LMFDB - Embedded newform 261.2.x.a.56.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$261 = 3^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	261.x (of order $84$ , degree $24$ , 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			56.26
Character	$\chi$	$=$	261.56
Dual form			261.2.x.a.14.26

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39950 - 1.89625i) q^{2} +(0.796871 + 1.53785i) q^{3} +(-1.04767 - 3.39645i) q^{4} +(1.30581 - 3.32715i) q^{5} +(4.03138 + 0.641157i) q^{6} +(-3.08282 - 0.950923i) q^{7} +(-3.45771 - 1.20991i) q^{8} +(-1.72999 + 2.45094i) q^{9} +(-4.48164 - 7.13249i) q^{10} +(-1.02242 + 5.40364i) q^{11} +(4.38840 - 4.31770i) q^{12} +(5.35389 - 0.401218i) q^{13} +(-6.11759 + 4.51498i) q^{14} +(6.15724 - 0.643162i) q^{15} +(-1.25983 + 0.858941i) q^{16} +(-0.320183 + 0.320183i) q^{17} +(2.22648 + 6.71059i) q^{18} +(-1.53180 + 0.962495i) q^{19} +(-12.6686 - 0.949379i) q^{20} +(-0.994225 - 5.49869i) q^{21} +(8.81579 + 9.50116i) q^{22} +(-0.344137 + 2.28320i) q^{23} +(-0.894689 - 6.28159i) q^{24} +(-5.69954 - 5.28840i) q^{25} +(6.73194 - 10.7138i) q^{26} +(-5.14778 - 0.707397i) q^{27} +11.4669i q^{28} +(5.20238 + 1.39113i) q^{29} +(7.39745 - 12.5758i) q^{30} +(3.98070 - 1.73676i) q^{31} +(0.139581 - 3.73039i) q^{32} +(-9.12476 + 2.73366i) q^{33} +(0.159052 + 1.05524i) q^{34} +(-7.18944 + 9.01528i) q^{35} +(10.1370 + 3.30808i) q^{36} +(-1.06614 + 3.04685i) q^{37} +(-0.318620 + 4.25169i) q^{38} +(4.88337 + 7.91378i) q^{39} +(-8.54066 + 9.92442i) q^{40} +(0.205283 - 0.766126i) q^{41} +(-11.8183 - 5.81010i) q^{42} +(-2.22810 + 5.10686i) q^{43} +(19.4244 - 2.18860i) q^{44} +(5.89561 + 8.95642i) q^{45} +(3.84791 + 3.84791i) q^{46} +(-10.4791 - 1.98276i) q^{47} +(-2.32485 - 1.25298i) q^{48} +(2.81584 + 1.91980i) q^{49} +(-18.0046 + 3.40666i) q^{50} +(-0.747540 - 0.237251i) q^{51} +(-6.97181 - 17.7639i) q^{52} +(-5.65175 + 4.50712i) q^{53} +(-8.54570 + 8.77148i) q^{54} +(16.6436 + 10.4579i) q^{55} +(9.50896 + 7.01793i) q^{56} +(-2.70082 - 1.58870i) q^{57} +(9.91866 - 7.91813i) q^{58} +(-2.18960 + 1.26417i) q^{59} +(-8.63521 - 20.2390i) q^{60} +(-1.47034 - 2.78201i) q^{61} +(2.27764 - 9.97900i) q^{62} +(7.66391 - 5.91072i) q^{63} +(-9.26266 - 7.38673i) q^{64} +(5.65625 - 18.3371i) q^{65} +(-7.58636 + 21.1286i) q^{66} +(1.75020 - 2.56707i) q^{67} +(1.42293 + 0.752043i) q^{68} +(-3.78547 + 1.29018i) q^{69} +(7.03363 + 26.2499i) q^{70} +(-6.93040 - 3.33751i) q^{71} +(8.94723 - 6.38152i) q^{72} +(-0.346814 - 3.07806i) q^{73} +(4.28554 + 6.28573i) q^{74} +(3.59100 - 12.9792i) q^{75} +(4.87389 + 4.19432i) q^{76} +(8.29040 - 15.6862i) q^{77} +(21.8408 + 1.81522i) q^{78} +(6.16533 - 5.30570i) q^{79} +(1.21272 + 5.31328i) q^{80} +(-3.01424 - 8.48023i) q^{81} +(-1.16547 - 1.46146i) q^{82} +(-9.35166 + 10.0787i) q^{83} +(-17.6344 + 9.13764i) q^{84} +(0.647200 + 1.48340i) q^{85} +(6.56567 + 11.3721i) q^{86} +(2.00626 + 9.10906i) q^{87} +(10.0731 - 17.4472i) q^{88} +(6.94131 + 0.782098i) q^{89} +(25.2345 + 1.35493i) q^{90} +(-16.8866 - 3.85425i) q^{91} +(8.11533 - 1.22319i) q^{92} +(5.84298 + 4.73776i) q^{93} +(-18.4253 + 17.0962i) q^{94} +(1.20212 + 6.35337i) q^{95} +(5.84803 - 2.75798i) q^{96} +(8.25739 - 0.308970i) q^{97} +(7.58119 - 2.65277i) q^{98} +(-11.4752 - 11.8542i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100})$ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$ .

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.39950	−	1.89625i	0.989594	−	1.34085i	0.0499307	−	0.998753i	$-0.484100\pi$
$2$	1.39950	−	1.89625i	0.989594	−	1.34085i	0.939664	−	0.342100i	$-0.111138\pi$
$3$	0.796871	+	1.53785i	0.460073	+	0.887881i
$3$	0.796871	+	1.53785i	0.460073	+	0.887881i
$4$	−1.04767	−	3.39645i	−0.523834	−	1.69823i
$5$	1.30581	−	3.32715i	0.583976	−	1.48795i	−0.267502	−	0.963557i	$-0.586198\pi$
$5$	1.30581	−	3.32715i	0.583976	−	1.48795i	0.851478	−	0.524390i	$-0.175707\pi$
$6$	4.03138	+	0.641157i	1.64580	+	0.261751i
$7$	−3.08282	−	0.950923i	−1.16520	−	0.359415i	−0.348962	−	0.937137i	$-0.613466\pi$
$7$	−3.08282	−	0.950923i	−1.16520	−	0.359415i	−0.816234	+	0.577722i	$0.803942\pi$
$8$	−3.45771	−	1.20991i	−1.22249	−	0.427766i
$9$	−1.72999	+	2.45094i	−0.576665	+	0.816981i
$10$	−4.48164	−	7.13249i	−1.41722	−	2.25549i
$11$	−1.02242	+	5.40364i	−0.308273	+	1.62926i	0.395241	+	0.918578i	$0.370661\pi$
$11$	−1.02242	+	5.40364i	−0.308273	+	1.62926i	−0.703513	+	0.710682i	$0.748387\pi$
$12$	4.38840	−	4.31770i	1.26682	−	1.24641i
$13$	5.35389	−	0.401218i	1.48490	−	0.111278i	0.692562	−	0.721359i	$-0.256482\pi$
$13$	5.35389	−	0.401218i	1.48490	−	0.111278i	0.792339	+	0.610081i	$0.208863\pi$
$14$	−6.11759	+	4.51498i	−1.63499	+	1.20668i
$15$	6.15724	−	0.643162i	1.58979	−	0.166064i
$16$	−1.25983	+	0.858941i	−0.314959	+	0.214735i
$17$	−0.320183	+	0.320183i	−0.0776559	+	0.0776559i	−0.744868	−	0.667212i	$-0.767488\pi$
$17$	−0.320183	+	0.320183i	−0.0776559	+	0.0776559i	0.667212	+	0.744868i	$0.267488\pi$
$18$	2.22648	+	6.71059i	0.524787	+	1.58170i
$19$	−1.53180	+	0.962495i	−0.351419	+	0.220811i	−0.696160	−	0.717886i	$-0.745110\pi$
$19$	−1.53180	+	0.962495i	−0.351419	+	0.220811i	0.344741	+	0.938698i	$0.387967\pi$
$20$	−12.6686	−	0.949379i	−2.83278	−	0.212288i
$21$	−0.994225	−	5.49869i	−0.216958	−	1.19991i
$22$	8.81579	+	9.50116i	1.87953	+	2.02565i
$23$	−0.344137	+	2.28320i	−0.0717576	+	0.476080i	0.923873	+	0.382700i	$0.125006\pi$
$23$	−0.344137	+	2.28320i	−0.0717576	+	0.476080i	−0.995630	+	0.0933809i	$0.970233\pi$
$24$	−0.894689	−	6.28159i	−0.182628	−	1.28223i
$25$	−5.69954	−	5.28840i	−1.13991	−	1.05768i
$26$	6.73194	−	10.7138i	1.32024	−	2.10115i
$27$	−5.14778	−	0.707397i	−0.990690	−	0.136139i
$28$			11.4669i			2.16704i
$29$	5.20238	+	1.39113i	0.966058	+	0.258327i
$29$	5.20238	+	1.39113i	0.966058	+	0.258327i
$30$	7.39745	−	12.5758i	1.35058	−	2.29601i
$31$	3.98070	−	1.73676i	0.714954	−	0.311931i	−0.0107461	−	0.999942i	$-0.503421\pi$
$31$	3.98070	−	1.73676i	0.714954	−	0.311931i	0.725700	+	0.688011i	$0.241516\pi$
$32$	0.139581	−	3.73039i	0.0246747	−	0.659446i
$33$	−9.12476	+	2.73366i	−1.58842	+	0.475870i
$34$	0.159052	+	1.05524i	0.0272773	+	0.180973i
$35$	−7.18944	+	9.01528i	−1.21524	+	1.52386i
$36$	10.1370	+	3.30808i	1.68950	+	0.551346i
$37$	−1.06614	+	3.04685i	−0.175272	+	0.500899i	−0.997686	−	0.0679905i	$-0.978341\pi$
$37$	−1.06614	+	3.04685i	−0.175272	+	0.500899i	0.822414	+	0.568890i	$0.192627\pi$
$38$	−0.318620	+	4.25169i	−0.0516870	+	0.689715i
$39$	4.88337	+	7.91378i	0.781965	+	1.26722i
$40$	−8.54066	+	9.92442i	−1.35040	+	1.56919i
$41$	0.205283	−	0.766126i	0.0320598	−	0.119649i	−0.948042	−	0.318147i	$-0.896940\pi$
$41$	0.205283	−	0.766126i	0.0320598	−	0.119649i	0.980101	+	0.198498i	$0.0636063\pi$
$42$	−11.8183	−	5.81010i	−1.82361	−	0.896518i
$43$	−2.22810	+	5.10686i	−0.339782	+	0.778789i	0.659843	+	0.751404i	$0.270623\pi$
$43$	−2.22810	+	5.10686i	−0.339782	+	0.778789i	−0.999625	+	0.0273852i	$0.991282\pi$
$44$	19.4244	−	2.18860i	2.92834	−	0.329944i
$45$	5.89561	+	8.95642i	0.878866	+	1.33514i
$46$	3.84791	+	3.84791i	0.567343	+	0.567343i
$47$	−10.4791	−	1.98276i	−1.52854	−	0.289215i	−0.647427	−	0.762127i	$-0.724155\pi$
$47$	−10.4791	−	1.98276i	−1.52854	−	0.289215i	−0.881109	+	0.472913i	$0.843203\pi$
$48$	−2.32485	−	1.25298i	−0.335563	−	0.180852i
$49$	2.81584	+	1.91980i	0.402262	+	0.274258i
$50$	−18.0046	+	3.40666i	−2.54624	+	0.481775i
$51$	−0.747540	−	0.237251i	−0.104677	−	0.0332218i
$52$	−6.97181	−	17.7639i	−0.966817	−	2.46341i
$53$	−5.65175	+	4.50712i	−0.776327	+	0.619100i	−0.929383	−	0.369117i	$-0.879660\pi$
$53$	−5.65175	+	4.50712i	−0.776327	+	0.619100i	0.153055	+	0.988218i	$0.451089\pi$
$54$	−8.54570	+	8.77148i	−1.16292	+	1.19365i
$55$	16.6436	+	10.4579i	2.24423	+	1.41014i
$56$	9.50896	+	7.01793i	1.27069	+	0.937811i
$57$	−2.70082	−	1.58870i	−0.357733	−	0.210429i
$58$	9.91866	−	7.91813i	1.30238	−	1.03970i
$59$	−2.18960	+	1.26417i	−0.285062	+	0.164580i	−0.635713	−	0.771926i	$-0.719294\pi$
$59$	−2.18960	+	1.26417i	−0.285062	+	0.164580i	0.350651	+	0.936506i	$0.385960\pi$
$60$	−8.63521	−	20.2390i	−1.11480	−	2.61284i
$61$	−1.47034	−	2.78201i	−0.188257	−	0.356200i	0.771862	−	0.635790i	$-0.219325\pi$
$61$	−1.47034	−	2.78201i	−0.188257	−	0.356200i	−0.960120	+	0.279590i	$0.909802\pi$
$62$	2.27764	−	9.97900i	0.289261	−	1.26733i
$63$	7.66391	−	5.91072i	0.965563	−	0.744680i
$64$	−9.26266	−	7.38673i	−1.15783	−	0.923341i
$65$	5.65625	−	18.3371i	0.701571	−	2.27444i
$66$	−7.58636	+	21.1286i	−0.933817	+	2.60075i
$67$	1.75020	−	2.56707i	0.213820	−	0.313617i	−0.704312	−	0.709891i	$-0.748744\pi$
$67$	1.75020	−	2.56707i	0.213820	−	0.313617i	0.918133	+	0.396273i	$0.129697\pi$
$68$	1.42293	+	0.752043i	0.172556	+	0.0911986i
$69$	−3.78547	+	1.29018i	−0.455716	+	0.155320i
$70$	7.03363	+	26.2499i	0.840679	+	3.13746i
$71$	−6.93040	−	3.33751i	−0.822488	−	0.396089i	−0.0251953	−	0.999683i	$-0.508021\pi$
$71$	−6.93040	−	3.33751i	−0.822488	−	0.396089i	−0.797292	+	0.603593i	$0.793735\pi$
$72$	8.94723	−	6.38152i	1.05444	−	0.752069i
$73$	−0.346814	−	3.07806i	−0.0405915	−	0.360259i	−0.997546	−	0.0700200i	$-0.977694\pi$
$73$	−0.346814	−	3.07806i	−0.0405915	−	0.360259i	0.956954	−	0.290239i	$-0.0937349\pi$
$74$	4.28554	+	6.28573i	0.498184	+	0.730702i
$75$	3.59100	−	12.9792i	0.414653	−	1.49871i
$76$	4.87389	+	4.19432i	0.559073	+	0.481122i
$77$	8.29040	−	15.6862i	0.944778	−	1.78761i
$78$	21.8408	+	1.81522i	2.47298	+	0.205533i
$79$	6.16533	−	5.30570i	0.693654	−	0.596938i	−0.233169	−	0.972436i	$-0.574909\pi$
$79$	6.16533	−	5.30570i	0.693654	−	0.596938i	0.926823	+	0.375499i	$0.122529\pi$
$80$	1.21272	+	5.31328i	0.135586	+	0.594042i
$81$	−3.01424	−	8.48023i	−0.334915	−	0.942248i
$82$	−1.16547	−	1.46146i	−0.128705	−	0.161391i
$83$	−9.35166	+	10.0787i	−1.02648	+	1.10628i	−0.0321977	+	0.999482i	$0.510251\pi$
$83$	−9.35166	+	10.0787i	−1.02648	+	1.10628i	−0.994281	+	0.106799i	$0.965940\pi$
$84$	−17.6344	+	9.13764i	−1.92407	+	0.996998i
$85$	0.647200	+	1.48340i	0.0701987	+	0.160897i
$86$	6.56567	+	11.3721i	0.707995	+	1.22628i
$87$	2.00626	+	9.10906i	0.215094	+	0.976593i
$88$	10.0731	−	17.4472i	1.07380	−	1.85988i
$89$	6.94131	+	0.782098i	0.735777	+	0.0829022i	0.471898	−	0.881653i	$-0.343569\pi$
$89$	6.94131	+	0.782098i	0.735777	+	0.0829022i	0.263880	+	0.964556i	$0.414998\pi$
$90$	25.2345	+	1.35493i	2.65995	+	0.142822i
$91$	−16.8866	−	3.85425i	−1.77019	−	0.404035i
$92$	8.11533	−	1.22319i	0.846082	−	0.127526i
$93$	5.84298	+	4.73776i	0.605889	+	0.491283i
$94$	−18.4253	+	17.0962i	−1.90042	+	1.76334i
$95$	1.20212	+	6.35337i	0.123335	+	0.651842i
$96$	5.84803	−	2.75798i	0.596862	−	0.281485i
$97$	8.25739	−	0.308970i	0.838411	−	0.0313711i	0.385263	−	0.922807i	$-0.374111\pi$
$97$	8.25739	−	0.308970i	0.838411	−	0.0313711i	0.453148	+	0.891436i	$0.350301\pi$
$98$	7.58119	−	2.65277i	0.765816	−	0.267970i
$99$	−11.4752	−	11.8542i	−1.15330	−	1.19139i
$100$	−11.9906	+	24.8987i	−1.19906	+	2.48987i
$101$	3.92107	+	1.71075i	0.390161	+	0.170226i	0.585810	−	0.810448i	$-0.300776\pi$
$101$	3.92107	+	1.71075i	0.390161	+	0.170226i	−0.195649	+	0.980674i	$0.562681\pi$
$102$	−1.49607	+	1.08549i	−0.148133	+	0.107480i
$103$	−0.681015	−	9.08751i	−0.0671024	−	0.895419i	−0.924602	−	0.380934i	$-0.875602\pi$
$103$	−0.681015	−	9.08751i	−0.0671024	−	0.895419i	0.857500	−	0.514485i	$-0.172017\pi$
$104$	−18.9976	−	5.09040i	−1.86287	−	0.499155i
$105$	−19.5932	−	3.87231i	−1.91210	−	0.377899i
$106$	0.637025	+	17.0248i	0.0618733	+	1.65360i
$107$	−6.62628	−	13.7596i	−0.640587	−	1.33019i	−0.928070	−	0.372407i	$-0.878533\pi$
$107$	−6.62628	−	13.7596i	−0.640587	−	1.33019i	0.287483	−	0.957786i	$-0.407182\pi$
$108$	2.99052	+	18.2253i	0.287763	+	1.75373i
$109$	−1.68836	+	0.385357i	−0.161716	+	0.0369106i	−0.302612	−	0.953114i	$-0.597859\pi$
$109$	−1.68836	+	0.385357i	−0.161716	+	0.0369106i	0.140896	+	0.990024i	$0.455002\pi$
$110$	43.1236	−	16.9247i	4.11167	−	1.61371i
$111$	−5.53519	+	0.788379i	−0.525377	+	0.0748296i
$112$	4.70063	−	1.44995i	0.444167	−	0.137007i
$113$	1.02858	+	0.0384869i	0.0967611	+	0.00362054i	0.0857279	−	0.996319i	$-0.472678\pi$
$113$	1.02858	+	0.0384869i	0.0967611	+	0.00362054i	0.0110332	+	0.999939i	$0.496488\pi$
$114$	−6.79238	+	2.89806i	−0.636165	+	0.271428i
$115$	7.14718	+	4.12643i	0.666478	+	0.384791i
$116$	−0.725442	−	19.1271i	−0.0673556	−	1.77591i
$117$	−8.27883	+	13.8162i	−0.765378	+	1.27731i
$118$	−0.667162	+	5.92123i	−0.0614173	+	0.545093i
$119$	1.29154	−	0.682597i	0.118395	−	0.0625736i
$120$	−22.0681	−	5.22581i	−2.01453	−	0.477049i
$121$	−17.9144	−	7.03088i	−1.62858	−	0.639171i
$122$	−7.33313	−	1.10529i	−0.663910	−	0.100068i
$123$	1.34177	−	0.294808i	0.120984	−	0.0265819i
$124$	−10.0693	−	11.7007i	−0.904247	−	1.05075i
$125$	−8.93651	+	4.30360i	−0.799306	+	0.384925i
$126$	−0.482575	−	22.8047i	−0.0429912	−	2.03161i
$127$	−2.19137	−	6.26259i	−0.194453	−	0.555715i	0.804833	−	0.593502i	$-0.202255\pi$
$127$	−2.19137	−	6.26259i	−0.194453	−	0.555715i	−0.999286	+	0.0377868i	$0.987969\pi$
$128$	−19.7586	+	5.29429i	−1.74643	+	0.467954i
$129$	−9.62912	+	0.643012i	−0.847796	+	0.0566140i
$130$	−26.8559	−	36.3884i	−2.35542	−	3.19148i
$131$	1.55094	+	2.10145i	0.135506	+	0.183605i	0.867097	−	0.498140i	$-0.165983\pi$
$131$	1.55094	+	2.10145i	0.135506	+	0.183605i	−0.731590	+	0.681745i	$0.761222\pi$
$132$	18.8445	+	28.1279i	1.64020	+	2.44822i
$133$	5.63752	−	1.51057i	0.488835	−	0.130983i
$134$	−2.41841	−	6.91142i	−0.208919	−	0.597055i
$135$	−9.07564	+	16.2037i	−0.781107	+	1.39459i
$136$	1.49449	−	0.719710i	0.128152	−	0.0617146i
$137$	4.48317	+	5.20953i	0.383023	+	0.445080i	0.916078	−	0.401000i	$-0.131337\pi$
$137$	4.48317	+	5.20953i	0.383023	+	0.445080i	−0.533055	+	0.846080i	$0.678956\pi$
$138$	−2.85124	+	8.98380i	−0.242713	+	0.764752i
$139$	11.5421	+	1.73969i	0.978989	+	0.147559i	0.618994	−	0.785395i	$-0.287540\pi$
$139$	11.5421	+	1.73969i	0.978989	+	0.147559i	0.359995	+	0.932954i	$0.382778\pi$
$140$	38.1521	+	14.9736i	3.22444	+	1.26550i
$141$	−5.30131	−	17.6954i	−0.446451	−	1.49022i
$142$	−16.0278	+	8.47096i	−1.34503	+	0.710867i
$143$	−3.30590	+	29.3407i	−0.276454	+	2.45359i
$144$	0.0742929	−	4.57374i	0.00619108	−	0.381145i
$145$	11.4218	−	15.4925i	0.948532	−	1.28659i
$146$	−6.32213	−	3.65009i	−0.523224	−	0.302083i
$147$	−0.708523	+	5.86018i	−0.0584380	+	0.483340i
$148$	11.4655	+	0.429007i	0.942455	+	0.0352642i
$149$	−20.0066	+	6.17122i	−1.63900	+	0.505566i	−0.971098	−	0.238679i	$-0.923285\pi$
$149$	−20.0066	+	6.17122i	−1.63900	+	0.505566i	−0.667906	+	0.744245i	$0.732809\pi$
$150$	−19.5863	−	24.9738i	−1.59922	−	2.03911i
$151$	5.58657	−	2.19257i	0.454629	−	0.178429i	−0.126966	−	0.991907i	$-0.540524\pi$
$151$	5.58657	−	2.19257i	0.454629	−	0.178429i	0.581595	+	0.813478i	$0.302429\pi$
$152$	6.46105	−	1.47469i	0.524061	−	0.119613i
$153$	−0.230836	−	1.33867i	−0.0186619	−	0.108225i
$154$	−18.1426	−	37.6735i	−1.46197	−	3.03581i
$155$	−0.580428	−	15.5123i	−0.0466211	−	1.24598i
$156$	21.7627	−	24.8772i	1.74241	−	1.99177i
$157$	10.4337	+	2.79570i	0.832700	+	0.223121i	0.649891	−	0.760027i	$-0.274814\pi$
$157$	10.4337	+	2.79570i	0.832700	+	0.223121i	0.182809	+	0.983148i	$0.441481\pi$
$158$	−1.43257	−	19.1163i	−0.113969	−	1.52081i
$159$	−11.4350	−	5.09998i	−0.906855	−	0.404455i
$160$	−12.2293	−	5.33559i	−0.966812	−	0.421816i
$161$	3.23206	−	6.71145i	0.254722	−	0.528936i
$162$	−20.2991	−	6.15231i	−1.59485	−	0.483371i
$163$	13.8854	−	4.85870i	1.08759	−	0.380563i	0.273835	−	0.961777i	$-0.411708\pi$
$163$	13.8854	−	4.85870i	1.08759	−	0.380563i	0.813751	+	0.581214i	$0.197422\pi$
$164$	−2.81718	+	0.105411i	−0.219985	+	0.00823125i
$165$	−2.81989	+	33.9291i	−0.219528	+	2.64138i
$166$	6.02412	+	31.8382i	0.467562	+	2.47112i
$167$	6.10084	−	5.66075i	0.472097	−	0.438042i	−0.407896	−	0.913028i	$-0.633737\pi$
$167$	6.10084	−	5.66075i	0.472097	−	0.438042i	0.879993	+	0.474986i	$0.157547\pi$
$168$	−3.21515	+	20.2158i	−0.248054	+	1.55968i
$169$	15.6483	−	2.35861i	1.20372	−	0.181431i
$170$	3.71865	+	0.848758i	0.285208	+	0.0650968i
$171$	0.290989	−	5.41947i	0.0222525	−	0.414437i
$172$	19.6795	+	2.21735i	1.50055	+	0.169071i
$173$	−3.50229	+	6.06614i	−0.266274	+	0.461200i	−0.967897	−	0.251349i	$-0.919126\pi$
$173$	−3.50229	+	6.06614i	−0.266274	+	0.461200i	0.701623	+	0.712549i	$0.252459\pi$
$174$	20.0808	+	8.94373i	1.52232	+	0.678022i
$175$	12.5418	+	21.7230i	0.948069	+	1.64210i
$176$	−3.35332	−	7.68590i	−0.252766	−	0.579346i
$177$	−3.68893	−	2.35991i	−0.277277	−	0.177382i
$178$	11.1974	−	12.0679i	0.839281	−	0.904529i
$179$	11.3960	+	14.2901i	0.851776	+	1.06809i	0.996900	+	0.0786804i	$0.0250707\pi$
$179$	11.3960	+	14.2901i	0.851776	+	1.06809i	−0.145123	+	0.989414i	$0.546358\pi$
$180$	24.2434	−	29.4075i	1.80700	−	2.19191i
$181$	4.89992	+	21.4679i	0.364208	+	1.59570i	0.742390	+	0.669968i	$0.233692\pi$
$181$	4.89992	+	21.4679i	0.364208	+	1.59570i	−0.378182	+	0.925731i	$0.623450\pi$
$182$	−30.9414	+	26.6272i	−2.29353	+	1.97374i
$183$	3.10666	−	4.47807i	0.229651	−	0.331028i
$184$	3.95238	−	7.47828i	0.291374	−	0.551306i
$185$	8.74516	+	7.52582i	0.642957	+	0.553310i
$186$	17.1612	−	4.44929i	1.25832	−	0.326238i
$187$	−1.40279	−	2.05752i	−0.102582	−	0.150461i
$188$	4.24429	+	37.6691i	0.309547	+	2.74730i
$189$	15.1970	+	7.07591i	1.10542	+	0.514697i
$190$	13.7300	+	6.61200i	0.996076	+	0.479685i
$191$	2.87790	+	10.7405i	0.208237	+	0.777153i	0.988438	+	0.151624i	$0.0484502\pi$
$191$	2.87790	+	10.7405i	0.208237	+	0.777153i	−0.780201	+	0.625529i	$0.784883\pi$
$192$	3.97857	−	20.1309i	0.287129	−	1.45282i
$193$	−12.2216	−	6.45930i	−0.879729	−	0.464950i	−0.0345309	−	0.999404i	$-0.510994\pi$
$193$	−12.2216	−	6.45930i	−0.879729	−	0.464950i	−0.845198	+	0.534453i	$0.820518\pi$
$194$	10.9703	−	16.0905i	0.787623	−	1.15523i
$195$	32.7071	−	5.91381i	2.34221	−	0.423497i
$196$	3.57047	−	11.5752i	0.255033	−	0.826798i
$197$	−11.8845	−	9.47755i	−0.846733	−	0.675247i	0.100799	−	0.994907i	$-0.467860\pi$
$197$	−11.8845	−	9.47755i	−0.846733	−	0.675247i	−0.947533	+	0.319659i	$0.896432\pi$
$198$	−38.5381	+	5.17003i	−2.73878	+	0.367418i
$199$	4.35430	−	19.0774i	0.308668	−	1.35236i	−0.547992	−	0.836484i	$-0.684608\pi$
$199$	4.35430	−	19.0774i	0.308668	−	1.35236i	0.856660	−	0.515881i	$-0.172535\pi$
$200$	13.3089	+	25.1817i	0.941081	+	1.78061i
$201$	5.34245	+	0.645928i	0.376828	+	0.0455602i
$202$	8.73154	−	5.04116i	0.614349	−	0.354695i
$203$	−14.7151	−	9.23567i	−1.03280	−	0.648217i
$204$	−0.0226381	+	2.78755i	−0.00158498	+	0.195167i
$205$	−2.28096	−	1.68342i	−0.159309	−	0.117575i
$206$	−18.1853	−	11.4266i	−1.26703	−	0.796127i
$207$	−5.00064	−	4.79339i	−0.347569	−	0.333163i
$208$	−6.40039	+	5.10414i	−0.443787	+	0.353908i
$209$	−3.63483	−	9.26139i	−0.251426	−	0.640624i
$210$	−34.7636	+	31.7344i	−2.39891	+	2.18988i
$211$	−2.61102	+	0.494031i	−0.179750	+	0.0340105i	−0.275007	−	0.961442i	$-0.588680\pi$
$211$	−2.61102	+	0.494031i	−0.179750	+	0.0340105i	0.0952573	+	0.995453i	$0.469633\pi$
$212$	21.2294	+	14.4739i	1.45804	+	0.994075i
$213$	−0.390034	−	13.3175i	−0.0267247	−	0.912501i
$214$	−35.3652	−	6.69145i	−2.41751	−	0.457418i
$215$	14.0818	+	14.0818i	0.960372	+	0.960372i
$216$	16.9436	+	8.67429i	1.15287	+	0.590211i
$217$	−13.9233	+	1.56878i	−0.945174	+	0.106496i
$218$	−1.63212	+	3.74087i	−0.110541	+	0.253363i
$219$	4.45724	−	2.98616i	0.301192	−	0.201786i
$220$	18.0828	−	67.4858i	1.21914	−	4.54989i
$221$	−1.58576	+	1.84269i	−0.106670	+	0.123953i
$222$	−6.25152	+	11.5995i	−0.419575	+	0.778504i
$223$	1.82291	−	24.3251i	0.122071	−	1.62893i	−0.514347	−	0.857582i	$-0.671966\pi$
$223$	1.82291	−	24.3251i	0.122071	−	1.62893i	0.636418	−	0.771344i	$-0.280415\pi$
$224$	−3.97762	+	11.3674i	−0.265766	+	0.759515i
$225$	22.8217	−	4.82034i	1.52145	−	0.321356i
$226$	1.51248	−	1.89659i	0.100609	−	0.126159i
$227$	−2.17663	−	14.4410i	−0.144468	−	0.958483i	−0.937170	−	0.348873i	$-0.886564\pi$
$227$	−2.17663	−	14.4410i	−0.144468	−	0.958483i	0.792702	−	0.609609i	$-0.208674\pi$
$228$	−2.56640	+	10.8377i	−0.169964	+	0.717742i
$229$	0.690849	−	18.4633i	0.0456526	−	1.22009i	−0.768657	−	0.639661i	$-0.779075\pi$
$229$	0.690849	−	18.4633i	0.0456526	−	1.22009i	0.814310	−	0.580430i	$-0.197116\pi$
$230$	17.8272	−	7.77793i	1.17549	−	0.512862i
$231$	30.7295	+	0.249558i	2.02185	+	0.0164197i
$232$	−16.3052	−	11.1045i	−1.07049	−	0.729048i
$233$		−	12.3880i		−	0.811565i	−0.913970	−	0.405782i	$-0.866999\pi$
$233$		−	12.3880i		−	0.811565i	0.913970	−	0.405782i	$-0.133001\pi$
$234$	14.6127	+	35.0345i	0.955265	+	2.29027i
$235$	−20.2807	+	32.2765i	−1.32297	+	2.10549i
$236$	6.58765	+	6.11245i	0.428820	+	0.397887i
$237$	13.0724	+	5.25343i	0.849141	+	0.341247i
$238$	0.513127	−	3.40437i	0.0332611	−	0.220673i
$239$	5.86660	+	6.32269i	0.379479	+	0.408981i	0.893692	−	0.448682i	$-0.148106\pi$
$239$	5.86660	+	6.32269i	0.379479	+	0.408981i	−0.514213	+	0.857663i	$0.671916\pi$
$240$	−7.20466	+	6.09898i	−0.465059	+	0.393688i
$241$	−17.8973	−	1.34122i	−1.15287	−	0.0863955i	−0.515454	−	0.856917i	$-0.672377\pi$
$241$	−17.8973	−	1.34122i	−1.15287	−	0.0863955i	−0.637414	+	0.770522i	$0.719996\pi$
$242$	−38.4035	+	24.1305i	−2.46867	+	1.55117i
$243$	10.6394	−	11.3931i	0.682519	−	0.730868i
$244$	−7.90855	+	7.90855i	−0.506293	+	0.506293i
$245$	10.0644	−	6.86181i	0.642993	−	0.438385i
$246$	1.31878	−	2.95693i	0.0840823	−	0.188527i
$247$	−7.81492	+	5.76768i	−0.497252	+	0.366988i
$248$	−15.8654	+	1.18895i	−1.00745	+	0.0754983i
$249$	−22.9516	−	6.35008i	−1.45450	−	0.402420i
$250$	−4.34592	+	22.9687i	−0.274860	+	1.45267i
$251$	11.1519	+	17.7482i	0.703904	+	1.12026i	0.986931	+	0.161145i	$0.0515186\pi$
$251$	11.1519	+	17.7482i	0.703904	+	1.12026i	−0.283027	+	0.959112i	$0.591339\pi$
$252$	−28.1047	−	19.8377i	−1.77043	−	1.24966i
$253$	−11.9858	−	4.19400i	−0.753538	−	0.263674i
$254$	−14.9423	−	4.60908i	−0.937561	−	0.289199i
$255$	−1.76552	+	2.17738i	−0.110561	+	0.136353i
$256$	−8.95608	+	22.8197i	−0.559755	+	1.42623i
$257$	8.65637	+	28.0633i	0.539970	+	1.75054i	0.653420	+	0.756995i	$0.273333\pi$
$257$	8.65637	+	28.0633i	0.539970	+	1.75054i	−0.113451	+	0.993544i	$0.536190\pi$
$258$	−12.2566	+	19.1591i	−0.763063	+	1.19279i
$259$	6.18404	−	8.37907i	0.384257	−	0.520650i
$260$	−68.2070			−4.23002
$261$	−12.4097	+	10.3441i	−0.768140	+	0.640282i
$262$	6.15542			0.380283
$263$	5.48122	−	7.42679i	0.337987	−	0.457956i	−0.602335	−	0.798244i	$-0.705763\pi$
$263$	5.48122	−	7.42679i	0.337987	−	0.457956i	0.940321	+	0.340288i	$0.110525\pi$
$264$	34.8582	+	1.58787i	2.14538	+	0.0977269i
$265$	7.61576	+	24.6897i	0.467832	+	1.51667i
$266$	5.02528	−	12.8042i	0.308120	−	0.785076i
$267$	4.32857	+	11.2980i	0.264904	+	0.691424i
$268$	−10.5525	−	3.25503i	−0.644599	−	0.198833i
$269$	−9.55569	−	3.34368i	−0.582621	−	0.203868i	0.0228452	−	0.999739i	$-0.492728\pi$
$269$	−9.55569	−	3.34368i	−0.582621	−	0.203868i	−0.605466	+	0.795871i	$0.707013\pi$
$270$	18.0250	+	39.8867i	1.09697	+	2.42743i
$271$	−1.82205	−	2.89977i	−0.110681	−	0.176148i	0.786790	−	0.617220i	$-0.211741\pi$
$271$	−1.82205	−	2.89977i	−0.110681	−	0.176148i	−0.897472	+	0.441072i	$0.854598\pi$
$272$	0.128360	−	0.678397i	0.00778294	−	0.0411338i
$273$	−7.52914	−	29.0404i	−0.455684	−	1.75761i
$274$	16.1528	−	1.21048i	0.975824	−	0.0731279i
$275$	34.4040	−	25.3913i	2.07464	−	1.53115i
$276$	8.34796	+	11.5055i	0.502488	+	0.692548i
$277$	2.65502	−	1.81016i	0.159525	−	0.108762i	−0.480927	−	0.876761i	$-0.659700\pi$
$277$	2.65502	−	1.81016i	0.159525	−	0.108762i	0.640451	+	0.767999i	$0.278747\pi$
$278$	19.4521	−	19.4521i	1.16666	−	1.16666i
$279$	−2.62988	+	12.7610i	−0.157447	+	0.763984i
$280$	35.7666	−	22.4737i	2.13747	−	1.34306i
$281$	−0.890928	−	0.0667659i	−0.0531483	−	0.00398292i	0.0481294	−	0.998841i	$-0.484674\pi$
$281$	−0.890928	−	0.0667659i	−0.0531483	−	0.00398292i	−0.101278	+	0.994858i	$0.532293\pi$
$282$	−40.9740	−	14.7120i	−2.43997	−	0.876087i
$283$	3.07613	+	3.31528i	0.182857	+	0.197073i	0.817828	−	0.575463i	$-0.195178\pi$
$283$	3.07613	+	3.31528i	0.182857	+	0.197073i	−0.634971	+	0.772536i	$0.718988\pi$
$284$	−4.07493	+	27.0354i	−0.241803	+	1.60426i
$285$	−8.81263	+	6.91151i	−0.522015	+	0.409402i
$286$	51.0108	+	47.3311i	3.01633	+	2.79874i
$287$	−1.36138	+	2.16662i	−0.0803595	+	0.127891i
$288$	8.90150	+	6.79566i	0.524526	+	0.400438i
$289$			16.7950i			0.987939i
$290$	−13.3929	−	43.3405i	−0.786461	−	2.54504i
$291$	7.05522	+	12.4525i	0.413584	+	0.729976i
$292$	−10.0911	+	4.40272i	−0.590539	+	0.257649i
$293$	−0.339959	+	9.08559i	−0.0198606	+	0.530786i	0.953485	+	0.301441i	$0.0974678\pi$
$293$	−0.339959	+	9.08559i	−0.0198606	+	0.530786i	−0.973345	+	0.229345i	$0.926342\pi$
$294$	10.1208	+	9.54485i	0.590257	+	0.556667i
$295$	1.34687	+	8.93589i	0.0784177	+	0.520268i
$296$	7.37281	−	9.24521i	0.428536	−	0.537367i
$297$	9.08573	−	27.0935i	0.527207	−	1.57212i
$298$	−16.2970	+	46.5742i	−0.944060	+	2.69797i
$299$	−0.926410	+	12.3621i	−0.0535757	+	0.714917i
$300$	−47.8456	+	1.40127i	−2.76236	+	0.0809023i
$301$	11.7251	−	13.6248i	0.675821	−	0.785318i
$302$	3.66073	−	13.6620i	0.210651	−	0.786162i
$303$	0.493708	+	7.39328i	0.0283628	+	0.424733i
$304$	1.10309	−	2.52831i	0.0632666	−	0.145009i
$305$	−11.1762	+	1.25925i	−0.639945	+	0.0721045i
$306$	−2.86150	−	1.43574i	−0.163581	−	0.0820757i
$307$	8.49534	+	8.49534i	0.484855	+	0.484855i	0.906678	−	0.421823i	$-0.138610\pi$
$307$	8.49534	+	8.49534i	0.484855	+	0.484855i	−0.421823	+	0.906678i	$0.638610\pi$
$308$	−61.9630	−	11.7240i	−3.53067	−	0.668039i
$309$	13.4326	−	8.28887i	0.764153	−	0.471537i
$310$	−30.2275	−	20.6087i	−1.71680	−	1.17050i
$311$	29.0740	−	5.50109i	1.64863	−	0.311938i	0.723140	−	0.690702i	$-0.242698\pi$
$311$	29.0740	−	5.50109i	1.64863	−	0.311938i	0.925493	+	0.378764i	$0.123651\pi$
$312$	−7.31036	−	33.2720i	−0.413867	−	1.88366i
$313$	4.34476	+	11.0703i	0.245580	+	0.625728i	0.999512	−	0.0312242i	$-0.00994060\pi$
$313$	4.34476	+	11.0703i	0.245580	+	0.625728i	−0.753932	+	0.656952i	$0.771845\pi$
$314$	19.9033	−	15.8724i	1.12321	−	0.895729i
$315$	−9.65823	−	33.2173i	−0.544179	−	1.87158i
$316$	−24.4798	−	15.3817i	−1.37710	−	0.865286i
$317$	5.69034	+	4.19967i	0.319602	+	0.235877i	0.741791	−	0.670631i	$-0.233976\pi$
$317$	5.69034	+	4.19967i	0.319602	+	0.235877i	−0.422190	+	0.906507i	$0.638738\pi$
$318$	−25.6741	+	14.5462i	−1.43973	+	0.815713i
$319$	−12.8362	+	26.6895i	−0.718691	+	1.49432i
$320$	−36.6721	+	21.1726i	−2.05003	+	1.18359i
$321$	15.8800	−	21.1549i	0.886335	−	1.18075i
$322$	−8.20333	−	15.5215i	−0.457154	−	0.864977i
$323$	0.182283	−	0.798632i	0.0101425	−	0.0444371i
$324$	−25.6448	+	19.1222i	−1.42471	+	1.06234i
$325$	−32.6365	−	26.0267i	−1.81035	−	1.44370i
$326$	10.2192	−	33.1299i	0.565991	−	1.83490i
$327$	−1.93803	−	2.28937i	−0.107173	−	0.126603i
$328$	−1.63675	+	2.40067i	−0.0903743	+	0.132555i
$329$	30.4198	+	16.0773i	1.67710	+	0.886371i
$330$	60.3917	+	52.8309i	3.32445	+	2.90825i
$331$	2.58943	+	9.66389i	0.142328	+	0.531175i	0.999860	+	0.0167444i	$0.00533016\pi$
$331$	2.58943	+	9.66389i	0.142328	+	0.531175i	−0.857532	+	0.514431i	$0.828003\pi$
$332$	44.0293	+	21.2034i	2.41642	+	1.16369i
$333$	−5.62324	−	7.88409i	−0.308152	−	0.432045i
$334$	−2.19610	−	19.4909i	−0.120165	−	1.06650i
$335$	−6.25559	−	9.17527i	−0.341780	−	0.501299i
$336$	5.97560	+	6.07346i	0.325996	+	0.331334i
$337$	−10.2800	−	8.84667i	−0.559988	−	0.481909i	0.326157	−	0.945315i	$-0.394246\pi$
$337$	−10.2800	−	8.84667i	−0.559988	−	0.481909i	−0.886146	+	0.463406i	$0.846627\pi$
$338$	17.4273	−	32.9740i	0.947919	−	1.79355i
$339$	0.760461	+	1.61248i	0.0413026	+	0.0875780i
$340$	4.36024	−	3.75229i	0.236467	−	0.203497i
$341$	5.31487	+	23.2860i	0.287816	+	1.26101i
$342$	−9.86944	−	8.13632i	−0.533678	−	0.439962i
$343$	7.22516	+	9.06007i	0.390122	+	0.489198i
$344$	13.8829	−	14.9623i	0.748518	−	0.806711i
$345$	−0.650467	+	14.2796i	−0.0350200	+	0.768785i
$346$	6.60148	+	15.1308i	0.354898	+	0.813435i
$347$	−4.57695	−	7.92751i	−0.245704	−	0.425571i	0.716626	−	0.697458i	$-0.245686\pi$
$347$	−4.57695	−	7.92751i	−0.245704	−	0.425571i	−0.962329	+	0.271887i	$0.912352\pi$
$348$	28.8366	−	16.3574i	1.54580	−	0.876851i
$349$	−8.60261	+	14.9002i	−0.460487	+	0.797587i	−0.998985	−	0.0450398i	$-0.985659\pi$
$349$	−8.60261	+	14.9002i	−0.460487	+	0.797587i	0.538498	+	0.842627i	$0.318992\pi$
$350$	58.7445	+	6.61891i	3.14002	+	0.353796i
$351$	−27.8444	−	1.72194i	−1.48623	−	0.0919103i
$352$	20.0150	+	4.56829i	1.06680	+	0.243491i
$353$	−31.0071	+	4.67357i	−1.65034	+	0.248749i	−0.907297	−	0.420491i	$-0.861858\pi$
$353$	−31.0071	+	4.67357i	−1.65034	+	0.248749i	−0.743046	+	0.669240i	$0.766620\pi$
$354$	−9.63763	+	3.69245i	−0.512234	+	0.196252i
$355$	−20.1542	+	18.7004i	−1.06967	+	0.992512i
$356$	−4.61583	−	24.3952i	−0.244638	−	1.29294i
$357$	2.07892	+	1.44225i	0.110028	+	0.0763322i
$358$	43.0463	−	1.61068i	2.27507	−	0.0851271i
$359$	1.99775	−	0.699041i	0.105437	−	0.0368940i	−0.277045	−	0.960857i	$-0.589355\pi$
$359$	1.99775	−	0.699041i	0.105437	−	0.0368940i	0.382482	+	0.923963i	$0.375069\pi$
$360$	−9.54890	−	38.1019i	−0.503271	−	2.00814i
$361$	−6.82377	+	14.1697i	−0.359146	+	0.745774i
$362$	47.5661	+	20.7529i	2.50002	+	1.09075i
$363$	−3.46298	−	33.1524i	−0.181759	−	1.74005i
$364$	4.60073	+	61.3925i	0.241144	+	3.21784i
$365$	−10.6940	−	2.86546i	−0.559751	−	0.149985i
$366$	−4.14378	−	12.1581i	−0.216599	−	0.635512i
$367$	0.399110	+	10.6664i	0.0208334	+	0.556784i	0.970156	+	0.242481i	$0.0779612\pi$
$367$	0.399110	+	10.6664i	0.0208334	+	0.556784i	−0.949323	+	0.314303i	$0.898229\pi$
$368$	−1.52758	−	3.17205i	−0.0796305	−	0.165355i
$369$	1.52259	+	1.82853i	0.0792630	+	0.0951895i
$370$	26.5097	−	6.05066i	1.37817	−	0.314559i
$371$	21.7092	−	8.52025i	1.12709	−	0.442349i
$372$	9.97008	−	24.8090i	0.516925	−	1.28629i
$373$	−1.85764	+	0.573007i	−0.0961852	+	0.0296692i	−0.342474	−	0.939527i	$-0.611265\pi$
$373$	−1.85764	+	0.573007i	−0.0961852	+	0.0296692i	0.246289	+	0.969196i	$0.420789\pi$
$374$	−5.86478	−	0.219445i	−0.303261	−	0.0113472i
$375$	−13.7395	−	10.3136i	−0.709507	−	0.532594i
$376$	33.8348	+	19.5345i	1.74490	+	1.00742i
$377$	28.4111	+	5.36068i	1.46325	+	0.276089i
$378$	34.6858	−	18.9146i	1.78405	−	0.972860i
$379$	1.85518	−	16.4652i	0.0952941	−	0.845759i	−0.851595	−	0.524200i	$-0.824365\pi$
$379$	1.85518	−	16.4652i	0.0952941	−	0.845759i	0.946890	−	0.321559i	$-0.104207\pi$
$380$	20.3195	−	10.7392i	1.04237	−	0.550908i
$381$	7.88471	−	8.36049i	0.403946	−	0.428321i
$382$	24.3942	+	9.57403i	1.24812	+	0.489850i
$383$	−26.8320	−	4.04427i	−1.37105	−	0.206653i	−0.578113	−	0.815957i	$-0.696211\pi$
$383$	−26.8320	−	4.04427i	−1.37105	−	0.206653i	−0.792937	+	0.609304i	$0.791449\pi$
$384$	−23.8869	−	26.1669i	−1.21897	−	1.33533i
$385$	−41.3647	−	48.0666i	−2.10814	−	2.44970i
$386$	−29.3525	+	14.1354i	−1.49400	+	0.719475i
$387$	−8.66202	−	14.2958i	−0.440315	−	0.726696i
$388$	−9.70040	−	27.7222i	−0.492463	−	1.40738i
$389$	6.93927	−	1.85937i	0.351835	−	0.0942738i	−0.0785731	−	0.996908i	$-0.525036\pi$
$389$	6.93927	−	1.85937i	0.351835	−	0.0942738i	0.430408	+	0.902635i	$0.358370\pi$
$390$	34.5594	−	70.2973i	1.74999	−	3.55964i
$391$	−0.620856	−	0.841230i	−0.0313980	−	0.0425428i
$392$	−7.41356	−	10.0450i	−0.374441	−	0.507350i
$393$	−1.99583	+	4.05971i	−0.100676	+	0.204785i
$394$	−34.6041	+	9.27214i	−1.74333	+	0.467124i
$395$	−9.60210	−	27.4412i	−0.483134	−	1.38072i
$396$	−28.2399	+	51.3943i	−1.41911	+	2.58266i
$397$	32.9873	−	15.8858i	1.65558	−	0.797287i	0.656506	−	0.754320i	$-0.272033\pi$
$397$	32.9873	−	15.8858i	1.65558	−	0.797287i	0.999077	−	0.0429663i	$-0.0136808\pi$
$398$	−30.0818	−	34.9557i	−1.50787	−	1.75217i
$399$	6.81541	+	7.46596i	0.341197	+	0.373766i
$400$	11.7229	+	1.76694i	0.586145	+	0.0883471i
$401$	3.31870	+	1.30249i	0.165728	+	0.0650434i	0.446755	−	0.894657i	$-0.352580\pi$
$401$	3.31870	+	1.30249i	0.165728	+	0.0650434i	−0.281027	+	0.959700i	$0.590675\pi$
$402$	8.70159	−	9.22667i	0.433996	−	0.460184i
$403$	20.6154	−	10.8955i	1.02693	−	0.542746i
$404$	1.70249	−	15.1100i	0.0847022	−	0.751753i
$405$	−32.1511	−	1.04476i	−1.59760	−	0.0519144i
$406$	−38.1069	+	14.9783i	−1.89122	+	0.743359i
$407$	−15.3741	−	8.87621i	−0.762064	−	0.439978i
$408$	2.29773	+	1.72480i	0.113754	+	0.0853902i
$409$	10.8565	+	0.406222i	0.536819	+	0.0200864i	0.304427	−	0.952536i	$-0.401535\pi$
$409$	10.8565	+	0.406222i	0.536819	+	0.0200864i	0.232392	+	0.972622i	$0.425345\pi$
$410$	−6.38439	+	1.96932i	−0.315302	+	0.0972579i
$411$	−4.43900	+	11.0458i	−0.218960	+	0.544848i
$412$	−30.1518	+	11.8337i	−1.48547	+	0.583006i
$413$	7.95226	−	1.81505i	0.391305	−	0.0893128i
$414$	−16.0879	+	2.77414i	−0.790675	+	0.136342i
$415$	21.3218	+	44.2753i	1.04665	+	2.17339i
$416$	−0.749398	−	20.0281i	−0.0367423	−	0.981958i
$417$	6.52217	+	19.1364i	0.319392	+	0.937114i
$418$	−22.6489	−	6.06874i	−1.10779	−	0.296832i
$419$	2.11745	+	28.2555i	0.103444	+	1.38037i	0.771486	+	0.636246i	$0.219514\pi$
$419$	2.11745	+	28.2555i	0.103444	+	1.38037i	−0.668042	+	0.744124i	$0.732867\pi$
$420$	7.37507	+	70.6045i	0.359867	+	3.44514i
$421$	−28.3292	−	12.3599i	−1.38068	−	0.602385i	−0.427288	−	0.904116i	$-0.640531\pi$
$421$	−28.3292	−	12.3599i	−1.38068	−	0.602385i	−0.953393	+	0.301731i	$0.902436\pi$
$422$	−2.71731	+	5.64255i	−0.132276	+	0.274675i
$423$	22.9884	−	22.2536i	1.11774	−	1.08200i
$424$	24.9953	−	8.74623i	1.21388	−	0.424755i
$425$	3.51816	−	0.131640i	0.170656	−	0.00638548i
$426$	−25.7992	−	17.8982i	−1.24998	−	0.867172i
$427$	1.88730	+	9.97461i	0.0913328	+	0.482705i
$428$	−39.7918	+	36.9214i	−1.92341	+	1.78466i
$429$	−47.7561	+	18.2967i	−2.30569	+	0.883375i
$430$	46.4102	−	6.99521i	2.23810	−	0.337339i
$431$	−8.59567	−	1.96191i	−0.414039	−	0.0945017i	0.0104269	−	0.999946i	$-0.496681\pi$
$431$	−8.59567	−	1.96191i	−0.414039	−	0.0945017i	−0.424466	+	0.905444i	$0.639538\pi$
$432$	7.09296	−	3.53043i	0.341260	−	0.169858i
$433$	−8.08849	−	0.911354i	−0.388708	−	0.0437969i	−0.0845520	−	0.996419i	$-0.526946\pi$
$433$	−8.08849	−	0.911354i	−0.388708	−	0.0437969i	−0.304156	+	0.952622i	$0.598374\pi$
$434$	−16.5108	+	28.5976i	−0.792544	+	1.37273i
$435$	32.9270	+	5.21957i	1.57873	+	0.250259i
$436$	3.07769	+	5.33072i	0.147395	+	0.255295i
$437$	−1.67042	−	3.82864i	−0.0799070	−	0.183149i
$438$	0.575379	−	12.6312i	0.0274927	−	0.603541i
$439$	1.42310	−	1.53374i	0.0679210	−	0.0732014i	−0.698177	−	0.715925i	$-0.746005\pi$
$439$	1.42310	−	1.53374i	0.0679210	−	0.0732014i	0.766098	+	0.642724i	$0.222196\pi$
$440$	−44.8959	−	56.2976i	−2.14033	−	2.68388i
$441$	−9.57671	+	3.58020i	−0.456034	+	0.170486i
$442$	1.27493	+	5.58584i	0.0606423	+	0.265691i
$443$	21.3453	−	18.3691i	1.01414	−	0.872741i	0.0222425	−	0.999753i	$-0.492919\pi$
$443$	21.3453	−	18.3691i	1.01414	−	0.872741i	0.991901	+	0.127011i	$0.0405385\pi$
$444$	8.47673	+	17.9741i	0.402288	+	0.853012i
$445$	11.6662	−	22.0735i	0.553031	−	1.04639i
$446$	−43.5753	−	37.4996i	−2.06335	−	1.77566i
$447$	−25.4331	−	25.8496i	−1.20294	−	1.22264i
$448$	21.5309	+	31.5800i	1.01724	+	1.49202i
$449$	−3.60772	−	32.0194i	−0.170259	−	1.51109i	−0.730587	−	0.682820i	$-0.760753\pi$
$449$	−3.60772	−	32.0194i	−0.170259	−	1.51109i	0.560328	−	0.828271i	$-0.310675\pi$
$450$	22.7984	−	50.0218i	1.07473	−	2.35805i
$451$	3.92998	+	1.89258i	0.185056	+	0.0891181i
$452$	−0.946895	−	3.53386i	−0.0445382	−	0.166219i
$453$	7.82362	+	6.84414i	0.367586	+	0.321566i
$454$	−30.4300	−	16.0827i	−1.42815	−	0.754799i
$455$	−34.8744	+	51.1513i	−1.63494	+	2.39801i
$456$	7.41649	+	8.76102i	0.347309	+	0.410273i
$457$	−8.17865	+	26.5145i	−0.382581	+	1.24030i	0.535713	+	0.844400i	$0.320043\pi$
$457$	−8.17865	+	26.5145i	−0.382581	+	1.24030i	−0.918294	+	0.395898i	$0.870433\pi$
$458$	−34.0443	−	27.1494i	−1.59079	−	1.26861i
$459$	1.87473	−	1.42174i	0.0875048	−	0.0663609i
$460$	6.52735	−	28.5982i	0.304339	−	1.33340i
$461$	10.0363	+	18.9896i	0.467437	+	0.884434i	0.999293	+	0.0375994i	$0.0119711\pi$
$461$	10.0363	+	18.9896i	0.467437	+	0.884434i	−0.531856	+	0.846835i	$0.678505\pi$
$462$	43.4790	−	57.9215i	2.02283	−	2.69475i
$463$	32.3329	−	18.6674i	1.50264	−	0.867547i	0.502640	−	0.864496i	$-0.332362\pi$
$463$	32.3329	−	18.6674i	1.50264	−	0.867547i	0.999995	−	0.00305157i	$-0.000971346\pi$
$464$	−7.74904	+	2.71594i	−0.359740	+	0.126084i
$465$	23.3931	−	13.2539i	1.08483	−	0.614634i
$466$	−23.4908	−	17.3370i	−1.08819	−	0.803120i
$467$	26.8496	+	16.8707i	1.24245	+	0.780683i	0.982738	−	0.185003i	$-0.0592295\pi$
$467$	26.8496	+	16.8707i	1.24245	+	0.780683i	0.259712	+	0.965686i	$0.416372\pi$
$468$	55.5995	+	13.6439i	2.57009	+	0.630691i
$469$	−7.83662	+	6.24949i	−0.361861	+	0.288575i
$470$	32.8216	+	83.6282i	1.51395	+	3.85748i
$471$	4.01493	+	18.2733i	0.184998	+	0.841991i
$472$	9.10052	−	1.72191i	0.418885	−	0.0792574i
$473$	−25.3176	−	17.2612i	−1.16410	−	0.793672i
$474$	28.2566	−	17.4363i	1.29787	−	0.800877i
$475$	13.8206	+	2.61500i	0.634134	+	0.119985i
$476$	−3.67151	−	3.67151i	−0.168283	−	0.168283i
$477$	−1.26919	−	21.6494i	−0.0581124	−	0.991258i
$478$	20.1997	−	2.27596i	0.923913	−	0.104100i
$479$	−2.43279	+	5.57601i	−0.111157	+	0.254774i	−0.963245	−	0.268624i	$-0.913431\pi$
$479$	−2.43279	+	5.57601i	−0.111157	+	0.254774i	0.852088	+	0.523398i	$0.175336\pi$
$480$	−1.53981	−	23.0587i	−0.0702824	−	1.05248i
$481$	−4.48554	+	16.7403i	−0.204523	+	0.763290i
$482$	−27.5905	+	32.0608i	−1.25672	+	1.46033i
$483$	12.8968	−	0.377712i	0.586823	−	0.0171865i
$484$	−5.11174	+	68.2114i	−0.232352	+	3.10052i
$485$	9.75460	−	27.8771i	0.442934	−	1.26583i
$486$	−6.71437	−	36.1196i	−0.304570	−	1.63842i
$487$	−7.02594	+	8.81025i	−0.318376	+	0.399231i	−0.915107	−	0.403210i	$-0.867894\pi$
$487$	−7.02594	+	8.81025i	−0.318376	+	0.399231i	0.596731	+	0.802441i	$0.296466\pi$
$488$	1.71803	+	11.3984i	0.0777714	+	0.515979i
$489$	18.5368	+	17.4819i	0.838264	+	0.790560i
$490$	1.07342	−	28.6878i	0.0484922	−	1.29598i
$491$	−35.0693	+	15.3006i	−1.58266	+	0.690505i	−0.993105	−	0.117226i	$-0.962600\pi$
$491$	−35.0693	+	15.3006i	−1.58266	+	0.690505i	−0.589550	+	0.807732i	$0.700695\pi$
$492$	−2.40704	−	4.24841i	−0.108518	−	0.191533i
$493$	−2.11113	+	1.22030i	−0.0950807	+	0.0549594i
$494$			22.8909i			1.02991i
$495$	−54.4251	+	22.7005i	−2.44623	+	1.02031i
$496$	−3.52324	+	5.60721i	−0.158198	+	0.251771i
$497$	18.1915	+	16.8792i	0.815998	+	0.757136i
$498$	−44.1621	+	34.6352i	−1.97895	+	1.55204i
$499$	0.164777	−	1.09322i	0.00737642	−	0.0489393i	−0.984840	−	0.173466i	$-0.944503\pi$
$499$	0.164777	−	1.09322i	0.00737642	−	0.0489393i	0.992216	+	0.124527i	$0.0397413\pi$
$500$	23.9795	+	25.8437i	1.07239	+	1.15577i
$501$	13.5670	+	4.87132i	0.606128	+	0.217634i
$502$	49.2622	+	3.69169i	2.19868	+	0.164768i
$503$	−16.9150	+	10.6284i	−0.754201	+	0.473896i	−0.853455	−	0.521166i	$-0.825497\pi$
$503$	−16.9150	+	10.6284i	−0.754201	+	0.473896i	0.0992539	+	0.995062i	$0.468354\pi$
$504$	−33.6510	+	11.1649i	−1.49893	+	0.497326i
$505$	10.8121	−	10.8121i	0.481132	−	0.481132i
$506$	−24.7269	+	16.8585i	−1.09924	+	0.749452i
$507$	16.0969	+	22.1853i	0.714888	+	0.985286i
$508$	−18.9748	+	14.0040i	−0.841869	+	0.621328i
$509$	24.5132	−	1.83701i	1.08653	−	0.0814242i	0.480598	−	0.876941i	$-0.340420\pi$
$509$	24.5132	−	1.83701i	1.08653	−	0.0814242i	0.605932	+	0.795517i	$0.292800\pi$
$510$	1.65802	+	6.39510i	0.0734182	+	0.283180i
$511$	−1.85783	+	9.81888i	−0.0821856	+	0.434362i
$512$	8.97189	+	14.2787i	0.396505	+	0.631034i
$513$	8.56624	−	3.87112i	0.378209	−	0.170914i
$514$	65.3296	+	22.8598i	2.88157	+	1.00830i
$515$	−31.1248	−	9.60073i	−1.37152	−	0.423059i
$516$	12.2721	+	32.0312i	0.540248	+	1.41009i
$517$	21.4282	−	54.5982i	0.942411	−	2.40123i
$518$	−7.23429	−	23.4530i	−0.317856	−	1.03046i
$519$	−12.1197	−	0.552081i	−0.531996	−	0.0242337i
$520$	−41.7438	+	56.5609i	−1.83059	+	2.48036i
$521$	−9.44830			−0.413938			−0.206969	−	0.978348i	$-0.566360\pi$
$521$	−9.44830			−0.413938			−0.206969	+	0.978348i	$0.566360\pi$
$522$	2.24767	+	38.0084i	0.0983777	+	1.66358i
$523$	−34.2714			−1.49859			−0.749293	−	0.662239i	$-0.769606\pi$
$523$	−34.2714			−1.49859			−0.749293	+	0.662239i	$0.769606\pi$
$524$	5.51261	−	7.46932i	0.240819	−	0.326299i
$525$	−23.4126	+	36.5979i	−1.02181	+	1.59726i
$526$	−6.41211	−	20.7876i	−0.279581	−	0.906381i
$527$	−0.718471	+	1.83063i	−0.0312971	+	0.0797437i
$528$	9.14763	−	11.2816i	0.398099	−	0.490968i
$529$	16.8836	+	5.20790i	0.734069	+	0.226430i
$530$	57.4761	+	20.1118i	2.49660	+	0.873599i
$531$	0.689597	−	7.55358i	0.0299260	−	0.327797i
$532$	−11.0368	−	17.5650i	−0.478507	−	0.761540i
$533$	0.791677	−	4.18411i	0.0342913	−	0.181234i
$534$	27.4816	+	7.60340i	1.18925	+	0.329031i
$535$	−54.4330	+	4.07919i	−2.35334	+	0.176359i
$536$	−9.15758	+	6.75860i	−0.395547	+	0.291927i
$537$	−12.8950	+	28.9128i	−0.556460	+	1.24768i
$538$	−19.7136	+	13.4405i	−0.849915	+	0.579462i
$539$	−13.2529	+	13.2529i	−0.570843	+	0.570843i
$540$	64.5434	+	13.8489i	2.77751	+	0.595962i
$541$	12.8823	−	8.09451i	0.553855	−	0.348010i	−0.225845	−	0.974163i	$-0.572514\pi$
$541$	12.8823	−	8.09451i	0.553855	−	0.348010i	0.779700	+	0.626153i	$0.215371\pi$
$542$	−8.04864	−	0.603162i	−0.345719	−	0.0259080i
$543$	−29.1100	+	24.6425i	−1.24923	+	1.05751i
$544$	1.14972	+	1.23910i	0.0492937	+	0.0531260i
$545$	−0.922538	+	6.12064i	−0.0395172	+	0.262179i
$546$	−65.6050	−	26.3649i	−2.80764	−	1.12831i
$547$	−32.6964	−	30.3379i	−1.39800	−	1.29715i	−0.903898	−	0.427748i	$-0.859307\pi$
$547$	−32.6964	−	30.3379i	−1.39800	−	1.29715i	−0.494101	−	0.869405i	$-0.664503\pi$
$548$	12.9971	−	20.6847i	0.555208	−	0.883608i
$549$	9.36222	+	1.20916i	0.399570	+	0.0516055i
$550$		−	100.774i		−	4.29700i
$551$	−9.30797	+	2.87632i	−0.396533	+	0.122535i
$552$	14.6500	+	0.118975i	0.623547	+	0.00506391i
$553$	−24.0519	+	10.4937i	−1.02279	+	0.446239i
$554$	0.283171	−	7.56790i	0.0120308	−	0.321529i
$555$	−4.60486	+	19.4459i	−0.195465	+	0.825433i
$556$	−6.18351	−	41.0249i	−0.262239	−	1.73984i
$557$	18.6580	−	23.3963i	0.790563	−	0.991335i	−0.209346	−	0.977842i	$-0.567133\pi$
$557$	18.6580	−	23.3963i	0.790563	−	0.991335i	0.999909	−	0.0134933i	$-0.00429518\pi$
$558$	20.5176	+	22.8460i	0.868581	+	0.967147i
$559$	−9.88003	+	28.2355i	−0.417881	+	1.19423i
$560$	1.31392	−	17.5331i	0.0555233	−	0.740907i
$561$	2.04632	−	3.79687i	0.0863958	−	0.160304i
$562$	−1.37346	+	1.59599i	−0.0579358	+	0.0673226i
$563$	6.51780	−	24.3248i	0.274692	−	1.02517i	−0.681355	−	0.731953i	$-0.738609\pi$
$563$	6.51780	−	24.3248i	0.274692	−	1.02517i	0.956047	−	0.293213i	$-0.0947244\pi$
$564$	−54.5475	+	36.5445i	−2.29686	+	1.53880i
$565$	1.47119	−	3.37200i	0.0618934	−	0.141861i
$566$	10.5916	−	1.19339i	0.445200	−	0.0501620i
$567$	1.22829	+	29.0093i	0.0515834	+	1.21828i
$568$	19.9253	+	19.9253i	0.836046	+	0.836046i
$569$	10.9844	+	2.07837i	0.460492	+	0.0871297i	0.410981	−	0.911644i	$-0.365186\pi$
$569$	10.9844	+	2.07837i	0.460492	+	0.0871297i	0.0495106	+	0.998774i	$0.484234\pi$
$570$	0.772705	+	26.3836i	0.0323651	+	1.10509i
$571$	7.64763	+	5.21407i	0.320043	+	0.218202i	0.712676	−	0.701494i	$-0.247483\pi$
$571$	7.64763	+	5.21407i	0.320043	+	0.218202i	−0.392632	+	0.919696i	$0.628436\pi$
$572$	103.118	−	19.5110i	4.31157	−	0.815794i
$573$	−14.2240	+	12.9846i	−0.594215	+	0.542437i
$574$	2.20321	+	5.61369i	0.0919602	+	0.234311i
$575$	14.0359	−	11.1933i	0.585338	−	0.466791i
$576$	34.1288	−	9.92326i	1.42203	−	0.413469i
$577$	−13.7996	−	8.67088i	−0.574486	−	0.360973i	0.213239	−	0.977000i	$-0.431599\pi$
$577$	−13.7996	−	8.67088i	−0.574486	−	0.360973i	−0.787725	+	0.616027i	$0.788741\pi$
$578$	31.8475	+	23.5045i	1.32468	+	0.977659i
$579$	0.194438	−	23.9422i	0.00808058	−	0.995006i
$580$	−64.5860	−	22.5627i	−2.68179	−	0.936866i
$581$	38.4135	−	22.1781i	1.59366	−	0.920101i
$582$	33.4868	+	4.04871i	1.38807	+	0.167824i
$583$	−18.5764	−	35.1482i	−0.769355	−	1.45569i
$584$	−2.52498	+	11.0626i	−0.104484	+	0.457775i
$585$	35.1579	+	45.5862i	1.45360	+	1.88476i
$586$	16.7528	+	13.3599i	0.692052	+	0.551893i
$587$	8.02554	−	26.0182i	0.331249	−	1.07388i	−0.624826	−	0.780764i	$-0.714830\pi$
$587$	8.02554	−	26.0182i	0.331249	−	1.07388i	0.956076	−	0.293120i	$-0.0946937\pi$
$588$	20.6461	−	3.73305i	0.851432	−	0.153949i
$589$	−4.42602	+	6.49177i	−0.182371	+	0.267489i
$590$	18.8296	+	9.95176i	0.775204	+	0.409707i
$591$	5.10471	−	25.8290i	0.209980	−	1.06246i
$592$	−1.27391	−	4.75428i	−0.0523572	−	0.195400i
$593$	−9.67498	−	4.65923i	−0.397304	−	0.191331i	0.224554	−	0.974462i	$-0.427908\pi$
$593$	−9.67498	−	4.65923i	−0.397304	−	0.191331i	−0.621858	+	0.783130i	$0.713622\pi$
$594$	−38.6606	−	55.1461i	−1.58626	−	2.26267i
$595$	−0.584602	−	5.18848i	−0.0239663	−	0.212707i
$596$	41.9205	+	61.4861i	1.71713	+	2.51857i
$597$	32.8082	−	8.50597i	1.34275	−	0.348126i
$598$	22.1451	+	19.0574i	0.905581	+	0.779315i
$599$	5.18875	−	9.81760i	0.212007	−	0.401136i	−0.755061	−	0.655654i	$-0.772393\pi$
$599$	5.18875	−	9.81760i	0.212007	−	0.401136i	0.967068	+	0.254518i	$0.0819168\pi$
$600$	−28.1203	+	40.5337i	−1.14801	+	1.65478i
$601$	−30.5752	+	26.3121i	−1.24719	+	1.07329i	−0.252799	+	0.967519i	$0.581351\pi$
$601$	−30.5752	+	26.3121i	−1.24719	+	1.07329i	−0.994390	+	0.105774i	$0.966268\pi$
$602$	−9.42679	−	41.3015i	−0.384207	−	1.68332i
$603$	3.26390	+	8.73064i	0.132916	+	0.355539i
$604$	−13.2998	−	16.6775i	−0.541162	−	0.678596i
$605$	−46.7856	+	50.4229i	−1.90211	+	2.04998i
$606$	14.7105	+	9.41069i	0.597572	+	0.382283i
$607$	3.28103	+	7.52020i	0.133173	+	0.305236i	0.970353	−	0.241692i	$-0.0777022\pi$
$607$	3.28103	+	7.52020i	0.133173	+	0.305236i	−0.837180	+	0.546927i	$0.815797\pi$
$608$	3.37667	+	5.84857i	0.136942	+	0.237191i
$609$	2.47708	−	29.9894i	0.100376	−	1.21523i
$610$	−13.2531	+	22.9551i	−0.536604	+	0.929426i
$611$	−56.8995	−	6.41104i	−2.30191	−	0.259363i
$612$	−4.30488	+	2.18650i	−0.174015	+	0.0883840i
$613$	−38.0411	−	8.68264i	−1.53647	−	0.350689i	−0.631230	−	0.775596i	$-0.717450\pi$
$613$	−38.0411	−	8.68264i	−1.53647	−	0.350689i	−0.905237	+	0.424907i	$0.860307\pi$
$614$	27.9985	−	4.22010i	1.12993	−	0.170309i
$615$	0.771232	−	4.84925i	0.0310991	−	0.195541i
$616$	−47.6446	+	44.2077i	−1.91966	+	1.78118i
$617$	−7.23006	−	38.2118i	−0.291071	−	1.53835i	−0.756934	−	0.653492i	$-0.773303\pi$
$617$	−7.23006	−	38.2118i	−0.291071	−	1.53835i	0.465862	−	0.884857i	$-0.345744\pi$
$618$	3.08109	−	37.0718i	0.123940	−	1.49125i
$619$	21.3537	−	0.799000i	0.858279	−	0.0321145i	0.395372	−	0.918521i	$-0.370616\pi$
$619$	21.3537	−	0.799000i	0.858279	−	0.0321145i	0.462907	+	0.886407i	$0.346806\pi$
$620$	−52.0786	+	18.2231i	−2.09153	+	0.731857i
$621$	3.38667	−	11.5100i	0.135902	−	0.461879i
$622$	30.2575	−	62.8303i	1.21321	−	2.51927i
$623$	−20.6551	−	9.01172i	−0.827528	−	0.361047i
$624$	−12.9497	−	5.77553i	−0.518403	−	0.231206i
$625$	−0.255837	−	3.41391i	−0.0102335	−	0.136556i
$626$	27.0725	+	7.25405i	1.08203	+	0.289930i
$627$	11.3462	−	12.9700i	0.453123	−	0.517970i
$628$	−1.43558	−	38.3666i	−0.0572857	−	1.53099i
$629$	−0.634191	−	1.31691i	−0.0252869	−	0.0525087i
$630$	−76.5050	−	28.1731i	−3.04803	−	1.12244i
$631$	−1.89374	+	0.432234i	−0.0753886	+	0.0172070i	−0.260049	−	0.965595i	$-0.583739\pi$
$631$	−1.89374	+	0.432234i	−0.0753886	+	0.0172070i	0.184660	+	0.982802i	$0.440882\pi$
$632$	−27.7373	+	10.8861i	−1.10333	+	0.433026i
$633$	−2.84039	−	3.62169i	−0.112895	−	0.143949i
$634$	15.9272	−	4.91291i	0.632552	−	0.195116i
$635$	−23.6981	−	0.886721i	−0.940431	−	0.0351884i
$636$	−5.34176	+	44.1816i	−0.211815	+	1.75191i
$637$	15.8459	+	9.14865i	0.627838	+	0.362483i
$638$	32.6457	+	61.6926i	1.29246	+	2.44243i
$639$	20.1696	−	11.2122i	0.797897	−	0.443546i
$640$	−8.18604	+	72.6531i	−0.323582	+	2.87187i
$641$	14.3229	−	7.56985i	0.565719	−	0.298991i	−0.159849	−	0.987141i	$-0.551101\pi$
$641$	14.3229	−	7.56985i	0.565719	−	0.298991i	0.725568	+	0.688150i	$0.241577\pi$
$642$	−17.8910	−	59.7187i	−0.706101	−	2.35691i
$643$	13.3138	+	5.22527i	0.525044	+	0.206065i	0.613034	−	0.790057i	$-0.289949\pi$
$643$	13.3138	+	5.22527i	0.525044	+	0.206065i	−0.0879896	+	0.996121i	$0.528044\pi$
$644$	−26.1812	−	3.94619i	−1.03169	−	0.155502i
$645$	−10.4344	+	32.8772i	−0.410854	+	1.29454i
$646$	−1.25930	−	1.46334i	−0.0495467	−	0.0575743i
$647$	−12.2459	+	5.89730i	−0.481435	+	0.231847i	−0.658828	−	0.752293i	$-0.728948\pi$
$647$	−12.2459	+	5.89730i	−0.481435	+	0.231847i	0.177394	+	0.984140i	$0.443233\pi$
$648$	0.162080	+	32.9691i	0.00636711	+	1.29515i
$649$	−4.59240	−	13.1243i	−0.180267	−	0.515175i
$650$	−95.0280	+	25.4627i	−3.72730	+	0.998728i
$651$	−13.5076	−	20.1619i	−0.529405	−	0.790206i
$652$	−31.0496	−	42.0707i	−1.21600	−	1.64762i
$653$	−2.89955	−	3.92875i	−0.113468	−	0.153744i	0.744183	−	0.667976i	$-0.232839\pi$
$653$	−2.89955	−	3.92875i	−0.113468	−	0.153744i	−0.857651	+	0.514232i	$0.828077\pi$
$654$	−7.05350	+	0.471018i	−0.275814	+	0.0184182i
$655$	9.01708	−	2.41612i	0.352326	−	0.0944056i
$656$	0.399434	+	1.14152i	0.0155953	+	0.0445688i
$657$	8.14412	+	4.47500i	0.317733	+	0.174586i
$658$	73.0590	−	35.1834i	2.84814	−	1.37159i
$659$	15.6323	+	18.1651i	0.608949	+	0.707612i	0.974805	−	0.223060i	$-0.0716045\pi$
$659$	15.6323	+	18.1651i	0.608949	+	0.707612i	−0.365856	+	0.930672i	$0.619224\pi$
$660$	118.193	−	25.9688i	4.60066	−	1.01083i
$661$	15.8232	+	2.38497i	0.615453	+	0.0927646i	0.449368	−	0.893347i	$-0.351649\pi$
$661$	15.8232	+	2.38497i	0.615453	+	0.0927646i	0.166085	+	0.986111i	$0.446887\pi$
$662$	21.9491	+	8.61438i	0.853075	+	0.334807i
$663$	−4.09744	−	0.970287i	−0.159131	−	0.0376828i
$664$	44.5296	−	23.5346i	1.72808	−	0.913319i
$665$	2.33564	−	20.7294i	0.0905724	−	0.803852i
$666$	−22.8199	−	0.370672i	−0.884254	−	0.0143632i
$667$	−4.96657	+	11.3993i	−0.192306	+	0.441384i
$668$	−25.6181	−	14.7906i	−0.991195	−	0.572267i
$669$	38.8610	−	16.5805i	1.50245	−	0.641041i
$670$	−26.1533	−	0.978588i	−1.01039	−	0.0378062i
$671$	16.5363	−	5.10077i	0.638377	−	0.196913i
$672$	−20.6510	+	2.94133i	−0.796631	+	0.113464i
$673$	−1.56894	+	0.615763i	−0.0604782	+	0.0237359i	−0.395387	−	0.918515i	$-0.629390\pi$
$673$	−1.56894	+	0.615763i	−0.0604782	+	0.0237359i	0.334909	+	0.942250i	$0.391294\pi$
$674$	−31.1624	+	7.11261i	−1.20033	+	0.273968i
$675$	25.5990	+	31.2553i	0.985304	+	1.20302i
$676$	−24.4051	−	50.6778i	−0.938659	−	1.94915i
$677$	0.694295	+	18.5554i	0.0266839	+	0.713143i	0.946861	+	0.321642i	$0.104235\pi$
$677$	0.694295	+	18.5554i	0.0266839	+	0.713143i	−0.920177	+	0.391502i	$0.871956\pi$
$678$	4.12194	+	0.814639i	0.158302	+	0.0312860i
$679$	−25.7498	−	6.89965i	−0.988188	−	0.264784i
$680$	−0.443059	−	5.91221i	−0.0169905	−	0.226723i
$681$	20.4737	−	14.8549i	0.784552	−	0.569243i
$682$	51.5942	+	22.5103i	1.97564	+	0.861965i
$683$	18.5321	−	38.4823i	0.709111	−	1.47248i	−0.164765	−	0.986333i	$-0.552686\pi$
$683$	18.5321	−	38.4823i	0.709111	−	1.47248i	0.873875	−	0.486150i	$-0.161599\pi$
$684$	−18.7118	+	4.68947i	−0.715465	+	0.179306i
$685$	23.1871	−	8.11351i	0.885933	−	0.310001i
$686$	27.2918	−	1.02119i	1.04200	−	0.0389891i
$687$	28.9444	−	13.6505i	1.10430	−	0.520798i
$688$	−1.57945	−	8.34760i	−0.0602160	−	0.318249i
$689$	−28.4505	+	26.3982i	−1.08388	+	1.00569i
$690$	26.1673	+	21.2177i	0.996172	+	0.807742i
$691$	−8.76447	+	1.32103i	−0.333416	+	0.0502544i	−0.313617	−	0.949550i	$-0.601541\pi$
$691$	−8.76447	+	1.32103i	−0.333416	+	0.0502544i	−0.0197992	+	0.999804i	$0.506303\pi$
$692$	24.2726	+	5.54006i	0.922705	+	0.210601i
$693$	24.1036	+	47.4563i	0.915621	+	1.80272i
$694$	−21.4380	−	2.41548i	−0.813775	−	0.0916904i
$695$	20.8600	−	36.1306i	0.791266	−	1.37051i
$696$	4.08402	−	33.9239i	0.154805	−	1.28588i
$697$	0.179573	+	0.311029i	0.00680180	+	0.0117811i
$698$	16.2151	+	37.1654i	0.613751	+	1.40673i
$699$	19.0509	−	9.87163i	0.720573	−	0.373379i
$700$	60.6416	−	65.3561i	2.29204	−	2.47023i
$701$	0.619060	+	0.776277i	0.0233816	+	0.0293196i	0.793385	−	0.608720i	$-0.208317\pi$
$701$	0.619060	+	0.776277i	0.0233816	+	0.0293196i	−0.770003	+	0.638040i	$0.779745\pi$
$702$	−42.2334	+	50.3902i	−1.59400	+	1.90186i
$703$	−1.29946	−	5.69333i	−0.0490102	−	0.214728i
$704$	49.3856	−	42.4998i	1.86129	−	1.60177i
$705$	−65.7977	−	5.46853i	−2.47808	−	0.205957i
$706$	−34.5321	+	65.3380i	−1.29963	+	2.45903i
$707$	−10.4612	−	9.00256i	−0.393433	−	0.338576i
$708$	−4.15055	+	15.0017i	−0.155987	+	0.563798i
$709$	19.2983	+	28.3054i	0.724763	+	1.06303i	0.994965	+	0.100228i	$0.0319571\pi$
$709$	19.2983	+	28.3054i	0.724763	+	1.06303i	−0.270202	+	0.962804i	$0.587090\pi$
$710$	7.25484	+	64.3885i	0.272269	+	2.41646i
$711$	2.33797	+	24.2897i	0.0876806	+	0.910935i
$712$	−23.0548	−	11.1026i	−0.864014	−	0.416087i
$713$	2.59547	+	9.68642i	0.0972010	+	0.362759i
$714$	5.64433	−	1.92373i	0.211234	−	0.0719938i
$715$	93.3041	+	49.3127i	3.48938	+	1.84419i
$716$	36.5965	−	53.6773i	1.36768	−	2.00601i
$717$	−5.04846	+	14.0603i	−0.188538	+	0.525093i
$718$	1.47028	−	4.76653i	0.0548704	−	0.177886i
$719$	−34.3429	−	27.3875i	−1.28077	−	1.02138i	−0.998065	−	0.0621768i	$-0.980196\pi$
$719$	−34.3429	−	27.3875i	−1.28077	−	1.02138i	−0.282708	−	0.959206i	$-0.591233\pi$
$720$	−15.1205	−	6.21963i	−0.563509	−	0.231792i
$721$	−6.54208	+	28.6627i	−0.243640	+	1.06746i
$722$	17.3195	+	32.7701i	0.644564	+	1.21958i
$723$	−12.1992	−	28.5923i	−0.453695	−	1.06336i
$724$	67.7814	−	39.1336i	2.51908	−	1.45439i
$725$	−22.2943	−	35.4411i	−0.827989	−	1.31625i
$726$	−67.7118	−	39.8301i	−2.51302	−	1.47823i
$727$	−10.5615	−	7.79473i	−0.391704	−	0.289091i	0.380107	−	0.924942i	$-0.375887\pi$
$727$	−10.5615	−	7.79473i	−0.391704	−	0.289091i	−0.771811	+	0.635852i	$0.780649\pi$
$728$	53.7256	+	33.7581i	1.99120	+	1.25116i
$729$	25.9992	+	7.28304i	0.962933	+	0.269742i
$730$	−20.3999	+	16.2684i	−0.755034	+	0.602120i
$731$	−0.921731	−	2.34853i	−0.0340915	−	0.0868636i
$732$	−18.4643	−	5.86011i	−0.682460	−	0.216596i
$733$	33.1903	−	6.27995i	1.22591	−	0.231955i	0.467656	−	0.883911i	$-0.345099\pi$
$733$	33.1903	−	6.27995i	1.22591	−	0.231955i	0.758257	+	0.651955i	$0.226051\pi$
$734$	20.7848	+	14.1708i	0.767181	+	0.523055i
$735$	18.5725	+	10.0097i	0.685058	+	0.369212i
$736$	8.46920	+	1.60246i	0.312179	+	0.0590674i
$737$	12.0821	+	12.0821i	0.445049	+	0.445049i
$738$	5.59822	−	0.328195i	0.206073	−	0.0120810i
$739$	−7.09425	+	0.799330i	−0.260966	+	0.0294038i	−0.241478	−	0.970406i	$-0.577632\pi$
$739$	−7.09425	+	0.799330i	−0.260966	+	0.0294038i	−0.0194880	+	0.999810i	$0.506204\pi$
$740$	16.3991	−	37.5871i	0.602843	−	1.38173i
$741$	−15.0973	−	7.42213i	−0.554614	−	0.272659i
$742$	14.2255	−	53.0902i	0.522234	−	1.94900i
$743$	−9.19794	+	10.6882i	−0.337440	+	0.392112i	−0.900897	−	0.434033i	$-0.857090\pi$
$743$	−9.19794	+	10.6882i	−0.337440	+	0.392112i	0.563457	+	0.826145i	$0.309471\pi$
$744$	−14.4711	−	23.4513i	−0.530537	−	0.859765i
$745$	−5.59225	+	74.6235i	−0.204884	+	2.73399i
$746$	−1.51320	+	4.32448i	−0.0554023	+	0.158331i
$747$	−8.52398	−	40.3565i	−0.311876	−	1.47657i
$748$	−5.51861	+	6.92012i	−0.201780	+	0.253025i
$749$	7.34328	+	48.7195i	0.268318	+	1.78017i
$750$	−38.7857	+	11.6197i	−1.41625	+	0.424292i
$751$	1.05270	−	28.1341i	0.0384137	−	1.02663i	−0.838179	−	0.545395i	$-0.816380\pi$
$751$	1.05270	−	28.1341i	0.0384137	−	1.02663i	0.876593	−	0.481233i	$-0.159811\pi$
$752$	14.9050	−	6.50299i	0.543530	−	0.237140i
$753$	−18.4075	+	31.2931i	−0.670807	+	1.14038i
$754$	49.9265	−	46.3723i	1.81821	−	1.68878i
$755$		−	21.4504i		−	0.780662i
$756$	8.11165	−	59.0290i	0.295018	−	2.14686i
$757$	13.6560	−	21.7333i	0.496335	−	0.789912i	−0.500800	−	0.865563i	$-0.666961\pi$
$757$	13.6560	−	21.7333i	0.496335	−	0.789912i	0.997134	+	0.0756513i	$0.0241036\pi$
$758$	−28.6258	−	26.5608i	−1.03974	−	0.964733i
$759$	−3.10134	−	21.7744i	−0.112571	−	0.790361i
$760$	3.53039	−	23.4226i	0.128061	−	0.849626i
$761$	0.140975	+	0.151935i	0.00511036	+	0.00550765i	0.735602	−	0.677414i	$-0.236899\pi$
$761$	0.140975	+	0.151935i	0.00511036	+	0.00550765i	−0.730492	+	0.682922i	$0.760709\pi$
$762$	−4.81896	−	26.6519i	−0.174572	−	0.965496i
$763$	5.57135	+	0.417515i	0.201697	+	0.0151151i
$764$	33.4644	−	21.0271i	1.21070	−	0.760733i
$765$	−4.75538	−	0.980021i	−0.171931	−	0.0354327i
$766$	−45.2202	+	45.2202i	−1.63387	+	1.63387i
$767$	−11.2157	+	7.64671i	−0.404974	+	0.276107i
$768$	−42.2303	+	4.41121i	−1.52385	+	0.159176i
$769$	−26.5426	+	19.5893i	−0.957149	+	0.706408i	−0.955931	−	0.293591i	$-0.905150\pi$
$769$	−26.5426	+	19.5893i	−0.957149	+	0.706408i	−0.00121797	+	0.999999i	$0.500388\pi$
$770$	−149.036	+	11.1687i	−5.37089	+	0.402493i
$771$	−36.2592	+	35.6750i	−1.30584	+	1.28481i
$772$	−9.13455	+	48.2773i	−0.328760	+	1.73754i
$773$	24.6365	+	39.2087i	0.886112	+	1.41024i	0.911829	+	0.410569i	$0.134670\pi$
$773$	24.6365	+	39.2087i	0.886112	+	1.41024i	−0.0257176	+	0.999669i	$0.508187\pi$
$774$	−39.2309	−	3.58155i	−1.41012	−	0.128736i
$775$	−31.8728	−	11.1528i	−1.14491	−	0.400620i
$776$	−28.9255	−	8.92233i	−1.03836	−	0.320293i
$777$	17.8137	+	2.83311i	0.639062	+	0.101637i
$778$	6.18565	−	15.7608i	0.221766	−	0.565051i
$779$	0.422940	+	1.37114i	0.0151534	+	0.0491261i
$780$	−54.3522	−	104.893i	−1.94612	−	3.75575i
$781$	25.1205	−	34.0371i	0.898882	−	1.21794i
$782$	−2.46407			−0.0881150
$783$	−25.7966	−	10.8414i	−0.921895	−	0.387440i
$784$	−5.19648			−0.185589
$785$	22.9262	−	31.0639i	0.818270	−	1.10872i
$786$	4.90507	+	9.46614i	0.174958	+	0.337646i
$787$	10.2986	+	33.3874i	0.367107	+	1.19013i	0.931227	+	0.364439i	$0.118739\pi$
$787$	10.2986	+	33.3874i	0.367107	+	1.19013i	−0.564121	+	0.825692i	$0.690785\pi$
$788$	−19.7391	+	50.2944i	−0.703176	+	1.79166i
$789$	15.7892	+	2.51113i	0.562109	+	0.0893987i
$790$	−65.4736	−	20.1959i	−2.32945	−	0.718539i
$791$	−3.13434	−	1.09675i	−0.111444	−	0.0389960i
$792$	25.3356	+	54.8722i	0.900261	+	1.94980i
$793$	−8.98821	−	14.3046i	−0.319181	−	0.507973i
$794$	16.0421	−	84.7843i	0.569311	−	3.00888i
$795$	−31.9004	+	31.3864i	−1.13139	+	1.11316i
$796$	−69.3576	+	5.19763i	−2.45831	+	0.184225i
$797$	−19.7004	+	14.5396i	−0.697825	+	0.515018i	−0.883993	−	0.467500i	$-0.845155\pi$
$797$	−19.7004	+	14.5396i	−0.697825	+	0.515018i	0.186168	+	0.982518i	$0.440393\pi$
$798$	23.6955	−	2.47514i	0.838812	−	0.0876191i
$799$	3.99008	−	2.72039i	0.141159	−	0.0962406i
$800$	−20.5234	+	20.5234i	−0.725610	+	0.725610i
$801$	−13.9253	+	15.6597i	−0.492026	+	0.553309i
$802$	7.11437	−	4.47026i	0.251217	−	0.157850i
$803$	16.9873	+	1.27302i	0.599469	+	0.0449240i
$804$	−3.40325	−	18.8221i	−0.120023	−	0.663805i
$805$	−18.1095	−	19.5174i	−0.638277	−	0.687899i
$806$	8.19047	−	54.3402i	0.288497	−	1.91405i
$807$	−2.47255	−	17.3597i	−0.0870380	−	0.611092i
$808$	−11.4881	−	10.6594i	−0.404150	−	0.374996i
$809$	−12.2838	+	19.5495i	−0.431875	+	0.687325i	−0.989784	−	0.142578i	$-0.954461\pi$
$809$	−12.2838	+	19.5495i	−0.431875	+	0.687325i	0.557909	+	0.829902i	$0.311604\pi$
$810$	−46.9764	+	59.5044i	−1.65058	+	2.09077i
$811$		−	42.9446i		−	1.50799i	−0.656880	−	0.753995i	$-0.728124\pi$
$811$		−	42.9446i		−	1.50799i	0.656880	−	0.753995i	$-0.271876\pi$
$812$	−15.9520	+	59.6552i	−0.559805	+	2.09349i
$813$	3.00749	−	5.11278i	0.105477	−	0.179313i
$814$	−38.3475	+	16.7308i	−1.34408	+	0.586416i
$815$	1.96603	−	52.5433i	0.0688671	−	1.84051i
$816$	1.14556	−	0.343196i	0.0401027	−	0.0120143i
$817$	−1.50232	−	9.96723i	−0.0525595	−	0.348709i
$818$	15.9639	−	20.0182i	0.558166	−	0.699918i
$819$	38.6602	−	34.7202i	1.35090	−	1.21322i
$820$	−3.32799	+	9.51084i	−0.116218	+	0.332133i
$821$	−2.39837	+	32.0040i	−0.0837036	+	1.11695i	0.784298	+	0.620385i	$0.213023\pi$
$821$	−2.39837	+	32.0040i	−0.0837036	+	1.11695i	−0.868001	+	0.496562i	$0.834596\pi$
$822$	14.7332	+	23.8760i	0.513880	+	0.832772i
$823$	−17.3713	+	20.1858i	−0.605525	+	0.703632i	−0.974139	−	0.225950i	$-0.927451\pi$
$823$	−17.3713	+	20.1858i	−0.605525	+	0.703632i	0.368614	+	0.929582i	$0.379832\pi$
$824$	−8.64027	+	32.2459i	−0.300998	+	1.12334i
$825$	66.4636	+	32.6747i	2.31397	+	1.13759i
$826$	7.68737	−	17.6196i	0.267478	−	0.613066i
$827$	30.4112	−	3.42652i	1.05750	−	0.119152i	0.433952	−	0.900936i	$-0.357119\pi$
$827$	30.4112	−	3.42652i	1.05750	−	0.119152i	0.623549	+	0.781784i	$0.285690\pi$
$828$	−11.0415	+	22.0063i	−0.383719	+	0.764773i
$829$	−2.80717	−	2.80717i	−0.0974971	−	0.0974971i	0.656676	−	0.754173i	$-0.271962\pi$
$829$	−2.80717	−	2.80717i	−0.0974971	−	0.0974971i	−0.754173	+	0.656676i	$0.771962\pi$
$830$	113.797	+	21.5315i	3.94995	+	0.747371i
$831$	4.89947	+	2.64057i	0.169961	+	0.0916003i
$832$	−52.5549	−	35.8314i	−1.82201	−	1.24223i
$833$	−1.51627	+	0.286894i	−0.0525357	+	0.00994030i
$834$	45.4152	+	14.4137i	1.57260	+	0.499104i
$835$	−10.8676	−	27.6903i	−0.376090	−	0.958262i
$836$	−27.6478	+	22.0484i	−0.956219	+	0.762559i
$837$	−21.7203	+	6.12452i	−0.750764	+	0.211694i
$838$	56.5429	+	35.5282i	1.95324	+	1.22730i
$839$	−10.8716	−	8.02360i	−0.375329	−	0.277006i	0.389778	−	0.920909i	$-0.372552\pi$
$839$	−10.8716	−	8.02360i	−0.375329	−	0.277006i	−0.765107	+	0.643904i	$0.777314\pi$
$840$	63.0626	+	37.0953i	2.17587	+	1.27991i
$841$	25.1295	+	14.4744i	0.866534	+	0.499118i
$842$	−63.0842	+	36.4217i	−2.17402	+	1.25517i
$843$	−0.607278	−	1.42332i	−0.0209158	−	0.0490218i
$844$	4.41344	+	8.35063i	0.151917	+	0.287440i
$845$	12.5863	−	55.1443i	0.432982	−	1.89702i
$846$	−10.0261	−	74.7357i	−0.344704	−	2.56947i
$847$	48.5410	+	38.7101i	1.66789	+	1.33010i
$848$	3.24892	−	10.5327i	0.111568	−	0.361696i
$849$	−2.64714	+	7.37249i	−0.0908497	+	0.253023i
$850$	4.67403	−	6.85554i	0.160318	−	0.235143i
$851$	−6.58968	−	3.48275i	−0.225891	−	0.119387i
$852$	−44.8237	+	15.2771i	−1.53564	+	0.523384i
$853$	1.83508	+	6.84863i	0.0628321	+	0.234492i	0.990200	−	0.139659i	$-0.0446007\pi$
$853$	1.83508	+	6.84863i	0.0628321	+	0.234492i	−0.927368	+	0.374152i	$0.877934\pi$
$854$	21.5556	+	10.3807i	0.737619	+	0.355219i
$855$	−17.6514	−	8.04497i	−0.603666	−	0.275132i
$856$	6.26393	+	55.5939i	0.214097	+	1.90016i
$857$	−24.4218	−	35.8201i	−0.834231	−	1.22359i	−0.972432	−	0.233188i	$-0.925084\pi$
$857$	−24.4218	−	35.8201i	−0.834231	−	1.22359i	0.138201	−	0.990404i	$-0.455868\pi$
$858$	−32.1393	+	116.164i	−1.09722	+	3.96577i
$859$	4.40889	+	3.79415i	0.150429	+	0.129455i	0.724283	−	0.689503i	$-0.242171\pi$
$859$	4.40889	+	3.79415i	0.150429	+	0.129455i	−0.573853	+	0.818958i	$0.694552\pi$
$860$	33.0752	−	62.5813i	1.12786	−	2.13401i
$861$	−4.41678	−	0.367085i	−0.150524	−	0.0125102i
$862$	−15.7499	+	13.5539i	−0.536443	+	0.461647i
$863$	10.6021	+	46.4506i	0.360898	+	1.58120i	0.750920	+	0.660393i	$0.229610\pi$
$863$	10.6021	+	46.4506i	0.360898	+	1.58120i	−0.390022	+	0.920805i	$0.627533\pi$
$864$	−3.35740	+	19.1045i	−0.114221	+	0.649947i
$865$	15.6096	+	19.5739i	0.530744	+	0.665531i
$866$	−13.0480	+	14.0624i	−0.443389	+	0.477859i
$867$	−25.8282	+	13.3834i	−0.877172	+	0.454525i
$868$	19.9153	+	45.6463i	0.675968	+	1.54933i
$869$	22.3665	+	38.7399i	0.758732	+	1.31416i
$870$	55.9789	−	55.1331i	1.89786	−	1.86919i
$871$	8.34040	−	14.4460i	0.282604	−	0.489484i
$872$	6.30411	+	0.710303i	0.213484	+	0.0240539i
$873$	−13.5280	+	20.7729i	−0.457853	+	0.703056i
$874$	−9.59782	−	2.19064i	−0.324651	−	0.0740995i
$875$	31.6420	−	4.76927i	1.06970	−	0.161231i
$876$	−14.8121	−	12.0103i	−0.500453	−	0.405791i
$877$	36.7312	−	34.0815i	1.24032	−	1.15085i	0.257505	−	0.966277i	$-0.417100\pi$
$877$	36.7312	−	34.0815i	1.24032	−	1.15085i	0.982818	−	0.184575i	$-0.0590909\pi$
$878$	−0.916728	−	4.84502i	−0.0309381	−	0.163512i
$879$	−14.2432	+	6.71723i	−0.480412	+	0.226567i
$880$	−29.9510	+	1.12069i	−1.00965	+	0.0377783i
$881$	41.1094	−	14.3848i	1.38501	−	0.484636i	0.468081	−	0.883685i	$-0.344945\pi$
$881$	41.1094	−	14.3848i	1.38501	−	0.484636i	0.916930	+	0.399049i	$0.130660\pi$
$882$	−6.61362	+	23.1703i	−0.222692	+	0.780186i
$883$	16.7178	−	34.7148i	0.562598	−	1.16825i	−0.404664	−	0.914465i	$-0.632612\pi$
$883$	16.7178	−	34.7148i	0.562598	−	1.16825i	0.967262	−	0.253781i	$-0.0816741\pi$
$884$	7.91996	+	3.45544i	0.266377	+	0.116219i
$885$	−12.6688	+	9.19204i	−0.425858	+	0.308987i
$886$	−4.95977	−	66.1835i	−0.166627	−	2.22348i
$887$	38.2316	+	10.2441i	1.28369	+	0.343964i	0.835261	−	0.549854i	$-0.185317\pi$
$887$	38.2316	+	10.2441i	1.28369	+	0.343964i	0.448430	+	0.893818i	$0.351983\pi$
$888$	20.0930	+	3.97107i	0.674275	+	0.133260i
$889$	0.800366	+	21.3902i	0.0268434	+	0.717406i
$890$	−25.5301	−	53.0139i	−0.855772	−	1.77703i
$891$	48.9060	−	7.61746i	1.63841	−	0.255195i
$892$	−84.5288	+	19.2931i	−2.83023	+	0.645982i
$893$	17.9603	−	7.04891i	0.601019	−	0.235883i
$894$	−84.6109	+	12.0512i	−2.82981	+	0.403051i
$895$	62.4264	−	19.2560i	2.08669	−	0.643657i
$896$	65.9465	+	2.46754i	2.20312	+	0.0824349i
$897$	−19.7493	+	8.42629i	−0.659410	+	0.281346i
$898$	−65.7659	−	37.9700i	−2.19464	−	1.26707i
$899$	23.1252	−	3.49760i	0.771267	−	0.116652i
$900$	−40.2817	−	72.4629i	−1.34272	−	2.41543i
$901$	0.366491	−	3.25270i	0.0122096	−	0.108363i
$902$	9.08881	−	4.80358i	0.302624	−	0.159942i
$903$	30.2963	+	7.17426i	1.00820	+	0.238744i
$904$	−3.50998	−	1.37757i	−0.116740	−	0.0458172i
$905$	77.8255	+	11.7303i	2.58701	+	0.389929i
$906$	23.9274	−	5.25720i	0.794933	−	0.174659i
$907$	−12.7902	−	14.8625i	−0.424691	−	0.493500i	0.504338	−	0.863506i	$-0.331736\pi$
$907$	−12.7902	−	14.8625i	−0.424691	−	0.493500i	−0.929029	+	0.370006i	$0.879355\pi$
$908$	−46.7678	+	22.5222i	−1.55204	+	0.747425i
$909$	−10.9764	+	6.65074i	−0.364063	+	0.220591i
$910$	48.1892	+	137.717i	1.59746	+	4.56526i
$911$	−46.1407	+	12.3634i	−1.52871	+	0.409617i	−0.922598	−	0.385762i	$-0.873939\pi$
$911$	−46.1407	+	12.3634i	−1.52871	+	0.409617i	−0.606112	+	0.795379i	$0.707272\pi$
$912$	4.76720	−	0.318343i	0.157858	−	0.0105414i
$913$	−44.9003	−	60.8377i	−1.48598	−	2.01344i
$914$	38.8322	+	52.6158i	1.28446	+	1.74038i
$915$	−10.8425	−	16.1838i	−0.358442	−	0.535021i
$916$	−63.4337	+	16.9970i	−2.09591	+	0.561597i
$917$	−2.78295	−	7.95321i	−0.0919011	−	0.262638i
$918$	−0.0722902	−	5.54467i	−0.00238593	−	0.183002i
$919$	−39.8479	+	19.1897i	−1.31446	+	0.633011i	−0.954012	−	0.299768i	$-0.903091\pi$
$919$	−39.8479	+	19.1897i	−1.31446	+	0.633011i	−0.360449	+	0.932779i	$0.617376\pi$
$920$	−19.7203	−	22.9154i	−0.650159	−	0.755498i
$921$	−6.29491	+	19.8343i	−0.207424	+	0.653562i
$922$	50.0549	+	7.54456i	1.64847	+	0.248467i
$923$	−38.4437	−	15.0880i	−1.26539	−	0.496628i
$924$	−31.3466	−	104.633i	−1.03123	−	3.44216i
$925$	22.1895	−	11.7275i	0.729586	−	0.385597i
$926$	9.85170	−	87.4362i	0.323747	−	2.87333i
$927$	23.4511	+	14.0522i	0.770236	+	0.461535i
$928$	5.91563	−	19.2127i	0.194190	−	0.630689i
$929$	9.34459	+	5.39510i	0.306586	+	0.177008i	0.645398	−	0.763847i	$-0.276692\pi$
$929$	9.34459	+	5.39510i	0.306586	+	0.177008i	−0.338812	+	0.940854i	$0.610025\pi$
$930$	7.60587	−	62.9080i	0.249406	−	2.06283i
$931$	−6.16110	−	0.230532i	−0.201922	−	0.00755539i
$932$	−42.0753	+	12.9785i	−1.37822	+	0.425125i
$933$	31.6281	+	40.3279i	1.03546	+	1.32028i
$934$	69.5670	−	27.3030i	2.27630	−	0.893383i
$935$	−8.67746	+	1.98057i	−0.283783	+	0.0647717i
$936$	45.3421	−	37.7557i	1.48205	−	1.23408i
$937$	3.94832	+	8.19877i	0.128986	+	0.267842i	0.955453	−	0.295143i	$-0.0953672\pi$
$937$	3.94832	+	8.19877i	0.128986	+	0.267842i	−0.826467	+	0.562985i	$0.809653\pi$
$938$	0.883287	+	23.6064i	0.0288404	+	0.770775i
$939$	−13.5622	+	15.5032i	−0.442587	+	0.505927i
$940$	130.873	+	35.0673i	4.26861	+	1.14377i
$941$	−3.78545	−	50.5133i	−0.123402	−	1.64669i	−0.624302	−	0.781183i	$-0.714617\pi$
$941$	−3.78545	−	50.5133i	−0.123402	−	1.64669i	0.500900	−	0.865505i	$-0.333002\pi$
$942$	40.2697	+	17.9602i	1.31206	+	0.585174i
$943$	1.67857	+	0.732355i	0.0546619	+	0.0238487i
$944$	1.67269	−	3.47337i	0.0544414	−	0.113049i
$945$	43.3870	−	41.3228i	1.41138	−	1.34423i
$946$	−68.1635	+	23.8515i	−2.21619	+	0.775478i
$947$	−47.6853	+	1.78426i	−1.54956	+	0.0579806i	−0.798397	−	0.602132i	$-0.794318\pi$
$947$	−47.6853	+	1.78426i	−1.54956	+	0.0579806i	−0.751167	+	0.660112i	$0.770509\pi$
$948$	4.14755	−	49.9035i	0.134706	−	1.62079i
$949$	−3.09177	−	16.3404i	−0.100363	−	0.530432i
$950$	24.3006	−	22.5477i	0.788417	−	0.731544i
$951$	−1.92401	+	12.0975i	−0.0623902	+	0.392289i
$952$	−5.29164	+	0.797586i	−0.171503	+	0.0258499i
$953$	−9.65880	−	2.20456i	−0.312879	−	0.0714127i	0.0631978	−	0.998001i	$-0.479870\pi$
$953$	−9.65880	−	2.20456i	−0.312879	−	0.0714127i	−0.376077	+	0.926588i	$0.622727\pi$
$954$	−42.8290	−	27.8916i	−1.38664	−	0.903023i
$955$	39.4932	+	4.44981i	1.27797	+	0.143992i
$956$	15.3285	−	26.5497i	0.495759	−	0.858680i
$957$	−51.2733	+	1.52780i	−1.65743	+	0.0493867i
$958$	7.16883	+	12.4168i	0.231615	+	0.401168i
$959$	−8.86691	−	20.3232i	−0.286328	−	0.656270i
$960$	−61.7833	−	39.5245i	−1.99405	−	1.27565i
$961$	−8.25575	+	8.89758i	−0.266314	+	0.287019i
$962$	25.4662	+	31.9337i	0.821065	+	1.02958i
$963$	45.1875	+	7.56343i	1.45615	+	0.243728i
$964$	14.1951	+	62.1926i	0.457192	+	2.00309i
$965$	−37.4501	+	32.2285i	−1.20556	+	1.03747i
$966$	17.3328	−	24.9841i	0.557672	−	0.803851i
$967$	−4.53337	+	8.57755i	−0.145783	+	0.275835i	−0.946184	−	0.323631i	$-0.895097\pi$
$967$	−4.53337	+	8.57755i	−0.145783	+	0.275835i	0.800400	+	0.599466i	$0.204620\pi$
$968$	53.4361	+	45.9855i	1.71750	+	1.47803i
$969$	1.37344	−	0.356082i	0.0441211	−	0.0114390i
$970$	−39.2104	−	57.5111i	−1.25897	−	1.84657i
$971$	4.25744	+	37.7859i	0.136628	+	1.21261i	0.855626	+	0.517594i	$0.173172\pi$
$971$	4.25744	+	37.7859i	0.136628	+	1.21261i	−0.718998	+	0.695012i	$0.755399\pi$
$972$	−49.8427	−	24.2001i	−1.59871	−	0.776218i
$973$	−33.9279	−	16.3388i	−1.08768	−	0.523798i
$974$	6.87367	+	25.6529i	0.220247	+	0.821972i
$975$	14.0183	−	70.9301i	0.448944	−	2.27158i
$976$	4.24196	+	2.24194i	0.135782	+	0.0717628i
$977$	−9.32942	+	13.6837i	−0.298475	+	0.437782i	−0.945954	−	0.324301i	$-0.894871\pi$
$977$	−9.32942	+	13.6837i	−0.298475	+	0.437782i	0.647479	+	0.762083i	$0.275823\pi$
$978$	59.0924	−	10.6846i	1.88957	−	0.341655i
$979$	−11.3231	+	36.7087i	−0.361889	+	1.17322i
$980$	−33.8500	−	26.9945i	−1.08130	−	0.862307i
$981$	1.97637	−	4.80474i	0.0631005	−	0.153404i
$982$	−20.0656	+	87.9134i	−0.640321	+	2.80543i
$983$	8.53507	+	16.1491i	0.272226	+	0.515078i	0.981887	−	0.189466i	$-0.0606756\pi$
$983$	8.53507	+	16.1491i	0.272226	+	0.515078i	−0.709661	+	0.704543i	$0.751152\pi$
$984$	−4.99616	−	0.604059i	−0.159272	−	0.0192567i
$985$	−47.0521	+	27.1656i	−1.49921	+	0.865567i
$986$	−0.640534	+	5.71104i	−0.0203988	+	0.181877i
$987$	−0.483960	+	59.5927i	−0.0154046	+	1.89686i
$988$	27.7771	+	20.5004i	0.883707	+	0.652205i
$989$	−10.8932	−	6.84466i	−0.346384	−	0.217648i
$990$	−33.1219	+	134.973i	−1.05268	+	4.28973i
$991$	31.1949	−	24.8771i	0.990939	−	0.790247i	0.0131656	−	0.999913i	$-0.495809\pi$
$991$	31.1949	−	24.8771i	0.990939	−	0.790247i	0.977773	+	0.209666i	$0.0672377\pi$
$992$	−5.92316	−	15.0920i	−0.188061	−	0.479171i
$993$	−12.7982	+	11.6830i	−0.406139	+	0.370750i
$994$	57.4661	−	10.8732i	1.82271	−	0.344876i
$995$	−57.7877	−	39.3990i	−1.83199	−	1.24903i
$996$	2.47791	+	84.6070i	0.0785156	+	2.68087i
$997$	−0.598961	−	0.113329i	−0.0189693	−	0.00358918i	0.176418	−	0.984315i	$-0.443549\pi$
$997$	−0.598961	−	0.113329i	−0.0189693	−	0.00358918i	−0.195388	+	0.980726i	$0.562596\pi$
$998$	−1.84242	−	1.84242i	−0.0583208	−	0.0583208i
$999$	7.64358	−	14.9303i	0.241832	−	0.472375i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.56.26	yes	672
3.2	odd	2		783.2.be.a.143.3		672
9.4	even	3		783.2.be.a.665.26		672
9.5	odd	6	inner	261.2.x.a.230.3	yes	672
29.14	odd	28	inner	261.2.x.a.101.3	yes	672
87.14	even	28		783.2.be.a.710.26		672
261.14	even	84	inner	261.2.x.a.14.26	✓	672
261.130	odd	84		783.2.be.a.449.3		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.26	✓	672	261.14	even	84	inner
261.2.x.a.56.26	yes	672	1.1	even	1	trivial
261.2.x.a.101.3	yes	672	29.14	odd	28	inner
261.2.x.a.230.3	yes	672	9.5	odd	6	inner
783.2.be.a.143.3		672	3.2	odd	2
783.2.be.a.449.3		672	261.130	odd	84
783.2.be.a.665.26		672	9.4	even	3
783.2.be.a.710.26		672	87.14	even	28

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

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Newspace parameters

Newform invariants

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	261.2.x.a.56.26

Level	$261$
Weight	$2$
Character	261.56
Analytic conductor	$2.084$
Analytic rank	$0$
Dimension	$672$
Inner twists	$4$