LMFDB - Embedded newform 672.4.bb.a.271.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,4,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.10
Character	$\chi$	$=$	672.271
Dual form			672.4.bb.a.367.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 + 1.50000i) q^{3} +(2.37912 - 4.12075i) q^{5} +(11.6311 + 14.4124i) q^{7} +(4.50000 - 7.79423i) q^{9} +(-11.1023 - 19.2297i) q^{11} -35.2705 q^{13} +14.2747i q^{15} +(25.4218 - 14.6773i) q^{17} +(-51.7365 - 29.8701i) q^{19} +(-51.8371 - 19.9980i) q^{21} +(-57.0064 - 32.9126i) q^{23} +(51.1796 + 88.6457i) q^{25} +27.0000i q^{27} -5.47499i q^{29} +(8.58171 + 14.8640i) q^{31} +(57.6891 + 33.3068i) q^{33} +(87.0617 - 13.6399i) q^{35} +(-10.7790 - 6.22327i) q^{37} +(91.6354 - 52.9057i) q^{39} -19.7660i q^{41} -297.874 q^{43} +(-21.4120 - 37.0867i) q^{45} +(165.783 - 287.145i) q^{47} +(-72.4363 + 335.264i) q^{49} +(-44.0318 + 76.2653i) q^{51} +(-114.567 + 66.1451i) q^{53} -105.654 q^{55} +179.221 q^{57} +(4.77742 - 2.75824i) q^{59} +(200.724 - 347.665i) q^{61} +(164.674 - 25.7993i) q^{63} +(-83.9126 + 145.341i) q^{65} +(-527.372 - 913.435i) q^{67} +197.476 q^{69} -273.718i q^{71} +(-781.728 + 451.331i) q^{73} +(-265.937 - 153.539i) q^{75} +(148.015 - 383.673i) q^{77} +(-719.113 - 415.180i) q^{79} +(-40.5000 - 70.1481i) q^{81} -208.136i q^{83} -139.676i q^{85} +(8.21248 + 14.2244i) q^{87} +(-1164.39 - 672.259i) q^{89} +(-410.234 - 508.334i) q^{91} +(-44.5919 - 25.7451i) q^{93} +(-246.174 + 142.129i) q^{95} +703.232i q^{97} -199.841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) $ 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$4$		0			0
$5$	2.37912	−	4.12075i	0.212795	−	0.368571i	−0.739794	−	0.672834i	$-0.765077\pi$
$5$	2.37912	−	4.12075i	0.212795	−	0.368571i	0.952588	+	0.304263i	$0.0984102\pi$
$6$		0			0
$7$	11.6311	+	14.4124i	0.628019	+	0.778198i
$7$	11.6311	+	14.4124i	0.628019	+	0.778198i
$8$		0			0
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$		0			0
$11$	−11.1023	−	19.2297i	−0.304315	−	0.527088i	0.672794	−	0.739830i	$-0.265094\pi$
$11$	−11.1023	−	19.2297i	−0.304315	−	0.527088i	−0.977108	+	0.212742i	$0.931761\pi$
$12$		0			0
$13$	−35.2705			−0.752483			−0.376241	−	0.926522i	$-0.622784\pi$
$13$	−35.2705			−0.752483			−0.376241	+	0.926522i	$0.622784\pi$
$14$		0			0
$15$			14.2747i			0.245714i
$16$		0			0
$17$	25.4218	−	14.6773i	0.362687	−	0.209398i	−0.307572	−	0.951525i	$-0.599516\pi$
$17$	25.4218	−	14.6773i	0.362687	−	0.209398i	0.670259	+	0.742127i	$0.266183\pi$
$18$		0			0
$19$	−51.7365	−	29.8701i	−0.624694	−	0.360667i	0.154001	−	0.988071i	$-0.450784\pi$
$19$	−51.7365	−	29.8701i	−0.624694	−	0.360667i	−0.778694	+	0.627404i	$0.784118\pi$
$20$		0			0
$21$	−51.8371	−	19.9980i	−0.538656	−	0.207806i
$22$		0			0
$23$	−57.0064	−	32.9126i	−0.516811	−	0.298381i	0.218818	−	0.975766i	$-0.429780\pi$
$23$	−57.0064	−	32.9126i	−0.516811	−	0.298381i	−0.735629	+	0.677385i	$0.763113\pi$
$24$		0			0
$25$	51.1796	+	88.6457i	0.409437	+	0.709166i
$26$		0			0
$27$			27.0000i			0.192450i
$28$		0			0
$29$		−	5.47499i		−	0.0350579i	−0.999846	−	0.0175290i	$-0.994420\pi$
$29$		−	5.47499i		−	0.0350579i	0.999846	−	0.0175290i	$-0.00557993\pi$
$30$		0			0
$31$	8.58171	+	14.8640i	0.0497200	+	0.0861176i	0.889814	−	0.456323i	$-0.150834\pi$
$31$	8.58171	+	14.8640i	0.0497200	+	0.0861176i	−0.840094	+	0.542440i	$0.817500\pi$
$32$		0			0
$33$	57.6891	+	33.3068i	0.304315	+	0.175696i
$34$		0			0
$35$	87.0617	−	13.6399i	0.420460	−	0.0658732i
$36$		0			0
$37$	−10.7790	−	6.22327i	−0.0478935	−	0.0276513i	0.475862	−	0.879520i	$-0.342136\pi$
$37$	−10.7790	−	6.22327i	−0.0478935	−	0.0276513i	−0.523756	+	0.851869i	$0.675469\pi$
$38$		0			0
$39$	91.6354	−	52.9057i	0.376241	−	0.217223i
$40$		0			0
$41$		−	19.7660i		−	0.0752910i	−0.999291	−	0.0376455i	$-0.988014\pi$
$41$		−	19.7660i		−	0.0752910i	0.999291	−	0.0376455i	$-0.0119858\pi$
$42$		0			0
$43$	−297.874			−1.05640			−0.528202	−	0.849119i	$-0.677134\pi$
$43$	−297.874			−1.05640			−0.528202	+	0.849119i	$0.677134\pi$
$44$		0			0
$45$	−21.4120	−	37.0867i	−0.0709315	−	0.122857i
$46$		0			0
$47$	165.783	−	287.145i	0.514510	−	0.891157i	−0.485348	−	0.874321i	$-0.661307\pi$
$47$	165.783	−	287.145i	0.514510	−	0.891157i	0.999858	−	0.0168365i	$-0.00535949\pi$
$48$		0			0
$49$	−72.4363	+	335.264i	−0.211185	+	0.977446i
$50$		0			0
$51$	−44.0318	+	76.2653i	−0.120896	+	0.209398i
$52$		0			0
$53$	−114.567	+	66.1451i	−0.296923	+	0.171429i	−0.641060	−	0.767491i	$-0.721505\pi$
$53$	−114.567	+	66.1451i	−0.296923	+	0.171429i	0.344137	+	0.938920i	$0.388172\pi$
$54$		0			0
$55$	−105.654			−0.259026
$56$		0			0
$57$	179.221			0.416462
$58$		0			0
$59$	4.77742	−	2.75824i	0.0105418	−	0.00608632i	−0.494720	−	0.869053i	$-0.664729\pi$
$59$	4.77742	−	2.75824i	0.0105418	−	0.00608632i	0.505262	+	0.862966i	$0.331396\pi$
$60$		0			0
$61$	200.724	−	347.665i	0.421313	−	0.729736i	−0.574755	−	0.818326i	$-0.694903\pi$
$61$	200.724	−	347.665i	0.421313	−	0.729736i	0.996068	+	0.0885896i	$0.0282360\pi$
$62$		0			0
$63$	164.674	−	25.7993i	0.329316	−	0.0515937i
$64$		0			0
$65$	−83.9126	+	145.341i	−0.160124	+	0.277343i
$66$		0			0
$67$	−527.372	−	913.435i	−0.961623	−	1.66558i	−0.718425	−	0.695604i	$-0.755137\pi$
$67$	−527.372	−	913.435i	−0.961623	−	1.66558i	−0.243198	−	0.969977i	$-0.578197\pi$
$68$		0			0
$69$	197.476			0.344541
$70$		0			0
$71$		−	273.718i		−	0.457526i	−0.973482	−	0.228763i	$-0.926532\pi$
$71$		−	273.718i		−	0.457526i	0.973482	−	0.228763i	$-0.0734681\pi$
$72$		0			0
$73$	−781.728	+	451.331i	−1.25335	+	0.723621i	−0.971773	−	0.235919i	$-0.924190\pi$
$73$	−781.728	+	451.331i	−1.25335	+	0.723621i	−0.281575	+	0.959539i	$0.590857\pi$
$74$		0			0
$75$	−265.937	−	153.539i	−0.409437	−	0.236389i
$76$		0			0
$77$	148.015	−	383.673i	0.219064	−	0.567838i
$78$		0			0
$79$	−719.113	−	415.180i	−1.02413	−	0.591284i	−0.108835	−	0.994060i	$-0.534712\pi$
$79$	−719.113	−	415.180i	−1.02413	−	0.591284i	−0.915298	+	0.402776i	$0.868045\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	208.136i		−	0.275251i	−0.990484	−	0.137626i	$-0.956053\pi$
$83$		−	208.136i		−	0.275251i	0.990484	−	0.137626i	$-0.0439471\pi$
$84$		0			0
$85$		−	139.676i		−	0.178235i
$86$		0			0
$87$	8.21248	+	14.2244i	0.0101204	+	0.0175290i
$88$		0			0
$89$	−1164.39	−	672.259i	−1.38679	−	0.800666i	−0.393842	−	0.919178i	$-0.628854\pi$
$89$	−1164.39	−	672.259i	−1.38679	−	0.800666i	−0.992953	+	0.118512i	$0.962188\pi$
$90$		0			0
$91$	−410.234	−	508.334i	−0.472573	−	0.585581i
$92$		0			0
$93$	−44.5919	−	25.7451i	−0.0497200	−	0.0287059i
$94$		0			0
$95$	−246.174	+	142.129i	−0.265863	+	0.153496i
$96$		0			0
$97$			703.232i			0.736107i	0.929805	+	0.368054i	$0.119976\pi$
$97$			703.232i			0.736107i	−0.929805	+	0.368054i	$0.880024\pi$
$98$		0			0
$99$	−199.841			−0.202876
$100$		0			0
$101$	−875.614	−	1516.61i	−0.862642	−	1.49414i	−0.869370	−	0.494162i	$-0.835475\pi$
$101$	−875.614	−	1516.61i	−0.862642	−	1.49414i	0.00672809	−	0.999977i	$-0.497858\pi$
$102$		0			0
$103$	798.830	−	1383.61i	0.764185	−	1.32361i	−0.176492	−	0.984302i	$-0.556475\pi$
$103$	798.830	−	1383.61i	0.764185	−	1.32361i	0.940677	−	0.339305i	$-0.110192\pi$
$104$		0			0
$105$	−205.733	+	166.030i	−0.191214	+	0.154313i
$106$		0			0
$107$	−533.169	+	923.476i	−0.481714	+	0.834353i	−0.999780	−	0.0209879i	$-0.993319\pi$
$107$	−533.169	+	923.476i	−0.481714	+	0.834353i	0.518066	+	0.855341i	$0.326652\pi$
$108$		0			0
$109$	499.543	−	288.411i	0.438969	−	0.253439i	−0.264191	−	0.964470i	$-0.585105\pi$
$109$	499.543	−	288.411i	0.438969	−	0.253439i	0.703160	+	0.711032i	$0.251772\pi$
$110$		0			0
$111$	37.3396			0.0319290
$112$		0			0
$113$	−383.291			−0.319088			−0.159544	−	0.987191i	$-0.551002\pi$
$113$	−383.291			−0.319088			−0.159544	+	0.987191i	$0.551002\pi$
$114$		0			0
$115$	−271.249	+	156.606i	−0.219949	+	0.126988i
$116$		0			0
$117$	−158.717	+	274.906i	−0.125414	+	0.217223i
$118$		0			0
$119$	507.218	+	195.677i	0.390727	+	0.150737i
$120$		0			0
$121$	418.979	−	725.693i	0.314785	−	0.545224i
$122$		0			0
$123$	29.6490	+	51.3536i	0.0217346	+	0.0376455i
$124$		0			0
$125$	1081.83			0.774093
$126$		0			0
$127$		−	2798.55i		−	1.95536i	−0.210098	−	0.977680i	$-0.567378\pi$
$127$		−	2798.55i		−	1.95536i	0.210098	−	0.977680i	$-0.432622\pi$
$128$		0			0
$129$	773.899	−	446.811i	0.528202	−	0.304957i
$130$		0			0
$131$	1467.12	+	847.041i	0.978494	+	0.564934i	0.901815	−	0.432122i	$-0.142235\pi$
$131$	1467.12	+	847.041i	0.978494	+	0.564934i	0.0766792	+	0.997056i	$0.475568\pi$
$132$		0			0
$133$	−171.251	−	1093.07i	−0.111649	−	0.712641i
$134$		0			0
$135$	111.260	+	64.2361i	0.0709315	+	0.0409523i
$136$		0			0
$137$	−1506.78	−	2609.83i	−0.939658	−	1.62754i	−0.766109	−	0.642711i	$-0.777810\pi$
$137$	−1506.78	−	2609.83i	−0.939658	−	1.62754i	−0.173550	−	0.984825i	$-0.555524\pi$
$138$		0			0
$139$			1912.12i			1.16679i	0.812189	+	0.583394i	$0.198276\pi$
$139$			1912.12i			1.16679i	−0.812189	+	0.583394i	$0.801724\pi$
$140$		0			0
$141$			994.699i			0.594105i
$142$		0			0
$143$	391.583	+	678.241i	0.228991	+	0.396625i
$144$		0			0
$145$	−22.5611	−	13.0256i	−0.0129213	−	0.00746014i
$146$		0			0
$147$	−314.701	−	979.696i	−0.176572	−	0.549687i
$148$		0			0
$149$	942.151	+	543.951i	0.518014	+	0.299075i	0.736122	−	0.676849i	$-0.236655\pi$
$149$	942.151	+	543.951i	0.518014	+	0.299075i	−0.218108	+	0.975925i	$0.569988\pi$
$150$		0			0
$151$	−612.435	+	353.589i	−0.330061	+	0.190561i	−0.655868	−	0.754875i	$-0.727697\pi$
$151$	−612.435	+	353.589i	−0.330061	+	0.190561i	0.325807	+	0.945436i	$0.394364\pi$
$152$		0			0
$153$		−	264.191i		−	0.139598i
$154$		0			0
$155$	81.6675			0.0423206
$156$		0			0
$157$	−1812.24	−	3138.90i	−0.921227	−	1.59561i	−0.797519	−	0.603294i	$-0.793854\pi$
$157$	−1812.24	−	3138.90i	−0.921227	−	1.59561i	−0.123709	−	0.992319i	$-0.539479\pi$
$158$		0			0
$159$	198.435	−	343.700i	0.0989744	−	0.171429i
$160$		0			0
$161$	−188.694	−	1204.41i	−0.0923675	−	0.589570i
$162$		0			0
$163$	−1322.37	+	2290.41i	−0.635434	+	1.10060i	0.350989	+	0.936380i	$0.385845\pi$
$163$	−1322.37	+	2290.41i	−0.635434	+	1.10060i	−0.986423	+	0.164224i	$0.947488\pi$
$164$		0			0
$165$	274.498	−	158.482i	0.129513	−	0.0747744i
$166$		0			0
$167$	−1429.17			−0.662229			−0.331114	−	0.943591i	$-0.607425\pi$
$167$	−1429.17			−0.662229			−0.331114	+	0.943591i	$0.607425\pi$
$168$		0			0
$169$	−952.992			−0.433770
$170$		0			0
$171$	−465.629	+	268.831i	−0.208231	+	0.120222i
$172$		0			0
$173$	649.225	−	1124.49i	0.285316	−	0.494182i	−0.687370	−	0.726308i	$-0.741235\pi$
$173$	649.225	−	1124.49i	0.285316	−	0.494182i	0.972686	+	0.232126i	$0.0745681\pi$
$174$		0			0
$175$	−682.326	+	1768.67i	−0.294737	+	0.763992i
$176$		0			0
$177$	−8.27473	+	14.3322i	−0.00351394	+	0.00608632i
$178$		0			0
$179$	1562.23	+	2705.86i	0.652327	+	1.12986i	0.982557	+	0.185963i	$0.0595406\pi$
$179$	1562.23	+	2705.86i	0.652327	+	1.12986i	−0.330229	+	0.943901i	$0.607126\pi$
$180$		0			0
$181$	−871.221			−0.357775			−0.178888	−	0.983870i	$-0.557250\pi$
$181$	−871.221			−0.357775			−0.178888	+	0.983870i	$0.557250\pi$
$182$		0			0
$183$			1204.35i			0.486491i
$184$		0			0
$185$	−51.2890	+	29.6117i	−0.0203829	+	0.0117681i
$186$		0			0
$187$	−564.479	−	325.902i	−0.220742	−	0.127446i
$188$		0			0
$189$	−389.136	+	314.039i	−0.149764	+	0.120862i
$190$		0			0
$191$	2526.95	+	1458.94i	0.957298	+	0.552696i	0.895340	−	0.445383i	$-0.146932\pi$
$191$	2526.95	+	1458.94i	0.957298	+	0.552696i	0.0619573	+	0.998079i	$0.480266\pi$
$192$		0			0
$193$	−708.867	−	1227.79i	−0.264380	−	0.457920i	0.703021	−	0.711169i	$-0.251834\pi$
$193$	−708.867	−	1227.79i	−0.264380	−	0.457920i	−0.967401	+	0.253249i	$0.918501\pi$
$194$		0			0
$195$		−	503.476i		−	0.184896i
$196$		0			0
$197$			5186.19i			1.87564i	0.347124	+	0.937819i	$0.387158\pi$
$197$			5186.19i			1.87564i	−0.347124	+	0.937819i	$0.612842\pi$
$198$		0			0
$199$	45.8417	+	79.4002i	0.0163298	+	0.0282841i	0.874075	−	0.485791i	$-0.161468\pi$
$199$	45.8417	+	79.4002i	0.0163298	+	0.0282841i	−0.857745	+	0.514075i	$0.828135\pi$
$200$		0			0
$201$	2740.31	+	1582.12i	0.961623	+	0.555194i
$202$		0			0
$203$	78.9079	−	63.6800i	0.0272820	−	0.0220170i
$204$		0			0
$205$	−81.4508	−	47.0256i	−0.0277501	−	0.0160215i
$206$		0			0
$207$	−513.057	+	296.214i	−0.172270	+	0.0994603i
$208$		0			0
$209$			1326.50i			0.439025i
$210$		0			0
$211$	−1708.65			−0.557481			−0.278740	−	0.960367i	$-0.589917\pi$
$211$	−1708.65			−0.557481			−0.278740	+	0.960367i	$0.589917\pi$
$212$		0			0
$213$	410.577	+	711.140i	0.132076	+	0.228763i
$214$		0			0
$215$	−708.677	+	1227.46i	−0.224797	+	0.389360i
$216$		0			0
$217$	−114.411	+	296.567i	−0.0357915	+	0.0927755i
$218$		0			0
$219$	1353.99	−	2345.19i	0.417783	−	0.723621i
$220$		0			0
$221$	−896.639	+	517.675i	−0.272916	+	0.157568i
$222$		0			0
$223$	−3519.46			−1.05686			−0.528432	−	0.848976i	$-0.677220\pi$
$223$	−3519.46			−1.05686			−0.528432	+	0.848976i	$0.677220\pi$
$224$		0			0
$225$	921.233			0.272958
$226$		0			0
$227$	5683.59	−	3281.42i	1.66182	−	0.959452i	0.689975	−	0.723833i	$-0.257622\pi$
$227$	5683.59	−	3281.42i	1.66182	−	0.959452i	0.971845	−	0.235619i	$-0.0757118\pi$
$228$		0			0
$229$	−1139.81	+	1974.20i	−0.328911	+	0.569690i	−0.982296	−	0.187336i	$-0.940015\pi$
$229$	−1139.81	+	1974.20i	−0.328911	+	0.569690i	0.653385	+	0.757025i	$0.273348\pi$
$230$		0			0
$231$	190.954	+	1218.83i	0.0543889	+	0.347158i
$232$		0			0
$233$	−1943.49	+	3366.22i	−0.546448	+	0.946475i	0.452067	+	0.891984i	$0.350687\pi$
$233$	−1943.49	+	3366.22i	−0.546448	+	0.946475i	−0.998514	+	0.0544907i	$0.982646\pi$
$234$		0			0
$235$	−788.835	−	1366.30i	−0.218970	−	0.379267i
$236$		0			0
$237$	2491.08			0.682755
$238$		0			0
$239$		−	2876.41i		−	0.778492i	−0.921134	−	0.389246i	$-0.872736\pi$
$239$		−	2876.41i		−	0.778492i	0.921134	−	0.389246i	$-0.127264\pi$
$240$		0			0
$241$	−436.769	+	252.169i	−0.116742	+	0.0674009i	−0.557234	−	0.830356i	$-0.688137\pi$
$241$	−436.769	+	252.169i	−0.116742	+	0.0674009i	0.440492	+	0.897756i	$0.354804\pi$
$242$		0			0
$243$	210.444	+	121.500i	0.0555556	+	0.0320750i
$244$		0			0
$245$	1209.20	+	1096.12i	0.315319	+	0.285832i
$246$		0			0
$247$	1824.77	+	1053.53i	0.470071	+	0.271396i
$248$		0			0
$249$	312.204	+	540.752i	0.0794582	+	0.137626i
$250$		0			0
$251$		−	2715.27i		−	0.682815i	−0.939915	−	0.341408i	$-0.889096\pi$
$251$		−	2715.27i		−	0.682815i	0.939915	−	0.341408i	$-0.110904\pi$
$252$		0			0
$253$			1461.62i			0.363207i
$254$		0			0
$255$	209.514	+	362.888i	0.0514519	+	0.0891174i
$256$		0			0
$257$	3494.82	+	2017.73i	0.848252	+	0.489739i	0.860061	−	0.510192i	$-0.170426\pi$
$257$	3494.82	+	2017.73i	0.848252	+	0.489739i	−0.0118086	+	0.999930i	$0.503759\pi$
$258$		0			0
$259$	−35.6791	−	227.735i	−0.00855981	−	0.0546362i
$260$		0			0
$261$	−42.6733	−	24.6374i	−0.0101204	−	0.00584299i
$262$		0			0
$263$	−3983.07	+	2299.63i	−0.933866	+	0.539168i	−0.888032	−	0.459781i	$-0.847928\pi$
$263$	−3983.07	+	2299.63i	−0.933866	+	0.539168i	−0.0458338	+	0.998949i	$0.514594\pi$
$264$		0			0
$265$			629.467i			0.145916i
$266$		0			0
$267$	4033.55			0.924530
$268$		0			0
$269$	1157.34	+	2004.56i	0.262320	+	0.454351i	0.966858	−	0.255315i	$-0.0821792\pi$
$269$	1157.34	+	2004.56i	0.262320	+	0.454351i	−0.704538	+	0.709666i	$0.748846\pi$
$270$		0			0
$271$	3501.99	−	6065.62i	0.784984	−	1.35963i	−0.144025	−	0.989574i	$-0.546005\pi$
$271$	3501.99	−	6065.62i	0.784984	−	1.35963i	0.929009	−	0.370058i	$-0.120662\pi$
$272$		0			0
$273$	1828.32	+	705.339i	0.405329	+	0.156370i
$274$		0			0
$275$	1136.42	−	1968.34i	0.249195	−	0.431619i
$276$		0			0
$277$	−3537.30	+	2042.26i	−0.767277	+	0.442987i	−0.831902	−	0.554922i	$-0.812748\pi$
$277$	−3537.30	+	2042.26i	−0.767277	+	0.442987i	0.0646255	+	0.997910i	$0.479415\pi$
$278$		0			0
$279$	154.471			0.0331467
$280$		0			0
$281$	6599.02			1.40094			0.700470	−	0.713682i	$-0.252974\pi$
$281$	6599.02			1.40094			0.700470	+	0.713682i	$0.252974\pi$
$282$		0			0
$283$	−1456.68	+	841.017i	−0.305975	+	0.176655i	−0.645124	−	0.764078i	$-0.723194\pi$
$283$	−1456.68	+	841.017i	−0.305975	+	0.176655i	0.339149	+	0.940733i	$0.389861\pi$
$284$		0			0
$285$	426.387	−	738.523i	0.0886209	−	0.153496i
$286$		0			0
$287$	284.876	−	229.900i	0.0585913	−	0.0472842i
$288$		0			0
$289$	−2025.66	+	3508.54i	−0.412305	+	0.714134i
$290$		0			0
$291$	−1054.85	−	1827.05i	−0.212496	−	0.368054i
$292$		0			0
$293$	4713.33			0.939780			0.469890	−	0.882725i	$-0.344294\pi$
$293$	4713.33			0.939780			0.469890	+	0.882725i	$0.344294\pi$
$294$		0			0
$295$		−	26.2487i		−	0.00518054i
$296$		0			0
$297$	519.202	−	299.761i	0.101438	−	0.0585654i
$298$		0			0
$299$	2010.64	+	1160.85i	0.388891	+	0.224526i
$300$		0			0
$301$	−3464.59	−	4293.09i	−0.663441	−	0.822091i
$302$		0			0
$303$	4549.82	+	2626.84i	0.862642	+	0.498046i
$304$		0			0
$305$	−955.092	−	1654.27i	−0.179306	−	0.310568i
$306$		0			0
$307$		−	384.191i		−	0.0714233i	−0.999362	−	0.0357116i	$-0.988630\pi$
$307$		−	384.191i		−	0.0714233i	0.999362	−	0.0357116i	$-0.0113698\pi$
$308$		0			0
$309$			4792.98i			0.882404i
$310$		0			0
$311$	4891.13	+	8471.69i	0.891803	+	1.54465i	0.837713	+	0.546111i	$0.183892\pi$
$311$	4891.13	+	8471.69i	0.891803	+	1.54465i	0.0540901	+	0.998536i	$0.482774\pi$
$312$		0			0
$313$	6043.10	+	3488.98i	1.09130	+	0.630061i	0.933922	−	0.357478i	$-0.116363\pi$
$313$	6043.10	+	3488.98i	1.09130	+	0.630061i	0.157376	+	0.987539i	$0.449697\pi$
$314$		0			0
$315$	285.465	−	739.958i	0.0510608	−	0.132355i
$316$		0			0
$317$	−3517.20	−	2030.66i	−0.623173	−	0.359789i	0.154930	−	0.987925i	$-0.450485\pi$
$317$	−3517.20	−	2030.66i	−0.623173	−	0.359789i	−0.778103	+	0.628136i	$0.783818\pi$
$318$		0			0
$319$	−105.282	+	60.7848i	−0.0184786	+	0.0106686i
$320$		0			0
$321$		−	3199.01i		−	0.556235i
$322$		0			0
$323$	−1753.65			−0.302091
$324$		0			0
$325$	−1805.13	−	3126.58i	−0.308094	−	0.533635i
$326$		0			0
$327$	−865.234	+	1498.63i	−0.146323	+	0.253439i
$328$		0			0
$329$	6066.69	−	950.464i	1.01662	−	0.159273i
$330$		0			0
$331$	−3756.03	+	6505.64i	−0.623717	+	1.08031i	0.365071	+	0.930980i	$0.381045\pi$
$331$	−3756.03	+	6505.64i	−0.623717	+	1.08031i	−0.988787	+	0.149330i	$0.952288\pi$
$332$		0			0
$333$	−97.0111	+	56.0094i	−0.0159645	+	0.00921711i
$334$		0			0
$335$	−5018.72			−0.818513
$336$		0			0
$337$	−5383.56			−0.870212			−0.435106	−	0.900379i	$-0.643289\pi$
$337$	−5383.56			−0.870212			−0.435106	+	0.900379i	$0.643289\pi$
$338$		0			0
$339$	995.819	−	574.937i	0.159544	−	0.0921129i
$340$		0			0
$341$	190.553	−	330.047i	0.0302611	−	0.0524137i
$342$		0			0
$343$	−5674.48	+	2855.50i	−0.893275	+	0.449511i
$344$		0			0
$345$	469.818	−	813.748i	0.0733164	−	0.126988i
$346$		0			0
$347$	−3326.59	−	5761.82i	−0.514641	−	0.891385i	−0.999856	−	0.0169898i	$-0.994592\pi$
$347$	−3326.59	−	5761.82i	−0.514641	−	0.891385i	0.485214	−	0.874395i	$-0.338742\pi$
$348$		0			0
$349$	8118.51			1.24520			0.622599	−	0.782541i	$-0.286077\pi$
$349$	8118.51			1.24520			0.622599	+	0.782541i	$0.286077\pi$
$350$		0			0
$351$		−	952.303i		−	0.144815i
$352$		0			0
$353$	6867.25	−	3964.81i	1.03543	−	0.597806i	0.116894	−	0.993144i	$-0.462706\pi$
$353$	6867.25	−	3964.81i	1.03543	−	0.597806i	0.918535	+	0.395339i	$0.129373\pi$
$354$		0			0
$355$	−1127.92	−	651.207i	−0.168631	−	0.0973591i
$356$		0			0
$357$	−1611.31	+	252.442i	−0.238878	+	0.0374248i
$358$		0			0
$359$	10088.9	+	5824.85i	1.48321	+	0.856334i	0.999818	−	0.0190675i	$-0.00606975\pi$
$359$	10088.9	+	5824.85i	1.48321	+	0.856334i	0.483396	+	0.875402i	$0.339403\pi$
$360$		0			0
$361$	−1645.05	−	2849.32i	−0.239839	−	0.415413i
$362$		0			0
$363$			2513.88i			0.363483i
$364$		0			0
$365$			4295.08i			0.615930i
$366$		0			0
$367$	−2069.11	−	3583.80i	−0.294296	−	0.509735i	0.680525	−	0.732725i	$-0.261752\pi$
$367$	−2069.11	−	3583.80i	−0.294296	−	0.509735i	−0.974821	+	0.222989i	$0.928418\pi$
$368$		0			0
$369$	−154.061	−	88.9470i	−0.0217346	−	0.0125485i
$370$		0			0
$371$	−2285.84	−	881.845i	−0.319879	−	0.123405i
$372$		0			0
$373$	−78.9240	−	45.5668i	−0.0109559	−	0.00632536i	0.494512	−	0.869171i	$-0.335347\pi$
$373$	−78.9240	−	45.5668i	−0.0109559	−	0.00632536i	−0.505468	+	0.862845i	$0.668680\pi$
$374$		0			0
$375$	−2810.67	+	1622.74i	−0.387046	+	0.223461i
$376$		0			0
$377$			193.106i			0.0263805i
$378$		0			0
$379$	6565.01			0.889768			0.444884	−	0.895588i	$-0.353245\pi$
$379$	6565.01			0.889768			0.444884	+	0.895588i	$0.353245\pi$
$380$		0			0
$381$	4197.82	+	7270.84i	0.564464	+	0.977680i
$382$		0			0
$383$	−70.5241	+	122.151i	−0.00940892	+	0.0162967i	−0.870692	−	0.491830i	$-0.836328\pi$
$383$	−70.5241	+	122.151i	−0.00940892	+	0.0162967i	0.861283	+	0.508126i	$0.169662\pi$
$384$		0			0
$385$	−1228.87	−	1522.74i	−0.162673	−	0.201574i
$386$		0			0
$387$	−1340.43	+	2321.70i	−0.176067	+	0.304957i
$388$		0			0
$389$	−12363.5	+	7138.09i	−1.61146	+	0.930374i	−0.622422	+	0.782682i	$0.713851\pi$
$389$	−12363.5	+	7138.09i	−1.61146	+	0.930374i	−0.989033	+	0.147692i	$0.952815\pi$
$390$		0			0
$391$	−1932.27			−0.249921
$392$		0			0
$393$	−5082.25			−0.652330
$394$		0			0
$395$	−3421.71	+	1975.52i	−0.435860	+	0.251644i
$396$		0			0
$397$	968.708	−	1677.85i	0.122464	−	0.212113i	−0.798275	−	0.602293i	$-0.794254\pi$
$397$	968.708	−	1677.85i	0.122464	−	0.212113i	0.920739	+	0.390180i	$0.127587\pi$
$398$		0			0
$399$	2084.53	+	2583.01i	0.261546	+	0.324090i
$400$		0			0
$401$	1359.48	−	2354.68i	0.169299	−	0.293235i	−0.768874	−	0.639400i	$-0.779183\pi$
$401$	1359.48	−	2354.68i	0.169299	−	0.293235i	0.938174	+	0.346165i	$0.112516\pi$
$402$		0			0
$403$	−302.681	−	524.259i	−0.0374135	−	0.0648020i
$404$		0			0
$405$	−385.417			−0.0472877
$406$		0			0
$407$			276.370i			0.0336588i
$408$		0			0
$409$	−3823.31	+	2207.39i	−0.462226	+	0.266866i	−0.712980	−	0.701185i	$-0.752655\pi$
$409$	−3823.31	+	2207.39i	−0.462226	+	0.266866i	0.250754	+	0.968051i	$0.419322\pi$
$410$		0			0
$411$	7829.48	+	4520.35i	0.939658	+	0.542512i
$412$		0			0
$413$	95.3195	+	36.7729i	0.0113568	+	0.00438129i
$414$		0			0
$415$	−857.675	−	495.179i	−0.101450	−	0.0585720i
$416$		0			0
$417$	−2868.18	−	4967.83i	−0.336823	−	0.583394i
$418$		0			0
$419$		−	3196.26i		−	0.372667i	−0.982487	−	0.186334i	$-0.940339\pi$
$419$		−	3196.26i		−	0.372667i	0.982487	−	0.186334i	$-0.0596605\pi$
$420$		0			0
$421$		−	423.986i		−	0.0490827i	−0.999699	−	0.0245414i	$-0.992187\pi$
$421$		−	423.986i		−	0.0490827i	0.999699	−	0.0245414i	$-0.00781254\pi$
$422$		0			0
$423$	−1492.05	−	2584.30i	−0.171503	−	0.297052i
$424$		0			0
$425$	2602.15	+	1502.35i	0.296995	+	0.171470i
$426$		0			0
$427$	7345.33	−	1150.79i	0.832472	−	0.130423i
$428$		0			0
$429$	−2034.72	−	1174.75i	−0.228991	−	0.132208i
$430$		0			0
$431$	8233.10	−	4753.38i	0.920126	−	0.531235i	0.0364510	−	0.999335i	$-0.488395\pi$
$431$	8233.10	−	4753.38i	0.920126	−	0.531235i	0.883675	+	0.468100i	$0.155061\pi$
$432$		0			0
$433$			7466.57i			0.828684i	0.910121	+	0.414342i	$0.135988\pi$
$433$			7466.57i			0.828684i	−0.910121	+	0.414342i	$0.864012\pi$
$434$		0			0
$435$	78.1538			0.00861422
$436$		0			0
$437$	1966.21	+	3405.57i	0.215232	+	0.372793i
$438$		0			0
$439$	−22.8451	+	39.5689i	−0.00248368	+	0.00430187i	−0.867265	−	0.497848i	$-0.834124\pi$
$439$	−22.8451	+	39.5689i	−0.00248368	+	0.00430187i	0.864781	+	0.502149i	$0.167457\pi$
$440$		0			0
$441$	2287.16	+	2073.27i	0.246967	+	0.223871i
$442$		0			0
$443$	−1968.74	+	3409.96i	−0.211146	+	0.365716i	−0.952073	−	0.305869i	$-0.901053\pi$
$443$	−1968.74	+	3409.96i	−0.211146	+	0.365716i	0.740927	+	0.671585i	$0.234386\pi$
$444$		0			0
$445$	−5540.42	+	3198.76i	−0.590205	+	0.340755i
$446$		0			0
$447$	−3263.71			−0.345342
$448$		0			0
$449$	−8972.29			−0.943048			−0.471524	−	0.881853i	$-0.656296\pi$
$449$	−8972.29			−0.943048			−0.471524	+	0.881853i	$0.656296\pi$
$450$		0			0
$451$	−380.094	+	219.448i	−0.0396850	+	0.0229122i
$452$		0			0
$453$	1060.77	−	1837.30i	0.110020	−	0.190561i
$454$		0			0
$455$	−3070.71	+	481.086i	−0.316389	+	0.0495684i
$456$		0			0
$457$	−1162.97	+	2014.32i	−0.119040	+	0.206183i	−0.919388	−	0.393353i	$-0.871315\pi$
$457$	−1162.97	+	2014.32i	−0.119040	+	0.206183i	0.800347	+	0.599536i	$0.204648\pi$
$458$		0			0
$459$	396.286	+	686.388i	0.0402986	+	0.0697992i
$460$		0			0
$461$	6874.77			0.694555			0.347277	−	0.937762i	$-0.387106\pi$
$461$	6874.77			0.694555			0.347277	+	0.937762i	$0.387106\pi$
$462$		0			0
$463$		−	8509.65i		−	0.854162i	−0.904213	−	0.427081i	$-0.859542\pi$
$463$		−	8509.65i		−	0.854162i	0.904213	−	0.427081i	$-0.140458\pi$
$464$		0			0
$465$	−212.179	+	122.501i	−0.0211603	+	0.0122169i
$466$		0			0
$467$	13878.0	+	8012.46i	1.37515	+	0.793945i	0.991571	−	0.129562i	$-0.0413572\pi$
$467$	13878.0	+	8012.46i	1.37515	+	0.793945i	0.383581	+	0.923507i	$0.374691\pi$
$468$		0			0
$469$	7030.92	−	18224.9i	0.692234	−	1.79435i
$470$		0			0
$471$	9416.69	+	5436.73i	0.921227	+	0.531871i
$472$		0			0
$473$	3307.08	+	5728.03i	0.321479	+	0.556818i
$474$		0			0
$475$		−	6114.96i		−	0.590682i
$476$		0			0
$477$			1190.61i			0.114286i
$478$		0			0
$479$	−3665.35	−	6348.58i	−0.349633	−	0.605582i	0.636551	−	0.771234i	$-0.280360\pi$
$479$	−3665.35	−	6348.58i	−0.349633	−	0.605582i	−0.986184	+	0.165652i	$0.947027\pi$
$480$		0			0
$481$	380.181	+	219.498i	0.0360390	+	0.0208071i
$482$		0			0
$483$	2296.86	+	2846.11i	0.216378	+	0.268121i
$484$		0			0
$485$	2897.84	+	1673.07i	0.271308	+	0.156640i
$486$		0			0
$487$	−3788.67	+	2187.39i	−0.352527	+	0.203532i	−0.665798	−	0.746132i	$-0.731909\pi$
$487$	−3788.67	+	2187.39i	−0.352527	+	0.203532i	0.313270	+	0.949664i	$0.398575\pi$
$488$		0			0
$489$		−	7934.20i		−	0.733736i
$490$		0			0
$491$	−11441.1			−1.05159			−0.525793	−	0.850613i	$-0.676231\pi$
$491$	−11441.1			−1.05159			−0.525793	+	0.850613i	$0.676231\pi$
$492$		0			0
$493$	−80.3579	−	139.184i	−0.00734105	−	0.0127151i
$494$		0			0
$495$	−475.445	+	823.494i	−0.0431710	+	0.0747744i
$496$		0			0
$497$	3944.94	−	3183.63i	0.356046	−	0.287335i
$498$		0			0
$499$	−6387.79	+	11064.0i	−0.573060	+	0.992569i	0.423189	+	0.906041i	$0.360911\pi$
$499$	−6387.79	+	11064.0i	−0.573060	+	0.992569i	−0.996249	+	0.0865279i	$0.972423\pi$
$500$		0			0
$501$	3713.08	−	2143.75i	0.331114	−	0.191169i
$502$		0			0
$503$	−12314.0			−1.09156			−0.545782	−	0.837928i	$-0.683767\pi$
$503$	−12314.0			−1.09156			−0.545782	+	0.837928i	$0.683767\pi$
$504$		0			0
$505$	−8332.74			−0.734262
$506$		0			0
$507$	2475.95	−	1429.49i	0.216885	−	0.125219i
$508$		0			0
$509$	9821.58	−	17011.5i	0.855273	−	1.48138i	−0.0211189	−	0.999777i	$-0.506723\pi$
$509$	9821.58	−	17011.5i	0.855273	−	1.48138i	0.876392	−	0.481599i	$-0.159944\pi$
$510$		0			0
$511$	−15597.1	−	6017.14i	−1.35025	−	0.520905i
$512$		0			0
$513$	806.493	−	1396.89i	0.0694104	−	0.120222i
$514$		0			0
$515$	−3801.02	−	6583.55i	−0.325229	−	0.563313i
$516$		0			0
$517$	−7362.28			−0.626292
$518$		0			0
$519$			3895.35i			0.329455i
$520$		0			0
$521$	−246.886	+	142.540i	−0.0207606	+	0.0119862i	−0.510344	−	0.859970i	$-0.670482\pi$
$521$	−246.886	+	142.540i	−0.0207606	+	0.0119862i	0.489584	+	0.871956i	$0.337149\pi$
$522$		0			0
$523$	10525.9	+	6077.12i	0.880047	+	0.508095i	0.870674	−	0.491861i	$-0.163683\pi$
$523$	10525.9	+	6077.12i	0.880047	+	0.508095i	0.00937313	+	0.999956i	$0.497016\pi$
$524$		0			0
$525$	−880.265	−	5618.62i	−0.0731770	−	0.467080i
$526$		0			0
$527$	436.325	+	251.912i	0.0360657	+	0.0208225i
$528$		0			0
$529$	−3917.02	−	6784.47i	−0.321938	−	0.557612i
$530$		0			0
$531$		−	49.6484i		−	0.00405754i
$532$		0			0
$533$			697.157i			0.0566552i
$534$		0			0
$535$	2536.94	+	4394.11i	0.205012	+	0.355092i
$536$		0			0
$537$	−8117.59	−	4686.69i	−0.652327	−	0.376621i
$538$		0			0
$539$	7251.23	−	2329.26i	0.579467	−	0.186138i
$540$		0			0
$541$	4080.03	+	2355.61i	0.324241	+	0.187200i	0.653281	−	0.757115i	$-0.273392\pi$
$541$	4080.03	+	2355.61i	0.324241	+	0.187200i	−0.329041	+	0.944316i	$0.606725\pi$
$542$		0			0
$543$	2263.50	−	1306.83i	0.178888	−	0.103281i
$544$		0			0
$545$		−	2744.66i		−	0.215721i
$546$		0			0
$547$	−4883.76			−0.381745			−0.190872	−	0.981615i	$-0.561132\pi$
$547$	−4883.76			−0.381745			−0.190872	+	0.981615i	$0.561132\pi$
$548$		0			0
$549$	−1806.52	−	3128.98i	−0.140438	−	0.243245i
$550$		0			0
$551$	−163.539	+	283.257i	−0.0126442	+	0.0219005i
$552$		0			0
$553$	−2380.30	−	15193.2i	−0.183039	−	1.16832i
$554$		0			0
$555$	88.8352	−	153.867i	0.00679432	−	0.0117681i
$556$		0			0
$557$	−14125.3	+	8155.23i	−1.07452	+	0.620374i	−0.929412	−	0.369043i	$-0.879686\pi$
$557$	−14125.3	+	8155.23i	−1.07452	+	0.620374i	−0.145106	+	0.989416i	$0.546352\pi$
$558$		0			0
$559$	10506.2			0.794925
$560$		0			0
$561$	1955.41			0.147161
$562$		0			0
$563$	−15216.0	+	8784.98i	−1.13904	+	0.657625i	−0.946193	−	0.323604i	$-0.895106\pi$
$563$	−15216.0	+	8784.98i	−1.13904	+	0.657625i	−0.192847	+	0.981229i	$0.561772\pi$
$564$		0			0
$565$	−911.894	+	1579.45i	−0.0679003	+	0.117607i
$566$		0			0
$567$	539.946	−	1399.60i	0.0399922	−	0.103664i
$568$		0			0
$569$	−4724.44	+	8182.97i	−0.348082	+	0.602896i	−0.985909	−	0.167284i	$-0.946500\pi$
$569$	−4724.44	+	8182.97i	−0.348082	+	0.602896i	0.637827	+	0.770180i	$0.279834\pi$
$570$		0			0
$571$	−7341.50	−	12715.8i	−0.538060	−	0.931947i	−0.999008	−	0.0445200i	$-0.985824\pi$
$571$	−7341.50	−	12715.8i	−0.538060	−	0.931947i	0.460949	−	0.887427i	$-0.347509\pi$
$572$		0			0
$573$	−8753.62			−0.638198
$574$		0			0
$575$		−	6737.83i		−	0.488673i
$576$		0			0
$577$	−14695.6	+	8484.48i	−1.06028	+	0.612155i	−0.925511	−	0.378721i	$-0.876364\pi$
$577$	−14695.6	+	8484.48i	−1.06028	+	0.612155i	−0.134773	+	0.990876i	$0.543031\pi$
$578$		0			0
$579$	3683.38	+	2126.60i	0.264380	+	0.152640i
$580$		0			0
$581$	2999.74	−	2420.84i	0.214200	−	0.172863i
$582$		0			0
$583$	2543.90	+	1468.72i	0.180716	+	0.104337i
$584$		0			0
$585$	755.213	+	1308.07i	0.0533748	+	0.0924478i
$586$		0			0
$587$		−	9958.87i		−	0.700250i	−0.936703	−	0.350125i	$-0.886139\pi$
$587$		−	9958.87i		−	0.700250i	0.936703	−	0.350125i	$-0.113861\pi$
$588$		0			0
$589$		−	1025.35i		−	0.0717295i
$590$		0			0
$591$	−7779.29	−	13474.1i	−0.541450	−	0.937819i
$592$		0			0
$593$	3833.34	+	2213.18i	0.265458	+	0.153262i	0.626822	−	0.779163i	$-0.284355\pi$
$593$	3833.34	+	2213.18i	0.265458	+	0.153262i	−0.361364	+	0.932425i	$0.617689\pi$
$594$		0			0
$595$	2013.07	−	1624.58i	0.138702	−	0.111935i
$596$		0			0
$597$	−238.200	−	137.525i	−0.0163298	−	0.00942802i
$598$		0			0
$599$	11021.3	−	6363.15i	0.751783	−	0.434042i	−0.0745547	−	0.997217i	$-0.523754\pi$
$599$	11021.3	−	6363.15i	0.751783	−	0.434042i	0.826338	+	0.563175i	$0.190420\pi$
$600$		0			0
$601$		−	13278.1i		−	0.901207i	−0.892724	−	0.450604i	$-0.851209\pi$
$601$		−	13278.1i		−	0.901207i	0.892724	−	0.450604i	$-0.148791\pi$
$602$		0			0
$603$	−9492.70			−0.641082
$604$		0			0
$605$	−1993.60	−	3453.02i	−0.133969	−	0.232041i
$606$		0			0
$607$	12177.6	−	21092.3i	0.814291	−	1.41039i	−0.0955456	−	0.995425i	$-0.530460\pi$
$607$	12177.6	−	21092.3i	0.814291	−	1.41039i	0.909836	−	0.414968i	$-0.136207\pi$
$608$		0			0
$609$	−109.489	+	283.807i	−0.00728523	+	0.0188842i
$610$		0			0
$611$	−5847.26	+	10127.7i	−0.387160	+	0.670581i
$612$		0			0
$613$	2250.29	−	1299.21i	0.148268	−	0.0856028i	−0.424030	−	0.905648i	$-0.639385\pi$
$613$	2250.29	−	1299.21i	0.148268	−	0.0856028i	0.572299	+	0.820045i	$0.306052\pi$
$614$		0			0
$615$	282.154			0.0185001
$616$		0			0
$617$	−16812.3			−1.09698			−0.548491	−	0.836156i	$-0.684798\pi$
$617$	−16812.3			−1.09698			−0.548491	+	0.836156i	$0.684798\pi$
$618$		0			0
$619$	−16632.8	+	9602.98i	−1.08002	+	0.623548i	−0.930901	−	0.365272i	$-0.880976\pi$
$619$	−16632.8	+	9602.98i	−1.08002	+	0.623548i	−0.149116	+	0.988820i	$0.547643\pi$
$620$		0			0
$621$	888.641	−	1539.17i	0.0574234	−	0.0994603i
$622$		0			0
$623$	−3854.18	−	24600.7i	−0.247856	−	1.58203i
$624$		0			0
$625$	−3823.66	+	6622.77i	−0.244714	+	0.423857i
$626$		0			0
$627$	−1989.76	−	3446.36i	−0.126736	−	0.219512i
$628$		0			0
$629$	−365.362			−0.0231605
$630$		0			0
$631$			16823.4i			1.06138i	0.847566	+	0.530689i	$0.178067\pi$
$631$			16823.4i			1.06138i	−0.847566	+	0.530689i	$0.821933\pi$
$632$		0			0
$633$	4439.21	−	2562.98i	0.278740	−	0.160931i
$634$		0			0
$635$	−11532.1	−	6658.06i	−0.720689	−	0.416090i
$636$		0			0
$637$	2554.87	−	11824.9i	0.158913	−	0.735511i
$638$		0			0
$639$	−2133.42	−	1231.73i	−0.132076	−	0.0762543i
$640$		0			0
$641$	2211.00	+	3829.57i	0.136239	+	0.235973i	0.926070	−	0.377351i	$-0.123165\pi$
$641$	2211.00	+	3829.57i	0.136239	+	0.235973i	−0.789831	+	0.613325i	$0.789832\pi$
$642$		0			0
$643$			1733.83i			0.106338i	0.998586	+	0.0531691i	$0.0169322\pi$
$643$			1733.83i			0.106338i	−0.998586	+	0.0531691i	$0.983068\pi$
$644$		0			0
$645$		−	4252.06i		−	0.259573i
$646$		0			0
$647$	6079.33	+	10529.7i	0.369402	+	0.639823i	0.989472	−	0.144723i	$-0.0462291\pi$
$647$	6079.33	+	10529.7i	0.369402	+	0.639823i	−0.620070	+	0.784546i	$0.712896\pi$
$648$		0			0
$649$	−106.080	−	61.2455i	−0.00641605	−	0.00370431i
$650$		0			0
$651$	−147.601	−	942.121i	−0.00888626	−	0.0567199i
$652$		0			0
$653$	−2133.27	−	1231.64i	−0.127843	−	0.0738100i	0.434715	−	0.900568i	$-0.356849\pi$
$653$	−2133.27	−	1231.64i	−0.127843	−	0.0738100i	−0.562557	+	0.826758i	$0.690183\pi$
$654$		0			0
$655$	6980.89	−	4030.42i	0.416437	−	0.240430i
$656$		0			0
$657$			8123.96i			0.482414i
$658$		0			0
$659$	−15114.9			−0.893461			−0.446731	−	0.894668i	$-0.647412\pi$
$659$	−15114.9			−0.893461			−0.446731	+	0.894668i	$0.647412\pi$
$660$		0			0
$661$	1247.13	+	2160.10i	0.0733856	+	0.127108i	0.900383	−	0.435098i	$-0.143286\pi$
$661$	1247.13	+	2160.10i	0.0733856	+	0.127108i	−0.826997	+	0.562206i	$0.809953\pi$
$662$		0			0
$663$	1553.02	−	2689.92i	0.0909720	−	0.157568i
$664$		0			0
$665$	−4911.70	−	1894.86i	−0.286417	−	0.110496i
$666$		0			0
$667$	−180.196	+	312.109i	−0.0104606	+	0.0181183i
$668$		0			0
$669$	9143.83	−	5279.19i	0.528432	−	0.305090i
$670$		0			0
$671$	−8913.98			−0.512847
$672$		0			0
$673$	13635.0			0.780966			0.390483	−	0.920610i	$-0.372308\pi$
$673$	13635.0			0.780966			0.390483	+	0.920610i	$0.372308\pi$
$674$		0			0
$675$	−2393.43	+	1381.85i	−0.136479	+	0.0787962i
$676$		0			0
$677$	12701.9	−	22000.4i	0.721086	−	1.24896i	−0.239479	−	0.970902i	$-0.576977\pi$
$677$	12701.9	−	22000.4i	0.721086	−	1.24896i	0.960565	−	0.278056i	$-0.0896900\pi$
$678$		0			0
$679$	−10135.3	+	8179.34i	−0.572837	+	0.462289i
$680$		0			0
$681$	−9844.27	+	17050.8i	−0.553940	+	0.959452i
$682$		0			0
$683$	3241.96	+	5615.25i	0.181626	+	0.314585i	0.942434	−	0.334391i	$-0.108531\pi$
$683$	3241.96	+	5615.25i	0.181626	+	0.314585i	−0.760809	+	0.648976i	$0.775197\pi$
$684$		0			0
$685$	−14339.2			−0.799817
$686$		0			0
$687$		−	6838.84i		−	0.379793i
$688$		0			0
$689$	4040.82	−	2332.97i	0.223430	−	0.128997i
$690$		0			0
$691$	−12707.4	−	7336.63i	−0.699585	−	0.403905i	0.107608	−	0.994193i	$-0.465681\pi$
$691$	−12707.4	−	7336.63i	−0.699585	−	0.403905i	−0.807193	+	0.590288i	$0.799014\pi$
$692$		0			0
$693$	−2324.36	−	2880.19i	−0.127410	−	0.157878i
$694$		0			0
$695$	7879.36	+	4549.15i	0.430045	+	0.248286i
$696$		0			0
$697$	−290.111	−	502.487i	−0.0157658	−	0.0273071i
$698$		0			0
$699$		−	11660.9i		−	0.630983i
$700$		0			0
$701$		−	16778.4i		−	0.904012i	−0.892015	−	0.452006i	$-0.850708\pi$
$701$		−	16778.4i		−	0.904012i	0.892015	−	0.452006i	$-0.149292\pi$
$702$		0			0
$703$	371.779	+	643.941i	0.0199458	+	0.0345472i
$704$		0			0
$705$	4098.91	+	2366.50i	0.218970	+	0.126422i
$706$		0			0
$707$	11673.7	−	30259.5i	0.620981	−	1.60965i
$708$		0			0
$709$	17892.0	+	10329.9i	0.947738	+	0.547177i	0.892378	−	0.451289i	$-0.149036\pi$
$709$	17892.0	+	10329.9i	0.947738	+	0.547177i	0.0553607	+	0.998466i	$0.482369\pi$
$710$		0			0
$711$	−6472.02	+	3736.62i	−0.341378	+	0.197095i
$712$		0			0
$713$		−	1129.79i		−	0.0593420i
$714$		0			0
$715$	3726.48			0.194913
$716$		0			0
$717$	4314.62	+	7473.13i	0.224731	+	0.389246i
$718$		0			0
$719$	14614.9	−	25313.8i	0.758060	−	1.31300i	−0.185779	−	0.982592i	$-0.559481\pi$
$719$	14614.9	−	25313.8i	0.758060	−	1.31300i	0.943839	−	0.330406i	$-0.107186\pi$
$720$		0			0
$721$	29232.5	−	4579.83i	1.50995	−	0.236563i
$722$		0			0
$723$	756.506	−	1310.31i	0.0389139	−	0.0674009i
$724$		0			0
$725$	485.334	−	280.208i	0.0248619	−	0.0143540i
$726$		0			0
$727$	19075.5			0.973136			0.486568	−	0.873643i	$-0.338249\pi$
$727$	19075.5			0.973136			0.486568	+	0.873643i	$0.338249\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$	−7572.48	+	4371.98i	−0.383144	+	0.221208i
$732$		0			0
$733$	−9651.80	+	16717.4i	−0.486354	+	0.842390i	−0.999877	−	0.0156862i	$-0.995007\pi$
$733$	−9651.80	+	16717.4i	−0.486354	+	0.842390i	0.513523	+	0.858076i	$0.328340\pi$
$734$		0			0
$735$	−4785.79	−	1034.01i	−0.240172	−	0.0518910i
$736$		0			0
$737$	−11710.1	+	20282.4i	−0.585272	+	1.01372i
$738$		0			0
$739$	−4366.02	−	7562.17i	−0.217330	−	0.376426i	0.736661	−	0.676262i	$-0.236401\pi$
$739$	−4366.02	−	7562.17i	−0.217330	−	0.376426i	−0.953991	+	0.299836i	$0.903068\pi$
$740$		0			0
$741$	−6321.20			−0.313381
$742$		0			0
$743$			31267.9i			1.54389i	0.635691	+	0.771944i	$0.280715\pi$
$743$			31267.9i			1.54389i	−0.635691	+	0.771944i	$0.719285\pi$
$744$		0			0
$745$	4482.97	−	2588.25i	0.220461	−	0.127283i
$746$		0			0
$747$	−1622.26	−	936.611i	−0.0794582	−	0.0458752i
$748$		0			0
$749$	−19510.9	+	3056.75i	−0.951817	+	0.149120i
$750$		0			0
$751$	5725.84	+	3305.82i	0.278214	+	0.160627i	0.632615	−	0.774467i	$-0.281982\pi$
$751$	5725.84	+	3305.82i	0.278214	+	0.160627i	−0.354400	+	0.935094i	$0.615315\pi$
$752$		0			0
$753$	4072.91	+	7054.49i	0.197112	+	0.341408i
$754$		0			0
$755$			3364.92i			0.162201i
$756$		0			0
$757$		−	1294.17i		−	0.0621366i	−0.999517	−	0.0310683i	$-0.990109\pi$
$757$		−	1294.17i		−	0.0621366i	0.999517	−	0.0310683i	$-0.00989095\pi$
$758$		0			0
$759$	−2192.43	−	3797.40i	−0.104849	−	0.181603i
$760$		0			0
$761$	25496.9	+	14720.6i	1.21454	+	0.701213i	0.963744	−	0.266828i	$-0.0859756\pi$
$761$	25496.9	+	14720.6i	1.21454	+	0.701213i	0.250792	+	0.968041i	$0.419309\pi$
$762$		0			0
$763$	9966.94	+	3845.10i	0.472906	+	0.182440i
$764$		0			0
$765$	−1088.66	−	628.541i	−0.0514519	−	0.0297058i
$766$		0			0
$767$	−168.502	+	97.2846i	−0.00793253	+	0.00457985i
$768$		0			0
$769$		−	1870.38i		−	0.0877084i	−0.999038	−	0.0438542i	$-0.986036\pi$
$769$		−	1870.38i		−	0.0877084i	0.999038	−	0.0438542i	$-0.0139637\pi$
$770$		0			0
$771$	−12106.4			−0.565501
$772$		0			0
$773$	−5789.10	−	10027.0i	−0.269365	−	0.466555i	0.699333	−	0.714796i	$-0.253481\pi$
$773$	−5789.10	−	10027.0i	−0.269365	−	0.466555i	−0.968698	+	0.248242i	$0.920147\pi$
$774$		0			0
$775$	−878.418	+	1521.46i	−0.0407144	+	0.0705195i
$776$		0			0
$777$	434.300	+	538.154i	0.0200520	+	0.0248471i
$778$		0			0
$779$	−590.413	+	1022.62i	−0.0271550	+	0.0470338i
$780$		0			0
$781$	−5263.51	+	3038.89i	−0.241157	+	0.139232i
$782$		0			0
$783$	147.825			0.00674690
$784$		0			0
$785$	−17246.1			−0.784129
$786$		0			0
$787$	29107.9	−	16805.4i	1.31840	−	0.761181i	0.334932	−	0.942242i	$-0.391287\pi$
$787$	29107.9	−	16805.4i	1.31840	−	0.761181i	0.983472	+	0.181061i	$0.0579533\pi$
$788$		0			0
$789$	6898.88	−	11949.2i	0.311289	−	0.539168i
$790$		0			0
$791$	−4458.09	−	5524.16i	−0.200394	−	0.248314i
$792$		0			0
$793$	−7079.64	+	12262.3i	−0.317031	+	0.549114i
$794$		0			0
$795$	−944.201	−	1635.40i	−0.0421224	−	0.0729582i
$796$		0			0
$797$	1179.48			0.0524206			0.0262103	−	0.999656i	$-0.491656\pi$
$797$	1179.48			0.0524206			0.0262103	+	0.999656i	$0.491656\pi$
$798$		0			0
$799$		−	9732.98i		−	0.430949i
$800$		0			0
$801$	−10479.5	+	6050.33i	−0.462265	+	0.266889i
$802$		0			0
$803$	17357.9	+	10021.6i	0.762824	+	0.440417i
$804$		0			0
$805$	−5412.00	−	2087.87i	−0.236954	−	0.0914133i
$806$		0			0
$807$	−6013.69	−	3472.01i	−0.262320	−	0.151450i
$808$		0			0
$809$	−21036.3	−	36436.0i	−0.914212	−	1.58346i	−0.808051	−	0.589112i	$-0.799477\pi$
$809$	−21036.3	−	36436.0i	−0.914212	−	1.58346i	−0.106161	−	0.994349i	$-0.533856\pi$
$810$		0			0
$811$		−	5872.04i		−	0.254248i	−0.991887	−	0.127124i	$-0.959425\pi$
$811$		−	5872.04i		−	0.254248i	0.991887	−	0.127124i	$-0.0405746\pi$
$812$		0			0
$813$			21011.9i			0.906421i
$814$		0			0
$815$	6292.12	+	10898.3i	0.270434	+	0.468405i
$816$		0			0
$817$	15411.0	+	8897.53i	0.659928	+	0.381010i
$818$		0			0
$819$	−5808.12	+	909.954i	−0.247805	+	0.0388234i
$820$		0			0
$821$	18927.6	+	10927.9i	0.804603	+	0.464538i	0.845078	−	0.534643i	$-0.179554\pi$
$821$	18927.6	+	10927.9i	0.804603	+	0.464538i	−0.0404753	+	0.999181i	$0.512887\pi$
$822$		0			0
$823$	−33335.2	+	19246.1i	−1.41190	+	0.815160i	−0.995567	−	0.0940531i	$-0.970018\pi$
$823$	−33335.2	+	19246.1i	−1.41190	+	0.815160i	−0.416331	+	0.909213i	$0.636684\pi$
$824$		0			0
$825$			6818.52i			0.287746i
$826$		0			0
$827$	28978.4			1.21848			0.609238	−	0.792988i	$-0.291476\pi$
$827$	28978.4			1.21848			0.609238	+	0.792988i	$0.291476\pi$
$828$		0			0
$829$	20169.2	+	34934.1i	0.845002	+	1.46359i	0.885619	+	0.464412i	$0.153734\pi$
$829$	20169.2	+	34934.1i	0.845002	+	1.46359i	−0.0406174	+	0.999175i	$0.512932\pi$
$830$		0			0
$831$	6126.78	−	10611.9i	0.255759	−	0.442987i
$832$		0			0
$833$	3079.30	+	9586.17i	0.128081	+	0.398729i
$834$		0			0
$835$	−3400.15	+	5889.23i	−0.140919	+	0.244078i
$836$		0			0
$837$	−401.327	+	231.706i	−0.0165733	+	0.00956863i
$838$		0			0
$839$	−46007.4			−1.89315			−0.946575	−	0.322485i	$-0.895482\pi$
$839$	−46007.4			−1.89315			−0.946575	+	0.322485i	$0.895482\pi$
$840$		0			0
$841$	24359.0			0.998771
$842$		0			0
$843$	−17144.7	+	9898.52i	−0.700470	+	0.404417i
$844$		0			0
$845$	−2267.28	+	3927.04i	−0.0923038	+	0.159875i
$846$		0			0
$847$	15332.2	−	2402.08i	0.621983	−	0.0974457i
$848$		0			0
$849$	2523.05	−	4370.05i	0.101992	−	0.176655i
$850$		0			0
$851$	409.648	+	709.532i	0.0165012	+	0.0285810i
$852$		0			0
$853$	−23484.4			−0.942663			−0.471331	−	0.881956i	$-0.656226\pi$
$853$	−23484.4			−0.942663			−0.471331	+	0.881956i	$0.656226\pi$
$854$		0			0
$855$			2558.32i			0.102331i
$856$		0			0
$857$	−18212.2	+	10514.8i	−0.725924	+	0.419112i	−0.816929	−	0.576738i	$-0.804325\pi$
$857$	−18212.2	+	10514.8i	−0.725924	+	0.419112i	0.0910052	+	0.995850i	$0.470992\pi$
$858$		0			0
$859$	2265.82	+	1308.17i	0.0899987	+	0.0519608i	0.544324	−	0.838875i	$-0.316786\pi$
$859$	2265.82	+	1308.17i	0.0899987	+	0.0519608i	−0.454325	+	0.890836i	$0.650120\pi$
$860$		0			0
$861$	−395.280	+	1024.61i	−0.0156459	+	0.0405559i
$862$		0			0
$863$	−33326.5	−	19241.1i	−1.31454	−	0.758949i	−0.331695	−	0.943387i	$-0.607620\pi$
$863$	−33326.5	−	19241.1i	−1.31454	−	0.758949i	−0.982844	+	0.184437i	$0.940954\pi$
$864$		0			0
$865$	−3089.17	−	5350.59i	−0.121427	−	0.210319i
$866$		0			0
$867$		−	12153.9i		−	0.476089i
$868$		0			0
$869$			18437.8i			0.719745i
$870$		0			0
$871$	18600.7	+	32217.3i	0.723605	+	1.25332i
$872$		0			0
$873$	5481.15	+	3164.54i	0.212496	+	0.122685i
$874$		0			0
$875$	12582.8	+	15591.8i	0.486145	+	0.602398i
$876$		0			0
$877$	39737.4	+	22942.4i	1.53003	+	0.883363i	0.999360	+	0.0357843i	$0.0113929\pi$
$877$	39737.4	+	22942.4i	1.53003	+	0.883363i	0.530670	+	0.847579i	$0.321940\pi$
$878$		0			0
$879$	−12245.6	+	7069.99i	−0.469890	+	0.271291i
$880$		0			0
$881$		−	32993.4i		−	1.26172i	−0.775896	−	0.630860i	$-0.782702\pi$
$881$		−	32993.4i		−	1.26172i	0.775896	−	0.630860i	$-0.217298\pi$
$882$		0			0
$883$	42541.9			1.62135			0.810674	−	0.585498i	$-0.199101\pi$
$883$	42541.9			1.62135			0.810674	+	0.585498i	$0.199101\pi$
$884$		0			0
$885$	39.3731	+	68.1962i	0.00149549	+	0.00259027i
$886$		0			0
$887$	−8772.25	+	15194.0i	−0.332067	+	0.575156i	−0.982917	−	0.184050i	$-0.941079\pi$
$887$	−8772.25	+	15194.0i	−0.332067	+	0.575156i	0.650850	+	0.759206i	$0.274413\pi$
$888$		0			0
$889$	40333.8	−	32550.1i	1.52166	−	1.22800i
$890$		0			0
$891$	−899.284	+	1557.61i	−0.0338127	+	0.0585654i
$892$		0			0
$893$	−17154.1	+	9903.93i	−0.642822	+	0.371134i
$894$		0			0
$895$	14866.9			0.555247
$896$		0			0
$897$	−6965.07			−0.259261
$898$		0			0
$899$	81.3800	−	46.9848i	0.00301911	−	0.00174308i
$900$		0			0
$901$	−1941.66	+	3363.05i	−0.0717936	+	0.124350i
$902$		0			0
$903$	15440.9	+	5956.88i	0.569038	+	0.219527i
$904$		0			0
$905$	−2072.73	+	3590.08i	−0.0761326	+	0.131866i
$906$		0			0
$907$	1398.50	+	2422.27i	0.0511977	+	0.0886770i	0.890488	−	0.455006i	$-0.150363\pi$
$907$	1398.50	+	2422.27i	0.0511977	+	0.0886770i	−0.839291	+	0.543683i	$0.817029\pi$
$908$		0			0
$909$	−15761.0			−0.575095
$910$		0			0
$911$			31110.0i			1.13142i	0.824605	+	0.565709i	$0.191397\pi$
$911$			31110.0i			1.13142i	−0.824605	+	0.565709i	$0.808603\pi$
$912$		0			0
$913$	−4002.39	+	2310.78i	−0.145082	+	0.0837630i
$914$		0			0
$915$	4962.81	+	2865.28i	0.179306	+	0.103523i
$916$		0			0
$917$	4856.24	+	30996.8i	0.174882	+	1.11625i
$918$		0			0
$919$	25609.3	+	14785.5i	0.919231	+	0.530718i	0.883390	−	0.468639i	$-0.155256\pi$
$919$	25609.3	+	14785.5i	0.919231	+	0.530718i	0.0358415	+	0.999357i	$0.488589\pi$
$920$		0			0
$921$	576.287	+	998.158i	0.0206181	+	0.0357116i
$922$		0			0
$923$			9654.17i			0.344280i
$924$		0			0
$925$		−	1274.02i		−	0.0452859i
$926$		0			0
$927$	−7189.47	−	12452.5i	−0.254728	−	0.441202i
$928$		0			0
$929$	−2107.56	−	1216.80i	−0.0744315	−	0.0429731i	0.462322	−	0.886712i	$-0.347016\pi$
$929$	−2107.56	−	1216.80i	−0.0744315	−	0.0429731i	−0.536754	+	0.843739i	$0.680350\pi$
$930$		0			0
$931$	13762.0	−	15181.7i	0.484458	−	0.534437i
$932$		0			0
$933$	−25415.1	−	14673.4i	−0.891803	−	0.514882i
$934$		0			0
$935$	−2685.92	+	1550.72i	−0.0939455	+	0.0542394i
$936$		0			0
$937$			23660.5i			0.824925i	0.910975	+	0.412462i	$0.135331\pi$
$937$			23660.5i			0.824925i	−0.910975	+	0.412462i	$0.864669\pi$
$938$		0			0
$939$	−20933.9			−0.727532
$940$		0			0
$941$	−17396.1	−	30130.9i	−0.602652	−	1.04382i	−0.992418	−	0.122910i	$-0.960777\pi$
$941$	−17396.1	−	30130.9i	−0.602652	−	1.04382i	0.389766	−	0.920914i	$-0.372556\pi$
$942$		0			0
$943$	−650.552	+	1126.79i	−0.0224654	+	0.0389112i
$944$		0			0
$945$	368.277	+	2350.67i	0.0126773	+	0.0809176i
$946$		0			0
$947$	−4163.32	+	7211.07i	−0.142861	+	0.247443i	−0.928573	−	0.371150i	$-0.878964\pi$
$947$	−4163.32	+	7211.07i	−0.142861	+	0.247443i	0.785712	+	0.618593i	$0.212297\pi$
$948$		0			0
$949$	27572.0	−	15918.7i	0.943123	−	0.544512i
$950$		0			0
$951$	12184.0			0.415449
$952$		0			0
$953$	−5396.93			−0.183446			−0.0917228	−	0.995785i	$-0.529237\pi$
$953$	−5396.93			−0.183446			−0.0917228	+	0.995785i	$0.529237\pi$
$954$		0			0
$955$	12023.8	−	6941.96i	0.407415	−	0.235221i
$956$		0			0
$957$	182.354	−	315.847i	0.00615954	−	0.0106686i
$958$		0			0
$959$	20088.4	−	52071.5i	0.676422	−	1.75336i
$960$		0			0
$961$	14748.2	−	25544.6i	0.495056	−	0.857462i
$962$		0			0
$963$	4798.52	+	8311.28i	0.160571	+	0.278118i
$964$		0			0
$965$	−6745.91			−0.225035
$966$		0			0
$967$			46588.0i			1.54930i	0.632393	+	0.774648i	$0.282073\pi$
$967$			46588.0i			1.54930i	−0.632393	+	0.774648i	$0.717927\pi$
$968$		0			0
$969$	4556.11	−	2630.47i	0.151046	−	0.0872063i
$970$		0			0
$971$	32953.1	+	19025.5i	1.08910	+	0.628792i	0.933336	−	0.359003i	$-0.116883\pi$
$971$	32953.1	+	19025.5i	1.08910	+	0.628792i	0.155763	+	0.987795i	$0.450216\pi$
$972$		0			0
$973$	−27558.3	+	22240.0i	−0.907993	+	0.732765i
$974$		0			0
$975$	9379.73	+	5415.39i	0.308094	+	0.177878i
$976$		0			0
$977$	−9751.93	−	16890.8i	−0.319337	−	0.553107i	0.661013	−	0.750374i	$-0.270127\pi$
$977$	−9751.93	−	16890.8i	−0.319337	−	0.553107i	−0.980350	+	0.197267i	$0.936793\pi$
$978$		0			0
$979$			29854.4i			0.974618i
$980$		0			0
$981$		−	5191.41i		−	0.168959i
$982$		0			0
$983$	17188.4	+	29771.1i	0.557705	+	0.965973i	0.997688	+	0.0679667i	$0.0216512\pi$
$983$	17188.4	+	29771.1i	0.557705	+	0.965973i	−0.439983	+	0.898006i	$0.645016\pi$
$984$		0			0
$985$	21371.0	+	12338.5i	0.691306	+	0.399126i
$986$		0			0
$987$	−14336.0	+	11569.4i	−0.462331	+	0.373109i
$988$		0			0
$989$	16980.7	+	9803.82i	0.545961	+	0.315211i
$990$		0			0
$991$	−37834.0	+	21843.5i	−1.21275	+	0.700183i	−0.963358	−	0.268219i	$-0.913565\pi$
$991$	−37834.0	+	21843.5i	−1.21275	+	0.700183i	−0.249395	+	0.968402i	$0.580232\pi$
$992$		0			0
$993$		−	22536.2i		−	0.720206i
$994$		0			0
$995$	436.251			0.0138996
$996$		0			0
$997$	16669.7	+	28872.8i	0.529523	+	0.917161i	0.999407	+	0.0344327i	$0.0109624\pi$
$997$	16669.7	+	28872.8i	0.529523	+	0.917161i	−0.469884	+	0.882728i	$0.655704\pi$
$998$		0			0
$999$	168.028	−	291.033i	0.00532150	−	0.00921711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.bb.a.271.10		96
4.3	odd	2		168.4.t.a.19.45	yes	96
7.3	odd	6	inner	672.4.bb.a.367.9		96
8.3	odd	2	inner	672.4.bb.a.271.9		96
8.5	even	2		168.4.t.a.19.20	✓	96
28.3	even	6		168.4.t.a.115.20	yes	96
56.3	even	6	inner	672.4.bb.a.367.10		96
56.45	odd	6		168.4.t.a.115.45	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.20	✓	96	8.5	even	2
168.4.t.a.19.45	yes	96	4.3	odd	2
168.4.t.a.115.20	yes	96	28.3	even	6
168.4.t.a.115.45	yes	96	56.45	odd	6
672.4.bb.a.271.9		96	8.3	odd	2	inner
672.4.bb.a.271.10		96	1.1	even	1	trivial
672.4.bb.a.367.9		96	7.3	odd	6	inner
672.4.bb.a.367.10		96	56.3	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{3} +(2.37912 - 4.12075i) q^{5} +(11.6311 + 14.4124i) q^{7} +(4.50000 - 7.79423i) q^{9} +(-11.1023 - 19.2297i) q^{11} -35.2705 q^{13} +14.2747i q^{15} +(25.4218 - 14.6773i) q^{17} +(-51.7365 - 29.8701i) q^{19} +(-51.8371 - 19.9980i) q^{21} +(-57.0064 - 32.9126i) q^{23} +(51.1796 + 88.6457i) q^{25} +27.0000i q^{27} -5.47499i q^{29} +(8.58171 + 14.8640i) q^{31} +(57.6891 + 33.3068i) q^{33} +(87.0617 - 13.6399i) q^{35} +(-10.7790 - 6.22327i) q^{37} +(91.6354 - 52.9057i) q^{39} -19.7660i q^{41} -297.874 q^{43} +(-21.4120 - 37.0867i) q^{45} +(165.783 - 287.145i) q^{47} +(-72.4363 + 335.264i) q^{49} +(-44.0318 + 76.2653i) q^{51} +(-114.567 + 66.1451i) q^{53} -105.654 q^{55} +179.221 q^{57} +(4.77742 - 2.75824i) q^{59} +(200.724 - 347.665i) q^{61} +(164.674 - 25.7993i) q^{63} +(-83.9126 + 145.341i) q^{65} +(-527.372 - 913.435i) q^{67} +197.476 q^{69} -273.718i q^{71} +(-781.728 + 451.331i) q^{73} +(-265.937 - 153.539i) q^{75} +(148.015 - 383.673i) q^{77} +(-719.113 - 415.180i) q^{79} +(-40.5000 - 70.1481i) q^{81} -208.136i q^{83} -139.676i q^{85} +(8.21248 + 14.2244i) q^{87} +(-1164.39 - 672.259i) q^{89} +(-410.234 - 508.334i) q^{91} +(-44.5919 - 25.7451i) q^{93} +(-246.174 + 142.129i) q^{95} +703.232i q^{97} -199.841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) \) 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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