LMFDB - Embedded newform 760.2.q.f.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(121,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("760.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$1.07988 - 1.87040i$ of defining polynomial
Character	$\chi$	$=$	760.201
Dual form			760.2.q.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.832272 + 1.44154i) q^{3} +(-0.500000 + 0.866025i) q^{5} +1.93047 q^{7} +(0.114645 + 0.198571i) q^{9} +1.38905 q^{11} +(0.362251 + 0.627436i) q^{13} +(-0.832272 - 1.44154i) q^{15} +(1.38535 - 2.39951i) q^{17} +(0.607771 + 4.31632i) q^{19} +(-1.60667 + 2.78284i) q^{21} +(4.34262 + 7.52163i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.37530 q^{27} +(-2.76753 - 4.79350i) q^{29} -2.37530 q^{31} +(-1.15606 + 2.00236i) q^{33} +(-0.965233 + 1.67183i) q^{35} -6.58865 q^{37} -1.20596 q^{39} +(1.62978 - 2.82286i) q^{41} +(-4.67968 + 8.10544i) q^{43} -0.229290 q^{45} +(5.78953 + 10.0278i) q^{47} -3.27330 q^{49} +(2.30599 + 3.99408i) q^{51} +(3.64491 + 6.31317i) q^{53} +(-0.694523 + 1.20295i) q^{55} +(-6.72797 - 2.71623i) q^{57} +(1.56156 - 2.70471i) q^{59} +(-1.44004 - 2.49423i) q^{61} +(0.221318 + 0.383335i) q^{63} -0.724501 q^{65} +(0.435255 + 0.753883i) q^{67} -14.4570 q^{69} +(1.16663 - 2.02066i) q^{71} +(-2.02310 + 3.50412i) q^{73} +1.66454 q^{75} +2.68151 q^{77} +(4.16801 - 7.21921i) q^{79} +(4.12978 - 7.15298i) q^{81} -9.97989 q^{83} +(1.38535 + 2.39951i) q^{85} +9.21335 q^{87} +(-2.41105 - 4.17606i) q^{89} +(0.699312 + 1.21124i) q^{91} +(1.97690 - 3.42408i) q^{93} +(-4.04193 - 1.63181i) q^{95} +(3.77232 - 6.53384i) q^{97} +(0.159247 + 0.275824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9} - 8 q^{11} + q^{13} + q^{15} + 13 q^{17} + q^{19} + 12 q^{21} + 8 q^{23} - 4 q^{25} - 20 q^{27} - 3 q^{29} + 4 q^{31} - 15 q^{33} - 2 q^{35} + 20 q^{37} - 2 q^{39}+ \cdots + 30 q^{99}+O(q^{100}) $ 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9 - 8 * q^11 + q^13 + q^15 + 13 * q^17 + q^19 + 12 * q^21 + 8 * q^23 - 4 * q^25 - 20 * q^27 - 3 * q^29 + 4 * q^31 - 15 * q^33 - 2 * q^35 + 20 * q^37 - 2 * q^39 - 8 * q^41 - 3 * q^43 + 2 * q^45 + 10 * q^47 + 12 * q^49 - 16 * q^51 - 11 * q^53 + 4 * q^55 - 29 * q^57 + q^59 - 25 * q^63 - 2 * q^65 - 8 * q^67 + 22 * q^69 - 4 * q^71 - 20 * q^73 - 2 * q^75 - 36 * q^77 - 3 * q^79 + 12 * q^81 - 30 * q^83 + 13 * q^85 + 24 * q^87 + 17 * q^89 - 4 * q^91 + 12 * q^93 + 4 * q^95 + 11 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.832272	+	1.44154i	−0.480513	+	0.832272i	−0.999750	−	0.0223576i	$-0.992883\pi$
$3$	−0.832272	+	1.44154i	−0.480513	+	0.832272i	0.519237	+	0.854630i	$0.326216\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.93047			0.729647			0.364824	−	0.931077i	$-0.381129\pi$
$7$	1.93047			0.729647			0.364824	+	0.931077i	$0.381129\pi$
$8$		0			0
$9$	0.114645	+	0.198571i	0.0382150	+	0.0661904i
$10$		0			0
$11$	1.38905			0.418813			0.209407	−	0.977829i	$-0.432847\pi$
$11$	1.38905			0.418813			0.209407	+	0.977829i	$0.432847\pi$
$12$		0			0
$13$	0.362251	+	0.627436i	0.100470	+	0.174020i	0.911878	−	0.410460i	$-0.134632\pi$
$13$	0.362251	+	0.627436i	0.100470	+	0.174020i	−0.811408	+	0.584480i	$0.801299\pi$
$14$		0			0
$15$	−0.832272	−	1.44154i	−0.214892	−	0.372204i
$16$		0			0
$17$	1.38535	−	2.39951i	0.335998	−	0.581965i	−0.647678	−	0.761914i	$-0.724260\pi$
$17$	1.38535	−	2.39951i	0.335998	−	0.581965i	0.983676	+	0.179949i	$0.0575932\pi$
$18$		0			0
$19$	0.607771	+	4.31632i	0.139432	+	0.990232i
$19$	0.607771	+	4.31632i	0.139432	+	0.990232i
$20$		0			0
$21$	−1.60667	+	2.78284i	−0.350605	+	0.607265i
$22$		0			0
$23$	4.34262	+	7.52163i	0.905498	+	1.56837i	0.820247	+	0.572009i	$0.193836\pi$
$23$	4.34262	+	7.52163i	0.905498	+	1.56837i	0.0852507	+	0.996360i	$0.472831\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−5.37530			−1.03448
$28$		0			0
$29$	−2.76753	−	4.79350i	−0.513917	−	0.890130i	−0.999870	−	0.0161451i	$-0.994861\pi$
$29$	−2.76753	−	4.79350i	−0.513917	−	0.890130i	0.485953	−	0.873985i	$-0.338473\pi$
$30$		0			0
$31$	−2.37530			−0.426616			−0.213308	−	0.976985i	$-0.568424\pi$
$31$	−2.37530			−0.426616			−0.213308	+	0.976985i	$0.568424\pi$
$32$		0			0
$33$	−1.15606	+	2.00236i	−0.201245	+	0.348567i
$34$		0			0
$35$	−0.965233	+	1.67183i	−0.163154	+	0.282591i
$36$		0			0
$37$	−6.58865			−1.08317			−0.541583	−	0.840647i	$-0.682175\pi$
$37$	−6.58865			−1.08317			−0.541583	+	0.840647i	$0.682175\pi$
$38$		0			0
$39$	−1.20596			−0.193109
$40$		0			0
$41$	1.62978	−	2.82286i	0.254529	−	0.440856i	−0.710239	−	0.703961i	$-0.751413\pi$
$41$	1.62978	−	2.82286i	0.254529	−	0.440856i	0.964767	+	0.263104i	$0.0847464\pi$
$42$		0			0
$43$	−4.67968	+	8.10544i	−0.713644	+	1.23607i	0.249836	+	0.968288i	$0.419623\pi$
$43$	−4.67968	+	8.10544i	−0.713644	+	1.23607i	−0.963480	+	0.267780i	$0.913710\pi$
$44$		0			0
$45$	−0.229290			−0.0341806
$46$		0			0
$47$	5.78953	+	10.0278i	0.844490	+	1.46270i	0.886063	+	0.463565i	$0.153430\pi$
$47$	5.78953	+	10.0278i	0.844490	+	1.46270i	−0.0415729	+	0.999135i	$0.513237\pi$
$48$		0			0
$49$	−3.27330			−0.467615
$50$		0			0
$51$	2.30599	+	3.99408i	0.322903	+	0.559284i
$52$		0			0
$53$	3.64491	+	6.31317i	0.500667	+	0.867181i	1.00000		0.000770280i	$0.000245188\pi$
$53$	3.64491	+	6.31317i	0.500667	+	0.867181i	−0.499333	+	0.866410i	$0.666421\pi$
$54$		0			0
$55$	−0.694523	+	1.20295i	−0.0936495	+	0.162206i
$56$		0			0
$57$	−6.72797	−	2.71623i	−0.891142	−	0.359773i
$58$		0			0
$59$	1.56156	−	2.70471i	0.203298	−	0.352123i	−0.746291	−	0.665620i	$-0.768167\pi$
$59$	1.56156	−	2.70471i	0.203298	−	0.352123i	0.949589	+	0.313497i	$0.101501\pi$
$60$		0			0
$61$	−1.44004	−	2.49423i	−0.184379	−	0.319353i	0.758988	−	0.651104i	$-0.225694\pi$
$61$	−1.44004	−	2.49423i	−0.184379	−	0.319353i	−0.943367	+	0.331751i	$0.892361\pi$
$62$		0			0
$63$	0.221318	+	0.383335i	0.0278835	+	0.0482956i
$64$		0			0
$65$	−0.724501			−0.0898633
$66$		0			0
$67$	0.435255	+	0.753883i	0.0531748	+	0.0921015i	0.891388	−	0.453242i	$-0.149733\pi$
$67$	0.435255	+	0.753883i	0.0531748	+	0.0921015i	−0.838213	+	0.545343i	$0.816399\pi$
$68$		0			0
$69$	−14.4570			−1.74041
$70$		0			0
$71$	1.16663	−	2.02066i	0.138453	−	0.239808i	−0.788458	−	0.615089i	$-0.789120\pi$
$71$	1.16663	−	2.02066i	0.138453	−	0.239808i	0.926911	+	0.375280i	$0.122454\pi$
$72$		0			0
$73$	−2.02310	+	3.50412i	−0.236786	+	0.410126i	−0.959790	−	0.280718i	$-0.909428\pi$
$73$	−2.02310	+	3.50412i	−0.236786	+	0.410126i	0.723004	+	0.690844i	$0.242761\pi$
$74$		0			0
$75$	1.66454			0.192205
$76$		0			0
$77$	2.68151			0.305586
$78$		0			0
$79$	4.16801	−	7.21921i	0.468938	−	0.812225i	−0.530431	−	0.847728i	$-0.677970\pi$
$79$	4.16801	−	7.21921i	0.468938	−	0.812225i	0.999370	+	0.0355030i	$0.0113033\pi$
$80$		0			0
$81$	4.12978	−	7.15298i	0.458864	−	0.794776i
$82$		0			0
$83$	−9.97989			−1.09543			−0.547717	−	0.836663i	$-0.684503\pi$
$83$	−9.97989			−1.09543			−0.547717	+	0.836663i	$0.684503\pi$
$84$		0			0
$85$	1.38535	+	2.39951i	0.150263	+	0.260263i
$86$		0			0
$87$	9.21335			0.987774
$88$		0			0
$89$	−2.41105	−	4.17606i	−0.255571	−	0.442662i	0.709479	−	0.704726i	$-0.248930\pi$
$89$	−2.41105	−	4.17606i	−0.255571	−	0.442662i	−0.965050	+	0.262064i	$0.915597\pi$
$90$		0			0
$91$	0.699312	+	1.21124i	0.0733078	+	0.126973i
$92$		0			0
$93$	1.97690	−	3.42408i	0.204995	−	0.355061i
$94$		0			0
$95$	−4.04193	−	1.63181i	−0.414693	−	0.167421i
$96$		0			0
$97$	3.77232	−	6.53384i	0.383021	−	0.663411i	−0.608472	−	0.793576i	$-0.708217\pi$
$97$	3.77232	−	6.53384i	0.383021	−	0.663411i	0.991492	+	0.130164i	$0.0415505\pi$
$98$		0			0
$99$	0.159247	+	0.275824i	0.0160050	+	0.0277214i
$100$		0			0
$101$	9.17171	+	15.8859i	0.912619	+	1.58070i	0.810351	+	0.585945i	$0.199277\pi$
$101$	9.17171	+	15.8859i	0.912619	+	1.58070i	0.102268	+	0.994757i	$0.467390\pi$
$102$		0			0
$103$	2.68523			0.264584			0.132292	−	0.991211i	$-0.457766\pi$
$103$	2.68523			0.264584			0.132292	+	0.991211i	$0.457766\pi$
$104$		0			0
$105$	−1.60667	−	2.78284i	−0.156795	−	0.271577i
$106$		0			0
$107$	12.0143			1.16147			0.580734	−	0.814093i	$-0.302766\pi$
$107$	12.0143			1.16147			0.580734	+	0.814093i	$0.302766\pi$
$108$		0			0
$109$	0.391751	−	0.678532i	0.0375229	−	0.0649916i	−0.846654	−	0.532144i	$-0.821387\pi$
$109$	0.391751	−	0.678532i	0.0375229	−	0.0649916i	0.884177	+	0.467152i	$0.154720\pi$
$110$		0			0
$111$	5.48355	−	9.49778i	0.520475	−	0.901490i
$112$		0			0
$113$	20.9151			1.96753			0.983763	−	0.179470i	$-0.0574384\pi$
$113$	20.9151			1.96753			0.983763	+	0.179470i	$0.0574384\pi$
$114$		0			0
$115$	−8.68523			−0.809902
$116$		0			0
$117$	−0.0830605	+	0.143865i	−0.00767895	+	0.0133003i
$118$		0			0
$119$	2.67438	−	4.63216i	0.245160	−	0.424630i
$120$		0			0
$121$	−9.07055			−0.824596
$122$		0			0
$123$	2.71284	+	4.69877i	0.244608	+	0.423674i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−3.14381	−	5.44524i	−0.278968	−	0.483187i	0.692160	−	0.721744i	$-0.256659\pi$
$127$	−3.14381	−	5.44524i	−0.278968	−	0.483187i	−0.971129	+	0.238557i	$0.923326\pi$
$128$		0			0
$129$	−7.78953	−	13.4919i	−0.685830	−	1.18789i
$130$		0			0
$131$	5.74332	−	9.94773i	0.501797	−	0.869137i	−0.498201	−	0.867061i	$-0.666006\pi$
$131$	5.74332	−	9.94773i	0.501797	−	0.869137i	0.999998	−	0.00207579i	$-0.000660744\pi$
$132$		0			0
$133$	1.17328	+	8.33251i	0.101736	+	0.722520i
$134$		0			0
$135$	2.68765	−	4.65515i	0.231316	−	0.400651i
$136$		0			0
$137$	−4.23484	−	7.33497i	−0.361807	−	0.626668i	0.626451	−	0.779461i	$-0.284507\pi$
$137$	−4.23484	−	7.33497i	−0.361807	−	0.626668i	−0.988258	+	0.152792i	$0.951173\pi$
$138$		0			0
$139$	−3.18655	−	5.51927i	−0.270280	−	0.468138i	0.698654	−	0.715460i	$-0.253783\pi$
$139$	−3.18655	−	5.51927i	−0.270280	−	0.468138i	−0.968933	+	0.247322i	$0.920450\pi$
$140$		0			0
$141$	−19.2739			−1.62315
$142$		0			0
$143$	0.503183	+	0.871538i	0.0420782	+	0.0728817i
$144$		0			0
$145$	5.53505			0.459661
$146$		0			0
$147$	2.72428	−	4.71859i	0.224695	−	0.389183i
$148$		0			0
$149$	8.28134	−	14.3437i	0.678434	−	1.17508i	−0.297019	−	0.954872i	$-0.595992\pi$
$149$	8.28134	−	14.3437i	0.678434	−	1.17508i	0.975452	−	0.220210i	$-0.0706743\pi$
$150$		0			0
$151$	11.1677			0.908816			0.454408	−	0.890794i	$-0.349851\pi$
$151$	11.1677			0.908816			0.454408	+	0.890794i	$0.349851\pi$
$152$		0			0
$153$	0.635297			0.0513607
$154$		0			0
$155$	1.18765	−	2.05707i	0.0953943	−	0.165228i
$156$		0			0
$157$	−4.63694	+	8.03141i	−0.370068	+	0.640977i	−0.989576	−	0.144014i	$-0.953999\pi$
$157$	−4.63694	+	8.03141i	−0.370068	+	0.640977i	0.619508	+	0.784991i	$0.287332\pi$
$158$		0			0
$159$	−12.1342			−0.962307
$160$		0			0
$161$	8.38327	+	14.5203i	0.660694	+	1.14436i
$162$		0			0
$163$	11.5680			0.906072			0.453036	−	0.891492i	$-0.350341\pi$
$163$	11.5680			0.906072			0.453036	+	0.891492i	$0.350341\pi$
$164$		0			0
$165$	−1.15606	−	2.00236i	−0.0899995	−	0.155884i
$166$		0			0
$167$	6.89891	+	11.9493i	0.533854	+	0.924662i	0.999218	+	0.0395425i	$0.0125901\pi$
$167$	6.89891	+	11.9493i	0.533854	+	0.924662i	−0.465364	+	0.885119i	$0.654077\pi$
$168$		0			0
$169$	6.23755	−	10.8038i	0.479811	−	0.831058i
$170$		0			0
$171$	−0.787418	+	0.615531i	−0.0602154	+	0.0470708i
$172$		0			0
$173$	3.90945	−	6.77136i	0.297230	−	0.514817i	−0.678271	−	0.734811i	$-0.737271\pi$
$173$	3.90945	−	6.77136i	0.297230	−	0.514817i	0.975501	+	0.219995i	$0.0706040\pi$
$174$		0			0
$175$	−0.965233	−	1.67183i	−0.0729647	−	0.126379i
$176$		0			0
$177$	2.59929	+	4.50210i	0.195375	+	0.338399i
$178$		0			0
$179$	−11.9978			−0.896758			−0.448379	−	0.893844i	$-0.647998\pi$
$179$	−11.9978			−0.896758			−0.448379	+	0.893844i	$0.647998\pi$
$180$		0			0
$181$	1.51243	+	2.61960i	0.112418	+	0.194713i	0.916745	−	0.399474i	$-0.130807\pi$
$181$	1.51243	+	2.61960i	0.112418	+	0.194713i	−0.804327	+	0.594187i	$0.797474\pi$
$182$		0			0
$183$	4.79404			0.354385
$184$		0			0
$185$	3.29432	−	5.70593i	0.242203	−	0.419509i
$186$		0			0
$187$	1.92432	−	3.33302i	0.140720	−	0.243735i
$188$		0			0
$189$	−10.3768			−0.754803
$190$		0			0
$191$	4.54836			0.329108			0.164554	−	0.986368i	$-0.447382\pi$
$191$	4.54836			0.329108			0.164554	+	0.986368i	$0.447382\pi$
$192$		0			0
$193$	5.20008	−	9.00680i	0.374310	−	0.648324i	−0.615914	−	0.787814i	$-0.711213\pi$
$193$	5.20008	−	9.00680i	0.374310	−	0.648324i	0.990223	+	0.139490i	$0.0445463\pi$
$194$		0			0
$195$	0.602982	−	1.04440i	0.0431805	−	0.0747907i
$196$		0			0
$197$	−3.41778			−0.243507			−0.121753	−	0.992560i	$-0.538852\pi$
$197$	−3.41778			−0.243507			−0.121753	+	0.992560i	$0.538852\pi$
$198$		0			0
$199$	−7.02120	−	12.1611i	−0.497719	−	0.862075i	0.502277	−	0.864707i	$-0.332496\pi$
$199$	−7.02120	−	12.1611i	−0.497719	−	0.862075i	−0.999997	+	0.00263148i	$0.999162\pi$
$200$		0			0
$201$	−1.44900			−0.102205
$202$		0			0
$203$	−5.34262	−	9.25368i	−0.374978	−	0.649481i
$204$		0			0
$205$	1.62978	+	2.82286i	0.113829	+	0.197157i
$206$		0			0
$207$	−0.995719	+	1.72464i	−0.0692073	+	0.119871i
$208$		0			0
$209$	0.844222	+	5.99557i	0.0583961	+	0.414722i
$210$		0			0
$211$	5.82562	−	10.0903i	0.401052	−	0.694643i	−0.592801	−	0.805349i	$-0.701978\pi$
$211$	5.82562	−	10.0903i	0.401052	−	0.694643i	0.993853	+	0.110706i	$0.0353113\pi$
$212$		0			0
$213$	1.94191	+	3.36348i	0.133057	+	0.230462i
$214$		0			0
$215$	−4.67968	−	8.10544i	−0.319151	−	0.552786i
$216$		0			0
$217$	−4.58543			−0.311279
$218$		0			0
$219$	−3.36755	−	5.83276i	−0.227558	−	0.394142i
$220$		0			0
$221$	2.00738			0.135031
$222$		0			0
$223$	−10.3115	+	17.8601i	−0.690512	+	1.19600i	0.281159	+	0.959661i	$0.409281\pi$
$223$	−10.3115	+	17.8601i	−0.690512	+	1.19600i	−0.971670	+	0.236340i	$0.924052\pi$
$224$		0			0
$225$	0.114645	−	0.198571i	0.00764301	−	0.0132381i
$226$		0			0
$227$	−16.5510			−1.09853			−0.549264	−	0.835649i	$-0.685092\pi$
$227$	−16.5510			−1.09853			−0.549264	+	0.835649i	$0.685092\pi$
$228$		0			0
$229$	−5.70856			−0.377232			−0.188616	−	0.982051i	$-0.560400\pi$
$229$	−5.70856			−0.377232			−0.188616	+	0.982051i	$0.560400\pi$
$230$		0			0
$231$	−2.23174	+	3.86549i	−0.146838	+	0.254331i
$232$		0			0
$233$	11.8471	−	20.5197i	0.776127	−	1.34429i	−0.158031	−	0.987434i	$-0.550515\pi$
$233$	11.8471	−	20.5197i	0.776127	−	1.34429i	0.934159	−	0.356858i	$-0.116152\pi$
$234$		0			0
$235$	−11.5791			−0.755335
$236$		0			0
$237$	6.93785	+	12.0167i	0.450662	+	0.780569i
$238$		0			0
$239$	21.1598			1.36871			0.684357	−	0.729147i	$-0.260083\pi$
$239$	21.1598			1.36871			0.684357	+	0.729147i	$0.260083\pi$
$240$		0			0
$241$	4.83673	+	8.37746i	0.311561	+	0.539640i	0.978701	−	0.205293i	$-0.0658148\pi$
$241$	4.83673	+	8.37746i	0.311561	+	0.539640i	−0.667139	+	0.744933i	$0.732481\pi$
$242$		0			0
$243$	−1.18875	−	2.05897i	−0.0762582	−	0.132083i
$244$		0			0
$245$	1.63665	−	2.83476i	0.104562	−	0.181106i
$246$		0			0
$247$	−2.48805	+	1.94493i	−0.158311	+	0.123753i
$248$		0			0
$249$	8.30599	−	14.3864i	0.526370	−	0.911700i
$250$		0			0
$251$	3.97002	+	6.87628i	0.250586	+	0.434027i	0.963687	−	0.267034i	$-0.0860435\pi$
$251$	3.97002	+	6.87628i	0.250586	+	0.434027i	−0.713102	+	0.701061i	$0.752710\pi$
$252$		0			0
$253$	6.03209	+	10.4479i	0.379234	+	0.656853i
$254$		0			0
$255$	−4.61197			−0.288813
$256$		0			0
$257$	−15.0297	−	26.0322i	−0.937525	−	1.62384i	−0.770068	−	0.637962i	$-0.779778\pi$
$257$	−15.0297	−	26.0322i	−0.937525	−	1.62384i	−0.167458	−	0.985879i	$-0.553556\pi$
$258$		0			0
$259$	−12.7192			−0.790330
$260$		0			0
$261$	0.634567	−	1.09910i	0.0392787	−	0.0680327i
$262$		0			0
$263$	−5.85457	+	10.1404i	−0.361008	+	0.625284i	−0.988127	−	0.153639i	$-0.950901\pi$
$263$	−5.85457	+	10.1404i	−0.361008	+	0.625284i	0.627119	+	0.778923i	$0.284234\pi$
$264$		0			0
$265$	−7.28982			−0.447810
$266$		0			0
$267$	8.02661			0.491221
$268$		0			0
$269$	−7.12528	+	12.3413i	−0.434436	+	0.752465i	−0.997249	−	0.0741190i	$-0.976386\pi$
$269$	−7.12528	+	12.3413i	−0.434436	+	0.752465i	0.562814	+	0.826584i	$0.309719\pi$
$270$		0			0
$271$	−13.2288	+	22.9129i	−0.803590	+	1.39186i	0.113648	+	0.993521i	$0.463746\pi$
$271$	−13.2288	+	22.9129i	−0.803590	+	1.39186i	−0.917239	+	0.398338i	$0.869587\pi$
$272$		0			0
$273$	−2.32807			−0.140901
$274$		0			0
$275$	−0.694523	−	1.20295i	−0.0418813	−	0.0725406i
$276$		0			0
$277$	10.5274			0.632533			0.316267	−	0.948670i	$-0.397571\pi$
$277$	10.5274			0.632533			0.316267	+	0.948670i	$0.397571\pi$
$278$		0			0
$279$	−0.272316	−	0.471666i	−0.0163032	−	0.0282379i
$280$		0			0
$281$	−9.20805	−	15.9488i	−0.549306	−	0.951426i	−0.998322	−	0.0579025i	$-0.981559\pi$
$281$	−9.20805	−	15.9488i	−0.549306	−	0.951426i	0.449016	−	0.893524i	$-0.351775\pi$
$282$		0			0
$283$	13.7527	−	23.8203i	0.817512	−	1.41597i	−0.0899979	−	0.995942i	$-0.528686\pi$
$283$	13.7527	−	23.8203i	0.817512	−	1.41597i	0.907510	−	0.420030i	$-0.137981\pi$
$284$		0			0
$285$	5.71631	−	4.46848i	0.338605	−	0.264690i
$286$		0			0
$287$	3.14623	−	5.44943i	0.185716	−	0.321670i
$288$		0			0
$289$	4.66158	+	8.07410i	0.274211	+	0.474947i
$290$		0			0
$291$	6.27919	+	10.8759i	0.368093	+	0.637555i
$292$		0			0
$293$	17.1119			0.999689			0.499845	−	0.866115i	$-0.333390\pi$
$293$	17.1119			0.999689			0.499845	+	0.866115i	$0.333390\pi$
$294$		0			0
$295$	1.56156	+	2.70471i	0.0909177	+	0.157474i
$296$		0			0
$297$	−7.46654			−0.433252
$298$		0			0
$299$	−3.14623	+	5.44943i	−0.181951	+	0.315149i
$300$		0			0
$301$	−9.03396	+	15.6473i	−0.520709	+	0.901894i
$302$		0			0
$303$	−30.5334			−1.75410
$304$		0			0
$305$	2.88009			0.164913
$306$		0			0
$307$	4.71236	−	8.16205i	0.268949	−	0.465833i	−0.699642	−	0.714494i	$-0.746657\pi$
$307$	4.71236	−	8.16205i	0.268949	−	0.465833i	0.968591	+	0.248661i	$0.0799905\pi$
$308$		0			0
$309$	−2.23484	+	3.87086i	−0.127136	+	0.220206i
$310$		0			0
$311$	−15.0791			−0.855058			−0.427529	−	0.904002i	$-0.640616\pi$
$311$	−15.0791			−0.855058			−0.427529	+	0.904002i	$0.640616\pi$
$312$		0			0
$313$	10.1399	+	17.5628i	0.573139	+	0.992706i	0.996241	+	0.0866239i	$0.0276078\pi$
$313$	10.1399	+	17.5628i	0.573139	+	0.992706i	−0.423102	+	0.906082i	$0.639059\pi$
$314$		0			0
$315$	−0.442637			−0.0249398
$316$		0			0
$317$	10.9297	+	18.9307i	0.613871	+	1.06325i	0.990582	+	0.136924i	$0.0437217\pi$
$317$	10.9297	+	18.9307i	0.613871	+	1.06325i	−0.376711	+	0.926331i	$0.622945\pi$
$318$		0			0
$319$	−3.84422	−	6.65839i	−0.215235	−	0.372798i
$320$		0			0
$321$	−9.99919	+	17.3191i	−0.558100	+	0.966658i
$322$		0			0
$323$	11.1990	+	4.52128i	0.623130	+	0.251571i
$324$		0			0
$325$	0.362251	−	0.627436i	0.0200940	−	0.0348039i
$326$		0			0
$327$	0.652086	+	1.12945i	0.0360605	+	0.0624586i
$328$		0			0
$329$	11.1765	+	19.3583i	0.616180	+	1.06726i
$330$		0			0
$331$	3.52548			0.193778			0.0968888	−	0.995295i	$-0.469111\pi$
$331$	3.52548			0.193778			0.0968888	+	0.995295i	$0.469111\pi$
$332$		0			0
$333$	−0.755356	−	1.30831i	−0.0413932	−	0.0716952i
$334$		0			0
$335$	−0.870509			−0.0475610
$336$		0			0
$337$	−10.8843	+	18.8521i	−0.592903	+	1.02694i	0.400936	+	0.916106i	$0.368685\pi$
$337$	−10.8843	+	18.8521i	−0.592903	+	1.02694i	−0.993839	+	0.110832i	$0.964648\pi$
$338$		0			0
$339$	−17.4071	+	30.1499i	−0.945422	+	1.63752i
$340$		0			0
$341$	−3.29940			−0.178672
$342$		0			0
$343$	−19.8323			−1.07084
$344$		0			0
$345$	7.22848	−	12.5201i	0.389168	−	0.674059i
$346$		0			0
$347$	−7.05498	+	12.2196i	−0.378731	+	0.655981i	−0.990878	−	0.134763i	$-0.956973\pi$
$347$	−7.05498	+	12.2196i	−0.378731	+	0.655981i	0.612147	+	0.790744i	$0.290306\pi$
$348$		0			0
$349$	−6.65401			−0.356181			−0.178091	−	0.984014i	$-0.556992\pi$
$349$	−6.65401			−0.356181			−0.178091	+	0.984014i	$0.556992\pi$
$350$		0			0
$351$	−1.94720	−	3.37266i	−0.103934	−	0.180019i
$352$		0			0
$353$	21.9755			1.16964			0.584819	−	0.811164i	$-0.301166\pi$
$353$	21.9755			1.16964			0.584819	+	0.811164i	$0.301166\pi$
$354$		0			0
$355$	1.16663	+	2.02066i	0.0619183	+	0.107246i
$356$		0			0
$357$	4.45163	+	7.71044i	0.235605	+	0.408080i
$358$		0			0
$359$	12.6449	−	21.9016i	0.667373	−	1.15592i	−0.311263	−	0.950324i	$-0.600752\pi$
$359$	12.6449	−	21.9016i	0.667373	−	1.15592i	0.978636	−	0.205600i	$-0.0659146\pi$
$360$		0			0
$361$	−18.2612	+	5.24667i	−0.961117	+	0.276141i
$362$		0			0
$363$	7.54917	−	13.0755i	0.396229	−	0.686288i
$364$		0			0
$365$	−2.02310	−	3.50412i	−0.105894	−	0.183414i
$366$		0			0
$367$	−15.0740	−	26.1090i	−0.786857	−	1.36288i	−0.927883	−	0.372871i	$-0.878373\pi$
$367$	−15.0740	−	26.1090i	−0.786857	−	1.36288i	0.141026	−	0.990006i	$-0.454960\pi$
$368$		0			0
$369$	0.747384			0.0389073
$370$		0			0
$371$	7.03637	+	12.1874i	0.365310	+	0.632736i
$372$		0			0
$373$	−1.71718			−0.0889122			−0.0444561	−	0.999011i	$-0.514155\pi$
$373$	−1.71718			−0.0889122			−0.0444561	+	0.999011i	$0.514155\pi$
$374$		0			0
$375$	−0.832272	+	1.44154i	−0.0429784	+	0.0744407i
$376$		0			0
$377$	2.00508	−	3.47289i	0.103267	−	0.178863i
$378$		0			0
$379$	6.63170			0.340648			0.170324	−	0.985388i	$-0.445519\pi$
$379$	6.63170			0.340648			0.170324	+	0.985388i	$0.445519\pi$
$380$		0			0
$381$	10.4660			0.536191
$382$		0			0
$383$	−0.516709	+	0.894966i	−0.0264026	+	0.0457306i	−0.878925	−	0.476960i	$-0.841739\pi$
$383$	−0.516709	+	0.894966i	−0.0264026	+	0.0457306i	0.852522	+	0.522691i	$0.175072\pi$
$384$		0			0
$385$	−1.34075	+	2.32225i	−0.0683311	+	0.118353i
$386$		0			0
$387$	−2.14601			−0.109088
$388$		0			0
$389$	13.8845	+	24.0487i	0.703974	+	1.21932i	0.967060	+	0.254547i	$0.0819263\pi$
$389$	13.8845	+	24.0487i	0.703974	+	1.21932i	−0.263086	+	0.964772i	$0.584740\pi$
$390$		0			0
$391$	24.0643			1.21698
$392$		0			0
$393$	9.56002	+	16.5584i	0.482239	+	0.835263i
$394$		0			0
$395$	4.16801	+	7.21921i	0.209716	+	0.363238i
$396$		0			0
$397$	−3.93554	+	6.81656i	−0.197519	+	0.342113i	−0.947723	−	0.319093i	$-0.896622\pi$
$397$	−3.93554	+	6.81656i	−0.197519	+	0.342113i	0.750204	+	0.661206i	$0.229955\pi$
$398$		0			0
$399$	−12.9881	−	5.24358i	−0.650219	−	0.262508i
$400$		0			0
$401$	10.9076	−	18.8926i	0.544702	−	0.943451i	−0.453924	−	0.891041i	$-0.649976\pi$
$401$	10.9076	−	18.8926i	0.544702	−	0.943451i	0.998626	−	0.0524109i	$-0.0166906\pi$
$402$		0			0
$403$	−0.860453	−	1.49035i	−0.0428622	−	0.0742396i
$404$		0			0
$405$	4.12978	+	7.15298i	0.205210	+	0.355435i
$406$		0			0
$407$	−9.15193			−0.453644
$408$		0			0
$409$	−9.72881	−	16.8508i	−0.481059	−	0.833218i	0.518705	−	0.854953i	$-0.326414\pi$
$409$	−9.72881	−	16.8508i	−0.481059	−	0.833218i	−0.999764	+	0.0217350i	$0.993081\pi$
$410$		0			0
$411$	14.0982			0.695412
$412$		0			0
$413$	3.01454	−	5.22134i	0.148336	−	0.256925i
$414$		0			0
$415$	4.98994	−	8.64284i	0.244947	−	0.424260i
$416$		0			0
$417$	10.6083			0.519491
$418$		0			0
$419$	6.06413			0.296252			0.148126	−	0.988969i	$-0.452676\pi$
$419$	6.06413			0.296252			0.148126	+	0.988969i	$0.452676\pi$
$420$		0			0
$421$	−8.70884	+	15.0842i	−0.424443	+	0.735157i	−0.996368	−	0.0851488i	$-0.972863\pi$
$421$	−8.70884	+	15.0842i	−0.424443	+	0.735157i	0.571925	+	0.820306i	$0.306197\pi$
$422$		0			0
$423$	−1.32748	+	2.29927i	−0.0645444	+	0.111794i
$424$		0			0
$425$	−2.77071			−0.134399
$426$		0			0
$427$	−2.77996	−	4.81502i	−0.134531	−	0.233015i
$428$		0			0
$429$	−1.67514			−0.0808765
$430$		0			0
$431$	2.16988	+	3.75834i	0.104519	+	0.181033i	0.913542	−	0.406745i	$-0.133336\pi$
$431$	2.16988	+	3.75834i	0.104519	+	0.181033i	−0.809022	+	0.587778i	$0.800003\pi$
$432$		0			0
$433$	−1.10083	−	1.90670i	−0.0529026	−	0.0916300i	0.838361	−	0.545115i	$-0.183514\pi$
$433$	−1.10083	−	1.90670i	−0.0529026	−	0.0916300i	−0.891264	+	0.453485i	$0.850181\pi$
$434$		0			0
$435$	−4.60667	+	7.97899i	−0.220873	+	0.382563i
$436$		0			0
$437$	−29.8264	+	23.3156i	−1.42679	+	1.11533i
$438$		0			0
$439$	5.81444	−	10.0709i	0.277508	−	0.480658i	−0.693257	−	0.720691i	$-0.743825\pi$
$439$	5.81444	−	10.0709i	0.277508	−	0.480658i	0.970765	+	0.240033i	$0.0771582\pi$
$440$		0			0
$441$	−0.375268	−	0.649983i	−0.0178699	−	0.0309516i
$442$		0			0
$443$	−2.08572	−	3.61257i	−0.0990955	−	0.171638i	0.812215	−	0.583358i	$-0.198262\pi$
$443$	−2.08572	−	3.61257i	−0.0990955	−	0.171638i	−0.911311	+	0.411720i	$0.864928\pi$
$444$		0			0
$445$	4.82210			0.228590
$446$		0			0
$447$	13.7847	+	23.8757i	0.651992	+	1.12928i
$448$		0			0
$449$	18.0392			0.851321			0.425661	−	0.904883i	$-0.360042\pi$
$449$	18.0392			0.851321			0.425661	+	0.904883i	$0.360042\pi$
$450$		0			0
$451$	2.26384	−	3.92108i	0.106600	−	0.184636i
$452$		0			0
$453$	−9.29458	+	16.0987i	−0.436697	+	0.756382i
$454$		0			0
$455$	−1.39862			−0.0655685
$456$		0			0
$457$	26.4990			1.23957			0.619785	−	0.784771i	$-0.287220\pi$
$457$	26.4990			1.23957			0.619785	+	0.784771i	$0.287220\pi$
$458$		0			0
$459$	−7.44670	+	12.8981i	−0.347582	+	0.602030i
$460$		0			0
$461$	0.151830	−	0.262977i	0.00707142	−	0.0122481i	−0.862468	−	0.506112i	$-0.831082\pi$
$461$	0.151830	−	0.262977i	0.00707142	−	0.0122481i	0.869539	+	0.493863i	$0.164416\pi$
$462$		0			0
$463$	−23.4781			−1.09112			−0.545560	−	0.838072i	$-0.683683\pi$
$463$	−23.4781			−1.09112			−0.545560	+	0.838072i	$0.683683\pi$
$464$		0			0
$465$	1.97690	+	3.42408i	0.0916763	+	0.158788i
$466$		0			0
$467$	10.8030			0.499905			0.249953	−	0.968258i	$-0.419585\pi$
$467$	10.8030			0.499905			0.249953	+	0.968258i	$0.419585\pi$
$468$		0			0
$469$	0.840244	+	1.45535i	0.0387989	+	0.0672016i
$470$		0			0
$471$	−7.71839	−	13.3686i	−0.355645	−	0.615995i
$472$		0			0
$473$	−6.50029	+	11.2588i	−0.298884	+	0.517681i
$474$		0			0
$475$	3.43416	−	2.68451i	0.157570	−	0.123174i
$476$		0			0
$477$	−0.835742	+	1.44755i	−0.0382660	+	0.0662787i
$478$		0			0
$479$	−4.08682	−	7.07858i	−0.186731	−	0.323428i	0.757427	−	0.652920i	$-0.226456\pi$
$479$	−4.08682	−	7.07858i	−0.186731	−	0.323428i	−0.944159	+	0.329491i	$0.893123\pi$
$480$		0			0
$481$	−2.38674	−	4.13396i	−0.108826	−	0.188492i
$482$		0			0
$483$	−27.9087			−1.26989
$484$		0			0
$485$	3.77232	+	6.53384i	0.171292	+	0.296687i
$486$		0			0
$487$	7.20822			0.326636			0.163318	−	0.986574i	$-0.447780\pi$
$487$	7.20822			0.326636			0.163318	+	0.986574i	$0.447780\pi$
$488$		0			0
$489$	−9.62769	+	16.6757i	−0.435379	+	0.754099i
$490$		0			0
$491$	15.5913	−	27.0049i	0.703624	−	1.21871i	−0.263561	−	0.964643i	$-0.584897\pi$
$491$	15.5913	−	27.0049i	0.703624	−	1.21871i	0.967186	−	0.254070i	$-0.0817695\pi$
$492$		0			0
$493$	−15.3360			−0.690700
$494$		0			0
$495$	−0.318495			−0.0143153
$496$		0			0
$497$	2.25214	−	3.90082i	0.101022	−	0.174976i
$498$		0			0
$499$	9.32828	−	16.1571i	0.417591	−	0.723289i	−0.578105	−	0.815962i	$-0.696208\pi$
$499$	9.32828	−	16.1571i	0.417591	−	0.723289i	0.995697	+	0.0926730i	$0.0295411\pi$
$500$		0			0
$501$	−22.9671			−1.02609
$502$		0			0
$503$	10.4018	+	18.0164i	0.463792	+	0.803311i	0.999146	−	0.0413169i	$-0.0131553\pi$
$503$	10.4018	+	18.0164i	0.463792	+	0.803311i	−0.535354	+	0.844627i	$0.679822\pi$
$504$		0			0
$505$	−18.3434			−0.816271
$506$		0			0
$507$	10.3827	+	17.9833i	0.461111	+	0.798668i
$508$		0			0
$509$	−21.0971	−	36.5413i	−0.935114	−	1.61966i	−0.774431	−	0.632658i	$-0.781964\pi$
$509$	−21.0971	−	36.5413i	−0.935114	−	1.61966i	−0.160682	−	0.987006i	$-0.551370\pi$
$510$		0			0
$511$	−3.90553	+	6.76458i	−0.172771	+	0.299247i
$512$		0			0
$513$	−3.26695	−	23.2015i	−0.144239	−	1.02437i
$514$		0			0
$515$	−1.34262	+	2.32548i	−0.0591627	+	0.102473i
$516$		0			0
$517$	8.04193	+	13.9290i	0.353684	+	0.612598i
$518$		0			0
$519$	6.50745	+	11.2712i	0.285645	+	0.494752i
$520$		0			0
$521$	−8.94530			−0.391901			−0.195950	−	0.980614i	$-0.562779\pi$
$521$	−8.94530			−0.391901			−0.195950	+	0.980614i	$0.562779\pi$
$522$		0			0
$523$	−4.64699	−	8.04883i	−0.203199	−	0.351951i	0.746358	−	0.665544i	$-0.231800\pi$
$523$	−4.64699	−	8.04883i	−0.203199	−	0.351951i	−0.949557	+	0.313593i	$0.898467\pi$
$524$		0			0
$525$	3.21335			0.140242
$526$		0			0
$527$	−3.29063	+	5.69954i	−0.143342	+	0.248276i
$528$		0			0
$529$	−26.2166	+	45.4085i	−1.13985	+	1.97428i
$530$		0			0
$531$	0.716102			0.0310762
$532$		0			0
$533$	2.36155			0.102290
$534$		0			0
$535$	−6.00716	+	10.4047i	−0.259712	+	0.449835i
$536$		0			0
$537$	9.98544	−	17.2953i	0.430904	−	0.746347i
$538$		0			0
$539$	−4.54677			−0.195843
$540$		0			0
$541$	6.87044	+	11.9000i	0.295383	+	0.511619i	0.975074	−	0.221880i	$-0.0712193\pi$
$541$	6.87044	+	11.9000i	0.295383	+	0.511619i	−0.679691	+	0.733499i	$0.737886\pi$
$542$		0			0
$543$	−5.03501			−0.216073
$544$		0			0
$545$	0.391751	+	0.678532i	0.0167808	+	0.0290651i
$546$		0			0
$547$	−14.9315	−	25.8621i	−0.638426	−	1.10579i	−0.985778	−	0.168051i	$-0.946253\pi$
$547$	−14.9315	−	25.8621i	−0.638426	−	1.10579i	0.347353	−	0.937735i	$-0.387081\pi$
$548$		0			0
$549$	0.330188	−	0.571902i	0.0140921	−	0.0244082i
$550$		0			0
$551$	19.0082	−	14.8589i	0.809778	−	0.633010i
$552$		0			0
$553$	8.04621	−	13.9364i	0.342160	−	0.592638i
$554$		0			0
$555$	5.48355	+	9.49778i	0.232764	+	0.403158i
$556$		0			0
$557$	0.167949	+	0.290896i	0.00711622	+	0.0123257i	0.869562	−	0.493825i	$-0.164401\pi$
$557$	0.167949	+	0.290896i	0.00711622	+	0.0123257i	−0.862445	+	0.506150i	$0.831068\pi$
$558$		0			0
$559$	−6.78086			−0.286800
$560$		0			0
$561$	3.20312	+	5.54797i	0.135236	+	0.234235i
$562$		0			0
$563$	−23.0854			−0.972933			−0.486467	−	0.873699i	$-0.661714\pi$
$563$	−23.0854			−0.972933			−0.486467	+	0.873699i	$0.661714\pi$
$564$		0			0
$565$	−10.4575	+	18.1130i	−0.439952	+	0.762020i
$566$		0			0
$567$	7.97239	−	13.8086i	0.334809	−	0.579906i
$568$		0			0
$569$	27.8284			1.16663			0.583314	−	0.812246i	$-0.301756\pi$
$569$	27.8284			1.16663			0.583314	+	0.812246i	$0.301756\pi$
$570$		0			0
$571$	−15.9821			−0.668829			−0.334415	−	0.942426i	$-0.608539\pi$
$571$	−15.9821			−0.668829			−0.334415	+	0.942426i	$0.608539\pi$
$572$		0			0
$573$	−3.78547	+	6.55663i	−0.158140	+	0.273907i
$574$		0			0
$575$	4.34262	−	7.52163i	0.181100	−	0.313674i
$576$		0			0
$577$	−32.6686			−1.36001			−0.680006	−	0.733206i	$-0.738023\pi$
$577$	−32.6686			−1.36001			−0.680006	+	0.733206i	$0.738023\pi$
$578$		0			0
$579$	8.65576	+	14.9922i	0.359721	+	0.623055i
$580$		0			0
$581$	−19.2658			−0.799281
$582$		0			0
$583$	5.06295	+	8.76928i	0.209686	+	0.363187i
$584$		0			0
$585$	−0.0830605	−	0.143865i	−0.00343413	−	0.00594809i
$586$		0			0
$587$	5.23774	−	9.07203i	0.216185	−	0.374443i	−0.737454	−	0.675398i	$-0.763972\pi$
$587$	5.23774	−	9.07203i	0.216185	−	0.374443i	0.953638	+	0.300955i	$0.0973053\pi$
$588$		0			0
$589$	−1.44364	−	10.2525i	−0.0594841	−	0.422449i
$590$		0			0
$591$	2.84452	−	4.92686i	0.117008	−	0.202664i
$592$		0			0
$593$	−2.74783	−	4.75938i	−0.112840	−	0.195444i	0.804074	−	0.594529i	$-0.202661\pi$
$593$	−2.74783	−	4.75938i	−0.112840	−	0.195444i	−0.916914	+	0.399085i	$0.869328\pi$
$594$		0			0
$595$	2.67438	+	4.63216i	0.109639	+	0.189900i
$596$		0			0
$597$	23.3742			0.956642
$598$		0			0
$599$	12.9435	+	22.4188i	0.528858	+	0.916008i	0.999434	+	0.0336489i	$0.0107128\pi$
$599$	12.9435	+	22.4188i	0.528858	+	0.916008i	−0.470576	+	0.882359i	$0.655954\pi$
$600$		0			0
$601$	−15.7448			−0.642244			−0.321122	−	0.947038i	$-0.604060\pi$
$601$	−15.7448			−0.642244			−0.321122	+	0.947038i	$0.604060\pi$
$602$		0			0
$603$	−0.0997996	+	0.172858i	−0.00406416	+	0.00703932i
$604$		0			0
$605$	4.53528	−	7.85533i	0.184385	−	0.319364i
$606$		0			0
$607$	−42.1534			−1.71095			−0.855477	−	0.517841i	$-0.826736\pi$
$607$	−42.1534			−1.71095			−0.855477	+	0.517841i	$0.826736\pi$
$608$		0			0
$609$	17.7860			0.720727
$610$		0			0
$611$	−4.19452	+	7.26513i	−0.169692	+	0.293916i
$612$		0			0
$613$	18.6686	−	32.3349i	0.754016	−	1.30599i	−0.191846	−	0.981425i	$-0.561448\pi$
$613$	18.6686	−	32.3349i	0.754016	−	1.30599i	0.945862	−	0.324569i	$-0.105219\pi$
$614$		0			0
$615$	−5.42568			−0.218784
$616$		0			0
$617$	−17.0655	−	29.5583i	−0.687031	−	1.18997i	−0.972794	−	0.231672i	$-0.925580\pi$
$617$	−17.0655	−	29.5583i	−0.687031	−	1.18997i	0.285763	−	0.958300i	$-0.407753\pi$
$618$		0			0
$619$	49.3884			1.98509			0.992545	−	0.121883i	$-0.0388931\pi$
$619$	49.3884			1.98509			0.992545	+	0.121883i	$0.0388931\pi$
$620$		0			0
$621$	−23.3429	−	40.4310i	−0.936717	−	1.62244i
$622$		0			0
$623$	−4.65445	−	8.06175i	−0.186477	−	0.322987i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−9.34546	−	3.77297i	−0.373222	−	0.150678i
$628$		0			0
$629$	−9.12761	+	15.8095i	−0.363942	+	0.630366i
$630$		0			0
$631$	7.21686	+	12.5000i	0.287299	+	0.497616i	0.973164	−	0.230112i	$-0.0739094\pi$
$631$	7.21686	+	12.5000i	0.287299	+	0.497616i	−0.685865	+	0.727729i	$0.740576\pi$
$632$		0			0
$633$	9.69701	+	16.7957i	0.385421	+	0.667569i
$634$		0			0
$635$	6.28762			0.249517
$636$		0			0
$637$	−1.18576	−	2.05379i	−0.0469813	−	0.0813741i
$638$		0			0
$639$	0.534993			0.0211640
$640$		0			0
$641$	17.2689	−	29.9106i	0.682079	−	1.18140i	−0.292266	−	0.956337i	$-0.594409\pi$
$641$	17.2689	−	29.9106i	0.682079	−	1.18140i	0.974345	−	0.225059i	$-0.0722574\pi$
$642$		0			0
$643$	−11.9859	+	20.7602i	−0.472679	+	0.818703i	−0.999511	−	0.0312659i	$-0.990046\pi$
$643$	−11.9859	+	20.7602i	−0.472679	+	0.818703i	0.526833	+	0.849969i	$0.323379\pi$
$644$		0			0
$645$	15.5791			0.613425
$646$		0			0
$647$	−1.02508			−0.0403000			−0.0201500	−	0.999797i	$-0.506414\pi$
$647$	−1.02508			−0.0403000			−0.0201500	+	0.999797i	$0.506414\pi$
$648$		0			0
$649$	2.16908	−	3.75696i	0.0851439	−	0.147474i
$650$		0			0
$651$	3.81633	−	6.61008i	0.149574	−	0.259069i
$652$		0			0
$653$	7.53629			0.294918			0.147459	−	0.989068i	$-0.452891\pi$
$653$	7.53629			0.294918			0.147459	+	0.989068i	$0.452891\pi$
$654$		0			0
$655$	5.74332	+	9.94773i	0.224410	+	0.388690i
$656$		0			0
$657$	−0.927756			−0.0361952
$658$		0			0
$659$	−13.9737	−	24.2032i	−0.544340	−	0.942824i	−0.998648	−	0.0519796i	$-0.983447\pi$
$659$	−13.9737	−	24.2032i	−0.544340	−	0.942824i	0.454308	−	0.890844i	$-0.349886\pi$
$660$		0			0
$661$	−17.3026	−	29.9690i	−0.672992	−	1.16566i	−0.977051	−	0.213004i	$-0.931675\pi$
$661$	−17.3026	−	29.9690i	−0.672992	−	1.16566i	0.304059	−	0.952653i	$-0.401658\pi$
$662$		0			0
$663$	−1.67069	+	2.89372i	−0.0648842	+	0.112383i
$664$		0			0
$665$	−7.80280	−	3.15016i	−0.302580	−	0.122158i
$666$		0			0
$667$	24.0366	−	41.6326i	0.930701	−	1.61202i
$668$		0			0
$669$	−17.1640	−	29.7290i	−0.663599	−	1.14939i
$670$		0			0
$671$	−2.00029	−	3.46460i	−0.0772202	−	0.133749i
$672$		0			0
$673$	2.79404			0.107702			0.0538511	−	0.998549i	$-0.482850\pi$
$673$	2.79404			0.107702			0.0538511	+	0.998549i	$0.482850\pi$
$674$		0			0
$675$	2.68765	+	4.65515i	0.103448	+	0.179177i
$676$		0			0
$677$	47.6578			1.83164			0.915819	−	0.401591i	$-0.131543\pi$
$677$	47.6578			1.83164			0.915819	+	0.401591i	$0.131543\pi$
$678$		0			0
$679$	7.28233	−	12.6134i	0.279470	−	0.484056i
$680$		0			0
$681$	13.7749	−	23.8589i	0.527857	−	0.914275i
$682$		0			0
$683$	−4.51475			−0.172752			−0.0863760	−	0.996263i	$-0.527529\pi$
$683$	−4.51475			−0.172752			−0.0863760	+	0.996263i	$0.527529\pi$
$684$		0			0
$685$	8.46969			0.323610
$686$		0			0
$687$	4.75108	−	8.22910i	0.181265	−	0.313960i
$688$		0			0
$689$	−2.64074	+	4.57390i	−0.100604	+	0.174252i
$690$		0			0
$691$	−23.5817			−0.897090			−0.448545	−	0.893760i	$-0.648058\pi$
$691$	−23.5817			−0.897090			−0.448545	+	0.893760i	$0.648058\pi$
$692$		0			0
$693$	0.307421	+	0.532470i	0.0116780	+	0.0202268i
$694$		0			0
$695$	6.37310			0.241746
$696$		0			0
$697$	−4.51564	−	7.82132i	−0.171042	−	0.296254i
$698$		0			0
$699$	19.7200	+	34.1560i	0.745878	+	1.29190i
$700$		0			0
$701$	22.3790	−	38.7616i	0.845244	−	1.46400i	−0.0401660	−	0.999193i	$-0.512789\pi$
$701$	22.3790	−	38.7616i	0.845244	−	1.46400i	0.885410	−	0.464812i	$-0.153878\pi$
$702$		0			0
$703$	−4.00439	−	28.4387i	−0.151028	−	1.07259i
$704$		0			0
$705$	9.63694	−	16.6917i	0.362948	−	0.628645i
$706$		0			0
$707$	17.7057	+	30.6671i	0.665890	+	1.15336i
$708$		0			0
$709$	15.5351	+	26.9076i	0.583432	+	1.01053i	0.995069	+	0.0991864i	$0.0316240\pi$
$709$	15.5351	+	26.9076i	0.583432	+	1.01053i	−0.411637	+	0.911348i	$0.635043\pi$
$710$		0			0
$711$	1.91137			0.0716820
$712$		0			0
$713$	−10.3150	−	17.8661i	−0.386300	−	0.669091i
$714$		0			0
$715$	−1.00637			−0.0376359
$716$		0			0
$717$	−17.6107	+	30.5027i	−0.657685	+	1.13914i
$718$		0			0
$719$	−4.93847	+	8.55368i	−0.184174	+	0.318998i	−0.943298	−	0.331948i	$-0.892294\pi$
$719$	−4.93847	+	8.55368i	−0.184174	+	0.318998i	0.759124	+	0.650946i	$0.225628\pi$
$720$		0			0
$721$	5.18375			0.193053
$722$		0			0
$723$	−16.1019			−0.598836
$724$		0			0
$725$	−2.76753	+	4.79350i	−0.102783	+	0.178026i
$726$		0			0
$727$	16.3627	−	28.3411i	0.606859	−	1.05111i	−0.384895	−	0.922960i	$-0.625762\pi$
$727$	16.3627	−	28.3411i	0.606859	−	1.05111i	0.991755	−	0.128151i	$-0.0409042\pi$
$728$		0			0
$729$	28.7361			1.06430
$730$		0			0
$731$	12.9660	+	22.4578i	0.479566	+	0.830632i
$732$		0			0
$733$	−5.88082			−0.217213			−0.108607	−	0.994085i	$-0.534639\pi$
$733$	−5.88082			−0.217213			−0.108607	+	0.994085i	$0.534639\pi$
$734$		0			0
$735$	2.72428	+	4.71859i	0.100487	+	0.174048i
$736$		0			0
$737$	0.604589	+	1.04718i	0.0222703	+	0.0385733i
$738$		0			0
$739$	6.61596	−	11.4592i	0.243372	−	0.421533i	−0.718301	−	0.695733i	$-0.755080\pi$
$739$	6.61596	−	11.4592i	0.243372	−	0.421533i	0.961673	+	0.274200i	$0.0884130\pi$
$740$		0			0
$741$	−0.732951	−	5.20533i	−0.0269256	−	0.191223i
$742$		0			0
$743$	5.70036	−	9.87332i	0.209126	−	0.362217i	−0.742313	−	0.670053i	$-0.766271\pi$
$743$	5.70036	−	9.87332i	0.209126	−	0.362217i	0.951439	+	0.307836i	$0.0996048\pi$
$744$		0			0
$745$	8.28134	+	14.3437i	0.303405	+	0.525513i
$746$		0			0
$747$	−1.14415	−	1.98172i	−0.0418621	−	0.0725073i
$748$		0			0
$749$	23.1932			0.847462
$750$		0			0
$751$	12.1592	+	21.0604i	0.443696	+	0.768504i	0.997960	−	0.0638367i	$-0.0203337\pi$
$751$	12.1592	+	21.0604i	0.443696	+	0.768504i	−0.554264	+	0.832341i	$0.687000\pi$
$752$		0			0
$753$	−13.2166			−0.481638
$754$		0			0
$755$	−5.58386	+	9.67152i	−0.203217	+	0.351983i
$756$		0			0
$757$	15.7200	−	27.2278i	0.571353	−	0.989612i	−0.425075	−	0.905158i	$-0.639752\pi$
$757$	15.7200	−	27.2278i	0.571353	−	0.989612i	0.996427	−	0.0844534i	$-0.0269144\pi$
$758$		0			0
$759$	−20.0814			−0.728908
$760$		0			0
$761$	−12.1438			−0.440211			−0.220105	−	0.975476i	$-0.570640\pi$
$761$	−12.1438			−0.440211			−0.220105	+	0.975476i	$0.570640\pi$
$762$		0			0
$763$	0.756261	−	1.30988i	0.0273785	−	0.0474209i
$764$		0			0
$765$	−0.317648	+	0.550183i	−0.0114846	+	0.0198919i
$766$		0			0
$767$	2.26271			0.0817016
$768$		0			0
$769$	3.81872	+	6.61421i	0.137706	+	0.238515i	0.926628	−	0.375979i	$-0.122694\pi$
$769$	3.81872	+	6.61421i	0.137706	+	0.238515i	−0.788922	+	0.614494i	$0.789360\pi$
$770$		0			0
$771$	50.0351			1.80197
$772$		0			0
$773$	−20.1630	−	34.9233i	−0.725212	−	1.25610i	−0.958887	−	0.283790i	$-0.908408\pi$
$773$	−20.1630	−	34.9233i	−0.725212	−	1.25610i	0.233674	−	0.972315i	$-0.424925\pi$
$774$		0			0
$775$	1.18765	+	2.05707i	0.0426616	+	0.0738921i
$776$		0			0
$777$	10.5858	−	18.3351i	0.379763	−	0.657770i
$778$		0			0
$779$	13.1749	+	5.31899i	0.472039	+	0.190573i
$780$		0			0
$781$	1.62050	−	2.80679i	0.0579861	−	0.100435i
$782$		0			0
$783$	14.8763	+	25.7665i	0.531635	+	0.920819i
$784$		0			0
$785$	−4.63694	−	8.03141i	−0.165499	−	0.286653i
$786$		0			0
$787$	16.8421			0.600355			0.300177	−	0.953883i	$-0.402954\pi$
$787$	16.8421			0.600355			0.300177	+	0.953883i	$0.402954\pi$
$788$		0			0
$789$	−9.74519	−	16.8792i	−0.346938	−	0.600914i
$790$		0			0
$791$	40.3759			1.43560
$792$		0			0
$793$	1.04331	−	1.80707i	0.0370491	−	0.0641710i
$794$		0			0
$795$	6.06712	−	10.5086i	0.215178	−	0.372700i
$796$		0			0
$797$	−49.5064			−1.75361			−0.876804	−	0.480848i	$-0.840329\pi$
$797$	−49.5064			−1.75361			−0.876804	+	0.480848i	$0.840329\pi$
$798$		0			0
$799$	32.0822			1.13499
$800$		0			0
$801$	0.552831	−	0.957531i	0.0195333	−	0.0338327i
$802$		0			0
$803$	−2.81018	+	4.86738i	−0.0991693	+	0.171766i
$804$		0			0
$805$	−16.7665			−0.590943
$806$		0			0
$807$	−11.8603	−	20.5427i	−0.417504	−	0.723138i
$808$		0			0
$809$	10.6840			0.375629			0.187815	−	0.982205i	$-0.439860\pi$
$809$	10.6840			0.375629			0.187815	+	0.982205i	$0.439860\pi$
$810$		0			0
$811$	−10.8753	−	18.8366i	−0.381883	−	0.661441i	0.609448	−	0.792826i	$-0.291391\pi$
$811$	−10.8753	−	18.8366i	−0.381883	−	0.661441i	−0.991331	+	0.131385i	$0.958058\pi$
$812$		0			0
$813$	−22.0199	−	38.1395i	−0.772271	−	1.33761i
$814$		0			0
$815$	−5.78398	+	10.0181i	−0.202604	+	0.350920i
$816$		0			0
$817$	−37.8298	−	15.2727i	−1.32350	−	0.534325i
$818$		0			0
$819$	−0.160345	+	0.277726i	−0.00560292	+	0.00970455i
$820$		0			0
$821$	−22.8956	−	39.6564i	−0.799063	−	1.38402i	−0.920227	−	0.391385i	$-0.871996\pi$
$821$	−22.8956	−	39.6564i	−0.799063	−	1.38402i	0.121165	−	0.992632i	$-0.461337\pi$
$822$		0			0
$823$	9.05095	+	15.6767i	0.315496	+	0.546456i	0.979543	−	0.201236i	$-0.0644957\pi$
$823$	9.05095	+	15.6767i	0.315496	+	0.546456i	−0.664047	+	0.747691i	$0.731162\pi$
$824$		0			0
$825$	2.31213			0.0804980
$826$		0			0
$827$	10.1157	+	17.5210i	0.351758	+	0.609263i	0.986558	−	0.163414i	$-0.0522506\pi$
$827$	10.1157	+	17.5210i	0.351758	+	0.609263i	−0.634799	+	0.772677i	$0.718917\pi$
$828$		0			0
$829$	35.7458			1.24150			0.620752	−	0.784007i	$-0.286827\pi$
$829$	35.7458			1.24150			0.620752	+	0.784007i	$0.286827\pi$
$830$		0			0
$831$	−8.76171	+	15.1757i	−0.303940	+	0.526440i
$832$		0			0
$833$	−4.53469	+	7.85431i	−0.157118	+	0.272136i
$834$		0			0
$835$	−13.7978			−0.477493
$836$		0			0
$837$	12.7679			0.441325
$838$		0			0
$839$	−21.2601	+	36.8236i	−0.733980	+	1.27129i	0.221189	+	0.975231i	$0.429006\pi$
$839$	−21.2601	+	36.8236i	−0.733980	+	1.27129i	−0.955169	+	0.296060i	$0.904327\pi$
$840$		0			0
$841$	−0.818413	+	1.41753i	−0.0282212	+	0.0488805i
$842$		0			0
$843$	30.6544			1.05579
$844$		0			0
$845$	6.23755	+	10.8038i	0.214578	+	0.371660i
$846$		0			0
$847$	−17.5104			−0.601664
$848$		0			0
$849$	22.8920	+	39.6500i	0.785650	+	1.36079i
$850$		0			0
$851$	−28.6120	−	49.5574i	−0.980805	−	1.69880i
$852$		0			0
$853$	1.85698	−	3.21639i	0.0635819	−	0.110127i	−0.832482	−	0.554052i	$-0.813081\pi$
$853$	1.85698	−	3.21639i	0.0635819	−	0.110127i	0.896064	+	0.443925i	$0.146414\pi$
$854$		0			0
$855$	−0.139356	−	0.989690i	−0.00476588	−	0.0338467i
$856$		0			0
$857$	−9.47155	+	16.4052i	−0.323542	+	0.560391i	−0.981216	−	0.192911i	$-0.938207\pi$
$857$	−9.47155	+	16.4052i	−0.323542	+	0.560391i	0.657674	+	0.753303i	$0.271540\pi$
$858$		0			0
$859$	21.0569	+	36.4716i	0.718451	+	1.24439i	0.961613	+	0.274408i	$0.0884819\pi$
$859$	21.0569	+	36.4716i	0.718451	+	1.24439i	−0.243162	+	0.969986i	$0.578185\pi$
$860$		0			0
$861$	5.23704	+	9.07082i	0.178478	+	0.309133i
$862$		0			0
$863$	−4.82943			−0.164396			−0.0821978	−	0.996616i	$-0.526194\pi$
$863$	−4.82943			−0.164396			−0.0821978	+	0.996616i	$0.526194\pi$
$864$		0			0
$865$	3.90945	+	6.77136i	0.132925	+	0.230233i
$866$		0			0
$867$	−15.5188			−0.527047
$868$		0			0
$869$	5.78956	−	10.0278i	0.196398	−	0.340170i
$870$		0			0
$871$	−0.315342	+	0.546189i	−0.0106850	+	0.0185069i
$872$		0			0
$873$	1.72991			0.0585486
$874$		0			0
$875$	1.93047			0.0652616
$876$		0			0
$877$	17.3361	−	30.0271i	0.585400	−	1.01394i	−0.409426	−	0.912343i	$-0.634271\pi$
$877$	17.3361	−	30.0271i	0.585400	−	1.01394i	0.994825	−	0.101599i	$-0.0323958\pi$
$878$		0			0
$879$	−14.2418	+	24.6675i	−0.480363	+	0.832014i
$880$		0			0
$881$	−4.36677			−0.147120			−0.0735601	−	0.997291i	$-0.523436\pi$
$881$	−4.36677			−0.147120			−0.0735601	+	0.997291i	$0.523436\pi$
$882$		0			0
$883$	−24.0703	−	41.6910i	−0.810031	−	1.40301i	−0.912842	−	0.408313i	$-0.866117\pi$
$883$	−24.0703	−	41.6910i	−0.810031	−	1.40301i	0.102811	−	0.994701i	$-0.467216\pi$
$884$		0			0
$885$	−5.19858			−0.174748
$886$		0			0
$887$	24.6682	+	42.7266i	0.828278	+	1.43462i	0.899388	+	0.437151i	$0.144012\pi$
$887$	24.6682	+	42.7266i	0.828278	+	1.43462i	−0.0711105	+	0.997468i	$0.522654\pi$
$888$		0			0
$889$	−6.06902	−	10.5119i	−0.203548	−	0.352556i
$890$		0			0
$891$	5.73645	−	9.93582i	0.192178	−	0.332863i
$892$		0			0
$893$	−39.7643	+	31.0841i	−1.33066	+	1.04019i
$894$		0			0
$895$	5.99890	−	10.3904i	0.200521	−	0.347313i
$896$		0			0
$897$	−5.23704	−	9.07082i	−0.174860	−	0.302866i
$898$		0			0
$899$	6.57370	+	11.3860i	0.219245	+	0.379744i
$900$		0			0
$901$	20.1980			0.672892
$902$		0			0
$903$	−15.0374	−	26.0456i	−0.500414	−	0.866743i
$904$		0			0
$905$	−3.02486			−0.100550
$906$		0			0
$907$	−12.6651	+	21.9366i	−0.420538	+	0.728394i	−0.995992	−	0.0894405i	$-0.971492\pi$
$907$	−12.6651	+	21.9366i	−0.420538	+	0.728394i	0.575454	+	0.817834i	$0.304825\pi$
$908$		0			0
$909$	−2.10298	+	3.64247i	−0.0697515	+	0.120813i
$910$		0			0
$911$	−22.6486			−0.750382			−0.375191	−	0.926948i	$-0.622423\pi$
$911$	−22.6486			−0.750382			−0.375191	+	0.926948i	$0.622423\pi$
$912$		0			0
$913$	−13.8625			−0.458783
$914$		0			0
$915$	−2.39702	+	4.15176i	−0.0792430	+	0.137253i
$916$		0			0
$917$	11.0873	−	19.2038i	0.366135	−	0.634164i
$918$		0			0
$919$	58.3992			1.92641			0.963207	−	0.268762i	$-0.0866146\pi$
$919$	58.3992			1.92641			0.963207	+	0.268762i	$0.0866146\pi$
$920$		0			0
$921$	7.84394	+	13.5861i	0.258466	+	0.447677i
$922$		0			0
$923$	1.69045			0.0556418
$924$		0			0
$925$	3.29432	+	5.70593i	0.108317	+	0.187610i
$926$		0			0
$927$	0.307849	+	0.533210i	0.0101111	+	0.0175129i
$928$		0			0
$929$	5.99093	−	10.3766i	0.196556	−	0.340445i	−0.750853	−	0.660469i	$-0.770358\pi$
$929$	5.99093	−	10.3766i	0.196556	−	0.340445i	0.947410	+	0.320024i	$0.103691\pi$
$930$		0			0
$931$	−1.98942	−	14.1286i	−0.0652006	−	0.463047i
$932$		0			0
$933$	12.5499	−	21.7371i	0.410866	−	0.711641i
$934$		0			0
$935$	1.92432	+	3.33302i	0.0629320	+	0.109002i
$936$		0			0
$937$	−25.1089	−	43.4899i	−0.820272	−	1.42075i	−0.905480	−	0.424389i	$-0.860489\pi$
$937$	−25.1089	−	43.4899i	−0.820272	−	1.42075i	0.0852086	−	0.996363i	$-0.472844\pi$
$938$		0			0
$939$	−33.7565			−1.10160
$940$		0			0
$941$	24.3909	+	42.2463i	0.795122	+	1.37719i	0.922762	+	0.385371i	$0.125927\pi$
$941$	24.3909	+	42.2463i	0.795122	+	1.37719i	−0.127640	+	0.991821i	$0.540740\pi$
$942$		0			0
$943$	28.3100			0.921900
$944$		0			0
$945$	5.18841	−	8.98660i	0.168779	−	0.292334i
$946$		0			0
$947$	−13.8072	+	23.9148i	−0.448675	+	0.777127i	−0.998300	−	0.0582840i	$-0.981437\pi$
$947$	−13.8072	+	23.9148i	−0.448675	+	0.777127i	0.549625	+	0.835411i	$0.314770\pi$
$948$		0			0
$949$	−2.93148			−0.0951599
$950$		0			0
$951$	−36.3858			−1.17989
$952$		0			0
$953$	−22.5584	+	39.0722i	−0.730737	+	1.26567i	0.225831	+	0.974166i	$0.427490\pi$
$953$	−22.5584	+	39.0722i	−0.730737	+	1.26567i	−0.956569	+	0.291507i	$0.905843\pi$
$954$		0			0
$955$	−2.27418	+	3.93899i	−0.0735907	+	0.127463i
$956$		0			0
$957$	12.7978			0.413693
$958$		0			0
$959$	−8.17522	−	14.1599i	−0.263992	−	0.457247i
$960$		0			0
$961$	−25.3580			−0.817999
$962$		0			0
$963$	1.37738	+	2.38570i	0.0443856	+	0.0768780i
$964$		0			0
$965$	5.20008	+	9.00680i	0.167396	+	0.289939i
$966$		0			0
$967$	16.5095	−	28.5953i	0.530911	−	0.919564i	−0.468439	−	0.883496i	$-0.655183\pi$
$967$	16.5095	−	28.5953i	0.530911	−	0.919564i	0.999349	−	0.0360684i	$-0.0114834\pi$
$968$		0			0
$969$	−15.8382	+	12.3809i	−0.508797	+	0.397731i
$970$		0			0
$971$	−12.0255	+	20.8288i	−0.385918	+	0.668430i	−0.991896	−	0.127052i	$-0.959449\pi$
$971$	−12.0255	+	20.8288i	−0.385918	+	0.668430i	0.605978	+	0.795481i	$0.292782\pi$
$972$		0			0
$973$	−6.15153	−	10.6548i	−0.197209	−	0.341576i
$974$		0			0
$975$	0.602982	+	1.04440i	0.0193109	+	0.0334474i
$976$		0			0
$977$	−30.6362			−0.980140			−0.490070	−	0.871683i	$-0.663029\pi$
$977$	−30.6362			−0.980140			−0.490070	+	0.871683i	$0.663029\pi$
$978$		0			0
$979$	−3.34906	−	5.80075i	−0.107036	−	0.185393i
$980$		0			0
$981$	0.179649			0.00573576
$982$		0			0
$983$	2.18447	−	3.78361i	0.0696737	−	0.120678i	−0.829084	−	0.559124i	$-0.811138\pi$
$983$	2.18447	−	3.78361i	0.0696737	−	0.120678i	0.898758	+	0.438446i	$0.144471\pi$
$984$		0			0
$985$	1.70889	−	2.95989i	0.0544498	−	0.0943098i
$986$		0			0
$987$	−37.2076			−1.18433
$988$		0			0
$989$	−81.2882			−2.58481
$990$		0			0
$991$	−19.4866	+	33.7519i	−0.619014	+	1.07216i	0.370652	+	0.928772i	$0.379134\pi$
$991$	−19.4866	+	33.7519i	−0.619014	+	1.07216i	−0.989666	+	0.143392i	$0.954199\pi$
$992$		0			0
$993$	−2.93416	+	5.08211i	−0.0931126	+	0.161276i
$994$		0			0
$995$	14.0424			0.445174
$996$		0			0
$997$	27.8963	+	48.3177i	0.883483	+	1.53024i	0.847442	+	0.530888i	$0.178141\pi$
$997$	27.8963	+	48.3177i	0.883483	+	1.53024i	0.0360412	+	0.999350i	$0.488525\pi$
$998$		0			0
$999$	35.4159			1.12051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.q.f.201.1	yes	8
4.3	odd	2		1520.2.q.k.961.4		8
19.7	even	3	inner	760.2.q.f.121.1	✓	8
76.7	odd	6		1520.2.q.k.881.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.q.f.121.1	✓	8	19.7	even	3	inner
760.2.q.f.201.1	yes	8	1.1	even	1	trivial
1520.2.q.k.881.4		8	76.7	odd	6
1520.2.q.k.961.4		8	4.3	odd	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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.832272 + 1.44154i) q^{3} +(-0.500000 + 0.866025i) q^{5} +1.93047 q^{7} +(0.114645 + 0.198571i) q^{9} +1.38905 q^{11} +(0.362251 + 0.627436i) q^{13} +(-0.832272 - 1.44154i) q^{15} +(1.38535 - 2.39951i) q^{17} +(0.607771 + 4.31632i) q^{19} +(-1.60667 + 2.78284i) q^{21} +(4.34262 + 7.52163i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.37530 q^{27} +(-2.76753 - 4.79350i) q^{29} -2.37530 q^{31} +(-1.15606 + 2.00236i) q^{33} +(-0.965233 + 1.67183i) q^{35} -6.58865 q^{37} -1.20596 q^{39} +(1.62978 - 2.82286i) q^{41} +(-4.67968 + 8.10544i) q^{43} -0.229290 q^{45} +(5.78953 + 10.0278i) q^{47} -3.27330 q^{49} +(2.30599 + 3.99408i) q^{51} +(3.64491 + 6.31317i) q^{53} +(-0.694523 + 1.20295i) q^{55} +(-6.72797 - 2.71623i) q^{57} +(1.56156 - 2.70471i) q^{59} +(-1.44004 - 2.49423i) q^{61} +(0.221318 + 0.383335i) q^{63} -0.724501 q^{65} +(0.435255 + 0.753883i) q^{67} -14.4570 q^{69} +(1.16663 - 2.02066i) q^{71} +(-2.02310 + 3.50412i) q^{73} +1.66454 q^{75} +2.68151 q^{77} +(4.16801 - 7.21921i) q^{79} +(4.12978 - 7.15298i) q^{81} -9.97989 q^{83} +(1.38535 + 2.39951i) q^{85} +9.21335 q^{87} +(-2.41105 - 4.17606i) q^{89} +(0.699312 + 1.21124i) q^{91} +(1.97690 - 3.42408i) q^{93} +(-4.04193 - 1.63181i) q^{95} +(3.77232 - 6.53384i) q^{97} +(0.159247 + 0.275824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9} - 8 q^{11} + q^{13} + q^{15} + 13 q^{17} + q^{19} + 12 q^{21} + 8 q^{23} - 4 q^{25} - 20 q^{27} - 3 q^{29} + 4 q^{31} - 15 q^{33} - 2 q^{35} + 20 q^{37} - 2 q^{39}+ \cdots + 30 q^{99}+O(q^{100}) \) 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9 - 8 * q^11 + q^13 + q^15 + 13 * q^17 + q^19 + 12 * q^21 + 8 * q^23 - 4 * q^25 - 20 * q^27 - 3 * q^29 + 4 * q^31 - 15 * q^33 - 2 * q^35 + 20 * q^37 - 2 * q^39 - 8 * q^41 - 3 * q^43 + 2 * q^45 + 10 * q^47 + 12 * q^49 - 16 * q^51 - 11 * q^53 + 4 * q^55 - 29 * q^57 + q^59 - 25 * q^63 - 2 * q^65 - 8 * q^67 + 22 * q^69 - 4 * q^71 - 20 * q^73 - 2 * q^75 - 36 * q^77 - 3 * q^79 + 12 * q^81 - 30 * q^83 + 13 * q^85 + 24 * q^87 + 17 * q^89 - 4 * q^91 + 12 * q^93 + 4 * q^95 + 11 * q^97 + 30 * q^99

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