LMFDB - Embedded newform 168.5.z.a.145.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,5,Mod(73,168)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("168.73");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	168.z (of order $6$, degree $2$, 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:	$17.3661537981$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 99 x^{14} - 1810 x^{13} + 14212 x^{12} - 199882 x^{11} + 1800935 x^{10} + \cdots + 41390114348800 $ x^16 - 6x^15 + 99x^14 - 1810x^13 + 14212x^12 - 199882x^11 + 1800935x^10 - 9073270x^9 + 62016647x^8 - 13497916x^7 - 872612906x^6 + 8208467240x^5 + 11144877252x^4 - 185824445600x^3 + 3750935164160x^2 - 13970712492800*x + 41390114348800
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{36}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.7
Root			$0.268520 + 7.69736i$ of defining polynomial
Character	$\chi$	$=$	168.145
Dual form			168.5.z.a.73.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 + 2.59808i) q^{3} +(25.2264 + 14.5645i) q^{5} +(14.3466 - 46.8527i) q^{7} +(13.5000 - 23.3827i) q^{9} +O(q^{10})$	\(q+(-4.50000 + 2.59808i) q^{3} +(25.2264 + 14.5645i) q^{5} +(14.3466 - 46.8527i) q^{7} +(13.5000 - 23.3827i) q^{9} +(-72.5287 - 125.623i) q^{11} +64.1998i q^{13} -151.359 q^{15} +(-50.6274 + 29.2298i) q^{17} +(347.153 + 200.429i) q^{19} +(57.1670 + 248.111i) q^{21} +(413.920 - 716.931i) q^{23} +(111.749 + 193.555i) q^{25} +140.296i q^{27} +344.644 q^{29} +(1161.22 - 670.431i) q^{31} +(652.758 + 376.870i) q^{33} +(1044.30 - 972.975i) q^{35} +(812.970 - 1408.11i) q^{37} +(-166.796 - 288.899i) q^{39} +90.9275i q^{41} +590.798 q^{43} +(681.114 - 393.241i) q^{45} +(1567.97 + 905.265i) q^{47} +(-1989.35 - 1344.36i) q^{49} +(151.882 - 263.068i) q^{51} +(2076.19 + 3596.07i) q^{53} -4225.37i q^{55} -2082.92 q^{57} +(-3930.89 + 2269.50i) q^{59} +(4218.43 + 2435.51i) q^{61} +(-901.862 - 967.974i) q^{63} +(-935.038 + 1619.53i) q^{65} +(-268.049 - 464.275i) q^{67} +4301.59i q^{69} -3979.64 q^{71} +(2038.90 - 1177.16i) q^{73} +(-1005.74 - 580.665i) q^{75} +(-6926.33 + 1595.89i) q^{77} +(5001.10 - 8662.16i) q^{79} +(-364.500 - 631.333i) q^{81} -9675.19i q^{83} -1702.87 q^{85} +(-1550.90 + 895.410i) q^{87} +(-488.319 - 281.931i) q^{89} +(3007.93 + 921.051i) q^{91} +(-3483.66 + 6033.88i) q^{93} +(5838.29 + 10112.2i) q^{95} +12456.1i q^{97} -3916.55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9}+O(q^{10}) $ 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9	$ 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9} - 108 q^{11} - 72 q^{15} - 168 q^{17} + 948 q^{19} - 252 q^{21} - 768 q^{23} + 1908 q^{25} - 1608 q^{29} - 3216 q^{31} + 972 q^{33} + 696 q^{35} - 1820 q^{37} - 1188 q^{39} + 2888 q^{43} + 324 q^{45} + 744 q^{47} - 3784 q^{49} + 504 q^{51} + 4476 q^{53} - 5688 q^{57} - 4668 q^{59} + 17760 q^{61} + 1188 q^{63} + 8760 q^{65} + 1580 q^{67} + 48 q^{71} + 588 q^{73} - 17172 q^{75} - 17508 q^{77} - 3824 q^{79} - 5832 q^{81} + 11440 q^{85} + 7236 q^{87} - 360 q^{89} + 25860 q^{91} + 9648 q^{93} - 21792 q^{95} - 5832 q^{99}+O(q^{100}) $ 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9 - 108 * q^11 - 72 * q^15 - 168 * q^17 + 948 * q^19 - 252 * q^21 - 768 * q^23 + 1908 * q^25 - 1608 * q^29 - 3216 * q^31 + 972 * q^33 + 696 * q^35 - 1820 * q^37 - 1188 * q^39 + 2888 * q^43 + 324 * q^45 + 744 * q^47 - 3784 * q^49 + 504 * q^51 + 4476 * q^53 - 5688 * q^57 - 4668 * q^59 + 17760 * q^61 + 1188 * q^63 + 8760 * q^65 + 1580 * q^67 + 48 * q^71 + 588 * q^73 - 17172 * q^75 - 17508 * q^77 - 3824 * q^79 - 5832 * q^81 + 11440 * q^85 + 7236 * q^87 - 360 * q^89 + 25860 * q^91 + 9648 * q^93 - 21792 * q^95 - 5832 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−4.50000	+	2.59808i	−0.500000	+	0.288675i
$3$	−4.50000	+	2.59808i	−0.500000	+	0.288675i
$4$		0			0
$5$	25.2264	+	14.5645i	1.00906	+	0.582580i	0.910916	−	0.412593i	$-0.135377\pi$
$5$	25.2264	+	14.5645i	1.00906	+	0.582580i	0.0981422	+	0.995172i	$0.468710\pi$
$6$		0			0
$7$	14.3466	−	46.8527i	0.292788	−	0.956177i
$7$	14.3466	−	46.8527i	0.292788	−	0.956177i
$8$		0			0
$9$	13.5000	−	23.3827i	0.166667	−	0.288675i
$10$		0			0
$11$	−72.5287	−	125.623i	−0.599411	−	1.03821i	−0.992908	−	0.118884i	$-0.962068\pi$
$11$	−72.5287	−	125.623i	−0.599411	−	1.03821i	0.393498	−	0.919326i	$-0.371265\pi$
$12$		0			0
$13$			64.1998i			0.379881i	0.981796	+	0.189940i	$0.0608294\pi$
$13$			64.1998i			0.379881i	−0.981796	+	0.189940i	$0.939171\pi$
$14$		0			0
$15$	−151.359			−0.672705
$16$		0			0
$17$	−50.6274	+	29.2298i	−0.175181	+	0.101141i	−0.585027	−	0.811014i	$-0.698916\pi$
$17$	−50.6274	+	29.2298i	−0.175181	+	0.101141i	0.409845	+	0.912155i	$0.365583\pi$
$18$		0			0
$19$	347.153	+	200.429i	0.961642	+	0.555204i	0.896678	−	0.442683i	$-0.145973\pi$
$19$	347.153	+	200.429i	0.961642	+	0.555204i	0.0649640	+	0.997888i	$0.479307\pi$
$20$		0			0
$21$	57.1670	+	248.111i	0.129630	+	0.562609i
$22$		0			0
$23$	413.920	−	716.931i	0.782458	−	1.35526i	−0.148048	−	0.988980i	$-0.547299\pi$
$23$	413.920	−	716.931i	0.782458	−	1.35526i	0.930506	−	0.366277i	$-0.119368\pi$
$24$		0			0
$25$	111.749	+	193.555i	0.178798	+	0.309688i
$26$		0			0
$27$			140.296i			0.192450i
$28$		0			0
$29$	344.644			0.409802			0.204901	−	0.978783i	$-0.434313\pi$
$29$	344.644			0.409802			0.204901	+	0.978783i	$0.434313\pi$
$30$		0			0
$31$	1161.22	−	670.431i	1.20835	−	0.697638i	0.245948	−	0.969283i	$-0.420901\pi$
$31$	1161.22	−	670.431i	1.20835	−	0.697638i	0.962398	+	0.271645i	$0.0875675\pi$
$32$		0			0
$33$	652.758	+	376.870i	0.599411	+	0.346070i
$34$		0			0
$35$	1044.30	−	972.975i	0.852490	−	0.794266i
$36$		0			0
$37$	812.970	−	1408.11i	0.593842	−	1.02856i	−0.399867	−	0.916573i	$-0.630944\pi$
$37$	812.970	−	1408.11i	0.593842	−	1.02856i	0.993709	−	0.111992i	$-0.0357230\pi$
$38$		0			0
$39$	−166.796	−	288.899i	−0.109662	−	0.189940i
$40$		0			0
$41$			90.9275i			0.0540913i	0.999634	+	0.0270457i	$0.00860995\pi$
$41$			90.9275i			0.0540913i	−0.999634	+	0.0270457i	$0.991390\pi$
$42$		0			0
$43$	590.798			0.319523			0.159761	−	0.987156i	$-0.448928\pi$
$43$	590.798			0.319523			0.159761	+	0.987156i	$0.448928\pi$
$44$		0			0
$45$	681.114	−	393.241i	0.336353	−	0.194193i
$46$		0			0
$47$	1567.97	+	905.265i	0.709808	+	0.409808i	0.810990	−	0.585060i	$-0.198929\pi$
$47$	1567.97	+	905.265i	0.709808	+	0.409808i	−0.101182	+	0.994868i	$0.532262\pi$
$48$		0			0
$49$	−1989.35	−	1344.36i	−0.828550	−	0.559915i
$50$		0			0
$51$	151.882	−	263.068i	0.0583938	−	0.101141i
$52$		0			0
$53$	2076.19	+	3596.07i	0.739122	+	1.28020i	0.952891	+	0.303313i	$0.0980928\pi$
$53$	2076.19	+	3596.07i	0.739122	+	1.28020i	−0.213769	+	0.976884i	$0.568574\pi$
$54$		0			0
$55$		−	4225.37i		−	1.39682i
$56$		0			0
$57$	−2082.92			−0.641095
$58$		0			0
$59$	−3930.89	+	2269.50i	−1.12924	+	0.651969i	−0.943744	−	0.330676i	$-0.892723\pi$
$59$	−3930.89	+	2269.50i	−1.12924	+	0.651969i	−0.185499	+	0.982645i	$0.559390\pi$
$60$		0			0
$61$	4218.43	+	2435.51i	1.13368	+	0.654531i	0.944858	−	0.327480i	$-0.106200\pi$
$61$	4218.43	+	2435.51i	1.13368	+	0.654531i	0.188823	+	0.982011i	$0.439533\pi$
$62$		0			0
$63$	−901.862	−	967.974i	−0.227227	−	0.243884i
$64$		0			0
$65$	−935.038	+	1619.53i	−0.221311	+	0.383321i
$66$		0			0
$67$	−268.049	−	464.275i	−0.0597125	−	0.103425i	0.834624	−	0.550820i	$-0.185685\pi$
$67$	−268.049	−	464.275i	−0.0597125	−	0.103425i	−0.894336	+	0.447395i	$0.852352\pi$
$68$		0			0
$69$			4301.59i			0.903505i
$70$		0			0
$71$	−3979.64			−0.789455			−0.394727	−	0.918798i	$-0.629161\pi$
$71$	−3979.64			−0.789455			−0.394727	+	0.918798i	$0.629161\pi$
$72$		0			0
$73$	2038.90	−	1177.16i	0.382604	−	0.220896i	−0.296347	−	0.955080i	$-0.595768\pi$
$73$	2038.90	−	1177.16i	0.382604	−	0.220896i	0.678951	+	0.734184i	$0.262435\pi$
$74$		0			0
$75$	−1005.74	−	580.665i	−0.178798	−	0.103229i
$76$		0			0
$77$	−6926.33	+	1595.89i	−1.16821	+	0.269167i
$78$		0			0
$79$	5001.10	−	8662.16i	0.801330	−	1.38794i	−0.117411	−	0.993083i	$-0.537460\pi$
$79$	5001.10	−	8662.16i	0.801330	−	1.38794i	0.918741	−	0.394861i	$-0.129207\pi$
$80$		0			0
$81$	−364.500	−	631.333i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	9675.19i		−	1.40444i	−0.711960	−	0.702220i	$-0.752192\pi$
$83$		−	9675.19i		−	1.40444i	0.711960	−	0.702220i	$-0.247808\pi$
$84$		0			0
$85$	−1702.87			−0.235691
$86$		0			0
$87$	−1550.90	+	895.410i	−0.204901	+	0.118300i
$88$		0			0
$89$	−488.319	−	281.931i	−0.0616487	−	0.0355929i	0.468859	−	0.883273i	$-0.344665\pi$
$89$	−488.319	−	281.931i	−0.0616487	−	0.0355929i	−0.530508	+	0.847680i	$0.677999\pi$
$90$		0			0
$91$	3007.93	+	921.051i	0.363233	+	0.111225i
$92$		0			0
$93$	−3483.66	+	6033.88i	−0.402782	+	0.697638i
$94$		0			0
$95$	5838.29	+	10112.2i	0.646902	+	1.12047i
$96$		0			0
$97$			12456.1i			1.32385i	0.749571	+	0.661924i	$0.230260\pi$
$97$			12456.1i			1.32385i	−0.749571	+	0.661924i	$0.769740\pi$
$98$		0			0
$99$	−3916.55			−0.399607
$100$		0			0
$101$	−411.873	+	237.795i	−0.0403757	+	0.0233109i	−0.520052	−	0.854135i	$-0.674087\pi$
$101$	−411.873	+	237.795i	−0.0403757	+	0.0233109i	0.479676	+	0.877446i	$0.340754\pi$
$102$		0			0
$103$	−12871.3	−	7431.25i	−1.21324	−	0.700466i	−0.249779	−	0.968303i	$-0.580358\pi$
$103$	−12871.3	−	7431.25i	−1.21324	−	0.700466i	−0.963464	+	0.267837i	$0.913691\pi$
$104$		0			0
$105$	−2171.49	+	7091.56i	−0.196960	+	0.643225i
$106$		0			0
$107$	−9866.21	+	17088.8i	−0.861753	+	1.49260i	0.00848183	+	0.999964i	$0.497300\pi$
$107$	−9866.21	+	17088.8i	−0.861753	+	1.49260i	−0.870235	+	0.492637i	$0.836033\pi$
$108$		0			0
$109$	−3606.37	−	6246.42i	−0.303541	−	0.525749i	0.673394	−	0.739284i	$-0.264836\pi$
$109$	−3606.37	−	6246.42i	−0.303541	−	0.525749i	−0.976935	+	0.213535i	$0.931502\pi$
$110$		0			0
$111$			8448.63i			0.685710i
$112$		0			0
$113$	−13699.9			−1.07290			−0.536450	−	0.843932i	$-0.680235\pi$
$113$	−13699.9			−1.07290			−0.536450	+	0.843932i	$0.680235\pi$
$114$		0			0
$115$	20883.5	−	12057.1i	1.57909	−	0.911689i
$116$		0			0
$117$	1501.16	+	866.697i	0.109662	+	0.0633134i
$118$		0			0
$119$	643.160	+	2791.38i	0.0454177	+	0.197117i
$120$		0			0
$121$	−3200.32	+	5543.12i	−0.218586	+	0.378602i
$122$		0			0
$123$	−236.237	−	409.174i	−0.0156148	−	0.0270457i
$124$		0			0
$125$		−	11695.3i		−	0.748502i
$126$		0			0
$127$	−30518.5			−1.89215			−0.946076	−	0.323946i	$-0.894990\pi$
$127$	−30518.5			−1.89215			−0.946076	+	0.323946i	$0.894990\pi$
$128$		0			0
$129$	−2658.59	+	1534.94i	−0.159761	+	0.0922383i
$130$		0			0
$131$	−7493.87	−	4326.59i	−0.436680	−	0.252117i	0.265508	−	0.964109i	$-0.414460\pi$
$131$	−7493.87	−	4326.59i	−0.436680	−	0.252117i	−0.702188	+	0.711991i	$0.747794\pi$
$132$		0			0
$133$	14371.1	−	13389.6i	0.812431	−	0.756943i
$134$		0			0
$135$	−2043.34	+	3539.17i	−0.112118	+	0.194193i
$136$		0			0
$137$	1666.30	+	2886.11i	0.0887793	+	0.153770i	0.906995	−	0.421141i	$-0.138370\pi$
$137$	1666.30	+	2886.11i	0.0887793	+	0.153770i	−0.818216	+	0.574911i	$0.805037\pi$
$138$		0			0
$139$		−	19490.3i		−	1.00876i	−0.863481	−	0.504381i	$-0.831721\pi$
$139$		−	19490.3i		−	1.00876i	0.863481	−	0.504381i	$-0.168279\pi$
$140$		0			0
$141$	−9407.79			−0.473205
$142$		0			0
$143$	8065.00	−	4656.33i	0.394396	−	0.227704i
$144$		0			0
$145$	8694.13	+	5019.56i	0.413514	+	0.238742i
$146$		0			0
$147$	12444.8	+	881.125i	0.575909	+	0.0407758i
$148$		0			0
$149$	−9694.13	+	16790.7i	−0.436653	+	0.756305i	−0.997429	−	0.0716628i	$-0.977169\pi$
$149$	−9694.13	+	16790.7i	−0.436653	+	0.756305i	0.560776	+	0.827967i	$0.310503\pi$
$150$		0			0
$151$	8668.06	+	15013.5i	0.380161	+	0.658459i	0.991085	−	0.133231i	$-0.0425351\pi$
$151$	8668.06	+	15013.5i	0.380161	+	0.658459i	−0.610924	+	0.791690i	$0.709202\pi$
$152$		0			0
$153$			1578.41i			0.0674274i
$154$		0			0
$155$	39057.9			1.62572
$156$		0			0
$157$	29734.8	−	17167.4i	1.20633	−	0.696473i	0.244372	−	0.969681i	$-0.421418\pi$
$157$	29734.8	−	17167.4i	1.20633	−	0.696473i	0.961955	+	0.273208i	$0.0880848\pi$
$158$		0			0
$159$	−18685.8	−	10788.2i	−0.739122	−	0.426733i
$160$		0			0
$161$	−27651.8	−	29678.8i	−1.06677	−	1.14497i
$162$		0			0
$163$	11923.8	−	20652.6i	0.448786	−	0.777320i	−0.549521	−	0.835480i	$-0.685190\pi$
$163$	11923.8	−	20652.6i	0.448786	−	0.777320i	0.998307	+	0.0581596i	$0.0185232\pi$
$164$		0			0
$165$	10977.8	+	19014.2i	0.403227	+	0.698409i
$166$		0			0
$167$			35538.6i			1.27429i	0.770745	+	0.637144i	$0.219884\pi$
$167$			35538.6i			1.27429i	−0.770745	+	0.637144i	$0.780116\pi$
$168$		0			0
$169$	24439.4			0.855691
$170$		0			0
$171$	9373.12	−	5411.58i	0.320547	−	0.185068i
$172$		0			0
$173$	−11016.7	−	6360.52i	−0.368096	−	0.212520i	0.304530	−	0.952503i	$-0.401500\pi$
$173$	−11016.7	−	6360.52i	−0.368096	−	0.212520i	−0.672626	+	0.739982i	$0.734834\pi$
$174$		0			0
$175$	10671.8	−	2458.88i	0.348467	−	0.0802900i
$176$		0			0
$177$	11792.7	−	20425.5i	0.376414	−	0.651969i
$178$		0			0
$179$	18131.8	+	31405.2i	0.565894	+	0.980158i	0.996966	+	0.0778401i	$0.0248024\pi$
$179$	18131.8	+	31405.2i	0.565894	+	0.980158i	−0.431071	+	0.902318i	$0.641864\pi$
$180$		0			0
$181$		−	27130.9i		−	0.828148i	−0.910243	−	0.414074i	$-0.864106\pi$
$181$		−	27130.9i		−	0.828148i	0.910243	−	0.414074i	$-0.135894\pi$
$182$		0			0
$183$	−25310.6			−0.755787
$184$		0			0
$185$	41016.7	−	23681.0i	1.19844	−	0.691921i
$186$		0			0
$187$	7343.88	+	4239.99i	0.210011	+	0.121250i
$188$		0			0
$189$	6573.25	+	2012.78i	0.184016	+	0.0563472i
$190$		0			0
$191$	−33177.4	+	57464.9i	−0.909443	+	1.57520i	−0.0946040	+	0.995515i	$0.530159\pi$
$191$	−33177.4	+	57464.9i	−0.909443	+	1.57520i	−0.814839	+	0.579687i	$0.803175\pi$
$192$		0			0
$193$	8619.47	+	14929.4i	0.231401	+	0.400799i	0.958221	−	0.286030i	$-0.0923356\pi$
$193$	8619.47	+	14929.4i	0.231401	+	0.400799i	−0.726819	+	0.686829i	$0.759002\pi$
$194$		0			0
$195$		−	9717.20i		−	0.255548i
$196$		0			0
$197$	34297.0			0.883738			0.441869	−	0.897079i	$-0.354316\pi$
$197$	34297.0			0.883738			0.441869	+	0.897079i	$0.354316\pi$
$198$		0			0
$199$	4867.03	−	2809.98i	0.122902	−	0.0709573i	−0.437289	−	0.899321i	$-0.644061\pi$
$199$	4867.03	−	2809.98i	0.122902	−	0.0709573i	0.560190	+	0.828364i	$0.310728\pi$
$200$		0			0
$201$	2412.44	+	1392.83i	0.0597125	+	0.0344750i
$202$		0			0
$203$	4944.47	−	16147.5i	0.119985	−	0.391843i
$204$		0			0
$205$	−1324.31	+	2293.78i	−0.0315125	+	0.0545813i
$206$		0			0
$207$	−11175.8	−	19357.1i	−0.260819	−	0.451752i
$208$		0			0
$209$		−	58147.3i		−	1.33118i
$210$		0			0
$211$	−1163.31			−0.0261296			−0.0130648	−	0.999915i	$-0.504159\pi$
$211$	−1163.31			−0.0261296			−0.0130648	+	0.999915i	$0.504159\pi$
$212$		0			0
$213$	17908.4	−	10339.4i	0.394727	−	0.227896i
$214$		0			0
$215$	14903.7	+	8604.67i	0.322417	+	0.186148i
$216$		0			0
$217$	−14751.9	−	64024.7i	−0.313277	−	1.35965i
$218$		0			0
$219$	−6116.69	+	10594.4i	−0.127535	+	0.220896i
$220$		0			0
$221$	−1876.55	−	3250.27i	−0.0384215	−	0.0665480i
$222$		0			0
$223$			87557.6i			1.76069i	0.474330	+	0.880347i	$0.342690\pi$
$223$			87557.6i			1.76069i	−0.474330	+	0.880347i	$0.657310\pi$
$224$		0			0
$225$	6034.45			0.119199
$226$		0			0
$227$	58528.2	−	33791.3i	1.13583	−	0.655772i	0.190435	−	0.981700i	$-0.439010\pi$
$227$	58528.2	−	33791.3i	1.13583	−	0.655772i	0.945395	+	0.325928i	$0.105677\pi$
$228$		0			0
$229$	−14100.5	−	8140.94i	−0.268884	−	0.155240i	0.359497	−	0.933146i	$-0.382948\pi$
$229$	−14100.5	−	8140.94i	−0.268884	−	0.155240i	−0.628380	+	0.777906i	$0.716282\pi$
$230$		0			0
$231$	27022.3	−	25176.7i	0.506405	−	0.471818i
$232$		0			0
$233$	38363.5	−	66447.6i	0.706654	−	1.22396i	−0.259437	−	0.965760i	$-0.583537\pi$
$233$	38363.5	−	66447.6i	0.706654	−	1.22396i	0.966091	−	0.258201i	$-0.0831296\pi$
$234$		0			0
$235$	26369.5	+	45673.2i	0.477491	+	0.827039i
$236$		0			0
$237$			51972.9i			0.925296i
$238$		0			0
$239$	−88558.8			−1.55037			−0.775186	−	0.631733i	$-0.782344\pi$
$239$	−88558.8			−1.55037			−0.775186	+	0.631733i	$0.782344\pi$
$240$		0			0
$241$	−73961.3	+	42701.6i	−1.27342	+	0.735208i	−0.975630	−	0.219424i	$-0.929582\pi$
$241$	−73961.3	+	42701.6i	−1.27342	+	0.735208i	−0.297788	+	0.954632i	$0.596249\pi$
$242$		0			0
$243$	3280.50	+	1894.00i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−30604.3	−	62887.2i	−0.509859	−	1.04768i
$246$		0			0
$247$	−12867.5	+	22287.1i	−0.210911	+	0.365309i
$248$		0			0
$249$	25136.9	+	43538.4i	0.405427	+	0.702220i
$250$		0			0
$251$			86543.3i			1.37368i	0.726808	+	0.686841i	$0.241003\pi$
$251$			86543.3i			1.37368i	−0.726808	+	0.686841i	$0.758997\pi$
$252$		0			0
$253$	−120084.			−1.87605
$254$		0			0
$255$	7662.90	−	4424.18i	0.117845	−	0.0680381i
$256$		0			0
$257$	−32975.8	−	19038.6i	−0.499263	−	0.288249i	0.229146	−	0.973392i	$-0.426407\pi$
$257$	−32975.8	−	19038.6i	−0.499263	−	0.288249i	−0.728409	+	0.685143i	$0.759740\pi$
$258$		0			0
$259$	−54310.1	−	58291.4i	−0.809620	−	0.868970i
$260$		0			0
$261$	4652.69	−	8058.69i	0.0683004	−	0.118300i
$262$		0			0
$263$	−2943.67	−	5098.58i	−0.0425576	−	0.0737120i	0.843962	−	0.536403i	$-0.180217\pi$
$263$	−2943.67	−	5098.58i	−0.0425576	−	0.0737120i	−0.886520	+	0.462691i	$0.846884\pi$
$264$		0			0
$265$			120955.i			1.72239i
$266$		0			0
$267$	2929.91			0.0410991
$268$		0			0
$269$	−25984.3	+	15002.1i	−0.359093	+	0.207322i	−0.668683	−	0.743548i	$-0.733142\pi$
$269$	−25984.3	+	15002.1i	−0.359093	+	0.207322i	0.309590	+	0.950870i	$0.399808\pi$
$270$		0			0
$271$	−69790.5	−	40293.5i	−0.950293	−	0.548652i	−0.0571211	−	0.998367i	$-0.518192\pi$
$271$	−69790.5	−	40293.5i	−0.950293	−	0.548652i	−0.893172	+	0.449715i	$0.851525\pi$
$272$		0			0
$273$	−15928.7	+	3670.11i	−0.213724	+	0.0492441i
$274$		0			0
$275$	16210.0	−	28076.6i	0.214347	−	0.371261i
$276$		0			0
$277$	70334.6	+	121823.i	0.916663	+	1.58771i	0.804448	+	0.594023i	$0.202461\pi$
$277$	70334.6	+	121823.i	0.916663	+	1.58771i	0.112214	+	0.993684i	$0.464206\pi$
$278$		0			0
$279$		−	36203.3i		−	0.465092i
$280$		0			0
$281$	−57441.6			−0.727468			−0.363734	−	0.931503i	$-0.618498\pi$
$281$	−57441.6			−0.727468			−0.363734	+	0.931503i	$0.618498\pi$
$282$		0			0
$283$	23484.5	−	13558.8i	0.293230	−	0.169297i	−0.346167	−	0.938173i	$-0.612517\pi$
$283$	23484.5	−	13558.8i	0.293230	−	0.169297i	0.639398	+	0.768876i	$0.279184\pi$
$284$		0			0
$285$	−52544.6	−	30336.6i	−0.646902	−	0.373489i
$286$		0			0
$287$	4260.20	+	1304.50i	0.0517209	+	0.0158373i
$288$		0			0
$289$	−40051.7	+	69371.7i	−0.479541	+	0.830589i
$290$		0			0
$291$	−32361.9	−	56052.4i	−0.382162	−	0.661924i
$292$		0			0
$293$		−	76646.3i		−	0.892803i	−0.894833	−	0.446402i	$-0.852705\pi$
$293$		−	76646.3i		−	0.892803i	0.894833	−	0.446402i	$-0.147295\pi$
$294$		0			0
$295$	−132217.			−1.51930
$296$		0			0
$297$	17624.5	−	10175.5i	0.199804	−	0.115357i
$298$		0			0
$299$	46026.8	+	26573.6i	0.514836	+	0.297241i
$300$		0			0
$301$	8475.96	−	27680.5i	0.0935526	−	0.305520i
$302$		0			0
$303$	1235.62	−	2140.15i	0.0134586	−	0.0233109i
$304$		0			0
$305$	70943.9	+	122878.i	0.762633	+	1.32092i
$306$		0			0
$307$			103676.i			1.10002i	0.835157	+	0.550011i	$0.185377\pi$
$307$			103676.i			1.10002i	−0.835157	+	0.550011i	$0.814623\pi$
$308$		0			0
$309$	77227.8			0.808829
$310$		0			0
$311$	49630.3	−	28654.1i	0.513129	−	0.296255i	−0.220990	−	0.975276i	$-0.570929\pi$
$311$	49630.3	−	28654.1i	0.513129	−	0.296255i	0.734119	+	0.679021i	$0.237596\pi$
$312$		0			0
$313$	147489.	+	85152.8i	1.50547	+	0.869181i	0.999980	+	0.00634608i	$0.00202003\pi$
$313$	147489.	+	85152.8i	1.50547	+	0.869181i	0.505486	+	0.862835i	$0.331313\pi$
$314$		0			0
$315$	−8652.72	−	37553.7i	−0.0872030	−	0.378470i
$316$		0			0
$317$	−85250.8	+	147659.i	−0.848359	+	1.46940i	0.0343128	+	0.999411i	$0.489076\pi$
$317$	−85250.8	+	147659.i	−0.848359	+	1.46940i	−0.882672	+	0.469990i	$0.844258\pi$
$318$		0			0
$319$	−24996.5	−	43295.3i	−0.245640	−	0.425461i
$320$		0			0
$321$		−	102533.i		−	0.995067i
$322$		0			0
$323$	−23433.9			−0.224616
$324$		0			0
$325$	−12426.2	+	7174.27i	−0.117644	+	0.0679221i
$326$		0			0
$327$	32457.4	+	18739.3i	0.303541	+	0.175250i
$328$		0			0
$329$	64909.1	−	60475.9i	0.599672	−	0.558715i
$330$		0			0
$331$	53722.4	−	93050.0i	0.490343	−	0.849298i	−0.509596	−	0.860414i	$-0.670205\pi$
$331$	53722.4	−	93050.0i	0.490343	−	0.849298i	0.999938	+	0.0111158i	$0.00353833\pi$
$332$		0			0
$333$	−21950.2	−	38018.8i	−0.197947	−	0.342855i
$334$		0			0
$335$		−	15616.0i		−	0.139149i
$336$		0			0
$337$	−6382.64			−0.0562006			−0.0281003	−	0.999605i	$-0.508946\pi$
$337$	−6382.64			−0.0562006			−0.0281003	+	0.999605i	$0.508946\pi$
$338$		0			0
$339$	61649.4	−	35593.3i	0.536450	−	0.309720i
$340$		0			0
$341$	−168443.	−	97250.9i	−1.44859	−	0.836344i
$342$		0			0
$343$	−91527.2	+	73919.3i	−0.777968	+	0.628304i
$344$		0			0
$345$	−62650.4	+	108514.i	−0.526364	+	0.911689i
$346$		0			0
$347$	8816.16	+	15270.0i	0.0732184	+	0.126818i	0.900310	−	0.435249i	$-0.143340\pi$
$347$	8816.16	+	15270.0i	0.0732184	+	0.126818i	−0.827092	+	0.562067i	$0.810006\pi$
$348$		0			0
$349$		−	137369.i		−	1.12781i	−0.825839	−	0.563907i	$-0.809298\pi$
$349$		−	137369.i		−	1.12781i	0.825839	−	0.563907i	$-0.190702\pi$
$350$		0			0
$351$	−9006.98			−0.0731080
$352$		0			0
$353$	−10297.6	+	5945.34i	−0.0826395	+	0.0477119i	−0.540750	−	0.841183i	$-0.681860\pi$
$353$	−10297.6	+	5945.34i	−0.0826395	+	0.0477119i	0.458111	+	0.888895i	$0.348526\pi$
$354$		0			0
$355$	−100392.	−	57961.5i	−0.796606	−	0.459920i
$356$		0			0
$357$	−10146.4	−	10890.2i	−0.0796118	−	0.0854478i
$358$		0			0
$359$	−9215.68	+	15962.0i	−0.0715053	+	0.123851i	−0.899561	−	0.436795i	$-0.856114\pi$
$359$	−9215.68	+	15962.0i	−0.0715053	+	0.123851i	0.828056	+	0.560646i	$0.189447\pi$
$360$		0			0
$361$	15182.9	+	26297.5i	0.116504	+	0.201790i
$362$		0			0
$363$		−	33258.7i		−	0.252402i
$364$		0			0
$365$	68578.8			0.514759
$366$		0			0
$367$	16711.0	−	9648.11i	0.124071	−	0.0716325i	−0.436680	−	0.899617i	$-0.643846\pi$
$367$	16711.0	−	9648.11i	0.124071	−	0.0716325i	0.560751	+	0.827984i	$0.310512\pi$
$368$		0			0
$369$	2126.13	+	1227.52i	0.0156148	+	0.00901522i
$370$		0			0
$371$	198272.	−	45683.7i	1.44050	−	0.331905i
$372$		0			0
$373$	−135022.	+	233865.i	−0.970480	+	1.68092i	−0.276372	+	0.961051i	$0.589132\pi$
$373$	−135022.	+	233865.i	−0.970480	+	1.68092i	−0.694108	+	0.719871i	$0.744201\pi$
$374$		0			0
$375$	30385.4	+	52629.1i	0.216074	+	0.374251i
$376$		0			0
$377$			22126.1i			0.155676i
$378$		0			0
$379$	42608.7			0.296633			0.148317	−	0.988940i	$-0.452614\pi$
$379$	42608.7			0.296633			0.148317	+	0.988940i	$0.452614\pi$
$380$		0			0
$381$	137333.	−	79289.4i	0.946076	−	0.546217i
$382$		0			0
$383$	−77072.1	−	44497.6i	−0.525411	−	0.303346i	0.213734	−	0.976892i	$-0.431437\pi$
$383$	−77072.1	−	44497.6i	−0.525411	−	0.303346i	−0.739146	+	0.673545i	$0.764771\pi$
$384$		0			0
$385$	−197970.	−	60619.9i	−1.33561	−	0.408972i
$386$		0			0
$387$	7975.77	−	13814.4i	0.0532538	−	0.0922383i
$388$		0			0
$389$	25608.2	+	44354.7i	0.169231	+	0.293116i	0.938150	−	0.346230i	$-0.112538\pi$
$389$	25608.2	+	44354.7i	0.169231	+	0.293116i	−0.768919	+	0.639346i	$0.779205\pi$
$390$		0			0
$391$			48395.2i			0.316555i
$392$		0			0
$393$	44963.2			0.291120
$394$		0			0
$395$	252320.	−	145677.i	1.61718	−	0.933677i
$396$		0			0
$397$	216088.	+	124758.i	1.37104	+	0.791569i	0.991059	−	0.133427i	$-0.0425981\pi$
$397$	216088.	+	124758.i	1.37104	+	0.791569i	0.379978	+	0.924995i	$0.375931\pi$
$398$		0			0
$399$	−29882.8	+	97590.2i	−0.187705	+	0.613000i
$400$		0			0
$401$	81034.8	−	140356.i	0.503945	−	0.872858i	−0.496045	−	0.868297i	$-0.665215\pi$
$401$	81034.8	−	140356.i	0.503945	−	0.872858i	0.999990	−	0.00456122i	$-0.00145189\pi$
$402$		0			0
$403$	43041.5	+	74550.1i	0.265019	+	0.459027i
$404$		0			0
$405$		−	21235.0i		−	0.129462i
$406$		0			0
$407$	−235855.			−1.42382
$408$		0			0
$409$	45755.7	−	26417.1i	0.273526	−	0.157920i	−0.356963	−	0.934119i	$-0.616188\pi$
$409$	45755.7	−	26417.1i	0.273526	−	0.157920i	0.630489	+	0.776198i	$0.282854\pi$
$410$		0			0
$411$	−14996.7	−	8658.34i	−0.0887793	−	0.0512567i
$412$		0			0
$413$	49937.2	+	216733.i	0.292768	+	1.27065i
$414$		0			0
$415$	140914.	−	244071.i	0.818199	−	1.41716i
$416$		0			0
$417$	50637.3	+	87706.4i	0.291205	+	0.504381i
$418$		0			0
$419$		−	7927.10i		−	0.0451530i	−0.999745	−	0.0225765i	$-0.992813\pi$
$419$		−	7927.10i		−	0.0451530i	0.999745	−	0.0225765i	$-0.00718693\pi$
$420$		0			0
$421$	110585.			0.623925			0.311962	−	0.950094i	$-0.399014\pi$
$421$	110585.			0.623925			0.311962	+	0.950094i	$0.399014\pi$
$422$		0			0
$423$	42335.1	−	24442.2i	0.236603	−	0.136603i
$424$		0			0
$425$	−11315.1	−	6532.80i	−0.0626444	−	0.0361677i
$426$		0			0
$427$	174630.	−	162703.i	0.957776	−	0.892361i
$428$		0			0
$429$	−24195.0	+	41906.9i	−0.131465	+	0.227704i
$430$		0			0
$431$	−52810.7	−	91470.9i	−0.284294	−	0.492412i	0.688144	−	0.725574i	$-0.258426\pi$
$431$	−52810.7	−	91470.9i	−0.284294	−	0.492412i	−0.972438	+	0.233163i	$0.925093\pi$
$432$		0			0
$433$		−	245956.i		−	1.31184i	−0.754830	−	0.655921i	$-0.772281\pi$
$433$		−	245956.i		−	1.31184i	0.754830	−	0.655921i	$-0.227719\pi$
$434$		0			0
$435$	−52164.8			−0.275676
$436$		0			0
$437$	287387.	−	165923.i	1.50489	−	0.868848i
$438$		0			0
$439$	50725.7	+	29286.5i	0.263208	+	0.151963i	0.625797	−	0.779986i	$-0.284774\pi$
$439$	50725.7	+	29286.5i	0.263208	+	0.151963i	−0.362589	+	0.931949i	$0.618107\pi$
$440$		0			0
$441$	−58290.9	+	28367.5i	−0.299725	+	0.145863i
$442$		0			0
$443$	112217.	−	194366.i	0.571811	−	0.990405i	−0.424570	−	0.905395i	$-0.639575\pi$
$443$	112217.	−	194366.i	0.571811	−	0.990405i	0.996380	−	0.0850096i	$-0.0270921\pi$
$444$		0			0
$445$	−8212.37	−	14224.2i	−0.0414714	−	0.0718305i
$446$		0			0
$447$		−	100744.i		−	0.504203i
$448$		0			0
$449$	115522.			0.573022			0.286511	−	0.958077i	$-0.407505\pi$
$449$	115522.			0.573022			0.286511	+	0.958077i	$0.407505\pi$
$450$		0			0
$451$	11422.6	−	6594.86i	0.0561582	−	0.0324229i
$452$		0			0
$453$	−78012.6	−	45040.6i	−0.380161	−	0.219486i
$454$		0			0
$455$	62464.8	+	67043.9i	0.301726	+	0.323844i
$456$		0			0
$457$	24574.2	−	42563.8i	0.117665	−	0.203802i	−0.801177	−	0.598427i	$-0.795792\pi$
$457$	24574.2	−	42563.8i	0.117665	−	0.203802i	0.918842	+	0.394626i	$0.129126\pi$
$458$		0			0
$459$	−4100.82	−	7102.83i	−0.0194646	−	0.0337137i
$460$		0			0
$461$			61543.1i			0.289586i	0.989462	+	0.144793i	$0.0462516\pi$
$461$			61543.1i			0.289586i	−0.989462	+	0.144793i	$0.953748\pi$
$462$		0			0
$463$	−25264.9			−0.117857			−0.0589285	−	0.998262i	$-0.518768\pi$
$463$	−25264.9			−0.117857			−0.0589285	+	0.998262i	$0.518768\pi$
$464$		0			0
$465$	−175761.	+	101475.i	−0.812860	+	0.469305i
$466$		0			0
$467$	−25858.1	−	14929.2i	−0.118567	−	0.0684544i	0.439544	−	0.898221i	$-0.355140\pi$
$467$	−25858.1	−	14929.2i	−0.118567	−	0.0684544i	−0.558110	+	0.829767i	$0.688473\pi$
$468$		0			0
$469$	−25598.1	+	5898.05i	−0.116376	+	0.0268141i
$470$		0			0
$471$	−89204.3	+	154506.i	−0.402109	+	0.696473i
$472$		0			0
$473$	−42849.8	−	74218.0i	−0.191525	−	0.331732i
$474$		0			0
$475$			89590.9i			0.397079i
$476$		0			0
$477$	112115.			0.492748
$478$		0			0
$479$	−124718.	+	72005.7i	−0.543572	+	0.313831i	−0.746525	−	0.665357i	$-0.768279\pi$
$479$	−124718.	+	72005.7i	−0.543572	+	0.313831i	0.202954	+	0.979188i	$0.434946\pi$
$480$		0			0
$481$	90400.1	+	52192.5i	0.390732	+	0.225589i
$482$		0			0
$483$	201541.	+	61713.3i	0.863911	+	0.264536i
$484$		0			0
$485$	−181417.	+	314223.i	−0.771247	+	1.33584i
$486$		0			0
$487$	160840.	+	278583.i	0.678167	+	1.17462i	0.975532	+	0.219855i	$0.0705585\pi$
$487$	160840.	+	278583.i	0.678167	+	1.17462i	−0.297366	+	0.954764i	$0.596108\pi$
$488$		0			0
$489$			123916.i			0.518213i
$490$		0			0
$491$	−389951.			−1.61751			−0.808754	−	0.588146i	$-0.799858\pi$
$491$	−389951.			−1.61751			−0.808754	+	0.588146i	$0.799858\pi$
$492$		0			0
$493$	−17448.4	+	10073.9i	−0.0717897	+	0.0414478i
$494$		0			0
$495$	−98800.6	−	57042.6i	−0.403227	−	0.232803i
$496$		0			0
$497$	−57094.5	+	186457.i	−0.231143	+	0.754859i
$498$		0			0
$499$	99056.1	−	171570.i	0.397814	−	0.689034i	−0.595642	−	0.803250i	$-0.703102\pi$
$499$	99056.1	−	171570.i	0.397814	−	0.689034i	0.993456	+	0.114216i	$0.0364356\pi$
$500$		0			0
$501$	−92332.0	−	159924.i	−0.367855	−	0.637144i
$502$		0			0
$503$			240418.i			0.950235i	0.879922	+	0.475118i	$0.157595\pi$
$503$			240418.i			0.950235i	−0.879922	+	0.475118i	$0.842405\pi$
$504$		0			0
$505$	−13853.5			−0.0543219
$506$		0			0
$507$	−109977.	+	63495.4i	−0.427845	+	0.247017i
$508$		0			0
$509$	−19660.6	−	11351.0i	−0.0758859	−	0.0438127i	0.461577	−	0.887100i	$-0.347284\pi$
$509$	−19660.6	−	11351.0i	−0.0758859	−	0.0438127i	−0.537463	+	0.843287i	$0.680617\pi$
$510$		0			0
$511$	−25901.7	−	112416.i	−0.0991941	−	0.430513i
$512$		0			0
$513$	−28119.4	+	48704.2i	−0.106849	+	0.185068i
$514$		0			0
$515$	−216465.	−	374928.i	−0.816155	−	1.41362i
$516$		0			0
$517$		−	262631.i		−	0.982572i
$518$		0			0
$519$	66100.4			0.245397
$520$		0			0
$521$	−276092.	+	159402.i	−1.01714	+	0.587243i	−0.913273	−	0.407348i	$-0.866454\pi$
$521$	−276092.	+	159402.i	−1.01714	+	0.587243i	−0.103863	+	0.994592i	$0.533120\pi$
$522$		0			0
$523$	398784.	+	230238.i	1.45792	+	0.841733i	0.998909	−	0.0466963i	$-0.0148693\pi$
$523$	398784.	+	230238.i	1.45792	+	0.841733i	0.459014	+	0.888429i	$0.348203\pi$
$524$		0			0
$525$	−41634.7	+	38791.1i	−0.151056	+	0.140739i
$526$		0			0
$527$	−39193.1	+	67884.4i	−0.141120	+	0.244427i
$528$		0			0
$529$	−202740.	−	351155.i	−0.724481	−	1.25484i
$530$		0			0
$531$			122553.i			0.434646i
$532$		0			0
$533$	−5837.53			−0.0205482
$534$		0			0
$535$	−497779.	+	287393.i	−1.73912	+	1.00408i
$536$		0			0
$537$	−163186.	−	94215.7i	−0.565894	−	0.326719i
$538$		0			0
$539$	−24597.8	+	347413.i	−0.0846678	+	1.19583i
$540$		0			0
$541$	206628.	−	357890.i	0.705983	−	1.22280i	−0.260352	−	0.965514i	$-0.583839\pi$
$541$	206628.	−	357890.i	0.705983	−	1.22280i	0.966335	−	0.257285i	$-0.0828281\pi$
$542$		0			0
$543$	70488.3	+	122089.i	0.239066	+	0.414074i
$544$		0			0
$545$		−	210100.i		−	0.707348i
$546$		0			0
$547$	−101659.			−0.339759			−0.169879	−	0.985465i	$-0.554338\pi$
$547$	−101659.			−0.339759			−0.169879	+	0.985465i	$0.554338\pi$
$548$		0			0
$549$	113898.	−	65758.8i	0.377894	−	0.218177i
$550$		0			0
$551$	119644.	+	69076.5i	0.394083	+	0.227524i
$552$		0			0
$553$	−334096.	−	358588.i	−1.09250	−	1.17259i
$554$		0			0
$555$	−123050.	+	213129.i	−0.399481	+	0.691921i
$556$		0			0
$557$	187074.	+	324022.i	0.602981	+	1.04439i	0.992367	+	0.123319i	$0.0393539\pi$
$557$	187074.	+	324022.i	0.602981	+	1.04439i	−0.389386	+	0.921075i	$0.627313\pi$
$558$		0			0
$559$			37929.1i			0.121381i
$560$		0			0
$561$	−44063.3			−0.140008
$562$		0			0
$563$	−319317.	+	184358.i	−1.00741	+	0.581627i	−0.910432	−	0.413659i	$-0.864250\pi$
$563$	−319317.	+	184358.i	−1.00741	+	0.581627i	−0.0969762	+	0.995287i	$0.530917\pi$
$564$		0			0
$565$	−345599.	−	199532.i	−1.08262	−	0.625050i
$566$		0			0
$567$	−34809.0	+	8020.31i	−0.108274	+	0.0249474i
$568$		0			0
$569$	−56631.1	+	98088.0i	−0.174916	+	0.302964i	−0.940132	−	0.340810i	$-0.889299\pi$
$569$	−56631.1	+	98088.0i	−0.174916	+	0.302964i	0.765216	+	0.643774i	$0.222632\pi$
$570$		0			0
$571$	−107712.	−	186563.i	−0.330364	−	0.572207i	0.652219	−	0.758030i	$-0.273838\pi$
$571$	−107712.	−	186563.i	−0.330364	−	0.572207i	−0.982583	+	0.185823i	$0.940505\pi$
$572$		0			0
$573$		−	344790.i		−	1.05013i
$574$		0			0
$575$	185021.			0.559609
$576$		0			0
$577$	−176127.	+	101687.i	−0.529023	+	0.305432i	−0.740619	−	0.671926i	$-0.765467\pi$
$577$	−176127.	+	101687.i	−0.529023	+	0.305432i	0.211595	+	0.977357i	$0.432134\pi$
$578$		0			0
$579$	−77575.2	−	44788.1i	−0.231401	−	0.133600i
$580$		0			0
$581$	−453309.	−	138806.i	−1.34289	−	0.411204i
$582$		0			0
$583$	301167.	−	521637.i	0.886076	−	1.53473i
$584$		0			0
$585$	25246.0	+	43727.4i	0.0737702	+	0.127774i
$586$		0			0
$587$			488438.i			1.41753i	0.705443	+	0.708766i	$0.250748\pi$
$587$			488438.i			1.41753i	−0.705443	+	0.708766i	$0.749252\pi$
$588$		0			0
$589$	537494.			1.54933
$590$		0			0
$591$	−154337.	+	89106.2i	−0.441869	+	0.255113i
$592$		0			0
$593$	403635.	+	233039.i	1.14784	+	0.662703i	0.948359	−	0.317199i	$-0.102742\pi$
$593$	403635.	+	233039.i	1.14784	+	0.662703i	0.199477	+	0.979903i	$0.436076\pi$
$594$		0			0
$595$	−24430.4	+	79783.9i	−0.0690076	+	0.225362i
$596$		0			0
$597$	−14601.1	+	25289.8i	−0.0409672	+	0.0709573i
$598$		0			0
$599$	−135564.	−	234804.i	−0.377825	−	0.654413i	0.612920	−	0.790145i	$-0.289995\pi$
$599$	−135564.	−	234804.i	−0.377825	−	0.654413i	−0.990746	+	0.135732i	$0.956661\pi$
$600$		0			0
$601$			180604.i			0.500010i	0.968245	+	0.250005i	$0.0804322\pi$
$601$			180604.i			0.500010i	−0.968245	+	0.250005i	$0.919568\pi$
$602$		0			0
$603$	−14474.7			−0.0398083
$604$		0			0
$605$	−161465.	+	93222.1i	−0.441132	+	0.254688i
$606$		0			0
$607$	637516.	+	368070.i	1.73027	+	0.998971i	0.887813	+	0.460205i	$0.152224\pi$
$607$	637516.	+	368070.i	1.73027	+	0.998971i	0.842456	+	0.538766i	$0.181109\pi$
$608$		0			0
$609$	19702.2	+	85509.8i	0.0531228	+	0.230559i
$610$		0			0
$611$	−58117.9	+	100663.i	−0.155678	+	0.269642i
$612$		0			0
$613$	−65209.9	−	112947.i	−0.173537	−	0.300575i	0.766117	−	0.642701i	$-0.222186\pi$
$613$	−65209.9	−	112947.i	−0.173537	−	0.300575i	−0.939654	+	0.342126i	$0.888853\pi$
$614$		0			0
$615$		−	13762.7i		−	0.0363875i
$616$		0			0
$617$	623632.			1.63817			0.819084	−	0.573674i	$-0.194482\pi$
$617$	623632.			1.63817			0.819084	+	0.573674i	$0.194482\pi$
$618$		0			0
$619$	−517688.	+	298887.i	−1.35110	+	0.780057i	−0.988403	−	0.151851i	$-0.951477\pi$
$619$	−517688.	+	298887.i	−1.35110	+	0.780057i	−0.362695	+	0.931908i	$0.618143\pi$
$620$		0			0
$621$	100583.	+	58071.4i	0.260819	+	0.150584i
$622$		0			0
$623$	−20215.0	+	18834.3i	−0.0520831	+	0.0485259i
$624$		0			0
$625$	240180.	−	416004.i	0.614861	−	1.06497i
$626$		0			0
$627$	151071.	+	261663.i	0.384279	+	0.665591i
$628$		0			0
$629$			95051.7i			0.240247i
$630$		0			0
$631$	−542123.			−1.36157			−0.680783	−	0.732485i	$-0.738361\pi$
$631$	−542123.			−1.36157			−0.680783	+	0.732485i	$0.738361\pi$
$632$		0			0
$633$	5234.92	−	3022.38i	0.0130648	−	0.00754296i
$634$		0			0
$635$	−769873.	−	444487.i	−1.90929	−	1.10233i
$636$		0			0
$637$	86307.4	−	127716.i	0.212701	−	0.314750i
$638$		0			0
$639$	−53725.2	+	93054.7i	−0.131576	+	0.227896i
$640$		0			0
$641$	−205470.	−	355885.i	−0.500073	−	0.866152i	−1.00000		8.42887e-5i	$-0.999973\pi$
$641$	−205470.	−	355885.i	−0.500073	−	0.866152i	0.499927	−	0.866068i	$-0.333360\pi$
$642$		0			0
$643$			501978.i			1.21412i	0.794654	+	0.607062i	$0.207652\pi$
$643$			501978.i			1.21412i	−0.794654	+	0.607062i	$0.792348\pi$
$644$		0			0
$645$	−89422.4			−0.214945
$646$		0			0
$647$	413841.	−	238931.i	0.988610	−	0.570774i	0.0837513	−	0.996487i	$-0.473310\pi$
$647$	413841.	−	238931.i	0.988610	−	0.570774i	0.904858	+	0.425713i	$0.139977\pi$
$648$		0			0
$649$	570205.	+	329208.i	1.35376	+	0.781594i
$650$		0			0
$651$	232724.	+	249785.i	0.549136	+	0.589391i
$652$		0			0
$653$	−335100.	+	580411.i	−0.785866	+	1.36116i	0.142614	+	0.989778i	$0.454449\pi$
$653$	−335100.	+	580411.i	−0.785866	+	1.36116i	−0.928480	+	0.371382i	$0.878884\pi$
$654$		0			0
$655$	−126029.	−	218289.i	−0.293757	−	0.508802i
$656$		0			0
$657$		−	63566.5i		−	0.147264i
$658$		0			0
$659$	481511.			1.10876			0.554378	−	0.832265i	$-0.312956\pi$
$659$	481511.			1.10876			0.554378	+	0.832265i	$0.312956\pi$
$660$		0			0
$661$	−325016.	+	187648.i	−0.743878	+	0.429478i	−0.823477	−	0.567349i	$-0.807969\pi$
$661$	−325016.	+	187648.i	−0.743878	+	0.429478i	0.0795999	+	0.996827i	$0.474636\pi$
$662$		0			0
$663$	16888.9	+	9750.82i	0.0384215	+	0.0221827i
$664$		0			0
$665$	557544.	−	128463.i	1.26077	−	0.290493i
$666$		0			0
$667$	142655.	−	247086.i	0.320653	−	0.555387i
$668$		0			0
$669$	−227481.	−	394009.i	−0.508269	−	0.880347i
$670$		0			0
$671$		−	706577.i		−	1.56933i
$672$		0			0
$673$	509800.			1.12556			0.562781	−	0.826606i	$-0.309731\pi$
$673$	509800.			1.12556			0.562781	+	0.826606i	$0.309731\pi$
$674$		0			0
$675$	−27155.0	+	15678.0i	−0.0595995	+	0.0344098i
$676$		0			0
$677$	−176095.	−	101668.i	−0.384210	−	0.221824i	0.295438	−	0.955362i	$-0.404534\pi$
$677$	−176095.	−	101668.i	−0.384210	−	0.221824i	−0.679648	+	0.733538i	$0.737868\pi$
$678$		0			0
$679$	583601.	+	178703.i	1.26583	+	0.387607i
$680$		0			0
$681$	−175585.	+	304121.i	−0.378610	+	0.655772i
$682$		0			0
$683$	−130320.	−	225721.i	−0.279364	−	0.483872i	0.691863	−	0.722029i	$-0.256790\pi$
$683$	−130320.	−	225721.i	−0.279364	−	0.483872i	−0.971227	+	0.238157i	$0.923457\pi$
$684$		0			0
$685$			97075.2i			0.206884i
$686$		0			0
$687$	84603.2			0.179256
$688$		0			0
$689$	−230867.	+	133291.i	−0.486322	+	0.280778i
$690$		0			0
$691$	−340943.	−	196844.i	−0.714046	−	0.412255i	0.0985114	−	0.995136i	$-0.468592\pi$
$691$	−340943.	−	196844.i	−0.714046	−	0.412255i	−0.812557	+	0.582881i	$0.801925\pi$
$692$		0			0
$693$	−56189.3	+	183501.i	−0.117000	+	0.382095i
$694$		0			0
$695$	283866.	−	491671.i	0.587685	−	1.01790i
$696$		0			0
$697$	−2657.79	−	4603.43i	−0.00547086	−	0.00947580i
$698$		0			0
$699$			398686.i			0.815974i
$700$		0			0
$701$	222381.			0.452546			0.226273	−	0.974064i	$-0.427346\pi$
$701$	222381.			0.452546			0.226273	+	0.974064i	$0.427346\pi$
$702$		0			0
$703$	564450.	−	325885.i	1.14213	−	0.659408i
$704$		0			0
$705$	−237325.	−	137020.i	−0.477491	−	0.275680i
$706$		0			0
$707$	5232.34	+	22708.9i	0.0104678	+	0.0454315i
$708$		0			0
$709$	387588.	−	671322.i	0.771041	−	1.33548i	−0.165951	−	0.986134i	$-0.553070\pi$
$709$	387588.	−	671322.i	0.771041	−	1.33548i	0.936993	−	0.349349i	$-0.113597\pi$
$710$		0			0
$711$	−135030.	−	233878.i	−0.267110	−	0.462648i
$712$		0			0
$713$		−	1.11002e6i		−	2.18349i
$714$		0			0
$715$	271268.			0.530624
$716$		0			0
$717$	398515.	−	230083.i	0.775186	−	0.447554i
$718$		0			0
$719$	100590.	+	58075.7i	0.194580	+	0.112341i	0.594125	−	0.804373i	$-0.297499\pi$
$719$	100590.	+	58075.7i	0.194580	+	0.112341i	−0.399545	+	0.916714i	$0.630832\pi$
$720$		0			0
$721$	−532834.	+	496441.i	−1.02499	+	0.954987i
$722$		0			0
$723$	221884.	−	384314.i	0.424472	−	0.735208i
$724$		0			0
$725$	38513.6	+	66707.5i	0.0732720	+	0.126911i
$726$		0			0
$727$			218654.i			0.413703i	0.978372	+	0.206851i	$0.0663217\pi$
$727$			218654.i			0.413703i	−0.978372	+	0.206851i	$0.933678\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	−29910.6	+	17268.9i	−0.0559745	+	0.0323169i
$732$		0			0
$733$	173822.	+	100356.i	0.323518	+	0.186783i	0.652959	−	0.757393i	$-0.273527\pi$
$733$	173822.	+	100356.i	0.323518	+	0.186783i	−0.329442	+	0.944176i	$0.606861\pi$
$734$		0			0
$735$	301105.	+	203480.i	0.557370	+	0.376658i
$736$		0			0
$737$	−38882.5	+	67346.5i	−0.0715846	+	0.123988i
$738$		0			0
$739$	−127506.	−	220846.i	−0.233475	−	0.404391i	0.725353	−	0.688377i	$-0.241676\pi$
$739$	−127506.	−	220846.i	−0.233475	−	0.404391i	−0.958828	+	0.283986i	$0.908343\pi$
$740$		0			0
$741$		−	133723.i		−	0.243539i
$742$		0			0
$743$	749838.			1.35828			0.679141	−	0.734008i	$-0.262352\pi$
$743$	749838.			1.35828			0.679141	+	0.734008i	$0.262352\pi$
$744$		0			0
$745$	−489097.	+	282380.i	−0.881216	+	0.508770i
$746$		0			0
$747$	−226232.	−	130615.i	−0.405427	−	0.234073i
$748$		0			0
$749$	659108.	+	707425.i	1.17488	+	1.26101i
$750$		0			0
$751$	157142.	−	272178.i	0.278620	−	0.482584i	−0.692422	−	0.721493i	$-0.743456\pi$
$751$	157142.	−	272178.i	0.278620	−	0.482584i	0.971042	+	0.238909i	$0.0767897\pi$
$752$		0			0
$753$	−224846.	−	389445.i	−0.396548	−	0.686841i
$754$		0			0
$755$			504984.i			0.885898i
$756$		0			0
$757$	−167897.			−0.292989			−0.146494	−	0.989212i	$-0.546799\pi$
$757$	−167897.			−0.292989			−0.146494	+	0.989212i	$0.546799\pi$
$758$		0			0
$759$	540380.	−	311988.i	0.938027	−	0.541570i
$760$		0			0
$761$	−225080.	−	129950.i	−0.388658	−	0.224392i	0.292921	−	0.956137i	$-0.405373\pi$
$761$	−225080.	−	129950.i	−0.388658	−	0.224392i	−0.681578	+	0.731745i	$0.738706\pi$
$762$		0			0
$763$	−344401.	+	79353.2i	−0.591583	+	0.136306i
$764$		0			0
$765$	−22988.7	+	39817.6i	−0.0392818	+	0.0680381i
$766$		0			0
$767$	−145702.	−	252363.i	−0.247670	−	0.428977i
$768$		0			0
$769$			695163.i			1.17553i	0.809031	+	0.587765i	$0.199992\pi$
$769$			695163.i			1.17553i	−0.809031	+	0.587765i	$0.800008\pi$
$770$		0			0
$771$	197855.			0.332842
$772$		0			0
$773$	−839814.	+	484867.i	−1.40548	+	0.811453i	−0.994948	−	0.100394i	$-0.967990\pi$
$773$	−839814.	+	484867.i	−1.40548	+	0.811453i	−0.410530	+	0.911847i	$0.634656\pi$
$774$		0			0
$775$	259530.	+	149840.i	0.432101	+	0.249473i
$776$		0			0
$777$	395841.	+	121209.i	0.655660	+	0.200768i
$778$		0			0
$779$	−18224.5	+	31565.8i	−0.0300317	+	0.0520165i
$780$		0			0
$781$	288638.	+	499936.i	0.473208	+	0.819620i
$782$		0			0
$783$			48352.2i			0.0788665i
$784$		0			0
$785$	1.00014e6			1.62301
$786$		0			0
$787$	−681977.	+	393740.i	−1.10108	+	0.635711i	−0.936505	−	0.350653i	$-0.885960\pi$
$787$	−681977.	+	393740.i	−1.10108	+	0.635711i	−0.164578	+	0.986364i	$0.552626\pi$
$788$		0			0
$789$	26493.0	+	15295.8i	0.0425576	+	0.0245707i
$790$		0			0
$791$	−196547.	+	641876.i	−0.314133	+	1.02588i
$792$		0			0
$793$	−156359.	+	270822.i	−0.248644	+	0.430663i
$794$		0			0
$795$	−314250.	−	544297.i	−0.497211	−	0.861196i
$796$		0			0
$797$		−	469149.i		−	0.738574i	−0.929315	−	0.369287i	$-0.879602\pi$
$797$		−	469149.i		−	0.738574i	0.929315	−	0.369287i	$-0.120398\pi$
$798$		0			0
$799$	−105843.			−0.165794
$800$		0			0
$801$	−13184.6	+	7612.14i	−0.0205496	+	0.0118643i
$802$		0			0
$803$	−295757.	−	170755.i	−0.458673	−	0.264815i
$804$		0			0
$805$	−265299.	−	1.15143e6i	−0.409396	−	1.77682i
$806$		0			0
$807$	77953.0	−	135019.i	0.119698	−	0.207322i
$808$		0			0
$809$	560505.	+	970823.i	0.856411	+	1.48335i	0.875329	+	0.483527i	$0.160645\pi$
$809$	560505.	+	970823.i	0.856411	+	1.48335i	−0.0189180	+	0.999821i	$0.506022\pi$
$810$		0			0
$811$		−	843629.i		−	1.28265i	−0.767267	−	0.641327i	$-0.778384\pi$
$811$		−	843629.i		−	1.28265i	0.767267	−	0.641327i	$-0.221616\pi$
$812$		0			0
$813$	418743.			0.633529
$814$		0			0
$815$	601590.	−	347328.i	0.905702	−	0.522907i
$816$		0			0
$817$	205097.	+	118413.i	0.307267	+	0.177400i
$818$		0			0
$819$	62143.8	−	57899.4i	0.0926466	−	0.0863189i
$820$		0			0
$821$	−174301.	+	301898.i	−0.258591	+	0.447892i	−0.965865	−	0.259047i	$-0.916591\pi$
$821$	−174301.	+	301898.i	−0.258591	+	0.447892i	0.707274	+	0.706940i	$0.249925\pi$
$822$		0			0
$823$	−476141.	−	824700.i	−0.702969	−	1.21758i	−0.967420	−	0.253178i	$-0.918524\pi$
$823$	−476141.	−	824700.i	−0.702969	−	1.21758i	0.264451	−	0.964399i	$-0.414809\pi$
$824$		0			0
$825$			168459.i			0.247507i
$826$		0			0
$827$	271034.			0.396290			0.198145	−	0.980173i	$-0.436508\pi$
$827$	271034.			0.396290			0.198145	+	0.980173i	$0.436508\pi$
$828$		0			0
$829$	−806917.	+	465874.i	−1.17414	+	0.677890i	−0.954652	−	0.297725i	$-0.903772\pi$
$829$	−806917.	+	465874.i	−1.17414	+	0.677890i	−0.219489	+	0.975615i	$0.570439\pi$
$830$		0			0
$831$	−633012.	−	365469.i	−0.916663	−	0.529236i
$832$		0			0
$833$	140011.	+	9913.14i	0.201777	+	0.0142863i
$834$		0			0
$835$	−517602.	+	896513.i	−0.742374	+	1.28583i
$836$		0			0
$837$	94058.8	+	162915.i	0.134261	+	0.232546i
$838$		0			0
$839$		−	947195.i		−	1.34560i	−0.739825	−	0.672799i	$-0.765092\pi$
$839$		−	947195.i		−	1.34560i	0.739825	−	0.672799i	$-0.234908\pi$
$840$		0			0
$841$	−588502.			−0.832062
$842$		0			0
$843$	258487.	−	149238.i	0.363734	−	0.210002i
$844$		0			0
$845$	616519.	+	355947.i	0.863441	+	0.498508i
$846$		0			0
$847$	213796.	+	229469.i	0.298011	+	0.319857i
$848$		0			0
$849$	−70453.6	+	122029.i	−0.0977435	+	0.169297i
$850$		0			0
$851$	−673010.	−	1.16569e6i	−0.929313	−	1.60962i
$852$		0			0
$853$			521356.i			0.716533i	0.933619	+	0.358267i	$0.116632\pi$
$853$			521356.i			0.716533i	−0.933619	+	0.358267i	$0.883368\pi$
$854$		0			0
$855$	315268.			0.431268
$856$		0			0
$857$	366814.	−	211780.i	0.499441	−	0.288353i	−0.229041	−	0.973417i	$-0.573559\pi$
$857$	366814.	−	211780.i	0.499441	−	0.288353i	0.728483	+	0.685064i	$0.240226\pi$
$858$		0			0
$859$	1.03093e6	+	595209.i	1.39715	+	0.806646i	0.994093	−	0.108529i	$-0.0346139\pi$
$859$	1.03093e6	+	595209.i	1.39715	+	0.806646i	0.403058	+	0.915174i	$0.367947\pi$
$860$		0			0
$861$	−22560.1	+	5198.06i	−0.0304323	+	0.00701188i
$862$		0			0
$863$	−612423.	+	1.06075e6i	−0.822300	+	1.42426i	0.0816662	+	0.996660i	$0.473976\pi$
$863$	−612423.	+	1.06075e6i	−0.822300	+	1.42426i	−0.903966	+	0.427605i	$0.859357\pi$
$864$		0			0
$865$	−185275.	−	320907.i	−0.247620	−	0.428890i
$866$		0			0
$867$		−	416230.i		−	0.553726i
$868$		0			0
$869$	−1.45089e6			−1.92130
$870$		0			0
$871$	29806.4	−	17208.7i	0.0392892	−	0.0226836i
$872$		0			0
$873$	291257.	+	168157.i	0.382162	+	0.220641i
$874$		0			0
$875$	−547958.	−	167789.i	−0.715701	−	0.219153i
$876$		0			0
$877$	27714.4	−	48002.8i	0.0360335	−	0.0624119i	−0.847446	−	0.530881i	$-0.821861\pi$
$877$	27714.4	−	48002.8i	0.0360335	−	0.0624119i	0.883480	+	0.468469i	$0.155194\pi$
$878$		0			0
$879$	199133.	+	344908.i	0.257730	+	0.446402i
$880$		0			0
$881$		−	1.10774e6i		−	1.42721i	−0.700549	−	0.713604i	$-0.747062\pi$
$881$		−	1.10774e6i		−	1.42721i	0.700549	−	0.713604i	$-0.252938\pi$
$882$		0			0
$883$	−211475.			−0.271230			−0.135615	−	0.990762i	$-0.543301\pi$
$883$	−211475.			−0.271230			−0.135615	+	0.990762i	$0.543301\pi$
$884$		0			0
$885$	594975.	−	343509.i	0.759648	−	0.438583i
$886$		0			0
$887$	127973.	+	73885.3i	0.162656	+	0.0939097i	0.579119	−	0.815243i	$-0.303397\pi$
$887$	127973.	+	73885.3i	0.162656	+	0.0939097i	−0.416462	+	0.909153i	$0.636730\pi$
$888$		0			0
$889$	−437838.	+	1.42987e6i	−0.554000	+	1.80923i
$890$		0			0
$891$	−52873.4	+	91579.4i	−0.0666012	+	0.115357i
$892$		0			0
$893$	362882.	+	628531.i	0.455054	+	0.788177i
$894$		0			0
$895$			1.05632e6i			1.31871i
$896$		0			0
$897$	−276161.			−0.343224
$898$		0			0
$899$	400207.	−	231060.i	0.495183	−	0.285894i
$900$		0			0
$901$	−210225.	−	121373.i	−0.258961	−	0.149511i
$902$		0			0
$903$	33774.1	+	146583.i	0.0414199	+	0.179767i
$904$		0			0
$905$	395149.	−	684417.i	0.482462	−	0.835649i
$906$		0			0
$907$	413229.	+	715734.i	0.502315	+	0.870036i	0.999996	+	0.00267567i	$0.000851692\pi$
$907$	413229.	+	715734.i	0.502315	+	0.870036i	−0.497681	+	0.867360i	$0.665815\pi$
$908$		0			0
$909$			12840.9i			0.0155406i
$910$		0			0
$911$	−516366.			−0.622187			−0.311093	−	0.950379i	$-0.600695\pi$
$911$	−516366.			−0.622187			−0.311093	+	0.950379i	$0.600695\pi$
$912$		0			0
$913$	−1.21543e6	+	701729.i	−1.45810	+	0.841837i
$914$		0			0
$915$	−638495.	−	368635.i	−0.762633	−	0.440306i
$916$		0			0
$917$	−310224.	+	289036.i	−0.368924	+	0.343727i
$918$		0			0
$919$	290517.	−	503189.i	0.343985	−	0.595800i	−0.641184	−	0.767388i	$-0.721556\pi$
$919$	290517.	−	503189.i	0.343985	−	0.595800i	0.985169	+	0.171587i	$0.0548896\pi$
$920$		0			0
$921$	−269358.	−	466542.i	−0.317549	−	0.550011i
$922$		0			0
$923$		−	255492.i		−	0.299899i
$924$		0			0
$925$	363394.			0.424712
$926$		0			0
$927$	−347525.	+	200644.i	−0.404414	+	0.233489i
$928$		0			0
$929$	−1.35034e6	−	779619.i	−1.56463	−	0.903340i	−0.996778	−	0.0802098i	$-0.974441\pi$
$929$	−1.35034e6	−	779619.i	−1.56463	−	0.903340i	−0.567853	−	0.823130i	$-0.692226\pi$
$930$		0			0
$931$	−421160.	−	865420.i	−0.485901	−	0.998452i
$932$		0			0
$933$	−148891.	+	257887.i	−0.171043	+	0.296255i
$934$		0			0
$935$	123507.	+	213920.i	0.141276	+	0.244697i
$936$		0			0
$937$			982922.i			1.11954i	0.828648	+	0.559770i	$0.189111\pi$
$937$			982922.i			1.11954i	−0.828648	+	0.559770i	$0.810889\pi$
$938$		0			0
$939$	−884934.			−1.00364
$940$		0			0
$941$	−888685.	+	513083.i	−1.00362	+	0.579439i	−0.909317	−	0.416104i	$-0.863395\pi$
$941$	−888685.	+	513083.i	−1.00362	+	0.579439i	−0.0943015	+	0.995544i	$0.530062\pi$
$942$		0			0
$943$	65188.8	+	37636.8i	0.0733077	+	0.0423242i
$944$		0			0
$945$	136505.	+	146511.i	0.152856	+	0.164062i
$946$		0			0
$947$	−290825.	+	503724.i	−0.324289	+	0.561684i	−0.981368	−	0.192137i	$-0.938458\pi$
$947$	−290825.	+	503724.i	−0.324289	+	0.561684i	0.657080	+	0.753821i	$0.271792\pi$
$948$		0			0
$949$	75573.2	+	130897.i	0.0839142	+	0.145344i
$950$		0			0
$951$		−	885952.i		−	0.979601i
$952$		0			0
$953$	925886.			1.01946			0.509732	−	0.860333i	$-0.329745\pi$
$953$	925886.			1.01946			0.509732	+	0.860333i	$0.329745\pi$
$954$		0			0
$955$	−1.67390e6	+	966424.i	−1.83536	+	1.05965i
$956$		0			0
$957$	224969.	+	129886.i	0.245640	+	0.141820i
$958$		0			0
$959$	159128.	−	36664.5i	0.173025	−	0.0398666i
$960$		0			0
$961$	437194.	−	757242.i	0.473399	−	0.819951i
$962$		0			0
$963$	266388.	+	461397.i	0.287251	+	0.497534i
$964$		0			0
$965$			502153.i			0.539239i
$966$		0			0
$967$	−1.69611e6			−1.81384			−0.906922	−	0.421298i	$-0.861575\pi$
$967$	−1.69611e6			−1.81384			−0.906922	+	0.421298i	$0.861575\pi$
$968$		0			0
$969$	105453.	−	60883.2i	0.112308	−	0.0648410i
$970$		0			0
$971$	666705.	+	384922.i	0.707124	+	0.408258i	0.809995	−	0.586437i	$-0.199470\pi$
$971$	666705.	+	384922.i	0.707124	+	0.408258i	−0.102871	+	0.994695i	$0.532803\pi$
$972$		0			0
$973$	−913173.	−	279620.i	−0.964556	−	0.295354i
$974$		0			0
$975$	37278.6	−	64568.4i	0.0392148	−	0.0679221i
$976$		0			0
$977$	−881749.	−	1.52723e6i	−0.923753	−	1.59999i	−0.793554	−	0.608499i	$-0.791772\pi$
$977$	−881749.	−	1.52723e6i	−0.923753	−	1.59999i	−0.130199	−	0.991488i	$-0.541562\pi$
$978$		0			0
$979$			81792.4i			0.0853390i
$980$		0			0
$981$	−194744.			−0.202361
$982$		0			0
$983$	454357.	−	262323.i	0.470209	−	0.271475i	−0.246118	−	0.969240i	$-0.579155\pi$
$983$	454357.	−	262323.i	0.470209	−	0.271475i	0.716327	+	0.697765i	$0.245822\pi$
$984$		0			0
$985$	865191.	+	499519.i	0.891743	+	0.514848i
$986$		0			0
$987$	−134970.	+	440780.i	−0.138549	+	0.452468i
$988$		0			0
$989$	244543.	−	423561.i	0.250013	−	0.433036i
$990$		0			0
$991$	159865.	+	276894.i	0.162782	+	0.281947i	0.935865	−	0.352358i	$-0.114620\pi$
$991$	159865.	+	276894.i	0.162782	+	0.281947i	−0.773083	+	0.634304i	$0.781287\pi$
$992$		0			0
$993$			558300.i			0.566199i
$994$		0			0
$995$	163704.			0.165353
$996$		0			0
$997$	1.55388e6	−	897132.i	1.56324	−	0.902539i	0.566318	−	0.824187i	$-0.308367\pi$
$997$	1.55388e6	−	897132.i	1.56324	−	0.902539i	0.996926	−	0.0783524i	$-0.0249659\pi$
$998$		0			0
$999$	197552.	+	114057.i	0.197947	+	0.114285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.5.z.a.145.7	yes	16
3.2	odd	2		504.5.by.a.145.2		16
4.3	odd	2		336.5.bh.i.145.7		16
7.2	even	3		1176.5.f.b.97.2		16
7.3	odd	6	inner	168.5.z.a.73.7	✓	16
7.5	odd	6		1176.5.f.b.97.15		16
21.17	even	6		504.5.by.a.73.2		16
28.3	even	6		336.5.bh.i.241.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.5.z.a.73.7	✓	16	7.3	odd	6	inner
168.5.z.a.145.7	yes	16	1.1	even	1	trivial
336.5.bh.i.145.7		16	4.3	odd	2
336.5.bh.i.241.7		16	28.3	even	6
504.5.by.a.73.2		16	21.17	even	6
504.5.by.a.145.2		16	3.2	odd	2
1176.5.f.b.97.2		16	7.2	even	3
1176.5.f.b.97.15		16	7.5	odd	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 + 2.59808i) q^{3} +(25.2264 + 14.5645i) q^{5} +(14.3466 - 46.8527i) q^{7} +(13.5000 - 23.3827i) q^{9} +O(q^{10})\)	\(q+(-4.50000 + 2.59808i) q^{3} +(25.2264 + 14.5645i) q^{5} +(14.3466 - 46.8527i) q^{7} +(13.5000 - 23.3827i) q^{9} +(-72.5287 - 125.623i) q^{11} +64.1998i q^{13} -151.359 q^{15} +(-50.6274 + 29.2298i) q^{17} +(347.153 + 200.429i) q^{19} +(57.1670 + 248.111i) q^{21} +(413.920 - 716.931i) q^{23} +(111.749 + 193.555i) q^{25} +140.296i q^{27} +344.644 q^{29} +(1161.22 - 670.431i) q^{31} +(652.758 + 376.870i) q^{33} +(1044.30 - 972.975i) q^{35} +(812.970 - 1408.11i) q^{37} +(-166.796 - 288.899i) q^{39} +90.9275i q^{41} +590.798 q^{43} +(681.114 - 393.241i) q^{45} +(1567.97 + 905.265i) q^{47} +(-1989.35 - 1344.36i) q^{49} +(151.882 - 263.068i) q^{51} +(2076.19 + 3596.07i) q^{53} -4225.37i q^{55} -2082.92 q^{57} +(-3930.89 + 2269.50i) q^{59} +(4218.43 + 2435.51i) q^{61} +(-901.862 - 967.974i) q^{63} +(-935.038 + 1619.53i) q^{65} +(-268.049 - 464.275i) q^{67} +4301.59i q^{69} -3979.64 q^{71} +(2038.90 - 1177.16i) q^{73} +(-1005.74 - 580.665i) q^{75} +(-6926.33 + 1595.89i) q^{77} +(5001.10 - 8662.16i) q^{79} +(-364.500 - 631.333i) q^{81} -9675.19i q^{83} -1702.87 q^{85} +(-1550.90 + 895.410i) q^{87} +(-488.319 - 281.931i) q^{89} +(3007.93 + 921.051i) q^{91} +(-3483.66 + 6033.88i) q^{93} +(5838.29 + 10112.2i) q^{95} +12456.1i q^{97} -3916.55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9}+O(q^{10}) \) 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9	\( 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9} - 108 q^{11} - 72 q^{15} - 168 q^{17} + 948 q^{19} - 252 q^{21} - 768 q^{23} + 1908 q^{25} - 1608 q^{29} - 3216 q^{31} + 972 q^{33} + 696 q^{35} - 1820 q^{37} - 1188 q^{39} + 2888 q^{43} + 324 q^{45} + 744 q^{47} - 3784 q^{49} + 504 q^{51} + 4476 q^{53} - 5688 q^{57} - 4668 q^{59} + 17760 q^{61} + 1188 q^{63} + 8760 q^{65} + 1580 q^{67} + 48 q^{71} + 588 q^{73} - 17172 q^{75} - 17508 q^{77} - 3824 q^{79} - 5832 q^{81} + 11440 q^{85} + 7236 q^{87} - 360 q^{89} + 25860 q^{91} + 9648 q^{93} - 21792 q^{95} - 5832 q^{99}+O(q^{100}) \) 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9 - 108 * q^11 - 72 * q^15 - 168 * q^17 + 948 * q^19 - 252 * q^21 - 768 * q^23 + 1908 * q^25 - 1608 * q^29 - 3216 * q^31 + 972 * q^33 + 696 * q^35 - 1820 * q^37 - 1188 * q^39 + 2888 * q^43 + 324 * q^45 + 744 * q^47 - 3784 * q^49 + 504 * q^51 + 4476 * q^53 - 5688 * q^57 - 4668 * q^59 + 17760 * q^61 + 1188 * q^63 + 8760 * q^65 + 1580 * q^67 + 48 * q^71 + 588 * q^73 - 17172 * q^75 - 17508 * q^77 - 3824 * q^79 - 5832 * q^81 + 11440 * q^85 + 7236 * q^87 - 360 * q^89 + 25860 * q^91 + 9648 * q^93 - 21792 * q^95 - 5832 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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