LMFDB - Embedded newform 300.5.c.c.151.11

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			151.11
Root			$-1.06635 + 3.85524i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.c.151.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.80556 - 2.85111i) q^{2} -5.19615i q^{3} +(-0.257663 - 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232i q^{7} +(-46.3347 - 44.1485i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(2.80556 - 2.85111i) q^{2} -5.19615i q^{3} +(-0.257663 - 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232i q^{7} +(-46.3347 - 44.1485i) q^{8} -27.0000 q^{9} +220.737i q^{11} +(-83.1277 + 1.33886i) q^{12} +236.856 q^{13} +(181.397 + 178.499i) q^{14} +(-255.867 + 8.24415i) q^{16} -46.7414 q^{17} +(-75.7501 + 76.9800i) q^{18} +195.899i q^{19} +330.596 q^{21} +(629.345 + 619.291i) q^{22} +741.830i q^{23} +(-229.402 + 240.762i) q^{24} +(664.512 - 675.301i) q^{26} +140.296i q^{27} +(1017.84 - 16.3934i) q^{28} +1059.06 q^{29} -1067.12i q^{31} +(-694.346 + 752.635i) q^{32} +1146.98 q^{33} +(-131.136 + 133.265i) q^{34} +(6.95691 + 431.944i) q^{36} -2287.23 q^{37} +(558.530 + 549.606i) q^{38} -1230.74i q^{39} -1141.57 q^{41} +(927.506 - 942.565i) q^{42} +1245.24i q^{43} +(3531.33 - 56.8758i) q^{44} +(2115.04 + 2081.25i) q^{46} -406.719i q^{47} +(42.8379 + 1329.53i) q^{48} -1646.91 q^{49} +242.875i q^{51} +(-61.0290 - 3789.20i) q^{52} +1442.39 q^{53} +(400.000 + 393.609i) q^{54} +(2808.87 - 2947.96i) q^{56} +1017.92 q^{57} +(2971.25 - 3019.49i) q^{58} -2472.02i q^{59} +4819.29 q^{61} +(-3042.47 - 2993.86i) q^{62} -1717.83i q^{63} +(197.817 + 4091.22i) q^{64} +(3217.93 - 3270.17i) q^{66} +5792.14i q^{67} +(12.0435 + 747.765i) q^{68} +3854.66 q^{69} +309.369i q^{71} +(1251.04 + 1192.01i) q^{72} +996.733 q^{73} +(-6416.96 + 6521.15i) q^{74} +(3133.98 - 50.4759i) q^{76} -14044.0 q^{77} +(-3508.97 - 3452.91i) q^{78} +1096.99i q^{79} +729.000 q^{81} +(-3202.76 + 3254.76i) q^{82} +3097.31i q^{83} +(-85.1824 - 5288.85i) q^{84} +(3550.32 + 3493.60i) q^{86} -5503.02i q^{87} +(9745.21 - 10227.8i) q^{88} +10965.3 q^{89} +15069.5i q^{91} +(11867.7 - 191.142i) q^{92} -5544.91 q^{93} +(-1159.60 - 1141.07i) q^{94} +(3910.81 + 3607.93i) q^{96} -12339.0 q^{97} +(-4620.50 + 4695.52i) q^{98} -5959.90i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.80556	−	2.85111i	0.701390	−	0.712778i
$2$	2.80556	−	2.85111i	0.701390	−	0.712778i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−0.257663	−	15.9979i	−0.0161040	−	0.999870i
$5$		0			0
$5$		0			0
$6$	−14.8148	−	14.5781i	−0.411522	−	0.404948i
$7$			63.6232i			1.29843i	0.760604	+	0.649216i	$0.224903\pi$
$7$			63.6232i			1.29843i	−0.760604	+	0.649216i	$0.775097\pi$
$8$	−46.3347	−	44.1485i	−0.723980	−	0.689821i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			220.737i			1.82427i	0.409888	+	0.912136i	$0.365568\pi$
$11$			220.737i			1.82427i	−0.409888	+	0.912136i	$0.634432\pi$
$12$	−83.1277	+	1.33886i	−0.577275	+	0.00929762i
$13$	236.856			1.40151			0.700756	−	0.713401i	$-0.252846\pi$
$13$	236.856			1.40151			0.700756	+	0.713401i	$0.252846\pi$
$14$	181.397	+	178.499i	0.925493	+	0.910707i
$15$		0			0
$16$	−255.867	+	8.24415i	−0.999481	+	0.0322037i
$17$	−46.7414			−0.161735			−0.0808674	−	0.996725i	$-0.525769\pi$
$17$	−46.7414			−0.161735			−0.0808674	+	0.996725i	$0.525769\pi$
$18$	−75.7501	+	76.9800i	−0.233797	+	0.237593i
$19$			195.899i			0.542656i	0.962487	+	0.271328i	$0.0874629\pi$
$19$			195.899i			0.542656i	−0.962487	+	0.271328i	$0.912537\pi$
$20$		0			0
$21$	330.596			0.749650
$22$	629.345	+	619.291i	1.30030	+	1.27953i
$23$			741.830i			1.40232i	0.713002	+	0.701162i	$0.247335\pi$
$23$			741.830i			1.40232i	−0.713002	+	0.701162i	$0.752665\pi$
$24$	−229.402	+	240.762i	−0.398268	+	0.417990i
$25$		0			0
$26$	664.512	−	675.301i	0.983007	−	0.998966i
$27$			140.296i			0.192450i
$28$	1017.84	−	16.3934i	1.29826	−	0.0209099i
$29$	1059.06			1.25928			0.629641	−	0.776886i	$-0.283202\pi$
$29$	1059.06			1.25928			0.629641	+	0.776886i	$0.283202\pi$
$30$		0			0
$31$		−	1067.12i		−	1.11042i	−0.831709	−	0.555212i	$-0.812637\pi$
$31$		−	1067.12i		−	1.11042i	0.831709	−	0.555212i	$-0.187363\pi$
$32$	−694.346	+	752.635i	−0.678072	+	0.734995i
$33$	1146.98			1.05324
$34$	−131.136	+	133.265i	−0.113439	+	0.115281i
$35$		0			0
$36$	6.95691	+	431.944i	0.00536798	+	0.333290i
$37$	−2287.23			−1.67073			−0.835366	−	0.549695i	$-0.814744\pi$
$37$	−2287.23			−1.67073			−0.835366	+	0.549695i	$0.814744\pi$
$38$	558.530	+	549.606i	0.386793	+	0.380614i
$39$		−	1230.74i		−	0.809163i
$40$		0			0
$41$	−1141.57			−0.679105			−0.339552	−	0.940587i	$-0.610276\pi$
$41$	−1141.57			−0.679105			−0.339552	+	0.940587i	$0.610276\pi$
$42$	927.506	−	942.565i	0.525797	−	0.534334i
$43$			1245.24i			0.673468i	0.941600	+	0.336734i	$0.109322\pi$
$43$			1245.24i			0.673468i	−0.941600	+	0.336734i	$0.890678\pi$
$44$	3531.33	−	56.8758i	1.82404	−	0.0293780i
$45$		0			0
$46$	2115.04	+	2081.25i	0.999546	+	0.983577i
$47$		−	406.719i		−	0.184119i	−0.995754	−	0.0920595i	$-0.970655\pi$
$47$		−	406.719i		−	0.184119i	0.995754	−	0.0920595i	$-0.0293450\pi$
$48$	42.8379	+	1329.53i	0.0185928	+	0.577051i
$49$	−1646.91			−0.685926
$50$		0			0
$51$			242.875i			0.0933777i
$52$	−61.0290	−	3789.20i	−0.0225699	−	1.40133i
$53$	1442.39			0.513488			0.256744	−	0.966479i	$-0.417350\pi$
$53$	1442.39			0.513488			0.256744	+	0.966479i	$0.417350\pi$
$54$	400.000	+	393.609i	0.137174	+	0.134983i
$55$		0			0
$56$	2808.87	−	2947.96i	0.895685	−	0.940039i
$57$	1017.92			0.313303
$58$	2971.25	−	3019.49i	0.883248	−	0.897588i
$59$		−	2472.02i		−	0.710147i	−0.934838	−	0.355074i	$-0.884456\pi$
$59$		−	2472.02i		−	0.710147i	0.934838	−	0.355074i	$-0.115544\pi$
$60$		0			0
$61$	4819.29			1.29516			0.647579	−	0.761998i	$-0.275781\pi$
$61$	4819.29			1.29516			0.647579	+	0.761998i	$0.275781\pi$
$62$	−3042.47	−	2993.86i	−0.791486	−	0.778841i
$63$		−	1717.83i		−	0.432811i
$64$	197.817	+	4091.22i	0.0482951	+	0.998833i
$65$		0			0
$66$	3217.93	−	3270.17i	0.738735	−	0.750729i
$67$			5792.14i			1.29030i	0.764057	+	0.645149i	$0.223205\pi$
$67$			5792.14i			1.29030i	−0.764057	+	0.645149i	$0.776795\pi$
$68$	12.0435	+	747.765i	0.00260457	+	0.161714i
$69$	3854.66			0.809633
$70$		0			0
$71$			309.369i			0.0613706i	0.999529	+	0.0306853i	$0.00976897\pi$
$71$			309.369i			0.0613706i	−0.999529	+	0.0306853i	$0.990231\pi$
$72$	1251.04	+	1192.01i	0.241327	+	0.229940i
$73$	996.733			0.187039			0.0935197	−	0.995617i	$-0.470188\pi$
$73$	996.733			0.187039			0.0935197	+	0.995617i	$0.470188\pi$
$74$	−6416.96	+	6521.15i	−1.17183	+	1.19086i
$75$		0			0
$76$	3133.98	−	50.4759i	0.542586	−	0.00873891i
$77$	−14044.0			−2.36869
$78$	−3508.97	−	3452.91i	−0.576754	−	0.567539i
$79$			1096.99i			0.175772i	0.996131	+	0.0878860i	$0.0280111\pi$
$79$			1096.99i			0.175772i	−0.996131	+	0.0878860i	$0.971989\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−3202.76	+	3254.76i	−0.476317	+	0.484051i
$83$			3097.31i			0.449603i	0.974405	+	0.224801i	$0.0721733\pi$
$83$			3097.31i			0.449603i	−0.974405	+	0.224801i	$0.927827\pi$
$84$	−85.1824	−	5288.85i	−0.0120723	−	0.749553i
$85$		0			0
$86$	3550.32	+	3493.60i	0.480033	+	0.472364i
$87$		−	5503.02i		−	0.727047i
$88$	9745.21	−	10227.8i	1.25842	−	1.32074i
$89$	10965.3			1.38433			0.692167	−	0.721738i	$-0.256656\pi$
$89$	10965.3			1.38433			0.692167	+	0.721738i	$0.256656\pi$
$90$		0			0
$91$			15069.5i			1.81977i
$92$	11867.7	−	191.142i	1.40214	−	0.0225830i
$93$	−5544.91			−0.641104
$94$	−1159.60	−	1141.07i	−0.131236	−	0.129139i
$95$		0			0
$96$	3910.81	+	3607.93i	0.424350	+	0.391485i
$97$	−12339.0			−1.31140			−0.655701	−	0.755020i	$-0.727627\pi$
$97$	−12339.0			−1.31140			−0.655701	+	0.755020i	$0.727627\pi$
$98$	−4620.50	+	4695.52i	−0.481102	+	0.488913i
$99$		−	5959.90i		−	0.608091i
$100$		0			0
$101$	14918.3			1.46244			0.731219	−	0.682143i	$-0.238952\pi$
$101$	14918.3			1.46244			0.731219	+	0.682143i	$0.238952\pi$
$102$	692.464	+	681.401i	0.0665575	+	0.0654942i
$103$		−	10083.1i		−	0.950433i	−0.879869	−	0.475216i	$-0.842370\pi$
$103$		−	10083.1i		−	0.950433i	0.879869	−	0.475216i	$-0.157630\pi$
$104$	−10974.6	−	10456.8i	−1.01467	−	0.966792i
$105$		0			0
$106$	4046.71	−	4112.41i	0.360155	−	0.366003i
$107$			18475.7i			1.61374i	0.590731	+	0.806869i	$0.298839\pi$
$107$			18475.7i			1.61374i	−0.590731	+	0.806869i	$0.701161\pi$
$108$	2244.45	−	36.1491i	0.192425	−	0.00309921i
$109$	−676.882			−0.0569718			−0.0284859	−	0.999594i	$-0.509069\pi$
$109$	−676.882			−0.0569718			−0.0284859	+	0.999594i	$0.509069\pi$
$110$		0			0
$111$			11884.8i			0.964597i
$112$	−524.519	−	16279.1i	−0.0418144	−	1.29776i
$113$	−5693.92			−0.445917			−0.222959	−	0.974828i	$-0.571571\pi$
$113$	−5693.92			−0.445917			−0.222959	+	0.974828i	$0.571571\pi$
$114$	2855.84	−	2902.20i	0.219747	−	0.223315i
$115$		0			0
$116$	−272.880	−	16942.7i	−0.0202794	−	1.25912i
$117$	−6395.10			−0.467171
$118$	−7048.01	−	6935.41i	−0.506177	−	0.498090i
$119$		−	2973.83i		−	0.210002i
$120$		0			0
$121$	−34083.8			−2.32797
$122$	13520.8	−	13740.3i	0.908412	−	0.923160i
$123$			5931.80i			0.392081i
$124$	−17071.7	+	274.957i	−1.11028	+	0.0178822i
$125$		0			0
$126$	−4897.71	−	4819.46i	−0.308498	−	0.303569i
$127$			21834.4i			1.35374i	0.736103	+	0.676869i	$0.236664\pi$
$127$			21834.4i			1.35374i	−0.736103	+	0.676869i	$0.763336\pi$
$128$	12219.5	+	10914.2i	0.745820	+	0.666148i
$129$	6470.47			0.388827
$130$		0			0
$131$		−	6919.28i		−	0.403198i	−0.979468	−	0.201599i	$-0.935386\pi$
$131$		−	6919.28i		−	0.403198i	0.979468	−	0.201599i	$-0.0646138\pi$
$132$	−295.535	−	18349.3i	−0.0169614	−	1.05311i
$133$	−12463.7			−0.704602
$134$	16514.0	+	16250.2i	0.919695	+	0.905002i
$135$		0			0
$136$	2165.75	+	2063.56i	0.117093	+	0.111568i
$137$	24619.2			1.31169			0.655846	−	0.754895i	$-0.272312\pi$
$137$	24619.2			1.31169			0.655846	+	0.754895i	$0.272312\pi$
$138$	10814.5	−	10990.1i	0.567868	−	0.577088i
$139$		−	18767.2i		−	0.971336i	−0.874143	−	0.485668i	$-0.838576\pi$
$139$		−	18767.2i		−	0.971336i	0.874143	−	0.485668i	$-0.161424\pi$
$140$		0			0
$141$	−2113.37			−0.106301
$142$	882.046	+	867.954i	0.0437436	+	0.0430447i
$143$			52282.8i			2.55674i
$144$	6908.41	−	222.592i	0.333160	−	0.0107346i
$145$		0			0
$146$	2796.39	−	2841.80i	0.131188	−	0.133318i
$147$			8557.59i			0.396020i
$148$	589.335	+	36590.9i	0.0269054	+	1.67051i
$149$	6573.00			0.296068			0.148034	−	0.988982i	$-0.452706\pi$
$149$	6573.00			0.296068			0.148034	+	0.988982i	$0.452706\pi$
$150$		0			0
$151$		−	7823.28i		−	0.343111i	−0.985174	−	0.171556i	$-0.945121\pi$
$151$		−	7823.28i		−	0.343111i	0.985174	−	0.171556i	$-0.0548793\pi$
$152$	8648.65	−	9076.93i	0.374335	−	0.392873i
$153$	1262.02			0.0539116
$154$	−39401.2	+	40041.0i	−1.66138	+	1.68835i
$155$		0			0
$156$	−19689.2	+	317.116i	−0.809058	+	0.0130307i
$157$	−9202.59			−0.373346			−0.186673	−	0.982422i	$-0.559770\pi$
$157$	−9202.59			−0.373346			−0.186673	+	0.982422i	$0.559770\pi$
$158$	3127.65	+	3077.68i	0.125286	+	0.123285i
$159$		−	7494.87i		−	0.296462i
$160$		0			0
$161$	−47197.6			−1.82082
$162$	2045.25	−	2078.46i	0.0779322	−	0.0791975i
$163$		−	43667.2i		−	1.64354i	−0.569820	−	0.821769i	$-0.692987\pi$
$163$		−	43667.2i		−	1.64354i	0.569820	−	0.821769i	$-0.307013\pi$
$164$	294.142	+	18262.8i	0.0109363	+	0.679017i
$165$		0			0
$166$	8830.78	+	8689.70i	0.320467	+	0.315347i
$167$			19662.7i			0.705034i	0.935805	+	0.352517i	$0.114674\pi$
$167$			19662.7i			0.705034i	−0.935805	+	0.352517i	$0.885326\pi$
$168$	−15318.1	−	14595.3i	−0.542732	−	0.517124i
$169$	27539.5			0.964236
$170$		0			0
$171$		−	5289.27i		−	0.180885i
$172$	19921.3	−	320.853i	0.673381	−	0.0108455i
$173$	−31871.9			−1.06492			−0.532459	−	0.846456i	$-0.678732\pi$
$173$	−31871.9			−1.06492			−0.532459	+	0.846456i	$0.678732\pi$
$174$	−15689.7	−	15439.1i	−0.518223	−	0.509944i
$175$		0			0
$176$	−1819.79	−	56479.3i	−0.0587484	−	1.82333i
$177$	−12845.0			−0.410004
$178$	30763.8	−	31263.3i	0.970958	−	0.986722i
$179$			52843.2i			1.64924i	0.565689	+	0.824619i	$0.308610\pi$
$179$			52843.2i			1.64924i	−0.565689	+	0.824619i	$0.691390\pi$
$180$		0			0
$181$	−63045.0			−1.92439			−0.962197	−	0.272356i	$-0.912197\pi$
$181$	−63045.0			−1.92439			−0.962197	+	0.272356i	$0.912197\pi$
$182$	42964.8	+	42278.4i	1.29709	+	1.27637i
$183$		−	25041.7i		−	0.747760i
$184$	32750.7	−	34372.5i	0.967352	−	1.01526i
$185$		0			0
$186$	−15556.6	+	15809.1i	−0.449664	+	0.456964i
$187$		−	10317.5i		−	0.295048i
$188$	−6506.66	+	104.796i	−0.184095	+	0.00296504i
$189$	−8926.08			−0.249883
$190$		0			0
$191$			20730.2i			0.568246i	0.958788	+	0.284123i	$0.0917024\pi$
$191$			20730.2i			0.568246i	−0.958788	+	0.284123i	$0.908298\pi$
$192$	21258.6	−	1027.89i	0.576677	−	0.0278832i
$193$	17567.6			0.471627			0.235813	−	0.971798i	$-0.424225\pi$
$193$	17567.6			0.471627			0.235813	+	0.971798i	$0.424225\pi$
$194$	−34617.8	+	35179.8i	−0.919805	+	0.934739i
$195$		0			0
$196$	424.348	+	26347.1i	0.0110461	+	0.685837i
$197$	−50800.9			−1.30900			−0.654499	−	0.756063i	$-0.727120\pi$
$197$	−50800.9			−1.30900			−0.654499	+	0.756063i	$0.727120\pi$
$198$	−16992.3	−	16720.8i	−0.433433	−	0.426509i
$199$		−	32141.3i		−	0.811629i	−0.913955	−	0.405814i	$-0.866988\pi$
$199$		−	32141.3i		−	0.811629i	0.913955	−	0.405814i	$-0.133012\pi$
$200$		0			0
$201$	30096.9			0.744953
$202$	41854.3	−	42533.8i	1.02574	−	1.04239i
$203$			67380.5i			1.63509i
$204$	3885.50	−	62.5800i	0.0933656	−	0.00150375i
$205$		0			0
$206$	−28748.1	−	28288.9i	−0.677447	−	0.666624i
$207$		−	20029.4i		−	0.467442i
$208$	−60603.6	+	1952.67i	−1.40079	+	0.0451339i
$209$	−43242.1			−0.989953
$210$		0			0
$211$			9541.34i			0.214311i	0.994242	+	0.107156i	$0.0341743\pi$
$211$			9541.34i			0.214311i	−0.994242	+	0.107156i	$0.965826\pi$
$212$	−371.650	−	23075.2i	−0.00826919	−	0.513421i
$213$	1607.53			0.0354323
$214$	52676.2	+	51834.6i	1.15024	+	1.13186i
$215$		0			0
$216$	6193.87	−	6500.58i	0.132756	−	0.139330i
$217$	67893.4			1.44181
$218$	−1899.03	+	1929.86i	−0.0399594	+	0.0406082i
$219$		−	5179.18i		−	0.107987i
$220$		0			0
$221$	−11071.0			−0.226673
$222$	33884.9	+	33343.5i	0.687543	+	0.676559i
$223$			33469.4i			0.673037i	0.941677	+	0.336518i	$0.109249\pi$
$223$			33469.4i			0.673037i	−0.941677	+	0.336518i	$0.890751\pi$
$224$	−47885.0	−	44176.5i	−0.954342	−	0.880431i
$225$		0			0
$226$	−15974.6	+	16234.0i	−0.312762	+	0.317840i
$227$			1149.27i			0.0223033i	0.999938	+	0.0111517i	$0.00354976\pi$
$227$			1149.27i			0.0223033i	−0.999938	+	0.0111517i	$0.996450\pi$
$228$	−262.281	−	16284.6i	−0.00504541	−	0.313262i
$229$	−49392.2			−0.941863			−0.470931	−	0.882170i	$-0.656082\pi$
$229$	−49392.2			−0.941863			−0.470931	+	0.882170i	$0.656082\pi$
$230$		0			0
$231$			72974.7i			1.36757i
$232$	−49071.1	−	46755.8i	−0.911696	−	0.868679i
$233$	42084.0			0.775184			0.387592	−	0.921831i	$-0.373307\pi$
$233$	42084.0			0.775184			0.387592	+	0.921831i	$0.373307\pi$
$234$	−17941.8	+	18233.1i	−0.327669	+	0.332989i
$235$		0			0
$236$	−39547.2	+	636.949i	−0.710055	+	0.0114362i
$237$	5700.14			0.101482
$238$	−8478.73	−	8343.27i	−0.149685	−	0.147293i
$239$		−	34540.4i		−	0.604689i	−0.953199	−	0.302345i	$-0.902231\pi$
$239$		−	34540.4i		−	0.604689i	0.953199	−	0.302345i	$-0.0977693\pi$
$240$		0			0
$241$	68666.9			1.18226			0.591131	−	0.806576i	$-0.298682\pi$
$241$	68666.9			1.18226			0.591131	+	0.806576i	$0.298682\pi$
$242$	−95624.1	+	97176.6i	−1.63281	+	1.65932i
$243$		−	3788.00i		−	0.0641500i
$244$	−1241.75	−	77098.6i	−0.0208572	−	1.29499i
$245$		0			0
$246$	16912.2	+	16642.0i	0.279467	+	0.275002i
$247$			46399.7i			0.760539i
$248$	−47111.7	+	49444.6i	−0.765994	+	0.803925i
$249$	16094.1			0.259578
$250$		0			0
$251$		−	62003.3i		−	0.984163i	−0.870549	−	0.492082i	$-0.836236\pi$
$251$		−	62003.3i		−	0.984163i	0.870549	−	0.492082i	$-0.163764\pi$
$252$	−27481.6	+	442.621i	−0.432755	+	0.00696996i
$253$	−163749.			−2.55822
$254$	62252.4	+	61257.9i	0.964914	+	0.949499i
$255$		0			0
$256$	65400.1	−	4218.82i	0.997926	−	0.0643740i
$257$	−65977.4			−0.998916			−0.499458	−	0.866338i	$-0.666468\pi$
$257$	−65977.4			−0.998916			−0.499458	+	0.866338i	$0.666468\pi$
$258$	18153.3	−	18448.0i	0.272719	−	0.277147i
$259$		−	145521.i		−	2.16933i
$260$		0			0
$261$	−28594.5			−0.419761
$262$	−19727.6	−	19412.5i	−0.287391	−	0.282799i
$263$		−	45889.4i		−	0.663439i	−0.943378	−	0.331719i	$-0.892371\pi$
$263$		−	45889.4i		−	0.663439i	0.943378	−	0.331719i	$-0.107629\pi$
$264$	−53145.1	−	50637.6i	−0.762528	−	0.726549i
$265$		0			0
$266$	−34967.7	+	35535.4i	−0.494201	+	0.502225i
$267$		−	56977.4i		−	0.799245i
$268$	92662.3	−	1492.42i	1.29013	−	0.0207789i
$269$	66600.2			0.920388			0.460194	−	0.887818i	$-0.347780\pi$
$269$	66600.2			0.920388			0.460194	+	0.887818i	$0.347780\pi$
$270$		0			0
$271$		−	107846.i		−	1.46848i	−0.678892	−	0.734239i	$-0.737539\pi$
$271$		−	107846.i		−	1.46848i	0.678892	−	0.734239i	$-0.262461\pi$
$272$	11959.6	−	385.343i	0.161651	−	0.00520847i
$273$	78303.4			1.05064
$274$	69070.5	−	70191.9i	0.920008	−	0.934945i
$275$		0			0
$276$	−993.204	−	61666.6i	−0.0130383	−	0.809528i
$277$	76120.9			0.992074			0.496037	−	0.868301i	$-0.334788\pi$
$277$	76120.9			0.992074			0.496037	+	0.868301i	$0.334788\pi$
$278$	−53507.3	−	52652.5i	−0.692347	−	0.681286i
$279$			28812.2i			0.370141i
$280$		0			0
$281$	127936.			1.62024			0.810120	−	0.586264i	$-0.199402\pi$
$281$	127936.			1.62024			0.810120	+	0.586264i	$0.199402\pi$
$282$	−5929.19	+	6025.46i	−0.0745586	+	0.0757691i
$283$		−	117792.i		−	1.47076i	−0.677655	−	0.735380i	$-0.737004\pi$
$283$		−	117792.i		−	1.47076i	0.677655	−	0.735380i	$-0.262996\pi$
$284$	4949.27	−	79.7131i	0.0613627	−	0.000988310i
$285$		0			0
$286$	149064.	+	146682.i	1.82239	+	1.79327i
$287$		−	72630.6i		−	0.881771i
$288$	18747.3	−	20321.2i	0.226024	−	0.244998i
$289$	−81336.2			−0.973842
$290$		0			0
$291$			64115.3i			0.757139i
$292$	−256.821	−	15945.7i	−0.00301207	−	0.187015i
$293$	120518.			1.40384			0.701918	−	0.712258i	$-0.252327\pi$
$293$	120518.			1.40384			0.701918	+	0.712258i	$0.252327\pi$
$294$	24398.6	+	24008.8i	0.282274	+	0.277764i
$295$		0			0
$296$	105978.	+	100978.i	1.20958	+	1.15250i
$297$	−30968.5			−0.351081
$298$	18441.0	−	18740.4i	0.207659	−	0.211031i
$299$			175706.i			1.96537i
$300$		0			0
$301$	−79226.3			−0.874453
$302$	−22305.0	−	21948.7i	−0.244562	−	0.240655i
$303$		−	77517.9i		−	0.844339i
$304$	−1615.02	−	50124.1i	−0.0174756	−	0.542375i
$305$		0			0
$306$	3540.67	−	3598.15i	0.0378131	−	0.0384270i
$307$		−	90003.1i		−	0.954950i	−0.878645	−	0.477475i	$-0.841552\pi$
$307$		−	90003.1i		−	0.954950i	0.878645	−	0.477475i	$-0.158448\pi$
$308$	3618.62	+	224675.i	0.0381453	+	2.36839i
$309$	−52393.5			−0.548732
$310$		0			0
$311$			35944.1i			0.371627i	0.982585	+	0.185813i	$0.0594920\pi$
$311$			35944.1i			0.371627i	−0.982585	+	0.185813i	$0.940508\pi$
$312$	−54335.2	+	57025.9i	−0.558178	+	0.585818i
$313$	−10420.7			−0.106368			−0.0531838	−	0.998585i	$-0.516937\pi$
$313$	−10420.7			−0.106368			−0.0531838	+	0.998585i	$0.516937\pi$
$314$	−25818.4	+	26237.6i	−0.261861	+	0.266112i
$315$		0			0
$316$	17549.6	−	282.655i	0.175749	−	0.00283062i
$317$	44276.9			0.440614			0.220307	−	0.975431i	$-0.429294\pi$
$317$	44276.9			0.440614			0.220307	+	0.975431i	$0.429294\pi$
$318$	−21368.7	−	21027.3i	−0.211312	−	0.207936i
$319$			233773.i			2.29727i
$320$		0			0
$321$	96002.4			0.931692
$322$	−132416.	+	134565.i	−1.27711	+	1.29784i
$323$		−	9156.59i		−	0.0877664i
$324$	−187.836	−	11662.5i	−0.00178933	−	0.111097i
$325$		0			0
$326$	−124500.	−	122511.i	−1.17148	−	1.15276i
$327$			3517.18i			0.0328927i
$328$	52894.6	+	50398.8i	0.491658	+	0.468460i
$329$	25876.7			0.239066
$330$		0			0
$331$		−	219017.i		−	1.99904i	−0.0309493	−	0.999521i	$-0.509853\pi$
$331$		−	219017.i		−	1.99904i	0.0309493	−	0.999521i	$-0.490147\pi$
$332$	49550.6	−	798.064i	0.449544	−	0.00724038i
$333$	61755.2			0.556910
$334$	56060.5	+	55164.9i	0.502533	+	0.494504i
$335$		0			0
$336$	−84588.6	+	2725.48i	−0.749261	+	0.0241415i
$337$	51173.5			0.450594			0.225297	−	0.974290i	$-0.427665\pi$
$337$	51173.5			0.450594			0.225297	+	0.974290i	$0.427665\pi$
$338$	77263.9	−	78518.3i	0.676306	−	0.687286i
$339$			29586.5i			0.257450i
$340$		0			0
$341$	235552.			2.02572
$342$	−15080.3	−	14839.4i	−0.128931	−	0.126871i
$343$			47977.7i			0.407804i
$344$	54975.6	−	57698.0i	0.464572	−	0.487578i
$345$		0			0
$346$	−89418.7	+	90870.4i	−0.746923	+	0.759050i
$347$			78897.6i			0.655247i	0.944808	+	0.327623i	$0.106248\pi$
$347$			78897.6i			0.655247i	−0.944808	+	0.327623i	$0.893752\pi$
$348$	−88036.9	+	1417.93i	−0.726953	+	0.0117083i
$349$	187086.			1.53599			0.767997	−	0.640454i	$-0.221254\pi$
$349$	187086.			1.53599			0.767997	+	0.640454i	$0.221254\pi$
$350$		0			0
$351$			33229.9i			0.269721i
$352$	−166134.	−	153268.i	−1.34083	−	1.23699i
$353$	26576.3			0.213278			0.106639	−	0.994298i	$-0.465991\pi$
$353$	26576.3			0.213278			0.106639	+	0.994298i	$0.465991\pi$
$354$	−36037.4	+	36622.5i	−0.287573	+	0.292242i
$355$		0			0
$356$	−2825.36	−	175422.i	−0.0222932	−	1.38415i
$357$	−15452.5			−0.121245
$358$	150662.	+	148255.i	1.17554	+	1.15676i
$359$			13211.6i			0.102510i	0.998686	+	0.0512552i	$0.0163222\pi$
$359$			13211.6i			0.102510i	−0.998686	+	0.0512552i	$0.983678\pi$
$360$		0			0
$361$	91944.6			0.705524
$362$	−176877.	+	179748.i	−1.34975	+	1.37166i
$363$			177105.i			1.34405i
$364$	241081.	−	3882.86i	1.81953	−	0.0293055i
$365$		0			0
$366$	−71396.8	−	70256.1i	−0.532987	−	0.524472i
$367$		−	46921.2i		−	0.348367i	−0.984713	−	0.174184i	$-0.944271\pi$
$367$		−	46921.2i		−	0.348367i	0.984713	−	0.174184i	$-0.0557286\pi$
$368$	−6115.76	−	189810.i	−0.0451601	−	1.40160i
$369$	30822.5			0.226368
$370$		0			0
$371$			91769.3i			0.666729i
$372$	1428.72	+	88707.0i	0.0103243	+	0.641021i
$373$	237489.			1.70697			0.853487	−	0.521115i	$-0.174484\pi$
$373$	237489.			1.70697			0.853487	+	0.521115i	$0.174484\pi$
$374$	−29416.5	−	28946.5i	−0.210304	−	0.206944i
$375$		0			0
$376$	−17956.0	+	18845.2i	−0.127009	+	0.133299i
$377$	250843.			1.76490
$378$	−25042.7	+	25449.3i	−0.175266	+	0.178111i
$379$		−	108145.i		−	0.752885i	−0.926440	−	0.376442i	$-0.877147\pi$
$379$		−	108145.i		−	0.752885i	0.926440	−	0.376442i	$-0.122853\pi$
$380$		0			0
$381$	113455.			0.781581
$382$	59104.0	+	58159.8i	0.405033	+	0.398562i
$383$			143109.i			0.975594i	0.872957	+	0.487797i	$0.162199\pi$
$383$			143109.i			0.975594i	−0.872957	+	0.487797i	$0.837801\pi$
$384$	56711.7	−	63494.4i	0.384601	−	0.430599i
$385$		0			0
$386$	49287.0	−	50087.3i	0.330794	−	0.336165i
$387$		−	33621.6i		−	0.224489i
$388$	3179.30	+	197398.i	0.0211188	+	1.31123i
$389$	−132061.			−0.872720			−0.436360	−	0.899772i	$-0.643733\pi$
$389$	−132061.			−0.872720			−0.436360	+	0.899772i	$0.643733\pi$
$390$		0			0
$391$		−	34674.1i		−	0.226805i
$392$	76309.1	+	72708.6i	0.496597	+	0.473166i
$393$	−35953.6			−0.232787
$394$	−142525.	+	144839.i	−0.918118	+	0.933024i
$395$		0			0
$396$	−95346.0	+	1535.65i	−0.608012	+	0.00979266i
$397$	46139.3			0.292745			0.146373	−	0.989230i	$-0.453240\pi$
$397$	46139.3			0.292745			0.146373	+	0.989230i	$0.453240\pi$
$398$	−91638.5	−	90174.4i	−0.578511	−	0.569269i
$399$			64763.3i			0.406802i
$400$		0			0
$401$	3244.97			0.0201800			0.0100900	−	0.999949i	$-0.496788\pi$
$401$	3244.97			0.0201800			0.0100900	+	0.999949i	$0.496788\pi$
$402$	84438.6	−	85809.5i	0.522503	−	0.530986i
$403$		−	252753.i		−	1.55627i
$404$	−3843.90	−	238662.i	−0.0235510	−	1.46225i
$405$		0			0
$406$	192109.	+	189040.i	1.16546	+	1.14684i
$407$		−	504876.i		−	3.04787i
$408$	10722.6	−	11253.6i	0.0644138	−	0.0676036i
$409$	−190227.			−1.13717			−0.568585	−	0.822625i	$-0.692509\pi$
$409$	−190227.			−1.13717			−0.568585	+	0.822625i	$0.692509\pi$
$410$		0			0
$411$		−	127925.i		−	0.757306i
$412$	−161309.	+	2598.05i	−0.950309	+	0.0153057i
$413$	157278.			0.922078
$414$	−57106.0	−	56193.7i	−0.333182	−	0.327859i
$415$		0			0
$416$	−164460.	+	178266.i	−0.950326	+	1.03010i
$417$	−97517.2			−0.560801
$418$	−121318.	+	123288.i	−0.694343	+	0.705616i
$419$			38663.2i			0.220226i	0.993919	+	0.110113i	$0.0351213\pi$
$419$			38663.2i			0.220226i	−0.993919	+	0.110113i	$0.964879\pi$
$420$		0			0
$421$	−215220.			−1.21428			−0.607140	−	0.794595i	$-0.707683\pi$
$421$	−215220.			−1.21428			−0.607140	+	0.794595i	$0.707683\pi$
$422$	27203.4	+	26768.8i	0.152756	+	0.150316i
$423$			10981.4i			0.0613730i
$424$	−66832.7	−	63679.3i	−0.371755	−	0.354215i
$425$		0			0
$426$	4510.02	−	4583.25i	0.0248519	−	0.0252554i
$427$			306618.i			1.68168i
$428$	295572.	−	4760.50i	1.61353	−	0.0259875i
$429$	271669.			1.47613
$430$		0			0
$431$			12832.4i			0.0690804i	0.999403	+	0.0345402i	$0.0109967\pi$
$431$			12832.4i			0.0690804i	−0.999403	+	0.0345402i	$0.989003\pi$
$432$	−1156.62	−	35897.2i	−0.00619761	−	0.192350i
$433$	−245264.			−1.30815			−0.654076	−	0.756429i	$-0.726942\pi$
$433$	−245264.			−1.30815			−0.654076	+	0.756429i	$0.726942\pi$
$434$	190479.	−	193572.i	1.01127	−	1.02769i
$435$		0			0
$436$	174.408	+	10828.7i	0.000917471	+	0.0569644i
$437$	−145324.			−0.760980
$438$	−14766.4	−	14530.5i	−0.0769709	−	0.0757412i
$439$		−	8320.58i		−	0.0431742i	−0.999767	−	0.0215871i	$-0.993128\pi$
$439$		−	8320.58i		−	0.0431742i	0.999767	−	0.0215871i	$-0.00687192\pi$
$440$		0			0
$441$	44466.5			0.228642
$442$	−31060.2	+	31564.5i	−0.158986	+	0.161568i
$443$		−	141239.i		−	0.719695i	−0.933011	−	0.359847i	$-0.882829\pi$
$443$		−	141239.i		−	0.719695i	0.933011	−	0.359847i	$-0.117171\pi$
$444$	190132.	−	3062.28i	0.964472	−	0.0155338i
$445$		0			0
$446$	95425.1	+	93900.6i	0.479726	+	0.472061i
$447$		−	34154.3i		−	0.170935i
$448$	−260296.	+	12585.7i	−1.29692	+	0.0627080i
$449$	−197626.			−0.980282			−0.490141	−	0.871643i	$-0.663055\pi$
$449$	−197626.			−0.980282			−0.490141	+	0.871643i	$0.663055\pi$
$450$		0			0
$451$		−	251988.i		−	1.23887i
$452$	1467.11	+	91090.9i	0.00718103	+	0.445859i
$453$	−40651.0			−0.198095
$454$	3276.69	+	3224.34i	0.0158973	+	0.0156433i
$455$		0			0
$456$	−47165.1	−	44939.7i	−0.226825	−	0.216123i
$457$	331333.			1.58647			0.793236	−	0.608915i	$-0.208395\pi$
$457$	331333.			1.58647			0.793236	+	0.608915i	$0.208395\pi$
$458$	−138573.	+	140823.i	−0.660613	+	0.671339i
$459$		−	6557.63i		−	0.0311259i
$460$		0			0
$461$	−196090.			−0.922687			−0.461343	−	0.887222i	$-0.652632\pi$
$461$	−196090.			−0.922687			−0.461343	+	0.887222i	$0.652632\pi$
$462$	208059.	+	204735.i	0.974770	+	0.959197i
$463$		−	168744.i		−	0.787164i	−0.919289	−	0.393582i	$-0.871236\pi$
$463$		−	168744.i		−	0.787164i	0.919289	−	0.393582i	$-0.128764\pi$
$464$	−270978.	+	8731.03i	−1.25863	+	0.0405536i
$465$		0			0
$466$	118069.	−	119986.i	0.543706	−	0.552534i
$467$			58203.8i			0.266881i	0.991057	+	0.133440i	$0.0426025\pi$
$467$			58203.8i			0.266881i	−0.991057	+	0.133440i	$0.957398\pi$
$468$	1647.78	+	102308.i	0.00752329	+	0.467110i
$469$	−368515.			−1.67536
$470$		0			0
$471$			47818.1i			0.215551i
$472$	−109136.	+	114541.i	−0.489874	+	0.514133i
$473$	−274871.			−1.22859
$474$	15992.1	−	16251.7i	0.0711785	−	0.0723341i
$475$		0			0
$476$	−47575.2	+	766.248i	−0.209975	+	0.00338186i
$477$	−38944.5			−0.171163
$478$	−98478.6	−	96905.3i	−0.431009	−	0.424123i
$479$		−	221700.i		−	0.966260i	−0.875549	−	0.483130i	$-0.839500\pi$
$479$		−	221700.i		−	0.966260i	0.875549	−	0.483130i	$-0.160500\pi$
$480$		0			0
$481$	−541743.			−2.34155
$482$	192649.	−	195777.i	0.829227	−	0.842690i
$483$			245246.i			1.05125i
$484$	8782.14	+	545270.i	0.0374895	+	2.32767i
$485$		0			0
$486$	−10800.0	−	10627.4i	−0.0457247	−	0.0449942i
$487$			145571.i			0.613788i	0.951744	+	0.306894i	$0.0992897\pi$
$487$			145571.i			0.613788i	−0.951744	+	0.306894i	$0.900710\pi$
$488$	−223300.	−	212764.i	−0.937670	−	0.893427i
$489$	−226901.			−0.948897
$490$		0			0
$491$			244597.i			1.01458i	0.861774	+	0.507292i	$0.169354\pi$
$491$			244597.i			1.01458i	−0.861774	+	0.507292i	$0.830646\pi$
$492$	94896.4	−	1528.41i	0.392030	−	0.00631406i
$493$	−49501.8			−0.203670
$494$	132291.	+	130177.i	0.542095	+	0.533435i
$495$		0			0
$496$	8797.48	+	273040.i	0.0357598	+	1.10985i
$497$	−19683.1			−0.0796856
$498$	45153.0	−	45886.1i	0.182066	−	0.185022i
$499$		−	113422.i		−	0.455507i	−0.973719	−	0.227754i	$-0.926862\pi$
$499$		−	113422.i		−	0.455507i	0.973719	−	0.227754i	$-0.0731381\pi$
$500$		0			0
$501$	102170.			0.407052
$502$	−176778.	−	173954.i	−0.701490	−	0.690282i
$503$		−	135516.i		−	0.535616i	−0.963472	−	0.267808i	$-0.913701\pi$
$503$		−	135516.i		−	0.535616i	0.963472	−	0.267808i	$-0.0862993\pi$
$504$	−75839.5	+	79595.0i	−0.298562	+	0.313346i
$505$		0			0
$506$	−459408.	+	466867.i	−1.79431	+	1.82344i
$507$		−	143100.i		−	0.556702i
$508$	349306.	−	5625.93i	1.35356	−	0.0218005i
$509$	393520.			1.51891			0.759454	−	0.650561i	$-0.225466\pi$
$509$	393520.			1.51891			0.759454	+	0.650561i	$0.225466\pi$
$510$		0			0
$511$			63415.3i			0.242858i
$512$	171456.	−	198299.i	0.654051	−	0.756451i
$513$	−27483.9			−0.104434
$514$	−185104.	+	188109.i	−0.700630	+	0.712005i
$515$		0			0
$516$	−1667.20	−	103514.i	−0.00626165	−	0.388777i
$517$	89777.9			0.335883
$518$	−414896.	−	408268.i	−1.54625	−	1.52155i
$519$			165611.i			0.614831i
$520$		0			0
$521$	309126.			1.13883			0.569416	−	0.822049i	$-0.307169\pi$
$521$	309126.			1.13883			0.569416	+	0.822049i	$0.307169\pi$
$522$	−80223.7	+	81526.2i	−0.294416	+	0.299196i
$523$			49369.3i			0.180490i	0.995920	+	0.0902452i	$0.0287651\pi$
$523$			49369.3i			0.180490i	−0.995920	+	0.0902452i	$0.971235\pi$
$524$	−110694.	+	1782.84i	−0.403146	+	0.00649308i
$525$		0			0
$526$	−130836.	−	128745.i	−0.472884	−	0.465329i
$527$			49878.6i			0.179594i
$528$	−293475.	+	9455.90i	−1.05270	+	0.0339184i
$529$	−270470.			−0.966514
$530$		0			0
$531$			66744.6i			0.236716i
$532$	3211.44	+	199394.i	0.0113469	+	0.704511i
$533$	−270388.			−0.951773
$534$	−162449.	−	159854.i	−0.569684	−	0.560583i
$535$		0			0
$536$	255715.	−	268377.i	0.890073	−	0.934150i
$537$	274581.			0.952188
$538$	186851.	−	189885.i	0.645551	−	0.656032i
$539$		−	363533.i		−	1.25132i
$540$		0			0
$541$	−102454.			−0.350053			−0.175027	−	0.984564i	$-0.556001\pi$
$541$	−102454.			−0.350053			−0.175027	+	0.984564i	$0.556001\pi$
$542$	−307482.	−	302570.i	−1.04670	−	1.02998i
$543$			327592.i			1.11105i
$544$	32454.7	−	35179.2i	0.109668	−	0.118874i
$545$		0			0
$546$	219685.	−	223252.i	0.736911	−	0.748875i
$547$		−	66168.6i		−	0.221145i	−0.993868	−	0.110573i	$-0.964732\pi$
$547$		−	66168.6i		−	0.221145i	0.993868	−	0.110573i	$-0.0352685\pi$
$548$	−6343.45	−	393855.i	−0.0211234	−	1.31152i
$549$	−130121.			−0.431720
$550$		0			0
$551$			207468.i			0.683358i
$552$	−178605.	−	170178.i	−0.586158	−	0.558501i
$553$	−69794.2			−0.228228
$554$	213562.	−	217029.i	0.695831	−	0.707128i
$555$		0			0
$556$	−300236.	+	4835.61i	−0.971210	+	0.0156424i
$557$	−344220.			−1.10950			−0.554749	−	0.832018i	$-0.687186\pi$
$557$	−344220.			−1.10950			−0.554749	+	0.832018i	$0.687186\pi$
$558$	82146.7	+	80834.3i	0.263829	+	0.259614i
$559$			294943.i			0.943874i
$560$		0			0
$561$	−53611.6			−0.170346
$562$	358931.	−	364759.i	1.13642	−	1.15487i
$563$		−	581940.i		−	1.83595i	−0.396637	−	0.917976i	$-0.629823\pi$
$563$		−	581940.i		−	1.83595i	0.396637	−	0.917976i	$-0.370177\pi$
$564$	544.538	+	33809.6i	0.00171187	+	0.106287i
$565$		0			0
$566$	−335837.	−	330472.i	−1.04833	−	1.03158i
$567$			46381.3i			0.144270i
$568$	13658.2	−	14334.5i	0.0423347	−	0.0444311i
$569$	269874.			0.833559			0.416779	−	0.909008i	$-0.363159\pi$
$569$	269874.			0.833559			0.416779	+	0.909008i	$0.363159\pi$
$570$		0			0
$571$		−	248959.i		−	0.763581i	−0.924249	−	0.381790i	$-0.875308\pi$
$571$		−	248959.i		−	0.763581i	0.924249	−	0.381790i	$-0.124692\pi$
$572$	836416.	−	13471.3i	2.55641	−	0.0411736i
$573$	107717.			0.328077
$574$	−207078.	−	203770.i	−0.628507	−	0.618466i
$575$		0			0
$576$	−5341.06	−	110463.i	−0.0160984	−	0.332944i
$577$	−389168.			−1.16892			−0.584461	−	0.811422i	$-0.698694\pi$
$577$	−389168.			−1.16892			−0.584461	+	0.811422i	$0.698694\pi$
$578$	−228194.	+	231899.i	−0.683043	+	0.694133i
$579$		−	91284.1i		−	0.272294i
$580$		0			0
$581$	−197061.			−0.583779
$582$	182800.	+	179879.i	0.539672	+	0.531050i
$583$			318388.i			0.936742i
$584$	−46183.4	−	44004.3i	−0.135413	−	0.129024i
$585$		0			0
$586$	338120.	−	343610.i	0.984636	−	1.00062i
$587$		−	67273.5i		−	0.195240i	−0.995224	−	0.0976198i	$-0.968877\pi$
$587$		−	67273.5i		−	0.195240i	0.995224	−	0.0976198i	$-0.0311229\pi$
$588$	136904.	−	2204.98i	0.395968	−	0.00637748i
$589$	209047.			0.602579
$590$		0			0
$591$			263969.i			0.755750i
$592$	585227.	−	18856.3i	1.66986	−	0.0538038i
$593$	483157.			1.37398			0.686988	−	0.726669i	$-0.258933\pi$
$593$	483157.			1.37398			0.686988	+	0.726669i	$0.258933\pi$
$594$	−86884.1	+	88294.7i	−0.246245	+	0.250243i
$595$		0			0
$596$	−1693.62	−	105154.i	−0.00476786	−	0.296029i
$597$	−167011.			−0.468594
$598$	500959.	+	492955.i	1.40088	+	1.37849i
$599$		−	361016.i		−	1.00617i	−0.864236	−	0.503086i	$-0.832198\pi$
$599$		−	361016.i		−	1.00617i	0.864236	−	0.503086i	$-0.167802\pi$
$600$		0			0
$601$	−329300.			−0.911681			−0.455841	−	0.890061i	$-0.650661\pi$
$601$	−329300.			−0.911681			−0.455841	+	0.890061i	$0.650661\pi$
$602$	−222274.	+	225883.i	−0.613333	+	0.623290i
$603$		−	156388.i		−	0.430099i
$604$	−125156.	+	2015.77i	−0.343067	+	0.00552545i
$605$		0			0
$606$	−221012.	−	217481.i	−0.601826	−	0.592211i
$607$			347112.i			0.942090i	0.882109	+	0.471045i	$0.156123\pi$
$607$			347112.i			0.942090i	−0.882109	+	0.471045i	$0.843877\pi$
$608$	−147440.	−	136022.i	−0.398850	−	0.367960i
$609$	350120.			0.944021
$610$		0			0
$611$		−	96333.6i		−	0.258045i
$612$	−325.175	−	20189.7i	−0.000868190	−	0.0539046i
$613$	−315831.			−0.840492			−0.420246	−	0.907410i	$-0.638056\pi$
$613$	−315831.			−0.840492			−0.420246	+	0.907410i	$0.638056\pi$
$614$	−256609.	−	252509.i	−0.680667	−	0.669792i
$615$		0			0
$616$	650724.	+	620021.i	1.71489	+	1.63397i
$617$	−302237.			−0.793920			−0.396960	−	0.917836i	$-0.629935\pi$
$617$	−302237.			−0.793920			−0.396960	+	0.917836i	$0.629935\pi$
$618$	−146993.	+	149380.i	−0.384876	+	0.391124i
$619$			367141.i			0.958190i	0.877763	+	0.479095i	$0.159035\pi$
$619$			367141.i			0.958190i	−0.877763	+	0.479095i	$0.840965\pi$
$620$		0			0
$621$	−104076.			−0.269878
$622$	102481.	+	100843.i	0.264887	+	0.260655i
$623$			697647.i			1.79746i
$624$	10146.4	+	314905.i	0.0260581	+	0.808744i
$625$		0			0
$626$	−29236.0	+	29710.7i	−0.0746052	+	0.0758165i
$627$			224693.i			0.571549i
$628$	2371.17	+	147222.i	0.00601234	+	0.373297i
$629$	106908.			0.270215
$630$		0			0
$631$			210709.i			0.529206i	0.964357	+	0.264603i	$0.0852409\pi$
$631$			210709.i			0.529206i	−0.964357	+	0.264603i	$0.914759\pi$
$632$	48430.6	−	50828.9i	0.121251	−	0.127255i
$633$	49578.3			0.123733
$634$	124221.	−	126238.i	0.309043	−	0.314060i
$635$		0			0
$636$	−119902.	+	1931.15i	−0.296424	+	0.00477422i
$637$	−390079.			−0.961334
$638$	666512.	+	655864.i	1.63745	+	1.61129i
$639$		−	8352.97i		−	0.0204569i
$640$		0			0
$641$	−415962.			−1.01237			−0.506183	−	0.862426i	$-0.668944\pi$
$641$	−415962.			−1.01237			−0.506183	+	0.862426i	$0.668944\pi$
$642$	269341.	−	273714.i	0.653479	−	0.664089i
$643$			732294.i			1.77118i	0.464465	+	0.885592i	$0.346247\pi$
$643$			732294.i			1.77118i	−0.464465	+	0.885592i	$0.653753\pi$
$644$	12161.1	+	755063.i	0.0293225	+	1.82059i
$645$		0			0
$646$	−26106.4	−	25689.4i	−0.0625580	−	0.0615585i
$647$			96321.2i			0.230098i	0.993360	+	0.115049i	$0.0367025\pi$
$647$			96321.2i			0.230098i	−0.993360	+	0.115049i	$0.963297\pi$
$648$	−33778.0	−	32184.3i	−0.0804423	−	0.0766467i
$649$	545667.			1.29550
$650$		0			0
$651$		−	352785.i		−	0.832430i
$652$	−698584.	+	11251.4i	−1.64333	+	0.0264675i
$653$	−274691.			−0.644196			−0.322098	−	0.946706i	$-0.604388\pi$
$653$	−274691.			−0.644196			−0.322098	+	0.946706i	$0.604388\pi$
$654$	10027.9	+	9867.66i	0.0234452	+	0.0230706i
$655$		0			0
$656$	292092.	−	9411.32i	0.678752	−	0.0218697i
$657$	−26911.8			−0.0623465
$658$	72598.8	−	73777.5i	0.167679	−	0.170401i
$659$			360421.i			0.829927i	0.909838	+	0.414963i	$0.136206\pi$
$659$			360421.i			0.829927i	−0.909838	+	0.414963i	$0.863794\pi$
$660$		0			0
$661$	461663.			1.05663			0.528314	−	0.849049i	$-0.322824\pi$
$661$	461663.			1.05663			0.528314	+	0.849049i	$0.322824\pi$
$662$	−624442.	−	614465.i	−1.42487	−	1.40211i
$663$			57526.4i			0.130870i
$664$	136742.	−	143513.i	0.310145	−	0.325504i
$665$		0			0
$666$	173258.	−	176071.i	0.390611	−	0.396953i
$667$			785640.i			1.76592i
$668$	314562.	−	5066.35i	0.704943	−	0.0113538i
$669$	173912.			0.388578
$670$		0			0
$671$			1.06379e6i			2.36272i
$672$	−229548.	+	248818.i	−0.508317	+	0.550989i
$673$	−295518.			−0.652459			−0.326230	−	0.945291i	$-0.605778\pi$
$673$	−295518.			−0.652459			−0.326230	+	0.945291i	$0.605778\pi$
$674$	143570.	−	145901.i	0.316042	−	0.321173i
$675$		0			0
$676$	−7095.93	−	440576.i	−0.0155280	−	0.964111i
$677$	865789.			1.88901			0.944506	−	0.328494i	$-0.106541\pi$
$677$	865789.			1.88901			0.944506	+	0.328494i	$0.106541\pi$
$678$	84354.3	+	83006.6i	0.183505	+	0.180573i
$679$		−	785046.i		−	1.70277i
$680$		0			0
$681$	5971.77			0.0128768
$682$	660856.	−	671586.i	1.42082	−	1.44389i
$683$		−	631289.i		−	1.35328i	−0.736316	−	0.676638i	$-0.763436\pi$
$683$		−	631289.i		−	1.35328i	0.736316	−	0.676638i	$-0.236564\pi$
$684$	−84617.4	+	1362.85i	−0.180862	+	0.00291297i
$685$		0			0
$686$	136790.	+	134604.i	0.290673	+	0.286029i
$687$			256650.i			0.543785i
$688$	−10266.0	−	318617.i	−0.0216882	−	0.673119i
$689$	341638.			0.719660
$690$		0			0
$691$		−	692970.i		−	1.45130i	−0.688062	−	0.725652i	$-0.741538\pi$
$691$		−	692970.i		−	1.45130i	0.688062	−	0.725652i	$-0.258462\pi$
$692$	8212.23	+	509885.i	0.0171494	+	1.06478i
$693$	379188.			0.789564
$694$	224946.	+	221352.i	0.467045	+	0.459584i
$695$		0			0
$696$	−242950.	+	254981.i	−0.501532	+	0.526368i
$697$	53358.8			0.109835
$698$	524880.	−	533402.i	1.07733	−	1.09482i
$699$		−	218675.i		−	0.447553i
$700$		0			0
$701$	−106868.			−0.217477			−0.108739	−	0.994070i	$-0.534681\pi$
$701$	−106868.			−0.217477			−0.108739	+	0.994070i	$0.534681\pi$
$702$	94742.2	+	93228.5i	0.192251	+	0.189180i
$703$		−	448066.i		−	0.906633i
$704$	−903083.	+	43665.5i	−1.82214	+	0.0881035i
$705$		0			0
$706$	74561.4	−	75772.0i	0.149591	−	0.152020i
$707$			949151.i			1.89888i
$708$	3309.69	+	205493.i	0.00660268	+	0.409951i
$709$	71602.5			0.142441			0.0712207	−	0.997461i	$-0.477311\pi$
$709$	71602.5			0.142441			0.0712207	+	0.997461i	$0.477311\pi$
$710$		0			0
$711$		−	29618.8i		−	0.0585906i
$712$	−508075.	−	484102.i	−1.00223	−	0.954942i
$713$	791620.			1.55718
$714$	−43352.9	+	44056.8i	−0.0850397	+	0.0864204i
$715$		0			0
$716$	845382.	−	13615.8i	1.64902	−	0.0265592i
$717$	−179477.			−0.349117
$718$	37667.8	+	37066.0i	0.0730671	+	0.0718997i
$719$			84839.0i			0.164111i	0.996628	+	0.0820555i	$0.0261485\pi$
$719$			84839.0i			0.164111i	−0.996628	+	0.0820555i	$0.973852\pi$
$720$		0			0
$721$	641521.			1.23407
$722$	257956.	−	262144.i	0.494848	−	0.502882i
$723$		−	356804.i		−	0.682579i
$724$	16244.4	+	1.00859e6i	0.0309903	+	1.92414i
$725$		0			0
$726$	504945.	+	496877.i	0.958011	+	0.942706i
$727$		−	80916.8i		−	0.153098i	−0.997066	−	0.0765491i	$-0.975610\pi$
$727$		−	80916.8i		−	0.153098i	0.997066	−	0.0765491i	$-0.0243902\pi$
$728$	665296.	−	698241.i	1.25531	−	1.31748i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	58204.4i		−	0.108923i
$732$	−400616.	+	6452.34i	−0.747663	+	0.0120419i
$733$	−62103.9			−0.115588			−0.0577938	−	0.998329i	$-0.518407\pi$
$733$	−62103.9			−0.115588			−0.0577938	+	0.998329i	$0.518407\pi$
$734$	−133778.	−	131640.i	−0.248308	−	0.244341i
$735$		0			0
$736$	−558327.	−	515086.i	−1.03070	−	0.950877i
$737$	−1.27854e6			−2.35385
$738$	86474.4	−	87878.4i	0.158772	−	0.161350i
$739$		−	268031.i		−	0.490790i	−0.969423	−	0.245395i	$-0.921082\pi$
$739$		−	268031.i		−	0.490790i	0.969423	−	0.245395i	$-0.0789176\pi$
$740$		0			0
$741$	241100.			0.439098
$742$	261644.	+	257464.i	0.475230	+	0.467637i
$743$			348633.i			0.631525i	0.948838	+	0.315763i	$0.102260\pi$
$743$			348633.i			0.631525i	−0.948838	+	0.315763i	$0.897740\pi$
$744$	256922.	+	244799.i	0.464147	+	0.442247i
$745$		0			0
$746$	666291.	−	677109.i	1.19725	−	1.21669i
$747$		−	83627.5i		−	0.149868i
$748$	−165059.	+	2658.45i	−0.295010	+	0.00475145i
$749$	−1.17548e6			−2.09533
$750$		0			0
$751$			757069.i			1.34232i	0.741313	+	0.671159i	$0.234203\pi$
$751$			757069.i			1.34232i	−0.741313	+	0.671159i	$0.765797\pi$
$752$	3353.05	+	104066.i	0.00592932	+	0.184023i
$753$	−322179.			−0.568207
$754$	703756.	−	715182.i	1.23788	−	1.25798i
$755$		0			0
$756$	2299.92	+	142799.i	0.00402411	+	0.249851i
$757$	−128542.			−0.224312			−0.112156	−	0.993691i	$-0.535776\pi$
$757$	−128542.			−0.224312			−0.112156	+	0.993691i	$0.535776\pi$
$758$	−308334.	−	303408.i	−0.536639	−	0.528066i
$759$			850866.i			1.47699i
$760$		0			0
$761$	460176.			0.794611			0.397306	−	0.917686i	$-0.369945\pi$
$761$	460176.			0.794611			0.397306	+	0.917686i	$0.369945\pi$
$762$	318305.	−	323473.i	0.548193	−	0.557094i
$763$		−	43065.4i		−	0.0739740i
$764$	331640.	−	5341.40i	0.568172	−	0.00915100i
$765$		0			0
$766$	408019.	+	401501.i	0.695382	+	0.684272i
$767$		−	585512.i		−	0.995280i
$768$	−21921.6	−	339829.i	−0.0371664	−	0.576153i
$769$	1.10194e6			1.86340			0.931701	−	0.363226i	$-0.118325\pi$
$769$	1.10194e6			1.86340			0.931701	+	0.363226i	$0.118325\pi$
$770$		0			0
$771$			342829.i			0.576725i
$772$	−4526.53	−	281046.i	−0.00759506	−	0.471566i
$773$	−809541.			−1.35481			−0.677407	−	0.735608i	$-0.736897\pi$
$773$	−809541.			−1.35481			−0.677407	+	0.735608i	$0.736897\pi$
$774$	−95858.8	−	94327.3i	−0.160011	−	0.157455i
$775$		0			0
$776$	571724.	+	544748.i	0.949430	+	0.904633i
$777$	−756149.			−1.25246
$778$	−370505.	+	376520.i	−0.612117	+	0.622055i
$779$		−	223633.i		−	0.368520i
$780$		0			0
$781$	−68289.2			−0.111957
$782$	−98859.8	−	97280.4i	−0.161661	−	0.159079i
$783$			148582.i			0.242349i
$784$	421390.	−	13577.4i	0.685570	−	0.0220894i
$785$		0			0
$786$	−100870.	+	102508.i	−0.163274	+	0.165925i
$787$		−	363079.i		−	0.586207i	−0.956081	−	0.293104i	$-0.905312\pi$
$787$		−	363079.i		−	0.586207i	0.956081	−	0.293104i	$-0.0946881\pi$
$788$	13089.5	+	812709.i	0.0210800	+	1.30883i
$789$	−238448.			−0.383036
$790$		0			0
$791$		−	362265.i		−	0.578993i
$792$	−263121.	+	276150.i	−0.419473	+	0.440246i
$793$	1.14147e6			1.81518
$794$	129446.	−	131548.i	0.205328	−	0.208662i
$795$		0			0
$796$	−514194.	+	8281.64i	−0.811524	+	0.0130704i
$797$	−483796.			−0.761633			−0.380816	−	0.924651i	$-0.624357\pi$
$797$	−483796.			−0.761633			−0.380816	+	0.924651i	$0.624357\pi$
$798$	184647.	+	181697.i	0.289960	+	0.285327i
$799$			19010.6i			0.0297785i
$800$		0			0
$801$	−296063.			−0.461444
$802$	9103.96	−	9251.77i	0.0141541	−	0.0143839i
$803$			220016.i			0.341211i
$804$	−7754.85	−	481487.i	−0.0119967	−	0.744857i
$805$		0			0
$806$	−720626.	−	709113.i	−1.10928	−	1.09155i
$807$		−	346065.i		−	0.531386i
$808$	−691237.	−	658622.i	−1.05878	−	1.00882i
$809$	483640.			0.738966			0.369483	−	0.929237i	$-0.379535\pi$
$809$	483640.			0.738966			0.369483	+	0.929237i	$0.379535\pi$
$810$		0			0
$811$			406318.i			0.617767i	0.951100	+	0.308883i	$0.0999553\pi$
$811$			406318.i			0.617767i	−0.951100	+	0.308883i	$0.900045\pi$
$812$	1.07795e6	−	17361.5i	1.63488	−	0.0263315i
$813$	−560386.			−0.847826
$814$	−1.43946e6	−	1.41646e6i	−2.17245	−	2.13774i
$815$		0			0
$816$	−2002.30	−	62143.8i	−0.00300711	−	0.0933292i
$817$	−243942.			−0.365462
$818$	−533693.	+	542358.i	−0.797599	+	0.810549i
$819$		−	406877.i		−	0.606589i
$820$		0			0
$821$	489931.			0.726857			0.363428	−	0.931622i	$-0.381606\pi$
$821$	489931.			0.726857			0.363428	+	0.931622i	$0.381606\pi$
$822$	−364728.	−	358901.i	−0.539791	−	0.531167i
$823$			372808.i			0.550408i	0.961386	+	0.275204i	$0.0887455\pi$
$823$			372808.i			0.550408i	−0.961386	+	0.275204i	$0.911255\pi$
$824$	−445156.	+	467200.i	−0.655628	+	0.688095i
$825$		0			0
$826$	441253.	−	448417.i	0.646736	−	0.657237i
$827$		−	222364.i		−	0.325127i	−0.986698	−	0.162563i	$-0.948024\pi$
$827$		−	222364.i		−	0.325127i	0.986698	−	0.162563i	$-0.0519762\pi$
$828$	−320429.	+	5160.84i	−0.467381	+	0.00752766i
$829$	127764.			0.185908			0.0929542	−	0.995670i	$-0.470369\pi$
$829$	127764.			0.185908			0.0929542	+	0.995670i	$0.470369\pi$
$830$		0			0
$831$		−	395536.i		−	0.572774i
$832$	46854.0	+	969028.i	0.0676862	+	1.39988i
$833$	76978.8			0.110938
$834$	−273590.	+	278032.i	−0.393341	+	0.399727i
$835$		0			0
$836$	11141.9	+	691784.i	0.0159422	+	0.989824i
$837$	149712.			0.213701
$838$	110233.	+	108472.i	0.156972	+	0.154465i
$839$			981082.i			1.39374i	0.717198	+	0.696870i	$0.245424\pi$
$839$			981082.i			1.39374i	−0.717198	+	0.696870i	$0.754576\pi$
$840$		0			0
$841$	414320.			0.585793
$842$	−603814.	+	613617.i	−0.851684	+	0.865512i
$843$		−	664774.i		−	0.935446i
$844$	152642.	−	2458.45i	0.214283	−	0.00345125i
$845$		0			0
$846$	31309.2	+	30809.0i	0.0437453	+	0.0430464i
$847$		−	2.16852e6i		−	3.02271i
$848$	−369060.	+	11891.3i	−0.513222	+	0.0165362i
$849$	−612064.			−0.849144
$850$		0			0
$851$		−	1.69674e6i		−	2.34291i
$852$	−414.201	−	25717.1i	−0.000570601	−	0.0354278i
$853$	192525.			0.264599			0.132299	−	0.991210i	$-0.457764\pi$
$853$	192525.			0.264599			0.132299	+	0.991210i	$0.457764\pi$
$854$	874203.	+	860236.i	1.19866	+	1.17951i
$855$		0			0
$856$	815674.	−	856066.i	1.11319	−	1.16831i
$857$	1.20031e6			1.63430			0.817151	−	0.576424i	$-0.195552\pi$
$857$	1.20031e6			1.63430			0.817151	+	0.576424i	$0.195552\pi$
$858$	762184.	−	774559.i	1.03535	−	1.05216i
$859$		−	1.29982e6i		−	1.76156i	−0.473529	−	0.880778i	$-0.657020\pi$
$859$		−	1.29982e6i		−	1.76156i	0.473529	−	0.880778i	$-0.342980\pi$
$860$		0			0
$861$	−377400.			−0.509091
$862$	36586.7	+	36002.2i	0.0492390	+	0.0484523i
$863$			148386.i			0.199238i	0.995026	+	0.0996188i	$0.0317623\pi$
$863$			148386.i			0.199238i	−0.995026	+	0.0996188i	$0.968238\pi$
$864$	−105592.	−	97414.0i	−0.141450	−	0.130495i
$865$		0			0
$866$	−688103.	+	699275.i	−0.917525	+	0.932421i
$867$			422636.i			0.562248i
$868$	−17493.6	−	1.08615e6i	−0.0232188	−	1.44162i
$869$	−242147.			−0.320656
$870$		0			0
$871$			1.37190e6i			1.80837i
$872$	31363.1	+	29883.3i	0.0412465	+	0.0393003i
$873$	333153.			0.437134
$874$	−407714.	+	414334.i	−0.533744	+	0.542410i
$875$		0			0
$876$	−82856.1	+	1334.48i	−0.107973	+	0.00173902i
$877$	144747.			0.188196			0.0940981	−	0.995563i	$-0.470003\pi$
$877$	144747.			0.188196			0.0940981	+	0.995563i	$0.470003\pi$
$878$	−23722.9	−	23343.9i	−0.0307736	−	0.0302820i
$879$		−	626229.i		−	0.810505i
$880$		0			0
$881$	281633.			0.362853			0.181427	−	0.983404i	$-0.441928\pi$
$881$	281633.			0.362853			0.181427	+	0.983404i	$0.441928\pi$
$882$	124754.	−	126779.i	0.160367	−	0.162971i
$883$		−	334210.i		−	0.428645i	−0.976763	−	0.214323i	$-0.931246\pi$
$883$		−	334210.i		−	0.428645i	0.976763	−	0.214323i	$-0.0687544\pi$
$884$	2852.58	+	177112.i	0.00365034	+	0.226644i
$885$		0			0
$886$	−402689.	−	396255.i	−0.512982	−	0.504787i
$887$			504313.i			0.640992i	0.947250	+	0.320496i	$0.103850\pi$
$887$			504313.i			0.640992i	−0.947250	+	0.320496i	$0.896150\pi$
$888$	524696.	−	550679.i	0.665399	−	0.698349i
$889$	−1.38918e6			−1.75774
$890$		0			0
$891$			160917.i			0.202697i
$892$	535442.	−	8623.85i	0.672950	−	0.0108386i
$893$	79675.8			0.0999133
$894$	−97377.7	−	95822.0i	−0.121839	−	0.119892i
$895$		0			0
$896$	−694394.	+	777444.i	−0.864948	+	0.968396i
$897$	912998.			1.13471
$898$	−554451.	+	563453.i	−0.687560	+	0.698723i
$899$		−	1.13014e6i		−	1.39834i
$900$		0			0
$901$	−67419.2			−0.0830489
$902$	−718445.	−	706967.i	−0.883040	−	0.868932i
$903$			411672.i			0.504866i
$904$	263826.	+	251378.i	0.322835	+	0.307603i
$905$		0			0
$906$	−114049.	+	115900.i	−0.138942	+	0.141198i
$907$			83306.2i			0.101266i	0.998717	+	0.0506329i	$0.0161239\pi$
$907$			83306.2i			0.101266i	−0.998717	+	0.0506329i	$0.983876\pi$
$908$	18385.9	−	296.124i	0.0223004	−	0.000359172i
$909$	−402795.			−0.487479
$910$		0			0
$911$			115795.i			0.139525i	0.997564	+	0.0697626i	$0.0222242\pi$
$911$			115795.i			0.139525i	−0.997564	+	0.0697626i	$0.977776\pi$
$912$	−260453.	+	8391.89i	−0.313140	+	0.0100895i
$913$	−683691.			−0.820198
$914$	929574.	−	944667.i	1.11274	−	1.13080i
$915$		0			0
$916$	12726.6	+	790173.i	0.0151677	+	0.941741i
$917$	440227.			0.523525
$918$	−18696.5	−	18397.8i	−0.0221858	−	0.0218314i
$919$			788234.i			0.933306i	0.884441	+	0.466653i	$0.154540\pi$
$919$			788234.i			0.933306i	−0.884441	+	0.466653i	$0.845460\pi$
$920$		0			0
$921$	−467670.			−0.551341
$922$	−550143.	+	559075.i	−0.647163	+	0.657671i
$923$			73275.8i			0.0860117i
$924$	1.16744e6	−	18802.9i	1.36739	−	0.0220232i
$925$		0			0
$926$	−481107.	−	473420.i	−0.561073	−	0.552109i
$927$			272245.i			0.316811i
$928$	−735352.	+	797083.i	−0.853884	+	0.925567i
$929$	−15865.8			−0.0183837			−0.00919183	−	0.999958i	$-0.502926\pi$
$929$	−15865.8			−0.0183837			−0.00919183	+	0.999958i	$0.502926\pi$
$930$		0			0
$931$		−	322628.i		−	0.372222i
$932$	−10843.5	−	673256.i	−0.0124835	−	0.775084i
$933$	186771.			0.214559
$934$	165945.	+	163294.i	0.190227	+	0.187188i
$935$		0			0
$936$	296315.	+	282334.i	0.338222	+	0.322264i
$937$	15433.2			0.0175783			0.00878913	−	0.999961i	$-0.497202\pi$
$937$	15433.2			0.0175783			0.00878913	+	0.999961i	$0.497202\pi$
$938$	−1.03389e6	+	1.05068e6i	−1.17508	+	1.19416i
$939$			54147.7i			0.0614114i
$940$		0			0
$941$	−550507.			−0.621704			−0.310852	−	0.950458i	$-0.600614\pi$
$941$	−550507.			−0.621704			−0.310852	+	0.950458i	$0.600614\pi$
$942$	136335.	+	134157.i	0.153640	+	0.151185i
$943$		−	846854.i		−	0.952325i
$944$	20379.7	+	632510.i	0.0228694	+	0.709779i
$945$		0			0
$946$	−771167.	+	783688.i	−0.861720	+	0.875711i
$947$			1.27984e6i			1.42710i	0.700602	+	0.713552i	$0.252915\pi$
$947$			1.27984e6i			1.42710i	−0.700602	+	0.713552i	$0.747085\pi$
$948$	−1468.72	−	91190.4i	−0.00163426	−	0.101469i
$949$	236082.			0.262138
$950$		0			0
$951$		−	230069.i		−	0.254389i
$952$	−131290.	+	137792.i	−0.144864	+	0.152037i
$953$	−491859.			−0.541571			−0.270785	−	0.962640i	$-0.587283\pi$
$953$	−491859.			−0.541571			−0.270785	+	0.962640i	$0.587283\pi$
$954$	−109261.	+	111035.i	−0.120052	+	0.122001i
$955$		0			0
$956$	−552575.	+	8899.80i	−0.604611	+	0.00973788i
$957$	1.21472e6			1.32633
$958$	−632090.	−	621992.i	−0.688729	−	0.677725i
$959$			1.56635e6i			1.70314i
$960$		0			0
$961$	−215219.			−0.233042
$962$	−1.51989e6	+	1.54457e6i	−1.64234	+	1.66900i
$963$		−	498843.i		−	0.537912i
$964$	−17692.9	−	1.09853e6i	−0.0190391	−	1.18211i
$965$		0			0
$966$	699223.	+	688052.i	0.749310	+	0.737338i
$967$		−	628976.i		−	0.672638i	−0.941748	−	0.336319i	$-0.890818\pi$
$967$		−	628976.i		−	0.672638i	0.941748	−	0.336319i	$-0.109182\pi$
$968$	1.57926e6	+	1.50475e6i	1.68540	+	1.60588i
$969$	−47579.0			−0.0506720
$970$		0			0
$971$		−	1.78700e6i		−	1.89533i	−0.319264	−	0.947666i	$-0.603436\pi$
$971$		−	1.78700e6i		−	1.89533i	0.319264	−	0.947666i	$-0.396564\pi$
$972$	−60600.1	+	976.027i	−0.0641417	+	0.00103307i
$973$	1.19403e6			1.26121
$974$	415040.	+	408409.i	0.437494	+	0.430505i
$975$		0			0
$976$	−1.23310e6	+	39730.9i	−1.29449	+	0.0417089i
$977$	842171.			0.882289			0.441145	−	0.897436i	$-0.354573\pi$
$977$	842171.			0.882289			0.441145	+	0.897436i	$0.354573\pi$
$978$	−636585.	+	646921.i	−0.665547	+	0.676353i
$979$			2.42045e6i			2.52540i
$980$		0			0
$981$	18275.8			0.0189906
$982$	697373.	+	686232.i	0.723173	+	0.711620i
$983$			877633.i			0.908251i	0.890938	+	0.454125i	$0.150048\pi$
$983$			877633.i			0.908251i	−0.890938	+	0.454125i	$0.849952\pi$
$984$	261880.	−	274848.i	0.270466	−	0.283859i
$985$		0			0
$986$	−138880.	+	141135.i	−0.142852	+	0.145171i
$987$		−	134459.i		−	0.138025i
$988$	742300.	−	11955.5i	0.760441	−	0.0122477i
$989$	−923758.			−0.944421
$990$		0			0
$991$			326910.i			0.332875i	0.986052	+	0.166437i	$0.0532264\pi$
$991$			326910.i			0.332875i	−0.986052	+	0.166437i	$0.946774\pi$
$992$	803150.	+	740949.i	0.816157	+	0.752948i
$993$	−1.13805e6			−1.15415
$994$	−55222.0	+	56118.6i	−0.0558907	+	0.0567981i
$995$		0			0
$996$	−4146.86	−	257472.i	−0.00418024	−	0.259545i
$997$	935659.			0.941298			0.470649	−	0.882320i	$-0.344020\pi$
$997$	935659.			0.941298			0.470649	+	0.882320i	$0.344020\pi$
$998$	−323378.	−	318212.i	−0.324676	−	0.319488i
$999$		−	320890.i		−	0.321532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.c.151.11	yes	16
4.3	odd	2	inner	300.5.c.c.151.12	yes	16
5.2	odd	4		300.5.f.c.199.26		32
5.3	odd	4		300.5.f.c.199.7		32
5.4	even	2		300.5.c.b.151.6	yes	16
20.3	even	4		300.5.f.c.199.25		32
20.7	even	4		300.5.f.c.199.8		32
20.19	odd	2		300.5.c.b.151.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.5.c.b.151.5	✓	16	20.19	odd	2
300.5.c.b.151.6	yes	16	5.4	even	2
300.5.c.c.151.11	yes	16	1.1	even	1	trivial
300.5.c.c.151.12	yes	16	4.3	odd	2	inner
300.5.f.c.199.7		32	5.3	odd	4
300.5.f.c.199.8		32	20.7	even	4
300.5.f.c.199.25		32	20.3	even	4
300.5.f.c.199.26		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)

\(f(q)\)	\(=\)	\(q+(2.80556 - 2.85111i) q^{2} -5.19615i q^{3} +(-0.257663 - 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232i q^{7} +(-46.3347 - 44.1485i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(2.80556 - 2.85111i) q^{2} -5.19615i q^{3} +(-0.257663 - 15.9979i) q^{4} +(-14.8148 - 14.5781i) q^{6} +63.6232i q^{7} +(-46.3347 - 44.1485i) q^{8} -27.0000 q^{9} +220.737i q^{11} +(-83.1277 + 1.33886i) q^{12} +236.856 q^{13} +(181.397 + 178.499i) q^{14} +(-255.867 + 8.24415i) q^{16} -46.7414 q^{17} +(-75.7501 + 76.9800i) q^{18} +195.899i q^{19} +330.596 q^{21} +(629.345 + 619.291i) q^{22} +741.830i q^{23} +(-229.402 + 240.762i) q^{24} +(664.512 - 675.301i) q^{26} +140.296i q^{27} +(1017.84 - 16.3934i) q^{28} +1059.06 q^{29} -1067.12i q^{31} +(-694.346 + 752.635i) q^{32} +1146.98 q^{33} +(-131.136 + 133.265i) q^{34} +(6.95691 + 431.944i) q^{36} -2287.23 q^{37} +(558.530 + 549.606i) q^{38} -1230.74i q^{39} -1141.57 q^{41} +(927.506 - 942.565i) q^{42} +1245.24i q^{43} +(3531.33 - 56.8758i) q^{44} +(2115.04 + 2081.25i) q^{46} -406.719i q^{47} +(42.8379 + 1329.53i) q^{48} -1646.91 q^{49} +242.875i q^{51} +(-61.0290 - 3789.20i) q^{52} +1442.39 q^{53} +(400.000 + 393.609i) q^{54} +(2808.87 - 2947.96i) q^{56} +1017.92 q^{57} +(2971.25 - 3019.49i) q^{58} -2472.02i q^{59} +4819.29 q^{61} +(-3042.47 - 2993.86i) q^{62} -1717.83i q^{63} +(197.817 + 4091.22i) q^{64} +(3217.93 - 3270.17i) q^{66} +5792.14i q^{67} +(12.0435 + 747.765i) q^{68} +3854.66 q^{69} +309.369i q^{71} +(1251.04 + 1192.01i) q^{72} +996.733 q^{73} +(-6416.96 + 6521.15i) q^{74} +(3133.98 - 50.4759i) q^{76} -14044.0 q^{77} +(-3508.97 - 3452.91i) q^{78} +1096.99i q^{79} +729.000 q^{81} +(-3202.76 + 3254.76i) q^{82} +3097.31i q^{83} +(-85.1824 - 5288.85i) q^{84} +(3550.32 + 3493.60i) q^{86} -5503.02i q^{87} +(9745.21 - 10227.8i) q^{88} +10965.3 q^{89} +15069.5i q^{91} +(11867.7 - 191.142i) q^{92} -5544.91 q^{93} +(-1159.60 - 1141.07i) q^{94} +(3910.81 + 3607.93i) q^{96} -12339.0 q^{97} +(-4620.50 + 4695.52i) q^{98} -5959.90i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 8 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 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

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