LMFDB - Embedded newform 256.3.h.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.97549476762$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	256.31
Dual form			256.3.h.a.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.68670 + 1.94129i) q^{3} +(4.51028 + 1.86822i) q^{5} +(3.85317 - 3.85317i) q^{7} +(11.8326 - 11.8326i) q^{9} +O(q^{10})$	\(q+(-4.68670 + 1.94129i) q^{3} +(4.51028 + 1.86822i) q^{5} +(3.85317 - 3.85317i) q^{7} +(11.8326 - 11.8326i) q^{9} +(-4.56441 - 1.89064i) q^{11} +(5.58307 - 2.31258i) q^{13} -24.7651 q^{15} +25.0539i q^{17} +(6.43433 + 15.5338i) q^{19} +(-10.5785 + 25.5388i) q^{21} +(26.9024 + 26.9024i) q^{23} +(-0.825315 - 0.825315i) q^{25} +(-15.0136 + 36.2460i) q^{27} +(0.210028 + 0.507052i) q^{29} +15.8372i q^{31} +25.0623 q^{33} +(24.5774 - 10.1803i) q^{35} +(2.18606 + 0.905498i) q^{37} +(-21.6768 + 21.6768i) q^{39} +(-31.1517 + 31.1517i) q^{41} +(12.9078 + 5.34659i) q^{43} +(75.4740 - 31.2624i) q^{45} -15.0033 q^{47} +19.3062i q^{49} +(-48.6370 - 117.420i) q^{51} +(15.4409 - 37.2776i) q^{53} +(-17.0546 - 17.0546i) q^{55} +(-60.3115 - 60.3115i) q^{57} +(-14.7242 + 35.5473i) q^{59} +(15.4603 + 37.3243i) q^{61} -91.1858i q^{63} +29.5016 q^{65} +(61.3598 - 25.4161i) q^{67} +(-178.309 - 73.8579i) q^{69} +(51.7789 - 51.7789i) q^{71} +(64.9440 - 64.9440i) q^{73} +(5.47018 + 2.26582i) q^{75} +(-24.8724 + 10.3025i) q^{77} +38.1202 q^{79} -48.4156i q^{81} +(15.9782 + 38.5748i) q^{83} +(-46.8061 + 113.000i) q^{85} +(-1.96868 - 1.96868i) q^{87} +(23.7666 + 23.7666i) q^{89} +(12.6017 - 30.4233i) q^{91} +(-30.7446 - 74.2241i) q^{93} +82.0827i q^{95} -118.710 q^{97} +(-76.3798 + 31.6376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{19} + 4 q^{21} + 68 q^{23} - 4 q^{25} - 100 q^{27} + 4 q^{29} - 8 q^{33} + 92 q^{35} + 4 q^{37} - 188 q^{39} - 4 q^{41} + 92 q^{43} + 40 q^{45} + 8 q^{47} + 224 q^{51} + 164 q^{53} - 252 q^{55} - 4 q^{57} + 124 q^{59} + 68 q^{61} - 8 q^{65} - 164 q^{67} - 188 q^{69} + 260 q^{71} - 4 q^{73} - 488 q^{75} - 220 q^{77} + 520 q^{79} - 484 q^{83} - 96 q^{85} + 452 q^{87} - 4 q^{89} - 196 q^{91} - 32 q^{93} - 8 q^{97} + 216 q^{99}+O(q^{100}) $ 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^19 + 4 * q^21 + 68 * q^23 - 4 * q^25 - 100 * q^27 + 4 * q^29 - 8 * q^33 + 92 * q^35 + 4 * q^37 - 188 * q^39 - 4 * q^41 + 92 * q^43 + 40 * q^45 + 8 * q^47 + 224 * q^51 + 164 * q^53 - 252 * q^55 - 4 * q^57 + 124 * q^59 + 68 * q^61 - 8 * q^65 - 164 * q^67 - 188 * q^69 + 260 * q^71 - 4 * q^73 - 488 * q^75 - 220 * q^77 + 520 * q^79 - 484 * q^83 - 96 * q^85 + 452 * q^87 - 4 * q^89 - 196 * q^91 - 32 * q^93 - 8 * q^97 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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			0
$2$		0			0
$3$	−4.68670	+	1.94129i	−1.56223	+	0.647098i	−0.985476	−	0.169817i	$-0.945682\pi$
$3$	−4.68670	+	1.94129i	−1.56223	+	0.647098i	−0.576758	+	0.816915i	$0.695682\pi$
$4$		0			0
$5$	4.51028	+	1.86822i	0.902055	+	0.373644i	0.785010	−	0.619483i	$-0.212658\pi$
$5$	4.51028	+	1.86822i	0.902055	+	0.373644i	0.117045	+	0.993127i	$0.462658\pi$
$6$		0			0
$7$	3.85317	−	3.85317i	0.550453	−	0.550453i	−0.376119	−	0.926571i	$-0.622742\pi$
$7$	3.85317	−	3.85317i	0.550453	−	0.550453i	0.926571	+	0.376119i	$0.122742\pi$
$8$		0			0
$9$	11.8326	−	11.8326i	1.31473	−	1.31473i
$10$		0			0
$11$	−4.56441	−	1.89064i	−0.414946	−	0.171876i	0.165436	−	0.986221i	$-0.447097\pi$
$11$	−4.56441	−	1.89064i	−0.414946	−	0.171876i	−0.580382	+	0.814344i	$0.697097\pi$
$12$		0			0
$13$	5.58307	−	2.31258i	0.429467	−	0.177891i	−0.157470	−	0.987524i	$-0.550334\pi$
$13$	5.58307	−	2.31258i	0.429467	−	0.177891i	0.586937	+	0.809633i	$0.300334\pi$
$14$		0			0
$15$	−24.7651			−1.65101
$16$		0			0
$17$			25.0539i			1.47376i	0.676025	+	0.736879i	$0.263701\pi$
$17$			25.0539i			1.47376i	−0.676025	+	0.736879i	$0.736299\pi$
$18$		0			0
$19$	6.43433	+	15.5338i	0.338649	+	0.817571i	0.997846	+	0.0656005i	$0.0208963\pi$
$19$	6.43433	+	15.5338i	0.338649	+	0.817571i	−0.659197	+	0.751970i	$0.729104\pi$
$20$		0			0
$21$	−10.5785	+	25.5388i	−0.503739	+	1.21613i
$22$		0			0
$23$	26.9024	+	26.9024i	1.16967	+	1.16967i	0.982287	+	0.187381i	$0.0600000\pi$
$23$	26.9024	+	26.9024i	1.16967	+	1.16967i	0.187381	+	0.982287i	$0.440000\pi$
$24$		0			0
$25$	−0.825315	−	0.825315i	−0.0330126	−	0.0330126i
$26$		0			0
$27$	−15.0136	+	36.2460i	−0.556058	+	1.34244i
$28$		0			0
$29$	0.210028	+	0.507052i	0.00724234	+	0.0174846i	0.927459	−	0.373924i	$-0.121988\pi$
$29$	0.210028	+	0.507052i	0.00724234	+	0.0174846i	−0.920217	+	0.391409i	$0.871988\pi$
$30$		0			0
$31$			15.8372i			0.510877i	0.966825	+	0.255438i	$0.0822198\pi$
$31$			15.8372i			0.510877i	−0.966825	+	0.255438i	$0.917780\pi$
$32$		0			0
$33$	25.0623			0.759464
$34$		0			0
$35$	24.5774	−	10.1803i	0.702212	−	0.290866i
$36$		0			0
$37$	2.18606	+	0.905498i	0.0590828	+	0.0244729i	0.412029	−	0.911171i	$-0.364820\pi$
$37$	2.18606	+	0.905498i	0.0590828	+	0.0244729i	−0.352946	+	0.935644i	$0.614820\pi$
$38$		0			0
$39$	−21.6768	+	21.6768i	−0.555814	+	0.555814i
$40$		0			0
$41$	−31.1517	+	31.1517i	−0.759798	+	0.759798i	−0.976285	−	0.216488i	$-0.930540\pi$
$41$	−31.1517	+	31.1517i	−0.759798	+	0.759798i	0.216488	+	0.976285i	$0.430540\pi$
$42$		0			0
$43$	12.9078	+	5.34659i	0.300182	+	0.124339i	0.527691	−	0.849437i	$-0.323058\pi$
$43$	12.9078	+	5.34659i	0.300182	+	0.124339i	−0.227509	+	0.973776i	$0.573058\pi$
$44$		0			0
$45$	75.4740	−	31.2624i	1.67720	−	0.694719i
$46$		0			0
$47$	−15.0033			−0.319220			−0.159610	−	0.987180i	$-0.551024\pi$
$47$	−15.0033			−0.319220			−0.159610	+	0.987180i	$0.551024\pi$
$48$		0			0
$49$			19.3062i			0.394004i
$50$		0			0
$51$	−48.6370	−	117.420i	−0.953666	−	2.30235i
$52$		0			0
$53$	15.4409	−	37.2776i	0.291338	−	0.703352i	−0.708660	−	0.705550i	$-0.750700\pi$
$53$	15.4409	−	37.2776i	0.291338	−	0.703352i	0.999998	+	0.00219873i	$0.000699877\pi$
$54$		0			0
$55$	−17.0546	−	17.0546i	−0.310084	−	0.310084i
$56$		0			0
$57$	−60.3115	−	60.3115i	−1.05810	−	1.05810i
$58$		0			0
$59$	−14.7242	+	35.5473i	−0.249562	+	0.602496i	−0.998167	−	0.0605202i	$-0.980724\pi$
$59$	−14.7242	+	35.5473i	−0.249562	+	0.602496i	0.748605	+	0.663016i	$0.230724\pi$
$60$		0			0
$61$	15.4603	+	37.3243i	0.253447	+	0.611875i	0.998478	−	0.0551552i	$-0.0175654\pi$
$61$	15.4603	+	37.3243i	0.253447	+	0.611875i	−0.745031	+	0.667030i	$0.767565\pi$
$62$		0			0
$63$		−	91.1858i		−	1.44739i
$64$		0			0
$65$	29.5016			0.453870
$66$		0			0
$67$	61.3598	−	25.4161i	0.915818	−	0.379344i	0.125537	−	0.992089i	$-0.459935\pi$
$67$	61.3598	−	25.4161i	0.915818	−	0.379344i	0.790281	+	0.612745i	$0.209935\pi$
$68$		0			0
$69$	−178.309	−	73.8579i	−2.58419	−	1.07040i
$70$		0			0
$71$	51.7789	−	51.7789i	0.729281	−	0.729281i	−0.241196	−	0.970477i	$-0.577540\pi$
$71$	51.7789	−	51.7789i	0.729281	−	0.729281i	0.970477	+	0.241196i	$0.0775395\pi$
$72$		0			0
$73$	64.9440	−	64.9440i	0.889643	−	0.889643i	−0.104845	−	0.994489i	$-0.533435\pi$
$73$	64.9440	−	64.9440i	0.889643	−	0.889643i	0.994489	+	0.104845i	$0.0334347\pi$
$74$		0			0
$75$	5.47018	+	2.26582i	0.0729358	+	0.0302110i
$76$		0			0
$77$	−24.8724	+	10.3025i	−0.323018	+	0.133798i
$78$		0			0
$79$	38.1202			0.482535			0.241267	−	0.970459i	$-0.422437\pi$
$79$	38.1202			0.482535			0.241267	+	0.970459i	$0.422437\pi$
$80$		0			0
$81$		−	48.4156i		−	0.597724i
$82$		0			0
$83$	15.9782	+	38.5748i	0.192509	+	0.464757i	0.990432	−	0.138002i	$-0.0440680\pi$
$83$	15.9782	+	38.5748i	0.192509	+	0.464757i	−0.797923	+	0.602759i	$0.794068\pi$
$84$		0			0
$85$	−46.8061	+	113.000i	−0.550660	+	1.32941i
$86$		0			0
$87$	−1.96868	−	1.96868i	−0.0226285	−	0.0226285i
$88$		0			0
$89$	23.7666	+	23.7666i	0.267040	+	0.267040i	0.827906	−	0.560866i	$-0.189532\pi$
$89$	23.7666	+	23.7666i	0.267040	+	0.267040i	−0.560866	+	0.827906i	$0.689532\pi$
$90$		0			0
$91$	12.6017	−	30.4233i	0.138481	−	0.334322i
$92$		0			0
$93$	−30.7446	−	74.2241i	−0.330587	−	0.798109i
$94$		0			0
$95$			82.0827i			0.864028i
$96$		0			0
$97$	−118.710			−1.22382			−0.611908	−	0.790929i	$-0.709598\pi$
$97$	−118.710			−1.22382			−0.611908	+	0.790929i	$0.709598\pi$
$98$		0			0
$99$	−76.3798	+	31.6376i	−0.771514	+	0.319571i
$100$		0			0
$101$	182.236	+	75.4846i	1.80432	+	0.747372i	0.984652	+	0.174529i	$0.0558402\pi$
$101$	182.236	+	75.4846i	1.80432	+	0.747372i	0.819665	+	0.572844i	$0.194160\pi$
$102$		0			0
$103$	80.3171	−	80.3171i	0.779777	−	0.779777i	−0.200016	−	0.979793i	$-0.564099\pi$
$103$	80.3171	−	80.3171i	0.779777	−	0.779777i	0.979793	+	0.200016i	$0.0640993\pi$
$104$		0			0
$105$	−95.4240	+	95.4240i	−0.908800	+	0.908800i
$106$		0			0
$107$	22.6854	+	9.39659i	0.212013	+	0.0878186i	0.486162	−	0.873868i	$-0.338396\pi$
$107$	22.6854	+	9.39659i	0.212013	+	0.0878186i	−0.274150	+	0.961687i	$0.588396\pi$
$108$		0			0
$109$	−181.428	+	75.1501i	−1.66448	+	0.689450i	−0.998406	−	0.0564360i	$-0.982026\pi$
$109$	−181.428	+	75.1501i	−1.66448	+	0.689450i	−0.666074	+	0.745886i	$0.732026\pi$
$110$		0			0
$111$	−12.0033			−0.108138
$112$		0			0
$113$			32.7876i			0.290156i	0.989420	+	0.145078i	$0.0463433\pi$
$113$			32.7876i			0.290156i	−0.989420	+	0.145078i	$0.953657\pi$
$114$		0			0
$115$	71.0777	+	171.597i	0.618067	+	1.49214i
$116$		0			0
$117$	38.6983	−	93.4259i	0.330754	−	0.798512i
$118$		0			0
$119$	96.5368	+	96.5368i	0.811234	+	0.811234i
$120$		0			0
$121$	−68.3006	−	68.3006i	−0.564468	−	0.564468i
$122$		0			0
$123$	85.5241	−	206.473i	0.695318	−	1.67865i
$124$		0			0
$125$	−48.8860	−	118.021i	−0.391088	−	0.944169i
$126$		0			0
$127$		−	130.165i		−	1.02492i	−0.858710	−	0.512462i	$-0.828734\pi$
$127$		−	130.165i		−	1.02492i	0.858710	−	0.512462i	$-0.171266\pi$
$128$		0			0
$129$	−70.8744			−0.549414
$130$		0			0
$131$	24.3356	−	10.0801i	0.185768	−	0.0769476i	−0.287861	−	0.957672i	$-0.592944\pi$
$131$	24.3356	−	10.0801i	0.185768	−	0.0769476i	0.473628	+	0.880725i	$0.342944\pi$
$132$		0			0
$133$	84.6471	+	35.0620i	0.636444	+	0.263624i
$134$		0			0
$135$	−135.431	+	135.431i	−1.00319	+	1.00319i
$136$		0			0
$137$	147.886	−	147.886i	1.07946	−	1.07946i	0.0829047	−	0.996557i	$-0.473580\pi$
$137$	147.886	−	147.886i	1.07946	−	1.07946i	0.996557	−	0.0829047i	$-0.0264197\pi$
$138$		0			0
$139$	−206.929	−	85.7129i	−1.48870	−	0.616639i	−0.517666	−	0.855583i	$-0.673199\pi$
$139$	−206.929	−	85.7129i	−1.48870	−	0.616639i	−0.971033	+	0.238944i	$0.923199\pi$
$140$		0			0
$141$	70.3162	−	29.1259i	0.498696	−	0.206567i
$142$		0			0
$143$	−29.8556			−0.208781
$144$		0			0
$145$			2.67932i			0.0184781i
$146$		0			0
$147$	−37.4790	−	90.4823i	−0.254959	−	0.615526i
$148$		0			0
$149$	20.4247	−	49.3095i	0.137078	−	0.330936i	−0.840402	−	0.541964i	$-0.817681\pi$
$149$	20.4247	−	49.3095i	0.137078	−	0.330936i	0.977480	+	0.211028i	$0.0676810\pi$
$150$		0			0
$151$	−180.137	−	180.137i	−1.19296	−	1.19296i	−0.976232	−	0.216726i	$-0.930462\pi$
$151$	−180.137	−	180.137i	−1.19296	−	1.19296i	−0.216726	−	0.976232i	$-0.569538\pi$
$152$		0			0
$153$	296.452	+	296.452i	1.93759	+	1.93759i
$154$		0			0
$155$	−29.5873	+	71.4300i	−0.190886	+	0.460839i
$156$		0			0
$157$	60.3999	+	145.818i	0.384713	+	0.928779i	0.991040	+	0.133564i	$0.0426422\pi$
$157$	60.3999	+	145.818i	0.384713	+	0.928779i	−0.606327	+	0.795215i	$0.707358\pi$
$158$		0			0
$159$			204.684i			1.28732i
$160$		0			0
$161$	207.319			1.28769
$162$		0			0
$163$	−152.162	+	63.0277i	−0.933512	+	0.386673i	−0.797010	−	0.603966i	$-0.793586\pi$
$163$	−152.162	+	63.0277i	−0.933512	+	0.386673i	−0.136502	+	0.990640i	$0.543586\pi$
$164$		0			0
$165$	113.038	+	46.8218i	0.685078	+	0.283769i
$166$		0			0
$167$	−94.8188	+	94.8188i	−0.567777	+	0.567777i	−0.931505	−	0.363728i	$-0.881504\pi$
$167$	−94.8188	+	94.8188i	−0.567777	+	0.567777i	0.363728	+	0.931505i	$0.381504\pi$
$168$		0			0
$169$	−93.6785	+	93.6785i	−0.554310	+	0.554310i
$170$		0			0
$171$	259.940	+	107.671i	1.52012	+	0.629653i
$172$		0			0
$173$	107.416	−	44.4930i	0.620900	−	0.257185i	−0.0499813	−	0.998750i	$-0.515916\pi$
$173$	107.416	−	44.4930i	0.620900	−	0.257185i	0.670881	+	0.741565i	$0.265916\pi$
$174$		0			0
$175$	−6.36016			−0.0363437
$176$		0			0
$177$		−	195.183i		−	1.10273i
$178$		0			0
$179$	54.7154	+	132.095i	0.305673	+	0.737959i	0.999835	+	0.0181410i	$0.00577478\pi$
$179$	54.7154	+	132.095i	0.305673	+	0.737959i	−0.694163	+	0.719818i	$0.744225\pi$
$180$		0			0
$181$	128.496	−	310.218i	0.709925	−	1.71391i	0.00973575	−	0.999953i	$-0.496901\pi$
$181$	128.496	−	310.218i	0.709925	−	1.71391i	0.700189	−	0.713957i	$-0.253099\pi$
$182$		0			0
$183$	−144.915	−	144.915i	−0.791886	−	0.791886i
$184$		0			0
$185$	8.16809	+	8.16809i	0.0441518	+	0.0441518i
$186$		0			0
$187$	47.3678	−	114.356i	0.253304	−	0.611530i
$188$		0			0
$189$	81.8120	+	197.512i	0.432868	+	1.04503i
$190$		0			0
$191$			312.806i			1.63773i	0.573986	+	0.818865i	$0.305396\pi$
$191$			312.806i			1.63773i	−0.573986	+	0.818865i	$0.694604\pi$
$192$		0			0
$193$	−70.6708			−0.366170			−0.183085	−	0.983097i	$-0.558608\pi$
$193$	−70.6708			−0.366170			−0.183085	+	0.983097i	$0.558608\pi$
$194$		0			0
$195$	−138.265	+	57.2713i	−0.709052	+	0.293699i
$196$		0			0
$197$	−81.5762	−	33.7900i	−0.414092	−	0.171523i	0.165904	−	0.986142i	$-0.446946\pi$
$197$	−81.5762	−	33.7900i	−0.414092	−	0.171523i	−0.579996	+	0.814619i	$0.696946\pi$
$198$		0			0
$199$	−102.666	+	102.666i	−0.515910	+	0.515910i	−0.916331	−	0.400421i	$-0.868864\pi$
$199$	−102.666	+	102.666i	−0.515910	+	0.515910i	0.400421	+	0.916331i	$0.368864\pi$
$200$		0			0
$201$	−238.235	+	238.235i	−1.18525	+	1.18525i
$202$		0			0
$203$	2.76303	+	1.14449i	0.0136110	+	0.00563786i
$204$		0			0
$205$	−198.701	+	82.3046i	−0.969273	+	0.401486i
$206$		0			0
$207$	636.649			3.07560
$208$		0			0
$209$		−	83.0678i		−	0.397454i
$210$		0			0
$211$	8.35160	+	20.1625i	0.0395810	+	0.0955571i	0.942434	−	0.334393i	$-0.108531\pi$
$211$	8.35160	+	20.1625i	0.0395810	+	0.0955571i	−0.902853	+	0.429950i	$0.858531\pi$
$212$		0			0
$213$	−142.154	+	343.191i	−0.667391	+	1.61122i
$214$		0			0
$215$	48.2292	+	48.2292i	0.224322	+	0.224322i
$216$		0			0
$217$	61.0233	+	61.0233i	0.281213	+	0.281213i
$218$		0			0
$219$	−178.298	+	430.448i	−0.814144	+	1.96552i
$220$		0			0
$221$	57.9391	+	139.877i	0.262168	+	0.632930i
$222$		0			0
$223$		−	131.685i		−	0.590516i	−0.955418	−	0.295258i	$-0.904594\pi$
$223$		−	131.685i		−	0.590516i	0.955418	−	0.295258i	$-0.0954056\pi$
$224$		0			0
$225$	−19.5312			−0.0868054
$226$		0			0
$227$	60.7552	−	25.1656i	0.267644	−	0.110862i	−0.244825	−	0.969567i	$-0.578731\pi$
$227$	60.7552	−	25.1656i	0.267644	−	0.110862i	0.512470	+	0.858705i	$0.328731\pi$
$228$		0			0
$229$	−123.210	−	51.0352i	−0.538035	−	0.222861i	0.0970835	−	0.995276i	$-0.469049\pi$
$229$	−123.210	−	51.0352i	−0.538035	−	0.222861i	−0.635118	+	0.772415i	$0.719049\pi$
$230$		0			0
$231$	96.5693	−	96.5693i	0.418049	−	0.418049i
$232$		0			0
$233$	110.005	−	110.005i	0.472124	−	0.472124i	−0.430477	−	0.902601i	$-0.641655\pi$
$233$	110.005	−	110.005i	0.472124	−	0.472124i	0.902601	+	0.430477i	$0.141655\pi$
$234$		0			0
$235$	−67.6692	−	28.0295i	−0.287954	−	0.119274i
$236$		0			0
$237$	−178.658	+	74.0026i	−0.753832	+	0.312247i
$238$		0			0
$239$	−277.831			−1.16247			−0.581236	−	0.813735i	$-0.697431\pi$
$239$	−277.831			−1.16247			−0.581236	+	0.813735i	$0.697431\pi$
$240$		0			0
$241$		−	52.0006i		−	0.215770i	−0.994163	−	0.107885i	$-0.965592\pi$
$241$		−	52.0006i		−	0.215770i	0.994163	−	0.107885i	$-0.0344079\pi$
$242$		0			0
$243$	−41.1331	−	99.3041i	−0.169272	−	0.408659i
$244$		0			0
$245$	−36.0681	+	87.0762i	−0.147217	+	0.355413i
$246$		0			0
$247$	71.8466	+	71.8466i	0.290877	+	0.290877i
$248$		0			0
$249$	−149.770	−	149.770i	−0.601487	−	0.601487i
$250$		0			0
$251$	28.7912	−	69.5080i	0.114706	−	0.276924i	−0.856092	−	0.516823i	$-0.827114\pi$
$251$	28.7912	−	69.5080i	0.114706	−	0.276924i	0.970798	+	0.239899i	$0.0771143\pi$
$252$		0			0
$253$	−71.9307	−	173.656i	−0.284311	−	0.686388i
$254$		0			0
$255$		−	620.461i		−	2.43318i
$256$		0			0
$257$	241.501			0.939692			0.469846	−	0.882748i	$-0.344309\pi$
$257$	241.501			0.939692			0.469846	+	0.882748i	$0.344309\pi$
$258$		0			0
$259$	11.9123	−	4.93424i	0.0459935	−	0.0190511i
$260$		0			0
$261$	8.48491	+	3.51456i	0.0325092	+	0.0134658i
$262$		0			0
$263$	118.637	−	118.637i	0.451090	−	0.451090i	−0.444626	−	0.895716i	$-0.646664\pi$
$263$	118.637	−	118.637i	0.451090	−	0.451090i	0.895716	+	0.444626i	$0.146664\pi$
$264$		0			0
$265$	139.285	−	139.285i	0.525606	−	0.525606i
$266$		0			0
$267$	−157.525	−	65.2489i	−0.589981	−	0.244378i
$268$		0			0
$269$	231.194	−	95.7638i	0.859459	−	0.355999i	0.0909629	−	0.995854i	$-0.471006\pi$
$269$	231.194	−	95.7638i	0.859459	−	0.355999i	0.768496	+	0.639855i	$0.221006\pi$
$270$		0			0
$271$	2.13724			0.00788650			0.00394325	−	0.999992i	$-0.498745\pi$
$271$	2.13724			0.00788650			0.00394325	+	0.999992i	$0.498745\pi$
$272$		0			0
$273$			167.048i			0.611899i
$274$		0			0
$275$	2.20670	+	5.32745i	0.00802437	+	0.0193725i
$276$		0			0
$277$	177.679	−	428.955i	0.641441	−	1.54857i	−0.183296	−	0.983058i	$-0.558677\pi$
$277$	177.679	−	428.955i	0.641441	−	1.54857i	0.824737	−	0.565517i	$-0.191323\pi$
$278$		0			0
$279$	187.395	+	187.395i	0.671665	+	0.671665i
$280$		0			0
$281$	−261.664	−	261.664i	−0.931188	−	0.931188i	0.0665922	−	0.997780i	$-0.478787\pi$
$281$	−261.664	−	261.664i	−0.931188	−	0.931188i	−0.997780	+	0.0665922i	$0.978787\pi$
$282$		0			0
$283$	160.904	−	388.456i	0.568564	−	1.37264i	−0.334201	−	0.942502i	$-0.608466\pi$
$283$	160.904	−	388.456i	0.568564	−	1.37264i	0.902765	−	0.430134i	$-0.141534\pi$
$284$		0			0
$285$	−159.347	−	384.697i	−0.559111	−	1.34981i
$286$		0			0
$287$			240.066i			0.836465i
$288$		0			0
$289$	−338.697			−1.17196
$290$		0			0
$291$	556.359	−	230.452i	1.91189	−	0.791930i
$292$		0			0
$293$	141.895	+	58.7749i	0.484284	+	0.200597i	0.611448	−	0.791285i	$-0.290587\pi$
$293$	141.895	+	58.7749i	0.484284	+	0.200597i	−0.127164	+	0.991882i	$0.540587\pi$
$294$		0			0
$295$	−132.820	+	132.820i	−0.450238	+	0.450238i
$296$		0			0
$297$	137.056	−	137.056i	0.461468	−	0.461468i
$298$		0			0
$299$	212.412	+	87.9838i	0.710407	+	0.294260i
$300$		0			0
$301$	70.3373	−	29.1347i	0.233679	−	0.0967929i
$302$		0			0
$303$	−1000.62			−3.30239
$304$		0			0
$305$			197.226i			0.646643i
$306$		0			0
$307$	−36.1806	−	87.3476i	−0.117852	−	0.284520i	0.853935	−	0.520379i	$-0.174209\pi$
$307$	−36.1806	−	87.3476i	−0.117852	−	0.284520i	−0.971787	+	0.235860i	$0.924209\pi$
$308$		0			0
$309$	−220.503	+	532.341i	−0.713602	+	1.72279i
$310$		0			0
$311$	−221.462	−	221.462i	−0.712098	−	0.712098i	0.254876	−	0.966974i	$-0.417965\pi$
$311$	−221.462	−	221.462i	−0.712098	−	0.712098i	−0.966974	+	0.254876i	$0.917965\pi$
$312$		0			0
$313$	280.384	+	280.384i	0.895795	+	0.895795i	0.995061	−	0.0992662i	$-0.0316495\pi$
$313$	280.384	+	280.384i	0.895795	+	0.895795i	−0.0992662	+	0.995061i	$0.531650\pi$
$314$		0			0
$315$	170.355	−	411.273i	0.540809	−	1.30563i
$316$		0			0
$317$	−155.972	−	376.549i	−0.492024	−	1.18785i	−0.953688	−	0.300796i	$-0.902748\pi$
$317$	−155.972	−	376.549i	−0.492024	−	1.18785i	0.461665	−	0.887055i	$-0.347252\pi$
$318$		0			0
$319$		−	2.71148i		−	0.00849994i
$320$		0			0
$321$	−124.561			−0.388041
$322$		0			0
$323$	−389.183	+	161.205i	−1.20490	+	0.499086i
$324$		0			0
$325$	−6.51640	−	2.69918i	−0.0200505	−	0.00830517i
$326$		0			0
$327$	704.412	−	704.412i	2.15416	−	2.15416i
$328$		0			0
$329$	−57.8104	+	57.8104i	−0.175715	+	0.175715i
$330$		0			0
$331$	−418.148	−	173.202i	−1.26329	−	0.523270i	−0.352370	−	0.935861i	$-0.614624\pi$
$331$	−418.148	−	173.202i	−1.26329	−	0.523270i	−0.910917	+	0.412591i	$0.864624\pi$
$332$		0			0
$333$	36.5812	−	15.1524i	0.109853	−	0.0455027i
$334$		0			0
$335$	324.232			0.967857
$336$		0			0
$337$			38.1203i			0.113116i	0.998399	+	0.0565582i	$0.0180127\pi$
$337$			38.1203i			0.113116i	−0.998399	+	0.0565582i	$0.981987\pi$
$338$		0			0
$339$	−63.6504	−	153.666i	−0.187759	−	0.453291i
$340$		0			0
$341$	29.9424	−	72.2873i	0.0878076	−	0.211986i
$342$		0			0
$343$	263.195	+	263.195i	0.767333	+	0.767333i
$344$		0			0
$345$	−666.239	−	666.239i	−1.93113	−	1.93113i
$346$		0			0
$347$	−201.452	+	486.348i	−0.580553	+	1.40158i	0.311760	+	0.950161i	$0.399082\pi$
$347$	−201.452	+	486.348i	−0.580553	+	1.40158i	−0.892313	+	0.451418i	$0.850918\pi$
$348$		0			0
$349$	53.2160	+	128.475i	0.152481	+	0.368122i	0.981600	−	0.190951i	$-0.0611571\pi$
$349$	53.2160	+	128.475i	0.152481	+	0.368122i	−0.829118	+	0.559073i	$0.811157\pi$
$350$		0			0
$351$			237.084i			0.675452i
$352$		0			0
$353$	−223.875			−0.634208			−0.317104	−	0.948391i	$-0.602710\pi$
$353$	−223.875			−0.634208			−0.317104	+	0.948391i	$0.602710\pi$
$354$		0			0
$355$	330.272	−	136.803i	0.930343	−	0.385361i
$356$		0			0
$357$	−639.846	−	265.033i	−1.79228	−	0.742389i
$358$		0			0
$359$	44.5652	−	44.5652i	0.124137	−	0.124137i	−0.642309	−	0.766446i	$-0.722023\pi$
$359$	44.5652	−	44.5652i	0.124137	−	0.124137i	0.766446	+	0.642309i	$0.222023\pi$
$360$		0			0
$361$	55.3658	−	55.3658i	0.153368	−	0.153368i
$362$		0			0
$363$	452.696	+	187.513i	1.24710	+	0.516565i
$364$		0			0
$365$	414.245	−	171.586i	1.13492	−	0.470098i
$366$		0			0
$367$	294.972			0.803739			0.401869	−	0.915697i	$-0.368361\pi$
$367$	294.972			0.803739			0.401869	+	0.915697i	$0.368361\pi$
$368$		0			0
$369$			737.210i			1.99786i
$370$		0			0
$371$	−84.1406	−	203.133i	−0.226794	−	0.547529i
$372$		0			0
$373$	−96.5187	+	233.017i	−0.258763	+	0.624710i	−0.998857	−	0.0477936i	$-0.984781\pi$
$373$	−96.5187	+	233.017i	−0.258763	+	0.624710i	0.740094	+	0.672504i	$0.234781\pi$
$374$		0			0
$375$	458.228	+	458.228i	1.22194	+	1.22194i
$376$		0			0
$377$	2.34520	+	2.34520i	0.00622069	+	0.00622069i
$378$		0			0
$379$	−70.2002	+	169.478i	−0.185225	+	0.447172i	−0.989029	−	0.147722i	$-0.952806\pi$
$379$	−70.2002	+	169.478i	−0.185225	+	0.447172i	0.803804	+	0.594894i	$0.202806\pi$
$380$		0			0
$381$	252.689	+	610.046i	0.663227	+	1.60117i
$382$		0			0
$383$		−	519.043i		−	1.35520i	−0.735429	−	0.677602i	$-0.763019\pi$
$383$		−	519.043i		−	1.35520i	0.735429	−	0.677602i	$-0.236981\pi$
$384$		0			0
$385$	−131.429			−0.341373
$386$		0			0
$387$	215.997	−	89.4688i	0.558131	−	0.231185i
$388$		0			0
$389$	−52.0121	−	21.5441i	−0.133707	−	0.0553834i	0.314827	−	0.949149i	$-0.398054\pi$
$389$	−52.0121	−	21.5441i	−0.133707	−	0.0553834i	−0.448534	+	0.893766i	$0.648054\pi$
$390$		0			0
$391$	−674.009	+	674.009i	−1.72381	+	1.72381i
$392$		0			0
$393$	−94.4851	+	94.4851i	−0.240420	+	0.240420i
$394$		0			0
$395$	171.933	+	71.2169i	0.435273	+	0.180296i
$396$		0			0
$397$	−138.533	+	57.3823i	−0.348950	+	0.144540i	−0.550272	−	0.834985i	$-0.685476\pi$
$397$	−138.533	+	57.3823i	−0.348950	+	0.144540i	0.201322	+	0.979525i	$0.435476\pi$
$398$		0			0
$399$	−464.781			−1.16487
$400$		0			0
$401$			11.3014i			0.0281830i	0.999901	+	0.0140915i	$0.00448560\pi$
$401$			11.3014i			0.0281830i	−0.999901	+	0.0140915i	$0.995514\pi$
$402$		0			0
$403$	36.6248	+	88.4200i	0.0908803	+	0.219404i
$404$		0			0
$405$	90.4509	−	218.368i	0.223336	−	0.539180i
$406$		0			0
$407$	−8.26612	−	8.26612i	−0.0203099	−	0.0203099i
$408$		0			0
$409$	188.958	+	188.958i	0.462001	+	0.462001i	0.899311	−	0.437310i	$-0.144069\pi$
$409$	188.958	+	188.958i	0.462001	+	0.462001i	−0.437310	+	0.899311i	$0.644069\pi$
$410$		0			0
$411$	−406.008	+	980.190i	−0.987854	+	2.38489i
$412$		0			0
$413$	80.2350	+	193.704i	0.194274	+	0.469018i
$414$		0			0
$415$			203.834i			0.491166i
$416$		0			0
$417$	1136.21			2.72472
$418$		0			0
$419$	−238.026	+	98.5936i	−0.568081	+	0.235307i	−0.648189	−	0.761479i	$-0.724473\pi$
$419$	−238.026	+	98.5936i	−0.568081	+	0.235307i	0.0801080	+	0.996786i	$0.474473\pi$
$420$		0			0
$421$	−324.923	−	134.588i	−0.771790	−	0.319686i	−0.0381925	−	0.999270i	$-0.512160\pi$
$421$	−324.923	−	134.588i	−0.771790	−	0.319686i	−0.733597	+	0.679585i	$0.762160\pi$
$422$		0			0
$423$	−177.528	+	177.528i	−0.419688	+	0.419688i
$424$		0			0
$425$	20.6773	−	20.6773i	0.0486526	−	0.0486526i
$426$		0			0
$427$	203.388	+	84.2461i	0.476318	+	0.197298i
$428$		0			0
$429$	139.924	−	57.9586i	0.326164	−	0.135102i
$430$		0			0
$431$	16.1400			0.0374479			0.0187239	−	0.999825i	$-0.494040\pi$
$431$	16.1400			0.0374479			0.0187239	+	0.999825i	$0.494040\pi$
$432$		0			0
$433$		−	732.781i		−	1.69233i	−0.532918	−	0.846167i	$-0.678905\pi$
$433$		−	732.781i		−	1.69233i	0.532918	−	0.846167i	$-0.321095\pi$
$434$		0			0
$435$	−5.20136	−	12.5572i	−0.0119571	−	0.0288671i
$436$		0			0
$437$	−244.799	+	590.996i	−0.560180	+	1.35239i
$438$		0			0
$439$	−460.630	−	460.630i	−1.04927	−	1.04927i	−0.998722	−	0.0505487i	$-0.983903\pi$
$439$	−460.630	−	460.630i	−1.04927	−	1.04927i	−0.0505487	−	0.998722i	$-0.516097\pi$
$440$		0			0
$441$	228.442	+	228.442i	0.518009	+	0.518009i
$442$		0			0
$443$	−55.5453	+	134.098i	−0.125384	+	0.302705i	−0.974090	−	0.226161i	$-0.927382\pi$
$443$	−55.5453	+	134.098i	−0.125384	+	0.302705i	0.848705	+	0.528866i	$0.177382\pi$
$444$		0			0
$445$	62.7927	+	151.595i	0.141107	+	0.340663i
$446$		0			0
$447$			270.749i			0.605703i
$448$		0			0
$449$	731.262			1.62865			0.814323	−	0.580412i	$-0.197108\pi$
$449$	731.262			1.62865			0.814323	+	0.580412i	$0.197108\pi$
$450$		0			0
$451$	201.086	−	83.2924i	0.445866	−	0.184684i
$452$		0			0
$453$	1193.95	+	494.549i	2.63564	+	1.09172i
$454$		0			0
$455$	113.675	−	113.675i	0.249834	−	0.249834i
$456$		0			0
$457$	−332.873	+	332.873i	−0.728388	+	0.728388i	−0.970298	−	0.241911i	$-0.922226\pi$
$457$	−332.873	+	332.873i	−0.728388	+	0.728388i	0.241911	+	0.970298i	$0.422226\pi$
$458$		0			0
$459$	−908.102	−	376.148i	−1.97844	−	0.819495i
$460$		0			0
$461$	132.650	−	54.9455i	0.287744	−	0.119188i	−0.234143	−	0.972202i	$-0.575228\pi$
$461$	132.650	−	54.9455i	0.287744	−	0.119188i	0.521887	+	0.853015i	$0.325228\pi$
$462$		0			0
$463$	873.591			1.88680			0.943402	−	0.331650i	$-0.107605\pi$
$463$	873.591			1.88680			0.943402	+	0.331650i	$0.107605\pi$
$464$		0			0
$465$		−	392.209i		−	0.843460i
$466$		0			0
$467$	−135.550	−	327.247i	−0.290258	−	0.700744i	0.709735	−	0.704468i	$-0.248814\pi$
$467$	−135.550	−	327.247i	−0.290258	−	0.700744i	−0.999993	+	0.00372448i	$0.998814\pi$
$468$		0			0
$469$	138.497	−	334.362i	0.295303	−	0.712925i
$470$		0			0
$471$	−566.153	−	566.153i	−1.20202	−	1.20202i
$472$		0			0
$473$	−48.8081	−	48.8081i	−0.103188	−	0.103188i
$474$		0			0
$475$	7.50997	−	18.1307i	0.0158105	−	0.0381698i
$476$		0			0
$477$	−258.385	−	623.796i	−0.541687	−	1.30775i
$478$		0			0
$479$		−	296.032i		−	0.618021i	−0.951059	−	0.309011i	$-0.900002\pi$
$479$		−	296.032i		−	0.618021i	0.951059	−	0.309011i	$-0.0999979\pi$
$480$		0			0
$481$	14.2990			0.0297276
$482$		0			0
$483$	−971.641	+	402.467i	−2.01168	+	0.833265i
$484$		0			0
$485$	−535.416	−	221.777i	−1.10395	−	0.457271i
$486$		0			0
$487$	232.632	−	232.632i	0.477683	−	0.477683i	−0.426707	−	0.904390i	$-0.640326\pi$
$487$	232.632	−	232.632i	0.477683	−	0.477683i	0.904390	+	0.426707i	$0.140326\pi$
$488$		0			0
$489$	590.784	−	590.784i	1.20815	−	1.20815i
$490$		0			0
$491$	217.435	+	90.0644i	0.442840	+	0.183430i	0.592951	−	0.805239i	$-0.297963\pi$
$491$	217.435	+	90.0644i	0.442840	+	0.183430i	−0.150110	+	0.988669i	$0.547963\pi$
$492$		0			0
$493$	−12.7036	+	5.26201i	−0.0257680	+	0.0106735i
$494$		0			0
$495$	−403.600			−0.815354
$496$		0			0
$497$		−	399.026i		−	0.802869i
$498$		0			0
$499$	64.7699	+	156.368i	0.129799	+	0.313364i	0.975396	−	0.220458i	$-0.0707553\pi$
$499$	64.7699	+	156.368i	0.129799	+	0.313364i	−0.845597	+	0.533822i	$0.820755\pi$
$500$		0			0
$501$	260.316	−	628.458i	0.519593	−	1.25441i
$502$		0			0
$503$	612.203	+	612.203i	1.21710	+	1.21710i	0.968642	+	0.248460i	$0.0799246\pi$
$503$	612.203	+	612.203i	1.21710	+	1.21710i	0.248460	+	0.968642i	$0.420075\pi$
$504$		0			0
$505$	680.913	+	680.913i	1.34834	+	1.34834i
$506$		0			0
$507$	257.185	−	620.900i	0.507269	−	1.22466i
$508$		0			0
$509$	273.870	+	661.182i	0.538056	+	1.29898i	0.926078	+	0.377332i	$0.123158\pi$
$509$	273.870	+	661.182i	0.538056	+	1.29898i	−0.388022	+	0.921650i	$0.626842\pi$
$510$		0			0
$511$		−	500.480i		−	0.979413i
$512$		0			0
$513$	−659.641			−1.28585
$514$		0			0
$515$	512.302	−	212.202i	0.994761	−	0.412043i
$516$		0			0
$517$	68.4813	+	28.3659i	0.132459	+	0.0548663i
$518$		0			0
$519$	−417.051	+	417.051i	−0.803566	+	0.803566i
$520$		0			0
$521$	−527.816	+	527.816i	−1.01308	+	1.01308i	−0.0131690	+	0.999913i	$0.504192\pi$
$521$	−527.816	+	527.816i	−1.01308	+	1.01308i	−0.999913	+	0.0131690i	$0.995808\pi$
$522$		0			0
$523$	5.01268	+	2.07632i	0.00958447	+	0.00397002i	0.387471	−	0.921882i	$-0.373349\pi$
$523$	5.01268	+	2.07632i	0.00958447	+	0.00397002i	−0.377886	+	0.925852i	$0.623349\pi$
$524$		0			0
$525$	29.8081	−	12.3469i	0.0567774	−	0.0235180i
$526$		0			0
$527$	−396.783			−0.752908
$528$		0			0
$529$			918.476i			1.73625i
$530$		0			0
$531$	246.391	+	594.841i	0.464013	+	1.12023i
$532$		0			0
$533$	−101.881	+	245.963i	−0.191147	+	0.461469i
$534$		0			0
$535$	84.7624	+	84.7624i	0.158434	+	0.158434i
$536$		0			0
$537$	−512.869	−	512.869i	−0.955064	−	0.955064i
$538$		0			0
$539$	36.5010	−	88.1213i	0.0677199	−	0.163490i
$540$		0			0
$541$	229.279	+	553.528i	0.423806	+	1.02316i	0.981215	+	0.192919i	$0.0617955\pi$
$541$	229.279	+	553.528i	0.423806	+	1.02316i	−0.557409	+	0.830238i	$0.688204\pi$
$542$		0			0
$543$			1703.35i			3.13692i
$544$		0			0
$545$	−958.688			−1.75906
$546$		0			0
$547$	−391.381	+	162.115i	−0.715504	+	0.296371i	−0.710580	−	0.703617i	$-0.751567\pi$
$547$	−391.381	+	162.115i	−0.715504	+	0.296371i	−0.00492387	+	0.999988i	$0.501567\pi$
$548$		0			0
$549$	624.578	+	258.709i	1.13766	+	0.471236i
$550$		0			0
$551$	−6.52508	+	6.52508i	−0.0118423	+	0.0118423i
$552$		0			0
$553$	146.884	−	146.884i	0.265613	−	0.265613i
$554$		0			0
$555$	−54.1381	−	22.4247i	−0.0975461	−	0.0404049i
$556$		0			0
$557$	−364.486	+	150.975i	−0.654374	+	0.271050i	−0.685069	−	0.728478i	$-0.740228\pi$
$557$	−364.486	+	150.975i	−0.654374	+	0.271050i	0.0306953	+	0.999529i	$0.490228\pi$
$558$		0			0
$559$	84.4296			0.151037
$560$		0			0
$561$			627.908i			1.11927i
$562$		0			0
$563$	114.762	+	277.059i	0.203840	+	0.492113i	0.992431	−	0.122805i	$-0.0391891\pi$
$563$	114.762	+	277.059i	0.203840	+	0.492113i	−0.788591	+	0.614918i	$0.789189\pi$
$564$		0			0
$565$	−61.2544	+	147.881i	−0.108415	+	0.261736i
$566$		0			0
$567$	−186.554	−	186.554i	−0.329019	−	0.329019i
$568$		0			0
$569$	172.424	+	172.424i	0.303029	+	0.303029i	0.842198	−	0.539169i	$-0.181261\pi$
$569$	172.424	+	172.424i	0.303029	+	0.303029i	−0.539169	+	0.842198i	$0.681261\pi$
$570$		0			0
$571$	295.206	−	712.690i	0.516998	−	1.24814i	−0.422740	−	0.906251i	$-0.638932\pi$
$571$	295.206	−	712.690i	0.516998	−	1.24814i	0.939739	−	0.341894i	$-0.111068\pi$
$572$		0			0
$573$	−607.250	−	1466.03i	−1.05977	−	2.55852i
$574$		0			0
$575$		−	44.4059i		−	0.0772276i
$576$		0			0
$577$	−756.330			−1.31080			−0.655398	−	0.755283i	$-0.727499\pi$
$577$	−756.330			−1.31080			−0.655398	+	0.755283i	$0.727499\pi$
$578$		0			0
$579$	331.213	−	137.193i	0.572043	−	0.236948i
$580$		0			0
$581$	210.202	+	87.0686i	0.361794	+	0.149860i
$582$		0			0
$583$	−140.957	+	140.957i	−0.241779	+	0.241779i
$584$		0			0
$585$	349.080	−	349.080i	0.596717	−	0.596717i
$586$		0			0
$587$	736.720	+	305.159i	1.25506	+	0.519863i	0.908390	−	0.418125i	$-0.137312\pi$
$587$	736.720	+	305.159i	1.25506	+	0.519863i	0.346670	+	0.937987i	$0.387312\pi$
$588$		0			0
$589$	−246.012	+	101.902i	−0.417678	+	0.173008i
$590$		0			0
$591$	447.919			0.757901
$592$		0			0
$593$		−	76.7003i		−	0.129343i	−0.997907	−	0.0646714i	$-0.979400\pi$
$593$		−	76.7003i		−	0.129343i	0.997907	−	0.0646714i	$-0.0205999\pi$
$594$		0			0
$595$	255.056	+	615.759i	0.428665	+	1.03489i
$596$		0			0
$597$	281.860	−	680.470i	0.472127	−	1.13982i
$598$		0			0
$599$	−34.1251	−	34.1251i	−0.0569702	−	0.0569702i	0.678048	−	0.735018i	$-0.262826\pi$
$599$	−34.1251	−	34.1251i	−0.0569702	−	0.0569702i	−0.735018	+	0.678048i	$0.762826\pi$
$600$		0			0
$601$	212.552	+	212.552i	0.353664	+	0.353664i	0.861471	−	0.507807i	$-0.169544\pi$
$601$	212.552	+	212.552i	0.353664	+	0.353664i	−0.507807	+	0.861471i	$0.669544\pi$
$602$		0			0
$603$	425.307	−	1026.78i	0.705318	−	1.70279i
$604$		0			0
$605$	−180.454	−	435.655i	−0.298271	−	0.720091i
$606$		0			0
$607$			56.8377i			0.0936371i	0.998903	+	0.0468186i	$0.0149083\pi$
$607$			56.8377i			0.0936371i	−0.998903	+	0.0468186i	$0.985092\pi$
$608$		0			0
$609$	−15.1713			−0.0249118
$610$		0			0
$611$	−83.7646	+	34.6964i	−0.137094	+	0.0567863i
$612$		0			0
$613$	7.45320	+	3.08722i	0.0121586	+	0.00503624i	0.388754	−	0.921341i	$-0.372905\pi$
$613$	7.45320	+	3.08722i	0.0121586	+	0.00503624i	−0.376596	+	0.926378i	$0.622905\pi$
$614$		0			0
$615$	771.474	−	771.474i	1.25443	−	1.25443i
$616$		0			0
$617$	−325.733	+	325.733i	−0.527931	+	0.527931i	−0.919955	−	0.392024i	$-0.871775\pi$
$617$	−325.733	+	325.733i	−0.527931	+	0.527931i	0.392024	+	0.919955i	$0.371775\pi$
$618$		0			0
$619$	76.1643	+	31.5483i	0.123044	+	0.0509665i	0.443356	−	0.896346i	$-0.353788\pi$
$619$	76.1643	+	31.5483i	0.123044	+	0.0509665i	−0.320312	+	0.947312i	$0.603788\pi$
$620$		0			0
$621$	−1379.00	+	571.202i	−2.22062	+	0.919810i
$622$		0			0
$623$	183.153			0.293986
$624$		0			0
$625$		−	594.458i		−	0.951133i
$626$		0			0
$627$	161.259	+	389.314i	0.257192	+	0.620915i
$628$		0			0
$629$	−22.6862	+	54.7694i	−0.0360671	+	0.0870738i
$630$		0			0
$631$	−70.1301	−	70.1301i	−0.111141	−	0.111141i	0.649349	−	0.760490i	$-0.275041\pi$
$631$	−70.1301	−	70.1301i	−0.111141	−	0.111141i	−0.760490	+	0.649349i	$0.775041\pi$
$632$		0			0
$633$	−78.2829	−	78.2829i	−0.123670	−	0.123670i
$634$		0			0
$635$	243.177	−	587.082i	0.382956	−	0.924538i
$636$		0			0
$637$	44.6471	+	107.788i	0.0700897	+	0.169211i
$638$		0			0
$639$		−	1225.36i		−	1.91762i
$640$		0			0
$641$	458.396			0.715126			0.357563	−	0.933889i	$-0.383608\pi$
$641$	458.396			0.715126			0.357563	+	0.933889i	$0.383608\pi$
$642$		0			0
$643$	−882.443	+	365.520i	−1.37238	+	0.568460i	−0.942434	−	0.334393i	$-0.891469\pi$
$643$	−882.443	+	365.520i	−1.37238	+	0.568460i	−0.429950	+	0.902853i	$0.641469\pi$
$644$		0			0
$645$	−319.663	−	132.409i	−0.495602	−	0.205285i
$646$		0			0
$647$	130.433	−	130.433i	0.201597	−	0.201597i	−0.599087	−	0.800684i	$-0.704470\pi$
$647$	130.433	−	130.433i	0.201597	−	0.201597i	0.800684	+	0.599087i	$0.204470\pi$
$648$		0			0
$649$	134.414	−	134.414i	0.207110	−	0.207110i
$650$		0			0
$651$	−404.462	−	167.534i	−0.621294	−	0.257348i
$652$		0			0
$653$	−989.811	+	409.993i	−1.51579	+	0.627861i	−0.976743	−	0.214415i	$-0.931216\pi$
$653$	−989.811	+	409.993i	−1.51579	+	0.627861i	−0.539047	+	0.842275i	$0.681216\pi$
$654$		0			0
$655$	128.592			0.196324
$656$		0			0
$657$		−	1536.91i		−	2.33928i
$658$		0			0
$659$	−457.745	−	1105.09i	−0.694605	−	1.67693i	−0.735289	−	0.677753i	$-0.762954\pi$
$659$	−457.745	−	1105.09i	−0.694605	−	1.67693i	0.0406841	−	0.999172i	$-0.487046\pi$
$660$		0			0
$661$	96.2729	−	232.423i	0.145647	−	0.351624i	−0.834173	−	0.551502i	$-0.814055\pi$
$661$	96.2729	−	232.423i	0.145647	−	0.351624i	0.979821	+	0.199879i	$0.0640548\pi$
$662$		0			0
$663$	−543.087	−	543.087i	−0.819135	−	0.819135i
$664$		0			0
$665$	316.278	+	316.278i	0.475607	+	0.475607i
$666$		0			0
$667$	−7.99066	+	19.2912i	−0.0119800	+	0.0289223i
$668$		0			0
$669$	255.640	+	617.168i	0.382122	+	0.922524i
$670$		0			0
$671$		−	199.593i		−	0.297456i
$672$		0			0
$673$	−135.640			−0.201545			−0.100772	−	0.994910i	$-0.532131\pi$
$673$	−135.640			−0.201545			−0.100772	+	0.994910i	$0.532131\pi$
$674$		0			0
$675$	42.3053	−	17.5234i	0.0626745	−	0.0259606i
$676$		0			0
$677$	348.196	+	144.228i	0.514322	+	0.213039i	0.624721	−	0.780848i	$-0.285213\pi$
$677$	348.196	+	144.228i	0.514322	+	0.213039i	−0.110399	+	0.993887i	$0.535213\pi$
$678$		0			0
$679$	−457.411	+	457.411i	−0.673653	+	0.673653i
$680$		0			0
$681$	−235.888	+	235.888i	−0.346384	+	0.346384i
$682$		0			0
$683$	−812.940	−	336.731i	−1.19025	−	0.493017i	−0.302413	−	0.953177i	$-0.597792\pi$
$683$	−812.940	−	336.731i	−1.19025	−	0.493017i	−0.887836	+	0.460159i	$0.847792\pi$
$684$		0			0
$685$	943.292	−	390.724i	1.37707	−	0.570400i
$686$		0			0
$687$	676.523			0.984749
$688$		0			0
$689$		−	243.832i		−	0.353892i
$690$		0			0
$691$	−78.3893	−	189.249i	−0.113443	−	0.273876i	0.856953	−	0.515395i	$-0.172355\pi$
$691$	−78.3893	−	189.249i	−0.113443	−	0.273876i	−0.970396	+	0.241518i	$0.922355\pi$
$692$		0			0
$693$	−172.400	+	416.209i	−0.248773	+	0.600591i
$694$		0			0
$695$	−773.177	−	773.177i	−1.11249	−	1.11249i
$696$		0			0
$697$	−780.471	−	780.471i	−1.11976	−	1.11976i
$698$		0			0
$699$	−302.008	+	729.112i	−0.432057	+	1.04308i
$700$		0			0
$701$	−432.140	−	1043.28i	−0.616463	−	1.48827i	−0.855785	−	0.517332i	$-0.826925\pi$
$701$	−432.140	−	1043.28i	−0.616463	−	1.48827i	0.239322	−	0.970940i	$-0.423075\pi$
$702$		0			0
$703$			39.7843i			0.0565921i
$704$		0			0
$705$	371.559			0.527034
$706$		0			0
$707$	993.041	−	411.331i	1.40458	−	0.581798i
$708$		0			0
$709$	−367.507	−	152.226i	−0.518345	−	0.214706i	0.108145	−	0.994135i	$-0.465509\pi$
$709$	−367.507	−	152.226i	−0.518345	−	0.214706i	−0.626490	+	0.779430i	$0.715509\pi$
$710$		0			0
$711$	451.061	−	451.061i	0.634403	−	0.634403i
$712$		0			0
$713$	−426.058	+	426.058i	−0.597556	+	0.597556i
$714$		0			0
$715$	−134.657	−	55.7768i	−0.188332	−	0.0780096i
$716$		0			0
$717$	1302.11	−	539.352i	1.81605	−	0.752234i
$718$		0			0
$719$	100.566			0.139869			0.0699344	−	0.997552i	$-0.477721\pi$
$719$	100.566			0.139869			0.0699344	+	0.997552i	$0.477721\pi$
$720$		0			0
$721$		−	618.950i		−	0.858461i
$722$		0			0
$723$	100.949	+	243.711i	0.139625	+	0.337084i
$724$		0			0
$725$	0.245139	−	0.591817i	0.000338122	−	0.000816300i
$726$		0			0
$727$	332.402	+	332.402i	0.457224	+	0.457224i	0.897743	−	0.440519i	$-0.145206\pi$
$727$	332.402	+	332.402i	0.457224	+	0.457224i	−0.440519	+	0.897743i	$0.645206\pi$
$728$		0			0
$729$	693.672	+	693.672i	0.951540	+	0.951540i
$730$		0			0
$731$	−133.953	+	323.391i	−0.183246	+	0.442395i
$732$		0			0
$733$	166.189	+	401.215i	0.226724	+	0.547360i	0.995775	−	0.0918276i	$-0.0292709\pi$
$733$	166.189	+	401.215i	0.226724	+	0.547360i	−0.769051	+	0.639187i	$0.779271\pi$
$734$		0			0
$735$		−	478.119i		−	0.650502i
$736$		0			0
$737$	−328.124			−0.445215
$738$		0			0
$739$	1011.25	−	418.874i	1.36840	−	0.566812i	0.427049	−	0.904229i	$-0.359553\pi$
$739$	1011.25	−	418.874i	1.36840	−	0.566812i	0.941355	+	0.337417i	$0.109553\pi$
$740$		0			0
$741$	−476.199	−	197.248i	−0.642643	−	0.266192i
$742$		0			0
$743$	−458.897	+	458.897i	−0.617627	+	0.617627i	−0.944922	−	0.327295i	$-0.893863\pi$
$743$	−458.897	+	458.897i	−0.617627	+	0.617627i	0.327295	+	0.944922i	$0.393863\pi$
$744$		0			0
$745$	184.242	−	184.242i	0.247304	−	0.247304i
$746$		0			0
$747$	645.503	+	267.376i	0.864128	+	0.357933i
$748$		0			0
$749$	123.617	−	51.2039i	0.165043	−	0.0683630i
$750$		0			0
$751$	636.920			0.848096			0.424048	−	0.905640i	$-0.360609\pi$
$751$	636.920			0.848096			0.424048	+	0.905640i	$0.360609\pi$
$752$		0			0
$753$			381.656i			0.506847i
$754$		0			0
$755$	−475.932	−	1149.00i	−0.630373	−	1.52186i
$756$		0			0
$757$	414.804	−	1001.43i	0.547958	−	1.32289i	−0.371038	−	0.928618i	$-0.620998\pi$
$757$	414.804	−	1001.43i	0.547958	−	1.32289i	0.918995	−	0.394269i	$-0.129002\pi$
$758$		0			0
$759$	674.236	+	674.236i	0.888321	+	0.888321i
$760$		0			0
$761$	−520.779	−	520.779i	−0.684334	−	0.684334i	0.276639	−	0.960974i	$-0.410779\pi$
$761$	−520.779	−	520.779i	−0.684334	−	0.684334i	−0.960974	+	0.276639i	$0.910779\pi$
$762$		0			0
$763$	−409.508	+	988.640i	−0.536708	+	1.29573i
$764$		0			0
$765$	783.243	+	1890.92i	1.02385	+	2.47179i
$766$		0			0
$767$			232.514i			0.303147i
$768$		0			0
$769$	973.035			1.26533			0.632663	−	0.774427i	$-0.281962\pi$
$769$	973.035			1.26533			0.632663	+	0.774427i	$0.281962\pi$
$770$		0			0
$771$	−1131.84	+	468.825i	−1.46802	+	0.608073i
$772$		0			0
$773$	−959.578	−	397.470i	−1.24137	−	0.514192i	−0.337227	−	0.941423i	$-0.609489\pi$
$773$	−959.578	−	397.470i	−1.24137	−	0.514192i	−0.904142	+	0.427232i	$0.859489\pi$
$774$		0			0
$775$	13.0707	−	13.0707i	0.0168654	−	0.0168654i
$776$		0			0
$777$	−46.2506	+	46.2506i	−0.0595246	+	0.0595246i
$778$		0			0
$779$	−684.346	−	283.465i	−0.878493	−	0.363884i
$780$		0			0
$781$	−334.236	+	138.445i	−0.427958	+	0.177266i
$782$		0			0
$783$	−21.5319			−0.0274992
$784$		0			0
$785$			770.521i			0.981556i
$786$		0			0
$787$	412.612	+	996.133i	0.524284	+	1.26573i	0.935219	+	0.354070i	$0.115202\pi$
$787$	412.612	+	996.133i	0.524284	+	1.26573i	−0.410935	+	0.911665i	$0.634798\pi$
$788$		0			0
$789$	−325.706	+	786.323i	−0.412808	+	0.996607i
$790$		0			0
$791$	126.336	+	126.336i	0.159717	+	0.159717i
$792$		0			0
$793$	172.631	+	172.631i	0.217694	+	0.217694i
$794$		0			0
$795$	−382.395	+	923.183i	−0.481000	+	1.16124i
$796$		0			0
$797$	46.5600	+	112.406i	0.0584191	+	0.141036i	0.950394	−	0.311049i	$-0.100680\pi$
$797$	46.5600	+	112.406i	0.0584191	+	0.141036i	−0.891975	+	0.452085i	$0.850680\pi$
$798$		0			0
$799$		−	375.892i		−	0.470453i
$800$		0			0
$801$	562.440			0.702172
$802$		0			0
$803$	−419.216	+	173.645i	−0.522063	+	0.216245i
$804$		0			0
$805$	935.065	+	387.317i	1.16157	+	0.481139i
$806$		0			0
$807$	−897.633	+	897.633i	−1.11231	+	1.11231i
$808$		0			0
$809$	−80.8371	+	80.8371i	−0.0999222	+	0.0999222i	−0.755301	−	0.655378i	$-0.772509\pi$
$809$	−80.8371	+	80.8371i	−0.0999222	+	0.0999222i	0.655378	+	0.755301i	$0.272509\pi$
$810$		0			0
$811$	1277.99	+	529.360i	1.57582	+	0.652725i	0.987744	−	0.156082i	$-0.0498865\pi$
$811$	1277.99	+	529.360i	1.57582	+	0.652725i	0.588074	+	0.808807i	$0.299886\pi$
$812$		0			0
$813$	−10.0166	+	4.14902i	−0.0123206	+	0.00510334i
$814$		0			0
$815$	−804.044			−0.986557
$816$		0			0
$817$			234.910i			0.287527i
$818$		0			0
$819$	−210.875	−	509.096i	−0.257478	−	0.621607i
$820$		0			0
$821$	−83.7084	+	202.090i	−0.101959	+	0.246151i	−0.966625	−	0.256197i	$-0.917530\pi$
$821$	−83.7084	+	202.090i	−0.101959	+	0.246151i	0.864666	+	0.502348i	$0.167530\pi$
$822$		0			0
$823$	−588.539	−	588.539i	−0.715114	−	0.715114i	0.252486	−	0.967601i	$-0.418752\pi$
$823$	−588.539	−	588.539i	−0.715114	−	0.715114i	−0.967601	+	0.252486i	$0.918752\pi$
$824$		0			0
$825$	−20.6843	−	20.6843i	−0.0250719	−	0.0250719i
$826$		0			0
$827$	281.470	−	679.529i	0.340351	−	0.821679i	−0.657329	−	0.753603i	$-0.728314\pi$
$827$	281.470	−	679.529i	0.340351	−	0.821679i	0.997680	−	0.0680759i	$-0.0216860\pi$
$828$		0			0
$829$	−6.83745	−	16.5071i	−0.00824783	−	0.0199120i	0.919702	−	0.392617i	$-0.128430\pi$
$829$	−6.83745	−	16.5071i	−0.00824783	−	0.0199120i	−0.927950	+	0.372705i	$0.878430\pi$
$830$		0			0
$831$			2355.31i			2.83431i
$832$		0			0
$833$	−483.695			−0.580666
$834$		0			0
$835$	−604.801	+	250.517i	−0.724313	+	0.300020i
$836$		0			0
$837$	−574.034	−	237.773i	−0.685823	−	0.284077i
$838$		0			0
$839$	358.991	−	358.991i	0.427879	−	0.427879i	−0.460026	−	0.887905i	$-0.652160\pi$
$839$	358.991	−	358.991i	0.427879	−	0.427879i	0.887905	+	0.460026i	$0.152160\pi$
$840$		0			0
$841$	594.464	−	594.464i	0.706854	−	0.706854i
$842$		0			0
$843$	1734.31	+	718.373i	2.05730	+	0.852163i
$844$		0			0
$845$	−597.527	+	247.504i	−0.707133	+	0.292904i
$846$		0			0
$847$	−526.348			−0.621426
$848$		0			0
$849$			2132.94i			2.51229i
$850$		0			0
$851$	34.4503	+	83.1704i	0.0404821	+	0.0977325i
$852$		0			0
$853$	−545.396	+	1316.70i	−0.639386	+	1.54361i	0.188114	+	0.982147i	$0.439763\pi$
$853$	−545.396	+	1316.70i	−0.639386	+	1.54361i	−0.827499	+	0.561467i	$0.810237\pi$
$854$		0			0
$855$	971.249	+	971.249i	1.13596	+	1.13596i
$856$		0			0
$857$	157.052	+	157.052i	0.183258	+	0.183258i	0.792774	−	0.609516i	$-0.208636\pi$
$857$	157.052	+	157.052i	0.183258	+	0.183258i	−0.609516	+	0.792774i	$0.708636\pi$
$858$		0			0
$859$	17.7307	−	42.8057i	0.0206411	−	0.0498321i	−0.913223	−	0.407460i	$-0.866414\pi$
$859$	17.7307	−	42.8057i	0.0206411	−	0.0498321i	0.933864	+	0.357628i	$0.116414\pi$
$860$		0			0
$861$	−466.038	−	1125.12i	−0.541275	−	1.30675i
$862$		0			0
$863$			186.088i			0.215629i	0.994171	+	0.107815i	$0.0343853\pi$
$863$			186.088i			0.215629i	−0.994171	+	0.107815i	$0.965615\pi$
$864$		0			0
$865$	567.597			0.656181
$866$		0			0
$867$	1587.37	−	657.510i	1.83088	−	0.758374i
$868$		0			0
$869$	−173.996	−	72.0716i	−0.200226	−	0.0829363i
$870$		0			0
$871$	283.799	−	283.799i	0.325831	−	0.325831i
$872$		0			0
$873$	−1404.65	+	1404.65i	−1.60899	+	1.60899i
$874$		0			0
$875$	−643.121	−	266.390i	−0.734996	−	0.304445i
$876$		0			0
$877$	216.654	−	89.7412i	0.247040	−	0.102328i	−0.255728	−	0.966749i	$-0.582315\pi$
$877$	216.654	−	89.7412i	0.247040	−	0.102328i	0.502768	+	0.864421i	$0.332315\pi$
$878$		0			0
$879$	−779.119			−0.886370
$880$		0			0
$881$		−	47.9671i		−	0.0544462i	−0.999629	−	0.0272231i	$-0.991334\pi$
$881$		−	47.9671i		−	0.0544462i	0.999629	−	0.0272231i	$-0.00866645\pi$
$882$		0			0
$883$	115.380	+	278.551i	0.130668	+	0.315460i	0.975650	−	0.219335i	$-0.0703888\pi$
$883$	115.380	+	278.551i	0.130668	+	0.315460i	−0.844982	+	0.534795i	$0.820389\pi$
$884$		0			0
$885$	364.645	−	880.331i	0.412028	−	0.994724i
$886$		0			0
$887$	−233.227	−	233.227i	−0.262939	−	0.262939i	0.563308	−	0.826247i	$-0.309528\pi$
$887$	−233.227	−	233.227i	−0.262939	−	0.262939i	−0.826247	+	0.563308i	$0.809528\pi$
$888$		0			0
$889$	−501.549	−	501.549i	−0.564172	−	0.564172i
$890$		0			0
$891$	−91.5365	+	220.989i	−0.102735	+	0.248023i
$892$		0			0
$893$	−96.5364	−	233.059i	−0.108103	−	0.260985i
$894$		0			0
$895$			698.004i			0.779892i
$896$		0			0
$897$	−1166.31			−1.30024
$898$		0			0
$899$	−8.03028	+	3.32625i	−0.00893246	+	0.00369994i
$900$		0			0
$901$	933.949	+	386.854i	1.03657	+	0.429361i
$902$		0			0
$903$	−273.091	+	273.091i	−0.302426	+	0.302426i
$904$		0			0
$905$	1159.11	−	1159.11i	1.28078	−	1.28078i
$906$		0			0
$907$	−827.946	−	342.947i	−0.912841	−	0.378111i	−0.123697	−	0.992320i	$-0.539475\pi$
$907$	−827.946	−	342.947i	−0.912841	−	0.378111i	−0.789143	+	0.614209i	$0.789475\pi$
$908$		0			0
$909$	3049.50	−	1263.14i	3.35478	−	1.38960i
$910$		0			0
$911$	−1321.92			−1.45107			−0.725534	−	0.688186i	$-0.758407\pi$
$911$	−1321.92			−1.45107			−0.725534	+	0.688186i	$0.758407\pi$
$912$		0			0
$913$		−	206.280i		−	0.225937i
$914$		0			0
$915$	−382.874	−	924.340i	−0.418442	−	1.01021i
$916$		0			0
$917$	54.9287	−	132.610i	0.0599004	−	0.144612i
$918$		0			0
$919$	717.026	+	717.026i	0.780224	+	0.780224i	0.979868	−	0.199645i	$-0.0639788\pi$
$919$	717.026	+	717.026i	0.780224	+	0.780224i	−0.199645	+	0.979868i	$0.563979\pi$
$920$		0			0
$921$	339.135	+	339.135i	0.368225	+	0.368225i
$922$		0			0
$923$	169.342	−	408.828i	0.183469	−	0.442934i
$924$		0			0
$925$	−1.05687	−	2.55151i	−0.00114256	−	0.00275839i
$926$		0			0
$927$		−	1900.72i		−	2.05039i
$928$		0			0
$929$	−430.578			−0.463485			−0.231743	−	0.972777i	$-0.574443\pi$
$929$	−430.578			−0.463485			−0.231743	+	0.972777i	$0.574443\pi$
$930$		0			0
$931$	−299.899	+	124.222i	−0.322126	+	0.133429i
$932$		0			0
$933$	1467.85	+	608.004i	1.57326	+	0.651666i
$934$		0			0
$935$	427.284	−	427.284i	0.456988	−	0.456988i
$936$		0			0
$937$	752.850	−	752.850i	0.803469	−	0.803469i	−0.180167	−	0.983636i	$-0.557664\pi$
$937$	752.850	−	752.850i	0.803469	−	0.803469i	0.983636	+	0.180167i	$0.0576639\pi$
$938$		0			0
$939$	−1858.38	−	769.767i	−1.97911	−	0.819773i
$940$		0			0
$941$	1482.20	−	613.948i	1.57513	−	0.652442i	0.587501	−	0.809223i	$-0.300112\pi$
$941$	1482.20	−	613.948i	1.57513	−	0.652442i	0.987633	+	0.156781i	$0.0501118\pi$
$942$		0			0
$943$	−1676.11			−1.77742
$944$		0			0
$945$			1043.67i			1.10442i
$946$		0			0
$947$	528.730	+	1276.47i	0.558321	+	1.34791i	0.911094	+	0.412198i	$0.135239\pi$
$947$	528.730	+	1276.47i	0.558321	+	1.34791i	−0.352773	+	0.935709i	$0.614761\pi$
$948$		0			0
$949$	212.398	−	512.775i	0.223813	−	0.540332i
$950$		0			0
$951$	1461.98	+	1461.98i	1.53731	+	1.53731i
$952$		0			0
$953$	−538.112	−	538.112i	−0.564650	−	0.564650i	0.365975	−	0.930625i	$-0.380736\pi$
$953$	−538.112	−	538.112i	−0.564650	−	0.564650i	−0.930625	+	0.365975i	$0.880736\pi$
$954$		0			0
$955$	−584.391	+	1410.84i	−0.611927	+	1.47732i
$956$		0			0
$957$	5.26378	+	12.7079i	0.00550030	+	0.0132789i
$958$		0			0
$959$		−	1139.66i		−	1.18839i
$960$		0			0
$961$	710.184			0.739005
$962$		0			0
$963$	379.612	−	157.240i	0.394197	−	0.163282i
$964$		0			0
$965$	−318.745	−	132.028i	−0.330306	−	0.136817i
$966$		0			0
$967$	380.769	−	380.769i	0.393763	−	0.393763i	−0.482263	−	0.876026i	$-0.660185\pi$
$967$	380.769	−	380.769i	0.393763	−	0.393763i	0.876026	+	0.482263i	$0.160185\pi$
$968$		0			0
$969$	1511.04	−	1511.04i	1.55938	−	1.55938i
$970$		0			0
$971$	−1000.67	−	414.490i	−1.03055	−	0.426869i	−0.197642	−	0.980274i	$-0.563328\pi$
$971$	−1000.67	−	414.490i	−1.03055	−	0.426869i	−0.832912	+	0.553405i	$0.813328\pi$
$972$		0			0
$973$	−1127.60	+	467.067i	−1.15889	+	0.480028i
$974$		0			0
$975$	35.7803			0.0366977
$976$		0			0
$977$			920.476i			0.942145i	0.882095	+	0.471072i	$0.156133\pi$
$977$			920.476i			0.942145i	−0.882095	+	0.471072i	$0.843867\pi$
$978$		0			0
$979$	−63.5463	−	153.414i	−0.0649094	−	0.156705i
$980$		0			0
$981$	−1257.55	+	3035.98i	−1.28190	+	3.09478i
$982$		0			0
$983$	−465.265	−	465.265i	−0.473312	−	0.473312i	0.429673	−	0.902985i	$-0.358629\pi$
$983$	−465.265	−	465.265i	−0.473312	−	0.473312i	−0.902985	+	0.429673i	$0.858629\pi$
$984$		0			0
$985$	−304.804	−	304.804i	−0.309446	−	0.309446i
$986$		0			0
$987$	158.713	−	383.167i	0.160803	−	0.388214i
$988$		0			0
$989$	203.415	+	491.087i	0.205677	+	0.496549i
$990$		0			0
$991$		−	365.984i		−	0.369307i	−0.982804	−	0.184654i	$-0.940884\pi$
$991$		−	365.984i		−	0.369307i	0.982804	−	0.184654i	$-0.0591164\pi$
$992$		0			0
$993$	2295.97			2.31216
$994$		0			0
$995$	−654.855	+	271.250i	−0.658146	+	0.272613i
$996$		0			0
$997$	77.3922	+	32.0569i	0.0776251	+	0.0321534i	0.421158	−	0.906987i	$-0.361624\pi$
$997$	77.3922	+	32.0569i	0.0776251	+	0.0321534i	−0.343533	+	0.939141i	$0.611624\pi$
$998$		0			0
$999$	−65.6413	+	65.6413i	−0.0657070	+	0.0657070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.3.h.a.31.1		28
4.3	odd	2		256.3.h.b.31.7		28
8.3	odd	2		32.3.h.a.27.2	yes	28
8.5	even	2		128.3.h.a.15.7		28
24.11	even	2		288.3.u.a.91.6		28
32.3	odd	8		128.3.h.a.111.7		28
32.13	even	8		256.3.h.b.223.7		28
32.19	odd	8	inner	256.3.h.a.223.1		28
32.29	even	8		32.3.h.a.19.2	✓	28
96.29	odd	8		288.3.u.a.19.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.2	✓	28	32.29	even	8
32.3.h.a.27.2	yes	28	8.3	odd	2
128.3.h.a.15.7		28	8.5	even	2
128.3.h.a.111.7		28	32.3	odd	8
256.3.h.a.31.1		28	1.1	even	1	trivial
256.3.h.a.223.1		28	32.19	odd	8	inner
256.3.h.b.31.7		28	4.3	odd	2
256.3.h.b.223.7		28	32.13	even	8
288.3.u.a.19.6		28	96.29	odd	8
288.3.u.a.91.6		28	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.68670 + 1.94129i) q^{3} +(4.51028 + 1.86822i) q^{5} +(3.85317 - 3.85317i) q^{7} +(11.8326 - 11.8326i) q^{9} +O(q^{10})\)	\(q+(-4.68670 + 1.94129i) q^{3} +(4.51028 + 1.86822i) q^{5} +(3.85317 - 3.85317i) q^{7} +(11.8326 - 11.8326i) q^{9} +(-4.56441 - 1.89064i) q^{11} +(5.58307 - 2.31258i) q^{13} -24.7651 q^{15} +25.0539i q^{17} +(6.43433 + 15.5338i) q^{19} +(-10.5785 + 25.5388i) q^{21} +(26.9024 + 26.9024i) q^{23} +(-0.825315 - 0.825315i) q^{25} +(-15.0136 + 36.2460i) q^{27} +(0.210028 + 0.507052i) q^{29} +15.8372i q^{31} +25.0623 q^{33} +(24.5774 - 10.1803i) q^{35} +(2.18606 + 0.905498i) q^{37} +(-21.6768 + 21.6768i) q^{39} +(-31.1517 + 31.1517i) q^{41} +(12.9078 + 5.34659i) q^{43} +(75.4740 - 31.2624i) q^{45} -15.0033 q^{47} +19.3062i q^{49} +(-48.6370 - 117.420i) q^{51} +(15.4409 - 37.2776i) q^{53} +(-17.0546 - 17.0546i) q^{55} +(-60.3115 - 60.3115i) q^{57} +(-14.7242 + 35.5473i) q^{59} +(15.4603 + 37.3243i) q^{61} -91.1858i q^{63} +29.5016 q^{65} +(61.3598 - 25.4161i) q^{67} +(-178.309 - 73.8579i) q^{69} +(51.7789 - 51.7789i) q^{71} +(64.9440 - 64.9440i) q^{73} +(5.47018 + 2.26582i) q^{75} +(-24.8724 + 10.3025i) q^{77} +38.1202 q^{79} -48.4156i q^{81} +(15.9782 + 38.5748i) q^{83} +(-46.8061 + 113.000i) q^{85} +(-1.96868 - 1.96868i) q^{87} +(23.7666 + 23.7666i) q^{89} +(12.6017 - 30.4233i) q^{91} +(-30.7446 - 74.2241i) q^{93} +82.0827i q^{95} -118.710 q^{97} +(-76.3798 + 31.6376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{19} + 4 q^{21} + 68 q^{23} - 4 q^{25} - 100 q^{27} + 4 q^{29} - 8 q^{33} + 92 q^{35} + 4 q^{37} - 188 q^{39} - 4 q^{41} + 92 q^{43} + 40 q^{45} + 8 q^{47} + 224 q^{51} + 164 q^{53} - 252 q^{55} - 4 q^{57} + 124 q^{59} + 68 q^{61} - 8 q^{65} - 164 q^{67} - 188 q^{69} + 260 q^{71} - 4 q^{73} - 488 q^{75} - 220 q^{77} + 520 q^{79} - 484 q^{83} - 96 q^{85} + 452 q^{87} - 4 q^{89} - 196 q^{91} - 32 q^{93} - 8 q^{97} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^19 + 4 * q^21 + 68 * q^23 - 4 * q^25 - 100 * q^27 + 4 * q^29 - 8 * q^33 + 92 * q^35 + 4 * q^37 - 188 * q^39 - 4 * q^41 + 92 * q^43 + 40 * q^45 + 8 * q^47 + 224 * q^51 + 164 * q^53 - 252 * q^55 - 4 * q^57 + 124 * q^59 + 68 * q^61 - 8 * q^65 - 164 * q^67 - 188 * q^69 + 260 * q^71 - 4 * q^73 - 488 * q^75 - 220 * q^77 + 520 * q^79 - 484 * q^83 - 96 * q^85 + 452 * q^87 - 4 * q^89 - 196 * q^91 - 32 * q^93 - 8 * q^97 + 216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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