LMFDB - Embedded newform 1368.2.e.g.379.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.17
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388306 - 1.35986i) q^{2} +(-1.69844 + 1.05608i) q^{4} +1.84435i q^{5} -2.17959i q^{7} +(2.09564 + 1.89955i) q^{8} +O(q^{10})$	\(q+(-0.388306 - 1.35986i) q^{2} +(-1.69844 + 1.05608i) q^{4} +1.84435i q^{5} -2.17959i q^{7} +(2.09564 + 1.89955i) q^{8} +(2.50805 - 0.716171i) q^{10} +4.96519 q^{11} -3.69149 q^{13} +(-2.96394 + 0.846348i) q^{14} +(1.76937 - 3.58738i) q^{16} +2.85570 q^{17} +(-3.47371 + 2.63312i) q^{19} +(-1.94778 - 3.13251i) q^{20} +(-1.92802 - 6.75197i) q^{22} +7.16583i q^{23} +1.59839 q^{25} +(1.43343 + 5.01991i) q^{26} +(2.30183 + 3.70190i) q^{28} -9.32113 q^{29} +4.76579 q^{31} +(-5.56540 - 1.01310i) q^{32} +(-1.10889 - 3.88335i) q^{34} +4.01992 q^{35} +2.36528 q^{37} +(4.92954 + 3.70130i) q^{38} +(-3.50343 + 3.86508i) q^{40} -0.613311i q^{41} -1.93580 q^{43} +(-8.43307 + 5.24366i) q^{44} +(9.74453 - 2.78254i) q^{46} +7.16015i q^{47} +2.24939 q^{49} +(-0.620663 - 2.17358i) q^{50} +(6.26977 - 3.89853i) q^{52} +11.4143 q^{53} +9.15754i q^{55} +(4.14024 - 4.56763i) q^{56} +(3.61945 + 12.6754i) q^{58} +4.64963i q^{59} +1.26055i q^{61} +(-1.85058 - 6.48080i) q^{62} +(0.783404 + 7.96155i) q^{64} -6.80839i q^{65} -3.30041i q^{67} +(-4.85022 + 3.01586i) q^{68} +(-1.56096 - 5.46652i) q^{70} +11.8343 q^{71} +15.7639 q^{73} +(-0.918453 - 3.21645i) q^{74} +(3.11908 - 8.14072i) q^{76} -10.8221i q^{77} +5.39784 q^{79} +(6.61638 + 3.26334i) q^{80} +(-0.834017 + 0.238153i) q^{82} +10.9571 q^{83} +5.26690i q^{85} +(0.751684 + 2.63242i) q^{86} +(10.4053 + 9.43165i) q^{88} -3.23446i q^{89} +8.04594i q^{91} +(-7.56772 - 12.1707i) q^{92} +(9.73679 - 2.78033i) q^{94} +(-4.85639 - 6.40673i) q^{95} +4.47099i q^{97} +(-0.873451 - 3.05885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.388306	−	1.35986i	−0.274574	−	0.961566i
$2$	−0.388306	−	1.35986i	−0.274574	−	0.961566i
$3$		0			0
$3$		0			0
$4$	−1.69844	+	1.05608i	−0.849218	+	0.528042i
$5$			1.84435i			0.824817i	0.910999	+	0.412408i	$0.135312\pi$
$5$			1.84435i			0.824817i	−0.910999	+	0.412408i	$0.864688\pi$
$6$		0			0
$7$		−	2.17959i		−	0.823808i	−0.911227	−	0.411904i	$-0.864864\pi$
$7$		−	2.17959i		−	0.823808i	0.911227	−	0.411904i	$-0.135136\pi$
$8$	2.09564	+	1.89955i	0.740920	+	0.671593i
$9$		0			0
$10$	2.50805	−	0.716171i	0.793116	−	0.226473i
$11$	4.96519			1.49706			0.748531	−	0.663100i	$-0.230759\pi$
$11$	4.96519			1.49706			0.748531	+	0.663100i	$0.230759\pi$
$12$		0			0
$13$	−3.69149			−1.02384			−0.511918	−	0.859034i	$-0.671065\pi$
$13$	−3.69149			−1.02384			−0.511918	+	0.859034i	$0.671065\pi$
$14$	−2.96394	+	0.846348i	−0.792145	+	0.226196i
$15$		0			0
$16$	1.76937	−	3.58738i	0.442344	−	0.896846i
$17$	2.85570			0.692609			0.346304	−	0.938122i	$-0.387436\pi$
$17$	2.85570			0.692609			0.346304	+	0.938122i	$0.387436\pi$
$18$		0			0
$19$	−3.47371	+	2.63312i	−0.796924	+	0.604079i
$19$	−3.47371	+	2.63312i	−0.796924	+	0.604079i
$20$	−1.94778	−	3.13251i	−0.435538	−	0.700449i
$21$		0			0
$22$	−1.92802	−	6.75197i	−0.411054	−	1.43952i
$23$			7.16583i			1.49418i	0.664723	+	0.747090i	$0.268550\pi$
$23$			7.16583i			1.49418i	−0.664723	+	0.747090i	$0.731450\pi$
$24$		0			0
$25$	1.59839			0.319677
$26$	1.43343	+	5.01991i	0.281119	+	0.984486i
$27$		0			0
$28$	2.30183	+	3.70190i	0.435005	+	0.699592i
$29$	−9.32113			−1.73089			−0.865445	−	0.501004i	$-0.832964\pi$
$29$	−9.32113			−1.73089			−0.865445	+	0.501004i	$0.832964\pi$
$30$		0			0
$31$	4.76579			0.855961			0.427980	−	0.903788i	$-0.359225\pi$
$31$	4.76579			0.855961			0.427980	+	0.903788i	$0.359225\pi$
$32$	−5.56540	−	1.01310i	−0.983832	−	0.179092i
$33$		0			0
$34$	−1.10889	−	3.88335i	−0.190172	−	0.665989i
$35$	4.01992			0.679490
$36$		0			0
$37$	2.36528			0.388850			0.194425	−	0.980917i	$-0.437716\pi$
$37$	2.36528			0.388850			0.194425	+	0.980917i	$0.437716\pi$
$38$	4.92954	+	3.70130i	0.799677	+	0.600431i
$39$		0			0
$40$	−3.50343	+	3.86508i	−0.553941	+	0.611123i
$41$		−	0.613311i		−	0.0957831i	−0.998853	−	0.0478916i	$-0.984750\pi$
$41$		−	0.613311i		−	0.0957831i	0.998853	−	0.0478916i	$-0.0152502\pi$
$42$		0			0
$43$	−1.93580			−0.295207			−0.147604	−	0.989047i	$-0.547156\pi$
$43$	−1.93580			−0.295207			−0.147604	+	0.989047i	$0.547156\pi$
$44$	−8.43307	+	5.24366i	−1.27133	+	0.790512i
$45$		0			0
$46$	9.74453	−	2.78254i	1.43675	−	0.410263i
$47$			7.16015i			1.04441i	0.852819	+	0.522207i	$0.174891\pi$
$47$			7.16015i			1.04441i	−0.852819	+	0.522207i	$0.825109\pi$
$48$		0			0
$49$	2.24939			0.321341
$50$	−0.620663	−	2.17358i	−0.0877751	−	0.307391i
$51$		0			0
$52$	6.26977	−	3.89853i	0.869461	−	0.540628i
$53$	11.4143			1.56787			0.783934	−	0.620844i	$-0.213210\pi$
$53$	11.4143			1.56787			0.783934	+	0.620844i	$0.213210\pi$
$54$		0			0
$55$			9.15754i			1.23480i
$56$	4.14024	−	4.56763i	0.553263	−	0.610376i
$57$		0			0
$58$	3.61945	+	12.6754i	0.475257	+	1.66437i
$59$			4.64963i			0.605330i	0.953097	+	0.302665i	$0.0978763\pi$
$59$			4.64963i			0.605330i	−0.953097	+	0.302665i	$0.902124\pi$
$60$		0			0
$61$			1.26055i			0.161397i	0.996739	+	0.0806986i	$0.0257151\pi$
$61$			1.26055i			0.161397i	−0.996739	+	0.0806986i	$0.974285\pi$
$62$	−1.85058	−	6.48080i	−0.235024	−	0.823063i
$63$		0			0
$64$	0.783404	+	7.96155i	0.0979256	+	0.995194i
$65$		−	6.80839i		−	0.844477i
$66$		0			0
$67$		−	3.30041i		−	0.403209i	−0.979467	−	0.201605i	$-0.935384\pi$
$67$		−	3.30041i		−	0.403209i	0.979467	−	0.201605i	$-0.0646156\pi$
$68$	−4.85022	+	3.01586i	−0.588176	+	0.365726i
$69$		0			0
$70$	−1.56096	−	5.46652i	−0.186570	−	0.653375i
$71$	11.8343			1.40448			0.702239	−	0.711942i	$-0.252184\pi$
$71$	11.8343			1.40448			0.702239	+	0.711942i	$0.252184\pi$
$72$		0			0
$73$	15.7639			1.84503			0.922515	−	0.385962i	$-0.126131\pi$
$73$	15.7639			1.84503			0.922515	+	0.385962i	$0.126131\pi$
$74$	−0.918453	−	3.21645i	−0.106768	−	0.373905i
$75$		0			0
$76$	3.11908	−	8.14072i	0.357783	−	0.933805i
$77$		−	10.8221i		−	1.23329i
$78$		0			0
$79$	5.39784			0.607305			0.303652	−	0.952783i	$-0.401794\pi$
$79$	5.39784			0.607305			0.303652	+	0.952783i	$0.401794\pi$
$80$	6.61638	+	3.26334i	0.739733	+	0.364852i
$81$		0			0
$82$	−0.834017	+	0.238153i	−0.0921018	+	0.0262995i
$83$	10.9571			1.20269			0.601346	−	0.798988i	$-0.294631\pi$
$83$	10.9571			1.20269			0.601346	+	0.798988i	$0.294631\pi$
$84$		0			0
$85$			5.26690i			0.571275i
$86$	0.751684	+	2.63242i	0.0810562	+	0.283861i
$87$		0			0
$88$	10.4053	+	9.43165i	1.10920	+	1.00542i
$89$		−	3.23446i		−	0.342853i	−0.985197	−	0.171426i	$-0.945162\pi$
$89$		−	3.23446i		−	0.342853i	0.985197	−	0.171426i	$-0.0548375\pi$
$90$		0			0
$91$			8.04594i			0.843444i
$92$	−7.56772	−	12.1707i	−0.788989	−	1.26888i
$93$		0			0
$94$	9.73679	−	2.78033i	1.00427	−	0.286769i
$95$	−4.85639	−	6.40673i	−0.498255	−	0.657316i
$96$		0			0
$97$			4.47099i			0.453961i	0.973899	+	0.226980i	$0.0728853\pi$
$97$			4.47099i			0.453961i	−0.973899	+	0.226980i	$0.927115\pi$
$98$	−0.873451	−	3.05885i	−0.0882319	−	0.308991i
$99$		0			0
$100$	−2.71476	+	1.68803i	−0.271476	+	0.168803i
$101$			16.5617i			1.64795i	0.566626	+	0.823975i	$0.308248\pi$
$101$			16.5617i			1.64795i	−0.566626	+	0.823975i	$0.691752\pi$
$102$		0			0
$103$	−7.10698			−0.700272			−0.350136	−	0.936699i	$-0.613865\pi$
$103$	−7.10698			−0.700272			−0.350136	+	0.936699i	$0.613865\pi$
$104$	−7.73604	−	7.01219i	−0.758581	−	0.687601i
$105$		0			0
$106$	−4.43223	−	15.5218i	−0.430496	−	1.50761i
$107$			20.4867i			1.98052i	0.139215	+	0.990262i	$0.455542\pi$
$107$			20.4867i			1.98052i	−0.139215	+	0.990262i	$0.544458\pi$
$108$		0			0
$109$	−0.203761			−0.0195168			−0.00975838	−	0.999952i	$-0.503106\pi$
$109$	−0.203761			−0.0195168			−0.00975838	+	0.999952i	$0.503106\pi$
$110$	12.4530	−	3.55593i	1.18734	−	0.339044i
$111$		0			0
$112$	−7.81902	−	3.85651i	−0.738828	−	0.364406i
$113$		−	10.0136i		−	0.941997i	−0.882134	−	0.470998i	$-0.843894\pi$
$113$		−	10.0136i		−	0.941997i	0.882134	−	0.470998i	$-0.156106\pi$
$114$		0			0
$115$	−13.2163			−1.23242
$116$	15.8313	−	9.84389i	1.46990	−	0.913982i
$117$		0			0
$118$	6.32284	−	1.80548i	0.582064	−	0.166208i
$119$		−	6.22425i		−	0.570576i
$120$		0			0
$121$	13.6532			1.24120
$122$	1.71417	−	0.489480i	0.155194	−	0.0443155i
$123$		0			0
$124$	−8.09439	+	5.03307i	−0.726898	+	0.451983i
$125$			12.1697i			1.08849i
$126$		0			0
$127$	−13.2985			−1.18005			−0.590025	−	0.807385i	$-0.700882\pi$
$127$	−13.2985			−1.18005			−0.590025	+	0.807385i	$0.700882\pi$
$128$	10.5224	−	4.15684i	0.930057	−	0.367416i
$129$		0			0
$130$	−9.25846	+	2.64374i	−0.812021	+	0.231871i
$131$	−13.8130			−1.20685			−0.603423	−	0.797421i	$-0.706197\pi$
$131$	−13.8130			−1.20685			−0.603423	+	0.797421i	$0.706197\pi$
$132$		0			0
$133$	5.73912	+	7.57127i	0.497645	+	0.656512i
$134$	−4.48809	+	1.28157i	−0.387712	+	0.110711i
$135$		0			0
$136$	5.98451	+	5.42455i	0.513168	+	0.465151i
$137$	7.87915			0.673161			0.336581	−	0.941655i	$-0.390730\pi$
$137$	7.87915			0.673161			0.336581	+	0.941655i	$0.390730\pi$
$138$		0			0
$139$	11.5642			0.980865			0.490433	−	0.871479i	$-0.336839\pi$
$139$	11.5642			0.980865			0.490433	+	0.871479i	$0.336839\pi$
$140$	−6.82758	+	4.24537i	−0.577036	+	0.358799i
$141$		0			0
$142$	−4.59534	−	16.0930i	−0.385633	−	1.35050i
$143$	−18.3290			−1.53275
$144$		0			0
$145$		−	17.1914i		−	1.42767i
$146$	−6.12123	−	21.4367i	−0.506597	−	1.77412i
$147$		0			0
$148$	−4.01728	+	2.49794i	−0.330219	+	0.205329i
$149$		−	19.1818i		−	1.57143i	−0.618586	−	0.785717i	$-0.712294\pi$
$149$		−	19.1818i		−	1.57143i	0.618586	−	0.785717i	$-0.287706\pi$
$150$		0			0
$151$	−6.84481			−0.557022			−0.278511	−	0.960433i	$-0.589841\pi$
$151$	−6.84481			−0.557022			−0.278511	+	0.960433i	$0.589841\pi$
$152$	−12.2814	−	1.08042i	−0.996153	−	0.0876340i
$153$		0			0
$154$	−14.7165	+	4.20228i	−1.18589	+	0.338630i
$155$			8.78976i			0.706011i
$156$		0			0
$157$			5.66411i			0.452045i	0.974122	+	0.226022i	$0.0725723\pi$
$157$			5.66411i			0.452045i	−0.974122	+	0.226022i	$0.927428\pi$
$158$	−2.09601	−	7.34031i	−0.166750	−	0.583963i
$159$		0			0
$160$	1.86851	−	10.2645i	0.147718	−	0.811481i
$161$	15.6186			1.23092
$162$		0			0
$163$	−19.0834			−1.49473			−0.747365	−	0.664413i	$-0.768681\pi$
$163$	−19.0834			−1.49473			−0.747365	+	0.664413i	$0.768681\pi$
$164$	0.647708	+	1.04167i	0.0505775	+	0.0813408i
$165$		0			0
$166$	−4.25469	−	14.9001i	−0.330228	−	1.15647i
$167$	−14.6821			−1.13614			−0.568069	−	0.822981i	$-0.692309\pi$
$167$	−14.6821			−1.13614			−0.568069	+	0.822981i	$0.692309\pi$
$168$		0			0
$169$	0.627133			0.0482410
$170$	7.16224	−	2.04517i	0.549319	−	0.156857i
$171$		0			0
$172$	3.28784	−	2.04437i	0.250695	−	0.155882i
$173$	7.14332			0.543097			0.271548	−	0.962425i	$-0.412464\pi$
$173$	7.14332			0.543097			0.271548	+	0.962425i	$0.412464\pi$
$174$		0			0
$175$		−	3.48383i		−	0.263353i
$176$	8.78529	−	17.8121i	0.662216	−	1.34263i
$177$		0			0
$178$	−4.39842	+	1.25596i	−0.329675	+	0.0941383i
$179$		−	13.2249i		−	0.988475i	−0.869327	−	0.494237i	$-0.835447\pi$
$179$		−	13.2249i		−	0.988475i	0.869327	−	0.494237i	$-0.164553\pi$
$180$		0			0
$181$	5.37220			0.399313			0.199656	−	0.979866i	$-0.436017\pi$
$181$	5.37220			0.399313			0.199656	+	0.979866i	$0.436017\pi$
$182$	10.9414	−	3.12429i	0.811027	−	0.231588i
$183$		0			0
$184$	−13.6119	+	15.0170i	−1.00348	+	1.10707i
$185$			4.36240i			0.320730i
$186$		0			0
$187$	14.1791			1.03688
$188$	−7.56171	−	12.1611i	−0.551495	−	0.886936i
$189$		0			0
$190$	−6.82648	+	9.09178i	−0.495245	+	0.659587i
$191$			8.64962i			0.625865i	0.949775	+	0.312932i	$0.101311\pi$
$191$			8.64962i			0.625865i	−0.949775	+	0.312932i	$0.898689\pi$
$192$		0			0
$193$			2.15616i			0.155204i	0.996984	+	0.0776018i	$0.0247263\pi$
$193$			2.15616i			0.155204i	−0.996984	+	0.0776018i	$0.975274\pi$
$194$	6.07992	−	1.73611i	0.436513	−	0.124646i
$195$		0			0
$196$	−3.82044	+	2.37554i	−0.272889	+	0.169682i
$197$			6.26682i			0.446493i	0.974762	+	0.223246i	$0.0716654\pi$
$197$			6.26682i			0.446493i	−0.974762	+	0.223246i	$0.928335\pi$
$198$		0			0
$199$		−	19.2477i		−	1.36443i	−0.731150	−	0.682216i	$-0.761016\pi$
$199$		−	19.2477i		−	1.36443i	0.731150	−	0.682216i	$-0.238984\pi$
$200$	3.34964	+	3.03622i	0.236855	+	0.214693i
$201$		0			0
$202$	22.5216	−	6.43100i	1.58461	−	0.452484i
$203$			20.3162i			1.42592i
$204$		0			0
$205$	1.13116			0.0790035
$206$	2.75968	+	9.66450i	0.192276	+	0.673357i
$207$		0			0
$208$	−6.53164	+	13.2428i	−0.452888	+	0.918223i
$209$	−17.2477	+	13.0740i	−1.19305	+	0.904345i
$210$		0			0
$211$			9.79567i			0.674362i	0.941440	+	0.337181i	$0.109473\pi$
$211$			9.79567i			0.674362i	−0.941440	+	0.337181i	$0.890527\pi$
$212$	−19.3864	+	12.0544i	−1.33146	+	0.827900i
$213$		0			0
$214$	27.8590	−	7.95511i	1.90441	−	0.543800i
$215$		−	3.57029i		−	0.243492i
$216$		0			0
$217$		−	10.3875i		−	0.705147i
$218$	0.0791216	+	0.277086i	0.00535879	+	0.0187667i
$219$		0			0
$220$	−9.67113	−	15.5535i	−0.652027	−	1.04862i
$221$	−10.5418			−0.709118
$222$		0			0
$223$	17.9777			1.20388			0.601938	−	0.798543i	$-0.294395\pi$
$223$	17.9777			1.20388			0.601938	+	0.798543i	$0.294395\pi$
$224$	−2.20814	+	12.1303i	−0.147538	+	0.810488i
$225$		0			0
$226$	−13.6170	+	3.88833i	−0.905792	+	0.258648i
$227$			3.71277i			0.246425i	0.992380	+	0.123213i	$0.0393197\pi$
$227$			3.71277i			0.246425i	−0.992380	+	0.123213i	$0.960680\pi$
$228$		0			0
$229$		−	12.1889i		−	0.805464i	−0.915318	−	0.402732i	$-0.868061\pi$
$229$		−	12.1889i		−	0.805464i	0.915318	−	0.402732i	$-0.131939\pi$
$230$	5.13196	+	17.9723i	0.338391	+	1.18506i
$231$		0			0
$232$	−19.5337	−	17.7060i	−1.28245	−	1.16245i
$233$	−8.30693			−0.544205			−0.272103	−	0.962268i	$-0.587719\pi$
$233$	−8.30693			−0.544205			−0.272103	+	0.962268i	$0.587719\pi$
$234$		0			0
$235$	−13.2058			−0.861451
$236$	−4.91039	−	7.89709i	−0.319639	−	0.514057i
$237$		0			0
$238$	−8.46411	+	2.41691i	−0.548647	+	0.156665i
$239$		−	10.5696i		−	0.683690i	−0.939756	−	0.341845i	$-0.888948\pi$
$239$		−	10.5696i		−	0.683690i	0.939756	−	0.341845i	$-0.111052\pi$
$240$		0			0
$241$		−	24.8552i		−	1.60106i	−0.599290	−	0.800532i	$-0.704551\pi$
$241$		−	24.8552i		−	1.60106i	0.599290	−	0.800532i	$-0.295449\pi$
$242$	−5.30160	−	18.5664i	−0.340800	−	1.19349i
$243$		0			0
$244$	−1.33125	−	2.14097i	−0.0852245	−	0.137061i
$245$			4.14865i			0.265048i
$246$		0			0
$247$	12.8232	−	9.72015i	0.815920	−	0.618479i
$248$	9.98737	+	9.05286i	0.634199	+	0.574857i
$249$		0			0
$250$	16.5491	−	4.72557i	1.04666	−	0.298871i
$251$	−4.52026			−0.285316			−0.142658	−	0.989772i	$-0.545565\pi$
$251$	−4.52026			−0.285316			−0.142658	+	0.989772i	$0.545565\pi$
$252$		0			0
$253$			35.5798i			2.23688i
$254$	5.16388	+	18.0841i	0.324011	+	1.13470i
$255$		0			0
$256$	−9.73863	−	12.6948i	−0.608664	−	0.793428i
$257$			25.3366i			1.58045i	0.612815	+	0.790226i	$0.290037\pi$
$257$			25.3366i			1.58045i	−0.612815	+	0.790226i	$0.709963\pi$
$258$		0			0
$259$		−	5.15534i		−	0.320338i
$260$	7.19023	+	11.5636i	0.445919	+	0.717146i
$261$		0			0
$262$	5.36367	+	18.7837i	0.331368	+	1.16046i
$263$			0.978384i			0.0603297i	0.999545	+	0.0301649i	$0.00960323\pi$
$263$			0.978384i			0.0603297i	−0.999545	+	0.0301649i	$0.990397\pi$
$264$		0			0
$265$			21.0518i			1.29320i
$266$	8.06732	−	10.7444i	0.494639	−	0.658780i
$267$		0			0
$268$	3.48551	+	5.60554i	0.212911	+	0.342413i
$269$	−2.96559			−0.180815			−0.0904075	−	0.995905i	$-0.528817\pi$
$269$	−2.96559			−0.180815			−0.0904075	+	0.995905i	$0.528817\pi$
$270$		0			0
$271$			5.79376i			0.351946i	0.984395	+	0.175973i	$0.0563071\pi$
$271$			5.79376i			0.351946i	−0.984395	+	0.175973i	$0.943693\pi$
$272$	5.05280	−	10.2445i	0.306371	−	0.621163i
$273$		0			0
$274$	−3.05952	−	10.7145i	−0.184833	−	0.647289i
$275$	7.93630			0.478577
$276$		0			0
$277$		−	30.9347i		−	1.85869i	−0.369218	−	0.929343i	$-0.620374\pi$
$277$		−	30.9347i		−	1.85869i	0.369218	−	0.929343i	$-0.379626\pi$
$278$	−4.49046	−	15.7257i	−0.269320	−	0.943166i
$279$		0			0
$280$	8.42430	+	7.63604i	0.503448	+	0.456341i
$281$			0.0986880i			0.00588724i	0.999996	+	0.00294362i	$0.000936984\pi$
$281$			0.0986880i			0.00588724i	−0.999996	+	0.00294362i	$0.999063\pi$
$282$		0			0
$283$	14.3319			0.851944			0.425972	−	0.904736i	$-0.359932\pi$
$283$	14.3319			0.851944			0.425972	+	0.904736i	$0.359932\pi$
$284$	−20.0999	+	12.4980i	−1.19271	+	0.741623i
$285$		0			0
$286$	7.11726	+	24.9249i	0.420852	+	1.47384i
$287$	−1.33677			−0.0789069
$288$		0			0
$289$	−8.84498			−0.520293
$290$	−23.3779	+	6.67552i	−1.37280	+	0.392000i
$291$		0			0
$292$	−26.7740	+	16.6480i	−1.56683	+	0.974252i
$293$	−13.4494			−0.785724			−0.392862	−	0.919598i	$-0.628515\pi$
$293$	−13.4494			−0.785724			−0.392862	+	0.919598i	$0.628515\pi$
$294$		0			0
$295$	−8.57552			−0.499286
$296$	4.95678	+	4.49298i	0.288107	+	0.261149i
$297$		0			0
$298$	−26.0846	+	7.44841i	−1.51104	+	0.431475i
$299$		−	26.4526i		−	1.52980i
$300$		0			0
$301$			4.21926i			0.243194i
$302$	2.65788	+	9.30798i	0.152944	+	0.535614i
$303$		0			0
$304$	3.29972	+	17.1205i	0.189252	+	0.981929i
$305$	−2.32490			−0.133123
$306$		0			0
$307$			31.7666i			1.81301i	0.422190	+	0.906507i	$0.361261\pi$
$307$			31.7666i			1.81301i	−0.422190	+	0.906507i	$0.638739\pi$
$308$	11.4290	+	18.3806i	0.651229	+	1.04733i
$309$		0			0
$310$	11.9528	−	3.41312i	0.678876	−	0.193852i
$311$			5.29321i			0.300150i	0.988675	+	0.150075i	$0.0479516\pi$
$311$			5.29321i			0.300150i	−0.988675	+	0.150075i	$0.952048\pi$
$312$		0			0
$313$	−12.5531			−0.709544			−0.354772	−	0.934953i	$-0.615442\pi$
$313$	−12.5531			−0.709544			−0.354772	+	0.934953i	$0.615442\pi$
$314$	7.70239	−	2.19941i	0.434671	−	0.124120i
$315$		0			0
$316$	−9.16789	+	5.70057i	−0.515734	+	0.320682i
$317$	−2.23959			−0.125788			−0.0628941	−	0.998020i	$-0.520033\pi$
$317$	−2.23959			−0.125788			−0.0628941	+	0.998020i	$0.520033\pi$
$318$		0			0
$319$	−46.2812			−2.59125
$320$	−14.6839	+	1.44487i	−0.820852	+	0.0807706i
$321$		0			0
$322$	−6.06479	−	21.2391i	−0.337977	−	1.18361i
$323$	−9.91987	+	7.51940i	−0.551957	+	0.418391i
$324$		0			0
$325$	−5.90044			−0.327297
$326$	7.41022	+	25.9508i	0.410414	+	1.43728i
$327$		0			0
$328$	1.16502	−	1.28528i	0.0643273	−	0.0709677i
$329$	15.6062			0.860397
$330$		0			0
$331$			10.4370i			0.573671i	0.957980	+	0.286835i	$0.0926033\pi$
$331$			10.4370i			0.573671i	−0.957980	+	0.286835i	$0.907397\pi$
$332$	−18.6099	+	11.5716i	−1.02135	+	0.635072i
$333$		0			0
$334$	5.70117	+	19.9657i	0.311954	+	1.09247i
$335$	6.08710			0.332574
$336$		0			0
$337$		−	4.47708i		−	0.243882i	−0.992537	−	0.121941i	$-0.961088\pi$
$337$		−	4.47708i		−	0.243882i	0.992537	−	0.121941i	$-0.0389119\pi$
$338$	−0.243520	−	0.852813i	−0.0132457	−	0.0463869i
$339$		0			0
$340$	−5.56228	−	8.94549i	−0.301657	−	0.485137i
$341$	23.6631			1.28143
$342$		0			0
$343$		−	20.1599i		−	1.08853i
$344$	−4.05674	−	3.67716i	−0.218725	−	0.198259i
$345$		0			0
$346$	−2.77379	−	9.71391i	−0.149120	−	0.522223i
$347$	−8.58895			−0.461079			−0.230540	−	0.973063i	$-0.574049\pi$
$347$	−8.58895			−0.461079			−0.230540	+	0.973063i	$0.574049\pi$
$348$		0			0
$349$		−	6.80028i		−	0.364011i	−0.983298	−	0.182005i	$-0.941741\pi$
$349$		−	6.80028i		−	0.364011i	0.983298	−	0.182005i	$-0.0582588\pi$
$350$	−4.73752	+	1.35279i	−0.253231	+	0.0723098i
$351$		0			0
$352$	−27.6333	−	5.03023i	−1.47286	−	0.268112i
$353$	3.51473			0.187070			0.0935350	−	0.995616i	$-0.470183\pi$
$353$	3.51473			0.187070			0.0935350	+	0.995616i	$0.470183\pi$
$354$		0			0
$355$			21.8266i			1.15844i
$356$	3.41586	+	5.49353i	0.181040	+	0.291157i
$357$		0			0
$358$	−17.9840	+	5.13530i	−0.950484	+	0.271409i
$359$		−	24.8768i		−	1.31295i	−0.754349	−	0.656474i	$-0.772047\pi$
$359$		−	24.8768i		−	1.31295i	0.754349	−	0.656474i	$-0.227953\pi$
$360$		0			0
$361$	5.13334	−	18.2934i	0.270176	−	0.962811i
$362$	−2.08606	−	7.30544i	−0.109641	−	0.383965i
$363$		0			0
$364$	−8.49719	−	13.6655i	−0.445374	−	0.716268i
$365$			29.0742i			1.52181i
$366$		0			0
$367$			26.7726i			1.39752i	0.715356	+	0.698760i	$0.246265\pi$
$367$			26.7726i			1.39752i	−0.715356	+	0.698760i	$0.753735\pi$
$368$	25.7066	+	12.6790i	1.34005	+	0.660941i
$369$		0			0
$370$	5.93225	−	1.69395i	0.308403	−	0.0880641i
$371$		−	24.8784i		−	1.29162i
$372$		0			0
$373$	31.4743			1.62968			0.814839	−	0.579687i	$-0.196825\pi$
$373$	31.4743			1.62968			0.814839	+	0.579687i	$0.196825\pi$
$374$	−5.50583	−	19.2816i	−0.284700	−	0.997027i
$375$		0			0
$376$	−13.6011	+	15.0051i	−0.701422	+	0.773828i
$377$	34.4089			1.77215
$378$		0			0
$379$			19.2363i			0.988104i	0.869432	+	0.494052i	$0.164485\pi$
$379$			19.2363i			0.988104i	−0.869432	+	0.494052i	$0.835515\pi$
$380$	15.0143	+	5.75267i	0.770218	+	0.295106i
$381$		0			0
$382$	11.7623	−	3.35870i	0.601810	−	0.171846i
$383$	13.1041			0.669589			0.334794	−	0.942291i	$-0.391333\pi$
$383$	13.1041			0.669589			0.334794	+	0.942291i	$0.391333\pi$
$384$		0			0
$385$	19.9597			1.01724
$386$	2.93207	−	0.837249i	0.149239	−	0.0426149i
$387$		0			0
$388$	−4.72174	−	7.59370i	−0.239710	−	0.385512i
$389$		−	1.08166i		−	0.0548423i	−0.999624	−	0.0274211i	$-0.991270\pi$
$389$		−	1.08166i		−	0.0548423i	0.999624	−	0.0274211i	$-0.00872951\pi$
$390$		0			0
$391$			20.4635i			1.03488i
$392$	4.71391	+	4.27283i	0.238088	+	0.215811i
$393$		0			0
$394$	8.52200	−	2.43345i	0.429332	−	0.122595i
$395$			9.95549i			0.500915i
$396$		0			0
$397$		−	35.9462i		−	1.80409i	−0.431643	−	0.902045i	$-0.642066\pi$
$397$		−	35.9462i		−	1.80409i	0.431643	−	0.902045i	$-0.357934\pi$
$398$	−26.1742	+	7.47400i	−1.31199	+	0.374638i
$399$		0			0
$400$	2.82815	−	5.73403i	0.141407	−	0.286701i
$401$		−	9.57558i		−	0.478182i	−0.970997	−	0.239091i	$-0.923151\pi$
$401$		−	9.57558i		−	0.478182i	0.970997	−	0.239091i	$-0.0768494\pi$
$402$		0			0
$403$	−17.5929			−0.876364
$404$	−17.4905	−	28.1290i	−0.870186	−	1.39947i
$405$		0			0
$406$	27.6272	−	7.88892i	1.37112	−	0.391520i
$407$	11.7441			0.582133
$408$		0			0
$409$			11.3502i			0.561230i	0.959820	+	0.280615i	$0.0905384\pi$
$409$			11.3502i			0.561230i	−0.959820	+	0.280615i	$0.909462\pi$
$410$	−0.439236	−	1.53822i	−0.0216923	−	0.0759671i
$411$		0			0
$412$	12.0708	−	7.50557i	0.594684	−	0.369773i
$413$	10.1343			0.498675
$414$		0			0
$415$			20.2086i			0.992001i
$416$	20.5446	+	3.73985i	1.00728	+	0.183361i
$417$		0			0
$418$	24.4761	+	18.3777i	1.19717	+	0.898882i
$419$	4.26913			0.208561			0.104280	−	0.994548i	$-0.466746\pi$
$419$	4.26913			0.208561			0.104280	+	0.994548i	$0.466746\pi$
$420$		0			0
$421$	−31.2645			−1.52374			−0.761869	−	0.647731i	$-0.775718\pi$
$421$	−31.2645			−1.52374			−0.761869	+	0.647731i	$0.775718\pi$
$422$	13.3207	−	3.80372i	0.648443	−	0.185162i
$423$		0			0
$424$	23.9202	+	21.6820i	1.16167	+	1.05297i
$425$	4.56451			0.221411
$426$		0			0
$427$	2.74749			0.132960
$428$	−21.6357	−	34.7954i	−1.04580	−	1.68190i
$429$		0			0
$430$	−4.85509	+	1.38637i	−0.234133	+	0.0668565i
$431$	−9.23965			−0.445058			−0.222529	−	0.974926i	$-0.571431\pi$
$431$	−9.23965			−0.445058			−0.222529	+	0.974926i	$0.571431\pi$
$432$		0			0
$433$		−	19.2732i		−	0.926210i	−0.886303	−	0.463105i	$-0.846735\pi$
$433$		−	19.2732i		−	0.926210i	0.886303	−	0.463105i	$-0.153265\pi$
$434$	−14.1255	+	4.03352i	−0.678045	+	0.193615i
$435$		0			0
$436$	0.346075	−	0.215189i	0.0165740	−	0.0103057i
$437$	−18.8685	−	24.8920i	−0.902603	−	1.19075i
$438$		0			0
$439$	−11.1076			−0.530136			−0.265068	−	0.964230i	$-0.585394\pi$
$439$	−11.1076			−0.530136			−0.265068	+	0.964230i	$0.585394\pi$
$440$	−17.3952	+	19.1909i	−0.829285	+	0.914890i
$441$		0			0
$442$	4.09344	+	14.3354i	0.194705	+	0.681864i
$443$	−25.1044			−1.19275			−0.596373	−	0.802707i	$-0.703392\pi$
$443$	−25.1044			−1.19275			−0.596373	+	0.802707i	$0.703392\pi$
$444$		0			0
$445$	5.96547			0.282790
$446$	−6.98085	−	24.4472i	−0.330553	−	1.15761i
$447$		0			0
$448$	17.3529	−	1.70750i	0.819848	−	0.0806718i
$449$		−	33.9705i		−	1.60317i	−0.597881	−	0.801585i	$-0.703991\pi$
$449$		−	33.9705i		−	1.60317i	0.597881	−	0.801585i	$-0.296009\pi$
$450$		0			0
$451$		−	3.04521i		−	0.143393i
$452$	10.5752	+	17.0074i	0.497414	+	0.799961i
$453$		0			0
$454$	5.04885	−	1.44169i	0.236954	−	0.0676620i
$455$	−14.8395			−0.695687
$456$		0			0
$457$	11.7002			0.547312			0.273656	−	0.961828i	$-0.411767\pi$
$457$	11.7002			0.547312			0.273656	+	0.961828i	$0.411767\pi$
$458$	−16.5752	+	4.73301i	−0.774506	+	0.221159i
$459$		0			0
$460$	22.4470	−	13.9575i	1.04660	−	0.650772i
$461$		−	21.3681i		−	0.995213i	−0.867403	−	0.497607i	$-0.834212\pi$
$461$		−	21.3681i		−	0.995213i	0.867403	−	0.497607i	$-0.165788\pi$
$462$		0			0
$463$		−	10.7136i		−	0.497905i	−0.968516	−	0.248952i	$-0.919914\pi$
$463$		−	10.7136i		−	0.497905i	0.968516	−	0.248952i	$-0.0800863\pi$
$464$	−16.4926	+	33.4385i	−0.765648	+	1.55234i
$465$		0			0
$466$	3.22563	+	11.2963i	0.149425	+	0.523289i
$467$	−12.0600			−0.558072			−0.279036	−	0.960281i	$-0.590015\pi$
$467$	−12.0600			−0.558072			−0.279036	+	0.960281i	$0.590015\pi$
$468$		0			0
$469$	−7.19354			−0.332167
$470$	5.12789	+	17.9580i	0.236532	+	0.828342i
$471$		0			0
$472$	−8.83220	+	9.74393i	−0.406535	+	0.448501i
$473$	−9.61164			−0.441943
$474$		0			0
$475$	−5.55234	+	4.20875i	−0.254759	+	0.193111i
$476$	6.57333	+	10.5715i	0.301288	+	0.484544i
$477$		0			0
$478$	−14.3732	+	4.10423i	−0.657413	+	0.187723i
$479$			36.0102i			1.64535i	0.568515	+	0.822673i	$0.307518\pi$
$479$			36.0102i			1.64535i	−0.568515	+	0.822673i	$0.692482\pi$
$480$		0			0
$481$	−8.73143			−0.398119
$482$	−33.7996	+	9.65142i	−1.53953	+	0.439610i
$483$		0			0
$484$	−23.1890	+	14.4189i	−1.05405	+	0.655403i
$485$	−8.24606			−0.374434
$486$		0			0
$487$	31.8174			1.44179			0.720893	−	0.693046i	$-0.243732\pi$
$487$	31.8174			1.44179			0.720893	+	0.693046i	$0.243732\pi$
$488$	−2.39449	+	2.64166i	−0.108393	+	0.119582i
$489$		0			0
$490$	5.64158	−	1.61095i	0.254861	−	0.0727751i
$491$	−41.3402			−1.86566			−0.932828	−	0.360321i	$-0.882667\pi$
$491$	−41.3402			−1.86566			−0.932828	+	0.360321i	$0.882667\pi$
$492$		0			0
$493$	−26.6183			−1.19883
$494$	−18.1974	−	13.6633i	−0.818738	−	0.614743i
$495$		0			0
$496$	8.43247	−	17.0967i	0.378629	−	0.767665i
$497$		−	25.7940i		−	1.15702i
$498$		0			0
$499$	−25.3722			−1.13581			−0.567907	−	0.823093i	$-0.692247\pi$
$499$	−25.3722			−1.13581			−0.567907	+	0.823093i	$0.692247\pi$
$500$	−12.8522	−	20.6695i	−0.574769	−	0.924367i
$501$		0			0
$502$	1.75524	+	6.14691i	0.0783403	+	0.274350i
$503$		−	12.7320i		−	0.567692i	−0.958870	−	0.283846i	$-0.908389\pi$
$503$		−	12.7320i		−	0.567692i	0.958870	−	0.283846i	$-0.0916105\pi$
$504$		0			0
$505$	−30.5455			−1.35926
$506$	48.3835	−	13.8158i	2.15091	−	0.614189i
$507$		0			0
$508$	22.5866	−	14.0443i	1.00212	−	0.623116i
$509$	15.8544			0.702733			0.351367	−	0.936238i	$-0.385717\pi$
$509$	15.8544			0.702733			0.351367	+	0.936238i	$0.385717\pi$
$510$		0			0
$511$		−	34.3589i		−	1.51995i
$512$	−13.4816	+	18.1727i	−0.595810	+	0.803125i
$513$		0			0
$514$	34.4542	−	9.83835i	1.51971	−	0.433951i
$515$		−	13.1077i		−	0.577596i
$516$		0			0
$517$			35.5515i			1.56355i
$518$	−7.01055	+	2.00185i	−0.308026	+	0.0879563i
$519$		0			0
$520$	12.9329	−	14.2679i	0.567145	−	0.625690i
$521$			1.81927i			0.0797035i	0.999206	+	0.0398518i	$0.0126886\pi$
$521$			1.81927i			0.0797035i	−0.999206	+	0.0398518i	$0.987311\pi$
$522$		0			0
$523$		−	39.1957i		−	1.71391i	−0.515391	−	0.856955i	$-0.672353\pi$
$523$		−	39.1957i		−	1.71391i	0.515391	−	0.856955i	$-0.327647\pi$
$524$	23.4605	−	14.5877i	1.02488	−	0.637265i
$525$		0			0
$526$	1.33046	−	0.379912i	0.0580110	−	0.0165650i
$527$	13.6097			0.592846
$528$		0			0
$529$	−28.3492			−1.23257
$530$	28.6275	−	8.17456i	1.24350	−	0.355080i
$531$		0			0
$532$	−17.7434	−	6.79832i	−0.769275	−	0.294745i
$533$			2.26404i			0.0980663i
$534$		0			0
$535$	−37.7846			−1.63357
$536$	6.26930	−	6.91647i	0.270793	−	0.298746i
$537$		0			0
$538$	1.15156	+	4.03278i	0.0496471	+	0.173866i
$539$	11.1687			0.481068
$540$		0			0
$541$		−	9.85972i		−	0.423902i	−0.977280	−	0.211951i	$-0.932018\pi$
$541$		−	9.85972i		−	0.423902i	0.977280	−	0.211951i	$-0.0679818\pi$
$542$	7.87870	−	2.24975i	0.338419	−	0.0966352i
$543$		0			0
$544$	−15.8931	−	2.89311i	−0.681411	−	0.124041i
$545$		−	0.375806i		−	0.0160977i
$546$		0			0
$547$			36.5530i			1.56289i	0.623972	+	0.781447i	$0.285518\pi$
$547$			36.5530i			1.56289i	−0.623972	+	0.781447i	$0.714482\pi$
$548$	−13.3822	+	8.32104i	−0.571661	+	0.355457i
$549$		0			0
$550$	−3.08171	−	10.7923i	−0.131405	−	0.460183i
$551$	32.3789	−	24.5437i	1.37939	−	1.04560i
$552$		0			0
$553$		−	11.7651i		−	0.500302i
$554$	−42.0669	+	12.0121i	−1.78725	+	0.510347i
$555$		0			0
$556$	−19.6411	+	12.2128i	−0.832969	+	0.517938i
$557$		−	5.51302i		−	0.233594i	−0.993156	−	0.116797i	$-0.962737\pi$
$557$		−	5.51302i		−	0.233594i	0.993156	−	0.116797i	$-0.0372627\pi$
$558$		0			0
$559$	7.14600			0.302244
$560$	7.11274	−	14.4210i	0.300568	−	0.609398i
$561$		0			0
$562$	0.134202	−	0.0383212i	0.00566097	−	0.00161648i
$563$			30.2801i			1.27615i	0.769973	+	0.638077i	$0.220270\pi$
$563$			30.2801i			1.27615i	−0.769973	+	0.638077i	$0.779730\pi$
$564$		0			0
$565$	18.4685			0.776975
$566$	−5.56517	−	19.4894i	−0.233921	−	0.819200i
$567$		0			0
$568$	24.8005	+	22.4799i	1.04061	+	0.943237i
$569$		−	15.2987i		−	0.641354i	−0.947189	−	0.320677i	$-0.896090\pi$
$569$		−	15.2987i		−	0.641354i	0.947189	−	0.320677i	$-0.103910\pi$
$570$		0			0
$571$	1.23253			0.0515797			0.0257899	−	0.999667i	$-0.491790\pi$
$571$	1.23253			0.0515797			0.0257899	+	0.999667i	$0.491790\pi$
$572$	31.1306	−	19.3569i	1.30164	−	0.809355i
$573$		0			0
$574$	0.519075	+	1.81782i	0.0216658	+	0.0758742i
$575$			11.4538i			0.477655i
$576$		0			0
$577$	−11.7401			−0.488747			−0.244374	−	0.969681i	$-0.578582\pi$
$577$	−11.7401			−0.488747			−0.244374	+	0.969681i	$0.578582\pi$
$578$	3.43456	+	12.0279i	0.142859	+	0.500296i
$579$		0			0
$580$	18.1555	+	29.1985i	0.753868	+	1.21240i
$581$		−	23.8819i		−	0.990787i
$582$		0			0
$583$	56.6740			2.34720
$584$	33.0355	+	29.9444i	1.36702	+	1.23911i
$585$		0			0
$586$	5.22249	+	18.2893i	0.215739	+	0.755525i
$587$	−18.0415			−0.744653			−0.372326	−	0.928102i	$-0.621440\pi$
$587$	−18.0415			−0.744653			−0.372326	+	0.928102i	$0.621440\pi$
$588$		0			0
$589$	−16.5550	+	12.5489i	−0.682136	+	0.517068i
$590$	3.32993	+	11.6615i	0.137091	+	0.480096i
$591$		0			0
$592$	4.18507	−	8.48517i	0.172005	−	0.348738i
$593$	−16.7690			−0.688620			−0.344310	−	0.938856i	$-0.611887\pi$
$593$	−16.7690			−0.688620			−0.344310	+	0.938856i	$0.611887\pi$
$594$		0			0
$595$	11.4797			0.470621
$596$	20.2576	+	32.5791i	0.829783	+	1.33449i
$597$		0			0
$598$	−35.9719	+	10.2717i	−1.47100	+	0.420042i
$599$	30.5577			1.24856			0.624278	−	0.781202i	$-0.285393\pi$
$599$	30.5577			1.24856			0.624278	+	0.781202i	$0.285393\pi$
$600$		0			0
$601$		−	39.5259i		−	1.61230i	−0.591714	−	0.806148i	$-0.701548\pi$
$601$		−	39.5259i		−	1.61230i	0.591714	−	0.806148i	$-0.298452\pi$
$602$	5.73760	−	1.63836i	0.233847	−	0.0667747i
$603$		0			0
$604$	11.6255	−	7.22869i	0.473034	−	0.294131i
$605$			25.1811i			1.02376i
$606$		0			0
$607$	5.27615			0.214152			0.107076	−	0.994251i	$-0.465851\pi$
$607$	5.27615			0.214152			0.107076	+	0.994251i	$0.465851\pi$
$608$	22.0002	−	11.1351i	0.892226	−	0.451590i
$609$		0			0
$610$	0.902771	+	3.16153i	0.0365521	+	0.128007i
$611$		−	26.4316i		−	1.06931i
$612$		0			0
$613$		−	14.1728i		−	0.572435i	−0.958165	−	0.286217i	$-0.907602\pi$
$613$		−	14.1728i		−	0.572435i	0.958165	−	0.286217i	$-0.0923979\pi$
$614$	43.1981	−	12.3352i	1.74333	−	0.497806i
$615$		0			0
$616$	20.5571	−	22.6792i	0.828270	−	0.913770i
$617$	23.6032			0.950229			0.475114	−	0.879924i	$-0.342407\pi$
$617$	23.6032			0.950229			0.475114	+	0.879924i	$0.342407\pi$
$618$		0			0
$619$	−3.61135			−0.145153			−0.0725763	−	0.997363i	$-0.523122\pi$
$619$	−3.61135			−0.145153			−0.0725763	+	0.997363i	$0.523122\pi$
$620$	−9.28272	−	14.9289i	−0.372803	−	0.599557i
$621$		0			0
$622$	7.19802	−	2.05538i	0.288614	−	0.0824134i
$623$	−7.04980			−0.282444
$624$		0			0
$625$	−14.4532			−0.578129
$626$	4.87445	+	17.0705i	0.194822	+	0.682273i
$627$		0			0
$628$	−5.98177	−	9.62013i	−0.238699	−	0.383885i
$629$	6.75453			0.269321
$630$		0			0
$631$			4.65771i			0.185421i	0.995693	+	0.0927103i	$0.0295530\pi$
$631$			4.65771i			0.185421i	−0.995693	+	0.0927103i	$0.970447\pi$
$632$	11.3119	+	10.2535i	0.449964	+	0.407862i
$633$		0			0
$634$	0.869648	+	3.04553i	0.0345381	+	0.120954i
$635$		−	24.5270i		−	0.973325i
$636$		0			0
$637$	−8.30361			−0.329001
$638$	17.9713	+	62.9360i	0.711490	+	2.49166i
$639$		0			0
$640$	7.66665	+	19.4069i	0.303051	+	0.767126i
$641$		−	10.6300i		−	0.419860i	−0.977716	−	0.209930i	$-0.932676\pi$
$641$		−	10.6300i		−	0.419860i	0.977716	−	0.209930i	$-0.0673236\pi$
$642$		0			0
$643$	37.4180			1.47562			0.737810	−	0.675008i	$-0.235860\pi$
$643$	37.4180			1.47562			0.737810	+	0.675008i	$0.235860\pi$
$644$	−26.5272	+	16.4945i	−1.04532	+	0.649975i
$645$		0			0
$646$	14.0773	+	10.5698i	0.553863	+	0.415863i
$647$		−	0.317549i		−	0.0124841i	−0.999981	−	0.00624207i	$-0.998013\pi$
$647$		−	0.317549i		−	0.0124841i	0.999981	−	0.00624207i	$-0.00198693\pi$
$648$		0			0
$649$			23.0863i			0.906216i
$650$	2.29118	+	8.02377i	0.0898673	+	0.314718i
$651$		0			0
$652$	32.4120	−	20.1537i	1.26935	−	0.789280i
$653$			31.8899i			1.24795i	0.781445	+	0.623974i	$0.214483\pi$
$653$			31.8899i			1.24795i	−0.781445	+	0.623974i	$0.785517\pi$
$654$		0			0
$655$		−	25.4759i		−	0.995427i
$656$	−2.20018	−	1.08518i	−0.0859027	−	0.0423691i
$657$		0			0
$658$	−6.05998	−	21.2222i	−0.236242	−	0.827328i
$659$		−	31.0470i		−	1.20942i	−0.796446	−	0.604710i	$-0.793289\pi$
$659$		−	31.0470i		−	1.20942i	0.796446	−	0.604710i	$-0.206711\pi$
$660$		0			0
$661$	43.8105			1.70403			0.852015	−	0.523517i	$-0.175380\pi$
$661$	43.8105			1.70403			0.852015	+	0.523517i	$0.175380\pi$
$662$	14.1929	−	4.05276i	0.551622	−	0.157515i
$663$		0			0
$664$	22.9620	+	20.8135i	0.891099	+	0.807720i
$665$	−13.9640	+	10.5849i	−0.541502	+	0.410466i
$666$		0			0
$667$		−	66.7937i		−	2.58626i
$668$	24.9367	−	15.5056i	0.964830	−	0.599929i
$669$		0			0
$670$	−2.36366	−	8.27760i	−0.0913161	−	0.319792i
$671$			6.25889i			0.241622i
$672$		0			0
$673$			28.6137i			1.10298i	0.834183	+	0.551488i	$0.185940\pi$
$673$			28.6137i			1.10298i	−0.834183	+	0.551488i	$0.814060\pi$
$674$	−6.08820	+	1.73848i	−0.234509	+	0.0669636i
$675$		0			0
$676$	−1.06515	+	0.662305i	−0.0409672	+	0.0254733i
$677$	20.5858			0.791178			0.395589	−	0.918428i	$-0.370541\pi$
$677$	20.5858			0.791178			0.395589	+	0.918428i	$0.370541\pi$
$678$		0			0
$679$	9.74493			0.373976
$680$	−10.0047	+	11.0375i	−0.383664	+	0.423269i
$681$		0			0
$682$	−9.18851	−	32.1784i	−0.351846	−	1.23218i
$683$			4.14039i			0.158428i	0.996858	+	0.0792138i	$0.0252410\pi$
$683$			4.14039i			0.158428i	−0.996858	+	0.0792138i	$0.974759\pi$
$684$		0			0
$685$			14.5319i			0.555235i
$686$	−27.4146	+	7.82820i	−1.04669	+	0.298882i
$687$		0			0
$688$	−3.42516	+	6.94446i	−0.130583	+	0.264755i
$689$	−42.1357			−1.60524
$690$		0			0
$691$	13.4721			0.512502			0.256251	−	0.966610i	$-0.417513\pi$
$691$	13.4721			0.512502			0.256251	+	0.966610i	$0.417513\pi$
$692$	−12.1325	+	7.54394i	−0.461208	+	0.286778i
$693$		0			0
$694$	3.33514	+	11.6798i	0.126600	+	0.443358i
$695$			21.3284i			0.809034i
$696$		0			0
$697$		−	1.75143i		−	0.0663402i
$698$	−9.24742	+	2.64059i	−0.350020	+	0.0999478i
$699$		0			0
$700$	3.67921	+	5.91706i	0.139061	+	0.223644i
$701$		−	36.6949i		−	1.38595i	−0.720964	−	0.692973i	$-0.756301\pi$
$701$		−	36.6949i		−	1.38595i	0.720964	−	0.692973i	$-0.243699\pi$
$702$		0			0
$703$	−8.21631	+	6.22807i	−0.309884	+	0.234896i
$704$	3.88976	+	39.5306i	0.146601	+	1.48987i
$705$		0			0
$706$	−1.36479	−	4.77954i	−0.0513646	−	0.179880i
$707$	36.0977			1.35759
$708$		0			0
$709$		−	36.5517i		−	1.37273i	−0.727258	−	0.686364i	$-0.759206\pi$
$709$		−	36.5517i		−	1.37273i	0.727258	−	0.686364i	$-0.240794\pi$
$710$	29.6811	−	8.47541i	1.11391	−	0.318076i
$711$		0			0
$712$	6.14403	−	6.77827i	0.230257	−	0.254026i
$713$			34.1508i			1.27896i
$714$		0			0
$715$		−	33.8050i		−	1.26424i
$716$	13.9666	+	22.4616i	0.521956	+	0.839431i
$717$		0			0
$718$	−33.8290	+	9.65982i	−1.26249	+	0.360501i
$719$		−	15.2082i		−	0.567170i	−0.958947	−	0.283585i	$-0.908476\pi$
$719$		−	15.2082i		−	0.567170i	0.958947	−	0.283585i	$-0.0915239\pi$
$720$		0			0
$721$			15.4903i			0.576889i
$722$	−26.8698	+	0.122815i	−0.999990	+	0.00457071i
$723$		0			0
$724$	−9.12435	+	5.67350i	−0.339104	+	0.210854i
$725$	−14.8988			−0.553326
$726$		0			0
$727$			21.4835i			0.796778i	0.917217	+	0.398389i	$0.130431\pi$
$727$			21.4835i			0.796778i	−0.917217	+	0.398389i	$0.869569\pi$
$728$	−15.2837	+	16.8614i	−0.566451	+	0.624925i
$729$		0			0
$730$	39.5368	−	11.2897i	1.46332	−	0.417849i
$731$	−5.52807			−0.204463
$732$		0			0
$733$			20.5095i			0.757535i	0.925492	+	0.378768i	$0.123652\pi$
$733$			20.5095i			0.757535i	−0.925492	+	0.378768i	$0.876348\pi$
$734$	36.4070	−	10.3960i	1.34381	−	0.383723i
$735$		0			0
$736$	7.25970	−	39.8807i	0.267596	−	1.47002i
$737$		−	16.3872i		−	0.603629i
$738$		0			0
$739$	−24.0241			−0.883740			−0.441870	−	0.897079i	$-0.645685\pi$
$739$	−24.0241			−0.883740			−0.441870	+	0.897079i	$0.645685\pi$
$740$	−4.60706	−	7.40926i	−0.169359	−	0.272370i
$741$		0			0
$742$	−33.8311	+	9.66043i	−1.24198	+	0.354646i
$743$	−37.3770			−1.37123			−0.685614	−	0.727965i	$-0.740466\pi$
$743$	−37.3770			−1.37123			−0.685614	+	0.727965i	$0.740466\pi$
$744$		0			0
$745$	35.3779			1.29615
$746$	−12.2217	−	42.8007i	−0.447467	−	1.56704i
$747$		0			0
$748$	−24.0823	+	14.9743i	−0.880536	+	0.547515i
$749$	44.6526			1.63157
$750$		0			0
$751$	4.48122			0.163522			0.0817610	−	0.996652i	$-0.473946\pi$
$751$	4.48122			0.163522			0.0817610	+	0.996652i	$0.473946\pi$
$752$	25.6862	+	12.6690i	0.936679	+	0.461990i
$753$		0			0
$754$	−13.3612	−	46.7913i	−0.486586	−	1.70404i
$755$		−	12.6242i		−	0.459441i
$756$		0			0
$757$		−	29.3408i		−	1.06641i	−0.845986	−	0.533206i	$-0.820987\pi$
$757$		−	29.3408i		−	1.06641i	0.845986	−	0.533206i	$-0.179013\pi$
$758$	26.1587	−	7.46958i	0.950127	−	0.271308i
$759$		0			0
$760$	1.99268	−	22.6511i	0.0722820	−	0.821643i
$761$	−36.1362			−1.30993			−0.654967	−	0.755657i	$-0.727318\pi$
$761$	−36.1362			−1.30993			−0.654967	+	0.755657i	$0.727318\pi$
$762$		0			0
$763$			0.444115i			0.0160781i
$764$	−9.13472	−	14.6908i	−0.330483	−	0.531496i
$765$		0			0
$766$	−5.08841	−	17.8198i	−0.183852	−	0.643854i
$767$		−	17.1641i		−	0.619759i
$768$		0			0
$769$	−5.23438			−0.188756			−0.0943782	−	0.995536i	$-0.530086\pi$
$769$	−5.23438			−0.188756			−0.0943782	+	0.995536i	$0.530086\pi$
$770$	−7.75046	−	27.1424i	−0.279307	−	0.978143i
$771$		0			0
$772$	−2.27708	−	3.66210i	−0.0819540	−	0.131802i
$773$	−16.8693			−0.606747			−0.303374	−	0.952872i	$-0.598113\pi$
$773$	−16.8693			−0.606747			−0.303374	+	0.952872i	$0.598113\pi$
$774$		0			0
$775$	7.61757			0.273631
$776$	−8.49289	+	9.36959i	−0.304877	+	0.336349i
$777$		0			0
$778$	−1.47090	+	0.420015i	−0.0527345	+	0.0150583i
$779$	1.61492	+	2.13047i	0.0578606	+	0.0763319i
$780$		0			0
$781$	58.7598			2.10259
$782$	27.8274	−	7.94609i	0.995107	−	0.284151i
$783$		0			0
$784$	3.98001	−	8.06942i	0.142143	−	0.288193i
$785$	−10.4466			−0.372854
$786$		0			0
$787$			11.4453i			0.407981i	0.978973	+	0.203991i	$0.0653912\pi$
$787$			11.4453i			0.407981i	−0.978973	+	0.203991i	$0.934609\pi$
$788$	−6.61829	−	10.6438i	−0.235767	−	0.379170i
$789$		0			0
$790$	13.5381	−	3.86578i	0.481663	−	0.137538i
$791$	−21.8255			−0.776024
$792$		0			0
$793$		−	4.65332i		−	0.165244i
$794$	−48.8818	+	13.9581i	−1.73475	+	0.495356i
$795$		0			0
$796$	20.3272	+	32.6910i	0.720478	+	1.15870i
$797$	−37.4188			−1.32544			−0.662720	−	0.748867i	$-0.730598\pi$
$797$	−37.4188			−1.32544			−0.662720	+	0.748867i	$0.730598\pi$
$798$		0			0
$799$			20.4472i			0.723371i
$800$	−8.89566	−	1.61932i	−0.314509	−	0.0572518i
$801$		0			0
$802$	−13.0214	+	3.71826i	−0.459803	+	0.131296i
$803$	78.2710			2.76212
$804$		0			0
$805$			28.8061i			1.01528i
$806$	6.83142	+	23.9239i	0.240627	+	0.842682i
$807$		0			0
$808$	−31.4598	+	34.7073i	−1.10675	+	1.22100i
$809$	−4.87679			−0.171459			−0.0857293	−	0.996318i	$-0.527322\pi$
$809$	−4.87679			−0.171459			−0.0857293	+	0.996318i	$0.527322\pi$
$810$		0			0
$811$		−	55.3830i		−	1.94476i	−0.233405	−	0.972380i	$-0.574987\pi$
$811$		−	55.3830i		−	1.94476i	0.233405	−	0.972380i	$-0.425013\pi$
$812$	−21.4556	−	34.5058i	−0.752945	−	1.21092i
$813$		0			0
$814$	−4.56030	−	15.9703i	−0.159838	−	0.559759i
$815$		−	35.1965i		−	1.23288i
$816$		0			0
$817$	6.72442	−	5.09720i	0.235258	−	0.178329i
$818$	15.4346	−	4.40734i	0.539659	−	0.154099i
$819$		0			0
$820$	−1.92120	+	1.19460i	−0.0670913	+	0.0417172i
$821$		−	22.6975i		−	0.792149i	−0.918218	−	0.396075i	$-0.870372\pi$
$821$		−	22.6975i		−	0.792149i	0.918218	−	0.396075i	$-0.129628\pi$
$822$		0			0
$823$			23.8641i			0.831852i	0.909399	+	0.415926i	$0.136542\pi$
$823$			23.8641i			0.831852i	−0.909399	+	0.415926i	$0.863458\pi$
$824$	−14.8937	−	13.5001i	−0.518845	−	0.470298i
$825$		0			0
$826$	−3.93520	−	13.7812i	−0.136923	−	0.479509i
$827$			35.5248i			1.23532i	0.786445	+	0.617660i	$0.211919\pi$
$827$			35.5248i			1.23532i	−0.786445	+	0.617660i	$0.788081\pi$
$828$		0			0
$829$	28.3353			0.984125			0.492062	−	0.870560i	$-0.336243\pi$
$829$	28.3353			0.984125			0.492062	+	0.870560i	$0.336243\pi$
$830$	27.4809	−	7.84712i	0.953875	−	0.272378i
$831$		0			0
$832$	−2.89193	−	29.3900i	−0.100260	−	1.01892i
$833$	6.42358			0.222564
$834$		0			0
$835$		−	27.0790i		−	0.937106i
$836$	15.4869	−	40.4203i	0.535624	−	1.39796i
$837$		0			0
$838$	−1.65773	−	5.80542i	−0.0572654	−	0.200545i
$839$	44.7633			1.54540			0.772701	−	0.634771i	$-0.218905\pi$
$839$	44.7633			1.54540			0.772701	+	0.634771i	$0.218905\pi$
$840$		0			0
$841$	57.8834			1.99598
$842$	12.1402	+	42.5153i	0.418379	+	1.46518i
$843$		0			0
$844$	−10.3450	−	16.6373i	−0.356091	−	0.572680i
$845$			1.15665i			0.0397900i
$846$		0			0
$847$		−	29.7583i		−	1.02251i
$848$	20.1961	−	40.9473i	0.693537	−	1.40614i
$849$		0			0
$850$	−1.77243	−	6.20710i	−0.0607938	−	0.212902i
$851$			16.9492i			0.581012i
$852$		0			0
$853$			26.5508i			0.909083i	0.890726	+	0.454542i	$0.150197\pi$
$853$			26.5508i			0.909083i	−0.890726	+	0.454542i	$0.849803\pi$
$854$	−1.06687	−	3.73620i	−0.0365074	−	0.127850i
$855$		0			0
$856$	−38.9156	+	42.9327i	−1.33011	+	1.46741i
$857$			52.4272i			1.79088i	0.445185	+	0.895439i	$0.353138\pi$
$857$			52.4272i			1.79088i	−0.445185	+	0.895439i	$0.646862\pi$
$858$		0			0
$859$	4.75338			0.162183			0.0810916	−	0.996707i	$-0.474159\pi$
$859$	4.75338			0.162183			0.0810916	+	0.996707i	$0.474159\pi$
$860$	3.77052	+	6.06391i	0.128574	+	0.206778i
$861$		0			0
$862$	3.58781	+	12.5646i	0.122201	+	0.427953i
$863$	42.5221			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$863$	42.5221			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$864$		0			0
$865$			13.1748i			0.447955i
$866$	−26.2088	+	7.48390i	−0.890613	+	0.254313i
$867$		0			0
$868$	10.9700	+	17.6424i	0.372347	+	0.598824i
$869$	26.8013			0.909173
$870$		0			0
$871$			12.1834i			0.412820i
$872$	−0.427009	−	0.387054i	−0.0144604	−	0.0131073i
$873$		0			0
$874$	−26.5229	+	35.3243i	−0.897151	+	1.19486i
$875$	26.5250			0.896708
$876$		0			0
$877$	−29.7302			−1.00392			−0.501958	−	0.864892i	$-0.667387\pi$
$877$	−29.7302			−1.00392			−0.501958	+	0.864892i	$0.667387\pi$
$878$	4.31314	+	15.1047i	0.145561	+	0.509761i
$879$		0			0
$880$	32.8516	+	16.2031i	1.10743	+	0.546207i
$881$	−11.0541			−0.372420			−0.186210	−	0.982510i	$-0.559621\pi$
$881$	−11.0541			−0.372420			−0.186210	+	0.982510i	$0.559621\pi$
$882$		0			0
$883$	22.8739			0.769769			0.384885	−	0.922965i	$-0.374241\pi$
$883$	22.8739			0.769769			0.384885	+	0.922965i	$0.374241\pi$
$884$	17.9046	−	11.1330i	0.602196	−	0.374444i
$885$		0			0
$886$	9.74819	+	34.1385i	0.327497	+	1.14690i
$887$	−19.2047			−0.644832			−0.322416	−	0.946598i	$-0.604495\pi$
$887$	−19.2047			−0.644832			−0.322416	+	0.946598i	$0.604495\pi$
$888$		0			0
$889$			28.9852i			0.972134i
$890$	−2.31643	−	8.11220i	−0.0776469	−	0.271922i
$891$		0			0
$892$	−30.5340	+	18.9860i	−1.02235	+	0.635697i
$893$	−18.8535	−	24.8723i	−0.630909	−	0.832319i
$894$		0			0
$895$	24.3913			0.815310
$896$	−9.06020	−	22.9345i	−0.302680	−	0.766188i
$897$		0			0
$898$	−46.1952	+	13.1910i	−1.54155	+	0.440188i
$899$	−44.4225			−1.48157
$900$		0			0
$901$	32.5957			1.08592
$902$	−4.14106	+	1.18247i	−0.137882	+	0.0393721i
$903$		0			0
$904$	19.0213	−	20.9848i	0.632639	−	0.697945i
$905$			9.90820i			0.329360i
$906$		0			0
$907$		−	6.75278i		−	0.224222i	−0.993696	−	0.112111i	$-0.964239\pi$
$907$		−	6.75278i		−	0.224222i	0.993696	−	0.112111i	$-0.0357613\pi$
$908$	−3.92100	−	6.30591i	−0.130123	−	0.209269i
$909$		0			0
$910$	5.76227	+	20.1796i	0.191017	+	0.668949i
$911$	18.5347			0.614083			0.307042	−	0.951696i	$-0.400661\pi$
$911$	18.5347			0.614083			0.307042	+	0.951696i	$0.400661\pi$
$912$		0			0
$913$	54.4039			1.80051
$914$	−4.54326	−	15.9106i	−0.150278	−	0.526277i
$915$		0			0
$916$	12.8725	+	20.7020i	0.425318	+	0.684015i
$917$			30.1066i			0.994209i
$918$		0			0
$919$		−	23.9508i		−	0.790065i	−0.918667	−	0.395033i	$-0.870733\pi$
$919$		−	23.9508i		−	0.790065i	0.918667	−	0.395033i	$-0.129267\pi$
$920$	−27.6965	−	25.1050i	−0.913128	−	0.827688i
$921$		0			0
$922$	−29.0577	+	8.29738i	−0.956963	+	0.273260i
$923$	−43.6864			−1.43795
$924$		0			0
$925$	3.78064			0.124307
$926$	−14.5690	+	4.16017i	−0.478768	+	0.136712i
$927$		0			0
$928$	51.8758	+	9.44323i	1.70291	+	0.309989i
$929$	−37.1420			−1.21859			−0.609295	−	0.792944i	$-0.708547\pi$
$929$	−37.1420			−1.21859			−0.609295	+	0.792944i	$0.708547\pi$
$930$		0			0
$931$	−7.81373	+	5.92291i	−0.256085	+	0.194116i
$932$	14.1088	−	8.77281i	0.462149	−	0.287363i
$933$		0			0
$934$	4.68299	+	16.4000i	0.153232	+	0.536623i
$935$			26.1512i			0.855235i
$936$		0			0
$937$	−53.6446			−1.75249			−0.876246	−	0.481864i	$-0.839960\pi$
$937$	−53.6446			−1.75249			−0.876246	+	0.481864i	$0.839960\pi$
$938$	2.79330	+	9.78221i	0.0912043	+	0.319400i
$939$		0			0
$940$	22.4292	−	13.9464i	0.731560	−	0.454882i
$941$	13.4007			0.436849			0.218425	−	0.975854i	$-0.429908\pi$
$941$	13.4007			0.436849			0.218425	+	0.975854i	$0.429908\pi$
$942$		0			0
$943$	4.39489			0.143117
$944$	16.6800	+	8.22693i	0.542887	+	0.267764i
$945$		0			0
$946$	3.73226	+	13.0705i	0.121346	+	0.424958i
$947$	34.2263			1.11221			0.556103	−	0.831114i	$-0.312296\pi$
$947$	34.2263			1.11221			0.556103	+	0.831114i	$0.312296\pi$
$948$		0			0
$949$	−58.1925			−1.88901
$950$	7.87931	+	5.91612i	0.255639	+	0.191944i
$951$		0			0
$952$	11.8233	−	13.0438i	0.383195	−	0.422751i
$953$		−	53.7074i		−	1.73975i	−0.493269	−	0.869877i	$-0.664198\pi$
$953$		−	53.7074i		−	1.73975i	0.493269	−	0.869877i	$-0.335802\pi$
$954$		0			0
$955$	−15.9529			−0.516224
$956$	11.1624	+	17.9518i	0.361017	+	0.580602i
$957$		0			0
$958$	48.9688	−	13.9830i	1.58211	−	0.451769i
$959$		−	17.1733i		−	0.554555i
$960$		0			0
$961$	−8.28726			−0.267331
$962$	3.39047	+	11.8735i	0.109313	+	0.382817i
$963$		0			0
$964$	26.2492	+	42.2150i	0.845428	+	1.35965i
$965$	−3.97670			−0.128015
$966$		0			0
$967$		−	29.3528i		−	0.943924i	−0.881619	−	0.471962i	$-0.843546\pi$
$967$		−	29.3528i		−	0.943924i	0.881619	−	0.471962i	$-0.156454\pi$
$968$	28.6121	+	25.9349i	0.919627	+	0.833579i
$969$		0			0
$970$	3.20200	+	11.2135i	0.102810	+	0.360043i
$971$			30.8032i			0.988522i	0.869314	+	0.494261i	$0.164561\pi$
$971$			30.8032i			0.988522i	−0.869314	+	0.494261i	$0.835439\pi$
$972$		0			0
$973$		−	25.2053i		−	0.808044i
$974$	−12.3549	−	43.2673i	−0.395877	−	1.38637i
$975$		0			0
$976$	4.52208	+	2.23039i	0.144748	+	0.0713931i
$977$		−	16.4474i		−	0.526198i	−0.964769	−	0.263099i	$-0.915255\pi$
$977$		−	16.4474i		−	0.526198i	0.964769	−	0.263099i	$-0.0847446\pi$
$978$		0			0
$979$		−	16.0597i		−	0.513272i
$980$	−4.38132	−	7.04622i	−0.139956	−	0.225083i
$981$		0			0
$982$	16.0526	+	56.2169i	0.512261	+	1.79395i
$983$	−52.9545			−1.68898			−0.844492	−	0.535568i	$-0.820098\pi$
$983$	−52.9545			−1.68898			−0.844492	+	0.535568i	$0.820098\pi$
$984$		0			0
$985$	−11.5582			−0.368275
$986$	10.3361	+	36.1972i	0.329167	+	1.15275i
$987$		0			0
$988$	−11.5141	+	30.0514i	−0.366312	+	0.956063i
$989$		−	13.8716i		−	0.441092i
$990$		0			0
$991$	47.4635			1.50773			0.753863	−	0.657032i	$-0.228188\pi$
$991$	47.4635			1.50773			0.753863	+	0.657032i	$0.228188\pi$
$992$	−26.5235	−	4.82822i	−0.842122	−	0.153296i
$993$		0			0
$994$	−35.0762	+	10.0160i	−1.11255	+	0.317687i
$995$	35.4994			1.12541
$996$		0			0
$997$		−	0.515627i		−	0.0163301i	−0.999967	−	0.00816504i	$-0.997401\pi$
$997$		−	0.515627i		−	0.0163301i	0.999967	−	0.00816504i	$-0.00259904\pi$
$998$	9.85217	+	34.5026i	0.311865	+	1.09216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.17		40
3.2	odd	2		456.2.e.a.379.24	yes	40
4.3	odd	2		5472.2.e.g.5167.18		40
8.3	odd	2	inner	1368.2.e.g.379.23		40
8.5	even	2		5472.2.e.g.5167.5		40
12.11	even	2		1824.2.e.a.1519.36		40
19.18	odd	2	inner	1368.2.e.g.379.24		40
24.5	odd	2		1824.2.e.a.1519.24		40
24.11	even	2		456.2.e.a.379.18	yes	40
57.56	even	2		456.2.e.a.379.17	✓	40
76.75	even	2		5472.2.e.g.5167.6		40
152.37	odd	2		5472.2.e.g.5167.17		40
152.75	even	2	inner	1368.2.e.g.379.18		40
228.227	odd	2		1824.2.e.a.1519.23		40
456.227	odd	2		456.2.e.a.379.23	yes	40
456.341	even	2		1824.2.e.a.1519.35		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.17	✓	40	57.56	even	2
456.2.e.a.379.18	yes	40	24.11	even	2
456.2.e.a.379.23	yes	40	456.227	odd	2
456.2.e.a.379.24	yes	40	3.2	odd	2
1368.2.e.g.379.17		40	1.1	even	1	trivial
1368.2.e.g.379.18		40	152.75	even	2	inner
1368.2.e.g.379.23		40	8.3	odd	2	inner
1368.2.e.g.379.24		40	19.18	odd	2	inner
1824.2.e.a.1519.23		40	228.227	odd	2
1824.2.e.a.1519.24		40	24.5	odd	2
1824.2.e.a.1519.35		40	456.341	even	2
1824.2.e.a.1519.36		40	12.11	even	2
5472.2.e.g.5167.5		40	8.5	even	2
5472.2.e.g.5167.6		40	76.75	even	2
5472.2.e.g.5167.17		40	152.37	odd	2
5472.2.e.g.5167.18		40	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.388306 - 1.35986i) q^{2} +(-1.69844 + 1.05608i) q^{4} +1.84435i q^{5} -2.17959i q^{7} +(2.09564 + 1.89955i) q^{8} +O(q^{10})\)	\(q+(-0.388306 - 1.35986i) q^{2} +(-1.69844 + 1.05608i) q^{4} +1.84435i q^{5} -2.17959i q^{7} +(2.09564 + 1.89955i) q^{8} +(2.50805 - 0.716171i) q^{10} +4.96519 q^{11} -3.69149 q^{13} +(-2.96394 + 0.846348i) q^{14} +(1.76937 - 3.58738i) q^{16} +2.85570 q^{17} +(-3.47371 + 2.63312i) q^{19} +(-1.94778 - 3.13251i) q^{20} +(-1.92802 - 6.75197i) q^{22} +7.16583i q^{23} +1.59839 q^{25} +(1.43343 + 5.01991i) q^{26} +(2.30183 + 3.70190i) q^{28} -9.32113 q^{29} +4.76579 q^{31} +(-5.56540 - 1.01310i) q^{32} +(-1.10889 - 3.88335i) q^{34} +4.01992 q^{35} +2.36528 q^{37} +(4.92954 + 3.70130i) q^{38} +(-3.50343 + 3.86508i) q^{40} -0.613311i q^{41} -1.93580 q^{43} +(-8.43307 + 5.24366i) q^{44} +(9.74453 - 2.78254i) q^{46} +7.16015i q^{47} +2.24939 q^{49} +(-0.620663 - 2.17358i) q^{50} +(6.26977 - 3.89853i) q^{52} +11.4143 q^{53} +9.15754i q^{55} +(4.14024 - 4.56763i) q^{56} +(3.61945 + 12.6754i) q^{58} +4.64963i q^{59} +1.26055i q^{61} +(-1.85058 - 6.48080i) q^{62} +(0.783404 + 7.96155i) q^{64} -6.80839i q^{65} -3.30041i q^{67} +(-4.85022 + 3.01586i) q^{68} +(-1.56096 - 5.46652i) q^{70} +11.8343 q^{71} +15.7639 q^{73} +(-0.918453 - 3.21645i) q^{74} +(3.11908 - 8.14072i) q^{76} -10.8221i q^{77} +5.39784 q^{79} +(6.61638 + 3.26334i) q^{80} +(-0.834017 + 0.238153i) q^{82} +10.9571 q^{83} +5.26690i q^{85} +(0.751684 + 2.63242i) q^{86} +(10.4053 + 9.43165i) q^{88} -3.23446i q^{89} +8.04594i q^{91} +(-7.56772 - 12.1707i) q^{92} +(9.73679 - 2.78033i) q^{94} +(-4.85639 - 6.40673i) q^{95} +4.47099i q^{97} +(-0.873451 - 3.05885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

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