LMFDB - Embedded newform 850.2.g.l.599.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(149,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.g (of order $4$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.23045668864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 $ x^8 + 26x^6 + 237x^4 + 892*x^2 + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			599.3
Root			$2.69904i$ of defining polynomial
Character	$\chi$	$=$	850.599
Dual form			850.2.g.l.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.20140 + 1.20140i) q^{3} +1.00000 q^{4} +(1.20140 + 1.20140i) q^{6} +(-1.69904 + 1.69904i) q^{7} +1.00000 q^{8} -0.113256i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.20140 + 1.20140i) q^{3} +1.00000 q^{4} +(1.20140 + 1.20140i) q^{6} +(-1.69904 + 1.69904i) q^{7} +1.00000 q^{8} -0.113256i q^{9} +(3.82843 + 3.82843i) q^{11} +(1.20140 + 1.20140i) q^{12} +2.28483i q^{13} +(-1.69904 + 1.69904i) q^{14} +1.00000 q^{16} +(-3.48623 - 2.20140i) q^{17} -0.113256i q^{18} +3.51606i q^{19} -4.08247 q^{21} +(3.82843 + 3.82843i) q^{22} +(-0.585786 + 0.585786i) q^{23} +(1.20140 + 1.20140i) q^{24} +2.28483i q^{26} +(3.74028 - 3.74028i) q^{27} +(-1.69904 + 1.69904i) q^{28} +(-0.384382 + 0.384382i) q^{29} +(6.72887 - 6.72887i) q^{31} +1.00000 q^{32} +9.19898i q^{33} +(-3.48623 - 2.20140i) q^{34} -0.113256i q^{36} +(-3.12938 - 3.12938i) q^{37} +3.51606i q^{38} +(-2.74500 + 2.74500i) q^{39} +(4.39808 + 4.39808i) q^{41} -4.08247 q^{42} +1.59719 q^{43} +(3.82843 + 3.82843i) q^{44} +(-0.585786 + 0.585786i) q^{46} +4.11798i q^{47} +(1.20140 + 1.20140i) q^{48} +1.22651i q^{49} +(-1.54360 - 6.83315i) q^{51} +2.28483i q^{52} +1.11326 q^{53} +(3.74028 - 3.74028i) q^{54} +(-1.69904 + 1.69904i) q^{56} +(-4.22421 + 4.22421i) q^{57} +(-0.384382 + 0.384382i) q^{58} -11.1729i q^{59} +(-9.01370 - 9.01370i) q^{61} +(6.72887 - 6.72887i) q^{62} +(0.192426 + 0.192426i) q^{63} +1.00000 q^{64} +9.19898i q^{66} +8.46247i q^{67} +(-3.48623 - 2.20140i) q^{68} -1.40753 q^{69} +(9.13168 - 9.13168i) q^{71} -0.113256i q^{72} +(-8.74028 - 8.74028i) q^{73} +(-3.12938 - 3.12938i) q^{74} +3.51606i q^{76} -13.0093 q^{77} +(-2.74500 + 2.74500i) q^{78} +(-11.6179 - 11.6179i) q^{79} +8.64741 q^{81} +(4.39808 + 4.39808i) q^{82} -10.9725 q^{83} -4.08247 q^{84} +1.59719 q^{86} -0.923597 q^{87} +(3.82843 + 3.82843i) q^{88} +10.7796 q^{89} +(-3.88202 - 3.88202i) q^{91} +(-0.585786 + 0.585786i) q^{92} +16.1682 q^{93} +4.11798i q^{94} +(1.20140 + 1.20140i) q^{96} +(10.5506 + 10.5506i) q^{97} +1.22651i q^{98} +(0.433591 - 0.433591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 4 q^{7} + 8 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 4 * q^7 + 8 * q^8	$ 8 q + 8 q^{2} + 8 q^{4} + 4 q^{7} + 8 q^{8} + 8 q^{11} + 4 q^{14} + 8 q^{16} - 12 q^{17} + 16 q^{21} + 8 q^{22} - 16 q^{23} - 12 q^{27} + 4 q^{28} - 24 q^{29} + 4 q^{31} + 8 q^{32} - 12 q^{34} - 20 q^{37} + 4 q^{39} + 16 q^{42} + 32 q^{43} + 8 q^{44} - 16 q^{46} + 4 q^{51} - 20 q^{53} - 12 q^{54} + 4 q^{56} - 40 q^{57} - 24 q^{58} - 16 q^{61} + 4 q^{62} + 64 q^{63} + 8 q^{64} - 12 q^{68} - 8 q^{69} + 4 q^{71} - 28 q^{73} - 20 q^{74} + 8 q^{77} + 4 q^{78} - 8 q^{79} - 8 q^{81} - 56 q^{83} + 16 q^{84} + 32 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 44 q^{91} - 16 q^{92} + 20 q^{93} + 20 q^{97} + 4 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 4 * q^7 + 8 * q^8 + 8 * q^11 + 4 * q^14 + 8 * q^16 - 12 * q^17 + 16 * q^21 + 8 * q^22 - 16 * q^23 - 12 * q^27 + 4 * q^28 - 24 * q^29 + 4 * q^31 + 8 * q^32 - 12 * q^34 - 20 * q^37 + 4 * q^39 + 16 * q^42 + 32 * q^43 + 8 * q^44 - 16 * q^46 + 4 * q^51 - 20 * q^53 - 12 * q^54 + 4 * q^56 - 40 * q^57 - 24 * q^58 - 16 * q^61 + 4 * q^62 + 64 * q^63 + 8 * q^64 - 12 * q^68 - 8 * q^69 + 4 * q^71 - 28 * q^73 - 20 * q^74 + 8 * q^77 + 4 * q^78 - 8 * q^79 - 8 * q^81 - 56 * q^83 + 16 * q^84 + 32 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 44 * q^91 - 16 * q^92 + 20 * q^93 + 20 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.20140	+	1.20140i	0.693631	+	0.693631i	0.963029	−	0.269398i	$-0.0868247\pi$
$3$	1.20140	+	1.20140i	0.693631	+	0.693631i	−0.269398	+	0.963029i	$0.586825\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	1.20140	+	1.20140i	0.490471	+	0.490471i
$7$	−1.69904	+	1.69904i	−0.642178	+	0.642178i	−0.951090	−	0.308913i	$-0.900035\pi$
$7$	−1.69904	+	1.69904i	−0.642178	+	0.642178i	0.308913	+	0.951090i	$0.400035\pi$
$8$	1.00000			0.353553
$9$		−	0.113256i		−	0.0377519i
$10$		0			0
$11$	3.82843	+	3.82843i	1.15431	+	1.15431i	0.985678	+	0.168636i	$0.0539362\pi$
$11$	3.82843	+	3.82843i	1.15431	+	1.15431i	0.168636	+	0.985678i	$0.446064\pi$
$12$	1.20140	+	1.20140i	0.346816	+	0.346816i
$13$			2.28483i			0.633697i	0.948476	+	0.316849i	$0.102625\pi$
$13$			2.28483i			0.633697i	−0.948476	+	0.316849i	$0.897375\pi$
$14$	−1.69904	+	1.69904i	−0.454088	+	0.454088i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.48623	−	2.20140i	−0.845536	−	0.533919i
$17$	−3.48623	−	2.20140i	−0.845536	−	0.533919i
$18$		−	0.113256i		−	0.0266946i
$19$			3.51606i			0.806640i	0.915059	+	0.403320i	$0.132144\pi$
$19$			3.51606i			0.806640i	−0.915059	+	0.403320i	$0.867856\pi$
$20$		0			0
$21$	−4.08247			−0.890869
$22$	3.82843	+	3.82843i	0.816223	+	0.816223i
$23$	−0.585786	+	0.585786i	−0.122145	+	0.122145i	−0.765537	−	0.643392i	$-0.777527\pi$
$23$	−0.585786	+	0.585786i	−0.122145	+	0.122145i	0.643392	+	0.765537i	$0.277527\pi$
$24$	1.20140	+	1.20140i	0.245236	+	0.245236i
$25$		0			0
$26$			2.28483i			0.448092i
$27$	3.74028	−	3.74028i	0.719817	−	0.719817i
$28$	−1.69904	+	1.69904i	−0.321089	+	0.321089i
$29$	−0.384382	+	0.384382i	−0.0713780	+	0.0713780i	−0.741895	−	0.670517i	$-0.766073\pi$
$29$	−0.384382	+	0.384382i	−0.0713780	+	0.0713780i	0.670517	+	0.741895i	$0.266073\pi$
$30$		0			0
$31$	6.72887	−	6.72887i	1.20854	−	1.20854i	0.237042	−	0.971499i	$-0.423822\pi$
$31$	6.72887	−	6.72887i	1.20854	−	1.20854i	0.971499	−	0.237042i	$-0.0761779\pi$
$32$	1.00000			0.176777
$33$			9.19898i			1.60134i
$34$	−3.48623	−	2.20140i	−0.597884	−	0.377538i
$35$		0			0
$36$		−	0.113256i		−	0.0188760i
$37$	−3.12938	−	3.12938i	−0.514468	−	0.514468i	0.401424	−	0.915892i	$-0.368515\pi$
$37$	−3.12938	−	3.12938i	−0.514468	−	0.514468i	−0.915892	+	0.401424i	$0.868515\pi$
$38$			3.51606i			0.570381i
$39$	−2.74500	+	2.74500i	−0.439552	+	0.439552i
$40$		0			0
$41$	4.39808	+	4.39808i	0.686865	+	0.686865i	0.961538	−	0.274672i	$-0.0885694\pi$
$41$	4.39808	+	4.39808i	0.686865	+	0.686865i	−0.274672	+	0.961538i	$0.588569\pi$
$42$	−4.08247			−0.629939
$43$	1.59719			0.243569			0.121785	−	0.992557i	$-0.461138\pi$
$43$	1.59719			0.243569			0.121785	+	0.992557i	$0.461138\pi$
$44$	3.82843	+	3.82843i	0.577157	+	0.577157i
$45$		0			0
$46$	−0.585786	+	0.585786i	−0.0863695	+	0.0863695i
$47$			4.11798i			0.600669i	0.953834	+	0.300335i	$0.0970983\pi$
$47$			4.11798i			0.600669i	−0.953834	+	0.300335i	$0.902902\pi$
$48$	1.20140	+	1.20140i	0.173408	+	0.173408i
$49$			1.22651i			0.175216i
$50$		0			0
$51$	−1.54360	−	6.83315i	−0.216147	−	0.956833i
$52$			2.28483i			0.316849i
$53$	1.11326			0.152917			0.0764587	−	0.997073i	$-0.475639\pi$
$53$	1.11326			0.152917			0.0764587	+	0.997073i	$0.475639\pi$
$54$	3.74028	−	3.74028i	0.508987	−	0.508987i
$55$		0			0
$56$	−1.69904	+	1.69904i	−0.227044	+	0.227044i
$57$	−4.22421	+	4.22421i	−0.559511	+	0.559511i
$58$	−0.384382	+	0.384382i	−0.0504719	+	0.0504719i
$59$		−	11.1729i		−	1.45459i	−0.686325	−	0.727295i	$-0.740777\pi$
$59$		−	11.1729i		−	1.45459i	0.686325	−	0.727295i	$-0.259223\pi$
$60$		0			0
$61$	−9.01370	−	9.01370i	−1.15409	−	1.15409i	−0.985725	−	0.168361i	$-0.946153\pi$
$61$	−9.01370	−	9.01370i	−1.15409	−	1.15409i	−0.168361	−	0.985725i	$-0.553847\pi$
$62$	6.72887	−	6.72887i	0.854568	−	0.854568i
$63$	0.192426	+	0.192426i	0.0242434	+	0.0242434i
$64$	1.00000			0.125000
$65$		0			0
$66$			9.19898i			1.13232i
$67$			8.46247i			1.03386i	0.856029	+	0.516928i	$0.172924\pi$
$67$			8.46247i			1.03386i	−0.856029	+	0.516928i	$0.827076\pi$
$68$	−3.48623	−	2.20140i	−0.422768	−	0.266959i
$69$	−1.40753			−0.169447
$70$		0			0
$71$	9.13168	−	9.13168i	1.08373	−	1.08373i	0.0875732	−	0.996158i	$-0.472089\pi$
$71$	9.13168	−	9.13168i	1.08373	−	1.08373i	0.996158	−	0.0875732i	$-0.0279112\pi$
$72$		−	0.113256i		−	0.0133473i
$73$	−8.74028	−	8.74028i	−1.02297	−	1.02297i	−0.999730	−	0.0232424i	$-0.992601\pi$
$73$	−8.74028	−	8.74028i	−1.02297	−	1.02297i	−0.0232424	−	0.999730i	$-0.507399\pi$
$74$	−3.12938	−	3.12938i	−0.363784	−	0.363784i
$75$		0			0
$76$			3.51606i			0.403320i
$77$	−13.0093			−1.48255
$78$	−2.74500	+	2.74500i	−0.310810	+	0.310810i
$79$	−11.6179	−	11.6179i	−1.30712	−	1.30712i	−0.923486	−	0.383631i	$-0.874673\pi$
$79$	−11.6179	−	11.6179i	−1.30712	−	1.30712i	−0.383631	−	0.923486i	$-0.625327\pi$
$80$		0			0
$81$	8.64741			0.960823
$82$	4.39808	+	4.39808i	0.485687	+	0.485687i
$83$	−10.9725			−1.20438			−0.602192	−	0.798351i	$-0.705706\pi$
$83$	−10.9725			−1.20438			−0.602192	+	0.798351i	$0.705706\pi$
$84$	−4.08247			−0.445434
$85$		0			0
$86$	1.59719			0.172230
$87$	−0.923597			−0.0990200
$88$	3.82843	+	3.82843i	0.408112	+	0.408112i
$89$	10.7796			1.14263			0.571315	−	0.820731i	$-0.306433\pi$
$89$	10.7796			1.14263			0.571315	+	0.820731i	$0.306433\pi$
$90$		0			0
$91$	−3.88202	−	3.88202i	−0.406946	−	0.406946i
$92$	−0.585786	+	0.585786i	−0.0610725	+	0.0610725i
$93$	16.1682			1.67656
$94$			4.11798i			0.424737i
$95$		0			0
$96$	1.20140	+	1.20140i	0.122618	+	0.122618i
$97$	10.5506	+	10.5506i	1.07125	+	1.07125i	0.997259	+	0.0739945i	$0.0235747\pi$
$97$	10.5506	+	10.5506i	1.07125	+	1.07125i	0.0739945	+	0.997259i	$0.476425\pi$
$98$			1.22651i			0.123896i
$99$	0.433591	−	0.433591i	0.0435776	−	0.0435776i
$100$		0			0
$101$	−3.65685			−0.363871			−0.181935	−	0.983311i	$-0.558236\pi$
$101$	−3.65685			−0.363871			−0.181935	+	0.983311i	$0.558236\pi$
$102$	−1.54360	−	6.83315i	−0.152839	−	0.676583i
$103$			2.02281i			0.199313i	0.995022	+	0.0996567i	$0.0317745\pi$
$103$			2.02281i			0.199313i	−0.995022	+	0.0996567i	$0.968226\pi$
$104$			2.28483i			0.224046i
$105$		0			0
$106$	1.11326			0.108129
$107$	−6.11326	−	6.11326i	−0.590991	−	0.590991i	0.346908	−	0.937899i	$-0.387232\pi$
$107$	−6.11326	−	6.11326i	−0.590991	−	0.590991i	−0.937899	+	0.346908i	$0.887232\pi$
$108$	3.74028	−	3.74028i	0.359908	−	0.359908i
$109$	0.384382	+	0.384382i	0.0368171	+	0.0368171i	0.725276	−	0.688459i	$-0.241712\pi$
$109$	0.384382	+	0.384382i	0.0368171	+	0.0368171i	−0.688459	+	0.725276i	$0.741712\pi$
$110$		0			0
$111$		−	7.51931i		−	0.713702i
$112$	−1.69904	+	1.69904i	−0.160544	+	0.160544i
$113$	5.14309	−	5.14309i	0.483821	−	0.483821i	−0.422529	−	0.906350i	$-0.638857\pi$
$113$	5.14309	−	5.14309i	0.483821	−	0.483821i	0.906350	+	0.422529i	$0.138857\pi$
$114$	−4.22421	+	4.22421i	−0.395634	+	0.395634i
$115$		0			0
$116$	−0.384382	+	0.384382i	−0.0356890	+	0.0356890i
$117$	0.258770			0.0239233
$118$		−	11.1729i		−	1.02855i
$119$	9.66354	−	2.18298i	0.885855	−	0.200113i
$120$		0			0
$121$			18.3137i			1.66488i
$122$	−9.01370	−	9.01370i	−0.816062	−	0.816062i
$123$			10.5678i			0.952862i
$124$	6.72887	−	6.72887i	0.604271	−	0.604271i
$125$		0			0
$126$	0.192426	+	0.192426i	0.0171427	+	0.0171427i
$127$	12.3217			1.09337			0.546686	−	0.837338i	$-0.315889\pi$
$127$	12.3217			1.09337			0.546686	+	0.837338i	$0.315889\pi$
$128$	1.00000			0.0883883
$129$	1.91887	+	1.91887i	0.168947	+	0.168947i
$130$		0			0
$131$	−8.45775	+	8.45775i	−0.738957	+	0.738957i	−0.972376	−	0.233419i	$-0.925009\pi$
$131$	−8.45775	+	8.45775i	−0.738957	+	0.738957i	0.233419	+	0.972376i	$0.425009\pi$
$132$			9.19898i			0.800668i
$133$	−5.97394	−	5.97394i	−0.518006	−	0.518006i
$134$			8.46247i			0.731046i
$135$		0			0
$136$	−3.48623	−	2.20140i	−0.298942	−	0.188769i
$137$		−	11.7781i		−	1.00627i	−0.864208	−	0.503135i	$-0.832180\pi$
$137$		−	11.7781i		−	1.00627i	0.864208	−	0.503135i	$-0.167820\pi$
$138$	−1.40753			−0.119817
$139$	4.97719	−	4.97719i	0.422160	−	0.422160i	−0.463787	−	0.885947i	$-0.653510\pi$
$139$	4.97719	−	4.97719i	0.422160	−	0.422160i	0.885947	+	0.463787i	$0.153510\pi$
$140$		0			0
$141$	−4.94736	+	4.94736i	−0.416643	+	0.416643i
$142$	9.13168	−	9.13168i	0.766314	−	0.766314i
$143$	−8.74730	+	8.74730i	−0.731486	+	0.731486i
$144$		−	0.113256i		−	0.00943798i
$145$		0			0
$146$	−8.74028	−	8.74028i	−0.723351	−	0.723351i
$147$	−1.47354	+	1.47354i	−0.121535	+	0.121535i
$148$	−3.12938	−	3.12938i	−0.257234	−	0.257234i
$149$	−3.25405			−0.266582			−0.133291	−	0.991077i	$-0.542554\pi$
$149$	−3.25405			−0.266582			−0.133291	+	0.991077i	$0.542554\pi$
$150$		0			0
$151$		−	3.39808i		−	0.276532i	−0.990395	−	0.138266i	$-0.955847\pi$
$151$		−	3.39808i		−	0.276532i	0.990395	−	0.138266i	$-0.0441529\pi$
$152$			3.51606i			0.285190i
$153$	−0.249322	+	0.394836i	−0.0201565	+	0.0319206i
$154$	−13.0093			−1.04832
$155$		0			0
$156$	−2.74500	+	2.74500i	−0.219776	+	0.219776i
$157$		−	11.5725i		−	0.923584i	−0.886988	−	0.461792i	$-0.847207\pi$
$157$		−	11.5725i		−	0.923584i	0.886988	−	0.461792i	$-0.152793\pi$
$158$	−11.6179	−	11.6179i	−0.924272	−	0.924272i
$159$	1.33747	+	1.33747i	0.106068	+	0.106068i
$160$		0			0
$161$		−	1.99055i		−	0.156877i
$162$	8.64741			0.679404
$163$	5.85449	−	5.85449i	0.458559	−	0.458559i	−0.439623	−	0.898182i	$-0.644888\pi$
$163$	5.85449	−	5.85449i	0.458559	−	0.458559i	0.898182	+	0.439623i	$0.144888\pi$
$164$	4.39808	+	4.39808i	0.343433	+	0.343433i
$165$		0			0
$166$	−10.9725			−0.851629
$167$	6.50141	+	6.50141i	0.503094	+	0.503094i	0.912398	−	0.409304i	$-0.134228\pi$
$167$	6.50141	+	6.50141i	0.503094	+	0.503094i	−0.409304	+	0.912398i	$0.634228\pi$
$168$	−4.08247			−0.314970
$169$	7.77956			0.598428
$170$		0			0
$171$	0.398214			0.0304522
$172$	1.59719			0.121785
$173$	−13.0483	−	13.0483i	−0.992041	−	0.992041i	0.00792792	−	0.999969i	$-0.497476\pi$
$173$	−13.0483	−	13.0483i	−0.992041	−	0.992041i	−0.999969	+	0.00792792i	$0.997476\pi$
$174$	−0.923597			−0.0700177
$175$		0			0
$176$	3.82843	+	3.82843i	0.288579	+	0.288579i
$177$	13.4232	−	13.4232i	1.00895	−	1.00895i
$178$	10.7796			0.807962
$179$			15.6018i			1.16613i	0.812425	+	0.583066i	$0.198147\pi$
$179$			15.6018i			1.16613i	−0.812425	+	0.583066i	$0.801853\pi$
$180$		0			0
$181$	−7.21511	−	7.21511i	−0.536295	−	0.536295i	0.386144	−	0.922439i	$-0.373807\pi$
$181$	−7.21511	−	7.21511i	−0.536295	−	0.536295i	−0.922439	+	0.386144i	$0.873807\pi$
$182$	−3.88202	−	3.88202i	−0.287754	−	0.287754i
$183$		−	21.6582i		−	1.60102i
$184$	−0.585786	+	0.585786i	−0.0431847	+	0.0431847i
$185$		0			0
$186$	16.1682			1.18551
$187$	−4.91887	−	21.7747i	−0.359704	−	1.59232i
$188$			4.11798i			0.300335i
$189$			12.7098i			0.924501i
$190$		0			0
$191$	−1.54212			−0.111584			−0.0557920	−	0.998442i	$-0.517768\pi$
$191$	−1.54212			−0.111584			−0.0557920	+	0.998442i	$0.517768\pi$
$192$	1.20140	+	1.20140i	0.0867039	+	0.0867039i
$193$	12.6601	−	12.6601i	0.911294	−	0.911294i	−0.0850800	−	0.996374i	$-0.527115\pi$
$193$	12.6601	−	12.6601i	0.911294	−	0.911294i	0.996374	+	0.0850800i	$0.0271146\pi$
$194$	10.5506	+	10.5506i	0.757490	+	0.757490i
$195$		0			0
$196$			1.22651i			0.0876080i
$197$	−6.76343	+	6.76343i	−0.481874	+	0.481874i	−0.905730	−	0.423855i	$-0.860676\pi$
$197$	−6.76343	+	6.76343i	−0.481874	+	0.481874i	0.423855	+	0.905730i	$0.360676\pi$
$198$	0.433591	−	0.433591i	0.0308140	−	0.0308140i
$199$	13.7013	−	13.7013i	0.971262	−	0.971262i	−0.0283363	−	0.999598i	$-0.509021\pi$
$199$	13.7013	−	13.7013i	0.971262	−	0.971262i	0.999598	+	0.0283363i	$0.00902092\pi$
$200$		0			0
$201$	−10.1668	+	10.1668i	−0.717114	+	0.717114i
$202$	−3.65685			−0.257295
$203$		−	1.30616i		−	0.0916747i
$204$	−1.54360	−	6.83315i	−0.108074	−	0.478416i
$205$		0			0
$206$			2.02281i			0.140936i
$207$	0.0663437	+	0.0663437i	0.00461120	+	0.00461120i
$208$			2.28483i			0.158424i
$209$	−13.4610	+	13.4610i	−0.931117	+	0.931117i
$210$		0			0
$211$	2.88202	+	2.88202i	0.198406	+	0.198406i	0.799317	−	0.600910i	$-0.205195\pi$
$211$	2.88202	+	2.88202i	0.198406	+	0.198406i	−0.600910	+	0.799317i	$0.705195\pi$
$212$	1.11326			0.0764587
$213$	21.9417			1.50342
$214$	−6.11326	−	6.11326i	−0.417894	−	0.417894i
$215$		0			0
$216$	3.74028	−	3.74028i	0.254494	−	0.254494i
$217$			22.8653i			1.55220i
$218$	0.384382	+	0.384382i	0.0260336	+	0.0260336i
$219$		−	21.0012i		−	1.41913i
$220$		0			0
$221$	5.02983	−	7.96544i	0.338343	−	0.535814i
$222$		−	7.51931i		−	0.504663i
$223$	10.0242			0.671267			0.335634	−	0.941993i	$-0.391050\pi$
$223$	10.0242			0.671267			0.335634	+	0.941993i	$0.391050\pi$
$224$	−1.69904	+	1.69904i	−0.113522	+	0.113522i
$225$		0			0
$226$	5.14309	−	5.14309i	0.342113	−	0.342113i
$227$	−10.6223	+	10.6223i	−0.705027	+	0.705027i	−0.965485	−	0.260458i	$-0.916126\pi$
$227$	−10.6223	+	10.6223i	−0.705027	+	0.705027i	0.260458	+	0.965485i	$0.416126\pi$
$228$	−4.22421	+	4.22421i	−0.279755	+	0.279755i
$229$			17.4483i			1.15302i	0.817091	+	0.576508i	$0.195585\pi$
$229$			17.4483i			1.15302i	−0.817091	+	0.576508i	$0.804415\pi$
$230$		0			0
$231$	−15.6294	−	15.6294i	−1.02834	−	1.02834i
$232$	−0.384382	+	0.384382i	−0.0252359	+	0.0252359i
$233$	20.3421	+	20.3421i	1.33265	+	1.33265i	0.902989	+	0.429664i	$0.141368\pi$
$233$	20.3421	+	20.3421i	1.33265	+	1.33265i	0.429664	+	0.902989i	$0.358632\pi$
$234$	0.258770			0.0169163
$235$		0			0
$236$		−	11.1729i		−	0.727295i
$237$		−	27.9156i		−	1.81331i
$238$	9.66354	−	2.18298i	0.626394	−	0.141501i
$239$	−19.0823			−1.23433			−0.617167	−	0.786832i	$-0.711720\pi$
$239$	−19.0823			−1.23433			−0.617167	+	0.786832i	$0.711720\pi$
$240$		0			0
$241$	−15.4302	+	15.4302i	−0.993947	+	0.993947i	−0.999982	−	0.00603442i	$-0.998079\pi$
$241$	−15.4302	+	15.4302i	−0.993947	+	0.993947i	0.00603442	+	0.999982i	$0.498079\pi$
$242$			18.3137i			1.17725i
$243$	−0.831806	−	0.831806i	−0.0533604	−	0.0533604i
$244$	−9.01370	−	9.01370i	−0.577043	−	0.577043i
$245$		0			0
$246$			10.5678i			0.673775i
$247$	−8.03360			−0.511166
$248$	6.72887	−	6.72887i	0.427284	−	0.427284i
$249$	−13.1824	−	13.1824i	−0.835399	−	0.835399i
$250$		0			0
$251$	−11.4209			−0.720880			−0.360440	−	0.932782i	$-0.617374\pi$
$251$	−11.4209			−0.720880			−0.360440	+	0.932782i	$0.617374\pi$
$252$	0.192426	+	0.192426i	0.0121217	+	0.0121217i
$253$	−4.48528			−0.281987
$254$	12.3217			0.773131
$255$		0			0
$256$	1.00000			0.0625000
$257$	−25.3278			−1.57990			−0.789951	−	0.613170i	$-0.789894\pi$
$257$	−25.3278			−1.57990			−0.789951	+	0.613170i	$0.789894\pi$
$258$	1.91887	+	1.91887i	0.119464	+	0.119464i
$259$	10.6339			0.660759
$260$		0			0
$261$	0.0435335	+	0.0435335i	0.00269466	+	0.00269466i
$262$	−8.45775	+	8.45775i	−0.522521	+	0.522521i
$263$	−14.5938			−0.899893			−0.449947	−	0.893055i	$-0.648557\pi$
$263$	−14.5938			−0.899893			−0.449947	+	0.893055i	$0.648557\pi$
$264$			9.19898i			0.566158i
$265$		0			0
$266$	−5.97394	−	5.97394i	−0.366286	−	0.366286i
$267$	12.9506	+	12.9506i	0.792564	+	0.792564i
$268$			8.46247i			0.516928i
$269$	−15.2128	+	15.2128i	−0.927541	+	0.927541i	−0.997547	−	0.0700053i	$-0.977698\pi$
$269$	−15.2128	+	15.2128i	−0.927541	+	0.927541i	0.0700053	+	0.997547i	$0.477698\pi$
$270$		0			0
$271$	20.4986			1.24520			0.622602	−	0.782539i	$-0.286076\pi$
$271$	20.4986			1.24520			0.622602	+	0.782539i	$0.286076\pi$
$272$	−3.48623	−	2.20140i	−0.211384	−	0.133480i
$273$		−	9.32775i		−	0.564541i
$274$		−	11.7781i		−	0.711540i
$275$		0			0
$276$	−1.40753			−0.0847235
$277$	7.40477	+	7.40477i	0.444909	+	0.444909i	0.893658	−	0.448749i	$-0.148130\pi$
$277$	7.40477	+	7.40477i	0.444909	+	0.444909i	−0.448749	+	0.893658i	$0.648130\pi$
$278$	4.97719	−	4.97719i	0.298512	−	0.298512i
$279$	−0.762083	−	0.762083i	−0.0456247	−	0.0456247i
$280$		0			0
$281$		−	15.8573i		−	0.945968i	−0.881071	−	0.472984i	$-0.843177\pi$
$281$		−	15.8573i		−	0.945968i	0.881071	−	0.472984i	$-0.156823\pi$
$282$	−4.94736	+	4.94736i	−0.294611	+	0.294611i
$283$	−3.97017	+	3.97017i	−0.236002	+	0.236002i	−0.815192	−	0.579190i	$-0.803369\pi$
$283$	−3.97017	+	3.97017i	−0.236002	+	0.236002i	0.579190	+	0.815192i	$0.303369\pi$
$284$	9.13168	−	9.13168i	0.541866	−	0.541866i
$285$		0			0
$286$	−8.74730	+	8.74730i	−0.517239	+	0.517239i
$287$	−14.9451			−0.882179
$288$		−	0.113256i		−	0.00667366i
$289$	7.30764	+	15.3492i	0.429861	+	0.902895i
$290$		0			0
$291$			25.3511i			1.48611i
$292$	−8.74028	−	8.74028i	−0.511486	−	0.511486i
$293$		−	27.9444i		−	1.63253i	−0.577679	−	0.816264i	$-0.696042\pi$
$293$		−	27.9444i		−	1.63253i	0.577679	−	0.816264i	$-0.303958\pi$
$294$	−1.47354	+	1.47354i	−0.0859384	+	0.0859384i
$295$		0			0
$296$	−3.12938	−	3.12938i	−0.181892	−	0.181892i
$297$	28.6388			1.66179
$298$	−3.25405			−0.188502
$299$	−1.33842	−	1.33842i	−0.0774029	−	0.0774029i
$300$		0			0
$301$	−2.71370	+	2.71370i	−0.156415	+	0.156415i
$302$		−	3.39808i		−	0.195538i
$303$	−4.39336	−	4.39336i	−0.252392	−	0.252392i
$304$			3.51606i			0.201660i
$305$		0			0
$306$	−0.249322	+	0.394836i	−0.0142528	+	0.0225713i
$307$		−	9.72597i		−	0.555090i	−0.960713	−	0.277545i	$-0.910479\pi$
$307$		−	9.72597i		−	0.555090i	0.960713	−	0.277545i	$-0.0895208\pi$
$308$	−13.0093			−0.741275
$309$	−2.43021	+	2.43021i	−0.138250	+	0.138250i
$310$		0			0
$311$	−16.7279	+	16.7279i	−0.948553	+	0.948553i	−0.998740	−	0.0501864i	$-0.984018\pi$
$311$	−16.7279	+	16.7279i	−0.948553	+	0.948553i	0.0501864	+	0.998740i	$0.484018\pi$
$312$	−2.74500	+	2.74500i	−0.155405	+	0.155405i
$313$	−17.7473	+	17.7473i	−1.00314	+	1.00314i	−0.00314163	+	0.999995i	$0.501000\pi$
$313$	−17.7473	+	17.7473i	−1.00314	+	1.00314i	−0.999995	+	0.00314163i	$0.999000\pi$
$314$		−	11.5725i		−	0.653073i
$315$		0			0
$316$	−11.6179	−	11.6179i	−0.653559	−	0.653559i
$317$	−0.784894	+	0.784894i	−0.0440840	+	0.0440840i	−0.728805	−	0.684721i	$-0.759924\pi$
$317$	−0.784894	+	0.784894i	−0.0440840	+	0.0440840i	0.684721	+	0.728805i	$0.259924\pi$
$318$	1.33747	+	1.33747i	0.0750016	+	0.0750016i
$319$	−2.94316			−0.164785
$320$		0			0
$321$		−	14.6890i		−	0.819859i
$322$		−	1.99055i		−	0.110929i
$323$	7.74028	−	12.2578i	0.430681	−	0.682043i
$324$	8.64741			0.480411
$325$		0			0
$326$	5.85449	−	5.85449i	0.324250	−	0.324250i
$327$			0.923597i			0.0510750i
$328$	4.39808	+	4.39808i	0.242844	+	0.242844i
$329$	−6.99662	−	6.99662i	−0.385736	−	0.385736i
$330$		0			0
$331$			3.90483i			0.214629i	0.994225	+	0.107314i	$0.0342252\pi$
$331$			3.90483i			0.214629i	−0.994225	+	0.107314i	$0.965775\pi$
$332$	−10.9725			−0.602192
$333$	−0.354421	+	0.354421i	−0.0194221	+	0.0194221i
$334$	6.50141	+	6.50141i	0.355741	+	0.355741i
$335$		0			0
$336$	−4.08247			−0.222717
$337$	18.9212	+	18.9212i	1.03070	+	1.03070i	0.999514	+	0.0311883i	$0.00992914\pi$
$337$	18.9212	+	18.9212i	1.03070	+	1.03070i	0.0311883	+	0.999514i	$0.490071\pi$
$338$	7.77956			0.423152
$339$	12.3579			0.671186
$340$		0			0
$341$	51.5220			2.79007
$342$	0.398214			0.0215330
$343$	−13.9772	−	13.9772i	−0.754697	−	0.754697i
$344$	1.59719			0.0861148
$345$		0			0
$346$	−13.0483	−	13.0483i	−0.701479	−	0.701479i
$347$	12.0526	−	12.0526i	0.647020	−	0.647020i	−0.305252	−	0.952272i	$-0.598741\pi$
$347$	12.0526	−	12.0526i	0.647020	−	0.647020i	0.952272	+	0.305252i	$0.0987407\pi$
$348$	−0.923597			−0.0495100
$349$		−	17.0455i		−	0.912424i	−0.889871	−	0.456212i	$-0.849206\pi$
$349$		−	17.0455i		−	0.912424i	0.889871	−	0.456212i	$-0.150794\pi$
$350$		0			0
$351$	8.54590	+	8.54590i	0.456146	+	0.456146i
$352$	3.82843	+	3.82843i	0.204056	+	0.204056i
$353$			30.0121i			1.59739i	0.601739	+	0.798693i	$0.294475\pi$
$353$			30.0121i			1.59739i	−0.601739	+	0.798693i	$0.705525\pi$
$354$	13.4232	−	13.4232i	0.713435	−	0.713435i
$355$		0			0
$356$	10.7796			0.571315
$357$	14.2325	+	8.98717i	0.753261	+	0.475652i
$358$			15.6018i			0.824580i
$359$			30.5514i			1.61244i	0.591614	+	0.806222i	$0.298491\pi$
$359$			30.5514i			1.61244i	−0.591614	+	0.806222i	$0.701509\pi$
$360$		0			0
$361$	6.63729			0.349331
$362$	−7.21511	−	7.21511i	−0.379218	−	0.379218i
$363$	−22.0022	+	22.0022i	−1.15481	+	1.15481i
$364$	−3.88202	−	3.88202i	−0.203473	−	0.203473i
$365$		0			0
$366$		−	21.6582i		−	1.13209i
$367$	−11.3820	+	11.3820i	−0.594133	+	0.594133i	−0.938745	−	0.344612i	$-0.888010\pi$
$367$	−11.3820	+	11.3820i	−0.594133	+	0.594133i	0.344612	+	0.938745i	$0.388010\pi$
$368$	−0.585786	+	0.585786i	−0.0305362	+	0.0305362i
$369$	0.498108	−	0.498108i	0.0259305	−	0.0259305i
$370$		0			0
$371$	−1.89147	+	1.89147i	−0.0982001	+	0.0982001i
$372$	16.1682			0.838282
$373$			13.0644i			0.676448i	0.941066	+	0.338224i	$0.109826\pi$
$373$			13.0644i			0.676448i	−0.941066	+	0.338224i	$0.890174\pi$
$374$	−4.91887	−	21.7747i	−0.254349	−	1.12594i
$375$		0			0
$376$			4.11798i			0.212369i
$377$	−0.878247	−	0.878247i	−0.0452320	−	0.0452320i
$378$			12.7098i			0.653721i
$379$	19.7607	−	19.7607i	1.01504	−	1.01504i	0.0151518	−	0.999885i	$-0.495177\pi$
$379$	19.7607	−	19.7607i	1.01504	−	1.01504i	0.999885	−	0.0151518i	$-0.00482315\pi$
$380$		0			0
$381$	14.8033	+	14.8033i	0.758397	+	0.758397i
$382$	−1.54212			−0.0789019
$383$	−29.9785			−1.53183			−0.765916	−	0.642941i	$-0.777714\pi$
$383$	−29.9785			−1.53183			−0.765916	+	0.642941i	$0.777714\pi$
$384$	1.20140	+	1.20140i	0.0613089	+	0.0613089i
$385$		0			0
$386$	12.6601	−	12.6601i	0.644382	−	0.644382i
$387$		−	0.180891i		−	0.00919521i
$388$	10.5506	+	10.5506i	0.535627	+	0.535627i
$389$			33.5174i			1.69940i	0.527266	+	0.849700i	$0.323217\pi$
$389$			33.5174i			1.69940i	−0.527266	+	0.849700i	$0.676783\pi$
$390$		0			0
$391$	3.33174	−	0.752635i	0.168493	−	0.0380624i
$392$			1.22651i			0.0619482i
$393$	−20.3223			−1.02513
$394$	−6.76343	+	6.76343i	−0.340737	+	0.340737i
$395$		0			0
$396$	0.433591	−	0.433591i	0.0217888	−	0.0217888i
$397$	−5.95647	+	5.95647i	−0.298946	+	0.298946i	−0.840601	−	0.541655i	$-0.817798\pi$
$397$	−5.95647	+	5.95647i	−0.298946	+	0.298946i	0.541655	+	0.840601i	$0.317798\pi$
$398$	13.7013	−	13.7013i	0.686786	−	0.686786i
$399$		−	14.3542i		−	0.718611i
$400$		0			0
$401$	12.8250	+	12.8250i	0.640452	+	0.640452i	0.950667	−	0.310214i	$-0.100401\pi$
$401$	12.8250	+	12.8250i	0.640452	+	0.640452i	−0.310214	+	0.950667i	$0.600401\pi$
$402$	−10.1668	+	10.1668i	−0.507076	+	0.507076i
$403$	15.3743	+	15.3743i	0.765850	+	0.765850i
$404$	−3.65685			−0.181935
$405$		0			0
$406$		−	1.30616i		−	0.0648238i
$407$		−	23.9612i		−	1.18771i
$408$	−1.54360	−	6.83315i	−0.0764195	−	0.338291i
$409$	17.7472			0.877541			0.438771	−	0.898599i	$-0.355414\pi$
$409$	17.7472			0.877541			0.438771	+	0.898599i	$0.355414\pi$
$410$		0			0
$411$	14.1502	−	14.1502i	0.697980	−	0.697980i
$412$			2.02281i			0.0996567i
$413$	18.9833	+	18.9833i	0.934105	+	0.934105i
$414$	0.0663437	+	0.0663437i	0.00326061	+	0.00326061i
$415$		0			0
$416$			2.28483i			0.112023i
$417$	11.9592			0.585646
$418$	−13.4610	+	13.4610i	−0.658399	+	0.658399i
$419$	−10.2896	−	10.2896i	−0.502678	−	0.502678i	0.409591	−	0.912269i	$-0.365671\pi$
$419$	−10.2896	−	10.2896i	−0.502678	−	0.502678i	−0.912269	+	0.409591i	$0.865671\pi$
$420$		0			0
$421$	−9.24460			−0.450554			−0.225277	−	0.974295i	$-0.572329\pi$
$421$	−9.24460			−0.450554			−0.225277	+	0.974295i	$0.572329\pi$
$422$	2.88202	+	2.88202i	0.140295	+	0.140295i
$423$	0.466385			0.0226764
$424$	1.11326			0.0540645
$425$		0			0
$426$	21.9417			1.06308
$427$	30.6293			1.48226
$428$	−6.11326	−	6.11326i	−0.295495	−	0.295495i
$429$	−21.0181			−1.01476
$430$		0			0
$431$	−27.3344	−	27.3344i	−1.31665	−	1.31665i	−0.916408	−	0.400245i	$-0.868925\pi$
$431$	−27.3344	−	27.3344i	−1.31665	−	1.31665i	−0.400245	−	0.916408i	$-0.631075\pi$
$432$	3.74028	−	3.74028i	0.179954	−	0.179954i
$433$	6.51944			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$433$	6.51944			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$434$			22.8653i			1.09757i
$435$		0			0
$436$	0.384382	+	0.384382i	0.0184086	+	0.0184086i
$437$	−2.05966	−	2.05966i	−0.0985270	−	0.0985270i
$438$		−	21.0012i		−	1.00348i
$439$	7.24736	−	7.24736i	0.345898	−	0.345898i	−0.512681	−	0.858579i	$-0.671348\pi$
$439$	7.24736	−	7.24736i	0.345898	−	0.345898i	0.858579	+	0.512681i	$0.171348\pi$
$440$		0			0
$441$	0.138909			0.00661474
$442$	5.02983	−	7.96544i	0.239245	−	0.378878i
$443$			24.2265i			1.15104i	0.817789	+	0.575518i	$0.195200\pi$
$443$			24.2265i			1.15104i	−0.817789	+	0.575518i	$0.804800\pi$
$444$		−	7.51931i		−	0.356851i
$445$		0			0
$446$	10.0242			0.474658
$447$	−3.90942	−	3.90942i	−0.184909	−	0.184909i
$448$	−1.69904	+	1.69904i	−0.0802722	+	0.0802722i
$449$	2.05034	+	2.05034i	0.0967617	+	0.0967617i	0.753831	−	0.657069i	$-0.228204\pi$
$449$	2.05034	+	2.05034i	0.0967617	+	0.0967617i	−0.657069	+	0.753831i	$0.728204\pi$
$450$		0			0
$451$			33.6755i			1.58572i
$452$	5.14309	−	5.14309i	0.241910	−	0.241910i
$453$	4.08247	−	4.08247i	0.191811	−	0.191811i
$454$	−10.6223	+	10.6223i	−0.498529	+	0.498529i
$455$		0			0
$456$	−4.22421	+	4.22421i	−0.197817	+	0.197817i
$457$	−22.7392			−1.06369			−0.531847	−	0.846840i	$-0.678502\pi$
$457$	−22.7392			−1.06369			−0.531847	+	0.846840i	$0.678502\pi$
$458$			17.4483i			0.815305i
$459$	−21.2733	+	4.80562i	−0.992955	+	0.224307i
$460$		0			0
$461$			28.4758i			1.32625i	0.748508	+	0.663126i	$0.230771\pi$
$461$			28.4758i			1.32625i	−0.748508	+	0.663126i	$0.769229\pi$
$462$	−15.6294	−	15.6294i	−0.727148	−	0.727148i
$463$			14.1542i			0.657799i	0.944365	+	0.328900i	$0.106678\pi$
$463$			14.1542i			0.657799i	−0.944365	+	0.328900i	$0.893322\pi$
$464$	−0.384382	+	0.384382i	−0.0178445	+	0.0178445i
$465$		0			0
$466$	20.3421	+	20.3421i	0.942328	+	0.942328i
$467$	18.1053			0.837813			0.418906	−	0.908029i	$-0.362414\pi$
$467$	18.1053			0.837813			0.418906	+	0.908029i	$0.362414\pi$
$468$	0.258770			0.0119616
$469$	−14.3781	−	14.3781i	−0.663919	−	0.663919i
$470$		0			0
$471$	13.9032	−	13.9032i	0.640627	−	0.640627i
$472$		−	11.1729i		−	0.514275i
$473$	6.11473	+	6.11473i	0.281156	+	0.281156i
$474$		−	27.9156i		−	1.28221i
$475$		0			0
$476$	9.66354	−	2.18298i	0.442927	−	0.100057i
$477$		−	0.126083i		−	0.00577293i
$478$	−19.0823			−0.872806
$479$	11.2757	−	11.2757i	0.515201	−	0.515201i	−0.400915	−	0.916115i	$-0.631308\pi$
$479$	11.2757	−	11.2757i	0.515201	−	0.515201i	0.916115	+	0.400915i	$0.131308\pi$
$480$		0			0
$481$	7.15011	−	7.15011i	0.326017	−	0.326017i
$482$	−15.4302	+	15.4302i	−0.702827	+	0.702827i
$483$	2.39146	−	2.39146i	0.108815	−	0.108815i
$484$			18.3137i			0.832441i
$485$		0			0
$486$	−0.831806	−	0.831806i	−0.0377315	−	0.0377315i
$487$	20.5047	−	20.5047i	0.929155	−	0.929155i	−0.0684966	−	0.997651i	$-0.521820\pi$
$487$	20.5047	−	20.5047i	0.929155	−	0.929155i	0.997651	+	0.0684966i	$0.0218202\pi$
$488$	−9.01370	−	9.01370i	−0.408031	−	0.408031i
$489$	14.0672			0.636141
$490$		0			0
$491$			23.3994i			1.05600i	0.849244	+	0.528001i	$0.177058\pi$
$491$			23.3994i			1.05600i	−0.849244	+	0.528001i	$0.822942\pi$
$492$			10.5678i			0.476431i
$493$	2.18623	−	0.493865i	0.0984627	−	0.0222426i
$494$	−8.03360			−0.361449
$495$		0			0
$496$	6.72887	−	6.72887i	0.302135	−	0.302135i
$497$			31.0302i			1.39190i
$498$	−13.1824	−	13.1824i	−0.590716	−	0.590716i
$499$	−9.37055	−	9.37055i	−0.419483	−	0.419483i	0.465542	−	0.885026i	$-0.345859\pi$
$499$	−9.37055	−	9.37055i	−0.419483	−	0.419483i	−0.885026	+	0.465542i	$0.845859\pi$
$500$		0			0
$501$			15.6216i			0.697924i
$502$	−11.4209			−0.509739
$503$	9.27018	−	9.27018i	0.413337	−	0.413337i	−0.469563	−	0.882899i	$-0.655588\pi$
$503$	9.27018	−	9.27018i	0.413337	−	0.413337i	0.882899	+	0.469563i	$0.155588\pi$
$504$	0.192426	+	0.192426i	0.00857135	+	0.00857135i
$505$		0			0
$506$	−4.48528			−0.199395
$507$	9.34639	+	9.34639i	0.415088	+	0.415088i
$508$	12.3217			0.546686
$509$	5.88337			0.260776			0.130388	−	0.991463i	$-0.458378\pi$
$509$	5.88337			0.260776			0.130388	+	0.991463i	$0.458378\pi$
$510$		0			0
$511$	29.7002			1.31386
$512$	1.00000			0.0441942
$513$	13.1511	+	13.1511i	0.580633	+	0.580633i
$514$	−25.3278			−1.11716
$515$		0			0
$516$	1.91887	+	1.91887i	0.0844737	+	0.0844737i
$517$	−15.7654	+	15.7654i	−0.693361	+	0.693361i
$518$	10.6339			0.467227
$519$		−	31.3525i		−	1.37622i
$520$		0			0
$521$	−5.28483	−	5.28483i	−0.231533	−	0.231533i	0.581800	−	0.813332i	$-0.302349\pi$
$521$	−5.28483	−	5.28483i	−0.231533	−	0.231533i	−0.813332	+	0.581800i	$0.802349\pi$
$522$	0.0435335	+	0.0435335i	0.00190541	+	0.00190541i
$523$		−	24.5081i		−	1.07166i	−0.844325	−	0.535832i	$-0.819998\pi$
$523$		−	24.5081i		−	1.07166i	0.844325	−	0.535832i	$-0.180002\pi$
$524$	−8.45775	+	8.45775i	−0.369478	+	0.369478i
$525$		0			0
$526$	−14.5938			−0.636320
$527$	−38.2714	+	8.64545i	−1.66713	+	0.376602i
$528$			9.19898i			0.400334i
$529$			22.3137i			0.970161i
$530$		0			0
$531$	−1.26540			−0.0549136
$532$	−5.97394	−	5.97394i	−0.259003	−	0.259003i
$533$	−10.0489	+	10.0489i	−0.435265	+	0.435265i
$534$	12.9506	+	12.9506i	0.560428	+	0.560428i
$535$		0			0
$536$			8.46247i			0.365523i
$537$	−18.7441	+	18.7441i	−0.808866	+	0.808866i
$538$	−15.2128	+	15.2128i	−0.655871	+	0.655871i
$539$	−4.69561	+	4.69561i	−0.202254	+	0.202254i
$540$		0			0
$541$	−27.6548	+	27.6548i	−1.18897	+	1.18897i	−0.211619	+	0.977352i	$0.567874\pi$
$541$	−27.6548	+	27.6548i	−1.18897	+	1.18897i	−0.977352	+	0.211619i	$0.932126\pi$
$542$	20.4986			0.880492
$543$		−	17.3365i		−	0.743981i
$544$	−3.48623	−	2.20140i	−0.149471	−	0.0943844i
$545$		0			0
$546$		−	9.32775i		−	0.399191i
$547$	5.16915	+	5.16915i	0.221017	+	0.221017i	0.808927	−	0.587910i	$-0.200049\pi$
$547$	5.16915	+	5.16915i	0.221017	+	0.221017i	−0.587910	+	0.808927i	$0.700049\pi$
$548$		−	11.7781i		−	0.503135i
$549$	−1.02085	+	1.02085i	−0.0435690	+	0.0435690i
$550$		0			0
$551$	−1.35151	−	1.35151i	−0.0575764	−	0.0575764i
$552$	−1.40753			−0.0599086
$553$	39.4787			1.67880
$554$	7.40477	+	7.40477i	0.314598	+	0.314598i
$555$		0			0
$556$	4.97719	−	4.97719i	0.211080	−	0.211080i
$557$		−	11.5891i		−	0.491045i	−0.969391	−	0.245523i	$-0.921040\pi$
$557$		−	11.5891i		−	0.491045i	0.969391	−	0.245523i	$-0.0789596\pi$
$558$	−0.762083	−	0.762083i	−0.0322616	−	0.0322616i
$559$			3.64931i			0.154349i
$560$		0			0
$561$	20.2507	−	32.0698i	0.854984	−	1.35399i
$562$		−	15.8573i		−	0.668900i
$563$	−13.6474			−0.575170			−0.287585	−	0.957755i	$-0.592852\pi$
$563$	−13.6474			−0.575170			−0.287585	+	0.957755i	$0.592852\pi$
$564$	−4.94736	+	4.94736i	−0.208321	+	0.208321i
$565$		0			0
$566$	−3.97017	+	3.97017i	−0.166879	+	0.166879i
$567$	−14.6923	+	14.6923i	−0.617019	+	0.617019i
$568$	9.13168	−	9.13168i	0.383157	−	0.383157i
$569$			14.0998i			0.591093i	0.955328	+	0.295546i	$0.0955017\pi$
$569$			14.0998i			0.591093i	−0.955328	+	0.295546i	$0.904498\pi$
$570$		0			0
$571$	−7.68439	−	7.68439i	−0.321582	−	0.321582i	0.527792	−	0.849374i	$-0.323020\pi$
$571$	−7.68439	−	7.68439i	−0.321582	−	0.321582i	−0.849374	+	0.527792i	$0.823020\pi$
$572$	−8.74730	+	8.74730i	−0.365743	+	0.365743i
$573$	−1.85271	−	1.85271i	−0.0773982	−	0.0773982i
$574$	−14.9451			−0.623795
$575$		0			0
$576$		−	0.113256i		−	0.00471899i
$577$		−	33.7732i		−	1.40600i	−0.711191	−	0.702999i	$-0.751844\pi$
$577$		−	33.7732i		−	1.40600i	0.711191	−	0.702999i	$-0.248156\pi$
$578$	7.30764	+	15.3492i	0.303958	+	0.638443i
$579$	30.4198			1.26420
$580$		0			0
$581$	18.6427	−	18.6427i	0.773429	−	0.773429i
$582$			25.3511i			1.05084i
$583$	4.26202	+	4.26202i	0.176515	+	0.176515i
$584$	−8.74028	−	8.74028i	−0.361675	−	0.361675i
$585$		0			0
$586$		−	27.9444i		−	1.15437i
$587$	31.3164			1.29257			0.646283	−	0.763098i	$-0.276323\pi$
$587$	31.3164			1.29257			0.646283	+	0.763098i	$0.276323\pi$
$588$	−1.47354	+	1.47354i	−0.0607676	+	0.0607676i
$589$	23.6592	+	23.6592i	0.974858	+	0.974858i
$590$		0			0
$591$	−16.2512			−0.668486
$592$	−3.12938	−	3.12938i	−0.128617	−	0.128617i
$593$	3.36583			0.138218			0.0691090	−	0.997609i	$-0.477984\pi$
$593$	3.36583			0.138218			0.0691090	+	0.997609i	$0.477984\pi$
$594$	28.6388			1.17506
$595$		0			0
$596$	−3.25405			−0.133291
$597$	32.9217			1.34740
$598$	−1.33842	−	1.33842i	−0.0547321	−	0.0547321i
$599$	−13.8928			−0.567645			−0.283822	−	0.958877i	$-0.591603\pi$
$599$	−13.8928			−0.567645			−0.283822	+	0.958877i	$0.591603\pi$
$600$		0			0
$601$	−14.1227	−	14.1227i	−0.576077	−	0.576077i	0.357743	−	0.933820i	$-0.383546\pi$
$601$	−14.1227	−	14.1227i	−0.576077	−	0.576077i	−0.933820	+	0.357743i	$0.883546\pi$
$602$	−2.71370	+	2.71370i	−0.110602	+	0.110602i
$603$	0.958423			0.0390300
$604$		−	3.39808i		−	0.138266i
$605$		0			0
$606$	−4.39336	−	4.39336i	−0.178468	−	0.178468i
$607$	16.1228	+	16.1228i	0.654403	+	0.654403i	0.954050	−	0.299647i	$-0.0968691\pi$
$607$	16.1228	+	16.1228i	0.654403	+	0.654403i	−0.299647	+	0.954050i	$0.596869\pi$
$608$			3.51606i			0.142595i
$609$	1.56923	−	1.56923i	0.0635884	−	0.0635884i
$610$		0			0
$611$	−9.40888			−0.380642
$612$	−0.249322	+	0.394836i	−0.0100782	+	0.0159603i
$613$			14.0705i			0.568300i	0.958780	+	0.284150i	$0.0917114\pi$
$613$			14.0705i			0.568300i	−0.958780	+	0.284150i	$0.908289\pi$
$614$		−	9.72597i		−	0.392508i
$615$		0			0
$616$	−13.0093			−0.524160
$617$	9.42657	+	9.42657i	0.379499	+	0.379499i	0.870922	−	0.491422i	$-0.163523\pi$
$617$	9.42657	+	9.42657i	0.379499	+	0.379499i	−0.491422	+	0.870922i	$0.663523\pi$
$618$	−2.43021	+	2.43021i	−0.0977575	+	0.0977575i
$619$	−19.8392	−	19.8392i	−0.797406	−	0.797406i	0.185280	−	0.982686i	$-0.440681\pi$
$619$	−19.8392	−	19.8392i	−0.797406	−	0.797406i	−0.982686	+	0.185280i	$0.940681\pi$
$620$		0			0
$621$			4.38201i			0.175844i
$622$	−16.7279	+	16.7279i	−0.670729	+	0.670729i
$623$	−18.3149	+	18.3149i	−0.733772	+	0.733772i
$624$	−2.74500	+	2.74500i	−0.109888	+	0.109888i
$625$		0			0
$626$	−17.7473	+	17.7473i	−0.709325	+	0.709325i
$627$	−32.3442			−1.29170
$628$		−	11.5725i		−	0.461792i
$629$	4.02072	+	17.7988i	0.160317	+	0.709685i
$630$		0			0
$631$			1.50527i			0.0599239i	0.999551	+	0.0299619i	$0.00953861\pi$
$631$			1.50527i			0.0599239i	−0.999551	+	0.0299619i	$0.990461\pi$
$632$	−11.6179	−	11.6179i	−0.462136	−	0.462136i
$633$			6.92494i			0.275242i
$634$	−0.784894	+	0.784894i	−0.0311721	+	0.0311721i
$635$		0			0
$636$	1.33747	+	1.33747i	0.0530341	+	0.0530341i
$637$	−2.80237			−0.111034
$638$	−2.94316			−0.116521
$639$	−1.03422	−	1.03422i	−0.0409129	−	0.0409129i
$640$		0			0
$641$	−16.3029	+	16.3029i	−0.643926	+	0.643926i	−0.951518	−	0.307592i	$-0.900477\pi$
$641$	−16.3029	+	16.3029i	−0.643926	+	0.643926i	0.307592	+	0.951518i	$0.400477\pi$
$642$		−	14.6890i		−	0.579728i
$643$	−26.8391	−	26.8391i	−1.05843	−	1.05843i	−0.998184	−	0.0602469i	$-0.980811\pi$
$643$	−26.8391	−	26.8391i	−1.05843	−	1.05843i	−0.0602469	−	0.998184i	$-0.519189\pi$
$644$		−	1.99055i		−	0.0784387i
$645$		0			0
$646$	7.74028	−	12.2578i	0.304537	−	0.482277i
$647$			0.182497i			0.00717469i	0.999994	+	0.00358734i	$0.00114189\pi$
$647$			0.182497i			0.00717469i	−0.999994	+	0.00358734i	$0.998858\pi$
$648$	8.64741			0.339702
$649$	42.7747	−	42.7747i	1.67905	−	1.67905i
$650$		0			0
$651$	−27.4704	+	27.4704i	−1.07665	+	1.07665i
$652$	5.85449	−	5.85449i	0.229279	−	0.229279i
$653$	3.84308	−	3.84308i	0.150391	−	0.150391i	−0.627901	−	0.778293i	$-0.716086\pi$
$653$	3.84308	−	3.84308i	0.150391	−	0.150391i	0.778293	+	0.627901i	$0.216086\pi$
$654$			0.923597i			0.0361155i
$655$		0			0
$656$	4.39808	+	4.39808i	0.171716	+	0.171716i
$657$	−0.989887	+	0.989887i	−0.0386192	+	0.0386192i
$658$	−6.99662	−	6.99662i	−0.272757	−	0.272757i
$659$	3.16347			0.123231			0.0616157	−	0.998100i	$-0.480375\pi$
$659$	3.16347			0.123231			0.0616157	+	0.998100i	$0.480375\pi$
$660$		0			0
$661$		−	22.2037i		−	0.863624i	−0.901964	−	0.431812i	$-0.857874\pi$
$661$		−	22.2037i		−	0.863624i	0.901964	−	0.431812i	$-0.142126\pi$
$662$			3.90483i			0.151766i
$663$	15.6126	−	3.52686i	0.606342	−	0.136972i
$664$	−10.9725			−0.425814
$665$		0			0
$666$	−0.354421	+	0.354421i	−0.0137335	+	0.0137335i
$667$		−	0.450332i		−	0.0174369i
$668$	6.50141	+	6.50141i	0.251547	+	0.251547i
$669$	12.0431	+	12.0431i	0.465612	+	0.465612i
$670$		0			0
$671$		−	69.0166i		−	2.66436i
$672$	−4.08247			−0.157485
$673$	27.9856	−	27.9856i	1.07876	−	1.07876i	0.0821434	−	0.996621i	$-0.473823\pi$
$673$	27.9856	−	27.9856i	1.07876	−	1.07876i	0.996621	−	0.0821434i	$-0.0261766\pi$
$674$	18.9212	+	18.9212i	0.728816	+	0.728816i
$675$		0			0
$676$	7.77956			0.299214
$677$	−33.6421	−	33.6421i	−1.29297	−	1.29297i	−0.932941	−	0.360029i	$-0.882767\pi$
$677$	−33.6421	−	33.6421i	−1.29297	−	1.29297i	−0.360029	−	0.932941i	$-0.617233\pi$
$678$	12.3579			0.474600
$679$	−35.8519			−1.37587
$680$		0			0
$681$	−25.5233			−0.978057
$682$	51.5220			1.97288
$683$	3.59962	+	3.59962i	0.137736	+	0.137736i	0.772613	−	0.634877i	$-0.218949\pi$
$683$	3.59962	+	3.59962i	0.137736	+	0.137736i	−0.634877	+	0.772613i	$0.718949\pi$
$684$	0.398214			0.0152261
$685$		0			0
$686$	−13.9772	−	13.9772i	−0.533652	−	0.533652i
$687$	−20.9625	+	20.9625i	−0.799768	+	0.799768i
$688$	1.59719			0.0608924
$689$			2.54360i			0.0969034i
$690$		0			0
$691$	24.3525	+	24.3525i	0.926411	+	0.926411i	0.997472	−	0.0710606i	$-0.0226384\pi$
$691$	24.3525	+	24.3525i	0.926411	+	0.926411i	−0.0710606	+	0.997472i	$0.522638\pi$
$692$	−13.0483	−	13.0483i	−0.496020	−	0.496020i
$693$			1.47338i			0.0559691i
$694$	12.0526	−	12.0526i	0.457512	−	0.457512i
$695$		0			0
$696$	−0.923597			−0.0350088
$697$	−5.65078	−	25.0147i	−0.214039	−	0.947500i
$698$		−	17.0455i		−	0.645181i
$699$			48.8781i			1.84874i
$700$		0			0
$701$	−10.0521			−0.379663			−0.189832	−	0.981817i	$-0.560794\pi$
$701$	−10.0521			−0.379663			−0.189832	+	0.981817i	$0.560794\pi$
$702$	8.54590	+	8.54590i	0.322544	+	0.322544i
$703$	11.0031	−	11.0031i	0.414990	−	0.414990i
$704$	3.82843	+	3.82843i	0.144289	+	0.144289i
$705$		0			0
$706$			30.0121i			1.12952i
$707$	6.21315	−	6.21315i	0.233670	−	0.233670i
$708$	13.4232	−	13.4232i	0.504474	−	0.504474i
$709$	−26.7993	+	26.7993i	−1.00647	+	1.00647i	−0.00649104	+	0.999979i	$0.502066\pi$
$709$	−26.7993	+	26.7993i	−1.00647	+	1.00647i	−0.999979	+	0.00649104i	$0.997934\pi$
$710$		0			0
$711$	−1.31580	+	1.31580i	−0.0493462	+	0.0493462i
$712$	10.7796			0.403981
$713$			7.88337i			0.295234i
$714$	14.2325	+	8.98717i	0.532636	+	0.336337i
$715$		0			0
$716$			15.6018i			0.583066i
$717$	−22.9256	−	22.9256i	−0.856173	−	0.856173i
$718$			30.5514i			1.14017i
$719$	−4.00763	+	4.00763i	−0.149459	+	0.149459i	−0.777877	−	0.628417i	$-0.783703\pi$
$719$	−4.00763	+	4.00763i	−0.149459	+	0.149459i	0.628417	+	0.777877i	$0.283703\pi$
$720$		0			0
$721$	−3.43684	−	3.43684i	−0.127995	−	0.127995i
$722$	6.63729			0.247014
$723$	−37.0758			−1.37887
$724$	−7.21511	−	7.21511i	−0.268147	−	0.268147i
$725$		0			0
$726$	−22.0022	+	22.0022i	−0.816577	+	0.816577i
$727$		−	6.36339i		−	0.236005i	−0.993013	−	0.118002i	$-0.962351\pi$
$727$		−	6.36339i		−	0.236005i	0.993013	−	0.118002i	$-0.0376491\pi$
$728$	−3.88202	−	3.88202i	−0.143877	−	0.143877i
$729$		−	27.9409i		−	1.03485i
$730$		0			0
$731$	−5.56818	−	3.51606i	−0.205947	−	0.130046i
$732$		−	21.6582i		−	0.800510i
$733$	3.82830			0.141401			0.0707007	−	0.997498i	$-0.477476\pi$
$733$	3.82830			0.141401			0.0707007	+	0.997498i	$0.477476\pi$
$734$	−11.3820	+	11.3820i	−0.420116	+	0.420116i
$735$		0			0
$736$	−0.585786	+	0.585786i	−0.0215924	+	0.0215924i
$737$	−32.3980	+	32.3980i	−1.19339	+	1.19339i
$738$	0.498108	−	0.498108i	0.0183356	−	0.0183356i
$739$			28.6554i			1.05411i	0.849833	+	0.527053i	$0.176703\pi$
$739$			28.6554i			1.05411i	−0.849833	+	0.527053i	$0.823297\pi$
$740$		0			0
$741$	−9.65161	−	9.65161i	−0.354561	−	0.354561i
$742$	−1.89147	+	1.89147i	−0.0694380	+	0.0694380i
$743$	1.66029	+	1.66029i	0.0609100	+	0.0609100i	0.736906	−	0.675996i	$-0.236286\pi$
$743$	1.66029	+	1.66029i	0.0609100	+	0.0609100i	−0.675996	+	0.736906i	$0.736286\pi$
$744$	16.1682			0.592755
$745$		0			0
$746$			13.0644i			0.478321i
$747$			1.24269i			0.0454678i
$748$	−4.91887	−	21.7747i	−0.179852	−	0.796162i
$749$	20.7734			0.759042
$750$		0			0
$751$	36.3675	−	36.3675i	1.32707	−	1.32707i	0.419154	−	0.907915i	$-0.362327\pi$
$751$	36.3675	−	36.3675i	1.32707	−	1.32707i	0.907915	−	0.419154i	$-0.137673\pi$
$752$			4.11798i			0.150167i
$753$	−13.7211	−	13.7211i	−0.500025	−	0.500025i
$754$	−0.878247	−	0.878247i	−0.0319839	−	0.0319839i
$755$		0			0
$756$			12.7098i			0.462250i
$757$	48.2458			1.75352			0.876762	−	0.480925i	$-0.159699\pi$
$757$	48.2458			1.75352			0.876762	+	0.480925i	$0.159699\pi$
$758$	19.7607	−	19.7607i	0.717740	−	0.717740i
$759$	−5.38864	−	5.38864i	−0.195595	−	0.195595i
$760$		0			0
$761$	−25.5040			−0.924521			−0.462261	−	0.886744i	$-0.652962\pi$
$761$	−25.5040			−0.924521			−0.462261	+	0.886744i	$0.652962\pi$
$762$	14.8033	+	14.8033i	0.536268	+	0.536268i
$763$	−1.30616			−0.0472863
$764$	−1.54212			−0.0557920
$765$		0			0
$766$	−29.9785			−1.08317
$767$	25.5282			0.921770
$768$	1.20140	+	1.20140i	0.0433519	+	0.0433519i
$769$	−15.9550			−0.575354			−0.287677	−	0.957728i	$-0.592883\pi$
$769$	−15.9550			−0.575354			−0.287677	+	0.957728i	$0.592883\pi$
$770$		0			0
$771$	−30.4289	−	30.4289i	−1.09587	−	1.09587i
$772$	12.6601	−	12.6601i	0.455647	−	0.455647i
$773$	−18.0027			−0.647512			−0.323756	−	0.946141i	$-0.604946\pi$
$773$	−18.0027			−0.647512			−0.323756	+	0.946141i	$0.604946\pi$
$774$		−	0.180891i		−	0.00650200i
$775$		0			0
$776$	10.5506	+	10.5506i	0.378745	+	0.378745i
$777$	12.7756	+	12.7756i	0.458323	+	0.458323i
$778$			33.5174i			1.20166i
$779$	−15.4639	+	15.4639i	−0.554053	+	0.554053i
$780$		0			0
$781$	69.9200			2.50193
$782$	3.33174	−	0.752635i	0.119143	−	0.0269142i
$783$			2.87539i			0.102758i
$784$			1.22651i			0.0438040i
$785$		0			0
$786$	−20.3223			−0.724874
$787$	14.0846	+	14.0846i	0.502063	+	0.502063i	0.912079	−	0.410015i	$-0.134477\pi$
$787$	14.0846	+	14.0846i	0.502063	+	0.502063i	−0.410015	+	0.912079i	$0.634477\pi$
$788$	−6.76343	+	6.76343i	−0.240937	+	0.240937i
$789$	−17.5331	−	17.5331i	−0.624194	−	0.624194i
$790$		0			0
$791$			17.4766i			0.621398i
$792$	0.433591	−	0.433591i	0.0154070	−	0.0154070i
$793$	20.5948	−	20.5948i	0.731342	−	0.731342i
$794$	−5.95647	+	5.95647i	−0.211387	+	0.211387i
$795$		0			0
$796$	13.7013	−	13.7013i	0.485631	−	0.485631i
$797$	−18.5240			−0.656155			−0.328078	−	0.944651i	$-0.606401\pi$
$797$	−18.5240			−0.656155			−0.328078	+	0.944651i	$0.606401\pi$
$798$		−	14.3542i		−	0.508134i
$799$	9.06534	−	14.3562i	0.320709	−	0.507887i
$800$		0			0
$801$		−	1.22085i		−	0.0431365i
$802$	12.8250	+	12.8250i	0.452868	+	0.452868i
$803$		−	66.9230i		−	2.36166i
$804$	−10.1668	+	10.1668i	−0.358557	+	0.358557i
$805$		0			0
$806$	15.3743	+	15.3743i	0.541537	+	0.541537i
$807$	−36.5535			−1.28674
$808$	−3.65685			−0.128648
$809$	−20.6246	−	20.6246i	−0.725122	−	0.725122i	0.244522	−	0.969644i	$-0.421369\pi$
$809$	−20.6246	−	20.6246i	−0.725122	−	0.725122i	−0.969644	+	0.244522i	$0.921369\pi$
$810$		0			0
$811$	7.91090	−	7.91090i	0.277789	−	0.277789i	−0.554437	−	0.832226i	$-0.687066\pi$
$811$	7.91090	−	7.91090i	0.277789	−	0.277789i	0.832226	+	0.554437i	$0.187066\pi$
$812$		−	1.30616i		−	0.0458373i
$813$	24.6272	+	24.6272i	0.863712	+	0.863712i
$814$		−	23.9612i		−	0.839841i
$815$		0			0
$816$	−1.54360	−	6.83315i	−0.0540368	−	0.239208i
$817$			5.61583i			0.196473i
$818$	17.7472			0.620515
$819$	−0.439661	+	0.439661i	−0.0153630	+	0.0153630i
$820$		0			0
$821$	−4.72563	+	4.72563i	−0.164925	+	0.164925i	−0.784745	−	0.619819i	$-0.787206\pi$
$821$	−4.72563	+	4.72563i	−0.164925	+	0.164925i	0.619819	+	0.784745i	$0.287206\pi$
$822$	14.1502	−	14.1502i	0.493546	−	0.493546i
$823$	13.8767	−	13.8767i	0.483711	−	0.483711i	−0.422604	−	0.906315i	$-0.638884\pi$
$823$	13.8767	−	13.8767i	0.483711	−	0.483711i	0.906315	+	0.422604i	$0.138884\pi$
$824$			2.02281i			0.0704679i
$825$		0			0
$826$	18.9833	+	18.9833i	0.660512	+	0.660512i
$827$	21.5436	−	21.5436i	0.749144	−	0.749144i	−0.225174	−	0.974319i	$-0.572295\pi$
$827$	21.5436	−	21.5436i	0.749144	−	0.749144i	0.974319	+	0.225174i	$0.0722951\pi$
$828$	0.0663437	+	0.0663437i	0.00230560	+	0.00230560i
$829$	−2.52404			−0.0876634			−0.0438317	−	0.999039i	$-0.513957\pi$
$829$	−2.52404			−0.0876634			−0.0438317	+	0.999039i	$0.513957\pi$
$830$		0			0
$831$			17.7922i			0.617206i
$832$			2.28483i			0.0792122i
$833$	2.70005	−	4.27590i	0.0935511	−	0.148151i
$834$	11.9592			0.414114
$835$		0			0
$836$	−13.4610	+	13.4610i	−0.465558	+	0.465558i
$837$		−	50.3357i		−	1.73986i
$838$	−10.2896	−	10.2896i	−0.355447	−	0.355447i
$839$	10.1638	+	10.1638i	0.350894	+	0.350894i	0.860442	−	0.509548i	$-0.170187\pi$
$839$	10.1638	+	10.1638i	0.350894	+	0.350894i	−0.509548	+	0.860442i	$0.670187\pi$
$840$		0			0
$841$			28.7045i			0.989810i
$842$	−9.24460			−0.318590
$843$	19.0510	−	19.0510i	0.656153	−	0.656153i
$844$	2.88202	+	2.88202i	0.0992032	+	0.0992032i
$845$		0			0
$846$	0.466385			0.0160346
$847$	−31.1158	−	31.1158i	−1.06915	−	1.06915i
$848$	1.11326			0.0382294
$849$	−9.53955			−0.327397
$850$		0			0
$851$	3.66630			0.125679
$852$	21.9417			0.751710
$853$	−24.7680	−	24.7680i	−0.848041	−	0.848041i	0.141848	−	0.989889i	$-0.454696\pi$
$853$	−24.7680	−	24.7680i	−0.848041	−	0.848041i	−0.989889	+	0.141848i	$0.954696\pi$
$854$	30.6293			1.04811
$855$		0			0
$856$	−6.11326	−	6.11326i	−0.208947	−	0.208947i
$857$	30.3695	−	30.3695i	1.03740	−	1.03740i	0.0381284	−	0.999273i	$-0.487860\pi$
$857$	30.3695	−	30.3695i	1.03740	−	1.03740i	0.999273	−	0.0381284i	$-0.0121396\pi$
$858$	−21.0181			−0.717546
$859$			5.90188i			0.201370i	0.994918	+	0.100685i	$0.0321034\pi$
$859$			5.90188i			0.201370i	−0.994918	+	0.100685i	$0.967897\pi$
$860$		0			0
$861$	−17.9551	−	17.9551i	−0.611907	−	0.611907i
$862$	−27.3344	−	27.3344i	−0.931014	−	0.931014i
$863$			6.32978i			0.215468i	0.994180	+	0.107734i	$0.0343595\pi$
$863$			6.32978i			0.215468i	−0.994180	+	0.107734i	$0.965640\pi$
$864$	3.74028	−	3.74028i	0.127247	−	0.127247i
$865$		0			0
$866$	6.51944			0.221540
$867$	−9.66118	+	27.2200i	−0.328111	+	0.924441i
$868$			22.8653i			0.776098i
$869$		−	88.9567i		−	3.01765i
$870$		0			0
$871$	−19.3353			−0.655152
$872$	0.384382	+	0.384382i	0.0130168	+	0.0130168i
$873$	1.19492	−	1.19492i	0.0404419	−	0.0404419i
$874$	−2.05966	−	2.05966i	−0.0696691	−	0.0696691i
$875$		0			0
$876$		−	21.0012i		−	0.709565i
$877$	−7.44027	+	7.44027i	−0.251240	+	0.251240i	−0.821479	−	0.570239i	$-0.806851\pi$
$877$	−7.44027	+	7.44027i	−0.251240	+	0.251240i	0.570239	+	0.821479i	$0.306851\pi$
$878$	7.24736	−	7.24736i	0.244587	−	0.244587i
$879$	33.5725	−	33.5725i	1.13237	−	1.13237i
$880$		0			0
$881$	−30.8068	+	30.8068i	−1.03791	+	1.03791i	−0.0386560	+	0.999253i	$0.512308\pi$
$881$	−30.8068	+	30.8068i	−1.03791	+	1.03791i	−0.999253	+	0.0386560i	$0.987692\pi$
$882$	0.138909			0.00467732
$883$		−	39.6614i		−	1.33471i	−0.744738	−	0.667357i	$-0.767426\pi$
$883$		−	39.6614i		−	1.33471i	0.744738	−	0.667357i	$-0.232574\pi$
$884$	5.02983	−	7.96544i	0.169172	−	0.267907i
$885$		0			0
$886$			24.2265i			0.813906i
$887$	−29.8799	−	29.8799i	−1.00327	−	1.00327i	−0.999995	−	0.00327533i	$-0.998957\pi$
$887$	−29.8799	−	29.8799i	−1.00327	−	1.00327i	−0.00327533	−	0.999995i	$-0.501043\pi$
$888$		−	7.51931i		−	0.252332i
$889$	−20.9351	+	20.9351i	−0.702139	+	0.702139i
$890$		0			0
$891$	33.1060	+	33.1060i	1.10909	+	1.10909i
$892$	10.0242			0.335634
$893$	−14.4791			−0.484524
$894$	−3.90942	−	3.90942i	−0.130751	−	0.130751i
$895$		0			0
$896$	−1.69904	+	1.69904i	−0.0567610	+	0.0567610i
$897$		−	3.21597i		−	0.107378i
$898$	2.05034	+	2.05034i	0.0684209	+	0.0684209i
$899$			5.17292i			0.172526i
$900$		0			0
$901$	−3.88107	−	2.45073i	−0.129297	−	0.0816455i
$902$			33.6755i			1.12127i
$903$	−6.52049			−0.216988
$904$	5.14309	−	5.14309i	0.171057	−	0.171057i
$905$		0			0
$906$	4.08247	−	4.08247i	0.135631	−	0.135631i
$907$	−13.3986	+	13.3986i	−0.444893	+	0.444893i	−0.893653	−	0.448759i	$-0.851866\pi$
$907$	−13.3986	+	13.3986i	−0.444893	+	0.444893i	0.448759	+	0.893653i	$0.351866\pi$
$908$	−10.6223	+	10.6223i	−0.352513	+	0.352513i
$909$			0.414160i			0.0137368i
$910$		0			0
$911$	−29.3865	−	29.3865i	−0.973620	−	0.973620i	0.0260411	−	0.999661i	$-0.491710\pi$
$911$	−29.3865	−	29.3865i	−0.973620	−	0.973620i	−0.999661	+	0.0260411i	$0.991710\pi$
$912$	−4.22421	+	4.22421i	−0.139878	+	0.139878i
$913$	−42.0073	−	42.0073i	−1.39024	−	1.39024i
$914$	−22.7392			−0.752146
$915$		0			0
$916$			17.4483i			0.576508i
$917$		−	28.7401i		−	0.949083i
$918$	−21.2733	+	4.80562i	−0.702125	+	0.158609i
$919$	45.1466			1.48925			0.744624	−	0.667484i	$-0.232629\pi$
$919$	45.1466			1.48925			0.744624	+	0.667484i	$0.232629\pi$
$920$		0			0
$921$	11.6848	−	11.6848i	0.385028	−	0.385028i
$922$			28.4758i			0.937802i
$923$	20.8643	+	20.8643i	0.686758	+	0.686758i
$924$	−15.6294	−	15.6294i	−0.514171	−	0.514171i
$925$		0			0
$926$			14.1542i			0.465134i
$927$	0.229095			0.00752446
$928$	−0.384382	+	0.384382i	−0.0126180	+	0.0126180i
$929$	−10.6246	−	10.6246i	−0.348582	−	0.348582i	0.510999	−	0.859581i	$-0.329275\pi$
$929$	−10.6246	−	10.6246i	−0.348582	−	0.348582i	−0.859581	+	0.510999i	$0.829275\pi$
$930$		0			0
$931$	−4.31249			−0.141336
$932$	20.3421	+	20.3421i	0.666326	+	0.666326i
$933$	−40.1940			−1.31589
$934$	18.1053			0.592423
$935$		0			0
$936$	0.258770			0.00845816
$937$	−19.0208			−0.621382			−0.310691	−	0.950511i	$-0.600560\pi$
$937$	−19.0208			−0.621382			−0.310691	+	0.950511i	$0.600560\pi$
$938$	−14.3781	−	14.3781i	−0.469461	−	0.469461i
$939$	−42.6434			−1.39161
$940$		0			0
$941$	−6.46686	−	6.46686i	−0.210813	−	0.210813i	0.593800	−	0.804613i	$-0.297627\pi$
$941$	−6.46686	−	6.46686i	−0.210813	−	0.210813i	−0.804613	+	0.593800i	$0.797627\pi$
$942$	13.9032	−	13.9032i	0.452992	−	0.452992i
$943$	−5.15268			−0.167794
$944$		−	11.1729i		−	0.363648i
$945$		0			0
$946$	6.11473	+	6.11473i	0.198807	+	0.198807i
$947$	−17.0004	−	17.0004i	−0.552439	−	0.552439i	0.374705	−	0.927144i	$-0.377744\pi$
$947$	−17.0004	−	17.0004i	−0.552439	−	0.552439i	−0.927144	+	0.374705i	$0.877744\pi$
$948$		−	27.9156i		−	0.906657i
$949$	19.9700	−	19.9700i	0.648255	−	0.648255i
$950$		0			0
$951$	−1.88595			−0.0611561
$952$	9.66354	−	2.18298i	0.313197	−	0.0707507i
$953$		−	44.4511i		−	1.43991i	−0.694019	−	0.719957i	$-0.744162\pi$
$953$		−	44.4511i		−	1.43991i	0.694019	−	0.719957i	$-0.255838\pi$
$954$		−	0.126083i		−	0.00408207i
$955$		0			0
$956$	−19.0823			−0.617167
$957$	−3.53592	−	3.53592i	−0.114300	−	0.114300i
$958$	11.2757	−	11.2757i	0.364302	−	0.364302i
$959$	20.0115	+	20.0115i	0.646204	+	0.646204i
$960$		0			0
$961$		−	59.5555i		−	1.92114i
$962$	7.15011	−	7.15011i	0.230529	−	0.230529i
$963$	−0.692361	+	0.692361i	−0.0223110	+	0.0223110i
$964$	−15.4302	+	15.4302i	−0.496974	+	0.496974i
$965$		0			0
$966$	2.39146	−	2.39146i	0.0769439	−	0.0769439i
$967$	−8.50514			−0.273507			−0.136753	−	0.990605i	$-0.543667\pi$
$967$	−8.50514			−0.273507			−0.136753	+	0.990605i	$0.543667\pi$
$968$			18.3137i			0.588625i
$969$	24.0258	−	5.42739i	0.771820	−	0.174353i
$970$		0			0
$971$		−	2.88215i		−	0.0924926i	−0.998930	−	0.0462463i	$-0.985274\pi$
$971$		−	2.88215i		−	0.0924926i	0.998930	−	0.0462463i	$-0.0147259\pi$
$972$	−0.831806	−	0.831806i	−0.0266802	−	0.0266802i
$973$			16.9129i			0.542203i
$974$	20.5047	−	20.5047i	0.657012	−	0.657012i
$975$		0			0
$976$	−9.01370	−	9.01370i	−0.288522	−	0.288522i
$977$	34.7030			1.11025			0.555124	−	0.831768i	$-0.312671\pi$
$977$	34.7030			1.11025			0.555124	+	0.831768i	$0.312671\pi$
$978$	14.0672			0.449820
$979$	41.2688	+	41.2688i	1.31896	+	1.31896i
$980$		0			0
$981$	0.0435335	−	0.0435335i	0.00138992	−	0.00138992i
$982$			23.3994i			0.746706i
$983$	24.4014	+	24.4014i	0.778283	+	0.778283i	0.979539	−	0.201255i	$-0.0645021\pi$
$983$	24.4014	+	24.4014i	0.778283	+	0.778283i	−0.201255	+	0.979539i	$0.564502\pi$
$984$			10.5678i			0.336888i
$985$		0			0
$986$	2.18623	−	0.493865i	0.0696236	−	0.0157279i
$987$		−	16.8115i		−	0.535117i
$988$	−8.03360			−0.255583
$989$	−0.935613	+	0.935613i	−0.0297508	+	0.0297508i
$990$		0			0
$991$	23.1043	−	23.1043i	0.733932	−	0.733932i	−0.237465	−	0.971396i	$-0.576316\pi$
$991$	23.1043	−	23.1043i	0.733932	−	0.733932i	0.971396	+	0.237465i	$0.0763164\pi$
$992$	6.72887	−	6.72887i	0.213642	−	0.213642i
$993$	−4.69128	+	4.69128i	−0.148873	+	0.148873i
$994$			31.0302i			0.984219i
$995$		0			0
$996$	−13.1824	−	13.1824i	−0.417699	−	0.417699i
$997$	−21.9490	+	21.9490i	−0.695133	+	0.695133i	−0.963357	−	0.268224i	$-0.913563\pi$
$997$	−21.9490	+	21.9490i	−0.695133	+	0.695133i	0.268224	+	0.963357i	$0.413563\pi$
$998$	−9.37055	−	9.37055i	−0.296620	−	0.296620i
$999$	−23.4095			−0.740645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.g.l.599.3		8
5.2	odd	4		850.2.h.n.701.3		8
5.3	odd	4		170.2.h.b.21.2	✓	8
5.4	even	2		850.2.g.i.599.2		8
15.8	even	4		1530.2.q.g.361.4		8
17.13	even	4		850.2.g.i.149.2		8
20.3	even	4		1360.2.bt.b.1041.3		8
85.8	odd	8		2890.2.a.bd.1.3		4
85.13	odd	4		170.2.h.b.81.2	yes	8
85.43	odd	8		2890.2.a.be.1.2		4
85.47	odd	4		850.2.h.n.251.3		8
85.53	odd	8		2890.2.b.o.2311.5		8
85.64	even	4	inner	850.2.g.l.149.3		8
85.83	odd	8		2890.2.b.o.2311.4		8
255.98	even	4		1530.2.q.g.1441.4		8
340.183	even	4		1360.2.bt.b.81.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.2	✓	8	5.3	odd	4
170.2.h.b.81.2	yes	8	85.13	odd	4
850.2.g.i.149.2		8	17.13	even	4
850.2.g.i.599.2		8	5.4	even	2
850.2.g.l.149.3		8	85.64	even	4	inner
850.2.g.l.599.3		8	1.1	even	1	trivial
850.2.h.n.251.3		8	85.47	odd	4
850.2.h.n.701.3		8	5.2	odd	4
1360.2.bt.b.81.3		8	340.183	even	4
1360.2.bt.b.1041.3		8	20.3	even	4
1530.2.q.g.361.4		8	15.8	even	4
1530.2.q.g.1441.4		8	255.98	even	4
2890.2.a.bd.1.3		4	85.8	odd	8
2890.2.a.be.1.2		4	85.43	odd	8
2890.2.b.o.2311.4		8	85.83	odd	8
2890.2.b.o.2311.5		8	85.53	odd	8

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.20140 + 1.20140i) q^{3} +1.00000 q^{4} +(1.20140 + 1.20140i) q^{6} +(-1.69904 + 1.69904i) q^{7} +1.00000 q^{8} -0.113256i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.20140 + 1.20140i) q^{3} +1.00000 q^{4} +(1.20140 + 1.20140i) q^{6} +(-1.69904 + 1.69904i) q^{7} +1.00000 q^{8} -0.113256i q^{9} +(3.82843 + 3.82843i) q^{11} +(1.20140 + 1.20140i) q^{12} +2.28483i q^{13} +(-1.69904 + 1.69904i) q^{14} +1.00000 q^{16} +(-3.48623 - 2.20140i) q^{17} -0.113256i q^{18} +3.51606i q^{19} -4.08247 q^{21} +(3.82843 + 3.82843i) q^{22} +(-0.585786 + 0.585786i) q^{23} +(1.20140 + 1.20140i) q^{24} +2.28483i q^{26} +(3.74028 - 3.74028i) q^{27} +(-1.69904 + 1.69904i) q^{28} +(-0.384382 + 0.384382i) q^{29} +(6.72887 - 6.72887i) q^{31} +1.00000 q^{32} +9.19898i q^{33} +(-3.48623 - 2.20140i) q^{34} -0.113256i q^{36} +(-3.12938 - 3.12938i) q^{37} +3.51606i q^{38} +(-2.74500 + 2.74500i) q^{39} +(4.39808 + 4.39808i) q^{41} -4.08247 q^{42} +1.59719 q^{43} +(3.82843 + 3.82843i) q^{44} +(-0.585786 + 0.585786i) q^{46} +4.11798i q^{47} +(1.20140 + 1.20140i) q^{48} +1.22651i q^{49} +(-1.54360 - 6.83315i) q^{51} +2.28483i q^{52} +1.11326 q^{53} +(3.74028 - 3.74028i) q^{54} +(-1.69904 + 1.69904i) q^{56} +(-4.22421 + 4.22421i) q^{57} +(-0.384382 + 0.384382i) q^{58} -11.1729i q^{59} +(-9.01370 - 9.01370i) q^{61} +(6.72887 - 6.72887i) q^{62} +(0.192426 + 0.192426i) q^{63} +1.00000 q^{64} +9.19898i q^{66} +8.46247i q^{67} +(-3.48623 - 2.20140i) q^{68} -1.40753 q^{69} +(9.13168 - 9.13168i) q^{71} -0.113256i q^{72} +(-8.74028 - 8.74028i) q^{73} +(-3.12938 - 3.12938i) q^{74} +3.51606i q^{76} -13.0093 q^{77} +(-2.74500 + 2.74500i) q^{78} +(-11.6179 - 11.6179i) q^{79} +8.64741 q^{81} +(4.39808 + 4.39808i) q^{82} -10.9725 q^{83} -4.08247 q^{84} +1.59719 q^{86} -0.923597 q^{87} +(3.82843 + 3.82843i) q^{88} +10.7796 q^{89} +(-3.88202 - 3.88202i) q^{91} +(-0.585786 + 0.585786i) q^{92} +16.1682 q^{93} +4.11798i q^{94} +(1.20140 + 1.20140i) q^{96} +(10.5506 + 10.5506i) q^{97} +1.22651i q^{98} +(0.433591 - 0.433591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 4 q^{7} + 8 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 4 * q^7 + 8 * q^8	\( 8 q + 8 q^{2} + 8 q^{4} + 4 q^{7} + 8 q^{8} + 8 q^{11} + 4 q^{14} + 8 q^{16} - 12 q^{17} + 16 q^{21} + 8 q^{22} - 16 q^{23} - 12 q^{27} + 4 q^{28} - 24 q^{29} + 4 q^{31} + 8 q^{32} - 12 q^{34} - 20 q^{37} + 4 q^{39} + 16 q^{42} + 32 q^{43} + 8 q^{44} - 16 q^{46} + 4 q^{51} - 20 q^{53} - 12 q^{54} + 4 q^{56} - 40 q^{57} - 24 q^{58} - 16 q^{61} + 4 q^{62} + 64 q^{63} + 8 q^{64} - 12 q^{68} - 8 q^{69} + 4 q^{71} - 28 q^{73} - 20 q^{74} + 8 q^{77} + 4 q^{78} - 8 q^{79} - 8 q^{81} - 56 q^{83} + 16 q^{84} + 32 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 44 q^{91} - 16 q^{92} + 20 q^{93} + 20 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 4 * q^7 + 8 * q^8 + 8 * q^11 + 4 * q^14 + 8 * q^16 - 12 * q^17 + 16 * q^21 + 8 * q^22 - 16 * q^23 - 12 * q^27 + 4 * q^28 - 24 * q^29 + 4 * q^31 + 8 * q^32 - 12 * q^34 - 20 * q^37 + 4 * q^39 + 16 * q^42 + 32 * q^43 + 8 * q^44 - 16 * q^46 + 4 * q^51 - 20 * q^53 - 12 * q^54 + 4 * q^56 - 40 * q^57 - 24 * q^58 - 16 * q^61 + 4 * q^62 + 64 * q^63 + 8 * q^64 - 12 * q^68 - 8 * q^69 + 4 * q^71 - 28 * q^73 - 20 * q^74 + 8 * q^77 + 4 * q^78 - 8 * q^79 - 8 * q^81 - 56 * q^83 + 16 * q^84 + 32 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 44 * q^91 - 16 * q^92 + 20 * q^93 + 20 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more