LMFDB - Embedded newform 668.2.e.a.9.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.8
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0433273 + 0.325140i) q^{3} +(3.41908 + 1.51194i) q^{5} +(-1.67119 + 3.59374i) q^{7} +(2.79147 - 0.757419i) q^{9} +O(q^{10})$	\(q+(0.0433273 + 0.325140i) q^{3} +(3.41908 + 1.51194i) q^{5} +(-1.67119 + 3.59374i) q^{7} +(2.79147 - 0.757419i) q^{9} +(3.68722 - 4.72762i) q^{11} +(0.965873 - 1.88680i) q^{13} +(-0.343455 + 1.17719i) q^{15} +(-2.68591 - 0.203715i) q^{17} +(-3.77888 + 5.68456i) q^{19} +(-1.24088 - 0.387664i) q^{21} +(-3.13185 - 1.24547i) q^{23} +(6.03974 + 6.64011i) q^{25} +(0.748089 + 1.78215i) q^{27} +(-2.45570 + 0.976584i) q^{29} +(1.67743 - 0.387636i) q^{31} +(1.69690 + 0.994029i) q^{33} +(-11.1474 + 9.76051i) q^{35} +(4.12317 + 1.11875i) q^{37} +(0.655322 + 0.232295i) q^{39} +(7.06029 - 3.44721i) q^{41} +(-0.853909 + 8.99707i) q^{43} +(10.6894 + 1.63088i) q^{45} +(-0.188917 - 9.98110i) q^{47} +(-5.61129 - 6.65879i) q^{49} +(-0.0501372 - 0.882124i) q^{51} +(-1.47669 - 8.58570i) q^{53} +(19.7548 - 10.5892i) q^{55} +(-2.01201 - 0.982371i) q^{57} +(-12.6765 + 0.961465i) q^{59} +(-1.28468 + 1.30922i) q^{61} +(-1.94312 + 11.2976i) q^{63} +(6.15512 - 4.99075i) q^{65} +(2.11722 - 0.936252i) q^{67} +(0.269260 - 1.07225i) q^{69} +(11.5437 - 1.31646i) q^{71} +(-12.5732 + 9.42903i) q^{73} +(-1.89728 + 2.25146i) q^{75} +(10.8278 + 21.1516i) q^{77} +(2.71245 - 7.21543i) q^{79} +(6.94014 - 4.06548i) q^{81} +(-3.89753 + 5.40742i) q^{83} +(-8.87532 - 4.75746i) q^{85} +(-0.423926 - 0.756135i) q^{87} +(2.75536 + 9.44398i) q^{89} +(5.16649 + 6.62429i) q^{91} +(0.198714 + 0.528604i) q^{93} +(-21.5150 + 13.7225i) q^{95} +(-16.6328 - 3.84367i) q^{97} +(6.71199 - 15.9898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.0433273	+	0.325140i	0.0250150	+	0.187720i	0.999292	−	0.0376362i	$-0.0119828\pi$
$3$	0.0433273	+	0.325140i	0.0250150	+	0.187720i	−0.974276	+	0.225356i	$0.927645\pi$
$4$		0			0
$5$	3.41908	+	1.51194i	1.52906	+	0.676162i	0.986486	−	0.163848i	$-0.0523906\pi$
$5$	3.41908	+	1.51194i	1.52906	+	0.676162i	0.542571	+	0.840010i	$0.317451\pi$
$6$		0			0
$7$	−1.67119	+	3.59374i	−0.631650	+	1.35830i	0.284967	+	0.958537i	$0.408017\pi$
$7$	−1.67119	+	3.59374i	−0.631650	+	1.35830i	−0.916617	+	0.399767i	$0.869091\pi$
$8$		0			0
$9$	2.79147	−	0.757419i	0.930492	−	0.252473i
$10$		0			0
$11$	3.68722	−	4.72762i	1.11174	−	1.42543i	0.218505	−	0.975836i	$-0.429882\pi$
$11$	3.68722	−	4.72762i	1.11174	−	1.42543i	0.893233	−	0.449594i	$-0.148431\pi$
$12$		0			0
$13$	0.965873	−	1.88680i	0.267885	−	0.523303i	−0.716879	−	0.697197i	$-0.754430\pi$
$13$	0.965873	−	1.88680i	0.267885	−	0.523303i	0.984764	+	0.173894i	$0.0556350\pi$
$14$		0			0
$15$	−0.343455	+	1.17719i	−0.0886796	+	0.303949i
$16$		0			0
$17$	−2.68591	−	0.203715i	−0.651429	−	0.0494082i	−0.254234	−	0.967143i	$-0.581823\pi$
$17$	−2.68591	−	0.203715i	−0.651429	−	0.0494082i	−0.397194	+	0.917734i	$0.630016\pi$
$18$		0			0
$19$	−3.77888	+	5.68456i	−0.866935	+	1.30413i	0.0845458	+	0.996420i	$0.473056\pi$
$19$	−3.77888	+	5.68456i	−0.866935	+	1.30413i	−0.951481	+	0.307708i	$0.900438\pi$
$20$		0			0
$21$	−1.24088	−	0.387664i	−0.270782	−	0.0845952i
$22$		0			0
$23$	−3.13185	−	1.24547i	−0.653035	−	0.259699i	0.0194488	−	0.999811i	$-0.493809\pi$
$23$	−3.13185	−	1.24547i	−0.653035	−	0.259699i	−0.672484	+	0.740111i	$0.734773\pi$
$24$		0			0
$25$	6.03974	+	6.64011i	1.20795	+	1.32802i
$26$		0			0
$27$	0.748089	+	1.78215i	0.143970	+	0.342975i
$28$		0			0
$29$	−2.45570	+	0.976584i	−0.456012	+	0.181347i	−0.586241	−	0.810137i	$-0.699393\pi$
$29$	−2.45570	+	0.976584i	−0.456012	+	0.181347i	0.130229	+	0.991484i	$0.458429\pi$
$30$		0			0
$31$	1.67743	−	0.387636i	0.301275	−	0.0696214i	−0.0718114	−	0.997418i	$-0.522878\pi$
$31$	1.67743	−	0.387636i	0.301275	−	0.0696214i	0.373086	+	0.927797i	$0.378300\pi$
$32$		0			0
$33$	1.69690	+	0.994029i	0.295392	+	0.173038i
$34$		0			0
$35$	−11.1474	+	9.76051i	−1.88426	+	1.64983i
$36$		0			0
$37$	4.12317	+	1.11875i	0.677845	+	0.183921i	0.584108	−	0.811676i	$-0.301444\pi$
$37$	4.12317	+	1.11875i	0.677845	+	0.183921i	0.0937363	+	0.995597i	$0.470119\pi$
$38$		0			0
$39$	0.655322	+	0.232295i	0.104936	+	0.0371969i
$40$		0			0
$41$	7.06029	−	3.44721i	1.10263	−	0.538363i	0.204845	−	0.978794i	$-0.434331\pi$
$41$	7.06029	−	3.44721i	1.10263	−	0.538363i	0.897786	+	0.440431i	$0.145174\pi$
$42$		0			0
$43$	−0.853909	+	8.99707i	−0.130220	+	1.37204i	0.656312	+	0.754490i	$0.272116\pi$
$43$	−0.853909	+	8.99707i	−0.130220	+	1.37204i	−0.786532	+	0.617550i	$0.788125\pi$
$44$		0			0
$45$	10.6894	+	1.63088i	1.59349	+	0.243118i
$46$		0			0
$47$	−0.188917	−	9.98110i	−0.0275564	−	1.45589i	−0.699151	−	0.714974i	$-0.746438\pi$
$47$	−0.188917	−	9.98110i	−0.0275564	−	1.45589i	0.671594	−	0.740919i	$-0.265610\pi$
$48$		0			0
$49$	−5.61129	−	6.65879i	−0.801613	−	0.951255i
$50$		0			0
$51$	−0.0501372	−	0.882124i	−0.00702061	−	0.123522i
$52$		0			0
$53$	−1.47669	−	8.58570i	−0.202839	−	1.17934i	−0.891077	−	0.453852i	$-0.850049\pi$
$53$	−1.47669	−	8.58570i	−0.202839	−	1.17934i	0.688238	−	0.725485i	$-0.258384\pi$
$54$		0			0
$55$	19.7548	−	10.5892i	2.66373	−	1.42785i
$56$		0			0
$57$	−2.01201	−	0.982371i	−0.266497	−	0.130118i
$58$		0			0
$59$	−12.6765	+	0.961465i	−1.65035	+	0.125172i	−0.867631	−	0.497209i	$-0.834358\pi$
$59$	−12.6765	+	0.961465i	−1.65035	+	0.125172i	−0.782714	+	0.622381i	$0.786165\pi$
$60$		0			0
$61$	−1.28468	+	1.30922i	−0.164486	+	0.167629i	−0.791071	−	0.611724i	$-0.790476\pi$
$61$	−1.28468	+	1.30922i	−0.164486	+	0.167629i	0.626585	+	0.779353i	$0.284452\pi$
$62$		0			0
$63$	−1.94312	+	11.2976i	−0.244810	+	1.42337i
$64$		0			0
$65$	6.15512	−	4.99075i	0.763449	−	0.619027i
$66$		0			0
$67$	2.11722	−	0.936252i	0.258659	−	0.114381i	−0.271036	−	0.962569i	$-0.587366\pi$
$67$	2.11722	−	0.936252i	0.258659	−	0.114381i	0.529696	+	0.848188i	$0.322306\pi$
$68$		0			0
$69$	0.269260	−	1.07225i	0.0324150	−	0.129084i
$70$		0			0
$71$	11.5437	−	1.31646i	1.36998	−	0.156236i	0.602916	−	0.797804i	$-0.294005\pi$
$71$	11.5437	−	1.31646i	1.36998	−	0.156236i	0.767065	+	0.641569i	$0.221716\pi$
$72$		0			0
$73$	−12.5732	+	9.42903i	−1.47158	+	1.10358i	−0.500236	+	0.865889i	$0.666754\pi$
$73$	−12.5732	+	9.42903i	−1.47158	+	1.10358i	−0.971340	+	0.237696i	$0.923608\pi$
$74$		0			0
$75$	−1.89728	+	2.25146i	−0.219079	+	0.259976i
$76$		0			0
$77$	10.8278	+	21.1516i	1.23394	+	2.41045i
$78$		0			0
$79$	2.71245	−	7.21543i	0.305174	−	0.811799i	−0.690873	−	0.722976i	$-0.742774\pi$
$79$	2.71245	−	7.21543i	0.305174	−	0.811799i	0.996047	−	0.0888232i	$-0.0283106\pi$
$80$		0			0
$81$	6.94014	−	4.06548i	0.771126	−	0.451720i
$82$		0			0
$83$	−3.89753	+	5.40742i	−0.427810	+	0.593541i	−0.968909	−	0.247418i	$-0.920418\pi$
$83$	−3.89753	+	5.40742i	−0.427810	+	0.593541i	0.541099	+	0.840959i	$0.318008\pi$
$84$		0			0
$85$	−8.87532	−	4.75746i	−0.962663	−	0.516019i
$86$		0			0
$87$	−0.423926	−	0.756135i	−0.0454496	−	0.0810661i
$88$		0			0
$89$	2.75536	+	9.44398i	0.292068	+	1.00106i	0.965195	+	0.261533i	$0.0842279\pi$
$89$	2.75536	+	9.44398i	0.292068	+	1.00106i	−0.673127	+	0.739527i	$0.735049\pi$
$90$		0			0
$91$	5.16649	+	6.62429i	0.541595	+	0.694414i
$92$		0			0
$93$	0.198714	+	0.528604i	0.0206057	+	0.0548137i
$94$		0			0
$95$	−21.5150	+	13.7225i	−2.20739	+	1.40790i
$96$		0			0
$97$	−16.6328	−	3.84367i	−1.68880	−	0.390265i	−0.732070	−	0.681229i	$-0.761446\pi$
$97$	−16.6328	−	3.84367i	−1.68880	−	0.390265i	−0.956734	+	0.290964i	$0.906024\pi$
$98$		0			0
$99$	6.71199	−	15.9898i	0.674581	−	1.60703i
$100$		0			0
$101$	−0.984855	−	10.3768i	−0.0979967	−	1.03253i	−0.900201	−	0.435476i	$-0.856580\pi$
$101$	−0.984855	−	10.3768i	−0.0979967	−	1.03253i	0.802204	−	0.597050i	$-0.203661\pi$
$102$		0			0
$103$	−1.36317	+	0.943859i	−0.134317	+	0.0930012i	−0.634518	−	0.772908i	$-0.718801\pi$
$103$	−1.36317	+	0.943859i	−0.134317	+	0.0930012i	0.500201	+	0.865909i	$0.333259\pi$
$104$		0			0
$105$	−3.65653	−	3.20159i	−0.356840	−	0.312443i
$106$		0			0
$107$	−5.59238	−	3.87217i	−0.540636	−	0.374337i	0.267295	−	0.963615i	$-0.413870\pi$
$107$	−5.59238	−	3.87217i	−0.540636	−	0.374337i	−0.807931	+	0.589278i	$0.799412\pi$
$108$		0			0
$109$	9.02259	+	5.75469i	0.864207	+	0.551200i	0.893853	−	0.448361i	$-0.147992\pi$
$109$	9.02259	+	5.75469i	0.864207	+	0.551200i	−0.0296455	+	0.999560i	$0.509438\pi$
$110$		0			0
$111$	−0.185105	+	1.38908i	−0.0175694	+	0.131846i
$112$		0			0
$113$	−2.38950	+	3.90760i	−0.224785	+	0.367596i	−0.945493	−	0.325643i	$-0.894419\pi$
$113$	−2.38950	+	3.90760i	−0.224785	+	0.367596i	0.720708	+	0.693239i	$0.243817\pi$
$114$		0			0
$115$	−8.82493	−	8.99355i	−0.822929	−	0.838653i
$116$		0			0
$117$	1.26712	−	5.99851i	0.117145	−	0.554563i
$118$		0			0
$119$	5.22076	−	9.31200i	0.478586	−	0.853630i
$120$		0			0
$121$	−6.07568	−	24.1947i	−0.552334	−	2.19952i
$122$		0			0
$123$	1.42673	+	2.14623i	0.128644	+	0.193519i
$124$		0			0
$125$	4.70020	+	14.1016i	0.420399	+	1.26129i
$126$		0			0
$127$	1.36216	+	0.155344i	0.120872	+	0.0137845i	0.173534	−	0.984828i	$-0.444481\pi$
$127$	1.36216	+	0.155344i	0.120872	+	0.0137845i	−0.0526618	+	0.998612i	$0.516771\pi$
$128$		0			0
$129$	−2.96231	+	0.112178i	−0.260817	+	0.00987676i
$130$		0			0
$131$	0.625911	−	11.0124i	0.0546861	−	0.962160i	−0.847495	−	0.530803i	$-0.821890\pi$
$131$	0.625911	−	11.0124i	0.0546861	−	0.962160i	0.902181	−	0.431357i	$-0.141965\pi$
$132$		0			0
$133$	−14.1136	−	23.0803i	−1.22380	−	2.00131i
$134$		0			0
$135$	−0.136739	+	7.22438i	−0.0117687	+	0.621775i
$136$		0			0
$137$	1.68894	−	0.598685i	0.144296	−	0.0511491i	−0.260976	−	0.965345i	$-0.584044\pi$
$137$	1.68894	−	0.598685i	0.144296	−	0.0511491i	0.405272	+	0.914196i	$0.367177\pi$
$138$		0			0
$139$	−3.92220	−	3.70560i	−0.332677	−	0.314305i	0.502190	−	0.864757i	$-0.332528\pi$
$139$	−3.92220	−	3.70560i	−0.332677	−	0.314305i	−0.834867	+	0.550452i	$0.814455\pi$
$140$		0			0
$141$	3.23707	−	0.493879i	0.272611	−	0.0415921i
$142$		0			0
$143$	−5.35866	−	11.5233i	−0.448114	−	0.963627i
$144$		0			0
$145$	−9.87276	−	0.373868i	−0.819888	−	0.0310480i
$146$		0			0
$147$	1.92192	−	2.11296i	0.158517	−	0.174274i
$148$		0			0
$149$	−6.67446	−	5.41185i	−0.546793	−	0.443356i	0.316112	−	0.948722i	$-0.397622\pi$
$149$	−6.67446	−	5.41185i	−0.546793	−	0.443356i	−0.862905	+	0.505366i	$0.831357\pi$
$150$		0			0
$151$	−10.1862	−	7.63897i	−0.828941	−	0.621651i	0.0987028	−	0.995117i	$-0.468531\pi$
$151$	−10.1862	−	7.63897i	−0.828941	−	0.621651i	−0.927644	+	0.373466i	$0.878169\pi$
$152$		0			0
$153$	−7.65195	+	1.46569i	−0.618623	+	0.118494i
$154$		0			0
$155$	6.32133	+	1.21082i	0.507741	+	0.0972553i
$156$		0			0
$157$	−2.73690	−	12.9565i	−0.218428	−	1.03404i	−0.939862	−	0.341554i	$-0.889047\pi$
$157$	−2.73690	−	12.9565i	−0.218428	−	1.03404i	0.721434	−	0.692483i	$-0.243483\pi$
$158$		0			0
$159$	2.72758	−	0.852127i	0.216311	−	0.0675780i
$160$		0			0
$161$	9.70982	−	9.17361i	0.765241	−	0.722982i
$162$		0			0
$163$	1.09154	−	3.27487i	0.0854964	−	0.256507i	−0.897233	−	0.441558i	$-0.854426\pi$
$163$	1.09154	−	3.27487i	0.0854964	−	0.256507i	0.982729	+	0.185051i	$0.0592451\pi$
$164$		0			0
$165$	4.29890	+	5.96427i	0.334669	+	0.464318i
$166$		0			0
$167$	2.67393	+	12.6432i	0.206915	+	0.978359i
$167$	2.67393	+	12.6432i	0.206915	+	0.978359i
$168$		0			0
$169$	4.97426	+	6.90126i	0.382635	+	0.530866i
$170$		0			0
$171$	−6.24306	+	18.7305i	−0.477419	+	1.43236i
$172$		0			0
$173$	5.10437	−	4.82249i	0.388078	−	0.366647i	−0.467792	−	0.883839i	$-0.654950\pi$
$173$	5.10437	−	4.82249i	0.388078	−	0.366647i	0.855870	+	0.517191i	$0.173022\pi$
$174$		0			0
$175$	−33.9563	+	10.6083i	−2.56686	+	0.801916i
$176$		0			0
$177$	−0.861852	−	4.08000i	−0.0647808	−	0.306672i
$178$		0			0
$179$	18.0325	+	3.45402i	1.34781	+	0.258166i	0.810757	−	0.585383i	$-0.199056\pi$
$179$	18.0325	+	3.45402i	1.34781	+	0.258166i	0.537052	+	0.843549i	$0.319538\pi$
$180$		0			0
$181$	−0.600379	+	0.114999i	−0.0446258	+	0.00854784i	−0.210389	−	0.977618i	$-0.567473\pi$
$181$	−0.600379	+	0.114999i	−0.0446258	+	0.00854784i	0.165763	+	0.986166i	$0.446991\pi$
$182$		0			0
$183$	−0.481343	−	0.360976i	−0.0355819	−	0.0266841i
$184$		0			0
$185$	12.4059	+	10.0591i	0.912102	+	0.739559i
$186$		0			0
$187$	−10.8666	+	11.9468i	−0.794646	+	0.873637i
$188$		0			0
$189$	−7.65478	−	0.289876i	−0.556803	−	0.0210854i
$190$		0			0
$191$	−6.42553	−	13.8175i	−0.464935	−	0.999799i	−0.988972	−	0.148104i	$-0.952683\pi$
$191$	−6.42553	−	13.8175i	−0.464935	−	0.999799i	0.524037	−	0.851696i	$-0.324425\pi$
$192$		0			0
$193$	13.1317	−	2.00350i	0.945241	−	0.144215i	0.340150	−	0.940371i	$-0.389522\pi$
$193$	13.1317	−	2.00350i	0.945241	−	0.144215i	0.605091	+	0.796156i	$0.293137\pi$
$194$		0			0
$195$	1.88938	+	1.78504i	0.135301	+	0.127830i
$196$		0			0
$197$	11.2667	−	3.99375i	0.802719	−	0.284543i	0.0990607	−	0.995081i	$-0.468416\pi$
$197$	11.2667	−	3.99375i	0.802719	−	0.284543i	0.703658	+	0.710539i	$0.251549\pi$
$198$		0			0
$199$	0.391700	−	20.6947i	0.0277669	−	1.46701i	−0.665537	−	0.746365i	$-0.731797\pi$
$199$	0.391700	−	20.6947i	0.0277669	−	1.46701i	0.693304	−	0.720645i	$-0.256154\pi$
$200$		0			0
$201$	0.396147	+	0.647828i	0.0279420	+	0.0456943i
$202$		0			0
$203$	0.594354	−	10.4572i	0.0417155	−	0.733951i
$204$		0			0
$205$	29.3516	−	1.11151i	2.05001	−	0.0776309i
$206$		0			0
$207$	−9.68582	−	1.10459i	−0.673211	−	0.0767744i
$208$		0			0
$209$	12.9409	+	38.8253i	0.895138	+	2.68560i
$210$		0			0
$211$	0.307953	+	0.463253i	0.0212004	+	0.0318917i	0.843229	−	0.537554i	$-0.180652\pi$
$211$	0.307953	+	0.463253i	0.0212004	+	0.0318917i	−0.822029	+	0.569446i	$0.807158\pi$
$212$		0			0
$213$	0.928192	+	3.69628i	0.0635987	+	0.253265i
$214$		0			0
$215$	−16.5226	+	29.4706i	−1.12683	+	2.00988i
$216$		0			0
$217$	−1.41023	+	6.67604i	−0.0957330	+	0.453199i
$218$		0			0
$219$	−3.61052	−	3.67951i	−0.243976	−	0.248638i
$220$		0			0
$221$	−2.97862	+	4.87100i	−0.200363	+	0.327659i
$222$		0			0
$223$	−3.00416	+	22.5441i	−0.201174	+	1.50966i	0.541893	+	0.840447i	$0.317708\pi$
$223$	−3.00416	+	22.5441i	−0.201174	+	1.50966i	−0.743067	+	0.669217i	$0.766630\pi$
$224$		0			0
$225$	21.8891	+	13.9611i	1.45927	+	0.930739i
$226$		0			0
$227$	−22.2126	−	15.3801i	−1.47431	−	1.02081i	−0.989235	−	0.146336i	$-0.953252\pi$
$227$	−22.2126	−	15.3801i	−1.47431	−	1.02081i	−0.485070	−	0.874475i	$-0.661206\pi$
$228$		0			0
$229$	−6.24724	−	5.46997i	−0.412829	−	0.361466i	0.427061	−	0.904223i	$-0.359549\pi$
$229$	−6.24724	−	5.46997i	−0.412829	−	0.361466i	−0.839890	+	0.542757i	$0.817380\pi$
$230$		0			0
$231$	−6.40811	+	4.43699i	−0.421623	+	0.291932i
$232$		0			0
$233$	1.44086	+	15.1814i	0.0943937	+	0.994563i	0.909626	+	0.415429i	$0.136368\pi$
$233$	1.44086	+	15.1814i	0.0943937	+	0.994563i	−0.815232	+	0.579135i	$0.803391\pi$
$234$		0			0
$235$	14.4449	−	34.4118i	0.942284	−	2.24478i
$236$		0			0
$237$	2.46355	+	0.569301i	0.160025	+	0.0369801i
$238$		0			0
$239$	16.9535	−	10.8131i	1.09663	−	0.699443i	0.139828	−	0.990176i	$-0.455345\pi$
$239$	16.9535	−	10.8131i	1.09663	−	0.699443i	0.956804	+	0.290733i	$0.0938991\pi$
$240$		0			0
$241$	−5.08334	−	13.5223i	−0.327447	−	0.871047i	−0.992276	−	0.124051i	$-0.960411\pi$
$241$	−5.08334	−	13.5223i	−0.327447	−	0.871047i	0.664829	−	0.746995i	$-0.268504\pi$
$242$		0			0
$243$	5.18855	+	6.65256i	0.332845	+	0.426762i
$244$		0			0
$245$	−9.11770	−	31.2508i	−0.582509	−	1.99654i
$246$		0			0
$247$	7.07569	+	12.6205i	0.450215	+	0.803026i
$248$		0			0
$249$	−1.92704	−	1.03296i	−0.122121	−	0.0654610i
$250$		0			0
$251$	−0.136789	+	0.189780i	−0.00863403	+	0.0119788i	−0.815531	−	0.578714i	$-0.803555\pi$
$251$	−0.136789	+	0.189780i	−0.00863403	+	0.0119788i	0.806897	+	0.590692i	$0.201145\pi$
$252$		0			0
$253$	−17.4359	+	10.2138i	−1.09619	+	0.642138i
$254$		0			0
$255$	1.16230	−	3.09185i	0.0727860	−	0.193619i
$256$		0			0
$257$	−7.84159	−	15.3183i	−0.489145	−	0.955527i	−0.995640	−	0.0932834i	$-0.970264\pi$
$257$	−7.84159	−	15.3183i	−0.489145	−	0.955527i	0.506494	−	0.862243i	$-0.330941\pi$
$258$		0			0
$259$	−10.9111	+	12.9479i	−0.677982	+	0.804546i
$260$		0			0
$261$	−6.11534	+	4.58610i	−0.378530	+	0.283873i
$262$		0			0
$263$	0.184467	−	0.0210370i	0.0113747	−	0.00129720i	−0.107618	−	0.994192i	$-0.534322\pi$
$263$	0.184467	−	0.0210370i	0.0113747	−	0.00129720i	0.118993	+	0.992895i	$0.462033\pi$
$264$		0			0
$265$	7.93220	−	31.5878i	0.487271	−	1.94043i
$266$		0			0
$267$	−2.95124	+	1.30506i	−0.180613	+	0.0798685i
$268$		0			0
$269$	2.47599	−	2.00760i	0.150964	−	0.122406i	−0.551348	−	0.834275i	$-0.685886\pi$
$269$	2.47599	−	2.00760i	0.150964	−	0.122406i	0.702311	+	0.711870i	$0.252151\pi$
$270$		0			0
$271$	0.409677	−	2.38193i	0.0248861	−	0.144692i	−0.970427	−	0.241394i	$-0.922396\pi$
$271$	0.409677	−	2.38193i	0.0248861	−	0.144692i	0.995313	+	0.0967016i	$0.0308293\pi$
$272$		0			0
$273$	−1.92997	+	1.96685i	−0.116807	+	0.119039i
$274$		0			0
$275$	53.6617	−	4.07002i	3.23592	−	0.245432i
$276$		0			0
$277$	13.7294	+	6.70340i	0.824917	+	0.402768i	0.802260	−	0.596975i	$-0.203631\pi$
$277$	13.7294	+	6.70340i	0.824917	+	0.402768i	0.0226569	+	0.999743i	$0.492787\pi$
$278$		0			0
$279$	4.38889	−	2.35259i	0.262756	−	0.140846i
$280$		0			0
$281$	4.38172	+	25.4760i	0.261392	+	1.51977i	0.758263	+	0.651949i	$0.226048\pi$
$281$	4.38172	+	25.4760i	0.261392	+	1.51977i	−0.496871	+	0.867824i	$0.665518\pi$
$282$		0			0
$283$	−1.09958	−	19.3463i	−0.0653633	−	1.15002i	−0.848859	−	0.528619i	$-0.822710\pi$
$283$	−1.09958	−	19.3463i	−0.0653633	−	1.15002i	0.783496	−	0.621397i	$-0.213434\pi$
$284$		0			0
$285$	−5.39392	−	6.40085i	−0.319508	−	0.379153i
$286$		0			0
$287$	0.589284	+	31.1337i	0.0347844	+	1.83777i
$288$		0			0
$289$	−9.63292	−	1.46969i	−0.566642	−	0.0864524i
$290$		0			0
$291$	0.529077	−	5.57453i	0.0310151	−	0.326785i
$292$		0			0
$293$	5.15600	−	2.51744i	0.301217	−	0.147070i	−0.281934	−	0.959434i	$-0.590976\pi$
$293$	5.15600	−	2.51744i	0.301217	−	0.147070i	0.583151	+	0.812364i	$0.301819\pi$
$294$		0			0
$295$	−44.7957	−	15.8789i	−2.60811	−	0.924506i
$296$		0			0
$297$	11.1837	+	3.03450i	0.648944	+	0.176080i
$298$		0			0
$299$	−5.37492	+	4.70619i	−0.310840	+	0.272166i
$300$		0			0
$301$	−30.9060	−	18.1045i	−1.78139	−	1.04353i
$302$		0			0
$303$	3.33123	−	0.769813i	0.191374	−	0.0442246i
$304$		0			0
$305$	−6.37188	+	2.53397i	−0.364853	+	0.145095i
$306$		0			0
$307$	6.54331	+	15.5879i	0.373447	+	0.889651i	0.994388	+	0.105794i	$0.0337384\pi$
$307$	6.54331	+	15.5879i	0.373447	+	0.889651i	−0.620941	+	0.783857i	$0.713250\pi$
$308$		0			0
$309$	−0.365949	−	0.402326i	−0.0208181	−	0.0228875i
$310$		0			0
$311$	14.3418	+	5.70346i	0.813250	+	0.323414i	0.738897	−	0.673818i	$-0.235347\pi$
$311$	14.3418	+	5.70346i	0.813250	+	0.323414i	0.0743532	+	0.997232i	$0.476311\pi$
$312$		0			0
$313$	−28.6027	−	8.93582i	−1.61672	−	0.505082i	−0.649789	−	0.760114i	$-0.725143\pi$
$313$	−28.6027	−	8.93582i	−1.61672	−	0.505082i	−0.966933	+	0.255032i	$0.917914\pi$
$314$		0			0
$315$	−23.7250	+	35.6895i	−1.33675	+	2.01088i
$316$		0			0
$317$	0.839528	+	0.0636748i	0.0471526	+	0.00357633i	0.0991839	−	0.995069i	$-0.468377\pi$
$317$	0.839528	+	0.0636748i	0.0471526	+	0.00357633i	−0.0520313	+	0.998645i	$0.516570\pi$
$318$		0			0
$319$	−4.43779	+	15.2105i	−0.248469	+	0.851624i
$320$		0			0
$321$	1.01670	−	1.98608i	0.0567465	−	0.110852i
$322$		0			0
$323$	11.3078	−	14.4984i	0.629181	−	0.806713i
$324$		0			0
$325$	18.3621	−	4.98225i	1.01855	−	0.276366i
$326$		0			0
$327$	−1.48016	+	3.18294i	−0.0818530	+	0.176017i
$328$		0			0
$329$	36.1852	+	16.0014i	1.99495	+	0.882185i
$330$		0			0
$331$	2.11036	+	15.8367i	0.115996	+	0.870465i	0.948573	+	0.316557i	$0.102527\pi$
$331$	2.11036	+	15.8367i	0.115996	+	0.870465i	−0.832578	+	0.553908i	$0.813136\pi$
$332$		0			0
$333$	12.3571			0.677164
$334$		0			0
$335$	8.65449			0.472845
$336$		0			0
$337$	1.59308	+	11.9549i	0.0867806	+	0.651226i	0.979621	+	0.200853i	$0.0643715\pi$
$337$	1.59308	+	11.9549i	0.0867806	+	0.651226i	−0.892841	+	0.450373i	$0.851291\pi$
$338$		0			0
$339$	−1.37405	−	0.607616i	−0.0746281	−	0.0330012i
$340$		0			0
$341$	4.35244	−	9.35952i	0.235698	−	0.506847i
$342$		0			0
$343$	6.53239	−	1.77245i	0.352716	−	0.0957034i
$344$		0			0
$345$	2.54181	−	3.25901i	0.136846	−	0.175459i
$346$		0			0
$347$	−1.42394	+	2.78161i	−0.0764411	+	0.149325i	−0.925230	−	0.379408i	$-0.876128\pi$
$347$	−1.42394	+	2.78161i	−0.0764411	+	0.149325i	0.848788	+	0.528733i	$0.177333\pi$
$348$		0			0
$349$	−1.42066	+	4.86930i	−0.0760462	+	0.260648i	−0.989112	−	0.147165i	$-0.952985\pi$
$349$	−1.42066	+	4.86930i	−0.0760462	+	0.260648i	0.913066	+	0.407812i	$0.133708\pi$
$350$		0			0
$351$	4.08511	+	0.309839i	0.218047	+	0.0165380i
$352$		0			0
$353$	14.2604	−	21.4518i	0.759003	−	1.14177i	−0.226814	−	0.973938i	$-0.572831\pi$
$353$	14.2604	−	21.4518i	0.759003	−	1.14177i	0.985816	−	0.167827i	$-0.0536752\pi$
$354$		0			0
$355$	41.4591	+	12.9523i	2.20042	+	0.687436i
$356$		0			0
$357$	3.25391	+	1.29402i	0.172215	+	0.0684866i
$358$		0			0
$359$	2.29129	+	2.51905i	0.120930	+	0.132951i	0.797230	−	0.603675i	$-0.206298\pi$
$359$	2.29129	+	2.51905i	0.120930	+	0.132951i	−0.676301	+	0.736626i	$0.736418\pi$
$360$		0			0
$361$	−10.6803	−	25.4435i	−0.562123	−	1.33913i
$362$		0			0
$363$	7.60345	−	3.02374i	0.399078	−	0.158705i
$364$		0			0
$365$	−57.2447	+	13.2287i	−2.99633	+	0.692420i
$366$		0			0
$367$	4.56517	+	2.67424i	0.238300	+	0.139594i	0.619761	−	0.784791i	$-0.287230\pi$
$367$	4.56517	+	2.67424i	0.238300	+	0.139594i	−0.381461	+	0.924385i	$0.624579\pi$
$368$		0			0
$369$	17.0976	−	14.9704i	0.890067	−	0.779327i
$370$		0			0
$371$	33.3226	+	9.04151i	1.73002	+	0.469412i
$372$		0			0
$373$	15.6843	+	5.55968i	0.812103	+	0.287869i	0.707562	−	0.706651i	$-0.249795\pi$
$373$	15.6843	+	5.55968i	0.812103	+	0.287869i	0.104542	+	0.994521i	$0.466662\pi$
$374$		0			0
$375$	−4.38135	+	2.13921i	−0.226252	+	0.110468i
$376$		0			0
$377$	−0.529279	+	5.57666i	−0.0272593	+	0.287213i
$378$		0			0
$379$	−3.56675	−	0.544178i	−0.183212	−	0.0279525i	0.0585695	−	0.998283i	$-0.481346\pi$
$379$	−3.56675	−	0.544178i	−0.183212	−	0.0279525i	−0.241781	+	0.970331i	$0.577732\pi$
$380$		0			0
$381$	0.00851027	+	0.449624i	0.000435994	+	0.0230349i
$382$		0			0
$383$	14.7633	+	17.5193i	0.754369	+	0.895192i	0.997193	−	0.0748785i	$-0.0238569\pi$
$383$	14.7633	+	17.5193i	0.754369	+	0.895192i	−0.242824	+	0.970070i	$0.578074\pi$
$384$		0			0
$385$	5.04086	+	88.6900i	0.256906	+	4.52006i
$386$		0			0
$387$	4.43088	+	25.7619i	0.225234	+	1.30955i
$388$		0			0
$389$	−31.6856	+	16.9845i	−1.60653	+	0.861150i	−0.608829	+	0.793301i	$0.708361\pi$
$389$	−31.6856	+	16.9845i	−1.60653	+	0.861150i	−0.997696	+	0.0678491i	$0.978386\pi$
$390$		0			0
$391$	8.15814	+	3.98324i	0.412575	+	0.201441i
$392$		0			0
$393$	3.60770	−	0.273630i	0.181985	−	0.0138028i
$394$		0			0
$395$	20.1834	−	20.5690i	1.01554	−	1.03494i
$396$		0			0
$397$	1.44525	−	8.40292i	0.0725350	−	0.421730i	−0.926439	−	0.376445i	$-0.877146\pi$
$397$	1.44525	−	8.40292i	0.0725350	−	0.421730i	0.998974	−	0.0452856i	$-0.0144198\pi$
$398$		0			0
$399$	6.89283	−	5.58891i	0.345073	−	0.279795i
$400$		0			0
$401$	−16.4575	+	7.27764i	−0.821847	+	0.363428i	−0.772232	−	0.635341i	$-0.780860\pi$
$401$	−16.4575	+	7.27764i	−0.821847	+	0.363428i	−0.0496152	+	0.998768i	$0.515799\pi$
$402$		0			0
$403$	0.888790	−	3.53937i	0.0442738	−	0.176308i
$404$		0			0
$405$	29.8756	−	3.40708i	1.48453	−	0.169299i
$406$		0			0
$407$	20.4920	−	15.3677i	1.01575	−	0.761748i
$408$		0			0
$409$	−25.6304	+	30.4151i	−1.26734	+	1.50393i	−0.494738	+	0.869042i	$0.664736\pi$
$409$	−25.6304	+	30.4151i	−1.26734	+	1.50393i	−0.772606	+	0.634886i	$0.781047\pi$
$410$		0			0
$411$	0.267834	+	0.523203i	0.0132113	+	0.0258077i
$412$		0			0
$413$	17.7296	−	47.1629i	0.872419	−	2.32074i
$414$		0			0
$415$	−21.5017	+	12.5955i	−1.05548	+	0.618290i
$416$		0			0
$417$	1.03490	−	1.43582i	0.0506794	−	0.0703124i
$418$		0			0
$419$	−10.4931	−	5.62465i	−0.512622	−	0.274782i	0.195710	−	0.980662i	$-0.437299\pi$
$419$	−10.4931	−	5.62465i	−0.512622	−	0.274782i	−0.708332	+	0.705880i	$0.750552\pi$
$420$		0			0
$421$	11.6523	+	20.7836i	0.567899	+	1.01293i	0.994117	+	0.108312i	$0.0345446\pi$
$421$	11.6523	+	20.7836i	0.567899	+	1.01293i	−0.426218	+	0.904621i	$0.640154\pi$
$422$		0			0
$423$	−8.08723	−	27.7189i	−0.393215	−	1.34774i
$424$		0			0
$425$	−14.8695	−	19.0651i	−0.721276	−	0.924794i
$426$		0			0
$427$	−2.55807	−	6.80475i	−0.123793	−	0.329305i
$428$		0			0
$429$	3.51452	−	2.24159i	0.169682	−	0.108225i
$430$		0			0
$431$	−29.4916	−	6.81520i	−1.42056	−	0.328276i	−0.556157	−	0.831078i	$-0.687725\pi$
$431$	−29.4916	−	6.81520i	−1.42056	−	0.328276i	−0.864402	+	0.502801i	$0.832303\pi$
$432$		0			0
$433$	−9.65936	+	23.0112i	−0.464199	+	1.10585i	0.505780	+	0.862662i	$0.331205\pi$
$433$	−9.65936	+	23.0112i	−0.464199	+	1.10585i	−0.969980	+	0.243186i	$0.921807\pi$
$434$		0			0
$435$	−0.306201	−	3.22623i	−0.0146812	−	0.154686i
$436$		0			0
$437$	18.9149	−	13.0967i	0.904820	−	0.626499i
$438$		0			0
$439$	8.82982	+	7.73124i	0.421424	+	0.368992i	0.843102	−	0.537754i	$-0.180727\pi$
$439$	8.82982	+	7.73124i	0.421424	+	0.368992i	−0.421677	+	0.906746i	$0.638558\pi$
$440$		0			0
$441$	−20.7073	−	14.3377i	−0.986060	−	0.682750i
$442$		0			0
$443$	14.7696	+	9.42021i	0.701726	+	0.447568i	0.839830	−	0.542850i	$-0.182655\pi$
$443$	14.7696	+	9.42021i	0.701726	+	0.447568i	−0.138104	+	0.990418i	$0.544101\pi$
$444$		0			0
$445$	−4.85798	+	36.4556i	−0.230290	+	1.72816i
$446$		0			0
$447$	1.47042	−	2.40462i	0.0695487	−	0.113735i
$448$		0			0
$449$	6.62126	+	6.74777i	0.312477	+	0.318447i	0.852018	−	0.523512i	$-0.175378\pi$
$449$	6.62126	+	6.74777i	0.312477	+	0.318447i	−0.539542	+	0.841959i	$0.681403\pi$
$450$		0			0
$451$	9.73574	−	46.0889i	0.458438	−	2.17024i
$452$		0			0
$453$	2.04240	−	3.64292i	0.0959603	−	0.171159i
$454$		0			0
$455$	7.64907	+	30.4604i	0.358594	+	1.42800i
$456$		0			0
$457$	3.63297	+	5.46506i	0.169943	+	0.255645i	0.907885	−	0.419219i	$-0.137696\pi$
$457$	3.63297	+	5.46506i	0.169943	+	0.255645i	−0.737942	+	0.674864i	$0.764202\pi$
$458$		0			0
$459$	−1.64625	−	4.93909i	−0.0768403	−	0.230537i
$460$		0			0
$461$	−14.5930	−	1.66422i	−0.679665	−	0.0775105i	−0.233359	−	0.972391i	$-0.574972\pi$
$461$	−14.5930	−	1.66422i	−0.679665	−	0.0775105i	−0.446306	+	0.894880i	$0.647261\pi$
$462$		0			0
$463$	25.8955	−	0.980628i	1.20347	−	0.0455736i	0.571522	−	0.820587i	$-0.306353\pi$
$463$	25.8955	−	0.980628i	1.20347	−	0.0455736i	0.631945	+	0.775013i	$0.282257\pi$
$464$		0			0
$465$	−0.119800	+	2.10778i	−0.00555558	+	0.0977460i
$466$		0			0
$467$	−11.7695	−	19.2469i	−0.544627	−	0.890641i	−1.00000		0.000340541i	$-0.999892\pi$
$467$	−11.7695	−	19.2469i	−0.544627	−	0.890641i	0.455373	−	0.890301i	$-0.349506\pi$
$468$		0			0
$469$	−0.173629	+	9.17338i	−0.00801746	+	0.423587i
$470$		0			0
$471$	4.09408	−	1.45124i	0.188645	−	0.0668698i
$472$		0			0
$473$	39.3861	+	37.2111i	1.81098	+	1.71097i
$474$		0			0
$475$	−60.5696	+	9.24107i	−2.77912	+	0.424010i
$476$		0			0
$477$	−10.6251	−	22.8483i	−0.486490	−	1.04615i
$478$		0			0
$479$	9.77007	+	0.369979i	0.446406	+	0.0169048i	0.260088	−	0.965585i	$-0.416248\pi$
$479$	9.77007	+	0.369979i	0.446406	+	0.0169048i	0.186318	+	0.982490i	$0.440345\pi$
$480$		0			0
$481$	6.09331	−	6.69901i	0.277831	−	0.305448i
$482$		0			0
$483$	3.40341	+	2.75959i	0.154861	+	0.125566i
$484$		0			0
$485$	−51.0574	−	38.2896i	−2.31840	−	1.73864i
$486$		0			0
$487$	30.0538	−	5.75664i	1.36187	−	0.260858i	0.545363	−	0.838200i	$-0.316392\pi$
$487$	30.0538	−	5.75664i	1.36187	−	0.260858i	0.816503	+	0.577341i	$0.195910\pi$
$488$		0			0
$489$	1.11209	+	0.213014i	0.0502902	+	0.00963284i
$490$		0			0
$491$	−1.38957	−	6.57820i	−0.0627103	−	0.296870i	0.935729	−	0.352720i	$-0.114743\pi$
$491$	−1.38957	−	6.57820i	−0.0627103	−	0.296870i	−0.998439	+	0.0558501i	$0.982213\pi$
$492$		0			0
$493$	6.79473	−	2.12275i	0.306019	−	0.0956039i
$494$		0			0
$495$	47.1245	−	44.5221i	2.11809	−	2.00112i
$496$		0			0
$497$	−14.5606	+	43.6850i	−0.653133	+	1.95954i
$498$		0			0
$499$	−8.02286	−	11.1309i	−0.359153	−	0.498287i	0.592454	−	0.805604i	$-0.298159\pi$
$499$	−8.02286	−	11.1309i	−0.359153	−	0.498287i	−0.951607	+	0.307317i	$0.900569\pi$
$500$		0			0
$501$	−3.99496	+	1.41720i	−0.178481	+	0.0633158i
$502$		0			0
$503$	6.15004	+	8.53254i	0.274217	+	0.380447i	0.925727	−	0.378193i	$-0.123454\pi$
$503$	6.15004	+	8.53254i	0.274217	+	0.380447i	−0.651510	+	0.758640i	$0.725864\pi$
$504$		0			0
$505$	12.3218	−	36.9680i	0.548312	−	1.64505i
$506$		0			0
$507$	−2.02836	+	1.91634i	−0.0900825	+	0.0851079i
$508$		0			0
$509$	−0.510991	+	0.159639i	−0.0226493	+	0.00707589i	−0.309502	−	0.950899i	$-0.600162\pi$
$509$	−0.510991	+	0.159639i	−0.0226493	+	0.00707589i	0.286852	+	0.957975i	$0.407391\pi$
$510$		0			0
$511$	−12.8733	−	60.9423i	−0.569483	−	2.69593i
$512$		0			0
$513$	−12.9577	−	2.48198i	−0.572096	−	0.109582i
$514$		0			0
$515$	−6.08783	+	1.16609i	−0.268262	+	0.0513842i
$516$		0			0
$517$	−47.8834	−	35.9094i	−2.10591	−	1.57929i
$518$		0			0
$519$	1.78915	+	1.45069i	0.0785348	+	0.0636783i
$520$		0			0
$521$	−25.5726	+	28.1146i	−1.12035	+	1.23172i	−0.150350	+	0.988633i	$0.548040\pi$
$521$	−25.5726	+	28.1146i	−1.12035	+	1.23172i	−0.970004	+	0.243088i	$0.921840\pi$
$522$		0			0
$523$	−8.91359	−	0.337545i	−0.389764	−	0.0147598i	−0.157767	−	0.987476i	$-0.550430\pi$
$523$	−8.91359	−	0.337545i	−0.389764	−	0.0147598i	−0.231997	+	0.972717i	$0.574526\pi$
$524$		0			0
$525$	−4.92044	−	10.5809i	−0.214746	−	0.461790i
$526$		0			0
$527$	−4.58438	+	0.699437i	−0.199699	+	0.0304680i
$528$		0			0
$529$	−8.46126	−	7.99401i	−0.367881	−	0.347566i
$530$		0			0
$531$	−34.6580	+	12.2854i	−1.50403	+	0.533139i
$532$		0			0
$533$	0.315160	−	16.6509i	0.0136511	−	0.721230i
$534$		0			0
$535$	−13.2663	−	21.6946i	−0.573550	−	0.937940i
$536$		0			0
$537$	−0.341745	+	6.01273i	−0.0147474	+	0.259469i
$538$		0			0
$539$	−52.1702	+	1.97561i	−2.24713	+	0.0850957i
$540$		0			0
$541$	−7.93652	−	0.905098i	−0.341218	−	0.0389132i	−0.0589842	−	0.998259i	$-0.518786\pi$
$541$	−7.93652	−	0.905098i	−0.341218	−	0.0389132i	−0.282234	+	0.959346i	$0.591075\pi$
$542$		0			0
$543$	−0.0634038	−	0.190225i	−0.00272092	−	0.00816333i
$544$		0			0
$545$	22.1481	+	33.3174i	0.948722	+	1.42716i
$546$		0			0
$547$	−3.31530	−	13.2023i	−0.141752	−	0.564490i	−0.998787	−	0.0492320i	$-0.984323\pi$
$547$	−3.31530	−	13.2023i	−0.141752	−	0.564490i	0.857035	−	0.515258i	$-0.172304\pi$
$548$		0			0
$549$	−2.59452	+	4.62770i	−0.110731	+	0.197506i
$550$		0			0
$551$	3.72835	−	17.6500i	0.158833	−	0.751914i
$552$		0			0
$553$	21.3973	+	21.8062i	0.909907	+	0.927292i
$554$		0			0
$555$	−2.73310	+	4.46951i	−0.116014	+	0.189720i
$556$		0			0
$557$	−4.90617	+	36.8173i	−0.207881	+	1.56000i	0.507740	+	0.861510i	$0.330481\pi$
$557$	−4.90617	+	36.8173i	−0.207881	+	1.56000i	−0.715621	+	0.698489i	$0.753856\pi$
$558$		0			0
$559$	16.1509	+	10.3012i	0.683109	+	0.435693i
$560$		0			0
$561$	−4.35521	−	3.01556i	−0.183877	−	0.127317i
$562$		0			0
$563$	22.7328	+	19.9044i	0.958072	+	0.838871i	0.987002	−	0.160711i	$-0.0513786\pi$
$563$	22.7328	+	19.9044i	0.958072	+	0.838871i	−0.0289298	+	0.999581i	$0.509210\pi$
$564$		0			0
$565$	−14.0779	+	9.74759i	−0.592263	+	0.410084i
$566$		0			0
$567$	3.01198	+	31.7352i	0.126491	+	1.33275i
$568$		0			0
$569$	−13.4461	+	32.0322i	−0.563688	+	1.34286i	0.350117	+	0.936706i	$0.386142\pi$
$569$	−13.4461	+	32.0322i	−0.563688	+	1.34286i	−0.913806	+	0.406152i	$0.866870\pi$
$570$		0			0
$571$	21.0654	+	4.86800i	0.881560	+	0.203719i	0.641578	−	0.767058i	$-0.278280\pi$
$571$	21.0654	+	4.86800i	0.881560	+	0.203719i	0.239982	+	0.970777i	$0.422858\pi$
$572$		0			0
$573$	4.21423	−	2.68787i	0.176052	−	0.112288i
$574$		0			0
$575$	−10.6455	−	28.3181i	−0.443946	−	1.18095i
$576$		0			0
$577$	22.8087	+	29.2444i	0.949538	+	1.21746i	0.975991	+	0.217812i	$0.0698920\pi$
$577$	22.8087	+	29.2444i	0.949538	+	1.21746i	−0.0264531	+	0.999650i	$0.508421\pi$
$578$		0			0
$579$	1.22038	+	4.18285i	0.0507173	+	0.173833i
$580$		0			0
$581$	−12.9193	−	23.0435i	−0.535984	−	0.956007i
$582$		0			0
$583$	−46.0348	−	24.6762i	−1.90657	−	1.02198i
$584$		0			0
$585$	13.4018	−	18.5936i	0.554095	−	0.768749i
$586$		0			0
$587$	−19.1741	+	11.2321i	−0.791400	+	0.463596i	−0.844869	−	0.534973i	$-0.820322\pi$
$587$	−19.1741	+	11.2321i	−0.791400	+	0.463596i	0.0534686	+	0.998570i	$0.482972\pi$
$588$		0			0
$589$	−4.13525	+	11.0003i	−0.170390	+	0.453258i
$590$		0			0
$591$	1.78668	+	3.49022i	0.0734944	+	0.143568i
$592$		0			0
$593$	−3.59942	+	4.27135i	−0.147811	+	0.175403i	−0.833550	−	0.552443i	$-0.813696\pi$
$593$	−3.59942	+	4.27135i	−0.147811	+	0.175403i	0.685740	+	0.727847i	$0.259479\pi$
$594$		0			0
$595$	31.9294	−	23.9449i	1.30898	−	0.981647i
$596$		0			0
$597$	6.74566	−	0.769290i	0.276082	−	0.0314849i
$598$		0			0
$599$	−1.34497	+	5.35598i	−0.0549540	+	0.218839i	−0.991172	−	0.132579i	$-0.957674\pi$
$599$	−1.34497	+	5.35598i	−0.0549540	+	0.218839i	0.936218	+	0.351419i	$0.114301\pi$
$600$		0			0
$601$	26.3553	−	11.6545i	1.07505	−	0.475398i	0.210323	−	0.977632i	$-0.432549\pi$
$601$	26.3553	−	11.6545i	1.07505	−	0.475398i	0.864732	+	0.502234i	$0.167488\pi$
$602$		0			0
$603$	5.20103	−	4.21714i	0.211802	−	0.171735i
$604$		0			0
$605$	15.8079	−	91.9097i	0.642683	−	3.73666i
$606$		0			0
$607$	−2.11141	+	2.15176i	−0.0856997	+	0.0873371i	−0.755279	−	0.655404i	$-0.772499\pi$
$607$	−2.11141	+	2.15176i	−0.0856997	+	0.0873371i	0.669579	+	0.742741i	$0.266474\pi$
$608$		0			0
$609$	3.42581	−	0.259834i	0.138821	−	0.0105290i
$610$		0			0
$611$	−19.0148	−	9.28403i	−0.769255	−	0.375592i
$612$		0			0
$613$	0.919069	−	0.492651i	0.0371208	−	0.0198980i	−0.453774	−	0.891117i	$-0.649923\pi$
$613$	0.919069	−	0.492651i	0.0371208	−	0.0198980i	0.490895	+	0.871219i	$0.336670\pi$
$614$		0			0
$615$	1.63312	+	9.49525i	0.0658539	+	0.382885i
$616$		0			0
$617$	1.22868	+	21.6176i	0.0494647	+	0.870292i	0.923302	+	0.384074i	$0.125479\pi$
$617$	1.22868	+	21.6176i	0.0494647	+	0.870292i	−0.873838	+	0.486218i	$0.838376\pi$
$618$		0			0
$619$	−0.674746	−	0.800705i	−0.0271203	−	0.0321831i	0.750962	−	0.660346i	$-0.229590\pi$
$619$	−0.674746	−	0.800705i	−0.0271203	−	0.0321831i	−0.778082	+	0.628163i	$0.783807\pi$
$620$		0			0
$621$	−0.123278	−	6.51315i	−0.00494697	−	0.261364i
$622$		0			0
$623$	−38.5439	−	5.88063i	−1.54423	−	0.235602i
$624$		0			0
$625$	−1.00997	+	10.6414i	−0.0403989	+	0.425656i
$626$		0			0
$627$	−12.0630	+	5.88980i	−0.481749	+	0.235216i
$628$		0			0
$629$	−10.8465	−	3.84482i	−0.432480	−	0.153303i
$630$		0			0
$631$	45.6317	+	12.3814i	1.81657	+	0.492895i	0.996810	−	0.0798119i	$-0.0254320\pi$
$631$	45.6317	+	12.3814i	1.81657	+	0.492895i	0.819760	+	0.572707i	$0.194107\pi$
$632$		0			0
$633$	−0.137280	+	0.120200i	−0.00545637	+	0.00477750i
$634$		0			0
$635$	4.42246	+	2.59064i	0.175500	+	0.102806i
$636$		0			0
$637$	−17.9836	+	4.15582i	−0.712535	+	0.164659i
$638$		0			0
$639$	31.2268	−	12.4183i	1.23531	−	0.491259i
$640$		0			0
$641$	10.8991	+	25.9646i	0.430489	+	1.02554i	0.981572	+	0.191091i	$0.0612025\pi$
$641$	10.8991	+	25.9646i	0.430489	+	1.02554i	−0.551084	+	0.834450i	$0.685785\pi$
$642$		0			0
$643$	3.85773	+	4.24120i	0.152134	+	0.167257i	0.811083	−	0.584931i	$-0.198878\pi$
$643$	3.85773	+	4.24120i	0.152134	+	0.167257i	−0.658949	+	0.752187i	$0.728999\pi$
$644$		0			0
$645$	−10.2980	−	4.09530i	−0.405482	−	0.161252i
$646$		0			0
$647$	−6.10429	−	1.90705i	−0.239984	−	0.0749738i	0.175840	−	0.984419i	$-0.443736\pi$
$647$	−6.10429	−	1.90705i	−0.239984	−	0.0749738i	−0.415824	+	0.909445i	$0.636507\pi$
$648$		0			0
$649$	−42.1958	+	63.4750i	−1.65633	+	2.49161i
$650$		0			0
$651$	−2.23175	−	0.169269i	−0.0874693	−	0.00663419i
$652$		0			0
$653$	2.54251	−	8.71444i	0.0994963	−	0.341023i	−0.894964	−	0.446139i	$-0.852799\pi$
$653$	2.54251	−	8.71444i	0.0994963	−	0.341023i	0.994460	+	0.105117i	$0.0335216\pi$
$654$		0			0
$655$	18.7902	−	36.7060i	0.734194	−	1.43422i
$656$		0			0
$657$	−27.9559	+	35.8440i	−1.09066	+	1.39841i
$658$		0			0
$659$	18.5782	−	5.04087i	0.723704	−	0.196365i	0.119090	−	0.992883i	$-0.462002\pi$
$659$	18.5782	−	5.04087i	0.723704	−	0.196365i	0.604614	+	0.796519i	$0.293328\pi$
$660$		0			0
$661$	11.9175	−	25.6274i	0.463535	−	0.996789i	−0.525729	−	0.850652i	$-0.676207\pi$
$661$	11.9175	−	25.6274i	0.463535	−	0.996789i	0.989264	−	0.146137i	$-0.0466841\pi$
$662$		0			0
$663$	−1.71281	−	0.757421i	−0.0665202	−	0.0294158i
$664$		0			0
$665$	−13.3593	−	100.252i	−0.518053	−	3.88761i
$666$		0			0
$667$	8.90719			0.344888
$668$		0			0
$669$	−7.46016			−0.288426
$670$		0			0
$671$	1.45262	+	10.9009i	0.0560777	+	0.420823i
$672$		0			0
$673$	−20.2335	−	8.94743i	−0.779945	−	0.344898i	−0.0241514	−	0.999708i	$-0.507688\pi$
$673$	−20.2335	−	8.94743i	−0.779945	−	0.344898i	−0.755793	+	0.654810i	$0.772749\pi$
$674$		0			0
$675$	−7.31541	+	15.7311i	−0.281570	+	0.605491i
$676$		0			0
$677$	−26.2783	+	7.13016i	−1.00996	+	0.274034i	−0.728136	−	0.685433i	$-0.759613\pi$
$677$	−26.2783	+	7.13016i	−1.00996	+	0.274034i	−0.281821	+	0.959467i	$0.590938\pi$
$678$		0			0
$679$	41.6097	−	53.3504i	1.59683	−	2.04740i
$680$		0			0
$681$	4.03827	−	7.88861i	0.154747	−	0.302292i
$682$		0			0
$683$	0.936443	−	3.20965i	0.0358320	−	0.122814i	−0.940094	−	0.340915i	$-0.889263\pi$
$683$	0.936443	−	3.20965i	0.0358320	−	0.122814i	0.975926	+	0.218101i	$0.0699862\pi$
$684$		0			0
$685$	6.67979	+	0.506635i	0.255222	+	0.0193575i
$686$		0			0
$687$	1.50783	−	2.26823i	0.0575274	−	0.0865383i
$688$		0			0
$689$	−17.6258	−	5.50649i	−0.671488	−	0.209781i
$690$		0			0
$691$	38.2254	+	15.2015i	1.45416	+	0.578293i	0.957187	−	0.289471i	$-0.0934794\pi$
$691$	38.2254	+	15.2015i	1.45416	+	0.578293i	0.496977	+	0.867764i	$0.334443\pi$
$692$		0			0
$693$	46.2461	+	50.8431i	1.75674	+	1.93137i
$694$		0			0
$695$	−7.80763	−	18.5999i	−0.296160	−	0.705534i
$696$		0			0
$697$	−19.6655	+	7.82060i	−0.744885	+	0.296226i
$698$		0			0
$699$	−4.87364	+	1.12625i	−0.184338	+	0.0425986i
$700$		0			0
$701$	−11.0730	−	6.48649i	−0.418222	−	0.244991i	0.281274	−	0.959627i	$-0.409243\pi$
$701$	−11.0730	−	6.48649i	−0.418222	−	0.244991i	−0.699496	+	0.714636i	$0.746592\pi$
$702$		0			0
$703$	−21.9406	+	19.2108i	−0.827504	+	0.724548i
$704$		0			0
$705$	11.8145	+	3.20567i	0.444961	+	0.120732i
$706$		0			0
$707$	38.9372	+	13.8022i	1.46438	+	0.519086i
$708$		0			0
$709$	0.460588	−	0.224883i	0.0172977	−	0.00844568i	−0.430080	−	0.902791i	$-0.641515\pi$
$709$	0.460588	−	0.224883i	0.0172977	−	0.00844568i	0.447378	+	0.894345i	$0.352358\pi$
$710$		0			0
$711$	2.10663	−	22.1961i	0.0790048	−	0.832420i
$712$		0			0
$713$	−5.73623	−	0.875175i	−0.214824	−	0.0327756i
$714$		0			0
$715$	−0.899077	−	47.5010i	−0.0336236	−	1.77644i
$716$		0			0
$717$	4.25033	+	5.04377i	0.158732	+	0.188363i
$718$		0			0
$719$	2.33367	+	41.0592i	0.0870314	+	1.53125i	0.684296	+	0.729205i	$0.260110\pi$
$719$	2.33367	+	41.0592i	0.0870314	+	1.53125i	−0.597264	+	0.802045i	$0.703746\pi$
$720$		0			0
$721$	−1.11387	−	6.47623i	−0.0414827	−	0.241187i
$722$		0			0
$723$	4.17639	−	2.23868i	0.155322	−	0.0832575i
$724$		0			0
$725$	−21.3164	−	10.4078i	−0.791671	−	0.386536i
$726$		0			0
$727$	−19.0324	+	1.44353i	−0.705872	+	0.0535375i	−0.423669	−	0.905817i	$-0.639258\pi$
$727$	−19.0324	+	1.44353i	−0.705872	+	0.0535375i	−0.282203	+	0.959355i	$0.591065\pi$
$728$		0			0
$729$	14.9618	−	15.2477i	0.554143	−	0.564730i
$730$		0			0
$731$	4.12636	−	23.9913i	0.152619	−	0.887352i
$732$		0			0
$733$	5.32864	−	4.32062i	0.196818	−	0.159586i	−0.526327	−	0.850283i	$-0.676431\pi$
$733$	5.32864	−	4.32062i	0.196818	−	0.159586i	0.723144	+	0.690697i	$0.242696\pi$
$734$		0			0
$735$	9.76587	−	4.31855i	0.360219	−	0.159292i
$736$		0			0
$737$	3.38041	−	13.4616i	0.124519	−	0.495863i
$738$		0			0
$739$	21.3713	−	2.43723i	0.786155	−	0.0896548i	0.289014	−	0.957325i	$-0.406672\pi$
$739$	21.3713	−	2.43723i	0.786155	−	0.0896548i	0.497141	+	0.867670i	$0.334383\pi$
$740$		0			0
$741$	−3.79688	+	2.84741i	−0.139482	+	0.104602i
$742$		0			0
$743$	22.1861	−	26.3277i	0.813929	−	0.965871i	−0.185932	−	0.982563i	$-0.559530\pi$
$743$	22.1861	−	26.3277i	0.813929	−	0.965871i	0.999861	+	0.0166921i	$0.00531351\pi$
$744$		0			0
$745$	−14.6381	−	28.5949i	−0.536297	−	1.04764i
$746$		0			0
$747$	−6.78419	+	18.0467i	−0.248221	+	0.660296i
$748$		0			0
$749$	23.2615	−	13.6264i	0.849957	−	0.497898i
$750$		0			0
$751$	−28.2764	+	39.2305i	−1.03182	+	1.43154i	−0.134104	+	0.990967i	$0.542816\pi$
$751$	−28.2764	+	39.2305i	−1.03182	+	1.43154i	−0.897716	+	0.440575i	$0.854775\pi$
$752$		0			0
$753$	−0.0676319	−	0.0362529i	−0.00246464	−	0.00132113i
$754$		0			0
$755$	−23.2777	−	41.5192i	−0.847161	−	1.51104i
$756$		0			0
$757$	−1.36056	−	4.66331i	−0.0494505	−	0.169491i	0.931503	−	0.363733i	$-0.118498\pi$
$757$	−1.36056	−	4.66331i	−0.0494505	−	0.169491i	−0.980954	+	0.194242i	$0.937775\pi$
$758$		0			0
$759$	−4.07638	−	5.22659i	−0.147963	−	0.189713i
$760$		0			0
$761$	11.1294	+	29.6056i	0.403441	+	1.07320i	0.968688	+	0.248279i	$0.0798651\pi$
$761$	11.1294	+	29.6056i	0.403441	+	1.07320i	−0.565247	+	0.824921i	$0.691219\pi$
$762$		0			0
$763$	−35.7593	+	22.8076i	−1.29457	+	0.825691i
$764$		0			0
$765$	−28.3786	−	6.55801i	−1.02603	−	0.237105i
$766$		0			0
$767$	−10.4298	+	24.8467i	−0.376600	+	0.897163i
$768$		0			0
$769$	−2.82823	−	29.7991i	−0.101988	−	1.07458i	−0.889081	−	0.457749i	$-0.848656\pi$
$769$	−2.82823	−	29.7991i	−0.101988	−	1.07458i	0.787093	−	0.616835i	$-0.211585\pi$
$770$		0			0
$771$	4.64083	−	3.21332i	0.167135	−	0.115725i
$772$		0			0
$773$	−8.10448	−	7.09614i	−0.291498	−	0.255230i	0.500525	−	0.865722i	$-0.333140\pi$
$773$	−8.10448	−	7.09614i	−0.291498	−	0.255230i	−0.792023	+	0.610492i	$0.790972\pi$
$774$		0			0
$775$	12.7052	+	8.79707i	0.456383	+	0.316000i
$776$		0			0
$777$	−4.68265	−	2.98664i	−0.167989	−	0.107145i
$778$		0			0
$779$	−7.08412	+	53.1612i	−0.253815	+	1.90470i
$780$		0			0
$781$	36.3403	−	59.4281i	1.30036	−	2.12651i
$782$		0			0
$783$	−3.57750	−	3.64586i	−0.127849	−	0.130292i
$784$		0			0
$785$	10.2318	−	48.4371i	0.365188	−	1.72880i
$786$		0			0
$787$	−12.7785	+	22.7924i	−0.455506	+	0.812462i	−0.999648	−	0.0265307i	$-0.991554\pi$
$787$	−12.7785	+	22.7924i	−0.455506	+	0.812462i	0.544142	+	0.838993i	$0.316855\pi$
$788$		0			0
$789$	0.0148325	+	0.0590663i	0.000528050	+	0.00210282i
$790$		0			0
$791$	−10.0496	−	15.1176i	−0.357322	−	0.537518i
$792$		0			0
$793$	1.22940	+	3.68847i	0.0436574	+	0.130981i
$794$		0			0
$795$	10.6142	+	1.21046i	0.376446	+	0.0429307i
$796$		0			0
$797$	−11.4231	+	0.432577i	−0.404627	+	0.0153226i	−0.239371	−	0.970928i	$-0.576941\pi$
$797$	−11.4231	+	0.432577i	−0.404627	+	0.0153226i	−0.165256	+	0.986251i	$0.552845\pi$
$798$		0			0
$799$	−1.52589	+	26.8468i	−0.0539821	+	0.949772i
$800$		0			0
$801$	14.8446	+	24.2757i	0.524507	+	0.857738i
$802$		0			0
$803$	−1.78312	+	94.2079i	−0.0629250	+	3.32453i
$804$		0			0
$805$	47.0686	−	16.6846i	1.65895	−	0.588054i
$806$		0			0
$807$	0.760030	+	0.718059i	0.0267543	+	0.0252769i
$808$		0			0
$809$	−22.7830	+	3.47599i	−0.801007	+	0.122209i	−0.538395	−	0.842692i	$-0.680969\pi$
$809$	−22.7830	+	3.47599i	−0.801007	+	0.122209i	−0.262611	+	0.964902i	$0.584584\pi$
$810$		0			0
$811$	−18.6349	−	40.0727i	−0.654361	−	1.40714i	−0.899182	−	0.437575i	$-0.855838\pi$
$811$	−18.6349	−	40.0727i	−0.654361	−	1.40714i	0.244821	−	0.969568i	$-0.421271\pi$
$812$		0			0
$813$	0.792212	+	0.0300000i	0.0277841	+	0.00105215i
$814$		0			0
$815$	8.68349	−	9.54666i	0.304169	−	0.334405i
$816$		0			0
$817$	−47.9176	−	38.8530i	−1.67642	−	1.35929i
$818$		0			0
$819$	19.4395	+	14.5783i	0.679271	+	0.509408i
$820$		0			0
$821$	−20.0871	+	3.84758i	−0.701045	+	0.134282i	−0.526258	−	0.850325i	$-0.676406\pi$
$821$	−20.0871	+	3.84758i	−0.701045	+	0.134282i	−0.174787	+	0.984606i	$0.555924\pi$
$822$		0			0
$823$	−12.0518	−	2.30846i	−0.420100	−	0.0804680i	−0.0262779	−	0.999655i	$-0.508365\pi$
$823$	−12.0518	−	2.30846i	−0.420100	−	0.0804680i	−0.393822	+	0.919187i	$0.628847\pi$
$824$		0			0
$825$	3.64835	+	17.2713i	0.127019	+	0.601308i
$826$		0			0
$827$	−20.4023	+	6.37390i	−0.709456	+	0.221642i	−0.631569	−	0.775320i	$-0.717589\pi$
$827$	−20.4023	+	6.37390i	−0.709456	+	0.221642i	−0.0778876	+	0.996962i	$0.524818\pi$
$828$		0			0
$829$	−34.3057	+	32.4112i	−1.19149	+	1.12569i	−0.202254	+	0.979333i	$0.564827\pi$
$829$	−34.3057	+	32.4112i	−1.19149	+	1.12569i	−0.989232	+	0.146356i	$0.953246\pi$
$830$		0			0
$831$	−1.58469	+	4.75441i	−0.0549723	+	0.164929i
$832$		0			0
$833$	13.7149	+	19.0280i	0.475194	+	0.659281i
$834$		0			0
$835$	−9.97342	+	47.2708i	−0.345144	+	1.63587i
$836$		0			0
$837$	1.94569	+	2.69944i	0.0672529	+	0.0933063i
$838$		0			0
$839$	−3.00074	+	9.00287i	−0.103597	+	0.310814i	−0.987673	−	0.156529i	$-0.949969\pi$
$839$	−3.00074	+	9.00287i	−0.103597	+	0.310814i	0.884076	+	0.467343i	$0.154789\pi$
$840$		0			0
$841$	−16.0031	+	15.1194i	−0.551832	+	0.521358i
$842$		0			0
$843$	−8.09345	+	2.52848i	−0.278753	+	0.0870856i
$844$		0			0
$845$	6.57304	+	31.1167i	0.226119	+	1.07045i
$846$		0			0
$847$	97.1031	+	18.5996i	3.33650	+	0.639090i
$848$		0			0
$849$	6.24261	−	1.19574i	0.214246	−	0.0410377i
$850$		0			0
$851$	−11.5198	−	8.63906i	−0.394892	−	0.296143i
$852$		0			0
$853$	−32.8271	−	26.6172i	−1.12398	−	0.911354i	−0.127225	−	0.991874i	$-0.540607\pi$
$853$	−32.8271	−	26.6172i	−1.12398	−	0.911354i	−0.996753	+	0.0805200i	$0.974342\pi$
$854$		0			0
$855$	−49.6650	+	54.6019i	−1.69851	+	1.86734i
$856$		0			0
$857$	28.1668	+	1.06664i	0.962158	+	0.0364356i	0.514247	−	0.857642i	$-0.328072\pi$
$857$	28.1668	+	1.06664i	0.962158	+	0.0364356i	0.447912	+	0.894078i	$0.352168\pi$
$858$		0			0
$859$	−3.80649	−	8.18550i	−0.129876	−	0.279286i	0.830997	−	0.556278i	$-0.187771\pi$
$859$	−3.80649	−	8.18550i	−0.129876	−	0.279286i	−0.960872	+	0.276992i	$0.910662\pi$
$860$		0			0
$861$	−10.0973	+	1.54054i	−0.344115	+	0.0525015i
$862$		0			0
$863$	−13.8774	−	13.1110i	−0.472392	−	0.446305i	0.413289	−	0.910600i	$-0.364380\pi$
$863$	−13.8774	−	13.1110i	−0.472392	−	0.446305i	−0.885681	+	0.464295i	$0.846308\pi$
$864$		0			0
$865$	24.7436	−	8.77094i	0.841307	−	0.298221i
$866$		0			0
$867$	0.0604872	−	3.19573i	0.00205425	−	0.108533i
$868$		0			0
$869$	−24.1104	−	39.4283i	−0.817889	−	1.33751i
$870$		0			0
$871$	0.278447	−	4.89906i	0.00943482	−	0.165998i
$872$		0			0
$873$	−49.3413	+	1.86849i	−1.66995	+	0.0632387i
$874$		0			0
$875$	−58.5323	−	6.67515i	−1.97875	−	0.225661i
$876$		0			0
$877$	10.8248	+	32.4767i	0.365528	+	1.09666i	0.956939	+	0.290291i	$0.0937520\pi$
$877$	10.8248	+	32.4767i	0.365528	+	1.09666i	−0.591411	+	0.806371i	$0.701429\pi$
$878$		0			0
$879$	1.04192	+	1.56735i	0.0351430	+	0.0528655i
$880$		0			0
$881$	4.90048	+	19.5148i	0.165101	+	0.657471i	0.995028	+	0.0995985i	$0.0317558\pi$
$881$	4.90048	+	19.5148i	0.165101	+	0.657471i	−0.829926	+	0.557873i	$0.811618\pi$
$882$		0			0
$883$	9.75554	−	17.4005i	0.328300	−	0.585572i	−0.657508	−	0.753448i	$-0.728389\pi$
$883$	9.75554	−	17.4005i	0.328300	−	0.585572i	0.985808	+	0.167875i	$0.0536906\pi$
$884$		0			0
$885$	3.22199	−	15.2529i	0.108306	−	0.512721i
$886$		0			0
$887$	10.0559	+	10.2481i	0.337646	+	0.344097i	0.861543	−	0.507684i	$-0.169498\pi$
$887$	10.0559	+	10.2481i	0.337646	+	0.344097i	−0.523897	+	0.851781i	$0.675522\pi$
$888$		0			0
$889$	−2.83469	+	4.63564i	−0.0950725	+	0.155474i
$890$		0			0
$891$	6.36978	−	47.8006i	0.213396	−	1.60138i
$892$		0			0
$893$	57.4521	+	36.6435i	1.92256	+	1.22623i
$894$		0			0
$895$	56.4320	+	39.0736i	1.88631	+	1.30609i
$896$		0			0
$897$	−1.76305	−	1.54370i	−0.0588666	−	0.0515426i
$898$		0			0
$899$	−3.74070	+	2.59006i	−0.124759	+	0.0863835i
$900$		0			0
$901$	2.21721	+	23.3612i	0.0738660	+	0.778276i
$902$		0			0
$903$	4.54744	−	10.8332i	0.151329	−	0.360507i
$904$		0			0
$905$	−2.22661	−	0.514547i	−0.0740151	−	0.0171041i
$906$		0			0
$907$	28.4191	−	18.1260i	0.943640	−	0.601863i	0.0261657	−	0.999658i	$-0.491670\pi$
$907$	28.4191	−	18.1260i	0.943640	−	0.601863i	0.917474	+	0.397795i	$0.130224\pi$
$908$		0			0
$909$	−10.6087	−	28.2205i	−0.351870	−	0.936015i
$910$		0			0
$911$	−12.6045	−	16.1610i	−0.417606	−	0.535439i	0.532887	−	0.846187i	$-0.321107\pi$
$911$	−12.6045	−	16.1610i	−0.417606	−	0.535439i	−0.950492	+	0.310748i	$0.899420\pi$
$912$		0			0
$913$	11.1931	+	38.3644i	0.370439	+	1.26968i
$914$		0			0
$915$	−1.09997	−	1.96197i	−0.0363640	−	0.0648606i
$916$		0			0
$917$	38.5297	+	20.6532i	1.27236	+	0.682029i
$918$		0			0
$919$	−27.6715	+	38.3912i	−0.912797	+	1.26641i	0.0507064	+	0.998714i	$0.483853\pi$
$919$	−27.6715	+	38.3912i	−0.912797	+	1.26641i	−0.963503	+	0.267696i	$0.913738\pi$
$920$		0			0
$921$	−4.78477	+	2.80288i	−0.157663	+	0.0923580i
$922$		0			0
$923$	8.66582	−	23.0521i	0.285239	−	0.758769i
$924$		0			0
$925$	17.4742	+	34.1352i	0.574549	+	1.12236i
$926$		0			0
$927$	−3.09035	+	3.66725i	−0.101500	+	0.120448i
$928$		0			0
$929$	40.4440	−	30.3303i	1.32692	−	0.995105i	0.328199	−	0.944609i	$-0.393558\pi$
$929$	40.4440	−	30.3303i	1.32692	−	0.995105i	0.998724	−	0.0504959i	$-0.0160802\pi$
$930$		0			0
$931$	59.0567	−	6.73495i	1.93550	−	0.220729i
$932$		0			0
$933$	−1.23303	+	4.91022i	−0.0403677	+	0.160754i
$934$		0			0
$935$	−55.2167	+	24.4173i	−1.80578	+	0.798531i
$936$		0			0
$937$	19.2137	−	15.5790i	0.627685	−	0.508945i	−0.262269	−	0.964995i	$-0.584471\pi$
$937$	19.2137	−	15.5790i	0.627685	−	0.508945i	0.889954	+	0.456049i	$0.150736\pi$
$938$		0			0
$939$	1.66612	−	9.68707i	0.0543716	−	0.316126i
$940$		0			0
$941$	33.1848	−	33.8188i	1.08179	−	1.10246i	0.0874573	−	0.996168i	$-0.472126\pi$
$941$	33.1848	−	33.8188i	1.08179	−	1.10246i	0.994335	−	0.106293i	$-0.0338982\pi$
$942$		0			0
$943$	−26.4052	+	2.00272i	−0.859870	+	0.0652177i
$944$		0			0
$945$	−25.7340	−	12.5647i	−0.837126	−	0.408730i
$946$		0			0
$947$	−4.38300	+	2.34943i	−0.142428	+	0.0763463i	−0.542109	−	0.840308i	$-0.682374\pi$
$947$	−4.38300	+	2.34943i	−0.142428	+	0.0763463i	0.399681	+	0.916654i	$0.369121\pi$
$948$		0			0
$949$	5.64659	+	32.8302i	0.183296	+	1.06571i
$950$		0			0
$951$	0.0156713	+	0.275723i	0.000508175	+	0.00894094i
$952$		0			0
$953$	−31.4825	−	37.3596i	−1.01982	−	1.21019i	−0.977466	−	0.211092i	$-0.932298\pi$
$953$	−31.4825	−	37.3596i	−1.01982	−	1.21019i	−0.0423519	−	0.999103i	$-0.513485\pi$
$954$		0			0
$955$	−1.07808	−	56.9581i	−0.0348857	−	1.84312i
$956$		0			0
$957$	−5.13782	−	0.783875i	−0.166082	−	0.0253391i
$958$		0			0
$959$	−0.671023	+	7.07012i	−0.0216685	+	0.228306i
$960$		0			0
$961$	−25.1934	+	12.3008i	−0.812690	+	0.396799i
$962$		0			0
$963$	−18.5438	−	6.57330i	−0.597567	−	0.211822i
$964$		0			0
$965$	47.9275	+	13.0043i	1.54284	+	0.418623i
$966$		0			0
$967$	−24.1838	+	21.1749i	−0.777699	+	0.680939i	−0.952796	−	0.303612i	$-0.901807\pi$
$967$	−24.1838	+	21.1749i	−0.777699	+	0.680939i	0.175097	+	0.984551i	$0.443976\pi$
$968$		0			0
$969$	5.20395	+	3.04844i	0.167175	+	0.0979299i
$970$		0			0
$971$	29.8784	−	6.90460i	0.958845	−	0.221579i	0.283410	−	0.958999i	$-0.408534\pi$
$971$	29.8784	−	6.90460i	0.958845	−	0.221579i	0.675435	+	0.737420i	$0.263956\pi$
$972$		0			0
$973$	19.8717	−	7.90259i	0.637057	−	0.253345i
$974$		0			0
$975$	2.41551	+	5.75441i	0.0773584	+	0.184289i
$976$		0			0
$977$	−17.5716	−	19.3182i	−0.562164	−	0.618045i	0.391040	−	0.920374i	$-0.372116\pi$
$977$	−17.5716	−	19.3182i	−0.562164	−	0.618045i	−0.953204	+	0.302329i	$0.902236\pi$
$978$		0			0
$979$	54.8071	+	21.7957i	1.75164	+	0.696594i
$980$		0			0
$981$	29.5450	+	9.23020i	0.943300	+	0.294698i
$982$		0			0
$983$	−11.0326	+	16.5963i	−0.351885	+	0.529340i	−0.965547	−	0.260229i	$-0.916202\pi$
$983$	−11.0326	+	16.5963i	−0.351885	+	0.529340i	0.613662	+	0.789569i	$0.289696\pi$
$984$		0			0
$985$	44.5600	+	3.37970i	1.41980	+	0.107686i
$986$		0			0
$987$	−3.63489	+	12.4586i	−0.115700	+	0.396560i
$988$		0			0
$989$	13.8799	−	27.1139i	0.441356	−	0.862172i
$990$		0			0
$991$	−1.73134	+	2.21986i	−0.0549979	+	0.0705163i	−0.815239	−	0.579125i	$-0.803394\pi$
$991$	−1.73134	+	2.21986i	−0.0549979	+	0.0705163i	0.760241	+	0.649641i	$0.225081\pi$
$992$		0			0
$993$	−5.05773	+	1.37233i	−0.160502	+	0.0435495i
$994$		0			0
$995$	32.6285	−	70.1646i	1.03439	−	2.22437i
$996$		0			0
$997$	22.4838	+	9.94252i	0.712068	+	0.314883i	0.728561	−	0.684981i	$-0.240190\pi$
$997$	22.4838	+	9.94252i	0.712068	+	0.314883i	−0.0164923	+	0.999864i	$0.505250\pi$
$998$		0			0
$999$	1.09072	+	8.18503i	0.0345087	+	0.258963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.8	✓	1148
167.130	even	83	inner	668.2.e.a.297.8	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.8	✓	1148	1.1	even	1	trivial
668.2.e.a.297.8	yes	1148	167.130	even	83	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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0433273 + 0.325140i) q^{3} +(3.41908 + 1.51194i) q^{5} +(-1.67119 + 3.59374i) q^{7} +(2.79147 - 0.757419i) q^{9} +O(q^{10})\)	\(q+(0.0433273 + 0.325140i) q^{3} +(3.41908 + 1.51194i) q^{5} +(-1.67119 + 3.59374i) q^{7} +(2.79147 - 0.757419i) q^{9} +(3.68722 - 4.72762i) q^{11} +(0.965873 - 1.88680i) q^{13} +(-0.343455 + 1.17719i) q^{15} +(-2.68591 - 0.203715i) q^{17} +(-3.77888 + 5.68456i) q^{19} +(-1.24088 - 0.387664i) q^{21} +(-3.13185 - 1.24547i) q^{23} +(6.03974 + 6.64011i) q^{25} +(0.748089 + 1.78215i) q^{27} +(-2.45570 + 0.976584i) q^{29} +(1.67743 - 0.387636i) q^{31} +(1.69690 + 0.994029i) q^{33} +(-11.1474 + 9.76051i) q^{35} +(4.12317 + 1.11875i) q^{37} +(0.655322 + 0.232295i) q^{39} +(7.06029 - 3.44721i) q^{41} +(-0.853909 + 8.99707i) q^{43} +(10.6894 + 1.63088i) q^{45} +(-0.188917 - 9.98110i) q^{47} +(-5.61129 - 6.65879i) q^{49} +(-0.0501372 - 0.882124i) q^{51} +(-1.47669 - 8.58570i) q^{53} +(19.7548 - 10.5892i) q^{55} +(-2.01201 - 0.982371i) q^{57} +(-12.6765 + 0.961465i) q^{59} +(-1.28468 + 1.30922i) q^{61} +(-1.94312 + 11.2976i) q^{63} +(6.15512 - 4.99075i) q^{65} +(2.11722 - 0.936252i) q^{67} +(0.269260 - 1.07225i) q^{69} +(11.5437 - 1.31646i) q^{71} +(-12.5732 + 9.42903i) q^{73} +(-1.89728 + 2.25146i) q^{75} +(10.8278 + 21.1516i) q^{77} +(2.71245 - 7.21543i) q^{79} +(6.94014 - 4.06548i) q^{81} +(-3.89753 + 5.40742i) q^{83} +(-8.87532 - 4.75746i) q^{85} +(-0.423926 - 0.756135i) q^{87} +(2.75536 + 9.44398i) q^{89} +(5.16649 + 6.62429i) q^{91} +(0.198714 + 0.528604i) q^{93} +(-21.5150 + 13.7225i) q^{95} +(-16.6328 - 3.84367i) q^{97} +(6.71199 - 15.9898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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