LMFDB - Embedded newform 425.2.n.e.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			349.2
Character	$\chi$	$=$	425.349
Dual form			425.2.n.e.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.813283 - 0.813283i) q^{2} +(-0.786634 + 1.89910i) q^{3} -0.677141i q^{4} +(2.18426 - 0.904752i) q^{6} +(0.346882 - 0.143683i) q^{7} +(-2.17727 + 2.17727i) q^{8} +(-0.866476 - 0.866476i) q^{9} +(0.0511675 - 0.0211943i) q^{11} +(1.28596 + 0.532662i) q^{12} +0.388558 q^{13} +(-0.398969 - 0.165258i) q^{14} +2.18720 q^{16} +(0.594174 + 4.08007i) q^{17} +1.40938i q^{18} +(-1.25108 + 1.25108i) q^{19} +0.771791i q^{21} +(-0.0588507 - 0.0243767i) q^{22} +(0.392870 + 0.948471i) q^{23} +(-2.42215 - 5.84758i) q^{24} +(-0.316007 - 0.316007i) q^{26} +(-3.37018 + 1.39597i) q^{27} +(-0.0972938 - 0.234888i) q^{28} +(-3.23410 + 7.80781i) q^{29} +(5.59808 + 2.31880i) q^{31} +(2.57573 + 2.57573i) q^{32} +0.113845i q^{33} +(2.83502 - 3.80148i) q^{34} +(-0.586726 + 0.586726i) q^{36} +(-3.63511 + 8.77594i) q^{37} +2.03496 q^{38} +(-0.305652 + 0.737910i) q^{39} +(2.93662 + 7.08964i) q^{41} +(0.627685 - 0.627685i) q^{42} +(4.77818 - 4.77818i) q^{43} +(-0.0143515 - 0.0346476i) q^{44} +(0.451862 - 1.09089i) q^{46} +1.84378 q^{47} +(-1.72053 + 4.15372i) q^{48} +(-4.85007 + 4.85007i) q^{49} +(-8.21586 - 2.08112i) q^{51} -0.263108i q^{52} +(-6.43330 - 6.43330i) q^{53} +(3.87624 + 1.60559i) q^{54} +(-0.442420 + 1.06810i) q^{56} +(-1.39178 - 3.36006i) q^{57} +(8.98020 - 3.71972i) q^{58} +(9.61131 + 9.61131i) q^{59} +(-2.22364 - 5.36835i) q^{61} +(-2.66698 - 6.43867i) q^{62} +(-0.425063 - 0.176067i) q^{63} -8.56400i q^{64} +(0.0925878 - 0.0925878i) q^{66} -14.4112i q^{67} +(2.76278 - 0.402339i) q^{68} -2.11029 q^{69} +(-1.04049 - 0.430984i) q^{71} +3.77311 q^{72} +(2.02455 + 0.838594i) q^{73} +(10.0937 - 4.18095i) q^{74} +(0.847155 + 0.847155i) q^{76} +(0.0147038 - 0.0147038i) q^{77} +(0.848712 - 0.351548i) q^{78} +(3.64157 - 1.50839i) q^{79} -11.1746i q^{81} +(3.37758 - 8.15419i) q^{82} +(-6.67554 - 6.67554i) q^{83} +0.522611 q^{84} -7.77202 q^{86} +(-12.2838 - 12.2838i) q^{87} +(-0.0652600 + 0.157551i) q^{88} +2.61320i q^{89} +(0.134784 - 0.0558293i) q^{91} +(0.642248 - 0.266028i) q^{92} +(-8.80728 + 8.80728i) q^{93} +(-1.49951 - 1.49951i) q^{94} +(-6.91774 + 2.86542i) q^{96} +(4.85551 + 2.01122i) q^{97} +7.88895 q^{98} +(-0.0626997 - 0.0259711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−0.813283	−	0.813283i	−0.575078	−	0.575078i	0.358465	−	0.933543i	$-0.383300\pi$
$2$	−0.813283	−	0.813283i	−0.575078	−	0.575078i	−0.933543	+	0.358465i	$0.883300\pi$
$3$	−0.786634	+	1.89910i	−0.454163	+	1.09645i	0.516561	+	0.856250i	$0.327212\pi$
$3$	−0.786634	+	1.89910i	−0.454163	+	1.09645i	−0.970724	+	0.240197i	$0.922788\pi$
$4$		−	0.677141i		−	0.338570i
$5$		0			0
$5$		0			0
$6$	2.18426	−	0.904752i	0.891722	−	0.369363i
$7$	0.346882	−	0.143683i	0.131109	−	0.0543072i	−0.316164	−	0.948704i	$-0.602395\pi$
$7$	0.346882	−	0.143683i	0.131109	−	0.0543072i	0.447273	+	0.894397i	$0.352395\pi$
$8$	−2.17727	+	2.17727i	−0.769782	+	0.769782i
$9$	−0.866476	−	0.866476i	−0.288825	−	0.288825i
$10$		0			0
$11$	0.0511675	−	0.0211943i	0.0154276	−	0.00639032i	−0.374956	−	0.927042i	$-0.622342\pi$
$11$	0.0511675	−	0.0211943i	0.0154276	−	0.00639032i	0.390384	+	0.920652i	$0.372342\pi$
$12$	1.28596	+	0.532662i	0.371224	+	0.153766i
$13$	0.388558			0.107766			0.0538832	−	0.998547i	$-0.482840\pi$
$13$	0.388558			0.107766			0.0538832	+	0.998547i	$0.482840\pi$
$14$	−0.398969	−	0.165258i	−0.106629	−	0.0441671i
$15$		0			0
$16$	2.18720			0.546800
$17$	0.594174	+	4.08007i	0.144108	+	0.989562i
$17$	0.594174	+	4.08007i	0.144108	+	0.989562i
$18$			1.40938i			0.332194i
$19$	−1.25108	+	1.25108i	−0.287017	+	0.287017i	−0.835899	−	0.548883i	$-0.815053\pi$
$19$	−1.25108	+	1.25108i	−0.287017	+	0.287017i	0.548883	+	0.835899i	$0.315053\pi$
$20$		0			0
$21$			0.771791i			0.168419i
$22$	−0.0588507	−	0.0243767i	−0.0125470	−	0.00519714i
$23$	0.392870	+	0.948471i	0.0819190	+	0.197770i	0.959532	−	0.281600i	$-0.0908652\pi$
$23$	0.392870	+	0.948471i	0.0819190	+	0.197770i	−0.877613	+	0.479370i	$0.840865\pi$
$24$	−2.42215	−	5.84758i	−0.494419	−	1.19363i
$25$		0			0
$26$	−0.316007	−	0.316007i	−0.0619741	−	0.0619741i
$27$	−3.37018	+	1.39597i	−0.648592	+	0.268656i
$28$	−0.0972938	−	0.234888i	−0.0183868	−	0.0443897i
$29$	−3.23410	+	7.80781i	−0.600557	+	1.44987i	0.272452	+	0.962169i	$0.412165\pi$
$29$	−3.23410	+	7.80781i	−0.600557	+	1.44987i	−0.873009	+	0.487704i	$0.837835\pi$
$30$		0			0
$31$	5.59808	+	2.31880i	1.00545	+	0.416469i	0.823791	−	0.566893i	$-0.191855\pi$
$31$	5.59808	+	2.31880i	1.00545	+	0.416469i	0.181654	+	0.983362i	$0.441855\pi$
$32$	2.57573	+	2.57573i	0.455330	+	0.455330i
$33$			0.113845i			0.0198178i
$34$	2.83502	−	3.80148i	0.486202	−	0.651949i
$35$		0			0
$36$	−0.586726	+	0.586726i	−0.0977876	+	0.0977876i
$37$	−3.63511	+	8.77594i	−0.597609	+	1.44276i	0.278402	+	0.960465i	$0.410195\pi$
$37$	−3.63511	+	8.77594i	−0.597609	+	1.44276i	−0.876011	+	0.482291i	$0.839805\pi$
$38$	2.03496			0.330114
$39$	−0.305652	+	0.737910i	−0.0489436	+	0.118160i
$40$		0			0
$41$	2.93662	+	7.08964i	0.458624	+	1.10722i	0.968955	+	0.247238i	$0.0795228\pi$
$41$	2.93662	+	7.08964i	0.458624	+	1.10722i	−0.510331	+	0.859978i	$0.670477\pi$
$42$	0.627685	−	0.627685i	0.0968539	−	0.0968539i
$43$	4.77818	−	4.77818i	0.728665	−	0.728665i	−0.241689	−	0.970354i	$-0.577701\pi$
$43$	4.77818	−	4.77818i	0.728665	−	0.728665i	0.970354	+	0.241689i	$0.0777013\pi$
$44$	−0.0143515	−	0.0346476i	−0.00216357	−	0.00522332i
$45$		0			0
$46$	0.451862	−	1.09089i	0.0666233	−	0.160843i
$47$	1.84378			0.268942			0.134471	−	0.990918i	$-0.457066\pi$
$47$	1.84378			0.268942			0.134471	+	0.990918i	$0.457066\pi$
$48$	−1.72053	+	4.15372i	−0.248336	+	0.599537i
$49$	−4.85007	+	4.85007i	−0.692866	+	0.692866i
$50$		0			0
$51$	−8.21586	−	2.08112i	−1.15045	−	0.291415i
$52$		−	0.263108i		−	0.0364865i
$53$	−6.43330	−	6.43330i	−0.883682	−	0.883682i	0.110224	−	0.993907i	$-0.464843\pi$
$53$	−6.43330	−	6.43330i	−0.883682	−	0.883682i	−0.993907	+	0.110224i	$0.964843\pi$
$54$	3.87624	+	1.60559i	0.527489	+	0.218493i
$55$		0			0
$56$	−0.442420	+	1.06810i	−0.0591208	+	0.142730i
$57$	−1.39178	−	3.36006i	−0.184346	−	0.445051i
$58$	8.98020	−	3.71972i	1.17916	−	0.488423i
$59$	9.61131	+	9.61131i	1.25129	+	1.25129i	0.955144	+	0.296143i	$0.0957004\pi$
$59$	9.61131	+	9.61131i	1.25129	+	1.25129i	0.296143	+	0.955144i	$0.404300\pi$
$60$		0			0
$61$	−2.22364	−	5.36835i	−0.284708	−	0.687347i	0.715225	−	0.698894i	$-0.246324\pi$
$61$	−2.22364	−	5.36835i	−0.284708	−	0.687347i	−0.999933	+	0.0115474i	$0.996324\pi$
$62$	−2.66698	−	6.43867i	−0.338707	−	0.817712i
$63$	−0.425063	−	0.176067i	−0.0535529	−	0.0221823i
$64$		−	8.56400i		−	1.07050i
$65$		0			0
$66$	0.0925878	−	0.0925878i	0.0113968	−	0.0113968i
$67$		−	14.4112i		−	1.76061i	−0.474412	−	0.880303i	$-0.657339\pi$
$67$		−	14.4112i		−	1.76061i	0.474412	−	0.880303i	$-0.342661\pi$
$68$	2.76278	−	0.402339i	0.335036	−	0.0487908i
$69$	−2.11029			−0.254049
$70$		0			0
$71$	−1.04049	−	0.430984i	−0.123483	−	0.0511484i	0.320086	−	0.947388i	$-0.396288\pi$
$71$	−1.04049	−	0.430984i	−0.123483	−	0.0511484i	−0.443570	+	0.896240i	$0.646288\pi$
$72$	3.77311			0.444665
$73$	2.02455	+	0.838594i	0.236955	+	0.0981500i	0.498001	−	0.867176i	$-0.334067\pi$
$73$	2.02455	+	0.838594i	0.236955	+	0.0981500i	−0.261046	+	0.965326i	$0.584067\pi$
$74$	10.0937	−	4.18095i	1.17337	−	0.486025i
$75$		0			0
$76$	0.847155	+	0.847155i	0.0971753	+	0.0971753i
$77$	0.0147038	−	0.0147038i	0.00167566	−	0.00167566i
$78$	0.848712	−	0.351548i	0.0960977	−	0.0398050i
$79$	3.64157	−	1.50839i	0.409709	−	0.169707i	−0.168303	−	0.985735i	$-0.553829\pi$
$79$	3.64157	−	1.50839i	0.409709	−	0.169707i	0.578012	+	0.816028i	$0.303829\pi$
$80$		0			0
$81$		−	11.1746i		−	1.24162i
$82$	3.37758	−	8.15419i	0.372991	−	0.900480i
$83$	−6.67554	−	6.67554i	−0.732735	−	0.732735i	0.238425	−	0.971161i	$-0.423369\pi$
$83$	−6.67554	−	6.67554i	−0.732735	−	0.732735i	−0.971161	+	0.238425i	$0.923369\pi$
$84$	0.522611			0.0570215
$85$		0			0
$86$	−7.77202			−0.838079
$87$	−12.2838	−	12.2838i	−1.31696	−	1.31696i
$88$	−0.0652600	+	0.157551i	−0.00695674	+	0.0167950i
$89$			2.61320i			0.276998i	0.990363	+	0.138499i	$0.0442278\pi$
$89$			2.61320i			0.276998i	−0.990363	+	0.138499i	$0.955772\pi$
$90$		0			0
$91$	0.134784	−	0.0558293i	0.0141292	−	0.00585250i
$92$	0.642248	−	0.266028i	0.0669590	−	0.0277353i
$93$	−8.80728	+	8.80728i	−0.913273	+	0.913273i
$94$	−1.49951	−	1.49951i	−0.154663	−	0.154663i
$95$		0			0
$96$	−6.91774	+	2.86542i	−0.706039	+	0.292451i
$97$	4.85551	+	2.01122i	0.493002	+	0.204208i	0.615312	−	0.788284i	$-0.289030\pi$
$97$	4.85551	+	2.01122i	0.493002	+	0.204208i	−0.122310	+	0.992492i	$0.539030\pi$
$98$	7.88895			0.796905
$99$	−0.0626997	−	0.0259711i	−0.00630156	−	0.00261019i
$100$		0			0
$101$	−4.03337			−0.401335			−0.200668	−	0.979659i	$-0.564311\pi$
$101$	−4.03337			−0.401335			−0.200668	+	0.979659i	$0.564311\pi$
$102$	4.98928	+	8.37437i	0.494013	+	0.829186i
$103$			3.21586i			0.316868i	0.987370	+	0.158434i	$0.0506446\pi$
$103$			3.21586i			0.316868i	−0.987370	+	0.158434i	$0.949355\pi$
$104$	−0.845996	+	0.845996i	−0.0829567	+	0.0829567i
$105$		0			0
$106$			10.4642i			1.01637i
$107$	10.9702	+	4.54399i	1.06052	+	0.439284i	0.843638	−	0.536913i	$-0.180410\pi$
$107$	10.9702	+	4.54399i	1.06052	+	0.439284i	0.216887	+	0.976197i	$0.430410\pi$
$108$	0.945271	+	2.28209i	0.0909588	+	0.219594i
$109$	−7.92218	−	19.1258i	−0.758807	−	1.83192i	−0.500106	−	0.865964i	$-0.666706\pi$
$109$	−7.92218	−	19.1258i	−0.758807	−	1.83192i	−0.258701	−	0.965957i	$-0.583294\pi$
$110$		0			0
$111$	−13.8069	−	13.8069i	−1.31049	−	1.31049i
$112$	0.758701	−	0.314264i	0.0716905	−	0.0296952i
$113$	−1.75294	−	4.23196i	−0.164902	−	0.398109i	0.819730	−	0.572750i	$-0.194124\pi$
$113$	−1.75294	−	4.23196i	−0.164902	−	0.398109i	−0.984632	+	0.174641i	$0.944124\pi$
$114$	−1.60077	+	3.86460i	−0.149926	+	0.361953i
$115$		0			0
$116$	5.28698	+	2.18994i	0.490884	+	0.203331i
$117$	−0.336676	−	0.336676i	−0.0311257	−	0.0311257i
$118$		−	15.6334i		−	1.43917i
$119$	0.792346	+	1.32993i	0.0726343	+	0.121915i
$120$		0			0
$121$	−7.77601	+	7.77601i	−0.706910	+	0.706910i
$122$	−2.55754	+	6.17444i	−0.231549	+	0.559008i
$123$	−15.7740			−1.42229
$124$	1.57015	−	3.79069i	0.141004	−	0.340414i
$125$		0			0
$126$	0.202505	+	0.488889i	0.0180405	+	0.0435537i
$127$	−0.0614833	+	0.0614833i	−0.00545576	+	0.00545576i	−0.709829	−	0.704374i	$-0.751228\pi$
$127$	−0.0614833	+	0.0614833i	−0.00545576	+	0.00545576i	0.704374	+	0.709829i	$0.251228\pi$
$128$	−1.81349	+	1.81349i	−0.160292	+	0.160292i
$129$	5.31557	+	12.8329i	0.468010	+	1.12988i
$130$		0			0
$131$	3.00793	−	7.26179i	0.262804	−	0.634465i	−0.736306	−	0.676649i	$-0.763431\pi$
$131$	3.00793	−	7.26179i	0.262804	−	0.634465i	0.999110	+	0.0421837i	$0.0134315\pi$
$132$	0.0770887			0.00670971
$133$	−0.254218	+	0.613736i	−0.0220435	+	0.0532176i
$134$	−11.7204	+	11.7204i	−1.01249	+	1.01249i
$135$		0			0
$136$	−10.1771	−	7.58975i	−0.872680	−	0.650815i
$137$			14.3733i			1.22800i	0.789307	+	0.613999i	$0.210440\pi$
$137$			14.3733i			1.22800i	−0.789307	+	0.613999i	$0.789560\pi$
$138$	1.71626	+	1.71626i	0.146098	+	0.146098i
$139$	−10.2198	−	4.23320i	−0.866836	−	0.359055i	−0.0954589	−	0.995433i	$-0.530432\pi$
$139$	−10.2198	−	4.23320i	−0.866836	−	0.359055i	−0.771377	+	0.636378i	$0.780432\pi$
$140$		0			0
$141$	−1.45038	+	3.50152i	−0.122144	+	0.294881i
$142$	0.495699	+	1.19672i	0.0415981	+	0.100427i
$143$	0.0198815	−	0.00823520i	0.00166258	−	0.000688662i
$144$	−1.89516	−	1.89516i	−0.157930	−	0.157930i
$145$		0			0
$146$	−0.964514	−	2.32854i	−0.0798238	−	0.192712i
$147$	−5.39554	−	13.0260i	−0.445017	−	1.07437i
$148$	5.94254	+	2.46148i	0.488474	+	0.202333i
$149$		−	5.19432i		−	0.425535i	−0.977103	−	0.212768i	$-0.931752\pi$
$149$		−	5.19432i		−	0.425535i	0.977103	−	0.212768i	$-0.0682478\pi$
$150$		0			0
$151$	4.97988	−	4.97988i	0.405257	−	0.405257i	−0.474824	−	0.880081i	$-0.657488\pi$
$151$	4.97988	−	4.97988i	0.405257	−	0.405257i	0.880081	+	0.474824i	$0.157488\pi$
$152$		−	5.44787i		−	0.441881i
$153$	3.02044	−	4.05012i	0.244188	−	0.327433i
$154$	−0.0239168			−0.00192727
$155$		0			0
$156$	0.499669	+	0.206970i	0.0400055	+	0.0165708i
$157$	15.8006			1.26103			0.630514	−	0.776178i	$-0.282844\pi$
$157$	15.8006			1.26103			0.630514	+	0.776178i	$0.282844\pi$
$158$	−4.18838	−	1.73488i	−0.333209	−	0.138020i
$159$	17.2782	−	7.15685i	1.37025	−	0.567575i
$160$		0			0
$161$	0.272559	+	0.272559i	0.0214807	+	0.0214807i
$162$	−9.08810	+	9.08810i	−0.714029	+	0.714029i
$163$	9.53178	−	3.94819i	0.746587	−	0.309246i	0.0232388	−	0.999730i	$-0.492602\pi$
$163$	9.53178	−	3.94819i	0.746587	−	0.309246i	0.723348	+	0.690483i	$0.242602\pi$
$164$	4.80068	−	1.98851i	0.374870	−	0.155276i
$165$		0			0
$166$			10.8582i			0.842760i
$167$	3.16461	−	7.64004i	0.244885	−	0.591204i	−0.752871	−	0.658168i	$-0.771331\pi$
$167$	3.16461	−	7.64004i	0.244885	−	0.591204i	0.997755	+	0.0669645i	$0.0213314\pi$
$168$	−1.68040	−	1.68040i	−0.129646	−	0.129646i
$169$	−12.8490			−0.988386
$170$		0			0
$171$	2.16806			0.165795
$172$	−3.23550	−	3.23550i	−0.246704	−	0.246704i
$173$	−5.55244	+	13.4048i	−0.422144	+	1.01915i	0.559570	+	0.828783i	$0.310966\pi$
$173$	−5.55244	+	13.4048i	−0.422144	+	1.01915i	−0.981714	+	0.190362i	$0.939034\pi$
$174$			19.9804i			1.51471i
$175$		0			0
$176$	0.111914	−	0.0463561i	0.00843581	−	0.00349423i
$177$	−25.8134	+	10.6923i	−1.94026	+	0.803681i
$178$	2.12527	−	2.12527i	0.159296	−	0.159296i
$179$	10.9353	+	10.9353i	0.817342	+	0.817342i	0.985722	−	0.168380i	$-0.0538535\pi$
$179$	10.9353	+	10.9353i	0.817342	+	0.817342i	−0.168380	+	0.985722i	$0.553854\pi$
$180$		0			0
$181$	22.1058	−	9.15653i	1.64311	−	0.680600i	0.646506	−	0.762909i	$-0.276229\pi$
$181$	22.1058	−	9.15653i	1.64311	−	0.680600i	0.996607	+	0.0823091i	$0.0262295\pi$
$182$	−0.155022	−	0.0642124i	−0.0114910	−	0.00475974i
$183$	11.9442			0.882944
$184$	−2.92047	−	1.20970i	−0.215300	−	0.0891800i
$185$		0			0
$186$	14.3256			1.05041
$187$	0.116877	+	0.196174i	0.00854686	+	0.0143457i
$188$		−	1.24849i		−	0.0910558i
$189$	−0.968478	+	0.968478i	−0.0704464	+	0.0704464i
$190$		0			0
$191$			22.0393i			1.59471i	0.603511	+	0.797355i	$0.293768\pi$
$191$			22.0393i			1.59471i	−0.603511	+	0.797355i	$0.706232\pi$
$192$	16.2639	+	6.73673i	1.17375	+	0.486182i
$193$	5.61741	+	13.5616i	0.404350	+	0.976187i	0.986597	+	0.163175i	$0.0521735\pi$
$193$	5.61741	+	13.5616i	0.404350	+	0.976187i	−0.582247	+	0.813012i	$0.697826\pi$
$194$	−2.31321	−	5.58459i	−0.166079	−	0.400950i
$195$		0			0
$196$	3.28418	+	3.28418i	0.234584	+	0.234584i
$197$	−9.05311	+	3.74992i	−0.645007	+	0.267171i	−0.681114	−	0.732177i	$-0.738504\pi$
$197$	−9.05311	+	3.74992i	−0.645007	+	0.267171i	0.0361070	+	0.999348i	$0.488504\pi$
$198$	0.0298708	+	0.0721145i	0.00212283	+	0.00512495i
$199$	5.41887	−	13.0823i	0.384134	−	0.927381i	−0.607023	−	0.794684i	$-0.707636\pi$
$199$	5.41887	−	13.0823i	0.384134	−	0.927381i	0.991157	−	0.132697i	$-0.0423636\pi$
$200$		0			0
$201$	27.3683	+	11.3363i	1.93041	+	0.799603i
$202$	3.28027	+	3.28027i	0.230799	+	0.230799i
$203$			3.17308i			0.222706i
$204$	−1.40921	+	5.56329i	−0.0986646	+	0.389508i
$205$		0			0
$206$	2.61541	−	2.61541i	0.182224	−	0.182224i
$207$	0.481415	−	1.16224i	0.0334607	−	0.0807812i
$208$	0.849853			0.0589267
$209$	−0.0374988	+	0.0905302i	−0.00259385	+	0.00626211i
$210$		0			0
$211$	2.00706	+	4.84546i	0.138172	+	0.333576i	0.977786	−	0.209608i	$-0.0672188\pi$
$211$	2.00706	+	4.84546i	0.138172	+	0.333576i	−0.839614	+	0.543184i	$0.817219\pi$
$212$	−4.35625	+	4.35625i	−0.299189	+	0.299189i
$213$	1.63697	−	1.63697i	0.112163	−	0.112163i
$214$	−5.22629	−	12.6174i	−0.357262	−	0.862507i
$215$		0			0
$216$	4.29839	−	10.3772i	0.292468	−	0.706081i
$217$	2.27505			0.154440
$218$	−9.11174	+	21.9977i	−0.617125	+	1.48987i
$219$	−3.18515	+	3.18515i	−0.215233	+	0.215233i
$220$		0			0
$221$	0.230871	+	1.58534i	0.0155300	+	0.106642i
$222$			22.4578i			1.50727i
$223$	−9.59168	−	9.59168i	−0.642306	−	0.642306i	0.308816	−	0.951122i	$-0.400067\pi$
$223$	−9.59168	−	9.59168i	−0.642306	−	0.642306i	−0.951122	+	0.308816i	$0.900067\pi$
$224$	1.26357	+	0.523387i	0.0844256	+	0.0349702i
$225$		0			0
$226$	−2.01615	+	4.86742i	−0.134112	+	0.323776i
$227$	−5.14308	−	12.4165i	−0.341358	−	0.824112i	−0.997579	−	0.0695428i	$-0.977846\pi$
$227$	−5.14308	−	12.4165i	−0.341358	−	0.824112i	0.656221	−	0.754569i	$-0.272154\pi$
$228$	−2.27523	+	0.942433i	−0.150681	+	0.0624142i
$229$	7.22635	+	7.22635i	0.477530	+	0.477530i	0.904341	−	0.426811i	$-0.140363\pi$
$229$	7.22635	+	7.22635i	0.477530	+	0.477530i	−0.426811	+	0.904341i	$0.640363\pi$
$230$		0			0
$231$	0.0163576	+	0.0394906i	0.00107625	+	0.00259829i
$232$	−9.95821	−	24.0413i	−0.653789	−	1.57839i
$233$	17.4631	+	7.23347i	1.14405	+	0.473880i	0.872534	−	0.488554i	$-0.162476\pi$
$233$	17.4631	+	7.23347i	1.14405	+	0.473880i	0.271514	+	0.962434i	$0.412476\pi$
$234$			0.547625i			0.0357994i
$235$		0			0
$236$	6.50821	−	6.50821i	0.423648	−	0.423648i
$237$			8.10226i			0.526299i
$238$	0.437208	−	1.72601i	0.0283400	−	0.111881i
$239$	−17.0192			−1.10088			−0.550440	−	0.834874i	$-0.685540\pi$
$239$	−17.0192			−1.10088			−0.550440	+	0.834874i	$0.685540\pi$
$240$		0			0
$241$	22.9284	+	9.49726i	1.47695	+	0.611772i	0.968432	−	0.249279i	$-0.0801937\pi$
$241$	22.9284	+	9.49726i	1.47695	+	0.611772i	0.508517	+	0.861052i	$0.330194\pi$
$242$	12.6482			0.813057
$243$	11.1111	+	4.60238i	0.712779	+	0.295243i
$244$	−3.63513	+	1.50572i	−0.232715	+	0.0963938i
$245$		0			0
$246$	12.8287	+	12.8287i	0.817930	+	0.817930i
$247$	−0.486115	+	0.486115i	−0.0309308	+	0.0309308i
$248$	−17.2372	+	7.13989i	−1.09457	+	0.453384i
$249$	17.9287	−	7.42632i	1.13619	−	0.470624i
$250$		0			0
$251$		−	18.0171i		−	1.13723i	−0.822604	−	0.568614i	$-0.807480\pi$
$251$		−	18.0171i		−	1.13723i	0.822604	−	0.568614i	$-0.192520\pi$
$252$	−0.119222	+	0.287828i	−0.00751028	+	0.0181314i
$253$	0.0402043	+	0.0402043i	0.00252763	+	0.00252763i
$254$	0.100007			0.00627497
$255$		0			0
$256$	−14.1782			−0.886140
$257$	−4.67554	−	4.67554i	−0.291652	−	0.291652i	0.546080	−	0.837733i	$-0.316119\pi$
$257$	−4.67554	−	4.67554i	−0.291652	−	0.291652i	−0.837733	+	0.546080i	$0.816119\pi$
$258$	6.11374	−	14.7599i	0.380625	−	0.918909i
$259$			3.56652i			0.221613i
$260$		0			0
$261$	9.56754	−	3.96301i	0.592216	−	0.245304i
$262$	−8.35219	+	3.45959i	−0.516000	+	0.213734i
$263$	7.47288	−	7.47288i	0.460798	−	0.460798i	−0.438119	−	0.898917i	$-0.644355\pi$
$263$	7.47288	−	7.47288i	0.460798	−	0.460798i	0.898917	+	0.438119i	$0.144355\pi$
$264$	−0.247871	−	0.247871i	−0.0152554	−	0.0152554i
$265$		0			0
$266$	0.705892	−	0.292390i	0.0432810	−	0.0179276i
$267$	−4.96273	−	2.05563i	−0.303714	−	0.125802i
$268$	−9.75840			−0.596089
$269$	−3.50830	−	1.45319i	−0.213905	−	0.0886024i	0.273158	−	0.961969i	$-0.411932\pi$
$269$	−3.50830	−	1.45319i	−0.213905	−	0.0886024i	−0.487063	+	0.873367i	$0.661932\pi$
$270$		0			0
$271$	−24.1996			−1.47002			−0.735010	−	0.678056i	$-0.762822\pi$
$271$	−24.1996			−1.47002			−0.735010	+	0.678056i	$0.762822\pi$
$272$	1.29958	+	8.92392i	0.0787984	+	0.541092i
$273$			0.299885i			0.0181499i
$274$	11.6896	−	11.6896i	0.706194	−	0.706194i
$275$		0			0
$276$			1.42896i			0.0860134i
$277$	20.9985	+	8.69785i	1.26168	+	0.522603i	0.910423	−	0.413678i	$-0.135756\pi$
$277$	20.9985	+	8.69785i	1.26168	+	0.522603i	0.351252	+	0.936281i	$0.385756\pi$
$278$	4.86884	+	11.7544i	0.292014	+	0.704983i
$279$	−2.84142	−	6.85979i	−0.170111	−	0.410685i
$280$		0			0
$281$	−7.92609	−	7.92609i	−0.472831	−	0.472831i	0.429998	−	0.902830i	$-0.358514\pi$
$281$	−7.92609	−	7.92609i	−0.472831	−	0.472831i	−0.902830	+	0.429998i	$0.858514\pi$
$282$	4.02729	−	1.66816i	0.239822	−	0.0993374i
$283$	5.37381	+	12.9735i	0.319440	+	0.771196i	0.999284	+	0.0378394i	$0.0120475\pi$
$283$	5.37381	+	12.9735i	0.319440	+	0.771196i	−0.679844	+	0.733357i	$0.737952\pi$
$284$	−0.291837	+	0.704556i	−0.0173173	+	0.0418077i
$285$		0			0
$286$	−0.0228669	−	0.00947177i	−0.00135215	−	0.000560077i
$287$	2.03733	+	2.03733i	0.120260	+	0.120260i
$288$		−	4.46362i		−	0.263021i
$289$	−16.2939	+	4.84854i	−0.958466	+	0.285208i
$290$		0			0
$291$	−7.63901	+	7.63901i	−0.447807	+	0.447807i
$292$	0.567846	−	1.37090i	0.0332307	−	0.0802259i
$293$	−27.9654			−1.63376			−0.816878	−	0.576811i	$-0.804297\pi$
$293$	−27.9654			−1.63376			−0.816878	+	0.576811i	$0.804297\pi$
$294$	−6.20572	+	14.9819i	−0.361925	+	0.873764i
$295$		0			0
$296$	−11.1930	−	27.0223i	−0.650579	−	1.57064i
$297$	−0.142857	+	0.142857i	−0.00828941	+	0.00828941i
$298$	−4.22446	+	4.22446i	−0.244716	+	0.244716i
$299$	0.152652	+	0.368536i	0.00882812	+	0.0213130i
$300$		0			0
$301$	0.970921	−	2.34401i	0.0559629	−	0.135106i
$302$	−8.10011			−0.466109
$303$	3.17278	−	7.65978i	0.182272	−	0.440043i
$304$	−2.73636	+	2.73636i	−0.156941	+	0.156941i
$305$		0			0
$306$	−5.75037	+	0.837417i	−0.328727	+	0.0478719i
$307$			20.4310i			1.16606i	0.812451	+	0.583029i	$0.198133\pi$
$307$			20.4310i			1.16606i	−0.812451	+	0.583029i	$0.801867\pi$
$308$	−0.00995657	−	0.00995657i	−0.000567328	−	0.000567328i
$309$	−6.10725	−	2.52971i	−0.347429	−	0.143910i
$310$		0			0
$311$	−4.76779	+	11.5105i	−0.270356	+	0.652698i	−0.999499	−	0.0316642i	$-0.989919\pi$
$311$	−4.76779	+	11.5105i	−0.270356	+	0.652698i	0.729142	+	0.684362i	$0.239919\pi$
$312$	−0.941144	−	2.27212i	−0.0532818	−	0.128634i
$313$	8.50641	−	3.52347i	0.480811	−	0.199158i	−0.129095	−	0.991632i	$-0.541207\pi$
$313$	8.50641	−	3.52347i	0.480811	−	0.199158i	0.609906	+	0.792474i	$0.291207\pi$
$314$	−12.8504	−	12.8504i	−0.725189	−	0.725189i
$315$		0			0
$316$	−1.02139	−	2.46586i	−0.0574577	−	0.138715i
$317$	−0.694093	−	1.67569i	−0.0389841	−	0.0941160i	0.903188	−	0.429245i	$-0.141220\pi$
$317$	−0.694093	−	1.67569i	−0.0389841	−	0.0941160i	−0.942172	+	0.335129i	$0.891220\pi$
$318$	−19.8726	−	8.23149i	−1.11440	−	0.461599i
$319$			0.468051i			0.0262058i
$320$		0			0
$321$	−17.2590	+	17.2590i	−0.963303	+	0.963303i
$322$		−	0.443336i		−	0.0247061i
$323$	−5.84784	−	4.36112i	−0.325382	−	0.242659i
$324$	−7.56676			−0.420376
$325$		0			0
$326$	−10.9630	−	4.54104i	−0.607187	−	0.251505i
$327$	42.5537			2.35323
$328$	−21.8299	−	9.04225i	−1.20536	−	0.499275i
$329$	0.639573	−	0.264920i	0.0352608	−	0.0146055i
$330$		0			0
$331$	−12.9804	−	12.9804i	−0.713470	−	0.713470i	0.253790	−	0.967259i	$-0.418323\pi$
$331$	−12.9804	−	12.9804i	−0.713470	−	0.713470i	−0.967259	+	0.253790i	$0.918323\pi$
$332$	−4.52028	+	4.52028i	−0.248082	+	0.248082i
$333$	10.7539	−	4.45440i	0.589309	−	0.244100i
$334$	−8.78724	+	3.63979i	−0.480816	+	0.199161i
$335$		0			0
$336$			1.68806i			0.0920913i
$337$	4.07140	−	9.82922i	0.221783	−	0.535432i	−0.773349	−	0.633980i	$-0.781420\pi$
$337$	4.07140	−	9.82922i	0.221783	−	0.535432i	0.995132	+	0.0985486i	$0.0314200\pi$
$338$	10.4499	+	10.4499i	0.568399	+	0.568399i
$339$	9.41585			0.511399
$340$		0			0
$341$	0.335585			0.0181730
$342$	−1.76324	−	1.76324i	−0.0953453	−	0.0953453i
$343$	−1.99131	+	4.80745i	−0.107521	+	0.259578i
$344$			20.8068i			1.12183i
$345$		0			0
$346$	15.4176	−	6.38617i	0.828854	−	0.343323i
$347$	−22.0704	+	9.14186i	−1.18480	+	0.490761i	−0.886059	−	0.463573i	$-0.846567\pi$
$347$	−22.0704	+	9.14186i	−1.18480	+	0.490761i	−0.298743	+	0.954334i	$0.596567\pi$
$348$	−8.31784	+	8.31784i	−0.445883	+	0.445883i
$349$	−18.5777	−	18.5777i	−0.994441	−	0.994441i	0.00554356	−	0.999985i	$-0.498235\pi$
$349$	−18.5777	−	18.5777i	−0.994441	−	0.994441i	−0.999985	+	0.00554356i	$0.998235\pi$
$350$		0			0
$351$	−1.30951	+	0.542417i	−0.0698964	+	0.0289521i
$352$	0.186385	+	0.0772031i	0.00993434	+	0.00411494i
$353$	4.10448			0.218460			0.109230	−	0.994017i	$-0.465162\pi$
$353$	4.10448			0.218460			0.109230	+	0.994017i	$0.465162\pi$
$354$	29.6895	+	12.2978i	1.57798	+	0.653620i
$355$		0			0
$356$	1.76950			0.0937834
$357$	−3.14896	+	0.458578i	−0.166661	+	0.0242705i
$358$		−	17.7870i		−	0.940071i
$359$	11.2487	−	11.2487i	0.593683	−	0.593683i	−0.344941	−	0.938624i	$-0.612101\pi$
$359$	11.2487	−	11.2487i	0.593683	−	0.593683i	0.938624	+	0.344941i	$0.112101\pi$
$360$		0			0
$361$			15.8696i			0.835243i
$362$	−25.4252	−	10.5314i	−1.33632	−	0.553520i
$363$	−8.65056	−	20.8843i	−0.454037	−	1.09614i
$364$	−0.0378042	−	0.0912675i	−0.00198148	−	0.00478372i
$365$		0			0
$366$	−9.71405	−	9.71405i	−0.507762	−	0.507762i
$367$	16.1023	−	6.66981i	0.840535	−	0.348161i	0.0794705	−	0.996837i	$-0.474677\pi$
$367$	16.1023	−	6.66981i	0.840535	−	0.348161i	0.761064	+	0.648676i	$0.224677\pi$
$368$	0.859284	+	2.07450i	0.0447933	+	0.108141i
$369$	3.59848	−	8.68751i	0.187330	−	0.452254i
$370$		0			0
$371$	−3.15596	−	1.30724i	−0.163849	−	0.0678686i
$372$	5.96377	+	5.96377i	0.309207	+	0.309207i
$373$			26.1546i			1.35423i	0.735875	+	0.677117i	$0.236771\pi$
$373$			26.1546i			1.35423i	−0.735875	+	0.677117i	$0.763229\pi$
$374$	0.0644912	−	0.254599i	0.00333476	−	0.0131650i
$375$		0			0
$376$	−4.01440	+	4.01440i	−0.207027	+	0.207027i
$377$	−1.25663	+	3.03378i	−0.0647199	+	0.156248i
$378$	1.57529			0.0810244
$379$	−6.79575	+	16.4064i	−0.349074	+	0.842740i	0.647656	+	0.761933i	$0.275750\pi$
$379$	−6.79575	+	16.4064i	−0.349074	+	0.842740i	−0.996730	+	0.0808066i	$0.974250\pi$
$380$		0			0
$381$	−0.0683982	−	0.165128i	−0.00350414	−	0.00845975i
$382$	17.9242	−	17.9242i	0.917083	−	0.917083i
$383$	20.3547	−	20.3547i	1.04008	−	1.04008i	0.0409141	−	0.999163i	$-0.486973\pi$
$383$	20.3547	−	20.3547i	1.04008	−	1.04008i	0.999163	−	0.0409141i	$-0.0130270\pi$
$384$	−2.01745	−	4.87056i	−0.102953	−	0.248550i
$385$		0			0
$386$	6.46090	−	15.5980i	0.328851	−	0.793916i
$387$	−8.28035			−0.420914
$388$	1.36188	−	3.28786i	0.0691388	−	0.166916i
$389$	18.9994	−	18.9994i	0.963308	−	0.963308i	−0.0360421	−	0.999350i	$-0.511475\pi$
$389$	18.9994	−	18.9994i	0.963308	−	0.963308i	0.999350	+	0.0360421i	$0.0114750\pi$
$390$		0			0
$391$	−3.63639	+	2.16649i	−0.183900	+	0.109564i
$392$		−	21.1198i		−	1.06671i
$393$	11.4247	+	11.4247i	0.576302	+	0.576302i
$394$	10.4125	+	4.31299i	0.524574	+	0.217285i
$395$		0			0
$396$	−0.0175861	+	0.0424565i	−0.000883733	+	0.00213352i
$397$	−10.1912	−	24.6038i	−0.511484	−	1.23483i	−0.943020	−	0.332736i	$-0.892028\pi$
$397$	−10.1912	−	24.6038i	−0.511484	−	1.23483i	0.431536	−	0.902096i	$-0.357972\pi$
$398$	−15.0467	+	6.23255i	−0.754223	+	0.312410i
$399$	−0.965570	−	0.965570i	−0.0483390	−	0.0483390i
$400$		0			0
$401$	1.03533	+	2.49950i	0.0517018	+	0.124819i	0.947620	−	0.319400i	$-0.103481\pi$
$401$	1.03533	+	2.49950i	0.0517018	+	0.124819i	−0.895918	+	0.444219i	$0.853481\pi$
$402$	−13.0385	−	31.4778i	−0.650303	−	1.56997i
$403$	2.17518	+	0.900988i	0.108353	+	0.0448814i
$404$			2.73116i			0.135880i
$405$		0			0
$406$	2.58061	−	2.58061i	0.128074	−	0.128074i
$407$			0.526087i			0.0260771i
$408$	22.4194	−	13.3570i	1.10992	−	0.661271i
$409$	0.665597			0.0329117			0.0164558	−	0.999865i	$-0.494762\pi$
$409$	0.665597			0.0329117			0.0164558	+	0.999865i	$0.494762\pi$
$410$		0			0
$411$	−27.2964	−	11.3066i	−1.34643	−	0.557711i
$412$	2.17759			0.107282
$413$	4.71498	+	1.95301i	0.232009	+	0.0961013i
$414$	−1.33676	+	0.553703i	−0.0656980	+	0.0272130i
$415$		0			0
$416$	1.00082	+	1.00082i	0.0490693	+	0.0490693i
$417$	16.0786	−	16.0786i	0.787370	−	0.787370i
$418$	0.104124	−	0.0431295i	0.00509287	−	0.00210953i
$419$	30.4600	−	12.6170i	1.48807	−	0.616379i	0.517175	−	0.855880i	$-0.326984\pi$
$419$	30.4600	−	12.6170i	1.48807	−	0.616379i	0.970896	+	0.239501i	$0.0769838\pi$
$420$		0			0
$421$		−	5.35373i		−	0.260925i	−0.991453	−	0.130462i	$-0.958354\pi$
$421$		−	5.35373i		−	0.260925i	0.991453	−	0.130462i	$-0.0416462\pi$
$422$	2.30843	−	5.57304i	0.112373	−	0.271291i
$423$	−1.59759	−	1.59759i	−0.0776773	−	0.0776773i
$424$	28.0141			1.36049
$425$		0			0
$426$	−2.66263			−0.129005
$427$	−1.54269	−	1.54269i	−0.0746558	−	0.0746558i
$428$	3.07692	−	7.42833i	0.148728	−	0.359062i
$429$			0.0442351i			0.00213569i
$430$		0			0
$431$	−10.2043	+	4.22676i	−0.491524	+	0.203596i	−0.614657	−	0.788794i	$-0.710706\pi$
$431$	−10.2043	+	4.22676i	−0.491524	+	0.203596i	0.123134	+	0.992390i	$0.460706\pi$
$432$	−7.37126	+	3.05328i	−0.354650	+	0.146901i
$433$	9.87103	−	9.87103i	0.474372	−	0.474372i	−0.428954	−	0.903326i	$-0.641118\pi$
$433$	9.87103	−	9.87103i	0.474372	−	0.474372i	0.903326	+	0.428954i	$0.141118\pi$
$434$	−1.85026	−	1.85026i	−0.0888153	−	0.0888153i
$435$		0			0
$436$	−12.9509	+	5.36443i	−0.620234	+	0.256909i
$437$	−1.67812	−	0.695100i	−0.0802754	−	0.0332512i
$438$	5.18086			0.247551
$439$	29.3045	+	12.1383i	1.39863	+	0.579330i	0.949395	−	0.314086i	$-0.101698\pi$
$439$	29.3045	+	12.1383i	1.39863	+	0.579330i	0.449231	+	0.893416i	$0.351698\pi$
$440$		0			0
$441$	8.40493			0.400235
$442$	1.10157	−	1.47709i	0.0523963	−	0.0702582i
$443$		−	37.4994i		−	1.78165i	−0.454345	−	0.890826i	$-0.650127\pi$
$443$		−	37.4994i		−	1.78165i	0.454345	−	0.890826i	$-0.349873\pi$
$444$	−9.34921	+	9.34921i	−0.443694	+	0.443694i
$445$		0			0
$446$			15.6015i			0.738753i
$447$	9.86455	+	4.08603i	0.466577	+	0.193263i
$448$	−1.23050	−	2.97070i	−0.0581359	−	0.140352i
$449$	4.39688	+	10.6150i	0.207502	+	0.500953i	0.993029	−	0.117874i	$-0.0376080\pi$
$449$	4.39688	+	10.6150i	0.207502	+	0.500953i	−0.785527	+	0.618827i	$0.787608\pi$
$450$		0			0
$451$	0.300520	+	0.300520i	0.0141509	+	0.0141509i
$452$	−2.86563	+	1.18698i	−0.134788	+	0.0558310i
$453$	5.53996	+	13.3746i	0.260290	+	0.628395i
$454$	−5.91535	+	14.2809i	−0.277621	+	0.670236i
$455$		0			0
$456$	10.3461	+	4.28548i	0.484499	+	0.200686i
$457$	17.1448	+	17.1448i	0.802002	+	0.802002i	0.983408	−	0.181407i	$-0.0580650\pi$
$457$	17.1448	+	17.1448i	0.802002	+	0.802002i	−0.181407	+	0.983408i	$0.558065\pi$
$458$		−	11.7541i		−	0.549235i
$459$	−7.69815	−	12.9211i	−0.359319	−	0.603106i
$460$		0			0
$461$	18.7157	−	18.7157i	0.871675	−	0.871675i	−0.120980	−	0.992655i	$-0.538604\pi$
$461$	18.7157	−	18.7157i	0.871675	−	0.871675i	0.992655	+	0.120980i	$0.0386037\pi$
$462$	0.0188138	−	0.0454204i	0.000875295	−	0.00211315i
$463$	16.0633			0.746523			0.373261	−	0.927726i	$-0.378239\pi$
$463$	16.0633			0.746523			0.373261	+	0.927726i	$0.378239\pi$
$464$	−7.07362	+	17.0772i	−0.328385	+	0.792791i
$465$		0			0
$466$	−8.31962	−	20.0853i	−0.385399	−	0.930435i
$467$	13.7863	−	13.7863i	0.637955	−	0.637955i	−0.312096	−	0.950051i	$-0.601031\pi$
$467$	13.7863	−	13.7863i	0.637955	−	0.637955i	0.950051	+	0.312096i	$0.101031\pi$
$468$	−0.227977	+	0.227977i	−0.0105382	+	0.0105382i
$469$	−2.07065	−	4.99898i	−0.0956136	−	0.230832i
$470$		0			0
$471$	−12.4293	+	30.0070i	−0.572712	+	1.38265i
$472$	−41.8529			−1.92644
$473$	0.143217	−	0.345758i	0.00658515	−	0.0158980i
$474$	6.58944	−	6.58944i	0.302663	−	0.302663i
$475$		0			0
$476$	0.900550	−	0.536530i	0.0412766	−	0.0245918i
$477$			11.1486i			0.510459i
$478$	13.8414	+	13.8414i	0.633093	+	0.633093i
$479$	−22.3277	−	9.24842i	−1.02018	−	0.422571i	−0.191020	−	0.981586i	$-0.561179\pi$
$479$	−22.3277	−	9.24842i	−1.02018	−	0.422571i	−0.829158	+	0.559015i	$0.811179\pi$
$480$		0			0
$481$	−1.41245	+	3.40996i	−0.0644022	+	0.155481i
$482$	−10.9233	−	26.3713i	−0.497544	−	1.20118i
$483$	−0.732022	+	0.303213i	−0.0333081	+	0.0137967i
$484$	5.26545	+	5.26545i	0.239339	+	0.239339i
$485$		0			0
$486$	−5.29346	−	12.7795i	−0.240116	−	0.579692i
$487$	13.9294	+	33.6285i	0.631200	+	1.52385i	0.838115	+	0.545493i	$0.183658\pi$
$487$	13.9294	+	33.6285i	0.631200	+	1.52385i	−0.206915	+	0.978359i	$0.566342\pi$
$488$	16.5299	+	6.84689i	0.748271	+	0.309944i
$489$			21.2076i			0.959041i
$490$		0			0
$491$	−27.2688	+	27.2688i	−1.23063	+	1.23063i	−0.266902	+	0.963724i	$0.586000\pi$
$491$	−27.2688	+	27.2688i	−1.23063	+	1.23063i	−0.963724	+	0.266902i	$0.914000\pi$
$492$			10.6812i			0.481546i
$493$	−33.7780	−	8.55615i	−1.52128	−	0.385350i
$494$	0.790699			0.0355752
$495$		0			0
$496$	12.2441	+	5.07168i	0.549778	+	0.227725i
$497$	−0.422852			−0.0189675
$498$	−20.6208	−	8.54143i	−0.924042	−	0.382751i
$499$	−33.5365	+	13.8913i	−1.50130	+	0.621859i	−0.973741	−	0.227659i	$-0.926893\pi$
$499$	−33.5365	+	13.8913i	−1.50130	+	0.621859i	−0.527559	+	0.849518i	$0.676893\pi$
$500$		0			0
$501$	12.0198	+	12.0198i	0.537006	+	0.537006i
$502$	−14.6530	+	14.6530i	−0.653995	+	0.653995i
$503$	9.30858	−	3.85574i	0.415049	−	0.171919i	−0.165380	−	0.986230i	$-0.552885\pi$
$503$	9.30858	−	3.85574i	0.415049	−	0.171919i	0.580429	+	0.814311i	$0.302885\pi$
$504$	1.30882	−	0.542133i	0.0582997	−	0.0241485i
$505$		0			0
$506$		−	0.0653950i		−	0.00290716i
$507$	10.1075	−	24.4016i	0.448889	−	1.08371i
$508$	0.0416328	+	0.0416328i	0.00184716	+	0.00184716i
$509$	17.8399			0.790740			0.395370	−	0.918522i	$-0.370616\pi$
$509$	17.8399			0.790740			0.395370	+	0.918522i	$0.370616\pi$
$510$		0			0
$511$	0.822771			0.0363972
$512$	15.1579	+	15.1579i	0.669891	+	0.669891i
$513$	2.46988	−	5.96283i	0.109048	−	0.263265i
$514$			7.60508i			0.335446i
$515$		0			0
$516$	8.68969	−	3.59939i	0.382542	−	0.158454i
$517$	0.0943414	−	0.0390775i	0.00414913	−	0.00171863i
$518$	2.90059	−	2.90059i	0.127445	−	0.127445i
$519$	−21.0893	−	21.0893i	−0.925717	−	0.925717i
$520$		0			0
$521$	33.1134	−	13.7160i	1.45073	−	0.600910i	0.488354	−	0.872646i	$-0.337598\pi$
$521$	33.1134	−	13.7160i	1.45073	−	0.600910i	0.962372	+	0.271736i	$0.0875976\pi$
$522$	−11.0042	−	4.55808i	−0.481639	−	0.199502i
$523$	−16.7275			−0.731444			−0.365722	−	0.930724i	$-0.619178\pi$
$523$	−16.7275			−0.731444			−0.365722	+	0.930724i	$0.619178\pi$
$524$	−4.91725	−	2.03679i	−0.214811	−	0.0889777i
$525$		0			0
$526$	−12.1551			−0.529989
$527$	−6.13464	+	24.2183i	−0.267229	+	1.05497i
$528$			0.249001i			0.0108364i
$529$	15.5182	−	15.5182i	0.674705	−	0.674705i
$530$		0			0
$531$		−	16.6559i		−	0.722806i
$532$	0.415585	+	0.172141i	0.0180179	+	0.00746326i
$533$	1.14105	+	2.75473i	0.0494242	+	0.119321i
$534$	2.36430	+	5.70791i	0.102313	+	0.247006i
$535$		0			0
$536$	31.3771	+	31.3771i	1.35528	+	1.35528i
$537$	−29.3693	+	12.1652i	−1.26738	+	0.524966i
$538$	1.67139	+	4.03510i	0.0720588	+	0.173965i
$539$	−0.145372	+	0.350960i	−0.00626162	+	0.0151169i
$540$		0			0
$541$	−12.1694	−	5.04072i	−0.523203	−	0.216718i	0.105420	−	0.994428i	$-0.466381\pi$
$541$	−12.1694	−	5.04072i	−0.523203	−	0.216718i	−0.628623	+	0.777710i	$0.716381\pi$
$542$	19.6811	+	19.6811i	0.845376	+	0.845376i
$543$			49.1841i			2.11069i
$544$	−8.97874	+	12.0396i	−0.384960	+	0.516194i
$545$		0			0
$546$	0.243892	−	0.243892i	0.0104376	−	0.0104376i
$547$	−5.03041	+	12.1445i	−0.215085	+	0.519260i	−0.994191	−	0.107632i	$-0.965673\pi$
$547$	−5.03041	+	12.1445i	−0.215085	+	0.519260i	0.779106	+	0.626892i	$0.215673\pi$
$548$	9.73277			0.415763
$549$	−2.72481	+	6.57828i	−0.116292	+	0.280754i
$550$		0			0
$551$	−5.72206	−	13.8143i	−0.243768	−	0.588508i
$552$	4.59468	−	4.59468i	0.195562	−	0.195562i
$553$	1.04647	−	1.04647i	0.0445003	−	0.0445003i
$554$	−10.0039	−	24.1515i	−0.425024	−	1.02610i
$555$		0			0
$556$	−2.86647	+	6.92027i	−0.121565	+	0.293485i
$557$	1.81038			0.0767084			0.0383542	−	0.999264i	$-0.487788\pi$
$557$	1.81038			0.0767084			0.0383542	+	0.999264i	$0.487788\pi$
$558$	−3.26807	+	7.88983i	−0.138349	+	0.334003i
$559$	1.85660	−	1.85660i	0.0785257	−	0.0785257i
$560$		0			0
$561$	−0.464493	+	0.0676434i	−0.0196109	+	0.00285591i
$562$			12.8923i			0.543830i
$563$	−15.2557	−	15.2557i	−0.642950	−	0.642950i	0.308330	−	0.951280i	$-0.400230\pi$
$563$	−15.2557	−	15.2557i	−0.642950	−	0.642950i	−0.951280	+	0.308330i	$0.900230\pi$
$564$	2.37102	+	0.982108i	0.0998379	+	0.0413542i
$565$		0			0
$566$	6.18072	−	14.9216i	0.259795	−	0.627201i
$567$	−1.60560	−	3.87627i	−0.0674289	−	0.162788i
$568$	3.20380	−	1.32706i	0.134428	−	0.0556820i
$569$	1.85776	+	1.85776i	0.0778815	+	0.0778815i	0.744974	−	0.667093i	$-0.232462\pi$
$569$	1.85776	+	1.85776i	0.0778815	+	0.0778815i	−0.667093	+	0.744974i	$0.732462\pi$
$570$		0			0
$571$	2.24262	+	5.41417i	0.0938509	+	0.226576i	0.963833	−	0.266507i	$-0.0858697\pi$
$571$	2.24262	+	5.41417i	0.0938509	+	0.226576i	−0.869982	+	0.493084i	$0.835870\pi$
$572$	−0.00557639	−	0.0134626i	−0.000233160	−	0.000562899i
$573$	−41.8549	−	17.3369i	−1.74851	−	0.724259i
$574$		−	3.31385i		−	0.138317i
$575$		0			0
$576$	−7.42050	+	7.42050i	−0.309187	+	0.309187i
$577$		−	20.9381i		−	0.871663i	−0.900028	−	0.435832i	$-0.856454\pi$
$577$		−	20.9381i		−	0.871663i	0.900028	−	0.435832i	$-0.143546\pi$
$578$	17.1948	+	9.30833i	0.715210	+	0.387176i
$579$	−30.1737			−1.25398
$580$		0			0
$581$	−3.27479	−	1.35646i	−0.135861	−	0.0562755i
$582$	12.4254			0.515048
$583$	−0.465526	−	0.192827i	−0.0192801	−	0.00798608i
$584$	−6.23384	+	2.58214i	−0.257958	+	0.106850i
$585$		0			0
$586$	22.7438	+	22.7438i	0.939537	+	0.939537i
$587$	−13.7302	+	13.7302i	−0.566706	+	0.566706i	−0.931204	−	0.364498i	$-0.881240\pi$
$587$	−13.7302	+	13.7302i	−0.566706	+	0.566706i	0.364498	+	0.931204i	$0.381240\pi$
$588$	−8.82043	+	3.65354i	−0.363748	+	0.150669i
$589$	−9.90463	+	4.10263i	−0.408113	+	0.169046i
$590$		0			0
$591$		−	20.1426i		−	0.828555i
$592$	−7.95072	+	19.1947i	−0.326772	+	0.788898i
$593$	14.9131	+	14.9131i	0.612407	+	0.612407i	0.943573	−	0.331166i	$-0.107442\pi$
$593$	14.9131	+	14.9131i	0.612407	+	0.612407i	−0.331166	+	0.943573i	$0.607442\pi$
$594$	0.232367			0.00953412
$595$		0			0
$596$	−3.51729			−0.144074
$597$	20.5820	+	20.5820i	0.842365	+	0.842365i
$598$	0.175574	−	0.423874i	0.00717976	−	0.0173335i
$599$		−	23.7029i		−	0.968476i	−0.874936	−	0.484238i	$-0.839097\pi$
$599$		−	23.7029i		−	0.968476i	0.874936	−	0.484238i	$-0.160903\pi$
$600$		0			0
$601$	19.7112	−	8.16463i	0.804035	−	0.333042i	0.0574636	−	0.998348i	$-0.481699\pi$
$601$	19.7112	−	8.16463i	0.804035	−	0.333042i	0.746571	+	0.665305i	$0.231699\pi$
$602$	−2.69598	+	1.11671i	−0.109880	+	0.0455137i
$603$	−12.4869	+	12.4869i	−0.508507	+	0.508507i
$604$	−3.37208	−	3.37208i	−0.137208	−	0.137208i
$605$		0			0
$606$	−8.80994	+	3.64920i	−0.357880	+	0.148239i
$607$	26.8048	+	11.1029i	1.08797	+	0.450653i	0.853299	−	0.521421i	$-0.174598\pi$
$607$	26.8048	+	11.1029i	1.08797	+	0.450653i	0.234673	+	0.972074i	$0.424598\pi$
$608$	−6.44488			−0.261375
$609$	−6.02600	−	2.49605i	−0.244186	−	0.101145i
$610$		0			0
$611$	0.716413			0.0289830
$612$	−2.74250	−	2.04526i	−0.110859	−	0.0826749i
$613$			26.9206i			1.08731i	0.839308	+	0.543657i	$0.182961\pi$
$613$			26.9206i			1.08731i	−0.839308	+	0.543657i	$0.817039\pi$
$614$	16.6162	−	16.6162i	0.670574	−	0.670574i
$615$		0			0
$616$			0.0640286i			0.00257979i
$617$	−13.7731	−	5.70499i	−0.554483	−	0.229674i	0.0878053	−	0.996138i	$-0.472015\pi$
$617$	−13.7731	−	5.70499i	−0.554483	−	0.229674i	−0.642288	+	0.766463i	$0.722015\pi$
$618$	2.90956	+	7.02429i	0.117040	+	0.282558i
$619$	13.1072	+	31.6435i	0.526822	+	1.27186i	0.933594	+	0.358332i	$0.116654\pi$
$619$	13.1072	+	31.6435i	0.526822	+	1.27186i	−0.406772	+	0.913530i	$0.633346\pi$
$620$		0			0
$621$	−2.64808	−	2.64808i	−0.106264	−	0.106264i
$622$	13.2388	−	5.48370i	0.530828	−	0.219876i
$623$	0.375473	+	0.906472i	0.0150430	+	0.0363170i
$624$	−0.668523	+	1.61396i	−0.0267623	+	0.0646100i
$625$		0			0
$626$	−9.78370	−	4.05254i	−0.391035	−	0.161972i
$627$	−0.142428	−	0.142428i	−0.00568804	−	0.00568804i
$628$		−	10.6992i		−	0.426946i
$629$	−37.9663	−	9.61707i	−1.51382	−	0.383458i
$630$		0			0
$631$	22.2493	−	22.2493i	0.885730	−	0.885730i	−0.108380	−	0.994110i	$-0.534566\pi$
$631$	22.2493	−	22.2493i	0.885730	−	0.885730i	0.994110	+	0.108380i	$0.0345662\pi$
$632$	−4.64452	+	11.2129i	−0.184749	+	0.446024i
$633$	−10.7809			−0.428500
$634$	−0.798315	+	1.92730i	−0.0317051	+	0.0765430i
$635$		0			0
$636$	−4.84619	−	11.6997i	−0.192164	−	0.463925i
$637$	−1.88453	+	1.88453i	−0.0746678	+	0.0746678i
$638$	0.380658	−	0.380658i	0.0150704	−	0.0150704i
$639$	0.528120	+	1.27499i	0.0208921	+	0.0504380i
$640$		0			0
$641$	−7.38863	+	17.8377i	−0.291833	+	0.704548i	−0.999999	−	0.00149842i	$-0.999523\pi$
$641$	−7.38863	+	17.8377i	−0.291833	+	0.704548i	0.708166	+	0.706046i	$0.249523\pi$
$642$	28.0729			1.10795
$643$	−6.65200	+	16.0593i	−0.262329	+	0.633319i	−0.999082	−	0.0428438i	$-0.986358\pi$
$643$	−6.65200	+	16.0593i	−0.262329	+	0.633319i	0.736753	+	0.676162i	$0.236358\pi$
$644$	0.184561	−	0.184561i	0.00727271	−	0.00727271i
$645$		0			0
$646$	1.20912	+	8.30278i	0.0475722	+	0.326668i
$647$		−	39.9032i		−	1.56876i	−0.620283	−	0.784378i	$-0.712982\pi$
$647$		−	39.9032i		−	1.56876i	0.620283	−	0.784378i	$-0.287018\pi$
$648$	24.3301	+	24.3301i	0.955778	+	0.955778i
$649$	0.695492	+	0.288082i	0.0273005	+	0.0113082i
$650$		0			0
$651$	−1.78963	+	4.32055i	−0.0701412	+	0.169336i
$652$	−2.67348	−	6.45436i	−0.104702	−	0.252772i
$653$	−11.5855	+	4.79886i	−0.453374	+	0.187794i	−0.597672	−	0.801740i	$-0.703908\pi$
$653$	−11.5855	+	4.79886i	−0.453374	+	0.187794i	0.144298	+	0.989534i	$0.453908\pi$
$654$	−34.6083	−	34.6083i	−1.35329	−	1.35329i
$655$		0			0
$656$	6.42298	+	15.5065i	0.250775	+	0.605425i
$657$	−1.02760	−	2.48084i	−0.0400904	−	0.0967868i
$658$	−0.735609	−	0.304699i	−0.0286770	−	0.0118784i
$659$			10.7616i			0.419214i	0.977786	+	0.209607i	$0.0672184\pi$
$659$			10.7616i			0.419214i	−0.977786	+	0.209607i	$0.932782\pi$
$660$		0			0
$661$	4.37383	−	4.37383i	0.170122	−	0.170122i	−0.616911	−	0.787033i	$-0.711616\pi$
$661$	4.37383	−	4.37383i	0.170122	−	0.170122i	0.787033	+	0.616911i	$0.211616\pi$
$662$			21.1136i			0.820602i
$663$	−3.19234	−	0.808636i	−0.123980	−	0.0314048i
$664$	29.0689			1.12809
$665$		0			0
$666$	−12.3686	−	5.12326i	−0.479275	−	0.198522i
$667$	−8.67606			−0.335938
$668$	−5.17338	−	2.14288i	−0.200164	−	0.0829107i
$669$	25.7607	−	10.6704i	0.995967	−	0.412543i
$670$		0			0
$671$	−0.227557	−	0.227557i	−0.00878473	−	0.00878473i
$672$	−1.98793	+	1.98793i	−0.0766860	+	0.0766860i
$673$	−4.45929	+	1.84710i	−0.171893	+	0.0712004i	−0.466970	−	0.884273i	$-0.654655\pi$
$673$	−4.45929	+	1.84710i	−0.171893	+	0.0712004i	0.295077	+	0.955473i	$0.404655\pi$
$674$	−11.3051	+	4.68274i	−0.435458	+	0.180373i
$675$		0			0
$676$			8.70059i			0.334638i
$677$	10.6989	−	25.8295i	0.411193	−	0.992709i	−0.573625	−	0.819118i	$-0.694463\pi$
$677$	10.6989	−	25.8295i	0.411193	−	0.992709i	0.984818	−	0.173590i	$-0.0555368\pi$
$678$	−7.65775	−	7.65775i	−0.294094	−	0.294094i
$679$	1.97327			0.0757271
$680$		0			0
$681$	27.6259			1.05863
$682$	−0.272926	−	0.272926i	−0.0104509	−	0.0104509i
$683$	4.46436	−	10.7779i	0.170824	−	0.412405i	−0.815162	−	0.579233i	$-0.803352\pi$
$683$	4.46436	−	10.7779i	0.170824	−	0.412405i	0.985986	+	0.166827i	$0.0533522\pi$
$684$		−	1.46808i		−	0.0561334i
$685$		0			0
$686$	5.52932	−	2.29032i	0.211110	−	0.0874448i
$687$	−19.4081	+	8.03908i	−0.740464	+	0.306710i
$688$	10.4508	−	10.4508i	0.398434	−	0.398434i
$689$	−2.49971	−	2.49971i	−0.0952313	−	0.0952313i
$690$		0			0
$691$	35.3606	−	14.6468i	1.34518	−	0.557192i	0.410233	−	0.911981i	$-0.365447\pi$
$691$	35.3606	−	14.6468i	1.34518	−	0.557192i	0.934946	+	0.354789i	$0.115447\pi$
$692$	9.07691	+	3.75978i	0.345052	+	0.142925i
$693$	−0.0254810			−0.000967945
$694$	25.3844	+	10.5146i	0.963580	+	0.399128i
$695$		0			0
$696$	53.4903			2.02754
$697$	−27.1813	+	16.1941i	−1.02957	+	0.613395i
$698$			30.2179i			1.14376i
$699$	−27.4742	+	27.4742i	−1.03917	+	1.03917i
$700$		0			0
$701$		−	13.5092i		−	0.510234i	−0.966910	−	0.255117i	$-0.917886\pi$
$701$		−	13.5092i		−	0.510234i	0.966910	−	0.255117i	$-0.0821141\pi$
$702$	1.50614	+	0.623864i	0.0568456	+	0.0235462i
$703$	−6.43157	−	15.5272i	−0.242571	−	0.585619i
$704$	−0.181508	−	0.438199i	−0.00684084	−	0.0165152i
$705$		0			0
$706$	−3.33811	−	3.33811i	−0.125631	−	0.125631i
$707$	−1.39910	+	0.579528i	−0.0526187	+	0.0217954i
$708$	7.24018	+	17.4793i	0.272102	+	0.656914i
$709$	9.05657	−	21.8645i	0.340127	−	0.821138i	−0.657576	−	0.753388i	$-0.728418\pi$
$709$	9.05657	−	21.8645i	0.340127	−	0.821138i	0.997702	−	0.0677499i	$-0.0215820\pi$
$710$		0			0
$711$	−4.46231	−	1.84835i	−0.167350	−	0.0693186i
$712$	−5.68965	−	5.68965i	−0.213229	−	0.213229i
$713$			6.22061i			0.232964i
$714$	2.93395	+	2.18804i	0.109800	+	0.0818855i
$715$		0			0
$716$	7.40473	−	7.40473i	0.276728	−	0.276728i
$717$	13.3879	−	32.3212i	0.499980	−	1.20706i
$718$	−18.2968			−0.682829
$719$	6.74163	−	16.2757i	0.251420	−	0.606982i	−0.746899	−	0.664938i	$-0.768458\pi$
$719$	6.74163	−	16.2757i	0.251420	−	0.606982i	0.998319	+	0.0579555i	$0.0184581\pi$
$720$		0			0
$721$	0.462066	+	1.11553i	0.0172082	+	0.0415443i
$722$	12.9065	−	12.9065i	0.480330	−	0.480330i
$723$	−36.0725	+	36.0725i	−1.34155	+	1.34155i
$724$	−6.20026	−	14.9687i	−0.230431	−	0.556309i
$725$		0			0
$726$	−9.94950	+	24.0202i	−0.369260	+	0.891473i
$727$	−38.2375			−1.41815			−0.709076	−	0.705132i	$-0.750888\pi$
$727$	−38.2375			−1.41815			−0.709076	+	0.705132i	$0.750888\pi$
$728$	−0.171906	+	0.415017i	−0.00637124	+	0.0153815i
$729$	6.22409	−	6.22409i	0.230522	−	0.230522i
$730$		0			0
$731$	22.3344	+	16.6562i	0.826066	+	0.616053i
$732$		−	8.08793i		−	0.298939i
$733$	25.7052	+	25.7052i	0.949443	+	0.949443i	0.998782	−	0.0493393i	$-0.0157116\pi$
$733$	25.7052	+	25.7052i	0.949443	+	0.949443i	−0.0493393	+	0.998782i	$0.515712\pi$
$734$	−18.5202	−	7.67132i	−0.683593	−	0.283154i
$735$		0			0
$736$	−1.43108	+	3.45494i	−0.0527504	+	0.127351i
$737$	−0.305435	−	0.737385i	−0.0112508	−	0.0271619i
$738$	−9.99200	+	4.13882i	−0.367810	+	0.152352i
$739$	31.5666	+	31.5666i	1.16120	+	1.16120i	0.984214	+	0.176982i	$0.0566336\pi$
$739$	31.5666	+	31.5666i	1.16120	+	1.16120i	0.176982	+	0.984214i	$0.443366\pi$
$740$		0			0
$741$	−0.540788	−	1.30558i	−0.0198663	−	0.0479616i
$742$	1.50353	+	3.62985i	0.0551964	+	0.133256i
$743$	3.00035	+	1.24279i	0.110072	+	0.0455935i	0.437040	−	0.899442i	$-0.356027\pi$
$743$	3.00035	+	1.24279i	0.110072	+	0.0455935i	−0.326968	+	0.945036i	$0.606027\pi$
$744$		−	38.3517i		−	1.40604i
$745$		0			0
$746$	21.2711	−	21.2711i	0.778790	−	0.778790i
$747$			11.5684i			0.423265i
$748$	0.132837	−	0.0791418i	0.00485701	−	0.00289371i
$749$	4.45825			0.162901
$750$		0			0
$751$	1.51618	+	0.628022i	0.0553262	+	0.0229169i	0.410175	−	0.912007i	$-0.365468\pi$
$751$	1.51618	+	0.628022i	0.0553262	+	0.0229169i	−0.354849	+	0.934924i	$0.615468\pi$
$752$	4.03270			0.147058
$753$	34.2163	+	14.1729i	1.24691	+	0.516487i
$754$	3.48932	−	1.44533i	0.127074	−	0.0526356i
$755$		0			0
$756$	0.655796	+	0.655796i	0.0238511	+	0.0238511i
$757$	−6.36808	+	6.36808i	−0.231452	+	0.231452i	−0.813298	−	0.581847i	$-0.802330\pi$
$757$	−6.36808	+	6.36808i	−0.231452	+	0.231452i	0.581847	+	0.813298i	$0.302330\pi$
$758$	18.8699	−	7.81618i	0.685386	−	0.283896i
$759$	−0.107978	+	0.0447261i	−0.00391936	+	0.00162345i
$760$		0			0
$761$			40.8543i			1.48097i	0.672075	+	0.740484i	$0.265403\pi$
$761$			40.8543i			1.48097i	−0.672075	+	0.740484i	$0.734597\pi$
$762$	−0.0786686	+	0.189923i	−0.00284986	+	0.00688018i
$763$	−5.49613	−	5.49613i	−0.198973	−	0.198973i
$764$	14.9237			0.539921
$765$		0			0
$766$	−33.1083			−1.19625
$767$	3.73455	+	3.73455i	0.134847	+	0.134847i
$768$	11.1531	−	26.9259i	0.402452	−	0.971606i
$769$			15.1859i			0.547617i	0.961784	+	0.273809i	$0.0882835\pi$
$769$			15.1859i			0.547617i	−0.961784	+	0.273809i	$0.911716\pi$
$770$		0			0
$771$	12.5573	−	5.20139i	0.452239	−	0.187324i
$772$	9.18312	−	3.80377i	0.330508	−	0.136901i
$773$	16.3437	−	16.3437i	0.587842	−	0.587842i	−0.349204	−	0.937047i	$-0.613548\pi$
$773$	16.3437	−	16.3437i	0.587842	−	0.587842i	0.937047	+	0.349204i	$0.113548\pi$
$774$	6.73427	+	6.73427i	0.242058	+	0.242058i
$775$		0			0
$776$	−14.9507	+	6.19280i	−0.536700	+	0.222308i
$777$	−6.77319	−	2.80555i	−0.242987	−	0.100648i
$778$	−30.9038			−1.10795
$779$	−12.5436	−	5.19574i	−0.449422	−	0.186157i
$780$		0			0
$781$	−0.0623736			−0.00223190
$782$	4.71939	+	1.19545i	0.168765	+	0.0427491i
$783$		−	30.8285i		−	1.10172i
$784$	−10.6081	+	10.6081i	−0.378859	+	0.378859i
$785$		0			0
$786$		−	18.5831i		−	0.662837i
$787$	−31.6938	−	13.1280i	−1.12976	−	0.467962i	−0.262061	−	0.965051i	$-0.584402\pi$
$787$	−31.6938	−	13.1280i	−1.12976	−	0.467962i	−0.867700	+	0.497089i	$0.834402\pi$
$788$	2.53922	+	6.13023i	0.0904561	+	0.218380i
$789$	8.31335	+	20.0702i	0.295963	+	0.714518i
$790$		0			0
$791$	−1.21612	−	1.21612i	−0.0432404	−	0.0432404i
$792$	0.193061	−	0.0799683i	0.00686011	−	0.00284155i
$793$	−0.864014	−	2.08591i	−0.0306820	−	0.0740730i
$794$	−11.7215	+	28.2983i	−0.415981	+	1.00427i
$795$		0			0
$796$	−8.85857	−	3.66934i	−0.313984	−	0.130056i
$797$	−7.47651	−	7.47651i	−0.264832	−	0.264832i	0.562182	−	0.827014i	$-0.309962\pi$
$797$	−7.47651	−	7.47651i	−0.264832	−	0.264832i	−0.827014	+	0.562182i	$0.809962\pi$
$798$			1.57056i			0.0555974i
$799$	1.09552	+	7.52273i	0.0387568	+	0.266135i
$800$		0			0
$801$	2.26427	−	2.26427i	0.0800041	−	0.0800041i
$802$	1.19079	−	2.87482i	0.0420482	−	0.101513i
$803$	0.121364			0.00428286
$804$	7.67628	−	18.5322i	0.270722	−	0.653580i
$805$		0			0
$806$	−1.03628	−	2.50179i	−0.0365013	−	0.0881219i
$807$	5.51950	−	5.51950i	0.194296	−	0.194296i
$808$	8.78175	−	8.78175i	0.308941	−	0.308941i
$809$	15.7502	+	38.0243i	0.553747	+	1.33686i	0.914645	+	0.404259i	$0.132471\pi$
$809$	15.7502	+	38.0243i	0.553747	+	1.33686i	−0.360897	+	0.932606i	$0.617529\pi$
$810$		0			0
$811$	1.73158	−	4.18040i	0.0608039	−	0.146794i	−0.890558	−	0.454871i	$-0.849685\pi$
$811$	1.73158	−	4.18040i	0.0608039	−	0.146794i	0.951361	+	0.308077i	$0.0996855\pi$
$812$	2.14862			0.0754017
$813$	19.0362	−	45.9575i	0.667629	−	1.61180i
$814$	0.427857	−	0.427857i	0.0149964	−	0.0149964i
$815$		0			0
$816$	−17.9697	−	4.55183i	−0.629067	−	0.159346i
$817$			11.9557i			0.418278i
$818$	−0.541319	−	0.541319i	−0.0189268	−	0.0189268i
$819$	−0.165162	−	0.0684121i	−0.00577121	−	0.00239051i
$820$		0			0
$821$	−7.96209	+	19.2222i	−0.277879	+	0.670859i	−0.999777	−	0.0211408i	$-0.993270\pi$
$821$	−7.96209	+	19.2222i	−0.277879	+	0.670859i	0.721898	+	0.692000i	$0.243270\pi$
$822$	13.0043	+	31.3952i	0.453577	+	1.09503i
$823$	42.3922	−	17.5594i	1.47770	−	0.612083i	0.509099	−	0.860708i	$-0.329979\pi$
$823$	42.3922	−	17.5594i	1.47770	−	0.612083i	0.968600	+	0.248626i	$0.0799789\pi$
$824$	−7.00181	−	7.00181i	−0.243920	−	0.243920i
$825$		0			0
$826$	−2.24627	−	5.42296i	−0.0781576	−	0.188689i
$827$	14.5723	+	35.1805i	0.506727	+	1.22335i	0.945757	+	0.324875i	$0.105322\pi$
$827$	14.5723	+	35.1805i	0.506727	+	1.22335i	−0.439030	+	0.898472i	$0.644678\pi$
$828$	−0.786999	−	0.325986i	−0.0273501	−	0.0113288i
$829$			36.1886i			1.25688i	0.777857	+	0.628441i	$0.216307\pi$
$829$			36.1886i			1.25688i	−0.777857	+	0.628441i	$0.783693\pi$
$830$		0			0
$831$	−33.0362	+	33.0362i	−1.14601	+	1.14601i
$832$		−	3.32761i		−	0.115364i
$833$	−22.6704	−	16.9068i	−0.785482	−	0.585786i
$834$	−26.1528			−0.905599
$835$		0			0
$836$	0.0613017	+	0.0253920i	0.00212016	+	0.000878200i
$837$	−22.1035			−0.764010
$838$	−35.0338	−	14.5115i	−1.21022	−	0.501291i
$839$	12.7679	−	5.28865i	0.440798	−	0.182585i	−0.151236	−	0.988498i	$-0.548325\pi$
$839$	12.7679	−	5.28865i	0.440798	−	0.182585i	0.592034	+	0.805913i	$0.298325\pi$
$840$		0			0
$841$	−29.9964	−	29.9964i	−1.03436	−	1.03436i
$842$	−4.35410	+	4.35410i	−0.150052	+	0.150052i
$843$	21.2874	−	8.81753i	0.733177	−	0.303692i
$844$	3.28106	−	1.35906i	0.112939	−	0.0467808i
$845$		0			0
$846$			2.59858i			0.0893410i
$847$	−1.58008	+	3.81464i	−0.0542921	+	0.131073i
$848$	−14.0709	−	14.0709i	−0.483197	−	0.483197i
$849$	−28.8653			−0.990654
$850$		0			0
$851$	−9.75185			−0.334289
$852$	−1.10846	−	1.10846i	−0.0379751	−	0.0379751i
$853$	−1.25777	+	3.03652i	−0.0430651	+	0.103968i	−0.943948	−	0.330093i	$-0.892920\pi$
$853$	−1.25777	+	3.03652i	−0.0430651	+	0.103968i	0.900883	+	0.434061i	$0.142920\pi$
$854$			2.50928i			0.0858658i
$855$		0			0
$856$	−33.7785	+	13.9915i	−1.15453	+	0.478220i
$857$	29.5906	−	12.2568i	1.01080	−	0.418686i	0.185051	−	0.982729i	$-0.440755\pi$
$857$	29.5906	−	12.2568i	1.01080	−	0.418686i	0.825745	+	0.564043i	$0.190755\pi$
$858$	0.0359757	−	0.0359757i	0.00122819	−	0.00122819i
$859$	22.5032	+	22.5032i	0.767801	+	0.767801i	0.977719	−	0.209918i	$-0.0673197\pi$
$859$	22.5032	+	22.5032i	0.767801	+	0.767801i	−0.209918	+	0.977719i	$0.567320\pi$
$860$		0			0
$861$	−5.47172	+	2.26646i	−0.186476	+	0.0772408i
$862$	11.7365	+	4.86143i	0.399748	+	0.165581i
$863$	35.8941			1.22185			0.610925	−	0.791688i	$-0.290798\pi$
$863$	35.8941			1.22185			0.610925	+	0.791688i	$0.290798\pi$
$864$	−12.2764	−	5.08503i	−0.417650	−	0.172996i
$865$		0			0
$866$	−16.0559			−0.545602
$867$	3.60947	−	34.7578i	0.122584	−	1.18044i
$868$		−	1.54053i		−	0.0522889i
$869$	0.154361	−	0.154361i	0.00523634	−	0.00523634i
$870$		0			0
$871$		−	5.59957i		−	0.189734i
$872$	58.8909	+	24.3934i	1.99430	+	0.826065i
$873$	−2.46451	−	5.94985i	−0.0834109	−	0.201372i
$874$	0.799474	+	1.93010i	0.0270426	+	0.0652867i
$875$		0			0
$876$	2.15680	+	2.15680i	0.0728714	+	0.0728714i
$877$	−29.9738	+	12.4156i	−1.01214	+	0.419243i	−0.826236	−	0.563324i	$-0.809522\pi$
$877$	−29.9738	+	12.4156i	−1.01214	+	0.419243i	−0.185907	+	0.982567i	$0.559522\pi$
$878$	−13.9609	−	33.7047i	−0.471159	−	1.13748i
$879$	21.9985	−	53.1091i	0.741992	−	1.79133i
$880$		0			0
$881$	−37.0581	−	15.3500i	−1.24852	−	0.517154i	−0.342153	−	0.939644i	$-0.611156\pi$
$881$	−37.0581	−	15.3500i	−1.24852	−	0.517154i	−0.906368	+	0.422490i	$0.861156\pi$
$882$	−6.83559	−	6.83559i	−0.230166	−	0.230166i
$883$		−	10.0633i		−	0.338656i	−0.985560	−	0.169328i	$-0.945840\pi$
$883$		−	10.0633i		−	0.338656i	0.985560	−	0.169328i	$-0.0541597\pi$
$884$	1.07350	−	0.156332i	0.0361057	−	0.00525801i
$885$		0			0
$886$	−30.4977	+	30.4977i	−1.02459	+	1.02459i
$887$	10.1549	−	24.5160i	0.340967	−	0.823167i	−0.656652	−	0.754194i	$-0.728028\pi$
$887$	10.1549	−	24.5160i	0.340967	−	0.823167i	0.997619	−	0.0689728i	$-0.0219722\pi$
$888$	60.1228			2.01759
$889$	−0.0124933	+	0.0301616i	−0.000419013	+	0.00101159i
$890$		0			0
$891$	−0.236837	−	0.571776i	−0.00793435	−	0.0191552i
$892$	−6.49491	+	6.49491i	−0.217466	+	0.217466i
$893$	−2.30670	+	2.30670i	−0.0771909	+	0.0771909i
$894$	−4.69957	−	11.3458i	−0.157177	−	0.379459i
$895$		0			0
$896$	−0.368500	+	0.889637i	−0.0123107	+	0.0297207i
$897$	−0.819968			−0.0273779
$898$	5.05710	−	12.2089i	0.168758	−	0.407417i
$899$	−36.2095	+	36.2095i	−1.20766	+	1.20766i
$900$		0			0
$901$	22.4258	−	30.0708i	0.747112	−	1.00180i
$902$		−	0.488815i		−	0.0162758i
$903$	3.68776	+	3.68776i	0.122721	+	0.122721i
$904$	13.0308	+	5.39752i	0.433397	+	0.179519i
$905$		0			0
$906$	6.37182	−	15.3829i	0.211689	−	0.511064i
$907$	3.16804	+	7.64833i	0.105193	+	0.253959i	0.967708	−	0.252072i	$-0.0811121\pi$
$907$	3.16804	+	7.64833i	0.105193	+	0.253959i	−0.862515	+	0.506031i	$0.831112\pi$
$908$	−8.40771	+	3.48259i	−0.279020	+	0.115574i
$909$	3.49482	+	3.49482i	0.115916	+	0.115916i
$910$		0			0
$911$	13.6431	+	32.9374i	0.452017	+	1.09126i	0.971554	+	0.236817i	$0.0761042\pi$
$911$	13.6431	+	32.9374i	0.452017	+	1.09126i	−0.519538	+	0.854448i	$0.673896\pi$
$912$	−3.04411	−	7.34913i	−0.100801	−	0.243354i
$913$	−0.483054	−	0.200088i	−0.0159868	−	0.00662193i
$914$		−	27.8872i		−	0.922427i
$915$		0			0
$916$	4.89325	−	4.89325i	0.161678	−	0.161678i
$917$		−	2.95118i		−	0.0974564i
$918$	−4.24776	+	16.7693i	−0.140197	+	0.553470i
$919$	44.5065			1.46813			0.734067	−	0.679077i	$-0.237620\pi$
$919$	44.5065			1.46813			0.734067	+	0.679077i	$0.237620\pi$
$920$		0			0
$921$	−38.8005	−	16.0717i	−1.27852	−	0.529581i
$922$	−30.4423			−1.00256
$923$	−0.404289	−	0.167462i	−0.0133073	−	0.00551208i
$924$	0.0267407	−	0.0110764i	0.000879705	−	0.000364386i
$925$		0			0
$926$	−13.0640	−	13.0640i	−0.429309	−	0.429309i
$927$	2.78647	−	2.78647i	0.0915195	−	0.0915195i
$928$	−28.4410	+	11.7807i	−0.933622	+	0.386719i
$929$	−3.92217	+	1.62462i	−0.128682	+	0.0533019i	−0.446095	−	0.894985i	$-0.647186\pi$
$929$	−3.92217	+	1.62462i	−0.128682	+	0.0533019i	0.317413	+	0.948287i	$0.397186\pi$
$930$		0			0
$931$		−	12.1356i		−	0.397729i
$932$	4.89807	−	11.8250i	0.160442	−	0.387341i
$933$	−18.1090	−	18.1090i	−0.592863	−	0.592863i
$934$	−22.4244			−0.733748
$935$		0			0
$936$	1.46607			0.0479200
$937$	7.19384	+	7.19384i	0.235012	+	0.235012i	0.814781	−	0.579769i	$-0.196857\pi$
$937$	7.19384	+	7.19384i	0.235012	+	0.235012i	−0.579769	+	0.814781i	$0.696857\pi$
$938$	−2.38157	+	5.74961i	−0.0777609	+	0.187732i
$939$			18.9262i			0.617634i
$940$		0			0
$941$	−28.1724	+	11.6694i	−0.918395	+	0.380412i	−0.791264	−	0.611474i	$-0.790577\pi$
$941$	−28.1724	+	11.6694i	−0.918395	+	0.380412i	−0.127131	+	0.991886i	$0.540577\pi$
$942$	34.5127	−	14.2956i	1.12449	−	0.465777i
$943$	−5.57061	+	5.57061i	−0.181404	+	0.181404i
$944$	21.0219	+	21.0219i	0.684203	+	0.684203i
$945$		0			0
$946$	−0.397675	+	0.164722i	−0.0129295	+	0.00535559i
$947$	−40.3302	−	16.7053i	−1.31056	−	0.542850i	−0.385509	−	0.922704i	$-0.625974\pi$
$947$	−40.3302	−	16.7053i	−1.31056	−	0.542850i	−0.925047	+	0.379854i	$0.875974\pi$
$948$	5.48637			0.178189
$949$	0.786652	+	0.325842i	0.0255358	+	0.0105773i
$950$		0			0
$951$	3.72830			0.120898
$952$	−4.62078	−	1.17047i	−0.149760	−	0.0379351i
$953$		−	6.19010i		−	0.200517i	−0.994961	−	0.100258i	$-0.968033\pi$
$953$		−	6.19010i		−	0.200517i	0.994961	−	0.100258i	$-0.0319670\pi$
$954$	9.06697	−	9.06697i	0.293554	−	0.293554i
$955$		0			0
$956$			11.5244i			0.372726i
$957$	−0.888876	−	0.368184i	−0.0287333	−	0.0119017i
$958$	10.6371	+	25.6803i	0.343670	+	0.829693i
$959$	2.06521	+	4.98586i	0.0666891	+	0.161002i
$960$		0			0
$961$	4.04139	+	4.04139i	0.130367	+	0.130367i
$962$	3.92198	−	1.62454i	0.126450	−	0.0523772i
$963$	−5.56812	−	13.4426i	−0.179430	−	0.433182i
$964$	6.43098	−	15.5258i	0.207128	−	0.500051i
$965$		0			0
$966$	0.841939	+	0.348743i	0.0270890	+	0.0112206i
$967$	−31.3914	−	31.3914i	−1.00948	−	1.00948i	−0.999955	−	0.00952406i	$-0.996968\pi$
$967$	−31.3914	−	31.3914i	−1.00948	−	1.00948i	−0.00952406	−	0.999955i	$-0.503032\pi$
$968$		−	33.8610i		−	1.08833i
$969$	12.8823	−	7.67503i	0.413840	−	0.246558i
$970$		0			0
$971$	34.3536	−	34.3536i	1.10246	−	1.10246i	0.108345	−	0.994113i	$-0.465445\pi$
$971$	34.3536	−	34.3536i	1.10246	−	1.10246i	0.994113	−	0.108345i	$-0.0345552\pi$
$972$	3.11646	−	7.52380i	0.0999605	−	0.241326i
$973$	−4.15333			−0.133149
$974$	16.0210	−	38.6780i	0.513345	−	1.23932i
$975$		0			0
$976$	−4.86355	−	11.7417i	−0.155679	−	0.375841i
$977$	−5.46940	+	5.46940i	−0.174982	+	0.174982i	−0.789164	−	0.614182i	$-0.789486\pi$
$977$	−5.46940	+	5.46940i	−0.174982	+	0.174982i	0.614182	+	0.789164i	$0.289486\pi$
$978$	17.2478	−	17.2478i	0.551524	−	0.551524i
$979$	0.0553849	+	0.133711i	0.00177011	+	0.00427342i
$980$		0			0
$981$	−9.70769	+	23.4364i	−0.309943	+	0.748268i
$982$	44.3546			1.41541
$983$	−7.28969	+	17.5989i	−0.232505	+	0.561317i	−0.996471	−	0.0839398i	$-0.973250\pi$
$983$	−7.28969	+	17.5989i	−0.232505	+	0.561317i	0.763966	+	0.645257i	$0.223250\pi$
$984$	34.3443	−	34.3443i	1.09486	−	1.09486i
$985$		0			0
$986$	20.5125	+	34.4297i	0.653251	+	1.09646i
$987$			1.42301i			0.0452949i
$988$	0.329168	+	0.329168i	0.0104722	+	0.0104722i
$989$	6.40917	+	2.65476i	0.203800	+	0.0844166i
$990$		0			0
$991$	4.66953	−	11.2732i	0.148332	−	0.358106i	−0.832196	−	0.554481i	$-0.812917\pi$
$991$	4.66953	−	11.2732i	0.148332	−	0.358106i	0.980529	+	0.196375i	$0.0629169\pi$
$992$	8.44656	+	20.3918i	0.268178	+	0.647440i
$993$	34.8621	−	14.4403i	1.10631	−	0.458250i
$994$	0.343898	+	0.343898i	0.0109078	+	0.0109078i
$995$		0			0
$996$	−5.02866	−	12.1403i	−0.159339	−	0.384679i
$997$	−8.44938	−	20.3986i	−0.267595	−	0.646031i	0.731774	−	0.681547i	$-0.238692\pi$
$997$	−8.44938	−	20.3986i	−0.267595	−	0.646031i	−0.999369	+	0.0355163i	$0.988692\pi$
$998$	38.5722	+	15.9771i	1.22098	+	0.505747i
$999$		−	34.6510i		−	1.09631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.e.349.2		24
5.2	odd	4		425.2.m.c.26.5	✓	24
5.3	odd	4		425.2.m.d.26.2	yes	24
5.4	even	2		425.2.n.d.349.5		24
17.2	even	8		425.2.n.d.274.5		24
85.2	odd	8		425.2.m.c.376.5	yes	24
85.19	even	8	inner	425.2.n.e.274.2		24
85.23	even	16		7225.2.a.cb.1.7		24
85.28	even	16		7225.2.a.cb.1.8		24
85.53	odd	8		425.2.m.d.376.2	yes	24
85.57	even	16		7225.2.a.bx.1.18		24
85.62	even	16		7225.2.a.bx.1.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.5	✓	24	5.2	odd	4
425.2.m.c.376.5	yes	24	85.2	odd	8
425.2.m.d.26.2	yes	24	5.3	odd	4
425.2.m.d.376.2	yes	24	85.53	odd	8
425.2.n.d.274.5		24	17.2	even	8
425.2.n.d.349.5		24	5.4	even	2
425.2.n.e.274.2		24	85.19	even	8	inner
425.2.n.e.349.2		24	1.1	even	1	trivial
7225.2.a.bx.1.17		24	85.62	even	16
7225.2.a.bx.1.18		24	85.57	even	16
7225.2.a.cb.1.7		24	85.23	even	16
7225.2.a.cb.1.8		24	85.28	even	16

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.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.813283 - 0.813283i) q^{2} +(-0.786634 + 1.89910i) q^{3} -0.677141i q^{4} +(2.18426 - 0.904752i) q^{6} +(0.346882 - 0.143683i) q^{7} +(-2.17727 + 2.17727i) q^{8} +(-0.866476 - 0.866476i) q^{9} +(0.0511675 - 0.0211943i) q^{11} +(1.28596 + 0.532662i) q^{12} +0.388558 q^{13} +(-0.398969 - 0.165258i) q^{14} +2.18720 q^{16} +(0.594174 + 4.08007i) q^{17} +1.40938i q^{18} +(-1.25108 + 1.25108i) q^{19} +0.771791i q^{21} +(-0.0588507 - 0.0243767i) q^{22} +(0.392870 + 0.948471i) q^{23} +(-2.42215 - 5.84758i) q^{24} +(-0.316007 - 0.316007i) q^{26} +(-3.37018 + 1.39597i) q^{27} +(-0.0972938 - 0.234888i) q^{28} +(-3.23410 + 7.80781i) q^{29} +(5.59808 + 2.31880i) q^{31} +(2.57573 + 2.57573i) q^{32} +0.113845i q^{33} +(2.83502 - 3.80148i) q^{34} +(-0.586726 + 0.586726i) q^{36} +(-3.63511 + 8.77594i) q^{37} +2.03496 q^{38} +(-0.305652 + 0.737910i) q^{39} +(2.93662 + 7.08964i) q^{41} +(0.627685 - 0.627685i) q^{42} +(4.77818 - 4.77818i) q^{43} +(-0.0143515 - 0.0346476i) q^{44} +(0.451862 - 1.09089i) q^{46} +1.84378 q^{47} +(-1.72053 + 4.15372i) q^{48} +(-4.85007 + 4.85007i) q^{49} +(-8.21586 - 2.08112i) q^{51} -0.263108i q^{52} +(-6.43330 - 6.43330i) q^{53} +(3.87624 + 1.60559i) q^{54} +(-0.442420 + 1.06810i) q^{56} +(-1.39178 - 3.36006i) q^{57} +(8.98020 - 3.71972i) q^{58} +(9.61131 + 9.61131i) q^{59} +(-2.22364 - 5.36835i) q^{61} +(-2.66698 - 6.43867i) q^{62} +(-0.425063 - 0.176067i) q^{63} -8.56400i q^{64} +(0.0925878 - 0.0925878i) q^{66} -14.4112i q^{67} +(2.76278 - 0.402339i) q^{68} -2.11029 q^{69} +(-1.04049 - 0.430984i) q^{71} +3.77311 q^{72} +(2.02455 + 0.838594i) q^{73} +(10.0937 - 4.18095i) q^{74} +(0.847155 + 0.847155i) q^{76} +(0.0147038 - 0.0147038i) q^{77} +(0.848712 - 0.351548i) q^{78} +(3.64157 - 1.50839i) q^{79} -11.1746i q^{81} +(3.37758 - 8.15419i) q^{82} +(-6.67554 - 6.67554i) q^{83} +0.522611 q^{84} -7.77202 q^{86} +(-12.2838 - 12.2838i) q^{87} +(-0.0652600 + 0.157551i) q^{88} +2.61320i q^{89} +(0.134784 - 0.0558293i) q^{91} +(0.642248 - 0.266028i) q^{92} +(-8.80728 + 8.80728i) q^{93} +(-1.49951 - 1.49951i) q^{94} +(-6.91774 + 2.86542i) q^{96} +(4.85551 + 2.01122i) q^{97} +7.88895 q^{98} +(-0.0626997 - 0.0259711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

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