LMFDB - Embedded newform 252.4.b.f.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.b (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 $ x^12 - x^11 - 2x^10 - 6x^9 + 56x^7 - 448x^6 + 448x^5 - 3072x^3 - 8192x^2 - 32768x + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.4
Root			$2.16644 + 1.81839i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.f.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16644 + 1.81839i) q^{2} +(1.38692 - 7.87886i) q^{4} +4.47531i q^{5} +(-14.9825 - 10.8869i) q^{7} +(11.3222 + 19.5910i) q^{8} +O(q^{10})$	\(q+(-2.16644 + 1.81839i) q^{2} +(1.38692 - 7.87886i) q^{4} +4.47531i q^{5} +(-14.9825 - 10.8869i) q^{7} +(11.3222 + 19.5910i) q^{8} +(-8.13786 - 9.69549i) q^{10} +7.61561i q^{11} -13.3620i q^{13} +(52.2553 - 3.65824i) q^{14} +(-60.1529 - 21.8547i) q^{16} +55.3574i q^{17} +73.9099 q^{19} +(35.2603 + 6.20690i) q^{20} +(-13.8481 - 16.4988i) q^{22} -133.446i q^{23} +104.972 q^{25} +(24.2974 + 28.9480i) q^{26} +(-106.556 + 102.946i) q^{28} -23.3760 q^{29} +241.005 q^{31} +(170.058 - 62.0345i) q^{32} +(-100.661 - 119.928i) q^{34} +(48.7222 - 67.0514i) q^{35} +178.979 q^{37} +(-160.121 + 134.397i) q^{38} +(-87.6760 + 50.6702i) q^{40} +494.101i q^{41} +72.6137i q^{43} +(60.0023 + 10.5622i) q^{44} +(242.657 + 289.103i) q^{46} +59.7992 q^{47} +(105.951 + 326.226i) q^{49} +(-227.415 + 190.879i) q^{50} +(-105.277 - 18.5320i) q^{52} +569.477 q^{53} -34.0822 q^{55} +(43.6512 - 416.786i) q^{56} +(50.6428 - 42.5068i) q^{58} +59.5343 q^{59} +629.889i q^{61} +(-522.123 + 438.241i) q^{62} +(-255.617 + 443.626i) q^{64} +59.7992 q^{65} -599.636i q^{67} +(436.153 + 76.7762i) q^{68} +(16.3717 + 233.859i) q^{70} +407.701i q^{71} +680.155i q^{73} +(-387.746 + 325.453i) q^{74} +(102.507 - 582.326i) q^{76} +(82.9103 - 114.101i) q^{77} -1084.52i q^{79} +(97.8065 - 269.203i) q^{80} +(-898.469 - 1070.44i) q^{82} +935.224 q^{83} -247.741 q^{85} +(-132.040 - 157.313i) q^{86} +(-149.198 + 86.2251i) q^{88} -12.1437i q^{89} +(-145.471 + 200.197i) q^{91} +(-1051.40 - 185.079i) q^{92} +(-129.551 + 108.738i) q^{94} +330.770i q^{95} -1433.48i q^{97} +(-822.742 - 514.088i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) $ 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8	$ 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8} + 56 q^{10} - 69 q^{14} + 41 q^{16} - 84 q^{19} - 172 q^{20} - 182 q^{22} - 216 q^{25} - 300 q^{26} + 309 q^{28} - 200 q^{29} - 384 q^{31} + 159 q^{32} - 164 q^{34} - 84 q^{35} - 244 q^{37} - 268 q^{38} - 316 q^{40} - 190 q^{44} + 894 q^{46} - 280 q^{47} - 424 q^{49} + 1771 q^{50} - 796 q^{52} + 16 q^{53} + 212 q^{55} + 7 q^{56} - 570 q^{58} - 1168 q^{59} + 384 q^{62} + 2705 q^{64} - 280 q^{65} - 1552 q^{68} + 968 q^{70} - 1622 q^{74} - 788 q^{76} - 968 q^{77} + 3060 q^{80} - 2540 q^{82} + 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} + 1648 q^{91} - 4298 q^{92} + 4256 q^{94} - 97 q^{98}+O(q^{100}) $ 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8 + 56 * q^10 - 69 * q^14 + 41 * q^16 - 84 * q^19 - 172 * q^20 - 182 * q^22 - 216 * q^25 - 300 * q^26 + 309 * q^28 - 200 * q^29 - 384 * q^31 + 159 * q^32 - 164 * q^34 - 84 * q^35 - 244 * q^37 - 268 * q^38 - 316 * q^40 - 190 * q^44 + 894 * q^46 - 280 * q^47 - 424 * q^49 + 1771 * q^50 - 796 * q^52 + 16 * q^53 + 212 * q^55 + 7 * q^56 - 570 * q^58 - 1168 * q^59 + 384 * q^62 + 2705 * q^64 - 280 * q^65 - 1552 * q^68 + 968 * q^70 - 1622 * q^74 - 788 * q^76 - 968 * q^77 + 3060 * q^80 - 2540 * q^82 + 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 + 1648 * q^91 - 4298 * q^92 + 4256 * q^94 - 97 * 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 $

$2$	−2.16644	+	1.81839i	−0.765952	+	0.642898i
$2$	−2.16644	+	1.81839i	−0.765952	+	0.642898i
$3$		0			0
$3$		0			0
$4$	1.38692	−	7.87886i	0.173365	−	0.984858i
$5$			4.47531i			0.400284i	0.979767	+	0.200142i	$0.0641403\pi$
$5$			4.47531i			0.400284i	−0.979767	+	0.200142i	$0.935860\pi$
$6$		0			0
$7$	−14.9825	−	10.8869i	−0.808979	−	0.587837i
$7$	−14.9825	−	10.8869i	−0.808979	−	0.587837i
$8$	11.3222	+	19.5910i	0.500374	+	0.865810i
$9$		0			0
$10$	−8.13786	−	9.69549i	−0.257342	−	0.306598i
$11$			7.61561i			0.208745i	0.994538	+	0.104372i	$0.0332834\pi$
$11$			7.61561i			0.208745i	−0.994538	+	0.104372i	$0.966717\pi$
$12$		0			0
$13$		−	13.3620i		−	0.285074i	−0.989790	−	0.142537i	$-0.954474\pi$
$13$		−	13.3620i		−	0.285074i	0.989790	−	0.142537i	$-0.0455259\pi$
$14$	52.2553	−	3.65824i	0.997558	−	0.0698361i
$15$		0			0
$16$	−60.1529	−	21.8547i	−0.939889	−	0.341480i
$17$			55.3574i			0.789773i	0.918730	+	0.394886i	$0.129216\pi$
$17$			55.3574i			0.789773i	−0.918730	+	0.394886i	$0.870784\pi$
$18$		0			0
$19$	73.9099			0.892426			0.446213	−	0.894927i	$-0.352772\pi$
$19$	73.9099			0.892426			0.446213	+	0.894927i	$0.352772\pi$
$20$	35.2603	+	6.20690i	0.394223	+	0.0693952i
$21$		0			0
$22$	−13.8481	−	16.4988i	−0.134202	−	0.159888i
$23$		−	133.446i		−	1.20980i	−0.796301	−	0.604901i	$-0.793213\pi$
$23$		−	133.446i		−	1.20980i	0.796301	−	0.604901i	$-0.206787\pi$
$24$		0			0
$25$	104.972			0.839773
$26$	24.2974	+	28.9480i	0.183273	+	0.218353i
$27$		0			0
$28$	−106.556	+	102.946i	−0.719184	+	0.694819i
$29$	−23.3760			−0.149684			−0.0748418	−	0.997195i	$-0.523845\pi$
$29$	−23.3760			−0.149684			−0.0748418	+	0.997195i	$0.523845\pi$
$30$		0			0
$31$	241.005			1.39632			0.698159	−	0.715943i	$-0.254003\pi$
$31$	241.005			1.39632			0.698159	+	0.715943i	$0.254003\pi$
$32$	170.058	−	62.0345i	0.939446	−	0.342696i
$33$		0			0
$34$	−100.661	−	119.928i	−0.507743	−	0.604928i
$35$	48.7222	−	67.0514i	0.235302	−	0.323821i
$36$		0			0
$37$	178.979			0.795240			0.397620	−	0.917550i	$-0.369836\pi$
$37$	178.979			0.795240			0.397620	+	0.917550i	$0.369836\pi$
$38$	−160.121	+	134.397i	−0.683556	+	0.573739i
$39$		0			0
$40$	−87.6760	+	50.6702i	−0.346570	+	0.200291i
$41$			494.101i			1.88209i	0.338282	+	0.941045i	$0.390154\pi$
$41$			494.101i			1.88209i	−0.338282	+	0.941045i	$0.609846\pi$
$42$		0			0
$43$			72.6137i			0.257523i	0.991676	+	0.128761i	$0.0411001\pi$
$43$			72.6137i			0.257523i	−0.991676	+	0.128761i	$0.958900\pi$
$44$	60.0023	+	10.5622i	0.205584	+	0.0361890i
$45$		0			0
$46$	242.657	+	289.103i	0.777779	+	0.926650i
$47$	59.7992			0.185587			0.0927937	−	0.995685i	$-0.470420\pi$
$47$	59.7992			0.185587			0.0927937	+	0.995685i	$0.470420\pi$
$48$		0			0
$49$	105.951	+	326.226i	0.308895	+	0.951096i
$50$	−227.415	+	190.879i	−0.643226	+	0.539888i
$51$		0			0
$52$	−105.277	−	18.5320i	−0.280757	−	0.0494218i
$53$	569.477			1.47592			0.737960	−	0.674845i	$-0.235789\pi$
$53$	569.477			1.47592			0.737960	+	0.674845i	$0.235789\pi$
$54$		0			0
$55$	−34.0822			−0.0835572
$56$	43.6512	−	416.786i	0.104163	−	0.994560i
$57$		0			0
$58$	50.6428	−	42.5068i	0.114650	−	0.0962312i
$59$	59.5343			0.131368			0.0656839	−	0.997840i	$-0.479077\pi$
$59$	59.5343			0.131368			0.0656839	+	0.997840i	$0.479077\pi$
$60$		0			0
$61$			629.889i			1.32212i	0.750335	+	0.661058i	$0.229892\pi$
$61$			629.889i			1.32212i	−0.750335	+	0.661058i	$0.770108\pi$
$62$	−522.123	+	438.241i	−1.06951	+	0.897689i
$63$		0			0
$64$	−255.617	+	443.626i	−0.499253	+	0.866456i
$65$	59.7992			0.114110
$66$		0			0
$67$		−	599.636i		−	1.09339i	−0.837332	−	0.546695i	$-0.815886\pi$
$67$		−	599.636i		−	1.09339i	0.837332	−	0.546695i	$-0.184114\pi$
$68$	436.153	+	76.7762i	0.777814	+	0.136919i
$69$		0			0
$70$	16.3717	+	233.859i	0.0279543	+	0.399307i
$71$			407.701i			0.681482i	0.940157	+	0.340741i	$0.110678\pi$
$71$			407.701i			0.681482i	−0.940157	+	0.340741i	$0.889322\pi$
$72$		0			0
$73$			680.155i			1.09050i	0.838275	+	0.545248i	$0.183564\pi$
$73$			680.155i			1.09050i	−0.838275	+	0.545248i	$0.816436\pi$
$74$	−387.746	+	325.453i	−0.609116	+	0.511258i
$75$		0			0
$76$	102.507	−	582.326i	0.154715	−	0.878913i
$77$	82.9103	−	114.101i	0.122708	−	0.168870i
$78$		0			0
$79$		−	1084.52i		−	1.54454i	−0.635296	−	0.772269i	$-0.719122\pi$
$79$		−	1084.52i		−	1.54454i	0.635296	−	0.772269i	$-0.280878\pi$
$80$	97.8065	−	269.203i	0.136689	−	0.376223i
$81$		0			0
$82$	−898.469	−	1070.44i	−1.20999	−	1.44159i
$83$	935.224			1.23680			0.618398	−	0.785865i	$-0.287782\pi$
$83$	935.224			1.23680			0.618398	+	0.785865i	$0.287782\pi$
$84$		0			0
$85$	−247.741			−0.316133
$86$	−132.040	−	157.313i	−0.165561	−	0.197250i
$87$		0			0
$88$	−149.198	+	86.2251i	−0.180733	+	0.104450i
$89$		−	12.1437i		−	0.0144633i	−0.999974	−	0.00723163i	$-0.997698\pi$
$89$		−	12.1437i		−	0.0144633i	0.999974	−	0.00723163i	$-0.00230192\pi$
$90$		0			0
$91$	−145.471	+	200.197i	−0.167577	+	0.230619i
$92$	−1051.40	−	185.079i	−1.19148	−	0.209737i
$93$		0			0
$94$	−129.551	+	108.738i	−0.142151	+	0.119314i
$95$			330.770i			0.357224i
$96$		0			0
$97$		−	1433.48i		−	1.50049i	−0.661160	−	0.750245i	$-0.729936\pi$
$97$		−	1433.48i		−	1.50049i	0.661160	−	0.750245i	$-0.270064\pi$
$98$	−822.742	−	514.088i	−0.848056	−	0.529906i
$99$		0			0
$100$	145.587	−	827.057i	0.145587	−	0.827057i
$101$		−	1771.45i		−	1.74521i	−0.488427	−	0.872605i	$-0.662429\pi$
$101$		−	1771.45i		−	1.74521i	0.488427	−	0.872605i	$-0.337571\pi$
$102$		0			0
$103$	1667.56			1.59524			0.797618	−	0.603163i	$-0.206093\pi$
$103$	1667.56			1.59524			0.797618	+	0.603163i	$0.206093\pi$
$104$	261.776	−	151.287i	0.246820	−	0.142643i
$105$		0			0
$106$	−1233.74	+	1035.53i	−1.13048	+	0.948865i
$107$		−	1105.21i		−	0.998551i	−0.866443	−	0.499276i	$-0.833600\pi$
$107$		−	1105.21i		−	0.998551i	0.866443	−	0.499276i	$-0.166400\pi$
$108$		0			0
$109$	−353.412			−0.310557			−0.155279	−	0.987871i	$-0.549628\pi$
$109$	−353.412			−0.310557			−0.155279	+	0.987871i	$0.549628\pi$
$110$	73.8370	−	61.9747i	0.0640008	−	0.0537187i
$111$		0			0
$112$	663.312	+	982.316i	0.559617	+	0.828752i
$113$	−796.483			−0.663070			−0.331535	−	0.943443i	$-0.607566\pi$
$113$	−796.483			−0.663070			−0.331535	+	0.943443i	$0.607566\pi$
$114$		0			0
$115$	597.213			0.484264
$116$	−32.4207	+	184.177i	−0.0259499	+	0.147417i
$117$		0			0
$118$	−128.977	+	108.256i	−0.100621	+	0.0844561i
$119$	602.670	−	829.392i	0.464258	−	0.638910i
$120$		0			0
$121$	1273.00			0.956426
$122$	−1145.38	−	1364.62i	−0.849985	−	1.01268i
$123$		0			0
$124$	334.255	−	1898.85i	0.242072	−	1.37517i
$125$			1029.19i			0.736431i
$126$		0			0
$127$			1382.89i			0.966230i	0.875557	+	0.483115i	$0.160495\pi$
$127$			1382.89i			0.966230i	−0.875557	+	0.483115i	$0.839505\pi$
$128$	−252.905	−	1425.90i	−0.174639	−	0.984632i
$129$		0			0
$130$	−129.551	+	108.738i	−0.0874031	+	0.0733613i
$131$	−2930.78			−1.95468			−0.977342	−	0.211668i	$-0.932111\pi$
$131$	−2930.78			−1.95468			−0.977342	+	0.211668i	$0.932111\pi$
$132$		0			0
$133$	−1107.36	−	804.649i	−0.721954	−	0.524601i
$134$	1090.37	+	1299.07i	0.702938	+	0.837485i
$135$		0			0
$136$	−1084.51	+	626.765i	−0.683793	+	0.395181i
$137$	−1514.84			−0.944685			−0.472343	−	0.881415i	$-0.656591\pi$
$137$	−1514.84			−0.944685			−0.472343	+	0.881415i	$0.656591\pi$
$138$		0			0
$139$	−1121.88			−0.684582			−0.342291	−	0.939594i	$-0.611203\pi$
$139$	−1121.88			−0.684582			−0.342291	+	0.939594i	$0.611203\pi$
$140$	−460.715	−	476.871i	−0.278125	−	0.287878i
$141$		0			0
$142$	−741.359	−	883.260i	−0.438123	−	0.521982i
$143$	101.760			0.0595076
$144$		0			0
$145$		−	104.615i		−	0.0599159i
$146$	−1236.79	−	1473.52i	−0.701077	−	0.835267i
$147$		0			0
$148$	248.229	−	1410.15i	0.137867	−	0.783199i
$149$	201.082			0.110559			0.0552796	−	0.998471i	$-0.482395\pi$
$149$	201.082			0.110559			0.0552796	+	0.998471i	$0.482395\pi$
$150$		0			0
$151$			1803.92i			0.972192i	0.873906	+	0.486096i	$0.161579\pi$
$151$			1803.92i			0.972192i	−0.873906	+	0.486096i	$0.838421\pi$
$152$	836.820	+	1447.97i	0.446546	+	0.772671i
$153$		0			0
$154$	27.8597	+	397.956i	0.0145779	+	0.208235i
$155$			1078.57i			0.558923i
$156$		0			0
$157$			1163.09i			0.591241i	0.955305	+	0.295621i	$0.0955265\pi$
$157$			1163.09i			0.591241i	−0.955305	+	0.295621i	$0.904474\pi$
$158$	1972.09	+	2349.56i	0.992980	+	1.18304i
$159$		0			0
$160$	277.624	+	761.062i	0.137176	+	0.376045i
$161$	−1452.81	+	1999.36i	−0.711166	+	0.978705i
$162$		0			0
$163$		−	1394.86i		−	0.670271i	−0.942170	−	0.335135i	$-0.891218\pi$
$163$		−	1394.86i		−	0.670271i	0.942170	−	0.335135i	$-0.108782\pi$
$164$	3892.96	+	685.279i	1.85359	+	0.326288i
$165$		0			0
$166$	−2026.11	+	1700.60i	−0.947327	+	0.795134i
$167$	1161.55			0.538222			0.269111	−	0.963109i	$-0.413270\pi$
$167$	1161.55			0.538222			0.269111	+	0.963109i	$0.413270\pi$
$168$		0			0
$169$	2018.46			0.918733
$170$	536.717	−	450.490i	0.242143	−	0.203241i
$171$		0			0
$172$	572.113	+	100.709i	0.253623	+	0.0446454i
$173$		−	2133.98i		−	0.937825i	−0.883245	−	0.468913i	$-0.844646\pi$
$173$		−	2133.98i		−	0.937825i	0.883245	−	0.468913i	$-0.155354\pi$
$174$		0			0
$175$	−1572.74	−	1142.81i	−0.679359	−	0.493650i
$176$	166.437	−	458.101i	0.0712821	−	0.196197i
$177$		0			0
$178$	22.0820	+	26.3086i	0.00929839	+	0.0110782i
$179$			2551.23i			1.06530i	0.846337	+	0.532648i	$0.178803\pi$
$179$			2551.23i			1.06530i	−0.846337	+	0.532648i	$0.821197\pi$
$180$		0			0
$181$		−	715.321i		−	0.293754i	−0.989155	−	0.146877i	$-0.953078\pi$
$181$		−	715.321i		−	0.293754i	0.989155	−	0.146877i	$-0.0469221\pi$
$182$	−48.8814	−	698.236i	−0.0199084	−	0.284378i
$183$		0			0
$184$	2614.35	−	1510.90i	1.04746	−	0.605353i
$185$			800.985i			0.318322i
$186$		0			0
$187$	−421.580			−0.164861
$188$	82.9367	−	471.149i	0.0321743	−	0.182777i
$189$		0			0
$190$	−601.468	−	716.593i	−0.229658	−	0.273616i
$191$		−	2766.30i		−	1.04797i	−0.851727	−	0.523986i	$-0.824444\pi$
$191$		−	2766.30i		−	1.04797i	0.851727	−	0.523986i	$-0.175556\pi$
$192$		0			0
$193$	1182.88			0.441169			0.220584	−	0.975368i	$-0.429204\pi$
$193$	1182.88			0.441169			0.220584	+	0.975368i	$0.429204\pi$
$194$	2606.62	+	3105.54i	0.964662	+	1.14930i
$195$		0			0
$196$	2717.23	−	382.325i	0.990246	−	0.139331i
$197$	4748.28			1.71726			0.858631	−	0.512593i	$-0.171315\pi$
$197$	4748.28			1.71726			0.858631	+	0.512593i	$0.171315\pi$
$198$		0			0
$199$	−918.553			−0.327209			−0.163604	−	0.986526i	$-0.552312\pi$
$199$	−918.553			−0.327209			−0.163604	+	0.986526i	$0.552312\pi$
$200$	1188.51	+	2056.50i	0.420200	+	0.727083i
$201$		0			0
$202$	3221.19	+	3837.75i	1.12199	+	1.33675i
$203$	350.232	+	254.493i	0.121091	+	0.0879895i
$204$		0			0
$205$	−2211.26			−0.753370
$206$	−3612.66	+	3032.27i	−1.22187	+	1.02557i
$207$		0			0
$208$	−292.023	+	803.764i	−0.0973468	+	0.267938i
$209$			562.869i			0.186289i
$210$		0			0
$211$			4595.79i			1.49946i	0.661742	+	0.749732i	$0.269818\pi$
$211$			4595.79i			1.49946i	−0.661742	+	0.749732i	$0.730182\pi$
$212$	789.819	−	4486.83i	0.255873	−	1.45357i
$213$		0			0
$214$	2009.71	+	2394.38i	0.641966	+	0.764842i
$215$	−324.969			−0.103082
$216$		0			0
$217$	−3610.86	−	2623.80i	−1.12959	−	0.820807i
$218$	765.646	−	642.641i	0.237872	−	0.199657i
$219$		0			0
$220$	−47.2693	+	268.529i	−0.0144859	+	0.0822919i
$221$	739.686			0.225143
$222$		0			0
$223$	−2989.01			−0.897575			−0.448787	−	0.893639i	$-0.648144\pi$
$223$	−2989.01			−0.897575			−0.448787	+	0.893639i	$0.648144\pi$
$224$	−3223.26	−	921.970i	−0.961442	−	0.275008i
$225$		0			0
$226$	1725.53	−	1448.32i	0.507879	−	0.426286i
$227$	−1938.17			−0.566698			−0.283349	−	0.959017i	$-0.591446\pi$
$227$	−1938.17			−0.566698			−0.283349	+	0.959017i	$0.591446\pi$
$228$		0			0
$229$			5281.13i			1.52396i	0.647600	+	0.761980i	$0.275773\pi$
$229$			5281.13i			1.52396i	−0.647600	+	0.761980i	$0.724227\pi$
$230$	−1293.83	+	1085.97i	−0.370923	+	0.311332i
$231$		0			0
$232$	−264.667	−	457.961i	−0.0748977	−	0.129597i
$233$	1490.57			0.419101			0.209550	−	0.977798i	$-0.432800\pi$
$233$	1490.57			0.419101			0.209550	+	0.977798i	$0.432800\pi$
$234$		0			0
$235$			267.620i			0.0742876i
$236$	82.5692	−	469.062i	0.0227746	−	0.129379i
$237$		0			0
$238$	202.510	+	2892.72i	0.0551546	+	0.787845i
$239$			2036.18i			0.551085i	0.961289	+	0.275543i	$0.0888575\pi$
$239$			2036.18i			0.551085i	−0.961289	+	0.275543i	$0.911142\pi$
$240$		0			0
$241$		−	6102.51i		−	1.63111i	−0.578681	−	0.815554i	$-0.696432\pi$
$241$		−	6102.51i		−	1.63111i	0.578681	−	0.815554i	$-0.303568\pi$
$242$	−2757.88	+	2314.81i	−0.732576	+	0.614884i
$243$		0			0
$244$	4962.81	+	873.606i	1.30210	+	0.229209i
$245$	−1459.96	+	474.164i	−0.380708	+	0.123646i
$246$		0			0
$247$		−	987.586i		−	0.254407i
$248$	2728.70	+	4721.54i	0.698680	+	1.20894i
$249$		0			0
$250$	−1871.48	−	2229.69i	−0.473450	−	0.564071i
$251$	−1319.61			−0.331846			−0.165923	−	0.986139i	$-0.553060\pi$
$251$	−1319.61			−0.331846			−0.165923	+	0.986139i	$0.553060\pi$
$252$		0			0
$253$	1016.27			0.252540
$254$	−2514.62	−	2995.94i	−0.621187	−	0.740086i
$255$		0			0
$256$	3140.74	+	2629.25i	0.766783	+	0.641906i
$257$		−	4469.92i		−	1.08492i	−0.840080	−	0.542462i	$-0.817492\pi$
$257$		−	4469.92i		−	1.08492i	0.840080	−	0.542462i	$-0.182508\pi$
$258$		0			0
$259$	−2681.55	−	1948.52i	−0.643333	−	0.467472i
$260$	82.9367	−	471.149i	0.0197827	−	0.112382i
$261$		0			0
$262$	6349.36	−	5329.30i	1.49719	−	1.25666i
$263$			4673.64i			1.09577i	0.836552	+	0.547887i	$0.184568\pi$
$263$			4673.64i			1.09577i	−0.836552	+	0.547887i	$0.815432\pi$
$264$		0			0
$265$			2548.59i			0.590787i
$266$	3862.19	−	270.380i	0.890247	−	0.0623235i
$267$		0			0
$268$	−4724.45	−	831.647i	−1.07683	−	0.189556i
$269$			4633.12i			1.05013i	0.851061	+	0.525067i	$0.175960\pi$
$269$			4633.12i			1.05013i	−0.851061	+	0.525067i	$0.824040\pi$
$270$		0			0
$271$	3004.01			0.673359			0.336680	−	0.941619i	$-0.390696\pi$
$271$	3004.01			0.673359			0.336680	+	0.941619i	$0.390696\pi$
$272$	1209.82	−	3329.91i	0.269691	−	0.742299i
$273$		0			0
$274$	3281.82	−	2754.58i	0.723584	−	0.607336i
$275$			799.423i			0.175298i
$276$		0			0
$277$	−8852.78			−1.92026			−0.960130	−	0.279552i	$-0.909814\pi$
$277$	−8852.78			−1.92026			−0.960130	+	0.279552i	$0.909814\pi$
$278$	2430.49	−	2040.02i	0.524357	−	0.440116i
$279$		0			0
$280$	1865.25	+	195.353i	0.398106	+	0.0416948i
$281$	−378.664			−0.0803885			−0.0401943	−	0.999192i	$-0.512798\pi$
$281$	−378.664			−0.0803885			−0.0401943	+	0.999192i	$0.512798\pi$
$282$		0			0
$283$	−1515.73			−0.318378			−0.159189	−	0.987248i	$-0.550888\pi$
$283$	−1515.73			−0.318378			−0.159189	+	0.987248i	$0.550888\pi$
$284$	3212.22	+	565.449i	0.671163	+	0.118145i
$285$		0			0
$286$	−220.457	+	185.039i	−0.0455800	+	0.0382573i
$287$	5379.23	−	7402.88i	1.10636	−	1.52257i
$288$		0			0
$289$	1848.56			0.376259
$290$	190.231	+	226.642i	0.0385198	+	0.0458927i
$291$		0			0
$292$	5358.85	+	943.321i	1.07398	+	0.189054i
$293$		−	5745.66i		−	1.14561i	−0.819690	−	0.572807i	$-0.805854\pi$
$293$		−	5745.66i		−	1.14561i	0.819690	−	0.572807i	$-0.194146\pi$
$294$		0			0
$295$			266.434i			0.0525844i
$296$	2026.42	+	3506.38i	0.397917	+	0.688527i
$297$		0			0
$298$	−435.633	+	365.646i	−0.0846830	+	0.0710782i
$299$	−1783.11			−0.344883
$300$		0			0
$301$	790.537	−	1087.93i	0.151381	−	0.208331i
$302$	−3280.23	−	3908.08i	−0.625020	−	0.744652i
$303$		0			0
$304$	−4445.90	−	1615.28i	−0.838782	−	0.304745i
$305$	−2818.95			−0.529222
$306$		0			0
$307$	−591.984			−0.110053			−0.0550265	−	0.998485i	$-0.517524\pi$
$307$	−591.984			−0.110053			−0.0550265	+	0.998485i	$0.517524\pi$
$308$	−783.995	−	811.488i	−0.145040	−	0.150126i
$309$		0			0
$310$	−1961.27	−	2336.66i	−0.359330	−	0.428108i
$311$	−2628.66			−0.479284			−0.239642	−	0.970861i	$-0.577030\pi$
$311$	−2628.66			−0.479284			−0.239642	+	0.970861i	$0.577030\pi$
$312$		0			0
$313$		−	3781.59i		−	0.682902i	−0.939900	−	0.341451i	$-0.889082\pi$
$313$		−	3781.59i		−	0.682902i	0.939900	−	0.341451i	$-0.110918\pi$
$314$	−2114.96	−	2519.77i	−0.380108	−	0.452863i
$315$		0			0
$316$	−8544.81	−	1504.15i	−1.52115	−	0.267769i
$317$	−3073.59			−0.544575			−0.272288	−	0.962216i	$-0.587780\pi$
$317$	−3073.59			−0.544575			−0.272288	+	0.962216i	$0.587780\pi$
$318$		0			0
$319$		−	178.023i		−	0.0312457i
$320$	−1985.36	−	1143.97i	−0.346829	−	0.199843i
$321$		0			0
$322$	−488.178	−	6973.27i	−0.0844878	−	1.20685i
$323$			4091.46i			0.704814i
$324$		0			0
$325$		−	1402.63i		−	0.239397i
$326$	2536.40	+	3021.89i	0.430915	+	0.513395i
$327$		0			0
$328$	−9679.96	+	5594.30i	−1.62953	+	0.941748i
$329$	−895.942	−	651.027i	−0.150136	−	0.109095i
$330$		0			0
$331$			6921.62i			1.14939i	0.818369	+	0.574693i	$0.194878\pi$
$331$			6921.62i			1.14939i	−0.818369	+	0.574693i	$0.805122\pi$
$332$	1297.08	−	7368.50i	0.214417	−	1.21807i
$333$		0			0
$334$	−2516.42	+	2112.14i	−0.412252	+	0.346022i
$335$	2683.56			0.437667
$336$		0			0
$337$	8596.94			1.38963			0.694815	−	0.719189i	$-0.255486\pi$
$337$	8596.94			1.38963			0.694815	+	0.719189i	$0.255486\pi$
$338$	−4372.86	+	3670.34i	−0.703705	+	0.590651i
$339$		0			0
$340$	−343.597	+	1951.92i	−0.0548064	+	0.311346i
$341$			1835.40i			0.291474i
$342$		0			0
$343$	1964.17	−	6041.16i	0.309200	−	0.950997i
$344$	−1422.58	+	822.143i	−0.222966	+	0.128858i
$345$		0			0
$346$	3880.41	+	4623.15i	0.602926	+	0.718329i
$347$			4939.05i			0.764098i	0.924142	+	0.382049i	$0.124781\pi$
$347$			4939.05i			0.764098i	−0.924142	+	0.382049i	$0.875219\pi$
$348$		0			0
$349$			195.755i			0.0300244i	0.999887	+	0.0150122i	$0.00477872\pi$
$349$			195.755i			0.0300244i	−0.999887	+	0.0150122i	$0.995221\pi$
$350$	5485.32	−	384.011i	0.837722	−	0.0586464i
$351$		0			0
$352$	472.431	+	1295.09i	0.0715359	+	0.196105i
$353$			837.552i			0.126284i	0.998005	+	0.0631422i	$0.0201122\pi$
$353$			837.552i			0.126284i	−0.998005	+	0.0631422i	$0.979888\pi$
$354$		0			0
$355$	−1824.59			−0.272786
$356$	−95.6785	−	16.8423i	−0.0142442	−	0.00250742i
$357$		0			0
$358$	−4639.13	−	5527.09i	−0.684876	−	0.815965i
$359$		−	5984.33i		−	0.879779i	−0.898052	−	0.439890i	$-0.855018\pi$
$359$		−	5984.33i		−	0.879779i	0.898052	−	0.439890i	$-0.144982\pi$
$360$		0			0
$361$	−1396.32			−0.203576
$362$	1300.73	+	1549.70i	0.188853	+	0.225001i
$363$		0			0
$364$	1375.56	+	1423.80i	0.198075	+	0.205021i
$365$	−3043.91			−0.436508
$366$		0			0
$367$	3550.58			0.505010			0.252505	−	0.967596i	$-0.418746\pi$
$367$	3550.58			0.505010			0.252505	+	0.967596i	$0.418746\pi$
$368$	−2916.42	+	8027.17i	−0.413123	+	1.13708i
$369$		0			0
$370$	−1456.50	−	1735.28i	−0.204648	−	0.243819i
$371$	−8532.20	−	6199.84i	−1.19399	−	0.867600i
$372$		0			0
$373$	4863.68			0.675152			0.337576	−	0.941298i	$-0.390393\pi$
$373$	4863.68			0.675152			0.337576	+	0.941298i	$0.390393\pi$
$374$	913.328	−	766.597i	0.126276	−	0.105989i
$375$		0			0
$376$	677.056	+	1171.53i	0.0928630	+	0.160683i
$377$			312.351i			0.0426708i
$378$		0			0
$379$			6050.73i			0.820066i	0.912071	+	0.410033i	$0.134483\pi$
$379$			6050.73i			0.820066i	−0.912071	+	0.410033i	$0.865517\pi$
$380$	2606.09	+	458.751i	0.351815	+	0.0619301i
$381$		0			0
$382$	5030.22	+	5993.03i	0.673739	+	0.802697i
$383$	3136.38			0.418437			0.209219	−	0.977869i	$-0.432908\pi$
$383$	3136.38			0.418437			0.209219	+	0.977869i	$0.432908\pi$
$384$		0			0
$385$	510.637	+	371.049i	0.0675960	+	0.0491180i
$386$	−2562.64	+	2150.94i	−0.337914	+	0.283626i
$387$		0			0
$388$	−11294.2	−	1988.12i	−1.47777	−	0.260132i
$389$	4086.79			0.532669			0.266335	−	0.963881i	$-0.414187\pi$
$389$	4086.79			0.532669			0.266335	+	0.963881i	$0.414187\pi$
$390$		0			0
$391$	7387.23			0.955469
$392$	−5191.51	+	5769.27i	−0.668905	+	0.743348i
$393$		0			0
$394$	−10286.9	+	8634.22i	−1.31534	+	1.10402i
$395$	4853.58			0.618254
$396$		0			0
$397$		−	4953.21i		−	0.626182i	−0.949723	−	0.313091i	$-0.898635\pi$
$397$		−	4953.21i		−	0.626182i	0.949723	−	0.313091i	$-0.101365\pi$
$398$	1989.99	−	1670.29i	0.250626	−	0.210362i
$399$		0			0
$400$	−6314.35	−	2294.12i	−0.789293	−	0.286765i
$401$	−6920.41			−0.861818			−0.430909	−	0.902396i	$-0.641807\pi$
$401$	−6920.41			−0.861818			−0.430909	+	0.902396i	$0.641807\pi$
$402$		0			0
$403$		−	3220.32i		−	0.398053i
$404$	−13957.0	−	2456.86i	−1.71878	−	0.302558i
$405$		0			0
$406$	−1221.52	+	85.5151i	−0.149318	+	0.0104533i
$407$			1363.03i			0.166002i
$408$		0			0
$409$			15351.1i			1.85590i	0.372710	+	0.927948i	$0.378429\pi$
$409$			15351.1i			1.85590i	−0.372710	+	0.927948i	$0.621571\pi$
$410$	4790.55	−	4020.93i	0.577045	−	0.484340i
$411$		0			0
$412$	2312.77	−	13138.4i	0.276558	−	1.57108i
$413$	−891.973	−	648.143i	−0.106274	−	0.0772229i
$414$		0			0
$415$			4185.42i			0.495070i
$416$	−828.907	−	2272.32i	−0.0976935	−	0.267811i
$417$		0			0
$418$	−1023.51	−	1219.42i	−0.119765	−	0.142689i
$419$	−12665.4			−1.47672			−0.738358	−	0.674409i	$-0.764399\pi$
$419$	−12665.4			−1.47672			−0.738358	+	0.674409i	$0.764399\pi$
$420$		0			0
$421$	11040.6			1.27812			0.639059	−	0.769158i	$-0.279324\pi$
$421$	11040.6			1.27812			0.639059	+	0.769158i	$0.279324\pi$
$422$	−8356.93	−	9956.49i	−0.964002	−	1.14852i
$423$		0			0
$424$	6447.71	+	11156.6i	0.738511	+	1.27787i
$425$			5810.95i			0.663230i
$426$		0			0
$427$	6857.54	−	9437.32i	0.777189	−	1.06956i
$428$	−8707.82	−	1532.84i	−0.983431	−	0.173114i
$429$		0			0
$430$	704.025	−	590.920i	0.0789560	−	0.0662713i
$431$		−	11223.6i		−	1.25434i	−0.778881	−	0.627171i	$-0.784213\pi$
$431$		−	11223.6i		−	1.25434i	0.778881	−	0.627171i	$-0.215787\pi$
$432$		0			0
$433$			3804.05i			0.422196i	0.977465	+	0.211098i	$0.0677040\pi$
$433$			3804.05i			0.422196i	−0.977465	+	0.211098i	$0.932296\pi$
$434$	12593.8	−	881.655i	1.39291	−	0.0975133i
$435$		0			0
$436$	−490.154	+	2784.49i	−0.0538398	+	0.305855i
$437$		−	9862.99i		−	1.07966i
$438$		0			0
$439$	729.294			0.0792877			0.0396438	−	0.999214i	$-0.487378\pi$
$439$	729.294			0.0792877			0.0396438	+	0.999214i	$0.487378\pi$
$440$	−385.884	−	667.706i	−0.0418098	−	0.0723446i
$441$		0			0
$442$	−1602.49	+	1345.04i	−0.172449	+	0.144744i
$443$			3801.56i			0.407714i	0.979001	+	0.203857i	$0.0653478\pi$
$443$			3801.56i			0.407714i	−0.979001	+	0.203857i	$0.934652\pi$
$444$		0			0
$445$	54.3468			0.00578941
$446$	6475.52	−	5435.19i	0.687499	−	0.577049i
$447$		0			0
$448$	8659.50	−	3863.75i	0.913220	−	0.407466i
$449$	14008.3			1.47237			0.736185	−	0.676780i	$-0.236625\pi$
$449$	14008.3			1.47237			0.736185	+	0.676780i	$0.236625\pi$
$450$		0			0
$451$	−3762.88			−0.392876
$452$	−1104.66	+	6275.38i	−0.114953	+	0.653029i
$453$		0			0
$454$	4198.92	−	3524.34i	0.434064	−	0.364329i
$455$	−895.942	−	651.027i	−0.0923130	−	0.0670783i
$456$		0			0
$457$	−15859.0			−1.62331			−0.811656	−	0.584136i	$-0.801434\pi$
$457$	−15859.0			−1.62331			−0.811656	+	0.584136i	$0.801434\pi$
$458$	−9603.15	−	11441.3i	−0.979751	−	1.16728i
$459$		0			0
$460$	828.286	−	4705.36i	0.0839544	−	0.476931i
$461$			7619.91i			0.769836i	0.922951	+	0.384918i	$0.125770\pi$
$461$			7619.91i			0.769836i	−0.922951	+	0.384918i	$0.874230\pi$
$462$		0			0
$463$		−	5312.60i		−	0.533255i	−0.963800	−	0.266628i	$-0.914091\pi$
$463$		−	5312.60i		−	0.533255i	0.963800	−	0.266628i	$-0.0859094\pi$
$464$	1406.14	+	510.876i	0.140686	+	0.0511139i
$465$		0			0
$466$	−3229.23	+	2710.44i	−0.321011	+	0.269439i
$467$	17971.9			1.78082			0.890408	−	0.455163i	$-0.150419\pi$
$467$	17971.9			1.78082			0.890408	+	0.455163i	$0.150419\pi$
$468$		0			0
$469$	−6528.17	+	8984.05i	−0.642735	+	0.884530i
$470$	−486.637	−	579.782i	−0.0477594	−	0.0569008i
$471$		0			0
$472$	674.057	+	1166.34i	0.0657330	+	0.113740i
$473$	−552.997			−0.0537565
$474$		0			0
$475$	7758.44			0.749435
$476$	−5698.81	−	5898.65i	−0.548749	−	0.567992i
$477$		0			0
$478$	−3702.56	−	4411.26i	−0.354292	−	0.422105i
$479$	11971.4			1.14194			0.570970	−	0.820971i	$-0.306567\pi$
$479$	11971.4			1.14194			0.570970	+	0.820971i	$0.306567\pi$
$480$		0			0
$481$		−	2391.52i		−	0.226702i
$482$	11096.7	+	13220.7i	1.04864	+	1.24935i
$483$		0			0
$484$	1765.55	−	10029.8i	0.165811	−	0.941943i
$485$	6415.25			0.600622
$486$		0			0
$487$		−	16208.1i		−	1.50813i	−0.656802	−	0.754063i	$-0.728091\pi$
$487$		−	16208.1i		−	1.50813i	0.656802	−	0.754063i	$-0.271909\pi$
$488$	−12340.2	+	7131.71i	−1.14470	+	0.661552i
$489$		0			0
$490$	2300.71	−	3682.03i	0.212113	−	0.339463i
$491$			4844.19i			0.445245i	0.974905	+	0.222622i	$0.0714617\pi$
$491$			4844.19i			0.445245i	−0.974905	+	0.222622i	$0.928538\pi$
$492$		0			0
$493$		−	1294.04i		−	0.118216i
$494$	1795.82	+	2139.54i	0.163558	+	0.194864i
$495$		0			0
$496$	−14497.2	−	5267.10i	−1.31238	−	0.476814i
$497$	4438.60	−	6108.39i	0.400600	−	0.551305i
$498$		0			0
$499$		−	3372.90i		−	0.302589i	−0.988489	−	0.151294i	$-0.951656\pi$
$499$		−	3372.90i		−	0.302589i	0.988489	−	0.151294i	$-0.0483441\pi$
$500$	8108.88	+	1427.41i	0.725280	+	0.127671i
$501$		0			0
$502$	2858.86	−	2399.57i	0.254178	−	0.213343i
$503$	18916.6			1.67684			0.838420	−	0.545024i	$-0.183480\pi$
$503$	18916.6			1.67684			0.838420	+	0.545024i	$0.183480\pi$
$504$		0			0
$505$	7927.80			0.698579
$506$	−2201.69	+	1847.98i	−0.193433	+	0.162357i
$507$		0			0
$508$	10895.6	+	1917.95i	0.951599	+	0.167510i
$509$			14473.0i			1.26033i	0.776463	+	0.630163i	$0.217012\pi$
$509$			14473.0i			1.26033i	−0.776463	+	0.630163i	$0.782988\pi$
$510$		0			0
$511$	7404.78	−	10190.4i	0.641033	−	0.882188i
$512$	−11585.2	+	14.9924i	−0.999999	+	0.00129410i
$513$		0			0
$514$	8128.05	+	9683.80i	0.697496	+	0.831000i
$515$			7462.83i			0.638547i
$516$		0			0
$517$			455.407i			0.0387404i
$518$	9352.58	−	654.746i	0.793299	−	0.0555365i
$519$		0			0
$520$	677.056	+	1171.53i	0.0570978	+	0.0987979i
$521$			3641.31i			0.306197i	0.988211	+	0.153098i	$0.0489251\pi$
$521$			3641.31i			0.306197i	−0.988211	+	0.153098i	$0.951075\pi$
$522$		0			0
$523$	−16089.9			−1.34525			−0.672623	−	0.739985i	$-0.734832\pi$
$523$	−16089.9			−1.34525			−0.672623	+	0.739985i	$0.734832\pi$
$524$	−4064.76	+	23091.2i	−0.338874	+	1.92508i
$525$		0			0
$526$	−8498.49	−	10125.2i	−0.704471	−	0.839311i
$527$			13341.4i			1.10277i
$528$		0			0
$529$	−5640.87			−0.463620
$530$	−4634.32	−	5521.36i	−0.379815	−	0.452514i
$531$		0			0
$532$	−7875.53	+	7608.72i	−0.641819	+	0.620075i
$533$	6602.19			0.536534
$534$		0			0
$535$	4946.17			0.399704
$536$	11747.5	−	6789.17i	0.946668	−	0.547104i
$537$		0			0
$538$	−8424.81	−	10037.4i	−0.675129	−	0.804352i
$539$	−2484.41	+	806.882i	−0.198536	+	0.0644803i
$540$		0			0
$541$	18144.0			1.44190			0.720952	−	0.692985i	$-0.243705\pi$
$541$	18144.0			1.44190			0.720952	+	0.692985i	$0.243705\pi$
$542$	−6508.00	+	5462.45i	−0.515761	+	0.432901i
$543$		0			0
$544$	3434.07	+	9413.96i	0.270652	+	0.741949i
$545$		−	1581.63i		−	0.124311i
$546$		0			0
$547$			12520.2i			0.978653i	0.872101	+	0.489326i	$0.162757\pi$
$547$			12520.2i			0.978653i	−0.872101	+	0.489326i	$0.837243\pi$
$548$	−2100.97	+	11935.2i	−0.163775	+	0.930381i
$549$		0			0
$550$	−1453.66	−	1731.90i	−0.112699	−	0.134270i
$551$	−1727.72			−0.133582
$552$		0			0
$553$	−11807.1	+	16248.9i	−0.907936	+	1.24950i
$554$	19179.0	−	16097.8i	1.47083	−	1.23453i
$555$		0			0
$556$	−1555.96	+	8839.17i	−0.118683	+	0.674216i
$557$	−8252.03			−0.627737			−0.313869	−	0.949466i	$-0.601625\pi$
$557$	−8252.03			−0.627737			−0.313869	+	0.949466i	$0.601625\pi$
$558$		0			0
$559$	970.265			0.0734130
$560$	−4396.17	+	2968.53i	−0.331736	+	0.224006i
$561$		0			0
$562$	820.352	−	688.558i	0.0615738	−	0.0516816i
$563$	−18486.4			−1.38386			−0.691928	−	0.721967i	$-0.743238\pi$
$563$	−18486.4			−1.38386			−0.691928	+	0.721967i	$0.743238\pi$
$564$		0			0
$565$		−	3564.51i		−	0.265416i
$566$	3283.74	−	2756.19i	0.243862	−	0.204684i
$567$		0			0
$568$	−7987.29	+	4616.06i	−0.590034	+	0.340996i
$569$	22842.2			1.68294			0.841471	−	0.540302i	$-0.181690\pi$
$569$	22842.2			1.68294			0.841471	+	0.540302i	$0.181690\pi$
$570$		0			0
$571$			7404.29i			0.542662i	0.962486	+	0.271331i	$0.0874638\pi$
$571$			7404.29i			0.542662i	−0.962486	+	0.271331i	$0.912536\pi$
$572$	141.133	−	801.752i	0.0103165	−	0.0586065i
$573$		0			0
$574$	1807.54	+	25819.4i	0.131438	+	1.87749i
$575$		−	14008.1i		−	1.01596i
$576$		0			0
$577$		−	680.722i		−	0.0491141i	−0.999698	−	0.0245570i	$-0.992182\pi$
$577$		−	680.722i		−	0.0491141i	0.999698	−	0.0245570i	$-0.00781753\pi$
$578$	−4004.79	+	3361.40i	−0.288196	+	0.241896i
$579$		0			0
$580$	−824.248	−	145.093i	−0.0590086	−	0.0103873i
$581$	−14012.0	−	10181.7i	−1.00054	−	0.727035i
$582$		0			0
$583$			4336.92i			0.308090i
$584$	−13324.9	+	7700.83i	−0.944161	+	0.545655i
$585$		0			0
$586$	10447.8	+	12447.6i	0.736513	+	0.877485i
$587$	−21647.2			−1.52210			−0.761052	−	0.648691i	$-0.775317\pi$
$587$	−21647.2			−1.52210			−0.761052	+	0.648691i	$0.775317\pi$
$588$		0			0
$589$	17812.7			1.24611
$590$	−484.481	−	577.214i	−0.0338064	−	0.0402771i
$591$		0			0
$592$	−10766.1	−	3911.52i	−0.747438	−	0.271558i
$593$			14571.9i			1.00910i	0.863383	+	0.504549i	$0.168341\pi$
$593$			14571.9i			1.00910i	−0.863383	+	0.504549i	$0.831659\pi$
$594$		0			0
$595$	3711.79	+	2697.13i	0.255745	+	0.185835i
$596$	278.885	−	1584.30i	0.0191671	−	0.108885i
$597$		0			0
$598$	3863.00	−	3242.39i	0.264164	−	0.221724i
$599$		−	23843.1i		−	1.62638i	−0.581997	−	0.813191i	$-0.697729\pi$
$599$		−	23843.1i		−	1.62638i	0.581997	−	0.813191i	$-0.302271\pi$
$600$		0			0
$601$		−	3664.55i		−	0.248719i	−0.992237	−	0.124360i	$-0.960312\pi$
$601$		−	3664.55i		−	0.248719i	0.992237	−	0.124360i	$-0.0396876\pi$
$602$	265.638	+	3794.45i	0.0179844	+	0.256894i
$603$		0			0
$604$	14212.8	+	2501.89i	0.957470	+	0.168544i
$605$			5697.08i			0.382842i
$606$		0			0
$607$	−1982.67			−0.132577			−0.0662885	−	0.997801i	$-0.521116\pi$
$607$	−1982.67			−0.132577			−0.0662885	+	0.997801i	$0.521116\pi$
$608$	12569.0	−	4584.97i	0.838387	−	0.305831i
$609$		0			0
$610$	6107.09	−	5125.95i	0.405358	−	0.340235i
$611$		−	799.038i		−	0.0529061i
$612$		0			0
$613$	−10215.4			−0.673077			−0.336538	−	0.941670i	$-0.609256\pi$
$613$	−10215.4			−0.673077			−0.336538	+	0.941670i	$0.609256\pi$
$614$	1282.50	−	1076.46i	0.0842954	−	0.0707529i
$615$		0			0
$616$	3174.08	+	332.430i	0.207609	+	0.0217435i
$617$	10912.4			0.712022			0.356011	−	0.934482i	$-0.384137\pi$
$617$	10912.4			0.712022			0.356011	+	0.934482i	$0.384137\pi$
$618$		0			0
$619$	−6816.95			−0.442644			−0.221322	−	0.975201i	$-0.571037\pi$
$619$	−6816.95			−0.442644			−0.221322	+	0.975201i	$0.571037\pi$
$620$	8497.93	+	1495.89i	0.550460	+	0.0968977i
$621$		0			0
$622$	5694.82	−	4779.92i	0.367109	−	0.308131i
$623$	−132.207	+	181.943i	−0.00850204	+	0.0117005i
$624$		0			0
$625$	8515.49			0.544991
$626$	6876.41	+	8192.59i	0.439036	+	0.523070i
$627$		0			0
$628$	9163.85	+	1613.12i	0.582289	+	0.102501i
$629$			9907.79i			0.628059i
$630$		0			0
$631$			27480.9i			1.73375i	0.498527	+	0.866874i	$0.333875\pi$
$631$			27480.9i			1.73375i	−0.498527	+	0.866874i	$0.666125\pi$
$632$	21246.9	−	12279.2i	1.33728	−	0.772846i
$633$		0			0
$634$	6658.76	−	5588.99i	0.417118	−	0.350106i
$635$	−6188.84			−0.386766
$636$		0			0
$637$	4359.04	−	1415.72i	0.271132	−	0.0880579i
$638$	323.715	+	385.676i	0.0200878	+	0.0239327i
$639$		0			0
$640$	6381.35	−	1131.83i	0.394133	−	0.0699053i
$641$	−31255.0			−1.92589			−0.962946	−	0.269694i	$-0.913077\pi$
$641$	−31255.0			−1.92589			−0.962946	+	0.269694i	$0.913077\pi$
$642$		0			0
$643$	3994.76			0.245004			0.122502	−	0.992468i	$-0.460908\pi$
$643$	3994.76			0.245004			0.122502	+	0.992468i	$0.460908\pi$
$644$	13737.7	+	14219.5i	0.840594	+	0.870071i
$645$		0			0
$646$	−7439.87	−	8863.90i	−0.453123	−	0.539854i
$647$	12996.2			0.789697			0.394848	−	0.918746i	$-0.370797\pi$
$647$	12996.2			0.789697			0.394848	+	0.918746i	$0.370797\pi$
$648$		0			0
$649$			453.390i			0.0274223i
$650$	2550.53	+	3038.72i	0.153908	+	0.183367i
$651$		0			0
$652$	−10989.9	−	1934.56i	−0.660121	−	0.116201i
$653$	−18282.4			−1.09563			−0.547814	−	0.836600i	$-0.684540\pi$
$653$	−18282.4			−1.09563			−0.547814	+	0.836600i	$0.684540\pi$
$654$		0			0
$655$		−	13116.2i		−	0.782428i
$656$	10798.4	−	29721.6i	0.642695	−	1.76896i
$657$		0			0
$658$	3124.82	−	218.760i	0.185134	−	0.0129607i
$659$			19470.9i			1.15095i	0.817818	+	0.575477i	$0.195184\pi$
$659$			19470.9i			1.15095i	−0.817818	+	0.575477i	$0.804816\pi$
$660$		0			0
$661$		−	25139.3i		−	1.47928i	−0.673000	−	0.739642i	$-0.734995\pi$
$661$		−	25139.3i		−	1.47928i	0.673000	−	0.739642i	$-0.265005\pi$
$662$	−12586.2	−	14995.3i	−0.738937	−	0.880374i
$663$		0			0
$664$	10588.8	+	18322.0i	0.618860	+	1.07083i
$665$	3601.06	−	4955.76i	0.209989	−	0.288987i
$666$		0			0
$667$			3119.44i			0.181087i
$668$	1610.97	−	9151.66i	0.0933089	−	0.530072i
$669$		0			0
$670$	−5813.76	+	4879.75i	−0.335232	+	0.281375i
$671$	−4796.99			−0.275985
$672$		0			0
$673$	12277.8			0.703232			0.351616	−	0.936144i	$-0.385632\pi$
$673$	12277.8			0.703232			0.351616	+	0.936144i	$0.385632\pi$
$674$	−18624.8	+	15632.6i	−1.06439	+	0.893390i
$675$		0			0
$676$	2799.44	−	15903.1i	0.159276	−	0.904821i
$677$		−	8737.50i		−	0.496026i	−0.968757	−	0.248013i	$-0.920222\pi$
$677$		−	8737.50i		−	0.496026i	0.968757	−	0.248013i	$-0.0797776\pi$
$678$		0			0
$679$	−15606.1	+	21477.1i	−0.882044	+	1.21387i
$680$	−2804.97	−	4853.51i	−0.158185	−	0.273711i
$681$		0			0
$682$	−3337.48	−	3976.29i	−0.187388	−	0.223255i
$683$		−	21358.4i		−	1.19657i	−0.801284	−	0.598284i	$-0.795849\pi$
$683$		−	21358.4i		−	1.19657i	0.801284	−	0.598284i	$-0.204151\pi$
$684$		0			0
$685$		−	6779.40i		−	0.378142i
$686$	6729.92	+	16659.4i	0.374562	+	0.927202i
$687$		0			0
$688$	1586.95	−	4367.92i	0.0879388	−	0.242043i
$689$		−	7609.37i		−	0.420746i
$690$		0			0
$691$	−27244.9			−1.49992			−0.749961	−	0.661483i	$-0.769928\pi$
$691$	−27244.9			−1.49992			−0.749961	+	0.661483i	$0.769928\pi$
$692$	−16813.4	−	2959.66i	−0.923624	−	0.162586i
$693$		0			0
$694$	−8981.11	−	10700.1i	−0.491237	−	0.585262i
$695$		−	5020.78i		−	0.274027i
$696$		0			0
$697$	−27352.2			−1.48642
$698$	−355.959	−	424.092i	−0.0193026	−	0.0229973i
$699$		0			0
$700$	−11185.3	+	10806.4i	−0.603952	+	0.583490i
$701$	−9913.36			−0.534126			−0.267063	−	0.963679i	$-0.586053\pi$
$701$	−9913.36			−0.534126			−0.267063	+	0.963679i	$0.586053\pi$
$702$		0			0
$703$	13228.3			0.709693
$704$	−3378.48	−	1946.68i	−0.180868	−	0.104216i
$705$		0			0
$706$	−1522.99	−	1814.50i	−0.0811879	−	0.0967277i
$707$	−19285.6	+	26540.8i	−1.02590	+	1.41184i
$708$		0			0
$709$	−4521.15			−0.239486			−0.119743	−	0.992805i	$-0.538207\pi$
$709$	−4521.15			−0.239486			−0.119743	+	0.992805i	$0.538207\pi$
$710$	3952.86	−	3317.81i	0.208941	−	0.175374i
$711$		0			0
$712$	237.908	−	137.493i	0.0125224	−	0.00723703i
$713$		−	32161.2i		−	1.68927i
$714$		0			0
$715$			455.407i			0.0238199i
$716$	20100.8	+	3538.35i	1.04916	+	0.184685i
$717$		0			0
$718$	10881.8	+	12964.7i	0.565608	+	0.673869i
$719$	14246.5			0.738948			0.369474	−	0.929241i	$-0.379538\pi$
$719$	14246.5			0.738948			0.369474	+	0.929241i	$0.379538\pi$
$720$		0			0
$721$	−24984.2	−	18154.5i	−1.29051	−	0.937738i
$722$	3025.05	−	2539.06i	0.155929	−	0.130878i
$723$		0			0
$724$	−5635.91	−	992.093i	−0.289305	−	0.0509266i
$725$	−2453.82			−0.125700
$726$		0			0
$727$	−13979.5			−0.713164			−0.356582	−	0.934264i	$-0.616058\pi$
$727$	−13979.5			−0.713164			−0.356582	+	0.934264i	$0.616058\pi$
$728$	−5569.10	−	583.268i	−0.283523	−	0.0296942i
$729$		0			0
$730$	6594.44	−	5535.01i	0.334344	−	0.280630i
$731$	−4019.70			−0.203384
$732$		0			0
$733$		−	22386.3i		−	1.12805i	−0.825759	−	0.564023i	$-0.809253\pi$
$733$		−	22386.3i		−	1.12805i	0.825759	−	0.564023i	$-0.190747\pi$
$734$	−7692.11	+	6456.33i	−0.386813	+	0.324670i
$735$		0			0
$736$	−8278.27	−	22693.6i	−0.414594	−	1.13654i
$737$	4566.59			0.228240
$738$		0			0
$739$		−	19233.7i		−	0.957406i	−0.877977	−	0.478703i	$-0.841107\pi$
$739$		−	19233.7i		−	0.957406i	0.877977	−	0.478703i	$-0.158893\pi$
$740$	6310.85	+	1110.90i	0.313502	+	0.0551859i
$741$		0			0
$742$	29758.2	−	2083.28i	1.47232	−	0.103072i
$743$			10980.6i			0.542181i	0.962554	+	0.271090i	$0.0873842\pi$
$743$			10980.6i			0.542181i	−0.962554	+	0.271090i	$0.912616\pi$
$744$		0			0
$745$			899.906i			0.0442550i
$746$	−10536.9	+	8844.07i	−0.517134	+	0.434054i
$747$		0			0
$748$	−584.698	+	3321.57i	−0.0285811	+	0.162365i
$749$	−12032.3	+	16558.9i	−0.586985	+	0.807807i
$750$		0			0
$751$			3799.25i			0.184603i	0.995731	+	0.0923014i	$0.0294223\pi$
$751$			3799.25i			0.184603i	−0.995731	+	0.0923014i	$0.970578\pi$
$752$	−3597.09	−	1306.89i	−0.174432	−	0.0633743i
$753$		0			0
$754$	−567.976	−	676.690i	−0.0274330	−	0.0326838i
$755$	−8073.10			−0.389153
$756$		0			0
$757$	−16774.7			−0.805400			−0.402700	−	0.915332i	$-0.631928\pi$
$757$	−16774.7			−0.805400			−0.402700	+	0.915332i	$0.631928\pi$
$758$	−11002.6	−	13108.5i	−0.527218	−	0.628131i
$759$		0			0
$760$	−6480.12	+	3745.03i	−0.309288	+	0.178745i
$761$		−	37256.0i		−	1.77468i	−0.461119	−	0.887338i	$-0.652552\pi$
$761$		−	37256.0i		−	1.77468i	0.461119	−	0.887338i	$-0.347448\pi$
$762$		0			0
$763$	5295.00	+	3847.56i	0.251235	+	0.182557i
$764$	−21795.3	−	3836.64i	−1.03210	−	0.181682i
$765$		0			0
$766$	−6794.77	+	5703.15i	−0.320503	+	0.269012i
$767$		−	795.498i		−	0.0374495i
$768$		0			0
$769$		−	3677.87i		−	0.172468i	−0.996275	−	0.0862338i	$-0.972517\pi$
$769$		−	3677.87i		−	0.172468i	0.996275	−	0.0862338i	$-0.0274832\pi$
$770$	−1780.98	+	124.681i	−0.0833532	+	0.00583530i
$771$		0			0
$772$	1640.56	−	9319.75i	0.0764832	−	0.434488i
$773$		−	1000.27i		−	0.0465421i	−0.999729	−	0.0232711i	$-0.992592\pi$
$773$		−	1000.27i		−	0.0465421i	0.999729	−	0.0232711i	$-0.00740808\pi$
$774$		0			0
$775$	25298.7			1.17259
$776$	28083.3	−	16230.1i	1.29914	−	0.750805i
$777$		0			0
$778$	−8853.78	+	7431.37i	−0.407999	+	0.342452i
$779$			36519.0i			1.67963i
$780$		0			0
$781$	−3104.89			−0.142256
$782$	−16004.0	+	13432.9i	−0.731843	+	0.614269i
$783$		0			0
$784$	756.303	−	21939.0i	0.0344526	−	0.999406i
$785$	−5205.20			−0.236664
$786$		0			0
$787$	−29106.1			−1.31832			−0.659161	−	0.752002i	$-0.729088\pi$
$787$	−29106.1			−1.31832			−0.659161	+	0.752002i	$0.729088\pi$
$788$	6585.48	−	37411.0i	0.297713	−	1.69126i
$789$		0			0
$790$	−10515.0	+	8825.70i	−0.473553	+	0.397474i
$791$	11933.3	+	8671.23i	0.536410	+	0.389777i
$792$		0			0
$793$	8416.59			0.376900
$794$	9006.86	+	10730.8i	0.402571	+	0.479626i
$795$		0			0
$796$	−1273.96	+	7237.15i	−0.0567265	+	0.322254i
$797$		−	26054.3i		−	1.15796i	−0.815343	−	0.578978i	$-0.803452\pi$
$797$		−	26054.3i		−	1.15796i	0.815343	−	0.578978i	$-0.196548\pi$
$798$		0			0
$799$			3310.33i			0.146572i
$800$	17851.3	−	6511.86i	0.788922	−	0.287786i
$801$		0			0
$802$	14992.7	−	12584.0i	0.660111	−	0.554061i
$803$	−5179.80			−0.227635
$804$		0			0
$805$	−8947.75	−	6501.79i	−0.391760	−	0.284668i
$806$	5855.79	+	6976.62i	0.255907	+	0.304890i
$807$		0			0
$808$	34704.6	−	20056.7i	1.51102	−	0.873257i
$809$	29749.3			1.29287			0.646433	−	0.762971i	$-0.276260\pi$
$809$	29749.3			1.29287			0.646433	+	0.762971i	$0.276260\pi$
$810$		0			0
$811$	−2585.38			−0.111942			−0.0559709	−	0.998432i	$-0.517825\pi$
$811$	−2585.38			−0.111942			−0.0559709	+	0.998432i	$0.517825\pi$
$812$	2490.85	−	2406.47i	0.107650	−	0.104003i
$813$		0			0
$814$	−2478.52	−	2952.92i	−0.106722	−	0.127150i
$815$	6242.44			0.268299
$816$		0			0
$817$			5366.87i			0.229820i
$818$	−27914.2	−	33257.2i	−1.19315	−	1.42153i
$819$		0			0
$820$	−3066.84	+	17422.2i	−0.130608	+	0.741962i
$821$	3421.88			0.145462			0.0727311	−	0.997352i	$-0.476829\pi$
$821$	3421.88			0.145462			0.0727311	+	0.997352i	$0.476829\pi$
$822$		0			0
$823$		−	16719.6i		−	0.708150i	−0.935217	−	0.354075i	$-0.884796\pi$
$823$		−	16719.6i		−	0.708150i	0.935217	−	0.354075i	$-0.115204\pi$
$824$	18880.3	+	32669.2i	0.798214	+	1.38117i
$825$		0			0
$826$	3110.98	−	217.790i	0.131047	−	0.00917421i
$827$			2715.80i			0.114193i	0.998369	+	0.0570966i	$0.0181843\pi$
$827$			2715.80i			0.114193i	−0.998369	+	0.0570966i	$0.981816\pi$
$828$		0			0
$829$		−	2183.04i		−	0.0914599i	−0.998954	−	0.0457299i	$-0.985439\pi$
$829$		−	2183.04i		−	0.0914599i	0.998954	−	0.0457299i	$-0.0145614\pi$
$830$	−7610.72	−	9067.45i	−0.318279	−	0.379200i
$831$		0			0
$832$	5927.74	+	3415.56i	0.247004	+	0.142324i
$833$	−18059.0	+	5865.17i	−0.751150	+	0.243957i
$834$		0			0
$835$			5198.28i			0.215442i
$836$	4434.77	+	780.654i	0.183468	+	0.0322960i
$837$		0			0
$838$	27438.8	−	23030.6i	1.13109	−	0.949378i
$839$	18292.1			0.752696			0.376348	−	0.926478i	$-0.377180\pi$
$839$	18292.1			0.752696			0.376348	+	0.926478i	$0.377180\pi$
$840$		0			0
$841$	−23842.6			−0.977595
$842$	−23918.9	+	20076.2i	−0.978977	+	0.821699i
$843$		0			0
$844$	36209.6	+	6373.99i	1.47676	+	0.259955i
$845$			9033.22i			0.367754i
$846$		0			0
$847$	−19072.8	−	13859.0i	−0.773729	−	0.562222i
$848$	−34255.7	−	12445.8i	−1.38720	−	0.503996i
$849$		0			0
$850$	−10566.6	−	12589.1i	−0.426389	−	0.508002i
$851$		−	23884.0i		−	0.962083i
$852$		0			0
$853$			39811.6i			1.59804i	0.601307	+	0.799018i	$0.294647\pi$
$853$			39811.6i			1.59804i	−0.601307	+	0.799018i	$0.705353\pi$
$854$	2304.29	+	32915.1i	0.0923314	+	1.31889i
$855$		0			0
$856$	21652.3	−	12513.4i	0.864555	−	0.499649i
$857$		−	8630.80i		−	0.344017i	−0.985095	−	0.172008i	$-0.944974\pi$
$857$		−	8630.80i		−	0.344017i	0.985095	−	0.172008i	$-0.0550256\pi$
$858$		0			0
$859$	1012.27			0.0402073			0.0201036	−	0.999798i	$-0.493600\pi$
$859$	1012.27			0.0402073			0.0201036	+	0.999798i	$0.493600\pi$
$860$	−450.705	+	2560.38i	−0.0178708	+	0.101521i
$861$		0			0
$862$	20408.9	+	24315.2i	0.806414	+	0.960766i
$863$		−	18567.1i		−	0.732367i	−0.930543	−	0.366184i	$-0.880664\pi$
$863$		−	18567.1i		−	0.732367i	0.930543	−	0.366184i	$-0.119336\pi$
$864$		0			0
$865$	9550.24			0.375396
$866$	−6917.25	−	8241.25i	−0.271429	−	0.323382i
$867$		0			0
$868$	−25680.5	+	24810.5i	−1.00421	+	0.970188i
$869$	8259.31			0.322414
$870$		0			0
$871$	−8012.34			−0.311697
$872$	−4001.39	−	6923.71i	−0.155395	−	0.268884i
$873$		0			0
$874$	17934.8	+	21367.6i	0.694110	+	0.826967i
$875$	11204.7	−	15419.9i	0.432902	−	0.595758i
$876$		0			0
$877$	−2228.75			−0.0858149			−0.0429075	−	0.999079i	$-0.513662\pi$
$877$	−2228.75			−0.0858149			−0.0429075	+	0.999079i	$0.513662\pi$
$878$	−1579.97	+	1326.14i	−0.0607305	+	0.0509739i
$879$		0			0
$880$	2050.14	+	744.856i	0.0785345	+	0.0285331i
$881$			28095.1i			1.07440i	0.843454	+	0.537201i	$0.180518\pi$
$881$			28095.1i			1.07440i	−0.843454	+	0.537201i	$0.819482\pi$
$882$		0			0
$883$			29038.8i			1.10672i	0.832942	+	0.553361i	$0.186655\pi$
$883$			29038.8i			1.10672i	−0.832942	+	0.553361i	$0.813345\pi$
$884$	1025.89	−	5827.89i	0.0390320	−	0.221734i
$885$		0			0
$886$	−6912.71	−	8235.84i	−0.262119	−	0.312290i
$887$	−45085.5			−1.70668			−0.853338	−	0.521357i	$-0.825426\pi$
$887$	−45085.5			−1.70668			−0.853338	+	0.521357i	$0.825426\pi$
$888$		0			0
$889$	15055.3	−	20719.1i	0.567986	−	0.781660i
$890$	−117.739	+	98.8237i	−0.00443441	+	0.00372200i
$891$		0			0
$892$	−4145.52	+	23550.0i	−0.155608	+	0.883983i
$893$	4419.75			0.165623
$894$		0			0
$895$	−11417.5			−0.426421
$896$	−11734.5	+	24116.9i	−0.437524	+	0.899207i
$897$		0			0
$898$	−30348.2	+	25472.6i	−1.12776	+	0.946583i
$899$	−5633.75			−0.209006
$900$		0			0
$901$			31524.8i			1.16564i
$902$	8152.06	−	6842.39i	0.300924	−	0.252579i
$903$		0			0
$904$	−9017.91	−	15603.9i	−0.331782	−	0.574092i
$905$	3201.28			0.117585
$906$		0			0
$907$		−	9186.50i		−	0.336309i	−0.985761	−	0.168155i	$-0.946219\pi$
$907$		−	9186.50i		−	0.336309i	0.985761	−	0.168155i	$-0.0537808\pi$
$908$	−2688.08	+	15270.5i	−0.0982457	+	0.558117i
$909$		0			0
$910$	3124.82	−	218.760i	0.113832	−	0.00796902i
$911$		−	13945.1i		−	0.507158i	−0.967315	−	0.253579i	$-0.918392\pi$
$911$		−	13945.1i		−	0.507158i	0.967315	−	0.253579i	$-0.0816077\pi$
$912$		0			0
$913$			7122.30i			0.258175i
$914$	34357.6	−	28837.9i	1.24338	−	1.04362i
$915$		0			0
$916$	41609.3	+	7324.50i	1.50088	+	0.264201i
$917$	43910.4	+	31907.1i	1.58130	+	1.14904i
$918$		0			0
$919$		−	16186.3i		−	0.580996i	−0.956876	−	0.290498i	$-0.906179\pi$
$919$		−	16186.3i		−	0.580996i	0.956876	−	0.290498i	$-0.0938209\pi$
$920$	6761.74	+	11700.0i	0.242313	+	0.419281i
$921$		0			0
$922$	−13856.0	−	16508.1i	−0.494926	−	0.589658i
$923$	5447.71			0.194273
$924$		0			0
$925$	18787.7			0.667821
$926$	9660.37	+	11509.4i	0.342829	+	0.408448i
$927$		0			0
$928$	−3975.28	+	1450.12i	−0.140620	+	0.0512959i
$929$			12983.8i			0.458541i	0.973363	+	0.229271i	$0.0736341\pi$
$929$			12983.8i			0.458541i	−0.973363	+	0.229271i	$0.926366\pi$
$930$		0			0
$931$	7830.84	+	24111.3i	0.275666	+	0.848783i
$932$	2067.30	−	11744.0i	0.0726574	−	0.412755i
$933$		0			0
$934$	−38935.1	+	32679.9i	−1.36402	+	1.14488i
$935$		−	1886.70i		−	0.0659912i
$936$		0			0
$937$			14063.8i			0.490335i	0.969481	+	0.245168i	$0.0788430\pi$
$937$			14063.8i			0.490335i	−0.969481	+	0.245168i	$0.921157\pi$
$938$	−2193.61	−	31334.1i	−0.0763581	−	1.09072i
$939$		0			0
$940$	2108.54	+	371.167i	0.0731628	+	0.0128789i
$941$			16064.3i			0.556517i	0.960506	+	0.278259i	$0.0897572\pi$
$941$			16064.3i			0.556517i	−0.960506	+	0.278259i	$0.910243\pi$
$942$		0			0
$943$	65935.9			2.27696
$944$	−3581.16	−	1301.10i	−0.123471	−	0.0448594i
$945$		0			0
$946$	1198.03	−	1005.56i	0.0411749	−	0.0345599i
$947$			4913.13i			0.168591i	0.996441	+	0.0842953i	$0.0268639\pi$
$947$			4913.13i			0.168591i	−0.996441	+	0.0842953i	$0.973136\pi$
$948$		0			0
$949$	9088.25			0.310871
$950$	−16808.2	+	14107.9i	−0.574031	+	0.481810i
$951$		0			0
$952$	23072.2	+	2416.41i	0.785477	+	0.0822652i
$953$	1609.89			0.0547215			0.0273607	−	0.999626i	$-0.491290\pi$
$953$	1609.89			0.0547215			0.0273607	+	0.999626i	$0.491290\pi$
$954$		0			0
$955$	12380.1			0.419487
$956$	16042.8	+	2824.02i	0.542741	+	0.0955389i
$957$		0			0
$958$	−25935.4	+	21768.8i	−0.874672	+	0.734151i
$959$	22696.2	+	16491.9i	0.764231	+	0.555321i
$960$		0			0
$961$	28292.5			0.949701
$962$	4348.71	+	5181.07i	0.145746	+	0.173643i
$963$		0			0
$964$	−48080.8	−	8463.68i	−1.60641	−	0.282777i
$965$			5293.75i			0.176593i
$966$		0			0
$967$		−	9176.82i		−	0.305177i	−0.988290	−	0.152589i	$-0.951239\pi$
$967$		−	9176.82i		−	0.305177i	0.988290	−	0.152589i	$-0.0487610\pi$
$968$	14413.1	+	24939.4i	0.478570	+	0.828083i
$969$		0			0
$970$	−13898.3	+	11665.4i	−0.460048	+	0.386139i
$971$	9484.07			0.313448			0.156724	−	0.987642i	$-0.449907\pi$
$971$	9484.07			0.313448			0.156724	+	0.987642i	$0.449907\pi$
$972$		0			0
$973$	16808.6	+	12213.8i	0.553813	+	0.402423i
$974$	29472.6	+	35113.8i	0.969571	+	1.15515i
$975$		0			0
$976$	13766.0	−	37889.7i	0.451476	−	1.24264i
$977$	−10671.9			−0.349461			−0.174731	−	0.984616i	$-0.555905\pi$
$977$	−10671.9			−0.349461			−0.174731	+	0.984616i	$0.555905\pi$
$978$		0			0
$979$	92.4817			0.00301913
$980$	1711.02	+	12160.5i	0.0557720	+	0.396379i
$981$		0			0
$982$	−8808.62	−	10494.6i	−0.286247	−	0.341036i
$983$	−18046.5			−0.585547			−0.292774	−	0.956182i	$-0.594578\pi$
$983$	−18046.5			−0.585547			−0.292774	+	0.956182i	$0.594578\pi$
$984$		0			0
$985$			21250.0i			0.687393i
$986$	2353.06	+	2803.45i	0.0760008	+	0.0905478i
$987$		0			0
$988$	−7781.05	−	1369.70i	−0.250555	−	0.0441053i
$989$	9690.01			0.311552
$990$		0			0
$991$		−	13201.9i		−	0.423181i	−0.977358	−	0.211590i	$-0.932136\pi$
$991$		−	13201.9i		−	0.423181i	0.977358	−	0.211590i	$-0.0678643\pi$
$992$	40984.9	−	14950.7i	1.31177	−	0.478512i
$993$		0			0
$994$	1491.47	+	21304.5i	0.0475920	+	0.679818i
$995$		−	4110.81i		−	0.130976i
$996$		0			0
$997$			30223.1i			0.960054i	0.877254	+	0.480027i	$0.159373\pi$
$997$			30223.1i			0.960054i	−0.877254	+	0.480027i	$0.840627\pi$
$998$	6133.25	+	7307.19i	0.194534	+	0.231768i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.f.55.4		12
3.2	odd	2		84.4.b.a.55.9	✓	12
4.3	odd	2		252.4.b.e.55.3		12
7.6	odd	2		252.4.b.e.55.4		12
12.11	even	2		84.4.b.b.55.10	yes	12
21.20	even	2		84.4.b.b.55.9	yes	12
24.5	odd	2		1344.4.b.h.895.7		12
24.11	even	2		1344.4.b.g.895.7		12
28.27	even	2	inner	252.4.b.f.55.3		12
84.83	odd	2		84.4.b.a.55.10	yes	12
168.83	odd	2		1344.4.b.h.895.6		12
168.125	even	2		1344.4.b.g.895.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.b.a.55.9	✓	12	3.2	odd	2
84.4.b.a.55.10	yes	12	84.83	odd	2
84.4.b.b.55.9	yes	12	21.20	even	2
84.4.b.b.55.10	yes	12	12.11	even	2
252.4.b.e.55.3		12	4.3	odd	2
252.4.b.e.55.4		12	7.6	odd	2
252.4.b.f.55.3		12	28.27	even	2	inner
252.4.b.f.55.4		12	1.1	even	1	trivial
1344.4.b.g.895.6		12	168.125	even	2
1344.4.b.g.895.7		12	24.11	even	2
1344.4.b.h.895.6		12	168.83	odd	2
1344.4.b.h.895.7		12	24.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16644 + 1.81839i) q^{2} +(1.38692 - 7.87886i) q^{4} +4.47531i q^{5} +(-14.9825 - 10.8869i) q^{7} +(11.3222 + 19.5910i) q^{8} +O(q^{10})\)	\(q+(-2.16644 + 1.81839i) q^{2} +(1.38692 - 7.87886i) q^{4} +4.47531i q^{5} +(-14.9825 - 10.8869i) q^{7} +(11.3222 + 19.5910i) q^{8} +(-8.13786 - 9.69549i) q^{10} +7.61561i q^{11} -13.3620i q^{13} +(52.2553 - 3.65824i) q^{14} +(-60.1529 - 21.8547i) q^{16} +55.3574i q^{17} +73.9099 q^{19} +(35.2603 + 6.20690i) q^{20} +(-13.8481 - 16.4988i) q^{22} -133.446i q^{23} +104.972 q^{25} +(24.2974 + 28.9480i) q^{26} +(-106.556 + 102.946i) q^{28} -23.3760 q^{29} +241.005 q^{31} +(170.058 - 62.0345i) q^{32} +(-100.661 - 119.928i) q^{34} +(48.7222 - 67.0514i) q^{35} +178.979 q^{37} +(-160.121 + 134.397i) q^{38} +(-87.6760 + 50.6702i) q^{40} +494.101i q^{41} +72.6137i q^{43} +(60.0023 + 10.5622i) q^{44} +(242.657 + 289.103i) q^{46} +59.7992 q^{47} +(105.951 + 326.226i) q^{49} +(-227.415 + 190.879i) q^{50} +(-105.277 - 18.5320i) q^{52} +569.477 q^{53} -34.0822 q^{55} +(43.6512 - 416.786i) q^{56} +(50.6428 - 42.5068i) q^{58} +59.5343 q^{59} +629.889i q^{61} +(-522.123 + 438.241i) q^{62} +(-255.617 + 443.626i) q^{64} +59.7992 q^{65} -599.636i q^{67} +(436.153 + 76.7762i) q^{68} +(16.3717 + 233.859i) q^{70} +407.701i q^{71} +680.155i q^{73} +(-387.746 + 325.453i) q^{74} +(102.507 - 582.326i) q^{76} +(82.9103 - 114.101i) q^{77} -1084.52i q^{79} +(97.8065 - 269.203i) q^{80} +(-898.469 - 1070.44i) q^{82} +935.224 q^{83} -247.741 q^{85} +(-132.040 - 157.313i) q^{86} +(-149.198 + 86.2251i) q^{88} -12.1437i q^{89} +(-145.471 + 200.197i) q^{91} +(-1051.40 - 185.079i) q^{92} +(-129.551 + 108.738i) q^{94} +330.770i q^{95} -1433.48i q^{97} +(-822.742 - 514.088i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) \) 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8} + 56 q^{10} - 69 q^{14} + 41 q^{16} - 84 q^{19} - 172 q^{20} - 182 q^{22} - 216 q^{25} - 300 q^{26} + 309 q^{28} - 200 q^{29} - 384 q^{31} + 159 q^{32} - 164 q^{34} - 84 q^{35} - 244 q^{37} - 268 q^{38} - 316 q^{40} - 190 q^{44} + 894 q^{46} - 280 q^{47} - 424 q^{49} + 1771 q^{50} - 796 q^{52} + 16 q^{53} + 212 q^{55} + 7 q^{56} - 570 q^{58} - 1168 q^{59} + 384 q^{62} + 2705 q^{64} - 280 q^{65} - 1552 q^{68} + 968 q^{70} - 1622 q^{74} - 788 q^{76} - 968 q^{77} + 3060 q^{80} - 2540 q^{82} + 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} + 1648 q^{91} - 4298 q^{92} + 4256 q^{94} - 97 q^{98}+O(q^{100}) \) 12 * q - q^2 + 5 * q^4 + 10 * q^7 - 25 * q^8 + 56 * q^10 - 69 * q^14 + 41 * q^16 - 84 * q^19 - 172 * q^20 - 182 * q^22 - 216 * q^25 - 300 * q^26 + 309 * q^28 - 200 * q^29 - 384 * q^31 + 159 * q^32 - 164 * q^34 - 84 * q^35 - 244 * q^37 - 268 * q^38 - 316 * q^40 - 190 * q^44 + 894 * q^46 - 280 * q^47 - 424 * q^49 + 1771 * q^50 - 796 * q^52 + 16 * q^53 + 212 * q^55 + 7 * q^56 - 570 * q^58 - 1168 * q^59 + 384 * q^62 + 2705 * q^64 - 280 * q^65 - 1552 * q^68 + 968 * q^70 - 1622 * q^74 - 788 * q^76 - 968 * q^77 + 3060 * q^80 - 2540 * q^82 + 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 + 1648 * q^91 - 4298 * q^92 + 4256 * q^94 - 97 * q^98

Introduction

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