LMFDB - Embedded newform 112.3.s.b.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(17,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("112.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.s (of order $6$, 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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	112.17
Dual form			112.3.s.b.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.62132 + 2.09077i) q^{3} +(2.74264 - 1.58346i) q^{5} +(2.24264 - 6.63103i) q^{7} +(4.24264 + 7.34847i) q^{9} +O(q^{10})$	\(q+(3.62132 + 2.09077i) q^{3} +(2.74264 - 1.58346i) q^{5} +(2.24264 - 6.63103i) q^{7} +(4.24264 + 7.34847i) q^{9} +(-6.62132 + 11.4685i) q^{11} +5.49333i q^{13} +13.2426 q^{15} +(-11.7426 - 6.77962i) q^{17} +(0.621320 - 0.358719i) q^{19} +(21.9853 - 19.3242i) q^{21} +(-1.13604 - 1.96768i) q^{23} +(-7.48528 + 12.9649i) q^{25} -2.15232i q^{27} +20.4853 q^{29} +(-21.3198 - 12.3090i) q^{31} +(-47.9558 + 27.6873i) q^{33} +(-4.34924 - 21.7377i) q^{35} +(-32.4706 - 56.2407i) q^{37} +(-11.4853 + 19.8931i) q^{39} +21.0308i q^{41} -6.48528 q^{43} +(23.2721 + 13.4361i) q^{45} +(-41.3787 + 23.8900i) q^{47} +(-38.9411 - 29.7420i) q^{49} +(-28.3492 - 49.1023i) q^{51} +(-11.0147 + 19.0781i) q^{53} +41.9385i q^{55} +3.00000 q^{57} +(72.5330 + 41.8770i) q^{59} +(57.3823 - 33.1297i) q^{61} +(58.2426 - 11.6531i) q^{63} +(8.69848 + 15.0662i) q^{65} +(46.3198 - 80.2283i) q^{67} -9.50079i q^{69} +48.4264 q^{71} +(113.441 + 65.4953i) q^{73} +(-54.2132 + 31.3000i) q^{75} +(61.1985 + 69.6258i) q^{77} +(-38.1066 - 66.0026i) q^{79} +(42.6838 - 73.9305i) q^{81} +107.981i q^{83} -42.9411 q^{85} +(74.1838 + 42.8300i) q^{87} +(-145.412 + 83.9535i) q^{89} +(36.4264 + 12.3196i) q^{91} +(-51.4706 - 89.1496i) q^{93} +(1.13604 - 1.96768i) q^{95} -25.5816i q^{97} -112.368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7	$ 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7} - 18 q^{11} + 36 q^{15} - 30 q^{17} - 6 q^{19} + 54 q^{21} - 30 q^{23} + 4 q^{25} + 48 q^{29} + 42 q^{31} - 90 q^{33} + 42 q^{35} - 62 q^{37} - 12 q^{39} + 8 q^{43} + 144 q^{45} - 174 q^{47} - 20 q^{49} - 54 q^{51} - 78 q^{53} + 12 q^{57} + 78 q^{59} - 42 q^{61} + 216 q^{63} - 84 q^{65} + 58 q^{67} + 24 q^{71} + 318 q^{73} - 132 q^{75} + 126 q^{77} - 110 q^{79} + 18 q^{81} - 36 q^{85} + 144 q^{87} - 378 q^{89} - 24 q^{91} - 138 q^{93} + 30 q^{95} - 144 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7 - 18 * q^11 + 36 * q^15 - 30 * q^17 - 6 * q^19 + 54 * q^21 - 30 * q^23 + 4 * q^25 + 48 * q^29 + 42 * q^31 - 90 * q^33 + 42 * q^35 - 62 * q^37 - 12 * q^39 + 8 * q^43 + 144 * q^45 - 174 * q^47 - 20 * q^49 - 54 * q^51 - 78 * q^53 + 12 * q^57 + 78 * q^59 - 42 * q^61 + 216 * q^63 - 84 * q^65 + 58 * q^67 + 24 * q^71 + 318 * q^73 - 132 * q^75 + 126 * q^77 - 110 * q^79 + 18 * q^81 - 36 * q^85 + 144 * q^87 - 378 * q^89 - 24 * q^91 - 138 * q^93 + 30 * q^95 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.62132	+	2.09077i	1.20711	+	0.696923i	0.962126	−	0.272605i	$-0.0878851\pi$
$3$	3.62132	+	2.09077i	1.20711	+	0.696923i	0.244981	+	0.969528i	$0.421218\pi$
$4$		0			0
$5$	2.74264	−	1.58346i	0.548528	−	0.316693i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	2.74264	−	1.58346i	0.548528	−	0.316693i	0.748528	+	0.663103i	$0.230761\pi$
$6$		0			0
$7$	2.24264	−	6.63103i	0.320377	−	0.947290i
$7$	2.24264	−	6.63103i	0.320377	−	0.947290i
$8$		0			0
$9$	4.24264	+	7.34847i	0.471405	+	0.816497i
$10$		0			0
$11$	−6.62132	+	11.4685i	−0.601938	+	1.04259i	0.390589	+	0.920565i	$0.372271\pi$
$11$	−6.62132	+	11.4685i	−0.601938	+	1.04259i	−0.992527	+	0.122022i	$0.961062\pi$
$12$		0			0
$13$			5.49333i			0.422563i	0.977425	+	0.211282i	$0.0677638\pi$
$13$			5.49333i			0.422563i	−0.977425	+	0.211282i	$0.932236\pi$
$14$		0			0
$15$	13.2426			0.882843
$16$		0			0
$17$	−11.7426	−	6.77962i	−0.690744	−	0.398801i	0.113147	−	0.993578i	$-0.463907\pi$
$17$	−11.7426	−	6.77962i	−0.690744	−	0.398801i	−0.803891	+	0.594777i	$0.797240\pi$
$18$		0			0
$19$	0.621320	−	0.358719i	0.0327011	−	0.0188800i	−0.483560	−	0.875311i	$-0.660657\pi$
$19$	0.621320	−	0.358719i	0.0327011	−	0.0188800i	0.516261	+	0.856431i	$0.327323\pi$
$20$		0			0
$21$	21.9853	−	19.3242i	1.04692	−	0.920202i
$22$		0			0
$23$	−1.13604	−	1.96768i	−0.0493930	−	0.0855512i	0.840272	−	0.542165i	$-0.182395\pi$
$23$	−1.13604	−	1.96768i	−0.0493930	−	0.0855512i	−0.889665	+	0.456614i	$0.849062\pi$
$24$		0			0
$25$	−7.48528	+	12.9649i	−0.299411	+	0.518596i
$26$		0			0
$27$		−	2.15232i		−	0.0797154i
$28$		0			0
$29$	20.4853			0.706389			0.353195	−	0.935550i	$-0.385095\pi$
$29$	20.4853			0.706389			0.353195	+	0.935550i	$0.385095\pi$
$30$		0			0
$31$	−21.3198	−	12.3090i	−0.687736	−	0.397064i	0.115028	−	0.993362i	$-0.463304\pi$
$31$	−21.3198	−	12.3090i	−0.687736	−	0.397064i	−0.802763	+	0.596298i	$0.796638\pi$
$32$		0			0
$33$	−47.9558	+	27.6873i	−1.45321	+	0.839010i
$34$		0			0
$35$	−4.34924	−	21.7377i	−0.124264	−	0.621076i
$36$		0			0
$37$	−32.4706	−	56.2407i	−0.877583	−	1.52002i	−0.853986	−	0.520296i	$-0.825821\pi$
$37$	−32.4706	−	56.2407i	−0.877583	−	1.52002i	−0.0235970	−	0.999722i	$-0.507512\pi$
$38$		0			0
$39$	−11.4853	+	19.8931i	−0.294494	+	0.510079i
$40$		0			0
$41$			21.0308i			0.512946i	0.966551	+	0.256473i	$0.0825605\pi$
$41$			21.0308i			0.512946i	−0.966551	+	0.256473i	$0.917439\pi$
$42$		0			0
$43$	−6.48528			−0.150820			−0.0754102	−	0.997153i	$-0.524027\pi$
$43$	−6.48528			−0.150820			−0.0754102	+	0.997153i	$0.524027\pi$
$44$		0			0
$45$	23.2721	+	13.4361i	0.517157	+	0.298581i
$46$		0			0
$47$	−41.3787	+	23.8900i	−0.880397	+	0.508298i	−0.870789	−	0.491656i	$-0.836392\pi$
$47$	−41.3787	+	23.8900i	−0.880397	+	0.508298i	−0.00960801	+	0.999954i	$0.503058\pi$
$48$		0			0
$49$	−38.9411	−	29.7420i	−0.794717	−	0.606980i
$50$		0			0
$51$	−28.3492	−	49.1023i	−0.555867	−	0.962791i
$52$		0			0
$53$	−11.0147	+	19.0781i	−0.207825	+	0.359963i	−0.951029	−	0.309101i	$-0.899972\pi$
$53$	−11.0147	+	19.0781i	−0.207825	+	0.359963i	0.743204	+	0.669065i	$0.233305\pi$
$54$		0			0
$55$			41.9385i			0.762518i
$56$		0			0
$57$	3.00000			0.0526316
$58$		0			0
$59$	72.5330	+	41.8770i	1.22937	+	0.709779i	0.966899	−	0.255160i	$-0.0821282\pi$
$59$	72.5330	+	41.8770i	1.22937	+	0.709779i	0.262474	+	0.964939i	$0.415462\pi$
$60$		0			0
$61$	57.3823	−	33.1297i	0.940693	−	0.543109i	0.0505153	−	0.998723i	$-0.483914\pi$
$61$	57.3823	−	33.1297i	0.940693	−	0.543109i	0.890177	+	0.455614i	$0.150580\pi$
$62$		0			0
$63$	58.2426	−	11.6531i	0.924486	−	0.184970i
$64$		0			0
$65$	8.69848	+	15.0662i	0.133823	+	0.231788i
$66$		0			0
$67$	46.3198	−	80.2283i	0.691340	−	1.19744i	−0.280058	−	0.959983i	$-0.590354\pi$
$67$	46.3198	−	80.2283i	0.691340	−	1.19744i	0.971399	−	0.237454i	$-0.0763128\pi$
$68$		0			0
$69$		−	9.50079i		−	0.137693i
$70$		0			0
$71$	48.4264			0.682062			0.341031	−	0.940052i	$-0.389224\pi$
$71$	48.4264			0.682062			0.341031	+	0.940052i	$0.389224\pi$
$72$		0			0
$73$	113.441	+	65.4953i	1.55399	+	0.897195i	0.997811	+	0.0661316i	$0.0210657\pi$
$73$	113.441	+	65.4953i	1.55399	+	0.897195i	0.556177	+	0.831064i	$0.312268\pi$
$74$		0			0
$75$	−54.2132	+	31.3000i	−0.722843	+	0.417333i
$76$		0			0
$77$	61.1985	+	69.6258i	0.794786	+	0.904231i
$78$		0			0
$79$	−38.1066	−	66.0026i	−0.482362	−	0.835476i	0.517433	−	0.855724i	$-0.326888\pi$
$79$	−38.1066	−	66.0026i	−0.482362	−	0.835476i	−0.999795	+	0.0202482i	$0.993554\pi$
$80$		0			0
$81$	42.6838	−	73.9305i	0.526960	−	0.912722i
$82$		0			0
$83$			107.981i			1.30098i	0.759514	+	0.650491i	$0.225437\pi$
$83$			107.981i			1.30098i	−0.759514	+	0.650491i	$0.774563\pi$
$84$		0			0
$85$	−42.9411			−0.505190
$86$		0			0
$87$	74.1838	+	42.8300i	0.852687	+	0.492299i
$88$		0			0
$89$	−145.412	+	83.9535i	−1.63384	+	0.943297i	−0.650945	+	0.759125i	$0.725627\pi$
$89$	−145.412	+	83.9535i	−1.63384	+	0.943297i	−0.982894	+	0.184173i	$0.941039\pi$
$90$		0			0
$91$	36.4264	+	12.3196i	0.400290	+	0.135380i
$92$		0			0
$93$	−51.4706	−	89.1496i	−0.553447	−	0.958598i
$94$		0			0
$95$	1.13604	−	1.96768i	0.0119583	−	0.0207124i
$96$		0			0
$97$		−	25.5816i		−	0.263728i	−0.991268	−	0.131864i	$-0.957904\pi$
$97$		−	25.5816i		−	0.263728i	0.991268	−	0.131864i	$-0.0420962\pi$
$98$		0			0
$99$	−112.368			−1.13503
$100$		0			0
$101$	24.6838	+	14.2512i	0.244394	+	0.141101i	0.617194	−	0.786811i	$-0.288269\pi$
$101$	24.6838	+	14.2512i	0.244394	+	0.141101i	−0.372801	+	0.927911i	$0.621603\pi$
$102$		0			0
$103$	−48.9228	+	28.2456i	−0.474979	+	0.274229i	−0.718322	−	0.695711i	$-0.755089\pi$
$103$	−48.9228	+	28.2456i	−0.474979	+	0.274229i	0.243343	+	0.969940i	$0.421756\pi$
$104$		0			0
$105$	29.6985	−	87.8124i	0.282843	−	0.836308i
$106$		0			0
$107$	23.8051	+	41.2316i	0.222477	+	0.385342i	0.955560	−	0.294798i	$-0.0952523\pi$
$107$	23.8051	+	41.2316i	0.222477	+	0.385342i	−0.733082	+	0.680140i	$0.761919\pi$
$108$		0			0
$109$	−37.6543	+	65.2192i	−0.345453	+	0.598341i	−0.985436	−	0.170047i	$-0.945608\pi$
$109$	−37.6543	+	65.2192i	−0.345453	+	0.598341i	0.639983	+	0.768389i	$0.278941\pi$
$110$		0			0
$111$		−	271.554i		−	2.44643i
$112$		0			0
$113$	85.4558			0.756246			0.378123	−	0.925755i	$-0.376570\pi$
$113$	85.4558			0.756246			0.378123	+	0.925755i	$0.376570\pi$
$114$		0			0
$115$	−6.23149	−	3.59775i	−0.0541869	−	0.0312848i
$116$		0			0
$117$	−40.3675	+	23.3062i	−0.345022	+	0.199198i
$118$		0			0
$119$	−71.2904	+	62.6616i	−0.599079	+	0.526568i
$120$		0			0
$121$	−27.1838	−	47.0837i	−0.224659	−	0.389121i
$122$		0			0
$123$	−43.9706	+	76.1592i	−0.357484	+	0.619181i
$124$		0			0
$125$			126.584i			1.01267i
$126$		0			0
$127$	60.6619			0.477653			0.238826	−	0.971062i	$-0.423237\pi$
$127$	60.6619			0.477653			0.238826	+	0.971062i	$0.423237\pi$
$128$		0			0
$129$	−23.4853	−	13.5592i	−0.182056	−	0.105110i
$130$		0			0
$131$	115.136	−	66.4738i	0.878901	−	0.507434i	0.00860515	−	0.999963i	$-0.497261\pi$
$131$	115.136	−	66.4738i	0.878901	−	0.507434i	0.870296	+	0.492529i	$0.163928\pi$
$132$		0			0
$133$	−0.985281	−	4.92447i	−0.00740813	−	0.0370261i
$134$		0			0
$135$	−3.40812	−	5.90303i	−0.0252453	−	0.0437262i
$136$		0			0
$137$	58.7132	−	101.694i	0.428564	−	0.742294i	−0.568182	−	0.822903i	$-0.692353\pi$
$137$	58.7132	−	101.694i	0.428564	−	0.742294i	0.996746	+	0.0806089i	$0.0256865\pi$
$138$		0			0
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$		0			0
$141$	−199.794			−1.41698
$142$		0			0
$143$	−63.0000	−	36.3731i	−0.440559	−	0.254357i
$144$		0			0
$145$	56.1838	−	32.4377i	0.387474	−	0.223708i
$146$		0			0
$147$	−78.8345	−	189.122i	−0.536289	−	1.28655i
$148$		0			0
$149$	13.1985	+	22.8604i	0.0885804	+	0.153426i	0.906911	−	0.421322i	$-0.138434\pi$
$149$	13.1985	+	22.8604i	0.0885804	+	0.153426i	−0.818331	+	0.574747i	$0.805100\pi$
$150$		0			0
$151$	−67.1066	+	116.232i	−0.444415	+	0.769749i	−0.998011	−	0.0630363i	$-0.979922\pi$
$151$	−67.1066	+	116.232i	−0.444415	+	0.769749i	0.553597	+	0.832785i	$0.313255\pi$
$152$		0			0
$153$		−	115.054i		−	0.751986i
$154$		0			0
$155$	−77.9634			−0.502990
$156$		0			0
$157$	−196.323	−	113.347i	−1.25047	−	0.721958i	−0.279265	−	0.960214i	$-0.590091\pi$
$157$	−196.323	−	113.347i	−1.25047	−	0.721958i	−0.971202	+	0.238256i	$0.923424\pi$
$158$		0			0
$159$	−79.7756	+	46.0585i	−0.501734	+	0.289676i
$160$		0			0
$161$	−15.5955	+	3.12032i	−0.0968662	+	0.0193808i
$162$		0			0
$163$	−45.9889	−	79.6550i	−0.282140	−	0.488681i	0.689771	−	0.724027i	$-0.257711\pi$
$163$	−45.9889	−	79.6550i	−0.282140	−	0.488681i	−0.971912	+	0.235346i	$0.924378\pi$
$164$		0			0
$165$	−87.6838	+	151.873i	−0.531417	+	0.920441i
$166$		0			0
$167$			203.482i			1.21845i	0.792996	+	0.609227i	$0.208520\pi$
$167$			203.482i			1.21845i	−0.792996	+	0.609227i	$0.791480\pi$
$168$		0			0
$169$	138.823			0.821440
$170$		0			0
$171$	5.27208	+	3.04384i	0.0308309	+	0.0178002i
$172$		0			0
$173$	61.3234	−	35.4051i	0.354470	−	0.204654i	−0.312182	−	0.950022i	$-0.601060\pi$
$173$	61.3234	−	35.4051i	0.354470	−	0.204654i	0.666652	+	0.745369i	$0.267727\pi$
$174$		0			0
$175$	69.1838	+	78.7107i	0.395336	+	0.449775i
$176$		0			0
$177$	175.110	+	303.300i	0.989323	+	1.71356i
$178$		0			0
$179$	54.4081	−	94.2376i	0.303956	−	0.526467i	−0.673072	−	0.739577i	$-0.735026\pi$
$179$	54.4081	−	94.2376i	0.303956	−	0.526467i	0.977028	+	0.213109i	$0.0683591\pi$
$180$		0			0
$181$			99.6607i			0.550611i	0.961357	+	0.275306i	$0.0887791\pi$
$181$			99.6607i			0.550611i	−0.961357	+	0.275306i	$0.911221\pi$
$182$		0			0
$183$	277.066			1.51402
$184$		0			0
$185$	−178.110	−	102.832i	−0.962758	−	0.555848i
$186$		0			0
$187$	155.504	−	89.7800i	0.831570	−	0.480107i
$188$		0			0
$189$	−14.2721	−	4.82687i	−0.0755136	−	0.0255390i
$190$		0			0
$191$	34.9523	+	60.5391i	0.182996	+	0.316959i	0.942899	−	0.333077i	$-0.108087\pi$
$191$	34.9523	+	60.5391i	0.182996	+	0.316959i	−0.759903	+	0.650036i	$0.774754\pi$
$192$		0			0
$193$	16.1690	−	28.0056i	0.0837774	−	0.145107i	−0.821092	−	0.570796i	$-0.806635\pi$
$193$	16.1690	−	28.0056i	0.0837774	−	0.145107i	0.904870	+	0.425689i	$0.139968\pi$
$194$		0			0
$195$			72.7461i			0.373057i
$196$		0			0
$197$	277.103			1.40661			0.703306	−	0.710887i	$-0.251706\pi$
$197$	277.103			1.40661			0.703306	+	0.710887i	$0.251706\pi$
$198$		0			0
$199$	−145.011	−	83.7222i	−0.728699	−	0.420715i	0.0892469	−	0.996010i	$-0.471554\pi$
$199$	−145.011	−	83.7222i	−0.728699	−	0.420715i	−0.817946	+	0.575295i	$0.804887\pi$
$200$		0			0
$201$	335.478	−	193.688i	1.66904	−	0.963623i
$202$		0			0
$203$	45.9411	−	135.839i	0.226311	−	0.669155i
$204$		0			0
$205$	33.3015	+	57.6799i	0.162446	+	0.281365i
$206$		0			0
$207$	9.63961	−	16.6963i	0.0465682	−	0.0806584i
$208$		0			0
$209$			9.50079i			0.0454583i
$210$		0			0
$211$	128.073			0.606982			0.303491	−	0.952834i	$-0.401848\pi$
$211$	128.073			0.606982			0.303491	+	0.952834i	$0.401848\pi$
$212$		0			0
$213$	175.368	+	101.248i	0.823322	+	0.475345i
$214$		0			0
$215$	−17.7868	+	10.2692i	−0.0827293	+	0.0477638i
$216$		0			0
$217$	−129.434	+	113.768i	−0.596470	+	0.524275i
$218$		0			0
$219$	273.871	+	474.359i	1.25055	+	2.16602i
$220$		0			0
$221$	37.2426	−	64.5061i	0.168519	−	0.291883i
$222$		0			0
$223$		−	417.169i		−	1.87071i	−0.353705	−	0.935357i	$-0.615078\pi$
$223$		−	417.169i		−	1.87071i	0.353705	−	0.935357i	$-0.384922\pi$
$224$		0			0
$225$	−127.029			−0.564575
$226$		0			0
$227$	−201.143	−	116.130i	−0.886093	−	0.511586i	−0.0134307	−	0.999910i	$-0.504275\pi$
$227$	−201.143	−	116.130i	−0.886093	−	0.511586i	−0.872663	+	0.488324i	$0.837609\pi$
$228$		0			0
$229$	−72.4188	+	41.8110i	−0.316239	+	0.182581i	−0.649715	−	0.760178i	$-0.725112\pi$
$229$	−72.4188	+	41.8110i	−0.316239	+	0.182581i	0.333476	+	0.942759i	$0.391778\pi$
$230$		0			0
$231$	76.0477	+	380.089i	0.329211	+	1.64541i
$232$		0			0
$233$	−109.537	−	189.723i	−0.470114	−	0.814261i	0.529302	−	0.848434i	$-0.322454\pi$
$233$	−109.537	−	189.723i	−0.470114	−	0.814261i	−0.999416	+	0.0341721i	$0.989121\pi$
$234$		0			0
$235$	−75.6579	+	131.043i	−0.321949	+	0.557631i
$236$		0			0
$237$		−	318.689i		−	1.34468i
$238$		0			0
$239$	−193.103			−0.807961			−0.403980	−	0.914768i	$-0.632374\pi$
$239$	−193.103			−0.807961			−0.403980	+	0.914768i	$0.632374\pi$
$240$		0			0
$241$	42.8970	+	24.7666i	0.177996	+	0.102766i	0.586351	−	0.810057i	$-0.300564\pi$
$241$	42.8970	+	24.7666i	0.177996	+	0.102766i	−0.408355	+	0.912823i	$0.633897\pi$
$242$		0			0
$243$	292.368	−	168.798i	1.20316	−	0.694644i
$244$		0			0
$245$	−153.897	−	19.9098i	−0.628151	−	0.0812646i
$246$		0			0
$247$	1.97056	+	3.41311i	0.00797799	+	0.0138183i
$248$		0			0
$249$	−225.765	+	391.036i	−0.906685	+	1.57042i
$250$		0			0
$251$			162.524i			0.647507i	0.946141	+	0.323754i	$0.104945\pi$
$251$			162.524i			0.647507i	−0.946141	+	0.323754i	$0.895055\pi$
$252$		0			0
$253$	30.0883			0.118926
$254$		0			0
$255$	−155.504	−	89.7800i	−0.609818	−	0.352079i
$256$		0			0
$257$	−85.8747	+	49.5798i	−0.334143	+	0.192917i	−0.657679	−	0.753298i	$-0.728462\pi$
$257$	−85.8747	+	49.5798i	−0.334143	+	0.192917i	0.323536	+	0.946216i	$0.395128\pi$
$258$		0			0
$259$	−445.753	+	89.1857i	−1.72106	+	0.344346i
$260$		0			0
$261$	86.9117	+	150.535i	0.332995	+	0.576764i
$262$		0			0
$263$	217.173	−	376.154i	0.825751	−	1.43024i	−0.0755923	−	0.997139i	$-0.524085\pi$
$263$	217.173	−	376.154i	0.825751	−	1.43024i	0.901344	−	0.433105i	$-0.142582\pi$
$264$		0			0
$265$			69.7657i			0.263267i
$266$		0			0
$267$	−702.110			−2.62962
$268$		0			0
$269$	−79.1619	−	45.7041i	−0.294282	−	0.169904i	0.345589	−	0.938386i	$-0.387679\pi$
$269$	−79.1619	−	45.7041i	−0.294282	−	0.169904i	−0.639871	+	0.768482i	$0.721012\pi$
$270$		0			0
$271$	−14.8051	+	8.54772i	−0.0546313	+	0.0315414i	−0.527067	−	0.849824i	$-0.676708\pi$
$271$	−14.8051	+	8.54772i	−0.0546313	+	0.0315414i	0.472436	+	0.881365i	$0.343375\pi$
$272$		0			0
$273$	106.154	+	120.772i	0.388844	+	0.442389i
$274$		0			0
$275$	−99.1249	−	171.689i	−0.360454	−	0.624325i
$276$		0			0
$277$	200.206	−	346.766i	0.722764	−	1.25186i	−0.237124	−	0.971479i	$-0.576205\pi$
$277$	200.206	−	346.766i	0.722764	−	1.25186i	0.959888	−	0.280385i	$-0.0904620\pi$
$278$		0			0
$279$		−	208.891i		−	0.748712i
$280$		0			0
$281$	−538.690			−1.91705			−0.958524	−	0.285012i	$-0.908002\pi$
$281$	−538.690			−1.91705			−0.958524	+	0.285012i	$0.908002\pi$
$282$		0			0
$283$	267.783	+	154.604i	0.946229	+	0.546306i	0.891907	−	0.452218i	$-0.149367\pi$
$283$	267.783	+	154.604i	0.946229	+	0.546306i	0.0543215	+	0.998523i	$0.482700\pi$
$284$		0			0
$285$	8.22792	−	4.75039i	0.0288699	−	0.0166680i
$286$		0			0
$287$	139.456	+	47.1645i	0.485909	+	0.164336i
$288$		0			0
$289$	−52.5736	−	91.0601i	−0.181916	−	0.315087i
$290$		0			0
$291$	53.4853	−	92.6392i	0.183798	−	0.318348i
$292$		0			0
$293$		−	327.391i		−	1.11738i	−0.829378	−	0.558688i	$-0.811305\pi$
$293$		−	327.391i		−	1.11738i	0.829378	−	0.558688i	$-0.188695\pi$
$294$		0			0
$295$	265.243			0.899128
$296$		0			0
$297$	24.6838	+	14.2512i	0.0831103	+	0.0479838i
$298$		0			0
$299$	10.8091	−	6.24063i	0.0361508	−	0.0208717i
$300$		0			0
$301$	−14.5442	+	43.0041i	−0.0483195	+	0.142871i
$302$		0			0
$303$	59.5919	+	103.216i	0.196673	+	0.340647i
$304$		0			0
$305$	104.919	−	181.725i	0.343998	−	0.595821i
$306$		0			0
$307$			256.140i			0.834331i	0.908831	+	0.417165i	$0.136976\pi$
$307$			256.140i			0.834331i	−0.908831	+	0.417165i	$0.863024\pi$
$308$		0			0
$309$	−236.220			−0.764467
$310$		0			0
$311$	−187.349	−	108.166i	−0.602409	−	0.347801i	0.167580	−	0.985859i	$-0.446405\pi$
$311$	−187.349	−	108.166i	−0.602409	−	0.347801i	−0.769989	+	0.638057i	$0.779738\pi$
$312$		0			0
$313$	135.809	−	78.4092i	0.433893	−	0.250509i	−0.267110	−	0.963666i	$-0.586069\pi$
$313$	135.809	−	78.4092i	0.433893	−	0.250509i	0.701004	+	0.713157i	$0.252736\pi$
$314$		0			0
$315$	141.286	−	124.185i	0.448528	−	0.394239i
$316$		0			0
$317$	224.015	+	388.005i	0.706671	+	1.22399i	0.966085	+	0.258224i	$0.0831372\pi$
$317$	224.015	+	388.005i	0.706671	+	1.22399i	−0.259414	+	0.965766i	$0.583529\pi$
$318$		0			0
$319$	−135.640	+	234.935i	−0.425203	+	0.736472i
$320$		0			0
$321$			199.084i			0.620199i
$322$		0			0
$323$	−9.72792			−0.0301174
$324$		0			0
$325$	−71.2203	−	41.1191i	−0.219140	−	0.126520i
$326$		0			0
$327$	−272.717	+	157.453i	−0.833996	+	0.481508i
$328$		0			0
$329$	65.6177	+	327.960i	0.199446	+	0.996839i
$330$		0			0
$331$	−27.5036	−	47.6376i	−0.0830924	−	0.143920i	0.821484	−	0.570231i	$-0.193146\pi$
$331$	−27.5036	−	47.6376i	−0.0830924	−	0.143920i	−0.904577	+	0.426311i	$0.859813\pi$
$332$		0			0
$333$	275.522	−	477.218i	0.827393	−	1.43309i
$334$		0			0
$335$		−	293.383i		−	0.875770i
$336$		0			0
$337$	−111.632			−0.331254			−0.165627	−	0.986189i	$-0.552965\pi$
$337$	−111.632			−0.331254			−0.165627	+	0.986189i	$0.552965\pi$
$338$		0			0
$339$	309.463	+	178.669i	0.912870	+	0.527046i
$340$		0			0
$341$	282.331	−	163.004i	0.827949	−	0.478016i
$342$		0			0
$343$	−284.551	+	191.519i	−0.829596	+	0.558365i
$344$		0			0
$345$	−15.0442	−	26.0572i	−0.0436062	−	0.0755282i
$346$		0			0
$347$	188.628	−	326.714i	0.543598	−	0.941539i	−0.455096	−	0.890442i	$-0.650395\pi$
$347$	188.628	−	326.714i	0.543598	−	0.941539i	0.998694	−	0.0510967i	$-0.0162717\pi$
$348$		0			0
$349$			204.034i			0.584624i	0.956323	+	0.292312i	$0.0944246\pi$
$349$			204.034i			0.584624i	−0.956323	+	0.292312i	$0.905575\pi$
$350$		0			0
$351$	11.8234			0.0336848
$352$		0			0
$353$	−361.198	−	208.538i	−1.02323	−	0.590759i	−0.108189	−	0.994130i	$-0.534505\pi$
$353$	−361.198	−	208.538i	−1.02323	−	0.590759i	−0.915036	+	0.403371i	$0.867838\pi$
$354$		0			0
$355$	132.816	−	76.6815i	0.374130	−	0.216004i
$356$		0			0
$357$	−389.176	+	77.8658i	−1.09013	+	0.218112i
$358$		0			0
$359$	−89.4153	−	154.872i	−0.249068	−	0.431398i	0.714200	−	0.699942i	$-0.246791\pi$
$359$	−89.4153	−	154.872i	−0.249068	−	0.431398i	−0.963267	+	0.268544i	$0.913457\pi$
$360$		0			0
$361$	−180.243	+	312.189i	−0.499287	+	0.864791i
$362$		0			0
$363$		−	227.340i		−	0.626281i
$364$		0			0
$365$	414.838			1.13654
$366$		0			0
$367$	544.724	+	314.497i	1.48426	+	0.856939i	0.999840	−	0.0178960i	$-0.00569679\pi$
$367$	544.724	+	314.497i	1.48426	+	0.856939i	0.484422	+	0.874835i	$0.339030\pi$
$368$		0			0
$369$	−154.544	+	89.2261i	−0.418819	+	0.241805i
$370$		0			0
$371$	101.805	+	115.824i	0.274407	+	0.312194i
$372$		0			0
$373$	127.779	+	221.320i	0.342572	+	0.593351i	0.984910	−	0.173070i	$-0.0553687\pi$
$373$	127.779	+	221.320i	0.342572	+	0.593351i	−0.642338	+	0.766422i	$0.722035\pi$
$374$		0			0
$375$	−264.658	+	458.401i	−0.705754	+	1.22240i
$376$		0			0
$377$			112.532i			0.298494i
$378$		0			0
$379$	−219.750			−0.579816			−0.289908	−	0.957055i	$-0.593625\pi$
$379$	−219.750			−0.579816			−0.289908	+	0.957055i	$0.593625\pi$
$380$		0			0
$381$	219.676	+	126.830i	0.576578	+	0.332887i
$382$		0			0
$383$	14.7534	−	8.51785i	0.0385205	−	0.0222398i	−0.480616	−	0.876931i	$-0.659587\pi$
$383$	14.7534	−	8.51785i	0.0385205	−	0.0222398i	0.519137	+	0.854691i	$0.326254\pi$
$384$		0			0
$385$	278.095	+	94.0530i	0.722326	+	0.244293i
$386$		0			0
$387$	−27.5147	−	47.6569i	−0.0710975	−	0.123144i
$388$		0			0
$389$	76.1102	−	131.827i	0.195656	−	0.338886i	−0.751459	−	0.659779i	$-0.770650\pi$
$389$	76.1102	−	131.827i	0.195656	−	0.338886i	0.947115	+	0.320893i	$0.103983\pi$
$390$		0			0
$391$			30.8076i			0.0787919i
$392$		0			0
$393$	555.926			1.41457
$394$		0			0
$395$	−209.025	−	120.681i	−0.529178	−	0.305521i
$396$		0			0
$397$	−322.786	+	186.361i	−0.813064	+	0.469423i	−0.848019	−	0.529966i	$-0.822205\pi$
$397$	−322.786	+	186.361i	−0.813064	+	0.469423i	0.0349549	+	0.999389i	$0.488871\pi$
$398$		0			0
$399$	6.72792	−	19.8931i	0.0168620	−	0.0498574i
$400$		0			0
$401$	−325.786	−	564.279i	−0.812435	−	1.40718i	−0.911155	−	0.412063i	$-0.864808\pi$
$401$	−325.786	−	564.279i	−0.812435	−	1.40718i	0.0987205	−	0.995115i	$-0.468525\pi$
$402$		0			0
$403$	67.6173	−	117.117i	0.167785	−	0.290612i
$404$		0			0
$405$		−	270.353i		−	0.667538i
$406$		0			0
$407$	859.992			2.11300
$408$		0			0
$409$	462.081	+	266.782i	1.12978	+	0.652280i	0.943880	−	0.330289i	$-0.107146\pi$
$409$	462.081	+	266.782i	1.12978	+	0.652280i	0.185902	+	0.982568i	$0.440479\pi$
$410$		0			0
$411$	425.239	−	245.512i	1.03464	−	0.597352i
$412$		0			0
$413$	440.353	−	387.054i	1.06623	−	0.937176i
$414$		0			0
$415$	170.985	+	296.154i	0.412012	+	0.713625i
$416$		0			0
$417$	−143.397	+	248.371i	−0.343878	+	0.595614i
$418$		0			0
$419$			534.252i			1.27507i	0.770423	+	0.637533i	$0.220045\pi$
$419$			534.252i			1.27507i	−0.770423	+	0.637533i	$0.779955\pi$
$420$		0			0
$421$	157.220			0.373445			0.186723	−	0.982413i	$-0.440213\pi$
$421$	157.220			0.373445			0.186723	+	0.982413i	$0.440213\pi$
$422$		0			0
$423$	−351.110	−	202.713i	−0.830047	−	0.479228i
$424$		0			0
$425$	175.794	−	101.495i	0.413633	−	0.238811i
$426$		0			0
$427$	−90.9960	−	454.801i	−0.213105	−	1.06511i
$428$		0			0
$429$	−152.095	−	263.437i	−0.354535	−	0.614072i
$430$		0			0
$431$	−114.268	+	197.918i	−0.265123	+	0.459207i	−0.967596	−	0.252504i	$-0.918746\pi$
$431$	−114.268	+	197.918i	−0.265123	+	0.459207i	0.702473	+	0.711711i	$0.252079\pi$
$432$		0			0
$433$			47.5549i			0.109827i	0.998491	+	0.0549133i	$0.0174882\pi$
$433$			47.5549i			0.109827i	−0.998491	+	0.0549133i	$0.982512\pi$
$434$		0			0
$435$	271.279			0.623630
$436$		0			0
$437$	−1.41169	−	0.815039i	−0.00323041	−	0.00186508i
$438$		0			0
$439$	63.9594	−	36.9270i	0.145693	−	0.0841161i	−0.425381	−	0.905014i	$-0.639860\pi$
$439$	63.9594	−	36.9270i	0.145693	−	0.0841161i	0.571075	+	0.820898i	$0.306527\pi$
$440$		0			0
$441$	53.3452	−	412.342i	0.120964	−	0.935017i
$442$		0			0
$443$	117.320	+	203.204i	0.264830	+	0.458699i	0.967519	−	0.252798i	$-0.0813507\pi$
$443$	117.320	+	203.204i	0.264830	+	0.458699i	−0.702689	+	0.711497i	$0.748017\pi$
$444$		0			0
$445$	−265.875	+	460.508i	−0.597471	+	1.03485i
$446$		0			0
$447$			110.380i			0.246935i
$448$		0			0
$449$	−255.161			−0.568288			−0.284144	−	0.958782i	$-0.591709\pi$
$449$	−255.161			−0.568288			−0.284144	+	0.958782i	$0.591709\pi$
$450$		0			0
$451$	−241.191	−	139.252i	−0.534791	−	0.308762i
$452$		0			0
$453$	−486.029	+	280.609i	−1.07291	+	0.619446i
$454$		0			0
$455$	119.412	−	23.8918i	0.262444	−	0.0525095i
$456$		0			0
$457$	72.8675	+	126.210i	0.159448	+	0.276171i	0.934670	−	0.355518i	$-0.115695\pi$
$457$	72.8675	+	126.210i	0.159448	+	0.276171i	−0.775222	+	0.631689i	$0.782362\pi$
$458$		0			0
$459$	−14.5919	+	25.2739i	−0.0317906	+	0.0550629i
$460$		0			0
$461$			888.329i			1.92696i	0.267777	+	0.963481i	$0.413711\pi$
$461$			888.329i			1.92696i	−0.267777	+	0.963481i	$0.586289\pi$
$462$		0			0
$463$	−234.014			−0.505430			−0.252715	−	0.967541i	$-0.581324\pi$
$463$	−234.014			−0.505430			−0.252715	+	0.967541i	$0.581324\pi$
$464$		0			0
$465$	−282.331	−	163.004i	−0.607162	−	0.350545i
$466$		0			0
$467$	−681.231	+	393.309i	−1.45874	+	0.842204i	−0.998950	−	0.0458237i	$-0.985409\pi$
$467$	−681.231	+	393.309i	−1.45874	+	0.842204i	−0.459790	+	0.888028i	$0.652075\pi$
$468$		0			0
$469$	−428.117	−	487.071i	−0.912830	−	1.03853i
$470$		0			0
$471$	−473.967	−	820.934i	−1.00630	−	1.74296i
$472$		0			0
$473$	42.9411	−	74.3762i	0.0907846	−	0.157244i
$474$		0			0
$475$			10.7405i			0.0226115i
$476$		0			0
$477$	−186.926			−0.391878
$478$		0			0
$479$	−638.202	−	368.466i	−1.33236	−	0.769240i	−0.346702	−	0.937975i	$-0.612698\pi$
$479$	−638.202	−	368.466i	−1.33236	−	0.769240i	−0.985661	+	0.168735i	$0.946032\pi$
$480$		0			0
$481$	308.948	−	178.371i	0.642304	−	0.370834i
$482$		0			0
$483$	−63.0000	−	21.3068i	−0.130435	−	0.0441136i
$484$		0			0
$485$	−40.5076	−	70.1612i	−0.0835208	−	0.144662i
$486$		0			0
$487$	135.349	−	234.432i	0.277925	−	0.481379i	−0.692944	−	0.720991i	$-0.743687\pi$
$487$	135.349	−	234.432i	0.277925	−	0.481379i	0.970869	+	0.239612i	$0.0770202\pi$
$488$		0			0
$489$		−	384.609i		−	0.786520i
$490$		0			0
$491$	−760.161			−1.54819			−0.774094	−	0.633070i	$-0.781794\pi$
$491$	−760.161			−1.54819			−0.774094	+	0.633070i	$0.781794\pi$
$492$		0			0
$493$	−240.551	−	138.882i	−0.487934	−	0.281709i
$494$		0			0
$495$	−308.184	+	177.930i	−0.622593	+	0.359455i
$496$		0			0
$497$	108.603	−	321.117i	0.218517	−	0.646111i
$498$		0			0
$499$	62.7462	+	108.680i	0.125744	+	0.217795i	0.922023	−	0.387134i	$-0.126535\pi$
$499$	62.7462	+	108.680i	0.125744	+	0.217795i	−0.796280	+	0.604929i	$0.793202\pi$
$500$		0			0
$501$	−425.434	+	736.873i	−0.849169	+	1.47080i
$502$		0			0
$503$		−	117.083i		−	0.232770i	−0.993204	−	0.116385i	$-0.962869\pi$
$503$		−	117.083i		−	0.232770i	0.993204	−	0.116385i	$-0.0371306\pi$
$504$		0			0
$505$	90.2649			0.178742
$506$		0			0
$507$	502.724	+	290.248i	0.991566	+	0.572481i
$508$		0			0
$509$	−574.110	+	331.463i	−1.12792	+	0.651204i	−0.943410	−	0.331627i	$-0.892402\pi$
$509$	−574.110	+	331.463i	−1.12792	+	0.651204i	−0.184507	+	0.982831i	$0.559069\pi$
$510$		0			0
$511$	688.709	−	605.349i	1.34777	−	1.18464i
$512$		0			0
$513$	−0.772078	−	1.33728i	−0.00150503	−	0.00260678i
$514$		0			0
$515$	−89.4518	+	154.935i	−0.173693	+	0.300845i
$516$		0			0
$517$		−	632.733i		−	1.22386i
$518$		0			0
$519$	296.095			0.570511
$520$		0			0
$521$	−40.8229	−	23.5691i	−0.0783550	−	0.0452383i	0.460311	−	0.887758i	$-0.347738\pi$
$521$	−40.8229	−	23.5691i	−0.0783550	−	0.0452383i	−0.538666	+	0.842520i	$0.681071\pi$
$522$		0			0
$523$	−432.554	+	249.735i	−0.827064	+	0.477506i	−0.852846	−	0.522162i	$-0.825126\pi$
$523$	−432.554	+	249.735i	−0.827064	+	0.477506i	0.0257824	+	0.999668i	$0.491792\pi$
$524$		0			0
$525$	85.9706	+	429.684i	0.163753	+	0.818446i
$526$		0			0
$527$	166.901	+	289.080i	0.316699	+	0.548539i
$528$		0			0
$529$	261.919	−	453.657i	0.495121	−	0.857574i
$530$		0			0
$531$			710.675i			1.33837i
$532$		0			0
$533$	−115.529			−0.216752
$534$		0			0
$535$	130.578	+	75.3890i	0.244070	+	0.140914i
$536$		0			0
$537$	394.058	−	227.510i	0.733815	−	0.423668i
$538$		0			0
$539$	598.937	−	249.663i	1.11120	−	0.463197i
$540$		0			0
$541$	−249.405	−	431.981i	−0.461007	−	0.798487i	0.538005	−	0.842942i	$-0.319178\pi$
$541$	−249.405	−	431.981i	−0.461007	−	0.798487i	−0.999011	+	0.0444550i	$0.985845\pi$
$542$		0			0
$543$	−208.368	+	360.903i	−0.383734	+	0.664647i
$544$		0			0
$545$			238.497i			0.437609i
$546$		0			0
$547$	279.897			0.511694			0.255847	−	0.966717i	$-0.417646\pi$
$547$	279.897			0.511694			0.255847	+	0.966717i	$0.417646\pi$
$548$		0			0
$549$	486.905	+	281.114i	0.886894	+	0.512048i
$550$		0			0
$551$	12.7279	−	7.34847i	0.0230997	−	0.0133366i
$552$		0			0
$553$	−523.124	+	104.666i	−0.945976	+	0.189269i
$554$		0			0
$555$	−429.996	−	744.775i	−0.774768	−	1.34194i
$556$		0			0
$557$	130.890	−	226.708i	0.234991	−	0.407016i	−0.724279	−	0.689507i	$-0.757827\pi$
$557$	130.890	−	226.708i	0.234991	−	0.407016i	0.959270	+	0.282491i	$0.0911607\pi$
$558$		0			0
$559$		−	35.6258i		−	0.0637312i
$560$		0			0
$561$	750.838			1.33839
$562$		0			0
$563$	420.076	+	242.531i	0.746139	+	0.430784i	0.824297	−	0.566157i	$-0.191571\pi$
$563$	420.076	+	242.531i	0.746139	+	0.430784i	−0.0781581	+	0.996941i	$0.524904\pi$
$564$		0			0
$565$	234.375	−	135.316i	0.414822	−	0.239498i
$566$		0			0
$567$	−394.511	−	448.837i	−0.695786	−	0.791599i
$568$		0			0
$569$	227.000	+	393.175i	0.398945	+	0.690993i	0.993596	−	0.112991i	$-0.0360432\pi$
$569$	227.000	+	393.175i	0.398945	+	0.690993i	−0.594651	+	0.803984i	$0.702710\pi$
$570$		0			0
$571$	−115.769	+	200.517i	−0.202747	+	0.351168i	−0.949413	−	0.314032i	$-0.898320\pi$
$571$	−115.769	+	200.517i	−0.202747	+	0.351168i	0.746666	+	0.665200i	$0.231654\pi$
$572$		0			0
$573$			292.309i			0.510137i
$574$		0			0
$575$	34.0143			0.0591553
$576$		0			0
$577$	564.014	+	325.634i	0.977494	+	0.564356i	0.901513	−	0.432753i	$-0.142458\pi$
$577$	564.014	+	325.634i	0.977494	+	0.564356i	0.0759812	+	0.997109i	$0.475791\pi$
$578$		0			0
$579$	117.107	−	67.6115i	0.202257	−	0.116773i
$580$		0			0
$581$	716.029	+	242.164i	1.23241	+	0.416805i
$582$		0			0
$583$	−145.864	−	252.644i	−0.250195	−	0.433351i
$584$		0			0
$585$	−73.8091	+	127.841i	−0.126169	+	0.218532i
$586$		0			0
$587$		−	823.029i		−	1.40209i	−0.713116	−	0.701046i	$-0.752717\pi$
$587$		−	823.029i		−	1.40209i	0.713116	−	0.701046i	$-0.247283\pi$
$588$		0			0
$589$	−17.6619			−0.0299863
$590$		0			0
$591$	1003.48	+	579.358i	1.69793	+	0.980301i
$592$		0			0
$593$	−700.110	+	404.209i	−1.18062	+	0.681634i	−0.956159	−	0.292848i	$-0.905397\pi$
$593$	−700.110	+	404.209i	−1.18062	+	0.681634i	−0.224465	+	0.974482i	$0.572064\pi$
$594$		0			0
$595$	−96.3015	+	284.744i	−0.161851	+	0.478561i
$596$		0			0
$597$	−350.088	−	606.370i	−0.586412	−	1.01570i
$598$		0			0
$599$	265.422	−	459.725i	0.443109	−	0.767488i	−0.554809	−	0.831978i	$-0.687209\pi$
$599$	265.422	−	459.725i	0.443109	−	0.767488i	0.997918	+	0.0644900i	$0.0205421\pi$
$600$		0			0
$601$		−	936.503i		−	1.55824i	−0.626874	−	0.779121i	$-0.715666\pi$
$601$		−	936.503i		−	1.55824i	0.626874	−	0.779121i	$-0.284334\pi$
$602$		0			0
$603$	786.073			1.30360
$604$		0			0
$605$	−149.111	−	86.0890i	−0.246464	−	0.142296i
$606$		0			0
$607$	−521.452	+	301.060i	−0.859064	+	0.495981i	−0.863699	−	0.504008i	$-0.831858\pi$
$607$	−521.452	+	301.060i	−0.859064	+	0.495981i	0.00463474	+	0.999989i	$0.498525\pi$
$608$		0			0
$609$	450.375	−	395.862i	0.739531	−	0.650020i
$610$		0			0
$611$	−131.235	−	227.307i	−0.214788	−	0.372024i
$612$		0			0
$613$	−548.448	+	949.940i	−0.894695	+	1.54966i	−0.0605142	+	0.998167i	$0.519274\pi$
$613$	−548.448	+	949.940i	−0.894695	+	1.54966i	−0.834181	+	0.551491i	$0.814059\pi$
$614$		0			0
$615$			278.503i			0.452851i
$616$		0			0
$617$	−432.956			−0.701712			−0.350856	−	0.936429i	$-0.614109\pi$
$617$	−432.956			−0.701712			−0.350856	+	0.936429i	$0.614109\pi$
$618$		0			0
$619$	−194.951	−	112.555i	−0.314946	−	0.181834i	0.334192	−	0.942505i	$-0.391537\pi$
$619$	−194.951	−	112.555i	−0.314946	−	0.181834i	−0.649137	+	0.760671i	$0.724870\pi$
$620$		0			0
$621$	−4.23506	+	2.44512i	−0.00681975	+	0.00393738i
$622$		0			0
$623$	230.592	+	1152.51i	0.370131	+	1.84993i
$624$		0			0
$625$	13.3091	+	23.0520i	0.0212945	+	0.0368832i
$626$		0			0
$627$	−19.8640	+	34.4054i	−0.0316810	+	0.0548730i
$628$		0			0
$629$			880.552i			1.39992i
$630$		0			0
$631$	−750.514			−1.18940			−0.594702	−	0.803946i	$-0.702730\pi$
$631$	−750.514			−1.18940			−0.594702	+	0.803946i	$0.702730\pi$
$632$		0			0
$633$	463.794	+	267.772i	0.732692	+	0.423020i
$634$		0			0
$635$	166.374	−	96.0560i	0.262006	−	0.151269i
$636$		0			0
$637$	163.383	−	213.916i	0.256488	−	0.335818i
$638$		0			0
$639$	205.456	+	355.860i	0.321527	+	0.556901i
$640$		0			0
$641$	580.926	−	1006.19i	0.906281	−	1.56973i	0.0870937	−	0.996200i	$-0.472242\pi$
$641$	580.926	−	1006.19i	0.906281	−	1.56973i	0.819188	−	0.573525i	$-0.194425\pi$
$642$		0			0
$643$		−	121.957i		−	0.189669i	−0.995493	−	0.0948347i	$-0.969768\pi$
$643$		−	121.957i		−	0.189669i	0.995493	−	0.0948347i	$-0.0302322\pi$
$644$		0			0
$645$	−85.8823			−0.133151
$646$		0			0
$647$	137.504	+	79.3877i	0.212525	+	0.122701i	0.602484	−	0.798131i	$-0.294178\pi$
$647$	137.504	+	79.3877i	0.212525	+	0.122701i	−0.389959	+	0.920832i	$0.627511\pi$
$648$		0			0
$649$	−960.529	+	554.561i	−1.48001	+	0.854486i
$650$		0			0
$651$	−706.584	+	141.372i	−1.08538	+	0.217162i
$652$		0			0
$653$	195.471	+	338.565i	0.299342	+	0.518476i	0.975986	−	0.217835i	$-0.0698994\pi$
$653$	195.471	+	338.565i	0.299342	+	0.518476i	−0.676643	+	0.736311i	$0.736566\pi$
$654$		0			0
$655$	210.518	−	364.628i	0.321401	−	0.556683i
$656$		0			0
$657$			1111.49i			1.69177i
$658$		0			0
$659$	331.955			0.503726			0.251863	−	0.967763i	$-0.418957\pi$
$659$	331.955			0.503726			0.251863	+	0.967763i	$0.418957\pi$
$660$		0			0
$661$	561.029	+	323.910i	0.848758	+	0.490031i	0.860232	−	0.509904i	$-0.170319\pi$
$661$	561.029	+	323.910i	0.848758	+	0.490031i	−0.0114736	+	0.999934i	$0.503652\pi$
$662$		0			0
$663$	269.735	−	155.732i	0.406840	−	0.234889i
$664$		0			0
$665$	−10.5000	−	11.9459i	−0.0157895	−	0.0179638i
$666$		0			0
$667$	−23.2721	−	40.3084i	−0.0348907	−	0.0604324i
$668$		0			0
$669$	872.205	−	1510.70i	1.30374	−	2.25815i
$670$		0			0
$671$			877.448i			1.30767i
$672$		0			0
$673$	100.956			0.150009			0.0750047	−	0.997183i	$-0.476103\pi$
$673$	100.956			0.150009			0.0750047	+	0.997183i	$0.476103\pi$
$674$		0			0
$675$	27.9045	+	16.1107i	0.0413401	+	0.0238677i
$676$		0			0
$677$	643.610	−	371.588i	0.950679	−	0.548875i	0.0573873	−	0.998352i	$-0.481723\pi$
$677$	643.610	−	371.588i	0.950679	−	0.548875i	0.893292	+	0.449477i	$0.148390\pi$
$678$		0			0
$679$	−169.632	−	57.3704i	−0.249827	−	0.0844924i
$680$		0			0
$681$	−485.603	−	841.088i	−0.713073	−	1.23508i
$682$		0			0
$683$	2.21721	−	3.84032i	0.00324628	−	0.00562272i	−0.864398	−	0.502809i	$-0.832300\pi$
$683$	2.21721	−	3.84032i	0.00324628	−	0.00562272i	0.867644	+	0.497186i	$0.165633\pi$
$684$		0			0
$685$		−	371.881i		−	0.542892i
$686$		0			0
$687$	−349.669			−0.508980
$688$		0			0
$689$	−104.802	−	60.5074i	−0.152107	−	0.0878192i
$690$		0			0
$691$	846.253	−	488.584i	1.22468	−	0.707069i	0.258767	−	0.965940i	$-0.416684\pi$
$691$	846.253	−	488.584i	1.22468	−	0.707069i	0.965912	+	0.258871i	$0.0833506\pi$
$692$		0			0
$693$	−252.000	+	745.113i	−0.363636	+	1.07520i
$694$		0			0
$695$	108.603	+	188.106i	0.156263	+	0.270656i
$696$		0			0
$697$	142.581	−	246.957i	0.204563	−	0.354314i
$698$		0			0
$699$		−	916.063i		−	1.31053i
$700$		0			0
$701$	−840.177			−1.19854			−0.599270	−	0.800547i	$-0.704542\pi$
$701$	−840.177			−1.19854			−0.599270	+	0.800547i	$0.704542\pi$
$702$		0			0
$703$	−40.3492	−	23.2956i	−0.0573958	−	0.0331375i
$704$		0			0
$705$	−547.963	+	316.367i	−0.777252	+	0.448747i
$706$		0			0
$707$	149.857	−	131.719i	0.211962	−	0.186306i
$708$		0			0
$709$	−341.279	−	591.112i	−0.481352	−	0.833727i	0.518419	−	0.855127i	$-0.326521\pi$
$709$	−341.279	−	591.112i	−0.481352	−	0.833727i	−0.999771	+	0.0214003i	$0.993188\pi$
$710$		0			0
$711$	323.345	−	560.050i	0.454775	−	0.787694i
$712$		0			0
$713$			55.9340i			0.0784488i
$714$		0			0
$715$	−230.382			−0.322212
$716$		0			0
$717$	−699.286	−	403.733i	−0.975295	−	0.563087i
$718$		0			0
$719$	−119.187	+	68.8126i	−0.165768	+	0.0957060i	−0.580589	−	0.814197i	$-0.697178\pi$
$719$	−119.187	+	68.8126i	−0.165768	+	0.0957060i	0.414821	+	0.909903i	$0.363844\pi$
$720$		0			0
$721$	77.5812	+	387.754i	0.107602	+	0.537800i
$722$		0			0
$723$	103.562	+	179.375i	0.143240	+	0.248099i
$724$		0			0
$725$	−153.338	+	265.589i	−0.211501	+	0.366330i
$726$		0			0
$727$		−	264.137i		−	0.363325i	−0.983361	−	0.181662i	$-0.941852\pi$
$727$		−	264.137i		−	0.363325i	0.983361	−	0.181662i	$-0.0581478\pi$
$728$		0			0
$729$	643.368			0.882534
$730$		0			0
$731$	76.1543	+	43.9677i	0.104178	+	0.0601474i
$732$		0			0
$733$	501.705	−	289.660i	0.684455	−	0.395170i	−0.117077	−	0.993123i	$-0.537352\pi$
$733$	501.705	−	289.660i	0.684455	−	0.395170i	0.801531	+	0.597953i	$0.204019\pi$
$734$		0			0
$735$	−515.683	−	393.863i	−0.701610	−	0.535868i
$736$		0			0
$737$	613.397	+	1062.43i	0.832288	+	1.44157i
$738$		0			0
$739$	−99.0477	+	171.556i	−0.134029	+	0.232146i	−0.925226	−	0.379416i	$-0.876125\pi$
$739$	−99.0477	+	171.556i	−0.134029	+	0.232146i	0.791197	+	0.611562i	$0.209458\pi$
$740$		0			0
$741$			16.4800i			0.0222402i
$742$		0			0
$743$	−976.690			−1.31452			−0.657261	−	0.753663i	$-0.728285\pi$
$743$	−976.690			−1.31452			−0.657261	+	0.753663i	$0.728285\pi$
$744$		0			0
$745$	72.3974	+	41.7987i	0.0971777	+	0.0561056i
$746$		0			0
$747$	−793.499	+	458.127i	−1.06225	+	0.613289i
$748$		0			0
$749$	326.794	−	65.3845i	0.436308	−	0.0872958i
$750$		0			0
$751$	−417.665	−	723.417i	−0.556145	−	0.963272i	−0.997813	−	0.0660933i	$-0.978947\pi$
$751$	−417.665	−	723.417i	−0.556145	−	0.963272i	0.441668	−	0.897178i	$-0.354387\pi$
$752$		0			0
$753$	−339.801	+	588.553i	−0.451263	+	0.781611i
$754$		0			0
$755$			425.044i			0.562972i
$756$		0			0
$757$	104.221			0.137677			0.0688383	−	0.997628i	$-0.478071\pi$
$757$	104.221			0.137677			0.0688383	+	0.997628i	$0.478071\pi$
$758$		0			0
$759$	108.959	+	62.9077i	0.143557	+	0.0828824i
$760$		0			0
$761$	−473.785	+	273.540i	−0.622583	+	0.359448i	−0.777874	−	0.628420i	$-0.783702\pi$
$761$	−473.785	+	273.540i	−0.622583	+	0.359448i	0.155291	+	0.987869i	$0.450368\pi$
$762$		0			0
$763$	348.025	+	395.950i	0.456128	+	0.518939i
$764$		0			0
$765$	−182.184	−	315.552i	−0.238149	−	0.412486i
$766$		0			0
$767$	−230.044	+	398.447i	−0.299927	+	0.519488i
$768$		0			0
$769$		−	341.205i		−	0.443700i	−0.975081	−	0.221850i	$-0.928790\pi$
$769$		−	341.205i		−	0.443700i	0.975081	−	0.221850i	$-0.0712095\pi$
$770$		0			0
$771$	−414.640			−0.537795
$772$		0			0
$773$	−425.213	−	245.497i	−0.550081	−	0.317590i	0.199074	−	0.979985i	$-0.436207\pi$
$773$	−425.213	−	245.497i	−0.550081	−	0.317590i	−0.749155	+	0.662395i	$0.769540\pi$
$774$		0			0
$775$	319.169	−	184.273i	0.411832	−	0.237771i
$776$		0			0
$777$	−1800.68	−	608.998i	−2.31748	−	0.783781i
$778$		0			0
$779$	7.54416	+	13.0669i	0.00968441	+	0.0167739i
$780$		0			0
$781$	−320.647	+	555.376i	−0.410559	+	0.711109i
$782$		0			0
$783$		−	44.0908i		−	0.0563101i
$784$		0			0
$785$	−717.926			−0.914555
$786$		0			0
$787$	−260.202	−	150.228i	−0.330625	−	0.190887i	0.325493	−	0.945544i	$-0.394470\pi$
$787$	−260.202	−	150.228i	−0.330625	−	0.190887i	−0.656119	+	0.754658i	$0.727803\pi$
$788$		0			0
$789$	1572.90	−	908.116i	1.99354	−	1.15097i
$790$		0			0
$791$	191.647	−	566.660i	0.242284	−	0.716385i
$792$		0			0
$793$	181.992	+	315.219i	0.229498	+	0.397502i
$794$		0			0
$795$	−145.864	+	252.644i	−0.183477	+	0.317791i
$796$		0			0
$797$		−	370.072i		−	0.464331i	−0.972676	−	0.232165i	$-0.925419\pi$
$797$		−	370.072i		−	0.464331i	0.972676	−	0.232165i	$-0.0745811\pi$
$798$		0			0
$799$	647.860			0.810838
$800$		0			0
$801$	−1233.86	−	712.369i	−1.54040	−	0.889349i
$802$		0			0
$803$	−1502.26	+	867.330i	−1.87081	+	1.08011i
$804$		0			0
$805$	−37.8318	+	33.2528i	−0.0469960	+	0.0413078i
$806$		0			0
$807$	−191.114	−	331.019i	−0.236820	−	0.410184i
$808$		0			0
$809$	−245.618	+	425.422i	−0.303607	+	0.525862i	−0.976950	−	0.213468i	$-0.931524\pi$
$809$	−245.618	+	425.422i	−0.303607	+	0.525862i	0.673344	+	0.739330i	$0.264858\pi$
$810$		0			0
$811$		−	156.802i		−	0.193344i	−0.995316	−	0.0966722i	$-0.969180\pi$
$811$		−	156.802i		−	0.193344i	0.995316	−	0.0966722i	$-0.0308199\pi$
$812$		0			0
$813$	−71.4853			−0.0879278
$814$		0			0
$815$	−252.262	−	145.643i	−0.309524	−	0.178704i
$816$		0			0
$817$	−4.02944	+	2.32640i	−0.00493199	+	0.00284749i
$818$		0			0
$819$	64.0143	+	319.946i	0.0781615	+	0.390654i
$820$		0			0
$821$	215.316	+	372.939i	0.262261	+	0.454249i	0.966842	−	0.255374i	$-0.0821986\pi$
$821$	215.316	+	372.939i	0.262261	+	0.454249i	−0.704581	+	0.709623i	$0.748865\pi$
$822$		0			0
$823$	−354.371	+	613.788i	−0.430584	+	0.745793i	−0.996924	−	0.0783785i	$-0.975026\pi$
$823$	−354.371	+	613.788i	−0.430584	+	0.745793i	0.566340	+	0.824172i	$0.308359\pi$
$824$		0			0
$825$		−	828.990i		−	1.00484i
$826$		0			0
$827$	1460.10			1.76554			0.882770	−	0.469805i	$-0.155676\pi$
$827$	1460.10			1.76554			0.882770	+	0.469805i	$0.155676\pi$
$828$		0			0
$829$	−223.095	−	128.804i	−0.269113	−	0.155373i	0.359371	−	0.933195i	$-0.382991\pi$
$829$	−223.095	−	128.804i	−0.269113	−	0.155373i	−0.628485	+	0.777822i	$0.716325\pi$
$830$		0			0
$831$	1450.02	−	837.168i	1.74491	−	1.00742i
$832$		0			0
$833$	255.632	+	613.256i	0.306881	+	0.736202i
$834$		0			0
$835$	322.206	+	558.077i	0.385876	+	0.668356i
$836$		0			0
$837$	−26.4929	+	45.8870i	−0.0316522	+	0.0548231i
$838$		0			0
$839$			213.621i			0.254613i	0.991863	+	0.127307i	$0.0406332\pi$
$839$			213.621i			0.254613i	−0.991863	+	0.127307i	$0.959367\pi$
$840$		0			0
$841$	−421.353			−0.501015
$842$		0			0
$843$	−1950.77	−	1126.28i	−2.31408	−	1.33604i
$844$		0			0
$845$	380.743	−	219.822i	0.450583	−	0.260144i
$846$		0			0
$847$	−373.177	+	74.6646i	−0.440586	+	0.0881519i
$848$		0			0
$849$	646.485	+	1119.74i	0.761466	+	1.31890i
$850$		0			0
$851$	−73.7756	+	127.783i	−0.0866929	+	0.150156i
$852$		0			0
$853$		−	1127.37i		−	1.32165i	−0.750539	−	0.660826i	$-0.770206\pi$
$853$		−	1127.37i		−	1.32165i	0.750539	−	0.660826i	$-0.229794\pi$
$854$		0			0
$855$	19.2792			0.0225488
$856$		0			0
$857$	1100.22	+	635.212i	1.28380	+	0.741204i	0.977541	−	0.210744i	$-0.0675885\pi$
$857$	1100.22	+	635.212i	1.28380	+	0.741204i	0.306261	+	0.951947i	$0.400922\pi$
$858$		0			0
$859$	221.488	−	127.876i	0.257844	−	0.148867i	−0.365506	−	0.930809i	$-0.619104\pi$
$859$	221.488	−	127.876i	0.257844	−	0.148867i	0.623351	+	0.781942i	$0.285771\pi$
$860$		0			0
$861$	406.404	+	462.368i	0.472014	+	0.537013i
$862$		0			0
$863$	557.364	+	965.382i	0.645844	+	1.11863i	0.984106	+	0.177583i	$0.0568278\pi$
$863$	557.364	+	965.382i	0.645844	+	1.11863i	−0.338262	+	0.941052i	$0.609839\pi$
$864$		0			0
$865$	112.125	−	194.207i	0.129625	−	0.224516i
$866$		0			0
$867$		−	439.677i		−	0.507125i
$868$		0			0
$869$	1009.26			1.16141
$870$		0			0
$871$	440.720	+	254.450i	0.505993	+	0.292135i
$872$		0			0
$873$	187.986	−	108.534i	0.215333	−	0.124323i
$874$		0			0
$875$	839.382	+	283.882i	0.959294	+	0.324437i
$876$		0			0
$877$	550.904	+	954.194i	0.628169	+	1.08802i	0.987919	+	0.154972i	$0.0495286\pi$
$877$	550.904	+	954.194i	0.628169	+	1.08802i	−0.359750	+	0.933049i	$0.617138\pi$
$878$		0			0
$879$	684.500	−	1185.59i	0.778725	−	1.34879i
$880$		0			0
$881$			217.067i			0.246387i	0.992383	+	0.123194i	$0.0393136\pi$
$881$			217.067i			0.246387i	−0.992383	+	0.123194i	$0.960686\pi$
$882$		0			0
$883$	516.544			0.584988			0.292494	−	0.956267i	$-0.405515\pi$
$883$	516.544			0.584988			0.292494	+	0.956267i	$0.405515\pi$
$884$		0			0
$885$	960.529	+	554.561i	1.08534	+	0.626623i
$886$		0			0
$887$	978.445	−	564.905i	1.10309	−	0.636872i	0.166062	−	0.986115i	$-0.446895\pi$
$887$	978.445	−	564.905i	1.10309	−	0.636872i	0.937032	+	0.349243i	$0.113561\pi$
$888$		0			0
$889$	136.043	−	402.251i	0.153029	−	0.452476i
$890$		0			0
$891$	565.246	+	979.034i	0.634395	+	1.09880i
$892$		0			0
$893$	−17.1396	+	29.6867i	−0.0191933	+	0.0332438i
$894$		0			0
$895$		−	344.613i		−	0.385043i
$896$		0			0
$897$	52.1909			0.0581838
$898$		0			0
$899$	−436.742	−	252.153i	−0.485809	−	0.280482i
$900$		0			0
$901$	258.684	−	149.351i	0.287107	−	0.165762i
$902$		0			0
$903$	−142.581	+	125.323i	−0.157897	+	0.138785i
$904$		0			0
$905$	157.809	+	273.333i	0.174375	+	0.302026i
$906$		0			0
$907$	30.0111	−	51.9808i	0.0330884	−	0.0573107i	−0.849007	−	0.528382i	$-0.822799\pi$
$907$	30.0111	−	51.9808i	0.0330884	−	0.0573107i	0.882095	+	0.471071i	$0.156132\pi$
$908$		0			0
$909$			241.851i			0.266062i
$910$		0			0
$911$	−1422.25			−1.56120			−0.780598	−	0.625033i	$-0.785085\pi$
$911$	−1422.25			−1.56120			−0.780598	+	0.625033i	$0.785085\pi$
$912$		0			0
$913$	−1238.38	−	714.980i	−1.35639	−	0.783111i
$914$		0			0
$915$	759.893	−	438.724i	0.830484	−	0.479480i
$916$		0			0
$917$	−182.581	−	912.547i	−0.199107	−	0.995144i
$918$		0			0
$919$	834.849	+	1446.00i	0.908432	+	1.57345i	0.816243	+	0.577708i	$0.196053\pi$
$919$	834.849	+	1446.00i	0.908432	+	1.57345i	0.0921886	+	0.995742i	$0.470614\pi$
$920$		0			0
$921$	−535.529	+	927.563i	−0.581465	+	1.00713i
$922$		0			0
$923$			266.022i			0.288215i
$924$		0			0
$925$	972.205			1.05103
$926$		0			0
$927$	−415.124	−	239.672i	−0.447814	−	0.258546i
$928$		0			0
$929$	839.058	−	484.430i	0.903184	−	0.521453i	0.0249519	−	0.999689i	$-0.492057\pi$
$929$	839.058	−	484.430i	0.903184	−	0.521453i	0.878232	+	0.478235i	$0.158723\pi$
$930$		0			0
$931$	−34.8640	−	4.51039i	−0.0374479	−	0.00484468i
$932$		0			0
$933$	−452.301	−	783.408i	−0.484781	−	0.839666i
$934$		0			0
$935$	284.327	−	492.469i	0.304093	−	0.526705i
$936$		0			0
$937$			1212.57i			1.29410i	0.762449	+	0.647049i	$0.223997\pi$
$937$			1212.57i			1.29410i	−0.762449	+	0.647049i	$0.776003\pi$
$938$		0			0
$939$	655.742			0.698341
$940$		0			0
$941$	−1293.90	−	747.032i	−1.37502	−	0.793870i	−0.383468	−	0.923554i	$-0.625270\pi$
$941$	−1293.90	−	747.032i	−1.37502	−	0.793870i	−0.991555	+	0.129684i	$0.958604\pi$
$942$		0			0
$943$	41.3818	−	23.8918i	0.0438832	−	0.0253360i
$944$		0			0
$945$	−46.7864	+	9.36095i	−0.0495094	+	0.00990576i
$946$		0			0
$947$	387.731	+	671.570i	0.409431	+	0.709155i	0.994826	−	0.101593i	$-0.0323939\pi$
$947$	387.731	+	671.570i	0.409431	+	0.709155i	−0.585395	+	0.810748i	$0.699061\pi$
$948$		0			0
$949$	−359.787	+	623.169i	−0.379122	+	0.656659i
$950$		0			0
$951$			1873.45i			1.96998i
$952$		0			0
$953$	1055.40			1.10745			0.553723	−	0.832701i	$-0.313206\pi$
$953$	1055.40			1.10745			0.553723	+	0.832701i	$0.313206\pi$
$954$		0			0
$955$	191.723	+	110.691i	0.200757	+	0.115907i
$956$		0			0
$957$	−982.389	+	567.183i	−1.02653	+	0.592667i
$958$		0			0
$959$	−542.665	−	617.393i	−0.565866	−	0.643788i
$960$		0			0
$961$	−177.477	−	307.400i	−0.184680	−	0.319875i
$962$		0			0
$963$	−201.993	+	349.862i	−0.209754	+	0.363304i
$964$		0			0
$965$		−	102.412i		−	0.106127i
$966$		0			0
$967$	−1221.63			−1.26332			−0.631661	−	0.775245i	$-0.717627\pi$
$967$	−1221.63			−1.26332			−0.631661	+	0.775245i	$0.717627\pi$
$968$		0			0
$969$	−35.2279	−	20.3389i	−0.0363549	−	0.0209895i
$970$		0			0
$971$	455.753	−	263.129i	0.469365	−	0.270988i	−0.246609	−	0.969115i	$-0.579316\pi$
$971$	455.753	−	263.129i	0.469365	−	0.270988i	0.715974	+	0.698127i	$0.245983\pi$
$972$		0			0
$973$	454.794	+	153.813i	0.467414	+	0.158081i
$974$		0			0
$975$	−171.941	−	297.811i	−0.176350	−	0.305447i
$976$		0			0
$977$	500.051	−	866.114i	0.511823	−	0.886504i	−0.488083	−	0.872797i	$-0.662304\pi$
$977$	500.051	−	866.114i	0.511823	−	0.886504i	0.999906	−	0.0137065i	$-0.00436306\pi$
$978$		0			0
$979$		−	2223.53i		−	2.27123i
$980$		0			0
$981$	−639.015			−0.651392
$982$		0			0
$983$	−931.584	−	537.850i	−0.947695	−	0.547152i	−0.0553306	−	0.998468i	$-0.517621\pi$
$983$	−931.584	−	537.850i	−0.947695	−	0.547152i	−0.892364	+	0.451316i	$0.850955\pi$
$984$		0			0
$985$	759.993	−	438.782i	0.771566	−	0.445464i
$986$		0			0
$987$	−448.066	+	1324.84i	−0.453968	+	1.34229i
$988$		0			0
$989$	7.36753	+	12.7609i	0.00744948	+	0.0129029i
$990$		0			0
$991$	−938.017	+	1624.69i	−0.946536	+	1.63945i	−0.193891	+	0.981023i	$0.562111\pi$
$991$	−938.017	+	1624.69i	−0.946536	+	1.63945i	−0.752646	+	0.658426i	$0.771223\pi$
$992$		0			0
$993$		−	230.015i		−	0.231636i
$994$		0			0
$995$	−530.285			−0.532949
$996$		0			0
$997$	504.221	+	291.112i	0.505738	+	0.291988i	0.731080	−	0.682292i	$-0.239017\pi$
$997$	504.221	+	291.112i	0.505738	+	0.291988i	−0.225342	+	0.974280i	$0.572350\pi$
$998$		0			0
$999$	−121.048	+	69.8869i	−0.121169	+	0.0699569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.s.b.17.2		4
3.2	odd	2		1008.3.cg.l.577.1		4
4.3	odd	2		14.3.d.a.3.2	✓	4
7.2	even	3		784.3.s.c.705.1		4
7.3	odd	6		784.3.c.e.97.4		4
7.4	even	3		784.3.c.e.97.1		4
7.5	odd	6	inner	112.3.s.b.33.2		4
7.6	odd	2		784.3.s.c.129.1		4
8.3	odd	2		448.3.s.d.129.2		4
8.5	even	2		448.3.s.c.129.1		4
12.11	even	2		126.3.n.c.73.1		4
20.3	even	4		350.3.i.a.199.4		8
20.7	even	4		350.3.i.a.199.1		8
20.19	odd	2		350.3.k.a.101.1		4
21.5	even	6		1008.3.cg.l.145.1		4
28.3	even	6		98.3.b.b.97.1		4
28.11	odd	6		98.3.b.b.97.2		4
28.19	even	6		14.3.d.a.5.2	yes	4
28.23	odd	6		98.3.d.a.19.2		4
28.27	even	2		98.3.d.a.31.2		4
56.5	odd	6		448.3.s.c.257.1		4
56.19	even	6		448.3.s.d.257.2		4
84.11	even	6		882.3.c.f.685.3		4
84.23	even	6		882.3.n.b.19.1		4
84.47	odd	6		126.3.n.c.19.1		4
84.59	odd	6		882.3.c.f.685.4		4
84.83	odd	2		882.3.n.b.325.1		4
140.19	even	6		350.3.k.a.201.1		4
140.47	odd	12		350.3.i.a.299.4		8
140.103	odd	12		350.3.i.a.299.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.2	✓	4	4.3	odd	2
14.3.d.a.5.2	yes	4	28.19	even	6
98.3.b.b.97.1		4	28.3	even	6
98.3.b.b.97.2		4	28.11	odd	6
98.3.d.a.19.2		4	28.23	odd	6
98.3.d.a.31.2		4	28.27	even	2
112.3.s.b.17.2		4	1.1	even	1	trivial
112.3.s.b.33.2		4	7.5	odd	6	inner
126.3.n.c.19.1		4	84.47	odd	6
126.3.n.c.73.1		4	12.11	even	2
350.3.i.a.199.1		8	20.7	even	4
350.3.i.a.199.4		8	20.3	even	4
350.3.i.a.299.1		8	140.103	odd	12
350.3.i.a.299.4		8	140.47	odd	12
350.3.k.a.101.1		4	20.19	odd	2
350.3.k.a.201.1		4	140.19	even	6
448.3.s.c.129.1		4	8.5	even	2
448.3.s.c.257.1		4	56.5	odd	6
448.3.s.d.129.2		4	8.3	odd	2
448.3.s.d.257.2		4	56.19	even	6
784.3.c.e.97.1		4	7.4	even	3
784.3.c.e.97.4		4	7.3	odd	6
784.3.s.c.129.1		4	7.6	odd	2
784.3.s.c.705.1		4	7.2	even	3
882.3.c.f.685.3		4	84.11	even	6
882.3.c.f.685.4		4	84.59	odd	6
882.3.n.b.19.1		4	84.23	even	6
882.3.n.b.325.1		4	84.83	odd	2
1008.3.cg.l.145.1		4	21.5	even	6
1008.3.cg.l.577.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.62132 + 2.09077i) q^{3} +(2.74264 - 1.58346i) q^{5} +(2.24264 - 6.63103i) q^{7} +(4.24264 + 7.34847i) q^{9} +O(q^{10})\)	\(q+(3.62132 + 2.09077i) q^{3} +(2.74264 - 1.58346i) q^{5} +(2.24264 - 6.63103i) q^{7} +(4.24264 + 7.34847i) q^{9} +(-6.62132 + 11.4685i) q^{11} +5.49333i q^{13} +13.2426 q^{15} +(-11.7426 - 6.77962i) q^{17} +(0.621320 - 0.358719i) q^{19} +(21.9853 - 19.3242i) q^{21} +(-1.13604 - 1.96768i) q^{23} +(-7.48528 + 12.9649i) q^{25} -2.15232i q^{27} +20.4853 q^{29} +(-21.3198 - 12.3090i) q^{31} +(-47.9558 + 27.6873i) q^{33} +(-4.34924 - 21.7377i) q^{35} +(-32.4706 - 56.2407i) q^{37} +(-11.4853 + 19.8931i) q^{39} +21.0308i q^{41} -6.48528 q^{43} +(23.2721 + 13.4361i) q^{45} +(-41.3787 + 23.8900i) q^{47} +(-38.9411 - 29.7420i) q^{49} +(-28.3492 - 49.1023i) q^{51} +(-11.0147 + 19.0781i) q^{53} +41.9385i q^{55} +3.00000 q^{57} +(72.5330 + 41.8770i) q^{59} +(57.3823 - 33.1297i) q^{61} +(58.2426 - 11.6531i) q^{63} +(8.69848 + 15.0662i) q^{65} +(46.3198 - 80.2283i) q^{67} -9.50079i q^{69} +48.4264 q^{71} +(113.441 + 65.4953i) q^{73} +(-54.2132 + 31.3000i) q^{75} +(61.1985 + 69.6258i) q^{77} +(-38.1066 - 66.0026i) q^{79} +(42.6838 - 73.9305i) q^{81} +107.981i q^{83} -42.9411 q^{85} +(74.1838 + 42.8300i) q^{87} +(-145.412 + 83.9535i) q^{89} +(36.4264 + 12.3196i) q^{91} +(-51.4706 - 89.1496i) q^{93} +(1.13604 - 1.96768i) q^{95} -25.5816i q^{97} -112.368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7	\( 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7} - 18 q^{11} + 36 q^{15} - 30 q^{17} - 6 q^{19} + 54 q^{21} - 30 q^{23} + 4 q^{25} + 48 q^{29} + 42 q^{31} - 90 q^{33} + 42 q^{35} - 62 q^{37} - 12 q^{39} + 8 q^{43} + 144 q^{45} - 174 q^{47} - 20 q^{49} - 54 q^{51} - 78 q^{53} + 12 q^{57} + 78 q^{59} - 42 q^{61} + 216 q^{63} - 84 q^{65} + 58 q^{67} + 24 q^{71} + 318 q^{73} - 132 q^{75} + 126 q^{77} - 110 q^{79} + 18 q^{81} - 36 q^{85} + 144 q^{87} - 378 q^{89} - 24 q^{91} - 138 q^{93} + 30 q^{95} - 144 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7 - 18 * q^11 + 36 * q^15 - 30 * q^17 - 6 * q^19 + 54 * q^21 - 30 * q^23 + 4 * q^25 + 48 * q^29 + 42 * q^31 - 90 * q^33 + 42 * q^35 - 62 * q^37 - 12 * q^39 + 8 * q^43 + 144 * q^45 - 174 * q^47 - 20 * q^49 - 54 * q^51 - 78 * q^53 + 12 * q^57 + 78 * q^59 - 42 * q^61 + 216 * q^63 - 84 * q^65 + 58 * q^67 + 24 * q^71 + 318 * q^73 - 132 * q^75 + 126 * q^77 - 110 * q^79 + 18 * q^81 - 36 * q^85 + 144 * q^87 - 378 * q^89 - 24 * q^91 - 138 * q^93 + 30 * q^95 - 144 * q^99

Introduction

L-functions

Modular forms

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