LMFDB - Embedded newform 300.5.c.d.151.8

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			151.8
Root			$2.77114 + 0.566380i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.5.c.d.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264404 + 3.99125i) q^{2} -5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} +(20.7392 + 1.37388i) q^{6} -29.5855i q^{7} +(12.6174 - 62.7439i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(-0.264404 + 3.99125i) q^{2} -5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} +(20.7392 + 1.37388i) q^{6} -29.5855i q^{7} +(12.6174 - 62.7439i) q^{8} -27.0000 q^{9} +210.571i q^{11} +(-10.9670 + 82.4119i) q^{12} +135.726 q^{13} +(118.083 + 7.82252i) q^{14} +(247.091 + 66.9491i) q^{16} +7.65200 q^{17} +(7.13890 - 107.764i) q^{18} -166.741i q^{19} -153.731 q^{21} +(-840.442 - 55.6758i) q^{22} -405.405i q^{23} +(-326.027 - 65.5622i) q^{24} +(-35.8866 + 541.718i) q^{26} +140.296i q^{27} +(-62.4433 + 469.231i) q^{28} -1646.13 q^{29} -1179.57i q^{31} +(-332.543 + 968.500i) q^{32} +1094.16 q^{33} +(-2.02322 + 30.5410i) q^{34} +(428.225 + 56.9863i) q^{36} -605.018 q^{37} +(665.506 + 44.0870i) q^{38} -705.255i q^{39} -1498.18 q^{41} +(40.6470 - 613.578i) q^{42} -1511.90i q^{43} +(444.432 - 3339.69i) q^{44} +(1618.07 + 107.191i) q^{46} -1880.00i q^{47} +(347.878 - 1283.92i) q^{48} +1525.70 q^{49} -39.7609i q^{51} +(-2152.65 - 286.465i) q^{52} -4955.24 q^{53} +(-559.957 - 37.0948i) q^{54} +(-1856.31 - 373.293i) q^{56} -866.413 q^{57} +(435.242 - 6570.10i) q^{58} -500.976i q^{59} -928.887 q^{61} +(4707.95 + 311.882i) q^{62} +798.809i q^{63} +(-3777.60 - 1583.34i) q^{64} +(-289.300 + 4367.06i) q^{66} -3041.07i q^{67} +(-121.362 - 16.1503i) q^{68} -2106.55 q^{69} +6963.76i q^{71} +(-340.671 + 1694.09i) q^{72} -7810.56 q^{73} +(159.969 - 2414.78i) q^{74} +(-351.925 + 2644.55i) q^{76} +6229.85 q^{77} +(2814.85 + 186.472i) q^{78} -9433.20i q^{79} +729.000 q^{81} +(396.124 - 5979.61i) q^{82} -9487.99i q^{83} +(2438.20 + 324.465i) q^{84} +(6034.36 + 399.751i) q^{86} +8553.52i q^{87} +(13212.1 + 2656.87i) q^{88} +13795.1 q^{89} -4015.54i q^{91} +(-855.649 + 6429.79i) q^{92} -6129.21 q^{93} +(7503.57 + 497.080i) q^{94} +(5032.47 + 1727.94i) q^{96} +7695.33 q^{97} +(-403.400 + 6089.45i) q^{98} -5685.42i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.264404	+	3.99125i	−0.0661009	+	0.997813i
$2$	−0.264404	+	3.99125i	−0.0661009	+	0.997813i
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−15.8602	−	2.11060i	−0.991261	−	0.131913i
$5$		0			0
$5$		0			0
$6$	20.7392	+	1.37388i	0.576088	+	0.0381634i
$7$		−	29.5855i		−	0.603786i	−0.953342	−	0.301893i	$-0.902382\pi$
$7$		−	29.5855i		−	0.603786i	0.953342	−	0.301893i	$-0.0976185\pi$
$8$	12.6174	−	62.7439i	0.197148	−	0.980374i
$9$	−27.0000			−0.333333
$10$		0			0
$11$			210.571i			1.74026i	0.492825	+	0.870128i	$0.335964\pi$
$11$			210.571i			1.74026i	−0.492825	+	0.870128i	$0.664036\pi$
$12$	−10.9670	+	82.4119i	−0.0761599	+	0.572305i
$13$	135.726			0.803115			0.401558	−	0.915834i	$-0.368469\pi$
$13$	135.726			0.803115			0.401558	+	0.915834i	$0.368469\pi$
$14$	118.083	+	7.82252i	0.602465	+	0.0399108i
$15$		0			0
$16$	247.091	+	66.9491i	0.965198	+	0.261520i
$17$	7.65200			0.0264775			0.0132387	−	0.999912i	$-0.495786\pi$
$17$	7.65200			0.0264775			0.0132387	+	0.999912i	$0.495786\pi$
$18$	7.13890	−	107.764i	0.0220336	−	0.332604i
$19$		−	166.741i		−	0.461887i	−0.972967	−	0.230943i	$-0.925819\pi$
$19$		−	166.741i		−	0.461887i	0.972967	−	0.230943i	$-0.0741812\pi$
$20$		0			0
$21$	−153.731			−0.348596
$22$	−840.442	−	55.6758i	−1.73645	−	0.115033i
$23$		−	405.405i		−	0.766361i	−0.923674	−	0.383180i	$-0.874829\pi$
$23$		−	405.405i		−	0.766361i	0.923674	−	0.383180i	$-0.125171\pi$
$24$	−326.027	−	65.5622i	−0.566019	−	0.113823i
$25$		0			0
$26$	−35.8866	+	541.718i	−0.0530867	+	0.801359i
$27$			140.296i			0.192450i
$28$	−62.4433	+	469.231i	−0.0796470	+	0.598509i
$29$	−1646.13			−1.95734			−0.978672	−	0.205431i	$-0.934140\pi$
$29$	−1646.13			−1.95734			−0.978672	+	0.205431i	$0.934140\pi$
$30$		0			0
$31$		−	1179.57i		−	1.22744i	−0.789525	−	0.613718i	$-0.789673\pi$
$31$		−	1179.57i		−	1.22744i	0.789525	−	0.613718i	$-0.210327\pi$
$32$	−332.543	+	968.500i	−0.324749	+	0.945800i
$33$	1094.16			1.00474
$34$	−2.02322	+	30.5410i	−0.00175019	+	0.0264196i
$35$		0			0
$36$	428.225	+	56.9863i	0.330420	+	0.0439709i
$37$	−605.018			−0.441941			−0.220971	−	0.975280i	$-0.570923\pi$
$37$	−605.018			−0.441941			−0.220971	+	0.975280i	$0.570923\pi$
$38$	665.506	+	44.0870i	0.460877	+	0.0305312i
$39$		−	705.255i		−	0.463679i
$40$		0			0
$41$	−1498.18			−0.891243			−0.445621	−	0.895222i	$-0.647017\pi$
$41$	−1498.18			−0.891243			−0.445621	+	0.895222i	$0.647017\pi$
$42$	40.6470	−	613.578i	0.0230425	−	0.347833i
$43$		−	1511.90i		−	0.817683i	−0.912605	−	0.408842i	$-0.865933\pi$
$43$		−	1511.90i		−	0.817683i	0.912605	−	0.408842i	$-0.134067\pi$
$44$	444.432	−	3339.69i	0.229562	−	1.72505i
$45$		0			0
$46$	1618.07	+	107.191i	0.764685	+	0.0506572i
$47$		−	1880.00i		−	0.851066i	−0.904943	−	0.425533i	$-0.860087\pi$
$47$		−	1880.00i		−	0.851066i	0.904943	−	0.425533i	$-0.139913\pi$
$48$	347.878	−	1283.92i	0.150989	−	0.557257i
$49$	1525.70			0.635443
$50$		0			0
$51$		−	39.7609i		−	0.0152868i
$52$	−2152.65	−	286.465i	−0.796097	−	0.105941i
$53$	−4955.24			−1.76406			−0.882029	−	0.471194i	$-0.843823\pi$
$53$	−4955.24			−1.76406			−0.882029	+	0.471194i	$0.843823\pi$
$54$	−559.957	−	37.0948i	−0.192029	−	0.0127211i
$55$		0			0
$56$	−1856.31	−	373.293i	−0.591936	−	0.119035i
$57$	−866.413			−0.266671
$58$	435.242	−	6570.10i	0.129382	−	1.95306i
$59$		−	500.976i		−	0.143917i	−0.997408	−	0.0719587i	$-0.977075\pi$
$59$		−	500.976i		−	0.143917i	0.997408	−	0.0719587i	$-0.0229250\pi$
$60$		0			0
$61$	−928.887			−0.249634			−0.124817	−	0.992180i	$-0.539834\pi$
$61$	−928.887			−0.249634			−0.124817	+	0.992180i	$0.539834\pi$
$62$	4707.95	+	311.882i	1.22475	+	0.0811347i
$63$			798.809i			0.201262i
$64$	−3777.60	−	1583.34i	−0.922266	−	0.386557i
$65$		0			0
$66$	−289.300	+	4367.06i	−0.0664141	+	1.00254i
$67$		−	3041.07i		−	0.677450i	−0.940885	−	0.338725i	$-0.890004\pi$
$67$		−	3041.07i		−	0.677450i	0.940885	−	0.338725i	$-0.109996\pi$
$68$	−121.362	−	16.1503i	−0.0262461	−	0.00349272i
$69$	−2106.55			−0.442459
$70$		0			0
$71$			6963.76i			1.38143i	0.723129	+	0.690713i	$0.242703\pi$
$71$			6963.76i			1.38143i	−0.723129	+	0.690713i	$0.757297\pi$
$72$	−340.671	+	1694.09i	−0.0657159	+	0.326791i
$73$	−7810.56			−1.46567			−0.732835	−	0.680406i	$-0.761803\pi$
$73$	−7810.56			−1.46567			−0.732835	+	0.680406i	$0.761803\pi$
$74$	159.969	−	2414.78i	0.0292127	−	0.440975i
$75$		0			0
$76$	−351.925	+	2644.55i	−0.0609288	+	0.457851i
$77$	6229.85			1.05074
$78$	2814.85	+	186.472i	0.462665	+	0.0306496i
$79$		−	9433.20i		−	1.51149i	−0.654867	−	0.755744i	$-0.727275\pi$
$79$		−	9433.20i		−	1.51149i	0.654867	−	0.755744i	$-0.272725\pi$
$80$		0			0
$81$	729.000			0.111111
$82$	396.124	−	5979.61i	0.0589120	−	0.889293i
$83$		−	9487.99i		−	1.37727i	−0.725110	−	0.688633i	$-0.758211\pi$
$83$		−	9487.99i		−	1.37727i	0.725110	−	0.688633i	$-0.241789\pi$
$84$	2438.20	+	324.465i	0.345550	+	0.0459842i
$85$		0			0
$86$	6034.36	+	399.751i	0.815895	+	0.0540496i
$87$			8553.52i			1.13007i
$88$	13212.1	+	2656.87i	1.70610	+	0.343087i
$89$	13795.1			1.74159			0.870794	−	0.491648i	$-0.163605\pi$
$89$	13795.1			1.74159			0.870794	+	0.491648i	$0.163605\pi$
$90$		0			0
$91$		−	4015.54i		−	0.484909i
$92$	−855.649	+	6429.79i	−0.101093	+	0.759664i
$93$	−6129.21			−0.708661
$94$	7503.57	+	497.080i	0.849204	+	0.0562562i
$95$		0			0
$96$	5032.47	+	1727.94i	0.546058	+	0.187494i
$97$	7695.33			0.817869			0.408934	−	0.912564i	$-0.365900\pi$
$97$	7695.33			0.817869			0.408934	+	0.912564i	$0.365900\pi$
$98$	−403.400	+	6089.45i	−0.0420034	+	0.634053i
$99$		−	5685.42i		−	0.580085i
$100$		0			0
$101$	−4743.34			−0.464988			−0.232494	−	0.972598i	$-0.574689\pi$
$101$	−4743.34			−0.464988			−0.232494	+	0.972598i	$0.574689\pi$
$102$	158.696	+	10.5129i	0.0152534	+	0.00101047i
$103$			549.159i			0.0517635i	0.999665	+	0.0258818i	$0.00823934\pi$
$103$			549.159i			0.0517635i	−0.999665	+	0.0258818i	$0.991761\pi$
$104$	1712.52	−	8516.01i	0.158332	−	0.787353i
$105$		0			0
$106$	1310.18	−	19777.6i	0.116606	−	1.76020i
$107$		−	1692.83i		−	0.147859i	−0.997263	−	0.0739293i	$-0.976446\pi$
$107$		−	1692.83i		−	0.147859i	0.997263	−	0.0739293i	$-0.0235539\pi$
$108$	296.110	−	2225.12i	0.0253866	−	0.190768i
$109$	−15885.9			−1.33708			−0.668542	−	0.743674i	$-0.733081\pi$
$109$	−15885.9			−1.33708			−0.668542	+	0.743674i	$0.733081\pi$
$110$		0			0
$111$			3143.76i			0.255155i
$112$	1980.72	−	7310.30i	0.157902	−	0.582773i
$113$	−8839.42			−0.692256			−0.346128	−	0.938187i	$-0.612504\pi$
$113$	−8839.42			−0.692256			−0.346128	+	0.938187i	$0.612504\pi$
$114$	229.083	−	3458.07i	0.0176272	−	0.266087i
$115$		0			0
$116$	26107.8	+	3474.32i	1.94024	+	0.258199i
$117$	−3664.61			−0.267705
$118$	1999.52	+	132.460i	0.143603	+	0.00951308i
$119$		−	226.388i		−	0.0159867i
$120$		0			0
$121$	−29699.2			−2.02849
$122$	245.601	−	3707.42i	0.0165010	−	0.249088i
$123$			7784.76i			0.514559i
$124$	−2489.60	+	18708.1i	−0.161915	+	1.21671i
$125$		0			0
$126$	−3188.25	−	211.208i	−0.200822	−	0.0133036i
$127$		−	2789.62i		−	0.172957i	−0.996254	−	0.0864784i	$-0.972439\pi$
$127$		−	2789.62i		−	0.172957i	0.996254	−	0.0864784i	$-0.0275614\pi$
$128$	7318.30	−	14658.7i	0.446674	−	0.894697i
$129$	−7856.04			−0.472090
$130$		0			0
$131$			11818.8i			0.688701i	0.938841	+	0.344350i	$0.111901\pi$
$131$			11818.8i			0.688701i	−0.938841	+	0.344350i	$0.888099\pi$
$132$	−17353.6	−	2309.34i	−0.995957	−	0.132538i
$133$	−4933.12			−0.278881
$134$	12137.7	+	804.071i	0.675969	+	0.0447801i
$135$		0			0
$136$	96.5486	−	480.116i	0.00521997	−	0.0259578i
$137$	29908.7			1.59352			0.796759	−	0.604297i	$-0.206546\pi$
$137$	29908.7			1.59352			0.796759	+	0.604297i	$0.206546\pi$
$138$	556.978	−	8407.75i	0.0292469	−	0.441491i
$139$			23947.7i			1.23947i	0.784812	+	0.619733i	$0.212759\pi$
$139$			23947.7i			1.23947i	−0.784812	+	0.619733i	$0.787241\pi$
$140$		0			0
$141$	−9768.79			−0.491363
$142$	−27794.1	−	1841.25i	−1.37840	−	0.0913135i
$143$			28580.1i			1.39763i
$144$	−6671.45	−	1807.63i	−0.321733	−	0.0871733i
$145$		0			0
$146$	2065.14	−	31173.9i	0.0968822	−	1.46246i
$147$		−	7927.76i		−	0.366873i
$148$	9595.69	+	1276.95i	0.438079	+	0.0582977i
$149$	−4438.67			−0.199931			−0.0999656	−	0.994991i	$-0.531873\pi$
$149$	−4438.67			−0.199931			−0.0999656	+	0.994991i	$0.531873\pi$
$150$		0			0
$151$		−	7753.12i		−	0.340034i	−0.985441	−	0.170017i	$-0.945618\pi$
$151$		−	7753.12i		−	0.340034i	0.985441	−	0.170017i	$-0.0543823\pi$
$152$	−10462.0	−	2103.85i	−0.452822	−	0.0910599i
$153$	−206.604			−0.00882583
$154$	−1647.20	+	24864.9i	−0.0694550	+	1.04844i
$155$		0			0
$156$	−1488.51	+	11185.5i	−0.0611651	+	0.459627i
$157$	−29000.7			−1.17655			−0.588273	−	0.808662i	$-0.700192\pi$
$157$	−29000.7			−1.17655			−0.588273	+	0.808662i	$0.700192\pi$
$158$	37650.3	+	2494.17i	1.50818	+	0.0999108i
$159$			25748.2i			1.01848i
$160$		0			0
$161$	−11994.1			−0.462718
$162$	−192.750	+	2909.62i	−0.00734455	+	0.110868i
$163$		−	14916.0i		−	0.561406i	−0.959795	−	0.280703i	$-0.909432\pi$
$163$		−	14916.0i		−	0.561406i	0.959795	−	0.280703i	$-0.0905676\pi$
$164$	23761.4	+	3162.06i	0.883454	+	0.117566i
$165$		0			0
$166$	37868.9	+	2508.66i	1.37425	+	0.0910386i
$167$			26694.7i			0.957178i	0.878039	+	0.478589i	$0.158852\pi$
$167$			26694.7i			0.957178i	−0.878039	+	0.478589i	$0.841148\pi$
$168$	−1939.69	+	9645.67i	−0.0687248	+	0.341754i
$169$	−10139.3			−0.355006
$170$		0			0
$171$			4502.01i			0.153962i
$172$	−3191.01	+	23979.0i	−0.107863	+	0.810538i
$173$	−41306.9			−1.38016			−0.690082	−	0.723731i	$-0.742426\pi$
$173$	−41306.9			−1.38016			−0.690082	+	0.723731i	$0.742426\pi$
$174$	−34139.2	−	2261.58i	−1.12760	−	0.0746989i
$175$		0			0
$176$	−14097.5	+	52030.1i	−0.455112	+	1.67969i
$177$	−2603.15			−0.0830907
$178$	−3647.48	+	55059.8i	−0.115121	+	1.73778i
$179$			30792.3i			0.961029i	0.876987	+	0.480515i	$0.159550\pi$
$179$			30792.3i			0.961029i	−0.876987	+	0.480515i	$0.840450\pi$
$180$		0			0
$181$	−5864.01			−0.178994			−0.0894968	−	0.995987i	$-0.528526\pi$
$181$	−5864.01			−0.178994			−0.0894968	+	0.995987i	$0.528526\pi$
$182$	16027.0	+	1061.72i	0.483849	+	0.0320530i
$183$			4826.64i			0.144126i
$184$	−25436.7	−	5115.17i	−0.751320	−	0.151086i
$185$		0			0
$186$	1620.59	−	24463.2i	0.0468432	−	0.707111i
$187$			1611.29i			0.0460776i
$188$	−3967.94	+	29817.2i	−0.112266	+	0.843629i
$189$	4150.73			0.116199
$190$		0			0
$191$		−	69081.5i		−	1.89363i	−0.321777	−	0.946815i	$-0.604280\pi$
$191$		−	69081.5i		−	1.89363i	0.321777	−	0.946815i	$-0.395720\pi$
$192$	−8227.26	+	19629.0i	−0.223179	+	0.532470i
$193$	−38834.2			−1.04256			−0.521279	−	0.853387i	$-0.674545\pi$
$193$	−38834.2			−1.04256			−0.521279	+	0.853387i	$0.674545\pi$
$194$	−2034.67	+	30714.0i	−0.0540619	+	0.816080i
$195$		0			0
$196$	−24197.8	−	3220.14i	−0.629890	−	0.0838230i
$197$	26569.0			0.684608			0.342304	−	0.939589i	$-0.388793\pi$
$197$	26569.0			0.684608			0.342304	+	0.939589i	$0.388793\pi$
$198$	22691.9	+	1503.25i	0.578817	+	0.0383442i
$199$		−	59241.5i		−	1.49596i	−0.663721	−	0.747980i	$-0.731024\pi$
$199$		−	59241.5i		−	1.49596i	0.663721	−	0.747980i	$-0.268976\pi$
$200$		0			0
$201$	−15801.9			−0.391126
$202$	1254.16	−	18931.9i	0.0307361	−	0.463971i
$203$			48701.4i			1.18182i
$204$	−83.9196	+	630.616i	−0.00201652	+	0.0151532i
$205$		0			0
$206$	−2191.83	−	145.200i	−0.0516503	−	0.00342162i
$207$			10945.9i			0.255454i
$208$	33536.7	+	9086.77i	0.775165	+	0.210031i
$209$	35110.9			0.803802
$210$		0			0
$211$			52946.2i			1.18924i	0.804007	+	0.594620i	$0.202698\pi$
$211$			52946.2i			1.18924i	−0.804007	+	0.594620i	$0.797302\pi$
$212$	78591.0	+	10458.6i	1.74864	+	0.232702i
$213$	36184.8			0.797566
$214$	6756.52	+	447.591i	0.147535	+	0.00977359i
$215$		0			0
$216$	8802.73	+	1770.18i	0.188673	+	0.0379411i
$217$	−34898.1			−0.741109
$218$	4200.29	−	63404.6i	0.0883825	−	1.33416i
$219$			40584.8i			0.846205i
$220$		0			0
$221$	1038.58			0.0212645
$222$	−12547.6	−	831.223i	−0.254597	−	0.0168660i
$223$		−	12221.6i		−	0.245764i	−0.992421	−	0.122882i	$-0.960786\pi$
$223$		−	12221.6i		−	0.245764i	0.992421	−	0.122882i	$-0.0392137\pi$
$224$	28653.5	+	9838.44i	0.571061	+	0.196079i
$225$		0			0
$226$	2337.17	−	35280.3i	0.0457588	−	0.690742i
$227$		−	52981.1i		−	1.02818i	−0.857736	−	0.514090i	$-0.828130\pi$
$227$		−	52981.1i		−	1.02818i	0.857736	−	0.514090i	$-0.171870\pi$
$228$	13741.5	+	1828.65i	0.264340	+	0.0351772i
$229$	26289.4			0.501315			0.250657	−	0.968076i	$-0.419353\pi$
$229$	26289.4			0.501315			0.250657	+	0.968076i	$0.419353\pi$
$230$		0			0
$231$		−	32371.2i		−	0.606646i
$232$	−20769.9	+	103284.i	−0.385885	+	1.91893i
$233$	−37894.8			−0.698020			−0.349010	−	0.937119i	$-0.613482\pi$
$233$	−37894.8			−0.698020			−0.349010	+	0.937119i	$0.613482\pi$
$234$	968.938	−	14626.4i	0.0176956	−	0.267120i
$235$		0			0
$236$	−1057.36	+	7945.58i	−0.0189845	+	0.142660i
$237$	−49016.3			−0.872658
$238$	903.572	+	59.8579i	0.0159518	+	0.00105674i
$239$			7490.41i			0.131132i	0.997848	+	0.0655662i	$0.0208853\pi$
$239$			7490.41i			0.131132i	−0.997848	+	0.0655662i	$0.979115\pi$
$240$		0			0
$241$	76034.4			1.30911			0.654555	−	0.756014i	$-0.272856\pi$
$241$	76034.4			1.30911			0.654555	+	0.756014i	$0.272856\pi$
$242$	7852.57	−	118537.i	0.134085	−	2.02406i
$243$		−	3788.00i		−	0.0641500i
$244$	14732.3	+	1960.51i	0.247452	+	0.0329299i
$245$		0			0
$246$	−31071.0	−	2058.32i	−0.513434	−	0.0340128i
$247$		−	22631.2i		−	0.370948i
$248$	−74010.6	−	14883.1i	−1.20335	−	0.241986i
$249$	−49301.0			−0.795165
$250$		0			0
$251$		−	40829.4i		−	0.648076i	−0.946044	−	0.324038i	$-0.894959\pi$
$251$		−	40829.4i		−	0.648076i	0.946044	−	0.324038i	$-0.105041\pi$
$252$	1685.97	−	12669.2i	0.0265490	−	0.199503i
$253$	85366.5			1.33366
$254$	11134.1	+	737.587i	0.172579	+	0.0114326i
$255$		0			0
$256$	56571.6	+	33085.0i	0.863215	+	0.504837i
$257$	89298.5			1.35200			0.676002	−	0.736900i	$-0.263711\pi$
$257$	89298.5			1.35200			0.676002	+	0.736900i	$0.263711\pi$
$258$	2077.17	−	31355.5i	0.0312056	−	0.471057i
$259$			17899.8i			0.266838i
$260$		0			0
$261$	44445.4			0.652448
$262$	−47171.8	−	3124.93i	−0.687195	−	0.0455238i
$263$			9881.37i			0.142858i	0.997446	+	0.0714292i	$0.0227560\pi$
$263$			9881.37i			0.142858i	−0.997446	+	0.0714292i	$0.977244\pi$
$264$	13805.5	−	68651.8i	0.198082	−	0.985018i
$265$		0			0
$266$	1304.34	−	19689.3i	0.0184343	−	0.278271i
$267$		−	71681.5i		−	1.00551i
$268$	−6418.50	+	48232.0i	−0.0893643	+	0.671530i
$269$	106250.			1.46833			0.734163	−	0.678974i	$-0.237575\pi$
$269$	106250.			1.46833			0.734163	+	0.678974i	$0.237575\pi$
$270$		0			0
$271$			64500.8i			0.878267i	0.898422	+	0.439133i	$0.144714\pi$
$271$			64500.8i			0.878267i	−0.898422	+	0.439133i	$0.855286\pi$
$272$	1890.74	+	512.294i	0.0255560	+	0.00692440i
$273$	−20865.3			−0.279963
$274$	−7907.98	+	119373.i	−0.105333	+	1.59003i
$275$		0			0
$276$	33410.2	+	4446.08i	0.438592	+	0.0583659i
$277$	99154.8			1.29227			0.646136	−	0.763222i	$-0.276384\pi$
$277$	99154.8			1.29227			0.646136	+	0.763222i	$0.276384\pi$
$278$	−95581.5	−	6331.87i	−1.23676	−	0.0819299i
$279$			31848.3i			0.409146i
$280$		0			0
$281$	−53023.5			−0.671515			−0.335758	−	0.941948i	$-0.608992\pi$
$281$	−53023.5			−0.671515			−0.335758	+	0.941948i	$0.608992\pi$
$282$	2582.90	−	38989.7i	0.0324796	−	0.490288i
$283$		−	135026.i		−	1.68596i	−0.537949	−	0.842978i	$-0.680801\pi$
$283$		−	135026.i		−	1.68596i	0.537949	−	0.842978i	$-0.319199\pi$
$284$	14697.8	−	110447.i	0.182228	−	1.36935i
$285$		0			0
$286$	−114070.	−	7556.68i	−1.39457	−	0.0923844i
$287$			44324.4i			0.538120i
$288$	8978.65	−	26149.5i	0.108250	−	0.315267i
$289$	−83462.4			−0.999299
$290$		0			0
$291$		−	39986.1i		−	0.472197i
$292$	123877.	+	16485.0i	1.45286	+	0.193341i
$293$	133739.			1.55784			0.778922	−	0.627120i	$-0.215767\pi$
$293$	133739.			1.55784			0.778922	+	0.627120i	$0.215767\pi$
$294$	31641.7	+	2096.13i	0.366071	+	0.0242507i
$295$		0			0
$296$	−7633.78	+	37961.2i	−0.0871277	+	0.433268i
$297$	−29542.3			−0.334913
$298$	1173.60	−	17715.9i	0.0132156	−	0.199494i
$299$		−	55024.2i		−	0.615476i
$300$		0			0
$301$	−44730.2			−0.493706
$302$	30944.7	+	2049.96i	0.339291	+	0.0224766i
$303$			24647.1i			0.268461i
$304$	11163.2	−	41200.2i	0.120793	−	0.445812i
$305$		0			0
$306$	54.6269	−	824.608i	0.000583396	−	0.00880653i
$307$			125386.i			1.33037i	0.746678	+	0.665185i	$0.231647\pi$
$307$			125386.i			1.33037i	−0.746678	+	0.665185i	$0.768353\pi$
$308$	−98806.5	−	13148.7i	−1.04156	−	0.138606i
$309$	2853.51			0.0298857
$310$		0			0
$311$			34537.2i			0.357080i	0.983933	+	0.178540i	$0.0571375\pi$
$311$			34537.2i			0.357080i	−0.983933	+	0.178540i	$0.942863\pi$
$312$	−44250.5	−	8898.52i	−0.454579	−	0.0914131i
$313$	16667.3			0.170129			0.0850644	−	0.996375i	$-0.472890\pi$
$313$	16667.3			0.170129			0.0850644	+	0.996375i	$0.472890\pi$
$314$	7667.89	−	115749.i	0.0777708	−	1.17397i
$315$		0			0
$316$	−19909.7	+	149612.i	−0.199385	+	1.49828i
$317$	−73762.0			−0.734030			−0.367015	−	0.930215i	$-0.619620\pi$
$317$	−73762.0			−0.734030			−0.367015	+	0.930215i	$0.619620\pi$
$318$	−102768.	−	6807.92i	−1.01625	−	0.0673225i
$319$		−	346626.i		−	3.40628i
$320$		0			0
$321$	−8796.21			−0.0853661
$322$	3171.29	−	47871.5i	0.0305861	−	0.461706i
$323$		−	1275.90i		−	0.0122296i
$324$	−11562.1	−	1538.63i	−0.110140	−	0.0146570i
$325$		0			0
$326$	59533.5	+	3943.85i	0.560178	+	0.0371095i
$327$			82545.6i			0.771966i
$328$	−18903.2	+	94001.6i	−0.175706	+	0.873751i
$329$	−55620.9			−0.513861
$330$		0			0
$331$			122804.i			1.12088i	0.828196	+	0.560438i	$0.189367\pi$
$331$			122804.i			1.12088i	−0.828196	+	0.560438i	$0.810633\pi$
$332$	−20025.4	+	150481.i	−0.181679	+	1.36523i
$333$	16335.5			0.147314
$334$	−106545.	−	7058.19i	−0.955085	−	0.0632704i
$335$		0			0
$336$	−37985.4	−	10292.1i	−0.336464	−	0.0911648i
$337$	−93476.4			−0.823081			−0.411540	−	0.911392i	$-0.635009\pi$
$337$	−93476.4			−0.823081			−0.411540	+	0.911392i	$0.635009\pi$
$338$	2680.88	−	40468.6i	0.0234662	−	0.354230i
$339$			45931.0i			0.399674i
$340$		0			0
$341$	248383.			2.13605
$342$	−17968.7	−	1190.35i	−0.153626	−	0.0101771i
$343$		−	116173.i		−	0.987457i
$344$	−94862.3	−	19076.3i	−0.801635	−	0.161204i
$345$		0			0
$346$	10921.7	−	164866.i	0.0912302	−	1.37715i
$347$		−	16526.2i		−	0.137251i	−0.997643	−	0.0686253i	$-0.978139\pi$
$347$		−	16526.2i		−	0.137251i	0.997643	−	0.0686253i	$-0.0218613\pi$
$348$	18053.1	−	135660.i	0.149071	−	1.12020i
$349$	−78324.9			−0.643056			−0.321528	−	0.946900i	$-0.604196\pi$
$349$	−78324.9			−0.643056			−0.321528	+	0.946900i	$0.604196\pi$
$350$		0			0
$351$			19041.9i			0.154560i
$352$	−203938.	−	70023.8i	−1.64594	−	0.565146i
$353$	89837.2			0.720953			0.360476	−	0.932768i	$-0.382614\pi$
$353$	89837.2			0.720953			0.360476	+	0.932768i	$0.382614\pi$
$354$	688.283	−	10389.8i	0.00549238	−	0.0829090i
$355$		0			0
$356$	−218793.	−	29116.0i	−1.72637	−	0.229738i
$357$	−1176.35			−0.00922995
$358$	−122900.	−	8141.61i	−0.958928	−	0.0635250i
$359$			152507.i			1.18332i	0.806188	+	0.591659i	$0.201527\pi$
$359$			152507.i			1.18332i	−0.806188	+	0.591659i	$0.798473\pi$
$360$		0			0
$361$	102518.			0.786660
$362$	1550.47	−	23404.8i	0.0118317	−	0.178602i
$363$			154321.i			1.17115i
$364$	−8475.21	+	63687.1i	−0.0639657	+	0.480672i
$365$		0			0
$366$	−19264.3	−	1276.18i	−0.143811	−	0.00952687i
$367$		−	110809.i		−	0.822700i	−0.911477	−	0.411350i	$-0.865057\pi$
$367$		−	110809.i		−	0.822700i	0.911477	−	0.411350i	$-0.134943\pi$
$368$	27141.5	−	100172.i	0.200419	−	0.739690i
$369$	40450.8			0.297081
$370$		0			0
$371$			146603.i			1.06511i
$372$	97210.3	+	12936.3i	0.702468	+	0.0934814i
$373$	146097.			1.05009			0.525043	−	0.851076i	$-0.324049\pi$
$373$	146097.			1.05009			0.525043	+	0.851076i	$0.324049\pi$
$374$	−6431.06	−	426.031i	−0.0459769	−	0.00304577i
$375$		0			0
$376$	−117959.	−	23720.8i	−0.834363	−	0.167786i
$377$	−223423.			−1.57197
$378$	−1097.47	+	16566.6i	−0.00768084	+	0.115944i
$379$		−	193663.i		−	1.34824i	−0.738620	−	0.674122i	$-0.764522\pi$
$379$		−	193663.i		−	1.34824i	0.738620	−	0.674122i	$-0.235478\pi$
$380$		0			0
$381$	−14495.3			−0.0998567
$382$	275722.	+	18265.4i	1.88949	+	0.125171i
$383$		−	144521.i		−	0.985223i	−0.870249	−	0.492612i	$-0.836042\pi$
$383$		−	144521.i		−	0.985223i	0.870249	−	0.492612i	$-0.163958\pi$
$384$	−76168.9	−	38027.0i	−0.516553	−	0.257887i
$385$		0			0
$386$	10267.9	−	154997.i	0.0689140	−	1.04028i
$387$			40821.2i			0.272561i
$388$	−122049.	−	16241.8i	−0.810722	−	0.107887i
$389$	−111547.			−0.737153			−0.368577	−	0.929597i	$-0.620155\pi$
$389$	−111547.			−0.737153			−0.368577	+	0.929597i	$0.620155\pi$
$390$		0			0
$391$		−	3102.16i		−	0.0202913i
$392$	19250.4	−	95728.3i	0.125276	−	0.622971i
$393$	61412.3			0.397622
$394$	−7024.93	+	106043.i	−0.0452533	+	0.683111i
$395$		0			0
$396$	−11999.7	+	90171.8i	−0.0765207	+	0.575016i
$397$	−151266.			−0.959756			−0.479878	−	0.877335i	$-0.659319\pi$
$397$	−151266.			−0.959756			−0.479878	+	0.877335i	$0.659319\pi$
$398$	236448.	+	15663.7i	1.49269	+	0.0988844i
$399$			25633.3i			0.161012i
$400$		0			0
$401$	79502.4			0.494415			0.247207	−	0.968963i	$-0.420487\pi$
$401$	79502.4			0.494415			0.247207	+	0.968963i	$0.420487\pi$
$402$	4178.08	−	63069.3i	0.0258538	−	0.390271i
$403$		−	160098.i		−	0.985773i
$404$	75230.3	+	10011.3i	0.460925	+	0.0613379i
$405$		0			0
$406$	−194380.	−	12876.8i	−1.17923	−	0.0781191i
$407$		−	127399.i		−	0.769091i
$408$	−2494.76	−	501.681i	−0.0149868	−	0.00301375i
$409$	294406.			1.75995			0.879975	−	0.475020i	$-0.157559\pi$
$409$	294406.			1.75995			0.879975	+	0.475020i	$0.157559\pi$
$410$		0			0
$411$		−	155410.i		−	0.920018i
$412$	1159.06	−	8709.76i	0.00682827	−	0.0513112i
$413$	−14821.6			−0.0868953
$414$	−43688.0	−	2894.15i	−0.254895	−	0.0168857i
$415$		0			0
$416$	−45134.8	+	131451.i	−0.260811	+	0.759587i
$417$	124436.			0.715607
$418$	−9283.44	+	140136.i	−0.0531321	+	0.802044i
$419$			250549.i			1.42713i	0.700587	+	0.713567i	$0.252921\pi$
$419$			250549.i			1.42713i	−0.700587	+	0.713567i	$0.747079\pi$
$420$		0			0
$421$	171788.			0.969234			0.484617	−	0.874726i	$-0.338959\pi$
$421$	171788.			0.969234			0.484617	+	0.874726i	$0.338959\pi$
$422$	−211322.	−	13999.2i	−1.18664	−	0.0786099i
$423$			50760.1i			0.283689i
$424$	−62522.5	+	310911.i	−0.347780	+	1.72944i
$425$		0			0
$426$	−9567.39	+	144423.i	−0.0527199	+	0.795822i
$427$			27481.6i			0.150725i
$428$	−3572.90	+	26848.6i	−0.0195044	+	0.146566i
$429$	148506.			0.806920
$430$		0			0
$431$		−	142972.i		−	0.769658i	−0.922988	−	0.384829i	$-0.874260\pi$
$431$		−	142972.i		−	0.769658i	0.922988	−	0.384829i	$-0.125740\pi$
$432$	−9392.70	+	34665.9i	−0.0503296	+	0.185752i
$433$	−77884.1			−0.415406			−0.207703	−	0.978192i	$-0.566599\pi$
$433$	−77884.1			−0.415406			−0.207703	+	0.978192i	$0.566599\pi$
$434$	9227.18	−	139287.i	0.0489880	−	0.739488i
$435$		0			0
$436$	251953.	+	33528.8i	1.32540	+	0.176379i
$437$	−67597.7			−0.353972
$438$	−161984.	−	10730.8i	−0.844354	−	0.0559350i
$439$			45863.6i			0.237979i	0.992895	+	0.118990i	$0.0379655\pi$
$439$			45863.6i			0.237979i	−0.992895	+	0.118990i	$0.962034\pi$
$440$		0			0
$441$	−41193.8			−0.211814
$442$	−274.604	+	4145.23i	−0.00140560	+	0.0212180i
$443$			178266.i			0.908367i	0.890908	+	0.454184i	$0.150069\pi$
$443$			178266.i			0.908367i	−0.890908	+	0.454184i	$0.849931\pi$
$444$	6635.24	−	49860.7i	0.0336582	−	0.252925i
$445$		0			0
$446$	48779.6	+	3231.44i	0.245227	+	0.0162453i
$447$			23064.0i			0.115430i
$448$	−46843.8	+	111762.i	−0.233397	+	0.556851i
$449$	−72533.3			−0.359786			−0.179893	−	0.983686i	$-0.557575\pi$
$449$	−72533.3			−0.359786			−0.179893	+	0.983686i	$0.557575\pi$
$450$		0			0
$451$		−	315473.i		−	1.55099i
$452$	140195.	+	18656.5i	0.686207	+	0.0913174i
$453$	−40286.4			−0.196319
$454$	211461.	+	14008.4i	1.02593	+	0.0679637i
$455$		0			0
$456$	−10931.9	+	54362.1i	−0.0525734	+	0.261437i
$457$	21324.1			0.102103			0.0510514	−	0.998696i	$-0.483743\pi$
$457$	21324.1			0.102103			0.0510514	+	0.998696i	$0.483743\pi$
$458$	−6951.03	+	104928.i	−0.0331374	+	0.500218i
$459$			1073.55i			0.00509560i
$460$		0			0
$461$	−24839.5			−0.116880			−0.0584401	−	0.998291i	$-0.518613\pi$
$461$	−24839.5			−0.116880			−0.0584401	+	0.998291i	$0.518613\pi$
$462$	129202.	+	8559.08i	0.605319	+	0.0400999i
$463$			64668.0i			0.301667i	0.988559	+	0.150833i	$0.0481957\pi$
$463$			64668.0i			0.301667i	−0.988559	+	0.150833i	$0.951804\pi$
$464$	−406742.	−	110207.i	−1.88922	−	0.511884i
$465$		0			0
$466$	10019.5	−	151248.i	0.0461398	−	0.696493i
$467$			172892.i			0.792761i	0.918086	+	0.396381i	$0.129734\pi$
$467$			172892.i			0.792761i	−0.918086	+	0.396381i	$0.870266\pi$
$468$	58121.4	+	7734.55i	0.265366	+	0.0353137i
$469$	−89971.7			−0.409035
$470$		0			0
$471$			150692.i			0.679279i
$472$	−31433.2	−	6321.04i	−0.141093	−	0.0283730i
$473$	318362.			1.42298
$474$	12960.1	−	195637.i	0.0576835	−	0.870750i
$475$		0			0
$476$	−477.816	+	3590.56i	−0.00210885	+	0.0158470i
$477$	133792.			0.588020
$478$	−29896.1	−	1980.49i	−0.130846	−	0.00866797i
$479$		−	19930.4i		−	0.0868652i	−0.999056	−	0.0434326i	$-0.986171\pi$
$479$		−	19930.4i		−	0.0868652i	0.999056	−	0.0434326i	$-0.0138294\pi$
$480$		0			0
$481$	−82116.9			−0.354930
$482$	−20103.8	+	303473.i	−0.0865334	+	1.30625i
$483$			62323.2i			0.267150i
$484$	471034.	+	62683.2i	2.01077	+	0.267584i
$485$		0			0
$486$	15118.8	+	1001.56i	0.0640097	+	0.00424038i
$487$		−	110147.i		−	0.464426i	−0.972665	−	0.232213i	$-0.925403\pi$
$487$		−	110147.i		−	0.464426i	0.972665	−	0.232213i	$-0.0745966\pi$
$488$	−11720.2	+	58282.0i	−0.0492147	+	0.244734i
$489$	−77505.8			−0.324128
$490$		0			0
$491$		−	164562.i		−	0.682599i	−0.939955	−	0.341300i	$-0.889133\pi$
$491$		−	164562.i		−	0.682599i	0.939955	−	0.341300i	$-0.110867\pi$
$492$	16430.6	−	123468.i	0.0678769	−	0.510063i
$493$	−12596.1			−0.0518255
$494$	90326.8	+	5983.77i	0.370137	+	0.0245200i
$495$		0			0
$496$	78971.0	−	291460.i	0.320999	−	1.18472i
$497$	206026.			0.834085
$498$	13035.4	−	196773.i	0.0525612	−	0.793426i
$499$			104374.i			0.419169i	0.977791	+	0.209585i	$0.0672112\pi$
$499$			104374.i			0.419169i	−0.977791	+	0.209585i	$0.932789\pi$
$500$		0			0
$501$	138710.			0.552627
$502$	162960.	+	10795.5i	0.646658	+	0.0428384i
$503$			177345.i			0.700945i	0.936573	+	0.350472i	$0.113979\pi$
$503$			177345.i			0.700945i	−0.936573	+	0.350472i	$0.886021\pi$
$504$	50120.4	+	10078.9i	0.197312	+	0.0396783i
$505$		0			0
$506$	−22571.2	+	340719.i	−0.0881565	+	1.33075i
$507$			52685.5i			0.204963i
$508$	−5887.79	+	44243.9i	−0.0228152	+	0.171445i
$509$	68651.6			0.264981			0.132491	−	0.991184i	$-0.457703\pi$
$509$	68651.6			0.264981			0.132491	+	0.991184i	$0.457703\pi$
$510$		0			0
$511$			231079.i			0.884951i
$512$	−147008.	+	217044.i	−0.560792	+	0.827956i
$513$	23393.1			0.0888902
$514$	−23610.9	+	356413.i	−0.0893687	+	1.34905i
$515$		0			0
$516$	124598.	+	16581.0i	0.467964	+	0.0622747i
$517$	395874.			1.48107
$518$	−71442.4	−	4732.76i	−0.266254	−	0.0176382i
$519$			214637.i			0.796838i
$520$		0			0
$521$	−371672.			−1.36926			−0.684628	−	0.728893i	$-0.740035\pi$
$521$	−371672.			−1.36926			−0.684628	+	0.728893i	$0.740035\pi$
$522$	−11751.5	+	177393.i	−0.0431274	+	0.651021i
$523$			247920.i			0.906376i	0.891415	+	0.453188i	$0.149713\pi$
$523$			247920.i			0.906376i	−0.891415	+	0.453188i	$0.850287\pi$
$524$	24944.8	−	187448.i	0.0908484	−	0.682683i
$525$		0			0
$526$	−39439.1	−	2612.67i	−0.142546	−	0.00944308i
$527$		−	9026.04i		−	0.0324994i
$528$	270357.	+	73253.0i	0.969771	+	0.262759i
$529$	115488.			0.412691
$530$		0			0
$531$			13526.4i			0.0479725i
$532$	78240.2	+	10411.9i	0.276444	+	0.0367879i
$533$	−203342.			−0.715770
$534$	286099.	+	18952.9i	1.00331	+	0.0664649i
$535$		0			0
$536$	−190809.	−	38370.6i	−0.664154	−	0.133558i
$537$	160002.			0.554851
$538$	−28092.8	+	424069.i	−0.0970577	+	1.46511i
$539$			321268.i			1.10583i
$540$		0			0
$541$	−283935.			−0.970119			−0.485059	−	0.874481i	$-0.661202\pi$
$541$	−283935.			−0.970119			−0.485059	+	0.874481i	$0.661202\pi$
$542$	−257439.	−	17054.3i	−0.876346	−	0.0580543i
$543$			30470.3i			0.103342i
$544$	−2544.61	+	7410.95i	−0.00859853	+	0.0250424i
$545$		0			0
$546$	5516.87	−	83278.8i	0.0185058	−	0.279350i
$547$		−	573141.i		−	1.91552i	−0.287567	−	0.957761i	$-0.592846\pi$
$547$		−	573141.i		−	1.91552i	0.287567	−	0.957761i	$-0.407154\pi$
$548$	−474358.	−	63125.5i	−1.57959	−	0.210205i
$549$	25080.0			0.0832113
$550$		0			0
$551$			274477.i			0.904071i
$552$	−26579.2	+	132173.i	−0.0872296	+	0.433775i
$553$	−279086.			−0.912615
$554$	−26216.9	+	395752.i	−0.0854204	+	1.28945i
$555$		0			0
$556$	50544.2	−	379815.i	0.163501	−	1.22864i
$557$	−148550.			−0.478810			−0.239405	−	0.970920i	$-0.576952\pi$
$557$	−148550.			−0.478810			−0.239405	+	0.970920i	$0.576952\pi$
$558$	−127115.	−	8420.81i	−0.408251	−	0.0270449i
$559$		−	205204.i		−	0.656694i
$560$		0			0
$561$	8372.50			0.0266029
$562$	14019.6	−	211630.i	0.0443878	−	0.670047i
$563$			518103.i			1.63455i	0.576246	+	0.817277i	$0.304517\pi$
$563$			518103.i			1.63455i	−0.576246	+	0.817277i	$0.695483\pi$
$564$	154935.	+	20618.0i	0.487069	+	0.0648171i
$565$		0			0
$566$	538925.	+	35701.5i	1.68227	+	0.111443i
$567$		−	21567.8i		−	0.0670873i
$568$	436934.	+	87864.9i	1.35431	+	0.272345i
$569$	−250898.			−0.774948			−0.387474	−	0.921881i	$-0.626652\pi$
$569$	−250898.			−0.774948			−0.387474	+	0.921881i	$0.626652\pi$
$570$		0			0
$571$		−	379446.i		−	1.16380i	−0.813261	−	0.581899i	$-0.802310\pi$
$571$		−	379446.i		−	1.16380i	0.813261	−	0.581899i	$-0.197690\pi$
$572$	60321.2	−	453285.i	0.184365	−	1.38541i
$573$	−358958.			−1.09329
$574$	−176910.	−	11719.5i	−0.536943	−	0.0355702i
$575$		0			0
$576$	101995.	+	42750.1i	0.307422	+	0.128852i
$577$	84917.5			0.255062			0.127531	−	0.991835i	$-0.459295\pi$
$577$	84917.5			0.255062			0.127531	+	0.991835i	$0.459295\pi$
$578$	22067.8	−	333120.i	0.0660546	−	0.997113i
$579$			201788.i			0.601921i
$580$		0			0
$581$	−280707.			−0.831574
$582$	159595.	+	10572.5i	0.471164	+	0.0312127i
$583$		−	1.04343e6i		−	3.06991i
$584$	−98549.3	+	490065.i	−0.288953	+	1.43690i
$585$		0			0
$586$	−35361.2	+	533788.i	−0.102975	+	1.55444i
$587$			540757.i			1.56937i	0.619893	+	0.784686i	$0.287176\pi$
$587$			540757.i			1.56937i	−0.619893	+	0.784686i	$0.712824\pi$
$588$	−16732.4	+	125736.i	−0.0483952	+	0.363667i
$589$	−196682.			−0.566937
$590$		0			0
$591$		−	138056.i		−	0.395259i
$592$	−149494.	−	40505.4i	−0.426561	−	0.115577i
$593$	−304664.			−0.866386			−0.433193	−	0.901301i	$-0.642613\pi$
$593$	−304664.			−0.866386			−0.433193	+	0.901301i	$0.642613\pi$
$594$	7811.10	−	117911.i	0.0221380	−	0.334180i
$595$		0			0
$596$	70398.2	+	9368.28i	0.198184	+	0.0263735i
$597$	−307828.			−0.863693
$598$	219615.	+	14548.6i	0.614130	+	0.0406835i
$599$		−	148036.i		−	0.412584i	−0.978490	−	0.206292i	$-0.933860\pi$
$599$		−	148036.i		−	0.412584i	0.978490	−	0.206292i	$-0.0661397\pi$
$600$		0			0
$601$	−149586.			−0.414134			−0.207067	−	0.978327i	$-0.566392\pi$
$601$	−149586.			−0.414134			−0.207067	+	0.978327i	$0.566392\pi$
$602$	11826.8	−	178530.i	0.0326344	−	0.492626i
$603$			82109.0i			0.225817i
$604$	−16363.8	+	122966.i	−0.0448549	+	0.337063i
$605$		0			0
$606$	−98372.9	−	6516.79i	−0.267874	−	0.0177455i
$607$			220755.i			0.599147i	0.954073	+	0.299574i	$0.0968445\pi$
$607$			220755.i			0.599147i	−0.954073	+	0.299574i	$0.903156\pi$
$608$	161489.	+	55448.5i	0.436853	+	0.149997i
$609$	253060.			0.682322
$610$		0			0
$611$		−	255166.i		−	0.683504i
$612$	3276.78	+	436.059i	0.00874871	+	0.00116424i
$613$	15013.9			0.0399551			0.0199776	−	0.999800i	$-0.493641\pi$
$613$	15013.9			0.0399551			0.0199776	+	0.999800i	$0.493641\pi$
$614$	−500447.	−	33152.6i	−1.32746	−	0.0879387i
$615$		0			0
$616$	78604.8	−	390885.i	0.207151	−	1.03012i
$617$	−537682.			−1.41239			−0.706196	−	0.708016i	$-0.749590\pi$
$617$	−537682.			−1.41239			−0.706196	+	0.708016i	$0.749590\pi$
$618$	−754.480	+	11389.1i	−0.00197547	+	0.0298203i
$619$		−	22215.9i		−	0.0579806i	−0.999580	−	0.0289903i	$-0.990771\pi$
$619$		−	22215.9i		−	0.0579806i	0.999580	−	0.0289903i	$-0.00922919\pi$
$620$		0			0
$621$	56876.7			0.147486
$622$	−137847.	−	9131.76i	−0.356299	−	0.0236034i
$623$		−	408135.i		−	1.05155i
$624$	47216.2	−	174262.i	0.121261	−	0.447542i
$625$		0			0
$626$	−4406.91	+	66523.6i	−0.0112457	+	0.169757i
$627$		−	182441.i		−	0.464075i
$628$	459956.	+	61209.0i	1.16626	+	0.155201i
$629$	−4629.59			−0.0117015
$630$		0			0
$631$			356750.i			0.895994i	0.894035	+	0.447997i	$0.147863\pi$
$631$			356750.i			0.895994i	−0.894035	+	0.447997i	$0.852137\pi$
$632$	−591876.	−	119023.i	−1.48182	−	0.297986i
$633$	275116.			0.686608
$634$	19502.9	−	294403.i	0.0485201	−	0.732425i
$635$		0			0
$636$	54344.2	−	408371.i	0.134350	−	1.00958i
$637$	207078.			0.510334
$638$	1.38347e6	+	91649.3i	3.39883	+	0.225158i
$639$		−	188022.i		−	0.460475i
$640$		0			0
$641$	41392.0			0.100740			0.0503698	−	0.998731i	$-0.483960\pi$
$641$	41392.0			0.100740			0.0503698	+	0.998731i	$0.483960\pi$
$642$	2325.75	−	35107.9i	0.00564278	−	0.0851794i
$643$			342725.i			0.828940i	0.910063	+	0.414470i	$0.136033\pi$
$643$			342725.i			0.828940i	−0.910063	+	0.414470i	$0.863967\pi$
$644$	190229.	+	25314.8i	0.458674	+	0.0610384i
$645$		0			0
$646$	5092.45	+	337.354i	0.0122029	+	0.000808389i
$647$		−	300662.i		−	0.718240i	−0.933291	−	0.359120i	$-0.883077\pi$
$647$		−	300662.i		−	0.718240i	0.933291	−	0.359120i	$-0.116923\pi$
$648$	9198.12	−	45740.3i	0.0219053	−	0.108930i
$649$	105491.			0.250453
$650$		0			0
$651$			181336.i			0.427879i
$652$	−31481.8	+	236571.i	−0.0740567	+	0.556500i
$653$	−127668.			−0.299402			−0.149701	−	0.988731i	$-0.547831\pi$
$653$	−127668.			−0.299402			−0.149701	+	0.988731i	$0.547831\pi$
$654$	−329460.	−	21825.4i	−0.770278	−	0.0510277i
$655$		0			0
$656$	−370186.	−	100302.i	−0.860226	−	0.233078i
$657$	210885.			0.488557
$658$	14706.4	−	221997.i	0.0339667	−	0.512738i
$659$		−	387877.i		−	0.893147i	−0.894747	−	0.446574i	$-0.852644\pi$
$659$		−	387877.i		−	0.893147i	0.894747	−	0.446574i	$-0.147356\pi$
$660$		0			0
$661$	116256.			0.266079			0.133040	−	0.991111i	$-0.457526\pi$
$661$	116256.			0.266079			0.133040	+	0.991111i	$0.457526\pi$
$662$	−490143.	−	32469.9i	−1.11842	−	0.0740910i
$663$		−	5396.61i		−	0.0122771i
$664$	−595314.	−	119714.i	−1.35024	−	0.271525i
$665$		0			0
$666$	−4319.16	+	65199.0i	−0.00973758	+	0.146992i
$667$			667347.i			1.50003i
$668$	56342.0	−	423384.i	0.126264	−	0.948814i
$669$	−63505.4			−0.141892
$670$		0			0
$671$		−	195597.i		−	0.434427i
$672$	51122.0	−	148888.i	0.113206	−	0.329702i
$673$	−764966.			−1.68893			−0.844466	−	0.535609i	$-0.820082\pi$
$673$	−764966.			−1.68893			−0.844466	+	0.535609i	$0.820082\pi$
$674$	24715.5	−	373088.i	0.0544064	−	0.821281i
$675$		0			0
$676$	160812.	+	21400.1i	0.351904	+	0.0468298i
$677$	−303589.			−0.662382			−0.331191	−	0.943564i	$-0.607450\pi$
$677$	−303589.			−0.662382			−0.331191	+	0.943564i	$0.607450\pi$
$678$	−183322.	−	12144.3i	−0.398800	−	0.0264188i
$679$		−	227670.i		−	0.493818i
$680$		0			0
$681$	−275298.			−0.593621
$682$	−65673.3	+	991357.i	−0.141195	+	2.13138i
$683$			541205.i			1.16017i	0.814557	+	0.580083i	$0.196980\pi$
$683$			541205.i			1.16017i	−0.814557	+	0.580083i	$0.803020\pi$
$684$	9501.96	−	71402.7i	0.0203096	−	0.152617i
$685$		0			0
$686$	463677.	+	30716.7i	0.985297	+	0.0652718i
$687$		−	136604.i		−	0.289434i
$688$	101220.	−	373576.i	0.213841	−	0.789226i
$689$	−672557.			−1.41674
$690$		0			0
$691$			902741.i			1.89063i	0.326155	+	0.945316i	$0.394247\pi$
$691$			902741.i			1.89063i	−0.326155	+	0.945316i	$0.605753\pi$
$692$	655136.	+	87182.6i	1.36810	+	0.182061i
$693$	−168206.			−0.350247
$694$	65960.3	+	4369.59i	0.136950	+	0.00907240i
$695$		0			0
$696$	536681.	+	107924.i	1.10789	+	0.222791i
$697$	−11464.1			−0.0235979
$698$	20709.4	−	312614.i	0.0425066	−	0.641650i
$699$			196907.i			0.403002i
$700$		0			0
$701$	16867.4			0.0343251			0.0171625	−	0.999853i	$-0.494537\pi$
$701$	16867.4			0.0343251			0.0171625	+	0.999853i	$0.494537\pi$
$702$	−76001.0	−	5034.75i	−0.154222	−	0.0102165i
$703$			100881.i			0.204127i
$704$	333405.	−	795453.i	0.672708	−	1.60498i
$705$		0			0
$706$	−23753.3	+	358563.i	−0.0476556	+	0.719376i
$707$			140334.i			0.280753i
$708$	41286.4	+	5494.22i	0.0823646	+	0.0109607i
$709$	231636.			0.460801			0.230400	−	0.973096i	$-0.425996\pi$
$709$	231636.			0.460801			0.230400	+	0.973096i	$0.425996\pi$
$710$		0			0
$711$			254696.i			0.503829i
$712$	174059.	−	865560.i	0.343350	−	1.70741i
$713$	−478202.			−0.940659
$714$	311.031	−	4695.10i	0.000610108	−	0.00920976i
$715$		0			0
$716$	64990.5	−	488372.i	0.126772	−	0.952631i
$717$	38921.3			0.0757093
$718$	−608695.	−	40323.5i	−1.18073	−	0.0782185i
$719$		−	283759.i		−	0.548898i	−0.961602	−	0.274449i	$-0.911504\pi$
$719$		−	283759.i		−	0.548898i	0.961602	−	0.274449i	$-0.0884955\pi$
$720$		0			0
$721$	16247.2			0.0312541
$722$	−27106.2	+	409177.i	−0.0519990	+	0.784940i
$723$		−	395087.i		−	0.755815i
$724$	93004.3	+	12376.6i	0.177430	+	0.0236116i
$725$		0			0
$726$	−615935.	−	40803.1i	−1.16859	−	0.0774142i
$727$		−	70775.4i		−	0.133910i	−0.997756	−	0.0669551i	$-0.978672\pi$
$727$		−	70775.4i		−	0.133910i	0.997756	−	0.0669551i	$-0.0213284\pi$
$728$	−251950.	−	50665.8i	−0.475393	−	0.0955987i
$729$	−19683.0			−0.0370370
$730$		0			0
$731$		−	11569.0i		−	0.0216502i
$732$	10187.1	−	76551.4i	0.0190121	−	0.142867i
$733$	195503.			0.363870			0.181935	−	0.983311i	$-0.441764\pi$
$733$	195503.			0.363870			0.181935	+	0.983311i	$0.441764\pi$
$734$	442265.	+	29298.2i	0.820901	+	0.0543813i
$735$		0			0
$736$	392634.	+	134814.i	0.724824	+	0.248875i
$737$	640362.			1.17894
$738$	−10695.4	+	161449.i	−0.0196373	+	0.296431i
$739$		−	193327.i		−	0.354001i	−0.984211	−	0.177000i	$-0.943361\pi$
$739$		−	193327.i		−	0.354001i	0.984211	−	0.177000i	$-0.0566394\pi$
$740$		0			0
$741$	−117595.			−0.214167
$742$	−585131.	−	38762.5i	−1.06278	−	0.0704050i
$743$		−	592034.i		−	1.07243i	−0.844082	−	0.536215i	$-0.819854\pi$
$743$		−	592034.i		−	1.07243i	0.844082	−	0.536215i	$-0.180146\pi$
$744$	−77334.9	+	384571.i	−0.139711	+	0.694753i
$745$		0			0
$746$	−38628.7	+	583111.i	−0.0694117	+	1.04779i
$747$			256176.i			0.459089i
$748$	3400.79	−	25555.3i	0.00607823	−	0.0456750i
$749$	−50083.3			−0.0892749
$750$		0			0
$751$			488630.i			0.866363i	0.901307	+	0.433181i	$0.142609\pi$
$751$			488630.i			0.866363i	−0.901307	+	0.433181i	$0.857391\pi$
$752$	125865.	−	464532.i	0.222571	−	0.821447i
$753$	−212156.			−0.374167
$754$	59073.8	−	891737.i	0.103909	−	1.56853i
$755$		0			0
$756$	−65831.3	−	8760.55i	−0.115183	−	0.0153281i
$757$	123002.			0.214645			0.107323	−	0.994224i	$-0.465772\pi$
$757$	123002.			0.214645			0.107323	+	0.994224i	$0.465772\pi$
$758$	772959.	+	51205.3i	1.34530	+	0.0891203i
$759$		−	443577.i		−	0.769991i
$760$		0			0
$761$	186320.			0.321729			0.160865	−	0.986976i	$-0.448572\pi$
$761$	186320.			0.321729			0.160865	+	0.986976i	$0.448572\pi$
$762$	3832.61	−	57854.4i	0.00660062	−	0.0996383i
$763$			469992.i			0.807313i
$764$	−145804.	+	1.09565e6i	−0.249794	+	1.87708i
$765$		0			0
$766$	576821.	+	38212.0i	0.983069	+	0.0651242i
$767$		−	67995.8i		−	0.115582i
$768$	171915.	−	293955.i	0.291468	−	0.498377i
$769$	305968.			0.517396			0.258698	−	0.965958i	$-0.416707\pi$
$769$	305968.			0.517396			0.258698	+	0.965958i	$0.416707\pi$
$770$		0			0
$771$		−	464009.i		−	0.780580i
$772$	615918.	+	81963.6i	1.03345	+	0.137527i
$773$	453241.			0.758526			0.379263	−	0.925289i	$-0.376178\pi$
$773$	453241.			0.758526			0.379263	+	0.925289i	$0.376178\pi$
$774$	−162928.	−	10793.3i	−0.271965	−	0.0180165i
$775$		0			0
$776$	97095.4	−	482835.i	0.161241	−	0.801817i
$777$	93009.9			0.154059
$778$	29493.4	−	445211.i	0.0487265	−	0.735541i
$779$			249808.i			0.411653i
$780$		0			0
$781$	−1.46637e6			−2.40403
$782$	12381.5	+	820.222i	0.0202469	+	0.00134127i
$783$		−	230945.i		−	0.376691i
$784$	376986.	+	102144.i	0.613328	+	0.166181i
$785$		0			0
$786$	−16237.6	+	245112.i	−0.0262832	+	0.396752i
$787$		−	590772.i		−	0.953829i	−0.878950	−	0.476915i	$-0.841755\pi$
$787$		−	590772.i		−	0.953829i	0.878950	−	0.476915i	$-0.158245\pi$
$788$	−421389.	−	56076.6i	−0.678626	−	0.0903086i
$789$	51345.1			0.0824794
$790$		0			0
$791$			261519.i			0.417974i
$792$	−356725.	−	71735.4i	−0.568701	−	0.114362i
$793$	−126075.			−0.200485
$794$	39995.4	−	603742.i	0.0634408	−	0.957657i
$795$		0			0
$796$	−125035.	+	939581.i	−0.197336	+	1.48289i
$797$	709741.			1.11734			0.558668	−	0.829392i	$-0.311313\pi$
$797$	709741.			1.11734			0.558668	+	0.829392i	$0.311313\pi$
$798$	−102309.	−	6777.53i	−0.160660	−	0.0106430i
$799$		−	14385.8i		−	0.0225341i
$800$		0			0
$801$	−372468.			−0.580529
$802$	−21020.7	+	317314.i	−0.0326813	+	0.493334i
$803$		−	1.64468e6i		−	2.55064i
$804$	250621.	+	33351.5i	0.387708	+	0.0515945i
$805$		0			0
$806$	638993.	+	42330.6i	0.983617	+	0.0651605i
$807$		−	552089.i		−	0.847738i
$808$	−59848.9	+	297616.i	−0.0916713	+	0.455862i
$809$	165063.			0.252204			0.126102	−	0.992017i	$-0.459753\pi$
$809$	165063.			0.252204			0.126102	+	0.992017i	$0.459753\pi$
$810$		0			0
$811$		−	1.10477e6i		−	1.67969i	−0.542823	−	0.839847i	$-0.682644\pi$
$811$		−	1.10477e6i		−	1.67969i	0.542823	−	0.839847i	$-0.317356\pi$
$812$	102789.	−	772414.i	0.155897	−	1.17149i
$813$	335156.			0.507068
$814$	508482.	+	33684.8i	0.767409	+	0.0508377i
$815$		0			0
$816$	2661.96	−	9824.56i	0.00399780	−	0.0147548i
$817$	−252095.			−0.377677
$818$	−77842.1	+	1.17505e6i	−0.116334	+	1.75610i
$819$			108419.i			0.161636i
$820$		0			0
$821$	−479717.			−0.711703			−0.355851	−	0.934543i	$-0.615809\pi$
$821$	−479717.			−0.711703			−0.355851	+	0.934543i	$0.615809\pi$
$822$	620282.	+	41091.1i	0.918006	+	0.0608141i
$823$		−	462067.i		−	0.682190i	−0.940029	−	0.341095i	$-0.889202\pi$
$823$		−	462067.i		−	0.682190i	0.940029	−	0.341095i	$-0.110798\pi$
$824$	34456.4	+	6928.99i	0.0507476	+	0.0102051i
$825$		0			0
$826$	3918.90	−	59156.9i	0.00574386	−	0.0867052i
$827$		−	986535.i		−	1.44245i	−0.692699	−	0.721226i	$-0.743579\pi$
$827$		−	986535.i		−	1.44245i	0.692699	−	0.721226i	$-0.256421\pi$
$828$	23102.5	−	173604.i	0.0336976	−	0.253221i
$829$	−919939.			−1.33860			−0.669298	−	0.742994i	$-0.733405\pi$
$829$	−919939.			−1.33860			−0.669298	+	0.742994i	$0.733405\pi$
$830$		0			0
$831$		−	515223.i		−	0.746094i
$832$	−512720.	−	214901.i	−0.740686	−	0.310449i
$833$	11674.6			0.0168249
$834$	−32901.4	+	496656.i	−0.0473023	+	0.714041i
$835$		0			0
$836$	−556865.	−	74105.1i	−0.796778	−	0.106032i
$837$	165489.			0.236220
$838$	−1.00000e6	−	66246.1i	−1.42401	−	0.0943349i
$839$		−	913352.i		−	1.29752i	−0.760993	−	0.648760i	$-0.775288\pi$
$839$		−	913352.i		−	1.29752i	0.760993	−	0.648760i	$-0.224712\pi$
$840$		0			0
$841$	2.00245e6			2.83119
$842$	−45421.4	+	685649.i	−0.0640673	+	0.967114i
$843$			275518.i			0.387699i
$844$	111748.	−	839736.i	0.156876	−	1.17885i
$845$		0			0
$846$	−202596.	−	13421.2i	−0.283068	−	0.0187521i
$847$			878664.i			1.22477i
$848$	−1.22439e6	−	331749.i	−1.70267	−	0.461337i
$849$	−701618.			−0.973387
$850$		0			0
$851$			245277.i			0.338687i
$852$	−573897.	−	76371.8i	−0.790597	−	0.105209i
$853$	−514313.			−0.706854			−0.353427	−	0.935462i	$-0.614984\pi$
$853$	−514313.			−0.706854			−0.353427	+	0.935462i	$0.614984\pi$
$854$	−109686.	−	7266.24i	−0.150396	−	0.00996309i
$855$		0			0
$856$	−106215.	−	21359.2i	−0.144957	−	0.0291499i
$857$	415272.			0.565420			0.282710	−	0.959205i	$-0.408767\pi$
$857$	415272.			0.565420			0.282710	+	0.959205i	$0.408767\pi$
$858$	−39265.6	+	592726.i	−0.0533382	+	0.805155i
$859$			516118.i			0.699459i	0.936851	+	0.349730i	$0.113727\pi$
$859$			516118.i			0.699459i	−0.936851	+	0.349730i	$0.886273\pi$
$860$		0			0
$861$	230316.			0.310683
$862$	570639.	+	37802.4i	0.767975	+	0.0508751i
$863$			535169.i			0.718570i	0.933228	+	0.359285i	$0.116979\pi$
$863$			535169.i			0.718570i	−0.933228	+	0.359285i	$0.883021\pi$
$864$	−135877.	−	46654.4i	−0.182019	−	0.0624979i
$865$		0			0
$866$	20592.9	−	310855.i	0.0274587	−	0.414498i
$867$			433684.i			0.576946i
$868$	553490.	+	73656.0i	0.734632	+	0.0977617i
$869$	1.98636e6			2.63038
$870$		0			0
$871$		−	412754.i		−	0.544071i
$872$	−200439.	+	996744.i	−0.263603	+	1.31084i
$873$	−207774.			−0.272623
$874$	17873.1	−	269799.i	0.0233979	−	0.353198i
$875$		0			0
$876$	85658.5	−	643683.i	0.111625	−	0.838810i
$877$	−70986.4			−0.0922945			−0.0461473	−	0.998935i	$-0.514694\pi$
$877$	−70986.4			−0.0922945			−0.0461473	+	0.998935i	$0.514694\pi$
$878$	−183053.	−	12126.5i	−0.237459	−	0.0157307i
$879$		−	694930.i		−	0.899422i
$880$		0			0
$881$	−348009.			−0.448372			−0.224186	−	0.974546i	$-0.571972\pi$
$881$	−348009.			−0.448372			−0.224186	+	0.974546i	$0.571972\pi$
$882$	10891.8	−	164415.i	0.0140011	−	0.211351i
$883$			1.32985e6i			1.70562i	0.522222	+	0.852810i	$0.325103\pi$
$883$			1.32985e6i			1.70562i	−0.522222	+	0.852810i	$0.674897\pi$
$884$	−16472.0	−	2192.03i	−0.0210787	−	0.00280506i
$885$		0			0
$886$	−711505.	−	47134.3i	−0.906381	−	0.0600439i
$887$		−	633096.i		−	0.804678i	−0.915491	−	0.402339i	$-0.868197\pi$
$887$		−	633096.i		−	0.804678i	0.915491	−	0.402339i	$-0.131803\pi$
$888$	197252.	+	39666.3i	0.250147	+	0.0503032i
$889$	−82532.4			−0.104429
$890$		0			0
$891$			153506.i			0.193362i
$892$	−25795.0	+	193837.i	−0.0324195	+	0.243617i
$893$	−313474.			−0.393096
$894$	−92054.3	−	6098.21i	−0.115178	−	0.00763005i
$895$		0			0
$896$	−433685.	−	216516.i	−0.540205	−	0.269695i
$897$	−285914.			−0.355345
$898$	19178.1	−	289499.i	0.0237822	−	0.359000i
$899$			1.94171e6i			2.40251i
$900$		0			0
$901$	−37917.5			−0.0467079
$902$	1.25913e6	+	83412.3i	1.54760	+	0.102522i
$903$			232425.i			0.285041i
$904$	−111531.	+	554620.i	−0.136477	+	0.678670i
$905$		0			0
$906$	10651.9	−	160793.i	0.0129769	−	0.195890i
$907$			375984.i			0.457041i	0.973539	+	0.228520i	$0.0733887\pi$
$907$			375984.i			0.457041i	−0.973539	+	0.228520i	$0.926611\pi$
$908$	−111822.	+	840290.i	−0.135630	+	1.01920i
$909$	128070.			0.154996
$910$		0			0
$911$			265425.i			0.319819i	0.987132	+	0.159910i	$0.0511203\pi$
$911$			265425.i			0.319819i	−0.987132	+	0.159910i	$0.948880\pi$
$912$	−214082.	−	58005.6i	−0.257390	−	0.0697397i
$913$	1.99790e6			2.39680
$914$	−5638.16	+	85109.7i	−0.00674909	+	0.101879i
$915$		0			0
$916$	−416955.	−	55486.6i	−0.496934	−	0.0661298i
$917$	349665.			0.415828
$918$	−4284.79	−	283.849i	−0.00508445	−	0.000336824i
$919$			283610.i			0.335808i	0.985803	+	0.167904i	$0.0536999\pi$
$919$			283610.i			0.335808i	−0.985803	+	0.167904i	$0.946300\pi$
$920$		0			0
$921$	651525.			0.768090
$922$	6567.66	−	99140.7i	0.00772589	−	0.116625i
$923$			945167.i			1.10944i
$924$	−68322.9	+	513414.i	−0.0800244	+	0.601345i
$925$		0			0
$926$	−258106.	−	17098.5i	−0.301007	−	0.0199405i
$927$		−	14827.3i		−	0.0172545i
$928$	547407.	−	1.59427e6i	0.635644	−	1.85126i
$929$	871065.			1.00930			0.504649	−	0.863325i	$-0.331622\pi$
$929$	871065.			1.00930			0.504649	+	0.863325i	$0.331622\pi$
$930$		0			0
$931$		−	254397.i		−	0.293503i
$932$	601018.	+	79980.9i	0.691920	+	0.0920777i
$933$	179460.			0.206160
$934$	−690057.	−	45713.4i	−0.791027	−	0.0524023i
$935$		0			0
$936$	−46238.1	+	229932.i	−0.0527774	+	0.262451i
$937$	−981541.			−1.11797			−0.558984	−	0.829178i	$-0.688809\pi$
$937$	−981541.			−1.11797			−0.558984	+	0.829178i	$0.688809\pi$
$938$	23788.9	−	359100.i	0.0270376	−	0.408140i
$939$		−	86606.0i		−	0.0982239i
$940$		0			0
$941$	1.53969e6			1.73882			0.869409	−	0.494094i	$-0.164500\pi$
$941$	1.53969e6			1.73882			0.869409	+	0.494094i	$0.164500\pi$
$942$	−601449.	−	39843.5i	−0.677793	−	0.0449010i
$943$			607369.i			0.683013i
$944$	33539.9	−	123787.i	0.0376373	−	0.138909i
$945$		0			0
$946$	−84176.0	+	1.27066e6i	−0.0940602	+	1.41987i
$947$		−	100610.i		−	0.112187i	−0.998426	−	0.0560933i	$-0.982136\pi$
$947$		−	100610.i		−	0.112187i	0.998426	−	0.0560933i	$-0.0178644\pi$
$948$	777408.	+	103454.i	0.865032	+	0.115115i
$949$	−1.06010e6			−1.17710
$950$		0			0
$951$			383279.i			0.423793i
$952$	−14204.5	−	2856.44i	−0.0156730	−	0.00315175i
$953$	1.47750e6			1.62683			0.813415	−	0.581683i	$-0.197606\pi$
$953$	1.47750e6			1.62683			0.813415	+	0.581683i	$0.197606\pi$
$954$	−35375.0	+	533996.i	−0.0388687	+	0.586734i
$955$		0			0
$956$	15809.3	−	118799.i	0.0172980	−	0.129986i
$957$	−1.80112e6			−1.96662
$958$	79547.4	+	5269.68i	0.0866752	+	0.00574187i
$959$		−	884865.i		−	0.962143i
$960$		0			0
$961$	−467856.			−0.506600
$962$	21712.0	−	327749.i	0.0234612	−	0.354154i
$963$			45706.5i			0.0492862i
$964$	−1.20592e6	−	160479.i	−1.29767	−	0.172688i
$965$		0			0
$966$	−248748.	−	16478.5i	−0.266566	−	0.0176589i
$967$			768191.i			0.821517i	0.911744	+	0.410758i	$0.134736\pi$
$967$			768191.i			0.821517i	−0.911744	+	0.410758i	$0.865264\pi$
$968$	−374727.	+	1.86344e6i	−0.399912	+	1.98868i
$969$	−6629.79			−0.00706077
$970$		0			0
$971$		−	458094.i		−	0.485866i	−0.970043	−	0.242933i	$-0.921891\pi$
$971$		−	458094.i		−	0.485866i	0.970043	−	0.242933i	$-0.0781094\pi$
$972$	−7994.96	+	60078.3i	−0.00846221	+	0.0635894i
$973$	708506.			0.748372
$974$	439626.	+	29123.4i	0.463410	+	0.0306990i
$975$		0			0
$976$	−229519.	−	62188.2i	−0.240946	−	0.0652842i
$977$	−905743.			−0.948890			−0.474445	−	0.880285i	$-0.657351\pi$
$977$	−905743.			−0.948890			−0.474445	+	0.880285i	$0.657351\pi$
$978$	20492.8	−	309345.i	0.0214252	−	0.323419i
$979$			2.90485e6i			3.03081i
$980$		0			0
$981$	428919.			0.445695
$982$	656807.	+	43510.7i	0.681106	+	0.0451205i
$983$		−	776569.i		−	0.803661i	−0.915714	−	0.401830i	$-0.868374\pi$
$983$		−	776569.i		−	0.803661i	0.915714	−	0.401830i	$-0.131626\pi$
$984$	488447.	+	98223.8i	0.504460	+	0.101444i
$985$		0			0
$986$	3330.47	−	50274.4i	0.00342572	−	0.0517122i
$987$			289015.i			0.296678i
$988$	−47765.5	+	358935.i	−0.0489328	+	0.367707i
$989$	−612930.			−0.626640
$990$		0			0
$991$		−	1.06325e6i		−	1.08265i	−0.840812	−	0.541327i	$-0.817922\pi$
$991$		−	1.06325e6i		−	1.08265i	0.840812	−	0.541327i	$-0.182078\pi$
$992$	1.14241e6	+	392256.i	1.16091	+	0.398608i
$993$	638110.			0.647138
$994$	−54474.2	+	822304.i	−0.0551338	+	0.832261i
$995$		0			0
$996$	781923.	+	104055.i	0.788216	+	0.104892i
$997$	−1.19772e6			−1.20494			−0.602470	−	0.798141i	$-0.705817\pi$
$997$	−1.19772e6			−1.20494			−0.602470	+	0.798141i	$0.705817\pi$
$998$	−416581.	−	27596.8i	−0.418252	−	0.0277075i
$999$		−	84881.7i		−	0.0850517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.5.c.d.151.8		16
4.3	odd	2	inner	300.5.c.d.151.7		16
5.2	odd	4		300.5.f.b.199.1		32
5.3	odd	4		300.5.f.b.199.32		32
5.4	even	2		60.5.c.a.31.9	✓	16
15.14	odd	2		180.5.c.c.91.8		16
20.3	even	4		300.5.f.b.199.2		32
20.7	even	4		300.5.f.b.199.31		32
20.19	odd	2		60.5.c.a.31.10	yes	16
40.19	odd	2		960.5.e.f.511.13		16
40.29	even	2		960.5.e.f.511.8		16
60.59	even	2		180.5.c.c.91.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.9	✓	16	5.4	even	2
60.5.c.a.31.10	yes	16	20.19	odd	2
180.5.c.c.91.7		16	60.59	even	2
180.5.c.c.91.8		16	15.14	odd	2
300.5.c.d.151.7		16	4.3	odd	2	inner
300.5.c.d.151.8		16	1.1	even	1	trivial
300.5.f.b.199.1		32	5.2	odd	4
300.5.f.b.199.2		32	20.3	even	4
300.5.f.b.199.31		32	20.7	even	4
300.5.f.b.199.32		32	5.3	odd	4
960.5.e.f.511.8		16	40.29	even	2
960.5.e.f.511.13		16	40.19	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.264404 + 3.99125i) q^{2} -5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} +(20.7392 + 1.37388i) q^{6} -29.5855i q^{7} +(12.6174 - 62.7439i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(-0.264404 + 3.99125i) q^{2} -5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} +(20.7392 + 1.37388i) q^{6} -29.5855i q^{7} +(12.6174 - 62.7439i) q^{8} -27.0000 q^{9} +210.571i q^{11} +(-10.9670 + 82.4119i) q^{12} +135.726 q^{13} +(118.083 + 7.82252i) q^{14} +(247.091 + 66.9491i) q^{16} +7.65200 q^{17} +(7.13890 - 107.764i) q^{18} -166.741i q^{19} -153.731 q^{21} +(-840.442 - 55.6758i) q^{22} -405.405i q^{23} +(-326.027 - 65.5622i) q^{24} +(-35.8866 + 541.718i) q^{26} +140.296i q^{27} +(-62.4433 + 469.231i) q^{28} -1646.13 q^{29} -1179.57i q^{31} +(-332.543 + 968.500i) q^{32} +1094.16 q^{33} +(-2.02322 + 30.5410i) q^{34} +(428.225 + 56.9863i) q^{36} -605.018 q^{37} +(665.506 + 44.0870i) q^{38} -705.255i q^{39} -1498.18 q^{41} +(40.6470 - 613.578i) q^{42} -1511.90i q^{43} +(444.432 - 3339.69i) q^{44} +(1618.07 + 107.191i) q^{46} -1880.00i q^{47} +(347.878 - 1283.92i) q^{48} +1525.70 q^{49} -39.7609i q^{51} +(-2152.65 - 286.465i) q^{52} -4955.24 q^{53} +(-559.957 - 37.0948i) q^{54} +(-1856.31 - 373.293i) q^{56} -866.413 q^{57} +(435.242 - 6570.10i) q^{58} -500.976i q^{59} -928.887 q^{61} +(4707.95 + 311.882i) q^{62} +798.809i q^{63} +(-3777.60 - 1583.34i) q^{64} +(-289.300 + 4367.06i) q^{66} -3041.07i q^{67} +(-121.362 - 16.1503i) q^{68} -2106.55 q^{69} +6963.76i q^{71} +(-340.671 + 1694.09i) q^{72} -7810.56 q^{73} +(159.969 - 2414.78i) q^{74} +(-351.925 + 2644.55i) q^{76} +6229.85 q^{77} +(2814.85 + 186.472i) q^{78} -9433.20i q^{79} +729.000 q^{81} +(396.124 - 5979.61i) q^{82} -9487.99i q^{83} +(2438.20 + 324.465i) q^{84} +(6034.36 + 399.751i) q^{86} +8553.52i q^{87} +(13212.1 + 2656.87i) q^{88} +13795.1 q^{89} -4015.54i q^{91} +(-855.649 + 6429.79i) q^{92} -6129.21 q^{93} +(7503.57 + 497.080i) q^{94} +(5032.47 + 1727.94i) q^{96} +7695.33 q^{97} +(-403.400 + 6089.45i) q^{98} -5685.42i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 26 q^{4} + 18 q^{6} + 180 q^{8} - 432 q^{9}+O(q^{10}) \) 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

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