LMFDB - Embedded newform 304.5.r.d.65.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.18
Character	$\chi$	$=$	304.65
Dual form			304.5.r.d.145.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.3222 + 6.53690i) q^{3} +(-19.8361 + 34.3572i) q^{5} +76.8642 q^{7} +(44.9621 + 77.8766i) q^{9} +O(q^{10})$	\(q+(11.3222 + 6.53690i) q^{3} +(-19.8361 + 34.3572i) q^{5} +76.8642 q^{7} +(44.9621 + 77.8766i) q^{9} -167.042 q^{11} +(-266.363 + 153.785i) q^{13} +(-449.179 + 259.334i) q^{15} +(73.9920 - 128.158i) q^{17} +(208.536 + 294.676i) q^{19} +(870.275 + 502.454i) q^{21} +(-22.2131 - 38.4743i) q^{23} +(-474.445 - 821.764i) q^{25} +116.673i q^{27} +(608.382 - 351.249i) q^{29} +596.777i q^{31} +(-1891.29 - 1091.94i) q^{33} +(-1524.69 + 2640.84i) q^{35} -300.577i q^{37} -4021.10 q^{39} +(-103.099 - 59.5244i) q^{41} +(-338.309 + 585.968i) q^{43} -3567.50 q^{45} +(-942.536 - 1632.52i) q^{47} +3507.11 q^{49} +(1675.51 - 967.357i) q^{51} +(-572.321 + 330.430i) q^{53} +(3313.46 - 5739.09i) q^{55} +(434.823 + 4699.57i) q^{57} +(-3737.52 - 2157.86i) q^{59} +(3355.06 + 5811.13i) q^{61} +(3455.98 + 5985.93i) q^{63} -12202.0i q^{65} +(-5778.80 + 3336.39i) q^{67} -580.820i q^{69} +(7207.51 + 4161.26i) q^{71} +(-3706.83 + 6420.42i) q^{73} -12405.6i q^{75} -12839.5 q^{77} +(5664.89 + 3270.62i) q^{79} +(2879.25 - 4987.01i) q^{81} +1526.28 q^{83} +(2935.43 + 5084.32i) q^{85} +9184.33 q^{87} +(-1121.63 + 647.575i) q^{89} +(-20473.8 + 11820.5i) q^{91} +(-3901.07 + 6756.86i) q^{93} +(-14260.8 + 1319.46i) q^{95} +(-5995.26 - 3461.36i) q^{97} +(-7510.55 - 13008.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	11.3222	+	6.53690i	1.25803	+	0.726322i	0.972691	−	0.232105i	$-0.0745614\pi$
$3$	11.3222	+	6.53690i	1.25803	+	0.726322i	0.285336	+	0.958427i	$0.407895\pi$
$4$		0			0
$5$	−19.8361	+	34.3572i	−0.793446	+	1.37429i	0.130375	+	0.991465i	$0.458382\pi$
$5$	−19.8361	+	34.3572i	−0.793446	+	1.37429i	−0.923821	+	0.382824i	$0.874952\pi$
$6$		0			0
$7$	76.8642			1.56866			0.784329	−	0.620345i	$-0.213007\pi$
$7$	76.8642			1.56866			0.784329	+	0.620345i	$0.213007\pi$
$8$		0			0
$9$	44.9621	+	77.8766i	0.555088	+	0.961440i
$10$		0			0
$11$	−167.042			−1.38051			−0.690255	−	0.723566i	$-0.742502\pi$
$11$	−167.042			−1.38051			−0.690255	+	0.723566i	$0.742502\pi$
$12$		0			0
$13$	−266.363	+	153.785i	−1.57611	+	0.909969i	−0.580718	+	0.814105i	$0.697228\pi$
$13$	−266.363	+	153.785i	−1.57611	+	0.909969i	−0.995394	+	0.0958637i	$0.969439\pi$
$14$		0			0
$15$	−449.179	+	259.334i	−1.99635	+	1.15259i
$16$		0			0
$17$	73.9920	−	128.158i	0.256028	−	0.443453i	−0.709146	−	0.705061i	$-0.750920\pi$
$17$	73.9920	−	128.158i	0.256028	−	0.443453i	0.965174	+	0.261608i	$0.0842528\pi$
$18$		0			0
$19$	208.536	+	294.676i	0.577661	+	0.816277i
$19$	208.536	+	294.676i	0.577661	+	0.816277i
$20$		0			0
$21$	870.275	+	502.454i	1.97341	+	1.13935i
$22$		0			0
$23$	−22.2131	−	38.4743i	−0.0419908	−	0.0727302i	0.844266	−	0.535924i	$-0.180037\pi$
$23$	−22.2131	−	38.4743i	−0.0419908	−	0.0727302i	−0.886257	+	0.463194i	$0.846703\pi$
$24$		0			0
$25$	−474.445	−	821.764i	−0.759113	−	1.31482i
$26$		0			0
$27$			116.673i			0.160046i
$28$		0			0
$29$	608.382	−	351.249i	0.723403	−	0.417657i	−0.0926009	−	0.995703i	$-0.529518\pi$
$29$	608.382	−	351.249i	0.723403	−	0.417657i	0.816004	+	0.578046i	$0.196185\pi$
$30$		0			0
$31$			596.777i			0.620996i	0.950574	+	0.310498i	$0.100496\pi$
$31$			596.777i			0.620996i	−0.950574	+	0.310498i	$0.899504\pi$
$32$		0			0
$33$	−1891.29	−	1091.94i	−1.73672	−	1.00270i
$34$		0			0
$35$	−1524.69	+	2640.84i	−1.24465	+	2.15579i
$36$		0			0
$37$		−	300.577i		−	0.219559i	−0.993956	−	0.109780i	$-0.964985\pi$
$37$		−	300.577i		−	0.219559i	0.993956	−	0.109780i	$-0.0350145\pi$
$38$		0			0
$39$	−4021.10			−2.64372
$40$		0			0
$41$	−103.099	−	59.5244i	−0.0613321	−	0.0354101i	0.469020	−	0.883187i	$-0.344607\pi$
$41$	−103.099	−	59.5244i	−0.0613321	−	0.0354101i	−0.530352	+	0.847777i	$0.677940\pi$
$42$		0			0
$43$	−338.309	+	585.968i	−0.182969	+	0.316911i	−0.942890	−	0.333104i	$-0.891904\pi$
$43$	−338.309	+	585.968i	−0.182969	+	0.316911i	0.759922	+	0.650015i	$0.225237\pi$
$44$		0			0
$45$	−3567.50			−1.76173
$46$		0			0
$47$	−942.536	−	1632.52i	−0.426680	−	0.739031i	0.569896	−	0.821717i	$-0.306984\pi$
$47$	−942.536	−	1632.52i	−0.426680	−	0.739031i	−0.996576	+	0.0826856i	$0.973650\pi$
$48$		0			0
$49$	3507.11			1.46069
$50$		0			0
$51$	1675.51	−	967.357i	0.644179	−	0.371917i
$52$		0			0
$53$	−572.321	+	330.430i	−0.203745	+	0.117632i	−0.598401	−	0.801197i	$-0.704197\pi$
$53$	−572.321	+	330.430i	−0.203745	+	0.117632i	0.394656	+	0.918829i	$0.370864\pi$
$54$		0			0
$55$	3313.46	−	5739.09i	1.09536	−	1.89722i
$56$		0			0
$57$	434.823	+	4699.57i	0.133833	+	1.44647i
$58$		0			0
$59$	−3737.52	−	2157.86i	−1.07369	−	0.619896i	−0.144503	−	0.989504i	$-0.546158\pi$
$59$	−3737.52	−	2157.86i	−1.07369	−	0.619896i	−0.929187	+	0.369609i	$0.879492\pi$
$60$		0			0
$61$	3355.06	+	5811.13i	0.901654	+	1.56171i	0.825346	+	0.564627i	$0.190980\pi$
$61$	3355.06	+	5811.13i	0.901654	+	1.56171i	0.0763082	+	0.997084i	$0.475687\pi$
$62$		0			0
$63$	3455.98	+	5985.93i	0.870743	+	1.50817i
$64$		0			0
$65$		−	12202.0i		−	2.88804i
$66$		0			0
$67$	−5778.80	+	3336.39i	−1.28732	+	0.743237i	−0.978176	−	0.207778i	$-0.933377\pi$
$67$	−5778.80	+	3336.39i	−1.28732	+	0.743237i	−0.309147	+	0.951014i	$0.600044\pi$
$68$		0			0
$69$		−	580.820i		−	0.121995i
$70$		0			0
$71$	7207.51	+	4161.26i	1.42978	+	0.825483i	0.997103	−	0.0760672i	$-0.0242363\pi$
$71$	7207.51	+	4161.26i	1.42978	+	0.825483i	0.432675	+	0.901550i	$0.357570\pi$
$72$		0			0
$73$	−3706.83	+	6420.42i	−0.695596	+	1.20481i	0.274383	+	0.961621i	$0.411526\pi$
$73$	−3706.83	+	6420.42i	−0.695596	+	1.20481i	−0.969979	+	0.243188i	$0.921807\pi$
$74$		0			0
$75$		−	12405.6i		−	2.20544i
$76$		0			0
$77$	−12839.5			−2.16555
$78$		0			0
$79$	5664.89	+	3270.62i	0.907689	+	0.524054i	0.879687	−	0.475554i	$-0.157752\pi$
$79$	5664.89	+	3270.62i	0.907689	+	0.524054i	0.0280020	+	0.999608i	$0.491086\pi$
$80$		0			0
$81$	2879.25	−	4987.01i	0.438843	−	0.760098i
$82$		0			0
$83$	1526.28			0.221554			0.110777	−	0.993845i	$-0.464666\pi$
$83$	1526.28			0.221554			0.110777	+	0.993845i	$0.464666\pi$
$84$		0			0
$85$	2935.43	+	5084.32i	0.406288	+	0.703712i
$86$		0			0
$87$	9184.33			1.21341
$88$		0			0
$89$	−1121.63	+	647.575i	−0.141602	+	0.0817541i	−0.569127	−	0.822249i	$-0.692719\pi$
$89$	−1121.63	+	647.575i	−0.141602	+	0.0817541i	0.427525	+	0.904003i	$0.359386\pi$
$90$		0			0
$91$	−20473.8	+	11820.5i	−2.47238	+	1.42743i
$92$		0			0
$93$	−3901.07	+	6756.86i	−0.451043	+	0.781230i
$94$		0			0
$95$	−14260.8	+	1319.46i	−1.58014	+	0.146201i
$96$		0			0
$97$	−5995.26	−	3461.36i	−0.637183	−	0.367878i	0.146346	−	0.989234i	$-0.453249\pi$
$97$	−5995.26	−	3461.36i	−0.637183	−	0.367878i	−0.783529	+	0.621356i	$0.786582\pi$
$98$		0			0
$99$	−7510.55	−	13008.7i	−0.766304	−	1.32728i
$100$		0			0
$101$	3845.97	+	6661.41i	0.377019	+	0.653016i	0.990627	−	0.136595i	$-0.0436159\pi$
$101$	3845.97	+	6661.41i	0.377019	+	0.653016i	−0.613608	+	0.789611i	$0.710283\pi$
$102$		0			0
$103$			11390.0i			1.07362i	0.843704	+	0.536809i	$0.180371\pi$
$103$			11390.0i			1.07362i	−0.843704	+	0.536809i	$0.819629\pi$
$104$		0			0
$105$	−34525.8	+	19933.5i	−3.13159	+	1.80803i
$106$		0			0
$107$		−	13180.8i		−	1.15126i	−0.817711	−	0.575629i	$-0.804757\pi$
$107$		−	13180.8i		−	1.15126i	0.817711	−	0.575629i	$-0.195243\pi$
$108$		0			0
$109$	11491.1	+	6634.39i	0.967183	+	0.558403i	0.898376	−	0.439227i	$-0.144748\pi$
$109$	11491.1	+	6634.39i	0.967183	+	0.558403i	0.0688066	+	0.997630i	$0.478081\pi$
$110$		0			0
$111$	1964.84	−	3403.20i	0.159471	−	0.276212i
$112$		0			0
$113$		−	20067.4i		−	1.57157i	−0.618498	−	0.785786i	$-0.712259\pi$
$113$		−	20067.4i		−	1.57157i	0.618498	−	0.785786i	$-0.287741\pi$
$114$		0			0
$115$	1762.49			0.133270
$116$		0			0
$117$	−23952.5	−	13829.0i	−1.74976	−	1.01022i
$118$		0			0
$119$	5687.34	−	9850.76i	0.401620	−	0.695626i
$120$		0			0
$121$	13261.9			0.905809
$122$		0			0
$123$	−778.209	−	1347.90i	−0.0514383	−	0.0890937i
$124$		0			0
$125$	12849.5			0.822368
$126$		0			0
$127$	−479.213	+	276.673i	−0.0297112	+	0.0171538i	−0.514782	−	0.857321i	$-0.672127\pi$
$127$	−479.213	+	276.673i	−0.0297112	+	0.0171538i	0.485071	+	0.874475i	$0.338794\pi$
$128$		0			0
$129$	−7660.83	+	4422.98i	−0.460359	+	0.265788i
$130$		0			0
$131$	−8858.51	+	15343.4i	−0.516200	+	0.894085i	0.483623	+	0.875276i	$0.339321\pi$
$131$	−8858.51	+	15343.4i	−0.516200	+	0.894085i	−0.999823	+	0.0188083i	$0.994013\pi$
$132$		0			0
$133$	16028.9	+	22650.0i	0.906152	+	1.28046i
$134$		0			0
$135$	−4008.57	−	2314.35i	−0.219949	−	0.126987i
$136$		0			0
$137$	13116.6	+	22718.7i	0.698846	+	1.21044i	0.968867	+	0.247583i	$0.0796362\pi$
$137$	13116.6	+	22718.7i	0.698846	+	1.21044i	−0.270021	+	0.962855i	$0.587030\pi$
$138$		0			0
$139$	8783.14	+	15212.8i	0.454590	+	0.787373i	0.998665	−	0.0516637i	$-0.0164524\pi$
$139$	8783.14	+	15212.8i	0.454590	+	0.787373i	−0.544074	+	0.839037i	$0.683119\pi$
$140$		0			0
$141$		−	24645.1i		−	1.23963i
$142$		0			0
$143$	44493.7	−	25688.5i	2.17584	−	1.25622i
$144$		0			0
$145$			27869.7i			1.32555i
$146$		0			0
$147$	39708.4	+	22925.6i	1.83758	+	1.06093i
$148$		0			0
$149$	11353.4	−	19664.6i	0.511390	−	0.885753i	−0.488523	−	0.872551i	$-0.662464\pi$
$149$	11353.4	−	19664.6i	0.511390	−	0.885753i	0.999913	−	0.0132022i	$-0.00420251\pi$
$150$		0			0
$151$			21631.4i			0.948703i	0.880336	+	0.474351i	$0.157317\pi$
$151$			21631.4i			0.948703i	−0.880336	+	0.474351i	$0.842683\pi$
$152$		0			0
$153$	13307.3			0.568471
$154$		0			0
$155$	−20503.6	−	11837.8i	−0.853428	−	0.492727i
$156$		0			0
$157$	18003.1	−	31182.3i	0.730379	−	1.26505i	−0.226343	−	0.974048i	$-0.572677\pi$
$157$	18003.1	−	31182.3i	0.730379	−	1.26505i	0.956721	−	0.291005i	$-0.0939897\pi$
$158$		0			0
$159$	−8639.94			−0.341756
$160$		0			0
$161$	−1707.40	−	2957.30i	−0.0658692	−	0.114089i
$162$		0			0
$163$	11908.8			0.448221			0.224111	−	0.974564i	$-0.428052\pi$
$163$	11908.8			0.448221			0.224111	+	0.974564i	$0.428052\pi$
$164$		0			0
$165$	75031.7	−	43319.6i	2.75599	−	1.59117i
$166$		0			0
$167$	−22590.0	+	13042.3i	−0.809997	+	0.467652i	−0.846955	−	0.531665i	$-0.821567\pi$
$167$	−22590.0	+	13042.3i	−0.809997	+	0.467652i	0.0369580	+	0.999317i	$0.488233\pi$
$168$		0			0
$169$	33019.0	−	57190.5i	1.15609	−	2.00240i
$170$		0			0
$171$	−13572.2	+	29489.3i	−0.464149	+	1.00849i
$172$		0			0
$173$	18044.3	+	10417.9i	0.602902	+	0.348086i	0.770182	−	0.637824i	$-0.220165\pi$
$173$	18044.3	+	10417.9i	0.602902	+	0.348086i	−0.167280	+	0.985909i	$0.553498\pi$
$174$		0			0
$175$	−36467.9	−	63164.2i	−1.19079	−	2.06251i
$176$		0			0
$177$	−28211.4	−	48863.5i	−0.900488	−	1.55969i
$178$		0			0
$179$		−	7060.12i		−	0.220346i	−0.993912	−	0.110173i	$-0.964859\pi$
$179$		−	7060.12i		−	0.220346i	0.993912	−	0.110173i	$-0.0351406\pi$
$180$		0			0
$181$	−3417.09	+	1972.86i	−0.104304	+	0.0602197i	−0.551244	−	0.834344i	$-0.685847\pi$
$181$	−3417.09	+	1972.86i	−0.104304	+	0.0602197i	0.446941	+	0.894564i	$0.352513\pi$
$182$		0			0
$183$			87726.7i			2.61957i
$184$		0			0
$185$	10327.0	+	5962.29i	0.301738	+	0.174209i
$186$		0			0
$187$	−12359.8	+	21407.7i	−0.353449	+	0.612191i
$188$		0			0
$189$			8968.00i			0.251057i
$190$		0			0
$191$	39437.1			1.08103			0.540515	−	0.841334i	$-0.318229\pi$
$191$	39437.1			1.08103			0.540515	+	0.841334i	$0.318229\pi$
$192$		0			0
$193$	10136.4	+	5852.26i	0.272126	+	0.157112i	0.629853	−	0.776714i	$-0.283115\pi$
$193$	10136.4	+	5852.26i	0.272126	+	0.157112i	−0.357728	+	0.933826i	$0.616448\pi$
$194$		0			0
$195$	79763.1	−	138154.i	2.09765	−	3.63324i
$196$		0			0
$197$	−12530.3			−0.322871			−0.161436	−	0.986883i	$-0.551612\pi$
$197$	−12530.3			−0.322871			−0.161436	+	0.986883i	$0.551612\pi$
$198$		0			0
$199$	−16606.8	−	28763.8i	−0.419353	−	0.726341i	0.576521	−	0.817082i	$-0.304410\pi$
$199$	−16606.8	−	28763.8i	−0.419353	−	0.726341i	−0.995875	+	0.0907411i	$0.971076\pi$
$200$		0			0
$201$	−87238.6			−2.15932
$202$		0			0
$203$	46762.8	−	26998.5i	1.13477	−	0.655161i
$204$		0			0
$205$	4090.18	−	2361.47i	0.0973273	−	0.0561920i
$206$		0			0
$207$	1997.50	−	3459.77i	0.0466172	−	0.0807433i
$208$		0			0
$209$	−34834.1	−	49223.2i	−0.797467	−	1.12688i
$210$		0			0
$211$	15910.7	+	9186.05i	0.357375	+	0.206331i	0.667929	−	0.744225i	$-0.267181\pi$
$211$	15910.7	+	9186.05i	0.357375	+	0.206331i	−0.310554	+	0.950556i	$0.600514\pi$
$212$		0			0
$213$	54403.5	+	94229.5i	1.19913	+	2.07696i
$214$		0			0
$215$	−13421.5	−	23246.7i	−0.290351	−	0.502903i
$216$		0			0
$217$			45870.8i			0.974130i
$218$		0			0
$219$	−83939.3	+	48462.4i	−1.75016	+	1.01045i
$220$		0			0
$221$			45515.4i			0.931909i
$222$		0			0
$223$	49826.1	+	28767.1i	1.00195	+	0.578477i	0.908825	−	0.417177i	$-0.136980\pi$
$223$	49826.1	+	28767.1i	1.00195	+	0.578477i	0.0931269	+	0.995654i	$0.470314\pi$
$224$		0			0
$225$	42664.1	−	73896.4i	0.842748	−	1.45968i
$226$		0			0
$227$			76720.4i			1.48888i	0.667691	+	0.744439i	$0.267283\pi$
$227$			76720.4i			1.48888i	−0.667691	+	0.744439i	$0.732717\pi$
$228$		0			0
$229$	−89074.7			−1.69857			−0.849285	−	0.527935i	$-0.822967\pi$
$229$	−89074.7			−1.69857			−0.849285	+	0.527935i	$0.822967\pi$
$230$		0			0
$231$	−145372.	−	83930.8i	−2.72432	−	1.57289i
$232$		0			0
$233$	2913.67	−	5046.62i	0.0536695	−	0.0929584i	−0.837942	−	0.545759i	$-0.816242\pi$
$233$	2913.67	−	5046.62i	0.0536695	−	0.0929584i	0.891612	+	0.452800i	$0.149575\pi$
$234$		0			0
$235$	74785.1			1.35419
$236$		0			0
$237$	42759.5	+	74061.6i	0.761265	+	1.31855i
$238$		0			0
$239$	71436.9			1.25062			0.625312	−	0.780375i	$-0.284972\pi$
$239$	71436.9			1.25062			0.625312	+	0.780375i	$0.284972\pi$
$240$		0			0
$241$	46155.9	−	26648.1i	0.794681	−	0.458809i	−0.0469267	−	0.998898i	$-0.514943\pi$
$241$	46155.9	−	26648.1i	0.794681	−	0.458809i	0.841608	+	0.540089i	$0.181609\pi$
$242$		0			0
$243$	73383.5	−	42368.0i	1.24276	−	0.717506i
$244$		0			0
$245$	−69567.6	+	120495.i	−1.15898	+	2.00741i
$246$		0			0
$247$	−100863.	−	46421.2i	−1.65324	−	0.760891i
$248$		0			0
$249$	17280.9	+	9977.16i	0.278720	+	0.160919i
$250$		0			0
$251$	32642.1	+	56537.8i	0.518121	+	0.897411i	0.999778	+	0.0210519i	$0.00670153\pi$
$251$	32642.1	+	56537.8i	0.518121	+	0.897411i	−0.481658	+	0.876359i	$0.659965\pi$
$252$		0			0
$253$	3710.52	+	6426.81i	0.0579688	+	0.100405i
$254$		0			0
$255$			76754.5i			1.18038i
$256$		0			0
$257$	41916.7	−	24200.6i	0.634631	−	0.366404i	−0.147912	−	0.989000i	$-0.547255\pi$
$257$	41916.7	−	24200.6i	0.634631	−	0.366404i	0.782543	+	0.622596i	$0.213922\pi$
$258$		0			0
$259$		−	23103.6i		−	0.344414i
$260$		0			0
$261$	54708.3	+	31585.8i	0.803104	+	0.463672i
$262$		0			0
$263$	23638.5	−	40943.1i	0.341750	−	0.591928i	−0.643008	−	0.765860i	$-0.722314\pi$
$263$	23638.5	−	40943.1i	0.341750	−	0.591928i	0.984758	+	0.173931i	$0.0556470\pi$
$264$		0			0
$265$		−	26217.8i		−	0.373340i
$266$		0			0
$267$	−16932.5			−0.237519
$268$		0			0
$269$	38299.5	+	22112.2i	0.529284	+	0.305582i	0.740725	−	0.671809i	$-0.234482\pi$
$269$	38299.5	+	22112.2i	0.529284	+	0.305582i	−0.211441	+	0.977391i	$0.567816\pi$
$270$		0			0
$271$	−8766.05	+	15183.2i	−0.119362	+	0.206741i	−0.919515	−	0.393055i	$-0.871418\pi$
$271$	−8766.05	+	15183.2i	−0.119362	+	0.206741i	0.800153	+	0.599796i	$0.204752\pi$
$272$		0			0
$273$	−309079.			−4.14710
$274$		0			0
$275$	79252.2	+	137269.i	1.04796	+	1.81513i
$276$		0			0
$277$	100392.			1.30840			0.654199	−	0.756322i	$-0.273006\pi$
$277$	100392.			1.30840			0.654199	+	0.756322i	$0.273006\pi$
$278$		0			0
$279$	−46475.0	+	26832.4i	−0.597050	+	0.344707i
$280$		0			0
$281$	20999.9	−	12124.3i	0.265953	−	0.153548i	−0.361094	−	0.932529i	$-0.617597\pi$
$281$	20999.9	−	12124.3i	0.265953	−	0.153548i	0.627047	+	0.778981i	$0.284263\pi$
$282$		0			0
$283$	−2816.84	+	4878.91i	−0.0351714	+	0.0609186i	−0.883075	−	0.469231i	$-0.844531\pi$
$283$	−2816.84	+	4878.91i	−0.0351714	+	0.0609186i	0.847904	+	0.530150i	$0.177864\pi$
$284$		0			0
$285$	−170089.	−	78282.0i	−2.09405	−	0.963768i
$286$		0			0
$287$	−7924.64	−	4575.29i	−0.0962090	−	0.0555463i
$288$		0			0
$289$	30810.9	+	53366.0i	0.368900	+	0.638953i
$290$		0			0
$291$	−45253.2	−	78380.8i	−0.534396	−	0.925600i
$292$		0			0
$293$		−	36761.9i		−	0.428216i	−0.976810	−	0.214108i	$-0.931316\pi$
$293$		−	36761.9i		−	0.428216i	0.976810	−	0.214108i	$-0.0686845\pi$
$294$		0			0
$295$	148276.	−	85607.1i	1.70383	−	0.983707i
$296$		0			0
$297$		−	19489.3i		−	0.220945i
$298$		0			0
$299$	11833.5	+	6832.08i	0.132364	+	0.0764207i
$300$		0			0
$301$	−26003.9	+	45040.0i	−0.287015	+	0.497125i
$302$		0			0
$303$			100563.i			1.09535i
$304$		0			0
$305$	−266206.			−2.86166
$306$		0			0
$307$	−93429.1	−	53941.3i	−0.991301	−	0.572328i	−0.0856380	−	0.996326i	$-0.527293\pi$
$307$	−93429.1	−	53941.3i	−0.991301	−	0.572328i	−0.905663	+	0.423999i	$0.860626\pi$
$308$		0			0
$309$	−74455.4	+	128961.i	−0.779793	+	1.35064i
$310$		0			0
$311$	−135845.			−1.40451			−0.702253	−	0.711927i	$-0.747822\pi$
$311$	−135845.			−1.40451			−0.702253	+	0.711927i	$0.747822\pi$
$312$		0			0
$313$	−935.538	−	1620.40i	−0.00954932	−	0.0165399i	0.861211	−	0.508247i	$-0.169706\pi$
$313$	−935.538	−	1620.40i	−0.00954932	−	0.0165399i	−0.870761	+	0.491707i	$0.836373\pi$
$314$		0			0
$315$	−274213.			−2.76355
$316$		0			0
$317$	72072.5	−	41611.0i	0.717217	−	0.414086i	−0.0965103	−	0.995332i	$-0.530768\pi$
$317$	72072.5	−	41611.0i	0.717217	−	0.414086i	0.813728	+	0.581246i	$0.197435\pi$
$318$		0			0
$319$	−101625.	+	58673.3i	−0.998665	+	0.576580i
$320$		0			0
$321$	86161.2	−	149236.i	0.836184	−	1.44831i
$322$		0			0
$323$	53195.0	−	4921.81i	0.509878	−	0.0471759i
$324$		0			0
$325$	252749.	+	145925.i	2.39289	+	1.38154i
$326$		0			0
$327$	86736.7	+	150232.i	0.811161	+	1.40497i
$328$		0			0
$329$	−72447.3	−	125482.i	−0.669315	−	1.15929i
$330$		0			0
$331$		−	68475.7i		−	0.625001i	−0.949918	−	0.312500i	$-0.898833\pi$
$331$		−	68475.7i		−	0.625001i	0.949918	−	0.312500i	$-0.101167\pi$
$332$		0			0
$333$	23407.9	−	13514.6i	0.211093	−	0.121875i
$334$		0			0
$335$		−	264724.i		−	2.35887i
$336$		0			0
$337$	157692.	+	91043.5i	1.38851	+	0.801658i	0.993148	−	0.116866i	$-0.0372849\pi$
$337$	157692.	+	91043.5i	1.38851	+	0.801658i	0.395365	+	0.918524i	$0.370618\pi$
$338$		0			0
$339$	131179.	−	227208.i	1.14147	−	1.97708i
$340$		0			0
$341$		−	99686.7i		−	0.857291i
$342$		0			0
$343$	85020.4			0.722662
$344$		0			0
$345$	19955.4	+	11521.2i	0.167657	+	0.0967968i
$346$		0			0
$347$	40266.3	−	69743.4i	0.334413	−	0.579220i	−0.648959	−	0.760824i	$-0.724795\pi$
$347$	40266.3	−	69743.4i	0.334413	−	0.579220i	0.983372	+	0.181603i	$0.0581286\pi$
$348$		0			0
$349$	−10451.9			−0.0858116			−0.0429058	−	0.999079i	$-0.513662\pi$
$349$	−10451.9			−0.0858116			−0.0429058	+	0.999079i	$0.513662\pi$
$350$		0			0
$351$	−17942.6	−	31077.4i	−0.145636	−	0.252250i
$352$		0			0
$353$	−101594.			−0.815302			−0.407651	−	0.913138i	$-0.633652\pi$
$353$	−101594.			−0.815302			−0.407651	+	0.913138i	$0.633652\pi$
$354$		0			0
$355$	−285938.	+	165087.i	−2.26890	+	1.30995i
$356$		0			0
$357$	128787.	−	74355.1i	1.01050	−	0.583411i
$358$		0			0
$359$	−98823.4	+	171167.i	−0.766780	+	1.32810i	0.172520	+	0.985006i	$0.444809\pi$
$359$	−98823.4	+	171167.i	−0.766780	+	1.32810i	−0.939300	+	0.343097i	$0.888524\pi$
$360$		0			0
$361$	−43346.9	+	122901.i	−0.332616	+	0.943062i
$362$		0			0
$363$	150155.	+	86692.0i	1.13953	+	0.657909i
$364$		0			0
$365$	−147059.	−	254713.i	−1.10384	−	1.91190i
$366$		0			0
$367$	−11874.6	−	20567.5i	−0.0881634	−	0.152703i	0.818571	−	0.574405i	$-0.194766\pi$
$367$	−11874.6	−	20567.5i	−0.0881634	−	0.152703i	−0.906735	+	0.421701i	$0.861433\pi$
$368$		0			0
$369$		−	10705.4i		−	0.0786228i
$370$		0			0
$371$	−43991.0	+	25398.2i	−0.319607	+	0.184525i
$372$		0			0
$373$		−	93642.3i		−	0.673061i	−0.941673	−	0.336531i	$-0.890746\pi$
$373$		−	93642.3i		−	0.673061i	0.941673	−	0.336531i	$-0.109254\pi$
$374$		0			0
$375$	145485.	+	83995.9i	1.03456	+	0.597304i
$376$		0			0
$377$	−108034.	+	187120.i	−0.760109	+	1.31655i
$378$		0			0
$379$		−	188058.i		−	1.30922i	−0.755965	−	0.654612i	$-0.772832\pi$
$379$		−	188058.i		−	1.30922i	0.755965	−	0.654612i	$-0.227168\pi$
$380$		0			0
$381$	−7234.35			−0.0498367
$382$		0			0
$383$	51550.6	+	29762.7i	0.351428	+	0.202897i	0.665314	−	0.746564i	$-0.268298\pi$
$383$	51550.6	+	29762.7i	0.351428	+	0.202897i	−0.313886	+	0.949461i	$0.601631\pi$
$384$		0			0
$385$	254687.	−	441131.i	1.71825	−	2.97609i
$386$		0			0
$387$	−60844.3			−0.406254
$388$		0			0
$389$	128489.	+	222550.i	0.849117	+	1.47071i	0.881997	+	0.471254i	$0.156199\pi$
$389$	128489.	+	222550.i	0.849117	+	1.47071i	−0.0328806	+	0.999459i	$0.510468\pi$
$390$		0			0
$391$	−6574.38			−0.0430032
$392$		0			0
$393$	−200596.	+	115814.i	−1.29879	+	0.749855i
$394$		0			0
$395$	−224739.	+	129753.i	−1.44040	+	0.831618i
$396$		0			0
$397$	−17505.0	+	30319.5i	−0.111066	+	0.192371i	−0.916200	−	0.400721i	$-0.868760\pi$
$397$	−17505.0	+	30319.5i	−0.111066	+	0.192371i	0.805134	+	0.593092i	$0.202093\pi$
$398$		0			0
$399$	33422.3	+	361229.i	0.209938	+	2.26901i
$400$		0			0
$401$	−94637.8	−	54639.2i	−0.588540	−	0.339794i	0.175980	−	0.984394i	$-0.443691\pi$
$401$	−94637.8	−	54639.2i	−0.588540	−	0.339794i	−0.764520	+	0.644600i	$0.777024\pi$
$402$		0			0
$403$	−91775.2	−	158959.i	−0.565087	−	0.978759i
$404$		0			0
$405$	114226.	+	197846.i	0.696396	+	1.20619i
$406$		0			0
$407$			50208.9i			0.303104i
$408$		0			0
$409$	211674.	−	122210.i	1.26538	−	0.730568i	0.291271	−	0.956641i	$-0.405922\pi$
$409$	211674.	−	122210.i	1.26538	−	0.730568i	0.974111	+	0.226072i	$0.0725885\pi$
$410$		0			0
$411$			342969.i			2.03035i
$412$		0			0
$413$	−287281.	−	165862.i	−1.68425	−	0.972404i
$414$		0			0
$415$	−30275.6	+	52438.8i	−0.175791	+	0.304479i
$416$		0			0
$417$			229658.i			1.32072i
$418$		0			0
$419$	−16629.2			−0.0947206			−0.0473603	−	0.998878i	$-0.515081\pi$
$419$	−16629.2			−0.0947206			−0.0473603	+	0.998878i	$0.515081\pi$
$420$		0			0
$421$	−232397.	−	134174.i	−1.31119	−	0.757016i	−0.328897	−	0.944366i	$-0.606677\pi$
$421$	−232397.	−	134174.i	−1.31119	−	0.757016i	−0.982293	+	0.187350i	$0.940010\pi$
$422$		0			0
$423$	84756.8	−	146803.i	0.473690	−	0.820454i
$424$		0			0
$425$	−140421.			−0.777416
$426$		0			0
$427$	257884.	+	446668.i	1.41439	+	2.44979i
$428$		0			0
$429$	671692.			3.64969
$430$		0			0
$431$	−232704.	+	134351.i	−1.25270	+	0.723249i	−0.971646	−	0.236441i	$-0.924019\pi$
$431$	−232704.	+	134351.i	−1.25270	+	0.723249i	−0.281059	+	0.959691i	$0.590686\pi$
$432$		0			0
$433$	−225551.	+	130222.i	−1.20301	+	0.694559i	−0.961224	−	0.275770i	$-0.911067\pi$
$433$	−225551.	+	130222.i	−1.20301	+	0.694559i	−0.241788	+	0.970329i	$0.577734\pi$
$434$		0			0
$435$	−182182.	+	315548.i	−0.962778	+	1.66758i
$436$		0			0
$437$	6705.22	−	14568.9i	0.0351116	−	0.0762895i
$438$		0			0
$439$	−157621.	−	91002.3i	−0.817869	−	0.472197i	0.0318121	−	0.999494i	$-0.489872\pi$
$439$	−157621.	−	91002.3i	−0.817869	−	0.472197i	−0.849681	+	0.527297i	$0.823206\pi$
$440$		0			0
$441$	157687.	+	273122.i	0.810810	+	1.40436i
$442$		0			0
$443$	−75748.2	−	131200.i	−0.385980	−	0.668537i	0.605925	−	0.795522i	$-0.292803\pi$
$443$	−75748.2	−	131200.i	−0.385980	−	0.668537i	−0.991905	+	0.126985i	$0.959470\pi$
$444$		0			0
$445$		−	51381.5i		−	0.259470i
$446$		0			0
$447$	257091.	−	148432.i	1.28668	−	0.742868i
$448$		0			0
$449$			8732.30i			0.0433147i	0.999765	+	0.0216574i	$0.00689430\pi$
$449$			8732.30i			0.0433147i	−0.999765	+	0.0216574i	$0.993106\pi$
$450$		0			0
$451$	17221.9	+	9943.05i	0.0846695	+	0.0488840i
$452$		0			0
$453$	−141402.	+	244916.i	−0.689064	+	1.19349i
$454$		0			0
$455$		−	937896.i		−	4.53035i
$456$		0			0
$457$	115906.			0.554977			0.277488	−	0.960729i	$-0.410498\pi$
$457$	115906.			0.554977			0.277488	+	0.960729i	$0.410498\pi$
$458$		0			0
$459$	14952.6	+	8632.88i	0.0709727	+	0.0409761i
$460$		0			0
$461$	−22093.0	+	38266.1i	−0.103957	+	0.180058i	−0.913311	−	0.407262i	$-0.866484\pi$
$461$	−22093.0	+	38266.1i	−0.103957	+	0.180058i	0.809355	+	0.587320i	$0.199817\pi$
$462$		0			0
$463$	−216008.			−1.00764			−0.503822	−	0.863808i	$-0.668073\pi$
$463$	−216008.			−1.00764			−0.503822	+	0.863808i	$0.668073\pi$
$464$		0			0
$465$	−154765.	−	268060.i	−0.715757	−	1.23973i
$466$		0			0
$467$	71782.8			0.329145			0.164572	−	0.986365i	$-0.447376\pi$
$467$	71782.8			0.329145			0.164572	+	0.986365i	$0.447376\pi$
$468$		0			0
$469$	−444183.	+	256449.i	−2.01937	+	1.16588i
$470$		0			0
$471$	407671.	−	235369.i	1.83767	−	1.06098i
$472$		0			0
$473$	56511.7	−	97881.2i	0.252590	−	0.437499i
$474$		0			0
$475$	143215.	−	311175.i	0.634749	−	1.37917i
$476$		0			0
$477$	−51465.5	−	29713.6i	−0.226193	−	0.130593i
$478$		0			0
$479$	−80897.0	−	140118.i	−0.352583	−	0.610691i	0.634118	−	0.773236i	$-0.281363\pi$
$479$	−80897.0	−	140118.i	−0.352583	−	0.610691i	−0.986701	+	0.162545i	$0.948030\pi$
$480$		0			0
$481$	46224.1	+	80062.6i	0.199792	+	0.346050i
$482$		0			0
$483$		−	44644.3i		−	0.191369i
$484$		0			0
$485$	237846.	−	137320.i	1.01114	−	0.583782i
$486$		0			0
$487$			281881.i			1.18852i	0.804271	+	0.594262i	$0.202556\pi$
$487$			281881.i			1.18852i	−0.804271	+	0.594262i	$0.797444\pi$
$488$		0			0
$489$	134834.	+	77846.6i	0.563874	+	0.325553i
$490$		0			0
$491$	51473.9	−	89155.4i	0.213513	−	0.369815i	−0.739299	−	0.673378i	$-0.764843\pi$
$491$	51473.9	−	89155.4i	0.213513	−	0.369815i	0.952812	+	0.303563i	$0.0981761\pi$
$492$		0			0
$493$		−	103959.i		−	0.427727i
$494$		0			0
$495$	595921.			2.43208
$496$		0			0
$497$	554000.	+	319852.i	2.24283	+	1.29490i
$498$		0			0
$499$	153525.	−	265914.i	0.616565	−	1.06792i	−0.373542	−	0.927613i	$-0.621857\pi$
$499$	153525.	−	265914.i	0.616565	−	1.06792i	0.990108	−	0.140310i	$-0.0448098\pi$
$500$		0			0
$501$	−341026.			−1.35866
$502$		0			0
$503$	−31471.2	−	54509.6i	−0.124388	−	0.215445i	0.797106	−	0.603840i	$-0.206363\pi$
$503$	−31471.2	−	54509.6i	−0.124388	−	0.215445i	−0.921493	+	0.388394i	$0.873030\pi$
$504$		0			0
$505$	−305157.			−1.19658
$506$		0			0
$507$	747698.	−	431683.i	2.90877	−	1.67938i
$508$		0			0
$509$	201053.	−	116078.i	0.776025	−	0.448038i	−0.0589946	−	0.998258i	$-0.518789\pi$
$509$	201053.	−	116078.i	0.776025	−	0.448038i	0.835020	+	0.550220i	$0.185456\pi$
$510$		0			0
$511$	−284923.	+	493501.i	−1.09115	+	1.88993i
$512$		0			0
$513$	−34380.8	+	24330.5i	−0.130641	+	0.0924520i
$514$		0			0
$515$	−391329.	−	225934.i	−1.47546	−	0.851858i
$516$		0			0
$517$	157443.	+	272699.i	0.589036	+	1.02024i
$518$		0			0
$519$	136201.	+	235907.i	0.505645	+	0.875802i
$520$		0			0
$521$		−	131421.i		−	0.484160i	−0.970256	−	0.242080i	$-0.922170\pi$
$521$		−	131421.i		−	0.484160i	0.970256	−	0.242080i	$-0.0778296\pi$
$522$		0			0
$523$	62017.6	−	35805.9i	0.226732	−	0.130904i	−0.382332	−	0.924025i	$-0.624879\pi$
$523$	62017.6	−	35805.9i	0.226732	−	0.130904i	0.609063	+	0.793122i	$0.291546\pi$
$524$		0			0
$525$		−	953548.i		−	3.45958i
$526$		0			0
$527$	76481.7	+	44156.7i	0.275383	+	0.158992i
$528$		0			0
$529$	138934.	−	240640.i	0.496474	−	0.859917i
$530$		0			0
$531$		−	388087.i		−	1.37639i
$532$		0			0
$533$	36615.7			0.128888
$534$		0			0
$535$	452854.	+	261455.i	1.58216	+	0.913461i
$536$		0			0
$537$	46151.3	−	79936.4i	0.160043	−	0.277202i
$538$		0			0
$539$	−585834.			−2.01649
$540$		0			0
$541$	−52685.5	−	91253.9i	−0.180010	−	0.311786i	0.761874	−	0.647726i	$-0.224280\pi$
$541$	−52685.5	−	91253.9i	−0.180010	−	0.311786i	−0.941884	+	0.335939i	$0.890946\pi$
$542$		0			0
$543$	−51585.5			−0.174956
$544$		0			0
$545$	−455878.	+	263201.i	−1.53481	+	0.886126i
$546$		0			0
$547$	−19037.0	+	10991.0i	−0.0636243	+	0.0367335i	−0.531475	−	0.847074i	$-0.678362\pi$
$547$	−19037.0	+	10991.0i	−0.0636243	+	0.0367335i	0.467850	+	0.883808i	$0.345029\pi$
$548$		0			0
$549$	−301701.	+	522561.i	−1.00099	+	1.73377i
$550$		0			0
$551$	230374.	+	106028.i	0.758805	+	0.349233i
$552$		0			0
$553$	435427.	+	251394.i	1.42385	+	0.822062i
$554$		0			0
$555$	77949.7	+	135013.i	0.253063	+	0.438318i
$556$		0			0
$557$	−271586.	−	470401.i	−0.875381	−	1.51620i	−0.856356	−	0.516386i	$-0.827277\pi$
$557$	−271586.	−	470401.i	−0.875381	−	1.51620i	−0.0190251	−	0.999819i	$-0.506056\pi$
$558$		0			0
$559$		−	208107.i		−	0.665983i
$560$		0			0
$561$	−279880.	+	161589.i	−0.889296	+	0.513435i
$562$		0			0
$563$			295758.i			0.933082i	0.884500	+	0.466541i	$0.154500\pi$
$563$			295758.i			0.933082i	−0.884500	+	0.466541i	$0.845500\pi$
$564$		0			0
$565$	689460.	+	398060.i	2.15979	+	1.24696i
$566$		0			0
$567$	221311.	−	383322.i	0.688395	−	1.19233i
$568$		0			0
$569$		−	81423.0i		−	0.251491i	−0.992063	−	0.125746i	$-0.959868\pi$
$569$		−	81423.0i		−	0.251491i	0.992063	−	0.125746i	$-0.0401323\pi$
$570$		0			0
$571$	−266632.			−0.817786			−0.408893	−	0.912582i	$-0.634085\pi$
$571$	−266632.			−0.817786			−0.408893	+	0.912582i	$0.634085\pi$
$572$		0			0
$573$	446516.	+	257796.i	1.35996	+	0.785176i
$574$		0			0
$575$	−21077.9	+	36507.9i	−0.0637515	+	0.110421i
$576$		0			0
$577$	134802.			0.404898			0.202449	−	0.979293i	$-0.435110\pi$
$577$	134802.			0.404898			0.202449	+	0.979293i	$0.435110\pi$
$578$		0			0
$579$	76511.3	+	132521.i	0.228228	+	0.395302i
$580$		0			0
$581$	117317.			0.347542
$582$		0			0
$583$	95601.5	−	55195.5i	0.281273	−	0.162393i
$584$		0			0
$585$	950250.	−	548627.i	2.77668	−	1.60312i
$586$		0			0
$587$	−22995.4	+	39829.3i	−0.0667368	+	0.115592i	−0.897463	−	0.441090i	$-0.854592\pi$
$587$	−22995.4	+	39829.3i	−0.0667368	+	0.115592i	0.830726	+	0.556681i	$0.187925\pi$
$588$		0			0
$589$	−175856.	+	124449.i	−0.506905	+	0.358725i
$590$		0			0
$591$	−141871.	−	81909.4i	−0.406181	−	0.234509i
$592$		0			0
$593$	−256767.	−	444733.i	−0.730179	−	1.26471i	−0.956806	−	0.290726i	$-0.906103\pi$
$593$	−256767.	−	444733.i	−0.730179	−	1.26471i	0.226627	−	0.973982i	$-0.427230\pi$
$594$		0			0
$595$	225630.	+	390802.i	0.637327	+	1.10388i
$596$		0			0
$597$		−	434228.i		−	1.21834i
$598$		0			0
$599$	−153194.	+	88446.7i	−0.426961	+	0.246506i	−0.698051	−	0.716048i	$-0.745949\pi$
$599$	−153194.	+	88446.7i	−0.426961	+	0.246506i	0.271090	+	0.962554i	$0.412616\pi$
$600$		0			0
$601$			2395.77i			0.00663278i	0.999995	+	0.00331639i	$0.00105564\pi$
$601$			2395.77i			0.00663278i	−0.999995	+	0.00331639i	$0.998944\pi$
$602$		0			0
$603$	−519654.	−	300022.i	−1.42915	−	0.825123i
$604$		0			0
$605$	−263066.	+	455643.i	−0.718710	+	1.24484i
$606$		0			0
$607$			675344.i			1.83294i	0.400105	+	0.916469i	$0.368974\pi$
$607$			675344.i			1.83294i	−0.400105	+	0.916469i	$0.631026\pi$
$608$		0			0
$609$	705947.			1.90343
$610$		0			0
$611$	502113.	+	289895.i	1.34499	+	0.776531i
$612$		0			0
$613$	133828.	−	231797.i	0.356145	−	0.616861i	−0.631169	−	0.775646i	$-0.717424\pi$
$613$	133828.	−	231797.i	0.356145	−	0.616861i	0.987313	+	0.158785i	$0.0507577\pi$
$614$		0			0
$615$	61746.7			0.163254
$616$		0			0
$617$	−193849.	−	335757.i	−0.509207	−	0.881972i	−0.999943	−	0.0106640i	$-0.996605\pi$
$617$	−193849.	−	335757.i	−0.509207	−	0.881972i	0.490736	−	0.871308i	$-0.336728\pi$
$618$		0			0
$619$	486832.			1.27057			0.635284	−	0.772278i	$-0.280883\pi$
$619$	486832.			1.27057			0.635284	+	0.772278i	$0.280883\pi$
$620$		0			0
$621$	4488.92	−	2591.68i	0.0116402	−	0.00672044i
$622$		0			0
$623$	−86213.4	+	49775.3i	−0.222126	+	0.128244i
$624$		0			0
$625$	41643.9	−	72129.4i	0.106608	−	0.184651i
$626$		0			0
$627$	−72633.5	−	785024.i	−0.184758	−	1.99686i
$628$		0			0
$629$	−38521.3	−	22240.3i	−0.0973643	−	0.0562133i
$630$		0			0
$631$	−144078.	−	249551.i	−0.361859	−	0.626758i	0.626408	−	0.779495i	$-0.284524\pi$
$631$	−144078.	−	249551.i	−0.361859	−	0.626758i	−0.988267	+	0.152737i	$0.951191\pi$
$632$		0			0
$633$	120097.	+	208013.i	0.299725	+	0.519139i
$634$		0			0
$635$		−	21952.5i		−	0.0544424i
$636$		0			0
$637$	−934165.	+	539340.i	−2.30221	+	1.32918i
$638$		0			0
$639$			748396.i			1.83286i
$640$		0			0
$641$	−194338.	−	112201.i	−0.472979	−	0.273074i	0.244507	−	0.969648i	$-0.421374\pi$
$641$	−194338.	−	112201.i	−0.472979	−	0.273074i	−0.717486	+	0.696573i	$0.754707\pi$
$642$		0			0
$643$	−139333.	+	241332.i	−0.337003	+	0.583706i	−0.983867	−	0.178899i	$-0.942746\pi$
$643$	−139333.	+	241332.i	−0.337003	+	0.583706i	0.646865	+	0.762605i	$0.276080\pi$
$644$		0			0
$645$		−	350940.i		−	0.843554i
$646$		0			0
$647$	285332.			0.681620			0.340810	−	0.940132i	$-0.389299\pi$
$647$	285332.			0.681620			0.340810	+	0.940132i	$0.389299\pi$
$648$		0			0
$649$	624321.	+	360452.i	1.48224	+	0.855772i
$650$		0			0
$651$	−299853.	+	519361.i	−0.707533	+	1.22548i
$652$		0			0
$653$	640489.			1.50205			0.751027	−	0.660272i	$-0.229559\pi$
$653$	640489.			1.50205			0.751027	+	0.660272i	$0.229559\pi$
$654$		0			0
$655$	−351437.	−	608707.i	−0.819154	−	1.41882i
$656$		0			0
$657$	−666668.			−1.54447
$658$		0			0
$659$	55947.7	−	32301.4i	0.128828	−	0.0743790i	−0.434201	−	0.900816i	$-0.642969\pi$
$659$	55947.7	−	32301.4i	0.128828	−	0.0743790i	0.563029	+	0.826437i	$0.309636\pi$
$660$		0			0
$661$	−337436.	+	194819.i	−0.772305	+	0.445891i	−0.833696	−	0.552223i	$-0.813780\pi$
$661$	−337436.	+	194819.i	−0.772305	+	0.445891i	0.0613911	+	0.998114i	$0.480446\pi$
$662$		0			0
$663$	−297529.	+	515336.i	−0.676866	+	1.17237i
$664$		0			0
$665$	−1.09614e6	+	101420.i	−2.47870	+	0.229339i
$666$		0			0
$667$	−27028.2	−	15604.7i	−0.0607526	−	0.0350755i
$668$		0			0
$669$	376095.	+	651416.i	0.840322	+	1.45548i
$670$		0			0
$671$	−560434.	−	970701.i	−1.24474	−	2.15596i
$672$		0			0
$673$		−	755036.i		−	1.66701i	−0.552514	−	0.833504i	$-0.686331\pi$
$673$		−	755036.i		−	1.66701i	0.552514	−	0.833504i	$-0.313669\pi$
$674$		0			0
$675$	95877.8	−	55355.1i	0.210431	−	0.121493i
$676$		0			0
$677$		−	481265.i		−	1.05004i	−0.851089	−	0.525022i	$-0.824057\pi$
$677$		−	481265.i		−	1.05004i	0.851089	−	0.525022i	$-0.175943\pi$
$678$		0			0
$679$	−460821.	−	266055.i	−0.999522	−	0.577074i
$680$		0			0
$681$	−501513.	+	868647.i	−1.08140	+	1.87305i
$682$		0			0
$683$		−	13212.6i		−	0.0283234i	−0.999900	−	0.0141617i	$-0.995492\pi$
$683$		−	13212.6i		−	0.0283234i	0.999900	−	0.0141617i	$-0.00450797\pi$
$684$		0			0
$685$	−1.04073e6			−2.21799
$686$		0			0
$687$	−1.00853e6	−	582272.i	−2.13685	−	1.23371i
$688$		0			0
$689$	101630.	−	176028.i	0.214084	−	0.370804i
$690$		0			0
$691$	−399708.			−0.837118			−0.418559	−	0.908190i	$-0.637465\pi$
$691$	−399708.			−0.837118			−0.418559	+	0.908190i	$0.637465\pi$
$692$		0			0
$693$	−577293.	−	999900.i	−1.20207	−	2.08205i
$694$		0			0
$695$	−696894.			−1.44277
$696$		0			0
$697$	−15257.0	+	8808.65i	−0.0314054	+	0.0181319i
$698$		0			0
$699$	65978.4	−	38092.7i	0.135035	−	0.0779627i
$700$		0			0
$701$	−56941.4	+	98625.4i	−0.115876	+	0.200703i	−0.918129	−	0.396281i	$-0.870301\pi$
$701$	−56941.4	+	98625.4i	−0.115876	+	0.200703i	0.802254	+	0.596983i	$0.203634\pi$
$702$		0			0
$703$	88572.8	−	62681.0i	0.179221	−	0.126831i
$704$		0			0
$705$	846735.	+	488863.i	1.70361	+	0.983578i
$706$		0			0
$707$	295617.	+	512024.i	0.591414	+	1.02436i
$708$		0			0
$709$	209822.	+	363422.i	0.417406	+	0.722968i	0.995678	−	0.0928763i	$-0.0296061\pi$
$709$	209822.	+	363422.i	0.417406	+	0.722968i	−0.578272	+	0.815844i	$0.696273\pi$
$710$		0			0
$711$			588216.i			1.16358i
$712$		0			0
$713$	22960.6	−	13256.3i	0.0451652	−	0.0260761i
$714$		0			0
$715$			2.03824e6i			3.98697i
$716$		0			0
$717$	808826.	+	466976.i	1.57332	+	0.908356i
$718$		0			0
$719$	−423881.	+	734184.i	−0.819949	+	1.42019i	0.0857707	+	0.996315i	$0.472665\pi$
$719$	−423881.	+	734184.i	−0.819949	+	1.42019i	−0.905719	+	0.423878i	$0.860669\pi$
$720$		0			0
$721$			875485.i			1.68414i
$722$		0			0
$723$	696784.			1.33297
$724$		0			0
$725$	−577288.	−	333297.i	−1.09829	−	0.634097i
$726$		0			0
$727$	267297.	−	462973.i	0.505738	−	0.875964i	−0.494240	−	0.869326i	$-0.664553\pi$
$727$	267297.	−	462973.i	0.505738	−	0.875964i	0.999978	−	0.00663874i	$-0.00211319\pi$
$728$		0			0
$729$	641383.			1.20687
$730$		0			0
$731$	50064.3	+	86713.9i	0.0936900	+	0.162276i
$732$		0			0
$733$	−725652.			−1.35058			−0.675290	−	0.737552i	$-0.735982\pi$
$733$	−725652.			−1.35058			−0.675290	+	0.737552i	$0.735982\pi$
$734$		0			0
$735$	−1.57532e6	+	909513.i	−2.91605	+	1.68358i
$736$		0			0
$737$	965300.	−	557316.i	1.77716	−	1.02605i
$738$		0			0
$739$	315188.	−	545921.i	0.577139	−	0.999634i	−0.418667	−	0.908140i	$-0.637502\pi$
$739$	315188.	−	545921.i	0.577139	−	0.999634i	0.995806	−	0.0914938i	$-0.0291642\pi$
$740$		0			0
$741$	−838542.	−	1.18492e6i	−1.52717	−	2.15801i
$742$		0			0
$743$	−611997.	−	353337.i	−1.10859	−	0.640046i	−0.170127	−	0.985422i	$-0.554418\pi$
$743$	−611997.	−	353337.i	−1.10859	−	0.640046i	−0.938464	+	0.345376i	$0.887751\pi$
$744$		0			0
$745$	450414.	+	780140.i	0.811520	+	1.40559i
$746$		0			0
$747$	68624.9	+	118862.i	0.122982	+	0.213010i
$748$		0			0
$749$		−	1.01313e6i		−	1.80593i
$750$		0			0
$751$	337824.	−	195043.i	0.598977	−	0.345820i	−0.169662	−	0.985502i	$-0.554268\pi$
$751$	337824.	−	195043.i	0.598977	−	0.345820i	0.768639	+	0.639683i	$0.220934\pi$
$752$		0			0
$753$			853513.i			1.50529i
$754$		0			0
$755$	−743194.	−	429083.i	−1.30379	−	0.752744i
$756$		0			0
$757$	475252.	−	823161.i	0.829340	−	1.43646i	−0.0692168	−	0.997602i	$-0.522050\pi$
$757$	475252.	−	823161.i	0.829340	−	1.43646i	0.898557	−	0.438857i	$-0.144617\pi$
$758$		0			0
$759$			97021.2i			0.168416i
$760$		0			0
$761$	−550760.			−0.951027			−0.475513	−	0.879709i	$-0.657738\pi$
$761$	−550760.			−0.951027			−0.475513	+	0.879709i	$0.657738\pi$
$762$		0			0
$763$	883255.	+	509947.i	1.51718	+	0.875944i
$764$		0			0
$765$	−263966.	+	457203.i	−0.451051	+	0.781244i
$766$		0			0
$767$	1.32738e6			2.25634
$768$		0			0
$769$	206275.	+	357278.i	0.348813	+	0.604162i	0.986039	−	0.166515i	$-0.0532514\pi$
$769$	206275.	+	357278.i	0.348813	+	0.604162i	−0.637226	+	0.770677i	$0.719918\pi$
$770$		0			0
$771$	632788.			1.06451
$772$		0			0
$773$	−591967.	+	341772.i	−0.990692	+	0.571976i	−0.905481	−	0.424387i	$-0.860490\pi$
$773$	−591967.	+	341772.i	−0.990692	+	0.571976i	−0.0852110	+	0.996363i	$0.527156\pi$
$774$		0			0
$775$	490410.	−	283138.i	0.816499	−	0.471406i
$776$		0			0
$777$	151026.	−	261585.i	0.250155	−	0.433282i
$778$		0			0
$779$	−3959.45	−	42793.8i	−0.00652469	−	0.0705190i
$780$		0			0
$781$	−1.20396e6	−	695104.i	−1.97382	−	1.13959i
$782$		0			0
$783$	40981.4	+	70981.9i	0.0668441	+	0.115777i
$784$		0			0
$785$	714224.	+	1.23707e6i	1.15903	+	2.00750i
$786$		0			0
$787$		−	35968.0i		−	0.0580719i	−0.999578	−	0.0290360i	$-0.990756\pi$
$787$		−	35968.0i		−	0.0580719i	0.999578	−	0.0290360i	$-0.00924374\pi$
$788$		0			0
$789$	535282.	−	309045.i	0.859861	−	0.496441i
$790$		0			0
$791$		−	1.54247e6i		−	2.46526i
$792$		0			0
$793$	−1.78733e6	−	1.03191e6i	−2.84222	−	1.64095i
$794$		0			0
$795$	171383.	−	296844.i	0.271165	−	0.469672i
$796$		0			0
$797$			1.02761e6i			1.61775i	0.587978	+	0.808877i	$0.299924\pi$
$797$			1.02761e6i			1.61775i	−0.587978	+	0.808877i	$0.700076\pi$
$798$		0			0
$799$	−278961.			−0.436968
$800$		0			0
$801$	−100862.	−	58232.6i	−0.157203	−	0.0907614i
$802$		0			0
$803$	619196.	−	1.07248e6i	0.960278	−	1.66325i
$804$		0			0
$805$	135473.			0.209055
$806$		0			0
$807$	289091.	+	500720.i	0.443902	+	0.768861i
$808$		0			0
$809$	785189.			1.19971			0.599856	−	0.800108i	$-0.295225\pi$
$809$	785189.			1.19971			0.599856	+	0.800108i	$0.295225\pi$
$810$		0			0
$811$	471647.	−	272305.i	0.717092	−	0.414014i	−0.0965891	−	0.995324i	$-0.530793\pi$
$811$	471647.	−	272305.i	0.717092	−	0.414014i	0.813682	+	0.581311i	$0.197460\pi$
$812$		0			0
$813$	−198503.	+	114606.i	−0.300321	+	0.173390i
$814$		0			0
$815$	−236225.	+	409153.i	−0.355639	+	0.615985i
$816$		0			0
$817$	−243220.	+	22503.7i	−0.364381	+	0.0337140i
$818$		0			0
$819$	−1.84109e6	−	1.06295e6i	−2.74478	−	1.58470i
$820$		0			0
$821$	−287358.	−	497719.i	−0.426321	−	0.738410i	0.570222	−	0.821491i	$-0.306857\pi$
$821$	−287358.	−	497719.i	−0.426321	−	0.738410i	−0.996543	+	0.0830808i	$0.973524\pi$
$822$		0			0
$823$	185898.	+	321985.i	0.274458	+	0.475375i	0.969998	−	0.243112i	$-0.0781683\pi$
$823$	185898.	+	321985.i	0.274458	+	0.475375i	−0.695540	+	0.718487i	$0.744835\pi$
$824$		0			0
$825$			2.07225e6i			3.04463i
$826$		0			0
$827$	−407789.	+	235437.i	−0.596244	+	0.344242i	−0.767563	−	0.640974i	$-0.778531\pi$
$827$	−407789.	+	235437.i	−0.596244	+	0.344242i	0.171318	+	0.985216i	$0.445197\pi$
$828$		0			0
$829$		−	611284.i		−	0.889476i	−0.895661	−	0.444738i	$-0.853297\pi$
$829$		−	611284.i		−	0.889476i	0.895661	−	0.444738i	$-0.146703\pi$
$830$		0			0
$831$	1.13666e6	+	656253.i	1.64600	+	0.950319i
$832$		0			0
$833$	259498.	−	449464.i	0.373977	−	0.647746i
$834$		0			0
$835$		−	1.03484e6i		−	1.48423i
$836$		0			0
$837$	−69627.9			−0.0993877
$838$		0			0
$839$	193199.	+	111544.i	0.274462	+	0.158461i	0.630914	−	0.775853i	$-0.282680\pi$
$839$	193199.	+	111544.i	0.274462	+	0.158461i	−0.356452	+	0.934314i	$0.616014\pi$
$840$		0			0
$841$	−106888.	+	185136.i	−0.151125	+	0.261757i
$842$		0			0
$843$	317021.			0.446101
$844$		0			0
$845$	1.30994e6	+	2.26888e6i	1.83458	+	3.17759i
$846$		0			0
$847$	1.01937e6			1.42090
$848$		0			0
$849$	−63785.9	+	36826.8i	−0.0884931	+	0.0510915i
$850$		0			0
$851$	−11564.5	+	6676.76i	−0.0159686	+	0.00921948i
$852$		0			0
$853$	695439.	−	1.20453e6i	0.955786	−	1.65547i	0.223227	−	0.974766i	$-0.428341\pi$
$853$	695439.	−	1.20453e6i	0.955786	−	1.65547i	0.732559	−	0.680704i	$-0.238326\pi$
$854$		0			0
$855$	−743950.	−	1.05126e6i	−1.01768	−	1.43806i
$856$		0			0
$857$	−421583.	−	243401.i	−0.574012	−	0.331406i	0.184738	−	0.982788i	$-0.440856\pi$
$857$	−421583.	−	243401.i	−0.574012	−	0.331406i	−0.758750	+	0.651382i	$0.774190\pi$
$858$		0			0
$859$	−182214.	−	315604.i	−0.246943	−	0.427717i	0.715733	−	0.698374i	$-0.246093\pi$
$859$	−182214.	−	315604.i	−0.246943	−	0.427717i	−0.962676	+	0.270656i	$0.912759\pi$
$860$		0			0
$861$	−59816.5	−	103605.i	−0.0806890	−	0.139757i
$862$		0			0
$863$		−	313552.i		−	0.421006i	−0.977593	−	0.210503i	$-0.932490\pi$
$863$		−	313552.i		−	0.421006i	0.977593	−	0.210503i	$-0.0675102\pi$
$864$		0			0
$865$	−715857.	+	413300.i	−0.956740	+	0.552374i
$866$		0			0
$867$			805630.i			1.07176i
$868$		0			0
$869$	−946272.	−	546331.i	−1.25307	−	0.723462i
$870$		0			0
$871$	1.02617e6	−	1.77738e6i	1.35264	−	2.34285i
$872$		0			0
$873$		−	622520.i		−	0.816818i
$874$		0			0
$875$	987667.			1.29001
$876$		0			0
$877$	641756.	+	370518.i	0.834393	+	0.481737i	0.855354	−	0.518043i	$-0.173339\pi$
$877$	641756.	+	370518.i	0.834393	+	0.481737i	−0.0209616	+	0.999780i	$0.506673\pi$
$878$		0			0
$879$	240309.	−	416227.i	0.311023	−	0.538707i
$880$		0			0
$881$	141027.			0.181699			0.0908493	−	0.995865i	$-0.471042\pi$
$881$	141027.			0.181699			0.0908493	+	0.995865i	$0.471042\pi$
$882$		0			0
$883$	132455.	+	229419.i	0.169882	+	0.294244i	0.938378	−	0.345610i	$-0.112328\pi$
$883$	132455.	+	229419.i	0.169882	+	0.294244i	−0.768496	+	0.639854i	$0.778995\pi$
$884$		0			0
$885$	2.23842e6			2.85795
$886$		0			0
$887$	−1.16073e6	+	670146.i	−1.47531	+	0.851770i	−0.999612	−	0.0278401i	$-0.991137\pi$
$887$	−1.16073e6	+	670146.i	−1.47531	+	0.851770i	−0.475696	+	0.879610i	$0.657804\pi$
$888$		0			0
$889$	−36834.3	+	21266.3i	−0.0466068	+	0.0269084i
$890$		0			0
$891$	−480955.	+	833038.i	−0.605827	+	1.04932i
$892$		0			0
$893$	284512.	−	618181.i	0.356778	−	0.775198i
$894$		0			0
$895$	242566.	+	140046.i	0.302820	+	0.174833i
$896$		0			0
$897$	89321.3	+	154709.i	0.111012	+	0.192278i
$898$		0			0
$899$	209618.	+	363068.i	0.259363	+	0.449230i
$900$		0			0
$901$			97796.6i			0.120469i
$902$		0			0
$903$	−588844.	+	339969.i	−0.722145	+	0.416931i
$904$		0			0
$905$		−	156536.i		−	0.191124i
$906$		0			0
$907$	572770.	+	330689.i	0.696250	+	0.401980i	0.805949	−	0.591985i	$-0.201655\pi$
$907$	572770.	+	330689.i	0.696250	+	0.401980i	−0.109699	+	0.993965i	$0.534989\pi$
$908$		0			0
$909$	−345846.	+	599022.i	−0.418557	+	0.724962i
$910$		0			0
$911$			802609.i			0.967091i	0.875319	+	0.483546i	$0.160651\pi$
$911$			802609.i			0.967091i	−0.875319	+	0.483546i	$0.839349\pi$
$912$		0			0
$913$	−254953.			−0.305857
$914$		0			0
$915$	−3.01404e6	−	1.74016e6i	−3.60004	−	2.07848i
$916$		0			0
$917$	−680903.	+	1.17936e6i	−0.809741	+	1.40251i
$918$		0			0
$919$	1.25329e6			1.48396			0.741979	−	0.670423i	$-0.233887\pi$
$919$	1.25329e6			1.48396			0.741979	+	0.670423i	$0.233887\pi$
$920$		0			0
$921$	−705218.	−	1.22147e6i	−0.831389	−	1.44001i
$922$		0			0
$923$	−2.55975e6			−3.00465
$924$		0			0
$925$	−247003.	+	142607.i	−0.288682	+	0.166670i
$926$		0			0
$927$	−887016.	+	512119.i	−1.03222	+	0.595952i
$928$		0			0
$929$	−336945.	+	583606.i	−0.390416	+	0.676221i	−0.992504	−	0.122209i	$-0.961002\pi$
$929$	−336945.	+	583606.i	−0.390416	+	0.676221i	0.602088	+	0.798430i	$0.294336\pi$
$930$		0			0
$931$	731357.	+	1.03346e6i	0.843782	+	1.19233i
$932$		0			0
$933$	−1.53807e6	−	888007.i	−1.76691	−	1.02012i
$934$		0			0
$935$	−490340.	−	849293.i	−0.560885	−	0.971481i
$936$		0			0
$937$	−155511.	−	269354.i	−0.177126	−	0.306792i	0.763769	−	0.645490i	$-0.223347\pi$
$937$	−155511.	−	269354.i	−0.177126	−	0.306792i	−0.940895	+	0.338698i	$0.890013\pi$
$938$		0			0
$939$		−	24462.1i		−	0.0277435i
$940$		0			0
$941$	−251667.	+	145300.i	−0.284215	+	0.164091i	−0.635330	−	0.772241i	$-0.719136\pi$
$941$	−251667.	+	145300.i	−0.284215	+	0.164091i	0.351115	+	0.936332i	$0.385803\pi$
$942$		0			0
$943$			5288.89i			0.00594759i
$944$		0			0
$945$	−308115.	−	177891.i	−0.345024	−	0.199200i
$946$		0			0
$947$	−80281.6	+	139052.i	−0.0895191	+	0.155052i	−0.907308	−	0.420467i	$-0.861866\pi$
$947$	−80281.6	+	139052.i	−0.0895191	+	0.155052i	0.817789	+	0.575518i	$0.195200\pi$
$948$		0			0
$949$		−	2.28022e6i		−	2.53188i
$950$		0			0
$951$	1.08803e6			1.20304
$952$		0			0
$953$	−17308.1	−	9992.82i	−0.0190574	−	0.0110028i	0.490441	−	0.871474i	$-0.336836\pi$
$953$	−17308.1	−	9992.82i	−0.0190574	−	0.0110028i	−0.509498	+	0.860472i	$0.670169\pi$
$954$		0			0
$955$	−782279.	+	1.35495e6i	−0.857739	+	1.48565i
$956$		0			0
$957$	−1.53417e6			−1.67513
$958$		0			0
$959$	1.00820e6	+	1.74626e6i	1.09625	+	1.89876i
$960$		0			0
$961$	567378.			0.614364
$962$		0			0
$963$	1.02647e6	−	592634.i	1.10687	−	0.639049i
$964$		0			0
$965$	−402135.	+	232173.i	−0.431834	+	0.249320i
$966$		0			0
$967$	359807.	−	623204.i	0.384783	−	0.666465i	−0.606956	−	0.794736i	$-0.707609\pi$
$967$	359807.	−	623204.i	0.384783	−	0.666465i	0.991739	+	0.128271i	$0.0409428\pi$
$968$		0			0
$969$	634460.	+	292005.i	0.675705	+	0.310987i
$970$		0			0
$971$	−885645.	−	511327.i	−0.939336	−	0.542326i	−0.0495841	−	0.998770i	$-0.515790\pi$
$971$	−885645.	−	511327.i	−0.939336	−	0.542326i	−0.889752	+	0.456444i	$0.849123\pi$
$972$		0			0
$973$	675109.	+	1.16932e6i	0.713097	+	1.23512i
$974$		0			0
$975$	1.90779e6	+	3.30439e6i	2.00688	+	3.47602i
$976$		0			0
$977$			35079.7i			0.0367508i	0.999831	+	0.0183754i	$0.00584941\pi$
$977$			35079.7i			0.0367508i	−0.999831	+	0.0183754i	$0.994151\pi$
$978$		0			0
$979$	187359.	−	108172.i	0.195483	−	0.112862i
$980$		0			0
$981$			1.19318e6i			1.23985i
$982$		0			0
$983$	−176477.	−	101889.i	−0.182634	−	0.105444i	0.405896	−	0.913919i	$-0.366960\pi$
$983$	−176477.	−	101889.i	−0.182634	−	0.105444i	−0.588530	+	0.808476i	$0.700293\pi$
$984$		0			0
$985$	248553.	−	430507.i	0.256181	−	0.443719i
$986$		0			0
$987$		−	1.89432e6i		−	1.94455i
$988$		0			0
$989$	30059.6			0.0307320
$990$		0			0
$991$	−170873.	−	98653.4i	−0.173990	−	0.100453i	0.410476	−	0.911872i	$-0.365363\pi$
$991$	−170873.	−	98653.4i	−0.173990	−	0.100453i	−0.584466	+	0.811418i	$0.698696\pi$
$992$		0			0
$993$	447619.	−	775298.i	0.453952	−	0.786268i
$994$		0			0
$995$	1.31766e6			1.33094
$996$		0			0
$997$	159089.	+	275550.i	0.160048	+	0.277211i	0.934886	−	0.354949i	$-0.115502\pi$
$997$	159089.	+	275550.i	0.160048	+	0.277211i	−0.774838	+	0.632160i	$0.782169\pi$
$998$		0			0
$999$	35069.3			0.0351395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.65.18		40
4.3	odd	2		152.5.n.a.65.3	✓	40
19.12	odd	6	inner	304.5.r.d.145.18		40
76.31	even	6		152.5.n.a.145.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.3	✓	40	4.3	odd	2
152.5.n.a.145.3	yes	40	76.31	even	6
304.5.r.d.65.18		40	1.1	even	1	trivial
304.5.r.d.145.18		40	19.12	odd	6	inner

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(11.3222 + 6.53690i) q^{3} +(-19.8361 + 34.3572i) q^{5} +76.8642 q^{7} +(44.9621 + 77.8766i) q^{9} +O(q^{10})\)	\(q+(11.3222 + 6.53690i) q^{3} +(-19.8361 + 34.3572i) q^{5} +76.8642 q^{7} +(44.9621 + 77.8766i) q^{9} -167.042 q^{11} +(-266.363 + 153.785i) q^{13} +(-449.179 + 259.334i) q^{15} +(73.9920 - 128.158i) q^{17} +(208.536 + 294.676i) q^{19} +(870.275 + 502.454i) q^{21} +(-22.2131 - 38.4743i) q^{23} +(-474.445 - 821.764i) q^{25} +116.673i q^{27} +(608.382 - 351.249i) q^{29} +596.777i q^{31} +(-1891.29 - 1091.94i) q^{33} +(-1524.69 + 2640.84i) q^{35} -300.577i q^{37} -4021.10 q^{39} +(-103.099 - 59.5244i) q^{41} +(-338.309 + 585.968i) q^{43} -3567.50 q^{45} +(-942.536 - 1632.52i) q^{47} +3507.11 q^{49} +(1675.51 - 967.357i) q^{51} +(-572.321 + 330.430i) q^{53} +(3313.46 - 5739.09i) q^{55} +(434.823 + 4699.57i) q^{57} +(-3737.52 - 2157.86i) q^{59} +(3355.06 + 5811.13i) q^{61} +(3455.98 + 5985.93i) q^{63} -12202.0i q^{65} +(-5778.80 + 3336.39i) q^{67} -580.820i q^{69} +(7207.51 + 4161.26i) q^{71} +(-3706.83 + 6420.42i) q^{73} -12405.6i q^{75} -12839.5 q^{77} +(5664.89 + 3270.62i) q^{79} +(2879.25 - 4987.01i) q^{81} +1526.28 q^{83} +(2935.43 + 5084.32i) q^{85} +9184.33 q^{87} +(-1121.63 + 647.575i) q^{89} +(-20473.8 + 11820.5i) q^{91} +(-3901.07 + 6756.86i) q^{93} +(-14260.8 + 1319.46i) q^{95} +(-5995.26 - 3461.36i) q^{97} +(-7510.55 - 13008.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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