LMFDB - Embedded newform 170.2.h.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(21,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("170.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.h (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:	$1.35745683436$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.2
Root			$-1.69904i$ of defining polynomial
Character	$\chi$	$=$	170.81
Dual form			170.2.h.b.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.20140 - 1.20140i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.20140 - 1.20140i) q^{6} +(1.69904 - 1.69904i) q^{7} -1.00000i q^{8} -0.113256i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.20140 - 1.20140i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.20140 - 1.20140i) q^{6} +(1.69904 - 1.69904i) q^{7} -1.00000i q^{8} -0.113256i q^{9} +(0.707107 - 0.707107i) q^{10} +(3.82843 - 3.82843i) q^{11} +(1.20140 + 1.20140i) q^{12} -2.28483 q^{13} +(1.69904 + 1.69904i) q^{14} +1.69904i q^{15} +1.00000 q^{16} +(-2.20140 - 3.48623i) q^{17} +0.113256 q^{18} +3.51606i q^{19} +(0.707107 + 0.707107i) q^{20} -4.08247 q^{21} +(3.82843 + 3.82843i) q^{22} +(-0.585786 + 0.585786i) q^{23} +(-1.20140 + 1.20140i) q^{24} +1.00000i q^{25} -2.28483i q^{26} +(-3.74028 + 3.74028i) q^{27} +(-1.69904 + 1.69904i) q^{28} +(0.384382 + 0.384382i) q^{29} -1.69904 q^{30} +(6.72887 + 6.72887i) q^{31} +1.00000i q^{32} -9.19898 q^{33} +(3.48623 - 2.20140i) q^{34} -2.40281 q^{35} +0.113256i q^{36} +(-3.12938 - 3.12938i) q^{37} -3.51606 q^{38} +(2.74500 + 2.74500i) q^{39} +(-0.707107 + 0.707107i) q^{40} +(4.39808 - 4.39808i) q^{41} -4.08247i q^{42} -1.59719i q^{43} +(-3.82843 + 3.82843i) q^{44} +(-0.0800839 + 0.0800839i) q^{45} +(-0.585786 - 0.585786i) q^{46} +4.11798 q^{47} +(-1.20140 - 1.20140i) q^{48} +1.22651i q^{49} -1.00000 q^{50} +(-1.54360 + 6.83315i) q^{51} +2.28483 q^{52} -1.11326i q^{53} +(-3.74028 - 3.74028i) q^{54} -5.41421 q^{55} +(-1.69904 - 1.69904i) q^{56} +(4.22421 - 4.22421i) q^{57} +(-0.384382 + 0.384382i) q^{58} -11.1729i q^{59} -1.69904i q^{60} +(-9.01370 + 9.01370i) q^{61} +(-6.72887 + 6.72887i) q^{62} +(-0.192426 - 0.192426i) q^{63} -1.00000 q^{64} +(1.61562 + 1.61562i) q^{65} -9.19898i q^{66} +8.46247 q^{67} +(2.20140 + 3.48623i) q^{68} +1.40753 q^{69} -2.40281i q^{70} +(9.13168 + 9.13168i) q^{71} -0.113256 q^{72} +(8.74028 + 8.74028i) q^{73} +(3.12938 - 3.12938i) q^{74} +(1.20140 - 1.20140i) q^{75} -3.51606i q^{76} -13.0093i q^{77} +(-2.74500 + 2.74500i) q^{78} +(11.6179 - 11.6179i) q^{79} +(-0.707107 - 0.707107i) q^{80} +8.64741 q^{81} +(4.39808 + 4.39808i) q^{82} +10.9725i q^{83} +4.08247 q^{84} +(-0.908511 + 4.02177i) q^{85} +1.59719 q^{86} -0.923597i q^{87} +(-3.82843 - 3.82843i) q^{88} -10.7796 q^{89} +(-0.0800839 - 0.0800839i) q^{90} +(-3.88202 + 3.88202i) q^{91} +(0.585786 - 0.585786i) q^{92} -16.1682i q^{93} +4.11798i q^{94} +(2.48623 - 2.48623i) q^{95} +(1.20140 - 1.20140i) q^{96} +(10.5506 + 10.5506i) q^{97} -1.22651 q^{98} +(-0.433591 - 0.433591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^7	$ 8 q - 8 q^{4} - 4 q^{7} + 8 q^{11} - 12 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} - 28 q^{18} + 16 q^{21} + 8 q^{22} - 16 q^{23} + 12 q^{27} + 4 q^{28} + 24 q^{29} + 4 q^{30} + 4 q^{31} + 16 q^{33} + 12 q^{34} - 20 q^{37} + 20 q^{38} - 4 q^{39} - 8 q^{44} - 8 q^{45} - 16 q^{46} + 20 q^{47} - 8 q^{50} + 4 q^{51} + 12 q^{52} + 12 q^{54} - 32 q^{55} + 4 q^{56} + 40 q^{57} - 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} - 8 q^{64} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 8 q^{69} + 4 q^{71} + 28 q^{72} + 28 q^{73} + 20 q^{74} + 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 8 q^{85} + 32 q^{86} - 8 q^{88} - 44 q^{89} - 8 q^{90} - 44 q^{91} + 16 q^{92} + 4 q^{95} + 20 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^7 + 8 * q^11 - 12 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 - 28 * q^18 + 16 * q^21 + 8 * q^22 - 16 * q^23 + 12 * q^27 + 4 * q^28 + 24 * q^29 + 4 * q^30 + 4 * q^31 + 16 * q^33 + 12 * q^34 - 20 * q^37 + 20 * q^38 - 4 * q^39 - 8 * q^44 - 8 * q^45 - 16 * q^46 + 20 * q^47 - 8 * q^50 + 4 * q^51 + 12 * q^52 + 12 * q^54 - 32 * q^55 + 4 * q^56 + 40 * q^57 - 24 * q^58 - 16 * q^61 - 4 * q^62 - 64 * q^63 - 8 * q^64 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 8 * q^69 + 4 * q^71 + 28 * q^72 + 28 * q^73 + 20 * q^74 + 4 * q^78 + 8 * q^79 - 8 * q^81 - 16 * q^84 + 8 * q^85 + 32 * q^86 - 8 * q^88 - 44 * q^89 - 8 * q^90 - 44 * q^91 + 16 * q^92 + 4 * q^95 + 20 * q^97 + 48 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.20140	−	1.20140i	−0.693631	−	0.693631i	0.269398	−	0.963029i	$-0.413175\pi$
$3$	−1.20140	−	1.20140i	−0.693631	−	0.693631i	−0.963029	+	0.269398i	$0.913175\pi$
$4$	−1.00000			−0.500000
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	1.20140	−	1.20140i	0.490471	−	0.490471i
$7$	1.69904	−	1.69904i	0.642178	−	0.642178i	−0.308913	−	0.951090i	$-0.599965\pi$
$7$	1.69904	−	1.69904i	0.642178	−	0.642178i	0.951090	+	0.308913i	$0.0999651\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	0.113256i		−	0.0377519i
$10$	0.707107	−	0.707107i	0.223607	−	0.223607i
$11$	3.82843	−	3.82843i	1.15431	−	1.15431i	0.168636	−	0.985678i	$-0.446064\pi$
$11$	3.82843	−	3.82843i	1.15431	−	1.15431i	0.985678	−	0.168636i	$-0.0539362\pi$
$12$	1.20140	+	1.20140i	0.346816	+	0.346816i
$13$	−2.28483			−0.633697			−0.316849	−	0.948476i	$-0.602625\pi$
$13$	−2.28483			−0.633697			−0.316849	+	0.948476i	$0.602625\pi$
$14$	1.69904	+	1.69904i	0.454088	+	0.454088i
$15$			1.69904i			0.438691i
$16$	1.00000			0.250000
$17$	−2.20140	−	3.48623i	−0.533919	−	0.845536i
$17$	−2.20140	−	3.48623i	−0.533919	−	0.845536i
$18$	0.113256			0.0266946
$19$			3.51606i			0.806640i	0.915059	+	0.403320i	$0.132144\pi$
$19$			3.51606i			0.806640i	−0.915059	+	0.403320i	$0.867856\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	−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
$25$			1.00000i			0.200000i
$26$		−	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	$-0.233927\pi$
$29$	0.384382	+	0.384382i	0.0713780	+	0.0713780i	−0.670517	+	0.741895i	$0.733927\pi$
$30$	−1.69904			−0.310201
$31$	6.72887	+	6.72887i	1.20854	+	1.20854i	0.971499	+	0.237042i	$0.0761779\pi$
$31$	6.72887	+	6.72887i	1.20854	+	1.20854i	0.237042	+	0.971499i	$0.423822\pi$
$32$			1.00000i			0.176777i
$33$	−9.19898			−1.60134
$34$	3.48623	−	2.20140i	0.597884	−	0.377538i
$35$	−2.40281			−0.406149
$36$			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	$0.868515\pi$
$38$	−3.51606			−0.570381
$39$	2.74500	+	2.74500i	0.439552	+	0.439552i
$40$	−0.707107	+	0.707107i	−0.111803	+	0.111803i
$41$	4.39808	−	4.39808i	0.686865	−	0.686865i	−0.274672	−	0.961538i	$-0.588569\pi$
$41$	4.39808	−	4.39808i	0.686865	−	0.686865i	0.961538	+	0.274672i	$0.0885694\pi$
$42$		−	4.08247i		−	0.629939i
$43$		−	1.59719i		−	0.243569i	−0.992557	−	0.121785i	$-0.961138\pi$
$43$		−	1.59719i		−	0.243569i	0.992557	−	0.121785i	$-0.0388617\pi$
$44$	−3.82843	+	3.82843i	−0.577157	+	0.577157i
$45$	−0.0800839	+	0.0800839i	−0.0119382	+	0.0119382i
$46$	−0.585786	−	0.585786i	−0.0863695	−	0.0863695i
$47$	4.11798			0.600669			0.300335	−	0.953834i	$-0.402902\pi$
$47$	4.11798			0.600669			0.300335	+	0.953834i	$0.402902\pi$
$48$	−1.20140	−	1.20140i	−0.173408	−	0.173408i
$49$			1.22651i			0.175216i
$50$	−1.00000			−0.141421
$51$	−1.54360	+	6.83315i	−0.216147	+	0.956833i
$52$	2.28483			0.316849
$53$		−	1.11326i		−	0.152917i	−0.997073	−	0.0764587i	$-0.975639\pi$
$53$		−	1.11326i		−	0.152917i	0.997073	−	0.0764587i	$-0.0243613\pi$
$54$	−3.74028	−	3.74028i	−0.508987	−	0.508987i
$55$	−5.41421			−0.730052
$56$	−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	$-0.259223\pi$
$60$		−	1.69904i		−	0.219345i
$61$	−9.01370	+	9.01370i	−1.15409	+	1.15409i	−0.168361	+	0.985725i	$0.553847\pi$
$61$	−9.01370	+	9.01370i	−1.15409	+	1.15409i	−0.985725	+	0.168361i	$0.946153\pi$
$62$	−6.72887	+	6.72887i	−0.854568	+	0.854568i
$63$	−0.192426	−	0.192426i	−0.0242434	−	0.0242434i
$64$	−1.00000			−0.125000
$65$	1.61562	+	1.61562i	0.200393	+	0.200393i
$66$		−	9.19898i		−	1.13232i
$67$	8.46247			1.03386			0.516928	−	0.856029i	$-0.327076\pi$
$67$	8.46247			1.03386			0.516928	+	0.856029i	$0.327076\pi$
$68$	2.20140	+	3.48623i	0.266959	+	0.422768i
$69$	1.40753			0.169447
$70$		−	2.40281i		−	0.287191i
$71$	9.13168	+	9.13168i	1.08373	+	1.08373i	0.996158	+	0.0875732i	$0.0279112\pi$
$71$	9.13168	+	9.13168i	1.08373	+	1.08373i	0.0875732	+	0.996158i	$0.472089\pi$
$72$	−0.113256			−0.0133473
$73$	8.74028	+	8.74028i	1.02297	+	1.02297i	0.999730	+	0.0232424i	$0.00739894\pi$
$73$	8.74028	+	8.74028i	1.02297	+	1.02297i	0.0232424	+	0.999730i	$0.492601\pi$
$74$	3.12938	−	3.12938i	0.363784	−	0.363784i
$75$	1.20140	−	1.20140i	0.138726	−	0.138726i
$76$		−	3.51606i		−	0.403320i
$77$		−	13.0093i		−	1.48255i
$78$	−2.74500	+	2.74500i	−0.310810	+	0.310810i
$79$	11.6179	−	11.6179i	1.30712	−	1.30712i	0.383631	−	0.923486i	$-0.374673\pi$
$79$	11.6179	−	11.6179i	1.30712	−	1.30712i	0.923486	−	0.383631i	$-0.125327\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	8.64741			0.960823
$82$	4.39808	+	4.39808i	0.485687	+	0.485687i
$83$			10.9725i			1.20438i	0.798351	+	0.602192i	$0.205706\pi$
$83$			10.9725i			1.20438i	−0.798351	+	0.602192i	$0.794294\pi$
$84$	4.08247			0.445434
$85$	−0.908511	+	4.02177i	−0.0985419	+	0.436222i
$86$	1.59719			0.172230
$87$		−	0.923597i		−	0.0990200i
$88$	−3.82843	−	3.82843i	−0.408112	−	0.408112i
$89$	−10.7796			−1.14263			−0.571315	−	0.820731i	$-0.693567\pi$
$89$	−10.7796			−1.14263			−0.571315	+	0.820731i	$0.693567\pi$
$90$	−0.0800839	−	0.0800839i	−0.00844158	−	0.00844158i
$91$	−3.88202	+	3.88202i	−0.406946	+	0.406946i
$92$	0.585786	−	0.585786i	0.0610725	−	0.0610725i
$93$		−	16.1682i		−	1.67656i
$94$			4.11798i			0.424737i
$95$	2.48623	−	2.48623i	0.255082	−	0.255082i
$96$	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	$0.476425\pi$
$98$	−1.22651			−0.123896
$99$	−0.433591	−	0.433591i	−0.0435776	−	0.0435776i
$100$		−	1.00000i		−	0.100000i
$101$	−3.65685			−0.363871			−0.181935	−	0.983311i	$-0.558236\pi$
$101$	−3.65685			−0.363871			−0.181935	+	0.983311i	$0.558236\pi$
$102$	−6.83315	−	1.54360i	−0.676583	−	0.152839i
$103$	−2.02281			−0.199313			−0.0996567	−	0.995022i	$-0.531774\pi$
$103$	−2.02281			−0.199313			−0.0996567	+	0.995022i	$0.531774\pi$
$104$			2.28483i			0.224046i
$105$	2.88674	+	2.88674i	0.281717	+	0.281717i
$106$	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	$-0.758288\pi$
$109$	−0.384382	+	0.384382i	−0.0368171	+	0.0368171i	0.688459	+	0.725276i	$0.258288\pi$
$110$		−	5.41421i		−	0.516225i
$111$			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
$115$	0.828427			0.0772512
$116$	−0.384382	−	0.384382i	−0.0356890	−	0.0356890i
$117$			0.258770i			0.0239233i
$118$	11.1729			1.02855
$119$	−9.66354	−	2.18298i	−0.885855	−	0.200113i
$120$	1.69904			0.155101
$121$		−	18.3137i		−	1.66488i
$122$	−9.01370	−	9.01370i	−0.816062	−	0.816062i
$123$	−10.5678			−0.952862
$124$	−6.72887	−	6.72887i	−0.604271	−	0.604271i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	0.192426	−	0.192426i	0.0171427	−	0.0171427i
$127$			12.3217i			1.09337i	0.837338	+	0.546686i	$0.184111\pi$
$127$			12.3217i			1.09337i	−0.837338	+	0.546686i	$0.815889\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.91887	+	1.91887i	−0.168947	+	0.168947i
$130$	−1.61562	+	1.61562i	−0.141699	+	0.141699i
$131$	−8.45775	−	8.45775i	−0.738957	−	0.738957i	0.233419	−	0.972376i	$-0.425009\pi$
$131$	−8.45775	−	8.45775i	−0.738957	−	0.738957i	−0.972376	+	0.233419i	$0.925009\pi$
$132$	9.19898			0.800668
$133$	5.97394	+	5.97394i	0.518006	+	0.518006i
$134$			8.46247i			0.731046i
$135$	5.28955			0.455252
$136$	−3.48623	+	2.20140i	−0.298942	+	0.188769i
$137$	−11.7781			−1.00627			−0.503135	−	0.864208i	$-0.667820\pi$
$137$	−11.7781			−1.00627			−0.503135	+	0.864208i	$0.667820\pi$
$138$			1.40753i			0.119817i
$139$	−4.97719	−	4.97719i	−0.422160	−	0.422160i	0.463787	−	0.885947i	$-0.346490\pi$
$139$	−4.97719	−	4.97719i	−0.422160	−	0.422160i	−0.885947	+	0.463787i	$0.846490\pi$
$140$	2.40281			0.203074
$141$	−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
$145$		−	0.543599i		−	0.0451434i
$146$	−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	$-0.457446\pi$
$149$	3.25405			0.266582			0.133291	+	0.991077i	$0.457446\pi$
$150$	1.20140	+	1.20140i	0.0980942	+	0.0980942i
$151$			3.39808i			0.276532i	0.990395	+	0.138266i	$0.0441529\pi$
$151$			3.39808i			0.276532i	−0.990395	+	0.138266i	$0.955847\pi$
$152$	3.51606			0.285190
$153$	−0.394836	+	0.249322i	−0.0319206	+	0.0201565i
$154$	13.0093			1.04832
$155$		−	9.51606i		−	0.764349i
$156$	−2.74500	−	2.74500i	−0.219776	−	0.219776i
$157$	−11.5725			−0.923584			−0.461792	−	0.886988i	$-0.652793\pi$
$157$	−11.5725			−0.923584			−0.461792	+	0.886988i	$0.652793\pi$
$158$	11.6179	+	11.6179i	0.924272	+	0.924272i
$159$	−1.33747	+	1.33747i	−0.106068	+	0.106068i
$160$	0.707107	−	0.707107i	0.0559017	−	0.0559017i
$161$			1.99055i			0.156877i
$162$			8.64741i			0.679404i
$163$	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
$165$	6.50466	+	6.50466i	0.506387	+	0.506387i
$166$	−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	$0.634228\pi$
$168$			4.08247i			0.314970i
$169$	−7.77956			−0.598428
$170$	−4.02177	−	0.908511i	−0.308455	−	0.0696796i
$171$	0.398214			0.0304522
$172$			1.59719i			0.121785i
$173$	13.0483	+	13.0483i	0.992041	+	0.992041i	0.999969	−	0.00792792i	$-0.00252356\pi$
$173$	13.0483	+	13.0483i	0.992041	+	0.992041i	−0.00792792	+	0.999969i	$0.502524\pi$
$174$	0.923597			0.0700177
$175$	1.69904	+	1.69904i	0.128436	+	0.128436i
$176$	3.82843	−	3.82843i	0.288579	−	0.288579i
$177$	−13.4232	+	13.4232i	−1.00895	+	1.00895i
$178$		−	10.7796i		−	0.807962i
$179$			15.6018i			1.16613i	0.812425	+	0.583066i	$0.198147\pi$
$179$			15.6018i			1.16613i	−0.812425	+	0.583066i	$0.801853\pi$
$180$	0.0800839	−	0.0800839i	0.00596910	−	0.00596910i
$181$	−7.21511	+	7.21511i	−0.536295	+	0.536295i	−0.922439	−	0.386144i	$-0.873807\pi$
$181$	−7.21511	+	7.21511i	−0.536295	+	0.536295i	0.386144	+	0.922439i	$0.373807\pi$
$182$	−3.88202	−	3.88202i	−0.287754	−	0.287754i
$183$	21.6582			1.60102
$184$	0.585786	+	0.585786i	0.0431847	+	0.0431847i
$185$			4.42562i			0.325378i
$186$	16.1682			1.18551
$187$	−21.7747	−	4.91887i	−1.59232	−	0.359704i
$188$	−4.11798			−0.300335
$189$			12.7098i			0.924501i
$190$	2.48623	+	2.48623i	0.180370	+	0.180370i
$191$	−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
$195$		−	3.88202i		−	0.277997i
$196$		−	1.22651i		−	0.0876080i
$197$	6.76343	−	6.76343i	0.481874	−	0.481874i	−0.423855	−	0.905730i	$-0.639324\pi$
$197$	6.76343	−	6.76343i	0.481874	−	0.481874i	0.905730	+	0.423855i	$0.139324\pi$
$198$	0.433591	−	0.433591i	0.0308140	−	0.0308140i
$199$	−13.7013	−	13.7013i	−0.971262	−	0.971262i	0.0283363	−	0.999598i	$-0.490979\pi$
$199$	−13.7013	−	13.7013i	−0.971262	−	0.971262i	−0.999598	+	0.0283363i	$0.990979\pi$
$200$	1.00000			0.0707107
$201$	−10.1668	−	10.1668i	−0.717114	−	0.717114i
$202$		−	3.65685i		−	0.257295i
$203$	1.30616			0.0916747
$204$	1.54360	−	6.83315i	0.108074	−	0.478416i
$205$	−6.21983			−0.434412
$206$		−	2.02281i		−	0.140936i
$207$	0.0663437	+	0.0663437i	0.00461120	+	0.00461120i
$208$	−2.28483			−0.158424
$209$	13.4610	+	13.4610i	0.931117	+	0.931117i
$210$	−2.88674	+	2.88674i	−0.199204	+	0.199204i
$211$	2.88202	−	2.88202i	0.198406	−	0.198406i	−0.600910	−	0.799317i	$-0.705195\pi$
$211$	2.88202	−	2.88202i	0.198406	−	0.198406i	0.799317	+	0.600910i	$0.205195\pi$
$212$			1.11326i			0.0764587i
$213$		−	21.9417i		−	1.50342i
$214$	6.11326	−	6.11326i	0.417894	−	0.417894i
$215$	−1.12938	+	1.12938i	−0.0770234	+	0.0770234i
$216$	3.74028	+	3.74028i	0.254494	+	0.254494i
$217$	22.8653			1.55220
$218$	−0.384382	−	0.384382i	−0.0260336	−	0.0260336i
$219$		−	21.0012i		−	1.41913i
$220$	5.41421			0.365026
$221$	5.02983	+	7.96544i	0.338343	+	0.535814i
$222$	−7.51931			−0.504663
$223$		−	10.0242i		−	0.671267i	−0.941993	−	0.335634i	$-0.891050\pi$
$223$		−	10.0242i		−	0.671267i	0.941993	−	0.335634i	$-0.108950\pi$
$224$	1.69904	+	1.69904i	0.113522	+	0.113522i
$225$	0.113256			0.00755038
$226$	5.14309	+	5.14309i	0.342113	+	0.342113i
$227$	10.6223	−	10.6223i	0.705027	−	0.705027i	−0.260458	−	0.965485i	$-0.583874\pi$
$227$	10.6223	−	10.6223i	0.705027	−	0.705027i	0.965485	+	0.260458i	$0.0838737\pi$
$228$	−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	$0.804415\pi$
$230$			0.828427i			0.0546249i
$231$	−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	$-0.858632\pi$
$233$	−20.3421	−	20.3421i	−1.33265	−	1.33265i	−0.429664	−	0.902989i	$-0.641368\pi$
$234$	−0.258770			−0.0169163
$235$	−2.91185	−	2.91185i	−0.189948	−	0.189948i
$236$			11.1729i			0.727295i
$237$	−27.9156			−1.81331
$238$	2.18298	−	9.66354i	0.141501	−	0.626394i
$239$	19.0823			1.23433			0.617167	−	0.786832i	$-0.288280\pi$
$239$	19.0823			1.23433			0.617167	+	0.786832i	$0.288280\pi$
$240$			1.69904i			0.109673i
$241$	−15.4302	−	15.4302i	−0.993947	−	0.993947i	0.00603442	−	0.999982i	$-0.498079\pi$
$241$	−15.4302	−	15.4302i	−0.993947	−	0.993947i	−0.999982	+	0.00603442i	$0.998079\pi$
$242$	18.3137			1.17725
$243$	0.831806	+	0.831806i	0.0533604	+	0.0533604i
$244$	9.01370	−	9.01370i	0.577043	−	0.577043i
$245$	0.867275	−	0.867275i	0.0554081	−	0.0554081i
$246$		−	10.5678i		−	0.673775i
$247$		−	8.03360i		−	0.511166i
$248$	6.72887	−	6.72887i	0.427284	−	0.427284i
$249$	13.1824	−	13.1824i	0.835399	−	0.835399i
$250$	0.707107	+	0.707107i	0.0447214	+	0.0447214i
$251$	−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
$253$			4.48528i			0.281987i
$254$	−12.3217			−0.773131
$255$	5.92326	−	3.74028i	0.370929	−	0.234225i
$256$	1.00000			0.0625000
$257$		−	25.3278i		−	1.57990i	−0.613170	−	0.789951i	$-0.710106\pi$
$257$		−	25.3278i		−	1.57990i	0.613170	−	0.789951i	$-0.289894\pi$
$258$	−1.91887	−	1.91887i	−0.119464	−	0.119464i
$259$	−10.6339			−0.660759
$260$	−1.61562	−	1.61562i	−0.100196	−	0.100196i
$261$	0.0435335	−	0.0435335i	0.00269466	−	0.00269466i
$262$	8.45775	−	8.45775i	0.522521	−	0.522521i
$263$			14.5938i			0.899893i	0.893055	+	0.449947i	$0.148557\pi$
$263$			14.5938i			0.899893i	−0.893055	+	0.449947i	$0.851443\pi$
$264$			9.19898i			0.566158i
$265$	−0.787191	+	0.787191i	−0.0483567	+	0.0483567i
$266$	−5.97394	+	5.97394i	−0.366286	+	0.366286i
$267$	12.9506	+	12.9506i	0.792564	+	0.792564i
$268$	−8.46247			−0.516928
$269$	15.2128	+	15.2128i	0.927541	+	0.927541i	0.997547	−	0.0700053i	$-0.0223016\pi$
$269$	15.2128	+	15.2128i	0.927541	+	0.927541i	−0.0700053	+	0.997547i	$0.522302\pi$
$270$			5.28955i			0.321912i
$271$	20.4986			1.24520			0.622602	−	0.782539i	$-0.286076\pi$
$271$	20.4986			1.24520			0.622602	+	0.782539i	$0.286076\pi$
$272$	−2.20140	−	3.48623i	−0.133480	−	0.211384i
$273$	9.32775			0.564541
$274$		−	11.7781i		−	0.711540i
$275$	3.82843	+	3.82843i	0.230863	+	0.230863i
$276$	−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
$280$			2.40281i			0.143595i
$281$			15.8573i			0.945968i	0.881071	+	0.472984i	$0.156823\pi$
$281$			15.8573i			0.945968i	−0.881071	+	0.472984i	$0.843177\pi$
$282$	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
$285$	−5.97394			−0.353866
$286$	−8.74730	−	8.74730i	−0.517239	−	0.517239i
$287$		−	14.9451i		−	0.882179i
$288$	0.113256			0.00667366
$289$	−7.30764	+	15.3492i	−0.429861	+	0.902895i
$290$	0.543599			0.0319212
$291$		−	25.3511i		−	1.48611i
$292$	−8.74028	−	8.74028i	−0.511486	−	0.511486i
$293$	27.9444			1.63253			0.816264	−	0.577679i	$-0.196042\pi$
$293$	27.9444			1.63253			0.816264	+	0.577679i	$0.196042\pi$
$294$	1.47354	+	1.47354i	0.0859384	+	0.0859384i
$295$	−7.90045	+	7.90045i	−0.459982	+	0.459982i
$296$	−3.12938	+	3.12938i	−0.181892	+	0.181892i
$297$			28.6388i			1.66179i
$298$			3.25405i			0.188502i
$299$	1.33842	−	1.33842i	0.0774029	−	0.0774029i
$300$	−1.20140	+	1.20140i	−0.0693631	+	0.0693631i
$301$	−2.71370	−	2.71370i	−0.156415	−	0.156415i
$302$	−3.39808			−0.195538
$303$	4.39336	+	4.39336i	0.252392	+	0.252392i
$304$			3.51606i			0.201660i
$305$	12.7473			0.729908
$306$	−0.249322	−	0.394836i	−0.0142528	−	0.0225713i
$307$	−9.72597			−0.555090			−0.277545	−	0.960713i	$-0.589521\pi$
$307$	−9.72597			−0.555090			−0.277545	+	0.960713i	$0.589521\pi$
$308$			13.0093i			0.741275i
$309$	2.43021	+	2.43021i	0.138250	+	0.138250i
$310$	9.51606			0.540476
$311$	−16.7279	−	16.7279i	−0.948553	−	0.948553i	0.0501864	−	0.998740i	$-0.484018\pi$
$311$	−16.7279	−	16.7279i	−0.948553	−	0.948553i	−0.998740	+	0.0501864i	$0.984018\pi$
$312$	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
$315$			0.272132i			0.0153329i
$316$	−11.6179	+	11.6179i	−0.653559	+	0.653559i
$317$	0.784894	−	0.784894i	0.0440840	−	0.0440840i	−0.684721	−	0.728805i	$-0.740076\pi$
$317$	0.784894	−	0.784894i	0.0440840	−	0.0440840i	0.728805	+	0.684721i	$0.240076\pi$
$318$	−1.33747	−	1.33747i	−0.0750016	−	0.0750016i
$319$	2.94316			0.164785
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$			14.6890i			0.819859i
$322$	−1.99055			−0.110929
$323$	12.2578	−	7.74028i	0.682043	−	0.430681i
$324$	−8.64741			−0.480411
$325$		−	2.28483i		−	0.126739i
$326$	5.85449	+	5.85449i	0.324250	+	0.324250i
$327$	0.923597			0.0510750
$328$	−4.39808	−	4.39808i	−0.242844	−	0.242844i
$329$	6.99662	−	6.99662i	0.385736	−	0.385736i
$330$	−6.50466	+	6.50466i	−0.358070	+	0.358070i
$331$		−	3.90483i		−	0.214629i	−0.994225	−	0.107314i	$-0.965775\pi$
$331$		−	3.90483i		−	0.214629i	0.994225	−	0.107314i	$-0.0342252\pi$
$332$		−	10.9725i		−	0.602192i
$333$	−0.354421	+	0.354421i	−0.0194221	+	0.0194221i
$334$	−6.50141	+	6.50141i	−0.355741	+	0.355741i
$335$	−5.98387	−	5.98387i	−0.326934	−	0.326934i
$336$	−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	$0.490071\pi$
$338$		−	7.77956i		−	0.423152i
$339$	−12.3579			−0.671186
$340$	0.908511	−	4.02177i	0.0492709	−	0.218111i
$341$	51.5220			2.79007
$342$			0.398214i			0.0215330i
$343$	13.9772	+	13.9772i	0.754697	+	0.754697i
$344$	−1.59719			−0.0861148
$345$	−0.995276	−	0.995276i	−0.0535839	−	0.0535839i
$346$	−13.0483	+	13.0483i	−0.701479	+	0.701479i
$347$	−12.0526	+	12.0526i	−0.647020	+	0.647020i	−0.952272	−	0.305252i	$-0.901259\pi$
$347$	−12.0526	+	12.0526i	−0.647020	+	0.647020i	0.305252	+	0.952272i	$0.401259\pi$
$348$			0.923597i			0.0495100i
$349$		−	17.0455i		−	0.912424i	−0.889871	−	0.456212i	$-0.849206\pi$
$349$		−	17.0455i		−	0.912424i	0.889871	−	0.456212i	$-0.150794\pi$
$350$	−1.69904	+	1.69904i	−0.0908176	+	0.0908176i
$351$	8.54590	−	8.54590i	0.456146	−	0.456146i
$352$	3.82843	+	3.82843i	0.204056	+	0.204056i
$353$	−30.0121			−1.59739			−0.798693	−	0.601739i	$-0.794475\pi$
$353$	−30.0121			−1.59739			−0.798693	+	0.601739i	$0.794475\pi$
$354$	−13.4232	−	13.4232i	−0.713435	−	0.713435i
$355$		−	12.9141i		−	0.685412i
$356$	10.7796			0.571315
$357$	8.98717	+	14.2325i	0.475652	+	0.753261i
$358$	−15.6018			−0.824580
$359$			30.5514i			1.61244i	0.591614	+	0.806222i	$0.298491\pi$
$359$			30.5514i			1.61244i	−0.591614	+	0.806222i	$0.701509\pi$
$360$	0.0800839	+	0.0800839i	0.00422079	+	0.00422079i
$361$	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
$365$		−	12.3606i		−	0.646984i
$366$			21.6582i			1.13209i
$367$	11.3820	−	11.3820i	0.594133	−	0.594133i	−0.344612	−	0.938745i	$-0.611990\pi$
$367$	11.3820	−	11.3820i	0.594133	−	0.594133i	0.938745	+	0.344612i	$0.111990\pi$
$368$	−0.585786	+	0.585786i	−0.0305362	+	0.0305362i
$369$	−0.498108	−	0.498108i	−0.0259305	−	0.0259305i
$370$	−4.42562			−0.230077
$371$	−1.89147	−	1.89147i	−0.0982001	−	0.0982001i
$372$			16.1682i			0.838282i
$373$	−13.0644			−0.676448			−0.338224	−	0.941066i	$-0.609826\pi$
$373$	−13.0644			−0.676448			−0.338224	+	0.941066i	$0.609826\pi$
$374$	4.91887	−	21.7747i	0.254349	−	1.12594i
$375$	−1.69904			−0.0877382
$376$		−	4.11798i		−	0.212369i
$377$	−0.878247	−	0.878247i	−0.0452320	−	0.0452320i
$378$	−12.7098			−0.653721
$379$	−19.7607	−	19.7607i	−1.01504	−	1.01504i	−0.999885	−	0.0151518i	$-0.995177\pi$
$379$	−19.7607	−	19.7607i	−1.01504	−	1.01504i	−0.0151518	−	0.999885i	$-0.504823\pi$
$380$	−2.48623	+	2.48623i	−0.127541	+	0.127541i
$381$	14.8033	−	14.8033i	0.758397	−	0.758397i
$382$		−	1.54212i		−	0.0789019i
$383$			29.9785i			1.53183i	0.642941	+	0.765916i	$0.277714\pi$
$383$			29.9785i			1.53183i	−0.642941	+	0.765916i	$0.722286\pi$
$384$	−1.20140	+	1.20140i	−0.0613089	+	0.0613089i
$385$	−9.19898	+	9.19898i	−0.468823	+	0.468823i
$386$	12.6601	+	12.6601i	0.644382	+	0.644382i
$387$	−0.180891			−0.00919521
$388$	−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	$0.676783\pi$
$390$	3.88202			0.196574
$391$	3.33174	+	0.752635i	0.168493	+	0.0380624i
$392$	1.22651			0.0619482
$393$			20.3223i			1.02513i
$394$	6.76343	+	6.76343i	0.340737	+	0.340737i
$395$	−16.4302			−0.826694
$396$	0.433591	+	0.433591i	0.0217888	+	0.0217888i
$397$	5.95647	−	5.95647i	0.298946	−	0.298946i	−0.541655	−	0.840601i	$-0.682202\pi$
$397$	5.95647	−	5.95647i	0.298946	−	0.298946i	0.840601	+	0.541655i	$0.182202\pi$
$398$	13.7013	−	13.7013i	0.686786	−	0.686786i
$399$		−	14.3542i		−	0.718611i
$400$			1.00000i			0.0500000i
$401$	12.8250	−	12.8250i	0.640452	−	0.640452i	−0.310214	−	0.950667i	$-0.600401\pi$
$401$	12.8250	−	12.8250i	0.640452	−	0.640452i	0.950667	+	0.310214i	$0.100401\pi$
$402$	10.1668	−	10.1668i	0.507076	−	0.507076i
$403$	−15.3743	−	15.3743i	−0.765850	−	0.765850i
$404$	3.65685			0.181935
$405$	−6.11464	−	6.11464i	−0.303839	−	0.303839i
$406$			1.30616i			0.0648238i
$407$	−23.9612			−1.18771
$408$	6.83315	+	1.54360i	0.338291	+	0.0764195i
$409$	−17.7472			−0.877541			−0.438771	−	0.898599i	$-0.644586\pi$
$409$	−17.7472			−0.877541			−0.438771	+	0.898599i	$0.644586\pi$
$410$		−	6.21983i		−	0.307176i
$411$	14.1502	+	14.1502i	0.697980	+	0.697980i
$412$	2.02281			0.0996567
$413$	−18.9833	−	18.9833i	−0.934105	−	0.934105i
$414$	−0.0663437	+	0.0663437i	−0.00326061	+	0.00326061i
$415$	7.75870	−	7.75870i	0.380860	−	0.380860i
$416$		−	2.28483i		−	0.112023i
$417$			11.9592i			0.585646i
$418$	−13.4610	+	13.4610i	−0.658399	+	0.658399i
$419$	10.2896	−	10.2896i	0.502678	−	0.502678i	−0.409591	−	0.912269i	$-0.634329\pi$
$419$	10.2896	−	10.2896i	0.502678	−	0.502678i	0.912269	+	0.409591i	$0.134329\pi$
$420$	−2.88674	−	2.88674i	−0.140859	−	0.140859i
$421$	−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
$423$		−	0.466385i		−	0.0226764i
$424$	−1.11326			−0.0540645
$425$	3.48623	−	2.20140i	0.169107	−	0.106784i
$426$	21.9417			1.06308
$427$			30.6293i			1.48226i
$428$	6.11326	+	6.11326i	0.295495	+	0.295495i
$429$	21.0181			1.01476
$430$	−1.12938	−	1.12938i	−0.0544638	−	0.0544638i
$431$	−27.3344	+	27.3344i	−1.31665	+	1.31665i	−0.400245	+	0.916408i	$0.631075\pi$
$431$	−27.3344	+	27.3344i	−1.31665	+	1.31665i	−0.916408	+	0.400245i	$0.868925\pi$
$432$	−3.74028	+	3.74028i	−0.179954	+	0.179954i
$433$		−	6.51944i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$433$		−	6.51944i		−	0.313304i	0.987654	−	0.156652i	$-0.0500702\pi$
$434$			22.8653i			1.09757i
$435$	−0.653082	+	0.653082i	−0.0313129	+	0.0313129i
$436$	0.384382	−	0.384382i	0.0184086	−	0.0184086i
$437$	−2.05966	−	2.05966i	−0.0985270	−	0.0985270i
$438$	21.0012			1.00348
$439$	−7.24736	−	7.24736i	−0.345898	−	0.345898i	0.512681	−	0.858579i	$-0.328652\pi$
$439$	−7.24736	−	7.24736i	−0.345898	−	0.345898i	−0.858579	+	0.512681i	$0.828652\pi$
$440$			5.41421i			0.258113i
$441$	0.138909			0.00661474
$442$	−7.96544	+	5.02983i	−0.378878	+	0.239245i
$443$	−24.2265			−1.15104			−0.575518	−	0.817789i	$-0.695200\pi$
$443$	−24.2265			−1.15104			−0.575518	+	0.817789i	$0.695200\pi$
$444$		−	7.51931i		−	0.356851i
$445$	7.62230	+	7.62230i	0.361332	+	0.361332i
$446$	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	$-0.771796\pi$
$449$	−2.05034	+	2.05034i	−0.0967617	+	0.0967617i	0.657069	+	0.753831i	$0.271796\pi$
$450$			0.113256i			0.00533893i
$451$		−	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
$455$	5.49001			0.257375
$456$	−4.22421	−	4.22421i	−0.197817	−	0.197817i
$457$		−	22.7392i		−	1.06369i	−0.846840	−	0.531847i	$-0.821498\pi$
$457$		−	22.7392i		−	1.06369i	0.846840	−	0.531847i	$-0.178502\pi$
$458$	−17.4483			−0.815305
$459$	21.2733	+	4.80562i	0.992955	+	0.224307i
$460$	−0.828427			−0.0386256
$461$		−	28.4758i		−	1.32625i	−0.748508	−	0.663126i	$-0.769229\pi$
$461$		−	28.4758i		−	1.32625i	0.748508	−	0.663126i	$-0.230771\pi$
$462$	−15.6294	−	15.6294i	−0.727148	−	0.727148i
$463$	−14.1542			−0.657799			−0.328900	−	0.944365i	$-0.606678\pi$
$463$	−14.1542			−0.657799			−0.328900	+	0.944365i	$0.606678\pi$
$464$	0.384382	+	0.384382i	0.0178445	+	0.0178445i
$465$	−11.4326	+	11.4326i	−0.530176	+	0.530176i
$466$	20.3421	−	20.3421i	0.942328	−	0.942328i
$467$			18.1053i			0.837813i	0.908029	+	0.418906i	$0.137586\pi$
$467$			18.1053i			0.837813i	−0.908029	+	0.418906i	$0.862414\pi$
$468$		−	0.258770i		−	0.0119616i
$469$	14.3781	−	14.3781i	0.663919	−	0.663919i
$470$	2.91185	−	2.91185i	0.134314	−	0.134314i
$471$	13.9032	+	13.9032i	0.640627	+	0.640627i
$472$	−11.1729			−0.514275
$473$	−6.11473	−	6.11473i	−0.281156	−	0.281156i
$474$		−	27.9156i		−	1.28221i
$475$	−3.51606			−0.161328
$476$	9.66354	+	2.18298i	0.442927	+	0.100057i
$477$	−0.126083			−0.00577293
$478$			19.0823i			0.872806i
$479$	−11.2757	−	11.2757i	−0.515201	−	0.515201i	0.400915	−	0.916115i	$-0.368692\pi$
$479$	−11.2757	−	11.2757i	−0.515201	−	0.515201i	−0.916115	+	0.400915i	$0.868692\pi$
$480$	−1.69904			−0.0775503
$481$	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
$485$		−	14.9208i		−	0.677520i
$486$	−0.831806	+	0.831806i	−0.0377315	+	0.0377315i
$487$	−20.5047	+	20.5047i	−0.929155	+	0.929155i	−0.997651	−	0.0684966i	$-0.978180\pi$
$487$	−20.5047	+	20.5047i	−0.929155	+	0.929155i	0.0684966	+	0.997651i	$0.478180\pi$
$488$	9.01370	+	9.01370i	0.408031	+	0.408031i
$489$	−14.0672			−0.636141
$490$	0.867275	+	0.867275i	0.0391795	+	0.0391795i
$491$		−	23.3994i		−	1.05600i	−0.849244	−	0.528001i	$-0.822942\pi$
$491$		−	23.3994i		−	1.05600i	0.849244	−	0.528001i	$-0.177058\pi$
$492$	10.5678			0.476431
$493$	0.493865	−	2.18623i	0.0222426	−	0.0984627i
$494$	8.03360			0.361449
$495$			0.613191i			0.0275609i
$496$	6.72887	+	6.72887i	0.302135	+	0.302135i
$497$	31.0302			1.39190
$498$	13.1824	+	13.1824i	0.590716	+	0.590716i
$499$	9.37055	−	9.37055i	0.419483	−	0.419483i	−0.465542	−	0.885026i	$-0.654141\pi$
$499$	9.37055	−	9.37055i	0.419483	−	0.419483i	0.885026	+	0.465542i	$0.154141\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$		−	15.6216i		−	0.697924i
$502$		−	11.4209i		−	0.509739i
$503$	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
$505$	2.58579	+	2.58579i	0.115066	+	0.115066i
$506$	−4.48528			−0.199395
$507$	9.34639	+	9.34639i	0.415088	+	0.415088i
$508$		−	12.3217i		−	0.546686i
$509$	−5.88337			−0.260776			−0.130388	−	0.991463i	$-0.541622\pi$
$509$	−5.88337			−0.260776			−0.130388	+	0.991463i	$0.541622\pi$
$510$	3.74028	+	5.92326i	0.165622	+	0.262286i
$511$	29.7002			1.31386
$512$			1.00000i			0.0441942i
$513$	−13.1511	−	13.1511i	−0.580633	−	0.580633i
$514$	25.3278			1.11716
$515$	1.43034	+	1.43034i	0.0630284	+	0.0630284i
$516$	1.91887	−	1.91887i	0.0844737	−	0.0844737i
$517$	15.7654	−	15.7654i	0.693361	−	0.693361i
$518$		−	10.6339i		−	0.467227i
$519$		−	31.3525i		−	1.37622i
$520$	1.61562	−	1.61562i	0.0708495	−	0.0708495i
$521$	−5.28483	+	5.28483i	−0.231533	+	0.231533i	−0.813332	−	0.581800i	$-0.802349\pi$
$521$	−5.28483	+	5.28483i	−0.231533	+	0.231533i	0.581800	+	0.813332i	$0.302349\pi$
$522$	0.0435335	+	0.0435335i	0.00190541	+	0.00190541i
$523$	24.5081			1.07166			0.535832	−	0.844325i	$-0.319998\pi$
$523$	24.5081			1.07166			0.535832	+	0.844325i	$0.319998\pi$
$524$	8.45775	+	8.45775i	0.369478	+	0.369478i
$525$		−	4.08247i		−	0.178174i
$526$	−14.5938			−0.636320
$527$	8.64545	−	38.2714i	0.376602	−	1.66713i
$528$	−9.19898			−0.400334
$529$			22.3137i			0.970161i
$530$	−0.787191	−	0.787191i	−0.0341934	−	0.0341934i
$531$	−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
$535$			8.64545i			0.373775i
$536$		−	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
$540$	−5.28955			−0.227626
$541$	−27.6548	−	27.6548i	−1.18897	−	1.18897i	−0.977352	−	0.211619i	$-0.932126\pi$
$541$	−27.6548	−	27.6548i	−1.18897	−	1.18897i	−0.211619	−	0.977352i	$-0.567874\pi$
$542$			20.4986i			0.880492i
$543$	17.3365			0.743981
$544$	3.48623	−	2.20140i	0.149471	−	0.0943844i
$545$	0.543599			0.0232852
$546$			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	$0.700049\pi$
$548$	11.7781			0.503135
$549$	1.02085	+	1.02085i	0.0435690	+	0.0435690i
$550$	−3.82843	+	3.82843i	−0.163245	+	0.163245i
$551$	−1.35151	+	1.35151i	−0.0575764	+	0.0575764i
$552$		−	1.40753i		−	0.0599086i
$553$		−	39.4787i		−	1.67880i
$554$	−7.40477	+	7.40477i	−0.314598	+	0.314598i
$555$	5.31696	−	5.31696i	0.225692	−	0.225692i
$556$	4.97719	+	4.97719i	0.211080	+	0.211080i
$557$	−11.5891			−0.491045			−0.245523	−	0.969391i	$-0.578960\pi$
$557$	−11.5891			−0.491045			−0.245523	+	0.969391i	$0.578960\pi$
$558$	0.762083	+	0.762083i	0.0322616	+	0.0322616i
$559$			3.64931i			0.154349i
$560$	−2.40281			−0.101537
$561$	20.2507	+	32.0698i	0.854984	+	1.35399i
$562$	−15.8573			−0.668900
$563$			13.6474i			0.575170i	0.957755	+	0.287585i	$0.0928523\pi$
$563$			13.6474i			0.575170i	−0.957755	+	0.287585i	$0.907148\pi$
$564$	4.94736	+	4.94736i	0.208321	+	0.208321i
$565$	−7.27342			−0.305995
$566$	−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	$0.904498\pi$
$570$		−	5.97394i		−	0.250221i
$571$	−7.68439	+	7.68439i	−0.321582	+	0.321582i	−0.849374	−	0.527792i	$-0.823020\pi$
$571$	−7.68439	+	7.68439i	−0.321582	+	0.321582i	0.527792	+	0.849374i	$0.323020\pi$
$572$	8.74730	−	8.74730i	0.365743	−	0.365743i
$573$	1.85271	+	1.85271i	0.0773982	+	0.0773982i
$574$	14.9451			0.623795
$575$	−0.585786	−	0.585786i	−0.0244290	−	0.0244290i
$576$			0.113256i			0.00471899i
$577$	−33.7732			−1.40600			−0.702999	−	0.711191i	$-0.748156\pi$
$577$	−33.7732			−1.40600			−0.702999	+	0.711191i	$0.748156\pi$
$578$	−15.3492	−	7.30764i	−0.638443	−	0.303958i
$579$	−30.4198			−1.26420
$580$			0.543599i			0.0225717i
$581$	18.6427	+	18.6427i	0.773429	+	0.773429i
$582$	25.3511			1.05084
$583$	−4.26202	−	4.26202i	−0.176515	−	0.176515i
$584$	8.74028	−	8.74028i	0.361675	−	0.361675i
$585$	0.182978	−	0.182978i	0.00756521	−	0.00756521i
$586$			27.9444i			1.15437i
$587$			31.3164i			1.29257i	0.763098	+	0.646283i	$0.223677\pi$
$587$			31.3164i			1.29257i	−0.763098	+	0.646283i	$0.776323\pi$
$588$	−1.47354	+	1.47354i	−0.0607676	+	0.0607676i
$589$	−23.6592	+	23.6592i	−0.974858	+	0.974858i
$590$	−7.90045	−	7.90045i	−0.325256	−	0.325256i
$591$	−16.2512			−0.668486
$592$	−3.12938	−	3.12938i	−0.128617	−	0.128617i
$593$		−	3.36583i		−	0.138218i	−0.997609	−	0.0691090i	$-0.977984\pi$
$593$		−	3.36583i		−	0.138218i	0.997609	−	0.0691090i	$-0.0220156\pi$
$594$	−28.6388			−1.17506
$595$	5.28955	+	8.37675i	0.216851	+	0.343413i
$596$	−3.25405			−0.133291
$597$			32.9217i			1.34740i
$598$	1.33842	+	1.33842i	0.0547321	+	0.0547321i
$599$	13.8928			0.567645			0.283822	−	0.958877i	$-0.408397\pi$
$599$	13.8928			0.567645			0.283822	+	0.958877i	$0.408397\pi$
$600$	−1.20140	−	1.20140i	−0.0490471	−	0.0490471i
$601$	−14.1227	+	14.1227i	−0.576077	+	0.576077i	−0.933820	−	0.357743i	$-0.883546\pi$
$601$	−14.1227	+	14.1227i	−0.576077	+	0.576077i	0.357743	+	0.933820i	$0.383546\pi$
$602$	2.71370	−	2.71370i	0.110602	−	0.110602i
$603$		−	0.958423i		−	0.0390300i
$604$		−	3.39808i		−	0.138266i
$605$	−12.9497	+	12.9497i	−0.526482	+	0.526482i
$606$	−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	$0.596869\pi$
$608$	−3.51606			−0.142595
$609$	−1.56923	−	1.56923i	−0.0635884	−	0.0635884i
$610$			12.7473i			0.516123i
$611$	−9.40888			−0.380642
$612$	0.394836	−	0.249322i	0.0159603	−	0.0100782i
$613$	−14.0705			−0.568300			−0.284150	−	0.958780i	$-0.591711\pi$
$613$	−14.0705			−0.568300			−0.284150	+	0.958780i	$0.591711\pi$
$614$		−	9.72597i		−	0.392508i
$615$	7.47253	+	7.47253i	0.301322	+	0.301322i
$616$	−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	$-0.559319\pi$
$619$	19.8392	−	19.8392i	0.797406	−	0.797406i	0.982686	+	0.185280i	$0.0593192\pi$
$620$			9.51606i			0.382174i
$621$		−	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
$625$	−1.00000			−0.0400000
$626$	−17.7473	−	17.7473i	−0.709325	−	0.709325i
$627$		−	32.3442i		−	1.29170i
$628$	11.5725			0.461792
$629$	−4.02072	+	17.7988i	−0.160317	+	0.709685i
$630$	−0.272132			−0.0108420
$631$		−	1.50527i		−	0.0599239i	−0.999551	−	0.0299619i	$-0.990461\pi$
$631$		−	1.50527i		−	0.0599239i	0.999551	−	0.0299619i	$-0.00953861\pi$
$632$	−11.6179	−	11.6179i	−0.462136	−	0.462136i
$633$	−6.92494			−0.275242
$634$	0.784894	+	0.784894i	0.0311721	+	0.0311721i
$635$	8.71274	−	8.71274i	0.345755	−	0.345755i
$636$	1.33747	−	1.33747i	0.0530341	−	0.0530341i
$637$		−	2.80237i		−	0.111034i
$638$			2.94316i			0.116521i
$639$	1.03422	−	1.03422i	0.0409129	−	0.0409129i
$640$	−0.707107	+	0.707107i	−0.0279508	+	0.0279508i
$641$	−16.3029	−	16.3029i	−0.643926	−	0.643926i	0.307592	−	0.951518i	$-0.400477\pi$
$641$	−16.3029	−	16.3029i	−0.643926	−	0.643926i	−0.951518	+	0.307592i	$0.900477\pi$
$642$	−14.6890			−0.579728
$643$	26.8391	+	26.8391i	1.05843	+	1.05843i	0.998184	+	0.0602469i	$0.0191888\pi$
$643$	26.8391	+	26.8391i	1.05843	+	1.05843i	0.0602469	+	0.998184i	$0.480811\pi$
$644$		−	1.99055i		−	0.0784387i
$645$	2.71370			0.106852
$646$	7.74028	+	12.2578i	0.304537	+	0.482277i
$647$	0.182497			0.00717469			0.00358734	−	0.999994i	$-0.498858\pi$
$647$	0.182497			0.00717469			0.00358734	+	0.999994i	$0.498858\pi$
$648$		−	8.64741i		−	0.339702i
$649$	−42.7747	−	42.7747i	−1.67905	−	1.67905i
$650$	2.28483			0.0896184
$651$	−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
$655$			11.9611i			0.467357i
$656$	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	$-0.519625\pi$
$659$	−3.16347			−0.123231			−0.0616157	+	0.998100i	$0.519625\pi$
$660$	−6.50466	−	6.50466i	−0.253194	−	0.253194i
$661$			22.2037i			0.863624i	0.901964	+	0.431812i	$0.142126\pi$
$661$			22.2037i			0.863624i	−0.901964	+	0.431812i	$0.857874\pi$
$662$	3.90483			0.151766
$663$	3.52686	−	15.6126i	0.136972	−	0.606342i
$664$	10.9725			0.425814
$665$		−	8.44843i		−	0.327616i
$666$	−0.354421	−	0.354421i	−0.0137335	−	0.0137335i
$667$	−0.450332			−0.0174369
$668$	−6.50141	−	6.50141i	−0.251547	−	0.251547i
$669$	−12.0431	+	12.0431i	−0.465612	+	0.465612i
$670$	5.98387	−	5.98387i	0.231177	−	0.231177i
$671$			69.0166i			2.66436i
$672$		−	4.08247i		−	0.157485i
$673$	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
$675$	−3.74028	−	3.74028i	−0.143963	−	0.143963i
$676$	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	$-0.617233\pi$
$678$		−	12.3579i		−	0.474600i
$679$	35.8519			1.37587
$680$	4.02177	+	0.908511i	0.154228	+	0.0348398i
$681$	−25.5233			−0.978057
$682$			51.5220i			1.97288i
$683$	−3.59962	−	3.59962i	−0.137736	−	0.137736i	0.634877	−	0.772613i	$-0.281051\pi$
$683$	−3.59962	−	3.59962i	−0.137736	−	0.137736i	−0.772613	+	0.634877i	$0.781051\pi$
$684$	−0.398214			−0.0152261
$685$	8.32836	+	8.32836i	0.318210	+	0.318210i
$686$	−13.9772	+	13.9772i	−0.533652	+	0.533652i
$687$	20.9625	−	20.9625i	0.799768	−	0.799768i
$688$		−	1.59719i		−	0.0608924i
$689$			2.54360i			0.0969034i
$690$	0.995276	−	0.995276i	0.0378895	−	0.0378895i
$691$	24.3525	−	24.3525i	0.926411	−	0.926411i	−0.0710606	−	0.997472i	$-0.522638\pi$
$691$	24.3525	−	24.3525i	0.926411	−	0.926411i	0.997472	+	0.0710606i	$0.0226384\pi$
$692$	−13.0483	−	13.0483i	−0.496020	−	0.496020i
$693$	−1.47338			−0.0559691
$694$	−12.0526	−	12.0526i	−0.457512	−	0.457512i
$695$			7.03881i			0.266997i
$696$	−0.923597			−0.0350088
$697$	−25.0147	−	5.65078i	−0.947500	−	0.214039i
$698$	17.0455			0.645181
$699$			48.8781i			1.84874i
$700$	−1.69904	−	1.69904i	−0.0642178	−	0.0642178i
$701$	−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
$705$			6.99662i			0.263508i
$706$		−	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	0.999979	+	0.00649104i	$0.00206618\pi$
$709$	26.7993	+	26.7993i	1.00647	+	1.00647i	0.00649104	+	0.999979i	$0.497934\pi$
$710$	12.9141			0.484659
$711$	−1.31580	−	1.31580i	−0.0493462	−	0.0493462i
$712$			10.7796i			0.403981i
$713$	−7.88337			−0.295234
$714$	−14.2325	+	8.98717i	−0.532636	+	0.336337i
$715$	12.3706			0.462632
$716$		−	15.6018i		−	0.583066i
$717$	−22.9256	−	22.9256i	−0.856173	−	0.856173i
$718$	−30.5514			−1.14017
$719$	4.00763	+	4.00763i	0.149459	+	0.149459i	0.777877	−	0.628417i	$-0.216297\pi$
$719$	4.00763	+	4.00763i	0.149459	+	0.149459i	−0.628417	+	0.777877i	$0.716297\pi$
$720$	−0.0800839	+	0.0800839i	−0.00298455	+	0.00298455i
$721$	−3.43684	+	3.43684i	−0.127995	+	0.127995i
$722$			6.63729i			0.247014i
$723$			37.0758i			1.37887i
$724$	7.21511	−	7.21511i	0.268147	−	0.268147i
$725$	−0.384382	+	0.384382i	−0.0142756	+	0.0142756i
$726$	−22.0022	−	22.0022i	−0.816577	−	0.816577i
$727$	−6.36339			−0.236005			−0.118002	−	0.993013i	$-0.537649\pi$
$727$	−6.36339			−0.236005			−0.118002	+	0.993013i	$0.537649\pi$
$728$	3.88202	+	3.88202i	0.143877	+	0.143877i
$729$		−	27.9409i		−	1.03485i
$730$	12.3606			0.457487
$731$	−5.56818	+	3.51606i	−0.205947	+	0.130046i
$732$	−21.6582			−0.800510
$733$		−	3.82830i		−	0.141401i	−0.997498	−	0.0707007i	$-0.977476\pi$
$733$		−	3.82830i		−	0.141401i	0.997498	−	0.0707007i	$-0.0225235\pi$
$734$	11.3820	+	11.3820i	0.420116	+	0.420116i
$735$	−2.08389			−0.0768656
$736$	−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	$0.823297\pi$
$740$		−	4.42562i		−	0.162689i
$741$	−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	0.675996	−	0.736906i	$-0.263714\pi$
$743$	−1.66029	−	1.66029i	−0.0609100	−	0.0609100i	−0.736906	+	0.675996i	$0.763714\pi$
$744$	−16.1682			−0.592755
$745$	−2.30096	−	2.30096i	−0.0843006	−	0.0843006i
$746$		−	13.0644i		−	0.478321i
$747$	1.24269			0.0454678
$748$	21.7747	+	4.91887i	0.796162	+	0.179852i
$749$	−20.7734			−0.759042
$750$		−	1.69904i		−	0.0620402i
$751$	36.3675	+	36.3675i	1.32707	+	1.32707i	0.907915	+	0.419154i	$0.137673\pi$
$751$	36.3675	+	36.3675i	1.32707	+	1.32707i	0.419154	+	0.907915i	$0.362327\pi$
$752$	4.11798			0.150167
$753$	13.7211	+	13.7211i	0.500025	+	0.500025i
$754$	0.878247	−	0.878247i	0.0319839	−	0.0319839i
$755$	2.40281	−	2.40281i	0.0874472	−	0.0874472i
$756$		−	12.7098i		−	0.462250i
$757$			48.2458i			1.75352i	0.480925	+	0.876762i	$0.340301\pi$
$757$			48.2458i			1.75352i	−0.480925	+	0.876762i	$0.659699\pi$
$758$	19.7607	−	19.7607i	0.717740	−	0.717740i
$759$	5.38864	−	5.38864i	0.195595	−	0.195595i
$760$	−2.48623	−	2.48623i	−0.0901851	−	0.0901851i
$761$	−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
$763$			1.30616i			0.0472863i
$764$	1.54212			0.0557920
$765$	0.455488	+	0.102894i	0.0164682	+	0.00372014i
$766$	−29.9785			−1.08317
$767$			25.5282i			0.921770i
$768$	−1.20140	−	1.20140i	−0.0433519	−	0.0433519i
$769$	15.9550			0.575354			0.287677	−	0.957728i	$-0.407117\pi$
$769$	15.9550			0.575354			0.287677	+	0.957728i	$0.407117\pi$
$770$	−9.19898	−	9.19898i	−0.331508	−	0.331508i
$771$	−30.4289	+	30.4289i	−1.09587	+	1.09587i
$772$	−12.6601	+	12.6601i	−0.455647	+	0.455647i
$773$			18.0027i			0.647512i	0.946141	+	0.323756i	$0.104946\pi$
$773$			18.0027i			0.647512i	−0.946141	+	0.323756i	$0.895054\pi$
$774$		−	0.180891i		−	0.00650200i
$775$	−6.72887	+	6.72887i	−0.241708	+	0.241708i
$776$	10.5506	−	10.5506i	0.378745	−	0.378745i
$777$	12.7756	+	12.7756i	0.458323	+	0.458323i
$778$	−33.5174			−1.20166
$779$	15.4639	+	15.4639i	0.554053	+	0.554053i
$780$			3.88202i			0.138999i
$781$	69.9200			2.50193
$782$	−0.752635	+	3.33174i	−0.0269142	+	0.119143i
$783$	−2.87539			−0.102758
$784$			1.22651i			0.0438040i
$785$	8.18298	+	8.18298i	0.292063	+	0.292063i
$786$	−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
$790$		−	16.4302i		−	0.584561i
$791$		−	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
$795$	1.89147			0.0670835
$796$	13.7013	+	13.7013i	0.485631	+	0.485631i
$797$		−	18.5240i		−	0.656155i	−0.944651	−	0.328078i	$-0.893599\pi$
$797$		−	18.5240i		−	0.656155i	0.944651	−	0.328078i	$-0.106401\pi$
$798$	14.3542			0.508134
$799$	−9.06534	−	14.3562i	−0.320709	−	0.507887i
$800$	−1.00000			−0.0353553
$801$			1.22085i			0.0431365i
$802$	12.8250	+	12.8250i	0.452868	+	0.452868i
$803$	66.9230			2.36166
$804$	10.1668	+	10.1668i	0.358557	+	0.358557i
$805$	1.40753	−	1.40753i	0.0496090	−	0.0496090i
$806$	15.3743	−	15.3743i	0.541537	−	0.541537i
$807$		−	36.5535i		−	1.28674i
$808$			3.65685i			0.128648i
$809$	20.6246	−	20.6246i	0.725122	−	0.725122i	−0.244522	−	0.969644i	$-0.578631\pi$
$809$	20.6246	−	20.6246i	0.725122	−	0.725122i	0.969644	+	0.244522i	$0.0786309\pi$
$810$	6.11464	−	6.11464i	0.214847	−	0.214847i
$811$	7.91090	+	7.91090i	0.277789	+	0.277789i	0.832226	−	0.554437i	$-0.187066\pi$
$811$	7.91090	+	7.91090i	0.277789	+	0.277789i	−0.554437	+	0.832226i	$0.687066\pi$
$812$	−1.30616			−0.0458373
$813$	−24.6272	−	24.6272i	−0.863712	−	0.863712i
$814$		−	23.9612i		−	0.839841i
$815$	−8.27949			−0.290018
$816$	−1.54360	+	6.83315i	−0.0540368	+	0.239208i
$817$	5.61583			0.196473
$818$		−	17.7472i		−	0.620515i
$819$	0.439661	+	0.439661i	0.0153630	+	0.0153630i
$820$	6.21983			0.217206
$821$	−4.72563	−	4.72563i	−0.164925	−	0.164925i	0.619819	−	0.784745i	$-0.287206\pi$
$821$	−4.72563	−	4.72563i	−0.164925	−	0.164925i	−0.784745	+	0.619819i	$0.787206\pi$
$822$	−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
$825$		−	9.19898i		−	0.320267i
$826$	18.9833	−	18.9833i	0.660512	−	0.660512i
$827$	−21.5436	+	21.5436i	−0.749144	+	0.749144i	−0.974319	−	0.225174i	$-0.927705\pi$
$827$	−21.5436	+	21.5436i	−0.749144	+	0.749144i	0.225174	+	0.974319i	$0.427705\pi$
$828$	−0.0663437	−	0.0663437i	−0.00230560	−	0.00230560i
$829$	2.52404			0.0876634			0.0438317	−	0.999039i	$-0.486043\pi$
$829$	2.52404			0.0876634			0.0438317	+	0.999039i	$0.486043\pi$
$830$	7.75870	+	7.75870i	0.269309	+	0.269309i
$831$		−	17.7922i		−	0.617206i
$832$	2.28483			0.0792122
$833$	4.27590	−	2.70005i	0.148151	−	0.0935511i
$834$	−11.9592			−0.414114
$835$		−	9.19438i		−	0.318185i
$836$	−13.4610	−	13.4610i	−0.465558	−	0.465558i
$837$	−50.3357			−1.73986
$838$	10.2896	+	10.2896i	0.355447	+	0.355447i
$839$	−10.1638	+	10.1638i	−0.350894	+	0.350894i	−0.860442	−	0.509548i	$-0.829813\pi$
$839$	−10.1638	+	10.1638i	−0.350894	+	0.350894i	0.509548	+	0.860442i	$0.329813\pi$
$840$	2.88674	−	2.88674i	0.0996021	−	0.0996021i
$841$		−	28.7045i		−	0.989810i
$842$		−	9.24460i		−	0.318590i
$843$	19.0510	−	19.0510i	0.656153	−	0.656153i
$844$	−2.88202	+	2.88202i	−0.0992032	+	0.0992032i
$845$	5.50098	+	5.50098i	0.189239	+	0.189239i
$846$	0.466385			0.0160346
$847$	−31.1158	−	31.1158i	−1.06915	−	1.06915i
$848$		−	1.11326i		−	0.0382294i
$849$	9.53955			0.327397
$850$	2.20140	+	3.48623i	0.0755075	+	0.119577i
$851$	3.66630			0.125679
$852$			21.9417i			0.751710i
$853$	24.7680	+	24.7680i	0.848041	+	0.848041i	0.989889	−	0.141848i	$-0.0453043\pi$
$853$	24.7680	+	24.7680i	0.848041	+	0.848041i	−0.141848	+	0.989889i	$0.545304\pi$
$854$	−30.6293			−1.04811
$855$	−0.281580	−	0.281580i	−0.00962984	−	0.00962984i
$856$	−6.11326	+	6.11326i	−0.208947	+	0.208947i
$857$	−30.3695	+	30.3695i	−1.03740	+	1.03740i	−0.0381284	+	0.999273i	$0.512140\pi$
$857$	−30.3695	+	30.3695i	−1.03740	+	1.03740i	−0.999273	+	0.0381284i	$0.987860\pi$
$858$			21.0181i			0.717546i
$859$			5.90188i			0.201370i	0.994918	+	0.100685i	$0.0321034\pi$
$859$			5.90188i			0.201370i	−0.994918	+	0.100685i	$0.967897\pi$
$860$	1.12938	−	1.12938i	0.0385117	−	0.0385117i
$861$	−17.9551	+	17.9551i	−0.611907	+	0.611907i
$862$	−27.3344	−	27.3344i	−0.931014	−	0.931014i
$863$	−6.32978			−0.215468			−0.107734	−	0.994180i	$-0.534360\pi$
$863$	−6.32978			−0.215468			−0.107734	+	0.994180i	$0.534360\pi$
$864$	−3.74028	−	3.74028i	−0.127247	−	0.127247i
$865$		−	18.4530i		−	0.627422i
$866$	6.51944			0.221540
$867$	27.2200	−	9.66118i	0.924441	−	0.328111i
$868$	−22.8653			−0.776098
$869$		−	88.9567i		−	3.01765i
$870$	−0.653082	−	0.653082i	−0.0221415	−	0.0221415i
$871$	−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
$875$		−	2.40281i		−	0.0812298i
$876$			21.0012i			0.709565i
$877$	7.44027	−	7.44027i	0.251240	−	0.251240i	−0.570239	−	0.821479i	$-0.693149\pi$
$877$	7.44027	−	7.44027i	0.251240	−	0.251240i	0.821479	+	0.570239i	$0.193149\pi$
$878$	7.24736	−	7.24736i	0.244587	−	0.244587i
$879$	−33.5725	−	33.5725i	−1.13237	−	1.13237i
$880$	−5.41421			−0.182513
$881$	−30.8068	−	30.8068i	−1.03791	−	1.03791i	−0.999253	−	0.0386560i	$-0.987692\pi$
$881$	−30.8068	−	30.8068i	−1.03791	−	1.03791i	−0.0386560	−	0.999253i	$-0.512308\pi$
$882$			0.138909i			0.00467732i
$883$	39.6614			1.33471			0.667357	−	0.744738i	$-0.267426\pi$
$883$	39.6614			1.33471			0.667357	+	0.744738i	$0.267426\pi$
$884$	−5.02983	−	7.96544i	−0.169172	−	0.267907i
$885$	18.9833			0.638115
$886$		−	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	$-0.501043\pi$
$888$	7.51931			0.252332
$889$	20.9351	+	20.9351i	0.702139	+	0.702139i
$890$	−7.62230	+	7.62230i	−0.255500	+	0.255500i
$891$	33.1060	−	33.1060i	1.10909	−	1.10909i
$892$			10.0242i			0.335634i
$893$			14.4791i			0.484524i
$894$	3.90942	−	3.90942i	0.130751	−	0.130751i
$895$	11.0321	−	11.0321i	0.368763	−	0.368763i
$896$	−1.69904	−	1.69904i	−0.0567610	−	0.0567610i
$897$	−3.21597			−0.107378
$898$	−2.05034	−	2.05034i	−0.0684209	−	0.0684209i
$899$			5.17292i			0.172526i
$900$	−0.113256			−0.00377519
$901$	−3.88107	+	2.45073i	−0.129297	+	0.0816455i
$902$	33.6755			1.12127
$903$			6.52049i			0.216988i
$904$	−5.14309	−	5.14309i	−0.171057	−	0.171057i
$905$	10.2037			0.339183
$906$	4.08247	+	4.08247i	0.135631	+	0.135631i
$907$	13.3986	−	13.3986i	0.444893	−	0.444893i	−0.448759	−	0.893653i	$-0.648134\pi$
$907$	13.3986	−	13.3986i	0.444893	−	0.444893i	0.893653	+	0.448759i	$0.148134\pi$
$908$	−10.6223	+	10.6223i	−0.352513	+	0.352513i
$909$			0.414160i			0.0137368i
$910$			5.49001i			0.181992i
$911$	−29.3865	+	29.3865i	−0.973620	+	0.973620i	−0.999661	−	0.0260411i	$-0.991710\pi$
$911$	−29.3865	+	29.3865i	−0.973620	+	0.973620i	0.0260411	+	0.999661i	$0.491710\pi$
$912$	4.22421	−	4.22421i	0.139878	−	0.139878i
$913$	42.0073	+	42.0073i	1.39024	+	1.39024i
$914$	22.7392			0.752146
$915$	−15.3147	−	15.3147i	−0.506287	−	0.506287i
$916$		−	17.4483i		−	0.576508i
$917$	−28.7401			−0.949083
$918$	−4.80562	+	21.2733i	−0.158609	+	0.702125i
$919$	−45.1466			−1.48925			−0.744624	−	0.667484i	$-0.767371\pi$
$919$	−45.1466			−1.48925			−0.744624	+	0.667484i	$0.767371\pi$
$920$		−	0.828427i		−	0.0273124i
$921$	11.6848	+	11.6848i	0.385028	+	0.385028i
$922$	28.4758			0.937802
$923$	−20.8643	−	20.8643i	−0.686758	−	0.686758i
$924$	15.6294	−	15.6294i	0.514171	−	0.514171i
$925$	3.12938	−	3.12938i	0.102894	−	0.102894i
$926$		−	14.1542i		−	0.465134i
$927$			0.229095i			0.00752446i
$928$	−0.384382	+	0.384382i	−0.0126180	+	0.0126180i
$929$	10.6246	−	10.6246i	0.348582	−	0.348582i	−0.510999	−	0.859581i	$-0.670725\pi$
$929$	10.6246	−	10.6246i	0.348582	−	0.348582i	0.859581	+	0.510999i	$0.170725\pi$
$930$	−11.4326	−	11.4326i	−0.374891	−	0.374891i
$931$	−4.31249			−0.141336
$932$	20.3421	+	20.3421i	0.666326	+	0.666326i
$933$			40.1940i			1.31589i
$934$	−18.1053			−0.592423
$935$	11.9189	+	18.8752i	0.389789	+	0.617285i
$936$	0.258770			0.00845816
$937$		−	19.0208i		−	0.621382i	−0.950511	−	0.310691i	$-0.899440\pi$
$937$		−	19.0208i		−	0.621382i	0.950511	−	0.310691i	$-0.100560\pi$
$938$	14.3781	+	14.3781i	0.469461	+	0.469461i
$939$	42.6434			1.39161
$940$	2.91185	+	2.91185i	0.0949741	+	0.0949741i
$941$	−6.46686	+	6.46686i	−0.210813	+	0.210813i	−0.804613	−	0.593800i	$-0.797627\pi$
$941$	−6.46686	+	6.46686i	−0.210813	+	0.210813i	0.593800	+	0.804613i	$0.297627\pi$
$942$	−13.9032	+	13.9032i	−0.452992	+	0.452992i
$943$			5.15268i			0.167794i
$944$		−	11.1729i		−	0.363648i
$945$	8.98717	−	8.98717i	0.292353	−	0.292353i
$946$	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	$0.877744\pi$
$948$	27.9156			0.906657
$949$	−19.9700	−	19.9700i	−0.648255	−	0.648255i
$950$		−	3.51606i		−	0.114076i
$951$	−1.88595			−0.0611561
$952$	−2.18298	+	9.66354i	−0.0707507	+	0.313197i
$953$	44.4511			1.43991			0.719957	−	0.694019i	$-0.244162\pi$
$953$	44.4511			1.43991			0.719957	+	0.694019i	$0.244162\pi$
$954$		−	0.126083i		−	0.00408207i
$955$	1.09045	+	1.09045i	0.0352860	+	0.0352860i
$956$	−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
$960$		−	1.69904i		−	0.0548364i
$961$			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
$965$	−17.9041			−0.576353
$966$	2.39146	+	2.39146i	0.0769439	+	0.0769439i
$967$		−	8.50514i		−	0.273507i	−0.990605	−	0.136753i	$-0.956333\pi$
$967$		−	8.50514i		−	0.273507i	0.990605	−	0.136753i	$-0.0436668\pi$
$968$	−18.3137			−0.588625
$969$	−24.0258	−	5.42739i	−0.771820	−	0.174353i
$970$	14.9208			0.479079
$971$			2.88215i			0.0924926i	0.998930	+	0.0462463i	$0.0147259\pi$
$971$			2.88215i			0.0924926i	−0.998930	+	0.0462463i	$0.985274\pi$
$972$	−0.831806	−	0.831806i	−0.0266802	−	0.0266802i
$973$	−16.9129			−0.542203
$974$	−20.5047	−	20.5047i	−0.657012	−	0.657012i
$975$	−2.74500	+	2.74500i	−0.0879104	+	0.0879104i
$976$	−9.01370	+	9.01370i	−0.288522	+	0.288522i
$977$			34.7030i			1.11025i	0.831768	+	0.555124i	$0.187329\pi$
$977$			34.7030i			1.11025i	−0.831768	+	0.555124i	$0.812671\pi$
$978$		−	14.0672i		−	0.449820i
$979$	−41.2688	+	41.2688i	−1.31896	+	1.31896i
$980$	−0.867275	+	0.867275i	−0.0277041	+	0.0277041i
$981$	0.0435335	+	0.0435335i	0.00138992	+	0.00138992i
$982$	23.3994			0.746706
$983$	−24.4014	−	24.4014i	−0.778283	−	0.778283i	0.201255	−	0.979539i	$-0.435498\pi$
$983$	−24.4014	−	24.4014i	−0.778283	−	0.778283i	−0.979539	+	0.201255i	$0.935498\pi$
$984$			10.5678i			0.336888i
$985$	−9.56493			−0.304764
$986$	2.18623	+	0.493865i	0.0696236	+	0.0157279i
$987$	−16.8115			−0.535117
$988$			8.03360i			0.255583i
$989$	0.935613	+	0.935613i	0.0297508	+	0.0297508i
$990$	−0.613191			−0.0194885
$991$	23.1043	+	23.1043i	0.733932	+	0.733932i	0.971396	−	0.237465i	$-0.0763164\pi$
$991$	23.1043	+	23.1043i	0.733932	+	0.733932i	−0.237465	+	0.971396i	$0.576316\pi$
$992$	−6.72887	+	6.72887i	−0.213642	+	0.213642i
$993$	−4.69128	+	4.69128i	−0.148873	+	0.148873i
$994$			31.0302i			0.984219i
$995$			19.3766i			0.614280i
$996$	−13.1824	+	13.1824i	−0.417699	+	0.417699i
$997$	21.9490	−	21.9490i	0.695133	−	0.695133i	−0.268224	−	0.963357i	$-0.586437\pi$
$997$	21.9490	−	21.9490i	0.695133	−	0.695133i	0.963357	+	0.268224i	$0.0864366\pi$
$998$	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	170.2.h.b.81.2	yes	8
3.2	odd	2		1530.2.q.g.1441.4		8
4.3	odd	2		1360.2.bt.b.81.3		8
5.2	odd	4		850.2.g.i.149.2		8
5.3	odd	4		850.2.g.l.149.3		8
5.4	even	2		850.2.h.n.251.3		8
17.2	even	8		2890.2.a.be.1.2		4
17.4	even	4	inner	170.2.h.b.21.2	✓	8
17.8	even	8		2890.2.b.o.2311.5		8
17.9	even	8		2890.2.b.o.2311.4		8
17.15	even	8		2890.2.a.bd.1.3		4
51.38	odd	4		1530.2.q.g.361.4		8
68.55	odd	4		1360.2.bt.b.1041.3		8
85.4	even	4		850.2.h.n.701.3		8
85.38	odd	4		850.2.g.i.599.2		8
85.72	odd	4		850.2.g.l.599.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.2	✓	8	17.4	even	4	inner
170.2.h.b.81.2	yes	8	1.1	even	1	trivial
850.2.g.i.149.2		8	5.2	odd	4
850.2.g.i.599.2		8	85.38	odd	4
850.2.g.l.149.3		8	5.3	odd	4
850.2.g.l.599.3		8	85.72	odd	4
850.2.h.n.251.3		8	5.4	even	2
850.2.h.n.701.3		8	85.4	even	4
1360.2.bt.b.81.3		8	4.3	odd	2
1360.2.bt.b.1041.3		8	68.55	odd	4
1530.2.q.g.361.4		8	51.38	odd	4
1530.2.q.g.1441.4		8	3.2	odd	2
2890.2.a.bd.1.3		4	17.15	even	8
2890.2.a.be.1.2		4	17.2	even	8
2890.2.b.o.2311.4		8	17.9	even	8
2890.2.b.o.2311.5		8	17.8	even	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.20140 - 1.20140i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.20140 - 1.20140i) q^{6} +(1.69904 - 1.69904i) q^{7} -1.00000i q^{8} -0.113256i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.20140 - 1.20140i) q^{3} -1.00000 q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.20140 - 1.20140i) q^{6} +(1.69904 - 1.69904i) q^{7} -1.00000i q^{8} -0.113256i q^{9} +(0.707107 - 0.707107i) q^{10} +(3.82843 - 3.82843i) q^{11} +(1.20140 + 1.20140i) q^{12} -2.28483 q^{13} +(1.69904 + 1.69904i) q^{14} +1.69904i q^{15} +1.00000 q^{16} +(-2.20140 - 3.48623i) q^{17} +0.113256 q^{18} +3.51606i q^{19} +(0.707107 + 0.707107i) q^{20} -4.08247 q^{21} +(3.82843 + 3.82843i) q^{22} +(-0.585786 + 0.585786i) q^{23} +(-1.20140 + 1.20140i) q^{24} +1.00000i q^{25} -2.28483i q^{26} +(-3.74028 + 3.74028i) q^{27} +(-1.69904 + 1.69904i) q^{28} +(0.384382 + 0.384382i) q^{29} -1.69904 q^{30} +(6.72887 + 6.72887i) q^{31} +1.00000i q^{32} -9.19898 q^{33} +(3.48623 - 2.20140i) q^{34} -2.40281 q^{35} +0.113256i q^{36} +(-3.12938 - 3.12938i) q^{37} -3.51606 q^{38} +(2.74500 + 2.74500i) q^{39} +(-0.707107 + 0.707107i) q^{40} +(4.39808 - 4.39808i) q^{41} -4.08247i q^{42} -1.59719i q^{43} +(-3.82843 + 3.82843i) q^{44} +(-0.0800839 + 0.0800839i) q^{45} +(-0.585786 - 0.585786i) q^{46} +4.11798 q^{47} +(-1.20140 - 1.20140i) q^{48} +1.22651i q^{49} -1.00000 q^{50} +(-1.54360 + 6.83315i) q^{51} +2.28483 q^{52} -1.11326i q^{53} +(-3.74028 - 3.74028i) q^{54} -5.41421 q^{55} +(-1.69904 - 1.69904i) q^{56} +(4.22421 - 4.22421i) q^{57} +(-0.384382 + 0.384382i) q^{58} -11.1729i q^{59} -1.69904i q^{60} +(-9.01370 + 9.01370i) q^{61} +(-6.72887 + 6.72887i) q^{62} +(-0.192426 - 0.192426i) q^{63} -1.00000 q^{64} +(1.61562 + 1.61562i) q^{65} -9.19898i q^{66} +8.46247 q^{67} +(2.20140 + 3.48623i) q^{68} +1.40753 q^{69} -2.40281i q^{70} +(9.13168 + 9.13168i) q^{71} -0.113256 q^{72} +(8.74028 + 8.74028i) q^{73} +(3.12938 - 3.12938i) q^{74} +(1.20140 - 1.20140i) q^{75} -3.51606i q^{76} -13.0093i q^{77} +(-2.74500 + 2.74500i) q^{78} +(11.6179 - 11.6179i) q^{79} +(-0.707107 - 0.707107i) q^{80} +8.64741 q^{81} +(4.39808 + 4.39808i) q^{82} +10.9725i q^{83} +4.08247 q^{84} +(-0.908511 + 4.02177i) q^{85} +1.59719 q^{86} -0.923597i q^{87} +(-3.82843 - 3.82843i) q^{88} -10.7796 q^{89} +(-0.0800839 - 0.0800839i) q^{90} +(-3.88202 + 3.88202i) q^{91} +(0.585786 - 0.585786i) q^{92} -16.1682i q^{93} +4.11798i q^{94} +(2.48623 - 2.48623i) q^{95} +(1.20140 - 1.20140i) q^{96} +(10.5506 + 10.5506i) q^{97} -1.22651 q^{98} +(-0.433591 - 0.433591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^7	\( 8 q - 8 q^{4} - 4 q^{7} + 8 q^{11} - 12 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} - 28 q^{18} + 16 q^{21} + 8 q^{22} - 16 q^{23} + 12 q^{27} + 4 q^{28} + 24 q^{29} + 4 q^{30} + 4 q^{31} + 16 q^{33} + 12 q^{34} - 20 q^{37} + 20 q^{38} - 4 q^{39} - 8 q^{44} - 8 q^{45} - 16 q^{46} + 20 q^{47} - 8 q^{50} + 4 q^{51} + 12 q^{52} + 12 q^{54} - 32 q^{55} + 4 q^{56} + 40 q^{57} - 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} - 8 q^{64} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 8 q^{69} + 4 q^{71} + 28 q^{72} + 28 q^{73} + 20 q^{74} + 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 8 q^{85} + 32 q^{86} - 8 q^{88} - 44 q^{89} - 8 q^{90} - 44 q^{91} + 16 q^{92} + 4 q^{95} + 20 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^7 + 8 * q^11 - 12 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 - 28 * q^18 + 16 * q^21 + 8 * q^22 - 16 * q^23 + 12 * q^27 + 4 * q^28 + 24 * q^29 + 4 * q^30 + 4 * q^31 + 16 * q^33 + 12 * q^34 - 20 * q^37 + 20 * q^38 - 4 * q^39 - 8 * q^44 - 8 * q^45 - 16 * q^46 + 20 * q^47 - 8 * q^50 + 4 * q^51 + 12 * q^52 + 12 * q^54 - 32 * q^55 + 4 * q^56 + 40 * q^57 - 24 * q^58 - 16 * q^61 - 4 * q^62 - 64 * q^63 - 8 * q^64 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 8 * q^69 + 4 * q^71 + 28 * q^72 + 28 * q^73 + 20 * q^74 + 4 * q^78 + 8 * q^79 - 8 * q^81 - 16 * q^84 + 8 * q^85 + 32 * q^86 - 8 * q^88 - 44 * q^89 - 8 * q^90 - 44 * q^91 + 16 * q^92 + 4 * q^95 + 20 * q^97 + 48 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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