LMFDB - Embedded newform 175.4.f.g.118.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(118,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("175.118");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.f (of order $4$, degree $2$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 10654x^{12} + 22102125x^{8} + 5700572500x^{4} + 44626562500 $ x^16 + 10654x^12 + 22102125x^8 + 5700572500*x^4 + 44626562500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.6
Root			$-2.91939 - 2.91939i$ of defining polynomial
Character	$\chi$	$=$	175.118
Dual form			175.4.f.g.132.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.172516 + 0.172516i) q^{2} +(2.91939 - 2.91939i) q^{3} +7.94048i q^{4} +1.00728i q^{6} +(-18.1737 + 3.56610i) q^{7} +(-2.74998 - 2.74998i) q^{8} +9.95432i q^{9} +O(q^{10})$	\(q+(-0.172516 + 0.172516i) q^{2} +(2.91939 - 2.91939i) q^{3} +7.94048i q^{4} +1.00728i q^{6} +(-18.1737 + 3.56610i) q^{7} +(-2.74998 - 2.74998i) q^{8} +9.95432i q^{9} -15.1443 q^{11} +(23.1814 + 23.1814i) q^{12} +(-40.2848 + 40.2848i) q^{13} +(2.52004 - 3.75045i) q^{14} -62.5750 q^{16} +(-30.0616 - 30.0616i) q^{17} +(-1.71728 - 1.71728i) q^{18} +65.1185 q^{19} +(-42.6452 + 63.4669i) q^{21} +(2.61264 - 2.61264i) q^{22} +(-56.5971 - 56.5971i) q^{23} -16.0565 q^{24} -13.8995i q^{26} +(107.884 + 107.884i) q^{27} +(-28.3165 - 144.308i) q^{28} +104.464i q^{29} +317.751i q^{31} +(32.7950 - 32.7950i) q^{32} +(-44.2123 + 44.2123i) q^{33} +10.3722 q^{34} -79.0420 q^{36} +(-190.864 + 190.864i) q^{37} +(-11.2340 + 11.2340i) q^{38} +235.214i q^{39} -370.814i q^{41} +(-3.59207 - 18.3060i) q^{42} +(-10.8913 - 10.8913i) q^{43} -120.253i q^{44} +19.5278 q^{46} +(100.476 + 100.476i) q^{47} +(-182.681 + 182.681i) q^{48} +(317.566 - 129.618i) q^{49} -175.523 q^{51} +(-319.881 - 319.881i) q^{52} +(332.255 + 332.255i) q^{53} -37.2234 q^{54} +(59.7840 + 40.1706i) q^{56} +(190.106 - 190.106i) q^{57} +(-18.0217 - 18.0217i) q^{58} -484.782 q^{59} -315.263i q^{61} +(-54.8170 - 54.8170i) q^{62} +(-35.4981 - 180.907i) q^{63} -489.285i q^{64} -15.2546i q^{66} +(40.1151 - 40.1151i) q^{67} +(238.704 - 238.704i) q^{68} -330.458 q^{69} +906.887 q^{71} +(27.3742 - 27.3742i) q^{72} +(96.5419 - 96.5419i) q^{73} -65.8540i q^{74} +517.072i q^{76} +(275.229 - 54.0063i) q^{77} +(-40.5781 - 40.5781i) q^{78} +354.468i q^{79} +361.145 q^{81} +(63.9712 + 63.9712i) q^{82} +(522.441 - 522.441i) q^{83} +(-503.958 - 338.624i) q^{84} +3.75783 q^{86} +(304.971 + 304.971i) q^{87} +(41.6467 + 41.6467i) q^{88} +1064.18 q^{89} +(588.464 - 875.783i) q^{91} +(449.408 - 449.408i) q^{92} +(927.639 + 927.639i) q^{93} -34.6673 q^{94} -191.483i q^{96} +(-577.458 - 577.458i) q^{97} +(-32.4239 + 77.1463i) q^{98} -150.752i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8}+O(q^{10}) $ 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8	$ 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8} - 152 q^{11} - 504 q^{16} - 288 q^{18} + 328 q^{21} - 348 q^{22} + 72 q^{23} + 528 q^{28} - 432 q^{32} + 344 q^{36} + 256 q^{37} + 1300 q^{42} + 312 q^{43} - 1856 q^{46} + 696 q^{51} - 1768 q^{53} + 1304 q^{56} + 3920 q^{57} + 4764 q^{58} - 2544 q^{63} - 4504 q^{67} + 6368 q^{71} - 7848 q^{72} + 3016 q^{77} - 5340 q^{78} - 3088 q^{81} - 9336 q^{86} + 2048 q^{88} + 1608 q^{91} + 6328 q^{92} + 3960 q^{93} - 3308 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8 - 152 * q^11 - 504 * q^16 - 288 * q^18 + 328 * q^21 - 348 * q^22 + 72 * q^23 + 528 * q^28 - 432 * q^32 + 344 * q^36 + 256 * q^37 + 1300 * q^42 + 312 * q^43 - 1856 * q^46 + 696 * q^51 - 1768 * q^53 + 1304 * q^56 + 3920 * q^57 + 4764 * q^58 - 2544 * q^63 - 4504 * q^67 + 6368 * q^71 - 7848 * q^72 + 3016 * q^77 - 5340 * q^78 - 3088 * q^81 - 9336 * q^86 + 2048 * q^88 + 1608 * q^91 + 6328 * q^92 + 3960 * q^93 - 3308 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.172516	+	0.172516i	−0.0609935	+	0.0609935i	−0.736946	−	0.675952i	$-0.763733\pi$
$2$	−0.172516	+	0.172516i	−0.0609935	+	0.0609935i	0.675952	+	0.736946i	$0.263733\pi$
$3$	2.91939	−	2.91939i	0.561837	−	0.561837i	−0.367992	−	0.929829i	$-0.619955\pi$
$3$	2.91939	−	2.91939i	0.561837	−	0.561837i	0.929829	+	0.367992i	$0.119955\pi$
$4$			7.94048i			0.992560i
$5$		0			0
$5$		0			0
$6$			1.00728i			0.0685368i
$7$	−18.1737	+	3.56610i	−0.981287	+	0.192551i
$7$	−18.1737	+	3.56610i	−0.981287	+	0.192551i
$8$	−2.74998	−	2.74998i	−0.121533	−	0.121533i
$9$			9.95432i			0.368678i
$10$		0			0
$11$	−15.1443			−0.415108			−0.207554	−	0.978224i	$-0.566550\pi$
$11$	−15.1443			−0.415108			−0.207554	+	0.978224i	$0.566550\pi$
$12$	23.1814	+	23.1814i	0.557657	+	0.557657i
$13$	−40.2848	+	40.2848i	−0.859461	+	0.859461i	−0.991275	−	0.131813i	$-0.957920\pi$
$13$	−40.2848	+	40.2848i	−0.859461	+	0.859461i	0.131813	+	0.991275i	$0.457920\pi$
$14$	2.52004	−	3.75045i	0.0481077	−	0.0715965i
$15$		0			0
$16$	−62.5750			−0.977734
$17$	−30.0616	−	30.0616i	−0.428883	−	0.428883i	0.459365	−	0.888248i	$-0.348077\pi$
$17$	−30.0616	−	30.0616i	−0.428883	−	0.428883i	−0.888248	+	0.459365i	$0.848077\pi$
$18$	−1.71728	−	1.71728i	−0.0224870	−	0.0224870i
$19$	65.1185			0.786274			0.393137	−	0.919480i	$-0.371390\pi$
$19$	65.1185			0.786274			0.393137	+	0.919480i	$0.371390\pi$
$20$		0			0
$21$	−42.6452	+	63.4669i	−0.443141	+	0.659506i
$22$	2.61264	−	2.61264i	0.0253189	−	0.0253189i
$23$	−56.5971	−	56.5971i	−0.513101	−	0.513101i	0.402375	−	0.915475i	$-0.368185\pi$
$23$	−56.5971	−	56.5971i	−0.513101	−	0.513101i	−0.915475	+	0.402375i	$0.868185\pi$
$24$	−16.0565			−0.136564
$25$		0			0
$26$		−	13.8995i		−	0.104843i
$27$	107.884	+	107.884i	0.768974	+	0.768974i
$28$	−28.3165	−	144.308i	−0.191119	−	0.973986i
$29$			104.464i			0.668913i	0.942411	+	0.334456i	$0.108553\pi$
$29$			104.464i			0.668913i	−0.942411	+	0.334456i	$0.891447\pi$
$30$		0			0
$31$			317.751i			1.84096i	0.390789	+	0.920480i	$0.372202\pi$
$31$			317.751i			1.84096i	−0.390789	+	0.920480i	$0.627798\pi$
$32$	32.7950	−	32.7950i	0.181169	−	0.181169i
$33$	−44.2123	+	44.2123i	−0.233223	+	0.233223i
$34$	10.3722			0.0523182
$35$		0			0
$36$	−79.0420			−0.365935
$37$	−190.864	+	190.864i	−0.848050	+	0.848050i	−0.989890	−	0.141840i	$-0.954698\pi$
$37$	−190.864	+	190.864i	−0.848050	+	0.848050i	0.141840	+	0.989890i	$0.454698\pi$
$38$	−11.2340	+	11.2340i	−0.0479576	+	0.0479576i
$39$			235.214i			0.965754i
$40$		0			0
$41$		−	370.814i		−	1.41247i	−0.707976	−	0.706236i	$-0.750392\pi$
$41$		−	370.814i		−	1.41247i	0.707976	−	0.706236i	$-0.249608\pi$
$42$	−3.59207	−	18.3060i	−0.0131968	−	0.0672542i
$43$	−10.8913	−	10.8913i	−0.0386257	−	0.0386257i	0.687530	−	0.726156i	$-0.258695\pi$
$43$	−10.8913	−	10.8913i	−0.0386257	−	0.0386257i	−0.726156	+	0.687530i	$0.758695\pi$
$44$		−	120.253i		−	0.412020i
$45$		0			0
$46$	19.5278			0.0625916
$47$	100.476	+	100.476i	0.311827	+	0.311827i	0.845617	−	0.533790i	$-0.179233\pi$
$47$	100.476	+	100.476i	0.311827	+	0.311827i	−0.533790	+	0.845617i	$0.679233\pi$
$48$	−182.681	+	182.681i	−0.549327	+	0.549327i
$49$	317.566	−	129.618i	0.925848	−	0.377896i
$50$		0			0
$51$	−175.523			−0.481925
$52$	−319.881	−	319.881i	−0.853066	−	0.853066i
$53$	332.255	+	332.255i	0.861108	+	0.861108i	0.991467	−	0.130359i	$-0.0416131\pi$
$53$	332.255	+	332.255i	0.861108	+	0.861108i	−0.130359	+	0.991467i	$0.541613\pi$
$54$	−37.2234			−0.0938048
$55$		0			0
$56$	59.7840	+	40.1706i	0.142660	+	0.0958575i
$57$	190.106	−	190.106i	0.441758	−	0.441758i
$58$	−18.0217	−	18.0217i	−0.0407993	−	0.0407993i
$59$	−484.782			−1.06971			−0.534857	−	0.844942i	$-0.679635\pi$
$59$	−484.782			−1.06971			−0.534857	+	0.844942i	$0.679635\pi$
$60$		0			0
$61$		−	315.263i		−	0.661726i	−0.943679	−	0.330863i	$-0.892660\pi$
$61$		−	315.263i		−	0.661726i	0.943679	−	0.330863i	$-0.107340\pi$
$62$	−54.8170	−	54.8170i	−0.112287	−	0.112287i
$63$	−35.4981	−	180.907i	−0.0709895	−	0.361779i
$64$		−	489.285i		−	0.955634i
$65$		0			0
$66$		−	15.2546i		−	0.0284502i
$67$	40.1151	−	40.1151i	0.0731468	−	0.0731468i	−0.669587	−	0.742734i	$-0.733529\pi$
$67$	40.1151	−	40.1151i	0.0731468	−	0.0731468i	0.742734	+	0.669587i	$0.233529\pi$
$68$	238.704	−	238.704i	0.425692	−	0.425692i
$69$	−330.458			−0.576558
$70$		0			0
$71$	906.887			1.51588			0.757942	−	0.652322i	$-0.226205\pi$
$71$	906.887			1.51588			0.757942	+	0.652322i	$0.226205\pi$
$72$	27.3742	−	27.3742i	0.0448067	−	0.0448067i
$73$	96.5419	−	96.5419i	0.154786	−	0.154786i	−0.625466	−	0.780252i	$-0.715091\pi$
$73$	96.5419	−	96.5419i	0.154786	−	0.154786i	0.780252	+	0.625466i	$0.215091\pi$
$74$		−	65.8540i		−	0.103451i
$75$		0			0
$76$			517.072i			0.780424i
$77$	275.229	−	54.0063i	0.407340	−	0.0799297i
$78$	−40.5781	−	40.5781i	−0.0589047	−	0.0589047i
$79$			354.468i			0.504820i	0.967620	+	0.252410i	$0.0812231\pi$
$79$			354.468i			0.504820i	−0.967620	+	0.252410i	$0.918777\pi$
$80$		0			0
$81$	361.145			0.495398
$82$	63.9712	+	63.9712i	0.0861516	+	0.0861516i
$83$	522.441	−	522.441i	0.690908	−	0.690908i	−0.271524	−	0.962432i	$-0.587528\pi$
$83$	522.441	−	522.441i	0.690908	−	0.690908i	0.962432	+	0.271524i	$0.0875276\pi$
$84$	−503.958	−	338.624i	−0.654599	−	0.439844i
$85$		0			0
$86$	3.75783			0.00471183
$87$	304.971	+	304.971i	0.375820	+	0.375820i
$88$	41.6467	+	41.6467i	0.0504494	+	0.0504494i
$89$	1064.18			1.26744			0.633722	−	0.773561i	$-0.281526\pi$
$89$	1064.18			1.26744			0.633722	+	0.773561i	$0.281526\pi$
$90$		0			0
$91$	588.464	−	875.783i	0.677888	−	1.00887i
$92$	449.408	−	449.408i	0.509283	−	0.509283i
$93$	927.639	+	927.639i	1.03432	+	1.03432i
$94$	−34.6673			−0.0380389
$95$		0			0
$96$		−	191.483i		−	0.203574i
$97$	−577.458	−	577.458i	−0.604454	−	0.604454i	0.337037	−	0.941491i	$-0.390575\pi$
$97$	−577.458	−	577.458i	−0.604454	−	0.604454i	−0.941491	+	0.337037i	$0.890575\pi$
$98$	−32.4239	+	77.1463i	−0.0334215	+	0.0795199i
$99$		−	150.752i		−	0.153041i
$100$		0			0
$101$		−	1057.45i		−	1.04178i	−0.853624	−	0.520890i	$-0.825600\pi$
$101$		−	1057.45i		−	1.04178i	0.853624	−	0.520890i	$-0.174400\pi$
$102$	30.2805	−	30.2805i	0.0293943	−	0.0293943i
$103$	56.1233	−	56.1233i	0.0536893	−	0.0536893i	−0.679752	−	0.733442i	$-0.737913\pi$
$103$	56.1233	−	56.1233i	0.0536893	−	0.0536893i	0.733442	+	0.679752i	$0.237913\pi$
$104$	221.565			0.208906
$105$		0			0
$106$	−114.638			−0.105044
$107$	−1335.01	+	1335.01i	−1.20617	+	1.20617i	−0.233914	+	0.972257i	$0.575153\pi$
$107$	−1335.01	+	1335.01i	−1.20617	+	1.20617i	−0.972257	+	0.233914i	$0.924847\pi$
$108$	−856.651	+	856.651i	−0.763253	+	0.763253i
$109$		−	324.403i		−	0.285065i	−0.989790	−	0.142533i	$-0.954475\pi$
$109$		−	324.403i		−	0.285065i	0.989790	−	0.142533i	$-0.0455246\pi$
$110$		0			0
$111$			1114.41i			0.952931i
$112$	1137.22	−	223.149i	0.959438	−	0.188264i
$113$	−136.101	−	136.101i	−0.113303	−	0.113303i	0.648182	−	0.761485i	$-0.275530\pi$
$113$	−136.101	−	136.101i	−0.113303	−	0.113303i	−0.761485	+	0.648182i	$0.775530\pi$
$114$			65.5926i			0.0538887i
$115$		0			0
$116$	−829.494			−0.663936
$117$	−401.008	−	401.008i	−0.316865	−	0.316865i
$118$	83.6324	−	83.6324i	0.0652456	−	0.0652456i
$119$	653.533	+	439.128i	0.503440	+	0.338275i
$120$		0			0
$121$	−1101.65			−0.827685
$122$	54.3878	+	54.3878i	0.0403610	+	0.0403610i
$123$	−1082.55	−	1082.55i	−0.793580	−	0.793580i
$124$	−2523.09			−1.82726
$125$		0			0
$126$	37.3332	+	25.0852i	0.0263961	+	0.0177363i
$127$	731.290	−	731.290i	0.510957	−	0.510957i	−0.403863	−	0.914820i	$-0.632333\pi$
$127$	731.290	−	731.290i	0.510957	−	0.510957i	0.914820	+	0.403863i	$0.132333\pi$
$128$	346.769	+	346.769i	0.239456	+	0.239456i
$129$	−63.5918			−0.0434027
$130$		0			0
$131$			1503.34i			1.00265i	0.865258	+	0.501327i	$0.167155\pi$
$131$			1503.34i			1.00265i	−0.865258	+	0.501327i	$0.832845\pi$
$132$	−351.066	−	351.066i	−0.231488	−	0.231488i
$133$	−1183.44	+	232.219i	−0.771560	+	0.151398i
$134$			13.8409i			0.00892295i
$135$		0			0
$136$			165.338i			0.104247i
$137$	−1918.81	+	1918.81i	−1.19660	+	1.19660i	−0.221426	+	0.975177i	$0.571071\pi$
$137$	−1918.81	+	1918.81i	−1.19660	+	1.19660i	−0.975177	+	0.221426i	$0.928929\pi$
$138$	57.0092	−	57.0092i	0.0351663	−	0.0351663i
$139$	658.997			0.402125			0.201063	−	0.979578i	$-0.435561\pi$
$139$	658.997			0.402125			0.201063	+	0.979578i	$0.435561\pi$
$140$		0			0
$141$	586.656			0.350392
$142$	−156.452	+	156.452i	−0.0924590	+	0.0924590i
$143$	610.087	−	610.087i	0.356769	−	0.356769i
$144$		−	622.891i		−	0.360470i
$145$		0			0
$146$			33.3100i			0.0188819i
$147$	548.692	−	1305.51i	0.307860	−	0.732492i
$148$	−1515.55	−	1515.55i	−0.841740	−	0.841740i
$149$			3027.11i			1.66437i	0.554500	+	0.832183i	$0.312909\pi$
$149$			3027.11i			1.66437i	−0.554500	+	0.832183i	$0.687091\pi$
$150$		0			0
$151$	−2127.15			−1.14639			−0.573195	−	0.819419i	$-0.694296\pi$
$151$	−2127.15			−1.14639			−0.573195	+	0.819419i	$0.694296\pi$
$152$	−179.075	−	179.075i	−0.0955583	−	0.0955583i
$153$	299.243	−	299.243i	0.158120	−	0.158120i
$154$	−38.1643	+	56.7981i	−0.0199699	+	0.0297203i
$155$		0			0
$156$	−1867.71			−0.958569
$157$	1563.61	+	1563.61i	0.794841	+	0.794841i	0.982277	−	0.187436i	$-0.0600177\pi$
$157$	1563.61	+	1563.61i	0.794841	+	0.794841i	−0.187436	+	0.982277i	$0.560018\pi$
$158$	−61.1512	−	61.1512i	−0.0307907	−	0.0307907i
$159$	1939.96			0.967604
$160$		0			0
$161$	1230.41	+	826.747i	0.602297	+	0.404701i
$162$	−62.3031	+	62.3031i	−0.0302160	+	0.0302160i
$163$	1344.83	+	1344.83i	0.646226	+	0.646226i	0.952079	−	0.305853i	$-0.0989415\pi$
$163$	1344.83	+	1344.83i	0.646226	+	0.646226i	−0.305853	+	0.952079i	$0.598942\pi$
$164$	2944.44			1.40196
$165$		0			0
$166$			180.258i			0.0842817i
$167$	1463.69	+	1463.69i	0.678228	+	0.678228i	0.959599	−	0.281371i	$-0.0907892\pi$
$167$	1463.69	+	1463.69i	0.678228	+	0.678228i	−0.281371	+	0.959599i	$0.590789\pi$
$168$	291.806	−	57.2592i	0.134008	−	0.0262955i
$169$		−	1048.73i		−	0.477347i
$170$		0			0
$171$			648.210i			0.289882i
$172$	86.4819	−	86.4819i	0.0383383	−	0.0383383i
$173$	−2017.91	+	2017.91i	−0.886814	+	0.886814i	−0.994216	−	0.107401i	$-0.965747\pi$
$173$	−2017.91	+	2017.91i	−0.886814	+	0.886814i	0.107401	+	0.994216i	$0.465747\pi$
$174$	−105.225			−0.0458451
$175$		0			0
$176$	947.657			0.405866
$177$	−1415.27	+	1415.27i	−0.601005	+	0.601005i
$178$	−183.587	+	183.587i	−0.0773059	+	0.0773059i
$179$			2212.81i			0.923985i	0.886884	+	0.461992i	$0.152865\pi$
$179$			2212.81i			0.923985i	−0.886884	+	0.461992i	$0.847135\pi$
$180$		0			0
$181$		−	2077.03i		−	0.852954i	−0.904498	−	0.426477i	$-0.859755\pi$
$181$		−	2077.03i		−	0.852954i	0.904498	−	0.426477i	$-0.140245\pi$
$182$	49.5671	+	252.605i	0.0201877	+	0.102881i
$183$	−920.375	−	920.375i	−0.371782	−	0.371782i
$184$			311.282i			0.124717i
$185$		0			0
$186$	−320.064			−0.126173
$187$	455.264	+	455.264i	0.178033	+	0.178033i
$188$	−797.825	+	797.825i	−0.309507	+	0.309507i
$189$	−2345.38	−	1575.93i	−0.902651	−	0.606517i
$190$		0			0
$191$	−2039.27			−0.772546			−0.386273	−	0.922385i	$-0.626238\pi$
$191$	−2039.27			−0.772546			−0.386273	+	0.922385i	$0.626238\pi$
$192$	−1428.41	−	1428.41i	−0.536910	−	0.536910i
$193$	403.319	+	403.319i	0.150423	+	0.150423i	0.778307	−	0.627884i	$-0.216079\pi$
$193$	403.319	+	403.319i	0.150423	+	0.150423i	−0.627884	+	0.778307i	$0.716079\pi$
$194$	199.241			0.0737355
$195$		0			0
$196$	1029.23	+	2521.62i	0.375085	+	0.918959i
$197$	2118.02	−	2118.02i	0.766003	−	0.766003i	−0.211397	−	0.977400i	$-0.567801\pi$
$197$	2118.02	−	2118.02i	0.766003	−	0.766003i	0.977400	+	0.211397i	$0.0678014\pi$
$198$	26.0070	+	26.0070i	0.00933453	+	0.00933453i
$199$	−543.669			−0.193667			−0.0968334	−	0.995301i	$-0.530871\pi$
$199$	−543.669			−0.193667			−0.0968334	+	0.995301i	$0.530871\pi$
$200$		0			0
$201$		−	234.223i		−	0.0821931i
$202$	182.426	+	182.426i	0.0635418	+	0.0635418i
$203$	−372.529	−	1898.50i	−0.128800	−	0.656395i
$204$		−	1393.74i		−	0.478339i
$205$		0			0
$206$			19.3643i			0.00654939i
$207$	563.386	−	563.386i	0.189169	−	0.189169i
$208$	2520.82	−	2520.82i	0.840325	−	0.840325i
$209$	−986.177			−0.326389
$210$		0			0
$211$	829.151			0.270526			0.135263	−	0.990810i	$-0.456812\pi$
$211$	829.151			0.270526			0.135263	+	0.990810i	$0.456812\pi$
$212$	−2638.26	+	2638.26i	−0.854701	+	0.854701i
$213$	2647.56	−	2647.56i	0.851679	−	0.851679i
$214$		−	460.620i		−	0.147137i
$215$		0			0
$216$		−	593.358i		−	0.186912i
$217$	−1133.13	−	5774.71i	−0.354479	−	1.80651i
$218$	55.9645	+	55.9645i	0.0173871	+	0.0173871i
$219$		−	563.687i		−	0.173929i
$220$		0			0
$221$	2422.05			0.737217
$222$	−192.254	−	192.254i	−0.0581226	−	0.0581226i
$223$	−2531.23	+	2531.23i	−0.760107	+	0.760107i	−0.976342	−	0.216234i	$-0.930623\pi$
$223$	−2531.23	+	2531.23i	−0.760107	+	0.760107i	0.216234	+	0.976342i	$0.430623\pi$
$224$	−479.056	+	712.957i	−0.142894	+	0.212663i
$225$		0			0
$226$	46.9589			0.0138215
$227$	−283.599	−	283.599i	−0.0829212	−	0.0829212i	0.664430	−	0.747351i	$-0.268675\pi$
$227$	−283.599	−	283.599i	−0.0829212	−	0.0829212i	−0.747351	+	0.664430i	$0.768675\pi$
$228$	1509.53	+	1509.53i	0.438471	+	0.438471i
$229$	−4475.13			−1.29138			−0.645688	−	0.763602i	$-0.723429\pi$
$229$	−4475.13			−1.29138			−0.645688	+	0.763602i	$0.723429\pi$
$230$		0			0
$231$	645.834	−	961.165i	0.183951	−	0.273766i
$232$	287.274	−	287.274i	0.0812951	−	0.0812951i
$233$	2075.27	+	2075.27i	0.583500	+	0.583500i	0.935863	−	0.352363i	$-0.114622\pi$
$233$	2075.27	+	2075.27i	0.583500	+	0.583500i	−0.352363	+	0.935863i	$0.614622\pi$
$234$	138.360			0.0386534
$235$		0			0
$236$		−	3849.40i		−	1.06176i
$237$	1034.83	+	1034.83i	0.283626	+	0.283626i
$238$	−188.501	+	36.9883i	−0.0513391	+	0.0100739i
$239$			561.502i			0.151969i	0.997109	+	0.0759844i	$0.0242099\pi$
$239$			561.502i			0.151969i	−0.997109	+	0.0759844i	$0.975790\pi$
$240$		0			0
$241$			491.727i			0.131431i	0.997838	+	0.0657156i	$0.0209330\pi$
$241$			491.727i			0.131431i	−0.997838	+	0.0657156i	$0.979067\pi$
$242$	190.052	−	190.052i	0.0504834	−	0.0504834i
$243$	−1858.55	+	1858.55i	−0.490641	+	0.490641i
$244$	2503.34			0.656802
$245$		0			0
$246$	373.514			0.0968063
$247$	−2623.29	+	2623.29i	−0.675772	+	0.675772i
$248$	873.809	−	873.809i	0.223738	−	0.223738i
$249$		−	3050.42i		−	0.776355i
$250$		0			0
$251$		−	4742.82i		−	1.19268i	−0.802730	−	0.596342i	$-0.796620\pi$
$251$		−	4742.82i		−	1.19268i	0.802730	−	0.596342i	$-0.203380\pi$
$252$	1436.49	−	281.872i	0.359088	−	0.0704614i
$253$	857.126	+	857.126i	0.212992	+	0.212992i
$254$			252.318i			0.0623301i
$255$		0			0
$256$	3794.63			0.926423
$257$	−906.753	−	906.753i	−0.220084	−	0.220084i	0.588450	−	0.808534i	$-0.299739\pi$
$257$	−906.753	−	906.753i	−0.220084	−	0.220084i	−0.808534	+	0.588450i	$0.799739\pi$
$258$	10.9706	−	10.9706i	0.00264728	−	0.00264728i
$259$	2788.06	−	4149.34i	0.668887	−	0.995473i
$260$		0			0
$261$	−1039.87			−0.246614
$262$	−259.350	−	259.350i	−0.0611554	−	0.0611554i
$263$	3713.61	+	3713.61i	0.870689	+	0.870689i	0.992547	−	0.121858i	$-0.0388854\pi$
$263$	3713.61	+	3713.61i	0.870689	+	0.870689i	−0.121858	+	0.992547i	$0.538885\pi$
$264$	243.166			0.0566887
$265$		0			0
$266$	164.101	−	244.224i	0.0378258	−	0.0562944i
$267$	3106.75	−	3106.75i	0.712097	−	0.712097i
$268$	318.533	+	318.533i	0.0726025	+	0.0726025i
$269$	140.328			0.0318065			0.0159033	−	0.999874i	$-0.494938\pi$
$269$	140.328			0.0318065			0.0159033	+	0.999874i	$0.494938\pi$
$270$		0			0
$271$			4266.09i			0.956260i	0.878289	+	0.478130i	$0.158685\pi$
$271$			4266.09i			0.956260i	−0.878289	+	0.478130i	$0.841315\pi$
$272$	1881.11	+	1881.11i	0.419334	+	0.419334i
$273$	−838.797	−	4274.71i	−0.185957	−	0.947682i
$274$		−	662.048i		−	0.145970i
$275$		0			0
$276$		−	2623.99i		−	0.572268i
$277$	1526.65	−	1526.65i	0.331146	−	0.331146i	−0.521876	−	0.853021i	$-0.674768\pi$
$277$	1526.65	−	1526.65i	0.331146	−	0.331146i	0.853021	+	0.521876i	$0.174768\pi$
$278$	−113.687	+	113.687i	−0.0245270	+	0.0245270i
$279$	−3163.00			−0.678722
$280$		0			0
$281$	7194.47			1.52735			0.763676	−	0.645600i	$-0.223393\pi$
$281$	7194.47			1.52735			0.763676	+	0.645600i	$0.223393\pi$
$282$	−101.207	+	101.207i	−0.0213716	+	0.0213716i
$283$	−2582.62	+	2582.62i	−0.542477	+	0.542477i	−0.924254	−	0.381777i	$-0.875312\pi$
$283$	−2582.62	+	2582.62i	−0.542477	+	0.542477i	0.381777	+	0.924254i	$0.375312\pi$
$284$			7201.12i			1.50460i
$285$		0			0
$286$			210.499i			0.0435212i
$287$	1322.36	+	6739.05i	0.271974	+	1.38604i
$288$	326.452	+	326.452i	0.0667929	+	0.0667929i
$289$		−	3105.60i		−	0.632118i
$290$		0			0
$291$	−3371.65			−0.679209
$292$	766.589	+	766.589i	0.153634	+	0.153634i
$293$	6367.25	−	6367.25i	1.26955	−	1.26955i	0.323231	−	0.946320i	$-0.395231\pi$
$293$	6367.25	−	6367.25i	1.26955	−	1.26955i	0.946320	−	0.323231i	$-0.104769\pi$
$294$	130.562	+	319.878i	0.0258998	+	0.0634546i
$295$		0			0
$296$	1049.74			0.206132
$297$	−1633.83	−	1633.83i	−0.319208	−	0.319208i
$298$	−522.224	−	522.224i	−0.101516	−	0.101516i
$299$	4560.01			0.881980
$300$		0			0
$301$	236.774	+	159.095i	0.0453403	+	0.0304655i
$302$	366.966	−	366.966i	0.0699223	−	0.0699223i
$303$	−3087.10	−	3087.10i	−0.585311	−	0.585311i
$304$	−4074.79			−0.768767
$305$		0			0
$306$			103.248i			0.0192886i
$307$	−5777.89	−	5777.89i	−1.07414	−	1.07414i	−0.997022	−	0.0771200i	$-0.975428\pi$
$307$	−5777.89	−	5777.89i	−1.07414	−	1.07414i	−0.0771200	−	0.997022i	$-0.524572\pi$
$308$	428.835	+	2185.45i	0.0793350	+	0.404310i
$309$		−	327.692i		−	0.0603292i
$310$		0			0
$311$			3724.71i			0.679128i	0.940583	+	0.339564i	$0.110279\pi$
$311$			3724.71i			0.679128i	−0.940583	+	0.339564i	$0.889721\pi$
$312$	646.834	−	646.834i	0.117371	−	0.117371i
$313$	3001.58	−	3001.58i	0.542042	−	0.542042i	−0.382085	−	0.924127i	$-0.624794\pi$
$313$	3001.58	−	3001.58i	0.542042	−	0.542042i	0.924127	+	0.382085i	$0.124794\pi$
$314$	−539.496			−0.0969602
$315$		0			0
$316$	−2814.64			−0.501064
$317$	2459.59	−	2459.59i	0.435786	−	0.435786i	−0.454805	−	0.890591i	$-0.650291\pi$
$317$	2459.59	−	2459.59i	0.435786	−	0.435786i	0.890591	+	0.454805i	$0.150291\pi$
$318$	−334.674	+	334.674i	−0.0590175	+	0.0590175i
$319$		−	1582.04i		−	0.277671i
$320$		0			0
$321$			7794.83i			1.35534i
$322$	−354.892	+	69.6380i	−0.0614203	+	0.0120521i
$323$	−1957.57	−	1957.57i	−0.337220	−	0.337220i
$324$			2867.66i			0.491712i
$325$		0			0
$326$	−464.007			−0.0788311
$327$	−947.058	−	947.058i	−0.160160	−	0.160160i
$328$	−1019.73	+	1019.73i	−0.171662	+	0.171662i
$329$	−2184.32	−	1467.71i	−0.366035	−	0.245949i
$330$		0			0
$331$	−6812.43			−1.13125			−0.565627	−	0.824661i	$-0.691366\pi$
$331$	−6812.43			−1.13125			−0.565627	+	0.824661i	$0.691366\pi$
$332$	4148.43	+	4148.43i	0.685767	+	0.685767i
$333$	−1899.92	−	1899.92i	−0.312658	−	0.312658i
$334$	−505.020			−0.0827350
$335$		0			0
$336$	2668.53	−	3971.44i	0.433274	−	0.644821i
$337$	−1850.53	+	1850.53i	−0.299124	+	0.299124i	−0.840671	−	0.541547i	$-0.817839\pi$
$337$	−1850.53	+	1850.53i	−0.299124	+	0.299124i	0.541547	+	0.840671i	$0.317839\pi$
$338$	180.923	+	180.923i	0.0291151	+	0.0291151i
$339$	−794.661			−0.127316
$340$		0			0
$341$		−	4812.13i		−	0.764198i
$342$	−111.826	−	111.826i	−0.0176809	−	0.0176809i
$343$	−5309.11	+	3488.12i	−0.835758	+	0.549098i
$344$			59.9016i			0.00938860i
$345$		0			0
$346$		−	696.242i		−	0.108180i
$347$	−4053.67	+	4053.67i	−0.627126	+	0.627126i	−0.947344	−	0.320218i	$-0.896244\pi$
$347$	−4053.67	+	4053.67i	−0.627126	+	0.627126i	0.320218	+	0.947344i	$0.396244\pi$
$348$	−2421.62	+	2421.62i	−0.373024	+	0.373024i
$349$	1734.54			0.266039			0.133020	−	0.991113i	$-0.457533\pi$
$349$	1734.54			0.266039			0.133020	+	0.991113i	$0.457533\pi$
$350$		0			0
$351$	−8692.18			−1.32181
$352$	−496.659	+	496.659i	−0.0752046	+	0.0752046i
$353$	−7713.10	+	7713.10i	−1.16297	+	1.16297i	−0.179143	+	0.983823i	$0.557333\pi$
$353$	−7713.10	+	7713.10i	−1.16297	+	1.16297i	−0.983823	+	0.179143i	$0.942667\pi$
$354$		−	488.311i		−	0.0733148i
$355$		0			0
$356$			8450.08i			1.25801i
$357$	3189.90	−	625.934i	0.472907	−	0.0927953i
$358$	−381.745	−	381.745i	−0.0563571	−	0.0563571i
$359$			1957.76i			0.287819i	0.989591	+	0.143909i	$0.0459673\pi$
$359$			1957.76i			0.287819i	−0.989591	+	0.143909i	$0.954033\pi$
$360$		0			0
$361$	−2618.58			−0.381773
$362$	358.321	+	358.321i	0.0520246	+	0.0520246i
$363$	−3216.14	+	3216.14i	−0.465024	+	0.465024i
$364$	6954.14	+	4672.68i	1.00136	+	0.672844i
$365$		0			0
$366$	317.558			0.0453526
$367$	−1489.90	−	1489.90i	−0.211913	−	0.211913i	0.593167	−	0.805080i	$-0.297877\pi$
$367$	−1489.90	−	1489.90i	−0.211913	−	0.211913i	−0.805080	+	0.593167i	$0.797877\pi$
$368$	3541.56	+	3541.56i	0.501676	+	0.501676i
$369$	3691.20			0.520748
$370$		0			0
$371$	−7223.15	−	4853.44i	−1.01080	−	0.679186i
$372$	−7365.90	+	7365.90i	−1.02662	+	1.02662i
$373$	−697.611	−	697.611i	−0.0968389	−	0.0968389i	0.657028	−	0.753867i	$-0.271813\pi$
$373$	−697.611	−	697.611i	−0.0968389	−	0.0968389i	−0.753867	+	0.657028i	$0.771813\pi$
$374$	−157.080			−0.0217177
$375$		0			0
$376$		−	552.613i		−	0.0757947i
$377$	−4208.31	−	4208.31i	−0.574905	−	0.574905i
$378$	676.486	−	132.742i	0.0920494	−	0.0180622i
$379$			7235.49i			0.980639i	0.871543	+	0.490319i	$0.163120\pi$
$379$			7235.49i			0.980639i	−0.871543	+	0.490319i	$0.836880\pi$
$380$		0			0
$381$		−	4269.84i		−	0.574149i
$382$	351.805	−	351.805i	0.0471202	−	0.0471202i
$383$	3851.00	−	3851.00i	0.513778	−	0.513778i	−0.401904	−	0.915682i	$-0.631651\pi$
$383$	3851.00	−	3851.00i	0.513778	−	0.513778i	0.915682	+	0.401904i	$0.131651\pi$
$384$	2024.71			0.269070
$385$		0			0
$386$	−139.158			−0.0183496
$387$	108.415	−	108.415i	0.0142405	−	0.0142405i
$388$	4585.30	−	4585.30i	0.599956	−	0.599956i
$389$		−	1416.54i		−	0.184631i	−0.995730	−	0.0923156i	$-0.970573\pi$
$389$		−	1416.54i		−	0.184631i	0.995730	−	0.0923156i	$-0.0294269\pi$
$390$		0			0
$391$			3402.80i			0.440120i
$392$	−1229.75	−	516.852i	−0.158448	−	0.0665943i
$393$	4388.85	+	4388.85i	0.563328	+	0.563328i
$394$			730.782i			0.0934423i
$395$		0			0
$396$	1197.04			0.151903
$397$	10286.6	+	10286.6i	1.30043	+	1.30043i	0.928098	+	0.372335i	$0.121443\pi$
$397$	10286.6	+	10286.6i	1.30043	+	1.30043i	0.372335	+	0.928098i	$0.378557\pi$
$398$	93.7914	−	93.7914i	0.0118124	−	0.0118124i
$399$	−2776.99	+	4132.87i	−0.348430	+	0.518552i
$400$		0			0
$401$	9804.91			1.22103			0.610516	−	0.792004i	$-0.290962\pi$
$401$	9804.91			1.22103			0.610516	+	0.792004i	$0.290962\pi$
$402$	40.4071	+	40.4071i	0.00501324	+	0.00501324i
$403$	−12800.5	−	12800.5i	−1.58223	−	1.58223i
$404$	8396.63			1.03403
$405$		0			0
$406$	391.787	+	263.253i	0.0478918	+	0.0321799i
$407$	2890.51	−	2890.51i	0.352033	−	0.352033i
$408$	482.686	+	482.686i	0.0585698	+	0.0585698i
$409$	−1485.98			−0.179651			−0.0898254	−	0.995958i	$-0.528631\pi$
$409$	−1485.98			−0.179651			−0.0898254	+	0.995958i	$0.528631\pi$
$410$		0			0
$411$			11203.5i			1.34459i
$412$	445.646	+	445.646i	0.0532898	+	0.0532898i
$413$	8810.27	−	1728.78i	1.04970	−	0.205975i
$414$			194.386i			0.0230762i
$415$		0			0
$416$			2642.28i			0.311415i
$417$	1923.87	−	1923.87i	0.225929	−	0.225929i
$418$	170.131	−	170.131i	0.0199076	−	0.0199076i
$419$	−4210.27			−0.490895			−0.245447	−	0.969410i	$-0.578935\pi$
$419$	−4210.27			−0.490895			−0.245447	+	0.969410i	$0.578935\pi$
$420$		0			0
$421$	−4272.21			−0.494571			−0.247286	−	0.968943i	$-0.579539\pi$
$421$	−4272.21			−0.494571			−0.247286	+	0.968943i	$0.579539\pi$
$422$	−143.041	+	143.041i	−0.0165004	+	0.0165004i
$423$	−1000.17	+	1000.17i	−0.114964	+	0.114964i
$424$		−	1827.39i		−	0.209306i
$425$		0			0
$426$			913.490i			0.103894i
$427$	1124.26	+	5729.49i	0.127416	+	0.649343i
$428$	−10600.6	−	10600.6i	−1.19720	−	1.19720i
$429$		−	3562.16i		−	0.400893i
$430$		0			0
$431$	−2055.39			−0.229710			−0.114855	−	0.993382i	$-0.536640\pi$
$431$	−2055.39			−0.229710			−0.114855	+	0.993382i	$0.536640\pi$
$432$	−6750.84	−	6750.84i	−0.751852	−	0.751852i
$433$	1679.54	−	1679.54i	0.186406	−	0.186406i	−0.607734	−	0.794140i	$-0.707922\pi$
$433$	1679.54	−	1679.54i	0.186406	−	0.186406i	0.794140	+	0.607734i	$0.207922\pi$
$434$	1191.71	+	800.744i	0.131806	+	0.0885644i
$435$		0			0
$436$	2575.91			0.282944
$437$	−3685.52	−	3685.52i	−0.403438	−	0.403438i
$438$	97.2448	+	97.2448i	0.0106085	+	0.0106085i
$439$	−9407.03			−1.02272			−0.511359	−	0.859367i	$-0.670858\pi$
$439$	−9407.03			−1.02272			−0.511359	+	0.859367i	$0.670858\pi$
$440$		0			0
$441$	1290.26	+	3161.15i	0.139322	+	0.341340i
$442$	−417.842	+	417.842i	−0.0449654	+	0.0449654i
$443$	−2276.99	−	2276.99i	−0.244205	−	0.244205i	0.574382	−	0.818587i	$-0.305242\pi$
$443$	−2276.99	−	2276.99i	−0.244205	−	0.244205i	−0.818587	+	0.574382i	$0.805242\pi$
$444$	−8848.97			−0.945841
$445$		0			0
$446$		−	873.355i		−	0.0927232i
$447$	8837.32	+	8837.32i	0.935103	+	0.935103i
$448$	1744.84	+	8892.11i	0.184009	+	0.937751i
$449$		−	5028.95i		−	0.528577i	−0.964444	−	0.264288i	$-0.914863\pi$
$449$		−	5028.95i		−	0.528577i	0.964444	−	0.264288i	$-0.0851371\pi$
$450$		0			0
$451$			5615.73i			0.586329i
$452$	1080.70	−	1080.70i	0.112460	−	0.112460i
$453$	−6209.98	+	6209.98i	−0.644084	+	0.644084i
$454$	97.8505			0.0101153
$455$		0			0
$456$	−1045.58			−0.107376
$457$	12754.2	−	12754.2i	1.30551	−	1.30551i	0.380890	−	0.924620i	$-0.375618\pi$
$457$	12754.2	−	12754.2i	1.30551	−	1.30551i	0.924620	−	0.380890i	$-0.124382\pi$
$458$	772.030	−	772.030i	0.0787655	−	0.0787655i
$459$		−	6486.34i		−	0.659600i
$460$		0			0
$461$		−	12702.8i		−	1.28336i	−0.766973	−	0.641680i	$-0.778238\pi$
$461$		−	12702.8i		−	1.28336i	0.766973	−	0.641680i	$-0.221762\pi$
$462$	54.3995	+	277.232i	0.00547812	+	0.0279178i
$463$	10925.8	+	10925.8i	1.09668	+	1.09668i	0.994796	+	0.101884i	$0.0324870\pi$
$463$	10925.8	+	10925.8i	1.09668	+	1.09668i	0.101884	+	0.994796i	$0.467513\pi$
$464$		−	6536.83i		−	0.654019i
$465$		0			0
$466$	−716.033			−0.0711794
$467$	−7125.70	−	7125.70i	−0.706077	−	0.706077i	0.259631	−	0.965708i	$-0.416399\pi$
$467$	−7125.70	−	7125.70i	−0.706077	−	0.706077i	−0.965708	+	0.259631i	$0.916399\pi$
$468$	3184.19	−	3184.19i	0.314507	−	0.314507i
$469$	−585.984	+	872.093i	−0.0576935	+	0.0858625i
$470$		0			0
$471$	9129.60			0.893142
$472$	1333.14	+	1333.14i	0.130006	+	0.130006i
$473$	164.941	+	164.941i	0.0160338	+	0.0160338i
$474$	−357.049			−0.0345987
$475$		0			0
$476$	−3486.88	+	5189.37i	−0.335759	+	0.499694i
$477$	−3307.37	+	3307.37i	−0.317472	+	0.317472i
$478$	−96.8679	−	96.8679i	−0.00926911	−	0.00926911i
$479$	12747.5			1.21597			0.607985	−	0.793949i	$-0.291978\pi$
$479$	12747.5			1.21597			0.607985	+	0.793949i	$0.291978\pi$
$480$		0			0
$481$		−	15377.8i		−	1.45773i
$482$	−84.8306	−	84.8306i	−0.00801645	−	0.00801645i
$483$	6005.64	−	1178.45i	0.565768	−	0.111017i
$484$		−	8747.62i		−	0.821527i
$485$		0			0
$486$		−	641.257i		−	0.0598518i
$487$	−4255.39	+	4255.39i	−0.395955	+	0.395955i	−0.876804	−	0.480849i	$-0.840329\pi$
$487$	−4255.39	+	4255.39i	−0.395955	+	0.395955i	0.480849	+	0.876804i	$0.340329\pi$
$488$	−866.967	+	866.967i	−0.0804216	+	0.0804216i
$489$	7852.14			0.726147
$490$		0			0
$491$	6284.86			0.577662			0.288831	−	0.957380i	$-0.406733\pi$
$491$	6284.86			0.577662			0.288831	+	0.957380i	$0.406733\pi$
$492$	8595.97	−	8595.97i	0.787675	−	0.787675i
$493$	3140.36	−	3140.36i	0.286885	−	0.286885i
$494$		−	905.115i		−	0.0824353i
$495$		0			0
$496$		−	19883.3i		−	1.79997i
$497$	−16481.5	+	3234.05i	−1.48752	+	0.291885i
$498$	526.245	+	526.245i	0.0473526	+	0.0473526i
$499$			6666.36i			0.598051i	0.954245	+	0.299025i	$0.0966615\pi$
$499$			6666.36i			0.598051i	−0.954245	+	0.299025i	$0.903338\pi$
$500$		0			0
$501$	8546.19			0.762107
$502$	818.210	+	818.210i	0.0727460	+	0.0727460i
$503$	−7649.95	+	7649.95i	−0.678120	+	0.678120i	−0.959575	−	0.281455i	$-0.909183\pi$
$503$	−7649.95	+	7649.95i	−0.678120	+	0.678120i	0.281455	+	0.959575i	$0.409183\pi$
$504$	−399.871	+	595.109i	−0.0353406	+	0.0525958i
$505$		0			0
$506$	−295.735			−0.0259823
$507$	−3061.66	−	3061.66i	−0.268191	−	0.268191i
$508$	5806.79	+	5806.79i	0.507155	+	0.507155i
$509$	−9472.50			−0.824875			−0.412437	−	0.910986i	$-0.635322\pi$
$509$	−9472.50			−0.824875			−0.412437	+	0.910986i	$0.635322\pi$
$510$		0			0
$511$	−1410.24	+	2098.80i	−0.122085	+	0.181694i
$512$	−3428.79	+	3428.79i	−0.295962	+	0.295962i
$513$	7025.25	+	7025.25i	0.604624	+	0.604624i
$514$	312.858			0.0268474
$515$		0			0
$516$		−	504.949i		−	0.0430797i
$517$	−1521.64	−	1521.64i	−0.129442	−	0.129442i
$518$	234.842	+	1196.81i	0.0199196	+	0.101515i
$519$			11782.1i			0.996490i
$520$		0			0
$521$		−	102.380i		−	0.00860914i	−0.999991	−	0.00430457i	$-0.998630\pi$
$521$		−	102.380i		−	0.00860914i	0.999991	−	0.00430457i	$-0.00137019\pi$
$522$	179.393	−	179.393i	0.0150418	−	0.0150418i
$523$	8434.43	−	8434.43i	0.705185	−	0.705185i	−0.260333	−	0.965519i	$-0.583832\pi$
$523$	8434.43	−	8434.43i	0.705185	−	0.705185i	0.965519	+	0.260333i	$0.0838325\pi$
$524$	−11937.3			−0.995194
$525$		0			0
$526$	−1281.31			−0.106213
$527$	9552.11	−	9552.11i	0.789557	−	0.789557i
$528$	2766.58	−	2766.58i	0.228030	−	0.228030i
$529$		−	5760.54i		−	0.473456i
$530$		0			0
$531$		−	4825.67i		−	0.394381i
$532$	−1843.93	−	9397.10i	−0.150272	−	0.765819i
$533$	14938.2	+	14938.2i	1.21397	+	1.21397i
$534$			1071.93i			0.0868666i
$535$		0			0
$536$	−220.631			−0.0177795
$537$	6460.06	+	6460.06i	0.519129	+	0.519129i
$538$	−24.2088	+	24.2088i	−0.00193999	+	0.00193999i
$539$	−4809.33	+	1962.99i	−0.384327	+	0.156868i
$540$		0			0
$541$	19779.3			1.57186			0.785931	−	0.618315i	$-0.212184\pi$
$541$	19779.3			1.57186			0.785931	+	0.618315i	$0.212184\pi$
$542$	−735.967	−	735.967i	−0.0583256	−	0.0583256i
$543$	−6063.67	−	6063.67i	−0.479221	−	0.479221i
$544$	−1971.74			−0.155400
$545$		0			0
$546$	882.160	+	592.748i	0.0691446	+	0.0464602i
$547$	−11797.7	+	11797.7i	−0.922180	+	0.922180i	−0.997183	−	0.0750033i	$-0.976103\pi$
$547$	−11797.7	+	11797.7i	−0.922180	+	0.922180i	0.0750033	+	0.997183i	$0.476103\pi$
$548$	−15236.2	−	15236.2i	−1.18770	−	1.18770i
$549$	3138.23			0.243964
$550$		0			0
$551$			6802.53i			0.525949i
$552$	908.753	+	908.753i	0.0700709	+	0.0700709i
$553$	−1264.07	−	6441.99i	−0.0972037	−	0.495373i
$554$			526.741i			0.0403954i
$555$		0			0
$556$			5232.75i			0.399133i
$557$	6016.09	−	6016.09i	0.457648	−	0.457648i	−0.440235	−	0.897883i	$-0.645105\pi$
$557$	6016.09	−	6016.09i	0.457648	−	0.457648i	0.897883	+	0.440235i	$0.145105\pi$
$558$	545.666	−	545.666i	0.0413976	−	0.0413976i
$559$	877.506			0.0663946
$560$		0			0
$561$	2658.18			0.200051
$562$	−1241.16	+	1241.16i	−0.0931585	+	0.0931585i
$563$	8887.62	−	8887.62i	0.665309	−	0.665309i	−0.291318	−	0.956626i	$-0.594094\pi$
$563$	8887.62	−	8887.62i	0.665309	−	0.665309i	0.956626	+	0.291318i	$0.0940937\pi$
$564$			4658.33i			0.347785i
$565$		0			0
$566$		−	891.085i		−	0.0661751i
$567$	−6563.33	+	1287.88i	−0.486127	+	0.0953895i
$568$	−2493.92	−	2493.92i	−0.184230	−	0.184230i
$569$		−	22877.9i		−	1.68558i	−0.538245	−	0.842788i	$-0.680913\pi$
$569$		−	22877.9i		−	1.68558i	0.538245	−	0.842788i	$-0.319087\pi$
$570$		0			0
$571$	5584.51			0.409290			0.204645	−	0.978836i	$-0.434396\pi$
$571$	5584.51			0.409290			0.204645	+	0.978836i	$0.434396\pi$
$572$	4844.38	+	4844.38i	0.354115	+	0.354115i
$573$	−5953.42	+	5953.42i	−0.434045	+	0.434045i
$574$	−1390.72	−	934.464i	−0.101128	−	0.0679509i
$575$		0			0
$576$	4870.49			0.352322
$577$	3145.37	+	3145.37i	0.226938	+	0.226938i	0.811412	−	0.584474i	$-0.198699\pi$
$577$	3145.37	+	3145.37i	0.226938	+	0.226938i	−0.584474	+	0.811412i	$0.698699\pi$
$578$	535.764	+	535.764i	0.0385551	+	0.0385551i
$579$	2354.89			0.169026
$580$		0			0
$581$	−7631.60	+	11357.8i	−0.544943	+	0.811014i
$582$	581.663	−	581.663i	0.0414273	−	0.0414273i
$583$	−5031.78	−	5031.78i	−0.357453	−	0.357453i
$584$	−530.977			−0.0376233
$585$		0			0
$586$			2196.90i			0.154869i
$587$	7974.07	+	7974.07i	0.560690	+	0.560690i	0.929503	−	0.368813i	$-0.120236\pi$
$587$	7974.07	+	7974.07i	0.560690	+	0.560690i	−0.368813	+	0.929503i	$0.620236\pi$
$588$	10366.3	+	4356.88i	0.727042	+	0.305569i
$589$			20691.5i			1.44750i
$590$		0			0
$591$		−	12366.6i		−	0.860737i
$592$	11943.3	−	11943.3i	0.829167	−	0.829167i
$593$	−6228.02	+	6228.02i	−0.431289	+	0.431289i	−0.889067	−	0.457778i	$-0.848645\pi$
$593$	−6228.02	+	6228.02i	−0.431289	+	0.431289i	0.457778	+	0.889067i	$0.348645\pi$
$594$	563.724			0.0389392
$595$		0			0
$596$	−24036.7			−1.65198
$597$	−1587.18	+	1587.18i	−0.108809	+	0.108809i
$598$	−786.672	+	786.672i	−0.0537950	+	0.0537950i
$599$			6066.56i			0.413811i	0.978361	+	0.206906i	$0.0663393\pi$
$599$			6066.56i			0.413811i	−0.978361	+	0.206906i	$0.933661\pi$
$600$		0			0
$601$			14162.7i			0.961245i	0.876928	+	0.480622i	$0.159589\pi$
$601$			14162.7i			0.961245i	−0.876928	+	0.480622i	$0.840411\pi$
$602$	−68.2936	+	13.4008i	−0.00462366	+	0.000907269i
$603$	399.318	+	399.318i	0.0269676	+	0.0269676i
$604$		−	16890.6i		−	1.13786i
$605$		0			0
$606$	1065.15			0.0714003
$607$	−13148.7	−	13148.7i	−0.879223	−	0.879223i	0.114231	−	0.993454i	$-0.463560\pi$
$607$	−13148.7	−	13148.7i	−0.879223	−	0.879223i	−0.993454	+	0.114231i	$0.963560\pi$
$608$	2135.56	−	2135.56i	0.142448	−	0.142448i
$609$	−6630.01	−	4454.89i	−0.441152	−	0.296422i
$610$		0			0
$611$	−8095.29			−0.536007
$612$	2376.13	+	2376.13i	0.156944	+	0.156944i
$613$	6838.92	+	6838.92i	0.450606	+	0.450606i	0.895556	−	0.444950i	$-0.146778\pi$
$613$	6838.92	+	6838.92i	0.450606	+	0.450606i	−0.444950	+	0.895556i	$0.646778\pi$
$614$	1993.55			0.131031
$615$		0			0
$616$	−905.389	−	608.357i	−0.0592194	−	0.0397912i
$617$	10902.0	−	10902.0i	0.711343	−	0.711343i	−0.255473	−	0.966816i	$-0.582231\pi$
$617$	10902.0	−	10902.0i	0.711343	−	0.711343i	0.966816	+	0.255473i	$0.0822313\pi$
$618$	56.5319	+	56.5319i	0.00367969	+	0.00367969i
$619$	19890.2			1.29153			0.645764	−	0.763537i	$-0.276539\pi$
$619$	19890.2			1.29153			0.645764	+	0.763537i	$0.276539\pi$
$620$		0			0
$621$		−	12211.9i		−	0.789122i
$622$	−642.570	−	642.570i	−0.0414223	−	0.0414223i
$623$	−19340.0	+	3794.96i	−1.24373	+	0.244048i
$624$		−	14718.5i		−	0.944251i
$625$		0			0
$626$			1035.64i			0.0661220i
$627$	−2879.03	+	2879.03i	−0.183377	+	0.183377i
$628$	−12415.8	+	12415.8i	−0.788927	+	0.788927i
$629$	11475.4			0.727429
$630$		0			0
$631$	−1793.20			−0.113132			−0.0565660	−	0.998399i	$-0.518015\pi$
$631$	−1793.20			−0.113132			−0.0565660	+	0.998399i	$0.518015\pi$
$632$	974.780	−	974.780i	0.0613523	−	0.0613523i
$633$	2420.61	−	2420.61i	0.151992	−	0.151992i
$634$			848.634i			0.0531602i
$635$		0			0
$636$			15404.2i			0.960405i
$637$	−7571.43	+	18014.7i	−0.470943	+	1.12052i
$638$	272.926	+	272.926i	0.0169361	+	0.0169361i
$639$			9027.45i			0.558874i
$640$		0			0
$641$	−6815.86			−0.419985			−0.209992	−	0.977703i	$-0.567344\pi$
$641$	−6815.86			−0.419985			−0.209992	+	0.977703i	$0.567344\pi$
$642$	−1344.73	−	1344.73i	−0.0826671	−	0.0826671i
$643$	5954.74	−	5954.74i	0.365213	−	0.365213i	−0.500515	−	0.865728i	$-0.666856\pi$
$643$	5954.74	−	5954.74i	0.365213	−	0.365213i	0.865728	+	0.500515i	$0.166856\pi$
$644$	−6564.77	+	9770.03i	−0.401689	+	0.597816i
$645$		0			0
$646$	675.422			0.0411364
$647$	10290.5	+	10290.5i	0.625288	+	0.625288i	0.946879	−	0.321591i	$-0.104218\pi$
$647$	10290.5	+	10290.5i	0.625288	+	0.625288i	−0.321591	+	0.946879i	$0.604218\pi$
$648$	−993.142	−	993.142i	−0.0602072	−	0.0602072i
$649$	7341.70			0.444048
$650$		0			0
$651$	−20166.7	−	13550.6i	−1.21412	−	0.815805i
$652$	−10678.6	+	10678.6i	−0.641418	+	0.641418i
$653$	−20937.8	−	20937.8i	−1.25476	−	1.25476i	−0.953561	−	0.301202i	$-0.902612\pi$
$653$	−20937.8	−	20937.8i	−1.25476	−	1.25476i	−0.301202	−	0.953561i	$-0.597388\pi$
$654$	326.765			0.0195375
$655$		0			0
$656$			23203.7i			1.38102i
$657$	961.009	+	961.009i	0.0570663	+	0.0570663i
$658$	630.032	−	123.627i	0.0373271	−	0.00732444i
$659$			4483.31i			0.265015i	0.991182	+	0.132508i	$0.0423029\pi$
$659$			4483.31i			0.265015i	−0.991182	+	0.132508i	$0.957697\pi$
$660$		0			0
$661$		−	10736.8i		−	0.631793i	−0.948794	−	0.315896i	$-0.897695\pi$
$661$		−	10736.8i		−	0.631793i	0.948794	−	0.315896i	$-0.102305\pi$
$662$	1175.25	−	1175.25i	0.0689991	−	0.0689991i
$663$	7070.92	−	7070.92i	0.414196	−	0.414196i
$664$	−2873.40			−0.167936
$665$		0			0
$666$	655.532			0.0381402
$667$	5912.36	−	5912.36i	0.343219	−	0.343219i
$668$	−11622.4	+	11622.4i	−0.673182	+	0.673182i
$669$			14779.3i			0.854113i
$670$		0			0
$671$			4774.45i			0.274688i
$672$	682.847	+	3479.95i	0.0391985	+	0.199765i
$673$	−1551.60	−	1551.60i	−0.0888706	−	0.0888706i	0.661274	−	0.750145i	$-0.270016\pi$
$673$	−1551.60	−	1551.60i	−0.0888706	−	0.0888706i	−0.750145	+	0.661274i	$0.770016\pi$
$674$		−	638.491i		−	0.0364893i
$675$		0			0
$676$	8327.43			0.473795
$677$	1139.42	+	1139.42i	0.0646844	+	0.0646844i	0.738709	−	0.674025i	$-0.235436\pi$
$677$	1139.42	+	1139.42i	0.0646844	+	0.0646844i	−0.674025	+	0.738709i	$0.735436\pi$
$678$	137.091	−	137.091i	0.00776543	−	0.00776543i
$679$	12553.8	+	8435.27i	0.709531	+	0.476754i
$680$		0			0
$681$	−1655.87			−0.0931764
$682$	830.168	+	830.168i	0.0466111	+	0.0466111i
$683$	6497.27	+	6497.27i	0.363999	+	0.363999i	0.865283	−	0.501284i	$-0.167139\pi$
$683$	6497.27	+	6497.27i	0.363999	+	0.363999i	−0.501284	+	0.865283i	$0.667139\pi$
$684$	−5147.10			−0.287725
$685$		0			0
$686$	314.150	−	1517.66i	0.0174844	−	0.0844672i
$687$	−13064.7	+	13064.7i	−0.725542	+	0.725542i
$688$	681.522	+	681.522i	0.0377657	+	0.0377657i
$689$	−26769.6			−1.48018
$690$		0			0
$691$			19123.4i			1.05280i	0.850236	+	0.526402i	$0.176459\pi$
$691$			19123.4i			1.05280i	−0.850236	+	0.526402i	$0.823541\pi$
$692$	−16023.2	−	16023.2i	−0.880216	−	0.880216i
$693$	537.596	+	2739.71i	0.0294683	+	0.150178i
$694$		−	1398.64i		−	0.0765011i
$695$		0			0
$696$		−	1677.33i		−	0.0913491i
$697$	−11147.3	+	11147.3i	−0.605786	+	0.605786i
$698$	−299.235	+	299.235i	−0.0162267	+	0.0162267i
$699$	12117.1			0.655664
$700$		0			0
$701$	1396.73			0.0752551			0.0376275	−	0.999292i	$-0.488020\pi$
$701$	1396.73			0.0752551			0.0376275	+	0.999292i	$0.488020\pi$
$702$	1499.54	−	1499.54i	0.0806216	−	0.0806216i
$703$	−12428.8	+	12428.8i	−0.666799	+	0.666799i
$704$			7409.89i			0.396692i
$705$		0			0
$706$		−	2661.26i		−	0.141867i
$707$	3770.96	+	19217.7i	0.200596	+	1.02229i
$708$	−11237.9	−	11237.9i	−0.596534	−	0.596534i
$709$			23710.1i			1.25592i	0.778244	+	0.627962i	$0.216111\pi$
$709$			23710.1i			1.25592i	−0.778244	+	0.627962i	$0.783889\pi$
$710$		0			0
$711$	−3528.49			−0.186116
$712$	−2926.47	−	2926.47i	−0.154037	−	0.154037i
$713$	17983.8	−	17983.8i	0.944598	−	0.944598i
$714$	−442.325	+	658.292i	−0.0231843	+	0.0345041i
$715$		0			0
$716$	−17570.8			−0.917110
$717$	1639.24	+	1639.24i	0.0853817	+	0.0853817i
$718$	−337.745	−	337.745i	−0.0175551	−	0.0175551i
$719$	−19736.1			−1.02369			−0.511844	−	0.859078i	$-0.671037\pi$
$719$	−19736.1			−1.02369			−0.511844	+	0.859078i	$0.671037\pi$
$720$		0			0
$721$	−819.826	+	1220.11i	−0.0423466	+	0.0630225i
$722$	451.747	−	451.747i	0.0232857	−	0.0232857i
$723$	1435.54	+	1435.54i	0.0738429	+	0.0738429i
$724$	16492.6			0.846608
$725$		0			0
$726$		−	1109.67i		−	0.0567269i
$727$	−6487.90	−	6487.90i	−0.330981	−	0.330981i	0.521978	−	0.852959i	$-0.325194\pi$
$727$	−6487.90	−	6487.90i	−0.330981	−	0.330981i	−0.852959	+	0.521978i	$0.825194\pi$
$728$	−4026.65	+	790.123i	−0.204997	+	0.0402251i
$729$			20602.6i			1.04672i
$730$		0			0
$731$			654.819i			0.0331318i
$732$	7308.22	−	7308.22i	0.369016	−	0.369016i
$733$	2787.63	−	2787.63i	0.140469	−	0.140469i	−0.633376	−	0.773844i	$-0.718331\pi$
$733$	2787.63	−	2787.63i	0.140469	−	0.140469i	0.773844	+	0.633376i	$0.218331\pi$
$734$	514.061			0.0258506
$735$		0			0
$736$	−3712.20			−0.185915
$737$	−607.516	+	607.516i	−0.0303638	+	0.0303638i
$738$	−636.789	+	636.789i	−0.0317623	+	0.0317623i
$739$		−	10052.4i		−	0.500384i	−0.968196	−	0.250192i	$-0.919506\pi$
$739$		−	10052.4i		−	0.500384i	0.968196	−	0.250192i	$-0.0804938\pi$
$740$		0			0
$741$			15316.8i			0.759347i
$742$	2083.40	−	408.812i	0.103078	−	0.0202263i
$743$	12894.8	+	12894.8i	0.636697	+	0.636697i	0.949739	−	0.313042i	$-0.101348\pi$
$743$	12894.8	+	12894.8i	0.636697	+	0.636697i	−0.313042	+	0.949739i	$0.601348\pi$
$744$		−	5101.98i		−	0.251408i
$745$		0			0
$746$	240.697			0.0118131
$747$	5200.54	+	5200.54i	0.254723	+	0.254723i
$748$	−3615.01	+	3615.01i	−0.176708	+	0.176708i
$749$	19501.3	−	29022.8i	0.951350	−	1.41585i
$750$		0			0
$751$	11311.9			0.549637			0.274818	−	0.961496i	$-0.411382\pi$
$751$	11311.9			0.549637			0.274818	+	0.961496i	$0.411382\pi$
$752$	−6287.27	−	6287.27i	−0.304884	−	0.304884i
$753$	−13846.1	−	13846.1i	−0.670094	−	0.670094i
$754$	1452.00			0.0701308
$755$		0			0
$756$	12513.6	−	18623.4i	0.602005	−	0.895935i
$757$	3513.21	−	3513.21i	0.168679	−	0.168679i	−0.617720	−	0.786398i	$-0.711943\pi$
$757$	3513.21	−	3513.21i	0.168679	−	0.168679i	0.786398	+	0.617720i	$0.211943\pi$
$758$	−1248.23	−	1248.23i	−0.0598126	−	0.0598126i
$759$	5004.57			0.239334
$760$		0			0
$761$		−	24202.1i		−	1.15286i	−0.817147	−	0.576430i	$-0.804446\pi$
$761$		−	24202.1i		−	1.15286i	0.817147	−	0.576430i	$-0.195554\pi$
$762$	736.615	+	736.615i	0.0350193	+	0.0350193i
$763$	1156.85	+	5895.59i	0.0548897	+	0.279731i
$764$		−	16192.8i		−	0.766797i
$765$		0			0
$766$			1328.72i			0.0626743i
$767$	19529.3	−	19529.3i	0.919379	−	0.919379i
$768$	11078.0	−	11078.0i	0.520499	−	0.520499i
$769$	−13151.0			−0.616691			−0.308346	−	0.951274i	$-0.599775\pi$
$769$	−13151.0			−0.616691			−0.308346	+	0.951274i	$0.599775\pi$
$770$		0			0
$771$	−5294.33			−0.247303
$772$	−3202.55	+	3202.55i	−0.149303	+	0.149303i
$773$	−1544.91	+	1544.91i	−0.0718842	+	0.0718842i	−0.742135	−	0.670251i	$-0.766187\pi$
$773$	−1544.91	+	1544.91i	−0.0718842	+	0.0718842i	0.670251	+	0.742135i	$0.266187\pi$
$774$			37.4066i			0.00173715i
$775$		0			0
$776$			3176.00i			0.146922i
$777$	−3974.11	−	20253.0i	−0.183488	−	0.935099i
$778$	244.376	+	244.376i	0.0112613	+	0.0112613i
$779$		−	24146.8i		−	1.11059i
$780$		0			0
$781$	−13734.2			−0.629256
$782$	−587.036	−	587.036i	−0.0268445	−	0.0268445i
$783$	−11270.0	+	11270.0i	−0.514377	+	0.514377i
$784$	−19871.7	+	8110.87i	−0.905233	+	0.369482i
$785$		0			0
$786$	−1514.29			−0.0687187
$787$	13390.9	+	13390.9i	0.606522	+	0.606522i	0.942035	−	0.335514i	$-0.108910\pi$
$787$	13390.9	+	13390.9i	0.606522	+	0.606522i	−0.335514	+	0.942035i	$0.608910\pi$
$788$	16818.1	+	16818.1i	0.760303	+	0.760303i
$789$	21683.0			0.978371
$790$		0			0
$791$	2958.80	+	1988.10i	0.133000	+	0.0893662i
$792$	−414.564	+	414.564i	−0.0185996	+	0.0185996i
$793$	12700.3	+	12700.3i	0.568728	+	0.568728i
$794$	−3549.21			−0.158636
$795$		0			0
$796$		−	4316.99i		−	0.192226i
$797$	−10313.5	−	10313.5i	−0.458372	−	0.458372i	0.439749	−	0.898121i	$-0.355067\pi$
$797$	−10313.5	−	10313.5i	−0.458372	−	0.458372i	−0.898121	+	0.439749i	$0.855067\pi$
$798$	−233.910	−	1192.06i	−0.0103763	−	0.0528802i
$799$		−	6040.93i		−	0.267475i
$800$		0			0
$801$			10593.2i			0.467280i
$802$	−1691.50	+	1691.50i	−0.0744750	+	0.0744750i
$803$	−1462.06	+	1462.06i	−0.0642530	+	0.0642530i
$804$	1859.84			0.0815816
$805$		0			0
$806$	4416.59			0.193012
$807$	409.673	−	409.673i	0.0178701	−	0.0178701i
$808$	−2907.96	+	2907.96i	−0.126611	+	0.126611i
$809$		−	18738.4i		−	0.814347i	−0.913351	−	0.407173i	$-0.866514\pi$
$809$		−	18738.4i		−	0.814347i	0.913351	−	0.407173i	$-0.133486\pi$
$810$		0			0
$811$		−	3494.94i		−	0.151324i	−0.997134	−	0.0756621i	$-0.975893\pi$
$811$		−	3494.94i		−	0.151324i	0.997134	−	0.0756621i	$-0.0241070\pi$
$812$	15075.0	−	2958.06i	0.651511	−	0.127842i
$813$	12454.4	+	12454.4i	0.537262	+	0.537262i
$814$			997.316i			0.0429434i
$815$		0			0
$816$	10983.4			0.471194
$817$	−709.224	−	709.224i	−0.0303704	−	0.0303704i
$818$	256.355	−	256.355i	0.0109575	−	0.0109575i
$819$	8717.83	+	5857.76i	0.371948	+	0.249923i
$820$		0			0
$821$	23319.4			0.991296			0.495648	−	0.868524i	$-0.334931\pi$
$821$	23319.4			0.991296			0.495648	+	0.868524i	$0.334931\pi$
$822$	−1932.78	−	1932.78i	−0.0820113	−	0.0820113i
$823$	−18512.9	−	18512.9i	−0.784105	−	0.784105i	0.196416	−	0.980521i	$-0.437070\pi$
$823$	−18512.9	−	18512.9i	−0.784105	−	0.784105i	−0.980521	+	0.196416i	$0.937070\pi$
$824$	−308.676			−0.0130500
$825$		0			0
$826$	−1221.67	+	1818.15i	−0.0514616	+	0.0765878i
$827$	17866.3	−	17866.3i	0.751236	−	0.751236i	−0.223474	−	0.974710i	$-0.571740\pi$
$827$	17866.3	−	17866.3i	0.751236	−	0.751236i	0.974710	+	0.223474i	$0.0717399\pi$
$828$	4473.55	+	4473.55i	0.187762	+	0.187762i
$829$	−31760.9			−1.33064			−0.665321	−	0.746557i	$-0.731706\pi$
$829$	−31760.9			−1.33064			−0.665321	+	0.746557i	$0.731706\pi$
$830$		0			0
$831$		−	8913.76i		−	0.372100i
$832$	19710.7	+	19710.7i	0.821330	+	0.821330i
$833$	−13443.1	−	5650.01i	−0.559154	−	0.235007i
$834$			663.795i			0.0275604i
$835$		0			0
$836$		−	7830.71i		−	0.323960i
$837$	−34280.3	+	34280.3i	−1.41565	+	1.41565i
$838$	726.336	−	726.336i	0.0299414	−	0.0299414i
$839$	−33411.9			−1.37486			−0.687429	−	0.726251i	$-0.741261\pi$
$839$	−33411.9			−1.37486			−0.687429	+	0.726251i	$0.741261\pi$
$840$		0			0
$841$	13476.3			0.552556
$842$	737.022	−	737.022i	0.0301656	−	0.0301656i
$843$	21003.5	−	21003.5i	0.858123	−	0.858123i
$844$			6583.85i			0.268514i
$845$		0			0
$846$		−	345.089i		−	0.0140241i
$847$	20021.0	−	3928.59i	0.812197	−	0.159372i
$848$	−20790.8	−	20790.8i	−0.841934	−	0.841934i
$849$			15079.4i			0.609567i
$850$		0			0
$851$	21604.7			0.870270
$852$	21022.9	+	21022.9i	0.845343	+	0.845343i
$853$	13286.0	−	13286.0i	0.533301	−	0.533301i	−0.388252	−	0.921553i	$-0.626921\pi$
$853$	13286.0	−	13286.0i	0.533301	−	0.533301i	0.921553	+	0.388252i	$0.126921\pi$
$854$	−1182.38	−	794.474i	−0.0473772	−	0.0318341i
$855$		0			0
$856$	7342.51			0.293180
$857$	−28818.2	−	28818.2i	−1.14867	−	1.14867i	−0.986814	−	0.161857i	$-0.948252\pi$
$857$	−28818.2	−	28818.2i	−1.14867	−	1.14867i	−0.161857	−	0.986814i	$-0.551748\pi$
$858$	614.529	+	614.529i	0.0244518	+	0.0244518i
$859$	39733.3			1.57821			0.789106	−	0.614258i	$-0.210544\pi$
$859$	39733.3			1.57821			0.789106	+	0.614258i	$0.210544\pi$
$860$		0			0
$861$	23534.4	+	15813.4i	0.931534	+	0.625924i
$862$	354.588	−	354.588i	0.0140108	−	0.0140108i
$863$	22961.7	+	22961.7i	0.905709	+	0.905709i	0.995922	−	0.0902133i	$-0.0287549\pi$
$863$	22961.7	+	22961.7i	0.905709	+	0.905709i	−0.0902133	+	0.995922i	$0.528755\pi$
$864$	7076.12			0.278628
$865$		0			0
$866$			579.495i			0.0227391i
$867$	−9066.45	−	9066.45i	−0.355147	−	0.355147i
$868$	45853.9	−	8997.61i	1.79307	−	0.351842i
$869$		−	5368.18i		−	0.209555i
$870$		0			0
$871$			3232.05i			0.125734i
$872$	−892.101	+	892.101i	−0.0346449	+	0.0346449i
$873$	5748.21	−	5748.21i	0.222849	−	0.222849i
$874$	1271.62			0.0492141
$875$		0			0
$876$	4475.95			0.172635
$877$	−154.614	+	154.614i	−0.00595319	+	0.00595319i	−0.710077	−	0.704124i	$-0.751340\pi$
$877$	−154.614	+	154.614i	−0.00595319	+	0.00595319i	0.704124	+	0.710077i	$0.251340\pi$
$878$	1622.86	−	1622.86i	0.0623791	−	0.0623791i
$879$		−	37177.0i		−	1.42656i
$880$		0			0
$881$		−	18280.7i		−	0.699082i	−0.936921	−	0.349541i	$-0.886338\pi$
$881$		−	18280.7i		−	0.699082i	0.936921	−	0.349541i	$-0.113662\pi$
$882$	−767.938	−	322.757i	−0.0293173	−	0.0123218i
$883$	571.541	+	571.541i	0.0217824	+	0.0217824i	0.717914	−	0.696132i	$-0.245097\pi$
$883$	571.541	+	571.541i	0.0217824	+	0.0217824i	−0.696132	+	0.717914i	$0.745097\pi$
$884$			19232.3i			0.731732i
$885$		0			0
$886$	785.632			0.0297899
$887$	−8548.86	−	8548.86i	−0.323611	−	0.323611i	0.526540	−	0.850151i	$-0.323489\pi$
$887$	−8548.86	−	8548.86i	−0.323611	−	0.323611i	−0.850151	+	0.526540i	$0.823489\pi$
$888$	3064.61	−	3064.61i	0.115813	−	0.115813i
$889$	−10682.4	+	15898.1i	−0.403010	+	0.599781i
$890$		0			0
$891$	−5469.30			−0.205644
$892$	−20099.2	−	20099.2i	−0.754452	−	0.754452i
$893$	6542.83	+	6542.83i	0.245182	+	0.245182i
$894$	−3049.15			−0.114070
$895$		0			0
$896$	−7538.69	−	5065.46i	−0.281083	−	0.188867i
$897$	13312.4	−	13312.4i	0.495529	−	0.495529i
$898$	867.573	+	867.573i	0.0322397	+	0.0322397i
$899$	−33193.5			−1.23144
$900$		0			0
$901$		−	19976.2i		−	0.738629i
$902$	−968.801	−	968.801i	−0.0357623	−	0.0357623i
$903$	1155.70	−	226.775i	0.0425905	−	0.00835724i
$904$			748.548i			0.0275402i
$905$		0			0
$906$		−	2142.64i		−	0.0785699i
$907$	−6054.46	+	6054.46i	−0.221648	+	0.221648i	−0.809192	−	0.587544i	$-0.800095\pi$
$907$	−6054.46	+	6054.46i	−0.221648	+	0.221648i	0.587544	+	0.809192i	$0.300095\pi$
$908$	2251.91	−	2251.91i	0.0823043	−	0.0823043i
$909$	10526.2			0.384082
$910$		0			0
$911$	23536.9			0.855995			0.427998	−	0.903780i	$-0.359219\pi$
$911$	23536.9			0.855995			0.427998	+	0.903780i	$0.359219\pi$
$912$	−11895.9	+	11895.9i	−0.431922	+	0.431922i
$913$	−7912.02	+	7912.02i	−0.286801	+	0.286801i
$914$			4400.61i			0.159255i
$915$		0			0
$916$		−	35534.7i		−	1.28177i
$917$	−5361.07	−	27321.3i	−0.193062	−	0.983891i
$918$	1119.00	+	1119.00i	0.0402313	+	0.0402313i
$919$			2009.73i			0.0721380i	0.999349	+	0.0360690i	$0.0114836\pi$
$919$			2009.73i			0.0721380i	−0.999349	+	0.0360690i	$0.988516\pi$
$920$		0			0
$921$	−33735.8			−1.20699
$922$	2191.43	+	2191.43i	0.0782766	+	0.0782766i
$923$	−36533.8	+	36533.8i	−1.30284	+	1.30284i
$924$	7632.11	+	5128.23i	0.271729	+	0.182583i
$925$		0			0
$926$	−3769.73			−0.133781
$927$	558.669	+	558.669i	0.0197941	+	0.0197941i
$928$	3425.90	+	3425.90i	0.121186	+	0.121186i
$929$	−23919.9			−0.844764			−0.422382	−	0.906418i	$-0.638806\pi$
$929$	−23919.9			−0.844764			−0.422382	+	0.906418i	$0.638806\pi$
$930$		0			0
$931$	20679.4	−	8440.55i	0.727970	−	0.297130i
$932$	−16478.6	+	16478.6i	−0.579159	+	0.579159i
$933$	10873.9	+	10873.9i	0.381559	+	0.381559i
$934$	2458.59			0.0861322
$935$		0			0
$936$			2205.53i			0.0770192i
$937$	31840.2	+	31840.2i	1.11011	+	1.11011i	0.993135	+	0.116976i	$0.0373201\pi$
$937$	31840.2	+	31840.2i	1.11011	+	1.11011i	0.116976	+	0.993135i	$0.462680\pi$
$938$	−49.3582	−	251.541i	−0.00171813	−	0.00875598i
$939$		−	17525.5i		−	0.609078i
$940$		0			0
$941$			34998.1i			1.21244i	0.795297	+	0.606220i	$0.207315\pi$
$941$			34998.1i			1.21244i	−0.795297	+	0.606220i	$0.792685\pi$
$942$	−1575.00	+	1575.00i	−0.0544758	+	0.0544758i
$943$	−20987.0	+	20987.0i	−0.724741	+	0.724741i
$944$	30335.2			1.04590
$945$		0			0
$946$	−56.9099			−0.00195592
$947$	−18008.6	+	18008.6i	−0.617951	+	0.617951i	−0.945005	−	0.327055i	$-0.893944\pi$
$947$	−18008.6	+	18008.6i	−0.617951	+	0.617951i	0.327055	+	0.945005i	$0.393944\pi$
$948$	−8217.05	+	8217.05i	−0.281516	+	0.281516i
$949$			7778.35i			0.266065i
$950$		0			0
$951$		−	14361.0i		−	0.489681i
$952$	−589.611	−	3004.80i	−0.0200729	−	0.102296i
$953$	−6157.51	−	6157.51i	−0.209298	−	0.209298i	0.594671	−	0.803969i	$-0.297282\pi$
$953$	−6157.51	−	6157.51i	−0.209298	−	0.209298i	−0.803969	+	0.594671i	$0.797282\pi$
$954$		−	1141.15i		−	0.0387274i
$955$		0			0
$956$	−4458.59			−0.150838
$957$	−4618.59	−	4618.59i	−0.156006	−	0.156006i
$958$	−2199.15	+	2199.15i	−0.0741662	+	0.0741662i
$959$	28029.1	−	41714.4i	0.943803	−	1.40462i
$960$		0			0
$961$	−71174.7			−2.38913
$962$	2652.92	+	2652.92i	0.0889121	+	0.0889121i
$963$	−13289.1	−	13289.1i	−0.444689	−	0.444689i
$964$	−3904.55			−0.130453
$965$		0			0
$966$	−832.766	+	1239.37i	−0.0277369	+	0.0412795i
$967$	28380.1	−	28380.1i	0.943788	−	0.943788i	−0.0547136	−	0.998502i	$-0.517425\pi$
$967$	28380.1	−	28380.1i	0.943788	−	0.943788i	0.998502	+	0.0547136i	$0.0174246\pi$
$968$	3029.51	+	3029.51i	0.100591	+	0.100591i
$969$	−11429.8			−0.378925
$970$		0			0
$971$			2873.09i			0.0949557i	0.998872	+	0.0474778i	$0.0151183\pi$
$971$			2873.09i			0.0949557i	−0.998872	+	0.0474778i	$0.984882\pi$
$972$	−14757.8	−	14757.8i	−0.486991	−	0.486991i
$973$	−11976.4	+	2350.05i	−0.394600	+	0.0774297i
$974$		−	1468.24i		−	0.0483013i
$975$		0			0
$976$			19727.6i			0.646992i
$977$	16501.7	−	16501.7i	0.540366	−	0.540366i	−0.383270	−	0.923636i	$-0.625202\pi$
$977$	16501.7	−	16501.7i	0.540366	−	0.540366i	0.923636	+	0.383270i	$0.125202\pi$
$978$	−1354.62	+	1354.62i	−0.0442903	+	0.0442903i
$979$	−16116.3			−0.526127
$980$		0			0
$981$	3229.21			0.105098
$982$	−1084.24	+	1084.24i	−0.0352336	+	0.0352336i
$983$	26447.8	−	26447.8i	0.858143	−	0.858143i	−0.132976	−	0.991119i	$-0.542453\pi$
$983$	26447.8	−	26447.8i	0.858143	−	0.858143i	0.991119	+	0.132976i	$0.0424534\pi$
$984$			5953.99i			0.192892i
$985$		0			0
$986$			1083.52i			0.0349963i
$987$	−10661.7	+	2092.07i	−0.343835	+	0.0674685i
$988$	−20830.1	−	20830.1i	−0.670744	−	0.670744i
$989$			1232.83i			0.0396377i
$990$		0			0
$991$	−15569.4			−0.499070			−0.249535	−	0.968366i	$-0.580278\pi$
$991$	−15569.4			−0.499070			−0.249535	+	0.968366i	$0.580278\pi$
$992$	10420.6	+	10420.6i	0.333524	+	0.333524i
$993$	−19888.2	+	19888.2i	−0.635581	+	0.635581i
$994$	2285.39	−	3401.24i	0.0729257	−	0.108532i
$995$		0			0
$996$	24221.8			0.770578
$997$	5027.25	+	5027.25i	0.159694	+	0.159694i	0.782431	−	0.622737i	$-0.213979\pi$
$997$	5027.25	+	5027.25i	0.159694	+	0.159694i	−0.622737	+	0.782431i	$0.713979\pi$
$998$	−1150.05	−	1150.05i	−0.0364772	−	0.0364772i
$999$	−41182.4			−1.30426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.f.g.118.6		16
5.2	odd	4	inner	175.4.f.g.132.5		16
5.3	odd	4		35.4.f.b.27.4	yes	16
5.4	even	2		35.4.f.b.13.3	✓	16
7.6	odd	2	inner	175.4.f.g.118.5		16
35.3	even	12		245.4.l.b.117.5		32
35.4	even	6		245.4.l.b.68.4		32
35.9	even	6		245.4.l.b.178.5		32
35.13	even	4		35.4.f.b.27.3	yes	16
35.18	odd	12		245.4.l.b.117.6		32
35.19	odd	6		245.4.l.b.178.6		32
35.23	odd	12		245.4.l.b.227.3		32
35.24	odd	6		245.4.l.b.68.3		32
35.27	even	4	inner	175.4.f.g.132.6		16
35.33	even	12		245.4.l.b.227.4		32
35.34	odd	2		35.4.f.b.13.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.3	✓	16	5.4	even	2
35.4.f.b.13.4	yes	16	35.34	odd	2
35.4.f.b.27.3	yes	16	35.13	even	4
35.4.f.b.27.4	yes	16	5.3	odd	4
175.4.f.g.118.5		16	7.6	odd	2	inner
175.4.f.g.118.6		16	1.1	even	1	trivial
175.4.f.g.132.5		16	5.2	odd	4	inner
175.4.f.g.132.6		16	35.27	even	4	inner
245.4.l.b.68.3		32	35.24	odd	6
245.4.l.b.68.4		32	35.4	even	6
245.4.l.b.117.5		32	35.3	even	12
245.4.l.b.117.6		32	35.18	odd	12
245.4.l.b.178.5		32	35.9	even	6
245.4.l.b.178.6		32	35.19	odd	6
245.4.l.b.227.3		32	35.23	odd	12
245.4.l.b.227.4		32	35.33	even	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.172516 + 0.172516i) q^{2} +(2.91939 - 2.91939i) q^{3} +7.94048i q^{4} +1.00728i q^{6} +(-18.1737 + 3.56610i) q^{7} +(-2.74998 - 2.74998i) q^{8} +9.95432i q^{9} +O(q^{10})\)	\(q+(-0.172516 + 0.172516i) q^{2} +(2.91939 - 2.91939i) q^{3} +7.94048i q^{4} +1.00728i q^{6} +(-18.1737 + 3.56610i) q^{7} +(-2.74998 - 2.74998i) q^{8} +9.95432i q^{9} -15.1443 q^{11} +(23.1814 + 23.1814i) q^{12} +(-40.2848 + 40.2848i) q^{13} +(2.52004 - 3.75045i) q^{14} -62.5750 q^{16} +(-30.0616 - 30.0616i) q^{17} +(-1.71728 - 1.71728i) q^{18} +65.1185 q^{19} +(-42.6452 + 63.4669i) q^{21} +(2.61264 - 2.61264i) q^{22} +(-56.5971 - 56.5971i) q^{23} -16.0565 q^{24} -13.8995i q^{26} +(107.884 + 107.884i) q^{27} +(-28.3165 - 144.308i) q^{28} +104.464i q^{29} +317.751i q^{31} +(32.7950 - 32.7950i) q^{32} +(-44.2123 + 44.2123i) q^{33} +10.3722 q^{34} -79.0420 q^{36} +(-190.864 + 190.864i) q^{37} +(-11.2340 + 11.2340i) q^{38} +235.214i q^{39} -370.814i q^{41} +(-3.59207 - 18.3060i) q^{42} +(-10.8913 - 10.8913i) q^{43} -120.253i q^{44} +19.5278 q^{46} +(100.476 + 100.476i) q^{47} +(-182.681 + 182.681i) q^{48} +(317.566 - 129.618i) q^{49} -175.523 q^{51} +(-319.881 - 319.881i) q^{52} +(332.255 + 332.255i) q^{53} -37.2234 q^{54} +(59.7840 + 40.1706i) q^{56} +(190.106 - 190.106i) q^{57} +(-18.0217 - 18.0217i) q^{58} -484.782 q^{59} -315.263i q^{61} +(-54.8170 - 54.8170i) q^{62} +(-35.4981 - 180.907i) q^{63} -489.285i q^{64} -15.2546i q^{66} +(40.1151 - 40.1151i) q^{67} +(238.704 - 238.704i) q^{68} -330.458 q^{69} +906.887 q^{71} +(27.3742 - 27.3742i) q^{72} +(96.5419 - 96.5419i) q^{73} -65.8540i q^{74} +517.072i q^{76} +(275.229 - 54.0063i) q^{77} +(-40.5781 - 40.5781i) q^{78} +354.468i q^{79} +361.145 q^{81} +(63.9712 + 63.9712i) q^{82} +(522.441 - 522.441i) q^{83} +(-503.958 - 338.624i) q^{84} +3.75783 q^{86} +(304.971 + 304.971i) q^{87} +(41.6467 + 41.6467i) q^{88} +1064.18 q^{89} +(588.464 - 875.783i) q^{91} +(449.408 - 449.408i) q^{92} +(927.639 + 927.639i) q^{93} -34.6673 q^{94} -191.483i q^{96} +(-577.458 - 577.458i) q^{97} +(-32.4239 + 77.1463i) q^{98} -150.752i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8}+O(q^{10}) \) 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8	\( 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8} - 152 q^{11} - 504 q^{16} - 288 q^{18} + 328 q^{21} - 348 q^{22} + 72 q^{23} + 528 q^{28} - 432 q^{32} + 344 q^{36} + 256 q^{37} + 1300 q^{42} + 312 q^{43} - 1856 q^{46} + 696 q^{51} - 1768 q^{53} + 1304 q^{56} + 3920 q^{57} + 4764 q^{58} - 2544 q^{63} - 4504 q^{67} + 6368 q^{71} - 7848 q^{72} + 3016 q^{77} - 5340 q^{78} - 3088 q^{81} - 9336 q^{86} + 2048 q^{88} + 1608 q^{91} + 6328 q^{92} + 3960 q^{93} - 3308 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8 - 152 * q^11 - 504 * q^16 - 288 * q^18 + 328 * q^21 - 348 * q^22 + 72 * q^23 + 528 * q^28 - 432 * q^32 + 344 * q^36 + 256 * q^37 + 1300 * q^42 + 312 * q^43 - 1856 * q^46 + 696 * q^51 - 1768 * q^53 + 1304 * q^56 + 3920 * q^57 + 4764 * q^58 - 2544 * q^63 - 4504 * q^67 + 6368 * q^71 - 7848 * q^72 + 3016 * q^77 - 5340 * q^78 - 3088 * q^81 - 9336 * q^86 + 2048 * q^88 + 1608 * q^91 + 6328 * q^92 + 3960 * q^93 - 3308 * q^98

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