LMFDB - Embedded newform 425.2.q.a.84.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

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([7, 5]))

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

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

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (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:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.20
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453067 + 0.623593i) q^{2} +(0.240491 + 0.740156i) q^{3} +(0.434435 + 1.33705i) q^{4} +(-2.23529 + 0.0588141i) q^{5} +(-0.570514 - 0.185371i) q^{6} -2.18212 q^{7} +(-2.49676 - 0.811247i) q^{8} +(1.93706 - 1.40735i) q^{9} +(0.976061 - 1.42056i) q^{10} +(-2.32047 + 3.19385i) q^{11} +(-0.885151 + 0.643100i) q^{12} +(-2.37819 - 3.27329i) q^{13} +(0.988648 - 1.36076i) q^{14} +(-0.581100 - 1.64032i) q^{15} +(-0.637648 + 0.463278i) q^{16} +(0.465129 - 4.09679i) q^{17} +1.84556i q^{18} +(-1.20332 + 3.70344i) q^{19} +(-1.04973 - 2.96316i) q^{20} +(-0.524782 - 1.61511i) q^{21} +(-0.940336 - 2.89406i) q^{22} +(-1.21493 - 0.882696i) q^{23} -2.04309i q^{24} +(4.99308 - 0.262933i) q^{25} +3.11868 q^{26} +(3.39635 + 2.46759i) q^{27} +(-0.947992 - 2.91762i) q^{28} +(-8.67033 + 2.81716i) q^{29} +(1.28617 + 0.380805i) q^{30} +(1.85861 + 0.603899i) q^{31} -5.85803i q^{32} +(-2.92200 - 0.949416i) q^{33} +(2.34399 + 2.14617i) q^{34} +(4.87769 - 0.128340i) q^{35} +(2.72324 + 1.97855i) q^{36} +(0.531257 - 0.385981i) q^{37} +(-1.76425 - 2.42829i) q^{38} +(1.85081 - 2.54743i) q^{39} +(5.62871 + 1.66653i) q^{40} +(-2.25941 - 3.10981i) q^{41} +(1.24493 + 0.404503i) q^{42} +10.0827i q^{43} +(-5.27845 - 1.71507i) q^{44} +(-4.24712 + 3.25978i) q^{45} +(1.10088 - 0.357699i) q^{46} +(4.67828 - 1.52006i) q^{47} +(-0.496247 - 0.360544i) q^{48} -2.23833 q^{49} +(-2.09824 + 3.23278i) q^{50} +(3.14412 - 0.640973i) q^{51} +(3.34340 - 4.60180i) q^{52} +(-9.85596 + 3.20240i) q^{53} +(-3.07754 + 0.999955i) q^{54} +(4.99909 - 7.27568i) q^{55} +(5.44824 + 1.77024i) q^{56} -3.03051 q^{57} +(2.17148 - 6.68312i) q^{58} +(-11.9770 + 8.70178i) q^{59} +(1.94075 - 1.48958i) q^{60} +(1.64612 - 2.26569i) q^{61} +(-1.21866 + 0.885409i) q^{62} +(-4.22690 + 3.07102i) q^{63} +(2.37773 + 1.72752i) q^{64} +(5.50846 + 7.17690i) q^{65} +(1.91591 - 1.39199i) q^{66} +(-4.45821 - 1.44856i) q^{67} +(5.67970 - 1.15789i) q^{68} +(0.361153 - 1.11152i) q^{69} +(-2.12989 + 3.09984i) q^{70} +(-7.01974 + 2.28085i) q^{71} +(-5.97808 + 1.94239i) q^{72} +(3.73499 + 2.71363i) q^{73} +0.506163i q^{74} +(1.39540 + 3.63243i) q^{75} -5.47447 q^{76} +(5.06356 - 6.96939i) q^{77} +(0.750015 + 2.30831i) q^{78} +(9.21871 - 2.99534i) q^{79} +(1.39808 - 1.07307i) q^{80} +(1.21006 - 3.72418i) q^{81} +2.96291 q^{82} +(-7.65726 - 2.48800i) q^{83} +(1.93151 - 1.40332i) q^{84} +(-0.798752 + 9.18488i) q^{85} +(-6.28753 - 4.56816i) q^{86} +(-4.17028 - 5.73989i) q^{87} +(8.38466 - 6.09181i) q^{88} +(13.3639 + 9.70947i) q^{89} +(-0.108545 - 4.12537i) q^{90} +(5.18950 + 7.14274i) q^{91} +(0.652405 - 2.00790i) q^{92} +1.52089i q^{93} +(-1.17167 + 3.60603i) q^{94} +(2.47196 - 8.34905i) q^{95} +(4.33585 - 1.40880i) q^{96} +(4.91324 + 15.1214i) q^{97} +(1.01411 - 1.39581i) q^{98} +9.45240i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.453067	+	0.623593i	−0.320366	+	0.440947i	−0.938579	−	0.345064i	$-0.887857\pi$
$2$	−0.453067	+	0.623593i	−0.320366	+	0.440947i	0.618213	+	0.786011i	$0.287857\pi$
$3$	0.240491	+	0.740156i	0.138848	+	0.427329i	0.996169	−	0.0874531i	$-0.0278728\pi$
$3$	0.240491	+	0.740156i	0.138848	+	0.427329i	−0.857321	+	0.514782i	$0.827873\pi$
$4$	0.434435	+	1.33705i	0.217218	+	0.668527i
$5$	−2.23529	+	0.0588141i	−0.999654	+	0.0263024i
$5$	−2.23529	+	0.0588141i	−0.999654	+	0.0263024i
$6$	−0.570514	−	0.185371i	−0.232911	−	0.0756775i
$7$	−2.18212			−0.824766			−0.412383	−	0.911011i	$-0.635303\pi$
$7$	−2.18212			−0.824766			−0.412383	+	0.911011i	$0.635303\pi$
$8$	−2.49676	−	0.811247i	−0.882738	−	0.286819i
$9$	1.93706	−	1.40735i	0.645685	−	0.469118i
$10$	0.976061	−	1.42056i	0.308658	−	0.449220i
$11$	−2.32047	+	3.19385i	−0.699648	+	0.962983i	0.300310	+	0.953842i	$0.402910\pi$
$11$	−2.32047	+	3.19385i	−0.699648	+	0.962983i	−0.999958	+	0.00914152i	$0.997090\pi$
$12$	−0.885151	+	0.643100i	−0.255521	+	0.185647i
$13$	−2.37819	−	3.27329i	−0.659590	−	0.907848i	0.339877	−	0.940470i	$-0.389614\pi$
$13$	−2.37819	−	3.27329i	−0.659590	−	0.907848i	−0.999468	+	0.0326214i	$0.989614\pi$
$14$	0.988648	−	1.36076i	0.264227	−	0.363678i
$15$	−0.581100	−	1.64032i	−0.150039	−	0.423529i
$16$	−0.637648	+	0.463278i	−0.159412	+	0.115820i
$17$	0.465129	−	4.09679i	0.112810	−	0.993617i
$17$	0.465129	−	4.09679i	0.112810	−	0.993617i
$18$			1.84556i			0.435003i
$19$	−1.20332	+	3.70344i	−0.276061	+	0.849628i	0.712876	+	0.701290i	$0.247392\pi$
$19$	−1.20332	+	3.70344i	−0.276061	+	0.849628i	−0.988937	+	0.148338i	$0.952608\pi$
$20$	−1.04973	−	2.96316i	−0.234727	−	0.662583i
$21$	−0.524782	−	1.61511i	−0.114517	−	0.352446i
$22$	−0.940336	−	2.89406i	−0.200480	−	0.617015i
$23$	−1.21493	−	0.882696i	−0.253330	−	0.184055i	0.453872	−	0.891067i	$-0.350042\pi$
$23$	−1.21493	−	0.882696i	−0.253330	−	0.184055i	−0.707201	+	0.707012i	$0.750042\pi$
$24$		−	2.04309i		−	0.417044i
$25$	4.99308	−	0.262933i	0.998616	−	0.0525867i
$26$	3.11868			0.611623
$27$	3.39635	+	2.46759i	0.653628	+	0.474888i
$28$	−0.947992	−	2.91762i	−0.179154	−	0.551378i
$29$	−8.67033	+	2.81716i	−1.61004	+	0.523134i	−0.969563	−	0.244843i	$-0.921264\pi$
$29$	−8.67033	+	2.81716i	−1.61004	+	0.523134i	−0.640478	+	0.767977i	$0.721264\pi$
$30$	1.28617	+	0.380805i	0.234821	+	0.0695252i
$31$	1.85861	+	0.603899i	0.333816	+	0.108463i	0.471129	−	0.882064i	$-0.343847\pi$
$31$	1.85861	+	0.603899i	0.333816	+	0.108463i	−0.137313	+	0.990528i	$0.543847\pi$
$32$		−	5.85803i		−	1.03556i
$33$	−2.92200	−	0.949416i	−0.508655	−	0.165272i
$34$	2.34399	+	2.14617i	0.401991	+	0.368065i
$35$	4.87769	−	0.128340i	0.824480	−	0.0216934i
$36$	2.72324	+	1.97855i	0.453873	+	0.329758i
$37$	0.531257	−	0.385981i	0.0873381	−	0.0634548i	−0.543259	−	0.839565i	$-0.682810\pi$
$37$	0.531257	−	0.385981i	0.0873381	−	0.0634548i	0.630597	+	0.776110i	$0.282810\pi$
$38$	−1.76425	−	2.42829i	−0.286200	−	0.393920i
$39$	1.85081	−	2.54743i	0.296367	−	0.407915i
$40$	5.62871	+	1.66653i	0.889977	+	0.263502i
$41$	−2.25941	−	3.10981i	−0.352860	−	0.485670i	0.595282	−	0.803517i	$-0.297040\pi$
$41$	−2.25941	−	3.10981i	−0.352860	−	0.485670i	−0.948142	+	0.317847i	$0.897040\pi$
$42$	1.24493	+	0.404503i	0.192097	+	0.0624162i
$43$			10.0827i			1.53760i	0.639487	+	0.768802i	$0.279147\pi$
$43$			10.0827i			1.53760i	−0.639487	+	0.768802i	$0.720853\pi$
$44$	−5.27845	−	1.71507i	−0.795757	−	0.258557i
$45$	−4.24712	+	3.25978i	−0.633123	+	0.485939i
$46$	1.10088	−	0.357699i	0.162317	−	0.0527399i
$47$	4.67828	−	1.52006i	0.682397	−	0.221724i	0.0527523	−	0.998608i	$-0.483201\pi$
$47$	4.67828	−	1.52006i	0.682397	−	0.221724i	0.629644	+	0.776884i	$0.283201\pi$
$48$	−0.496247	−	0.360544i	−0.0716270	−	0.0520401i
$49$	−2.23833			−0.319762
$50$	−2.09824	+	3.23278i	−0.296735	+	0.457184i
$51$	3.14412	−	0.640973i	0.440265	−	0.0897541i
$52$	3.34340	−	4.60180i	0.463647	−	0.638155i
$53$	−9.85596	+	3.20240i	−1.35382	+	0.439883i	−0.893975	−	0.448116i	$-0.852095\pi$
$53$	−9.85596	+	3.20240i	−1.35382	+	0.439883i	−0.459845	+	0.887999i	$0.652095\pi$
$54$	−3.07754	+	0.999955i	−0.418801	+	0.136077i
$55$	4.99909	−	7.27568i	0.674077	−	0.981052i
$56$	5.44824	+	1.77024i	0.728052	+	0.236558i
$57$	−3.03051			−0.401401
$58$	2.17148	−	6.68312i	0.285129	−	0.877536i
$59$	−11.9770	+	8.70178i	−1.55927	+	1.13287i	−0.622662	+	0.782491i	$0.713949\pi$
$59$	−11.9770	+	8.70178i	−1.55927	+	1.13287i	−0.936606	+	0.350384i	$0.886051\pi$
$60$	1.94075	−	1.48958i	0.250550	−	0.192304i
$61$	1.64612	−	2.26569i	0.210764	−	0.290092i	−0.690526	−	0.723307i	$-0.742621\pi$
$61$	1.64612	−	2.26569i	0.210764	−	0.290092i	0.901290	+	0.433215i	$0.142621\pi$
$62$	−1.21866	+	0.885409i	−0.154770	+	0.112447i
$63$	−4.22690	+	3.07102i	−0.532539	+	0.386912i
$64$	2.37773	+	1.72752i	0.297216	+	0.215940i
$65$	5.50846	+	7.17690i	0.683241	+	0.890185i
$66$	1.91591	−	1.39199i	0.235832	−	0.171342i
$67$	−4.45821	−	1.44856i	−0.544657	−	0.176970i	0.0237490	−	0.999718i	$-0.492440\pi$
$67$	−4.45821	−	1.44856i	−0.544657	−	0.176970i	−0.568406	+	0.822748i	$0.692440\pi$
$68$	5.67970	−	1.15789i	0.688764	−	0.140414i
$69$	0.361153	−	1.11152i	0.0434777	−	0.133811i
$70$	−2.12989	+	3.09984i	−0.254570	+	0.370502i
$71$	−7.01974	+	2.28085i	−0.833090	+	0.270687i	−0.694346	−	0.719641i	$-0.744306\pi$
$71$	−7.01974	+	2.28085i	−0.833090	+	0.270687i	−0.138743	+	0.990328i	$0.544306\pi$
$72$	−5.97808	+	1.94239i	−0.704523	+	0.228913i
$73$	3.73499	+	2.71363i	0.437147	+	0.317606i	0.784500	−	0.620128i	$-0.212919\pi$
$73$	3.73499	+	2.71363i	0.437147	+	0.317606i	−0.347353	+	0.937734i	$0.612919\pi$
$74$			0.506163i			0.0588402i
$75$	1.39540	+	3.63243i	0.161127	+	0.419436i
$76$	−5.47447			−0.627965
$77$	5.06356	−	6.96939i	0.577046	−	0.794235i
$78$	0.750015	+	2.30831i	0.0849225	+	0.261364i
$79$	9.21871	−	2.99534i	1.03719	−	0.337002i	0.259558	−	0.965727i	$-0.416423\pi$
$79$	9.21871	−	2.99534i	1.03719	−	0.337002i	0.777627	+	0.628725i	$0.216423\pi$
$80$	1.39808	−	1.07307i	0.156310	−	0.119972i
$81$	1.21006	−	3.72418i	0.134451	−	0.413798i
$82$	2.96291			0.327199
$83$	−7.65726	−	2.48800i	−0.840494	−	0.273093i	−0.143035	−	0.989718i	$-0.545686\pi$
$83$	−7.65726	−	2.48800i	−0.840494	−	0.273093i	−0.697459	+	0.716625i	$0.745686\pi$
$84$	1.93151	−	1.40332i	0.210745	−	0.153115i
$85$	−0.798752	+	9.18488i	−0.0866369	+	0.996240i
$86$	−6.28753	−	4.56816i	−0.678001	−	0.492597i
$87$	−4.17028	−	5.73989i	−0.447101	−	0.615381i
$88$	8.38466	−	6.09181i	0.893808	−	0.649390i
$89$	13.3639	+	9.70947i	1.41657	+	1.02920i	0.992325	+	0.123656i	$0.0394618\pi$
$89$	13.3639	+	9.70947i	1.41657	+	1.02920i	0.424249	+	0.905546i	$0.360538\pi$
$90$	−0.108545	−	4.12537i	−0.0114416	−	0.434852i
$91$	5.18950	+	7.14274i	0.544008	+	0.748762i
$92$	0.652405	−	2.00790i	0.0680180	−	0.209338i
$93$			1.52089i			0.157709i
$94$	−1.17167	+	3.60603i	−0.120849	+	0.371933i
$95$	2.47196	−	8.34905i	0.253618	−	0.856595i
$96$	4.33585	−	1.40880i	0.442526	−	0.143785i
$97$	4.91324	+	15.1214i	0.498864	+	1.53534i	0.810848	+	0.585257i	$0.199006\pi$
$97$	4.91324	+	15.1214i	0.498864	+	1.53534i	−0.311984	+	0.950087i	$0.600994\pi$
$98$	1.01411	−	1.39581i	0.102441	−	0.140998i
$99$			9.45240i			0.950002i
$100$	2.52073	+	6.56180i	0.252073	+	0.656180i
$101$	13.0301			1.29654			0.648272	−	0.761409i	$-0.275492\pi$
$101$	13.0301			1.29654			0.648272	+	0.761409i	$0.275492\pi$
$102$	−1.02479	+	2.25105i	−0.101469	+	0.222887i
$103$	−7.66475	+	2.49043i	−0.755230	+	0.245389i	−0.661230	−	0.750183i	$-0.729965\pi$
$103$	−7.66475	+	2.49043i	−0.755230	+	0.245389i	−0.0939999	+	0.995572i	$0.529965\pi$
$104$	3.28232	+	10.1019i	0.321857	+	0.990575i
$105$	1.26803	+	3.57939i	0.123747	+	0.349312i
$106$	2.46842	−	7.59700i	0.239754	−	0.737886i
$107$	7.94649			0.768216			0.384108	−	0.923288i	$-0.374509\pi$
$107$	7.94649			0.768216			0.384108	+	0.923288i	$0.374509\pi$
$108$	−1.82381	+	5.61311i	−0.175496	+	0.540122i
$109$	5.76721	+	7.93789i	0.552399	+	0.760312i	0.990335	−	0.138694i	$-0.0442906\pi$
$109$	5.76721	+	7.93789i	0.552399	+	0.760312i	−0.437937	+	0.899006i	$0.644291\pi$
$110$	2.27214	+	6.41376i	0.216640	+	0.611528i
$111$	0.413448	+	0.300388i	0.0392428	+	0.0285115i
$112$	1.39143	−	1.01093i	0.131477	−	0.0955239i
$113$	−14.5970	+	10.6053i	−1.37317	+	0.997667i	−0.375689	+	0.926746i	$0.622594\pi$
$113$	−14.5970	+	10.6053i	−1.37317	+	0.997667i	−0.997482	+	0.0709208i	$0.977406\pi$
$114$	1.37302	−	1.88980i	0.128595	−	0.176996i
$115$	2.76763	+	1.90163i	0.258083	+	0.177328i
$116$	−7.53340	−	10.3688i	−0.699459	−	0.962722i
$117$	−9.21337	−	2.99360i	−0.851776	−	0.276759i
$118$		−	11.4112i		−	1.05049i
$119$	−1.01497	+	8.93970i	−0.0930422	+	0.819501i
$120$	0.120162	+	4.56691i	0.0109693	+	0.416900i
$121$	−1.41693	−	4.36087i	−0.128812	−	0.396442i
$122$	0.667065	+	2.05302i	0.0603932	+	0.185871i
$123$	1.75837	−	2.42019i	0.158547	−	0.218222i
$124$			2.74742i			0.246725i
$125$	−11.1455	+	0.881397i	−0.996888	+	0.0788346i
$126$		−	4.02724i		−	0.358775i
$127$	1.02806	−	1.41500i	0.0912255	−	0.125561i	−0.760965	−	0.648793i	$-0.775274\pi$
$127$	1.02806	−	1.41500i	0.0912255	−	0.125561i	0.852190	+	0.523232i	$0.175274\pi$
$128$	8.98809	−	2.92041i	0.794442	−	0.258130i
$129$	−7.46280	+	2.42481i	−0.657063	+	0.213493i
$130$	−6.97117	+	0.183422i	−0.611412	+	0.0160872i
$131$	12.4029	+	4.02994i	1.08364	+	0.352097i	0.795787	−	0.605576i	$-0.207057\pi$
$131$	12.4029	+	4.02994i	1.08364	+	0.352097i	0.287857	+	0.957673i	$0.407057\pi$
$132$		−	4.31934i		−	0.375950i
$133$	2.62580	−	8.08137i	0.227685	−	0.700744i
$134$	2.92318	−	2.12381i	0.252524	−	0.183470i
$135$	−7.73697	−	5.31604i	−0.665892	−	0.457532i
$136$	−4.48482	+	9.85136i	−0.384570	+	0.844747i
$137$	−4.27198	−	5.87988i	−0.364980	−	0.502352i	0.586548	−	0.809915i	$-0.300487\pi$
$137$	−4.27198	−	5.87988i	−0.364980	−	0.502352i	−0.951528	+	0.307563i	$0.900487\pi$
$138$	0.529506	+	0.728803i	0.0450746	+	0.0620398i
$139$	7.88081	−	10.8470i	0.668442	−	0.920031i	−0.331282	−	0.943532i	$-0.607481\pi$
$139$	7.88081	−	10.8470i	0.668442	−	0.920031i	0.999724	+	0.0235005i	$0.00748114\pi$
$140$	2.29064	+	6.46599i	0.193594	+	0.546476i
$141$	2.25017	+	3.09709i	0.189498	+	0.260822i
$142$	1.75809	−	5.41083i	0.147535	−	0.454067i
$143$	15.9729			1.33572
$144$	−0.583163	+	1.79479i	−0.0485969	+	0.149566i
$145$	19.2151	−	6.80712i	1.59572	−	0.565301i
$146$	−3.38440	+	1.09966i	−0.280095	+	0.0910083i
$147$	−0.538299	−	1.65671i	−0.0443982	−	0.136643i
$148$	0.746874	+	0.542636i	0.0613927	+	0.0446044i
$149$	−11.9172			−0.976293			−0.488147	−	0.872762i	$-0.662327\pi$
$149$	−11.9172			−0.976293			−0.488147	+	0.872762i	$0.662327\pi$
$150$	−2.89736	−	0.775567i	−0.236569	−	0.0633248i
$151$	−7.60060			−0.618528			−0.309264	−	0.950976i	$-0.600083\pi$
$151$	−7.60060			−0.618528			−0.309264	+	0.950976i	$0.600083\pi$
$152$	6.00881	−	8.27042i	0.487379	−	0.670819i
$153$	−4.86465	−	8.59031i	−0.393283	−	0.694485i
$154$	2.05193	+	6.31519i	0.165349	+	0.508893i
$155$	−4.19006	−	1.24058i	−0.336554	−	0.0996457i
$156$	4.21011	+	1.36795i	0.337079	+	0.109523i
$157$		−	2.99678i		−	0.239169i	−0.992824	−	0.119584i	$-0.961844\pi$
$157$		−	2.99678i		−	0.239169i	0.992824	−	0.119584i	$-0.0381562\pi$
$158$	−2.30882	+	7.10581i	−0.183680	+	0.565308i
$159$	−4.74054	−	6.52480i	−0.375950	−	0.517450i
$160$	0.344534	+	13.0944i	0.0272378	+	1.03520i
$161$	2.65112	+	1.92615i	0.208938	+	0.151802i
$162$	1.77413	+	2.44188i	0.139389	+	0.191853i
$163$	−10.3135	+	7.49317i	−0.807813	+	0.586910i	−0.913196	−	0.407521i	$-0.866393\pi$
$163$	−10.3135	+	7.49317i	−0.807813	+	0.586910i	0.105383	+	0.994432i	$0.466393\pi$
$164$	3.17642	−	4.37196i	0.248036	−	0.341393i
$165$	6.58737	+	1.95037i	0.512826	+	0.151836i
$166$	5.02075	−	3.64779i	0.389685	−	0.283123i
$167$	1.09302	−	3.36397i	0.0845805	−	0.260312i	−0.899818	−	0.436266i	$-0.856301\pi$
$167$	1.09302	−	3.36397i	0.0845805	−	0.260312i	0.984398	+	0.175953i	$0.0563008\pi$
$168$			4.45828i			0.343963i
$169$	−1.04146	+	3.20528i	−0.0801121	+	0.246560i
$170$	−5.36574	−	4.65946i	−0.411533	−	0.357364i
$171$	2.88115	+	8.86727i	0.220327	+	0.678097i
$172$	−13.4812	+	4.38030i	−1.02793	+	0.333995i
$173$	−16.1053	−	11.7012i	−1.22446	−	0.889623i	−0.227999	−	0.973661i	$-0.573218\pi$
$173$	−16.1053	−	11.7012i	−1.22446	−	0.889623i	−0.996463	+	0.0840384i	$0.973218\pi$
$174$	5.46877			0.414586
$175$	−10.8955	+	0.573754i	−0.823624	+	0.0433717i
$176$		−	3.11158i		−	0.234544i
$177$	−9.32102	−	6.77212i	−0.700611	−	0.509024i
$178$	−12.1095	+	3.93462i	−0.907646	+	0.294912i
$179$	−4.82967	−	14.8642i	−0.360986	−	1.11100i	−0.952456	−	0.304675i	$-0.901452\pi$
$179$	−4.82967	−	14.8642i	−0.360986	−	1.11100i	0.591470	−	0.806327i	$-0.298548\pi$
$180$	−6.20360	−	4.26247i	−0.462389	−	0.317706i
$181$	10.9367	+	3.55354i	0.812916	+	0.264132i	0.685832	−	0.727760i	$-0.259438\pi$
$181$	10.9367	+	3.55354i	0.812916	+	0.264132i	0.127084	+	0.991892i	$0.459438\pi$
$182$	−6.80535			−0.504446
$183$	2.07284	+	0.673506i	0.153229	+	0.0497870i
$184$	2.31730	+	3.18948i	0.170833	+	0.235132i
$185$	−1.16481	+	0.894026i	−0.0856388	+	0.0657301i
$186$	−0.948418	−	0.689066i	−0.0695414	−	0.0505248i
$187$	12.0052	+	10.9920i	0.877908	+	0.803817i
$188$	4.06482	+	5.59474i	0.296457	+	0.408038i
$189$	−7.41126	−	5.38459i	−0.539090	−	0.391671i
$190$	4.08645	+	5.32418i	0.296462	+	0.386256i
$191$	15.7937	−	11.4748i	1.14280	−	0.830289i	0.155289	−	0.987869i	$-0.450369\pi$
$191$	15.7937	−	11.4748i	1.14280	−	0.830289i	0.987506	+	0.157580i	$0.0503692\pi$
$192$	−0.706811	+	2.17534i	−0.0510097	+	0.156992i
$193$	3.42804			0.246756			0.123378	−	0.992360i	$-0.460627\pi$
$193$	3.42804			0.246756			0.123378	+	0.992360i	$0.460627\pi$
$194$	−11.6556	−	3.78714i	−0.836824	−	0.271901i
$195$	−3.98729	+	5.80310i	−0.285536	+	0.415569i
$196$	−0.972411	−	2.99277i	−0.0694579	−	0.213769i
$197$	−1.57210	−	4.83841i	−0.112007	−	0.344723i	0.879304	−	0.476261i	$-0.158008\pi$
$197$	−1.57210	−	4.83841i	−0.112007	−	0.344723i	−0.991311	+	0.131538i	$0.958008\pi$
$198$	−5.89445	−	4.28257i	−0.418900	−	0.304349i
$199$		−	8.72891i		−	0.618776i	−0.950936	−	0.309388i	$-0.899876\pi$
$199$		−	8.72891i		−	0.618776i	0.950936	−	0.309388i	$-0.100124\pi$
$200$	−12.6798	−	3.39414i	−0.896600	−	0.240002i
$201$		−	3.64814i		−	0.257320i
$202$	−5.90351	+	8.12548i	−0.415369	+	0.571707i
$203$	18.9197	−	6.14740i	1.32791	−	0.431463i
$204$	2.22293	+	3.92540i	0.155636	+	0.274833i
$205$	5.23334	+	6.81845i	0.365512	+	0.476221i
$206$	1.91963	−	5.90801i	0.133747	−	0.411631i
$207$	−3.59565			−0.249915
$208$	3.03289	+	0.985446i	0.210293	+	0.0683284i
$209$	−9.03598	−	12.4370i	−0.625032	−	0.860282i
$210$	−2.80658	−	0.830964i	−0.193673	−	0.0573420i
$211$	3.59267	−	4.94489i	0.247330	−	0.340420i	−0.667244	−	0.744839i	$-0.732526\pi$
$211$	3.59267	−	4.94489i	0.247330	−	0.340420i	0.914574	+	0.404419i	$0.132526\pi$
$212$	−8.56356	−	11.7867i	−0.588148	−	0.809516i
$213$	−3.37637	−	4.64717i	−0.231345	−	0.318419i
$214$	−3.60029	+	4.95537i	−0.246111	+	0.338742i
$215$	−0.593007	−	22.5379i	−0.0404428	−	1.53707i
$216$	−6.47804	−	8.91626i	−0.440775	−	0.606675i
$217$	−4.05572	−	1.31778i	−0.275320	−	0.0894569i
$218$	−7.56294			−0.512227
$219$	−1.11028	+	3.41708i	−0.0750255	+	0.230905i
$220$	11.8998	+	3.52325i	0.802282	+	0.237537i
$221$	−14.5161	+	8.22042i	−0.976462	+	0.552965i
$222$	−0.374639	+	0.121728i	−0.0251441	+	0.00816983i
$223$	−12.4463	+	17.1308i	−0.833464	+	1.14716i	0.153804	+	0.988101i	$0.450847\pi$
$223$	−12.4463	+	17.1308i	−0.833464	+	1.14716i	−0.987268	+	0.159064i	$0.949153\pi$
$224$			12.7829i			0.854096i
$225$	9.30184	−	7.53635i	0.620123	−	0.502423i
$226$		−	13.9075i		−	0.925114i
$227$	−2.61836	−	1.90235i	−0.173787	−	0.126264i	0.497492	−	0.867469i	$-0.334255\pi$
$227$	−2.61836	−	1.90235i	−0.173787	−	0.126264i	−0.671278	+	0.741205i	$0.734255\pi$
$228$	−1.31656	−	4.05196i	−0.0871914	−	0.268348i
$229$	−5.80641	−	17.8703i	−0.383698	−	1.18090i	−0.937420	−	0.348200i	$-0.886793\pi$
$229$	−5.80641	−	17.8703i	−0.383698	−	1.18090i	0.553722	−	0.832702i	$-0.313207\pi$
$230$	−2.43976	+	0.864311i	−0.160873	+	0.0569909i
$231$	6.37617	+	2.07174i	0.419521	+	0.136311i
$232$	23.9332			1.57129
$233$	2.82107	−	8.68237i	0.184815	−	0.568801i	−0.815130	−	0.579277i	$-0.803335\pi$
$233$	2.82107	−	8.68237i	0.184815	−	0.568801i	0.999945	+	0.0104763i	$0.00333478\pi$
$234$	6.04106	−	4.38909i	0.394916	−	0.286924i
$235$	−10.3679	+	3.67294i	−0.676329	+	0.239596i
$236$	−16.8380	−	12.2335i	−1.09606	−	0.796333i
$237$	4.43403	+	6.10293i	0.288022	+	0.396428i
$238$	−5.11488	−	4.68321i	−0.331548	−	0.303567i
$239$	−11.9265	−	8.66514i	−0.771464	−	0.560502i	0.130941	−	0.991390i	$-0.458200\pi$
$239$	−11.9265	−	8.66514i	−0.771464	−	0.560502i	−0.902405	+	0.430889i	$0.858200\pi$
$240$	1.13046	+	0.776736i	0.0729710	+	0.0501381i
$241$	−9.59986	−	13.2131i	−0.618381	−	0.851129i	0.378853	−	0.925457i	$-0.376319\pi$
$241$	−9.59986	−	13.2131i	−0.618381	−	0.851129i	−0.997234	+	0.0743283i	$0.976319\pi$
$242$	3.36137	+	1.09218i	0.216077	+	0.0702077i
$243$	15.6418			1.00342
$244$	3.74448	+	1.21666i	0.239716	+	0.0778884i
$245$	5.00333	−	0.131645i	0.319651	−	0.00841052i
$246$	0.712555	+	2.19302i	0.0454308	+	0.139822i
$247$	14.9842	−	4.86865i	0.953420	−	0.309785i
$248$	−4.15059	−	3.01558i	−0.263563	−	0.191490i
$249$		−	6.26591i		−	0.397086i
$250$	4.50004	−	7.34961i	0.284608	−	0.464830i
$251$	12.2334			0.772168			0.386084	−	0.922464i	$-0.373827\pi$
$251$	12.2334			0.772168			0.386084	+	0.922464i	$0.373827\pi$
$252$	−5.94244	−	4.31744i	−0.374339	−	0.271973i
$253$	5.63840	−	1.83203i	0.354483	−	0.115179i
$254$	0.416606	+	1.28218i	0.0261402	+	0.0804512i
$255$	−6.99033	+	1.61768i	−0.437752	+	0.101303i
$256$	−4.06748	+	12.5184i	−0.254218	+	0.782401i
$257$			22.2697i			1.38915i	0.719422	+	0.694573i	$0.244407\pi$
$257$			22.2697i			1.38915i	−0.719422	+	0.694573i	$0.755593\pi$
$258$	1.86905	−	5.75235i	0.116362	−	0.358126i
$259$	−1.15927	+	0.842258i	−0.0720334	+	0.0523354i
$260$	−7.20284	+	10.4830i	−0.446701	+	0.650129i
$261$	−12.8302	+	17.6592i	−0.794168	+	1.09308i
$262$	−8.13237	+	5.90851i	−0.502420	+	0.365029i
$263$	10.6525	+	14.6619i	0.656859	+	0.904089i	0.999372	−	0.0354243i	$-0.0112783\pi$
$263$	10.6525	+	14.6619i	0.656859	+	0.904089i	−0.342514	+	0.939513i	$0.611278\pi$
$264$	6.52533	+	4.74093i	0.401606	+	0.291784i
$265$	21.8426	−	7.73797i	1.34178	−	0.475340i
$266$	3.84982	+	5.29883i	0.236048	+	0.324892i
$267$	−3.97261	+	12.2264i	−0.243120	+	0.748246i
$268$		−	6.59018i		−	0.402559i
$269$	22.2740	+	7.23726i	1.35807	+	0.441264i	0.895398	−	0.445266i	$-0.146891\pi$
$269$	22.2740	+	7.23726i	1.35807	+	0.441264i	0.462672	+	0.886530i	$0.346891\pi$
$270$	6.82041	−	2.41620i	0.415077	−	0.147045i
$271$	1.87474	+	5.76985i	0.113882	+	0.350493i	0.991712	−	0.128479i	$-0.0410095\pi$
$271$	1.87474	+	5.76985i	0.113882	+	0.350493i	−0.877830	+	0.478972i	$0.841009\pi$
$272$	1.60136	+	2.82779i	0.0970969	+	0.171460i
$273$	−4.03871	+	5.55880i	−0.244434	+	0.336434i
$274$	5.60214			0.338438
$275$	−10.7465	+	16.5573i	−0.648040	+	0.998443i
$276$	1.64305			0.0989003
$277$	−14.4467	−	10.4961i	−0.868015	−	0.630650i	0.0620382	−	0.998074i	$-0.480240\pi$
$277$	−14.4467	−	10.4961i	−0.868015	−	0.630650i	−0.930054	+	0.367424i	$0.880240\pi$
$278$	3.19358	+	9.82883i	0.191538	+	0.589494i
$279$	4.45013	−	1.44594i	0.266422	−	0.0865659i
$280$	−12.2825	−	3.63658i	−0.734022	−	0.217327i
$281$	6.08219	−	18.7191i	0.362833	−	1.11668i	−0.588494	−	0.808502i	$-0.700279\pi$
$281$	6.08219	−	18.7191i	0.362833	−	1.11668i	0.951327	−	0.308183i	$-0.0997210\pi$
$282$	−2.95080			−0.175718
$283$	1.96819	−	6.05746i	0.116997	−	0.360079i	−0.875362	−	0.483469i	$-0.839377\pi$
$283$	1.96819	−	6.05746i	0.116997	−	0.360079i	0.992358	+	0.123390i	$0.0393766\pi$
$284$	−6.09925	−	8.39489i	−0.361924	−	0.498145i
$285$	6.77409	−	0.178237i	0.401262	−	0.0105578i
$286$	−7.23680	+	9.96061i	−0.427921	+	0.588983i
$287$	4.93031	+	6.78599i	0.291027	+	0.400564i
$288$	−8.24432	−	11.3473i	−0.485801	−	0.668648i
$289$	−16.5673	−	3.81107i	−0.974548	−	0.224181i
$290$	−4.46083	+	15.0664i	−0.261949	+	0.884732i
$291$	−10.0106	+	7.27312i	−0.586831	+	0.426358i
$292$	−2.00566	+	6.17278i	−0.117372	+	0.361235i
$293$			5.22242i			0.305097i	0.988296	+	0.152548i	$0.0487480\pi$
$293$			5.22242i			0.305097i	−0.988296	+	0.152548i	$0.951252\pi$
$294$	1.27700	+	0.414923i	0.0744762	+	0.0241988i
$295$	26.2603	−	20.1554i	1.52893	−	1.17350i
$296$	−1.63955	+	0.532721i	−0.0952967	+	0.0309638i
$297$	−15.7623	+	5.12147i	−0.914619	+	0.297178i
$298$	5.39928	−	7.43147i	0.312772	−	0.430493i
$299$			6.07603i			0.351386i
$300$	−4.25054	+	3.44379i	−0.245405	+	0.198827i
$301$		−	22.0018i		−	1.26816i
$302$	3.44358	−	4.73968i	0.198156	−	0.272738i
$303$	3.13363	+	9.64431i	0.180022	+	0.554051i
$304$	−0.948428	−	2.91896i	−0.0543961	−	0.167414i
$305$	−3.54631	+	5.16130i	−0.203061	+	0.295535i
$306$	7.56086	+	0.858424i	0.432226	+	0.0490728i
$307$			5.89713i			0.336567i	0.985739	+	0.168283i	$0.0538224\pi$
$307$			5.89713i			0.336567i	−0.985739	+	0.168283i	$0.946178\pi$
$308$	11.5182	+	3.74250i	0.656313	+	0.213249i
$309$	−3.68661	−	5.07418i	−0.209724	−	0.288660i
$310$	2.67199	−	2.05082i	0.151759	−	0.116479i
$311$	−16.9049	+	23.2676i	−0.958588	+	1.31938i	−0.0109821	+	0.999940i	$0.503496\pi$
$311$	−16.9049	+	23.2676i	−0.958588	+	1.31938i	−0.947606	+	0.319443i	$0.896504\pi$
$312$	−6.68763	+	4.85885i	−0.378613	+	0.275078i
$313$	−26.1145	+	18.9733i	−1.47608	+	1.07243i	−0.497282	+	0.867589i	$0.665669\pi$
$313$	−26.1145	+	18.9733i	−1.47608	+	1.07243i	−0.978795	+	0.204844i	$0.934331\pi$
$314$	1.86877	+	1.35774i	0.105461	+	0.0766217i
$315$	9.26774	−	7.11324i	0.522178	−	0.400786i
$316$	8.00987	+	11.0246i	0.450590	+	0.620184i
$317$	−3.53803	+	10.8889i	−0.198715	+	0.611583i	0.801198	+	0.598400i	$0.204197\pi$
$317$	−3.53803	+	10.8889i	−0.198715	+	0.611583i	−0.999913	+	0.0131834i	$0.995803\pi$
$318$	6.21660			0.348610
$319$	11.1216	−	34.2289i	0.622693	−	1.91645i
$320$	−5.41652	−	3.72167i	−0.302793	−	0.208048i
$321$	1.91106	+	5.88164i	0.106665	+	0.328281i
$322$	−2.40227	+	0.780544i	−0.133873	+	0.0434980i
$323$	14.6125	+	6.65233i	0.813062	+	0.370145i
$324$	5.50512			0.305840
$325$	−12.7351	−	15.7185i	−0.706419	−	0.871907i
$326$		−	9.82630i		−	0.544229i
$327$	−4.48831	+	6.17763i	−0.248204	+	0.341623i
$328$	3.11838	+	9.59738i	0.172184	+	0.529926i
$329$	−10.2086	+	3.31697i	−0.562817	+	0.182870i
$330$	−4.20076	+	3.22419i	−0.231244	+	0.177486i
$331$	−4.11225	+	12.6562i	−0.226030	+	0.695648i	0.772156	+	0.635433i	$0.219179\pi$
$331$	−4.11225	+	12.6562i	−0.226030	+	0.695648i	−0.998185	+	0.0602148i	$0.980821\pi$
$332$		−	11.3191i		−	0.621214i
$333$	0.485863	−	1.49533i	0.0266251	−	0.0819437i
$334$	1.60254	+	2.20570i	0.0876870	+	0.120691i
$335$	10.0506	+	2.97575i	0.549123	+	0.162583i
$336$	1.08287	+	0.786752i	0.0590755	+	0.0429209i
$337$	3.67462	−	2.66977i	0.200170	−	0.145432i	−0.483185	−	0.875518i	$-0.660520\pi$
$337$	3.67462	−	2.66977i	0.200170	−	0.145432i	0.683355	+	0.730086i	$0.260520\pi$
$338$	−1.52694	−	2.10165i	−0.0830545	−	0.114315i
$339$	−11.3601	−	8.25356i	−0.616994	−	0.448272i
$340$	−12.6277	+	2.92226i	−0.684833	+	0.158482i
$341$	−6.24161	+	4.53480i	−0.338002	+	0.245573i
$342$	−6.83492	−	2.22080i	−0.369590	−	0.120087i
$343$	20.1592			1.08849
$344$	8.17959	−	25.1742i	0.441014	−	1.35730i
$345$	−0.741911	+	2.50580i	−0.0399431	+	0.134908i
$346$	14.5935	−	4.74172i	0.784553	−	0.254917i
$347$	−5.18585	−	15.9604i	−0.278391	−	0.856799i	−0.988302	−	0.152508i	$-0.951265\pi$
$347$	−5.18585	−	15.9604i	−0.278391	−	0.856799i	0.709912	−	0.704291i	$-0.248735\pi$
$348$	5.86284	−	8.06950i	0.314281	−	0.432571i
$349$	−5.42076			−0.290166			−0.145083	−	0.989419i	$-0.546345\pi$
$349$	−5.42076			−0.290166			−0.145083	+	0.989419i	$0.546345\pi$
$350$	4.57861	−	7.05432i	0.244737	−	0.377069i
$351$		−	16.9856i		−	0.906626i
$352$	18.7097	+	13.5934i	0.997229	+	0.724530i
$353$	1.31632	−	0.427699i	0.0700608	−	0.0227641i	−0.273777	−	0.961793i	$-0.588273\pi$
$353$	1.31632	−	0.427699i	0.0700608	−	0.0227641i	0.343838	+	0.939029i	$0.388273\pi$
$354$	8.44609	−	2.74430i	0.448905	−	0.145858i
$355$	15.5570	−	5.51123i	0.825682	−	0.292506i
$356$	−7.17632	+	22.0864i	−0.380344	+	1.17058i
$357$	−6.86086	+	1.39868i	−0.363115	+	0.0740261i
$358$	11.4574	+	3.72272i	0.605540	+	0.196752i
$359$	−20.4734	+	14.8748i	−1.08055	+	0.785063i	−0.977778	−	0.209642i	$-0.932770\pi$
$359$	−20.4734	+	14.8748i	−1.08055	+	0.785063i	−0.102769	+	0.994705i	$0.532770\pi$
$360$	13.2485	−	4.69342i	0.698258	−	0.247365i
$361$	3.10383	+	2.25506i	0.163359	+	0.118687i
$362$	−7.17100	+	5.21004i	−0.376899	+	0.273833i
$363$	2.88696	−	2.09750i	0.151526	−	0.110090i
$364$	−7.29573	+	10.0417i	−0.382400	+	0.526328i
$365$	−8.50840	−	5.84609i	−0.445350	−	0.305998i
$366$	−1.35913	+	0.987464i	−0.0710428	+	0.0516156i
$367$	6.70807	−	20.6453i	0.350159	−	1.07768i	−0.608605	−	0.793473i	$-0.708271\pi$
$367$	6.70807	−	20.6453i	0.350159	−	1.07768i	0.958764	−	0.284204i	$-0.0917294\pi$
$368$	1.18363			0.0617009
$369$	−8.75320	−	2.84409i	−0.455673	−	0.148057i
$370$	−0.0297695	−	1.13142i	−0.00154764	−	0.0588199i
$371$	21.5069	−	6.98803i	1.11658	−	0.362800i
$372$	−2.03352	+	0.660730i	−0.105433	+	0.0342573i
$373$	−1.50063	+	2.06543i	−0.0776994	+	0.106944i	−0.846098	−	0.533028i	$-0.821054\pi$
$373$	−1.50063	+	2.06543i	−0.0776994	+	0.106944i	0.768398	+	0.639972i	$0.221054\pi$
$374$	−12.2937	+	2.50624i	−0.635693	+	0.129595i
$375$	−3.33278	−	8.03747i	−0.172104	−	0.415053i
$376$	−12.9137			−0.665972
$377$	29.8411	+	21.6808i	1.53689	+	1.11662i
$378$	6.71558	−	2.18203i	0.345412	−	0.112231i
$379$	−12.3170	+	4.00204i	−0.632683	+	0.205571i	−0.607763	−	0.794118i	$-0.707933\pi$
$379$	−12.3170	+	4.00204i	−0.632683	+	0.205571i	−0.0249196	+	0.999689i	$0.507933\pi$
$380$	12.2371	−	0.321976i	0.627748	−	0.0165170i
$381$	1.29456	+	0.420629i	0.0663224	+	0.0215495i
$382$			15.0477i			0.769908i
$383$	15.7473	+	5.11662i	0.804652	+	0.261447i	0.682331	−	0.731043i	$-0.260966\pi$
$383$	15.7473	+	5.11662i	0.804652	+	0.261447i	0.122321	+	0.992491i	$0.460966\pi$
$384$	4.32311	+	5.95025i	0.220613	+	0.303648i
$385$	−10.9086	+	15.8764i	−0.555956	+	0.809138i
$386$	−1.55313	+	2.13770i	−0.0790522	+	0.108806i
$387$	14.1900	+	19.5308i	0.721318	+	0.992809i
$388$	−18.0836	+	13.1385i	−0.918058	+	0.667008i
$389$	18.7687	+	13.6362i	0.951610	+	0.691385i	0.951187	−	0.308615i	$-0.0998655\pi$
$389$	18.7687	+	13.6362i	0.951610	+	0.691385i	0.000422561		1.00000i	$0.499865\pi$
$390$	−1.81227	−	5.11564i	−0.0917676	−	0.259040i
$391$	−4.18131	+	4.56672i	−0.211458	+	0.230949i
$392$	5.58858	+	1.81584i	0.282266	+	0.0917137i
$393$			10.1492i			0.511961i
$394$	3.72946	+	1.21178i	0.187888	+	0.0610484i
$395$	−20.4304	+	7.23765i	−1.02796	+	0.364166i
$396$	−12.6384	+	4.10646i	−0.635102	+	0.206357i
$397$	−7.35291	−	22.6299i	−0.369032	−	1.13576i	−0.947418	−	0.320000i	$-0.896317\pi$
$397$	−7.35291	−	22.6299i	−0.369032	−	1.13576i	0.578386	−	0.815763i	$-0.303683\pi$
$398$	5.44329	+	3.95478i	0.272847	+	0.198235i
$399$	6.61295			0.331062
$400$	−3.06201	+	2.48084i	−0.153101	+	0.124042i
$401$			16.5828i			0.828105i	0.910253	+	0.414053i	$0.135887\pi$
$401$			16.5828i			0.828105i	−0.910253	+	0.414053i	$0.864113\pi$
$402$	2.27495	+	1.65285i	0.113464	+	0.0824366i
$403$	−2.44338	−	7.51996i	−0.121714	−	0.374596i
$404$	5.66074	+	17.4220i	0.281632	+	0.866776i
$405$	−2.48580	+	8.39580i	−0.123521	+	0.417191i
$406$	−4.73843	+	14.5834i	−0.235164	+	0.723762i
$407$			2.59241i			0.128501i
$408$	−8.37010	−	0.950301i	−0.414382	−	0.0470469i
$409$	14.2417	−	10.3472i	0.704206	−	0.511635i	−0.177093	−	0.984194i	$-0.556669\pi$
$409$	14.2417	−	10.3472i	0.704206	−	0.511635i	0.881299	+	0.472559i	$0.156669\pi$
$410$	−6.62299	+	0.174261i	−0.327086	+	0.00860614i
$411$	3.32465	−	4.57599i	0.163993	−	0.225717i
$412$	−6.65968	−	9.16626i	−0.328099	−	0.451589i
$413$	26.1352	−	18.9884i	1.28603	−	0.934356i
$414$	1.62907	−	2.24222i	0.0800643	−	0.110199i
$415$	17.2626	+	5.11105i	0.847386	+	0.250891i
$416$	−19.1750	+	13.9315i	−0.940134	+	0.683047i
$417$	9.92374	+	3.22442i	0.485968	+	0.157900i
$418$	11.8495			0.579578
$419$	25.8969	+	8.41440i	1.26514	+	0.411070i	0.863325	−	0.504649i	$-0.168378\pi$
$419$	25.8969	+	8.41440i	1.26514	+	0.411070i	0.401819	+	0.915719i	$0.368378\pi$
$420$	−4.23496	+	3.25044i	−0.206645	+	0.158605i
$421$	−2.93049	−	9.01912i	−0.142823	−	0.439565i	0.853901	−	0.520435i	$-0.174230\pi$
$421$	−2.93049	−	9.01912i	−0.142823	−	0.439565i	−0.996725	+	0.0808699i	$0.974230\pi$
$422$	1.45588	+	4.48073i	0.0708709	+	0.218118i
$423$	6.92282	−	9.52844i	0.336599	−	0.463289i
$424$	27.2059			1.32124
$425$	1.24525	−	20.5779i	0.0604034	−	0.998174i
$426$	4.42766			0.214521
$427$	−3.59204	+	4.94401i	−0.173831	+	0.239258i
$428$	3.45224	+	10.6249i	0.166870	+	0.513574i
$429$	3.84135	+	11.8225i	0.185462	+	0.570794i
$430$	14.3231	+	9.84138i	0.690723	+	0.474593i
$431$	20.4439	+	6.64261i	0.984746	+	0.319963i	0.756754	−	0.653700i	$-0.226784\pi$
$431$	20.4439	+	6.64261i	0.984746	+	0.319963i	0.227992	+	0.973663i	$0.426784\pi$
$432$	−3.30885			−0.159197
$433$	−0.161272	−	0.0524005i	−0.00775025	−	0.00251821i	0.305139	−	0.952308i	$-0.401297\pi$
$433$	−0.161272	−	0.0524005i	−0.00775025	−	0.00251821i	−0.312890	+	0.949790i	$0.601297\pi$
$434$	2.65927	−	1.93207i	0.127649	−	0.0927425i
$435$	9.65938	+	12.5851i	0.463132	+	0.603408i
$436$	−8.10791	+	11.1596i	−0.388298	+	0.534447i
$437$	4.73096	−	3.43724i	0.226312	−	0.164426i
$438$	−1.62784	−	2.24052i	−0.0777810	−	0.107056i
$439$	1.99365	−	2.74402i	0.0951517	−	0.130965i	−0.758787	−	0.651339i	$-0.774208\pi$
$439$	1.99365	−	2.74402i	0.0951517	−	0.130965i	0.853938	+	0.520374i	$0.174208\pi$
$440$	−18.3839	+	14.1101i	−0.876418	+	0.672674i
$441$	−4.33578	+	3.15013i	−0.206465	+	0.150006i
$442$	1.45059	−	12.7766i	0.0689975	−	0.607719i
$443$		−	33.0979i		−	1.57253i	−0.617891	−	0.786264i	$-0.712013\pi$
$443$		−	33.0979i		−	1.57253i	0.617891	−	0.786264i	$-0.287987\pi$
$444$	−0.222018	+	0.683302i	−0.0105365	+	0.0324281i
$445$	−30.4434	−	20.9175i	−1.44315	−	0.991586i
$446$	−5.04367	−	15.5228i	−0.238825	−	0.735026i
$447$	−2.86598	−	8.82057i	−0.135556	−	0.417199i
$448$	−5.18850	−	3.76966i	−0.245133	−	0.178100i
$449$		−	2.00501i		−	0.0946224i	−0.998880	−	0.0473112i	$-0.984935\pi$
$449$		−	2.00501i		−	0.0946224i	0.998880	−	0.0473112i	$-0.0150652\pi$
$450$	0.485259	+	9.21503i	0.0228753	+	0.434401i
$451$	15.1752			0.714570
$452$	−20.5214	−	14.9097i	−0.965245	−	0.701291i
$453$	−1.82788	−	5.62563i	−0.0858812	−	0.264315i
$454$	2.37259	−	0.770900i	0.111351	−	0.0361801i
$455$	−12.0202	−	15.6609i	−0.563514	−	0.734194i
$456$	7.56646	+	2.45849i	0.354332	+	0.115129i
$457$			9.16451i			0.428698i	0.976757	+	0.214349i	$0.0687630\pi$
$457$			9.16451i			0.428698i	−0.976757	+	0.214349i	$0.931237\pi$
$458$	13.7745	+	4.47560i	0.643639	+	0.209131i
$459$	11.6889	−	12.7664i	0.545593	−	0.595883i
$460$	−1.34023	+	4.52661i	−0.0624883	+	0.211054i
$461$	−12.8318	−	9.32287i	−0.597638	−	0.434209i	0.247402	−	0.968913i	$-0.420423\pi$
$461$	−12.8318	−	9.32287i	−0.597638	−	0.434209i	−0.845040	+	0.534704i	$0.820423\pi$
$462$	−4.18076	+	3.03750i	−0.194506	+	0.141317i
$463$	4.91179	+	6.76050i	0.228270	+	0.314187i	0.907754	−	0.419504i	$-0.137796\pi$
$463$	4.91179	+	6.76050i	0.228270	+	0.314187i	−0.679483	+	0.733691i	$0.737796\pi$
$464$	4.22349	−	5.81313i	0.196070	−	0.269868i
$465$	−0.0894499	−	3.39964i	−0.00414814	−	0.157655i
$466$	4.13613	+	5.69289i	0.191603	+	0.263718i
$467$	24.8582	+	8.07692i	1.15030	+	0.373755i	0.821256	−	0.570559i	$-0.193274\pi$
$467$	24.8582	+	8.07692i	1.15030	+	0.373755i	0.329044	+	0.944315i	$0.393274\pi$
$468$		−	13.6193i		−	0.629553i
$469$	9.72837	+	3.16094i	0.449214	+	0.145959i
$470$	2.40694	−	8.12945i	0.111024	−	0.374983i
$471$	2.21808	−	0.720698i	0.102204	−	0.0332080i
$472$	36.9629	−	12.0100i	1.70136	−	0.552804i
$473$	−32.2028	−	23.3967i	−1.48069	−	1.07578i
$474$	−5.81465			−0.267076
$475$	−5.03452	+	18.8080i	−0.231000	+	0.862969i
$476$	−12.3938	+	2.52665i	−0.568069	+	0.115809i
$477$	−14.5846	+	20.0740i	−0.667785	+	0.919127i
$478$	10.8070	−	3.51142i	0.494303	−	0.160609i
$479$	−4.28302	+	1.39164i	−0.195696	+	0.0635856i	−0.405225	−	0.914217i	$-0.632807\pi$
$479$	−4.28302	+	1.39164i	−0.195696	+	0.0635856i	0.209529	+	0.977802i	$0.432807\pi$
$480$	−9.60905	+	3.40410i	−0.438591	+	0.155375i
$481$	−2.52686	−	0.821025i	−0.115215	−	0.0374355i
$482$	12.5889			0.573411
$483$	−0.788081	+	2.42546i	−0.0358589	+	0.110362i
$484$	5.21515	−	3.78903i	0.237052	−	0.172229i
$485$	−11.8719	−	33.5118i	−0.539074	−	1.52169i
$486$	−7.08679	+	9.75413i	−0.321463	+	0.442456i
$487$	−2.33647	+	1.69754i	−0.105875	+	0.0769230i	−0.639463	−	0.768822i	$-0.720843\pi$
$487$	−2.33647	+	1.69754i	−0.105875	+	0.0769230i	0.533588	+	0.845745i	$0.320843\pi$
$488$	−5.94800	+	4.32147i	−0.269253	+	0.195624i
$489$	−8.02641	−	5.83153i	−0.362967	−	0.263711i
$490$	−2.18475	+	3.17968i	−0.0986969	+	0.143644i
$491$	−6.88785	+	5.00431i	−0.310844	+	0.225841i	−0.732259	−	0.681027i	$-0.761534\pi$
$491$	−6.88785	+	5.00431i	−0.310844	+	0.225841i	0.421414	+	0.906868i	$0.361534\pi$
$492$	3.99983	+	1.29962i	0.180326	+	0.0585916i
$493$	7.50848	+	36.8308i	0.338165	+	1.65878i
$494$	−3.75277	+	11.5498i	−0.168845	+	0.519652i
$495$	−0.555934	−	21.1289i	−0.0249874	−	0.949673i
$496$	−1.46491	+	0.475978i	−0.0657764	+	0.0213721i
$497$	15.3179	−	4.97710i	0.687104	−	0.223253i
$498$	3.90737	+	2.83887i	0.175094	+	0.127213i
$499$			5.00286i			0.223959i	0.993711	+	0.111979i	$0.0357191\pi$
$499$			5.00286i			0.223959i	−0.993711	+	0.111979i	$0.964281\pi$
$500$	−6.02050	−	14.5193i	−0.269245	−	0.649323i
$501$	2.75273			0.122983
$502$	−5.54256	+	7.62869i	−0.247377	+	0.340485i
$503$	6.48087	+	19.9461i	0.288968	+	0.889351i	0.985181	+	0.171516i	$0.0548665\pi$
$503$	6.48087	+	19.9461i	0.288968	+	0.889351i	−0.696214	+	0.717834i	$0.745133\pi$
$504$	13.0449	−	4.23855i	0.581066	−	0.188800i
$505$	−29.1261	+	0.766354i	−1.29610	+	0.0341023i
$506$	−1.41213	+	4.34610i	−0.0627769	+	0.193208i
$507$	−2.62287			−0.116486
$508$	2.33856	+	0.759845i	0.103757	+	0.0337127i
$509$	−11.6766	+	8.48351i	−0.517554	+	0.376025i	−0.815682	−	0.578501i	$-0.803638\pi$
$509$	−11.6766	+	8.48351i	−0.517554	+	0.376025i	0.298128	+	0.954526i	$0.403638\pi$
$510$	2.15831	−	5.09204i	0.0955717	−	0.225479i
$511$	−8.15021	−	5.92147i	−0.360544	−	0.261951i
$512$	5.14634	+	7.08332i	0.227438	+	0.313042i
$513$	−13.2255	+	9.60887i	−0.583919	+	0.424242i
$514$	−13.8872	−	10.0897i	−0.612539	−	0.445036i
$515$	16.9865	−	6.01763i	0.748514	−	0.265169i
$516$	−6.48421	−	8.92475i	−0.285452	−	0.392890i
$517$	−6.00094	+	18.4690i	−0.263921	+	0.812265i
$518$		−	1.10451i		−	0.0485294i
$519$	4.78751	−	14.7344i	0.210148	−	0.646770i
$520$	−7.93108	−	22.3877i	−0.347801	−	0.981767i
$521$	−5.61513	+	1.82447i	−0.246003	+	0.0799313i	−0.429423	−	0.903103i	$-0.641283\pi$
$521$	−5.61513	+	1.82447i	−0.246003	+	0.0799313i	0.183420	+	0.983035i	$0.441283\pi$
$522$	−5.19924	−	16.0016i	−0.227565	−	0.700372i
$523$	8.10231	−	11.1519i	0.354289	−	0.487637i	−0.594257	−	0.804275i	$-0.702554\pi$
$523$	8.10231	−	11.1519i	0.354289	−	0.487637i	0.948547	+	0.316638i	$0.102554\pi$
$524$			18.3341i			0.800928i
$525$	−3.04495	−	7.92640i	−0.132892	−	0.345937i
$526$	−13.9693			−0.609090
$527$	3.33854	−	7.33344i	0.145429	−	0.319449i
$528$	2.30305	−	0.748307i	0.100227	−	0.0325659i
$529$	−6.41050	−	19.7295i	−0.278717	−	0.857803i
$530$	−5.07083	+	17.1267i	−0.220263	+	0.743937i
$531$	−10.9536	+	33.7117i	−0.475345	+	1.46296i
$532$	11.9460			0.517924
$533$	−4.80602	+	14.7914i	−0.208172	+	0.640687i
$534$	−5.82446	−	8.01668i	−0.252049	−	0.346916i
$535$	−17.7627	+	0.467365i	−0.767950	+	0.0202060i
$536$	9.95594	+	7.23342i	0.430031	+	0.312436i
$537$	9.84032	−	7.14941i	0.424641	−	0.308520i
$538$	−14.6047	+	10.6109i	−0.629654	+	0.457470i
$539$	5.19398	−	7.14891i	0.223721	−	0.307925i
$540$	3.74662	−	12.6542i	0.161229	−	0.544551i
$541$	−22.5576	−	31.0479i	−0.969828	−	1.33485i	−0.942134	−	0.335237i	$-0.891184\pi$
$541$	−22.5576	−	31.0479i	−0.969828	−	1.33485i	−0.0276940	−	0.999616i	$-0.508816\pi$
$542$	−4.44742	−	1.44505i	−0.191033	−	0.0620703i
$543$			8.94943i			0.384057i
$544$	−23.9991	−	2.72474i	−1.02895	−	0.116822i
$545$	−13.3583	−	17.4043i	−0.572206	−	0.745519i
$546$	−1.63663	−	5.03702i	−0.0700411	−	0.215564i
$547$	13.7314	+	42.2609i	0.587112	+	1.80694i	0.590619	+	0.806950i	$0.298883\pi$
$547$	13.7314	+	42.2609i	0.587112	+	1.80694i	−0.00350774	+	0.999994i	$0.501117\pi$
$548$	6.00582	−	8.26631i	0.256556	−	0.353119i
$549$		−	6.70544i		−	0.286181i
$550$	−5.45612	−	14.2030i	−0.232650	−	0.605619i
$551$		−	35.5000i		−	1.51235i
$552$	−1.80343	+	2.48220i	−0.0767589	+	0.105650i
$553$	−20.1164	+	6.53620i	−0.855435	+	0.277948i
$554$	13.0906	−	4.25339i	0.556166	−	0.180709i
$555$	−0.941846	−	0.647139i	−0.0399791	−	0.0274695i
$556$	17.9268	+	5.82475i	0.760264	+	0.247025i
$557$		−	19.4807i		−	0.825424i	−0.910861	−	0.412712i	$-0.864582\pi$
$557$		−	19.4807i		−	0.825424i	0.910861	−	0.412712i	$-0.135418\pi$
$558$	−1.11453	+	3.43017i	−0.0471819	+	0.145211i
$559$	33.0038	−	23.9787i	1.39591	−	1.01419i
$560$	−3.05079	+	2.34156i	−0.128919	+	0.0989491i
$561$	−5.24866	+	11.5292i	−0.221599	+	0.486764i
$562$	8.91743	+	12.2738i	0.376159	+	0.517738i
$563$	−10.4074	−	14.3246i	−0.438621	−	0.603709i	0.531284	−	0.847194i	$-0.321710\pi$
$563$	−10.4074	−	14.3246i	−0.438621	−	0.603709i	−0.969905	+	0.243484i	$0.921710\pi$
$564$	−3.16343	+	4.35408i	−0.133204	+	0.183340i
$565$	32.0049	−	24.5646i	1.34645	−	1.03344i
$566$	2.88567	+	3.97178i	0.121294	+	0.166946i
$567$	−2.64050	+	8.12662i	−0.110891	+	0.341286i
$568$	19.3769			0.813038
$569$	−13.8404	+	42.5963i	−0.580219	+	1.78573i	0.0374577	+	0.999298i	$0.488074\pi$
$569$	−13.8404	+	42.5963i	−0.580219	+	1.78573i	−0.617677	+	0.786432i	$0.711926\pi$
$570$	−2.95796	+	4.30502i	−0.123896	+	0.180318i
$571$	−39.5751	+	12.8587i	−1.65617	+	0.538122i	−0.980064	−	0.198684i	$-0.936333\pi$
$571$	−39.5751	+	12.8587i	−1.65617	+	0.538122i	−0.676104	+	0.736806i	$0.736333\pi$
$572$	6.93921	+	21.3567i	0.290143	+	0.892968i
$573$	12.2914	+	8.93023i	0.513481	+	0.373066i
$574$	−6.46545			−0.269863
$575$	−6.29832	−	4.08793i	−0.262658	−	0.170478i
$576$	7.03702			0.293209
$577$	8.98172	−	12.3623i	0.373914	−	0.514648i	−0.580045	−	0.814584i	$-0.696965\pi$
$577$	8.98172	−	12.3623i	0.373914	−	0.514648i	0.953959	+	0.299936i	$0.0969652\pi$
$578$	9.88265	−	8.60458i	0.411064	−	0.357904i
$579$	0.824413	+	2.53728i	0.0342614	+	0.105446i
$580$	17.4492	+	22.7343i	0.724539	+	0.943992i
$581$	16.7091	+	5.42912i	0.693210	+	0.225238i
$582$		−	9.53774i		−	0.395352i
$583$	12.6425	−	38.9096i	0.523598	−	1.61147i
$584$	−7.12395	−	9.80527i	−0.294791	−	0.405745i
$585$	20.7707	+	6.14971i	0.858761	+	0.254259i
$586$	−3.25666	−	2.36610i	−0.134531	−	0.0977428i
$587$	−0.944551	−	1.30006i	−0.0389858	−	0.0536593i	0.789079	−	0.614292i	$-0.210558\pi$
$587$	−0.944551	−	1.30006i	−0.0389858	−	0.0536593i	−0.828065	+	0.560632i	$0.810558\pi$
$588$	1.98126	−	1.43947i	0.0817059	−	0.0593628i
$589$	−4.47301	+	6.15657i	−0.184307	+	0.253677i
$590$	0.671141	+	25.5075i	0.0276304	+	1.05013i
$591$	3.20311	−	2.32719i	0.131758	−	0.0957279i
$592$	−0.159938	+	0.492239i	−0.00657342	+	0.0202309i
$593$			22.4143i			0.920443i	0.887804	+	0.460222i	$0.152230\pi$
$593$			22.4143i			0.920443i	−0.887804	+	0.460222i	$0.847770\pi$
$594$	3.94764	−	12.1496i	0.161974	−	0.498504i
$595$	1.74298	−	20.0426i	0.0714551	−	0.821664i
$596$	−5.17725	−	15.9339i	−0.212068	−	0.652679i
$597$	6.46076	−	2.09923i	0.264421	−	0.0859156i
$598$	−3.78897	−	2.75284i	−0.154942	−	0.112572i
$599$	9.75063			0.398400			0.199200	−	0.979959i	$-0.436166\pi$
$599$	9.75063			0.398400			0.199200	+	0.979959i	$0.436166\pi$
$600$	−0.537197	−	10.2013i	−0.0219310	−	0.416467i
$601$		−	1.80049i		−	0.0734434i	−0.999326	−	0.0367217i	$-0.988308\pi$
$601$		−	1.80049i		−	0.0734434i	0.999326	−	0.0367217i	$-0.0116915\pi$
$602$	13.7202	+	9.96828i	0.559192	+	0.406277i
$603$	−10.6744	+	3.46834i	−0.434697	+	0.141242i
$604$	−3.30197	−	10.1624i	−0.134355	−	0.413503i
$605$	3.42374	+	9.66449i	0.139195	+	0.392917i
$606$	−7.43386	−	2.41541i	−0.301980	−	0.0981193i
$607$	−47.4972			−1.92785			−0.963926	−	0.266171i	$-0.914241\pi$
$607$	−47.4972			−1.92785			−0.963926	+	0.266171i	$0.914241\pi$
$608$	21.6949	+	7.04909i	0.879843	+	0.285878i
$609$	9.10006	+	12.5252i	0.368753	+	0.507545i
$610$	−1.61183	−	4.54986i	−0.0652612	−	0.184219i
$611$	−16.1014	−	11.6984i	−0.651394	−	0.473266i
$612$	9.37234	−	10.2362i	0.378854	−	0.413775i
$613$	1.43126	+	1.96996i	0.0578079	+	0.0795658i	0.836942	−	0.547291i	$-0.184341\pi$
$613$	1.43126	+	1.96996i	0.0578079	+	0.0795658i	−0.779134	+	0.626857i	$0.784341\pi$
$614$	−3.67740	−	2.67179i	−0.148408	−	0.107825i
$615$	−3.78814	+	5.51326i	−0.152753	+	0.222316i
$616$	−18.2964	+	13.2931i	−0.737182	+	0.535594i
$617$	−13.2666	+	40.8303i	−0.534092	+	1.64377i	0.211510	+	0.977376i	$0.432162\pi$
$617$	−13.2666	+	40.8303i	−0.534092	+	1.64377i	−0.745602	+	0.666391i	$0.767838\pi$
$618$	4.83450			0.194472
$619$	2.75232	+	0.894282i	0.110625	+	0.0359442i	0.363806	−	0.931475i	$-0.381477\pi$
$619$	2.75232	+	0.894282i	0.110625	+	0.0359442i	−0.253181	+	0.967419i	$0.581477\pi$
$620$	−0.161587	−	6.14129i	−0.00648948	−	0.246640i
$621$	−1.94818	−	5.99588i	−0.0781778	−	0.240606i
$622$	−6.85045	−	21.0835i	−0.274678	−	0.845372i
$623$	−29.1618	−	21.1873i	−1.16834	−	0.848850i
$624$			2.48180i			0.0993516i
$625$	24.8617	−	2.62570i	0.994469	−	0.105028i
$626$		−	24.8809i		−	0.994442i
$627$	7.03221	−	9.67901i	0.280840	−	0.386542i
$628$	4.00685	−	1.30191i	0.159891	−	0.0519517i
$629$	−1.33418	−	2.35598i	−0.0531971	−	0.0939389i
$630$	0.236858	+	9.00207i	0.00943666	+	0.358651i
$631$	−12.0198	+	36.9931i	−0.478500	+	1.47267i	0.362679	+	0.931914i	$0.381862\pi$
$631$	−12.0198	+	36.9931i	−0.478500	+	1.47267i	−0.841179	+	0.540757i	$0.818138\pi$
$632$	−25.4469			−1.01222
$633$	4.52399	+	1.46993i	0.179813	+	0.0584246i
$634$	−5.18729	−	7.13970i	−0.206014	−	0.283554i
$635$	−2.21479	+	3.22341i	−0.0878914	+	0.127917i
$636$	6.66455	−	9.17297i	0.264267	−	0.363732i
$637$	5.32317	+	7.32672i	0.210912	+	0.290295i
$638$	16.3061	+	22.4434i	0.645563	+	0.888541i
$639$	−10.3877	+	14.2974i	−0.410930	+	0.565596i
$640$	−19.9193	+	7.05660i	−0.787378	+	0.278936i
$641$	−21.1484	−	29.1082i	−0.835310	−	1.14971i	−0.986911	−	0.161264i	$-0.948443\pi$
$641$	−21.1484	−	29.1082i	−0.835310	−	1.14971i	0.151601	−	0.988442i	$-0.451557\pi$
$642$	−4.53359	−	1.47305i	−0.178926	−	0.0581367i
$643$	−28.6714			−1.13069			−0.565344	−	0.824855i	$-0.691257\pi$
$643$	−28.6714			−1.13069			−0.565344	+	0.824855i	$0.691257\pi$
$644$	−1.42363	+	4.38148i	−0.0560989	+	0.172655i
$645$	16.5389	−	5.85908i	0.651220	−	0.230701i
$646$	−10.7688	+	6.09830i	−0.423692	+	0.239935i
$647$	−5.04271	+	1.63847i	−0.198249	+	0.0644151i	−0.406459	−	0.913669i	$-0.633236\pi$
$647$	−5.04271	+	1.63847i	−0.198249	+	0.0644151i	0.208209	+	0.978084i	$0.433236\pi$
$648$	−6.04245	+	8.31673i	−0.237370	+	0.326712i
$649$		−	58.4449i		−	2.29416i
$650$	15.5718	−	0.820005i	0.610777	−	0.0321633i
$651$		−	3.31878i		−	0.130073i
$652$	−14.4993	−	10.5344i	−0.567837	−	0.412558i
$653$	8.52512	+	26.2376i	0.333614	+	1.02676i	0.967401	+	0.253250i	$0.0814996\pi$
$653$	8.52512	+	26.2376i	0.333614	+	1.02676i	−0.633787	+	0.773508i	$0.718500\pi$
$654$	−1.81882	−	5.59775i	−0.0711215	−	0.218889i
$655$	−27.9611	−	8.27864i	−1.09253	−	0.323473i
$656$	2.88141	+	0.936227i	0.112500	+	0.0365535i
$657$	11.0539			0.431254
$658$	2.55673	−	7.86880i	0.0996717	−	0.306758i
$659$	1.55716	−	1.13134i	0.0606582	−	0.0440708i	−0.557043	−	0.830484i	$-0.688064\pi$
$659$	1.55716	−	1.13134i	0.0606582	−	0.0440708i	0.617701	+	0.786413i	$0.288064\pi$
$660$	0.254038	+	9.65499i	0.00988841	+	0.375820i
$661$	33.6454	+	24.4448i	1.30866	+	0.950794i	1.00000		0.000380495i	$-0.000121115\pi$
$661$	33.6454	+	24.4448i	1.30866	+	0.950794i	0.308655	+	0.951174i	$0.400121\pi$
$662$	−6.02920	−	8.29848i	−0.234331	−	0.322529i
$663$	−9.57540	−	8.76727i	−0.371878	−	0.340493i
$664$	17.1000	+	12.4239i	0.663608	+	0.482139i
$665$	−5.39413	+	18.2187i	−0.209175	+	0.706490i
$666$	0.712350	+	0.980466i	0.0276030	+	0.0379923i
$667$	13.0205	+	4.23062i	0.504156	+	0.163810i
$668$	4.97267			0.192398
$669$	−15.6727	−	5.09237i	−0.605942	−	0.196882i
$670$	−6.40925	+	4.91927i	−0.247611	+	0.190048i
$671$	3.41651	+	10.5149i	0.131893	+	0.405924i
$672$	−9.46137	+	3.07419i	−0.364980	+	0.118589i
$673$	3.95308	+	2.87208i	0.152380	+	0.110711i	0.661363	−	0.750066i	$-0.269978\pi$
$673$	3.95308	+	2.87208i	0.152380	+	0.110711i	−0.508983	+	0.860777i	$0.669978\pi$
$674$			3.50105i			0.134855i
$675$	17.6071	+	11.4279i	0.677696	+	0.439859i
$676$	−4.73808			−0.182234
$677$	5.26088	+	3.82226i	0.202192	+	0.146901i	0.684274	−	0.729225i	$-0.260119\pi$
$677$	5.26088	+	3.82226i	0.202192	+	0.146901i	−0.482082	+	0.876126i	$0.660119\pi$
$678$	10.2937	−	3.34463i	0.395328	−	0.128450i
$679$	−10.7213	−	32.9967i	−0.411445	−	1.26630i
$680$	9.44550	−	22.2845i	0.362218	−	0.854570i
$681$	0.778344	−	2.39550i	0.0298262	−	0.0917956i
$682$		−	5.94679i		−	0.227714i
$683$	2.47777	−	7.62578i	0.0948090	−	0.291792i	−0.892395	−	0.451255i	$-0.850976\pi$
$683$	2.47777	−	7.62578i	0.0948090	−	0.291792i	0.987204	+	0.159463i	$0.0509763\pi$
$684$	−10.6044	+	7.70452i	−0.405468	+	0.294590i
$685$	9.89496	+	12.8920i	0.378067	+	0.492578i
$686$	−9.13346	+	12.5711i	−0.348717	+	0.479968i
$687$	11.8304	−	8.59529i	0.451358	−	0.327931i
$688$	−4.67111	−	6.42924i	−0.178085	−	0.245112i
$689$	33.9217	+	24.6456i	1.29231	+	0.938921i
$690$	−1.22647	−	1.59795i	−0.0466908	−	0.0608328i
$691$	−8.97314	−	12.3505i	−0.341354	−	0.469834i	0.603482	−	0.797377i	$-0.293779\pi$
$691$	−8.97314	−	12.3505i	−0.341354	−	0.469834i	−0.944836	+	0.327543i	$0.893779\pi$
$692$	8.64840	−	26.6170i	0.328763	−	1.01183i
$693$		−	20.6263i		−	0.783529i
$694$	12.3023	+	3.99727i	0.466990	+	0.151734i
$695$	−16.9780	+	24.7098i	−0.644011	+	0.937295i
$696$	5.75571	+	17.7143i	0.218170	+	0.671457i
$697$	−13.7911	+	7.80984i	−0.522376	+	0.295819i
$698$	2.45596	−	3.38034i	0.0929596	−	0.127948i
$699$	7.10475			0.268726
$700$	−5.50054	−	14.3187i	−0.207901	−	0.541194i
$701$	−30.7067			−1.15978			−0.579888	−	0.814696i	$-0.696904\pi$
$701$	−30.7067			−1.15978			−0.579888	+	0.814696i	$0.696904\pi$
$702$	10.5921	+	7.69563i	0.399774	+	0.290453i
$703$	0.790184	+	2.43194i	0.0298024	+	0.0917222i
$704$	−11.0349	+	3.58545i	−0.415893	+	0.135132i
$705$	−5.21194	−	6.79057i	−0.196293	−	0.255748i
$706$	−0.329672	+	1.01463i	−0.0124074	+	0.0381860i
$707$	−28.4333			−1.06935
$708$	5.00531	−	15.4048i	0.188111	−	0.578947i
$709$	18.3763	+	25.2928i	0.690137	+	0.949892i	1.00000		0.000889169i	$-0.000283031\pi$
$709$	18.3763	+	25.2928i	0.690137	+	0.949892i	−0.309863	+	0.950781i	$0.600283\pi$
$710$	−3.61161	+	12.1982i	−0.135541	+	0.457791i
$711$	13.6417	−	18.7761i	0.511602	−	0.704160i
$712$	−25.4898	−	35.0837i	−0.955269	−	1.31482i
$713$	−1.72501	−	2.37428i	−0.0646023	−	0.0889175i
$714$	2.23622	−	4.91208i	0.0836884	−	0.183830i
$715$	−35.7042	+	0.939433i	−1.33526	+	0.0351328i
$716$	17.7761	−	12.9151i	0.664323	−	0.482659i
$717$	3.54533	−	10.9114i	0.132403	−	0.407493i
$718$		−	19.5064i		−	0.727972i
$719$	−21.1046	−	6.85731i	−0.787070	−	0.255735i	−0.112214	−	0.993684i	$-0.535794\pi$
$719$	−21.1046	−	6.85731i	−0.787070	−	0.255735i	−0.674856	+	0.737949i	$0.735794\pi$
$720$	1.19798	−	4.04619i	0.0446462	−	0.150792i
$721$	16.7254	−	5.43442i	0.622888	−	0.202389i
$722$	−2.81248	+	0.913830i	−0.104670	+	0.0340092i
$723$	7.47105	−	10.2830i	0.277851	−	0.382430i
$724$			16.1667i			0.600831i
$725$	−42.5510	+	16.3460i	−1.58030	+	0.607077i
$726$			2.75060i			0.102084i
$727$	−23.6813	+	32.5945i	−0.878291	+	1.20886i	0.0985997	+	0.995127i	$0.468564\pi$
$727$	−23.6813	+	32.5945i	−0.878291	+	1.20886i	−0.976891	+	0.213737i	$0.931436\pi$
$728$	−7.16242	−	22.0437i	−0.265457	−	0.816993i
$729$	0.131546	+	0.404857i	0.00487207	+	0.0149947i
$730$	7.50045	−	2.65711i	0.277604	−	0.0983440i
$731$	41.3068	+	4.68978i	1.52779	+	0.173458i
$732$			3.06410i			0.113252i
$733$	−10.3238	−	3.35441i	−0.381318	−	0.123898i	0.112085	−	0.993699i	$-0.464247\pi$
$733$	−10.3238	−	3.35441i	−0.381318	−	0.123898i	−0.493403	+	0.869801i	$0.664247\pi$
$734$	9.83507	+	13.5368i	0.363019	+	0.499653i
$735$	1.30070	+	3.67158i	0.0479769	+	0.135428i
$736$	−5.17085	+	7.11707i	−0.190600	+	0.262339i
$737$	14.9716	−	10.8775i	0.551487	−	0.400679i
$738$	5.73933	−	4.16987i	0.211268	−	0.153495i
$739$	−22.7661	−	16.5406i	−0.837465	−	0.608454i	0.0841963	−	0.996449i	$-0.473168\pi$
$739$	−22.7661	−	16.5406i	−0.837465	−	0.608454i	−0.921661	+	0.387995i	$0.873168\pi$
$740$	−1.70140	−	1.16902i	−0.0625446	−	0.0429742i
$741$	7.20712	+	9.91976i	0.264760	+	0.364411i
$742$	−5.38639	+	16.5776i	−0.197741	+	0.608583i
$743$	−10.5356			−0.386513			−0.193256	−	0.981148i	$-0.561905\pi$
$743$	−10.5356			−0.386513			−0.193256	+	0.981148i	$0.561905\pi$
$744$	1.23382	−	3.79731i	0.0452340	−	0.139216i
$745$	26.6384	−	0.700898i	0.975956	−	0.0256789i
$746$	−0.608106	−	1.87156i	−0.0222643	−	0.0685226i
$747$	−18.3340	+	5.95709i	−0.670807	+	0.217959i
$748$	−9.48145	+	20.8270i	−0.346676	+	0.761509i
$749$	−17.3402			−0.633598
$750$	6.52208	+	1.56321i	0.238153	+	0.0570805i
$751$			18.5771i			0.677888i	0.940807	+	0.338944i	$0.110070\pi$
$751$			18.5771i			0.677888i	−0.940807	+	0.338944i	$0.889930\pi$
$752$	−2.27888	+	3.13661i	−0.0831022	+	0.114380i
$753$	2.94204	+	9.05465i	0.107214	+	0.329970i
$754$	−27.0400	+	8.78582i	−0.984738	+	0.319961i
$755$	16.9896	−	0.447022i	0.618314	−	0.0162688i
$756$	3.97978	−	12.2485i	0.144743	−	0.445474i
$757$			19.8141i			0.720155i	0.932922	+	0.360078i	$0.117250\pi$
$757$			19.8141i			0.720155i	−0.932922	+	0.360078i	$0.882750\pi$
$758$	3.08479	−	9.49399i	0.112044	−	0.344837i
$759$	2.71197	+	3.73271i	0.0984383	+	0.135489i
$760$	−12.9450	+	18.8402i	−0.469566	+	0.683406i
$761$	1.65165	+	1.20000i	0.0598724	+	0.0434998i	0.617319	−	0.786713i	$-0.288219\pi$
$761$	1.65165	+	1.20000i	0.0598724	+	0.0434998i	−0.557447	+	0.830213i	$0.688219\pi$
$762$	−0.848824	+	0.616706i	−0.0307496	+	0.0223409i
$763$	−12.5848	−	17.3215i	−0.455599	−	0.627079i
$764$	22.2038	+	16.1320i	0.803307	+	0.583636i
$765$	11.3791	+	18.9158i	0.411414	+	0.683901i
$766$	−10.3253	+	7.50176i	−0.373068	+	0.271050i
$767$	56.9669	+	18.5097i	2.05696	+	0.668346i
$768$	−10.2438			−0.369640
$769$	7.29689	−	22.4575i	0.263133	−	0.809839i	−0.728985	−	0.684529i	$-0.760008\pi$
$769$	7.29689	−	22.4575i	0.263133	−	0.809839i	0.992118	−	0.125309i	$-0.0399923\pi$
$770$	−4.95809	−	13.9956i	−0.178677	−	0.504368i
$771$	−16.4831	+	5.35567i	−0.593623	+	0.192880i

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.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453067 + 0.623593i) q^{2} +(0.240491 + 0.740156i) q^{3} +(0.434435 + 1.33705i) q^{4} +(-2.23529 + 0.0588141i) q^{5} +(-0.570514 - 0.185371i) q^{6} -2.18212 q^{7} +(-2.49676 - 0.811247i) q^{8} +(1.93706 - 1.40735i) q^{9} +(0.976061 - 1.42056i) q^{10} +(-2.32047 + 3.19385i) q^{11} +(-0.885151 + 0.643100i) q^{12} +(-2.37819 - 3.27329i) q^{13} +(0.988648 - 1.36076i) q^{14} +(-0.581100 - 1.64032i) q^{15} +(-0.637648 + 0.463278i) q^{16} +(0.465129 - 4.09679i) q^{17} +1.84556i q^{18} +(-1.20332 + 3.70344i) q^{19} +(-1.04973 - 2.96316i) q^{20} +(-0.524782 - 1.61511i) q^{21} +(-0.940336 - 2.89406i) q^{22} +(-1.21493 - 0.882696i) q^{23} -2.04309i q^{24} +(4.99308 - 0.262933i) q^{25} +3.11868 q^{26} +(3.39635 + 2.46759i) q^{27} +(-0.947992 - 2.91762i) q^{28} +(-8.67033 + 2.81716i) q^{29} +(1.28617 + 0.380805i) q^{30} +(1.85861 + 0.603899i) q^{31} -5.85803i q^{32} +(-2.92200 - 0.949416i) q^{33} +(2.34399 + 2.14617i) q^{34} +(4.87769 - 0.128340i) q^{35} +(2.72324 + 1.97855i) q^{36} +(0.531257 - 0.385981i) q^{37} +(-1.76425 - 2.42829i) q^{38} +(1.85081 - 2.54743i) q^{39} +(5.62871 + 1.66653i) q^{40} +(-2.25941 - 3.10981i) q^{41} +(1.24493 + 0.404503i) q^{42} +10.0827i q^{43} +(-5.27845 - 1.71507i) q^{44} +(-4.24712 + 3.25978i) q^{45} +(1.10088 - 0.357699i) q^{46} +(4.67828 - 1.52006i) q^{47} +(-0.496247 - 0.360544i) q^{48} -2.23833 q^{49} +(-2.09824 + 3.23278i) q^{50} +(3.14412 - 0.640973i) q^{51} +(3.34340 - 4.60180i) q^{52} +(-9.85596 + 3.20240i) q^{53} +(-3.07754 + 0.999955i) q^{54} +(4.99909 - 7.27568i) q^{55} +(5.44824 + 1.77024i) q^{56} -3.03051 q^{57} +(2.17148 - 6.68312i) q^{58} +(-11.9770 + 8.70178i) q^{59} +(1.94075 - 1.48958i) q^{60} +(1.64612 - 2.26569i) q^{61} +(-1.21866 + 0.885409i) q^{62} +(-4.22690 + 3.07102i) q^{63} +(2.37773 + 1.72752i) q^{64} +(5.50846 + 7.17690i) q^{65} +(1.91591 - 1.39199i) q^{66} +(-4.45821 - 1.44856i) q^{67} +(5.67970 - 1.15789i) q^{68} +(0.361153 - 1.11152i) q^{69} +(-2.12989 + 3.09984i) q^{70} +(-7.01974 + 2.28085i) q^{71} +(-5.97808 + 1.94239i) q^{72} +(3.73499 + 2.71363i) q^{73} +0.506163i q^{74} +(1.39540 + 3.63243i) q^{75} -5.47447 q^{76} +(5.06356 - 6.96939i) q^{77} +(0.750015 + 2.30831i) q^{78} +(9.21871 - 2.99534i) q^{79} +(1.39808 - 1.07307i) q^{80} +(1.21006 - 3.72418i) q^{81} +2.96291 q^{82} +(-7.65726 - 2.48800i) q^{83} +(1.93151 - 1.40332i) q^{84} +(-0.798752 + 9.18488i) q^{85} +(-6.28753 - 4.56816i) q^{86} +(-4.17028 - 5.73989i) q^{87} +(8.38466 - 6.09181i) q^{88} +(13.3639 + 9.70947i) q^{89} +(-0.108545 - 4.12537i) q^{90} +(5.18950 + 7.14274i) q^{91} +(0.652405 - 2.00790i) q^{92} +1.52089i q^{93} +(-1.17167 + 3.60603i) q^{94} +(2.47196 - 8.34905i) q^{95} +(4.33585 - 1.40880i) q^{96} +(4.91324 + 15.1214i) q^{97} +(1.01411 - 1.39581i) q^{98} +9.45240i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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