LMFDB - Embedded newform 300.5.c.d.151.4

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			151.4
Root			$-2.48191 - 1.35651i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.d.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37483 + 3.21872i) q^{2} +5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} +(-16.7250 - 12.3400i) q^{6} +19.2859i q^{7} +(60.4174 + 21.1124i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-2.37483 + 3.21872i) q^{2} +5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} +(-16.7250 - 12.3400i) q^{6} +19.2859i q^{7} +(60.4174 + 21.1124i) q^{8} -27.0000 q^{9} -28.1695i q^{11} +(79.4379 - 24.5278i) q^{12} +28.6347 q^{13} +(-62.0759 - 45.8006i) q^{14} +(-211.436 + 144.329i) q^{16} -290.124 q^{17} +(64.1204 - 86.9056i) q^{18} -459.035i q^{19} -100.212 q^{21} +(90.6699 + 66.8978i) q^{22} +63.0305i q^{23} +(-109.703 + 313.938i) q^{24} +(-68.0024 + 92.1671i) q^{26} -140.296i q^{27} +(294.839 - 91.0366i) q^{28} +1141.80 q^{29} -1335.53i q^{31} +(37.5694 - 1023.31i) q^{32} +146.373 q^{33} +(688.996 - 933.831i) q^{34} +(127.450 + 412.772i) q^{36} -1365.02 q^{37} +(1477.51 + 1090.13i) q^{38} +148.790i q^{39} +1242.93 q^{41} +(237.987 - 322.556i) q^{42} +663.357i q^{43} +(-430.651 + 132.971i) q^{44} +(-202.878 - 149.687i) q^{46} -3936.26i q^{47} +(-749.955 - 1098.65i) q^{48} +2029.06 q^{49} -1507.53i q^{51} +(-135.166 - 437.762i) q^{52} +4618.99 q^{53} +(451.575 + 333.179i) q^{54} +(-407.170 + 1165.20i) q^{56} +2385.22 q^{57} +(-2711.59 + 3675.15i) q^{58} +2602.83i q^{59} -5396.32 q^{61} +(4298.69 + 3171.64i) q^{62} -520.718i q^{63} +(3204.53 + 2551.11i) q^{64} +(-347.611 + 471.135i) q^{66} +6033.14i q^{67} +(1369.50 + 4435.38i) q^{68} -327.516 q^{69} +955.221i q^{71} +(-1631.27 - 570.034i) q^{72} +8814.75 q^{73} +(3241.68 - 4393.61i) q^{74} +(-7017.65 + 2166.82i) q^{76} +543.273 q^{77} +(-478.914 - 353.351i) q^{78} +3717.96i q^{79} +729.000 q^{81} +(-2951.75 + 4000.66i) q^{82} -5992.78i q^{83} +(473.040 + 1532.03i) q^{84} +(-2135.16 - 1575.36i) q^{86} +5932.99i q^{87} +(594.726 - 1701.93i) q^{88} +10839.6 q^{89} +552.244i q^{91} +(963.600 - 297.528i) q^{92} +6939.59 q^{93} +(12669.8 + 9347.95i) q^{94} +(5317.28 + 195.216i) q^{96} -5581.91 q^{97} +(-4818.66 + 6530.97i) q^{98} +760.577i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.37483	+	3.21872i	−0.593707	+	0.804681i
$2$	−2.37483	+	3.21872i	−0.593707	+	0.804681i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−4.72038	−	15.2878i	−0.295024	−	0.955490i
$5$		0			0
$5$		0			0
$6$	−16.7250	−	12.3400i	−0.464583	−	0.342777i
$7$			19.2859i			0.393589i	0.980445	+	0.196794i	$0.0630532\pi$
$7$			19.2859i			0.393589i	−0.980445	+	0.196794i	$0.936947\pi$
$8$	60.4174	+	21.1124i	0.944023	+	0.329881i
$9$	−27.0000			−0.333333
$10$		0			0
$11$		−	28.1695i		−	0.232806i	−0.993202	−	0.116403i	$-0.962864\pi$
$11$		−	28.1695i		−	0.232806i	0.993202	−	0.116403i	$-0.0371364\pi$
$12$	79.4379	−	24.5278i	0.551652	−	0.170332i
$13$	28.6347			0.169436			0.0847179	−	0.996405i	$-0.473001\pi$
$13$	28.6347			0.169436			0.0847179	+	0.996405i	$0.473001\pi$
$14$	−62.0759	−	45.8006i	−0.316714	−	0.233677i
$15$		0			0
$16$	−211.436	+	144.329i	−0.825922	+	0.563785i
$17$	−290.124			−1.00389			−0.501945	−	0.864899i	$-0.667382\pi$
$17$	−290.124			−1.00389			−0.501945	+	0.864899i	$0.667382\pi$
$18$	64.1204	−	86.9056i	0.197902	−	0.268227i
$19$		−	459.035i		−	1.27156i	−0.771868	−	0.635782i	$-0.780678\pi$
$19$		−	459.035i		−	1.27156i	0.771868	−	0.635782i	$-0.219322\pi$
$20$		0			0
$21$	−100.212			−0.227239
$22$	90.6699	+	66.8978i	0.187335	+	0.138219i
$23$			63.0305i			0.119150i	0.998224	+	0.0595752i	$0.0189746\pi$
$23$			63.0305i			0.119150i	−0.998224	+	0.0595752i	$0.981025\pi$
$24$	−109.703	+	313.938i	−0.190457	+	0.545032i
$25$		0			0
$26$	−68.0024	+	92.1671i	−0.100595	+	0.136342i
$27$		−	140.296i		−	0.192450i
$28$	294.839	−	91.0366i	0.376070	−	0.116118i
$29$	1141.80			1.35767			0.678837	−	0.734289i	$-0.262484\pi$
$29$	1141.80			1.35767			0.678837	+	0.734289i	$0.262484\pi$
$30$		0			0
$31$		−	1335.53i		−	1.38972i	−0.719143	−	0.694862i	$-0.755465\pi$
$31$		−	1335.53i		−	1.38972i	0.719143	−	0.694862i	$-0.244535\pi$
$32$	37.5694	−	1023.31i	0.0366889	−	0.999327i
$33$	146.373			0.134411
$34$	688.996	−	933.831i	0.596017	−	0.807812i
$35$		0			0
$36$	127.450	+	412.772i	0.0983413	+	0.318497i
$37$	−1365.02			−0.997090			−0.498545	−	0.866864i	$-0.666132\pi$
$37$	−1365.02			−0.997090			−0.498545	+	0.866864i	$0.666132\pi$
$38$	1477.51	+	1090.13i	1.02320	+	0.754937i
$39$			148.790i			0.0978238i
$40$		0			0
$41$	1242.93			0.739401			0.369700	−	0.929151i	$-0.379460\pi$
$41$	1242.93			0.739401			0.369700	+	0.929151i	$0.379460\pi$
$42$	237.987	−	322.556i	0.134913	−	0.182855i
$43$			663.357i			0.358765i	0.983779	+	0.179383i	$0.0574100\pi$
$43$			663.357i			0.358765i	−0.983779	+	0.179383i	$0.942590\pi$
$44$	−430.651	+	132.971i	−0.222444	+	0.0686833i
$45$		0			0
$46$	−202.878	−	149.687i	−0.0958780	−	0.0707404i
$47$		−	3936.26i		−	1.78192i	−0.454080	−	0.890961i	$-0.650032\pi$
$47$		−	3936.26i		−	1.78192i	0.454080	−	0.890961i	$-0.349968\pi$
$48$	−749.955	−	1098.65i	−0.325501	−	0.476846i
$49$	2029.06			0.845088
$50$		0			0
$51$		−	1507.53i		−	0.579597i
$52$	−135.166	−	437.762i	−0.0499876	−	0.161894i
$53$	4618.99			1.64435			0.822177	−	0.569232i	$-0.192760\pi$
$53$	4618.99			1.64435			0.822177	+	0.569232i	$0.192760\pi$
$54$	451.575	+	333.179i	0.154861	+	0.114259i
$55$		0			0
$56$	−407.170	+	1165.20i	−0.129838	+	0.371557i
$57$	2385.22			0.734138
$58$	−2711.59	+	3675.15i	−0.806061	+	1.09250i
$59$			2602.83i			0.747725i	0.927484	+	0.373862i	$0.121967\pi$
$59$			2602.83i			0.747725i	−0.927484	+	0.373862i	$0.878033\pi$
$60$		0			0
$61$	−5396.32			−1.45023			−0.725117	−	0.688626i	$-0.758214\pi$
$61$	−5396.32			−1.45023			−0.725117	+	0.688626i	$0.758214\pi$
$62$	4298.69	+	3171.64i	1.11829	+	0.825089i
$63$		−	520.718i		−	0.131196i
$64$	3204.53	+	2551.11i	0.782357	+	0.622830i
$65$		0			0
$66$	−347.611	+	471.135i	−0.0798005	+	0.108158i
$67$			6033.14i			1.34398i	0.740559	+	0.671991i	$0.234561\pi$
$67$			6033.14i			1.34398i	−0.740559	+	0.671991i	$0.765439\pi$
$68$	1369.50	+	4435.38i	0.296172	+	0.959208i
$69$	−327.516			−0.0687915
$70$		0			0
$71$			955.221i			0.189490i	0.995502	+	0.0947452i	$0.0302036\pi$
$71$			955.221i			0.189490i	−0.995502	+	0.0947452i	$0.969796\pi$
$72$	−1631.27	−	570.034i	−0.314674	−	0.109960i
$73$	8814.75			1.65411			0.827055	−	0.562121i	$-0.190014\pi$
$73$	8814.75			1.65411			0.827055	+	0.562121i	$0.190014\pi$
$74$	3241.68	−	4393.61i	0.591979	−	0.802340i
$75$		0			0
$76$	−7017.65	+	2166.82i	−1.21497	+	0.375142i
$77$	543.273			0.0916298
$78$	−478.914	−	353.351i	−0.0787170	−	0.0580787i
$79$			3717.96i			0.595731i	0.954608	+	0.297866i	$0.0962747\pi$
$79$			3717.96i			0.595731i	−0.954608	+	0.297866i	$0.903725\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	−2951.75	+	4000.66i	−0.438988	+	0.594982i
$83$		−	5992.78i		−	0.869905i	−0.900453	−	0.434953i	$-0.856765\pi$
$83$		−	5992.78i		−	0.869905i	0.900453	−	0.434953i	$-0.143235\pi$
$84$	473.040	+	1532.03i	0.0670408	+	0.217124i
$85$		0			0
$86$	−2135.16	−	1575.36i	−0.288692	−	0.213002i
$87$			5932.99i			0.783854i
$88$	594.726	−	1701.93i	0.0767983	−	0.219774i
$89$	10839.6			1.36847			0.684233	−	0.729263i	$-0.260137\pi$
$89$	10839.6			1.36847			0.684233	+	0.729263i	$0.260137\pi$
$90$		0			0
$91$			552.244i			0.0666881i
$92$	963.600	−	297.528i	0.113847	−	0.0351522i
$93$	6939.59			0.802358
$94$	12669.8	+	9347.95i	1.43388	+	1.05794i
$95$		0			0
$96$	5317.28	+	195.216i	0.576962	+	0.0211823i
$97$	−5581.91			−0.593253			−0.296626	−	0.954994i	$-0.595862\pi$
$97$	−5581.91			−0.593253			−0.296626	+	0.954994i	$0.595862\pi$
$98$	−4818.66	+	6530.97i	−0.501735	+	0.680026i
$99$			760.577i			0.0776020i
$100$		0			0
$101$	18138.4			1.77810			0.889050	−	0.457809i	$-0.151366\pi$
$101$	18138.4			1.77810			0.889050	+	0.457809i	$0.151366\pi$
$102$	4852.33	+	3580.13i	0.466391	+	0.344111i
$103$		−	15849.0i		−	1.49392i	−0.664869	−	0.746960i	$-0.731513\pi$
$103$		−	15849.0i		−	1.49392i	0.664869	−	0.746960i	$-0.268487\pi$
$104$	1730.03	+	604.546i	0.159951	+	0.0558937i
$105$		0			0
$106$	−10969.3	+	14867.3i	−0.976264	+	1.32318i
$107$			2519.57i			0.220069i	0.993928	+	0.110035i	$0.0350962\pi$
$107$			2519.57i			0.220069i	−0.993928	+	0.110035i	$0.964904\pi$
$108$	−2144.82	+	662.251i	−0.183884	+	0.0567774i
$109$	1083.02			0.0911555			0.0455778	−	0.998961i	$-0.485487\pi$
$109$	1083.02			0.0911555			0.0455778	+	0.998961i	$0.485487\pi$
$110$		0			0
$111$		−	7092.83i		−	0.575670i
$112$	−2783.51	−	4077.72i	−0.221899	−	0.325074i
$113$	665.859			0.0521466			0.0260733	−	0.999660i	$-0.491700\pi$
$113$	665.859			0.0521466			0.0260733	+	0.999660i	$0.491700\pi$
$114$	−5664.48	+	7677.35i	−0.435863	+	0.590747i
$115$		0			0
$116$	−5389.75	−	17455.7i	−0.400546	−	1.29724i
$117$	−773.136			−0.0564786
$118$	−8377.79	−	6181.27i	−0.601680	−	0.443929i
$119$		−	5595.30i		−	0.395120i
$120$		0			0
$121$	13847.5			0.945801
$122$	12815.3	−	17369.3i	0.861014	−	1.16698i
$123$			6458.47i			0.426893i
$124$	−20417.3	+	6304.19i	−1.32787	+	0.410002i
$125$		0			0
$126$	1676.05	+	1236.62i	0.105571	+	0.0778922i
$127$			9928.67i			0.615579i	0.951454	+	0.307789i	$0.0995892\pi$
$127$			9928.67i			0.615579i	−0.951454	+	0.307789i	$0.900411\pi$
$128$	−15821.5	+	4256.06i	−0.965671	+	0.259769i
$129$	−3446.90			−0.207133
$130$		0			0
$131$		−	25186.1i		−	1.46764i	−0.679346	−	0.733818i	$-0.737736\pi$
$131$		−	25186.1i		−	1.46764i	0.679346	−	0.733818i	$-0.262264\pi$
$132$	−690.937	−	2237.73i	−0.0396543	−	0.128428i
$133$	8852.88			0.500474
$134$	−19419.0	−	14327.7i	−1.08148	−	0.797932i
$135$		0			0
$136$	−17528.6	−	6125.22i	−0.947696	−	0.331165i
$137$	3063.11			0.163200			0.0816002	−	0.996665i	$-0.473997\pi$
$137$	3063.11			0.163200			0.0816002	+	0.996665i	$0.473997\pi$
$138$	777.795	−	1054.18i	0.0408420	−	0.0553552i
$139$		−	23379.5i		−	1.21006i	−0.796204	−	0.605028i	$-0.793162\pi$
$139$		−	23379.5i		−	1.21006i	0.796204	−	0.605028i	$-0.206838\pi$
$140$		0			0
$141$	20453.4			1.02879
$142$	−3074.59	−	2268.49i	−0.152479	−	0.112502i
$143$		−	806.624i		−	0.0394457i
$144$	5708.77	−	3896.88i	0.275307	−	0.187928i
$145$		0			0
$146$	−20933.5	+	28372.3i	−0.982057	+	1.33103i
$147$			10543.3i			0.487912i
$148$	6443.40	+	20868.1i	0.294165	+	0.952709i
$149$	−14924.8			−0.672257			−0.336129	−	0.941816i	$-0.609118\pi$
$149$	−14924.8			−0.672257			−0.336129	+	0.941816i	$0.609118\pi$
$150$		0			0
$151$			5685.42i			0.249350i	0.992198	+	0.124675i	$0.0397888\pi$
$151$			5685.42i			0.249350i	−0.992198	+	0.124675i	$0.960211\pi$
$152$	9691.32	−	27733.7i	0.419465	−	1.20039i
$153$	7833.36			0.334630
$154$	−1290.18	+	1748.65i	−0.0544013	+	0.0737328i
$155$		0			0
$156$	2274.68	−	702.346i	0.0934697	−	0.0288604i
$157$	−29681.0			−1.20415			−0.602073	−	0.798441i	$-0.705659\pi$
$157$	−29681.0			−1.20415			−0.602073	+	0.798441i	$0.705659\pi$
$158$	−11967.1	−	8829.51i	−0.479374	−	0.353690i
$159$			24001.0i			0.949368i
$160$		0			0
$161$	−1215.60			−0.0468962
$162$	−1731.25	+	2346.45i	−0.0659675	+	0.0894090i
$163$		−	11159.3i		−	0.420011i	−0.977700	−	0.210005i	$-0.932652\pi$
$163$		−	11159.3i		−	0.420011i	0.977700	−	0.210005i	$-0.0673482\pi$
$164$	−5867.12	−	19001.8i	−0.218141	−	0.706490i
$165$		0			0
$166$	19289.1	+	14231.8i	0.699996	+	0.516469i
$167$		−	45348.0i		−	1.62602i	−0.582251	−	0.813009i	$-0.697828\pi$
$167$		−	45348.0i		−	1.62602i	0.582251	−	0.813009i	$-0.302172\pi$
$168$	−6054.57	−	2115.72i	−0.214518	−	0.0749617i
$169$	−27741.1			−0.971291
$170$		0			0
$171$			12393.9i			0.423855i
$172$	10141.3	−	3131.30i	0.342797	−	0.105844i
$173$	18639.7			0.622797			0.311399	−	0.950279i	$-0.399203\pi$
$173$	18639.7			0.622797			0.311399	+	0.950279i	$0.399203\pi$
$174$	−19096.7	−	14089.8i	−0.630752	−	0.465380i
$175$		0			0
$176$	4065.67	+	5956.05i	0.131252	+	0.192280i
$177$	−13524.7			−0.431699
$178$	−25742.2	+	34889.8i	−0.812468	+	1.10118i
$179$		−	59685.9i		−	1.86280i	−0.364001	−	0.931399i	$-0.618589\pi$
$179$		−	59685.9i		−	1.86280i	0.364001	−	0.931399i	$-0.381411\pi$
$180$		0			0
$181$	23124.2			0.705845			0.352923	−	0.935653i	$-0.385188\pi$
$181$	23124.2			0.705845			0.352923	+	0.935653i	$0.385188\pi$
$182$	−1777.52	−	1311.48i	−0.0536626	−	0.0395932i
$183$		−	28040.1i		−	0.837293i
$184$	−1330.72	+	3808.14i	−0.0393054	+	0.112481i
$185$		0			0
$186$	−16480.3	+	22336.6i	−0.476366	+	0.645642i
$187$			8172.67i			0.233712i
$188$	−60177.0	+	18580.7i	−1.70261	+	0.525709i
$189$	2705.73			0.0757462
$190$		0			0
$191$			4215.25i			0.115547i	0.998330	+	0.0577733i	$0.0184001\pi$
$191$			4215.25i			0.115547i	−0.998330	+	0.0577733i	$0.981600\pi$
$192$	−13256.0	+	16651.2i	−0.359591	+	0.451694i
$193$	−42051.8			−1.12894			−0.564469	−	0.825454i	$-0.690919\pi$
$193$	−42051.8			−1.12894			−0.564469	+	0.825454i	$0.690919\pi$
$194$	13256.1	−	17966.6i	0.352218	−	0.477379i
$195$		0			0
$196$	−9577.92	−	31019.9i	−0.249321	−	0.807473i
$197$	3599.70			0.0927542			0.0463771	−	0.998924i	$-0.485232\pi$
$197$	3599.70			0.0927542			0.0463771	+	0.998924i	$0.485232\pi$
$198$	−2448.09	−	1806.24i	−0.0624449	−	0.0460728i
$199$			13966.2i			0.352673i	0.984330	+	0.176336i	$0.0564246\pi$
$199$			13966.2i			0.352673i	−0.984330	+	0.176336i	$0.943575\pi$
$200$		0			0
$201$	−31349.1			−0.775949
$202$	−43075.6	+	58382.5i	−1.05567	+	1.43080i
$203$			22020.7i			0.534366i
$204$	−23046.9	+	7116.12i	−0.553799	+	0.170995i
$205$		0			0
$206$	51013.6	+	37638.6i	1.20213	+	0.886951i
$207$		−	1701.82i		−	0.0397168i
$208$	−6054.40	+	4132.81i	−0.139941	+	0.0955253i
$209$	−12930.8			−0.296028
$210$		0			0
$211$		−	22691.1i		−	0.509673i	−0.966984	−	0.254836i	$-0.917978\pi$
$211$		−	22691.1i		−	0.509673i	0.966984	−	0.254836i	$-0.0820216\pi$
$212$	−21803.4	−	70614.3i	−0.485123	−	1.57116i
$213$	−4963.47			−0.109402
$214$	−8109.81	−	5983.55i	−0.177086	−	0.130657i
$215$		0			0
$216$	2961.99	−	8476.33i	0.0634856	−	0.181677i
$217$	25756.8			0.546980
$218$	−2571.98	+	3485.94i	−0.0541197	+	0.0733512i
$219$			45802.8i			0.955001i
$220$		0			0
$221$	−8307.61			−0.170095
$222$	22829.9	+	16844.3i	0.463231	+	0.341779i
$223$		−	84540.5i		−	1.70002i	−0.526763	−	0.850012i	$-0.676595\pi$
$223$		−	84540.5i		−	1.70002i	0.526763	−	0.850012i	$-0.323405\pi$
$224$	19735.4	+	724.558i	0.393324	+	0.0144403i
$225$		0			0
$226$	−1581.30	+	2143.22i	−0.0309598	+	0.0419614i
$227$		−	739.621i		−	0.0143535i	−0.999974	−	0.00717674i	$-0.997716\pi$
$227$		−	739.621i		−	0.0143535i	0.999974	−	0.00717674i	$-0.00228445\pi$
$228$	−11259.1	−	36464.8i	−0.216588	−	0.701462i
$229$	−60378.3			−1.15136			−0.575679	−	0.817676i	$-0.695262\pi$
$229$	−60378.3			−1.15136			−0.575679	+	0.817676i	$0.695262\pi$
$230$		0			0
$231$			2822.93i			0.0529025i
$232$	68984.9	+	24106.2i	1.28168	+	0.447871i
$233$	26943.7			0.496301			0.248151	−	0.968721i	$-0.420177\pi$
$233$	26943.7			0.496301			0.248151	+	0.968721i	$0.420177\pi$
$234$	1836.06	−	2488.51i	0.0335318	−	0.0454473i
$235$		0			0
$236$	39791.6	−	12286.3i	0.714443	−	0.220597i
$237$	−19319.1			−0.343945
$238$	18009.7	+	13287.9i	0.317946	+	0.234586i
$239$			35882.1i			0.628177i	0.949394	+	0.314089i	$0.101699\pi$
$239$			35882.1i			0.628177i	−0.949394	+	0.314089i	$0.898301\pi$
$240$		0			0
$241$	47555.3			0.818776			0.409388	−	0.912360i	$-0.365742\pi$
$241$	47555.3			0.818776			0.409388	+	0.912360i	$0.365742\pi$
$242$	−32885.4	+	44571.2i	−0.561529	+	0.761069i
$243$			3788.00i			0.0641500i
$244$	25472.7	+	82498.0i	0.427853	+	1.38568i
$245$		0			0
$246$	−20788.0	−	15337.8i	−0.343513	−	0.253450i
$247$		−	13144.3i		−	0.215449i
$248$	28196.1	−	80689.0i	0.458444	−	1.31193i
$249$	31139.4			0.502240
$250$		0			0
$251$		−	64104.2i		−	1.01751i	−0.860911	−	0.508756i	$-0.830106\pi$
$251$		−	64104.2i		−	1.01751i	0.860911	−	0.508756i	$-0.169894\pi$
$252$	−7960.65	+	2457.99i	−0.125357	+	0.0387060i
$253$	1775.54			0.0277389
$254$	−31957.7	−	23578.9i	−0.495345	−	0.365474i
$255$		0			0
$256$	23874.4	−	61032.6i	0.364294	−	0.931284i
$257$	38018.5			0.575611			0.287806	−	0.957689i	$-0.407074\pi$
$257$	38018.5			0.575611			0.287806	+	0.957689i	$0.407074\pi$
$258$	8185.81	−	11094.6i	0.122976	−	0.166676i
$259$		−	26325.5i		−	0.392444i
$260$		0			0
$261$	−30828.7			−0.452558
$262$	81067.2	+	59812.7i	1.18098	+	0.871346i
$263$			101432.i			1.46644i	0.679994	+	0.733218i	$0.261982\pi$
$263$			101432.i			1.46644i	−0.679994	+	0.733218i	$0.738018\pi$
$264$	8843.49	+	3090.29i	0.126887	+	0.0443395i
$265$		0			0
$266$	−21024.1	+	28495.0i	−0.297135	+	0.402722i
$267$			56324.3i			0.790084i
$268$	92233.6	−	28478.7i	1.28416	−	0.396507i
$269$	118525.			1.63796			0.818982	−	0.573819i	$-0.194539\pi$
$269$	118525.			1.63796			0.818982	+	0.573819i	$0.194539\pi$
$270$		0			0
$271$			48236.2i			0.656802i	0.944538	+	0.328401i	$0.106510\pi$
$271$			48236.2i			0.656802i	−0.944538	+	0.328401i	$0.893490\pi$
$272$	61342.8	−	41873.3i	0.829136	−	0.565978i
$273$	−2869.54			−0.0385024
$274$	−7274.35	+	9859.30i	−0.0968932	+	0.131324i
$275$		0			0
$276$	1546.00	+	5007.01i	0.0202951	+	0.0657296i
$277$	17265.4			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$277$	17265.4			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$278$	75252.2	+	55522.3i	0.973709	+	0.718419i
$279$			36059.2i			0.463242i
$280$		0			0
$281$	−80910.7			−1.02469			−0.512346	−	0.858779i	$-0.671224\pi$
$281$	−80910.7			−1.02469			−0.512346	+	0.858779i	$0.671224\pi$
$282$	−48573.4	+	65834.0i	−0.610802	+	0.827850i
$283$		−	44418.4i		−	0.554613i	−0.960782	−	0.277306i	$-0.910558\pi$
$283$		−	44418.4i		−	0.554613i	0.960782	−	0.277306i	$-0.0894417\pi$
$284$	14603.3	−	4509.01i	0.181056	−	0.0559042i
$285$		0			0
$286$	2596.30	+	1915.59i	0.0317412	+	0.0234192i
$287$			23971.0i			0.291020i
$288$	−1014.37	+	27629.4i	−0.0122296	+	0.333109i
$289$	651.209			0.00779695
$290$		0			0
$291$		−	29004.5i		−	0.342515i
$292$	−41609.0	−	134759.i	−0.488002	−	1.58049i
$293$	−12219.3			−0.142335			−0.0711677	−	0.997464i	$-0.522673\pi$
$293$	−12219.3			−0.142335			−0.0711677	+	0.997464i	$0.522673\pi$
$294$	−33935.9	−	25038.5i	−0.392613	−	0.289677i
$295$		0			0
$296$	−82470.8	−	28818.7i	−0.941275	−	0.328921i
$297$	−3952.07			−0.0448035
$298$	35443.8	−	48038.8i	0.399124	−	0.540953i
$299$			1804.86i			0.0201883i
$300$		0			0
$301$	−12793.4			−0.141206
$302$	−18299.8	−	13501.9i	−0.200647	−	0.148041i
$303$			94249.9i			1.02659i
$304$	66252.0	+	97056.5i	0.716889	+	1.05021i
$305$		0			0
$306$	−18602.9	+	25213.4i	−0.198672	+	0.269271i
$307$			45783.2i			0.485768i	0.970055	+	0.242884i	$0.0780934\pi$
$307$			45783.2i			0.485768i	−0.970055	+	0.242884i	$0.921907\pi$
$308$	−2564.46	−	8305.47i	−0.0270330	−	0.0875514i
$309$	82353.8			0.862515
$310$		0			0
$311$			93050.8i			0.962054i	0.876706	+	0.481027i	$0.159736\pi$
$311$			93050.8i			0.962054i	−0.876706	+	0.481027i	$0.840264\pi$
$312$	−3141.31	+	8989.51i	−0.0322702	+	0.0923479i
$313$	−153178.			−1.56353			−0.781767	−	0.623571i	$-0.785681\pi$
$313$	−153178.			−1.56353			−0.781767	+	0.623571i	$0.785681\pi$
$314$	70487.3	−	95535.0i	0.714910	−	0.968954i
$315$		0			0
$316$	56839.5	−	17550.2i	0.569215	−	0.175755i
$317$	−25234.5			−0.251117			−0.125559	−	0.992086i	$-0.540072\pi$
$317$	−25234.5			−0.251117			−0.125559	+	0.992086i	$0.540072\pi$
$318$	−77252.5	−	56998.2i	−0.763938	−	0.563646i
$319$		−	32164.1i		−	0.316075i
$320$		0			0
$321$	−13092.1			−0.127057
$322$	2886.84	−	3912.67i	0.0278426	−	0.0377365i
$323$			133177.i			1.27651i
$324$	−3441.16	−	11144.8i	−0.0327804	−	0.106166i
$325$		0			0
$326$	35918.6	+	26501.4i	0.337975	+	0.249363i
$327$			5627.53i			0.0526287i
$328$	75094.8	+	26241.3i	0.698011	+	0.243914i
$329$	75914.2			0.701345
$330$		0			0
$331$			158659.i			1.44813i	0.689730	+	0.724066i	$0.257729\pi$
$331$			158659.i			1.44813i	−0.689730	+	0.724066i	$0.742271\pi$
$332$	−91616.6	+	28288.2i	−0.831186	+	0.256643i
$333$	36855.4			0.332363
$334$	145963.	+	107694.i	1.30843	+	0.965379i
$335$		0			0
$336$	21188.5	−	14463.5i	0.187681	−	0.128114i
$337$	15308.6			0.134796			0.0673980	−	0.997726i	$-0.478530\pi$
$337$	15308.6			0.134796			0.0673980	+	0.997726i	$0.478530\pi$
$338$	65880.2	−	89290.8i	0.576663	−	0.781580i
$339$			3459.91i			0.0301068i
$340$		0			0
$341$	−37621.1			−0.323536
$342$	−39892.7	−	29433.5i	−0.341068	−	0.251646i
$343$			85437.4i			0.726206i
$344$	−14005.1	+	40078.3i	−0.118350	+	0.338683i
$345$		0			0
$346$	−44266.1	+	59996.1i	−0.369759	+	0.501153i
$347$		−	145358.i		−	1.20720i	−0.797288	−	0.603599i	$-0.793733\pi$
$347$		−	145358.i		−	1.20720i	0.797288	−	0.603599i	$-0.206267\pi$
$348$	90702.6	−	28006.0i	0.748964	−	0.231256i
$349$	−91594.6			−0.752002			−0.376001	−	0.926619i	$-0.622701\pi$
$349$	−91594.6			−0.752002			−0.376001	+	0.926619i	$0.622701\pi$
$350$		0			0
$351$		−	4017.33i		−	0.0326079i
$352$	−28826.2	−	1058.31i	−0.232649	−	0.00854139i
$353$	−84192.7			−0.675655			−0.337827	−	0.941208i	$-0.609692\pi$
$353$	−84192.7			−0.675655			−0.337827	+	0.941208i	$0.609692\pi$
$354$	32118.8	−	43532.3i	0.256303	−	0.347380i
$355$		0			0
$356$	−51167.1	−	165714.i	−0.403730	−	1.30756i
$357$	29074.0			0.228123
$358$	192112.	+	141744.i	1.49896	+	1.10596i
$359$			53396.4i			0.414308i	0.978308	+	0.207154i	$0.0664201\pi$
$359$			53396.4i			0.414308i	−0.978308	+	0.207154i	$0.933580\pi$
$360$		0			0
$361$	−80392.1			−0.616877
$362$	−54916.0	+	74430.4i	−0.419065	+	0.567980i
$363$			71953.6i			0.546059i
$364$	8442.62	−	2606.80i	0.0637198	−	0.0196746i
$365$		0			0
$366$	90253.3	+	66590.4i	0.673754	+	0.497107i
$367$		−	141341.i		−	1.04938i	−0.851292	−	0.524692i	$-0.824180\pi$
$367$		−	141341.i		−	1.04938i	0.851292	−	0.524692i	$-0.175820\pi$
$368$	−9097.12	−	13326.9i	−0.0671751	−	0.0984089i
$369$	−33559.2			−0.246467
$370$		0			0
$371$			89081.1i			0.647199i
$372$	−32757.5	−	106091.i	−0.236715	−	0.766645i
$373$	98354.8			0.706932			0.353466	−	0.935447i	$-0.385003\pi$
$373$	98354.8			0.706932			0.353466	+	0.935447i	$0.385003\pi$
$374$	−26305.6	−	19408.7i	−0.188063	−	0.138756i
$375$		0			0
$376$	83103.9	−	237819.i	0.587822	−	1.68217i
$377$	32695.2			0.230039
$378$	−6425.65	+	8709.00i	−0.0449711	+	0.0609516i
$379$		−	233635.i		−	1.62652i	−0.581902	−	0.813259i	$-0.697691\pi$
$379$		−	233635.i		−	1.62652i	0.581902	−	0.813259i	$-0.302309\pi$
$380$		0			0
$381$	−51590.9			−0.355405
$382$	−13567.7	−	10010.5i	−0.0929782	−	0.0686008i
$383$		−	70931.0i		−	0.483547i	−0.970333	−	0.241773i	$-0.922271\pi$
$383$		−	70931.0i		−	0.483547i	0.970333	−	0.241773i	$-0.0777291\pi$
$384$	−22115.1	−	82211.2i	−0.149978	−	0.557530i
$385$		0			0
$386$	99865.8	−	135353.i	0.670258	−	0.908435i
$387$		−	17910.6i		−	0.119588i
$388$	26348.8	+	85335.4i	0.175024	+	0.566847i
$389$	5365.04			0.0354547			0.0177274	−	0.999843i	$-0.494357\pi$
$389$	5365.04			0.0354547			0.0177274	+	0.999843i	$0.494357\pi$
$390$		0			0
$391$		−	18286.7i		−	0.119614i
$392$	122590.	+	42838.2i	0.797782	+	0.278778i
$393$	130871.			0.847340
$394$	−8548.67	+	11586.4i	−0.0550688	+	0.0746376i
$395$		0			0
$396$	11627.6	−	3590.21i	0.0741479	−	0.0228944i
$397$	228645.			1.45071			0.725356	−	0.688374i	$-0.241675\pi$
$397$	228645.			1.45071			0.725356	+	0.688374i	$0.241675\pi$
$398$	−44953.3	−	33167.3i	−0.283789	−	0.209384i
$399$			46000.9i			0.288949i
$400$		0			0
$401$	−182899.			−1.13743			−0.568714	−	0.822536i	$-0.692559\pi$
$401$	−182899.			−1.13743			−0.568714	+	0.822536i	$0.692559\pi$
$402$	74448.7	−	100904.i	0.460686	−	0.624391i
$403$		−	38242.3i		−	0.235469i
$404$	−85620.2	−	277297.i	−0.524582	−	1.69896i
$405$		0			0
$406$	−70878.5	−	52295.3i	−0.429994	−	0.317257i
$407$			38451.8i			0.232128i
$408$	31827.6	−	91081.2i	0.191198	−	0.547152i
$409$	−132579.			−0.792552			−0.396276	−	0.918131i	$-0.629698\pi$
$409$	−132579.			−0.792552			−0.396276	+	0.918131i	$0.629698\pi$
$410$		0			0
$411$			15916.4i			0.0942238i
$412$	−242297.	+	74813.3i	−1.42743	+	0.440742i
$413$	−50197.8			−0.294296
$414$	5477.70	+	4041.54i	0.0319593	+	0.0235801i
$415$		0			0
$416$	1075.79	−	29302.1i	0.00621641	−	0.169322i
$417$	121483.			0.698626
$418$	30708.4	−	41620.7i	0.175754	−	0.238208i
$419$			291072.i			1.65795i	0.559283	+	0.828976i	$0.311076\pi$
$419$			291072.i			1.65795i	−0.559283	+	0.828976i	$0.688924\pi$
$420$		0			0
$421$	−33411.3			−0.188508			−0.0942540	−	0.995548i	$-0.530047\pi$
$421$	−33411.3			−0.188508			−0.0942540	+	0.995548i	$0.530047\pi$
$422$	73036.5	+	53887.5i	0.410124	+	0.302596i
$423$			106279.i			0.593974i
$424$	279067.	+	97517.9i	1.55231	+	0.542441i
$425$		0			0
$426$	11787.4	−	15976.1i	0.0649529	−	0.0880340i
$427$		−	104073.i		−	0.570796i
$428$	38518.8	−	11893.3i	0.210274	−	0.0649256i
$429$	4191.34			0.0227740
$430$		0			0
$431$		−	91506.5i		−	0.492603i	−0.969193	−	0.246302i	$-0.920785\pi$
$431$		−	91506.5i		−	0.492603i	0.969193	−	0.246302i	$-0.0792154\pi$
$432$	20248.8	+	29663.7i	0.108500	+	0.158949i
$433$	−301690.			−1.60911			−0.804553	−	0.593881i	$-0.797595\pi$
$433$	−301690.			−1.60911			−0.804553	+	0.593881i	$0.797595\pi$
$434$	−61167.9	+	82903.9i	−0.324746	+	0.440145i
$435$		0			0
$436$	−5112.26	−	16557.0i	−0.0268931	−	0.0870982i
$437$	28933.2			0.151507
$438$	−147427.	−	108774.i	−0.768471	−	0.566991i
$439$		−	176051.i		−	0.913502i	−0.889594	−	0.456751i	$-0.849013\pi$
$439$		−	176051.i		−	0.913502i	0.889594	−	0.456751i	$-0.150987\pi$
$440$		0			0
$441$	−54784.5			−0.281696
$442$	19729.2	−	26739.9i	0.100987	−	0.136872i
$443$		−	189794.i		−	0.967108i	−0.875315	−	0.483554i	$-0.839346\pi$
$443$		−	189794.i		−	0.967108i	0.875315	−	0.483554i	$-0.160654\pi$
$444$	−108434.	+	33480.9i	−0.550047	+	0.169836i
$445$		0			0
$446$	272113.	+	200769.i	1.36798	+	1.00932i
$447$		−	77551.4i		−	0.388128i
$448$	−49200.4	+	61802.2i	−0.245139	+	0.307927i
$449$	−55275.5			−0.274183			−0.137091	−	0.990558i	$-0.543775\pi$
$449$	−55275.5			−0.274183			−0.137091	+	0.990558i	$0.543775\pi$
$450$		0			0
$451$		−	35012.8i		−	0.172137i
$452$	−3143.11	−	10179.6i	−0.0153845	−	0.0498255i
$453$	−29542.3			−0.143962
$454$	2380.64	+	1756.47i	0.0115500	+	0.00852177i
$455$		0			0
$456$	144109.	+	50357.6i	0.693043	+	0.242178i
$457$	−401864.			−1.92418			−0.962091	−	0.272728i	$-0.912074\pi$
$457$	−401864.			−1.92418			−0.962091	+	0.272728i	$0.912074\pi$
$458$	143388.	−	194341.i	0.683569	−	0.926476i
$459$			40703.3i			0.193199i
$460$		0			0
$461$	231421.			1.08893			0.544467	−	0.838782i	$-0.316732\pi$
$461$	231421.			1.08893			0.544467	+	0.838782i	$0.316732\pi$
$462$	−9086.24	−	6703.98i	−0.0425697	−	0.0314086i
$463$			34800.1i			0.162337i	0.996700	+	0.0811687i	$0.0258652\pi$
$463$			34800.1i			0.162337i	−0.996700	+	0.0811687i	$0.974135\pi$
$464$	−241419.	+	164795.i	−1.12133	+	0.765436i
$465$		0			0
$466$	−63986.7	+	86724.3i	−0.294658	+	0.399364i
$467$			182183.i			0.835359i	0.908594	+	0.417679i	$0.137156\pi$
$467$			182183.i			0.835359i	−0.908594	+	0.417679i	$0.862844\pi$
$468$	3649.49	+	11819.6i	0.0166625	+	0.0539647i
$469$	−116354.			−0.528977
$470$		0			0
$471$		−	154227.i		−	0.695214i
$472$	−54951.9	+	157256.i	−0.246660	+	0.705869i
$473$	18686.4			0.0835227
$474$	45879.5	−	62182.8i	0.204203	−	0.276766i
$475$		0			0
$476$	−85540.0	+	26411.9i	−0.377533	+	0.116570i
$477$	−124713.			−0.548118
$478$	−115495.	−	85213.8i	−0.505482	−	0.372953i
$479$			388419.i			1.69289i	0.532473	+	0.846447i	$0.321263\pi$
$479$			388419.i			1.69289i	−0.532473	+	0.846447i	$0.678737\pi$
$480$		0			0
$481$	−39086.8			−0.168943
$482$	−112936.	+	153068.i	−0.486113	+	0.658854i
$483$		−	6316.43i		−	0.0270756i
$484$	−65365.4	−	211698.i	−0.279034	−	0.903704i
$485$		0			0
$486$	−12192.5	−	8995.84i	−0.0516203	−	0.0380863i
$487$			320680.i			1.35212i	0.736849	+	0.676058i	$0.236313\pi$
$487$			320680.i			1.35212i	−0.736849	+	0.676058i	$0.763687\pi$
$488$	−326032.	−	113929.i	−1.36905	−	0.478404i
$489$	57985.3			0.242493
$490$		0			0
$491$			206317.i			0.855800i	0.903826	+	0.427900i	$0.140746\pi$
$491$			206317.i			0.855800i	−0.903826	+	0.427900i	$0.859254\pi$
$492$	98736.0	−	30486.4i	0.407892	−	0.125944i
$493$	−331265.			−1.36296
$494$	42307.9	+	31215.5i	0.173367	+	0.127913i
$495$		0			0
$496$	192755.	+	282378.i	0.783505	+	1.14780i
$497$	−18422.3			−0.0745813
$498$	−73950.7	+	100229.i	−0.298183	+	0.404143i
$499$		−	465187.i		−	1.86821i	−0.356993	−	0.934107i	$-0.616198\pi$
$499$		−	465187.i		−	1.86821i	0.356993	−	0.934107i	$-0.383802\pi$
$500$		0			0
$501$	235635.			0.938782
$502$	206334.	+	152237.i	0.818772	+	0.604104i
$503$			227645.i			0.899750i	0.893092	+	0.449875i	$0.148531\pi$
$503$			227645.i			0.899750i	−0.893092	+	0.449875i	$0.851469\pi$
$504$	10993.6	−	31460.5i	0.0432792	−	0.123852i
$505$		0			0
$506$	−4216.60	+	5714.97i	−0.0164688	+	0.0223210i
$507$		−	144147.i		−	0.560775i
$508$	151788.	−	46867.1i	0.588179	−	0.181610i
$509$	9630.55			0.0371720			0.0185860	−	0.999827i	$-0.494084\pi$
$509$	9630.55			0.0371720			0.0185860	+	0.999827i	$0.494084\pi$
$510$		0			0
$511$			170000.i			0.651039i
$512$	139750.	+	221787.i	0.533103	+	0.846050i
$513$	−64400.8			−0.244713
$514$	−90287.5	+	122371.i	−0.341744	+	0.463183i
$515$		0			0
$516$	16270.7	+	52695.7i	0.0611092	+	0.197914i
$517$	−110883.			−0.414842
$518$	84734.6	+	62518.6i	0.315792	+	0.232997i
$519$			96854.7i			0.359572i
$520$		0			0
$521$	112120.			0.413053			0.206527	−	0.978441i	$-0.433784\pi$
$521$	112120.			0.413053			0.206527	+	0.978441i	$0.433784\pi$
$522$	73212.9	−	99229.2i	0.268687	−	0.364165i
$523$		−	448729.i		−	1.64052i	−0.571993	−	0.820258i	$-0.693830\pi$
$523$		−	448729.i		−	1.64052i	0.571993	−	0.820258i	$-0.306170\pi$
$524$	−385041.	+	118888.i	−1.40231	+	0.432988i
$525$		0			0
$526$	−326481.	−	240883.i	−1.18001	−	0.870633i
$527$			387469.i			1.39513i
$528$	−30948.5	+	21125.9i	−0.111013	+	0.0757786i
$529$	275868.			0.985803
$530$		0			0
$531$		−	70276.4i		−	0.249242i
$532$	−41789.0	−	135341.i	−0.147652	−	0.478198i
$533$	35591.0			0.125281
$534$	−181292.	−	133761.i	−0.635766	−	0.469079i
$535$		0			0
$536$	−127374.	+	364507.i	−0.443354	+	1.26875i
$537$	310137.			1.07549
$538$	−281476.	+	381499.i	−0.972471	+	1.31804i
$539$		−	57157.5i		−	0.196741i
$540$		0			0
$541$	−101996.			−0.348487			−0.174244	−	0.984703i	$-0.555748\pi$
$541$	−101996.			−0.348487			−0.174244	+	0.984703i	$0.555748\pi$
$542$	−155259.	−	114553.i	−0.528516	−	0.389948i
$543$			120157.i			0.407520i
$544$	−10899.8	+	296887.i	−0.0368316	+	1.00322i
$545$		0			0
$546$	6814.67	−	9236.27i	0.0228591	−	0.0309821i
$547$		−	368616.i		−	1.23197i	−0.787758	−	0.615984i	$-0.788758\pi$
$547$		−	368616.i		−	1.23197i	0.787758	−	0.615984i	$-0.211242\pi$
$548$	−14459.0	−	46828.3i	−0.0481480	−	0.155936i
$549$	145701.			0.483411
$550$		0			0
$551$		−	524128.i		−	1.72637i
$552$	−19787.7	−	6914.65i	−0.0649407	−	0.0226930i
$553$	−71704.0			−0.234473
$554$	−41002.3	+	55572.5i	−0.133595	+	0.181067i
$555$		0			0
$556$	−357422.	+	110360.i	−1.15620	+	0.356995i
$557$	−303706.			−0.978910			−0.489455	−	0.872028i	$-0.662804\pi$
$557$	−303706.			−0.978910			−0.489455	+	0.872028i	$0.662804\pi$
$558$	−116065.	−	85634.4i	−0.372762	−	0.275030i
$559$			18995.0i			0.0607877i
$560$		0			0
$561$	−42466.4			−0.134934
$562$	192149.	−	260429.i	0.608367	−	0.824551i
$563$		−	29621.8i		−	0.0934534i	−0.998908	−	0.0467267i	$-0.985121\pi$
$563$		−	29621.8i		−	0.0934534i	0.998908	−	0.0467267i	$-0.0148790\pi$
$564$	−96548.0	−	312689.i	−0.303518	−	0.983001i
$565$		0			0
$566$	142971.	+	105486.i	0.446286	+	0.329278i
$567$			14059.4i			0.0437321i
$568$	−20167.0	+	57712.0i	−0.0625093	+	0.178883i
$569$	−498051.			−1.53833			−0.769164	−	0.639052i	$-0.779327\pi$
$569$	−498051.			−1.53833			−0.769164	+	0.639052i	$0.779327\pi$
$570$		0			0
$571$			196843.i			0.603736i	0.953350	+	0.301868i	$0.0976103\pi$
$571$			196843.i			0.603736i	−0.953350	+	0.301868i	$0.902390\pi$
$572$	−12331.5	+	3807.57i	−0.0376899	+	0.0116374i
$573$	−21903.1			−0.0667109
$574$	−77156.1	−	56927.1i	−0.234178	−	0.172781i
$575$		0			0
$576$	−86522.4	−	68880.0i	−0.260786	−	0.207610i
$577$	135033.			0.405591			0.202795	−	0.979221i	$-0.434997\pi$
$577$	135033.			0.405591			0.202795	+	0.979221i	$0.434997\pi$
$578$	−1546.51	+	2096.06i	−0.00462911	+	0.00627406i
$579$		−	218508.i		−	0.651793i
$580$		0			0
$581$	115576.			0.342385
$582$	93357.4	+	68880.7i	0.275615	+	0.203353i
$583$		−	130115.i		−	0.382815i
$584$	532565.	+	186100.i	1.56152	+	0.545660i
$585$		0			0
$586$	29018.8	−	39330.7i	0.0845055	−	0.114535i
$587$			35351.5i			0.102596i	0.998683	+	0.0512981i	$0.0163359\pi$
$587$			35351.5i			0.102596i	−0.998683	+	0.0512981i	$0.983664\pi$
$588$	161184.	−	49768.3i	0.466195	−	0.143946i
$589$	−613053.			−1.76713
$590$		0			0
$591$			18704.6i			0.0535517i
$592$	288614.	−	197011.i	0.823519	−	0.562144i
$593$	553805.			1.57488			0.787440	−	0.616392i	$-0.211406\pi$
$593$	553805.			1.57488			0.787440	+	0.616392i	$0.211406\pi$
$594$	9385.50	−	12720.6i	0.0266002	−	0.0360526i
$595$		0			0
$596$	70450.7	+	228168.i	0.198332	+	0.642335i
$597$	−72570.4			−0.203616
$598$	−5809.34	−	4286.23i	−0.0162452	−	0.0119860i
$599$		−	284209.i		−	0.792108i	−0.918227	−	0.396054i	$-0.870379\pi$
$599$		−	284209.i		−	0.792108i	0.918227	−	0.396054i	$-0.129621\pi$
$600$		0			0
$601$	517703.			1.43328			0.716641	−	0.697442i	$-0.245679\pi$
$601$	517703.			1.43328			0.716641	+	0.697442i	$0.245679\pi$
$602$	30382.2	−	41178.5i	0.0838350	−	0.113626i
$603$		−	162895.i		−	0.447994i
$604$	86917.8	−	26837.4i	0.238251	−	0.0735641i
$605$		0			0
$606$	−303365.	−	223827.i	−0.826075	−	0.609492i
$607$		−	287344.i		−	0.779876i	−0.920841	−	0.389938i	$-0.872496\pi$
$607$		−	287344.i		−	0.779876i	0.920841	−	0.389938i	$-0.127504\pi$
$608$	−469735.	−	17245.7i	−1.27071	−	0.0466523i
$609$	−114423.			−0.308516
$610$		0			0
$611$		−	112714.i		−	0.301921i
$612$	−36976.4	−	119755.i	−0.0987239	−	0.319736i
$613$	467697.			1.24464			0.622319	−	0.782763i	$-0.286190\pi$
$613$	467697.			1.24464			0.622319	+	0.782763i	$0.286190\pi$
$614$	−147363.	−	108727.i	−0.390888	−	0.288404i
$615$		0			0
$616$	32823.2	+	11469.8i	0.0865006	+	0.0302269i
$617$	94926.6			0.249355			0.124677	−	0.992197i	$-0.460210\pi$
$617$	94926.6			0.249355			0.124677	+	0.992197i	$0.460210\pi$
$618$	−195576.	+	265074.i	−0.512081	+	0.694050i
$619$			371758.i			0.970238i	0.874448	+	0.485119i	$0.161224\pi$
$619$			371758.i			0.970238i	−0.874448	+	0.485119i	$0.838776\pi$
$620$		0			0
$621$	8842.94			0.0229305
$622$	−299505.	−	220980.i	−0.774147	−	0.571178i
$623$			209051.i			0.538613i
$624$	−21474.7	−	31459.6i	−0.0551516	−	0.0807948i
$625$		0			0
$626$	363771.	−	493037.i	0.928281	−	1.25815i
$627$		−	67190.4i		−	0.170912i
$628$	140106.	+	453758.i	0.355252	+	1.15055i
$629$	396025.			1.00097
$630$		0			0
$631$		−	545789.i		−	1.37078i	−0.728178	−	0.685388i	$-0.759633\pi$
$631$		−	545789.i		−	1.37078i	0.728178	−	0.685388i	$-0.240367\pi$
$632$	−78494.9	+	224629.i	−0.196520	+	0.562384i
$633$	117907.			0.294260
$634$	59927.7	−	81223.0i	0.149090	−	0.202069i
$635$		0			0
$636$	366923.	−	113294.i	0.907111	−	0.280086i
$637$	58101.3			0.143188
$638$	103527.	+	76384.2i	0.254339	+	0.187656i
$639$		−	25791.0i		−	0.0631634i
$640$		0			0
$641$	176298.			0.429072			0.214536	−	0.976716i	$-0.431176\pi$
$641$	176298.			0.429072			0.214536	+	0.976716i	$0.431176\pi$
$642$	31091.4	−	42139.8i	0.0754346	−	0.102240i
$643$		−	569717.i		−	1.37796i	−0.724779	−	0.688981i	$-0.758058\pi$
$643$		−	569717.i		−	1.37796i	0.724779	−	0.688981i	$-0.241942\pi$
$644$	5738.08	+	18583.9i	0.0138355	+	0.0448089i
$645$		0			0
$646$	−428661.	−	316273.i	−1.02719	−	0.757874i
$647$			314453.i			0.751186i	0.926785	+	0.375593i	$0.122561\pi$
$647$			314453.i			0.751186i	−0.926785	+	0.375593i	$0.877439\pi$
$648$	44044.3	+	15390.9i	0.104891	+	0.0366534i
$649$	73320.4			0.174075
$650$		0			0
$651$			133836.i			0.315799i
$652$	−170601.	+	52676.0i	−0.401316	+	0.123913i
$653$	488553.			1.14574			0.572869	−	0.819647i	$-0.305830\pi$
$653$	488553.			1.14574			0.572869	+	0.819647i	$0.305830\pi$
$654$	−18113.5	−	13364.4i	−0.0423493	−	0.0312460i
$655$		0			0
$656$	−262801.	+	179391.i	−0.610687	+	0.416863i
$657$	−237998.			−0.551370
$658$	−180283.	+	244347.i	−0.416393	+	0.564359i
$659$		−	76000.3i		−	0.175003i	−0.996164	−	0.0875013i	$-0.972112\pi$
$659$		−	76000.3i		−	0.175003i	0.996164	−	0.0875013i	$-0.0278882\pi$
$660$		0			0
$661$	200869.			0.459738			0.229869	−	0.973222i	$-0.426170\pi$
$661$	200869.			0.459738			0.229869	+	0.973222i	$0.426170\pi$
$662$	−510679.	−	376788.i	−1.16529	−	0.859767i
$663$		−	43167.6i		−	0.0982044i
$664$	126522.	−	362068.i	0.286965	−	0.821210i
$665$		0			0
$666$	−87525.3	+	118628.i	−0.197326	+	0.267447i
$667$			71968.5i			0.161767i
$668$	−693274.	+	214060.i	−1.55364	+	0.479714i
$669$	439285.			0.981509
$670$		0			0
$671$			152012.i			0.337623i
$672$	−3764.91	+	102548.i	−0.00833713	+	0.227086i
$673$	341117.			0.753135			0.376568	−	0.926389i	$-0.377104\pi$
$673$	341117.			0.753135			0.376568	+	0.926389i	$0.377104\pi$
$674$	−36355.4	+	49274.3i	−0.0800293	+	0.108468i
$675$		0			0
$676$	130948.	+	424101.i	0.286554	+	0.928059i
$677$	113833.			0.248366			0.124183	−	0.992259i	$-0.460369\pi$
$677$	113833.			0.248366			0.124183	+	0.992259i	$0.460369\pi$
$678$	−11136.5	−	8216.68i	−0.0242264	−	0.0178746i
$679$		−	107652.i		−	0.233498i
$680$		0			0
$681$	3843.18			0.00828699
$682$	89343.7	−	121092.i	0.192086	−	0.260343i
$683$		−	879589.i		−	1.88555i	−0.333428	−	0.942775i	$-0.608206\pi$
$683$		−	879589.i		−	1.88555i	0.333428	−	0.942775i	$-0.391794\pi$
$684$	189477.	−	58504.1i	0.404989	−	0.125047i
$685$		0			0
$686$	−275000.	−	202899.i	−0.584364	−	0.431154i
$687$		−	313735.i		−	0.664736i
$688$	−95741.6	−	140258.i	−0.202266	−	0.296312i
$689$	132263.			0.278612
$690$		0			0
$691$			558055.i			1.16875i	0.811484	+	0.584374i	$0.198660\pi$
$691$			558055.i			1.16875i	−0.811484	+	0.584374i	$0.801340\pi$
$692$	−87986.5	−	284961.i	−0.183740	−	0.595076i
$693$	−14668.4			−0.0305433
$694$	467866.	+	345199.i	0.971410	+	0.716722i
$695$		0			0
$696$	−125260.	+	358456.i	−0.258579	+	0.739976i
$697$	−360605.			−0.742278
$698$	217521.	−	294818.i	0.446469	−	0.605122i
$699$			140004.i			0.286540i
$700$		0			0
$701$	−513378.			−1.04472			−0.522362	−	0.852724i	$-0.674949\pi$
$701$	−513378.			−1.04472			−0.522362	+	0.852724i	$0.674949\pi$
$702$	12930.7	+	9540.47i	0.0262390	+	0.0193596i
$703$			626590.i			1.26786i
$704$	71863.6	−	90270.2i	0.144999	−	0.182137i
$705$		0			0
$706$	199943.	−	270993.i	0.401141	−	0.543687i
$707$			349815.i			0.699841i
$708$	63841.7	+	206763.i	0.127361	+	0.412484i
$709$	440653.			0.876605			0.438302	−	0.898828i	$-0.355580\pi$
$709$	440653.			0.876605			0.438302	+	0.898828i	$0.355580\pi$
$710$		0			0
$711$		−	100385.i		−	0.198577i
$712$	654902.	+	228850.i	1.29186	+	0.451431i
$713$	84178.9			0.165586
$714$	−69045.8	+	93581.3i	−0.135438	+	0.183566i
$715$		0			0
$716$	−912468.	+	281740.i	−1.77988	+	0.549570i
$717$	−186449.			−0.362678
$718$	−171868.	−	126807.i	−0.333386	−	0.245978i
$719$			594526.i			1.15004i	0.818139	+	0.575021i	$0.195006\pi$
$719$			594526.i			1.15004i	−0.818139	+	0.575021i	$0.804994\pi$
$720$		0			0
$721$	305661.			0.587990
$722$	190917.	−	258760.i	0.366244	−	0.496390i
$723$			247105.i			0.472720i
$724$	−109155.	−	353519.i	−0.208241	−	0.674428i
$725$		0			0
$726$	−231599.	−	170877.i	−0.439403	−	0.324199i
$727$		−	77530.5i		−	0.146691i	−0.997307	−	0.0733455i	$-0.976632\pi$
$727$		−	77530.5i		−	0.146691i	0.997307	−	0.0733455i	$-0.0233676\pi$
$728$	−11659.2	+	33365.2i	−0.0219991	+	0.0629550i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	192456.i		−	0.360161i
$732$	−428672.	+	132360.i	−0.800025	+	0.247021i
$733$	739223.			1.37584			0.687920	−	0.725787i	$-0.258524\pi$
$733$	739223.			1.37584			0.687920	+	0.725787i	$0.258524\pi$
$734$	454936.	+	335660.i	0.844420	+	0.623027i
$735$		0			0
$736$	64499.8	+	2368.02i	0.119070	+	0.00437149i
$737$	169951.			0.312887
$738$	79697.3	−	108018.i	0.146329	−	0.198327i
$739$		−	730948.i		−	1.33844i	−0.743066	−	0.669218i	$-0.766629\pi$
$739$		−	730948.i		−	1.33844i	0.743066	−	0.669218i	$-0.233371\pi$
$740$		0			0
$741$	68299.8			0.124389
$742$	−286728.	−	211552.i	−0.520789	−	0.384247i
$743$			380418.i			0.689102i	0.938768	+	0.344551i	$0.111969\pi$
$743$			380418.i			0.689102i	−0.938768	+	0.344551i	$0.888031\pi$
$744$	419272.	+	146511.i	0.757444	+	0.264683i
$745$		0			0
$746$	−233576.	+	316577.i	−0.419711	+	0.568855i
$747$			161805.i			0.289968i
$748$	124942.	−	38578.1i	0.223309	−	0.0689505i
$749$	−48592.1			−0.0866168
$750$		0			0
$751$		−	839595.i		−	1.48864i	−0.667822	−	0.744321i	$-0.732773\pi$
$751$		−	839595.i		−	1.48864i	0.667822	−	0.744321i	$-0.267227\pi$
$752$	568116.	+	832268.i	1.00462	+	1.47173i
$753$	333095.			0.587461
$754$	−77645.4	+	105237.i	−0.136576	+	0.185108i
$755$		0			0
$756$	−12772.1	−	41364.8i	−0.0223469	−	0.0723748i
$757$	411596.			0.718256			0.359128	−	0.933288i	$-0.383074\pi$
$757$	411596.			0.718256			0.359128	+	0.933288i	$0.383074\pi$
$758$	752006.	+	554842.i	1.30883	+	0.965675i
$759$			9225.97i			0.0160151i
$760$		0			0
$761$	−152823.			−0.263888			−0.131944	−	0.991257i	$-0.542122\pi$
$761$	−152823.			−0.263888			−0.131944	+	0.991257i	$0.542122\pi$
$762$	122520.	−	166057.i	0.211006	−	0.285987i
$763$			20887.0i			0.0358778i
$764$	64442.1	−	19897.6i	0.110404	−	0.0340890i
$765$		0			0
$766$	228307.	+	168449.i	0.389101	+	0.287085i
$767$			74531.1i			0.126691i
$768$	317135.	+	124055.i	0.537677	+	0.210325i
$769$	888025.			1.50166			0.750832	−	0.660494i	$-0.229653\pi$
$769$	888025.			1.50166			0.750832	+	0.660494i	$0.229653\pi$
$770$		0			0
$771$			197550.i			0.332329i
$772$	198501.	+	642881.i	0.333064	+	1.07869i
$773$	−84232.3			−0.140968			−0.0704839	−	0.997513i	$-0.522454\pi$
$773$	−84232.3			−0.140968			−0.0704839	+	0.997513i	$0.522454\pi$
$774$	57649.4	+	42534.7i	0.0962306	+	0.0710005i
$775$		0			0
$776$	−337245.	−	117848.i	−0.560044	−	0.195703i
$777$	136791.			0.226577
$778$	−12741.1	+	17268.6i	−0.0210497	+	0.0285297i
$779$		−	570550.i		−	0.940196i
$780$		0			0
$781$	26908.1			0.0441145
$782$	58859.8	+	43427.8i	0.0962511	+	0.0710156i
$783$		−	160191.i		−	0.261285i
$784$	−429015.	+	292851.i	−0.697977	+	0.476447i
$785$		0			0
$786$	−310796.	+	421237.i	−0.503072	+	0.681839i
$787$			971179.i			1.56801i	0.620752	+	0.784007i	$0.286827\pi$
$787$			971179.i			1.56801i	−0.620752	+	0.784007i	$0.713173\pi$
$788$	−16991.9	−	55031.6i	−0.0273647	−	0.0886257i
$789$	−527056.			−0.846647
$790$		0			0
$791$			12841.7i			0.0205243i
$792$	−16057.6	+	45952.1i	−0.0255994	+	0.0732580i
$793$	−154522.			−0.245721
$794$	−542993.	+	735946.i	−0.861298	+	1.16736i
$795$		0			0
$796$	213513.	−	65925.7i	0.336975	−	0.104047i
$797$	−274894.			−0.432761			−0.216381	−	0.976309i	$-0.569425\pi$
$797$	−274894.			−0.432761			−0.216381	+	0.976309i	$0.569425\pi$
$798$	−148064.	−	109244.i	−0.232512	−	0.171551i
$799$			1.14201e6i			1.78885i
$800$		0			0
$801$	−292670.			−0.456155
$802$	434355.	−	588703.i	0.675299	−	0.915267i
$803$		−	248307.i		−	0.385087i
$804$	147980.	+	479260.i	0.228923	+	0.741411i
$805$		0			0
$806$	123091.	+	90818.9i	0.189478	+	0.139800i
$807$			615873.i			0.945679i
$808$	1.09588e6	+	382945.i	1.67857	+	0.586562i
$809$	863110.			1.31877			0.659385	−	0.751805i	$-0.270817\pi$
$809$	863110.			1.31877			0.659385	+	0.751805i	$0.270817\pi$
$810$		0			0
$811$		−	391388.i		−	0.595067i	−0.954711	−	0.297534i	$-0.903836\pi$
$811$		−	391388.i		−	0.595067i	0.954711	−	0.297534i	$-0.0961640\pi$
$812$	336649.	−	103946.i	0.510581	−	0.157651i
$813$	−250643.			−0.379205
$814$	−123766.	−	91316.5i	−0.186789	−	0.137816i
$815$		0			0
$816$	217580.	+	318746.i	0.326768	+	0.478702i
$817$	304504.			0.456193
$818$	314852.	−	426735.i	0.470544	−	0.637752i
$819$		−	14910.6i		−	0.0222294i
$820$		0			0
$821$	420749.			0.624219			0.312109	−	0.950046i	$-0.398964\pi$
$821$	420749.			0.624219			0.312109	+	0.950046i	$0.398964\pi$
$822$	−51230.4	−	37798.7i	−0.0758201	−	0.0559413i
$823$			412920.i			0.609630i	0.952412	+	0.304815i	$0.0985946\pi$
$823$			412920.i			0.609630i	−0.952412	+	0.304815i	$0.901405\pi$
$824$	334610.	−	957556.i	0.492816	−	1.41029i
$825$		0			0
$826$	119211.	−	161573.i	0.174726	−	0.236815i
$827$		−	1.35535e6i		−	1.98171i	−0.134932	−	0.990855i	$-0.543082\pi$
$827$		−	1.35535e6i		−	1.98171i	0.134932	−	0.990855i	$-0.456918\pi$
$828$	−26017.2	+	8033.26i	−0.0379490	+	0.0117174i
$829$	−441966.			−0.643102			−0.321551	−	0.946892i	$-0.604204\pi$
$829$	−441966.			−0.643102			−0.321551	+	0.946892i	$0.604204\pi$
$830$		0			0
$831$			89713.5i			0.129914i
$832$	91760.7	+	73050.2i	0.132559	+	0.105530i
$833$	−588679.			−0.848376
$834$	−288502.	+	391022.i	−0.414779	+	0.562171i
$835$		0			0
$836$	61038.3	+	197684.i	0.0873353	+	0.282852i
$837$	−187369.			−0.267453
$838$	−936880.	−	691246.i	−1.33412	−	0.984338i
$839$			606640.i			0.861801i	0.902399	+	0.430901i	$0.141804\pi$
$839$			606640.i			0.861801i	−0.902399	+	0.430901i	$0.858196\pi$
$840$		0			0
$841$	596436.			0.843281
$842$	79346.2	−	107542.i	0.111918	−	0.151689i
$843$		−	420425.i		−	0.591606i
$844$	−346898.	+	107111.i	−0.486987	+	0.150366i
$845$		0			0
$846$	−342083.	−	252395.i	−0.477960	−	0.352646i
$847$			267060.i			0.372257i
$848$	−976620.	+	666653.i	−1.35811	+	0.927061i
$849$	230805.			0.320206
$850$		0			0
$851$		−	86037.7i		−	0.118804i
$852$	23429.5	+	75880.8i	0.0322763	+	0.104533i
$853$	−167085.			−0.229636			−0.114818	−	0.993387i	$-0.536628\pi$
$853$	−167085.			−0.229636			−0.114818	+	0.993387i	$0.536628\pi$
$854$	334981.	+	247155.i	0.459309	+	0.338885i
$855$		0			0
$856$	−53194.2	+	152226.i	−0.0725966	+	0.207750i
$857$	−1.08085e6			−1.47164			−0.735822	−	0.677175i	$-0.763204\pi$
$857$	−1.08085e6			−1.47164			−0.735822	+	0.677175i	$0.763204\pi$
$858$	−9953.72	+	13490.8i	−0.0135211	+	0.0183258i
$859$			501417.i			0.679536i	0.940509	+	0.339768i	$0.110349\pi$
$859$			501417.i			0.679536i	−0.940509	+	0.339768i	$0.889651\pi$
$860$		0			0
$861$	−124557.			−0.168020
$862$	294534.	+	217312.i	0.396389	+	0.292462i
$863$		−	334736.i		−	0.449449i	−0.974422	−	0.224725i	$-0.927852\pi$
$863$		−	334736.i		−	0.449449i	0.974422	−	0.224725i	$-0.0721483\pi$
$864$	−143566.	−	5270.84i	−0.192321	−	0.00706078i
$865$		0			0
$866$	716461.	−	971056.i	0.955337	−	1.29482i
$867$			3383.78i			0.00450157i
$868$	−121582.	−	393765.i	−0.161372	−	0.522634i
$869$	104733.			0.138690
$870$		0			0
$871$			172757.i			0.227719i
$872$	65433.2	+	22865.1i	0.0860529	+	0.0300705i
$873$	150712.			0.197751
$874$	−68711.4	+	93128.0i	−0.0899510	+	0.121915i
$875$		0			0
$876$	700226.	−	216207.i	0.912494	−	0.281748i
$877$	393662.			0.511829			0.255914	−	0.966699i	$-0.417623\pi$
$877$	393662.			0.511829			0.255914	+	0.966699i	$0.417623\pi$
$878$	566660.	+	418091.i	0.735078	+	0.542353i
$879$		−	63493.6i		−	0.0821773i
$880$		0			0
$881$	−354446.			−0.456665			−0.228333	−	0.973583i	$-0.573327\pi$
$881$	−354446.			−0.456665			−0.228333	+	0.973583i	$0.573327\pi$
$882$	130104.	−	176336.i	0.167245	−	0.226675i
$883$			852839.i			1.09382i	0.837192	+	0.546910i	$0.184196\pi$
$883$			852839.i			1.09382i	−0.837192	+	0.546910i	$0.815804\pi$
$884$	39215.1	+	127005.i	0.0501821	+	0.162524i
$885$		0			0
$886$	610895.	+	450728.i	0.778214	+	0.574179i
$887$		−	620430.i		−	0.788579i	−0.918986	−	0.394290i	$-0.870991\pi$
$887$		−	620430.i		−	0.788579i	0.918986	−	0.394290i	$-0.129009\pi$
$888$	149747.	−	428531.i	0.189903	−	0.543446i
$889$	−191483.			−0.242285
$890$		0			0
$891$		−	20535.6i		−	0.0258673i
$892$	−1.29244e6	+	399063.i	−1.62436	+	0.501547i
$893$	−1.80688e6			−2.26583
$894$	249617.	+	184171.i	0.312319	+	0.230434i
$895$		0			0
$896$	−82081.8	−	305132.i	−0.102242	−	0.380077i
$897$	−9378.31			−0.0116557
$898$	131270.	−	177917.i	0.162784	−	0.220630i
$899$		−	1.52491e6i		−	1.88679i
$900$		0			0
$901$	−1.34008e6			−1.65075
$902$	112697.	+	83149.4i	0.138515	+	0.102199i
$903$		−	66476.5i		−	0.0815254i
$904$	40229.5	+	14057.9i	0.0492275	+	0.0172022i
$905$		0			0
$906$	70157.9	−	95088.6i	0.0854713	−	0.115844i
$907$		−	1.05362e6i		−	1.28077i	−0.768054	−	0.640385i	$-0.778775\pi$
$907$		−	1.05362e6i		−	1.28077i	0.768054	−	0.640385i	$-0.221225\pi$
$908$	−11307.2	+	3491.29i	−0.0137146	+	0.00423462i
$909$	−489737.			−0.592700
$910$		0			0
$911$			1.11079e6i			1.33842i	0.743071	+	0.669212i	$0.233368\pi$
$911$			1.11079e6i			1.33842i	−0.743071	+	0.669212i	$0.766632\pi$
$912$	−504320.	+	344255.i	−0.606341	+	0.413896i
$913$	−168814.			−0.202519
$914$	954357.	−	1.29349e6i	1.14240	−	1.54835i
$915$		0			0
$916$	285009.	+	923054.i	0.339678	+	1.10011i
$917$	485736.			0.577645
$918$	−131013.	−	96663.4i	−0.155464	−	0.114704i
$919$			1.10097e6i			1.30360i	0.758390	+	0.651801i	$0.225986\pi$
$919$			1.10097e6i			1.30360i	−0.758390	+	0.651801i	$0.774014\pi$
$920$		0			0
$921$	−237896.			−0.280458
$922$	−549586.	+	744882.i	−0.646508	+	0.876245i
$923$			27352.4i			0.0321064i
$924$	43156.5	−	13325.3i	0.0505478	−	0.0156075i
$925$		0			0
$926$	−112012.	−	82644.2i	−0.130630	−	0.0963808i
$927$			427923.i			0.497973i
$928$	42896.9	−	1.16842e6i	0.0498116	−	1.35676i
$929$	−1.41544e6			−1.64006			−0.820031	−	0.572319i	$-0.806044\pi$
$929$	−1.41544e6			−1.64006			−0.820031	+	0.572319i	$0.806044\pi$
$930$		0			0
$931$		−	931407.i		−	1.07458i
$932$	−127185.	−	411911.i	−0.146421	−	0.474211i
$933$	−483506.			−0.555442
$934$	−586396.	−	432652.i	−0.672198	−	0.495958i
$935$		0			0
$936$	−46710.9	−	16322.7i	−0.0533171	−	0.0186312i
$937$	250113.			0.284877			0.142439	−	0.989804i	$-0.454506\pi$
$937$	250113.			0.284877			0.142439	+	0.989804i	$0.454506\pi$
$938$	276321.	−	374512.i	0.314057	−	0.425657i
$939$		−	795935.i		−	0.902706i
$940$		0			0
$941$	538389.			0.608019			0.304010	−	0.952669i	$-0.401675\pi$
$941$	538389.			0.608019			0.304010	+	0.952669i	$0.401675\pi$
$942$	496414.	+	366263.i	0.559426	+	0.412754i
$943$			78342.7i			0.0880999i
$944$	−375663.	−	550332.i	−0.421556	−	0.617562i
$945$		0			0
$946$	−44377.1	+	60146.5i	−0.0495880	+	0.0672091i
$947$		−	106656.i		−	0.118928i	−0.998230	−	0.0594640i	$-0.981061\pi$
$947$		−	106656.i		−	0.118928i	0.998230	−	0.0594640i	$-0.0189391\pi$
$948$	91193.4	+	295347.i	0.101472	+	0.328636i
$949$	252407.			0.280266
$950$		0			0
$951$		−	131122.i		−	0.144983i
$952$	118130.	−	338054.i	0.130343	−	0.373002i
$953$	1.33258e6			1.46726			0.733631	−	0.679548i	$-0.237824\pi$
$953$	1.33258e6			1.46726			0.733631	+	0.679548i	$0.237824\pi$
$954$	296171.	−	401416.i	0.325421	−	0.441060i
$955$		0			0
$956$	548560.	−	169377.i	0.600217	−	0.185327i
$957$	167129.			0.182486
$958$	−1.25022e6	−	922429.i	−1.36224	−	1.00508i
$959$			59074.7i			0.0642339i
$960$		0			0
$961$	−860107.			−0.931335
$962$	92824.4	−	125810.i	0.100303	−	0.135945i
$963$		−	68028.4i		−	0.0733564i
$964$	−224479.	−	727018.i	−0.241558	−	0.782332i
$965$		0			0
$966$	20330.9	+	15000.4i	0.0217872	+	0.0160750i
$967$			541951.i			0.579571i	0.957092	+	0.289786i	$0.0935840\pi$
$967$			541951.i			0.579571i	−0.957092	+	0.289786i	$0.906416\pi$
$968$	836629.	+	292353.i	0.892858	+	0.312002i
$969$	−692009.			−0.736995
$970$		0			0
$971$			1.19103e6i			1.26323i	0.775281	+	0.631617i	$0.217608\pi$
$971$			1.19103e6i			1.26323i	−0.775281	+	0.631617i	$0.782392\pi$
$972$	57910.3	−	17880.8i	0.0612947	−	0.0189258i
$973$	450894.			0.476265
$974$	−1.03218e6	−	761560.i	−1.08802	−	0.802761i
$975$		0			0
$976$	1.14098e6	−	778844.i	1.19778	−	0.817619i
$977$	546137.			0.572153			0.286077	−	0.958207i	$-0.407649\pi$
$977$	546137.			0.572153			0.286077	+	0.958207i	$0.407649\pi$
$978$	−137705.	+	186639.i	−0.143970	+	0.195130i
$979$		−	305347.i		−	0.318587i
$980$		0			0
$981$	−29241.5			−0.0303852
$982$	−664078.	−	489968.i	−0.688646	−	0.508094i
$983$			1.29131e6i			1.33636i	0.744001	+	0.668179i	$0.232926\pi$
$983$			1.29131e6i			1.33636i	−0.744001	+	0.668179i	$0.767074\pi$
$984$	−136354.	+	390204.i	−0.140824	+	0.402997i
$985$		0			0
$986$	786698.	−	1.06625e6i	0.809197	−	1.09675i
$987$			394462.i			0.404921i
$988$	−200948.	+	62046.1i	−0.205859	+	0.0635625i
$989$	−41811.7			−0.0427470
$990$		0			0
$991$			1.36845e6i			1.39342i	0.717353	+	0.696709i	$0.245353\pi$
$991$			1.36845e6i			1.39342i	−0.717353	+	0.696709i	$0.754647\pi$
$992$	−1.36666e6	−	50174.9i	−1.38879	−	0.0509874i
$993$	−824416.			−0.836080
$994$	43749.7	−	59296.2i	0.0442794	−	0.0600142i
$995$		0			0
$996$	−146990.	−	476054.i	−0.148173	−	0.479885i
$997$	−533291.			−0.536505			−0.268252	−	0.963349i	$-0.586446\pi$
$997$	−533291.			−0.536505			−0.268252	+	0.963349i	$0.586446\pi$
$998$	1.49731e6	+	1.10474e6i	1.50332	+	1.10917i
$999$			191506.i			0.191890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.d.151.4		16
4.3	odd	2	inner	300.5.c.d.151.3		16
5.2	odd	4		300.5.f.b.199.5		32
5.3	odd	4		300.5.f.b.199.28		32
5.4	even	2		60.5.c.a.31.13	✓	16
15.14	odd	2		180.5.c.c.91.4		16
20.3	even	4		300.5.f.b.199.6		32
20.7	even	4		300.5.f.b.199.27		32
20.19	odd	2		60.5.c.a.31.14	yes	16
40.19	odd	2		960.5.e.f.511.7		16
40.29	even	2		960.5.e.f.511.14		16
60.59	even	2		180.5.c.c.91.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.13	✓	16	5.4	even	2
60.5.c.a.31.14	yes	16	20.19	odd	2
180.5.c.c.91.3		16	60.59	even	2
180.5.c.c.91.4		16	15.14	odd	2
300.5.c.d.151.3		16	4.3	odd	2	inner
300.5.c.d.151.4		16	1.1	even	1	trivial
300.5.f.b.199.5		32	5.2	odd	4
300.5.f.b.199.6		32	20.3	even	4
300.5.f.b.199.27		32	20.7	even	4
300.5.f.b.199.28		32	5.3	odd	4
960.5.e.f.511.7		16	40.19	odd	2
960.5.e.f.511.14		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)

\(f(q)\)	\(=\)	\(q+(-2.37483 + 3.21872i) q^{2} +5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} +(-16.7250 - 12.3400i) q^{6} +19.2859i q^{7} +(60.4174 + 21.1124i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-2.37483 + 3.21872i) q^{2} +5.19615i q^{3} +(-4.72038 - 15.2878i) q^{4} +(-16.7250 - 12.3400i) q^{6} +19.2859i q^{7} +(60.4174 + 21.1124i) q^{8} -27.0000 q^{9} -28.1695i q^{11} +(79.4379 - 24.5278i) q^{12} +28.6347 q^{13} +(-62.0759 - 45.8006i) q^{14} +(-211.436 + 144.329i) q^{16} -290.124 q^{17} +(64.1204 - 86.9056i) q^{18} -459.035i q^{19} -100.212 q^{21} +(90.6699 + 66.8978i) q^{22} +63.0305i q^{23} +(-109.703 + 313.938i) q^{24} +(-68.0024 + 92.1671i) q^{26} -140.296i q^{27} +(294.839 - 91.0366i) q^{28} +1141.80 q^{29} -1335.53i q^{31} +(37.5694 - 1023.31i) q^{32} +146.373 q^{33} +(688.996 - 933.831i) q^{34} +(127.450 + 412.772i) q^{36} -1365.02 q^{37} +(1477.51 + 1090.13i) q^{38} +148.790i q^{39} +1242.93 q^{41} +(237.987 - 322.556i) q^{42} +663.357i q^{43} +(-430.651 + 132.971i) q^{44} +(-202.878 - 149.687i) q^{46} -3936.26i q^{47} +(-749.955 - 1098.65i) q^{48} +2029.06 q^{49} -1507.53i q^{51} +(-135.166 - 437.762i) q^{52} +4618.99 q^{53} +(451.575 + 333.179i) q^{54} +(-407.170 + 1165.20i) q^{56} +2385.22 q^{57} +(-2711.59 + 3675.15i) q^{58} +2602.83i q^{59} -5396.32 q^{61} +(4298.69 + 3171.64i) q^{62} -520.718i q^{63} +(3204.53 + 2551.11i) q^{64} +(-347.611 + 471.135i) q^{66} +6033.14i q^{67} +(1369.50 + 4435.38i) q^{68} -327.516 q^{69} +955.221i q^{71} +(-1631.27 - 570.034i) q^{72} +8814.75 q^{73} +(3241.68 - 4393.61i) q^{74} +(-7017.65 + 2166.82i) q^{76} +543.273 q^{77} +(-478.914 - 353.351i) q^{78} +3717.96i q^{79} +729.000 q^{81} +(-2951.75 + 4000.66i) q^{82} -5992.78i q^{83} +(473.040 + 1532.03i) q^{84} +(-2135.16 - 1575.36i) q^{86} +5932.99i q^{87} +(594.726 - 1701.93i) q^{88} +10839.6 q^{89} +552.244i q^{91} +(963.600 - 297.528i) q^{92} +6939.59 q^{93} +(12669.8 + 9347.95i) q^{94} +(5317.28 + 195.216i) q^{96} -5581.91 q^{97} +(-4818.66 + 6530.97i) q^{98} +760.577i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 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

Properties

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