LMFDB - Embedded newform 640.2.s.c.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(223,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("640.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.2
Root			$0.0376504 + 1.41371i$ of defining polynomial
Character	$\chi$	$=$	640.223
Dual form			640.2.s.c.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55161 q^{3} +(-1.49107 + 1.66635i) q^{5} +(-2.40368 + 2.40368i) q^{7} +3.51070 q^{9} +O(q^{10})$	\(q-2.55161 q^{3} +(-1.49107 + 1.66635i) q^{5} +(-2.40368 + 2.40368i) q^{7} +3.51070 q^{9} +(-2.67707 - 2.67707i) q^{11} +2.40164i q^{13} +(3.80462 - 4.25187i) q^{15} +(-0.0750544 + 0.0750544i) q^{17} +(2.67236 + 2.67236i) q^{19} +(6.13324 - 6.13324i) q^{21} +(-2.12375 - 2.12375i) q^{23} +(-0.553442 - 4.96928i) q^{25} -1.30310 q^{27} +(3.95795 - 3.95795i) q^{29} -1.65367i q^{31} +(6.83083 + 6.83083i) q^{33} +(-0.421324 - 7.58941i) q^{35} -2.53082i q^{37} -6.12803i q^{39} -1.70882i q^{41} -3.84601i q^{43} +(-5.23469 + 5.85005i) q^{45} +(-2.15264 - 2.15264i) q^{47} -4.55532i q^{49} +(0.191509 - 0.191509i) q^{51} +1.29475 q^{53} +(8.45262 - 0.469246i) q^{55} +(-6.81881 - 6.81881i) q^{57} +(5.29614 - 5.29614i) q^{59} +(-10.2413 - 10.2413i) q^{61} +(-8.43858 + 8.43858i) q^{63} +(-4.00197 - 3.58100i) q^{65} +10.6230i q^{67} +(5.41898 + 5.41898i) q^{69} -2.27322 q^{71} +(-9.99096 + 9.99096i) q^{73} +(1.41217 + 12.6796i) q^{75} +12.8696 q^{77} +8.70617 q^{79} -7.20709 q^{81} +11.1310 q^{83} +(-0.0131558 - 0.236978i) q^{85} +(-10.0991 + 10.0991i) q^{87} +15.6390 q^{89} +(-5.77276 - 5.77276i) q^{91} +4.21952i q^{93} +(-8.43775 + 0.468420i) q^{95} +(5.00672 - 5.00672i) q^{97} +(-9.39839 - 9.39839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	$ 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9 - 2 * q^11 + 20 * q^15 - 6 * q^17 - 2 * q^19 + 16 * q^21 + 2 * q^23 - 6 * q^25 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.55161			−1.47317			−0.736586	−	0.676344i	$-0.763563\pi$
$3$	−2.55161			−1.47317			−0.736586	+	0.676344i	$0.763563\pi$
$4$		0			0
$5$	−1.49107	+	1.66635i	−0.666825	+	0.745214i
$5$	−1.49107	+	1.66635i	−0.666825	+	0.745214i
$6$		0			0
$7$	−2.40368	+	2.40368i	−0.908504	+	0.908504i	−0.996152	−	0.0876474i	$-0.972065\pi$
$7$	−2.40368	+	2.40368i	−0.908504	+	0.908504i	0.0876474	+	0.996152i	$0.472065\pi$
$8$		0			0
$9$	3.51070			1.17023
$10$		0			0
$11$	−2.67707	−	2.67707i	−0.807167	−	0.807167i	0.177037	−	0.984204i	$-0.443349\pi$
$11$	−2.67707	−	2.67707i	−0.807167	−	0.807167i	−0.984204	+	0.177037i	$0.943349\pi$
$12$		0			0
$13$			2.40164i			0.666094i	0.942910	+	0.333047i	$0.108077\pi$
$13$			2.40164i			0.666094i	−0.942910	+	0.333047i	$0.891923\pi$
$14$		0			0
$15$	3.80462	−	4.25187i	0.982348	−	1.09783i
$16$		0			0
$17$	−0.0750544	+	0.0750544i	−0.0182034	+	0.0182034i	−0.716150	−	0.697947i	$-0.754097\pi$
$17$	−0.0750544	+	0.0750544i	−0.0182034	+	0.0182034i	0.697947	+	0.716150i	$0.254097\pi$
$18$		0			0
$19$	2.67236	+	2.67236i	0.613081	+	0.613081i	0.943748	−	0.330666i	$-0.107274\pi$
$19$	2.67236	+	2.67236i	0.613081	+	0.613081i	−0.330666	+	0.943748i	$0.607274\pi$
$20$		0			0
$21$	6.13324	−	6.13324i	1.33838	−	1.33838i
$22$		0			0
$23$	−2.12375	−	2.12375i	−0.442833	−	0.442833i	0.450130	−	0.892963i	$-0.351378\pi$
$23$	−2.12375	−	2.12375i	−0.442833	−	0.442833i	−0.892963	+	0.450130i	$0.851378\pi$
$24$		0			0
$25$	−0.553442	−	4.96928i	−0.110688	−	0.993855i
$26$		0			0
$27$	−1.30310			−0.250783
$28$		0			0
$29$	3.95795	−	3.95795i	0.734974	−	0.734974i	−0.236627	−	0.971601i	$-0.576042\pi$
$29$	3.95795	−	3.95795i	0.734974	−	0.734974i	0.971601	+	0.236627i	$0.0760419\pi$
$30$		0			0
$31$		−	1.65367i		−	0.297008i	−0.988912	−	0.148504i	$-0.952554\pi$
$31$		−	1.65367i		−	0.297008i	0.988912	−	0.148504i	$-0.0474458\pi$
$32$		0			0
$33$	6.83083	+	6.83083i	1.18909	+	1.18909i
$34$		0			0
$35$	−0.421324	−	7.58941i	−0.0712168	−	1.28284i
$36$		0			0
$37$		−	2.53082i		−	0.416064i	−0.978122	−	0.208032i	$-0.933294\pi$
$37$		−	2.53082i		−	0.416064i	0.978122	−	0.208032i	$-0.0667059\pi$
$38$		0			0
$39$		−	6.12803i		−	0.981271i
$40$		0			0
$41$		−	1.70882i		−	0.266873i	−0.991057	−	0.133436i	$-0.957399\pi$
$41$		−	1.70882i		−	0.266873i	0.991057	−	0.133436i	$-0.0426012\pi$
$42$		0			0
$43$		−	3.84601i		−	0.586510i	−0.956034	−	0.293255i	$-0.905261\pi$
$43$		−	3.84601i		−	0.586510i	0.956034	−	0.293255i	$-0.0947386\pi$
$44$		0			0
$45$	−5.23469	+	5.85005i	−0.780341	+	0.872074i
$46$		0			0
$47$	−2.15264	−	2.15264i	−0.313995	−	0.313995i	0.532460	−	0.846455i	$-0.321268\pi$
$47$	−2.15264	−	2.15264i	−0.313995	−	0.313995i	−0.846455	+	0.532460i	$0.821268\pi$
$48$		0			0
$49$		−	4.55532i		−	0.650760i
$50$		0			0
$51$	0.191509	−	0.191509i	0.0268167	−	0.0268167i
$52$		0			0
$53$	1.29475			0.177848			0.0889239	−	0.996038i	$-0.471657\pi$
$53$	1.29475			0.177848			0.0889239	+	0.996038i	$0.471657\pi$
$54$		0			0
$55$	8.45262	−	0.469246i	1.13975	−	0.0632731i
$56$		0			0
$57$	−6.81881	−	6.81881i	−0.903174	−	0.903174i
$58$		0			0
$59$	5.29614	−	5.29614i	0.689499	−	0.689499i	−0.272622	−	0.962121i	$-0.587891\pi$
$59$	5.29614	−	5.29614i	0.689499	−	0.689499i	0.962121	+	0.272622i	$0.0878908\pi$
$60$		0			0
$61$	−10.2413	−	10.2413i	−1.31126	−	1.31126i	−0.920484	−	0.390780i	$-0.872205\pi$
$61$	−10.2413	−	10.2413i	−1.31126	−	1.31126i	−0.390780	−	0.920484i	$-0.627795\pi$
$62$		0			0
$63$	−8.43858	+	8.43858i	−1.06316	+	1.06316i
$64$		0			0
$65$	−4.00197	−	3.58100i	−0.496383	−	0.444168i
$66$		0			0
$67$			10.6230i			1.29780i	0.760873	+	0.648901i	$0.224771\pi$
$67$			10.6230i			1.29780i	−0.760873	+	0.648901i	$0.775229\pi$
$68$		0			0
$69$	5.41898	+	5.41898i	0.652369	+	0.652369i
$70$		0			0
$71$	−2.27322			−0.269781			−0.134891	−	0.990860i	$-0.543068\pi$
$71$	−2.27322			−0.269781			−0.134891	+	0.990860i	$0.543068\pi$
$72$		0			0
$73$	−9.99096	+	9.99096i	−1.16935	+	1.16935i	−0.186992	+	0.982361i	$0.559874\pi$
$73$	−9.99096	+	9.99096i	−1.16935	+	1.16935i	−0.982361	+	0.186992i	$0.940126\pi$
$74$		0			0
$75$	1.41217	+	12.6796i	0.163063	+	1.46412i
$76$		0			0
$77$	12.8696			1.46663
$78$		0			0
$79$	8.70617			0.979520			0.489760	−	0.871857i	$-0.337084\pi$
$79$	8.70617			0.979520			0.489760	+	0.871857i	$0.337084\pi$
$80$		0			0
$81$	−7.20709			−0.800787
$82$		0			0
$83$	11.1310			1.22178			0.610890	−	0.791715i	$-0.290812\pi$
$83$	11.1310			1.22178			0.610890	+	0.791715i	$0.290812\pi$
$84$		0			0
$85$	−0.0131558	−	0.236978i	−0.00142695	−	0.0257039i
$86$		0			0
$87$	−10.0991	+	10.0991i	−1.08274	+	1.08274i
$88$		0			0
$89$	15.6390			1.65773			0.828866	−	0.559447i	$-0.188986\pi$
$89$	15.6390			1.65773			0.828866	+	0.559447i	$0.188986\pi$
$90$		0			0
$91$	−5.77276	−	5.77276i	−0.605149	−	0.605149i
$92$		0			0
$93$			4.21952i			0.437544i
$94$		0			0
$95$	−8.43775	+	0.468420i	−0.865695	+	0.0480589i
$96$		0			0
$97$	5.00672	−	5.00672i	0.508355	−	0.508355i	−0.405666	−	0.914021i	$-0.632960\pi$
$97$	5.00672	−	5.00672i	0.508355	−	0.508355i	0.914021	+	0.405666i	$0.132960\pi$
$98$		0			0
$99$	−9.39839	−	9.39839i	−0.944573	−	0.944573i
$100$		0			0
$101$	−6.37101	+	6.37101i	−0.633939	+	0.633939i	−0.949054	−	0.315115i	$-0.897957\pi$
$101$	−6.37101	+	6.37101i	−0.633939	+	0.633939i	0.315115	+	0.949054i	$0.397957\pi$
$102$		0			0
$103$	1.93695	+	1.93695i	0.190854	+	0.190854i	0.796065	−	0.605211i	$-0.206911\pi$
$103$	1.93695	+	1.93695i	0.190854	+	0.190854i	−0.605211	+	0.796065i	$0.706911\pi$
$104$		0			0
$105$	1.07505	+	19.3652i	0.104915	+	1.88985i
$106$		0			0
$107$	6.97778			0.674568			0.337284	−	0.941403i	$-0.390492\pi$
$107$	6.97778			0.674568			0.337284	+	0.941403i	$0.390492\pi$
$108$		0			0
$109$	−0.277748	+	0.277748i	−0.0266034	+	0.0266034i	−0.720283	−	0.693680i	$-0.755988\pi$
$109$	−0.277748	+	0.277748i	−0.0266034	+	0.0266034i	0.693680	+	0.720283i	$0.255988\pi$
$110$		0			0
$111$			6.45766i			0.612934i
$112$		0			0
$113$	−8.75577	−	8.75577i	−0.823674	−	0.823674i	0.162959	−	0.986633i	$-0.447896\pi$
$113$	−8.75577	−	8.75577i	−0.823674	−	0.823674i	−0.986633	+	0.162959i	$0.947896\pi$
$114$		0			0
$115$	6.70557	−	0.372258i	0.625298	−	0.0347133i
$116$		0			0
$117$			8.43142i			0.779485i
$118$		0			0
$119$		−	0.360813i		−	0.0330757i
$120$		0			0
$121$			3.33340i			0.303036i
$122$		0			0
$123$			4.36024i			0.393149i
$124$		0			0
$125$	9.10577	+	6.48729i	0.814445	+	0.580241i
$126$		0			0
$127$	0.679502	+	0.679502i	0.0602961	+	0.0602961i	0.736612	−	0.676316i	$-0.236424\pi$
$127$	0.679502	+	0.679502i	0.0602961	+	0.0602961i	−0.676316	+	0.736612i	$0.736424\pi$
$128$		0			0
$129$			9.81350i			0.864030i
$130$		0			0
$131$	−5.43859	+	5.43859i	−0.475172	+	0.475172i	−0.903584	−	0.428412i	$-0.859073\pi$
$131$	−5.43859	+	5.43859i	−0.475172	+	0.475172i	0.428412	+	0.903584i	$0.359073\pi$
$132$		0			0
$133$	−12.8470			−1.11397
$134$		0			0
$135$	1.94302	−	2.17143i	0.167228	−	0.186887i
$136$		0			0
$137$	−7.47496	−	7.47496i	−0.638629	−	0.638629i	0.311588	−	0.950217i	$-0.399139\pi$
$137$	−7.47496	−	7.47496i	−0.638629	−	0.638629i	−0.950217	+	0.311588i	$0.899139\pi$
$138$		0			0
$139$	−11.5307	+	11.5307i	−0.978023	+	0.978023i	−0.999764	−	0.0217404i	$-0.993079\pi$
$139$	−11.5307	+	11.5307i	−0.978023	+	0.978023i	0.0217404	+	0.999764i	$0.493079\pi$
$140$		0			0
$141$	5.49270	+	5.49270i	0.462568	+	0.462568i
$142$		0			0
$143$	6.42935	−	6.42935i	0.537649	−	0.537649i
$144$		0			0
$145$	0.693763	+	12.4969i	0.0576139	+	1.03781i
$146$		0			0
$147$			11.6234i			0.958680i
$148$		0			0
$149$	−5.51174	−	5.51174i	−0.451539	−	0.451539i	0.444326	−	0.895865i	$-0.353443\pi$
$149$	−5.51174	−	5.51174i	−0.451539	−	0.451539i	−0.895865	+	0.444326i	$0.853443\pi$
$150$		0			0
$151$	4.13617			0.336597			0.168299	−	0.985736i	$-0.446173\pi$
$151$	4.13617			0.336597			0.168299	+	0.985736i	$0.446173\pi$
$152$		0			0
$153$	−0.263494	+	0.263494i	−0.0213022	+	0.0213022i
$154$		0			0
$155$	2.75559	+	2.46573i	0.221335	+	0.198052i
$156$		0			0
$157$	−20.2700			−1.61772			−0.808861	−	0.587999i	$-0.799916\pi$
$157$	−20.2700			−1.61772			−0.808861	+	0.587999i	$0.799916\pi$
$158$		0			0
$159$	−3.30370			−0.262000
$160$		0			0
$161$	10.2096			0.804631
$162$		0			0
$163$	−13.1835			−1.03262			−0.516308	−	0.856403i	$-0.672694\pi$
$163$	−13.1835			−1.03262			−0.516308	+	0.856403i	$0.672694\pi$
$164$		0			0
$165$	−21.5678	+	1.19733i	−1.67905	+	0.0932121i
$166$		0			0
$167$	11.8190	−	11.8190i	0.914585	−	0.914585i	−0.0820441	−	0.996629i	$-0.526145\pi$
$167$	11.8190	−	11.8190i	0.914585	−	0.914585i	0.996629	+	0.0820441i	$0.0261448\pi$
$168$		0			0
$169$	7.23214			0.556319
$170$		0			0
$171$	9.38185	+	9.38185i	0.717448	+	0.717448i
$172$		0			0
$173$		−	15.5763i		−	1.18424i	−0.805849	−	0.592120i	$-0.798291\pi$
$173$		−	15.5763i		−	1.18424i	0.805849	−	0.592120i	$-0.201709\pi$
$174$		0			0
$175$	13.2748	+	10.6142i	1.00348	+	0.802361i
$176$		0			0
$177$	−13.5137	+	13.5137i	−1.01575	+	1.01575i
$178$		0			0
$179$	−15.5963	−	15.5963i	−1.16572	−	1.16572i	−0.983202	−	0.182523i	$-0.941574\pi$
$179$	−15.5963	−	15.5963i	−1.16572	−	1.16572i	−0.182523	−	0.983202i	$-0.558426\pi$
$180$		0			0
$181$	−2.98705	+	2.98705i	−0.222026	+	0.222026i	−0.809351	−	0.587325i	$-0.800181\pi$
$181$	−2.98705	+	2.98705i	−0.222026	+	0.222026i	0.587325	+	0.809351i	$0.300181\pi$
$182$		0			0
$183$	26.1318	+	26.1318i	1.93172	+	1.93172i
$184$		0			0
$185$	4.21723	+	3.77362i	0.310057	+	0.277442i
$186$		0			0
$187$	0.401852			0.0293863
$188$		0			0
$189$	3.13224	−	3.13224i	0.227837	−	0.227837i
$190$		0			0
$191$			6.47168i			0.468274i	0.972204	+	0.234137i	$0.0752264\pi$
$191$			6.47168i			0.468274i	−0.972204	+	0.234137i	$0.924774\pi$
$192$		0			0
$193$	−11.1131	−	11.1131i	−0.799936	−	0.799936i	0.183149	−	0.983085i	$-0.441371\pi$
$193$	−11.1131	−	11.1131i	−0.799936	−	0.799936i	−0.983085	+	0.183149i	$0.941371\pi$
$194$		0			0
$195$	10.2114	+	9.13730i	0.731257	+	0.654336i
$196$		0			0
$197$		−	25.0927i		−	1.78778i	−0.448288	−	0.893889i	$-0.647966\pi$
$197$		−	25.0927i		−	1.78778i	0.448288	−	0.893889i	$-0.352034\pi$
$198$		0			0
$199$		−	18.7579i		−	1.32972i	−0.746970	−	0.664858i	$-0.768492\pi$
$199$		−	18.7579i		−	1.32972i	0.746970	−	0.664858i	$-0.231508\pi$
$200$		0			0
$201$		−	27.1056i		−	1.91188i
$202$		0			0
$203$			19.0273i			1.33545i
$204$		0			0
$205$	2.84749	+	2.54796i	0.198877	+	0.177958i
$206$		0			0
$207$	−7.45586	−	7.45586i	−0.518218	−	0.518218i
$208$		0			0
$209$		−	14.3082i		−	0.989718i
$210$		0			0
$211$	6.38863	−	6.38863i	0.439811	−	0.439811i	−0.452137	−	0.891948i	$-0.649338\pi$
$211$	6.38863	−	6.38863i	0.439811	−	0.439811i	0.891948	+	0.452137i	$0.149338\pi$
$212$		0			0
$213$	5.80036			0.397434
$214$		0			0
$215$	6.40879	+	5.73465i	0.437076	+	0.391100i
$216$		0			0
$217$	3.97489	+	3.97489i	0.269833	+	0.269833i
$218$		0			0
$219$	25.4930	−	25.4930i	1.72266	−	1.72266i
$220$		0			0
$221$	−0.180253	−	0.180253i	−0.0121252	−	0.0121252i
$222$		0			0
$223$	4.29779	−	4.29779i	0.287801	−	0.287801i	−0.548409	−	0.836210i	$-0.684766\pi$
$223$	4.29779	−	4.29779i	0.287801	−	0.287801i	0.836210	+	0.548409i	$0.184766\pi$
$224$		0			0
$225$	−1.94297	−	17.4456i	−0.129531	−	1.16304i
$226$		0			0
$227$		−	29.1029i		−	1.93163i	−0.259241	−	0.965813i	$-0.583472\pi$
$227$		−	29.1029i		−	1.93163i	0.259241	−	0.965813i	$-0.416528\pi$
$228$		0			0
$229$	18.3405	+	18.3405i	1.21198	+	1.21198i	0.970376	+	0.241600i	$0.0776721\pi$
$229$	18.3405	+	18.3405i	1.21198	+	1.21198i	0.241600	+	0.970376i	$0.422328\pi$
$230$		0			0
$231$	−32.8382			−2.16060
$232$		0			0
$233$	1.46663	−	1.46663i	0.0960824	−	0.0960824i	−0.657432	−	0.753514i	$-0.728357\pi$
$233$	1.46663	−	1.46663i	0.0960824	−	0.0960824i	0.753514	+	0.657432i	$0.228357\pi$
$234$		0			0
$235$	6.79678	−	0.377322i	0.443373	−	0.0246138i
$236$		0			0
$237$	−22.2147			−1.44300
$238$		0			0
$239$	−12.5432			−0.811352			−0.405676	−	0.914017i	$-0.632964\pi$
$239$	−12.5432			−0.811352			−0.405676	+	0.914017i	$0.632964\pi$
$240$		0			0
$241$	14.8870			0.958954			0.479477	−	0.877554i	$-0.340826\pi$
$241$	14.8870			0.958954			0.479477	+	0.877554i	$0.340826\pi$
$242$		0			0
$243$	22.2990			1.43048
$244$		0			0
$245$	7.59075	+	6.79228i	0.484955	+	0.433943i
$246$		0			0
$247$	−6.41803	+	6.41803i	−0.408370	+	0.408370i
$248$		0			0
$249$	−28.4018			−1.79989
$250$		0			0
$251$	−5.38459	−	5.38459i	−0.339872	−	0.339872i	0.516447	−	0.856319i	$-0.327254\pi$
$251$	−5.38459	−	5.38459i	−0.339872	−	0.339872i	−0.856319	+	0.516447i	$0.827254\pi$
$252$		0			0
$253$			11.3709i			0.714880i
$254$		0			0
$255$	0.0335684	+	0.604675i	0.00210214	+	0.0378662i
$256$		0			0
$257$	−3.88657	+	3.88657i	−0.242437	+	0.242437i	−0.817858	−	0.575420i	$-0.804838\pi$
$257$	−3.88657	+	3.88657i	−0.242437	+	0.242437i	0.575420	+	0.817858i	$0.304838\pi$
$258$		0			0
$259$	6.08327	+	6.08327i	0.377996	+	0.377996i
$260$		0			0
$261$	13.8952	−	13.8952i	0.860090	−	0.860090i
$262$		0			0
$263$	−16.9658	−	16.9658i	−1.04615	−	1.04615i	−0.998882	−	0.0472716i	$-0.984947\pi$
$263$	−16.9658	−	16.9658i	−1.04615	−	1.04615i	−0.0472716	−	0.998882i	$-0.515053\pi$
$264$		0			0
$265$	−1.93056	+	2.15751i	−0.118593	+	0.132535i
$266$		0			0
$267$	−39.9046			−2.44212
$268$		0			0
$269$	−2.55482	+	2.55482i	−0.155770	+	0.155770i	−0.780689	−	0.624919i	$-0.785132\pi$
$269$	−2.55482	+	2.55482i	−0.155770	+	0.155770i	0.624919	+	0.780689i	$0.285132\pi$
$270$		0			0
$271$		−	3.33684i		−	0.202698i	−0.994851	−	0.101349i	$-0.967684\pi$
$271$		−	3.33684i		−	0.202698i	0.994851	−	0.101349i	$-0.0323159\pi$
$272$		0			0
$273$	14.7298	+	14.7298i	0.891488	+	0.891488i
$274$		0			0
$275$	−11.8215	+	14.7847i	−0.712863	+	0.891551i
$276$		0			0
$277$			4.60736i			0.276830i	0.990374	+	0.138415i	$0.0442007\pi$
$277$			4.60736i			0.276830i	−0.990374	+	0.138415i	$0.955799\pi$
$278$		0			0
$279$		−	5.80554i		−	0.347569i
$280$		0			0
$281$			22.1178i			1.31944i	0.751513	+	0.659718i	$0.229324\pi$
$281$			22.1178i			1.31944i	−0.751513	+	0.659718i	$0.770676\pi$
$282$		0			0
$283$		−	10.8629i		−	0.645734i	−0.946444	−	0.322867i	$-0.895353\pi$
$283$		−	10.8629i		−	0.645734i	0.946444	−	0.322867i	$-0.104647\pi$
$284$		0			0
$285$	21.5298	−	1.19522i	1.27532	−	0.0707990i
$286$		0			0
$287$	4.10745	+	4.10745i	0.242455	+	0.242455i
$288$		0			0
$289$			16.9887i			0.999337i
$290$		0			0
$291$	−12.7752	+	12.7752i	−0.748895	+	0.748895i
$292$		0			0
$293$	18.4067			1.07533			0.537665	−	0.843159i	$-0.319307\pi$
$293$	18.4067			1.07533			0.537665	+	0.843159i	$0.319307\pi$
$294$		0			0
$295$	0.928326	+	16.7221i	0.0540492	+	0.973600i
$296$		0			0
$297$	3.48850	+	3.48850i	0.202423	+	0.202423i
$298$		0			0
$299$	5.10048	−	5.10048i	0.294968	−	0.294968i
$300$		0			0
$301$	9.24455	+	9.24455i	0.532847	+	0.532847i
$302$		0			0
$303$	16.2563	−	16.2563i	0.933900	−	0.933900i
$304$		0			0
$305$	32.3360	−	1.79513i	1.85156	−	0.102789i
$306$		0			0
$307$			6.60872i			0.377180i	0.982056	+	0.188590i	$0.0603917\pi$
$307$			6.60872i			0.377180i	−0.982056	+	0.188590i	$0.939608\pi$
$308$		0			0
$309$	−4.94234	−	4.94234i	−0.281160	−	0.281160i
$310$		0			0
$311$	0.606102			0.0343689			0.0171845	−	0.999852i	$-0.494530\pi$
$311$	0.606102			0.0343689			0.0171845	+	0.999852i	$0.494530\pi$
$312$		0			0
$313$	19.3708	−	19.3708i	1.09490	−	1.09490i	0.0999032	−	0.994997i	$-0.468147\pi$
$313$	19.3708	−	19.3708i	1.09490	−	1.09490i	0.994997	−	0.0999032i	$-0.0318533\pi$
$314$		0			0
$315$	−1.47914	−	26.6441i	−0.0833403	−	1.50123i
$316$		0			0
$317$	7.04328			0.395590			0.197795	−	0.980243i	$-0.436622\pi$
$317$	7.04328			0.395590			0.197795	+	0.980243i	$0.436622\pi$
$318$		0			0
$319$	−21.1914			−1.18649
$320$		0			0
$321$	−17.8046			−0.993753
$322$		0			0
$323$	−0.401145			−0.0223203
$324$		0			0
$325$	11.9344	−	1.32917i	0.662001	−	0.0737290i
$326$		0			0
$327$	0.708703	−	0.708703i	0.0391914	−	0.0391914i
$328$		0			0
$329$	10.3485			0.570532
$330$		0			0
$331$	−13.2275	−	13.2275i	−0.727047	−	0.727047i	0.242983	−	0.970031i	$-0.421874\pi$
$331$	−13.2275	−	13.2275i	−0.727047	−	0.727047i	−0.970031	+	0.242983i	$0.921874\pi$
$332$		0			0
$333$		−	8.88495i		−	0.486892i
$334$		0			0
$335$	−17.7016	−	15.8395i	−0.967140	−	0.865407i
$336$		0			0
$337$	7.73287	−	7.73287i	0.421236	−	0.421236i	−0.464393	−	0.885629i	$-0.653727\pi$
$337$	7.73287	−	7.73287i	0.421236	−	0.421236i	0.885629	+	0.464393i	$0.153727\pi$
$338$		0			0
$339$	22.3413	+	22.3413i	1.21341	+	1.21341i
$340$		0			0
$341$	−4.42699	+	4.42699i	−0.239735	+	0.239735i
$342$		0			0
$343$	−5.87623	−	5.87623i	−0.317286	−	0.317286i
$344$		0			0
$345$	−17.1100	+	0.949857i	−0.921170	+	0.0511386i
$346$		0			0
$347$	−11.3945			−0.611691			−0.305845	−	0.952081i	$-0.598939\pi$
$347$	−11.3945			−0.611691			−0.305845	+	0.952081i	$0.598939\pi$
$348$		0			0
$349$	12.0508	−	12.0508i	0.645066	−	0.645066i	−0.306730	−	0.951796i	$-0.599235\pi$
$349$	12.0508	−	12.0508i	0.645066	−	0.645066i	0.951796	+	0.306730i	$0.0992350\pi$
$350$		0			0
$351$		−	3.12958i		−	0.167045i
$352$		0			0
$353$	−6.47876	−	6.47876i	−0.344830	−	0.344830i	0.513350	−	0.858179i	$-0.328404\pi$
$353$	−6.47876	−	6.47876i	−0.344830	−	0.344830i	−0.858179	+	0.513350i	$0.828404\pi$
$354$		0			0
$355$	3.38952	−	3.78798i	0.179897	−	0.201045i
$356$		0			0
$357$			0.920653i			0.0487261i
$358$		0			0
$359$		−	3.25098i		−	0.171580i	−0.996313	−	0.0857902i	$-0.972659\pi$
$359$		−	3.25098i		−	0.171580i	0.996313	−	0.0857902i	$-0.0273415\pi$
$360$		0			0
$361$		−	4.71699i		−	0.248263i
$362$		0			0
$363$		−	8.50553i		−	0.446424i
$364$		0			0
$365$	−1.75125	−	31.5456i	−0.0916646	−	1.65117i
$366$		0			0
$367$	12.7038	+	12.7038i	0.663132	+	0.663132i	0.956117	−	0.292985i	$-0.0946487\pi$
$367$	12.7038	+	12.7038i	0.663132	+	0.663132i	−0.292985	+	0.956117i	$0.594649\pi$
$368$		0			0
$369$		−	5.99916i		−	0.312304i
$370$		0			0
$371$	−3.11216	+	3.11216i	−0.161575	+	0.161575i
$372$		0			0
$373$	−21.9761			−1.13788			−0.568939	−	0.822379i	$-0.692646\pi$
$373$	−21.9761			−1.13788			−0.568939	+	0.822379i	$0.692646\pi$
$374$		0			0
$375$	−23.2343	−	16.5530i	−1.19982	−	0.854794i
$376$		0			0
$377$	9.50557	+	9.50557i	0.489562	+	0.489562i
$378$		0			0
$379$	−17.0642	+	17.0642i	−0.876527	+	0.876527i	−0.993174	−	0.116646i	$-0.962786\pi$
$379$	−17.0642	+	17.0642i	−0.876527	+	0.876527i	0.116646	+	0.993174i	$0.462786\pi$
$380$		0			0
$381$	−1.73382	−	1.73382i	−0.0888264	−	0.0888264i
$382$		0			0
$383$	0.228058	−	0.228058i	0.0116532	−	0.0116532i	−0.701256	−	0.712909i	$-0.747377\pi$
$383$	0.228058	−	0.228058i	0.0116532	−	0.0116532i	0.712909	+	0.701256i	$0.247377\pi$
$384$		0			0
$385$	−19.1894	+	21.4453i	−0.977985	+	1.09295i
$386$		0			0
$387$		−	13.5022i		−	0.686354i
$388$		0			0
$389$	14.3036	+	14.3036i	0.725221	+	0.725221i	0.969664	−	0.244443i	$-0.0786050\pi$
$389$	14.3036	+	14.3036i	0.725221	+	0.725221i	−0.244443	+	0.969664i	$0.578605\pi$
$390$		0			0
$391$	0.318794			0.0161221
$392$		0			0
$393$	13.8771	−	13.8771i	0.700009	−	0.700009i
$394$		0			0
$395$	−12.9815	+	14.5075i	−0.653169	+	0.729953i
$396$		0			0
$397$	−5.11618			−0.256774			−0.128387	−	0.991724i	$-0.540980\pi$
$397$	−5.11618			−0.256774			−0.128387	+	0.991724i	$0.540980\pi$
$398$		0			0
$399$	32.7804			1.64107
$400$		0			0
$401$	−16.2837			−0.813170			−0.406585	−	0.913613i	$-0.633281\pi$
$401$	−16.2837			−0.813170			−0.406585	+	0.913613i	$0.633281\pi$
$402$		0			0
$403$	3.97152			0.197835
$404$		0			0
$405$	10.7462	−	12.0095i	0.533985	−	0.596758i
$406$		0			0
$407$	−6.77518	+	6.77518i	−0.335833	+	0.335833i
$408$		0			0
$409$	−17.4256			−0.861640			−0.430820	−	0.902438i	$-0.641776\pi$
$409$	−17.4256			−0.861640			−0.430820	+	0.902438i	$0.641776\pi$
$410$		0			0
$411$	19.0732	+	19.0732i	0.940810	+	0.940810i
$412$		0			0
$413$			25.4604i			1.25283i
$414$		0			0
$415$	−16.5970	+	18.5481i	−0.814714	+	0.910488i
$416$		0			0
$417$	29.4219	−	29.4219i	1.44080	−	1.44080i
$418$		0			0
$419$	−11.7257	−	11.7257i	−0.572837	−	0.572837i	0.360083	−	0.932920i	$-0.382748\pi$
$419$	−11.7257	−	11.7257i	−0.572837	−	0.572837i	−0.932920	+	0.360083i	$0.882748\pi$
$420$		0			0
$421$	23.5406	−	23.5406i	1.14730	−	1.14730i	0.160216	−	0.987082i	$-0.448781\pi$
$421$	23.5406	−	23.5406i	1.14730	−	1.14730i	0.987082	−	0.160216i	$-0.0512191\pi$
$422$		0			0
$423$	−7.55728	−	7.55728i	−0.367447	−	0.367447i
$424$		0			0
$425$	0.414505	+	0.331428i	0.0201064	+	0.0160766i
$426$		0			0
$427$	49.2335			2.38258
$428$		0			0
$429$	−16.4052	+	16.4052i	−0.792049	+	0.792049i
$430$		0			0
$431$		−	35.0243i		−	1.68706i	−0.537079	−	0.843532i	$-0.680472\pi$
$431$		−	35.0243i		−	1.68706i	0.537079	−	0.843532i	$-0.319528\pi$
$432$		0			0
$433$	10.1094	+	10.1094i	0.485828	+	0.485828i	0.906987	−	0.421159i	$-0.138376\pi$
$433$	10.1094	+	10.1094i	0.485828	+	0.485828i	−0.421159	+	0.906987i	$0.638376\pi$
$434$		0			0
$435$	−1.77021	−	31.8872i	−0.0848752	−	1.52887i
$436$		0			0
$437$		−	11.3509i		−	0.542985i
$438$		0			0
$439$			22.6071i			1.07898i	0.841993	+	0.539488i	$0.181382\pi$
$439$			22.6071i			1.07898i	−0.841993	+	0.539488i	$0.818618\pi$
$440$		0			0
$441$		−	15.9923i		−	0.761540i
$442$		0			0
$443$		−	10.9178i		−	0.518721i	−0.965781	−	0.259360i	$-0.916488\pi$
$443$		−	10.9178i		−	0.518721i	0.965781	−	0.259360i	$-0.0835118\pi$
$444$		0			0
$445$	−23.3188	+	26.0601i	−1.10542	+	1.23537i
$446$		0			0
$447$	14.0638	+	14.0638i	0.665195	+	0.665195i
$448$		0			0
$449$			28.8112i			1.35969i	0.733358	+	0.679843i	$0.237952\pi$
$449$			28.8112i			1.35969i	−0.733358	+	0.679843i	$0.762048\pi$
$450$		0			0
$451$	−4.57463	+	4.57463i	−0.215411	+	0.215411i
$452$		0			0
$453$	−10.5539			−0.495865
$454$		0			0
$455$	18.2270	−	1.01187i	0.854495	−	0.0474371i
$456$		0			0
$457$	−19.1653	−	19.1653i	−0.896513	−	0.896513i	0.0986128	−	0.995126i	$-0.468559\pi$
$457$	−19.1653	−	19.1653i	−0.896513	−	0.896513i	−0.995126	+	0.0986128i	$0.968559\pi$
$458$		0			0
$459$	0.0978038	−	0.0978038i	0.00456509	−	0.00456509i
$460$		0			0
$461$	−4.43227	−	4.43227i	−0.206431	−	0.206431i	0.596317	−	0.802749i	$-0.296630\pi$
$461$	−4.43227	−	4.43227i	−0.206431	−	0.206431i	−0.802749	+	0.596317i	$0.796630\pi$
$462$		0			0
$463$	−20.1518	+	20.1518i	−0.936534	+	0.936534i	−0.998103	−	0.0615691i	$-0.980390\pi$
$463$	−20.1518	+	20.1518i	−0.936534	+	0.936534i	0.0615691	+	0.998103i	$0.480390\pi$
$464$		0			0
$465$	−7.03120	−	6.29158i	−0.326064	−	0.291765i
$466$		0			0
$467$			3.89858i			0.180405i	0.995923	+	0.0902025i	$0.0287514\pi$
$467$			3.89858i			0.180405i	−0.995923	+	0.0902025i	$0.971249\pi$
$468$		0			0
$469$	−25.5342	−	25.5342i	−1.17906	−	1.17906i
$470$		0			0
$471$	51.7211			2.38318
$472$		0			0
$473$	−10.2960	+	10.2960i	−0.473412	+	0.473412i
$474$		0			0
$475$	11.8007	−	14.7587i	0.541453	−	0.677175i
$476$		0			0
$477$	4.54548			0.208123
$478$		0			0
$479$	−9.85299			−0.450194			−0.225097	−	0.974336i	$-0.572270\pi$
$479$	−9.85299			−0.450194			−0.225097	+	0.974336i	$0.572270\pi$
$480$		0			0
$481$	6.07811			0.277138
$482$		0			0
$483$	−26.0510			−1.18536
$484$		0			0
$485$	0.877595	+	15.8083i	0.0398495	+	0.717818i
$486$		0			0
$487$	13.9164	−	13.9164i	0.630611	−	0.630611i	−0.317610	−	0.948221i	$-0.602880\pi$
$487$	13.9164	−	13.9164i	0.630611	−	0.630611i	0.948221	+	0.317610i	$0.102880\pi$
$488$		0			0
$489$	33.6392			1.52122
$490$		0			0
$491$	2.39213	+	2.39213i	0.107955	+	0.107955i	0.759021	−	0.651066i	$-0.225678\pi$
$491$	2.39213	+	2.39213i	0.107955	+	0.107955i	−0.651066	+	0.759021i	$0.725678\pi$
$492$		0			0
$493$			0.594124i			0.0267580i
$494$		0			0
$495$	29.6746	−	1.64738i	1.33377	−	0.0740443i
$496$		0			0
$497$	5.46408	−	5.46408i	0.245098	−	0.245098i
$498$		0			0
$499$	−9.87034	−	9.87034i	−0.441857	−	0.441857i	0.450779	−	0.892636i	$-0.351146\pi$
$499$	−9.87034	−	9.87034i	−0.441857	−	0.441857i	−0.892636	+	0.450779i	$0.851146\pi$
$500$		0			0
$501$	−30.1575	+	30.1575i	−1.34734	+	1.34734i
$502$		0			0
$503$	−9.29035	−	9.29035i	−0.414236	−	0.414236i	0.468975	−	0.883211i	$-0.344623\pi$
$503$	−9.29035	−	9.29035i	−0.414236	−	0.414236i	−0.883211	+	0.468975i	$0.844623\pi$
$504$		0			0
$505$	−1.11673	−	20.1159i	−0.0496939	−	0.895146i
$506$		0			0
$507$	−18.4536			−0.819553
$508$		0			0
$509$	6.53818	−	6.53818i	0.289800	−	0.289800i	−0.547201	−	0.837001i	$-0.684307\pi$
$509$	6.53818	−	6.53818i	0.289800	−	0.289800i	0.837001	+	0.547201i	$0.184307\pi$
$510$		0			0
$511$		−	48.0301i		−	2.12473i
$512$		0			0
$513$	−3.48236	−	3.48236i	−0.153750	−	0.153750i
$514$		0			0
$515$	−6.11577	+	0.339516i	−0.269493	+	0.0149608i
$516$		0			0
$517$			11.5255i			0.506893i
$518$		0			0
$519$			39.7445i			1.74459i
$520$		0			0
$521$		−	14.2961i		−	0.626324i	−0.949700	−	0.313162i	$-0.898612\pi$
$521$		−	14.2961i		−	0.626324i	0.949700	−	0.313162i	$-0.101388\pi$
$522$		0			0
$523$			16.0319i			0.701027i	0.936558	+	0.350513i	$0.113993\pi$
$523$			16.0319i			0.701027i	−0.936558	+	0.350513i	$0.886007\pi$
$524$		0			0
$525$	−33.8721	−	27.0834i	−1.47830	−	1.18201i
$526$		0			0
$527$	0.124115	+	0.124115i	0.00540655	+	0.00540655i
$528$		0			0
$529$		−	13.9794i		−	0.607798i
$530$		0			0
$531$	18.5932	−	18.5932i	0.806875	−	0.806875i
$532$		0			0
$533$	4.10397			0.177762
$534$		0			0
$535$	−10.4043	+	11.6274i	−0.449819	+	0.502697i
$536$		0			0
$537$	39.7957	+	39.7957i	1.71731	+	1.71731i
$538$		0			0
$539$	−12.1949	+	12.1949i	−0.525271	+	0.525271i
$540$		0			0
$541$	14.3926	+	14.3926i	0.618785	+	0.618785i	0.945220	−	0.326435i	$-0.105847\pi$
$541$	14.3926	+	14.3926i	0.618785	+	0.618785i	−0.326435	+	0.945220i	$0.605847\pi$
$542$		0			0
$543$	7.62178	−	7.62178i	0.327082	−	0.327082i
$544$		0			0
$545$	−0.0486846	−	0.876965i	−0.00208542	−	0.0375651i
$546$		0			0
$547$			11.6741i			0.499148i	0.968356	+	0.249574i	$0.0802905\pi$
$547$			11.6741i			0.499148i	−0.968356	+	0.249574i	$0.919709\pi$
$548$		0			0
$549$	−35.9541	−	35.9541i	−1.53448	−	1.53448i
$550$		0			0
$551$	21.1541			0.901197
$552$		0			0
$553$	−20.9268	+	20.9268i	−0.889898	+	0.889898i
$554$		0			0
$555$	−10.7607	−	9.62880i	−0.456767	−	0.408720i
$556$		0			0
$557$	39.6712			1.68092			0.840460	−	0.541873i	$-0.182285\pi$
$557$	39.6712			1.68092			0.840460	+	0.541873i	$0.182285\pi$
$558$		0			0
$559$	9.23671			0.390671
$560$		0			0
$561$	−1.02537			−0.0432911
$562$		0			0
$563$	−12.4534			−0.524850			−0.262425	−	0.964952i	$-0.584522\pi$
$563$	−12.4534			−0.524850			−0.262425	+	0.964952i	$0.584522\pi$
$564$		0			0
$565$	27.6456	−	1.53474i	1.16306	−	0.0645671i
$566$		0			0
$567$	17.3235	−	17.3235i	0.727519	−	0.727519i
$568$		0			0
$569$	−5.62622			−0.235863			−0.117932	−	0.993022i	$-0.537626\pi$
$569$	−5.62622			−0.235863			−0.117932	+	0.993022i	$0.537626\pi$
$570$		0			0
$571$	23.1808	+	23.1808i	0.970086	+	0.970086i	0.999565	−	0.0294797i	$-0.00938505\pi$
$571$	23.1808	+	23.1808i	0.970086	+	0.970086i	−0.0294797	+	0.999565i	$0.509385\pi$
$572$		0			0
$573$		−	16.5132i		−	0.689848i
$574$		0			0
$575$	−9.37814	+	11.7289i	−0.391095	+	0.489128i
$576$		0			0
$577$	−25.6307	+	25.6307i	−1.06702	+	1.06702i	−0.0694322	+	0.997587i	$0.522119\pi$
$577$	−25.6307	+	25.6307i	−1.06702	+	1.06702i	−0.997587	+	0.0694322i	$0.977881\pi$
$578$		0			0
$579$	28.3562	+	28.3562i	1.17844	+	1.17844i
$580$		0			0
$581$	−26.7552	+	26.7552i	−1.10999	+	1.10999i
$582$		0			0
$583$	−3.46614	−	3.46614i	−0.143553	−	0.143553i
$584$		0			0
$585$	−14.0497	−	12.5718i	−0.580884	−	0.519780i
$586$		0			0
$587$	25.5579			1.05489			0.527444	−	0.849590i	$-0.323151\pi$
$587$	25.5579			1.05489			0.527444	+	0.849590i	$0.323151\pi$
$588$		0			0
$589$	4.41920	−	4.41920i	0.182090	−	0.182090i
$590$		0			0
$591$			64.0266i			2.63370i
$592$		0			0
$593$	2.96607	+	2.96607i	0.121802	+	0.121802i	0.765380	−	0.643578i	$-0.222551\pi$
$593$	2.96607	+	2.96607i	0.121802	+	0.121802i	−0.643578	+	0.765380i	$0.722551\pi$
$594$		0			0
$595$	0.601241	+	0.537996i	0.0246485	+	0.0220557i
$596$		0			0
$597$			47.8629i			1.95890i
$598$		0			0
$599$			5.14724i			0.210311i	0.994456	+	0.105155i	$0.0335340\pi$
$599$			5.14724i			0.210311i	−0.994456	+	0.105155i	$0.966466\pi$
$600$		0			0
$601$			33.5619i			1.36902i	0.729005	+	0.684509i	$0.239983\pi$
$601$			33.5619i			1.36902i	−0.729005	+	0.684509i	$0.760017\pi$
$602$		0			0
$603$			37.2940i			1.51873i
$604$		0			0
$605$	−5.55461	−	4.97032i	−0.225827	−	0.202072i
$606$		0			0
$607$	3.29572	+	3.29572i	0.133769	+	0.133769i	0.770821	−	0.637052i	$-0.219846\pi$
$607$	3.29572	+	3.29572i	0.133769	+	0.133769i	−0.637052	+	0.770821i	$0.719846\pi$
$608$		0			0
$609$		−	48.5501i		−	1.96735i
$610$		0			0
$611$	5.16986	−	5.16986i	0.209150	−	0.209150i
$612$		0			0
$613$	−0.261903			−0.0105781			−0.00528907	−	0.999986i	$-0.501684\pi$
$613$	−0.261903			−0.0105781			−0.00528907	+	0.999986i	$0.501684\pi$
$614$		0			0
$615$	−7.26568	−	6.50140i	−0.292981	−	0.262162i
$616$		0			0
$617$	12.1529	+	12.1529i	0.489259	+	0.489259i	0.908072	−	0.418813i	$-0.137554\pi$
$617$	12.1529	+	12.1529i	0.489259	+	0.489259i	−0.418813	+	0.908072i	$0.637554\pi$
$618$		0			0
$619$	−12.1134	+	12.1134i	−0.486877	+	0.486877i	−0.907319	−	0.420442i	$-0.861875\pi$
$619$	−12.1134	+	12.1134i	−0.486877	+	0.486877i	0.420442	+	0.907319i	$0.361875\pi$
$620$		0			0
$621$	2.76747	+	2.76747i	0.111055	+	0.111055i
$622$		0			0
$623$	−37.5911	+	37.5911i	−1.50606	+	1.50606i
$624$		0			0
$625$	−24.3874	+	5.50042i	−0.975496	+	0.220017i
$626$		0			0
$627$			36.5089i			1.45802i
$628$		0			0
$629$	0.189949	+	0.189949i	0.00757377	+	0.00757377i
$630$		0			0
$631$	−49.8568			−1.98477			−0.992384	−	0.123179i	$-0.960691\pi$
$631$	−49.8568			−1.98477			−0.992384	+	0.123179i	$0.960691\pi$
$632$		0			0
$633$	−16.3013	+	16.3013i	−0.647917	+	0.647917i
$634$		0			0
$635$	−2.14547	+	0.119105i	−0.0851404	+	0.00472656i
$636$		0			0
$637$	10.9402			0.433467
$638$		0			0
$639$	−7.98059			−0.315707
$640$		0			0
$641$	−4.10036			−0.161954			−0.0809772	−	0.996716i	$-0.525804\pi$
$641$	−4.10036			−0.161954			−0.0809772	+	0.996716i	$0.525804\pi$
$642$		0			0
$643$	−18.7451			−0.739233			−0.369617	−	0.929184i	$-0.620511\pi$
$643$	−18.7451			−0.739233			−0.369617	+	0.929184i	$0.620511\pi$
$644$		0			0
$645$	−16.3527	−	14.6326i	−0.643888	−	0.576157i
$646$		0			0
$647$	−5.46529	+	5.46529i	−0.214863	+	0.214863i	−0.806330	−	0.591467i	$-0.798549\pi$
$647$	−5.46529	+	5.46529i	−0.214863	+	0.214863i	0.591467	+	0.806330i	$0.298549\pi$
$648$		0			0
$649$	−28.3563			−1.11308
$650$		0			0
$651$	−10.1424	−	10.1424i	−0.397510	−	0.397510i
$652$		0			0
$653$			33.9219i			1.32747i	0.747970	+	0.663733i	$0.231029\pi$
$653$			33.9219i			1.32747i	−0.747970	+	0.663733i	$0.768971\pi$
$654$		0			0
$655$	−0.953294	−	17.1719i	−0.0372483	−	0.670961i
$656$		0			0
$657$	−35.0753	+	35.0753i	−1.36842	+	1.36842i
$658$		0			0
$659$	26.4961	+	26.4961i	1.03214	+	1.03214i	0.999466	+	0.0326746i	$0.0104025\pi$
$659$	26.4961	+	26.4961i	1.03214	+	1.03214i	0.0326746	+	0.999466i	$0.489598\pi$
$660$		0			0
$661$	−10.6974	+	10.6974i	−0.416081	+	0.416081i	−0.883851	−	0.467769i	$-0.845058\pi$
$661$	−10.6974	+	10.6974i	−0.416081	+	0.416081i	0.467769	+	0.883851i	$0.345058\pi$
$662$		0			0
$663$	0.459936	+	0.459936i	0.0178624	+	0.0178624i
$664$		0			0
$665$	19.1557	−	21.4075i	0.742826	−	0.830149i
$666$		0			0
$667$	−16.8114			−0.650941
$668$		0			0
$669$	−10.9663	+	10.9663i	−0.423980	+	0.423980i
$670$		0			0
$671$			54.8333i			2.11682i
$672$		0			0
$673$	−6.70854	−	6.70854i	−0.258595	−	0.258595i	0.565887	−	0.824483i	$-0.308534\pi$
$673$	−6.70854	−	6.70854i	−0.258595	−	0.258595i	−0.824483	+	0.565887i	$0.808534\pi$
$674$		0			0
$675$	0.721194	+	6.47549i	0.0277588	+	0.249242i
$676$		0			0
$677$			13.1970i			0.507200i	0.967309	+	0.253600i	$0.0816147\pi$
$677$			13.1970i			0.507200i	−0.967309	+	0.253600i	$0.918385\pi$
$678$		0			0
$679$			24.0691i			0.923686i
$680$		0			0
$681$			74.2591i			2.84561i
$682$		0			0
$683$		−	37.9089i		−	1.45054i	−0.688462	−	0.725272i	$-0.741714\pi$
$683$		−	37.9089i		−	1.45054i	0.688462	−	0.725272i	$-0.258286\pi$
$684$		0			0
$685$	23.6016	−	1.31024i	0.901770	−	0.0500616i
$686$		0			0
$687$	−46.7978	−	46.7978i	−1.78545	−	1.78545i
$688$		0			0
$689$			3.10952i			0.118463i
$690$		0			0
$691$	20.8280	−	20.8280i	0.792335	−	0.792335i	−0.189538	−	0.981873i	$-0.560699\pi$
$691$	20.8280	−	20.8280i	0.792335	−	0.792335i	0.981873	+	0.189538i	$0.0606991\pi$
$692$		0			0
$693$	45.1813			1.71630
$694$		0			0
$695$	−2.02114	−	36.4073i	−0.0766664	−	1.38101i
$696$		0			0
$697$	0.128255	+	0.128255i	0.00485799	+	0.00485799i
$698$		0			0
$699$	−3.74227	+	3.74227i	−0.141546	+	0.141546i
$700$		0			0
$701$	−19.9053	−	19.9053i	−0.751812	−	0.751812i	0.223005	−	0.974817i	$-0.428413\pi$
$701$	−19.9053	−	19.9053i	−0.751812	−	0.751812i	−0.974817	+	0.223005i	$0.928413\pi$
$702$		0			0
$703$	6.76326	−	6.76326i	0.255081	−	0.255081i
$704$		0			0
$705$	−17.3427	+	0.962778i	−0.653165	+	0.0362603i
$706$		0			0
$707$		−	30.6277i		−	1.15187i
$708$		0			0
$709$	8.57112	+	8.57112i	0.321895	+	0.321895i	0.849494	−	0.527599i	$-0.176908\pi$
$709$	8.57112	+	8.57112i	0.321895	+	0.321895i	−0.527599	+	0.849494i	$0.676908\pi$
$710$		0			0
$711$	30.5647			1.14627
$712$		0			0
$713$	−3.51199	+	3.51199i	−0.131525	+	0.131525i
$714$		0			0
$715$	1.12696	+	20.3001i	0.0421458	+	0.759182i
$716$		0			0
$717$	32.0053			1.19526
$718$		0			0
$719$	33.1900			1.23778			0.618889	−	0.785478i	$-0.287583\pi$
$719$	33.1900			1.23778			0.618889	+	0.785478i	$0.287583\pi$
$720$		0			0
$721$	−9.31162			−0.346783
$722$		0			0
$723$	−37.9857			−1.41270
$724$		0			0
$725$	−21.8587	−	17.4777i	−0.811810	−	0.649104i
$726$		0			0
$727$	−5.06503	+	5.06503i	−0.187852	+	0.187852i	−0.794767	−	0.606915i	$-0.792407\pi$
$727$	−5.06503	+	5.06503i	−0.187852	+	0.187852i	0.606915	+	0.794767i	$0.292407\pi$
$728$		0			0
$729$	−35.2770			−1.30655
$730$		0			0
$731$	0.288660	+	0.288660i	0.0106765	+	0.0106765i
$732$		0			0
$733$		−	43.0744i		−	1.59099i	−0.605961	−	0.795494i	$-0.707211\pi$
$733$		−	43.0744i		−	1.59099i	0.605961	−	0.795494i	$-0.292789\pi$
$734$		0			0
$735$	−19.3686	−	17.3312i	−0.714422	−	0.639272i
$736$		0			0
$737$	28.4384	−	28.4384i	1.04754	−	1.04754i
$738$		0			0
$739$	11.3838	+	11.3838i	0.418762	+	0.418762i	0.884777	−	0.466015i	$-0.154311\pi$
$739$	11.3838	+	11.3838i	0.418762	+	0.418762i	−0.466015	+	0.884777i	$0.654311\pi$
$740$		0			0
$741$	16.3763	−	16.3763i	0.601599	−	0.601599i
$742$		0			0
$743$	−1.54795	−	1.54795i	−0.0567888	−	0.0567888i	0.678142	−	0.734931i	$-0.262785\pi$
$743$	−1.54795	−	1.54795i	−0.0567888	−	0.0567888i	−0.734931	+	0.678142i	$0.762785\pi$
$744$		0			0
$745$	17.4029	−	0.966116i	0.637591	−	0.0353958i
$746$		0			0
$747$	39.0774			1.42977
$748$		0			0
$749$	−16.7723	+	16.7723i	−0.612847	+	0.612847i
$750$		0			0
$751$			1.49244i			0.0544600i	0.999629	+	0.0272300i	$0.00866865\pi$
$751$			1.49244i			0.0544600i	−0.999629	+	0.0272300i	$0.991331\pi$
$752$		0			0
$753$	13.7394	+	13.7394i	0.500690	+	0.500690i
$754$		0			0
$755$	−6.16731	+	6.89231i	−0.224451	+	0.250837i
$756$		0			0
$757$		−	22.7030i		−	0.825154i	−0.910923	−	0.412577i	$-0.864629\pi$
$757$		−	22.7030i		−	0.825154i	0.910923	−	0.412577i	$-0.135371\pi$
$758$		0			0
$759$		−	29.0140i		−	1.05314i
$760$		0			0
$761$		−	33.6599i		−	1.22017i	−0.792335	−	0.610086i	$-0.791135\pi$
$761$		−	33.6599i		−	1.22017i	0.792335	−	0.610086i	$-0.208865\pi$
$762$		0			0
$763$		−	1.33523i		−	0.0483386i
$764$		0			0
$765$	−0.0461860	−	0.831959i	−0.00166986	−	0.0300795i
$766$		0			0
$767$	12.7194	+	12.7194i	0.459271	+	0.459271i
$768$		0			0
$769$		−	10.1943i		−	0.367615i	−0.982962	−	0.183808i	$-0.941158\pi$
$769$		−	10.1943i		−	0.367615i	0.982962	−	0.183808i	$-0.0588423\pi$
$770$		0			0
$771$	9.91699	−	9.91699i	0.357152	−	0.357152i
$772$		0			0
$773$	−7.34419			−0.264152			−0.132076	−	0.991240i	$-0.542164\pi$
$773$	−7.34419			−0.264152			−0.132076	+	0.991240i	$0.542164\pi$
$774$		0			0
$775$	−8.21755	+	0.915212i	−0.295183	+	0.0328754i
$776$		0			0
$777$	−15.5221	−	15.5221i	−0.556853	−	0.556853i
$778$		0			0
$779$	4.56658	−	4.56658i	0.163615	−	0.163615i
$780$		0			0
$781$	6.08556	+	6.08556i	0.217759	+	0.217759i
$782$		0			0
$783$	−5.15763	+	5.15763i	−0.184319	+	0.184319i
$784$		0			0
$785$	30.2239	−	33.7769i	1.07874	−	1.20555i
$786$		0			0
$787$		−	29.4359i		−	1.04928i	−0.851326	−	0.524638i	$-0.824201\pi$
$787$		−	29.4359i		−	1.04928i	0.851326	−	0.524638i	$-0.175799\pi$
$788$		0			0
$789$	43.2900	+	43.2900i	1.54116	+	1.54116i
$790$		0			0
$791$	42.0921			1.49662
$792$		0			0
$793$	24.5959	−	24.5959i	0.873425	−	0.873425i
$794$		0			0
$795$	4.92603	−	5.50511i	0.174708	−	0.195246i
$796$		0			0
$797$	−50.3934			−1.78503			−0.892513	−	0.451022i	$-0.851060\pi$
$797$	−50.3934			−1.78503			−0.892513	+	0.451022i	$0.851060\pi$
$798$		0			0
$799$	0.323131			0.0114315
$800$		0			0
$801$	54.9039			1.93993
$802$		0			0
$803$	53.4930			1.88773
$804$		0			0
$805$	−15.2232	+	17.0128i	−0.536548	+	0.599623i
$806$		0			0
$807$	6.51890	−	6.51890i	0.229476	−	0.229476i
$808$		0			0
$809$	−27.1588			−0.954851			−0.477426	−	0.878672i	$-0.658430\pi$
$809$	−27.1588			−0.954851			−0.477426	+	0.878672i	$0.658430\pi$
$810$		0			0
$811$	−11.5416	−	11.5416i	−0.405280	−	0.405280i	0.474809	−	0.880089i	$-0.342517\pi$
$811$	−11.5416	−	11.5416i	−0.405280	−	0.405280i	−0.880089	+	0.474809i	$0.842517\pi$
$812$		0			0
$813$			8.51429i			0.298609i
$814$		0			0
$815$	19.6575	−	21.9684i	0.688574	−	0.769520i
$816$		0			0
$817$	10.2779	−	10.2779i	0.359579	−	0.359579i
$818$		0			0
$819$	−20.2664	−	20.2664i	−0.708166	−	0.708166i
$820$		0			0
$821$	20.2900	−	20.2900i	0.708126	−	0.708126i	−0.258015	−	0.966141i	$-0.583068\pi$
$821$	20.2900	−	20.2900i	0.708126	−	0.708126i	0.966141	+	0.258015i	$0.0830684\pi$
$822$		0			0
$823$	31.4540	+	31.4540i	1.09642	+	1.09642i	0.994826	+	0.101592i	$0.0323936\pi$
$823$	31.4540	+	31.4540i	1.09642	+	1.09642i	0.101592	+	0.994826i	$0.467606\pi$
$824$		0			0
$825$	30.1638	−	37.7247i	1.05017	−	1.31341i
$826$		0			0
$827$	15.3304			0.533090			0.266545	−	0.963822i	$-0.414118\pi$
$827$	15.3304			0.533090			0.266545	+	0.963822i	$0.414118\pi$
$828$		0			0
$829$	0.896046	−	0.896046i	0.0311210	−	0.0311210i	−0.691375	−	0.722496i	$-0.742995\pi$
$829$	0.896046	−	0.896046i	0.0311210	−	0.0311210i	0.722496	+	0.691375i	$0.242995\pi$
$830$		0			0
$831$		−	11.7562i		−	0.407817i
$832$		0			0
$833$	0.341897	+	0.341897i	0.0118460	+	0.0118460i
$834$		0			0
$835$	2.07168	+	37.3176i	0.0716935	+	1.29143i
$836$		0			0
$837$			2.15491i			0.0744845i
$838$		0			0
$839$			48.1891i			1.66367i	0.555021	+	0.831837i	$0.312710\pi$
$839$			48.1891i			1.66367i	−0.555021	+	0.831837i	$0.687290\pi$
$840$		0			0
$841$		−	2.33080i		−	0.0803723i
$842$		0			0
$843$		−	56.4359i		−	1.94376i
$844$		0			0
$845$	−10.7836	+	12.0513i	−0.370967	+	0.414577i
$846$		0			0
$847$	−8.01241	−	8.01241i	−0.275310	−	0.275310i
$848$		0			0
$849$			27.7179i			0.951277i
$850$		0			0
$851$	−5.37484	+	5.37484i	−0.184247	+	0.184247i
$852$		0			0
$853$	13.7426			0.470537			0.235268	−	0.971930i	$-0.424403\pi$
$853$	13.7426			0.470537			0.235268	+	0.971930i	$0.424403\pi$
$854$		0			0
$855$	−29.6224	+	1.64448i	−1.01306	+	0.0562401i
$856$		0			0
$857$	−13.4366	−	13.4366i	−0.458986	−	0.458986i	0.439336	−	0.898323i	$-0.355214\pi$
$857$	−13.4366	−	13.4366i	−0.458986	−	0.458986i	−0.898323	+	0.439336i	$0.855214\pi$
$858$		0			0
$859$	7.00719	−	7.00719i	0.239082	−	0.239082i	−0.577388	−	0.816470i	$-0.695928\pi$
$859$	7.00719	−	7.00719i	0.239082	−	0.239082i	0.816470	+	0.577388i	$0.195928\pi$
$860$		0			0
$861$	−10.4806	−	10.4806i	−0.357178	−	0.357178i
$862$		0			0
$863$	41.4708	−	41.4708i	1.41168	−	1.41168i	0.663560	−	0.748123i	$-0.269045\pi$
$863$	41.4708	−	41.4708i	1.41168	−	1.41168i	0.748123	−	0.663560i	$-0.230955\pi$
$864$		0			0
$865$	25.9555	+	23.2252i	0.882513	+	0.789682i
$866$		0			0
$867$		−	43.3486i		−	1.47219i
$868$		0			0
$869$	−23.3070	−	23.3070i	−0.790636	−	0.790636i
$870$		0			0
$871$	−25.5125			−0.864458
$872$		0			0
$873$	17.5771	−	17.5771i	0.594894	−	0.594894i
$874$		0			0
$875$	−37.4807	+	6.29398i	−1.26708	+	0.212775i
$876$		0			0
$877$	5.34168			0.180376			0.0901879	−	0.995925i	$-0.471253\pi$
$877$	5.34168			0.180376			0.0901879	+	0.995925i	$0.471253\pi$
$878$		0			0
$879$	−46.9666			−1.58414
$880$		0			0
$881$	−45.9723			−1.54885			−0.774423	−	0.632668i	$-0.781960\pi$
$881$	−45.9723			−1.54885			−0.774423	+	0.632668i	$0.781960\pi$
$882$		0			0
$883$	2.64739			0.0890918			0.0445459	−	0.999007i	$-0.485816\pi$
$883$	2.64739			0.0890918			0.0445459	+	0.999007i	$0.485816\pi$
$884$		0			0
$885$	−2.36872	−	42.6683i	−0.0796238	−	1.43428i
$886$		0			0
$887$	−3.87171	+	3.87171i	−0.129999	+	0.129999i	−0.769113	−	0.639113i	$-0.779301\pi$
$887$	−3.87171	+	3.87171i	−0.129999	+	0.129999i	0.639113	+	0.769113i	$0.279301\pi$
$888$		0			0
$889$	−3.26661			−0.109558
$890$		0			0
$891$	19.2939	+	19.2939i	0.646369	+	0.646369i
$892$		0			0
$893$		−	11.5053i		−	0.385009i
$894$		0			0
$895$	49.2441	−	2.73378i	1.64605	−	0.0913801i
$896$		0			0
$897$	−13.0144	+	13.0144i	−0.434539	+	0.434539i
$898$		0			0
$899$	−6.54516	−	6.54516i	−0.218293	−	0.218293i
$900$		0			0
$901$	−0.0971768	+	0.0971768i	−0.00323743	+	0.00323743i
$902$		0			0
$903$	−23.5885	−	23.5885i	−0.784975	−	0.784975i
$904$		0			0
$905$	−0.523580	−	9.43136i	−0.0174044	−	0.313509i
$906$		0			0
$907$	26.2062			0.870163			0.435081	−	0.900391i	$-0.356720\pi$
$907$	26.2062			0.870163			0.435081	+	0.900391i	$0.356720\pi$
$908$		0			0
$909$	−22.3667	+	22.3667i	−0.741856	+	0.741856i
$910$		0			0
$911$			24.2898i			0.804757i	0.915473	+	0.402378i	$0.131816\pi$
$911$			24.2898i			0.804757i	−0.915473	+	0.402378i	$0.868184\pi$
$912$		0			0
$913$	−29.7983	−	29.7983i	−0.986181	−	0.986181i
$914$		0			0
$915$	−82.5089	+	4.58047i	−2.72766	+	0.151426i
$916$		0			0
$917$		−	26.1452i		−	0.863391i
$918$		0			0
$919$		−	41.1294i		−	1.35673i	−0.734723	−	0.678367i	$-0.762688\pi$
$919$		−	41.1294i		−	1.35673i	0.734723	−	0.678367i	$-0.237312\pi$
$920$		0			0
$921$		−	16.8629i		−	0.555650i
$922$		0			0
$923$		−	5.45944i		−	0.179700i
$924$		0			0
$925$	−12.5763	+	1.40066i	−0.413508	+	0.0460535i
$926$		0			0
$927$	6.80006	+	6.80006i	0.223343	+	0.223343i
$928$		0			0
$929$			43.4799i			1.42653i	0.700894	+	0.713265i	$0.252785\pi$
$929$			43.4799i			1.42653i	−0.700894	+	0.713265i	$0.747215\pi$
$930$		0			0
$931$	12.1734	−	12.1734i	0.398968	−	0.398968i
$932$		0			0
$933$	−1.54653			−0.0506313
$934$		0			0
$935$	−0.599188	+	0.669626i	−0.0195955	+	0.0218991i
$936$		0			0
$937$	13.0565	+	13.0565i	0.426537	+	0.426537i	0.887447	−	0.460910i	$-0.152477\pi$
$937$	13.0565	+	13.0565i	0.426537	+	0.426537i	−0.460910	+	0.887447i	$0.652477\pi$
$938$		0			0
$939$	−49.4266	+	49.4266i	−1.61298	+	1.61298i
$940$		0			0
$941$	5.53494	+	5.53494i	0.180434	+	0.180434i	0.791545	−	0.611111i	$-0.209277\pi$
$941$	5.53494	+	5.53494i	0.180434	+	0.180434i	−0.611111	+	0.791545i	$0.709277\pi$
$942$		0			0
$943$	−3.62911	+	3.62911i	−0.118180	+	0.118180i
$944$		0			0
$945$	0.549030	+	9.88979i	0.0178599	+	0.321715i
$946$		0			0
$947$			31.6905i			1.02980i	0.857249	+	0.514902i	$0.172172\pi$
$947$			31.6905i			1.02980i	−0.857249	+	0.514902i	$0.827828\pi$
$948$		0			0
$949$	−23.9947	−	23.9947i	−0.778900	−	0.778900i
$950$		0			0
$951$	−17.9717			−0.582772
$952$		0			0
$953$	2.85543	−	2.85543i	0.0924965	−	0.0924965i	−0.659344	−	0.751841i	$-0.729166\pi$
$953$	2.85543	−	2.85543i	0.0924965	−	0.0924965i	0.751841	+	0.659344i	$0.229166\pi$
$954$		0			0
$955$	−10.7841	−	9.64970i	−0.348964	−	0.312257i
$956$		0			0
$957$	54.0722			1.74791
$958$		0			0
$959$	35.9348			1.16039
$960$		0			0
$961$	28.2654			0.911786
$962$		0			0
$963$	24.4969			0.789401
$964$		0			0
$965$	35.0886	−	1.94793i	1.12954	−	0.0627062i
$966$		0			0
$967$	40.1144	−	40.1144i	1.28999	−	1.28999i	0.355202	−	0.934790i	$-0.384412\pi$
$967$	40.1144	−	40.1144i	1.28999	−	1.28999i	0.934790	−	0.355202i	$-0.115588\pi$
$968$		0			0
$969$	1.02356			0.0328816
$970$		0			0
$971$	−17.3439	−	17.3439i	−0.556592	−	0.556592i	0.371743	−	0.928335i	$-0.378760\pi$
$971$	−17.3439	−	17.3439i	−0.556592	−	0.556592i	−0.928335	+	0.371743i	$0.878760\pi$
$972$		0			0
$973$		−	55.4322i		−	1.77708i
$974$		0			0
$975$	−30.4519	+	3.39151i	−0.975241	+	0.108615i
$976$		0			0
$977$	−12.2234	+	12.2234i	−0.391060	+	0.391060i	−0.875065	−	0.484005i	$-0.839182\pi$
$977$	−12.2234	+	12.2234i	−0.391060	+	0.391060i	0.484005	+	0.875065i	$0.339182\pi$
$978$		0			0
$979$	−41.8667	−	41.8667i	−1.33807	−	1.33807i
$980$		0			0
$981$	−0.975089	+	0.975089i	−0.0311322	+	0.0311322i
$982$		0			0
$983$	−13.6091	−	13.6091i	−0.434063	−	0.434063i	0.455945	−	0.890008i	$-0.349301\pi$
$983$	−13.6091	−	13.6091i	−0.434063	−	0.434063i	−0.890008	+	0.455945i	$0.849301\pi$
$984$		0			0
$985$	41.8132	+	37.4148i	1.33228	+	1.19214i
$986$		0			0
$987$	−26.4053			−0.840491
$988$		0			0
$989$	−8.16797	+	8.16797i	−0.259726	+	0.259726i
$990$		0			0
$991$		−	52.9400i		−	1.68169i	−0.541273	−	0.840847i	$-0.682058\pi$
$991$		−	52.9400i		−	1.68169i	0.541273	−	0.840847i	$-0.317942\pi$
$992$		0			0
$993$	33.7513	+	33.7513i	1.07107	+	1.07107i
$994$		0			0
$995$	31.2573	+	27.9693i	0.990923	+	0.886688i
$996$		0			0
$997$			3.67381i			0.116351i	0.998306	+	0.0581754i	$0.0185283\pi$
$997$			3.67381i			0.116351i	−0.998306	+	0.0581754i	$0.981472\pi$
$998$		0			0
$999$			3.29792i			0.104342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.s.c.223.2		18
4.3	odd	2		640.2.s.d.223.8		18
5.2	odd	4		640.2.j.c.607.8		18
8.3	odd	2		80.2.s.b.3.2	yes	18
8.5	even	2		320.2.s.b.303.8		18
16.3	odd	4		320.2.j.b.143.8		18
16.5	even	4		640.2.j.d.543.8		18
16.11	odd	4		640.2.j.c.543.2		18
16.13	even	4		80.2.j.b.43.4	✓	18
20.7	even	4		640.2.j.d.607.2		18
24.11	even	2		720.2.z.g.163.8		18
40.3	even	4		400.2.j.d.307.6		18
40.13	odd	4		1600.2.j.d.1007.8		18
40.19	odd	2		400.2.s.d.243.8		18
40.27	even	4		80.2.j.b.67.4	yes	18
40.29	even	2		1600.2.s.d.943.2		18
40.37	odd	4		320.2.j.b.47.2		18
48.29	odd	4		720.2.bd.g.523.6		18
80.3	even	4		1600.2.s.d.207.2		18
80.13	odd	4		400.2.s.d.107.8		18
80.19	odd	4		1600.2.j.d.143.2		18
80.27	even	4	inner	640.2.s.c.287.2		18
80.29	even	4		400.2.j.d.43.6		18
80.37	odd	4		640.2.s.d.287.8		18
80.67	even	4		320.2.s.b.207.8		18
80.77	odd	4		80.2.s.b.27.2	yes	18
120.107	odd	4		720.2.bd.g.307.6		18
240.77	even	4		720.2.z.g.667.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.4	✓	18	16.13	even	4
80.2.j.b.67.4	yes	18	40.27	even	4
80.2.s.b.3.2	yes	18	8.3	odd	2
80.2.s.b.27.2	yes	18	80.77	odd	4
320.2.j.b.47.2		18	40.37	odd	4
320.2.j.b.143.8		18	16.3	odd	4
320.2.s.b.207.8		18	80.67	even	4
320.2.s.b.303.8		18	8.5	even	2
400.2.j.d.43.6		18	80.29	even	4
400.2.j.d.307.6		18	40.3	even	4
400.2.s.d.107.8		18	80.13	odd	4
400.2.s.d.243.8		18	40.19	odd	2
640.2.j.c.543.2		18	16.11	odd	4
640.2.j.c.607.8		18	5.2	odd	4
640.2.j.d.543.8		18	16.5	even	4
640.2.j.d.607.2		18	20.7	even	4
640.2.s.c.223.2		18	1.1	even	1	trivial
640.2.s.c.287.2		18	80.27	even	4	inner
640.2.s.d.223.8		18	4.3	odd	2
640.2.s.d.287.8		18	80.37	odd	4
720.2.z.g.163.8		18	24.11	even	2
720.2.z.g.667.8		18	240.77	even	4
720.2.bd.g.307.6		18	120.107	odd	4
720.2.bd.g.523.6		18	48.29	odd	4
1600.2.j.d.143.2		18	80.19	odd	4
1600.2.j.d.1007.8		18	40.13	odd	4
1600.2.s.d.207.2		18	80.3	even	4
1600.2.s.d.943.2		18	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.55161 q^{3} +(-1.49107 + 1.66635i) q^{5} +(-2.40368 + 2.40368i) q^{7} +3.51070 q^{9} +O(q^{10})\)	\(q-2.55161 q^{3} +(-1.49107 + 1.66635i) q^{5} +(-2.40368 + 2.40368i) q^{7} +3.51070 q^{9} +(-2.67707 - 2.67707i) q^{11} +2.40164i q^{13} +(3.80462 - 4.25187i) q^{15} +(-0.0750544 + 0.0750544i) q^{17} +(2.67236 + 2.67236i) q^{19} +(6.13324 - 6.13324i) q^{21} +(-2.12375 - 2.12375i) q^{23} +(-0.553442 - 4.96928i) q^{25} -1.30310 q^{27} +(3.95795 - 3.95795i) q^{29} -1.65367i q^{31} +(6.83083 + 6.83083i) q^{33} +(-0.421324 - 7.58941i) q^{35} -2.53082i q^{37} -6.12803i q^{39} -1.70882i q^{41} -3.84601i q^{43} +(-5.23469 + 5.85005i) q^{45} +(-2.15264 - 2.15264i) q^{47} -4.55532i q^{49} +(0.191509 - 0.191509i) q^{51} +1.29475 q^{53} +(8.45262 - 0.469246i) q^{55} +(-6.81881 - 6.81881i) q^{57} +(5.29614 - 5.29614i) q^{59} +(-10.2413 - 10.2413i) q^{61} +(-8.43858 + 8.43858i) q^{63} +(-4.00197 - 3.58100i) q^{65} +10.6230i q^{67} +(5.41898 + 5.41898i) q^{69} -2.27322 q^{71} +(-9.99096 + 9.99096i) q^{73} +(1.41217 + 12.6796i) q^{75} +12.8696 q^{77} +8.70617 q^{79} -7.20709 q^{81} +11.1310 q^{83} +(-0.0131558 - 0.236978i) q^{85} +(-10.0991 + 10.0991i) q^{87} +15.6390 q^{89} +(-5.77276 - 5.77276i) q^{91} +4.21952i q^{93} +(-8.43775 + 0.468420i) q^{95} +(5.00672 - 5.00672i) q^{97} +(-9.39839 - 9.39839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9} - 2 q^{11} + 20 q^{15} - 6 q^{17} - 2 q^{19} + 16 q^{21} + 2 q^{23} - 6 q^{25} - 24 q^{27} - 14 q^{29} - 8 q^{33} + 2 q^{35} + 14 q^{45} - 38 q^{47} + 8 q^{51} - 12 q^{53} + 6 q^{55} - 24 q^{57} + 10 q^{59} - 14 q^{61} + 6 q^{63} + 32 q^{69} - 24 q^{71} - 14 q^{73} + 16 q^{75} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} - 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q - 2 * q^5 - 2 * q^7 + 10 * q^9 - 2 * q^11 + 20 * q^15 - 6 * q^17 - 2 * q^19 + 16 * q^21 + 2 * q^23 - 6 * q^25 - 24 * q^27 - 14 * q^29 - 8 * q^33 + 2 * q^35 + 14 * q^45 - 38 * q^47 + 8 * q^51 - 12 * q^53 + 6 * q^55 - 24 * q^57 + 10 * q^59 - 14 * q^61 + 6 * q^63 + 32 * q^69 - 24 * q^71 - 14 * q^73 + 16 * q^75 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 - 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more