LMFDB - Embedded newform 76.2.k.a.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.6
Character	$\chi$	$=$	76.51
Dual form			76.2.k.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.719007 - 1.21780i) q^{2} +(1.09089 + 0.397053i) q^{3} +(-0.966058 - 1.75121i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.26789 - 1.04300i) q^{6} +(-3.53555 - 2.04125i) q^{7} +(-2.82722 - 0.0826699i) q^{8} +(-1.26573 - 1.06208i) q^{9} +O(q^{10})$	\(q+(0.719007 - 1.21780i) q^{2} +(1.09089 + 0.397053i) q^{3} +(-0.966058 - 1.75121i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.26789 - 1.04300i) q^{6} +(-3.53555 - 2.04125i) q^{7} +(-2.82722 - 0.0826699i) q^{8} +(-1.26573 - 1.06208i) q^{9} +(4.69669 + 1.76147i) q^{10} +(0.260098 - 0.150167i) q^{11} +(-0.358544 - 2.29396i) q^{12} +(0.546397 + 1.50121i) q^{13} +(-5.02792 + 2.83791i) q^{14} +(-0.715025 + 4.05511i) q^{15} +(-2.13347 + 3.38354i) q^{16} +(3.58623 - 3.00920i) q^{17} +(-2.20347 + 0.777766i) q^{18} +(3.34958 + 2.78932i) q^{19} +(5.52206 - 4.45310i) q^{20} +(-3.04643 - 3.63059i) q^{21} +(0.00413863 - 0.424718i) q^{22} +(3.07108 + 0.541514i) q^{23} +(-3.05137 - 1.21274i) q^{24} +(-7.12363 + 2.59279i) q^{25} +(2.22104 + 0.413983i) q^{26} +(-2.70044 - 4.67730i) q^{27} +(-0.159112 + 8.16346i) q^{28} +(0.344669 - 0.410760i) q^{29} +(4.42419 + 3.78641i) q^{30} +(-2.08054 + 3.60361i) q^{31} +(2.58648 + 5.03091i) q^{32} +(0.343363 - 0.0605442i) q^{33} +(-1.08607 - 6.53093i) q^{34} +(4.95259 - 13.6071i) q^{35} +(-0.637147 + 3.24259i) q^{36} -2.42729i q^{37} +(5.80520 - 2.07357i) q^{38} +1.85461i q^{39} +(-1.45257 - 9.92656i) q^{40} +(2.70395 - 7.42905i) q^{41} +(-6.61173 + 1.09951i) q^{42} +(-2.23149 + 0.393472i) q^{43} +(-0.514244 - 0.310415i) q^{44} +(2.93031 - 5.07544i) q^{45} +(2.86758 - 3.35060i) q^{46} +(-2.11323 + 2.51844i) q^{47} +(-3.67083 + 2.84398i) q^{48} +(4.83342 + 8.37173i) q^{49} +(-1.96445 + 10.5394i) q^{50} +(5.10701 - 1.85880i) q^{51} +(2.10109 - 2.40712i) q^{52} +(-5.12508 - 0.903690i) q^{53} +(-7.63763 - 0.0744244i) q^{54} +(0.684743 + 0.816045i) q^{55} +(9.82703 + 6.06335i) q^{56} +(2.54653 + 4.37281i) q^{57} +(-0.252403 - 0.715076i) q^{58} +(-4.17166 + 3.50044i) q^{59} +(7.79210 - 2.66531i) q^{60} +(-0.594383 + 3.37091i) q^{61} +(2.89253 + 5.12470i) q^{62} +(2.30710 + 6.33871i) q^{63} +(7.98633 + 0.467452i) q^{64} +(-4.90729 + 2.83323i) q^{65} +(0.173150 - 0.461679i) q^{66} +(-5.29646 - 4.44426i) q^{67} +(-8.73424 - 3.37317i) q^{68} +(3.13521 + 1.81012i) q^{69} +(-13.0098 - 15.8149i) q^{70} +(0.743257 + 4.21522i) q^{71} +(3.49071 + 3.10736i) q^{72} +(-8.50411 - 3.09524i) q^{73} +(-2.95595 - 1.74524i) q^{74} -8.80060 q^{75} +(1.64879 - 8.56046i) q^{76} -1.22612 q^{77} +(2.25854 + 1.33348i) q^{78} +(-0.187126 - 0.0681083i) q^{79} +(-13.1329 - 5.36833i) q^{80} +(-0.228002 - 1.29306i) q^{81} +(-7.10291 - 8.63440i) q^{82} +(12.9034 + 7.44977i) q^{83} +(-3.41490 + 8.84229i) q^{84} +(12.7201 + 10.6735i) q^{85} +(-1.12529 + 3.00041i) q^{86} +(0.539091 - 0.311244i) q^{87} +(-0.747767 + 0.403054i) q^{88} +(2.26220 + 6.21534i) q^{89} +(-4.07394 - 7.21779i) q^{90} +(1.13254 - 6.42296i) q^{91} +(-2.01854 - 5.90124i) q^{92} +(-3.70047 + 3.10507i) q^{93} +(1.54753 + 4.38426i) q^{94} +(-7.68017 + 13.4183i) q^{95} +(0.824040 + 6.51517i) q^{96} +(3.90012 + 4.64798i) q^{97} +(13.6703 + 0.133210i) q^{98} +(-0.488704 - 0.0861717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	0.719007	−	1.21780i	0.508415	−	0.861112i
$2$	0.719007	−	1.21780i	0.508415	−	0.861112i
$3$	1.09089	+	0.397053i	0.629828	+	0.229239i	0.637156	−	0.770734i	$-0.280111\pi$
$3$	1.09089	+	0.397053i	0.629828	+	0.229239i	−0.00732842	+	0.999973i	$0.502333\pi$
$4$	−0.966058	−	1.75121i	−0.483029	−	0.875604i
$5$	0.615920	+	3.49306i	0.275448	+	1.56214i	0.737535	+	0.675309i	$0.235990\pi$
$5$	0.615920	+	3.49306i	0.275448	+	1.56214i	−0.462087	+	0.886834i	$0.652899\pi$
$6$	1.26789	−	1.04300i	0.517614	−	0.425804i
$7$	−3.53555	−	2.04125i	−1.33631	−	0.771521i	−0.350055	−	0.936729i	$-0.613837\pi$
$7$	−3.53555	−	2.04125i	−1.33631	−	0.771521i	−0.986259	+	0.165208i	$0.947170\pi$
$8$	−2.82722	−	0.0826699i	−0.999573	−	0.0292282i
$9$	−1.26573	−	1.06208i	−0.421911	−	0.354026i
$10$	4.69669	+	1.76147i	1.48522	+	0.557025i
$11$	0.260098	−	0.150167i	0.0784224	−	0.0452772i	−0.460276	−	0.887776i	$-0.652250\pi$
$11$	0.260098	−	0.150167i	0.0784224	−	0.0452772i	0.538698	+	0.842499i	$0.318916\pi$
$12$	−0.358544	−	2.29396i	−0.103503	−	0.662209i
$13$	0.546397	+	1.50121i	0.151543	+	0.416362i	0.992114	−	0.125340i	$-0.0400023\pi$
$13$	0.546397	+	1.50121i	0.151543	+	0.416362i	−0.840570	+	0.541702i	$0.817780\pi$
$14$	−5.02792	+	2.83791i	−1.34377	+	0.758463i
$15$	−0.715025	+	4.05511i	−0.184619	+	1.04702i
$16$	−2.13347	+	3.38354i	−0.533366	+	0.845884i
$17$	3.58623	−	3.00920i	0.869788	−	0.729839i	−0.0942656	−	0.995547i	$-0.530050\pi$
$17$	3.58623	−	3.00920i	0.869788	−	0.729839i	0.964053	+	0.265708i	$0.0856058\pi$
$18$	−2.20347	+	0.777766i	−0.519362	+	0.183321i
$19$	3.34958	+	2.78932i	0.768447	+	0.639914i
$19$	3.34958	+	2.78932i	0.768447	+	0.639914i
$20$	5.52206	−	4.45310i	1.23477	−	0.995743i
$21$	−3.04643	−	3.63059i	−0.664785	−	0.792260i
$22$	0.00413863	−	0.424718i	0.000882360	−	0.0905501i
$23$	3.07108	+	0.541514i	0.640365	+	0.112914i	0.484397	−	0.874849i	$-0.339039\pi$
$23$	3.07108	+	0.541514i	0.640365	+	0.112914i	0.155968	+	0.987762i	$0.450150\pi$
$24$	−3.05137	−	1.21274i	−0.622859	−	0.247549i
$25$	−7.12363	+	2.59279i	−1.42473	+	0.518558i
$26$	2.22104	+	0.413983i	0.435581	+	0.0811887i
$27$	−2.70044	−	4.67730i	−0.519700	−	0.900146i
$28$	−0.159112	+	8.16346i	−0.0300693	+	1.54275i
$29$	0.344669	−	0.410760i	0.0640034	−	0.0762762i	−0.733093	−	0.680129i	$-0.761924\pi$
$29$	0.344669	−	0.410760i	0.0640034	−	0.0762762i	0.797096	+	0.603852i	$0.206368\pi$
$30$	4.42419	+	3.78641i	0.807743	+	0.691300i
$31$	−2.08054	+	3.60361i	−0.373676	+	0.647227i	−0.990128	−	0.140166i	$-0.955236\pi$
$31$	−2.08054	+	3.60361i	−0.373676	+	0.647227i	0.616452	+	0.787393i	$0.288570\pi$
$32$	2.58648	+	5.03091i	0.457230	+	0.889348i
$33$	0.343363	−	0.0605442i	0.0597719	−	0.0105394i
$34$	−1.08607	−	6.53093i	−0.186260	−	1.12005i
$35$	4.95259	−	13.6071i	0.837141	−	2.30003i
$36$	−0.637147	+	3.24259i	−0.106191	+	0.540432i
$37$		−	2.42729i		−	0.399044i	−0.979893	−	0.199522i	$-0.936061\pi$
$37$		−	2.42729i		−	0.399044i	0.979893	−	0.199522i	$-0.0639389\pi$
$38$	5.80520	−	2.07357i	0.941727	−	0.336378i
$39$			1.85461i			0.296976i
$40$	−1.45257	−	9.92656i	−0.229672	−	1.56953i
$41$	2.70395	−	7.42905i	0.422286	−	1.16022i	−0.528109	−	0.849177i	$-0.677099\pi$
$41$	2.70395	−	7.42905i	0.422286	−	1.16022i	0.950395	−	0.311045i	$-0.100679\pi$
$42$	−6.61173	+	1.09951i	−1.02021	+	0.169658i
$43$	−2.23149	+	0.393472i	−0.340299	+	0.0600039i	−0.341186	−	0.939996i	$-0.610829\pi$
$43$	−2.23149	+	0.393472i	−0.340299	+	0.0600039i	0.000887115		1.00000i	$0.499718\pi$
$44$	−0.514244	−	0.310415i	−0.0775252	−	0.0467968i
$45$	2.93031	−	5.07544i	0.436824	−	0.756602i
$46$	2.86758	−	3.35060i	0.422802	−	0.494019i
$47$	−2.11323	+	2.51844i	−0.308246	+	0.367353i	−0.897821	−	0.440360i	$-0.854851\pi$
$47$	−2.11323	+	2.51844i	−0.308246	+	0.367353i	0.589575	+	0.807713i	$0.299295\pi$
$48$	−3.67083	+	2.84398i	−0.529838	+	0.410493i
$49$	4.83342	+	8.37173i	0.690489	+	1.19596i
$50$	−1.96445	+	10.5394i	−0.277815	+	1.49049i
$51$	5.10701	−	1.85880i	0.715124	−	0.260284i
$52$	2.10109	−	2.40712i	0.291369	−	0.333807i
$53$	−5.12508	−	0.903690i	−0.703984	−	0.124131i	−0.189814	−	0.981820i	$-0.560789\pi$
$53$	−5.12508	−	0.903690i	−0.703984	−	0.124131i	−0.514169	+	0.857689i	$0.671900\pi$
$54$	−7.63763	−	0.0744244i	−1.03935	−	0.0101279i
$55$	0.684743	+	0.816045i	0.0923307	+	0.110035i
$56$	9.82703	+	6.06335i	1.31319	+	0.810249i
$57$	2.54653	+	4.37281i	0.337296	+	0.579193i
$58$	−0.252403	−	0.715076i	−0.0331422	−	0.0938941i
$59$	−4.17166	+	3.50044i	−0.543104	+	0.455719i	−0.872598	−	0.488439i	$-0.837566\pi$
$59$	−4.17166	+	3.50044i	−0.543104	+	0.455719i	0.329494	+	0.944158i	$0.393122\pi$
$60$	7.79210	−	2.66531i	1.00596	−	0.344090i
$61$	−0.594383	+	3.37091i	−0.0761029	+	0.431601i	0.922821	+	0.385228i	$0.125877\pi$
$61$	−0.594383	+	3.37091i	−0.0761029	+	0.431601i	−0.998924	+	0.0463728i	$0.985234\pi$
$62$	2.89253	+	5.12470i	0.367352	+	0.650837i
$63$	2.30710	+	6.33871i	0.290668	+	0.798603i
$64$	7.98633	+	0.467452i	0.998291	+	0.0584315i
$65$	−4.90729	+	2.83323i	−0.608675	+	0.351418i
$66$	0.173150	−	0.461679i	0.0213133	−	0.0568287i
$67$	−5.29646	−	4.44426i	−0.647066	−	0.542953i	0.259113	−	0.965847i	$-0.416570\pi$
$67$	−5.29646	−	4.44426i	−0.647066	−	0.542953i	−0.906179	+	0.422894i	$0.861014\pi$
$68$	−8.73424	−	3.37317i	−1.05918	−	0.409057i
$69$	3.13521	+	1.81012i	0.377435	+	0.217912i
$70$	−13.0098	−	15.8149i	−1.55497	−	1.89024i
$71$	0.743257	+	4.21522i	0.0882084	+	0.500254i	0.996618	+	0.0821733i	$0.0261861\pi$
$71$	0.743257	+	4.21522i	0.0882084	+	0.500254i	−0.908410	+	0.418081i	$0.862703\pi$
$72$	3.49071	+	3.10736i	0.411384	+	0.366206i
$73$	−8.50411	−	3.09524i	−0.995331	−	0.362271i	−0.207549	−	0.978225i	$-0.566549\pi$
$73$	−8.50411	−	3.09524i	−0.995331	−	0.362271i	−0.787782	+	0.615954i	$0.788771\pi$
$74$	−2.95595	−	1.74524i	−0.343622	−	0.202880i
$75$	−8.80060			−1.01621
$76$	1.64879	−	8.56046i	0.189129	−	0.981952i
$77$	−1.22612			−0.139729
$78$	2.25854	+	1.33348i	0.255730	+	0.150987i
$79$	−0.187126	−	0.0681083i	−0.0210533	−	0.00766278i	0.331472	−	0.943465i	$-0.392455\pi$
$79$	−0.187126	−	0.0681083i	−0.0210533	−	0.00766278i	−0.352525	+	0.935802i	$0.614677\pi$
$80$	−13.1329	−	5.36833i	−1.46831	−	0.600197i
$81$	−0.228002	−	1.29306i	−0.0253336	−	0.143674i
$82$	−7.10291	−	8.63440i	−0.784385	−	0.953510i
$83$	12.9034	+	7.44977i	1.41633	+	0.817719i	0.995974	−	0.0896401i	$-0.0285717\pi$
$83$	12.9034	+	7.44977i	1.41633	+	0.817719i	0.420356	+	0.907359i	$0.361905\pi$
$84$	−3.41490	+	8.84229i	−0.372596	+	0.964773i
$85$	12.7201	+	10.6735i	1.37969	+	1.15770i
$86$	−1.12529	+	3.00041i	−0.121343	+	0.323543i
$87$	0.539091	−	0.311244i	0.0577966	−	0.0333689i
$88$	−0.747767	+	0.403054i	−0.0797123	+	0.0429657i
$89$	2.26220	+	6.21534i	0.239793	+	0.658825i	0.999959	+	0.00909600i	$0.00289539\pi$
$89$	2.26220	+	6.21534i	0.239793	+	0.658825i	−0.760166	+	0.649729i	$0.774882\pi$
$90$	−4.07394	−	7.21779i	−0.429431	−	0.760822i
$91$	1.13254	−	6.42296i	0.118723	−	0.673309i
$92$	−2.01854	−	5.90124i	−0.210447	−	0.615247i
$93$	−3.70047	+	3.10507i	−0.383721	+	0.321980i
$94$	1.54753	+	4.38426i	0.159615	+	0.452202i
$95$	−7.68017	+	13.4183i	−0.787969	+	1.37669i
$96$	0.824040	+	6.51517i	0.0841033	+	0.664951i
$97$	3.90012	+	4.64798i	0.395997	+	0.471931i	0.926795	−	0.375567i	$-0.122552\pi$
$97$	3.90012	+	4.64798i	0.395997	+	0.471931i	−0.530798	+	0.847498i	$0.678108\pi$
$98$	13.6703	+	0.133210i	1.38091	+	0.0134562i
$99$	−0.488704	−	0.0861717i	−0.0491166	−	0.00866058i
$100$	11.4224	+	9.97018i	1.14224	+	0.997018i
$101$	5.15199	−	1.87517i	0.512642	−	0.186586i	−0.0727293	−	0.997352i	$-0.523171\pi$
$101$	5.15199	−	1.87517i	0.512642	−	0.186586i	0.585371	+	0.810765i	$0.300949\pi$
$102$	1.40834	−	7.55579i	0.139446	−	0.748134i
$103$	−9.18625	−	15.9110i	−0.905148	−	1.56776i	−0.820719	−	0.571333i	$-0.806427\pi$
$103$	−9.18625	−	15.9110i	−0.905148	−	1.56776i	−0.0844294	−	0.996429i	$-0.526907\pi$
$104$	−1.42068	−	4.28943i	−0.139309	−	0.420613i
$105$	10.8055	−	12.8775i	1.05451	−	1.25672i
$106$	−4.78548	+	5.59155i	−0.464807	+	0.543099i
$107$	8.31778	−	14.4068i	0.804110	−	1.39276i	−0.112780	−	0.993620i	$-0.535975\pi$
$107$	8.31778	−	14.4068i	0.804110	−	1.39276i	0.916890	−	0.399140i	$-0.130691\pi$
$108$	−5.58215	+	9.24757i	−0.537142	+	0.889848i
$109$	−8.39330	+	1.47996i	−0.803932	+	0.141755i	−0.560491	−	0.828161i	$-0.689387\pi$
$109$	−8.39330	+	1.47996i	−0.803932	+	0.141755i	−0.243441	+	0.969916i	$0.578276\pi$
$110$	1.48611	−	0.247136i	0.141695	−	0.0235635i
$111$	0.963763	−	2.64792i	0.0914763	−	0.251329i
$112$	14.4496	−	7.60773i	1.36536	−	0.718863i
$113$		−	10.6541i		−	1.00226i	−0.865373	−	0.501129i	$-0.832918\pi$
$113$		−	10.6541i		−	1.00226i	0.865373	−	0.501129i	$-0.167082\pi$
$114$	7.15617	+	0.0429244i	0.670237	+	0.00402024i
$115$			11.0610i			1.03144i
$116$	−1.05230	−	0.206769i	−0.0977033	−	0.0191980i
$117$	0.902812	−	2.48046i	0.0834650	−	0.229318i
$118$	1.26337	+	7.59708i	0.116303	+	0.699368i
$119$	−18.8218	+	3.31880i	−1.72539	+	0.304234i
$120$	2.35677	−	11.4056i	0.215143	−	1.04118i
$121$	−5.45490	+	9.44816i	−0.495900	+	0.858924i
$122$	3.67772	+	3.14755i	0.332965	+	0.284966i
$123$	5.89945	−	7.03069i	0.531935	−	0.633936i
$124$	8.32059	+	0.162174i	0.747211	+	0.0145637i
$125$	−4.57699	−	7.92759i	−0.409379	−	0.709065i
$126$	9.37809	+	1.74800i	0.835466	+	0.155724i
$127$	17.1851	−	6.25486i	1.52493	−	0.555029i	0.562556	−	0.826759i	$-0.309818\pi$
$127$	17.1851	−	6.25486i	1.52493	−	0.555029i	0.962373	+	0.271730i	$0.0875959\pi$
$128$	6.31149	−	9.38963i	0.557862	−	0.829934i
$129$	−2.59055	−	0.456784i	−0.228085	−	0.0402176i
$130$	−0.0780841	+	8.01319i	−0.00684843	+	0.702804i
$131$	1.78093	+	2.12243i	0.155601	+	0.185438i	0.838213	−	0.545343i	$-0.183601\pi$
$131$	1.78093	+	2.12243i	0.155601	+	0.185438i	−0.682612	+	0.730781i	$0.739156\pi$
$132$	−0.437735	−	0.542812i	−0.0380999	−	0.0472457i
$133$	−6.14892	−	16.6991i	−0.533179	−	1.44800i
$134$	−9.22040	+	3.25456i	−0.796521	+	0.281151i
$135$	14.6748	−	12.3136i	1.26301	−	1.05979i
$136$	−10.3878	+	8.21120i	−0.890748	+	0.704104i
$137$	−1.84783	+	10.4796i	−0.157871	+	0.895330i	0.798243	+	0.602335i	$0.205763\pi$
$137$	−1.84783	+	10.4796i	−0.157871	+	0.895330i	−0.956114	+	0.292995i	$0.905348\pi$
$138$	4.45860	−	2.51657i	0.379541	−	0.214224i
$139$	6.24308	+	17.1527i	0.529531	+	1.45487i	0.859624	+	0.510927i	$0.170698\pi$
$139$	6.24308	+	17.1527i	0.529531	+	1.45487i	−0.330093	+	0.943948i	$0.607080\pi$
$140$	−28.6134	+	4.47225i	−2.41828	+	0.377974i
$141$	−3.30526	+	1.90829i	−0.278353	+	0.160707i
$142$	5.66769	+	2.12564i	0.475622	+	0.178379i
$143$	0.367550	+	0.308411i	0.0307361	+	0.0257906i
$144$	6.29398	−	2.01675i	0.524498	−	0.168063i
$145$	1.64710	+	0.950952i	0.136784	+	0.0789723i
$146$	−9.88389	+	8.13078i	−0.817997	+	0.672908i
$147$	1.94873	+	11.0518i	0.160729	+	0.911537i
$148$	−4.25069	+	2.34490i	−0.349405	+	0.192750i
$149$	14.1321	+	5.14368i	1.15775	+	0.421387i	0.848293	−	0.529527i	$-0.177630\pi$
$149$	14.1321	+	5.14368i	1.15775	+	0.421387i	0.309457	+	0.950913i	$0.399853\pi$
$150$	−6.32770	+	10.7173i	−0.516654	+	0.875068i
$151$	−15.0749			−1.22678			−0.613389	−	0.789781i	$-0.710194\pi$
$151$	−15.0749			−1.22678			−0.613389	+	0.789781i	$0.710194\pi$
$152$	−9.23941	−	8.16292i	−0.749415	−	0.662100i
$153$	−7.73522			−0.625355
$154$	−0.881588	+	1.49316i	−0.0710404	+	0.120323i
$155$	−13.8691	−	5.04792i	−1.11399	−	0.405459i
$156$	3.24782	−	1.79166i	0.260034	−	0.143448i
$157$	−2.81624	−	15.9717i	−0.224761	−	1.27468i	−0.863142	−	0.504961i	$-0.831507\pi$
$157$	−2.81624	−	15.9717i	−0.224761	−	1.27468i	0.638381	−	0.769720i	$-0.279604\pi$
$158$	−0.217487	+	0.178911i	−0.0173023	+	0.0142334i
$159$	−5.23211	−	3.02076i	−0.414933	−	0.239562i
$160$	−15.9802	+	12.1334i	−1.26335	+	0.959228i
$161$	−9.75260	−	8.18340i	−0.768613	−	0.644942i
$162$	−1.73862	−	0.652062i	−0.136599	−	0.0512308i
$163$	−5.45589	+	3.14996i	−0.427338	+	0.246724i	−0.698212	−	0.715891i	$-0.746021\pi$
$163$	−5.45589	+	3.14996i	−0.427338	+	0.246724i	0.270874	+	0.962615i	$0.412687\pi$
$164$	−15.6220	+	2.44170i	−1.21987	+	0.190665i
$165$	0.422969	+	1.16210i	0.0329281	+	0.0904692i
$166$	18.3499	−	10.3573i	1.42423	−	0.803879i
$167$	−0.932562	+	5.28882i	−0.0721638	+	0.409261i	0.927231	+	0.374489i	$0.122182\pi$
$167$	−0.932562	+	5.28882i	−0.0721638	+	0.409261i	−0.999395	+	0.0347725i	$0.988929\pi$
$168$	8.31278	+	10.5163i	0.641345	+	0.811352i
$169$	8.00348	−	6.71572i	0.615653	−	0.516594i
$170$	22.1440	−	7.81625i	1.69837	−	0.599479i
$171$	−1.27721	−	7.08805i	−0.0976707	−	0.542037i
$172$	2.84480	+	3.52769i	0.216914	+	0.268984i
$173$	−9.95804	−	11.8675i	−0.757096	−	0.902271i	0.240565	−	0.970633i	$-0.422667\pi$
$173$	−9.95804	−	11.8675i	−0.757096	−	0.902271i	−0.997661	+	0.0683617i	$0.978223\pi$
$174$	0.00857793	−	0.880289i	0.000650291	−	0.0667346i
$175$	30.4785	+	5.37418i	2.30396	+	0.406250i
$176$	−0.0468122	+	1.20043i	−0.00352860	+	0.0904856i
$177$	−5.94070	+	2.16224i	−0.446531	+	0.162524i
$178$	9.19556	+	1.71398i	0.689236	+	0.128468i
$179$	4.09294	+	7.08919i	0.305921	+	0.529871i	0.977466	−	0.211093i	$-0.0677023\pi$
$179$	4.09294	+	7.08919i	0.305921	+	0.529871i	−0.671545	+	0.740964i	$0.734369\pi$
$180$	−11.7190	−	0.228412i	−0.873482	−	0.0170248i
$181$	−11.2531	+	13.4109i	−0.836434	+	0.996823i	0.163514	+	0.986541i	$0.447717\pi$
$181$	−11.2531	+	13.4109i	−0.836434	+	0.996823i	−0.999947	+	0.0102816i	$0.996727\pi$
$182$	−7.00755	−	5.99736i	−0.519434	−	0.444554i
$183$	−1.98684	+	3.44131i	−0.146871	+	0.254389i
$184$	−8.63785	−	1.78487i	−0.636791	−	0.131582i
$185$	8.47866	−	1.49502i	0.623364	−	0.109916i
$186$	1.12067	+	6.73899i	0.0821717	+	0.494127i
$187$	0.480885	−	1.32122i	0.0351658	−	0.0966173i
$188$	6.45182	+	1.26774i	0.470547	+	0.0924593i
$189$			22.0491i			1.60384i
$190$	10.8186	+	19.0007i	0.784867	+	1.37846i
$191$		−	5.42765i		−	0.392731i	−0.980531	−	0.196366i	$-0.937086\pi$
$191$		−	5.42765i		−	0.392731i	0.980531	−	0.196366i	$-0.0629139\pi$
$192$	8.52664	+	3.68094i	0.615357	+	0.265649i
$193$	−3.00336	+	8.25165i	−0.216186	+	0.593967i	−0.999622	−	0.0275063i	$-0.991243\pi$
$193$	−3.00336	+	8.25165i	−0.216186	+	0.593967i	0.783435	+	0.621473i	$0.213466\pi$
$194$	8.46451	−	1.40762i	0.607716	−	0.101061i
$195$	−6.47828	+	1.14230i	−0.463919	+	0.0818014i
$196$	9.99129	−	16.5519i	0.713663	−	1.18228i
$197$	1.49191	−	2.58406i	0.106294	−	0.184107i	−0.807972	−	0.589221i	$-0.799435\pi$
$197$	1.49191	−	2.58406i	0.106294	−	0.184107i	0.914266	+	0.405114i	$0.132768\pi$
$198$	−0.456321	+	0.533184i	−0.0324293	+	0.0378917i
$199$	−0.554813	+	0.661200i	−0.0393297	+	0.0468713i	−0.785351	−	0.619051i	$-0.787517\pi$
$199$	−0.554813	+	0.661200i	−0.0393297	+	0.0468713i	0.746021	+	0.665922i	$0.231962\pi$
$200$	20.3544	−	6.74147i	1.43927	−	0.476694i
$201$	−4.01327	−	6.95119i	−0.283075	−	0.490299i
$202$	1.42074	−	7.62234i	0.0999629	−	0.536306i
$203$	−2.05706	+	0.748708i	−0.144377	+	0.0525490i
$204$	−8.18881	−	7.14773i	−0.573331	−	0.500441i
$205$	27.6155	+	4.86936i	1.92875	+	0.340091i
$206$	−25.9814	−	0.253174i	−1.81021	−	0.0176395i
$207$	−3.31204	−	3.94714i	−0.230203	−	0.274345i
$208$	−6.24514	−	1.35403i	−0.433022	−	0.0938853i
$209$	1.29008	+	0.222497i	0.0892369	+	0.0153904i
$210$	−7.91295	−	22.4179i	−0.546045	−	1.54698i
$211$	−6.79371	+	5.70060i	−0.467698	+	0.392446i	−0.845954	−	0.533256i	$-0.820968\pi$
$211$	−6.79371	+	5.70060i	−0.467698	+	0.392446i	0.378256	+	0.925701i	$0.376524\pi$
$212$	3.36857	+	9.84810i	0.231355	+	0.676371i
$213$	−0.862851	+	4.89347i	−0.0591216	+	0.335295i
$214$	−11.5640	−	20.4880i	−0.790501	−	1.40053i
$215$	−2.74884	−	7.55238i	−0.187469	−	0.515068i
$216$	7.24806	+	13.4470i	0.493168	+	0.914952i
$217$	14.7117	−	8.49382i	0.998698	−	0.576598i
$218$	−4.23254	+	11.2854i	−0.286664	+	0.764346i
$219$	−8.04811	−	6.75317i	−0.543841	−	0.456337i
$220$	0.767564	−	1.98747i	0.0517492	−	0.133996i
$221$	6.47696	+	3.73948i	0.435688	+	0.251544i
$222$	−2.53167	−	3.07754i	−0.169915	−	0.206551i
$223$	−2.08177	−	11.8063i	−0.139406	−	0.790610i	−0.971690	−	0.236260i	$-0.924078\pi$
$223$	−2.08177	−	11.8063i	−0.139406	−	0.790610i	0.832284	−	0.554350i	$-0.187033\pi$
$224$	1.12472	−	23.0667i	0.0751483	−	1.54121i
$225$	11.7704	+	4.28406i	0.784691	+	0.285604i
$226$	−12.9746	−	7.66040i	−0.863056	−	0.509562i
$227$	−3.59398			−0.238541			−0.119270	−	0.992862i	$-0.538056\pi$
$227$	−3.59398			−0.238541			−0.119270	+	0.992862i	$0.538056\pi$
$228$	5.19761	−	8.68390i	0.344220	−	0.575105i
$229$	8.48334			0.560595			0.280297	−	0.959913i	$-0.409567\pi$
$229$	8.48334			0.560595			0.280297	+	0.959913i	$0.409567\pi$
$230$	13.4700	+	7.95293i	0.888188	+	0.524401i
$231$	−1.33757	−	0.486834i	−0.0880054	−	0.0320313i
$232$	−1.00841	+	1.13282i	−0.0662054	+	0.0743730i
$233$	3.62386	+	20.5519i	0.237407	+	1.34640i	0.837485	+	0.546461i	$0.184025\pi$
$233$	3.62386	+	20.5519i	0.237407	+	1.34640i	−0.600078	+	0.799942i	$0.704864\pi$
$234$	−2.37156	−	2.88291i	−0.155034	−	0.188461i
$235$	−10.0987	−	5.83046i	−0.658763	−	0.380337i
$236$	10.1601	+	3.92383i	0.661364	+	0.255419i
$237$	−0.177092	−	0.148598i	−0.0115034	−	0.00965247i
$238$	−9.49141	+	25.3074i	−0.615237	+	1.64044i
$239$	22.9107	−	13.2275i	1.48197	−	0.855617i	0.482182	−	0.876071i	$-0.339844\pi$
$239$	22.9107	−	13.2275i	1.48197	−	0.855617i	0.999791	+	0.0204539i	$0.00651115\pi$
$240$	−12.1951	−	11.0708i	−0.787192	−	0.714614i
$241$	−5.36811	−	14.7488i	−0.345790	−	0.950051i	−0.983681	−	0.179924i	$-0.942415\pi$
$241$	−5.36811	−	14.7488i	−0.345790	−	0.950051i	0.637890	−	0.770127i	$-0.279807\pi$
$242$	7.58383	+	13.4363i	0.487507	+	0.863715i
$243$	−2.54887	+	14.4554i	−0.163510	+	0.927312i
$244$	6.47738	−	2.21561i	0.414672	−	0.141840i
$245$	−26.2659	+	22.0397i	−1.67807	+	1.40807i
$246$	−4.32021	−	12.2394i	−0.275446	−	0.780359i
$247$	−2.35716	+	6.55252i	−0.149983	+	0.416927i
$248$	6.18006	−	10.0162i	0.392434	−	0.636028i
$249$	11.1183	+	13.2502i	0.704592	+	0.839700i
$250$	−12.9451	−	0.126143i	−0.818719	−	0.00797796i
$251$	−1.99182	−	0.351211i	−0.125722	−	0.0221682i	0.110433	−	0.993884i	$-0.464776\pi$
$251$	−1.99182	−	0.351211i	−0.125722	−	0.0221682i	−0.236155	+	0.971715i	$0.575887\pi$
$252$	8.87162	−	10.1638i	0.558859	−	0.640258i
$253$	0.880099	−	0.320330i	0.0553313	−	0.0201390i
$254$	4.73905	−	25.4252i	0.297354	−	1.59532i
$255$	9.63840	+	16.6942i	0.603580	+	1.04543i
$256$	−6.89665	−	14.4373i	−0.431041	−	0.902333i
$257$	−2.96164	+	3.52955i	−0.184742	+	0.220167i	−0.850465	−	0.526032i	$-0.823679\pi$
$257$	−2.96164	+	3.52955i	−0.184742	+	0.220167i	0.665722	+	0.746200i	$0.268124\pi$
$258$	−2.41889	+	2.82633i	−0.150594	+	0.175960i
$259$	−4.95471	+	8.58181i	−0.307871	+	0.533248i
$260$	9.70230	+	5.85663i	0.601711	+	0.363213i
$261$	−0.872518	+	0.153848i	−0.0540075	+	0.00952298i
$262$	3.86519	−	0.642769i	0.238792	−	0.0397104i
$263$	3.03627	−	8.34207i	0.187224	−	0.514394i	−0.810198	−	0.586157i	$-0.800640\pi$
$263$	3.03627	−	8.34207i	0.187224	−	0.514394i	0.997422	+	0.0717627i	$0.0228624\pi$
$264$	−0.975769	+	0.142786i	−0.0600544	+	0.00878787i
$265$		−	18.4588i		−	1.13392i
$266$	−24.7573	−	4.51865i	−1.51796	−	0.277056i
$267$			7.67849i			0.469916i
$268$	−2.66614	+	13.5686i	−0.162860	+	0.828836i
$269$	−2.44696	+	6.72295i	−0.149193	+	0.409906i	−0.991666	−	0.128833i	$-0.958877\pi$
$269$	−2.44696	+	6.72295i	−0.149193	+	0.409906i	0.842473	+	0.538739i	$0.181099\pi$
$270$	−4.44420	−	26.7245i	−0.270466	−	1.62640i
$271$	31.4126	−	5.53889i	1.90818	−	0.336464i	0.911059	−	0.412277i	$-0.135266\pi$
$271$	31.4126	−	5.53889i	1.90818	−	0.336464i	0.997122	+	0.0758130i	$0.0241552\pi$
$272$	2.53066	+	18.5542i	0.153444	+	1.12501i
$273$	3.78574	−	6.55709i	0.229123	−	0.396853i
$274$	11.4334	+	9.78517i	0.690716	+	0.591144i
$275$	−1.46349	+	1.74412i	−0.0882516	+	0.105174i
$276$	0.141095	−	7.23909i	0.00849293	−	0.435742i
$277$	−5.16272	−	8.94209i	−0.310198	−	0.537278i	0.668207	−	0.743975i	$-0.267062\pi$
$277$	−5.16272	−	8.94209i	−0.310198	−	0.537278i	−0.978405	+	0.206697i	$0.933729\pi$
$278$	25.3773	+	4.73013i	1.52203	+	0.283694i
$279$	6.46072	−	2.35151i	0.386793	−	0.140781i
$280$	−15.1270	+	38.0609i	−0.904009	+	2.27458i
$281$	−24.7357	−	4.36157i	−1.47561	−	0.260190i	−0.622787	−	0.782391i	$-0.714000\pi$
$281$	−24.7357	−	4.36157i	−1.47561	−	0.260190i	−0.852822	+	0.522202i	$0.825111\pi$
$282$	−0.0525928	+	5.39721i	−0.00313186	+	0.321399i
$283$	−9.40772	−	11.2117i	−0.559231	−	0.666465i	0.410153	−	0.912017i	$-0.365475\pi$
$283$	−9.40772	−	11.2117i	−0.559231	−	0.666465i	−0.969384	+	0.245552i	$0.921031\pi$
$284$	6.66370	−	5.37374i	0.395418	−	0.318873i
$285$	−13.7060	+	11.5885i	−0.811875	+	0.686443i
$286$	0.639854	−	0.225852i	0.0378353	−	0.0133549i
$287$	−24.7245	+	20.7463i	−1.45944	+	1.22462i
$288$	2.06942	−	9.11485i	0.121942	−	0.537098i
$289$	0.853710	−	4.84163i	0.0502183	−	0.284802i
$290$	2.34234	−	1.32209i	0.137547	−	0.0776357i
$291$	2.40912	+	6.61901i	0.141225	+	0.388013i
$292$	2.79504	+	17.8827i	0.163568	+	1.04650i
$293$	25.4984	−	14.7215i	1.48963	−	0.860039i	0.489701	−	0.871890i	$-0.337106\pi$
$293$	25.4984	−	14.7215i	1.48963	−	0.860039i	0.999930	+	0.0118513i	$0.00377249\pi$
$294$	14.8600	+	5.57316i	0.866652	+	0.325034i
$295$	−14.7967	−	12.4159i	−0.861494	−	0.722880i
$296$	−0.200664	+	6.86248i	−0.0116633	+	0.398874i
$297$	−1.40476	−	0.811036i	−0.0815122	−	0.0470611i
$298$	16.4251	−	13.5117i	0.951479	−	0.782714i
$299$	0.865101	+	4.90623i	0.0500301	+	0.283735i
$300$	8.50189	+	15.4117i	0.490857	+	0.889795i
$301$	8.69273	+	3.16390i	0.501041	+	0.182364i
$302$	−10.8390	+	18.3582i	−0.623712	+	1.05639i
$303$	6.36482			0.365649
$304$	−16.5840	+	5.38252i	−0.951157	+	0.308709i
$305$	−12.1409			−0.695185
$306$	−5.56168	+	9.41992i	−0.317940	+	0.538501i
$307$	14.8744	+	5.41384i	0.848926	+	0.308984i	0.729602	−	0.683872i	$-0.239705\pi$
$307$	14.8744	+	5.41384i	0.848926	+	0.308984i	0.119324	+	0.992855i	$0.461927\pi$
$308$	1.18450	+	2.14719i	0.0674932	+	0.122348i
$309$	−3.70369	−	21.0047i	−0.210696	−	1.19492i
$310$	−16.1193	+	13.2602i	−0.915514	+	0.753128i
$311$	−11.3865	−	6.57399i	−0.645669	−	0.372777i	0.141126	−	0.989992i	$-0.454928\pi$
$311$	−11.3865	−	6.57399i	−0.645669	−	0.372777i	−0.786795	+	0.617215i	$0.788261\pi$
$312$	0.153321	−	5.24340i	0.00868008	−	0.296849i
$313$	−15.0193	−	12.6027i	−0.848944	−	0.712348i	0.110613	−	0.993864i	$-0.464719\pi$
$313$	−15.0193	−	12.6027i	−0.848944	−	0.712348i	−0.959557	+	0.281515i	$0.909163\pi$
$314$	−21.4752	−	8.05416i	−1.21192	−	0.454523i
$315$	−20.7205	+	11.9630i	−1.16747	+	0.674038i
$316$	0.0615026	+	0.393493i	0.00345979	+	0.0221357i
$317$	2.06718	+	5.67953i	0.116104	+	0.318994i	0.984110	−	0.177560i	$-0.0568205\pi$
$317$	2.06718	+	5.67953i	0.116104	+	0.318994i	−0.868005	+	0.496555i	$0.834598\pi$
$318$	−7.44059	+	4.19970i	−0.417248	+	0.235507i
$319$	0.0279647	−	0.158596i	0.00156572	−	0.00887966i
$320$	3.28611	+	28.1846i	0.183699	+	1.57557i
$321$	14.7941	−	12.4137i	0.825726	−	0.692866i
$322$	−16.9779	+	5.99276i	−0.946142	+	0.333963i
$323$	20.4060	−	0.0764404i	1.13542	−	0.00425326i
$324$	−2.04416	+	1.64845i	−0.113565	+	0.0915808i
$325$	−7.78467	−	9.27741i	−0.431816	−	0.514618i
$326$	−0.0868132	+	8.90900i	−0.00480814	+	0.493424i
$327$	−9.74382	−	1.71810i	−0.538835	−	0.0950111i
$328$	−8.25882	+	20.7800i	−0.456017	+	1.14738i
$329$	12.6122	−	4.59047i	0.695333	−	0.253081i
$330$	1.71932	+	0.320466i	0.0946453	+	0.0176411i
$331$	1.83555	+	3.17926i	0.100891	+	0.174748i	0.912052	−	0.410075i	$-0.134497\pi$
$331$	1.83555	+	3.17926i	0.100891	+	0.174748i	−0.811161	+	0.584823i	$0.801164\pi$
$332$	0.580696	−	29.7934i	0.0318698	−	1.63513i
$333$	−2.57797	+	3.07230i	−0.141272	+	0.168361i
$334$	5.77019	+	4.93837i	0.315731	+	0.270216i
$335$	12.2619	−	21.2382i	0.669937	−	1.16036i
$336$	18.7837	−	2.56196i	1.02473	−	0.139766i
$337$	−17.7177	+	3.12412i	−0.965147	+	0.170181i	−0.633945	−	0.773378i	$-0.718565\pi$
$337$	−17.7177	+	3.12412i	−0.965147	+	0.170181i	−0.331202	+	0.943560i	$0.607454\pi$
$338$	−2.42382	−	14.5753i	−0.131838	−	0.792790i
$339$	4.23026	−	11.6225i	0.229756	−	0.631250i
$340$	6.40308	−	32.5868i	0.347256	−	1.76727i
$341$			1.24972i			0.0676761i
$342$	−9.55013	−	3.54098i	−0.516412	−	0.191474i
$343$		−	10.8874i		−	0.587864i
$344$	6.34144	−	0.927955i	0.341908	−	0.0500320i
$345$	−4.39180	+	12.0664i	−0.236447	+	0.649632i
$346$	−21.6121	+	3.59403i	−1.16188	+	0.193216i
$347$	16.0384	−	2.82801i	0.860988	−	0.151815i	0.274316	−	0.961640i	$-0.411549\pi$
$347$	16.0384	−	2.82801i	0.860988	−	0.151815i	0.586672	+	0.809824i	$0.300438\pi$
$348$	−1.06585	−	0.643381i	−0.0571353	−	0.0344888i
$349$	5.92019	−	10.2541i	0.316901	−	0.548888i	−0.662939	−	0.748673i	$-0.730691\pi$
$349$	5.92019	−	10.2541i	0.316901	−	0.548888i	0.979840	+	0.199785i	$0.0640245\pi$
$350$	28.4589	−	33.2526i	1.52119	−	1.77742i
$351$	5.54611	−	6.60960i	0.296030	−	0.352794i
$352$	1.42822	+	0.920123i	0.0761243	+	0.0490427i
$353$	12.9044	+	22.3511i	0.686833	+	1.18963i	0.972857	+	0.231408i	$0.0743331\pi$
$353$	12.9044	+	22.3511i	0.686833	+	1.18963i	−0.286023	+	0.958223i	$0.592334\pi$
$354$	−1.63824	+	8.78923i	−0.0870715	+	0.467142i
$355$	−14.2662	+	5.19248i	−0.757172	+	0.275588i
$356$	8.69895	−	9.96596i	0.461043	−	0.528195i
$357$	−21.8504	−	3.85281i	−1.15644	−	0.203912i
$358$	11.5760	+	0.112802i	0.611813	+	0.00596177i
$359$	2.73656	+	3.26130i	0.144430	+	0.172125i	0.833410	−	0.552656i	$-0.186386\pi$
$359$	2.73656	+	3.26130i	0.144430	+	0.172125i	−0.688980	+	0.724781i	$0.741941\pi$
$360$	−8.70420	+	14.1071i	−0.458752	+	0.743511i
$361$	3.43941	+	18.6861i	0.181021	+	0.983479i
$362$	8.24069	+	23.3465i	0.433121	+	1.22706i
$363$	−9.70214	+	8.14106i	−0.509230	+	0.427295i
$364$	−12.3420	+	4.22163i	−0.646899	+	0.221274i
$365$	5.57401	−	31.6118i	0.291757	−	1.65464i
$366$	2.76226	+	4.89389i	0.144386	+	0.255808i
$367$	−0.887138	−	2.43739i	−0.0463082	−	0.127231i	0.914383	−	0.404851i	$-0.132677\pi$
$367$	−0.887138	−	2.43739i	−0.0463082	−	0.127231i	−0.960691	+	0.277620i	$0.910454\pi$
$368$	−8.38428	+	9.23581i	−0.437061	+	0.481450i
$369$	−11.3127	+	6.53139i	−0.588916	+	0.340011i
$370$	4.27559	−	11.4002i	0.222277	−	0.592669i
$371$	16.2753	+	13.6566i	0.844973	+	0.709017i
$372$	9.01249	+	3.48063i	0.467276	+	0.180462i
$373$	−32.6213	−	18.8339i	−1.68907	−	0.975183i	−0.955233	−	0.295854i	$-0.904396\pi$
$373$	−32.6213	−	18.8339i	−1.68907	−	0.975183i	−0.733833	−	0.679330i	$-0.762271\pi$
$374$	−1.26322	−	1.53559i	−0.0653195	−	0.0794033i
$375$	−1.84534	−	10.4655i	−0.0952932	−	0.540434i
$376$	6.18275	−	6.94549i	0.318851	−	0.358187i
$377$	0.804965	+	0.292983i	0.0414578	+	0.0150894i
$378$	26.8513	+	15.8535i	1.38108	+	0.815414i
$379$	17.6837			0.908353			0.454177	−	0.890912i	$-0.349934\pi$
$379$	17.6837			0.908353			0.454177	+	0.890912i	$0.349934\pi$
$380$	30.9177	+	0.486756i	1.58604	+	0.0249701i
$381$	21.2306			1.08768
$382$	−6.60978	−	3.90252i	−0.338186	−	0.199670i
$383$	−18.5485	−	6.75110i	−0.947785	−	0.344965i	−0.178549	−	0.983931i	$-0.557140\pi$
$383$	−18.5485	−	6.75110i	−0.947785	−	0.344965i	−0.769235	+	0.638966i	$0.779363\pi$
$384$	10.6133	−	7.73709i	0.541610	−	0.394832i
$385$	−0.755191	−	4.28290i	−0.0384881	−	0.218277i
$386$	7.88940	+	9.59048i	0.401560	+	0.488142i
$387$	3.24237	+	1.87199i	0.164819	+	0.0951584i
$388$	4.37185	−	11.3201i	0.221947	−	0.574693i
$389$	15.7275	+	13.1970i	0.797418	+	0.669113i	0.947569	−	0.319550i	$-0.103532\pi$
$389$	15.7275	+	13.1970i	0.797418	+	0.669113i	−0.150152	+	0.988663i	$0.547976\pi$
$390$	−3.26684	+	8.71054i	−0.165423	+	0.441075i
$391$	12.6431	−	7.29951i	0.639390	−	0.369152i
$392$	−12.9730	−	24.0683i	−0.655238	−	1.21563i
$393$	1.10009	+	3.02247i	0.0554922	+	0.152463i
$394$	−2.07417	−	3.67480i	−0.104495	−	0.185134i
$395$	0.122651	−	0.695591i	0.00617127	−	0.0349990i
$396$	0.321212	+	0.939070i	0.0161415	+	0.0471900i
$397$	4.01047	−	3.36518i	0.201280	−	0.168894i	−0.536577	−	0.843852i	$-0.680283\pi$
$397$	4.01047	−	3.36518i	0.201280	−	0.168894i	0.737856	+	0.674958i	$0.235838\pi$
$398$	0.406293	+	1.15106i	0.0203656	+	0.0576973i
$399$	−0.0773861	−	20.6584i	−0.00387415	−	1.03421i
$400$	6.42522	−	29.6347i	0.321261	−	1.48174i
$401$	16.5098	+	19.6756i	0.824458	+	0.982550i	0.999998	−	0.00192191i	$-0.000611762\pi$
$401$	16.5098	+	19.6756i	0.824458	+	0.982550i	−0.175541	+	0.984472i	$0.556167\pi$
$402$	−11.3507	−	0.110606i	−0.566122	−	0.00551654i
$403$	−6.54659	−	1.15434i	−0.326109	−	0.0575018i
$404$	−8.26093	−	7.21069i	−0.410997	−	0.358745i
$405$	4.37632	−	1.59285i	0.217461	−	0.0791493i
$406$	−0.567266	+	3.04341i	−0.0281529	+	0.151042i
$407$	−0.364500	−	0.631333i	−0.0180676	−	0.0312940i
$408$	−14.5923	+	4.83303i	−0.722426	+	0.239271i
$409$	15.6062	−	18.5987i	0.771676	−	0.919648i	−0.226850	−	0.973930i	$-0.572843\pi$
$409$	15.6062	−	18.5987i	0.771676	−	0.919648i	0.998526	+	0.0542822i	$0.0172871\pi$
$410$	25.7856	−	30.1290i	1.27346	−	1.48796i
$411$	−6.17673	+	10.6984i	−0.304676	+	0.527714i
$412$	−18.9891	+	31.4580i	−0.935527	+	1.54983i
$413$	21.8944	−	3.86058i	1.07735	−	0.189967i
$414$	−7.18819	+	1.19537i	−0.353280	+	0.0587494i
$415$	−18.0750	+	49.6607i	−0.887268	+	2.43775i
$416$	−6.13923	+	6.63175i	−0.301001	+	0.325148i
$417$			21.1906i			1.03771i
$418$	1.19854	−	1.41108i	0.0586223	−	0.0690183i
$419$		−	3.51321i		−	0.171632i	−0.996311	−	0.0858159i	$-0.972650\pi$
$419$		−	3.51321i		−	0.171632i	0.996311	−	0.0858159i	$-0.0273497\pi$
$420$	−32.9899	−	6.48229i	−1.60974	−	0.316304i
$421$	−0.483024	+	1.32710i	−0.0235412	+	0.0646788i	−0.950907	−	0.309478i	$-0.899846\pi$
$421$	−0.483024	+	1.32710i	−0.0235412	+	0.0646788i	0.927365	+	0.374157i	$0.122068\pi$
$422$	2.05745	+	12.3721i	0.100155	+	0.602266i
$423$	5.34957	−	0.943273i	0.260105	−	0.0458635i
$424$	14.4150	+	2.97862i	0.700055	+	0.144655i
$425$	−17.7447	+	30.7348i	−0.860746	+	1.49086i
$426$	5.33886	+	4.56922i	0.258668	+	0.221379i
$427$	8.98236	−	10.7048i	0.434687	−	0.518039i
$428$	−33.2648	−	0.648355i	−1.60792	−	0.0313394i
$429$	0.278503	+	0.482381i	0.0134462	+	0.0232896i
$430$	−11.1737	−	2.08269i	−0.538844	−	0.100436i
$431$	−29.6032	+	10.7747i	−1.42594	+	0.518998i	−0.935764	−	0.352628i	$-0.885288\pi$
$431$	−29.6032	+	10.7747i	−1.42594	+	0.518998i	−0.490172	+	0.871626i	$0.663066\pi$
$432$	21.5871	+	0.841817i	1.03861	+	0.0405019i
$433$	32.3517	+	5.70447i	1.55472	+	0.274139i	0.883970	−	0.467543i	$-0.154861\pi$
$433$	32.3517	+	5.70447i	1.55472	+	0.274139i	0.670751	+	0.741683i	$0.265972\pi$
$434$	0.234091	−	24.0230i	0.0112367	−	1.15314i
$435$	1.41923	+	1.69137i	0.0680469	+	0.0810951i
$436$	10.7001	+	13.2687i	0.512444	+	0.635455i
$437$	8.77638	+	10.3801i	0.419831	+	0.496546i
$438$	−14.0106	+	4.94539i	−0.669454	+	0.236300i
$439$	1.21027	−	1.01554i	0.0577630	−	0.0484689i	−0.613449	−	0.789734i	$-0.710218\pi$
$439$	1.21027	−	1.01554i	0.0577630	−	0.0484689i	0.671212	+	0.741265i	$0.265774\pi$
$440$	−1.86846	−	2.36375i	−0.0890751	−	0.112687i
$441$	2.77360	−	15.7299i	0.132076	−	0.749041i
$442$	9.21090	−	5.19891i	0.438118	−	0.247287i
$443$	0.331536	+	0.910886i	0.0157517	+	0.0432775i	0.947319	−	0.320291i	$-0.103781\pi$
$443$	0.331536	+	0.910886i	0.0157517	+	0.0432775i	−0.931568	+	0.363568i	$0.881558\pi$
$444$	−5.56811	+	0.870290i	−0.264251	+	0.0413021i
$445$	−20.3172	+	11.7301i	−0.963128	+	0.556062i
$446$	−15.8745	−	5.95365i	−0.751680	−	0.281914i
$447$	13.3744	+	11.2224i	0.632586	+	0.530802i
$448$	−27.2819	−	17.9548i	−1.28895	−	0.848285i
$449$	−18.7171	−	10.8063i	−0.883312	−	0.509981i	−0.0115631	−	0.999933i	$-0.503681\pi$
$449$	−18.7171	−	10.8063i	−0.883312	−	0.509981i	−0.871749	+	0.489953i	$0.837014\pi$
$450$	13.6801	−	11.2536i	0.644886	−	0.530502i
$451$	−0.412309	−	2.33832i	−0.0194149	−	0.110107i
$452$	−18.6576	+	10.2925i	−0.877581	+	0.484119i
$453$	−16.4451	−	5.98554i	−0.772659	−	0.281225i
$454$	−2.58410	+	4.37673i	−0.121278	+	0.205410i
$455$	23.1333			1.08451
$456$	−6.83810	−	12.5734i	−0.320224	−	0.588804i
$457$	−14.8816			−0.696132			−0.348066	−	0.937470i	$-0.613162\pi$
$457$	−14.8816			−0.696132			−0.348066	+	0.937470i	$0.613162\pi$
$458$	6.09958	−	10.3310i	0.285015	−	0.482735i
$459$	−23.7593	−	8.64769i	−1.10899	−	0.403639i
$460$	19.3701	−	10.6856i	0.903136	−	0.498217i
$461$	0.538610	+	3.05461i	0.0250856	+	0.142267i	0.994778	−	0.102061i	$-0.0325437\pi$
$461$	0.538610	+	3.05461i	0.0250856	+	0.142267i	−0.969693	+	0.244328i	$0.921433\pi$
$462$	−1.55458	+	1.27885i	−0.0723258	+	0.0594973i
$463$	10.3891	+	5.99813i	0.482821	+	0.278757i	0.721591	−	0.692319i	$-0.243411\pi$
$463$	10.3891	+	5.99813i	0.482821	+	0.278757i	−0.238771	+	0.971076i	$0.576744\pi$
$464$	0.654484	+	2.04254i	0.0303836	+	0.0948226i
$465$	−13.1254	−	11.0135i	−0.608675	−	0.510739i
$466$	27.6337	+	10.3639i	1.28011	+	0.480097i
$467$	6.20648	−	3.58331i	0.287202	−	0.165816i	−0.349478	−	0.936945i	$-0.613641\pi$
$467$	6.20648	−	3.58331i	0.287202	−	0.165816i	0.636679	+	0.771129i	$0.280308\pi$
$468$	−5.21596	+	0.815250i	−0.241108	+	0.0376850i
$469$	9.65407	+	26.5243i	0.445783	+	1.22478i
$470$	−14.3613	+	8.10596i	−0.662438	+	0.373900i
$471$	3.26939	−	18.5416i	0.150646	−	0.854354i
$472$	12.0836	−	9.55164i	0.556192	−	0.439650i
$473$	−0.521319	+	0.437439i	−0.0239703	+	0.0201134i
$474$	−0.308292	+	0.108819i	−0.0141603	+	0.00499823i
$475$	−31.0933	−	11.1853i	−1.42666	−	0.513217i
$476$	23.9949	+	29.7548i	1.09980	+	1.36381i
$477$	5.52720	+	6.58706i	0.253073	+	0.301601i
$478$	0.364552	−	37.4113i	0.0166742	−	1.71115i
$479$	−30.0195	−	5.29324i	−1.37162	−	0.241854i	−0.561192	−	0.827686i	$-0.689657\pi$
$479$	−30.0195	−	5.29324i	−1.37162	−	0.241854i	−0.810433	+	0.585831i	$0.800768\pi$
$480$	−22.2503	+	6.89124i	−1.01558	+	0.314541i
$481$	3.64388	−	1.32627i	0.166147	−	0.0604725i
$482$	−21.8207	−	4.06720i	−0.993906	−	0.185256i
$483$	−7.38981	−	12.7995i	−0.336248	−	0.582399i
$484$	21.8155	+	0.425199i	0.991612	+	0.0193272i
$485$	−13.8335	+	16.4861i	−0.628147	+	0.748597i
$486$	15.7710	+	13.4975i	0.715388	+	0.612259i
$487$	−14.6412	+	25.3593i	−0.663455	+	1.14914i	0.316246	+	0.948677i	$0.397577\pi$
$487$	−14.6412	+	25.3593i	−0.663455	+	1.14914i	−0.979702	+	0.200461i	$0.935756\pi$
$488$	1.95912	−	9.48117i	0.0886854	−	0.429192i
$489$	−7.20250	+	1.26999i	−0.325708	+	0.0574311i
$490$	7.95453	+	47.8333i	0.359349	+	2.16089i
$491$	−8.64980	+	23.7651i	−0.390360	+	1.07250i	0.576478	+	0.817113i	$0.304427\pi$
$491$	−8.64980	+	23.7651i	−0.390360	+	1.07250i	−0.966838	+	0.255392i	$0.917795\pi$
$492$	−18.0114	−	3.53912i	−0.812017	−	0.159556i
$493$		−	2.51026i		−	0.113056i
$494$	6.28482	+	7.58185i	0.282767	+	0.341124i
$495$		−	1.76015i		−	0.0791127i
$496$	−7.75417	−	14.7278i	−0.348172	−	0.661296i
$497$	5.97650	−	16.4203i	0.268083	−	0.736551i
$498$	24.1302	−	4.01278i	1.08130	−	0.179817i
$499$	−19.5472	+	3.44669i	−0.875052	+	0.154295i	−0.593096	−	0.805132i	$-0.702094\pi$
$499$	−19.5472	+	3.44669i	−0.875052	+	0.154295i	−0.281956	+	0.959427i	$0.590983\pi$
$500$	−9.46122	+	15.6738i	−0.423119	+	0.700953i
$501$	−3.11727	+	5.39927i	−0.139269	+	0.241221i
$502$	−1.85983	+	2.17310i	−0.0830084	+	0.0969903i
$503$	−10.8354	+	12.9131i	−0.483127	+	0.575768i	−0.951456	−	0.307786i	$-0.900412\pi$
$503$	−10.8354	+	12.9131i	−0.483127	+	0.575768i	0.468329	+	0.883554i	$0.344856\pi$
$504$	−5.99866	−	18.1117i	−0.267202	−	0.806757i
$505$	9.72330	+	16.8412i	0.432681	+	0.749425i
$506$	0.242701	−	1.30210i	0.0107894	−	0.0578854i
$507$	11.3974	−	4.14833i	0.506178	−	0.184234i
$508$	−27.5553	−	24.0521i	−1.22257	−	1.06714i
$509$	−5.53279	−	0.975580i	−0.245237	−	0.0432418i	0.0496786	−	0.998765i	$-0.484180\pi$
$509$	−5.53279	−	0.975580i	−0.245237	−	0.0432418i	−0.294915	+	0.955523i	$0.595291\pi$
$510$	27.2602	+	0.265636i	1.20710	+	0.0117625i
$511$	23.7486	+	28.3024i	1.05057	+	1.25203i
$512$	−22.5405	−	1.98182i	−0.996157	−	0.0875848i
$513$	4.00113	−	23.1994i	0.176654	−	1.02428i
$514$	2.16883	+	6.14445i	0.0956630	+	0.271020i
$515$	49.9202	−	41.8880i	2.19975	−	1.84581i
$516$	1.70270	+	4.97787i	0.0749570	+	0.219139i
$517$	−0.171457	+	0.972379i	−0.00754066	+	0.0427652i
$518$	6.88843	+	12.2042i	0.302660	+	0.536222i
$519$	−6.15113	−	16.9001i	−0.270005	−	0.741831i
$520$	14.1082	−	7.60447i	0.618686	−	0.333478i
$521$	10.7604	−	6.21252i	0.471422	−	0.272175i	−0.245413	−	0.969419i	$-0.578924\pi$
$521$	10.7604	−	6.21252i	0.471422	−	0.272175i	0.716835	+	0.697243i	$0.245590\pi$
$522$	−0.439990	+	1.17317i	−0.0192579	+	0.0513482i
$523$	9.51699	+	7.98570i	0.416149	+	0.349190i	0.826696	−	0.562649i	$-0.190218\pi$
$523$	9.51699	+	7.98570i	0.416149	+	0.349190i	−0.410547	+	0.911839i	$0.634662\pi$
$524$	1.99634	−	5.16917i	0.0872104	−	0.225816i
$525$	31.1150	+	17.9643i	1.35797	+	0.784024i
$526$	−7.97585	−	9.69556i	−0.347764	−	0.422747i
$527$	3.38268	+	19.1841i	0.147352	+	0.835673i
$528$	−0.527700	+	1.29095i	−0.0229652	+	0.0561815i
$529$	−12.4746	−	4.54039i	−0.542375	−	0.197408i
$530$	−22.4791	−	13.2720i	−0.976428	−	0.576499i
$531$	8.99795			0.390478
$532$	−23.3034	+	26.9004i	−1.01033	+	1.16628i
$533$	12.6300			0.547067
$534$	9.35084	+	5.52089i	0.404651	+	0.238912i
$535$	55.4469	+	20.1810i	2.39718	+	0.872502i
$536$	14.6069	+	13.0028i	0.630920	+	0.561633i
$537$	1.65019	+	9.35867i	0.0712108	+	0.403856i
$538$	6.42781	+	7.81375i	0.277123	+	0.336875i
$539$	2.51432	+	1.45165i	0.108300	+	0.0625268i
$540$	−35.7405	−	13.8030i	−1.53802	−	0.593986i
$541$	1.32512	+	1.11191i	0.0569713	+	0.0478046i	0.670829	−	0.741612i	$-0.265939\pi$
$541$	1.32512	+	1.11191i	0.0569713	+	0.0478046i	−0.613857	+	0.789417i	$0.710383\pi$
$542$	15.8407	−	42.2367i	0.680414	−	1.81422i
$543$	−17.6007	+	10.1618i	−0.755320	+	0.436084i
$544$	24.4148	+	10.2588i	1.04677	+	0.439840i
$545$	−10.3392	−	28.4067i	−0.442883	−	1.21681i
$546$	−5.26323	−	9.32485i	−0.225245	−	0.399067i
$547$	1.45078	−	8.22779i	0.0620309	−	0.351795i	−0.937956	−	0.346753i	$-0.887284\pi$
$547$	1.45078	−	8.22779i	0.0620309	−	0.351795i	0.999987	−	0.00504147i	$-0.00160476\pi$
$548$	20.1370	−	6.88793i	0.860211	−	0.294238i
$549$	4.33250	−	3.63540i	0.184907	−	0.155155i
$550$	1.07172	+	3.03626i	0.0456983	+	0.129467i
$551$	2.30024	−	0.414484i	0.0979934	−	0.0176576i
$552$	−8.71429	−	5.37678i	−0.370905	−	0.228851i
$553$	0.522568	+	0.622772i	0.0222218	+	0.0264829i
$554$	−14.6017	−	0.142285i	−0.620366	−	0.00604512i
$555$	9.84293	+	1.73557i	0.417809	+	0.0736710i
$556$	24.0068	−	27.5035i	1.01812	−	1.16641i
$557$	−29.6978	+	10.8091i	−1.25834	+	0.457997i	−0.883210	−	0.468977i	$-0.844623\pi$
$557$	−29.6978	+	10.8091i	−1.25834	+	0.457997i	−0.375126	+	0.926974i	$0.622400\pi$
$558$	1.78164	−	9.55860i	0.0754230	−	0.404648i
$559$	−1.80997	−	3.13496i	−0.0765535	−	0.132594i
$560$	35.4741	+	45.7876i	1.49905	+	1.93488i
$561$	1.04919	−	1.25038i	0.0442968	−	0.0527909i
$562$	−23.0967	+	26.9871i	−0.974274	+	1.13838i
$563$	6.50555	−	11.2679i	0.274176	−	0.474887i	−0.695751	−	0.718283i	$-0.744928\pi$
$563$	6.50555	−	11.2679i	0.274176	−	0.474887i	0.969927	+	0.243396i	$0.0782615\pi$
$564$	6.53490	+	3.94468i	0.275169	+	0.166101i
$565$	37.2155	−	6.56210i	1.56567	−	0.276070i
$566$	−20.4178	+	3.39541i	−0.858223	+	0.142720i
$567$	−1.83336	+	5.03711i	−0.0769938	+	0.211539i
$568$	−1.75288	−	11.9788i	−0.0735491	−	0.502619i
$569$		−	36.1864i		−	1.51701i	−0.651665	−	0.758507i	$-0.725929\pi$
$569$		−	36.1864i		−	1.51701i	0.651665	−	0.758507i	$-0.274071\pi$
$570$	4.25769	+	25.0234i	0.178335	+	1.04811i
$571$		−	45.6728i		−	1.91135i	−0.294430	−	0.955673i	$-0.595130\pi$
$571$		−	45.6728i		−	1.91135i	0.294430	−	0.955673i	$-0.404870\pi$
$572$	0.185018	−	0.941600i	0.00773599	−	0.0393703i
$573$	2.15507	−	5.92099i	0.0900292	−	0.247353i
$574$	7.48771	+	45.0262i	0.312531	+	1.87936i
$575$	−23.2813	+	4.10512i	−0.970896	+	0.171195i
$576$	−9.61210	−	9.07377i	−0.400504	−	0.378074i
$577$	7.41053	−	12.8354i	0.308504	−	0.534345i	−0.669531	−	0.742784i	$-0.733505\pi$
$577$	7.41053	−	12.8354i	0.308504	−	0.534345i	0.978035	+	0.208439i	$0.0668383\pi$
$578$	−5.28230	−	4.52081i	−0.219715	−	0.188041i
$579$	−6.55269	+	7.80919i	−0.272320	+	0.324539i
$580$	0.0741249	−	3.80309i	0.00307787	−	0.157915i
$581$	−30.4137	−	52.6781i	−1.26177	−	2.18546i
$582$	9.79279	+	1.82529i	0.405924	+	0.0756609i
$583$	−1.46873	+	0.534573i	−0.0608284	+	0.0221397i
$584$	23.7871	+	9.45396i	0.984317	+	0.391208i
$585$	9.22043	+	1.62581i	0.381218	+	0.0672190i
$586$	0.405726	−	41.6367i	0.0167604	−	1.72000i
$587$	−27.2045	−	32.4211i	−1.12285	−	1.33816i	−0.934460	−	0.356067i	$-0.884117\pi$
$587$	−27.2045	−	32.4211i	−1.12285	−	1.33816i	−0.188391	−	0.982094i	$-0.560327\pi$
$588$	17.4714	−	14.0893i	0.720509	−	0.581033i
$589$	−17.0206	+	6.26728i	−0.701320	+	0.258239i
$590$	−25.7589	+	9.09222i	−1.06048	+	0.374321i
$591$	2.65352	−	2.22657i	0.109151	−	0.0915888i
$592$	8.21283	+	5.17854i	0.337545	+	0.212837i
$593$	−4.25553	+	24.1343i	−0.174754	+	0.991077i	0.763674	+	0.645602i	$0.223393\pi$
$593$	−4.25553	+	24.1343i	−0.174754	+	0.991077i	−0.938428	+	0.345475i	$0.887718\pi$
$594$	−1.99771	+	1.12757i	−0.0819669	+	0.0462646i
$595$	−23.1855	−	63.7016i	−0.950513	−	2.61151i
$596$	−4.64481	−	29.7174i	−0.190259	−	1.21727i
$597$	−0.867774	+	0.501010i	−0.0355156	+	0.0205050i
$598$	6.59681	+	2.47410i	0.269764	+	0.101173i
$599$	3.72253	+	3.12357i	0.152098	+	0.127626i	0.715661	−	0.698447i	$-0.246125\pi$
$599$	3.72253	+	3.12357i	0.152098	+	0.127626i	−0.563563	+	0.826073i	$0.690570\pi$
$600$	24.8812	+	0.727545i	1.01577	+	0.0297019i
$601$	13.4093	+	7.74187i	0.546978	+	0.315798i	0.747902	−	0.663809i	$-0.231061\pi$
$601$	13.4093	+	7.74187i	0.546978	+	0.315798i	−0.200925	+	0.979607i	$0.564395\pi$
$602$	10.1031	−	8.31112i	0.411772	−	0.338736i
$603$	1.98377	+	11.2505i	0.0807853	+	0.458156i
$604$	14.5632	+	26.3993i	0.592569	+	1.07417i
$605$	−36.3628	−	13.2350i	−1.47836	−	0.538078i
$606$	4.57635	−	7.75105i	0.185901	−	0.314865i
$607$	−18.2620			−0.741230			−0.370615	−	0.928787i	$-0.620853\pi$
$607$	−18.2620			−0.741230			−0.370615	+	0.928787i	$0.620853\pi$
$608$	−5.36918	+	24.0660i	−0.217749	+	0.976005i
$609$	−2.54131			−0.102979
$610$	−8.72938	+	14.7851i	−0.353442	+	0.598632i
$611$	−4.93539	−	1.79633i	−0.199664	−	0.0726719i
$612$	7.47266	+	13.5460i	0.302065	+	0.547564i
$613$	7.49765	+	42.5213i	0.302827	+	1.71742i	0.633560	+	0.773694i	$0.281593\pi$
$613$	7.49765	+	42.5213i	0.302827	+	1.71742i	−0.330732	+	0.943725i	$0.607296\pi$
$614$	17.2877	−	14.2214i	0.697676	−	0.573929i
$615$	28.1922	+	16.2768i	1.13682	+	0.656343i
$616$	3.46651	+	0.101363i	0.139669	+	0.00408404i
$617$	−2.81302	−	2.36041i	−0.113248	−	0.0950264i	0.584405	−	0.811462i	$-0.301328\pi$
$617$	−2.81302	−	2.36041i	−0.113248	−	0.0950264i	−0.697653	+	0.716436i	$0.745772\pi$
$618$	−28.2424	−	10.5922i	−1.13608	−	0.426080i
$619$	13.5511	−	7.82373i	0.544665	−	0.314462i	−0.202303	−	0.979323i	$-0.564842\pi$
$619$	13.5511	−	7.82373i	0.544665	−	0.314462i	0.746967	+	0.664861i	$0.231509\pi$
$620$	4.55834	+	29.1642i	0.183067	+	1.17126i
$621$	−5.76044	−	15.8267i	−0.231159	−	0.635103i
$622$	−16.1928	+	9.13968i	−0.649270	+	0.366468i
$623$	4.68896	−	26.5924i	0.187859	−	1.06540i
$624$	−6.27516	−	3.95676i	−0.251207	−	0.158397i
$625$	−4.16373	+	3.49379i	−0.166549	+	0.139751i
$626$	−26.1466	+	9.22906i	−1.04503	+	0.368867i
$627$	1.31900	+	0.754952i	0.0526758	+	0.0301499i
$628$	−25.2491	+	20.3614i	−1.00755	+	0.812509i
$629$	−7.30421	−	8.70481i	−0.291238	−	0.347084i
$630$	−0.329701	+	33.8348i	−0.0131356	+	1.34801i
$631$	−38.6875	−	6.82166i	−1.54013	−	0.271566i	−0.661820	−	0.749663i	$-0.730216\pi$
$631$	−38.6875	−	6.82166i	−1.54013	−	0.271566i	−0.878307	+	0.478097i	$0.841327\pi$
$632$	0.523416	+	0.208027i	0.0208204	+	0.00827486i
$633$	−9.67466	+	3.52129i	−0.384533	+	0.139959i
$634$	8.40283	+	1.56622i	0.333719	+	0.0622025i
$635$	32.4332	+	56.1760i	1.28707	+	2.22928i
$636$	−0.235462	+	12.0807i	−0.00933669	+	0.479033i
$637$	−9.92680	+	11.8303i	−0.393314	+	0.468733i
$638$	−0.173031	−	0.148087i	−0.00685035	−	0.00586281i
$639$	3.53612	−	6.12474i	0.139887	−	0.242291i
$640$	36.6859	+	16.2631i	1.45014	+	0.642857i
$641$	−34.0089	+	5.99669i	−1.34327	+	0.236855i	−0.798635	−	0.601816i	$-0.794444\pi$
$641$	−34.0089	+	5.99669i	−1.34327	+	0.236855i	−0.544638	+	0.838671i	$0.683333\pi$
$642$	−4.48033	−	26.9417i	−0.176824	−	1.06331i
$643$	−8.89830	+	24.4479i	−0.350915	+	0.964130i	0.631162	+	0.775651i	$0.282578\pi$
$643$	−8.89830	+	24.4479i	−0.350915	+	0.964130i	−0.982077	+	0.188479i	$0.939644\pi$
$644$	−4.90928	+	24.9845i	−0.193453	+	0.984526i
$645$		−	9.33028i		−	0.367380i
$646$	14.5790	−	24.9053i	0.573602	−	0.979886i
$647$			29.4173i			1.15651i	0.815855	+	0.578256i	$0.196267\pi$
$647$			29.4173i			1.15651i	−0.815855	+	0.578256i	$0.803733\pi$
$648$	0.537714	+	3.67462i	0.0211234	+	0.144353i
$649$	−0.559387	+	1.53690i	−0.0219579	+	0.0603288i
$650$	−16.8952	+	2.80962i	−0.662685	+	0.110202i
$651$	19.4214	−	3.42452i	0.761186	−	0.134218i
$652$	10.7869	+	6.51136i	0.422449	+	0.255004i
$653$	5.77812	−	10.0080i	0.226115	−	0.391643i	−0.730538	−	0.682872i	$-0.760731\pi$
$653$	5.77812	−	10.0080i	0.226115	−	0.391643i	0.956654	+	0.291229i	$0.0940640\pi$
$654$	−9.09817	+	10.6307i	−0.355767	+	0.415692i
$655$	−6.31686	+	7.52814i	−0.246820	+	0.294149i
$656$	19.3677	+	24.9985i	0.756180	+	0.976029i
$657$	7.47656	+	12.9498i	0.291688	+	0.505219i
$658$	3.47801	−	18.6597i	0.135587	−	0.727430i
$659$	−7.45091	+	2.71191i	−0.290246	+	0.105641i	−0.483040	−	0.875598i	$-0.660467\pi$
$659$	−7.45091	+	2.71191i	−0.290246	+	0.105641i	0.192794	+	0.981239i	$0.438245\pi$
$660$	1.62646	−	1.86336i	0.0633100	−	0.0725312i
$661$	8.97455	+	1.58246i	0.349070	+	0.0615504i	0.345434	−	0.938443i	$-0.387732\pi$
$661$	8.97455	+	1.58246i	0.349070	+	0.0615504i	0.00363550	+	0.999993i	$0.498843\pi$
$662$	5.19146	+	0.0505879i	0.201772	+	0.00196615i
$663$	5.58091	+	6.65107i	0.216745	+	0.258306i
$664$	−35.8648	−	22.1289i	−1.39183	−	0.858766i
$665$	54.5438	−	31.7639i	2.11512	−	1.23175i
$666$	1.88786	+	5.34845i	0.0731532	+	0.207248i
$667$	1.28094	−	1.07483i	0.0495981	−	0.0416178i
$668$	10.1627	−	3.47619i	0.393208	−	0.134498i
$669$	2.41674	−	13.7060i	0.0934366	−	0.529905i
$670$	−17.0474	−	30.2028i	−0.658599	−	1.16684i
$671$	0.351604	+	0.966024i	0.0135735	+	0.0372929i
$672$	10.3857	−	24.7168i	0.400636	−	0.953471i
$673$	−12.1210	+	6.99808i	−0.467231	+	0.269756i	−0.715080	−	0.699043i	$-0.753610\pi$
$673$	−12.1210	+	6.99808i	−0.467231	+	0.269756i	0.247849	+	0.968799i	$0.420276\pi$
$674$	−8.93465	+	23.8229i	−0.344150	+	0.917623i
$675$	31.3642	+	26.3177i	1.20721	+	1.01297i
$676$	−19.4925	−	7.52800i	−0.749710	−	0.289538i
$677$	38.4118	+	22.1771i	1.47629	+	0.852334i	0.999642	−	0.0267620i	$-0.00851964\pi$
$677$	38.4118	+	22.1771i	1.47629	+	0.852334i	0.476644	+	0.879096i	$0.341853\pi$
$678$	−11.1123	−	13.5083i	−0.426766	−	0.518783i
$679$	−4.30138	−	24.3943i	−0.165072	−	0.936168i
$680$	−35.0803	−	31.2278i	−1.34527	−	1.19753i
$681$	−3.92065	−	1.42700i	−0.150240	−	0.0546827i
$682$	1.52190	+	0.898557i	0.0582767	+	0.0344075i
$683$	31.4233			1.20238			0.601190	−	0.799106i	$-0.294693\pi$
$683$	31.4233			1.20238			0.601190	+	0.799106i	$0.294693\pi$
$684$	−11.1788	+	9.08413i	−0.427432	+	0.347340i
$685$	−37.7439			−1.44212
$686$	−13.2586	−	7.82812i	−0.506217	−	0.298879i
$687$	9.25442	+	3.36833i	0.353078	+	0.128510i
$688$	3.42948	−	8.38979i	0.130748	−	0.319858i
$689$	−1.44370	−	8.18762i	−0.0550005	−	0.311923i
$690$	11.5367	+	14.0241i	0.439193	+	0.533889i
$691$	1.99231	+	1.15026i	0.0757911	+	0.0437580i	0.537417	−	0.843317i	$-0.319400\pi$
$691$	1.99231	+	1.15026i	0.0757911	+	0.0437580i	−0.461626	+	0.887075i	$0.652734\pi$
$692$	−11.1625	+	28.9033i	−0.424334	+	1.09874i
$693$	1.55194	+	1.30223i	0.0589533	+	0.0494677i
$694$	8.08781	−	21.5649i	0.307009	−	0.818593i
$695$	−56.0702	+	32.3721i	−2.12686	+	1.22795i
$696$	−1.54986	+	0.835389i	−0.0587472	+	0.0316653i
$697$	−12.6585	−	34.7790i	−0.479475	−	1.31735i
$698$	−8.23072	−	14.5823i	−0.311537	−	0.551950i
$699$	−4.20696	+	23.8589i	−0.159122	+	0.902425i
$700$	−20.0327	−	58.5660i	−0.757164	−	2.21359i
$701$	21.6513	−	18.1676i	0.817757	−	0.686180i	−0.134689	−	0.990888i	$-0.543003\pi$
$701$	21.6513	−	18.1676i	0.817757	−	0.686180i	0.952446	+	0.304708i	$0.0985590\pi$
$702$	−4.06146	−	11.5064i	−0.153290	−	0.434281i
$703$	6.77049	−	8.13041i	0.255354	−	0.306644i
$704$	2.14742	−	1.07770i	0.0809340	−	0.0406175i
$705$	−8.70156	−	10.3701i	−0.327720	−	0.390561i
$706$	36.4975	+	0.355648i	1.37360	+	0.0133850i
$707$	−22.0428	−	3.88675i	−0.829006	−	0.146176i
$708$	9.52559	+	8.31456i	0.357994	+	0.312480i
$709$	22.1340	−	8.05611i	0.831259	−	0.302553i	0.108883	−	0.994055i	$-0.465272\pi$
$709$	22.1340	−	8.05611i	0.831259	−	0.302553i	0.722375	+	0.691501i	$0.243050\pi$
$710$	−3.93413	+	21.1068i	−0.147645	+	0.792123i
$711$	0.164516	+	0.284949i	0.00616981	+	0.0106864i
$712$	−5.88191	−	17.7591i	−0.220434	−	0.665552i
$713$	−8.34092	+	9.94032i	−0.312370	+	0.372268i
$714$	−20.4025	+	23.8391i	−0.763545	+	0.892156i
$715$	−0.850917	+	1.47383i	−0.0318225	+	0.0551182i
$716$	8.46063	−	14.0162i	0.316189	−	0.523809i
$717$	30.2452	−	5.33305i	1.12953	−	0.199166i
$718$	5.93921	−	0.987671i	0.221649	−	0.0368596i
$719$	6.03096	−	16.5699i	0.224917	−	0.617954i	−0.774985	−	0.631980i	$-0.782243\pi$
$719$	6.03096	−	16.5699i	0.224917	−	0.617954i	0.999902	+	0.0140260i	$0.00446476\pi$
$720$	10.9212	+	20.7431i	0.407010	+	0.773049i
$721$			75.0058i			2.79336i
$722$	25.2288	+	9.24694i	0.938920	+	0.344136i
$723$		−	18.2208i		−	0.677638i
$724$	34.3564	+	6.75078i	1.27684	+	0.250891i
$725$	−1.39028	+	3.81976i	−0.0516336	+	0.141862i
$726$	2.93825	+	17.6687i	0.109049	+	0.655747i
$727$	4.39466	−	0.774896i	0.162989	−	0.0287393i	−0.0915582	−	0.995800i	$-0.529185\pi$
$727$	4.39466	−	0.774896i	0.162989	−	0.0287393i	0.254547	+	0.967060i	$0.418074\pi$
$728$	−3.73293	+	18.0655i	−0.138351	+	0.669551i
$729$	−10.4896	+	18.1685i	−0.388504	+	0.672909i
$730$	−34.4890	−	29.5171i	−1.27649	−	1.09248i
$731$	−6.81860	+	8.12609i	−0.252195	+	0.300554i
$732$	7.94585	+	0.154870i	0.293687	+	0.00572418i
$733$	18.5155	+	32.0698i	0.683886	+	1.18453i	0.973785	+	0.227469i	$0.0730450\pi$
$733$	18.5155	+	32.0698i	0.683886	+	1.18453i	−0.289899	+	0.957057i	$0.593622\pi$
$734$	−3.60610	−	0.672148i	−0.133104	−	0.0248094i
$735$	−37.4043	+	13.6141i	−1.37968	+	0.502162i
$736$	5.21899	+	16.8510i	0.192374	+	0.621135i
$737$	−2.04498	−	0.360585i	−0.0753279	−	0.0132823i
$738$	−0.180006	+	18.4727i	−0.00662611	+	0.679989i
$739$	33.1809	+	39.5434i	1.22058	+	1.45463i	0.850785	+	0.525513i	$0.176127\pi$
$739$	33.1809	+	39.5434i	1.22058	+	1.45463i	0.369792	+	0.929114i	$0.379429\pi$
$740$	−10.8090	−	13.4036i	−0.397346	−	0.492728i
$741$	−5.17311	+	6.21219i	−0.190039	+	0.228210i
$742$	28.3331	−	10.0008i	1.04014	−	0.367142i
$743$	1.13874	−	0.955514i	0.0417762	−	0.0350544i	−0.621660	−	0.783287i	$-0.713542\pi$
$743$	1.13874	−	0.955514i	0.0417762	−	0.0350544i	0.663437	+	0.748232i	$0.269097\pi$
$744$	10.7187	−	8.47278i	0.392968	−	0.310627i
$745$	−9.26290	+	52.5325i	−0.339366	+	1.92464i
$746$	−46.3908	+	26.1844i	−1.69849	+	0.958679i
$747$	−8.42002	−	23.1338i	−0.308073	−	0.846423i
$748$	−2.77830	+	0.434245i	−0.101585	+	0.0158776i
$749$	−58.8159	+	33.9574i	−2.14909	+	1.24078i
$750$	−14.0716	−	5.27749i	−0.513823	−	0.192707i
$751$	−24.8869	−	20.8826i	−0.908134	−	0.762015i	0.0636288	−	0.997974i	$-0.479733\pi$
$751$	−24.8869	−	20.8826i	−0.908134	−	0.762015i	−0.971763	+	0.235958i	$0.924177\pi$
$752$	−4.01276	−	12.5232i	−0.146330	−	0.456674i
$753$	−2.03341	−	1.17399i	−0.0741016	−	0.0427826i
$754$	0.935570	−	0.769627i	0.0340714	−	0.0280282i
$755$	−9.28494	−	52.6575i	−0.337914	−	1.91640i
$756$	38.6126	−	21.3007i	1.40433	−	0.774699i
$757$	−14.9991	−	5.45921i	−0.545150	−	0.198418i	0.0547403	−	0.998501i	$-0.482567\pi$
$757$	−14.9991	−	5.45921i	−0.545150	−	0.198418i	−0.599890	+	0.800082i	$0.704789\pi$
$758$	12.7147	−	21.5352i	0.461820	−	0.782194i
$759$	1.08728			0.0394659
$760$	22.8228	−	37.3015i	0.827871	−	1.35307i
$761$	37.3192			1.35282			0.676410	−	0.736526i	$-0.263535\pi$
$761$	37.3192			1.35282			0.676410	+	0.736526i	$0.263535\pi$
$762$	15.2650	−	25.8546i	0.552991	−	0.936612i
$763$	32.6959	+	11.9003i	1.18367	+	0.430821i
$764$	−9.50495	+	5.24343i	−0.343877	+	0.189700i
$765$	−4.76428	−	27.0196i	−0.172253	−	0.976894i
$766$	−21.5580	+	17.7342i	−0.778922	+	0.640763i
$767$	−7.53430	−	4.34993i	−0.272048	−	0.157067i
$768$	−1.79113	−	18.4879i	−0.0646320	−	0.667125i
$769$	0.934238	+	0.783919i	0.0336895	+	0.0282688i	0.659477	−	0.751725i	$-0.270778\pi$
$769$	0.934238	+	0.783919i	0.0336895	+	0.0282688i	−0.625787	+	0.779994i	$0.715222\pi$
$770$	−5.75869	−	2.15977i	−0.207529	−	0.0778326i
$771$	−4.63226	+	2.67443i	−0.166827	+	0.0963174i
$772$	17.3518	−	2.71207i	0.624504	−	0.0976095i
$773$	14.4258	+	39.6345i	0.518859	+	1.42555i	0.871778	+	0.489901i	$0.162967\pi$
$773$	14.4258	+	39.6345i	0.518859	+	1.42555i	−0.352919	+	0.935654i	$0.614811\pi$
$774$	4.61099	−	2.60258i	0.165738	−	0.0935478i
$775$	5.47763	−	31.0652i	0.196762	−	1.11589i
$776$	−10.6422	−	13.4633i	−0.382034	−	0.483304i
$777$	−8.81250	+	7.39457i	−0.316147	+	0.265279i
$778$	27.3794	−	9.66423i	0.981600	−	0.346479i
$779$	29.7791	−	17.3420i	1.06695	−	0.621342i
$780$	8.25879	+	10.2413i	0.295712	+	0.366697i
$781$	0.826308	+	0.984756i	0.0295676	+	0.0352373i
$782$	0.201175	−	20.6451i	0.00719402	−	0.738269i
$783$	−2.85200	−	0.502885i	−0.101922	−	0.0179717i
$784$	−38.6380	−	1.50674i	−1.37993	−	0.0538121i
$785$	54.0555	−	19.6746i	1.92932	−	0.702217i
$786$	4.47173	+	0.833492i	0.159501	+	0.0297297i
$787$	−18.2059	−	31.5336i	−0.648972	−	1.12405i	−0.983369	−	0.181620i	$-0.941866\pi$
$787$	−18.2059	−	31.5336i	−0.648972	−	1.12405i	0.334397	−	0.942432i	$-0.391467\pi$
$788$	−5.96650	−	0.116291i	−0.212548	−	0.00414271i
$789$	6.62449	−	7.89476i	0.235838	−	0.281061i
$790$	−0.758901	−	0.649499i	−0.0270005	−	0.0231082i
$791$	−21.7478	+	37.6683i	−0.773262	+	1.33933i
$792$	1.37455	+	0.284027i	0.0488425	+	0.0100925i
$793$	−5.38523	+	0.949562i	−0.191235	+	0.0337199i
$794$	−1.21455	−	7.30352i	−0.0431029	−	0.259192i
$795$	7.32912	−	20.1366i	0.259937	−	0.714172i
$796$	1.69388	+	0.332836i	0.0600380	+	0.0117971i
$797$		−	13.4658i		−	0.476984i	−0.971145	−	0.238492i	$-0.923347\pi$
$797$		−	13.4658i		−	0.476984i	0.971145	−	0.238492i	$-0.0766530\pi$
$798$	−25.2134	−	14.7593i	−0.892545	−	0.522474i
$799$			15.3908i			0.544489i
$800$	−31.4693	−	29.1322i	−1.11261	−	1.02998i
$801$	3.73783	−	10.2696i	0.132070	−	0.362859i
$802$	35.8315	−	5.95866i	1.26525	−	0.210407i
$803$	−2.67670	+	0.471975i	−0.0944588	+	0.0166556i
$804$	−8.29594	+	13.7433i	−0.292575	+	0.484690i
$805$	22.5783	−	39.1067i	0.795780	−	1.37833i
$806$	−6.11279	+	7.14243i	−0.215314	+	0.251582i
$807$	−5.33874	+	6.36246i	−0.187932	+	0.223969i
$808$	−14.7208	+	4.87560i	−0.517877	+	0.171523i
$809$	−9.76161	−	16.9076i	−0.343200	−	0.594440i	0.641825	−	0.766851i	$-0.278178\pi$
$809$	−9.76161	−	16.9076i	−0.343200	−	0.594440i	−0.985025	+	0.172411i	$0.944844\pi$
$810$	1.20684	−	6.47473i	0.0424039	−	0.227499i
$811$	−28.8297	+	10.4931i	−1.01235	+	0.368464i	−0.794334	−	0.607482i	$-0.792180\pi$
$811$	−28.8297	+	10.4931i	−1.01235	+	0.368464i	−0.218013	+	0.975946i	$0.569958\pi$
$812$	3.29838	+	2.87905i	0.115751	+	0.101035i
$813$	36.4671	+	6.43013i	1.27896	+	0.225514i
$814$	−1.03091	−	0.0100457i	−0.0361335	−	0.000352100i
$815$	−14.3634	−	17.1176i	−0.503127	−	0.599604i
$816$	−4.60631	+	21.2454i	−0.161253	+	0.743739i
$817$	−8.57208	−	4.90637i	−0.299899	−	0.171652i
$818$	−11.4285	−	32.3778i	−0.399588	−	1.13206i
$819$	−8.25517	+	6.92691i	−0.288459	+	0.242046i
$820$	−18.1509	−	53.0646i	−0.633857	−	1.85310i
$821$	−0.782765	+	4.43928i	−0.0273187	+	0.154932i	−0.995416	−	0.0956441i	$-0.969509\pi$
$821$	−0.782765	+	4.43928i	−0.0273187	+	0.154932i	0.968097	+	0.250576i	$0.0806200\pi$
$822$	8.58738	+	15.2142i	0.299519	+	0.530658i
$823$	12.8016	+	35.1722i	0.446237	+	1.22603i	0.935325	+	0.353791i	$0.115108\pi$
$823$	12.8016	+	35.1722i	0.446237	+	1.22603i	−0.489088	+	0.872235i	$0.662670\pi$
$824$	24.6562	+	45.7434i	0.858938	+	1.59355i
$825$	−2.28902	+	1.32156i	−0.0796933	+	0.0460110i
$826$	11.0408	−	29.4387i	0.384160	−	1.02430i
$827$	9.25002	+	7.76169i	0.321655	+	0.269900i	0.789289	−	0.614022i	$-0.210449\pi$
$827$	9.25002	+	7.76169i	0.321655	+	0.269900i	−0.467635	+	0.883922i	$0.654894\pi$
$828$	−3.71264	+	9.61324i	−0.129023	+	0.334083i
$829$	−30.8649	−	17.8198i	−1.07198	−	0.618909i	−0.143259	−	0.989685i	$-0.545758\pi$
$829$	−30.8649	−	17.8198i	−1.07198	−	0.618909i	−0.928722	+	0.370776i	$0.879092\pi$
$830$	47.4806	+	57.7181i	1.64808	+	2.00343i
$831$	−2.08150	−	11.8047i	−0.0722063	−	0.409502i
$832$	3.66197	+	12.2446i	0.126956	+	0.424506i
$833$	42.5260	+	15.4782i	1.47344	+	0.536288i
$834$	25.8059	+	15.2362i	0.893585	+	0.527587i
$835$	−19.0485			−0.659202
$836$	−0.856656	−	2.47415i	−0.0296281	−	0.0855703i
$837$	22.4735			0.776798
$838$	−4.27838	−	2.52603i	−0.147794	−	0.0872601i
$839$	35.3858	+	12.8794i	1.22165	+	0.444646i	0.870731	−	0.491759i	$-0.163646\pi$
$839$	35.3858	+	12.8794i	1.22165	+	0.444646i	0.350922	+	0.936405i	$0.385868\pi$
$840$	−31.6141	+	35.5142i	−1.09079	+	1.22536i
$841$	4.98587	+	28.2763i	0.171927	+	0.975044i
$842$	1.26884	+	1.54242i	0.0437270	+	0.0531552i
$843$	−25.2523	−	14.5794i	−0.869734	−	0.502141i
$844$	16.5461	+	6.39010i	0.569539	+	0.219956i
$845$	28.3879	+	23.8203i	0.976574	+	0.819443i
$846$	2.69766	−	7.19290i	0.0927475	−	0.247297i
$847$	38.5722	−	22.2697i	1.32536	−	0.765194i
$848$	13.9919	−	15.4129i	0.480482	−	0.529282i
$849$	−5.81119	−	15.9661i	−0.199440	−	0.547956i
$850$	24.6701	+	43.7080i	0.846178	+	1.49917i
$851$	1.31441	−	7.45440i	0.0450575	−	0.255534i
$852$	9.40305	−	3.21634i	0.322143	−	0.110190i
$853$	−19.0885	+	16.0172i	−0.653578	+	0.548417i	−0.908154	−	0.418636i	$-0.862508\pi$
$853$	−19.0885	+	16.0172i	−0.653578	+	0.548417i	0.254576	+	0.967053i	$0.418064\pi$
$854$	−6.57784	−	18.6355i	−0.225089	−	0.637693i
$855$	23.9723	−	8.82704i	0.819836	−	0.301879i
$856$	−24.7072	+	40.0436i	−0.844475	+	1.36866i
$857$	−17.9448	−	21.3858i	−0.612983	−	0.730525i	0.366864	−	0.930275i	$-0.380431\pi$
$857$	−17.9448	−	21.3858i	−0.612983	−	0.730525i	−0.979847	+	0.199750i	$0.935987\pi$
$858$	0.787688	+	0.00767557i	0.0268912	+	0.000262040i
$859$	19.9915	+	3.52504i	0.682100	+	0.120273i	0.503953	−	0.863731i	$-0.331878\pi$
$859$	19.9915	+	3.52504i	0.682100	+	0.120273i	0.178147	+	0.984004i	$0.442990\pi$
$860$	−10.5703	+	12.1098i	−0.360443	+	0.412942i
$861$	−35.2092	+	12.8151i	−1.19993	+	0.436738i
$862$	−8.16354	+	43.7977i	−0.278051	+	1.49176i
$863$	5.87734	+	10.1799i	0.200067	+	0.346526i	0.948550	−	0.316628i	$-0.102551\pi$
$863$	5.87734	+	10.1799i	0.200067	+	0.346526i	−0.748483	+	0.663154i	$0.769217\pi$
$864$	16.5464	−	25.6834i	0.562921	−	0.873768i
$865$	35.3206	−	42.0934i	1.20094	−	1.43122i
$866$	30.2080	−	35.2962i	1.02651	−	1.19941i
$867$	2.85369	−	4.94274i	0.0969165	−	0.167864i
$868$	−29.0868	−	17.5578i	−0.987272	−	0.595951i
$869$	−0.0588987	+	0.0103854i	−0.00199800	+	0.000352301i
$870$	3.08019	−	0.512225i	0.104428	−	0.0173661i
$871$	3.77781	−	10.3795i	0.128006	−	0.351695i
$872$	23.8520	−	3.49031i	0.807732	−	0.118197i
$873$		−	10.0253i		−	0.339306i
$874$	18.9511	−	3.22451i	0.641030	−	0.109071i
$875$			37.3712i			1.26338i
$876$	−4.05127	+	20.6179i	−0.136880	+	0.696613i
$877$	1.10391	−	3.03297i	0.0372764	−	0.102416i	−0.919658	−	0.392720i	$-0.871534\pi$
$877$	1.10391	−	3.03297i	0.0372764	−	0.102416i	0.956935	+	0.290304i	$0.0937564\pi$
$878$	−0.366525	−	2.20404i	−0.0123696	−	0.0743827i
$879$	33.6612	−	5.93539i	1.13537	−	0.200196i
$880$	−4.22199	+	0.575850i	−0.142323	+	0.0194119i
$881$	−1.25716	+	2.17746i	−0.0423546	+	0.0733604i	−0.886426	−	0.462871i	$-0.846819\pi$
$881$	−1.25716	+	2.17746i	−0.0423546	+	0.0733604i	0.844071	+	0.536232i	$0.180153\pi$
$882$	−17.1615	−	14.6876i	−0.577859	−	0.494556i
$883$	−32.5538	+	38.7961i	−1.09552	+	1.30559i	−0.146910	+	0.989150i	$0.546933\pi$
$883$	−32.5538	+	38.7961i	−1.09552	+	1.30559i	−0.948612	+	0.316442i	$0.897512\pi$
$884$	0.291485	−	14.9551i	0.00980370	−	0.502993i
$885$	−11.2118	−	19.4194i	−0.376881	−	0.652778i
$886$	1.34765	+	0.251191i	0.0452752	+	0.00843892i
$887$	3.33576	−	1.21412i	0.112004	−	0.0407661i	−0.285410	−	0.958405i	$-0.592130\pi$
$887$	3.33576	−	1.21412i	0.112004	−	0.0407661i	0.397414	+	0.917639i	$0.369908\pi$
$888$	−2.94367	+	7.40657i	−0.0987831	+	0.248548i
$889$	−73.5265	−	12.9647i	−2.46600	−	0.434822i
$890$	−0.323284	+	33.1763i	−0.0108365	+	1.11207i
$891$	−0.253479	−	0.302085i	−0.00849187	−	0.0101202i
$892$	−18.6642	+	15.0512i	−0.624924	+	0.503952i
$893$	−14.1032	+	2.54128i	−0.471945	+	0.0850406i
$894$	23.2829	−	8.21825i	0.778696	−	0.274859i
$895$	−22.2420	+	18.6633i	−0.743468	+	0.623844i
$896$	−41.4812	+	20.3142i	−1.38579	+	0.678649i
$897$	−1.00430	+	5.69567i	−0.0335326	+	0.190173i
$898$	−26.6176	+	15.0238i	−0.888240	+	0.501349i
$899$	0.763120	+	2.09665i	0.0254515	+	0.0699273i
$900$	−3.86856	−	24.7510i	−0.128952	−	0.825034i
$901$	−21.0991	+	12.1816i	−0.702913	+	0.405827i
$902$	−3.14406	−	1.17916i	−0.104686	−	0.0392618i
$903$	8.22662	+	6.90295i	0.273765	+	0.229716i
$904$	−0.880777	+	30.1216i	−0.0292942	+	1.00183i
$905$	−53.7760	−	31.0476i	−1.78757	−	1.03206i
$906$	−19.1133	+	15.7232i	−0.634998	+	0.522368i
$907$	−3.97715	−	22.5555i	−0.132059	−	0.748944i	−0.976863	−	0.213867i	$-0.931394\pi$
$907$	−3.97715	−	22.5555i	−0.132059	−	0.748944i	0.844804	−	0.535076i	$-0.179717\pi$
$908$	3.47199	+	6.29380i	0.115222	+	0.208867i
$909$	−8.51263	−	3.09834i	−0.282346	−	0.102766i
$910$	16.6330	−	28.1717i	0.551379	−	0.933882i
$911$	21.7119			0.719347			0.359673	−	0.933078i	$-0.382888\pi$
$911$	21.7119			0.719347			0.359673	+	0.933078i	$0.382888\pi$
$912$	−20.2285	−	0.712957i	−0.669833	−	0.0236084i
$913$	4.47485			0.148096
$914$	−10.7000	+	18.1228i	−0.353924	+	0.599448i
$915$	−13.2444	−	4.82058i	−0.437847	−	0.159363i
$916$	−8.19539	−	14.8561i	−0.270783	−	0.490859i
$917$	−1.96416	−	11.1393i	−0.0648622	−	0.367852i
$918$	−27.6142	+	22.7163i	−0.911406	+	0.749749i
$919$	−20.5068	−	11.8396i	−0.676457	−	0.390552i	0.122062	−	0.992522i	$-0.461049\pi$
$919$	−20.5068	−	11.8396i	−0.676457	−	0.390552i	−0.798519	+	0.601970i	$0.794383\pi$
$920$	0.914411	−	31.2718i	0.0301472	−	1.03100i
$921$	14.0768	+	11.8118i	0.463847	+	0.389213i
$922$	4.10716	+	1.54037i	0.135262	+	0.0507293i
$923$	−5.92183	+	3.41897i	−0.194920	+	0.112537i
$924$	0.439617	+	2.81267i	0.0144623	+	0.0925299i
$925$	6.29345	+	17.2911i	0.206927	+	0.568529i
$926$	14.7743	−	8.33907i	0.485514	−	0.274039i
$927$	−5.27141	+	29.8957i	−0.173136	+	0.981903i
$928$	2.95798	+	0.671574i	0.0971004	+	0.0220455i
$929$	−14.5821	+	12.2359i	−0.478425	+	0.401446i	−0.849856	−	0.527014i	$-0.823311\pi$
$929$	−14.5821	+	12.2359i	−0.478425	+	0.401446i	0.371432	+	0.928460i	$0.378867\pi$
$930$	−22.8494	+	8.06525i	−0.749263	+	0.264470i
$931$	−7.16148	+	41.5238i	−0.234708	+	1.36089i
$932$	32.4899	−	26.2005i	1.06424	−	0.858226i
$933$	−9.81123	−	11.6926i	−0.321205	−	0.382798i
$934$	0.0987565	−	10.1347i	0.00323141	−	0.331616i
$935$	4.91129	+	0.865993i	0.160616	+	0.0283210i
$936$	−2.75751	+	6.93815i	−0.0901319	+	0.226781i
$937$	28.0788	−	10.2198i	0.917294	−	0.333868i	0.160133	−	0.987095i	$-0.448808\pi$
$937$	28.0788	−	10.2198i	0.917294	−	0.333868i	0.757162	+	0.653228i	$0.226586\pi$
$938$	39.2426	+	7.31449i	1.28132	+	0.238827i
$939$	−11.3806	−	19.7117i	−0.371391	−	0.643268i
$940$	−0.454473	+	23.3174i	−0.0148233	+	0.760530i
$941$	7.50705	−	8.94655i	0.244723	−	0.291649i	−0.629675	−	0.776858i	$-0.716812\pi$
$941$	7.50705	−	8.94655i	0.244723	−	0.291649i	0.874398	+	0.485209i	$0.161257\pi$
$942$	−20.2292	−	17.3130i	−0.659104	−	0.564089i
$943$	12.3270	−	21.3510i	0.401422	−	0.695283i
$944$	−2.94377	−	21.5830i	−0.0958117	−	0.702468i
$945$	−77.0188	+	13.5805i	−2.50542	+	0.441774i
$946$	0.157879	+	0.949382i	0.00513310	+	0.0308671i
$947$	4.69128	−	12.8892i	0.152446	−	0.418843i	−0.839836	−	0.542840i	$-0.817349\pi$
$947$	4.69128	−	12.8892i	0.152446	−	0.418843i	0.992283	+	0.123997i	$0.0395714\pi$
$948$	−0.0891448	+	0.453679i	−0.00289529	+	0.0147348i
$949$		−	14.4577i		−	0.469318i
$950$	−35.9777	+	29.8230i	−1.16727	+	0.967586i
$951$			7.01655i			0.227527i
$952$	53.4878	−	7.82697i	1.73355	−	0.253673i
$953$	−3.90387	+	10.7258i	−0.126459	+	0.347443i	−0.986724	−	0.162403i	$-0.948075\pi$
$953$	−3.90387	+	10.7258i	−0.126459	+	0.347443i	0.860266	+	0.509846i	$0.170298\pi$
$954$	11.9958	−	1.99486i	0.388378	−	0.0645861i
$955$	18.9591	−	3.34300i	0.613502	−	0.108177i
$956$	−45.2972	−	27.3429i	−1.46502	−	0.884334i
$957$	0.0934775	−	0.161908i	0.00302170	−	0.00523373i
$958$	−28.0303	+	32.7517i	−0.905618	+	1.05816i
$959$	27.9246	−	33.2792i	0.901731	−	1.07464i
$960$	−7.60600	+	32.0512i	−0.245482	+	1.03445i
$961$	6.84269	+	11.8519i	0.220732	+	0.382319i
$962$	1.00486	−	5.39110i	0.0323979	−	0.173816i
$963$	−25.8293	+	9.40108i	−0.832336	+	0.302946i
$964$	−20.6423	+	23.6488i	−0.664843	+	0.761678i
$965$	−30.6733	−	5.40854i	−0.987409	−	0.174107i
$966$	−20.9005	−	0.203664i	−0.672464	−	0.00655278i
$967$	0.279271	+	0.332822i	0.00898075	+	0.0107028i	0.770516	−	0.637421i	$-0.219999\pi$
$967$	0.279271	+	0.332822i	0.00898075	+	0.0107028i	−0.761535	+	0.648123i	$0.775554\pi$
$968$	16.2033	−	26.2611i	0.520793	−	0.844063i
$969$	22.2911	+	8.01887i	0.716094	+	0.257603i
$970$	10.1304	+	28.7000i	0.325266	+	0.921503i
$971$	42.2441	−	35.4470i	1.35568	−	1.13755i	0.378388	−	0.925647i	$-0.376479\pi$
$971$	42.2441	−	35.4470i	1.35568	−	1.13755i	0.977291	−	0.211902i	$-0.0679659\pi$
$972$	27.7767	−	9.50110i	0.890938	−	0.304748i
$973$	12.9403	−	73.3881i	0.414847	−	2.35271i
$974$	20.3553	+	36.0635i	0.652227	+	1.15555i
$975$	−4.80863	−	13.2116i	−0.153999	−	0.423110i
$976$	−10.1375	−	9.20284i	−0.324494	−	0.294576i
$977$	50.6858	−	29.2635i	1.62158	−	0.936221i	0.635085	−	0.772442i	$-0.280965\pi$
$977$	50.6858	−	29.2635i	1.62158	−	0.936221i	0.986497	−	0.163779i	$-0.0523683\pi$
$978$	−3.63205	+	9.68431i	−0.116140	+	0.309670i
$979$	1.52174	+	1.27689i	0.0486349	+	0.0408095i
$980$	63.9706	+	24.7055i	2.04347	+	0.789188i
$981$	12.1955	+	7.04109i	0.389373	+	0.224805i
$982$	22.7218	+	27.6210i	0.725082	+	0.881421i
$983$	5.85032	+	33.1788i	0.186596	+	1.05824i	0.923887	+	0.382665i	$0.124994\pi$
$983$	5.85032	+	33.1788i	0.186596	+	1.05824i	−0.737291	+	0.675575i	$0.763895\pi$
$984$	−17.2603	+	19.3896i	−0.550237	+	0.618118i
$985$	9.94517	+	3.61974i	0.316879	+	0.115335i
$986$	−3.05698	−	1.80489i	−0.0973542	−	0.0574795i
$987$	15.5812			0.495956
$988$	13.7520	−	2.20223i	0.437509	−	0.0700622i
$989$	−7.06616			−0.224691
$990$	−2.14350	−	1.26556i	−0.0681249	−	0.0402221i
$991$	−41.2012	−	14.9960i	−1.30880	−	0.476364i	−0.408948	−	0.912558i	$-0.634104\pi$
$991$	−41.2012	−	14.9960i	−1.30880	−	0.476364i	−0.899853	+	0.436193i	$0.856326\pi$
$992$	−23.5107	−	1.14636i	−0.746466	−	0.0363971i
$993$	0.740052	+	4.19705i	0.0234849	+	0.133189i
$994$	−15.6994	−	19.0845i	−0.497956	−	0.605323i
$995$	−2.65133	−	1.53075i	−0.0840529	−	0.0485279i
$996$	12.4631	−	32.2709i	0.394907	−	1.02254i
$997$	16.0473	+	13.4653i	0.508224	+	0.426451i	0.860504	−	0.509444i	$-0.170149\pi$
$997$	16.0473	+	13.4653i	0.508224	+	0.426451i	−0.352280	+	0.935895i	$0.614593\pi$
$998$	−9.85719	+	26.2827i	−0.312024	+	0.831964i
$999$	−11.3532	+	6.55475i	−0.359198	+	0.207383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.51.6	yes	48
3.2	odd	2		684.2.cf.a.127.3		48
4.3	odd	2	inner	76.2.k.a.51.2	yes	48
12.11	even	2		684.2.cf.a.127.7		48
19.3	odd	18	inner	76.2.k.a.3.2	✓	48
57.41	even	18		684.2.cf.a.307.7		48
76.3	even	18	inner	76.2.k.a.3.6	yes	48
228.155	odd	18		684.2.cf.a.307.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.2	✓	48	19.3	odd	18	inner
76.2.k.a.3.6	yes	48	76.3	even	18	inner
76.2.k.a.51.2	yes	48	4.3	odd	2	inner
76.2.k.a.51.6	yes	48	1.1	even	1	trivial
684.2.cf.a.127.3		48	3.2	odd	2
684.2.cf.a.127.7		48	12.11	even	2
684.2.cf.a.307.3		48	228.155	odd	18
684.2.cf.a.307.7		48	57.41	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.719007 - 1.21780i) q^{2} +(1.09089 + 0.397053i) q^{3} +(-0.966058 - 1.75121i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.26789 - 1.04300i) q^{6} +(-3.53555 - 2.04125i) q^{7} +(-2.82722 - 0.0826699i) q^{8} +(-1.26573 - 1.06208i) q^{9} +O(q^{10})\)	\(q+(0.719007 - 1.21780i) q^{2} +(1.09089 + 0.397053i) q^{3} +(-0.966058 - 1.75121i) q^{4} +(0.615920 + 3.49306i) q^{5} +(1.26789 - 1.04300i) q^{6} +(-3.53555 - 2.04125i) q^{7} +(-2.82722 - 0.0826699i) q^{8} +(-1.26573 - 1.06208i) q^{9} +(4.69669 + 1.76147i) q^{10} +(0.260098 - 0.150167i) q^{11} +(-0.358544 - 2.29396i) q^{12} +(0.546397 + 1.50121i) q^{13} +(-5.02792 + 2.83791i) q^{14} +(-0.715025 + 4.05511i) q^{15} +(-2.13347 + 3.38354i) q^{16} +(3.58623 - 3.00920i) q^{17} +(-2.20347 + 0.777766i) q^{18} +(3.34958 + 2.78932i) q^{19} +(5.52206 - 4.45310i) q^{20} +(-3.04643 - 3.63059i) q^{21} +(0.00413863 - 0.424718i) q^{22} +(3.07108 + 0.541514i) q^{23} +(-3.05137 - 1.21274i) q^{24} +(-7.12363 + 2.59279i) q^{25} +(2.22104 + 0.413983i) q^{26} +(-2.70044 - 4.67730i) q^{27} +(-0.159112 + 8.16346i) q^{28} +(0.344669 - 0.410760i) q^{29} +(4.42419 + 3.78641i) q^{30} +(-2.08054 + 3.60361i) q^{31} +(2.58648 + 5.03091i) q^{32} +(0.343363 - 0.0605442i) q^{33} +(-1.08607 - 6.53093i) q^{34} +(4.95259 - 13.6071i) q^{35} +(-0.637147 + 3.24259i) q^{36} -2.42729i q^{37} +(5.80520 - 2.07357i) q^{38} +1.85461i q^{39} +(-1.45257 - 9.92656i) q^{40} +(2.70395 - 7.42905i) q^{41} +(-6.61173 + 1.09951i) q^{42} +(-2.23149 + 0.393472i) q^{43} +(-0.514244 - 0.310415i) q^{44} +(2.93031 - 5.07544i) q^{45} +(2.86758 - 3.35060i) q^{46} +(-2.11323 + 2.51844i) q^{47} +(-3.67083 + 2.84398i) q^{48} +(4.83342 + 8.37173i) q^{49} +(-1.96445 + 10.5394i) q^{50} +(5.10701 - 1.85880i) q^{51} +(2.10109 - 2.40712i) q^{52} +(-5.12508 - 0.903690i) q^{53} +(-7.63763 - 0.0744244i) q^{54} +(0.684743 + 0.816045i) q^{55} +(9.82703 + 6.06335i) q^{56} +(2.54653 + 4.37281i) q^{57} +(-0.252403 - 0.715076i) q^{58} +(-4.17166 + 3.50044i) q^{59} +(7.79210 - 2.66531i) q^{60} +(-0.594383 + 3.37091i) q^{61} +(2.89253 + 5.12470i) q^{62} +(2.30710 + 6.33871i) q^{63} +(7.98633 + 0.467452i) q^{64} +(-4.90729 + 2.83323i) q^{65} +(0.173150 - 0.461679i) q^{66} +(-5.29646 - 4.44426i) q^{67} +(-8.73424 - 3.37317i) q^{68} +(3.13521 + 1.81012i) q^{69} +(-13.0098 - 15.8149i) q^{70} +(0.743257 + 4.21522i) q^{71} +(3.49071 + 3.10736i) q^{72} +(-8.50411 - 3.09524i) q^{73} +(-2.95595 - 1.74524i) q^{74} -8.80060 q^{75} +(1.64879 - 8.56046i) q^{76} -1.22612 q^{77} +(2.25854 + 1.33348i) q^{78} +(-0.187126 - 0.0681083i) q^{79} +(-13.1329 - 5.36833i) q^{80} +(-0.228002 - 1.29306i) q^{81} +(-7.10291 - 8.63440i) q^{82} +(12.9034 + 7.44977i) q^{83} +(-3.41490 + 8.84229i) q^{84} +(12.7201 + 10.6735i) q^{85} +(-1.12529 + 3.00041i) q^{86} +(0.539091 - 0.311244i) q^{87} +(-0.747767 + 0.403054i) q^{88} +(2.26220 + 6.21534i) q^{89} +(-4.07394 - 7.21779i) q^{90} +(1.13254 - 6.42296i) q^{91} +(-2.01854 - 5.90124i) q^{92} +(-3.70047 + 3.10507i) q^{93} +(1.54753 + 4.38426i) q^{94} +(-7.68017 + 13.4183i) q^{95} +(0.824040 + 6.51517i) q^{96} +(3.90012 + 4.64798i) q^{97} +(13.6703 + 0.133210i) q^{98} +(-0.488704 - 0.0861717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more