LMFDB - Embedded newform 725.2.p.b.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(149,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("725.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.p (of order $14$, degree $6$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			274.2
Character	$\chi$	$=$	725.274
Dual form			725.2.p.b.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20749 - 0.581499i) q^{2} +(-0.772561 + 0.968761i) q^{3} +(-0.127077 - 0.159349i) q^{4} +(1.49620 - 0.720531i) q^{6} +(3.02093 + 2.40911i) q^{7} +(0.657236 + 2.87954i) q^{8} +(0.325916 + 1.42793i) q^{9} +(-4.90945 - 1.12055i) q^{11} +0.252546 q^{12} +(3.13465 + 0.715462i) q^{13} +(-2.24686 - 4.66565i) q^{14} +(0.790134 - 3.46180i) q^{16} -5.75831 q^{17} +(0.436798 - 1.91374i) q^{18} +(3.76970 - 3.00623i) q^{19} +(-4.66770 + 1.06537i) q^{21} +(5.27653 + 4.20790i) q^{22} +(1.51507 + 3.14607i) q^{23} +(-3.29734 - 1.58792i) q^{24} +(-3.36903 - 2.68671i) q^{26} +(-4.98426 - 2.40029i) q^{27} -0.787523i q^{28} +(-2.84467 - 4.57251i) q^{29} +(-1.34746 + 2.79803i) q^{31} +(0.715953 - 0.897777i) q^{32} +(4.87839 - 3.89039i) q^{33} +(6.95313 + 3.34845i) q^{34} +(0.186123 - 0.233391i) q^{36} +(0.603935 + 2.64601i) q^{37} +(-6.30001 + 1.43794i) q^{38} +(-3.11482 + 2.48398i) q^{39} +12.5230i q^{41} +(6.25574 + 1.42783i) q^{42} +(-7.79009 + 3.75151i) q^{43} +(0.445317 + 0.924711i) q^{44} -4.67987i q^{46} +(0.0495957 - 0.217293i) q^{47} +(2.74323 + 3.43991i) q^{48} +(1.76454 + 7.73097i) q^{49} +(4.44865 - 5.57843i) q^{51} +(-0.284332 - 0.590421i) q^{52} +(-2.90224 + 6.02657i) q^{53} +(4.62270 + 5.79669i) q^{54} +(-4.95166 + 10.2822i) q^{56} +5.97443i q^{57} +(0.776019 + 7.17546i) q^{58} +4.63118 q^{59} +(-7.39623 - 5.89830i) q^{61} +(3.25411 - 2.59506i) q^{62} +(-2.45547 + 5.09883i) q^{63} +(-7.78494 + 3.74903i) q^{64} +(-8.15289 + 1.86084i) q^{66} +(-12.6590 + 2.88934i) q^{67} +(0.731747 + 0.917581i) q^{68} +(-4.21827 - 0.962792i) q^{69} +(1.66939 - 7.31408i) q^{71} +(-3.89758 + 1.87697i) q^{72} +(-3.18450 + 1.53357i) q^{73} +(0.809405 - 3.54623i) q^{74} +(-0.958080 - 0.218676i) q^{76} +(-12.1315 - 15.2125i) q^{77} +(5.20556 - 1.18814i) q^{78} +(4.33934 - 0.990426i) q^{79} +(2.21714 - 1.06772i) q^{81} +(7.28211 - 15.1215i) q^{82} +(-6.59115 + 5.25627i) q^{83} +(0.762921 + 0.608409i) q^{84} +11.5880 q^{86} +(6.62735 + 0.776735i) q^{87} -14.8734i q^{88} +(-4.20382 + 8.72932i) q^{89} +(7.74590 + 9.71306i) q^{91} +(0.308793 - 0.641215i) q^{92} +(-1.66963 - 3.46702i) q^{93} +(-0.186242 + 0.233540i) q^{94} +(0.316614 + 1.38718i) q^{96} +(9.77776 + 12.2609i) q^{97} +(2.36487 - 10.3612i) q^{98} -7.37555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56}+ \cdots - 2 q^{96}+O(q^{100}) $ 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

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 $

$2$	−1.20749	−	0.581499i	−0.853828	−	0.411182i	−0.0448309	−	0.998995i	$-0.514275\pi$
$2$	−1.20749	−	0.581499i	−0.853828	−	0.411182i	−0.808997	+	0.587813i	$0.799989\pi$
$3$	−0.772561	+	0.968761i	−0.446038	+	0.559314i	−0.953124	−	0.302582i	$-0.902152\pi$
$3$	−0.772561	+	0.968761i	−0.446038	+	0.559314i	0.507085	+	0.861896i	$0.330723\pi$
$4$	−0.127077	−	0.159349i	−0.0635383	−	0.0796745i
$5$		0			0
$5$		0			0
$6$	1.49620	−	0.720531i	0.610820	−	0.294155i
$7$	3.02093	+	2.40911i	1.14180	+	0.910557i	0.996884	−	0.0788865i	$-0.0251365\pi$
$7$	3.02093	+	2.40911i	1.14180	+	0.910557i	0.144919	+	0.989444i	$0.453708\pi$
$8$	0.657236	+	2.87954i	0.232368	+	1.01807i
$9$	0.325916	+	1.42793i	0.108639	+	0.475976i
$10$		0			0
$11$	−4.90945	−	1.12055i	−1.48025	−	0.337858i	−0.595287	−	0.803513i	$-0.702962\pi$
$11$	−4.90945	−	1.12055i	−1.48025	−	0.337858i	−0.884967	+	0.465655i	$0.845819\pi$
$12$	0.252546			0.0729036
$13$	3.13465	+	0.715462i	0.869394	+	0.198434i	0.633874	−	0.773436i	$-0.281464\pi$
$13$	3.13465	+	0.715462i	0.869394	+	0.198434i	0.235520	+	0.971870i	$0.424321\pi$
$14$	−2.24686	−	4.66565i	−0.600498	−	1.24695i
$15$		0			0
$16$	0.790134	−	3.46180i	0.197533	−	0.865451i
$17$	−5.75831			−1.39660			−0.698298	−	0.715807i	$-0.746059\pi$
$17$	−5.75831			−1.39660			−0.698298	+	0.715807i	$0.746059\pi$
$18$	0.436798	−	1.91374i	0.102954	−	0.451072i
$19$	3.76970	−	3.00623i	0.864828	−	0.689677i	−0.0870338	−	0.996205i	$-0.527739\pi$
$19$	3.76970	−	3.00623i	0.864828	−	0.689677i	0.951862	+	0.306528i	$0.0991674\pi$
$20$		0			0
$21$	−4.66770	+	1.06537i	−1.01858	+	0.232483i
$22$	5.27653	+	4.20790i	1.12496	+	0.897126i
$23$	1.51507	+	3.14607i	0.315913	+	0.656000i	0.997099	−	0.0761100i	$-0.0242500\pi$
$23$	1.51507	+	3.14607i	0.315913	+	0.656000i	−0.681186	+	0.732110i	$0.738536\pi$
$24$	−3.29734	−	1.58792i	−0.673067	−	0.324132i
$25$		0			0
$26$	−3.36903	−	2.68671i	−0.660721	−	0.526907i
$27$	−4.98426	−	2.40029i	−0.959222	−	0.461937i
$28$		−	0.787523i		−	0.148828i
$29$	−2.84467	−	4.57251i	−0.528242	−	0.849094i
$29$	−2.84467	−	4.57251i	−0.528242	−	0.849094i
$30$		0			0
$31$	−1.34746	+	2.79803i	−0.242011	+	0.502542i	−0.986227	−	0.165398i	$-0.947109\pi$
$31$	−1.34746	+	2.79803i	−0.242011	+	0.502542i	0.744216	+	0.667939i	$0.232823\pi$
$32$	0.715953	−	0.897777i	0.126564	−	0.158706i
$33$	4.87839	−	3.89039i	0.849219	−	0.677230i
$34$	6.95313	+	3.34845i	1.19245	+	0.574255i
$35$		0			0
$36$	0.186123	−	0.233391i	0.0310205	−	0.0388985i
$37$	0.603935	+	2.64601i	0.0992863	+	0.435002i	1.00000		0.000588127i	$0.000187207\pi$
$37$	0.603935	+	2.64601i	0.0992863	+	0.435002i	−0.900714	+	0.434414i	$0.856956\pi$
$38$	−6.30001	+	1.43794i	−1.02200	+	0.233264i
$39$	−3.11482	+	2.48398i	−0.498770	+	0.397756i
$40$		0			0
$41$			12.5230i			1.95576i	0.209157	+	0.977882i	$0.432928\pi$
$41$			12.5230i			1.95576i	−0.209157	+	0.977882i	$0.567072\pi$
$42$	6.25574	+	1.42783i	0.965281	+	0.220319i
$43$	−7.79009	+	3.75151i	−1.18798	+	0.572100i	−0.920226	−	0.391388i	$-0.871995\pi$
$43$	−7.79009	+	3.75151i	−1.18798	+	0.572100i	−0.267752	+	0.963488i	$0.586281\pi$
$44$	0.445317	+	0.924711i	0.0671341	+	0.139405i
$45$		0			0
$46$		−	4.67987i		−	0.690009i
$47$	0.0495957	−	0.217293i	0.00723428	−	0.0316954i	−0.971182	−	0.238339i	$-0.923397\pi$
$47$	0.0495957	−	0.217293i	0.00723428	−	0.0316954i	0.978416	+	0.206644i	$0.0662541\pi$
$48$	2.74323	+	3.43991i	0.395952	+	0.496508i
$49$	1.76454	+	7.73097i	0.252078	+	1.10442i
$50$		0			0
$51$	4.44865	−	5.57843i	0.622935	−	0.781136i
$52$	−0.284332	−	0.590421i	−0.0394297	−	0.0818767i
$53$	−2.90224	+	6.02657i	−0.398653	+	0.827812i	0.600940	+	0.799294i	$0.294793\pi$
$53$	−2.90224	+	6.02657i	−0.398653	+	0.827812i	−0.999593	+	0.0285181i	$0.990921\pi$
$54$	4.62270	+	5.79669i	0.629070	+	0.788829i
$55$		0			0
$56$	−4.95166	+	10.2822i	−0.661693	+	1.37402i
$57$			5.97443i			0.791333i
$58$	0.776019	+	7.17546i	0.101896	+	0.942183i
$59$	4.63118			0.602928			0.301464	−	0.953478i	$-0.402525\pi$
$59$	4.63118			0.602928			0.301464	+	0.953478i	$0.402525\pi$
$60$		0			0
$61$	−7.39623	−	5.89830i	−0.946990	−	0.755199i	0.0226481	−	0.999743i	$-0.492790\pi$
$61$	−7.39623	−	5.89830i	−0.946990	−	0.755199i	−0.969638	+	0.244544i	$0.921362\pi$
$62$	3.25411	−	2.59506i	0.413272	−	0.329573i
$63$	−2.45547	+	5.09883i	−0.309360	+	0.642393i
$64$	−7.78494	+	3.74903i	−0.973117	+	0.468629i
$65$		0			0
$66$	−8.15289	+	1.86084i	−1.00355	+	0.229054i
$67$	−12.6590	+	2.88934i	−1.54655	+	0.352989i	−0.908792	−	0.417250i	$-0.862994\pi$
$67$	−12.6590	+	2.88934i	−1.54655	+	0.352989i	−0.637755	+	0.770239i	$0.720137\pi$
$68$	0.731747	+	0.917581i	0.0887373	+	0.111273i
$69$	−4.21827	−	0.962792i	−0.507820	−	0.115907i
$70$		0			0
$71$	1.66939	−	7.31408i	0.198120	−	0.868021i	−0.773934	−	0.633266i	$-0.781714\pi$
$71$	1.66939	−	7.31408i	0.198120	−	0.868021i	0.972054	−	0.234755i	$-0.0754289\pi$
$72$	−3.89758	+	1.87697i	−0.459334	+	0.221204i
$73$	−3.18450	+	1.53357i	−0.372718	+	0.179491i	−0.610859	−	0.791739i	$-0.709176\pi$
$73$	−3.18450	+	1.53357i	−0.372718	+	0.179491i	0.238142	+	0.971230i	$0.423462\pi$
$74$	0.809405	−	3.54623i	0.0940914	−	0.412241i
$75$		0			0
$76$	−0.958080	−	0.218676i	−0.109899	−	0.0250838i
$77$	−12.1315	−	15.2125i	−1.38252	−	1.73362i
$78$	5.20556	−	1.18814i	0.589414	−	0.134530i
$79$	4.33934	−	0.990426i	0.488214	−	0.111432i	0.0286740	−	0.999589i	$-0.490872\pi$
$79$	4.33934	−	0.990426i	0.488214	−	0.111432i	0.459540	+	0.888157i	$0.348014\pi$
$80$		0			0
$81$	2.21714	−	1.06772i	0.246349	−	0.118635i
$82$	7.28211	−	15.1215i	0.804175	−	1.66989i
$83$	−6.59115	+	5.25627i	−0.723473	+	0.576950i	−0.914477	−	0.404639i	$-0.867397\pi$
$83$	−6.59115	+	5.25627i	−0.723473	+	0.576950i	0.191004	+	0.981589i	$0.438826\pi$
$84$	0.762921	+	0.608409i	0.0832415	+	0.0663829i
$85$		0			0
$86$	11.5880			1.24957
$87$	6.62735	+	0.776735i	0.710527	+	0.0832747i
$88$		−	14.8734i		−	1.58551i
$89$	−4.20382	+	8.72932i	−0.445604	+	0.925306i	0.550307	+	0.834963i	$0.314511\pi$
$89$	−4.20382	+	8.72932i	−0.445604	+	0.925306i	−0.995911	+	0.0903436i	$0.971203\pi$
$90$		0			0
$91$	7.74590	+	9.71306i	0.811991	+	1.01820i
$92$	0.308793	−	0.641215i	0.0321939	−	0.0668513i
$93$	−1.66963	−	3.46702i	−0.173132	−	0.359513i
$94$	−0.186242	+	0.233540i	−0.0192094	+	0.0240878i
$95$		0			0
$96$	0.316614	+	1.38718i	0.0323142	+	0.141578i
$97$	9.77776	+	12.2609i	0.992781	+	1.24491i	0.969478	+	0.245180i	$0.0788470\pi$
$97$	9.77776	+	12.2609i	0.992781	+	1.24491i	0.0233037	+	0.999728i	$0.492582\pi$
$98$	2.36487	−	10.3612i	0.238888	−	1.04664i
$99$		−	7.37555i		−	0.741271i
$100$		0			0
$101$	1.83592	+	3.81234i	0.182681	+	0.379342i	0.972119	−	0.234490i	$-0.0753419\pi$
$101$	1.83592	+	3.81234i	0.182681	+	0.379342i	−0.789437	+	0.613831i	$0.789628\pi$
$102$	−8.61557	+	4.14904i	−0.853069	+	0.410816i
$103$	1.88882	+	0.431110i	0.186111	+	0.0424785i	0.314560	−	0.949237i	$-0.398143\pi$
$103$	1.88882	+	0.431110i	0.186111	+	0.0424785i	−0.128450	+	0.991716i	$0.541000\pi$
$104$			9.49657i			0.931215i
$105$		0			0
$106$	7.00888	−	5.58940i	0.680763	−	0.542890i
$107$	5.21382	−	1.19002i	0.504039	−	0.115044i	0.0370620	−	0.999313i	$-0.488200\pi$
$107$	5.21382	−	1.19002i	0.504039	−	0.115044i	0.466977	+	0.884269i	$0.345343\pi$
$108$	0.250899	+	1.09926i	0.0241427	+	0.105776i
$109$	−2.27679	+	2.85501i	−0.218077	+	0.273460i	−0.878821	−	0.477151i	$-0.841669\pi$
$109$	−2.27679	+	2.85501i	−0.218077	+	0.273460i	0.660744	+	0.750611i	$0.270241\pi$
$110$		0			0
$111$	−3.02993	−	1.45914i	−0.287588	−	0.138495i
$112$	10.7268	−	8.55433i	1.01359	−	0.808308i
$113$	5.71530	−	7.16676i	0.537650	−	0.674192i	−0.436602	−	0.899655i	$-0.643818\pi$
$113$	5.71530	−	7.16676i	0.537650	−	0.674192i	0.974252	+	0.225463i	$0.0723896\pi$
$114$	3.47413	−	7.21410i	0.325382	−	0.675662i
$115$		0			0
$116$	−0.367133	+	1.03435i	−0.0340875	+	0.0960374i
$117$			4.70923i			0.435369i
$118$	−5.59213	−	2.69303i	−0.514797	−	0.247913i
$119$	−17.3954	−	13.8724i	−1.59464	−	1.27168i
$120$		0			0
$121$	12.9364	+	6.22983i	1.17603	+	0.566349i
$122$	5.50106	+	11.4231i	0.498042	+	1.03420i
$123$	−12.1318	−	9.67478i	−1.09389	−	0.872346i
$124$	0.617095	−	0.140848i	0.0554167	−	0.0126485i
$125$		0			0
$126$	5.92993	−	4.72896i	0.528280	−	0.421290i
$127$	1.38816	−	6.08193i	0.123179	−	0.539684i	−0.875251	−	0.483670i	$-0.839304\pi$
$127$	1.38816	−	6.08193i	0.123179	−	0.539684i	0.998430	−	0.0560143i	$-0.0178392\pi$
$128$	9.28373			0.820574
$129$	2.38401	−	10.4450i	0.209900	−	0.919632i
$130$		0			0
$131$	0.283798	+	0.589312i	0.0247955	+	0.0514884i	0.912999	−	0.407962i	$-0.133761\pi$
$131$	0.283798	+	0.589312i	0.0247955	+	0.0514884i	−0.888203	+	0.459451i	$0.848046\pi$
$132$	−1.23986	−	0.282990i	−0.107916	−	0.0246311i
$133$	18.6303			1.61545
$134$	16.9659	+	3.87235i	1.46563	+	0.334520i
$135$		0			0
$136$	−3.78457	−	16.5813i	−0.324524	−	1.42183i
$137$	0.580302	+	2.54247i	0.0495785	+	0.217218i	0.993649	−	0.112527i	$-0.0358945\pi$
$137$	0.580302	+	2.54247i	0.0495785	+	0.217218i	−0.944070	+	0.329745i	$0.893037\pi$
$138$	4.53367	+	3.61548i	0.385932	+	0.307770i
$139$	5.28787	−	2.54651i	0.448512	−	0.215992i	−0.195973	−	0.980609i	$-0.562786\pi$
$139$	5.28787	−	2.54651i	0.448512	−	0.215992i	0.644484	+	0.764618i	$0.277072\pi$
$140$		0			0
$141$	0.172189	+	0.215919i	0.0145010	+	0.0181836i
$142$	−6.26891	+	7.86096i	−0.526075	+	0.659677i
$143$	−14.5877	−	7.02505i	−1.21988	−	0.587464i
$144$	5.20073			0.433394
$145$		0			0
$146$	4.73704			0.392040
$147$	−8.85268	−	4.26323i	−0.730157	−	0.351625i
$148$	0.344893	−	0.432483i	0.0283501	−	0.0355498i
$149$	6.48457	+	8.13139i	0.531237	+	0.666150i	0.972952	−	0.231005i	$-0.0742015\pi$
$149$	6.48457	+	8.13139i	0.531237	+	0.666150i	−0.441716	+	0.897155i	$0.645630\pi$
$150$		0			0
$151$	−3.13545	+	1.50995i	−0.255160	+	0.122878i	−0.557091	−	0.830451i	$-0.688083\pi$
$151$	−3.13545	+	1.50995i	−0.255160	+	0.122878i	0.301932	+	0.953329i	$0.402368\pi$
$152$	11.1342	+	8.87919i	0.903099	+	0.720197i
$153$	−1.87672	−	8.22246i	−0.151724	−	0.664747i
$154$	5.80274	+	25.4235i	0.467598	+	2.04868i
$155$		0			0
$156$	0.791641	+	0.180687i	0.0633820	+	0.0144665i
$157$	−9.31575			−0.743478			−0.371739	−	0.928337i	$-0.621238\pi$
$157$	−9.31575			−0.743478			−0.371739	+	0.928337i	$0.621238\pi$
$158$	−5.81566	−	1.32739i	−0.462669	−	0.105601i
$159$	−3.59614	−	7.46747i	−0.285193	−	0.592209i
$160$		0			0
$161$	−3.00231	+	13.1540i	−0.236615	+	1.03668i
$162$	−3.29807			−0.259121
$163$	−0.0927873	+	0.406528i	−0.00726767	+	0.0318417i	−0.978432	−	0.206570i	$-0.933770\pi$
$163$	−0.0927873	+	0.406528i	−0.00726767	+	0.0318417i	0.971164	+	0.238412i	$0.0766269\pi$
$164$	1.99553	−	1.59138i	0.155825	−	0.124266i
$165$		0			0
$166$	11.0153	−	2.51417i	0.854953	−	0.195137i
$167$	−9.26143	−	7.38574i	−0.716671	−	0.571526i	0.195812	−	0.980641i	$-0.437266\pi$
$167$	−9.26143	−	7.38574i	−0.716671	−	0.571526i	−0.912483	+	0.409116i	$0.865837\pi$
$168$	−6.13556	−	12.7406i	−0.473369	−	0.982961i
$169$	−2.39848	−	1.15505i	−0.184498	−	0.0888498i
$170$		0			0
$171$	5.52129	+	4.40308i	0.422224	+	0.336712i
$172$	1.58774	+	0.764614i	0.121064	+	0.0583013i
$173$			5.01268i			0.381107i	0.981677	+	0.190553i	$0.0610282\pi$
$173$			5.01268i			0.381107i	−0.981677	+	0.190553i	$0.938972\pi$
$174$	−7.55082	−	4.79170i	−0.572426	−	0.363258i
$175$		0			0
$176$	−7.75824	+	16.1102i	−0.584799	+	1.21435i
$177$	−3.57787	+	4.48651i	−0.268929	+	0.337226i
$178$	10.1522	−	8.09609i	0.760938	−	0.606828i
$179$	4.12590	+	1.98693i	0.308384	+	0.148510i	0.581675	−	0.813422i	$-0.302398\pi$
$179$	4.12590	+	1.98693i	0.308384	+	0.148510i	−0.273290	+	0.961932i	$0.588112\pi$
$180$		0			0
$181$	0.861425	−	1.08019i	0.0640292	−	0.0802901i	−0.748786	−	0.662812i	$-0.769363\pi$
$181$	0.861425	−	1.08019i	0.0640292	−	0.0802901i	0.812815	+	0.582522i	$0.197934\pi$
$182$	−3.70501	−	16.2327i	−0.274633	−	1.20325i
$183$	11.4281	−	2.60838i	0.844788	−	0.192817i
$184$	−8.06347	+	6.43040i	−0.594447	+	0.474055i
$185$		0			0
$186$			5.15730i			0.378151i
$187$	28.2701	+	6.45247i	2.06732	+	0.471852i
$188$	−0.0409279	+	0.0197098i	−0.00298497	+	0.00143749i
$189$	−9.27452	−	19.2587i	−0.674622	−	1.40087i
$190$		0			0
$191$		−	25.0514i		−	1.81265i	−0.422577	−	0.906327i	$-0.638874\pi$
$191$		−	25.0514i		−	1.81265i	0.422577	−	0.906327i	$-0.361126\pi$
$192$	2.38243	−	10.4381i	0.171937	−	0.753305i
$193$	7.21168	+	9.04317i	0.519108	+	0.650941i	0.970419	−	0.241425i	$-0.0776149\pi$
$193$	7.21168	+	9.04317i	0.519108	+	0.650941i	−0.451311	+	0.892367i	$0.649043\pi$
$194$	−4.67688	−	20.4908i	−0.335781	−	1.47115i
$195$		0			0
$196$	1.00769	−	1.26360i	0.0719779	−	0.0902574i
$197$	−9.62495	−	19.9864i	−0.685750	−	1.42397i	−0.894980	−	0.446107i	$-0.852810\pi$
$197$	−9.62495	−	19.9864i	−0.685750	−	1.42397i	0.209230	−	0.977866i	$-0.432904\pi$
$198$	−4.28887	+	8.90594i	−0.304797	+	0.632917i
$199$	−12.8258	−	16.0831i	−0.909198	−	1.14010i	−0.989673	−	0.143342i	$-0.954215\pi$
$199$	−12.8258	−	16.0831i	−0.909198	−	1.14010i	0.0804754	−	0.996757i	$-0.474356\pi$
$200$		0			0
$201$	6.98079	−	14.4958i	0.492387	−	1.02245i
$202$		−	5.67096i		−	0.399008i
$203$	2.42212	−	20.6663i	0.170000	−	1.45049i
$204$	−1.45424			−0.101817
$205$		0			0
$206$	−2.03005	−	1.61891i	−0.141440	−	0.112795i
$207$	−3.99858	+	3.18876i	−0.277920	+	0.221634i
$208$	4.95358	−	10.2862i	0.343469	−	0.713221i
$209$	−21.8758	+	10.5348i	−1.51318	+	0.728708i
$210$		0			0
$211$	−4.26387	+	0.973201i	−0.293537	+	0.0669979i	−0.366753	−	0.930318i	$-0.619531\pi$
$211$	−4.26387	+	0.973201i	−0.293537	+	0.0669979i	0.0732165	+	0.997316i	$0.476674\pi$
$212$	1.32913	−	0.303366i	0.0912853	−	0.0208353i
$213$	5.79589	+	7.26781i	0.397128	+	0.497982i
$214$	−6.98766	−	1.59489i	−0.477667	−	0.109024i
$215$		0			0
$216$	3.63591	−	15.9299i	0.247392	−	1.08390i
$217$	−10.8113	+	5.20647i	−0.733922	+	0.353438i
$218$	4.40940	−	2.12346i	0.298642	−	0.143819i
$219$	0.974554	−	4.26980i	0.0658543	−	0.288526i
$220$		0			0
$221$	−18.0503	−	4.11986i	−1.21419	−	0.277131i
$222$	2.81014	+	3.52380i	0.188604	+	0.236502i
$223$	−0.492588	+	0.112430i	−0.0329861	+	0.00752886i	−0.238982	−	0.971024i	$-0.576814\pi$
$223$	−0.492588	+	0.112430i	−0.0329861	+	0.00752886i	0.205996	+	0.978553i	$0.433957\pi$
$224$	4.32568	−	0.987309i	0.289022	−	0.0659673i
$225$		0			0
$226$	−11.0687	+	5.33038i	−0.736276	+	0.354572i
$227$	1.06106	−	2.20331i	0.0704249	−	0.146239i	−0.862784	−	0.505572i	$-0.831282\pi$
$227$	1.06106	−	2.20331i	0.0704249	−	0.146239i	0.933209	+	0.359333i	$0.116996\pi$
$228$	0.952020	−	0.759211i	0.0630491	−	0.0502800i
$229$	8.61682	+	6.87169i	0.569416	+	0.454094i	0.865388	−	0.501103i	$-0.167072\pi$
$229$	8.61682	+	6.87169i	0.569416	+	0.454094i	−0.295972	+	0.955197i	$0.595644\pi$
$230$		0			0
$231$	24.1096			1.58630
$232$	11.2971	−	11.1966i	0.741691	−	0.735091i
$233$			11.0552i			0.724252i	0.932129	+	0.362126i	$0.117949\pi$
$233$			11.0552i			0.724252i	−0.932129	+	0.362126i	$0.882051\pi$
$234$	2.73841	−	5.68638i	0.179016	−	0.371730i
$235$		0			0
$236$	−0.588514	−	0.737974i	−0.0383090	−	0.0480380i
$237$	−2.39292	+	4.96895i	−0.155437	+	0.322768i
$238$	12.9381	+	26.8663i	0.838653	+	1.74148i
$239$	−7.88050	+	9.88184i	−0.509747	+	0.639203i	−0.968397	−	0.249414i	$-0.919762\pi$
$239$	−7.88050	+	9.88184i	−0.509747	+	0.639203i	0.458650	+	0.888617i	$0.348333\pi$
$240$		0			0
$241$	4.57172	+	20.0300i	0.294490	+	1.29025i	0.878204	+	0.478286i	$0.158742\pi$
$241$	4.57172	+	20.0300i	0.294490	+	1.29025i	−0.583714	+	0.811959i	$0.698401\pi$
$242$	−11.9980	−	15.0450i	−0.771259	−	0.967128i
$243$	3.01452	−	13.2075i	0.193382	−	0.847260i
$244$			1.92812i			0.123435i
$245$		0			0
$246$	9.02321	+	18.7369i	0.575299	+	1.19462i
$247$	13.9675	−	6.72640i	0.888731	−	0.427990i
$248$	−8.94265	−	2.04110i	−0.567859	−	0.129610i
$249$		−	10.4460i		−	0.661991i
$250$		0			0
$251$	−5.43666	+	4.33559i	−0.343159	+	0.273660i	−0.779870	−	0.625942i	$-0.784715\pi$
$251$	−5.43666	+	4.33559i	−0.343159	+	0.273660i	0.436711	+	0.899602i	$0.356143\pi$
$252$	1.12453	−	0.256666i	0.0708385	−	0.0161684i
$253$	−3.91281	−	17.1431i	−0.245996	−	1.07778i
$254$	−5.21283	+	6.53669i	−0.327082	+	0.410148i
$255$		0			0
$256$	4.35982	+	2.09958i	0.272489	+	0.131224i
$257$	−16.1208	+	12.8559i	−1.00559	+	0.801931i	−0.980253	−	0.197748i	$-0.936637\pi$
$257$	−16.1208	+	12.8559i	−1.00559	+	0.801931i	−0.0253371	+	0.999679i	$0.508066\pi$
$258$	−8.95244	+	11.2260i	−0.557354	+	0.698900i
$259$	−4.55008	+	9.44835i	−0.282729	+	0.587092i
$260$		0			0
$261$	5.60210	−	5.55224i	0.346761	−	0.343675i
$262$		−	0.876619i		−	0.0541577i
$263$	19.3853	+	9.33549i	1.19535	+	0.575651i	0.922347	−	0.386362i	$-0.126268\pi$
$263$	19.3853	+	9.33549i	1.19535	+	0.575651i	0.273004	+	0.962013i	$0.411983\pi$
$264$	14.4088	+	11.4906i	0.886800	+	0.707199i
$265$		0			0
$266$	−22.4960	−	10.8335i	−1.37932	−	0.664245i
$267$	−5.20892	−	10.8164i	−0.318781	−	0.661955i
$268$	2.06908	+	1.65004i	0.126389	+	0.100792i
$269$	21.1832	−	4.83494i	1.29156	−	0.294791i	0.479079	−	0.877772i	$-0.340971\pi$
$269$	21.1832	−	4.83494i	1.29156	−	0.294791i	0.812486	+	0.582981i	$0.198114\pi$
$270$		0			0
$271$	−2.89671	+	2.31005i	−0.175962	+	0.140325i	−0.707511	−	0.706703i	$-0.750182\pi$
$271$	−2.89671	+	2.31005i	−0.175962	+	0.140325i	0.531548	+	0.847028i	$0.321610\pi$
$272$	−4.54984	+	19.9341i	−0.275874	+	1.20868i
$273$	−15.3938			−0.931676
$274$	0.777731	−	3.40746i	0.0469844	−	0.205852i
$275$		0			0
$276$	0.382623	+	0.794525i	0.0230312	+	0.0478248i
$277$	2.59813	+	0.593007i	0.156107	+	0.0356303i	0.299860	−	0.953983i	$-0.403060\pi$
$277$	2.59813	+	0.593007i	0.156107	+	0.0356303i	−0.143753	+	0.989614i	$0.545917\pi$
$278$	−7.86587			−0.471764
$279$	−4.43455	−	1.01216i	−0.265490	−	0.0605963i
$280$		0			0
$281$	−0.0589884	−	0.258445i	−0.00351895	−	0.0154175i	0.973138	−	0.230223i	$-0.0739455\pi$
$281$	−0.0589884	−	0.258445i	−0.00351895	−	0.0154175i	−0.976657	+	0.214805i	$0.931088\pi$
$282$	−0.0823613	−	0.360848i	−0.00490454	−	0.0214882i
$283$	−5.98619	−	4.77383i	−0.355842	−	0.283775i	0.429209	−	0.903205i	$-0.358792\pi$
$283$	−5.98619	−	4.77383i	−0.355842	−	0.283775i	−0.785052	+	0.619430i	$0.787364\pi$
$284$	−1.37763	+	0.663432i	−0.0817474	+	0.0393675i
$285$		0			0
$286$	13.5295	+	16.9654i	0.800015	+	1.00319i
$287$	−30.1693	+	37.8311i	−1.78083	+	2.23310i
$288$	1.51530	+	0.729731i	0.0892900	+	0.0429998i
$289$	16.1582			0.950480
$290$		0			0
$291$	−19.4318			−1.13911
$292$	0.649049	+	0.312566i	0.0379827	+	0.0182915i
$293$	3.38364	−	4.24295i	0.197674	−	0.247876i	−0.673108	−	0.739544i	$-0.735041\pi$
$293$	3.38364	−	4.24295i	0.197674	−	0.247876i	0.870783	+	0.491668i	$0.163613\pi$
$294$	8.21051	+	10.2957i	0.478847	+	0.600455i
$295$		0			0
$296$	−7.22237	+	3.47811i	−0.419792	+	0.202161i
$297$	21.7803	+	17.3692i	1.26382	+	1.00786i
$298$	−3.10169	−	13.5894i	−0.179676	−	0.787212i
$299$	2.49830	+	10.9458i	0.144480	+	0.633010i
$300$		0			0
$301$	−32.5711	−	7.43414i	−1.87737	−	0.428497i
$302$	4.66408			0.268388
$303$	−5.11161	−	1.16669i	−0.293654	−	0.0670246i
$304$	−7.42842	−	15.4253i	−0.426049	−	0.884700i
$305$		0			0
$306$	−2.51522	+	11.0199i	−0.143786	+	0.629966i
$307$	23.3143			1.33062			0.665309	−	0.746568i	$-0.268300\pi$
$307$	23.3143			1.33062			0.665309	+	0.746568i	$0.268300\pi$
$308$	−0.882458	+	3.86630i	−0.0502827	+	0.220303i
$309$	−1.87687	+	1.49675i	−0.106771	+	0.0851473i
$310$		0			0
$311$	29.0583	−	6.63237i	1.64775	−	0.376087i	0.704898	−	0.709309i	$-0.250993\pi$
$311$	29.0583	−	6.63237i	1.64775	−	0.376087i	0.942848	+	0.333222i	$0.108136\pi$
$312$	−9.19990	−	7.33668i	−0.520842	−	0.415358i
$313$	8.07225	+	16.7622i	0.456271	+	0.947456i	0.994508	+	0.104662i	$0.0333762\pi$
$313$	8.07225	+	16.7622i	0.456271	+	0.947456i	−0.538237	+	0.842793i	$0.680910\pi$
$314$	11.2487	+	5.41710i	0.634802	+	0.305705i
$315$		0			0
$316$	−0.709252	−	0.565609i	−0.0398985	−	0.0318180i
$317$	3.07158	+	1.47919i	0.172517	+	0.0830797i	0.518149	−	0.855290i	$-0.326621\pi$
$317$	3.07158	+	1.47919i	0.172517	+	0.0830797i	−0.345632	+	0.938370i	$0.612336\pi$
$318$			11.1081i			0.622910i
$319$	8.84205	+	25.6361i	0.495060	+	1.43535i
$320$		0			0
$321$	−2.87515	+	5.97031i	−0.160475	+	0.333230i
$322$	11.2743	−	14.1375i	0.628292	−	0.787854i
$323$	−21.7071	+	17.3108i	−1.20781	+	0.963200i
$324$	−0.451887	−	0.217617i	−0.0251048	−	0.0120898i
$325$		0			0
$326$	0.348436	−	0.436925i	0.0192981	−	0.0241990i
$327$	−1.00686	−	4.41134i	−0.0556794	−	0.243948i
$328$	−36.0605	+	8.23057i	−1.99111	+	0.454457i
$329$	0.673307	−	0.536945i	0.0371206	−	0.0296027i
$330$		0			0
$331$		−	17.8368i		−	0.980399i	−0.871610	−	0.490200i	$-0.836924\pi$
$331$		−	17.8368i		−	0.980399i	0.871610	−	0.490200i	$-0.163076\pi$
$332$	1.67516	+	0.382345i	0.0919365	+	0.0209839i
$333$	−3.58149	+	1.72475i	−0.196264	+	0.0945159i
$334$	6.88833	+	14.3038i	0.376912	+	0.782667i
$335$		0			0
$336$			17.0004i			0.927450i
$337$	2.15836	−	9.45638i	0.117573	−	0.515122i	−0.881504	−	0.472176i	$-0.843469\pi$
$337$	2.15836	−	9.45638i	0.117573	−	0.515122i	0.999077	−	0.0429458i	$-0.0136743\pi$
$338$	2.22449	+	2.78943i	0.120996	+	0.151725i
$339$	2.52746	+	11.0735i	0.137273	+	0.601431i
$340$		0			0
$341$	9.75063	−	12.2269i	0.528026	−	0.662124i
$342$	−4.10654	−	8.52733i	−0.222056	−	0.461105i
$343$	−1.55878	+	3.23684i	−0.0841662	+	0.174773i
$344$	−15.9226	−	19.9663i	−0.858487	−	1.07651i
$345$		0			0
$346$	2.91487	−	6.05278i	0.156704	−	0.325399i
$347$			27.8087i			1.49285i	0.665469	+	0.746425i	$0.268231\pi$
$347$			27.8087i			1.49285i	−0.665469	+	0.746425i	$0.731769\pi$
$348$	−0.718409	−	1.15477i	−0.0385108	−	0.0619020i
$349$	31.0380			1.66142			0.830712	−	0.556703i	$-0.187934\pi$
$349$	31.0380			1.66142			0.830712	+	0.556703i	$0.187934\pi$
$350$		0			0
$351$	−13.9066	−	11.0901i	−0.742278	−	0.591947i
$352$	−4.52094	+	3.60533i	−0.240967	+	0.192165i
$353$	−2.58841	+	5.37488i	−0.137767	+	0.286076i	−0.958425	−	0.285343i	$-0.907893\pi$
$353$	−2.58841	+	5.37488i	−0.137767	+	0.286076i	0.820659	+	0.571419i	$0.193607\pi$
$354$	6.92916	−	3.33691i	0.368281	−	0.177355i
$355$		0			0
$356$	1.92522	−	0.439418i	0.102036	−	0.0232891i
$357$	26.8781	−	6.13474i	1.42254	−	0.324685i
$358$	−3.82661	−	4.79841i	−0.202243	−	0.253604i
$359$	13.5567	+	3.09422i	0.715494	+	0.163307i	0.564745	−	0.825265i	$-0.308975\pi$
$359$	13.5567	+	3.09422i	0.715494	+	0.163307i	0.150748	+	0.988572i	$0.451832\pi$
$360$		0			0
$361$	0.945280	−	4.14154i	0.0497516	−	0.217976i
$362$	−1.66830	+	0.803410i	−0.0876838	+	0.0422263i
$363$	−16.0294	+	7.71934i	−0.841324	+	0.405160i
$364$	0.563443	−	2.46860i	0.0295324	−	0.129390i
$365$		0			0
$366$	−15.3161	−	3.49580i	−0.800586	−	0.182729i
$367$	10.8925	+	13.6588i	0.568586	+	0.712985i	0.980119	−	0.198410i	$-0.0635778\pi$
$367$	10.8925	+	13.6588i	0.568586	+	0.712985i	−0.411533	+	0.911395i	$0.635006\pi$
$368$	12.0882	−	2.75904i	0.630139	−	0.143825i
$369$	−17.8820	+	4.08144i	−0.930898	+	0.212471i
$370$		0			0
$371$	−23.2861	+	11.2140i	−1.20895	+	0.582202i
$372$	−0.340295	+	0.706631i	−0.0176435	+	0.0366371i
$373$	−1.13223	+	0.902920i	−0.0586244	+	0.0467514i	−0.652364	−	0.757906i	$-0.726223\pi$
$373$	−1.13223	+	0.902920i	−0.0586244	+	0.0467514i	0.593739	+	0.804658i	$0.297651\pi$
$374$	−30.3839	−	24.2304i	−1.57112	−	1.25292i
$375$		0			0
$376$	0.658300			0.0339492
$377$	−5.64558	−	16.3685i	−0.290762	−	0.843018i
$378$			28.6479i			1.47349i
$379$	−1.77584	+	3.68757i	−0.0912189	+	0.189418i	−0.941587	−	0.336771i	$-0.890665\pi$
$379$	−1.77584	+	3.68757i	−0.0912189	+	0.189418i	0.850368	+	0.526189i	$0.176379\pi$
$380$		0			0
$381$	4.81950	+	6.04346i	0.246910	+	0.309616i
$382$	−14.5673	+	30.2494i	−0.745330	+	1.54769i
$383$	0.130413	+	0.270806i	0.00666380	+	0.0138375i	0.904274	−	0.426952i	$-0.140413\pi$
$383$	0.130413	+	0.270806i	0.00666380	+	0.0138375i	−0.897610	+	0.440790i	$0.854698\pi$
$384$	−7.17225	+	8.99372i	−0.366007	+	0.458959i
$385$		0			0
$386$	−3.44948	−	15.1132i	−0.175574	−	0.769240i
$387$	−7.89581	−	9.90103i	−0.401366	−	0.503297i
$388$	0.711242	−	3.11615i	0.0361078	−	0.158199i
$389$		−	17.2457i		−	0.874393i	−0.899366	−	0.437197i	$-0.855971\pi$
$389$		−	17.2457i		−	0.874393i	0.899366	−	0.437197i	$-0.144029\pi$
$390$		0			0
$391$	−8.72422	−	18.1160i	−0.441203	−	0.916167i
$392$	−21.1019	+	10.1622i	−1.06581	+	0.513266i
$393$	−0.790153	−	0.180347i	−0.0398580	−	0.00909732i
$394$			29.7304i			1.49780i
$395$		0			0
$396$	−1.17529	+	0.937259i	−0.0590604	+	0.0470991i
$397$	26.6130	−	6.07424i	1.33567	−	0.304857i	0.505719	−	0.862698i	$-0.331227\pi$
$397$	26.6130	−	6.07424i	1.33567	−	0.304857i	0.829948	+	0.557841i	$0.188370\pi$
$398$	6.13482	+	26.8784i	0.307511	+	1.34729i
$399$	−14.3931	+	18.0483i	−0.720554	+	0.903546i
$400$		0			0
$401$	8.08532	+	3.89369i	0.403762	+	0.194441i	0.624732	−	0.780839i	$-0.285208\pi$
$401$	8.08532	+	3.89369i	0.403762	+	0.194441i	−0.220970	+	0.975281i	$0.570922\pi$
$402$	−16.8585	+	13.4442i	−0.840828	+	0.670538i
$403$	−6.22570	+	7.80679i	−0.310124	+	0.388884i
$404$	0.374189	−	0.777011i	0.0186166	−	0.0386577i
$405$		0			0
$406$	−14.9421	+	23.5460i	−0.741566	+	1.16857i
$407$		−	13.6672i		−	0.677458i
$408$	18.9871	+	9.14372i	0.940003	+	0.452681i
$409$	−12.3651	−	9.86086i	−0.611416	−	0.487588i	0.268142	−	0.963379i	$-0.413590\pi$
$409$	−12.3651	−	9.86086i	−0.611416	−	0.487588i	−0.879558	+	0.475791i	$0.842162\pi$
$410$		0			0
$411$	−2.91136	−	1.40204i	−0.143607	−	0.0691574i
$412$	−0.171327	−	0.355765i	−0.00844070	−	0.0175273i
$413$	13.9904	+	11.1570i	0.688425	+	0.549001i
$414$	6.68252	−	1.52524i	0.328428	−	0.0749615i
$415$		0			0
$416$	2.88658	−	2.30197i	0.141526	−	0.112864i
$417$	−1.61825	+	7.09002i	−0.0792461	+	0.347200i
$418$	32.5409			1.59163
$419$	8.72261	−	38.2163i	0.426127	−	1.86699i	−0.0681390	−	0.997676i	$-0.521706\pi$
$419$	8.72261	−	38.2163i	0.426127	−	1.86699i	0.494266	−	0.869310i	$-0.335437\pi$
$420$		0			0
$421$	17.1631	+	35.6395i	0.836477	+	1.73696i	0.658000	+	0.753018i	$0.271403\pi$
$421$	17.1631	+	35.6395i	0.836477	+	1.73696i	0.178477	+	0.983944i	$0.442883\pi$
$422$	5.71452	+	1.30430i	0.278178	+	0.0634924i
$423$	0.326443			0.0158722
$424$	−19.2612	−	4.39624i	−0.935406	−	0.213500i
$425$		0			0
$426$	−2.77228	−	12.1462i	−0.134317	−	0.588483i
$427$	−8.13383	−	35.6366i	−0.393623	−	1.72458i
$428$	−0.852184	−	0.679594i	−0.0411919	−	0.0328494i
$429$	18.0755	−	8.70468i	0.872691	−	0.420266i
$430$		0			0
$431$	−1.94340	−	2.43695i	−0.0936103	−	0.117384i	0.732820	−	0.680422i	$-0.238204\pi$
$431$	−1.94340	−	2.43695i	−0.0936103	−	0.117384i	−0.826431	+	0.563039i	$0.809632\pi$
$432$	−12.2476	+	15.3580i	−0.589262	+	0.738911i
$433$	1.88837	+	0.909391i	0.0907493	+	0.0437026i	0.478708	−	0.877974i	$-0.341105\pi$
$433$	1.88837	+	0.909391i	0.0907493	+	0.0437026i	−0.387959	+	0.921677i	$0.626820\pi$
$434$	16.0822			0.771970
$435$		0			0
$436$	0.744270			0.0356441
$437$	15.1691	+	7.30507i	0.725638	+	0.349449i
$438$	−3.65965	+	4.58906i	−0.174865	+	0.219274i
$439$	1.93738	+	2.42939i	0.0924660	+	0.115949i	0.825912	−	0.563799i	$-0.190661\pi$
$439$	1.93738	+	2.42939i	0.0924660	+	0.115949i	−0.733446	+	0.679748i	$0.762089\pi$
$440$		0			0
$441$	−10.4642	+	5.03929i	−0.498295	+	0.239966i
$442$	19.3999	+	15.4709i	0.922760	+	0.735876i
$443$	−2.51820	−	11.0329i	−0.119643	−	0.524191i	−0.998859	−	0.0477664i	$-0.984790\pi$
$443$	−2.51820	−	11.0329i	−0.119643	−	0.524191i	0.879215	−	0.476425i	$-0.158067\pi$
$444$	0.152521	+	0.668238i	0.00723833	+	0.0317132i
$445$		0			0
$446$	0.660175	+	0.150681i	0.0312602	+	0.00713493i
$447$	−12.8871			−0.609539
$448$	−32.5495	−	7.42922i	−1.53782	−	0.350998i
$449$	15.2346	+	31.6351i	0.718968	+	1.49295i	0.863982	+	0.503522i	$0.167963\pi$
$449$	15.2346	+	31.6351i	0.718968	+	1.49295i	−0.145015	+	0.989429i	$0.546323\pi$
$450$		0			0
$451$	14.0326	−	61.4810i	0.660771	−	2.89503i
$452$	−1.86830			−0.0878772
$453$	0.959544	−	4.20404i	0.0450833	−	0.197523i
$454$	−2.56244	+	2.04348i	−0.120261	+	0.0959053i
$455$		0			0
$456$	−17.2036	+	3.92662i	−0.805634	+	0.183881i
$457$	26.0316	+	20.7595i	1.21771	+	0.971090i	0.999988	−	0.00492096i	$-0.00156640\pi$
$457$	26.0316	+	20.7595i	1.21771	+	0.971090i	0.217721	+	0.976011i	$0.430138\pi$
$458$	−6.40889	−	13.3082i	−0.299468	−	0.621851i
$459$	28.7009	+	13.8216i	1.33964	+	0.645139i
$460$		0			0
$461$	25.0026	+	19.9389i	1.16449	+	0.928649i	0.998348	−	0.0574532i	$-0.0182980\pi$
$461$	25.0026	+	19.9389i	1.16449	+	0.928649i	0.166141	+	0.986102i	$0.446869\pi$
$462$	−29.1122	−	14.0197i	−1.35442	−	0.652256i
$463$			21.7185i			1.00934i	0.863311	+	0.504672i	$0.168387\pi$
$463$			21.7185i			1.00934i	−0.863311	+	0.504672i	$0.831613\pi$
$464$	−18.0768	+	6.23480i	−0.839194	+	0.289443i
$465$		0			0
$466$	6.42860	−	13.3491i	0.297799	−	0.618387i
$467$	−10.7006	+	13.4181i	−0.495162	+	0.620914i	−0.965130	−	0.261769i	$-0.915694\pi$
$467$	−10.7006	+	13.4181i	−0.495162	+	0.620914i	0.469968	+	0.882683i	$0.344265\pi$
$468$	0.750411	−	0.598433i	0.0346878	−	0.0276626i
$469$	−45.2027	−	21.7685i	−2.08727	−	1.00518i
$470$		0			0
$471$	7.19699	−	9.02474i	0.331620	−	0.415838i
$472$	3.04378	+	13.3357i	0.140101	+	0.613824i
$473$	42.4488	−	9.68866i	1.95180	−	0.445485i
$474$	5.77887	−	4.60850i	0.265432	−	0.211675i
$475$		0			0
$476$			4.53480i			0.207852i
$477$	−9.55140	−	2.18004i	−0.437328	−	0.0998173i
$478$	15.2619	−	7.34976i	0.698065	−	0.336170i
$479$	11.3447	+	23.5575i	0.518351	+	1.07637i	0.981743	+	0.190214i	$0.0609181\pi$
$479$	11.3447	+	23.5575i	0.518351	+	1.07637i	−0.463391	+	0.886154i	$0.653368\pi$
$480$		0			0
$481$			8.72640i			0.397890i
$482$	6.12710	−	26.8446i	0.279082	−	1.22274i
$483$	−10.4236	−	13.0708i	−0.474290	−	0.594741i
$484$	−0.651194	−	2.85307i	−0.0295997	−	0.129685i
$485$		0			0
$486$	−11.3201	+	14.1950i	−0.513492	+	0.643899i
$487$	−10.0045	−	20.7745i	−0.453347	−	0.941384i	−0.994914	−	0.100727i	$-0.967883\pi$
$487$	−10.0045	−	20.7745i	−0.453347	−	0.941384i	0.541568	−	0.840657i	$-0.317831\pi$
$488$	12.1233	−	25.1743i	0.548796	−	1.13959i
$489$	−0.322145	−	0.403956i	−0.0145679	−	0.0182675i
$490$		0			0
$491$	0.926899	−	1.92472i	0.0418303	−	0.0868616i	−0.879006	−	0.476810i	$-0.841793\pi$
$491$	0.926899	−	1.92472i	0.0418303	−	0.0868616i	0.920837	+	0.389949i	$0.127507\pi$
$492$			3.16263i			0.142582i
$493$	16.3805	+	26.3299i	0.737741	+	1.18584i
$494$	−20.7771			−0.934806
$495$		0			0
$496$	8.62157	+	6.87547i	0.387120	+	0.308718i
$497$	22.6635	−	18.0735i	1.01660	−	0.810709i
$498$	−6.07436	+	12.6135i	−0.272199	+	0.565226i
$499$	−8.68887	+	4.18434i	−0.388967	+	0.187317i	−0.618138	−	0.786069i	$-0.712113\pi$
$499$	−8.68887	+	4.18434i	−0.388967	+	0.187317i	0.229171	+	0.973386i	$0.426398\pi$
$500$		0			0
$501$	14.3100	−	3.26617i	0.639325	−	0.145922i
$502$	9.08588	−	2.07379i	0.405523	−	0.0925579i
$503$	−21.0456	−	26.3903i	−0.938375	−	1.17669i	−0.984079	−	0.177730i	$-0.943125\pi$
$503$	−21.0456	−	26.3903i	−0.938375	−	1.17669i	0.0457040	−	0.998955i	$-0.485447\pi$
$504$	−16.2961	−	3.71948i	−0.725887	−	0.165679i
$505$		0			0
$506$	−5.24402	+	22.9756i	−0.233125	+	1.02139i
$507$	2.97194	−	1.43121i	0.131988	−	0.0635622i
$508$	−1.14555	+	0.551669i	−0.0508257	+	0.0244763i
$509$	5.07511	−	22.2355i	0.224950	−	0.985572i	−0.728742	−	0.684788i	$-0.759895\pi$
$509$	5.07511	−	22.2355i	0.224950	−	0.985572i	0.953692	−	0.300784i	$-0.0972482\pi$
$510$		0			0
$511$	−13.3147	−	3.03899i	−0.589007	−	0.134437i
$512$	−15.6202	−	19.5871i	−0.690321	−	0.865635i
$513$	−26.0050	+	5.93547i	−1.14815	+	0.262057i
$514$	26.9415	−	6.14923i	1.18834	−	0.271231i
$515$		0			0
$516$	−1.96735	+	0.947427i	−0.0866079	+	0.0417082i
$517$	−0.486975	+	1.01121i	−0.0214171	+	0.0444731i
$518$	10.9884	−	8.76296i	0.482803	−	0.385023i
$519$	−4.85608	−	3.87260i	−0.213158	−	0.169988i
$520$		0			0
$521$	34.9903			1.53295			0.766476	−	0.642272i	$-0.222008\pi$
$521$	34.9903			1.53295			0.766476	+	0.642272i	$0.222008\pi$
$522$	−9.99313	+	3.44669i	−0.437387	+	0.150858i
$523$		−	21.9987i		−	0.961936i	−0.876738	−	0.480968i	$-0.840285\pi$
$523$		−	21.9987i		−	0.961936i	0.876738	−	0.480968i	$-0.159715\pi$
$524$	0.0578422	−	0.120111i	0.00252685	−	0.00524705i
$525$		0			0
$526$	−17.9791	−	22.5451i	−0.783927	−	0.983013i
$527$	7.75911	−	16.1120i	0.337992	−	0.701848i
$528$	−9.61317	−	19.9620i	−0.418360	−	0.868733i
$529$	6.73796	−	8.44914i	0.292955	−	0.367354i
$530$		0			0
$531$	1.50937	+	6.61300i	0.0655012	+	0.286980i
$532$	−2.36748	−	2.96872i	−0.102643	−	0.128710i
$533$	−8.95974	+	39.2552i	−0.388089	+	1.70033i
$534$			16.0898i			0.696272i
$535$		0			0
$536$	−16.6399	−	34.5532i	−0.718736	−	1.49247i
$537$	−5.11237	+	2.46199i	−0.220615	+	0.106243i
$538$	−28.3902	−	6.47987i	−1.22399	−	0.279367i
$539$		−	39.9321i		−	1.72000i
$540$		0			0
$541$	−29.7630	+	23.7352i	−1.27961	+	1.02046i	−0.281468	+	0.959571i	$0.590821\pi$
$541$	−29.7630	+	23.7352i	−1.27961	+	1.02046i	−0.998145	+	0.0608863i	$0.980607\pi$
$542$	4.84105	−	1.10494i	0.207941	−	0.0474612i
$543$	0.380945	+	1.66903i	0.0163479	+	0.0716249i
$544$	−4.12268	+	5.16968i	−0.176759	+	0.221648i
$545$		0			0
$546$	18.5880	+	8.95149i	0.795491	+	0.383088i
$547$	−28.7854	+	22.9556i	−1.23077	+	0.981510i	−0.230811	+	0.972999i	$0.574138\pi$
$547$	−28.7854	+	22.9556i	−1.23077	+	0.981510i	−0.999964	+	0.00851144i	$0.997291\pi$
$548$	0.331397	−	0.415559i	0.0141566	−	0.0177518i
$549$	6.01180	−	12.4836i	0.256578	−	0.532789i
$550$		0			0
$551$	−24.4696	−	8.68522i	−1.04244	−	0.370003i
$552$		−	12.7794i		−	0.543929i
$553$	15.4949	+	7.46193i	0.658908	+	0.317314i
$554$	−2.79240	−	2.22686i	−0.118638	−	0.0946104i
$555$		0			0
$556$	−1.07775	−	0.519016i	−0.0457067	−	0.0220112i
$557$	−6.98964	−	14.5141i	−0.296161	−	0.614984i	0.698793	−	0.715324i	$-0.253721\pi$
$557$	−6.98964	−	14.5141i	−0.296161	−	0.614984i	−0.994953	+	0.100341i	$0.968007\pi$
$558$	4.76613	+	3.80086i	0.201766	+	0.160903i
$559$	−27.1032	+	6.18614i	−1.14635	+	0.261646i
$560$		0			0
$561$	−28.0913	+	22.4021i	−1.18602	+	0.945816i
$562$	−0.0790573	+	0.346373i	−0.00333483	+	0.0146109i
$563$	2.46470			0.103875			0.0519374	−	0.998650i	$-0.483460\pi$
$563$	2.46470			0.103875			0.0519374	+	0.998650i	$0.483460\pi$
$564$	0.0125252	−	0.0548764i	0.000527405	−	0.00231071i
$565$		0			0
$566$	4.45232	+	9.24534i	0.187145	+	0.388611i
$567$	9.27007	+	2.11583i	0.389306	+	0.0888567i
$568$	22.1584			0.929745
$569$	24.4808	+	5.58758i	1.02629	+	0.234243i	0.702348	−	0.711834i	$-0.252135\pi$
$569$	24.4808	+	5.58758i	1.02629	+	0.234243i	0.323940	+	0.946078i	$0.394992\pi$
$570$		0			0
$571$	8.21338	+	35.9852i	0.343719	+	1.50593i	0.791155	+	0.611616i	$0.209480\pi$
$571$	8.21338	+	35.9852i	0.343719	+	1.50593i	−0.447436	+	0.894316i	$0.647663\pi$
$572$	0.734316	+	3.21725i	0.0307033	+	0.134520i
$573$	24.2688	+	19.3537i	1.01384	+	0.808513i
$574$	58.4279	−	28.1374i	2.43874	−	1.17443i
$575$		0			0
$576$	−7.89058	−	9.89448i	−0.328774	−	0.412270i
$577$	−12.7696	+	16.0126i	−0.531606	+	0.666613i	−0.973028	−	0.230687i	$-0.925903\pi$
$577$	−12.7696	+	16.0126i	−0.531606	+	0.666613i	0.441422	+	0.897300i	$0.354474\pi$
$578$	−19.5109	−	9.39595i	−0.811546	−	0.390820i
$579$	−14.3321			−0.595623
$580$		0			0
$581$	−32.5743			−1.35141
$582$	23.4638	+	11.2996i	0.972607	+	0.468383i
$583$	21.0015	−	26.3350i	0.869792	−	1.09068i
$584$	−6.50896	−	8.16198i	−0.269343	−	0.337745i
$585$		0			0
$586$	−6.55300	+	3.15576i	−0.270702	+	0.130363i
$587$	−1.02486	−	0.817302i	−0.0423007	−	0.0337337i	0.602111	−	0.798412i	$-0.294326\pi$
$587$	−1.02486	−	0.817302i	−0.0423007	−	0.0337337i	−0.644412	+	0.764679i	$0.722898\pi$
$588$	0.445628	+	1.95242i	0.0183774	+	0.0805165i
$589$	3.33202	+	14.5985i	0.137293	+	0.601522i
$590$		0			0
$591$	26.7979	+	6.11645i	1.10232	+	0.251597i
$592$	9.63716			0.396085
$593$	7.01853	+	1.60193i	0.288217	+	0.0657836i	0.364185	−	0.931327i	$-0.381348\pi$
$593$	7.01853	+	1.60193i	0.288217	+	0.0657836i	−0.0759683	+	0.997110i	$0.524205\pi$
$594$	−16.1994	−	33.6385i	−0.664671	−	1.38020i
$595$		0			0
$596$	0.471692	−	2.06662i	0.0193213	−	0.0846520i
$597$	25.4894			1.04321
$598$	3.34827	−	14.6697i	0.136921	−	0.599890i
$599$	−31.3897	+	25.0325i	−1.28255	+	1.02280i	−0.284610	+	0.958643i	$0.591864\pi$
$599$	−31.3897	+	25.0325i	−1.28255	+	1.02280i	−0.997940	+	0.0641559i	$0.979565\pi$
$600$		0			0
$601$	−25.1547	+	5.74139i	−1.02608	+	0.234196i	−0.702259	−	0.711922i	$-0.747825\pi$
$601$	−25.1547	+	5.74139i	−1.02608	+	0.234196i	−0.323822	+	0.946118i	$0.604968\pi$
$602$	35.0065	+	27.9167i	1.42676	+	1.13780i
$603$	−8.25155	−	17.1345i	−0.336029	−	0.697772i
$604$	0.639052	+	0.307751i	0.0260027	+	0.0125222i
$605$		0			0
$606$	5.49381	+	4.38117i	0.223171	+	0.177973i
$607$	−20.9327	−	10.0807i	−0.849634	−	0.409162i	−0.0421920	−	0.999110i	$-0.513434\pi$
$607$	−20.9327	−	10.0807i	−0.849634	−	0.409162i	−0.807442	+	0.589948i	$0.799148\pi$
$608$		−	5.53667i		−	0.224542i
$609$	18.1495	+	18.3125i	0.735455	+	0.742058i
$610$		0			0
$611$	0.310930	−	0.645653i	0.0125789	−	0.0261203i
$612$	−1.07175	+	1.34394i	−0.0433231	+	0.0543254i
$613$	33.9398	−	27.0661i	1.37081	−	1.09319i	0.385449	−	0.922729i	$-0.374046\pi$
$613$	33.9398	−	27.0661i	1.37081	−	1.09319i	0.985365	−	0.170459i	$-0.0545250\pi$
$614$	−28.1519	−	13.5572i	−1.13612	−	0.547126i
$615$		0			0
$616$	35.8317	−	44.9315i	1.44370	−	1.81034i
$617$	−0.649973	−	2.84772i	−0.0261669	−	0.114645i	0.960158	−	0.279458i	$-0.0901549\pi$
$617$	−0.649973	−	2.84772i	−0.0261669	−	0.114645i	−0.986325	+	0.164814i	$0.947298\pi$
$618$	3.13667	−	0.715925i	0.126175	−	0.0287987i
$619$	−5.30577	+	4.23121i	−0.213257	+	0.170067i	−0.724293	−	0.689493i	$-0.757833\pi$
$619$	−5.30577	+	4.23121i	−0.213257	+	0.170067i	0.511036	+	0.859560i	$0.329262\pi$
$620$		0			0
$621$		−	19.3174i		−	0.775181i
$622$	−38.9445	−	8.88882i	−1.56153	−	0.356409i
$623$	−33.7293	+	16.2432i	−1.35134	+	0.650769i
$624$	6.13794	+	12.7456i	0.245714	+	0.510231i
$625$		0			0
$626$		−	24.9343i		−	0.996574i
$627$	6.69465	−	29.3312i	0.267358	−	1.17137i
$628$	1.18381	+	1.48446i	0.0472393	+	0.0592362i
$629$	−3.47765	−	15.2366i	−0.138663	−	0.607522i
$630$		0			0
$631$	8.15797	−	10.2298i	0.324764	−	0.407241i	−0.592469	−	0.805594i	$-0.701847\pi$
$631$	8.15797	−	10.2298i	0.324764	−	0.407241i	0.917232	+	0.398353i	$0.130418\pi$
$632$	5.70394	+	11.8444i	0.226891	+	0.471143i
$633$	2.35130	−	4.88253i	0.0934559	−	0.194063i
$634$	−2.84876	−	3.57224i	−0.113139	−	0.141872i
$635$		0			0
$636$	−0.732948	+	1.52198i	−0.0290633	+	0.0603505i
$637$			25.4963i			1.01020i
$638$	4.23063	−	36.0971i	0.167492	−	1.42910i
$639$	10.9881			0.434681
$640$		0			0
$641$	−11.9956	−	9.56620i	−0.473799	−	0.377842i	0.357279	−	0.933998i	$-0.383705\pi$
$641$	−11.9956	−	9.56620i	−0.473799	−	0.377842i	−0.831078	+	0.556155i	$0.812276\pi$
$642$	6.94346	−	5.53723i	0.274037	−	0.218537i
$643$	6.37331	−	13.2343i	0.251339	−	0.521911i	−0.736680	−	0.676241i	$-0.763608\pi$
$643$	6.37331	−	13.2343i	0.251339	−	0.521911i	0.988019	+	0.154331i	$0.0493221\pi$
$644$	2.47760	−	1.19315i	0.0976310	−	0.0470166i
$645$		0			0
$646$	36.2774	−	8.28009i	1.42732	−	0.325776i
$647$	6.99109	−	1.59567i	0.274848	−	0.0627323i	−0.0828751	−	0.996560i	$-0.526410\pi$
$647$	6.99109	−	1.59567i	0.274848	−	0.0627323i	0.357723	+	0.933828i	$0.383553\pi$
$648$	4.53173	+	5.68261i	0.178023	+	0.223234i
$649$	−22.7365	−	5.18947i	−0.892487	−	0.203704i
$650$		0			0
$651$	3.30860	−	14.4959i	0.129674	−	0.568140i
$652$	0.0765709	−	0.0368746i	0.00299875	−	0.00144412i
$653$	−7.23483	+	3.48411i	−0.283121	+	0.136344i	−0.570055	−	0.821607i	$-0.693078\pi$
$653$	−7.23483	+	3.48411i	−0.283121	+	0.136344i	0.286934	+	0.957950i	$0.407364\pi$
$654$	−1.34941	+	5.91216i	−0.0527661	+	0.231184i
$655$		0			0
$656$	43.3522	+	9.89485i	1.69262	+	0.386329i
$657$	−3.22772	−	4.04743i	−0.125925	−	0.157905i
$658$	−1.12525	+	0.256830i	−0.0438667	+	0.0100123i
$659$	36.5138	−	8.33404i	1.42238	−	0.324648i	0.558983	−	0.829179i	$-0.311192\pi$
$659$	36.5138	−	8.33404i	1.42238	−	0.324648i	0.863393	+	0.504531i	$0.168335\pi$
$660$		0			0
$661$	21.4073	−	10.3092i	0.832649	−	0.400983i	0.0315411	−	0.999502i	$-0.489958\pi$
$661$	21.4073	−	10.3092i	0.832649	−	0.400983i	0.801108	+	0.598520i	$0.204244\pi$
$662$	−10.3721	+	21.5378i	−0.403122	+	0.837092i
$663$	17.9361	−	14.3036i	0.696580	−	0.555504i
$664$	−19.4676	−	15.5249i	−0.755489	−	0.602482i
$665$		0			0
$666$	5.32757			0.206439
$667$	10.0755	−	15.8772i	0.390127	−	0.614767i
$668$			2.41435i			0.0934142i
$669$	0.271636	−	0.564059i	0.0105021	−	0.0218078i
$670$		0			0
$671$	29.7021	+	37.2452i	1.14664	+	1.43784i
$672$	−2.38539	+	4.95331i	−0.0920183	+	0.191078i
$673$	−11.6134	−	24.1155i	−0.447663	−	0.929582i	−0.995657	−	0.0930999i	$-0.970322\pi$
$673$	−11.6134	−	24.1155i	−0.447663	−	0.929582i	0.547993	−	0.836483i	$-0.315392\pi$
$674$	−8.10508	+	10.1635i	−0.312196	+	0.391482i
$675$		0			0
$676$	0.120735	+	0.528975i	0.00464365	+	0.0203452i
$677$	4.84564	+	6.07624i	0.186233	+	0.233529i	0.866180	−	0.499733i	$-0.166568\pi$
$677$	4.84564	+	6.07624i	0.186233	+	0.233529i	−0.679946	+	0.733262i	$0.737997\pi$
$678$	3.38734	−	14.8409i	0.130090	−	0.569962i
$679$			60.5950i			2.32542i
$680$		0			0
$681$	1.31475	+	2.73010i	0.0503813	+	0.104618i
$682$	−18.8838	+	9.09394i	−0.723097	+	0.348225i
$683$	11.0484	+	2.52173i	0.422755	+	0.0964911i	0.428605	−	0.903492i	$-0.359005\pi$
$683$	11.0484	+	2.52173i	0.422755	+	0.0964911i	−0.00585019	+	0.999983i	$0.501862\pi$
$684$		−	1.43934i		−	0.0550346i
$685$		0			0
$686$	3.76444	−	3.00204i	0.143727	−	0.114618i
$687$	−13.3140	+	3.03884i	−0.507963	+	0.115939i
$688$	6.83177	+	29.9320i	0.260459	+	1.14115i
$689$	−13.4093	+	16.8147i	−0.510853	+	0.640589i
$690$		0			0
$691$	−17.8906	−	8.61567i	−0.680591	−	0.327756i	0.0614495	−	0.998110i	$-0.480428\pi$
$691$	−17.8906	−	8.61567i	−0.680591	−	0.327756i	−0.742041	+	0.670355i	$0.766142\pi$
$692$	0.798765	−	0.636994i	0.0303645	−	0.0242149i
$693$	17.7685	−	22.2810i	0.674969	−	0.846385i
$694$	16.1707	−	33.5789i	0.613833	−	1.27464i
$695$		0			0
$696$	2.11910	+	19.5942i	0.0803242	+	0.742717i
$697$		−	72.1114i		−	2.73141i
$698$	−37.4782	−	18.0485i	−1.41857	−	0.683147i
$699$	−10.7099	−	8.54084i	−0.405085	−	0.323044i
$700$		0			0
$701$	28.4759	+	13.7133i	1.07552	+	0.517944i	0.885882	−	0.463910i	$-0.153554\pi$
$701$	28.4759	+	13.7133i	1.07552	+	0.517944i	0.189639	+	0.981854i	$0.439268\pi$
$702$	10.3432	+	21.4779i	0.390380	+	0.810632i
$703$	10.2312	+	8.15909i	0.385876	+	0.307726i
$704$	42.4207	−	9.68225i	1.59879	−	0.364914i
$705$		0			0
$706$	6.25097	−	4.98498i	0.235258	−	0.187612i
$707$	−3.63814	+	15.9397i	−0.136826	+	0.599475i
$708$	1.16958			0.0439556
$709$	−8.72768	+	38.2384i	−0.327775	+	1.43608i	0.495587	+	0.868558i	$0.334953\pi$
$709$	−8.72768	+	38.2384i	−0.327775	+	1.43608i	−0.823362	+	0.567517i	$0.807904\pi$
$710$		0			0
$711$	2.82852	+	5.87347i	0.106078	+	0.220272i
$712$	−27.8993	−	6.36784i	−1.04557	−	0.238645i
$713$	−10.8443			−0.406122
$714$	−36.0225	−	8.22190i	−1.34811	−	0.307697i
$715$		0			0
$716$	−0.207690	−	0.909950i	−0.00776175	−	0.0340064i
$717$	−3.48497	−	15.2686i	−0.130149	−	0.570218i
$718$	−14.5703	−	11.6194i	−0.543760	−	0.433634i
$719$	−1.50781	+	0.726122i	−0.0562317	+	0.0270798i	−0.461788	−	0.886990i	$-0.652792\pi$
$719$	−1.50781	+	0.726122i	−0.0562317	+	0.0270798i	0.405557	+	0.914070i	$0.367078\pi$
$720$		0			0
$721$	4.66738	+	5.85272i	0.173822	+	0.217967i
$722$	−3.54972	+	4.45121i	−0.132107	+	0.165657i
$723$	−22.9362	−	11.0455i	−0.853007	−	0.410786i
$724$	−0.281595			−0.0104654
$725$		0			0
$726$	23.8442			0.884940
$727$	−34.6894	−	16.7055i	−1.28656	−	0.619574i	−0.339491	−	0.940609i	$-0.610255\pi$
$727$	−34.6894	−	16.7055i	−1.28656	−	0.619574i	−0.947067	+	0.321035i	$0.895969\pi$
$728$	−22.8782	+	28.6884i	−0.847924	+	1.06326i
$729$	15.0689	+	18.8958i	0.558108	+	0.699845i
$730$		0			0
$731$	44.8578	−	21.6024i	1.65913	−	0.798993i
$732$	−1.86788	−	1.48959i	−0.0690390	−	0.0550568i
$733$	−2.49071	−	10.9125i	−0.0919966	−	0.403064i	0.907872	−	0.419247i	$-0.137706\pi$
$733$	−2.49071	−	10.9125i	−0.0919966	−	0.403064i	−0.999869	+	0.0161830i	$0.994849\pi$
$734$	−5.21011	−	22.8270i	−0.192309	−	0.842559i
$735$		0			0
$736$	3.90918	+	0.892245i	0.144094	+	0.0328886i
$737$	65.3865			2.40854
$738$	23.9657	+	5.47002i	0.882191	+	0.201354i
$739$	−19.6187	−	40.7386i	−0.721685	−	1.49859i	−0.861141	−	0.508366i	$-0.830250\pi$
$739$	−19.6187	−	40.7386i	−0.721685	−	1.49859i	0.139456	−	0.990228i	$-0.455465\pi$
$740$		0			0
$741$	−4.27448	+	18.7277i	−0.157027	+	0.687980i
$742$	34.6388			1.27163
$743$	−5.32485	+	23.3297i	−0.195350	+	0.855884i	0.778310	+	0.627880i	$0.216077\pi$
$743$	−5.32485	+	23.3297i	−0.195350	+	0.855884i	−0.973660	+	0.228004i	$0.926780\pi$
$744$	8.88609	−	7.08642i	0.325780	−	0.259801i
$745$		0			0
$746$	1.89220	−	0.431883i	0.0692785	−	0.0158124i
$747$	−9.65374	−	7.69860i	−0.353212	−	0.281677i
$748$	−2.56428	−	5.32477i	−0.0937592	−	0.194693i
$749$	18.6175	+	8.96570i	0.680267	+	0.327599i
$750$		0			0
$751$	34.3700	+	27.4091i	1.25418	+	1.00017i	0.999450	+	0.0331610i	$0.0105574\pi$
$751$	34.3700	+	27.4091i	1.25418	+	1.00017i	0.254728	+	0.967013i	$0.418014\pi$
$752$	−0.713038	−	0.343381i	−0.0260018	−	0.0125218i
$753$		−	8.61633i		−	0.313997i
$754$	−2.70122	+	23.0477i	−0.0983728	+	0.839349i
$755$		0			0
$756$	−1.89029	+	3.92522i	−0.0687490	+	0.142759i
$757$	26.3065	−	32.9873i	0.956125	−	1.19894i	−0.0238279	−	0.999716i	$-0.507585\pi$
$757$	26.3065	−	32.9873i	0.956125	−	1.19894i	0.979953	−	0.199227i	$-0.0638432\pi$
$758$	4.28864	−	3.42008i	0.155770	−	0.124223i
$759$	19.6305	+	9.45355i	0.712542	+	0.343142i
$760$		0			0
$761$	9.04819	−	11.3461i	0.327997	−	0.411295i	−0.590302	−	0.807182i	$-0.700992\pi$
$761$	9.04819	−	11.3461i	0.327997	−	0.411295i	0.918299	+	0.395887i	$0.129563\pi$
$762$	−2.30525	−	10.1000i	−0.0835105	−	0.365884i
$763$	−13.7560	+	3.13973i	−0.498002	+	0.113666i
$764$	−3.99191	+	3.18344i	−0.144422	+	0.115173i
$765$		0			0
$766$		−	0.402831i		−	0.0145549i
$767$	14.5171	+	3.31343i	0.524182	+	0.119641i
$768$	−5.40222	+	2.60157i	−0.194936	+	0.0938761i
$769$	5.19669	+	10.7910i	0.187397	+	0.389135i	0.973408	−	0.229078i	$-0.0735712\pi$
$769$	5.19669	+	10.7910i	0.187397	+	0.389135i	−0.786011	+	0.618213i	$0.787857\pi$
$770$		0			0
$771$		−	25.5492i		−	0.920133i
$772$	0.524583	−	2.29835i	0.0188802	−	0.0827194i
$773$	−12.7880	−	16.0357i	−0.459954	−	0.576764i	0.496725	−	0.867908i	$-0.334536\pi$
$773$	−12.7880	−	16.0357i	−0.459954	−	0.576764i	−0.956679	+	0.291144i	$0.905964\pi$
$774$	3.77671	+	16.5468i	0.135751	+	0.594764i
$775$		0			0
$776$	−28.8795	+	36.2138i	−1.03671	+	1.30000i
$777$	−5.63797	−	11.7074i	−0.202261	−	0.420000i
$778$	−10.0284	+	20.8241i	−0.359535	+	0.746581i
$779$	37.6471	+	47.2079i	1.34885	+	1.69140i
$780$		0			0
$781$	−16.3916	+	34.0374i	−0.586537	+	1.21796i
$782$			26.9481i			0.963663i
$783$	3.20323	+	29.6186i	0.114474	+	1.05848i
$784$	28.1573			1.00562
$785$		0			0
$786$	0.849234	+	0.677242i	0.0302912	+	0.0241564i
$787$	8.87316	−	7.07611i	0.316294	−	0.252236i	−0.452454	−	0.891788i	$-0.649451\pi$
$787$	8.87316	−	7.07611i	0.316294	−	0.252236i	0.768748	+	0.639552i	$0.220880\pi$
$788$	−1.96171	+	4.07353i	−0.0698830	+	0.145114i
$789$	−24.0202	+	11.5675i	−0.855142	+	0.411815i
$790$		0			0
$791$	34.5310	−	7.88147i	1.22778	−	0.280233i
$792$	21.2382	−	4.84748i	0.754666	−	0.172248i
$793$	−18.9645	−	23.7808i	−0.673451	−	0.844481i
$794$	−35.6672	−	8.14080i	−1.26578	−	0.288906i
$795$		0			0
$796$	−0.932959	+	4.08756i	−0.0330679	+	0.144880i
$797$	−4.01159	+	1.93188i	−0.142098	+	0.0684308i	−0.503582	−	0.863948i	$-0.667985\pi$
$797$	−4.01159	+	1.93188i	−0.142098	+	0.0684308i	0.361484	+	0.932378i	$0.382270\pi$
$798$	27.8746	−	13.4237i	0.986751	−	0.475194i
$799$	−0.285588	+	1.25124i	−0.0101034	+	0.0442657i
$800$		0			0
$801$	−13.8349	−	3.15774i	−0.488834	−	0.111573i
$802$	−7.49881	−	9.40321i	−0.264792	−	0.332039i
$803$	17.3526	−	3.96061i	0.612359	−	0.139767i
$804$	−3.19698	+	0.729690i	−0.112749	+	0.0257342i
$805$		0			0
$806$	12.0571	−	5.80641i	0.424695	−	0.204522i
$807$	−11.6815	+	24.2568i	−0.411207	+	0.853879i
$808$	−9.77114	+	7.79222i	−0.343747	+	0.274129i
$809$	−2.30156	−	1.83543i	−0.0809184	−	0.0645303i	0.582195	−	0.813049i	$-0.302194\pi$
$809$	−2.30156	−	1.83543i	−0.0809184	−	0.0645303i	−0.663114	+	0.748519i	$0.730765\pi$
$810$		0			0
$811$	−52.6587			−1.84910			−0.924548	−	0.381066i	$-0.875557\pi$
$811$	−52.6587			−1.84910			−0.924548	+	0.381066i	$0.875557\pi$
$812$	−3.60095	+	2.24024i	−0.126369	+	0.0786171i
$813$		−	4.59087i		−	0.161009i
$814$	−7.94746	+	16.5031i	−0.278558	+	0.578432i
$815$		0			0
$816$	−15.7964	−	19.8080i	−0.552984	−	0.693420i
$817$	−18.0884	+	37.5609i	−0.632832	+	1.31409i
$818$	9.19675	+	19.0972i	0.321557	+	0.667719i
$819$	−11.3450	+	14.2262i	−0.396428	+	0.497105i
$820$		0			0
$821$	−0.360547	−	1.57966i	−0.0125832	−	0.0551306i	0.968247	−	0.249997i	$-0.0804297\pi$
$821$	−0.360547	−	1.57966i	−0.0125832	−	0.0551306i	−0.980830	+	0.194867i	$0.937573\pi$
$822$	2.70017	+	3.38591i	0.0941793	+	0.118097i
$823$	−8.35401	+	36.6013i	−0.291202	+	1.27584i	0.591652	+	0.806194i	$0.298476\pi$
$823$	−8.35401	+	36.6013i	−0.291202	+	1.27584i	−0.882854	+	0.469647i	$0.844381\pi$
$824$			5.72227i			0.199345i
$825$		0			0
$826$	−10.4056	−	21.6075i	−0.362057	−	0.751820i
$827$	7.84779	−	3.77930i	0.272894	−	0.131419i	−0.292432	−	0.956286i	$-0.594464\pi$
$827$	7.84779	−	3.77930i	0.272894	−	0.131419i	0.565326	+	0.824867i	$0.308750\pi$
$828$	1.01625	+	0.231953i	0.0353172	+	0.00806091i
$829$		−	1.94099i		−	0.0674135i	−0.999432	−	0.0337067i	$-0.989269\pi$
$829$		−	1.94099i		−	0.0674135i	0.999432	−	0.0337067i	$-0.0107312\pi$
$830$		0			0
$831$	−2.58170	+	2.05884i	−0.0895581	+	0.0714202i
$832$	−27.0853	+	6.18205i	−0.939014	+	0.214324i
$833$	−10.1608	−	44.5174i	−0.352051	−	1.54243i
$834$	6.07687	−	7.62015i	0.210425	−	0.263864i
$835$		0			0
$836$	4.45861	+	2.14715i	0.154204	+	0.0742608i
$837$	13.4322	−	10.7118i	0.464285	−	0.370255i
$838$	−32.7552	+	41.0737i	−1.13151	+	1.41887i
$839$	15.7021	−	32.6058i	0.542098	−	1.12568i	−0.432482	−	0.901642i	$-0.642362\pi$
$839$	15.7021	−	32.6058i	0.542098	−	1.12568i	0.974581	−	0.224036i	$-0.0719234\pi$
$840$		0			0
$841$	−12.8157	+	26.0146i	−0.441920	+	0.897055i
$842$		−	53.0148i		−	1.82701i
$843$	0.295944	+	0.142519i	0.0101928	+	0.00490861i
$844$	0.696917	+	0.555772i	0.0239889	+	0.0191305i
$845$		0			0
$846$	−0.394178	−	0.189826i	−0.0135521	−	0.00652636i
$847$	24.0715	+	49.9850i	0.827107	+	1.71751i
$848$	18.5696	+	14.8088i	0.637683	+	0.508536i
$849$	9.24940	−	2.11111i	0.317439	−	0.0724533i
$850$		0			0
$851$	−7.40953	+	5.90890i	−0.253995	+	0.202554i
$852$	0.421597	−	1.84714i	0.0144437	−	0.0632819i
$853$	0.842759			0.0288555			0.0144278	−	0.999896i	$-0.495407\pi$
$853$	0.842759			0.0288555			0.0144278	+	0.999896i	$0.495407\pi$
$854$	−10.9011	+	47.7609i	−0.373028	+	1.63434i
$855$		0			0
$856$	6.85343	+	14.2313i	0.234245	+	0.486416i
$857$	−18.3036	−	4.17767i	−0.625237	−	0.142706i	−0.101848	−	0.994800i	$-0.532476\pi$
$857$	−18.3036	−	4.17767i	−0.625237	−	0.142706i	−0.523389	+	0.852094i	$0.675333\pi$
$858$	−26.8878			−0.917934
$859$	31.4029	+	7.16751i	1.07145	+	0.244552i	0.721641	−	0.692267i	$-0.243388\pi$
$859$	31.4029	+	7.16751i	1.07145	+	0.244552i	0.349813	+	0.936820i	$0.386245\pi$
$860$		0			0
$861$	−13.3417	−	58.4536i	−0.454682	−	1.99209i
$862$	0.929564	+	4.07269i	0.0316611	+	0.138716i
$863$	−36.8294	−	29.3705i	−1.25369	−	0.999782i	−0.999467	−	0.0326357i	$-0.989610\pi$
$863$	−36.8294	−	29.3705i	−1.25369	−	0.999782i	−0.254220	−	0.967146i	$-0.581819\pi$
$864$	−5.72343	+	2.75626i	−0.194715	+	0.0937698i
$865$		0			0
$866$	−1.75139	−	2.19617i	−0.0595146	−	0.0746289i
$867$	−12.4832	+	15.6534i	−0.423951	+	0.531617i
$868$	2.20351	+	1.06116i	0.0747922	+	0.0360180i
$869$	−22.4136			−0.760328
$870$		0			0
$871$	−41.7488			−1.41460
$872$	−9.71751	−	4.67970i	−0.329076	−	0.158475i
$873$	−14.3210	+	17.9580i	−0.484693	+	0.607786i
$874$	−14.0688	−	17.6417i	−0.475883	−	0.596739i
$875$		0			0
$876$	−0.804231	+	0.387297i	−0.0271725	+	0.0130856i
$877$	24.8892	+	19.8485i	0.840450	+	0.670236i	0.945996	−	0.324178i	$-0.105088\pi$
$877$	24.8892	+	19.8485i	0.840450	+	0.670236i	−0.105546	+	0.994414i	$0.533659\pi$
$878$	−0.926683	−	4.06006i	−0.0312740	−	0.137021i
$879$	1.49634	+	6.55588i	0.0504702	+	0.221124i
$880$		0			0
$881$	−31.7553	−	7.24794i	−1.06986	−	0.244189i	−0.348898	−	0.937161i	$-0.613444\pi$
$881$	−31.7553	−	7.24794i	−1.06986	−	0.244189i	−0.720965	+	0.692971i	$0.756301\pi$
$882$	15.5658			0.524128
$883$	53.5623	+	12.2253i	1.80252	+	0.411412i	0.986114	−	0.166072i	$-0.0531083\pi$
$883$	53.5623	+	12.2253i	1.80252	+	0.411412i	0.816402	+	0.577484i	$0.195965\pi$
$884$	1.63727	+	3.39983i	0.0550674	+	0.114349i
$885$		0			0
$886$	−3.37493	+	14.7866i	−0.113383	+	0.496764i
$887$	29.8115			1.00097			0.500486	−	0.865745i	$-0.333155\pi$
$887$	29.8115			1.00097			0.500486	+	0.865745i	$0.333155\pi$
$888$	2.21026	−	9.68380i	0.0741716	−	0.324967i
$889$	18.8456	−	15.0288i	0.632060	−	0.504051i
$890$		0			0
$891$	−12.0814	+	2.75750i	−0.404741	+	0.0923796i
$892$	0.0805119	+	0.0642061i	0.00269574	+	0.00214978i
$893$	−0.466273	−	0.968225i	−0.0156032	−	0.0324004i
$894$	15.5611	+	7.49384i	0.520441	+	0.250631i
$895$		0			0
$896$	28.0455	+	22.3655i	0.936933	+	0.747179i
$897$	−12.5339	−	6.03602i	−0.418496	−	0.201537i
$898$		−	47.0581i		−	1.57035i
$899$	16.6271	−	1.79821i	0.554546	−	0.0599736i
$900$		0			0
$901$	16.7120	−	34.7028i	0.556758	−	1.15612i
$902$	−52.6955	+	66.0780i	−1.75457	+	2.20016i
$903$	32.3651	−	25.8103i	1.07704	−	0.858912i
$904$	24.3933	+	11.7472i	0.811308	+	0.390705i
$905$		0			0
$906$	−3.60329	+	4.51838i	−0.119711	+	0.150113i
$907$	−6.96687	−	30.5239i	−0.231331	−	1.01353i	−0.948537	−	0.316666i	$-0.897436\pi$
$907$	−6.96687	−	30.5239i	−0.231331	−	1.01353i	0.717206	−	0.696861i	$-0.245421\pi$
$908$	−0.485931	+	0.110911i	−0.0161262	+	0.00368069i
$909$	−4.84539	+	3.86407i	−0.160711	+	0.128163i
$910$		0			0
$911$			30.4463i			1.00873i	0.863490	+	0.504365i	$0.168273\pi$
$911$			30.4463i			1.00873i	−0.863490	+	0.504365i	$0.831727\pi$
$912$	20.6823	+	4.72060i	0.684860	+	0.156315i
$913$	38.2488	−	18.4197i	1.26585	−	0.609602i
$914$	−19.3614	−	40.2044i	−0.640419	−	1.32984i
$915$		0			0
$916$		−	2.24631i		−	0.0742203i
$917$	−0.562384	+	2.46397i	−0.0185716	+	0.0813673i
$918$	−26.6190	−	33.3791i	−0.878557	−	1.10168i
$919$	−8.50473	−	37.2616i	−0.280545	−	1.22915i	−0.897097	−	0.441834i	$-0.854328\pi$
$919$	−8.50473	−	37.2616i	−0.280545	−	1.22915i	0.616552	−	0.787314i	$-0.288529\pi$
$920$		0			0
$921$	−18.0117	+	22.5860i	−0.593507	+	0.744234i
$922$	−18.5961	−	38.6152i	−0.612429	−	1.27172i
$923$	10.4659	−	21.7327i	0.344489	−	0.715339i
$924$	−3.06377	−	3.84184i	−0.100791	−	0.126387i
$925$		0			0
$926$	12.6293	−	26.2250i	0.415024	−	0.861806i
$927$			2.83760i			0.0931991i
$928$	−6.14175	−	0.719821i	−0.201613	−	0.0236293i
$929$	−7.40994			−0.243112			−0.121556	−	0.992585i	$-0.538788\pi$
$929$	−7.40994			−0.243112			−0.121556	+	0.992585i	$0.538788\pi$
$930$		0			0
$931$	29.8929	+	23.8388i	0.979700	+	0.781285i
$932$	1.76164	−	1.40486i	0.0577044	−	0.0460177i
$933$	−16.0241	+	33.2745i	−0.524607	+	1.08936i
$934$	20.7235	−	9.97989i	0.678092	−	0.326552i
$935$		0			0
$936$	−13.5604	+	3.09508i	−0.443236	+	0.101166i
$937$	−36.6242	+	8.35924i	−1.19646	+	0.273085i	−0.773934	−	0.633266i	$-0.781714\pi$
$937$	−36.6242	+	8.35924i	−1.19646	+	0.273085i	−0.422527	+	0.906350i	$0.638857\pi$
$938$	41.9237	+	52.5707i	1.36886	+	1.71649i
$939$	−22.4749	−	5.12974i	−0.733440	−	0.167403i
$940$		0			0
$941$	9.63473	−	42.2125i	0.314083	−	1.37609i	−0.533668	−	0.845694i	$-0.679187\pi$
$941$	9.63473	−	42.2125i	0.314083	−	1.37609i	0.847751	−	0.530394i	$-0.177956\pi$
$942$	−13.9382	+	6.71228i	−0.454131	+	0.218698i
$943$	−39.3982	+	18.9732i	−1.28298	+	0.617851i
$944$	3.65925	−	16.0322i	0.119099	−	0.521805i
$945$		0			0
$946$	−56.8907	−	12.9849i	−1.84967	−	0.422176i
$947$	9.07894	+	11.3846i	0.295026	+	0.369951i	0.907147	−	0.420813i	$-0.138255\pi$
$947$	9.07894	+	11.3846i	0.295026	+	0.369951i	−0.612121	+	0.790764i	$0.709684\pi$
$948$	1.09588	−	0.250128i	0.0355925	−	0.00812376i
$949$	−11.0795	+	2.52882i	−0.359656	+	0.0820891i
$950$		0			0
$951$	−3.80596	+	1.83286i	−0.123417	+	0.0594344i
$952$	28.5132	−	59.2083i	0.924118	−	1.91895i
$953$	6.39582	−	5.10050i	0.207181	−	0.165221i	−0.514402	−	0.857549i	$-0.671986\pi$
$953$	6.39582	−	5.10050i	0.207181	−	0.165221i	0.721583	+	0.692328i	$0.243415\pi$
$954$	10.2656	+	8.18652i	0.332360	+	0.265048i
$955$		0			0
$956$	2.57609			0.0833166
$957$	−31.6663	−	11.2396i	−1.02362	−	0.363325i
$958$		−	35.0424i		−	1.13217i
$959$	−4.37203	+	9.07861i	−0.141180	+	0.293164i
$960$		0			0
$961$	13.3148	+	16.6963i	0.429511	+	0.538590i
$962$	5.07439	−	10.5371i	0.163605	−	0.339729i
$963$	3.39853	+	7.05713i	0.109516	+	0.227413i
$964$	2.61080	−	3.27384i	0.0840882	−	0.105443i
$965$		0			0
$966$	4.98580	+	21.8442i	0.160415	+	0.702826i
$967$	13.5770	+	17.0250i	0.436606	+	0.547487i	0.950645	−	0.310280i	$-0.100423\pi$
$967$	13.5770	+	17.0250i	0.436606	+	0.547487i	−0.514039	+	0.857767i	$0.671851\pi$
$968$	−9.43680	+	41.3453i	−0.303310	+	1.32889i
$969$		−	34.4027i		−	1.10517i
$970$		0			0
$971$	10.8622	+	22.5556i	0.348584	+	0.723842i	0.999373	−	0.0354167i	$-0.0112759\pi$
$971$	10.8622	+	22.5556i	0.348584	+	0.723842i	−0.650789	+	0.759259i	$0.725562\pi$
$972$	−2.48767	+	1.19800i	−0.0797921	+	0.0384259i
$973$	22.1091	+	5.04625i	0.708785	+	0.161775i
$974$			30.9027i			0.990187i
$975$		0			0
$976$	−26.2627	+	20.9438i	−0.840650	+	0.670396i
$977$	−24.7038	+	5.63849i	−0.790345	+	0.180391i	−0.598594	−	0.801052i	$-0.704274\pi$
$977$	−24.7038	+	5.63849i	−0.790345	+	0.180391i	−0.191751	+	0.981444i	$0.561417\pi$
$978$	0.154088	+	0.675102i	0.00492718	+	0.0215874i
$979$	30.4201	−	38.1456i	0.972229	−	1.21914i
$980$		0			0
$981$	−4.81879	−	2.32061i	−0.153852	−	0.0740913i
$982$	−2.23845	+	1.78510i	−0.0714318	+	0.0569650i
$983$	0.439068	−	0.550574i	0.0140041	−	0.0175606i	−0.774780	−	0.632231i	$-0.782139\pi$
$983$	0.439068	−	0.550574i	0.0140041	−	0.0175606i	0.788784	+	0.614670i	$0.210711\pi$
$984$	19.8855	−	41.2926i	0.633926	−	1.31636i
$985$		0			0
$986$	−4.46856	−	41.3185i	−0.142308	−	1.31585i
$987$			1.06710i			0.0339660i
$988$	−2.84679	−	1.37094i	−0.0905684	−	0.0436154i
$989$	−23.6050	−	18.8244i	−0.750595	−	0.598580i
$990$		0			0
$991$	−24.4697	−	11.7840i	−0.777307	−	0.374331i	0.00278497	−	0.999996i	$-0.499114\pi$
$991$	−24.4697	−	11.7840i	−0.777307	−	0.374331i	−0.780092	+	0.625665i	$0.784828\pi$
$992$	1.54729	+	3.21298i	0.0491265	+	0.102012i
$993$	17.2796	+	13.7800i	0.548351	+	0.437296i
$994$	−37.8758	+	8.64491i	−1.20135	+	0.274200i
$995$		0			0
$996$	−1.66457	+	1.32745i	−0.0527438	+	0.0420618i
$997$	1.20743	−	5.29010i	0.0382398	−	0.167539i	−0.952202	−	0.305468i	$-0.901187\pi$
$997$	1.20743	−	5.29010i	0.0382398	−	0.167539i	0.990442	+	0.137928i	$0.0440444\pi$
$998$	12.9250			0.409132
$999$	3.34104	−	14.6380i	0.105706	−	0.463127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.p.b.274.2		48
5.2	odd	4		145.2.m.a.71.3	✓	24
5.3	odd	4		725.2.q.b.651.2		24
5.4	even	2	inner	725.2.p.b.274.7		48
29.9	even	14	inner	725.2.p.b.299.7		48
145.9	even	14	inner	725.2.p.b.299.2		48
145.32	even	28		4205.2.a.y.1.19		24
145.38	odd	28		725.2.q.b.676.2		24
145.67	odd	28		145.2.m.a.96.3	yes	24
145.142	even	28		4205.2.a.y.1.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.m.a.71.3	✓	24	5.2	odd	4
145.2.m.a.96.3	yes	24	145.67	odd	28
725.2.p.b.274.2		48	1.1	even	1	trivial
725.2.p.b.274.7		48	5.4	even	2	inner
725.2.p.b.299.2		48	145.9	even	14	inner
725.2.p.b.299.7		48	29.9	even	14	inner
725.2.q.b.651.2		24	5.3	odd	4
725.2.q.b.676.2		24	145.38	odd	28
4205.2.a.y.1.6		24	145.142	even	28
4205.2.a.y.1.19		24	145.32	even	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.p (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20749 - 0.581499i) q^{2} +(-0.772561 + 0.968761i) q^{3} +(-0.127077 - 0.159349i) q^{4} +(1.49620 - 0.720531i) q^{6} +(3.02093 + 2.40911i) q^{7} +(0.657236 + 2.87954i) q^{8} +(0.325916 + 1.42793i) q^{9} +(-4.90945 - 1.12055i) q^{11} +0.252546 q^{12} +(3.13465 + 0.715462i) q^{13} +(-2.24686 - 4.66565i) q^{14} +(0.790134 - 3.46180i) q^{16} -5.75831 q^{17} +(0.436798 - 1.91374i) q^{18} +(3.76970 - 3.00623i) q^{19} +(-4.66770 + 1.06537i) q^{21} +(5.27653 + 4.20790i) q^{22} +(1.51507 + 3.14607i) q^{23} +(-3.29734 - 1.58792i) q^{24} +(-3.36903 - 2.68671i) q^{26} +(-4.98426 - 2.40029i) q^{27} -0.787523i q^{28} +(-2.84467 - 4.57251i) q^{29} +(-1.34746 + 2.79803i) q^{31} +(0.715953 - 0.897777i) q^{32} +(4.87839 - 3.89039i) q^{33} +(6.95313 + 3.34845i) q^{34} +(0.186123 - 0.233391i) q^{36} +(0.603935 + 2.64601i) q^{37} +(-6.30001 + 1.43794i) q^{38} +(-3.11482 + 2.48398i) q^{39} +12.5230i q^{41} +(6.25574 + 1.42783i) q^{42} +(-7.79009 + 3.75151i) q^{43} +(0.445317 + 0.924711i) q^{44} -4.67987i q^{46} +(0.0495957 - 0.217293i) q^{47} +(2.74323 + 3.43991i) q^{48} +(1.76454 + 7.73097i) q^{49} +(4.44865 - 5.57843i) q^{51} +(-0.284332 - 0.590421i) q^{52} +(-2.90224 + 6.02657i) q^{53} +(4.62270 + 5.79669i) q^{54} +(-4.95166 + 10.2822i) q^{56} +5.97443i q^{57} +(0.776019 + 7.17546i) q^{58} +4.63118 q^{59} +(-7.39623 - 5.89830i) q^{61} +(3.25411 - 2.59506i) q^{62} +(-2.45547 + 5.09883i) q^{63} +(-7.78494 + 3.74903i) q^{64} +(-8.15289 + 1.86084i) q^{66} +(-12.6590 + 2.88934i) q^{67} +(0.731747 + 0.917581i) q^{68} +(-4.21827 - 0.962792i) q^{69} +(1.66939 - 7.31408i) q^{71} +(-3.89758 + 1.87697i) q^{72} +(-3.18450 + 1.53357i) q^{73} +(0.809405 - 3.54623i) q^{74} +(-0.958080 - 0.218676i) q^{76} +(-12.1315 - 15.2125i) q^{77} +(5.20556 - 1.18814i) q^{78} +(4.33934 - 0.990426i) q^{79} +(2.21714 - 1.06772i) q^{81} +(7.28211 - 15.1215i) q^{82} +(-6.59115 + 5.25627i) q^{83} +(0.762921 + 0.608409i) q^{84} +11.5880 q^{86} +(6.62735 + 0.776735i) q^{87} -14.8734i q^{88} +(-4.20382 + 8.72932i) q^{89} +(7.74590 + 9.71306i) q^{91} +(0.308793 - 0.641215i) q^{92} +(-1.66963 - 3.46702i) q^{93} +(-0.186242 + 0.233540i) q^{94} +(0.316614 + 1.38718i) q^{96} +(9.77776 + 12.2609i) q^{97} +(2.36487 - 10.3612i) q^{98} -7.37555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56}+ \cdots - 2 q^{96}+O(q^{100}) \) 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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