LMFDB - Embedded newform 675.2.r.a.181.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			181.23
Character	$\chi$	$=$	675.181
Dual form			675.2.r.a.496.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68376 + 0.357895i) q^{2} +(0.879882 + 0.391749i) q^{4} +(-1.96791 - 1.06176i) q^{5} +(-2.11497 + 3.66323i) q^{7} +(-1.44394 - 1.04909i) q^{8} +(-2.93350 - 2.49206i) q^{10} +(-5.35421 - 1.13807i) q^{11} +(-2.27272 + 0.483081i) q^{13} +(-4.87216 + 5.41109i) q^{14} +(-3.34474 - 3.71472i) q^{16} +(1.13466 + 0.824379i) q^{17} +(4.74872 + 3.45015i) q^{19} +(-1.31559 - 1.70515i) q^{20} +(-8.60791 - 3.83249i) q^{22} +(-2.33826 + 2.59691i) q^{23} +(2.74534 + 4.17889i) q^{25} -3.99961 q^{26} +(-3.29599 + 2.39468i) q^{28} +(-0.451070 - 4.29164i) q^{29} +(0.330923 - 3.14852i) q^{31} +(-2.51747 - 4.36039i) q^{32} +(1.61546 + 1.79415i) q^{34} +(8.05154 - 4.96333i) q^{35} +(0.930443 - 2.86361i) q^{37} +(6.76093 + 7.50877i) q^{38} +(1.72767 + 3.59763i) q^{40} +(4.52265 - 0.961319i) q^{41} +(-2.17619 + 3.76927i) q^{43} +(-4.26523 - 3.09887i) q^{44} +(-4.86650 + 3.53572i) q^{46} +(-0.300021 - 2.85451i) q^{47} +(-5.44619 - 9.43308i) q^{49} +(3.12690 + 8.01881i) q^{50} +(-2.18897 - 0.465280i) q^{52} +(-4.61926 + 3.35609i) q^{53} +(9.32824 + 7.92450i) q^{55} +(6.89694 - 3.07072i) q^{56} +(0.776463 - 7.38755i) q^{58} +(-11.3426 + 2.41094i) q^{59} +(-10.6036 - 2.25387i) q^{61} +(1.68404 - 5.18293i) q^{62} +(0.411065 + 1.26513i) q^{64} +(4.98542 + 1.46242i) q^{65} +(-1.17916 + 11.2190i) q^{67} +(0.675418 + 1.16986i) q^{68} +(15.3332 - 5.47547i) q^{70} +(5.34318 - 3.88205i) q^{71} +(1.20170 + 3.69845i) q^{73} +(2.59152 - 4.48864i) q^{74} +(2.82672 + 4.89603i) q^{76} +(15.4930 - 17.2067i) q^{77} +(0.299995 + 2.85427i) q^{79} +(2.63803 + 10.8615i) q^{80} +7.95913 q^{82} +(-6.23662 + 2.77672i) q^{83} +(-1.35762 - 2.82704i) q^{85} +(-5.01319 + 5.56772i) q^{86} +(6.53724 + 7.26034i) q^{88} +(1.41471 + 4.35403i) q^{89} +(3.03709 - 9.34720i) q^{91} +(-3.07473 + 1.36896i) q^{92} +(0.516451 - 4.91370i) q^{94} +(-5.68183 - 11.8316i) q^{95} +(-1.44531 - 13.7512i) q^{97} +(-5.79405 - 17.8322i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.68376	+	0.357895i	1.19060	+	0.253070i	0.760274	−	0.649603i	$-0.225065\pi$
$2$	1.68376	+	0.357895i	1.19060	+	0.253070i	0.430327	+	0.902673i	$0.358398\pi$
$3$		0			0
$3$		0			0
$4$	0.879882	+	0.391749i	0.439941	+	0.195874i
$5$	−1.96791	−	1.06176i	−0.880076	−	0.474833i
$5$	−1.96791	−	1.06176i	−0.880076	−	0.474833i
$6$		0			0
$7$	−2.11497	+	3.66323i	−0.799383	+	1.38457i	0.120635	+	0.992697i	$0.461507\pi$
$7$	−2.11497	+	3.66323i	−0.799383	+	1.38457i	−0.920018	+	0.391876i	$0.871826\pi$
$8$	−1.44394	−	1.04909i	−0.510511	−	0.370908i
$9$		0			0
$10$	−2.93350	−	2.49206i	−0.927654	−	0.788057i
$11$	−5.35421	−	1.13807i	−1.61435	−	0.343142i	−0.689743	−	0.724054i	$-0.742277\pi$
$11$	−5.35421	−	1.13807i	−1.61435	−	0.343142i	−0.924611	+	0.380912i	$0.875610\pi$
$12$		0			0
$13$	−2.27272	+	0.483081i	−0.630338	+	0.133983i	−0.511992	−	0.858990i	$-0.671092\pi$
$13$	−2.27272	+	0.483081i	−0.630338	+	0.133983i	−0.118346	+	0.992972i	$0.537759\pi$
$14$	−4.87216	+	5.41109i	−1.30214	+	1.44617i
$15$		0			0
$16$	−3.34474	−	3.71472i	−0.836186	−	0.928679i
$17$	1.13466	+	0.824379i	0.275195	+	0.199941i	0.716819	−	0.697259i	$-0.245597\pi$
$17$	1.13466	+	0.824379i	0.275195	+	0.199941i	−0.441624	+	0.897200i	$0.645597\pi$
$18$		0			0
$19$	4.74872	+	3.45015i	1.08943	+	0.791518i	0.979303	−	0.202400i	$-0.0648740\pi$
$19$	4.74872	+	3.45015i	1.08943	+	0.791518i	0.110128	+	0.993917i	$0.464874\pi$
$20$	−1.31559	−	1.70515i	−0.294174	−	0.381283i
$21$		0			0
$22$	−8.60791	−	3.83249i	−1.83521	−	0.817090i
$23$	−2.33826	+	2.59691i	−0.487562	+	0.541492i	−0.935851	−	0.352396i	$-0.885367\pi$
$23$	−2.33826	+	2.59691i	−0.487562	+	0.541492i	0.448289	+	0.893889i	$0.352034\pi$
$24$		0			0
$25$	2.74534	+	4.17889i	0.549068	+	0.835778i
$26$	−3.99961			−0.784388
$27$		0			0
$28$	−3.29599	+	2.39468i	−0.622884	+	0.452552i
$29$	−0.451070	−	4.29164i	−0.0837616	−	0.796938i	−0.953087	−	0.302698i	$-0.902113\pi$
$29$	−0.451070	−	4.29164i	−0.0837616	−	0.796938i	0.869325	−	0.494241i	$-0.164554\pi$
$30$		0			0
$31$	0.330923	−	3.14852i	0.0594355	−	0.565491i	−0.923765	−	0.382961i	$-0.874904\pi$
$31$	0.330923	−	3.14852i	0.0594355	−	0.565491i	0.983200	−	0.182531i	$-0.0584289\pi$
$32$	−2.51747	−	4.36039i	−0.445030	−	0.770815i
$33$		0			0
$34$	1.61546	+	1.79415i	0.277049	+	0.307694i
$35$	8.05154	−	4.96333i	1.36096	−	0.838956i
$36$		0			0
$37$	0.930443	−	2.86361i	0.152964	−	0.470775i	−0.844985	−	0.534790i	$-0.820391\pi$
$37$	0.930443	−	2.86361i	0.152964	−	0.470775i	0.997949	+	0.0640154i	$0.0203907\pi$
$38$	6.76093	+	7.50877i	1.09677	+	1.21808i
$39$		0			0
$40$	1.72767	+	3.59763i	0.273169	+	0.568835i
$41$	4.52265	−	0.961319i	0.706319	−	0.150133i	0.159272	−	0.987235i	$-0.449085\pi$
$41$	4.52265	−	0.961319i	0.706319	−	0.150133i	0.547047	+	0.837102i	$0.315752\pi$
$42$		0			0
$43$	−2.17619	+	3.76927i	−0.331866	+	0.574809i	−0.982878	−	0.184259i	$-0.941011\pi$
$43$	−2.17619	+	3.76927i	−0.331866	+	0.574809i	0.651012	+	0.759068i	$0.274345\pi$
$44$	−4.26523	−	3.09887i	−0.643008	−	0.467173i
$45$		0			0
$46$	−4.86650	+	3.53572i	−0.717527	+	0.521314i
$47$	−0.300021	−	2.85451i	−0.0437626	−	0.416374i	−0.994369	−	0.105974i	$-0.966204\pi$
$47$	−0.300021	−	2.85451i	−0.0437626	−	0.416374i	0.950606	−	0.310399i	$-0.100463\pi$
$48$		0			0
$49$	−5.44619	−	9.43308i	−0.778027	−	1.34758i
$50$	3.12690	+	8.01881i	0.442210	+	1.13403i
$51$		0			0
$52$	−2.18897	−	0.465280i	−0.303555	−	0.0645227i
$53$	−4.61926	+	3.35609i	−0.634504	+	0.460994i	−0.857958	−	0.513720i	$-0.828267\pi$
$53$	−4.61926	+	3.35609i	−0.634504	+	0.460994i	0.223454	+	0.974715i	$0.428267\pi$
$54$		0			0
$55$	9.32824	+	7.92450i	1.25782	+	1.06854i
$56$	6.89694	−	3.07072i	0.921643	−	0.410342i
$57$		0			0
$58$	0.776463	−	7.38755i	0.101955	−	0.970033i
$59$	−11.3426	+	2.41094i	−1.47668	+	0.313877i	−0.874711	−	0.484645i	$-0.838949\pi$
$59$	−11.3426	+	2.41094i	−1.47668	+	0.313877i	−0.601966	+	0.798522i	$0.705616\pi$
$60$		0			0
$61$	−10.6036	−	2.25387i	−1.35766	−	0.288579i	−0.529136	−	0.848537i	$-0.677484\pi$
$61$	−10.6036	−	2.25387i	−1.35766	−	0.288579i	−0.828521	+	0.559958i	$0.810817\pi$
$62$	1.68404	−	5.18293i	0.213873	−	0.658233i
$63$		0			0
$64$	0.411065	+	1.26513i	0.0513831	+	0.158141i
$65$	4.98542	+	1.46242i	0.618365	+	0.181390i
$66$		0			0
$67$	−1.17916	+	11.2190i	−0.144058	+	1.37062i	0.648683	+	0.761059i	$0.275320\pi$
$67$	−1.17916	+	11.2190i	−0.144058	+	1.37062i	−0.792741	+	0.609559i	$0.791347\pi$
$68$	0.675418	+	1.16986i	0.0819064	+	0.141866i
$69$		0			0
$70$	15.3332	−	5.47547i	1.83267	−	0.654444i
$71$	5.34318	−	3.88205i	0.634119	−	0.460714i	−0.223706	−	0.974657i	$-0.571816\pi$
$71$	5.34318	−	3.88205i	0.634119	−	0.460714i	0.857825	+	0.513942i	$0.171816\pi$
$72$		0			0
$73$	1.20170	+	3.69845i	0.140648	+	0.432871i	0.996426	−	0.0844731i	$-0.0269207\pi$
$73$	1.20170	+	3.69845i	0.140648	+	0.432871i	−0.855777	+	0.517344i	$0.826921\pi$
$74$	2.59152	−	4.48864i	0.301258	−	0.521794i
$75$		0			0
$76$	2.82672	+	4.89603i	0.324247	+	0.561613i
$77$	15.4930	−	17.2067i	1.76559	−	1.96089i
$78$		0			0
$79$	0.299995	+	2.85427i	0.0337521	+	0.321130i	0.998351	+	0.0574078i	$0.0182835\pi$
$79$	0.299995	+	2.85427i	0.0337521	+	0.321130i	−0.964599	+	0.263722i	$0.915050\pi$
$80$	2.63803	+	10.8615i	0.294940	+	1.21436i
$81$		0			0
$82$	7.95913			0.878938
$83$	−6.23662	+	2.77672i	−0.684558	+	0.304785i	−0.719388	−	0.694608i	$-0.755578\pi$
$83$	−6.23662	+	2.77672i	−0.684558	+	0.304785i	0.0348298	+	0.999393i	$0.488911\pi$
$84$		0			0
$85$	−1.35762	−	2.82704i	−0.147254	−	0.306635i
$86$	−5.01319	+	5.56772i	−0.540587	+	0.600382i
$87$		0			0
$88$	6.53724	+	7.26034i	0.696872	+	0.773955i
$89$	1.41471	+	4.35403i	0.149959	+	0.461526i	0.997615	−	0.0690197i	$-0.0219871\pi$
$89$	1.41471	+	4.35403i	0.149959	+	0.461526i	−0.847656	+	0.530545i	$0.821987\pi$
$90$		0			0
$91$	3.03709	−	9.34720i	0.318373	−	0.979852i
$92$	−3.07473	+	1.36896i	−0.320563	+	0.142724i
$93$		0			0
$94$	0.516451	−	4.91370i	0.0532679	−	0.506810i
$95$	−5.68183	−	11.8316i	−0.582943	−	1.21389i
$96$		0			0
$97$	−1.44531	−	13.7512i	−0.146749	−	1.39623i	−0.781691	−	0.623666i	$-0.785643\pi$
$97$	−1.44531	−	13.7512i	−0.146749	−	1.39623i	0.634942	−	0.772560i	$-0.281024\pi$
$98$	−5.79405	−	17.8322i	−0.585287	−	1.80133i
$99$		0			0
$100$	0.778500	+	4.75241i	0.0778500	+	0.475241i
$101$	4.29330	−	7.43621i	0.427199	−	0.739930i	−0.569424	−	0.822044i	$-0.692834\pi$
$101$	4.29330	−	7.43621i	0.427199	−	0.739930i	0.996623	+	0.0821135i	$0.0261670\pi$
$102$		0			0
$103$	0.0160907	+	0.00716406i	0.00158547	+	0.000705896i	0.407529	−	0.913192i	$-0.366390\pi$
$103$	0.0160907	+	0.00716406i	0.00158547	+	0.000705896i	−0.405944	+	0.913898i	$0.633057\pi$
$104$	3.78847	+	1.68673i	0.371490	+	0.165398i
$105$		0			0
$106$	−8.97887	+	3.99765i	−0.872105	+	0.388286i
$107$	−3.33334			−0.322246			−0.161123	−	0.986934i	$-0.551512\pi$
$107$	−3.33334			−0.322246			−0.161123	+	0.986934i	$0.551512\pi$
$108$		0			0
$109$	0.885216	−	2.72442i	0.0847883	−	0.260952i	−0.899670	−	0.436571i	$-0.856193\pi$
$109$	0.885216	−	2.72442i	0.0847883	−	0.260952i	0.984458	+	0.175619i	$0.0561928\pi$
$110$	12.8704	+	16.6815i	1.22715	+	1.59052i
$111$		0			0
$112$	20.6819	−	4.39607i	1.95426	−	0.415390i
$113$	−7.87550	+	1.67399i	−0.740864	+	0.157476i	−0.562858	−	0.826554i	$-0.690298\pi$
$113$	−7.87550	+	1.67399i	−0.740864	+	0.157476i	−0.178007	+	0.984029i	$0.556965\pi$
$114$		0			0
$115$	7.35878	−	2.62780i	0.686210	−	0.245044i
$116$	1.28436	−	3.95285i	0.119250	−	0.367013i
$117$		0			0
$118$	−19.9611			−1.83757
$119$	−5.41966	+	2.41299i	−0.496820	+	0.221198i
$120$		0			0
$121$	17.3233	+	7.71285i	1.57485	+	0.701168i
$122$	−17.0474	−	7.58998i	−1.54340	−	0.687165i
$123$		0			0
$124$	1.52460	−	2.64069i	0.136913	−	0.237141i
$125$	−0.965608	−	11.1386i	−0.0863666	−	0.996263i
$126$		0			0
$127$	−1.46943	−	4.52243i	−0.130391	−	0.401301i	0.864454	−	0.502712i	$-0.167664\pi$
$127$	−1.46943	−	4.52243i	−0.130391	−	0.401301i	−0.994845	+	0.101411i	$0.967664\pi$
$128$	1.29194	+	12.2920i	0.114193	+	1.08647i
$129$		0			0
$130$	7.87087	+	4.24662i	0.690321	+	0.372453i
$131$	−1.92495	+	18.3147i	−0.168184	+	1.60016i	0.506623	+	0.862168i	$0.330894\pi$
$131$	−1.92495	+	18.3147i	−0.168184	+	1.60016i	−0.674807	+	0.737995i	$0.735773\pi$
$132$		0			0
$133$	−22.6821	+	10.0987i	−1.96679	+	0.875670i
$134$	−6.00065	+	18.4681i	−0.518377	+	1.59540i
$135$		0			0
$136$	−0.773540	−	2.38071i	−0.0663305	−	0.204144i
$137$	11.0852	+	12.3114i	0.947074	+	1.05183i	0.998586	+	0.0531595i	$0.0169292\pi$
$137$	11.0852	+	12.3114i	0.947074	+	1.05183i	−0.0515124	+	0.998672i	$0.516404\pi$
$138$		0			0
$139$	−7.23633	+	8.03676i	−0.613778	+	0.681669i	−0.967265	−	0.253770i	$-0.918329\pi$
$139$	−7.23633	+	8.03676i	−0.613778	+	0.681669i	0.353487	+	0.935440i	$0.384996\pi$
$140$	9.02878	−	1.21296i	0.763071	−	0.102514i
$141$		0			0
$142$	10.3860	−	4.62415i	0.871575	−	0.388050i
$143$	12.7184			1.06356
$144$		0			0
$145$	−3.66902	+	8.92450i	−0.304696	+	0.741139i
$146$	0.699721	+	6.65740i	0.0579094	+	0.550971i
$147$		0			0
$148$	1.94050	−	2.15514i	0.159508	−	0.177151i
$149$	4.92744	+	8.53458i	0.403672	+	0.699180i	0.994166	−	0.107862i	$-0.0344004\pi$
$149$	4.92744	+	8.53458i	0.403672	+	0.699180i	−0.590494	+	0.807042i	$0.701067\pi$
$150$		0			0
$151$	9.07209	−	15.7133i	0.738276	−	1.27873i	−0.214994	−	0.976615i	$-0.568973\pi$
$151$	9.07209	−	15.7133i	0.738276	−	1.27873i	0.953271	−	0.302117i	$-0.0976934\pi$
$152$	−3.23738	−	9.96363i	−0.262586	−	0.808157i
$153$		0			0
$154$	32.2448	−	23.4272i	2.59836	−	1.88782i
$155$	−3.99420	+	5.84465i	−0.320822	+	0.469453i
$156$		0			0
$157$	−1.33107	−	2.30547i	−0.106231	−	0.183997i	0.808010	−	0.589169i	$-0.200545\pi$
$157$	−1.33107	−	2.30547i	−0.106231	−	0.183997i	−0.914240	+	0.405172i	$0.867212\pi$
$158$	−0.516406	+	4.91328i	−0.0410831	+	0.390879i
$159$		0			0
$160$	0.324478	+	11.2538i	0.0256522	+	0.889691i
$161$	−4.56772	−	14.0580i	−0.359986	−	1.10792i
$162$		0			0
$163$	1.19215	−	3.66905i	0.0933761	−	0.287382i	−0.893451	−	0.449161i	$-0.851723\pi$
$163$	1.19215	−	3.66905i	0.0933761	−	0.287382i	0.986827	+	0.161779i	$0.0517230\pi$
$164$	4.35599	+	0.925895i	0.340146	+	0.0723003i
$165$		0			0
$166$	−11.4948	+	2.44329i	−0.892168	+	0.189636i
$167$	−1.09890	+	10.4554i	−0.0850358	+	0.809061i	0.866013	+	0.500021i	$0.166674\pi$
$167$	−1.09890	+	10.4554i	−0.0850358	+	0.809061i	−0.951049	+	0.309040i	$0.899992\pi$
$168$		0			0
$169$	−6.94422	+	3.09176i	−0.534170	+	0.237828i
$170$	−1.27412	−	5.24595i	−0.0977209	−	0.402346i
$171$		0			0
$172$	−3.39140	+	2.46399i	−0.258592	+	0.187878i
$173$	6.01334	+	1.27818i	0.457186	+	0.0971779i	0.430747	−	0.902473i	$-0.358250\pi$
$173$	6.01334	+	1.27818i	0.457186	+	0.0971779i	0.0264386	+	0.999650i	$0.491583\pi$
$174$		0			0
$175$	−21.1146	+	1.21860i	−1.59611	+	0.0921172i
$176$	13.6808	+	23.6959i	1.03123	+	1.78615i
$177$		0			0
$178$	0.823751	+	7.83747i	0.0617428	+	0.587443i
$179$	−5.82725	+	4.23375i	−0.435549	+	0.316445i	−0.783864	−	0.620933i	$-0.786754\pi$
$179$	−5.82725	+	4.23375i	−0.435549	+	0.316445i	0.348315	+	0.937378i	$0.386754\pi$
$180$		0			0
$181$	−18.3734	−	13.3490i	−1.36568	−	0.992226i	−0.998061	−	0.0622510i	$-0.980172\pi$
$181$	−18.3734	−	13.3490i	−1.36568	−	0.992226i	−0.367622	−	0.929975i	$-0.619828\pi$
$182$	8.45906	−	14.6515i	0.627027	−	1.08604i
$183$		0			0
$184$	6.10070	−	1.29674i	0.449749	−	0.0955972i
$185$	−4.87149	+	4.64742i	−0.358159	+	0.341685i
$186$		0			0
$187$	−5.13700	−	5.70522i	−0.375655	−	0.417207i
$188$	0.854269	−	2.62917i	0.0623039	−	0.191752i
$189$		0			0
$190$	−5.33240	−	21.9551i	−0.386853	−	1.59279i
$191$	7.18086	+	7.97515i	0.519589	+	0.577062i	0.944641	−	0.328107i	$-0.106411\pi$
$191$	7.18086	+	7.97515i	0.519589	+	0.577062i	−0.425052	+	0.905169i	$0.639744\pi$
$192$		0			0
$193$	7.49531	+	12.9823i	0.539524	+	0.934483i	0.998930	+	0.0462566i	$0.0147292\pi$
$193$	7.49531	+	12.9823i	0.539524	+	0.934483i	−0.459405	+	0.888227i	$0.651937\pi$
$194$	2.48793	−	23.6711i	0.178623	−	1.69949i
$195$		0			0
$196$	−1.09661	−	10.4335i	−0.0783292	−	0.745253i
$197$	−6.42527	+	4.66823i	−0.457782	+	0.332598i	−0.792660	−	0.609663i	$-0.791305\pi$
$197$	−6.42527	+	4.66823i	−0.457782	+	0.332598i	0.334879	+	0.942261i	$0.391305\pi$
$198$		0			0
$199$	−14.1116			−1.00034			−0.500172	−	0.865926i	$-0.666730\pi$
$199$	−14.1116			−1.00034			−0.500172	+	0.865926i	$0.666730\pi$
$200$	0.419902	−	8.91418i	0.0296916	−	0.630327i
$201$		0			0
$202$	9.89028	−	10.9843i	0.695878	−	0.772851i
$203$	16.6753	+	7.42432i	1.17038	+	0.521085i
$204$		0			0
$205$	−9.92085	−	2.91017i	−0.692903	−	0.203255i
$206$	0.0245290	+	0.0178214i	0.00170902	+	0.00124167i
$207$		0			0
$208$	9.39616	+	6.82671i	0.651507	+	0.473347i
$209$	−21.4991	−	23.8772i	−1.48712	−	1.65162i
$210$		0			0
$211$	4.89947	−	5.44141i	0.337293	−	0.374602i	−0.550507	−	0.834830i	$-0.685566\pi$
$211$	4.89947	−	5.44141i	0.337293	−	0.374602i	0.887801	+	0.460228i	$0.152232\pi$
$212$	−5.37915	+	1.14337i	−0.369441	+	0.0785272i
$213$		0			0
$214$	−5.61255	−	1.19299i	−0.383666	−	0.0815508i
$215$	8.28460	−	5.10700i	0.565005	−	0.348294i
$216$		0			0
$217$	10.8339	+	7.87128i	0.735452	+	0.534337i
$218$	2.46555	−	4.27046i	0.166988	−	0.289232i
$219$		0			0
$220$	5.10334	+	10.6270i	0.344067	+	0.716469i
$221$	−2.97700	−	1.32545i	−0.200255	−	0.0891592i
$222$		0			0
$223$	19.8964	+	4.22911i	1.33236	+	0.283202i	0.818419	−	0.574622i	$-0.194851\pi$
$223$	19.8964	+	4.22911i	1.33236	+	0.283202i	0.513943	+	0.857825i	$0.328184\pi$
$224$	21.2975			1.42300
$225$		0			0
$226$	−13.8596			−0.921926
$227$	−21.2885	−	4.52501i	−1.41297	−	0.300335i	−0.562689	−	0.826669i	$-0.690233\pi$
$227$	−21.2885	−	4.52501i	−1.41297	−	0.300335i	−0.850278	+	0.526333i	$0.823566\pi$
$228$		0			0
$229$	−17.1567	−	7.63866i	−1.13375	−	0.504777i	−0.247915	−	0.968782i	$-0.579745\pi$
$229$	−17.1567	−	7.63866i	−1.13375	−	0.504777i	−0.885833	+	0.464005i	$0.846412\pi$
$230$	13.3309	−	1.79093i	0.879015	−	0.118091i
$231$		0			0
$232$	−3.85098	+	6.67010i	−0.252830	+	0.437914i
$233$	5.17867	+	3.76252i	0.339266	+	0.246491i	0.744352	−	0.667787i	$-0.232758\pi$
$233$	5.17867	+	3.76252i	0.339266	+	0.246491i	−0.405086	+	0.914279i	$0.632758\pi$
$234$		0			0
$235$	−2.44039	+	5.93598i	−0.159193	+	0.387220i
$236$	−10.9246	−	2.32210i	−0.711131	−	0.151156i
$237$		0			0
$238$	−9.98903	+	2.12323i	−0.647493	+	0.137629i
$239$	11.7685	−	13.0702i	0.761238	−	0.845440i	−0.230586	−	0.973052i	$-0.574064\pi$
$239$	11.7685	−	13.0702i	0.761238	−	0.845440i	0.991824	+	0.127612i	$0.0407311\pi$
$240$		0			0
$241$	5.08374	+	5.64606i	0.327472	+	0.363695i	0.884289	−	0.466941i	$-0.154644\pi$
$241$	5.08374	+	5.64606i	0.327472	+	0.363695i	−0.556816	+	0.830636i	$0.687977\pi$
$242$	26.4080	+	19.1866i	1.69757	+	1.23336i
$243$		0			0
$244$	−8.44700	−	6.13711i	−0.540764	−	0.392888i
$245$	0.701962	+	24.3460i	0.0448467	+	1.55541i
$246$		0			0
$247$	−12.4592	−	5.54719i	−0.792759	−	0.352959i
$248$	−3.78091	+	4.19912i	−0.240088	+	0.266644i
$249$		0			0
$250$	2.36058	−	19.1003i	0.149296	−	1.20801i
$251$	−25.9812			−1.63992			−0.819959	−	0.572422i	$-0.806004\pi$
$251$	−25.9812			−1.63992			−0.819959	+	0.572422i	$0.806004\pi$
$252$		0			0
$253$	15.4750	−	11.2433i	0.972906	−	0.706858i
$254$	−0.855612	−	8.14061i	−0.0536859	−	0.510787i
$255$		0			0
$256$	−1.94583	+	18.5133i	−0.121614	+	1.15708i
$257$	−0.478674	−	0.829088i	−0.0298589	−	0.0517171i	0.850710	−	0.525636i	$-0.176172\pi$
$257$	−0.478674	−	0.829088i	−0.0298589	−	0.0517171i	−0.880569	+	0.473919i	$0.842839\pi$
$258$		0			0
$259$	8.52222	+	9.46488i	0.529545	+	0.588119i
$260$	3.81368	+	3.23978i	0.236514	+	0.200923i
$261$		0			0
$262$	−9.79591	+	30.1487i	−0.605193	+	1.86259i
$263$	3.53512	+	3.92615i	0.217985	+	0.242097i	0.842213	−	0.539146i	$-0.181253\pi$
$263$	3.53512	+	3.92615i	0.217985	+	0.242097i	−0.624227	+	0.781243i	$0.714586\pi$
$264$		0			0
$265$	12.6536	−	1.69994i	0.777307	−	0.104427i
$266$	−41.8056	+	8.88605i	−2.56326	+	0.544838i
$267$		0			0
$268$	−5.43255	+	9.40945i	−0.331846	+	0.574774i
$269$	−14.1657	−	10.2920i	−0.863699	−	0.627514i	0.0651897	−	0.997873i	$-0.479235\pi$
$269$	−14.1657	−	10.2920i	−0.863699	−	0.627514i	−0.928889	+	0.370359i	$0.879235\pi$
$270$		0			0
$271$	−10.8922	+	7.91361i	−0.661651	+	0.480718i	−0.867220	−	0.497925i	$-0.834096\pi$
$271$	−10.8922	+	7.91361i	−0.661651	+	0.480718i	0.205569	+	0.978643i	$0.434096\pi$
$272$	−0.732816	−	6.97227i	−0.0444335	−	0.422756i
$273$		0			0
$274$	14.2587	+	24.6968i	0.861400	+	1.49199i
$275$	−9.94324	−	25.4990i	−0.599600	−	1.53765i
$276$		0			0
$277$	25.7950	+	5.48290i	1.54987	+	0.329436i	0.901804	−	0.432146i	$-0.142244\pi$
$277$	25.7950	+	5.48290i	1.54987	+	0.329436i	0.648069	+	0.761582i	$0.275577\pi$
$278$	−15.0606	+	10.9422i	−0.903274	+	0.656267i
$279$		0			0
$280$	−16.8329	−	1.27999i	−1.00596	−	0.0764942i
$281$	−22.9358	+	10.2117i	−1.36823	+	0.609176i	−0.953673	−	0.300846i	$-0.902731\pi$
$281$	−22.9358	+	10.2117i	−1.36823	+	0.609176i	−0.414559	+	0.910022i	$0.636064\pi$
$282$		0			0
$283$	1.50697	−	14.3378i	0.0895798	−	0.852295i	−0.853805	−	0.520593i	$-0.825711\pi$
$283$	1.50697	−	14.3378i	0.0895798	−	0.852295i	0.943385	−	0.331701i	$-0.107623\pi$
$284$	6.22215	−	1.32256i	0.369217	−	0.0784795i
$285$		0			0
$286$	21.4148	+	4.55185i	1.26628	+	0.269156i
$287$	−6.04373	+	18.6007i	−0.356750	+	1.09796i
$288$		0			0
$289$	−4.64544	−	14.2972i	−0.273261	−	0.841011i
$290$	−9.37180	+	13.7136i	−0.550331	+	0.805292i
$291$		0			0
$292$	−0.391510	+	3.72497i	−0.0229114	+	0.217987i
$293$	−3.34662	−	5.79652i	−0.195512	−	0.338636i	0.751556	−	0.659669i	$-0.229303\pi$
$293$	−3.34662	−	5.79652i	−0.195512	−	0.338636i	−0.947068	+	0.321033i	$0.895970\pi$
$294$		0			0
$295$	24.8810	+	7.29856i	1.44863	+	0.424939i
$296$	−4.34768	+	3.15878i	−0.252704	+	0.183600i
$297$		0			0
$298$	5.24217	+	16.1337i	0.303671	+	0.934602i
$299$	4.05970	−	7.03160i	0.234778	−	0.406648i
$300$		0			0
$301$	−9.20515	−	15.9438i	−0.530576	−	0.918985i
$302$	20.8990	−	23.2107i	1.20260	−	1.33562i
$303$		0			0
$304$	−3.06694	−	29.1800i	−0.175901	−	1.67359i
$305$	18.4739	+	15.6939i	1.05781	+	0.898631i
$306$		0			0
$307$	3.26128			0.186131			0.0930657	−	0.995660i	$-0.470333\pi$
$307$	3.26128			0.186131			0.0930657	+	0.995660i	$0.470333\pi$
$308$	20.3727	−	9.07053i	1.16084	−	0.516841i
$309$		0			0
$310$	−8.81706	+	8.41151i	−0.500775	+	0.477741i
$311$	21.5663	−	23.9518i	1.22291	−	1.35818i	0.309629	−	0.950858i	$-0.399795\pi$
$311$	21.5663	−	23.9518i	1.22291	−	1.35818i	0.913284	−	0.407324i	$-0.133538\pi$
$312$		0			0
$313$	−13.7340	−	15.2532i	−0.776292	−	0.862159i	0.217193	−	0.976129i	$-0.430310\pi$
$313$	−13.7340	−	15.2532i	−0.776292	−	0.862159i	−0.993484	+	0.113969i	$0.963643\pi$
$314$	−1.41608	−	4.35826i	−0.0799142	−	0.245951i
$315$		0			0
$316$	−0.854194	+	2.62894i	−0.0480522	+	0.147889i
$317$	3.65413	−	1.62692i	0.205236	−	0.0913771i	−0.301544	−	0.953452i	$-0.597502\pi$
$317$	3.65413	−	1.62692i	0.205236	−	0.0913771i	0.506781	+	0.862075i	$0.330835\pi$
$318$		0			0
$319$	−2.46908	+	23.4917i	−0.138242	+	1.31528i
$320$	0.534321	−	2.92611i	0.0298695	−	0.163575i
$321$		0			0
$322$	−2.65967	−	25.3051i	−0.148218	−	1.41020i
$323$	2.54395	+	7.82948i	0.141549	+	0.435644i
$324$		0			0
$325$	−8.25812	−	8.17121i	−0.458078	−	0.453257i
$326$	3.32043	−	5.75115i	0.183902	−	0.318527i
$327$		0			0
$328$	−7.53895	−	3.35656i	−0.416269	−	0.185335i
$329$	11.0913	+	4.93816i	0.611483	+	0.272250i
$330$		0			0
$331$	1.34664	−	0.599564i	0.0740181	−	0.0329550i	−0.369394	−	0.929273i	$-0.620435\pi$
$331$	1.34664	−	0.599564i	0.0740181	−	0.0329550i	0.443412	+	0.896318i	$0.353768\pi$
$332$	−6.57527			−0.360865
$333$		0			0
$334$	−5.59222	+	17.2111i	−0.305993	+	0.941749i
$335$	14.2323	−	20.8260i	0.777596	−	1.13784i
$336$		0			0
$337$	9.11619	−	1.93771i	0.496590	−	0.105554i	0.0471935	−	0.998886i	$-0.484972\pi$
$337$	9.11619	−	1.93771i	0.496590	−	0.105554i	0.449397	+	0.893332i	$0.351639\pi$
$338$	−12.7990	+	2.72050i	−0.696171	+	0.147976i
$339$		0			0
$340$	−0.0870549	−	3.01930i	−0.00472122	−	0.163745i
$341$	−5.35508	+	16.4812i	−0.289994	+	0.892509i
$342$		0			0
$343$	16.4645			0.889001
$344$	7.09658	−	3.15960i	0.382622	−	0.170354i
$345$		0			0
$346$	9.66760	+	4.30429i	0.519733	+	0.231400i
$347$	6.09966	+	2.71574i	0.327447	+	0.145789i	0.563875	−	0.825860i	$-0.309310\pi$
$347$	6.09966	+	2.71574i	0.327447	+	0.145789i	−0.236428	+	0.971649i	$0.575977\pi$
$348$		0			0
$349$	2.17204	−	3.76209i	0.116267	−	0.201380i	−0.802019	−	0.597299i	$-0.796241\pi$
$349$	2.17204	−	3.76209i	0.116267	−	0.201380i	0.918285	+	0.395919i	$0.129574\pi$
$350$	−35.9881	−	5.50497i	−1.92364	−	0.294253i
$351$		0			0
$352$	8.51663	+	26.2115i	0.453938	+	1.39708i
$353$	−0.483612	−	4.60126i	−0.0257401	−	0.244900i	−0.999825	−	0.0187171i	$-0.994042\pi$
$353$	−0.483612	−	4.60126i	−0.0257401	−	0.244900i	0.974085	−	0.226183i	$-0.0726248\pi$
$354$		0			0
$355$	−14.6367	+	1.96635i	−0.776835	+	0.104363i
$356$	−0.460907	+	4.38524i	−0.0244280	+	0.232417i
$357$		0			0
$358$	−11.3270	+	5.04309i	−0.598648	+	0.266535i
$359$	2.78646	−	8.57585i	0.147064	−	0.452616i	−0.850207	−	0.526449i	$-0.823523\pi$
$359$	2.78646	−	8.57585i	0.147064	−	0.452616i	0.997271	+	0.0738329i	$0.0235232\pi$
$360$		0			0
$361$	4.77550	+	14.6975i	0.251342	+	0.773551i
$362$	−26.1589	−	29.0524i	−1.37488	−	1.52696i
$363$		0			0
$364$	6.33403	−	7.03465i	0.331993	−	0.368716i
$365$	1.56203	−	8.55414i	0.0817601	−	0.447744i
$366$		0			0
$367$	−8.45692	+	3.76527i	−0.441448	+	0.196545i	−0.615410	−	0.788207i	$-0.711010\pi$
$367$	−8.45692	+	3.76527i	−0.441448	+	0.196545i	0.173962	+	0.984752i	$0.444343\pi$
$368$	17.4677			0.910565
$369$		0			0
$370$	−9.86573	+	6.08168i	−0.512895	+	0.316171i
$371$	−2.52455	−	24.0194i	−0.131068	−	1.24703i
$372$		0			0
$373$	−3.62568	+	4.02673i	−0.187731	+	0.208496i	−0.829662	−	0.558266i	$-0.811467\pi$
$373$	−3.62568	+	4.02673i	−0.187731	+	0.208496i	0.641931	+	0.766762i	$0.278133\pi$
$374$	−6.60763	−	11.4448i	−0.341673	−	0.591794i
$375$		0			0
$376$	−2.56142	+	4.43650i	−0.132095	+	0.228795i
$377$	3.09837	+	9.53579i	0.159574	+	0.491118i
$378$		0			0
$379$	7.21488	−	5.24191i	0.370603	−	0.269259i	−0.386858	−	0.922139i	$-0.626440\pi$
$379$	7.21488	−	5.24191i	0.370603	−	0.269259i	0.757461	+	0.652880i	$0.226440\pi$
$380$	−0.364338	−	12.6362i	−0.0186901	−	0.648225i
$381$		0			0
$382$	9.23661	+	15.9983i	0.472586	+	0.818543i
$383$	−1.92865	+	18.3499i	−0.0985493	+	0.937634i	0.827814	+	0.561003i	$0.189584\pi$
$383$	−1.92865	+	18.3499i	−0.0985493	+	0.937634i	−0.926363	+	0.376631i	$0.877082\pi$
$384$		0			0
$385$	−48.7582	+	17.4115i	−2.48495	+	0.887370i
$386$	7.97405	+	24.5416i	0.405868	+	1.24913i
$387$		0			0
$388$	4.11532	−	12.6657i	0.208924	−	0.643001i
$389$	−12.3953	−	2.63469i	−0.628465	−	0.133584i	−0.117341	−	0.993092i	$-0.537437\pi$
$389$	−12.3953	−	2.63469i	−0.628465	−	0.133584i	−0.511123	+	0.859507i	$0.670770\pi$
$390$		0			0
$391$	−4.79397	+	1.01899i	−0.242441	+	0.0515325i
$392$	−2.03212	+	19.3344i	−0.102638	+	0.976532i
$393$		0			0
$394$	−12.4894	+	5.56063i	−0.629206	+	0.280140i
$395$	2.44018	−	5.93546i	0.122779	−	0.298645i
$396$		0			0
$397$	5.05655	−	3.67380i	0.253781	−	0.184383i	−0.453620	−	0.891195i	$-0.649868\pi$
$397$	5.05655	−	3.67380i	0.253781	−	0.184383i	0.707401	+	0.706813i	$0.249868\pi$
$398$	−23.7606	−	5.05047i	−1.19101	−	0.253157i
$399$		0			0
$400$	6.34093	−	24.1755i	0.317046	−	1.20877i
$401$	−13.3637	−	23.1466i	−0.667352	−	1.15589i	−0.978642	−	0.205572i	$-0.934094\pi$
$401$	−13.3637	−	23.1466i	−0.667352	−	1.15589i	0.311290	−	0.950315i	$-0.399239\pi$
$402$		0			0
$403$	0.768897	+	7.31556i	0.0383015	+	0.364414i
$404$	6.69072	−	4.86109i	0.332876	−	0.241848i
$405$		0			0
$406$	25.4201	+	18.4688i	1.26158	+	0.916592i
$407$	−8.24078	+	14.2735i	−0.408480	+	0.707509i
$408$		0			0
$409$	−23.4005	+	4.97392i	−1.15708	+	0.245945i	−0.746185	−	0.665739i	$-0.768117\pi$
$409$	−23.4005	+	4.97392i	−1.15708	+	0.245945i	−0.410893	+	0.911683i	$0.634783\pi$
$410$	−15.6628	−	8.45067i	−0.773533	−	0.417349i
$411$		0			0
$412$	0.0113514	+	0.0126071i	0.000559246	+	0.000621105i
$413$	15.1574	−	46.6496i	0.745845	−	2.29547i
$414$		0			0
$415$	15.2213	+	1.15744i	0.747185	+	0.0568167i
$416$	7.82792	+	8.69378i	0.383795	+	0.426248i
$417$		0			0
$418$	−27.6539	−	47.8980i	−1.35260	−	2.34277i
$419$	−1.31148	+	12.4779i	−0.0640699	+	0.609584i	0.914631	+	0.404291i	$0.132482\pi$
$419$	−1.31148	+	12.4779i	−0.0640699	+	0.609584i	−0.978700	+	0.205294i	$0.934185\pi$
$420$		0			0
$421$	0.123363	+	1.17372i	0.00601232	+	0.0572034i	0.997117	−	0.0758835i	$-0.0241777\pi$
$421$	0.123363	+	1.17372i	0.00601232	+	0.0572034i	−0.991104	+	0.133087i	$0.957511\pi$
$422$	10.1970	−	7.40856i	0.496382	−	0.360643i
$423$		0			0
$424$	10.1908			0.494908
$425$	−0.329962	+	7.00482i	−0.0160055	+	0.339784i
$426$		0			0
$427$	30.6828	−	34.0767i	1.48485	−	1.64909i
$428$	−2.93294	−	1.30583i	−0.141769	−	0.0631197i
$429$		0			0
$430$	15.7771	−	5.63396i	0.760839	−	0.271694i
$431$	20.3282	+	14.7693i	0.979174	+	0.711412i	0.957524	−	0.288354i	$-0.0931080\pi$
$431$	20.3282	+	14.7693i	0.979174	+	0.711412i	0.0216502	+	0.999766i	$0.493108\pi$
$432$		0			0
$433$	16.1875	+	11.7609i	0.777922	+	0.565193i	0.904355	−	0.426782i	$-0.140353\pi$
$433$	16.1875	+	11.7609i	0.777922	+	0.565193i	−0.126433	+	0.991975i	$0.540353\pi$
$434$	15.4246	+	17.1308i	0.740405	+	0.822303i
$435$		0			0
$436$	1.84617	−	2.05038i	0.0884156	−	0.0981955i
$437$	−20.0635	+	4.26462i	−0.959765	+	0.204004i
$438$		0			0
$439$	22.1767	+	4.71380i	1.05844	+	0.224977i	0.704071	−	0.710130i	$-0.251364\pi$
$439$	22.1767	+	4.71380i	1.05844	+	0.224977i	0.354365	+	0.935107i	$0.384697\pi$
$440$	−5.15597	−	21.2287i	−0.245801	−	1.01204i
$441$		0			0
$442$	−4.53820	−	3.29719i	−0.215860	−	0.156832i
$443$	−2.48298	+	4.30064i	−0.117970	+	0.204330i	−0.918963	−	0.394344i	$-0.870972\pi$
$443$	−2.48298	+	4.30064i	−0.117970	+	0.204330i	0.800993	+	0.598673i	$0.204305\pi$
$444$		0			0
$445$	1.83890	−	10.0704i	0.0871724	−	0.477383i
$446$	31.9873	+	14.2416i	1.51464	+	0.674362i
$447$		0			0
$448$	−5.50385	−	1.16988i	−0.260032	−	0.0552716i
$449$	−17.7685			−0.838548			−0.419274	−	0.907860i	$-0.637715\pi$
$449$	−17.7685			−0.838548			−0.419274	+	0.907860i	$0.637715\pi$
$450$		0			0
$451$	−25.3093			−1.19177
$452$	−7.58529	−	1.61230i	−0.356782	−	0.0758364i
$453$		0			0
$454$	−34.2253	−	15.2381i	−1.60627	−	0.715159i
$455$	−15.9012	+	15.1698i	−0.745459	+	0.711170i
$456$		0			0
$457$	−10.0171	+	17.3501i	−0.468579	+	0.811602i	−0.999355	−	0.0359099i	$-0.988567\pi$
$457$	−10.0171	+	17.3501i	−0.468579	+	0.811602i	0.530776	+	0.847512i	$0.321900\pi$
$458$	−26.1540	−	19.0020i	−1.22210	−	0.887906i
$459$		0			0
$460$	7.50430	+	0.570634i	0.349890	+	0.0266060i
$461$	−12.3278	−	2.62035i	−0.574161	−	0.122042i	−0.0883252	−	0.996092i	$-0.528151\pi$
$461$	−12.3278	−	2.62035i	−0.574161	−	0.122042i	−0.485836	+	0.874050i	$0.661485\pi$
$462$		0			0
$463$	24.3569	−	5.17722i	1.13196	−	0.240606i	0.396409	−	0.918074i	$-0.370256\pi$
$463$	24.3569	−	5.17722i	1.13196	−	0.240606i	0.735552	+	0.677469i	$0.236923\pi$
$464$	−14.4335	+	16.0300i	−0.670059	+	0.744176i
$465$		0			0
$466$	7.37307	+	8.18862i	0.341551	+	0.379331i
$467$	29.6418	+	21.5361i	1.37166	+	0.996570i	0.997605	+	0.0691640i	$0.0220332\pi$
$467$	29.6418	+	21.5361i	1.37166	+	0.996570i	0.374056	+	0.927406i	$0.377967\pi$
$468$		0			0
$469$	−38.6039	−	28.0474i	−1.78256	−	1.29511i
$470$	−6.23350	+	9.12138i	−0.287530	+	0.420738i
$471$		0			0
$472$	18.9073	+	8.41808i	0.870279	+	0.387473i
$473$	15.9415	−	17.7048i	0.732990	−	0.814068i
$474$		0			0
$475$	−1.38094	+	29.3162i	−0.0633618	+	1.34512i
$476$	−5.71395			−0.261899
$477$		0			0
$478$	24.4931	−	17.7952i	1.12029	−	0.813936i
$479$	0.763778	+	7.26686i	0.0348979	+	0.332031i	0.998016	+	0.0629539i	$0.0200521\pi$
$479$	0.763778	+	7.26686i	0.0348979	+	0.332031i	−0.963119	+	0.269078i	$0.913281\pi$
$480$		0			0
$481$	−0.731279	+	6.95766i	−0.0333435	+	0.317242i
$482$	6.53911	+	11.3261i	0.297849	+	0.515889i
$483$		0			0
$484$	12.2210	+	13.5728i	0.555500	+	0.616945i
$485$	−11.7562	+	28.5957i	−0.533823	+	1.29847i
$486$		0			0
$487$	−7.65681	+	23.5652i	−0.346963	+	1.06784i	0.613561	+	0.789647i	$0.289736\pi$
$487$	−7.65681	+	23.5652i	−0.346963	+	1.06784i	−0.960524	+	0.278195i	$0.910264\pi$
$488$	12.9465	+	14.3786i	0.586063	+	0.650889i
$489$		0			0
$490$	−7.53137	+	41.2441i	−0.340233	+	1.86322i
$491$	−19.9579	+	4.24219i	−0.900690	+	0.191447i	−0.634910	−	0.772586i	$-0.718963\pi$
$491$	−19.9579	+	4.24219i	−0.900690	+	0.191447i	−0.265780	+	0.964034i	$0.585629\pi$
$492$		0			0
$493$	3.02613	−	5.24141i	0.136290	−	0.236061i
$494$	−18.9930	−	13.7992i	−0.854537	−	0.620857i
$495$		0			0
$496$	−12.8027	+	9.30172i	−0.574859	+	0.417659i
$497$	2.92019	+	27.7837i	0.130988	+	1.24627i
$498$		0			0
$499$	−10.7311	−	18.5869i	−0.480392	−	0.832064i	0.519355	−	0.854559i	$-0.326172\pi$
$499$	−10.7311	−	18.5869i	−0.480392	−	0.832064i	−0.999747	+	0.0224950i	$0.992839\pi$
$500$	3.51390	−	10.1789i	0.157146	−	0.455214i
$501$		0			0
$502$	−43.7462	−	9.29854i	−1.95249	−	0.415014i
$503$	8.58020	−	6.23388i	0.382572	−	0.277955i	−0.379833	−	0.925055i	$-0.624019\pi$
$503$	8.58020	−	6.23388i	0.382572	−	0.277955i	0.762405	+	0.647100i	$0.224019\pi$
$504$		0			0
$505$	−16.3443	+	10.0753i	−0.727311	+	0.448347i
$506$	30.0802	−	13.3926i	1.33723	−	0.595372i
$507$		0			0
$508$	0.478734	−	4.55485i	0.0212404	−	0.202089i
$509$	4.48811	−	0.953978i	0.198932	−	0.0422843i	−0.107368	−	0.994219i	$-0.534242\pi$
$509$	4.48811	−	0.953978i	0.198932	−	0.0422843i	0.306300	+	0.951935i	$0.400909\pi$
$510$		0			0
$511$	−16.0899	−	3.42000i	−0.711773	−	0.151292i
$512$	−2.26343	+	6.96611i	−0.100030	+	0.307861i
$513$		0			0
$514$	−0.509248	−	1.56730i	−0.0224620	−	0.0691308i
$515$	−0.0240586	−	0.0311827i	−0.00106015	−	0.00137407i
$516$		0			0
$517$	−1.64226	+	15.6251i	−0.0722267	+	0.687191i
$518$	10.9620	+	18.9867i	0.481641	+	0.834227i
$519$		0			0
$520$	−5.66446	−	7.34178i	−0.248403	−	0.321958i
$521$	−9.38013	+	6.81506i	−0.410951	+	0.298573i	−0.773987	−	0.633202i	$-0.781740\pi$
$521$	−9.38013	+	6.81506i	−0.410951	+	0.298573i	0.363036	+	0.931775i	$0.381740\pi$
$522$		0			0
$523$	−2.58596	−	7.95877i	−0.113076	−	0.348013i	0.878465	−	0.477807i	$-0.158568\pi$
$523$	−2.58596	−	7.95877i	−0.113076	−	0.348013i	−0.991541	+	0.129794i	$0.958568\pi$
$524$	−8.86849	+	15.3607i	−0.387422	+	0.671034i
$525$		0			0
$526$	4.54717	+	7.87592i	0.198266	+	0.343407i
$527$	2.97106	−	3.29970i	0.129421	−	0.143737i
$528$		0			0
$529$	1.12772	+	10.7295i	0.0490311	+	0.466500i
$530$	21.9141	+	1.66637i	0.951890	+	0.0723827i
$531$		0			0
$532$	−23.9137			−1.03679
$533$	−9.81431	+	4.36961i	−0.425105	+	0.189269i
$534$		0			0
$535$	6.55971	+	3.53920i	0.283601	+	0.153013i
$536$	13.4723	−	14.9625i	0.581916	−	0.646283i
$537$		0			0
$538$	−20.1683	−	22.3991i	−0.869516	−	0.965695i
$539$	18.4245	+	56.7048i	0.793600	+	2.44245i
$540$		0			0
$541$	6.73533	−	20.7292i	0.289575	−	0.891219i	−0.695416	−	0.718608i	$-0.744780\pi$
$541$	6.73533	−	20.7292i	0.289575	−	0.891219i	0.984990	−	0.172611i	$-0.0552203\pi$
$542$	−21.1721	+	9.42641i	−0.909418	+	0.404899i
$543$		0			0
$544$	0.738137	−	7.02291i	0.0316474	−	0.301105i
$545$	−4.63470	+	4.42152i	−0.198529	+	0.189397i
$546$		0			0
$547$	−3.48938	−	33.1992i	−0.149195	−	1.41950i	−0.771255	−	0.636526i	$-0.780371\pi$
$547$	−3.48938	−	33.1992i	−0.149195	−	1.41950i	0.622060	−	0.782969i	$-0.286296\pi$
$548$	4.93071	+	15.1752i	0.210630	+	0.648251i
$549$		0			0
$550$	−7.61609	−	46.4930i	−0.324751	−	1.98247i
$551$	12.6648	−	21.9361i	0.539538	−	0.934508i
$552$		0			0
$553$	−11.0903	−	4.93773i	−0.471609	−	0.209974i
$554$	41.4704	+	18.4638i	1.76191	+	0.784453i
$555$		0			0
$556$	−9.51551	+	4.23658i	−0.403548	+	0.179671i
$557$	−0.351013			−0.0148729			−0.00743646	−	0.999972i	$-0.502367\pi$
$557$	−0.351013			−0.0148729			−0.00743646	+	0.999972i	$0.502367\pi$
$558$		0			0
$559$	3.12500	−	9.61776i	0.132173	−	0.406788i
$560$	−45.3677	−	13.3081i	−1.91713	−	0.562370i
$561$		0			0
$562$	−42.2731	+	8.98542i	−1.78318	+	0.379027i
$563$	6.71206	−	1.42669i	0.282879	−	0.0601279i	−0.0642869	−	0.997931i	$-0.520477\pi$
$563$	6.71206	−	1.42669i	0.282879	−	0.0601279i	0.347166	+	0.937804i	$0.387144\pi$
$564$		0			0
$565$	17.2756	+	5.06762i	0.726792	+	0.213196i
$566$	7.66881	−	23.6022i	0.322344	−	0.992073i
$567$		0			0
$568$	−11.7878			−0.494607
$569$	−13.8450	+	6.16417i	−0.580411	+	0.258416i	−0.675874	−	0.737017i	$-0.736234\pi$
$569$	−13.8450	+	6.16417i	−0.580411	+	0.258416i	0.0954629	+	0.995433i	$0.469567\pi$
$570$		0			0
$571$	36.1997	+	16.1171i	1.51491	+	0.674481i	0.984839	−	0.173473i	$-0.0554989\pi$
$571$	36.1997	+	16.1171i	1.51491	+	0.674481i	0.530070	+	0.847954i	$0.322166\pi$
$572$	11.1907	+	4.98241i	0.467906	+	0.208325i
$573$		0			0
$574$	−16.8333	+	29.1561i	−0.702609	+	1.21695i
$575$	−17.2715	−	2.64196i	−0.720272	−	0.110177i
$576$		0			0
$577$	−3.56209	−	10.9630i	−0.148292	−	0.456396i	0.849128	−	0.528188i	$-0.177128\pi$
$577$	−3.56209	−	10.9630i	−0.148292	−	0.456396i	−0.997420	+	0.0717920i	$0.977128\pi$
$578$	−2.70493	−	25.7357i	−0.112510	−	1.07046i
$579$		0			0
$580$	−6.72447	+	6.41517i	−0.279218	+	0.266375i
$581$	3.01848	−	28.7189i	0.125228	−	1.19146i
$582$		0			0
$583$	28.5519	−	12.7121i	1.18250	−	0.526483i
$584$	2.14481	−	6.60104i	0.0887528	−	0.273153i
$585$		0			0
$586$	−3.56038	−	10.9577i	−0.147078	−	0.452659i
$587$	26.2637	+	29.1688i	1.08402	+	1.20393i	0.977791	+	0.209583i	$0.0672108\pi$
$587$	26.2637	+	29.1688i	1.08402	+	1.20393i	0.106228	+	0.994342i	$0.466123\pi$
$588$		0			0
$589$	12.4343	−	13.8097i	0.512347	−	0.569019i
$590$	39.2816	+	21.1938i	1.61720	+	0.872537i
$591$		0			0
$592$	−13.7496	+	6.12171i	−0.565105	+	0.251601i
$593$	2.11729			0.0869465			0.0434733	−	0.999055i	$-0.486158\pi$
$593$	2.11729			0.0869465			0.0434733	+	0.999055i	$0.486158\pi$
$594$		0			0
$595$	13.2274	+	1.00583i	0.542271	+	0.0412349i
$596$	0.992157	+	9.43975i	0.0406403	+	0.386667i
$597$		0			0
$598$	9.35215	−	10.3866i	0.382438	−	0.424740i
$599$	1.13371	+	1.96364i	0.0463219	+	0.0802320i	0.888257	−	0.459347i	$-0.151917\pi$
$599$	1.13371	+	1.96364i	0.0463219	+	0.0802320i	−0.841935	+	0.539579i	$0.818583\pi$
$600$		0			0
$601$	17.8254	−	30.8745i	0.727113	−	1.25940i	−0.230985	−	0.972957i	$-0.574195\pi$
$601$	17.8254	−	30.8745i	0.727113	−	1.25940i	0.958098	−	0.286440i	$-0.0924718\pi$
$602$	−9.79310	−	30.1401i	−0.399137	−	1.22842i
$603$		0			0
$604$	14.1380	−	10.2719i	0.575269	−	0.417957i
$605$	−25.9016	−	33.5714i	−1.05305	−	1.36487i
$606$		0			0
$607$	−12.5954	−	21.8159i	−0.511231	−	0.885478i	−0.999915	−	0.0130175i	$-0.995856\pi$
$607$	−12.5954	−	21.8159i	−0.511231	−	0.885478i	0.488684	−	0.872461i	$-0.337477\pi$
$608$	3.08921	−	29.3919i	0.125284	−	1.19200i
$609$		0			0
$610$	25.4890	+	33.0366i	1.03202	+	1.33761i
$611$	2.06082	+	6.34257i	0.0833720	+	0.256593i
$612$		0			0
$613$	−13.2971	+	40.9242i	−0.537063	+	1.65291i	0.202085	+	0.979368i	$0.435228\pi$
$613$	−13.2971	+	40.9242i	−0.537063	+	1.65291i	−0.739148	+	0.673543i	$0.764772\pi$
$614$	5.49123	+	1.16720i	0.221608	+	0.0471043i
$615$		0			0
$616$	−40.4224	+	8.59204i	−1.62866	+	0.346183i
$617$	3.34729	−	31.8474i	0.134757	−	1.28213i	−0.692958	−	0.720978i	$-0.743693\pi$
$617$	3.34729	−	31.8474i	0.134757	−	1.28213i	0.827715	−	0.561149i	$-0.189640\pi$
$618$		0			0
$619$	−11.9559	+	5.32313i	−0.480550	+	0.213955i	−0.632691	−	0.774404i	$-0.718050\pi$
$619$	−11.9559	+	5.32313i	−0.480550	+	0.213955i	0.152141	+	0.988359i	$0.451383\pi$
$620$	−5.80406	+	3.57788i	−0.233096	+	0.143691i
$621$		0			0
$622$	44.8848	−	32.6107i	1.79972	−	1.30757i
$623$	−18.9419	−	4.02622i	−0.758890	−	0.161307i
$624$		0			0
$625$	−9.92623	+	22.9449i	−0.397049	+	0.917797i
$626$	−17.6658	−	30.5980i	−0.706067	−	1.22294i
$627$		0			0
$628$	−0.268015	−	2.54999i	−0.0106949	−	0.101756i
$629$	3.41644	−	2.48219i	0.136222	−	0.0989713i
$630$		0			0
$631$	34.4722	+	25.0455i	1.37232	+	0.997047i	0.997552	+	0.0699268i	$0.0222766\pi$
$631$	34.4722	+	25.0455i	1.37232	+	0.997047i	0.374765	+	0.927120i	$0.377723\pi$
$632$	2.56119	−	4.43612i	0.101879	−	0.176459i
$633$		0			0
$634$	6.73496	−	1.43156i	0.267479	−	0.0568545i
$635$	−1.91003	+	10.4599i	−0.0757972	+	0.415089i
$636$		0			0
$637$	16.9346	+	18.8078i	0.670973	+	0.745191i
$638$	−12.5649	+	38.6708i	−0.497450	+	1.53099i
$639$		0			0
$640$	10.5087	−	25.5613i	0.415394	−	1.01040i
$641$	1.78356	+	1.98084i	0.0704464	+	0.0782386i	0.777338	−	0.629084i	$-0.216570\pi$
$641$	1.78356	+	1.98084i	0.0704464	+	0.0782386i	−0.706891	+	0.707322i	$0.749903\pi$
$642$		0			0
$643$	19.1382	+	33.1483i	0.754736	+	1.30724i	0.945505	+	0.325607i	$0.105569\pi$
$643$	19.1382	+	33.1483i	0.754736	+	1.30724i	−0.190769	+	0.981635i	$0.561098\pi$
$644$	1.48815	−	14.1588i	0.0586412	−	0.557934i
$645$		0			0
$646$	1.48128	+	14.0935i	0.0582803	+	0.554500i
$647$	−29.1546	+	21.1821i	−1.14619	+	0.832753i	−0.987969	−	0.154651i	$-0.950575\pi$
$647$	−29.1546	+	21.1821i	−1.14619	+	0.832753i	−0.158217	+	0.987404i	$0.550575\pi$
$648$		0			0
$649$	63.4743			2.49158
$650$	−10.9803	−	16.7139i	−0.430682	−	0.655574i
$651$		0			0
$652$	2.48629	−	2.76131i	0.0973708	−	0.108141i
$653$	−25.9936	−	11.5731i	−1.01721	−	0.452890i	−0.170732	−	0.985318i	$-0.554613\pi$
$653$	−25.9936	−	11.5731i	−1.01721	−	0.452890i	−0.846476	+	0.532428i	$0.821280\pi$
$654$		0			0
$655$	23.2339	−	33.9978i	0.907824	−	1.32841i
$656$	−18.6981	−	13.5850i	−0.730039	−	0.530405i
$657$		0			0
$658$	16.9078	+	12.2842i	0.659134	+	0.478889i
$659$	21.6918	+	24.0912i	0.844993	+	0.938460i	0.998767	−	0.0496464i	$-0.0158094\pi$
$659$	21.6918	+	24.0912i	0.844993	+	0.938460i	−0.153774	+	0.988106i	$0.549143\pi$
$660$		0			0
$661$	31.0769	−	34.5144i	1.20875	−	1.34245i	0.285443	−	0.958396i	$-0.407859\pi$
$661$	31.0769	−	34.5144i	1.20875	−	1.34245i	0.923309	−	0.384059i	$-0.125474\pi$
$662$	2.48201	−	0.527567i	0.0964660	−	0.0205045i
$663$		0			0
$664$	11.9184	+	2.53332i	0.462522	+	0.0983120i
$665$	55.3587	+	4.20953i	2.14672	+	0.163239i
$666$		0			0
$667$	12.1997	+	8.86361i	0.472375	+	0.343200i
$668$	−5.06279	+	8.76900i	−0.195885	+	0.339283i
$669$		0			0
$670$	31.4174	−	29.9723i	1.21376	−	1.15793i
$671$	54.2090	+	24.1354i	2.09272	+	0.931737i
$672$		0			0
$673$	−5.72623	−	1.21715i	−0.220730	−	0.0469176i	0.0962191	−	0.995360i	$-0.469325\pi$
$673$	−5.72623	−	1.21715i	−0.220730	−	0.0469176i	−0.316949	+	0.948443i	$0.602658\pi$
$674$	16.0430			0.617953
$675$		0			0
$676$	−7.32129			−0.281588
$677$	19.4462	+	4.13342i	0.747379	+	0.158860i	0.565830	−	0.824522i	$-0.308556\pi$
$677$	19.4462	+	4.13342i	0.747379	+	0.158860i	0.181549	+	0.983382i	$0.441889\pi$
$678$		0			0
$679$	53.4307	+	23.7889i	2.05048	+	0.912934i
$680$	−1.00548	+	5.50634i	−0.0385585	+	0.211158i
$681$		0			0
$682$	−14.9152	+	25.8340i	−0.571134	+	0.989233i
$683$	36.4251	+	26.4644i	1.39377	+	1.01263i	0.995440	+	0.0953885i	$0.0304093\pi$
$683$	36.4251	+	26.4644i	1.39377	+	1.01263i	0.398328	+	0.917243i	$0.369591\pi$
$684$		0			0
$685$	−8.74299	−	35.9975i	−0.334053	−	1.37539i
$686$	27.7224	+	5.89258i	1.05845	+	0.224980i
$687$		0			0
$688$	21.2806	−	4.52332i	0.811314	−	0.172450i
$689$	8.87700	−	9.85891i	0.338187	−	0.375595i
$690$		0			0
$691$	0.672969	+	0.747407i	0.0256009	+	0.0284327i	0.755809	−	0.654792i	$-0.227244\pi$
$691$	0.672969	+	0.747407i	0.0256009	+	0.0284327i	−0.730208	+	0.683225i	$0.760577\pi$
$692$	4.79031	+	3.48036i	0.182100	+	0.132304i
$693$		0			0
$694$	9.29844	+	6.75571i	0.352964	+	0.256443i
$695$	22.7735	−	8.13239i	0.863850	−	0.308479i
$696$		0			0
$697$	5.92416	+	2.63761i	0.224394	+	0.0999065i
$698$	5.00364	−	5.55710i	0.189390	−	0.210339i
$699$		0			0
$700$	−19.0557	−	7.19938i	−0.720238	−	0.272111i
$701$	8.14396			0.307593			0.153797	−	0.988103i	$-0.450850\pi$
$701$	8.14396			0.307593			0.153797	+	0.988103i	$0.450850\pi$
$702$		0			0
$703$	14.2983	−	10.3883i	0.539270	−	0.391803i
$704$	−0.761121	−	7.24158i	−0.0286858	−	0.272927i
$705$		0			0
$706$	0.832480	−	7.92052i	0.0313308	−	0.298093i
$707$	18.1604	+	31.4547i	0.682992	+	1.18298i
$708$		0			0
$709$	27.5012	+	30.5431i	1.03283	+	1.14707i	0.988982	+	0.148033i	$0.0472941\pi$
$709$	27.5012	+	30.5431i	1.03283	+	1.14707i	0.0438449	+	0.999038i	$0.486039\pi$
$710$	−25.3485	−	1.92752i	−0.951312	−	0.0723387i
$711$		0			0
$712$	2.52499	−	7.77112i	0.0946279	−	0.291235i
$713$	7.40263	+	8.22145i	0.277231	+	0.307896i
$714$		0			0
$715$	−25.0286	−	13.5038i	−0.936018	−	0.505015i
$716$	−6.78586	+	1.44238i	−0.253600	+	0.0539042i
$717$		0			0
$718$	7.76100	−	13.4424i	0.289638	−	0.501668i
$719$	−39.3653	−	28.6006i	−1.46808	−	1.06662i	−0.981165	−	0.193173i	$-0.938122\pi$
$719$	−39.3653	−	28.6006i	−1.46808	−	1.06662i	−0.486915	−	0.873449i	$-0.661878\pi$
$720$		0			0
$721$	−0.0602751	+	0.0437924i	−0.00224476	+	0.00163091i
$722$	2.78066	+	26.4562i	0.103485	+	0.984597i
$723$		0			0
$724$	−10.9369	−	18.9433i	−0.406468	−	0.704023i
$725$	16.6960	−	13.6670i	0.620073	−	0.507579i
$726$		0			0
$727$	−38.1966	−	8.11893i	−1.41663	−	0.301115i	−0.564929	−	0.825139i	$-0.691097\pi$
$727$	−38.1966	−	8.11893i	−1.41663	−	0.301115i	−0.851703	+	0.524025i	$0.824430\pi$
$728$	−14.1914	+	10.3107i	−0.525968	+	0.382138i
$729$		0			0
$730$	5.69157	−	13.8441i	0.210654	−	0.512393i
$731$	−5.57654	+	2.48284i	−0.206256	+	0.0918310i
$732$		0			0
$733$	−0.0804066	+	0.765018i	−0.00296989	+	0.0282566i	−0.995906	−	0.0903896i	$-0.971189\pi$
$733$	−0.0804066	+	0.765018i	−0.00296989	+	0.0282566i	0.992937	+	0.118646i	$0.0378554\pi$
$734$	−15.5870	+	3.31313i	−0.575328	+	0.122290i
$735$		0			0
$736$	17.2100	+	3.65810i	0.634370	+	0.134839i
$737$	19.0815	−	58.7268i	0.702876	−	2.16323i
$738$		0			0
$739$	16.0888	+	49.5162i	0.591835	+	1.82148i	0.569888	+	0.821723i	$0.306987\pi$
$739$	16.0888	+	49.5162i	0.591835	+	1.82148i	0.0219476	+	0.999759i	$0.493013\pi$
$740$	−6.10696	+	2.18078i	−0.224496	+	0.0801672i
$741$		0			0
$742$	4.34570	−	41.3466i	0.159536	−	1.51788i
$743$	−19.6551	−	34.0437i	−0.721076	−	1.24894i	−0.960569	−	0.278043i	$-0.910314\pi$
$743$	−19.6551	−	34.0437i	−0.721076	−	1.24894i	0.239492	−	0.970898i	$-0.423019\pi$
$744$		0			0
$745$	−0.635101	−	22.0270i	−0.0232683	−	0.807008i
$746$	−7.54594	+	5.48244i	−0.276276	+	0.200727i
$747$		0			0
$748$	−2.28494	−	7.03234i	−0.0835458	−	0.257128i
$749$	7.04991	−	12.2108i	0.257598	−	0.446173i
$750$		0			0
$751$	19.8565	+	34.3925i	0.724575	+	1.25500i	0.959149	+	0.282903i	$0.0912973\pi$
$751$	19.8565	+	34.3925i	0.724575	+	1.25500i	−0.234573	+	0.972098i	$0.575369\pi$
$752$	−9.60021	+	10.6621i	−0.350084	+	0.388807i
$753$		0			0
$754$	1.80410	+	17.1649i	0.0657016	+	0.625109i
$755$	−34.5368	+	21.2900i	−1.25692	+	0.774824i
$756$		0			0
$757$	−30.6481			−1.11392			−0.556961	−	0.830538i	$-0.688033\pi$
$757$	−30.6481			−1.11392			−0.556961	+	0.830538i	$0.688033\pi$
$758$	14.0242	−	6.24398i	0.509382	−	0.226792i
$759$		0			0
$760$	−4.20809	+	23.0448i	−0.152644	+	0.835924i
$761$	12.5617	−	13.9511i	0.455360	−	0.505729i	−0.471122	−	0.882068i	$-0.656151\pi$
$761$	12.5617	−	13.9511i	0.455360	−	0.505729i	0.926482	+	0.376340i	$0.122817\pi$
$762$		0			0
$763$	8.10797	+	9.00481i	0.293528	+	0.325996i
$764$	3.19405	+	9.83029i	0.115557	+	0.355647i
$765$		0			0
$766$	−9.81472	+	30.2066i	−0.354620	+	1.09141i
$767$	24.6138	−	10.9588i	0.888752	−	0.395698i
$768$		0			0
$769$	3.95016	−	37.5833i	0.142446	−	1.35529i	−0.656700	−	0.754152i	$-0.728048\pi$
$769$	3.95016	−	37.5833i	0.142446	−	1.35529i	0.799147	−	0.601136i	$-0.205285\pi$
$770$	−88.3289	+	11.8665i	−3.18315	+	0.427638i
$771$		0			0
$772$	1.50921	+	14.3591i	0.0543175	+	0.516796i
$773$	8.44199	+	25.9818i	0.303637	+	0.934500i	0.980182	+	0.198098i	$0.0634765\pi$
$773$	8.44199	+	25.9818i	0.303637	+	0.934500i	−0.676545	+	0.736401i	$0.736524\pi$
$774$		0			0
$775$	14.0658	−	7.26087i	0.505259	−	0.260818i
$776$	−12.3393	+	21.3722i	−0.442954	+	0.767219i
$777$		0			0
$778$	−19.9278	−	8.87241i	−0.714445	−	0.318091i
$779$	24.7935	+	11.0388i	0.888318	+	0.395505i
$780$		0			0
$781$	−33.0265	+	14.7044i	−1.18178	+	0.526164i
$782$	−8.43660			−0.301692
$783$		0			0
$784$	−16.8251	+	51.7823i	−0.600896	+	1.84937i
$785$	0.171562	+	5.95023i	0.00612330	+	0.212373i
$786$		0			0
$787$	15.6555	−	3.32767i	0.558057	−	0.118619i	0.0797556	−	0.996814i	$-0.474586\pi$
$787$	15.6555	−	3.32767i	0.558057	−	0.118619i	0.478301	+	0.878196i	$0.341253\pi$
$788$	−7.48226	+	1.59040i	−0.266544	+	0.0566557i
$789$		0			0
$790$	6.23295	−	9.12059i	0.221759	−	0.324496i
$791$	10.5242	−	32.3902i	0.374198	−	1.15166i
$792$		0			0
$793$	25.1879			0.894448
$794$	9.82887	−	4.37610i	0.348814	−	0.155302i
$795$		0			0
$796$	−12.4165	−	5.52819i	−0.440092	−	0.195942i
$797$	15.8206	+	7.04381i	0.560396	+	0.249504i	0.667331	−	0.744762i	$-0.267437\pi$
$797$	15.8206	+	7.04381i	0.560396	+	0.249504i	−0.106934	+	0.994266i	$0.534103\pi$
$798$		0			0
$799$	2.01278	−	3.48623i	0.0712070	−	0.123334i
$800$	11.3103	−	22.4910i	0.399878	−	0.795176i
$801$		0			0
$802$	−14.2173	−	43.7563i	−0.502029	−	1.54509i
$803$	−2.22505	−	21.1699i	−0.0785202	−	0.747070i
$804$		0			0
$805$	−5.93733	+	32.5147i	−0.209263	+	1.14599i
$806$	−1.32356	+	12.5929i	−0.0466205	+	0.443565i
$807$		0			0
$808$	−14.0005	+	6.23342i	−0.492536	+	0.219291i
$809$	−3.76845	+	11.5981i	−0.132492	+	0.407767i	−0.995191	−	0.0979492i	$-0.968772\pi$
$809$	−3.76845	+	11.5981i	−0.132492	+	0.407767i	0.862700	+	0.505716i	$0.168772\pi$
$810$		0			0
$811$	1.10851	+	3.41163i	0.0389249	+	0.119799i	0.968631	−	0.248504i	$-0.0799390\pi$
$811$	1.10851	+	3.41163i	0.0389249	+	0.119799i	−0.929706	+	0.368303i	$0.879939\pi$
$812$	11.7638	+	13.0651i	0.412829	+	0.458493i
$813$		0			0
$814$	−18.9839	+	21.0838i	−0.665387	+	0.738987i
$815$	−6.24168	+	5.95459i	−0.218637	+	0.208580i
$816$		0			0
$817$	−23.3386	+	10.3910i	−0.816516	+	0.363536i
$818$	−41.1810			−1.43986
$819$		0			0
$820$	−7.58913	−	6.44709i	−0.265024	−	0.225142i
$821$	−0.975788	−	9.28401i	−0.0340552	−	0.324014i	−0.998265	−	0.0588748i	$-0.981249\pi$
$821$	−0.975788	−	9.28401i	−0.0340552	−	0.324014i	0.964210	−	0.265139i	$-0.0854179\pi$
$822$		0			0
$823$	−32.2029	+	35.7650i	−1.12252	+	1.24669i	−0.156656	+	0.987653i	$0.550071\pi$
$823$	−32.2029	+	35.7650i	−1.12252	+	1.24669i	−0.965868	+	0.259035i	$0.916595\pi$
$824$	−0.0157184	−	0.0272251i	−0.000547576	−	0.000948430i
$825$		0			0
$826$	42.2171	−	73.1221i	1.46892	−	2.54424i
$827$	−8.29286	−	25.5228i	−0.288371	−	0.887515i	−0.985368	−	0.170441i	$-0.945481\pi$
$827$	−8.29286	−	25.5228i	−0.288371	−	0.887515i	0.696997	−	0.717074i	$-0.254519\pi$
$828$		0			0
$829$	−27.4122	+	19.9161i	−0.952065	+	0.691716i	−0.951294	−	0.308284i	$-0.900245\pi$
$829$	−27.4122	+	19.9161i	−0.952065	+	0.691716i	−0.000770971		1.00000i	$0.500245\pi$
$830$	25.2149	+	7.39650i	0.875221	+	0.256736i
$831$		0			0
$832$	−1.54539	−	2.67670i	−0.0535769	−	0.0927979i
$833$	1.59686	−	15.1931i	0.0553278	−	0.526408i
$834$		0			0
$835$	13.2636	−	19.4085i	0.459007	−	0.671658i
$836$	−9.56283	−	29.4314i	−0.330737	−	1.01790i
$837$		0			0
$838$	−6.67399	+	20.5404i	−0.230549	+	0.709558i
$839$	−17.6290	−	3.74715i	−0.608620	−	0.129366i	−0.106716	−	0.994290i	$-0.534034\pi$
$839$	−17.6290	−	3.74715i	−0.608620	−	0.129366i	−0.501904	+	0.864923i	$0.667367\pi$
$840$		0			0
$841$	10.1515	−	2.15778i	0.350053	−	0.0744061i
$842$	−0.212354	+	2.02041i	−0.00731820	+	0.0696280i
$843$		0			0
$844$	6.44262	−	2.86844i	0.221764	−	0.0987358i
$845$	16.9483	+	1.28877i	0.583039	+	0.0443349i
$846$		0			0
$847$	−64.8923	+	47.1470i	−2.22973	+	1.61999i
$848$	27.9171	+	5.93397i	0.958679	+	0.203773i
$849$		0			0
$850$	−3.06257	+	11.6764i	−0.105045	+	0.400496i
$851$	5.26090	+	9.11215i	0.180341	+	0.312361i
$852$		0			0
$853$	−4.26725	−	40.6001i	−0.146108	−	1.39012i	−0.784365	−	0.620299i	$-0.787011\pi$
$853$	−4.26725	−	40.6001i	−0.146108	−	1.39012i	0.638257	−	0.769823i	$-0.279656\pi$
$854$	63.8586	−	46.3960i	2.18520	−	1.58764i
$855$		0			0
$856$	4.81315	+	3.49696i	0.164510	+	0.119524i
$857$	0.284511	−	0.492787i	0.00971870	−	0.0168333i	−0.861125	−	0.508393i	$-0.830240\pi$
$857$	0.284511	−	0.492787i	0.00971870	−	0.0168333i	0.870844	+	0.491560i	$0.163573\pi$
$858$		0			0
$859$	−34.4947	+	7.33208i	−1.17695	+	0.250167i	−0.754549	−	0.656244i	$-0.772144\pi$
$859$	−34.4947	+	7.33208i	−1.17695	+	0.250167i	−0.422396	+	0.906411i	$0.638811\pi$
$860$	9.29013	−	1.24807i	0.316791	−	0.0425590i
$861$		0			0
$862$	28.9420	+	32.1434i	0.985769	+	1.09481i
$863$	−7.48769	+	23.0447i	−0.254884	+	0.784452i	0.738968	+	0.673740i	$0.235313\pi$
$863$	−7.48769	+	23.0447i	−0.254884	+	0.784452i	−0.993852	+	0.110712i	$0.964687\pi$
$864$		0			0
$865$	−10.4766	−	8.90005i	−0.356215	−	0.302611i
$866$	23.0468	+	25.5960i	0.783161	+	0.869789i
$867$		0			0
$868$	6.44898	+	11.1700i	0.218893	+	0.379133i
$869$	1.64212	−	15.6237i	0.0557052	−	0.529999i
$870$		0			0
$871$	−2.73977	−	26.0672i	−0.0928337	−	0.883254i
$872$	−4.13635	+	3.00523i	−0.140074	+	0.101770i
$873$		0			0
$874$	−35.3084			−1.19433
$875$	42.8454	+	20.0205i	1.44844	+	0.676815i
$876$		0			0
$877$	−32.8680	+	36.5036i	−1.10987	+	1.23264i	−0.139710	+	0.990193i	$0.544617\pi$
$877$	−32.8680	+	36.5036i	−1.10987	+	1.23264i	−0.970165	+	0.242448i	$0.922050\pi$
$878$	35.6533	+	15.8739i	1.20324	+	0.535717i
$879$		0			0
$880$	−1.76333	−	61.1572i	−0.0594419	−	2.06161i
$881$	9.93477	+	7.21804i	0.334711	+	0.243182i	0.742427	−	0.669927i	$-0.233675\pi$
$881$	9.93477	+	7.21804i	0.334711	+	0.243182i	−0.407716	+	0.913109i	$0.633675\pi$
$882$		0			0
$883$	−40.0558	−	29.1022i	−1.34798	−	0.979367i	−0.999109	−	0.0421976i	$-0.986564\pi$
$883$	−40.0558	−	29.1022i	−1.34798	−	0.979367i	−0.348874	−	0.937170i	$-0.613436\pi$
$884$	−2.10017	−	2.33247i	−0.0706363	−	0.0784496i
$885$		0			0
$886$	−5.71992	+	6.35262i	−0.192165	+	0.213420i
$887$	−46.9880	+	9.98760i	−1.57770	+	0.335351i	−0.911783	−	0.410673i	$-0.865294\pi$
$887$	−46.9880	+	9.98760i	−1.57770	+	0.335351i	−0.665919	+	0.746024i	$0.731960\pi$
$888$		0			0
$889$	19.6745	+	4.18195i	0.659862	+	0.140258i
$890$	6.70043	−	16.2981i	0.224599	−	0.546312i
$891$		0			0
$892$	15.8497	+	11.5155i	0.530688	+	0.385568i
$893$	8.42377	−	14.5904i	0.281891	−	0.488249i
$894$		0			0
$895$	15.9627	−	2.14450i	0.533575	−	0.0716827i
$896$	−47.7609	−	21.2645i	−1.59558	−	0.710399i
$897$		0			0
$898$	−29.9180	−	6.35927i	−0.998376	−	0.212211i
$899$	−13.6616			−0.455640
$900$		0			0
$901$	−8.00797			−0.266784
$902$	−42.6148	−	9.05806i	−1.41892	−	0.301600i
$903$		0			0
$904$	13.1279	+	5.84493i	0.436628	+	0.194399i
$905$	21.9837	+	45.7778i	0.730763	+	1.52171i
$906$		0			0
$907$	−4.54408	+	7.87058i	−0.150884	+	0.261338i	−0.931553	−	0.363607i	$-0.881545\pi$
$907$	−4.54408	+	7.87058i	−0.150884	+	0.261338i	0.780669	+	0.624945i	$0.214879\pi$
$908$	−16.9587	−	12.3212i	−0.562794	−	0.408894i
$909$		0			0
$910$	−32.2030	+	19.8514i	−1.06752	+	0.658067i
$911$	2.29989	+	0.488856i	0.0761987	+	0.0161965i	0.245853	−	0.969307i	$-0.420932\pi$
$911$	2.29989	+	0.488856i	0.0761987	+	0.0161965i	−0.169655	+	0.985504i	$0.554265\pi$
$912$		0			0
$913$	36.5523	−	7.76943i	1.20970	−	0.257131i
$914$	−23.0759	+	25.6284i	−0.763282	+	0.847711i
$915$		0			0
$916$	−12.1035	−	13.4422i	−0.399909	−	0.444144i
$917$	−63.0198	−	45.7866i	−2.08110	−	1.51201i
$918$		0			0
$919$	−35.1878	−	25.5654i	−1.16074	−	0.843325i	−0.170866	−	0.985294i	$-0.554657\pi$
$919$	−35.1878	−	25.5654i	−1.16074	−	0.843325i	−0.989871	+	0.141969i	$0.954657\pi$
$920$	−13.3825	−	3.92559i	−0.441206	−	0.129423i
$921$		0			0
$922$	−19.8192	−	8.82409i	−0.652712	−	0.290606i
$923$	−10.2682	+	11.4040i	−0.337982	+	0.375367i
$924$		0			0
$925$	14.5211	−	3.97336i	0.477451	−	0.130643i
$926$	42.8642			1.40860
$927$		0			0
$928$	−17.5777	+	12.7709i	−0.577015	+	0.419226i
$929$	5.37815	+	51.1697i	0.176451	+	1.67882i	0.621576	+	0.783354i	$0.286493\pi$
$929$	5.37815	+	51.1697i	0.176451	+	1.67882i	−0.445125	+	0.895469i	$0.646841\pi$
$930$		0			0
$931$	6.68307	−	63.5852i	0.219029	−	2.08392i
$932$	3.08265	+	5.33931i	0.100976	+	0.174895i
$933$		0			0
$934$	42.2022	+	46.8703i	1.38090	+	1.53364i
$935$	4.05159	+	16.6816i	0.132501	+	0.545547i
$936$		0			0
$937$	−1.71388	+	5.27478i	−0.0559900	+	0.172320i	−0.975141	−	0.221587i	$-0.928876\pi$
$937$	−1.71388	+	5.27478i	−0.0559900	+	0.172320i	0.919151	+	0.393906i	$0.128876\pi$
$938$	−54.9618	−	61.0413i	−1.79457	−	1.99307i
$939$		0			0
$940$	−4.47267	+	4.26694i	−0.145882	+	0.139172i
$941$	34.3030	−	7.29133i	1.11825	−	0.237691i	0.388527	−	0.921437i	$-0.372984\pi$
$941$	34.3030	−	7.29133i	1.11825	−	0.237691i	0.729720	+	0.683746i	$0.239651\pi$
$942$		0			0
$943$	−8.07869	+	13.9927i	−0.263078	+	0.455665i
$944$	46.8939	+	34.0704i	1.52627	+	1.10890i
$945$		0			0
$946$	33.1782	−	24.1053i	1.07871	−	0.783732i
$947$	−5.85222	−	55.6801i	−0.190172	−	1.80936i	−0.508155	−	0.861265i	$-0.669672\pi$
$947$	−5.85222	−	55.6801i	−0.190172	−	1.80936i	0.317984	−	0.948096i	$-0.396994\pi$
$948$		0			0
$949$	−4.51778	−	7.82502i	−0.146653	−	0.254011i
$950$	−12.8173	+	48.8673i	−0.415848	+	1.58546i
$951$		0			0
$952$	10.3571	+	2.20147i	0.335676	+	0.0713502i
$953$	5.24619	−	3.81158i	0.169941	−	0.123469i	−0.499564	−	0.866277i	$-0.666506\pi$
$953$	5.24619	−	3.81158i	0.169941	−	0.123469i	0.669505	+	0.742808i	$0.266506\pi$
$954$		0			0
$955$	−5.66360	−	23.3187i	−0.183270	−	0.754576i
$956$	15.4751	−	6.88995i	0.500500	−	0.222837i
$957$		0			0
$958$	−1.31475	+	12.5090i	−0.0424777	+	0.404149i
$959$	−68.5443	+	14.5696i	−2.21341	+	0.470475i
$960$		0			0
$961$	20.5189	+	4.36143i	0.661900	+	0.140691i
$962$	−3.72141	+	11.4533i	−0.119983	+	0.369270i
$963$		0			0
$964$	2.26125	+	6.95941i	0.0728300	+	0.224148i
$965$	−0.966074	−	33.5061i	−0.0310990	−	1.07860i
$966$		0			0
$967$	−0.523420	+	4.98001i	−0.0168321	+	0.160146i	−0.999709	−	0.0241160i	$-0.992323\pi$
$967$	−0.523420	+	4.98001i	−0.0168321	+	0.160146i	0.982877	+	0.184262i	$0.0589896\pi$
$968$	−16.9225	−	29.3106i	−0.543909	−	0.942078i
$969$		0			0
$970$	−30.0290	+	43.9410i	−0.964173	+	1.41086i
$971$	40.8653	−	29.6904i	1.31143	−	0.952810i	0.311434	−	0.950268i	$-0.399191\pi$
$971$	40.8653	−	29.6904i	1.31143	−	0.952810i	0.999997	−	0.00254202i	$-0.000809152\pi$
$972$		0			0
$973$	−14.1359	−	43.5059i	−0.453177	−	1.39473i
$974$	−21.3261	+	36.9380i	−0.683333	+	1.18357i
$975$		0			0
$976$	27.0940	+	46.9281i	0.867257	+	1.50213i
$977$	−15.9615	+	17.7270i	−0.510653	+	0.567138i	−0.942242	−	0.334933i	$-0.891286\pi$
$977$	−15.9615	+	17.7270i	−0.510653	+	0.567138i	0.431589	+	0.902070i	$0.357953\pi$
$978$		0			0
$979$	−2.61945	−	24.9224i	−0.0837180	−	0.796523i
$980$	−8.91987	+	21.6966i	−0.284935	+	0.693072i
$981$		0			0
$982$	−35.1227			−1.12081
$983$	−8.65772	+	3.85467i	−0.276138	+	0.122945i	−0.540134	−	0.841579i	$-0.681626\pi$
$983$	−8.65772	+	3.85467i	−0.276138	+	0.122945i	0.263995	+	0.964524i	$0.414960\pi$
$984$		0			0
$985$	17.6009	−	2.36458i	0.560811	−	0.0753417i
$986$	6.97116	−	7.74226i	0.222007	−	0.246564i
$987$		0			0
$988$	−8.78951	−	9.76174i	−0.279632	−	0.310562i
$989$	−4.69993	−	14.4649i	−0.149449	−	0.459957i
$990$		0			0
$991$	8.47195	−	26.0740i	0.269120	−	0.828268i	−0.721595	−	0.692316i	$-0.756591\pi$
$991$	8.47195	−	26.0740i	0.269120	−	0.828268i	0.990715	−	0.135952i	$-0.0434093\pi$
$992$	−14.5619	+	6.48336i	−0.462340	+	0.205847i
$993$		0			0
$994$	−5.02675	+	47.8264i	−0.159439	+	1.51696i
$995$	27.7703	+	14.9831i	0.880378	+	0.474996i
$996$		0			0
$997$	−2.65815	−	25.2906i	−0.0841844	−	0.800961i	−0.952416	−	0.304802i	$-0.901410\pi$
$997$	−2.65815	−	25.2906i	−0.0841844	−	0.800961i	0.868232	−	0.496159i	$-0.165257\pi$
$998$	−11.4166	−	35.1366i	−0.361385	−	1.11223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.181.23		224
3.2	odd	2		225.2.q.a.106.6	yes	224
9.4	even	3	inner	675.2.r.a.631.6		224
9.5	odd	6		225.2.q.a.31.23	✓	224
25.21	even	5	inner	675.2.r.a.46.6		224
75.71	odd	10		225.2.q.a.196.23	yes	224
225.121	even	15	inner	675.2.r.a.496.23		224
225.221	odd	30		225.2.q.a.121.6	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.23	✓	224	9.5	odd	6
225.2.q.a.106.6	yes	224	3.2	odd	2
225.2.q.a.121.6	yes	224	225.221	odd	30
225.2.q.a.196.23	yes	224	75.71	odd	10
675.2.r.a.46.6		224	25.21	even	5	inner
675.2.r.a.181.23		224	1.1	even	1	trivial
675.2.r.a.496.23		224	225.121	even	15	inner
675.2.r.a.631.6		224	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68376 + 0.357895i) q^{2} +(0.879882 + 0.391749i) q^{4} +(-1.96791 - 1.06176i) q^{5} +(-2.11497 + 3.66323i) q^{7} +(-1.44394 - 1.04909i) q^{8} +(-2.93350 - 2.49206i) q^{10} +(-5.35421 - 1.13807i) q^{11} +(-2.27272 + 0.483081i) q^{13} +(-4.87216 + 5.41109i) q^{14} +(-3.34474 - 3.71472i) q^{16} +(1.13466 + 0.824379i) q^{17} +(4.74872 + 3.45015i) q^{19} +(-1.31559 - 1.70515i) q^{20} +(-8.60791 - 3.83249i) q^{22} +(-2.33826 + 2.59691i) q^{23} +(2.74534 + 4.17889i) q^{25} -3.99961 q^{26} +(-3.29599 + 2.39468i) q^{28} +(-0.451070 - 4.29164i) q^{29} +(0.330923 - 3.14852i) q^{31} +(-2.51747 - 4.36039i) q^{32} +(1.61546 + 1.79415i) q^{34} +(8.05154 - 4.96333i) q^{35} +(0.930443 - 2.86361i) q^{37} +(6.76093 + 7.50877i) q^{38} +(1.72767 + 3.59763i) q^{40} +(4.52265 - 0.961319i) q^{41} +(-2.17619 + 3.76927i) q^{43} +(-4.26523 - 3.09887i) q^{44} +(-4.86650 + 3.53572i) q^{46} +(-0.300021 - 2.85451i) q^{47} +(-5.44619 - 9.43308i) q^{49} +(3.12690 + 8.01881i) q^{50} +(-2.18897 - 0.465280i) q^{52} +(-4.61926 + 3.35609i) q^{53} +(9.32824 + 7.92450i) q^{55} +(6.89694 - 3.07072i) q^{56} +(0.776463 - 7.38755i) q^{58} +(-11.3426 + 2.41094i) q^{59} +(-10.6036 - 2.25387i) q^{61} +(1.68404 - 5.18293i) q^{62} +(0.411065 + 1.26513i) q^{64} +(4.98542 + 1.46242i) q^{65} +(-1.17916 + 11.2190i) q^{67} +(0.675418 + 1.16986i) q^{68} +(15.3332 - 5.47547i) q^{70} +(5.34318 - 3.88205i) q^{71} +(1.20170 + 3.69845i) q^{73} +(2.59152 - 4.48864i) q^{74} +(2.82672 + 4.89603i) q^{76} +(15.4930 - 17.2067i) q^{77} +(0.299995 + 2.85427i) q^{79} +(2.63803 + 10.8615i) q^{80} +7.95913 q^{82} +(-6.23662 + 2.77672i) q^{83} +(-1.35762 - 2.82704i) q^{85} +(-5.01319 + 5.56772i) q^{86} +(6.53724 + 7.26034i) q^{88} +(1.41471 + 4.35403i) q^{89} +(3.03709 - 9.34720i) q^{91} +(-3.07473 + 1.36896i) q^{92} +(0.516451 - 4.91370i) q^{94} +(-5.68183 - 11.8316i) q^{95} +(-1.44531 - 13.7512i) q^{97} +(-5.79405 - 17.8322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

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