LMFDB - Embedded newform 300.5.c.c.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,5,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	300.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$31.0109889252$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 $ x^16 - 6x^15 + 20x^14 - 108x^13 + 492x^12 - 2160x^11 + 7360x^10 - 39552x^9 + 234752x^8 - 632832x^7 + 1884160x^6 - 8847360x^5 + 32243712x^4 - 113246208x^3 + 335544320x^2 - 1610612736*x + 4294967296
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.3
Root			$-3.55818 - 1.82740i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.c.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.36166 - 2.16777i) q^{2} -5.19615i q^{3} +(6.60152 + 14.5746i) q^{4} +(-11.2641 + 17.4677i) q^{6} -36.6738i q^{7} +(9.40241 - 63.3056i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-3.36166 - 2.16777i) q^{2} -5.19615i q^{3} +(6.60152 + 14.5746i) q^{4} +(-11.2641 + 17.4677i) q^{6} -36.6738i q^{7} +(9.40241 - 63.3056i) q^{8} -27.0000 q^{9} -56.2282i q^{11} +(75.7320 - 34.3025i) q^{12} +219.043 q^{13} +(-79.5004 + 123.285i) q^{14} +(-168.840 + 192.430i) q^{16} +54.4527 q^{17} +(90.7648 + 58.5299i) q^{18} +155.937i q^{19} -190.562 q^{21} +(-121.890 + 189.020i) q^{22} -322.708i q^{23} +(-328.945 - 48.8564i) q^{24} +(-736.347 - 474.834i) q^{26} +140.296i q^{27} +(534.506 - 242.103i) q^{28} +989.618 q^{29} -847.804i q^{31} +(984.726 - 280.876i) q^{32} -292.171 q^{33} +(-183.051 - 118.041i) q^{34} +(-178.241 - 393.515i) q^{36} +1837.88 q^{37} +(338.035 - 524.206i) q^{38} -1138.18i q^{39} -2470.86 q^{41} +(640.606 + 413.096i) q^{42} -171.009i q^{43} +(819.506 - 371.192i) q^{44} +(-699.557 + 1084.83i) q^{46} -3346.60i q^{47} +(999.893 + 877.317i) q^{48} +1056.04 q^{49} -282.944i q^{51} +(1446.01 + 3192.46i) q^{52} -2748.29 q^{53} +(304.130 - 471.628i) q^{54} +(-2321.65 - 344.822i) q^{56} +810.271 q^{57} +(-3326.76 - 2145.27i) q^{58} -1780.57i q^{59} -5039.83 q^{61} +(-1837.85 + 2850.03i) q^{62} +990.191i q^{63} +(-3919.19 - 1190.45i) q^{64} +(982.178 + 633.359i) q^{66} +4015.61i q^{67} +(359.470 + 793.628i) q^{68} -1676.84 q^{69} -5381.54i q^{71} +(-253.865 + 1709.25i) q^{72} -6555.14 q^{73} +(-6178.33 - 3984.11i) q^{74} +(-2272.72 + 1029.42i) q^{76} -2062.10 q^{77} +(-2467.31 + 3826.17i) q^{78} +11497.9i q^{79} +729.000 q^{81} +(8306.20 + 5356.27i) q^{82} -8231.85i q^{83} +(-1258.00 - 2777.38i) q^{84} +(-370.709 + 574.874i) q^{86} -5142.21i q^{87} +(-3559.56 - 528.681i) q^{88} -5360.84 q^{89} -8033.11i q^{91} +(4703.34 - 2130.36i) q^{92} -4405.32 q^{93} +(-7254.66 + 11250.1i) q^{94} +(-1459.48 - 5116.78i) q^{96} -12933.5 q^{97} +(-3550.03 - 2289.25i) q^{98} +1518.16i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) $ 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−3.36166	−	2.16777i	−0.840415	−	0.541943i
$2$	−3.36166	−	2.16777i	−0.840415	−	0.541943i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	6.60152	+	14.5746i	0.412595	+	0.910915i
$5$		0			0
$5$		0			0
$6$	−11.2641	+	17.4677i	−0.312891	+	0.485214i
$7$		−	36.6738i		−	0.748444i	−0.927339	−	0.374222i	$-0.877910\pi$
$7$		−	36.6738i		−	0.748444i	0.927339	−	0.374222i	$-0.122090\pi$
$8$	9.40241	−	63.3056i	0.146913	−	0.989149i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	56.2282i		−	0.464696i	−0.972633	−	0.232348i	$-0.925359\pi$
$11$		−	56.2282i		−	0.464696i	0.972633	−	0.232348i	$-0.0746409\pi$
$12$	75.7320	−	34.3025i	0.525917	−	0.238212i
$13$	219.043			1.29611			0.648055	−	0.761594i	$-0.275583\pi$
$13$	219.043			1.29611			0.648055	+	0.761594i	$0.275583\pi$
$14$	−79.5004	+	123.285i	−0.405614	+	0.629004i
$15$		0			0
$16$	−168.840	+	192.430i	−0.659530	+	0.751678i
$17$	54.4527			0.188418			0.0942088	−	0.995552i	$-0.469968\pi$
$17$	54.4527			0.188418			0.0942088	+	0.995552i	$0.469968\pi$
$18$	90.7648	+	58.5299i	0.280138	+	0.180648i
$19$			155.937i			0.431957i	0.976398	+	0.215979i	$0.0692942\pi$
$19$			155.937i			0.431957i	−0.976398	+	0.215979i	$0.930706\pi$
$20$		0			0
$21$	−190.562			−0.432114
$22$	−121.890	+	189.020i	−0.251839	+	0.390538i
$23$		−	322.708i		−	0.610033i	−0.952347	−	0.305017i	$-0.901338\pi$
$23$		−	322.708i		−	0.610033i	0.952347	−	0.305017i	$-0.0986620\pi$
$24$	−328.945	−	48.8564i	−0.571086	−	0.0848201i
$25$		0			0
$26$	−736.347	−	474.834i	−1.08927	−	0.702418i
$27$			140.296i			0.192450i
$28$	534.506	−	242.103i	0.681768	−	0.308804i
$29$	989.618			1.17672			0.588358	−	0.808601i	$-0.299775\pi$
$29$	989.618			1.17672			0.588358	+	0.808601i	$0.299775\pi$
$30$		0			0
$31$		−	847.804i		−	0.882210i	−0.897456	−	0.441105i	$-0.854587\pi$
$31$		−	847.804i		−	0.882210i	0.897456	−	0.441105i	$-0.145413\pi$
$32$	984.726	−	280.876i	0.961646	−	0.274293i
$33$	−292.171			−0.268292
$34$	−183.051	−	118.041i	−0.158349	−	0.102112i
$35$		0			0
$36$	−178.241	−	393.515i	−0.137532	−	0.303638i
$37$	1837.88			1.34250			0.671249	−	0.741232i	$-0.265758\pi$
$37$	1837.88			1.34250			0.671249	+	0.741232i	$0.265758\pi$
$38$	338.035	−	524.206i	0.234096	−	0.363024i
$39$		−	1138.18i		−	0.748309i
$40$		0			0
$41$	−2470.86			−1.46988			−0.734939	−	0.678134i	$-0.762789\pi$
$41$	−2470.86			−1.46988			−0.734939	+	0.678134i	$0.762789\pi$
$42$	640.606	+	413.096i	0.363155	+	0.234181i
$43$		−	171.009i		−	0.0924873i	−0.998930	−	0.0462436i	$-0.985275\pi$
$43$		−	171.009i		−	0.0924873i	0.998930	−	0.0462436i	$-0.0147251\pi$
$44$	819.506	−	371.192i	0.423299	−	0.191731i
$45$		0			0
$46$	−699.557	+	1084.83i	−0.330603	+	0.512681i
$47$		−	3346.60i		−	1.51498i	−0.652845	−	0.757492i	$-0.726425\pi$
$47$		−	3346.60i		−	1.51498i	0.652845	−	0.757492i	$-0.273575\pi$
$48$	999.893	+	877.317i	0.433981	+	0.380780i
$49$	1056.04			0.439832
$50$		0			0
$51$		−	282.944i		−	0.108783i
$52$	1446.01	+	3192.46i	0.534769	+	1.18065i
$53$	−2748.29			−0.978386			−0.489193	−	0.872176i	$-0.662709\pi$
$53$	−2748.29			−0.978386			−0.489193	+	0.872176i	$0.662709\pi$
$54$	304.130	−	471.628i	0.104297	−	0.161738i
$55$		0			0
$56$	−2321.65	−	344.822i	−0.740323	−	0.109956i
$57$	810.271			0.249391
$58$	−3326.76	−	2145.27i	−0.988930	−	0.637713i
$59$		−	1780.57i		−	0.511511i	−0.966742	−	0.255755i	$-0.917676\pi$
$59$		−	1780.57i		−	0.511511i	0.966742	−	0.255755i	$-0.0823242\pi$
$60$		0			0
$61$	−5039.83			−1.35443			−0.677214	−	0.735786i	$-0.736813\pi$
$61$	−5039.83			−1.35443			−0.677214	+	0.735786i	$0.736813\pi$
$62$	−1837.85	+	2850.03i	−0.478108	+	0.741422i
$63$			990.191i			0.249481i
$64$	−3919.19	−	1190.45i	−0.956833	−	0.290637i
$65$		0			0
$66$	982.178	+	633.359i	0.225477	+	0.145399i
$67$			4015.61i			0.894543i	0.894398	+	0.447272i	$0.147604\pi$
$67$			4015.61i			0.894543i	−0.894398	+	0.447272i	$0.852396\pi$
$68$	359.470	+	793.628i	0.0777402	+	0.171632i
$69$	−1676.84			−0.352203
$70$		0			0
$71$		−	5381.54i		−	1.06755i	−0.845625	−	0.533777i	$-0.820772\pi$
$71$		−	5381.54i		−	1.06755i	0.845625	−	0.533777i	$-0.179228\pi$
$72$	−253.865	+	1709.25i	−0.0489709	+	0.329716i
$73$	−6555.14			−1.23009			−0.615044	−	0.788493i	$-0.710862\pi$
$73$	−6555.14			−1.23009			−0.615044	+	0.788493i	$0.710862\pi$
$74$	−6178.33	−	3984.11i	−1.12826	−	0.727558i
$75$		0			0
$76$	−2272.72	+	1029.42i	−0.393476	+	0.178224i
$77$	−2062.10			−0.347799
$78$	−2467.31	+	3826.17i	−0.405541	+	0.628890i
$79$			11497.9i			1.84232i	0.389188	+	0.921158i	$0.372756\pi$
$79$			11497.9i			1.84232i	−0.389188	+	0.921158i	$0.627244\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	8306.20	+	5356.27i	1.23531	+	0.796590i
$83$		−	8231.85i		−	1.19493i	−0.801896	−	0.597463i	$-0.796175\pi$
$83$		−	8231.85i		−	1.19493i	0.801896	−	0.597463i	$-0.203825\pi$
$84$	−1258.00	−	2777.38i	−0.178288	−	0.393619i
$85$		0			0
$86$	−370.709	+	574.874i	−0.0501229	+	0.0777277i
$87$		−	5142.21i		−	0.679377i
$88$	−3559.56	−	528.681i	−0.459654	−	0.0682698i
$89$	−5360.84			−0.676788			−0.338394	−	0.941005i	$-0.609884\pi$
$89$	−5360.84			−0.676788			−0.338394	+	0.941005i	$0.609884\pi$
$90$		0			0
$91$		−	8033.11i		−	0.970065i
$92$	4703.34	−	2130.36i	0.555688	−	0.251697i
$93$	−4405.32			−0.509344
$94$	−7254.66	+	11250.1i	−0.821035	+	1.27321i
$95$		0			0
$96$	−1459.48	−	5116.78i	−0.158363	−	0.555207i
$97$	−12933.5			−1.37459			−0.687295	−	0.726379i	$-0.741202\pi$
$97$	−12933.5			−1.37459			−0.687295	+	0.726379i	$0.741202\pi$
$98$	−3550.03	−	2289.25i	−0.369641	−	0.238364i
$99$			1518.16i			0.154899i
$100$		0			0
$101$	−10633.8			−1.04243			−0.521216	−	0.853425i	$-0.674521\pi$
$101$	−10633.8			−1.04243			−0.521216	+	0.853425i	$0.674521\pi$
$102$	−613.359	+	951.163i	−0.0589542	+	0.0914228i
$103$		−	10524.5i		−	0.992031i	−0.868314	−	0.496016i	$-0.834796\pi$
$103$		−	10524.5i		−	0.992031i	0.868314	−	0.496016i	$-0.165204\pi$
$104$	2059.53	−	13866.6i	0.190415	−	1.28205i
$105$		0			0
$106$	9238.81	+	5957.66i	0.822250	+	0.530230i
$107$		−	16409.2i		−	1.43324i	−0.697462	−	0.716621i	$-0.745688\pi$
$107$		−	16409.2i		−	1.43324i	0.697462	−	0.716621i	$-0.254312\pi$
$108$	−2044.76	+	926.168i	−0.175306	+	0.0794040i
$109$	2190.64			0.184382			0.0921908	−	0.995741i	$-0.470613\pi$
$109$	2190.64			0.184382			0.0921908	+	0.995741i	$0.470613\pi$
$110$		0			0
$111$		−	9549.91i		−	0.775092i
$112$	7057.11	+	6191.99i	0.562589	+	0.493622i
$113$	−235.041			−0.0184072			−0.00920358	−	0.999958i	$-0.502930\pi$
$113$	−235.041			−0.0184072			−0.00920358	+	0.999958i	$0.502930\pi$
$114$	−2723.85	−	1756.48i	−0.209592	−	0.135156i
$115$		0			0
$116$	6532.99	+	14423.3i	0.485507	+	1.07189i
$117$	−5914.15			−0.432037
$118$	−3859.87	+	5985.67i	−0.277210	+	0.429881i
$119$		−	1996.98i		−	0.141020i
$120$		0			0
$121$	11479.4			0.784057
$122$	16942.2	+	10925.2i	1.13828	+	0.734023i
$123$			12839.0i			0.848634i
$124$	12356.4	−	5596.79i	0.803618	−	0.363996i
$125$		0			0
$126$	2146.51	−	3328.69i	0.135205	−	0.209668i
$127$		−	18937.2i		−	1.17411i	−0.809548	−	0.587054i	$-0.800288\pi$
$127$		−	18937.2i		−	1.17411i	0.809548	−	0.587054i	$-0.199712\pi$
$128$	10594.4	+	12497.8i	0.646628	+	0.762805i
$129$	−888.589			−0.0533976
$130$		0			0
$131$			8486.92i			0.494547i	0.968946	+	0.247273i	$0.0795346\pi$
$131$			8486.92i			0.494547i	−0.968946	+	0.247273i	$0.920465\pi$
$132$	−1928.77	−	4258.28i	−0.110696	−	0.244392i
$133$	5718.78			0.323296
$134$	8704.92	−	13499.1i	0.484792	−	0.751788i
$135$		0			0
$136$	511.986	−	3447.16i	0.0276809	−	0.186373i
$137$	307.323			0.0163740			0.00818699	−	0.999966i	$-0.497394\pi$
$137$	307.323			0.0163740			0.00818699	+	0.999966i	$0.497394\pi$
$138$	5636.96	+	3635.00i	0.295997	+	0.190874i
$139$			33154.2i			1.71597i	0.513677	+	0.857984i	$0.328283\pi$
$139$			33154.2i			1.71597i	−0.513677	+	0.857984i	$0.671717\pi$
$140$		0			0
$141$	−17389.4			−0.874676
$142$	−11666.0	+	18090.9i	−0.578554	+	0.897189i
$143$		−	12316.4i		−	0.602297i
$144$	4558.67	−	5195.60i	0.219843	−	0.250559i
$145$		0			0
$146$	22036.2	+	14210.1i	1.03378	+	0.666638i
$147$		−	5487.32i		−	0.253937i
$148$	12132.8	+	26786.4i	0.553908	+	1.22290i
$149$	33856.8			1.52501			0.762506	−	0.646981i	$-0.223969\pi$
$149$	33856.8			1.52501			0.762506	+	0.646981i	$0.223969\pi$
$150$		0			0
$151$		−	12036.5i		−	0.527894i	−0.964537	−	0.263947i	$-0.914976\pi$
$151$		−	12036.5i		−	0.527894i	0.964537	−	0.263947i	$-0.0850244\pi$
$152$	9871.66	+	1466.18i	0.427270	+	0.0634600i
$153$	−1470.22			−0.0628058
$154$	6932.08	+	4470.17i	0.292296	+	0.188487i
$155$		0			0
$156$	16588.5	−	7513.71i	0.681646	−	0.308749i
$157$	−29036.3			−1.17799			−0.588995	−	0.808137i	$-0.700476\pi$
$157$	−29036.3			−1.17799			−0.588995	+	0.808137i	$0.700476\pi$
$158$	24924.8	−	38652.0i	0.998431	−	1.54831i
$159$			14280.5i			0.564871i
$160$		0			0
$161$	−11834.9			−0.456576
$162$	−2450.65	−	1580.31i	−0.0933795	−	0.0602159i
$163$		−	14158.1i		−	0.532879i	−0.963852	−	0.266439i	$-0.914153\pi$
$163$		−	14158.1i		−	0.532879i	0.963852	−	0.266439i	$-0.0858472\pi$
$164$	−16311.5	−	36011.9i	−0.606464	−	1.33893i
$165$		0			0
$166$	−17844.8	+	27672.7i	−0.647582	+	1.00423i
$167$		−	24992.4i		−	0.896139i	−0.893999	−	0.448069i	$-0.852112\pi$
$167$		−	24992.4i		−	0.896139i	0.893999	−	0.448069i	$-0.147888\pi$
$168$	−1791.75	+	12063.7i	−0.0634831	+	0.427426i
$169$	19418.6			0.679900
$170$		0			0
$171$		−	4210.29i		−	0.143986i
$172$	2492.39	−	1128.92i	0.0842480	−	0.0381598i
$173$	49606.1			1.65746			0.828730	−	0.559648i	$-0.189064\pi$
$173$	49606.1			1.65746			0.828730	+	0.559648i	$0.189064\pi$
$174$	−11147.1	+	17286.4i	−0.368184	+	0.570959i
$175$		0			0
$176$	10820.0	+	9493.56i	0.349302	+	0.306481i
$177$	−9252.11			−0.295321
$178$	18021.3	+	11621.1i	0.568783	+	0.366780i
$179$		−	6175.50i		−	0.192737i	−0.995346	−	0.0963687i	$-0.969277\pi$
$179$		−	6175.50i		−	0.192737i	0.995346	−	0.0963687i	$-0.0307228\pi$
$180$		0			0
$181$	24421.3			0.745437			0.372719	−	0.927944i	$-0.378426\pi$
$181$	24421.3			0.745437			0.372719	+	0.927944i	$0.378426\pi$
$182$	−17414.0	+	27004.6i	−0.525720	+	0.815258i
$183$			26187.7i			0.781980i
$184$	−20429.2	−	3034.23i	−0.603414	−	0.0896216i
$185$		0			0
$186$	14809.2	+	9549.73i	0.428060	+	0.276036i
$187$		−	3061.78i		−	0.0875569i
$188$	48775.4	−	22092.6i	1.38002	−	0.625075i
$189$	5145.19			0.144038
$190$		0			0
$191$			47105.7i			1.29124i	0.763659	+	0.645620i	$0.223401\pi$
$191$			47105.7i			1.29124i	−0.763659	+	0.645620i	$0.776599\pi$
$192$	−6185.76	+	20364.7i	−0.167799	+	0.552428i
$193$	18873.5			0.506686			0.253343	−	0.967377i	$-0.418470\pi$
$193$	18873.5			0.506686			0.253343	+	0.967377i	$0.418470\pi$
$194$	43478.1	+	28036.9i	1.15523	+	0.744950i
$195$		0			0
$196$	6971.44	+	15391.3i	0.181472	+	0.400649i
$197$	−35212.2			−0.907319			−0.453660	−	0.891175i	$-0.649882\pi$
$197$	−35212.2			−0.907319			−0.453660	+	0.891175i	$0.649882\pi$
$198$	3291.03	−	5103.55i	0.0839463	−	0.130179i
$199$		−	31238.6i		−	0.788834i	−0.918932	−	0.394417i	$-0.870947\pi$
$199$		−	31238.6i		−	0.788834i	0.918932	−	0.394417i	$-0.129053\pi$
$200$		0			0
$201$	20865.7			0.516465
$202$	35747.4	+	23051.7i	0.876075	+	0.564938i
$203$		−	36293.0i		−	0.880706i
$204$	4123.81	−	1867.86i	0.0990919	−	0.0448833i
$205$		0			0
$206$	−22814.6	+	35379.7i	−0.537624	+	0.833718i
$207$			8713.11i			0.203344i
$208$	−36983.1	+	42150.3i	−0.854824	+	0.974257i
$209$	8768.04			0.200729
$210$		0			0
$211$		−	59099.8i		−	1.32746i	−0.747973	−	0.663730i	$-0.768973\pi$
$211$		−	59099.8i		−	1.32746i	0.747973	−	0.663730i	$-0.231027\pi$
$212$	−18142.9	−	40055.3i	−0.403677	−	0.891226i
$213$	−27963.3			−0.616353
$214$	−35571.4	+	55162.1i	−0.776736	+	1.20452i
$215$		0			0
$216$	8881.52	+	1319.12i	0.190362	+	0.0282734i
$217$	−31092.1			−0.660285
$218$	−7364.18	−	4748.80i	−0.154957	−	0.0999243i
$219$			34061.5i			0.710192i
$220$		0			0
$221$	11927.4			0.244210
$222$	−20702.0	+	32103.5i	−0.420056	+	0.651399i
$223$			63431.3i			1.27554i	0.770227	+	0.637769i	$0.220143\pi$
$223$			63431.3i			1.27554i	−0.770227	+	0.637769i	$0.779857\pi$
$224$	−10300.8	−	36113.6i	−0.205293	−	0.719738i
$225$		0			0
$226$	790.128	+	509.515i	0.0154697	+	0.00997563i
$227$		−	81211.1i		−	1.57603i	−0.615658	−	0.788013i	$-0.711110\pi$
$227$		−	81211.1i		−	1.57603i	0.615658	−	0.788013i	$-0.288890\pi$
$228$	5349.02	+	11809.4i	0.102897	+	0.227174i
$229$	37312.5			0.711513			0.355757	−	0.934579i	$-0.384223\pi$
$229$	37312.5			0.711513			0.355757	+	0.934579i	$0.384223\pi$
$230$		0			0
$231$			10715.0i			0.200802i
$232$	9304.80	−	62648.3i	0.172875	−	1.16395i
$233$	−59419.3			−1.09450			−0.547250	−	0.836969i	$-0.684325\pi$
$233$	−59419.3			−1.09450			−0.547250	+	0.836969i	$0.684325\pi$
$234$	19881.4	+	12820.5i	0.363090	+	0.234139i
$235$		0			0
$236$	25951.1	−	11754.5i	0.465943	−	0.211047i
$237$	59744.8			1.06366
$238$	−4329.01	+	6713.18i	−0.0764248	+	0.118515i
$239$			15215.1i			0.266365i	0.991092	+	0.133183i	$0.0425197\pi$
$239$			15215.1i			0.266365i	−0.991092	+	0.133183i	$0.957480\pi$
$240$		0			0
$241$	113924.			1.96146			0.980732	−	0.195356i	$-0.0625862\pi$
$241$	113924.			1.96146			0.980732	+	0.195356i	$0.0625862\pi$
$242$	−38589.8	−	24884.7i	−0.658934	−	0.424915i
$243$		−	3788.00i		−	0.0641500i
$244$	−33270.5	−	73453.6i	−0.558831	−	1.23377i
$245$		0			0
$246$	27832.0	−	43160.3i	0.459911	−	0.713205i
$247$			34156.8i			0.559864i
$248$	−53670.7	−	7971.40i	−0.872637	−	0.129608i
$249$	−42773.9			−0.689891
$250$		0			0
$251$		−	6177.27i		−	0.0980504i	−0.998798	−	0.0490252i	$-0.984389\pi$
$251$		−	6177.27i		−	0.0980504i	0.998798	−	0.0490252i	$-0.0156115\pi$
$252$	−14431.7	+	6536.77i	−0.227256	+	0.102935i
$253$	−18145.3			−0.283480
$254$	−41051.5	+	63660.4i	−0.636300	+	0.986739i
$255$		0			0
$256$	−8522.24	−	64979.5i	−0.130039	−	0.991509i
$257$	104659.			1.58457			0.792286	−	0.610150i	$-0.208891\pi$
$257$	104659.			1.58457			0.792286	+	0.610150i	$0.208891\pi$
$258$	2987.13	+	1926.26i	0.0448761	+	0.0289384i
$259$		−	67402.0i		−	1.00478i
$260$		0			0
$261$	−26719.7			−0.392239
$262$	18397.7	−	28530.1i	0.268016	−	0.415625i
$263$		−	74062.0i		−	1.07074i	−0.844618	−	0.535370i	$-0.820172\pi$
$263$		−	74062.0i		−	1.07074i	0.844618	−	0.535370i	$-0.179828\pi$
$264$	−2747.11	+	18496.0i	−0.0394156	+	0.265381i
$265$		0			0
$266$	−19224.6	−	12397.0i	−0.271703	−	0.175208i
$267$			27855.7i			0.390744i
$268$	−58526.0	+	26509.1i	−0.814853	+	0.369084i
$269$	−21868.5			−0.302213			−0.151107	−	0.988517i	$-0.548284\pi$
$269$	−21868.5			−0.302213			−0.151107	+	0.988517i	$0.548284\pi$
$270$		0			0
$271$		−	40797.1i		−	0.555508i	−0.960652	−	0.277754i	$-0.910410\pi$
$271$		−	40797.1i		−	0.555508i	0.960652	−	0.277754i	$-0.0895900\pi$
$272$	−9193.78	+	10478.3i	−0.124267	+	0.141629i
$273$	−41741.3			−0.560068
$274$	−1033.12	−	666.207i	−0.0137609	−	0.00887376i
$275$		0			0
$276$	−11069.7	−	24439.3i	−0.145317	−	0.320827i
$277$	−43989.6			−0.573311			−0.286655	−	0.958034i	$-0.592544\pi$
$277$	−43989.6			−0.573311			−0.286655	+	0.958034i	$0.592544\pi$
$278$	71870.8	−	111453.i	0.929957	−	1.44213i
$279$			22890.7i			0.294070i
$280$		0			0
$281$	−135950.			−1.72174			−0.860869	−	0.508827i	$-0.830079\pi$
$281$	−135950.			−1.72174			−0.860869	+	0.508827i	$0.830079\pi$
$282$	58457.4	+	37696.3i	0.735091	+	0.474025i
$283$			78066.1i			0.974742i	0.873195	+	0.487371i	$0.162044\pi$
$283$			78066.1i			0.974742i	−0.873195	+	0.487371i	$0.837956\pi$
$284$	78434.0	−	35526.4i	0.972451	−	0.440468i
$285$		0			0
$286$	−26699.1	+	41403.5i	−0.326411	+	0.506180i
$287$			90615.8i			1.10012i
$288$	−26587.6	+	7583.66i	−0.320549	+	0.0914311i
$289$	−80555.9			−0.964499
$290$		0			0
$291$			67204.5i			0.793620i
$292$	−43273.9	−	95538.7i	−0.507528	−	1.12050i
$293$	−61325.1			−0.714337			−0.357169	−	0.934040i	$-0.616258\pi$
$293$	−61325.1			−0.714337			−0.357169	+	0.934040i	$0.616258\pi$
$294$	−11895.3	+	18446.5i	−0.137619	+	0.213412i
$295$		0			0
$296$	17280.5	−	116348.i	0.197230	−	1.32793i
$297$	7888.60			0.0894308
$298$	−113815.	−	73393.8i	−1.28164	−	0.826470i
$299$		−	70686.7i		−	0.790670i
$300$		0			0
$301$	−6271.54			−0.0692215
$302$	−26092.4	+	40462.7i	−0.286088	+	0.443650i
$303$			55255.0i			0.601848i
$304$	−30006.8	−	26328.3i	−0.324693	−	0.284889i
$305$		0			0
$306$	4942.39	+	3187.11i	0.0527830	+	0.0340372i
$307$			126561.i			1.34283i	0.741080	+	0.671417i	$0.234314\pi$
$307$			126561.i			1.34283i	−0.741080	+	0.671417i	$0.765686\pi$
$308$	−13613.0	−	30054.4i	−0.143500	−	0.316815i
$309$	−54686.7			−0.572749
$310$		0			0
$311$			147924.i			1.52939i	0.644395	+	0.764693i	$0.277109\pi$
$311$			147924.i			1.52939i	−0.644395	+	0.764693i	$0.722891\pi$
$312$	−72053.0	−	10701.6i	−0.740190	−	0.109936i
$313$	154062.			1.57256			0.786278	−	0.617872i	$-0.212005\pi$
$313$	154062.			1.57256			0.786278	+	0.617872i	$0.212005\pi$
$314$	97610.1	+	62944.0i	0.990001	+	0.638404i
$315$		0			0
$316$	−167578.	+	75903.6i	−1.67819	+	0.760131i
$317$	40362.8			0.401664			0.200832	−	0.979626i	$-0.435635\pi$
$317$	40362.8			0.401664			0.200832	+	0.979626i	$0.435635\pi$
$318$	30956.9	−	48006.2i	0.306128	−	0.474727i
$319$		−	55644.5i		−	0.546815i
$320$		0			0
$321$	−85264.7			−0.827483
$322$	39784.9	+	25655.4i	0.383713	+	0.247438i
$323$			8491.16i			0.0813883i
$324$	4812.51	+	10624.9i	0.0458439	+	0.101213i
$325$		0			0
$326$	−30691.5	+	47594.6i	−0.288790	+	0.447840i
$327$		−	11382.9i		−	0.106453i
$328$	−23232.1	+	156419.i	−0.215944	+	1.45393i
$329$	−122732.			−1.13388
$330$		0			0
$331$		−	103314.i		−	0.942982i	−0.881871	−	0.471491i	$-0.843716\pi$
$331$		−	103314.i		−	0.942982i	0.881871	−	0.471491i	$-0.156284\pi$
$332$	119976.	−	54342.7i	1.08848	−	0.493021i
$333$	−49622.8			−0.447499
$334$	−54177.9	+	84016.0i	−0.485656	+	0.753129i
$335$		0			0
$336$	32174.5	−	36669.8i	0.284993	−	0.324811i
$337$	132569.			1.16730			0.583649	−	0.812006i	$-0.301625\pi$
$337$	132569.			1.16730			0.583649	+	0.812006i	$0.301625\pi$
$338$	−65278.8	−	42095.2i	−0.571398	−	0.368467i
$339$			1221.31i			0.0106274i
$340$		0			0
$341$	−47670.5			−0.409960
$342$	−9126.95	+	14153.6i	−0.0780321	+	0.121008i
$343$		−	126782.i		−	1.07763i
$344$	−10825.8	−	1607.90i	−0.0914837	−	0.0135876i
$345$		0			0
$346$	−166759.	−	107535.i	−1.39295	−	0.898249i
$347$			235031.i			1.95194i	0.217916	+	0.975968i	$0.430074\pi$
$347$			235031.i			1.95194i	−0.217916	+	0.975968i	$0.569926\pi$
$348$	74945.8	−	33946.4i	0.618855	−	0.280308i
$349$	−10835.2			−0.0889583			−0.0444791	−	0.999010i	$-0.514163\pi$
$349$	−10835.2			−0.0889583			−0.0444791	+	0.999010i	$0.514163\pi$
$350$		0			0
$351$			30730.8i			0.249436i
$352$	−15793.2	−	55369.4i	−0.127463	−	0.446873i
$353$	87770.7			0.704369			0.352184	−	0.935931i	$-0.385439\pi$
$353$	87770.7			0.704369			0.352184	+	0.935931i	$0.385439\pi$
$354$	31102.5	+	20056.5i	0.248192	+	0.160047i
$355$		0			0
$356$	−35389.7	−	78132.2i	−0.279239	−	0.616496i
$357$	−10376.6			−0.0814179
$358$	−13387.1	+	20759.9i	−0.104453	+	0.161979i
$359$			32404.1i			0.251427i	0.992067	+	0.125713i	$0.0401219\pi$
$359$			32404.1i			0.251427i	−0.992067	+	0.125713i	$0.959878\pi$
$360$		0			0
$361$	106005.			0.813413
$362$	−82096.0	−	52939.8i	−0.626477	−	0.403985i
$363$		−	59648.6i		−	0.452676i
$364$	117080.	−	53030.8i	0.883647	−	0.400244i
$365$		0			0
$366$	56769.0	−	88034.2i	0.423789	−	0.657187i
$367$			98110.7i			0.728424i	0.931316	+	0.364212i	$0.118662\pi$
$367$			98110.7i			0.728424i	−0.931316	+	0.364212i	$0.881338\pi$
$368$	62098.5	+	54485.9i	0.458548	+	0.402336i
$369$	66713.3			0.489959
$370$		0			0
$371$			100790.i			0.732267i
$372$	−29081.8	−	64205.9i	−0.210153	−	0.463969i
$373$	113856.			0.818345			0.409172	−	0.912457i	$-0.365817\pi$
$373$	113856.			0.818345			0.409172	+	0.912457i	$0.365817\pi$
$374$	−6637.24	+	10292.7i	−0.0474509	+	0.0735841i
$375$		0			0
$376$	−211858.	−	31466.1i	−1.49854	−	0.222570i
$377$	216768.			1.52515
$378$	−17296.4	−	11153.6i	−0.121052	−	0.0780605i
$379$		−	97914.7i		−	0.681663i	−0.940124	−	0.340831i	$-0.889292\pi$
$379$		−	97914.7i		−	0.681663i	0.940124	−	0.340831i	$-0.110708\pi$
$380$		0			0
$381$	−98400.6			−0.677872
$382$	102114.	−	158353.i	0.699778	−	1.08518i
$383$			199529.i			1.36022i	0.733112	+	0.680108i	$0.238067\pi$
$383$			199529.i			1.36022i	−0.733112	+	0.680108i	$0.761933\pi$
$384$	64940.5	−	55049.9i	0.440406	−	0.373331i
$385$		0			0
$386$	−63446.4	−	40913.5i	−0.425826	−	0.274595i
$387$			4617.24i			0.0308291i
$388$	−85380.9	−	188501.i	−0.567149	−	1.25213i
$389$	−28806.1			−0.190364			−0.0951820	−	0.995460i	$-0.530343\pi$
$389$	−28806.1			−0.190364			−0.0951820	+	0.995460i	$0.530343\pi$
$390$		0			0
$391$		−	17572.3i		−	0.114941i
$392$	9929.29	−	66852.9i	0.0646169	−	0.435059i
$393$	44099.3			0.285527
$394$	118371.	+	76332.0i	0.762525	+	0.491716i
$395$		0			0
$396$	−22126.7	+	10022.2i	−0.141100	+	0.0639105i
$397$	−108324.			−0.687293			−0.343646	−	0.939099i	$-0.611662\pi$
$397$	−108324.			−0.687293			−0.343646	+	0.939099i	$0.611662\pi$
$398$	−67718.2	+	105014.i	−0.427503	+	0.662948i
$399$		−	29715.7i		−	0.186655i
$400$		0			0
$401$	23481.5			0.146028			0.0730141	−	0.997331i	$-0.476738\pi$
$401$	23481.5			0.146028			0.0730141	+	0.997331i	$0.476738\pi$
$402$	−70143.4	−	45232.1i	−0.434045	−	0.279895i
$403$		−	185705.i		−	1.14344i
$404$	−70199.5	−	154984.i	−0.430102	−	0.949566i
$405$		0			0
$406$	−78675.0	+	122005.i	−0.477293	+	0.740159i
$407$		−	103341.i		−	0.623854i
$408$	−17912.0	−	2660.36i	−0.107603	−	0.0159816i
$409$	129856.			0.776272			0.388136	−	0.921602i	$-0.373119\pi$
$409$	129856.			0.776272			0.388136	+	0.921602i	$0.373119\pi$
$410$		0			0
$411$		−	1596.90i		−	0.00945352i
$412$	153390.	−	69477.4i	0.903655	−	0.409307i
$413$	−65300.2			−0.382837
$414$	18888.0	−	29290.5i	0.110201	−	0.170894i
$415$		0			0
$416$	215697.	−	61523.9i	1.24640	−	0.355514i
$417$	172274.			0.990714
$418$	−29475.2	−	19007.1i	−0.168696	−	0.108784i
$419$		−	193614.i		−	1.10283i	−0.834230	−	0.551416i	$-0.814088\pi$
$419$		−	193614.i		−	1.10283i	0.834230	−	0.551416i	$-0.185912\pi$
$420$		0			0
$421$	185577.			1.04703			0.523515	−	0.852016i	$-0.324620\pi$
$421$	185577.			1.04703			0.523515	+	0.852016i	$0.324620\pi$
$422$	−128115.	+	198674.i	−0.719407	+	1.11562i
$423$			90358.1i			0.504994i
$424$	−25840.5	+	173982.i	−0.143737	+	0.967770i
$425$		0			0
$426$	94003.2	+	60618.1i	0.517992	+	0.334028i
$427$			184829.i			1.01371i
$428$	239158.	−	108326.i	1.30556	−	0.591349i
$429$	−63997.8			−0.347736
$430$		0			0
$431$		−	37823.7i		−	0.203615i	−0.994804	−	0.101808i	$-0.967537\pi$
$431$		−	37823.7i		−	0.203615i	0.994804	−	0.101808i	$-0.0324626\pi$
$432$	−26997.1	−	23687.6i	−0.144660	−	0.126927i
$433$	−13758.6			−0.0733834			−0.0366917	−	0.999327i	$-0.511682\pi$
$433$	−13758.6			−0.0733834			−0.0366917	+	0.999327i	$0.511682\pi$
$434$	104521.	+	67400.7i	0.554913	+	0.357837i
$435$		0			0
$436$	14461.5	+	31927.7i	0.0760749	+	0.167956i
$437$	50321.9			0.263508
$438$	73837.6	−	114503.i	0.384884	−	0.596856i
$439$		−	100071.i		−	0.519252i	−0.965709	−	0.259626i	$-0.916401\pi$
$439$		−	100071.i		−	0.519252i	0.965709	−	0.259626i	$-0.0835993\pi$
$440$		0			0
$441$	−28513.0			−0.146611
$442$	−40096.0	−	25856.0i	−0.205238	−	0.132348i
$443$			314053.i			1.60028i	0.599815	+	0.800139i	$0.295241\pi$
$443$			314053.i			1.60028i	−0.599815	+	0.800139i	$0.704759\pi$
$444$	139186.	−	63043.9i	0.706042	−	0.319799i
$445$		0			0
$446$	137505.	−	213234.i	0.691270	−	1.07198i
$447$		−	175925.i		−	0.880466i
$448$	−43658.3	+	143731.i	−0.217526	+	0.716136i
$449$	−104489.			−0.518294			−0.259147	−	0.965838i	$-0.583441\pi$
$449$	−104489.			−0.518294			−0.259147	+	0.965838i	$0.583441\pi$
$450$		0			0
$451$			138932.i			0.683046i
$452$	−1551.63	−	3425.64i	−0.00759470	−	0.0167673i
$453$	−62543.5			−0.304780
$454$	−176047.	+	273004.i	−0.854117	+	1.32452i
$455$		0			0
$456$	7618.50	−	51294.6i	0.0366387	−	0.246685i
$457$	−227716.			−1.09034			−0.545169	−	0.838326i	$-0.683535\pi$
$457$	−227716.			−1.09034			−0.545169	+	0.838326i	$0.683535\pi$
$458$	−125432.	−	80885.0i	−0.597967	−	0.385600i
$459$			7639.50i			0.0362610i
$460$		0			0
$461$	39587.7			0.186276			0.0931382	−	0.995653i	$-0.470310\pi$
$461$	39587.7			0.186276			0.0931382	+	0.995653i	$0.470310\pi$
$462$	23227.7	−	36020.2i	0.108823	−	0.168757i
$463$		−	68330.8i		−	0.318753i	−0.987218	−	0.159377i	$-0.949052\pi$
$463$		−	68330.8i		−	0.318753i	0.987218	−	0.159377i	$-0.0509484\pi$
$464$	−167087.	+	190432.i	−0.776080	+	0.884511i
$465$		0			0
$466$	199748.	+	128808.i	0.919834	+	0.593157i
$467$		−	51291.7i		−	0.235187i	−0.993062	−	0.117594i	$-0.962482\pi$
$467$		−	51291.7i		−	0.235187i	0.993062	−	0.117594i	$-0.0375180\pi$
$468$	−39042.4	−	86196.5i	−0.178256	−	0.393548i
$469$	147267.			0.669516
$470$		0			0
$471$			150877.i			0.680113i
$472$	−112720.	−	16741.6i	−0.505961	−	0.0751474i
$473$	−9615.53			−0.0429785
$474$	−200842.	−	129513.i	−0.893918	−	0.576444i
$475$		0			0
$476$	29105.3	−	13183.1i	0.128457	−	0.0581841i
$477$	74203.7			0.326129
$478$	32982.8	−	51147.9i	0.144355	−	0.223858i
$479$			420785.i			1.83396i	0.398935	+	0.916979i	$0.369380\pi$
$479$			420785.i			1.83396i	−0.398935	+	0.916979i	$0.630620\pi$
$480$		0			0
$481$	402574.			1.74003
$482$	−382973.	−	246961.i	−1.64844	−	1.06300i
$483$			61495.9i			0.263604i
$484$	75781.4	+	167308.i	0.323498	+	0.714209i
$485$		0			0
$486$	−8211.51	+	12734.0i	−0.0347657	+	0.0539127i
$487$		−	62163.7i		−	0.262107i	−0.991375	−	0.131054i	$-0.958164\pi$
$487$		−	62163.7i		−	0.262107i	0.991375	−	0.131054i	$-0.0418360\pi$
$488$	−47386.5	+	319049.i	−0.198983	+	1.33973i
$489$	−73567.4			−0.307658
$490$		0			0
$491$		−	244825.i		−	1.01553i	−0.861496	−	0.507764i	$-0.830472\pi$
$491$		−	244825.i		−	1.01553i	0.861496	−	0.507764i	$-0.169528\pi$
$492$	−187123.	+	84756.8i	−0.773033	+	0.350142i
$493$	53887.3			0.221714
$494$	74044.1	−	114823.i	0.303415	−	0.470518i
$495$		0			0
$496$	163142.	+	143143.i	0.663138	+	0.581844i
$497$	−197361.			−0.799005
$498$	143791.	+	92724.2i	0.579795	+	0.373882i
$499$			248564.i			0.998245i	0.866532	+	0.499122i	$0.166344\pi$
$499$			248564.i			0.998245i	−0.866532	+	0.499122i	$0.833656\pi$
$500$		0			0
$501$	−129864.			−0.517386
$502$	−13390.9	+	20765.9i	−0.0531377	+	0.0824030i
$503$			222640.i			0.879970i	0.898005	+	0.439985i	$0.145016\pi$
$503$			222640.i			0.879970i	−0.898005	+	0.439985i	$0.854984\pi$
$504$	62684.6	+	9310.19i	0.246774	+	0.0366520i
$505$		0			0
$506$	60998.3	+	39334.8i	0.238241	+	0.153630i
$507$		−	100902.i		−	0.392541i
$508$	276003.	−	125014.i	1.06951	−	0.484431i
$509$	−119110.			−0.459741			−0.229870	−	0.973221i	$-0.573830\pi$
$509$	−119110.			−0.459741			−0.229870	+	0.973221i	$0.573830\pi$
$510$		0			0
$511$			240402.i			0.920652i
$512$	−112212.	+	236913.i	−0.428055	+	0.903753i
$513$	−21877.3			−0.0831302
$514$	−351829.	−	226878.i	−1.33170	−	0.858748i
$515$		0			0
$516$	−5866.04	−	12950.9i	−0.0220316	−	0.0486406i
$517$	−188173.			−0.704007
$518$	−146112.	+	226583.i	−0.544536	+	0.844436i
$519$		−	257761.i		−	0.956935i
$520$		0			0
$521$	191412.			0.705170			0.352585	−	0.935780i	$-0.385303\pi$
$521$	191412.			0.705170			0.352585	+	0.935780i	$0.385303\pi$
$522$	89822.5	+	57922.2i	0.329643	+	0.212571i
$523$		−	393137.i		−	1.43728i	−0.695383	−	0.718639i	$-0.744765\pi$
$523$		−	393137.i		−	1.43728i	0.695383	−	0.718639i	$-0.255235\pi$
$524$	−123694.	+	56026.6i	−0.450490	+	0.204048i
$525$		0			0
$526$	−160550.	+	248971.i	−0.580280	+	0.899866i
$527$		−	46165.2i		−	0.166224i
$528$	49330.0	−	56222.2i	0.176947	−	0.201669i
$529$	175701.			0.627859
$530$		0			0
$531$			48075.4i			0.170504i
$532$	37752.7	+	83349.1i	0.133390	+	0.294495i
$533$	−541224.			−1.90512
$534$	60384.9	−	93641.5i	0.211761	−	0.328387i
$535$		0			0
$536$	254210.	+	37756.4i	0.884837	+	0.131420i
$537$	−32088.8			−0.111277
$538$	73514.3	+	47405.8i	0.253985	+	0.163782i
$539$		−	59379.0i		−	0.204388i
$540$		0			0
$541$	466336.			1.59333			0.796663	−	0.604423i	$-0.206596\pi$
$541$	466336.			1.59333			0.796663	+	0.604423i	$0.206596\pi$
$542$	−88438.8	+	137146.i	−0.301054	+	0.466858i
$543$		−	126897.i		−	0.430378i
$544$	53620.9	−	15294.5i	0.181191	−	0.0516817i
$545$		0			0
$546$	140320.	+	90485.6i	0.470689	+	0.303525i
$547$			188282.i			0.629265i	0.949214	+	0.314632i	$0.101881\pi$
$547$			188282.i			0.629265i	−0.949214	+	0.314632i	$0.898119\pi$
$548$	2028.80	+	4479.12i	0.00675582	+	0.0149153i
$549$	136075.			0.451476
$550$		0			0
$551$			154318.i			0.508291i
$552$	−15766.3	+	106153.i	−0.0517431	+	0.348381i
$553$	421671.			1.37887
$554$	147878.	+	95359.4i	0.481819	+	0.310702i
$555$		0			0
$556$	−483210.	+	218868.i	−1.56310	+	0.708000i
$557$	−267269.			−0.861466			−0.430733	−	0.902479i	$-0.641745\pi$
$557$	−267269.			−0.861466			−0.430733	+	0.902479i	$0.641745\pi$
$558$	49621.8	−	76950.8i	0.159369	−	0.247141i
$559$		−	37458.2i		−	0.119874i
$560$		0			0
$561$	−15909.5			−0.0505510
$562$	457018.	+	294709.i	1.44697	+	0.933084i
$563$			41516.3i			0.130979i	0.997853	+	0.0654896i	$0.0208609\pi$
$563$			41516.3i			0.130979i	−0.997853	+	0.0654896i	$0.979139\pi$
$564$	−114797.	−	253445.i	−0.360887	−	0.796755i
$565$		0			0
$566$	169230.	−	262432.i	0.528255	−	0.819188i
$567$		−	26735.2i		−	0.0831604i
$568$	−340682.	−	50599.5i	−1.05597	−	0.156837i
$569$	432092.			1.33460			0.667301	−	0.744788i	$-0.267450\pi$
$569$	432092.			1.33460			0.667301	+	0.744788i	$0.267450\pi$
$570$		0			0
$571$		−	568904.i		−	1.74488i	−0.488717	−	0.872442i	$-0.662535\pi$
$571$		−	568904.i		−	1.74488i	0.488717	−	0.872442i	$-0.337465\pi$
$572$	179507.	−	81306.8i	0.548641	−	0.248505i
$573$	244768.			0.745497
$574$	196435.	−	304620.i	0.596203	−	0.924558i
$575$		0			0
$576$	105818.	+	32142.2i	0.318944	+	0.0968791i
$577$	−81702.4			−0.245405			−0.122702	−	0.992444i	$-0.539156\pi$
$577$	−81702.4			−0.245405			−0.122702	+	0.992444i	$0.539156\pi$
$578$	270802.	+	174627.i	0.810579	+	0.522704i
$579$		−	98069.8i		−	0.292535i
$580$		0			0
$581$	−301893.			−0.894335
$582$	145684.	−	225919.i	0.430097	−	0.666970i
$583$			154531.i			0.454652i
$584$	−61634.1	+	414977.i	−0.180716	+	1.21674i
$585$		0			0
$586$	206154.	+	132939.i	0.600340	+	0.387130i
$587$		−	435087.i		−	1.26270i	−0.775498	−	0.631350i	$-0.782501\pi$
$587$		−	435087.i		−	1.26270i	0.775498	−	0.631350i	$-0.217499\pi$
$588$	79975.7	−	36224.7i	0.231315	−	0.104773i
$589$	132204.			0.381077
$590$		0			0
$591$			182968.i			0.523841i
$592$	−310307.	+	353662.i	−0.885419	+	1.00913i
$593$	−13910.0			−0.0395566			−0.0197783	−	0.999804i	$-0.506296\pi$
$593$	−13910.0			−0.0395566			−0.0197783	+	0.999804i	$0.506296\pi$
$594$	−26518.8	−	17100.7i	−0.0751590	−	0.0484664i
$595$		0			0
$596$	223506.	+	493450.i	0.629212	+	1.38916i
$597$	−162321.			−0.455434
$598$	−153233.	+	237625.i	−0.428498	+	0.664491i
$599$			252321.i			0.703233i	0.936144	+	0.351616i	$0.114368\pi$
$599$			252321.i			0.703233i	−0.936144	+	0.351616i	$0.885632\pi$
$600$		0			0
$601$	−546279.			−1.51240			−0.756198	−	0.654342i	$-0.772945\pi$
$601$	−546279.			−1.51240			−0.756198	+	0.654342i	$0.772945\pi$
$602$	21082.8	+	13595.3i	0.0581748	+	0.0375141i
$603$		−	108421.i		−	0.298181i
$604$	175428.	−	79459.3i	0.480866	−	0.217806i
$605$		0			0
$606$	119780.	−	185749.i	0.326167	−	0.505802i
$607$		−	538337.i		−	1.46109i	−0.682865	−	0.730544i	$-0.739266\pi$
$607$		−	538337.i		−	1.46109i	0.682865	−	0.730544i	$-0.260734\pi$
$608$	43798.9	+	153555.i	0.118483	+	0.415390i
$609$	−188584.			−0.508476
$610$		0			0
$611$		−	733047.i		−	1.96358i
$612$	−9705.70	−	21427.9i	−0.0259134	−	0.0572107i
$613$	238346.			0.634289			0.317144	−	0.948377i	$-0.397276\pi$
$613$	238346.			0.634289			0.317144	+	0.948377i	$0.397276\pi$
$614$	274355.	−	425454.i	0.727739	−	1.12854i
$615$		0			0
$616$	−19388.7	+	130542.i	−0.0510961	+	0.344025i
$617$	−233463.			−0.613264			−0.306632	−	0.951828i	$-0.599202\pi$
$617$	−233463.			−0.613264			−0.306632	+	0.951828i	$0.599202\pi$
$618$	183838.	+	118548.i	0.481347	+	0.310398i
$619$			18530.9i			0.0483633i	0.999708	+	0.0241816i	$0.00769800\pi$
$619$			18530.9i			0.0483633i	−0.999708	+	0.0241816i	$0.992302\pi$
$620$		0			0
$621$	45274.6			0.117401
$622$	320665.	−	497269.i	0.828840	−	1.28532i
$623$			196602.i			0.506538i
$624$	219019.	+	192170.i	0.562487	+	0.493533i
$625$		0			0
$626$	−517904.	−	333971.i	−1.32160	−	0.852237i
$627$		−	45560.1i		−	0.115891i
$628$	−191684.	−	423193.i	−0.486033	−	1.07305i
$629$	100077.			0.252950
$630$		0			0
$631$			2833.16i			0.00711560i	0.999994	+	0.00355780i	$0.00113249\pi$
$631$			2833.16i			0.00711560i	−0.999994	+	0.00355780i	$0.998868\pi$
$632$	727881.	+	108108.i	1.82233	+	0.270660i
$633$	−307092.			−0.766409
$634$	−135686.	−	87497.5i	−0.337565	−	0.217679i
$635$		0			0
$636$	−208133.	+	94273.1i	−0.514550	+	0.233063i
$637$	231317.			0.570070
$638$	−120625.	+	187058.i	−0.296343	+	0.459552i
$639$			145302.i			0.355852i
$640$		0			0
$641$	−14308.7			−0.0348244			−0.0174122	−	0.999848i	$-0.505543\pi$
$641$	−14308.7			−0.0348244			−0.0174122	+	0.999848i	$0.505543\pi$
$642$	286631.	+	184834.i	0.695429	+	0.448449i
$643$		−	436544.i		−	1.05586i	−0.849288	−	0.527930i	$-0.822968\pi$
$643$		−	436544.i		−	1.05586i	0.849288	−	0.527930i	$-0.177032\pi$
$644$	−78128.4	−	172489.i	−0.188381	−	0.415901i
$645$		0			0
$646$	18406.9	−	28544.4i	0.0441079	−	0.0684000i
$647$		−	104345.i		−	0.249266i	−0.992203	−	0.124633i	$-0.960225\pi$
$647$		−	104345.i		−	0.249266i	0.992203	−	0.124633i	$-0.0397753\pi$
$648$	6854.36	−	46149.8i	0.0163236	−	0.109905i
$649$	−100118.			−0.237697
$650$		0			0
$651$			161560.i			0.381216i
$652$	206349.	−	93464.8i	0.485407	−	0.219863i
$653$	382198.			0.896317			0.448159	−	0.893954i	$-0.352080\pi$
$653$	382198.			0.896317			0.448159	+	0.893954i	$0.352080\pi$
$654$	−24675.5	+	38265.4i	−0.0576913	+	0.0894645i
$655$		0			0
$656$	417180.	−	475467.i	0.969429	−	1.10487i
$657$	176989.			0.410029
$658$	412584.	+	266056.i	0.952930	+	0.614498i
$659$			663093.i			1.52688i	0.645881	+	0.763438i	$0.276490\pi$
$659$			663093.i			1.52688i	−0.645881	+	0.763438i	$0.723510\pi$
$660$		0			0
$661$	−510788.			−1.16906			−0.584531	−	0.811371i	$-0.698721\pi$
$661$	−510788.			−1.16906			−0.584531	+	0.811371i	$0.698721\pi$
$662$	−223961.	+	347307.i	−0.511043	+	0.792496i
$663$		−	61976.8i		−	0.140995i
$664$	−521122.	−	77399.2i	−1.18196	−	0.175550i
$665$		0			0
$666$	166815.	+	107571.i	0.376085	+	0.242519i
$667$		−	319357.i		−	0.717836i
$668$	364255.	−	164988.i	0.816306	−	0.369743i
$669$	329599.			0.736433
$670$		0			0
$671$			283381.i			0.629398i
$672$	−187652.	+	53524.5i	−0.415541	+	0.118526i
$673$	−367929.			−0.812332			−0.406166	−	0.913799i	$-0.633134\pi$
$673$	−367929.			−0.812332			−0.406166	+	0.913799i	$0.633134\pi$
$674$	−445651.	−	287379.i	−0.981014	−	0.632609i
$675$		0			0
$676$	128193.	+	283019.i	0.280524	+	0.619331i
$677$	87657.7			0.191255			0.0956275	−	0.995417i	$-0.469514\pi$
$677$	87657.7			0.191255			0.0956275	+	0.995417i	$0.469514\pi$
$678$	2647.52	−	4105.63i	0.00575943	−	0.00893141i
$679$			474321.i			1.02880i
$680$		0			0
$681$	−421985.			−0.909919
$682$	160252.	+	103339.i	0.344536	+	0.222175i
$683$		−	694219.i		−	1.48818i	−0.668080	−	0.744090i	$-0.732884\pi$
$683$		−	694219.i		−	1.48818i	0.668080	−	0.744090i	$-0.267116\pi$
$684$	61363.4	−	27794.3i	0.131159	−	0.0594078i
$685$		0			0
$686$	−274836.	+	426200.i	−0.584016	+	0.905659i
$687$		−	193881.i		−	0.410793i
$688$	32907.2	+	28873.1i	0.0695206	+	0.0609982i
$689$	−601992.			−1.26810
$690$		0			0
$691$		−	538950.i		−	1.12874i	−0.825523	−	0.564368i	$-0.809120\pi$
$691$		−	538950.i		−	1.12874i	0.825523	−	0.564368i	$-0.190880\pi$
$692$	327476.	+	722991.i	0.683860	+	1.50980i
$693$	55676.7			0.115933
$694$	509493.	−	790093.i	1.05784	−	1.64044i
$695$		0			0
$696$	−325530.	−	48349.2i	−0.672006	−	0.0998092i
$697$	−134545.			−0.276951
$698$	36424.3	+	23488.3i	0.0747619	+	0.0482103i
$699$			308752.i			0.631910i
$700$		0			0
$701$	−741852.			−1.50967			−0.754834	−	0.655916i	$-0.772283\pi$
$701$	−741852.			−1.50967			−0.754834	+	0.655916i	$0.772283\pi$
$702$	66617.4	−	103307.i	0.135180	−	0.209630i
$703$			286593.i			0.579902i
$704$	−66936.9	+	220369.i	−0.135058	+	0.444637i
$705$		0			0
$706$	−295055.	−	190267.i	−0.591962	−	0.381728i
$707$			389983.i			0.780201i
$708$	−61078.0	−	134846.i	−0.121848	−	0.269012i
$709$	199695.			0.397260			0.198630	−	0.980075i	$-0.436351\pi$
$709$	199695.			0.397260			0.198630	+	0.980075i	$0.436351\pi$
$710$		0			0
$711$		−	310443.i		−	0.614106i
$712$	−50404.8	+	339371.i	−0.0994287	+	0.669444i
$713$	−273593.			−0.538177
$714$	34882.7	+	22494.2i	0.0684248	+	0.0441239i
$715$		0			0
$716$	90005.6	−	40767.7i	0.175567	−	0.0795225i
$717$	79059.8			0.153786
$718$	70244.8	−	108932.i	0.136259	−	0.211303i
$719$		−	142037.i		−	0.274755i	−0.990519	−	0.137377i	$-0.956133\pi$
$719$		−	142037.i		−	0.274755i	0.990519	−	0.137377i	$-0.0438673\pi$
$720$		0			0
$721$	−385971.			−0.742480
$722$	−356352.	−	229794.i	−0.683604	−	0.440824i
$723$		−	591966.i		−	1.13245i
$724$	161218.	+	355931.i	0.307564	+	0.679030i
$725$		0			0
$726$	−129305.	+	200518.i	−0.245325	+	0.380436i
$727$		−	85013.5i		−	0.160849i	−0.996761	−	0.0804247i	$-0.974372\pi$
$727$		−	85013.5i		−	0.160849i	0.996761	−	0.0804247i	$-0.0256276\pi$
$728$	−508541.	−	75530.6i	−0.959540	−	0.142515i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	9311.89i		−	0.0174262i
$732$	−381676.	+	172879.i	−0.712317	+	0.322641i
$733$	−3612.19			−0.00672300			−0.00336150	−	0.999994i	$-0.501070\pi$
$733$	−3612.19			−0.00672300			−0.00336150	+	0.999994i	$0.501070\pi$
$734$	212682.	−	329815.i	0.394764	−	0.612179i
$735$		0			0
$736$	−90641.0	−	317778.i	−0.167328	−	0.586636i
$737$	225790.			0.415691
$738$	−224267.	−	144619.i	−0.411769	−	0.265530i
$739$		−	644842.i		−	1.18077i	−0.807123	−	0.590384i	$-0.798976\pi$
$739$		−	644842.i		−	1.18077i	0.807123	−	0.590384i	$-0.201024\pi$
$740$		0			0
$741$	177484.			0.323238
$742$	218490.	−	338822.i	0.396847	−	0.615408i
$743$		−	78321.7i		−	0.141875i	−0.997481	−	0.0709373i	$-0.977401\pi$
$743$		−	78321.7i		−	0.141875i	0.997481	−	0.0709373i	$-0.0225990\pi$
$744$	−41420.6	+	278881.i	−0.0748291	+	0.503817i
$745$		0			0
$746$	−382744.	−	246813.i	−0.687750	−	0.443496i
$747$			222260.i			0.398309i
$748$	44624.3	−	20212.4i	0.0797569	−	0.0361256i
$749$	−601787.			−1.07270
$750$		0			0
$751$			72594.7i			0.128714i	0.997927	+	0.0643569i	$0.0204996\pi$
$751$			72594.7i			0.128714i	−0.997927	+	0.0643569i	$0.979500\pi$
$752$	643984.	+	565039.i	1.13878	+	0.999177i
$753$	−32098.1			−0.0566094
$754$	−728702.	−	469905.i	−1.28176	−	0.826546i
$755$		0			0
$756$	33966.1	+	74989.2i	0.0594294	+	0.131206i
$757$	−627366.			−1.09479			−0.547393	−	0.836876i	$-0.684380\pi$
$757$	−627366.			−1.09479			−0.547393	+	0.836876i	$0.684380\pi$
$758$	−212257.	+	329156.i	−0.369422	+	0.572880i
$759$			94285.6i			0.163667i
$760$		0			0
$761$	95973.0			0.165722			0.0828609	−	0.996561i	$-0.473594\pi$
$761$	95973.0			0.165722			0.0828609	+	0.996561i	$0.473594\pi$
$762$	330789.	+	213310.i	0.569694	+	0.367368i
$763$		−	80338.9i		−	0.137999i
$764$	−686548.	+	310969.i	−1.17621	+	0.532759i
$765$		0			0
$766$	432533.	−	670748.i	0.737160	−	1.14315i
$767$		−	390020.i		−	0.662974i
$768$	−337644.	+	44282.9i	−0.572448	+	0.0750781i
$769$	−309887.			−0.524023			−0.262011	−	0.965065i	$-0.584386\pi$
$769$	−309887.			−0.524023			−0.262011	+	0.965065i	$0.584386\pi$
$770$		0			0
$771$		−	543826.i		−	0.914853i
$772$	124594.	+	275075.i	0.209056	+	0.461547i
$773$	−377481.			−0.631737			−0.315869	−	0.948803i	$-0.602296\pi$
$773$	−377481.			−0.631737			−0.315869	+	0.948803i	$0.602296\pi$
$774$	10009.1	−	15521.6i	0.0167076	−	0.0259092i
$775$		0			0
$776$	−121606.	+	818763.i	−0.201945	+	1.35967i
$777$	−350231.			−0.580113
$778$	96836.2	+	62445.0i	0.159985	+	0.103166i
$779$		−	385298.i		−	0.634924i
$780$		0			0
$781$	−302595.			−0.496089
$782$	−38092.7	+	59072.1i	−0.0622915	+	0.0965981i
$783$			138840.i			0.226459i
$784$	−178301.	+	203212.i	−0.290082	+	0.330612i
$785$		0			0
$786$	−148247.	−	95597.3i	−0.239961	−	0.154739i
$787$		−	254689.i		−	0.411208i	−0.978635	−	0.205604i	$-0.934084\pi$
$787$		−	254689.i		−	0.411208i	0.978635	−	0.205604i	$-0.0659158\pi$
$788$	−232454.	−	513204.i	−0.374356	−	0.826490i
$789$	−384838.			−0.618192
$790$		0			0
$791$			8619.83i			0.0137767i
$792$	96108.1	+	14274.4i	0.153218	+	0.0227566i
$793$	−1.10394e6			−1.75549
$794$	364147.	+	234821.i	0.577611	+	0.372474i
$795$		0			0
$796$	455291.	−	206222.i	0.718560	−	0.325469i
$797$	553547.			0.871440			0.435720	−	0.900082i	$-0.356494\pi$
$797$	553547.			0.871440			0.435720	+	0.900082i	$0.356494\pi$
$798$	−64416.8	+	99894.0i	−0.101156	+	0.156868i
$799$		−	182231.i		−	0.285449i
$800$		0			0
$801$	144743.			0.225596
$802$	−78936.8	−	50902.5i	−0.122724	−	0.0791390i
$803$			368584.i			0.571617i
$804$	137745.	+	304110.i	0.213091	+	0.470455i
$805$		0			0
$806$	−402566.	+	624277.i	−0.619680	+	0.960965i
$807$			113632.i			0.174483i
$808$	−99983.8	+	673181.i	−0.153146	+	1.03112i
$809$	1.16526e6			1.78043			0.890214	−	0.455543i	$-0.150555\pi$
$809$	1.16526e6			1.78043			0.890214	+	0.455543i	$0.150555\pi$
$810$		0			0
$811$		−	183530.i		−	0.279039i	−0.990219	−	0.139520i	$-0.955444\pi$
$811$		−	183530.i		−	0.279039i	0.990219	−	0.139520i	$-0.0445559\pi$
$812$	528957.	−	239589.i	0.802248	−	0.363375i
$813$	−211988.			−0.320723
$814$	−224019.	+	347397.i	−0.338093	+	0.524296i
$815$		0			0
$816$	54446.8	+	47772.3i	0.0817697	+	0.0717456i
$817$	26666.6			0.0399506
$818$	−436530.	−	281497.i	−0.652391	−	0.420695i
$819$			216894.i			0.323355i
$820$		0			0
$821$	1.04846e6			1.55548			0.777740	−	0.628587i	$-0.216366\pi$
$821$	1.04846e6			1.55548			0.777740	+	0.628587i	$0.216366\pi$
$822$	−3461.71	+	5368.23i	−0.00512327	+	0.00794488i
$823$			769461.i			1.13602i	0.823021	+	0.568011i	$0.192287\pi$
$823$			769461.i			1.13602i	−0.823021	+	0.568011i	$0.807713\pi$
$824$	−666257.	−	98955.3i	−0.981267	−	0.145742i
$825$		0			0
$826$	219517.	+	141556.i	0.321742	+	0.207476i
$827$			962782.i			1.40772i	0.710338	+	0.703861i	$0.248542\pi$
$827$			962782.i			1.40772i	−0.710338	+	0.703861i	$0.751458\pi$
$828$	−126990.	+	57519.8i	−0.185229	+	0.0838989i
$829$	6742.46			0.00981091			0.00490546	−	0.999988i	$-0.498439\pi$
$829$	6742.46			0.00981091			0.00490546	+	0.999988i	$0.498439\pi$
$830$		0			0
$831$			228577.i			0.331001i
$832$	−858469.	−	260759.i	−1.24016	−	0.376698i
$833$	57504.0			0.0828720
$834$	−579128.	−	373452.i	−0.832611	−	0.536911i
$835$		0			0
$836$	57882.4	+	127791.i	0.0828198	+	0.182847i
$837$	118944.			0.169781
$838$	−419712.	+	650866.i	−0.597673	+	0.926837i
$839$			89293.9i			0.126852i	0.997987	+	0.0634261i	$0.0202027\pi$
$839$			89293.9i			0.126852i	−0.997987	+	0.0634261i	$0.979797\pi$
$840$		0			0
$841$	272063.			0.384660
$842$	−623846.	−	402288.i	−0.879940	−	0.567431i
$843$			706417.i			0.994045i
$844$	861358.	−	390149.i	1.20920	−	0.547703i
$845$		0			0
$846$	195876.	−	303753.i	0.273678	−	0.424405i
$847$		−	420992.i		−	0.586823i
$848$	464020.	−	528851.i	0.645275	−	0.735431i
$849$	405643.			0.562767
$850$		0			0
$851$		−	593098.i		−	0.818969i
$852$	−184600.	−	407555.i	−0.254304	−	0.561445i
$853$	−350724.			−0.482023			−0.241011	−	0.970522i	$-0.577479\pi$
$853$	−350724.			−0.482023			−0.241011	+	0.970522i	$0.577479\pi$
$854$	400668.	−	621334.i	0.549375	−	0.851940i
$855$		0			0
$856$	−1.03879e6	−	154286.i	−1.41769	−	0.210562i
$857$	−627010.			−0.853715			−0.426857	−	0.904319i	$-0.640379\pi$
$857$	−627010.			−0.853715			−0.426857	+	0.904319i	$0.640379\pi$
$858$	215139.	+	138733.i	0.292243	+	0.188453i
$859$		−	830100.i		−	1.12498i	−0.826805	−	0.562489i	$-0.809844\pi$
$859$		−	830100.i		−	1.12498i	0.826805	−	0.562489i	$-0.190156\pi$
$860$		0			0
$861$	470854.			0.635155
$862$	−81993.3	+	127151.i	−0.110348	+	0.171121i
$863$		−	898913.i		−	1.20697i	−0.797375	−	0.603485i	$-0.793779\pi$
$863$		−	898913.i		−	1.20697i	0.797375	−	0.603485i	$-0.206221\pi$
$864$	39405.9	+	138153.i	0.0527878	+	0.185069i
$865$		0			0
$866$	46251.7	+	29825.5i	0.0616726	+	0.0397697i
$867$			418581.i			0.556854i
$868$	−205255.	−	453157.i	−0.272430	−	0.601463i
$869$	646507.			0.856118
$870$		0			0
$871$			879588.i			1.15943i
$872$	20597.3	−	138680.i	0.0270880	−	0.182381i
$873$	349205.			0.458197
$874$	−169165.	−	109087.i	−0.221456	−	0.142807i
$875$		0			0
$876$	−496434.	+	224858.i	−0.646924	+	0.293022i
$877$	1.35617e6			1.76325			0.881625	−	0.471951i	$-0.156450\pi$
$877$	1.35617e6			1.76325			0.881625	+	0.471951i	$0.156450\pi$
$878$	−216931.	+	336404.i	−0.281405	+	0.436387i
$879$			318655.i			0.412423i
$880$		0			0
$881$	−198041.			−0.255155			−0.127577	−	0.991829i	$-0.540720\pi$
$881$	−198041.			−0.255155			−0.127577	+	0.991829i	$0.540720\pi$
$882$	95850.9	+	61809.6i	0.123214	+	0.0794546i
$883$			424914.i			0.544978i	0.962159	+	0.272489i	$0.0878469\pi$
$883$			424914.i			0.544978i	−0.962159	+	0.272489i	$0.912153\pi$
$884$	78739.3	+	173838.i	0.100760	+	0.222454i
$885$		0			0
$886$	680795.	−	1.05574e6i	0.867259	−	1.34490i
$887$		−	251270.i		−	0.319370i	−0.987168	−	0.159685i	$-0.948952\pi$
$887$		−	251270.i		−	0.319370i	0.987168	−	0.159685i	$-0.0510478\pi$
$888$	−604562.	−	89792.2i	−0.766682	−	0.113871i
$889$	−694498.			−0.878754
$890$		0			0
$891$		−	40990.4i		−	0.0516329i
$892$	−924487.	+	418743.i	−1.16191	+	0.526281i
$893$	521857.			0.654408
$894$	−381365.	+	591400.i	−0.477163	+	0.739957i
$895$		0			0
$896$	458341.	−	388535.i	0.570917	−	0.483965i
$897$	−367299.			−0.456494
$898$	351255.	+	226507.i	0.435582	+	0.280886i
$899$		−	839002.i		−	1.03811i
$900$		0			0
$901$	−149652.			−0.184345
$902$	301174.	−	467043.i	0.370172	−	0.574042i
$903$			32587.9i			0.0399651i
$904$	−2209.95	+	14879.4i	−0.00270424	+	0.0182074i
$905$		0			0
$906$	210250.	+	135580.i	0.256141	+	0.165173i
$907$			767484.i			0.932943i	0.884536	+	0.466471i	$0.154475\pi$
$907$			767484.i			0.932943i	−0.884536	+	0.466471i	$0.845525\pi$
$908$	1.18362e6	−	536117.i	1.43563	−	0.650261i
$909$	287114.			0.347477
$910$		0			0
$911$			1.57220e6i			1.89440i	0.320644	+	0.947200i	$0.396101\pi$
$911$			1.57220e6i			1.89440i	−0.320644	+	0.947200i	$0.603899\pi$
$912$	−136806.	+	155920.i	−0.164481	+	0.187461i
$913$	−462862.			−0.555278
$914$	765504.	+	493637.i	0.916337	+	0.590901i
$915$		0			0
$916$	246319.	+	543816.i	0.293567	+	0.648128i
$917$	311247.			0.370141
$918$	16560.7	−	25681.4i	0.0196514	−	0.0304743i
$919$			966072.i			1.14388i	0.820297	+	0.571938i	$0.193808\pi$
$919$			966072.i			1.14388i	−0.820297	+	0.571938i	$0.806192\pi$
$920$		0			0
$921$	657629.			0.775285
$922$	−133080.	−	85817.0i	−0.156550	−	0.100951i
$923$		−	1.17879e6i		−	1.38367i
$924$	−156167.	+	70735.2i	−0.182913	+	0.0828499i
$925$		0			0
$926$	−148126.	+	229705.i	−0.172746	+	0.267885i
$927$			284160.i			0.330677i
$928$	974502.	−	277960.i	1.13158	−	0.322765i
$929$	−70858.7			−0.0821035			−0.0410518	−	0.999157i	$-0.513071\pi$
$929$	−70858.7			−0.0821035			−0.0410518	+	0.999157i	$0.513071\pi$
$930$		0			0
$931$			164675.i			0.189989i
$932$	−392258.	−	866014.i	−0.451585	−	0.996996i
$933$	768634.			0.882991
$934$	−111189.	+	172425.i	−0.127458	+	0.197655i
$935$		0			0
$936$	−55607.3	+	374399.i	−0.0634717	+	0.427349i
$937$	1.17870e6			1.34253			0.671264	−	0.741218i	$-0.265752\pi$
$937$	1.17870e6			1.34253			0.671264	+	0.741218i	$0.265752\pi$
$938$	−495063.	−	319242.i	−0.562671	−	0.362839i
$939$		−	800529.i		−	0.907916i
$940$		0			0
$941$	531033.			0.599711			0.299856	−	0.953985i	$-0.403061\pi$
$941$	531033.			0.599711			0.299856	+	0.953985i	$0.403061\pi$
$942$	327067.	−	507197.i	0.368583	−	0.571577i
$943$			797366.i			0.896674i
$944$	342634.	+	300631.i	0.384491	+	0.337357i
$945$		0			0
$946$	32324.2	+	20844.3i	0.0361198	+	0.0232919i
$947$		−	62301.1i		−	0.0694698i	−0.999397	−	0.0347349i	$-0.988941\pi$
$947$		−	62301.1i		−	0.0694698i	0.999397	−	0.0347349i	$-0.0110587\pi$
$948$	394407.	+	870759.i	0.438862	+	0.968905i
$949$	−1.43585e6			−1.59433
$950$		0			0
$951$		−	209731.i		−	0.231901i
$952$	−126420.	−	18776.5i	−0.139490	−	0.0207176i
$953$	1.59019e6			1.75091			0.875453	−	0.483304i	$-0.160563\pi$
$953$	1.59019e6			1.75091			0.875453	+	0.483304i	$0.160563\pi$
$954$	−249448.	−	160857.i	−0.274083	−	0.176743i
$955$		0			0
$956$	−221754.	+	100443.i	−0.242636	+	0.109901i
$957$	−289137.			−0.315704
$958$	912167.	−	1.41454e6i	0.993901	−	1.54129i
$959$		−	11270.7i		−	0.0122550i
$960$		0			0
$961$	204750.			0.221706
$962$	−1.35332e6	−	872689.i	−1.46234	−	0.942995i
$963$			443048.i			0.477748i
$964$	752071.	+	1.66040e6i	0.809291	+	1.78673i
$965$		0			0
$966$	133309.	−	206728.i	0.142858	−	0.221537i
$967$		−	1.28376e6i		−	1.37287i	−0.727189	−	0.686437i	$-0.759174\pi$
$967$		−	1.28376e6i		−	1.37287i	0.727189	−	0.686437i	$-0.240826\pi$
$968$	107934.	−	726709.i	0.115188	−	0.775550i
$969$	44121.4			0.0469896
$970$		0			0
$971$		−	778263.i		−	0.825445i	−0.910857	−	0.412722i	$-0.864578\pi$
$971$		−	778263.i		−	0.825445i	0.910857	−	0.412722i	$-0.135422\pi$
$972$	55208.6	−	25006.5i	0.0584352	−	0.0264680i
$973$	1.21589e6			1.28431
$974$	−134757.	+	208973.i	−0.142047	+	0.220279i
$975$		0			0
$976$	850924.	−	969812.i	0.893287	−	1.01809i
$977$	−774448.			−0.811341			−0.405670	−	0.914019i	$-0.632962\pi$
$977$	−774448.			−0.811341			−0.405670	+	0.914019i	$0.632962\pi$
$978$	247309.	+	159477.i	0.258560	+	0.166733i
$979$			301430.i			0.314501i
$980$		0			0
$981$	−59147.2			−0.0614605
$982$	−530724.	+	823017.i	−0.550359	+	0.853466i
$983$			1.11526e6i			1.15417i	0.816685	+	0.577083i	$0.195809\pi$
$983$			1.11526e6i			1.15417i	−0.816685	+	0.577083i	$0.804191\pi$
$984$	812779.	+	120717.i	0.839426	+	0.124675i
$985$		0			0
$986$	−181151.	−	116816.i	−0.186332	−	0.120156i
$987$			637736.i			0.654646i
$988$	−497822.	+	225487.i	−0.509988	+	0.230997i
$989$	−55185.9			−0.0564203
$990$		0			0
$991$			1.63570e6i			1.66554i	0.553619	+	0.832770i	$0.313246\pi$
$991$			1.63570e6i			1.66554i	−0.553619	+	0.832770i	$0.686754\pi$
$992$	−238128.	−	834854.i	−0.241984	−	0.848374i
$993$	−536836.			−0.544431
$994$	663462.	+	427835.i	0.671496	+	0.433015i
$995$		0			0
$996$	−282373.	−	623414.i	−0.284646	−	0.628432i
$997$	228598.			0.229976			0.114988	−	0.993367i	$-0.463317\pi$
$997$	228598.			0.229976			0.114988	+	0.993367i	$0.463317\pi$
$998$	538830.	−	835587.i	0.540992	−	0.838940i
$999$			257847.i			0.258364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.c.151.3	yes	16
4.3	odd	2	inner	300.5.c.c.151.4	yes	16
5.2	odd	4		300.5.f.c.199.21		32
5.3	odd	4		300.5.f.c.199.12		32
5.4	even	2		300.5.c.b.151.14	yes	16
20.3	even	4		300.5.f.c.199.22		32
20.7	even	4		300.5.f.c.199.11		32
20.19	odd	2		300.5.c.b.151.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.13	✓	16	20.19	odd	2
300.5.c.b.151.14	yes	16	5.4	even	2
300.5.c.c.151.3	yes	16	1.1	even	1	trivial
300.5.c.c.151.4	yes	16	4.3	odd	2	inner
300.5.f.c.199.11		32	20.7	even	4
300.5.f.c.199.12		32	5.3	odd	4
300.5.f.c.199.21		32	5.2	odd	4
300.5.f.c.199.22		32	20.3	even	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.36166 - 2.16777i) q^{2} -5.19615i q^{3} +(6.60152 + 14.5746i) q^{4} +(-11.2641 + 17.4677i) q^{6} -36.6738i q^{7} +(9.40241 - 63.3056i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-3.36166 - 2.16777i) q^{2} -5.19615i q^{3} +(6.60152 + 14.5746i) q^{4} +(-11.2641 + 17.4677i) q^{6} -36.6738i q^{7} +(9.40241 - 63.3056i) q^{8} -27.0000 q^{9} -56.2282i q^{11} +(75.7320 - 34.3025i) q^{12} +219.043 q^{13} +(-79.5004 + 123.285i) q^{14} +(-168.840 + 192.430i) q^{16} +54.4527 q^{17} +(90.7648 + 58.5299i) q^{18} +155.937i q^{19} -190.562 q^{21} +(-121.890 + 189.020i) q^{22} -322.708i q^{23} +(-328.945 - 48.8564i) q^{24} +(-736.347 - 474.834i) q^{26} +140.296i q^{27} +(534.506 - 242.103i) q^{28} +989.618 q^{29} -847.804i q^{31} +(984.726 - 280.876i) q^{32} -292.171 q^{33} +(-183.051 - 118.041i) q^{34} +(-178.241 - 393.515i) q^{36} +1837.88 q^{37} +(338.035 - 524.206i) q^{38} -1138.18i q^{39} -2470.86 q^{41} +(640.606 + 413.096i) q^{42} -171.009i q^{43} +(819.506 - 371.192i) q^{44} +(-699.557 + 1084.83i) q^{46} -3346.60i q^{47} +(999.893 + 877.317i) q^{48} +1056.04 q^{49} -282.944i q^{51} +(1446.01 + 3192.46i) q^{52} -2748.29 q^{53} +(304.130 - 471.628i) q^{54} +(-2321.65 - 344.822i) q^{56} +810.271 q^{57} +(-3326.76 - 2145.27i) q^{58} -1780.57i q^{59} -5039.83 q^{61} +(-1837.85 + 2850.03i) q^{62} +990.191i q^{63} +(-3919.19 - 1190.45i) q^{64} +(982.178 + 633.359i) q^{66} +4015.61i q^{67} +(359.470 + 793.628i) q^{68} -1676.84 q^{69} -5381.54i q^{71} +(-253.865 + 1709.25i) q^{72} -6555.14 q^{73} +(-6178.33 - 3984.11i) q^{74} +(-2272.72 + 1029.42i) q^{76} -2062.10 q^{77} +(-2467.31 + 3826.17i) q^{78} +11497.9i q^{79} +729.000 q^{81} +(8306.20 + 5356.27i) q^{82} -8231.85i q^{83} +(-1258.00 - 2777.38i) q^{84} +(-370.709 + 574.874i) q^{86} -5142.21i q^{87} +(-3559.56 - 528.681i) q^{88} -5360.84 q^{89} -8033.11i q^{91} +(4703.34 - 2130.36i) q^{92} -4405.32 q^{93} +(-7254.66 + 11250.1i) q^{94} +(-1459.48 - 5116.78i) q^{96} -12933.5 q^{97} +(-3550.03 - 2289.25i) q^{98} +1518.16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 176 q^{13} + 78 q^{14} - 376 q^{16} - 162 q^{18} - 144 q^{21} - 788 q^{22} + 108 q^{24} + 678 q^{26} + 3368 q^{28} + 1728 q^{29} + 2016 q^{32} - 2932 q^{34} - 216 q^{36} - 1568 q^{37} - 6990 q^{38} + 1248 q^{41} + 162 q^{42} + 8088 q^{44} + 5956 q^{46} + 2088 q^{48} - 10720 q^{49} + 3128 q^{52} - 288 q^{53} - 486 q^{54} - 10236 q^{56} + 5616 q^{57} - 16164 q^{58} - 3760 q^{61} - 12714 q^{62} + 10544 q^{64} + 8100 q^{66} + 26136 q^{68} + 9792 q^{69} + 4860 q^{72} + 11040 q^{73} - 17004 q^{74} - 28344 q^{76} + 768 q^{77} - 16830 q^{78} + 11664 q^{81} - 21280 q^{82} + 15120 q^{84} + 24414 q^{86} + 52840 q^{88} - 768 q^{89} + 23736 q^{92} - 9936 q^{93} - 45156 q^{94} - 11088 q^{96} + 7248 q^{97} - 58140 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 8 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 176 * q^13 + 78 * q^14 - 376 * q^16 - 162 * q^18 - 144 * q^21 - 788 * q^22 + 108 * q^24 + 678 * q^26 + 3368 * q^28 + 1728 * q^29 + 2016 * q^32 - 2932 * q^34 - 216 * q^36 - 1568 * q^37 - 6990 * q^38 + 1248 * q^41 + 162 * q^42 + 8088 * q^44 + 5956 * q^46 + 2088 * q^48 - 10720 * q^49 + 3128 * q^52 - 288 * q^53 - 486 * q^54 - 10236 * q^56 + 5616 * q^57 - 16164 * q^58 - 3760 * q^61 - 12714 * q^62 + 10544 * q^64 + 8100 * q^66 + 26136 * q^68 + 9792 * q^69 + 4860 * q^72 + 11040 * q^73 - 17004 * q^74 - 28344 * q^76 + 768 * q^77 - 16830 * q^78 + 11664 * q^81 - 21280 * q^82 + 15120 * q^84 + 24414 * q^86 + 52840 * q^88 - 768 * q^89 + 23736 * q^92 - 9936 * q^93 - 45156 * q^94 - 11088 * q^96 + 7248 * q^97 - 58140 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more