LMFDB - Embedded newform 750.2.l.c.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	750.143
Dual form			750.2.l.c.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.207905 + 1.71953i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(2.58285 - 2.58285i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.91355 - 0.714995i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.207905 + 1.71953i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(2.58285 - 2.58285i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.91355 - 0.714995i) q^{9} +(-1.45719 + 0.473470i) q^{11} +(1.51333 - 0.842515i) q^{12} +(4.48435 - 2.28489i) q^{13} +(1.12875 + 3.47393i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.806752 - 5.09363i) q^{17} +(1.95979 - 2.27139i) q^{18} +(1.27450 - 1.75421i) q^{19} +(3.90430 + 4.97827i) q^{21} +(0.239686 - 1.51332i) q^{22} +(5.66723 + 2.88760i) q^{23} +(0.0636485 + 1.73088i) q^{24} +5.03290i q^{26} +(1.83520 - 4.86128i) q^{27} +(-3.60774 - 0.571409i) q^{28} +(5.64831 - 4.10373i) q^{29} +(-5.95310 - 4.32518i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.511188 - 2.60412i) q^{33} +(4.90472 + 1.59364i) q^{34} +(1.13410 + 2.77738i) q^{36} +(3.48561 + 6.84089i) q^{37} +(0.984395 + 1.93198i) q^{38} +(2.99661 + 8.18600i) q^{39} +(-2.85939 - 0.929072i) q^{41} +(-6.20819 + 1.21867i) q^{42} +(3.24693 + 3.24693i) q^{43} +(1.23956 + 0.900593i) q^{44} +(-5.14573 + 3.73859i) q^{46} +(-2.81716 - 0.446195i) q^{47} +(-1.57112 - 0.729092i) q^{48} -6.34226i q^{49} +(8.92637 - 0.328243i) q^{51} +(-4.48435 - 2.28489i) q^{52} +(-0.161639 + 1.02055i) q^{53} +(3.49827 + 3.84215i) q^{54} +(2.14701 - 2.95510i) q^{56} +(2.75143 + 2.55625i) q^{57} +(1.09218 + 6.89573i) q^{58} +(-2.10801 + 6.48779i) q^{59} +(1.78395 + 5.49044i) q^{61} +(6.55641 - 3.34066i) q^{62} +(-9.37200 + 5.67855i) q^{63} +(0.951057 - 0.309017i) q^{64} +(2.55236 + 0.726772i) q^{66} +(-3.33029 + 0.527466i) q^{67} +(-3.64664 + 3.64664i) q^{68} +(-6.14354 + 9.14461i) q^{69} +(2.18090 + 3.00175i) q^{71} +(-2.98953 - 0.250413i) q^{72} +(0.270757 - 0.531390i) q^{73} -7.67771 q^{74} -2.16832 q^{76} +(-2.54081 + 4.98661i) q^{77} +(-8.65421 - 1.04636i) q^{78} +(0.782199 + 1.07660i) q^{79} +(7.97756 + 4.16635i) q^{81} +(2.12595 - 2.12595i) q^{82} +(-2.73356 + 0.432953i) q^{83} +(1.73262 - 6.08480i) q^{84} +(-4.36710 + 1.41896i) q^{86} +(5.88218 + 10.5656i) q^{87} +(-1.36518 + 0.695596i) q^{88} +(-1.98939 - 6.12272i) q^{89} +(5.68088 - 17.4839i) q^{91} +(-0.994998 - 6.28217i) q^{92} +(8.67494 - 9.33729i) q^{93} +(1.67653 - 2.30754i) q^{94} +(1.36290 - 1.06888i) q^{96} +(2.14067 - 13.5156i) q^{97} +(5.65100 + 2.87933i) q^{98} +(4.58413 - 0.337594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.207905	+	1.71953i	−0.120034	+	0.992770i
$3$	−0.207905	+	1.71953i	−0.120034	+	0.992770i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.43772	−	0.965894i	−0.586948	−	0.394324i
$7$	2.58285	−	2.58285i	0.976227	−	0.976227i	−0.0234972	−	0.999724i	$-0.507480\pi$
$7$	2.58285	−	2.58285i	0.976227	−	0.976227i	0.999724	+	0.0234972i	$0.00748007\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−2.91355	−	0.714995i	−0.971184	−	0.238332i
$10$		0			0
$11$	−1.45719	+	0.473470i	−0.439360	+	0.142757i	−0.520340	−	0.853959i	$-0.674195\pi$
$11$	−1.45719	+	0.473470i	−0.439360	+	0.142757i	0.0809806	+	0.996716i	$0.474195\pi$
$12$	1.51333	−	0.842515i	0.436861	−	0.243213i
$13$	4.48435	−	2.28489i	1.24373	−	0.633714i	0.296738	−	0.954959i	$-0.404101\pi$
$13$	4.48435	−	2.28489i	1.24373	−	0.633714i	0.946996	+	0.321245i	$0.104101\pi$
$14$	1.12875	+	3.47393i	0.301671	+	0.928447i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.806752	−	5.09363i	−0.195666	−	1.23539i	−0.868536	−	0.495626i	$-0.834939\pi$
$17$	−0.806752	−	5.09363i	−0.195666	−	1.23539i	0.672870	−	0.739761i	$-0.265061\pi$
$18$	1.95979	−	2.27139i	0.461927	−	0.535372i
$19$	1.27450	−	1.75421i	0.292391	−	0.402442i	−0.637398	−	0.770535i	$-0.719989\pi$
$19$	1.27450	−	1.75421i	0.292391	−	0.402442i	0.929789	+	0.368093i	$0.119989\pi$
$20$		0			0
$21$	3.90430	+	4.97827i	0.851988	+	1.08635i
$22$	0.239686	−	1.51332i	0.0511012	−	0.322640i
$23$	5.66723	+	2.88760i	1.18170	+	0.602105i	0.930665	−	0.365873i	$-0.119230\pi$
$23$	5.66723	+	2.88760i	1.18170	+	0.602105i	0.251034	+	0.967978i	$0.419230\pi$
$24$	0.0636485	+	1.73088i	0.0129922	+	0.353315i
$25$		0			0
$26$			5.03290i			0.987033i
$27$	1.83520	−	4.86128i	0.353183	−	0.935554i
$28$	−3.60774	−	0.571409i	−0.681798	−	0.107986i
$29$	5.64831	−	4.10373i	1.04886	−	0.762044i	0.0768679	−	0.997041i	$-0.475508\pi$
$29$	5.64831	−	4.10373i	1.04886	−	0.762044i	0.971996	+	0.234997i	$0.0755080\pi$
$30$		0			0
$31$	−5.95310	−	4.32518i	−1.06921	−	0.776825i	−0.0934378	−	0.995625i	$-0.529786\pi$
$31$	−5.95310	−	4.32518i	−1.06921	−	0.776825i	−0.975770	+	0.218800i	$0.929786\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.511188	−	2.60412i	−0.0889864	−	0.453318i
$34$	4.90472	+	1.59364i	0.841152	+	0.273307i
$35$		0			0
$36$	1.13410	+	2.77738i	0.189017	+	0.462896i
$37$	3.48561	+	6.84089i	0.573031	+	1.12464i	0.977667	+	0.210158i	$0.0673979\pi$
$37$	3.48561	+	6.84089i	0.573031	+	1.12464i	−0.404637	+	0.914477i	$0.632602\pi$
$38$	0.984395	+	1.93198i	0.159690	+	0.313409i
$39$	2.99661	+	8.18600i	0.479842	+	1.31081i
$40$		0			0
$41$	−2.85939	−	0.929072i	−0.446562	−	0.145097i	0.0770993	−	0.997023i	$-0.475434\pi$
$41$	−2.85939	−	0.929072i	−0.446562	−	0.145097i	−0.523661	+	0.851927i	$0.675434\pi$
$42$	−6.20819	+	1.21867i	−0.957945	+	0.188045i
$43$	3.24693	+	3.24693i	0.495151	+	0.495151i	0.909925	−	0.414773i	$-0.136139\pi$
$43$	3.24693	+	3.24693i	0.495151	+	0.495151i	−0.414773	+	0.909925i	$0.636139\pi$
$44$	1.23956	+	0.900593i	0.186871	+	0.135770i
$45$		0			0
$46$	−5.14573	+	3.73859i	−0.758697	+	0.551226i
$47$	−2.81716	−	0.446195i	−0.410925	−	0.0650842i	−0.0524505	−	0.998624i	$-0.516703\pi$
$47$	−2.81716	−	0.446195i	−0.410925	−	0.0650842i	−0.358475	+	0.933539i	$0.616703\pi$
$48$	−1.57112	−	0.729092i	−0.226772	−	0.105235i
$49$		−	6.34226i		−	0.906037i
$50$		0			0
$51$	8.92637	−	0.328243i	1.24994	−	0.0459632i
$52$	−4.48435	−	2.28489i	−0.621867	−	0.316857i
$53$	−0.161639	+	1.02055i	−0.0222028	+	0.140183i	−0.996300	−	0.0859487i	$-0.972608\pi$
$53$	−0.161639	+	1.02055i	−0.0222028	+	0.140183i	0.974097	+	0.226131i	$0.0726079\pi$
$54$	3.49827	+	3.84215i	0.476055	+	0.522850i
$55$		0			0
$56$	2.14701	−	2.95510i	0.286906	−	0.394892i
$57$	2.75143	+	2.55625i	0.364436	+	0.338584i
$58$	1.09218	+	6.89573i	0.143410	+	0.905454i
$59$	−2.10801	+	6.48779i	−0.274439	+	0.844638i	0.714928	+	0.699198i	$0.246460\pi$
$59$	−2.10801	+	6.48779i	−0.274439	+	0.844638i	−0.989367	+	0.145439i	$0.953540\pi$
$60$		0			0
$61$	1.78395	+	5.49044i	0.228412	+	0.702979i	0.997927	+	0.0643507i	$0.0204976\pi$
$61$	1.78395	+	5.49044i	0.228412	+	0.702979i	−0.769516	+	0.638628i	$0.779502\pi$
$62$	6.55641	−	3.34066i	0.832665	−	0.424264i
$63$	−9.37200	+	5.67855i	−1.18076	+	0.715430i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	2.55236	+	0.726772i	0.314174	+	0.0894595i
$67$	−3.33029	+	0.527466i	−0.406859	+	0.0644402i	−0.356510	−	0.934291i	$-0.616033\pi$
$67$	−3.33029	+	0.527466i	−0.406859	+	0.0644402i	−0.0503493	+	0.998732i	$0.516033\pi$
$68$	−3.64664	+	3.64664i	−0.442220	+	0.442220i
$69$	−6.14354	+	9.14461i	−0.739596	+	1.10088i
$70$		0			0
$71$	2.18090	+	3.00175i	0.258825	+	0.356242i	0.918578	−	0.395241i	$-0.129339\pi$
$71$	2.18090	+	3.00175i	0.258825	+	0.356242i	−0.659752	+	0.751483i	$0.729339\pi$
$72$	−2.98953	−	0.250413i	−0.352320	−	0.0295114i
$73$	0.270757	−	0.531390i	0.0316897	−	0.0621945i	−0.874619	−	0.484811i	$-0.838888\pi$
$73$	0.270757	−	0.531390i	0.0316897	−	0.0621945i	0.906309	+	0.422617i	$0.138888\pi$
$74$	−7.67771			−0.892516
$75$		0			0
$76$	−2.16832			−0.248723
$77$	−2.54081	+	4.98661i	−0.289552	+	0.568277i
$78$	−8.65421	−	1.04636i	−0.979897	−	0.118477i
$79$	0.782199	+	1.07660i	0.0880042	+	0.121127i	0.850749	−	0.525572i	$-0.176149\pi$
$79$	0.782199	+	1.07660i	0.0880042	+	0.121127i	−0.762745	+	0.646700i	$0.776149\pi$
$80$		0			0
$81$	7.97756	+	4.16635i	0.886396	+	0.462928i
$82$	2.12595	−	2.12595i	0.234771	−	0.234771i
$83$	−2.73356	+	0.432953i	−0.300047	+	0.0475228i	−0.304643	−	0.952467i	$-0.598537\pi$
$83$	−2.73356	+	0.432953i	−0.300047	+	0.0475228i	0.00459575	+	0.999989i	$0.498537\pi$
$84$	1.73262	−	6.08480i	0.189044	−	0.663906i
$85$		0			0
$86$	−4.36710	+	1.41896i	−0.470917	+	0.153010i
$87$	5.88218	+	10.5656i	0.630635	+	1.13275i
$88$	−1.36518	+	0.695596i	−0.145529	+	0.0741507i
$89$	−1.98939	−	6.12272i	−0.210875	−	0.649007i	−0.999421	−	0.0340306i	$-0.989166\pi$
$89$	−1.98939	−	6.12272i	−0.210875	−	0.649007i	0.788546	−	0.614976i	$-0.210834\pi$
$90$		0			0
$91$	5.68088	−	17.4839i	0.595518	−	1.83282i
$92$	−0.994998	−	6.28217i	−0.103736	−	0.654961i
$93$	8.67494	−	9.33729i	0.899549	−	0.968232i
$94$	1.67653	−	2.30754i	0.172921	−	0.238005i
$95$		0			0
$96$	1.36290	−	1.06888i	0.139100	−	0.109092i
$97$	2.14067	−	13.5156i	0.217352	−	1.37230i	−0.601763	−	0.798675i	$-0.705535\pi$
$97$	2.14067	−	13.5156i	0.217352	−	1.37230i	0.819114	−	0.573630i	$-0.194465\pi$
$98$	5.65100	+	2.87933i	0.570837	+	0.290856i
$99$	4.58413	−	0.337594i	0.460722	−	0.0339295i
$100$		0			0
$101$			0.146560i			0.0145833i	0.999973	+	0.00729163i	$0.00232102\pi$
$101$			0.146560i			0.0145833i	−0.999973	+	0.00729163i	$0.997679\pi$
$102$	−3.76002	+	8.10247i	−0.372297	+	0.802264i
$103$	15.4311	+	2.44405i	1.52047	+	0.240819i	0.860103	−	0.510120i	$-0.170399\pi$
$103$	15.4311	+	2.44405i	1.52047	+	0.240819i	0.660371	+	0.750939i	$0.270399\pi$
$104$	4.07170	−	2.95827i	0.399263	−	0.290082i
$105$		0			0
$106$	−0.835930	−	0.607339i	−0.0811927	−	0.0589900i
$107$	1.77141	+	1.77141i	0.171249	+	0.171249i	0.787528	−	0.616279i	$-0.211361\pi$
$107$	1.77141	+	1.77141i	0.171249	+	0.171249i	−0.616279	+	0.787528i	$0.711361\pi$
$108$	−5.01156	+	1.37269i	−0.482238	+	0.132087i
$109$	−7.65945	−	2.48870i	−0.733642	−	0.238375i	−0.0817142	−	0.996656i	$-0.526039\pi$
$109$	−7.65945	−	2.48870i	−0.733642	−	0.238375i	−0.651928	+	0.758281i	$0.726039\pi$
$110$		0			0
$111$	−12.4878	+	4.57135i	−1.18529	+	0.433893i
$112$	1.65829	+	3.25458i	0.156694	+	0.307529i
$113$	−4.92541	−	9.66667i	−0.463344	−	0.909364i	−0.997934	−	0.0642521i	$-0.979534\pi$
$113$	−4.92541	−	9.66667i	−0.463344	−	0.909364i	0.534590	−	0.845112i	$-0.320466\pi$
$114$	−3.52676	+	1.29103i	−0.330311	+	0.120916i
$115$		0			0
$116$	−6.63998	−	2.15746i	−0.616507	−	0.200315i
$117$	−14.6991	+	3.45085i	−1.35893	+	0.319032i
$118$	−4.82364	−	4.82364i	−0.444052	−	0.444052i
$119$	−15.2398	−	11.0724i	−1.39703	−	1.01500i
$120$		0			0
$121$	−6.99996	+	5.08577i	−0.636360	+	0.462342i
$122$	−5.70191	−	0.903094i	−0.516227	−	0.0817623i
$123$	2.19205	−	4.72364i	0.197650	−	0.425916i
$124$			7.35843i			0.660807i
$125$		0			0
$126$	−0.804822	−	10.9285i	−0.0716992	−	0.973590i
$127$	16.4638	+	8.38871i	1.46092	+	0.744378i	0.990429	−	0.138025i	$-0.0440754\pi$
$127$	16.4638	+	8.38871i	1.46092	+	0.744378i	0.470495	+	0.882403i	$0.344075\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−6.25823	+	4.90813i	−0.551006	+	0.432137i
$130$		0			0
$131$	7.79711	−	10.7318i	0.681236	−	0.937641i	−0.318712	−	0.947852i	$-0.603250\pi$
$131$	7.79711	−	10.7318i	0.681236	−	0.937641i	0.999948	+	0.0102104i	$0.00325012\pi$
$132$	−1.80631	+	1.94422i	−0.157219	+	0.169223i
$133$	−1.23900	−	7.82271i	−0.107435	−	0.678315i
$134$	1.04194	−	3.20677i	0.0900102	−	0.277023i
$135$		0			0
$136$	−1.59364	−	4.90472i	−0.136653	−	0.420576i
$137$	−8.69698	+	4.43133i	−0.743033	+	0.378594i	−0.784159	−	0.620560i	$-0.786905\pi$
$137$	−8.69698	+	4.43133i	−0.743033	+	0.378594i	0.0411262	+	0.999154i	$0.486905\pi$
$138$	−5.35879	−	9.62550i	−0.456171	−	0.819377i
$139$	4.61980	−	1.50106i	0.391846	−	0.127319i	−0.106466	−	0.994316i	$-0.533953\pi$
$139$	4.61980	−	1.50106i	0.391846	−	0.127319i	0.498312	+	0.866998i	$0.333953\pi$
$140$		0			0
$141$	1.35295	−	4.75142i	0.113939	−	0.400142i
$142$	−3.66469	+	0.580430i	−0.307534	+	0.0487086i
$143$	−5.45272	+	5.45272i	−0.455980	+	0.455980i
$144$	1.58034	−	2.55001i	0.131695	−	0.212501i
$145$		0			0
$146$	0.350551	+	0.482492i	0.0290118	+	0.0399313i
$147$	10.9057	+	1.31859i	0.899486	+	0.108755i
$148$	3.48561	−	6.84089i	0.286515	−	0.562318i
$149$	6.55688			0.537160			0.268580	−	0.963257i	$-0.413446\pi$
$149$	6.55688			0.537160			0.268580	+	0.963257i	$0.413446\pi$
$150$		0			0
$151$	1.06618			0.0867647			0.0433824	−	0.999059i	$-0.486187\pi$
$151$	1.06618			0.0867647			0.0433824	+	0.999059i	$0.486187\pi$
$152$	0.984395	−	1.93198i	0.0798450	−	0.156705i
$153$	−1.29141	+	15.4174i	−0.104404	+	1.24642i
$154$	−3.28960	−	4.52775i	−0.265084	−	0.364856i
$155$		0			0
$156$	4.86125	−	7.23592i	0.389211	−	0.579337i
$157$	15.3342	−	15.3342i	1.22380	−	1.22380i	0.257528	−	0.966271i	$-0.417092\pi$
$157$	15.3342	−	15.3342i	1.22380	−	1.22380i	0.966271	−	0.257528i	$-0.0829078\pi$
$158$	−1.31437	+	0.208176i	−0.104566	+	0.0165616i
$159$	−1.72125	−	0.490118i	−0.136504	−	0.0388689i
$160$		0			0
$161$	22.0958	−	7.17938i	1.74140	−	0.565814i
$162$	−7.33398	+	5.21658i	−0.576212	+	0.409853i
$163$	9.16108	−	4.66780i	0.717551	−	0.365610i	−0.0567839	−	0.998386i	$-0.518085\pi$
$163$	9.16108	−	4.66780i	0.717551	−	0.365610i	0.774335	+	0.632776i	$0.218085\pi$
$164$	0.929072	+	2.85939i	0.0725483	+	0.223281i
$165$		0			0
$166$	0.855246	−	2.63218i	0.0663800	−	0.204297i
$167$	3.76955	+	23.8000i	0.291697	+	1.84170i	0.503008	+	0.864282i	$0.332227\pi$
$167$	3.76955	+	23.8000i	0.291697	+	1.84170i	−0.211311	+	0.977419i	$0.567773\pi$
$168$	4.63501	+	4.30622i	0.357598	+	0.332232i
$169$	7.24745	−	9.97526i	0.557496	−	0.767327i
$170$		0			0
$171$	−4.96758	+	4.19970i	−0.379881	+	0.321159i
$172$	0.718323	−	4.53531i	0.0547716	−	0.345814i
$173$	−21.3945	−	10.9010i	−1.62659	−	0.828791i	−0.998725	−	0.0504717i	$-0.983928\pi$
$173$	−21.3945	−	10.9010i	−1.62659	−	0.828791i	−0.627869	−	0.778319i	$-0.716072\pi$
$174$	−12.0845	+	0.444374i	−0.916122	+	0.0336879i
$175$		0			0
$176$		−	1.53218i		−	0.115492i
$177$	−10.7177	−	4.97362i	−0.805589	−	0.373840i
$178$	6.35855	+	1.00709i	0.476593	+	0.0754849i
$179$	−3.64757	+	2.65012i	−0.272632	+	0.198079i	−0.715697	−	0.698410i	$-0.753891\pi$
$179$	−3.64757	+	2.65012i	−0.272632	+	0.198079i	0.443065	+	0.896489i	$0.353891\pi$
$180$		0			0
$181$	−11.4405	−	8.31202i	−0.850367	−	0.617828i	0.0748802	−	0.997193i	$-0.476143\pi$
$181$	−11.4405	−	8.31202i	−0.850367	−	0.617828i	−0.925247	+	0.379365i	$0.876143\pi$
$182$	12.9992	+	12.9992i	0.963568	+	0.963568i
$183$	−9.81185	+	1.92607i	−0.725313	+	0.142379i
$184$	6.04917	+	1.96550i	0.445951	+	0.144898i
$185$		0			0
$186$	4.38125	+	11.9685i	0.321249	+	0.877571i
$187$	3.58727	+	7.04042i	0.262327	+	0.514846i
$188$	1.29491	+	2.54140i	0.0944409	+	0.185351i
$189$	−7.81594	−	17.2960i	−0.568526	−	1.25810i
$190$		0			0
$191$	−12.1952	−	3.96247i	−0.882416	−	0.286714i	−0.167456	−	0.985880i	$-0.553555\pi$
$191$	−12.1952	−	3.96247i	−0.882416	−	0.286714i	−0.714960	+	0.699165i	$0.753555\pi$
$192$	0.333634	+	1.69961i	0.0240780	+	0.122659i
$193$	−9.89879	−	9.89879i	−0.712531	−	0.712531i	0.254533	−	0.967064i	$-0.418078\pi$
$193$	−9.89879	−	9.89879i	−0.712531	−	0.712531i	−0.967064	+	0.254533i	$0.918078\pi$
$194$	11.0707	+	8.04332i	0.794828	+	0.577477i
$195$		0			0
$196$	−5.13100	+	3.72789i	−0.366500	+	0.266278i
$197$	6.72363	+	1.06492i	0.479039	+	0.0758723i	0.391284	−	0.920270i	$-0.372031\pi$
$197$	6.72363	+	1.06492i	0.479039	+	0.0758723i	0.0877545	+	0.996142i	$0.472031\pi$
$198$	−1.78035	+	4.23775i	−0.126524	+	0.301164i
$199$			5.40490i			0.383143i	0.981479	+	0.191572i	$0.0613585\pi$
$199$			5.40490i			0.383143i	−0.981479	+	0.191572i	$0.938642\pi$
$200$		0			0
$201$	−0.214610	−	5.83618i	−0.0151374	−	0.411653i
$202$	−0.130586	−	0.0665368i	−0.00918799	−	0.00468151i
$203$	3.98940	−	25.1881i	0.280001	−	1.76786i
$204$	−5.51234	−	7.02865i	−0.385941	−	0.492104i
$205$		0			0
$206$	−9.18325	+	12.6397i	−0.639827	+	0.880647i
$207$	−14.4471	−	12.4652i	−1.00415	−	0.866391i
$208$	0.787319	+	4.97094i	0.0545908	+	0.344673i
$209$	−1.02663	+	3.15965i	−0.0710137	+	0.218558i
$210$		0			0
$211$	3.95464	+	12.1711i	0.272249	+	0.837896i	0.989934	+	0.141529i	$0.0452017\pi$
$211$	3.95464	+	12.1711i	0.272249	+	0.837896i	−0.717685	+	0.696368i	$0.754798\pi$
$212$	0.920647	−	0.469093i	0.0632303	−	0.0322175i
$213$	−5.61502	+	3.12604i	−0.384735	+	0.214193i
$214$	−2.38255	+	0.774136i	−0.162868	+	0.0529189i
$215$		0			0
$216$	1.05213	−	5.08852i	0.0715883	−	0.346230i
$217$	−26.5473	+	4.20467i	−1.80215	+	0.285432i
$218$	5.69477	−	5.69477i	0.385698	−	0.385698i
$219$	0.857448	+	0.576052i	0.0579410	+	0.0389260i
$220$		0			0
$221$	−15.2561	−	20.9983i	−1.02624	−	1.41250i
$222$	1.59623	−	13.2020i	0.107132	−	0.886063i
$223$	−13.1811	+	25.8694i	−0.882673	+	1.73234i	−0.232437	+	0.972611i	$0.574670\pi$
$223$	−13.1811	+	25.8694i	−0.882673	+	1.73234i	−0.650236	+	0.759732i	$0.725330\pi$
$224$	−3.65271			−0.244057
$225$		0			0
$226$	10.8492			0.721675
$227$	1.79400	−	3.52093i	0.119072	−	0.233692i	−0.823776	−	0.566916i	$-0.808136\pi$
$227$	1.79400	−	3.52093i	0.119072	−	0.233692i	0.942848	+	0.333224i	$0.108136\pi$
$228$	0.450803	−	3.72848i	0.0298552	−	0.246925i
$229$	−7.75981	−	10.6805i	−0.512783	−	0.705785i	0.471603	−	0.881811i	$-0.343676\pi$
$229$	−7.75981	−	10.6805i	−0.512783	−	0.705785i	−0.984386	+	0.176026i	$0.943676\pi$
$230$		0			0
$231$	−8.04637	−	5.40573i	−0.529413	−	0.355671i
$232$	4.93680	−	4.93680i	0.324117	−	0.324117i
$233$	8.65736	−	1.37119i	0.567163	−	0.0898297i	0.133733	−	0.991017i	$-0.457303\pi$
$233$	8.65736	−	1.37119i	0.567163	−	0.0898297i	0.433429	+	0.901188i	$0.357303\pi$
$234$	3.59850	−	14.6636i	0.235241	−	0.958591i
$235$		0			0
$236$	6.48779	−	2.10801i	0.422319	−	0.137220i
$237$	−2.01387	+	1.12118i	−0.130815	+	0.0728285i
$238$	16.7843	−	8.55203i	1.08796	−	0.554345i
$239$	−5.85405	−	18.0169i	−0.378667	−	1.16542i	−0.940971	−	0.338486i	$-0.890085\pi$
$239$	−5.85405	−	18.0169i	−0.378667	−	1.16542i	0.562305	−	0.826930i	$-0.309915\pi$
$240$		0			0
$241$	−7.26464	+	22.3583i	−0.467957	+	1.44022i	0.387269	+	0.921967i	$0.373418\pi$
$241$	−7.26464	+	22.3583i	−0.467957	+	1.44022i	−0.855226	+	0.518256i	$0.826582\pi$
$242$	−1.35354	−	8.54590i	−0.0870087	−	0.549351i
$243$	−8.82273	+	12.8514i	−0.565978	+	0.824420i
$244$	3.39328	−	4.67045i	0.217232	−	0.298995i
$245$		0			0
$246$	3.21363	+	4.09762i	0.204893	+	0.261254i
$247$	1.70716	−	10.7786i	0.108624	−	0.685824i
$248$	−6.55641	−	3.34066i	−0.416332	−	0.212132i
$249$	−0.176156	−	4.79044i	−0.0111634	−	0.303582i
$250$		0			0
$251$			13.6488i			0.861504i	0.902470	+	0.430752i	$0.141752\pi$
$251$			13.6488i			0.861504i	−0.902470	+	0.430752i	$0.858248\pi$
$252$	10.1028	+	4.24434i	0.636414	+	0.267369i
$253$	−9.62542	−	1.52452i	−0.605145	−	0.0958455i
$254$	−14.9488	+	10.8609i	−0.937971	+	0.681476i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−14.2769	−	14.2769i	−0.890571	−	0.890571i	0.104006	−	0.994577i	$-0.466834\pi$
$257$	−14.2769	−	14.2769i	−0.890571	−	0.890571i	−0.994577	+	0.104006i	$0.966834\pi$
$258$	−1.53200	−	7.80437i	−0.0953780	−	0.485879i
$259$	26.6718	+	8.66620i	1.65731	+	0.538492i
$260$		0			0
$261$	−19.3908	+	7.91793i	−1.20026	+	0.490107i
$262$	6.02229	+	11.8194i	0.372058	+	0.730205i
$263$	7.39734	+	14.5181i	0.456139	+	0.895224i	0.998483	+	0.0550670i	$0.0175372\pi$
$263$	7.39734	+	14.5181i	0.456139	+	0.895224i	−0.542343	+	0.840157i	$0.682463\pi$
$264$	−0.912268	−	2.49209i	−0.0561462	−	0.153377i
$265$		0			0
$266$	7.53258	+	2.44748i	0.461852	+	0.150065i
$267$	10.9418	−	2.14787i	0.669626	−	0.131448i
$268$	2.38422	+	2.38422i	0.145640	+	0.145640i
$269$	8.83824	+	6.42136i	0.538877	+	0.391517i	0.823668	−	0.567073i	$-0.191924\pi$
$269$	8.83824	+	6.42136i	0.538877	+	0.391517i	−0.284791	+	0.958590i	$0.591924\pi$
$270$		0			0
$271$	−2.71650	+	1.97365i	−0.165016	+	0.119891i	−0.667228	−	0.744853i	$-0.732519\pi$
$271$	−2.71650	+	1.97365i	−0.165016	+	0.119891i	0.502213	+	0.864744i	$0.332519\pi$
$272$	5.09363	+	0.806752i	0.308847	+	0.0489165i
$273$	28.8830	+	13.4034i	1.74808	+	0.811212i
$274$		−	9.76085i		−	0.589674i
$275$		0			0
$276$	11.0092	−	0.404835i	0.662678	−	0.0243682i
$277$	−25.0088	−	12.7426i	−1.50263	−	0.765631i	−0.507269	−	0.861788i	$-0.669345\pi$
$277$	−25.0088	−	12.7426i	−1.50263	−	0.765631i	−0.995366	+	0.0961574i	$0.969345\pi$
$278$	−0.759888	+	4.79774i	−0.0455750	+	0.287749i
$279$	14.2522	+	16.8581i	0.853255	+	1.00927i
$280$		0			0
$281$	−0.417572	+	0.574739i	−0.0249103	+	0.0342861i	−0.821290	−	0.570510i	$-0.806745\pi$
$281$	−0.417572	+	0.574739i	−0.0249103	+	0.0342861i	0.796380	+	0.604796i	$0.206745\pi$
$282$	3.61933	+	3.36258i	0.215528	+	0.200239i
$283$	1.44181	+	9.10320i	0.0857064	+	0.541129i	0.992760	+	0.120114i	$0.0383260\pi$
$283$	1.44181	+	9.10320i	0.0857064	+	0.541129i	−0.907054	+	0.421015i	$0.861674\pi$
$284$	1.14657	−	3.52877i	0.0680363	−	0.209394i
$285$		0			0
$286$	−2.38293	−	7.33390i	−0.140905	−	0.433662i
$287$	−9.78504	+	4.98573i	−0.577593	+	0.294298i
$288$	1.55461	+	2.56577i	0.0916065	+	0.151189i
$289$	−9.12626	+	2.96530i	−0.536839	+	0.174430i
$290$		0			0
$291$	22.7955	+	6.49090i	1.33629	+	0.380503i
$292$	−0.589050	+	0.0932964i	−0.0344716	+	0.00545976i
$293$	1.97743	−	1.97743i	0.115523	−	0.115523i	−0.646982	−	0.762505i	$-0.723969\pi$
$293$	1.97743	−	1.97743i	0.115523	−	0.115523i	0.762505	+	0.646982i	$0.223969\pi$
$294$	−6.12595	+	9.11842i	−0.357273	+	0.531797i
$295$		0			0
$296$	4.51285	+	6.21140i	0.262304	+	0.361030i
$297$	−0.372559	+	7.95272i	−0.0216180	+	0.461464i
$298$	−2.97676	+	5.84222i	−0.172439	+	0.338431i
$299$	32.0116			1.85128
$300$		0			0
$301$	16.7727			0.966760
$302$	−0.484037	+	0.949976i	−0.0278532	+	0.0546650i
$303$	−0.252014	−	0.0304705i	−0.0144778	−	0.00175048i
$304$	1.27450	+	1.75421i	0.0730979	+	0.100611i
$305$		0			0
$306$	−13.1507	−	8.15000i	−0.751775	−	0.465904i
$307$	−11.7511	+	11.7511i	−0.670673	+	0.670673i	−0.957871	−	0.287198i	$-0.907276\pi$
$307$	−11.7511	+	11.7511i	−0.670673	+	0.670673i	0.287198	+	0.957871i	$0.407276\pi$
$308$	5.52770	−	0.875502i	0.314970	−	0.0498864i
$309$	−7.41082	+	26.0261i	−0.421587	+	1.48057i
$310$		0			0
$311$	3.30339	−	1.07334i	0.187318	−	0.0608633i	−0.213856	−	0.976865i	$-0.568602\pi$
$311$	3.30339	−	1.07334i	0.187318	−	0.0608633i	0.401174	+	0.916002i	$0.368602\pi$
$312$	4.24029	+	7.61644i	0.240059	+	0.431196i
$313$	−7.56390	+	3.85400i	−0.427537	+	0.217841i	−0.654499	−	0.756063i	$-0.727121\pi$
$313$	−7.56390	+	3.85400i	−0.427537	+	0.217841i	0.226962	+	0.973904i	$0.427121\pi$
$314$	6.70127	+	20.6244i	0.378175	+	1.16390i
$315$		0			0
$316$	0.411226	−	1.26562i	0.0231333	−	0.0711969i
$317$	1.54252	+	9.73906i	0.0866363	+	0.547000i	0.992384	+	0.123183i	$0.0393101\pi$
$317$	1.54252	+	9.73906i	0.0866363	+	0.547000i	−0.905748	+	0.423817i	$0.860690\pi$
$318$	1.21813	−	1.31114i	0.0683093	−	0.0735249i
$319$	−6.28766	+	8.65423i	−0.352042	+	0.484544i
$320$		0			0
$321$	−3.41428	+	2.67771i	−0.190567	+	0.149455i
$322$	−3.63443	+	22.9469i	−0.202539	+	1.27878i
$323$	−9.96348	−	5.07665i	−0.554383	−	0.282472i
$324$	−1.31844	−	8.90290i	−0.0732469	−	0.494606i
$325$		0			0
$326$			10.2817i			0.569452i
$327$	5.87183	−	12.6532i	0.324713	−	0.699724i
$328$	−2.96952	−	0.470327i	−0.163965	−	0.0259694i
$329$	−8.42877	+	6.12386i	−0.464693	+	0.337619i
$330$		0			0
$331$	−13.3891	−	9.72777i	−0.735933	−	0.534687i	0.155502	−	0.987836i	$-0.450301\pi$
$331$	−13.3891	−	9.72777i	−0.735933	−	0.534687i	−0.891435	+	0.453149i	$0.850301\pi$
$332$	1.95701	+	1.95701i	0.107405	+	0.107405i
$333$	−5.26429	−	22.4235i	−0.288481	−	1.22880i
$334$	−22.9173	−	7.44629i	−1.25398	−	0.407443i
$335$		0			0
$336$	−5.94112	+	2.17484i	−0.324114	+	0.118647i
$337$	11.9038	+	23.3624i	0.648439	+	1.27263i	0.947913	+	0.318528i	$0.103189\pi$
$337$	11.9038	+	23.3624i	0.648439	+	1.27263i	−0.299475	+	0.954104i	$0.596811\pi$
$338$	5.59775	+	10.9862i	0.304477	+	0.597570i
$339$	17.6461	−	6.45964i	0.958406	−	0.350840i
$340$		0			0
$341$	10.7226	+	3.48400i	0.580663	+	0.188669i
$342$	−1.48673	−	6.33277i	−0.0803929	−	0.342437i
$343$	1.69884	+	1.69884i	0.0917290	+	0.0917290i
$344$	3.71488	+	2.69902i	0.200293	+	0.145521i
$345$		0			0
$346$	19.4258	−	14.1137i	1.04434	−	0.758756i
$347$	11.7554	+	1.86187i	0.631061	+	0.0999502i	0.463768	−	0.885957i	$-0.346497\pi$
$347$	11.7554	+	1.86187i	0.631061	+	0.0999502i	0.167293	+	0.985907i	$0.446497\pi$
$348$	5.09030	−	10.9691i	0.272869	−	0.588005i
$349$			25.4721i			1.36349i	0.731591	+	0.681744i	$0.238778\pi$
$349$			25.4721i			1.36349i	−0.731591	+	0.681744i	$0.761222\pi$
$350$		0			0
$351$	−2.87784	−	25.9929i	−0.153608	−	1.38740i
$352$	1.36518	+	0.695596i	0.0727645	+	0.0370754i
$353$	−1.37767	+	8.69825i	−0.0733258	+	0.462961i	0.923517	+	0.383558i	$0.125301\pi$
$353$	−1.37767	+	8.69825i	−0.0733258	+	0.462961i	−0.996843	+	0.0794030i	$0.974699\pi$
$354$	9.29725	−	7.29153i	0.494143	−	0.387541i
$355$		0			0
$356$	−3.78405	+	5.20829i	−0.200554	+	0.276039i
$357$	22.2077	−	23.9033i	1.17536	−	1.26510i
$358$	−0.705308	−	4.45314i	−0.0372767	−	0.235356i
$359$	−2.11987	+	6.52428i	−0.111882	+	0.344338i	−0.991284	−	0.131742i	$-0.957943\pi$
$359$	−2.11987	+	6.52428i	−0.111882	+	0.344338i	0.879402	+	0.476080i	$0.157943\pi$
$360$		0			0
$361$	4.41845	+	13.5986i	0.232550	+	0.715715i
$362$	12.6000	−	6.42000i	0.662239	−	0.337428i
$363$	−7.28979	−	13.0940i	−0.382615	−	0.687255i
$364$	−17.4839	+	5.68088i	−0.916408	+	0.297759i
$365$		0			0
$366$	2.73835	−	9.61684i	0.143136	−	0.502680i
$367$	−14.6468	+	2.31983i	−0.764559	+	0.121094i	−0.526522	−	0.850162i	$-0.676504\pi$
$367$	−14.6468	+	2.31983i	−0.764559	+	0.121094i	−0.238038	+	0.971256i	$0.576504\pi$
$368$	−4.49754	+	4.49754i	−0.234450	+	0.234450i
$369$	7.66670	+	4.75135i	0.399112	+	0.247345i
$370$		0			0
$371$	2.21843	+	3.05341i	0.115175	+	0.158525i
$372$	−12.6530	−	1.52985i	−0.656029	−	0.0793191i
$373$	7.85384	−	15.4140i	0.406656	−	0.798108i	−0.593320	−	0.804967i	$-0.702183\pi$
$373$	7.85384	−	15.4140i	0.406656	−	0.798108i	0.999976	+	0.00685847i	$0.00218314\pi$
$374$	−7.90165			−0.408584
$375$		0			0
$376$	−2.85228			−0.147095
$377$	15.9524	−	31.3083i	0.821590	−	1.61246i
$378$	18.9592	+	0.888176i	0.975157	+	0.0456829i
$379$	3.34257	+	4.60065i	0.171696	+	0.236319i	0.886190	−	0.463323i	$-0.153343\pi$
$379$	3.34257	+	4.60065i	0.171696	+	0.236319i	−0.714494	+	0.699642i	$0.753343\pi$
$380$		0			0
$381$	−17.8475	+	26.5659i	−0.914356	+	1.36101i
$382$	9.06711	−	9.06711i	0.463914	−	0.463914i
$383$	29.9833	−	4.74888i	1.53207	−	0.242657i	0.667289	−	0.744799i	$-0.267455\pi$
$383$	29.9833	−	4.74888i	1.53207	−	0.242657i	0.864785	+	0.502143i	$0.167455\pi$
$384$	−1.66583	−	0.474338i	−0.0850092	−	0.0242060i
$385$		0			0
$386$	13.3138	−	4.32593i	0.677657	−	0.220184i
$387$	−7.13855	−	11.7816i	−0.362873	−	0.598893i
$388$	−12.1926	+	6.21246i	−0.618987	+	0.315390i
$389$	−0.407506	−	1.25417i	−0.0206613	−	0.0635891i	0.940194	−	0.340639i	$-0.110643\pi$
$389$	−0.407506	−	1.25417i	−0.0206613	−	0.0635891i	−0.960856	+	0.277050i	$0.910643\pi$
$390$		0			0
$391$	10.1363	−	31.1963i	0.512615	−	1.57767i
$392$	−0.992148	−	6.26418i	−0.0501110	−	0.316389i
$393$	16.8326	+	15.6385i	0.849091	+	0.788860i
$394$	−4.00131	+	5.50734i	−0.201583	+	0.277456i
$395$		0			0
$396$	−2.96760	−	3.51020i	−0.149128	−	0.176394i
$397$	1.73643	−	10.9634i	0.0871491	−	0.550238i	−0.905023	−	0.425362i	$-0.860147\pi$
$397$	1.73643	−	10.9634i	0.0871491	−	0.550238i	0.992172	−	0.124876i	$-0.0398532\pi$
$398$	−4.81580	−	2.45377i	−0.241394	−	0.122997i
$399$	13.7090	−	0.504110i	0.686307	−	0.0252371i
$400$		0			0
$401$			38.4533i			1.92026i	0.279545	+	0.960132i	$0.409816\pi$
$401$			38.4533i			1.92026i	−0.279545	+	0.960132i	$0.590184\pi$
$402$	5.29751	+	2.45835i	0.264216	+	0.122612i
$403$	−36.5783	−	5.79343i	−1.82209	−	0.288591i
$404$	0.118569	−	0.0861458i	0.00589905	−	0.00428591i
$405$		0			0
$406$	20.6316	+	14.9897i	1.02393	+	0.743928i
$407$	−8.31815	−	8.31815i	−0.412316	−	0.412316i
$408$	8.76512	−	1.72059i	0.433938	−	0.0851820i
$409$	−10.8096	−	3.51227i	−0.534502	−	0.173670i	0.0293144	−	0.999570i	$-0.490668\pi$
$409$	−10.8096	−	3.51227i	−0.534502	−	0.173670i	−0.563817	+	0.825900i	$0.690668\pi$
$410$		0			0
$411$	−5.81166	−	15.8760i	−0.286668	−	0.783105i
$412$	−7.09291	−	13.9206i	−0.349443	−	0.685820i
$413$	11.3123	+	22.2017i	0.556643	+	1.09247i
$414$	17.6654	−	7.21341i	0.868209	−	0.354520i
$415$		0			0
$416$	−4.78657	−	1.55525i	−0.234681	−	0.0762525i
$417$	1.62064	+	8.25595i	0.0793633	+	0.404296i
$418$	−2.34919	−	2.34919i	−0.114903	−	0.114903i
$419$	−4.06691	−	2.95479i	−0.198682	−	0.144351i	0.483996	−	0.875070i	$-0.339185\pi$
$419$	−4.06691	−	2.95479i	−0.198682	−	0.144351i	−0.682678	+	0.730719i	$0.739185\pi$
$420$		0			0
$421$	−7.36850	+	5.35353i	−0.359119	+	0.260915i	−0.752684	−	0.658382i	$-0.771241\pi$
$421$	−7.36850	+	5.35353i	−0.359119	+	0.260915i	0.393566	+	0.919296i	$0.371241\pi$
$422$	−12.6399	−	2.00197i	−0.615303	−	0.0974544i
$423$	7.88892	+	3.31427i	0.383573	+	0.161145i
$424$			1.03327i			0.0501799i
$425$		0			0
$426$	−0.236159	−	6.42221i	−0.0114420	−	0.311157i
$427$	18.7887	+	9.57331i	0.909248	+	0.463285i
$428$	0.391893	−	2.47432i	0.0189429	−	0.119601i
$429$	−8.24246	−	10.5098i	−0.397950	−	0.507416i
$430$		0			0
$431$	−14.5495	+	20.0257i	−0.700824	+	0.964602i	0.299122	+	0.954215i	$0.403306\pi$
$431$	−14.5495	+	20.0257i	−0.700824	+	0.964602i	−0.999946	+	0.0103868i	$0.996694\pi$
$432$	4.05625	+	3.24759i	0.195156	+	0.156250i
$433$	3.46945	+	21.9052i	0.166731	+	1.05270i	0.919119	+	0.393979i	$0.128902\pi$
$433$	3.46945	+	21.9052i	0.166731	+	1.05270i	−0.752388	+	0.658720i	$0.771098\pi$
$434$	8.30582	−	25.5627i	0.398692	−	1.22705i
$435$		0			0
$436$	2.48870	+	7.65945i	0.119187	+	0.366821i
$437$	12.2883	−	6.26122i	0.587831	−	0.299515i
$438$	−0.902539	+	0.502470i	−0.0431250	+	0.0240089i
$439$	−1.62057	+	0.526555i	−0.0773456	+	0.0251311i	−0.347434	−	0.937704i	$-0.612947\pi$
$439$	−1.62057	+	0.526555i	−0.0773456	+	0.0251311i	0.270089	+	0.962835i	$0.412947\pi$
$440$		0			0
$441$	−4.53469	+	18.4785i	−0.215937	+	0.879929i
$442$	25.6357	−	4.06030i	1.21937	−	0.193129i
$443$	−0.713085	+	0.713085i	−0.0338797	+	0.0338797i	−0.723844	−	0.689964i	$-0.757626\pi$
$443$	−0.713085	+	0.713085i	−0.0338797	+	0.0338797i	0.689964	+	0.723844i	$0.257626\pi$
$444$	11.0384	+	7.41585i	0.523861	+	0.351941i
$445$		0			0
$446$	−17.0657	−	23.4889i	−0.808085	−	1.11223i
$447$	−1.36321	+	11.2747i	−0.0644774	+	0.533277i
$448$	1.65829	−	3.25458i	0.0783470	−	0.153765i
$449$	12.4310			0.586657			0.293329	−	0.956012i	$-0.405237\pi$
$449$	12.4310			0.586657			0.293329	+	0.956012i	$0.405237\pi$
$450$		0			0
$451$	4.60656			0.216915
$452$	−4.92541	+	9.66667i	−0.231672	+	0.454682i
$453$	−0.221664	+	1.83333i	−0.0104147	+	0.0861374i
$454$	2.32271	+	3.19694i	0.109010	+	0.150040i
$455$		0			0
$456$	3.11744	+	2.09436i	0.145988	+	0.0980776i
$457$	−25.4659	+	25.4659i	−1.19125	+	1.19125i	−0.214529	+	0.976718i	$0.568822\pi$
$457$	−25.4659	+	25.4659i	−1.19125	+	1.19125i	−0.976718	+	0.214529i	$0.931178\pi$
$458$	13.0392	−	2.06521i	0.609284	−	0.0965011i
$459$	−26.2421	−	5.42596i	−1.22488	−	0.253262i
$460$		0			0
$461$	34.8009	−	11.3075i	1.62084	−	0.526642i	0.648699	−	0.761045i	$-0.275314\pi$
$461$	34.8009	−	11.3075i	1.62084	−	0.526642i	0.972140	+	0.234403i	$0.0753135\pi$
$462$	8.46951	−	4.71522i	0.394037	−	0.219372i
$463$	−5.89566	+	3.00399i	−0.273994	+	0.139607i	−0.585589	−	0.810608i	$-0.699137\pi$
$463$	−5.89566	+	3.00399i	−0.273994	+	0.139607i	0.311595	+	0.950215i	$0.399137\pi$
$464$	2.15746	+	6.63998i	0.100158	+	0.308253i
$465$		0			0
$466$	−2.70862	+	8.33627i	−0.125474	+	0.386170i
$467$	−5.97151	−	37.7026i	−0.276328	−	1.74467i	−0.601371	−	0.798970i	$-0.705379\pi$
$467$	−5.97151	−	37.7026i	−0.276328	−	1.74467i	0.325043	−	0.945699i	$-0.394621\pi$
$468$	11.4317	+	9.86343i	0.528430	+	0.455937i
$469$	−7.23928	+	9.96401i	−0.334279	+	0.460095i
$470$		0			0
$471$	23.1795	+	29.5555i	1.06805	+	1.36185i
$472$	−1.06714	+	6.73768i	−0.0491192	+	0.310127i
$473$	−6.26871	−	3.19407i	−0.288236	−	0.146863i
$474$	−0.0847006	−	2.30338i	−0.00389043	−	0.105798i
$475$		0			0
$476$			18.8375i			0.863413i
$477$	1.20063	−	2.85784i	0.0549730	−	0.130852i
$478$	18.7109	+	2.96351i	0.855815	+	0.135548i
$479$	−9.41843	+	6.84289i	−0.430339	+	0.312660i	−0.781785	−	0.623549i	$-0.785690\pi$
$479$	−9.41843	+	6.84289i	−0.430339	+	0.312660i	0.351445	+	0.936208i	$0.385690\pi$
$480$		0			0
$481$	31.2614	+	22.7127i	1.42540	+	1.03561i
$482$	−16.6233	−	16.6233i	−0.757170	−	0.757170i
$483$	7.75131	+	39.4870i	0.352697	+	1.79672i
$484$	8.22894	+	2.67375i	0.374043	+	0.121534i
$485$		0			0
$486$	−7.44528	−	13.6955i	−0.337725	−	0.621242i
$487$	−16.1262	−	31.6495i	−0.730750	−	1.43418i	−0.894219	−	0.447629i	$-0.852269\pi$
$487$	−16.1262	−	31.6495i	−0.730750	−	1.43418i	0.163470	−	0.986548i	$-0.447731\pi$
$488$	2.62088	+	5.14377i	0.118642	+	0.232848i
$489$	6.12178	+	16.7232i	0.276837	+	0.756249i
$490$		0			0
$491$	3.18688	+	1.03548i	0.143822	+	0.0467305i	0.380043	−	0.924969i	$-0.375909\pi$
$491$	3.18688	+	1.03548i	0.143822	+	0.0467305i	−0.236222	+	0.971699i	$0.575909\pi$
$492$	−5.10996	+	1.00308i	−0.230375	+	0.0452226i
$493$	−25.4597	−	25.4597i	−1.14665	−	1.14665i
$494$	8.82874	+	6.41446i	0.397224	+	0.288600i
$495$		0			0
$496$	5.95310	−	4.32518i	0.267302	−	0.194206i
$497$	13.3860	+	2.12014i	0.600446	+	0.0951012i
$498$	4.34829	+	2.01786i	0.194852	+	0.0904225i
$499$		−	2.56390i		−	0.114776i	−0.998352	−	0.0573880i	$-0.981723\pi$
$499$		−	2.56390i		−	0.114776i	0.998352	−	0.0573880i	$-0.0182772\pi$
$500$		0			0
$501$	−41.7085	+	1.53372i	−1.86340	+	0.0685214i
$502$	−12.1612	−	6.19642i	−0.542779	−	0.276560i
$503$	2.27523	−	14.3652i	0.101448	−	0.640515i	−0.883601	−	0.468240i	$-0.844888\pi$
$503$	2.27523	−	14.3652i	0.101448	−	0.640515i	0.985049	−	0.172275i	$-0.0551117\pi$
$504$	−8.36830	+	7.07474i	−0.372754	+	0.315134i
$505$		0			0
$506$	5.72820	−	7.88419i	0.254650	−	0.350495i
$507$	15.6460	+	14.5361i	0.694861	+	0.645570i
$508$	−2.89055	−	18.2502i	−0.128248	−	0.809723i
$509$	−2.88278	+	8.87228i	−0.127777	+	0.393257i	−0.994397	−	0.105712i	$-0.966288\pi$
$509$	−2.88278	+	8.87228i	−0.127777	+	0.393257i	0.866620	+	0.498969i	$0.166288\pi$
$510$		0			0
$511$	−0.673177	−	2.07183i	−0.0297796	−	0.0916522i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−6.18872	−	9.41504i	−0.273239	−	0.415684i
$514$	19.2024	−	6.23925i	0.846983	−	0.275202i
$515$		0			0
$516$	7.64925	+	2.17809i	0.336740	+	0.0958850i
$517$	4.31640	−	0.683651i	0.189835	−	0.0300669i
$518$	−19.8304	+	19.8304i	−0.871298	+	0.871298i
$519$	23.1927	−	34.5221i	1.01804	−	1.51535i
$520$		0			0
$521$	−19.0337	−	26.1976i	−0.833881	−	1.14774i	−0.987188	−	0.159560i	$-0.948993\pi$
$521$	−19.0337	−	26.1976i	−0.833881	−	1.14774i	0.153308	−	0.988179i	$-0.451007\pi$
$522$	1.74830	−	20.8720i	0.0765212	−	0.913541i
$523$	10.0842	−	19.7913i	0.440950	−	0.865413i	−0.558408	−	0.829567i	$-0.688587\pi$
$523$	10.0842	−	19.7913i	0.440950	−	0.865413i	0.999357	−	0.0358458i	$-0.0114125\pi$
$524$	−13.2652			−0.579494
$525$		0			0
$526$	−16.2940			−0.710454
$527$	−17.2282	+	33.8122i	−0.750471	+	1.47288i
$528$	2.63463	+	0.318547i	0.114657	+	0.0138630i
$529$	10.2602	+	14.1219i	0.446095	+	0.613997i
$530$		0			0
$531$	10.7805	−	17.3953i	0.467835	−	0.754891i
$532$	−5.60044	+	5.60044i	−0.242810	+	0.242810i
$533$	−14.9453	+	2.36711i	−0.647354	+	0.102531i
$534$	−3.05370	+	10.7243i	−0.132146	+	0.464087i
$535$		0			0
$536$	−3.20677	+	1.04194i	−0.138511	+	0.0450051i
$537$	−3.79860	−	6.82307i	−0.163922	−	0.294437i
$538$	−9.73395	+	4.95969i	−0.419660	+	0.213828i
$539$	3.00287	+	9.24188i	0.129343	+	0.398076i
$540$		0			0
$541$	−0.547811	+	1.68599i	−0.0235522	+	0.0724863i	−0.962142	−	0.272549i	$-0.912133\pi$
$541$	−0.547811	+	1.68599i	−0.0235522	+	0.0724863i	0.938590	+	0.345036i	$0.112133\pi$
$542$	−0.525272	−	3.31644i	−0.0225624	−	0.142453i
$543$	16.6713	−	17.9442i	0.715434	−	0.770058i
$544$	−3.03128	+	4.17220i	−0.129965	+	0.178882i
$545$		0			0
$546$	−25.0552	+	19.6500i	−1.07226	+	0.840941i
$547$	−1.96467	+	12.4044i	−0.0840033	+	0.530376i	0.909420	+	0.415878i	$0.136526\pi$
$547$	−1.96467	+	12.4044i	−0.0840033	+	0.530376i	−0.993424	+	0.114497i	$0.963474\pi$
$548$	8.69698	+	4.43133i	0.371517	+	0.189297i
$549$	−1.27200	−	17.2722i	−0.0542875	−	0.737159i
$550$		0			0
$551$		−	15.1385i		−	0.644922i
$552$	−4.63737	+	9.99308i	−0.197380	+	0.425334i
$553$	4.80101	+	0.760406i	0.204160	+	0.0323357i
$554$	22.7075	−	16.4980i	0.964751	−	0.700933i
$555$		0			0
$556$	−3.92984	−	2.85519i	−0.166662	−	0.121087i
$557$	19.4225	+	19.4225i	0.822959	+	0.822959i	0.986531	−	0.163573i	$-0.0523018\pi$
$557$	19.4225	+	19.4225i	0.822959	+	0.822959i	−0.163573	+	0.986531i	$0.552302\pi$
$558$	−21.4910	+	5.04537i	−0.909786	+	0.213588i
$559$	21.9792	+	7.14148i	0.929621	+	0.302052i
$560$		0			0
$561$	−12.8520	+	4.70468i	−0.542612	+	0.198632i
$562$	−0.322522	−	0.632986i	−0.0136048	−	0.0267009i
$563$	11.4362	+	22.4447i	0.481977	+	0.945933i	0.996101	+	0.0882171i	$0.0281169\pi$
$563$	11.4362	+	22.4447i	0.481977	+	0.945933i	−0.514125	+	0.857716i	$0.671883\pi$
$564$	−4.63922	+	1.69826i	−0.195347	+	0.0715097i
$565$		0			0
$566$	−8.76558	−	2.84811i	−0.368445	−	0.119715i
$567$	31.3659	−	9.84380i	1.31725	−	0.413401i
$568$	2.62363	+	2.62363i	0.110085	+	0.110085i
$569$	−24.7435	−	17.9772i	−1.03730	−	0.753643i	−0.0675439	−	0.997716i	$-0.521516\pi$
$569$	−24.7435	−	17.9772i	−1.03730	−	0.753643i	−0.969757	+	0.244073i	$0.921516\pi$
$570$		0			0
$571$	−8.91080	+	6.47408i	−0.372905	+	0.270932i	−0.758415	−	0.651772i	$-0.774026\pi$
$571$	−8.91080	+	6.47408i	−0.372905	+	0.270932i	0.385509	+	0.922704i	$0.374026\pi$
$572$	7.61638	+	1.20632i	0.318457	+	0.0504386i
$573$	9.34903	−	20.1462i	0.390561	−	0.841621i
$574$		−	10.9820i		−	0.458380i
$575$		0			0
$576$	−2.99190	+	0.220336i	−0.124662	+	0.00918066i
$577$	3.45787	+	1.76187i	0.143953	+	0.0733478i	0.524483	−	0.851421i	$-0.324259\pi$
$577$	3.45787	+	1.76187i	0.143953	+	0.0733478i	−0.380530	+	0.924768i	$0.624259\pi$
$578$	1.50113	−	9.47778i	0.0624389	−	0.394224i
$579$	19.0793	−	14.9632i	0.792907	−	0.621851i
$580$		0			0
$581$	−5.94213	+	8.17864i	−0.246521	+	0.339307i
$582$	−16.1324	+	17.3641i	−0.668708	+	0.719765i
$583$	−0.247659	−	1.56366i	−0.0102570	−	0.0647602i
$584$	0.184296	−	0.567203i	0.00762620	−	0.0234710i
$585$		0			0
$586$	0.864170	+	2.65964i	0.0356985	+	0.109869i
$587$	−39.5031	+	20.1279i	−1.63047	+	0.830766i	−0.632028	+	0.774945i	$0.717777\pi$
$587$	−39.5031	+	20.1279i	−1.63047	+	0.830766i	−0.998441	+	0.0558204i	$0.982223\pi$
$588$	−5.34345	−	9.59794i	−0.220360	−	0.395812i
$589$	−15.1745	+	4.93049i	−0.625254	+	0.203157i
$590$		0			0
$591$	−3.22903	+	11.3401i	−0.132825	+	0.466468i
$592$	−7.58319	+	1.20106i	−0.311667	+	0.0493632i
$593$	−11.0677	+	11.0677i	−0.454495	+	0.454495i	−0.896843	−	0.442348i	$-0.854145\pi$
$593$	−11.0677	+	11.0677i	−0.454495	+	0.454495i	0.442348	+	0.896843i	$0.354145\pi$
$594$	−6.91679	−	3.94241i	−0.283799	−	0.161759i
$595$		0			0
$596$	−3.85404	−	5.30463i	−0.157868	−	0.217286i
$597$	−9.29388	−	1.12370i	−0.380373	−	0.0459902i
$598$	−14.5330	+	28.5226i	−0.594298	+	1.16638i
$599$	−39.0036			−1.59364			−0.796822	−	0.604215i	$-0.793487\pi$
$599$	−39.0036			−1.59364			−0.796822	+	0.604215i	$0.793487\pi$
$600$		0			0
$601$	−25.7471			−1.05025			−0.525123	−	0.851027i	$-0.675981\pi$
$601$	−25.7471			−1.05025			−0.525123	+	0.851027i	$0.675981\pi$
$602$	−7.61463	+	14.9446i	−0.310349	+	0.609094i
$603$	10.0801	+	0.844342i	0.410493	+	0.0343843i
$604$	−0.626686	−	0.862560i	−0.0254995	−	0.0350971i
$605$		0			0
$606$	0.141561	−	0.210713i	0.00575054	−	0.00855962i
$607$	−14.3533	+	14.3533i	−0.582583	+	0.582583i	−0.935612	−	0.353030i	$-0.885152\pi$
$607$	−14.3533	+	14.3533i	−0.582583	+	0.582583i	0.353030	+	0.935612i	$0.385152\pi$
$608$	−2.14162	+	0.339200i	−0.0868542	+	0.0137564i
$609$	42.4822	+	12.0966i	1.72147	+	0.490179i
$610$		0			0
$611$	−13.6526	+	4.43601i	−0.552327	+	0.179462i
$612$	13.2320	−	8.01733i	0.534872	−	0.324082i
$613$	25.0841	−	12.7810i	1.01314	−	0.516219i	0.133089	−	0.991104i	$-0.457510\pi$
$613$	25.0841	−	12.7810i	1.01314	−	0.516219i	0.880048	+	0.474885i	$0.157510\pi$
$614$	−5.13543	−	15.8052i	−0.207249	−	0.637848i
$615$		0			0
$616$	−1.72945	+	5.32269i	−0.0696814	+	0.214457i
$617$	3.61324	+	22.8131i	0.145464	+	0.918421i	0.947177	+	0.320712i	$0.103922\pi$
$617$	3.61324	+	22.8131i	0.145464	+	0.918421i	−0.801713	+	0.597709i	$0.796078\pi$
$618$	−19.8250	−	18.4187i	−0.797479	−	0.740909i
$619$	−5.12654	+	7.05608i	−0.206053	+	0.283608i	−0.899519	−	0.436882i	$-0.856083\pi$
$619$	−5.12654	+	7.05608i	−0.206053	+	0.283608i	0.693466	+	0.720489i	$0.256083\pi$
$620$		0			0
$621$	24.4379	−	22.2507i	0.980658	−	0.892889i
$622$	−0.543357	+	3.43062i	−0.0217866	+	0.137555i
$623$	−20.9524	−	10.6758i	−0.839440	−	0.427716i
$624$	−8.71135	+	0.320336i	−0.348733	+	0.0128237i
$625$		0			0
$626$		−	8.48916i		−	0.339295i
$627$	−5.21967	−	2.42223i	−0.208453	−	0.0967345i
$628$	−21.4188	−	3.39240i	−0.854702	−	0.135372i
$629$	32.0330	−	23.2733i	1.27724	−	0.927967i
$630$		0			0
$631$	20.4095	+	14.8283i	0.812488	+	0.590307i	0.914551	−	0.404471i	$-0.132544\pi$
$631$	20.4095	+	14.8283i	0.812488	+	0.590307i	−0.102063	+	0.994778i	$0.532544\pi$
$632$	0.940986	+	0.940986i	0.0374304	+	0.0374304i
$633$	−21.7508	+	4.26968i	−0.864517	+	0.169705i
$634$	−9.37785	−	3.04705i	−0.372442	−	0.121014i
$635$		0			0
$636$	0.615212	+	1.68061i	0.0243947	+	0.0666403i
$637$	−14.4914	−	28.4409i	−0.574169	−	1.12687i
$638$	−4.85643	−	9.53128i	−0.192268	−	0.377347i
$639$	−4.20793	−	10.3051i	−0.166463	−	0.407663i
$640$		0			0
$641$	−30.1335	−	9.79096i	−1.19020	−	0.386720i	−0.354054	−	0.935225i	$-0.615197\pi$
$641$	−30.1335	−	9.79096i	−1.19020	−	0.386720i	−0.836147	+	0.548505i	$0.815197\pi$
$642$	−0.835807	−	4.25780i	−0.0329867	−	0.168042i
$643$	11.3185	+	11.3185i	0.446357	+	0.446357i	0.894142	−	0.447785i	$-0.147787\pi$
$643$	11.3185	+	11.3185i	0.446357	+	0.446357i	−0.447785	+	0.894142i	$0.647787\pi$
$644$	−18.7959	−	13.6560i	−0.740660	−	0.538121i
$645$		0			0
$646$	9.04665	−	6.57278i	0.355936	−	0.258602i
$647$	−30.8296	−	4.88293i	−1.21204	−	0.191968i	−0.482491	−	0.875901i	$-0.660268\pi$
$647$	−30.8296	−	4.88293i	−1.21204	−	0.191968i	−0.729545	+	0.683933i	$0.760268\pi$
$648$	8.53111	+	2.86709i	0.335134	+	0.112630i
$649$		−	10.4520i		−	0.410278i
$650$		0			0
$651$	−1.71075	−	46.5229i	−0.0670498	−	1.82338i
$652$	−9.16108	−	4.66780i	−0.358775	−	0.182805i
$653$	0.252918	−	1.59686i	0.00989744	−	0.0624900i	−0.982245	−	0.187601i	$-0.939929\pi$
$653$	0.252918	−	1.59686i	0.00989744	−	0.0624900i	0.992143	+	0.125111i	$0.0399288\pi$
$654$	8.60834	+	10.9763i	0.336613	+	0.429207i
$655$		0			0
$656$	1.76720	−	2.43234i	0.0689976	−	0.0949670i
$657$	−1.16880	+	1.35464i	−0.0455994	+	0.0528496i
$658$	−1.62982	−	10.2903i	−0.0635369	−	0.401156i
$659$	−1.49604	+	4.60434i	−0.0582774	+	0.179360i	−0.975958	−	0.217960i	$-0.930060\pi$
$659$	−1.49604	+	4.60434i	−0.0582774	+	0.179360i	0.917680	+	0.397320i	$0.130060\pi$
$660$		0			0
$661$	−14.5577	−	44.8040i	−0.566229	−	1.74267i	−0.664271	−	0.747492i	$-0.731258\pi$
$661$	−14.5577	−	44.8040i	−0.566229	−	1.74267i	0.0980414	−	0.995182i	$-0.468742\pi$
$662$	14.7460	−	7.51349i	0.573121	−	0.292020i
$663$	39.2789	−	21.8677i	1.52547	−	0.849272i
$664$	−2.63218	+	0.855246i	−0.102148	+	0.0331900i
$665$		0			0
$666$	22.3694	+	5.48953i	0.866797	+	0.212715i
$667$	43.8601	−	6.94676i	1.69827	−	0.268980i
$668$	17.0389	−	17.0389i	0.659256	−	0.659256i
$669$	−41.7427	−	28.0437i	−1.61387	−	1.08423i
$670$		0			0
$671$	−5.19911	−	7.15597i	−0.200710	−	0.276253i
$672$	0.759414	−	6.28093i	0.0292950	−	0.242292i
$673$	−11.6331	+	22.8312i	−0.448422	+	0.880077i	0.550553	+	0.834800i	$0.314417\pi$
$673$	−11.6331	+	22.8312i	−0.448422	+	0.880077i	−0.998974	+	0.0452767i	$0.985583\pi$
$674$	−26.2203			−1.00997
$675$		0			0
$676$	−12.3301			−0.474234
$677$	8.38373	−	16.4540i	0.322213	−	0.632379i	−0.671910	−	0.740633i	$-0.734526\pi$
$677$	8.38373	−	16.4540i	0.322213	−	0.632379i	0.994123	+	0.108254i	$0.0345260\pi$
$678$	−2.25559	+	18.6554i	−0.0866254	+	0.716457i
$679$	−29.3799	−	40.4379i	−1.12750	−	1.55187i
$680$		0			0
$681$	5.68136	+	3.81686i	0.217710	+	0.146262i
$682$	−7.97224	+	7.97224i	−0.305273	+	0.305273i
$683$	16.2967	−	2.58115i	0.623578	−	0.0987650i	0.163353	−	0.986568i	$-0.447769\pi$
$683$	16.2967	−	2.58115i	0.623578	−	0.0987650i	0.460224	+	0.887803i	$0.347769\pi$
$684$	6.31750	+	1.55034i	0.241556	+	0.0592786i
$685$		0			0
$686$	−2.28494	+	0.742422i	−0.0872394	+	0.0283458i
$687$	19.9787	−	11.1227i	0.762234	−	0.424357i
$688$	−4.09136	+	2.08465i	−0.155982	+	0.0794767i
$689$	1.60699	+	4.94581i	0.0612214	+	0.188420i
$690$		0			0
$691$	−10.6221	+	32.6914i	−0.404084	+	1.24364i	0.517574	+	0.855638i	$0.326835\pi$
$691$	−10.6221	+	32.6914i	−0.404084	+	1.24364i	−0.921658	+	0.388003i	$0.873165\pi$
$692$	3.75624	+	23.7160i	0.142791	+	0.901547i
$693$	10.9682	−	12.7121i	0.416646	−	0.482892i
$694$	−6.99576	+	9.62884i	−0.265555	+	0.365506i
$695$		0			0
$696$	7.46258	+	9.51535i	0.282868	+	0.360678i
$697$	−2.42553	+	15.3142i	−0.0918736	+	0.580067i
$698$	−22.6958	−	11.5641i	−0.859048	−	0.437707i
$699$	0.557896	+	15.1717i	0.0211016	+	0.573845i
$700$		0			0
$701$		−	14.8859i		−	0.562232i	−0.959674	−	0.281116i	$-0.909295\pi$
$701$		−	14.8859i		−	0.562232i	0.959674	−	0.281116i	$-0.0907045\pi$
$702$	24.4663	+	9.23636i	0.923423	+	0.348604i
$703$	16.4428	+	2.60428i	0.620150	+	0.0982222i
$704$	−1.23956	+	0.900593i	−0.0467177	+	0.0339424i
$705$		0			0
$706$	−7.12475	−	5.17643i	−0.268143	−	0.194818i
$707$	0.378543	+	0.378543i	0.0142366	+	0.0142366i
$708$	2.27594	+	11.5942i	0.0855351	+	0.435736i
$709$	−38.5502	−	12.5257i	−1.44778	−	0.470413i	−0.523468	−	0.852045i	$-0.675362\pi$
$709$	−38.5502	−	12.5257i	−1.44778	−	0.470413i	−0.924314	+	0.381632i	$0.875362\pi$
$710$		0			0
$711$	−1.50921	−	3.69601i	−0.0565998	−	0.138611i
$712$	−2.92270	−	5.73613i	−0.109533	−	0.214970i
$713$	−21.2482	−	41.7019i	−0.795750	−	1.56175i
$714$	11.2159	+	30.6391i	0.419745	+	1.14664i
$715$		0			0
$716$	4.28798	+	1.39325i	0.160249	+	0.0520681i
$717$	32.1976	−	6.32040i	1.20244	−	0.236040i
$718$	−4.85077	−	4.85077i	−0.181029	−	0.181029i
$719$	17.9319	+	13.0283i	0.668748	+	0.485874i	0.869606	−	0.493746i	$-0.164373\pi$
$719$	17.9319	+	13.0283i	0.668748	+	0.485874i	−0.200858	+	0.979620i	$0.564373\pi$
$720$		0			0
$721$	46.1690	−	33.5437i	1.71942	−	1.24923i
$722$	−14.1224	−	2.23676i	−0.525580	−	0.0832437i
$723$	−36.9353	−	17.1401i	−1.37364	−	0.637449i
$724$			14.1413i			0.525556i
$725$		0			0
$726$	14.9763	−	0.550713i	0.555823	−	0.0204389i
$727$	16.6015	+	8.45889i	0.615716	+	0.313723i	0.733888	−	0.679270i	$-0.237704\pi$
$727$	16.6015	+	8.45889i	0.615716	+	0.313723i	−0.118172	+	0.992993i	$0.537704\pi$
$728$	2.87585	−	18.1574i	0.106586	−	0.672957i
$729$	−20.2641	−	17.8428i	−0.750523	−	0.660844i
$730$		0			0
$731$	13.9192	−	19.1581i	0.514819	−	0.708588i
$732$	7.32548	+	6.80584i	0.270758	+	0.251551i
$733$	0.339633	+	2.14436i	0.0125446	+	0.0792038i	0.993166	−	0.116707i	$-0.0372338\pi$
$733$	0.339633	+	2.14436i	0.0125446	+	0.0792038i	−0.980622	+	0.195911i	$0.937234\pi$
$734$	4.58254	−	14.1036i	0.169145	−	0.520574i
$735$		0			0
$736$	−1.96550	−	6.04917i	−0.0724491	−	0.222975i
$737$	4.60312	−	2.34541i	0.169558	−	0.0863942i
$738$	−7.71409	+	4.67401i	−0.283960	+	0.172053i
$739$	−25.4696	+	8.27559i	−0.936916	+	0.304423i	−0.737388	−	0.675470i	$-0.763941\pi$
$739$	−25.4696	+	8.27559i	−0.936916	+	0.304423i	−0.199528	+	0.979892i	$0.563941\pi$
$740$		0			0
$741$	18.1791	+	5.17642i	0.667827	+	0.190161i
$742$	−3.72775	+	0.590418i	−0.136850	+	0.0216749i
$743$	−30.8466	+	30.8466i	−1.13165	+	1.13165i	−0.141749	+	0.989903i	$0.545273\pi$
$743$	−30.8466	+	30.8466i	−1.13165	+	1.13165i	−0.989903	+	0.141749i	$0.954727\pi$
$744$	7.10746	−	10.5794i	0.260572	−	0.387859i
$745$		0			0
$746$	10.1684	+	13.9956i	0.372293	+	0.512417i
$747$	8.27393	+	0.693051i	0.302727	+	0.0253574i
$748$	3.58727	−	7.04042i	0.131164	−	0.257423i
$749$	9.15060			0.334356
$750$		0			0
$751$	48.1007			1.75522			0.877610	−	0.479376i	$-0.159137\pi$
$751$	48.1007			1.75522			0.877610	+	0.479376i	$0.159137\pi$
$752$	1.29491	−	2.54140i	0.0472204	−	0.0926753i
$753$	−23.4695	−	2.83765i	−0.855275	−	0.103410i
$754$	20.6537	+	28.4274i	0.752163	+	1.03526i
$755$		0			0
$756$	−9.39868	+	16.4896i	−0.341827	+	0.599720i
$757$	2.64953	−	2.64953i	0.0962989	−	0.0962989i	−0.657316	−	0.753615i	$-0.728308\pi$
$757$	2.64953	−	2.64953i	0.0962989	−	0.0962989i	0.753615	+	0.657316i	$0.228308\pi$
$758$	−5.61670	+	0.889598i	−0.204008	+	0.0323117i
$759$	4.62262	−	16.2342i	0.167790	−	0.589265i
$760$		0			0
$761$	37.7032	−	12.2505i	1.36674	−	0.444080i	0.468452	−	0.883489i	$-0.344812\pi$
$761$	37.7032	−	12.2505i	1.36674	−	0.444080i	0.898287	+	0.439409i	$0.144812\pi$
$762$	−15.5678	−	27.9629i	−0.563960	−	1.01299i
$763$	−26.2112	+	13.3553i	−0.948909	+	0.483493i
$764$	3.96247	+	12.1952i	0.143357	+	0.441208i
$765$		0			0
$766$	−9.38083	+	28.8712i	−0.338943	+	1.04316i
$767$	5.37083	+	33.9101i	0.193929	+	1.22442i
$768$	1.17891	−	1.26892i	0.0425403	−	0.0457883i
$769$	13.8631	−	19.0810i	0.499918	−	0.688078i	−0.482261	−	0.876028i	$-0.660184\pi$
$769$	13.8631	−	19.0810i	0.499918	−	0.688078i	0.982179	+	0.187950i	$0.0601843\pi$
$770$		0			0
$771$	27.5178	−	21.5814i	0.991031	−	0.777233i
$772$	−2.18993	+	13.8267i	−0.0788172	+	0.497632i
$773$	37.0692	+	18.8877i	1.33329	+	0.679344i	0.967859	−	0.251495i	$-0.0809223\pi$
$773$	37.0692	+	18.8877i	1.33329	+	0.679344i	0.365429	+	0.930839i	$0.380922\pi$
$774$	13.7383	−	1.01175i	0.493814	−	0.0363665i
$775$		0			0
$776$		−	13.6841i		−	0.491231i
$777$	−20.4470	+	44.0612i	−0.733531	+	1.58069i
$778$	1.30248	+	0.206293i	0.0466962	+	0.00739595i
$779$	−5.27409	+	3.83185i	−0.188964	+	0.137290i
$780$		0			0
$781$	−4.59923	−	3.34153i	−0.164573	−	0.119570i
$782$	23.1943	+	23.1943i	0.829428	+	0.829428i
$783$	−9.58366	−	34.9892i	−0.342492	−	1.25041i
$784$	6.03185	+	1.95987i	0.215423	+	0.0699952i
$785$		0			0
$786$	−21.5759	+	7.89818i	−0.769585	+	0.281719i
$787$	−2.05558	−	4.03430i	−0.0732734	−	0.143807i	0.851464	−	0.524413i	$-0.175715\pi$
$787$	−2.05558	−	4.03430i	−0.0732734	−	0.143807i	−0.924737	+	0.380606i	$0.875715\pi$
$788$	−3.09051	−	6.06547i	−0.110095	−	0.216074i
$789$	−26.5022	+	9.70155i	−0.943503	+	0.345384i
$790$		0			0
$791$	−37.6892	−	12.2460i	−1.34007	−	0.435416i
$792$	4.47488	−	1.05055i	0.159008	−	0.0373298i
$793$	20.5449	+	20.5449i	0.729571	+	0.729571i
$794$	8.98015	+	6.52446i	0.318693	+	0.231544i
$795$		0			0
$796$	4.37266	−	3.17692i	0.154985	−	0.112603i
$797$	−12.9409	−	2.04964i	−0.458392	−	0.0726021i	−0.0770316	−	0.997029i	$-0.524544\pi$
$797$	−12.9409	−	2.04964i	−0.458392	−	0.0726021i	−0.381360	+	0.924427i	$0.624544\pi$
$798$	−5.77457	+	12.4436i	−0.204418	+	0.440500i
$799$			14.7096i			0.520387i
$800$		0			0
$801$	1.41848	+	19.2613i	0.0501195	+	0.680563i
$802$	−34.2621	−	17.4574i	−1.20984	−	0.616443i
$803$	−0.142947	+	0.902532i	−0.00504449	+	0.0318496i
$804$	−4.59543	+	3.60405i	−0.162068	+	0.127105i
$805$		0			0
$806$	21.7682	−	29.9613i	0.766752	−	1.05534i
$807$	−12.8792	+	13.8626i	−0.453370	+	0.487985i
$808$	0.0229270	+	0.144756i	0.000806570	+	0.00509248i
$809$	10.9215	−	33.6130i	0.383980	−	1.18177i	−0.553237	−	0.833024i	$-0.686608\pi$
$809$	10.9215	−	33.6130i	0.383980	−	1.18177i	0.937217	−	0.348746i	$-0.113392\pi$
$810$		0			0
$811$	0.0429712	+	0.132252i	0.00150892	+	0.00464399i	0.951808	−	0.306694i	$-0.0992228\pi$
$811$	0.0429712	+	0.132252i	0.00150892	+	0.00464399i	−0.950299	+	0.311338i	$0.899223\pi$
$812$	−22.7225	+	11.5777i	−0.797403	+	0.406297i
$813$	−2.82898	−	5.08143i	−0.0992166	−	0.178213i
$814$	11.1879	−	3.63517i	0.392135	−	0.127413i
$815$		0			0
$816$	−2.44622	+	8.59091i	−0.0856349	+	0.300742i
$817$	9.83400	−	1.55755i	0.344048	−	0.0544918i
$818$	8.03693	−	8.03693i	0.281005	−	0.281005i
$819$	−29.0525	+	46.8786i	−1.01518	+	1.63807i
$820$		0			0
$821$	−1.62196	−	2.23243i	−0.0566067	−	0.0779125i	0.779775	−	0.626060i	$-0.215333\pi$
$821$	−1.62196	−	2.23243i	−0.0566067	−	0.0779125i	−0.836382	+	0.548147i	$0.815333\pi$
$822$	16.7840	+	2.02932i	0.585411	+	0.0707808i
$823$	9.20610	−	18.0680i	0.320905	−	0.629811i	−0.673051	−	0.739596i	$-0.735016\pi$
$823$	9.20610	−	18.0680i	0.320905	−	0.629811i	0.993955	+	0.109786i	$0.0350164\pi$
$824$	15.6235			0.544270
$825$		0			0
$826$	−24.9175			−0.866992
$827$	1.51186	−	2.96720i	0.0525726	−	0.103180i	−0.863225	−	0.504819i	$-0.831559\pi$
$827$	1.51186	−	2.96720i	0.0525726	−	0.103180i	0.915798	+	0.401639i	$0.131559\pi$
$828$	−1.59274	+	19.0148i	−0.0553517	+	0.660811i
$829$	17.4925	+	24.0763i	0.607539	+	0.836206i	0.996372	−	0.0851024i	$-0.0271218\pi$
$829$	17.4925	+	24.0763i	0.607539	+	0.836206i	−0.388833	+	0.921308i	$0.627122\pi$
$830$		0			0
$831$	27.1108	−	40.3541i	0.940462	−	1.39987i
$832$	3.55880	−	3.55880i	0.123379	−	0.123379i
$833$	−32.3051	+	5.11663i	−1.11931	+	0.177281i
$834$	−8.09187	−	2.30412i	−0.280198	−	0.0797852i
$835$		0			0
$836$	3.15965	−	1.02663i	0.109279	−	0.0355068i
$837$	−31.9510	+	21.0021i	−1.10439	+	0.725940i
$838$	4.47907	−	2.28220i	0.154727	−	0.0788374i
$839$	−5.16619	−	15.8999i	−0.178357	−	0.548926i	0.821414	−	0.570332i	$-0.193186\pi$
$839$	−5.16619	−	15.8999i	−0.178357	−	0.548926i	−0.999771	+	0.0214067i	$0.993186\pi$
$840$		0			0
$841$	6.10123	−	18.7776i	0.210387	−	0.647505i
$842$	−1.42480	−	8.99583i	−0.0491018	−	0.310017i
$843$	−0.901465	−	0.837518i	−0.0310481	−	0.0288457i
$844$	7.52218	−	10.3534i	0.258924	−	0.356379i
$845$		0			0
$846$	−6.53453	+	5.52443i	−0.224662	+	0.189934i
$847$	−4.94407	+	31.2156i	−0.169880	+	1.07258i
$848$	−0.920647	−	0.469093i	−0.0316152	−	0.0161087i
$849$	−15.9530	+	0.586627i	−0.547504	+	0.0201330i
$850$		0			0
$851$			48.8339i			1.67400i
$852$	5.82944	+	2.70520i	0.199713	+	0.0926787i
$853$	−2.82627	−	0.447638i	−0.0967698	−	0.0153268i	0.107862	−	0.994166i	$-0.465600\pi$
$853$	−2.82627	−	0.447638i	−0.0967698	−	0.0153268i	−0.204632	+	0.978839i	$0.565600\pi$
$854$	−17.0598	+	12.3946i	−0.583773	+	0.424136i
$855$		0			0
$856$	2.02672	+	1.47249i	0.0692717	+	0.0503288i
$857$	−8.27926	−	8.27926i	−0.282814	−	0.282814i	0.551416	−	0.834230i	$-0.314088\pi$
$857$	−8.27926	−	8.27926i	−0.282814	−	0.282814i	−0.834230	+	0.551416i	$0.814088\pi$
$858$	13.1063	−	2.57276i	0.447440	−	0.0878325i
$859$	−21.3255	−	6.92908i	−0.727617	−	0.236417i	−0.0782946	−	0.996930i	$-0.524947\pi$
$859$	−21.3255	−	6.92908i	−0.727617	−	0.236417i	−0.649323	+	0.760513i	$0.724947\pi$
$860$		0			0
$861$	−6.53874	−	17.8622i	−0.222840	−	0.608742i
$862$	−11.2377	−	22.0551i	−0.382756	−	0.751201i
$863$	8.33881	+	16.3658i	0.283857	+	0.557100i	0.988275	−	0.152685i	$-0.0487921\pi$
$863$	8.33881	+	16.3658i	0.283857	+	0.557100i	−0.704418	+	0.709785i	$0.748792\pi$
$864$	−4.73512	+	2.13977i	−0.161092	+	0.0727963i
$865$		0			0
$866$	−21.0928	−	6.85347i	−0.716763	−	0.232890i
$867$	−3.20153	−	16.3094i	−0.108730	−	0.553895i
$868$	19.0057	+	19.0057i	0.645097	+	0.645097i
$869$	−1.64955	−	1.19847i	−0.0559572	−	0.0406553i
$870$		0			0
$871$	−13.7290	+	9.97468i	−0.465188	+	0.337979i
$872$	−7.95446	−	1.25986i	−0.269372	−	0.0426644i
$873$	−15.9006	+	37.8479i	−0.538152	+	1.28096i
$874$			13.7915i			0.466505i
$875$		0			0
$876$	−0.0379595	−	1.03228i	−0.00128253	−	0.0348777i
$877$	34.8578	+	17.7609i	1.17706	+	0.599744i	0.929390	−	0.369100i	$-0.120334\pi$
$877$	34.8578	+	17.7609i	1.17706	+	0.599744i	0.247673	+	0.968844i	$0.420334\pi$
$878$	0.266559	−	1.68299i	0.00899594	−	0.0567981i
$879$	2.98913	+	3.81137i	0.100821	+	0.128554i
$880$		0			0
$881$	0.436643	−	0.600988i	0.0147109	−	0.0202478i	−0.801598	−	0.597863i	$-0.796017\pi$
$881$	0.436643	−	0.600988i	0.0147109	−	0.0202478i	0.816309	+	0.577615i	$0.196017\pi$
$882$	−14.4058	−	12.4295i	−0.485067	−	0.418523i
$883$	−4.62830	−	29.2220i	−0.155755	−	0.983397i	−0.934476	−	0.356027i	$-0.884131\pi$
$883$	−4.62830	−	29.2220i	−0.155755	−	0.983397i	0.778721	−	0.627371i	$-0.215869\pi$
$884$	−8.02063	+	24.6849i	−0.269763	+	0.830245i
$885$		0			0
$886$	−0.311629	−	0.959097i	−0.0104694	−	0.0322215i
$887$	52.4089	−	26.7037i	1.75972	−	0.896621i	0.808270	−	0.588813i	$-0.200404\pi$
$887$	52.4089	−	26.7037i	1.75972	−	0.896621i	0.951448	−	0.307809i	$-0.0995956\pi$
$888$	−11.6189	+	6.46859i	−0.389905	+	0.217072i
$889$	64.1903	−	20.8567i	2.15287	−	0.699511i
$890$		0			0
$891$	−13.5975	−	2.29403i	−0.455532	−	0.0768530i
$892$	28.6765	−	4.54190i	0.960159	−	0.152074i
$893$	−4.37321	+	4.37321i	−0.146344	+	0.146344i
$894$	−9.42698	−	6.33325i	−0.315285	−	0.211815i
$895$		0			0
$896$	2.14701	+	2.95510i	0.0717265	+	0.0987230i
$897$	−6.65537	+	55.0449i	−0.222216	+	1.83790i
$898$	−5.64357	+	11.0761i	−0.188329	+	0.369616i
$899$	−51.3743			−1.71343
$900$		0			0
$901$	5.32868			0.177524
$902$	−2.09134	+	4.10448i	−0.0696339	+	0.136664i
$903$	−3.48711	+	28.8411i	−0.116044	+	0.959770i
$904$	−6.37698	−	8.77715i	−0.212095	−	0.291924i
$905$		0			0
$906$	−1.53288	−	1.02982i	−0.0509264	−	0.0342134i
$907$	−8.72011	+	8.72011i	−0.289547	+	0.289547i	−0.836901	−	0.547354i	$-0.815635\pi$
$907$	−8.72011	+	8.72011i	−0.289547	+	0.289547i	0.547354	+	0.836901i	$0.315635\pi$
$908$	−3.90298	+	0.618172i	−0.129525	+	0.0205148i
$909$	0.104790	−	0.427010i	0.00347565	−	0.0141630i
$910$		0			0
$911$	−35.6554	+	11.5852i	−1.18132	+	0.383833i	−0.832856	−	0.553490i	$-0.813296\pi$
$911$	−35.6554	+	11.5852i	−1.18132	+	0.383833i	−0.348461	+	0.937323i	$0.613296\pi$
$912$	−3.28138	+	1.82684i	−0.108657	+	0.0604927i
$913$	3.77833	−	1.92515i	0.125044	−	0.0637133i
$914$	−11.1290	−	34.2516i	−0.368116	−	1.13294i
$915$		0			0
$916$	−4.07958	+	12.5556i	−0.134793	+	0.414850i
$917$	−7.57987	−	47.8574i	−0.250309	−	1.58039i
$918$	16.7482	−	20.9186i	0.552774	−	0.690416i
$919$	17.9736	−	24.7386i	0.592896	−	0.816051i	−0.402139	−	0.915579i	$-0.631733\pi$
$919$	17.9736	−	24.7386i	0.592896	−	0.816051i	0.995035	+	0.0995274i	$0.0317331\pi$
$920$		0			0
$921$	−17.7633	−	22.6495i	−0.585320	−	0.746327i
$922$	−5.72422	+	36.1413i	−0.188517	+	1.19025i
$923$	16.6386	+	8.47779i	0.547666	+	0.279050i
$924$	0.356215	+	9.68706i	0.0117186	+	0.318681i
$925$		0			0
$926$		−	6.61685i		−	0.217443i
$927$	−43.2119	−	18.1541i	−1.41926	−	0.596257i
$928$	−6.89573	−	1.09218i	−0.226364	−	0.0358525i
$929$	0.652608	−	0.474147i	0.0214114	−	0.0155563i	−0.577028	−	0.816724i	$-0.695788\pi$
$929$	0.652608	−	0.474147i	0.0214114	−	0.0155563i	0.598439	+	0.801168i	$0.295788\pi$
$930$		0			0
$931$	−11.1256	−	8.08324i	−0.364628	−	0.264918i
$932$	−6.19799	−	6.19799i	−0.203022	−	0.203022i
$933$	1.15884	+	5.90342i	0.0379387	+	0.193269i
$934$	36.3043	+	11.7960i	1.18791	+	0.385976i
$935$		0			0
$936$	−13.9783	+	5.70781i	−0.456894	+	0.186566i
$937$	−3.87770	−	7.61042i	−0.126679	−	0.248622i	0.818953	−	0.573861i	$-0.194555\pi$
$937$	−3.87770	−	7.61042i	−0.126679	−	0.248622i	−0.945632	+	0.325240i	$0.894555\pi$
$938$	−5.59143	−	10.9738i	−0.182567	−	0.358308i
$939$	−5.05449	−	13.8076i	−0.164947	−	0.450594i
$940$		0			0
$941$	17.4242	+	5.66148i	0.568014	+	0.184559i	0.578924	−	0.815382i	$-0.303473\pi$
$941$	17.4242	+	5.66148i	0.568014	+	0.184559i	−0.0109101	+	0.999940i	$0.503473\pi$
$942$	−36.8574	+	7.23511i	−1.20088	+	0.235733i
$943$	−13.5220	−	13.5220i	−0.440338	−	0.440338i
$944$	−5.51884	−	4.00967i	−0.179623	−	0.130504i
$945$		0			0
$946$	5.69187	−	4.13539i	0.185059	−	0.134453i
$947$	35.5120	+	5.62455i	1.15398	+	0.182773i	0.703958	−	0.710242i	$-0.251414\pi$
$947$	35.5120	+	5.62455i	1.15398	+	0.182773i	0.450027	+	0.893015i	$0.351414\pi$
$948$	2.09078	+	0.970244i	0.0679054	+	0.0315121i
$949$		−	3.00159i		−	0.0974356i
$950$		0			0
$951$	−17.0673	+	0.627603i	−0.553444	+	0.0203514i
$952$	−16.7843	−	8.55203i	−0.543982	−	0.277173i
$953$	1.94289	−	12.2669i	0.0629365	−	0.397365i	−0.936030	−	0.351919i	$-0.885529\pi$
$953$	1.94289	−	12.2669i	0.0629365	−	0.397365i	0.998967	−	0.0454459i	$-0.0144709\pi$
$954$	2.00128	+	2.36720i	0.0647939	+	0.0766409i
$955$		0			0
$956$	−11.1351	+	15.3261i	−0.360133	+	0.495681i
$957$	−13.5739	−	12.6111i	−0.438783	−	0.407658i
$958$	−1.82118	−	11.4985i	−0.0588397	−	0.371500i
$959$	−11.0175	+	33.9085i	−0.355775	+	1.09496i
$960$		0			0
$961$	7.15266	+	22.0136i	0.230731	+	0.710117i
$962$	−34.4295	+	17.5427i	−1.11005	+	0.565600i
$963$	−3.89455	−	6.42766i	−0.125500	−	0.207128i
$964$	22.3583	−	7.26464i	0.720111	−	0.233978i
$965$		0			0
$966$	−38.7022	−	11.0203i	−1.24522	−	0.354572i
$967$	5.27370	−	0.835271i	0.169591	−	0.0268605i	−0.0710616	−	0.997472i	$-0.522639\pi$
$967$	5.27370	−	0.835271i	0.169591	−	0.0268605i	0.240652	+	0.970611i	$0.422639\pi$
$968$	−6.11819	+	6.11819i	−0.196646	+	0.196646i
$969$	10.8009	−	16.0770i	0.346975	−	0.516469i
$970$		0			0
$971$	33.9216	+	46.6890i	1.08859	+	1.49832i	0.849693	+	0.527278i	$0.176788\pi$
$971$	33.9216	+	46.6890i	1.08859	+	1.49832i	0.238902	+	0.971044i	$0.423212\pi$
$972$	15.5829	−	0.416147i	0.499822	−	0.0133479i
$973$	8.05524	−	15.8093i	0.258239	−	0.506823i
$974$	35.5211			1.13817
$975$		0			0
$976$	−5.77299			−0.184789
$977$	4.68324	−	9.19137i	0.149830	−	0.294058i	−0.803877	−	0.594796i	$-0.797233\pi$
$977$	4.68324	−	9.19137i	0.149830	−	0.294058i	0.953707	+	0.300738i	$0.0972329\pi$
$978$	−17.6797	−	2.13762i	−0.565334	−	0.0683534i
$979$	5.79785	+	7.98005i	0.185300	+	0.255043i
$980$		0			0
$981$	20.5368	+	12.7274i	0.655689	+	0.406356i
$982$	−2.36943	+	2.36943i	−0.0756116	+	0.0756116i
$983$	39.7879	−	6.30178i	1.26904	−	0.200996i	0.514635	−	0.857409i	$-0.327927\pi$
$983$	39.7879	−	6.30178i	1.26904	−	0.200996i	0.754401	+	0.656413i	$0.227927\pi$
$984$	1.42612	−	5.00840i	0.0454630	−	0.159662i
$985$		0			0
$986$	34.2432	−	11.1263i	1.09053	−	0.354333i
$987$	−8.77777	−	15.7667i	−0.279400	−	0.501859i
$988$	−9.72349	+	4.95436i	−0.309345	+	0.157619i
$989$	9.02525	+	27.7769i	0.286986	+	0.883253i
$990$		0			0
$991$	−7.61373	+	23.4326i	−0.241858	+	0.744362i	0.754279	+	0.656554i	$0.227986\pi$
$991$	−7.61373	+	23.4326i	−0.241858	+	0.744362i	−0.996137	+	0.0878088i	$0.972014\pi$
$992$	1.15111	+	7.26784i	0.0365478	+	0.230754i
$993$	19.5108	−	21.0005i	0.619158	−	0.666432i
$994$	−7.96619	+	10.9645i	−0.252672	+	0.347773i
$995$		0			0
$996$	−3.77201	+	2.95827i	−0.119521	+	0.0937362i
$997$	5.80306	−	36.6391i	0.183785	−	1.16037i	−0.707428	−	0.706785i	$-0.750145\pi$
$997$	5.80306	−	36.6391i	0.183785	−	1.16037i	0.891213	−	0.453585i	$-0.149855\pi$
$998$	2.28445	+	1.16399i	0.0723131	+	0.0368454i
$999$	39.6523	−	4.39015i	1.25454	−	0.138898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.143.3		80
3.2	odd	2	inner	750.2.l.c.143.9		80
5.2	odd	4		150.2.l.a.17.5	✓	80
5.3	odd	4		750.2.l.b.107.6		80
5.4	even	2		750.2.l.a.143.8		80
15.2	even	4		150.2.l.a.17.6	yes	80
15.8	even	4		750.2.l.b.107.5		80
15.14	odd	2		750.2.l.a.143.2		80
25.3	odd	20		750.2.l.a.257.2		80
25.4	even	10		750.2.l.b.743.5		80
25.21	even	5		150.2.l.a.53.6	yes	80
25.22	odd	20	inner	750.2.l.c.257.9		80
75.29	odd	10		750.2.l.b.743.6		80
75.47	even	20	inner	750.2.l.c.257.3		80
75.53	even	20		750.2.l.a.257.8		80
75.71	odd	10		150.2.l.a.53.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.5	✓	80	5.2	odd	4
150.2.l.a.17.6	yes	80	15.2	even	4
150.2.l.a.53.5	yes	80	75.71	odd	10
150.2.l.a.53.6	yes	80	25.21	even	5
750.2.l.a.143.2		80	15.14	odd	2
750.2.l.a.143.8		80	5.4	even	2
750.2.l.a.257.2		80	25.3	odd	20
750.2.l.a.257.8		80	75.53	even	20
750.2.l.b.107.5		80	15.8	even	4
750.2.l.b.107.6		80	5.3	odd	4
750.2.l.b.743.5		80	25.4	even	10
750.2.l.b.743.6		80	75.29	odd	10
750.2.l.c.143.3		80	1.1	even	1	trivial
750.2.l.c.143.9		80	3.2	odd	2	inner
750.2.l.c.257.3		80	75.47	even	20	inner
750.2.l.c.257.9		80	25.22	odd	20	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.207905 + 1.71953i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(2.58285 - 2.58285i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.91355 - 0.714995i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.207905 + 1.71953i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.43772 - 0.965894i) q^{6} +(2.58285 - 2.58285i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.91355 - 0.714995i) q^{9} +(-1.45719 + 0.473470i) q^{11} +(1.51333 - 0.842515i) q^{12} +(4.48435 - 2.28489i) q^{13} +(1.12875 + 3.47393i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.806752 - 5.09363i) q^{17} +(1.95979 - 2.27139i) q^{18} +(1.27450 - 1.75421i) q^{19} +(3.90430 + 4.97827i) q^{21} +(0.239686 - 1.51332i) q^{22} +(5.66723 + 2.88760i) q^{23} +(0.0636485 + 1.73088i) q^{24} +5.03290i q^{26} +(1.83520 - 4.86128i) q^{27} +(-3.60774 - 0.571409i) q^{28} +(5.64831 - 4.10373i) q^{29} +(-5.95310 - 4.32518i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.511188 - 2.60412i) q^{33} +(4.90472 + 1.59364i) q^{34} +(1.13410 + 2.77738i) q^{36} +(3.48561 + 6.84089i) q^{37} +(0.984395 + 1.93198i) q^{38} +(2.99661 + 8.18600i) q^{39} +(-2.85939 - 0.929072i) q^{41} +(-6.20819 + 1.21867i) q^{42} +(3.24693 + 3.24693i) q^{43} +(1.23956 + 0.900593i) q^{44} +(-5.14573 + 3.73859i) q^{46} +(-2.81716 - 0.446195i) q^{47} +(-1.57112 - 0.729092i) q^{48} -6.34226i q^{49} +(8.92637 - 0.328243i) q^{51} +(-4.48435 - 2.28489i) q^{52} +(-0.161639 + 1.02055i) q^{53} +(3.49827 + 3.84215i) q^{54} +(2.14701 - 2.95510i) q^{56} +(2.75143 + 2.55625i) q^{57} +(1.09218 + 6.89573i) q^{58} +(-2.10801 + 6.48779i) q^{59} +(1.78395 + 5.49044i) q^{61} +(6.55641 - 3.34066i) q^{62} +(-9.37200 + 5.67855i) q^{63} +(0.951057 - 0.309017i) q^{64} +(2.55236 + 0.726772i) q^{66} +(-3.33029 + 0.527466i) q^{67} +(-3.64664 + 3.64664i) q^{68} +(-6.14354 + 9.14461i) q^{69} +(2.18090 + 3.00175i) q^{71} +(-2.98953 - 0.250413i) q^{72} +(0.270757 - 0.531390i) q^{73} -7.67771 q^{74} -2.16832 q^{76} +(-2.54081 + 4.98661i) q^{77} +(-8.65421 - 1.04636i) q^{78} +(0.782199 + 1.07660i) q^{79} +(7.97756 + 4.16635i) q^{81} +(2.12595 - 2.12595i) q^{82} +(-2.73356 + 0.432953i) q^{83} +(1.73262 - 6.08480i) q^{84} +(-4.36710 + 1.41896i) q^{86} +(5.88218 + 10.5656i) q^{87} +(-1.36518 + 0.695596i) q^{88} +(-1.98939 - 6.12272i) q^{89} +(5.68088 - 17.4839i) q^{91} +(-0.994998 - 6.28217i) q^{92} +(8.67494 - 9.33729i) q^{93} +(1.67653 - 2.30754i) q^{94} +(1.36290 - 1.06888i) q^{96} +(2.14067 - 13.5156i) q^{97} +(5.65100 + 2.87933i) q^{98} +(4.58413 - 0.337594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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