LMFDB - Embedded newform 308.4.i.a.221.4

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			221.4
Root			$-1.14233 - 1.97858i$ of defining polynomial
Character	$\chi$	$=$	308.221
Dual form			308.4.i.a.177.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.64233 + 2.84460i) q^{3} +(-10.0843 - 17.4664i) q^{5} +(15.8994 + 9.49786i) q^{7} +(8.10549 + 14.0391i) q^{9} +(-5.50000 + 9.52628i) q^{11} +18.0138 q^{13} +66.2468 q^{15} +(-3.37085 + 5.83848i) q^{17} +(-79.1022 - 137.009i) q^{19} +(-53.1297 + 29.6288i) q^{21} +(-42.5354 - 73.6735i) q^{23} +(-140.884 + 244.019i) q^{25} -141.934 q^{27} -49.3654 q^{29} +(74.7462 - 129.464i) q^{31} +(-18.0657 - 31.2906i) q^{33} +(5.56034 - 373.485i) q^{35} +(-142.061 - 246.057i) q^{37} +(-29.5847 + 51.2421i) q^{39} -223.913 q^{41} -38.0640 q^{43} +(163.476 - 283.148i) q^{45} +(-205.534 - 355.996i) q^{47} +(162.581 + 302.020i) q^{49} +(-11.0721 - 19.1775i) q^{51} +(178.729 - 309.568i) q^{53} +221.854 q^{55} +519.648 q^{57} +(374.003 - 647.792i) q^{59} +(62.5723 + 108.378i) q^{61} +(-4.46927 + 300.198i) q^{63} +(-181.656 - 314.637i) q^{65} +(-318.986 + 552.499i) q^{67} +279.429 q^{69} -176.322 q^{71} +(-526.722 + 912.308i) q^{73} +(-462.758 - 801.520i) q^{75} +(-177.926 + 99.2238i) q^{77} +(-209.993 - 363.719i) q^{79} +(14.2540 - 24.6887i) q^{81} -1472.87 q^{83} +135.970 q^{85} +(81.0744 - 140.425i) q^{87} +(-671.059 - 1162.31i) q^{89} +(286.409 + 171.093i) q^{91} +(245.516 + 425.247i) q^{93} +(-1595.37 + 2763.27i) q^{95} +1289.25 q^{97} -178.321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.64233	+	2.84460i	−0.316067	+	0.547444i	−0.979664	−	0.200646i	$-0.935696\pi$
$3$	−1.64233	+	2.84460i	−0.316067	+	0.547444i	0.663597	+	0.748091i	$0.269029\pi$
$4$		0			0
$5$	−10.0843	−	17.4664i	−0.901963	−	1.56225i	−0.824943	−	0.565216i	$-0.808793\pi$
$5$	−10.0843	−	17.4664i	−0.901963	−	1.56225i	−0.0770204	−	0.997030i	$-0.524541\pi$
$6$		0			0
$7$	15.8994	+	9.49786i	0.858486	+	0.512836i
$7$	15.8994	+	9.49786i	0.858486	+	0.512836i
$8$		0			0
$9$	8.10549	+	14.0391i	0.300203	+	0.519967i
$10$		0			0
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$		0			0
$13$	18.0138			0.384318			0.192159	−	0.981364i	$-0.438451\pi$
$13$	18.0138			0.384318			0.192159	+	0.981364i	$0.438451\pi$
$14$		0			0
$15$	66.2468			1.14032
$16$		0			0
$17$	−3.37085	+	5.83848i	−0.0480912	+	0.0832965i	−0.889069	−	0.457773i	$-0.848647\pi$
$17$	−3.37085	+	5.83848i	−0.0480912	+	0.0832965i	0.840978	+	0.541070i	$0.181980\pi$
$18$		0			0
$19$	−79.1022	−	137.009i	−0.955120	−	1.65432i	−0.734093	−	0.679049i	$-0.762393\pi$
$19$	−79.1022	−	137.009i	−0.955120	−	1.65432i	−0.221027	−	0.975268i	$-0.570941\pi$
$20$		0			0
$21$	−53.1297	+	29.6288i	−0.552089	+	0.307883i
$22$		0			0
$23$	−42.5354	−	73.6735i	−0.385619	−	0.667912i	0.606236	−	0.795285i	$-0.292679\pi$
$23$	−42.5354	−	73.6735i	−0.385619	−	0.667912i	−0.991855	+	0.127373i	$0.959346\pi$
$24$		0			0
$25$	−140.884	+	244.019i	−1.12707	+	1.95215i
$26$		0			0
$27$	−141.934			−1.01167
$28$		0			0
$29$	−49.3654			−0.316101			−0.158050	−	0.987431i	$-0.550521\pi$
$29$	−49.3654			−0.316101			−0.158050	+	0.987431i	$0.550521\pi$
$30$		0			0
$31$	74.7462	−	129.464i	0.433059	−	0.750080i	−0.564076	−	0.825723i	$-0.690768\pi$
$31$	74.7462	−	129.464i	0.433059	−	0.750080i	0.997135	+	0.0756430i	$0.0241009\pi$
$32$		0			0
$33$	−18.0657	−	31.2906i	−0.0952978	−	0.165061i
$34$		0			0
$35$	5.56034	−	373.485i	0.0268534	−	1.80373i
$36$		0			0
$37$	−142.061	−	246.057i	−0.631207	−	1.09328i	−0.987305	−	0.158834i	$-0.949226\pi$
$37$	−142.061	−	246.057i	−0.631207	−	1.09328i	0.356098	−	0.934449i	$-0.384107\pi$
$38$		0			0
$39$	−29.5847	+	51.2421i	−0.121470	+	0.210393i
$40$		0			0
$41$	−223.913			−0.852911			−0.426456	−	0.904509i	$-0.640238\pi$
$41$	−223.913			−0.852911			−0.426456	+	0.904509i	$0.640238\pi$
$42$		0			0
$43$	−38.0640			−0.134993			−0.0674965	−	0.997720i	$-0.521501\pi$
$43$	−38.0640			−0.134993			−0.0674965	+	0.997720i	$0.521501\pi$
$44$		0			0
$45$	163.476	−	283.148i	0.541544	−	0.937982i
$46$		0			0
$47$	−205.534	−	355.996i	−0.637878	−	1.10484i	−0.985898	−	0.167349i	$-0.946479\pi$
$47$	−205.534	−	355.996i	−0.637878	−	1.10484i	0.348020	−	0.937487i	$-0.386854\pi$
$48$		0			0
$49$	162.581	+	302.020i	0.473998	+	0.880526i
$50$		0			0
$51$	−11.0721	−	19.1775i	−0.0304001	−	0.0526545i
$52$		0			0
$53$	178.729	−	309.568i	0.463213	−	0.802309i	−0.535906	−	0.844278i	$-0.680030\pi$
$53$	178.729	−	309.568i	0.463213	−	0.802309i	0.999119	+	0.0419689i	$0.0133630\pi$
$54$		0			0
$55$	221.854			0.543904
$56$		0			0
$57$	519.648			1.20753
$58$		0			0
$59$	374.003	−	647.792i	0.825272	−	1.42941i	−0.0764390	−	0.997074i	$-0.524355\pi$
$59$	374.003	−	647.792i	0.825272	−	1.42941i	0.901711	−	0.432339i	$-0.142312\pi$
$60$		0			0
$61$	62.5723	+	108.378i	0.131337	+	0.227482i	0.924192	−	0.381928i	$-0.124740\pi$
$61$	62.5723	+	108.378i	0.131337	+	0.227482i	−0.792855	+	0.609410i	$0.791406\pi$
$62$		0			0
$63$	−4.46927	+	300.198i	−0.00893770	+	0.600340i
$64$		0			0
$65$	−181.656	−	314.637i	−0.346640	−	0.600399i
$66$		0			0
$67$	−318.986	+	552.499i	−0.581646	+	1.00744i	0.413638	+	0.910441i	$0.364258\pi$
$67$	−318.986	+	552.499i	−0.581646	+	1.00744i	−0.995284	+	0.0969997i	$0.969075\pi$
$68$		0			0
$69$	279.429			0.487526
$70$		0			0
$71$	−176.322			−0.294727			−0.147363	−	0.989082i	$-0.547079\pi$
$71$	−176.322			−0.294727			−0.147363	+	0.989082i	$0.547079\pi$
$72$		0			0
$73$	−526.722	+	912.308i	−0.844494	+	1.46271i	0.0415651	+	0.999136i	$0.486766\pi$
$73$	−526.722	+	912.308i	−0.844494	+	1.46271i	−0.886060	+	0.463571i	$0.846568\pi$
$74$		0			0
$75$	−462.758	−	801.520i	−0.712463	−	1.23402i
$76$		0			0
$77$	−177.926	+	99.2238i	−0.263332	+	0.146852i
$78$		0			0
$79$	−209.993	−	363.719i	−0.299064	−	0.517994i	0.676858	−	0.736114i	$-0.263341\pi$
$79$	−209.993	−	363.719i	−0.299064	−	0.517994i	−0.975922	+	0.218119i	$0.930008\pi$
$80$		0			0
$81$	14.2540	−	24.6887i	0.0195528	−	0.0338665i
$82$		0			0
$83$	−1472.87			−1.94781			−0.973907	−	0.226949i	$-0.927125\pi$
$83$	−1472.87			−1.94781			−0.973907	+	0.226949i	$0.927125\pi$
$84$		0			0
$85$	135.970			0.173506
$86$		0			0
$87$	81.0744	−	140.425i	0.0999091	−	0.173048i
$88$		0			0
$89$	−671.059	−	1162.31i	−0.799237	−	1.38432i	−0.920114	−	0.391651i	$-0.871904\pi$
$89$	−671.059	−	1162.31i	−0.799237	−	1.38432i	0.120877	−	0.992667i	$-0.461429\pi$
$90$		0			0
$91$	286.409	+	171.093i	0.329932	+	0.197092i
$92$		0			0
$93$	245.516	+	425.247i	0.273751	+	0.474151i
$94$		0			0
$95$	−1595.37	+	2763.27i	−1.72297	+	2.98426i
$96$		0			0
$97$	1289.25			1.34952			0.674759	−	0.738038i	$-0.264248\pi$
$97$	1289.25			1.34952			0.674759	+	0.738038i	$0.264248\pi$
$98$		0			0
$99$	−178.321			−0.181029
$100$		0			0
$101$	679.118	−	1176.27i	0.669057	−	1.15884i	−0.309112	−	0.951026i	$-0.600032\pi$
$101$	679.118	−	1176.27i	0.669057	−	1.15884i	0.978168	−	0.207814i	$-0.0666350\pi$
$102$		0			0
$103$	574.860	+	995.687i	0.549929	+	0.952505i	0.998279	+	0.0586465i	$0.0186785\pi$
$103$	574.860	+	995.687i	0.549929	+	0.952505i	−0.448350	+	0.893858i	$0.647988\pi$
$104$		0			0
$105$	1053.28	+	629.203i	0.978952	+	0.584799i
$106$		0			0
$107$	−715.764	−	1239.74i	−0.646687	−	1.12010i	−0.983909	−	0.178670i	$-0.942821\pi$
$107$	−715.764	−	1239.74i	−0.646687	−	1.12010i	0.337222	−	0.941425i	$-0.390513\pi$
$108$		0			0
$109$	−559.031	+	968.271i	−0.491243	+	0.850858i	−0.999949	−	0.0100822i	$-0.996791\pi$
$109$	−559.031	+	968.271i	−0.491243	+	0.850858i	0.508706	+	0.860940i	$0.330124\pi$
$110$		0			0
$111$	933.245			0.798015
$112$		0			0
$113$	584.060			0.486228			0.243114	−	0.969998i	$-0.421831\pi$
$113$	584.060			0.486228			0.243114	+	0.969998i	$0.421831\pi$
$114$		0			0
$115$	−857.876	+	1485.88i	−0.695629	+	1.20486i
$116$		0			0
$117$	146.011	+	252.898i	0.115373	+	0.199833i
$118$		0			0
$119$	−109.048	+	60.8125i	−0.0840031	+	0.0468460i
$120$		0			0
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	367.740	−	636.944i	0.269577	−	0.466921i
$124$		0			0
$125$	3161.79			2.26239
$126$		0			0
$127$	137.723			0.0962277			0.0481139	−	0.998842i	$-0.484679\pi$
$127$	137.723			0.0962277			0.0481139	+	0.998842i	$0.484679\pi$
$128$		0			0
$129$	62.5137	−	108.277i	0.0426669	−	0.0739012i
$130$		0			0
$131$	773.723	+	1340.13i	0.516034	+	0.893798i	0.999827	+	0.0186149i	$0.00592564\pi$
$131$	773.723	+	1340.13i	0.516034	+	0.893798i	−0.483792	+	0.875183i	$0.660741\pi$
$132$		0			0
$133$	43.6160	−	2929.66i	0.0284360	−	1.91003i
$134$		0			0
$135$	1431.29	+	2479.07i	0.912490	+	1.58048i
$136$		0			0
$137$	299.607	−	518.935i	0.186841	−	0.323617i	−0.757355	−	0.653004i	$-0.773509\pi$
$137$	299.607	−	518.935i	0.186841	−	0.323617i	0.944195	+	0.329386i	$0.106842\pi$
$138$		0			0
$139$	1760.91			1.07452			0.537260	−	0.843417i	$-0.319459\pi$
$139$	1760.91			1.07452			0.537260	+	0.843417i	$0.319459\pi$
$140$		0			0
$141$	1350.22			0.806448
$142$		0			0
$143$	−99.0759	+	171.605i	−0.0579381	+	0.100352i
$144$		0			0
$145$	497.813	+	862.238i	0.285111	+	0.493827i
$146$		0			0
$147$	−1126.14	−	33.5388i	−0.631854	−	0.0188179i
$148$		0			0
$149$	1237.46	+	2143.34i	0.680379	+	1.17845i	0.974865	+	0.222795i	$0.0715181\pi$
$149$	1237.46	+	2143.34i	0.680379	+	1.17845i	−0.294486	+	0.955656i	$0.595149\pi$
$150$		0			0
$151$	209.888	−	363.537i	0.113116	−	0.195922i	−0.803909	−	0.594752i	$-0.797250\pi$
$151$	209.888	−	363.537i	0.113116	−	0.195922i	0.917025	+	0.398830i	$0.130584\pi$
$152$		0			0
$153$	−109.290			−0.0577486
$154$		0			0
$155$	−3015.04			−1.56241
$156$		0			0
$157$	−638.799	+	1106.43i	−0.324724	+	0.562439i	−0.981457	−	0.191685i	$-0.938605\pi$
$157$	−638.799	+	1106.43i	−0.324724	+	0.562439i	0.656732	+	0.754124i	$0.271938\pi$
$158$		0			0
$159$	587.065	+	1016.83i	0.292813	+	0.507167i
$160$		0			0
$161$	23.4535	−	1575.36i	0.0114807	−	0.771153i
$162$		0			0
$163$	−1326.92	−	2298.29i	−0.637620	−	1.10439i	−0.985954	−	0.167020i	$-0.946586\pi$
$163$	−1326.92	−	2298.29i	−0.637620	−	1.10439i	0.348333	−	0.937371i	$-0.386748\pi$
$164$		0			0
$165$	−364.357	+	631.086i	−0.171910	+	0.297757i
$166$		0			0
$167$	3219.63			1.49187			0.745935	−	0.666019i	$-0.232003\pi$
$167$	3219.63			1.49187			0.745935	+	0.666019i	$0.232003\pi$
$168$		0			0
$169$	−1872.50			−0.852300
$170$		0			0
$171$	1282.32	−	2221.05i	0.573460	−	0.993262i
$172$		0			0
$173$	−455.813	−	789.491i	−0.200317	−	0.346959i	0.748314	−	0.663345i	$-0.230864\pi$
$173$	−455.813	−	789.491i	−0.200317	−	0.346959i	−0.948631	+	0.316386i	$0.897531\pi$
$174$		0			0
$175$	−4557.63	+	2541.65i	−1.96871	+	1.09789i
$176$		0			0
$177$	1228.48	+	2127.78i	0.521683	+	0.903581i
$178$		0			0
$179$	746.808	−	1293.51i	0.311838	−	0.540120i	−0.666922	−	0.745128i	$-0.732389\pi$
$179$	746.808	−	1293.51i	0.311838	−	0.540120i	0.978760	+	0.205008i	$0.0657219\pi$
$180$		0			0
$181$	−1967.65			−0.808035			−0.404018	−	0.914751i	$-0.632387\pi$
$181$	−1967.65			−0.808035			−0.404018	+	0.914751i	$0.632387\pi$
$182$		0			0
$183$	−411.058			−0.166045
$184$		0			0
$185$	−2865.16	+	4962.60i	−1.13865	+	1.97220i
$186$		0			0
$187$	−37.0793	−	64.2233i	−0.0145001	−	0.0251148i
$188$		0			0
$189$	−2256.66	−	1348.07i	−0.868506	−	0.518822i
$190$		0			0
$191$	−168.090	−	291.141i	−0.0636784	−	0.110294i	0.832429	−	0.554132i	$-0.186950\pi$
$191$	−168.090	−	291.141i	−0.0636784	−	0.110294i	−0.896107	+	0.443838i	$0.853617\pi$
$192$		0			0
$193$	1140.94	−	1976.16i	0.425526	−	0.737033i	−0.570943	−	0.820990i	$-0.693422\pi$
$193$	1140.94	−	1976.16i	0.425526	−	0.737033i	0.996469	+	0.0839566i	$0.0267557\pi$
$194$		0			0
$195$	1193.36			0.438247
$196$		0			0
$197$	1810.04			0.654619			0.327309	−	0.944917i	$-0.393858\pi$
$197$	1810.04			0.654619			0.327309	+	0.944917i	$0.393858\pi$
$198$		0			0
$199$	−896.689	+	1553.11i	−0.319420	+	0.553252i	−0.980367	−	0.197181i	$-0.936821\pi$
$199$	−896.689	+	1553.11i	−0.319420	+	0.553252i	0.660947	+	0.750433i	$0.270155\pi$
$200$		0			0
$201$	−1047.76	−	1814.78i	−0.367679	−	0.636838i
$202$		0			0
$203$	−784.880	−	468.866i	−0.271368	−	0.162108i
$204$		0			0
$205$	2258.00	+	3910.96i	0.769294	+	1.33246i
$206$		0			0
$207$	689.540	−	1194.32i	0.231528	−	0.401019i
$208$		0			0
$209$	1740.25			0.575959
$210$		0			0
$211$	−701.349			−0.228829			−0.114414	−	0.993433i	$-0.536499\pi$
$211$	−701.349			−0.228829			−0.114414	+	0.993433i	$0.536499\pi$
$212$		0			0
$213$	289.580	−	501.567i	0.0931535	−	0.161347i
$214$		0			0
$215$	383.847	+	664.842i	0.121759	+	0.210892i
$216$		0			0
$217$	2418.05	−	1348.47i	0.756443	−	0.421845i
$218$		0			0
$219$	−1730.10	−	2996.63i	−0.533834	−	0.924627i
$220$		0			0
$221$	−60.7218	+	105.173i	−0.0184823	+	0.0320123i
$222$		0			0
$223$	3527.11			1.05916			0.529580	−	0.848260i	$-0.322350\pi$
$223$	3527.11			1.05916			0.529580	+	0.848260i	$0.322350\pi$
$224$		0			0
$225$	−4567.75			−1.35341
$226$		0			0
$227$	797.408	−	1381.15i	0.233153	−	0.403833i	−0.725581	−	0.688137i	$-0.758429\pi$
$227$	797.408	−	1381.15i	0.233153	−	0.403833i	0.958734	+	0.284303i	$0.0917623\pi$
$228$		0			0
$229$	1482.74	+	2568.18i	0.427870	+	0.741093i	0.996684	−	0.0813734i	$-0.0259306\pi$
$229$	1482.74	+	2568.18i	0.427870	+	0.741093i	−0.568813	+	0.822467i	$0.692597\pi$
$230$		0			0
$231$	9.96120	−	669.087i	0.00283722	−	0.190574i
$232$		0			0
$233$	1837.81	+	3183.19i	0.516734	+	0.895010i	0.999811	+	0.0194323i	$0.00618588\pi$
$233$	1837.81	+	3183.19i	0.516734	+	0.895010i	−0.483077	+	0.875578i	$0.660481\pi$
$234$		0			0
$235$	−4145.32	+	7179.90i	−1.15068	+	1.99304i
$236$		0			0
$237$	1379.51			0.378097
$238$		0			0
$239$	−3671.87			−0.993780			−0.496890	−	0.867814i	$-0.665525\pi$
$239$	−3671.87			−0.993780			−0.496890	+	0.867814i	$0.665525\pi$
$240$		0			0
$241$	1995.43	−	3456.18i	0.533348	−	0.923786i	−0.465893	−	0.884841i	$-0.654267\pi$
$241$	1995.43	−	3456.18i	0.533348	−	0.923786i	0.999241	−	0.0389450i	$-0.0123997\pi$
$242$		0			0
$243$	−1869.28	−	3237.69i	−0.493476	−	0.854725i
$244$		0			0
$245$	3635.71	−	5885.37i	0.948070	−	1.53470i
$246$		0			0
$247$	−1424.93	−	2468.05i	−0.367070	−	0.635783i
$248$		0			0
$249$	2418.94	−	4189.73i	0.615640	−	1.06632i
$250$		0			0
$251$	777.368			0.195486			0.0977430	−	0.995212i	$-0.468838\pi$
$251$	777.368			0.195486			0.0977430	+	0.995212i	$0.468838\pi$
$252$		0			0
$253$	935.779			0.232537
$254$		0			0
$255$	−223.308	+	386.781i	−0.0548396	+	0.0949849i
$256$		0			0
$257$	1648.95	+	2856.07i	0.400229	+	0.693216i	0.993753	−	0.111600i	$-0.0355974\pi$
$257$	1648.95	+	2856.07i	0.400229	+	0.693216i	−0.593525	+	0.804816i	$0.702264\pi$
$258$		0			0
$259$	78.3307	−	5261.42i	0.0187924	−	1.26227i
$260$		0			0
$261$	−400.131	−	693.047i	−0.0948945	−	0.164362i
$262$		0			0
$263$	−2009.46	+	3480.49i	−0.471136	+	0.816032i	−0.999455	−	0.0330140i	$-0.989489\pi$
$263$	−2009.46	+	3480.49i	−0.471136	+	0.816032i	0.528318	+	0.849046i	$0.322823\pi$
$264$		0			0
$265$	−7209.39			−1.67121
$266$		0			0
$267$	4408.41			1.01045
$268$		0			0
$269$	1433.96	−	2483.68i	0.325018	−	0.562948i	−0.656498	−	0.754328i	$-0.727963\pi$
$269$	1433.96	−	2483.68i	0.325018	−	0.562948i	0.981516	+	0.191380i	$0.0612963\pi$
$270$		0			0
$271$	−3791.79	−	6567.57i	−0.849943	−	1.47215i	−0.881258	−	0.472636i	$-0.843303\pi$
$271$	−3791.79	−	6567.57i	−0.849943	−	1.47215i	0.0313146	−	0.999510i	$-0.490031\pi$
$272$		0			0
$273$	−957.069	+	533.728i	−0.212177	+	0.118325i
$274$		0			0
$275$	−1549.73	−	2684.21i	−0.339826	−	0.588596i
$276$		0			0
$277$	−928.332	+	1607.92i	−0.201365	+	0.348774i	−0.948968	−	0.315371i	$-0.897871\pi$
$277$	−928.332	+	1607.92i	−0.201365	+	0.348774i	0.747604	+	0.664145i	$0.231204\pi$
$278$		0			0
$279$	2423.42			0.520023
$280$		0			0
$281$	146.754			0.0311551			0.0155776	−	0.999879i	$-0.495041\pi$
$281$	146.754			0.0311551			0.0155776	+	0.999879i	$0.495041\pi$
$282$		0			0
$283$	−588.434	+	1019.20i	−0.123600	+	0.214081i	−0.921185	−	0.389125i	$-0.872777\pi$
$283$	−588.434	+	1019.20i	−0.123600	+	0.214081i	0.797585	+	0.603207i	$0.206111\pi$
$284$		0			0
$285$	−5240.26	−	9076.41i	−1.08915	−	1.88646i
$286$		0			0
$287$	−3560.08	−	2126.70i	−0.732213	−	0.437404i
$288$		0			0
$289$	2433.77	+	4215.42i	0.495374	+	0.858014i
$290$		0			0
$291$	−2117.37	+	3667.40i	−0.426538	+	0.738786i
$292$		0			0
$293$	−2767.43			−0.551792			−0.275896	−	0.961187i	$-0.588975\pi$
$293$	−2767.43			−0.551792			−0.275896	+	0.961187i	$0.588975\pi$
$294$		0			0
$295$	−15086.2			−2.97746
$296$		0			0
$297$	780.635	−	1352.10i	0.152515	−	0.264164i
$298$		0			0
$299$	−766.225	−	1327.14i	−0.148200	−	0.256691i
$300$		0			0
$301$	−605.194	−	361.526i	−0.115890	−	0.0692294i
$302$		0			0
$303$	2230.67	+	3863.64i	0.422934	+	0.732542i
$304$		0			0
$305$	1261.99	−	2185.83i	0.236922	−	0.410361i
$306$		0			0
$307$	2937.35			0.546069			0.273035	−	0.962004i	$-0.411973\pi$
$307$	2937.35			0.546069			0.273035	+	0.962004i	$0.411973\pi$
$308$		0			0
$309$	−3776.45			−0.695258
$310$		0			0
$311$	−1617.87	+	2802.24i	−0.294987	+	0.510933i	−0.974982	−	0.222284i	$-0.928649\pi$
$311$	−1617.87	+	2802.24i	−0.294987	+	0.510933i	0.679995	+	0.733217i	$0.261982\pi$
$312$		0			0
$313$	−4754.84	−	8235.63i	−0.858657	−	1.48724i	−0.873210	−	0.487344i	$-0.837966\pi$
$313$	−4754.84	−	8235.63i	−0.858657	−	1.48724i	0.0145529	−	0.999894i	$-0.495367\pi$
$314$		0			0
$315$	5288.46	−	2949.21i	0.945940	−	0.527522i
$316$		0			0
$317$	2217.77	+	3841.29i	0.392941	+	0.680595i	0.992836	−	0.119484i	$-0.0381242\pi$
$317$	2217.77	+	3841.29i	0.392941	+	0.680595i	−0.599895	+	0.800079i	$0.704791\pi$
$318$		0			0
$319$	271.510	−	470.269i	0.0476540	−	0.0825391i
$320$		0			0
$321$	4702.09			0.817586
$322$		0			0
$323$	1066.57			0.183732
$324$		0			0
$325$	−2537.86	+	4395.71i	−0.433155	+	0.750246i
$326$		0			0
$327$	−1836.23	−	3180.45i	−0.310532	−	0.537856i
$328$		0			0
$329$	113.329	−	7612.25i	0.0189910	−	1.27561i
$330$		0			0
$331$	1355.88	+	2348.45i	0.225153	+	0.389977i	0.956365	−	0.292173i	$-0.0943784\pi$
$331$	1355.88	+	2348.45i	0.225153	+	0.389977i	−0.731212	+	0.682150i	$0.761045\pi$
$332$		0			0
$333$	2302.94	−	3988.82i	0.378981	−	0.656414i
$334$		0			0
$335$	12866.9			2.09849
$336$		0			0
$337$	3897.67			0.630029			0.315015	−	0.949087i	$-0.397991\pi$
$337$	3897.67			0.630029			0.315015	+	0.949087i	$0.397991\pi$
$338$		0			0
$339$	−959.221	+	1661.42i	−0.153681	+	0.266183i
$340$		0			0
$341$	822.209	+	1424.11i	0.130572	+	0.226158i
$342$		0			0
$343$	−283.606	+	6346.11i	−0.0446451	+	0.999003i
$344$		0			0
$345$	−2817.83	−	4880.63i	−0.439731	−	0.761636i
$346$		0			0
$347$	−104.007	+	180.145i	−0.0160904	+	0.0278694i	−0.873958	−	0.486001i	$-0.838455\pi$
$347$	−104.007	+	180.145i	−0.0160904	+	0.0278694i	0.857868	+	0.513870i	$0.171789\pi$
$348$		0			0
$349$	2513.14			0.385459			0.192729	−	0.981252i	$-0.438266\pi$
$349$	2513.14			0.385459			0.192729	+	0.981252i	$0.438266\pi$
$350$		0			0
$351$	−2556.76			−0.388803
$352$		0			0
$353$	−4394.08	+	7610.78i	−0.662531	+	1.14754i	0.317417	+	0.948286i	$0.397184\pi$
$353$	−4394.08	+	7610.78i	−0.662531	+	1.14754i	−0.979948	+	0.199252i	$0.936149\pi$
$354$		0			0
$355$	1778.08	+	3079.72i	0.265833	+	0.460436i
$356$		0			0
$357$	6.10504	−	410.071i	0.000905078	−	0.0607935i
$358$		0			0
$359$	−3882.41	−	6724.53i	−0.570768	−	0.988600i	−0.996487	−	0.0837443i	$-0.973312\pi$
$359$	−3882.41	−	6724.53i	−0.570768	−	0.988600i	0.425719	−	0.904855i	$-0.360021\pi$
$360$		0			0
$361$	−9084.80	+	15735.3i	−1.32451	+	2.29412i
$362$		0			0
$363$	397.445			0.0574667
$364$		0			0
$365$	21246.4			3.04681
$366$		0			0
$367$	1847.67	−	3200.25i	0.262800	−	0.455182i	−0.704185	−	0.710016i	$-0.748688\pi$
$367$	1847.67	−	3200.25i	0.262800	−	0.455182i	0.966985	+	0.254834i	$0.0820209\pi$
$368$		0			0
$369$	−1814.92	−	3143.54i	−0.256047	−	0.443486i
$370$		0			0
$371$	5781.91	−	3224.39i	0.809116	−	0.451219i
$372$		0			0
$373$	5369.48	+	9300.22i	0.745366	+	1.29101i	0.950024	+	0.312178i	$0.101058\pi$
$373$	5369.48	+	9300.22i	0.745366	+	1.29101i	−0.204658	+	0.978833i	$0.565608\pi$
$374$		0			0
$375$	−5192.71	+	8994.04i	−0.715068	+	1.23853i
$376$		0			0
$377$	−889.259			−0.121483
$378$		0			0
$379$	3267.42			0.442839			0.221419	−	0.975179i	$-0.428931\pi$
$379$	3267.42			0.442839			0.221419	+	0.975179i	$0.428931\pi$
$380$		0			0
$381$	−226.187	+	391.767i	−0.0304144	+	0.0526793i
$382$		0			0
$383$	−7259.62	−	12574.0i	−0.968536	−	1.67755i	−0.699798	−	0.714341i	$-0.746727\pi$
$383$	−7259.62	−	12574.0i	−0.968536	−	1.67755i	−0.268738	−	0.963213i	$-0.586607\pi$
$384$		0			0
$385$	3527.34	+	2107.13i	0.466934	+	0.278934i
$386$		0			0
$387$	−308.527	−	534.385i	−0.0405254	−	0.0701920i
$388$		0			0
$389$	57.8990	−	100.284i	0.00754652	−	0.0130709i	−0.862227	−	0.506521i	$-0.830931\pi$
$389$	57.8990	−	100.284i	0.00754652	−	0.0130709i	0.869774	+	0.493450i	$0.164265\pi$
$390$		0			0
$391$	573.522			0.0741797
$392$		0			0
$393$	−5082.84			−0.652406
$394$		0			0
$395$	−4235.25	+	7335.67i	−0.539490	+	0.934424i
$396$		0			0
$397$	5082.64	+	8803.39i	0.642545	+	1.11292i	0.984863	+	0.173337i	$0.0554549\pi$
$397$	5082.64	+	8803.39i	0.642545	+	1.11292i	−0.342317	+	0.939584i	$0.611212\pi$
$398$		0			0
$399$	8262.09	+	4935.55i	1.03665	+	0.619264i
$400$		0			0
$401$	−6938.02	−	12017.0i	−0.864011	−	1.49651i	−0.868026	−	0.496519i	$-0.834611\pi$
$401$	−6938.02	−	12017.0i	−0.864011	−	1.49651i	0.00401504	−	0.999992i	$-0.498722\pi$
$402$		0			0
$403$	1346.46	−	2332.14i	0.166432	−	0.288269i
$404$		0			0
$405$	−574.965			−0.0705438
$406$		0			0
$407$	3125.34			0.380632
$408$		0			0
$409$	5760.31	−	9977.14i	0.696403	−	1.20621i	−0.273302	−	0.961928i	$-0.588116\pi$
$409$	5760.31	−	9977.14i	0.696403	−	1.20621i	0.969705	−	0.244277i	$-0.0785507\pi$
$410$		0			0
$411$	984.109	+	1704.53i	0.118108	+	0.204570i
$412$		0			0
$413$	12099.1	−	6747.27i	1.44154	−	0.803902i
$414$		0			0
$415$	14852.8	+	25725.8i	1.75686	+	3.04296i
$416$		0			0
$417$	−2892.00	+	5009.08i	−0.339620	+	0.588240i
$418$		0			0
$419$	−14017.0			−1.63431			−0.817155	−	0.576419i	$-0.804450\pi$
$419$	−14017.0			−1.63431			−0.817155	+	0.576419i	$0.804450\pi$
$420$		0			0
$421$	−7481.04			−0.866042			−0.433021	−	0.901384i	$-0.642552\pi$
$421$	−7481.04			−0.866042			−0.433021	+	0.901384i	$0.642552\pi$
$422$		0			0
$423$	3331.91	−	5771.04i	0.382986	−	0.663351i
$424$		0			0
$425$	−949.800	−	1645.10i	−0.108405	−	0.187763i
$426$		0			0
$427$	−34.5016	+	2317.45i	−0.00391019	+	0.262645i
$428$		0			0
$429$	−325.431	−	563.664i	−0.0366246	−	0.0634357i
$430$		0			0
$431$	−3428.67	+	5938.63i	−0.383186	+	0.663698i	−0.991516	−	0.129987i	$-0.958506\pi$
$431$	−3428.67	+	5938.63i	−0.383186	+	0.663698i	0.608330	+	0.793684i	$0.291840\pi$
$432$		0			0
$433$	−6537.32			−0.725551			−0.362775	−	0.931877i	$-0.618171\pi$
$433$	−6537.32			−0.725551			−0.362775	+	0.931877i	$0.618171\pi$
$434$		0			0
$435$	−3270.30			−0.360457
$436$		0			0
$437$	−6729.29	+	11655.5i	−0.736626	+	1.27587i
$438$		0			0
$439$	−2714.96	−	4702.44i	−0.295166	−	0.511242i	0.679858	−	0.733344i	$-0.262042\pi$
$439$	−2714.96	−	4702.44i	−0.295166	−	0.511242i	−0.975023	+	0.222102i	$0.928708\pi$
$440$		0			0
$441$	−2922.30	+	4730.52i	−0.315549	+	0.510800i
$442$		0			0
$443$	1959.86	+	3394.58i	0.210194	+	0.364067i	0.951775	−	0.306797i	$-0.0992571\pi$
$443$	1959.86	+	3394.58i	0.210194	+	0.364067i	−0.741581	+	0.670863i	$0.765924\pi$
$444$		0			0
$445$	−13534.2	+	23442.0i	−1.44176	+	2.49721i
$446$		0			0
$447$	−8129.27			−0.860181
$448$		0			0
$449$	9796.86			1.02972			0.514858	−	0.857275i	$-0.327845\pi$
$449$	9796.86			1.02972			0.514858	+	0.857275i	$0.327845\pi$
$450$		0			0
$451$	1231.52	−	2133.06i	0.128581	−	0.222709i
$452$		0			0
$453$	689.412	+	1194.10i	0.0715042	+	0.123849i
$454$		0			0
$455$	100.163	−	6727.88i	0.0103202	−	0.693204i
$456$		0			0
$457$	9253.49	+	16027.5i	0.947177	+	1.64056i	0.751333	+	0.659924i	$0.229411\pi$
$457$	9253.49	+	16027.5i	0.947177	+	1.64056i	0.195844	+	0.980635i	$0.437255\pi$
$458$		0			0
$459$	478.437	−	828.677i	0.0486525	−	0.0842687i
$460$		0			0
$461$	−4871.70			−0.492185			−0.246093	−	0.969246i	$-0.579147\pi$
$461$	−4871.70			−0.492185			−0.246093	+	0.969246i	$0.579147\pi$
$462$		0			0
$463$	6158.63			0.618177			0.309088	−	0.951033i	$-0.399976\pi$
$463$	6158.63			0.618177			0.309088	+	0.951033i	$0.399976\pi$
$464$		0			0
$465$	4951.70	−	8576.59i	0.493827	−	0.855333i
$466$		0			0
$467$	1842.96	+	3192.10i	0.182617	+	0.316302i	0.942771	−	0.333441i	$-0.108210\pi$
$467$	1842.96	+	3192.10i	0.182617	+	0.316302i	−0.760154	+	0.649743i	$0.774877\pi$
$468$		0			0
$469$	−10319.2	+	5754.72i	−1.01599	+	0.566585i
$470$		0			0
$471$	−2098.24	−	3634.26i	−0.205269	−	0.355537i
$472$		0			0
$473$	209.352	−	362.608i	0.0203510	−	0.0352489i
$474$		0			0
$475$	44577.0			4.30597
$476$		0			0
$477$	5794.74			0.556232
$478$		0			0
$479$	5170.98	−	8956.41i	0.493253	−	0.854340i	−0.506717	−	0.862113i	$-0.669141\pi$
$479$	5170.98	−	8956.41i	0.493253	−	0.854340i	0.999970	+	0.00777309i	$0.00247428\pi$
$480$		0			0
$481$	−2559.06	−	4432.42i	−0.242584	−	0.420168i
$482$		0			0
$483$	4442.75	+	2653.98i	0.418535	+	0.250021i
$484$		0			0
$485$	−13001.1	−	22518.6i	−1.21722	−	2.10828i
$486$		0			0
$487$	5101.96	−	8836.86i	0.474727	−	0.822251i	−0.524854	−	0.851192i	$-0.675880\pi$
$487$	5101.96	−	8836.86i	0.474727	−	0.822251i	0.999581	+	0.0289408i	$0.00921344\pi$
$488$		0			0
$489$	8716.95			0.806123
$490$		0			0
$491$	2590.24			0.238078			0.119039	−	0.992890i	$-0.462019\pi$
$491$	2590.24			0.238078			0.119039	+	0.992890i	$0.462019\pi$
$492$		0			0
$493$	166.403	−	288.219i	0.0152017	−	0.0263301i
$494$		0			0
$495$	1798.23	+	3114.63i	0.163282	+	0.282812i
$496$		0			0
$497$	−2803.42	−	1674.69i	−0.253019	−	0.151147i
$498$		0			0
$499$	1853.03	+	3209.54i	0.166238	+	0.287933i	0.937094	−	0.349076i	$-0.113505\pi$
$499$	1853.03	+	3209.54i	0.166238	+	0.287933i	−0.770856	+	0.637009i	$0.780171\pi$
$500$		0			0
$501$	−5287.70	+	9158.56i	−0.471531	+	0.816715i
$502$		0			0
$503$	−10724.5			−0.950661			−0.475330	−	0.879807i	$-0.657671\pi$
$503$	−10724.5			−0.950661			−0.475330	+	0.879807i	$0.657671\pi$
$504$		0			0
$505$	−27393.6			−2.41386
$506$		0			0
$507$	3075.27	−	5326.53i	0.269384	−	0.466587i
$508$		0			0
$509$	966.221	+	1673.54i	0.0841395	+	0.145734i	0.905024	−	0.425360i	$-0.139853\pi$
$509$	966.221	+	1673.54i	0.0841395	+	0.145734i	−0.820885	+	0.571094i	$0.806519\pi$
$510$		0			0
$511$	−17039.5	+	9502.42i	−1.47512	+	0.822627i
$512$		0			0
$513$	11227.3	+	19446.2i	0.966268	+	1.67362i
$514$		0			0
$515$	11594.1	−	20081.5i	0.992031	−	1.71825i
$516$		0			0
$517$	4521.75			0.384655
$518$		0			0
$519$	2994.39			0.253254
$520$		0			0
$521$	−3558.30	+	6163.16i	−0.299217	+	0.518259i	−0.975957	−	0.217963i	$-0.930059\pi$
$521$	−3558.30	+	6163.16i	−0.299217	+	0.518259i	0.676740	+	0.736222i	$0.263392\pi$
$522$		0			0
$523$	−3109.84	−	5386.40i	−0.260007	−	0.450346i	0.706236	−	0.707976i	$-0.250392\pi$
$523$	−3109.84	−	5386.40i	−0.260007	−	0.450346i	−0.966244	+	0.257630i	$0.917058\pi$
$524$		0			0
$525$	255.159	−	17138.9i	0.0212116	−	1.42477i
$526$		0			0
$527$	503.917	+	872.809i	0.0416527	+	0.0721445i
$528$		0			0
$529$	2464.98	−	4269.47i	0.202595	−	0.350906i
$530$		0			0
$531$	12125.9			0.990997
$532$		0			0
$533$	−4033.53			−0.327789
$534$		0			0
$535$	−14435.9	+	25003.7i	−1.16658	+	2.02057i
$536$		0			0
$537$	2453.02	+	4248.75i	0.197124	+	0.341428i
$538$		0			0
$539$	−3771.33	−	112.318i	−0.301378	−	0.00897565i
$540$		0			0
$541$	−5625.92	−	9744.38i	−0.447093	−	0.774388i	0.551102	−	0.834438i	$-0.314207\pi$
$541$	−5625.92	−	9744.38i	−0.447093	−	0.774388i	−0.998195	+	0.0600499i	$0.980874\pi$
$542$		0			0
$543$	3231.54	−	5597.19i	0.255393	−	0.442354i
$544$		0			0
$545$	22549.7			1.77233
$546$		0			0
$547$	4334.19			0.338787			0.169393	−	0.985548i	$-0.445819\pi$
$547$	4334.19			0.338787			0.169393	+	0.985548i	$0.445819\pi$
$548$		0			0
$549$	−1014.36	+	1756.92i	−0.0788556	+	0.136582i
$550$		0			0
$551$	3904.91	+	6763.50i	0.301914	+	0.522931i
$552$		0			0
$553$	115.788	−	7777.39i	0.00890379	−	0.598062i
$554$		0			0
$555$	−9411.08	−	16300.5i	−0.719780	−	1.24670i
$556$		0			0
$557$	468.201	−	810.947i	0.0356163	−	0.0616893i	−0.847668	−	0.530527i	$-0.821994\pi$
$557$	468.201	−	810.947i	0.0356163	−	0.0616893i	0.883284	+	0.468838i	$0.155327\pi$
$558$		0			0
$559$	−685.677			−0.0518802
$560$		0			0
$561$	243.586			0.0183320
$562$		0			0
$563$	5869.25	−	10165.8i	0.439360	−	0.760993i	−0.558281	−	0.829652i	$-0.688539\pi$
$563$	5869.25	−	10165.8i	0.439360	−	0.760993i	0.997640	+	0.0686591i	$0.0218721\pi$
$564$		0			0
$565$	−5889.81	−	10201.4i	−0.438559	−	0.759607i
$566$		0			0
$567$	461.120	−	257.152i	0.0341538	−	0.0190465i
$568$		0			0
$569$	11962.3	+	20719.3i	0.881345	+	1.52653i	0.849847	+	0.527030i	$0.176695\pi$
$569$	11962.3	+	20719.3i	0.881345	+	1.52653i	0.0314982	+	0.999504i	$0.489972\pi$
$570$		0			0
$571$	3392.23	−	5875.52i	0.248617	−	0.430618i	−0.714525	−	0.699610i	$-0.753357\pi$
$571$	3392.23	−	5875.52i	0.248617	−	0.430618i	0.963142	+	0.268992i	$0.0866905\pi$
$572$		0			0
$573$	1104.24			0.0805066
$574$		0			0
$575$	23970.3			1.73849
$576$		0			0
$577$	3943.64	−	6830.58i	0.284534	−	0.492827i	−0.687962	−	0.725746i	$-0.741495\pi$
$577$	3943.64	−	6830.58i	0.284534	−	0.492827i	0.972496	+	0.232920i	$0.0748280\pi$
$578$		0			0
$579$	3747.60	+	6491.03i	0.268990	+	0.465904i
$580$		0			0
$581$	−23417.7	−	13989.1i	−1.67217	−	0.998910i
$582$		0			0
$583$	1966.02	+	3405.24i	0.139664	+	0.241905i
$584$		0			0
$585$	2944.82	−	5100.57i	0.208125	−	0.360483i
$586$		0			0
$587$	11414.7			0.802613			0.401306	−	0.915944i	$-0.368556\pi$
$587$	11414.7			0.802613			0.401306	+	0.915944i	$0.368556\pi$
$588$		0			0
$589$	−23650.4			−1.65449
$590$		0			0
$591$	−2972.69	+	5148.84i	−0.206903	+	0.358367i
$592$		0			0
$593$	6788.85	+	11758.6i	0.470126	+	0.814282i	0.999416	−	0.0341584i	$-0.0108751\pi$
$593$	6788.85	+	11758.6i	0.470126	+	0.814282i	−0.529290	+	0.848441i	$0.677542\pi$
$594$		0			0
$595$	2161.84	+	1291.42i	0.148953	+	0.0889802i
$596$		0			0
$597$	−2945.32	−	5101.45i	−0.201916	−	0.349729i
$598$		0			0
$599$	−12394.9	+	21468.5i	−0.845476	+	1.46441i	0.0397319	+	0.999210i	$0.487350\pi$
$599$	−12394.9	+	21468.5i	−0.845476	+	1.46441i	−0.885208	+	0.465196i	$0.845984\pi$
$600$		0			0
$601$	−27467.5			−1.86426			−0.932132	−	0.362119i	$-0.882054\pi$
$601$	−27467.5			−1.86426			−0.932132	+	0.362119i	$0.882054\pi$
$602$		0			0
$603$	−10342.1			−0.698448
$604$		0			0
$605$	−1220.19	+	2113.44i	−0.0819966	+	0.142022i
$606$		0			0
$607$	8324.29	+	14418.1i	0.556627	+	0.964106i	0.997775	+	0.0666717i	$0.0212380\pi$
$607$	8324.29	+	14418.1i	0.556627	+	0.964106i	−0.441148	+	0.897434i	$0.645429\pi$
$608$		0			0
$609$	2622.77	−	1462.64i	0.174516	−	0.0973220i
$610$		0			0
$611$	−3702.45	−	6412.84i	−0.245148	−	0.424608i
$612$		0			0
$613$	12883.4	−	22314.6i	0.848864	−	1.47028i	−0.0333584	−	0.999443i	$-0.510620\pi$
$613$	12883.4	−	22314.6i	0.848864	−	1.47028i	0.882223	−	0.470832i	$-0.156046\pi$
$614$		0			0
$615$	−14833.5			−0.972594
$616$		0			0
$617$	−21818.5			−1.42363			−0.711815	−	0.702367i	$-0.752126\pi$
$617$	−21818.5			−1.42363			−0.711815	+	0.702367i	$0.752126\pi$
$618$		0			0
$619$	−2656.72	+	4601.58i	−0.172509	+	0.298794i	−0.939296	−	0.343107i	$-0.888521\pi$
$619$	−2656.72	+	4601.58i	−0.172509	+	0.298794i	0.766788	+	0.641901i	$0.221854\pi$
$620$		0			0
$621$	6037.20	+	10456.7i	0.390120	+	0.675708i
$622$		0			0
$623$	370.014	−	24853.6i	0.0237950	−	1.59830i
$624$		0			0
$625$	−14273.8	−	24722.9i	−0.913521	−	1.58226i
$626$		0			0
$627$	−2858.07	+	4950.31i	−0.182042	+	0.315305i
$628$		0			0
$629$	1915.46			0.121422
$630$		0			0
$631$	−26807.8			−1.69129			−0.845645	−	0.533746i	$-0.820784\pi$
$631$	−26807.8			−1.69129			−0.845645	+	0.533746i	$0.820784\pi$
$632$		0			0
$633$	1151.85	−	1995.06i	0.0723252	−	0.125271i
$634$		0			0
$635$	−1388.83	−	2405.53i	−0.0867939	−	0.150331i
$636$		0			0
$637$	2928.71	+	5440.54i	0.182166	+	0.338402i
$638$		0			0
$639$	−1429.18	−	2475.41i	−0.0884780	−	0.153248i
$640$		0			0
$641$	2334.68	−	4043.78i	0.143860	−	0.249173i	−0.785087	−	0.619385i	$-0.787382\pi$
$641$	2334.68	−	4043.78i	0.143860	−	0.249173i	0.928947	+	0.370213i	$0.120715\pi$
$642$		0			0
$643$	15653.7			0.960067			0.480033	−	0.877250i	$-0.340625\pi$
$643$	15653.7			0.960067			0.480033	+	0.877250i	$0.340625\pi$
$644$		0			0
$645$	−2521.62			−0.153936
$646$		0			0
$647$	2340.45	−	4053.78i	0.142214	−	0.246322i	−0.786116	−	0.618079i	$-0.787911\pi$
$647$	2340.45	−	4053.78i	0.142214	−	0.246322i	0.928330	+	0.371757i	$0.121244\pi$
$648$		0			0
$649$	4114.03	+	7125.72i	0.248829	+	0.430984i
$650$		0			0
$651$	−135.375	+	9093.05i	−0.00815017	+	0.547442i
$652$		0			0
$653$	−10738.3	−	18599.3i	−0.643528	−	1.11462i	−0.984639	−	0.174600i	$-0.944137\pi$
$653$	−10738.3	−	18599.3i	−0.643528	−	1.11462i	0.341112	−	0.940023i	$-0.389197\pi$
$654$		0			0
$655$	15604.8	−	27028.4i	0.930888	−	1.61235i
$656$		0			0
$657$	−17077.3			−1.01408
$658$		0			0
$659$	−17974.1			−1.06248			−0.531239	−	0.847222i	$-0.678273\pi$
$659$	−17974.1			−1.06248			−0.531239	+	0.847222i	$0.678273\pi$
$660$		0			0
$661$	−6640.39	+	11501.5i	−0.390743	+	0.676787i	−0.992548	−	0.121856i	$-0.961115\pi$
$661$	−6640.39	+	11501.5i	−0.390743	+	0.676787i	0.601804	+	0.798643i	$0.294449\pi$
$662$		0			0
$663$	−199.451	−	345.459i	−0.0116833	−	0.0202361i
$664$		0			0
$665$	−51610.6	+	28781.6i	−3.00958	+	1.67835i
$666$		0			0
$667$	2099.78	+	3636.92i	0.121895	+	0.211128i
$668$		0			0
$669$	−5792.68	+	10033.2i	−0.334765	+	0.579831i
$670$		0			0
$671$	−1376.59			−0.0791992
$672$		0			0
$673$	28060.2			1.60719			0.803596	−	0.595176i	$-0.202917\pi$
$673$	28060.2			1.60719			0.803596	+	0.595176i	$0.202917\pi$
$674$		0			0
$675$	19996.2	−	34634.5i	1.14023	−	1.97494i
$676$		0			0
$677$	7242.46	+	12544.3i	0.411152	+	0.712137i	0.995016	−	0.0997149i	$-0.0317931\pi$
$677$	7242.46	+	12544.3i	0.411152	+	0.712137i	−0.583864	+	0.811852i	$0.698460\pi$
$678$		0			0
$679$	20498.2	+	12245.1i	1.15854	+	0.692082i
$680$		0			0
$681$	2619.22	+	4536.62i	0.147384	+	0.255277i
$682$		0			0
$683$	−4240.18	+	7344.21i	−0.237549	+	0.411447i	−0.960010	−	0.279964i	$-0.909677\pi$
$683$	−4240.18	+	7344.21i	−0.237549	+	0.411447i	0.722461	+	0.691411i	$0.243011\pi$
$684$		0			0
$685$	−12085.3			−0.674093
$686$		0			0
$687$	−9740.62			−0.540943
$688$		0			0
$689$	3219.59	−	5576.49i	0.178021	−	0.308342i
$690$		0			0
$691$	−12283.9	−	21276.4i	−0.676270	−	1.17133i	−0.976096	−	0.217340i	$-0.930262\pi$
$691$	−12283.9	−	21276.4i	−0.676270	−	1.17133i	0.299826	−	0.953994i	$-0.403071\pi$
$692$		0			0
$693$	−2835.19	−	1693.67i	−0.155411	−	0.0928384i
$694$		0			0
$695$	−17757.4	−	30756.8i	−0.969177	−	1.67866i
$696$		0			0
$697$	754.777	−	1307.31i	0.0410176	−	0.0710445i
$698$		0			0
$699$	−12073.2			−0.653291
$700$		0			0
$701$	23325.9			1.25679			0.628394	−	0.777895i	$-0.283712\pi$
$701$	23325.9			1.25679			0.628394	+	0.777895i	$0.283712\pi$
$702$		0			0
$703$	−22474.6	+	38927.2i	−1.20576	+	2.08843i
$704$		0			0
$705$	−13616.0	−	23583.6i	−0.727387	−	1.25987i
$706$		0			0
$707$	21969.6	−	12251.7i	1.16867	−	0.651732i
$708$		0			0
$709$	−14574.3	−	25243.4i	−0.772001	−	1.33715i	−0.936465	−	0.350762i	$-0.885923\pi$
$709$	−14574.3	−	25243.4i	−0.772001	−	1.33715i	0.164464	−	0.986383i	$-0.447411\pi$
$710$		0			0
$711$	3404.19	−	5896.24i	0.179560	−	0.311007i
$712$		0			0
$713$	−12717.4			−0.667983
$714$		0			0
$715$	3996.43			0.209032
$716$		0			0
$717$	6030.43	−	10445.0i	0.314101	−	0.544039i
$718$		0			0
$719$	6665.58	+	11545.1i	0.345736	+	0.598832i	0.985487	−	0.169750i	$-0.0542959\pi$
$719$	6665.58	+	11545.1i	0.345736	+	0.598832i	−0.639751	+	0.768582i	$0.720963\pi$
$720$		0			0
$721$	−316.971	+	21290.8i	−0.0163726	+	1.09974i
$722$		0			0
$723$	6554.32	+	11352.4i	0.337148	+	0.583957i
$724$		0			0
$725$	6954.81	−	12046.1i	0.356269	−	0.617077i
$726$		0			0
$727$	18836.0			0.960920			0.480460	−	0.877017i	$-0.340470\pi$
$727$	18836.0			0.960920			0.480460	+	0.877017i	$0.340470\pi$
$728$		0			0
$729$	13049.7			0.662991
$730$		0			0
$731$	128.308	−	222.236i	0.00649198	−	0.0112444i
$732$		0			0
$733$	−5787.15	−	10023.6i	−0.291614	−	0.505091i	0.682577	−	0.730813i	$-0.260859\pi$
$733$	−5787.15	−	10023.6i	−0.291614	−	0.505091i	−0.974192	+	0.225723i	$0.927526\pi$
$734$		0			0
$735$	10770.5	+	20007.9i	0.540511	+	1.00408i
$736$		0			0
$737$	−3508.84	−	6077.49i	−0.175373	−	0.303755i
$738$		0			0
$739$	8143.74	−	14105.4i	0.405375	−	0.702130i	−0.588990	−	0.808140i	$-0.700474\pi$
$739$	8143.74	−	14105.4i	0.405375	−	0.702130i	0.994365	+	0.106010i	$0.0338076\pi$
$740$		0			0
$741$	9360.84			0.464074
$742$		0			0
$743$	18975.7			0.936947			0.468473	−	0.883478i	$-0.344804\pi$
$743$	18975.7			0.936947			0.468473	+	0.883478i	$0.344804\pi$
$744$		0			0
$745$	24957.7	−	43227.9i	1.22735	−	2.12584i
$746$		0			0
$747$	−11938.3	−	20677.8i	−0.584740	−	1.01280i
$748$		0			0
$749$	394.664	−	26509.3i	0.0192533	−	1.29323i
$750$		0			0
$751$	6534.14	+	11317.5i	0.317489	+	0.549907i	0.979963	−	0.199178i	$-0.0638271\pi$
$751$	6534.14	+	11317.5i	0.317489	+	0.549907i	−0.662475	+	0.749084i	$0.730494\pi$
$752$		0			0
$753$	−1276.70	+	2211.30i	−0.0617867	+	0.107018i
$754$		0			0
$755$	−8466.26			−0.408104
$756$		0			0
$757$	12393.2			0.595030			0.297515	−	0.954717i	$-0.403842\pi$
$757$	12393.2			0.595030			0.297515	+	0.954717i	$0.403842\pi$
$758$		0			0
$759$	−1536.86	+	2661.92i	−0.0734974	+	0.127301i
$760$		0			0
$761$	12227.3	+	21178.4i	0.582445	+	1.00882i	0.995189	+	0.0979767i	$0.0312371\pi$
$761$	12227.3	+	21178.4i	0.582445	+	1.00882i	−0.412744	+	0.910847i	$0.635430\pi$
$762$		0			0
$763$	−18084.8	+	10085.3i	−0.858077	+	0.478523i
$764$		0			0
$765$	1102.10	+	1908.90i	0.0520871	+	0.0902175i
$766$		0			0
$767$	6737.22	−	11669.2i	0.317167	−	0.549349i
$768$		0			0
$769$	9229.19			0.432787			0.216393	−	0.976306i	$-0.430571\pi$
$769$	9229.19			0.432787			0.216393	+	0.976306i	$0.430571\pi$
$770$		0			0
$771$	−10832.5			−0.505996
$772$		0			0
$773$	−12471.8	+	21601.7i	−0.580308	+	1.00512i	0.415134	+	0.909760i	$0.363735\pi$
$773$	−12471.8	+	21601.7i	−0.580308	+	1.00512i	−0.995443	+	0.0953630i	$0.969599\pi$
$774$		0			0
$775$	21061.2	+	36479.0i	0.976179	+	1.69079i
$776$		0			0
$777$	14838.0	+	8863.83i	0.685085	+	0.409251i
$778$		0			0
$779$	17712.0	+	30678.1i	0.814632	+	1.41098i
$780$		0			0
$781$	969.773	−	1679.70i	0.0444318	−	0.0769581i
$782$		0			0
$783$	7006.61			0.319790
$784$		0			0
$785$	25767.3			1.17156
$786$		0			0
$787$	4126.58	−	7147.44i	0.186908	−	0.323734i	−0.757310	−	0.653056i	$-0.773487\pi$
$787$	4126.58	−	7147.44i	0.186908	−	0.323734i	0.944218	+	0.329322i	$0.106820\pi$
$788$		0			0
$789$	−6600.42	−	11432.3i	−0.297821	−	0.515842i
$790$		0			0
$791$	9286.20	+	5547.32i	0.417420	+	0.249355i
$792$		0			0
$793$	1127.16	+	1952.31i	0.0504751	+	0.0874255i
$794$		0			0
$795$	11840.2	−	20507.9i	0.528213	−	0.914892i
$796$		0			0
$797$	12314.7			0.547315			0.273657	−	0.961827i	$-0.411767\pi$
$797$	12314.7			0.547315			0.273657	+	0.961827i	$0.411767\pi$
$798$		0			0
$799$	2771.30			0.122705
$800$		0			0
$801$	10878.5	−	18842.1i	0.479867	−	0.831154i
$802$		0			0
$803$	−5793.94	−	10035.4i	−0.254625	−	0.441023i
$804$		0			0
$805$	−27752.4	+	15476.7i	−1.21509	+	0.677616i
$806$		0			0
$807$	4710.06	+	8158.07i	0.205455	+	0.355858i
$808$		0			0
$809$	10920.4	−	18914.7i	0.474588	−	0.822010i	−0.524989	−	0.851109i	$-0.675931\pi$
$809$	10920.4	−	18914.7i	0.474588	−	0.822010i	0.999577	+	0.0290992i	$0.00926387\pi$
$810$		0			0
$811$	−42180.2			−1.82632			−0.913161	−	0.407600i	$-0.866366\pi$
$811$	−42180.2			−1.82632			−0.913161	+	0.407600i	$0.866366\pi$
$812$		0			0
$813$	24909.5			1.07456
$814$		0			0
$815$	−26761.9	+	46353.0i	−1.15022	+	1.99224i
$816$		0			0
$817$	3010.94	+	5215.11i	0.128935	+	0.223321i
$818$		0			0
$819$	−80.5086	+	5407.71i	−0.00343492	+	0.230721i
$820$		0			0
$821$	9809.13	+	16989.9i	0.416980	+	0.722231i	0.995634	−	0.0933421i	$-0.0297550\pi$
$821$	9809.13	+	16989.9i	0.416980	+	0.722231i	−0.578654	+	0.815573i	$0.696422\pi$
$822$		0			0
$823$	−11817.3	+	20468.1i	−0.500516	+	0.866920i	0.499484	+	0.866323i	$0.333523\pi$
$823$	−11817.3	+	20468.1i	−0.500516	+	0.866920i	−1.00000		0.000596246i	$0.999810\pi$
$824$		0			0
$825$	10180.7			0.429631
$826$		0			0
$827$	1479.01			0.0621888			0.0310944	−	0.999516i	$-0.490101\pi$
$827$	1479.01			0.0621888			0.0310944	+	0.999516i	$0.490101\pi$
$828$		0			0
$829$	−13307.3	+	23048.8i	−0.557515	+	0.965645i	0.440188	+	0.897906i	$0.354912\pi$
$829$	−13307.3	+	23048.8i	−0.557515	+	0.965645i	−0.997703	+	0.0677391i	$0.978421\pi$
$830$		0			0
$831$	−3049.26	−	5281.47i	−0.127290	−	0.220472i
$832$		0			0
$833$	−2311.38	−	68.8376i	−0.0961399	−	0.00286324i
$834$		0			0
$835$	−32467.5	−	56235.4i	−1.34561	−	2.33067i
$836$		0			0
$837$	−10609.0	+	18375.3i	−0.438113	+	0.758834i
$838$		0			0
$839$	−56.5620			−0.00232746			−0.00116373	−	0.999999i	$-0.500370\pi$
$839$	−56.5620			−0.00232746			−0.00116373	+	0.999999i	$0.500370\pi$
$840$		0			0
$841$	−21952.1			−0.900080
$842$		0			0
$843$	−241.018	+	417.456i	−0.00984711	+	0.0170557i
$844$		0			0
$845$	18882.8	+	32706.0i	0.768743	+	1.33150i
$846$		0			0
$847$	33.3590	−	2240.70i	0.00135328	−	0.0908990i
$848$		0			0
$849$	−1932.81	−	3347.72i	−0.0781317	−	0.135328i
$850$		0			0
$851$	−12085.2	+	20932.2i	−0.486811	+	0.843182i
$852$		0			0
$853$	−40634.3			−1.63106			−0.815529	−	0.578716i	$-0.803554\pi$
$853$	−40634.3			−1.63106			−0.815529	+	0.578716i	$0.803554\pi$
$854$		0			0
$855$	−51725.1			−2.06896
$856$		0			0
$857$	17672.3	−	30609.3i	0.704403	−	1.22006i	−0.262503	−	0.964931i	$-0.584548\pi$
$857$	17672.3	−	30609.3i	0.704403	−	1.22006i	0.966906	−	0.255131i	$-0.0821187\pi$
$858$		0			0
$859$	−8997.92	−	15584.8i	−0.357398	−	0.619032i	0.630127	−	0.776492i	$-0.283003\pi$
$859$	−8997.92	−	15584.8i	−0.357398	−	0.619032i	−0.987525	+	0.157460i	$0.949669\pi$
$860$		0			0
$861$	11896.4	−	6634.28i	0.470882	−	0.262597i
$862$		0			0
$863$	−10758.1	−	18633.5i	−0.424344	−	0.734986i	0.572015	−	0.820243i	$-0.306162\pi$
$863$	−10758.1	−	18633.5i	−0.424344	−	0.734986i	−0.996359	+	0.0852576i	$0.972829\pi$
$864$		0			0
$865$	−9193.07	+	15922.9i	−0.361357	+	0.625889i
$866$		0			0
$867$	−15988.3			−0.626286
$868$		0			0
$869$	4619.85			0.180343
$870$		0			0
$871$	−5746.15	+	9952.62i	−0.223537	+	0.387178i
$872$		0			0
$873$	10450.0	+	18099.9i	0.405130	+	0.701705i
$874$		0			0
$875$	50270.6	+	30030.3i	1.94223	+	1.16024i
$876$		0			0
$877$	14944.2	+	25884.1i	0.575405	+	0.996630i	0.995998	+	0.0893806i	$0.0284888\pi$
$877$	14944.2	+	25884.1i	0.575405	+	0.996630i	−0.420593	+	0.907249i	$0.638178\pi$
$878$		0			0
$879$	4545.05	−	7872.25i	0.174403	−	0.302076i
$880$		0			0
$881$	−42643.4			−1.63075			−0.815376	−	0.578932i	$-0.803470\pi$
$881$	−42643.4			−1.63075			−0.815376	+	0.578932i	$0.803470\pi$
$882$		0			0
$883$	−9486.36			−0.361542			−0.180771	−	0.983525i	$-0.557859\pi$
$883$	−9486.36			−0.361542			−0.180771	+	0.983525i	$0.557859\pi$
$884$		0			0
$885$	24776.5	−	42914.2i	0.941077	−	1.62999i
$886$		0			0
$887$	7531.41	+	13044.8i	0.285096	+	0.493800i	0.972632	−	0.232349i	$-0.0746413\pi$
$887$	7531.41	+	13044.8i	0.285096	+	0.493800i	−0.687537	+	0.726150i	$0.741308\pi$
$888$		0			0
$889$	2189.71	+	1308.07i	0.0826102	+	0.0493491i
$890$		0			0
$891$	156.794	+	271.576i	0.00589541	+	0.0102111i
$892$		0			0
$893$	−32516.4	+	56320.1i	−1.21850	+	2.11050i
$894$		0			0
$895$	−30124.0			−1.12507
$896$		0			0
$897$	5033.58			0.187365
$898$		0			0
$899$	−3689.88	+	6391.06i	−0.136890	+	0.237101i
$900$		0			0
$901$	1204.94	+	2087.01i	0.0445530	+	0.0771681i
$902$		0			0
$903$	2022.33	−	1127.79i	0.0745281	−	0.0415620i
$904$		0			0
$905$	19842.3	+	34367.9i	0.728818	+	1.26235i
$906$		0			0
$907$	21568.3	−	37357.5i	0.789598	−	1.36762i	−0.136616	−	0.990624i	$-0.543623\pi$
$907$	21568.3	−	37357.5i	0.789598	−	1.36762i	0.926213	−	0.376999i	$-0.123044\pi$
$908$		0			0
$909$	22018.3			0.803412
$910$		0			0
$911$	−3708.67			−0.134878			−0.0674390	−	0.997723i	$-0.521483\pi$
$911$	−3708.67			−0.134878			−0.0674390	+	0.997723i	$0.521483\pi$
$912$		0			0
$913$	8100.79	−	14031.0i	0.293644	−	0.508606i
$914$		0			0
$915$	4145.21	+	7179.72i	0.149767	+	0.259403i
$916$		0			0
$917$	−426.622	+	28655.9i	−0.0153635	+	1.03195i
$918$		0			0
$919$	24372.4	+	42214.3i	0.874834	+	1.51526i	0.856939	+	0.515417i	$0.172363\pi$
$919$	24372.4	+	42214.3i	0.874834	+	1.51526i	0.0178947	+	0.999840i	$0.494304\pi$
$920$		0			0
$921$	−4824.10	+	8355.59i	−0.172595	+	0.298942i
$922$		0			0
$923$	−3176.24			−0.113269
$924$		0			0
$925$	80056.6			2.84567
$926$		0			0
$927$	−9319.04	+	16141.1i	−0.330181	+	0.571890i
$928$		0			0
$929$	2501.80	+	4333.25i	0.0883547	+	0.153035i	0.906816	−	0.421527i	$-0.138506\pi$
$929$	2501.80	+	4333.25i	0.0883547	+	0.153035i	−0.818461	+	0.574562i	$0.805172\pi$
$930$		0			0
$931$	28519.0	−	46165.6i	1.00394	−	1.62515i
$932$		0			0
$933$	−5314.17	−	9204.41i	−0.186472	−	0.322978i
$934$		0			0
$935$	−747.835	+	1295.29i	−0.0261570	+	0.0453053i
$936$		0			0
$937$	34591.3			1.20603			0.603014	−	0.797731i	$-0.293966\pi$
$937$	34591.3			1.20603			0.603014	+	0.797731i	$0.293966\pi$
$938$		0			0
$939$	31236.1			1.08557
$940$		0			0
$941$	−1352.21	+	2342.10i	−0.0468446	+	0.0811373i	−0.888497	−	0.458882i	$-0.848250\pi$
$941$	−1352.21	+	2342.10i	−0.0468446	+	0.0811373i	0.841652	+	0.540020i	$0.181583\pi$
$942$		0			0
$943$	9524.24	+	16496.5i	0.328899	+	0.569670i
$944$		0			0
$945$	−789.199	+	53010.0i	−0.0271668	+	1.82478i
$946$		0			0
$947$	−5521.24	−	9563.06i	−0.189457	−	0.328150i	0.755612	−	0.655019i	$-0.227340\pi$
$947$	−5521.24	−	9563.06i	−0.189457	−	0.328150i	−0.945069	+	0.326870i	$0.894006\pi$
$948$		0			0
$949$	−9488.26	+	16434.1i	−0.324554	+	0.562144i
$950$		0			0
$951$	−14569.3			−0.496783
$952$		0			0
$953$	14088.1			0.478864			0.239432	−	0.970913i	$-0.423039\pi$
$953$	14088.1			0.478864			0.239432	+	0.970913i	$0.423039\pi$
$954$		0			0
$955$	−3390.13	+	5871.88i	−0.114871	+	0.198963i
$956$		0			0
$957$	891.819	+	1544.68i	0.0301237	+	0.0521758i
$958$		0			0
$959$	9692.34	−	5405.12i	0.326363	−	0.182003i
$960$		0			0
$961$	3721.50	+	6445.83i	0.124920	+	0.216368i
$962$		0			0
$963$	11603.2	−	20097.4i	0.388275	−	0.672512i
$964$		0			0
$965$	−46022.0			−1.53524
$966$		0			0
$967$	42880.4			1.42600			0.712999	−	0.701165i	$-0.247336\pi$
$967$	42880.4			1.42600			0.712999	+	0.701165i	$0.247336\pi$
$968$		0			0
$969$	−1751.66	+	3033.96i	−0.0580715	+	0.100583i
$970$		0			0
$971$	−25902.6	−	44864.6i	−0.856079	−	1.48277i	−0.875640	−	0.482964i	$-0.839560\pi$
$971$	−25902.6	−	44864.6i	−0.856079	−	1.48277i	0.0195610	−	0.999809i	$-0.493773\pi$
$972$		0			0
$973$	27997.4	+	16724.9i	0.922461	+	0.551053i
$974$		0			0
$975$	−8336.03	−	14438.4i	−0.273812	−	0.474256i
$976$		0			0
$977$	−1160.79	+	2010.54i	−0.0380111	+	0.0658372i	−0.884405	−	0.466720i	$-0.845436\pi$
$977$	−1160.79	+	2010.54i	−0.0380111	+	0.0658372i	0.846394	+	0.532557i	$0.178769\pi$
$978$		0			0
$979$	14763.3			0.481958
$980$		0			0
$981$	−18124.9			−0.589891
$982$		0			0
$983$	7795.68	−	13502.5i	0.252943	−	0.438111i	−0.711391	−	0.702796i	$-0.751935\pi$
$983$	7795.68	−	13502.5i	0.252943	−	0.438111i	0.964335	+	0.264685i	$0.0852680\pi$
$984$		0			0
$985$	−18252.9	−	31614.9i	−0.590442	−	1.02268i
$986$		0			0
$987$	21467.7	+	12824.2i	0.692325	+	0.413576i
$988$		0			0
$989$	1619.07	+	2804.31i	0.0520559	+	0.0901635i
$990$		0			0
$991$	5846.09	−	10125.7i	0.187394	−	0.324575i	−0.756987	−	0.653430i	$-0.773329\pi$
$991$	5846.09	−	10125.7i	0.187394	−	0.324575i	0.944381	+	0.328855i	$0.106663\pi$
$992$		0			0
$993$	−8907.20			−0.284654
$994$		0			0
$995$	36169.8			1.15242
$996$		0			0
$997$	15392.7	−	26660.9i	0.488959	−	0.846901i	−0.510961	−	0.859604i	$-0.670710\pi$
$997$	15392.7	−	26660.9i	0.488959	−	0.846901i	0.999919	+	0.0127030i	$0.00404359\pi$
$998$		0			0
$999$	20163.2	+	34923.7i	0.638574	+	1.10604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.4.i.a.221.4	yes	20
7.2	even	3	inner	308.4.i.a.177.4	✓	20
7.3	odd	6		2156.4.a.j.1.4		10
7.4	even	3		2156.4.a.m.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.4.i.a.177.4	✓	20	7.2	even	3	inner
308.4.i.a.221.4	yes	20	1.1	even	1	trivial
2156.4.a.j.1.4		10	7.3	odd	6
2156.4.a.m.1.7		10	7.4	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)

\(f(q)\)	\(=\)	\(q+(-1.64233 + 2.84460i) q^{3} +(-10.0843 - 17.4664i) q^{5} +(15.8994 + 9.49786i) q^{7} +(8.10549 + 14.0391i) q^{9} +(-5.50000 + 9.52628i) q^{11} +18.0138 q^{13} +66.2468 q^{15} +(-3.37085 + 5.83848i) q^{17} +(-79.1022 - 137.009i) q^{19} +(-53.1297 + 29.6288i) q^{21} +(-42.5354 - 73.6735i) q^{23} +(-140.884 + 244.019i) q^{25} -141.934 q^{27} -49.3654 q^{29} +(74.7462 - 129.464i) q^{31} +(-18.0657 - 31.2906i) q^{33} +(5.56034 - 373.485i) q^{35} +(-142.061 - 246.057i) q^{37} +(-29.5847 + 51.2421i) q^{39} -223.913 q^{41} -38.0640 q^{43} +(163.476 - 283.148i) q^{45} +(-205.534 - 355.996i) q^{47} +(162.581 + 302.020i) q^{49} +(-11.0721 - 19.1775i) q^{51} +(178.729 - 309.568i) q^{53} +221.854 q^{55} +519.648 q^{57} +(374.003 - 647.792i) q^{59} +(62.5723 + 108.378i) q^{61} +(-4.46927 + 300.198i) q^{63} +(-181.656 - 314.637i) q^{65} +(-318.986 + 552.499i) q^{67} +279.429 q^{69} -176.322 q^{71} +(-526.722 + 912.308i) q^{73} +(-462.758 - 801.520i) q^{75} +(-177.926 + 99.2238i) q^{77} +(-209.993 - 363.719i) q^{79} +(14.2540 - 24.6887i) q^{81} -1472.87 q^{83} +135.970 q^{85} +(81.0744 - 140.425i) q^{87} +(-671.059 - 1162.31i) q^{89} +(286.409 + 171.093i) q^{91} +(245.516 + 425.247i) q^{93} +(-1595.37 + 2763.27i) q^{95} +1289.25 q^{97} -178.321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} - 10 q^{5} - 20 q^{7} - 104 q^{9} - 110 q^{11} + 16 q^{13} + 108 q^{15} - 166 q^{17} - 342 q^{19} - 42 q^{21} + 54 q^{23} - 198 q^{25} + 612 q^{27} - 160 q^{29} - 492 q^{31} - 66 q^{33} + 310 q^{35}+ \cdots + 2288 q^{99}+O(q^{100}) \) 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

L-functions

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