	25.2142i	−0.348436	+	1.01673i
$616$	2.76534	−	2.00914i	0.111419	−	0.0809504i
$617$	8.35129	+	2.71350i	0.336210	+	0.109241i	0.472256	−	0.881461i	$-0.343440\pi$
$617$	8.35129	+	2.71350i	0.336210	+	0.109241i	−0.136046	+	0.990702i	$0.543440\pi$
$618$			46.8114i			1.88303i
$619$	2.48420	+	0.807167i	0.0998486	+	0.0324428i	0.358515	−	0.933524i	$-0.383283\pi$
$619$	2.48420	+	0.807167i	0.0998486	+	0.0324428i	−0.258667	+	0.965967i	$0.583283\pi$
$620$	4.70256	−	1.44520i	0.188859	−	0.0580405i
$621$	4.50089	+	13.8523i	0.180615	+	0.555874i
$622$	41.6564	−	13.5350i	1.67027	−	0.542703i
$623$	5.81481	−	8.00340i	0.232966	−	0.320650i
$624$		−	24.8378i		−	0.994306i
$625$	9.23016	−	23.2337i	0.369206	−	0.929347i
$626$		−	44.5479i		−	1.78049i
$627$	13.7806	+	10.0122i	0.550345	+	0.399849i
$628$	−3.89530	−	11.9885i	−0.155440	−	0.478394i
$629$	−20.2669	−	33.4412i	−0.808093	−	1.33339i
$630$	45.1539	−	13.8768i	1.79898	−	0.552864i
$631$	−2.06171	+	6.34528i	−0.0820752	+	0.252601i	−0.983670	−	0.179979i	$-0.942397\pi$
$631$	−2.06171	+	6.34528i	−0.0820752	+	0.252601i	0.901595	+	0.432581i	$0.142397\pi$
$632$			1.36649i			0.0543561i
$633$	−10.5735	+	32.5419i	−0.420259	+	1.29342i
$634$	−17.8453	−	24.5619i	−0.708726	−	0.975478i
$635$	−13.7294	+	40.0624i	−0.544836	+	1.58983i
$636$	24.4746	−	33.6863i	0.970479	−	1.33575i
$637$	2.28118	−	1.65738i	0.0903837	−	0.0656676i
$638$	79.5275	−	57.7801i	3.14852	−	2.28754i
$639$	−22.5567	+	31.0466i	−0.892329	+	1.22819i
$640$	−4.30707	+	3.02519i	−0.170252	+	0.119581i
$641$	−3.50908	−	4.82983i	−0.138600	−	0.190767i	0.734074	−	0.679069i	$-0.237616\pi$
$641$	−3.50908	−	4.82983i	−0.138600	−	0.190767i	−0.872675	+	0.488302i	$0.837616\pi$
$642$	9.34610	−	28.7643i	0.368861	−	1.13524i
$643$			25.6744i			1.01250i	0.862387	+	0.506250i	$0.168969\pi$
$643$			25.6744i			1.01250i	−0.862387	+	0.506250i	$0.831031\pi$
$644$	4.74597	−	14.6066i	0.187017	−	0.575580i
$645$	−23.6219	−	33.6314i	−0.930112	−	1.32423i
$646$	−8.83011	+	5.35144i	−0.347416	+	0.210550i
$647$	−11.4475	−	35.2317i	−0.450047	−	1.38510i	−0.876853	−	0.480759i	$-0.840361\pi$
$647$	−11.4475	−	35.2317i	−0.450047	−	1.38510i	0.426805	−	0.904343i	$-0.359639\pi$
$648$	−0.504622	−	0.366629i	−0.0198234	−	0.0144026i
$649$			32.2276i			1.26504i
$650$	17.1819	−	11.6622i	0.673928	−	0.457428i
$651$		−	7.76713i		−	0.304418i
$652$	−15.1109	+	20.7984i	−0.591790	+	0.814529i
$653$	−16.6710	+	5.41675i	−0.652388	+	0.211974i	−0.616467	−	0.787381i	$-0.711437\pi$
$653$	−16.6710	+	5.41675i	−0.652388	+	0.211974i	−0.0359212	+	0.999355i	$0.511437\pi$
$654$	1.81939	+	5.59950i	0.0711436	+	0.218958i
$655$	−0.592607	+	37.0372i	−0.0231551	+	1.44716i
$656$	17.6828	+	5.74550i	0.690399	+	0.224324i
$657$		−	6.64477i		−	0.259237i
$658$	5.77293	+	1.87574i	0.225052	+	0.0731239i
$659$	11.1103	−	8.07208i	0.432794	−	0.314443i	−0.349971	−	0.936761i	$-0.613809\pi$
$659$	11.1103	−	8.07208i	0.432794	−	0.314443i	0.782765	+	0.622317i	$0.213809\pi$
$660$	−16.2147	−	52.7615i	−0.631158	−	2.05374i
$661$	−8.39265	−	6.09762i	−0.326436	−	0.237170i	0.412481	−	0.910966i	$-0.364662\pi$
$661$	−8.39265	−	6.09762i	−0.326436	−	0.237170i	−0.738917	+	0.673797i	$0.764662\pi$
$662$	0.891334	−	0.647592i	0.0346427	−	0.0251694i
$663$	15.6357	−	18.1255i	0.607240	−	0.703935i
$664$	−1.91035	−	1.38795i	−0.0741361	−	0.0538631i
$665$	−0.108701	+	6.79367i	−0.00421524	+	0.263447i
$666$	49.4655	+	68.0834i	1.91675	+	2.63818i
$667$	−11.0973	+	34.1541i	−0.429690	+	1.32245i
$668$		−	17.8101i		−	0.689094i
$669$	−5.21006	−	1.69285i	−0.201433	−	0.0654494i
$670$	−25.7618	−	19.3542i	−0.995264	−	0.747718i
$671$	19.5267	+	60.0970i	0.753820	+	2.32002i
$672$	−15.7465	−	48.4628i	−0.607435	−	1.86949i
$673$	3.97595	−	5.47243i	0.153262	−	0.210947i	−0.725481	−	0.688242i	$-0.758383\pi$
$673$	3.97595	−	5.47243i	0.153262	−	0.210947i	0.878743	+	0.477295i	$0.158383\pi$
$674$			43.0299i			1.65745i
$675$	−0.668011	+	20.8696i	−0.0257118	+	0.803272i
$676$	−15.7574			−0.606056
$677$	−9.35719	+	12.8791i	−0.359626	+	0.494983i	−0.950044	−	0.312115i	$-0.898963\pi$
$677$	−9.35719	+	12.8791i	−0.359626	+	0.494983i	0.590419	+	0.807097i	$0.298963\pi$
$678$	16.1850	+	49.8124i	0.621582	+	1.91303i
$679$	−7.13995	−	21.9745i	−0.274006	−	0.843304i
$680$	−2.70690	−	0.270134i	−0.103805	−	0.0103592i
$681$	11.8080	−	36.3414i	0.452485	−	1.39260i
$682$	−11.3563			−0.434856
$683$	44.8767	+	14.5813i	1.71716	+	0.557939i	0.991499	−	0.130115i	$-0.0415346\pi$
$683$	44.8767	+	14.5813i	1.71716	+	0.557939i	0.725660	+	0.688053i	$0.241535\pi$
$684$	8.63753	−	6.27553i	0.330264	−	0.239951i
$685$	−9.03682	−	6.78915i	−0.345279	−	0.259400i
$686$	22.8767	−	31.4870i	0.873435	−	1.20218i
$687$	−47.7949	−	65.7840i	−1.82349	−	2.50982i
$688$	−23.1936	+	16.8512i	−0.884249	+	0.642444i
$689$	−14.0560	−	10.2123i	−0.535490	−	0.389056i
$690$	33.5545	+	25.2087i	1.27740	+	0.959678i
$691$	−7.84311	−	10.7951i	−0.298366	−	0.410665i	0.633343	−	0.773871i	$-0.281682\pi$
$691$	−7.84311	−	10.7951i	−0.298366	−	0.410665i	−0.931709	+	0.363206i	$0.881682\pi$
$692$	27.7750	+	9.02463i	1.05585	+	0.343065i
$693$	−52.3918			−1.99020
$694$	−12.9897	−	4.22063i	−0.493084	−	0.160213i
$695$	23.3813	+	8.01282i	0.886905	+	0.303944i
$696$	2.57494	+	7.92486i	0.0976030	+	0.300391i
$697$	9.28727	+	15.3244i	0.351780	+	0.580453i
$698$	−1.42410	−	1.03467i	−0.0539030	−	0.0391629i
$699$	−23.8833			−0.903349
$700$	13.5046	−	17.3892i	0.510428	−	0.657249i
$701$	49.9601			1.88697			0.943483	−	0.331422i	$-0.107528\pi$
$701$	49.9601			1.88697			0.943483	+	0.331422i	$0.107528\pi$
$702$	−10.1945	+	14.0315i	−0.384767	+	0.529586i
$703$	−11.5122	+	3.74053i	−0.434190	+	0.141077i
$704$	−31.2609	+	10.1573i	−1.17819	+	0.382817i
$705$	−4.78698	+	6.37180i	−0.180288	+	0.239976i
$706$	−11.6127	+	35.7404i	−0.437052	+	1.34511i
$707$		−	45.4714i		−	1.71013i
$708$	31.9547	+	10.3827i	1.20093	+	0.390207i
$709$	21.6747	+	29.8326i	0.814009	+	1.12039i	0.990692	+	0.136120i	$0.0434632\pi$
$709$	21.6747	+	29.8326i	0.814009	+	1.12039i	−0.176683	+	0.984268i	$0.556537\pi$
$710$	−0.595574	+	37.2227i	−0.0223515	+	1.39694i
$711$	12.3111	−	16.9448i	0.461703	−	0.635480i
$712$	0.991923	−	0.720674i	0.0371739	−	0.0270084i
$713$	3.35639	−	2.43856i	0.125698	−	0.0913247i
$714$	20.4549	−	48.7025i	0.765506	−	1.82265i
$715$	−22.0153	+	6.76577i	−0.823325	+	0.253025i
$716$	−10.4101	+	7.56337i	−0.389043	+	0.282656i
$717$	−40.6642	−	13.2126i	−1.51863	−	0.493433i
$718$	−62.5836			−2.33560
$719$	24.8906	+	8.08744i	0.928262	+	0.301611i	0.733852	−	0.679310i	$-0.237721\pi$
$719$	24.8906	+	8.08744i	0.928262	+	0.301611i	0.194410	+	0.980920i	$0.437721\pi$
$720$	43.2587	+	0.692152i	1.61216	+	0.0257950i
$721$	19.6960	−	6.39961i	0.733516	−	0.238334i
$722$	−10.5321	−	32.4145i	−0.391964	−	1.20634i
$723$	41.1649	+	29.9081i	1.53094	+	1.11229i
$724$			19.9845i			0.742717i
$725$	−31.5774	+	40.6605i	−1.17276	+	1.51009i
$726$			68.2200i			2.53188i
$727$	5.27260	+	3.83077i	0.195550	+	0.142075i	0.681252	−	0.732049i	$-0.261436\pi$
$727$	5.27260	+	3.83077i	0.195550	+	0.142075i	−0.485702	+	0.874125i	$0.661436\pi$
$728$	−1.41418	+	0.459496i	−0.0524131	+	0.0170300i
$729$	13.5726	+	41.7723i	0.502690	+	1.54712i
$730$	−3.70492	−	5.27482i	−0.137125	−	0.195230i
$731$	−27.5337	−	2.30349i	−1.01837	−	0.0851975i
$732$	65.8791			2.43496
$733$	4.68692	−	14.4249i	0.173115	−	0.532794i	−0.826427	−	0.563044i	$-0.809630\pi$
$733$	4.68692	−	14.4249i	0.173115	−	0.532794i	0.999542	+	0.0302496i	$0.00963022\pi$
$734$	8.42330	+	11.5937i	0.310910	+	0.427930i
$735$	4.69560	+	6.68529i	0.173200	+	0.246591i
$736$	15.9983	−	22.0198i	0.589706	−	0.811660i
$737$	21.0059	+	28.9121i	0.773762	+	1.06499i
$738$	−22.6675	−	31.1991i	−0.834402	−	1.14846i
$739$	26.3106	+	19.1158i	0.967852	+	0.703186i	0.954961	−	0.296731i	$-0.0958964\pi$
$739$	26.3106	+	19.1158i	0.967852	+	0.703186i	0.0128913	+	0.999917i	$0.495896\pi$
$740$	37.1057	+	12.7162i	1.36403	+	0.467457i
$741$	−4.35550	−	5.99483i	−0.160003	−	0.220226i
$742$	−36.4635	−	11.8477i	−1.33862	−	0.434943i
$743$		−	48.3362i		−	1.77328i	−0.462457	−	0.886642i	$-0.653032\pi$
$743$		−	48.3362i		−	1.77328i	0.462457	−	0.886642i	$-0.346968\pi$
$744$	0.297472	−	0.915525i	0.0109059	−	0.0335648i
$745$	12.1097	+	39.4041i	0.443666	+	1.44365i
$746$	6.33163	+	19.4868i	0.231818	+	0.713461i
$747$	11.1844	+	34.4219i	0.409214	+	1.25943i
$748$	−34.2131	−	14.3694i	−1.25096	−	0.525398i
$749$	−13.3804			−0.488908
$750$	32.9883	+	50.3156i	1.20456	+	1.83726i
$751$			12.2741i			0.447889i	0.974602	+	0.223945i	$0.0718935\pi$
$751$			12.2741i			0.447889i	−0.974602	+	0.223945i	$0.928107\pi$
$752$	4.49763	+	3.26772i	0.164012	+	0.119162i
$753$	−20.2676	+	6.58533i	−0.738591	+	0.239983i
$754$	−40.6700	+	13.2145i	−1.48111	+	0.481243i
$755$	7.24973	+	23.5900i	0.263845	+	0.858529i
$756$	−5.68254	+	17.4891i	−0.206672	+	0.636071i
$757$	−44.6286			−1.62205			−0.811027	−	0.585009i	$-0.801091\pi$
$757$	−44.6286			−1.62205			−0.811027	+	0.585009i	$0.801091\pi$
$758$	−22.8946	−	7.43890i	−0.831568	−	0.270193i
$759$	−27.3600	−	37.6578i	−0.993105	−	1.36689i
$760$	−0.273002	+	0.796618i	−0.00990284	+	0.0288964i
$761$	−21.7300	−	15.7878i	−0.787714	−	0.572307i	0.119570	−	0.992826i	$-0.461848\pi$
$761$	−21.7300	−	15.7878i	−0.787714	−	0.572307i	−0.907284	+	0.420518i	$0.861848\pi$
$762$	−59.9067	−	82.4545i	−2.17019	−	2.98701i
$763$	2.10727	−	1.53102i	0.0762882	−	0.0554266i
$764$	5.35346	+	3.88951i	0.193681	+	0.140718i
$765$	31.1325	+	27.7370i	1.12560	+	1.00283i
$766$	−17.3964	+	12.6392i	−0.628558	+	0.456674i
$767$	4.33230	−	13.3335i	0.156430	−	0.481443i
$768$		−	49.7216i		−	1.79417i
$769$	−0.683133	+	2.10247i	−0.0246344	+	0.0758169i	−0.962618	−	0.270863i	$-0.912691\pi$
$769$	−0.683133	+	2.10247i	−0.0246344	+	0.0758169i	0.937984	+	0.346680i	$0.112691\pi$
$770$	−41.5902	+	29.2120i	−1.49881	+	1.05273i
$771$	−5.00556	+	1.62640i	−0.180271	+	0.0585735i
$772$	12.2508	−	3.98052

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+(-1.58733 - 1.15326i) q^{2} +(2.60850 - 0.847551i) q^{3} +(0.571562 + 1.75909i) q^{4} +(0.656872 + 2.13741i) q^{5} +(-5.11798 - 1.66293i) q^{6} +2.38074i q^{7} +(-0.0911795 + 0.280622i) q^{8} +(3.65885 - 2.65831i) q^{9} +(1.42232 - 4.15031i) q^{10} +(-2.86011 + 3.93660i) q^{11} +(2.98183 + 4.10414i) q^{12} +(1.71250 - 1.24420i) q^{13} +(2.74561 - 3.77901i) q^{14} +(3.52501 + 5.01869i) q^{15} +(3.46110 - 2.51464i) q^{16} +(4.10875 + 0.343741i) q^{17} -8.87352 q^{18} +(0.394408 - 1.21386i) q^{19} +(-3.38445 + 2.37716i) q^{20} +(2.01780 + 6.21015i) q^{21} +(9.07986 - 2.95022i) q^{22} +(-2.05007 + 2.82167i) q^{23} +0.809280i q^{24} +(-4.13704 + 2.80801i) q^{25} -4.15318 q^{26} +(2.45463 - 3.37850i) q^{27} +(-4.18793 + 1.36074i) q^{28} +(9.79249 - 3.18177i) q^{29} +(0.192508 - 12.0316i) q^{30} +(-1.13128 - 0.367576i) q^{31} -7.80380 q^{32} +(-4.12411 + 12.6927i) q^{33} +(-6.12551 - 5.28409i) q^{34} +(-5.08862 + 1.56384i) q^{35} +(6.76747 + 4.91685i) q^{36} +(-5.57451 - 7.67265i) q^{37} +(-2.02595 + 1.47194i) q^{38} +(3.41252 - 4.69692i) q^{39} +(-0.659697 - 0.0105553i) q^{40} +(2.55451 + 3.51598i) q^{41} +(3.95901 - 12.1846i) q^{42} -6.70123 q^{43} +(-8.55956 - 2.78117i) q^{44} +(8.08530 + 6.07429i) q^{45} +(6.50825 - 2.11466i) q^{46} +(0.401562 + 1.23588i) q^{47} +(6.89698 - 9.49288i) q^{48} +1.33208 q^{49} +(9.80520 + 0.313852i) q^{50} +(11.0090 - 2.58573i) q^{51} +(3.16746 + 2.30129i) q^{52} +(-2.53638 - 7.80616i) q^{53} +(-7.79259 + 2.53197i) q^{54} +(-10.2929 - 3.52738i) q^{55} +(-0.668087 - 0.217075i) q^{56} -3.50064i q^{57} +(-19.2133 - 6.24278i) q^{58} +(5.35824 - 3.89299i) q^{59} +(-6.81355 + 9.06930i) q^{60} +(7.63310 - 10.5061i) q^{61} +(1.37181 + 1.88813i) q^{62} +(6.32875 + 8.71078i) q^{63} +(5.46498 + 3.97054i) q^{64} +(3.78426 + 2.84303i) q^{65} +(21.1843 - 15.3913i) q^{66} +(2.26955 - 6.98497i) q^{67} +(1.74374 + 7.42412i) q^{68} +(-2.95607 + 9.09786i) q^{69} +(9.88081 + 3.38617i) q^{70} +(-8.07004 + 2.62211i) q^{71} +(0.412368 + 1.26914i) q^{72} +(0.863598 - 1.18864i) q^{73} +18.6079i q^{74} +(-8.41151 + 10.8310i) q^{75} +2.36072 q^{76} +(-9.37203 - 6.80918i) q^{77} +(-10.8336 + 3.52003i) q^{78} +(4.40451 - 1.43111i) q^{79} +(7.64831 + 5.74599i) q^{80} +(-0.653245 + 2.01048i) q^{81} -8.52703i q^{82} +(-2.47300 + 7.61111i) q^{83} +(-9.77090 + 7.09897i) q^{84} +(1.96421 + 9.00788i) q^{85} +(10.6370 + 7.72826i) q^{86} +(22.8469 - 16.5993i) q^{87} +(-0.843913 - 1.16155i) q^{88} +(-3.36173 - 2.44244i) q^{89} +(-5.82877 - 18.9663i) q^{90} +(2.96212 + 4.07701i) q^{91} +(-6.13531 - 1.99348i) q^{92} -3.26249 q^{93} +(0.787881 - 2.42485i) q^{94} +(2.85360 + 0.0456584i) q^{95} +(-20.3562 + 6.61412i) q^{96} +(-9.23012 + 2.99905i) q^{97} +(-2.11444 - 1.53623i) q^{98} +22.0065i 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

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