LMFDB - Embedded newform 275.3.f.c.232.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			232.11
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31629 + 2.31629i) q^{2} +(0.535688 - 0.535688i) q^{3} +6.73036i q^{4} +2.48161 q^{6} +(2.25638 + 2.25638i) q^{7} +(-6.32430 + 6.32430i) q^{8} +8.42608i q^{9} +3.31662 q^{11} +(3.60537 + 3.60537i) q^{12} +(-7.80868 + 7.80868i) q^{13} +10.4529i q^{14} -2.37634 q^{16} +(6.60411 + 6.60411i) q^{17} +(-19.5172 + 19.5172i) q^{18} -14.8216i q^{19} +2.41743 q^{21} +(7.68225 + 7.68225i) q^{22} +(-6.20520 + 6.20520i) q^{23} +6.77570i q^{24} -36.1743 q^{26} +(9.33493 + 9.33493i) q^{27} +(-15.1863 + 15.1863i) q^{28} -55.3363i q^{29} +7.07201 q^{31} +(19.7929 + 19.7929i) q^{32} +(1.77667 - 1.77667i) q^{33} +30.5940i q^{34} -56.7106 q^{36} +(-22.2145 - 22.2145i) q^{37} +(34.3310 - 34.3310i) q^{38} +8.36603i q^{39} -36.8039 q^{41} +(5.59946 + 5.59946i) q^{42} +(50.8752 - 50.8752i) q^{43} +22.3221i q^{44} -28.7460 q^{46} +(45.9755 + 45.9755i) q^{47} +(-1.27298 + 1.27298i) q^{48} -38.8175i q^{49} +7.07547 q^{51} +(-52.5553 - 52.5553i) q^{52} +(-5.18836 + 5.18836i) q^{53} +43.2448i q^{54} -28.5401 q^{56} +(-7.93973 - 7.93973i) q^{57} +(128.175 - 128.175i) q^{58} -94.6910i q^{59} +102.761 q^{61} +(16.3808 + 16.3808i) q^{62} +(-19.0124 + 19.0124i) q^{63} +101.198i q^{64} +8.23057 q^{66} +(-16.0072 - 16.0072i) q^{67} +(-44.4480 + 44.4480i) q^{68} +6.64810i q^{69} -12.0687 q^{71} +(-53.2891 - 53.2891i) q^{72} +(-86.2203 + 86.2203i) q^{73} -102.910i q^{74} +99.7545 q^{76} +(7.48357 + 7.48357i) q^{77} +(-19.3781 + 19.3781i) q^{78} -76.3614i q^{79} -65.8335 q^{81} +(-85.2483 - 85.2483i) q^{82} +(-85.3715 + 85.3715i) q^{83} +16.2702i q^{84} +235.683 q^{86} +(-29.6430 - 29.6430i) q^{87} +(-20.9753 + 20.9753i) q^{88} -3.80628i q^{89} -35.2387 q^{91} +(-41.7633 - 41.7633i) q^{92} +(3.78839 - 3.78839i) q^{93} +212.985i q^{94} +21.2057 q^{96} +(33.8246 + 33.8246i) q^{97} +(89.9124 - 89.9124i) q^{98} +27.9461i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.31629	+	2.31629i	1.15814	+	1.15814i	0.984875	+	0.173268i	$0.0554328\pi$
$2$	2.31629	+	2.31629i	1.15814	+	1.15814i	0.173268	+	0.984875i	$0.444567\pi$
$3$	0.535688	−	0.535688i	0.178563	−	0.178563i	−0.612166	−	0.790729i	$-0.709702\pi$
$3$	0.535688	−	0.535688i	0.178563	−	0.178563i	0.790729	+	0.612166i	$0.209702\pi$
$4$			6.73036i			1.68259i
$5$		0			0
$5$		0			0
$6$	2.48161			0.413602
$7$	2.25638	+	2.25638i	0.322340	+	0.322340i	0.849664	−	0.527324i	$-0.176805\pi$
$7$	2.25638	+	2.25638i	0.322340	+	0.322340i	−0.527324	+	0.849664i	$0.676805\pi$
$8$	−6.32430	+	6.32430i	−0.790538	+	0.790538i
$9$			8.42608i			0.936231i
$10$		0			0
$11$	3.31662			0.301511
$11$	3.31662			0.301511
$12$	3.60537	+	3.60537i	0.300448	+	0.300448i
$13$	−7.80868	+	7.80868i	−0.600668	+	0.600668i	−0.940490	−	0.339822i	$-0.889633\pi$
$13$	−7.80868	+	7.80868i	−0.600668	+	0.600668i	0.339822	+	0.940490i	$0.389633\pi$
$14$			10.4529i			0.746632i
$15$		0			0
$16$	−2.37634			−0.148521
$17$	6.60411	+	6.60411i	0.388477	+	0.388477i	0.874144	−	0.485667i	$-0.161423\pi$
$17$	6.60411	+	6.60411i	0.388477	+	0.388477i	−0.485667	+	0.874144i	$0.661423\pi$
$18$	−19.5172	+	19.5172i	−1.08429	+	1.08429i
$19$		−	14.8216i		−	0.780082i	−0.920797	−	0.390041i	$-0.872461\pi$
$19$		−	14.8216i		−	0.780082i	0.920797	−	0.390041i	$-0.127539\pi$
$20$		0			0
$21$	2.41743			0.115116
$22$	7.68225	+	7.68225i	0.349193	+	0.349193i
$23$	−6.20520	+	6.20520i	−0.269791	+	0.269791i	−0.829016	−	0.559225i	$-0.811099\pi$
$23$	−6.20520	+	6.20520i	−0.269791	+	0.269791i	0.559225	+	0.829016i	$0.311099\pi$
$24$			6.77570i			0.282321i
$25$		0			0
$26$	−36.1743			−1.39132
$27$	9.33493	+	9.33493i	0.345738	+	0.345738i
$28$	−15.1863	+	15.1863i	−0.542367	+	0.542367i
$29$		−	55.3363i		−	1.90815i	−0.299570	−	0.954074i	$-0.596843\pi$
$29$		−	55.3363i		−	1.90815i	0.299570	−	0.954074i	$-0.403157\pi$
$30$		0			0
$31$	7.07201			0.228129			0.114065	−	0.993473i	$-0.463613\pi$
$31$	7.07201			0.228129			0.114065	+	0.993473i	$0.463613\pi$
$32$	19.7929	+	19.7929i	0.618529	+	0.618529i
$33$	1.77667	−	1.77667i	0.0538386	−	0.0538386i
$34$			30.5940i			0.899823i
$35$		0			0
$36$	−56.7106			−1.57529
$37$	−22.2145	−	22.2145i	−0.600393	−	0.600393i	0.340024	−	0.940417i	$-0.389565\pi$
$37$	−22.2145	−	22.2145i	−0.600393	−	0.600393i	−0.940417	+	0.340024i	$0.889565\pi$
$38$	34.3310	−	34.3310i	0.903447	−	0.903447i
$39$			8.36603i			0.214514i
$40$		0			0
$41$	−36.8039			−0.897655			−0.448828	−	0.893618i	$-0.648158\pi$
$41$	−36.8039			−0.897655			−0.448828	+	0.893618i	$0.648158\pi$
$42$	5.59946	+	5.59946i	0.133321	+	0.133321i
$43$	50.8752	−	50.8752i	1.18314	−	1.18314i	0.204219	−	0.978925i	$-0.434534\pi$
$43$	50.8752	−	50.8752i	1.18314	−	1.18314i	0.978925	−	0.204219i	$-0.0654656\pi$
$44$			22.3221i			0.507320i
$45$		0			0
$46$	−28.7460			−0.624914
$47$	45.9755	+	45.9755i	0.978203	+	0.978203i	0.999767	−	0.0215644i	$-0.00686468\pi$
$47$	45.9755	+	45.9755i	0.978203	+	0.978203i	−0.0215644	+	0.999767i	$0.506865\pi$
$48$	−1.27298	+	1.27298i	−0.0265203	+	0.0265203i
$49$		−	38.8175i		−	0.792194i
$50$		0			0
$51$	7.07547			0.138735
$52$	−52.5553	−	52.5553i	−1.01068	−	1.01068i
$53$	−5.18836	+	5.18836i	−0.0978936	+	0.0978936i	−0.754357	−	0.656464i	$-0.772051\pi$
$53$	−5.18836	+	5.18836i	−0.0978936	+	0.0978936i	0.656464	+	0.754357i	$0.272051\pi$
$54$			43.2448i			0.800829i
$55$		0			0
$56$	−28.5401			−0.509644
$57$	−7.93973	−	7.93973i	−0.139293	−	0.139293i
$58$	128.175	−	128.175i	2.20991	−	2.20991i
$59$		−	94.6910i		−	1.60493i	−0.596698	−	0.802466i	$-0.703521\pi$
$59$		−	94.6910i		−	1.60493i	0.596698	−	0.802466i	$-0.296479\pi$
$60$		0			0
$61$	102.761			1.68460			0.842302	−	0.539006i	$-0.181200\pi$
$61$	102.761			1.68460			0.842302	+	0.539006i	$0.181200\pi$
$62$	16.3808	+	16.3808i	0.264207	+	0.264207i
$63$	−19.0124	+	19.0124i	−0.301785	+	0.301785i
$64$			101.198i			1.58121i
$65$		0			0
$66$	8.23057			0.124706
$67$	−16.0072	−	16.0072i	−0.238914	−	0.238914i	0.577486	−	0.816400i	$-0.304034\pi$
$67$	−16.0072	−	16.0072i	−0.238914	−	0.238914i	−0.816400	+	0.577486i	$0.804034\pi$
$68$	−44.4480	+	44.4480i	−0.653648	+	0.653648i
$69$			6.64810i			0.0963493i
$70$		0			0
$71$	−12.0687			−0.169982			−0.0849908	−	0.996382i	$-0.527086\pi$
$71$	−12.0687			−0.169982			−0.0849908	+	0.996382i	$0.527086\pi$
$72$	−53.2891	−	53.2891i	−0.740126	−	0.740126i
$73$	−86.2203	+	86.2203i	−1.18110	+	1.18110i	−0.201641	+	0.979460i	$0.564627\pi$
$73$	−86.2203	+	86.2203i	−1.18110	+	1.18110i	−0.979460	+	0.201641i	$0.935373\pi$
$74$		−	102.910i		−	1.39068i
$75$		0			0
$76$	99.7545			1.31256
$77$	7.48357	+	7.48357i	0.0971892	+	0.0971892i
$78$	−19.3781	+	19.3781i	−0.248437	+	0.248437i
$79$		−	76.3614i		−	0.966600i	−0.875455	−	0.483300i	$-0.839438\pi$
$79$		−	76.3614i		−	0.966600i	0.875455	−	0.483300i	$-0.160562\pi$
$80$		0			0
$81$	−65.8335			−0.812759
$82$	−85.2483	−	85.2483i	−1.03961	−	1.03961i
$83$	−85.3715	+	85.3715i	−1.02857	+	1.02857i	−0.0289933	+	0.999580i	$0.509230\pi$
$83$	−85.3715	+	85.3715i	−1.02857	+	1.02857i	−0.999580	+	0.0289933i	$0.990770\pi$
$84$			16.2702i			0.193693i
$85$		0			0
$86$	235.683			2.74050
$87$	−29.6430	−	29.6430i	−0.340724	−	0.340724i
$88$	−20.9753	+	20.9753i	−0.238356	+	0.238356i
$89$		−	3.80628i		−	0.0427672i	−0.999771	−	0.0213836i	$-0.993193\pi$
$89$		−	3.80628i		−	0.0427672i	0.999771	−	0.0213836i	$-0.00680713\pi$
$90$		0			0
$91$	−35.2387			−0.387239
$92$	−41.7633	−	41.7633i	−0.453949	−	0.453949i
$93$	3.78839	−	3.78839i	0.0407354	−	0.0407354i
$94$			212.985i			2.26580i
$95$		0			0
$96$	21.2057			0.220892
$97$	33.8246	+	33.8246i	0.348707	+	0.348707i	0.859628	−	0.510921i	$-0.170695\pi$
$97$	33.8246	+	33.8246i	0.348707	+	0.348707i	−0.510921	+	0.859628i	$0.670695\pi$
$98$	89.9124	−	89.9124i	0.917473	−	0.917473i
$99$			27.9461i			0.282284i
$100$		0			0
$101$	132.615			1.31302			0.656510	−	0.754317i	$-0.272032\pi$
$101$	132.615			1.31302			0.656510	+	0.754317i	$0.272032\pi$
$102$	16.3888	+	16.3888i	0.160675	+	0.160675i
$103$	−26.3409	+	26.3409i	−0.255737	+	0.255737i	−0.823318	−	0.567581i	$-0.807879\pi$
$103$	−26.3409	+	26.3409i	−0.255737	+	0.255737i	0.567581	+	0.823318i	$0.307879\pi$
$104$		−	98.7690i		−	0.949702i
$105$		0			0
$106$	−24.0355			−0.226750
$107$	6.67005	+	6.67005i	0.0623370	+	0.0623370i	0.737588	−	0.675251i	$-0.235965\pi$
$107$	6.67005	+	6.67005i	0.0623370	+	0.0623370i	−0.675251	+	0.737588i	$0.735965\pi$
$108$	−62.8275	+	62.8275i	−0.581736	+	0.581736i
$109$			48.5455i			0.445372i	0.974890	+	0.222686i	$0.0714825\pi$
$109$			48.5455i			0.445372i	−0.974890	+	0.222686i	$0.928518\pi$
$110$		0			0
$111$	−23.8001			−0.214415
$112$	−5.36193	−	5.36193i	−0.0478744	−	0.0478744i
$113$	97.1769	−	97.1769i	0.859973	−	0.859973i	−0.131362	−	0.991334i	$-0.541935\pi$
$113$	97.1769	−	97.1769i	0.859973	−	0.859973i	0.991334	+	0.131362i	$0.0419349\pi$
$114$		−	36.7814i		−	0.322644i
$115$		0			0
$116$	372.433			3.21063
$117$	−65.7966	−	65.7966i	−0.562364	−	0.562364i
$118$	219.331	−	219.331i	1.85874	−	1.85874i
$119$			29.8028i			0.250443i
$120$		0			0
$121$	11.0000			0.0909091
$122$	238.023	+	238.023i	1.95101	+	1.95101i
$123$	−19.7154	+	19.7154i	−0.160288	+	0.160288i
$124$			47.5972i			0.383848i
$125$		0			0
$126$	−88.0765			−0.699020
$127$	−12.2300	−	12.2300i	−0.0962992	−	0.0962992i	0.657316	−	0.753615i	$-0.271692\pi$
$127$	−12.2300	−	12.2300i	−0.0962992	−	0.0962992i	−0.753615	+	0.657316i	$0.771692\pi$
$128$	−155.231	+	155.231i	−1.21274	+	1.21274i
$129$		−	54.5064i		−	0.422530i
$130$		0			0
$131$	−93.1147			−0.710800			−0.355400	−	0.934714i	$-0.615655\pi$
$131$	−93.1147			−0.710800			−0.355400	+	0.934714i	$0.615655\pi$
$132$	11.9577	+	11.9577i	0.0905884	+	0.0905884i
$133$	33.4431	−	33.4431i	0.251452	−	0.251452i
$134$		−	74.1547i		−	0.553393i
$135$		0			0
$136$	−83.5327			−0.614211
$137$	−132.310	−	132.310i	−0.965764	−	0.965764i	0.0336695	−	0.999433i	$-0.489281\pi$
$137$	−132.310	−	132.310i	−0.965764	−	0.965764i	−0.999433	+	0.0336695i	$0.989281\pi$
$138$	−15.3989	+	15.3989i	−0.111586	+	0.111586i
$139$			180.635i			1.29954i	0.760133	+	0.649768i	$0.225134\pi$
$139$			180.635i			1.29954i	−0.760133	+	0.649768i	$0.774866\pi$
$140$		0			0
$141$	49.2571			0.349341
$142$	−27.9545	−	27.9545i	−0.196863	−	0.196863i
$143$	−25.8985	+	25.8985i	−0.181108	+	0.181108i
$144$		−	20.0232i		−	0.139050i
$145$		0			0
$146$	−399.422			−2.73577
$147$	−20.7940	−	20.7940i	−0.141456	−	0.141456i
$148$	149.512	−	149.512i	1.01022	−	1.01022i
$149$		−	39.4408i		−	0.264703i	−0.991203	−	0.132352i	$-0.957747\pi$
$149$		−	39.4408i		−	0.264703i	0.991203	−	0.132352i	$-0.0422528\pi$
$150$		0			0
$151$	−151.320			−1.00212			−0.501060	−	0.865412i	$-0.667057\pi$
$151$	−151.320			−1.00212			−0.501060	+	0.865412i	$0.667057\pi$
$152$	93.7361	+	93.7361i	0.616685	+	0.616685i
$153$	−55.6467	+	55.6467i	−0.363704	+	0.363704i
$154$			34.6682i			0.225118i
$155$		0			0
$156$	−56.3064			−0.360939
$157$	−38.3532	−	38.3532i	−0.244288	−	0.244288i	0.574333	−	0.818621i	$-0.305261\pi$
$157$	−38.3532	−	38.3532i	−0.244288	−	0.244288i	−0.818621	+	0.574333i	$0.805261\pi$
$158$	176.875	−	176.875i	1.11946	−	1.11946i
$159$			5.55868i			0.0349602i
$160$		0			0
$161$	−28.0026			−0.173929
$162$	−152.489	−	152.489i	−0.941291	−	0.941291i
$163$	−170.729	+	170.729i	−1.04741	+	1.04741i	−0.0485963	+	0.998818i	$0.515475\pi$
$163$	−170.729	+	170.729i	−1.04741	+	1.04741i	−0.998818	+	0.0485963i	$0.984525\pi$
$164$		−	247.703i		−	1.51039i
$165$		0			0
$166$	−395.490			−2.38247
$167$	52.4959	+	52.4959i	0.314347	+	0.314347i	0.846591	−	0.532244i	$-0.178651\pi$
$167$	52.4959	+	52.4959i	0.314347	+	0.314347i	−0.532244	+	0.846591i	$0.678651\pi$
$168$	−15.2886	+	15.2886i	−0.0910034	+	0.0910034i
$169$			47.0489i			0.278396i
$170$		0			0
$171$	124.888			0.730337
$172$	342.409	+	342.409i	1.99075	+	1.99075i
$173$	50.0798	−	50.0798i	0.289478	−	0.289478i	−0.547396	−	0.836874i	$-0.684381\pi$
$173$	50.0798	−	50.0798i	0.289478	−	0.289478i	0.836874	+	0.547396i	$0.184381\pi$
$174$		−	137.323i		−	0.789214i
$175$		0			0
$176$	−7.88143			−0.0447809
$177$	−50.7248	−	50.7248i	−0.286581	−	0.286581i
$178$	8.81644	−	8.81644i	0.0495306	−	0.0495306i
$179$		−	338.727i		−	1.89233i	−0.323689	−	0.946164i	$-0.604923\pi$
$179$		−	338.727i		−	1.89233i	0.323689	−	0.946164i	$-0.395077\pi$
$180$		0			0
$181$	−253.266			−1.39926			−0.699629	−	0.714506i	$-0.746652\pi$
$181$	−253.266			−1.39926			−0.699629	+	0.714506i	$0.746652\pi$
$182$	−81.6230	−	81.6230i	−0.448478	−	0.448478i
$183$	55.0477	−	55.0477i	0.300807	−	0.300807i
$184$		−	78.4872i		−	0.426561i
$185$		0			0
$186$	17.5500			0.0943548
$187$	21.9033	+	21.9033i	0.117130	+	0.117130i
$188$	−309.432	+	309.432i	−1.64592	+	1.64592i
$189$			42.1263i			0.222891i
$190$		0			0
$191$	−108.158			−0.566274			−0.283137	−	0.959079i	$-0.591375\pi$
$191$	−108.158			−0.566274			−0.283137	+	0.959079i	$0.591375\pi$
$192$	54.2103	+	54.2103i	0.282345	+	0.282345i
$193$	−47.4394	+	47.4394i	−0.245800	+	0.245800i	−0.819244	−	0.573445i	$-0.805607\pi$
$193$	−47.4394	+	47.4394i	−0.245800	+	0.245800i	0.573445	+	0.819244i	$0.305607\pi$
$194$			156.695i			0.807706i
$195$		0			0
$196$	261.256			1.33294
$197$	−179.302	−	179.302i	−0.910161	−	0.910161i	0.0861231	−	0.996285i	$-0.472552\pi$
$197$	−179.302	−	179.302i	−0.910161	−	0.910161i	−0.996285	+	0.0861231i	$0.972552\pi$
$198$	−64.7313	+	64.7313i	−0.326926	+	0.326926i
$199$			196.013i			0.984989i	0.870315	+	0.492495i	$0.163915\pi$
$199$			196.013i			0.984989i	−0.870315	+	0.492495i	$0.836085\pi$
$200$		0			0
$201$	−17.1497			−0.0853221
$202$	307.174	+	307.174i	1.52067	+	1.52067i
$203$	124.860	−	124.860i	0.615073	−	0.615073i
$204$			47.6205i			0.233434i
$205$		0			0
$206$	−122.026			−0.592360
$207$	−52.2855	−	52.2855i	−0.252587	−	0.252587i
$208$	18.5561	−	18.5561i	0.0892120	−	0.0892120i
$209$		−	49.1576i		−	0.235204i
$210$		0			0
$211$	−37.5901			−0.178152			−0.0890761	−	0.996025i	$-0.528391\pi$
$211$	−37.5901			−0.178152			−0.0890761	+	0.996025i	$0.528391\pi$
$212$	−34.9195	−	34.9195i	−0.164715	−	0.164715i
$213$	−6.46505	+	6.46505i	−0.0303523	+	0.0303523i
$214$			30.8995i			0.144390i
$215$		0			0
$216$	−118.074			−0.546638
$217$	15.9572	+	15.9572i	0.0735353	+	0.0735353i
$218$	−112.445	+	112.445i	−0.515804	+	0.515804i
$219$			92.3743i			0.421800i
$220$		0			0
$221$	−103.139			−0.466691
$222$	−55.1278	−	55.1278i	−0.248324	−	0.248324i
$223$	−174.596	+	174.596i	−0.782941	+	0.782941i	−0.980326	−	0.197385i	$-0.936755\pi$
$223$	−174.596	+	174.596i	−0.782941	+	0.782941i	0.197385	+	0.980326i	$0.436755\pi$
$224$			89.3208i			0.398754i
$225$		0			0
$226$	450.179			1.99194
$227$	254.298	+	254.298i	1.12026	+	1.12026i	0.991702	+	0.128555i	$0.0410339\pi$
$227$	254.298	+	254.298i	1.12026	+	1.12026i	0.128555	+	0.991702i	$0.458966\pi$
$228$	53.4373	−	53.4373i	0.234374	−	0.234374i
$229$			344.525i			1.50448i	0.658891	+	0.752238i	$0.271026\pi$
$229$			344.525i			1.50448i	−0.658891	+	0.752238i	$0.728974\pi$
$230$		0			0
$231$	8.01771			0.0347087
$232$	349.964	+	349.964i	1.50846	+	1.50846i
$233$	266.136	−	266.136i	1.14222	−	1.14222i	0.154172	−	0.988044i	$-0.450729\pi$
$233$	266.136	−	266.136i	1.14222	−	1.14222i	0.988044	−	0.154172i	$-0.0492708\pi$
$234$		−	304.807i		−	1.30260i
$235$		0			0
$236$	637.305			2.70044
$237$	−40.9059	−	40.9059i	−0.172599	−	0.172599i
$238$	−69.0317	+	69.0317i	−0.290049	+	0.290049i
$239$			275.134i			1.15119i	0.817735	+	0.575594i	$0.195229\pi$
$239$			275.134i			1.15119i	−0.817735	+	0.575594i	$0.804771\pi$
$240$		0			0
$241$	187.853			0.779475			0.389738	−	0.920926i	$-0.372566\pi$
$241$	187.853			0.779475			0.389738	+	0.920926i	$0.372566\pi$
$242$	25.4791	+	25.4791i	0.105286	+	0.105286i
$243$	−119.281	+	119.281i	−0.490867	+	0.490867i
$244$			691.618i			2.83450i
$245$		0			0
$246$	−91.3329			−0.371272
$247$	115.737	+	115.737i	0.468571	+	0.468571i
$248$	−44.7256	+	44.7256i	−0.180345	+	0.180345i
$249$			91.4649i			0.367329i
$250$		0			0
$251$	−228.760			−0.911395			−0.455697	−	0.890135i	$-0.650610\pi$
$251$	−228.760			−0.911395			−0.455697	+	0.890135i	$0.650610\pi$
$252$	−127.961	−	127.961i	−0.507781	−	0.507781i
$253$	−20.5803	+	20.5803i	−0.0813452	+	0.0813452i
$254$		−	56.6564i		−	0.223057i
$255$		0			0
$256$	−314.328			−1.22784
$257$	−199.176	−	199.176i	−0.775003	−	0.775003i	0.203973	−	0.978976i	$-0.434614\pi$
$257$	−199.176	−	199.176i	−0.775003	−	0.775003i	−0.978976	+	0.203973i	$0.934614\pi$
$258$	126.252	−	126.252i	0.489351	−	0.489351i
$259$		−	100.249i		−	0.387062i
$260$		0			0
$261$	466.268			1.78647
$262$	−215.680	−	215.680i	−0.823208	−	0.823208i
$263$	−168.588	+	168.588i	−0.641019	+	0.641019i	−0.950806	−	0.309787i	$-0.899742\pi$
$263$	−168.588	+	168.588i	−0.641019	+	0.641019i	0.309787	+	0.950806i	$0.399742\pi$
$264$			22.4725i			0.0851230i
$265$		0			0
$266$	154.928			0.582435
$267$	−2.03898	−	2.03898i	−0.00763662	−	0.00763662i
$268$	107.734	−	107.734i	0.401994	−	0.401994i
$269$		−	82.2687i		−	0.305832i	−0.988239	−	0.152916i	$-0.951134\pi$
$269$		−	82.2687i		−	0.305832i	0.988239	−	0.152916i	$-0.0488664\pi$
$270$		0			0
$271$	151.503			0.559051			0.279525	−	0.960138i	$-0.409823\pi$
$271$	151.503			0.559051			0.279525	+	0.960138i	$0.409823\pi$
$272$	−15.6936	−	15.6936i	−0.0576971	−	0.0576971i
$273$	−18.8770	+	18.8770i	−0.0691464	+	0.0691464i
$274$		−	612.934i		−	2.23698i
$275$		0			0
$276$	−44.7441			−0.162116
$277$	340.510	+	340.510i	1.22928	+	1.22928i	0.964237	+	0.265041i	$0.0853855\pi$
$277$	340.510	+	340.510i	1.22928	+	1.22928i	0.265041	+	0.964237i	$0.414615\pi$
$278$	−418.403	+	418.403i	−1.50505	+	1.50505i
$279$			59.5893i			0.213582i
$280$		0			0
$281$	−11.0542			−0.0393386			−0.0196693	−	0.999807i	$-0.506261\pi$
$281$	−11.0542			−0.0393386			−0.0196693	+	0.999807i	$0.506261\pi$
$282$	114.093	+	114.093i	0.404587	+	0.404587i
$283$	202.451	−	202.451i	0.715376	−	0.715376i	−0.252279	−	0.967655i	$-0.581180\pi$
$283$	202.451	−	202.451i	0.715376	−	0.715376i	0.967655	+	0.252279i	$0.0811800\pi$
$284$		−	81.2267i		−	0.286009i
$285$		0			0
$286$	−119.977			−0.419498
$287$	−83.0436	−	83.0436i	−0.289350	−	0.289350i
$288$	−166.777	+	166.777i	−0.579086	+	0.579086i
$289$		−	201.772i		−	0.698172i
$290$		0			0
$291$	36.2388			0.124532
$292$	−580.294	−	580.294i	−1.98731	−	1.98731i
$293$	161.658	−	161.658i	0.551734	−	0.551734i	−0.375207	−	0.926941i	$-0.622428\pi$
$293$	161.658	−	161.658i	0.551734	−	0.551734i	0.926941	+	0.375207i	$0.122428\pi$
$294$		−	96.3299i		−	0.327653i
$295$		0			0
$296$	280.983			0.949267
$297$	30.9605	+	30.9605i	0.104244	+	0.104244i
$298$	91.3562	−	91.3562i	0.306565	−	0.306565i
$299$		−	96.9089i		−	0.324110i
$300$		0			0
$301$	229.588			0.762750
$302$	−350.501	−	350.501i	−1.16060	−	1.16060i
$303$	71.0402	−	71.0402i	0.234456	−	0.234456i
$304$			35.2211i			0.115859i
$305$		0			0
$306$	−257.787			−0.842443
$307$	24.1388	+	24.1388i	0.0786280	+	0.0786280i	0.745327	−	0.666699i	$-0.232293\pi$
$307$	24.1388	+	24.1388i	0.0786280	+	0.0786280i	−0.666699	+	0.745327i	$0.732293\pi$
$308$	−50.3672	+	50.3672i	−0.163530	+	0.163530i
$309$			28.2210i			0.0913301i
$310$		0			0
$311$	−35.5406			−0.114278			−0.0571392	−	0.998366i	$-0.518198\pi$
$311$	−35.5406			−0.114278			−0.0571392	+	0.998366i	$0.518198\pi$
$312$	−52.9093	−	52.9093i	−0.169581	−	0.169581i
$313$	−12.7719	+	12.7719i	−0.0408047	+	0.0408047i	−0.727215	−	0.686410i	$-0.759186\pi$
$313$	−12.7719	+	12.7719i	−0.0408047	+	0.0408047i	0.686410	+	0.727215i	$0.259186\pi$
$314$		−	177.674i		−	0.565841i
$315$		0			0
$316$	513.940			1.62639
$317$	−290.699	−	290.699i	−0.917033	−	0.917033i	0.0797797	−	0.996813i	$-0.474578\pi$
$317$	−290.699	−	290.699i	−0.917033	−	0.917033i	−0.996813	+	0.0797797i	$0.974578\pi$
$318$	−12.8755	+	12.8755i	−0.0404890	+	0.0404890i
$319$		−	183.530i		−	0.575328i
$320$		0			0
$321$	7.14613			0.0222621
$322$	−64.8621	−	64.8621i	−0.201435	−	0.201435i
$323$	97.8832	−	97.8832i	0.303044	−	0.303044i
$324$		−	443.083i		−	1.36754i
$325$		0			0
$326$	−790.913			−2.42611
$327$	26.0052	+	26.0052i	0.0795267	+	0.0795267i
$328$	232.759	−	232.759i	0.709631	−	0.709631i
$329$			207.477i			0.630628i
$330$		0			0
$331$	−324.542			−0.980489			−0.490244	−	0.871585i	$-0.663093\pi$
$331$	−324.542			−0.980489			−0.490244	+	0.871585i	$0.663093\pi$
$332$	−574.582	−	574.582i	−1.73067	−	1.73067i
$333$	187.181	−	187.181i	0.562106	−	0.562106i
$334$			243.191i			0.728117i
$335$		0			0
$336$	−5.74464			−0.0170971
$337$	−144.992	−	144.992i	−0.430242	−	0.430242i	0.458468	−	0.888711i	$-0.348398\pi$
$337$	−144.992	−	144.992i	−0.430242	−	0.430242i	−0.888711	+	0.458468i	$0.848398\pi$
$338$	−108.979	+	108.979i	−0.322422	+	0.322422i
$339$		−	104.113i		−	0.307118i
$340$		0			0
$341$	23.4552			0.0687836
$342$	289.276	+	289.276i	0.845835	+	0.845835i
$343$	198.150	−	198.150i	0.577696	−	0.577696i
$344$			643.501i			1.87064i
$345$		0			0
$346$	231.998			0.670515
$347$	306.003	+	306.003i	0.881852	+	0.881852i	0.993723	−	0.111871i	$-0.0356843\pi$
$347$	306.003	+	306.003i	0.881852	+	0.881852i	−0.111871	+	0.993723i	$0.535684\pi$
$348$	199.508	−	199.508i	0.573299	−	0.573299i
$349$		−	241.147i		−	0.690965i	−0.938425	−	0.345483i	$-0.887715\pi$
$349$		−	241.147i		−	0.690965i	0.938425	−	0.345483i	$-0.112285\pi$
$350$		0			0
$351$	−145.787			−0.415348
$352$	65.6457	+	65.6457i	0.186494	+	0.186494i
$353$	−115.582	+	115.582i	−0.327429	+	0.327429i	−0.851608	−	0.524179i	$-0.824372\pi$
$353$	−115.582	+	115.582i	−0.327429	+	0.327429i	0.524179	+	0.851608i	$0.324372\pi$
$354$		−	234.986i		−	0.663803i
$355$		0			0
$356$	25.6177			0.0719597
$357$	15.9650	+	15.9650i	0.0447198	+	0.0447198i
$358$	784.588	−	784.588i	2.19159	−	2.19159i
$359$			119.466i			0.332775i	0.986060	+	0.166387i	$0.0532103\pi$
$359$			119.466i			0.332775i	−0.986060	+	0.166387i	$0.946790\pi$
$360$		0			0
$361$	141.321			0.391471
$362$	−586.636	−	586.636i	−1.62054	−	1.62054i
$363$	5.89256	−	5.89256i	0.0162330	−	0.0162330i
$364$		−	237.170i		−	0.651565i
$365$		0			0
$366$	255.012			0.696755
$367$	397.007	+	397.007i	1.08176	+	1.08176i	0.996345	+	0.0854192i	$0.0272229\pi$
$367$	397.007	+	397.007i	1.08176	+	1.08176i	0.0854192	+	0.996345i	$0.472777\pi$
$368$	14.7457	−	14.7457i	0.0400698	−	0.0400698i
$369$		−	310.112i		−	0.840413i
$370$		0			0
$371$	−23.4138			−0.0631101
$372$	25.4972	+	25.4972i	0.0685409	+	0.0685409i
$373$	382.736	−	382.736i	1.02610	−	1.02610i	0.0264513	−	0.999650i	$-0.491579\pi$
$373$	382.736	−	382.736i	1.02610	−	1.02610i	0.999650	−	0.0264513i	$-0.00842070\pi$
$374$			101.469i			0.271307i
$375$		0			0
$376$	−581.527			−1.54661
$377$	432.104	+	432.104i	1.14616	+	1.14616i
$378$	−97.5767	+	97.5767i	−0.258139	+	0.258139i
$379$			664.428i			1.75311i	0.481303	+	0.876554i	$0.340164\pi$
$379$			664.428i			1.75311i	−0.481303	+	0.876554i	$0.659836\pi$
$380$		0			0
$381$	−13.1029			−0.0343909
$382$	−250.526	−	250.526i	−0.655826	−	0.655826i
$383$	493.549	−	493.549i	1.28864	−	1.28864i	0.353025	−	0.935614i	$-0.385153\pi$
$383$	493.549	−	493.549i	1.28864	−	1.28864i	0.935614	−	0.353025i	$-0.114847\pi$
$384$			166.310i			0.433100i
$385$		0			0
$386$	−219.766			−0.569343
$387$	428.678	+	428.678i	1.10770	+	1.10770i
$388$	−227.652	+	227.652i	−0.586732	+	0.586732i
$389$		−	283.340i		−	0.728380i	−0.931325	−	0.364190i	$-0.881346\pi$
$389$		−	283.340i		−	0.728380i	0.931325	−	0.364190i	$-0.118654\pi$
$390$		0			0
$391$	−81.9596			−0.209615
$392$	245.494	+	245.494i	0.626259	+	0.626259i
$393$	−49.8804	+	49.8804i	−0.126922	+	0.126922i
$394$		−	830.629i		−	2.10819i
$395$		0			0
$396$	−188.088			−0.474969
$397$	−196.379	−	196.379i	−0.494657	−	0.494657i	0.415113	−	0.909770i	$-0.363742\pi$
$397$	−196.379	−	196.379i	−0.494657	−	0.494657i	−0.909770	+	0.415113i	$0.863742\pi$
$398$	−454.022	+	454.022i	−1.14076	+	1.14076i
$399$		−	35.8301i		−	0.0897998i
$400$		0			0
$401$	377.835			0.942232			0.471116	−	0.882071i	$-0.343851\pi$
$401$	377.835			0.942232			0.471116	+	0.882071i	$0.343851\pi$
$402$	−39.7237	−	39.7237i	−0.0988152	−	0.0988152i
$403$	−55.2231	+	55.2231i	−0.137030	+	0.137030i
$404$			892.547i			2.20928i
$405$		0			0
$406$	578.422			1.42469
$407$	−73.6773	−	73.6773i	−0.181025	−	0.181025i
$408$	−44.7474	+	44.7474i	−0.109675	+	0.109675i
$409$		−	593.471i		−	1.45103i	−0.688207	−	0.725515i	$-0.741602\pi$
$409$		−	593.471i		−	1.45103i	0.688207	−	0.725515i	$-0.258398\pi$
$410$		0			0
$411$	−141.753			−0.344898
$412$	−177.284	−	177.284i	−0.430301	−	0.430301i
$413$	213.659	−	213.659i	0.517334	−	0.517334i
$414$		−	242.216i		−	0.585064i
$415$		0			0
$416$	−309.113			−0.743061
$417$	96.7642	+	96.7642i	0.232048	+	0.232048i
$418$	113.863	−	113.863i	0.272400	−	0.272400i
$419$			475.070i			1.13382i	0.823781	+	0.566909i	$0.191861\pi$
$419$			475.070i			1.13382i	−0.823781	+	0.566909i	$0.808139\pi$
$420$		0			0
$421$	780.496			1.85391			0.926955	−	0.375173i	$-0.122417\pi$
$421$	780.496			1.85391			0.926955	+	0.375173i	$0.122417\pi$
$422$	−87.0695	−	87.0695i	−0.206326	−	0.206326i
$423$	−387.394	+	387.394i	−0.915824	+	0.915824i
$424$		−	65.6255i		−	0.154777i
$425$		0			0
$426$	−29.9498			−0.0703047
$427$	231.868	+	231.868i	0.543016	+	0.543016i
$428$	−44.8919	+	44.8919i	−0.104888	+	0.104888i
$429$			27.7470i			0.0646783i
$430$		0			0
$431$	371.853			0.862768			0.431384	−	0.902168i	$-0.358025\pi$
$431$	371.853			0.862768			0.431384	+	0.902168i	$0.358025\pi$
$432$	−22.1830	−	22.1830i	−0.0513495	−	0.0513495i
$433$	−542.802	+	542.802i	−1.25358	+	1.25358i	−0.299483	+	0.954102i	$0.596814\pi$
$433$	−542.802	+	542.802i	−1.25358	+	1.25358i	−0.954102	+	0.299483i	$0.903186\pi$
$434$			73.9227i			0.170329i
$435$		0			0
$436$	−326.729			−0.749379
$437$	91.9708	+	91.9708i	0.210460	+	0.210460i
$438$	−213.965	+	213.965i	−0.488505	+	0.488505i
$439$			270.318i			0.615759i	0.951425	+	0.307880i	$0.0996194\pi$
$439$			270.318i			0.615759i	−0.951425	+	0.307880i	$0.900381\pi$
$440$		0			0
$441$	327.079			0.741676
$442$	−238.899	−	238.899i	−0.540495	−	0.540495i
$443$	−123.199	+	123.199i	−0.278102	+	0.278102i	−0.832351	−	0.554249i	$-0.813006\pi$
$443$	−123.199	+	123.199i	−0.278102	+	0.278102i	0.554249	+	0.832351i	$0.313006\pi$
$444$		−	160.183i		−	0.360773i
$445$		0			0
$446$	−808.828			−1.81352
$447$	−21.1280	−	21.1280i	−0.0472661	−	0.0472661i
$448$	−228.340	+	228.340i	−0.509688	+	0.509688i
$449$			72.9616i			0.162498i	0.996694	+	0.0812490i	$0.0258909\pi$
$449$			72.9616i			0.162498i	−0.996694	+	0.0812490i	$0.974109\pi$
$450$		0			0
$451$	−122.065			−0.270653
$452$	654.036	+	654.036i	1.44698	+	1.44698i
$453$	−81.0603	+	81.0603i	−0.178941	+	0.178941i
$454$			1178.06i			2.59484i
$455$		0			0
$456$	100.427			0.220234
$457$	−258.612	−	258.612i	−0.565890	−	0.565890i	0.365084	−	0.930974i	$-0.381040\pi$
$457$	−258.612	−	258.612i	−0.565890	−	0.565890i	−0.930974	+	0.365084i	$0.881040\pi$
$458$	−798.019	+	798.019i	−1.74240	+	1.74240i
$459$			123.298i			0.268623i
$460$		0			0
$461$	−436.020			−0.945813			−0.472906	−	0.881113i	$-0.656795\pi$
$461$	−436.020			−0.945813			−0.472906	+	0.881113i	$0.656795\pi$
$462$	18.5713	+	18.5713i	0.0401977	+	0.0401977i
$463$	−144.556	+	144.556i	−0.312216	+	0.312216i	−0.845768	−	0.533551i	$-0.820857\pi$
$463$	−144.556	+	144.556i	−0.312216	+	0.312216i	0.533551	+	0.845768i	$0.320857\pi$
$464$			131.498i			0.283401i
$465$		0			0
$466$	1232.90			2.64570
$467$	−577.283	−	577.283i	−1.23615	−	1.23615i	−0.961561	−	0.274591i	$-0.911458\pi$
$467$	−577.283	−	577.283i	−1.23615	−	1.23615i	−0.274591	−	0.961561i	$-0.588542\pi$
$468$	442.835	−	442.835i	0.946228	−	0.946228i
$469$		−	72.2368i		−	0.154023i
$470$		0			0
$471$	−41.0907			−0.0872414
$472$	598.855	+	598.855i	1.26876	+	1.26876i
$473$	168.734	−	168.734i	0.356731	−	0.356731i
$474$		−	189.499i		−	0.399788i
$475$		0			0
$476$	−200.583			−0.421394
$477$	−43.7175	−	43.7175i	−0.0916510	−	0.0916510i
$478$	−637.289	+	637.289i	−1.33324	+	1.33324i
$479$		−	654.219i		−	1.36580i	−0.730511	−	0.682901i	$-0.760718\pi$
$479$		−	654.219i		−	1.36580i	0.730511	−	0.682901i	$-0.239282\pi$
$480$		0			0
$481$	346.933			0.721274
$482$	435.122	+	435.122i	0.902744	+	0.902744i
$483$	−15.0006	+	15.0006i	−0.0310572	+	0.0310572i
$484$			74.0340i			0.152963i
$485$		0			0
$486$	−552.576			−1.13699
$487$	504.551	+	504.551i	1.03604	+	1.03604i	0.999326	+	0.0367134i	$0.0116889\pi$
$487$	504.551	+	504.551i	1.03604	+	1.03604i	0.0367134	+	0.999326i	$0.488311\pi$
$488$	−649.891	+	649.891i	−1.33174	+	1.33174i
$489$			182.914i			0.374058i
$490$		0			0
$491$	−523.273			−1.06573			−0.532865	−	0.846200i	$-0.678885\pi$
$491$	−523.273			−1.06573			−0.532865	+	0.846200i	$0.678885\pi$
$492$	−132.692	−	132.692i	−0.269698	−	0.269698i
$493$	365.447	−	365.447i	0.741271	−	0.741271i
$494$			536.160i			1.08534i
$495$		0			0
$496$	−16.8055			−0.0338821
$497$	−27.2316	−	27.2316i	−0.0547919	−	0.0547919i
$498$	−211.859	+	211.859i	−0.425420	+	0.425420i
$499$		−	648.175i		−	1.29895i	−0.760384	−	0.649474i	$-0.774989\pi$
$499$		−	648.175i		−	1.29895i	0.760384	−	0.649474i	$-0.225011\pi$
$500$		0			0
$501$	56.2428			0.112261
$502$	−529.874	−	529.874i	−1.05553	−	1.05553i
$503$	−539.158	+	539.158i	−1.07188	+	1.07188i	−0.0746767	+	0.997208i	$0.523792\pi$
$503$	−539.158	+	539.158i	−1.07188	+	1.07188i	−0.997208	+	0.0746767i	$0.976208\pi$
$504$		−	240.481i		−	0.477145i
$505$		0			0
$506$	−95.3399			−0.188419
$507$	25.2035	+	25.2035i	0.0497111	+	0.0497111i
$508$	82.3123	−	82.3123i	0.162032	−	0.162032i
$509$			663.413i			1.30336i	0.758492	+	0.651682i	$0.225936\pi$
$509$			663.413i			1.30336i	−0.758492	+	0.651682i	$0.774064\pi$
$510$		0			0
$511$	−389.092			−0.761432
$512$	−107.150	−	107.150i	−0.209276	−	0.209276i
$513$	138.358	−	138.358i	0.269704	−	0.269704i
$514$		−	922.696i		−	1.79513i
$515$		0			0
$516$	366.848			0.710946
$517$	152.484	+	152.484i	0.294939	+	0.294939i
$518$	232.205	−	232.205i	0.448273	−	0.448273i
$519$		−	53.6542i		−	0.103380i
$520$		0			0
$521$	−90.7825			−0.174247			−0.0871233	−	0.996198i	$-0.527767\pi$
$521$	−90.7825			−0.174247			−0.0871233	+	0.996198i	$0.527767\pi$
$522$	1080.01	+	1080.01i	2.06898	+	2.06898i
$523$	−259.722	+	259.722i	−0.496600	+	0.496600i	−0.910378	−	0.413778i	$-0.864209\pi$
$523$	−259.722	+	259.722i	−0.496600	+	0.496600i	0.413778	+	0.910378i	$0.364209\pi$
$524$		−	626.696i		−	1.19598i
$525$		0			0
$526$	−780.996			−1.48478
$527$	46.7043	+	46.7043i	0.0886230	+	0.0886230i
$528$	−4.22198	+	4.22198i	−0.00799618	+	0.00799618i
$529$			451.991i			0.854425i
$530$		0			0
$531$	797.874			1.50259
$532$	225.084	+	225.084i	0.423091	+	0.423091i
$533$	287.390	−	287.390i	0.539193	−	0.539193i
$534$		−	9.44571i		−	0.0176886i
$535$		0			0
$536$	202.469			0.377741
$537$	−181.452	−	181.452i	−0.337899	−	0.337899i
$538$	190.558	−	190.558i	0.354197	−	0.354197i
$539$		−	128.743i		−	0.238855i
$540$		0			0
$541$	258.243			0.477345			0.238672	−	0.971100i	$-0.423288\pi$
$541$	258.243			0.477345			0.238672	+	0.971100i	$0.423288\pi$
$542$	350.924	+	350.924i	0.647461	+	0.647461i
$543$	−135.671	+	135.671i	−0.249855	+	0.249855i
$544$			261.429i			0.480568i
$545$		0			0
$546$	−87.4489			−0.160163
$547$	−14.6234	−	14.6234i	−0.0267339	−	0.0267339i	0.693613	−	0.720347i	$-0.256018\pi$
$547$	−14.6234	−	14.6234i	−0.0267339	−	0.0267339i	−0.720347	+	0.693613i	$0.756018\pi$
$548$	890.492	−	890.492i	1.62499	−	1.62499i
$549$			865.871i			1.57718i
$550$		0			0
$551$	−820.171			−1.48851
$552$	−42.0446	−	42.0446i	−0.0761677	−	0.0761677i
$553$	172.301	−	172.301i	0.311574	−	0.311574i
$554$			1577.44i			2.84736i
$555$		0			0
$556$	−1215.74			−2.18659
$557$	−114.984	−	114.984i	−0.206434	−	0.206434i	0.596316	−	0.802750i	$-0.296631\pi$
$557$	−114.984	−	114.984i	−0.206434	−	0.206434i	−0.802750	+	0.596316i	$0.796631\pi$
$558$	−138.026	+	138.026i	−0.247358	+	0.247358i
$559$			794.537i			1.42135i
$560$		0			0
$561$	23.4667			0.0418301
$562$	−25.6046	−	25.6046i	−0.0455598	−	0.0455598i
$563$	492.621	−	492.621i	0.874992	−	0.874992i	−0.118019	−	0.993011i	$-0.537654\pi$
$563$	492.621	−	492.621i	0.874992	−	0.874992i	0.993011	+	0.118019i	$0.0376544\pi$
$564$			331.518i			0.587798i
$565$		0			0
$566$	937.870			1.65701
$567$	−148.545	−	148.545i	−0.261985	−	0.261985i
$568$	76.3261	−	76.3261i	0.134377	−	0.134377i
$569$		−	518.523i		−	0.911288i	−0.890162	−	0.455644i	$-0.849409\pi$
$569$		−	518.523i		−	0.911288i	0.890162	−	0.455644i	$-0.150591\pi$
$570$		0			0
$571$	−168.460			−0.295027			−0.147513	−	0.989060i	$-0.547127\pi$
$571$	−168.460			−0.295027			−0.147513	+	0.989060i	$0.547127\pi$
$572$	−174.306	−	174.306i	−0.304731	−	0.304731i
$573$	−57.9391	+	57.9391i	−0.101115	+	0.101115i
$574$		−	384.705i		−	0.670218i
$575$		0			0
$576$	−852.698			−1.48038
$577$	−337.711	−	337.711i	−0.585288	−	0.585288i	0.351063	−	0.936352i	$-0.385820\pi$
$577$	−337.711	−	337.711i	−0.585288	−	0.585288i	−0.936352	+	0.351063i	$0.885820\pi$
$578$	467.361	−	467.361i	0.808583	−	0.808583i
$579$			50.8254i			0.0877813i
$580$		0			0
$581$	−385.262			−0.663101
$582$	83.9395	+	83.9395i	0.144226	+	0.144226i
$583$	−17.2078	+	17.2078i	−0.0295160	+	0.0295160i
$584$		−	1090.57i		−	1.86741i
$585$		0			0
$586$	748.893			1.27797
$587$	−566.152	−	566.152i	−0.964484	−	0.964484i	0.0349064	−	0.999391i	$-0.488887\pi$
$587$	−566.152	−	566.152i	−0.964484	−	0.964484i	−0.999391	+	0.0349064i	$0.988887\pi$
$588$	139.951	−	139.951i	0.238013	−	0.238013i
$589$		−	104.818i		−	0.177960i
$590$		0			0
$591$	−192.099			−0.325041
$592$	52.7893	+	52.7893i	0.0891711	+	0.0891711i
$593$	252.393	−	252.393i	0.425620	−	0.425620i	−0.461513	−	0.887133i	$-0.652693\pi$
$593$	252.393	−	252.393i	0.425620	−	0.425620i	0.887133	+	0.461513i	$0.152693\pi$
$594$			143.427i			0.241459i
$595$		0			0
$596$	265.451			0.445388
$597$	105.002	+	105.002i	0.175882	+	0.175882i
$598$	224.469	−	224.469i	0.375366	−	0.375366i
$599$		−	365.644i		−	0.610423i	−0.952285	−	0.305212i	$-0.901273\pi$
$599$		−	365.644i		−	0.610423i	0.952285	−	0.305212i	$-0.0987272\pi$
$600$		0			0
$601$	−213.337			−0.354969			−0.177485	−	0.984124i	$-0.556796\pi$
$601$	−213.337			−0.354969			−0.177485	+	0.984124i	$0.556796\pi$
$602$	531.791	+	531.791i	0.883374	+	0.883374i
$603$	134.878	−	134.878i	0.223679	−	0.223679i
$604$		−	1018.44i		−	1.68616i
$605$		0			0
$606$	329.099			0.543068
$607$	363.922	+	363.922i	0.599543	+	0.599543i	0.940191	−	0.340648i	$-0.110646\pi$
$607$	363.922	+	363.922i	0.599543	+	0.599543i	−0.340648	+	0.940191i	$0.610646\pi$
$608$	293.362	−	293.362i	0.482504	−	0.482504i
$609$		−	133.772i		−	0.219658i
$610$		0			0
$611$	−718.017			−1.17515
$612$	−374.523	−	374.523i	−0.611965	−	0.611965i
$613$	−254.795	+	254.795i	−0.415653	+	0.415653i	−0.883702	−	0.468049i	$-0.844957\pi$
$613$	−254.795	+	254.795i	−0.415653	+	0.415653i	0.468049	+	0.883702i	$0.344957\pi$
$614$			111.825i			0.182125i
$615$		0			0
$616$	−94.6568			−0.153664
$617$	−617.888	−	617.888i	−1.00144	−	1.00144i	−0.999999	−	0.00144021i	$-0.999542\pi$
$617$	−617.888	−	617.888i	−1.00144	−	1.00144i	−0.00144021	−	0.999999i	$-0.500458\pi$
$618$	−65.3679	+	65.3679i	−0.105773	+	0.105773i
$619$		−	49.4374i		−	0.0798665i	−0.999202	−	0.0399333i	$-0.987285\pi$
$619$		−	49.4374i		−	0.0798665i	0.999202	−	0.0399333i	$-0.0127145\pi$
$620$		0			0
$621$	−115.850			−0.186554
$622$	−82.3222	−	82.3222i	−0.132351	−	0.132351i
$623$	8.58843	−	8.58843i	0.0137856	−	0.0137856i
$624$		−	19.8805i		−	0.0318598i
$625$		0			0
$626$	−59.1667			−0.0945154
$627$	−26.3331	−	26.3331i	−0.0419986	−	0.0419986i
$628$	258.131	−	258.131i	0.411037	−	0.411037i
$629$		−	293.414i		−	0.466477i
$630$		0			0
$631$	160.479			0.254326			0.127163	−	0.991882i	$-0.459413\pi$
$631$	160.479			0.254326			0.127163	+	0.991882i	$0.459413\pi$
$632$	482.933	+	482.933i	0.764134	+	0.764134i
$633$	−20.1366	+	20.1366i	−0.0318113	+	0.0318113i
$634$		−	1346.69i		−	2.12411i
$635$		0			0
$636$	−37.4119			−0.0588238
$637$	303.113	+	303.113i	0.475845	+	0.475845i
$638$	425.107	−	425.107i	0.666313	−	0.666313i
$639$		−	101.692i		−	0.159142i
$640$		0			0
$641$	229.507			0.358045			0.179022	−	0.983845i	$-0.442707\pi$
$641$	229.507			0.358045			0.179022	+	0.983845i	$0.442707\pi$
$642$	16.5525	+	16.5525i	0.0257827	+	0.0257827i
$643$	−484.144	+	484.144i	−0.752946	+	0.752946i	−0.975028	−	0.222082i	$-0.928715\pi$
$643$	−484.144	+	484.144i	−0.752946	+	0.752946i	0.222082	+	0.975028i	$0.428715\pi$
$644$		−	188.468i		−	0.292652i
$645$		0			0
$646$	453.451			0.701936
$647$	−561.713	−	561.713i	−0.868181	−	0.868181i	0.124090	−	0.992271i	$-0.460399\pi$
$647$	−561.713	−	561.713i	−0.868181	−	0.868181i	−0.992271	+	0.124090i	$0.960399\pi$
$648$	416.351	−	416.351i	0.642517	−	0.642517i
$649$		−	314.054i		−	0.483905i
$650$		0			0
$651$	17.0961			0.0262613
$652$	−1149.07	−	1149.07i	−1.76237	−	1.76237i
$653$	−217.884	+	217.884i	−0.333666	+	0.333666i	−0.853977	−	0.520311i	$-0.825816\pi$
$653$	−217.884	+	217.884i	−0.333666	+	0.333666i	0.520311	+	0.853977i	$0.325816\pi$
$654$			120.471i			0.184207i
$655$		0			0
$656$	87.4585			0.133321
$657$	−726.499	−	726.499i	−1.10578	−	1.10578i
$658$	−480.576	+	480.576i	−0.730358	+	0.730358i
$659$		−	67.5668i		−	0.102529i	−0.998685	−	0.0512646i	$-0.983675\pi$
$659$		−	67.5668i		−	0.102529i	0.998685	−	0.0512646i	$-0.0163252\pi$
$660$		0			0
$661$	−652.282			−0.986811			−0.493406	−	0.869799i	$-0.664248\pi$
$661$	−652.282			−0.986811			−0.493406	+	0.869799i	$0.664248\pi$
$662$	−751.732	−	751.732i	−1.13555	−	1.13555i
$663$	−55.2501	+	55.2501i	−0.0833335	+	0.0833335i
$664$		−	1079.83i		−	1.62625i
$665$		0			0
$666$	867.131			1.30200
$667$	343.373	+	343.373i	0.514802	+	0.514802i
$668$	−353.317	+	353.317i	−0.528917	+	0.528917i
$669$			187.058i			0.279608i
$670$		0			0
$671$	340.819			0.507927
$672$	47.8480	+	47.8480i	0.0712024	+	0.0712024i
$673$	−414.530	+	414.530i	−0.615943	+	0.615943i	−0.944488	−	0.328545i	$-0.893442\pi$
$673$	−414.530	+	414.530i	−0.615943	+	0.615943i	0.328545	+	0.944488i	$0.393442\pi$
$674$		−	671.684i		−	0.996564i
$675$		0			0
$676$	−316.656			−0.468426
$677$	73.4867	+	73.4867i	0.108548	+	0.108548i	0.759295	−	0.650747i	$-0.225544\pi$
$677$	73.4867	+	73.4867i	0.108548	+	0.108548i	−0.650747	+	0.759295i	$0.725544\pi$
$678$	241.155	−	241.155i	0.355686	−	0.355686i
$679$			152.642i			0.224805i
$680$		0			0
$681$	272.449			0.400072
$682$	54.3290	+	54.3290i	0.0796613	+	0.0796613i
$683$	21.5357	−	21.5357i	0.0315310	−	0.0315310i	−0.691166	−	0.722697i	$-0.742902\pi$
$683$	21.5357	−	21.5357i	0.0315310	−	0.0315310i	0.722697	+	0.691166i	$0.242902\pi$
$684$			840.539i			1.22886i
$685$		0			0
$686$	917.943			1.33811
$687$	184.558	+	184.558i	0.268643	+	0.268643i
$688$	−120.897	+	120.897i	−0.175722	+	0.175722i
$689$		−	81.0285i		−	0.117603i
$690$		0			0
$691$	−911.677			−1.31936			−0.659679	−	0.751547i	$-0.729308\pi$
$691$	−911.677			−1.31936			−0.659679	+	0.751547i	$0.729308\pi$
$692$	337.055	+	337.055i	0.487074	+	0.487074i
$693$	−63.0572	+	63.0572i	−0.0909916	+	0.0909916i
$694$			1417.58i			2.04262i
$695$		0			0
$696$	374.942			0.538710
$697$	−243.057	−	243.057i	−0.348718	−	0.348718i
$698$	558.565	−	558.565i	0.800236	−	0.800236i
$699$		−	285.132i		−	0.407914i
$700$		0			0
$701$	−377.613			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$701$	−377.613			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$702$	−337.685	−	337.685i	−0.481032	−	0.481032i
$703$	−329.254	+	329.254i	−0.468356	+	0.468356i
$704$			335.634i			0.476753i
$705$		0			0
$706$	−535.443			−0.758418
$707$	299.230	+	299.230i	0.423239	+	0.423239i
$708$	341.396	−	341.396i	0.482198	−	0.482198i
$709$			621.973i			0.877253i	0.898669	+	0.438627i	$0.144535\pi$
$709$			621.973i			0.877253i	−0.898669	+	0.438627i	$0.855465\pi$
$710$		0			0
$711$	643.427			0.904961
$712$	24.0721	+	24.0721i	0.0338091	+	0.0338091i
$713$	−43.8833	+	43.8833i	−0.0615474	+	0.0615474i
$714$			73.9589i			0.103584i
$715$		0			0
$716$	2279.75			3.18401
$717$	147.386	+	147.386i	0.205559	+	0.205559i
$718$	−276.718	+	276.718i	−0.385401	+	0.385401i
$719$			325.457i			0.452653i	0.974051	+	0.226326i	$0.0726716\pi$
$719$			325.457i			0.452653i	−0.974051	+	0.226326i	$0.927328\pi$
$720$		0			0
$721$	−118.870			−0.164869
$722$	327.340	+	327.340i	0.453380	+	0.453380i
$723$	100.631	−	100.631i	0.139185	−	0.139185i
$724$		−	1704.57i		−	2.35438i
$725$		0			0
$726$	27.2977			0.0376002
$727$	−956.282	−	956.282i	−1.31538	−	1.31538i	−0.917389	−	0.397992i	$-0.869707\pi$
$727$	−956.282	−	956.282i	−1.31538	−	1.31538i	−0.397992	−	0.917389i	$-0.630293\pi$
$728$	222.861	−	222.861i	0.306127	−	0.306127i
$729$		−	464.707i		−	0.637458i
$730$		0			0
$731$	671.971			0.919248
$732$	370.491	+	370.491i	0.506135	+	0.506135i
$733$	299.492	−	299.492i	0.408584	−	0.408584i	−0.472660	−	0.881245i	$-0.656706\pi$
$733$	299.492	−	299.492i	0.408584	−	0.408584i	0.881245	+	0.472660i	$0.156706\pi$
$734$			1839.17i			2.50568i
$735$		0			0
$736$	−245.638			−0.333748
$737$	−53.0900	−	53.0900i	−0.0720352	−	0.0720352i
$738$	718.309	−	718.309i	0.973318	−	0.973318i
$739$			522.550i			0.707104i	0.935415	+	0.353552i	$0.115026\pi$
$739$			522.550i			0.707104i	−0.935415	+	0.353552i	$0.884974\pi$
$740$		0			0
$741$	123.998			0.167338
$742$	−54.2332	−	54.2332i	−0.0730905	−	0.0730905i
$743$	−480.166	+	480.166i	−0.646253	+	0.646253i	−0.952085	−	0.305833i	$-0.901065\pi$
$743$	−480.166	+	480.166i	−0.646253	+	0.646253i	0.305833	+	0.952085i	$0.401065\pi$
$744$			47.9178i			0.0644057i
$745$		0			0
$746$	1773.05			2.37674
$747$	−719.347	−	719.347i	−0.962982	−	0.962982i
$748$	−147.417	+	147.417i	−0.197082	+	0.197082i
$749$			30.1004i			0.0401874i
$750$		0			0
$751$	−858.032			−1.14252			−0.571259	−	0.820770i	$-0.693545\pi$
$751$	−858.032			−1.14252			−0.571259	+	0.820770i	$0.693545\pi$
$752$	−109.254	−	109.254i	−0.145284	−	0.145284i
$753$	−122.544	+	122.544i	−0.162741	+	0.162741i
$754$			2001.75i			2.65484i
$755$		0			0
$756$	−283.526			−0.375034
$757$	369.714	+	369.714i	0.488394	+	0.488394i	0.907799	−	0.419405i	$-0.137761\pi$
$757$	369.714	+	369.714i	0.488394	+	0.488394i	−0.419405	+	0.907799i	$0.637761\pi$
$758$	−1539.01	+	1539.01i	−2.03035	+	2.03035i
$759$			22.0492i			0.0290504i
$760$		0			0
$761$	894.818			1.17585			0.587923	−	0.808917i	$-0.299946\pi$
$761$	894.818			1.17585			0.587923	+	0.808917i	$0.299946\pi$
$762$	−30.3501	−	30.3501i	−0.0398295	−	0.0398295i
$763$	−109.537	+	109.537i	−0.143561	+	0.143561i
$764$		−	727.945i		−	0.952807i
$765$		0			0
$766$	2286.40			2.98486
$767$	739.412	+	739.412i	0.964031	+	0.964031i
$768$	−168.381	+	168.381i	−0.219247	+	0.219247i
$769$		−	53.0200i		−	0.0689467i	−0.999406	−	0.0344734i	$-0.989025\pi$
$769$		−	53.0200i		−	0.0689467i	0.999406	−	0.0344734i	$-0.0109754\pi$
$770$		0			0
$771$	−213.392			−0.276773
$772$	−319.284	−	319.284i	−0.413581	−	0.413581i
$773$	−75.9189	+	75.9189i	−0.0982133	+	0.0982133i	−0.754506	−	0.656293i	$-0.772124\pi$
$773$	−75.9189	+	75.9189i	−0.0982133	+	0.0982133i	0.656293	+	0.754506i	$0.272124\pi$
$774$			1985.88i			2.56574i
$775$		0			0
$776$	−427.834			−0.551333
$777$	−53.7021	−	53.7021i	−0.0691147	−	0.0691147i
$778$	656.296	−	656.296i	0.843568	−	0.843568i
$779$			545.491i			0.700245i
$780$		0			0
$781$	−40.0273			−0.0512514
$782$	−189.842	−	189.842i	−0.242765	−	0.242765i
$783$	516.561	−	516.561i	0.659720	−	0.659720i
$784$			92.2436i			0.117658i
$785$		0			0
$786$	−231.075			−0.293988
$787$	166.709	+	166.709i	0.211829	+	0.211829i	0.805044	−	0.593215i	$-0.202142\pi$
$787$	166.709	+	166.709i	0.211829	+	0.211829i	−0.593215	+	0.805044i	$0.702142\pi$
$788$	1206.77	−	1206.77i	1.53143	−	1.53143i
$789$			180.621i			0.228924i
$790$		0			0
$791$	438.536			0.554408
$792$	−176.740	−	176.740i	−0.223156	−	0.223156i
$793$	−802.427	+	802.427i	−1.01189	+	1.01189i
$794$		−	909.740i		−	1.14577i
$795$		0			0
$796$	−1319.24			−1.65733
$797$	244.912	+	244.912i	0.307292	+	0.307292i	0.843858	−	0.536566i	$-0.180279\pi$
$797$	244.912	+	244.912i	0.307292	+	0.307292i	−0.536566	+	0.843858i	$0.680279\pi$
$798$	82.9928	−	82.9928i	0.104001	−	0.104001i
$799$			607.255i			0.760018i
$800$		0			0
$801$	32.0720			0.0400400
$802$	875.174	+	875.174i	1.09124	+	1.09124i
$803$	−285.960	+	285.960i	−0.356115	+	0.356115i
$804$		−	115.424i		−	0.143562i
$805$		0			0
$806$	−255.825			−0.317401
$807$	−44.0703	−	44.0703i	−0.0546101	−	0.0546101i
$808$	−838.698	+	838.698i	−1.03799	+	1.03799i
$809$		−	998.342i		−	1.23404i	−0.786946	−	0.617022i	$-0.788339\pi$
$809$		−	998.342i		−	1.23404i	0.786946	−	0.617022i	$-0.211661\pi$
$810$		0			0
$811$	753.628			0.929258			0.464629	−	0.885505i	$-0.346188\pi$
$811$	753.628			0.929258			0.464629	+	0.885505i	$0.346188\pi$
$812$	840.352	+	840.352i	1.03492	+	1.03492i
$813$	81.1581	−	81.1581i	0.0998255	−	0.0998255i
$814$		−	341.315i		−	0.419306i
$815$		0			0
$816$	−16.8137			−0.0206051
$817$	−754.050	−	754.050i	−0.922950	−	0.922950i
$818$	1374.65	−	1374.65i	1.68050	−	1.68050i
$819$		−	296.924i		−	0.362545i
$820$		0			0
$821$	507.827			0.618547			0.309274	−	0.950973i	$-0.399914\pi$
$821$	507.827			0.618547			0.309274	+	0.950973i	$0.399914\pi$
$822$	−328.341	−	328.341i	−0.399442	−	0.399442i
$823$	−657.940	+	657.940i	−0.799441	+	0.799441i	−0.983007	−	0.183566i	$-0.941236\pi$
$823$	−657.940	+	657.940i	−0.799441	+	0.799441i	0.183566	+	0.983007i	$0.441236\pi$
$824$		−	333.176i		−	0.404340i
$825$		0			0
$826$	989.791			1.19829
$827$	296.348	+	296.348i	0.358341	+	0.358341i	0.863201	−	0.504860i	$-0.168456\pi$
$827$	296.348	+	296.348i	0.358341	+	0.358341i	−0.504860	+	0.863201i	$0.668456\pi$
$828$	351.901	−	351.901i	0.425001	−	0.425001i
$829$		−	856.072i		−	1.03266i	−0.856391	−	0.516328i	$-0.827298\pi$
$829$		−	856.072i		−	1.03266i	0.856391	−	0.516328i	$-0.172702\pi$
$830$		0			0
$831$	364.814			0.439006
$832$	−790.220	−	790.220i	−0.949783	−	0.949783i
$833$	256.355	−	256.355i	0.307749	−	0.307749i
$834$			448.267i			0.537490i
$835$		0			0
$836$	330.848			0.395752
$837$	66.0168	+	66.0168i	0.0788731	+	0.0788731i
$838$	−1100.40	+	1100.40i	−1.31312	+	1.31312i
$839$		−	1313.02i		−	1.56498i	−0.622663	−	0.782490i	$-0.713949\pi$
$839$		−	1313.02i		−	1.56498i	0.622663	−	0.782490i	$-0.286051\pi$
$840$		0			0
$841$	−2221.11			−2.64103
$842$	1807.85	+	1807.85i	2.14709	+	2.14709i
$843$	−5.92157	+	5.92157i	−0.00702441	+	0.00702441i
$844$		−	252.995i		−	0.299757i
$845$		0			0
$846$	−1794.63			−2.12131
$847$	24.8202	+	24.8202i	0.0293037	+	0.0293037i
$848$	12.3293	−	12.3293i	0.0145393	−	0.0145393i
$849$		−	216.901i		−	0.255479i
$850$		0			0
$851$	275.691			0.323962
$852$	−43.5121	−	43.5121i	−0.0510706	−	0.0510706i
$853$	−426.296	+	426.296i	−0.499761	+	0.499761i	−0.911363	−	0.411603i	$-0.864969\pi$
$853$	−426.296	+	426.296i	−0.499761	+	0.499761i	0.411603	+	0.911363i	$0.364969\pi$
$854$			1074.14i			1.25778i
$855$		0			0
$856$	−84.3669			−0.0985595
$857$	−874.858	−	874.858i	−1.02084	−	1.02084i	−0.999778	−	0.0210593i	$-0.993296\pi$
$857$	−874.858	−	874.858i	−1.02084	−	1.02084i	−0.0210593	−	0.999778i	$-0.506704\pi$
$858$	−64.2699	+	64.2699i	−0.0749067	+	0.0749067i
$859$		−	777.425i		−	0.905035i	−0.891756	−	0.452517i	$-0.850526\pi$
$859$		−	777.425i		−	0.905035i	0.891756	−	0.452517i	$-0.149474\pi$
$860$		0			0
$861$	−88.9708			−0.103334
$862$	861.318	+	861.318i	0.999209	+	0.999209i
$863$	836.459	−	836.459i	0.969246	−	0.969246i	−0.0302952	−	0.999541i	$-0.509645\pi$
$863$	836.459	−	836.459i	0.969246	−	0.969246i	0.999541	+	0.0302952i	$0.00964474\pi$
$864$			369.531i			0.427698i
$865$		0			0
$866$	−2514.57			−2.90366
$867$	−108.087	−	108.087i	−0.124667	−	0.124667i
$868$	−107.397	+	107.397i	−0.123730	+	0.123730i
$869$		−	253.262i		−	0.291441i
$870$		0			0
$871$	249.991			0.287016
$872$	−307.017	−	307.017i	−0.352083	−	0.352083i
$873$	−285.009	+	285.009i	−0.326471	+	0.326471i
$874$			426.061i			0.487484i
$875$		0			0
$876$	−621.713			−0.709718
$877$	649.687	+	649.687i	0.740806	+	0.740806i	0.972733	−	0.231927i	$-0.0745031\pi$
$877$	649.687	+	649.687i	0.740806	+	0.740806i	−0.231927	+	0.972733i	$0.574503\pi$
$878$	−626.135	+	626.135i	−0.713137	+	0.713137i
$879$		−	173.197i		−	0.197038i
$880$		0			0
$881$	162.266			0.184184			0.0920921	−	0.995750i	$-0.470645\pi$
$881$	162.266			0.184184			0.0920921	+	0.995750i	$0.470645\pi$
$882$	757.609	+	757.609i	0.858967	+	0.858967i
$883$	34.2561	−	34.2561i	0.0387951	−	0.0387951i	−0.687443	−	0.726238i	$-0.741267\pi$
$883$	34.2561	−	34.2561i	0.0387951	−	0.0387951i	0.726238	+	0.687443i	$0.241267\pi$
$884$		−	694.161i		−	0.785250i
$885$		0			0
$886$	−570.729			−0.644164
$887$	175.705	+	175.705i	0.198089	+	0.198089i	0.799180	−	0.601091i	$-0.205267\pi$
$887$	175.705	+	175.705i	0.198089	+	0.198089i	−0.601091	+	0.799180i	$0.705267\pi$
$888$	150.519	−	150.519i	0.169503	−	0.169503i
$889$		−	55.1911i		−	0.0620822i
$890$		0			0
$891$	−218.345			−0.245056
$892$	−1175.09	−	1175.09i	−1.31737	−	1.31737i
$893$	681.430	−	681.430i	0.763079	−	0.763079i
$894$		−	97.8768i		−	0.109482i
$895$		0			0
$896$	−700.520			−0.781830
$897$	−51.9129	−	51.9129i	−0.0578739	−	0.0578739i
$898$	−169.000	+	169.000i	−0.188196	+	0.188196i
$899$		−	391.339i		−	0.435305i
$900$		0			0
$901$	−68.5289			−0.0760588
$902$	−282.737	−	282.737i	−0.313455	−	0.313455i
$903$	122.987	−	122.987i	0.136199	−	0.136199i
$904$			1229.15i			1.35968i
$905$		0			0
$906$	−375.518			−0.414479
$907$	−913.002	−	913.002i	−1.00662	−	1.00662i	−0.999978	−	0.00663968i	$-0.997887\pi$
$907$	−913.002	−	913.002i	−1.00662	−	1.00662i	−0.00663968	−	0.999978i	$-0.502113\pi$
$908$	−1711.52	+	1711.52i	−1.88494	+	1.88494i
$909$			1117.42i			1.22929i
$910$		0			0
$911$	414.304			0.454779			0.227390	−	0.973804i	$-0.426981\pi$
$911$	414.304			0.454779			0.227390	+	0.973804i	$0.426981\pi$
$912$	18.8675	+	18.8675i	0.0206880	+	0.0206880i
$913$	−283.145	+	283.145i	−0.310126	+	0.310126i
$914$		−	1198.04i		−	1.31076i
$915$		0			0
$916$	−2318.78			−2.53142
$917$	−210.102	−	210.102i	−0.229119	−	0.229119i
$918$	−285.593	+	285.593i	−0.311103	+	0.311103i
$919$			333.359i			0.362741i	0.983415	+	0.181371i	$0.0580533\pi$
$919$			333.359i			0.362741i	−0.983415	+	0.181371i	$0.941947\pi$
$920$		0			0
$921$	25.8617			0.0280800
$922$	−1009.95	−	1009.95i	−1.09539	−	1.09539i
$923$	94.2406	−	94.2406i	0.102102	−	0.102102i
$924$			53.9621i			0.0584006i
$925$		0			0
$926$	−669.667			−0.723183
$927$	−221.951	−	221.951i	−0.239429	−	0.239429i
$928$	1095.27	−	1095.27i	1.18025	−	1.18025i
$929$		−	488.198i		−	0.525509i	−0.964863	−	0.262755i	$-0.915369\pi$
$929$		−	488.198i		−	0.525509i	0.964863	−	0.262755i	$-0.0846309\pi$
$930$		0			0
$931$	−575.336			−0.617976
$932$	1791.19	+	1791.19i	1.92188	+	1.92188i
$933$	−19.0387	+	19.0387i	−0.0204059	+	0.0204059i
$934$		−	2674.30i		−	2.86328i
$935$		0			0
$936$	832.235			0.889140
$937$	1156.79	+	1156.79i	1.23457	+	1.23457i	0.962191	+	0.272377i	$0.0878098\pi$
$937$	1156.79	+	1156.79i	1.23457	+	1.23457i	0.272377	+	0.962191i	$0.412190\pi$
$938$	167.321	−	167.321i	0.178381	−	0.178381i
$939$			13.6835i			0.0145724i
$940$		0			0
$941$	684.642			0.727569			0.363784	−	0.931483i	$-0.381485\pi$
$941$	684.642			0.727569			0.363784	+	0.931483i	$0.381485\pi$
$942$	−95.1778	−	95.1778i	−0.101038	−	0.101038i
$943$	228.375	−	228.375i	0.242180	−	0.242180i
$944$			225.018i			0.238367i
$945$		0			0
$946$	781.672			0.826292
$947$	209.592	+	209.592i	0.221322	+	0.221322i	0.809055	−	0.587733i	$-0.199979\pi$
$947$	209.592	+	209.592i	0.221322	+	0.221322i	−0.587733	+	0.809055i	$0.699979\pi$
$948$	275.311	−	275.311i	0.290413	−	0.290413i
$949$		−	1346.53i		−	1.41890i
$950$		0			0
$951$	−311.448			−0.327495
$952$	−188.482	−	188.482i	−0.197985	−	0.197985i
$953$	219.429	−	219.429i	0.230251	−	0.230251i	−0.582546	−	0.812798i	$-0.697944\pi$
$953$	219.429	−	219.429i	0.230251	−	0.230251i	0.812798	+	0.582546i	$0.197944\pi$
$954$		−	202.525i		−	0.212290i
$955$		0			0
$956$	−1851.75			−1.93698
$957$	−98.3146	−	98.3146i	−0.102732	−	0.102732i
$958$	1515.36	−	1515.36i	1.58179	−	1.58179i
$959$		−	597.082i		−	0.622609i
$960$		0			0
$961$	−910.987			−0.947957
$962$	803.595	+	803.595i	0.835338	+	0.835338i
$963$	−56.2024	+	56.2024i	−0.0583618	+	0.0583618i
$964$			1264.32i			1.31154i
$965$		0			0
$966$	−69.4916			−0.0719375
$967$	949.654	+	949.654i	0.982062	+	0.982062i	0.999842	−	0.0177798i	$-0.00565978\pi$
$967$	949.654	+	949.654i	0.982062	+	0.982062i	−0.0177798	+	0.999842i	$0.505660\pi$
$968$	−69.5673	+	69.5673i	−0.0718671	+	0.0718671i
$969$		−	104.870i		−	0.108225i
$970$		0			0
$971$	−149.959			−0.154437			−0.0772186	−	0.997014i	$-0.524604\pi$
$971$	−149.959			−0.154437			−0.0772186	+	0.997014i	$0.524604\pi$
$972$	−802.802	−	802.802i	−0.825928	−	0.825928i
$973$	−407.583	+	407.583i	−0.418893	+	0.418893i
$974$			2337.37i			2.39976i
$975$		0			0
$976$	−244.195			−0.250200
$977$	1123.34	+	1123.34i	1.14978	+	1.14978i	0.986595	+	0.163186i	$0.0521770\pi$
$977$	1123.34	+	1123.34i	1.14978	+	1.14978i	0.163186	+	0.986595i	$0.447823\pi$
$978$	−423.682	+	423.682i	−0.433213	+	0.433213i
$979$		−	12.6240i		−	0.0128948i
$980$		0			0
$981$	−409.049			−0.416971
$982$	−1212.05	−	1212.05i	−1.23427	−	1.23427i
$983$	−547.724	+	547.724i	−0.557196	+	0.557196i	−0.928508	−	0.371312i	$-0.878908\pi$
$983$	−547.724	+	547.724i	−0.557196	+	0.557196i	0.371312	+	0.928508i	$0.378908\pi$
$984$		−	249.372i		−	0.253427i
$985$		0			0
$986$	1692.96			1.71700
$987$	111.143	+	111.143i	0.112607	+	0.112607i
$988$	−778.952	+	778.952i	−0.788413	+	0.788413i
$989$			631.382i			0.638404i
$990$		0			0
$991$	1405.64			1.41841			0.709205	−	0.705002i	$-0.249054\pi$
$991$	1405.64			1.41841			0.709205	+	0.705002i	$0.249054\pi$
$992$	139.976	+	139.976i	0.141105	+	0.141105i
$993$	−173.853	+	173.853i	−0.175079	+	0.175079i
$994$		−	126.152i		−	0.126914i
$995$		0			0
$996$	−615.592			−0.618065
$997$	75.6789	+	75.6789i	0.0759066	+	0.0759066i	0.744041	−	0.668134i	$-0.232907\pi$
$997$	75.6789	+	75.6789i	0.0759066	+	0.0759066i	−0.668134	+	0.744041i	$0.732907\pi$
$998$	1501.36	−	1501.36i	1.50437	−	1.50437i
$999$		−	414.742i		−	0.415158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.232.11	yes	24
5.2	odd	4	inner	275.3.f.c.243.2	yes	24
5.3	odd	4	inner	275.3.f.c.243.11	yes	24
5.4	even	2	inner	275.3.f.c.232.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.2	✓	24	5.4	even	2	inner
275.3.f.c.232.11	yes	24	1.1	even	1	trivial
275.3.f.c.243.2	yes	24	5.2	odd	4	inner
275.3.f.c.243.11	yes	24	5.3	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.31629 + 2.31629i) q^{2} +(0.535688 - 0.535688i) q^{3} +6.73036i q^{4} +2.48161 q^{6} +(2.25638 + 2.25638i) q^{7} +(-6.32430 + 6.32430i) q^{8} +8.42608i q^{9} +3.31662 q^{11} +(3.60537 + 3.60537i) q^{12} +(-7.80868 + 7.80868i) q^{13} +10.4529i q^{14} -2.37634 q^{16} +(6.60411 + 6.60411i) q^{17} +(-19.5172 + 19.5172i) q^{18} -14.8216i q^{19} +2.41743 q^{21} +(7.68225 + 7.68225i) q^{22} +(-6.20520 + 6.20520i) q^{23} +6.77570i q^{24} -36.1743 q^{26} +(9.33493 + 9.33493i) q^{27} +(-15.1863 + 15.1863i) q^{28} -55.3363i q^{29} +7.07201 q^{31} +(19.7929 + 19.7929i) q^{32} +(1.77667 - 1.77667i) q^{33} +30.5940i q^{34} -56.7106 q^{36} +(-22.2145 - 22.2145i) q^{37} +(34.3310 - 34.3310i) q^{38} +8.36603i q^{39} -36.8039 q^{41} +(5.59946 + 5.59946i) q^{42} +(50.8752 - 50.8752i) q^{43} +22.3221i q^{44} -28.7460 q^{46} +(45.9755 + 45.9755i) q^{47} +(-1.27298 + 1.27298i) q^{48} -38.8175i q^{49} +7.07547 q^{51} +(-52.5553 - 52.5553i) q^{52} +(-5.18836 + 5.18836i) q^{53} +43.2448i q^{54} -28.5401 q^{56} +(-7.93973 - 7.93973i) q^{57} +(128.175 - 128.175i) q^{58} -94.6910i q^{59} +102.761 q^{61} +(16.3808 + 16.3808i) q^{62} +(-19.0124 + 19.0124i) q^{63} +101.198i q^{64} +8.23057 q^{66} +(-16.0072 - 16.0072i) q^{67} +(-44.4480 + 44.4480i) q^{68} +6.64810i q^{69} -12.0687 q^{71} +(-53.2891 - 53.2891i) q^{72} +(-86.2203 + 86.2203i) q^{73} -102.910i q^{74} +99.7545 q^{76} +(7.48357 + 7.48357i) q^{77} +(-19.3781 + 19.3781i) q^{78} -76.3614i q^{79} -65.8335 q^{81} +(-85.2483 - 85.2483i) q^{82} +(-85.3715 + 85.3715i) q^{83} +16.2702i q^{84} +235.683 q^{86} +(-29.6430 - 29.6430i) q^{87} +(-20.9753 + 20.9753i) q^{88} -3.80628i q^{89} -35.2387 q^{91} +(-41.7633 - 41.7633i) q^{92} +(3.78839 - 3.78839i) q^{93} +212.985i q^{94} +21.2057 q^{96} +(33.8246 + 33.8246i) q^{97} +(89.9124 - 89.9124i) q^{98} +27.9461i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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