LMFDB - Embedded newform 74.2.h.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(3,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("74.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.h (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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.2
Root			$0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	74.41
Dual form			74.2.h.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.266044 - 1.50881i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.247315 - 0.294739i) q^{5} -1.53209i q^{6} +(-2.50048 + 2.09815i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.613341 - 0.223238i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.266044 - 1.50881i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.247315 - 0.294739i) q^{5} -1.53209i q^{6} +(-2.50048 + 2.09815i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.613341 - 0.223238i) q^{9} +(-0.192377 - 0.333207i) q^{10} +(-1.29236 + 2.23843i) q^{11} +(0.266044 - 1.50881i) q^{12} +(-0.466831 + 1.28261i) q^{13} +(-2.82683 + 1.63207i) q^{14} +(-0.378909 + 0.451566i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.13965 - 3.13118i) q^{17} +(0.642788 - 0.113341i) q^{18} +(-5.89485 + 1.03942i) q^{19} +(-0.131594 - 0.361551i) q^{20} +(3.83095 + 3.21455i) q^{21} +(-1.66142 + 1.98001i) q^{22} +(6.53507 - 3.77303i) q^{23} +(0.524005 - 1.43969i) q^{24} +(0.842535 - 4.77825i) q^{25} +(-0.682461 + 1.18206i) q^{26} +(-2.79813 - 4.84651i) q^{27} +(-3.06729 + 1.11640i) q^{28} +(2.78251 + 1.60649i) q^{29} +(-0.451566 + 0.378909i) q^{30} +2.53737i q^{31} +(0.642788 + 0.766044i) q^{32} +(3.72120 + 1.35440i) q^{33} +(-0.578618 - 3.28150i) q^{34} +(1.23681 + 0.218083i) q^{35} +0.652704 q^{36} +(0.543196 + 6.05846i) q^{37} -5.98578 q^{38} +(2.05941 + 0.363130i) q^{39} +(-0.0668119 - 0.378909i) q^{40} +(7.77046 + 2.82822i) q^{41} +(3.21455 + 3.83095i) q^{42} -4.33920i q^{43} +(-1.98001 + 1.66142i) q^{44} +(-0.217486 - 0.125565i) q^{45} +(7.09097 - 2.58090i) q^{46} +(-2.61455 - 4.52853i) q^{47} +(0.766044 - 1.32683i) q^{48} +(0.634616 - 3.59909i) q^{49} +(1.65947 - 4.55935i) q^{50} +(-4.42116 + 2.55256i) q^{51} +(-0.877355 + 1.04559i) q^{52} +(-6.64254 - 5.57375i) q^{53} +(-1.91404 - 5.25877i) q^{54} +(0.979373 - 0.172690i) q^{55} +(-3.21455 + 0.566812i) q^{56} +(3.13658 + 8.61769i) q^{57} +(2.46128 + 2.06526i) q^{58} +(8.33530 - 9.93362i) q^{59} +(-0.510503 + 0.294739i) q^{60} +(-2.39847 + 6.58973i) q^{61} +(-0.440610 + 2.49882i) q^{62} +(-1.06526 + 1.84508i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.493489 - 0.179615i) q^{65} +(3.42947 + 1.98001i) q^{66} +(-8.60881 + 7.22365i) q^{67} -3.33213i q^{68} +(-7.43141 - 8.85641i) q^{69} +(1.18015 + 0.429540i) q^{70} +(2.60464 + 14.7717i) q^{71} +(0.642788 + 0.113341i) q^{72} -15.0792 q^{73} +(-0.517097 + 6.06074i) q^{74} -7.43364 q^{75} +(-5.89485 - 1.03942i) q^{76} +(-1.46505 - 8.30870i) q^{77} +(1.96507 + 0.715227i) q^{78} +(0.940587 + 1.12095i) q^{79} -0.384754i q^{80} +(-5.06805 + 4.25260i) q^{81} +(7.16130 + 4.13458i) q^{82} +(0.0104473 - 0.00380252i) q^{83} +(2.50048 + 4.33095i) q^{84} +(-0.641025 + 1.11029i) q^{85} +(0.753494 - 4.27328i) q^{86} +(1.68361 - 4.62569i) q^{87} +(-2.23843 + 1.29236i) q^{88} +(-0.612745 + 0.730241i) q^{89} +(-0.192377 - 0.161424i) q^{90} +(-1.52380 - 4.18661i) q^{91} +(7.43141 - 1.31036i) q^{92} +(3.82842 - 0.675054i) q^{93} +(-1.78845 - 4.91374i) q^{94} +(1.76424 + 1.48038i) q^{95} +(0.984808 - 1.17365i) q^{96} +(12.8332 - 7.40927i) q^{97} +(1.24995 - 3.43421i) q^{98} +(-0.292954 + 1.66142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.266044	−	1.50881i	−0.153601	−	0.871114i	−0.960054	−	0.279815i	$-0.909727\pi$
$3$	−0.266044	−	1.50881i	−0.153601	−	0.871114i	0.806453	−	0.591298i	$-0.201384\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−0.247315	−	0.294739i	−0.110603	−	0.131811i	0.707903	−	0.706310i	$-0.249641\pi$
$5$	−0.247315	−	0.294739i	−0.110603	−	0.131811i	−0.818506	+	0.574499i	$0.805197\pi$
$6$		−	1.53209i		−	0.625473i
$7$	−2.50048	+	2.09815i	−0.945091	+	0.793026i	−0.978464	−	0.206417i	$-0.933820\pi$
$7$	−2.50048	+	2.09815i	−0.945091	+	0.793026i	0.0333729	+	0.999443i	$0.489375\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	0.613341	−	0.223238i	0.204447	−	0.0744126i
$10$	−0.192377	−	0.333207i	−0.0608350	−	0.105369i
$11$	−1.29236	+	2.23843i	−0.389661	+	0.674912i	−0.992404	−	0.123023i	$-0.960741\pi$
$11$	−1.29236	+	2.23843i	−0.389661	+	0.674912i	0.602743	+	0.797935i	$0.294074\pi$
$12$	0.266044	−	1.50881i	0.0768004	−	0.435557i
$13$	−0.466831	+	1.28261i	−0.129476	+	0.355731i	−0.987444	−	0.157972i	$-0.949504\pi$
$13$	−0.466831	+	1.28261i	−0.129476	+	0.355731i	0.857968	+	0.513703i	$0.171727\pi$
$14$	−2.82683	+	1.63207i	−0.755502	+	0.436189i
$15$	−0.378909	+	0.451566i	−0.0978339	+	0.116594i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.13965	−	3.13118i	−0.276407	−	0.759422i	−0.997763	−	0.0668568i	$-0.978703\pi$
$17$	−1.13965	−	3.13118i	−0.276407	−	0.759422i	0.721356	−	0.692565i	$-0.243519\pi$
$18$	0.642788	−	0.113341i	0.151506	−	0.0267147i
$19$	−5.89485	+	1.03942i	−1.35237	+	0.238459i	−0.802431	−	0.596745i	$-0.796460\pi$
$19$	−5.89485	+	1.03942i	−1.35237	+	0.238459i	−0.549939	+	0.835205i	$0.685349\pi$
$20$	−0.131594	−	0.361551i	−0.0294253	−	0.0808452i
$21$	3.83095	+	3.21455i	0.835982	+	0.701472i
$22$	−1.66142	+	1.98001i	−0.354217	+	0.422139i
$23$	6.53507	−	3.77303i	1.36266	−	0.786730i	0.372680	−	0.927960i	$-0.378439\pi$
$23$	6.53507	−	3.77303i	1.36266	−	0.786730i	0.989977	+	0.141230i	$0.0451057\pi$
$24$	0.524005	−	1.43969i	0.106962	−	0.293876i
$25$	0.842535	−	4.77825i	0.168507	−	0.955650i
$26$	−0.682461	+	1.18206i	−0.133842	+	0.231821i
$27$	−2.79813	−	4.84651i	−0.538501	−	0.932711i
$28$	−3.06729	+	1.11640i	−0.579663	+	0.210980i
$29$	2.78251	+	1.60649i	0.516700	+	0.298317i	0.735583	−	0.677434i	$-0.236908\pi$
$29$	2.78251	+	1.60649i	0.516700	+	0.298317i	−0.218883	+	0.975751i	$0.570241\pi$
$30$	−0.451566	+	0.378909i	−0.0824444	+	0.0691790i
$31$			2.53737i			0.455726i	0.973693	+	0.227863i	$0.0731738\pi$
$31$			2.53737i			0.455726i	−0.973693	+	0.227863i	$0.926826\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	3.72120	+	1.35440i	0.647777	+	0.235772i
$34$	−0.578618	−	3.28150i	−0.0992321	−	0.562773i
$35$	1.23681	+	0.218083i	0.209059	+	0.0368628i
$36$	0.652704			0.108784
$37$	0.543196	+	6.05846i	0.0893009	+	0.996005i
$37$	0.543196	+	6.05846i	0.0893009	+	0.996005i
$38$	−5.98578			−0.971022
$39$	2.05941	+	0.363130i	0.329770	+	0.0581473i
$40$	−0.0668119	−	0.378909i	−0.0105639	−	0.0599108i
$41$	7.77046	+	2.82822i	1.21354	+	0.441693i	0.867931	−	0.496685i	$-0.165449\pi$
$41$	7.77046	+	2.82822i	1.21354	+	0.441693i	0.345611	+	0.938378i	$0.387672\pi$
$42$	3.21455	+	3.83095i	0.496016	+	0.591129i
$43$		−	4.33920i		−	0.661722i	−0.943680	−	0.330861i	$-0.892661\pi$
$43$		−	4.33920i		−	0.661722i	0.943680	−	0.330861i	$-0.107339\pi$
$44$	−1.98001	+	1.66142i	−0.298497	+	0.250469i
$45$	−0.217486	−	0.125565i	−0.0324208	−	0.0187182i
$46$	7.09097	−	2.58090i	1.04551	−	0.380533i
$47$	−2.61455	−	4.52853i	−0.381371	−	0.660554i	0.609888	−	0.792488i	$-0.291215\pi$
$47$	−2.61455	−	4.52853i	−0.381371	−	0.660554i	−0.991258	+	0.131934i	$0.957881\pi$
$48$	0.766044	−	1.32683i	0.110569	−	0.191511i
$49$	0.634616	−	3.59909i	0.0906594	−	0.514155i
$50$	1.65947	−	4.55935i	0.234684	−	0.644790i
$51$	−4.42116	+	2.55256i	−0.619086	+	0.357430i
$52$	−0.877355	+	1.04559i	−0.121667	+	0.144997i
$53$	−6.64254	−	5.57375i	−0.912423	−	0.765614i	0.0601551	−	0.998189i	$-0.480840\pi$
$53$	−6.64254	−	5.57375i	−0.912423	−	0.765614i	−0.972578	+	0.232575i	$0.925285\pi$
$54$	−1.91404	−	5.25877i	−0.260467	−	0.715628i
$55$	0.979373	−	0.172690i	0.132059	−	0.0232855i
$56$	−3.21455	+	0.566812i	−0.429562	+	0.0757434i
$57$	3.13658	+	8.61769i	0.415450	+	1.14144i
$58$	2.46128	+	2.06526i	0.323182	+	0.271182i
$59$	8.33530	−	9.93362i	1.08516	−	1.29325i	0.131849	−	0.991270i	$-0.457909\pi$
$59$	8.33530	−	9.93362i	1.08516	−	1.29325i	0.953315	−	0.301978i	$-0.0976469\pi$
$60$	−0.510503	+	0.294739i	−0.0659056	+	0.0380506i
$61$	−2.39847	+	6.58973i	−0.307092	+	0.843728i	0.686128	+	0.727481i	$0.259309\pi$
$61$	−2.39847	+	6.58973i	−0.307092	+	0.843728i	−0.993220	+	0.116248i	$0.962913\pi$
$62$	−0.440610	+	2.49882i	−0.0559576	+	0.317351i
$63$	−1.06526	+	1.84508i	−0.134210	+	0.232458i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	0.493489	−	0.179615i	0.0612098	−	0.0222785i
$66$	3.42947	+	1.98001i	0.422139	+	0.243722i
$67$	−8.60881	+	7.22365i	−1.05173	+	0.882509i	−0.993275	−	0.115781i	$-0.963063\pi$
$67$	−8.60881	+	7.22365i	−1.05173	+	0.882509i	−0.0584586	+	0.998290i	$0.518619\pi$
$68$		−	3.33213i		−	0.404080i
$69$	−7.43141	−	8.85641i	−0.894636	−	1.06619i
$70$	1.18015	+	0.429540i	0.141055	+	0.0513399i
$71$	2.60464	+	14.7717i	0.309114	+	1.75307i	0.603477	+	0.797380i	$0.293781\pi$
$71$	2.60464	+	14.7717i	0.309114	+	1.75307i	−0.294363	+	0.955694i	$0.595107\pi$
$72$	0.642788	+	0.113341i	0.0757532	+	0.0133573i
$73$	−15.0792			−1.76489			−0.882445	−	0.470416i	$-0.844104\pi$
$73$	−15.0792			−1.76489			−0.882445	+	0.470416i	$0.844104\pi$
$74$	−0.517097	+	6.06074i	−0.0601113	+	0.704547i
$75$	−7.43364			−0.858363
$76$	−5.89485	−	1.03942i	−0.676185	−	0.119230i
$77$	−1.46505	−	8.30870i	−0.166958	−	0.946864i
$78$	1.96507	+	0.715227i	0.222500	+	0.0809835i
$79$	0.940587	+	1.12095i	0.105824	+	0.126117i	0.816357	−	0.577548i	$-0.195990\pi$
$79$	0.940587	+	1.12095i	0.105824	+	0.126117i	−0.710532	+	0.703664i	$0.751546\pi$
$80$		−	0.384754i		−	0.0430169i
$81$	−5.06805	+	4.25260i	−0.563116	+	0.472511i
$82$	7.16130	+	4.13458i	0.790833	+	0.456588i
$83$	0.0104473	−	0.00380252i	0.00114674	−	0.000417381i	−0.341447	−	0.939901i	$-0.610917\pi$
$83$	0.0104473	−	0.00380252i	0.00114674	−	0.000417381i	0.342593	+	0.939484i	$0.388695\pi$
$84$	2.50048	+	4.33095i	0.272824	+	0.472546i
$85$	−0.641025	+	1.11029i	−0.0695290	+	0.120428i
$86$	0.753494	−	4.27328i	0.0812514	−	0.460799i
$87$	1.68361	−	4.62569i	0.180502	−	0.495926i
$88$	−2.23843	+	1.29236i	−0.238617	+	0.137766i
$89$	−0.612745	+	0.730241i	−0.0649509	+	0.0774054i	−0.797542	−	0.603264i	$-0.793867\pi$
$89$	−0.612745	+	0.730241i	−0.0649509	+	0.0774054i	0.732591	+	0.680669i	$0.238311\pi$
$90$	−0.192377	−	0.161424i	−0.0202783	−	0.0170155i
$91$	−1.52380	−	4.18661i	−0.159738	−	0.438876i
$92$	7.43141	−	1.31036i	0.774778	−	0.136614i
$93$	3.82842	−	0.675054i	0.396989	−	0.0699998i
$94$	−1.78845	−	4.91374i	−0.184465	−	0.506814i
$95$	1.76424	+	1.48038i	0.181008	+	0.151883i
$96$	0.984808	−	1.17365i	0.100512	−	0.119785i
$97$	12.8332	−	7.40927i	1.30302	−	0.752297i	0.322097	−	0.946707i	$-0.395612\pi$
$97$	12.8332	−	7.40927i	1.30302	−	0.752297i	0.980920	+	0.194410i	$0.0622791\pi$
$98$	1.24995	−	3.43421i	0.126264	−	0.346907i
$99$	−0.292954	+	1.66142i	−0.0294430	+	0.166979i
$100$	2.42598	−	4.20192i	0.242598	−	0.420192i
$101$	−0.636260	−	1.10204i	−0.0633103	−	0.109657i	0.832633	−	0.553825i	$-0.186832\pi$
$101$	−0.636260	−	1.10204i	−0.0633103	−	0.109657i	−0.895943	+	0.444169i	$0.853499\pi$
$102$	−4.79724	+	1.74605i	−0.474997	+	0.172885i
$103$	9.39301	+	5.42306i	0.925521	+	0.534350i	0.885392	−	0.464845i	$-0.153890\pi$
$103$	9.39301	+	5.42306i	0.925521	+	0.534350i	0.0401287	+	0.999195i	$0.487223\pi$
$104$	−1.04559	+	0.877355i	−0.102529	+	0.0860318i
$105$		−	1.92414i		−	0.187777i
$106$	−5.57375	−	6.64254i	−0.541371	−	0.645181i
$107$	4.47254	+	1.62787i	0.432377	+	0.157372i	0.549034	−	0.835800i	$-0.314996\pi$
$107$	4.47254	+	1.62787i	0.432377	+	0.157372i	−0.116657	+	0.993172i	$0.537218\pi$
$108$	−0.971782	−	5.51125i	−0.0935097	−	0.530320i
$109$	9.49102	+	1.67352i	0.909075	+	0.160294i	0.608583	−	0.793490i	$-0.291738\pi$
$109$	9.49102	+	1.67352i	0.909075	+	0.160294i	0.300492	+	0.953784i	$0.402849\pi$
$110$	0.994481			0.0948201
$111$	8.99657	−	2.43140i	0.853917	−	0.230778i
$112$	−3.26414			−0.308432
$113$	−12.7581	−	2.24960i	−1.20018	−	0.211624i	−0.462405	−	0.886669i	$-0.653013\pi$
$113$	−12.7581	−	2.24960i	−1.20018	−	0.211624i	−0.737777	+	0.675044i	$0.764124\pi$
$114$	1.59248	+	9.03143i	0.149150	+	0.845871i
$115$	−2.72828	−	0.993013i	−0.254414	−	0.0925990i
$116$	2.06526	+	2.46128i	0.191754	+	0.228524i
$117$			0.890890i			0.0823628i
$118$	9.93362	−	8.33530i	0.914464	−	0.767327i
$119$	9.41935	+	5.43826i	0.863470	+	0.498525i
$120$	−0.553928	+	0.201613i	−0.0505665	+	0.0184047i
$121$	2.15962	+	3.74057i	0.196329	+	0.340052i
$122$	−3.50632	+	6.07313i	−0.317447	+	0.549835i
$123$	2.19996	−	12.4766i	0.198364	−	1.12498i
$124$	−0.867833	+	2.38435i	−0.0779337	+	0.214121i
$125$	−3.28274	+	1.89529i	−0.293618	+	0.169520i
$126$	−1.36947	+	1.63207i	−0.122002	+	0.145396i
$127$	8.61094	+	7.22543i	0.764097	+	0.641154i	0.939190	−	0.343398i	$-0.111578\pi$
$127$	8.61094	+	7.22543i	0.764097	+	0.641154i	−0.175093	+	0.984552i	$0.556023\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−6.54704	+	1.15442i	−0.576435	+	0.101641i
$130$	0.517182	−	0.0911931i	0.0453598	−	0.00799816i
$131$	2.86257	+	7.86484i	0.250104	+	0.687154i	0.999681	+	0.0252378i	$0.00803431\pi$
$131$	2.86257	+	7.86484i	0.250104	+	0.687154i	−0.749578	+	0.661916i	$0.769743\pi$
$132$	3.03355	+	2.54545i	0.264036	+	0.221553i
$133$	12.5591	−	14.9673i	1.08901	−	1.29783i
$134$	−9.73239	+	5.61900i	−0.840751	+	0.485408i
$135$	−0.736434	+	2.02334i	−0.0633821	+	0.174141i
$136$	0.578618	−	3.28150i	0.0496161	−	0.281387i
$137$	1.99206	−	3.45036i	0.170194	−	0.294784i	−0.768294	−	0.640097i	$-0.778894\pi$
$137$	1.99206	−	3.45036i	0.170194	−	0.294784i	0.938487	+	0.345313i	$0.112227\pi$
$138$	−5.78061	−	10.0123i	−0.492078	−	0.852304i
$139$	−4.80315	+	1.74820i	−0.407398	+	0.148281i	−0.537586	−	0.843209i	$-0.680664\pi$
$139$	−4.80315	+	1.74820i	−0.407398	+	0.148281i	0.130189	+	0.991489i	$0.458442\pi$
$140$	1.08763	+	0.627946i	0.0919219	+	0.0530711i
$141$	−6.13711	+	5.14965i	−0.516838	+	0.433679i
$142$			14.9995i			1.25873i
$143$	−2.26771	−	2.70256i	−0.189636	−	0.225999i
$144$	0.613341	+	0.223238i	0.0511117	+	0.0186031i
$145$	−0.214665	−	1.21742i	−0.0178269	−	0.101102i
$146$	−14.8501	−	2.61848i	−1.22901	−	0.216707i
$147$	−5.59918			−0.461813
$148$	−1.56168	+	5.87887i	−0.128369	+	0.483240i
$149$	−15.8700			−1.30012			−0.650060	−	0.759883i	$-0.725256\pi$
$149$	−15.8700			−1.30012			−0.650060	+	0.759883i	$0.725256\pi$
$150$	−7.32071	−	1.29084i	−0.597733	−	0.105396i
$151$	−3.77998	−	21.4373i	−0.307611	−	1.74455i	−0.610955	−	0.791665i	$-0.709214\pi$
$151$	−3.77998	−	21.4373i	−0.307611	−	1.74455i	0.303344	−	0.952881i	$-0.401897\pi$
$152$	−5.62480	−	2.04726i	−0.456231	−	0.166055i
$153$	−1.39799	−	1.66606i	−0.113021	−	0.134693i
$154$		−	8.43688i		−	0.679863i
$155$	0.747863	−	0.627531i	0.0600698	−	0.0504045i
$156$	1.81102	+	1.04559i	0.144997	+	0.0837143i
$157$	9.16333	−	3.33518i	0.731314	−	0.266176i	0.0505928	−	0.998719i	$-0.483889\pi$
$157$	9.16333	−	3.33518i	0.731314	−	0.266176i	0.680721	+	0.732543i	$0.261667\pi$
$158$	0.731647	+	1.26725i	0.0582067	+	0.100817i
$159$	−6.64254	+	11.5052i	−0.526788	+	0.912423i
$160$	0.0668119	−	0.378909i	0.00528195	−	0.0299554i
$161$	−8.42442	+	23.1459i	−0.663937	+	1.82415i
$162$	−5.72951	+	3.30793i	−0.450153	+	0.259896i
$163$	8.46213	−	10.0848i	0.662805	−	0.789901i	−0.324980	−	0.945721i	$-0.605358\pi$
$163$	8.46213	−	10.0848i	0.662805	−	0.789901i	0.987785	+	0.155820i	$0.0498021\pi$
$164$	6.33454	+	5.31531i	0.494644	+	0.415056i
$165$	−0.521113	−	1.43175i	−0.0405686	−	0.111461i
$166$	0.0109489	−	0.00193059i	0.000849801	−	0.000149843i
$167$	5.51717	−	0.972826i	0.426932	−	0.0752796i	0.0439461	−	0.999034i	$-0.486007\pi$
$167$	5.51717	−	0.972826i	0.426932	−	0.0752796i	0.382986	+	0.923754i	$0.374896\pi$
$168$	1.71043	+	4.69936i	0.131962	+	0.362563i
$169$	8.53143	+	7.15872i	0.656264	+	0.550671i
$170$	−0.824086	+	0.982108i	−0.0632045	+	0.0753242i
$171$	−3.38351	+	1.95347i	−0.258744	+	0.149386i
$172$	1.48409	−	4.07751i	0.113161	−	0.310908i
$173$	−1.88155	+	10.6708i	−0.143051	+	0.811285i	0.825860	+	0.563876i	$0.190690\pi$
$173$	−1.88155	+	10.6708i	−0.143051	+	0.811285i	−0.968911	+	0.247409i	$0.920421\pi$
$174$	2.46128	−	4.26306i	0.186589	−	0.323182i
$175$	7.91874	+	13.7157i	0.598601	+	1.03681i
$176$	−2.42884	+	0.884025i	−0.183081	+	0.0666359i
$177$	−17.2055	−	9.93362i	−1.29325	−	0.746657i
$178$	−0.730241	+	0.612745i	−0.0547339	+	0.0459272i
$179$		−	6.07192i		−	0.453837i	−0.973914	−	0.226918i	$-0.927135\pi$
$179$		−	6.07192i		−	0.453837i	0.973914	−	0.226918i	$-0.0728651\pi$
$180$	−0.161424	−	0.192377i	−0.0120318	−	0.0143390i
$181$	−20.2540	−	7.37185i	−1.50547	−	0.547945i	−0.547997	−	0.836480i	$-0.684610\pi$
$181$	−20.2540	−	7.37185i	−1.50547	−	0.547945i	−0.957469	+	0.288535i	$0.906832\pi$
$182$	−0.773654	−	4.38761i	−0.0573471	−	0.325231i
$183$	10.5808	+	1.86567i	0.782153	+	0.137915i
$184$	7.54605			0.556302
$185$	1.65132	−	1.65845i	0.121408	−	0.121932i
$186$	3.88748			0.285044
$187$	8.48176	+	1.49556i	0.620248	+	0.109366i
$188$	−0.908022	−	5.14965i	−0.0662243	−	0.375577i
$189$	17.1654	+	6.24768i	1.24860	+	0.454452i
$190$	1.48038	+	1.76424i	0.107398	+	0.127992i
$191$		−	6.62693i		−	0.479508i	−0.970834	−	0.239754i	$-0.922933\pi$
$191$		−	6.62693i		−	0.479508i	0.970834	−	0.239754i	$-0.0770668\pi$
$192$	1.17365	−	0.984808i	0.0847008	−	0.0710724i
$193$	−19.7925	−	11.4272i	−1.42469	−	0.822548i	−0.428000	−	0.903779i	$-0.640782\pi$
$193$	−19.7925	−	11.4272i	−1.42469	−	0.822548i	−0.996695	+	0.0812309i	$0.974115\pi$
$194$	13.9249	−	5.06824i	0.999747	−	0.363878i
$195$	−0.402296	−	0.696797i	−0.0288090	−	0.0498987i
$196$	1.82730	−	3.16498i	0.130522	−	0.226070i
$197$	−2.56236	+	14.5319i	−0.182561	+	1.03535i	0.746488	+	0.665398i	$0.231738\pi$
$197$	−2.56236	+	14.5319i	−0.182561	+	1.03535i	−0.929049	+	0.369956i	$0.879373\pi$
$198$	−0.577006	+	1.58531i	−0.0410061	+	0.112663i
$199$	−1.27720	+	0.737389i	−0.0905380	+	0.0522721i	−0.544585	−	0.838705i	$-0.683313\pi$
$199$	−1.27720	+	0.737389i	−0.0905380	+	0.0522721i	0.454047	+	0.890978i	$0.349980\pi$
$200$	3.11878	−	3.71682i	0.220531	−	0.262819i
$201$	13.1895	+	11.0673i	0.930313	+	0.780625i
$202$	−0.435228	−	1.19578i	−0.0306225	−	0.0841347i
$203$	−10.3283	+	1.82115i	−0.724901	+	0.127820i
$204$	−5.02756	+	0.886494i	−0.351999	+	0.0620670i
$205$	−1.08817	−	2.98972i	−0.0760010	−	0.208811i
$206$	8.30861	+	6.97175i	0.578888	+	0.485745i
$207$	3.16594	−	3.77303i	0.220048	−	0.262243i
$208$	−1.18206	+	0.682461i	−0.0819609	+	0.0473202i
$209$	5.29158	−	14.5385i	0.366026	−	1.00565i
$210$	0.334123	−	1.89491i	0.0230567	−	0.130761i
$211$	1.20976	−	2.09537i	0.0832835	−	0.144251i	−0.821375	−	0.570389i	$-0.806793\pi$
$211$	1.20976	−	2.09537i	0.0832835	−	0.144251i	0.904658	+	0.426137i	$0.140126\pi$
$212$	−4.33561	−	7.50950i	−0.297771	−	0.515755i
$213$	21.5947	−	7.85984i	1.47965	−	0.538547i
$214$	4.12192	+	2.37979i	0.281769	+	0.162679i
$215$	−1.27893	+	1.07315i	−0.0872224	+	0.0731883i
$216$		−	5.59627i		−	0.380778i
$217$	−5.32379	−	6.34464i	−0.361402	−	0.430702i
$218$	9.05623	+	3.29620i	0.613365	+	0.223247i
$219$	4.01174	+	22.7517i	0.271089	+	1.53742i
$220$	0.979373	+	0.172690i	0.0660293	+	0.0116427i
$221$	4.54809			0.305938
$222$	9.28210	−	0.832224i	0.622974	−	0.0558552i
$223$	−6.94726			−0.465223			−0.232611	−	0.972570i	$-0.574727\pi$
$223$	−6.94726			−0.465223			−0.232611	+	0.972570i	$0.574727\pi$
$224$	−3.21455	−	0.566812i	−0.214781	−	0.0378717i
$225$	−0.549925	−	3.11878i	−0.0366617	−	0.207919i
$226$	−12.1736	−	4.43084i	−0.809779	−	0.294735i
$227$	−14.0443	−	16.7373i	−0.932150	−	1.11089i	−0.993619	−	0.112785i	$-0.964023\pi$
$227$	−14.0443	−	16.7373i	−0.932150	−	1.11089i	0.0614692	−	0.998109i	$-0.480421\pi$
$228$			9.17075i			0.607348i
$229$	−3.25576	+	2.73191i	−0.215147	+	0.180530i	−0.743992	−	0.668189i	$-0.767070\pi$
$229$	−3.25576	+	2.73191i	−0.215147	+	0.180530i	0.528845	+	0.848719i	$0.322625\pi$
$230$	−2.51440	−	1.45169i	−0.165794	−	0.0957215i
$231$	−12.1465	+	4.42097i	−0.799181	+	0.290878i
$232$	1.60649	+	2.78251i	0.105471	+	0.182681i
$233$	−8.67215	+	15.0206i	−0.568131	+	0.984032i	0.428619	+	0.903485i	$0.359000\pi$
$233$	−8.67215	+	15.0206i	−0.568131	+	0.984032i	−0.996751	+	0.0805473i	$0.974333\pi$
$234$	−0.154701	+	0.877355i	−0.0101131	+	0.0573545i
$235$	−0.688116	+	1.89058i	−0.0448877	+	0.123328i
$236$	11.2301	−	6.48371i	0.731019	−	0.422054i
$237$	1.44106	−	1.71739i	0.0936071	−	0.111557i
$238$	8.33190	+	6.99130i	0.540077	+	0.453178i
$239$	−6.27893	−	17.2512i	−0.406150	−	1.11589i	−0.959197	−	0.282738i	$-0.908757\pi$
$239$	−6.27893	−	17.2512i	−0.406150	−	1.11589i	0.553047	−	0.833150i	$-0.313465\pi$
$240$	−0.580523	+	0.102362i	−0.0374726	+	0.00660742i
$241$	23.1096	−	4.07485i	1.48862	−	0.262484i	0.630604	−	0.776105i	$-0.282807\pi$
$241$	23.1096	−	4.07485i	1.48862	−	0.262484i	0.858017	+	0.513621i	$0.171696\pi$
$242$	1.47727	+	4.05876i	0.0949624	+	0.260907i
$243$	−5.09627	−	4.27628i	−0.326926	−	0.274323i
$244$	−4.50764	+	5.37200i	−0.288572	+	0.343907i
$245$	−1.21774	+	0.703063i	−0.0777986	+	0.0449171i
$246$	4.33308	−	11.9050i	0.276267	−	0.759037i
$247$	1.41873	−	8.04601i	0.0902715	−	0.511955i
$248$	−1.26869	+	2.19743i	−0.0805617	+	0.139537i
$249$	−0.00851674	−	0.0147514i	−0.000539727	−	0.000934834i
$250$	−3.56199	+	1.29646i	−0.225280	+	0.0819951i
$251$	5.28405	+	3.05074i	0.333526	+	0.192561i	0.657405	−	0.753537i	$-0.271654\pi$
$251$	5.28405	+	3.05074i	0.333526	+	0.192561i	−0.323879	+	0.946098i	$0.604987\pi$
$252$	−1.63207	+	1.36947i	−0.102811	+	0.0862685i
$253$			19.5044i			1.22623i
$254$	7.22543	+	8.61094i	0.453364	+	0.540298i
$255$	1.84576	+	0.671801i	0.115586	+	0.0420698i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	4.28106	+	0.754866i	0.267045	+	0.0470873i	0.305567	−	0.952170i	$-0.401154\pi$
$257$	4.28106	+	0.754866i	0.267045	+	0.0470873i	−0.0385222	+	0.999258i	$0.512265\pi$
$258$	−6.64804			−0.413889
$259$	−14.0698	−	14.0093i	−0.874255	−	0.870497i
$260$	0.525160			0.0325690
$261$	2.06526	+	0.364161i	0.127836	+	0.0225410i
$262$	1.45336	+	8.24243i	0.0897891	+	0.509219i
$263$	3.81031	+	1.38684i	0.234954	+	0.0855163i	0.456814	−	0.889562i	$-0.348991\pi$
$263$	3.81031	+	1.38684i	0.234954	+	0.0855163i	−0.221860	+	0.975079i	$0.571213\pi$
$264$	2.54545	+	3.03355i	0.156662	+	0.186702i
$265$			3.33629i			0.204947i
$266$	14.9673	−	12.5591i	0.917704	−	0.770045i
$267$	1.26481	+	0.730241i	0.0774054	+	0.0446900i
$268$	−10.5603	+	3.84362i	−0.645071	+	0.234787i
$269$	−4.39669	−	7.61528i	−0.268071	−	0.464312i	0.700293	−	0.713856i	$-0.253053\pi$
$269$	−4.39669	−	7.61528i	−0.268071	−	0.464312i	−0.968364	+	0.249544i	$0.919719\pi$
$270$	−1.07659	+	1.86472i	−0.0655194	+	0.113483i
$271$	−2.24218	+	12.7160i	−0.136203	+	0.772444i	0.837812	+	0.545959i	$0.183835\pi$
$271$	−2.24218	+	12.7160i	−0.136203	+	0.772444i	−0.974015	+	0.226485i	$0.927276\pi$
$272$	1.13965	−	3.13118i	0.0691017	−	0.189855i
$273$	−5.91141	+	3.41296i	−0.357775	+	0.206561i
$274$	2.56095	−	3.05202i	0.154713	−	0.184379i
$275$	9.60693	+	8.06117i	0.579319	+	0.486107i
$276$	−3.95417	−	10.8640i	−0.238013	−	0.653936i
$277$	7.65829	−	1.35036i	0.460142	−	0.0811355i	0.0612280	−	0.998124i	$-0.480498\pi$
$277$	7.65829	−	1.35036i	0.460142	−	0.0811355i	0.398914	+	0.916988i	$0.369387\pi$
$278$	−5.03375	+	0.887586i	−0.301904	+	0.0532338i
$279$	0.566438	+	1.55627i	0.0339117	+	0.0931717i
$280$	0.962069	+	0.807272i	0.0574946	+	0.0482437i
$281$	0.149454	−	0.178113i	0.00891569	−	0.0106253i	−0.761568	−	0.648085i	$-0.775570\pi$
$281$	0.149454	−	0.178113i	0.00891569	−	0.0106253i	0.770484	+	0.637459i	$0.220015\pi$
$282$	−6.93811	+	4.00572i	−0.413158	+	0.238537i
$283$	−4.38915	+	12.0591i	−0.260908	+	0.716838i	0.738199	+	0.674583i	$0.235676\pi$
$283$	−4.38915	+	12.0591i	−0.260908	+	0.716838i	−0.999107	+	0.0422550i	$0.986546\pi$
$284$	−2.60464	+	14.7717i	−0.154557	+	0.876537i
$285$	1.76424	−	3.05576i	0.104505	−	0.181008i
$286$	−1.76397	−	3.05528i	−0.104306	−	0.180663i
$287$	−25.3639	+	9.23169i	−1.49718	+	0.544930i
$288$	0.565258	+	0.326352i	0.0333081	+	0.0192305i
$289$	4.51731	−	3.79047i	0.265724	−	0.222969i
$290$		−	1.23620i		−	0.0725925i
$291$	−14.5934	−	17.3917i	−0.855481	−	1.01952i
$292$	−14.1698	−	5.15740i	−0.829227	−	0.301814i
$293$	−4.27944	−	24.2699i	−0.250007	−	1.41786i	−0.808570	−	0.588400i	$-0.799758\pi$
$293$	−4.27944	−	24.2699i	−0.250007	−	1.41786i	0.558563	−	0.829462i	$-0.311353\pi$
$294$	−5.51412	−	0.972288i	−0.321590	−	0.0567050i
$295$	−4.98927			−0.290487
$296$	−2.55881	+	5.51838i	−0.148728	+	0.320749i
$297$	14.4648			0.839331
$298$	−15.6289	−	2.75579i	−0.905357	−	0.159639i
$299$	1.78854	+	10.1433i	0.103434	+	0.586602i
$300$	−6.98534	−	2.54245i	−0.403299	−	0.146789i
$301$	9.10429	+	10.8501i	0.524762	+	0.625387i
$302$		−	21.7680i		−	1.25261i
$303$	−1.49349	+	1.25319i	−0.0857988	+	0.0719938i
$304$	−5.18384	−	2.99289i	−0.297314	−	0.171654i
$305$	2.53543	−	0.922820i	0.145178	−	0.0528405i
$306$	−1.08745	−	1.88351i	−0.0621651	−	0.107673i
$307$	−3.45566	+	5.98538i	−0.197225	+	0.341604i	−0.947628	−	0.319377i	$-0.896526\pi$
$307$	−3.45566	+	5.98538i	−0.197225	+	0.341604i	0.750403	+	0.660981i	$0.229860\pi$
$308$	1.46505	−	8.30870i	0.0834789	−	0.473432i
$309$	5.68342	−	15.6151i	0.323319	−	0.888310i
$310$	0.845471	−	0.488133i	0.0480195	−	0.0277241i
$311$	1.06612	−	1.27056i	0.0604542	−	0.0720466i	−0.734970	−	0.678100i	$-0.762804\pi$
$311$	1.06612	−	1.27056i	0.0604542	−	0.0720466i	0.795424	+	0.606053i	$0.207248\pi$
$312$	1.60194	+	1.34419i	0.0906919	+	0.0760996i
$313$	8.87573	+	24.3859i	0.501686	+	1.37837i	0.889628	+	0.456687i	$0.150964\pi$
$313$	8.87573	+	24.3859i	0.501686	+	1.37837i	−0.387942	+	0.921684i	$0.626814\pi$
$314$	9.60327	−	1.69332i	0.541944	−	0.0955593i
$315$	0.807272	−	0.142344i	0.0454846	−	0.00802017i
$316$	0.500476	+	1.37505i	0.0281540	+	0.0773524i
$317$	−8.69447	−	7.29553i	−0.488330	−	0.409758i	0.365097	−	0.930969i	$-0.381036\pi$
$317$	−8.69447	−	7.29553i	−0.488330	−	0.409758i	−0.853427	+	0.521212i	$0.825480\pi$
$318$	−8.53949	+	10.1770i	−0.478871	+	0.570696i
$319$	−7.19201	+	4.15231i	−0.402675	+	0.232485i
$320$	0.131594	−	0.361551i	0.00735632	−	0.0202113i
$321$	1.26626	−	7.18132i	0.0706758	−	0.400822i
$322$	−12.3157	+	21.3314i	−0.686326	+	1.18875i
$323$	9.97269	+	17.2732i	0.554896	+	0.961107i
$324$	−6.21688	+	2.26276i	−0.345382	+	0.125709i
$325$	5.73530	+	3.31128i	0.318137	+	0.183677i
$326$	10.0848	−	8.46213i	0.558544	−	0.468674i
$327$		−	14.7654i		−	0.816529i
$328$	5.31531	+	6.33454i	0.293489	+	0.349766i
$329$	16.0391	+	5.83777i	0.884266	+	0.321847i
$330$	−0.264576	−	1.50049i	−0.0145644	−	0.0825990i
$331$	−12.6426	−	2.22924i	−0.694903	−	0.122530i	−0.184970	−	0.982744i	$-0.559219\pi$
$331$	−12.6426	−	2.22924i	−0.694903	−	0.122530i	−0.509933	+	0.860214i	$0.670330\pi$
$332$	0.0111178			0.000610170
$333$	1.68564	+	3.59464i	0.0923726	+	0.196985i
$334$	5.60228			0.306543
$335$	4.25818	+	0.750832i	0.232649	+	0.0410224i
$336$	0.868406	+	4.92498i	0.0473754	+	0.268679i
$337$	−5.36736	−	1.95356i	−0.292379	−	0.106417i	0.191666	−	0.981460i	$-0.438611\pi$
$337$	−5.36736	−	1.95356i	−0.292379	−	0.106417i	−0.484045	+	0.875043i	$0.660833\pi$
$338$	7.15872	+	8.53143i	0.389383	+	0.464048i
$339$			19.8481i			1.07800i
$340$	−0.982108	+	0.824086i	−0.0532623	+	0.0446924i
$341$	−5.67973	−	3.27919i	−0.307575	−	0.177578i
$342$	−3.67132	+	1.33625i	−0.198523	+	0.0722563i
$343$	−5.45991	−	9.45685i	−0.294808	−	0.510622i
$344$	2.16960	−	3.75786i	0.116977	−	0.202610i
$345$	−0.772427	+	4.38065i	−0.0415861	+	0.235846i
$346$	−3.70592	+	10.1819i	−0.199232	+	0.547385i
$347$	28.0087	−	16.1708i	1.50358	−	0.868095i	0.503593	−	0.863941i	$-0.332011\pi$
$347$	28.0087	−	16.1708i	1.50358	−	0.868095i	0.999991	−	0.00415382i	$-0.00132221\pi$
$348$	3.16416	−	3.77090i	0.169617	−	0.202141i
$349$	−19.0990	−	16.0260i	−1.02235	−	0.857852i	−0.0324270	−	0.999474i	$-0.510324\pi$
$349$	−19.0990	−	16.0260i	−1.02235	−	0.857852i	−0.989921	+	0.141622i	$0.954768\pi$
$350$	5.41674	+	14.8824i	0.289537	+	0.795496i
$351$	7.52242	−	1.32641i	0.401517	−	0.0707983i
$352$	−2.54545	+	0.448831i	−0.135673	+	0.0239228i
$353$	2.95544	+	8.12001i	0.157302	+	0.432185i	0.993160	−	0.116762i	$-0.0372513\pi$
$353$	2.95544	+	8.12001i	0.157302	+	0.432185i	−0.835858	+	0.548946i	$0.815029\pi$
$354$	−15.2192	−	12.7704i	−0.808891	−	0.678740i
$355$	3.70962	−	4.42095i	0.196886	−	0.234640i
$356$	−0.825549	+	0.476631i	−0.0437540	+	0.0252614i
$357$	5.69936	−	15.6589i	0.301642	−	0.828755i
$358$	1.05438	−	5.97968i	0.0557256	−	0.316036i
$359$	−1.92924	+	3.34154i	−0.101821	+	0.176360i	−0.912435	−	0.409221i	$-0.865800\pi$
$359$	−1.92924	+	3.34154i	−0.101821	+	0.176360i	0.810614	+	0.585581i	$0.199134\pi$
$360$	−0.125565	−	0.217486i	−0.00661787	−	0.0114625i
$361$	15.8146	−	5.75606i	0.832350	−	0.302951i
$362$	−18.6662	−	10.7769i	−0.981072	−	0.566422i
$363$	5.06927	−	4.25362i	0.266068	−	0.223257i
$364$		−	4.45530i		−	0.233521i
$365$	3.72932	+	4.44444i	0.195202	+	0.232632i
$366$	10.0960	+	3.67466i	0.527729	+	0.192078i
$367$	1.81571	+	10.2974i	0.0947794	+	0.537521i	0.994815	+	0.101704i	$0.0324294\pi$
$367$	1.81571	+	10.2974i	0.0947794	+	0.537521i	−0.900035	+	0.435817i	$0.856460\pi$
$368$	7.43141	+	1.31036i	0.387389	+	0.0683071i
$369$	5.39731			0.280973
$370$	1.91422	−	1.34651i	0.0995157	−	0.0700015i
$371$	28.3041			1.46947
$372$	3.82842	+	0.675054i	0.198494	+	0.0349999i
$373$	1.71315	+	9.71578i	0.0887038	+	0.503064i	0.996496	+	0.0836434i	$0.0266557\pi$
$373$	1.71315	+	9.71578i	0.0887038	+	0.503064i	−0.907792	+	0.419421i	$0.862233\pi$
$374$	8.09320	+	2.94568i	0.418489	+	0.152318i
$375$	3.73300	+	4.44882i	0.192771	+	0.229736i
$376$		−	5.22909i		−	0.269670i
$377$	−3.35945	+	2.81892i	−0.173021	+	0.145182i
$378$	15.8197	+	9.13350i	0.813677	+	0.469776i
$379$	−2.33157	+	0.848623i	−0.119765	+	0.0435908i	−0.401207	−	0.915987i	$-0.631409\pi$
$379$	−2.33157	+	0.848623i	−0.119765	+	0.0435908i	0.281443	+	0.959578i	$0.409187\pi$
$380$	1.15153	+	1.99451i	0.0590722	+	0.102316i
$381$	8.61094	−	14.9146i	0.441152	−	0.764097i
$382$	1.15075	−	6.52625i	0.0588777	−	0.333912i
$383$	8.74336	−	24.0222i	0.446765	−	1.22748i	−0.488199	−	0.872733i	$-0.662346\pi$
$383$	8.74336	−	24.0222i	0.446765	−	1.22748i	0.934963	−	0.354744i	$-0.115432\pi$
$384$	1.32683	−	0.766044i	0.0677094	−	0.0390920i
$385$	−2.08657	+	2.48668i	−0.106341	+	0.126733i
$386$	−17.5075	−	14.6905i	−0.891108	−	0.747728i
$387$	−0.968674	−	2.66141i	−0.0492404	−	0.135287i
$388$	14.5934	−	2.57321i	0.740868	−	0.130635i
$389$	−6.27824	+	1.10702i	−0.318319	+	0.0561283i	−0.330525	−	0.943797i	$-0.607226\pi$
$389$	−6.27824	+	1.10702i	−0.318319	+	0.0561283i	0.0122057	+	0.999926i	$0.496115\pi$
$390$	−0.275187	−	0.756069i	−0.0139346	−	0.0382850i
$391$	−19.2617	−	16.1625i	−0.974107	−	0.817373i
$392$	2.34914	−	2.79959i	0.118649	−	0.141401i
$393$	11.1050	−	6.41147i	0.560173	−	0.323416i
$394$	−5.04687	+	13.8662i	−0.254258	+	0.698567i
$395$	0.0977655	−	0.554456i	0.00491911	−	0.0278977i
$396$	−0.843527	+	1.46103i	−0.0423888	+	0.0734196i
$397$	18.7489	+	32.4740i	0.940979	+	1.62982i	0.763609	+	0.645679i	$0.223426\pi$
$397$	18.7489	+	32.4740i	0.940979	+	1.62982i	0.177370	+	0.984144i	$0.443241\pi$
$398$	−1.38584	+	0.504404i	−0.0694658	+	0.0252835i
$399$	−25.9241	−	14.9673i	−1.29783	−	0.749303i
$400$	3.71682	−	3.11878i	0.185841	−	0.155939i
$401$		−	35.1464i		−	1.75513i	−0.479462	−	0.877563i	$-0.659168\pi$
$401$		−	35.1464i		−	1.75513i	0.479462	−	0.877563i	$-0.340832\pi$
$402$	11.0673	+	13.1895i	0.551985	+	0.657830i
$403$	−3.25445	−	1.18452i	−0.162116	−	0.0590054i
$404$	−0.220971	−	1.25319i	−0.0109937	−	0.0623484i
$405$	2.50681	+	0.442019i	0.124565	+	0.0219641i
$406$	−10.4876			−0.520490
$407$	−14.2634	−	6.61379i	−0.707013	−	0.327834i
$408$	−5.10511			−0.252741
$409$	0.443894	+	0.0782704i	0.0219491	+	0.00387022i	0.184612	−	0.982811i	$-0.440897\pi$
$409$	0.443894	+	0.0782704i	0.0219491	+	0.00387022i	−0.162663	+	0.986682i	$0.552008\pi$
$410$	−0.552478	−	3.13326i	−0.0272849	−	0.154741i
$411$	−5.73592	−	2.08770i	−0.282932	−	0.102979i
$412$	6.97175	+	8.30861i	0.343473	+	0.409336i
$413$			42.3275i			2.08280i
$414$	3.77303	−	3.16594i	0.185434	−	0.155598i
$415$	−0.00370454	−	0.00213882i	−0.000181849	−	0.000104990i
$416$	−1.28261	+	0.466831i	−0.0628850	+	0.0228883i
$417$	3.91556	+	6.78195i	0.191746	+	0.332114i
$418$	7.73578	−	13.3988i	0.378369	−	0.655355i
$419$	−2.65878	+	15.0787i	−0.129890	+	0.736642i	0.848393	+	0.529367i	$0.177571\pi$
$419$	−2.65878	+	15.0787i	−0.129890	+	0.736642i	−0.978283	+	0.207275i	$0.933541\pi$
$420$	0.658094	−	1.80810i	0.0321117	−	0.0882262i
$421$	−19.3959	+	11.1982i	−0.945299	+	0.545769i	−0.891617	−	0.452789i	$-0.850429\pi$
$421$	−19.3959	+	11.1982i	−0.945299	+	0.545769i	−0.0536815	+	0.998558i	$0.517096\pi$
$422$	1.55524	−	1.85346i	0.0757079	−	0.0902252i
$423$	−2.61455	−	2.19386i	−0.127124	−	0.106669i
$424$	−2.96573	−	8.14828i	−0.144029	−	0.395716i
$425$	−15.9217	+	2.80743i	−0.772318	+	0.136180i
$426$	22.6315	−	3.99054i	1.09650	−	0.193343i
$427$	−7.82893	−	21.5098i	−0.378868	−	1.04093i
$428$	3.64605	+	3.05940i	0.176239	+	0.147882i
$429$	−3.47434	+	4.14056i	−0.167743	+	0.199908i
$430$	−1.44585	+	0.834763i	−0.0697252	+	0.0402559i
$431$	−0.0349134	+	0.0959236i	−0.00168172	+	0.00462048i	−0.940531	−	0.339709i	$-0.889671\pi$
$431$	−0.0349134	+	0.0959236i	−0.00168172	+	0.00462048i	0.938849	+	0.344329i	$0.111894\pi$
$432$	0.971782	−	5.51125i	0.0467549	−	0.265160i
$433$	−3.96357	+	6.86510i	−0.190477	+	0.329916i	−0.945408	−	0.325888i	$-0.894337\pi$
$433$	−3.96357	+	6.86510i	−0.190477	+	0.329916i	0.754931	+	0.655804i	$0.227670\pi$
$434$	−4.14117	−	7.17272i	−0.198783	−	0.344301i
$435$	−1.77976	+	0.647778i	−0.0853327	+	0.0310586i
$436$	8.34627	+	4.81872i	0.399714	+	0.230775i
$437$	−34.6015	+	29.0341i	−1.65521	+	1.38889i
$438$			23.1027i			1.10389i
$439$	4.86630	+	5.79944i	0.232256	+	0.276792i	0.869567	−	0.493815i	$-0.164398\pi$
$439$	4.86630	+	5.79944i	0.232256	+	0.276792i	−0.637311	+	0.770607i	$0.719953\pi$
$440$	0.934507	+	0.340133i	0.0445509	+	0.0162152i
$441$	−0.414216	−	2.34914i	−0.0197246	−	0.111864i
$442$	4.47900	+	0.789768i	0.213044	+	0.0375654i
$443$	15.9856			0.759499			0.379749	−	0.925089i	$-0.376010\pi$
$443$	15.9856			0.759499			0.379749	+	0.925089i	$0.376010\pi$
$444$	9.28560	+	0.792239i	0.440675	+	0.0375980i
$445$	0.366772			0.0173867
$446$	−6.84171	−	1.20638i	−0.323964	−	0.0571237i
$447$	4.22212	+	23.9448i	0.199700	+	1.13255i
$448$	−3.06729	−	1.11640i	−0.144916	−	0.0527450i
$449$	−18.4321	−	21.9666i	−0.869866	−	1.03667i	−0.998985	−	0.0450373i	$-0.985659\pi$
$449$	−18.4321	−	21.9666i	−0.869866	−	1.03667i	0.129119	−	0.991629i	$-0.458785\pi$
$450$		−	3.16689i		−	0.149289i
$451$	−16.3730	+	13.7386i	−0.770974	+	0.646924i
$452$	−11.2193	−	6.47746i	−0.527711	−	0.304674i
$453$	−31.3393	+	11.4066i	−1.47245	+	0.535928i
$454$	−10.9245	−	18.9218i	−0.512712	−	0.888043i
$455$	−0.857098	+	1.48454i	−0.0401814	+	0.0695962i
$456$	−1.59248	+	9.03143i	−0.0745749	+	0.422935i
$457$	0.0359519	−	0.0987770i	0.00168176	−	0.00462059i	−0.938849	−	0.344329i	$-0.888106\pi$
$457$	0.0359519	−	0.0987770i	0.00168176	−	0.00462059i	0.940531	+	0.339709i	$0.110329\pi$
$458$	−3.68069	+	2.12505i	−0.171987	+	0.0992970i
$459$	−11.9864	+	14.2848i	−0.559476	+	0.666757i
$460$	−2.22412	−	1.86625i	−0.103700	−	0.0870146i
$461$	8.19825	+	22.5245i	0.381831	+	1.04907i	0.970585	+	0.240759i	$0.0773964\pi$
$461$	8.19825	+	22.5245i	0.381831	+	1.04907i	−0.588754	+	0.808312i	$0.700381\pi$
$462$	−12.7297	+	2.24458i	−0.592238	+	0.104427i
$463$	−20.4361	+	3.60344i	−0.949747	+	0.167466i	−0.627000	−	0.779019i	$-0.715717\pi$
$463$	−20.4361	+	3.60344i	−0.949747	+	0.167466i	−0.322747	+	0.946485i	$0.604606\pi$
$464$	1.09890	+	3.01921i	0.0510152	+	0.140163i
$465$	−1.14579	−	0.961434i	−0.0531348	−	0.0445854i
$466$	−11.1487	+	13.2865i	−0.516454	+	0.615485i
$467$	15.1492	−	8.74642i	0.701023	−	0.404736i	−0.106705	−	0.994291i	$-0.534030\pi$
$467$	15.1492	−	8.74642i	0.701023	−	0.404736i	0.807728	+	0.589555i	$0.200697\pi$
$468$	−0.304702	+	0.837163i	−0.0140849	+	0.0386979i
$469$	6.36983	−	36.1251i	0.294132	−	1.66810i
$470$	−1.00596	+	1.74237i	−0.0464014	+	0.0803696i
$471$	−7.47002	−	12.9385i	−0.344200	−	0.596172i
$472$	12.1854	−	4.43512i	0.560878	−	0.204143i
$473$	9.71300	+	5.60780i	0.446604	+	0.257847i
$474$	1.71739	−	1.44106i	0.0788825	−	0.0661902i
$475$			29.0428i			1.33258i
$476$	6.99130	+	8.33190i	0.320446	+	0.381892i
$477$	−5.31841	−	1.93574i	−0.243513	−	0.0886317i
$478$	−3.18790	−	18.0795i	−0.145811	−	0.826935i
$479$	−6.77593	−	1.19478i	−0.309600	−	0.0545909i	0.0166894	−	0.999861i	$-0.494687\pi$
$479$	−6.77593	−	1.19478i	−0.309600	−	0.0545909i	−0.326290	+	0.945270i	$0.605798\pi$
$480$	−0.589478			−0.0269059
$481$	−8.02421	−	2.13157i	−0.365872	−	0.0971912i
$482$	23.4661			1.06885
$483$	37.1641	+	6.55304i	1.69103	+	0.298174i
$484$	0.750028	+	4.25362i	0.0340922	+	0.193346i
$485$	−5.35766	−	1.95003i	−0.243279	−	0.0885462i
$486$	−4.27628	−	5.09627i	−0.193976	−	0.231171i
$487$		−	1.70810i		−	0.0774014i	−0.999251	−	0.0387007i	$-0.987678\pi$
$487$		−	1.70810i		−	0.0774014i	0.999251	−	0.0387007i	$-0.0123219\pi$
$488$	−5.37200	+	4.50764i	−0.243179	+	0.204051i
$489$	−17.4673	−	10.0848i	−0.789901	−	0.456049i
$490$	−1.32133	+	0.480924i	−0.0596915	+	0.0217259i
$491$	−5.31153	−	9.19983i	−0.239706	−	0.415183i	0.720924	−	0.693014i	$-0.243718\pi$
$491$	−5.31153	−	9.19983i	−0.239706	−	0.415183i	−0.960630	+	0.277831i	$0.910384\pi$
$492$	6.33454	−	10.9717i	0.285583	−	0.494644i
$493$	1.85908	−	10.5434i	0.0837288	−	0.474850i
$494$	2.79435	−	7.67741i	0.125724	−	0.345423i
$495$	0.562138	−	0.324551i	0.0252662	−	0.0145875i
$496$	−1.63099	+	1.94374i	−0.0732337	+	0.0872765i
$497$	−37.5060	−	31.4713i	−1.68237	−	1.41168i
$498$	−0.00582580	−	0.0160062i	−0.000261060	−	0.000717257i
$499$	34.9319	−	6.15943i	1.56376	−	0.275734i	0.676306	−	0.736621i	$-0.263580\pi$
$499$	34.9319	−	6.15943i	1.56376	−	0.275734i	0.887459	+	0.460887i	$0.152469\pi$
$500$	−3.73300	+	0.658229i	−0.166945	+	0.0294369i
$501$	−2.93563	−	8.06557i	−0.131154	−	0.360343i
$502$	4.67401	+	3.92196i	0.208611	+	0.175046i
$503$	−19.3402	+	23.0487i	−0.862336	+	1.02769i	0.136975	+	0.990574i	$0.456262\pi$
$503$	−19.3402	+	23.0487i	−0.862336	+	1.02769i	−0.999311	+	0.0371171i	$0.988183\pi$
$504$	−1.84508	+	1.06526i	−0.0821864	+	0.0474504i
$505$	−0.167456	+	0.460081i	−0.00745168	+	0.0204733i
$506$	−3.38690	+	19.2081i	−0.150566	+	0.853903i
$507$	8.53143	−	14.7769i	0.378894	−	0.656264i
$508$	5.62039	+	9.73480i	0.249364	+	0.431912i
$509$	22.6380	−	8.23957i	1.00341	−	0.365213i	0.212513	−	0.977158i	$-0.431835\pi$
$509$	22.6380	−	8.23957i	1.00341	−	0.365213i	0.790900	+	0.611946i	$0.209613\pi$
$510$	1.70106	+	0.982108i	0.0753242	+	0.0434885i
$511$	37.7052	−	31.6385i	1.66798	−	1.39960i
$512$			1.00000i			0.0441942i
$513$	21.5321	+	25.6610i	0.950666	+	1.13296i
$514$	4.08494	+	1.48680i	0.180179	+	0.0655798i
$515$	−0.724650	−	4.10969i	−0.0319319	−	0.181095i
$516$	−6.54704	−	1.15442i	−0.288217	−	0.0508205i
$517$	13.5157			0.594421
$518$	−11.4234	−	16.2397i	−0.501913	−	0.713531i
$519$	16.6008			0.728694
$520$	0.517182	+	0.0911931i	0.0226799	+	0.00399908i
$521$	−0.130158	−	0.738160i	−0.00570231	−	0.0323394i	0.981824	−	0.189794i	$-0.0607822\pi$
$521$	−0.130158	−	0.738160i	−0.00570231	−	0.0323394i	−0.987526	+	0.157455i	$0.949671\pi$
$522$	1.97065	+	0.717257i	0.0862528	+	0.0313935i
$523$	1.31038	+	1.56165i	0.0572989	+	0.0682862i	0.793933	−	0.608006i	$-0.208030\pi$
$523$	1.31038	+	1.56165i	0.0572989	+	0.0682862i	−0.736634	+	0.676292i	$0.763586\pi$
$524$			8.36959i			0.365627i
$525$	18.5876	−	15.5969i	0.811231	−	0.680704i
$526$	3.51160	+	2.02743i	0.153113	+	0.0884000i
$527$	7.94496	−	2.89173i	0.346088	−	0.125966i
$528$	1.98001	+	3.42947i	0.0861688	+	0.149249i
$529$	16.9714	−	29.3954i	0.737889	−	1.27806i
$530$	−0.579341	+	3.28561i	−0.0251650	+	0.142718i
$531$	2.89482	−	7.95345i	0.125624	−	0.345150i
$532$	16.9208	−	9.76922i	0.733609	−	0.423549i
$533$	−7.25498	+	8.64615i	−0.314248	+	0.374506i
$534$	1.11879	+	0.938780i	0.0484150	+	0.0406250i
$535$	−0.626331	−	1.72083i	−0.0270787	−	0.0743980i
$536$	−11.0673	+	1.95146i	−0.478033	+	0.0842902i
$537$	−9.16140	+	1.61540i	−0.395343	+	0.0697097i
$538$	−3.00751	−	8.26307i	−0.129663	−	0.356246i
$539$	7.23615	+	6.07185i	0.311683	+	0.261533i
$540$	−1.38404	+	1.64944i	−0.0595597	+	0.0709805i
$541$	−27.1442	+	15.6717i	−1.16702	+	0.673778i	−0.952976	−	0.303046i	$-0.901996\pi$
$541$	−27.1442	+	15.6717i	−1.16702	+	0.673778i	−0.214042	+	0.976824i	$0.568663\pi$
$542$	−4.41623	+	12.1335i	−0.189694	+	0.521179i
$543$	−5.73428	+	32.5207i	−0.246081	+	1.39560i
$544$	1.66606	−	2.88571i	0.0714319	−	0.123724i
$545$	−1.85402	−	3.21126i	−0.0794176	−	0.137555i
$546$	−6.41426	+	2.33460i	−0.274505	+	0.0999116i
$547$	15.7325	+	9.08317i	0.672674	+	0.388368i	0.797089	−	0.603862i	$-0.206372\pi$
$547$	15.7325	+	9.08317i	0.672674	+	0.388368i	−0.124415	+	0.992230i	$0.539706\pi$
$548$	3.05202	−	2.56095i	0.130376	−	0.109398i
$549$			4.57718i			0.195349i
$550$	8.06117	+	9.60693i	0.343729	+	0.409641i
$551$	−18.0723	−	6.57778i	−0.769906	−	0.280223i
$552$	−2.00758	−	11.3856i	−0.0854485	−	0.484602i
$553$	−4.70383	−	0.829413i	−0.200027	−	0.0352702i
$554$	7.77643			0.330389
$555$	−2.94162	−	2.05032i	−0.124865	−	0.0870311i
$556$	−5.11140			−0.216772
$557$	32.4061	+	5.71408i	1.37309	+	0.242113i	0.811041	−	0.584989i	$-0.198901\pi$
$557$	32.4061	+	5.71408i	1.37309	+	0.242113i	0.562051	+	0.827102i	$0.310012\pi$
$558$	0.287588	+	1.63099i	0.0121746	+	0.0690454i
$559$	5.56549	+	2.02567i	0.235395	+	0.0856768i
$560$	0.807272	+	0.962069i	0.0341135	+	0.0406548i
$561$		−	13.1953i		−	0.557105i
$562$	0.178113	−	0.149454i	0.00751323	−	0.00630435i
$563$	29.7054	+	17.1504i	1.25193	+	0.722804i	0.971493	−	0.237068i	$-0.0761864\pi$
$563$	29.7054	+	17.1504i	1.25193	+	0.722804i	0.280440	+	0.959872i	$0.409520\pi$
$564$	−7.52829	+	2.74007i	−0.316998	+	0.115378i
$565$	2.49223	+	4.31667i	0.104849	+	0.181604i
$566$	−6.41650	+	11.1137i	−0.269706	+	0.467144i
$567$	3.74995	−	21.2670i	0.157483	−	0.893132i
$568$	−5.13014	+	14.0950i	−0.215256	+	0.591411i
$569$	18.3769	−	10.6099i	0.770398	−	0.444789i	−0.0626186	−	0.998038i	$-0.519945\pi$
$569$	18.3769	−	10.6099i	0.770398	−	0.444789i	0.833017	+	0.553248i	$0.186612\pi$
$570$	2.26807	−	2.70298i	0.0949989	−	0.113215i
$571$	12.5989	+	10.5717i	0.527247	+	0.442413i	0.867150	−	0.498048i	$-0.165950\pi$
$571$	12.5989	+	10.5717i	0.527247	+	0.442413i	−0.339902	+	0.940461i	$0.610394\pi$
$572$	−1.20663	−	3.31518i	−0.0504516	−	0.138614i
$573$	−9.99880	+	1.76306i	−0.417706	+	0.0736528i
$574$	−26.5816	+	4.68705i	−1.10949	+	0.195634i
$575$	−12.5224	−	34.4051i	−0.522222	−	1.43479i
$576$	0.500000	+	0.419550i	0.0208333	+	0.0174812i
$577$	−23.3471	+	27.8240i	−0.971952	+	1.15833i	0.0154162	+	0.999881i	$0.495093\pi$
$577$	−23.3471	+	27.8240i	−0.971952	+	1.15833i	−0.987368	+	0.158446i	$0.949352\pi$
$578$	5.10689	−	2.94846i	0.212419	−	0.122640i
$579$	−11.9758	+	32.9033i	−0.497698	+	1.36742i
$580$	0.214665	−	1.21742i	0.00891347	−	0.0505508i
$581$	−0.0181451	+	0.0314282i	−0.000752784	+	0.00130386i
$582$	−11.3517	−	19.6616i	−0.470541	−	0.815001i
$583$	21.0610	−	7.66558i	0.872258	−	0.317476i
$584$	−13.0590	−	7.53961i	−0.540385	−	0.311991i
$585$	0.262580	−	0.220331i	0.0108563	−	0.00910956i
$586$		−	24.6443i		−	1.01805i
$587$	24.1202	+	28.7453i	0.995547	+	1.18645i	0.982449	+	0.186532i	$0.0597249\pi$
$587$	24.1202	+	28.7453i	0.995547	+	1.18645i	0.0130981	+	0.999914i	$0.495831\pi$
$588$	−5.26151	−	1.91503i	−0.216981	−	0.0789747i
$589$	−2.63740	−	14.9574i	−0.108672	−	0.616310i
$590$	−4.91348	−	0.866378i	−0.202285	−	0.0356682i
$591$	22.6076			0.929953
$592$	−3.47819	+	4.99021i	−0.142953	+	0.205096i
$593$	−10.0159			−0.411302			−0.205651	−	0.978625i	$-0.565931\pi$
$593$	−10.0159			−0.411302			−0.205651	+	0.978625i	$0.565931\pi$
$594$	14.2450	+	2.51178i	0.584480	+	0.103060i
$595$	−0.726682	−	4.12122i	−0.0297910	−	0.168953i
$596$	−14.9129	−	5.42786i	−0.610857	−	0.222334i
$597$	1.45237	+	1.73087i	0.0594417	+	0.0708398i
$598$			10.2998i			0.421189i
$599$	−25.7808	+	21.6326i	−1.05337	+	0.883886i	−0.993444	−	0.114317i	$-0.963532\pi$
$599$	−25.7808	+	21.6326i	−1.05337	+	0.883886i	−0.0599300	+	0.998203i	$0.519088\pi$
$600$	−6.43772	−	3.71682i	−0.262819	−	0.151739i
$601$	40.2252	−	14.6408i	1.64082	−	0.597209i	0.653637	−	0.756808i	$-0.273242\pi$
$601$	40.2252	−	14.6408i	1.64082	−	0.597209i	0.987182	+	0.159599i	$0.0510202\pi$
$602$	7.08188	+	12.2662i	0.288636	+	0.499932i
$603$	−3.66754	+	6.35237i	−0.149354	+	0.258688i
$604$	3.77998	−	21.4373i	0.153805	−	0.872273i
$605$	0.568385	−	1.56163i	0.0231081	−	0.0634891i
$606$	−1.68842	+	0.974807i	−0.0685872	+	0.0395988i
$607$	3.45545	−	4.11804i	0.140252	−	0.167146i	−0.691346	−	0.722524i	$-0.742982\pi$
$607$	3.45545	−	4.11804i	0.140252	−	0.167146i	0.831598	+	0.555378i	$0.187426\pi$
$608$	−4.58538	−	3.84759i	−0.185962	−	0.156040i
$609$	5.49555	+	15.0989i	0.222691	+	0.611838i
$610$	2.65715	−	0.468528i	0.107585	−	0.0189701i
$611$	7.02887	−	1.23938i	0.284358	−	0.0501400i
$612$	−0.743857	−	2.04373i	−0.0300686	−	0.0826129i
$613$	−25.6002	−	21.4811i	−1.03398	−	0.867614i	−0.0426623	−	0.999090i	$-0.513584\pi$
$613$	−25.6002	−	21.4811i	−1.03398	−	0.867614i	−0.991319	+	0.131476i	$0.958028\pi$
$614$	−4.44251	+	5.29438i	−0.179285	+	0.213664i
$615$	−4.22143	+	2.43724i	−0.170224	+	0.0982791i
$616$	2.88558	−	7.92807i	0.116263	−	0.319431i
$617$	−0.878588	+	4.98272i	−0.0353706	+	0.200597i	−0.997372	−	0.0724469i	$-0.976919\pi$
$617$	−0.878588	+	4.98272i	−0.0353706	+	0.200597i	0.962002	+	0.273044i	$0.0880303\pi$
$618$	8.30861	−	14.3909i	0.334221	−	0.578888i
$619$	−17.8909	−	30.9879i	−0.719096	−	1.24551i	−0.961358	−	0.275300i	$-0.911223\pi$
$619$	−17.8909	−	30.9879i	−0.719096	−	1.24551i	0.242263	−	0.970211i	$-0.422110\pi$
$620$	0.917390	−	0.333902i	0.0368433	−	0.0134098i
$621$	−36.5720	−	21.1149i	−1.46758	−	0.847310i
$622$	1.27056	−	1.06612i	0.0509446	−	0.0427476i
$623$		−	3.11158i		−	0.124663i
$624$	1.34419	+	1.60194i	0.0538105	+	0.0641289i
$625$	−21.4263	−	7.79853i	−0.857051	−	0.311941i
$626$	4.50633	+	25.5566i	0.180109	+	1.02145i
$627$	−23.3437	−	4.11612i	−0.932257	−	0.164382i
$628$	9.75142			0.389124
$629$	18.3510	−	8.60539i	0.731704	−	0.343119i
$630$	0.819725			0.0326586
$631$	6.52046	+	1.14973i	0.259576	+	0.0457702i	0.301921	−	0.953333i	$-0.402372\pi$
$631$	6.52046	+	1.14973i	0.259576	+	0.0457702i	−0.0423458	+	0.999103i	$0.513483\pi$
$632$	0.254098	+	1.44106i	0.0101075	+	0.0573224i
$633$	−3.48337	−	1.26784i	−0.138452	−	0.0503923i
$634$	−7.29553	−	8.69447i	−0.289742	−	0.345301i
$635$		−	4.32494i		−	0.171630i
$636$	−10.1770	+	8.53949i	−0.403543	+	0.338613i
$637$	4.31996	+	2.49413i	0.171163	+	0.0988210i
$638$	−7.80379	+	2.84035i	−0.308955	+	0.112450i
$639$	4.89513	+	8.47861i	0.193648	+	0.335409i
$640$	0.192377	−	0.333207i	0.00760438	−	0.0131712i
$641$	−6.18098	+	35.0541i	−0.244134	+	1.38455i	0.578361	+	0.815781i	$0.303693\pi$
$641$	−6.18098	+	35.0541i	−0.244134	+	1.38455i	−0.822495	+	0.568772i	$0.807418\pi$
$642$	2.49405	−	6.85234i	0.0984322	−	0.270440i
$643$	4.34087	−	2.50620i	0.171187	−	0.0988350i	−0.411958	−	0.911203i	$-0.635155\pi$
$643$	4.34087	−	2.50620i	0.171187	−	0.0988350i	0.583146	+	0.812368i	$0.301822\pi$
$644$	−15.8327	+	18.8687i	−0.623897	+	0.743532i
$645$	1.95944	+	1.64416i	0.0771528	+	0.0647388i
$646$	6.82172	+	18.7425i	0.268397	+	0.737415i
$647$	−34.7348	+	6.12469i	−1.36557	+	0.240786i	−0.807920	−	0.589292i	$-0.799407\pi$
$647$	−34.7348	+	6.12469i	−1.36557	+	0.240786i	−0.557647	+	0.830078i	$0.688296\pi$
$648$	−6.51536	+	1.14883i	−0.255947	+	0.0451304i
$649$	11.4635	+	31.4958i	0.449983	+	1.23632i
$650$	5.07317	+	4.25690i	0.198986	+	0.166969i
$651$	−8.15651	+	9.72055i	−0.319679	+	0.380979i
$652$	11.4010	−	6.58237i	0.446498	−	0.257785i
$653$	0.925218	−	2.54201i	0.0362066	−	0.0994767i	−0.920272	−	0.391279i	$-0.872033\pi$
$653$	0.925218	−	2.54201i	0.0362066	−	0.0994767i	0.956479	+	0.291802i	$0.0942549\pi$
$654$	2.56399	−	14.5411i	0.100260	−	0.568602i
$655$	1.61012	−	2.78881i	0.0629125	−	0.108968i
$656$	4.13458	+	7.16130i	0.161428	+	0.279602i
$657$	−9.24871	+	3.36625i	−0.360826	+	0.131330i
$658$	14.7817	+	8.53424i	0.576252	+	0.332699i
$659$	21.3419	−	17.9080i	0.831363	−	0.697597i	−0.124240	−	0.992252i	$-0.539649\pi$
$659$	21.3419	−	17.9080i	0.831363	−	0.697597i	0.955604	+	0.294655i	$0.0952049\pi$
$660$		−	1.52363i		−	0.0593074i
$661$	−6.82156	−	8.12962i	−0.265328	−	0.316205i	0.616888	−	0.787051i	$-0.288393\pi$
$661$	−6.82156	−	8.12962i	−0.265328	−	0.316205i	−0.882216	+	0.470846i	$0.843949\pi$
$662$	−12.0635	−	4.39075i	−0.468860	−	0.170651i
$663$	−1.21000	−	6.86222i	−0.0469923	−	0.266507i
$664$	0.0109489	+	0.00193059i	0.000424900	+	7.49214e-5i
$665$	−7.51750			−0.291516
$666$	1.03583	+	3.83274i	0.0401376	+	0.148516i
$667$	24.2452			0.938779
$668$	5.51717	+	0.972826i	0.213466	+	0.0376398i
$669$	1.84828	+	10.4821i	0.0714586	+	0.405262i
$670$	4.06311	+	1.47885i	0.156972	+	0.0571330i
$671$	−11.6510	−	13.8851i	−0.449781	−	0.536028i
$672$			5.00095i			0.192916i
$673$	−0.503594	+	0.422565i	−0.0194121	+	0.0162887i	−0.652442	−	0.757839i	$-0.726255\pi$
$673$	−0.503594	+	0.422565i	−0.0194121	+	0.0162887i	0.633030	+	0.774127i	$0.281811\pi$
$674$	−4.94659	−	2.85591i	−0.190535	−	0.110006i
$675$	−25.5154	+	9.28683i	−0.982087	+	0.357450i
$676$	5.56849	+	9.64491i	0.214173	+	0.370958i
$677$	16.0036	−	27.7190i	0.615067	−	1.06533i	−0.375306	−	0.926901i	$-0.622462\pi$
$677$	16.0036	−	27.7190i	0.615067	−	1.06533i	0.990373	−	0.138426i	$-0.0442043\pi$
$678$	−3.44659	+	19.5466i	−0.132365	+	0.750681i
$679$	−16.5434	+	45.4527i	−0.634879	+	1.74432i
$680$	−1.11029	+	0.641025i	−0.0425776	+	0.0245822i
$681$	−21.5171	+	25.6430i	−0.824535	+	0.982643i
$682$	−5.02402	−	4.21565i	−0.192380	−	0.161426i
$683$	−1.36647	−	3.75435i	−0.0522866	−	0.143656i	0.910800	−	0.412848i	$-0.135466\pi$
$683$	−1.36647	−	3.75435i	−0.0522866	−	0.143656i	−0.963087	+	0.269191i	$0.913244\pi$
$684$	−3.84759	+	0.678433i	−0.147116	+	0.0259405i
$685$	−1.50962	+	0.266187i	−0.0576797	+	0.0101705i
$686$	−3.73480	−	10.2613i	−0.142595	−	0.391778i
$687$	4.98812	+	4.18553i	0.190309	+	0.159688i
$688$	2.78918	−	3.32402i	0.106337	−	0.126727i
$689$	10.2499	−	5.91777i	0.390489	−	0.225449i
$690$	−1.52138	+	4.17997i	−0.0579181	+	0.159129i
$691$	−0.763380	+	4.32934i	−0.0290404	+	0.164696i	−0.995879	−	0.0906920i	$-0.971092\pi$
$691$	−0.763380	+	4.32934i	−0.0290404	+	0.164696i	0.966839	+	0.255388i	$0.0822032\pi$
$692$	−5.41770	+	9.38373i	−0.205950	+	0.356716i
$693$	−2.75339	−	4.76901i	−0.104593	−	0.181160i
$694$	30.3912	−	11.0615i	1.15363	−	0.419888i
$695$	1.70316	+	0.983317i	0.0646044	+	0.0372993i
$696$	3.77090	−	3.16416i	0.142936	−	0.119937i
$697$		−	27.5539i		−	1.04368i
$698$	−16.0260	−	19.0990i	−0.606593	−	0.722909i
$699$	24.9705	+	9.08850i	0.944469	+	0.343759i
$700$	2.75015	+	15.5969i	0.103946	+	0.589507i
$701$	14.1350	+	2.49237i	0.533870	+	0.0941356i	0.434082	−	0.900873i	$-0.357073\pi$
$701$	14.1350	+	2.49237i	0.533870	+	0.0941356i	0.0997873	+	0.995009i	$0.468184\pi$
$702$	7.63847			0.288295
$703$	−9.49934	−	35.1491i	−0.358274	−	1.32567i
$704$	−2.58472			−0.0974152
$705$	3.03561	+	0.535259i	0.114328	+	0.0201590i
$706$	1.50052	+	8.50986i	0.0564727	+	0.320273i
$707$	3.90319	+	1.42064i	0.146794	+	0.0534288i
$708$	−12.7704	−	15.2192i	−0.479942	−	0.571972i
$709$		−	6.87475i		−	0.258187i	−0.991632	−	0.129093i	$-0.958793\pi$
$709$		−	6.87475i		−	0.258187i	0.991632	−	0.129093i	$-0.0412067\pi$
$710$	4.42095	−	3.70962i	0.165915	−	0.139219i
$711$	0.827139	+	0.477549i	0.0310201	+	0.0179095i
$712$	−0.895774	+	0.326035i	−0.0335705	+	0.0122187i
$713$	9.57357	+	16.5819i	0.358533	+	0.620998i
$714$	8.33190	−	14.4313i	0.311814	−	0.540077i
$715$	−0.235708	+	1.33677i	−0.00881499	+	0.0499923i
$716$	2.07672	−	5.70574i	0.0776107	−	0.213234i
$717$	−24.3584	+	14.0633i	−0.909681	+	0.525204i
$718$	−2.48018	+	2.95577i	−0.0925596	+	0.110308i
$719$	−13.0967	−	10.9894i	−0.488424	−	0.409836i	0.365037	−	0.930993i	$-0.381056\pi$
$719$	−13.0967	−	10.9894i	−0.488424	−	0.409836i	−0.853461	+	0.521157i	$0.825501\pi$
$720$	−0.0858917	−	0.235986i	−0.00320100	−	0.00879466i
$721$	−34.8654	+	6.14771i	−1.29845	+	0.228953i
$722$	16.5739	−	2.92243i	0.616817	−	0.108762i
$723$	−12.2964	−	33.7840i	−0.457307	−	1.25644i
$724$	−16.5112	−	13.8545i	−0.613634	−	0.514900i
$725$	10.0206	−	11.9420i	0.372154	−	0.443516i
$726$	5.73089	−	3.30873i	0.212693	−	0.122799i
$727$	−14.5792	+	40.0561i	−0.540713	+	1.48560i	0.305206	+	0.952286i	$0.401275\pi$
$727$	−14.5792	+	40.0561i	−0.540713	+	1.48560i	−0.845919	+	0.533311i	$0.820948\pi$
$728$	0.773654	−	4.38761i	0.0286735	−	0.162616i
$729$	−15.0201	+	26.0155i	−0.556299	+	0.963538i
$730$	2.90090	+	5.02451i	0.107367	+	0.185965i
$731$	−13.5868	+	4.94519i	−0.502526	+	0.182904i
$732$	9.30457	+	5.37200i	0.343907	+	0.198555i
$733$	32.6482	−	27.3951i	1.20589	−	1.01186i	0.206447	−	0.978458i	$-0.433810\pi$
$733$	32.6482	−	27.3951i	1.20589	−	1.01186i	0.999442	−	0.0334033i	$-0.0106346\pi$
$734$			10.4563i			0.385948i
$735$	1.38476	+	1.65030i	0.0510778	+	0.0608722i
$736$	7.09097	+	2.58090i	0.261377	+	0.0951333i
$737$	−5.04397	−	28.6058i	−0.185797	−	1.05371i
$738$	5.31531	+	0.937232i	0.195659	+	0.0345000i
$739$	1.69175			0.0622321			0.0311161	−	0.999516i	$-0.490094\pi$
$739$	1.69175			0.0622321			0.0311161	+	0.999516i	$0.490094\pi$
$740$	2.11896	−	0.993649i	0.0778945	−	0.0365272i
$741$	−12.5174			−0.459837
$742$	27.8741	+	4.91495i	1.02329	+	0.180434i
$743$	−2.22382	−	12.6119i	−0.0815839	−	0.462685i	−0.998042	−	0.0625538i	$-0.980076\pi$
$743$	−2.22382	−	12.6119i	−0.0815839	−	0.462685i	0.916458	−	0.400132i	$-0.131036\pi$
$744$	3.65304	+	1.32960i	0.133927	+	0.0487454i
$745$	3.92489	+	4.67751i	0.143797	+	0.171371i
$746$			9.86566i			0.361208i
$747$	0.00555891	−	0.00466448i	0.000203390	−	0.000170664i
$748$	7.45873	+	4.30630i	0.272718	+	0.157454i
$749$	−14.5990	+	5.31360i	−0.533436	+	0.194155i
$750$	2.90376	+	5.02946i	0.106030	+	0.183650i
$751$	24.2360	−	41.9780i	0.884384	−	1.53180i	0.0379668	−	0.999279i	$-0.487912\pi$
$751$	24.2360	−	41.9780i	0.884384	−	1.53180i	0.846418	−	0.532520i	$-0.178755\pi$
$752$	0.908022	−	5.14965i	0.0331122	−	0.187788i
$753$	3.19721	−	8.78427i	0.116513	−	0.320117i
$754$	−3.79792	+	2.19273i	−0.138312	+	0.0798544i
$755$	−5.38357	+	6.41589i	−0.195928	+	0.233498i
$756$	13.9933	+	11.7418i	0.508933	+	0.427045i
$757$	10.9913	+	30.1984i	0.399486	+	1.09758i	0.962535	+	0.271156i	$0.0874060\pi$
$757$	10.9913	+	30.1984i	0.399486	+	1.09758i	−0.563049	+	0.826424i	$0.690372\pi$
$758$	−2.44351	+	0.430857i	−0.0887524	+	0.0156494i
$759$	29.4285	−	5.18904i	1.06819	−	0.188350i
$760$	0.787692	+	2.16417i	0.0285726	+	0.0785025i
$761$	7.94619	+	6.66765i	0.288049	+	0.241702i	0.775349	−	0.631533i	$-0.217574\pi$
$761$	7.94619	+	6.66765i	0.288049	+	0.241702i	−0.487300	+	0.873235i	$0.662018\pi$
$762$	11.0700	−	13.1927i	0.401024	−	0.477922i
$763$	−27.2434	+	15.7290i	−0.986277	+	0.569427i
$764$	2.26654	−	6.22728i	0.0820007	−	0.225295i
$765$	−0.145309	+	0.824086i	−0.00525365	+	0.0297949i
$766$	12.7819	−	22.1390i	0.461830	−	0.799913i
$767$	8.84976	+	15.3282i	0.319546	+	0.553471i
$768$	1.43969	−	0.524005i	0.0519504	−	0.0189084i
$769$	29.3819	+	16.9637i	1.05954	+	0.611725i	0.925305	−	0.379225i	$-0.123809\pi$
$769$	29.3819	+	16.9637i	1.05954	+	0.611725i	0.134234	+	0.990950i	$0.457143\pi$
$770$	−2.48668	+	2.08657i	−0.0896136	+	0.0751947i
$771$		−	6.66015i		−	0.239859i
$772$	−14.6905	−	17.5075i	−0.528724	−	0.630108i
$773$	27.2363	+	9.91322i	0.979623	+	0.356554i	0.781694	−	0.623662i	$-0.214356\pi$
$773$	27.2363	+	9.91322i	0.979623	+	0.356554i	0.197930	+	0.980216i	$0.436578\pi$
$774$	−0.491808	−	2.78918i	−0.0176777	−	0.100255i
$775$	12.1242	+	2.13782i	0.435514	+	0.0767929i
$776$	14.8185			0.531954
$777$	−17.3943	+	24.9558i	−0.624016	+	0.895284i
$778$	−6.37509			−0.228558
$779$	−48.7454	−	8.59512i	−1.74648	−	0.307952i
$780$	−0.139716	−	0.792368i	−0.00500263	−	0.0283713i
$781$	−36.4315	−	13.2600i	−1.30362	−	0.474479i
$782$	−16.1625	−	19.2617i	−0.577970	−	0.688798i
$783$		−	17.9806i		−	0.642576i
$784$	2.79959	−	2.34914i	0.0999854	−	0.0838977i
$785$	−3.24924	−	1.87595i	−0.115970	−	0.0669555i
$786$	12.0496	−	4.38571i	0.429796	−	0.156433i
$787$	8.35500	+	14.4713i	0.297823	+	0.515845i	0.975638	−	0.219388i	$-0.0704060\pi$
$787$	8.35500	+	14.4713i	0.297823	+	0.515845i	−0.677814	+	0.735233i	$0.737073\pi$
$788$	−7.37803	+	12.7791i	−0.262832	+	0.455238i
$789$	1.07877	−	6.11801i	0.0384052	−	0.217807i
$790$	0.192560	−	0.529055i	0.00685099	−	0.0188229i
$791$	36.6213	−	21.1433i	1.30210	−	0.751771i
$792$	−1.08442	+	1.29236i	−0.0385331	+	0.0459219i
$793$	−7.33236	−	6.15258i	−0.260380	−	0.218484i
$794$	12.8250	+	35.2364i	0.455142	+	1.25049i
$795$	5.03384	−	0.887602i	0.178532	−	0.0314800i
$796$	−1.45237	+	0.256093i	−0.0514780	+	0.00907696i
$797$	1.78348	+	4.90007i	0.0631741	+	0.173569i	0.967264	−	0.253774i	$-0.0816719\pi$
$797$	1.78348	+	4.90007i	0.0631741	+	0.173569i	−0.904090	+	0.427343i	$0.859450\pi$
$798$	−22.9312	−	19.2416i	−0.811757	−	0.681145i
$799$	−11.1999	+	13.3476i	−0.396225	+	0.472203i
$800$	4.20192	−	2.42598i	0.148560	−	0.0857714i
$801$	−0.212804	+	0.584675i	−0.00751907	+	0.0206585i
$802$	6.10310	−	34.6124i	0.215508	−	1.22221i
$803$	19.4878	−	33.7538i	0.687708	−	1.19115i
$804$	8.60881	+	14.9109i	0.303609	+	0.525867i
$805$	8.90549	−	3.24133i	0.313877	−	0.114242i
$806$	−2.99932	−	1.73166i	−0.105647	−	0.0609951i
$807$	−10.3203	+	8.65978i	−0.363293	+	0.304839i
$808$		−	1.27252i		−	0.0447671i
$809$	32.5001	+	38.7321i	1.14264	+	1.36175i	0.922369	+	0.386310i	$0.126251\pi$
$809$	32.5001	+	38.7321i	1.14264	+	1.36175i	0.220274	+	0.975438i	$0.429305\pi$
$810$	2.39197	+	0.870607i	0.0840454	+	0.0305900i
$811$	6.26321	+	35.5205i	0.219931	+	1.24729i	0.872141	+	0.489254i	$0.162731\pi$
$811$	6.26321	+	35.5205i	0.219931	+	1.24729i	−0.652210	+	0.758038i	$0.726158\pi$
$812$	−10.3283	−	1.82115i	−0.362451	−	0.0639098i
$813$	19.7826			0.693808
$814$	−12.8983	−	8.99014i	−0.452084	−	0.315104i
$815$	−5.06519			−0.177426
$816$	−5.02756	−	0.886494i	−0.176000	−	0.0310335i
$817$	4.51025	+	25.5789i	0.157794	+	0.894893i
$818$	0.423558	+	0.154163i	0.0148094	+	0.00539017i
$819$	−1.86922	−	2.22765i	−0.0653158	−	0.0778403i
$820$		−	3.18159i		−	0.111106i
$821$	39.1705	−	32.8679i	1.36706	−	1.14710i	0.393328	−	0.919398i	$-0.371324\pi$
$821$	39.1705	−	32.8679i	1.36706	−	1.14710i	0.973731	−	0.227701i	$-0.0731208\pi$
$822$	−5.28625	−	3.05202i	−0.184379	−	0.106451i
$823$	−7.59472	+	2.76425i	−0.264735	+	0.0963558i	−0.470978	−	0.882145i	$-0.656099\pi$
$823$	−7.59472	+	2.76425i	−0.264735	+	0.0963558i	0.206242	+	0.978501i	$0.433877\pi$
$824$	5.42306	+	9.39301i	0.188921	+	0.327221i
$825$	9.60693	−	16.6397i	0.334470	−	0.579319i
$826$	−7.35009	+	41.6844i	−0.255742	+	1.45039i
$827$	8.84209	−	24.2934i	0.307469	−	0.844765i	−0.685679	−	0.727904i	$-0.740495\pi$
$827$	8.84209	−	24.2934i	0.307469	−	0.844765i	0.993148	−	0.116861i	$-0.0372833\pi$
$828$	4.26546	−	2.46267i	0.148235	−	0.0855836i
$829$	5.26941	−	6.27984i	0.183014	−	0.218108i	−0.666735	−	0.745295i	$-0.732309\pi$
$829$	5.26941	−	6.27984i	0.183014	−	0.218108i	0.849749	+	0.527187i	$0.176753\pi$
$830$	−0.00327685	−	0.00274961i	−0.000113741	−	9.54403e-5i
$831$	−4.07489	−	11.1957i	−0.141356	−	0.388373i
$832$	−1.34419	+	0.237016i	−0.0466013	+	0.00821706i
$833$	−11.9926	+	2.11462i	−0.415519	+	0.0732673i
$834$	2.67840	+	7.35885i	0.0927454	+	0.254816i
$835$	−1.65121	−	1.38553i	−0.0571425	−	0.0479483i
$836$	9.94492	−	11.8519i	0.343952	−	0.409906i
$837$	12.2974	−	7.09991i	0.425060	−	0.245409i
$838$	−5.23677	+	14.3879i	−0.180901	+	0.497022i
$839$	−9.17699	+	52.0453i	−0.316825	+	1.79680i	0.244975	+	0.969529i	$0.421220\pi$
$839$	−9.17699	+	52.0453i	−0.316825	+	1.79680i	−0.561800	+	0.827273i	$0.689891\pi$
$840$	0.962069	−	1.66635i	0.0331945	−	0.0574946i
$841$	−9.33841	−	16.1746i	−0.322014	−	0.557745i
$842$	−21.0458	+	7.66004i	−0.725286	+	0.263983i
$843$	−0.308500	−	0.178113i	−0.0106253	−	0.00613453i
$844$	1.85346	−	1.55524i	0.0637988	−	0.0535336i
$845$		−	4.28501i		−	0.147409i
$846$	−2.19386	−	2.61455i	−0.0754266	−	0.0898900i
$847$	−13.2484	−	4.82201i	−0.455219	−	0.165686i
$848$	−1.50574	−	8.53949i	−0.0517074	−	0.293247i
$849$	19.3626	+	3.41415i	0.664523	+	0.117173i
$850$	−16.1674			−0.554536
$851$	26.4085	+	37.5430i	0.905273	+	1.28696i
$852$	22.9806			0.787303
$853$	−32.4894	−	5.72875i	−1.11241	−	0.196149i	−0.412907	−	0.910773i	$-0.635486\pi$
$853$	−32.4894	−	5.72875i	−1.11241	−	0.196149i	−0.699508	+	0.714625i	$0.746598\pi$
$854$	−3.97485	−	22.5425i	−0.136017	−	0.771388i
$855$	1.41256	+	0.514129i	0.0483085	+	0.0175828i
$856$	3.05940	+	3.64605i	0.104568	+	0.124619i
$857$		−	38.4078i		−	1.31199i	−0.754767	−	0.655993i	$-0.772250\pi$
$857$		−	38.4078i		−	1.31199i	0.754767	−	0.655993i	$-0.227750\pi$
$858$	−4.14056	+	3.47434i	−0.141356	+	0.118612i
$859$	−17.9404	−	10.3579i	−0.612119	−	0.353407i	0.161676	−	0.986844i	$-0.448310\pi$
$859$	−17.9404	−	10.3579i	−0.612119	−	0.353407i	−0.773794	+	0.633437i	$0.781644\pi$
$860$	−1.56884	+	0.571012i	−0.0534971	+	0.0194713i
$861$	20.6768	+	35.8133i	0.704664	+	1.22051i
$862$	−0.0510399	+	0.0884037i	−0.00173843	+	0.00301104i
$863$	6.14125	−	34.8288i	0.209051	−	1.18559i	−0.681886	−	0.731458i	$-0.738840\pi$
$863$	6.14125	−	34.8288i	0.209051	−	1.18559i	0.890937	−	0.454127i	$-0.150049\pi$
$864$	1.91404	−	5.25877i	0.0651168	−	0.178907i
$865$	3.61043	−	2.08448i	0.122758	−	0.0708746i
$866$	−5.09547	+	6.07254i	−0.173151	+	0.206353i
$867$	−6.92092	−	5.80734i	−0.235047	−	0.197228i
$868$	−2.83273	−	7.78285i	−0.0961490	−	0.264167i
$869$	−3.72474	+	0.656772i	−0.126353	+	0.0222795i
$870$	−1.86520	+	0.328885i	−0.0632363	+	0.0111503i
$871$	−5.24625	−	14.4139i	−0.177762	−	0.488398i
$872$	7.38271	+	6.19483i	0.250010	+	0.209783i
$873$	6.21711	−	7.40927i	0.210417	−	0.250766i
$874$	−39.1175	+	22.5845i	−1.32317	+	0.763932i
$875$	4.23182	−	11.6268i	0.143062	−	0.393058i
$876$	−4.01174	+	22.7517i	−0.135544	+	0.768710i
$877$	−13.1851	+	22.8373i	−0.445230	+	0.771160i	−0.998068	−	0.0621282i	$-0.980211\pi$
$877$	−13.1851	+	22.8373i	−0.445230	+	0.771160i	0.552839	+	0.833288i	$0.313545\pi$
$878$	3.78531	+	6.55635i	0.127748	+	0.221266i
$879$	−35.4802	+	12.9137i	−1.19672	+	0.435570i
$880$	0.861246	+	0.497241i	0.0290326	+	0.0167620i
$881$	25.8314	−	21.6752i	0.870283	−	0.730254i	−0.0938745	−	0.995584i	$-0.529925\pi$
$881$	25.8314	−	21.6752i	0.870283	−	0.730254i	0.964158	+	0.265330i	$0.0854808\pi$
$882$		−	2.38538i		−	0.0803198i
$883$	−37.1901	−	44.3215i	−1.25155	−	1.49154i	−0.800857	−	0.598856i	$-0.795622\pi$
$883$	−37.1901	−	44.3215i	−1.25155	−	1.49154i	−0.450690	−	0.892680i	$-0.648822\pi$
$884$	4.27381	+	1.55554i	0.143744	+	0.0523185i
$885$	1.32737	+	7.52788i	0.0446190	+	0.253047i
$886$	15.7427	+	2.77587i	0.528888	+	0.0932572i
$887$	−44.4679			−1.49309			−0.746544	−	0.665336i	$-0.768288\pi$
$887$	−44.4679			−1.49309			−0.746544	+	0.665336i	$0.768288\pi$
$888$	9.00696	+	2.39263i	0.302254	+	0.0802914i
$889$	−36.6915			−1.23059
$890$	0.361200	+	0.0636893i	0.0121074	+	0.00213487i
$891$	−2.96941	−	16.8404i	−0.0994789	−	0.564173i
$892$	−6.52829	−	2.37610i	−0.218583	−	0.0795578i
$893$	20.1194	+	23.9774i	0.673270	+	0.802372i
$894$			24.3142i			0.813190i
$895$	−1.78963	+	1.50168i	−0.0598208	+	0.0501956i
$896$	−2.82683	−	1.63207i	−0.0944377	−	0.0545236i
$897$	14.8285	−	5.39714i	0.495109	−	0.180205i
$898$	−14.3377	−	24.8336i	−0.478454	−	0.828706i
$899$	−4.07625	+	7.06028i	−0.135951	+	0.235473i
$900$	0.549925	−	3.11878i	0.0183308	−	0.103959i
$901$	−9.88220	+	27.1511i	−0.329224	+	0.904535i
$902$	−18.5099	+	10.6867i	−0.616313	+	0.355828i
$903$	13.9486	−	16.6233i	0.464180	−	0.553188i
$904$	−9.92405	−	8.32726i	−0.330069	−	0.276961i
$905$	2.83635	+	7.79281i	0.0942835	+	0.259042i
$906$	−32.8439	+	5.79127i	−1.09117	+	0.192402i
$907$	−12.8961	+	2.27393i	−0.428209	+	0.0755048i	−0.383599	−	0.923500i	$-0.625316\pi$
$907$	−12.8961	+	2.27393i	−0.428209	+	0.0755048i	−0.0446097	+	0.999004i	$0.514204\pi$
$908$	−7.47280	−	20.5313i	−0.247993	−	0.681356i
$909$	−0.636260	−	0.533886i	−0.0211034	−	0.0177079i
$910$	−1.10186	+	1.31315i	−0.0365264	+	0.0435305i
$911$	−33.2957	+	19.2233i	−1.10314	+	0.636896i	−0.937043	−	0.349215i	$-0.886448\pi$
$911$	−33.2957	+	19.2233i	−1.10314	+	0.636896i	−0.166093	+	0.986110i	$0.553115\pi$
$912$	−3.13658	+	8.61769i	−0.103863	+	0.285360i
$913$	−0.00499003	+	0.0282998i	−0.000165146	+	0.000936588i
$914$	0.0525581	−	0.0910334i	0.00173847	−	0.00301112i
$915$	−2.06690	−	3.57997i	−0.0683296	−	0.118350i
$916$	−3.99379	+	1.45362i	−0.131958	+	0.0480289i
$917$	−23.6594	−	13.6597i	−0.781301	−	0.451085i
$918$	−14.2848	+	11.9864i	−0.471468	+	0.395609i
$919$			14.8613i			0.490229i	0.969494	+	0.245115i	$0.0788256\pi$
$919$			14.8613i			0.490229i	−0.969494	+	0.245115i	$0.921174\pi$
$920$	−1.86625	−	2.22412i	−0.0615286	−	0.0733269i
$921$	9.95018	+	3.62157i	0.327869	+	0.119335i
$922$	4.16236	+	23.6059i	0.137080	+	0.777420i
$923$	−20.1622	−	3.55514i	−0.663646	−	0.117019i
$924$	−12.9260			−0.425236
$925$	29.4065	+	2.50894i	0.966880	+	0.0824933i
$926$	−20.7514			−0.681933
$927$	6.97175	+	1.22931i	0.228982	+	0.0403757i
$928$	0.557927	+	3.16416i	0.0183148	+	0.103869i
$929$	−6.82712	−	2.48487i	−0.223990	−	0.0815258i	0.227587	−	0.973758i	$-0.426916\pi$
$929$	−6.82712	−	2.48487i	−0.223990	−	0.0815258i	−0.451578	+	0.892232i	$0.649139\pi$
$930$	−0.961434	−	1.14579i	−0.0315267	−	0.0375720i
$931$			21.8757i			0.716947i
$932$	−13.2865	+	11.1487i	−0.435214	+	0.365188i
$933$	−2.20067	−	1.27056i	−0.0720466	−	0.0415961i
$934$	16.4379	−	5.98290i	0.537864	−	0.195767i
$935$	−1.65687	−	2.86978i	−0.0541854	−	0.0938519i
$936$	−0.445445	+	0.771533i	−0.0145598	+	0.0252184i
$937$	−4.58137	+	25.9822i	−0.149667	+	0.848802i	0.813834	+	0.581097i	$0.197376\pi$
$937$	−4.58137	+	25.9822i	−0.149667	+	0.848802i	−0.963501	+	0.267705i	$0.913735\pi$
$938$	12.5461	−	34.4702i	0.409645	−	1.12549i
$939$	34.4324	−	19.8795i	1.12366	−	0.648744i
$940$	−1.29324	+	1.54122i	−0.0421807	+	0.0502690i
$941$	27.6990	+	23.2422i	0.902961	+	0.757674i	0.970767	−	0.240025i	$-0.0771555\pi$
$941$	27.6990	+	23.2422i	0.902961	+	0.757674i	−0.0678062	+	0.997699i	$0.521600\pi$
$942$	−5.10979	−	14.0390i	−0.166486	−	0.457417i
$943$	61.4514	−	10.8355i	2.00113	−	0.352854i
$944$	12.7704	−	2.25177i	0.415642	−	0.0732889i
$945$	−2.40382	−	6.60445i	−0.0781964	−	0.214843i
$946$	8.59165	+	7.20925i	0.279339	+	0.234393i
$947$	−30.2846	+	36.0917i	−0.984116	+	1.17282i	0.000836789		1.00000i	$0.499734\pi$
$947$	−30.2846	+	36.0917i	−0.984116	+	1.17282i	−0.984953	+	0.172824i	$0.944711\pi$
$948$	1.94154	−	1.12095i	0.0630583	−	0.0364067i
$949$	7.03945	−	19.3407i	0.228510	−	0.627827i
$950$	−5.04323	+	28.6016i	−0.163624	+	0.927958i
$951$	−8.69447	+	15.0593i	−0.281937	+	0.488330i
$952$	5.43826	+	9.41935i	0.176255	+	0.305283i
$953$	−8.78776	+	3.19848i	−0.284663	+	0.103609i	−0.480406	−	0.877046i	$-0.659511\pi$
$953$	−8.78776	+	3.19848i	−0.284663	+	0.103609i	0.195742	+	0.980655i	$0.437288\pi$
$954$	−4.90148	−	2.82987i	−0.158691	−	0.0916204i
$955$	−1.95322	+	1.63894i	−0.0632046	+	0.0530349i
$956$		−	18.3584i		−	0.593752i
$957$	8.17845	+	9.74670i	0.264372	+	0.315066i
$958$	−6.46552	−	2.35326i	−0.208891	−	0.0760303i
$959$	2.25825	+	12.8072i	0.0729228	+	0.413565i
$960$	−0.580523	−	0.102362i	−0.0187363	−	0.00330371i
$961$	24.5617			0.792314
$962$	−7.53216	−	3.49258i	−0.242847	−	0.112605i
$963$	3.10660			0.100109
$964$	23.1096	+	4.07485i	0.744310	+	0.131242i
$965$	1.52695	+	8.65974i	0.0491541	+	0.278767i
$966$	35.4616	+	12.9070i	1.14096	+	0.415275i
$967$	32.1046	+	38.2608i	1.03242	+	1.23039i	0.972675	+	0.232171i	$0.0745830\pi$
$967$	32.1046	+	38.2608i	1.03242	+	1.23039i	0.0597409	+	0.998214i	$0.480973\pi$
$968$			4.31924i			0.138826i
$969$	23.4089	−	19.6424i	0.752001	−	0.631004i
$970$	−4.93764	−	2.85075i	−0.158538	−	0.0915320i
$971$	−35.3500	+	12.8664i	−1.13444	+	0.412901i	−0.839901	−	0.542739i	$-0.817387\pi$
$971$	−35.3500	+	12.8664i	−1.13444	+	0.412901i	−0.294536	+	0.955641i	$0.595165\pi$
$972$	−3.32635	−	5.76141i	−0.106693	−	0.184797i
$973$	8.34216	−	14.4491i	0.267437	−	0.463215i
$974$	0.296609	−	1.68215i	0.00950395	−	0.0538996i
$975$	3.47025	−	9.53444i	0.111137	−	0.305347i
$976$	−6.07313	+	3.50632i	−0.194396	+	0.112235i
$977$	18.0852	−	21.5531i	0.578597	−	0.689545i	−0.394775	−	0.918778i	$-0.629177\pi$
$977$	18.0852	−	21.5531i	0.578597	−	0.689545i	0.973372	+	0.229233i	$0.0736219\pi$
$978$	−15.4508	−	12.9647i	−0.494061	−	0.414567i
$979$	−0.842708	−	2.31532i	−0.0269331	−	0.0739980i
$980$	−1.38476	+	0.244171i	−0.0442347	+	0.00779977i
$981$	6.19483	−	1.09231i	0.197786	−	0.0348749i
$982$	−3.63330	−	9.98241i	−0.115943	−	0.318551i
$983$	−25.2349	−	21.1746i	−0.804867	−	0.675364i	0.144510	−	0.989503i	$-0.453840\pi$
$983$	−25.2349	−	21.1746i	−0.804867	−	0.675364i	−0.949377	+	0.314140i	$0.898284\pi$
$984$	8.14352	−	9.70508i	0.259606	−	0.309386i
$985$	4.91683	−	2.83873i	0.156663	−	0.0904495i
$986$	3.66168	−	10.0604i	0.116612	−	0.320388i
$987$	4.54098	−	25.7532i	0.144541	−	0.819732i
$988$	4.08506	−	7.07554i	0.129963	−	0.225103i
$989$	−16.3719	−	28.3570i	−0.520597	−	0.901700i
$990$	0.609956	−	0.222006i	0.0193857	−	0.00705581i
$991$	33.7743	+	19.4996i	1.07288	+	0.619426i	0.928966	−	0.370164i	$-0.120699\pi$
$991$	33.7743	+	19.4996i	1.07288	+	0.619426i	0.143911	+	0.989591i	$0.454032\pi$
$992$	−1.94374	+	1.63099i	−0.0617138	+	0.0517840i
$993$			19.6685i			0.624160i
$994$	−31.4713	−	37.5060i	−0.998208	−	1.18962i
$995$	0.533207	+	0.194072i	0.0169038	+	0.00615248i
$996$	−0.00295783	−	0.0167747i	−9.37226e−5	−	0.000531527i
$997$	−7.85922	−	1.38579i	−0.248904	−	0.0438885i	0.0478041	−	0.998857i	$-0.484778\pi$
$997$	−7.85922	−	1.38579i	−0.248904	−	0.0438885i	−0.296708	+	0.954968i	$0.595889\pi$
$998$	35.4707			1.12281
$999$	27.8424	−	19.5850i	0.880896	−	0.619641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.h.a.41.2	✓	12
3.2	odd	2		666.2.bj.c.559.1		12
4.3	odd	2		592.2.bq.b.337.2		12
37.18	odd	36		2738.2.a.r.1.5		6
37.19	odd	36		2738.2.a.s.1.6		6
37.28	even	18	inner	74.2.h.a.65.2	yes	12
111.65	odd	18		666.2.bj.c.361.1		12
148.139	odd	18		592.2.bq.b.65.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.2	✓	12	1.1	even	1	trivial
74.2.h.a.65.2	yes	12	37.28	even	18	inner
592.2.bq.b.65.2		12	148.139	odd	18
592.2.bq.b.337.2		12	4.3	odd	2
666.2.bj.c.361.1		12	111.65	odd	18
666.2.bj.c.559.1		12	3.2	odd	2
2738.2.a.r.1.5		6	37.18	odd	36
2738.2.a.s.1.6		6	37.19	odd	36

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.266044 - 1.50881i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.247315 - 0.294739i) q^{5} -1.53209i q^{6} +(-2.50048 + 2.09815i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.613341 - 0.223238i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.266044 - 1.50881i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.247315 - 0.294739i) q^{5} -1.53209i q^{6} +(-2.50048 + 2.09815i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.613341 - 0.223238i) q^{9} +(-0.192377 - 0.333207i) q^{10} +(-1.29236 + 2.23843i) q^{11} +(0.266044 - 1.50881i) q^{12} +(-0.466831 + 1.28261i) q^{13} +(-2.82683 + 1.63207i) q^{14} +(-0.378909 + 0.451566i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.13965 - 3.13118i) q^{17} +(0.642788 - 0.113341i) q^{18} +(-5.89485 + 1.03942i) q^{19} +(-0.131594 - 0.361551i) q^{20} +(3.83095 + 3.21455i) q^{21} +(-1.66142 + 1.98001i) q^{22} +(6.53507 - 3.77303i) q^{23} +(0.524005 - 1.43969i) q^{24} +(0.842535 - 4.77825i) q^{25} +(-0.682461 + 1.18206i) q^{26} +(-2.79813 - 4.84651i) q^{27} +(-3.06729 + 1.11640i) q^{28} +(2.78251 + 1.60649i) q^{29} +(-0.451566 + 0.378909i) q^{30} +2.53737i q^{31} +(0.642788 + 0.766044i) q^{32} +(3.72120 + 1.35440i) q^{33} +(-0.578618 - 3.28150i) q^{34} +(1.23681 + 0.218083i) q^{35} +0.652704 q^{36} +(0.543196 + 6.05846i) q^{37} -5.98578 q^{38} +(2.05941 + 0.363130i) q^{39} +(-0.0668119 - 0.378909i) q^{40} +(7.77046 + 2.82822i) q^{41} +(3.21455 + 3.83095i) q^{42} -4.33920i q^{43} +(-1.98001 + 1.66142i) q^{44} +(-0.217486 - 0.125565i) q^{45} +(7.09097 - 2.58090i) q^{46} +(-2.61455 - 4.52853i) q^{47} +(0.766044 - 1.32683i) q^{48} +(0.634616 - 3.59909i) q^{49} +(1.65947 - 4.55935i) q^{50} +(-4.42116 + 2.55256i) q^{51} +(-0.877355 + 1.04559i) q^{52} +(-6.64254 - 5.57375i) q^{53} +(-1.91404 - 5.25877i) q^{54} +(0.979373 - 0.172690i) q^{55} +(-3.21455 + 0.566812i) q^{56} +(3.13658 + 8.61769i) q^{57} +(2.46128 + 2.06526i) q^{58} +(8.33530 - 9.93362i) q^{59} +(-0.510503 + 0.294739i) q^{60} +(-2.39847 + 6.58973i) q^{61} +(-0.440610 + 2.49882i) q^{62} +(-1.06526 + 1.84508i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.493489 - 0.179615i) q^{65} +(3.42947 + 1.98001i) q^{66} +(-8.60881 + 7.22365i) q^{67} -3.33213i q^{68} +(-7.43141 - 8.85641i) q^{69} +(1.18015 + 0.429540i) q^{70} +(2.60464 + 14.7717i) q^{71} +(0.642788 + 0.113341i) q^{72} -15.0792 q^{73} +(-0.517097 + 6.06074i) q^{74} -7.43364 q^{75} +(-5.89485 - 1.03942i) q^{76} +(-1.46505 - 8.30870i) q^{77} +(1.96507 + 0.715227i) q^{78} +(0.940587 + 1.12095i) q^{79} -0.384754i q^{80} +(-5.06805 + 4.25260i) q^{81} +(7.16130 + 4.13458i) q^{82} +(0.0104473 - 0.00380252i) q^{83} +(2.50048 + 4.33095i) q^{84} +(-0.641025 + 1.11029i) q^{85} +(0.753494 - 4.27328i) q^{86} +(1.68361 - 4.62569i) q^{87} +(-2.23843 + 1.29236i) q^{88} +(-0.612745 + 0.730241i) q^{89} +(-0.192377 - 0.161424i) q^{90} +(-1.52380 - 4.18661i) q^{91} +(7.43141 - 1.31036i) q^{92} +(3.82842 - 0.675054i) q^{93} +(-1.78845 - 4.91374i) q^{94} +(1.76424 + 1.48038i) q^{95} +(0.984808 - 1.17365i) q^{96} +(12.8332 - 7.40927i) q^{97} +(1.24995 - 3.43421i) q^{98} +(-0.292954 + 1.66142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Introduction

L-functions

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