LMFDB - Embedded newform 252.4.b.f.55.10

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			55.10
Root			$-1.72458 + 2.24184i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.f.55.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72458 + 2.24184i) q^{2} +(-2.05167 + 7.73244i) q^{4} -6.58775i q^{5} +(15.1925 - 10.5918i) q^{7} +(-20.8731 + 8.73568i) q^{8} +O(q^{10})$	\(q+(1.72458 + 2.24184i) q^{2} +(-2.05167 + 7.73244i) q^{4} -6.58775i q^{5} +(15.1925 - 10.5918i) q^{7} +(-20.8731 + 8.73568i) q^{8} +(14.7687 - 11.3611i) q^{10} +54.2380i q^{11} +40.9722i q^{13} +(49.9458 + 15.7928i) q^{14} +(-55.5813 - 31.7288i) q^{16} +69.4988i q^{17} +160.189 q^{19} +(50.9394 + 13.5159i) q^{20} +(-121.593 + 93.5376i) q^{22} +87.8244i q^{23} +81.6016 q^{25} +(-91.8529 + 70.6596i) q^{26} +(50.7305 + 139.206i) q^{28} -236.369 q^{29} -131.598 q^{31} +(-24.7233 - 179.323i) q^{32} +(-155.805 + 119.856i) q^{34} +(-69.7762 - 100.085i) q^{35} -23.6257 q^{37} +(276.258 + 359.118i) q^{38} +(57.5485 + 137.507i) q^{40} -112.106i q^{41} +194.017i q^{43} +(-419.392 - 111.279i) q^{44} +(-196.888 + 151.460i) q^{46} +269.914 q^{47} +(118.627 - 321.833i) q^{49} +(140.728 + 182.937i) q^{50} +(-316.815 - 84.0613i) q^{52} +120.407 q^{53} +357.307 q^{55} +(-224.590 + 353.802i) q^{56} +(-407.637 - 529.902i) q^{58} +338.109 q^{59} +267.146i q^{61} +(-226.951 - 295.022i) q^{62} +(359.376 - 364.682i) q^{64} +269.914 q^{65} -275.691i q^{67} +(-537.395 - 142.589i) q^{68} +(104.039 - 329.031i) q^{70} +270.482i q^{71} -1237.57i q^{73} +(-40.7444 - 52.9651i) q^{74} +(-328.655 + 1238.65i) q^{76} +(574.479 + 824.014i) q^{77} +691.966i q^{79} +(-209.022 + 366.156i) q^{80} +(251.323 - 193.335i) q^{82} -430.482 q^{83} +457.841 q^{85} +(-434.954 + 334.596i) q^{86} +(-473.806 - 1132.12i) q^{88} -1220.75i q^{89} +(433.969 + 622.472i) q^{91} +(-679.097 - 180.187i) q^{92} +(465.488 + 605.104i) q^{94} -1055.28i q^{95} -381.884i q^{97} +(926.079 - 289.083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.72458	+	2.24184i	0.609730	+	0.792609i
$2$	1.72458	+	2.24184i	0.609730	+	0.792609i
$3$		0			0
$3$		0			0
$4$	−2.05167	+	7.73244i	−0.256459	+	0.966555i
$5$		−	6.58775i		−	0.589226i	−0.955617	−	0.294613i	$-0.904809\pi$
$5$		−	6.58775i		−	0.589226i	0.955617	−	0.294613i	$-0.0951908\pi$
$6$		0			0
$7$	15.1925	−	10.5918i	0.820321	−	0.571904i
$7$	15.1925	−	10.5918i	0.820321	−	0.571904i
$8$	−20.8731	+	8.73568i	−0.922471	+	0.386066i
$9$		0			0
$10$	14.7687	−	11.3611i	0.467026	−	0.359269i
$11$			54.2380i			1.48667i	0.668919	+	0.743335i	$0.266757\pi$
$11$			54.2380i			1.48667i	−0.668919	+	0.743335i	$0.733243\pi$
$12$		0			0
$13$			40.9722i			0.874125i	0.899431	+	0.437063i	$0.143981\pi$
$13$			40.9722i			0.874125i	−0.899431	+	0.437063i	$0.856019\pi$
$14$	49.9458	+	15.7928i	0.953470	+	0.301487i
$15$		0			0
$16$	−55.5813	−	31.7288i	−0.868458	−	0.495763i
$17$			69.4988i			0.991526i	0.868458	+	0.495763i	$0.165111\pi$
$17$			69.4988i			0.991526i	−0.868458	+	0.495763i	$0.834889\pi$
$18$		0			0
$19$	160.189			1.93420			0.967102	−	0.254389i	$-0.0818744\pi$
$19$	160.189			1.93420			0.967102	+	0.254389i	$0.0818744\pi$
$20$	50.9394	+	13.5159i	0.569520	+	0.151112i
$21$		0			0
$22$	−121.593	+	93.5376i	−1.17835	+	0.906468i
$23$			87.8244i			0.796202i	0.917342	+	0.398101i	$0.130331\pi$
$23$			87.8244i			0.796202i	−0.917342	+	0.398101i	$0.869669\pi$
$24$		0			0
$25$	81.6016			0.652812
$26$	−91.8529	+	70.6596i	−0.692840	+	0.532981i
$27$		0			0
$28$	50.7305	+	139.206i	0.342398	+	0.939555i
$29$	−236.369			−1.51354			−0.756771	−	0.653680i	$-0.773224\pi$
$29$	−236.369			−1.51354			−0.756771	+	0.653680i	$0.773224\pi$
$30$		0			0
$31$	−131.598			−0.762443			−0.381222	−	0.924484i	$-0.624497\pi$
$31$	−131.598			−0.762443			−0.381222	+	0.924484i	$0.624497\pi$
$32$	−24.7233	−	179.323i	−0.136578	−	0.990629i
$33$		0			0
$34$	−155.805	+	119.856i	−0.785892	+	0.604563i
$35$	−69.7762	−	100.085i	−0.336981	−	0.483354i
$36$		0			0
$37$	−23.6257			−0.104974			−0.0524871	−	0.998622i	$-0.516715\pi$
$37$	−23.6257			−0.104974			−0.0524871	+	0.998622i	$0.516715\pi$
$38$	276.258	+	359.118i	1.17934	+	1.53307i
$39$		0			0
$40$	57.5485	+	137.507i	0.227480	+	0.543544i
$41$		−	112.106i		−	0.427024i	−0.976940	−	0.213512i	$-0.931510\pi$
$41$		−	112.106i		−	0.427024i	0.976940	−	0.213512i	$-0.0684903\pi$
$42$		0			0
$43$			194.017i			0.688076i	0.938956	+	0.344038i	$0.111795\pi$
$43$			194.017i			0.688076i	−0.938956	+	0.344038i	$0.888205\pi$
$44$	−419.392	−	111.279i	−1.43695	−	0.381270i
$45$		0			0
$46$	−196.888	+	151.460i	−0.631077	+	0.485468i
$47$	269.914			0.837682			0.418841	−	0.908060i	$-0.362436\pi$
$47$	269.914			0.837682			0.418841	+	0.908060i	$0.362436\pi$
$48$		0			0
$49$	118.627	−	321.833i	0.345852	−	0.938289i
$50$	140.728	+	182.937i	0.398039	+	0.517425i
$51$		0			0
$52$	−316.815	−	84.0613i	−0.844891	−	0.224177i
$53$	120.407			0.312059			0.156030	−	0.987752i	$-0.450130\pi$
$53$	120.407			0.312059			0.156030	+	0.987752i	$0.450130\pi$
$54$		0			0
$55$	357.307			0.875985
$56$	−224.590	+	353.802i	−0.535929	+	0.844263i
$57$		0			0
$58$	−407.637	−	529.902i	−0.922852	−	1.19965i
$59$	338.109			0.746069			0.373035	−	0.927817i	$-0.378317\pi$
$59$	338.109			0.746069			0.373035	+	0.927817i	$0.378317\pi$
$60$		0			0
$61$			267.146i			0.560729i	0.959894	+	0.280365i	$0.0904554\pi$
$61$			267.146i			0.560729i	−0.959894	+	0.280365i	$0.909545\pi$
$62$	−226.951	−	295.022i	−0.464885	−	0.604320i
$63$		0			0
$64$	359.376	−	364.682i	0.701906	−	0.712270i
$65$	269.914			0.515058
$66$		0			0
$67$		−	275.691i		−	0.502702i	−0.967896	−	0.251351i	$-0.919125\pi$
$67$		−	275.691i		−	0.502702i	0.967896	−	0.251351i	$-0.0808749\pi$
$68$	−537.395	−	142.589i	−0.958364	−	0.254285i
$69$		0			0
$70$	104.039	−	329.031i	0.177644	−	0.561810i
$71$			270.482i			0.452117i	0.974114	+	0.226058i	$0.0725840\pi$
$71$			270.482i			0.452117i	−0.974114	+	0.226058i	$0.927416\pi$
$72$		0			0
$73$		−	1237.57i		−	1.98420i	−0.125469	−	0.992098i	$-0.540044\pi$
$73$		−	1237.57i		−	1.98420i	0.125469	−	0.992098i	$-0.459956\pi$
$74$	−40.7444	−	52.9651i	−0.0640060	−	0.0832036i
$75$		0			0
$76$	−328.655	+	1238.65i	−0.496044	+	1.86951i
$77$	574.479	+	824.014i	0.850233	+	1.21955i
$78$		0			0
$79$			691.966i			0.985472i	0.870179	+	0.492736i	$0.164003\pi$
$79$			691.966i			0.985472i	−0.870179	+	0.492736i	$0.835997\pi$
$80$	−209.022	+	366.156i	−0.292117	+	0.511718i
$81$		0			0
$82$	251.323	−	193.335i	0.338463	−	0.260369i
$83$	−430.482			−0.569296			−0.284648	−	0.958632i	$-0.591877\pi$
$83$	−430.482			−0.569296			−0.284648	+	0.958632i	$0.591877\pi$
$84$		0			0
$85$	457.841			0.584233
$86$	−434.954	+	334.596i	−0.545375	+	0.419540i
$87$		0			0
$88$	−473.806	−	1132.12i	−0.573953	−	1.37141i
$89$		−	1220.75i		−	1.45392i	−0.686680	−	0.726960i	$-0.740933\pi$
$89$		−	1220.75i		−	1.45392i	0.686680	−	0.726960i	$-0.259067\pi$
$90$		0			0
$91$	433.969	+	622.472i	0.499916	+	0.717063i
$92$	−679.097	−	180.187i	−0.769573	−	0.204193i
$93$		0			0
$94$	465.488	+	605.104i	0.510760	+	0.663954i
$95$		−	1055.28i		−	1.13968i
$96$		0			0
$97$		−	381.884i		−	0.399736i	−0.979823	−	0.199868i	$-0.935949\pi$
$97$		−	381.884i		−	0.399736i	0.979823	−	0.199868i	$-0.0640513\pi$
$98$	926.079	−	289.083i	0.954573	−	0.297978i
$99$		0			0
$100$	−167.419	+	630.979i	−0.167419	+	0.630979i
$101$		−	696.862i		−	0.686538i	−0.939237	−	0.343269i	$-0.888466\pi$
$101$		−	696.862i		−	0.686538i	0.939237	−	0.343269i	$-0.111534\pi$
$102$		0			0
$103$	−621.333			−0.594386			−0.297193	−	0.954817i	$-0.596050\pi$
$103$	−621.333			−0.594386			−0.297193	+	0.954817i	$0.596050\pi$
$104$	−357.920	−	855.218i	−0.337470	−	0.806356i
$105$		0			0
$106$	207.651	+	269.932i	0.190272	+	0.247341i
$107$			295.518i			0.266999i	0.991049	+	0.133499i	$0.0426214\pi$
$107$			295.518i			0.266999i	−0.991049	+	0.133499i	$0.957379\pi$
$108$		0			0
$109$	669.548			0.588358			0.294179	−	0.955750i	$-0.404954\pi$
$109$	669.548			0.588358			0.294179	+	0.955750i	$0.404954\pi$
$110$	616.203	+	801.023i	0.534115	+	0.694314i
$111$		0			0
$112$	−1180.49	+	106.665i	−0.995943	+	0.0899898i
$113$	1093.94			0.910703			0.455352	−	0.890312i	$-0.349514\pi$
$113$	1093.94			0.910703			0.455352	+	0.890312i	$0.349514\pi$
$114$		0			0
$115$	578.565			0.469143
$116$	484.952	−	1827.71i	0.388161	−	1.46292i
$117$		0			0
$118$	583.096	+	757.986i	0.454901	+	0.591342i
$119$	736.118	+	1055.86i	0.567058	+	0.813369i
$120$		0			0
$121$	−1610.76			−1.21019
$122$	−598.897	+	460.713i	−0.444439	+	0.341894i
$123$		0			0
$124$	269.996	−	1017.58i	0.195535	−	0.736944i
$125$		−	1361.04i		−	0.973880i
$126$		0			0
$127$			837.266i			0.585003i	0.956265	+	0.292501i	$0.0944876\pi$
$127$			837.266i			0.585003i	−0.956265	+	0.292501i	$0.905512\pi$
$128$	1437.33	+	176.740i	0.992525	+	0.122045i
$129$		0			0
$130$	465.488	+	605.104i	0.314046	+	0.408239i
$131$	1821.00			1.21452			0.607258	−	0.794504i	$-0.292269\pi$
$131$	1821.00			1.21452			0.607258	+	0.794504i	$0.292269\pi$
$132$		0			0
$133$	2433.68	−	1696.69i	1.58667	−	1.10618i
$134$	618.055	−	475.451i	0.398447	−	0.306513i
$135$		0			0
$136$	−607.119	−	1450.66i	−0.382794	−	0.914654i
$137$	−321.471			−0.200475			−0.100238	−	0.994964i	$-0.531960\pi$
$137$	−321.471			−0.200475			−0.100238	+	0.994964i	$0.531960\pi$
$138$		0			0
$139$	1339.35			0.817284			0.408642	−	0.912695i	$-0.366002\pi$
$139$	1339.35			0.817284			0.408642	+	0.912695i	$0.366002\pi$
$140$	917.057	−	334.200i	0.553610	−	0.201750i
$141$		0			0
$142$	−606.376	+	466.467i	−0.358352	+	0.275669i
$143$	−2222.25			−1.29954
$144$		0			0
$145$			1557.14i			0.891818i
$146$	2774.42	−	2134.28i	1.57269	−	1.20982i
$147$		0			0
$148$	48.4722	−	182.685i	0.0269216	−	0.101463i
$149$	−2748.96			−1.51144			−0.755718	−	0.654898i	$-0.772712\pi$
$149$	−2748.96			−1.51144			−0.755718	+	0.654898i	$0.772712\pi$
$150$		0			0
$151$		−	1950.99i		−	1.05145i	−0.850655	−	0.525725i	$-0.823794\pi$
$151$		−	1950.99i		−	1.05145i	0.850655	−	0.525725i	$-0.176206\pi$
$152$	−3343.65	+	1399.36i	−1.78425	+	0.746731i
$153$		0			0
$154$	−856.572	+	2708.96i	−0.448211	+	1.41750i
$155$			866.936i			0.449252i
$156$		0			0
$157$			3019.82i			1.53508i	0.641000	+	0.767540i	$0.278520\pi$
$157$			3019.82i			1.53508i	−0.641000	+	0.767540i	$0.721480\pi$
$158$	−1551.28	+	1193.35i	−0.781094	+	0.600872i
$159$		0			0
$160$	−1181.34	+	162.871i	−0.583705	+	0.0804756i
$161$	930.219	+	1334.28i	0.455351	+	0.653141i
$162$		0			0
$163$		−	2882.36i		−	1.38506i	−0.721391	−	0.692528i	$-0.756497\pi$
$163$		−	2882.36i		−	1.38506i	0.721391	−	0.692528i	$-0.243503\pi$
$164$	866.852	+	230.004i	0.412743	+	0.109514i
$165$		0			0
$166$	−742.400	−	965.071i	−0.347117	−	0.451229i
$167$	−2512.97			−1.16443			−0.582213	−	0.813036i	$-0.697813\pi$
$167$	−2512.97			−1.16443			−0.582213	+	0.813036i	$0.697813\pi$
$168$		0			0
$169$	518.282			0.235905
$170$	789.581	+	1026.40i	0.356224	+	0.463068i
$171$		0			0
$172$	−1500.22	−	398.058i	−0.665063	−	0.176463i
$173$		−	1307.12i		−	0.574442i	−0.957864	−	0.287221i	$-0.907269\pi$
$173$		−	1307.12i		−	0.574442i	0.957864	−	0.287221i	$-0.0927314\pi$
$174$		0			0
$175$	1239.74	−	864.308i	0.535515	−	0.373346i
$176$	1720.91	−	3014.62i	0.737037	−	1.29111i
$177$		0			0
$178$	2736.72	−	2105.27i	1.15239	−	0.886499i
$179$		−	3555.19i		−	1.48451i	−0.670117	−	0.742256i	$-0.733756\pi$
$179$		−	3555.19i		−	1.48451i	0.670117	−	0.742256i	$-0.266244\pi$
$180$		0			0
$181$		−	1746.96i		−	0.717406i	−0.933452	−	0.358703i	$-0.883219\pi$
$181$		−	1746.96i		−	0.717406i	0.933452	−	0.358703i	$-0.116781\pi$
$182$	−647.067	+	2046.39i	−0.263537	+	0.833453i
$183$		0			0
$184$	−767.205	−	1833.17i	−0.307387	−	0.734473i
$185$			155.640i			0.0618536i
$186$		0			0
$187$	−3769.48			−1.47407
$188$	−553.775	+	2087.10i	−0.214831	+	0.809666i
$189$		0			0
$190$	2365.78	−	1819.92i	0.903324	−	0.694899i
$191$			1935.70i			0.733310i	0.930357	+	0.366655i	$0.119497\pi$
$191$			1935.70i			0.733310i	−0.930357	+	0.366655i	$0.880503\pi$
$192$		0			0
$193$	−3842.27			−1.43302			−0.716509	−	0.697578i	$-0.754261\pi$
$193$	−3842.27			−1.43302			−0.716509	+	0.697578i	$0.754261\pi$
$194$	856.121	−	658.588i	0.316835	−	0.243731i
$195$		0			0
$196$	2245.17	+	1577.57i	0.818212	+	0.574917i
$197$	−490.616			−0.177436			−0.0887181	−	0.996057i	$-0.528277\pi$
$197$	−490.616			−0.177436			−0.0887181	+	0.996057i	$0.528277\pi$
$198$		0			0
$199$	−3630.14			−1.29314			−0.646568	−	0.762857i	$-0.723796\pi$
$199$	−3630.14			−1.29314			−0.646568	+	0.762857i	$0.723796\pi$
$200$	−1703.28	+	712.845i	−0.602201	+	0.252029i
$201$		0			0
$202$	1562.25	−	1201.79i	0.544157	−	0.418603i
$203$	−3591.05	+	2503.58i	−1.24159	+	0.865600i
$204$		0			0
$205$	−738.525			−0.251614
$206$	−1071.54	−	1392.93i	−0.362415	−	0.471116i
$207$		0			0
$208$	1300.00	−	2277.29i	0.433359	−	0.759141i
$209$			8688.33i			2.87552i
$210$		0			0
$211$			2486.62i			0.811308i	0.914027	+	0.405654i	$0.132956\pi$
$211$			2486.62i			0.811308i	−0.914027	+	0.405654i	$0.867044\pi$
$212$	−247.035	+	931.039i	−0.0800304	+	0.301623i
$213$		0			0
$214$	−662.504	+	509.644i	−0.211625	+	0.162797i
$215$	1278.13			0.405432
$216$		0			0
$217$	−1999.31	+	1393.86i	−0.625448	+	0.436044i
$218$	1154.69	+	1501.02i	0.358740	+	0.466338i
$219$		0			0
$220$	−733.075	+	2762.85i	−0.224654	+	0.846688i
$221$	−2847.52			−0.866718
$222$		0			0
$223$	−992.723			−0.298106			−0.149053	−	0.988829i	$-0.547623\pi$
$223$	−992.723			−0.298106			−0.149053	+	0.988829i	$0.547623\pi$
$224$	−2274.97	−	2462.51i	−0.678583	−	0.734524i
$225$		0			0
$226$	1886.59	+	2452.44i	0.555283	+	0.721832i
$227$	5666.03			1.65668			0.828342	−	0.560223i	$-0.189284\pi$
$227$	5666.03			1.65668			0.828342	+	0.560223i	$0.189284\pi$
$228$		0			0
$229$			6488.31i			1.87231i	0.351583	+	0.936157i	$0.385643\pi$
$229$			6488.31i			1.87231i	−0.351583	+	0.936157i	$0.614357\pi$
$230$	997.780	+	1297.05i	0.286051	+	0.371847i
$231$		0			0
$232$	4933.77	−	2064.85i	1.39620	−	0.584327i
$233$	3657.30			1.02832			0.514158	−	0.857696i	$-0.328105\pi$
$233$	3657.30			1.02832			0.514158	+	0.857696i	$0.328105\pi$
$234$		0			0
$235$		−	1778.13i		−	0.493584i
$236$	−693.689	+	2614.41i	−0.191336	+	0.721117i
$237$		0			0
$238$	−1097.58	+	3471.18i	−0.298932	+	0.945390i
$239$		−	5806.11i		−	1.57141i	−0.618604	−	0.785703i	$-0.712302\pi$
$239$		−	5806.11i		−	1.57141i	0.618604	−	0.785703i	$-0.287698\pi$
$240$		0			0
$241$			584.133i			0.156130i	0.996948	+	0.0780649i	$0.0248741\pi$
$241$			584.133i			0.156130i	−0.996948	+	0.0780649i	$0.975126\pi$
$242$	−2777.89	−	3611.07i	−0.737889	−	0.959208i
$243$		0			0
$244$	−2065.69	−	548.095i	−0.541976	−	0.143804i
$245$	−2120.16	−	781.486i	−0.552865	−	0.203785i
$246$		0			0
$247$			6563.29i			1.69074i
$248$	2746.87	−	1149.60i	0.703332	−	0.294354i
$249$		0			0
$250$	3051.23	−	2347.22i	0.771907	−	0.593804i
$251$	3459.63			0.870000			0.435000	−	0.900430i	$-0.356748\pi$
$251$	3459.63			0.870000			0.435000	+	0.900430i	$0.356748\pi$
$252$		0			0
$253$	−4763.42			−1.18369
$254$	−1877.01	+	1443.93i	−0.463679	+	0.356694i
$255$		0			0
$256$	2082.56	+	3527.06i	0.508438	+	0.861099i
$257$			1501.55i			0.364453i	0.983257	+	0.182226i	$0.0583304\pi$
$257$			1501.55i			0.364453i	−0.983257	+	0.182226i	$0.941670\pi$
$258$		0			0
$259$	−358.935	+	250.239i	−0.0861125	+	0.0600352i
$260$	−553.775	+	2087.10i	−0.132091	+	0.497832i
$261$		0			0
$262$	3140.46	+	4082.39i	0.740527	+	0.962637i
$263$		−	5235.13i		−	1.22742i	−0.789531	−	0.613711i	$-0.789676\pi$
$263$		−	5235.13i		−	1.22742i	0.789531	−	0.613711i	$-0.210324\pi$
$264$		0			0
$265$		−	793.210i		−	0.183874i
$266$	8000.77	+	2529.84i	1.84421	+	0.583137i
$267$		0			0
$268$	2131.77	+	565.628i	0.485890	+	0.128922i
$269$			34.2010i			0.00775193i	0.999992	+	0.00387597i	$0.00123376\pi$
$269$			34.2010i			0.00775193i	−0.999992	+	0.00387597i	$0.998766\pi$
$270$		0			0
$271$	653.935			0.146582			0.0732910	−	0.997311i	$-0.476650\pi$
$271$	653.935			0.146582			0.0732910	+	0.997311i	$0.476650\pi$
$272$	2205.12	−	3862.83i	0.491562	−	0.861098i
$273$		0			0
$274$	−554.401	−	720.686i	−0.122236	−	0.158899i
$275$			4425.91i			0.970517i
$276$		0			0
$277$	2250.58			0.488174			0.244087	−	0.969753i	$-0.421512\pi$
$277$	2250.58			0.488174			0.244087	+	0.969753i	$0.421512\pi$
$278$	2309.82	+	3002.61i	0.498323	+	0.647787i
$279$		0			0
$280$	2330.76	+	1479.54i	0.497462	+	0.315784i
$281$	−4213.47			−0.894500			−0.447250	−	0.894409i	$-0.647597\pi$
$281$	−4213.47			−0.894500			−0.447250	+	0.894409i	$0.647597\pi$
$282$		0			0
$283$	2069.17			0.434627			0.217313	−	0.976102i	$-0.430271\pi$
$283$	2069.17			0.434627			0.217313	+	0.976102i	$0.430271\pi$
$284$	−2091.49	−	554.940i	−0.436996	−	0.115949i
$285$		0			0
$286$	−3832.44	−	4981.92i	−0.792367	−	1.03002i
$287$	−1187.40	−	1703.17i	−0.244217	−	0.350297i
$288$		0			0
$289$	82.9156			0.0168768
$290$	−3490.86	+	2685.41i	−0.706863	+	0.543768i
$291$		0			0
$292$	9569.41	+	2539.08i	1.91783	+	0.508864i
$293$			2027.49i			0.404257i	0.979359	+	0.202128i	$0.0647859\pi$
$293$			2027.49i			0.404257i	−0.979359	+	0.202128i	$0.935214\pi$
$294$		0			0
$295$		−	2227.38i		−	0.439604i
$296$	493.143	−	206.387i	0.0968357	−	0.0405270i
$297$		0			0
$298$	−4740.80	−	6162.73i	−0.921567	−	1.19798i
$299$	−3598.35			−0.695981
$300$		0			0
$301$	2054.99	+	2947.61i	0.393513	+	0.564443i
$302$	4373.79	−	3364.62i	0.833389	−	0.641101i
$303$		0			0
$304$	−8903.51	−	5082.61i	−1.67977	−	0.958907i
$305$	1759.89			0.330396
$306$		0			0
$307$	167.377			0.0311162			0.0155581	−	0.999879i	$-0.495047\pi$
$307$	167.377			0.0311162			0.0155581	+	0.999879i	$0.495047\pi$
$308$	−7550.28	+	2751.52i	−1.39681	+	0.509034i
$309$		0			0
$310$	−1943.53	+	1495.10i	−0.356081	+	0.273922i
$311$	−4720.36			−0.860666			−0.430333	−	0.902670i	$-0.641604\pi$
$311$	−4720.36			−0.860666			−0.430333	+	0.902670i	$0.641604\pi$
$312$		0			0
$313$		−	6008.08i		−	1.08497i	−0.840064	−	0.542487i	$-0.817483\pi$
$313$		−	6008.08i		−	1.08497i	0.840064	−	0.542487i	$-0.182517\pi$
$314$	−6769.94	+	5207.91i	−1.21672	+	0.935985i
$315$		0			0
$316$	−5350.59	−	1419.69i	−0.952513	−	0.252733i
$317$	1790.11			0.317170			0.158585	−	0.987345i	$-0.449307\pi$
$317$	1790.11			0.317170			0.158585	+	0.987345i	$0.449307\pi$
$318$		0			0
$319$		−	12820.2i		−	2.25014i
$320$	−2402.43	−	2367.48i	−0.419688	−	0.413581i
$321$		0			0
$322$	−1387.00	+	4386.46i	−0.240044	+	0.759155i
$323$			11132.9i			1.91781i
$324$		0			0
$325$			3343.39i			0.570640i
$326$	6461.79	−	4970.86i	1.09781	−	0.844510i
$327$		0			0
$328$	979.321	+	2340.00i	0.164860	+	0.393918i
$329$	4100.69	−	2858.88i	0.687168	−	0.479074i
$330$		0			0
$331$			5059.04i			0.840090i	0.907503	+	0.420045i	$0.137986\pi$
$331$			5059.04i			0.840090i	−0.907503	+	0.420045i	$0.862014\pi$
$332$	883.208	−	3328.68i	0.146001	−	0.550256i
$333$		0			0
$334$	−4333.80	−	5633.66i	−0.709985	−	0.922935i
$335$	−1816.19			−0.296205
$336$		0			0
$337$	−12120.3			−1.95915			−0.979574	−	0.201084i	$-0.935554\pi$
$337$	−12120.3			−1.95915			−0.979574	+	0.201084i	$0.935554\pi$
$338$	893.818	+	1161.90i	0.143838	+	0.186980i
$339$		0			0
$340$	−939.338	+	3540.23i	−0.149832	+	0.564693i
$341$		−	7137.63i		−	1.13350i
$342$		0			0
$343$	−1606.55	−	6145.94i	−0.252902	−	0.967492i
$344$	−1694.87	−	4049.73i	−0.265643	−	0.634730i
$345$		0			0
$346$	2930.35	−	2254.23i	0.455308	−	0.350254i
$347$		−	6366.23i		−	0.984892i	−0.870343	−	0.492446i	$-0.836103\pi$
$347$		−	6366.23i		−	0.984892i	0.870343	−	0.492446i	$-0.163897\pi$
$348$		0			0
$349$		−	4912.76i		−	0.753508i	−0.926313	−	0.376754i	$-0.877040\pi$
$349$		−	4912.76i		−	0.753508i	0.926313	−	0.376754i	$-0.122960\pi$
$350$	4075.66	+	1288.72i	0.622437	+	0.196814i
$351$		0			0
$352$	9726.13	−	1340.94i	1.47274	−	0.203047i
$353$		−	5847.50i		−	0.881674i	−0.897587	−	0.440837i	$-0.854682\pi$
$353$		−	5847.50i		−	0.881674i	0.897587	−	0.440837i	$-0.145318\pi$
$354$		0			0
$355$	1781.87			0.266399
$356$	9439.35	+	2504.57i	1.40529	+	0.372871i
$357$		0			0
$358$	7970.16	−	6131.20i	1.17664	−	0.905151i
$359$			7074.15i			1.04000i	0.854167	+	0.519999i	$0.174068\pi$
$359$			7074.15i			1.04000i	−0.854167	+	0.519999i	$0.825932\pi$
$360$		0			0
$361$	18801.5			2.74114
$362$	3916.40	−	3012.76i	0.568622	−	0.437424i
$363$		0			0
$364$	−5703.59	+	2078.54i	−0.821289	+	0.299299i
$365$	−8152.78			−1.16914
$366$		0			0
$367$	3730.67			0.530625			0.265312	−	0.964163i	$-0.414525\pi$
$367$	3730.67			0.530625			0.265312	+	0.964163i	$0.414525\pi$
$368$	2786.57	−	4881.39i	0.394728	−	0.691468i
$369$		0			0
$370$	−348.921	+	268.414i	−0.0490257	+	0.0377140i
$371$	1829.29	−	1275.33i	0.255989	−	0.178468i
$372$		0			0
$373$	9966.13			1.38345			0.691725	−	0.722161i	$-0.256851\pi$
$373$	9966.13			1.38345			0.691725	+	0.722161i	$0.256851\pi$
$374$	−6500.75	−	8450.56i	−0.898786	−	1.16836i
$375$		0			0
$376$	−5633.96	+	2357.88i	−0.772737	+	0.323401i
$377$		−	9684.57i		−	1.32303i
$378$		0			0
$379$			11391.4i			1.54390i	0.635686	+	0.771948i	$0.280717\pi$
$379$			11391.4i			1.54390i	−0.635686	+	0.771948i	$0.719283\pi$
$380$	8159.93	+	2165.10i	1.10157	+	0.292282i
$381$		0			0
$382$	−4339.52	+	3338.26i	−0.581228	+	0.447121i
$383$	−3889.70			−0.518941			−0.259471	−	0.965751i	$-0.583548\pi$
$383$	−3889.70			−0.518941			−0.259471	+	0.965751i	$0.583548\pi$
$384$		0			0
$385$	5428.40	−	3784.52i	0.718589	−	0.500980i
$386$	−6626.29	−	8613.74i	−0.873754	−	1.13582i
$387$		0			0
$388$	2952.89	+	783.499i	0.386367	+	0.102516i
$389$	9689.51			1.26292			0.631462	−	0.775407i	$-0.282455\pi$
$389$	9689.51			1.26292			0.631462	+	0.775407i	$0.282455\pi$
$390$		0			0
$391$	−6103.69			−0.789455
$392$	335.311	+	7753.96i	0.0432035	+	0.999066i
$393$		0			0
$394$	−846.105	−	1099.88i	−0.108188	−	0.140638i
$395$	4558.50			0.580666
$396$		0			0
$397$		−	10767.0i		−	1.36116i	−0.732672	−	0.680582i	$-0.761727\pi$
$397$		−	10767.0i		−	1.36116i	0.732672	−	0.680582i	$-0.238273\pi$
$398$	−6260.46	−	8138.19i	−0.788463	−	1.02495i
$399$		0			0
$400$	−4535.52	−	2589.12i	−0.566940	−	0.323640i
$401$	4053.14			0.504749			0.252374	−	0.967630i	$-0.418789\pi$
$401$	4053.14			0.504749			0.252374	+	0.967630i	$0.418789\pi$
$402$		0			0
$403$		−	5391.86i		−	0.666471i
$404$	5388.45	+	1429.73i	0.663577	+	0.176069i
$405$		0			0
$406$	−11805.7	−	3732.94i	−1.44312	−	0.456313i
$407$		−	1281.41i		−	0.156062i
$408$		0			0
$409$		−	1517.85i		−	0.183503i	−0.995782	−	0.0917517i	$-0.970753\pi$
$409$		−	1517.85i		−	0.183503i	0.995782	−	0.0917517i	$-0.0292466\pi$
$410$	−1273.64	−	1655.65i	−0.153417	−	0.199431i
$411$		0			0
$412$	1274.77	−	4804.42i	0.152435	−	0.574507i
$413$	5136.74	−	3581.19i	0.612016	−	0.426680i
$414$		0			0
$415$			2835.91i			0.335444i
$416$	7347.25	−	1012.97i	0.865934	−	0.119387i
$417$		0			0
$418$	−19477.8	+	14983.7i	−2.27917	+	1.75329i
$419$	−1429.41			−0.166662			−0.0833310	−	0.996522i	$-0.526556\pi$
$419$	−1429.41			−0.166662			−0.0833310	+	0.996522i	$0.526556\pi$
$420$		0			0
$421$	−924.052			−0.106973			−0.0534864	−	0.998569i	$-0.517033\pi$
$421$	−924.052			−0.106973			−0.0534864	+	0.998569i	$0.517033\pi$
$422$	−5574.60	+	4288.37i	−0.643050	+	0.494679i
$423$		0			0
$424$	−2513.27	+	1051.84i	−0.287866	+	0.120476i
$425$			5671.21i			0.647280i
$426$		0			0
$427$	2829.56	+	4058.62i	0.320683	+	0.459978i
$428$	−2285.08	−	606.306i	−0.258069	−	0.0684741i
$429$		0			0
$430$	2204.24	+	2865.37i	0.247204	+	0.321349i
$431$		−	4099.49i		−	0.458157i	−0.973408	−	0.229078i	$-0.926429\pi$
$431$		−	4099.49i		−	0.458157i	0.973408	−	0.229078i	$-0.0735712\pi$
$432$		0			0
$433$			6350.16i			0.704779i	0.935853	+	0.352390i	$0.114631\pi$
$433$			6350.16i			0.704779i	−0.935853	+	0.352390i	$0.885369\pi$
$434$	−6572.79	−	2078.31i	−0.726967	−	0.229867i
$435$		0			0
$436$	−1373.69	+	5177.24i	−0.150890	+	0.568680i
$437$			14068.5i			1.54002i
$438$		0			0
$439$	5385.88			0.585545			0.292772	−	0.956182i	$-0.405422\pi$
$439$	5385.88			0.585545			0.292772	+	0.956182i	$0.405422\pi$
$440$	−7458.11	+	3121.31i	−0.808071	+	0.338188i
$441$		0			0
$442$	−4910.76	−	6383.67i	−0.528464	−	0.686969i
$443$		−	1259.12i		−	0.135040i	−0.997718	−	0.0675200i	$-0.978491\pi$
$443$		−	1259.12i		−	0.135040i	0.997718	−	0.0675200i	$-0.0215087\pi$
$444$		0			0
$445$	−8041.97			−0.856688
$446$	−1712.03	−	2225.52i	−0.181764	−	0.236282i
$447$		0			0
$448$	1597.19	−	9346.89i	0.168438	−	0.985712i
$449$	−434.975			−0.0457187			−0.0228594	−	0.999739i	$-0.507277\pi$
$449$	−434.975			−0.0457187			−0.0228594	+	0.999739i	$0.507277\pi$
$450$		0			0
$451$	6080.40			0.634845
$452$	−2244.41	+	8458.85i	−0.233558	+	0.880245i
$453$		0			0
$454$	9771.50	+	12702.3i	1.01013	+	1.31310i
$455$	4100.69	−	2858.88i	0.422512	−	0.294564i
$456$		0			0
$457$	−3172.32			−0.324715			−0.162357	−	0.986732i	$-0.551910\pi$
$457$	−3172.32			−0.324715			−0.162357	+	0.986732i	$0.551910\pi$
$458$	−14545.7	+	11189.6i	−1.48401	+	1.14161i
$459$		0			0
$460$	−1187.02	+	4473.72i	−0.120316	+	0.453453i
$461$		−	12644.2i		−	1.27744i	−0.769441	−	0.638718i	$-0.779465\pi$
$461$		−	12644.2i		−	1.27744i	0.769441	−	0.638718i	$-0.220535\pi$
$462$		0			0
$463$			13829.8i			1.38818i	0.719890	+	0.694089i	$0.244192\pi$
$463$			13829.8i			1.38818i	−0.719890	+	0.694089i	$0.755808\pi$
$464$	13137.7	+	7499.73i	1.31445	+	0.750358i
$465$		0			0
$466$	6307.29	+	8199.06i	0.626995	+	0.815052i
$467$	17043.7			1.68884			0.844419	−	0.535684i	$-0.179946\pi$
$467$	17043.7			1.68884			0.844419	+	0.535684i	$0.179946\pi$
$468$		0			0
$469$	−2920.07	−	4188.45i	−0.287497	−	0.412377i
$470$	3986.27	−	3066.52i	0.391219	−	0.300953i
$471$		0			0
$472$	−7057.40	+	2953.62i	−0.688228	+	0.288032i
$473$	−10523.1			−1.02294
$474$		0			0
$475$	13071.7			1.26267
$476$	−9674.68	+	3525.71i	−0.931593	+	0.339497i
$477$		0			0
$478$	13016.4	−	10013.1i	1.24551	−	0.958133i
$479$	−4131.98			−0.394144			−0.197072	−	0.980389i	$-0.563143\pi$
$479$	−4131.98			−0.394144			−0.197072	+	0.980389i	$0.563143\pi$
$480$		0			0
$481$		−	967.997i		−	0.0917607i
$482$	−1309.53	+	1007.38i	−0.123750	+	0.0951970i
$483$		0			0
$484$	3304.76	−	12455.1i	0.310364	−	1.16972i
$485$	−2515.75			−0.235535
$486$		0			0
$487$			11356.0i			1.05665i	0.849042	+	0.528325i	$0.177180\pi$
$487$			11356.0i			1.05665i	−0.849042	+	0.528325i	$0.822820\pi$
$488$	−2333.70	−	5576.17i	−0.216479	−	0.517257i
$489$		0			0
$490$	−1904.41	−	6100.78i	−0.175576	−	0.562459i
$491$			7964.89i			0.732079i	0.930599	+	0.366039i	$0.119286\pi$
$491$			7964.89i			0.732079i	−0.930599	+	0.366039i	$0.880714\pi$
$492$		0			0
$493$		−	16427.4i		−	1.50072i
$494$	−14713.8	+	11318.9i	−1.34009	+	1.03089i
$495$		0			0
$496$	7314.40	+	4175.46i	0.662150	+	0.377991i
$497$	2864.89	+	4109.31i	0.258567	+	0.370881i
$498$		0			0
$499$			2086.90i			0.187219i	0.995609	+	0.0936096i	$0.0298406\pi$
$499$			2086.90i			0.187219i	−0.995609	+	0.0936096i	$0.970159\pi$
$500$	10524.2	+	2792.40i	0.941309	+	0.249760i
$501$		0			0
$502$	5966.40	+	7755.93i	0.530465	+	0.689570i
$503$	10945.8			0.970277			0.485138	−	0.874437i	$-0.338769\pi$
$503$	10945.8			0.970277			0.485138	+	0.874437i	$0.338769\pi$
$504$		0			0
$505$	−4590.75			−0.404526
$506$	−8214.88	−	10678.8i	−0.721732	−	0.938204i
$507$		0			0
$508$	−6474.11	−	1717.79i	−0.565438	−	0.150029i
$509$			21490.9i			1.87145i	0.352732	+	0.935724i	$0.385253\pi$
$509$			21490.9i			1.87145i	−0.352732	+	0.935724i	$0.614747\pi$
$510$		0			0
$511$	−13108.1	−	18801.8i	−1.13477	−	1.62768i
$512$	−4315.56	+	10751.5i	−0.372505	+	0.928030i
$513$		0			0
$514$	−3366.24	+	2589.55i	−0.288869	+	0.222218i
$515$			4093.18i			0.350228i
$516$		0			0
$517$			14639.6i			1.24536i
$518$	−1180.01	−	373.117i	−0.100090	−	0.0316483i
$519$		0			0
$520$	−5633.96	+	2357.88i	−0.475126	+	0.198846i
$521$		−	6155.93i		−	0.517651i	−0.965924	−	0.258826i	$-0.916665\pi$
$521$		−	6155.93i		−	0.517651i	0.965924	−	0.258826i	$-0.0833355\pi$
$522$		0			0
$523$	5018.12			0.419555			0.209777	−	0.977749i	$-0.432726\pi$
$523$	5018.12			0.419555			0.209777	+	0.977749i	$0.432726\pi$
$524$	−3736.09	+	14080.8i	−0.311473	+	1.17390i
$525$		0			0
$526$	11736.3	−	9028.38i	0.972865	−	0.748395i
$527$		−	9145.92i		−	0.755982i
$528$		0			0
$529$	4453.88			0.366062
$530$	1778.25	−	1367.95i	0.145740	−	0.112113i
$531$		0			0
$532$	8126.46	+	22299.3i	0.662268	+	1.81729i
$533$	4593.22			0.373273
$534$		0			0
$535$	1946.80			0.157323
$536$	2408.35	+	5754.54i	0.194076	+	0.463728i
$537$		0			0
$538$	−76.6730	+	58.9822i	−0.00614425	+	0.00472659i
$539$	17455.6	+	6434.10i	1.39493	+	0.514168i
$540$		0			0
$541$	−1260.99			−0.100211			−0.0501055	−	0.998744i	$-0.515956\pi$
$541$	−1260.99			−0.100211			−0.0501055	+	0.998744i	$0.515956\pi$
$542$	1127.76	+	1466.02i	0.0893754	+	0.116182i
$543$		0			0
$544$	12462.7	−	1718.24i	0.982234	−	0.135421i
$545$		−	4410.81i		−	0.346676i
$546$		0			0
$547$			16180.1i			1.26474i	0.774666	+	0.632370i	$0.217918\pi$
$547$			16180.1i			1.26474i	−0.774666	+	0.632370i	$0.782082\pi$
$548$	659.552	−	2485.76i	0.0514137	−	0.193770i
$549$		0			0
$550$	−9922.16	+	7632.82i	−0.769241	+	0.591753i
$551$	−37863.8			−2.92750
$552$		0			0
$553$	7329.17	+	10512.7i	0.563595	+	0.808403i
$554$	3881.30	+	5045.44i	0.297654	+	0.386931i
$555$		0			0
$556$	−2747.91	+	10356.5i	−0.209600	+	0.789950i
$557$	21384.1			1.62670			0.813351	−	0.581774i	$-0.197641\pi$
$557$	21384.1			1.62670			0.813351	+	0.581774i	$0.197641\pi$
$558$		0			0
$559$	−7949.28			−0.601464
$560$	702.680	+	7776.76i	0.0530244	+	0.586836i
$561$		0			0
$562$	−7266.45	−	9445.91i	−0.545403	−	0.708989i
$563$	−2029.82			−0.151948			−0.0759739	−	0.997110i	$-0.524207\pi$
$563$	−2029.82			−0.151948			−0.0759739	+	0.997110i	$0.524207\pi$
$564$		0			0
$565$		−	7206.62i		−	0.536610i
$566$	3568.44	+	4638.74i	0.265005	+	0.344489i
$567$		0			0
$568$	−2362.84	−	5645.81i	−0.174547	−	0.417065i
$569$	−21597.4			−1.59123			−0.795616	−	0.605801i	$-0.792853\pi$
$569$	−21597.4			−1.59123			−0.795616	+	0.605801i	$0.792853\pi$
$570$		0			0
$571$		−	13250.6i		−	0.971137i	−0.874199	−	0.485568i	$-0.838613\pi$
$571$		−	13250.6i		−	0.971137i	0.874199	−	0.485568i	$-0.161387\pi$
$572$	4559.32	−	17183.4i	0.333278	−	1.25607i
$573$		0			0
$574$	1770.47	−	5599.22i	0.128742	−	0.407155i
$575$			7166.61i			0.519771i
$576$		0			0
$577$		−	17602.4i		−	1.27001i	−0.772507	−	0.635006i	$-0.780998\pi$
$577$		−	17602.4i		−	1.27001i	0.772507	−	0.635006i	$-0.219002\pi$
$578$	142.994	+	185.883i	0.0102903	+	0.0133767i
$579$		0			0
$580$	−12040.5	−	3194.74i	−0.861992	−	0.228715i
$581$	−6540.12	+	4559.59i	−0.467005	+	0.325583i
$582$		0			0
$583$			6530.63i			0.463930i
$584$	10811.0	+	25831.9i	0.766030	+	1.83036i
$585$		0			0
$586$	−4545.31	+	3496.56i	−0.320418	+	0.246488i
$587$	10190.1			0.716510			0.358255	−	0.933624i	$-0.383372\pi$
$587$	10190.1			0.716510			0.358255	+	0.933624i	$0.383372\pi$
$588$		0			0
$589$	−21080.6			−1.47472
$590$	4993.42	−	3841.29i	0.348434	−	0.268040i
$591$		0			0
$592$	1313.15	+	749.617i	0.0911657	+	0.0520424i
$593$		−	1211.86i		−	0.0839213i	−0.999119	−	0.0419606i	$-0.986640\pi$
$593$		−	1211.86i		−	0.0839213i	0.999119	−	0.0419606i	$-0.0133604\pi$
$594$		0			0
$595$	6955.77	−	4849.36i	0.479258	−	0.334125i
$596$	5639.96	−	21256.2i	0.387621	−	1.46089i
$597$		0			0
$598$	−6205.64	−	8066.92i	−0.424360	−	0.551641i
$599$		−	9213.72i		−	0.628485i	−0.949343	−	0.314243i	$-0.898249\pi$
$599$		−	9213.72i		−	0.628485i	0.949343	−	0.314243i	$-0.101751\pi$
$600$		0			0
$601$			17051.3i			1.15730i	0.815575	+	0.578651i	$0.196421\pi$
$601$			17051.3i			1.15730i	−0.815575	+	0.578651i	$0.803579\pi$
$602$	−3064.07	+	9690.32i	−0.207446	+	0.656060i
$603$		0			0
$604$	15085.9	+	4002.78i	1.01628	+	0.269654i
$605$			10611.3i			0.713076i
$606$		0			0
$607$	9836.13			0.657721			0.328860	−	0.944379i	$-0.393335\pi$
$607$	9836.13			0.657721			0.328860	+	0.944379i	$0.393335\pi$
$608$	−3960.40	−	28725.6i	−0.264170	−	1.91608i
$609$		0			0
$610$	3035.06	+	3945.38i	0.201453	+	0.261875i
$611$			11059.0i			0.732239i
$612$		0			0
$613$	10697.4			0.704837			0.352418	−	0.935843i	$-0.385359\pi$
$613$	10697.4			0.704837			0.352418	+	0.935843i	$0.385359\pi$
$614$	288.654	+	375.231i	0.0189725	+	0.0246630i
$615$		0			0
$616$	−19189.5	−	12181.3i	−1.25514	−	0.796751i
$617$	−18439.5			−1.20316			−0.601578	−	0.798814i	$-0.705461\pi$
$617$	−18439.5			−1.20316			−0.601578	+	0.798814i	$0.705461\pi$
$618$		0			0
$619$	−26672.5			−1.73192			−0.865960	−	0.500113i	$-0.833292\pi$
$619$	−26672.5			−1.73192			−0.865960	+	0.500113i	$0.833292\pi$
$620$	−6703.54	−	1778.67i	−0.434227	−	0.115215i
$621$		0			0
$622$	−8140.63	−	10582.3i	−0.524774	−	0.682172i
$623$	−12929.9	−	18546.3i	−0.831503	−	1.19268i
$624$		0			0
$625$	1234.01			0.0789766
$626$	13469.1	−	10361.4i	0.859961	−	0.661541i
$627$		0			0
$628$	−23350.6	−	6195.67i	−1.48374	−	0.393685i
$629$		−	1641.96i		−	0.104085i
$630$		0			0
$631$		−	10491.0i		−	0.661870i	−0.943653	−	0.330935i	$-0.892636\pi$
$631$		−	10491.0i		−	0.661870i	0.943653	−	0.330935i	$-0.107364\pi$
$632$	−6044.79	−	14443.5i	−0.380457	−	0.909069i
$633$		0			0
$634$	3087.19	+	4013.15i	0.193388	+	0.251392i
$635$	5515.70			0.344699
$636$		0			0
$637$	13186.2	+	4860.41i	0.820183	+	0.302318i
$638$	28740.8	−	22109.4i	1.78348	−	1.37198i
$639$		0			0
$640$	1164.32	−	9468.76i	0.0719121	−	0.584821i
$641$	−2839.23			−0.174950			−0.0874749	−	0.996167i	$-0.527880\pi$
$641$	−2839.23			−0.174950			−0.0874749	+	0.996167i	$0.527880\pi$
$642$		0			0
$643$	−6153.86			−0.377426			−0.188713	−	0.982032i	$-0.560432\pi$
$643$	−6153.86			−0.377426			−0.188713	+	0.982032i	$0.560432\pi$
$644$	−12225.7	+	4455.37i	−0.748076	+	0.272618i
$645$		0			0
$646$	−24958.3	+	19199.6i	−1.52008	+	1.16935i
$647$	3054.45			0.185599			0.0927996	−	0.995685i	$-0.470418\pi$
$647$	3054.45			0.185599			0.0927996	+	0.995685i	$0.470418\pi$
$648$		0			0
$649$			18338.4i			1.10916i
$650$	−7495.34	+	5765.94i	−0.452295	+	0.347936i
$651$		0			0
$652$	22287.7	+	5913.66i	1.33873	+	0.355210i
$653$	17522.7			1.05010			0.525052	−	0.851070i	$-0.324046\pi$
$653$	17522.7			1.05010			0.525052	+	0.851070i	$0.324046\pi$
$654$		0			0
$655$		−	11996.3i		−	0.715625i
$656$	−3556.99	+	6230.99i	−0.211703	+	0.370853i
$657$		0			0
$658$	13481.1	+	4262.71i	0.798705	+	0.252550i
$659$			131.768i			0.00778899i	0.999992	+	0.00389450i	$0.00123966\pi$
$659$			131.768i			0.00778899i	−0.999992	+	0.00389450i	$0.998760\pi$
$660$		0			0
$661$			21150.0i			1.24454i	0.782803	+	0.622270i	$0.213789\pi$
$661$			21150.0i			1.24454i	−0.782803	+	0.622270i	$0.786211\pi$
$662$	−11341.5	+	8724.69i	−0.665863	+	0.512228i
$663$		0			0
$664$	8985.52	−	3760.56i	0.525159	−	0.219786i
$665$	−11177.4	−	16032.5i	−0.651790	−	0.934906i
$666$		0			0
$667$		−	20759.0i		−	1.20508i
$668$	5155.78	−	19431.4i	0.298627	−	1.12548i
$669$		0			0
$670$	−3132.15	−	4071.59i	−0.180605	−	0.234775i
$671$	−14489.5			−0.833620
$672$		0			0
$673$	11238.3			0.643693			0.321846	−	0.946792i	$-0.395697\pi$
$673$	11238.3			0.643693			0.321846	+	0.946792i	$0.395697\pi$
$674$	−20902.3	−	27171.7i	−1.19455	−	1.55284i
$675$		0			0
$676$	−1063.34	+	4007.59i	−0.0604998	+	0.228015i
$677$		−	4728.28i		−	0.268423i	−0.990953	−	0.134212i	$-0.957150\pi$
$677$		−	4728.28i		−	0.268423i	0.990953	−	0.134212i	$-0.0428502\pi$
$678$		0			0
$679$	−4044.84	−	5801.78i	−0.228611	−	0.327912i
$680$	−9556.57	+	3999.55i	−0.538938	+	0.225553i
$681$		0			0
$682$	16001.4	−	12309.4i	0.898425	−	0.691130i
$683$			26608.6i			1.49070i	0.666673	+	0.745350i	$0.267718\pi$
$683$			26608.6i			1.49070i	−0.666673	+	0.745350i	$0.732282\pi$
$684$		0			0
$685$			2117.77i			0.118125i
$686$	11007.6	−	14200.8i	0.612641	−	0.790361i
$687$		0			0
$688$	6155.92	−	10783.7i	0.341122	−	0.597565i
$689$			4933.33i			0.272779i
$690$		0			0
$691$	9292.47			0.511580			0.255790	−	0.966732i	$-0.417664\pi$
$691$	9292.47			0.511580			0.255790	+	0.966732i	$0.417664\pi$
$692$	10107.2	+	2681.78i	0.555230	+	0.147321i
$693$		0			0
$694$	14272.1	−	10979.1i	0.780634	−	0.600518i
$695$		−	8823.33i		−	0.481565i
$696$		0			0
$697$	7791.22			0.423406
$698$	11013.6	−	8472.44i	0.597237	−	0.459436i
$699$		0			0
$700$	4139.68	+	11359.5i	0.223522	+	0.613353i
$701$	13950.7			0.751657			0.375829	−	0.926689i	$-0.377358\pi$
$701$	13950.7			0.751657			0.375829	+	0.926689i	$0.377358\pi$
$702$		0			0
$703$	−3784.58			−0.203042
$704$	19779.6	+	19491.8i	1.05891	+	1.04350i
$705$		0			0
$706$	13109.1	−	10084.5i	0.698823	−	0.537583i
$707$	−7381.03	−	10587.1i	−0.392634	−	0.563181i
$708$		0			0
$709$	−29363.4			−1.55538			−0.777691	−	0.628646i	$-0.783609\pi$
$709$	−29363.4			−1.55538			−0.777691	+	0.628646i	$0.783609\pi$
$710$	3072.97	+	3994.66i	0.162432	+	0.211150i
$711$		0			0
$712$	10664.1	+	25480.8i	0.561309	+	1.34120i
$713$		−	11557.5i		−	0.607059i
$714$		0			0
$715$			14639.6i			0.765721i
$716$	27490.3	+	7294.08i	1.43486	+	0.380716i
$717$		0			0
$718$	−15859.1	+	12199.9i	−0.824312	+	0.634118i
$719$	−8612.18			−0.446704			−0.223352	−	0.974738i	$-0.571700\pi$
$719$	−8612.18			−0.446704			−0.223352	+	0.974738i	$0.571700\pi$
$720$		0			0
$721$	−9439.63	+	6581.04i	−0.487587	+	0.339932i
$722$	32424.7	+	42149.9i	1.67136	+	2.17266i
$723$		0			0
$724$	13508.3	+	3584.18i	0.693412	+	0.183985i
$725$	−19288.1			−0.988059
$726$		0			0
$727$	−19226.6			−0.980846			−0.490423	−	0.871484i	$-0.663158\pi$
$727$	−19226.6			−0.980846			−0.490423	+	0.871484i	$0.663158\pi$
$728$	−14496.0	−	9201.92i	−0.737992	−	0.468469i
$729$		0			0
$730$	−14060.1	−	18277.2i	−0.712860	−	0.926671i
$731$	−13483.9			−0.682245
$732$		0			0
$733$		−	33053.9i		−	1.66559i	−0.553584	−	0.832793i	$-0.686740\pi$
$733$		−	33053.9i		−	1.66559i	0.553584	−	0.832793i	$-0.313260\pi$
$734$	6433.82	+	8363.55i	0.323538	+	0.420578i
$735$		0			0
$736$	15748.9	−	2171.31i	0.788741	−	0.108744i
$737$	14953.0			0.747353
$738$		0			0
$739$			4071.71i			0.202679i	0.994852	+	0.101340i	$0.0323129\pi$
$739$			4071.71i			0.202679i	−0.994852	+	0.101340i	$0.967687\pi$
$740$	−1203.48	−	319.323i	−0.0597849	−	0.0158629i
$741$		0			0
$742$	6013.82	+	1901.56i	0.297539	+	0.0940817i
$743$			807.693i			0.0398807i	0.999801	+	0.0199404i	$0.00634763\pi$
$743$			807.693i			0.0398807i	−0.999801	+	0.0199404i	$0.993652\pi$
$744$		0			0
$745$			18109.5i			0.890577i
$746$	17187.4	+	22342.4i	0.843531	+	1.09653i
$747$		0			0
$748$	7733.73	−	29147.3i	0.378039	−	1.42477i
$749$	3130.07	+	4489.68i	0.152698	+	0.219024i
$750$		0			0
$751$		−	12604.7i		−	0.612454i	−0.951959	−	0.306227i	$-0.900933\pi$
$751$		−	12604.7i		−	0.612454i	0.951959	−	0.306227i	$-0.0990666\pi$
$752$	−15002.2	−	8564.07i	−0.727491	−	0.415292i
$753$		0			0
$754$	21711.2	−	16701.8i	1.04864	−	0.806688i
$755$	−12852.6			−0.619542
$756$		0			0
$757$	−18825.2			−0.903848			−0.451924	−	0.892056i	$-0.649262\pi$
$757$	−18825.2			−0.903848			−0.451924	+	0.892056i	$0.649262\pi$
$758$	−25537.6	+	19645.3i	−1.22371	+	0.941359i
$759$		0			0
$760$	9218.63	+	22027.1i	0.439993	+	1.05133i
$761$			7341.96i			0.349732i	0.984592	+	0.174866i	$0.0559492\pi$
$761$			7341.96i			0.349732i	−0.984592	+	0.174866i	$0.944051\pi$
$762$		0			0
$763$	10172.1	−	7091.72i	0.482642	−	0.336484i
$764$	−14967.7	−	3971.41i	−0.708785	−	0.188064i
$765$		0			0
$766$	−6708.09	−	8720.08i	−0.316414	−	0.411318i
$767$			13853.1i			0.652158i
$768$		0			0
$769$		−	37425.8i		−	1.75502i	−0.479560	−	0.877509i	$-0.659204\pi$
$769$		−	37425.8i		−	1.75502i	0.479560	−	0.877509i	$-0.340796\pi$
$770$	17846.0	+	5642.88i	0.835226	+	0.264098i
$771$		0			0
$772$	7883.07	−	29710.1i	0.367510	−	1.38509i
$773$		−	36961.6i		−	1.71982i	−0.510449	−	0.859908i	$-0.670521\pi$
$773$		−	36961.6i		−	1.71982i	0.510449	−	0.859908i	$-0.329479\pi$
$774$		0			0
$775$	−10738.6			−0.497733
$776$	3336.01	+	7971.11i	0.154325	+	0.368745i
$777$		0			0
$778$	16710.3	+	21722.3i	0.770043	+	1.00101i
$779$		−	17958.1i		−	0.825952i
$780$		0			0
$781$	−14670.4			−0.672149
$782$	−10526.3	−	13683.5i	−0.481354	−	0.625729i
$783$		0			0
$784$	−16804.8	+	14124.0i	−0.765527	+	0.643404i
$785$	19893.8			0.904510
$786$		0			0
$787$	22096.0			1.00081			0.500406	−	0.865791i	$-0.333184\pi$
$787$	22096.0			1.00081			0.500406	+	0.865791i	$0.333184\pi$
$788$	1006.58	−	3793.66i	0.0455051	−	0.171502i
$789$		0			0
$790$	7861.48	+	10219.4i	0.354049	+	0.460241i
$791$	16619.8	−	11586.8i	0.747068	−	0.520835i
$792$		0			0
$793$	−10945.5			−0.490148
$794$	24137.9	−	18568.6i	1.07887	−	0.829942i
$795$		0			0
$796$	7447.85	−	28069.9i	0.331636	−	1.24989i
$797$			40538.6i			1.80170i	0.434134	+	0.900848i	$0.357054\pi$
$797$			40538.6i			1.80170i	−0.434134	+	0.900848i	$0.642946\pi$
$798$		0			0
$799$			18758.7i			0.830583i
$800$	−2017.46	−	14633.0i	−0.0891601	−	0.646695i
$801$		0			0
$802$	6989.95	+	9086.48i	0.307760	+	0.400068i
$803$	67123.2			2.94985
$804$		0			0
$805$	8789.88	−	6128.05i	0.384848	−	0.268305i
$806$	12087.7	−	9298.68i	0.528251	−	0.406367i
$807$		0			0
$808$	6087.56	+	14545.7i	0.265049	+	0.633312i
$809$	15624.5			0.679022			0.339511	−	0.940602i	$-0.389738\pi$
$809$	15624.5			0.679022			0.339511	+	0.940602i	$0.389738\pi$
$810$		0			0
$811$	4997.93			0.216401			0.108200	−	0.994129i	$-0.465491\pi$
$811$	4997.93			0.216401			0.108200	+	0.994129i	$0.465491\pi$
$812$	−11991.1	−	32904.1i	−0.518234	−	1.42206i
$813$		0			0
$814$	2872.72	−	2209.90i	0.123696	−	0.0951558i
$815$	−18988.3			−0.816111
$816$		0			0
$817$			31079.3i			1.33088i
$818$	3402.78	−	2617.65i	0.145447	−	0.111888i
$819$		0			0
$820$	1515.21	−	5710.60i	0.0645286	−	0.243199i
$821$	−45367.1			−1.92853			−0.964266	−	0.264937i	$-0.914649\pi$
$821$	−45367.1			−1.92853			−0.964266	+	0.264937i	$0.914649\pi$
$822$		0			0
$823$			3913.77i			0.165766i	0.996559	+	0.0828829i	$0.0264128\pi$
$823$			3913.77i			0.165766i	−0.996559	+	0.0828829i	$0.973587\pi$
$824$	12969.2	−	5427.76i	0.548304	−	0.229472i
$825$		0			0
$826$	16887.2	+	5339.71i	0.711355	+	0.224930i
$827$			7368.11i			0.309812i	0.987929	+	0.154906i	$0.0495074\pi$
$827$			7368.11i			0.309812i	−0.987929	+	0.154906i	$0.950493\pi$
$828$		0			0
$829$			25074.8i			1.05052i	0.850941	+	0.525261i	$0.176032\pi$
$829$			25074.8i			1.05052i	−0.850941	+	0.525261i	$0.823968\pi$
$830$	−6357.65	+	4890.74i	−0.265876	+	0.204530i
$831$		0			0
$832$	14941.8	+	14724.4i	0.622613	+	0.613554i
$833$	22367.0	+	8244.44i	0.930338	+	0.342921i
$834$		0			0
$835$			16554.8i			0.686110i
$836$	−67182.0	−	17825.6i	−2.77935	−	0.737453i
$837$		0			0
$838$	−2465.13	−	3204.51i	−0.101619	−	0.132098i
$839$	11380.1			0.468279			0.234139	−	0.972203i	$-0.424773\pi$
$839$	11380.1			0.468279			0.234139	+	0.972203i	$0.424773\pi$
$840$		0			0
$841$	31481.5			1.29081
$842$	−1593.60	−	2071.58i	−0.0652245	−	0.0847876i
$843$		0			0
$844$	−19227.7	−	5101.73i	−0.784174	−	0.208067i
$845$		−	3414.31i		−	0.139001i
$846$		0			0
$847$	−24471.6	+	17060.9i	−0.992744	+	0.692113i
$848$	−6692.37	−	3820.37i	−0.271010	−	0.154708i
$849$		0			0
$850$	−12713.9	+	9780.44i	−0.513040	+	0.394666i
$851$		−	2074.92i		−	0.0835807i
$852$		0			0
$853$			2040.57i			0.0819082i	0.999161	+	0.0409541i	$0.0130397\pi$
$853$			2040.57i			0.0819082i	−0.999161	+	0.0409541i	$0.986960\pi$
$854$	−4218.99	+	13342.8i	−0.169052	+	0.534639i
$855$		0			0
$856$	−2581.55	−	6168.40i	−0.103079	−	0.246298i
$857$			14755.7i			0.588152i	0.955782	+	0.294076i	$0.0950120\pi$
$857$			14755.7i			0.588152i	−0.955782	+	0.294076i	$0.904988\pi$
$858$		0			0
$859$	−44194.2			−1.75540			−0.877698	−	0.479213i	$-0.840922\pi$
$859$	−44194.2			−1.75540			−0.877698	+	0.479213i	$0.840922\pi$
$860$	−2622.31	+	9883.08i	−0.103977	+	0.391873i
$861$		0			0
$862$	9190.39	−	7069.89i	0.363139	−	0.279352i
$863$		−	47866.0i		−	1.88804i	−0.329888	−	0.944020i	$-0.607011\pi$
$863$		−	47866.0i		−	1.88804i	0.329888	−	0.944020i	$-0.392989\pi$
$864$		0			0
$865$	−8610.97			−0.338476
$866$	−14236.0	+	10951.3i	−0.558615	+	0.429725i
$867$		0			0
$868$	−6676.04	−	18319.3i	−0.261059	−	0.716357i
$869$	−37530.9			−1.46507
$870$		0			0
$871$	11295.7			0.439425
$872$	−13975.6	+	5848.95i	−0.542743	+	0.227145i
$873$		0			0
$874$	−31539.3	+	24262.2i	−1.22063	+	0.938995i
$875$	−14415.9	−	20677.7i	−0.556966	−	0.798894i
$876$		0			0
$877$	−25430.0			−0.979146			−0.489573	−	0.871962i	$-0.662847\pi$
$877$	−25430.0			−0.979146			−0.489573	+	0.871962i	$0.662847\pi$
$878$	9288.36	+	12074.3i	0.357024	+	0.464108i
$879$		0			0
$880$	−19859.6	−	11336.9i	−0.760756	−	0.434281i
$881$			13602.8i			0.520192i	0.965583	+	0.260096i	$0.0837541\pi$
$881$			13602.8i			0.520192i	−0.965583	+	0.260096i	$0.916246\pi$
$882$		0			0
$883$			16042.8i			0.611419i	0.952125	+	0.305710i	$0.0988937\pi$
$883$			16042.8i			0.611419i	−0.952125	+	0.305710i	$0.901106\pi$
$884$	5842.16	−	22018.3i	0.222277	−	0.837731i
$885$		0			0
$886$	2822.75	−	2171.45i	0.107034	−	0.0823380i
$887$	−45834.8			−1.73504			−0.867520	−	0.497402i	$-0.834287\pi$
$887$	−45834.8			−1.73504			−0.867520	+	0.497402i	$0.834287\pi$
$888$		0			0
$889$	8868.17	+	12720.2i	0.334565	+	0.479890i
$890$	−13869.0	−	18028.8i	−0.522348	−	0.679019i
$891$		0			0
$892$	2036.74	−	7676.17i	0.0764519	−	0.288136i
$893$	43237.3			1.62025
$894$		0			0
$895$	−23420.7			−0.874713
$896$	23708.7	−	12538.8i	0.883986	−	0.467513i
$897$		0			0
$898$	−750.147	−	975.142i	−0.0278761	−	0.0362371i
$899$	31105.8			1.15399
$900$		0			0
$901$			8368.13i			0.309415i
$902$	10486.1	+	13631.3i	0.387084	+	0.503184i
$903$		0			0
$904$	−22834.0	+	9556.33i	−0.840097	+	0.351592i
$905$	−11508.5			−0.422714
$906$		0			0
$907$			11789.5i			0.431603i	0.976437	+	0.215801i	$0.0692363\pi$
$907$			11789.5i			0.431603i	−0.976437	+	0.215801i	$0.930764\pi$
$908$	−11624.8	+	43812.2i	−0.424871	+	1.60128i
$909$		0			0
$910$	13481.1	+	4262.71i	0.491092	+	0.155283i
$911$			34980.3i			1.27217i	0.771618	+	0.636087i	$0.219448\pi$
$911$			34980.3i			1.27217i	−0.771618	+	0.636087i	$0.780552\pi$
$912$		0			0
$913$		−	23348.5i		−	0.846356i
$914$	−5470.90	−	7111.82i	−0.197988	−	0.257372i
$915$		0			0
$916$	−50170.5	−	13311.9i	−1.80969	−	0.480171i
$917$	27665.7	−	19287.7i	0.996293	−	0.694587i
$918$		0			0
$919$		−	34836.9i		−	1.25045i	−0.780444	−	0.625225i	$-0.785007\pi$
$919$		−	34836.9i		−	1.25045i	0.780444	−	0.625225i	$-0.214993\pi$
$920$	−12076.5	+	5054.16i	−0.432771	+	0.181120i
$921$		0			0
$922$	28346.2	−	21805.8i	1.01251	−	0.778891i
$923$	−11082.2			−0.395207
$924$		0			0
$925$	−1927.90			−0.0685285
$926$	−31004.2	+	23850.6i	−1.10028	+	0.846413i
$927$		0			0
$928$	5843.84	+	42386.5i	0.206717	+	1.49936i
$929$			8027.80i			0.283513i	0.989902	+	0.141757i	$0.0452750\pi$
$929$			8027.80i			0.283513i	−0.989902	+	0.141757i	$0.954725\pi$
$930$		0			0
$931$	19002.8	−	51554.1i	0.668948	−	1.81484i
$932$	−7503.57	+	28279.8i	−0.263720	+	0.993923i
$933$		0			0
$934$	29393.1	+	38209.1i	1.02973	+	1.33859i
$935$			24832.4i			0.868562i
$936$		0			0
$937$		−	31147.0i		−	1.08594i	−0.839751	−	0.542972i	$-0.817299\pi$
$937$		−	31147.0i		−	1.08594i	0.839751	−	0.542972i	$-0.182701\pi$
$938$	4353.95	−	13769.6i	0.151558	−	0.479312i
$939$		0			0
$940$	13749.3	+	3648.13i	0.477076	+	0.126584i
$941$		−	14386.4i		−	0.498389i	−0.968453	−	0.249195i	$-0.919834\pi$
$941$		−	14386.4i		−	0.498389i	0.968453	−	0.249195i	$-0.0801659\pi$
$942$		0			0
$943$	9845.63			0.339998
$944$	−18792.6	−	10727.8i	−0.647930	−	0.369874i
$945$		0			0
$946$	−18147.9	−	23591.0i	−0.623718	−	0.810793i
$947$		−	1481.87i		−	0.0508494i	−0.999677	−	0.0254247i	$-0.991906\pi$
$947$		−	1481.87i		−	0.0508494i	0.999677	−	0.0254247i	$-0.00809380\pi$
$948$		0			0
$949$	50705.8			1.73444
$950$	22543.1	+	29304.6i	0.769889	+	1.00081i
$951$		0			0
$952$	−24588.8	−	15608.7i	−0.837108	−	0.531388i
$953$	4125.04			0.140213			0.0701065	−	0.997540i	$-0.477666\pi$
$953$	4125.04			0.140213			0.0701065	+	0.997540i	$0.477666\pi$
$954$		0			0
$955$	12751.9			0.432086
$956$	44895.4	+	11912.2i	1.51885	+	0.403001i
$957$		0			0
$958$	−7125.92	−	9263.24i	−0.240322	−	0.312402i
$959$	−4883.96	+	3404.96i	−0.164454	+	0.114653i
$960$		0			0
$961$	−12472.9			−0.418680
$962$	2170.09	−	1669.39i	0.0727304	−	0.0559492i
$963$		0			0
$964$	−4516.77	−	1198.45i	−0.150908	−	0.0400409i
$965$			25311.9i			0.844372i
$966$		0			0
$967$			17872.4i			0.594351i	0.954823	+	0.297175i	$0.0960446\pi$
$967$			17872.4i			0.594351i	−0.954823	+	0.297175i	$0.903955\pi$
$968$	33621.7	−	14071.1i	1.11637	−	0.467213i
$969$		0			0
$970$	−4338.61	−	5639.91i	−0.143613	−	0.186687i
$971$	6473.23			0.213940			0.106970	−	0.994262i	$-0.465885\pi$
$971$	6473.23			0.213940			0.106970	+	0.994262i	$0.465885\pi$
$972$		0			0
$973$	20348.2	−	14186.2i	0.670435	−	0.467408i
$974$	−25458.3	+	19584.3i	−0.837511	+	0.644271i
$975$		0			0
$976$	8476.22	−	14848.3i	0.277989	−	0.486970i
$977$	−32958.4			−1.07926			−0.539628	−	0.841904i	$-0.681435\pi$
$977$	−32958.4			−1.07926			−0.539628	+	0.841904i	$0.681435\pi$
$978$		0			0
$979$	66210.9			2.16150
$980$	10392.7	−	14790.6i	0.338756	−	0.482112i
$981$		0			0
$982$	−17856.0	+	13736.1i	−0.580252	+	0.446370i
$983$	11342.0			0.368010			0.184005	−	0.982925i	$-0.441094\pi$
$983$	11342.0			0.368010			0.184005	+	0.982925i	$0.441094\pi$
$984$		0			0
$985$			3232.06i			0.104550i
$986$	36827.5	−	28330.3i	1.18948	−	0.915031i
$987$		0			0
$988$	−50750.2	−	13465.7i	−1.63419	−	0.433604i
$989$	−17039.4			−0.547847
$990$		0			0
$991$		−	15910.0i		−	0.509987i	−0.966943	−	0.254994i	$-0.917927\pi$
$991$		−	15910.0i		−	0.509987i	0.966943	−	0.254994i	$-0.0820733\pi$
$992$	3253.55	+	23598.6i	0.104133	+	0.755299i
$993$		0			0
$994$	−4271.68	+	13509.4i	−0.136307	+	0.431080i
$995$			23914.5i			0.761949i
$996$		0			0
$997$		−	3756.74i		−	0.119335i	−0.998218	−	0.0596676i	$-0.980996\pi$
$997$		−	3756.74i		−	0.119335i	0.998218	−	0.0596676i	$-0.0190041\pi$
$998$	−4678.49	+	3599.02i	−0.148392	+	0.114153i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.f.55.10		12
3.2	odd	2		84.4.b.a.55.3	✓	12
4.3	odd	2		252.4.b.e.55.9		12
7.6	odd	2		252.4.b.e.55.10		12
12.11	even	2		84.4.b.b.55.4	yes	12
21.20	even	2		84.4.b.b.55.3	yes	12
24.5	odd	2		1344.4.b.h.895.4		12
24.11	even	2		1344.4.b.g.895.4		12
28.27	even	2	inner	252.4.b.f.55.9		12
84.83	odd	2		84.4.b.a.55.4	yes	12
168.83	odd	2		1344.4.b.h.895.9		12
168.125	even	2		1344.4.b.g.895.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.b.a.55.3	✓	12	3.2	odd	2
84.4.b.a.55.4	yes	12	84.83	odd	2
84.4.b.b.55.3	yes	12	21.20	even	2
84.4.b.b.55.4	yes	12	12.11	even	2
252.4.b.e.55.9		12	4.3	odd	2
252.4.b.e.55.10		12	7.6	odd	2
252.4.b.f.55.9		12	28.27	even	2	inner
252.4.b.f.55.10		12	1.1	even	1	trivial
1344.4.b.g.895.4		12	24.11	even	2
1344.4.b.g.895.9		12	168.125	even	2
1344.4.b.h.895.4		12	24.5	odd	2
1344.4.b.h.895.9		12	168.83	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)

\(f(q)\)	\(=\)	\(q+(1.72458 + 2.24184i) q^{2} +(-2.05167 + 7.73244i) q^{4} -6.58775i q^{5} +(15.1925 - 10.5918i) q^{7} +(-20.8731 + 8.73568i) q^{8} +O(q^{10})\)	\(q+(1.72458 + 2.24184i) q^{2} +(-2.05167 + 7.73244i) q^{4} -6.58775i q^{5} +(15.1925 - 10.5918i) q^{7} +(-20.8731 + 8.73568i) q^{8} +(14.7687 - 11.3611i) q^{10} +54.2380i q^{11} +40.9722i q^{13} +(49.9458 + 15.7928i) q^{14} +(-55.5813 - 31.7288i) q^{16} +69.4988i q^{17} +160.189 q^{19} +(50.9394 + 13.5159i) q^{20} +(-121.593 + 93.5376i) q^{22} +87.8244i q^{23} +81.6016 q^{25} +(-91.8529 + 70.6596i) q^{26} +(50.7305 + 139.206i) q^{28} -236.369 q^{29} -131.598 q^{31} +(-24.7233 - 179.323i) q^{32} +(-155.805 + 119.856i) q^{34} +(-69.7762 - 100.085i) q^{35} -23.6257 q^{37} +(276.258 + 359.118i) q^{38} +(57.5485 + 137.507i) q^{40} -112.106i q^{41} +194.017i q^{43} +(-419.392 - 111.279i) q^{44} +(-196.888 + 151.460i) q^{46} +269.914 q^{47} +(118.627 - 321.833i) q^{49} +(140.728 + 182.937i) q^{50} +(-316.815 - 84.0613i) q^{52} +120.407 q^{53} +357.307 q^{55} +(-224.590 + 353.802i) q^{56} +(-407.637 - 529.902i) q^{58} +338.109 q^{59} +267.146i q^{61} +(-226.951 - 295.022i) q^{62} +(359.376 - 364.682i) q^{64} +269.914 q^{65} -275.691i q^{67} +(-537.395 - 142.589i) q^{68} +(104.039 - 329.031i) q^{70} +270.482i q^{71} -1237.57i q^{73} +(-40.7444 - 52.9651i) q^{74} +(-328.655 + 1238.65i) q^{76} +(574.479 + 824.014i) q^{77} +691.966i q^{79} +(-209.022 + 366.156i) q^{80} +(251.323 - 193.335i) q^{82} -430.482 q^{83} +457.841 q^{85} +(-434.954 + 334.596i) q^{86} +(-473.806 - 1132.12i) q^{88} -1220.75i q^{89} +(433.969 + 622.472i) q^{91} +(-679.097 - 180.187i) q^{92} +(465.488 + 605.104i) q^{94} -1055.28i q^{95} -381.884i q^{97} +(926.079 - 289.083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} + 10 q^{7} - 25 q^{8}+O(q^{10}) \) 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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