LMFDB - Embedded newform 300.5.c.b.151.13

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			151.13
Root			$-3.55818 - 1.82740i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.b.151.14

$q$-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	$0.0746409\pi$
$11$			56.2282i			0.464696i	−0.972633	+	0.232348i	$0.925359\pi$
$12$	−75.7320	−	34.3025i	−0.525917	−	0.238212i
$13$	−219.043			−1.29611			−0.648055	−	0.761594i	$-0.724417\pi$
$13$	−219.043			−1.29611			−0.648055	+	0.761594i	$0.724417\pi$
$14$	−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	$-0.530032\pi$
$17$	−54.4527			−0.188418			−0.0942088	+	0.995552i	$0.530032\pi$
$18$	−90.7648	+	58.5299i	−0.280138	+	0.180648i
$19$		−	155.937i		−	0.431957i	−0.976398	−	0.215979i	$-0.930706\pi$
$19$		−	155.937i		−	0.431957i	0.976398	−	0.215979i	$-0.0692942\pi$
$20$		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	$0.145413\pi$
$31$			847.804i			0.882210i	−0.897456	+	0.441105i	$0.854587\pi$
$32$	−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	$-0.734242\pi$
$37$	−1837.88			−1.34250			−0.671249	+	0.741232i	$0.734242\pi$
$38$	−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	$-0.337291\pi$
$53$	2748.29			0.978386			0.489193	+	0.872176i	$0.337291\pi$
$54$	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	$0.0823242\pi$
$59$			1780.57i			0.511511i	−0.966742	+	0.255755i	$0.917676\pi$
$60$		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	$0.179228\pi$
$71$			5381.54i			1.06755i	−0.845625	+	0.533777i	$0.820772\pi$
$72$	253.865	+	1709.25i	0.0489709	+	0.329716i
$73$	6555.14			1.23009			0.615044	−	0.788493i	$-0.289138\pi$
$73$	6555.14			1.23009			0.615044	+	0.788493i	$0.289138\pi$
$74$	−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	$-0.627244\pi$
$79$		−	11497.9i		−	1.84232i	0.389188	−	0.921158i	$-0.372756\pi$
$80$		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	$-0.258798\pi$
$97$	12933.5			1.37459			0.687295	+	0.726379i	$0.258798\pi$
$98$	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	$-0.497070\pi$
$113$	235.041			0.0184072			0.00920358	+	0.999958i	$0.497070\pi$
$114$	−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	$-0.920465\pi$
$131$		−	8486.92i		−	0.494547i	0.968946	−	0.247273i	$-0.0795346\pi$
$132$	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	$-0.502606\pi$
$137$	−307.323			−0.0163740			−0.00818699	+	0.999966i	$0.502606\pi$
$138$	−5636.96	+	3635.00i	−0.295997	+	0.190874i
$139$		−	33154.2i		−	1.71597i	−0.513677	−	0.857984i	$-0.671717\pi$
$139$		−	33154.2i		−	1.71597i	0.513677	−	0.857984i	$-0.328283\pi$
$140$		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	$0.0850244\pi$
$151$			12036.5i			0.527894i	−0.964537	+	0.263947i	$0.914976\pi$
$152$	−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	$-0.299524\pi$
$157$	29036.3			1.17799			0.588995	+	0.808137i	$0.299524\pi$
$158$	−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	$-0.810936\pi$
$173$	−49606.1			−1.65746			−0.828730	+	0.559648i	$0.810936\pi$
$174$	−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	$0.0307228\pi$
$179$			6175.50i			0.192737i	−0.995346	+	0.0963687i	$0.969277\pi$
$180$		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	$-0.776599\pi$
$191$		−	47105.7i		−	1.29124i	0.763659	−	0.645620i	$-0.223401\pi$
$192$	6185.76	+	20364.7i	0.167799	+	0.552428i
$193$	−18873.5			−0.506686			−0.253343	−	0.967377i	$-0.581530\pi$
$193$	−18873.5			−0.506686			−0.253343	+	0.967377i	$0.581530\pi$
$194$	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	$-0.350118\pi$
$197$	35212.2			0.907319			0.453660	+	0.891175i	$0.350118\pi$
$198$	−3291.03	−	5103.55i	−0.0839463	−	0.130179i
$199$			31238.6i			0.788834i	0.918932	+	0.394417i	$0.129053\pi$
$199$			31238.6i			0.788834i	−0.918932	+	0.394417i	$0.870947\pi$
$200$		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	$0.231027\pi$
$211$			59099.8i			1.32746i	−0.747973	+	0.663730i	$0.768973\pi$
$212$	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	$-0.315675\pi$
$233$	59419.3			1.09450			0.547250	+	0.836969i	$0.315675\pi$
$234$	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	$-0.957480\pi$
$239$		−	15215.1i		−	0.266365i	0.991092	−	0.133183i	$-0.0425197\pi$
$240$		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	$0.0156115\pi$
$251$			6177.27i			0.0980504i	−0.998798	+	0.0490252i	$0.984389\pi$
$252$	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	$-0.791109\pi$
$257$	−104659.			−1.58457			−0.792286	+	0.610150i	$0.791109\pi$
$258$	−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	$0.0895900\pi$
$271$			40797.1i			0.555508i	−0.960652	+	0.277754i	$0.910410\pi$
$272$	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	$-0.407456\pi$
$277$	43989.6			0.573311			0.286655	+	0.958034i	$0.407456\pi$
$278$	−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	$-0.383742\pi$
$293$	61325.1			0.714337			0.357169	+	0.934040i	$0.383742\pi$
$294$	−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	$-0.722891\pi$
$311$		−	147924.i		−	1.52939i	0.644395	−	0.764693i	$-0.277109\pi$
$312$	72053.0	−	10701.6i	0.740190	−	0.109936i
$313$	−154062.			−1.57256			−0.786278	−	0.617872i	$-0.787995\pi$
$313$	−154062.			−1.57256			−0.786278	+	0.617872i	$0.787995\pi$
$314$	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	$-0.564365\pi$
$317$	−40362.8			−0.401664			−0.200832	+	0.979626i	$0.564365\pi$
$318$	−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	$0.156284\pi$
$331$			103314.i			0.942982i	−0.881871	+	0.471491i	$0.843716\pi$
$332$	−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	$-0.698375\pi$
$337$	−132569.			−1.16730			−0.583649	+	0.812006i	$0.698375\pi$
$338$	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	$-0.614561\pi$
$353$	−87770.7			−0.704369			−0.352184	+	0.935931i	$0.614561\pi$
$354$	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	$-0.959878\pi$
$359$		−	32404.1i		−	0.251427i	0.992067	−	0.125713i	$-0.0401219\pi$
$360$		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	$-0.634183\pi$
$373$	−113856.			−0.818345			−0.409172	+	0.912457i	$0.634183\pi$
$374$	−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	$0.110708\pi$
$379$			97914.7i			0.681663i	−0.940124	+	0.340831i	$0.889292\pi$
$380$		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	$-0.388338\pi$
$397$	108324.			0.687293			0.343646	+	0.939099i	$0.388338\pi$
$398$	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	$0.185912\pi$
$419$			193614.i			1.10283i	−0.834230	+	0.551416i	$0.814088\pi$
$420$		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	$0.0324626\pi$
$431$			37823.7i			0.203615i	−0.994804	+	0.101808i	$0.967537\pi$
$432$	26997.1	−	23687.6i	0.144660	−	0.126927i
$433$	13758.6			0.0733834			0.0366917	−	0.999327i	$-0.488318\pi$
$433$	13758.6			0.0733834			0.0366917	+	0.999327i	$0.488318\pi$
$434$	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	$0.0835993\pi$
$439$			100071.i			0.519252i	−0.965709	+	0.259626i	$0.916401\pi$
$440$		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	$-0.316465\pi$
$457$	227716.			1.09034			0.545169	+	0.838326i	$0.316465\pi$
$458$	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	$-0.630620\pi$
$479$		−	420785.i		−	1.83396i	0.398935	−	0.916979i	$-0.369380\pi$
$480$		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	$0.169528\pi$
$491$			244825.i			1.01553i	−0.861496	+	0.507764i	$0.830472\pi$
$492$	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	$-0.833656\pi$
$499$		−	248564.i		−	0.998245i	0.866532	−	0.499122i	$-0.166344\pi$
$500$		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	$-0.358255\pi$
$557$	267269.			0.861466			0.430733	+	0.902479i	$0.358255\pi$
$558$	−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	$0.337465\pi$
$571$			568904.i			1.74488i	−0.488717	+	0.872442i	$0.662535\pi$
$572$	−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	$-0.460844\pi$
$577$	81702.4			0.245405			0.122702	+	0.992444i	$0.460844\pi$
$578$	−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	$-0.493704\pi$
$593$	13910.0			0.0395566			0.0197783	+	0.999804i	$0.493704\pi$
$594$	−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	$-0.885632\pi$
$599$		−	252321.i		−	0.703233i	0.936144	−	0.351616i	$-0.114368\pi$
$600$		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	$-0.602724\pi$
$613$	−238346.			−0.634289			−0.317144	+	0.948377i	$0.602724\pi$
$614$	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	$-0.400798\pi$
$617$	233463.			0.613264			0.306632	+	0.951828i	$0.400798\pi$
$618$	−183838.	+	118548.i	−0.481347	+	0.310398i
$619$		−	18530.9i		−	0.0483633i	−0.999708	−	0.0241816i	$-0.992302\pi$
$619$		−	18530.9i		−	0.0483633i	0.999708	−	0.0241816i	$-0.00769800\pi$
$620$		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	$-0.998868\pi$
$631$		−	2833.16i		−	0.00711560i	0.999994	−	0.00355780i	$-0.00113249\pi$
$632$	−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	$-0.647920\pi$
$653$	−382198.			−0.896317			−0.448159	+	0.893954i	$0.647920\pi$
$654$	−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	$-0.723510\pi$
$659$		−	663093.i		−	1.52688i	0.645881	−	0.763438i	$-0.276490\pi$
$660$		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	$-0.366866\pi$
$673$	367929.			0.812332			0.406166	+	0.913799i	$0.366866\pi$
$674$	−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	$-0.530486\pi$
$677$	−87657.7			−0.191255			−0.0956275	+	0.995417i	$0.530486\pi$
$678$	−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	$0.190880\pi$
$691$			538950.i			1.12874i	−0.825523	+	0.564368i	$0.809120\pi$
$692$	−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	$0.0438673\pi$
$719$			142037.i			0.274755i	−0.990519	+	0.137377i	$0.956133\pi$
$720$		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	$-0.498930\pi$
$733$	3612.19			0.00672300			0.00336150	+	0.999994i	$0.498930\pi$
$734$	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	$0.201024\pi$
$739$			644842.i			1.18077i	−0.807123	+	0.590384i	$0.798976\pi$
$740$		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	$-0.979500\pi$
$751$		−	72594.7i		−	0.128714i	0.997927	−	0.0643569i	$-0.0204996\pi$
$752$	−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	$-0.315620\pi$
$757$	627366.			1.09479			0.547393	+	0.836876i	$0.315620\pi$
$758$	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	$-0.397704\pi$
$773$	377481.			0.631737			0.315869	+	0.948803i	$0.397704\pi$
$774$	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	$-0.643506\pi$
$797$	−553547.			−0.871440			−0.435720	+	0.900082i	$0.643506\pi$
$798$	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	$0.0445559\pi$
$811$			183530.i			0.279039i	−0.990219	+	0.139520i	$0.955444\pi$
$812$	−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	$-0.979797\pi$
$839$		−	89293.9i		−	0.126852i	0.997987	−	0.0634261i	$-0.0202027\pi$
$840$		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	$-0.422521\pi$
$853$	350724.			0.482023			0.241011	+	0.970522i	$0.422521\pi$
$854$	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	$-0.359621\pi$
$857$	627010.			0.853715			0.426857	+	0.904319i	$0.359621\pi$
$858$	−215139.	+	138733.i	−0.292243	+	0.188453i
$859$			830100.i			1.12498i	0.826805	+	0.562489i	$0.190156\pi$
$859$			830100.i			1.12498i	−0.826805	+	0.562489i	$0.809844\pi$
$860$		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	$-0.843550\pi$
$877$	−1.35617e6			−1.76325			−0.881625	+	0.471951i	$0.843550\pi$
$878$	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	$-0.603899\pi$
$911$		−	1.57220e6i		−	1.89440i	0.320644	−	0.947200i	$-0.396101\pi$
$912$	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	$-0.806192\pi$
$919$		−	966072.i		−	1.14388i	0.820297	−	0.571938i	$-0.193808\pi$
$920$		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	$-0.734248\pi$
$937$	−1.17870e6			−1.34253			−0.671264	+	0.741218i	$0.734248\pi$
$938$	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	$-0.839437\pi$
$953$	−1.59019e6			−1.75091			−0.875453	+	0.483304i	$0.839437\pi$
$954$	−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	$0.135422\pi$
$971$			778263.i			0.825445i	−0.910857	+	0.412722i	$0.864578\pi$
$972$	−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	$-0.367038\pi$
$977$	774448.			0.811341			0.405670	+	0.914019i	$0.367038\pi$
$978$	−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	$-0.686754\pi$
$991$		−	1.63570e6i		−	1.66554i	0.553619	−	0.832770i	$-0.313246\pi$
$992$	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	$-0.536683\pi$
$997$	−228598.			−0.229976			−0.114988	+	0.993367i	$0.536683\pi$
$998$	−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.b.151.13	✓	16
4.3	odd	2	inner	300.5.c.b.151.14	yes	16
5.2	odd	4		300.5.f.c.199.22		32
5.3	odd	4		300.5.f.c.199.11		32
5.4	even	2		300.5.c.c.151.4	yes	16
20.3	even	4		300.5.f.c.199.21		32
20.7	even	4		300.5.f.c.199.12		32
20.19	odd	2		300.5.c.c.151.3	yes	16

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

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Database

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