LMFDB - Embedded newform 36.6.e.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,6,Mod(13,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("36.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	36.e (of order $3$, 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:	$5.77381751327$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 $ x^10 + 175x^8 + 8800x^6 + 124623x^4 + 498609x^2 + 442368
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.1
Root			$2.13639i$ of defining polynomial
Character	$\chi$	$=$	36.13
Dual form			36.6.e.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.2647 - 9.62174i) q^{3} +(-14.0718 + 24.3731i) q^{5} +(75.7039 + 131.123i) q^{7} +(57.8441 + 236.015i) q^{9} +O(q^{10})$	\(q+(-12.2647 - 9.62174i) q^{3} +(-14.0718 + 24.3731i) q^{5} +(75.7039 + 131.123i) q^{7} +(57.8441 + 236.015i) q^{9} +(138.873 + 240.536i) q^{11} +(-291.929 + 505.636i) q^{13} +(407.098 - 163.533i) q^{15} -1612.01 q^{17} +1368.76 q^{19} +(333.149 - 2336.58i) q^{21} +(-428.014 + 741.342i) q^{23} +(1166.47 + 2020.38i) q^{25} +(1561.44 - 3451.21i) q^{27} +(-4267.49 - 7391.50i) q^{29} +(-1469.19 + 2544.71i) q^{31} +(611.138 - 4286.30i) q^{33} -4261.17 q^{35} +4036.80 q^{37} +(8445.52 - 3392.59i) q^{39} +(-9449.81 + 16367.5i) q^{41} +(10158.6 + 17595.1i) q^{43} +(-6566.39 - 1911.32i) q^{45} +(147.890 + 256.152i) q^{47} +(-3058.67 + 5297.78i) q^{49} +(19770.7 + 15510.3i) q^{51} +3039.13 q^{53} -7816.81 q^{55} +(-16787.4 - 13169.9i) q^{57} +(8618.31 - 14927.4i) q^{59} +(-12826.2 - 22215.7i) q^{61} +(-26568.0 + 25452.0i) q^{63} +(-8215.95 - 14230.4i) q^{65} +(13140.1 - 22759.4i) q^{67} +(12382.5 - 4974.07i) q^{69} +76665.7 q^{71} +1496.33 q^{73} +(5133.25 - 36002.8i) q^{75} +(-21026.5 + 36419.0i) q^{77} +(-49637.1 - 85974.0i) q^{79} +(-52357.1 + 27304.1i) q^{81} +(-25025.7 - 43345.7i) q^{83} +(22683.8 - 39289.6i) q^{85} +(-18779.8 + 131715. i) q^{87} +136635. q^{89} -88400.8 q^{91} +(42503.6 - 17073.9i) q^{93} +(-19261.0 + 33361.0i) q^{95} +(33325.0 + 57720.5i) q^{97} +(-48737.1 + 46689.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9}+O(q^{10}) $ 10 * q + 12 * q^3 - 21 * q^5 + 29 * q^7 + 12 * q^9	$ 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9} + 177 q^{11} - 181 q^{13} + 117 q^{15} + 2280 q^{17} - 832 q^{19} - 207 q^{21} + 399 q^{23} - 4778 q^{25} - 7128 q^{27} - 6033 q^{29} + 2759 q^{31} + 9603 q^{33} + 37146 q^{35} - 15172 q^{37} + 5529 q^{39} - 18435 q^{41} + 1469 q^{43} - 64089 q^{45} - 25155 q^{47} - 4056 q^{49} + 90612 q^{51} + 116844 q^{53} + 14778 q^{55} + 26934 q^{57} - 90537 q^{59} + 1403 q^{61} - 198255 q^{63} - 148407 q^{65} + 13907 q^{67} + 214425 q^{69} + 229368 q^{71} + 15200 q^{73} + 44640 q^{75} - 211983 q^{77} + 29993 q^{79} - 404172 q^{81} - 228951 q^{83} - 49662 q^{85} + 397323 q^{87} + 598332 q^{89} + 124930 q^{91} + 250041 q^{93} - 394764 q^{95} + 40541 q^{97} - 697239 q^{99}+O(q^{100}) $ 10 * q + 12 * q^3 - 21 * q^5 + 29 * q^7 + 12 * q^9 + 177 * q^11 - 181 * q^13 + 117 * q^15 + 2280 * q^17 - 832 * q^19 - 207 * q^21 + 399 * q^23 - 4778 * q^25 - 7128 * q^27 - 6033 * q^29 + 2759 * q^31 + 9603 * q^33 + 37146 * q^35 - 15172 * q^37 + 5529 * q^39 - 18435 * q^41 + 1469 * q^43 - 64089 * q^45 - 25155 * q^47 - 4056 * q^49 + 90612 * q^51 + 116844 * q^53 + 14778 * q^55 + 26934 * q^57 - 90537 * q^59 + 1403 * q^61 - 198255 * q^63 - 148407 * q^65 + 13907 * q^67 + 214425 * q^69 + 229368 * q^71 + 15200 * q^73 + 44640 * q^75 - 211983 * q^77 + 29993 * q^79 - 404172 * q^81 - 228951 * q^83 - 49662 * q^85 + 397323 * q^87 + 598332 * q^89 + 124930 * q^91 + 250041 * q^93 - 394764 * q^95 + 40541 * q^97 - 697239 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−12.2647	−	9.62174i	−0.786779	−	0.617235i
$3$	−12.2647	−	9.62174i	−0.786779	−	0.617235i
$4$		0			0
$5$	−14.0718	+	24.3731i	−0.251724	+	0.435999i	−0.964001	−	0.265900i	$-0.914331\pi$
$5$	−14.0718	+	24.3731i	−0.251724	+	0.435999i	0.712276	+	0.701899i	$0.247664\pi$
$6$		0			0
$7$	75.7039	+	131.123i	0.583947	+	1.01143i	0.995006	+	0.0998170i	$0.0318257\pi$
$7$	75.7039	+	131.123i	0.583947	+	1.01143i	−0.411059	+	0.911609i	$0.634841\pi$
$8$		0			0
$9$	57.8441	+	236.015i	0.238042	+	0.971255i
$10$		0			0
$11$	138.873	+	240.536i	0.346049	+	0.599374i	0.985544	−	0.169421i	$-0.0541898\pi$
$11$	138.873	+	240.536i	0.346049	+	0.599374i	−0.639495	+	0.768795i	$0.720856\pi$
$12$		0			0
$13$	−291.929	+	505.636i	−0.479092	+	0.829812i	−0.999713	−	0.0239762i	$-0.992367\pi$
$13$	−291.929	+	505.636i	−0.479092	+	0.829812i	0.520620	+	0.853788i	$0.325701\pi$
$14$		0			0
$15$	407.098	−	163.533i	0.467165	−	0.187662i
$16$		0			0
$17$	−1612.01			−1.35283			−0.676417	−	0.736519i	$-0.736468\pi$
$17$	−1612.01			−1.35283			−0.676417	+	0.736519i	$0.736468\pi$
$18$		0			0
$19$	1368.76			0.869851			0.434925	−	0.900467i	$-0.356775\pi$
$19$	1368.76			0.869851			0.434925	+	0.900467i	$0.356775\pi$
$20$		0			0
$21$	333.149	−	2336.58i	0.164850	−	1.15620i
$22$		0			0
$23$	−428.014	+	741.342i	−0.168709	+	0.292213i	−0.937966	−	0.346727i	$-0.887293\pi$
$23$	−428.014	+	741.342i	−0.168709	+	0.292213i	0.769257	+	0.638939i	$0.220627\pi$
$24$		0			0
$25$	1166.47	+	2020.38i	0.373270	+	0.646522i
$26$		0			0
$27$	1561.44	−	3451.21i	0.412207	−	0.911090i
$28$		0			0
$29$	−4267.49	−	7391.50i	−0.942274	−	1.63207i	−0.761120	−	0.648611i	$-0.775350\pi$
$29$	−4267.49	−	7391.50i	−0.942274	−	1.63207i	−0.181154	−	0.983455i	$-0.557983\pi$
$30$		0			0
$31$	−1469.19	+	2544.71i	−0.274583	+	0.475591i	−0.970030	−	0.242986i	$-0.921873\pi$
$31$	−1469.19	+	2544.71i	−0.274583	+	0.475591i	0.695447	+	0.718577i	$0.255206\pi$
$32$		0			0
$33$	611.138	−	4286.30i	0.0976910	−	0.685169i
$34$		0			0
$35$	−4261.17			−0.587975
$36$		0			0
$37$	4036.80			0.484767			0.242383	−	0.970181i	$-0.422071\pi$
$37$	4036.80			0.484767			0.242383	+	0.970181i	$0.422071\pi$
$38$		0			0
$39$	8445.52	−	3392.59i	0.889129	−	0.357166i
$40$		0			0
$41$	−9449.81	+	16367.5i	−0.877937	+	1.52063i	−0.0243361	+	0.999704i	$0.507747\pi$
$41$	−9449.81	+	16367.5i	−0.877937	+	1.52063i	−0.853601	+	0.520928i	$0.825586\pi$
$42$		0			0
$43$	10158.6	+	17595.1i	0.837840	+	1.45118i	0.891697	+	0.452632i	$0.149515\pi$
$43$	10158.6	+	17595.1i	0.837840	+	1.45118i	−0.0538576	+	0.998549i	$0.517152\pi$
$44$		0			0
$45$	−6566.39	−	1911.32i	−0.483387	−	0.140703i
$46$		0			0
$47$	147.890	+	256.152i	0.00976546	+	0.0169143i	0.870867	−	0.491519i	$-0.163558\pi$
$47$	147.890	+	256.152i	0.00976546	+	0.0169143i	−0.861101	+	0.508433i	$0.830225\pi$
$48$		0			0
$49$	−3058.67	+	5297.78i	−0.181988	+	0.315213i
$50$		0			0
$51$	19770.7	+	15510.3i	1.06438	+	0.835016i
$52$		0			0
$53$	3039.13			0.148614			0.0743069	−	0.997235i	$-0.476326\pi$
$53$	3039.13			0.148614			0.0743069	+	0.997235i	$0.476326\pi$
$54$		0			0
$55$	−7816.81			−0.348436
$56$		0			0
$57$	−16787.4	−	13169.9i	−0.684380	−	0.536902i
$58$		0			0
$59$	8618.31	−	14927.4i	0.322324	−	0.558281i	−0.658643	−	0.752455i	$-0.728869\pi$
$59$	8618.31	−	14927.4i	0.322324	−	0.558281i	0.980967	+	0.194174i	$0.0622027\pi$
$60$		0			0
$61$	−12826.2	−	22215.7i	−0.441342	−	0.764426i	0.556448	−	0.830883i	$-0.312164\pi$
$61$	−12826.2	−	22215.7i	−0.441342	−	0.764426i	−0.997789	+	0.0664565i	$0.978831\pi$
$62$		0			0
$63$	−26568.0	+	25452.0i	−0.843349	+	0.807923i
$64$		0			0
$65$	−8215.95	−	14230.4i	−0.241198	−	0.417768i
$66$		0			0
$67$	13140.1	−	22759.4i	0.357613	−	0.619403i	−0.629949	−	0.776637i	$-0.716924\pi$
$67$	13140.1	−	22759.4i	0.357613	−	0.619403i	0.987561	+	0.157233i	$0.0502575\pi$
$68$		0			0
$69$	12382.5	−	4974.07i	0.313101	−	0.125774i
$70$		0			0
$71$	76665.7			1.80491			0.902454	−	0.430786i	$-0.141764\pi$
$71$	76665.7			1.80491			0.902454	+	0.430786i	$0.141764\pi$
$72$		0			0
$73$	1496.33			0.0328640			0.0164320	−	0.999865i	$-0.494769\pi$
$73$	1496.33			0.0328640			0.0164320	+	0.999865i	$0.494769\pi$
$74$		0			0
$75$	5133.25	−	36002.8i	0.105375	−	0.739065i
$76$		0			0
$77$	−21026.5	+	36419.0i	−0.404148	+	0.700006i
$78$		0			0
$79$	−49637.1	−	85974.0i	−0.894826	−	1.54988i	−0.834019	−	0.551735i	$-0.813966\pi$
$79$	−49637.1	−	85974.0i	−0.894826	−	1.54988i	−0.0608070	−	0.998150i	$-0.519367\pi$
$80$		0			0
$81$	−52357.1	+	27304.1i	−0.886672	+	0.462398i
$82$		0			0
$83$	−25025.7	−	43345.7i	−0.398740	−	0.690639i	0.594830	−	0.803851i	$-0.297219\pi$
$83$	−25025.7	−	43345.7i	−0.398740	−	0.690639i	−0.993571	+	0.113213i	$0.963886\pi$
$84$		0			0
$85$	22683.8	−	39289.6i	0.340541	−	0.589834i
$86$		0			0
$87$	−18779.8	+	131715.i	−0.266008	+	1.86568i
$88$		0			0
$89$	136635.			1.82847			0.914235	−	0.405185i	$-0.132793\pi$
$89$	136635.			1.82847			0.914235	+	0.405185i	$0.132793\pi$
$90$		0			0
$91$	−88400.8			−1.11906
$92$		0			0
$93$	42503.6	−	17073.9i	0.509588	−	0.204703i
$94$		0			0
$95$	−19261.0	+	33361.0i	−0.218963	+	0.379254i
$96$		0			0
$97$	33325.0	+	57720.5i	0.359617	+	0.622875i	0.987897	−	0.155113i	$-0.0495740\pi$
$97$	33325.0	+	57720.5i	0.359617	+	0.622875i	−0.628280	+	0.777987i	$0.716241\pi$
$98$		0			0
$99$	−48737.1	+	46689.8i	−0.499771	+	0.478778i
$100$		0			0
$101$	12338.7	+	21371.2i	0.120355	+	0.208462i	0.919908	−	0.392135i	$-0.128263\pi$
$101$	12338.7	+	21371.2i	0.120355	+	0.208462i	−0.799552	+	0.600596i	$0.794930\pi$
$102$		0			0
$103$	−57883.5	+	100257.i	−0.537603	+	0.931155i	0.461430	+	0.887177i	$0.347337\pi$
$103$	−57883.5	+	100257.i	−0.537603	+	0.931155i	−0.999032	+	0.0439785i	$0.985997\pi$
$104$		0			0
$105$	52261.8	+	40999.9i	0.462606	+	0.362919i
$106$		0			0
$107$	84364.3			0.712360			0.356180	−	0.934417i	$-0.384079\pi$
$107$	84364.3			0.712360			0.356180	+	0.934417i	$0.384079\pi$
$108$		0			0
$109$	198400.			1.59947			0.799735	−	0.600354i	$-0.204973\pi$
$109$	198400.			1.59947			0.799735	+	0.600354i	$0.204973\pi$
$110$		0			0
$111$	−49510.0	−	38841.1i	−0.381404	−	0.299215i
$112$		0			0
$113$	−114453.	+	198238.i	−0.843199	+	1.46046i	0.0439777	+	0.999033i	$0.485997\pi$
$113$	−114453.	+	198238.i	−0.843199	+	1.46046i	−0.887176	+	0.461430i	$0.847336\pi$
$114$		0			0
$115$	−12045.9	−	20864.1i	−0.0849364	−	0.147114i
$116$		0			0
$117$	−136224.	−	39651.6i	−0.920003	−	0.267791i
$118$		0			0
$119$	−122035.	−	211371.i	−0.789983	−	1.36829i
$120$		0			0
$121$	41953.8	−	72666.2i	0.260500	−	0.451200i
$122$		0			0
$123$	273383.	−	109819.i	1.62933	−	0.654507i
$124$		0			0
$125$	−153606.			−0.879293
$126$		0			0
$127$	−246629.			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$127$	−246629.			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$128$		0			0
$129$	44704.6	−	313542.i	0.236525	−	1.65890i
$130$		0			0
$131$	84612.6	−	146553.i	0.430781	−	0.746135i	−0.566159	−	0.824296i	$-0.691571\pi$
$131$	84612.6	−	146553.i	0.430781	−	0.746135i	0.996941	+	0.0781606i	$0.0249047\pi$
$132$		0			0
$133$	103621.	+	179477.i	0.507947	+	0.879789i
$134$		0			0
$135$	62144.3	+	86621.8i	0.293472	+	0.409065i
$136$		0			0
$137$	−49985.3	−	86577.0i	−0.227531	−	0.394095i	0.729545	−	0.683933i	$-0.239732\pi$
$137$	−49985.3	−	86577.0i	−0.227531	−	0.394095i	−0.957076	+	0.289838i	$0.906399\pi$
$138$		0			0
$139$	18699.4	−	32388.2i	0.0820899	−	0.142184i	−0.822058	−	0.569404i	$-0.807174\pi$
$139$	18699.4	−	32388.2i	0.0820899	−	0.142184i	0.904147	+	0.427221i	$0.140507\pi$
$140$		0			0
$141$	650.815	−	4564.58i	0.00275683	−	0.0193354i
$142$		0			0
$143$	−162165.			−0.663158
$144$		0			0
$145$	240205.			0.948773
$146$		0			0
$147$	88487.5	−	35545.7i	0.337745	−	0.135673i
$148$		0			0
$149$	−127267.	+	220433.i	−0.469623	+	0.813411i	−0.999397	−	0.0347281i	$-0.988943\pi$
$149$	−127267.	+	220433.i	−0.469623	+	0.813411i	0.529774	+	0.848139i	$0.322277\pi$
$150$		0			0
$151$	118363.	+	205010.i	0.422448	+	0.731701i	0.996178	−	0.0873434i	$-0.0278377\pi$
$151$	118363.	+	205010.i	0.422448	+	0.731701i	−0.573731	+	0.819044i	$0.694504\pi$
$152$		0			0
$153$	−93245.0	−	380457.i	−0.322031	−	1.31395i
$154$		0			0
$155$	−41348.3	−	71617.4i	−0.138238	−	0.239436i
$156$		0			0
$157$	−127406.	+	220673.i	−0.412515	+	0.714497i	−0.995164	−	0.0982266i	$-0.968683\pi$
$157$	−127406.	+	220673.i	−0.412515	+	0.714497i	0.582649	+	0.812724i	$0.302016\pi$
$158$		0			0
$159$	−37273.9	−	29241.7i	−0.116926	−	0.0917297i
$160$		0			0
$161$	−129609.			−0.394069
$162$		0			0
$163$	215050.			0.633973			0.316987	−	0.948430i	$-0.397329\pi$
$163$	215050.			0.633973			0.316987	+	0.948430i	$0.397329\pi$
$164$		0			0
$165$	95870.5	+	75211.3i	0.274142	+	0.215067i
$166$		0			0
$167$	−96168.5	+	166569.i	−0.266834	+	0.462171i	−0.968043	−	0.250786i	$-0.919311\pi$
$167$	−96168.5	+	166569.i	−0.266834	+	0.462171i	0.701208	+	0.712956i	$0.252644\pi$
$168$		0			0
$169$	15201.2	+	26329.2i	0.0409411	+	0.0709121i
$170$		0			0
$171$	79174.9	+	323049.i	0.207061	+	0.844847i
$172$		0			0
$173$	4150.57	+	7189.00i	0.0105437	+	0.0182622i	0.871249	−	0.490841i	$-0.163310\pi$
$173$	4150.57	+	7189.00i	0.0105437	+	0.0182622i	−0.860705	+	0.509103i	$0.829977\pi$
$174$		0			0
$175$	−176612.	+	305902.i	−0.435939	+	0.755069i
$176$		0			0
$177$	−249328.	+	100156.i	−0.598188	+	0.240294i
$178$		0			0
$179$	574496.			1.34015			0.670077	−	0.742292i	$-0.266261\pi$
$179$	574496.			1.34015			0.670077	+	0.742292i	$0.266261\pi$
$180$		0			0
$181$	−224707.			−0.509823			−0.254912	−	0.966964i	$-0.582046\pi$
$181$	−224707.			−0.509823			−0.254912	+	0.966964i	$0.582046\pi$
$182$		0			0
$183$	−56444.2	+	395879.i	−0.124592	+	0.873846i
$184$		0			0
$185$	−56805.1	+	98389.3i	−0.122028	+	0.211358i
$186$		0			0
$187$	−223865.	−	387745.i	−0.468147	−	0.810854i
$188$		0			0
$189$	570740.	−	56529.5i	1.16221	−	0.115112i
$190$		0			0
$191$	239041.	+	414031.i	0.474121	+	0.821201i	0.999561	−	0.0296294i	$-0.00943271\pi$
$191$	239041.	+	414031.i	0.474121	+	0.821201i	−0.525440	+	0.850830i	$0.676099\pi$
$192$		0			0
$193$	263025.	−	455572.i	0.508281	−	0.880368i	−0.491673	−	0.870780i	$-0.663615\pi$
$193$	263025.	−	455572.i	0.508281	−	0.880368i	0.999954	−	0.00958824i	$-0.00305208\pi$
$194$		0			0
$195$	−36155.8	+	253583.i	−0.0680912	+	0.477567i
$196$		0			0
$197$	−222278.			−0.408067			−0.204034	−	0.978964i	$-0.565405\pi$
$197$	−222278.			−0.408067			−0.204034	+	0.978964i	$0.565405\pi$
$198$		0			0
$199$	−109696.			−0.196363			−0.0981813	−	0.995169i	$-0.531303\pi$
$199$	−109696.			−0.196363			−0.0981813	+	0.995169i	$0.531303\pi$
$200$		0			0
$201$	−380144.	+	152705.i	−0.663679	+	0.266602i
$202$		0			0
$203$	646131.	−	1.11913e6i	1.10048	−	1.90608i
$204$		0			0
$205$	−265952.	−	460642.i	−0.441996	−	0.765560i
$206$		0			0
$207$	−199726.	−	58135.5i	−0.323973	−	0.0943008i
$208$		0			0
$209$	190085.	+	329237.i	0.301011	+	0.521366i
$210$		0			0
$211$	309436.	−	535959.i	0.478482	−	0.828754i	−0.521214	−	0.853426i	$-0.674521\pi$
$211$	309436.	−	535959.i	0.478482	−	0.828754i	0.999696	+	0.0246717i	$0.00785404\pi$
$212$		0			0
$213$	−940279.	−	737657.i	−1.42006	−	1.11405i
$214$		0			0
$215$	−571797.			−0.843618
$216$		0			0
$217$	−444893.			−0.641367
$218$		0			0
$219$	−18352.0	−	14397.3i	−0.0258567	−	0.0202848i
$220$		0			0
$221$	470592.	−	815089.i	0.648132	−	1.12260i
$222$		0			0
$223$	−231653.	−	401234.i	−0.311943	−	0.540301i	0.666840	−	0.745201i	$-0.267646\pi$
$223$	−231653.	−	401234.i	−0.311943	−	0.540301i	−0.978783	+	0.204900i	$0.934313\pi$
$224$		0			0
$225$	−409367.	+	392171.i	−0.539084	+	0.516439i
$226$		0			0
$227$	573326.	+	993029.i	0.738477	+	1.27908i	0.953181	+	0.302400i	$0.0977878\pi$
$227$	573326.	+	993029.i	0.738477	+	1.27908i	−0.214704	+	0.976679i	$0.568879\pi$
$228$		0			0
$229$	175527.	−	304022.i	0.221185	−	0.383104i	−0.733983	−	0.679168i	$-0.762341\pi$
$229$	175527.	−	304022.i	0.221185	−	0.383104i	0.955168	+	0.296064i	$0.0956741\pi$
$230$		0			0
$231$	608298.	−	244355.i	0.750043	−	0.301295i
$232$		0			0
$233$	814275.			0.982610			0.491305	−	0.870988i	$-0.336520\pi$
$233$	814275.			0.982610			0.491305	+	0.870988i	$0.336520\pi$
$234$		0			0
$235$	−8324.30			−0.00983281
$236$		0			0
$237$	−218437.	+	1.53204e6i	−0.252613	+	1.77173i
$238$		0			0
$239$	357452.	−	619124.i	0.404783	−	0.701105i	−0.589513	−	0.807759i	$-0.700680\pi$
$239$	357452.	−	619124.i	0.404783	−	0.701105i	0.994296	+	0.106654i	$0.0340137\pi$
$240$		0			0
$241$	−22648.5	−	39228.3i	−0.0251186	−	0.0435068i	0.853193	−	0.521596i	$-0.174663\pi$
$241$	−22648.5	−	39228.3i	−0.0251186	−	0.0435068i	−0.878311	+	0.478089i	$0.841330\pi$
$242$		0			0
$243$	904856.	+	168891.i	0.983023	+	0.183480i
$244$		0			0
$245$	−86082.2	−	149099.i	−0.0916216	−	0.158693i
$246$		0			0
$247$	−399582.	+	692097.i	−0.416739	+	0.721813i
$248$		0			0
$249$	−110130.	+	772411.i	−0.112566	+	0.789496i
$250$		0			0
$251$	−1.35110e6			−1.35364			−0.676822	−	0.736147i	$-0.736643\pi$
$251$	−1.35110e6			−1.35364			−0.676822	+	0.736147i	$0.736643\pi$
$252$		0			0
$253$	−237759.			−0.233526
$254$		0			0
$255$	−656244.	+	263615.i	−0.631997	+	0.253875i
$256$		0			0
$257$	−600097.	+	1.03940e6i	−0.566747	+	0.981634i	0.430138	+	0.902763i	$0.358465\pi$
$257$	−600097.	+	1.03940e6i	−0.566747	+	0.981634i	−0.996885	+	0.0788708i	$0.974869\pi$
$258$		0			0
$259$	305602.	+	529318.i	0.283078	+	0.490306i
$260$		0			0
$261$	1.49766e6	−	1.43475e6i	1.36085	−	1.30369i
$262$		0			0
$263$	656802.	+	1.13761e6i	0.585525	+	1.01416i	0.994810	+	0.101752i	$0.0324449\pi$
$263$	656802.	+	1.13761e6i	0.585525	+	1.01416i	−0.409285	+	0.912407i	$0.634222\pi$
$264$		0			0
$265$	−42766.1	+	74073.0i	−0.0374097	+	0.0647956i
$266$		0			0
$267$	−1.67579e6	−	1.31467e6i	−1.43860	−	1.12860i
$268$		0			0
$269$	321363.			0.270779			0.135389	−	0.990792i	$-0.456771\pi$
$269$	321363.			0.270779			0.135389	+	0.990792i	$0.456771\pi$
$270$		0			0
$271$	384928.			0.318388			0.159194	−	0.987247i	$-0.449110\pi$
$271$	384928.			0.318388			0.159194	+	0.987247i	$0.449110\pi$
$272$		0			0
$273$	1.08421e6	+	850570.i	0.880451	+	0.690722i
$274$		0			0
$275$	−323983.	+	561155.i	−0.258339	+	0.447457i
$276$		0			0
$277$	847964.	+	1.46872e6i	0.664015	+	1.15011i	0.979551	+	0.201194i	$0.0644822\pi$
$277$	847964.	+	1.46872e6i	0.664015	+	1.15011i	−0.315536	+	0.948913i	$0.602184\pi$
$278$		0			0
$279$	−685573.	−	199554.i	−0.527283	−	0.153479i
$280$		0			0
$281$	−530669.	−	919146.i	−0.400920	−	0.694415i	0.592917	−	0.805264i	$-0.297976\pi$
$281$	−530669.	−	919146.i	−0.400920	−	0.694415i	−0.993837	+	0.110849i	$0.964643\pi$
$282$		0			0
$283$	192313.	−	333096.i	0.142739	−	0.247231i	−0.785788	−	0.618496i	$-0.787742\pi$
$283$	192313.	−	333096.i	0.142739	−	0.247231i	0.928527	+	0.371265i	$0.121076\pi$
$284$		0			0
$285$	557221.	−	223838.i	0.406364	−	0.163238i
$286$		0			0
$287$	−2.86155e6			−2.05067
$288$		0			0
$289$	1.17871e6			0.830158
$290$		0			0
$291$	146653.	−	1.02857e6i	0.101521	−	0.712033i
$292$		0			0
$293$	667643.	−	1.15639e6i	0.454334	−	0.786929i	−0.544316	−	0.838880i	$-0.683211\pi$
$293$	667643.	−	1.15639e6i	0.454334	−	0.786929i	0.998650	+	0.0519513i	$0.0165441\pi$
$294$		0			0
$295$	242551.	+	420110.i	0.162273	+	0.281066i
$296$		0			0
$297$	1.04698e6	−	103699.i	0.688728	−	0.0682158i
$298$		0			0
$299$	−249900.	−	432839.i	−0.161655	−	0.279994i
$300$		0			0
$301$	−1.53809e6	+	2.66404e6i	−0.978508	+	1.69483i
$302$		0			0
$303$	54298.7	−	380831.i	0.0339768	−	0.238301i
$304$		0			0
$305$	721954.			0.444386
$306$		0			0
$307$	636269.			0.385296			0.192648	−	0.981268i	$-0.438292\pi$
$307$	636269.			0.385296			0.192648	+	0.981268i	$0.438292\pi$
$308$		0			0
$309$	1.67457e6	−	672680.i	0.997716	−	0.400786i
$310$		0			0
$311$	269890.	−	467464.i	0.158229	−	0.274061i	−0.776001	−	0.630732i	$-0.782755\pi$
$311$	269890.	−	467464.i	0.158229	−	0.274061i	0.934230	+	0.356671i	$0.116088\pi$
$312$		0			0
$313$	−976605.	−	1.69153e6i	−0.563454	−	0.975931i	−0.997192	−	0.0748915i	$-0.976139\pi$
$313$	−976605.	−	1.69153e6i	−0.563454	−	0.975931i	0.433738	−	0.901039i	$-0.357194\pi$
$314$		0			0
$315$	−246483.	−	1.00570e6i	−0.139962	−	0.571073i
$316$		0			0
$317$	−781983.	−	1.35443e6i	−0.437068	−	0.757024i	0.560394	−	0.828226i	$-0.310650\pi$
$317$	−781983.	−	1.35443e6i	−0.437068	−	0.757024i	−0.997462	+	0.0712021i	$0.977316\pi$
$318$		0			0
$319$	1.18528e6	−	2.05297e6i	0.652146	−	1.12955i
$320$		0			0
$321$	−1.03470e6	−	811732.i	−0.560469	−	0.439693i
$322$		0			0
$323$	−2.20646e6			−1.17676
$324$		0			0
$325$	−1.36210e6			−0.715323
$326$		0			0
$327$	−2.43331e6	−	1.90896e6i	−1.25843	−	0.987249i
$328$		0			0
$329$	−22391.6	+	38783.5i	−0.0114050	+	0.0197541i
$330$		0			0
$331$	1.28000e6	+	2.21702e6i	0.642154	+	1.11224i	0.984951	+	0.172834i	$0.0552925\pi$
$331$	1.28000e6	+	2.21702e6i	0.642154	+	1.11224i	−0.342796	+	0.939410i	$0.611374\pi$
$332$		0			0
$333$	233505.	+	952745.i	0.115395	+	0.470832i
$334$		0			0
$335$	369811.	+	640532.i	0.180040	+	0.311838i
$336$		0			0
$337$	299646.	−	519002.i	0.143725	−	0.248940i	−0.785171	−	0.619279i	$-0.787425\pi$
$337$	299646.	−	519002.i	0.143725	−	0.248940i	0.928897	+	0.370339i	$0.120758\pi$
$338$		0			0
$339$	3.31112e6	−	1.33009e6i	1.56486	−	0.628609i
$340$		0			0
$341$	−816125.			−0.380076
$342$		0			0
$343$	1.61850e6			0.742808
$344$		0			0
$345$	−53010.1	+	371793.i	−0.0239779	+	0.168172i
$346$		0			0
$347$	−1.34386e6	+	2.32764e6i	−0.599144	+	1.03775i	0.393804	+	0.919195i	$0.371159\pi$
$347$	−1.34386e6	+	2.32764e6i	−0.599144	+	1.03775i	−0.992948	+	0.118553i	$0.962174\pi$
$348$		0			0
$349$	−335807.	−	581635.i	−0.147580	−	0.255615i	0.782753	−	0.622333i	$-0.213815\pi$
$349$	−335807.	−	581635.i	−0.147580	−	0.255615i	−0.930332	+	0.366717i	$0.880482\pi$
$350$		0			0
$351$	1.28923e6	+	1.79703e6i	0.558549	+	0.778550i
$352$		0			0
$353$	764881.	+	1.32481e6i	0.326706	+	0.565871i	0.981856	−	0.189627i	$-0.0607280\pi$
$353$	764881.	+	1.32481e6i	0.326706	+	0.565871i	−0.655150	+	0.755499i	$0.727395\pi$
$354$		0			0
$355$	−1.07883e6	+	1.86858e6i	−0.454339	+	0.786939i
$356$		0			0
$357$	−537038.	+	3.76659e6i	−0.223015	+	1.56415i
$358$		0			0
$359$	3.27210e6			1.33996			0.669978	−	0.742381i	$-0.266303\pi$
$359$	3.27210e6			1.33996			0.669978	+	0.742381i	$0.266303\pi$
$360$		0			0
$361$	−602583.			−0.243360
$362$		0			0
$363$	−1.21372e6	+	487557.i	−0.483452	+	0.194204i
$364$		0			0
$365$	−21056.1	+	36470.2i	−0.00827267	+	0.0143287i
$366$		0			0
$367$	−313571.	−	543121.i	−0.121526	−	0.210490i	0.798843	−	0.601539i	$-0.205446\pi$
$367$	−313571.	−	543121.i	−0.121526	−	0.210490i	−0.920370	+	0.391049i	$0.872112\pi$
$368$		0			0
$369$	−4.40960e6	−	1.28353e6i	−1.68591	−	0.490727i
$370$		0			0
$371$	230074.	+	398500.i	0.0867826	+	0.150312i
$372$		0			0
$373$	−66186.8	+	114639.i	−0.0246320	+	0.0426638i	−0.878079	−	0.478516i	$-0.841175\pi$
$373$	−66186.8	+	114639.i	−0.0246320	+	0.0426638i	0.853447	+	0.521180i	$0.174508\pi$
$374$		0			0
$375$	1.88393e6	+	1.47796e6i	0.691809	+	0.542730i
$376$		0			0
$377$	4.98322e6			1.80574
$378$		0			0
$379$	−163225.			−0.0583700			−0.0291850	−	0.999574i	$-0.509291\pi$
$379$	−163225.			−0.0583700			−0.0291850	+	0.999574i	$0.509291\pi$
$380$		0			0
$381$	3.02482e6	+	2.37300e6i	1.06755	+	0.837501i
$382$		0			0
$383$	398301.	−	689877.i	0.138744	−	0.240312i	−0.788277	−	0.615320i	$-0.789027\pi$
$383$	398301.	−	689877.i	0.138744	−	0.240312i	0.927021	+	0.375008i	$0.122360\pi$
$384$		0			0
$385$	−591763.	−	1.02496e6i	−0.203468	−	0.352417i
$386$		0			0
$387$	−3.56510e6	+	3.41535e6i	−1.21003	+	1.15920i
$388$		0			0
$389$	−2.04745e6	−	3.54629e6i	−0.686024	−	1.18823i	−0.973114	−	0.230325i	$-0.926021\pi$
$389$	−2.04745e6	−	3.54629e6i	−0.686024	−	1.18823i	0.287089	−	0.957904i	$-0.407312\pi$
$390$		0			0
$391$	689961.	−	1.19505e6i	0.228235	−	0.395315i
$392$		0			0
$393$	−2.44784e6	+	983307.i	−0.799470	+	0.321150i
$394$		0			0
$395$	2.79394e6			0.900998
$396$		0			0
$397$	−5.58867e6			−1.77964			−0.889820	−	0.456312i	$-0.849170\pi$
$397$	−5.58867e6			−1.77964			−0.889820	+	0.456312i	$0.849170\pi$
$398$		0			0
$399$	456002.	−	3.19823e6i	0.143395	−	1.00572i
$400$		0			0
$401$	−1.11676e6	+	1.93429e6i	−0.346817	+	0.600705i	−0.985682	−	0.168614i	$-0.946071\pi$
$401$	−1.11676e6	+	1.93429e6i	−0.346817	+	0.600705i	0.638865	+	0.769319i	$0.279404\pi$
$402$		0			0
$403$	−857798.	−	1.48575e6i	−0.263101	−	0.455704i
$404$		0			0
$405$	71273.1	−	1.66032e6i	0.0215918	−	0.502985i
$406$		0			0
$407$	560604.	+	970995.i	0.167753	+	0.290557i
$408$		0			0
$409$	2.30256e6	−	3.98815e6i	0.680617	−	1.17886i	−0.294176	−	0.955751i	$-0.595045\pi$
$409$	2.30256e6	−	3.98815e6i	0.680617	−	1.17886i	0.974793	−	0.223111i	$-0.0716214\pi$
$410$		0			0
$411$	−219969.	+	1.54278e6i	−0.0642329	+	0.450506i
$412$		0			0
$413$	2.60976e6			0.752880
$414$		0			0
$415$	1.40863e6			0.401491
$416$		0			0
$417$	−540973.	+	217310.i	−0.152347	+	0.0611985i
$418$		0			0
$419$	−571064.	+	989112.i	−0.158909	+	0.275239i	−0.934476	−	0.356027i	$-0.884131\pi$
$419$	−571064.	+	989112.i	−0.158909	+	0.275239i	0.775566	+	0.631266i	$0.217464\pi$
$420$		0			0
$421$	−962383.	−	1.66690e6i	−0.264632	−	0.458356i	0.702835	−	0.711353i	$-0.251917\pi$
$421$	−962383.	−	1.66690e6i	−0.264632	−	0.458356i	−0.967467	+	0.252996i	$0.918584\pi$
$422$		0			0
$423$	−51901.2	+	49721.0i	−0.0141035	+	0.0135111i
$424$		0			0
$425$	−1.88035e6	−	3.25687e6i	−0.504972	−	0.874637i
$426$		0			0
$427$	1.94199e6	−	3.36363e6i	0.515440	−	0.892769i
$428$		0			0
$429$	1.98890e6	+	1.56031e6i	0.521758	+	0.409324i
$430$		0			0
$431$	2.21303e6			0.573843			0.286922	−	0.957954i	$-0.407368\pi$
$431$	2.21303e6			0.573843			0.286922	+	0.957954i	$0.407368\pi$
$432$		0			0
$433$	3.00235e6			0.769558			0.384779	−	0.923009i	$-0.374278\pi$
$433$	3.00235e6			0.769558			0.384779	+	0.923009i	$0.374278\pi$
$434$		0			0
$435$	−2.94604e6	−	2.31119e6i	−0.746474	−	0.585616i
$436$		0			0
$437$	−585851.	+	1.01472e6i	−0.146752	+	0.254181i
$438$		0			0
$439$	−960857.	−	1.66425e6i	−0.237956	−	0.412153i	0.722171	−	0.691714i	$-0.243144\pi$
$439$	−960857.	−	1.66425e6i	−0.237956	−	0.412153i	−0.960128	+	0.279562i	$0.909811\pi$
$440$		0			0
$441$	−1.42728e6	−	415447.i	−0.349472	−	0.101723i
$442$		0			0
$443$	924258.	+	1.60086e6i	0.223761	+	0.387565i	0.955947	−	0.293540i	$-0.0948332\pi$
$443$	924258.	+	1.60086e6i	0.223761	+	0.387565i	−0.732186	+	0.681105i	$0.761500\pi$
$444$		0			0
$445$	−1.92271e6	+	3.33022e6i	−0.460270	+	0.797211i
$446$		0			0
$447$	3.68183e6	−	1.47900e6i	0.871555	−	0.350107i
$448$		0			0
$449$	3.45640e6			0.809110			0.404555	−	0.914514i	$-0.367426\pi$
$449$	3.45640e6			0.809110			0.404555	+	0.914514i	$0.367426\pi$
$450$		0			0
$451$	−5.24931e6			−1.21524
$452$		0			0
$453$	520877.	−	3.65324e6i	0.119259	−	0.836436i
$454$		0			0
$455$	1.24396e6	−	2.15460e6i	0.281694	−	0.487908i
$456$		0			0
$457$	−1.79319e6	−	3.10589e6i	−0.401638	−	0.695658i	0.592286	−	0.805728i	$-0.298226\pi$
$457$	−1.79319e6	−	3.10589e6i	−0.401638	−	0.695658i	−0.993924	+	0.110070i	$0.964892\pi$
$458$		0			0
$459$	−2.51704e6	+	5.56336e6i	−0.557647	+	1.23255i
$460$		0			0
$461$	−4.21775e6	−	7.30536e6i	−0.924333	−	1.60099i	−0.792630	−	0.609703i	$-0.791289\pi$
$461$	−4.21775e6	−	7.30536e6i	−0.924333	−	1.60099i	−0.131703	−	0.991289i	$-0.542045\pi$
$462$		0			0
$463$	−2.47237e6	+	4.28227e6i	−0.535995	+	0.928370i	0.463120	+	0.886296i	$0.346730\pi$
$463$	−2.47237e6	+	4.28227e6i	−0.535995	+	0.928370i	−0.999114	+	0.0420745i	$0.986603\pi$
$464$		0			0
$465$	−181961.	+	1.27621e6i	−0.0390252	+	0.273709i
$466$		0			0
$467$	−4.12589e6			−0.875438			−0.437719	−	0.899112i	$-0.644213\pi$
$467$	−4.12589e6			−0.875438			−0.437719	+	0.899112i	$0.644213\pi$
$468$		0			0
$469$	3.97904e6			0.835307
$470$		0			0
$471$	3.68585e6	−	1.48062e6i	0.765571	−	0.307532i
$472$		0			0
$473$	−2.82151e6	+	4.88700e6i	−0.579867	+	1.00436i
$474$		0			0
$475$	1.59662e6	+	2.76543e6i	0.324689	+	0.562378i
$476$		0			0
$477$	175796.	+	717280.i	0.0353763	+	0.144342i
$478$		0			0
$479$	561301.	+	972203.i	0.111778	+	0.193606i	0.916487	−	0.400064i	$-0.131012\pi$
$479$	561301.	+	972203.i	0.111778	+	0.193606i	−0.804709	+	0.593669i	$0.797679\pi$
$480$		0			0
$481$	−1.17846e6	+	2.04115e6i	−0.232248	+	0.402265i
$482$		0			0
$483$	1.58962e6	+	1.24707e6i	0.310045	+	0.243233i
$484$		0			0
$485$	−1.87577e6			−0.362097
$486$		0			0
$487$	8.11380e6			1.55025			0.775126	−	0.631807i	$-0.217687\pi$
$487$	8.11380e6			1.55025			0.775126	+	0.631807i	$0.217687\pi$
$488$		0			0
$489$	−2.63752e6	−	2.06916e6i	−0.498797	−	0.391310i
$490$		0			0
$491$	1.66481e6	−	2.88353e6i	0.311645	−	0.539786i	−0.667073	−	0.744992i	$-0.732453\pi$
$491$	1.66481e6	−	2.88353e6i	0.311645	−	0.539786i	0.978719	+	0.205207i	$0.0657866\pi$
$492$		0			0
$493$	6.87921e6	+	1.19151e7i	1.27474	+	2.20791i
$494$		0			0
$495$	−452156.	−	1.84488e6i	−0.0829422	−	0.338420i
$496$		0			0
$497$	5.80389e6	+	1.00526e7i	1.05397	+	1.82553i
$498$		0			0
$499$	−940630.	+	1.62922e6i	−0.169109	+	0.292906i	−0.938107	−	0.346346i	$-0.887422\pi$
$499$	−940630.	+	1.62922e6i	−0.169109	+	0.292906i	0.768998	+	0.639252i	$0.220756\pi$
$500$		0			0
$501$	2.78216e6	−	1.11760e6i	0.495207	−	0.198926i
$502$		0			0
$503$	−7.96749e6			−1.40411			−0.702056	−	0.712122i	$-0.747734\pi$
$503$	−7.96749e6			−1.40411			−0.702056	+	0.712122i	$0.747734\pi$
$504$		0			0
$505$	−694511.			−0.121186
$506$		0			0
$507$	66895.5	−	469180.i	0.0115578	−	0.0810625i
$508$		0			0
$509$	−5.40561e6	+	9.36279e6i	−0.924805	+	1.60181i	−0.132931	+	0.991125i	$0.542439\pi$
$509$	−5.40561e6	+	9.36279e6i	−0.924805	+	1.60181i	−0.791874	+	0.610684i	$0.790894\pi$
$510$		0			0
$511$	113278.	+	196204.i	0.0191908	+	0.0332395i
$512$		0			0
$513$	2.13724e6	−	4.72389e6i	0.358558	−	0.792512i
$514$		0			0
$515$	−1.62905e6	−	2.82160e6i	−0.270655	−	0.468789i
$516$		0			0
$517$	−41075.9	+	71145.5i	−0.00675865	+	0.0117063i
$518$		0			0
$519$	18265.4	−	128106.i	0.00297653	−	0.0208763i
$520$		0			0
$521$	−1.19670e6			−0.193148			−0.0965740	−	0.995326i	$-0.530788\pi$
$521$	−1.19670e6			−0.193148			−0.0965740	+	0.995326i	$0.530788\pi$
$522$		0			0
$523$	−6.43371e6			−1.02851			−0.514254	−	0.857638i	$-0.671931\pi$
$523$	−6.43371e6			−1.02851			−0.514254	+	0.857638i	$0.671931\pi$
$524$		0			0
$525$	5.10940e6	−	2.05246e6i	0.809043	−	0.324995i
$526$		0			0
$527$	2.36834e6	−	4.10209e6i	0.371465	−	0.643396i
$528$		0			0
$529$	2.85178e6	+	4.93943e6i	0.443074	+	0.767427i
$530$		0			0
$531$	4.02160e6	+	1.17059e6i	0.618960	+	0.180164i
$532$		0			0
$533$	−5.51735e6	−	9.55633e6i	−0.841226	−	1.45705i
$534$		0			0
$535$	−1.18716e6	+	2.05622e6i	−0.179318	+	0.310588i
$536$		0			0
$537$	−7.04600e6	−	5.52765e6i	−1.05440	−	0.827190i
$538$		0			0
$539$	−1.69907e6			−0.251907
$540$		0			0
$541$	5.85989e6			0.860788			0.430394	−	0.902641i	$-0.358375\pi$
$541$	5.85989e6			0.860788			0.430394	+	0.902641i	$0.358375\pi$
$542$		0			0
$543$	2.75595e6	+	2.16207e6i	0.401118	+	0.314681i
$544$		0			0
$545$	−2.79185e6	+	4.83563e6i	−0.402625	+	0.697368i
$546$		0			0
$547$	−2.59436e6	−	4.49357e6i	−0.370734	−	0.642130i	0.618945	−	0.785434i	$-0.287560\pi$
$547$	−2.59436e6	−	4.49357e6i	−0.370734	−	0.642130i	−0.989679	+	0.143305i	$0.954227\pi$
$548$		0			0
$549$	4.50132e6	−	4.31223e6i	0.637395	−	0.610621i
$550$		0			0
$551$	−5.84118e6	−	1.01172e7i	−0.819637	−	1.41965i
$552$		0			0
$553$	7.51545e6	−	1.30171e7i	1.04506	−	1.81010i
$554$		0			0
$555$	1.64337e6	−	660148.i	0.226466	−	0.0909723i
$556$		0			0
$557$	5.07405e6			0.692973			0.346487	−	0.938055i	$-0.387375\pi$
$557$	5.07405e6			0.692973			0.346487	+	0.938055i	$0.387375\pi$
$558$		0			0
$559$	−1.18623e7			−1.60561
$560$		0			0
$561$	−985158.	+	6.90954e6i	−0.132160	+	0.926919i
$562$		0			0
$563$	3.05439e6	−	5.29036e6i	0.406119	−	0.703419i	−0.588332	−	0.808620i	$-0.700215\pi$
$563$	3.05439e6	−	5.29036e6i	0.406119	−	0.703419i	0.994451	+	0.105200i	$0.0335484\pi$
$564$		0			0
$565$	−3.22111e6	−	5.57913e6i	−0.424507	−	0.735268i
$566$		0			0
$567$	−7.54384e6	−	4.79819e6i	−0.985451	−	0.626787i
$568$		0			0
$569$	5.40483e6	+	9.36143e6i	0.699844	+	1.21216i	0.968520	+	0.248934i	$0.0800803\pi$
$569$	5.40483e6	+	9.36143e6i	0.699844	+	1.21216i	−0.268677	+	0.963230i	$0.586586\pi$
$570$		0			0
$571$	−6.02796e6	+	1.04407e7i	−0.773714	+	1.34011i	0.161801	+	0.986823i	$0.448270\pi$
$571$	−6.02796e6	+	1.04407e7i	−0.773714	+	1.34011i	−0.935515	+	0.353288i	$0.885063\pi$
$572$		0			0
$573$	1.05194e6	−	7.37794e6i	0.133846	−	0.938747i
$574$		0			0
$575$	−1.99706e6			−0.251896
$576$		0			0
$577$	1.22323e7			1.52957			0.764786	−	0.644285i	$-0.222845\pi$
$577$	1.22323e7			1.52957			0.764786	+	0.644285i	$0.222845\pi$
$578$		0			0
$579$	−7.60931e6	+	3.05669e6i	−0.943298	+	0.378926i
$580$		0			0
$581$	3.78908e6	−	6.56288e6i	0.465686	−	0.806593i
$582$		0			0
$583$	422054.	+	731019.i	0.0514277	+	0.0890754i
$584$		0			0
$585$	2.88335e6	−	2.76223e6i	0.348344	−	0.333711i
$586$		0			0
$587$	4.29817e6	+	7.44465e6i	0.514859	+	0.891762i	0.999851	+	0.0172439i	$0.00548917\pi$
$587$	4.29817e6	+	7.44465e6i	0.514859	+	0.891762i	−0.484992	+	0.874519i	$0.661177\pi$
$588$		0			0
$589$	−2.01097e6	+	3.48311e6i	−0.238846	+	0.413693i
$590$		0			0
$591$	2.72617e6	+	2.13871e6i	0.321059	+	0.251874i
$592$		0			0
$593$	−5.78455e6			−0.675511			−0.337756	−	0.941234i	$-0.609668\pi$
$593$	−5.78455e6			−0.675511			−0.337756	+	0.941234i	$0.609668\pi$
$594$		0			0
$595$	6.86903e6			0.795432
$596$		0			0
$597$	1.34539e6	+	1.05547e6i	0.154494	+	0.121202i
$598$		0			0
$599$	2.62557e6	−	4.54761e6i	0.298989	−	0.517865i	−0.676916	−	0.736061i	$-0.736684\pi$
$599$	2.62557e6	−	4.54761e6i	0.298989	−	0.517865i	0.975905	+	0.218196i	$0.0700172\pi$
$600$		0			0
$601$	3.11169e6	+	5.38960e6i	0.351407	+	0.608654i	0.986496	−	0.163784i	$-0.0523701\pi$
$601$	3.11169e6	+	5.38960e6i	0.351407	+	0.608654i	−0.635090	+	0.772439i	$0.719037\pi$
$602$		0			0
$603$	6.13163e6	+	1.78477e6i	0.686725	+	0.199889i
$604$		0			0
$605$	1.18073e6	+	2.04509e6i	0.131148	+	0.227156i
$606$		0			0
$607$	7.94049e6	−	1.37533e7i	0.874733	−	1.51508i	0.0176871	−	0.999844i	$-0.494370\pi$
$607$	7.94049e6	−	1.37533e7i	0.874733	−	1.51508i	0.857046	−	0.515239i	$-0.172297\pi$
$608$		0			0
$609$	−1.86926e7	+	7.50887e6i	−2.04233	+	0.820411i
$610$		0			0
$611$	−172693.			−0.0187142
$612$		0			0
$613$	−1.28661e7			−1.38292			−0.691458	−	0.722417i	$-0.743031\pi$
$613$	−1.28661e7			−1.38292			−0.691458	+	0.722417i	$0.743031\pi$
$614$		0			0
$615$	−1.17037e6	+	8.20854e6i	−0.124777	+	0.875142i
$616$		0			0
$617$	3.43797e6	−	5.95473e6i	0.363571	−	0.629723i	−0.624975	−	0.780645i	$-0.714891\pi$
$617$	3.43797e6	−	5.95473e6i	0.363571	−	0.629723i	0.988546	+	0.150922i	$0.0482242\pi$
$618$		0			0
$619$	−6.52408e6	−	1.13000e7i	−0.684373	−	1.18537i	−0.973633	−	0.228118i	$-0.926743\pi$
$619$	−6.52408e6	−	1.13000e7i	−0.684373	−	1.18537i	0.289261	−	0.957250i	$-0.406591\pi$
$620$		0			0
$621$	1.89021e6	+	2.63472e6i	0.196689	+	0.274161i
$622$		0			0
$623$	1.03438e7	+	1.79160e7i	1.06773	+	1.84936i
$624$		0			0
$625$	−1.48369e6	+	2.56983e6i	−0.151930	+	0.263151i
$626$		0			0
$627$	836504.	−	5.86693e6i	0.0849765	−	0.595994i
$628$		0			0
$629$	−6.50734e6			−0.655809
$630$		0			0
$631$	−1.52784e7			−1.52758			−0.763790	−	0.645464i	$-0.776664\pi$
$631$	−1.52784e7			−1.52758			−0.763790	+	0.645464i	$0.776664\pi$
$632$		0			0
$633$	−8.95200e6	+	3.59605e6i	−0.887995	+	0.356711i
$634$		0			0
$635$	3.47052e6	−	6.01111e6i	0.341554	−	0.591590i
$636$		0			0
$637$	−1.78583e6	−	3.09315e6i	−0.174378	−	0.302032i
$638$		0			0
$639$	4.43466e6	+	1.80942e7i	0.429643	+	1.75303i
$640$		0			0
$641$	5.96157e6	+	1.03257e7i	0.573080	+	0.992604i	0.996247	+	0.0865524i	$0.0275850\pi$
$641$	5.96157e6	+	1.03257e7i	0.573080	+	0.992604i	−0.423167	+	0.906052i	$0.639082\pi$
$642$		0			0
$643$	3.00302e6	−	5.20137e6i	0.286438	−	0.496125i	−0.686519	−	0.727112i	$-0.740862\pi$
$643$	3.00302e6	−	5.20137e6i	0.286438	−	0.496125i	0.972957	+	0.230987i	$0.0741955\pi$
$644$		0			0
$645$	7.01291e6	+	5.50169e6i	0.663741	+	0.520711i
$646$		0			0
$647$	1.19440e7			1.12173			0.560864	−	0.827908i	$-0.310469\pi$
$647$	1.19440e7			1.12173			0.560864	+	0.827908i	$0.310469\pi$
$648$		0			0
$649$	4.78742e6			0.446159
$650$		0			0
$651$	5.45647e6	+	4.28065e6i	0.504614	+	0.395874i
$652$		0			0
$653$	1.53297e6	−	2.65518e6i	0.140686	−	0.243675i	−0.787069	−	0.616864i	$-0.788403\pi$
$653$	1.53297e6	−	2.65518e6i	0.140686	−	0.243675i	0.927755	+	0.373190i	$0.121736\pi$
$654$		0			0
$655$	2.38131e6	+	4.12454e6i	0.216876	+	0.375641i
$656$		0			0
$657$	86553.9	+	353157.i	0.00782300	+	0.0319193i
$658$		0			0
$659$	1.55065e6	+	2.68581e6i	0.139092	+	0.240914i	0.927153	−	0.374683i	$-0.122248\pi$
$659$	1.55065e6	+	2.68581e6i	0.139092	+	0.240914i	−0.788061	+	0.615597i	$0.788915\pi$
$660$		0			0
$661$	−6.48853e6	+	1.12385e7i	−0.577621	+	1.00047i	0.418130	+	0.908387i	$0.362685\pi$
$661$	−6.48853e6	+	1.12385e7i	−0.577621	+	1.00047i	−0.995751	+	0.0920819i	$0.970648\pi$
$662$		0			0
$663$	−1.36142e7	+	5.46888e6i	−1.20284	+	0.483186i
$664$		0			0
$665$	−5.83253e6			−0.511450
$666$		0			0
$667$	7.30618e6			0.635881
$668$		0			0
$669$	−1.01943e6	+	7.14991e6i	−0.0880627	+	0.617640i
$670$		0			0
$671$	3.56245e6	−	6.17034e6i	0.305452	−	0.529058i
$672$		0			0
$673$	−1.10703e7	−	1.91743e7i	−0.942154	−	1.63186i	−0.761352	−	0.648338i	$-0.775464\pi$
$673$	−1.10703e7	−	1.91743e7i	−0.942154	−	1.63186i	−0.180801	−	0.983520i	$-0.557869\pi$
$674$		0			0
$675$	8.79412e6	−	871023.i	0.742904	−	0.0735817i
$676$		0			0
$677$	−799850.	−	1.38538e6i	−0.0670713	−	0.116171i	0.830540	−	0.556960i	$-0.188032\pi$
$677$	−799850.	−	1.38538e6i	−0.0670713	−	0.116171i	−0.897611	+	0.440789i	$0.854699\pi$
$678$		0			0
$679$	−5.04566e6	+	8.73934e6i	−0.419994	+	0.727452i
$680$		0			0
$681$	2.52302e6	−	1.76956e7i	0.208475	−	1.46217i
$682$		0			0
$683$	1.36986e7			1.12363			0.561816	−	0.827262i	$-0.310103\pi$
$683$	1.36986e7			1.12363			0.561816	+	0.827262i	$0.310103\pi$
$684$		0			0
$685$	2.81353e6			0.229100
$686$		0			0
$687$	−5.07801e6	+	2.03985e6i	−0.410489	+	0.164895i
$688$		0			0
$689$	−887210.	+	1.53669e6i	−0.0711998	+	0.123322i
$690$		0			0
$691$	2.09107e6	+	3.62183e6i	0.166599	+	0.288558i	0.937222	−	0.348733i	$-0.113388\pi$
$691$	2.09107e6	+	3.62183e6i	0.166599	+	0.288558i	−0.770623	+	0.637291i	$0.780055\pi$
$692$		0			0
$693$	−9.81170e6	−	2.85595e6i	−0.776088	−	0.225901i
$694$		0			0
$695$	526268.	+	911522.i	0.0413280	+	0.0715822i
$696$		0			0
$697$	1.52331e7	−	2.63846e7i	1.18770	−	2.05716i
$698$		0			0
$699$	−9.98681e6	−	7.83474e6i	−0.773097	−	0.606501i
$700$		0			0
$701$	−1.47134e7			−1.13089			−0.565443	−	0.824788i	$-0.691295\pi$
$701$	−1.47134e7			−1.13089			−0.565443	+	0.824788i	$0.691295\pi$
$702$		0			0
$703$	5.52543e6			0.421675
$704$		0			0
$705$	102095.	+	80094.2i	0.00773625	+	0.00606916i
$706$		0			0
$707$	−1.86818e6	+	3.23577e6i	−0.140562	+	0.243461i
$708$		0			0
$709$	4.25908e6	+	7.37694e6i	0.318200	+	0.551139i	0.980113	−	0.198442i	$-0.0635883\pi$
$709$	4.25908e6	+	7.37694e6i	0.318200	+	0.551139i	−0.661913	+	0.749581i	$0.730255\pi$
$710$		0			0
$711$	1.74199e7	−	1.66882e7i	1.29233	−	1.23804i
$712$		0			0
$713$	−1.25767e6	−	2.17834e6i	−0.0926493	−	0.160473i
$714$		0			0
$715$	2.28195e6	−	3.95246e6i	0.166933	−	0.289136i
$716$		0			0
$717$	−1.03411e7	+	4.15404e6i	−0.751221	+	0.301768i
$718$		0			0
$719$	−1.20183e7			−0.867003			−0.433502	−	0.901153i	$-0.642722\pi$
$719$	−1.20183e7			−0.867003			−0.433502	+	0.901153i	$0.642722\pi$
$720$		0			0
$721$	−1.75280e7			−1.25573
$722$		0			0
$723$	−99668.7	+	699040.i	−0.00709109	+	0.0497343i
$724$		0			0
$725$	9.95577e6	−	1.72439e7i	0.703445	−	1.21840i
$726$		0			0
$727$	−1.49257e6	−	2.58521e6i	−0.104737	−	0.181409i	0.808894	−	0.587955i	$-0.200067\pi$
$727$	−1.49257e6	−	2.58521e6i	−0.104737	−	0.181409i	−0.913631	+	0.406545i	$0.866733\pi$
$728$		0			0
$729$	−9.47274e6	−	1.07777e7i	−0.660171	−	0.751115i
$730$		0			0
$731$	−1.63757e7	−	2.83635e7i	−1.13346	−	1.96321i
$732$		0			0
$733$	−1.05675e7	+	1.83035e7i	−0.726464	+	1.25827i	0.231905	+	0.972739i	$0.425504\pi$
$733$	−1.05675e7	+	1.83035e7i	−0.726464	+	1.25827i	−0.958369	+	0.285534i	$0.907829\pi$
$734$		0			0
$735$	−378820.	+	2.65691e6i	−0.0258651	+	0.181409i
$736$		0			0
$737$	7.29926e6			0.495006
$738$		0			0
$739$	1.33961e7			0.902337			0.451168	−	0.892439i	$-0.351007\pi$
$739$	1.33961e7			0.902337			0.451168	+	0.892439i	$0.351007\pi$
$740$		0			0
$741$	1.15599e7	−	4.64366e6i	0.773409	−	0.310681i
$742$		0			0
$743$	−5.95418e6	+	1.03129e7i	−0.395685	+	0.685347i	−0.993188	−	0.116519i	$-0.962826\pi$
$743$	−5.95418e6	+	1.03129e7i	−0.395685	+	0.685347i	0.597503	+	0.801867i	$0.296160\pi$
$744$		0			0
$745$	−3.58175e6	−	6.20377e6i	−0.236431	−	0.409511i
$746$		0			0
$747$	8.78265e6	−	8.41372e6i	0.575869	−	0.551679i
$748$		0			0
$749$	6.38671e6	+	1.10621e7i	0.415980	+	0.720499i
$750$		0			0
$751$	−2.33184e6	+	4.03886e6i	−0.150868	+	0.261312i	−0.931547	−	0.363621i	$-0.881540\pi$
$751$	−2.33184e6	+	4.03886e6i	−0.150868	+	0.261312i	0.780679	+	0.624933i	$0.214874\pi$
$752$		0			0
$753$	1.65708e7	+	1.30000e7i	1.06502	+	0.835517i
$754$		0			0
$755$	−6.66232e6			−0.425361
$756$		0			0
$757$	138599.			0.00879065			0.00439532	−	0.999990i	$-0.498601\pi$
$757$	138599.			0.00879065			0.00439532	+	0.999990i	$0.498601\pi$
$758$		0			0
$759$	2.91604e6	+	2.28766e6i	0.183734	+	0.144141i
$760$		0			0
$761$	−1.19856e6	+	2.07597e6i	−0.0750237	+	0.129945i	−0.901097	−	0.433618i	$-0.857237\pi$
$761$	−1.19856e6	+	2.07597e6i	−0.0750237	+	0.129945i	0.826073	+	0.563563i	$0.190570\pi$
$762$		0			0
$763$	1.50197e7	+	2.60148e7i	0.934005	+	1.61774i
$764$		0			0
$765$	1.05851e7	+	3.08106e6i	0.653942	+	0.190347i
$766$		0			0
$767$	5.03188e6	+	8.71546e6i	0.308846	+	0.534936i
$768$		0			0
$769$	−399739.	+	692369.i	−0.0243759	+	0.0422203i	−0.877956	−	0.478741i	$-0.841093\pi$
$769$	−399739.	+	692369.i	−0.0243759	+	0.0422203i	0.853580	+	0.520962i	$0.174427\pi$
$770$		0			0
$771$	1.73608e7	−	6.97390e6i	1.05180	−	0.422513i
$772$		0			0
$773$	1.07743e6			0.0648546			0.0324273	−	0.999474i	$-0.489676\pi$
$773$	1.07743e6			0.0648546			0.0324273	+	0.999474i	$0.489676\pi$
$774$		0			0
$775$	−6.85505e6			−0.409974
$776$		0			0
$777$	1.34486e6	−	9.43232e6i	0.0799140	−	0.560488i
$778$		0			0
$779$	−1.29346e7	+	2.24033e7i	−0.763674	+	1.32272i
$780$		0			0
$781$	1.06468e7	+	1.84408e7i	0.624586	+	1.08182i
$782$		0			0
$783$	−3.21730e7	+	3.18661e6i	−1.87537	+	0.185748i
$784$		0			0
$785$	−3.58566e6	−	6.21055e6i	−0.207680	−	0.359713i
$786$		0			0
$787$	−1.53546e6	+	2.65949e6i	−0.0883692	+	0.153060i	−0.906822	−	0.421514i	$-0.861499\pi$
$787$	−1.53546e6	+	2.65949e6i	−0.0883692	+	0.153060i	0.818453	+	0.574574i	$0.194832\pi$
$788$		0			0
$789$	2.89038e6	−	2.02721e7i	0.165296	−	1.15932i
$790$		0			0
$791$	−3.46581e7			−1.96953
$792$		0			0
$793$	1.49774e7			0.845774
$794$		0			0
$795$	1.23722e6	−	496996.i	0.0694273	−	0.0278892i
$796$		0			0
$797$	−7.49242e6	+	1.29772e7i	−0.417808	+	0.723664i	−0.995719	−	0.0924359i	$-0.970535\pi$
$797$	−7.49242e6	+	1.29772e7i	−0.417808	+	0.723664i	0.577911	+	0.816100i	$0.303868\pi$
$798$		0			0
$799$	−238399.	−	412919.i	−0.0132110	−	0.0228822i
$800$		0			0
$801$	7.90354e6	+	3.22480e7i	0.435252	+	1.77591i
$802$		0			0
$803$	207801.	+	359921.i	0.0113726	+	0.0196978i
$804$		0			0
$805$	1.82384e6	−	3.15898e6i	0.0991967	−	0.171814i
$806$		0			0
$807$	−3.94141e6	−	3.09207e6i	−0.213043	−	0.167134i
$808$		0			0
$809$	−3.11069e6			−0.167103			−0.0835516	−	0.996503i	$-0.526626\pi$
$809$	−3.11069e6			−0.167103			−0.0835516	+	0.996503i	$0.526626\pi$
$810$		0			0
$811$	1.12694e7			0.601659			0.300830	−	0.953678i	$-0.402736\pi$
$811$	1.12694e7			0.601659			0.300830	+	0.953678i	$0.402736\pi$
$812$		0			0
$813$	−4.72102e6	−	3.70368e6i	−0.250501	−	0.196520i
$814$		0			0
$815$	−3.02615e6	+	5.24144e6i	−0.159586	+	0.276412i
$816$		0			0
$817$	1.39047e7	+	2.40836e7i	0.728795	+	1.26231i
$818$		0			0
$819$	−5.11346e6	−	2.08639e7i	−0.266382	−	1.08689i
$820$		0			0
$821$	−1.04769e7	−	1.81465e7i	−0.542467	−	0.939580i	−0.998762	−	0.0497515i	$-0.984157\pi$
$821$	−1.04769e7	−	1.81465e7i	−0.542467	−	0.939580i	0.456295	−	0.889829i	$-0.349176\pi$
$822$		0			0
$823$	−974079.	+	1.68715e6i	−0.0501296	+	0.0868271i	−0.890001	−	0.455958i	$-0.849297\pi$
$823$	−974079.	+	1.68715e6i	−0.0501296	+	0.0868271i	0.839872	+	0.542785i	$0.182630\pi$
$824$		0			0
$825$	9.37283e6	−	3.76510e6i	0.479442	−	0.192593i
$826$		0			0
$827$	3.11807e7			1.58534			0.792671	−	0.609650i	$-0.208690\pi$
$827$	3.11807e7			1.58534			0.792671	+	0.609650i	$0.208690\pi$
$828$		0			0
$829$	−1.67293e7			−0.845455			−0.422727	−	0.906257i	$-0.638927\pi$
$829$	−1.67293e7			−0.845455			−0.422727	+	0.906257i	$0.638927\pi$
$830$		0			0
$831$	3.73162e6	−	2.61722e7i	0.187454	−	1.31473i
$832$		0			0
$833$	4.93060e6	−	8.54005e6i	0.246199	−	0.426430i
$834$		0			0
$835$	−2.70653e6	−	4.68785e6i	−0.134337	−	0.232679i
$836$		0			0
$837$	6.48827e6	+	9.04387e6i	0.320122	+	0.446212i
$838$		0			0
$839$	4.13660e6	+	7.16481e6i	0.202880	+	0.351398i	0.949455	−	0.313903i	$-0.101637\pi$
$839$	4.13660e6	+	7.16481e6i	0.202880	+	0.351398i	−0.746575	+	0.665301i	$0.768303\pi$
$840$		0			0
$841$	−2.61673e7	+	4.53231e7i	−1.27576	+	2.20968i
$842$		0			0
$843$	−2.33531e6	+	1.63790e7i	−0.113181	+	0.793813i
$844$		0			0
$845$	−855632.			−0.0412235
$846$		0			0
$847$	1.27043e7			0.608473
$848$		0			0
$849$	−5.56362e6	+	2.23492e6i	−0.264904	+	0.106413i
$850$		0			0
$851$	−1.72781e6	+	2.99265e6i	−0.0817846	+	0.141655i
$852$		0			0
$853$	−1.73469e7	−	3.00458e7i	−0.816300	−	1.41387i	−0.908391	−	0.418123i	$-0.862688\pi$
$853$	−1.73469e7	−	3.00458e7i	−0.816300	−	1.41387i	0.0920905	−	0.995751i	$-0.470645\pi$
$854$		0			0
$855$	−8.98784e6	−	2.61615e6i	−0.420475	−	0.122390i
$856$		0			0
$857$	−2.51863e6	−	4.36239e6i	−0.117142	−	0.202895i	0.801492	−	0.598005i	$-0.204040\pi$
$857$	−2.51863e6	−	4.36239e6i	−0.117142	−	0.202895i	−0.918634	+	0.395110i	$0.870707\pi$
$858$		0			0
$859$	2.13910e7	−	3.70502e7i	0.989116	−	1.71320i	0.367132	−	0.930169i	$-0.380340\pi$
$859$	2.13910e7	−	3.70502e7i	0.989116	−	1.71320i	0.621984	−	0.783030i	$-0.286327\pi$
$860$		0			0
$861$	3.50960e7	+	2.75331e7i	1.61343	+	1.26575i
$862$		0			0
$863$	1.50904e6			0.0689721			0.0344861	−	0.999405i	$-0.489021\pi$
$863$	1.50904e6			0.0689721			0.0344861	+	0.999405i	$0.489021\pi$
$864$		0			0
$865$	−233624.			−0.0106164
$866$		0			0
$867$	−1.44564e7	−	1.13412e7i	−0.653151	−	0.512403i
$868$		0			0
$869$	1.37866e7	−	2.38790e7i	0.619307	−	1.07267i
$870$		0			0
$871$	7.67198e6	+	1.32883e7i	0.342659	+	0.593503i
$872$		0			0
$873$	−1.16953e7	+	1.12040e7i	−0.519367	+	0.497550i
$874$		0			0
$875$	−1.16286e7	−	2.01413e7i	−0.513460	−	0.889339i
$876$		0			0
$877$	1.64700e7	−	2.85268e7i	0.723092	−	1.25243i	−0.236663	−	0.971592i	$-0.576054\pi$
$877$	1.64700e7	−	2.85268e7i	0.723092	−	1.25243i	0.959755	−	0.280840i	$-0.0906131\pi$
$878$		0			0
$879$	−1.93149e7	+	7.75886e6i	−0.843180	+	0.338708i
$880$		0			0
$881$	2.62885e7			1.14110			0.570552	−	0.821261i	$-0.306729\pi$
$881$	2.62885e7			1.14110			0.570552	+	0.821261i	$0.306729\pi$
$882$		0			0
$883$	−2.07499e7			−0.895602			−0.447801	−	0.894133i	$-0.647793\pi$
$883$	−2.07499e7			−0.895602			−0.447801	+	0.894133i	$0.647793\pi$
$884$		0			0
$885$	1.06739e6	−	7.48627e6i	0.0458104	−	0.321297i
$886$		0			0
$887$	−1.64291e7	+	2.84561e7i	−0.701140	+	1.21441i	0.266926	+	0.963717i	$0.413992\pi$
$887$	−1.64291e7	+	2.84561e7i	−0.701140	+	1.21441i	−0.968066	+	0.250694i	$0.919341\pi$
$888$		0			0
$889$	−1.86708e7	−	3.23387e7i	−0.792334	−	1.37236i
$890$		0			0
$891$	−1.38386e7	−	8.80194e6i	−0.583982	−	0.371436i
$892$		0			0
$893$	202426.	+	350612.i	0.00849449	+	0.0147129i
$894$		0			0
$895$	−8.08420e6	+	1.40022e7i	−0.337349	+	0.584306i
$896$		0			0
$897$	−1.09973e6	+	7.71310e6i	−0.0456357	+	0.320072i
$898$		0			0
$899$	2.50790e7			1.03493
$900$		0			0
$901$	−4.89909e6			−0.201050
$902$		0			0
$903$	4.44968e7	−	1.78745e7i	1.81597	−	0.729483i
$904$		0			0
$905$	3.16203e6	−	5.47680e6i	0.128335	−	0.222283i
$906$		0			0
$907$	−2.35836e7	−	4.08480e7i	−0.951900	−	1.64874i	−0.741307	−	0.671166i	$-0.765794\pi$
$907$	−2.35836e7	−	4.08480e7i	−0.951900	−	1.64874i	−0.210593	−	0.977574i	$-0.567540\pi$
$908$		0			0
$909$	−4.33021e6	+	4.14832e6i	−0.173820	+	0.166518i
$910$		0			0
$911$	−1.90246e7	−	3.29516e7i	−0.759486	−	1.31547i	−0.943113	−	0.332472i	$-0.892117\pi$
$911$	−1.90246e7	−	3.29516e7i	−0.759486	−	1.31547i	0.183627	−	0.982996i	$-0.441216\pi$
$912$		0			0
$913$	6.95080e6	−	1.20391e7i	0.275967	−	0.477990i
$914$		0			0
$915$	−8.85453e6	−	6.94646e6i	−0.349633	−	0.274290i
$916$		0			0
$917$	2.56220e7			1.00621
$918$		0			0
$919$	2.54292e7			0.993215			0.496607	−	0.867975i	$-0.334579\pi$
$919$	2.54292e7			0.993215			0.496607	+	0.867975i	$0.334579\pi$
$920$		0			0
$921$	−7.80363e6	−	6.12202e6i	−0.303143	−	0.237818i
$922$		0			0
$923$	−2.23809e7	+	3.87649e7i	−0.864717	+	1.49773i
$924$		0			0
$925$	4.70880e6	+	8.15588e6i	0.180949	+	0.313412i
$926$		0			0
$927$	−2.70104e7	−	7.86208e6i	−1.03236	−	0.300496i
$928$		0			0
$929$	7.00472e6	+	1.21325e7i	0.266288	+	0.461224i	0.967900	−	0.251335i	$-0.0808695\pi$
$929$	7.00472e6	+	1.21325e7i	0.266288	+	0.461224i	−0.701612	+	0.712559i	$0.747536\pi$
$930$		0			0
$931$	−4.18660e6	+	7.25141e6i	−0.158302	+	0.274188i
$932$		0			0
$933$	−7.80793e6	+	3.13647e6i	−0.293651	+	0.117961i
$934$		0			0
$935$	1.26007e7			0.471375
$936$		0			0
$937$	−1.29313e7			−0.481164			−0.240582	−	0.970629i	$-0.577338\pi$
$937$	−1.29313e7			−0.481164			−0.240582	+	0.970629i	$0.577338\pi$
$938$		0			0
$939$	−4.29773e6	+	3.01427e7i	−0.159065	+	1.11562i
$940$		0			0
$941$	4.79973e6	−	8.31337e6i	0.176702	−	0.306058i	−0.764047	−	0.645161i	$-0.776790\pi$
$941$	4.79973e6	−	8.31337e6i	0.176702	−	0.306058i	0.940749	+	0.339103i	$0.110124\pi$
$942$		0			0
$943$	−8.08930e6	−	1.40111e7i	−0.296232	−	0.513089i
$944$		0			0
$945$	−6.65354e6	+	1.47062e7i	−0.242367	+	0.535698i
$946$		0			0
$947$	7.16687e6	+	1.24134e7i	0.259690	+	0.449796i	0.966159	−	0.257948i	$-0.0830464\pi$
$947$	7.16687e6	+	1.24134e7i	0.259690	+	0.449796i	−0.706469	+	0.707744i	$0.749713\pi$
$948$		0			0
$949$	−436823.	+	756599.i	−0.0157449	+	0.0272710i
$950$		0			0
$951$	−3.44126e6	+	2.41357e7i	−0.123386	+	0.865384i
$952$		0			0
$953$	3.14184e7			1.12060			0.560302	−	0.828289i	$-0.310685\pi$
$953$	3.14184e7			1.12060			0.560302	+	0.828289i	$0.310685\pi$
$954$		0			0
$955$	−1.34550e7			−0.477391
$956$		0			0
$957$	−3.42902e7	+	1.37745e7i	−1.21029	+	0.486178i
$958$		0			0
$959$	7.56817e6	−	1.31084e7i	0.265732	−	0.460262i
$960$		0			0
$961$	9.99755e6	+	1.73163e7i	0.349209	+	0.604847i
$962$		0			0
$963$	4.87998e6	+	1.99112e7i	0.169571	+	0.691883i
$964$		0			0
$965$	7.40248e6	+	1.28215e7i	0.255893	+	0.443220i
$966$		0			0
$967$	6.76319e6	−	1.17142e7i	0.232587	−	0.402852i	−0.725982	−	0.687714i	$-0.758614\pi$
$967$	6.76319e6	−	1.17142e7i	0.232587	−	0.402852i	0.958569	+	0.284862i	$0.0919477\pi$
$968$		0			0
$969$	2.70614e7	+	2.12300e7i	0.925852	+	0.726339i
$970$		0			0
$971$	3.90534e7			1.32926			0.664632	−	0.747171i	$-0.268588\pi$
$971$	3.90534e7			1.32926			0.664632	+	0.747171i	$0.268588\pi$
$972$		0			0
$973$	5.66246e6			0.191744
$974$		0			0
$975$	1.67058e7	+	1.31058e7i	0.562801	+	0.441522i
$976$		0			0
$977$	−9.45244e6	+	1.63721e7i	−0.316816	+	0.548742i	−0.979822	−	0.199873i	$-0.935947\pi$
$977$	−9.45244e6	+	1.63721e7i	−0.316816	+	0.548742i	0.663006	+	0.748614i	$0.269280\pi$
$978$		0			0
$979$	1.89750e7	+	3.28657e7i	0.632740	+	1.09594i
$980$		0			0
$981$	1.14763e7	+	4.68254e7i	0.380740	+	1.55349i
$982$		0			0
$983$	2.95013e6	+	5.10977e6i	0.0973771	+	0.168662i	0.910598	−	0.413293i	$-0.135621\pi$
$983$	2.95013e6	+	5.10977e6i	0.0973771	+	0.168662i	−0.813221	+	0.581955i	$0.802288\pi$
$984$		0			0
$985$	3.12786e6	−	5.41762e6i	0.102720	−	0.177917i
$986$		0			0
$987$	647790.	−	260220.i	0.0211661	−	0.00850251i
$988$		0			0
$989$	−1.73920e7			−0.565405
$990$		0			0
$991$	−3.67515e7			−1.18875			−0.594375	−	0.804188i	$-0.702601\pi$
$991$	−3.67515e7			−1.18875			−0.594375	+	0.804188i	$0.702601\pi$
$992$		0			0
$993$	5.63287e6	−	3.95069e7i	0.181283	−	1.27145i
$994$		0			0
$995$	1.54362e6	−	2.67364e6i	0.0494293	−	0.0856140i
$996$		0			0
$997$	−1.46074e7	−	2.53008e7i	−0.465410	−	0.806114i	0.533810	−	0.845605i	$-0.320760\pi$
$997$	−1.46074e7	−	2.53008e7i	−0.465410	−	0.806114i	−0.999220	+	0.0394905i	$0.987427\pi$
$998$		0			0
$999$	6.30321e6	−	1.39318e7i	0.199824	−	0.441666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.6.e.a.13.1	✓	10
3.2	odd	2		108.6.e.a.37.4		10
4.3	odd	2		144.6.i.d.49.5		10
9.2	odd	6		108.6.e.a.73.4		10
9.4	even	3		324.6.a.e.1.4		5
9.5	odd	6		324.6.a.d.1.2		5
9.7	even	3	inner	36.6.e.a.25.1	yes	10
12.11	even	2		432.6.i.d.145.4		10
36.7	odd	6		144.6.i.d.97.5		10
36.11	even	6		432.6.i.d.289.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.e.a.13.1	✓	10	1.1	even	1	trivial
36.6.e.a.25.1	yes	10	9.7	even	3	inner
108.6.e.a.37.4		10	3.2	odd	2
108.6.e.a.73.4		10	9.2	odd	6
144.6.i.d.49.5		10	4.3	odd	2
144.6.i.d.97.5		10	36.7	odd	6
324.6.a.d.1.2		5	9.5	odd	6
324.6.a.e.1.4		5	9.4	even	3
432.6.i.d.145.4		10	12.11	even	2
432.6.i.d.289.4		10	36.11	even	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	36.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.2647 - 9.62174i) q^{3} +(-14.0718 + 24.3731i) q^{5} +(75.7039 + 131.123i) q^{7} +(57.8441 + 236.015i) q^{9} +O(q^{10})\)	\(q+(-12.2647 - 9.62174i) q^{3} +(-14.0718 + 24.3731i) q^{5} +(75.7039 + 131.123i) q^{7} +(57.8441 + 236.015i) q^{9} +(138.873 + 240.536i) q^{11} +(-291.929 + 505.636i) q^{13} +(407.098 - 163.533i) q^{15} -1612.01 q^{17} +1368.76 q^{19} +(333.149 - 2336.58i) q^{21} +(-428.014 + 741.342i) q^{23} +(1166.47 + 2020.38i) q^{25} +(1561.44 - 3451.21i) q^{27} +(-4267.49 - 7391.50i) q^{29} +(-1469.19 + 2544.71i) q^{31} +(611.138 - 4286.30i) q^{33} -4261.17 q^{35} +4036.80 q^{37} +(8445.52 - 3392.59i) q^{39} +(-9449.81 + 16367.5i) q^{41} +(10158.6 + 17595.1i) q^{43} +(-6566.39 - 1911.32i) q^{45} +(147.890 + 256.152i) q^{47} +(-3058.67 + 5297.78i) q^{49} +(19770.7 + 15510.3i) q^{51} +3039.13 q^{53} -7816.81 q^{55} +(-16787.4 - 13169.9i) q^{57} +(8618.31 - 14927.4i) q^{59} +(-12826.2 - 22215.7i) q^{61} +(-26568.0 + 25452.0i) q^{63} +(-8215.95 - 14230.4i) q^{65} +(13140.1 - 22759.4i) q^{67} +(12382.5 - 4974.07i) q^{69} +76665.7 q^{71} +1496.33 q^{73} +(5133.25 - 36002.8i) q^{75} +(-21026.5 + 36419.0i) q^{77} +(-49637.1 - 85974.0i) q^{79} +(-52357.1 + 27304.1i) q^{81} +(-25025.7 - 43345.7i) q^{83} +(22683.8 - 39289.6i) q^{85} +(-18779.8 + 131715. i) q^{87} +136635. q^{89} -88400.8 q^{91} +(42503.6 - 17073.9i) q^{93} +(-19261.0 + 33361.0i) q^{95} +(33325.0 + 57720.5i) q^{97} +(-48737.1 + 46689.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9}+O(q^{10}) \) 10 * q + 12 * q^3 - 21 * q^5 + 29 * q^7 + 12 * q^9	\( 10 q + 12 q^{3} - 21 q^{5} + 29 q^{7} + 12 q^{9} + 177 q^{11} - 181 q^{13} + 117 q^{15} + 2280 q^{17} - 832 q^{19} - 207 q^{21} + 399 q^{23} - 4778 q^{25} - 7128 q^{27} - 6033 q^{29} + 2759 q^{31} + 9603 q^{33} + 37146 q^{35} - 15172 q^{37} + 5529 q^{39} - 18435 q^{41} + 1469 q^{43} - 64089 q^{45} - 25155 q^{47} - 4056 q^{49} + 90612 q^{51} + 116844 q^{53} + 14778 q^{55} + 26934 q^{57} - 90537 q^{59} + 1403 q^{61} - 198255 q^{63} - 148407 q^{65} + 13907 q^{67} + 214425 q^{69} + 229368 q^{71} + 15200 q^{73} + 44640 q^{75} - 211983 q^{77} + 29993 q^{79} - 404172 q^{81} - 228951 q^{83} - 49662 q^{85} + 397323 q^{87} + 598332 q^{89} + 124930 q^{91} + 250041 q^{93} - 394764 q^{95} + 40541 q^{97} - 697239 q^{99}+O(q^{100}) \) 10 * q + 12 * q^3 - 21 * q^5 + 29 * q^7 + 12 * q^9 + 177 * q^11 - 181 * q^13 + 117 * q^15 + 2280 * q^17 - 832 * q^19 - 207 * q^21 + 399 * q^23 - 4778 * q^25 - 7128 * q^27 - 6033 * q^29 + 2759 * q^31 + 9603 * q^33 + 37146 * q^35 - 15172 * q^37 + 5529 * q^39 - 18435 * q^41 + 1469 * q^43 - 64089 * q^45 - 25155 * q^47 - 4056 * q^49 + 90612 * q^51 + 116844 * q^53 + 14778 * q^55 + 26934 * q^57 - 90537 * q^59 + 1403 * q^61 - 198255 * q^63 - 148407 * q^65 + 13907 * q^67 + 214425 * q^69 + 229368 * q^71 + 15200 * q^73 + 44640 * q^75 - 211983 * q^77 + 29993 * q^79 - 404172 * q^81 - 228951 * q^83 - 49662 * q^85 + 397323 * q^87 + 598332 * q^89 + 124930 * q^91 + 250041 * q^93 - 394764 * q^95 + 40541 * q^97 - 697239 * q^99

Introduction

L-functions

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Database

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