LMFDB - Embedded newform 308.4.i.a.177.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,4,Mod(177,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("308.177");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	308.i (of order $3$, degree $2$, 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:	$18.1725882818$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 194 x^{18} - 432 x^{17} + 24205 x^{16} - 47156 x^{15} + 1632616 x^{14} + \cdots + 7996651776 $ x^20 - 4x^19 + 194x^18 - 432x^17 + 24205x^16 - 47156x^15 + 1632616x^14 - 1838210x^13 + 75876043x^12 - 82333872x^11 + 1801672853x^10 - 471307576x^9 + 27041915377x^8 - 14255551602x^7 + 176709560868x^6 - 669217680x^5 + 678547482048x^4 - 436737562560x^3 + 226025971776x^2 - 48231013248*x + 7996651776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.6
Root			$0.192948 - 0.334196i$ of defining polynomial
Character	$\chi$	$=$	308.177
Dual form			308.4.i.a.221.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.307052 - 0.531830i) q^{3} +(-0.388866 + 0.673536i) q^{5} +(6.69839 + 17.2665i) q^{7} +(13.3114 - 23.0561i) q^{9} +(-5.50000 - 9.52628i) q^{11} +2.92263 q^{13} +0.477608 q^{15} +(21.1983 + 36.7165i) q^{17} +(-6.76559 + 11.7184i) q^{19} +(7.12608 - 8.86411i) q^{21} +(-13.2164 + 22.8915i) q^{23} +(62.1976 + 107.729i) q^{25} -32.9300 q^{27} +158.877 q^{29} +(94.4858 + 163.654i) q^{31} +(-3.37757 + 5.85013i) q^{33} +(-14.2344 - 2.20274i) q^{35} +(98.0421 - 169.814i) q^{37} +(-0.897400 - 1.55434i) q^{39} +370.208 q^{41} +423.999 q^{43} +(10.3527 + 17.9315i) q^{45} +(52.6992 - 91.2777i) q^{47} +(-253.263 + 231.315i) q^{49} +(13.0180 - 22.5478i) q^{51} +(-81.5097 - 141.179i) q^{53} +8.55505 q^{55} +8.30956 q^{57} +(187.419 + 324.619i) q^{59} +(-104.713 + 181.369i) q^{61} +(487.263 + 75.4031i) q^{63} +(-1.13651 + 1.96850i) q^{65} +(251.786 + 436.106i) q^{67} +16.2325 q^{69} -588.616 q^{71} +(120.465 + 208.651i) q^{73} +(38.1958 - 66.1570i) q^{75} +(127.644 - 158.776i) q^{77} +(-182.911 + 316.812i) q^{79} +(-349.298 - 605.001i) q^{81} +985.073 q^{83} -32.9732 q^{85} +(-48.7834 - 84.4953i) q^{87} +(-18.6680 + 32.3340i) q^{89} +(19.5769 + 50.4636i) q^{91} +(58.0241 - 100.501i) q^{93} +(-5.26182 - 9.11374i) q^{95} -79.8620 q^{97} -292.852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} - 10 q^{5} - 20 q^{7} - 104 q^{9} - 110 q^{11} + 16 q^{13} + 108 q^{15} - 166 q^{17} - 342 q^{19} - 42 q^{21} + 54 q^{23} - 198 q^{25} + 612 q^{27} - 160 q^{29} - 492 q^{31} - 66 q^{33} + 310 q^{35}+ \cdots + 2288 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 - 10 * q^5 - 20 * q^7 - 104 * q^9 - 110 * q^11 + 16 * q^13 + 108 * q^15 - 166 * q^17 - 342 * q^19 - 42 * q^21 + 54 * q^23 - 198 * q^25 + 612 * q^27 - 160 * q^29 - 492 * q^31 - 66 * q^33 + 310 * q^35 - 258 * q^37 + 418 * q^39 + 1268 * q^41 - 548 * q^43 - 138 * q^45 - 312 * q^47 + 572 * q^49 + 196 * q^51 - 656 * q^53 + 220 * q^55 - 1476 * q^57 - 934 * q^59 + 228 * q^61 - 1270 * q^63 - 524 * q^65 - 478 * q^67 + 3144 * q^69 + 276 * q^71 + 364 * q^73 - 234 * q^75 - 154 * q^77 + 616 * q^79 - 4082 * q^81 - 264 * q^83 - 992 * q^85 + 2120 * q^87 - 1906 * q^89 - 94 * q^91 + 2984 * q^93 - 2322 * q^95 + 2700 * q^97 + 2288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−0.307052	−	0.531830i	−0.0590922	−	0.102351i	0.834966	−	0.550302i	$-0.185487\pi$
$3$	−0.307052	−	0.531830i	−0.0590922	−	0.102351i	−0.894058	+	0.447951i	$0.852154\pi$
$4$		0			0
$5$	−0.388866	+	0.673536i	−0.0347812	+	0.0602429i	−0.882892	−	0.469576i	$-0.844407\pi$
$5$	−0.388866	+	0.673536i	−0.0347812	+	0.0602429i	0.848111	+	0.529819i	$0.177740\pi$
$6$		0			0
$7$	6.69839	+	17.2665i	0.361679	+	0.932303i
$7$	6.69839	+	17.2665i	0.361679	+	0.932303i
$8$		0			0
$9$	13.3114	−	23.0561i	0.493016	−	0.853929i
$10$		0			0
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$12$		0			0
$13$	2.92263			0.0623533			0.0311766	−	0.999514i	$-0.490075\pi$
$13$	2.92263			0.0623533			0.0311766	+	0.999514i	$0.490075\pi$
$14$		0			0
$15$	0.477608			0.00822120
$16$		0			0
$17$	21.1983	+	36.7165i	0.302432	+	0.523827i	0.976686	−	0.214672i	$-0.0688682\pi$
$17$	21.1983	+	36.7165i	0.302432	+	0.523827i	−0.674254	+	0.738499i	$0.735535\pi$
$18$		0			0
$19$	−6.76559	+	11.7184i	−0.0816912	+	0.141493i	−0.903976	−	0.427582i	$-0.859365\pi$
$19$	−6.76559	+	11.7184i	−0.0816912	+	0.141493i	0.822285	+	0.569076i	$0.192699\pi$
$20$		0			0
$21$	7.12608	−	8.86411i	0.0740494	−	0.0921099i
$22$		0			0
$23$	−13.2164	+	22.8915i	−0.119818	+	0.207531i	−0.919695	−	0.392633i	$-0.871564\pi$
$23$	−13.2164	+	22.8915i	−0.119818	+	0.207531i	0.799877	+	0.600163i	$0.204898\pi$
$24$		0			0
$25$	62.1976	+	107.729i	0.497581	+	0.861835i
$26$		0			0
$27$	−32.9300			−0.234718
$28$		0			0
$29$	158.877			1.01733			0.508667	−	0.860964i	$-0.330139\pi$
$29$	158.877			1.01733			0.508667	+	0.860964i	$0.330139\pi$
$30$		0			0
$31$	94.4858	+	163.654i	0.547424	+	0.948166i	0.998450	+	0.0556554i	$0.0177248\pi$
$31$	94.4858	+	163.654i	0.547424	+	0.948166i	−0.451026	+	0.892511i	$0.648942\pi$
$32$		0			0
$33$	−3.37757	+	5.85013i	−0.0178170	+	0.0308599i
$34$		0			0
$35$	−14.2344	−	2.20274i	−0.0687442	−	0.0106380i
$36$		0			0
$37$	98.0421	−	169.814i	0.435622	−	0.754520i	−0.561724	−	0.827325i	$-0.689862\pi$
$37$	98.0421	−	169.814i	0.435622	−	0.754520i	0.997346	+	0.0728048i	$0.0231950\pi$
$38$		0			0
$39$	−0.897400	−	1.55434i	−0.00368459	−	0.00638190i
$40$		0			0
$41$	370.208			1.41017			0.705084	−	0.709124i	$-0.250909\pi$
$41$	370.208			1.41017			0.705084	+	0.709124i	$0.250909\pi$
$42$		0			0
$43$	423.999			1.50370			0.751851	−	0.659333i	$-0.229161\pi$
$43$	423.999			1.50370			0.751851	+	0.659333i	$0.229161\pi$
$44$		0			0
$45$	10.3527	+	17.9315i	0.0342954	+	0.0594014i
$46$		0			0
$47$	52.6992	−	91.2777i	0.163553	−	0.283281i	−0.772588	−	0.634908i	$-0.781038\pi$
$47$	52.6992	−	91.2777i	0.163553	−	0.283281i	0.936140	+	0.351627i	$0.114371\pi$
$48$		0			0
$49$	−253.263	+	231.315i	−0.738376	+	0.674389i
$50$		0			0
$51$	13.0180	−	22.5478i	0.0357427	−	0.0619082i
$52$		0			0
$53$	−81.5097	−	141.179i	−0.211249	−	0.365894i	0.740856	−	0.671663i	$-0.234420\pi$
$53$	−81.5097	−	141.179i	−0.211249	−	0.365894i	−0.952106	+	0.305769i	$0.901087\pi$
$54$		0			0
$55$	8.55505			0.0209739
$56$		0			0
$57$	8.30956			0.0193093
$58$		0			0
$59$	187.419	+	324.619i	0.413557	+	0.716302i	0.995276	−	0.0970882i	$-0.0309529\pi$
$59$	187.419	+	324.619i	0.413557	+	0.716302i	−0.581719	+	0.813390i	$0.697620\pi$
$60$		0			0
$61$	−104.713	+	181.369i	−0.219790	+	0.380687i	−0.954744	−	0.297430i	$-0.903871\pi$
$61$	−104.713	+	181.369i	−0.219790	+	0.380687i	0.734954	+	0.678117i	$0.237204\pi$
$62$		0			0
$63$	487.263	+	75.4031i	0.974434	+	0.150792i
$64$		0			0
$65$	−1.13651	+	1.96850i	−0.00216872	+	0.00375634i
$66$		0			0
$67$	251.786	+	436.106i	0.459113	+	0.795207i	0.998914	−	0.0465854i	$-0.0148340\pi$
$67$	251.786	+	436.106i	0.459113	+	0.795207i	−0.539801	+	0.841792i	$0.681501\pi$
$68$		0			0
$69$	16.2325			0.0283212
$70$		0			0
$71$	−588.616			−0.983885			−0.491943	−	0.870628i	$-0.663713\pi$
$71$	−588.616			−0.983885			−0.491943	+	0.870628i	$0.663713\pi$
$72$		0			0
$73$	120.465	+	208.651i	0.193142	+	0.334531i	0.946290	−	0.323320i	$-0.104799\pi$
$73$	120.465	+	208.651i	0.193142	+	0.334531i	−0.753148	+	0.657851i	$0.771466\pi$
$74$		0			0
$75$	38.1958	−	66.1570i	0.0588062	−	0.101855i
$76$		0			0
$77$	127.644	−	158.776i	0.188914	−	0.234990i
$78$		0			0
$79$	−182.911	+	316.812i	−0.260495	+	0.451191i	−0.966374	−	0.257142i	$-0.917219\pi$
$79$	−182.911	+	316.812i	−0.260495	+	0.451191i	0.705878	+	0.708333i	$0.250552\pi$
$80$		0			0
$81$	−349.298	−	605.001i	−0.479146	−	0.829906i
$82$		0			0
$83$	985.073			1.30272			0.651360	−	0.758768i	$-0.274199\pi$
$83$	985.073			1.30272			0.651360	+	0.758768i	$0.274199\pi$
$84$		0			0
$85$	−32.9732			−0.0420758
$86$		0			0
$87$	−48.7834	−	84.4953i	−0.0601164	−	0.104125i
$88$		0			0
$89$	−18.6680	+	32.3340i	−0.0222338	+	0.0385101i	−0.876928	−	0.480621i	$-0.840411\pi$
$89$	−18.6680	+	32.3340i	−0.0222338	+	0.0385101i	0.854694	+	0.519131i	$0.173744\pi$
$90$		0			0
$91$	19.5769	+	50.4636i	0.0225519	+	0.0581321i
$92$		0			0
$93$	58.0241	−	100.501i	0.0646970	−	0.112058i
$94$		0			0
$95$	−5.26182	−	9.11374i	−0.00568264	−	0.00984263i
$96$		0			0
$97$	−79.8620			−0.0835954			−0.0417977	−	0.999126i	$-0.513309\pi$
$97$	−79.8620			−0.0835954			−0.0417977	+	0.999126i	$0.513309\pi$
$98$		0			0
$99$	−292.852			−0.297300
$100$		0			0
$101$	−965.030	−	1671.48i	−0.950734	−	1.64672i	−0.743842	−	0.668355i	$-0.766999\pi$
$101$	−965.030	−	1671.48i	−0.950734	−	1.64672i	−0.206891	−	0.978364i	$-0.566335\pi$
$102$		0			0
$103$	−62.9437	+	109.022i	−0.0602139	+	0.104293i	−0.894561	−	0.446946i	$-0.852512\pi$
$103$	−62.9437	+	109.022i	−0.0602139	+	0.104293i	0.834347	+	0.551239i	$0.185845\pi$
$104$		0			0
$105$	3.19921	+	8.24662i	0.00297344	+	0.00766464i
$106$		0			0
$107$	−245.224	+	424.741i	−0.221558	+	0.383750i	−0.955281	−	0.295698i	$-0.904448\pi$
$107$	−245.224	+	424.741i	−0.221558	+	0.383750i	0.733723	+	0.679449i	$0.237781\pi$
$108$		0			0
$109$	−447.232	−	774.628i	−0.393000	−	0.680697i	0.599843	−	0.800118i	$-0.295230\pi$
$109$	−447.232	−	774.628i	−0.393000	−	0.680697i	−0.992844	+	0.119421i	$0.961896\pi$
$110$		0			0
$111$	−120.416			−0.102967
$112$		0			0
$113$	346.489			0.288450			0.144225	−	0.989545i	$-0.453931\pi$
$113$	346.489			0.288450			0.144225	+	0.989545i	$0.453931\pi$
$114$		0			0
$115$	−10.2788	−	17.8034i	−0.00833483	−	0.0144363i
$116$		0			0
$117$	38.9044	−	67.3845i	0.0307412	−	0.0532453i
$118$		0			0
$119$	−491.971	+	611.961i	−0.378982	+	0.471415i
$120$		0			0
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−113.673	−	196.888i	−0.0833299	−	0.144332i
$124$		0			0
$125$	−193.963			−0.138788
$126$		0			0
$127$	−2039.36			−1.42491			−0.712457	−	0.701716i	$-0.752418\pi$
$127$	−2039.36			−1.42491			−0.712457	+	0.701716i	$0.752418\pi$
$128$		0			0
$129$	−130.190	−	225.495i	−0.0888570	−	0.153905i
$130$		0			0
$131$	−1076.72	+	1864.93i	−0.718117	+	1.24382i	0.243627	+	0.969869i	$0.421663\pi$
$131$	−1076.72	+	1864.93i	−0.718117	+	1.24382i	−0.961745	+	0.273947i	$0.911671\pi$
$132$		0			0
$133$	−247.653	−	38.3239i	−0.161461	−	0.0249858i
$134$		0			0
$135$	12.8054	−	22.1795i	0.00816378	−	0.0141401i
$136$		0			0
$137$	−207.156	−	358.804i	−0.129186	−	0.223757i	0.794175	−	0.607689i	$-0.207903\pi$
$137$	−207.156	−	358.804i	−0.129186	−	0.223757i	−0.923361	+	0.383932i	$0.874570\pi$
$138$		0			0
$139$	−965.844			−0.589366			−0.294683	−	0.955595i	$-0.595214\pi$
$139$	−965.844			−0.589366			−0.294683	+	0.955595i	$0.595214\pi$
$140$		0			0
$141$	−64.7256			−0.0386587
$142$		0			0
$143$	−16.0745	−	27.8418i	−0.00940011	−	0.0162815i
$144$		0			0
$145$	−61.7817	+	107.009i	−0.0353841	+	0.0612871i
$146$		0			0
$147$	200.785	+	63.6670i	0.112656	+	0.0357222i
$148$		0			0
$149$	1006.10	−	1742.62i	0.553176	−	0.958128i	−0.444867	−	0.895597i	$-0.646749\pi$
$149$	1006.10	−	1742.62i	0.553176	−	0.958128i	0.998043	−	0.0625319i	$-0.0199175\pi$
$150$		0			0
$151$	−853.320	−	1477.99i	−0.459882	−	0.796539i	0.539072	−	0.842260i	$-0.318775\pi$
$151$	−853.320	−	1477.99i	−0.459882	−	0.796539i	−0.998954	+	0.0457205i	$0.985442\pi$
$152$		0			0
$153$	1128.72			0.596415
$154$		0			0
$155$	−146.969			−0.0761603
$156$		0			0
$157$	−1379.71	−	2389.72i	−0.701354	−	1.21478i	−0.967991	−	0.250984i	$-0.919246\pi$
$157$	−1379.71	−	2389.72i	−0.701354	−	1.21478i	0.266637	−	0.963797i	$-0.414088\pi$
$158$		0			0
$159$	−50.0554	+	86.6985i	−0.0249664	+	0.0432430i
$160$		0			0
$161$	−483.784	−	74.8648i	−0.236817	−	0.0366470i
$162$		0			0
$163$	313.400	−	542.825i	0.150598	−	0.260843i	−0.780850	−	0.624719i	$-0.785214\pi$
$163$	313.400	−	542.825i	0.150598	−	0.260843i	0.931447	+	0.363876i	$0.118547\pi$
$164$		0			0
$165$	−2.62685	−	4.54983i	−0.00123939	−	0.00214669i
$166$		0			0
$167$	1952.08			0.904529			0.452265	−	0.891884i	$-0.350616\pi$
$167$	1952.08			0.904529			0.452265	+	0.891884i	$0.350616\pi$
$168$		0			0
$169$	−2188.46			−0.996112
$170$		0			0
$171$	180.120	+	311.976i	0.0805502	+	0.139517i
$172$		0			0
$173$	−165.093	+	285.950i	−0.0725538	+	0.125667i	−0.900020	−	0.435849i	$-0.856448\pi$
$173$	−165.093	+	285.950i	−0.0725538	+	0.125667i	0.827466	+	0.561516i	$0.189782\pi$
$174$		0			0
$175$	−1443.48	+	1795.55i	−0.623526	+	0.775603i
$176$		0			0
$177$	115.095	−	199.350i	0.0488760	−	0.0846557i
$178$		0			0
$179$	−1159.90	−	2009.00i	−0.484329	−	0.838883i	0.515509	−	0.856884i	$-0.327603\pi$
$179$	−1159.90	−	2009.00i	−0.484329	−	0.838883i	−0.999838	+	0.0180013i	$0.994270\pi$
$180$		0			0
$181$	2064.16			0.847668			0.423834	−	0.905740i	$-0.360684\pi$
$181$	2064.16			0.847668			0.423834	+	0.905740i	$0.360684\pi$
$182$		0			0
$183$	128.610			0.0519515
$184$		0			0
$185$	76.2505	+	132.070i	0.0303030	+	0.0524863i
$186$		0			0
$187$	233.181	−	403.882i	0.0911866	−	0.157940i
$188$		0			0
$189$	−220.578	−	568.586i	−0.0848926	−	0.218828i
$190$		0			0
$191$	−694.827	+	1203.48i	−0.263225	+	0.455919i	−0.967097	−	0.254408i	$-0.918119\pi$
$191$	−694.827	+	1203.48i	−0.263225	+	0.455919i	0.703872	+	0.710327i	$0.251453\pi$
$192$		0			0
$193$	−1554.86	−	2693.10i	−0.579903	−	1.00442i	−0.995490	−	0.0948675i	$-0.969757\pi$
$193$	−1554.86	−	2693.10i	−0.579903	−	1.00442i	0.415587	−	0.909553i	$-0.363576\pi$
$194$		0			0
$195$	1.39587			0.000512618
$196$		0			0
$197$	−478.386			−0.173013			−0.0865067	−	0.996251i	$-0.527570\pi$
$197$	−478.386			−0.173013			−0.0865067	+	0.996251i	$0.527570\pi$
$198$		0			0
$199$	2082.32	+	3606.69i	0.741768	+	1.28478i	0.951689	+	0.307062i	$0.0993460\pi$
$199$	2082.32	+	3606.69i	0.741768	+	1.28478i	−0.209921	+	0.977718i	$0.567321\pi$
$200$		0			0
$201$	154.623	−	267.815i	0.0542600	−	0.0939810i
$202$		0			0
$203$	1064.22	+	2743.24i	0.367948	+	0.948462i
$204$		0			0
$205$	−143.961	+	249.349i	−0.0490473	+	0.0849525i
$206$		0			0
$207$	351.859	+	609.437i	0.118144	+	0.204632i
$208$		0			0
$209$	148.843			0.0492617
$210$		0			0
$211$	1053.87			0.343844			0.171922	−	0.985111i	$-0.445002\pi$
$211$	1053.87			0.343844			0.171922	+	0.985111i	$0.445002\pi$
$212$		0			0
$213$	180.736	+	313.043i	0.0581399	+	0.100701i
$214$		0			0
$215$	−164.879	+	285.578i	−0.0523006	+	0.0905873i
$216$		0			0
$217$	−2192.83	+	2727.66i	−0.685986	+	0.853297i
$218$		0			0
$219$	73.9779	−	128.134i	0.0228263	−	0.0395364i
$220$		0			0
$221$	61.9548	+	107.309i	0.0188576	+	0.0326623i
$222$		0			0
$223$	1069.13			0.321050			0.160525	−	0.987032i	$-0.448681\pi$
$223$	1069.13			0.321050			0.160525	+	0.987032i	$0.448681\pi$
$224$		0			0
$225$	3311.76			0.981261
$226$		0			0
$227$	−726.734	−	1258.74i	−0.212489	−	0.368042i	0.740004	−	0.672603i	$-0.234824\pi$
$227$	−726.734	−	1258.74i	−0.212489	−	0.368042i	−0.952493	+	0.304561i	$0.901490\pi$
$228$		0			0
$229$	−2902.06	+	5026.52i	−0.837440	+	1.45049i	0.0545885	+	0.998509i	$0.482615\pi$
$229$	−2902.06	+	5026.52i	−0.837440	+	1.45049i	−0.892028	+	0.451979i	$0.850718\pi$
$230$		0			0
$231$	−123.635	−	19.1324i	−0.0352148	−	0.00544943i
$232$		0			0
$233$	2948.92	−	5107.68i	0.829143	−	1.43612i	−0.0695692	−	0.997577i	$-0.522162\pi$
$233$	2948.92	−	5107.68i	0.829143	−	1.43612i	0.898712	−	0.438540i	$-0.144504\pi$
$234$		0			0
$235$	40.9859	+	70.9896i	0.0113771	+	0.0197057i
$236$		0			0
$237$	224.653			0.0615729
$238$		0			0
$239$	−183.362			−0.0496263			−0.0248131	−	0.999692i	$-0.507899\pi$
$239$	−183.362			−0.0496263			−0.0248131	+	0.999692i	$0.507899\pi$
$240$		0			0
$241$	441.072	+	763.959i	0.117892	+	0.204195i	0.918932	−	0.394416i	$-0.129053\pi$
$241$	441.072	+	763.959i	0.117892	+	0.204195i	−0.801040	+	0.598611i	$0.795720\pi$
$242$		0			0
$243$	−659.060	+	1141.53i	−0.173987	+	0.301354i
$244$		0			0
$245$	−57.3137	−	260.532i	−0.0149455	−	0.0679380i
$246$		0			0
$247$	−19.7733	+	34.2484i	−0.00509372	+	0.00882257i
$248$		0			0
$249$	−302.469	−	523.891i	−0.0769806	−	0.133334i
$250$		0			0
$251$	5270.37			1.32535			0.662675	−	0.748907i	$-0.269421\pi$
$251$	5270.37			1.32535			0.662675	+	0.748907i	$0.269421\pi$
$252$		0			0
$253$	290.761			0.0722529
$254$		0			0
$255$	10.1245	+	17.5361i	0.00248635	+	0.00430649i
$256$		0			0
$257$	2651.53	−	4592.59i	0.643573	−	1.11470i	−0.341057	−	0.940043i	$-0.610785\pi$
$257$	2651.53	−	4592.59i	0.643573	−	1.11470i	0.984629	−	0.174658i	$-0.0558819\pi$
$258$		0			0
$259$	3588.81	+	555.363i	0.860996	+	0.133238i
$260$		0			0
$261$	2114.88	−	3663.07i	0.501562	−	0.868730i
$262$		0			0
$263$	2198.60	+	3808.09i	0.515481	+	0.892840i	0.999839	+	0.0179696i	$0.00572022\pi$
$263$	2198.60	+	3808.09i	0.515481	+	0.892840i	−0.484357	+	0.874870i	$0.660946\pi$
$264$		0			0
$265$	126.785			0.0293900
$266$		0			0
$267$	22.9282			0.00525538
$268$		0			0
$269$	1523.07	+	2638.04i	0.345217	+	0.597933i	0.985393	−	0.170295i	$-0.0544721\pi$
$269$	1523.07	+	2638.04i	0.345217	+	0.597933i	−0.640176	+	0.768228i	$0.721139\pi$
$270$		0			0
$271$	−2777.55	+	4810.85i	−0.622597	+	1.07837i	0.366403	+	0.930456i	$0.380589\pi$
$271$	−2777.55	+	4810.85i	−0.622597	+	1.07837i	−0.989000	+	0.147914i	$0.952744\pi$
$272$		0			0
$273$	20.8269	−	25.9065i	0.00461722	−	0.00574335i
$274$		0			0
$275$	684.173	−	1185.02i	0.150026	−	0.259853i
$276$		0			0
$277$	−2665.52	−	4616.81i	−0.578178	−	1.00143i	−0.995688	−	0.0927620i	$-0.970430\pi$
$277$	−2665.52	−	4616.81i	−0.578178	−	1.00143i	0.417510	−	0.908672i	$-0.362903\pi$
$278$		0			0
$279$	5030.97			1.07956
$280$		0			0
$281$	−2917.59			−0.619390			−0.309695	−	0.950836i	$-0.600227\pi$
$281$	−2917.59			−0.619390			−0.309695	+	0.950836i	$0.600227\pi$
$282$		0			0
$283$	−529.171	−	916.552i	−0.111152	−	0.192521i	0.805083	−	0.593162i	$-0.202121\pi$
$283$	−529.171	−	916.552i	−0.111152	−	0.192521i	−0.916235	+	0.400641i	$0.868787\pi$
$284$		0			0
$285$	−3.23130	+	5.59678i	−0.000671600	+	0.00116324i
$286$		0			0
$287$	2479.80	+	6392.20i	0.510028	+	1.31470i
$288$		0			0
$289$	1557.77	−	2698.13i	0.317070	−	0.549181i
$290$		0			0
$291$	24.5218	+	42.4730i	0.00493984	+	0.00855605i
$292$		0			0
$293$	7625.47			1.52043			0.760213	−	0.649674i	$-0.225095\pi$
$293$	7625.47			1.52043			0.760213	+	0.649674i	$0.225095\pi$
$294$		0			0
$295$	−291.523			−0.0575361
$296$		0			0
$297$	181.115	+	313.701i	0.0353851	+	0.0612887i
$298$		0			0
$299$	−38.6267	+	66.9034i	−0.00747104	+	0.0129402i
$300$		0			0
$301$	2840.11	+	7320.97i	0.543858	+	1.40191i
$302$		0			0
$303$	−592.629	+	1026.46i	−0.112362	+	0.194616i
$304$		0			0
$305$	−81.4390	−	141.057i	−0.0152891	−	0.0264816i
$306$		0			0
$307$	5138.09			0.955199			0.477600	−	0.878578i	$-0.341507\pi$
$307$	5138.09			0.955199			0.477600	+	0.878578i	$0.341507\pi$
$308$		0			0
$309$	77.3080			0.0142327
$310$		0			0
$311$	−2640.95	−	4574.26i	−0.481526	−	0.834027i	0.518250	−	0.855229i	$-0.326584\pi$
$311$	−2640.95	−	4574.26i	−0.481526	−	0.834027i	−0.999775	+	0.0212025i	$0.993251\pi$
$312$		0			0
$313$	−4103.85	+	7108.07i	−0.741097	+	1.28362i	0.210900	+	0.977508i	$0.432361\pi$
$313$	−4103.85	+	7108.07i	−0.741097	+	1.28362i	−0.951996	+	0.306109i	$0.900973\pi$
$314$		0			0
$315$	−240.267	+	298.867i	−0.0429762	+	0.0534580i
$316$		0			0
$317$	−697.788	+	1208.60i	−0.123633	+	0.214139i	−0.921198	−	0.389095i	$-0.872788\pi$
$317$	−697.788	+	1208.60i	−0.123633	+	0.214139i	0.797565	+	0.603233i	$0.206121\pi$
$318$		0			0
$319$	−873.822	−	1513.50i	−0.153369	−	0.265642i
$320$		0			0
$321$	301.187			0.0523694
$322$		0			0
$323$	−573.676			−0.0988241
$324$		0			0
$325$	181.781	+	314.853i	0.0310258	+	0.0537382i
$326$		0			0
$327$	−274.647	+	475.702i	−0.0464465	+	0.0804477i
$328$		0			0
$329$	1929.05	+	298.516i	0.323257	+	0.0500235i
$330$		0			0
$331$	−4567.17	+	7910.58i	−0.758413	+	1.31361i	0.185247	+	0.982692i	$0.440691\pi$
$331$	−4567.17	+	7910.58i	−0.758413	+	1.31361i	−0.943660	+	0.330917i	$0.892642\pi$
$332$		0			0
$333$	−2610.16	−	4520.93i	−0.429538	−	0.743981i
$334$		0			0
$335$	−391.644			−0.0638741
$336$		0			0
$337$	−2501.41			−0.404333			−0.202166	−	0.979351i	$-0.564798\pi$
$337$	−2501.41			−0.404333			−0.202166	+	0.979351i	$0.564798\pi$
$338$		0			0
$339$	−106.390	−	184.273i	−0.0170452	−	0.0295231i
$340$		0			0
$341$	1039.34	−	1800.20i	0.165055	−	0.285883i
$342$		0			0
$343$	−5690.46	−	2823.52i	−0.895790	−	0.444478i
$344$		0			0
$345$	−6.31227	+	10.9332i	−0.000985047	+	0.00170615i
$346$		0			0
$347$	−2747.24	−	4758.36i	−0.425013	−	0.736144i	0.571409	−	0.820666i	$-0.306397\pi$
$347$	−2747.24	−	4758.36i	−0.425013	−	0.736144i	−0.996422	+	0.0845217i	$0.973064\pi$
$348$		0			0
$349$	4763.86			0.730670			0.365335	−	0.930876i	$-0.380954\pi$
$349$	4763.86			0.730670			0.365335	+	0.930876i	$0.380954\pi$
$350$		0			0
$351$	−96.2424			−0.0146354
$352$		0			0
$353$	−5.04275	−	8.73430i	−0.000760335	−	0.00131694i	0.865645	−	0.500658i	$-0.166909\pi$
$353$	−5.04275	−	8.73430i	−0.000760335	−	0.00131694i	−0.866405	+	0.499341i	$0.833575\pi$
$354$		0			0
$355$	228.893	−	396.454i	0.0342207	−	0.0592721i
$356$		0			0
$357$	476.520	+	73.7406i	0.0706446	+	0.0109321i
$358$		0			0
$359$	3220.84	−	5578.67i	0.473509	−	0.820141i	−0.526031	−	0.850465i	$-0.676321\pi$
$359$	3220.84	−	5578.67i	0.473509	−	0.820141i	0.999540	+	0.0303239i	$0.00965386\pi$
$360$		0			0
$361$	3337.95	+	5781.51i	0.486653	+	0.842908i
$362$		0			0
$363$	74.3066			0.0107440
$364$		0			0
$365$	−187.379			−0.0268708
$366$		0			0
$367$	−1696.89	−	2939.10i	−0.241354	−	0.418037i	0.719746	−	0.694237i	$-0.244258\pi$
$367$	−1696.89	−	2939.10i	−0.241354	−	0.418037i	−0.961100	+	0.276200i	$0.910925\pi$
$368$		0			0
$369$	4928.01	−	8535.56i	0.695235	−	1.20418i
$370$		0			0
$371$	1891.68	−	2353.06i	0.264720	−	0.329285i
$372$		0			0
$373$	−1576.88	+	2731.24i	−0.218895	+	0.379138i	−0.954471	−	0.298305i	$-0.903579\pi$
$373$	−1576.88	+	2731.24i	−0.218895	+	0.379138i	0.735575	+	0.677443i	$0.236912\pi$
$374$		0			0
$375$	59.5566	+	103.155i	0.00820131	+	0.0142051i
$376$		0			0
$377$	464.338			0.0634340
$378$		0			0
$379$	−7645.29			−1.03618			−0.518090	−	0.855326i	$-0.673357\pi$
$379$	−7645.29			−1.03618			−0.518090	+	0.855326i	$0.673357\pi$
$380$		0			0
$381$	626.190	+	1084.59i	0.0842013	+	0.145841i
$382$		0			0
$383$	−4080.84	+	7068.23i	−0.544442	+	0.943001i	0.454200	+	0.890900i	$0.349925\pi$
$383$	−4080.84	+	7068.23i	−0.544442	+	0.943001i	−0.998642	+	0.0521013i	$0.983408\pi$
$384$		0			0
$385$	57.3051	+	147.716i	0.00758581	+	0.0195540i
$386$		0			0
$387$	5644.03	−	9775.75i	0.741349	−	1.28405i
$388$		0			0
$389$	−5887.53	−	10197.5i	−0.767377	−	1.32914i	−0.938981	−	0.343970i	$-0.888228\pi$
$389$	−5887.53	−	10197.5i	−0.767377	−	1.32914i	0.171603	−	0.985166i	$-0.445105\pi$
$390$		0			0
$391$	−1120.66			−0.144947
$392$		0			0
$393$	1322.44			0.169741
$394$		0			0
$395$	−142.256	−	246.394i	−0.0181207	−	0.0313860i
$396$		0			0
$397$	−5045.80	+	8739.58i	−0.637888	+	1.10485i	0.348008	+	0.937492i	$0.386858\pi$
$397$	−5045.80	+	8739.58i	−0.637888	+	1.10485i	−0.985895	+	0.167363i	$0.946475\pi$
$398$		0			0
$399$	55.6607	+	143.477i	0.00698375	+	0.0180021i
$400$		0			0
$401$	−4345.00	+	7525.76i	−0.541095	+	0.937203i	0.457747	+	0.889082i	$0.348657\pi$
$401$	−4345.00	+	7525.76i	−0.541095	+	0.937203i	−0.998842	+	0.0481207i	$0.984677\pi$
$402$		0			0
$403$	276.147	+	478.301i	0.0341337	+	0.0591213i
$404$		0			0
$405$	543.320			0.0666612
$406$		0			0
$407$	−2156.93			−0.262690
$408$		0			0
$409$	−6752.35	−	11695.4i	−0.816337	−	1.41394i	−0.908364	−	0.418181i	$-0.862668\pi$
$409$	−6752.35	−	11695.4i	−0.816337	−	1.41394i	0.0920263	−	0.995757i	$-0.470666\pi$
$410$		0			0
$411$	−127.215	+	220.343i	−0.0152678	+	0.0264446i
$412$		0			0
$413$	−4349.63	+	5410.49i	−0.518235	+	0.644632i
$414$		0			0
$415$	−383.061	+	663.482i	−0.0453102	+	0.0784796i
$416$		0			0
$417$	296.564	+	513.665i	0.0348269	+	0.0603220i
$418$		0			0
$419$	12360.1			1.44112			0.720559	−	0.693394i	$-0.243885\pi$
$419$	12360.1			1.44112			0.720559	+	0.693394i	$0.243885\pi$
$420$		0			0
$421$	−2082.48			−0.241078			−0.120539	−	0.992709i	$-0.538462\pi$
$421$	−2082.48			−0.241078			−0.120539	+	0.992709i	$0.538462\pi$
$422$		0			0
$423$	−1403.00	−	2430.07i	−0.161268	−	0.279325i
$424$		0			0
$425$	−2636.96	+	4567.36i	−0.300968	+	0.521292i
$426$		0			0
$427$	−3833.02	−	593.153i	−0.434409	−	0.0672241i
$428$		0			0
$429$	−9.87140	+	17.0978i	−0.00111095	+	0.00192421i
$430$		0			0
$431$	−6230.17	−	10791.0i	−0.696280	−	1.20599i	−0.969747	−	0.244111i	$-0.921504\pi$
$431$	−6230.17	−	10791.0i	−0.696280	−	1.20599i	0.273468	−	0.961881i	$-0.411829\pi$
$432$		0			0
$433$	−9716.57			−1.07840			−0.539201	−	0.842177i	$-0.681274\pi$
$433$	−9716.57			−1.07840			−0.539201	+	0.842177i	$0.681274\pi$
$434$		0			0
$435$	75.8808			0.00836370
$436$		0			0
$437$	−178.834	−	309.749i	−0.0195762	−	0.0339069i
$438$		0			0
$439$	−7512.57	+	13012.1i	−0.816755	+	1.41466i	0.0913066	+	0.995823i	$0.470896\pi$
$439$	−7512.57	+	13012.1i	−0.816755	+	1.41466i	−0.908061	+	0.418838i	$0.862438\pi$
$440$		0			0
$441$	1961.93	+	8918.40i	0.211849	+	0.963006i
$442$		0			0
$443$	7254.42	−	12565.0i	0.778032	−	1.34759i	−0.155043	−	0.987908i	$-0.549552\pi$
$443$	7254.42	−	12565.0i	0.778032	−	1.34759i	0.933075	−	0.359683i	$-0.117115\pi$
$444$		0			0
$445$	−14.5187	−	25.1472i	−0.00154664	−	0.00267886i
$446$		0			0
$447$	−1235.70			−0.130753
$448$		0			0
$449$	−1320.31			−0.138774			−0.0693869	−	0.997590i	$-0.522104\pi$
$449$	−1320.31			−0.138774			−0.0693869	+	0.997590i	$0.522104\pi$
$450$		0			0
$451$	−2036.15	−	3526.71i	−0.212591	−	0.368218i
$452$		0			0
$453$	−524.027	+	907.642i	−0.0543509	+	0.0941385i
$454$		0			0
$455$	−41.6018	−	6.43781i	−0.00428643	−	0.000663317i
$456$		0			0
$457$	2948.18	−	5106.40i	0.301773	−	0.522686i	−0.674765	−	0.738033i	$-0.735755\pi$
$457$	2948.18	−	5106.40i	0.301773	−	0.522686i	0.976538	+	0.215347i	$0.0690883\pi$
$458$		0			0
$459$	−698.060	−	1209.08i	−0.0709862	−	0.122952i
$460$		0			0
$461$	−2076.99			−0.209837			−0.104919	−	0.994481i	$-0.533458\pi$
$461$	−2076.99			−0.209837			−0.104919	+	0.994481i	$0.533458\pi$
$462$		0			0
$463$	−13195.4			−1.32450			−0.662249	−	0.749284i	$-0.730398\pi$
$463$	−13195.4			−1.32450			−0.662249	+	0.749284i	$0.730398\pi$
$464$		0			0
$465$	45.1272	+	78.1626i	0.00450048	+	0.00779506i
$466$		0			0
$467$	2433.80	−	4215.46i	0.241162	−	0.417705i	−0.719883	−	0.694095i	$-0.755805\pi$
$467$	2433.80	−	4215.46i	0.241162	−	0.417705i	0.961046	+	0.276390i	$0.0891381\pi$
$468$		0			0
$469$	−5843.46	+	7268.67i	−0.575322	+	0.715642i
$470$		0			0
$471$	−847.284	+	1467.54i	−0.0828891	+	0.143568i
$472$		0			0
$473$	−2331.99	−	4039.13i	−0.226692	−	0.392641i
$474$		0			0
$475$	−1683.21			−0.162592
$476$		0			0
$477$	−4340.04			−0.416597
$478$		0			0
$479$	−1491.85	−	2583.97i	−0.142306	−	0.246481i	0.786059	−	0.618152i	$-0.212118\pi$
$479$	−1491.85	−	2583.97i	−0.142306	−	0.246481i	−0.928365	+	0.371671i	$0.878785\pi$
$480$		0			0
$481$	286.541	−	496.304i	0.0271625	−	0.0470468i
$482$		0			0
$483$	108.732	+	280.278i	0.0102432	+	0.0264039i
$484$		0			0
$485$	31.0556	−	53.7899i	0.00290755	−	0.00503603i
$486$		0			0
$487$	−6612.45	−	11453.1i	−0.615274	−	1.06569i	−0.990336	−	0.138687i	$-0.955712\pi$
$487$	−6612.45	−	11453.1i	−0.615274	−	1.06569i	0.375062	−	0.927000i	$-0.377621\pi$
$488$		0			0
$489$	−384.921			−0.0355966
$490$		0			0
$491$	13182.9			1.21168			0.605841	−	0.795586i	$-0.292837\pi$
$491$	13182.9			1.21168			0.605841	+	0.795586i	$0.292837\pi$
$492$		0			0
$493$	3367.91	+	5833.40i	0.307674	+	0.532907i
$494$		0			0
$495$	113.880	−	197.246i	0.0103405	−	0.0179102i
$496$		0			0
$497$	−3942.78	−	10163.3i	−0.355851	−	0.917279i
$498$		0			0
$499$	808.066	−	1399.61i	0.0724930	−	0.125562i	−0.827500	−	0.561465i	$-0.810238\pi$
$499$	808.066	−	1399.61i	0.0724930	−	0.125562i	0.899993	+	0.435904i	$0.143571\pi$
$500$		0			0
$501$	−599.390	−	1038.17i	−0.0534506	−	0.0925792i
$502$		0			0
$503$	−7369.76			−0.653283			−0.326642	−	0.945148i	$-0.605917\pi$
$503$	−7369.76			−0.653283			−0.326642	+	0.945148i	$0.605917\pi$
$504$		0			0
$505$	1501.07			0.132271
$506$		0			0
$507$	671.971	+	1163.89i	0.0588624	+	0.101953i
$508$		0			0
$509$	6434.20	−	11144.4i	0.560296	−	0.970461i	−0.437174	−	0.899377i	$-0.644021\pi$
$509$	6434.20	−	11144.4i	0.560296	−	0.970461i	0.997470	−	0.0710845i	$-0.0226460\pi$
$510$		0			0
$511$	−2795.75	+	3477.63i	−0.242029	+	0.301059i
$512$		0			0
$513$	222.791	−	385.886i	0.0191744	−	0.0332110i
$514$		0			0
$515$	−48.9533	−	84.7897i	−0.00418862	−	0.00725491i
$516$		0			0
$517$	−1159.38			−0.0986259
$518$		0			0
$519$	202.769			0.0171494
$520$		0			0
$521$	10943.1	+	18954.0i	0.920201	+	1.59383i	0.799103	+	0.601194i	$0.205308\pi$
$521$	10943.1	+	18954.0i	0.920201	+	1.59383i	0.121098	+	0.992641i	$0.461359\pi$
$522$		0			0
$523$	5529.04	−	9576.58i	0.462272	−	0.800678i	−0.536802	−	0.843708i	$-0.680368\pi$
$523$	5529.04	−	9576.58i	0.462272	−	0.800678i	0.999074	+	0.0430303i	$0.0137012\pi$
$524$		0			0
$525$	1398.15	+	216.361i	0.116229	+	0.0179862i
$526$		0			0
$527$	−4005.87	+	6938.38i	−0.331117	+	0.573511i
$528$		0			0
$529$	5734.15	+	9931.84i	0.471287	+	0.816294i
$530$		0			0
$531$	9979.26			0.815561
$532$		0			0
$533$	1081.98			0.0879285
$534$		0			0
$535$	−190.719	−	330.335i	−0.0154121	−	0.0266946i
$536$		0			0
$537$	−712.299	+	1233.74i	−0.0572402	+	0.0991429i
$538$		0			0
$539$	3596.52	+	1140.42i	0.287408	+	0.0911343i
$540$		0			0
$541$	3696.83	−	6403.09i	0.293788	−	0.508855i	−0.680915	−	0.732363i	$-0.738418\pi$
$541$	3696.83	−	6403.09i	0.293788	−	0.508855i	0.974702	+	0.223508i	$0.0717508\pi$
$542$		0			0
$543$	−633.805	−	1097.78i	−0.0500906	−	0.0867594i
$544$		0			0
$545$	695.653			0.0546762
$546$		0			0
$547$	−7218.17			−0.564217			−0.282108	−	0.959383i	$-0.591034\pi$
$547$	−7218.17			−0.564217			−0.282108	+	0.959383i	$0.591034\pi$
$548$		0			0
$549$	2787.77	+	4828.57i	0.216720	+	0.375370i
$550$		0			0
$551$	−1074.90	+	1861.77i	−0.0831072	+	0.143946i
$552$		0			0
$553$	−6695.43	−	1036.11i	−0.514862	−	0.0796740i
$554$		0			0
$555$	46.8257	−	81.1045i	0.00358134	−	0.00620306i
$556$		0			0
$557$	−1890.80	−	3274.97i	−0.143835	−	0.249129i	0.785103	−	0.619365i	$-0.212610\pi$
$557$	−1890.80	−	3274.97i	−0.143835	−	0.249129i	−0.928938	+	0.370236i	$0.879277\pi$
$558$		0			0
$559$	1239.19			0.0937607
$560$		0			0
$561$	−286.395			−0.0215537
$562$		0			0
$563$	−8866.86	−	15357.9i	−0.663754	−	1.14966i	−0.979621	−	0.200853i	$-0.935629\pi$
$563$	−8866.86	−	15357.9i	−0.663754	−	1.14966i	0.315867	−	0.948803i	$-0.397705\pi$
$564$		0			0
$565$	−134.738	+	233.372i	−0.0100327	+	0.0173771i
$566$		0			0
$567$	8106.51	−	10083.7i	0.600426	−	0.746869i
$568$		0			0
$569$	814.217	−	1410.26i	0.0599890	−	0.103904i	−0.834471	−	0.551052i	$-0.814227\pi$
$569$	814.217	−	1410.26i	0.0599890	−	0.103904i	0.894460	+	0.447148i	$0.147560\pi$
$570$		0			0
$571$	3126.26	+	5414.83i	0.229124	+	0.396854i	0.957549	−	0.288272i	$-0.0930806\pi$
$571$	3126.26	+	5414.83i	0.229124	+	0.396854i	−0.728425	+	0.685126i	$0.759747\pi$
$572$		0			0
$573$	853.392			0.0622181
$574$		0			0
$575$	−3288.11			−0.238476
$576$		0			0
$577$	8488.32	+	14702.2i	0.612432	+	1.06076i	0.990829	+	0.135120i	$0.0431420\pi$
$577$	8488.32	+	14702.2i	0.612432	+	1.06076i	−0.378397	+	0.925643i	$0.623525\pi$
$578$		0			0
$579$	−954.845	+	1653.84i	−0.0685354	+	0.118707i
$580$		0			0
$581$	6598.41	+	17008.8i	0.471167	+	1.21453i
$582$		0			0
$583$	−896.606	+	1552.97i	−0.0636941	+	0.110321i
$584$		0			0
$585$	30.2572	+	52.4071i	0.00213843	+	0.00370387i
$586$		0			0
$587$	6987.50			0.491320			0.245660	−	0.969356i	$-0.420995\pi$
$587$	6987.50			0.491320			0.245660	+	0.969356i	$0.420995\pi$
$588$		0			0
$589$	−2557.01			−0.178879
$590$		0			0
$591$	146.890	+	254.420i	0.0102237	+	0.0177080i
$592$		0			0
$593$	−8175.55	+	14160.5i	−0.566154	+	0.980608i	0.430787	+	0.902454i	$0.358236\pi$
$593$	−8175.55	+	14160.5i	−0.566154	+	0.980608i	−0.996941	+	0.0781545i	$0.975097\pi$
$594$		0			0
$595$	−220.867	−	569.331i	−0.0152179	−	0.0392274i
$596$		0			0
$597$	1278.76	−	2214.88i	0.0876654	−	0.151841i
$598$		0			0
$599$	8466.18	+	14663.9i	0.577494	+	1.00025i	0.995766	+	0.0919269i	$0.0293026\pi$
$599$	8466.18	+	14663.9i	0.577494	+	1.00025i	−0.418272	+	0.908322i	$0.637364\pi$
$600$		0			0
$601$	−6651.59			−0.451454			−0.225727	−	0.974191i	$-0.572476\pi$
$601$	−6651.59			−0.451454			−0.225727	+	0.974191i	$0.572476\pi$
$602$		0			0
$603$	13406.5			0.905401
$604$		0			0
$605$	−47.0528	−	81.4978i	−0.00316193	−	0.00547662i
$606$		0			0
$607$	5761.25	−	9978.77i	0.385242	−	0.667258i	−0.606561	−	0.795037i	$-0.707451\pi$
$607$	5761.25	−	9978.77i	0.385242	−	0.667258i	0.991803	+	0.127779i	$0.0407847\pi$
$608$		0			0
$609$	1132.17	−	1408.30i	0.0753329	−	0.0937065i
$610$		0			0
$611$	154.020	−	266.771i	0.0101980	−	0.0176635i
$612$		0			0
$613$	−2445.04	−	4234.94i	−0.161100	−	0.279034i	0.774163	−	0.632986i	$-0.218171\pi$
$613$	−2445.04	−	4234.94i	−0.161100	−	0.279034i	−0.935263	+	0.353952i	$0.884838\pi$
$614$		0			0
$615$	176.815			0.0115933
$616$		0			0
$617$	18700.2			1.22016			0.610082	−	0.792338i	$-0.291137\pi$
$617$	18700.2			1.22016			0.610082	+	0.792338i	$0.291137\pi$
$618$		0			0
$619$	−10163.7	−	17604.0i	−0.659955	−	1.14308i	−0.980627	−	0.195886i	$-0.937242\pi$
$619$	−10163.7	−	17604.0i	−0.659955	−	1.14308i	0.320671	−	0.947191i	$-0.396092\pi$
$620$		0			0
$621$	435.217	−	753.818i	0.0281234	−	0.0487112i
$622$		0			0
$623$	−683.340	−	105.746i	−0.0439446	−	0.00680034i
$624$		0			0
$625$	−7699.27	+	13335.5i	−0.492753	+	0.853474i
$626$		0			0
$627$	−45.7026	−	79.1592i	−0.00291098	−	0.00504197i
$628$		0			0
$629$	8313.30			0.526984
$630$		0			0
$631$	−5658.00			−0.356959			−0.178480	−	0.983944i	$-0.557118\pi$
$631$	−5658.00			−0.356959			−0.178480	+	0.983944i	$0.557118\pi$
$632$		0			0
$633$	−323.592	−	560.478i	−0.0203185	−	0.0351927i
$634$		0			0
$635$	793.039	−	1373.58i	0.0495603	−	0.0858409i
$636$		0			0
$637$	−740.195	+	676.050i	−0.0460402	+	0.0420503i
$638$		0			0
$639$	−7835.32	+	13571.2i	−0.485071	+	0.840168i
$640$		0			0
$641$	4061.92	+	7035.45i	0.250291	+	0.433516i	0.963606	−	0.267327i	$-0.0861405\pi$
$641$	4061.92	+	7035.45i	0.250291	+	0.433516i	−0.713315	+	0.700843i	$0.752807\pi$
$642$		0			0
$643$	21274.9			1.30482			0.652411	−	0.757865i	$-0.273758\pi$
$643$	21274.9			1.30482			0.652411	+	0.757865i	$0.273758\pi$
$644$		0			0
$645$	202.505			0.0123622
$646$		0			0
$647$	−1545.18	−	2676.34i	−0.0938909	−	0.162624i	0.815254	−	0.579103i	$-0.196597\pi$
$647$	−1545.18	−	2676.34i	−0.0938909	−	0.162624i	−0.909145	+	0.416479i	$0.863264\pi$
$648$		0			0
$649$	2061.61	−	3570.81i	0.124692	−	0.215973i
$650$		0			0
$651$	2123.96	+	328.679i	0.127872	+	0.0197880i
$652$		0			0
$653$	2826.85	−	4896.25i	0.169408	−	0.293423i	−0.768804	−	0.639484i	$-0.779148\pi$
$653$	2826.85	−	4896.25i	0.169408	−	0.293423i	0.938212	+	0.346062i	$0.112481\pi$
$654$		0			0
$655$	−837.399	−	1450.42i	−0.0499540	−	0.0865229i
$656$		0			0
$657$	6414.24			0.380888
$658$		0			0
$659$	4493.32			0.265607			0.132803	−	0.991142i	$-0.457602\pi$
$659$	4493.32			0.265607			0.132803	+	0.991142i	$0.457602\pi$
$660$		0			0
$661$	14381.9	+	24910.2i	0.846282	+	1.46580i	0.884503	+	0.466535i	$0.154498\pi$
$661$	14381.9	+	24910.2i	0.846282	+	1.46580i	−0.0382207	+	0.999269i	$0.512169\pi$
$662$		0			0
$663$	38.0467	−	65.8988i	0.00222867	−	0.00386018i
$664$		0			0
$665$	122.116	−	151.900i	0.00712101	−	0.00885782i
$666$		0			0
$667$	−2099.78	+	3636.93i	−0.121895	+	0.211128i
$668$		0			0
$669$	−328.278	−	568.595i	−0.0189716	−	0.0328597i
$670$		0			0
$671$	2303.70			0.132538
$672$		0			0
$673$	23237.8			1.33098			0.665492	−	0.746405i	$-0.268222\pi$
$673$	23237.8			1.33098			0.665492	+	0.746405i	$0.268222\pi$
$674$		0			0
$675$	−2048.17	−	3547.53i	−0.116791	−	0.202288i
$676$		0			0
$677$	−4622.69	+	8006.73i	−0.262429	+	0.454540i	−0.966887	−	0.255206i	$-0.917857\pi$
$677$	−4622.69	+	8006.73i	−0.262429	+	0.454540i	0.704458	+	0.709746i	$0.251190\pi$
$678$		0			0
$679$	−534.947	−	1378.94i	−0.0302347	−	0.0779362i
$680$		0			0
$681$	−446.291	+	772.998i	−0.0251129	+	0.0434968i
$682$		0			0
$683$	5013.31	+	8683.30i	0.280862	+	0.486467i	0.971597	−	0.236640i	$-0.0760463\pi$
$683$	5013.31	+	8683.30i	0.280862	+	0.486467i	−0.690735	+	0.723108i	$0.742713\pi$
$684$		0			0
$685$	322.223			0.0179730
$686$		0			0
$687$	3564.34			0.197945
$688$		0			0
$689$	−238.223	−	412.614i	−0.0131721	−	0.0228147i
$690$		0			0
$691$	1120.34	−	1940.48i	0.0616783	−	0.106830i	−0.833537	−	0.552463i	$-0.813688\pi$
$691$	1120.34	−	1940.48i	0.0616783	−	0.106830i	0.895216	+	0.445633i	$0.147021\pi$
$692$		0			0
$693$	−1961.63	−	5056.52i	−0.107527	−	0.277174i
$694$		0			0
$695$	375.584	−	650.531i	0.0204989	−	0.0355051i
$696$		0			0
$697$	7847.79	+	13592.8i	0.426479	+	0.738684i
$698$		0			0
$699$	−3621.89			−0.195983
$700$		0			0
$701$	−2362.56			−0.127293			−0.0636467	−	0.997972i	$-0.520273\pi$
$701$	−2362.56			−0.127293			−0.0636467	+	0.997972i	$0.520273\pi$
$702$		0			0
$703$	1326.63	+	2297.78i	0.0711730	+	0.123275i
$704$		0			0
$705$	25.1696	−	43.5950i	0.00134460	−	0.00232891i
$706$		0			0
$707$	22396.5	−	27858.9i	1.19138	−	1.48196i
$708$		0			0
$709$	3202.58	−	5547.03i	0.169641	−	0.293827i	−0.768653	−	0.639666i	$-0.779073\pi$
$709$	3202.58	−	5547.03i	0.169641	−	0.293827i	0.938294	+	0.345840i	$0.112406\pi$
$710$		0			0
$711$	4869.62	+	8434.44i	0.256857	+	0.444889i
$712$		0			0
$713$	−4995.05			−0.262365
$714$		0			0
$715$	25.0033			0.00130779
$716$		0			0
$717$	56.3015	+	97.5171i	0.00293252	+	0.00507928i
$718$		0			0
$719$	4851.51	−	8403.07i	0.251642	−	0.435857i	−0.712336	−	0.701839i	$-0.752363\pi$
$719$	4851.51	−	8403.07i	0.251642	−	0.435857i	0.963978	+	0.265981i	$0.0856960\pi$
$720$		0			0
$721$	−2304.04	−	356.547i	−0.119011	−	0.0184168i
$722$		0			0
$723$	270.864	−	469.150i	0.0139330	−	0.0241326i
$724$		0			0
$725$	9881.74	+	17115.7i	0.506205	+	0.876773i
$726$		0			0
$727$	−23233.2			−1.18524			−0.592621	−	0.805481i	$-0.701907\pi$
$727$	−23233.2			−1.18524			−0.592621	+	0.805481i	$0.701907\pi$
$728$		0			0
$729$	−18052.6			−0.917167
$730$		0			0
$731$	8988.04	+	15567.7i	0.454767	+	0.787680i
$732$		0			0
$733$	1072.05	−	1856.85i	0.0540206	−	0.0935664i	−0.837751	−	0.546053i	$-0.816130\pi$
$733$	1072.05	−	1856.85i	0.0540206	−	0.0935664i	0.891771	+	0.452487i	$0.149463\pi$
$734$		0			0
$735$	−120.961	+	110.478i	−0.00607034	+	0.00554428i
$736$		0			0
$737$	2769.65	−	4797.17i	0.138428	−	0.239764i
$738$		0			0
$739$	−5149.39	−	8919.01i	−0.256324	−	0.443966i	0.708930	−	0.705279i	$-0.249178\pi$
$739$	−5149.39	−	8919.01i	−0.256324	−	0.443966i	−0.965254	+	0.261312i	$0.915845\pi$
$740$		0			0
$741$	24.2858			0.00120400
$742$		0			0
$743$	−7196.07			−0.355314			−0.177657	−	0.984092i	$-0.556852\pi$
$743$	−7196.07			−0.355314			−0.177657	+	0.984092i	$0.556852\pi$
$744$		0			0
$745$	782.479	+	1355.29i	0.0384803	+	0.0666498i
$746$		0			0
$747$	13112.7	−	22711.9i	0.642263	−	1.11243i
$748$		0			0
$749$	−8976.39	−	1389.08i	−0.437904	−	0.0677649i
$750$		0			0
$751$	−13040.4	+	22586.7i	−0.633624	+	1.09747i	0.353180	+	0.935555i	$0.385100\pi$
$751$	−13040.4	+	22586.7i	−0.633624	+	1.09747i	−0.986805	+	0.161915i	$0.948233\pi$
$752$		0			0
$753$	−1618.28	−	2802.94i	−0.0783178	−	0.135650i
$754$		0			0
$755$	1327.31			0.0639811
$756$		0			0
$757$	11607.4			0.557302			0.278651	−	0.960392i	$-0.410113\pi$
$757$	11607.4			0.557302			0.278651	+	0.960392i	$0.410113\pi$
$758$		0			0
$759$	−89.2788	−	154.635i	−0.00426958	−	0.00739514i
$760$		0			0
$761$	9518.76	−	16487.0i	0.453423	−	0.785351i	−0.545173	−	0.838323i	$-0.683536\pi$
$761$	9518.76	−	16487.0i	0.453423	−	0.785351i	0.998596	+	0.0529723i	$0.0168695\pi$
$762$		0			0
$763$	10379.4	−	12910.9i	0.492475	−	0.612589i
$764$		0			0
$765$	−438.920	+	760.232i	−0.0207441	+	0.0359297i
$766$		0			0
$767$	547.757	+	948.742i	0.0257866	+	0.0446638i
$768$		0			0
$769$	6598.66			0.309433			0.154716	−	0.987959i	$-0.450554\pi$
$769$	6598.66			0.309433			0.154716	+	0.987959i	$0.450554\pi$
$770$		0			0
$771$	−3256.64			−0.152120
$772$		0			0
$773$	−9933.59	−	17205.5i	−0.462207	−	0.800567i	0.536863	−	0.843669i	$-0.319609\pi$
$773$	−9933.59	−	17205.5i	−0.462207	−	0.800567i	−0.999071	+	0.0431025i	$0.986276\pi$
$774$		0			0
$775$	−11753.6	+	20357.8i	−0.544775	+	0.943578i
$776$		0			0
$777$	−806.594	−	2079.16i	−0.0372412	−	0.0959969i
$778$		0			0
$779$	−2504.68	+	4338.23i	−0.115198	+	0.199529i
$780$		0			0
$781$	3237.39	+	5607.32i	0.148326	+	0.256909i
$782$		0			0
$783$	−5231.81			−0.238786
$784$		0			0
$785$	2146.08			0.0975759
$786$		0			0
$787$	−10806.5	−	18717.4i	−0.489466	−	0.847779i	0.510461	−	0.859901i	$-0.329475\pi$
$787$	−10806.5	−	18717.4i	−0.489466	−	0.847779i	−0.999927	+	0.0121217i	$0.996141\pi$
$788$		0			0
$789$	1350.17	−	2338.56i	0.0609219	−	0.105520i
$790$		0			0
$791$	2320.92	+	5982.64i	0.104326	+	0.268923i
$792$		0			0
$793$	−306.039	+	530.075i	−0.0137046	+	0.0237371i
$794$		0			0
$795$	−38.9297	−	67.4282i	−0.00173672	−	0.00300809i
$796$		0			0
$797$	−34265.2			−1.52288			−0.761441	−	0.648234i	$-0.775508\pi$
$797$	−34265.2			−1.52288			−0.761441	+	0.648234i	$0.775508\pi$
$798$		0			0
$799$	4468.53			0.197854
$800$		0			0
$801$	496.997	+	860.824i	0.0219233	+	0.0379722i
$802$		0			0
$803$	1325.11	−	2295.16i	0.0582344	−	0.100865i
$804$		0			0
$805$	238.551	−	296.734i	0.0104445	−	0.0129919i
$806$		0			0
$807$	935.324	−	1620.03i	0.0407992	−	0.0706663i
$808$		0			0
$809$	−6359.67	−	11015.3i	−0.276383	−	0.478710i	0.694100	−	0.719879i	$-0.255803\pi$
$809$	−6359.67	−	11015.3i	−0.276383	−	0.478710i	−0.970483	+	0.241169i	$0.922469\pi$
$810$		0			0
$811$	−24550.0			−1.06297			−0.531483	−	0.847069i	$-0.678365\pi$
$811$	−24550.0			−1.06297			−0.531483	+	0.847069i	$0.678365\pi$
$812$		0			0
$813$	3411.40			0.147163
$814$		0			0
$815$	243.741	+	422.173i	0.0104759	+	0.0181449i
$816$		0			0
$817$	−2868.60	+	4968.56i	−0.122839	+	0.212764i
$818$		0			0
$819$	1424.09	+	220.376i	0.0607591	+	0.00940237i
$820$		0			0
$821$	−6241.28	+	10810.2i	−0.265313	+	0.459536i	−0.967646	−	0.252313i	$-0.918809\pi$
$821$	−6241.28	+	10810.2i	−0.265313	+	0.459536i	0.702332	+	0.711849i	$0.252142\pi$
$822$		0			0
$823$	17471.3	+	30261.2i	0.739990	+	1.28170i	0.952499	+	0.304541i	$0.0985029\pi$
$823$	17471.3	+	30261.2i	0.739990	+	1.28170i	−0.212510	+	0.977159i	$0.568164\pi$
$824$		0			0
$825$	−840.307			−0.0354615
$826$		0			0
$827$	−16671.7			−0.701007			−0.350503	−	0.936561i	$-0.613989\pi$
$827$	−16671.7			−0.701007			−0.350503	+	0.936561i	$0.613989\pi$
$828$		0			0
$829$	−1201.84	−	2081.66i	−0.0503520	−	0.0872122i	0.839751	−	0.542972i	$-0.182701\pi$
$829$	−1201.84	−	2081.66i	−0.0503520	−	0.0872122i	−0.890103	+	0.455760i	$0.849368\pi$
$830$		0			0
$831$	−1636.91	+	2835.20i	−0.0683317	+	0.118354i
$832$		0			0
$833$	−13861.8	−	4395.45i	−0.576572	−	0.182825i
$834$		0			0
$835$	−759.097	+	1314.79i	−0.0314606	+	0.0544914i
$836$		0			0
$837$	−3111.42	−	5389.13i	−0.128490	−	0.222552i
$838$		0			0
$839$	−25451.3			−1.04729			−0.523646	−	0.851936i	$-0.675428\pi$
$839$	−25451.3			−1.04729			−0.523646	+	0.851936i	$0.675428\pi$
$840$		0			0
$841$	852.803			0.0349667
$842$		0			0
$843$	895.851	+	1551.66i	0.0366011	+	0.0633950i
$844$		0			0
$845$	851.017	−	1474.00i	0.0346460	−	0.0600086i
$846$		0			0
$847$	−2214.59	−	342.704i	−0.0898398	−	0.0139025i
$848$		0			0
$849$	−324.966	+	562.858i	−0.0131364	+	0.0227529i
$850$		0			0
$851$	2591.53	+	4488.66i	0.104391	+	0.180810i
$852$		0			0
$853$	−360.609			−0.0144748			−0.00723741	−	0.999974i	$-0.502304\pi$
$853$	−360.609			−0.0144748			−0.00723741	+	0.999974i	$0.502304\pi$
$854$		0			0
$855$	−280.169			−0.0112065
$856$		0			0
$857$	−5909.27	−	10235.2i	−0.235539	−	0.407966i	0.723890	−	0.689915i	$-0.242352\pi$
$857$	−5909.27	−	10235.2i	−0.235539	−	0.407966i	−0.959429	+	0.281950i	$0.909019\pi$
$858$		0			0
$859$	−2655.32	+	4599.14i	−0.105469	+	0.182678i	−0.913930	−	0.405872i	$-0.866968\pi$
$859$	−2655.32	+	4599.14i	−0.105469	+	0.182678i	0.808461	+	0.588550i	$0.200301\pi$
$860$		0			0
$861$	2638.13	−	3281.57i	0.104422	−	0.129890i
$862$		0			0
$863$	−7320.55	+	12679.6i	−0.288754	+	0.500136i	−0.973513	−	0.228634i	$-0.926574\pi$
$863$	−7320.55	+	12679.6i	−0.288754	+	0.500136i	0.684759	+	0.728770i	$0.259908\pi$
$864$		0			0
$865$	−128.398	−	222.392i	−0.00504702	−	0.00874169i
$866$		0			0
$867$	−1913.26			−0.0749455
$868$		0			0
$869$	4024.05			0.157085
$870$		0			0
$871$	735.878	+	1274.58i	0.0286272	+	0.0495838i
$872$		0			0
$873$	−1063.08	+	1841.30i	−0.0412139	+	0.0713846i
$874$		0			0
$875$	−1299.24	−	3349.05i	−0.0501968	−	0.129393i
$876$		0			0
$877$	25370.5	−	43942.9i	0.976852	−	1.69196i	0.303169	−	0.952937i	$-0.401955\pi$
$877$	25370.5	−	43942.9i	0.976852	−	1.69196i	0.673683	−	0.739021i	$-0.264711\pi$
$878$		0			0
$879$	−2341.42	−	4055.45i	−0.0898452	−	0.155617i
$880$		0			0
$881$	−23328.6			−0.892122			−0.446061	−	0.895003i	$-0.647174\pi$
$881$	−23328.6			−0.892122			−0.446061	+	0.895003i	$0.647174\pi$
$882$		0			0
$883$	27284.1			1.03985			0.519923	−	0.854213i	$-0.325961\pi$
$883$	27284.1			1.03985			0.519923	+	0.854213i	$0.325961\pi$
$884$		0			0
$885$	89.5128	+	155.041i	0.00339993	+	0.00588886i
$886$		0			0
$887$	22661.1	−	39250.2i	0.857819	−	1.48579i	−0.0161863	−	0.999869i	$-0.505152\pi$
$887$	22661.1	−	39250.2i	0.857819	−	1.48579i	0.874005	−	0.485917i	$-0.161514\pi$
$888$		0			0
$889$	−13660.4	−	35212.6i	−0.515362	−	1.32845i
$890$		0			0
$891$	−3842.27	+	6655.01i	−0.144468	+	0.250226i
$892$		0			0
$893$	713.083	+	1235.10i	0.0267216	+	0.0462832i
$894$		0			0
$895$	1804.18			0.0673823
$896$		0			0
$897$	47.4416			0.00176592
$898$		0			0
$899$	15011.6	+	26000.8i	0.556913	+	0.964601i
$900$		0			0
$901$	3455.73	−	5985.50i	0.127777	−	0.221316i
$902$		0			0
$903$	3021.45	−	3758.37i	0.111348	−	0.138506i
$904$		0			0
$905$	−802.682	+	1390.29i	−0.0294829	+	0.0510660i
$906$		0			0
$907$	−7640.29	−	13233.4i	−0.279704	−	0.484462i	0.691607	−	0.722274i	$-0.256903\pi$
$907$	−7640.29	−	13233.4i	−0.279704	−	0.484462i	−0.971311	+	0.237812i	$0.923570\pi$
$908$		0			0
$909$	−51383.8			−1.87491
$910$		0			0
$911$	−34690.9			−1.26165			−0.630824	−	0.775926i	$-0.717283\pi$
$911$	−34690.9			−1.26165			−0.630824	+	0.775926i	$0.717283\pi$
$912$		0			0
$913$	−5417.90	−	9384.08i	−0.196393	−	0.340162i
$914$		0			0
$915$	−50.0120	+	86.6234i	−0.00180694	+	0.00312971i
$916$		0			0
$917$	−39413.1	−	6099.11i	−1.41934	−	0.219641i
$918$		0			0
$919$	−4162.22	+	7209.18i	−0.149401	+	0.258769i	−0.931006	−	0.365004i	$-0.881068\pi$
$919$	−4162.22	+	7209.18i	−0.149401	+	0.258769i	0.781606	+	0.623773i	$0.214401\pi$
$920$		0			0
$921$	−1577.66	−	2732.59i	−0.0564448	−	0.0977653i
$922$		0			0
$923$	−1720.31			−0.0613485
$924$		0			0
$925$	24391.9			0.867029
$926$		0			0
$927$	1675.74	+	2902.47i	0.0593728	+	0.102837i
$928$		0			0
$929$	8095.37	−	14021.6i	0.285899	−	0.495192i	−0.686927	−	0.726726i	$-0.741041\pi$
$929$	8095.37	−	14021.6i	0.285899	−	0.495192i	0.972827	+	0.231534i	$0.0743743\pi$
$930$		0			0
$931$	−997.159	−	4532.81i	−0.0351027	−	0.159567i
$932$		0			0
$933$	−1621.82	+	2809.07i	−0.0569088	+	0.0985690i
$934$		0			0
$935$	181.352	+	314.112i	0.00634316	+	0.0109867i
$936$		0			0
$937$	−43218.7			−1.50682			−0.753411	−	0.657550i	$-0.771593\pi$
$937$	−43218.7			−1.50682			−0.753411	+	0.657550i	$0.771593\pi$
$938$		0			0
$939$	5040.38			0.175172
$940$		0			0
$941$	10615.2	+	18386.0i	0.367741	+	0.636947i	0.989212	−	0.146491i	$-0.0467979\pi$
$941$	10615.2	+	18386.0i	0.367741	+	0.636947i	−0.621471	+	0.783437i	$0.713465\pi$
$942$		0			0
$943$	−4892.83	+	8474.63i	−0.168963	+	0.292653i
$944$		0			0
$945$	468.738	+	72.5364i	0.0161355	+	0.00249694i
$946$		0			0
$947$	−2135.57	+	3698.91i	−0.0732805	+	0.126926i	−0.900337	−	0.435193i	$-0.856680\pi$
$947$	−2135.57	+	3698.91i	−0.0732805	+	0.126926i	0.827057	+	0.562118i	$0.190014\pi$
$948$		0			0
$949$	352.074	+	609.811i	0.0120430	+	0.0208591i
$950$		0			0
$951$	857.029			0.0292230
$952$		0			0
$953$	7808.73			0.265425			0.132712	−	0.991155i	$-0.457631\pi$
$953$	7808.73			0.265425			0.132712	+	0.991155i	$0.457631\pi$
$954$		0			0
$955$	−540.389	−	935.982i	−0.0183106	−	0.0317148i
$956$		0			0
$957$	−536.617	+	929.449i	−0.0181258	+	0.0313948i
$958$		0			0
$959$	4807.67	−	5980.26i	0.161885	−	0.201369i
$960$		0			0
$961$	−2959.62	+	5126.21i	−0.0993461	+	0.172072i
$962$		0			0
$963$	6528.58	+	11307.8i	0.218464	+	0.378390i
$964$		0			0
$965$	2418.53			0.0806789
$966$		0			0
$967$	−42531.9			−1.41441			−0.707205	−	0.707009i	$-0.750044\pi$
$967$	−42531.9			−1.41441			−0.707205	+	0.707009i	$0.750044\pi$
$968$		0			0
$969$	176.148	+	305.098i	0.00583973	+	0.0101147i
$970$		0			0
$971$	5644.05	−	9775.78i	0.186536	−	0.323089i	−0.757557	−	0.652769i	$-0.773607\pi$
$971$	5644.05	−	9775.78i	0.186536	−	0.323089i	0.944093	+	0.329679i	$0.106941\pi$
$972$		0			0
$973$	−6469.60	−	16676.7i	−0.213161	−	0.549467i
$974$		0			0
$975$	111.632	−	193.353i	0.00366676	−	0.00635102i
$976$		0			0
$977$	−13220.8	−	22899.1i	−0.432928	−	0.749853i	0.564196	−	0.825641i	$-0.309186\pi$
$977$	−13220.8	−	22899.1i	−0.432928	−	0.749853i	−0.997124	+	0.0757877i	$0.975853\pi$
$978$		0			0
$979$	410.697			0.0134075
$980$		0			0
$981$	−23813.2			−0.775022
$982$		0			0
$983$	−7703.39	−	13342.7i	−0.249949	−	0.432925i	0.713562	−	0.700592i	$-0.247081\pi$
$983$	−7703.39	−	13342.7i	−0.249949	−	0.432925i	−0.963511	+	0.267667i	$0.913747\pi$
$984$		0			0
$985$	186.028	−	322.210i	0.00601762	−	0.0104228i
$986$		0			0
$987$	−433.557	−	1117.58i	−0.0139820	−	0.0360416i
$988$		0			0
$989$	−5603.74	+	9705.96i	−0.180170	+	0.312064i
$990$		0			0
$991$	13907.8	+	24089.0i	0.445807	+	0.772160i	0.998108	−	0.0614844i	$-0.0195834\pi$
$991$	13907.8	+	24089.0i	0.445807	+	0.772160i	−0.552301	+	0.833645i	$0.686250\pi$
$992$		0			0
$993$	5609.44			0.179265
$994$		0			0
$995$	−3238.98			−0.103198
$996$		0			0
$997$	16624.7	+	28794.8i	0.528093	+	0.914683i	0.999464	+	0.0327484i	$0.0104260\pi$
$997$	16624.7	+	28794.8i	0.528093	+	0.914683i	−0.471371	+	0.881935i	$0.656241\pi$
$998$		0			0
$999$	−3228.53	+	5591.98i	−0.102248	+	0.177099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.4.i.a.177.6	✓	20
7.2	even	3		2156.4.a.m.1.5		10
7.4	even	3	inner	308.4.i.a.221.6	yes	20
7.5	odd	6		2156.4.a.j.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.4.i.a.177.6	✓	20	1.1	even	1	trivial
308.4.i.a.221.6	yes	20	7.4	even	3	inner
2156.4.a.j.1.6		10	7.5	odd	6
2156.4.a.m.1.5		10	7.2	even	3

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	308.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.307052 - 0.531830i) q^{3} +(-0.388866 + 0.673536i) q^{5} +(6.69839 + 17.2665i) q^{7} +(13.3114 - 23.0561i) q^{9} +(-5.50000 - 9.52628i) q^{11} +2.92263 q^{13} +0.477608 q^{15} +(21.1983 + 36.7165i) q^{17} +(-6.76559 + 11.7184i) q^{19} +(7.12608 - 8.86411i) q^{21} +(-13.2164 + 22.8915i) q^{23} +(62.1976 + 107.729i) q^{25} -32.9300 q^{27} +158.877 q^{29} +(94.4858 + 163.654i) q^{31} +(-3.37757 + 5.85013i) q^{33} +(-14.2344 - 2.20274i) q^{35} +(98.0421 - 169.814i) q^{37} +(-0.897400 - 1.55434i) q^{39} +370.208 q^{41} +423.999 q^{43} +(10.3527 + 17.9315i) q^{45} +(52.6992 - 91.2777i) q^{47} +(-253.263 + 231.315i) q^{49} +(13.0180 - 22.5478i) q^{51} +(-81.5097 - 141.179i) q^{53} +8.55505 q^{55} +8.30956 q^{57} +(187.419 + 324.619i) q^{59} +(-104.713 + 181.369i) q^{61} +(487.263 + 75.4031i) q^{63} +(-1.13651 + 1.96850i) q^{65} +(251.786 + 436.106i) q^{67} +16.2325 q^{69} -588.616 q^{71} +(120.465 + 208.651i) q^{73} +(38.1958 - 66.1570i) q^{75} +(127.644 - 158.776i) q^{77} +(-182.911 + 316.812i) q^{79} +(-349.298 - 605.001i) q^{81} +985.073 q^{83} -32.9732 q^{85} +(-48.7834 - 84.4953i) q^{87} +(-18.6680 + 32.3340i) q^{89} +(19.5769 + 50.4636i) q^{91} +(58.0241 - 100.501i) q^{93} +(-5.26182 - 9.11374i) q^{95} -79.8620 q^{97} -292.852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} - 10 q^{5} - 20 q^{7} - 104 q^{9} - 110 q^{11} + 16 q^{13} + 108 q^{15} - 166 q^{17} - 342 q^{19} - 42 q^{21} + 54 q^{23} - 198 q^{25} + 612 q^{27} - 160 q^{29} - 492 q^{31} - 66 q^{33} + 310 q^{35}+ \cdots + 2288 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 - 10 * q^5 - 20 * q^7 - 104 * q^9 - 110 * q^11 + 16 * q^13 + 108 * q^15 - 166 * q^17 - 342 * q^19 - 42 * q^21 + 54 * q^23 - 198 * q^25 + 612 * q^27 - 160 * q^29 - 492 * q^31 - 66 * q^33 + 310 * q^35 - 258 * q^37 + 418 * q^39 + 1268 * q^41 - 548 * q^43 - 138 * q^45 - 312 * q^47 + 572 * q^49 + 196 * q^51 - 656 * q^53 + 220 * q^55 - 1476 * q^57 - 934 * q^59 + 228 * q^61 - 1270 * q^63 - 524 * q^65 - 478 * q^67 + 3144 * q^69 + 276 * q^71 + 364 * q^73 - 234 * q^75 - 154 * q^77 + 616 * q^79 - 4082 * q^81 - 264 * q^83 - 992 * q^85 + 2120 * q^87 - 1906 * q^89 - 94 * q^91 + 2984 * q^93 - 2322 * q^95 + 2700 * q^97 + 2288 * q^99

Introduction

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