LMFDB - Embedded newform 637.2.g.m.263.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.6
Root			$0.141226 + 0.244611i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.m.373.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760387 - 1.31703i) q^{2} +2.12621 q^{3} +(-0.156376 - 0.270851i) q^{4} +(0.294696 + 0.510428i) q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +1.52077 q^{9} +O(q^{10})$	\(q+(0.760387 - 1.31703i) q^{2} +2.12621 q^{3} +(-0.156376 - 0.270851i) q^{4} +(0.294696 + 0.510428i) q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +1.52077 q^{9} +0.896331 q^{10} +1.52077 q^{11} +(-0.332488 - 0.575886i) q^{12} +(-3.32565 - 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} +(2.26384 - 3.92109i) q^{16} +(2.39740 + 4.15241i) q^{17} +(1.15638 - 2.00290i) q^{18} -1.68391 q^{19} +(0.0921666 - 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +(-0.886972 + 1.53628i) q^{23} +5.45569 q^{24} +(2.32631 - 4.02929i) q^{25} +(-4.36321 + 3.32087i) q^{26} -3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +1.90579 q^{30} +(-3.04320 + 5.27098i) q^{31} +(-0.876873 - 1.51879i) q^{32} +3.23349 q^{33} +7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +(-0.704563 + 1.22034i) q^{37} +(-1.28043 + 2.21776i) q^{38} +(-7.07104 - 2.96150i) q^{39} +(0.756166 + 1.30972i) q^{40} +(0.677729 + 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +(-0.237812 - 0.411903i) q^{44} +(0.448165 + 0.776245i) q^{45} +(1.34888 + 2.33633i) q^{46} +(-0.232416 - 0.402556i) q^{47} +(4.81341 - 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} +(5.09737 + 8.82890i) q^{51} +(0.142796 + 1.11856i) q^{52} +(-4.12340 + 7.14194i) q^{53} +(-2.39153 + 4.14225i) q^{54} +(0.448165 + 0.776245i) q^{55} -3.58035 q^{57} -10.4819 q^{58} +(-5.93782 - 10.2846i) q^{59} +(0.195966 - 0.339422i) q^{60} -2.48017 q^{61} +(4.62802 + 8.01596i) q^{62} +6.38833 q^{64} +(-0.269104 - 2.10797i) q^{65} +(2.45870 - 4.25859i) q^{66} -7.57284 q^{67} +(0.749790 - 1.29867i) q^{68} +(-1.88589 + 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +3.90219 q^{72} +(-8.18558 + 14.1778i) q^{73} +(1.07148 + 1.85586i) q^{74} +(4.94622 - 8.56711i) q^{75} +(0.263323 + 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} +(7.48116 + 12.9577i) q^{79} +2.66858 q^{80} -11.2496 q^{81} +2.06134 q^{82} -10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +(-8.78973 - 15.2243i) q^{86} +(-7.32746 - 12.6915i) q^{87} +3.90219 q^{88} +(8.24250 - 14.2764i) q^{89} +1.36312 q^{90} +0.554804 q^{92} +(-6.47049 + 11.2072i) q^{93} -0.706904 q^{94} +(-0.496242 - 0.859516i) q^{95} +(-1.86442 - 3.22927i) q^{96} +(-0.486935 + 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.760387	−	1.31703i	0.537675	−	0.931280i	−0.461354	−	0.887216i	$-0.652636\pi$
$2$	0.760387	−	1.31703i	0.537675	−	0.931280i	0.999029	−	0.0440636i	$-0.0140304\pi$
$3$	2.12621			1.22757			0.613784	−	0.789474i	$-0.289646\pi$
$3$	2.12621			1.22757			0.613784	+	0.789474i	$0.289646\pi$
$4$	−0.156376	−	0.270851i	−0.0781880	−	0.135426i
$5$	0.294696	+	0.510428i	0.131792	+	0.228270i	0.924367	−	0.381504i	$-0.124594\pi$
$5$	0.294696	+	0.510428i	0.131792	+	0.228270i	−0.792575	+	0.609774i	$0.791260\pi$
$6$	1.61674	−	2.80028i	0.660032	−	1.14321i
$7$		0			0
$7$		0			0
$8$	2.56592			0.907190
$9$	1.52077			0.506924
$10$	0.896331			0.283445
$11$	1.52077			0.458530			0.229265	−	0.973364i	$-0.426368\pi$
$11$	1.52077			0.458530			0.229265	+	0.973364i	$0.426368\pi$
$12$	−0.332488	−	0.575886i	−0.0959811	−	0.166244i
$13$	−3.32565	−	1.39285i	−0.922370	−	0.386308i
$13$	−3.32565	−	1.39285i	−0.922370	−	0.386308i
$14$		0			0
$15$	0.626585	+	1.08528i	0.161784	+	0.280217i
$16$	2.26384	−	3.92109i	0.565961	−	0.980274i
$17$	2.39740	+	4.15241i	0.581454	+	1.00711i	0.995307	+	0.0967643i	$0.0308493\pi$
$17$	2.39740	+	4.15241i	0.581454	+	1.00711i	−0.413853	+	0.910344i	$0.635817\pi$
$18$	1.15638	−	2.00290i	0.272560	−	0.472088i
$19$	−1.68391			−0.386316			−0.193158	−	0.981168i	$-0.561873\pi$
$19$	−1.68391			−0.386316			−0.193158	+	0.981168i	$0.561873\pi$
$20$	0.0921666	−	0.159637i	0.0206091	−	0.0356960i
$21$		0			0
$22$	1.15638	−	2.00290i	0.246540	−	0.427020i
$23$	−0.886972	+	1.53628i	−0.184946	+	0.320337i	−0.943558	−	0.331206i	$-0.892544\pi$
$23$	−0.886972	+	1.53628i	−0.184946	+	0.320337i	0.758612	+	0.651543i	$0.225878\pi$
$24$	5.45569			1.11364
$25$	2.32631	−	4.02929i	0.465262	−	0.805857i
$26$	−4.36321	+	3.32087i	−0.855696	+	0.651276i
$27$	−3.14515			−0.605284
$28$		0			0
$29$	−3.44625	−	5.96909i	−0.639953	−	1.10843i	−0.985443	−	0.170009i	$-0.945620\pi$
$29$	−3.44625	−	5.96909i	−0.639953	−	1.10843i	0.345489	−	0.938423i	$-0.387713\pi$
$30$	1.90579			0.347948
$31$	−3.04320	+	5.27098i	−0.546575	+	0.946695i	0.451931	+	0.892053i	$0.350735\pi$
$31$	−3.04320	+	5.27098i	−0.546575	+	0.946695i	−0.998506	+	0.0546426i	$0.982598\pi$
$32$	−0.876873	−	1.51879i	−0.155011	−	0.268486i
$33$	3.23349			0.562878
$34$	7.29179			1.25053
$35$		0			0
$36$	−0.237812	−	0.411903i	−0.0396354	−	0.0686505i
$37$	−0.704563	+	1.22034i	−0.115830	+	0.200623i	−0.918111	−	0.396323i	$-0.870286\pi$
$37$	−0.704563	+	1.22034i	−0.115830	+	0.200623i	0.802282	+	0.596946i	$0.203619\pi$
$38$	−1.28043	+	2.21776i	−0.207712	+	0.359768i
$39$	−7.07104	−	2.96150i	−1.13227	−	0.474219i
$40$	0.756166	+	1.30972i	0.119560	+	0.207085i
$41$	0.677729	+	1.17386i	0.105843	+	0.183326i	0.914082	−	0.405528i	$-0.132912\pi$
$41$	0.677729	+	1.17386i	0.105843	+	0.183326i	−0.808239	+	0.588855i	$0.799579\pi$
$42$		0			0
$43$	5.77978	−	10.0109i	0.881408	−	1.52664i	0.0316319	−	0.999500i	$-0.489930\pi$
$43$	5.77978	−	10.0109i	0.881408	−	1.52664i	0.849776	−	0.527144i	$-0.176737\pi$
$44$	−0.237812	−	0.411903i	−0.0358516	−	0.0620967i
$45$	0.448165	+	0.776245i	0.0668085	+	0.115716i
$46$	1.34888	+	2.33633i	0.198882	+	0.344474i
$47$	−0.232416	−	0.402556i	−0.0339013	−	0.0587188i	0.848577	−	0.529072i	$-0.177460\pi$
$47$	−0.232416	−	0.402556i	−0.0339013	−	0.0587188i	−0.882478	+	0.470353i	$0.844127\pi$
$48$	4.81341	−	8.33707i	0.694756	−	1.20335i
$49$		0			0
$50$	−3.53779	−	6.12763i	−0.500319	−	0.866578i
$51$	5.09737	+	8.82890i	0.713775	+	1.23629i
$52$	0.142796	+	1.11856i	0.0198023	+	0.155117i
$53$	−4.12340	+	7.14194i	−0.566393	+	0.981021i	0.430526	+	0.902578i	$0.358328\pi$
$53$	−4.12340	+	7.14194i	−0.566393	+	0.981021i	−0.996919	+	0.0784430i	$0.975005\pi$
$54$	−2.39153	+	4.14225i	−0.325446	+	0.563689i
$55$	0.448165	+	0.776245i	0.0604306	+	0.104669i
$56$		0			0
$57$	−3.58035			−0.474230
$58$	−10.4819			−1.37635
$59$	−5.93782	−	10.2846i	−0.773038	−	1.33894i	−0.935890	−	0.352291i	$-0.885403\pi$
$59$	−5.93782	−	10.2846i	−0.773038	−	1.33894i	0.162852	−	0.986651i	$-0.447931\pi$
$60$	0.195966	−	0.339422i	0.0252991	−	0.0438193i
$61$	−2.48017			−0.317553			−0.158777	−	0.987315i	$-0.550755\pi$
$61$	−2.48017			−0.317553			−0.158777	+	0.987315i	$0.550755\pi$
$62$	4.62802	+	8.01596i	0.587759	+	1.01803i
$63$		0			0
$64$	6.38833			0.798541
$65$	−0.269104	−	2.10797i	−0.0333783	−	0.261462i
$66$	2.45870	−	4.25859i	0.302645	−	0.524196i
$67$	−7.57284			−0.925169			−0.462585	−	0.886575i	$-0.653078\pi$
$67$	−7.57284			−0.925169			−0.462585	+	0.886575i	$0.653078\pi$
$68$	0.749790	−	1.29867i	0.0909254	−	0.157487i
$69$	−1.88589	+	3.26646i	−0.227034	+	0.393235i
$70$		0			0
$71$	−3.30235	+	5.71984i	−0.391917	+	0.678821i	−0.992702	−	0.120590i	$-0.961521\pi$
$71$	−3.30235	+	5.71984i	−0.391917	+	0.678821i	0.600785	+	0.799411i	$0.294855\pi$
$72$	3.90219			0.459877
$73$	−8.18558	+	14.1778i	−0.958049	+	1.65939i	−0.230819	+	0.972997i	$0.574140\pi$
$73$	−8.18558	+	14.1778i	−0.958049	+	1.65939i	−0.727231	+	0.686393i	$0.759193\pi$
$74$	1.07148	+	1.85586i	0.124557	+	0.215739i
$75$	4.94622	−	8.56711i	0.571141	−	0.989245i
$76$	0.263323	+	0.456090i	0.0302053	+	0.0523171i
$77$		0			0
$78$	−9.27710	+	7.06087i	−1.05042	+	0.799486i
$79$	7.48116	+	12.9577i	0.841696	+	1.45786i	0.888460	+	0.458955i	$0.151776\pi$
$79$	7.48116	+	12.9577i	0.841696	+	1.45786i	−0.0467635	+	0.998906i	$0.514891\pi$
$80$	2.66858			0.298356
$81$	−11.2496			−1.24995
$82$	2.06134			0.227637
$83$	−10.1222			−1.11105			−0.555526	−	0.831499i	$-0.687483\pi$
$83$	−10.1222			−1.11105			−0.555526	+	0.831499i	$0.687483\pi$
$84$		0			0
$85$	−1.41300	+	2.44740i	−0.153262	+	0.265457i
$86$	−8.78973	−	15.2243i	−0.947821	−	1.64167i
$87$	−7.32746	−	12.6915i	−0.785586	−	1.36068i
$88$	3.90219			0.415974
$89$	8.24250	−	14.2764i	0.873703	−	1.51330i	0.0155650	−	0.999879i	$-0.495045\pi$
$89$	8.24250	−	14.2764i	0.873703	−	1.51330i	0.858138	−	0.513419i	$-0.171621\pi$
$90$	1.36312			0.143685
$91$		0			0
$92$	0.554804			0.0578423
$93$	−6.47049	+	11.2072i	−0.670958	+	1.16213i
$94$	−0.706904			−0.0729115
$95$	−0.496242	−	0.859516i	−0.0509133	−	0.0881845i
$96$	−1.86442	−	3.22927i	−0.190286	−	0.329586i
$97$	−0.486935	+	0.843396i	−0.0494407	+	0.0856338i	−0.889687	−	0.456572i	$-0.849077\pi$
$97$	−0.486935	+	0.843396i	−0.0494407	+	0.0856338i	0.840246	+	0.542205i	$0.182411\pi$
$98$		0			0
$99$	2.31275			0.232440
$100$	−1.45511			−0.145511
$101$	2.94023			0.292564			0.146282	−	0.989243i	$-0.453269\pi$
$101$	2.94023			0.292564			0.146282	+	0.989243i	$0.453269\pi$
$102$	15.5039			1.53511
$103$	0.264341	+	0.457852i	0.0260463	+	0.0451135i	0.878755	−	0.477274i	$-0.158375\pi$
$103$	0.264341	+	0.457852i	0.0260463	+	0.0451135i	−0.852708	+	0.522387i	$0.825042\pi$
$104$	−8.53336	−	3.57395i	−0.836765	−	0.350455i
$105$		0			0
$106$	6.27076	+	10.8613i	0.609070	+	1.05494i
$107$	9.66119	−	16.7337i	0.933983	−	1.61771i	0.157545	−	0.987512i	$-0.449642\pi$
$107$	9.66119	−	16.7337i	0.933983	−	1.61771i	0.776438	−	0.630194i	$-0.217024\pi$
$108$	0.491825	+	0.851866i	0.0473259	+	0.0819709i
$109$	2.86620	−	4.96440i	0.274532	−	0.475503i	−0.695485	−	0.718541i	$-0.744810\pi$
$109$	2.86620	−	4.96440i	0.274532	−	0.475503i	0.970017	+	0.243037i	$0.0781437\pi$
$110$	1.36312			0.129968
$111$	−1.49805	+	2.59470i	−0.142189	+	0.246278i
$112$		0			0
$113$	−2.57480	+	4.45968i	−0.242216	+	0.419531i	−0.961345	−	0.275346i	$-0.911208\pi$
$113$	−2.57480	+	4.45968i	−0.242216	+	0.419531i	0.719129	+	0.694877i	$0.244541\pi$
$114$	−2.72245	+	4.71543i	−0.254981	+	0.441640i
$115$	−1.04555			−0.0974978
$116$	−1.07782	+	1.86684i	−0.100073	+	0.173332i
$117$	−5.05756	−	2.11821i	−0.467572	−	0.195829i
$118$	−18.0602			−1.66257
$119$		0			0
$120$	1.60777	+	2.78474i	0.146769	+	0.254211i
$121$	−8.68725			−0.789750
$122$	−1.88589	+	3.26646i	−0.170740	+	0.295731i
$123$	1.44099	+	2.49588i	0.129930	+	0.225045i
$124$	1.90353			0.170942
$125$	5.68917			0.508855
$126$		0			0
$127$	4.50166	+	7.79710i	0.399457	+	0.691881i	0.993659	−	0.112436i	$-0.0358652\pi$
$127$	4.50166	+	7.79710i	0.399457	+	0.691881i	−0.594202	+	0.804316i	$0.702532\pi$
$128$	6.61135	−	11.4512i	0.584366	−	1.01215i
$129$	12.2890	−	21.2852i	1.08199	−	1.87406i
$130$	−2.98088	−	1.24846i	−0.261441	−	0.109497i
$131$	3.39920	+	5.88758i	0.296989	+	0.514401i	0.975446	−	0.220240i	$-0.0706841\pi$
$131$	3.39920	+	5.88758i	0.296989	+	0.514401i	−0.678456	+	0.734641i	$0.737351\pi$
$132$	−0.505639	−	0.875793i	−0.0440102	−	0.0762280i
$133$		0			0
$134$	−5.75829	+	9.97364i	−0.497440	+	0.861592i
$135$	−0.926861	−	1.60537i	−0.0797715	−	0.138168i
$136$	6.15153	+	10.6548i	0.527490	+	0.913639i
$137$	7.03779	+	12.1898i	0.601279	+	1.04145i	0.992628	+	0.121203i	$0.0386753\pi$
$137$	7.03779	+	12.1898i	0.601279	+	1.04145i	−0.391349	+	0.920242i	$0.627991\pi$
$138$	2.86801	+	4.96754i	0.244141	+	0.422865i
$139$	8.64313	−	14.9703i	0.733101	−	1.26977i	−0.222451	−	0.974944i	$-0.571406\pi$
$139$	8.64313	−	14.9703i	0.733101	−	1.26977i	0.955552	−	0.294824i	$-0.0952611\pi$
$140$		0			0
$141$	−0.494165	−	0.855919i	−0.0416162	−	0.0720814i
$142$	5.02213	+	8.69859i	0.421448	+	0.729969i
$143$	−5.05756	−	2.11821i	−0.422935	−	0.177134i
$144$	3.44280	−	5.96310i	0.286900	−	0.496925i
$145$	2.03119	−	3.51813i	0.168681	−	0.292165i
$146$	12.4484	+	21.5613i	1.03024	+	1.78442i
$147$		0			0
$148$	0.440707			0.0362259
$149$	−17.1252			−1.40295			−0.701475	−	0.712694i	$-0.747475\pi$
$149$	−17.1252			−1.40295			−0.701475	+	0.712694i	$0.747475\pi$
$150$	−7.52209	−	13.0286i	−0.614176	−	1.06378i
$151$	−7.89873	+	13.6810i	−0.642789	+	1.11334i	0.342018	+	0.939693i	$0.388890\pi$
$151$	−7.89873	+	13.6810i	−0.642789	+	1.11334i	−0.984807	+	0.173650i	$0.944444\pi$
$152$	−4.32079			−0.350462
$153$	3.64590	+	6.31488i	0.294753	+	0.510528i
$154$		0			0
$155$	−3.58727			−0.288137
$156$	0.303615	+	2.37830i	0.0243086	+	0.190417i
$157$	−1.89176	+	3.27662i	−0.150979	+	0.261503i	−0.931587	−	0.363517i	$-0.881576\pi$
$157$	−1.89176	+	3.27662i	−0.150979	+	0.261503i	0.780609	+	0.625020i	$0.214909\pi$
$158$	22.7543			1.81023
$159$	−8.76722	+	15.1853i	−0.695286	+	1.20427i
$160$	0.516821	−	0.895161i	0.0408583	−	0.0707687i
$161$		0			0
$162$	−8.55402	+	14.8160i	−0.672067	+	1.16406i
$163$	1.71551			0.134369			0.0671847	−	0.997741i	$-0.478598\pi$
$163$	1.71551			0.134369			0.0671847	+	0.997741i	$0.478598\pi$
$164$	0.211961	−	0.367127i	0.0165514	−	0.0286678i
$165$	0.952894	+	1.65046i	0.0741827	+	0.128488i
$166$	−7.69677	+	13.3312i	−0.597385	+	1.03470i
$167$	6.32605	+	10.9570i	0.489524	+	0.847881i	0.999927	−	0.0120542i	$-0.00383706\pi$
$167$	6.32605	+	10.9570i	0.489524	+	0.847881i	−0.510403	+	0.859935i	$0.670504\pi$
$168$		0			0
$169$	9.11992	+	9.26429i	0.701532	+	0.712638i
$170$	2.14886	+	3.72193i	0.164810	+	0.285459i
$171$	−2.56085			−0.195833
$172$	−3.61527			−0.275662
$173$	11.4874			0.873372			0.436686	−	0.899614i	$-0.356152\pi$
$173$	11.4874			0.873372			0.436686	+	0.899614i	$0.356152\pi$
$174$	−22.2868			−1.68956
$175$		0			0
$176$	3.44280	−	5.96310i	0.259510	−	0.449485i
$177$	−12.6251	−	21.8672i	−0.948958	−	1.64364i
$178$	−12.5350	−	21.7112i	−0.939536	−	1.62732i
$179$	−2.18451			−0.163278			−0.0816389	−	0.996662i	$-0.526015\pi$
$179$	−2.18451			−0.163278			−0.0816389	+	0.996662i	$0.526015\pi$
$180$	0.140165	−	0.242772i	0.0104472	−	0.0180952i
$181$	11.5981			0.862081			0.431041	−	0.902333i	$-0.358147\pi$
$181$	11.5981			0.862081			0.431041	+	0.902333i	$0.358147\pi$
$182$		0			0
$183$	−5.27337			−0.389819
$184$	−2.27590	+	3.94198i	−0.167782	+	0.290606i
$185$	−0.830527			−0.0610616
$186$	9.84014	+	17.0436i	0.721514	+	1.24970i
$187$	3.64590	+	6.31488i	0.266614	+	0.461790i
$188$	−0.0726885	+	0.125900i	−0.00530135	+	0.00918221i
$189$		0			0
$190$	−1.50934			−0.109499
$191$	17.7592			1.28501			0.642506	−	0.766281i	$-0.277895\pi$
$191$	17.7592			1.28501			0.642506	+	0.766281i	$0.277895\pi$
$192$	13.5829			0.980264
$193$	22.6379			1.62951			0.814756	−	0.579804i	$-0.196871\pi$
$193$	22.6379			1.62951			0.814756	+	0.579804i	$0.196871\pi$
$194$	0.740517	+	1.28261i	0.0531660	+	0.0920863i
$195$	−0.572172	−	4.48200i	−0.0409741	−	0.320962i
$196$		0			0
$197$	−10.0032	−	17.3260i	−0.712696	−	1.23442i	−0.963842	−	0.266476i	$-0.914141\pi$
$197$	−10.0032	−	17.3260i	−0.712696	−	1.23442i	0.251146	−	0.967949i	$-0.419193\pi$
$198$	1.75859	−	3.04596i	0.124977	−	0.216467i
$199$	−0.924426	−	1.60115i	−0.0655309	−	0.113503i	0.831398	−	0.555677i	$-0.187541\pi$
$199$	−0.924426	−	1.60115i	−0.0655309	−	0.113503i	−0.896929	+	0.442174i	$0.854207\pi$
$200$	5.96913	−	10.3388i	0.422081	−	0.731066i
$201$	−16.1015			−1.13571
$202$	2.23572	−	3.87237i	0.157304	−	0.272459i
$203$		0			0
$204$	1.59421	−	2.76126i	0.111617	−	0.193327i
$205$	−0.399447	+	0.691863i	−0.0278986	+	0.0483218i
$206$	0.804005			0.0560177
$207$	−1.34888	+	2.33633i	−0.0937539	+	0.162386i
$208$	−12.9903	+	9.88699i	−0.900713	+	0.685540i
$209$	−2.56085			−0.177138
$210$		0			0
$211$	8.08474	+	14.0032i	0.556576	+	0.964019i	0.997779	+	0.0666110i	$0.0212187\pi$
$211$	8.08474	+	14.0032i	0.556576	+	0.964019i	−0.441203	+	0.897407i	$0.645448\pi$
$212$	2.57920			0.177140
$213$	−7.02150	+	12.1616i	−0.481105	+	0.833299i
$214$	−14.6925	−	25.4481i	−1.00436	−	1.73960i
$215$	6.81310			0.464650
$216$	−8.07020			−0.549108
$217$		0			0
$218$	−4.35884	−	7.54973i	−0.295218	−	0.511332i
$219$	−17.4043	+	30.1451i	−1.17607	+	2.03701i
$220$	0.140165	−	0.242772i	0.00944989	−	0.0163677i
$221$	−2.18921	−	17.1487i	−0.147262	−	1.15355i
$222$	2.27820	+	3.94595i	0.152902	+	0.264835i
$223$	−6.21589	−	10.7662i	−0.416247	−	0.720961i	0.579312	−	0.815106i	$-0.303321\pi$
$223$	−6.21589	−	10.7662i	−0.416247	−	0.720961i	−0.995558	+	0.0941455i	$0.969988\pi$
$224$		0			0
$225$	3.53779	−	6.12763i	0.235853	−	0.408509i
$226$	3.91568	+	6.78216i	0.260467	+	0.451142i
$227$	0.617487	+	1.06952i	0.0409841	+	0.0709865i	0.885790	−	0.464087i	$-0.153617\pi$
$227$	0.617487	+	1.06952i	0.0409841	+	0.0709865i	−0.844806	+	0.535073i	$0.820284\pi$
$228$	0.559881	+	0.969743i	0.0370790	+	0.0642228i
$229$	3.27757	+	5.67692i	0.216588	+	0.375141i	0.953763	−	0.300561i	$-0.0971739\pi$
$229$	3.27757	+	5.67692i	0.216588	+	0.375141i	−0.737175	+	0.675702i	$0.763841\pi$
$230$	−0.795020	+	1.37702i	−0.0524221	+	0.0907977i
$231$		0			0
$232$	−8.84282	−	15.3162i	−0.580559	−	1.00556i
$233$	−3.14944	−	5.45498i	−0.206326	−	0.357368i	0.744228	−	0.667925i	$-0.232818\pi$
$233$	−3.14944	−	5.45498i	−0.206326	−	0.357368i	−0.950555	+	0.310558i	$0.899484\pi$
$234$	−6.63545	+	5.05029i	−0.433773	+	0.330148i
$235$	0.136984	−	0.237263i	0.00893584	−	0.0154773i
$236$	−1.85706	+	3.21653i	−0.120885	+	0.209378i
$237$	15.9065	+	27.5509i	1.03324	+	1.78962i
$238$		0			0
$239$	−18.9193			−1.22379			−0.611895	−	0.790939i	$-0.709592\pi$
$239$	−18.9193			−1.22379			−0.611895	+	0.790939i	$0.709592\pi$
$240$	5.67397			0.366253
$241$	11.1484	+	19.3096i	0.718131	+	1.24384i	0.961740	+	0.273965i	$0.0883353\pi$
$241$	11.1484	+	19.3096i	0.718131	+	1.24384i	−0.243609	+	0.969874i	$0.578331\pi$
$242$	−6.60567	+	11.4414i	−0.424628	+	0.735478i
$243$	−14.4835			−0.929118
$244$	0.387839	+	0.671757i	0.0248289	+	0.0430048i
$245$		0			0
$246$	4.38285			0.279440
$247$	5.60011	+	2.34544i	0.356326	+	0.149237i
$248$	−7.80861	+	13.5249i	−0.495847	+	0.858833i
$249$	−21.5219			−1.36389
$250$	4.32597	−	7.49280i	0.273598	−	0.473886i
$251$	−3.47657	+	6.02160i	−0.219439	+	0.380080i	−0.954637	−	0.297773i	$-0.903756\pi$
$251$	−3.47657	+	6.02160i	−0.219439	+	0.380080i	0.735197	+	0.677853i	$0.237090\pi$
$252$		0			0
$253$	−1.34888	+	2.33633i	−0.0848036	+	0.146884i
$254$	13.6920			0.859113
$255$	−3.00435	+	5.20368i	−0.188139	+	0.325867i
$256$	−3.66603	−	6.34975i	−0.229127	−	0.396860i
$257$	10.5776	−	18.3209i	0.659811	−	1.14283i	−0.320853	−	0.947129i	$-0.603970\pi$
$257$	10.5776	−	18.3209i	0.659811	−	1.14283i	0.980664	−	0.195697i	$-0.0626970\pi$
$258$	−18.6888	−	32.3700i	−1.16352	−	2.01527i
$259$		0			0
$260$	−0.528865	+	0.402523i	−0.0327988	+	0.0249634i
$261$	−5.24097	−	9.07763i	−0.324408	−	0.561891i
$262$	10.3388			0.638735
$263$	−8.42992			−0.519811			−0.259906	−	0.965634i	$-0.583691\pi$
$263$	−8.42992			−0.519811			−0.259906	+	0.965634i	$0.583691\pi$
$264$	8.29687			0.510637
$265$	−4.86060			−0.298584
$266$		0			0
$267$	17.5253	−	30.3547i	1.07253	−	1.85768i
$268$	1.18421	+	2.05111i	0.0723371	+	0.125292i
$269$	−2.91519	−	5.04926i	−0.177743	−	0.307859i	0.763364	−	0.645968i	$-0.223546\pi$
$269$	−2.91519	−	5.04926i	−0.177743	−	0.307859i	−0.941107	+	0.338109i	$0.890213\pi$
$270$	−2.81909			−0.171565
$271$	9.21497	−	15.9608i	0.559769	−	0.969549i	−0.437746	−	0.899099i	$-0.644223\pi$
$271$	9.21497	−	15.9608i	0.559769	−	0.969549i	0.997515	−	0.0704502i	$-0.0224436\pi$
$272$	21.7093			1.31632
$273$		0			0
$274$	21.4058			1.29317
$275$	3.53779	−	6.12763i	0.213337	−	0.369510i
$276$	1.17963			0.0710054
$277$	3.09154	+	5.35470i	0.185752	+	0.321733i	0.943830	−	0.330432i	$-0.107194\pi$
$277$	3.09154	+	5.35470i	0.185752	+	0.321733i	−0.758077	+	0.652165i	$0.773861\pi$
$278$	−13.1442	−	22.7665i	−0.788340	−	1.36544i
$279$	−4.62802	+	8.01596i	−0.277072	+	0.479903i
$280$		0			0
$281$	−5.64049			−0.336483			−0.168242	−	0.985746i	$-0.553809\pi$
$281$	−5.64049			−0.336483			−0.168242	+	0.985746i	$0.553809\pi$
$282$	−1.50303			−0.0895039
$283$	16.4554			0.978173			0.489086	−	0.872235i	$-0.337330\pi$
$283$	16.4554			0.978173			0.489086	+	0.872235i	$0.337330\pi$
$284$	2.06563			0.122573
$285$	−1.05512	−	1.82751i	−0.0624996	−	0.108253i
$286$	−6.63545	+	5.05029i	−0.392362	+	0.298630i
$287$		0			0
$288$	−1.33353	−	2.30973i	−0.0785787	−	0.136102i
$289$	−2.99502	+	5.18752i	−0.176177	+	0.305148i
$290$	−3.08898	−	5.35028i	−0.181391	−	0.314179i
$291$	−1.03533	+	1.79324i	−0.0606919	+	0.105121i
$292$	5.12011			0.299632
$293$	15.3086	−	26.5152i	0.894335	−	1.54903i	0.0597104	−	0.998216i	$-0.480982\pi$
$293$	15.3086	−	26.5152i	0.894335	−	1.54903i	0.834625	−	0.550819i	$-0.185684\pi$
$294$		0			0
$295$	3.49970	−	6.06166i	0.203760	−	0.352923i
$296$	−1.80785	+	3.13130i	−0.105079	+	0.182003i
$297$	−4.78306			−0.277541
$298$	−13.0218	+	22.5544i	−0.754331	+	1.30654i
$299$	5.08957	−	3.87371i	0.294338	−	0.224023i
$300$	−3.09388			−0.178625
$301$		0			0
$302$	12.0122	+	20.8057i	0.691223	+	1.19723i
$303$	6.25156			0.359143
$304$	−3.81212	+	6.60278i	−0.218640	+	0.378696i
$305$	−0.730896	−	1.26595i	−0.0418510	−	0.0724880i
$306$	11.0892			0.633925
$307$	9.96020			0.568459			0.284229	−	0.958756i	$-0.408262\pi$
$307$	9.96020			0.568459			0.284229	+	0.958756i	$0.408262\pi$
$308$		0			0
$309$	0.562044	+	0.973489i	0.0319736	+	0.0553799i
$310$	−2.72771	+	4.72454i	−0.154924	+	0.268336i
$311$	13.8734	−	24.0294i	0.786687	−	1.36258i	−0.141299	−	0.989967i	$-0.545128\pi$
$311$	13.8734	−	24.0294i	0.786687	−	1.36258i	0.927986	−	0.372615i	$-0.121539\pi$
$312$	−18.1437	−	7.59898i	−1.02719	−	0.430207i
$313$	−8.26136	−	14.3091i	−0.466960	−	0.808798i	0.532328	−	0.846538i	$-0.321317\pi$
$313$	−8.26136	−	14.3091i	−0.466960	−	0.808798i	−0.999288	+	0.0377401i	$0.987984\pi$
$314$	2.87693	+	4.98300i	0.162355	+	0.281207i
$315$		0			0
$316$	2.33975	−	4.05256i	0.131621	−	0.227974i
$317$	−11.8396	−	20.5069i	−0.664980	−	1.15178i	−0.979291	−	0.202459i	$-0.935107\pi$
$317$	−11.8396	−	20.5069i	−0.664980	−	1.15178i	0.314310	−	0.949320i	$-0.398227\pi$
$318$	13.3330	+	23.0934i	0.747675	+	1.29501i
$319$	−5.24097	−	9.07763i	−0.293438	−	0.508250i
$320$	1.88261	+	3.26078i	0.105241	+	0.182283i
$321$	20.5417	−	35.5793i	1.14653	−	1.98584i
$322$		0			0
$323$	−4.03701	−	6.99230i	−0.224625	−	0.389062i
$324$	1.75916	+	3.04696i	0.0977312	+	0.169275i
$325$	−13.3487	+	10.1598i	−0.740452	+	0.563564i
$326$	1.30445	−	2.25938i	0.0722470	−	0.125136i
$327$	6.09414	−	10.5554i	0.337007	−	0.583713i
$328$	1.73900	+	3.01203i	0.0960202	+	0.166312i
$329$		0			0
$330$	2.89827			0.159545
$331$	7.95209			0.437086			0.218543	−	0.975827i	$-0.429870\pi$
$331$	7.95209			0.437086			0.218543	+	0.975827i	$0.429870\pi$
$332$	1.58286	+	2.74160i	0.0868710	+	0.150465i
$333$	−1.07148	+	1.85586i	−0.0587168	+	0.101700i
$334$	19.2410			1.05282
$335$	−2.23168	−	3.86539i	−0.121930	−	0.211189i
$336$		0			0
$337$	−7.91326			−0.431063			−0.215531	−	0.976497i	$-0.569148\pi$
$337$	−7.91326			−0.431063			−0.215531	+	0.976497i	$0.569148\pi$
$338$	19.1360	−	4.96675i	1.04086	−	0.270156i
$339$	−5.47456	+	9.48221i	−0.297337	+	0.515003i
$340$	0.883839			0.0479329
$341$	−4.62802	+	8.01596i	−0.250621	+	0.434089i
$342$	−1.94724	+	3.37271i	−0.105294	+	0.182375i
$343$		0			0
$344$	14.8305	−	25.6871i	0.799605	−	1.38496i
$345$	−2.22305			−0.119685
$346$	8.73488	−	15.1292i	0.469590	−	0.813353i
$347$	−3.56786	−	6.17971i	−0.191533	−	0.331744i	0.754226	−	0.656615i	$-0.228012\pi$
$347$	−3.56786	−	6.17971i	−0.191533	−	0.331744i	−0.945758	+	0.324871i	$0.894679\pi$
$348$	−2.29168	+	3.96930i	−0.122847	+	0.212777i
$349$	−0.688402	−	1.19235i	−0.0368493	−	0.0638249i	0.847013	−	0.531573i	$-0.178399\pi$
$349$	−0.688402	−	1.19235i	−0.0368493	−	0.0638249i	−0.883862	+	0.467748i	$0.845065\pi$
$350$		0			0
$351$	10.4597	+	4.38073i	0.558296	+	0.233826i
$352$	−1.33353	−	2.30973i	−0.0710771	−	0.123109i
$353$	0.693215			0.0368961			0.0184481	−	0.999830i	$-0.494127\pi$
$353$	0.693215			0.0368961			0.0184481	+	0.999830i	$0.494127\pi$
$354$	−38.3997			−2.04092
$355$	−3.89276			−0.206606
$356$	−5.15571			−0.273252
$357$		0			0
$358$	−1.66107	+	2.87706i	−0.0877904	+	0.152057i
$359$	2.90182	+	5.02611i	0.153152	+	0.265268i	0.932385	−	0.361467i	$-0.117724\pi$
$359$	2.90182	+	5.02611i	0.153152	+	0.265268i	−0.779232	+	0.626735i	$0.784391\pi$
$360$	1.14996	+	1.99178i	0.0606081	+	0.104976i
$361$	−16.1644			−0.850760
$362$	8.81905	−	15.2750i	0.463519	−	0.802839i
$363$	−18.4709			−0.969472
$364$		0			0
$365$	−9.64902			−0.505053
$366$	−4.00980	+	6.94518i	−0.209596	+	0.363030i
$367$	7.35157			0.383749			0.191874	−	0.981420i	$-0.438543\pi$
$367$	7.35157			0.383749			0.191874	+	0.981420i	$0.438543\pi$
$368$	4.01593	+	6.95580i	0.209345	+	0.362596i
$369$	1.03067	+	1.78518i	0.0536546	+	0.0929325i
$370$	−0.631522	+	1.09383i	−0.0328313	+	0.0568654i
$371$		0			0
$372$	4.04731			0.209843
$373$	18.3988			0.952656			0.476328	−	0.879268i	$-0.341967\pi$
$373$	18.3988			0.952656			0.476328	+	0.879268i	$0.341967\pi$
$374$	11.0892			0.573407
$375$	12.0964			0.624654
$376$	−0.596361	−	1.03293i	−0.0307550	−	0.0532692i
$377$	3.14698	+	24.6512i	0.162078	+	1.26960i
$378$		0			0
$379$	2.42550	+	4.20110i	0.124590	+	0.215796i	0.921573	−	0.388206i	$-0.126905\pi$
$379$	2.42550	+	4.20110i	0.124590	+	0.215796i	−0.796983	+	0.604002i	$0.793572\pi$
$380$	−0.155201	+	0.268815i	−0.00796162	+	0.0137899i
$381$	9.57147	+	16.5783i	0.490361	+	0.849331i
$382$	13.5039	−	23.3894i	0.690918	−	1.19671i
$383$	−22.8205			−1.16607			−0.583037	−	0.812446i	$-0.698136\pi$
$383$	−22.8205			−1.16607			−0.583037	+	0.812446i	$0.698136\pi$
$384$	14.0571	−	24.3476i	0.717349	−	1.24249i
$385$		0			0
$386$	17.2136	−	29.8148i	0.876147	−	1.51753i
$387$	8.78973	−	15.2243i	0.446807	−	0.773893i
$388$	0.304579			0.0154627
$389$	10.1561	−	17.5908i	0.514933	−	0.891891i	−0.484916	−	0.874561i	$-0.661150\pi$
$389$	10.1561	−	17.5908i	0.514933	−	0.891891i	0.999850	−	0.0173304i	$-0.00551672\pi$
$390$	−6.33799	−	2.65448i	−0.320937	−	0.134415i
$391$	−8.50569			−0.430151
$392$		0			0
$393$	7.22741	+	12.5182i	0.364575	+	0.631462i
$394$	−30.4251			−1.53279
$395$	−4.40933	+	7.63719i	−0.221858	+	0.384268i
$396$	−0.361659	−	0.626411i	−0.0181740	−	0.0314783i
$397$	−34.1377			−1.71332			−0.856662	−	0.515878i	$-0.827466\pi$
$397$	−34.1377			−1.71332			−0.856662	+	0.515878i	$0.827466\pi$
$398$	−2.81169			−0.140937
$399$		0			0
$400$	−10.5328	−	18.2434i	−0.526640	−	0.912168i
$401$	1.51298	−	2.62056i	0.0755547	−	0.130865i	−0.825773	−	0.564003i	$-0.809261\pi$
$401$	1.51298	−	2.62056i	0.0755547	−	0.130865i	0.901327	+	0.433139i	$0.142594\pi$
$402$	−12.2433	+	21.2061i	−0.610642	+	1.05766i
$403$	17.4623	−	13.2907i	0.869860	−	0.662057i
$404$	−0.459782	−	0.796365i	−0.0228750	−	0.0396207i
$405$	−3.31520	−	5.74209i	−0.164734	−	0.285327i
$406$		0			0
$407$	−1.07148	+	1.85586i	−0.0531114	+	0.0919916i
$408$	13.0795	+	22.6543i	0.647530	+	1.12155i
$409$	−2.69162	−	4.66203i	−0.133092	−	0.230523i	0.791775	−	0.610813i	$-0.209157\pi$
$409$	−2.69162	−	4.66203i	−0.133092	−	0.230523i	−0.924867	+	0.380291i	$0.875824\pi$
$410$	0.607469	+	1.05217i	0.0300008	+	0.0519628i
$411$	14.9638	+	25.9181i	0.738111	+	1.27845i
$412$	0.0826731	−	0.143194i	0.00407301	−	0.00705466i
$413$		0			0
$414$	2.05135	+	3.55304i	0.100818	+	0.174622i
$415$	−2.98296	−	5.16664i	−0.146428	−	0.253620i
$416$	0.800725	+	6.27232i	0.0392588	+	0.307526i
$417$	18.3771	−	31.8301i	0.899932	−	1.55873i
$418$	−1.94724	+	3.37271i	−0.0952425	+	0.164965i
$419$	−2.94117	−	5.09426i	−0.143686	−	0.248871i	0.785196	−	0.619247i	$-0.212562\pi$
$419$	−2.94117	−	5.09426i	−0.143686	−	0.248871i	−0.928882	+	0.370376i	$0.879229\pi$
$420$		0			0
$421$	−28.7614			−1.40174			−0.700872	−	0.713287i	$-0.747206\pi$
$421$	−28.7614			−1.40174			−0.700872	+	0.713287i	$0.747206\pi$
$422$	24.5901			1.19703
$423$	−0.353452	−	0.612196i	−0.0171854	−	0.0297660i
$424$	−10.5803	+	18.3257i	−0.513826	+	0.889973i
$425$	22.3083			1.08211
$426$	10.6781	+	18.4950i	0.517356	+	0.896087i
$427$		0			0
$428$	−6.04311			−0.292105
$429$	−10.7534	−	4.50377i	−0.519181	−	0.217444i
$430$	5.18059	−	8.97305i	0.249830	−	0.432719i
$431$	8.38588			0.403934			0.201967	−	0.979392i	$-0.435267\pi$
$431$	8.38588			0.403934			0.201967	+	0.979392i	$0.435267\pi$
$432$	−7.12013	+	12.3324i	−0.342567	+	0.593344i
$433$	13.7996	−	23.9017i	0.663168	−	1.14864i	−0.316611	−	0.948556i	$-0.602545\pi$
$433$	13.7996	−	23.9017i	0.663168	−	1.14864i	0.979779	−	0.200085i	$-0.0641218\pi$
$434$		0			0
$435$	4.31874	−	7.48028i	0.207068	−	0.358652i
$436$	−1.79282			−0.0858604
$437$	1.49358	−	2.58696i	0.0714478	−	0.123751i
$438$	26.4679	+	45.8438i	1.26469	+	2.19050i
$439$	−15.5869	+	26.9973i	−0.743921	+	1.28851i	0.206776	+	0.978388i	$0.433703\pi$
$439$	−15.5869	+	26.9973i	−0.743921	+	1.28851i	−0.950697	+	0.310121i	$0.899631\pi$
$440$	1.14996	+	1.99178i	0.0548221	+	0.0949546i
$441$		0			0
$442$	−24.2500	−	10.1564i	−1.15345	−	0.483090i
$443$	11.7941	+	20.4281i	0.560357	+	0.970566i	0.997465	+	0.0711573i	$0.0226692\pi$
$443$	11.7941	+	20.4281i	0.560357	+	0.970566i	−0.437109	+	0.899409i	$0.643997\pi$
$444$	0.937036			0.0444698
$445$	9.71611			0.460588
$446$	−18.9059			−0.895221
$447$	−36.4118			−1.72222
$448$		0			0
$449$	−1.41328	+	2.44787i	−0.0666968	+	0.115522i	−0.897445	−	0.441125i	$-0.854579\pi$
$449$	−1.41328	+	2.44787i	−0.0666968	+	0.115522i	0.830749	+	0.556648i	$0.187913\pi$
$450$	−5.38018	−	9.31874i	−0.253624	−	0.439289i
$451$	1.03067	+	1.78518i	0.0485324	+	0.0840607i
$452$	1.61054			0.0757536
$453$	−16.7944	+	29.0887i	−0.789068	+	1.36671i
$454$	1.87812			0.0881444
$455$		0			0
$456$	−9.18691			−0.430217
$457$	18.8716	−	32.6866i	0.882776	−	1.52901i	0.0345338	−	0.999404i	$-0.489005\pi$
$457$	18.8716	−	32.6866i	0.882776	−	1.52901i	0.848242	−	0.529609i	$-0.177661\pi$
$458$	9.96888			0.465815
$459$	−7.54017	−	13.0599i	−0.351945	−	0.609586i
$460$	0.163498	+	0.283188i	0.00762315	+	0.0132037i
$461$	−17.3293	+	30.0152i	−0.807106	+	1.39795i	0.107754	+	0.994178i	$0.465634\pi$
$461$	−17.3293	+	30.0152i	−0.807106	+	1.39795i	−0.914860	+	0.403771i	$0.867699\pi$
$462$		0			0
$463$	18.5114			0.860296			0.430148	−	0.902758i	$-0.358461\pi$
$463$	18.5114			0.860296			0.430148	+	0.902758i	$0.358461\pi$
$464$	−31.2071			−1.44875
$465$	−7.62730			−0.353707
$466$	−9.57916			−0.443746
$467$	−3.31392	−	5.73987i	−0.153350	−	0.265610i	0.779107	−	0.626891i	$-0.215673\pi$
$467$	−3.31392	−	5.73987i	−0.153350	−	0.265610i	−0.932457	+	0.361281i	$0.882339\pi$
$468$	0.217161	+	1.70108i	0.0100383	+	0.0786326i
$469$		0			0
$470$	−0.208321	−	0.360823i	−0.00960915	−	0.0166435i
$471$	−4.02227	+	6.96678i	−0.185337	+	0.321012i
$472$	−15.2360	−	26.3895i	−0.701293	−	1.21468i
$473$	8.78973	−	15.2243i	0.404152	−	0.700012i
$474$	48.3804			2.22219
$475$	−3.91730	+	6.78497i	−0.179738	+	0.311316i
$476$		0			0
$477$	−6.27076	+	10.8613i	−0.287118	+	0.497304i
$478$	−14.3860	+	24.9173i	−0.658001	+	1.13969i
$479$	−17.4526			−0.797430			−0.398715	−	0.917075i	$-0.630544\pi$
$479$	−17.4526			−0.797430			−0.398715	+	0.917075i	$0.630544\pi$
$480$	1.09887	−	1.90330i	0.0501564	−	0.0868734i
$481$	4.04289	−	3.07707i	0.184340	−	0.140302i
$482$	33.9083			1.54448
$483$		0			0
$484$	1.35848	+	2.35295i	0.0617489	+	0.106952i
$485$	−0.573990			−0.0260635
$486$	−11.0131	+	19.0752i	−0.499563	+	0.865269i
$487$	17.7569	+	30.7558i	0.804641	+	1.39368i	0.916533	+	0.399959i	$0.130976\pi$
$487$	17.7569	+	30.7558i	0.804641	+	1.39368i	−0.111892	+	0.993720i	$0.535691\pi$
$488$	−6.36393			−0.288081
$489$	3.64754			0.164948
$490$		0			0
$491$	14.9059	+	25.8178i	0.672695	+	1.16514i	0.977137	+	0.212611i	$0.0681966\pi$
$491$	14.9059	+	25.8178i	0.672695	+	1.16514i	−0.304442	+	0.952531i	$0.598470\pi$
$492$	0.450674	−	0.780590i	0.0203179	−	0.0351917i
$493$	16.5241	−	28.6205i	0.744207	−	1.28900i
$494$	7.34726	−	5.59206i	0.330569	−	0.251599i
$495$	0.681558	+	1.18049i	0.0306338	+	0.0530592i
$496$	13.7787	+	23.8653i	0.618680	+	1.07159i
$497$		0			0
$498$	−16.3649	+	28.3449i	−0.733331	+	1.27017i
$499$	3.75483	+	6.50355i	0.168089	+	0.291139i	0.937748	−	0.347316i	$-0.112907\pi$
$499$	3.75483	+	6.50355i	0.168089	+	0.291139i	−0.769659	+	0.638455i	$0.779574\pi$
$500$	−0.889649	−	1.54092i	−0.0397863	−	0.0689119i
$501$	13.4505	+	23.2970i	0.600925	+	1.04083i
$502$	5.28708	+	9.15750i	0.235974	+	0.408719i
$503$	−0.492171	+	0.852466i	−0.0219448	+	0.0380096i	−0.876789	−	0.480875i	$-0.840319\pi$
$503$	−0.492171	+	0.852466i	−0.0219448	+	0.0380096i	0.854844	+	0.518884i	$0.173652\pi$
$504$		0			0
$505$	0.866474	+	1.50078i	0.0385576	+	0.0667837i
$506$	2.05135	+	3.55304i	0.0911934	+	0.157952i
$507$	19.3909	+	19.6978i	0.861179	+	0.874811i
$508$	1.40790	−	2.43856i	0.0624655	−	0.108193i
$509$	−6.48958	+	11.2403i	−0.287646	+	0.498217i	−0.973247	−	0.229760i	$-0.926206\pi$
$509$	−6.48958	+	11.2403i	−0.287646	+	0.498217i	0.685602	+	0.727977i	$0.259539\pi$
$510$	4.56893	+	7.91362i	0.202316	+	0.350421i
$511$		0			0
$512$	15.2950			0.675949
$513$	5.29616			0.233831
$514$	−16.0861	−	27.8619i	−0.709527	−	1.22894i
$515$	−0.155800	+	0.269854i	−0.00686538	+	0.0118912i
$516$	−7.68683			−0.338394
$517$	−0.353452	−	0.612196i	−0.0155448	−	0.0269244i
$518$		0			0
$519$	24.4247			1.07212
$520$	−0.690500	−	5.40890i	−0.0302804	−	0.237196i
$521$	9.70730	−	16.8135i	0.425285	−	0.736614i	−0.571162	−	0.820837i	$-0.693507\pi$
$521$	9.70730	−	16.8135i	0.425285	−	0.736614i	0.996447	+	0.0842226i	$0.0268407\pi$
$522$	−15.9407			−0.697704
$523$	−13.6360	+	23.6182i	−0.596259	+	1.03275i	0.397109	+	0.917771i	$0.370013\pi$
$523$	−13.6360	+	23.6182i	−0.596259	+	1.03275i	−0.993368	+	0.114979i	$0.963320\pi$
$524$	1.06311	−	1.84135i	0.0464420	−	0.0804399i
$525$		0			0
$526$	−6.41000	+	11.1024i	−0.279489	+	0.484090i
$527$	−29.1830			−1.27123
$528$	7.32011	−	12.6788i	0.318567	−	0.551774i
$529$	9.92656	+	17.1933i	0.431590	+	0.747535i
$530$	−3.69593	+	6.40154i	−0.160541	+	0.278065i
$531$	−9.03008	−	15.6406i	−0.391872	−	0.678742i
$532$		0			0
$533$	−0.618874	−	4.84783i	−0.0268064	−	0.209983i
$534$	−26.6520	−	46.1626i	−1.15334	−	1.99765i
$535$	11.3884			0.492365
$536$	−19.4313			−0.839305
$537$	−4.64473			−0.200435
$538$	−8.86670			−0.382271
$539$		0			0
$540$	−0.289878	+	0.502083i	−0.0124743	+	0.0216062i
$541$	15.0495	+	26.0665i	0.647029	+	1.12069i	0.983829	+	0.179111i	$0.0573223\pi$
$541$	15.0495	+	26.0665i	0.647029	+	1.12069i	−0.336799	+	0.941576i	$0.609344\pi$
$542$	−14.0139	−	24.2727i	−0.601947	−	1.04260i
$543$	24.6600			1.05826
$544$	4.20442	−	7.28228i	0.180263	−	0.312225i
$545$	3.37863			0.144724
$546$		0			0
$547$	−26.1451			−1.11788			−0.558942	−	0.829207i	$-0.688793\pi$
$547$	−26.1451			−1.11788			−0.558942	+	0.829207i	$0.688793\pi$
$548$	2.20108	−	3.81238i	0.0940255	−	0.162857i
$549$	−3.77178			−0.160976
$550$	−5.38018	−	9.31874i	−0.229411	−	0.397352i
$551$	5.80319	+	10.0514i	0.247224	+	0.428205i
$552$	−4.83905	+	8.38147i	−0.205963	+	0.356739i
$553$		0			0
$554$	9.40305			0.399497
$555$	−1.76588			−0.0749573
$556$	−5.40631			−0.229279
$557$	17.9063			0.758716			0.379358	−	0.925250i	$-0.376145\pi$
$557$	17.9063			0.758716			0.379358	+	0.925250i	$0.376145\pi$
$558$	7.03817	+	12.1905i	0.297949	+	0.516063i
$559$	−33.1652	+	25.2423i	−1.40274	+	1.06764i
$560$		0			0
$561$	7.75195	+	13.4268i	0.327287	+	0.566878i
$562$	−4.28895	+	7.42868i	−0.180919	+	0.313360i
$563$	15.8275	+	27.4140i	0.667048	+	1.15536i	0.978726	+	0.205173i	$0.0657756\pi$
$563$	15.8275	+	27.4140i	0.667048	+	1.15536i	−0.311678	+	0.950188i	$0.600891\pi$
$564$	−0.154551	+	0.267690i	−0.00650777	+	0.0112718i
$565$	−3.03512			−0.127689
$566$	12.5125	−	21.6722i	0.525939	−	0.910953i
$567$		0			0
$568$	−8.47358	+	14.6767i	−0.355544	+	0.615820i
$569$	13.0555	−	22.6129i	0.547317	−	0.947981i	−0.451140	−	0.892453i	$-0.648983\pi$
$569$	13.0555	−	22.6129i	0.547317	−	0.947981i	0.998457	−	0.0555278i	$-0.0176841\pi$
$570$	−3.20918			−0.134418
$571$	−6.65205	+	11.5217i	−0.278380	+	0.482168i	−0.970982	−	0.239152i	$-0.923131\pi$
$571$	−6.65205	+	11.5217i	−0.278380	+	0.482168i	0.692602	+	0.721320i	$0.256464\pi$
$572$	0.217161	+	1.70108i	0.00907994	+	0.0711259i
$573$	37.7599			1.57744
$574$		0			0
$575$	4.12674	+	7.14773i	0.172097	+	0.298081i
$576$	9.71520			0.404800
$577$	8.38564	−	14.5244i	0.349099	−	0.604657i	−0.636991	−	0.770871i	$-0.719821\pi$
$577$	8.38564	−	14.5244i	0.349099	−	0.604657i	0.986090	+	0.166214i	$0.0531544\pi$
$578$	4.55474	+	7.88904i	0.189452	+	0.328141i
$579$	48.1329			2.00034
$580$	−1.27052			−0.0527554
$581$		0			0
$582$	1.57450	+	2.72711i	0.0652650	+	0.113042i
$583$	−6.27076	+	10.8613i	−0.259708	+	0.449828i
$584$	−21.0036	+	36.3792i	−0.869133	+	1.50538i
$585$	−0.409246	−	3.20575i	−0.0169203	−	0.132541i
$586$	−23.2808	−	40.3236i	−0.961723	−	1.66575i
$587$	5.03261	+	8.71673i	0.207718	+	0.359778i	0.950995	−	0.309205i	$-0.100063\pi$
$587$	5.03261	+	8.71673i	0.207718	+	0.359778i	−0.743277	+	0.668983i	$0.766730\pi$
$588$		0			0
$589$	5.12448	−	8.87587i	0.211151	−	0.365724i
$590$	−5.32225	−	9.21841i	−0.219114	−	0.379516i
$591$	−21.2688	−	36.8387i	−0.874883	−	1.51534i
$592$	3.19004	+	5.52532i	0.131110	+	0.227089i
$593$	−19.7161	−	34.1493i	−0.809643	−	1.40234i	−0.913111	−	0.407710i	$-0.866327\pi$
$593$	−19.7161	−	34.1493i	−0.809643	−	1.40234i	0.103468	−	0.994633i	$-0.467006\pi$
$594$	−3.63697	+	6.29942i	−0.149227	+	0.258468i
$595$		0			0
$596$	2.67797	+	4.63838i	0.109694	+	0.189995i
$597$	−1.96553	−	3.40439i	−0.0804436	−	0.139332i
$598$	−1.23175	−	9.64863i	−0.0503698	−	0.394562i
$599$	−6.88601	+	11.9269i	−0.281355	+	0.487321i	−0.971719	−	0.236142i	$-0.924117\pi$
$599$	−6.88601	+	11.9269i	−0.281355	+	0.487321i	0.690364	+	0.723462i	$0.257450\pi$
$600$	12.6916	−	21.9825i	0.518133	−	0.897433i
$601$	−16.6312	−	28.8060i	−0.678399	−	1.17502i	−0.975463	−	0.220164i	$-0.929341\pi$
$601$	−16.6312	−	28.8060i	−0.678399	−	1.17502i	0.297064	−	0.954858i	$-0.403993\pi$
$602$		0			0
$603$	−11.5166			−0.468991
$604$	4.94068			0.201034
$605$	−2.56009	−	4.43421i	−0.104083	−	0.180276i
$606$	4.75360	−	8.23348i	0.193102	−	0.334462i
$607$	43.9649			1.78448			0.892240	−	0.451562i	$-0.149133\pi$
$607$	43.9649			1.78448			0.892240	+	0.451562i	$0.149133\pi$
$608$	1.47658	+	2.55751i	0.0598831	+	0.103721i
$609$		0			0
$610$	−2.22305			−0.0900088
$611$	0.212233	+	1.66248i	0.00858602	+	0.0672568i
$612$	1.14026	−	1.97499i	0.0460923	−	0.0798342i
$613$	2.70091			0.109089			0.0545443	−	0.998511i	$-0.482629\pi$
$613$	2.70091			0.109089			0.0545443	+	0.998511i	$0.482629\pi$
$614$	7.57361	−	13.1179i	0.305646	−	0.529394i
$615$	−0.849310	+	1.47105i	−0.0342475	+	0.0593184i
$616$		0			0
$617$	−3.00208	+	5.19975i	−0.120859	+	0.209334i	−0.920107	−	0.391668i	$-0.871898\pi$
$617$	−3.00208	+	5.19975i	−0.120859	+	0.209334i	0.799248	+	0.601002i	$0.205232\pi$
$618$	1.70948			0.0687655
$619$	6.68204	−	11.5736i	0.268574	−	0.465184i	−0.699920	−	0.714221i	$-0.746781\pi$
$619$	6.68204	−	11.5736i	0.268574	−	0.465184i	0.968494	+	0.249038i	$0.0801143\pi$
$620$	0.560963	+	0.971616i	0.0225288	+	0.0390210i
$621$	2.78966	−	4.83183i	0.111945	−	0.193895i
$622$	−21.0983	−	36.5433i	−0.845963	−	1.46525i
$623$		0			0
$624$	−27.6201	+	21.0218i	−1.10569	+	0.841547i
$625$	−9.95497	−	17.2425i	−0.398199	−	0.689701i
$626$	−25.1273			−1.00429
$627$	−5.44491			−0.217449
$628$	1.18330			0.0472188
$629$	−6.75647			−0.269398
$630$		0			0
$631$	−20.2228	+	35.0270i	−0.805059	+	1.39440i	0.111192	+	0.993799i	$0.464533\pi$
$631$	−20.2228	+	35.0270i	−0.805059	+	1.39440i	−0.916251	+	0.400604i	$0.868800\pi$
$632$	19.1961	+	33.2486i	0.763579	+	1.32256i
$633$	17.1899	+	29.7737i	0.683236	+	1.18340i
$634$	−36.0108			−1.43017
$635$	−2.65324	+	4.59554i	−0.105291	+	0.182369i
$636$	5.48393			0.217452
$637$		0			0
$638$	−15.9407			−0.631097
$639$	−5.02213	+	8.69859i	−0.198672	+	0.344111i
$640$	7.79334			0.308059
$641$	−5.10991	−	8.85062i	−0.201829	−	0.349578i	0.747289	−	0.664500i	$-0.231355\pi$
$641$	−5.10991	−	8.85062i	−0.201829	−	0.349578i	−0.949118	+	0.314921i	$0.898022\pi$
$642$	−31.2393	−	54.1081i	−1.23292	−	2.13548i
$643$	−15.9014	+	27.5420i	−0.627088	+	1.08615i	0.361045	+	0.932548i	$0.382420\pi$
$643$	−15.9014	+	27.5420i	−0.627088	+	1.08615i	−0.988133	+	0.153600i	$0.950913\pi$
$644$		0			0
$645$	14.4861			0.570389
$646$	−12.2787			−0.483101
$647$	−34.5233			−1.35725			−0.678626	−	0.734484i	$-0.737424\pi$
$647$	−34.5233			−1.35725			−0.678626	+	0.734484i	$0.737424\pi$
$648$	−28.8655			−1.13394
$649$	−9.03008	−	15.6406i	−0.354462	−	0.613946i
$650$	3.23057	+	25.3060i	0.126713	+	0.992582i
$651$		0			0
$652$	−0.268265	−	0.464649i	−0.0105061	−	0.0181970i
$653$	−5.05899	+	8.76244i	−0.197974	+	0.342901i	−0.947871	−	0.318653i	$-0.896769\pi$
$653$	−5.05899	+	8.76244i	−0.197974	+	0.342901i	0.749898	+	0.661554i	$0.230103\pi$
$654$	−9.26781	−	16.0523i	−0.362400	−	0.627695i
$655$	−2.00346	+	3.47009i	−0.0782816	+	0.135588i
$656$	6.13709			0.239613
$657$	−12.4484	+	21.5613i	−0.485659	+	0.841185i
$658$		0			0
$659$	17.3841	−	30.1101i	0.677187	−	1.17292i	−0.298637	−	0.954367i	$-0.596532\pi$
$659$	17.3841	−	30.1101i	0.677187	−	1.17292i	0.975824	−	0.218556i	$-0.0701345\pi$
$660$	0.298019	−	0.516185i	0.0116004	−	0.0200925i
$661$	−16.5615			−0.644168			−0.322084	−	0.946711i	$-0.604383\pi$
$661$	−16.5615			−0.644168			−0.322084	+	0.946711i	$0.604383\pi$
$662$	6.04666	−	10.4731i	0.235010	−	0.407050i
$663$	−4.65471	−	36.4617i	−0.180774	−	1.41606i
$664$	−25.9727			−1.00794
$665$		0			0
$666$	1.62948	+	2.82234i	0.0631411	+	0.109364i
$667$	12.2269			0.473428
$668$	1.97848	−	3.42683i	0.0765498	−	0.132588i
$669$	−13.2163	−	22.8913i	−0.510972	−	0.885029i
$670$	−6.78777			−0.262234
$671$	−3.77178			−0.145608
$672$		0			0
$673$	20.9437	+	36.2756i	0.807321	+	1.39832i	0.914713	+	0.404104i	$0.132417\pi$
$673$	20.9437	+	36.2756i	0.807321	+	1.39832i	−0.107393	+	0.994217i	$0.534250\pi$
$674$	−6.01714	+	10.4220i	−0.231771	+	0.401440i
$675$	−7.31659	+	12.6727i	−0.281616	+	0.487772i
$676$	1.08311	−	3.91885i	0.0416579	−	0.150725i
$677$	15.7858	+	27.3417i	0.606696	+	1.05083i	0.991781	+	0.127947i	$0.0408387\pi$
$677$	15.7858	+	27.3417i	0.606696	+	1.05083i	−0.385085	+	0.922881i	$0.625828\pi$
$678$	8.32556	+	14.4203i	0.319741	+	0.553808i
$679$		0			0
$680$	−3.62566	+	6.27983i	−0.139038	+	0.240820i
$681$	1.31291	+	2.27402i	0.0503107	+	0.0871408i
$682$	7.03817	+	12.1905i	0.269505	+	0.466797i
$683$	13.1338	+	22.7484i	0.502551	+	0.870444i	0.999996	+	0.00294809i	$0.000938408\pi$
$683$	13.1338	+	22.7484i	0.502551	+	0.870444i	−0.497445	+	0.867496i	$0.665728\pi$
$684$	0.400455	+	0.693609i	0.0153118	+	0.0265208i
$685$	−4.14801	+	7.18457i	−0.158487	+	0.274508i
$686$		0			0
$687$	6.96880	+	12.0703i	0.265876	+	0.460512i
$688$	−26.1690	−	45.3261i	−0.997686	−	1.72804i
$689$	23.6607	−	18.0083i	0.901400	−	0.686062i
$690$	−1.69038	+	2.92783i	−0.0643517	+	0.111460i
$691$	−3.05047	+	5.28358i	−0.116046	+	0.200997i	−0.918197	−	0.396124i	$-0.870355\pi$
$691$	−3.05047	+	5.28358i	−0.116046	+	0.200997i	0.802152	+	0.597120i	$0.203689\pi$
$692$	−1.79635	−	3.11138i	−0.0682872	−	0.118277i
$693$		0			0
$694$	−10.8518			−0.411929
$695$	10.1884			0.386467
$696$	−18.8017	−	32.5655i	−0.712677	−	1.23439i
$697$	−3.24957	+	5.62842i	−0.123086	+	0.213192i
$698$	−2.09381			−0.0792518
$699$	−6.69636	−	11.5984i	−0.253280	−	0.438693i
$700$		0			0
$701$	−20.5701			−0.776921			−0.388461	−	0.921465i	$-0.626993\pi$
$701$	−20.5701			−0.776921			−0.388461	+	0.921465i	$0.626993\pi$
$702$	13.7229	−	10.4446i	0.517939	−	0.394207i
$703$	1.18642	−	2.05495i	0.0447468	−	0.0775038i
$704$	9.71520			0.366155
$705$	0.291257	−	0.504471i	0.0109694	−	0.0189995i
$706$	0.527111	−	0.912984i	0.0198381	−	0.0343606i
$707$		0			0
$708$	−3.94851	+	6.83902i	−0.148394	+	0.257026i
$709$	−43.1529			−1.62064			−0.810320	−	0.585988i	$-0.800707\pi$
$709$	−43.1529			−1.62064			−0.810320	+	0.585988i	$0.800707\pi$
$710$	−2.96000	+	5.12687i	−0.111087	+	0.192408i
$711$	11.3771	+	19.7058i	0.426676	+	0.739025i
$712$	21.1496	−	36.6322i	0.792615	−	1.37285i
$713$	−5.39847	−	9.35042i	−0.202174	−	0.350176i
$714$		0			0
$715$	−0.409246	−	3.20575i	−0.0153050	−	0.119888i
$716$	0.341605	+	0.591677i	0.0127664	+	0.0221120i
$717$	−40.2265			−1.50229
$718$	8.82603			0.329385
$719$	28.2084			1.05200			0.525999	−	0.850485i	$-0.323692\pi$
$719$	28.2084			1.05200			0.525999	+	0.850485i	$0.323692\pi$
$720$	4.05831			0.151244
$721$		0			0
$722$	−12.2912	+	21.2890i	−0.457432	+	0.792295i
$723$	23.7038	+	41.0562i	0.881555	+	1.52690i
$724$	−1.81367	−	3.14136i	−0.0674044	−	0.116748i
$725$	−32.0682			−1.19098
$726$	−14.0450	+	24.3267i	−0.521260	+	0.902850i
$727$	19.5116			0.723646			0.361823	−	0.932247i	$-0.382155\pi$
$727$	19.5116			0.723646			0.361823	+	0.932247i	$0.382155\pi$
$728$		0			0
$729$	2.95370			0.109396
$730$	−7.33698	+	12.7080i	−0.271554	+	0.470345i
$731$	55.4257			2.04999
$732$	0.824628	+	1.42830i	0.0304791	+	0.0527914i
$733$	10.1833	+	17.6380i	0.376129	+	0.651475i	0.990495	−	0.137546i	$-0.0439215\pi$
$733$	10.1833	+	17.6380i	0.376129	+	0.651475i	−0.614366	+	0.789021i	$0.710588\pi$
$734$	5.59003	−	9.68222i	0.206332	−	0.357377i
$735$		0			0
$736$	3.11105			0.114675
$737$	−11.5166			−0.424218
$738$	3.13484			0.115395
$739$	−10.4199			−0.383303			−0.191651	−	0.981463i	$-0.561384\pi$
$739$	−10.4199			−0.383303			−0.191651	+	0.981463i	$0.561384\pi$
$740$	0.129874	+	0.224949i	0.00477428	+	0.00826929i
$741$	11.9070	+	4.98691i	0.437415	+	0.183199i
$742$		0			0
$743$	8.70470	+	15.0770i	0.319344	+	0.553121i	0.980351	−	0.197259i	$-0.0632040\pi$
$743$	8.70470	+	15.0770i	0.319344	+	0.553121i	−0.661007	+	0.750380i	$0.729871\pi$
$744$	−16.6028	+	28.7568i	−0.608687	+	1.05428i
$745$	−5.04672	−	8.74118i	−0.184898	−	0.320252i
$746$	13.9902	−	24.2318i	0.512219	−	0.887189i
$747$	−15.3935			−0.563220
$748$	1.14026	−	1.97499i	0.0416921	−	0.0722128i
$749$		0			0
$750$	9.19792	−	15.9313i	0.335861	−	0.581728i
$751$	0.907626	−	1.57205i	0.0331197	−	0.0573651i	−0.848990	−	0.528408i	$-0.822789\pi$
$751$	0.907626	−	1.57205i	0.0331197	−	0.0573651i	0.882110	+	0.471043i	$0.156122\pi$
$752$	−2.10461			−0.0767474
$753$	−7.39193	+	12.8032i	−0.269377	+	0.466575i
$754$	34.8593	+	14.5998i	1.26950	+	0.531694i
$755$	−9.31088			−0.338858
$756$		0			0
$757$	−26.7814	−	46.3867i	−0.973385	−	1.68595i	−0.685165	−	0.728388i	$-0.740270\pi$
$757$	−26.7814	−	46.3867i	−0.973385	−	1.68595i	−0.288220	−	0.957564i	$-0.593063\pi$
$758$	7.37728			0.267955
$759$	−2.86801	+	4.96754i	−0.104102	+	0.180310i
$760$	−1.27332	−	2.20545i	−0.0461881	−	0.0800001i
$761$	−3.68166			−0.133460			−0.0667300	−	0.997771i	$-0.521257\pi$
$761$	−3.68166			−0.133460			−0.0667300	+	0.997771i	$0.521257\pi$
$762$	29.1121			1.05462
$763$		0			0
$764$	−2.77711	−	4.81010i	−0.100472	−	0.174023i
$765$	−2.14886	+	3.72193i	−0.0776922	+	0.134567i
$766$	−17.3524	+	30.0553i	−0.626968	+	1.08594i
$767$	5.42218	+	42.4735i	0.195783	+	1.53363i
$768$	−7.79476	−	13.5009i	−0.281269	−	0.487172i
$769$	2.61897	+	4.53619i	0.0944424	+	0.163579i	0.909376	−	0.415976i	$-0.136560\pi$
$769$	2.61897	+	4.53619i	0.0944424	+	0.163579i	−0.814933	+	0.579555i	$0.803227\pi$
$770$		0			0
$771$	22.4902	−	38.9541i	0.809963	−	1.40290i
$772$	−3.54002	−	6.13150i	−0.127408	−	0.220677i
$773$	−20.3069	−	35.1726i	−0.730388	−	1.26507i	−0.956717	−	0.291019i	$-0.906006\pi$
$773$	−20.3069	−	35.1726i	−0.730388	−	1.26507i	0.226329	−	0.974051i	$-0.427328\pi$
$774$	−13.3672	−	23.1527i	−0.480474	−	0.832205i
$775$	14.1588	+	24.5238i	0.508601	+	0.880922i
$776$	−1.24944	+	2.16409i	−0.0448522	+	0.0776862i
$777$		0			0
$778$	−15.4451	−	26.7517i	−0.553733	−	0.959094i
$779$	−1.14124	−	1.97668i	−0.0408890	−	0.0708219i
$780$	−1.12448	+	0.855850i	−0.0402628	+	0.0306443i
$781$	−5.02213	+	8.69859i	−0.179706	+	0.311260i
$782$	−6.46762	+	11.2022i	−0.231281	+	0.400591i
$783$	10.8390	+	18.7737i	0.387353	+	0.670916i
$784$		0			0
$785$	−2.22997			−0.0795911
$786$	21.9825			0.784090
$787$	17.1000	+	29.6181i	0.609550	+	1.05577i	0.991315	+	0.131512i	$0.0419830\pi$
$787$	17.1000	+	29.6181i	0.609550	+	1.05577i	−0.381765	+	0.924259i	$0.624684\pi$
$788$	−3.12851	+	5.41873i	−0.111448	+	0.193034i
$789$	−17.9238			−0.638104
$790$	6.70559	+	11.6144i	0.238574	+	0.413223i
$791$		0			0
$792$	5.93434			0.210868
$793$	8.24819	+	3.45451i	0.292902	+	0.122673i
$794$	−25.9579	+	44.9604i	−0.921211	+	1.59558i
$795$	−10.3347			−0.366532
$796$	−0.289116	+	0.500764i	−0.0102474	+	0.0177491i
$797$	15.6903	−	27.1763i	0.555778	−	0.962635i	−0.442065	−	0.896983i	$-0.645754\pi$
$797$	15.6903	−	27.1763i	0.555778	−	0.962635i	0.997843	−	0.0656522i	$-0.0209128\pi$
$798$		0			0
$799$	1.11439	−	1.93017i	0.0394241	−	0.0682846i
$800$	−8.15951			−0.288482
$801$	12.5350	−	21.7112i	0.442901	−	0.767128i
$802$	−2.30090	−	3.98528i	−0.0812477	−	0.140725i
$803$	−12.4484	+	21.5613i	−0.439295	+	0.760881i
$804$	2.51788	+	4.36109i	0.0887988	+	0.153804i
$805$		0			0
$806$	−4.22612	−	33.1044i	−0.148859	−	1.16605i
$807$	−6.19832	−	10.7358i	−0.218191	−	0.377918i
$808$	7.54441			0.265412
$809$	−37.9418			−1.33396			−0.666981	−	0.745075i	$-0.732414\pi$
$809$	−37.9418			−1.33396			−0.666981	+	0.745075i	$0.732414\pi$
$810$	−10.0833			−0.354292
$811$	32.1023			1.12726			0.563632	−	0.826026i	$-0.309403\pi$
$811$	32.1023			1.12726			0.563632	+	0.826026i	$0.309403\pi$
$812$		0			0
$813$	19.5930	−	33.9360i	0.687155	−	1.19019i
$814$	1.62948	+	2.82234i	0.0571133	+	0.0989231i
$815$	0.505555	+	0.875646i	0.0177088	+	0.0306725i
$816$	46.1586			1.61588
$817$	−9.73265	+	16.8574i	−0.340502	+	0.589767i
$818$	−8.18670			−0.286241
$819$		0			0
$820$	0.249856			0.00872534
$821$	8.46117	−	14.6552i	0.295297	−	0.511469i	−0.679757	−	0.733437i	$-0.737915\pi$
$821$	8.46117	−	14.6552i	0.295297	−	0.511469i	0.975054	+	0.221968i	$0.0712481\pi$
$822$	45.5132			1.58745
$823$	7.23666	+	12.5343i	0.252254	+	0.436917i	0.964146	−	0.265372i	$-0.0854948\pi$
$823$	7.23666	+	12.5343i	0.252254	+	0.436917i	−0.711892	+	0.702289i	$0.752161\pi$
$824$	0.678278	+	1.17481i	0.0236289	+	0.0409265i
$825$	7.52209	−	13.0286i	0.261885	−	0.453599i
$826$		0			0
$827$	27.5792			0.959021			0.479511	−	0.877536i	$-0.340814\pi$
$827$	27.5792			0.959021			0.479511	+	0.877536i	$0.340814\pi$
$828$	0.843731			0.0293217
$829$	−21.0930			−0.732592			−0.366296	−	0.930498i	$-0.619374\pi$
$829$	−21.0930			−0.732592			−0.366296	+	0.930498i	$0.619374\pi$
$830$	−9.07281			−0.314922
$831$	6.57326	+	11.3852i	0.228024	+	0.394949i
$832$	−21.2454	−	8.89800i	−0.736550	−	0.308483i
$833$		0			0
$834$	−27.9474	−	48.4064i	−0.967741	−	1.67618i
$835$	−3.72852	+	6.45798i	−0.129031	+	0.223488i
$836$	0.400455	+	0.693609i	0.0138500	+	0.0239890i
$837$	9.57131	−	16.5780i	0.330833	−	0.573020i
$838$	−8.94572			−0.309025
$839$	−6.35488	+	11.0070i	−0.219395	+	0.380003i	−0.954623	−	0.297817i	$-0.903742\pi$
$839$	−6.35488	+	11.0070i	−0.219395	+	0.380003i	0.735228	+	0.677819i	$0.237075\pi$
$840$		0			0
$841$	−9.25333	+	16.0272i	−0.319080	+	0.552663i
$842$	−21.8698	+	37.8796i	−0.753682	+	1.30542i
$843$	−11.9929			−0.413056
$844$	2.52852	−	4.37952i	0.0870351	−	0.150749i
$845$	−2.04115	+	7.38521i	−0.0702177	+	0.254059i
$846$	−1.07504			−0.0369606
$847$		0			0
$848$	18.6695	+	32.3365i	0.641113	+	1.11044i
$849$	34.9877			1.20077
$850$	16.9630	−	29.3807i	0.581825	−	1.00775i
$851$	−1.24986	−	2.16481i	−0.0428445	−	0.0742089i
$852$	4.39197			0.150467
$853$	35.0471			1.19999			0.599996	−	0.800003i	$-0.295169\pi$
$853$	35.0471			1.19999			0.599996	+	0.800003i	$0.295169\pi$
$854$		0			0
$855$	−0.754672	−	1.30713i	−0.0258092	−	0.0447029i
$856$	24.7899	−	42.9373i	0.847300	−	1.46757i
$857$	−12.7970	+	22.1651i	−0.437138	+	0.757145i	−0.997467	−	0.0711250i	$-0.977341\pi$
$857$	−12.7970	+	22.1651i	−0.437138	+	0.757145i	0.560330	+	0.828270i	$0.310674\pi$
$858$	−14.1084	+	10.7380i	−0.481652	+	0.366589i
$859$	0.372743	+	0.645610i	0.0127178	+	0.0220279i	0.872314	−	0.488946i	$-0.162618\pi$
$859$	0.372743	+	0.645610i	0.0127178	+	0.0220279i	−0.859596	+	0.510974i	$0.829285\pi$
$860$	−1.06541	−	1.84534i	−0.0363300	−	0.0629254i
$861$		0			0
$862$	6.37651	−	11.0444i	0.217185	−	0.376175i
$863$	10.9908	+	19.0367i	0.374132	+	0.648015i	0.990197	−	0.139680i	$-0.0446075\pi$
$863$	10.9908	+	19.0367i	0.374132	+	0.648015i	−0.616065	+	0.787695i	$0.711274\pi$
$864$	2.75790	+	4.77682i	0.0938255	+	0.162511i
$865$	3.38529	+	5.86350i	0.115103	+	0.199365i
$866$	−20.9861	−	36.3490i	−0.713137	−	1.23519i
$867$	−6.36804	+	11.0298i	−0.216270	+	0.374590i
$868$		0			0
$869$	11.3771	+	19.7058i	0.385943	+	0.668473i
$870$	−6.56783	−	11.3758i	−0.222670	−	0.385676i
$871$	25.1846	+	10.5479i	0.853348	+	0.357400i
$872$	7.35444	−	12.7383i	0.249053	−	0.431372i
$873$	−0.740517	+	1.28261i	−0.0250627	+	0.0434099i
$874$	−2.27140	−	3.93418i	−0.0768313	−	0.133076i
$875$		0			0
$876$	10.8864			0.367818
$877$	29.4190			0.993411			0.496705	−	0.867919i	$-0.334543\pi$
$877$	29.4190			0.993411			0.496705	+	0.867919i	$0.334543\pi$
$878$	23.7041	+	41.0567i	0.799975	+	1.38560i
$879$	32.5492	−	56.3769i	1.09786	−	1.90155i
$880$	4.05831			0.136806
$881$	−24.1414	−	41.8142i	−0.813345	−	1.40876i	−0.910510	−	0.413487i	$-0.864311\pi$
$881$	−24.1414	−	41.8142i	−0.813345	−	1.40876i	0.0971649	−	0.995268i	$-0.469023\pi$
$882$		0			0
$883$	16.4465			0.553469			0.276735	−	0.960946i	$-0.410748\pi$
$883$	16.4465			0.553469			0.276735	+	0.960946i	$0.410748\pi$
$884$	−4.30240	+	3.27459i	−0.144705	+	0.110136i
$885$	7.44110	−	12.8884i	0.250130	−	0.433238i
$886$	35.8724			1.20516
$887$	−14.5827	+	25.2579i	−0.489638	+	0.848078i	−0.999929	−	0.0119239i	$-0.996204\pi$
$887$	−14.5827	+	25.2579i	−0.489638	+	0.848078i	0.510291	+	0.860002i	$0.329538\pi$
$888$	−3.84388	+	6.65780i	−0.128992	+	0.223421i
$889$		0			0
$890$	7.38800	−	12.7964i	0.247646	−	0.428936i
$891$	−17.1080			−0.573141
$892$	−1.94403	+	3.36716i	−0.0650910	+	0.112741i
$893$	0.391368	+	0.677869i	0.0130966	+	0.0226840i
$894$	−27.6870	+	47.9553i	−0.925993	+	1.60387i
$895$	−0.643765	−	1.11503i	−0.0215187	−	0.0372715i
$896$		0			0
$897$	10.8215	−	8.23633i	0.361320	−	0.275003i
$898$	2.14928	+	3.72266i	0.0717224	+	0.124227i
$899$	41.9506			1.39913
$900$	−2.21290			−0.0737633
$901$	−39.5417			−1.31733
$902$	3.13484			0.104379
$903$		0			0
$904$	−6.60673	+	11.4432i	−0.219736	+	0.380595i
$905$	3.41791	+	5.92000i	0.113615	+	0.196787i
$906$	25.5404	+	44.2373i	0.848524	+	1.46969i
$907$	−35.3215			−1.17283			−0.586416	−	0.810010i	$-0.699461\pi$
$907$	−35.3215			−1.17283			−0.586416	+	0.810010i	$0.699461\pi$
$908$	0.193120	−	0.334494i	0.00640892	−	0.0111006i
$909$	4.47143			0.148308
$910$		0			0
$911$	−43.6496			−1.44617			−0.723087	−	0.690757i	$-0.757278\pi$
$911$	−43.6496			−1.44617			−0.723087	+	0.690757i	$0.757278\pi$
$912$	−8.10537	+	14.0389i	−0.268396	+	0.464875i
$913$	−15.3935			−0.509452
$914$	−28.6994	−	49.7088i	−0.949292	−	1.64422i
$915$	−1.55404	−	2.69167i	−0.0513749	−	0.0889840i
$916$	1.02507	−	1.77547i	0.0338691	−	0.0586630i
$917$		0			0
$918$	−22.9338			−0.756927
$919$	−17.7878			−0.586765			−0.293382	−	0.955995i	$-0.594781\pi$
$919$	−17.7878			−0.586765			−0.293382	+	0.955995i	$0.594781\pi$
$920$	−2.68279			−0.0884491
$921$	21.1775			0.697822
$922$	26.3539	+	45.6463i	0.867921	+	1.50328i
$923$	18.9494	−	14.4225i	0.623726	−	0.474723i
$924$		0			0
$925$	3.27806	+	5.67777i	0.107782	+	0.186684i
$926$	14.0758	−	24.3800i	0.462559	−	0.801176i
$927$	0.402003	+	0.696289i	0.0132035	+	0.0228691i
$928$	−6.04385	+	10.4683i	−0.198399	+	0.343638i
$929$	3.91420			0.128421			0.0642103	−	0.997936i	$-0.479547\pi$
$929$	3.91420			0.128421			0.0642103	+	0.997936i	$0.479547\pi$
$930$	−5.79969	+	10.0454i	−0.190179	+	0.329401i
$931$		0			0
$932$	−0.984992	+	1.70606i	−0.0322645	+	0.0558837i
$933$	29.4977	−	51.0916i	0.965712	−	1.67266i
$934$	−10.0794			−0.329809
$935$	−2.14886	+	3.72193i	−0.0702752	+	0.121720i
$936$	−12.9773	−	5.43517i	−0.424177	−	0.177654i
$937$	−0.207362			−0.00677421			−0.00338710	−	0.999994i	$-0.501078\pi$
$937$	−0.207362			−0.00677421			−0.00338710	+	0.999994i	$0.501078\pi$
$938$		0			0
$939$	−17.5654	−	30.4242i	−0.573225	−	0.992855i
$940$	−0.0856839			−0.00279470
$941$	−13.7328	+	23.7859i	−0.447677	+	0.775400i	−0.998234	−	0.0593977i	$-0.981082\pi$
$941$	−13.7328	+	23.7859i	−0.447677	+	0.775400i	0.550557	+	0.834797i	$0.314415\pi$
$942$	6.11697	+	10.5949i	0.199302	+	0.345200i
$943$	−2.40451			−0.0783015
$944$	−53.7692			−1.75004
$945$		0			0
$946$	−13.3672	−	23.1527i	−0.434605	−	0.752758i
$947$	11.5182	−	19.9501i	0.374290	−	0.648290i	−0.615930	−	0.787801i	$-0.711220\pi$
$947$	11.5182	−	19.9501i	0.374290	−	0.648290i	0.990221	+	0.139511i	$0.0445531\pi$
$948$	4.97479	−	8.61660i	0.161574	−	0.279854i
$949$	46.9700	−	35.7492i	1.52471	−	1.16047i
$950$	5.95733	+	10.3184i	0.193281	+	0.334773i
$951$	−25.1736	−	43.6019i	−0.816309	−	1.41389i
$952$		0			0
$953$	−7.22808	+	12.5194i	−0.234140	+	0.405543i	−0.959022	−	0.283330i	$-0.908561\pi$
$953$	−7.22808	+	12.5194i	−0.234140	+	0.405543i	0.724882	+	0.688873i	$0.241894\pi$
$954$	9.53641	+	16.5175i	0.308753	+	0.534775i
$955$	5.23357	+	9.06480i	0.169354	+	0.293330i
$956$	2.95853	+	5.12432i	0.0956856	+	0.165732i
$957$	−11.1434	−	19.3010i	−0.360215	−	0.623911i
$958$	−13.2707	+	22.9856i	−0.428758	+	0.742630i
$959$		0			0
$960$	4.00283	+	6.93311i	0.129191	+	0.223765i
$961$	−3.02213	−	5.23448i	−0.0974881	−	0.168854i
$962$	−0.978433	−	7.66436i	−0.0315460	−	0.247109i
$963$	14.6925	−	25.4481i	0.473459	−	0.820054i
$964$	3.48668	−	6.03910i	0.112298	−	0.194506i
$965$	6.67129	+	11.5550i	0.214756	+	0.371969i
$966$		0			0
$967$	32.3357			1.03984			0.519922	−	0.854213i	$-0.325961\pi$
$967$	32.3357			1.03984			0.519922	+	0.854213i	$0.325961\pi$
$968$	−22.2908			−0.716454
$969$	−8.58353	−	14.8671i	−0.275743	−	0.477600i
$970$	−0.436454	+	0.755961i	−0.0140137	+	0.0242725i
$971$	24.6235			0.790206			0.395103	−	0.918637i	$-0.370709\pi$
$971$	24.6235			0.790206			0.395103	+	0.918637i	$0.370709\pi$
$972$	2.26487	+	3.92287i	0.0726458	+	0.125826i
$973$		0			0
$974$	54.0084			1.73054
$975$	−28.3821	+	21.6019i	−0.908956	+	0.691813i
$976$	−5.61472	+	9.72499i	−0.179723	+	0.311289i
$977$	6.00992			0.192274			0.0961372	−	0.995368i	$-0.469351\pi$
$977$	6.00992			0.192274			0.0961372	+	0.995368i	$0.469351\pi$
$978$	2.77354	−	4.80392i	0.0886882	−	0.153612i
$979$	12.5350	−	21.7112i	0.400619	−	0.693893i
$980$		0			0
$981$	4.35884	−	7.54973i	0.139167	−	0.241044i
$982$	45.3371			1.44676
$983$	17.9546	−	31.0984i	0.572664	−	0.991884i	−0.423627	−	0.905837i	$-0.639243\pi$
$983$	17.9546	−	31.0984i	0.572664	−	0.991884i	0.996291	−	0.0860467i	$-0.0274234\pi$
$984$	3.69748	+	6.40422i	0.117871	+	0.204159i
$985$	5.89578	−	10.2118i	0.187855	−	0.325374i
$986$	−25.1294	−	43.5253i	−0.800282	−	1.38613i
$987$		0			0
$988$	−0.240456	−	1.88357i	−0.00764994	−	0.0599242i
$989$	10.2530	+	17.7587i	0.326027	+	0.564694i
$990$	2.07299			0.0658840
$991$	28.0000			0.889449			0.444724	−	0.895668i	$-0.353302\pi$
$991$	28.0000			0.889449			0.444724	+	0.895668i	$0.353302\pi$
$992$	10.6740			0.338900
$993$	16.9078			0.536553
$994$		0			0
$995$	0.544849	−	0.943706i	0.0172729	−	0.0299175i
$996$	3.36550	+	5.82922i	0.106640	+	0.184706i
$997$	16.5040	+	28.5858i	0.522688	+	0.905323i	0.999651	+	0.0263994i	$0.00840416\pi$
$997$	16.5040	+	28.5858i	0.522688	+	0.905323i	−0.476963	+	0.878923i	$0.658263\pi$
$998$	11.4205			0.361509
$999$	2.21596	−	3.83815i	0.0701097	−	0.121434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.m.263.6		16
7.2	even	3		637.2.h.m.471.3		16
7.3	odd	6		637.2.f.l.393.6	yes	16
7.4	even	3		637.2.f.l.393.5	yes	16
7.5	odd	6		637.2.h.m.471.4		16
7.6	odd	2	inner	637.2.g.m.263.5		16
13.9	even	3		637.2.h.m.165.3		16
91.3	odd	6		8281.2.a.ci.1.3		8
91.9	even	3	inner	637.2.g.m.373.6		16
91.10	odd	6		8281.2.a.cl.1.5		8
91.48	odd	6		637.2.h.m.165.4		16
91.61	odd	6	inner	637.2.g.m.373.5		16
91.74	even	3		637.2.f.l.295.5	✓	16
91.81	even	3		8281.2.a.ci.1.4		8
91.87	odd	6		637.2.f.l.295.6	yes	16
91.88	even	6		8281.2.a.cl.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.5	✓	16	91.74	even	3
637.2.f.l.295.6	yes	16	91.87	odd	6
637.2.f.l.393.5	yes	16	7.4	even	3
637.2.f.l.393.6	yes	16	7.3	odd	6
637.2.g.m.263.5		16	7.6	odd	2	inner
637.2.g.m.263.6		16	1.1	even	1	trivial
637.2.g.m.373.5		16	91.61	odd	6	inner
637.2.g.m.373.6		16	91.9	even	3	inner
637.2.h.m.165.3		16	13.9	even	3
637.2.h.m.165.4		16	91.48	odd	6
637.2.h.m.471.3		16	7.2	even	3
637.2.h.m.471.4		16	7.5	odd	6
8281.2.a.ci.1.3		8	91.3	odd	6
8281.2.a.ci.1.4		8	91.81	even	3
8281.2.a.cl.1.5		8	91.10	odd	6
8281.2.a.cl.1.6		8	91.88	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.760387 - 1.31703i) q^{2} +2.12621 q^{3} +(-0.156376 - 0.270851i) q^{4} +(0.294696 + 0.510428i) q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +1.52077 q^{9} +O(q^{10})\)	\(q+(0.760387 - 1.31703i) q^{2} +2.12621 q^{3} +(-0.156376 - 0.270851i) q^{4} +(0.294696 + 0.510428i) q^{5} +(1.61674 - 2.80028i) q^{6} +2.56592 q^{8} +1.52077 q^{9} +0.896331 q^{10} +1.52077 q^{11} +(-0.332488 - 0.575886i) q^{12} +(-3.32565 - 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} +(2.26384 - 3.92109i) q^{16} +(2.39740 + 4.15241i) q^{17} +(1.15638 - 2.00290i) q^{18} -1.68391 q^{19} +(0.0921666 - 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +(-0.886972 + 1.53628i) q^{23} +5.45569 q^{24} +(2.32631 - 4.02929i) q^{25} +(-4.36321 + 3.32087i) q^{26} -3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +1.90579 q^{30} +(-3.04320 + 5.27098i) q^{31} +(-0.876873 - 1.51879i) q^{32} +3.23349 q^{33} +7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +(-0.704563 + 1.22034i) q^{37} +(-1.28043 + 2.21776i) q^{38} +(-7.07104 - 2.96150i) q^{39} +(0.756166 + 1.30972i) q^{40} +(0.677729 + 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +(-0.237812 - 0.411903i) q^{44} +(0.448165 + 0.776245i) q^{45} +(1.34888 + 2.33633i) q^{46} +(-0.232416 - 0.402556i) q^{47} +(4.81341 - 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} +(5.09737 + 8.82890i) q^{51} +(0.142796 + 1.11856i) q^{52} +(-4.12340 + 7.14194i) q^{53} +(-2.39153 + 4.14225i) q^{54} +(0.448165 + 0.776245i) q^{55} -3.58035 q^{57} -10.4819 q^{58} +(-5.93782 - 10.2846i) q^{59} +(0.195966 - 0.339422i) q^{60} -2.48017 q^{61} +(4.62802 + 8.01596i) q^{62} +6.38833 q^{64} +(-0.269104 - 2.10797i) q^{65} +(2.45870 - 4.25859i) q^{66} -7.57284 q^{67} +(0.749790 - 1.29867i) q^{68} +(-1.88589 + 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +3.90219 q^{72} +(-8.18558 + 14.1778i) q^{73} +(1.07148 + 1.85586i) q^{74} +(4.94622 - 8.56711i) q^{75} +(0.263323 + 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} +(7.48116 + 12.9577i) q^{79} +2.66858 q^{80} -11.2496 q^{81} +2.06134 q^{82} -10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +(-8.78973 - 15.2243i) q^{86} +(-7.32746 - 12.6915i) q^{87} +3.90219 q^{88} +(8.24250 - 14.2764i) q^{89} +1.36312 q^{90} +0.554804 q^{92} +(-6.47049 + 11.2072i) q^{93} -0.706904 q^{94} +(-0.496242 - 0.859516i) q^{95} +(-1.86442 - 3.22927i) q^{96} +(-0.486935 + 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

L-functions

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