LMFDB - Embedded newform 968.2.c.i.485.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(485,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("968.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.c (of order $2$ , degree $1$ , 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024$ x^20 - x^18 - 2x^16 - 2x^15 - 4x^14 - 4x^13 + 12x^12 + 16x^11 + 32x^9 + 48x^8 - 32x^7 - 64x^6 - 64x^5 - 128x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{4}$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.18
Root			$-1.30820 + 0.537231i$ of defining polynomial
Character	$\chi$	$=$	968.485
Dual form			968.2.c.i.485.17

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30820 + 0.537231i) q^{2} +1.28633i q^{3} +(1.42276 + 1.40561i) q^{4} +1.58193i q^{5} +(-0.691057 + 1.68277i) q^{6} +1.86825 q^{7} +(1.10612 + 2.60317i) q^{8} +1.34535 q^{9} +(-0.849862 + 2.06948i) q^{10} +(-1.80808 + 1.83015i) q^{12} +0.322072i q^{13} +(2.44404 + 1.00368i) q^{14} -2.03488 q^{15} +(0.0485202 + 3.99971i) q^{16} -4.79250 q^{17} +(1.75999 + 0.722767i) q^{18} -3.38629i q^{19} +(-2.22357 + 2.25071i) q^{20} +2.40318i q^{21} +3.08044 q^{23} +(-3.34854 + 1.42284i) q^{24} +2.49750 q^{25} +(-0.173027 + 0.421335i) q^{26} +5.58956i q^{27} +(2.65808 + 2.62603i) q^{28} -10.4131i q^{29} +(-2.66203 - 1.09320i) q^{30} -2.82067 q^{31} +(-2.08529 + 5.25847i) q^{32} +(-6.26955 - 2.57468i) q^{34} +2.95543i q^{35} +(1.91412 + 1.89104i) q^{36} -3.57225i q^{37} +(1.81922 - 4.42993i) q^{38} -0.414291 q^{39} +(-4.11803 + 1.74980i) q^{40} +4.49931 q^{41} +(-1.29107 + 3.14384i) q^{42} -3.61796i q^{43} +2.12826i q^{45} +(4.02982 + 1.65491i) q^{46} -12.7265 q^{47} +(-5.14494 + 0.0624130i) q^{48} -3.50965 q^{49} +(3.26723 + 1.34174i) q^{50} -6.16474i q^{51} +(-0.452708 + 0.458233i) q^{52} +5.65725i q^{53} +(-3.00289 + 7.31225i) q^{54} +(2.06651 + 4.86337i) q^{56} +4.35588 q^{57} +(5.59423 - 13.6224i) q^{58} +5.38428i q^{59} +(-2.89516 - 2.86025i) q^{60} +10.9289i q^{61} +(-3.68999 - 1.51535i) q^{62} +2.51346 q^{63} +(-5.55299 + 5.75884i) q^{64} -0.509496 q^{65} -10.9885i q^{67} +(-6.81861 - 6.73639i) q^{68} +3.96246i q^{69} +(-1.58775 + 3.86629i) q^{70} -11.1359 q^{71} +(1.48812 + 3.50219i) q^{72} +12.6094 q^{73} +(1.91912 - 4.67321i) q^{74} +3.21261i q^{75} +(4.75980 - 4.81789i) q^{76} +(-0.541975 - 0.222570i) q^{78} -5.97994 q^{79} +(-6.32725 + 0.0767555i) q^{80} -3.15396 q^{81} +(5.88599 + 2.41717i) q^{82} -0.139643i q^{83} +(-3.37794 + 3.41917i) q^{84} -7.58140i q^{85} +(1.94368 - 4.73301i) q^{86} +13.3946 q^{87} +4.28990 q^{89} +(-1.14337 + 2.78418i) q^{90} +0.601711i q^{91} +(4.38274 + 4.32989i) q^{92} -3.62831i q^{93} +(-16.6488 - 6.83706i) q^{94} +5.35686 q^{95} +(-6.76413 - 2.68238i) q^{96} +12.3942 q^{97} +(-4.59132 - 1.88549i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 2 q^{4} + q^{6} - 10 q^{7} - 10 q^{9} + 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} - 2 q^{17} + 5 q^{18} - 16 q^{20} - 4 q^{23} - 15 q^{24} - 2 q^{25} + 30 q^{26} + 14 q^{28} - 16 q^{30}+ \cdots + 72 q^{98}+O(q^{100})$ 20 * q + 2 * q^4 + q^6 - 10 * q^7 - 10 * q^9 + 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 - 2 * q^17 + 5 * q^18 - 16 * q^20 - 4 * q^23 - 15 * q^24 - 2 * q^25 + 30 * q^26 + 14 * q^28 - 16 * q^30 + 2 * q^31 - 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 - 28 * q^39 - 10 * q^40 + 2 * q^41 - 20 * q^42 - 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 + 22 * q^50 + 20 * q^52 - 54 * q^54 - 16 * q^56 - 22 * q^57 + 12 * q^58 - 48 * q^60 - 4 * q^62 + 30 * q^63 + 38 * q^64 + 18 * q^65 + 21 * q^68 - 44 * q^70 - 34 * q^71 - 57 * q^72 - 2 * q^73 + 28 * q^74 + 67 * q^76 - 6 * q^78 + 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 + 44 * q^84 + 25 * q^86 - 34 * q^87 - 8 * q^89 + 42 * q^90 + 68 * q^92 - 60 * q^94 + 92 * q^95 - 35 * q^96 + 10 * q^97 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$ .

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.30820	+	0.537231i	0.925036	+	0.379880i
$2$	1.30820	+	0.537231i	0.925036	+	0.379880i
$3$			1.28633i			0.742663i	0.928500	+	0.371332i	$0.121099\pi$
$3$			1.28633i			0.742663i	−0.928500	+	0.371332i	$0.878901\pi$
$4$	1.42276	+	1.40561i	0.711382	+	0.702805i
$5$			1.58193i			0.707460i	0.935348	+	0.353730i	$0.115087\pi$
$5$			1.58193i			0.707460i	−0.935348	+	0.353730i	$0.884913\pi$
$6$	−0.691057	+	1.68277i	−0.282123	+	0.686990i
$7$	1.86825			0.706131			0.353066	−	0.935599i	$-0.385139\pi$
$7$	1.86825			0.706131			0.353066	+	0.935599i	$0.385139\pi$
$8$	1.10612	+	2.60317i	0.391073	+	0.920360i
$9$	1.34535			0.448452
$10$	−0.849862	+	2.06948i	−0.268750	+	0.654426i
$11$		0			0
$11$		0			0
$12$	−1.80808	+	1.83015i	−0.521947	+	0.528317i
$13$			0.322072i			0.0893268i	0.999002	+	0.0446634i	$0.0142215\pi$
$13$			0.322072i			0.0893268i	−0.999002	+	0.0446634i	$0.985778\pi$
$14$	2.44404	+	1.00368i	0.653197	+	0.268245i
$15$	−2.03488			−0.525404
$16$	0.0485202	+	3.99971i	0.0121300	+	0.999926i
$17$	−4.79250			−1.16235			−0.581177	−	0.813778i	$-0.697407\pi$
$17$	−4.79250			−1.16235			−0.581177	+	0.813778i	$0.697407\pi$
$18$	1.75999	+	0.722767i	0.414834	+	0.170358i
$19$		−	3.38629i		−	0.776867i	−0.921477	−	0.388434i	$-0.873016\pi$
$19$		−	3.38629i		−	0.776867i	0.921477	−	0.388434i	$-0.126984\pi$
$20$	−2.22357	+	2.25071i	−0.497206	+	0.503275i
$21$			2.40318i			0.524418i
$22$		0			0
$23$	3.08044			0.642316			0.321158	−	0.947026i	$-0.395928\pi$
$23$	3.08044			0.642316			0.321158	+	0.947026i	$0.395928\pi$
$24$	−3.34854	+	1.42284i	−0.683517	+	0.290435i
$25$	2.49750			0.499500
$26$	−0.173027	+	0.421335i	−0.0339335	+	0.0826305i
$27$			5.58956i			1.07571i
$28$	2.65808	+	2.62603i	0.502330	+	0.496273i
$29$		−	10.4131i		−	1.93366i	−0.255422	−	0.966830i	$-0.582215\pi$
$29$		−	10.4131i		−	1.93366i	0.255422	−	0.966830i	$-0.417785\pi$
$30$	−2.66203	−	1.09320i	−0.486018	−	0.199591i
$31$	−2.82067			−0.506607			−0.253303	−	0.967387i	$-0.581517\pi$
$31$	−2.82067			−0.506607			−0.253303	+	0.967387i	$0.581517\pi$
$32$	−2.08529	+	5.25847i	−0.368631	+	0.929576i
$33$		0			0
$34$	−6.26955	−	2.57468i	−1.07522	−	0.441555i
$35$			2.95543i			0.499560i
$36$	1.91412	+	1.89104i	0.319021	+	0.315174i
$37$		−	3.57225i		−	0.587274i	−0.955917	−	0.293637i	$-0.905134\pi$
$37$		−	3.57225i		−	0.587274i	0.955917	−	0.293637i	$-0.0948657\pi$
$38$	1.81922	−	4.42993i	0.295116	−	0.718630i
$39$	−0.414291			−0.0663397
$40$	−4.11803	+	1.74980i	−0.651118	+	0.276668i
$41$	4.49931			0.702674			0.351337	−	0.936249i	$-0.385727\pi$
$41$	4.49931			0.702674			0.351337	+	0.936249i	$0.385727\pi$
$42$	−1.29107	+	3.14384i	−0.199216	+	0.485105i
$43$		−	3.61796i		−	0.551734i	−0.961196	−	0.275867i	$-0.911035\pi$
$43$		−	3.61796i		−	0.551734i	0.961196	−	0.275867i	$-0.0889649\pi$
$44$		0			0
$45$			2.12826i			0.317262i
$46$	4.02982	+	1.65491i	0.594165	+	0.244003i
$47$	−12.7265			−1.85635			−0.928174	−	0.372147i	$-0.878622\pi$
$47$	−12.7265			−1.85635			−0.928174	+	0.372147i	$0.878622\pi$
$48$	−5.14494	+	0.0624130i	−0.742608	+	0.00900854i
$49$	−3.50965			−0.501378
$50$	3.26723	+	1.34174i	0.462056	+	0.189750i
$51$		−	6.16474i		−	0.863237i
$52$	−0.452708	+	0.458233i	−0.0627793	+	0.0635455i
$53$			5.65725i			0.777083i	0.921431	+	0.388541i	$0.127021\pi$
$53$			5.65725i			0.777083i	−0.921431	+	0.388541i	$0.872979\pi$
$54$	−3.00289	+	7.31225i	−0.408641	+	0.995072i
$55$		0			0
$56$	2.06651	+	4.86337i	0.276149	+	0.649895i
$57$	4.35588			0.576951
$58$	5.59423	−	13.6224i	0.734558	−	1.78870i
$59$			5.38428i			0.700973i	0.936568	+	0.350487i	$0.113984\pi$
$59$			5.38428i			0.700973i	−0.936568	+	0.350487i	$0.886016\pi$
$60$	−2.89516	−	2.86025i	−0.373763	−	0.369257i
$61$			10.9289i			1.39931i	0.714482	+	0.699654i	$0.246662\pi$
$61$			10.9289i			1.39931i	−0.714482	+	0.699654i	$0.753338\pi$
$62$	−3.68999	−	1.51535i	−0.468630	−	0.192450i
$63$	2.51346			0.316666
$64$	−5.55299	+	5.75884i	−0.694124	+	0.719855i
$65$	−0.509496			−0.0631951
$66$		0			0
$67$		−	10.9885i		−	1.34246i	−0.741249	−	0.671230i	$-0.765766\pi$
$67$		−	10.9885i		−	1.34246i	0.741249	−	0.671230i	$-0.234234\pi$
$68$	−6.81861	−	6.73639i	−0.826878	−	0.816908i
$69$			3.96246i			0.477024i
$70$	−1.58775	+	3.86629i	−0.189773	+	0.462111i
$71$	−11.1359			−1.32159			−0.660795	−	0.750566i	$-0.729781\pi$
$71$	−11.1359			−1.32159			−0.660795	+	0.750566i	$0.729781\pi$
$72$	1.48812	+	3.50219i	0.175377	+	0.412737i
$73$	12.6094			1.47582			0.737912	−	0.674897i	$-0.235812\pi$
$73$	12.6094			1.47582			0.737912	+	0.674897i	$0.235812\pi$
$74$	1.91912	−	4.67321i	0.223094	−	0.543250i
$75$			3.21261i			0.370961i
$76$	4.75980	−	4.81789i	0.545986	−	0.552650i
$77$		0			0
$78$	−0.541975	−	0.222570i	−0.0613666	−	0.0252011i
$79$	−5.97994			−0.672796			−0.336398	−	0.941720i	$-0.609209\pi$
$79$	−5.97994			−0.672796			−0.336398	+	0.941720i	$0.609209\pi$
$80$	−6.32725	+	0.0767555i	−0.707408	+	0.00858152i
$81$	−3.15396			−0.350440
$82$	5.88599	+	2.41717i	0.649999	+	0.266932i
$83$		−	0.139643i		−	0.0153279i	−0.999971	−	0.00766393i	$-0.997560\pi$
$83$		−	0.139643i		−	0.0153279i	0.999971	−	0.00766393i	$-0.00243953\pi$
$84$	−3.37794	+	3.41917i	−0.368563	+	0.373062i
$85$		−	7.58140i		−	0.822318i
$86$	1.94368	−	4.73301i	0.209593	−	0.510373i
$87$	13.3946			1.43606
$88$		0			0
$89$	4.28990			0.454729			0.227364	−	0.973810i	$-0.426989\pi$
$89$	4.28990			0.454729			0.227364	+	0.973810i	$0.426989\pi$
$90$	−1.14337	+	2.78418i	−0.120521	+	0.293478i
$91$			0.601711i			0.0630765i
$92$	4.38274	+	4.32989i	0.456932	+	0.451423i
$93$		−	3.62831i		−	0.376238i
$94$	−16.6488	−	6.83706i	−1.71719	−	0.705189i
$95$	5.35686			0.549602
$96$	−6.76413	−	2.68238i	−0.690362	−	0.273769i
$97$	12.3942			1.25844			0.629218	−	0.777229i	$-0.283375\pi$
$97$	12.3942			1.25844			0.629218	+	0.777229i	$0.283375\pi$
$98$	−4.59132	−	1.88549i	−0.463793	−	0.190464i
$99$		0			0
$100$	3.55336	+	3.51051i	0.355336	+	0.351051i
$101$		−	15.3627i		−	1.52865i	−0.644831	−	0.764325i	$-0.723072\pi$
$101$		−	15.3627i		−	1.52865i	0.644831	−	0.764325i	$-0.276928\pi$
$102$	3.31189	−	8.06471i	0.327926	−	0.798525i
$103$	8.17691			0.805695			0.402848	−	0.915267i	$-0.368020\pi$
$103$	8.17691			0.805695			0.402848	+	0.915267i	$0.368020\pi$
$104$	−0.838409	+	0.356251i	−0.0822128	+	0.0349333i
$105$	−3.80166			−0.371005
$106$	−3.03925	+	7.40080i	−0.295198	+	0.718829i
$107$		−	5.03234i		−	0.486494i	−0.969964	−	0.243247i	$-0.921787\pi$
$107$		−	5.03234i		−	0.486494i	0.969964	−	0.243247i	$-0.0782126\pi$
$108$	−7.85674	+	7.95263i	−0.756015	+	0.765242i
$109$		−	10.1839i		−	0.975439i	−0.873000	−	0.487720i	$-0.837829\pi$
$109$		−	10.1839i		−	0.975439i	0.873000	−	0.487720i	$-0.162171\pi$
$110$		0			0
$111$	4.59509			0.436147
$112$	0.0906477	+	7.47244i	0.00856541	+	0.706079i
$113$	8.05191			0.757460			0.378730	−	0.925507i	$-0.376361\pi$
$113$	8.05191			0.757460			0.378730	+	0.925507i	$0.376361\pi$
$114$	5.69836	+	2.34012i	0.533700	+	0.219172i
$115$			4.87303i			0.454413i
$116$	14.6367	−	14.8154i	1.35899	−	1.37557i
$117$			0.433302i			0.0400588i
$118$	−2.89260	+	7.04370i	−0.266286	+	0.648425i
$119$	−8.95359			−0.820774
$120$	−2.25083	−	5.29715i	−0.205471	−	0.483561i
$121$		0			0
$122$	−5.87137	+	14.2972i	−0.531569	+	1.29441i
$123$			5.78760i			0.521850i
$124$	−4.01315	−	3.96476i	−0.360391	−	0.356046i
$125$			11.8605i			1.06084i
$126$	3.28810	+	1.35031i	0.292927	+	0.120295i
$127$	13.0462			1.15766			0.578830	−	0.815448i	$-0.303510\pi$
$127$	13.0462			1.15766			0.578830	+	0.815448i	$0.303510\pi$
$128$	−10.3582	+	4.55046i	−0.915548	+	0.402208i
$129$	4.65389			0.409752
$130$	−0.666521	−	0.273717i	−0.0584578	−	0.0240066i
$131$		−	11.5519i		−	1.00930i	−0.863325	−	0.504648i	$-0.831622\pi$
$131$		−	11.5519i		−	1.00930i	0.863325	−	0.504648i	$-0.168378\pi$
$132$		0			0
$133$		−	6.32642i		−	0.548570i
$134$	5.90338	−	14.3752i	0.509974	−	1.24182i
$135$	−8.84229			−0.761023
$136$	−5.30109	−	12.4757i	−0.454565	−	1.06978i
$137$	18.0192			1.53948			0.769742	−	0.638355i	$-0.220385\pi$
$137$	18.0192			1.53948			0.769742	+	0.638355i	$0.220385\pi$
$138$	−2.12876	+	5.18368i	−0.181212	+	0.441264i
$139$			6.70490i			0.568702i	0.958720	+	0.284351i	$0.0917781\pi$
$139$			6.70490i			0.568702i	−0.958720	+	0.284351i	$0.908222\pi$
$140$	−4.15419	+	4.20489i	−0.351093	+	0.355378i
$141$		−	16.3705i		−	1.37864i
$142$	−14.5680	−	5.98257i	−1.22252	−	0.502046i
$143$		0			0
$144$	0.0652769	+	5.38102i	0.00543974	+	0.448419i
$145$	16.4727			1.36799
$146$	16.4956	+	6.77419i	1.36519	+	0.560636i
$147$		−	4.51457i		−	0.372355i
$148$	5.02119	−	5.08247i	0.412739	−	0.417776i
$149$		−	4.00757i		−	0.328313i	−0.986434	−	0.164156i	$-0.947510\pi$
$149$		−	4.00757i		−	0.328313i	0.986434	−	0.164156i	$-0.0524902\pi$
$150$	−1.72592	+	4.20273i	−0.140920	+	0.343152i
$151$	2.33413			0.189948			0.0949742	−	0.995480i	$-0.469723\pi$
$151$	2.33413			0.189948			0.0949742	+	0.995480i	$0.469723\pi$
$152$	8.81508	−	3.74564i	0.714997	−	0.303812i
$153$	−6.44762			−0.521259
$154$		0			0
$155$		−	4.46210i		−	0.358404i
$156$	−0.589439	−	0.582332i	−0.0471929	−	0.0466239i
$157$		−	7.94584i		−	0.634147i	−0.948401	−	0.317073i	$-0.897300\pi$
$157$		−	7.94584i		−	0.634147i	0.948401	−	0.317073i	$-0.102700\pi$
$158$	−7.82295	−	3.21261i	−0.622361	−	0.255582i
$159$	−7.27709			−0.577111
$160$	−8.31853	−	3.29878i	−0.657638	−	0.260792i
$161$	5.75502			0.453559
$162$	−4.12600	−	1.69440i	−0.324169	−	0.133125i
$163$		−	5.61529i		−	0.439823i	−0.975520	−	0.219912i	$-0.929423\pi$
$163$		−	5.61529i		−	0.439823i	0.975520	−	0.219912i	$-0.0705769\pi$
$164$	6.40146	+	6.32428i	0.499870	+	0.493843i
$165$		0			0
$166$	0.0750208	−	0.182681i	0.00582275	−	0.0141788i
$167$	−18.0271			−1.39498			−0.697489	−	0.716595i	$-0.745700\pi$
$167$	−18.0271			−1.39498			−0.697489	+	0.716595i	$0.745700\pi$
$168$	−6.25590	+	2.65821i	−0.482653	+	0.205085i
$169$	12.8963			0.992021
$170$	4.07297	−	9.91797i	0.312382	−	0.760674i
$171$		−	4.55576i		−	0.348387i
$172$	5.08544	−	5.14751i	0.387761	−	0.392494i
$173$			15.0682i			1.14562i	0.819689	+	0.572809i	$0.194146\pi$
$173$			15.0682i			1.14562i	−0.819689	+	0.572809i	$0.805854\pi$
$174$	17.5229	+	7.19603i	1.32840	+	0.545529i
$175$	4.66595			0.352713
$176$		0			0
$177$	−6.92596			−0.520587
$178$	5.61204	+	2.30467i	0.420641	+	0.172742i
$179$			22.2870i			1.66581i	0.553419	+	0.832903i	$0.313323\pi$
$179$			22.2870i			1.66581i	−0.553419	+	0.832903i	$0.686677\pi$
$180$	−2.99150	+	3.02801i	−0.222973	+	0.225694i
$181$			11.5115i			0.855643i	0.903863	+	0.427822i	$0.140719\pi$
$181$			11.5115i			0.855643i	−0.903863	+	0.427822i	$0.859281\pi$
$182$	−0.323258	+	0.787158i	−0.0239615	+	0.0583480i
$183$	−14.0582			−1.03921
$184$	3.40734	+	8.01891i	0.251192	+	0.591162i
$185$	5.65104			0.415473
$186$	1.94924	−	4.74655i	0.142925	−	0.348034i
$187$		0			0
$188$	−18.1068	−	17.8885i	−1.32057	−	1.30465i
$189$			10.4427i			0.759594i
$190$	7.00784	+	2.87787i	0.508402	+	0.208783i
$191$	−10.7973			−0.781262			−0.390631	−	0.920547i	$-0.627743\pi$
$191$	−10.7973			−0.781262			−0.390631	+	0.920547i	$0.627743\pi$
$192$	−7.40777	−	7.14298i	−0.534610	−	0.515500i
$193$	−9.05654			−0.651904			−0.325952	−	0.945386i	$-0.605685\pi$
$193$	−9.05654			−0.651904			−0.325952	+	0.945386i	$0.605685\pi$
$194$	16.2140	+	6.65853i	1.16410	+	0.478054i
$195$		−	0.655379i		−	0.0469327i
$196$	−4.99341	−	4.93320i	−0.356672	−	0.352371i
$197$			8.74114i			0.622780i	0.950282	+	0.311390i	$0.100795\pi$
$197$			8.74114i			0.622780i	−0.950282	+	0.311390i	$0.899205\pi$
$198$		0			0
$199$	2.55580			0.181176			0.0905878	−	0.995888i	$-0.471125\pi$
$199$	2.55580			0.181176			0.0905878	+	0.995888i	$0.471125\pi$
$200$	2.76254	+	6.50142i	0.195341	+	0.459720i
$201$	14.1349			0.996996
$202$	8.25335	−	20.0975i	0.580703	−	1.41406i
$203$		−	19.4542i		−	1.36542i
$204$	8.66522	−	8.77098i	0.606687	−	0.614091i
$205$			7.11759i			0.497114i
$206$	10.6970	+	4.39289i	0.745297	+	0.306067i
$207$	4.14428			0.288048
$208$	−1.28819	+	0.0156270i	−0.0893202	+	0.00108354i
$209$		0			0
$210$	−4.97333	−	2.04237i	−0.343192	−	0.140937i
$211$		−	3.31568i		−	0.228261i	−0.993466	−	0.114130i	$-0.963592\pi$
$211$		−	3.31568i		−	0.228261i	0.993466	−	0.114130i	$-0.0364082\pi$
$212$	−7.95189	+	8.04893i	−0.546138	+	0.552803i
$213$		−	14.3245i		−	0.981497i
$214$	2.70353	−	6.58329i	0.184809	−	0.450025i
$215$	5.72335			0.390330
$216$	−14.5506	+	6.18273i	−0.990042	+	0.420681i
$217$	−5.26971			−0.357731
$218$	5.47110	−	13.3225i	0.370550	−	0.902316i
$219$			16.2199i			1.09604i
$220$		0			0
$221$		−	1.54353i		−	0.103829i
$222$	6.01129	+	2.46863i	0.403451	+	0.165683i
$223$	−14.9051			−0.998121			−0.499061	−	0.866567i	$-0.666322\pi$
$223$	−14.9051			−0.998121			−0.499061	+	0.866567i	$0.666322\pi$
$224$	−3.89585	+	9.82413i	−0.260302	+	0.656403i
$225$	3.36003			0.224002
$226$	10.5335	+	4.32574i	0.700677	+	0.287744i
$227$		−	1.32270i		−	0.0877904i	−0.999036	−	0.0438952i	$-0.986023\pi$
$227$		−	1.32270i		−	0.0877904i	0.999036	−	0.0438952i	$-0.0139768\pi$
$228$	6.19740	+	6.12267i	0.410433	+	0.405484i
$229$		−	23.6029i		−	1.55972i	−0.625953	−	0.779861i	$-0.715290\pi$
$229$		−	23.6029i		−	1.55972i	0.625953	−	0.779861i	$-0.284710\pi$
$230$	−2.61795	+	6.37489i	−0.172622	+	0.420348i
$231$		0			0
$232$	27.1070	−	11.5181i	1.77966	−	0.756201i
$233$	−2.47082			−0.161869			−0.0809343	−	0.996719i	$-0.525790\pi$
$233$	−2.47082			−0.161869			−0.0809343	+	0.996719i	$0.525790\pi$
$234$	−0.232783	+	0.566844i	−0.0152175	+	0.0370558i
$235$		−	20.1324i		−	1.31329i
$236$	−7.56820	+	7.66056i	−0.492648	+	0.498660i
$237$		−	7.69218i		−	0.499661i
$238$	−11.7131	−	4.81015i	−0.759245	−	0.311796i
$239$	−15.8198			−1.02330			−0.511648	−	0.859195i	$-0.670965\pi$
$239$	−15.8198			−1.02330			−0.511648	+	0.859195i	$0.670965\pi$
$240$	−0.0987329	−	8.13893i	−0.00637318	−	0.525366i
$241$	3.22511			0.207748			0.103874	−	0.994590i	$-0.466876\pi$
$241$	3.22511			0.207748			0.103874	+	0.994590i	$0.466876\pi$
$242$		0			0
$243$			12.7117i			0.815453i
$244$	−15.3618	+	15.5493i	−0.983441	+	0.995443i
$245$		−	5.55201i		−	0.354705i
$246$	−3.10928	+	7.57133i	−0.198240	+	0.482730i
$247$	1.09063			0.0693951
$248$	−3.12000	−	7.34268i	−0.198120	−	0.466261i
$249$	0.179628			0.0113834
$250$	−6.37184	+	15.5159i	−0.402990	+	0.981312i
$251$		−	0.345844i		−	0.0218295i	−0.999940	−	0.0109147i	$-0.996526\pi$
$251$		−	0.345844i		−	0.0218295i	0.999940	−	0.0109147i	$-0.00347434\pi$
$252$	3.57606	+	3.53294i	0.225270	+	0.222554i
$253$		0			0
$254$	17.0670	+	7.00881i	1.07088	+	0.439772i
$255$	9.75218			0.610705
$256$	−15.9953	+	0.388133i	−0.999706	+	0.0242583i
$257$	−0.421872			−0.0263157			−0.0131578	−	0.999913i	$-0.504188\pi$
$257$	−0.421872			−0.0263157			−0.0131578	+	0.999913i	$0.504188\pi$
$258$	6.08821	+	2.50022i	0.379036	+	0.155657i
$259$		−	6.67385i		−	0.414693i
$260$	−0.724892	−	0.716152i	−0.0449559	−	0.0444139i
$261$		−	14.0093i		−	0.867153i
$262$	6.20605	−	15.1122i	0.383411	−	0.933634i
$263$	2.35352			0.145124			0.0725621	−	0.997364i	$-0.476882\pi$
$263$	2.35352			0.145124			0.0725621	+	0.997364i	$0.476882\pi$
$264$		0			0
$265$	−8.94936			−0.549755
$266$	3.39875	−	8.27621i	0.208391	−	0.507447i
$267$			5.51823i			0.337710i
$268$	15.4456	−	15.6341i	0.943488	−	0.955003i
$269$		−	23.0569i		−	1.40580i	−0.711287	−	0.702901i	$-0.751888\pi$
$269$		−	23.0569i		−	1.40580i	0.711287	−	0.702901i	$-0.248112\pi$
$270$	−11.5675	−	4.75035i	−0.703973	−	0.289097i
$271$	−4.37644			−0.265850			−0.132925	−	0.991126i	$-0.542437\pi$
$271$	−4.37644			−0.265850			−0.132925	+	0.991126i	$0.542437\pi$
$272$	−0.232533	−	19.1686i	−0.0140994	−	1.16227i
$273$	−0.773999			−0.0468446
$274$	23.5727	+	9.68048i	1.42408	+	0.584819i
$275$		0			0
$276$	−5.56967	+	5.63765i	−0.335255	+	0.339347i
$277$		−	6.26661i		−	0.376524i	−0.982119	−	0.188262i	$-0.939715\pi$
$277$		−	6.26661i		−	0.376524i	0.982119	−	0.188262i	$-0.0602854\pi$
$278$	−3.60208	+	8.77133i	−0.216038	+	0.526070i
$279$	−3.79480			−0.227189
$280$	−7.69350	+	3.26907i	−0.459775	+	0.195364i
$281$	−11.1852			−0.667250			−0.333625	−	0.942706i	$-0.608272\pi$
$281$	−11.1852			−0.667250			−0.333625	+	0.942706i	$0.608272\pi$
$282$	8.79472	−	21.4158i	0.523718	−	1.27529i
$283$			31.9805i			1.90104i	0.310662	+	0.950521i	$0.399449\pi$
$283$			31.9805i			1.90104i	−0.310662	+	0.950521i	$0.600551\pi$
$284$	−15.8438	−	15.6528i	−0.940157	−	0.928821i
$285$			6.89069i			0.408169i
$286$		0			0
$287$	8.40583			0.496180
$288$	−2.80546	+	7.07451i	−0.165313	+	0.416870i
$289$	5.96810			0.351065
$290$	21.5496	+	8.84967i	1.26544	+	0.519671i
$291$			15.9430i			0.934594i
$292$	17.9403	+	17.7240i	1.04987	+	1.03722i
$293$			7.66484i			0.447785i	0.974614	+	0.223892i	$0.0718764\pi$
$293$			7.66484i			0.447785i	−0.974614	+	0.223892i	$0.928124\pi$
$294$	2.42537	−	5.90595i	0.141450	−	0.344442i
$295$	−8.51754			−0.495911
$296$	9.29917	−	3.95134i	0.540503	−	0.229667i
$297$		0			0
$298$	2.15299	−	5.24269i	0.124719	−	0.303701i
$299$			0.992124i			0.0573760i
$300$	−4.51568	+	4.57079i	−0.260713	+	0.263895i
$301$		−	6.75925i		−	0.389597i
$302$	3.05350	+	1.25397i	0.175709	+	0.0721576i
$303$	19.7616			1.13527
$304$	13.5441	−	0.164303i	0.776810	−	0.00942343i
$305$	−17.2888			−0.989954
$306$	−8.43476	−	3.46386i	−0.482183	−	0.198016i
$307$		−	3.57511i		−	0.204042i	−0.994782	−	0.102021i	$-0.967469\pi$
$307$		−	3.57511i		−	0.204042i	0.994782	−	0.102021i	$-0.0325309\pi$
$308$		0			0
$309$			10.5182i			0.598360i
$310$	2.39718	−	5.83730i	0.136151	−	0.331537i
$311$	−0.0783210			−0.00444118			−0.00222059	−	0.999998i	$-0.500707\pi$
$311$	−0.0783210			−0.00444118			−0.00222059	+	0.999998i	$0.500707\pi$
$312$	−0.458256	−	1.07847i	−0.0259437	−	0.0610564i
$313$	−8.94774			−0.505756			−0.252878	−	0.967498i	$-0.581377\pi$
$313$	−8.94774			−0.505756			−0.252878	+	0.967498i	$0.581377\pi$
$314$	4.26875	−	10.3947i	0.240900	−	0.586608i
$315$			3.97611i			0.224028i
$316$	−8.50805	−	8.40547i	−0.478615	−	0.472845i
$317$			24.4832i			1.37512i	0.726129	+	0.687558i	$0.241317\pi$
$317$			24.4832i			1.37512i	−0.726129	+	0.687558i	$0.758683\pi$
$318$	−9.51987	−	3.90948i	−0.533848	−	0.219233i
$319$		0			0
$320$	−9.11008	−	8.78444i	−0.509269	−	0.491065i
$321$	6.47324			0.361301
$322$	7.52871	+	3.09178i	0.419559	+	0.172298i
$323$			16.2288i			0.902994i
$324$	−4.48734	−	4.43323i	−0.249297	−	0.246291i
$325$			0.804377i			0.0446188i
$326$	3.01671	−	7.34591i	0.167080	−	0.406852i
$327$	13.0998			0.724423
$328$	4.97678	+	11.7125i	0.274797	+	0.646713i
$329$	−23.7762			−1.31083
$330$		0			0
$331$			24.2083i			1.33061i	0.746572	+	0.665305i	$0.231698\pi$
$331$			24.2083i			1.33061i	−0.746572	+	0.665305i	$0.768302\pi$
$332$	0.196284	−	0.198680i	0.0107725	−	0.0109040i
$333$		−	4.80594i		−	0.263364i
$334$	−23.5830	−	9.68472i	−1.29041	−	0.529924i
$335$	17.3830			0.949737
$336$	−9.61203	+	0.116603i	−0.524379	+	0.00636121i
$337$	−22.3046			−1.21501			−0.607505	−	0.794315i	$-0.707830\pi$
$337$	−22.3046			−1.21501			−0.607505	+	0.794315i	$0.707830\pi$
$338$	16.8709	+	6.92828i	0.917655	+	0.376849i
$339$			10.3574i			0.562537i
$340$	10.6565	−	10.7865i	0.577929	−	0.584983i
$341$		0			0
$342$	2.44749	−	5.95983i	0.132345	−	0.322271i
$343$	−19.6346			−1.06017
$344$	9.41817	−	4.00190i	0.507794	−	0.215768i
$345$	−6.26833			−0.337475
$346$	−8.09514	+	19.7123i	−0.435197	+	1.05974i
$347$		−	16.8395i		−	0.903991i	−0.892020	−	0.451996i	$-0.850712\pi$
$347$		−	16.8395i		−	0.903991i	0.892020	−	0.451996i	$-0.149288\pi$
$348$	19.0574	+	18.8277i	1.02159	+	1.00927i
$349$			5.97392i			0.319777i	0.987135	+	0.159888i	$0.0511134\pi$
$349$			5.97392i			0.319777i	−0.987135	+	0.159888i	$0.948887\pi$
$350$	6.10399	+	2.50670i	0.326272	+	0.133989i
$351$	−1.80024			−0.0960899
$352$		0			0
$353$	−6.69469			−0.356322			−0.178161	−	0.984001i	$-0.557015\pi$
$353$	−6.69469			−0.356322			−0.178161	+	0.984001i	$0.557015\pi$
$354$	−9.06053	−	3.72084i	−0.481562	−	0.197761i
$355$		−	17.6162i		−	0.934973i
$356$	6.10353	+	6.02993i	0.323486	+	0.319586i
$357$		−	11.5173i		−	0.609559i
$358$	−11.9733	+	29.1558i	−0.632806	+	1.54093i
$359$	−20.1204			−1.06191			−0.530957	−	0.847399i	$-0.678167\pi$
$359$	−20.1204			−1.06191			−0.530957	+	0.847399i	$0.678167\pi$
$360$	−5.54021	+	2.35411i	−0.291995	+	0.124072i
$361$	7.53307			0.396477
$362$	−6.18434	+	15.0593i	−0.325042	+	0.791501i
$363$		0			0
$364$	−0.845771	+	0.856094i	−0.0443305	+	0.0448715i
$365$			19.9472i			1.04409i
$366$	−18.3909	−	7.55252i	−0.961310	−	0.394777i
$367$	7.45942			0.389378			0.194689	−	0.980865i	$-0.437630\pi$
$367$	7.45942			0.389378			0.194689	+	0.980865i	$0.437630\pi$
$368$	0.149463	+	12.3208i	0.00779132	+	0.642268i
$369$	6.05317			0.315115
$370$	7.39268	+	3.03592i	0.384327	+	0.157830i
$371$			10.5691i			0.548723i
$372$	5.09999	−	5.16223i	0.264422	−	0.267649i
$373$		−	1.53907i		−	0.0796902i	−0.999206	−	0.0398451i	$-0.987314\pi$
$373$		−	1.53907i		−	0.0796902i	0.999206	−	0.0398451i	$-0.0126864\pi$
$374$		0			0
$375$	−15.2565			−0.787844
$376$	−14.0770	−	33.1292i	−0.725967	−	1.70851i
$377$	3.35376			0.172728
$378$	−5.61014	+	13.6611i	−0.288554	+	0.702651i
$379$			5.35013i			0.274818i	0.990514	+	0.137409i	$0.0438774\pi$
$379$			5.35013i			0.274818i	−0.990514	+	0.137409i	$0.956123\pi$
$380$	7.62156	+	7.52966i	0.390978	+	0.386263i
$381$			16.7817i			0.859751i
$382$	−14.1250	−	5.80063i	−0.722696	−	0.296786i
$383$	−9.59330			−0.490195			−0.245097	−	0.969498i	$-0.578820\pi$
$383$	−9.59330			−0.490195			−0.245097	+	0.969498i	$0.578820\pi$
$384$	−5.85340	−	13.3241i	−0.298705	−	0.679944i
$385$		0			0
$386$	−11.8478	−	4.86546i	−0.603035	−	0.247645i
$387$		−	4.86744i		−	0.247426i
$388$	17.6340	+	17.4213i	0.895229	+	0.884435i
$389$			11.2345i			0.569614i	0.958585	+	0.284807i	$0.0919294\pi$
$389$			11.2345i			0.569614i	−0.958585	+	0.284807i	$0.908071\pi$
$390$	0.352090	−	0.857366i	0.0178288	−	0.0434144i
$391$	−14.7630			−0.746598
$392$	−3.88210	−	9.13621i	−0.196075	−	0.461449i
$393$	14.8596			0.749566
$394$	−4.69601	+	11.4351i	−0.236582	+	0.576094i
$395$		−	9.45984i		−	0.475976i
$396$		0			0
$397$		−	9.83583i		−	0.493646i	−0.969061	−	0.246823i	$-0.920613\pi$
$397$		−	9.83583i		−	0.493646i	0.969061	−	0.246823i	$-0.0793866\pi$
$398$	3.34349	+	1.37305i	0.167594	+	0.0688250i
$399$	8.13787			0.407403
$400$	0.121179	+	9.98927i	0.00605896	+	0.499464i
$401$	10.7477			0.536714			0.268357	−	0.963319i	$-0.413519\pi$
$401$	10.7477			0.536714			0.268357	+	0.963319i	$0.413519\pi$
$402$	18.4912	+	7.59369i	0.922257	+	0.378739i
$403$		−	0.908459i		−	0.0452536i
$404$	21.5940	−	21.8576i	1.07434	−	1.08745i
$405$		−	4.98933i		−	0.247922i
$406$	10.4514	−	25.4500i	0.518695	−	1.26306i
$407$		0			0
$408$	16.0479	−	6.81895i	0.794488	−	0.337588i
$409$	6.33056			0.313026			0.156513	−	0.987676i	$-0.449975\pi$
$409$	6.33056			0.313026			0.156513	+	0.987676i	$0.449975\pi$
$410$	−3.82379	+	9.31122i	−0.188844	+	0.459848i
$411$			23.1786i			1.14332i
$412$	11.6338	+	11.4936i	0.573157	+	0.566247i
$413$			10.0592i			0.494979i
$414$	5.42154	+	2.22644i	0.266454	+	0.109423i
$415$	0.220906			0.0108438
$416$	−1.69361	−	0.671615i	−0.0830360	−	0.0329287i
$417$	−8.62471			−0.422354
$418$		0			0
$419$		−	8.63496i		−	0.421846i	−0.977503	−	0.210923i	$-0.932353\pi$
$419$		−	8.63496i		−	0.421846i	0.977503	−	0.210923i	$-0.0676469\pi$
$420$	−5.40888	−	5.34366i	−0.263926	−	0.260744i
$421$		−	29.4762i		−	1.43658i	−0.695743	−	0.718291i	$-0.744925\pi$
$421$		−	29.4762i		−	1.43658i	0.695743	−	0.718291i	$-0.255075\pi$
$422$	1.78129	−	4.33757i	0.0867117	−	0.211149i
$423$	−17.1216			−0.832482
$424$	−14.7268	+	6.25760i	−0.715196	+	0.303896i
$425$	−11.9693			−0.580596
$426$	7.69556	−	18.7392i	0.372851	−	0.907920i
$427$			20.4180i			0.988095i
$428$	7.07350	−	7.15983i	0.341911	−	0.346083i
$429$		0			0
$430$	7.48728	+	3.07477i	0.361069	+	0.148278i
$431$	21.6684			1.04373			0.521864	−	0.853029i	$-0.325237\pi$
$431$	21.6684			1.04373			0.521864	+	0.853029i	$0.325237\pi$
$432$	−22.3566	+	0.271207i	−1.07563	+	0.0130484i
$433$	−11.5153			−0.553392			−0.276696	−	0.960957i	$-0.589240\pi$
$433$	−11.5153			−0.553392			−0.276696	+	0.960957i	$0.589240\pi$
$434$	−6.89382	−	2.83105i	−0.330914	−	0.135895i
$435$			21.1894i			1.01595i
$436$	14.3146	−	14.4893i	0.685544	−	0.693910i
$437$		−	10.4312i		−	0.498994i
$438$	−8.71384	+	21.2188i	−0.416363	+	1.01388i
$439$	−35.9563			−1.71610			−0.858049	−	0.513567i	$-0.828324\pi$
$439$	−35.9563			−1.71610			−0.858049	+	0.513567i	$0.828324\pi$
$440$		0			0
$441$	−4.72172			−0.224844
$442$	0.829235	−	2.01925i	0.0394427	−	0.0960458i
$443$		−	27.8156i		−	1.32156i	−0.750581	−	0.660779i	$-0.770226\pi$
$443$		−	27.8156i		−	1.32156i	0.750581	−	0.660779i	$-0.229774\pi$
$444$	6.53773	+	6.45891i	0.310267	+	0.306526i
$445$			6.78632i			0.321702i
$446$	−19.4989	−	8.00750i	−0.923298	−	0.379166i
$447$	5.15506			0.243826
$448$	−10.3744	+	10.7589i	−0.490143	+	0.508312i
$449$	−13.0847			−0.617505			−0.308753	−	0.951142i	$-0.599912\pi$
$449$	−13.0847			−0.617505			−0.308753	+	0.951142i	$0.599912\pi$
$450$	4.39558	+	1.80511i	0.207210	+	0.0850938i
$451$		0			0
$452$	11.4560	+	11.3178i	0.538843	+	0.532346i
$453$			3.00246i			0.141068i
$454$	0.710593	−	1.73035i	0.0333498	−	0.0812092i
$455$	−0.951864			−0.0446241
$456$	4.81813	+	11.3391i	0.225630	+	0.531002i
$457$	6.63015			0.310145			0.155073	−	0.987903i	$-0.450439\pi$
$457$	6.63015			0.310145			0.155073	+	0.987903i	$0.450439\pi$
$458$	12.6802	−	30.8772i	0.592507	−	1.44280i
$459$		−	26.7880i		−	1.25036i
$460$	−6.84958	+	6.93318i	−0.319364	+	0.323261i
$461$			8.43029i			0.392638i	0.980540	+	0.196319i	$0.0628988\pi$
$461$			8.43029i			0.392638i	−0.980540	+	0.196319i	$0.937101\pi$
$462$		0			0
$463$	9.16056			0.425727			0.212864	−	0.977082i	$-0.431721\pi$
$463$	9.16056			0.425727			0.212864	+	0.977082i	$0.431721\pi$
$464$	41.6492	−	0.505244i	1.93352	−	0.0234554i
$465$	5.73973			0.266173
$466$	−3.23232	−	1.32740i	−0.149734	−	0.0614907i
$467$		−	11.5736i		−	0.535560i	−0.963480	−	0.267780i	$-0.913710\pi$
$467$		−	11.5736i		−	0.535560i	0.963480	−	0.267780i	$-0.0862900\pi$
$468$	−0.609053	+	0.616486i	−0.0281535	+	0.0284971i
$469$		−	20.5293i		−	0.947954i
$470$	10.8157	−	26.3371i	0.498893	−	1.21484i
$471$	10.2210			0.470957
$472$	−14.0162	+	5.95566i	−0.645148	+	0.274132i
$473$		0			0
$474$	4.13248	−	10.0629i	0.189811	−	0.462204i
$475$		−	8.45726i		−	0.388046i
$476$	−12.7389	−	12.5853i	−0.583884	−	0.576844i
$477$			7.61101i			0.348484i
$478$	−20.6954	−	8.49888i	−0.946586	−	0.388730i
$479$	−19.1582			−0.875360			−0.437680	−	0.899131i	$-0.644200\pi$
$479$	−19.1582			−0.875360			−0.437680	+	0.899131i	$0.644200\pi$
$480$	4.24333	−	10.7004i	0.193680	−	0.488403i
$481$	1.15052			0.0524593
$482$	4.21909	+	1.73263i	0.192174	+	0.0789192i
$483$			7.40286i			0.336842i
$484$		0			0
$485$			19.6067i			0.890293i
$486$	−6.82910	+	16.6294i	−0.309774	+	0.754323i
$487$	42.4387			1.92308			0.961540	−	0.274664i	$-0.0885667\pi$
$487$	42.4387			1.92308			0.961540	+	0.274664i	$0.0885667\pi$
$488$	−28.4499	+	12.0887i	−1.28787	+	0.547231i
$489$	7.22312			0.326641
$490$	2.98272	−	7.26313i	0.134745	−	0.328115i
$491$			39.2592i			1.77174i	0.463930	+	0.885872i	$0.346439\pi$
$491$			39.2592i			1.77174i	−0.463930	+	0.885872i	$0.653561\pi$
$492$	−8.13511	+	8.23439i	−0.366759	+	0.371235i
$493$			49.9047i			2.24759i
$494$	1.42676	+	0.585920i	0.0641929	+	0.0263618i
$495$		0			0
$496$	−0.136859	−	11.2818i	−0.00614517	−	0.506570i
$497$	−20.8047			−0.933217
$498$	0.234988	+	0.0965016i	0.0105301	+	0.00432434i
$499$		−	22.6637i		−	1.01457i	−0.861779	−	0.507284i	$-0.830649\pi$
$499$		−	22.6637i		−	1.01457i	0.861779	−	0.507284i	$-0.169351\pi$
$500$	−16.6713	+	16.8747i	−0.745561	+	0.754660i
$501$		−	23.1888i		−	1.03600i
$502$	0.185798	−	0.452433i	0.00829259	−	0.0201931i
$503$	−15.5389			−0.692847			−0.346424	−	0.938078i	$-0.612604\pi$
$503$	−15.5389			−0.692847			−0.346424	+	0.938078i	$0.612604\pi$
$504$	2.78019	+	6.54296i	0.123839	+	0.291446i
$505$	24.3028			1.08146
$506$		0			0
$507$			16.5889i			0.736737i
$508$	18.5616	+	18.3378i	0.823539	+	0.813609i
$509$			13.4499i			0.596156i	0.954542	+	0.298078i	$0.0963455\pi$
$509$			13.4499i			0.596156i	−0.954542	+	0.298078i	$0.903654\pi$
$510$	12.7578	+	5.23918i	0.564924	+	0.231995i
$511$	23.5576			1.04213
$512$	−21.1335	−	8.08542i	−0.933979	−	0.357328i
$513$	18.9278			0.835685
$514$	−0.551893	−	0.226643i	−0.0243429	−	0.00999679i
$515$			12.9353i			0.569997i
$516$	6.62139	+	6.54156i	0.291491	+	0.287976i
$517$		0			0
$518$	3.58540	−	8.73071i	0.157533	−	0.383606i
$519$	−19.3827			−0.850808
$520$	−0.563564	−	1.32630i	−0.0247139	−	0.0581623i
$521$	−6.69298			−0.293225			−0.146612	−	0.989194i	$-0.546837\pi$
$521$	−6.69298			−0.293225			−0.146612	+	0.989194i	$0.546837\pi$
$522$	7.52622	−	18.3269i	0.329414	−	0.802147i
$523$			23.7587i			1.03889i	0.854503	+	0.519447i	$0.173862\pi$
$523$			23.7587i			1.03889i	−0.854503	+	0.519447i	$0.826138\pi$
$524$	16.2375	−	16.4357i	0.709338	−	0.717995i
$525$			6.00196i			0.261947i
$526$	3.07887	+	1.26438i	0.134245	+	0.0551298i
$527$	13.5181			0.588856
$528$		0			0
$529$	−13.5109			−0.587431
$530$	−11.7075	−	4.80788i	−0.508543	−	0.208841i
$531$			7.24376i			0.314353i
$532$	8.89248	−	9.00101i	0.385538	−	0.390243i
$533$			1.44910i			0.0627677i
$534$	−2.96457	+	7.21894i	−0.128289	+	0.312394i
$535$	7.96080			0.344175
$536$	28.6050	−	12.1546i	1.23555	−	0.525000i
$537$	−28.6684			−1.23713
$538$	12.3869	−	30.1630i	0.534036	−	1.30042i
$539$		0			0
$540$	−12.5805	−	12.4288i	−0.541378	−	0.534851i
$541$		−	28.5717i		−	1.22839i	−0.789153	−	0.614197i	$-0.789480\pi$
$541$		−	28.5717i		−	1.22839i	0.789153	−	0.614197i	$-0.210520\pi$
$542$	−5.72524	−	2.35116i	−0.245920	−	0.100991i
$543$	−14.8076			−0.635455
$544$	9.99378	−	25.2013i	0.428480	−	1.08050i
$545$	16.1102			0.690084
$546$	−1.01254	−	0.415817i	−0.0433329	−	0.0177953i
$547$		−	30.2265i		−	1.29239i	−0.763172	−	0.646195i	$-0.776359\pi$
$547$		−	30.2265i		−	1.29239i	0.763172	−	0.646195i	$-0.223641\pi$
$548$	25.6371	+	25.3280i	1.09516	+	1.08196i
$549$			14.7033i			0.627522i
$550$		0			0
$551$	−35.2616			−1.50220
$552$	−10.3150	+	4.38296i	−0.439034	+	0.186551i
$553$	−11.1720			−0.475083
$554$	3.36662	−	8.19796i	0.143034	−	0.348298i
$555$			7.26911i			0.308556i
$556$	−9.42447	+	9.53949i	−0.399687	+	0.404565i
$557$		−	7.94247i		−	0.336533i	−0.985742	−	0.168267i	$-0.946183\pi$
$557$		−	7.94247i		−	0.336533i	0.985742	−	0.168267i	$-0.0538170\pi$
$558$	−4.96435	−	2.03869i	−0.210158	−	0.0863044i
$559$	1.16525			0.0492846
$560$	−11.8209	+	0.143398i	−0.499523	+	0.00605968i
$561$		0			0
$562$	−14.6324	−	6.00901i	−0.617230	−	0.253475i
$563$			17.7730i			0.749043i	0.927218	+	0.374521i	$0.122193\pi$
$563$			17.7730i			0.749043i	−0.927218	+	0.374521i	$0.877807\pi$
$564$	23.0105	−	23.2913i	0.968916	−	0.980741i
$565$			12.7375i			0.535872i
$566$	−17.1809	+	41.8368i	−0.722167	+	1.75853i
$567$	−5.89237			−0.247456
$568$	−12.3177	−	28.9887i	−0.516838	−	1.21634i
$569$	−28.3627			−1.18903			−0.594513	−	0.804086i	$-0.702655\pi$
$569$	−28.3627			−1.18903			−0.594513	+	0.804086i	$0.702655\pi$
$570$	−3.70190	+	9.01439i	−0.155055	+	0.377571i
$571$			11.9221i			0.498923i	0.968385	+	0.249461i	$0.0802535\pi$
$571$			11.9221i			0.498923i	−0.968385	+	0.249461i	$0.919746\pi$
$572$		0			0
$573$		−	13.8888i		−	0.580215i
$574$	10.9965	+	4.51587i	0.458985	+	0.188489i
$575$	7.69340			0.320837
$576$	−7.47075	+	7.74769i	−0.311281	+	0.322820i
$577$	−24.5999			−1.02411			−0.512053	−	0.858954i	$-0.671115\pi$
$577$	−24.5999			−1.02411			−0.512053	+	0.858954i	$0.671115\pi$
$578$	7.80745	+	3.20625i	0.324747	+	0.133362i
$579$		−	11.6497i		−	0.484145i
$580$	23.4368	+	23.1542i	0.973161	+	0.961428i
$581$		−	0.260889i		−	0.0108235i
$582$	−8.56506	+	20.8566i	−0.355033	+	0.864532i
$583$		0			0
$584$	13.9476	+	32.8245i	0.577154	+	1.35829i
$585$	−0.685452			−0.0283400
$586$	−4.11779	+	10.0271i	−0.170104	+	0.414217i
$587$			12.0954i			0.499229i	0.968345	+	0.249614i	$0.0803039\pi$
$587$			12.0954i			0.499229i	−0.968345	+	0.249614i	$0.919696\pi$
$588$	6.34572	−	6.42317i	0.261693	−	0.264887i
$589$			9.55159i			0.393566i
$590$	−11.1426	−	4.57589i	−0.458735	−	0.188386i
$591$	−11.2440			−0.462516
$592$	14.2879	−	0.173326i	0.587231	−	0.00712366i
$593$	1.77063			0.0727109			0.0363554	−	0.999339i	$-0.488425\pi$
$593$	1.77063			0.0727109			0.0363554	+	0.999339i	$0.488425\pi$
$594$		0			0
$595$		−	14.1639i		−	0.580665i
$596$	5.63308	−	5.70183i	0.230740	−	0.233556i
$597$			3.28760i			0.134552i
$598$	−0.533000	+	1.29790i	−0.0217960	+	0.0530749i
$599$	−14.3212			−0.585149			−0.292574	−	0.956243i	$-0.594512\pi$
$599$	−14.3212			−0.585149			−0.292574	+	0.956243i	$0.594512\pi$
$600$	−8.36298	+	3.55354i	−0.341417	+	0.145073i
$601$	−20.9923			−0.856293			−0.428147	−	0.903709i	$-0.640833\pi$
$601$	−20.9923			−0.856293			−0.428147	+	0.903709i	$0.640833\pi$
$602$	3.63128	−	8.84244i	0.148000	−	0.360391i
$603$		−	14.7835i		−	0.602029i
$604$	3.32091	+	3.28087i	0.135126	+	0.133497i
$605$		0			0
$606$	25.8520	+	10.6165i	1.05017	+	0.431267i
$607$	34.0000			1.38002			0.690009	−	0.723800i	$-0.257606\pi$
$607$	34.0000			1.38002			0.690009	+	0.723800i	$0.257606\pi$
$608$	17.8067	+	7.06140i	0.722157	+	0.286378i
$609$	25.0245			1.01405
$610$	−22.6172	−	9.28809i	−0.915743	−	0.376064i
$611$		−	4.09885i		−	0.165822i
$612$	−9.17345	−	9.06284i	−0.370815	−	0.366344i
$613$			13.3983i			0.541152i	0.962699	+	0.270576i	$0.0872141\pi$
$613$			13.3983i			0.541152i	−0.962699	+	0.270576i	$0.912786\pi$
$614$	1.92066	−	4.67695i	0.0775115	−	0.188746i
$615$	−9.15557			−0.369188
$616$		0			0
$617$	24.0930			0.969946			0.484973	−	0.874529i	$-0.338829\pi$
$617$	24.0930			0.969946			0.484973	+	0.874529i	$0.338829\pi$
$618$	−5.65071	+	13.7599i	−0.227305	+	0.553504i
$619$			2.41918i			0.0972349i	0.998817	+	0.0486175i	$0.0154815\pi$
$619$			2.41918i			0.0972349i	−0.998817	+	0.0486175i	$0.984518\pi$
$620$	6.27197	−	6.34851i	0.251888	−	0.254962i
$621$			17.2183i			0.690946i
$622$	−0.102459	−	0.0420765i	−0.00410825	−	0.00168711i
$623$	8.01461			0.321098
$624$	−0.0201015	−	1.65704i	−0.000804704	−	0.0663348i
$625$	−6.27497			−0.250999
$626$	−11.7054	−	4.80701i	−0.467843	−	0.192127i
$627$		0			0
$628$	11.1687	−	11.3051i	0.445682	−	0.451121i
$629$			17.1200i			0.682620i
$630$	−2.13609	+	5.20154i	−0.0851039	+	0.207234i
$631$	40.5047			1.61247			0.806234	−	0.591596i	$-0.201502\pi$
$631$	40.5047			1.61247			0.806234	+	0.591596i	$0.201502\pi$
$632$	−6.61454	−	15.5668i	−0.263112	−	0.619215i
$633$	4.26506			0.169521
$634$	−13.1532	+	32.0289i	−0.522379	+	1.27203i
$635$			20.6381i			0.818998i
$636$	−10.3536	−	10.2287i	−0.410546	−	0.405596i
$637$		−	1.13036i		−	0.0447865i
$638$		0			0
$639$	−14.9818			−0.592670
$640$	−7.19851	−	16.3860i	−0.284546	−	0.647714i
$641$	−22.2703			−0.879624			−0.439812	−	0.898090i	$-0.644955\pi$
$641$	−22.2703			−0.879624			−0.439812	+	0.898090i	$0.644955\pi$
$642$	8.46829	+	3.47763i	0.334217	+	0.137251i
$643$		−	24.9678i		−	0.984633i	−0.870416	−	0.492316i	$-0.836150\pi$
$643$		−	24.9678i		−	0.984633i	0.870416	−	0.492316i	$-0.163850\pi$
$644$	8.18804	+	8.08932i	0.322654	+	0.318764i
$645$			7.36212i			0.289883i
$646$	−8.71861	+	21.2305i	−0.343029	+	0.835302i
$647$	−12.3518			−0.485599			−0.242799	−	0.970077i	$-0.578066\pi$
$647$	−12.3518			−0.485599			−0.242799	+	0.970077i	$0.578066\pi$
$648$	−3.48866	−	8.21028i	−0.137047	−	0.322530i
$649$		0			0
$650$	−0.432136	+	1.05228i	−0.0169498	+	0.0412740i
$651$		−	6.77858i		−	0.265674i
$652$	7.89291	−	7.98924i	0.309110	−	0.312883i
$653$		−	4.78361i		−	0.187197i	−0.995610	−	0.0935987i	$-0.970163\pi$
$653$		−	4.78361i		−	0.187197i	0.995610	−	0.0935987i	$-0.0298371\pi$
$654$	17.1372	+	7.03764i	0.670117	+	0.275194i
$655$	18.2743			0.714036
$656$	0.218307	+	17.9959i	0.00852347	+	0.702623i
$657$	16.9642			0.661835
$658$	−31.1040	−	12.7733i	−1.21256	−	0.497956i
$659$			34.4552i			1.34219i	0.741374	+	0.671093i	$0.234175\pi$
$659$			34.4552i			1.34219i	−0.741374	+	0.671093i	$0.765825\pi$
$660$		0			0
$661$			39.9505i			1.55389i	0.629567	+	0.776947i	$0.283233\pi$
$661$			39.9505i			1.55389i	−0.629567	+	0.776947i	$0.716767\pi$
$662$	−13.0055	+	31.6693i	−0.505472	+	1.23086i
$663$	1.98549			0.0771102
$664$	0.363516	−	0.154463i	0.0141071	−	0.00599431i
$665$	10.0079			0.388092
$666$	2.58190	−	6.28712i	0.100047	−	0.243621i
$667$		−	32.0768i		−	1.24202i
$668$	−25.6483	−	25.3391i	−0.992363	−	0.980398i
$669$		−	19.1729i		−	0.741268i
$670$	22.7405	+	9.33872i	0.878541	+	0.360786i
$671$		0			0
$672$	−12.6371	−	5.01134i	−0.487486	−	0.193317i
$673$	−10.8179			−0.417000			−0.208500	−	0.978022i	$-0.566858\pi$
$673$	−10.8179			−0.417000			−0.208500	+	0.978022i	$0.566858\pi$
$674$	−29.1789	−	11.9828i	−1.12393	−	0.461558i
$675$			13.9599i			0.537318i
$676$	18.3484	+	18.1271i	0.705706	+	0.697197i
$677$			37.4282i			1.43848i	0.694761	+	0.719241i	$0.255510\pi$
$677$			37.4282i			1.43848i	−0.694761	+	0.719241i	$0.744490\pi$
$678$	−5.56432	+	13.5495i	−0.213697	+	0.520367i
$679$	23.1554			0.888621
$680$	19.7357	−	8.38594i	0.756829	−	0.321586i
$681$	1.70142			0.0651987
$682$		0			0
$683$		−	24.1362i		−	0.923545i	−0.886998	−	0.461772i	$-0.847214\pi$
$683$		−	24.1362i		−	0.923545i	0.886998	−	0.461772i	$-0.152786\pi$
$684$	6.40362	−	6.48177i	0.244848	−	0.247837i
$685$			28.5051i			1.08912i
$686$	−25.6860	−	10.5483i	−0.980696	−	0.402737i
$687$	30.3611			1.15835
$688$	14.4708	−	0.175544i	0.551693	−	0.00669256i
$689$	−1.82204			−0.0694143
$690$	−8.20022	−	3.36754i	−0.312177	−	0.128200i
$691$		−	44.8113i		−	1.70470i	−0.522969	−	0.852352i	$-0.675176\pi$
$691$		−	44.8113i		−	1.70470i	0.522969	−	0.852352i	$-0.324824\pi$
$692$	−21.1801	+	21.4386i	−0.805146	+	0.814972i
$693$		0			0
$694$	9.04670	−	22.0294i	0.343408	−	0.836224i
$695$	−10.6067			−0.402334
$696$	14.8161	+	34.8686i	0.561603	+	1.32169i
$697$	−21.5630			−0.816756
$698$	−3.20938	+	7.81507i	−0.121477	+	0.295805i
$699$		−	3.17829i		−	0.120214i
$700$	6.63856	+	6.55851i	0.250914	+	0.247888i
$701$			22.9120i			0.865376i	0.901544	+	0.432688i	$0.142435\pi$
$701$			22.9120i			0.865376i	−0.901544	+	0.432688i	$0.857565\pi$
$702$	−2.35508	−	0.967147i	−0.0888866	−	0.0365026i
$703$	−12.0967			−0.456234
$704$		0			0
$705$	25.8969			0.975333
$706$	−8.75798	−	3.59660i	−0.329611	−	0.135360i
$707$		−	28.7014i		−	1.07943i
$708$	−9.85401	−	9.73520i	−0.370336	−	0.365871i
$709$			39.8708i			1.49738i	0.662920	+	0.748690i	$0.269317\pi$
$709$			39.8708i			1.49738i	−0.662920	+	0.748690i	$0.730683\pi$
$710$	9.46399	−	23.0455i	0.355177	−	0.864883i
$711$	−8.04515			−0.301717
$712$	4.74515	+	11.1674i	0.177832	+	0.418514i
$713$	−8.68889			−0.325402
$714$	6.18744	−	15.0669i	0.231559	−	0.563863i
$715$		0			0
$716$	−31.3268	+	31.7091i	−1.17074	+	1.18502i
$717$		−	20.3495i		−	0.759965i
$718$	−26.3215	−	10.8093i	−0.982308	−	0.403400i
$719$	−36.2649			−1.35245			−0.676227	−	0.736693i	$-0.736386\pi$
$719$	−36.2649			−1.35245			−0.676227	+	0.736693i	$0.736386\pi$
$720$	−8.51239	+	0.103263i	−0.317238	+	0.00384840i
$721$	15.2765			0.568927
$722$	9.85475	+	4.04700i	0.366756	+	0.150614i
$723$			4.14856i			0.154287i
$724$	−16.1807	+	16.3782i	−0.601350	+	0.608690i
$725$		−	26.0067i		−	0.965864i
$726$		0			0
$727$	4.42926			0.164272			0.0821360	−	0.996621i	$-0.473826\pi$
$727$	4.42926			0.164272			0.0821360	+	0.996621i	$0.473826\pi$
$728$	−1.56636	+	0.665565i	−0.0580530	+	0.0246675i
$729$	−25.8133			−0.956046
$730$	−10.7163	+	26.0949i	−0.396627	+	0.965817i
$731$			17.3391i			0.641309i
$732$	−20.0016	−	19.7604i	−0.739279	−	0.730365i
$733$			27.2599i			1.00687i	0.864034	+	0.503434i	$0.167930\pi$
$733$			27.2599i			1.00687i	−0.864034	+	0.503434i	$0.832070\pi$
$734$	9.75840	+	4.00743i	0.360189	+	0.147917i
$735$	7.14172			0.263426
$736$	−6.42362	+	16.1984i	−0.236778	+	0.597081i
$737$		0			0
$738$	7.91875	+	3.25195i	0.291493	+	0.119706i
$739$		−	1.16933i		−	0.0430146i	−0.999769	−	0.0215073i	$-0.993153\pi$
$739$		−	1.16933i		−	0.0430146i	0.999769	−	0.0215073i	$-0.00684651\pi$
$740$	8.04010	+	7.94316i	0.295560	+	0.291996i
$741$			1.40291i			0.0515372i
$742$	−5.67808	+	13.8265i	−0.208449	+	0.507588i
$743$	−39.6565			−1.45486			−0.727429	−	0.686183i	$-0.759285\pi$
$743$	−39.6565			−1.45486			−0.727429	+	0.686183i	$0.759285\pi$
$744$	9.44511	−	4.01335i	0.346275	−	0.147137i
$745$	6.33969			0.232268
$746$	0.826838	−	2.01341i	0.0302727	−	0.0737163i
$747$		−	0.187870i		−	0.00687380i
$748$		0			0
$749$		−	9.40165i		−	0.343529i
$750$	−19.9586	−	8.19629i	−0.728784	−	0.299286i
$751$	−6.61284			−0.241306			−0.120653	−	0.992695i	$-0.538499\pi$
$751$	−6.61284			−0.241306			−0.120653	+	0.992695i	$0.538499\pi$
$752$	−0.617491	−	50.9022i	−0.0225176	−	1.85621i
$753$	0.444870			0.0162120
$754$	4.38739	+	1.80175i	0.159779	+	0.0656158i
$755$			3.69242i			0.134381i
$756$	−14.6783	+	14.8575i	−0.533846	+	0.540362i
$757$		−	20.6836i		−	0.751759i	−0.926668	−	0.375880i	$-0.877341\pi$
$757$		−	20.6836i		−	0.751759i	0.926668	−	0.375880i	$-0.122659\pi$
$758$	−2.87426	+	6.99903i	−0.104398	+	0.254216i
$759$		0			0
$760$	5.92534	+	13.9448i	0.214935	+	0.505832i
$761$	−45.5490			−1.65115			−0.825575	−	0.564293i	$-0.809149\pi$
$761$	−45.5490			−1.65115			−0.825575	+	0.564293i	$0.809149\pi$
$762$	−9.01564	+	21.9538i	−0.326602	+	0.795300i
$763$		−	19.0260i		−	0.688788i
$764$	−15.3620	−	15.1767i	−0.555776	−	0.549075i
$765$		−	10.1997i		−	0.368770i
$766$	−12.5499	−	5.15382i	−0.453447	−	0.186215i
$767$	−1.73413			−0.0626157
$768$	−0.499267	−	20.5752i	−0.0180157	−	0.742444i
$769$	19.1817			0.691711			0.345856	−	0.938288i	$-0.387589\pi$
$769$	19.1817			0.691711			0.345856	+	0.938288i	$0.387589\pi$
$770$		0			0
$771$		−	0.542667i		−	0.0195437i
$772$	−12.8853	−	12.7300i	−0.463753	−	0.458162i
$773$			50.1410i			1.80345i	0.432314	+	0.901723i	$0.357697\pi$
$773$			50.1410i			1.80345i	−0.432314	+	0.901723i	$0.642303\pi$
$774$	2.61494	−	6.36758i	0.0939921	−	0.228878i
$775$	−7.04463			−0.253050
$776$	13.7094	+	32.2641i	0.492140	+	1.15821i
$777$	8.58477			0.307977
$778$	−6.03554	+	14.6970i	−0.216385	+	0.526913i
$779$		−	15.2360i		−	0.545885i
$780$	0.921208	−	0.932451i	0.0329845	−	0.0333871i
$781$		0			0
$782$	−19.3129	−	7.93115i	−0.690630	−	0.283617i
$783$	58.2045			2.08006
$784$	−0.170289	−	14.0376i	−0.00608174	−	0.501342i
$785$	12.5697			0.448633
$786$	19.4393	+	7.98303i	0.693376	+	0.284745i
$787$		−	22.8144i		−	0.813246i	−0.913596	−	0.406623i	$-0.866706\pi$
$787$		−	22.8144i		−	0.813246i	0.913596	−	0.406623i	$-0.133294\pi$
$788$	−12.2866	+	12.4366i	−0.437693	+	0.443035i
$789$			3.02740i			0.107778i
$790$	5.08212	−	12.3753i	0.180814	−	0.440295i
$791$	15.0430			0.534866
$792$		0			0
$793$	−3.51991			−0.124996
$794$	5.28412	−	12.8672i	0.187526	−	0.456640i
$795$		−	11.5118i		−	0.408283i
$796$	3.63630	+	3.59245i	0.128885	+	0.127331i
$797$		−	26.6673i		−	0.944604i	−0.881437	−	0.472302i	$-0.843423\pi$
$797$		−	26.6673i		−	0.944604i	0.881437	−	0.472302i	$-0.156577\pi$
$798$	10.6459	+	4.37192i	0.376862	+	0.154764i
$799$	60.9917			2.15773
$800$	−5.20802	+	13.1331i	−0.184131	+	0.464323i
$801$	5.77144			0.203924
$802$	14.0601	+	5.77400i	0.496480	+	0.203887i
$803$		0			0
$804$	20.1106	+	19.8681i	0.709246	+	0.700694i
$805$			9.10403i			0.320875i
$806$	0.488053	−	1.18844i	0.0171909	−	0.0418612i
$807$	29.6588			1.04404
$808$	39.9918	−	16.9930i	1.40691	−	0.597813i
$809$	38.5665			1.35592			0.677962	−	0.735097i	$-0.262863\pi$
$809$	38.5665			1.35592			0.677962	+	0.735097i	$0.262863\pi$
$810$	2.68043	−	6.52704i	0.0941806	−	0.229337i
$811$		−	16.8283i		−	0.590922i	−0.955355	−	0.295461i	$-0.904527\pi$
$811$		−	16.8283i		−	0.590922i	0.955355	−	0.295461i	$-0.0954733\pi$
$812$	27.3450	−	27.6788i	0.959622	−	0.971334i
$813$		−	5.62954i		−	0.197437i
$814$		0			0
$815$	8.88299			0.311157
$816$	24.6572	−	0.299114i	0.863173	−	0.0104711i
$817$	−12.2514			−0.428624
$818$	8.28162	+	3.40097i	0.289560	+	0.118912i
$819$			0.809515i			0.0282867i
$820$	−10.0046	+	10.1267i	−0.349374	+	0.353638i
$821$		−	1.25448i		−	0.0437816i	−0.999760	−	0.0218908i	$-0.993031\pi$
$821$		−	1.25448i		−	0.0437816i	0.999760	−	0.0218908i	$-0.00696862\pi$
$822$	−12.4523	+	30.3223i	−0.434324	+	1.05761i
$823$	50.2585			1.75190			0.875950	−	0.482402i	$-0.160236\pi$
$823$	50.2585			1.75190			0.875950	+	0.482402i	$0.160236\pi$
$824$	9.04465	+	21.2859i	0.315085	+	0.741529i
$825$		0			0
$826$	−5.40410	+	13.1594i	−0.188033	+	0.457874i
$827$			23.6885i			0.823732i	0.911245	+	0.411866i	$0.135123\pi$
$827$			23.6885i			0.823732i	−0.911245	+	0.411866i	$0.864877\pi$
$828$	5.89634	+	5.82525i	0.204912	+	0.202441i
$829$		−	33.4106i		−	1.16040i	−0.814475	−	0.580199i	$-0.802975\pi$
$829$		−	33.4106i		−	1.16040i	0.814475	−	0.580199i	$-0.197025\pi$
$830$	0.288989	+	0.118678i	0.0100309	+	0.00411936i
$831$	8.06092			0.279630
$832$	−1.85476	−	1.78847i	−0.0643024	−	0.0620039i
$833$	16.8200			0.582779
$834$	−11.2828	−	4.63346i	−0.390692	−	0.160444i
$835$		−	28.5176i		−	0.986892i
$836$		0			0
$837$		−	15.7663i		−	0.544963i
$838$	4.63897	−	11.2962i	0.160251	−	0.390222i
$839$	18.8019			0.649113			0.324557	−	0.945866i	$-0.394785\pi$
$839$	18.8019			0.649113			0.324557	+	0.945866i	$0.394785\pi$
$840$	−4.20510	−	9.89638i	−0.145090	−	0.341458i
$841$	−79.4321			−2.73904
$842$	15.8355	−	38.5607i	0.545728	−	1.32889i
$843$		−	14.3878i		−	0.495542i
$844$	4.66055	−	4.71743i	0.160423	−	0.162381i
$845$			20.4010i			0.701815i
$846$	−22.3985	−	9.19828i	−0.770076	−	0.316243i
$847$		0			0
$848$	−22.6273	+	0.274491i	−0.777026	+	0.00942605i
$849$	−41.1374			−1.41183
$850$	−15.6582	−	6.43028i	−0.537072	−	0.220557i
$851$		−	11.0041i		−	0.377215i
$852$	20.1346	−	20.3804i	0.689801	−	0.698220i
$853$		−	43.9013i		−	1.50315i	−0.659647	−	0.751575i	$-0.729294\pi$
$853$		−	43.9013i		−	1.50315i	0.659647	−	0.751575i	$-0.270706\pi$
$854$	−10.9692	+	26.7108i	−0.375358	+	0.914023i
$855$	7.20688			0.246470
$856$	13.1000	−	5.56637i	0.447750	−	0.190255i
$857$	35.4141			1.20972			0.604861	−	0.796331i	$-0.293229\pi$
$857$	35.4141			1.20972			0.604861	+	0.796331i	$0.293229\pi$
$858$		0			0
$859$		−	36.4697i		−	1.24433i	−0.782886	−	0.622165i	$-0.786253\pi$
$859$		−	36.4697i		−	1.24433i	0.782886	−	0.622165i	$-0.213747\pi$
$860$	8.14299	+	8.04481i	0.277674	+	0.274326i
$861$			10.8127i			0.368495i
$862$	28.3465	+	11.6409i	0.965486	+	0.396492i
$863$	24.0325			0.818075			0.409037	−	0.912518i	$-0.365865\pi$
$863$	24.0325			0.818075			0.409037	+	0.912518i	$0.365865\pi$
$864$	−29.3926	−	11.6559i	−0.999955	−	0.396541i
$865$	−23.8369			−0.810479
$866$	−15.0644	−	6.18641i	−0.511908	−	0.210223i
$867$			7.67694i			0.260723i
$868$	−7.49756	−	7.40716i	−0.254484	−	0.251415i
$869$		0			0
$870$	−11.3836	+	27.7199i	−0.385940	+	0.939793i
$871$	3.53910			0.119918
$872$	26.5104	−	11.2646i	0.897755	−	0.381468i
$873$	16.6745			0.564347
$874$	5.60399	−	13.6461i	0.189558	−	0.461587i
$875$			22.1584i			0.749090i
$876$	−22.7989	+	23.0771i	−0.770302	+	0.779703i
$877$		−	18.6541i		−	0.629904i	−0.949108	−	0.314952i	$-0.898012\pi$
$877$		−	18.6541i		−	0.629904i	0.949108	−	0.314952i	$-0.101988\pi$
$878$	−47.0379	−	19.3168i	−1.58745	−	0.651912i
$879$	−9.85952			−0.332553
$880$		0			0
$881$	32.4553			1.09345			0.546723	−	0.837314i	$-0.315875\pi$
$881$	32.4553			1.09345			0.546723	+	0.837314i	$0.315875\pi$
$882$	−6.17695	−	2.53666i	−0.207989	−	0.0854137i
$883$			13.0200i			0.438157i	0.975707	+	0.219079i	$0.0703051\pi$
$883$			13.0200i			0.438157i	−0.975707	+	0.219079i	$0.929695\pi$
$884$	2.16961	−	2.19609i	0.0729718	−	0.0738623i
$885$		−	10.9564i		−	0.368294i
$886$	14.9434	−	36.3883i	0.502033	−	1.22249i
$887$	−19.1455			−0.642843			−0.321422	−	0.946936i	$-0.604161\pi$
$887$	−19.1455			−0.642843			−0.321422	+	0.946936i	$0.604161\pi$
$888$	5.08273	+	11.9618i	0.170565	+	0.401412i
$889$	24.3735			0.817460
$890$	−3.64582	+	8.87785i	−0.122208	+	0.297586i
$891$		0			0
$892$	−21.2065	−	20.9508i	−0.710046	−	0.701485i
$893$			43.0955i			1.44214i
$894$	6.74383	+	2.76946i	0.225548	+	0.0926245i
$895$	−35.2564			−1.17849
$896$	−19.3518	+	8.50139i	−0.646497	+	0.284012i
$897$	−1.27620			−0.0426110
$898$	−17.1174	−	7.02951i	−0.571215	−	0.234578i
$899$			29.3718i			0.979605i
$900$	4.78053	+	4.72289i	0.159351	+	0.157430i
$901$		−	27.1124i		−	0.903245i
$902$		0			0
$903$	8.69462			0.289339
$904$	8.90638	+	20.9605i	0.296222	+	0.697135i
$905$	−18.2104			−0.605333
$906$	−1.61301	+	3.92781i	−0.0535888	+	0.130493i
$907$		−	53.3243i		−	1.77060i	−0.465017	−	0.885302i	$-0.653952\pi$
$907$		−	53.3243i		−	1.77060i	0.465017	−	0.885302i	$-0.346048\pi$
$908$	1.85919	−	1.88188i	0.0616995	−	0.0624525i
$909$		−	20.6683i		−	0.685525i
$910$	−1.24523	−	0.511371i	−0.0412789	−	0.0169518i
$911$	47.3265			1.56800			0.783999	−	0.620762i	$-0.213177\pi$
$911$	47.3265			1.56800			0.783999	+	0.620762i	$0.213177\pi$
$912$	0.211348	+	17.4222i	0.00699844	+	0.576908i
$913$		0			0
$914$	8.67355	+	3.56193i	0.286896	+	0.117818i
$915$		−	22.2391i		−	0.735202i
$916$	33.1764	−	33.5814i	1.09618	−	1.10956i
$917$		−	21.5818i		−	0.712695i
$918$	14.3914	−	35.0440i	0.474985	−	1.15662i
$919$	−55.9089			−1.84427			−0.922133	−	0.386874i	$-0.873555\pi$
$919$	−55.9089			−1.84427			−0.922133	+	0.386874i	$0.873555\pi$
$920$	−12.6853	+	5.39016i	−0.418223	+	0.177708i
$921$	4.59877			0.151535
$922$	−4.52902	+	11.0285i	−0.149155	+	0.363204i
$923$		−	3.58657i		−	0.118054i
$924$		0			0
$925$		−	8.92170i		−	0.293344i
$926$	11.9838	+	4.92134i	0.393813	+	0.161725i
$927$	11.0008			0.361315
$928$	54.7569	+	21.7143i	1.79748	+	0.712807i
$929$	20.2505			0.664396			0.332198	−	0.943210i	$-0.392210\pi$
$929$	20.2505			0.664396			0.332198	+	0.943210i	$0.392210\pi$
$930$	7.50870	+	3.08356i	0.246220	+	0.101114i
$931$			11.8847i			0.389504i
$932$	−3.51539	−	3.47301i	−0.115151	−	0.113762i
$933$		−	0.100747i		−	0.00329830i
$934$	6.21767	−	15.1405i	0.203449	−	0.495412i
$935$		0			0
$936$	−1.12796	+	0.479284i	−0.0368685	+	0.0156659i
$937$	40.6651			1.32847			0.664235	−	0.747524i	$-0.268757\pi$
$937$	40.6651			1.32847			0.664235	+	0.747524i	$0.268757\pi$
$938$	11.0290	−	26.8564i	0.360109	−	0.876891i
$939$		−	11.5097i		−	0.375606i
$940$	28.2983	−	28.6436i	0.922988	−	0.934253i
$941$		−	2.23992i		−	0.0730194i	−0.999333	−	0.0365097i	$-0.988376\pi$
$941$		−	2.23992i		−	0.0730194i	0.999333	−	0.0365097i	$-0.0116240\pi$
$942$	13.3711	+	5.49102i	0.435652	+	0.178907i
$943$	13.8598			0.451339
$944$	−21.5355	+	0.261246i	−0.700922	+	0.00850284i
$945$	−16.5196			−0.537382
$946$		0			0
$947$			14.7173i			0.478247i	0.970989	+	0.239123i	$0.0768601\pi$
$947$			14.7173i			0.478247i	−0.970989	+	0.239123i	$0.923140\pi$
$948$	10.8122	−	10.9442i	0.351164	−	0.355450i
$949$			4.06115i			0.131831i
$950$	4.54350	−	11.0638i	0.147411	−	0.358956i
$951$	−31.4935			−1.02125
$952$	−9.90375	−	23.3077i	−0.320982	−	0.755407i
$953$	18.3058			0.592984			0.296492	−	0.955035i	$-0.404183\pi$
$953$	18.3058			0.592984			0.296492	+	0.955035i	$0.404183\pi$
$954$	−4.08887	+	9.95670i	−0.132382	+	0.322360i
$955$		−	17.0805i		−	0.552712i
$956$	−22.5078	−	22.2364i	−0.727955	−	0.719178i
$957$		0			0
$958$	−25.0627	−	10.2924i	−0.809739	−	0.332532i
$959$	33.6643			1.08708
$960$	11.2997	−	11.7186i	0.364696	−	0.378215i
$961$	−23.0438			−0.743349
$962$	1.50511	+	0.618097i	0.0485268	+	0.0199282i
$963$		−	6.77028i		−	0.218169i
$964$	4.58858	+	4.53325i	0.147788	+	0.146006i
$965$		−	14.3268i		−	0.461196i
$966$	−3.97705	+	9.68441i	−0.127959	+	0.311591i
$967$	−7.98210			−0.256687			−0.128343	−	0.991730i	$-0.540966\pi$
$967$	−7.98210			−0.256687			−0.128343	+	0.991730i	$0.540966\pi$
$968$		0			0
$969$	−20.8756			−0.670620
$970$	−10.5333	+	25.6494i	−0.338204	+	0.823553i
$971$			35.5820i			1.14188i	0.820992	+	0.570940i	$0.193421\pi$
$971$			35.5820i			1.14188i	−0.820992	+	0.570940i	$0.806579\pi$
$972$	−17.8676	+	18.0857i	−0.573104	+	0.580099i
$973$			12.5264i			0.401578i
$974$	55.5182	+	22.7994i	1.77892	+	0.730540i
$975$	−1.03469			−0.0331367
$976$	−43.7126	+	0.530274i	−1.39920	+	0.0169737i
$977$	−38.5825			−1.23436			−0.617181	−	0.786821i	$-0.711726\pi$
$977$	−38.5825			−1.23436			−0.617181	+	0.786821i	$0.711726\pi$
$978$	9.44927	+	3.88048i	0.302154	+	0.124084i
$979$		0			0
$980$	7.80397	−	7.89921i	0.249289	−	0.252331i
$981$		−	13.7009i		−	0.437437i
$982$	−21.0913	+	51.3588i	−0.673050	+	1.63893i
$983$	33.6443			1.07309			0.536543	−	0.843873i	$-0.319730\pi$
$983$	33.6443			1.07309			0.536543	+	0.843873i	$0.319730\pi$
$984$	−15.0661	+	6.40178i	−0.480290	+	0.204081i
$985$	−13.8279			−0.440592
$986$	−26.8104	+	65.2852i	−0.853816	+	2.07911i
$987$		−	30.5841i		−	0.973502i
$988$	1.55171	+	1.53300i	0.0493664	+	0.0487712i
$989$		−	11.1449i		−	0.354387i
$990$		0			0
$991$	34.6130			1.09952			0.549758	−	0.835324i	$-0.314720\pi$
$991$	34.6130			1.09952			0.549758	+	0.835324i	$0.314720\pi$
$992$	5.88192	−	14.8324i	0.186751	−	0.470930i
$993$	−31.1399			−0.988194
$994$	−27.2166	−	11.1769i	−0.863259	−	0.354510i
$995$			4.04309i			0.128174i
$996$	0.255568	+	0.252486i	0.00809798	+	0.00800034i
$997$		−	14.2720i		−	0.452000i	−0.974127	−	0.226000i	$-0.927435\pi$
$997$		−	14.2720i		−	0.452000i	0.974127	−	0.226000i	$-0.0725649\pi$
$998$	12.1757	−	29.6487i	0.385414	−	0.938512i
$999$	19.9673			0.631737

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.c.i.485.18		20
4.3	odd	2		3872.2.c.i.1937.6		20
8.3	odd	2		3872.2.c.i.1937.15		20
8.5	even	2	inner	968.2.c.i.485.17		20
11.2	odd	10		88.2.o.a.37.8	✓	40
11.3	even	5		968.2.o.d.493.8		40
11.4	even	5		968.2.o.d.269.6		40
11.5	even	5		968.2.o.i.245.1		40
11.6	odd	10		88.2.o.a.69.10	yes	40
11.7	odd	10		968.2.o.j.269.5		40
11.8	odd	10		968.2.o.j.493.3		40
11.9	even	5		968.2.o.i.565.3		40
11.10	odd	2		968.2.c.h.485.3		20
33.2	even	10		792.2.br.b.37.3		40
33.17	even	10		792.2.br.b.685.1		40
44.35	even	10		352.2.w.a.81.3		40
44.39	even	10		352.2.w.a.113.8		40
44.43	even	2		3872.2.c.h.1937.6		20
88.5	even	10		968.2.o.i.245.3		40
88.13	odd	10		88.2.o.a.37.10	yes	40
88.21	odd	2		968.2.c.h.485.4		20
88.29	odd	10		968.2.o.j.269.3		40
88.35	even	10		352.2.w.a.81.8		40
88.37	even	10		968.2.o.d.269.8		40
88.43	even	2		3872.2.c.h.1937.15		20
88.53	even	10		968.2.o.i.565.1		40
88.61	odd	10		88.2.o.a.69.8	yes	40
88.69	even	10		968.2.o.d.493.6		40
88.83	even	10		352.2.w.a.113.3		40
88.85	odd	10		968.2.o.j.493.5		40
264.101	even	10		792.2.br.b.37.1		40
264.149	even	10		792.2.br.b.685.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.8	✓	40	11.2	odd	10
88.2.o.a.37.10	yes	40	88.13	odd	10
88.2.o.a.69.8	yes	40	88.61	odd	10
88.2.o.a.69.10	yes	40	11.6	odd	10
352.2.w.a.81.3		40	44.35	even	10
352.2.w.a.81.8		40	88.35	even	10
352.2.w.a.113.3		40	88.83	even	10
352.2.w.a.113.8		40	44.39	even	10
792.2.br.b.37.1		40	264.101	even	10
792.2.br.b.37.3		40	33.2	even	10
792.2.br.b.685.1		40	33.17	even	10
792.2.br.b.685.3		40	264.149	even	10
968.2.c.h.485.3		20	11.10	odd	2
968.2.c.h.485.4		20	88.21	odd	2
968.2.c.i.485.17		20	8.5	even	2	inner
968.2.c.i.485.18		20	1.1	even	1	trivial
968.2.o.d.269.6		40	11.4	even	5
968.2.o.d.269.8		40	88.37	even	10
968.2.o.d.493.6		40	88.69	even	10
968.2.o.d.493.8		40	11.3	even	5
968.2.o.i.245.1		40	11.5	even	5
968.2.o.i.245.3		40	88.5	even	10
968.2.o.i.565.1		40	88.53	even	10
968.2.o.i.565.3		40	11.9	even	5
968.2.o.j.269.3		40	88.29	odd	10
968.2.o.j.269.5		40	11.7	odd	10
968.2.o.j.493.3		40	11.8	odd	10
968.2.o.j.493.5		40	88.85	odd	10
3872.2.c.h.1937.6		20	44.43	even	2
3872.2.c.h.1937.15		20	88.43	even	2
3872.2.c.i.1937.6		20	4.3	odd	2
3872.2.c.i.1937.15		20	8.3	odd	2

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	968.2.c.i.485.18

Level	$968$
Weight	$2$
Character	968.485
Analytic conductor	$7.730$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$