LMFDB - Embedded newform 300.5.c.d.151.14

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} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.14
Root			$-1.14149 + 2.58786i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.d.151.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.40825 + 2.09376i) q^{2} +5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} +(-10.8795 + 17.7098i) q^{6} -61.3317i q^{7} +(-5.23271 + 63.7857i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(3.40825 + 2.09376i) q^{2} +5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} +(-10.8795 + 17.7098i) q^{6} -61.3317i q^{7} +(-5.23271 + 63.7857i) q^{8} -27.0000 q^{9} +74.1525i q^{11} +(-74.1601 + 37.5804i) q^{12} -181.358 q^{13} +(128.414 - 209.034i) q^{14} +(-151.386 + 206.442i) q^{16} -516.182 q^{17} +(-92.0228 - 56.5315i) q^{18} +407.870i q^{19} +318.689 q^{21} +(-155.258 + 252.730i) q^{22} +7.48405i q^{23} +(-331.440 - 27.1900i) q^{24} +(-618.114 - 379.720i) q^{26} -140.296i q^{27} +(875.333 - 443.572i) q^{28} -1473.47 q^{29} +1041.01i q^{31} +(-948.202 + 386.639i) q^{32} -385.308 q^{33} +(-1759.28 - 1080.76i) q^{34} +(-195.273 - 385.347i) q^{36} +667.800 q^{37} +(-853.982 + 1390.12i) q^{38} -942.365i q^{39} +1215.10 q^{41} +(1086.17 + 667.258i) q^{42} -987.639i q^{43} +(-1058.31 + 536.297i) q^{44} +(-15.6698 + 25.5075i) q^{46} -2943.18i q^{47} +(-1072.70 - 786.626i) q^{48} -1360.58 q^{49} -2682.16i q^{51} +(-1311.64 - 2588.36i) q^{52} +2287.61 q^{53} +(293.746 - 478.164i) q^{54} +(3912.09 + 320.931i) q^{56} -2119.36 q^{57} +(-5021.96 - 3085.09i) q^{58} -390.685i q^{59} +4108.86 q^{61} +(-2179.63 + 3548.03i) q^{62} +1655.96i q^{63} +(-4041.24 - 667.545i) q^{64} +(-1313.23 - 806.742i) q^{66} +6166.96i q^{67} +(-3733.20 - 7367.00i) q^{68} -38.8883 q^{69} +4462.68i q^{71} +(141.283 - 1722.21i) q^{72} -3369.06 q^{73} +(2276.03 + 1398.21i) q^{74} +(-5821.17 + 2949.86i) q^{76} +4547.90 q^{77} +(1973.08 - 3211.81i) q^{78} -7060.25i q^{79} +729.000 q^{81} +(4141.36 + 2544.12i) q^{82} +4972.33i q^{83} +(2304.87 + 4548.36i) q^{84} +(2067.88 - 3366.12i) q^{86} -7656.38i q^{87} +(-4729.87 - 388.019i) q^{88} -12370.7 q^{89} +11123.0i q^{91} +(-106.813 + 54.1273i) q^{92} -5409.26 q^{93} +(6162.30 - 10031.1i) q^{94} +(-2009.03 - 4927.00i) q^{96} -2516.32 q^{97} +(-4637.19 - 2848.72i) q^{98} -2002.12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	$ 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) $ 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 + 352 * q^13 - 804 * q^14 - 190 * q^16 - 324 * q^18 + 288 * q^21 - 436 * q^22 - 1998 * q^24 - 852 * q^26 + 1156 * q^28 - 3456 * q^29 - 7668 * q^32 + 4772 * q^34 - 702 * q^36 - 9376 * q^37 + 1320 * q^38 + 1248 * q^41 + 324 * q^42 - 6420 * q^44 - 1112 * q^46 + 4176 * q^48 - 3952 * q^49 - 12704 * q^52 + 5184 * q^53 - 486 * q^54 - 2604 * q^56 + 11232 * q^57 - 12708 * q^58 - 3808 * q^61 + 16152 * q^62 - 11902 * q^64 - 2916 * q^66 + 12312 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 + 30516 * q^74 - 5160 * q^76 + 27456 * q^77 + 3600 * q^78 + 11664 * q^81 + 54040 * q^82 - 2052 * q^84 + 39768 * q^86 + 7220 * q^88 + 7584 * q^89 - 28848 * q^92 - 19872 * q^93 + 49776 * q^94 + 18882 * q^96 + 14496 * q^97 - 23940 * 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 $

$2$	3.40825	+	2.09376i	0.852063	+	0.523440i
$2$	3.40825	+	2.09376i	0.852063	+	0.523440i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	7.23235	+	14.2721i	0.452022	+	0.892007i
$5$		0			0
$5$		0			0
$6$	−10.8795	+	17.7098i	−0.302208	+	0.491939i
$7$		−	61.3317i		−	1.25167i	−0.779956	−	0.625834i	$-0.784759\pi$
$7$		−	61.3317i		−	1.25167i	0.779956	−	0.625834i	$-0.215241\pi$
$8$	−5.23271	+	63.7857i	−0.0817612	+	0.996652i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			74.1525i			0.612831i	0.951898	+	0.306415i	$0.0991297\pi$
$11$			74.1525i			0.612831i	−0.951898	+	0.306415i	$0.900870\pi$
$12$	−74.1601	+	37.5804i	−0.515000	+	0.260975i
$13$	−181.358			−1.07313			−0.536563	−	0.843861i	$-0.680277\pi$
$13$	−181.358			−1.07313			−0.536563	+	0.843861i	$0.680277\pi$
$14$	128.414	−	209.034i	0.655173	−	1.06650i
$15$		0			0
$16$	−151.386	+	206.442i	−0.591353	+	0.806413i
$17$	−516.182			−1.78610			−0.893048	−	0.449962i	$-0.851438\pi$
$17$	−516.182			−1.78610			−0.893048	+	0.449962i	$0.851438\pi$
$18$	−92.0228	−	56.5315i	−0.284021	−	0.174480i
$19$			407.870i			1.12983i	0.825147	+	0.564917i	$0.191092\pi$
$19$			407.870i			1.12983i	−0.825147	+	0.564917i	$0.808908\pi$
$20$		0			0
$21$	318.689			0.722651
$22$	−155.258	+	252.730i	−0.320780	+	0.522170i
$23$			7.48405i			0.0141475i	0.999975	+	0.00707377i	$0.00225167\pi$
$23$			7.48405i			0.0141475i	−0.999975	+	0.00707377i	$0.997748\pi$
$24$	−331.440	−	27.1900i	−0.575417	−	0.0472048i
$25$		0			0
$26$	−618.114	−	379.720i	−0.914370	−	0.561716i
$27$		−	140.296i		−	0.192450i
$28$	875.333	−	443.572i	1.11650	−	0.565781i
$29$	−1473.47			−1.75205			−0.876023	−	0.482270i	$-0.839812\pi$
$29$	−1473.47			−1.75205			−0.876023	+	0.482270i	$0.839812\pi$
$30$		0			0
$31$			1041.01i			1.08326i	0.840617	+	0.541630i	$0.182192\pi$
$31$			1041.01i			1.08326i	−0.840617	+	0.541630i	$0.817808\pi$
$32$	−948.202	+	386.639i	−0.925978	+	0.377577i
$33$	−385.308			−0.353818
$34$	−1759.28	−	1080.76i	−1.52187	−	0.934913i
$35$		0			0
$36$	−195.273	−	385.347i	−0.150674	−	0.297336i
$37$	667.800			0.487802			0.243901	−	0.969800i	$-0.421573\pi$
$37$	667.800			0.487802			0.243901	+	0.969800i	$0.421573\pi$
$38$	−853.982	+	1390.12i	−0.591400	+	0.962690i
$39$		−	942.365i		−	0.619569i
$40$		0			0
$41$	1215.10			0.722842			0.361421	−	0.932403i	$-0.382292\pi$
$41$	1215.10			0.722842			0.361421	+	0.932403i	$0.382292\pi$
$42$	1086.17	+	667.258i	0.615744	+	0.378264i
$43$		−	987.639i		−	0.534148i	−0.963676	−	0.267074i	$-0.913943\pi$
$43$		−	987.639i		−	0.534148i	0.963676	−	0.267074i	$-0.0860568\pi$
$44$	−1058.31	+	536.297i	−0.546649	+	0.277013i
$45$		0			0
$46$	−15.6698	+	25.5075i	−0.00740539	+	0.0120546i
$47$		−	2943.18i		−	1.33236i	−0.745792	−	0.666178i	$-0.767929\pi$
$47$		−	2943.18i		−	1.33236i	0.745792	−	0.666178i	$-0.232071\pi$
$48$	−1072.70	−	786.626i	−0.465583	−	0.341418i
$49$	−1360.58			−0.566672
$50$		0			0
$51$		−	2682.16i		−	1.03120i
$52$	−1311.64	−	2588.36i	−0.485076	−	0.957235i
$53$	2287.61			0.814384			0.407192	−	0.913343i	$-0.366508\pi$
$53$	2287.61			0.814384			0.407192	+	0.913343i	$0.366508\pi$
$54$	293.746	−	478.164i	0.100736	−	0.163980i
$55$		0			0
$56$	3912.09	+	320.931i	1.24748	+	0.102338i
$57$	−2119.36			−0.652310
$58$	−5021.96	−	3085.09i	−1.49285	−	0.917090i
$59$		−	390.685i		−	0.112234i	−0.998424	−	0.0561168i	$-0.982128\pi$
$59$		−	390.685i		−	0.112234i	0.998424	−	0.0561168i	$-0.0178719\pi$
$60$		0			0
$61$	4108.86			1.10424			0.552118	−	0.833766i	$-0.313820\pi$
$61$	4108.86			1.10424			0.552118	+	0.833766i	$0.313820\pi$
$62$	−2179.63	+	3548.03i	−0.567021	+	0.923005i
$63$			1655.96i			0.417223i
$64$	−4041.24	−	667.545i	−0.986630	−	0.162975i
$65$		0			0
$66$	−1313.23	−	806.742i	−0.301475	−	0.185202i
$67$			6166.96i			1.37379i	0.726755	+	0.686897i	$0.241028\pi$
$67$			6166.96i			1.37379i	−0.726755	+	0.686897i	$0.758972\pi$
$68$	−3733.20	−	7367.00i	−0.807354	−	1.59321i
$69$	−38.8883			−0.00816809
$70$		0			0
$71$			4462.68i			0.885276i	0.896700	+	0.442638i	$0.145957\pi$
$71$			4462.68i			0.885276i	−0.896700	+	0.442638i	$0.854043\pi$
$72$	141.283	−	1722.21i	0.0272537	−	0.332217i
$73$	−3369.06			−0.632213			−0.316106	−	0.948724i	$-0.602376\pi$
$73$	−3369.06			−0.632213			−0.316106	+	0.948724i	$0.602376\pi$
$74$	2276.03	+	1398.21i	0.415638	+	0.255335i
$75$		0			0
$76$	−5821.17	+	2949.86i	−1.00782	+	0.510710i
$77$	4547.90			0.767061
$78$	1973.08	−	3211.81i	0.324307	−	0.527912i
$79$		−	7060.25i		−	1.13127i	−0.824656	−	0.565635i	$-0.808631\pi$
$79$		−	7060.25i		−	1.13127i	0.824656	−	0.565635i	$-0.191369\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	4141.36	+	2544.12i	0.615907	+	0.378364i
$83$			4972.33i			0.721777i	0.932609	+	0.360889i	$0.117527\pi$
$83$			4972.33i			0.721777i	−0.932609	+	0.360889i	$0.882473\pi$
$84$	2304.87	+	4548.36i	0.326654	+	0.644609i
$85$		0			0
$86$	2067.88	−	3366.12i	0.279594	−	0.455127i
$87$		−	7656.38i		−	1.01154i
$88$	−4729.87	−	388.019i	−0.610779	−	0.0501058i
$89$	−12370.7			−1.56175			−0.780877	−	0.624685i	$-0.785227\pi$
$89$	−12370.7			−1.56175			−0.780877	+	0.624685i	$0.785227\pi$
$90$		0			0
$91$			11123.0i			1.34320i
$92$	−106.813	+	54.1273i	−0.0126197	+	0.00639500i
$93$	−5409.26			−0.625420
$94$	6162.30	−	10031.1i	0.697408	−	1.13525i
$95$		0			0
$96$	−2009.03	−	4927.00i	−0.217994	−	0.534614i
$97$	−2516.32			−0.267438			−0.133719	−	0.991019i	$-0.542692\pi$
$97$	−2516.32			−0.267438			−0.133719	+	0.991019i	$0.542692\pi$
$98$	−4637.19	−	2848.72i	−0.482840	−	0.296619i
$99$		−	2002.12i		−	0.204277i
$100$		0			0
$101$	−2974.94			−0.291632			−0.145816	−	0.989312i	$-0.546581\pi$
$101$	−2974.94			−0.291632			−0.145816	+	0.989312i	$0.546581\pi$
$102$	5615.79	−	9141.47i	0.539773	−	0.878649i
$103$			17963.5i			1.69323i	0.532202	+	0.846617i	$0.321365\pi$
$103$			17963.5i			1.69323i	−0.532202	+	0.846617i	$0.678635\pi$
$104$	948.995	−	11568.1i	0.0877399	−	1.06953i
$105$		0			0
$106$	7796.73	+	4789.69i	0.693906	+	0.426281i
$107$			1200.48i			0.104854i	0.998625	+	0.0524272i	$0.0166958\pi$
$107$			1200.48i			0.104854i	−0.998625	+	0.0524272i	$0.983304\pi$
$108$	2002.32	−	1014.67i	0.171667	−	0.0869916i
$109$	16500.9			1.38884			0.694422	−	0.719568i	$-0.255660\pi$
$109$	16500.9			1.38884			0.694422	+	0.719568i	$0.255660\pi$
$110$		0			0
$111$			3469.99i			0.281632i
$112$	12661.4	+	9284.78i	1.00936	+	0.740177i
$113$	6037.80			0.472849			0.236424	−	0.971650i	$-0.424024\pi$
$113$	6037.80			0.472849			0.236424	+	0.971650i	$0.424024\pi$
$114$	−7223.30	−	4437.42i	−0.555809	−	0.341445i
$115$		0			0
$116$	−10656.6	−	21029.5i	−0.791962	−	1.56284i
$117$	4896.67			0.357708
$118$	818.000	−	1331.55i	0.0587475	−	0.0956300i
$119$			31658.3i			2.23560i
$120$		0			0
$121$	9142.40			0.624438
$122$	14004.0	+	8602.97i	0.940878	+	0.578001i
$123$			6313.83i			0.417333i
$124$	−14857.4	+	7528.96i	−0.966275	+	0.489657i
$125$		0			0
$126$	−3467.17	+	5643.91i	−0.218391	+	0.355500i
$127$		−	17483.7i		−	1.08399i	−0.840382	−	0.541995i	$-0.817669\pi$
$127$		−	17483.7i		−	1.08399i	0.840382	−	0.541995i	$-0.182331\pi$
$128$	−12375.9	−	10736.5i	−0.755363	−	0.655306i
$129$	5131.92			0.308390
$130$		0			0
$131$			10698.3i			0.623408i	0.950179	+	0.311704i	$0.100900\pi$
$131$			10698.3i			0.623408i	−0.950179	+	0.311704i	$0.899100\pi$
$132$	−2786.68	−	5499.16i	−0.159933	−	0.315608i
$133$	25015.4			1.41418
$134$	−12912.1	+	21018.6i	−0.719099	+	1.17056i
$135$		0			0
$136$	2701.03	−	32925.0i	0.146033	−	1.78012i
$137$	−31259.4			−1.66548			−0.832740	−	0.553665i	$-0.813229\pi$
$137$	−31259.4			−1.66548			−0.832740	+	0.553665i	$0.813229\pi$
$138$	−132.541	−	81.4227i	−0.00695972	−	0.00427550i
$139$		−	22483.1i		−	1.16366i	−0.813310	−	0.581831i	$-0.802337\pi$
$139$		−	22483.1i		−	1.16366i	0.813310	−	0.581831i	$-0.197663\pi$
$140$		0			0
$141$	15293.2			0.769236
$142$	−9343.77	+	15209.9i	−0.463389	+	0.754311i
$143$		−	13448.2i		−	0.657644i
$144$	4087.43	−	5573.93i	0.197118	−	0.268804i
$145$		0			0
$146$	−11482.6	−	7054.01i	−0.538685	−	0.330925i
$147$		−	7069.78i		−	0.327168i
$148$	4829.76	+	9530.92i	0.220497	+	0.435122i
$149$	19244.0			0.866808			0.433404	−	0.901200i	$-0.357312\pi$
$149$	19244.0			0.866808			0.433404	+	0.901200i	$0.357312\pi$
$150$		0			0
$151$			42406.7i			1.85986i	0.367735	+	0.929931i	$0.380133\pi$
$151$			42406.7i			1.85986i	−0.367735	+	0.929931i	$0.619867\pi$
$152$	−26016.3	−	2134.27i	−1.12605	−	0.0923766i
$153$	13936.9			0.595365
$154$	15500.4	+	9522.21i	0.653584	+	0.401510i
$155$		0			0
$156$	13449.5	−	6815.51i	0.552660	−	0.280059i
$157$	−13979.2			−0.567129			−0.283565	−	0.958953i	$-0.591517\pi$
$157$	−13979.2			−0.567129			−0.283565	+	0.958953i	$0.591517\pi$
$158$	14782.5	−	24063.1i	0.592151	−	0.963913i
$159$			11886.7i			0.470185i
$160$		0			0
$161$	459.010			0.0177080
$162$	2484.61	+	1526.35i	0.0946736	+	0.0581600i
$163$			31094.2i			1.17032i	0.810919	+	0.585159i	$0.198968\pi$
$163$			31094.2i			1.17032i	−0.810919	+	0.585159i	$0.801032\pi$
$164$	8788.00	+	17342.0i	0.326740	+	0.644780i
$165$		0			0
$166$	−10410.9	+	16946.9i	−0.377807	+	0.615000i
$167$			30204.9i			1.08304i	0.840687	+	0.541521i	$0.182151\pi$
$167$			30204.9i			1.08304i	−0.840687	+	0.541521i	$0.817849\pi$
$168$	−1667.61	+	20327.8i	−0.0590847	+	0.720231i
$169$	4329.78			0.151598
$170$		0			0
$171$		−	11012.5i		−	0.376612i
$172$	14095.7	−	7142.95i	0.476463	−	0.241446i
$173$	22061.5			0.737128			0.368564	−	0.929602i	$-0.379850\pi$
$173$	22061.5			0.737128			0.368564	+	0.929602i	$0.379850\pi$
$174$	16030.6	−	26094.8i	0.529482	−	0.861899i
$175$		0			0
$176$	−15308.2	−	11225.7i	−0.494195	−	0.362399i
$177$	2030.06			0.0647981
$178$	−42162.3	−	25901.2i	−1.33071	−	0.817484i
$179$			4300.24i			0.134210i	0.997746	+	0.0671052i	$0.0213763\pi$
$179$			4300.24i			0.134210i	−0.997746	+	0.0671052i	$0.978624\pi$
$180$		0			0
$181$	−32288.1			−0.985566			−0.492783	−	0.870152i	$-0.664020\pi$
$181$	−32288.1			−0.985566			−0.492783	+	0.870152i	$0.664020\pi$
$182$	−23288.9	+	37910.0i	−0.703082	+	1.14449i
$183$			21350.3i			0.637531i
$184$	−477.376	−	39.1619i	−0.0141002	−	0.00115672i
$185$		0			0
$186$	−18436.1	−	11325.7i	−0.532897	−	0.327370i
$187$		−	38276.2i		−	1.09457i
$188$	42005.3	−	21286.1i	1.18847	−	0.602254i
$189$	−8604.60			−0.240884
$190$		0			0
$191$		−	23139.2i		−	0.634279i	−0.948379	−	0.317140i	$-0.897278\pi$
$191$		−	23139.2i		−	0.634279i	0.948379	−	0.317140i	$-0.102722\pi$
$192$	3468.66	−	20998.9i	0.0940936	−	0.569631i
$193$	64774.6			1.73896			0.869481	−	0.493966i	$-0.164453\pi$
$193$	64774.6			1.73896			0.869481	+	0.493966i	$0.164453\pi$
$194$	−8576.25	−	5268.57i	−0.227874	−	0.139988i
$195$		0			0
$196$	−9840.18	−	19418.3i	−0.256148	−	0.505475i
$197$	−317.341			−0.00817699			−0.00408850	−	0.999992i	$-0.501301\pi$
$197$	−317.341			−0.00817699			−0.00408850	+	0.999992i	$0.501301\pi$
$198$	4191.95	−	6823.72i	0.106927	−	0.174057i
$199$			18051.2i			0.455828i	0.973681	+	0.227914i	$0.0731905\pi$
$199$			18051.2i			0.455828i	−0.973681	+	0.227914i	$0.926810\pi$
$200$		0			0
$201$	−32044.5			−0.793161
$202$	−10139.3	−	6228.80i	−0.248489	−	0.152652i
$203$			90370.5i			2.19298i
$204$	38280.1	−	19398.3i	0.919840	−	0.466126i
$205$		0			0
$206$	−37611.3	+	61224.2i	−0.886306	+	1.44274i
$207$		−	202.069i		−	0.00471585i
$208$	27455.1	−	37439.9i	0.634596	−	0.865382i
$209$	−30244.6			−0.692398
$210$		0			0
$211$		−	62848.8i		−	1.41167i	−0.708378	−	0.705833i	$-0.750573\pi$
$211$		−	62848.8i		−	1.41167i	0.708378	−	0.705833i	$-0.249427\pi$
$212$	16544.8	+	32649.0i	0.368119	+	0.726436i
$213$	−23188.8			−0.511115
$214$	−2513.51	+	4091.53i	−0.0548850	+	0.0893426i
$215$		0			0
$216$	8948.89	+	734.129i	0.191806	+	0.0157349i
$217$	63847.1			1.35588
$218$	56239.1	+	34548.8i	1.18338	+	0.726976i
$219$		−	17506.2i		−	0.365008i
$220$		0			0
$221$	93613.7			1.91670
$222$	−7265.33	+	11826.6i	−0.147418	+	0.239968i
$223$		−	60726.4i		−	1.22115i	−0.791960	−	0.610573i	$-0.790939\pi$
$223$		−	60726.4i		−	1.22115i	0.791960	−	0.610573i	$-0.209061\pi$
$224$	23713.2	+	58154.8i	0.472601	+	1.15902i
$225$		0			0
$226$	20578.4	+	12641.7i	0.402897	+	0.247508i
$227$			98629.1i			1.91405i	0.290006	+	0.957025i	$0.406343\pi$
$227$			98629.1i			1.91405i	−0.290006	+	0.957025i	$0.593657\pi$
$228$	−15327.9	−	30247.7i	−0.294858	−	0.581865i
$229$	56329.9			1.07416			0.537079	−	0.843532i	$-0.319528\pi$
$229$	56329.9			1.07416			0.537079	+	0.843532i	$0.319528\pi$
$230$		0			0
$231$			23631.6i			0.442863i
$232$	7710.25	−	93986.4i	0.143249	−	1.74618i
$233$	−52509.1			−0.967215			−0.483608	−	0.875285i	$-0.660674\pi$
$233$	−52509.1			−0.967215			−0.483608	+	0.875285i	$0.660674\pi$
$234$	16689.1	+	10252.4i	0.304790	+	0.187239i
$235$		0			0
$236$	5575.90	−	2825.57i	0.100113	−	0.0507320i
$237$	36686.2			0.653139
$238$	−66284.9	+	107899.i	−1.17020	+	1.90487i
$239$			51142.5i			0.895336i	0.894200	+	0.447668i	$0.147745\pi$
$239$			51142.5i			0.895336i	−0.894200	+	0.447668i	$0.852255\pi$
$240$		0			0
$241$	7.06147			0.000121580			6.07899e−5	−	1.00000i	$-0.499981\pi$
$241$	7.06147			0.000121580			6.07899e−5		1.00000i	$0.499981\pi$
$242$	31159.6	+	19142.0i	0.532061	+	0.326856i
$243$			3788.00i			0.0641500i
$244$	29716.7	+	58642.1i	0.499139	+	0.984986i
$245$		0			0
$246$	−13219.6	+	21519.1i	−0.218449	+	0.355594i
$247$		−	73970.6i		−	1.21245i
$248$	−66401.7	−	5447.32i	−1.07963	−	0.0885685i
$249$	−25837.0			−0.416718
$250$		0			0
$251$			60466.9i			0.959776i	0.877330	+	0.479888i	$0.159323\pi$
$251$			60466.9i			0.959776i	−0.877330	+	0.479888i	$0.840677\pi$
$252$	−23634.0	+	11976.4i	−0.372165	+	0.188594i
$253$	−554.961			−0.00867005
$254$	36606.6	−	59588.7i	0.567403	−	0.923627i
$255$		0			0
$256$	−19700.4	−	62504.9i	−0.300604	−	0.953749i
$257$	−38335.4			−0.580408			−0.290204	−	0.956965i	$-0.593723\pi$
$257$	−38335.4			−0.580408			−0.290204	+	0.956965i	$0.593723\pi$
$258$	17490.9	+	10745.0i	0.262768	+	0.161424i
$259$		−	40957.3i		−	0.610566i
$260$		0			0
$261$	39783.7			0.584015
$262$	−22399.7	+	36462.5i	−0.326316	+	0.531183i
$263$		−	38851.9i		−	0.561696i	−0.959752	−	0.280848i	$-0.909384\pi$
$263$		−	38851.9i		−	0.561696i	0.959752	−	0.280848i	$-0.0906156\pi$
$264$	2016.21	−	24577.1i	0.0289286	−	0.352634i
$265$		0			0
$266$	85258.7	+	52376.2i	1.20497	+	0.740237i
$267$		−	64279.8i		−	0.901679i
$268$	−88015.6	+	44601.6i	−1.22543	+	0.620985i
$269$	−18724.5			−0.258765			−0.129382	−	0.991595i	$-0.541299\pi$
$269$	−18724.5			−0.258765			−0.129382	+	0.991595i	$0.541299\pi$
$270$		0			0
$271$		−	25639.5i		−	0.349117i	−0.984647	−	0.174559i	$-0.944150\pi$
$271$		−	25639.5i		−	0.349117i	0.984647	−	0.174559i	$-0.0558499\pi$
$272$	78142.8	−	106561.i	1.05621	−	1.44033i
$273$	−57796.8			−0.775495
$274$	−106540.	−	65449.6i	−1.41909	−	0.871778i
$275$		0			0
$276$	−281.253	−	555.018i	−0.00369215	−	0.00728599i
$277$	69695.7			0.908335			0.454168	−	0.890916i	$-0.349937\pi$
$277$	69695.7			0.908335			0.454168	+	0.890916i	$0.349937\pi$
$278$	47074.2	−	76628.1i	0.609107	−	0.991513i
$279$		−	28107.3i		−	0.361086i
$280$		0			0
$281$	−69900.0			−0.885248			−0.442624	−	0.896707i	$-0.645952\pi$
$281$	−69900.0			−0.885248			−0.442624	+	0.896707i	$0.645952\pi$
$282$	52123.0	+	32020.3i	0.655438	+	0.402649i
$283$		−	107624.i		−	1.34381i	−0.740637	−	0.671905i	$-0.765476\pi$
$283$		−	107624.i		−	1.34381i	0.740637	−	0.671905i	$-0.234524\pi$
$284$	−63691.8	+	32275.6i	−0.789673	+	0.400164i
$285$		0			0
$286$	28157.2	−	45834.7i	0.344237	−	0.560354i
$287$		−	74524.0i		−	0.904758i
$288$	25601.4	−	10439.2i	0.308659	−	0.125859i
$289$	182922.			2.19014
$290$		0			0
$291$		−	13075.2i		−	0.154405i
$292$	−24366.2	−	48083.6i	−0.285774	−	0.563938i
$293$	−21779.0			−0.253689			−0.126845	−	0.991923i	$-0.540485\pi$
$293$	−21779.0			−0.253689			−0.126845	+	0.991923i	$0.540485\pi$
$294$	14802.4	−	24095.6i	0.171253	−	0.278768i
$295$		0			0
$296$	−3494.41	+	42596.1i	−0.0398832	+	0.486168i
$297$	10403.3			0.117939
$298$	65588.4	+	40292.3i	0.738574	+	0.453722i
$299$		−	1357.29i		−	0.0151821i
$300$		0			0
$301$	−60573.6			−0.668575
$302$	−88789.4	+	144533.i	−0.973525	+	1.58472i
$303$		−	15458.2i		−	0.168374i
$304$	−84201.5	−	61746.0i	−0.911113	−	0.668131i
$305$		0			0
$306$	47500.5	+	29180.5i	0.507288	+	0.311638i
$307$			129208.i			1.37092i	0.728111	+	0.685460i	$0.240399\pi$
$307$			129208.i			1.37092i	−0.728111	+	0.685460i	$0.759601\pi$
$308$	32892.0	+	64908.2i	0.346728	+	0.684223i
$309$	−93341.2			−0.977590
$310$		0			0
$311$		−	39962.2i		−	0.413170i	−0.978429	−	0.206585i	$-0.933765\pi$
$311$		−	39962.2i		−	0.413170i	0.978429	−	0.206585i	$-0.0662351\pi$
$312$	60109.4	+	4931.12i	0.617495	+	0.0506567i
$313$	−99259.1			−1.01317			−0.506584	−	0.862191i	$-0.669092\pi$
$313$	−99259.1			−1.01317			−0.506584	+	0.862191i	$0.669092\pi$
$314$	−47644.5	−	29269.0i	−0.483230	−	0.296858i
$315$		0			0
$316$	100765.	−	51062.2i	1.00910	−	0.511358i
$317$	−92350.2			−0.919008			−0.459504	−	0.888176i	$-0.651973\pi$
$317$	−92350.2			−0.919008			−0.459504	+	0.888176i	$0.651973\pi$
$318$	−24888.0	+	40513.0i	−0.246114	+	0.400627i
$319$		−	109262.i		−	1.07371i
$320$		0			0
$321$	−6237.87			−0.0605378
$322$	1564.42	+	961.056i	0.0150883	+	0.00926908i
$323$		−	210535.i		−	2.01799i
$324$	5272.38	+	10404.4i	0.0502246	+	0.0991119i
$325$		0			0
$326$	−65103.7	+	105977.i	−0.612591	+	0.997184i
$327$			85741.0i			0.801850i
$328$	−6358.25	+	77505.8i	−0.0591004	+	0.720422i
$329$	−180510.			−1.66767
$330$		0			0
$331$		−	37376.0i		−	0.341143i	−0.985345	−	0.170572i	$-0.945439\pi$
$331$		−	37376.0i		−	0.341143i	0.985345	−	0.170572i	$-0.0545614\pi$
$332$	−70965.6	+	35961.6i	−0.643831	+	0.326259i
$333$	−18030.6			−0.162601
$334$	−63241.9	+	102946.i	−0.566907	+	0.922819i
$335$		0			0
$336$	−48245.2	+	65790.7i	−0.427342	+	0.582755i
$337$	−119047.			−1.04824			−0.524118	−	0.851645i	$-0.675605\pi$
$337$	−119047.			−1.04824			−0.524118	+	0.851645i	$0.675605\pi$
$338$	14757.0	+	9065.51i	0.129171	+	0.0793522i
$339$			31373.4i			0.272999i
$340$		0			0
$341$	−77193.7			−0.663855
$342$	23057.5	−	37533.4i	0.197133	−	0.320897i
$343$		−	63810.8i		−	0.542383i
$344$	62997.3	+	5168.03i	0.532359	+	0.0436725i
$345$		0			0
$346$	75191.1	+	46191.5i	0.628079	+	0.385842i
$347$			84780.6i			0.704105i	0.935980	+	0.352052i	$0.114516\pi$
$347$			84780.6i			0.704105i	−0.935980	+	0.352052i	$0.885484\pi$
$348$	109273.	−	55373.6i	0.902304	−	0.457240i
$349$	−171629.			−1.40909			−0.704545	−	0.709659i	$-0.748849\pi$
$349$	−171629.			−1.40909			−0.704545	+	0.709659i	$0.748849\pi$
$350$		0			0
$351$			25443.8i			0.206523i
$352$	−28670.2	−	70311.6i	−0.231391	−	0.567468i
$353$	−195140.			−1.56602			−0.783010	−	0.622009i	$-0.786317\pi$
$353$	−195140.			−1.56602			−0.783010	+	0.622009i	$0.786317\pi$
$354$	6918.95	+	4250.45i	0.0552120	+	0.0339179i
$355$		0			0
$356$	−89468.9	−	176555.i	−0.705947	−	1.39310i
$357$	−164501.			−1.29072
$358$	−9003.66	+	14656.3i	−0.0702511	+	0.114356i
$359$			50318.4i			0.390426i	0.980761	+	0.195213i	$0.0625398\pi$
$359$			50318.4i			0.390426i	−0.980761	+	0.195213i	$0.937460\pi$
$360$		0			0
$361$	−36037.2			−0.276527
$362$	−110046.	−	67603.6i	−0.839764	−	0.515884i
$363$			47505.3i			0.360520i
$364$	−158749.	+	80445.4i	−1.19814	+	0.607154i
$365$		0			0
$366$	−44702.3	+	72767.1i	−0.333709	+	0.543216i
$367$			50718.2i			0.376558i	0.982116	+	0.188279i	$0.0602909\pi$
$367$			50718.2i			0.376558i	−0.982116	+	0.188279i	$0.939709\pi$
$368$	−1545.02	−	1132.98i	−0.0114088	−	0.00836619i
$369$	−32807.6			−0.240947
$370$		0			0
$371$		−	140303.i		−	1.01934i
$372$	−39121.6	−	77201.5i	−0.282703	−	0.557879i
$373$	119570.			0.859417			0.429709	−	0.902968i	$-0.358616\pi$
$373$	119570.			0.859417			0.429709	+	0.902968i	$0.358616\pi$
$374$	80141.1	−	130455.i	0.572944	−	0.932646i
$375$		0			0
$376$	187733.	+	15400.8i	1.32790	+	0.108935i
$377$	267226.			1.88016
$378$	−29326.6	−	18016.0i	−0.205248	−	0.126088i
$379$		−	104060.i		−	0.724447i	−0.932091	−	0.362223i	$-0.882018\pi$
$379$		−	104060.i		−	0.724447i	0.932091	−	0.362223i	$-0.117982\pi$
$380$		0			0
$381$	90847.8			0.625842
$382$	48447.8	−	78864.0i	0.332007	−	0.540446i
$383$			72442.8i			0.493853i	0.969034	+	0.246926i	$0.0794206\pi$
$383$			72442.8i			0.493853i	−0.969034	+	0.246926i	$0.920579\pi$
$384$	55788.7	−	64306.9i	0.378341	−	0.436109i
$385$		0			0
$386$	220768.	+	135622.i	1.48171	+	0.910242i
$387$			26666.3i			0.178049i
$388$	−18198.9	−	35913.2i	−0.120888	−	0.238556i
$389$	−162511.			−1.07395			−0.536975	−	0.843598i	$-0.680433\pi$
$389$	−162511.			−1.07395			−0.536975	+	0.843598i	$0.680433\pi$
$390$		0			0
$391$		−	3863.13i		−	0.0252689i
$392$	7119.52	−	86785.5i	0.0463317	−	0.564775i
$393$	−55590.0			−0.359925
$394$	−1081.58	−	664.435i	−0.00696731	−	0.00428016i
$395$		0			0
$396$	28574.5	−	14480.0i	0.182216	−	0.0923376i
$397$	−53291.6			−0.338125			−0.169063	−	0.985605i	$-0.554074\pi$
$397$	−53291.6			−0.338125			−0.169063	+	0.985605i	$0.554074\pi$
$398$	−37794.9	+	61523.1i	−0.238598	+	0.388394i
$399$			129984.i			0.816476i
$400$		0			0
$401$	−33793.7			−0.210159			−0.105079	−	0.994464i	$-0.533510\pi$
$401$	−33793.7			−0.210159			−0.105079	+	0.994464i	$0.533510\pi$
$402$	−109216.	−	67093.4i	−0.675823	−	0.415172i
$403$		−	188796.i		−	1.16247i
$404$	−21515.8	−	42458.6i	−0.131824	−	0.260138i
$405$		0			0
$406$	−189214.	+	308005.i	−1.14789	+	1.86856i
$407$			49519.1i			0.298940i
$408$	171083.	+	14035.0i	1.02775	+	0.0843123i
$409$	192978.			1.15361			0.576807	−	0.816881i	$-0.304299\pi$
$409$	192978.			1.15361			0.576807	+	0.816881i	$0.304299\pi$
$410$		0			0
$411$		−	162429.i		−	0.961565i
$412$	−256377.	+	129918.i	−1.51038	+	0.765379i
$413$	−23961.4			−0.140479
$414$	423.085	−	688.703i	0.00246846	−	0.00401820i
$415$		0			0
$416$	171964.	−	70120.1i	0.993691	−	0.405187i
$417$	116826.			0.671840
$418$	−103081.	−	63325.0i	−0.589966	−	0.362428i
$419$		−	207731.i		−	1.18324i	−0.806216	−	0.591621i	$-0.798488\pi$
$419$		−	207731.i		−	1.18324i	0.806216	−	0.591621i	$-0.201512\pi$
$420$		0			0
$421$	−135957.			−0.767075			−0.383538	−	0.923525i	$-0.625294\pi$
$421$	−135957.			−0.767075			−0.383538	+	0.923525i	$0.625294\pi$
$422$	131590.	−	214204.i	0.738922	−	1.20283i
$423$			79465.8i			0.444119i
$424$	−11970.4	+	145917.i	−0.0665850	+	0.811658i
$425$		0			0
$426$	−79033.1	−	48551.7i	−0.435502	−	0.267538i
$427$		−	252004.i		−	1.38214i
$428$	−17133.4	+	8682.28i	−0.0935309	+	0.0473965i
$429$	69878.7			0.379691
$430$		0			0
$431$		−	151994.i		−	0.818222i	−0.912485	−	0.409111i	$-0.865839\pi$
$431$		−	151994.i		−	0.818222i	0.912485	−	0.409111i	$-0.134161\pi$
$432$	28963.0	+	21238.9i	0.155194	+	0.113806i
$433$	36457.2			0.194450			0.0972249	−	0.995262i	$-0.469003\pi$
$433$	36457.2			0.194450			0.0972249	+	0.995262i	$0.469003\pi$
$434$	217607.	+	133680.i	1.15530	+	0.709722i
$435$		0			0
$436$	119340.	+	235502.i	0.627788	+	1.23886i
$437$	−3052.52			−0.0159844
$438$	36653.7	−	59665.4i	0.191060	−	0.311010i
$439$		−	118065.i		−	0.612620i	−0.951932	−	0.306310i	$-0.900906\pi$
$439$		−	118065.i		−	0.612620i	0.951932	−	0.306310i	$-0.0990944\pi$
$440$		0			0
$441$	36735.6			0.188891
$442$	319059.	+	196005.i	1.63315	+	1.00328i
$443$		−	113592.i		−	0.578817i	−0.957206	−	0.289409i	$-0.906541\pi$
$443$		−	113592.i		−	0.578817i	0.957206	−	0.289409i	$-0.0934587\pi$
$444$	−49524.1	+	25096.2i	−0.251218	+	0.127304i
$445$		0			0
$446$	127146.	−	206971.i	0.639196	−	1.04049i
$447$			99994.7i			0.500452i
$448$	−40941.7	+	247856.i	−0.203990	+	1.23493i
$449$	−1745.18			−0.00865662			−0.00432831	−	0.999991i	$-0.501378\pi$
$449$	−1745.18			−0.00865662			−0.00432831	+	0.999991i	$0.501378\pi$
$450$		0			0
$451$			90102.5i			0.442980i
$452$	43667.5	+	86172.2i	0.213738	+	0.421784i
$453$	−220352.			−1.07379
$454$	−206506.	+	336153.i	−1.00189	+	1.63089i
$455$		0			0
$456$	11090.0	−	135185.i	0.0533337	−	0.650126i
$457$	74606.1			0.357225			0.178613	−	0.983919i	$-0.442839\pi$
$457$	74606.1			0.357225			0.178613	+	0.983919i	$0.442839\pi$
$458$	191987.	+	117941.i	0.915250	+	0.562257i
$459$			72418.3i			0.343734i
$460$		0			0
$461$	17305.9			0.0814314			0.0407157	−	0.999171i	$-0.487036\pi$
$461$	17305.9			0.0814314			0.0407157	+	0.999171i	$0.487036\pi$
$462$	−49478.9	+	80542.4i	−0.231812	+	0.377347i
$463$			124639.i			0.581422i	0.956811	+	0.290711i	$0.0938918\pi$
$463$			124639.i			0.581422i	−0.956811	+	0.290711i	$0.906108\pi$
$464$	223063.	−	304186.i	1.03608	−	1.41287i
$465$		0			0
$466$	−178964.	−	109941.i	−0.824128	−	0.506279i
$467$		−	208541.i		−	0.956219i	−0.878300	−	0.478110i	$-0.841322\pi$
$467$		−	208541.i		−	0.956219i	0.878300	−	0.478110i	$-0.158678\pi$
$468$	35414.4	+	69885.8i	0.161692	+	0.319078i
$469$	378230.			1.71953
$470$		0			0
$471$		−	72637.9i		−	0.327432i
$472$	24920.1	+	2044.34i	0.111858	+	0.00917634i
$473$	73235.9			0.327342
$474$	125036.	+	76812.0i	0.556515	+	0.341879i
$475$		0			0
$476$	−451831.	+	228964.i	−1.99417	+	1.01054i
$477$	−61765.3			−0.271461
$478$	−107080.	+	174306.i	−0.468654	+	0.762882i
$479$			399291.i			1.74028i	0.492805	+	0.870140i	$0.335972\pi$
$479$			399291.i			1.74028i	−0.492805	+	0.870140i	$0.664028\pi$
$480$		0			0
$481$	−121111.			−0.523472
$482$	24.0673	+	14.7850i	0.000103594	+	6.36397e-5i
$483$			2385.08i			0.0102237i
$484$	66121.0	+	130481.i	0.282260	+	0.557003i
$485$		0			0
$486$	−7931.15	+	12910.4i	−0.0335787	+	0.0546598i
$487$			432403.i			1.82318i	0.411097	+	0.911592i	$0.365146\pi$
$487$			432403.i			1.82318i	−0.411097	+	0.911592i	$0.634854\pi$
$488$	−21500.5	+	262087.i	−0.0902836	+	1.10054i
$489$	−161570.			−0.675683
$490$		0			0
$491$			266902.i			1.10710i	0.832814	+	0.553552i	$0.186728\pi$
$491$			266902.i			1.10710i	−0.832814	+	0.553552i	$0.813272\pi$
$492$	−90111.7	+	45663.8i	−0.372264	+	0.188643i
$493$	760578.			3.12932
$494$	154877.	−	252110.i	0.634647	−	1.03309i
$495$		0			0
$496$	−214908.	−	157595.i	−0.873554	−	0.640589i
$497$	273704.			1.10807
$498$	−88058.8	−	54096.4i	−0.355070	−	0.218127i
$499$		−	21287.2i		−	0.0854905i	−0.999086	−	0.0427452i	$-0.986390\pi$
$499$		−	21287.2i		−	0.0854905i	0.999086	−	0.0427452i	$-0.0136104\pi$
$500$		0			0
$501$	−156949.			−0.625294
$502$	−126603.	+	206086.i	−0.502385	+	0.817790i
$503$			267207.i			1.05612i	0.849208	+	0.528058i	$0.177080\pi$
$503$			267207.i			1.05612i	−0.849208	+	0.528058i	$0.822920\pi$
$504$	−105626.	−	8665.15i	−0.415826	−	0.0341126i
$505$		0			0
$506$	−1891.45	−	1161.96i	−0.00738743	−	0.00453825i
$507$			22498.2i			0.0875249i
$508$	249529.	−	126448.i	0.966926	−	0.489987i
$509$	449991.			1.73687			0.868437	−	0.495800i	$-0.165125\pi$
$509$	449991.			1.73687			0.868437	+	0.495800i	$0.165125\pi$
$510$		0			0
$511$			206630.i			0.791320i
$512$	63726.5	−	254280.i	0.243097	−	0.970002i
$513$	57222.6			0.217437
$514$	−130657.	−	80265.0i	−0.494544	−	0.303809i
$515$		0			0
$516$	37115.8	+	73243.4i	0.139399	+	0.275086i
$517$	218244.			0.816509
$518$	85754.8	−	139593.i	0.319594	−	0.520240i
$519$			114635.i			0.425581i
$520$		0			0
$521$	147922.			0.544951			0.272475	−	0.962163i	$-0.412158\pi$
$521$	147922.			0.544951			0.272475	+	0.962163i	$0.412158\pi$
$522$	135593.	+	83297.5i	0.497618	+	0.305697i
$523$		−	329638.i		−	1.20513i	−0.798070	−	0.602565i	$-0.794145\pi$
$523$		−	329638.i		−	1.20513i	0.798070	−	0.602565i	$-0.205855\pi$
$524$	−152687.	+	77373.8i	−0.556084	+	0.281794i
$525$		0			0
$526$	81346.6	−	132417.i	0.294014	−	0.478600i
$527$		−	537351.i		−	1.93480i
$528$	58330.4	−	79543.6i	0.209231	−	0.285323i
$529$	279785.			0.999800
$530$		0			0
$531$			10548.5i			0.0374112i
$532$	180920.	+	357022.i	0.639239	+	1.26146i
$533$	−220368.			−0.775700
$534$	134586.	−	219082.i	0.471975	−	0.768287i
$535$		0			0
$536$	−393364.	−	32270.0i	−1.36919	−	0.112323i
$537$	−22344.7			−0.0774865
$538$	−63817.7	−	39204.6i	−0.220484	−	0.135448i
$539$		−	100890.i		−	0.347274i
$540$		0			0
$541$	412276.			1.40862			0.704309	−	0.709894i	$-0.251257\pi$
$541$	412276.			1.40862			0.704309	+	0.709894i	$0.251257\pi$
$542$	53683.0	−	87385.9i	0.182742	−	0.297470i
$543$		−	167774.i		−	0.569017i
$544$	489444.	−	199576.i	1.65389	−	0.674388i
$545$		0			0
$546$	−196986.	−	121013.i	−0.660770	−	0.405925i
$547$			37918.1i			0.126728i	0.997990	+	0.0633638i	$0.0201829\pi$
$547$			37918.1i			0.126728i	−0.997990	+	0.0633638i	$0.979817\pi$
$548$	−226079.	−	446137.i	−0.752833	−	1.48562i
$549$	−110939.			−0.368079
$550$		0			0
$551$		−	600985.i		−	1.97952i
$552$	203.491	−	2480.52i	0.000667832	−	0.00814074i
$553$	−433017.			−1.41597
$554$	237540.	+	145926.i	0.773959	+	0.475459i
$555$		0			0
$556$	320881.	−	162606.i	1.03799	−	0.526000i
$557$	−229026.			−0.738200			−0.369100	−	0.929390i	$-0.620334\pi$
$557$	−229026.			−0.738200			−0.369100	+	0.929390i	$0.620334\pi$
$558$	58850.0	−	95796.8i	0.189007	−	0.307668i
$559$			179116.i			0.573207i
$560$		0			0
$561$	198889.			0.631953
$562$	−238237.	−	146354.i	−0.754286	−	0.463374i
$563$			529561.i			1.67070i	0.549717	+	0.835351i	$0.314735\pi$
$563$			529561.i			1.67070i	−0.549717	+	0.835351i	$0.685265\pi$
$564$	110606.	+	218266.i	0.347712	+	0.686164i
$565$		0			0
$566$	225340.	−	366811.i	0.703403	−	1.14501i
$567$		−	44710.8i		−	0.139074i
$568$	−284655.	−	23351.9i	−0.882312	−	0.0723812i
$569$	273177.			0.843760			0.421880	−	0.906652i	$-0.361370\pi$
$569$	273177.			0.843760			0.421880	+	0.906652i	$0.361370\pi$
$570$		0			0
$571$			465596.i			1.42803i	0.700132	+	0.714014i	$0.253125\pi$
$571$			465596.i			1.42803i	−0.700132	+	0.714014i	$0.746875\pi$
$572$	191934.	−	97261.8i	0.586623	−	0.297269i
$573$	120235.			0.366201
$574$	156035.	−	253996.i	0.473586	−	0.770910i
$575$		0			0
$576$	109113.	+	18023.7i	0.328877	+	0.0543249i
$577$	−292168.			−0.877570			−0.438785	−	0.898592i	$-0.644591\pi$
$577$	−292168.			−0.877570			−0.438785	+	0.898592i	$0.644591\pi$
$578$	623446.	+	382996.i	1.86613	+	1.14641i
$579$			336579.i			1.00399i
$580$		0			0
$581$	304961.			0.903426
$582$	27376.3	−	44563.5i	0.0808218	−	0.131563i
$583$			169632.i			0.499080i
$584$	17629.3	−	214898.i	0.0516905	−	0.630096i
$585$		0			0
$586$	−74228.2	−	45599.9i	−0.216159	−	0.132791i
$587$		−	184222.i		−	0.534644i	−0.963607	−	0.267322i	$-0.913861\pi$
$587$		−	184222.i		−	0.534644i	0.963607	−	0.267322i	$-0.0861387\pi$
$588$	100901.	−	51131.1i	0.291836	−	0.147887i
$589$	−424598.			−1.22390
$590$		0			0
$591$		−	1648.95i		−	0.00472099i
$592$	−101096.	+	137862.i	−0.288463	+	0.393370i
$593$	385641.			1.09666			0.548332	−	0.836261i	$-0.315263\pi$
$593$	385641.			1.09666			0.548332	+	0.836261i	$0.315263\pi$
$594$	35457.1	+	21782.0i	0.100492	+	0.0617342i
$595$		0			0
$596$	139179.	+	274652.i	0.391816	+	0.773198i
$597$	−93797.0			−0.263172
$598$	2841.85	−	4626.00i	0.00794691	−	0.0129361i
$599$		−	316862.i		−	0.883115i	−0.897233	−	0.441557i	$-0.854426\pi$
$599$		−	316862.i		−	0.883115i	0.897233	−	0.441557i	$-0.145574\pi$
$600$		0			0
$601$	−388882.			−1.07663			−0.538317	−	0.842742i	$-0.680940\pi$
$601$	−388882.			−1.07663			−0.538317	+	0.842742i	$0.680940\pi$
$602$	−206450.	−	126827.i	−0.569668	−	0.349959i
$603$		−	166508.i		−	0.457931i
$604$	−605233.	+	306700.i	−1.65901	+	0.840698i
$605$		0			0
$606$	32365.8	−	52685.5i	0.0881335	−	0.143465i
$607$			235572.i			0.639362i	0.947525	+	0.319681i	$0.103576\pi$
$607$			235572.i			0.639362i	−0.947525	+	0.319681i	$0.896424\pi$
$608$	−157698.	−	386743.i	−0.426599	−	1.04620i
$609$	−469579.			−1.26612
$610$		0			0
$611$			533769.i			1.42979i
$612$	100797.	+	198909.i	0.269118	+	0.531070i
$613$	74819.9			0.199111			0.0995557	−	0.995032i	$-0.468258\pi$
$613$	74819.9			0.199111			0.0995557	+	0.995032i	$0.468258\pi$
$614$	−270530.	+	440372.i	−0.717594	+	1.16811i
$615$		0			0
$616$	−23797.9	+	290091.i	−0.0627158	+	0.764493i
$617$	−476184.			−1.25085			−0.625424	−	0.780285i	$-0.715074\pi$
$617$	−476184.			−1.25085			−0.625424	+	0.780285i	$0.715074\pi$
$618$	−318130.	−	195434.i	−0.832968	−	0.511709i
$619$			95751.1i			0.249898i	0.992163	+	0.124949i	$0.0398767\pi$
$619$			95751.1i			0.249898i	−0.992163	+	0.124949i	$0.960123\pi$
$620$		0			0
$621$	1049.98			0.00272270
$622$	83671.3	−	136201.i	0.216270	−	0.352047i
$623$			758713.i			1.95480i
$624$	194543.	+	142661.i	0.499628	+	0.366384i
$625$		0			0
$626$	−338300.	−	207825.i	−0.863283	−	0.530332i
$627$		−	157156.i		−	0.399756i
$628$	−101102.	−	199512.i	−0.256355	−	0.505883i
$629$	−344706.			−0.871260
$630$		0			0
$631$		−	363696.i		−	0.913439i	−0.889611	−	0.456720i	$-0.849024\pi$
$631$		−	363696.i		−	0.913439i	0.889611	−	0.456720i	$-0.150976\pi$
$632$	450343.	+	36944.3i	1.12748	+	0.0924939i
$633$	326572.			0.815026
$634$	−314753.	−	193359.i	−0.783053	−	0.481045i
$635$		0			0
$636$	−169649.	+	85969.1i	−0.419408	+	0.212534i
$637$	246752.			0.608110
$638$	228767.	−	372391.i	0.562021	−	0.914866i
$639$		−	120492.i		−	0.295092i
$640$		0			0
$641$	11650.4			0.0283547			0.0141773	−	0.999899i	$-0.495487\pi$
$641$	11650.4			0.0283547			0.0141773	+	0.999899i	$0.495487\pi$
$642$	−21260.2	−	13060.6i	−0.0515820	−	0.0316879i
$643$			477647.i			1.15527i	0.816294	+	0.577637i	$0.196025\pi$
$643$			477647.i			1.15527i	−0.816294	+	0.577637i	$0.803975\pi$
$644$	3319.72	+	6551.04i	0.00800441	+	0.0157957i
$645$		0			0
$646$	440810.	−	717557.i	1.05630	−	1.71946i
$647$			184457.i			0.440642i	0.975427	+	0.220321i	$0.0707105\pi$
$647$			184457.i			0.440642i	−0.975427	+	0.220321i	$0.929289\pi$
$648$	−3814.65	+	46499.8i	−0.00908457	+	0.110739i
$649$	28970.3			0.0687802
$650$		0			0
$651$			331759.i			0.782818i
$652$	−443779.	+	224884.i	−1.04393	+	0.529009i
$653$	−105463.			−0.247329			−0.123664	−	0.992324i	$-0.539465\pi$
$653$	−105463.			−0.247329			−0.123664	+	0.992324i	$0.539465\pi$
$654$	−179521.	+	292227.i	−0.419720	+	0.683226i
$655$		0			0
$656$	−183949.	+	250847.i	−0.427455	+	0.582909i
$657$	90964.7			0.210738
$658$	−615223.	−	377944.i	−1.42096	−	0.872924i
$659$		−	434371.i		−	1.00021i	−0.865966	−	0.500103i	$-0.833295\pi$
$659$		−	434371.i		−	1.00021i	0.865966	−	0.500103i	$-0.166705\pi$
$660$		0			0
$661$	−474718.			−1.08651			−0.543254	−	0.839568i	$-0.682808\pi$
$661$	−474718.			−1.08651			−0.543254	+	0.839568i	$0.682808\pi$
$662$	78256.3	−	127387.i	0.178568	−	0.290675i
$663$			486431.i			1.10661i
$664$	−317163.	−	26018.8i	−0.719361	−	0.0590134i
$665$		0			0
$666$	−61452.8	−	37751.8i	−0.138546	−	0.0851116i
$667$		−	11027.5i		−	0.0247871i
$668$	−431088.	+	218453.i	−0.966080	+	0.489558i
$669$	315544.			0.705029
$670$		0			0
$671$			304683.i			0.676710i
$672$	−302181.	+	123217.i	−0.669159	+	0.272856i
$673$	701401.			1.54859			0.774295	−	0.632825i	$-0.218105\pi$
$673$	701401.			1.54859			0.774295	+	0.632825i	$0.218105\pi$
$674$	−405743.	−	249256.i	−0.893164	−	0.548689i
$675$		0			0
$676$	31314.4	+	61795.1i	0.0685254	+	0.135226i
$677$	284255.			0.620199			0.310100	−	0.950704i	$-0.399638\pi$
$677$	284255.			0.620199			0.310100	+	0.950704i	$0.399638\pi$
$678$	−65688.2	+	106928.i	−0.142899	+	0.232613i
$679$			154330.i			0.334743i
$680$		0			0
$681$	−512492.			−1.10508
$682$	−263096.	−	161625.i	−0.565646	−	0.347488i
$683$		−	659478.i		−	1.41371i	−0.707361	−	0.706853i	$-0.750114\pi$
$683$		−	659478.i		−	1.41371i	0.707361	−	0.706853i	$-0.249886\pi$
$684$	157172.	−	79646.2i	0.335940	−	0.170237i
$685$		0			0
$686$	133604.	−	217483.i	0.283905	−	0.462144i
$687$			292699.i			0.620166i
$688$	203890.	+	149515.i	0.430744	+	0.315870i
$689$	−414876.			−0.873936
$690$		0			0
$691$			163007.i			0.341390i	0.985324	+	0.170695i	$0.0546012\pi$
$691$			163007.i			0.341390i	−0.985324	+	0.170695i	$0.945399\pi$
$692$	159556.	+	314864.i	0.333198	+	0.657523i
$693$	−122793.			−0.255687
$694$	−177510.	+	288953.i	−0.368556	+	0.599941i
$695$		0			0
$696$	488367.	+	40063.6i	1.00816	+	0.0827050i
$697$	−627211.			−1.29106
$698$	−584953.	−	359349.i	−1.20063	−	0.737574i
$699$		−	272846.i		−	0.558422i
$700$		0			0
$701$	270195.			0.549847			0.274924	−	0.961466i	$-0.411347\pi$
$701$	270195.			0.549847			0.274924	+	0.961466i	$0.411347\pi$
$702$	−53273.3	+	86719.0i	−0.108102	+	0.175971i
$703$			272376.i			0.551135i
$704$	49500.2	−	299668.i	0.0998760	−	0.604638i
$705$		0			0
$706$	−665087.	−	408577.i	−1.33435	−	0.819717i
$707$			182458.i			0.365026i
$708$	14682.1	+	28973.2i	0.0292901	+	0.0578003i
$709$	40040.3			0.0796534			0.0398267	−	0.999207i	$-0.487319\pi$
$709$	40040.3			0.0796534			0.0398267	+	0.999207i	$0.487319\pi$
$710$		0			0
$711$			190627.i			0.377090i
$712$	64732.1	−	789071.i	0.127691	−	1.55653i
$713$	−7790.99			−0.0153255
$714$	−560662.	−	344426.i	−1.09978	−	0.675616i
$715$		0			0
$716$	−61373.5	+	31100.8i	−0.119717	+	0.0606660i
$717$	−265744.			−0.516922
$718$	−105355.	+	171498.i	−0.204364	+	0.332667i
$719$		−	388789.i		−	0.752066i	−0.926606	−	0.376033i	$-0.877288\pi$
$719$		−	388789.i		−	0.752066i	0.926606	−	0.376033i	$-0.122712\pi$
$720$		0			0
$721$	1.10173e6			2.11937
$722$	−122824.	−	75453.3i	−0.235618	−	0.144745i
$723$			36.6925i			7.01941e-5i
$724$	−233519.	−	460820.i	−0.445497	−	0.879132i
$725$		0			0
$726$	−99464.7	+	161910.i	−0.188710	+	0.307185i
$727$		−	569739.i		−	1.07797i	−0.842315	−	0.538985i	$-0.818808\pi$
$727$		−	569739.i		−	1.07797i	0.842315	−	0.538985i	$-0.181192\pi$
$728$	−709489.	−	58203.5i	−1.33870	−	0.109821i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$			509801.i			0.954039i
$732$	−304714.	+	154413.i	−0.568682	+	0.288178i
$733$	−119853.			−0.223070			−0.111535	−	0.993760i	$-0.535577\pi$
$733$	−119853.			−0.223070			−0.111535	+	0.993760i	$0.535577\pi$
$734$	−106192.	+	172860.i	−0.197105	+	0.320851i
$735$		0			0
$736$	−2893.62	−	7096.39i	−0.00534178	−	0.0131003i
$737$	−457296.			−0.841904
$738$	−111817.	−	68691.3i	−0.205302	−	0.126121i
$739$		−	543414.i		−	0.995044i	−0.867451	−	0.497522i	$-0.834243\pi$
$739$		−	543414.i		−	0.995044i	0.867451	−	0.497522i	$-0.165757\pi$
$740$		0			0
$741$	384363.			0.700011
$742$	293760.	−	478187.i	0.533562	−	0.868540i
$743$		−	33513.7i		−	0.0607078i	−0.999539	−	0.0303539i	$-0.990337\pi$
$743$		−	33513.7i		−	0.0607078i	0.999539	−	0.0303539i	$-0.00966343\pi$
$744$	28305.1	−	345033.i	0.0511351	−	0.623326i
$745$		0			0
$746$	407524.	+	250351.i	0.732277	+	0.449853i
$747$		−	134253.i		−	0.240592i
$748$	546282.	−	276827.i	0.976368	−	0.494771i
$749$	73627.4			0.131243
$750$		0			0
$751$			483614.i			0.857471i	0.903430	+	0.428735i	$0.141041\pi$
$751$			483614.i			0.857471i	−0.903430	+	0.428735i	$0.858959\pi$
$752$	607594.	+	445557.i	1.07443	+	0.787893i
$753$	−314195.			−0.554127
$754$	910773.	+	559506.i	1.60202	+	0.984153i
$755$		0			0
$756$	−62231.5	−	122806.i	−0.108885	−	0.214870i
$757$	154021.			0.268774			0.134387	−	0.990929i	$-0.457094\pi$
$757$	154021.			0.268774			0.134387	+	0.990929i	$0.457094\pi$
$758$	217877.	−	354663.i	0.379204	−	0.617274i
$759$		−	2883.66i		−	0.00500566i
$760$		0			0
$761$	−242974.			−0.419557			−0.209779	−	0.977749i	$-0.567274\pi$
$761$	−242974.			−0.419557			−0.209779	+	0.977749i	$0.567274\pi$
$762$	309632.	+	190213.i	0.533256	+	0.327590i
$763$		−	1.01203e6i		−	1.73837i
$764$	330245.	−	167350.i	0.565782	−	0.286708i
$765$		0			0
$766$	−151678.	+	246903.i	−0.258502	+	0.420794i
$767$			70853.9i			0.120441i
$768$	324785.	−	102366.i	0.550647	−	0.173554i
$769$	−86574.7			−0.146399			−0.0731995	−	0.997317i	$-0.523321\pi$
$769$	−86574.7			−0.146399			−0.0731995	+	0.997317i	$0.523321\pi$
$770$		0			0
$771$		−	199196.i		−	0.335099i
$772$	468473.	+	924471.i	0.786049	+	1.55117i
$773$	−1.07093e6			−1.79227			−0.896133	−	0.443785i	$-0.853635\pi$
$773$	−1.07093e6			−1.79227			−0.896133	+	0.443785i	$0.853635\pi$
$774$	−55832.7	+	90885.3i	−0.0931980	+	0.151709i
$775$		0			0
$776$	13167.2	−	160505.i	0.0218660	−	0.266542i
$777$	212821.			0.352510
$778$	−553879.	−	340259.i	−0.915073	−	0.562148i
$779$			495602.i			0.816692i
$780$		0			0
$781$	−330919.			−0.542525
$782$	8088.46	−	13166.5i	0.0132267	−	0.0215307i
$783$			206722.i			0.337181i
$784$	205973.	−	280880.i	0.335103	−	0.456972i
$785$		0			0
$786$	−189465.	−	116392.i	−0.306678	−	0.188399i
$787$		−	751269.i		−	1.21296i	−0.795099	−	0.606479i	$-0.792581\pi$
$787$		−	751269.i		−	1.21296i	0.795099	−	0.606479i	$-0.207419\pi$
$788$	−2295.12	−	4529.12i	−0.00369618	−	0.00729393i
$789$	201881.			0.324295
$790$		0			0
$791$		−	370309.i		−	0.591849i
$792$	127707.	+	10476.5i	0.203593	+	0.0167019i
$793$	−745176.			−1.18498
$794$	−181631.	−	111580.i	−0.288104	−	0.176988i
$795$		0			0
$796$	−257629.	+	130553.i	−0.406601	+	0.206044i
$797$	410930.			0.646921			0.323461	−	0.946242i	$-0.395154\pi$
$797$	410930.			0.646921			0.323461	+	0.946242i	$0.395154\pi$
$798$	−272155.	+	443017.i	−0.427376	+	0.695689i
$799$			1.51921e6i			2.37972i
$800$		0			0
$801$	334008.			0.520585
$802$	−115177.	−	70755.9i	−0.179068	−	0.110005i
$803$		−	249825.i		−	0.387440i
$804$	−231757.	−	457342.i	−0.358526	−	0.707505i
$805$		0			0
$806$	395293.	−	643464.i	0.608484	−	0.990500i
$807$		−	97295.3i		−	0.149398i
$808$	15567.0	−	189758.i	0.0238442	−	0.290655i
$809$	−81222.3			−0.124102			−0.0620510	−	0.998073i	$-0.519764\pi$
$809$	−81222.3			−0.124102			−0.0620510	+	0.998073i	$0.519764\pi$
$810$		0			0
$811$		−	665948.i		−	1.01251i	−0.862384	−	0.506254i	$-0.831030\pi$
$811$		−	665948.i		−	1.01251i	0.862384	−	0.506254i	$-0.168970\pi$
$812$	−1.28978e6	+	653590.i	−1.95615	+	0.991274i
$813$	133227.			0.201563
$814$	−103681.	+	168774.i	−0.156477	+	0.254716i
$815$		0			0
$816$	553709.	+	406042.i	0.831575	+	0.609805i
$817$	402829.			0.603499
$818$	657716.	+	404049.i	0.982951	+	0.603847i
$819$		−	300321.i		−	0.447732i
$820$		0			0
$821$	175974.			0.261074			0.130537	−	0.991443i	$-0.458330\pi$
$821$	175974.			0.261074			0.130537	+	0.991443i	$0.458330\pi$
$822$	340086.	−	553597.i	0.503321	−	0.819314i
$823$			825656.i			1.21899i	0.792790	+	0.609494i	$0.208627\pi$
$823$			825656.i			1.21899i	−0.792790	+	0.609494i	$0.791373\pi$
$824$	−1.14582e6	−	93998.0i	−1.68757	−	0.138441i
$825$		0			0
$826$	−81666.4	−	50169.4i	−0.119697	−	0.0735324i
$827$			184129.i			0.269222i	0.990899	+	0.134611i	$0.0429785\pi$
$827$			184129.i			0.269222i	−0.990899	+	0.134611i	$0.957022\pi$
$828$	2883.96	−	1461.44i	0.00420657	−	0.00213167i
$829$	−713518.			−1.03824			−0.519118	−	0.854703i	$-0.673739\pi$
$829$	−713518.			−1.03824			−0.519118	+	0.854703i	$0.673739\pi$
$830$		0			0
$831$			362149.i			0.524428i
$832$	732911.	+	121065.i	1.05878	+	0.174892i
$833$	702306.			1.01213
$834$	398171.	+	244605.i	0.572450	+	0.351668i
$835$		0			0
$836$	−218740.	−	431655.i	−0.312979	−	0.617624i
$837$	146050.			0.208473
$838$	434939.	−	708000.i	0.619356	−	1.00820i
$839$			1.30678e6i			1.85643i	0.372047	+	0.928214i	$0.378656\pi$
$839$			1.30678e6i			1.85643i	−0.372047	+	0.928214i	$0.621344\pi$
$840$		0			0
$841$	1.46383e6			2.06966
$842$	−463376.	−	284662.i	−0.653596	−	0.401518i
$843$		−	363211.i		−	0.511098i
$844$	896985.	−	454544.i	1.25922	−	0.638104i
$845$		0			0
$846$	−166382.	+	270839.i	−0.232469	+	0.378417i
$847$		−	560719.i		−	0.781589i
$848$	−346312.	+	472257.i	−0.481589	+	0.656730i
$849$	559233.			0.775849
$850$		0			0
$851$			4997.85i			0.00690120i
$852$	−167709.	−	330952.i	−0.231035	−	0.455918i
$853$	−590922.			−0.812143			−0.406071	−	0.913841i	$-0.633102\pi$
$853$	−590922.			−0.812143			−0.406071	+	0.913841i	$0.633102\pi$
$854$	527635.	−	858891.i	0.723465	−	1.17767i
$855$		0			0
$856$	−76573.4	−	6281.76i	−0.104503	−	0.00857302i
$857$	756073.			1.02944			0.514721	−	0.857358i	$-0.327895\pi$
$857$	756073.			1.02944			0.514721	+	0.857358i	$0.327895\pi$
$858$	238164.	+	146309.i	0.323521	+	0.198745i
$859$		−	1.02880e6i		−	1.39426i	−0.716945	−	0.697130i	$-0.754460\pi$
$859$		−	1.02880e6i		−	1.39426i	0.716945	−	0.697130i	$-0.245540\pi$
$860$		0			0
$861$	387238.			0.522362
$862$	318238.	−	518033.i	0.428290	−	0.697176i
$863$		−	520287.i		−	0.698589i	−0.937013	−	0.349294i	$-0.886421\pi$
$863$		−	520287.i		−	0.698589i	0.937013	−	0.349294i	$-0.113579\pi$
$864$	54243.9	+	133029.i	0.0726647	+	0.178205i
$865$		0			0
$866$	124255.	+	76332.6i	0.165683	+	0.101783i
$867$			950493.i			1.26448i
$868$	461764.	+	911232.i	0.612887	+	1.20946i
$869$	523536.			0.693277
$870$		0			0
$871$		−	1.11843e6i		−	1.47425i
$872$	−86344.3	+	1.05252e6i	−0.113554	+	1.38419i
$873$	67940.7			0.0891459
$874$	−10403.8	−	6391.25i	−0.0136197	−	0.00836686i
$875$		0			0
$876$	249850.	−	126611.i	0.325590	−	0.164992i
$877$	132059.			0.171699			0.0858496	−	0.996308i	$-0.472640\pi$
$877$	132059.			0.171699			0.0858496	+	0.996308i	$0.472640\pi$
$878$	247199.	−	402394.i	0.320670	−	0.521990i
$879$		−	113167.i		−	0.146468i
$880$		0			0
$881$	−485203.			−0.625132			−0.312566	−	0.949896i	$-0.601189\pi$
$881$	−485203.			−0.625132			−0.312566	+	0.949896i	$0.601189\pi$
$882$	125204.	+	76915.6i	0.160947	+	0.0988729i
$883$			454909.i			0.583449i	0.956502	+	0.291725i	$0.0942291\pi$
$883$			454909.i			0.583449i	−0.956502	+	0.291725i	$0.905771\pi$
$884$	677047.	+	1.33607e6i	0.866392	+	1.70971i
$885$		0			0
$886$	237835.	−	387151.i	0.302976	−	0.493189i
$887$			372656.i			0.473654i	0.971552	+	0.236827i	$0.0761075\pi$
$887$			372656.i			0.473654i	−0.971552	+	0.236827i	$0.923893\pi$
$888$	−221336.	−	18157.5i	−0.280689	−	0.0230266i
$889$	−1.07230e6			−1.35679
$890$		0			0
$891$			54057.2i			0.0680923i
$892$	866694.	−	439194.i	1.08927	−	0.551985i
$893$	1.20043e6			1.50534
$894$	−209365.	+	340807.i	−0.261956	+	0.426416i
$895$		0			0
$896$	−658490.	+	759033.i	−0.820226	+	0.945464i
$897$	7052.71			0.00876538
$898$	−5948.02	−	3653.99i	−0.00737598	−	0.00453122i
$899$		−	1.53390e6i		−	1.89792i
$900$		0			0
$901$	−1.18082e6			−1.45457
$902$	−188653.	+	307092.i	−0.231873	+	0.377447i
$903$		−	314750.i		−	0.386002i
$904$	−31594.1	+	385126.i	−0.0386607	+	0.471266i
$905$		0			0
$906$	−751014.	−	461363.i	−0.914938	−	0.562065i
$907$		−	354962.i		−	0.431487i	−0.976450	−	0.215743i	$-0.930783\pi$
$907$		−	354962.i		−	0.431487i	0.976450	−	0.215743i	$-0.0692175\pi$
$908$	−1.40765e6	+	713320.i	−1.70735	+	0.865192i
$909$	80323.3			0.0972106
$910$		0			0
$911$			108935.i			0.131260i	0.997844	+	0.0656298i	$0.0209056\pi$
$911$			108935.i			0.131260i	−0.997844	+	0.0656298i	$0.979094\pi$
$912$	320842.	−	437524.i	0.385746	−	0.526032i
$913$	−368711.			−0.442328
$914$	254276.	+	156207.i	0.304378	+	0.186986i
$915$		0			0
$916$	407398.	+	803947.i	0.485543	+	0.958157i
$917$	656145.			0.780299
$918$	−151626.	+	246820.i	−0.179924	+	0.292883i
$919$		−	306482.i		−	0.362889i	−0.983401	−	0.181444i	$-0.941923\pi$
$919$		−	306482.i		−	0.362889i	0.983401	−	0.181444i	$-0.0580772\pi$
$920$		0			0
$921$	−671383.			−0.791500
$922$	58982.8	+	36234.3i	0.0693846	+	0.0426244i
$923$		−	809343.i		−	0.950012i
$924$	−337273.	+	170912.i	−0.395037	+	0.200184i
$925$		0			0
$926$	−260964.	+	424800.i	−0.304339	+	0.495408i
$927$		−	485015.i		−	0.564412i
$928$	1.39715e6	−	569700.i	1.62236	−	0.661532i
$929$	230175.			0.266702			0.133351	−	0.991069i	$-0.457426\pi$
$929$	230175.			0.266702			0.133351	+	0.991069i	$0.457426\pi$
$930$		0			0
$931$		−	554940.i		−	0.640246i
$932$	−379764.	−	749416.i	−0.437202	−	0.862763i
$933$	207650.			0.238544
$934$	436634.	−	710760.i	0.500523	−	0.814759i
$935$		0			0
$936$	−25622.9	+	312338.i	−0.0292466	+	0.356511i
$937$	−1.06117e6			−1.20867			−0.604333	−	0.796732i	$-0.706560\pi$
$937$	−1.06117e6			−1.20867			−0.604333	+	0.796732i	$0.706560\pi$
$938$	1.28910e6	+	791923.i	1.46515	+	0.900073i
$939$		−	515765.i		−	0.584953i
$940$		0			0
$941$	−1.17032e6			−1.32168			−0.660838	−	0.750529i	$-0.729799\pi$
$941$	−1.17032e6			−1.32168			−0.660838	+	0.750529i	$0.729799\pi$
$942$	152086.	−	247568.i	0.171391	−	0.278993i
$943$			9093.85i			0.0102264i
$944$	80653.7	+	59144.4i	0.0905066	+	0.0663696i
$945$		0			0
$946$	249606.	+	153338.i	0.278916	+	0.171344i
$947$			605186.i			0.674822i	0.941357	+	0.337411i	$0.109551\pi$
$947$			605186.i			0.674822i	−0.941357	+	0.337411i	$0.890449\pi$
$948$	265327.	+	523589.i	0.295233	+	0.582604i
$949$	611007.			0.678444
$950$		0			0
$951$		−	479866.i		−	0.530590i
$952$	−2.01935e6	−	165659.i	−2.22811	−	0.182785i
$953$	1.26323e6			1.39090			0.695452	−	0.718572i	$-0.255204\pi$
$953$	1.26323e6			1.39090			0.695452	+	0.718572i	$0.255204\pi$
$954$	−210512.	−	129322.i	−0.231302	−	0.142094i
$955$		0			0
$956$	−729911.	+	369880.i	−0.798646	+	0.404711i
$957$	567740.			0.619905
$958$	−836020.	+	1.36089e6i	−0.910931	+	1.48283i
$959$			1.91719e6i			2.08463i
$960$		0			0
$961$	−160185.			−0.173451
$962$	−412777.	−	253577.i	−0.446031	−	0.274006i
$963$		−	32412.9i		−	0.0349515i
$964$	51.0710	+	100.782i	5.49567e−5	+	0.000108450i
$965$		0			0
$966$	−4993.79	+	8128.97i	−0.00535151	+	0.00871126i
$967$			1.65602e6i			1.77098i	0.464657	+	0.885491i	$0.346177\pi$
$967$			1.65602e6i			1.77098i	−0.464657	+	0.885491i	$0.653823\pi$
$968$	−47839.6	+	583155.i	−0.0510548	+	0.622348i
$969$	1.09397e6			1.16509
$970$		0			0
$971$		−	538842.i		−	0.571508i	−0.958303	−	0.285754i	$-0.907756\pi$
$971$		−	538842.i		−	0.571508i	0.958303	−	0.285754i	$-0.0922441\pi$
$972$	−54062.7	+	27396.1i	−0.0572223	+	0.0289972i
$973$	−1.37893e6			−1.45652
$974$	−905347.	+	1.47374e6i	−0.954327	+	1.55347i
$975$		0			0
$976$	−622026.	+	848241.i	−0.652993	+	0.890470i
$977$	−962571.			−1.00843			−0.504213	−	0.863579i	$-0.668217\pi$
$977$	−962571.			−1.00843			−0.504213	+	0.863579i	$0.668217\pi$
$978$	−550671.	−	338289.i	−0.575724	−	0.353679i
$979$		−	917315.i		−	0.957091i
$980$		0			0
$981$	−445523.			−0.462948
$982$	−558828.	+	909669.i	−0.579503	+	0.943323i
$983$			386329.i			0.399807i	0.979816	+	0.199903i	$0.0640628\pi$
$983$			386329.i			0.399807i	−0.979816	+	0.199903i	$0.935937\pi$
$984$	−402732.	−	33038.5i	−0.415936	−	0.0341216i
$985$		0			0
$986$	2.59224e6	+	1.59247e6i	2.66638	+	1.63801i
$987$		−	937958.i		−	0.962828i
$988$	1.05572e6	−	534981.i	1.08152	−	0.548055i
$989$	7391.54			0.00755688
$990$		0			0
$991$		−	18475.3i		−	0.0188124i	−0.999956	−	0.00940620i	$-0.997006\pi$
$991$		−	18475.3i		−	0.0188124i	0.999956	−	0.00940620i	$-0.00299413\pi$
$992$	−402495.	−	987090.i	−0.409014	−	1.00307i
$993$	194211.			0.196959
$994$	932851.	+	573070.i	0.944147	+	0.580009i
$995$		0			0
$996$	−186862.	−	368748.i	−0.188366	−	0.371716i
$997$	−177630.			−0.178701			−0.0893503	−	0.996000i	$-0.528479\pi$
$997$	−177630.			−0.178701			−0.0893503	+	0.996000i	$0.528479\pi$
$998$	44570.3	−	72552.1i	0.0447491	−	0.0728432i
$999$		−	93689.8i		−	0.0938775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.d.151.14		16
4.3	odd	2	inner	300.5.c.d.151.13		16
5.2	odd	4		300.5.f.b.199.12		32
5.3	odd	4		300.5.f.b.199.21		32
5.4	even	2		60.5.c.a.31.3	✓	16
15.14	odd	2		180.5.c.c.91.14		16
20.3	even	4		300.5.f.b.199.11		32
20.7	even	4		300.5.f.b.199.22		32
20.19	odd	2		60.5.c.a.31.4	yes	16
40.19	odd	2		960.5.e.f.511.5		16
40.29	even	2		960.5.e.f.511.16		16
60.59	even	2		180.5.c.c.91.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.3	✓	16	5.4	even	2
60.5.c.a.31.4	yes	16	20.19	odd	2
180.5.c.c.91.13		16	60.59	even	2
180.5.c.c.91.14		16	15.14	odd	2
300.5.c.d.151.13		16	4.3	odd	2	inner
300.5.c.d.151.14		16	1.1	even	1	trivial
300.5.f.b.199.11		32	20.3	even	4
300.5.f.b.199.12		32	5.2	odd	4
300.5.f.b.199.21		32	5.3	odd	4
300.5.f.b.199.22		32	20.7	even	4
960.5.e.f.511.5		16	40.19	odd	2
960.5.e.f.511.16		16	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(3.40825 + 2.09376i) q^{2} +5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} +(-10.8795 + 17.7098i) q^{6} -61.3317i q^{7} +(-5.23271 + 63.7857i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(3.40825 + 2.09376i) q^{2} +5.19615i q^{3} +(7.23235 + 14.2721i) q^{4} +(-10.8795 + 17.7098i) q^{6} -61.3317i q^{7} +(-5.23271 + 63.7857i) q^{8} -27.0000 q^{9} +74.1525i q^{11} +(-74.1601 + 37.5804i) q^{12} -181.358 q^{13} +(128.414 - 209.034i) q^{14} +(-151.386 + 206.442i) q^{16} -516.182 q^{17} +(-92.0228 - 56.5315i) q^{18} +407.870i q^{19} +318.689 q^{21} +(-155.258 + 252.730i) q^{22} +7.48405i q^{23} +(-331.440 - 27.1900i) q^{24} +(-618.114 - 379.720i) q^{26} -140.296i q^{27} +(875.333 - 443.572i) q^{28} -1473.47 q^{29} +1041.01i q^{31} +(-948.202 + 386.639i) q^{32} -385.308 q^{33} +(-1759.28 - 1080.76i) q^{34} +(-195.273 - 385.347i) q^{36} +667.800 q^{37} +(-853.982 + 1390.12i) q^{38} -942.365i q^{39} +1215.10 q^{41} +(1086.17 + 667.258i) q^{42} -987.639i q^{43} +(-1058.31 + 536.297i) q^{44} +(-15.6698 + 25.5075i) q^{46} -2943.18i q^{47} +(-1072.70 - 786.626i) q^{48} -1360.58 q^{49} -2682.16i q^{51} +(-1311.64 - 2588.36i) q^{52} +2287.61 q^{53} +(293.746 - 478.164i) q^{54} +(3912.09 + 320.931i) q^{56} -2119.36 q^{57} +(-5021.96 - 3085.09i) q^{58} -390.685i q^{59} +4108.86 q^{61} +(-2179.63 + 3548.03i) q^{62} +1655.96i q^{63} +(-4041.24 - 667.545i) q^{64} +(-1313.23 - 806.742i) q^{66} +6166.96i q^{67} +(-3733.20 - 7367.00i) q^{68} -38.8883 q^{69} +4462.68i q^{71} +(141.283 - 1722.21i) q^{72} -3369.06 q^{73} +(2276.03 + 1398.21i) q^{74} +(-5821.17 + 2949.86i) q^{76} +4547.90 q^{77} +(1973.08 - 3211.81i) q^{78} -7060.25i q^{79} +729.000 q^{81} +(4141.36 + 2544.12i) q^{82} +4972.33i q^{83} +(2304.87 + 4548.36i) q^{84} +(2067.88 - 3366.12i) q^{86} -7656.38i q^{87} +(-4729.87 - 388.019i) q^{88} -12370.7 q^{89} +11123.0i q^{91} +(-106.813 + 54.1273i) q^{92} -5409.26 q^{93} +(6162.30 - 10031.1i) q^{94} +(-2009.03 - 4927.00i) q^{96} -2516.32 q^{97} +(-4637.19 - 2848.72i) q^{98} -2002.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9} + 352 q^{13} - 804 q^{14} - 190 q^{16} - 324 q^{18} + 288 q^{21} - 436 q^{22} - 1998 q^{24} - 852 q^{26} + 1156 q^{28} - 3456 q^{29} - 7668 q^{32} + 4772 q^{34} - 702 q^{36} - 9376 q^{37} + 1320 q^{38} + 1248 q^{41} + 324 q^{42} - 6420 q^{44} - 1112 q^{46} + 4176 q^{48} - 3952 q^{49} - 12704 q^{52} + 5184 q^{53} - 486 q^{54} - 2604 q^{56} + 11232 q^{57} - 12708 q^{58} - 3808 q^{61} + 16152 q^{62} - 11902 q^{64} - 2916 q^{66} + 12312 q^{68} + 9792 q^{69} - 4860 q^{72} - 11040 q^{73} + 30516 q^{74} - 5160 q^{76} + 27456 q^{77} + 3600 q^{78} + 11664 q^{81} + 54040 q^{82} - 2052 q^{84} + 39768 q^{86} + 7220 q^{88} + 7584 q^{89} - 28848 q^{92} - 19872 q^{93} + 49776 q^{94} + 18882 q^{96} + 14496 q^{97} - 23940 q^{98}+O(q^{100}) \) 16 * q + 12 * q^2 + 26 * q^4 + 18 * q^6 + 180 * q^8 - 432 * q^9 + 352 * q^13 - 804 * q^14 - 190 * q^16 - 324 * q^18 + 288 * q^21 - 436 * q^22 - 1998 * q^24 - 852 * q^26 + 1156 * q^28 - 3456 * q^29 - 7668 * q^32 + 4772 * q^34 - 702 * q^36 - 9376 * q^37 + 1320 * q^38 + 1248 * q^41 + 324 * q^42 - 6420 * q^44 - 1112 * q^46 + 4176 * q^48 - 3952 * q^49 - 12704 * q^52 + 5184 * q^53 - 486 * q^54 - 2604 * q^56 + 11232 * q^57 - 12708 * q^58 - 3808 * q^61 + 16152 * q^62 - 11902 * q^64 - 2916 * q^66 + 12312 * q^68 + 9792 * q^69 - 4860 * q^72 - 11040 * q^73 + 30516 * q^74 - 5160 * q^76 + 27456 * q^77 + 3600 * q^78 + 11664 * q^81 + 54040 * q^82 - 2052 * q^84 + 39768 * q^86 + 7220 * q^88 + 7584 * q^89 - 28848 * q^92 - 19872 * q^93 + 49776 * q^94 + 18882 * q^96 + 14496 * q^97 - 23940 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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