LMFDB - Embedded newform 36.6.b.b.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,6,Mod(35,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("36.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	36.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.77381751327$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 58x^{6} - 160x^{5} + 805x^{4} - 1348x^{3} + 3024x^{2} - 2376x + 972 $ x^8 - 4x^7 + 58x^6 - 160x^5 + 805x^4 - 1348x^3 + 3024x^2 - 2376*x + 972
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.2
Root			$0.500000 + 2.36350i$ of defining polynomial
Character	$\chi$	$=$	36.35
Dual form			36.6.b.b.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.11240 + 2.42144i) q^{2} +(20.2733 - 24.7587i) q^{4} +49.0700i q^{5} -12.2745i q^{7} +(-43.6935 + 175.667i) q^{8} +(-118.820 - 250.865i) q^{10} -706.464 q^{11} -795.304 q^{13} +(29.7220 + 62.7523i) q^{14} +(-201.988 - 1003.88i) q^{16} -363.652i q^{17} +2776.33i q^{19} +(1214.91 + 994.810i) q^{20} +(3611.73 - 1710.66i) q^{22} -1048.39 q^{23} +717.137 q^{25} +(4065.91 - 1925.78i) q^{26} +(-303.902 - 248.845i) q^{28} -4961.79i q^{29} +5933.17i q^{31} +(3463.48 + 4643.14i) q^{32} +(880.560 + 1859.13i) q^{34} +602.311 q^{35} -5625.73 q^{37} +(-6722.71 - 14193.7i) q^{38} +(-8619.97 - 2144.04i) q^{40} +8665.30i q^{41} -17517.2i q^{43} +(-14322.3 + 17491.1i) q^{44} +(5359.80 - 2538.62i) q^{46} -97.2886 q^{47} +16656.3 q^{49} +(-3666.29 + 1736.50i) q^{50} +(-16123.4 + 19690.7i) q^{52} +21872.7i q^{53} -34666.2i q^{55} +(2156.23 + 536.317i) q^{56} +(12014.7 + 25366.7i) q^{58} +19260.2 q^{59} +931.610 q^{61} +(-14366.8 - 30332.7i) q^{62} +(-28949.8 - 15351.0i) q^{64} -39025.6i q^{65} +30412.3i q^{67} +(-9003.55 - 7372.42i) q^{68} +(-3079.25 + 1458.46i) q^{70} +42335.7 q^{71} +146.390 q^{73} +(28761.0 - 13622.3i) q^{74} +(68738.4 + 56285.3i) q^{76} +8671.51i q^{77} +37898.9i q^{79} +(49260.4 - 9911.53i) q^{80} +(-20982.5 - 44300.5i) q^{82} -62590.3 q^{83} +17844.4 q^{85} +(42416.8 + 89554.9i) q^{86} +(30867.9 - 124102. i) q^{88} -35939.1i q^{89} +9761.98i q^{91} +(-21254.4 + 25956.8i) q^{92} +(497.378 - 235.578i) q^{94} -136234. q^{95} -96305.1 q^{97} +(-85153.9 + 40332.3i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 44 q^{4} - 596 q^{10} + 256 q^{13} - 4216 q^{16} + 9984 q^{22} + 15192 q^{25} - 23232 q^{28} + 23236 q^{34} - 26096 q^{37} - 36104 q^{40} + 84480 q^{46} + 4664 q^{49} - 96368 q^{52} + 126964 q^{58}+ \cdots + 229888 q^{97}+O(q^{100}) $ 8 * q + 44 * q^4 - 596 * q^10 + 256 * q^13 - 4216 * q^16 + 9984 * q^22 + 15192 * q^25 - 23232 * q^28 + 23236 * q^34 - 26096 * q^37 - 36104 * q^40 + 84480 * q^46 + 4664 * q^49 - 96368 * q^52 + 126964 * q^58 - 102224 * q^61 - 14608 * q^64 - 28416 * q^70 + 110848 * q^73 + 50688 * q^76 - 240308 * q^82 + 100208 * q^85 + 349056 * q^88 - 287232 * q^94 + 229888 * q^97

Character values

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

$n$	$19$	$29$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−5.11240	+	2.42144i	−0.903753	+	0.428054i
$2$	−5.11240	+	2.42144i	−0.903753	+	0.428054i
$3$		0			0
$3$		0			0
$4$	20.2733	−	24.7587i	0.633540	−	0.773710i
$5$			49.0700i			0.877790i	0.898538	+	0.438895i	$0.144630\pi$
$5$			49.0700i			0.877790i	−0.898538	+	0.438895i	$0.855370\pi$
$6$		0			0
$7$		−	12.2745i		−	0.0946803i	−0.998879	−	0.0473402i	$-0.984926\pi$
$7$		−	12.2745i		−	0.0946803i	0.998879	−	0.0473402i	$-0.0150745\pi$
$8$	−43.6935	+	175.667i	−0.241375	+	0.970432i
$9$		0			0
$10$	−118.820	−	250.865i	−0.375741	−	0.793306i
$11$	−706.464			−1.76039			−0.880194	−	0.474615i	$-0.842587\pi$
$11$	−706.464			−1.76039			−0.880194	+	0.474615i	$0.842587\pi$
$12$		0			0
$13$	−795.304			−1.30519			−0.652597	−	0.757706i	$-0.726320\pi$
$13$	−795.304			−1.30519			−0.652597	+	0.757706i	$0.726320\pi$
$14$	29.7220	+	62.7523i	0.0405283	+	0.0855677i
$15$		0			0
$16$	−201.988	−	1003.88i	−0.197254	−	0.980352i
$17$		−	363.652i		−	0.305185i	−0.988289	−	0.152593i	$-0.951238\pi$
$17$		−	363.652i		−	0.305185i	0.988289	−	0.152593i	$-0.0487622\pi$
$18$		0			0
$19$			2776.33i			1.76436i	0.470913	+	0.882180i	$0.343925\pi$
$19$			2776.33i			1.76436i	−0.470913	+	0.882180i	$0.656075\pi$
$20$	1214.91	+	994.810i	0.679155	+	0.556116i
$21$		0			0
$22$	3611.73	−	1710.66i	1.59096	−	0.753540i
$23$	−1048.39			−0.413242			−0.206621	−	0.978421i	$-0.566247\pi$
$23$	−1048.39			−0.413242			−0.206621	+	0.978421i	$0.566247\pi$
$24$		0			0
$25$	717.137			0.229484
$26$	4065.91	−	1925.78i	1.17957	−	0.558693i
$27$		0			0
$28$	−303.902	−	248.845i	−0.0732551	−	0.0599838i
$29$		−	4961.79i		−	1.09558i	−0.836616	−	0.547790i	$-0.815469\pi$
$29$		−	4961.79i		−	1.09558i	0.836616	−	0.547790i	$-0.184531\pi$
$30$		0			0
$31$			5933.17i			1.10888i	0.832225	+	0.554438i	$0.187067\pi$
$31$			5933.17i			1.10888i	−0.832225	+	0.554438i	$0.812933\pi$
$32$	3463.48	+	4643.14i	0.597912	+	0.801562i
$33$		0			0
$34$	880.560	+	1859.13i	0.130636	+	0.275812i
$35$	602.311			0.0831095
$36$		0			0
$37$	−5625.73			−0.675576			−0.337788	−	0.941222i	$-0.609679\pi$
$37$	−5625.73			−0.675576			−0.337788	+	0.941222i	$0.609679\pi$
$38$	−6722.71	−	14193.7i	−0.755241	−	1.59455i
$39$		0			0
$40$	−8619.97	−	2144.04i	−0.851836	−	0.211877i
$41$			8665.30i			0.805052i	0.915409	+	0.402526i	$0.131868\pi$
$41$			8665.30i			0.805052i	−0.915409	+	0.402526i	$0.868132\pi$
$42$		0			0
$43$		−	17517.2i		−	1.44475i	−0.691500	−	0.722376i	$-0.743050\pi$
$43$		−	17517.2i		−	1.44475i	0.691500	−	0.722376i	$-0.256950\pi$
$44$	−14322.3	+	17491.1i	−1.11528	+	1.36203i
$45$		0			0
$46$	5359.80	−	2538.62i	0.373469	−	0.176890i
$47$	−97.2886			−0.00642418			−0.00321209	−	0.999995i	$-0.501022\pi$
$47$	−97.2886			−0.00642418			−0.00321209	+	0.999995i	$0.501022\pi$
$48$		0			0
$49$	16656.3			0.991036
$50$	−3666.29	+	1736.50i	−0.207397	+	0.0982314i
$51$		0			0
$52$	−16123.4	+	19690.7i	−0.826892	+	1.00984i
$53$			21872.7i			1.06958i	0.844986	+	0.534788i	$0.179609\pi$
$53$			21872.7i			1.06958i	−0.844986	+	0.534788i	$0.820391\pi$
$54$		0			0
$55$		−	34666.2i		−	1.54525i
$56$	2156.23	+	536.317i	0.0918808	+	0.0228534i
$57$		0			0
$58$	12014.7	+	25366.7i	0.468967	+	0.990133i
$59$	19260.2			0.720330			0.360165	−	0.932889i	$-0.382720\pi$
$59$	19260.2			0.720330			0.360165	+	0.932889i	$0.382720\pi$
$60$		0			0
$61$	931.610			0.0320560			0.0160280	−	0.999872i	$-0.494898\pi$
$61$	931.610			0.0320560			0.0160280	+	0.999872i	$0.494898\pi$
$62$	−14366.8	−	30332.7i	−0.474658	−	1.00215i
$63$		0			0
$64$	−28949.8	−	15351.0i	−0.883476	−	0.468476i
$65$		−	39025.6i		−	1.14569i
$66$		0			0
$67$			30412.3i			0.827680i	0.910350	+	0.413840i	$0.135813\pi$
$67$			30412.3i			0.827680i	−0.910350	+	0.413840i	$0.864187\pi$
$68$	−9003.55	−	7372.42i	−0.236125	−	0.193347i
$69$		0			0
$70$	−3079.25	+	1458.46i	−0.0751105	+	0.0355753i
$71$	42335.7			0.996693			0.498346	−	0.866978i	$-0.333941\pi$
$71$	42335.7			0.996693			0.498346	+	0.866978i	$0.333941\pi$
$72$		0			0
$73$	146.390			0.00321517			0.00160759	−	0.999999i	$-0.499488\pi$
$73$	146.390			0.00321517			0.00160759	+	0.999999i	$0.499488\pi$
$74$	28761.0	−	13622.3i	0.610554	−	0.289183i
$75$		0			0
$76$	68738.4	+	56285.3i	1.36510	+	1.11779i
$77$			8671.51i			0.166674i
$78$		0			0
$79$			37898.9i			0.683218i	0.939842	+	0.341609i	$0.110972\pi$
$79$			37898.9i			0.683218i	−0.939842	+	0.341609i	$0.889028\pi$
$80$	49260.4	−	9911.53i	0.860544	−	0.173147i
$81$		0			0
$82$	−20982.5	−	44300.5i	−0.344605	−	0.727568i
$83$	−62590.3			−0.997267			−0.498634	−	0.866813i	$-0.666165\pi$
$83$	−62590.3			−0.997267			−0.498634	+	0.866813i	$0.666165\pi$
$84$		0			0
$85$	17844.4			0.267889
$86$	42416.8	+	89554.9i	0.618432	+	1.30570i
$87$		0			0
$88$	30867.9	−	124102.i	0.424913	−	1.70834i
$89$		−	35939.1i		−	0.480941i	−0.970656	−	0.240470i	$-0.922698\pi$
$89$		−	35939.1i		−	0.480941i	0.970656	−	0.240470i	$-0.0773017\pi$
$90$		0			0
$91$			9761.98i			0.123576i
$92$	−21254.4	+	25956.8i	−0.261805	+	0.319729i
$93$		0			0
$94$	497.378	−	235.578i	0.00580587	−	0.00274989i
$95$	−136234.			−1.54874
$96$		0			0
$97$	−96305.1			−1.03925			−0.519625	−	0.854395i	$-0.673928\pi$
$97$	−96305.1			−1.03925			−0.519625	+	0.854395i	$0.673928\pi$
$98$	−85153.9	+	40332.3i	−0.895652	+	0.424216i
$99$		0			0
$100$	14538.7	−	17755.4i	0.145387	−	0.177554i
$101$			106306.i			1.03694i	0.855095	+	0.518472i	$0.173499\pi$
$101$			106306.i			1.03694i	−0.855095	+	0.518472i	$0.826501\pi$
$102$		0			0
$103$			114350.i			1.06205i	0.847356	+	0.531025i	$0.178193\pi$
$103$			114350.i			1.06205i	−0.847356	+	0.531025i	$0.821807\pi$
$104$	34749.6	−	139709.i	0.315041	−	1.26660i
$105$		0			0
$106$	−52963.3	−	111822.i	−0.457836	−	0.966634i
$107$	20578.7			0.173763			0.0868817	−	0.996219i	$-0.472310\pi$
$107$	20578.7			0.173763			0.0868817	+	0.996219i	$0.472310\pi$
$108$		0			0
$109$	−182954.			−1.47494			−0.737470	−	0.675380i	$-0.763980\pi$
$109$	−182954.			−1.47494			−0.737470	+	0.675380i	$0.763980\pi$
$110$	83941.9	+	177227.i	0.661450	+	1.39653i
$111$		0			0
$112$	−12322.2	+	2479.30i	−0.0928201	+	0.0186760i
$113$		−	181726.i		−	1.33882i	−0.742894	−	0.669409i	$-0.766547\pi$
$113$		−	181726.i		−	1.33882i	0.742894	−	0.669409i	$-0.233453\pi$
$114$		0			0
$115$		−	51444.6i		−	0.362740i
$116$	−122848.	−	100592.i	−0.847660	−	0.694093i
$117$		0			0
$118$	−98466.0	+	46637.4i	−0.651000	+	0.308340i
$119$	−4463.65			−0.0288950
$120$		0			0
$121$	338040.			2.09896
$122$	−4762.76	+	2255.83i	−0.0289707	+	0.0137217i
$123$		0			0
$124$	146898.	+	120285.i	0.857947	+	0.702517i
$125$			188534.i			1.07923i
$126$		0			0
$127$		−	171256.i		−	0.942188i	−0.882083	−	0.471094i	$-0.843859\pi$
$127$		−	171256.i		−	0.942188i	0.882083	−	0.471094i	$-0.156141\pi$
$128$	185174.	+	8380.52i	0.998977	+	0.0452112i
$129$		0			0
$130$	94497.9	+	199514.i	0.490415	+	1.03542i
$131$	164660.			0.838321			0.419160	−	0.907912i	$-0.362324\pi$
$131$	164660.			0.838321			0.419160	+	0.907912i	$0.362324\pi$
$132$		0			0
$133$	34078.1			0.167050
$134$	−73641.5	−	155480.i	−0.354291	−	0.748019i
$135$		0			0
$136$	63881.6	+	15889.2i	0.296161	+	0.0736640i
$137$		−	148406.i		−	0.675537i	−0.941229	−	0.337769i	$-0.890328\pi$
$137$		−	148406.i		−	0.675537i	0.941229	−	0.337769i	$-0.109672\pi$
$138$		0			0
$139$			33933.7i			0.148968i	0.997222	+	0.0744841i	$0.0237310\pi$
$139$			33933.7i			0.148968i	−0.997222	+	0.0744841i	$0.976269\pi$
$140$	12210.8	−	14912.4i	0.0526532	−	0.0643026i
$141$		0			0
$142$	−216437.	+	102513.i	−0.900765	+	0.426638i
$143$	561853.			2.29765
$144$		0			0
$145$	243475.			0.961689
$146$	−748.404	+	354.474i	−0.00290572	+	0.00137627i
$147$		0			0
$148$	−114052.	+	139286.i	−0.428005	+	0.522700i
$149$			127386.i			0.470063i	0.971988	+	0.235032i	$0.0755194\pi$
$149$			127386.i			0.470063i	−0.971988	+	0.235032i	$0.924481\pi$
$150$		0			0
$151$		−	233416.i		−	0.833082i	−0.909117	−	0.416541i	$-0.863242\pi$
$151$		−	233416.i		−	0.833082i	0.909117	−	0.416541i	$-0.136758\pi$
$152$	−487709.	−	121308.i	−1.71219	−	0.425872i
$153$		0			0
$154$	−20997.5	−	44332.2i	−0.0713454	−	0.150632i
$155$	−291141.			−0.973360
$156$		0			0
$157$	−489218.			−1.58399			−0.791996	−	0.610526i	$-0.790958\pi$
$157$	−489218.			−1.58399			−0.791996	+	0.610526i	$0.790958\pi$
$158$	−91769.9	−	193755.i	−0.292454	−	0.617461i
$159$		0			0
$160$	−227839.	+	169953.i	−0.703603	+	0.524841i
$161$			12868.5i			0.0391259i
$162$		0			0
$163$		−	186891.i		−	0.550959i	−0.961307	−	0.275480i	$-0.911163\pi$
$163$		−	186891.i		−	0.550959i	0.961307	−	0.275480i	$-0.0888367\pi$
$164$	214542.	+	175674.i	0.622877	+	0.510033i
$165$		0			0
$166$	319987.	−	151558.i	0.901284	−	0.426884i
$167$	−533479.			−1.48022			−0.740110	−	0.672485i	$-0.765227\pi$
$167$	−533479.			−1.48022			−0.740110	+	0.672485i	$0.765227\pi$
$168$		0			0
$169$	261216.			0.703529
$170$	−91227.6	+	43209.0i	−0.242105	+	0.114671i
$171$		0			0
$172$	−433703.	−	355131.i	−1.11782	−	0.915309i
$173$			249914.i			0.634856i	0.948282	+	0.317428i	$0.102819\pi$
$173$			249914.i			0.634856i	−0.948282	+	0.317428i	$0.897181\pi$
$174$		0			0
$175$		−	8802.52i		−	0.0217276i
$176$	142697.	+	709205.i	0.347243	+	1.72580i
$177$		0			0
$178$	87024.2	+	183735.i	0.205869	+	0.434652i
$179$	314346.			0.733289			0.366644	−	0.930361i	$-0.380507\pi$
$179$	314346.			0.733289			0.366644	+	0.930361i	$0.380507\pi$
$180$		0			0
$181$	−179049.			−0.406233			−0.203116	−	0.979155i	$-0.565107\pi$
$181$	−179049.			−0.406233			−0.203116	+	0.979155i	$0.565107\pi$
$182$	−23638.0	−	49907.2i	−0.0528972	−	0.111682i
$183$		0			0
$184$	45808.0	−	184168.i	0.0997462	−	0.401023i
$185$		−	276054.i		−	0.593014i
$186$		0			0
$187$			256907.i			0.537244i
$188$	−1972.36	+	2408.74i	−0.00406997	+	0.00497045i
$189$		0			0
$190$	696485.	−	329883.i	1.39968	−	0.662943i
$191$	−608739.			−1.20739			−0.603695	−	0.797215i	$-0.706306\pi$
$191$	−608739.			−1.20739			−0.603695	+	0.797215i	$0.706306\pi$
$192$		0			0
$193$	−441.035			−0.000852276			−0.000426138	−	1.00000i	$-0.500136\pi$
$193$	−441.035			−0.000852276			−0.000426138		1.00000i	$0.500136\pi$
$194$	492350.	−	233197.i	0.939225	−	0.444855i
$195$		0			0
$196$	337679.	−	412389.i	0.627861	−	0.766774i
$197$			686826.i			1.26090i	0.776229	+	0.630451i	$0.217130\pi$
$197$			686826.i			1.26090i	−0.776229	+	0.630451i	$0.782870\pi$
$198$		0			0
$199$			1.09668e6i			1.96313i	0.191132	+	0.981564i	$0.438784\pi$
$199$			1.09668e6i			1.96313i	−0.191132	+	0.981564i	$0.561216\pi$
$200$	−31334.2	+	125977.i	−0.0553916	+	0.222698i
$201$		0			0
$202$	−257414.	−	543480.i	−0.443868	−	0.937142i
$203$	−60903.7			−0.103730
$204$		0			0
$205$	−425206.			−0.706667
$206$	−276892.	−	584606.i	−0.454614	−	0.959831i
$207$		0			0
$208$	160642.	+	798391.i	0.257454	+	1.27955i
$209$		−	1.96138e6i		−	3.10596i
$210$		0			0
$211$			174943.i			0.270514i	0.990811	+	0.135257i	$0.0431860\pi$
$211$			174943.i			0.270514i	−0.990811	+	0.135257i	$0.956814\pi$
$212$	541539.	+	443431.i	0.827542	+	0.677620i
$213$		0			0
$214$	−105207.	+	49830.0i	−0.157039	+	0.0743801i
$215$	859569.			1.26819
$216$		0			0
$217$	72826.9			0.104989
$218$	935332.	−	443010.i	1.33298	−	0.631354i
$219$		0			0
$220$	−858290.	−	702797.i	−1.19558	−	0.978979i
$221$			289214.i			0.398326i
$222$		0			0
$223$			285814.i			0.384877i	0.981309	+	0.192438i	$0.0616396\pi$
$223$			285814.i			0.384877i	−0.981309	+	0.192438i	$0.938360\pi$
$224$	56992.4	−	42512.5i	0.0758921	−	0.0566105i
$225$		0			0
$226$	440039.	+	929057.i	0.573086	+	1.20996i
$227$	−876427.			−1.12889			−0.564444	−	0.825471i	$-0.690909\pi$
$227$	−876427.			−1.12889			−0.564444	+	0.825471i	$0.690909\pi$
$228$		0			0
$229$	−73250.8			−0.0923047			−0.0461524	−	0.998934i	$-0.514696\pi$
$229$	−73250.8			−0.0923047			−0.0461524	+	0.998934i	$0.514696\pi$
$230$	124570.	+	263005.i	0.155272	+	0.327827i
$231$		0			0
$232$	871623.	+	216798.i	1.06319	+	0.264445i
$233$			313500.i			0.378310i	0.981947	+	0.189155i	$0.0605748\pi$
$233$			313500.i			0.378310i	−0.981947	+	0.189155i	$0.939425\pi$
$234$		0			0
$235$		−	4773.95i		−	0.00563908i
$236$	390468.	−	476858.i	0.456358	−	0.557326i
$237$		0			0
$238$	22820.0	−	10808.5i	0.0261140	−	0.0123686i
$239$	−15468.8			−0.0175171			−0.00875854	−	0.999962i	$-0.502788\pi$
$239$	−15468.8			−0.0175171			−0.00875854	+	0.999962i	$0.502788\pi$
$240$		0			0
$241$	653692.			0.724987			0.362494	−	0.931986i	$-0.381925\pi$
$241$	653692.			0.724987			0.362494	+	0.931986i	$0.381925\pi$
$242$	−1.72820e6	+	818543.i	−1.89694	+	0.898468i
$243$		0			0
$244$	18886.8	−	23065.5i	0.0203088	−	0.0248021i
$245$			817326.i			0.869922i
$246$		0			0
$247$		−	2.20803e6i		−	2.30283i
$248$	−1.04226e6	−	259241.i	−1.07609	−	0.267655i
$249$		0			0
$250$	−456522.	−	963859.i	−0.461968	−	0.975357i
$251$	1.15934e6			1.16152			0.580760	−	0.814075i	$-0.302755\pi$
$251$	1.15934e6			1.16152			0.580760	+	0.814075i	$0.302755\pi$
$252$		0			0
$253$	740651.			0.727466
$254$	414687.	+	875531.i	0.403307	+	0.851505i
$255$		0			0
$256$	−966978.	+	405543.i	−0.922182	+	0.386756i
$257$			660113.i			0.623427i	0.950176	+	0.311713i	$0.100903\pi$
$257$			660113.i			0.623427i	−0.950176	+	0.311713i	$0.899097\pi$
$258$		0			0
$259$			69053.1i			0.0639638i
$260$	−966222.	−	791176.i	−0.886429	−	0.725838i
$261$		0			0
$262$	−841809.	+	398714.i	−0.757635	+	0.358846i
$263$	56534.1			0.0503989			0.0251995	−	0.999682i	$-0.491978\pi$
$263$	56534.1			0.0503989			0.0251995	+	0.999682i	$0.491978\pi$
$264$		0			0
$265$	−1.07329e6			−0.938864
$266$	−174221.	+	82518.1i	−0.150972	+	0.0715064i
$267$		0			0
$268$	752970.	+	616558.i	0.640384	+	0.524369i
$269$			688131.i			0.579816i	0.957054	+	0.289908i	$0.0936248\pi$
$269$			688131.i			0.579816i	−0.957054	+	0.289908i	$0.906375\pi$
$270$		0			0
$271$		−	669194.i		−	0.553514i	−0.960940	−	0.276757i	$-0.910740\pi$
$271$		−	669194.i		−	0.553514i	0.960940	−	0.276757i	$-0.0892598\pi$
$272$	−365063.	+	73453.2i	−0.299189	+	0.0601989i
$273$		0			0
$274$	359355.	+	758710.i	0.289166	+	0.610519i
$275$	−506631.			−0.403980
$276$		0			0
$277$	−333722.			−0.261328			−0.130664	−	0.991427i	$-0.541711\pi$
$277$	−333722.			−0.261328			−0.130664	+	0.991427i	$0.541711\pi$
$278$	−82168.2	−	173482.i	−0.0637664	−	0.134631i
$279$		0			0
$280$	−26317.1	+	105806.i	−0.0200605	+	0.0806521i
$281$		−	59934.8i		−	0.0452807i	−0.999744	−	0.0226404i	$-0.992793\pi$
$281$		−	59934.8i		−	0.0452807i	0.999744	−	0.0226404i	$-0.00720726\pi$
$282$		0			0
$283$		−	1.72304e6i		−	1.27888i	−0.768841	−	0.639440i	$-0.779166\pi$
$283$		−	1.72304e6i		−	1.27888i	0.768841	−	0.639440i	$-0.220834\pi$
$284$	858285.	−	1.04818e6i	0.631445	−	0.771151i
$285$		0			0
$286$	−2.87242e6	+	1.36049e6i	−2.07650	+	0.983515i
$287$	106362.			0.0762226
$288$		0			0
$289$	1.28761e6			0.906862
$290$	−1.24474e6	+	589560.i	−0.869130	+	0.411654i
$291$		0			0
$292$	2967.81	−	3624.43i	0.00203694	−	0.00248761i
$293$		−	2.17996e6i		−	1.48347i	−0.670692	−	0.741736i	$-0.734003\pi$
$293$		−	2.17996e6i		−	1.48347i	0.670692	−	0.741736i	$-0.265997\pi$
$294$		0			0
$295$			945099.i			0.632298i
$296$	245808.	−	988254.i	0.163067	−	0.655601i
$297$		0			0
$298$	−308457.	−	651249.i	−0.201212	−	0.424821i
$299$	833791.			0.539361
$300$		0			0
$301$	−215015.			−0.136790
$302$	565202.	+	1.19332e6i	0.356604	+	0.752901i
$303$		0			0
$304$	2.78711e6	−	560785.i	1.72969	−	0.348026i
$305$			45714.1i			0.0281385i
$306$		0			0
$307$			623275.i			0.377428i	0.982032	+	0.188714i	$0.0604319\pi$
$307$			623275.i			0.377428i	−0.982032	+	0.188714i	$0.939568\pi$
$308$	214695.	+	175800.i	0.128957	+	0.105595i
$309$		0			0
$310$	1.48843e6	−	704979.i	0.879677	−	0.416650i
$311$	706360.			0.414119			0.207059	−	0.978328i	$-0.433611\pi$
$311$	706360.			0.414119			0.207059	+	0.978328i	$0.433611\pi$
$312$		0			0
$313$	963254.			0.555750			0.277875	−	0.960617i	$-0.410370\pi$
$313$	963254.			0.555750			0.277875	+	0.960617i	$0.410370\pi$
$314$	2.50108e6	−	1.18461e6i	1.43154	−	0.678033i
$315$		0			0
$316$	938329.	+	768336.i	0.528612	+	0.432846i
$317$			1.49739e6i			0.836927i	0.908234	+	0.418463i	$0.137431\pi$
$317$			1.49739e6i			0.836927i	−0.908234	+	0.418463i	$0.862569\pi$
$318$		0			0
$319$			3.50533e6i			1.92864i
$320$	753274.	−	1.42056e6i	0.411223	−	0.775507i
$321$		0			0
$322$	−31160.3	−	65789.1i	−0.0167480	−	0.0353601i
$323$	1.00962e6			0.538456
$324$		0			0
$325$	−570342.			−0.299521
$326$	452545.	+	955462.i	0.235840	+	0.497931i
$327$		0			0
$328$	−1.52221e6	−	378617.i	−0.781248	−	0.194319i
$329$			1194.17i			0.000608243i
$330$		0			0
$331$			530245.i			0.266015i	0.991115	+	0.133008i	$0.0424635\pi$
$331$			530245.i			0.266015i	−0.991115	+	0.133008i	$0.957536\pi$
$332$	−1.26891e6	+	1.54965e6i	−0.631809	+	0.771595i
$333$		0			0
$334$	2.72736e6	−	1.29179e6i	1.33775	−	0.633614i
$335$	−1.49233e6			−0.726530
$336$		0			0
$337$	135027.			0.0647658			0.0323829	−	0.999476i	$-0.489690\pi$
$337$	135027.			0.0647658			0.0323829	+	0.999476i	$0.489690\pi$
$338$	−1.33544e6	+	632517.i	−0.635817	+	0.301148i
$339$		0			0
$340$	361764.	−	441804.i	0.169718	−	0.207268i
$341$		−	4.19157e6i		−	1.95205i
$342$		0			0
$343$		−	410747.i		−	0.188512i
$344$	3.07719e6	+	765388.i	1.40203	+	0.348727i
$345$		0			0
$346$	−605151.	−	1.27766e6i	−0.271753	−	0.573753i
$347$	−3.36046e6			−1.49822			−0.749108	−	0.662448i	$-0.769518\pi$
$347$	−3.36046e6			−1.49822			−0.749108	+	0.662448i	$0.769518\pi$
$348$		0			0
$349$	−1.82741e6			−0.803106			−0.401553	−	0.915836i	$-0.631529\pi$
$349$	−1.82741e6			−0.803106			−0.401553	+	0.915836i	$0.631529\pi$
$350$	21314.7	+	45002.0i	0.00930058	+	0.0196364i
$351$		0			0
$352$	−2.44682e6	−	3.28021e6i	−1.05256	−	1.41106i
$353$			1.55874e6i			0.665788i	0.942964	+	0.332894i	$0.108025\pi$
$353$			1.55874e6i			0.665788i	−0.942964	+	0.332894i	$0.891975\pi$
$354$		0			0
$355$			2.07741e6i			0.874888i
$356$	−889805.	−	728603.i	−0.372109	−	0.304695i
$357$		0			0
$358$	−1.60706e6	+	761168.i	−0.662712	+	0.313887i
$359$	−3.96723e6			−1.62462			−0.812308	−	0.583229i	$-0.801789\pi$
$359$	−3.96723e6			−1.62462			−0.812308	+	0.583229i	$0.801789\pi$
$360$		0			0
$361$	−5.23191e6			−2.11297
$362$	915369.	−	433555.i	0.367134	−	0.173889i
$363$		0			0
$364$	241694.	+	197907.i	0.0956121	+	0.0782904i
$365$			7183.35i			0.00282225i
$366$		0			0
$367$		−	3.09712e6i		−	1.20031i	−0.799884	−	0.600154i	$-0.795106\pi$
$367$		−	3.09712e6i		−	1.20031i	0.799884	−	0.600154i	$-0.204894\pi$
$368$	211762.	+	1.05246e6i	0.0815135	+	0.405123i
$369$		0			0
$370$	668448.	+	1.41130e6i	0.253842	+	0.535939i
$371$	268477.			0.101268
$372$		0			0
$373$	3.19318e6			1.18837			0.594185	−	0.804329i	$-0.297475\pi$
$373$	3.19318e6			1.18837			0.594185	+	0.804329i	$0.297475\pi$
$374$	−622084.	−	1.31341e6i	−0.229969	−	0.485536i
$375$		0			0
$376$	4250.88	−	17090.4i	0.00155063	−	0.00623423i
$377$			3.94614e6i			1.42994i
$378$		0			0
$379$			2.20894e6i			0.789925i	0.918697	+	0.394963i	$0.129242\pi$
$379$			2.20894e6i			0.789925i	−0.918697	+	0.394963i	$0.870758\pi$
$380$	−2.76192e6	+	3.37299e6i	−0.981188	+	1.19827i
$381$		0			0
$382$	3.11212e6	−	1.47402e6i	1.09118	−	0.516828i
$383$	4.28671e6			1.49323			0.746615	−	0.665256i	$-0.231678\pi$
$383$	4.28671e6			1.49323			0.746615	+	0.665256i	$0.231678\pi$
$384$		0			0
$385$	−425511.			−0.146305
$386$	2254.75	−	1067.94i	0.000770247	−	0.000364820i
$387$		0			0
$388$	−1.95242e6	+	2.38439e6i	−0.658407	+	0.804078i
$389$		−	2.57450e6i		−	0.862618i	−0.902204	−	0.431309i	$-0.858052\pi$
$389$		−	2.57450e6i		−	0.862618i	0.902204	−	0.431309i	$-0.141948\pi$
$390$		0			0
$391$			381250.i			0.126115i
$392$	−727774.	+	2.92597e6i	−0.239211	+	0.961733i
$393$		0			0
$394$	−1.66311e6	−	3.51133e6i	−0.539734	−	1.13954i
$395$	−1.85970e6			−0.599722
$396$		0			0
$397$	3.61737e6			1.15191			0.575953	−	0.817483i	$-0.304631\pi$
$397$	3.61737e6			1.15191			0.575953	+	0.817483i	$0.304631\pi$
$398$	−2.65555e6	−	5.60669e6i	−0.840324	−	1.77418i
$399$		0			0
$400$	−144853.	−	719920.i	−0.0452665	−	0.224975i
$401$			2.51173e6i			0.780032i	0.920808	+	0.390016i	$0.127530\pi$
$401$			2.51173e6i			0.780032i	−0.920808	+	0.390016i	$0.872470\pi$
$402$		0			0
$403$		−	4.71867e6i		−	1.44730i
$404$	2.63201e6	+	2.15518e6i	0.802294	+	0.656946i
$405$		0			0
$406$	311364.	−	147474.i	0.0937461	−	0.0444019i
$407$	3.97437e6			1.18928
$408$		0			0
$409$	−960413.			−0.283890			−0.141945	−	0.989875i	$-0.545336\pi$
$409$	−960413.			−0.283890			−0.141945	+	0.989875i	$0.545336\pi$
$410$	2.17382e6	−	1.02961e6i	0.638653	−	0.302491i
$411$		0			0
$412$	2.83117e6	+	2.31826e6i	0.821718	+	0.672851i
$413$		−	236410.i		−	0.0682010i
$414$		0			0
$415$		−	3.07130e6i		−	0.875392i
$416$	−2.75452e6	−	3.69271e6i	−0.780391	−	1.04619i
$417$		0			0
$418$	4.74935e6	+	1.00273e7i	1.32952	+	2.80702i
$419$	2.90137e6			0.807361			0.403680	−	0.914900i	$-0.367731\pi$
$419$	2.90137e6			0.807361			0.403680	+	0.914900i	$0.367731\pi$
$420$		0			0
$421$	5.00572e6			1.37645			0.688226	−	0.725496i	$-0.258390\pi$
$421$	5.00572e6			1.37645			0.688226	+	0.725496i	$0.258390\pi$
$422$	−423612.	−	894376.i	−0.115794	−	0.244478i
$423$		0			0
$424$	−3.84230e6	−	955693.i	−1.03795	−	0.258169i
$425$		−	260788.i		−	0.0700351i
$426$		0			0
$427$		−	11435.1i		−	0.00303507i
$428$	417198.	−	509502.i	0.110086	−	0.134442i
$429$		0			0
$430$	−4.39446e6	+	2.08139e6i	−1.14613	+	0.542853i
$431$	−1.08969e6			−0.282558			−0.141279	−	0.989970i	$-0.545122\pi$
$431$	−1.08969e6			−0.282558			−0.141279	+	0.989970i	$0.545122\pi$
$432$		0			0
$433$	−322643.			−0.0826994			−0.0413497	−	0.999145i	$-0.513166\pi$
$433$	−322643.			−0.0826994			−0.0413497	+	0.999145i	$0.513166\pi$
$434$	−372320.	+	176346.i	−0.0948838	+	0.0449408i
$435$		0			0
$436$	−3.70907e6	+	4.52969e6i	−0.934434	+	1.14118i
$437$		−	2.91068e6i		−	0.729107i
$438$		0			0
$439$			4.70640e6i			1.16554i	0.812637	+	0.582770i	$0.198031\pi$
$439$			4.70640e6i			1.16554i	−0.812637	+	0.582770i	$0.801969\pi$
$440$	6.08970e6	+	1.51469e6i	1.49956	+	0.372985i
$441$		0			0
$442$	−700313.	−	1.47858e6i	−0.170505	−	0.359988i
$443$	6.83494e6			1.65472			0.827362	−	0.561669i	$-0.189841\pi$
$443$	6.83494e6			1.65472			0.827362	+	0.561669i	$0.189841\pi$
$444$		0			0
$445$	1.76353e6			0.422165
$446$	−692081.	−	1.46120e6i	−0.164748	−	0.347834i
$447$		0			0
$448$	−188426.	+	355345.i	−0.0443554	+	0.0836478i
$449$		−	4.80959e6i		−	1.12588i	−0.826498	−	0.562940i	$-0.809670\pi$
$449$		−	4.80959e6i		−	1.12588i	0.826498	−	0.562940i	$-0.190330\pi$
$450$		0			0
$451$		−	6.12172e6i		−	1.41720i
$452$	−4.49931e6	−	3.68419e6i	−1.03586	−	0.848195i
$453$		0			0
$454$	4.48065e6	−	2.12221e6i	1.02024	−	0.483225i
$455$	−479020.			−0.108474
$456$		0			0
$457$	−6.10756e6			−1.36797			−0.683986	−	0.729495i	$-0.739755\pi$
$457$	−6.10756e6			−1.36797			−0.683986	+	0.729495i	$0.739755\pi$
$458$	374488.	−	177372.i	0.0834207	−	0.0395114i
$459$		0			0
$460$	−1.27370e6	−	1.04295e6i	−0.280655	−	0.229810i
$461$			2.67820e6i			0.586936i	0.955969	+	0.293468i	$0.0948094\pi$
$461$			2.67820e6i			0.586936i	−0.955969	+	0.293468i	$0.905191\pi$
$462$		0			0
$463$		−	992564.i		−	0.215182i	−0.994195	−	0.107591i	$-0.965686\pi$
$463$		−	992564.i		−	0.215182i	0.994195	−	0.107591i	$-0.0343137\pi$
$464$	−4.98105e6	+	1.00222e6i	−1.07405	+	0.216107i
$465$		0			0
$466$	−759120.	−	1.60274e6i	−0.161937	−	0.341899i
$467$	−2.95034e6			−0.626009			−0.313004	−	0.949752i	$-0.601335\pi$
$467$	−2.95034e6			−0.626009			−0.313004	+	0.949752i	$0.601335\pi$
$468$		0			0
$469$	373297.			0.0783650
$470$	11559.8	+	24406.3i	0.00241383	+	0.00509634i
$471$		0			0
$472$	−841547.	+	3.38338e6i	−0.173869	+	0.699031i
$473$			1.23753e7i			2.54332i
$474$		0			0
$475$			1.99101e6i			0.404892i
$476$	−90492.9	+	110514.i	−0.0183062	+	0.0223564i
$477$		0			0
$478$	79082.7	−	37456.7i	0.0158311	−	0.00749825i
$479$	−3.80895e6			−0.758519			−0.379259	−	0.925290i	$-0.623821\pi$
$479$	−3.80895e6			−0.758519			−0.379259	+	0.925290i	$0.623821\pi$
$480$		0			0
$481$	4.47416e6			0.881757
$482$	−3.34193e6	+	1.58287e6i	−0.655210	+	0.310333i
$483$		0			0
$484$	6.85318e6	−	8.36944e6i	1.32978	−	1.62399i
$485$		−	4.72569e6i		−	0.912244i
$486$		0			0
$487$		−	1.27019e6i		−	0.242687i	−0.992611	−	0.121344i	$-0.961280\pi$
$487$		−	1.27019e6i		−	0.242687i	0.992611	−	0.121344i	$-0.0387203\pi$
$488$	−40705.3	+	163653.i	−0.00773752	+	0.0311082i
$489$		0			0
$490$	−1.97910e6	−	4.17850e6i	−0.372373	−	0.786195i
$491$	−685153.			−0.128258			−0.0641289	−	0.997942i	$-0.520427\pi$
$491$	−685153.			−0.128258			−0.0641289	+	0.997942i	$0.520427\pi$
$492$		0			0
$493$	−1.80437e6			−0.334354
$494$	5.34660e6	+	1.12883e7i	0.985735	+	2.08119i
$495$		0			0
$496$	5.95620e6	−	1.19843e6i	1.08709	−	0.218730i
$497$		−	519651.i		−	0.0943672i
$498$		0			0
$499$			6.74866e6i			1.21329i	0.794971	+	0.606647i	$0.207486\pi$
$499$			6.74866e6i			1.21329i	−0.794971	+	0.606647i	$0.792514\pi$
$500$	4.66785e6	+	3.82220e6i	0.835010	+	0.683735i
$501$		0			0
$502$	−5.92702e6	+	2.80727e6i	−1.04973	+	0.497193i
$503$	−6.00484e6			−1.05823			−0.529117	−	0.848549i	$-0.677477\pi$
$503$	−6.00484e6			−1.05823			−0.529117	+	0.848549i	$0.677477\pi$
$504$		0			0
$505$	−5.21645e6			−0.910220
$506$	−3.78651e6	+	1.79344e6i	−0.657450	+	0.311394i
$507$		0			0
$508$	−4.24009e6	−	3.47193e6i	−0.728980	−	0.596914i
$509$		−	3.46748e6i		−	0.593225i	−0.954998	−	0.296612i	$-0.904143\pi$
$509$		−	3.46748e6i		−	0.593225i	0.954998	−	0.296612i	$-0.0958569\pi$
$510$		0			0
$511$		−	1796.87i		−	0.000304413i
$512$	3.96158e6	−	4.41478e6i	0.667873	−	0.744275i
$513$		0			0
$514$	−1.59842e6	−	3.37476e6i	−0.266860	−	0.563424i
$515$	−5.61118e6			−0.932257
$516$		0			0
$517$	68730.9			0.0113090
$518$	−167208.	−	353027.i	−0.0273799	−	0.0578075i
$519$		0			0
$520$	6.85550e6	+	1.70516e6i	1.11181	+	0.276540i
$521$			5.52394e6i			0.891569i	0.895140	+	0.445784i	$0.147075\pi$
$521$			5.52394e6i			0.891569i	−0.895140	+	0.445784i	$0.852925\pi$
$522$		0			0
$523$			438511.i			0.0701013i	0.999386	+	0.0350506i	$0.0111592\pi$
$523$			438511.i			0.0701013i	−0.999386	+	0.0350506i	$0.988841\pi$
$524$	3.33820e6	−	4.07677e6i	0.531110	−	0.648617i
$525$		0			0
$526$	−289025.	+	136894.i	−0.0455482	+	0.0215734i
$527$	2.15761e6			0.338412
$528$		0			0
$529$	−5.33722e6			−0.829231
$530$	5.48709e6	−	2.59891e6i	0.848502	−	0.401884i
$531$		0			0
$532$	690876.	−	843731.i	0.105833	−	0.129248i
$533$		−	6.89155e6i		−	1.05075i
$534$		0			0
$535$			1.00980e6i			0.152528i
$536$	−5.34244e6	−	1.32882e6i	−0.803207	−	0.199781i
$537$		0			0
$538$	−1.66627e6	−	3.51800e6i	−0.248193	−	0.524011i
$539$	−1.17671e7			−1.74461
$540$		0			0
$541$	−3.99542e6			−0.586908			−0.293454	−	0.955973i	$-0.594805\pi$
$541$	−3.99542e6			−0.586908			−0.293454	+	0.955973i	$0.594805\pi$
$542$	1.62041e6	+	3.42119e6i	0.236934	+	0.500240i
$543$		0			0
$544$	1.68849e6	−	1.25950e6i	0.244625	−	0.182474i
$545$		−	8.97753e6i		−	1.29469i
$546$		0			0
$547$			1.10987e7i			1.58601i	0.609217	+	0.793004i	$0.291484\pi$
$547$			1.10987e7i			1.58601i	−0.609217	+	0.793004i	$0.708516\pi$
$548$	−3.67434e6	−	3.00867e6i	−0.522670	−	0.427980i
$549$		0			0
$550$	2.59010e6	−	1.22678e6i	0.365099	−	0.172925i
$551$	1.37756e7			1.93300
$552$		0			0
$553$	465192.			0.0646873
$554$	1.70612e6	−	808087.i	0.236176	−	0.111862i
$555$		0			0
$556$	840154.	+	687947.i	0.115258	+	0.0943774i
$557$		−	4.66176e6i		−	0.636666i	−0.947979	−	0.318333i	$-0.896877\pi$
$557$		−	4.66176e6i		−	0.636666i	0.947979	−	0.318333i	$-0.103123\pi$
$558$		0			0
$559$			1.39315e7i			1.88568i
$560$	−121659.	−	604648.i	−0.0163936	−	0.0814766i
$561$		0			0
$562$	145128.	+	306411.i	0.0193826	+	0.0409226i
$563$	9.51764e6			1.26549			0.632744	−	0.774361i	$-0.281928\pi$
$563$	9.51764e6			1.26549			0.632744	+	0.774361i	$0.281928\pi$
$564$		0			0
$565$	8.91730e6			1.17520
$566$	4.17224e6	+	8.80889e6i	0.547430	+	1.15579i
$567$		0			0
$568$	−1.84980e6	+	7.43699e6i	−0.240577	+	0.967223i
$569$			1.24323e7i			1.60979i	0.593416	+	0.804896i	$0.297779\pi$
$569$			1.24323e7i			1.60979i	−0.593416	+	0.804896i	$0.702221\pi$
$570$		0			0
$571$		−	8.54645e6i		−	1.09697i	−0.836160	−	0.548486i	$-0.815205\pi$
$571$		−	8.54645e6i		−	1.09697i	0.836160	−	0.548486i	$-0.184795\pi$
$572$	1.13906e7	−	1.39108e7i	1.45565	−	1.77771i
$573$		0			0
$574$	−543768.	+	257550.i	−0.0688864	+	0.0326274i
$575$	−751841.			−0.0948323
$576$		0			0
$577$	1.17304e7			1.46680			0.733402	−	0.679795i	$-0.237931\pi$
$577$	1.17304e7			1.46680			0.733402	+	0.679795i	$0.237931\pi$
$578$	−6.58280e6	+	3.11788e6i	−0.819580	+	0.388186i
$579$		0			0
$580$	4.93604e6	−	6.02813e6i	0.609269	−	0.744068i
$581$			768266.i			0.0944216i
$582$		0			0
$583$		−	1.54522e7i		−	1.88287i
$584$	−6396.29	+	25715.9i	−0.000776061	+	0.00312010i
$585$		0			0
$586$	5.27863e6	+	1.11448e7i	0.635005	+	1.34069i
$587$	1.03092e7			1.23489			0.617444	−	0.786615i	$-0.288168\pi$
$587$	1.03092e7			1.23489			0.617444	+	0.786615i	$0.288168\pi$
$588$		0			0
$589$	−1.64724e7			−1.95645
$590$	−2.28850e6	−	4.83172e6i	−0.270658	−	0.571442i
$591$		0			0
$592$	1.13633e6	+	5.64756e6i	0.133260	+	0.662303i
$593$		−	8.53081e6i		−	0.996216i	−0.867115	−	0.498108i	$-0.834028\pi$
$593$		−	8.53081e6i		−	0.996216i	0.867115	−	0.498108i	$-0.165972\pi$
$594$		0			0
$595$		−	219031.i		−	0.0253638i
$596$	3.15392e6	+	2.58254e6i	0.363693	+	0.297804i
$597$		0			0
$598$	−4.26267e6	+	2.01897e6i	−0.487449	+	0.230875i
$599$	−1.46201e7			−1.66489			−0.832443	−	0.554110i	$-0.813059\pi$
$599$	−1.46201e7			−1.66489			−0.832443	+	0.554110i	$0.813059\pi$
$600$		0			0
$601$	1.37185e7			1.54925			0.774623	−	0.632423i	$-0.217940\pi$
$601$	1.37185e7			1.54925			0.774623	+	0.632423i	$0.217940\pi$
$602$	1.09924e6	−	520646.i	0.123624	−	0.0585533i
$603$		0			0
$604$	−5.77908e6	−	4.73211e6i	−0.644564	−	0.527791i
$605$			1.65876e7i			1.84245i
$606$		0			0
$607$		−	5.51308e6i		−	0.607327i	−0.952779	−	0.303663i	$-0.901790\pi$
$607$		−	5.51308e6i		−	0.607327i	0.952779	−	0.303663i	$-0.0982098\pi$
$608$	−1.28909e7	+	9.61575e6i	−1.41424	+	1.05493i
$609$		0			0
$610$	−110694.	−	233709.i	−0.0120448	−	0.0254302i
$611$	77374.0			0.00838479
$612$		0			0
$613$	1.13872e7			1.22395			0.611976	−	0.790876i	$-0.290375\pi$
$613$	1.13872e7			1.22395			0.611976	+	0.790876i	$0.290375\pi$
$614$	−1.50922e6	−	3.18643e6i	−0.161559	−	0.341102i
$615$		0			0
$616$	−1.52330e6	−	378889.i	−0.161746	−	0.0402309i
$617$		−	5.15049e6i		−	0.544673i	−0.962202	−	0.272336i	$-0.912204\pi$
$617$		−	5.15049e6i		−	0.544673i	0.962202	−	0.272336i	$-0.0877963\pi$
$618$		0			0
$619$		−	1.08291e7i		−	1.13597i	−0.823039	−	0.567984i	$-0.807723\pi$
$619$		−	1.08291e7i		−	1.13597i	0.823039	−	0.567984i	$-0.192277\pi$
$620$	−5.90238e6	+	7.20827e6i	−0.616663	+	0.753098i
$621$		0			0
$622$	−3.61119e6	+	1.71041e6i	−0.374261	+	0.177265i
$623$	−441135.			−0.0455356
$624$		0			0
$625$	−7.01029e6			−0.717853
$626$	−4.92454e6	+	2.33246e6i	−0.502261	+	0.237891i
$627$		0			0
$628$	−9.91805e6	+	1.21124e7i	−1.00352	+	1.22555i
$629$			2.04580e6i			0.206176i
$630$		0			0
$631$			155430.i			0.0155404i	0.999970	+	0.00777021i	$0.00247336\pi$
$631$			155430.i			0.0155404i	−0.999970	+	0.00777021i	$0.997527\pi$
$632$	−6.65759e6	−	1.65594e6i	−0.663017	−	0.164912i
$633$		0			0
$634$	−3.62584e6	−	7.65527e6i	−0.358250	−	0.756376i
$635$	8.40355e6			0.827044
$636$		0			0
$637$	−1.32469e7			−1.29349
$638$	−8.48793e6	−	1.79206e7i	−0.825563	−	1.74302i
$639$		0			0
$640$	−411232.	+	9.08650e6i	−0.0396860	+	0.876893i
$641$		−	2.71820e6i		−	0.261298i	−0.991429	−	0.130649i	$-0.958294\pi$
$641$		−	2.71820e6i		−	0.261298i	0.991429	−	0.130649i	$-0.0417062\pi$
$642$		0			0
$643$		−	1.66240e7i		−	1.58566i	−0.609445	−	0.792828i	$-0.708608\pi$
$643$		−	1.66240e7i		−	1.58566i	0.609445	−	0.792828i	$-0.291392\pi$
$644$	318608.	+	260887.i	0.0302721	+	0.0247878i
$645$		0			0
$646$	−5.16157e6	+	2.44472e6i	−0.486632	+	0.230488i
$647$	1.27360e7			1.19611			0.598057	−	0.801454i	$-0.295940\pi$
$647$	1.27360e7			1.19611			0.598057	+	0.801454i	$0.295940\pi$
$648$		0			0
$649$	−1.36066e7			−1.26806
$650$	2.91582e6	−	1.38105e6i	0.270693	−	0.128211i
$651$		0			0
$652$	−4.62718e6	−	3.78890e6i	−0.426283	−	0.349055i
$653$			2.05017e7i			1.88151i	0.339086	+	0.940755i	$0.389882\pi$
$653$			2.05017e7i			1.88151i	−0.339086	+	0.940755i	$0.610118\pi$
$654$		0			0
$655$			8.07987e6i			0.735870i
$656$	8.69893e6	−	1.75028e6i	0.789235	−	0.158799i
$657$		0			0
$658$	−2891.61	−	6105.09i	−0.000260361	−	0.000549702i
$659$	−1.44326e7			−1.29459			−0.647294	−	0.762241i	$-0.724099\pi$
$659$	−1.44326e7			−1.29459			−0.647294	+	0.762241i	$0.724099\pi$
$660$		0			0
$661$	8.96109e6			0.797733			0.398866	−	0.917009i	$-0.369404\pi$
$661$	8.96109e6			0.797733			0.398866	+	0.917009i	$0.369404\pi$
$662$	−1.28396e6	−	2.71083e6i	−0.113869	−	0.240412i
$663$		0			0
$664$	2.73479e6	−	1.09950e7i	0.240715	−	0.967780i
$665$			1.67221e6i			0.146635i
$666$		0			0
$667$			5.20191e6i			0.452739i
$668$	−1.08154e7	+	1.32083e7i	−0.937779	+	1.14526i
$669$		0			0
$670$	7.62940e6	−	3.61359e6i	0.656604	−	0.310994i
$671$	−658149.			−0.0564310
$672$		0			0
$673$	1.16050e7			0.987663			0.493831	−	0.869558i	$-0.335596\pi$
$673$	1.16050e7			0.987663			0.493831	+	0.869558i	$0.335596\pi$
$674$	−690312.	+	326959.i	−0.0585323	+	0.0277232i
$675$		0			0
$676$	5.29570e6	−	6.46736e6i	0.445714	−	0.544328i
$677$		−	1.43607e7i		−	1.20422i	−0.798414	−	0.602109i	$-0.794327\pi$
$677$		−	1.43607e7i		−	1.20422i	0.798414	−	0.602109i	$-0.205673\pi$
$678$		0			0
$679$			1.18210e6i			0.0983965i
$680$	−779684.	+	3.13467e6i	−0.0646616	+	0.259968i
$681$		0			0
$682$	1.01496e7	+	2.14290e7i	0.835582	+	1.76417i
$683$	−1.01202e6			−0.0830116			−0.0415058	−	0.999138i	$-0.513215\pi$
$683$	−1.01202e6			−0.0830116			−0.0415058	+	0.999138i	$0.513215\pi$
$684$		0			0
$685$	7.28227e6			0.592980
$686$	994597.	+	2.09990e6i	0.0806932	+	0.170368i
$687$		0			0
$688$	−1.75852e7	+	3.53826e6i	−1.41637	+	0.284983i
$689$		−	1.73954e7i		−	1.39600i
$690$		0			0
$691$			5.32225e6i			0.424034i	0.977266	+	0.212017i	$0.0680032\pi$
$691$			5.32225e6i			0.424034i	−0.977266	+	0.212017i	$0.931997\pi$
$692$	6.18755e6	+	5.06658e6i	0.491195	+	0.402207i
$693$		0			0
$694$	1.71800e7	−	8.13713e6i	1.35402	−	0.641317i
$695$	−1.66512e6			−0.130763
$696$		0			0
$697$	3.15115e6			0.245690
$698$	9.34246e6	−	4.42496e6i	0.725810	−	0.343772i
$699$		0			0
$700$	−217939.	−	178456.i	−0.0168109	−	0.0137653i
$701$			1.62964e7i			1.25255i	0.779601	+	0.626277i	$0.215422\pi$
$701$			1.62964e7i			1.25255i	−0.779601	+	0.626277i	$0.784578\pi$
$702$		0			0
$703$		−	1.56189e7i		−	1.19196i
$704$	2.04520e7	+	1.08449e7i	1.55526	+	0.824699i
$705$		0			0
$706$	−3.77438e6	−	7.96888e6i	−0.284993	−	0.601708i
$707$	1.30486e6			0.0981782
$708$		0			0
$709$	−4.36798e6			−0.326336			−0.163168	−	0.986598i	$-0.552171\pi$
$709$	−4.36798e6			−0.326336			−0.163168	+	0.986598i	$0.552171\pi$
$710$	−5.03033e6	−	1.06206e7i	−0.374499	−	0.790683i
$711$		0			0
$712$	6.31331e6	+	1.57030e6i	0.466720	+	0.116087i
$713$		−	6.22029e6i		−	0.458234i
$714$		0			0
$715$			2.75701e7i			2.01685i
$716$	6.37282e6	−	7.78279e6i	0.464568	−	0.567353i
$717$		0			0
$718$	2.02820e7	−	9.60639e6i	1.46825	−	0.695423i
$719$	5.23447e6			0.377616			0.188808	−	0.982014i	$-0.439538\pi$
$719$	5.23447e6			0.377616			0.188808	+	0.982014i	$0.439538\pi$
$720$		0			0
$721$	1.40360e6			0.100555
$722$	2.67476e7	−	1.26687e7i	1.90960	−	0.904462i
$723$		0			0
$724$	−3.62991e6	+	4.43302e6i	−0.257365	+	0.314306i
$725$		−	3.55829e6i		−	0.251418i
$726$		0			0
$727$			2.28365e7i			1.60248i	0.598341	+	0.801242i	$0.295827\pi$
$727$			2.28365e7i			1.60248i	−0.598341	+	0.801242i	$0.704173\pi$
$728$	−1.71486e6	−	426535.i	−0.119922	−	0.0298282i
$729$		0			0
$730$	−17394.0	−	36724.2i	−0.00120807	−	0.00255061i
$731$	−6.37016e6			−0.440917
$732$		0			0
$733$	−1.85011e7			−1.27186			−0.635928	−	0.771749i	$-0.719382\pi$
$733$	−1.85011e7			−1.27186			−0.635928	+	0.771749i	$0.719382\pi$
$734$	7.49948e6	+	1.58337e7i	0.513796	+	1.08478i
$735$		0			0
$736$	−3.63108e6	−	4.86783e6i	−0.247082	−	0.331239i
$737$		−	2.14852e7i		−	1.45704i
$738$		0			0
$739$			1.90057e7i			1.28018i	0.768299	+	0.640091i	$0.221103\pi$
$739$			1.90057e7i			1.28018i	−0.768299	+	0.640091i	$0.778897\pi$
$740$	−6.83475e6	−	5.59653e6i	−0.458821	−	0.375698i
$741$		0			0
$742$	−1.37256e6	+	650099.i	−0.0915212	+	0.0433481i
$743$	−6.44452e6			−0.428271			−0.214136	−	0.976804i	$-0.568693\pi$
$743$	−6.44452e6			−0.428271			−0.214136	+	0.976804i	$0.568693\pi$
$744$		0			0
$745$	−6.25084e6			−0.412617
$746$	−1.63248e7	+	7.73208e6i	−1.07399	+	0.508686i
$747$		0			0
$748$	6.36068e6	+	5.20834e6i	0.415671	+	0.340366i
$749$		−	252594.i		−	0.0164520i
$750$		0			0
$751$		−	8.18850e6i		−	0.529791i	−0.964277	−	0.264896i	$-0.914663\pi$
$751$		−	8.18850e6i		−	0.529791i	0.964277	−	0.264896i	$-0.0853375\pi$
$752$	19651.1	+	97666.2i	0.00126719	+	0.00629796i
$753$		0			0
$754$	−9.55532e6	−	2.01742e7i	−0.612092	−	1.29232i
$755$	1.14537e7			0.731272
$756$		0			0
$757$	−4.18430e6			−0.265389			−0.132694	−	0.991157i	$-0.542363\pi$
$757$	−4.18430e6			−0.265389			−0.132694	+	0.991157i	$0.542363\pi$
$758$	−5.34881e6	−	1.12930e7i	−0.338130	−	0.713897i
$759$		0			0
$760$	5.95256e6	−	2.39319e7i	0.373826	−	1.50295i
$761$		−	1.61530e6i		−	0.101110i	−0.998721	−	0.0505548i	$-0.983901\pi$
$761$		−	1.61530e6i		−	0.101110i	0.998721	−	0.0505548i	$-0.0160990\pi$
$762$		0			0
$763$			2.24567e6i			0.139648i
$764$	−1.23411e7	+	1.50716e7i	−0.764931	+	0.934170i
$765$		0			0
$766$	−2.19154e7	+	1.03800e7i	−1.34951	+	0.639183i
$767$	−1.53177e7			−0.940169
$768$		0			0
$769$	1.54128e7			0.939864			0.469932	−	0.882703i	$-0.344278\pi$
$769$	1.54128e7			0.939864			0.469932	+	0.882703i	$0.344278\pi$
$770$	2.17538e6	−	1.03035e6i	0.132224	−	0.0626263i
$771$		0			0
$772$	−8941.23	+	10919.5i	−0.000539951	+	0.000659414i
$773$			2.31379e7i			1.39276i	0.717674	+	0.696379i	$0.245207\pi$
$773$			2.31379e7i			1.39276i	−0.717674	+	0.696379i	$0.754793\pi$
$774$		0			0
$775$			4.25490e6i			0.254469i
$776$	4.20791e6	−	1.69176e7i	0.250849	−	1.00852i
$777$		0			0
$778$	6.23399e6	+	1.31619e7i	0.369247	+	0.779594i
$779$	−2.40577e7			−1.42040
$780$		0			0
$781$	−2.99087e7			−1.75457
$782$	−923172.	−	1.94910e6i	−0.0539841	−	0.113977i
$783$		0			0
$784$	−3.36437e6	−	1.67210e7i	−0.195485	−	0.971564i
$785$		−	2.40059e7i		−	1.39041i
$786$		0			0
$787$		−	2.90198e7i		−	1.67016i	−0.550130	−	0.835079i	$-0.685422\pi$
$787$		−	2.90198e7i		−	1.67016i	0.550130	−	0.835079i	$-0.314578\pi$
$788$	1.70049e7	+	1.39242e7i	0.975572	+	0.798832i
$789$		0			0
$790$	9.50753e6	−	4.50315e6i	0.542001	−	0.256713i
$791$	−2.23060e6			−0.126760
$792$		0			0
$793$	−740913.			−0.0418393
$794$	−1.84935e7	+	8.75924e6i	−1.04104	+	0.493077i
$795$		0			0
$796$	2.71525e7	+	2.22334e7i	1.51889	+	1.24372i
$797$			3.03335e7i			1.69152i	0.533565	+	0.845759i	$0.320852\pi$
$797$			3.03335e7i			1.69152i	−0.533565	+	0.845759i	$0.679148\pi$
$798$		0			0
$799$			35379.2i			0.00196056i
$800$	2.48379e6	+	3.32977e6i	0.137211	+	0.183945i
$801$		0			0
$802$	−6.08200e6	−	1.28410e7i	−0.333895	−	0.704956i
$803$	−103419.			−0.00565995
$804$		0			0
$805$	−631458.			−0.0343443
$806$	1.14260e7	+	2.41238e7i	0.619520	+	1.30800i
$807$		0			0
$808$	−1.86745e7	−	4.64489e6i	−1.00628	−	0.250292i
$809$			2.52104e7i			1.35428i	0.735854	+	0.677140i	$0.236781\pi$
$809$			2.52104e7i			1.35428i	−0.735854	+	0.677140i	$0.763219\pi$
$810$		0			0
$811$		−	2.17678e7i		−	1.16215i	−0.813849	−	0.581076i	$-0.802632\pi$
$811$		−	2.17678e7i		−	1.16215i	0.813849	−	0.581076i	$-0.197368\pi$
$812$	−1.23472e6	+	1.50790e6i	−0.0657170	+	0.0802568i
$813$		0			0
$814$	−2.03186e7	+	9.62369e6i	−1.07481	+	0.509074i
$815$	9.17074e6			0.483627
$816$		0			0
$817$	4.86335e7			2.54906
$818$	4.91002e6	−	2.32558e6i	0.256566	−	0.121520i
$819$		0			0
$820$	−8.62032e6	+	1.05276e7i	−0.447702	+	0.546755i
$821$		−	1.68043e7i		−	0.870087i	−0.900409	−	0.435044i	$-0.856733\pi$
$821$		−	1.68043e7i		−	0.870087i	0.900409	−	0.435044i	$-0.143267\pi$
$822$		0			0
$823$			8.63167e6i			0.444217i	0.975022	+	0.222108i	$0.0712939\pi$
$823$			8.63167e6i			0.444217i	−0.975022	+	0.222108i	$0.928706\pi$
$824$	−2.00876e7	−	4.99637e6i	−1.03065	−	0.256352i
$825$		0			0
$826$	572452.	+	1.20862e6i	0.0291937	+	0.0616369i
$827$	2.57523e7			1.30934			0.654668	−	0.755916i	$-0.272808\pi$
$827$	2.57523e7			1.30934			0.654668	+	0.755916i	$0.272808\pi$
$828$		0			0
$829$	6.21533e6			0.314107			0.157054	−	0.987590i	$-0.449800\pi$
$829$	6.21533e6			0.314107			0.157054	+	0.987590i	$0.449800\pi$
$830$	7.43697e6	+	1.57017e7i	0.374715	+	0.791138i
$831$		0			0
$832$	2.30239e7	+	1.22087e7i	1.15311	+	0.611451i
$833$		−	6.05711e6i		−	0.302449i
$834$		0			0
$835$		−	2.61778e7i		−	1.29932i
$836$	−4.85612e7	−	3.97636e7i	−2.40311	−	1.96775i
$837$		0			0
$838$	−1.48330e7	+	7.02548e6i	−0.729655	+	0.345594i
$839$	−1.38503e7			−0.679287			−0.339644	−	0.940554i	$-0.610306\pi$
$839$	−1.38503e7			−0.679287			−0.339644	+	0.940554i	$0.610306\pi$
$840$		0			0
$841$	−4.10826e6			−0.200294
$842$	−2.55912e7	+	1.21210e7i	−1.24397	+	0.589195i
$843$		0			0
$844$	4.33135e6	+	3.54666e6i	0.209299	+	0.171381i
$845$			1.28178e7i			0.617551i
$846$		0			0
$847$		−	4.14928e6i		−	0.198730i
$848$	2.19575e7	−	4.41801e6i	1.04856	−	0.210978i
$849$		0			0
$850$	631482.	+	1.33325e6i	0.0299788	+	0.0632944i
$851$	5.89797e6			0.279176
$852$		0			0
$853$	−1.81244e7			−0.852886			−0.426443	−	0.904515i	$-0.640233\pi$
$853$	−1.81244e7			−0.852886			−0.426443	+	0.904515i	$0.640233\pi$
$854$	27689.3	+	58460.7i	0.00129917	+	0.00274296i
$855$		0			0
$856$	−899155.	+	3.61500e6i	−0.0419421	+	0.168626i
$857$			1.66848e7i			0.776011i	0.921657	+	0.388006i	$0.126836\pi$
$857$			1.66848e7i			0.776011i	−0.921657	+	0.388006i	$0.873164\pi$
$858$		0			0
$859$			1.14999e7i			0.531756i	0.964007	+	0.265878i	$0.0856618\pi$
$859$			1.14999e7i			0.531756i	−0.964007	+	0.265878i	$0.914338\pi$
$860$	1.74263e7	−	2.12818e7i	0.803449	−	0.981211i
$861$		0			0
$862$	5.57091e6	−	2.63861e6i	0.255363	−	0.120950i
$863$	3.96199e7			1.81086			0.905432	−	0.424491i	$-0.139547\pi$
$863$	3.96199e7			1.81086			0.905432	+	0.424491i	$0.139547\pi$
$864$		0			0
$865$	−1.22633e7			−0.557271
$866$	1.64948e6	−	781259.i	0.0747399	−	0.0353998i
$867$		0			0
$868$	1.47644e6	−	1.80310e6i	0.0665145	−	0.0812307i
$869$		−	2.67742e7i		−	1.20273i
$870$		0			0
$871$		−	2.41870e7i		−	1.08028i
$872$	7.99388e6	−	3.21389e7i	0.356014	−	1.43133i
$873$		0			0
$874$	7.04804e6	+	1.48806e7i	0.312097	+	0.658933i
$875$	2.31416e6			0.102182
$876$		0			0
$877$	2.19126e7			0.962045			0.481022	−	0.876708i	$-0.340266\pi$
$877$	2.19126e7			0.962045			0.481022	+	0.876708i	$0.340266\pi$
$878$	−1.13962e7	−	2.40610e7i	−0.498914	−	1.05336i
$879$		0			0
$880$	−3.48007e7	+	7.00214e6i	−1.51489	+	0.304806i
$881$		−	1.94063e7i		−	0.842371i	−0.906974	−	0.421186i	$-0.861614\pi$
$881$		−	1.94063e7i		−	0.842371i	0.906974	−	0.421186i	$-0.138386\pi$
$882$		0			0
$883$			1.49520e7i			0.645353i	0.946509	+	0.322677i	$0.104583\pi$
$883$			1.49520e7i			0.645353i	−0.946509	+	0.322677i	$0.895417\pi$
$884$	7.16056e6	+	5.86331e6i	0.308188	+	0.252355i
$885$		0			0
$886$	−3.49430e7	+	1.65504e7i	−1.49546	+	0.708310i
$887$	1.73689e7			0.741246			0.370623	−	0.928783i	$-0.379144\pi$
$887$	1.73689e7			0.741246			0.370623	+	0.928783i	$0.379144\pi$
$888$		0			0
$889$	−2.10209e6			−0.0892067
$890$	−9.01587e6	+	4.27027e6i	−0.381533	+	0.180709i
$891$		0			0
$892$	7.07640e6	+	5.79440e6i	0.297783	+	0.243835i
$893$		−	270105.i		−	0.0113346i
$894$		0			0
$895$			1.54249e7i			0.643674i
$896$	102867.	−	2.27293e6i	0.00428061	−	0.0945835i
$897$		0			0
$898$	1.16461e7	+	2.45885e7i	0.481937	+	1.01752i
$899$	2.94392e7			1.21486
$900$		0			0
$901$	7.95403e6			0.326419
$902$	1.48234e7	+	3.12967e7i	0.606639	+	1.28080i
$903$		0			0
$904$	3.19233e7	+	7.94026e6i	1.29923	+	0.323157i
$905$		−	8.78592e6i		−	0.356587i
$906$		0			0
$907$			1.98414e6i			0.0800854i	0.999198	+	0.0400427i	$0.0127494\pi$
$907$			1.98414e6i			0.0800854i	−0.999198	+	0.0400427i	$0.987251\pi$
$908$	−1.77681e7	+	2.16992e7i	−0.715196	+	0.873432i
$909$		0			0
$910$	2.44894e6	−	1.15992e6i	0.0980337	−	0.0464327i
$911$	−2.02590e7			−0.808766			−0.404383	−	0.914590i	$-0.632514\pi$
$911$	−2.02590e7			−0.808766			−0.404383	+	0.914590i	$0.632514\pi$
$912$		0			0
$913$	4.42178e7			1.75558
$914$	3.12243e7	−	1.47891e7i	1.23631	−	0.585566i
$915$		0			0
$916$	−1.48504e6	+	1.81360e6i	−0.0584788	+	0.0714171i
$917$		−	2.02113e6i		−	0.0793725i
$918$		0			0
$919$		−	3.99374e7i		−	1.55988i	−0.625856	−	0.779939i	$-0.715250\pi$
$919$		−	3.99374e7i		−	1.55988i	0.625856	−	0.779939i	$-0.284750\pi$
$920$	9.03712e6	+	2.24780e6i	0.352014	+	0.0875563i
$921$		0			0
$922$	−6.48509e6	−	1.36920e7i	−0.251240	−	0.530445i
$923$	−3.36698e7			−1.30088
$924$		0			0
$925$	−4.03442e6			−0.155034
$926$	2.40343e6	+	5.07439e6i	0.0921095	+	0.194472i
$927$		0			0
$928$	2.30383e7	−	1.71851e7i	0.878174	−	0.655060i
$929$			2.41714e7i			0.918888i	0.888207	+	0.459444i	$0.151951\pi$
$929$			2.41714e7i			0.918888i	−0.888207	+	0.459444i	$0.848049\pi$
$930$		0			0
$931$			4.62435e7i			1.74854i
$932$	7.76185e6	+	6.35567e6i	0.292702	+	0.239674i
$933$		0			0
$934$	1.50833e7	−	7.14407e6i	0.565757	−	0.267965i
$935$	−1.26064e7			−0.471588
$936$		0			0
$937$	−4.42022e7			−1.64473			−0.822366	−	0.568959i	$-0.807346\pi$
$937$	−4.42022e7			−1.64473			−0.822366	+	0.568959i	$0.807346\pi$
$938$	−1.90844e6	+	903915.i	−0.0708226	+	0.0335444i
$939$		0			0
$940$	−118197.	−	96783.7i	−0.00436301	−	0.00357258i
$941$			1.51502e7i			0.557756i	0.960327	+	0.278878i	$0.0899625\pi$
$941$			1.51502e7i			0.557756i	−0.960327	+	0.278878i	$0.910038\pi$
$942$		0			0
$943$		−	9.08464e6i		−	0.332681i
$944$	−3.89033e6	−	1.93350e7i	−0.142088	−	0.706177i
$945$		0			0
$946$	−2.99659e7	−	6.32673e7i	−1.08868	−	2.29854i
$947$	−2.47403e7			−0.896459			−0.448229	−	0.893919i	$-0.647945\pi$
$947$	−2.47403e7			−0.896459			−0.448229	+	0.893919i	$0.647945\pi$
$948$		0			0
$949$	−116425.			−0.00419642
$950$	−4.82110e6	−	1.01788e7i	−0.173316	−	0.365923i
$951$		0			0
$952$	195033.	−	784116.i	0.00697453	−	0.0280407i
$953$		−	3.53865e6i		−	0.126213i	−0.998007	−	0.0631067i	$-0.979899\pi$
$953$		−	3.53865e6i		−	0.126213i	0.998007	−	0.0631067i	$-0.0201009\pi$
$954$		0			0
$955$		−	2.98708e7i		−	1.05984i
$956$	−313603.	+	382988.i	−0.0110978	+	0.0135531i
$957$		0			0
$958$	1.94729e7	−	9.22313e6i	0.685514	−	0.324687i
$959$	−1.82161e6			−0.0639601
$960$		0			0
$961$	−6.57337e6			−0.229604
$962$	−2.28737e7	+	1.08339e7i	−0.796891	+	0.377439i
$963$		0			0
$964$	1.32525e7	−	1.61846e7i	0.459309	−	0.560930i
$965$		−	21641.6i		−	0.000748119i
$966$		0			0
$967$			3.30528e7i			1.13669i	0.822790	+	0.568345i	$0.192416\pi$
$967$			3.30528e7i			1.13669i	−0.822790	+	0.568345i	$0.807584\pi$
$968$	−1.47702e7	+	5.93825e7i	−0.506637	+	2.03690i
$969$		0			0
$970$	1.14430e7	+	2.41596e7i	0.390489	+	0.824443i
$971$	6.44600e6			0.219403			0.109701	−	0.993965i	$-0.465011\pi$
$971$	6.44600e6			0.219403			0.109701	+	0.993965i	$0.465011\pi$
$972$		0			0
$973$	416520.			0.0141044
$974$	3.07569e6	+	6.49373e6i	0.103883	+	0.219329i
$975$		0			0
$976$	−188174.	−	935226.i	−0.00632317	−	0.0314262i
$977$		−	1.22343e7i		−	0.410056i	−0.978756	−	0.205028i	$-0.934271\pi$
$977$		−	1.22343e7i		−	0.410056i	0.978756	−	0.205028i	$-0.0657286\pi$
$978$		0			0
$979$			2.53896e7i			0.846642i
$980$	2.02359e7	+	1.65699e7i	0.673067	+	0.551130i
$981$		0			0
$982$	3.50278e6	−	1.65905e6i	0.115913	−	0.0549012i
$983$	1.56050e7			0.515086			0.257543	−	0.966267i	$-0.417087\pi$
$983$	1.56050e7			0.515086			0.257543	+	0.966267i	$0.417087\pi$
$984$		0			0
$985$	−3.37025e7			−1.10681
$986$	9.22464e6	−	4.36916e6i	0.302174	−	0.143122i
$987$		0			0
$988$	−5.46679e7	−	4.47640e7i	−1.78172	−	1.45894i
$989$			1.83649e7i			0.597032i
$990$		0			0
$991$			5.84661e7i			1.89112i	0.325443	+	0.945562i	$0.394487\pi$
$991$			5.84661e7i			1.89112i	−0.325443	+	0.945562i	$0.605513\pi$
$992$	−2.75486e7	+	2.05494e7i	−0.888832	+	0.663010i
$993$		0			0
$994$	1.25830e6	+	2.65667e6i	0.0403942	+	0.0852847i
$995$	−5.38143e7			−1.72322
$996$		0			0
$997$	−9.50143e6			−0.302727			−0.151364	−	0.988478i	$-0.548366\pi$
$997$	−9.50143e6			−0.302727			−0.151364	+	0.988478i	$0.548366\pi$
$998$	−1.63414e7	−	3.45018e7i	−0.519355	−	1.09652i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.6.b.b.35.2	yes	8
3.2	odd	2	inner	36.6.b.b.35.7	yes	8
4.3	odd	2	inner	36.6.b.b.35.8	yes	8
8.3	odd	2		576.6.c.c.575.2		8
8.5	even	2		576.6.c.c.575.1		8
12.11	even	2	inner	36.6.b.b.35.1	✓	8
24.5	odd	2		576.6.c.c.575.7		8
24.11	even	2		576.6.c.c.575.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.b.b.35.1	✓	8	12.11	even	2	inner
36.6.b.b.35.2	yes	8	1.1	even	1	trivial
36.6.b.b.35.7	yes	8	3.2	odd	2	inner
36.6.b.b.35.8	yes	8	4.3	odd	2	inner
576.6.c.c.575.1		8	8.5	even	2
576.6.c.c.575.2		8	8.3	odd	2
576.6.c.c.575.7		8	24.5	odd	2
576.6.c.c.575.8		8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	36.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.11240 + 2.42144i) q^{2} +(20.2733 - 24.7587i) q^{4} +49.0700i q^{5} -12.2745i q^{7} +(-43.6935 + 175.667i) q^{8} +(-118.820 - 250.865i) q^{10} -706.464 q^{11} -795.304 q^{13} +(29.7220 + 62.7523i) q^{14} +(-201.988 - 1003.88i) q^{16} -363.652i q^{17} +2776.33i q^{19} +(1214.91 + 994.810i) q^{20} +(3611.73 - 1710.66i) q^{22} -1048.39 q^{23} +717.137 q^{25} +(4065.91 - 1925.78i) q^{26} +(-303.902 - 248.845i) q^{28} -4961.79i q^{29} +5933.17i q^{31} +(3463.48 + 4643.14i) q^{32} +(880.560 + 1859.13i) q^{34} +602.311 q^{35} -5625.73 q^{37} +(-6722.71 - 14193.7i) q^{38} +(-8619.97 - 2144.04i) q^{40} +8665.30i q^{41} -17517.2i q^{43} +(-14322.3 + 17491.1i) q^{44} +(5359.80 - 2538.62i) q^{46} -97.2886 q^{47} +16656.3 q^{49} +(-3666.29 + 1736.50i) q^{50} +(-16123.4 + 19690.7i) q^{52} +21872.7i q^{53} -34666.2i q^{55} +(2156.23 + 536.317i) q^{56} +(12014.7 + 25366.7i) q^{58} +19260.2 q^{59} +931.610 q^{61} +(-14366.8 - 30332.7i) q^{62} +(-28949.8 - 15351.0i) q^{64} -39025.6i q^{65} +30412.3i q^{67} +(-9003.55 - 7372.42i) q^{68} +(-3079.25 + 1458.46i) q^{70} +42335.7 q^{71} +146.390 q^{73} +(28761.0 - 13622.3i) q^{74} +(68738.4 + 56285.3i) q^{76} +8671.51i q^{77} +37898.9i q^{79} +(49260.4 - 9911.53i) q^{80} +(-20982.5 - 44300.5i) q^{82} -62590.3 q^{83} +17844.4 q^{85} +(42416.8 + 89554.9i) q^{86} +(30867.9 - 124102. i) q^{88} -35939.1i q^{89} +9761.98i q^{91} +(-21254.4 + 25956.8i) q^{92} +(497.378 - 235.578i) q^{94} -136234. q^{95} -96305.1 q^{97} +(-85153.9 + 40332.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 44 q^{4} - 596 q^{10} + 256 q^{13} - 4216 q^{16} + 9984 q^{22} + 15192 q^{25} - 23232 q^{28} + 23236 q^{34} - 26096 q^{37} - 36104 q^{40} + 84480 q^{46} + 4664 q^{49} - 96368 q^{52} + 126964 q^{58}+ \cdots + 229888 q^{97}+O(q^{100}) \) 8 * q + 44 * q^4 - 596 * q^10 + 256 * q^13 - 4216 * q^16 + 9984 * q^22 + 15192 * q^25 - 23232 * q^28 + 23236 * q^34 - 26096 * q^37 - 36104 * q^40 + 84480 * q^46 + 4664 * q^49 - 96368 * q^52 + 126964 * q^58 - 102224 * q^61 - 14608 * q^64 - 28416 * q^70 + 110848 * q^73 + 50688 * q^76 - 240308 * q^82 + 100208 * q^85 + 349056 * q^88 - 287232 * q^94 + 229888 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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