LMFDB - Embedded newform 252.3.g.b.127.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,3,Mod(127,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("252.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.g (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:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.489494783471841.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 18 x^{8} - 22 x^{7} + 33 x^{6} - 44 x^{5} + 72 x^{4} + \cdots + 64 $ x^12 - 3x^11 + 7x^10 - 11x^9 + 18x^8 - 22x^7 + 33x^6 - 44x^5 + 72x^4 - 88x^3 + 112x^2 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{19} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			127.7
Root			$1.10978 - 0.876576i$ of defining polynomial
Character	$\chi$	$=$	252.127
Dual form			252.3.g.b.127.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0345996 - 1.99970i) q^{2} +(-3.99761 + 0.138378i) q^{4} +6.29204 q^{5} +2.64575i q^{7} +(0.415030 + 7.98923i) q^{8} +O(q^{10})$	\(q+(-0.0345996 - 1.99970i) q^{2} +(-3.99761 + 0.138378i) q^{4} +6.29204 q^{5} +2.64575i q^{7} +(0.415030 + 7.98923i) q^{8} +(-0.217702 - 12.5822i) q^{10} -16.5803i q^{11} +14.1288 q^{13} +(5.29071 - 0.0915421i) q^{14} +(15.9617 - 1.10636i) q^{16} +20.4687 q^{17} +6.39258i q^{19} +(-25.1531 + 0.870679i) q^{20} +(-33.1556 + 0.573671i) q^{22} -29.0945i q^{23} +14.5898 q^{25} +(-0.488852 - 28.2534i) q^{26} +(-0.366113 - 10.5767i) q^{28} -54.6984 q^{29} -14.7296i q^{31} +(-2.76466 - 31.8803i) q^{32} +(-0.708210 - 40.9313i) q^{34} +16.6472i q^{35} +26.8040 q^{37} +(12.7833 - 0.221181i) q^{38} +(2.61139 + 50.2685i) q^{40} +33.5802 q^{41} +3.83239i q^{43} +(2.29434 + 66.2814i) q^{44} +(-58.1804 + 1.00666i) q^{46} +27.4693i q^{47} -7.00000 q^{49} +(-0.504801 - 29.1752i) q^{50} +(-56.4815 + 1.95512i) q^{52} +21.7113 q^{53} -104.324i q^{55} +(-21.1375 + 1.09807i) q^{56} +(1.89254 + 109.380i) q^{58} +54.1344i q^{59} -35.7188 q^{61} +(-29.4549 + 0.509641i) q^{62} +(-63.6555 + 6.63154i) q^{64} +88.8991 q^{65} +95.4255i q^{67} +(-81.8258 + 2.83241i) q^{68} +(33.2894 - 0.575986i) q^{70} +55.6524i q^{71} +130.476 q^{73} +(-0.927408 - 53.5999i) q^{74} +(-0.884592 - 25.5550i) q^{76} +43.8673 q^{77} +15.6309i q^{79} +(100.432 - 6.96126i) q^{80} +(-1.16186 - 67.1503i) q^{82} -49.4495i q^{83} +128.790 q^{85} +(7.66363 - 0.132599i) q^{86} +(132.464 - 6.88131i) q^{88} -39.2530 q^{89} +37.3813i q^{91} +(4.02604 + 116.309i) q^{92} +(54.9303 - 0.950427i) q^{94} +40.2224i q^{95} -171.943 q^{97} +(0.242198 + 13.9979i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8	$ 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8} + 28 q^{10} - 24 q^{13} + 14 q^{14} - 14 q^{16} + 40 q^{17} + 20 q^{20} - 88 q^{22} + 180 q^{25} - 100 q^{26} + 14 q^{28} - 72 q^{29} - 142 q^{32} - 100 q^{34} - 88 q^{37} - 128 q^{38} - 28 q^{40} + 200 q^{41} + 40 q^{44} - 24 q^{46} - 84 q^{49} + 346 q^{50} - 364 q^{52} - 104 q^{53} - 98 q^{56} + 148 q^{58} + 104 q^{61} - 64 q^{62} - 70 q^{64} - 176 q^{65} - 188 q^{68} - 84 q^{70} + 312 q^{73} - 4 q^{74} + 432 q^{76} + 224 q^{77} + 564 q^{80} + 332 q^{82} + 352 q^{85} - 160 q^{86} + 328 q^{88} + 552 q^{89} - 232 q^{92} - 144 q^{94} - 264 q^{97} + 14 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8 + 28 * q^10 - 24 * q^13 + 14 * q^14 - 14 * q^16 + 40 * q^17 + 20 * q^20 - 88 * q^22 + 180 * q^25 - 100 * q^26 + 14 * q^28 - 72 * q^29 - 142 * q^32 - 100 * q^34 - 88 * q^37 - 128 * q^38 - 28 * q^40 + 200 * q^41 + 40 * q^44 - 24 * q^46 - 84 * q^49 + 346 * q^50 - 364 * q^52 - 104 * q^53 - 98 * q^56 + 148 * q^58 + 104 * q^61 - 64 * q^62 - 70 * q^64 - 176 * q^65 - 188 * q^68 - 84 * q^70 + 312 * q^73 - 4 * q^74 + 432 * q^76 + 224 * q^77 + 564 * q^80 + 332 * q^82 + 352 * q^85 - 160 * q^86 + 328 * q^88 + 552 * q^89 - 232 * q^92 - 144 * q^94 - 264 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−0.0345996	−	1.99970i	−0.0172998	−	0.999850i
$2$	−0.0345996	−	1.99970i	−0.0172998	−	0.999850i
$3$		0			0
$3$		0			0
$4$	−3.99761	+	0.138378i	−0.999401	+	0.0345945i
$5$	6.29204			1.25841			0.629204	−	0.777240i	$-0.283381\pi$
$5$	6.29204			1.25841			0.629204	+	0.777240i	$0.283381\pi$
$6$		0			0
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	0.415030	+	7.98923i	0.0518788	+	0.998653i
$9$		0			0
$10$	−0.217702	−	12.5822i	−0.0217702	−	1.25822i
$11$		−	16.5803i		−	1.50730i	−0.657278	−	0.753649i	$-0.728292\pi$
$11$		−	16.5803i		−	1.50730i	0.657278	−	0.753649i	$-0.271708\pi$
$12$		0			0
$13$	14.1288			1.08683			0.543416	−	0.839463i	$-0.317131\pi$
$13$	14.1288			1.08683			0.543416	+	0.839463i	$0.317131\pi$
$14$	5.29071	−	0.0915421i	0.377908	−	0.00653872i
$15$		0			0
$16$	15.9617	−	1.10636i	0.997606	−	0.0691475i
$17$	20.4687			1.20404			0.602020	−	0.798481i	$-0.294363\pi$
$17$	20.4687			1.20404			0.602020	+	0.798481i	$0.294363\pi$
$18$		0			0
$19$			6.39258i			0.336452i	0.985748	+	0.168226i	$0.0538038\pi$
$19$			6.39258i			0.336452i	−0.985748	+	0.168226i	$0.946196\pi$
$20$	−25.1531	+	0.870679i	−1.25765	+	0.0435340i
$21$		0			0
$22$	−33.1556	+	0.573671i	−1.50707	+	0.0260760i
$23$		−	29.0945i		−	1.26498i	−0.774568	−	0.632490i	$-0.782033\pi$
$23$		−	29.0945i		−	1.26498i	0.774568	−	0.632490i	$-0.217967\pi$
$24$		0			0
$25$	14.5898			0.583591
$26$	−0.488852	−	28.2534i	−0.0188020	−	1.08667i
$27$		0			0
$28$	−0.366113	−	10.5767i	−0.0130755	−	0.377738i
$29$	−54.6984			−1.88615			−0.943075	−	0.332579i	$-0.892081\pi$
$29$	−54.6984			−1.88615			−0.943075	+	0.332579i	$0.892081\pi$
$30$		0			0
$31$		−	14.7296i		−	0.475150i	−0.971369	−	0.237575i	$-0.923647\pi$
$31$		−	14.7296i		−	0.475150i	0.971369	−	0.237575i	$-0.0763525\pi$
$32$	−2.76466	−	31.8803i	−0.0863956	−	0.996261i
$33$		0			0
$34$	−0.708210	−	40.9313i	−0.0208297	−	1.20386i
$35$			16.6472i			0.475633i
$36$		0			0
$37$	26.8040			0.724431			0.362216	−	0.932094i	$-0.382020\pi$
$37$	26.8040			0.724431			0.362216	+	0.932094i	$0.382020\pi$
$38$	12.7833	−	0.221181i	0.336401	−	0.00582055i
$39$		0			0
$40$	2.61139	+	50.2685i	0.0652846	+	1.25671i
$41$	33.5802			0.819029			0.409515	−	0.912304i	$-0.365698\pi$
$41$	33.5802			0.819029			0.409515	+	0.912304i	$0.365698\pi$
$42$		0			0
$43$			3.83239i			0.0891253i	0.999007	+	0.0445627i	$0.0141894\pi$
$43$			3.83239i			0.0891253i	−0.999007	+	0.0445627i	$0.985811\pi$
$44$	2.29434	+	66.2814i	0.0521441	+	1.50639i
$45$		0			0
$46$	−58.1804	+	1.00666i	−1.26479	+	0.0218839i
$47$			27.4693i			0.584453i	0.956349	+	0.292226i	$0.0943961\pi$
$47$			27.4693i			0.584453i	−0.956349	+	0.292226i	$0.905604\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−0.504801	−	29.1752i	−0.0100960	−	0.583503i
$51$		0			0
$52$	−56.4815	+	1.95512i	−1.08618	+	0.0375984i
$53$	21.7113			0.409648			0.204824	−	0.978799i	$-0.434338\pi$
$53$	21.7113			0.409648			0.204824	+	0.978799i	$0.434338\pi$
$54$		0			0
$55$		−	104.324i		−	1.89679i
$56$	−21.1375	+	1.09807i	−0.377456	+	0.0196083i
$57$		0			0
$58$	1.89254	+	109.380i	0.0326301	+	1.88587i
$59$			54.1344i			0.917532i	0.888557	+	0.458766i	$0.151708\pi$
$59$			54.1344i			0.917532i	−0.888557	+	0.458766i	$0.848292\pi$
$60$		0			0
$61$	−35.7188			−0.585554			−0.292777	−	0.956181i	$-0.594579\pi$
$61$	−35.7188			−0.585554			−0.292777	+	0.956181i	$0.594579\pi$
$62$	−29.4549	+	0.509641i	−0.475079	+	0.00822001i
$63$		0			0
$64$	−63.6555	+	6.63154i	−0.994617	+	0.103618i
$65$	88.8991			1.36768
$66$		0			0
$67$			95.4255i			1.42426i	0.702047	+	0.712131i	$0.252270\pi$
$67$			95.4255i			1.42426i	−0.702047	+	0.712131i	$0.747730\pi$
$68$	−81.8258	+	2.83241i	−1.20332	+	0.0416532i
$69$		0			0
$70$	33.2894	−	0.575986i	0.475562	−	0.00822837i
$71$			55.6524i			0.783837i	0.920000	+	0.391919i	$0.128189\pi$
$71$			55.6524i			0.783837i	−0.920000	+	0.391919i	$0.871811\pi$
$72$		0			0
$73$	130.476			1.78735			0.893673	−	0.448719i	$-0.148119\pi$
$73$	130.476			1.78735			0.893673	+	0.448719i	$0.148119\pi$
$74$	−0.927408	−	53.5999i	−0.0125325	−	0.724323i
$75$		0			0
$76$	−0.884592	−	25.5550i	−0.0116394	−	0.336250i
$77$	43.8673			0.569705
$78$		0			0
$79$			15.6309i			0.197859i	0.995094	+	0.0989295i	$0.0315418\pi$
$79$			15.6309i			0.197859i	−0.995094	+	0.0989295i	$0.968458\pi$
$80$	100.432	−	6.96126i	1.25540	−	0.0870158i
$81$		0			0
$82$	−1.16186	−	67.1503i	−0.0141691	−	0.818907i
$83$		−	49.4495i		−	0.595777i	−0.954601	−	0.297889i	$-0.903718\pi$
$83$		−	49.4495i		−	0.595777i	0.954601	−	0.297889i	$-0.0962824\pi$
$84$		0			0
$85$	128.790			1.51517
$86$	7.66363	−	0.132599i	0.0891120	−	0.00154185i
$87$		0			0
$88$	132.464	−	6.88131i	1.50527	−	0.0781967i
$89$	−39.2530			−0.441045			−0.220522	−	0.975382i	$-0.570776\pi$
$89$	−39.2530			−0.441045			−0.220522	+	0.975382i	$0.570776\pi$
$90$		0			0
$91$			37.3813i			0.410784i
$92$	4.02604	+	116.309i	0.0437613	+	1.26422i
$93$		0			0
$94$	54.9303	−	0.950427i	0.584365	−	0.0101109i
$95$			40.2224i			0.423394i
$96$		0			0
$97$	−171.943			−1.77261			−0.886303	−	0.463106i	$-0.846735\pi$
$97$	−171.943			−1.77261			−0.886303	+	0.463106i	$0.846735\pi$
$98$	0.242198	+	13.9979i	0.00247140	+	0.142836i
$99$		0			0
$100$	−58.3241	+	2.01890i	−0.583241	+	0.0201890i
$101$	−113.883			−1.12755			−0.563777	−	0.825927i	$-0.690652\pi$
$101$	−113.883			−1.12755			−0.563777	+	0.825927i	$0.690652\pi$
$102$		0			0
$103$			93.7629i			0.910319i	0.890410	+	0.455160i	$0.150418\pi$
$103$			93.7629i			0.910319i	−0.890410	+	0.455160i	$0.849582\pi$
$104$	5.86389	+	112.878i	0.0563835	+	1.08537i
$105$		0			0
$106$	−0.751204	−	43.4161i	−0.00708683	−	0.409586i
$107$		−	48.2088i		−	0.450549i	−0.974295	−	0.225275i	$-0.927672\pi$
$107$		−	48.2088i		−	0.450549i	0.974295	−	0.225275i	$-0.0723279\pi$
$108$		0			0
$109$	89.3790			0.819991			0.409996	−	0.912088i	$-0.365530\pi$
$109$	89.3790			0.819991			0.409996	+	0.912088i	$0.365530\pi$
$110$	−208.616	+	3.60956i	−1.89651	+	0.0328142i
$111$		0			0
$112$	2.92715	+	42.2307i	0.0261353	+	0.377060i
$113$	−93.4667			−0.827139			−0.413569	−	0.910473i	$-0.635718\pi$
$113$	−93.4667			−0.827139			−0.413569	+	0.910473i	$0.635718\pi$
$114$		0			0
$115$		−	183.064i		−	1.59186i
$116$	218.662	−	7.56904i	1.88502	−	0.0652504i
$117$		0			0
$118$	108.253	−	1.87303i	0.917395	−	0.0158731i
$119$			54.1551i			0.455085i
$120$		0			0
$121$	−153.905			−1.27194
$122$	1.23586	+	71.4269i	0.0101300	+	0.585466i
$123$		0			0
$124$	2.03826	+	58.8833i	0.0164376	+	0.474866i
$125$	−65.5016			−0.524013
$126$		0			0
$127$			208.300i			1.64016i	0.572248	+	0.820081i	$0.306071\pi$
$127$			208.300i			1.64016i	−0.572248	+	0.820081i	$0.693929\pi$
$128$	15.4635	+	127.062i	0.120809	+	0.992676i
$129$		0			0
$130$	−3.07588	−	177.772i	−0.0236606	−	1.36747i
$131$		−	67.7695i		−	0.517324i	−0.965968	−	0.258662i	$-0.916718\pi$
$131$		−	67.7695i		−	0.517324i	0.965968	−	0.258662i	$-0.0832816\pi$
$132$		0			0
$133$	−16.9132			−0.127167
$134$	190.823	−	3.30169i	1.42405	−	0.0246395i
$135$		0			0
$136$	8.49512	+	163.529i	0.0624641	+	1.20242i
$137$	13.4127			0.0979029			0.0489514	−	0.998801i	$-0.484412\pi$
$137$	13.4127			0.0979029			0.0489514	+	0.998801i	$0.484412\pi$
$138$		0			0
$139$			160.382i			1.15383i	0.816804	+	0.576915i	$0.195744\pi$
$139$			160.382i			1.15383i	−0.816804	+	0.576915i	$0.804256\pi$
$140$	−2.30360	−	66.5488i	−0.0164543	−	0.475349i
$141$		0			0
$142$	111.288	−	1.92555i	0.783720	−	0.0135602i
$143$		−	234.260i		−	1.63818i
$144$		0			0
$145$	−344.164			−2.37355
$146$	−4.51443	−	260.914i	−0.0309208	−	1.78708i
$147$		0			0
$148$	−107.152	+	3.70908i	−0.723998	+	0.0250613i
$149$	130.824			0.878015			0.439007	−	0.898483i	$-0.355330\pi$
$149$	130.824			0.878015			0.439007	+	0.898483i	$0.355330\pi$
$150$		0			0
$151$		−	175.855i		−	1.16460i	−0.812974	−	0.582300i	$-0.802153\pi$
$151$		−	175.855i		−	1.16460i	0.812974	−	0.582300i	$-0.197847\pi$
$152$	−51.0718	+	2.65311i	−0.335999	+	0.0174547i
$153$		0			0
$154$	−1.51779	−	87.7214i	−0.00985579	−	0.569620i
$155$		−	92.6795i		−	0.597932i
$156$		0			0
$157$	−167.199			−1.06496			−0.532482	−	0.846441i	$-0.678741\pi$
$157$	−167.199			−1.06496			−0.532482	+	0.846441i	$0.678741\pi$
$158$	31.2570	−	0.540822i	0.197829	−	0.00342293i
$159$		0			0
$160$	−17.3953	−	200.592i	−0.108721	−	1.25370i
$161$	76.9769			0.478118
$162$		0			0
$163$		−	220.591i		−	1.35332i	−0.736295	−	0.676661i	$-0.763426\pi$
$163$		−	220.591i		−	1.35332i	0.736295	−	0.676661i	$-0.236574\pi$
$164$	−134.240	+	4.64676i	−0.818539	+	0.0283339i
$165$		0			0
$166$	−98.8842	+	1.71093i	−0.595688	+	0.0103068i
$167$			64.6529i			0.387143i	0.981086	+	0.193572i	$0.0620072\pi$
$167$			64.6529i			0.387143i	−0.981086	+	0.193572i	$0.937993\pi$
$168$		0			0
$169$	30.6236			0.181205
$170$	−4.45608	−	257.541i	−0.0262123	−	1.51495i
$171$		0			0
$172$	−0.530318	−	15.3204i	−0.00308324	−	0.0890720i
$173$	−237.146			−1.37078			−0.685392	−	0.728174i	$-0.740369\pi$
$173$	−237.146			−1.37078			−0.685392	+	0.728174i	$0.740369\pi$
$174$		0			0
$175$			38.6009i			0.220577i
$176$	−18.3438	−	264.649i	−0.104226	−	1.50369i
$177$		0			0
$178$	1.35814	+	78.4942i	0.00763000	+	0.440979i
$179$			103.153i			0.576275i	0.957589	+	0.288137i	$0.0930360\pi$
$179$			103.153i			0.576275i	−0.957589	+	0.288137i	$0.906964\pi$
$180$		0			0
$181$	43.5702			0.240719			0.120360	−	0.992730i	$-0.461595\pi$
$181$	43.5702			0.240719			0.120360	+	0.992730i	$0.461595\pi$
$182$	74.7515	−	1.29338i	0.410723	−	0.00710649i
$183$		0			0
$184$	232.443	−	12.0751i	1.26328	−	0.0656256i
$185$	168.652			0.911630
$186$		0			0
$187$		−	339.376i		−	1.81485i
$188$	−3.80114	−	109.811i	−0.0202188	−	0.584103i
$189$		0			0
$190$	80.4327	−	1.39168i	0.423330	−	0.00732463i
$191$			219.309i			1.14822i	0.818779	+	0.574109i	$0.194651\pi$
$191$			219.309i			1.14822i	−0.818779	+	0.574109i	$0.805349\pi$
$192$		0			0
$193$	9.40273			0.0487188			0.0243594	−	0.999703i	$-0.492245\pi$
$193$	9.40273			0.0487188			0.0243594	+	0.999703i	$0.492245\pi$
$194$	5.94916	+	343.834i	0.0306658	+	1.77234i
$195$		0			0
$196$	27.9832	−	0.968645i	0.142772	−	0.00494207i
$197$	−329.193			−1.67103			−0.835514	−	0.549469i	$-0.814830\pi$
$197$	−329.193			−1.67103			−0.835514	+	0.549469i	$0.814830\pi$
$198$		0			0
$199$		−	63.0050i		−	0.316608i	−0.987390	−	0.158304i	$-0.949397\pi$
$199$		−	63.0050i		−	0.316608i	0.987390	−	0.158304i	$-0.0506026\pi$
$200$	6.05519	+	116.561i	0.0302760	+	0.582805i
$201$		0			0
$202$	3.94031	+	227.732i	0.0195065	+	1.12739i
$203$		−	144.718i		−	0.712898i
$204$		0			0
$205$	211.288			1.03067
$206$	187.498	−	3.24416i	0.910183	−	0.0157484i
$207$		0			0
$208$	225.520	−	15.6316i	1.08423	−	0.0751518i
$209$	105.991			0.507133
$210$		0			0
$211$			0.702405i			0.00332893i	0.999999	+	0.00166447i	$0.000529817\pi$
$211$			0.702405i			0.00332893i	−0.999999	+	0.00166447i	$0.999470\pi$
$212$	−86.7933	+	3.00437i	−0.409402	+	0.0141715i
$213$		0			0
$214$	−96.4031	+	1.66801i	−0.450482	+	0.00779442i
$215$			24.1135i			0.112156i
$216$		0			0
$217$	38.9710			0.179590
$218$	−3.09248	−	178.731i	−0.0141857	−	0.819868i
$219$		0			0
$220$	14.4361	+	417.045i	0.0656186	+	1.89566i
$221$	289.199			1.30859
$222$		0			0
$223$			260.543i			1.16835i	0.811627	+	0.584177i	$0.198582\pi$
$223$			260.543i			1.16835i	−0.811627	+	0.584177i	$0.801418\pi$
$224$	84.3475	−	7.31460i	0.376551	−	0.0326545i
$225$		0			0
$226$	3.23391	+	186.905i	0.0143094	+	0.827015i
$227$		−	222.146i		−	0.978617i	−0.872111	−	0.489308i	$-0.837249\pi$
$227$		−	222.146i		−	0.978617i	0.872111	−	0.489308i	$-0.162751\pi$
$228$		0			0
$229$	124.781			0.544893			0.272447	−	0.962171i	$-0.412167\pi$
$229$	124.781			0.544893			0.272447	+	0.962171i	$0.412167\pi$
$230$	−366.073	+	6.33395i	−1.59162	+	0.0275389i
$231$		0			0
$232$	−22.7015	−	436.998i	−0.0978511	−	1.88361i
$233$	−332.321			−1.42627			−0.713135	−	0.701027i	$-0.752725\pi$
$233$	−332.321			−1.42627			−0.713135	+	0.701027i	$0.752725\pi$
$234$		0			0
$235$			172.838i			0.735480i
$236$	−7.49100	−	216.408i	−0.0317415	−	0.916983i
$237$		0			0
$238$	108.294	−	1.87375i	0.455017	−	0.00787288i
$239$			285.085i			1.19282i	0.802679	+	0.596412i	$0.203407\pi$
$239$			285.085i			1.19282i	−0.802679	+	0.596412i	$0.796593\pi$
$240$		0			0
$241$	89.2332			0.370262			0.185131	−	0.982714i	$-0.440729\pi$
$241$	89.2332			0.370262			0.185131	+	0.982714i	$0.440729\pi$
$242$	5.32507	+	307.765i	0.0220044	+	1.27175i
$243$		0			0
$244$	142.790	−	4.94269i	0.585204	−	0.0202569i
$245$	−44.0443			−0.179773
$246$		0			0
$247$			90.3197i			0.365667i
$248$	117.679	−	6.11325i	0.474510	−	0.0246502i
$249$		0			0
$250$	2.26633	+	130.984i	0.00906533	+	0.523935i
$251$			83.4611i			0.332514i	0.986082	+	0.166257i	$0.0531682\pi$
$251$			83.4611i			0.332514i	−0.986082	+	0.166257i	$0.946832\pi$
$252$		0			0
$253$	−482.395			−1.90670
$254$	416.539	−	7.20712i	1.63992	−	0.0283745i
$255$		0			0
$256$	253.552	−	35.3188i	0.990437	−	0.137964i
$257$	29.8619			0.116194			0.0580971	−	0.998311i	$-0.481497\pi$
$257$	29.8619			0.116194			0.0580971	+	0.998311i	$0.481497\pi$
$258$		0			0
$259$			70.9166i			0.273809i
$260$	−355.384	+	12.3017i	−1.36686	+	0.0473141i
$261$		0			0
$262$	−135.519	+	2.34480i	−0.517247	+	0.00894962i
$263$			245.304i			0.932717i	0.884596	+	0.466358i	$0.154434\pi$
$263$			245.304i			0.932717i	−0.884596	+	0.466358i	$0.845566\pi$
$264$		0			0
$265$	136.608			0.515504
$266$	0.585190	+	33.8213i	0.00219996	+	0.127148i
$267$		0			0
$268$	−13.2048	−	381.474i	−0.0492716	−	1.42341i
$269$	18.9441			0.0704241			0.0352120	−	0.999380i	$-0.488789\pi$
$269$	18.9441			0.0704241			0.0352120	+	0.999380i	$0.488789\pi$
$270$		0			0
$271$		−	278.928i		−	1.02925i	−0.857414	−	0.514626i	$-0.827931\pi$
$271$		−	278.928i		−	1.02925i	0.857414	−	0.514626i	$-0.172069\pi$
$272$	326.715	−	22.6458i	1.20116	−	0.0832564i
$273$		0			0
$274$	−0.464074	−	26.8214i	−0.00169370	−	0.0978882i
$275$		−	241.902i		−	0.879644i
$276$		0			0
$277$	−206.348			−0.744938			−0.372469	−	0.928045i	$-0.621489\pi$
$277$	−206.348			−0.744938			−0.372469	+	0.928045i	$0.621489\pi$
$278$	320.717	−	5.54917i	1.15366	−	0.0199610i
$279$		0			0
$280$	−132.998	+	6.90908i	−0.474993	+	0.0246753i
$281$	262.775			0.935142			0.467571	−	0.883956i	$-0.345129\pi$
$281$	262.775			0.935142			0.467571	+	0.883956i	$0.345129\pi$
$282$		0			0
$283$		−	543.508i		−	1.92052i	−0.279101	−	0.960262i	$-0.590037\pi$
$283$		−	543.508i		−	1.92052i	0.279101	−	0.960262i	$-0.409963\pi$
$284$	−7.70107	−	222.477i	−0.0271164	−	0.783368i
$285$		0			0
$286$	−468.449	+	8.10530i	−1.63793	+	0.0283402i
$287$			88.8448i			0.309564i
$288$		0			0
$289$	129.967			0.449714
$290$	11.9080	+	688.226i	0.0410619	+	2.37319i
$291$		0			0
$292$	−521.593	+	18.0550i	−1.78628	+	0.0618323i
$293$	−19.1934			−0.0655064			−0.0327532	−	0.999463i	$-0.510428\pi$
$293$	−19.1934			−0.0655064			−0.0327532	+	0.999463i	$0.510428\pi$
$294$		0			0
$295$			340.616i			1.15463i
$296$	11.1245	+	214.143i	0.0375826	+	0.723456i
$297$		0			0
$298$	−4.52647	−	261.609i	−0.0151895	−	0.877883i
$299$		−	411.072i		−	1.37482i
$300$		0			0
$301$	−10.1395			−0.0336862
$302$	−351.657	+	6.08451i	−1.16443	+	0.0201474i
$303$		0			0
$304$	7.07250	+	102.037i	0.0232648	+	0.335646i
$305$	−224.744			−0.736866
$306$		0			0
$307$			543.121i			1.76912i	0.466423	+	0.884562i	$0.345542\pi$
$307$			543.121i			1.76912i	−0.466423	+	0.884562i	$0.654458\pi$
$308$	−175.364	+	6.07026i	−0.569364	+	0.0197086i
$309$		0			0
$310$	−185.331	+	3.20668i	−0.597843	+	0.0103441i
$311$		−	183.154i		−	0.588920i	−0.955664	−	0.294460i	$-0.904860\pi$
$311$		−	183.154i		−	0.588920i	0.955664	−	0.294460i	$-0.0951398\pi$
$312$		0			0
$313$	513.858			1.64172			0.820859	−	0.571131i	$-0.193495\pi$
$313$	513.858			1.64172			0.820859	+	0.571131i	$0.193495\pi$
$314$	5.78504	+	334.349i	0.0184237	+	1.06481i
$315$		0			0
$316$	−2.16297	−	62.4860i	−0.00684483	−	0.197741i
$317$	559.731			1.76571			0.882857	−	0.469642i	$-0.155617\pi$
$317$	559.731			1.76571			0.882857	+	0.469642i	$0.155617\pi$
$318$		0			0
$319$			906.914i			2.84299i
$320$	−400.523	+	41.7259i	−1.25163	+	0.130393i
$321$		0			0
$322$	−2.66337	−	153.931i	−0.00827135	−	0.478046i
$323$			130.848i			0.405102i
$324$		0			0
$325$	206.136			0.634265
$326$	−441.117	+	7.63239i	−1.35312	+	0.0234122i
$327$		0			0
$328$	13.9368	+	268.280i	0.0424902	+	0.817926i
$329$	−72.6769			−0.220902
$330$		0			0
$331$		−	379.794i		−	1.14741i	−0.819061	−	0.573707i	$-0.805505\pi$
$331$		−	379.794i		−	1.14741i	0.819061	−	0.573707i	$-0.194495\pi$
$332$	6.84271	+	197.680i	0.0206106	+	0.595420i
$333$		0			0
$334$	129.286	−	2.23697i	0.387085	−	0.00669751i
$335$			600.421i			1.79230i
$336$		0			0
$337$	−117.618			−0.349015			−0.174507	−	0.984656i	$-0.555833\pi$
$337$	−117.618			−0.349015			−0.174507	+	0.984656i	$0.555833\pi$
$338$	−1.05957	−	61.2380i	−0.00313481	−	0.181178i
$339$		0			0
$340$	−514.851	+	17.8217i	−1.51427	+	0.0524167i
$341$	−244.222			−0.716192
$342$		0			0
$343$		−	18.5203i		−	0.0539949i
$344$	−30.6178	+	1.59056i	−0.0890053	+	0.00462371i
$345$		0			0
$346$	8.20516	+	474.221i	0.0237143	+	1.37058i
$347$		−	302.706i		−	0.872351i	−0.899862	−	0.436175i	$-0.856333\pi$
$347$		−	302.706i		−	0.872351i	0.899862	−	0.436175i	$-0.143667\pi$
$348$		0			0
$349$	83.1588			0.238277			0.119139	−	0.992878i	$-0.461987\pi$
$349$	83.1588			0.238277			0.119139	+	0.992878i	$0.461987\pi$
$350$	77.1902	−	1.33558i	0.220543	−	0.00381593i
$351$		0			0
$352$	−528.585	+	45.8388i	−1.50166	+	0.130224i
$353$	277.478			0.786057			0.393028	−	0.919526i	$-0.371427\pi$
$353$	277.478			0.786057			0.393028	+	0.919526i	$0.371427\pi$
$354$		0			0
$355$			350.167i			0.986387i
$356$	156.918	−	5.43175i	0.440781	−	0.0152577i
$357$		0			0
$358$	206.276	−	3.56906i	0.576189	−	0.00996945i
$359$			76.3214i			0.212594i	0.994334	+	0.106297i	$0.0338995\pi$
$359$			76.3214i			0.212594i	−0.994334	+	0.106297i	$0.966101\pi$
$360$		0			0
$361$	320.135			0.886800
$362$	−1.50751	−	87.1273i	−0.00416440	−	0.240683i
$363$		0			0
$364$	−5.17275	−	149.436i	−0.0142109	−	0.410538i
$365$	820.962			2.24921
$366$		0			0
$367$		−	176.403i		−	0.480663i	−0.970691	−	0.240332i	$-0.922744\pi$
$367$		−	176.403i		−	0.480663i	0.970691	−	0.240332i	$-0.0772562\pi$
$368$	−32.1890	−	464.398i	−0.0874702	−	1.26195i
$369$		0			0
$370$	−5.83529	−	337.253i	−0.0157710	−	0.911494i
$371$			57.4428i			0.154832i
$372$		0			0
$373$	57.5272			0.154229			0.0771143	−	0.997022i	$-0.475429\pi$
$373$	57.5272			0.154229			0.0771143	+	0.997022i	$0.475429\pi$
$374$	−678.651	+	11.7423i	−1.81458	+	0.0313965i
$375$		0			0
$376$	−219.458	+	11.4006i	−0.583666	+	0.0303207i
$377$	−772.823			−2.04993
$378$		0			0
$379$		−	412.402i		−	1.08813i	−0.839042	−	0.544066i	$-0.816884\pi$
$379$		−	412.402i		−	1.08813i	0.839042	−	0.544066i	$-0.183116\pi$
$380$	−5.56589	−	160.793i	−0.0146471	−	0.423140i
$381$		0			0
$382$	438.553	−	7.58803i	1.14805	−	0.0198640i
$383$			583.323i			1.52304i	0.648143	+	0.761518i	$0.275546\pi$
$383$			583.323i			1.52304i	−0.648143	+	0.761518i	$0.724454\pi$
$384$		0			0
$385$	276.015			0.716921
$386$	−0.325331	−	18.8026i	−0.000842826	−	0.0487115i
$387$		0			0
$388$	687.360	−	23.7931i	1.77155	−	0.0613224i
$389$	−64.4937			−0.165794			−0.0828968	−	0.996558i	$-0.526417\pi$
$389$	−64.4937			−0.165794			−0.0828968	+	0.996558i	$0.526417\pi$
$390$		0			0
$391$		−	595.527i		−	1.52309i
$392$	−2.90521	−	55.9246i	−0.00741125	−	0.142665i
$393$		0			0
$394$	11.3899	+	658.287i	0.0289085	+	1.67078i
$395$			98.3500i			0.248987i
$396$		0			0
$397$	−0.702051			−0.00176839			−0.000884195	−	1.00000i	$-0.500281\pi$
$397$	−0.702051			−0.00176839			−0.000884195		1.00000i	$0.500281\pi$
$398$	−125.991	+	2.17995i	−0.316561	+	0.00547727i
$399$		0			0
$400$	232.877	−	16.1415i	0.582194	−	0.0403538i
$401$	−61.3178			−0.152912			−0.0764561	−	0.997073i	$-0.524360\pi$
$401$	−61.3178			−0.152912			−0.0764561	+	0.997073i	$0.524360\pi$
$402$		0			0
$403$		−	208.113i		−	0.516408i
$404$	455.259	−	15.7589i	1.12688	−	0.0390071i
$405$		0			0
$406$	−289.393	+	5.00720i	−0.712791	+	0.0123330i
$407$		−	444.417i		−	1.09193i
$408$		0			0
$409$	−109.489			−0.267700			−0.133850	−	0.991002i	$-0.542734\pi$
$409$	−109.489			−0.267700			−0.133850	+	0.991002i	$0.542734\pi$
$410$	−7.31049	−	422.513i	−0.0178305	−	1.03052i
$411$		0			0
$412$	−12.9747	−	374.827i	−0.0314920	−	0.909774i
$413$	−143.226			−0.346795
$414$		0			0
$415$		−	311.138i		−	0.749731i
$416$	−39.0614	−	450.432i	−0.0938975	−	1.08277i
$417$		0			0
$418$	−3.66724	−	211.950i	−0.00877331	−	0.507057i
$419$		−	312.627i		−	0.746128i	−0.927806	−	0.373064i	$-0.878307\pi$
$419$		−	312.627i		−	0.746128i	0.927806	−	0.373064i	$-0.121693\pi$
$420$		0			0
$421$	633.267			1.50420			0.752099	−	0.659050i	$-0.229042\pi$
$421$	633.267			1.50420			0.752099	+	0.659050i	$0.229042\pi$
$422$	1.40460	−	0.0243030i	0.00332844	−	5.75900e-5i
$423$		0			0
$424$	9.01085	+	173.457i	0.0212520	+	0.409096i
$425$	298.633			0.702667
$426$		0			0
$427$		−	94.5031i		−	0.221319i
$428$	6.67103	+	192.720i	0.0155865	+	0.450280i
$429$		0			0
$430$	48.2199	−	0.834320i	0.112139	−	0.00194028i
$431$		−	46.7851i		−	0.108550i	−0.998526	−	0.0542750i	$-0.982715\pi$
$431$		−	46.7851i		−	0.108550i	0.998526	−	0.0542750i	$-0.0172848\pi$
$432$		0			0
$433$	71.4224			0.164948			0.0824739	−	0.996593i	$-0.473718\pi$
$433$	71.4224			0.164948			0.0824739	+	0.996593i	$0.473718\pi$
$434$	−1.34838	−	77.9303i	−0.00310687	−	0.179563i
$435$		0			0
$436$	−357.302	+	12.3681i	−0.819500	+	0.0283672i
$437$	185.989			0.425605
$438$		0			0
$439$		−	0.829943i		−	0.00189053i	−1.00000		0.000945266i	$-0.999699\pi$
$439$		−	0.829943i		−	0.00189053i	1.00000		0.000945266i	$-0.000300887\pi$
$440$	833.466	−	43.2975i	1.89424	−	0.0984033i
$441$		0			0
$442$	−10.0062	−	578.311i	−0.0226384	−	1.30839i
$443$		−	770.065i		−	1.73830i	−0.494552	−	0.869148i	$-0.664668\pi$
$443$		−	770.065i		−	1.73830i	0.494552	−	0.869148i	$-0.335332\pi$
$444$		0			0
$445$	−246.981			−0.555014
$446$	521.008	−	9.01469i	1.16818	−	0.0202123i
$447$		0			0
$448$	−17.5454	−	168.417i	−0.0391638	−	0.375930i
$449$	80.0955			0.178386			0.0891932	−	0.996014i	$-0.471571\pi$
$449$	80.0955			0.178386			0.0891932	+	0.996014i	$0.471571\pi$
$450$		0			0
$451$		−	556.769i		−	1.23452i
$452$	373.643	−	12.9337i	0.826644	−	0.0286144i
$453$		0			0
$454$	−444.226	+	7.68617i	−0.978470	+	0.0169299i
$455$			235.205i			0.516934i
$456$		0			0
$457$	−178.912			−0.391493			−0.195747	−	0.980654i	$-0.562713\pi$
$457$	−178.912			−0.391493			−0.195747	+	0.980654i	$0.562713\pi$
$458$	−4.31736	−	249.524i	−0.00942656	−	0.544812i
$459$		0			0
$460$	25.3320	+	731.818i	0.0550696	+	1.59091i
$461$	320.864			0.696017			0.348009	−	0.937491i	$-0.386858\pi$
$461$	320.864			0.696017			0.348009	+	0.937491i	$0.386858\pi$
$462$		0			0
$463$			597.651i			1.29082i	0.763835	+	0.645411i	$0.223314\pi$
$463$			597.651i			1.29082i	−0.763835	+	0.645411i	$0.776686\pi$
$464$	−873.079	+	60.5161i	−1.88164	+	0.130423i
$465$		0			0
$466$	11.4982	+	664.542i	0.0246742	+	1.42606i
$467$		−	578.307i		−	1.23834i	−0.785255	−	0.619172i	$-0.787468\pi$
$467$		−	578.307i		−	1.23834i	0.785255	−	0.619172i	$-0.212532\pi$
$468$		0			0
$469$	−252.472			−0.538320
$470$	345.624	−	5.98013i	0.735370	−	0.0127237i
$471$		0			0
$472$	−432.492	+	22.4674i	−0.916297	+	0.0476004i
$473$	63.5420			0.134338
$474$		0			0
$475$			93.2663i			0.196350i
$476$	−7.49386	−	216.491i	−0.0157434	−	0.454812i
$477$		0			0
$478$	570.084	−	9.86383i	1.19264	−	0.0206356i
$479$			543.921i			1.13554i	0.823189	+	0.567768i	$0.192193\pi$
$479$			543.921i			1.13554i	−0.823189	+	0.567768i	$0.807807\pi$
$480$		0			0
$481$	378.708			0.787336
$482$	−3.08744	−	178.440i	−0.00640547	−	0.370207i
$483$		0			0
$484$	615.253	−	21.2971i	1.27118	−	0.0440022i
$485$	−1081.87			−2.23066
$486$		0			0
$487$			25.1657i			0.0516750i	0.999666	+	0.0258375i	$0.00822524\pi$
$487$			25.1657i			0.0516750i	−0.999666	+	0.0258375i	$0.991775\pi$
$488$	−14.8244	−	285.366i	−0.0303778	−	0.584766i
$489$		0			0
$490$	1.52392	+	88.0754i	0.00311003	+	0.179746i
$491$			876.015i			1.78414i	0.451894	+	0.892072i	$0.350749\pi$
$491$			876.015i			1.78414i	−0.451894	+	0.892072i	$0.649251\pi$
$492$		0			0
$493$	−1119.60			−2.27100
$494$	180.612	−	3.12503i	0.365612	−	0.00632597i
$495$		0			0
$496$	−16.2963	−	235.110i	−0.0328554	−	0.474013i
$497$	−147.243			−0.296263
$498$		0			0
$499$		−	9.06767i		−	0.0181717i	−0.999959	−	0.00908584i	$-0.997108\pi$
$499$		−	9.06767i		−	0.0181717i	0.999959	−	0.00908584i	$-0.00289215\pi$
$500$	261.850	−	9.06397i	0.523699	−	0.0181279i
$501$		0			0
$502$	166.897	−	2.88772i	0.332465	−	0.00575244i
$503$		−	433.976i		−	0.862774i	−0.902167	−	0.431387i	$-0.858024\pi$
$503$		−	433.976i		−	0.862774i	0.902167	−	0.431387i	$-0.141976\pi$
$504$		0			0
$505$	−716.556			−1.41892
$506$	16.6907	+	964.646i	0.0329856	+	1.90642i
$507$		0			0
$508$	−28.8242	−	832.703i	−0.0567405	−	1.63918i
$509$	335.775			0.659675			0.329838	−	0.944038i	$-0.393006\pi$
$509$	335.775			0.659675			0.329838	+	0.944038i	$0.393006\pi$
$510$		0			0
$511$			345.208i			0.675553i
$512$	−79.3998	−	505.806i	−0.155078	−	0.987902i
$513$		0			0
$514$	−1.03321	−	59.7149i	−0.00201014	−	0.116177i
$515$			589.960i			1.14555i
$516$		0			0
$517$	455.448			0.880944
$518$	141.812	−	2.45369i	0.273768	−	0.00473685i
$519$		0			0
$520$	36.8958	+	710.235i	0.0709535	+	1.36584i
$521$	−540.822			−1.03805			−0.519023	−	0.854760i	$-0.673704\pi$
$521$	−540.822			−1.03805			−0.519023	+	0.854760i	$0.673704\pi$
$522$		0			0
$523$			337.109i			0.644568i	0.946643	+	0.322284i	$0.104451\pi$
$523$			337.109i			0.644568i	−0.946643	+	0.322284i	$0.895549\pi$
$524$	9.37780	+	270.916i	0.0178966	+	0.517015i
$525$		0			0
$526$	490.535	−	8.48745i	0.932577	−	0.0161358i
$527$		−	301.497i		−	0.572100i
$528$		0			0
$529$	−317.492			−0.600175
$530$	−4.72661	−	273.176i	−0.00891812	−	0.515427i
$531$		0			0
$532$	67.6122	−	2.34041i	0.127091	−	0.00439927i
$533$	474.449			0.890147
$534$		0			0
$535$		−	303.331i		−	0.566975i
$536$	−762.376	+	39.6045i	−1.42234	+	0.0738889i
$537$		0			0
$538$	−0.655458	−	37.8825i	−0.00121832	−	0.0704135i
$539$			116.062i			0.215328i
$540$		0			0
$541$	210.355			0.388827			0.194413	−	0.980920i	$-0.437720\pi$
$541$	210.355			0.388827			0.194413	+	0.980920i	$0.437720\pi$
$542$	−557.772	+	9.65079i	−1.02910	+	0.0178059i
$543$		0			0
$544$	−56.5890	−	652.549i	−0.104024	−	1.19954i
$545$	562.376			1.03188
$546$		0			0
$547$			228.588i			0.417894i	0.977927	+	0.208947i	$0.0670036\pi$
$547$			228.588i			0.417894i	−0.977927	+	0.208947i	$0.932996\pi$
$548$	−53.6187	+	1.85602i	−0.0978443	+	0.00338690i
$549$		0			0
$550$	−483.732	+	8.36973i	−0.879513	+	0.0152177i
$551$		−	349.664i		−	0.634599i
$552$		0			0
$553$	−41.3554			−0.0747837
$554$	7.13956	+	412.634i	0.0128873	+	0.744826i
$555$		0			0
$556$	−22.1934	−	641.145i	−0.0399161	−	1.15314i
$557$	−129.632			−0.232732			−0.116366	−	0.993206i	$-0.537125\pi$
$557$	−129.632			−0.232732			−0.116366	+	0.993206i	$0.537125\pi$
$558$		0			0
$559$			54.1471i			0.0968643i
$560$	18.4178	+	265.717i	0.0328889	+	0.474495i
$561$		0			0
$562$	−9.09192	−	525.471i	−0.0161778	−	0.935002i
$563$		−	718.440i		−	1.27609i	−0.769998	−	0.638046i	$-0.779743\pi$
$563$		−	718.440i		−	1.27609i	0.769998	−	0.638046i	$-0.220257\pi$
$564$		0			0
$565$	−588.096			−1.04088
$566$	−1086.85	+	18.8052i	−1.92024	+	0.0332247i
$567$		0			0
$568$	−444.620	+	23.0974i	−0.782782	+	0.0406645i
$569$	−736.365			−1.29414			−0.647069	−	0.762431i	$-0.724006\pi$
$569$	−736.365			−1.29414			−0.647069	+	0.762431i	$0.724006\pi$
$570$		0			0
$571$			161.022i			0.282001i	0.990010	+	0.141000i	$0.0450319\pi$
$571$			161.022i			0.282001i	−0.990010	+	0.141000i	$0.954968\pi$
$572$	32.4163	+	936.478i	0.0566719	+	1.63720i
$573$		0			0
$574$	177.663	−	3.07400i	0.309518	−	0.00535540i
$575$		−	424.483i		−	0.738230i
$576$		0			0
$577$	748.940			1.29799			0.648995	−	0.760793i	$-0.275190\pi$
$577$	748.940			1.29799			0.648995	+	0.760793i	$0.275190\pi$
$578$	−4.49683	−	259.896i	−0.00777998	−	0.449647i
$579$		0			0
$580$	1375.83	−	47.6247i	2.37213	−	0.0821116i
$581$	130.831			0.225183
$582$		0			0
$583$		−	359.980i		−	0.617461i
$584$	54.1516	+	1042.40i	0.0927253	+	1.78494i
$585$		0			0
$586$	0.664084	+	38.3810i	0.00113325	+	0.0654966i
$587$		−	261.696i		−	0.445819i	−0.974839	−	0.222910i	$-0.928444\pi$
$587$		−	261.696i		−	0.445819i	0.974839	−	0.222910i	$-0.0715555\pi$
$588$		0			0
$589$	94.1605			0.159865
$590$	681.130	−	11.7852i	1.15446	−	0.0199749i
$591$		0			0
$592$	427.837	−	29.6548i	0.722698	−	0.0500926i
$593$	284.492			0.479750			0.239875	−	0.970804i	$-0.422894\pi$
$593$	284.492			0.479750			0.239875	+	0.970804i	$0.422894\pi$
$594$		0			0
$595$			340.746i			0.572682i
$596$	−522.984	+	18.1032i	−0.877489	+	0.0303745i
$597$		0			0
$598$	−822.020	+	14.2229i	−1.37462	+	0.0237842i
$599$		−	358.608i		−	0.598678i	−0.954147	−	0.299339i	$-0.903234\pi$
$599$		−	358.608i		−	0.598678i	0.954147	−	0.299339i	$-0.0967662\pi$
$600$		0			0
$601$	−404.112			−0.672399			−0.336200	−	0.941791i	$-0.609142\pi$
$601$	−404.112			−0.672399			−0.336200	+	0.941791i	$0.609142\pi$
$602$	0.350825	+	20.2761i	0.000582765	+	0.0336812i
$603$		0			0
$604$	24.3344	+	702.997i	0.0402887	+	1.16390i
$605$	−968.378			−1.60063
$606$		0			0
$607$		−	608.215i		−	1.00200i	−0.865447	−	0.501001i	$-0.832965\pi$
$607$		−	608.215i		−	1.00200i	0.865447	−	0.501001i	$-0.167035\pi$
$608$	203.798	−	17.6733i	0.335194	−	0.0290679i
$609$		0			0
$610$	7.77607	+	449.421i	0.0127476	+	0.736756i
$611$			388.108i			0.635202i
$612$		0			0
$613$	−741.906			−1.21029			−0.605143	−	0.796117i	$-0.706884\pi$
$613$	−741.906			−1.21029			−0.605143	+	0.796117i	$0.706884\pi$
$614$	1086.08	−	18.7918i	1.76886	−	0.0306055i
$615$		0			0
$616$	18.2062	+	350.466i	0.0295556	+	0.568938i
$617$	−788.372			−1.27775			−0.638875	−	0.769310i	$-0.720600\pi$
$617$	−788.372			−1.27775			−0.638875	+	0.769310i	$0.720600\pi$
$618$		0			0
$619$			1053.85i			1.70251i	0.524754	+	0.851254i	$0.324157\pi$
$619$			1053.85i			1.70251i	−0.524754	+	0.851254i	$0.675843\pi$
$620$	12.8248	+	370.496i	0.0206852	+	0.597575i
$621$		0			0
$622$	−366.253	+	6.33707i	−0.588832	+	0.0101882i
$623$		−	103.854i		−	0.166699i
$624$		0			0
$625$	−776.883			−1.24301
$626$	−17.7793	−	1027.56i	−0.0284014	−	1.64147i
$627$		0			0
$628$	668.398	−	23.1367i	1.06433	−	0.0368419i
$629$	548.642			0.872245
$630$		0			0
$631$			729.494i			1.15609i	0.816004	+	0.578046i	$0.196185\pi$
$631$			729.494i			1.15609i	−0.816004	+	0.578046i	$0.803815\pi$
$632$	−124.879	+	6.48728i	−0.197593	+	0.0102647i
$633$		0			0
$634$	−19.3665	−	1119.30i	−0.0305465	−	1.76545i
$635$			1310.63i			2.06399i
$636$		0			0
$637$	−98.9018			−0.155262
$638$	1813.56	−	31.3789i	2.84256	−	0.0491832i
$639$		0			0
$640$	97.2973	+	799.482i	0.152027	+	1.24919i
$641$	−258.186			−0.402787			−0.201393	−	0.979510i	$-0.564547\pi$
$641$	−258.186			−0.402787			−0.201393	+	0.979510i	$0.564547\pi$
$642$		0			0
$643$		−	844.440i		−	1.31328i	−0.754203	−	0.656641i	$-0.771977\pi$
$643$		−	844.440i		−	1.31328i	0.754203	−	0.656641i	$-0.228023\pi$
$644$	−307.723	+	10.6519i	−0.477831	+	0.0165402i
$645$		0			0
$646$	261.656	−	4.52729i	0.405041	−	0.00700819i
$647$			94.5538i			0.146142i	0.997327	+	0.0730709i	$0.0232799\pi$
$647$			94.5538i			0.146142i	−0.997327	+	0.0730709i	$0.976720\pi$
$648$		0			0
$649$	897.563			1.38299
$650$	−7.13224	−	412.211i	−0.0109727	−	0.634170i
$651$		0			0
$652$	30.5250	+	881.838i	0.0468174	+	1.35251i
$653$	239.621			0.366954			0.183477	−	0.983024i	$-0.441265\pi$
$653$	239.621			0.366954			0.183477	+	0.983024i	$0.441265\pi$
$654$		0			0
$655$		−	426.408i		−	0.651005i
$656$	535.997	−	37.1518i	0.817069	−	0.0566338i
$657$		0			0
$658$	2.51459	+	145.332i	0.00382157	+	0.220869i
$659$			150.618i			0.228555i	0.993449	+	0.114278i	$0.0364553\pi$
$659$			150.618i			0.228555i	−0.993449	+	0.114278i	$0.963545\pi$
$660$		0			0
$661$	−575.893			−0.871246			−0.435623	−	0.900129i	$-0.643472\pi$
$661$	−575.893			−0.871246			−0.435623	+	0.900129i	$0.643472\pi$
$662$	−759.474	+	13.1407i	−1.14724	+	0.0198500i
$663$		0			0
$664$	395.063	−	20.5230i	0.594975	−	0.0309082i
$665$	−106.418			−0.160028
$666$		0			0
$667$			1591.42i			2.38594i
$668$	−8.94653	−	258.457i	−0.0133930	−	0.386912i
$669$		0			0
$670$	1200.66	−	20.7744i	1.79203	−	0.0310065i
$671$			592.227i			0.882604i
$672$		0			0
$673$	−614.833			−0.913571			−0.456785	−	0.889577i	$-0.650999\pi$
$673$	−614.833			−0.913571			−0.456785	+	0.889577i	$0.650999\pi$
$674$	4.06954	+	235.201i	0.00603789	+	0.348962i
$675$		0			0
$676$	−122.421	+	4.23763i	−0.181096	+	0.00626868i
$677$	308.666			0.455933			0.227966	−	0.973669i	$-0.426792\pi$
$677$	308.666			0.455933			0.227966	+	0.973669i	$0.426792\pi$
$678$		0			0
$679$		−	454.918i		−	0.669982i
$680$	53.4517	+	1028.93i	0.0786054	+	1.51313i
$681$		0			0
$682$	8.44998	+	488.370i	0.0123900	+	0.716085i
$683$			143.442i			0.210018i	0.994471	+	0.105009i	$0.0334871\pi$
$683$			143.442i			0.210018i	−0.994471	+	0.105009i	$0.966513\pi$
$684$		0			0
$685$	84.3932			0.123202
$686$	−37.0350	+	0.640794i	−0.0539868	+	0.000934103i
$687$		0			0
$688$	4.24000	+	61.1715i	0.00616279	+	0.0889120i
$689$	306.755			0.445218
$690$		0			0
$691$			366.656i			0.530616i	0.964164	+	0.265308i	$0.0854737\pi$
$691$			366.656i			0.530616i	−0.964164	+	0.265308i	$0.914526\pi$
$692$	948.015	−	32.8157i	1.36996	−	0.0474216i
$693$		0			0
$694$	−605.321	+	10.4735i	−0.872220	+	0.0150915i
$695$			1009.13i			1.45199i
$696$		0			0
$697$	687.343			0.986145
$698$	−2.87726	−	166.293i	−0.00412215	−	0.238242i
$699$		0			0
$700$	−5.34151	−	154.311i	−0.00763073	−	0.220444i
$701$	−125.995			−0.179736			−0.0898681	−	0.995954i	$-0.528645\pi$
$701$	−125.995			−0.179736			−0.0898681	+	0.995954i	$0.528645\pi$
$702$		0			0
$703$			171.347i			0.243736i
$704$	109.953	+	1055.43i	0.156183	+	1.49918i
$705$		0			0
$706$	−9.60064	−	554.873i	−0.0135986	−	0.785939i
$707$		−	301.306i		−	0.426175i
$708$		0			0
$709$	−159.688			−0.225230			−0.112615	−	0.993639i	$-0.535923\pi$
$709$	−159.688			−0.225230			−0.112615	+	0.993639i	$0.535923\pi$
$710$	700.230	−	12.1157i	0.986239	−	0.0170643i
$711$		0			0
$712$	−16.2912	−	313.601i	−0.0228809	−	0.440451i
$713$	−428.552			−0.601055
$714$		0			0
$715$		−	1473.97i		−	2.06150i
$716$	−14.2741	−	412.366i	−0.0199359	−	0.575930i
$717$		0			0
$718$	152.620	−	2.64069i	0.212563	−	0.00367785i
$719$			1368.60i			1.90348i	0.306899	+	0.951742i	$0.400708\pi$
$719$			1368.60i			1.90348i	−0.306899	+	0.951742i	$0.599292\pi$
$720$		0			0
$721$	−248.073			−0.344068
$722$	−11.0766	−	640.174i	−0.0153415	−	0.886668i
$723$		0			0
$724$	−174.176	+	6.02914i	−0.240575	+	0.00832755i
$725$	−798.036			−1.10074
$726$		0			0
$727$			510.747i			0.702540i	0.936274	+	0.351270i	$0.114250\pi$
$727$			510.747i			0.702540i	−0.936274	+	0.351270i	$0.885750\pi$
$728$	−298.648	+	15.5144i	−0.410231	+	0.0213110i
$729$		0			0
$730$	−28.4050	−	1641.68i	−0.0389109	−	2.24887i
$731$			78.4440i			0.107311i
$732$		0			0
$733$	−774.969			−1.05726			−0.528628	−	0.848853i	$-0.677293\pi$
$733$	−774.969			−1.05726			−0.528628	+	0.848853i	$0.677293\pi$
$734$	−352.754	+	6.10350i	−0.480592	+	0.00831539i
$735$		0			0
$736$	−927.544	+	80.4365i	−1.26025	+	0.109289i
$737$	1582.18			2.14679
$738$		0			0
$739$		−	1349.26i		−	1.82579i	−0.408194	−	0.912895i	$-0.633841\pi$
$739$		−	1349.26i		−	1.82579i	0.408194	−	0.912895i	$-0.366159\pi$
$740$	−674.203	+	23.3376i	−0.911085	+	0.0315374i
$741$		0			0
$742$	114.868	−	1.98750i	0.154809	−	0.00267857i
$743$		−	853.994i		−	1.14939i	−0.818369	−	0.574693i	$-0.805122\pi$
$743$		−	853.994i		−	1.14939i	0.818369	−	0.574693i	$-0.194878\pi$
$744$		0			0
$745$	823.151			1.10490
$746$	−1.99042	−	115.037i	−0.00266813	−	0.154205i
$747$		0			0
$748$	46.9622	+	1356.69i	0.0627837	+	1.81376i
$749$	127.548			0.170292
$750$		0			0
$751$		−	509.524i		−	0.678460i	−0.940703	−	0.339230i	$-0.889833\pi$
$751$		−	509.524i		−	0.678460i	0.940703	−	0.339230i	$-0.110167\pi$
$752$	30.3909	+	438.456i	0.0404135	+	0.583054i
$753$		0			0
$754$	26.7394	+	1545.42i	0.0354634	+	2.04962i
$755$		−	1106.48i		−	1.46554i
$756$		0			0
$757$	1373.83			1.81484			0.907418	−	0.420228i	$-0.138050\pi$
$757$	1373.83			1.81484			0.907418	+	0.420228i	$0.138050\pi$
$758$	−824.681	+	14.2690i	−1.08797	+	0.0188245i
$759$		0			0
$760$	−321.346	+	16.6935i	−0.422823	+	0.0219651i
$761$	1165.32			1.53130			0.765652	−	0.643255i	$-0.222417\pi$
$761$	1165.32			1.53130			0.765652	+	0.643255i	$0.222417\pi$
$762$		0			0
$763$			236.475i			0.309927i
$764$	−30.3476	−	876.713i	−0.0397220	−	1.14753i
$765$		0			0
$766$	1166.47	−	20.1828i	1.52281	−	0.0263483i
$767$			764.855i			0.997204i
$768$		0			0
$769$	−686.335			−0.892503			−0.446251	−	0.894908i	$-0.647241\pi$
$769$	−686.335			−0.892503			−0.446251	+	0.894908i	$0.647241\pi$
$770$	−9.55001	−	551.947i	−0.0124026	−	0.716814i
$771$		0			0
$772$	−37.5884	+	1.30113i	−0.0486896	+	0.00168540i
$773$	−244.058			−0.315729			−0.157864	−	0.987461i	$-0.550461\pi$
$773$	−244.058			−0.315729			−0.157864	+	0.987461i	$0.550461\pi$
$774$		0			0
$775$		−	214.902i		−	0.277293i
$776$	−71.3614	−	1373.69i	−0.0919606	−	1.77022i
$777$		0			0
$778$	2.23146	+	128.968i	0.00286820	+	0.165769i
$779$			214.664i			0.275564i
$780$		0			0
$781$	922.733			1.18148
$782$	−1190.88	+	20.6050i	−1.52286	+	0.0263491i
$783$		0			0
$784$	−111.732	+	7.74452i	−0.142515	+	0.00987822i
$785$	−1052.03			−1.34016
$786$		0			0
$787$		−	959.027i		−	1.21859i	−0.792945	−	0.609293i	$-0.791453\pi$
$787$		−	959.027i		−	1.21859i	0.792945	−	0.609293i	$-0.208547\pi$
$788$	1315.98	−	45.5530i	1.67003	−	0.0578083i
$789$		0			0
$790$	196.671	−	3.40288i	0.248950	−	0.00430744i
$791$		−	247.290i		−	0.312629i
$792$		0			0
$793$	−504.665			−0.636399
$794$	0.0242907	+	1.40389i	3.05928e−5	+	0.00176812i
$795$		0			0
$796$	8.71850	+	251.869i	0.0109529	+	0.316419i
$797$	−24.5322			−0.0307807			−0.0153903	−	0.999882i	$-0.504899\pi$
$797$	−24.5322			−0.0307807			−0.0153903	+	0.999882i	$0.504899\pi$
$798$		0			0
$799$			562.260i			0.703705i
$800$	−40.3357	−	465.127i	−0.0504196	−	0.581408i
$801$		0			0
$802$	2.12157	+	122.617i	0.00264535	+	0.152889i
$803$		−	2163.33i		−	2.69406i
$804$		0			0
$805$	484.342			0.601667
$806$	−416.163	+	7.20062i	−0.516331	+	0.00893377i
$807$		0			0
$808$	−47.2649	−	909.837i	−0.0584961	−	1.12604i
$809$	−673.148			−0.832074			−0.416037	−	0.909348i	$-0.636581\pi$
$809$	−673.148			−0.832074			−0.416037	+	0.909348i	$0.636581\pi$
$810$		0			0
$811$		−	386.219i		−	0.476226i	−0.971237	−	0.238113i	$-0.923471\pi$
$811$		−	386.219i		−	0.476226i	0.971237	−	0.238113i	$-0.0765288\pi$
$812$	20.0258	+	578.527i	0.0246623	+	0.712471i
$813$		0			0
$814$	−888.701	+	15.3767i	−1.09177	+	0.0188903i
$815$		−	1387.97i		−	1.70303i
$816$		0			0
$817$	−24.4989			−0.0299864
$818$	3.78830	+	218.946i	0.00463117	+	0.267660i
$819$		0			0
$820$	−844.646	+	29.2376i	−1.03006	+	0.0356556i
$821$	−5.93033			−0.00722330			−0.00361165	−	0.999993i	$-0.501150\pi$
$821$	−5.93033			−0.00722330			−0.00361165	+	0.999993i	$0.501150\pi$
$822$		0			0
$823$			365.439i			0.444033i	0.975043	+	0.222016i	$0.0712638\pi$
$823$			365.439i			0.444033i	−0.975043	+	0.222016i	$0.928736\pi$
$824$	−749.093	+	38.9144i	−0.909093	+	0.0472262i
$825$		0			0
$826$	4.95558	+	286.410i	0.00599949	+	0.346743i
$827$			1236.80i			1.49552i	0.663968	+	0.747761i	$0.268871\pi$
$827$			1236.80i			1.49552i	−0.663968	+	0.747761i	$0.731129\pi$
$828$		0			0
$829$	899.957			1.08559			0.542797	−	0.839864i	$-0.317365\pi$
$829$	899.957			1.08559			0.542797	+	0.839864i	$0.317365\pi$
$830$	−622.183	+	10.7653i	−0.749618	+	0.0129702i
$831$		0			0
$832$	−899.377	+	93.6958i	−1.08098	+	0.112615i
$833$	−143.281			−0.172006
$834$		0			0
$835$			406.799i			0.487184i
$836$	−423.709	+	14.6668i	−0.506829	+	0.0175440i
$837$		0			0
$838$	−625.161	+	10.8168i	−0.746016	+	0.0129079i
$839$			473.095i			0.563880i	0.959432	+	0.281940i	$0.0909779\pi$
$839$			473.095i			0.563880i	−0.959432	+	0.281940i	$0.909022\pi$
$840$		0			0
$841$	2150.91			2.55756
$842$	−21.9108	−	1266.35i	−0.0260224	−	1.50397i
$843$		0			0
$844$	−0.0971973	−	2.80794i	−0.000115163	−	0.00332694i
$845$	192.685			0.228029
$846$		0			0
$847$		−	407.195i		−	0.480750i
$848$	346.550	−	24.0205i	0.408667	−	0.0283261i
$849$		0			0
$850$	−10.3326	−	597.177i	−0.0121560	−	0.702562i
$851$		−	779.849i		−	0.916391i
$852$		0			0
$853$	−456.925			−0.535668			−0.267834	−	0.963465i	$-0.586308\pi$
$853$	−456.925			−0.535668			−0.267834	+	0.963465i	$0.586308\pi$
$854$	−188.978	+	3.26977i	−0.221286	+	0.00382877i
$855$		0			0
$856$	385.151	−	20.0081i	0.449943	−	0.0233739i
$857$	1460.48			1.70417			0.852087	−	0.523401i	$-0.175337\pi$
$857$	1460.48			1.70417			0.852087	+	0.523401i	$0.175337\pi$
$858$		0			0
$859$			329.072i			0.383087i	0.981484	+	0.191544i	$0.0613493\pi$
$859$			329.072i			0.383087i	−0.981484	+	0.191544i	$0.938651\pi$
$860$	−3.33678	−	96.3964i	−0.00387998	−	0.112089i
$861$		0			0
$862$	−93.5562	+	1.61875i	−0.108534	+	0.00187790i
$863$			528.421i			0.612307i	0.951982	+	0.306154i	$0.0990421\pi$
$863$			528.421i			0.612307i	−0.951982	+	0.306154i	$0.900958\pi$
$864$		0			0
$865$	−1492.13			−1.72501
$866$	−2.47119	−	142.823i	−0.00285357	−	0.164923i
$867$		0			0
$868$	−155.791	+	5.39272i	−0.179482	+	0.00621281i
$869$	259.164			0.298232
$870$		0			0
$871$			1348.25i			1.54793i
$872$	37.0950	+	714.069i	0.0425401	+	0.818887i
$873$		0			0
$874$	−6.43516	−	371.923i	−0.00736289	−	0.425541i
$875$		−	173.301i		−	0.198058i
$876$		0			0
$877$	532.559			0.607250			0.303625	−	0.952792i	$-0.401803\pi$
$877$	532.559			0.607250			0.303625	+	0.952792i	$0.401803\pi$
$878$	−1.65964	+	0.0287157i	−0.00189025	+	3.27058e-5i
$879$		0			0
$880$	−115.420	−	1665.18i	−0.131159	−	1.89225i
$881$	326.517			0.370621			0.185310	−	0.982680i	$-0.440671\pi$
$881$	326.517			0.370621			0.185310	+	0.982680i	$0.440671\pi$
$882$		0			0
$883$		−	31.0138i		−	0.0351232i	−0.999846	−	0.0175616i	$-0.994410\pi$
$883$		−	31.0138i		−	0.0351232i	0.999846	−	0.0175616i	$-0.00559032\pi$
$884$	−1156.10	+	40.0187i	−1.30781	+	0.0452700i
$885$		0			0
$886$	−1539.90	+	26.6440i	−1.73804	+	0.0300722i
$887$		−	414.448i		−	0.467247i	−0.972327	−	0.233623i	$-0.924942\pi$
$887$		−	414.448i		−	0.467247i	0.972327	−	0.233623i	$-0.0750583\pi$
$888$		0			0
$889$	−551.111			−0.619923
$890$	8.54547	+	493.889i	0.00960165	+	0.554931i
$891$		0			0
$892$	−36.0534	−	1041.55i	−0.0404186	−	1.16765i
$893$	−175.600			−0.196640
$894$		0			0
$895$			649.044i			0.725189i
$896$	−336.176	+	40.9127i	−0.375196	+	0.0456615i
$897$		0			0
$898$	−2.77127	−	160.167i	−0.00308605	−	0.178360i
$899$			805.688i			0.896204i
$900$		0			0
$901$	444.402			0.493232
$902$	−1113.37	+	19.2640i	−1.23434	+	0.0213570i
$903$		0			0
$904$	−38.7915	−	746.726i	−0.0429109	−	0.826025i
$905$	274.145			0.302923
$906$		0			0
$907$		−	388.080i		−	0.427872i	−0.976848	−	0.213936i	$-0.931372\pi$
$907$		−	388.080i		−	0.427872i	0.976848	−	0.213936i	$-0.0686283\pi$
$908$	30.7401	+	888.052i	0.0338547	+	0.978031i
$909$		0			0
$910$	470.339	−	8.13801i	0.516857	−	0.00894286i
$911$		−	891.807i		−	0.978932i	−0.872023	−	0.489466i	$-0.837192\pi$
$911$		−	891.807i		−	0.978932i	0.872023	−	0.489466i	$-0.162808\pi$
$912$		0			0
$913$	−819.886			−0.898013
$914$	6.19031	+	357.771i	0.00677277	+	0.391435i
$915$		0			0
$916$	−498.824	+	17.2669i	−0.544567	+	0.0188503i
$917$	179.301			0.195530
$918$		0			0
$919$		−	390.619i		−	0.425048i	−0.977156	−	0.212524i	$-0.931832\pi$
$919$		−	390.619i		−	0.425048i	0.977156	−	0.212524i	$-0.0681684\pi$
$920$	1462.54	−	75.9771i	1.58972	−	0.0825838i
$921$		0			0
$922$	−11.1018	−	641.632i	−0.0120410	−	0.695913i
$923$			786.304i			0.851900i
$924$		0			0
$925$	391.064			0.422771
$926$	1195.12	−	20.6785i	1.29063	−	0.0223310i
$927$		0			0
$928$	151.222	+	1743.80i	0.162955	+	1.87910i
$929$	241.450			0.259903			0.129952	−	0.991520i	$-0.458518\pi$
$929$	241.450			0.259903			0.129952	+	0.991520i	$0.458518\pi$
$930$		0			0
$931$		−	44.7481i		−	0.0480645i
$932$	1328.49	−	45.9859i	1.42542	−	0.0493410i
$933$		0			0
$934$	−1156.44	+	20.0092i	−1.23816	+	0.0214231i
$935$		−	2135.37i		−	2.28382i
$936$		0			0
$937$	−753.075			−0.803709			−0.401855	−	0.915703i	$-0.631634\pi$
$937$	−753.075			−0.803709			−0.401855	+	0.915703i	$0.631634\pi$
$938$	8.73545	+	504.869i	0.00931285	+	0.538240i
$939$		0			0
$940$	−23.9169	−	690.937i	−0.0254435	−	0.735040i
$941$	−1372.35			−1.45840			−0.729199	−	0.684302i	$-0.760107\pi$
$941$	−1372.35			−1.45840			−0.729199	+	0.684302i	$0.760107\pi$
$942$		0			0
$943$		−	977.000i		−	1.03606i
$944$	59.8922	+	864.077i	0.0634451	+	0.915336i
$945$		0			0
$946$	−2.19853	−	127.065i	−0.00232403	−	0.134318i
$947$		−	498.081i		−	0.525957i	−0.964802	−	0.262979i	$-0.915295\pi$
$947$		−	498.081i		−	0.525957i	0.964802	−	0.262979i	$-0.0847048\pi$
$948$		0			0
$949$	1843.48			1.94255
$950$	186.505	−	3.22698i	0.196321	−	0.00339682i
$951$		0			0
$952$	−432.657	+	22.4760i	−0.454472	+	0.0236092i
$953$	117.526			0.123322			0.0616610	−	0.998097i	$-0.480360\pi$
$953$	117.526			0.123322			0.0616610	+	0.998097i	$0.480360\pi$
$954$		0			0
$955$			1379.90i			1.44493i
$956$	−39.4494	−	1139.66i	−0.0412651	−	1.19211i
$957$		0			0
$958$	1087.68	−	18.8195i	1.13537	−	0.0196446i
$959$			35.4867i			0.0370038i
$960$		0			0
$961$	744.037			0.774233
$962$	−13.1032	−	757.304i	−0.0136208	−	0.787218i
$963$		0			0
$964$	−356.719	+	12.3479i	−0.370041	+	0.0128090i
$965$	59.1623			0.0613081
$966$		0			0
$967$		−	1016.54i		−	1.05123i	−0.850723	−	0.525614i	$-0.823836\pi$
$967$		−	1016.54i		−	1.05123i	0.850723	−	0.525614i	$-0.176164\pi$
$968$	−63.8753	−	1229.58i	−0.0659869	−	1.27023i
$969$		0			0
$970$	37.4324	+	2163.42i	0.0385901	+	2.23033i
$971$		−	760.606i		−	0.783323i	−0.920109	−	0.391661i	$-0.871900\pi$
$971$		−	760.606i		−	0.783323i	0.920109	−	0.391661i	$-0.128100\pi$
$972$		0			0
$973$	−424.332			−0.436107
$974$	50.3239	−	0.870724i	0.0516672	−	0.000893967i
$975$		0			0
$976$	−570.133	+	39.5179i	−0.584153	+	0.0404896i
$977$	1823.13			1.86605			0.933026	−	0.359809i	$-0.117158\pi$
$977$	1823.13			1.86605			0.933026	+	0.359809i	$0.117158\pi$
$978$		0			0
$979$			650.825i			0.664786i
$980$	176.072	−	6.09475i	0.179665	−	0.00621914i
$981$		0			0
$982$	1751.77	−	30.3098i	1.78388	−	0.0308654i
$983$			1400.51i			1.42473i	0.701809	+	0.712365i	$0.252376\pi$
$983$			1400.51i			1.42473i	−0.701809	+	0.712365i	$0.747624\pi$
$984$		0			0
$985$	−2071.29			−2.10284
$986$	38.7379	+	2238.87i	0.0392879	+	2.27066i
$987$		0			0
$988$	−12.4982	−	361.062i	−0.0126500	−	0.365448i
$989$	111.502			0.112742
$990$		0			0
$991$			508.288i			0.512904i	0.966557	+	0.256452i	$0.0825536\pi$
$991$			508.288i			0.512904i	−0.966557	+	0.256452i	$0.917446\pi$
$992$	−469.586	+	40.7225i	−0.473373	+	0.0410509i
$993$		0			0
$994$	5.09454	+	294.441i	0.00512529	+	0.296218i
$995$		−	396.430i		−	0.398422i
$996$		0			0
$997$	1357.91			1.36199			0.680997	−	0.732286i	$-0.261547\pi$
$997$	1357.91			1.36199			0.680997	+	0.732286i	$0.261547\pi$
$998$	−18.1326	+	0.313738i	−0.0181690	+	0.000314367i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.g.b.127.7		12
3.2	odd	2		84.3.g.a.43.6	yes	12
4.3	odd	2	inner	252.3.g.b.127.8		12
12.11	even	2		84.3.g.a.43.5	✓	12
21.20	even	2		588.3.g.d.295.6		12
24.5	odd	2		1344.3.m.e.127.5		12
24.11	even	2		1344.3.m.e.127.11		12
84.83	odd	2		588.3.g.d.295.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.g.a.43.5	✓	12	12.11	even	2
84.3.g.a.43.6	yes	12	3.2	odd	2
252.3.g.b.127.7		12	1.1	even	1	trivial
252.3.g.b.127.8		12	4.3	odd	2	inner
588.3.g.d.295.5		12	84.83	odd	2
588.3.g.d.295.6		12	21.20	even	2
1344.3.m.e.127.5		12	24.5	odd	2
1344.3.m.e.127.11		12	24.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0345996 - 1.99970i) q^{2} +(-3.99761 + 0.138378i) q^{4} +6.29204 q^{5} +2.64575i q^{7} +(0.415030 + 7.98923i) q^{8} +O(q^{10})\)	\(q+(-0.0345996 - 1.99970i) q^{2} +(-3.99761 + 0.138378i) q^{4} +6.29204 q^{5} +2.64575i q^{7} +(0.415030 + 7.98923i) q^{8} +(-0.217702 - 12.5822i) q^{10} -16.5803i q^{11} +14.1288 q^{13} +(5.29071 - 0.0915421i) q^{14} +(15.9617 - 1.10636i) q^{16} +20.4687 q^{17} +6.39258i q^{19} +(-25.1531 + 0.870679i) q^{20} +(-33.1556 + 0.573671i) q^{22} -29.0945i q^{23} +14.5898 q^{25} +(-0.488852 - 28.2534i) q^{26} +(-0.366113 - 10.5767i) q^{28} -54.6984 q^{29} -14.7296i q^{31} +(-2.76466 - 31.8803i) q^{32} +(-0.708210 - 40.9313i) q^{34} +16.6472i q^{35} +26.8040 q^{37} +(12.7833 - 0.221181i) q^{38} +(2.61139 + 50.2685i) q^{40} +33.5802 q^{41} +3.83239i q^{43} +(2.29434 + 66.2814i) q^{44} +(-58.1804 + 1.00666i) q^{46} +27.4693i q^{47} -7.00000 q^{49} +(-0.504801 - 29.1752i) q^{50} +(-56.4815 + 1.95512i) q^{52} +21.7113 q^{53} -104.324i q^{55} +(-21.1375 + 1.09807i) q^{56} +(1.89254 + 109.380i) q^{58} +54.1344i q^{59} -35.7188 q^{61} +(-29.4549 + 0.509641i) q^{62} +(-63.6555 + 6.63154i) q^{64} +88.8991 q^{65} +95.4255i q^{67} +(-81.8258 + 2.83241i) q^{68} +(33.2894 - 0.575986i) q^{70} +55.6524i q^{71} +130.476 q^{73} +(-0.927408 - 53.5999i) q^{74} +(-0.884592 - 25.5550i) q^{76} +43.8673 q^{77} +15.6309i q^{79} +(100.432 - 6.96126i) q^{80} +(-1.16186 - 67.1503i) q^{82} -49.4495i q^{83} +128.790 q^{85} +(7.66363 - 0.132599i) q^{86} +(132.464 - 6.88131i) q^{88} -39.2530 q^{89} +37.3813i q^{91} +(4.02604 + 116.309i) q^{92} +(54.9303 - 0.950427i) q^{94} +40.2224i q^{95} -171.943 q^{97} +(0.242198 + 13.9979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8	\( 12 q - 2 q^{2} + 2 q^{4} - 8 q^{5} + 10 q^{8} + 28 q^{10} - 24 q^{13} + 14 q^{14} - 14 q^{16} + 40 q^{17} + 20 q^{20} - 88 q^{22} + 180 q^{25} - 100 q^{26} + 14 q^{28} - 72 q^{29} - 142 q^{32} - 100 q^{34} - 88 q^{37} - 128 q^{38} - 28 q^{40} + 200 q^{41} + 40 q^{44} - 24 q^{46} - 84 q^{49} + 346 q^{50} - 364 q^{52} - 104 q^{53} - 98 q^{56} + 148 q^{58} + 104 q^{61} - 64 q^{62} - 70 q^{64} - 176 q^{65} - 188 q^{68} - 84 q^{70} + 312 q^{73} - 4 q^{74} + 432 q^{76} + 224 q^{77} + 564 q^{80} + 332 q^{82} + 352 q^{85} - 160 q^{86} + 328 q^{88} + 552 q^{89} - 232 q^{92} - 144 q^{94} - 264 q^{97} + 14 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 8 * q^5 + 10 * q^8 + 28 * q^10 - 24 * q^13 + 14 * q^14 - 14 * q^16 + 40 * q^17 + 20 * q^20 - 88 * q^22 + 180 * q^25 - 100 * q^26 + 14 * q^28 - 72 * q^29 - 142 * q^32 - 100 * q^34 - 88 * q^37 - 128 * q^38 - 28 * q^40 + 200 * q^41 + 40 * q^44 - 24 * q^46 - 84 * q^49 + 346 * q^50 - 364 * q^52 - 104 * q^53 - 98 * q^56 + 148 * q^58 + 104 * q^61 - 64 * q^62 - 70 * q^64 - 176 * q^65 - 188 * q^68 - 84 * q^70 + 312 * q^73 - 4 * q^74 + 432 * q^76 + 224 * q^77 + 564 * q^80 + 332 * q^82 + 352 * q^85 - 160 * q^86 + 328 * q^88 + 552 * q^89 - 232 * q^92 - 144 * q^94 - 264 * q^97 + 14 * q^98

Introduction

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