LMFDB - Embedded newform 1155.2.i.a.76.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.6
Root			$-1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.a.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.792287i q^{2} +1.00000i q^{3} +1.37228 q^{4} -1.00000i q^{5} -0.792287 q^{6} +(-0.792287 - 2.52434i) q^{7} +2.67181i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.792287i q^{2} +1.00000i q^{3} +1.37228 q^{4} -1.00000i q^{5} -0.792287 q^{6} +(-0.792287 - 2.52434i) q^{7} +2.67181i q^{8} -1.00000 q^{9} +0.792287 q^{10} -3.31662i q^{11} +1.37228i q^{12} +(2.00000 - 0.627719i) q^{14} +1.00000 q^{15} +0.627719 q^{16} +4.10891 q^{17} -0.792287i q^{18} -4.40387 q^{19} -1.37228i q^{20} +(2.52434 - 0.792287i) q^{21} +2.62772 q^{22} +9.11684 q^{23} -2.67181 q^{24} -1.00000 q^{25} -1.00000i q^{27} +(-1.08724 - 3.46410i) q^{28} -5.98844i q^{29} +0.792287i q^{30} +6.74456i q^{31} +5.84096i q^{32} +3.31662 q^{33} +3.25544i q^{34} +(-2.52434 + 0.792287i) q^{35} -1.37228 q^{36} +10.7446 q^{37} -3.48913i q^{38} +2.67181 q^{40} +11.6819 q^{41} +(0.627719 + 2.00000i) q^{42} -4.10891i q^{43} -4.55134i q^{44} +1.00000i q^{45} +7.22316i q^{46} -12.7446i q^{47} +0.627719i q^{48} +(-5.74456 + 4.00000i) q^{49} -0.792287i q^{50} +4.10891i q^{51} -1.62772 q^{53} +0.792287 q^{54} -3.31662 q^{55} +(6.74456 - 2.11684i) q^{56} -4.40387i q^{57} +4.74456 q^{58} -1.62772i q^{59} +1.37228 q^{60} -11.0371 q^{61} -5.34363 q^{62} +(0.792287 + 2.52434i) q^{63} -3.37228 q^{64} +2.62772i q^{66} -4.74456 q^{67} +5.63858 q^{68} +9.11684i q^{69} +(-0.627719 - 2.00000i) q^{70} +3.25544 q^{71} -2.67181i q^{72} +6.92820 q^{73} +8.51278i q^{74} -1.00000i q^{75} -6.04334 q^{76} +(-8.37228 + 2.62772i) q^{77} +0.294954i q^{79} -0.627719i q^{80} +1.00000 q^{81} +9.25544i q^{82} -9.45254 q^{83} +(3.46410 - 1.08724i) q^{84} -4.10891i q^{85} +3.25544 q^{86} +5.98844 q^{87} +8.86141 q^{88} +8.37228i q^{89} -0.792287 q^{90} +12.5109 q^{92} -6.74456 q^{93} +10.0974 q^{94} +4.40387i q^{95} -5.84096 q^{96} -8.37228i q^{97} +(-3.16915 - 4.55134i) q^{98} +3.31662i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} - 8 q^{9}+O(q^{10}) $ 8 * q - 12 * q^4 - 8 * q^9	$ 8 q - 12 q^{4} - 8 q^{9} + 16 q^{14} + 8 q^{15} + 28 q^{16} + 44 q^{22} + 4 q^{23} - 8 q^{25} + 12 q^{36} + 40 q^{37} + 28 q^{42} - 36 q^{53} + 8 q^{56} - 8 q^{58} - 12 q^{60} - 4 q^{64} + 8 q^{67} - 28 q^{70} + 72 q^{71} - 44 q^{77} + 8 q^{81} + 72 q^{86} - 44 q^{88} + 192 q^{92} - 8 q^{93}+O(q^{100}) $ 8 * q - 12 * q^4 - 8 * q^9 + 16 * q^14 + 8 * q^15 + 28 * q^16 + 44 * q^22 + 4 * q^23 - 8 * q^25 + 12 * q^36 + 40 * q^37 + 28 * q^42 - 36 * q^53 + 8 * q^56 - 8 * q^58 - 12 * q^60 - 4 * q^64 + 8 * q^67 - 28 * q^70 + 72 * q^71 - 44 * q^77 + 8 * q^81 + 72 * q^86 - 44 * q^88 + 192 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			0.792287i			0.560232i	0.959966	+	0.280116i	$0.0903729\pi$
$2$			0.792287i			0.560232i	−0.959966	+	0.280116i	$0.909627\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.37228			0.686141
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.792287			−0.323450
$7$	−0.792287	−	2.52434i	−0.299456	−	0.954110i
$7$	−0.792287	−	2.52434i	−0.299456	−	0.954110i
$8$			2.67181i			0.944629i
$9$	−1.00000			−0.333333
$10$	0.792287			0.250543
$11$		−	3.31662i		−	1.00000i
$11$		−	3.31662i		−	1.00000i
$12$			1.37228i			0.396143i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.00000	−	0.627719i	0.534522	−	0.167765i
$15$	1.00000			0.258199
$16$	0.627719			0.156930
$17$	4.10891			0.996557			0.498279	−	0.867017i	$-0.333966\pi$
$17$	4.10891			0.996557			0.498279	+	0.867017i	$0.333966\pi$
$18$		−	0.792287i		−	0.186744i
$19$	−4.40387			−1.01032			−0.505158	−	0.863027i	$-0.668566\pi$
$19$	−4.40387			−1.01032			−0.505158	+	0.863027i	$0.668566\pi$
$20$		−	1.37228i		−	0.306851i
$21$	2.52434	−	0.792287i	0.550856	−	0.172891i
$22$	2.62772			0.560232
$23$	9.11684			1.90099			0.950497	−	0.310735i	$-0.100575\pi$
$23$	9.11684			1.90099			0.950497	+	0.310735i	$0.100575\pi$
$24$	−2.67181			−0.545382
$25$	−1.00000			−0.200000
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$	−1.08724	−	3.46410i	−0.205469	−	0.654654i
$29$		−	5.98844i		−	1.11203i	−0.831174	−	0.556013i	$-0.812331\pi$
$29$		−	5.98844i		−	1.11203i	0.831174	−	0.556013i	$-0.187669\pi$
$30$			0.792287i			0.144651i
$31$			6.74456i			1.21136i	0.795709	+	0.605680i	$0.207099\pi$
$31$			6.74456i			1.21136i	−0.795709	+	0.605680i	$0.792901\pi$
$32$			5.84096i			1.03255i
$33$	3.31662			0.577350
$34$			3.25544i			0.558303i
$35$	−2.52434	+	0.792287i	−0.426691	+	0.133921i
$36$	−1.37228			−0.228714
$37$	10.7446			1.76640			0.883198	−	0.469001i	$-0.155386\pi$
$37$	10.7446			1.76640			0.883198	+	0.469001i	$0.155386\pi$
$38$		−	3.48913i		−	0.566011i
$39$		0			0
$40$	2.67181			0.422451
$41$	11.6819			1.82441			0.912205	−	0.409734i	$-0.134378\pi$
$41$	11.6819			1.82441			0.912205	+	0.409734i	$0.134378\pi$
$42$	0.627719	+	2.00000i	0.0968591	+	0.308607i
$43$		−	4.10891i		−	0.626603i	−0.949654	−	0.313302i	$-0.898565\pi$
$43$		−	4.10891i		−	0.626603i	0.949654	−	0.313302i	$-0.101435\pi$
$44$		−	4.55134i		−	0.686141i
$45$			1.00000i			0.149071i
$46$			7.22316i			1.06500i
$47$		−	12.7446i		−	1.85899i	−0.368840	−	0.929493i	$-0.620245\pi$
$47$		−	12.7446i		−	1.85899i	0.368840	−	0.929493i	$-0.379755\pi$
$48$			0.627719i			0.0906034i
$49$	−5.74456	+	4.00000i	−0.820652	+	0.571429i
$50$		−	0.792287i		−	0.112046i
$51$			4.10891i			0.575363i
$52$		0			0
$53$	−1.62772			−0.223584			−0.111792	−	0.993732i	$-0.535659\pi$
$53$	−1.62772			−0.223584			−0.111792	+	0.993732i	$0.535659\pi$
$54$	0.792287			0.107817
$55$	−3.31662			−0.447214
$56$	6.74456	−	2.11684i	0.901280	−	0.282875i
$57$		−	4.40387i		−	0.583306i
$58$	4.74456			0.622992
$59$		−	1.62772i		−	0.211911i	−0.994371	−	0.105955i	$-0.966210\pi$
$59$		−	1.62772i		−	0.211911i	0.994371	−	0.105955i	$-0.0337901\pi$
$60$	1.37228			0.177161
$61$	−11.0371			−1.41316			−0.706579	−	0.707634i	$-0.749762\pi$
$61$	−11.0371			−1.41316			−0.706579	+	0.707634i	$0.749762\pi$
$62$	−5.34363			−0.678642
$63$	0.792287	+	2.52434i	0.0998188	+	0.318037i
$64$	−3.37228			−0.421535
$65$		0			0
$66$			2.62772i			0.323450i
$67$	−4.74456			−0.579641			−0.289820	−	0.957081i	$-0.593596\pi$
$67$	−4.74456			−0.579641			−0.289820	+	0.957081i	$0.593596\pi$
$68$	5.63858			0.683779
$69$			9.11684i			1.09754i
$70$	−0.627719	−	2.00000i	−0.0750267	−	0.239046i
$71$	3.25544			0.386349			0.193175	−	0.981164i	$-0.438122\pi$
$71$	3.25544			0.386349			0.193175	+	0.981164i	$0.438122\pi$
$72$		−	2.67181i		−	0.314876i
$73$	6.92820			0.810885			0.405442	−	0.914121i	$-0.367117\pi$
$73$	6.92820			0.810885			0.405442	+	0.914121i	$0.367117\pi$
$74$			8.51278i			0.989590i
$75$		−	1.00000i		−	0.115470i
$76$	−6.04334			−0.693219
$77$	−8.37228	+	2.62772i	−0.954110	+	0.299456i
$78$		0			0
$79$			0.294954i			0.0331849i	0.999862	+	0.0165924i	$0.00528178\pi$
$79$			0.294954i			0.0331849i	−0.999862	+	0.0165924i	$0.994718\pi$
$80$		−	0.627719i		−	0.0701811i
$81$	1.00000			0.111111
$82$			9.25544i			1.02209i
$83$	−9.45254			−1.03755			−0.518776	−	0.854910i	$-0.673612\pi$
$83$	−9.45254			−1.03755			−0.518776	+	0.854910i	$0.673612\pi$
$84$	3.46410	−	1.08724i	0.377964	−	0.118628i
$85$		−	4.10891i		−	0.445674i
$86$	3.25544			0.351043
$87$	5.98844			0.642028
$88$	8.86141			0.944629
$89$			8.37228i			0.887460i	0.896161	+	0.443730i	$0.146345\pi$
$89$			8.37228i			0.887460i	−0.896161	+	0.443730i	$0.853655\pi$
$90$	−0.792287			−0.0835144
$91$		0			0
$92$	12.5109			1.30435
$93$	−6.74456			−0.699379
$94$	10.0974			1.04146
$95$			4.40387i			0.451827i
$96$	−5.84096			−0.596141
$97$		−	8.37228i		−	0.850076i	−0.905175	−	0.425038i	$-0.860261\pi$
$97$		−	8.37228i		−	0.850076i	0.905175	−	0.425038i	$-0.139739\pi$
$98$	−3.16915	−	4.55134i	−0.320132	−	0.459755i
$99$			3.31662i			0.333333i
$100$	−1.37228			−0.137228
$101$	−10.3923			−1.03407			−0.517036	−	0.855963i	$-0.672965\pi$
$101$	−10.3923			−1.03407			−0.517036	+	0.855963i	$0.672965\pi$
$102$	−3.25544			−0.322336
$103$			11.1168i			1.09538i	0.836683	+	0.547688i	$0.184492\pi$
$103$			11.1168i			1.09538i	−0.836683	+	0.547688i	$0.815508\pi$
$104$		0			0
$105$	−0.792287	−	2.52434i	−0.0773193	−	0.246350i
$106$		−	1.28962i		−	0.125259i
$107$			4.75372i			0.459560i	0.973243	+	0.229780i	$0.0738006\pi$
$107$			4.75372i			0.459560i	−0.973243	+	0.229780i	$0.926199\pi$
$108$		−	1.37228i		−	0.132048i
$109$			1.87953i			0.180026i	0.995941	+	0.0900130i	$0.0286909\pi$
$109$			1.87953i			0.180026i	−0.995941	+	0.0900130i	$0.971309\pi$
$110$		−	2.62772i		−	0.250543i
$111$			10.7446i			1.01983i
$112$	−0.497333	−	1.58457i	−0.0469936	−	0.149728i
$113$	−1.62772			−0.153123			−0.0765614	−	0.997065i	$-0.524394\pi$
$113$	−1.62772			−0.153123			−0.0765614	+	0.997065i	$0.524394\pi$
$114$	3.48913			0.326787
$115$		−	9.11684i		−	0.850150i
$116$		−	8.21782i		−	0.763006i
$117$		0			0
$118$	1.28962			0.118719
$119$	−3.25544	−	10.3723i	−0.298425	−	0.950825i
$120$			2.67181i			0.243902i
$121$	−11.0000			−1.00000
$122$		−	8.74456i		−	0.791696i
$123$			11.6819i			1.05332i
$124$			9.25544i			0.831163i
$125$			1.00000i			0.0894427i
$126$	−2.00000	+	0.627719i	−0.178174	+	0.0559216i
$127$			9.74749i			0.864950i	0.901646	+	0.432475i	$0.142360\pi$
$127$			9.74749i			0.864950i	−0.901646	+	0.432475i	$0.857640\pi$
$128$			9.01011i			0.796389i
$129$	4.10891			0.361770
$130$		0			0
$131$	−1.28962			−0.112675			−0.0563373	−	0.998412i	$-0.517942\pi$
$131$	−1.28962			−0.112675			−0.0563373	+	0.998412i	$0.517942\pi$
$132$	4.55134			0.396143
$133$	3.48913	+	11.1168i	0.302546	+	0.963953i
$134$		−	3.75906i		−	0.324733i
$135$	−1.00000			−0.0860663
$136$			10.9783i			0.941377i
$137$	12.7446			1.08884			0.544421	−	0.838812i	$-0.316750\pi$
$137$	12.7446			1.08884			0.544421	+	0.838812i	$0.316750\pi$
$138$	−7.22316			−0.614876
$139$	3.46410			0.293821			0.146911	−	0.989150i	$-0.453067\pi$
$139$	3.46410			0.293821			0.146911	+	0.989150i	$0.453067\pi$
$140$	−3.46410	+	1.08724i	−0.292770	+	0.0918886i
$141$	12.7446			1.07329
$142$			2.57924i			0.216445i
$143$		0			0
$144$	−0.627719			−0.0523099
$145$	−5.98844			−0.497313
$146$			5.48913i			0.454283i
$147$	−4.00000	−	5.74456i	−0.329914	−	0.473804i
$148$	14.7446			1.21200
$149$			13.8564i			1.13516i	0.823318	+	0.567581i	$0.192120\pi$
$149$			13.8564i			1.13516i	−0.823318	+	0.567581i	$0.807880\pi$
$150$	0.792287			0.0646900
$151$			8.51278i			0.692760i	0.938094	+	0.346380i	$0.112589\pi$
$151$			8.51278i			0.692760i	−0.938094	+	0.346380i	$0.887411\pi$
$152$		−	11.7663i		−	0.954374i
$153$	−4.10891			−0.332186
$154$	−2.08191	−	6.63325i	−0.167765	−	0.534522i
$155$	6.74456			0.541736
$156$		0			0
$157$		−	2.88316i		−	0.230101i	−0.993360	−	0.115050i	$-0.963297\pi$
$157$		−	2.88316i		−	0.230101i	0.993360	−	0.115050i	$-0.0367030\pi$
$158$	−0.233688			−0.0185912
$159$		−	1.62772i		−	0.129086i
$160$	5.84096			0.461769
$161$	−7.22316	−	23.0140i	−0.569265	−	1.81376i
$162$			0.792287i			0.0622479i
$163$	−18.2337			−1.42817			−0.714086	−	0.700058i	$-0.753158\pi$
$163$	−18.2337			−1.42817			−0.714086	+	0.700058i	$0.753158\pi$
$164$	16.0309			1.25180
$165$		−	3.31662i		−	0.258199i
$166$		−	7.48913i		−	0.581269i
$167$	2.87419			0.222412			0.111206	−	0.993797i	$-0.464529\pi$
$167$	2.87419			0.222412			0.111206	+	0.993797i	$0.464529\pi$
$168$	2.11684	+	6.74456i	0.163318	+	0.520354i
$169$	−13.0000			−1.00000
$170$	3.25544			0.249681
$171$	4.40387			0.336772
$172$		−	5.63858i		−	0.429938i
$173$	6.92820			0.526742			0.263371	−	0.964695i	$-0.415166\pi$
$173$	6.92820			0.526742			0.263371	+	0.964695i	$0.415166\pi$
$174$			4.74456i			0.359684i
$175$	0.792287	+	2.52434i	0.0598913	+	0.190822i
$176$		−	2.08191i		−	0.156930i
$177$	1.62772			0.122347
$178$	−6.63325			−0.497183
$179$	−21.4891			−1.60617			−0.803086	−	0.595863i	$-0.796810\pi$
$179$	−21.4891			−1.60617			−0.803086	+	0.595863i	$0.796810\pi$
$180$			1.37228i			0.102284i
$181$		−	16.7446i		−	1.24461i	−0.782773	−	0.622307i	$-0.786196\pi$
$181$		−	16.7446i		−	1.24461i	0.782773	−	0.622307i	$-0.213804\pi$
$182$		0			0
$183$		−	11.0371i		−	0.815887i
$184$			24.3585i			1.79573i
$185$		−	10.7446i		−	0.789956i
$186$		−	5.34363i		−	0.391814i
$187$		−	13.6277i		−	0.996557i
$188$		−	17.4891i		−	1.27553i
$189$	−2.52434	+	0.792287i	−0.183619	+	0.0576304i
$190$	−3.48913			−0.253128
$191$	−8.74456			−0.632734			−0.316367	−	0.948637i	$-0.602463\pi$
$191$	−8.74456			−0.632734			−0.316367	+	0.948637i	$0.602463\pi$
$192$		−	3.37228i		−	0.243373i
$193$			4.75372i			0.342180i	0.985255	+	0.171090i	$0.0547290\pi$
$193$			4.75372i			0.342180i	−0.985255	+	0.171090i	$0.945271\pi$
$194$	6.63325			0.476240
$195$		0			0
$196$	−7.88316	+	5.48913i	−0.563083	+	0.392080i
$197$			3.16915i			0.225792i	0.993607	+	0.112896i	$0.0360128\pi$
$197$			3.16915i			0.225792i	−0.993607	+	0.112896i	$0.963987\pi$
$198$	−2.62772			−0.186744
$199$			6.74456i			0.478109i	0.971006	+	0.239055i	$0.0768375\pi$
$199$			6.74456i			0.478109i	−0.971006	+	0.239055i	$0.923162\pi$
$200$		−	2.67181i		−	0.188926i
$201$		−	4.74456i		−	0.334656i
$202$		−	8.23369i		−	0.579320i
$203$	−15.1168	+	4.74456i	−1.06099	+	0.333003i
$204$			5.63858i			0.394780i
$205$		−	11.6819i		−	0.815901i
$206$	−8.80773			−0.613664
$207$	−9.11684			−0.633664
$208$		0			0
$209$			14.6060i			1.01032i
$210$	2.00000	−	0.627719i	0.138013	−	0.0433167i
$211$		−	3.46410i		−	0.238479i	−0.992866	−	0.119239i	$-0.961954\pi$
$211$		−	3.46410i		−	0.238479i	0.992866	−	0.119239i	$-0.0380456\pi$
$212$	−2.23369			−0.153410
$213$			3.25544i			0.223059i
$214$	−3.76631			−0.257460
$215$	−4.10891			−0.280225
$216$	2.67181			0.181794
$217$	17.0256	−	5.34363i	1.15577	−	0.362749i
$218$	−1.48913			−0.100856
$219$			6.92820i			0.468165i
$220$	−4.55134			−0.306851
$221$		0			0
$222$	−8.51278			−0.571340
$223$		−	14.3723i		−	0.962439i	−0.876600	−	0.481220i	$-0.840194\pi$
$223$		−	14.3723i		−	0.962439i	0.876600	−	0.481220i	$-0.159806\pi$
$224$	14.7446	−	4.62772i	0.985163	−	0.309202i
$225$	1.00000			0.0666667
$226$		−	1.28962i		−	0.0857843i
$227$	24.5986			1.63266			0.816332	−	0.577583i	$-0.196004\pi$
$227$	24.5986			1.63266			0.816332	+	0.577583i	$0.196004\pi$
$228$		−	6.04334i		−	0.400230i
$229$			11.2554i			0.743780i	0.928277	+	0.371890i	$0.121290\pi$
$229$			11.2554i			0.743780i	−0.928277	+	0.371890i	$0.878710\pi$
$230$	7.22316			0.476281
$231$	−2.62772	−	8.37228i	−0.172891	−	0.550856i
$232$	16.0000			1.05045
$233$			16.4356i			1.07674i	0.842710	+	0.538368i	$0.180959\pi$
$233$			16.4356i			1.07674i	−0.842710	+	0.538368i	$0.819041\pi$
$234$		0			0
$235$	−12.7446			−0.831364
$236$		−	2.23369i		−	0.145401i
$237$	−0.294954			−0.0191593
$238$	8.21782	−	2.57924i	0.532682	−	0.167187i
$239$		−	20.8395i		−	1.34800i	−0.738733	−	0.673998i	$-0.764576\pi$
$239$		−	20.8395i		−	1.34800i	0.738733	−	0.673998i	$-0.235424\pi$
$240$	0.627719			0.0405191
$241$	−13.8564			−0.892570			−0.446285	−	0.894891i	$-0.647253\pi$
$241$	−13.8564			−0.892570			−0.446285	+	0.894891i	$0.647253\pi$
$242$		−	8.71516i		−	0.560232i
$243$			1.00000i			0.0641500i
$244$	−15.1460			−0.969625
$245$	4.00000	+	5.74456i	0.255551	+	0.367007i
$246$	−9.25544			−0.590105
$247$		0			0
$248$	−18.0202			−1.14429
$249$		−	9.45254i		−	0.599030i
$250$	−0.792287			−0.0501086
$251$		−	17.4891i		−	1.10390i	−0.833876	−	0.551952i	$-0.813883\pi$
$251$		−	17.4891i		−	1.10390i	0.833876	−	0.551952i	$-0.186117\pi$
$252$	1.08724	+	3.46410i	0.0684897	+	0.218218i
$253$		−	30.2372i		−	1.90099i
$254$	−7.72281			−0.484572
$255$	4.10891			0.257310
$256$	−13.8832			−0.867697
$257$		−	24.2337i		−	1.51166i	−0.654770	−	0.755828i	$-0.727235\pi$
$257$		−	24.2337i		−	1.51166i	0.654770	−	0.755828i	$-0.272765\pi$
$258$			3.25544i			0.202675i
$259$	−8.51278	−	27.1229i	−0.528958	−	1.68534i
$260$		0			0
$261$			5.98844i			0.370675i
$262$		−	1.02175i		−	0.0631239i
$263$			16.7306i			1.03165i	0.856693	+	0.515827i	$0.172515\pi$
$263$			16.7306i			1.03165i	−0.856693	+	0.515827i	$0.827485\pi$
$264$			8.86141i			0.545382i
$265$			1.62772i			0.0999900i
$266$	−8.80773	+	2.76439i	−0.540037	+	0.169496i
$267$	−8.37228			−0.512375
$268$	−6.51087			−0.397715
$269$			19.6277i			1.19672i	0.801226	+	0.598362i	$0.204181\pi$
$269$			19.6277i			1.19672i	−0.801226	+	0.598362i	$0.795819\pi$
$270$		−	0.792287i		−	0.0482171i
$271$	−2.52434			−0.153343			−0.0766713	−	0.997056i	$-0.524429\pi$
$271$	−2.52434			−0.153343			−0.0766713	+	0.997056i	$0.524429\pi$
$272$	2.57924			0.156389
$273$		0			0
$274$			10.0974i			0.610003i
$275$			3.31662i			0.200000i
$276$			12.5109i			0.753066i
$277$			22.3692i			1.34403i	0.740536	+	0.672017i	$0.234572\pi$
$277$			22.3692i			1.34403i	−0.740536	+	0.672017i	$0.765428\pi$
$278$			2.74456i			0.164608i
$279$		−	6.74456i		−	0.403786i
$280$	−2.11684	−	6.74456i	−0.126506	−	0.403065i
$281$			0.589907i			0.0351909i	0.999845	+	0.0175955i	$0.00560110\pi$
$281$			0.589907i			0.0351909i	−0.999845	+	0.0175955i	$0.994399\pi$
$282$			10.0974i			0.601289i
$283$	−2.17448			−0.129259			−0.0646297	−	0.997909i	$-0.520587\pi$
$283$	−2.17448			−0.129259			−0.0646297	+	0.997909i	$0.520587\pi$
$284$	4.46738			0.265090
$285$	−4.40387			−0.260862
$286$		0			0
$287$	−9.25544	−	29.4891i	−0.546331	−	1.74069i
$288$		−	5.84096i		−	0.344182i
$289$	−0.116844			−0.00687317
$290$		−	4.74456i		−	0.278610i
$291$	8.37228			0.490792
$292$	9.50744			0.556381
$293$	21.7244			1.26915			0.634576	−	0.772861i	$-0.281175\pi$
$293$	21.7244			1.26915			0.634576	+	0.772861i	$0.281175\pi$
$294$	4.55134	−	3.16915i	0.265440	−	0.184828i
$295$	−1.62772			−0.0947694
$296$			28.7075i			1.66859i
$297$	−3.31662			−0.192450
$298$	−10.9783			−0.635953
$299$		0			0
$300$		−	1.37228i		−	0.0792287i
$301$	−10.3723	+	3.25544i	−0.597848	+	0.187640i
$302$	−6.74456			−0.388106
$303$		−	10.3923i		−	0.597022i
$304$	−2.76439			−0.158549
$305$			11.0371i			0.631983i
$306$		−	3.25544i		−	0.186101i
$307$	−15.4410			−0.881263			−0.440632	−	0.897688i	$-0.645245\pi$
$307$	−15.4410			−0.881263			−0.440632	+	0.897688i	$0.645245\pi$
$308$	−11.4891	+	3.60597i	−0.654654	+	0.205469i
$309$	−11.1168			−0.632415
$310$			5.34363i			0.303498i
$311$		−	16.0000i		−	0.907277i	−0.891186	−	0.453638i	$-0.850126\pi$
$311$		−	16.0000i		−	0.907277i	0.891186	−	0.453638i	$-0.149874\pi$
$312$		0			0
$313$			21.8614i			1.23568i	0.786304	+	0.617840i	$0.211992\pi$
$313$			21.8614i			1.23568i	−0.786304	+	0.617840i	$0.788008\pi$
$314$	2.28429			0.128910
$315$	2.52434	−	0.792287i	0.142230	−	0.0446403i
$316$			0.404759i			0.0227695i
$317$	−24.7446			−1.38979			−0.694897	−	0.719110i	$-0.744550\pi$
$317$	−24.7446			−1.38979			−0.694897	+	0.719110i	$0.744550\pi$
$318$	1.28962			0.0723183
$319$	−19.8614			−1.11203
$320$			3.37228i			0.188516i
$321$	−4.75372			−0.265327
$322$	18.2337	−	5.72281i	1.01612	−	0.318920i
$323$	−18.0951			−1.00684
$324$	1.37228			0.0762379
$325$		0			0
$326$		−	14.4463i		−	0.800107i
$327$	−1.87953			−0.103938
$328$			31.2119i			1.72339i
$329$	−32.1716	+	10.0974i	−1.77368	+	0.556685i
$330$	2.62772			0.144651
$331$	−9.62772			−0.529187			−0.264594	−	0.964360i	$-0.585238\pi$
$331$	−9.62772			−0.529187			−0.264594	+	0.964360i	$0.585238\pi$
$332$	−12.9715			−0.711906
$333$	−10.7446			−0.588798
$334$			2.27719i			0.124602i
$335$			4.74456i			0.259223i
$336$	1.58457	−	0.497333i	0.0864456	−	0.0271318i
$337$		−	13.9113i		−	0.757797i	−0.925438	−	0.378899i	$-0.876303\pi$
$337$		−	13.9113i		−	0.757797i	0.925438	−	0.378899i	$-0.123697\pi$
$338$		−	10.2997i		−	0.560232i
$339$		−	1.62772i		−	0.0884055i
$340$		−	5.63858i		−	0.305795i
$341$	22.3692			1.21136
$342$			3.48913i			0.188670i
$343$	14.6487	+	11.3321i	0.790955	+	0.611874i
$344$	10.9783			0.591908
$345$	9.11684			0.490834
$346$			5.48913i			0.295097i
$347$		−	24.2487i		−	1.30174i	−0.759190	−	0.650870i	$-0.774404\pi$
$347$		−	24.2487i		−	1.30174i	0.759190	−	0.650870i	$-0.225596\pi$
$348$	8.21782			0.440522
$349$	12.3267			0.659835			0.329918	−	0.944010i	$-0.392979\pi$
$349$	12.3267			0.659835			0.329918	+	0.944010i	$0.392979\pi$
$350$	−2.00000	+	0.627719i	−0.106904	+	0.0335530i
$351$		0			0
$352$	19.3723			1.03255
$353$			17.2554i			0.918414i	0.888329	+	0.459207i	$0.151866\pi$
$353$			17.2554i			0.918414i	−0.888329	+	0.459207i	$0.848134\pi$
$354$			1.28962i			0.0685425i
$355$		−	3.25544i		−	0.172781i
$356$			11.4891i			0.608922i
$357$	10.3723	−	3.25544i	0.548959	−	0.172296i
$358$		−	17.0256i		−	0.899829i
$359$		−	13.9113i		−	0.734211i	−0.930179	−	0.367105i	$-0.880349\pi$
$359$		−	13.9113i		−	0.734211i	0.930179	−	0.367105i	$-0.119651\pi$
$360$	−2.67181			−0.140817
$361$	0.394031			0.0207385
$362$	13.2665			0.697272
$363$		−	11.0000i		−	0.577350i
$364$		0			0
$365$		−	6.92820i		−	0.362639i
$366$	8.74456			0.457086
$367$		−	11.1168i		−	0.580295i	−0.956982	−	0.290147i	$-0.906296\pi$
$367$		−	11.1168i		−	0.580295i	0.956982	−	0.290147i	$-0.0937043\pi$
$368$	5.72281			0.298322
$369$	−11.6819			−0.608137
$370$	8.51278			0.442558
$371$	1.28962	+	4.10891i	0.0669538	+	0.213324i
$372$	−9.25544			−0.479872
$373$			28.3576i			1.46830i	0.678986	+	0.734151i	$0.262420\pi$
$373$			28.3576i			1.46830i	−0.678986	+	0.734151i	$0.737580\pi$
$374$	10.7971			0.558303
$375$	−1.00000			−0.0516398
$376$	34.0511			1.75605
$377$		0			0
$378$	−0.627719	−	2.00000i	−0.0322864	−	0.102869i
$379$	30.3723			1.56012			0.780060	−	0.625705i	$-0.215189\pi$
$379$	30.3723			1.56012			0.780060	+	0.625705i	$0.215189\pi$
$380$			6.04334i			0.310017i
$381$	−9.74749			−0.499379
$382$		−	6.92820i		−	0.354478i
$383$			30.2337i			1.54487i	0.635094	+	0.772435i	$0.280961\pi$
$383$			30.2337i			1.54487i	−0.635094	+	0.772435i	$0.719039\pi$
$384$	−9.01011			−0.459795
$385$	2.62772	+	8.37228i	0.133921	+	0.426691i
$386$	−3.76631			−0.191700
$387$			4.10891i			0.208868i
$388$		−	11.4891i		−	0.583272i
$389$	−2.00000			−0.101404			−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000			−0.101404			−0.0507020	+	0.998714i	$0.516146\pi$
$390$		0			0
$391$	37.4603			1.89445
$392$	−10.6873	−	15.3484i	−0.539788	−	0.775212i
$393$		−	1.28962i		−	0.0650527i
$394$	−2.51087			−0.126496
$395$	0.294954			0.0148407
$396$			4.55134i			0.228714i
$397$		−	27.4891i		−	1.37964i	−0.723981	−	0.689820i	$-0.757690\pi$
$397$		−	27.4891i		−	1.37964i	0.723981	−	0.689820i	$-0.242310\pi$
$398$	−5.34363			−0.267852
$399$	−11.1168	+	3.48913i	−0.556538	+	0.174675i
$400$	−0.627719			−0.0313859
$401$	29.7228			1.48429			0.742143	−	0.670241i	$-0.233809\pi$
$401$	29.7228			1.48429			0.742143	+	0.670241i	$0.233809\pi$
$402$	3.75906			0.187485
$403$		0			0
$404$	−14.2612			−0.709520
$405$		−	1.00000i		−	0.0496904i
$406$	−3.75906	−	11.9769i	−0.186559	−	0.594403i
$407$		−	35.6357i		−	1.76640i
$408$	−10.9783			−0.543504
$409$	34.6410			1.71289			0.856444	−	0.516240i	$-0.172669\pi$
$409$	34.6410			1.71289			0.856444	+	0.516240i	$0.172669\pi$
$410$	9.25544			0.457093
$411$			12.7446i			0.628643i
$412$			15.2554i			0.751581i
$413$	−4.10891	+	1.28962i	−0.202186	+	0.0634581i
$414$		−	7.22316i		−	0.354999i
$415$			9.45254i			0.464007i
$416$		0			0
$417$			3.46410i			0.169638i
$418$	−11.5721			−0.566011
$419$		−	10.3723i		−	0.506719i	−0.967372	−	0.253360i	$-0.918464\pi$
$419$		−	10.3723i		−	0.506719i	0.967372	−	0.253360i	$-0.0815356\pi$
$420$	−1.08724	−	3.46410i	−0.0530519	−	0.169031i
$421$	−9.86141			−0.480616			−0.240308	−	0.970697i	$-0.577248\pi$
$421$	−9.86141			−0.480616			−0.240308	+	0.970697i	$0.577248\pi$
$422$	2.74456			0.133603
$423$			12.7446i			0.619662i
$424$		−	4.34896i		−	0.211204i
$425$	−4.10891			−0.199311
$426$	−2.57924			−0.124965
$427$	8.74456	+	27.8614i	0.423179	+	1.34831i
$428$			6.52344i			0.315323i
$429$		0			0
$430$		−	3.25544i		−	0.156991i
$431$			12.9715i			0.624817i	0.949948	+	0.312409i	$0.101136\pi$
$431$			12.9715i			0.624817i	−0.949948	+	0.312409i	$0.898864\pi$
$432$		−	0.627719i		−	0.0302011i
$433$			12.9783i			0.623695i	0.950132	+	0.311847i	$0.100948\pi$
$433$			12.9783i			0.623695i	−0.950132	+	0.311847i	$0.899052\pi$
$434$	4.23369	+	13.4891i	0.203224	+	0.647499i
$435$		−	5.98844i		−	0.287124i
$436$			2.57924i			0.123523i
$437$	−40.1494			−1.92060
$438$	−5.48913			−0.262281
$439$	−30.9369			−1.47654			−0.738268	−	0.674508i	$-0.764356\pi$
$439$	−30.9369			−1.47654			−0.738268	+	0.674508i	$0.764356\pi$
$440$		−	8.86141i		−	0.422451i
$441$	5.74456	−	4.00000i	0.273551	−	0.190476i
$442$		0			0
$443$	0.233688			0.0111028			0.00555142	−	0.999985i	$-0.498233\pi$
$443$	0.233688			0.0111028			0.00555142	+	0.999985i	$0.498233\pi$
$444$			14.7446i			0.699746i
$445$	8.37228			0.396884
$446$	11.3870			0.539189
$447$	−13.8564			−0.655386
$448$	2.67181	+	8.51278i	0.126231	+	0.402191i
$449$	25.7228			1.21393			0.606967	−	0.794727i	$-0.292386\pi$
$449$	25.7228			1.21393			0.606967	+	0.794727i	$0.292386\pi$
$450$			0.792287i			0.0373488i
$451$		−	38.7446i		−	1.82441i
$452$	−2.23369			−0.105064
$453$	−8.51278			−0.399965
$454$			19.4891i			0.914670i
$455$		0			0
$456$	11.7663			0.551008
$457$			31.5268i			1.47476i	0.675478	+	0.737380i	$0.263937\pi$
$457$			31.5268i			1.47476i	−0.675478	+	0.737380i	$0.736063\pi$
$458$	−8.91754			−0.416689
$459$		−	4.10891i		−	0.191788i
$460$		−	12.5109i		−	0.583323i
$461$	16.7306			0.779222			0.389611	−	0.920980i	$-0.372610\pi$
$461$	16.7306			0.779222			0.389611	+	0.920980i	$0.372610\pi$
$462$	6.63325	−	2.08191i	0.308607	−	0.0968591i
$463$	−2.51087			−0.116690			−0.0583451	−	0.998296i	$-0.518582\pi$
$463$	−2.51087			−0.116690			−0.0583451	+	0.998296i	$0.518582\pi$
$464$		−	3.75906i		−	0.174510i
$465$			6.74456i			0.312772i
$466$	−13.0217			−0.603221
$467$			6.97825i			0.322915i	0.986880	+	0.161457i	$0.0516195\pi$
$467$			6.97825i			0.322915i	−0.986880	+	0.161457i	$0.948381\pi$
$468$		0			0
$469$	3.75906	+	11.9769i	0.173577	+	0.553041i
$470$		−	10.0974i		−	0.465756i
$471$	2.88316			0.132849
$472$	4.34896			0.200177
$473$	−13.6277			−0.626603
$474$		−	0.233688i		−	0.0107336i
$475$	4.40387			0.202063
$476$	−4.46738	−	14.2337i	−0.204762	−	0.652400i
$477$	1.62772			0.0745281
$478$	16.5109			0.755190
$479$	−34.0511			−1.55583			−0.777917	−	0.628367i	$-0.783724\pi$
$479$	−34.0511			−1.55583			−0.777917	+	0.628367i	$0.783724\pi$
$480$			5.84096i			0.266602i
$481$		0			0
$482$		−	10.9783i		−	0.500046i
$483$	23.0140	−	7.22316i	1.04717	−	0.328665i
$484$	−15.0951			−0.686141
$485$	−8.37228			−0.380166
$486$	−0.792287			−0.0359389
$487$	30.9783			1.40376			0.701879	−	0.712296i	$-0.252345\pi$
$487$	30.9783			1.40376			0.701879	+	0.712296i	$0.252345\pi$
$488$		−	29.4891i		−	1.33491i
$489$		−	18.2337i		−	0.824556i
$490$	−4.55134	+	3.16915i	−0.205609	+	0.143168i
$491$			3.81396i			0.172122i	0.996290	+	0.0860608i	$0.0274279\pi$
$491$			3.81396i			0.172122i	−0.996290	+	0.0860608i	$0.972572\pi$
$492$			16.0309i			0.722728i
$493$		−	24.6060i		−	1.10820i
$494$		0			0
$495$	3.31662			0.149071
$496$			4.23369i			0.190098i
$497$	−2.57924	−	8.21782i	−0.115695	−	0.368620i
$498$	7.48913			0.335596
$499$	17.3505			0.776716			0.388358	−	0.921508i	$-0.373042\pi$
$499$	17.3505			0.776716			0.388358	+	0.921508i	$0.373042\pi$
$500$			1.37228i			0.0613703i
$501$			2.87419i			0.128410i
$502$	13.8564			0.618442
$503$	5.69349			0.253860			0.126930	−	0.991912i	$-0.459488\pi$
$503$	5.69349			0.253860			0.126930	+	0.991912i	$0.459488\pi$
$504$	−6.74456	+	2.11684i	−0.300427	+	0.0942917i
$505$			10.3923i			0.462451i
$506$	23.9565			1.06500
$507$		−	13.0000i		−	0.577350i
$508$			13.3763i			0.593478i
$509$			16.3723i			0.725689i	0.931850	+	0.362844i	$0.118194\pi$
$509$			16.3723i			0.725689i	−0.931850	+	0.362844i	$0.881806\pi$
$510$			3.25544i			0.144153i
$511$	−5.48913	−	17.4891i	−0.242825	−	0.773673i
$512$			7.02078i			0.310277i
$513$			4.40387i			0.194435i
$514$	19.2000			0.846877
$515$	11.1168			0.489867
$516$	5.63858			0.248225
$517$	−42.2689			−1.85899
$518$	21.4891	−	6.74456i	0.944178	−	0.296339i
$519$			6.92820i			0.304114i
$520$		0			0
$521$			28.3723i			1.24301i	0.783409	+	0.621506i	$0.213479\pi$
$521$			28.3723i			1.24301i	−0.783409	+	0.621506i	$0.786521\pi$
$522$	−4.74456			−0.207664
$523$	10.3923			0.454424			0.227212	−	0.973845i	$-0.427039\pi$
$523$	10.3923			0.454424			0.227212	+	0.973845i	$0.427039\pi$
$524$	−1.76972			−0.0773107
$525$	−2.52434	+	0.792287i	−0.110171	+	0.0345782i
$526$	−13.2554			−0.577965
$527$			27.7128i			1.20719i
$528$	2.08191			0.0906034
$529$	60.1168			2.61378
$530$	−1.28962			−0.0560175
$531$			1.62772i			0.0706370i
$532$	4.78806	+	15.2554i	0.207589	+	0.661407i
$533$		0			0
$534$		−	6.63325i		−	0.287049i
$535$	4.75372			0.205521
$536$		−	12.6766i		−	0.547545i
$537$		−	21.4891i		−	0.927324i
$538$	−15.5508			−0.670442
$539$	13.2665	+	19.0526i	0.571429	+	0.820652i
$540$	−1.37228			−0.0590536
$541$			30.2921i			1.30236i	0.758925	+	0.651179i	$0.225725\pi$
$541$			30.2921i			1.30236i	−0.758925	+	0.651179i	$0.774275\pi$
$542$		−	2.00000i		−	0.0859074i
$543$	16.7446			0.718578
$544$			24.0000i			1.02899i
$545$	1.87953			0.0805101
$546$		0			0
$547$			5.39853i			0.230825i	0.993318	+	0.115412i	$0.0368189\pi$
$547$			5.39853i			0.230825i	−0.993318	+	0.115412i	$0.963181\pi$
$548$	17.4891			0.747098
$549$	11.0371			0.471053
$550$	−2.62772			−0.112046
$551$			26.3723i			1.12350i
$552$	−24.3585			−1.03677
$553$	0.744563	−	0.233688i	0.0316620	−	0.00993742i
$554$	−17.7228			−0.752970
$555$	10.7446			0.456081
$556$	4.75372			0.201603
$557$			19.6048i			0.830682i	0.909666	+	0.415341i	$0.136338\pi$
$557$			19.6048i			0.830682i	−0.909666	+	0.415341i	$0.863662\pi$
$558$	5.34363			0.226214
$559$		0			0
$560$	−1.58457	+	0.497333i	−0.0669605	+	0.0210162i
$561$	13.6277			0.575363
$562$	−0.467376			−0.0197151
$563$	−44.4434			−1.87307			−0.936533	−	0.350579i	$-0.885985\pi$
$563$	−44.4434			−1.87307			−0.936533	+	0.350579i	$0.885985\pi$
$564$	17.4891			0.736425
$565$			1.62772i			0.0684786i
$566$		−	1.72281i		−	0.0724152i
$567$	−0.792287	−	2.52434i	−0.0332729	−	0.106012i
$568$			8.69793i			0.364957i
$569$			31.2318i			1.30931i	0.755930	+	0.654653i	$0.227185\pi$
$569$			31.2318i			1.30931i	−0.755930	+	0.654653i	$0.772815\pi$
$570$		−	3.48913i		−	0.146143i
$571$		−	10.3923i		−	0.434904i	−0.976071	−	0.217452i	$-0.930225\pi$
$571$		−	10.3923i		−	0.434904i	0.976071	−	0.217452i	$-0.0697746\pi$
$572$		0			0
$573$		−	8.74456i		−	0.365309i
$574$	23.3639	−	7.33296i	0.975188	−	0.306072i
$575$	−9.11684			−0.380199
$576$	3.37228			0.140512
$577$		−	26.4674i		−	1.10185i	−0.834554	−	0.550926i	$-0.814275\pi$
$577$		−	26.4674i		−	1.10185i	0.834554	−	0.550926i	$-0.185725\pi$
$578$		−	0.0925740i		−	0.00385057i
$579$	−4.75372			−0.197558
$580$	−8.21782			−0.341227
$581$	7.48913	+	23.8614i	0.310701	+	0.989938i
$582$			6.63325i			0.274957i
$583$			5.39853i			0.223584i
$584$			18.5109i			0.765985i
$585$		0			0
$586$			17.2119i			0.711019i
$587$		−	4.00000i		−	0.165098i	−0.996587	−	0.0825488i	$-0.973694\pi$
$587$		−	4.00000i		−	0.165098i	0.996587	−	0.0825488i	$-0.0263060\pi$
$588$	−5.48913	−	7.88316i	−0.226368	−	0.325096i
$589$		−	29.7021i		−	1.22386i
$590$		−	1.28962i		−	0.0530928i
$591$	−3.16915			−0.130361
$592$	6.74456			0.277200
$593$	12.6766			0.520565			0.260283	−	0.965532i	$-0.416184\pi$
$593$	12.6766			0.520565			0.260283	+	0.965532i	$0.416184\pi$
$594$		−	2.62772i		−	0.107817i
$595$	−10.3723	+	3.25544i	−0.425222	+	0.133460i
$596$			19.0149i			0.778880i
$597$	−6.74456			−0.276037
$598$		0			0
$599$	−43.7228			−1.78647			−0.893233	−	0.449594i	$-0.851569\pi$
$599$	−43.7228			−1.78647			−0.893233	+	0.449594i	$0.851569\pi$
$600$	2.67181			0.109076
$601$	−19.8448			−0.809488			−0.404744	−	0.914430i	$-0.632639\pi$
$601$	−19.8448			−0.809488			−0.404744	+	0.914430i	$0.632639\pi$
$602$	−2.57924	−	8.21782i	−0.105122	−	0.334933i
$603$	4.74456			0.193214
$604$			11.6819i			0.475331i
$605$			11.0000i			0.447214i
$606$	8.23369			0.334471
$607$	−33.7562			−1.37012			−0.685060	−	0.728487i	$-0.740224\pi$
$607$	−33.7562			−1.37012			−0.685060	+	0.728487i	$0.740224\pi$
$608$		−	25.7228i		−	1.04320i
$609$	−4.74456	−	15.1168i	−0.192259	−	0.612565i
$610$	−8.74456			−0.354057
$611$		0			0
$612$	−5.63858			−0.227926
$613$		−	25.5383i		−	1.03148i	−0.856744	−	0.515742i	$-0.827516\pi$
$613$		−	25.5383i		−	1.03148i	0.856744	−	0.515742i	$-0.172484\pi$
$614$		−	12.2337i		−	0.493711i
$615$	11.6819			0.471061
$616$	−7.02078	−	22.3692i	−0.282875	−	0.901280i
$617$	3.25544			0.131059			0.0655295	−	0.997851i	$-0.479126\pi$
$617$	3.25544			0.131059			0.0655295	+	0.997851i	$0.479126\pi$
$618$		−	8.80773i		−	0.354299i
$619$			3.48913i			0.140240i	0.997539	+	0.0701199i	$0.0223382\pi$
$619$			3.48913i			0.140240i	−0.997539	+	0.0701199i	$0.977662\pi$
$620$	9.25544			0.371707
$621$		−	9.11684i		−	0.365846i
$622$	12.6766			0.508285
$623$	21.1345	−	6.63325i	0.846735	−	0.265756i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−17.3205			−0.692267
$627$	−14.6060			−0.583306
$628$		−	3.95650i		−	0.157882i
$629$	44.1485			1.76031
$630$	0.627719	+	2.00000i	0.0250089	+	0.0796819i
$631$	−16.6060			−0.661073			−0.330537	−	0.943793i	$-0.607230\pi$
$631$	−16.6060			−0.661073			−0.330537	+	0.943793i	$0.607230\pi$
$632$	−0.788061			−0.0313474
$633$	3.46410			0.137686
$634$		−	19.6048i		−	0.778606i
$635$	9.74749			0.386818
$636$		−	2.23369i		−	0.0885715i
$637$		0			0
$638$		−	15.7359i		−	0.622992i
$639$	−3.25544			−0.128783
$640$	9.01011			0.356156
$641$	33.2554			1.31351			0.656755	−	0.754104i	$-0.271928\pi$
$641$	33.2554			1.31351			0.656755	+	0.754104i	$0.271928\pi$
$642$		−	3.76631i		−	0.148644i
$643$		−	6.37228i		−	0.251298i	−0.992075	−	0.125649i	$-0.959899\pi$
$643$		−	6.37228i		−	0.251298i	0.992075	−	0.125649i	$-0.0401014\pi$
$644$	−9.91220	−	31.5817i	−0.390596	−	1.24449i
$645$		−	4.10891i		−	0.161788i
$646$		−	14.3365i		−	0.564062i
$647$			38.2337i			1.50312i	0.659664	+	0.751561i	$0.270699\pi$
$647$			38.2337i			1.50312i	−0.659664	+	0.751561i	$0.729301\pi$
$648$			2.67181i			0.104959i
$649$	−5.39853			−0.211911
$650$		0			0
$651$	5.34363	+	17.0256i	0.209433	+	0.667284i
$652$	−25.0217			−0.979927
$653$	13.3505			0.522447			0.261223	−	0.965278i	$-0.415874\pi$
$653$	13.3505			0.522447			0.261223	+	0.965278i	$0.415874\pi$
$654$		−	1.48913i		−	0.0582294i
$655$			1.28962i			0.0503896i
$656$	7.33296			0.286304
$657$	−6.92820			−0.270295
$658$	−8.00000	−	25.4891i	−0.311872	−	0.993670i
$659$			23.3089i			0.907988i	0.891005	+	0.453994i	$0.150001\pi$
$659$			23.3089i			0.907988i	−0.891005	+	0.453994i	$0.849999\pi$
$660$		−	4.55134i		−	0.177161i
$661$			14.2337i			0.553626i	0.960924	+	0.276813i	$0.0892783\pi$
$661$			14.2337i			0.553626i	−0.960924	+	0.276813i	$0.910722\pi$
$662$		−	7.62792i		−	0.296467i
$663$		0			0
$664$		−	25.2554i		−	0.980101i
$665$	11.1168	−	3.48913i	0.431093	−	0.135302i
$666$		−	8.51278i		−	0.329863i
$667$		−	54.5957i		−	2.11395i
$668$	3.94420			0.152606
$669$	14.3723			0.555664
$670$	−3.75906			−0.145225
$671$			36.6060i			1.41316i
$672$	4.62772	+	14.7446i	0.178518	+	0.568784i
$673$		−	8.16292i		−	0.314657i	−0.987546	−	0.157329i	$-0.949712\pi$
$673$		−	8.16292i		−	0.314657i	0.987546	−	0.157329i	$-0.0502882\pi$
$674$	11.0217			0.424542
$675$			1.00000i			0.0384900i
$676$	−17.8397			−0.686141
$677$	48.8473			1.87735			0.938677	−	0.344799i	$-0.112053\pi$
$677$	48.8473			1.87735			0.938677	+	0.344799i	$0.112053\pi$
$678$	1.28962			0.0495276
$679$	−21.1345	+	6.63325i	−0.811066	+	0.254561i
$680$	10.9783			0.420997
$681$			24.5986i			0.942619i
$682$			17.7228i			0.678642i
$683$	2.74456			0.105018			0.0525089	−	0.998620i	$-0.483278\pi$
$683$	2.74456			0.105018			0.0525089	+	0.998620i	$0.483278\pi$
$684$	6.04334			0.231073
$685$		−	12.7446i		−	0.486945i
$686$	−8.97825	+	11.6060i	−0.342791	+	0.443118i
$687$	−11.2554			−0.429422
$688$		−	2.57924i		−	0.0983326i
$689$		0			0
$690$			7.22316i			0.274981i
$691$		−	42.4674i		−	1.61554i	−0.589501	−	0.807768i	$-0.700676\pi$
$691$		−	42.4674i		−	1.61554i	0.589501	−	0.807768i	$-0.299324\pi$
$692$	9.50744			0.361419
$693$	8.37228	−	2.62772i	0.318037	−	0.0998188i
$694$	19.2119			0.729275
$695$		−	3.46410i		−	0.131401i
$696$			16.0000i			0.606478i
$697$	48.0000			1.81813
$698$			9.76631i			0.369660i
$699$	−16.4356			−0.621653
$700$	1.08724	+	3.46410i	0.0410938	+	0.130931i
$701$		−	41.9191i		−	1.58326i	−0.611000	−	0.791631i	$-0.709232\pi$
$701$		−	41.9191i		−	1.58326i	0.611000	−	0.791631i	$-0.290768\pi$
$702$		0			0
$703$	−47.3176			−1.78462
$704$			11.1846i			0.421535i
$705$		−	12.7446i		−	0.479988i
$706$	−13.6713			−0.514525
$707$	8.23369	+	26.2337i	0.309660	+	0.986619i
$708$	2.23369			0.0839471
$709$	20.0951			0.754687			0.377344	−	0.926073i	$-0.376838\pi$
$709$	20.0951			0.754687			0.377344	+	0.926073i	$0.376838\pi$
$710$	2.57924			0.0967972
$711$		−	0.294954i		−	0.0110616i
$712$	−22.3692			−0.838321
$713$			61.4891i			2.30279i
$714$	2.57924	+	8.21782i	0.0965257	+	0.307544i
$715$		0			0
$716$	−29.4891			−1.10206
$717$	20.8395			0.778266
$718$	11.0217			0.411328
$719$		−	5.62772i		−	0.209878i	−0.994479	−	0.104939i	$-0.966535\pi$
$719$		−	5.62772i		−	0.209878i	0.994479	−	0.104939i	$-0.0334648\pi$
$720$			0.627719i			0.0233937i
$721$	28.0627	−	8.80773i	1.04511	−	0.328017i
$722$			0.312185i			0.0116183i
$723$		−	13.8564i		−	0.515325i
$724$		−	22.9783i		−	0.853980i
$725$			5.98844i			0.222405i
$726$	8.71516			0.323450
$727$			24.8832i			0.922865i	0.887175	+	0.461433i	$0.152664\pi$
$727$			24.8832i			0.922865i	−0.887175	+	0.461433i	$0.847336\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	5.48913			0.203162
$731$		−	16.8832i		−	0.624446i
$732$		−	15.1460i		−	0.559813i
$733$	0.699713			0.0258445			0.0129222	−	0.999917i	$-0.495887\pi$
$733$	0.699713			0.0258445			0.0129222	+	0.999917i	$0.495887\pi$
$734$	8.80773			0.325099
$735$	−5.74456	+	4.00000i	−0.211891	+	0.147542i
$736$			53.2511i			1.96286i
$737$			15.7359i			0.579641i
$738$		−	9.25544i		−	0.340697i
$739$			49.4921i			1.82060i	0.413954	+	0.910298i	$0.364148\pi$
$739$			49.4921i			1.82060i	−0.413954	+	0.910298i	$0.635852\pi$
$740$		−	14.7446i		−	0.542021i
$741$		0			0
$742$	−3.25544	+	1.02175i	−0.119511	+	0.0375096i
$743$		−	2.17448i		−	0.0797740i	−0.999204	−	0.0398870i	$-0.987300\pi$
$743$		−	2.17448i		−	0.0797740i	0.999204	−	0.0398870i	$-0.0126998\pi$
$744$		−	18.0202i		−	0.660653i
$745$	13.8564			0.507659
$746$	−22.4674			−0.822589
$747$	9.45254			0.345850
$748$		−	18.7011i		−	0.683779i
$749$	12.0000	−	3.76631i	0.438470	−	0.137618i
$750$		−	0.792287i		−	0.0289302i
$751$	−27.8614			−1.01668			−0.508339	−	0.861157i	$-0.669740\pi$
$751$	−27.8614			−1.01668			−0.508339	+	0.861157i	$0.669740\pi$
$752$		−	8.00000i		−	0.291730i
$753$	17.4891			0.637339
$754$		0			0
$755$	8.51278			0.309812
$756$	−3.46410	+	1.08724i	−0.125988	+	0.0395426i
$757$	44.9783			1.63476			0.817381	−	0.576097i	$-0.195425\pi$
$757$	44.9783			1.63476			0.817381	+	0.576097i	$0.195425\pi$
$758$			24.0636i			0.874028i
$759$	30.2372			1.09754
$760$	−11.7663			−0.426809
$761$	8.51278			0.308588			0.154294	−	0.988025i	$-0.450690\pi$
$761$	8.51278			0.308588			0.154294	+	0.988025i	$0.450690\pi$
$762$		−	7.72281i		−	0.279768i
$763$	4.74456	−	1.48913i	0.171765	−	0.0539100i
$764$	−12.0000			−0.434145
$765$			4.10891i			0.148558i
$766$	−23.9538			−0.865484
$767$		0			0
$768$		−	13.8832i		−	0.500965i
$769$	−45.0882			−1.62592			−0.812961	−	0.582317i	$-0.802146\pi$
$769$	−45.0882			−1.62592			−0.812961	+	0.582317i	$0.802146\pi$
$770$	−6.63325	+	2.08191i	−0.239046	+	0.0750267i
$771$	24.2337			0.872755
$772$			6.52344i			0.234784i
$773$			34.4674i			1.23971i	0.784718	+	0.619853i	$0.212808\pi$
$773$			34.4674i			1.23971i	−0.784718	+	0.619853i	$0.787192\pi$
$774$	−3.25544			−0.117014
$775$		−	6.74456i		−	0.242272i
$776$	22.3692			0.803007
$777$	27.1229	−	8.51278i	0.973029	−	0.305394i
$778$		−	1.58457i		−	0.0568097i
$779$	−51.4456			−1.84323
$780$		0			0
$781$		−	10.7971i		−	0.386349i
$782$			29.6793i			1.06133i
$783$	−5.98844			−0.214009
$784$	−3.60597	+	2.51087i	−0.128785	+	0.0896741i
$785$	−2.88316			−0.102904
$786$	1.02175			0.0364446
$787$	48.2025			1.71823			0.859116	−	0.511781i	$-0.171014\pi$
$787$	48.2025			1.71823			0.859116	+	0.511781i	$0.171014\pi$
$788$			4.34896i			0.154925i
$789$	−16.7306			−0.595625
$790$			0.233688i			0.00831424i
$791$	1.28962	+	4.10891i	0.0458536	+	0.146096i
$792$	−8.86141			−0.314876
$793$		0			0
$794$	21.7793			0.772918
$795$	−1.62772			−0.0577292
$796$			9.25544i			0.328050i
$797$			46.0000i			1.62940i	0.579880	+	0.814702i	$0.303099\pi$
$797$			46.0000i			1.62940i	−0.579880	+	0.814702i	$0.696901\pi$
$798$	−2.76439	−	8.80773i	−0.0978583	−	0.311790i
$799$		−	52.3663i		−	1.85259i
$800$		−	5.84096i		−	0.206509i
$801$		−	8.37228i		−	0.295820i
$802$			23.5490i			0.831544i
$803$		−	22.9783i		−	0.810885i
$804$		−	6.51087i		−	0.229621i
$805$	−23.0140	+	7.22316i	−0.811137	+	0.254583i
$806$		0			0
$807$	−19.6277			−0.690928
$808$		−	27.7663i		−	0.976815i
$809$		−	13.2665i		−	0.466425i	−0.972426	−	0.233213i	$-0.925076\pi$
$809$		−	13.2665i		−	0.466425i	0.972426	−	0.233213i	$-0.0749238\pi$
$810$	0.792287			0.0278381
$811$	6.63325			0.232925			0.116462	−	0.993195i	$-0.462845\pi$
$811$	6.63325			0.232925			0.116462	+	0.993195i	$0.462845\pi$
$812$	−20.7446	+	6.51087i	−0.727991	+	0.228487i
$813$		−	2.52434i		−	0.0885324i
$814$	28.2337			0.989590
$815$			18.2337i			0.638698i
$816$			2.57924i			0.0902915i
$817$			18.0951i			0.633067i
$818$			27.4456i			0.959614i
$819$		0			0
$820$		−	16.0309i		−	0.559823i
$821$		−	19.8448i		−	0.692590i	−0.938126	−	0.346295i	$-0.887440\pi$
$821$		−	19.8448i		−	0.692590i	0.938126	−	0.346295i	$-0.112560\pi$
$822$	−10.0974			−0.352186
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$	−29.7021			−1.03472
$825$	−3.31662			−0.115470
$826$	−1.02175	−	3.25544i	−0.0355512	−	0.113271i
$827$			5.34363i			0.185816i	0.995675	+	0.0929081i	$0.0296163\pi$
$827$			5.34363i			0.185816i	−0.995675	+	0.0929081i	$0.970384\pi$
$828$	−12.5109			−0.434783
$829$			1.48913i			0.0517195i	0.999666	+	0.0258597i	$0.00823233\pi$
$829$			1.48913i			0.0517195i	−0.999666	+	0.0258597i	$0.991768\pi$
$830$	−7.48913			−0.259951
$831$	−22.3692			−0.775978
$832$		0			0
$833$	−23.6039	+	16.4356i	−0.817827	+	0.569461i
$834$	−2.74456			−0.0950364
$835$		−	2.87419i		−	0.0994656i
$836$			20.0435i			0.693219i
$837$	6.74456			0.233126
$838$	8.21782			0.283880
$839$		−	11.1168i		−	0.383796i	−0.981415	−	0.191898i	$-0.938536\pi$
$839$		−	11.1168i		−	0.383796i	0.981415	−	0.191898i	$-0.0614643\pi$
$840$	6.74456	−	2.11684i	0.232710	−	0.0730381i
$841$	−6.86141			−0.236600
$842$		−	7.81306i		−	0.269256i
$843$	−0.589907			−0.0203175
$844$		−	4.75372i		−	0.163630i
$845$			13.0000i			0.447214i
$846$	−10.0974			−0.347154
$847$	8.71516	+	27.7677i	0.299456	+	0.954110i
$848$	−1.02175			−0.0350870
$849$		−	2.17448i		−	0.0746280i
$850$		−	3.25544i		−	0.111661i
$851$	97.9565			3.35791
$852$			4.46738i			0.153050i
$853$	−51.6666			−1.76903			−0.884515	−	0.466512i	$-0.845510\pi$
$853$	−51.6666			−1.76903			−0.884515	+	0.466512i	$0.845510\pi$
$854$	−22.0742	+	6.92820i	−0.755365	+	0.237078i
$855$		−	4.40387i		−	0.150609i
$856$	−12.7011			−0.434113
$857$	−20.7846			−0.709989			−0.354994	−	0.934868i	$-0.615517\pi$
$857$	−20.7846			−0.709989			−0.354994	+	0.934868i	$0.615517\pi$
$858$		0			0
$859$			9.72281i			0.331738i	0.986148	+	0.165869i	$0.0530429\pi$
$859$			9.72281i			0.331738i	−0.986148	+	0.165869i	$0.946957\pi$
$860$	−5.63858			−0.192274
$861$	29.4891	−	9.25544i	1.00499	−	0.315424i
$862$	−10.2772			−0.350042
$863$	−26.8832			−0.915113			−0.457557	−	0.889180i	$-0.651275\pi$
$863$	−26.8832			−0.915113			−0.457557	+	0.889180i	$0.651275\pi$
$864$	5.84096			0.198714
$865$		−	6.92820i		−	0.235566i
$866$	−10.2825			−0.349414
$867$		−	0.116844i		−	0.00396823i
$868$	23.3639	−	7.33296i	0.793021	−	0.248897i
$869$	0.978251			0.0331849
$870$	4.74456			0.160856
$871$		0			0
$872$	−5.02175			−0.170058
$873$			8.37228i			0.283359i
$874$		−	31.8098i		−	1.07598i
$875$	2.52434	−	0.792287i	0.0853382	−	0.0267842i
$876$			9.50744i			0.321227i
$877$		−	43.5036i		−	1.46901i	−0.678601	−	0.734507i	$-0.737414\pi$
$877$		−	43.5036i		−	1.46901i	0.678601	−	0.734507i	$-0.262586\pi$
$878$		−	24.5109i		−	0.827202i
$879$			21.7244i			0.732745i
$880$	−2.08191			−0.0701811
$881$		−	4.37228i		−	0.147306i	−0.997284	−	0.0736530i	$-0.976534\pi$
$881$		−	4.37228i		−	0.147306i	0.997284	−	0.0736530i	$-0.0234657\pi$
$882$	3.16915	+	4.55134i	0.106711	+	0.153252i
$883$	7.72281			0.259893			0.129947	−	0.991521i	$-0.458519\pi$
$883$	7.72281			0.259893			0.129947	+	0.991521i	$0.458519\pi$
$884$		0			0
$885$		−	1.62772i		−	0.0547152i
$886$			0.185148i			0.00622017i
$887$	−44.0936			−1.48052			−0.740258	−	0.672322i	$-0.765297\pi$
$887$	−44.0936			−1.48052			−0.740258	+	0.672322i	$0.765297\pi$
$888$	−28.7075			−0.963360
$889$	24.6060	−	7.72281i	0.825258	−	0.259015i
$890$			6.63325i			0.222347i
$891$		−	3.31662i		−	0.111111i
$892$		−	19.7228i		−	0.660369i
$893$			56.1253i			1.87816i
$894$		−	10.9783i		−	0.367168i
$895$			21.4891i			0.718302i
$896$	22.7446	−	7.13859i	0.759843	−	0.238484i
$897$		0			0
$898$			20.3799i			0.680084i
$899$	40.3894			1.34706
$900$	1.37228			0.0457427
$901$	−6.68815			−0.222815
$902$	30.6968			1.02209
$903$	−3.25544	−	10.3723i	−0.108334	−	0.345168i
$904$		−	4.34896i		−	0.144644i
$905$	−16.7446			−0.556608
$906$		−	6.74456i		−	0.224073i
$907$	−44.4674			−1.47651			−0.738257	−	0.674519i	$-0.764351\pi$
$907$	−44.4674			−1.47651			−0.738257	+	0.674519i	$0.764351\pi$
$908$	33.7562			1.12024
$909$	10.3923			0.344691
$910$		0			0
$911$	−24.7446			−0.819824			−0.409912	−	0.912125i	$-0.634441\pi$
$911$	−24.7446			−0.819824			−0.409912	+	0.912125i	$0.634441\pi$
$912$		−	2.76439i		−	0.0915381i
$913$			31.3505i			1.03755i
$914$	−24.9783			−0.826207
$915$	−11.0371			−0.364876
$916$			15.4456i			0.510338i
$917$	1.02175	+	3.25544i	0.0337411	+	0.107504i
$918$	3.25544			0.107445
$919$			23.0689i			0.760973i	0.924787	+	0.380486i	$0.124243\pi$
$919$			23.0689i			0.760973i	−0.924787	+	0.380486i	$0.875757\pi$
$920$	24.3585			0.803077
$921$		−	15.4410i		−	0.508798i
$922$			13.2554i			0.436545i
$923$		0			0
$924$	−3.60597	−	11.4891i	−0.118628	−	0.377964i
$925$	−10.7446			−0.353279
$926$		−	1.98933i		−	0.0653736i
$927$		−	11.1168i		−	0.365125i
$928$	34.9783			1.14822
$929$			36.5109i			1.19788i	0.800793	+	0.598941i	$0.204412\pi$
$929$			36.5109i			1.19788i	−0.800793	+	0.598941i	$0.795588\pi$
$930$	−5.34363			−0.175225
$931$	25.2983	−	17.6155i	0.829118	−	0.577323i
$932$			22.5543i			0.738792i
$933$	16.0000			0.523816
$934$	−5.52878			−0.180907
$935$	−13.6277			−0.445674
$936$		0			0
$937$	25.2434			0.824665			0.412333	−	0.911033i	$-0.364714\pi$
$937$	25.2434			0.824665			0.412333	+	0.911033i	$0.364714\pi$
$938$	−9.48913	+	2.97825i	−0.309831	+	0.0972433i
$939$	−21.8614			−0.713420
$940$	−17.4891			−0.570432
$941$	−46.3229			−1.51008			−0.755042	−	0.655676i	$-0.772384\pi$
$941$	−46.3229			−1.51008			−0.755042	+	0.655676i	$0.772384\pi$
$942$			2.28429i			0.0744261i
$943$	106.502			3.46819
$944$		−	1.02175i		−	0.0332551i
$945$	0.792287	+	2.52434i	0.0257731	+	0.0821167i
$946$		−	10.7971i		−	0.351043i
$947$	−3.35053			−0.108878			−0.0544388	−	0.998517i	$-0.517337\pi$
$947$	−3.35053			−0.108878			−0.0544388	+	0.998517i	$0.517337\pi$
$948$	−0.404759			−0.0131460
$949$		0			0
$950$			3.48913i			0.113202i
$951$		−	24.7446i		−	0.802397i
$952$	27.7128	−	8.69793i	0.898177	−	0.281901i
$953$		−	44.8482i		−	1.45277i	−0.687285	−	0.726387i	$-0.741198\pi$
$953$		−	44.8482i		−	1.45277i	0.687285	−	0.726387i	$-0.258802\pi$
$954$			1.28962i			0.0417530i
$955$			8.74456i			0.282967i
$956$		−	28.5977i		−	0.924915i
$957$		−	19.8614i		−	0.642028i
$958$		−	26.9783i		−	0.871628i
$959$	−10.0974	−	32.1716i	−0.326060	−	1.03887i
$960$	−3.37228			−0.108840
$961$	−14.4891			−0.467391
$962$		0			0
$963$		−	4.75372i		−	0.153187i
$964$	−19.0149			−0.612428
$965$	4.75372			0.153028
$966$	5.72281	+	18.2337i	0.184128	+	0.586659i
$967$			17.9653i			0.577726i	0.957370	+	0.288863i	$0.0932772\pi$
$967$			17.9653i			0.577726i	−0.957370	+	0.288863i	$0.906723\pi$
$968$		−	29.3900i		−	0.944629i
$969$		−	18.0951i		−	0.581298i
$970$		−	6.63325i		−	0.212981i
$971$		−	1.62772i		−	0.0522360i	−0.999659	−	0.0261180i	$-0.991685\pi$
$971$		−	1.62772i		−	0.0522360i	0.999659	−	0.0261180i	$-0.00831456\pi$
$972$			1.37228i			0.0440159i
$973$	−2.74456	−	8.74456i	−0.0879866	−	0.280338i
$974$			24.5437i			0.786430i
$975$		0			0
$976$	−6.92820			−0.221766
$977$	−30.0951			−0.962827			−0.481414	−	0.876494i	$-0.659877\pi$
$977$	−30.0951			−0.962827			−0.481414	+	0.876494i	$0.659877\pi$
$978$	14.4463			0.461942
$979$	27.7677			0.887460
$980$	5.48913	+	7.88316i	0.175344	+	0.251818i
$981$		−	1.87953i		−	0.0600087i
$982$	−3.02175			−0.0964279
$983$		−	28.4674i		−	0.907968i	−0.891010	−	0.453984i	$-0.850002\pi$
$983$		−	28.4674i		−	0.907968i	0.891010	−	0.453984i	$-0.149998\pi$
$984$	−31.2119			−0.995000
$985$	3.16915			0.100977
$986$	19.4950			0.620847
$987$	−10.0974	−	32.1716i	−0.321402	−	1.02403i
$988$		0			0
$989$		−	37.4603i		−	1.19117i
$990$			2.62772i			0.0835144i
$991$	−50.3723			−1.60013			−0.800064	−	0.599914i	$-0.795201\pi$
$991$	−50.3723			−1.60013			−0.800064	+	0.599914i	$0.795201\pi$
$992$	−39.3947			−1.25078
$993$		−	9.62772i		−	0.305526i
$994$	6.51087	−	2.04350i	0.206512	−	0.0648158i
$995$	6.74456			0.213817
$996$		−	12.9715i		−	0.411019i
$997$	−19.4950			−0.617413			−0.308706	−	0.951157i	$-0.599896\pi$
$997$	−19.4950			−0.617413			−0.308706	+	0.951157i	$0.599896\pi$
$998$			13.7466i			0.435141i
$999$		−	10.7446i		−	0.339943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.a.76.6	yes	8
7.6	odd	2	inner	1155.2.i.a.76.5	yes	8
11.10	odd	2	inner	1155.2.i.a.76.4	yes	8
77.76	even	2	inner	1155.2.i.a.76.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.a.76.3	✓	8	77.76	even	2	inner
1155.2.i.a.76.4	yes	8	11.10	odd	2	inner
1155.2.i.a.76.5	yes	8	7.6	odd	2	inner
1155.2.i.a.76.6	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.792287i q^{2} +1.00000i q^{3} +1.37228 q^{4} -1.00000i q^{5} -0.792287 q^{6} +(-0.792287 - 2.52434i) q^{7} +2.67181i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.792287i q^{2} +1.00000i q^{3} +1.37228 q^{4} -1.00000i q^{5} -0.792287 q^{6} +(-0.792287 - 2.52434i) q^{7} +2.67181i q^{8} -1.00000 q^{9} +0.792287 q^{10} -3.31662i q^{11} +1.37228i q^{12} +(2.00000 - 0.627719i) q^{14} +1.00000 q^{15} +0.627719 q^{16} +4.10891 q^{17} -0.792287i q^{18} -4.40387 q^{19} -1.37228i q^{20} +(2.52434 - 0.792287i) q^{21} +2.62772 q^{22} +9.11684 q^{23} -2.67181 q^{24} -1.00000 q^{25} -1.00000i q^{27} +(-1.08724 - 3.46410i) q^{28} -5.98844i q^{29} +0.792287i q^{30} +6.74456i q^{31} +5.84096i q^{32} +3.31662 q^{33} +3.25544i q^{34} +(-2.52434 + 0.792287i) q^{35} -1.37228 q^{36} +10.7446 q^{37} -3.48913i q^{38} +2.67181 q^{40} +11.6819 q^{41} +(0.627719 + 2.00000i) q^{42} -4.10891i q^{43} -4.55134i q^{44} +1.00000i q^{45} +7.22316i q^{46} -12.7446i q^{47} +0.627719i q^{48} +(-5.74456 + 4.00000i) q^{49} -0.792287i q^{50} +4.10891i q^{51} -1.62772 q^{53} +0.792287 q^{54} -3.31662 q^{55} +(6.74456 - 2.11684i) q^{56} -4.40387i q^{57} +4.74456 q^{58} -1.62772i q^{59} +1.37228 q^{60} -11.0371 q^{61} -5.34363 q^{62} +(0.792287 + 2.52434i) q^{63} -3.37228 q^{64} +2.62772i q^{66} -4.74456 q^{67} +5.63858 q^{68} +9.11684i q^{69} +(-0.627719 - 2.00000i) q^{70} +3.25544 q^{71} -2.67181i q^{72} +6.92820 q^{73} +8.51278i q^{74} -1.00000i q^{75} -6.04334 q^{76} +(-8.37228 + 2.62772i) q^{77} +0.294954i q^{79} -0.627719i q^{80} +1.00000 q^{81} +9.25544i q^{82} -9.45254 q^{83} +(3.46410 - 1.08724i) q^{84} -4.10891i q^{85} +3.25544 q^{86} +5.98844 q^{87} +8.86141 q^{88} +8.37228i q^{89} -0.792287 q^{90} +12.5109 q^{92} -6.74456 q^{93} +10.0974 q^{94} +4.40387i q^{95} -5.84096 q^{96} -8.37228i q^{97} +(-3.16915 - 4.55134i) q^{98} +3.31662i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} - 8 q^{9}+O(q^{10}) \) 8 * q - 12 * q^4 - 8 * q^9	\( 8 q - 12 q^{4} - 8 q^{9} + 16 q^{14} + 8 q^{15} + 28 q^{16} + 44 q^{22} + 4 q^{23} - 8 q^{25} + 12 q^{36} + 40 q^{37} + 28 q^{42} - 36 q^{53} + 8 q^{56} - 8 q^{58} - 12 q^{60} - 4 q^{64} + 8 q^{67} - 28 q^{70} + 72 q^{71} - 44 q^{77} + 8 q^{81} + 72 q^{86} - 44 q^{88} + 192 q^{92} - 8 q^{93}+O(q^{100}) \) 8 * q - 12 * q^4 - 8 * q^9 + 16 * q^14 + 8 * q^15 + 28 * q^16 + 44 * q^22 + 4 * q^23 - 8 * q^25 + 12 * q^36 + 40 * q^37 + 28 * q^42 - 36 * q^53 + 8 * q^56 - 8 * q^58 - 12 * q^60 - 4 * q^64 + 8 * q^67 - 28 * q^70 + 72 * q^71 - 44 * q^77 + 8 * q^81 + 72 * q^86 - 44 * q^88 + 192 * q^92 - 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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