LMFDB - Embedded newform 76.6.i.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	76.17
Dual form			76.6.i.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.670817 - 0.562882i) q^{3} +(-12.4943 + 4.54757i) q^{5} +(41.6708 + 72.1759i) q^{7} +(-42.0633 - 238.553i) q^{9} +O(q^{10})$	\(q+(-0.670817 - 0.562882i) q^{3} +(-12.4943 + 4.54757i) q^{5} +(41.6708 + 72.1759i) q^{7} +(-42.0633 - 238.553i) q^{9} +(-226.700 + 392.656i) q^{11} +(-370.814 + 311.150i) q^{13} +(10.9412 + 3.98225i) q^{15} +(-138.347 + 784.604i) q^{17} +(-2.60199 + 1573.56i) q^{19} +(12.6731 - 71.8725i) q^{21} +(-3264.71 - 1188.26i) q^{23} +(-2258.46 + 1895.07i) q^{25} +(-212.457 + 367.986i) q^{27} +(1083.32 + 6143.80i) q^{29} +(816.303 + 1413.88i) q^{31} +(373.093 - 135.795i) q^{33} +(-848.873 - 712.289i) q^{35} -4167.20 q^{37} +423.889 q^{39} +(-11740.2 - 9851.22i) q^{41} +(19818.8 - 7213.47i) q^{43} +(1610.39 + 2789.28i) q^{45} +(961.691 + 5454.02i) q^{47} +(4930.59 - 8540.04i) q^{49} +(534.444 - 448.452i) q^{51} +(19335.8 + 7037.65i) q^{53} +(1046.84 - 5936.91i) q^{55} +(887.474 - 1054.11i) q^{57} +(6806.67 - 38602.6i) q^{59} +(-24885.4 - 9057.56i) q^{61} +(15465.0 - 12976.7i) q^{63} +(3218.10 - 5573.91i) q^{65} +(725.150 + 4112.53i) q^{67} +(1521.17 + 2634.75i) q^{69} +(35214.4 - 12817.0i) q^{71} +(24304.4 + 20393.8i) q^{73} +2581.72 q^{75} -37787.1 q^{77} +(26470.6 + 22211.4i) q^{79} +(-54963.2 + 20005.0i) q^{81} +(-2051.52 - 3553.34i) q^{83} +(-1839.49 - 10432.2i) q^{85} +(2731.53 - 4731.14i) q^{87} +(-80831.0 + 67825.2i) q^{89} +(-37909.6 - 13798.0i) q^{91} +(248.257 - 1407.94i) q^{93} +(-7123.36 - 19672.4i) q^{95} +(-16543.4 + 93822.2i) q^{97} +(103205. + 37563.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.670817	−	0.562882i	−0.0430329	−	0.0361089i	0.621018	−	0.783797i	$-0.286720\pi$
$3$	−0.670817	−	0.562882i	−0.0430329	−	0.0361089i	−0.664050	+	0.747688i	$0.731164\pi$
$4$		0			0
$5$	−12.4943	+	4.54757i	−0.223506	+	0.0813494i	−0.451346	−	0.892349i	$-0.649056\pi$
$5$	−12.4943	+	4.54757i	−0.223506	+	0.0813494i	0.227840	+	0.973699i	$0.426834\pi$
$6$		0			0
$7$	41.6708	+	72.1759i	0.321430	+	0.556733i	0.980783	−	0.195100i	$-0.0625032\pi$
$7$	41.6708	+	72.1759i	0.321430	+	0.556733i	−0.659353	+	0.751833i	$0.729170\pi$
$8$		0			0
$9$	−42.0633	−	238.553i	−0.173100	−	0.981700i
$10$		0			0
$11$	−226.700	+	392.656i	−0.564898	+	0.978432i	0.432161	+	0.901796i	$0.357751\pi$
$11$	−226.700	+	392.656i	−0.564898	+	0.978432i	−0.997059	+	0.0766357i	$0.975582\pi$
$12$		0			0
$13$	−370.814	+	311.150i	−0.608552	+	0.510636i	−0.894182	−	0.447704i	$-0.852242\pi$
$13$	−370.814	+	311.150i	−0.608552	+	0.510636i	0.285630	+	0.958340i	$0.407797\pi$
$14$		0			0
$15$	10.9412	+	3.98225i	0.0125555	+	0.00456984i
$16$		0			0
$17$	−138.347	+	784.604i	−0.116104	+	0.658458i	0.870094	+	0.492886i	$0.164058\pi$
$17$	−138.347	+	784.604i	−0.116104	+	0.658458i	−0.986198	+	0.165572i	$0.947053\pi$
$18$		0			0
$19$	−2.60199	+	1573.56i	−0.00165357	+	0.999999i
$19$	−2.60199	+	1573.56i	−0.00165357	+	0.999999i
$20$		0			0
$21$	12.6731	−	71.8725i	0.00627095	−	0.0355643i
$22$		0			0
$23$	−3264.71	−	1188.26i	−1.28684	−	0.468372i	−0.394152	−	0.919045i	$-0.628962\pi$
$23$	−3264.71	−	1188.26i	−1.28684	−	0.468372i	−0.892689	+	0.450674i	$0.851184\pi$
$24$		0			0
$25$	−2258.46	+	1895.07i	−0.722707	+	0.606424i
$26$		0			0
$27$	−212.457	+	367.986i	−0.0560868	+	0.0971452i
$28$		0			0
$29$	1083.32	+	6143.80i	0.239200	+	1.35657i	0.833586	+	0.552389i	$0.186284\pi$
$29$	1083.32	+	6143.80i	0.239200	+	1.35657i	−0.594387	+	0.804179i	$0.702605\pi$
$30$		0			0
$31$	816.303	+	1413.88i	0.152562	+	0.264246i	0.932169	−	0.362024i	$-0.117914\pi$
$31$	816.303	+	1413.88i	0.152562	+	0.264246i	−0.779606	+	0.626270i	$0.784581\pi$
$32$		0			0
$33$	373.093	−	135.795i	0.0596393	−	0.0217069i
$34$		0			0
$35$	−848.873	−	712.289i	−0.117131	−	0.0982848i
$36$		0			0
$37$	−4167.20			−0.500427			−0.250213	−	0.968191i	$-0.580501\pi$
$37$	−4167.20			−0.500427			−0.250213	+	0.968191i	$0.580501\pi$
$38$		0			0
$39$	423.889			0.0446263
$40$		0			0
$41$	−11740.2	−	9851.22i	−1.09073	−	0.915230i	−0.0939616	−	0.995576i	$-0.529953\pi$
$41$	−11740.2	−	9851.22i	−1.09073	−	0.915230i	−0.996767	+	0.0803458i	$0.974398\pi$
$42$		0			0
$43$	19818.8	−	7213.47i	1.63458	−	0.594940i	0.648504	−	0.761211i	$-0.275395\pi$
$43$	19818.8	−	7213.47i	1.63458	−	0.594940i	0.986080	+	0.166271i	$0.0531727\pi$
$44$		0			0
$45$	1610.39	+	2789.28i	0.118550	+	0.205334i
$46$		0			0
$47$	961.691	+	5454.02i	0.0635025	+	0.360141i	0.999956	+	0.00934971i	$0.00297615\pi$
$47$	961.691	+	5454.02i	0.0635025	+	0.360141i	−0.936454	+	0.350791i	$0.885913\pi$
$48$		0			0
$49$	4930.59	−	8540.04i	0.293366	−	0.508124i
$50$		0			0
$51$	534.444	−	448.452i	0.0287725	−	0.0241430i
$52$		0			0
$53$	19335.8	+	7037.65i	0.945523	+	0.344142i	0.768345	−	0.640036i	$-0.221081\pi$
$53$	19335.8	+	7037.65i	0.945523	+	0.344142i	0.177179	+	0.984179i	$0.443303\pi$
$54$		0			0
$55$	1046.84	−	5936.91i	0.0466630	−	0.264639i
$56$		0			0
$57$	887.474	−	1054.11i	0.0361800	−	0.0429731i
$58$		0			0
$59$	6806.67	−	38602.6i	0.254569	−	1.44373i	−0.542609	−	0.839986i	$-0.682563\pi$
$59$	6806.67	−	38602.6i	0.254569	−	1.44373i	0.797177	−	0.603745i	$-0.206326\pi$
$60$		0			0
$61$	−24885.4	−	9057.56i	−0.856290	−	0.311664i	−0.123688	−	0.992321i	$-0.539472\pi$
$61$	−24885.4	−	9057.56i	−0.856290	−	0.311664i	−0.732602	+	0.680657i	$0.761694\pi$
$62$		0			0
$63$	15465.0	−	12976.7i	0.490905	−	0.411918i
$64$		0			0
$65$	3218.10	−	5573.91i	0.0944748	−	0.163635i
$66$		0			0
$67$	725.150	+	4112.53i	0.0197352	+	0.111924i	0.993084	−	0.117406i	$-0.0374578\pi$
$67$	725.150	+	4112.53i	0.0197352	+	0.111924i	−0.973349	+	0.229329i	$0.926347\pi$
$68$		0			0
$69$	1521.17	+	2634.75i	0.0384641	+	0.0666218i
$70$		0			0
$71$	35214.4	−	12817.0i	0.829037	−	0.301745i	0.107574	−	0.994197i	$-0.465692\pi$
$71$	35214.4	−	12817.0i	0.829037	−	0.301745i	0.721464	+	0.692452i	$0.243470\pi$
$72$		0			0
$73$	24304.4	+	20393.8i	0.533798	+	0.447910i	0.869411	−	0.494090i	$-0.164499\pi$
$73$	24304.4	+	20393.8i	0.533798	+	0.447910i	−0.335613	+	0.942000i	$0.608943\pi$
$74$		0			0
$75$	2581.72			0.0529975
$76$		0			0
$77$	−37787.1			−0.726301
$78$		0			0
$79$	26470.6	+	22211.4i	0.477195	+	0.400414i	0.849411	−	0.527732i	$-0.176958\pi$
$79$	26470.6	+	22211.4i	0.477195	+	0.400414i	−0.372216	+	0.928146i	$0.621402\pi$
$80$		0			0
$81$	−54963.2	+	20005.0i	−0.930806	+	0.338786i
$82$		0			0
$83$	−2051.52	−	3553.34i	−0.0326874	−	0.0566162i	0.849219	−	0.528041i	$-0.177073\pi$
$83$	−2051.52	−	3553.34i	−0.0326874	−	0.0566162i	−0.881906	+	0.471425i	$0.843740\pi$
$84$		0			0
$85$	−1839.49	−	10432.2i	−0.0276153	−	0.156614i
$86$		0			0
$87$	2731.53	−	4731.14i	0.0386907	−	0.0670143i
$88$		0			0
$89$	−80831.0	+	67825.2i	−1.08169	+	0.907646i	−0.996060	−	0.0886813i	$-0.971735\pi$
$89$	−80831.0	+	67825.2i	−1.08169	+	0.907646i	−0.0856300	+	0.996327i	$0.527290\pi$
$90$		0			0
$91$	−37909.6	−	13798.0i	−0.479895	−	0.174667i
$92$		0			0
$93$	248.257	−	1407.94i	0.00297642	−	0.0168801i
$94$		0			0
$95$	−7123.36	−	19672.4i	−0.0809797	−	0.223640i
$96$		0			0
$97$	−16543.4	+	93822.2i	−0.178523	+	1.01246i	0.755475	+	0.655178i	$0.227406\pi$
$97$	−16543.4	+	93822.2i	−0.178523	+	1.01246i	−0.933998	+	0.357278i	$0.883705\pi$
$98$		0			0
$99$	103205.	+	37563.6i	1.05831	+	0.385194i
$100$		0			0
$101$	−36897.9	+	30961.0i	−0.359913	+	0.302003i	−0.804756	−	0.593605i	$-0.797704\pi$
$101$	−36897.9	+	30961.0i	−0.359913	+	0.302003i	0.444843	+	0.895609i	$0.353260\pi$
$102$		0			0
$103$	−47681.9	+	82587.5i	−0.442854	+	0.767046i	−0.997900	−	0.0647738i	$-0.979367\pi$
$103$	−47681.9	+	82587.5i	−0.442854	+	0.767046i	0.555046	+	0.831820i	$0.312701\pi$
$104$		0			0
$105$	168.504	+	955.631i	0.00149154	+	0.00845896i
$106$		0			0
$107$	−27703.2	−	47983.3i	−0.233922	−	0.405164i	0.725037	−	0.688710i	$-0.241823\pi$
$107$	−27703.2	−	47983.3i	−0.233922	−	0.405164i	−0.958959	+	0.283546i	$0.908489\pi$
$108$		0			0
$109$	−43256.7	+	15744.2i	−0.348729	+	0.126927i	−0.510445	−	0.859910i	$-0.670519\pi$
$109$	−43256.7	+	15744.2i	−0.348729	+	0.126927i	0.161716	+	0.986837i	$0.448297\pi$
$110$		0			0
$111$	2795.43	+	2345.64i	0.0215348	+	0.0180699i
$112$		0			0
$113$	−141896.			−1.04538			−0.522690	−	0.852523i	$-0.675071\pi$
$113$	−141896.			−1.04538			−0.522690	+	0.852523i	$0.675071\pi$
$114$		0			0
$115$	46194.0			0.325718
$116$		0			0
$117$	89823.4	+	75370.8i	0.606632	+	0.509024i
$118$		0			0
$119$	−62394.5	+	22709.7i	−0.403905	+	0.147009i
$120$		0			0
$121$	−22260.4	−	38556.2i	−0.138220	−	0.239403i
$122$		0			0
$123$	2330.46	+	13216.7i	0.0138893	+	0.0787700i
$124$		0			0
$125$	40375.3	−	69932.1i	0.231122	−	0.400315i
$126$		0			0
$127$	245301.	−	205832.i	1.34955	−	1.13241i	0.370492	−	0.928836i	$-0.379189\pi$
$127$	245301.	−	205832.i	1.34955	−	1.13241i	0.979060	−	0.203573i	$-0.0652553\pi$
$128$		0			0
$129$	−17355.1	−	6316.76i	−0.0918235	−	0.0334210i
$130$		0			0
$131$	−14599.3	+	82797.0i	−0.0743285	+	0.421538i	0.924825	+	0.380393i	$0.124211\pi$
$131$	−14599.3	+	82797.0i	−0.0743285	+	0.421538i	−0.999153	+	0.0411443i	$0.986900\pi$
$132$		0			0
$133$	−113682.	+	65383.7i	−0.557264	+	0.320509i
$134$		0			0
$135$	981.065	−	5563.90i	0.00463301	−	0.0262751i
$136$		0			0
$137$	6618.08	+	2408.78i	0.0301252	+	0.0109647i	0.357039	−	0.934090i	$-0.383786\pi$
$137$	6618.08	+	2408.78i	0.0301252	+	0.0109647i	−0.326914	+	0.945054i	$0.606009\pi$
$138$		0			0
$139$	151353.	−	127001.i	0.664439	−	0.557531i	−0.246974	−	0.969022i	$-0.579436\pi$
$139$	151353.	−	127001.i	0.664439	−	0.557531i	0.911414	+	0.411491i	$0.134992\pi$
$140$		0			0
$141$	2424.85	−	4199.97i	0.0102716	−	0.0177909i
$142$		0			0
$143$	−38111.3	−	216140.i	−0.155853	−	0.883884i
$144$		0			0
$145$	−41474.7	−	71836.2i	−0.163818	−	0.283742i
$146$		0			0
$147$	−8114.56	+	2953.46i	−0.0309722	+	0.0112729i
$148$		0			0
$149$	−58362.3	−	48971.7i	−0.215361	−	0.180709i	0.528725	−	0.848793i	$-0.322670\pi$
$149$	−58362.3	−	48971.7i	−0.215361	−	0.180709i	−0.744086	+	0.668084i	$0.767115\pi$
$150$		0			0
$151$	319845.			1.14156			0.570778	−	0.821105i	$-0.306642\pi$
$151$	319845.			1.14156			0.570778	+	0.821105i	$0.306642\pi$
$152$		0			0
$153$	192989.			0.666506
$154$		0			0
$155$	−16628.9	−	13953.3i	−0.0555947	−	0.0466495i
$156$		0			0
$157$	498916.	−	181591.i	1.61539	−	0.587956i	0.632898	−	0.774235i	$-0.281865\pi$
$157$	498916.	−	181591.i	1.61539	−	0.587956i	0.982497	+	0.186280i	$0.0596431\pi$
$158$		0			0
$159$	−9009.40	−	15604.7i	−0.0282620	−	0.0489512i
$160$		0			0
$161$	−50279.4	−	285149.i	−0.152871	−	0.866976i
$162$		0			0
$163$	−159204.	+	275749.i	−0.469337	+	0.812915i	−0.999385	−	0.0350522i	$-0.988840\pi$
$163$	−159204.	+	275749.i	−0.469337	+	0.812915i	0.530049	+	0.847967i	$0.322174\pi$
$164$		0			0
$165$	−4044.02	+	3393.33i	−0.0115639	+	0.00970324i
$166$		0			0
$167$	−424782.	−	154608.i	−1.17862	−	0.428984i	−0.322907	−	0.946431i	$-0.604660\pi$
$167$	−424782.	−	154608.i	−1.17862	−	0.428984i	−0.855715	+	0.517447i	$0.826882\pi$
$168$		0			0
$169$	−23785.6	+	134895.i	−0.0640615	+	0.363311i
$170$		0			0
$171$	375487.	−	65568.5i	0.981985	−	0.171477i
$172$		0			0
$173$	65648.1	−	372309.i	0.166766	−	0.945776i	−0.780459	−	0.625207i	$-0.785015\pi$
$173$	65648.1	−	372309.i	0.166766	−	0.945776i	0.947225	−	0.320569i	$-0.103874\pi$
$174$		0			0
$175$	−230890.	−	84037.2i	−0.569916	−	0.207432i
$176$		0			0
$177$	−26294.7	+	22063.9i	−0.0630863	+	0.0529357i
$178$		0			0
$179$	−52850.8	+	91540.2i	−0.123287	+	0.213540i	−0.921062	−	0.389415i	$-0.872677\pi$
$179$	−52850.8	+	91540.2i	−0.123287	+	0.213540i	0.797775	+	0.602956i	$0.206010\pi$
$180$		0			0
$181$	128043.	+	726167.i	0.290509	+	1.64756i	0.684917	+	0.728621i	$0.259838\pi$
$181$	128043.	+	726167.i	0.290509	+	1.64756i	−0.394409	+	0.918935i	$0.629051\pi$
$182$		0			0
$183$	11595.2	+	20083.5i	0.0255948	+	0.0443315i
$184$		0			0
$185$	52066.5	−	18950.6i	0.111848	−	0.0407094i
$186$		0			0
$187$	−276716.	−	232192.i	−0.578669	−	0.485561i
$188$		0			0
$189$	−35412.9			−0.0721120
$190$		0			0
$191$	−133895.			−0.265571			−0.132786	−	0.991145i	$-0.542392\pi$
$191$	−133895.			−0.265571			−0.132786	+	0.991145i	$0.542392\pi$
$192$		0			0
$193$	38799.9	+	32557.0i	0.0749787	+	0.0629146i	0.679507	−	0.733669i	$-0.262194\pi$
$193$	38799.9	+	32557.0i	0.0749787	+	0.0629146i	−0.604528	+	0.796584i	$0.706638\pi$
$194$		0			0
$195$	−5296.21	+	1927.66i	−0.00997421	+	0.00363032i
$196$		0			0
$197$	−99526.8	−	172385.i	−0.182715	−	0.316472i	0.760089	−	0.649819i	$-0.225155\pi$
$197$	−99526.8	−	172385.i	−0.182715	−	0.316472i	−0.942804	+	0.333347i	$0.891822\pi$
$198$		0			0
$199$	137507.	+	779840.i	0.246145	+	1.39596i	0.817818	+	0.575477i	$0.195184\pi$
$199$	137507.	+	779840.i	0.246145	+	1.39596i	−0.571673	+	0.820482i	$0.693705\pi$
$200$		0			0
$201$	1828.43	−	3166.93i	0.00319218	−	0.00552902i
$202$		0			0
$203$	−398291.	+	334206.i	−0.678361	+	0.569212i
$204$		0			0
$205$	191485.	+	69695.0i	0.318237	+	0.115829i
$206$		0			0
$207$	−146138.	+	828788.i	−0.237048	+	1.34437i
$208$		0			0
$209$	−617278.	−	357748.i	−0.977497	−	0.566515i
$210$		0			0
$211$	21074.4	−	119519.i	0.0325874	−	0.184812i	−0.964169	−	0.265288i	$-0.914533\pi$
$211$	21074.4	−	119519.i	0.0325874	−	0.184812i	0.996757	+	0.0804760i	$0.0256440\pi$
$212$		0			0
$213$	−30836.8	−	11223.7i	−0.0465716	−	0.0169507i
$214$		0			0
$215$	−214820.	+	180255.i	−0.316941	+	0.265945i
$216$		0			0
$217$	−68032.0	+	117835.i	−0.0980762	+	0.169873i
$218$		0			0
$219$	−4824.48	−	27361.0i	−0.00679735	−	0.0385497i
$220$		0			0
$221$	−192828.	−	333989.i	−0.265577	−	0.459993i
$222$		0			0
$223$	13860.1	−	5044.66i	0.0186640	−	0.00679313i	−0.332671	−	0.943043i	$-0.607950\pi$
$223$	13860.1	−	5044.66i	0.0186640	−	0.00679313i	0.351335	+	0.936250i	$0.385728\pi$
$224$		0			0
$225$	547074.	+	459050.i	0.720427	+	0.604510i
$226$		0			0
$227$	−1.11830e6			−1.44044			−0.720218	−	0.693748i	$-0.755958\pi$
$227$	−1.11830e6			−1.44044			−0.720218	+	0.693748i	$0.755958\pi$
$228$		0			0
$229$	846872.			1.06716			0.533579	−	0.845750i	$-0.320847\pi$
$229$	846872.			1.06716			0.533579	+	0.845750i	$0.320847\pi$
$230$		0			0
$231$	25348.2	+	21269.7i	0.0312548	+	0.0262259i
$232$		0			0
$233$	307002.	−	111740.i	0.370469	−	0.134840i	−0.150075	−	0.988675i	$-0.547951\pi$
$233$	307002.	−	111740.i	0.370469	−	0.134840i	0.520544	+	0.853835i	$0.325729\pi$
$234$		0			0
$235$	−36818.2	−	63771.0i	−0.0434904	−	0.0753276i
$236$		0			0
$237$	−5254.47	−	29799.6i	−0.00607657	−	0.0344619i
$238$		0			0
$239$	−383103.	+	663554.i	−0.433831	+	0.751418i	−0.997199	−	0.0747881i	$-0.976172\pi$
$239$	−383103.	+	663554.i	−0.433831	+	0.751418i	0.563368	+	0.826206i	$0.309505\pi$
$240$		0			0
$241$	−898627.	+	754037.i	−0.996636	+	0.836277i	−0.986515	−	0.163672i	$-0.947666\pi$
$241$	−898627.	+	754037.i	−0.996636	+	0.836277i	−0.0101213	+	0.999949i	$0.503222\pi$
$242$		0			0
$243$	145158.	+	52833.0i	0.157697	+	0.0573971i
$244$		0			0
$245$	−22768.1	+	129124.i	−0.0242333	+	0.137434i
$246$		0			0
$247$	−488648.	−	584308.i	−0.509629	−	0.609396i
$248$		0			0
$249$	−623.915	+	3538.40i	−0.000637716	+	0.00361667i
$250$		0			0
$251$	259043.	+	94283.8i	0.259530	+	0.0944611i	0.468508	−	0.883459i	$-0.344792\pi$
$251$	259043.	+	94283.8i	0.259530	+	0.0944611i	−0.208978	+	0.977920i	$0.567014\pi$
$252$		0			0
$253$	1.20669e6	−	1.01253e6i	1.18520	−	0.994504i
$254$		0			0
$255$	−4638.16	+	8033.54i	−0.00446679	+	0.00773671i
$256$		0			0
$257$	−91681.0	−	519949.i	−0.0865858	−	0.491052i	−0.997003	−	0.0773614i	$-0.975350\pi$
$257$	−91681.0	−	519949.i	−0.0865858	−	0.491052i	0.910417	−	0.413691i	$-0.135761\pi$
$258$		0			0
$259$	−173651.	−	300772.i	−0.160852	−	0.278604i
$260$		0			0
$261$	1.42005e6	−	516857.i	1.29034	−	0.469645i
$262$		0			0
$263$	277869.	+	233160.i	0.247714	+	0.207857i	0.758187	−	0.652037i	$-0.226085\pi$
$263$	277869.	+	233160.i	0.247714	+	0.207857i	−0.510473	+	0.859894i	$0.670530\pi$
$264$		0			0
$265$	−273592.			−0.239325
$266$		0			0
$267$	92400.4			0.0793223
$268$		0			0
$269$	524178.	+	439838.i	0.441670	+	0.370606i	0.836334	−	0.548220i	$-0.184694\pi$
$269$	524178.	+	439838.i	0.441670	+	0.370606i	−0.394664	+	0.918826i	$0.629139\pi$
$270$		0			0
$271$	746656.	−	271760.i	0.617586	−	0.224783i	−0.0142335	−	0.999899i	$-0.504531\pi$
$271$	746656.	−	271760.i	0.617586	−	0.224783i	0.631819	+	0.775116i	$0.282309\pi$
$272$		0			0
$273$	17663.8	+	30594.5i	0.0143442	+	0.0248449i
$274$		0			0
$275$	−232119.	−	1.31641e6i	−0.185088	−	1.04969i
$276$		0			0
$277$	1.09292e6	−	1.89300e6i	0.855836	−	1.48235i	−0.0200322	−	0.999799i	$-0.506377\pi$
$277$	1.09292e6	−	1.89300e6i	0.855836	−	1.48235i	0.875868	−	0.482551i	$-0.160290\pi$
$278$		0			0
$279$	302949.	−	254204.i	0.233001	−	0.195511i
$280$		0			0
$281$	−2.40001e6	−	873532.i	−1.81321	−	0.659953i	−0.996566	−	0.0828074i	$-0.973611\pi$
$281$	−2.40001e6	−	873532.i	−1.81321	−	0.659953i	−0.816641	−	0.577146i	$-0.804166\pi$
$282$		0			0
$283$	−230484.	+	1.30714e6i	−0.171070	+	0.970189i	0.771512	+	0.636215i	$0.219501\pi$
$283$	−230484.	+	1.30714e6i	−0.171070	+	0.970189i	−0.942582	+	0.333974i	$0.891610\pi$
$284$		0			0
$285$	−6294.79	+	17206.2i	−0.00459059	+	0.0125480i
$286$		0			0
$287$	221796.	−	1.25787e6i	0.158946	−	0.901427i
$288$		0			0
$289$	737766.	+	268525.i	0.519606	+	0.189121i
$290$		0			0
$291$	63908.4	−	53625.5i	0.0442410	−	0.0371226i
$292$		0			0
$293$	−561017.	+	971710.i	−0.381775	+	0.661253i	−0.991316	−	0.131501i	$-0.958020\pi$
$293$	−561017.	+	971710.i	−0.381775	+	0.661253i	0.609541	+	0.792754i	$0.291354\pi$
$294$		0			0
$295$	90502.9	+	513267.i	0.0605491	+	0.343391i
$296$		0			0
$297$	−96327.9	−	166845.i	−0.0633667	−	0.109754i
$298$		0			0
$299$	1.58033e6	−	575191.i	1.02228	−	0.372078i
$300$		0			0
$301$	1.34651e6	+	1.12985e6i	0.856627	+	0.718796i
$302$		0			0
$303$	42179.1			0.0263931
$304$		0			0
$305$	352117.			0.216739
$306$		0			0
$307$	1.39789e6	+	1.17297e6i	0.846502	+	0.710299i	0.959016	−	0.283351i	$-0.0914461\pi$
$307$	1.39789e6	+	1.17297e6i	0.846502	+	0.710299i	−0.112515	+	0.993650i	$0.535891\pi$
$308$		0			0
$309$	78472.9	−	28561.8i	0.0467545	−	0.0170172i
$310$		0			0
$311$	−869763.	−	1.50647e6i	−0.509918	−	0.883203i	−0.999934	−	0.0114901i	$-0.996343\pi$
$311$	−869763.	−	1.50647e6i	−0.509918	−	0.883203i	0.490016	−	0.871713i	$-0.336991\pi$
$312$		0			0
$313$	−69691.3	−	395239.i	−0.0402085	−	0.228034i	0.958081	−	0.286497i	$-0.0924909\pi$
$313$	−69691.3	−	395239.i	−0.0402085	−	0.228034i	−0.998290	+	0.0584637i	$0.981380\pi$
$314$		0			0
$315$	−134212.	+	232463.i	−0.0762107	+	0.132001i
$316$		0			0
$317$	864165.	−	725121.i	0.483002	−	0.405287i	−0.368509	−	0.929624i	$-0.620132\pi$
$317$	864165.	−	725121.i	0.483002	−	0.405287i	0.851510	+	0.524338i	$0.175687\pi$
$318$		0			0
$319$	−2.65799e6	−	967428.i	−1.46243	−	0.532282i
$320$		0			0
$321$	−8425.19	+	47781.6i	−0.00456370	+	0.0258820i
$322$		0			0
$323$	−1.23426e6	−	219739.i	−0.658265	−	0.117193i
$324$		0			0
$325$	247817.	−	1.40544e6i	0.130144	−	0.738081i
$326$		0			0
$327$	37879.4	+	13787.0i	0.0195900	+	0.00713017i
$328$		0			0
$329$	−353574.	+	296684.i	−0.180091	+	0.151114i
$330$		0			0
$331$	−1.48398e6	+	2.57033e6i	−0.744489	+	1.28949i	0.205945	+	0.978564i	$0.433973\pi$
$331$	−1.48398e6	+	2.57033e6i	−0.744489	+	1.28949i	−0.950433	+	0.310928i	$0.899360\pi$
$332$		0			0
$333$	175287.	+	994100.i	0.0866240	+	0.491269i
$334$		0			0
$335$	−27762.3	−	48085.7i	−0.0135158	−	0.0234101i
$336$		0			0
$337$	−2.38540e6	+	868214.i	−1.14416	+	0.416440i	−0.843414	−	0.537265i	$-0.819458\pi$
$337$	−2.38540e6	+	868214.i	−1.14416	+	0.416440i	−0.300745	+	0.953704i	$0.597235\pi$
$338$		0			0
$339$	95186.2	+	79870.7i	0.0449857	+	0.0377475i
$340$		0			0
$341$	−740224.			−0.344729
$342$		0			0
$343$	2.22257e6			1.02005
$344$		0			0
$345$	−30987.7	−	26001.8i	−0.0140166	−	0.0117613i
$346$		0			0
$347$	3.57211e6	−	1.30014e6i	1.59258	−	0.579652i	0.614690	−	0.788769i	$-0.289281\pi$
$347$	3.57211e6	−	1.30014e6i	1.59258	−	0.579652i	0.977891	+	0.209116i	$0.0670588\pi$
$348$		0			0
$349$	386343.	+	669165.i	0.169789	+	0.294083i	0.938346	−	0.345699i	$-0.112358\pi$
$349$	386343.	+	669165.i	0.169789	+	0.294083i	−0.768557	+	0.639782i	$0.779025\pi$
$350$		0			0
$351$	−35716.8	−	202560.i	−0.0154741	−	0.0877579i
$352$		0			0
$353$	−2.03191e6	+	3.51937e6i	−0.867895	+	1.50324i	−0.00375215	+	0.999993i	$0.501194\pi$
$353$	−2.03191e6	+	3.51937e6i	−0.867895	+	1.50324i	−0.864143	+	0.503246i	$0.832139\pi$
$354$		0			0
$355$	−381694.	+	320279.i	−0.160748	+	0.134883i
$356$		0			0
$357$	54638.1	+	19886.7i	0.0226895	+	0.00825831i
$358$		0			0
$359$	−774844.	+	4.39436e6i	−0.317306	+	1.79953i	0.241682	+	0.970355i	$0.422301\pi$
$359$	−774844.	+	4.39436e6i	−0.317306	+	1.79953i	−0.558988	+	0.829176i	$0.688810\pi$
$360$		0			0
$361$	−2.47609e6	−	8188.78i	−0.999995	−	0.00330713i
$362$		0			0
$363$	−6769.91	+	38394.1i	−0.00269660	+	0.0152932i
$364$		0			0
$365$	−396409.	−	144281.i	−0.155744	−	0.0566862i
$366$		0			0
$367$	2.45612e6	−	2.06093e6i	0.951883	−	0.798725i	−0.0277306	−	0.999615i	$-0.508828\pi$
$367$	2.45612e6	−	2.06093e6i	0.951883	−	0.798725i	0.979614	+	0.200891i	$0.0643836\pi$
$368$		0			0
$369$	−1.85621e6	+	3.21504e6i	−0.709676	+	1.22919i
$370$		0			0
$371$	297788.	+	1.68884e6i	0.112324	+	0.637022i
$372$		0			0
$373$	−1.59428e6	−	2.76137e6i	−0.593325	−	1.02767i	−0.993781	−	0.111353i	$-0.964482\pi$
$373$	−1.59428e6	−	2.76137e6i	−0.593325	−	1.02767i	0.400456	−	0.916316i	$-0.368852\pi$
$374$		0			0
$375$	−66447.9	+	24185.1i	−0.0244008	+	0.00888115i
$376$		0			0
$377$	−2.31335e6	−	1.94113e6i	−0.838278	−	0.703399i
$378$		0			0
$379$	−2.33738e6			−0.835857			−0.417928	−	0.908480i	$-0.637244\pi$
$379$	−2.33738e6			−0.835857			−0.417928	+	0.908480i	$0.637244\pi$
$380$		0			0
$381$	−280411.			−0.0989651
$382$		0			0
$383$	2.05330e6	+	1.72293e6i	0.715247	+	0.600164i	0.926066	−	0.377361i	$-0.123169\pi$
$383$	2.05330e6	+	1.72293e6i	0.715247	+	0.600164i	−0.210819	+	0.977525i	$0.567613\pi$
$384$		0			0
$385$	472124.	−	171839.i	0.162332	−	0.0590841i
$386$		0			0
$387$	−2.55444e6	−	4.42443e6i	−0.866999	−	1.50169i
$388$		0			0
$389$	846388.	+	4.80011e6i	0.283593	+	1.60834i	0.710268	+	0.703931i	$0.248574\pi$
$389$	846388.	+	4.80011e6i	0.283593	+	1.60834i	−0.426675	+	0.904405i	$0.640315\pi$
$390$		0			0
$391$	1.38397e6	−	2.39711e6i	0.457810	−	0.792951i
$392$		0			0
$393$	56398.4	−	47323.9i	0.0184198	−	0.0154561i
$394$		0			0
$395$	−431740.	−	157141.i	−0.139229	−	0.0506752i
$396$		0			0
$397$	−881237.	+	4.99774e6i	−0.280619	+	1.59147i	0.439910	+	0.898042i	$0.355010\pi$
$397$	−881237.	+	4.99774e6i	−0.280619	+	1.59147i	−0.720529	+	0.693425i	$0.756101\pi$
$398$		0			0
$399$	113063.	+	20128.8i	0.0355539	+	0.00632975i
$400$		0			0
$401$	579046.	−	3.28393e6i	0.179826	−	1.01984i	−0.752599	−	0.658479i	$-0.771200\pi$
$401$	579046.	−	3.28393e6i	0.179826	−	1.01984i	0.932425	−	0.361364i	$-0.117689\pi$
$402$		0			0
$403$	−742625.	−	270293.i	−0.227775	−	0.0829035i
$404$		0			0
$405$	595754.	−	499897.i	0.180480	−	0.151441i
$406$		0			0
$407$	944706.	−	1.63628e6i	0.282690	−	0.489634i
$408$		0			0
$409$	538031.	+	3.05132e6i	0.159037	+	0.901945i	0.955001	+	0.296601i	$0.0958532\pi$
$409$	538031.	+	3.05132e6i	0.159037	+	0.901945i	−0.795964	+	0.605344i	$0.793036\pi$
$410$		0			0
$411$	−3083.66	−	5341.05i	−0.000900454	−	0.00155963i
$412$		0			0
$413$	3.06981e6	−	1.11732e6i	0.885599	−	0.322332i
$414$		0			0
$415$	41791.4	+	35067.2i	0.0119115	+	0.00999494i
$416$		0			0
$417$	−173017.			−0.0487246
$418$		0			0
$419$	5.22406e6			1.45370			0.726848	−	0.686799i	$-0.240985\pi$
$419$	5.22406e6			1.45370			0.726848	+	0.686799i	$0.240985\pi$
$420$		0			0
$421$	3.66828e6	+	3.07805e6i	1.00869	+	0.846391i	0.988164	−	0.153398i	$-0.0490218\pi$
$421$	3.66828e6	+	3.07805e6i	1.00869	+	0.846391i	0.0205250	+	0.999789i	$0.493466\pi$
$422$		0			0
$423$	1.26062e6	−	458829.i	0.342558	−	0.124681i
$424$		0			0
$425$	−1.17443e6	−	2.03417e6i	−0.315395	−	0.546281i
$426$		0			0
$427$	−383258.	−	2.17356e6i	−0.101724	−	0.576903i
$428$		0			0
$429$	−96095.6	+	166443.i	−0.0252093	+	0.0436638i
$430$		0			0
$431$	−2.90633e6	+	2.43870e6i	−0.753619	+	0.632361i	−0.936457	−	0.350782i	$-0.885916\pi$
$431$	−2.90633e6	+	2.43870e6i	−0.753619	+	0.632361i	0.182838	+	0.983143i	$0.441471\pi$
$432$		0			0
$433$	−6.84218e6	−	2.49035e6i	−1.75378	−	0.638323i	−0.753951	−	0.656931i	$-0.771854\pi$
$433$	−6.84218e6	−	2.49035e6i	−1.75378	−	0.638323i	−0.999827	+	0.0186076i	$0.994077\pi$
$434$		0			0
$435$	−12613.4	+	71534.3i	−0.00319602	+	0.0181255i
$436$		0			0
$437$	1.87829e6	−	5.13412e6i	0.470499	−	1.28606i
$438$		0			0
$439$	341451.	−	1.93647e6i	0.0845604	−	0.479566i	−0.912890	−	0.408205i	$-0.866155\pi$
$439$	341451.	−	1.93647e6i	0.0845604	−	0.479566i	0.997451	−	0.0713607i	$-0.0227341\pi$
$440$		0			0
$441$	−2.24465e6	−	816986.i	−0.549607	−	0.200041i
$442$		0			0
$443$	1.51850e6	−	1.27418e6i	0.367626	−	0.308475i	−0.440196	−	0.897902i	$-0.645091\pi$
$443$	1.51850e6	−	1.27418e6i	0.367626	−	0.308475i	0.807822	+	0.589427i	$0.200646\pi$
$444$		0			0
$445$	701490.	−	1.21502e6i	0.167927	−	0.290859i
$446$		0			0
$447$	11585.1	+	65702.1i	0.00274239	+	0.0155529i
$448$		0			0
$449$	−1.58316e6	−	2.74211e6i	−0.370603	−	0.641903i	0.619055	−	0.785347i	$-0.287516\pi$
$449$	−1.58316e6	−	2.74211e6i	−0.370603	−	0.641903i	−0.989658	+	0.143444i	$0.954182\pi$
$450$		0			0
$451$	6.52965e6	−	2.37660e6i	1.51164	−	0.550192i
$452$		0			0
$453$	−214557.	−	180035.i	−0.0491245	−	0.0412203i
$454$		0			0
$455$	536403.			0.121468
$456$		0			0
$457$	1.76366e6			0.395025			0.197512	−	0.980300i	$-0.436714\pi$
$457$	1.76366e6			0.395025			0.197512	+	0.980300i	$0.436714\pi$
$458$		0			0
$459$	−259330.	−	217604.i	−0.0574541	−	0.0482098i
$460$		0			0
$461$	6.22908e6	−	2.26720e6i	1.36512	−	0.496864i	0.447487	−	0.894290i	$-0.352319\pi$
$461$	6.22908e6	−	2.26720e6i	1.36512	−	0.496864i	0.917634	+	0.397427i	$0.130097\pi$
$462$		0			0
$463$	1.32607e6	+	2.29682e6i	0.287484	+	0.497937i	0.973209	−	0.229924i	$-0.0738479\pi$
$463$	1.32607e6	+	2.29682e6i	0.287484	+	0.497937i	−0.685725	+	0.727861i	$0.740515\pi$
$464$		0			0
$465$	3300.87	+	18720.2i	0.000707940	+	0.00401493i
$466$		0			0
$467$	−958220.	+	1.65969e6i	−0.203317	+	0.352155i	−0.949595	−	0.313479i	$-0.898505\pi$
$467$	−958220.	+	1.65969e6i	−0.203317	+	0.352155i	0.746278	+	0.665634i	$0.231839\pi$
$468$		0			0
$469$	−266608.	+	223711.i	−0.0559682	+	0.0469629i
$470$		0			0
$471$	−436896.	−	159017.i	−0.0907455	−	0.0330287i
$472$		0			0
$473$	−1.66052e6	+	9.41729e6i	−0.341265	+	1.93541i
$474$		0			0
$475$	−2.97614e6	−	3.55876e6i	−0.605228	−	0.723709i
$476$		0			0
$477$	865526.	−	4.90864e6i	0.174174	−	0.987791i
$478$		0			0
$479$	4.02793e6	+	1.46605e6i	0.802127	+	0.291950i	0.710367	−	0.703831i	$-0.248529\pi$
$479$	4.02793e6	+	1.46605e6i	0.802127	+	0.291950i	0.0917592	+	0.995781i	$0.470751\pi$
$480$		0			0
$481$	1.54526e6	−	1.29663e6i	0.304536	−	0.255536i
$482$		0			0
$483$	−126777.	+	219584.i	−0.0247270	+	0.0428285i
$484$		0			0
$485$	−219964.	−	1.24748e6i	−0.0424617	−	0.240812i
$486$		0			0
$487$	−4.04172e6	−	7.00046e6i	−0.772225	−	1.33753i	−0.936341	−	0.351091i	$-0.885811\pi$
$487$	−4.04172e6	−	7.00046e6i	−0.772225	−	1.33753i	0.164117	−	0.986441i	$-0.447523\pi$
$488$		0			0
$489$	262011.	−	95364.1i	0.0495504	−	0.0180349i
$490$		0			0
$491$	6.05314e6	+	5.07918e6i	1.13312	+	0.950802i	0.999192	−	0.0401884i	$-0.0127958\pi$
$491$	6.05314e6	+	5.07918e6i	1.13312	+	0.950802i	0.133930	+	0.990991i	$0.457240\pi$
$492$		0			0
$493$	−4.97032e6			−0.921015
$494$		0			0
$495$	−1.46030e6			−0.267874
$496$		0			0
$497$	2.39249e6	+	2.00753e6i	0.434469	+	0.364563i
$498$		0			0
$499$	−1.31951e6	+	480264.i	−0.237226	+	0.0863433i	−0.457898	−	0.889005i	$-0.651397\pi$
$499$	−1.31951e6	+	480264.i	−0.237226	+	0.0863433i	0.220671	+	0.975348i	$0.429175\pi$
$500$		0			0
$501$	197925.	+	342816.i	0.0352294	+	0.0610192i
$502$		0			0
$503$	25080.2	+	142237.i	0.00441988	+	0.0250664i	0.986938	−	0.161101i	$-0.0515045\pi$
$503$	25080.2	+	142237.i	0.00441988	+	0.0250664i	−0.982518	+	0.186167i	$0.940393\pi$
$504$		0			0
$505$	320217.	−	554633.i	0.0558749	−	0.0967781i
$506$		0			0
$507$	91885.6	−	77101.2i	0.0158755	−	0.0133211i
$508$		0			0
$509$	−2.86479e6	−	1.04270e6i	−0.490115	−	0.178387i	0.0851275	−	0.996370i	$-0.472870\pi$
$509$	−2.86479e6	−	1.04270e6i	−0.490115	−	0.178387i	−0.575243	+	0.817983i	$0.695092\pi$
$510$		0			0
$511$	−459158.	+	2.60401e6i	−0.0777875	+	0.441155i
$512$		0			0
$513$	−578495.	−	335271.i	−0.0970524	−	0.0562474i
$514$		0			0
$515$	220182.	−	1.24871e6i	0.0365817	−	0.207465i
$516$		0			0
$517$	−2.35957e6	−	858814.i	−0.388246	−	0.141310i
$518$		0			0
$519$	−253604.	+	212799.i	−0.0413273	+	0.0346777i
$520$		0			0
$521$	−4.27482e6	+	7.40421e6i	−0.689960	+	1.19505i	0.281891	+	0.959446i	$0.409038\pi$
$521$	−4.27482e6	+	7.40421e6i	−0.689960	+	1.19505i	−0.971850	+	0.235599i	$0.924295\pi$
$522$		0			0
$523$	28953.3	+	164203.i	0.00462854	+	0.0262498i	0.987035	−	0.160508i	$-0.0513132\pi$
$523$	28953.3	+	164203.i	0.00462854	+	0.0262498i	−0.982406	+	0.186758i	$0.940202\pi$
$524$		0			0
$525$	107582.	+	186338.i	0.0170350	+	0.0295055i
$526$		0			0
$527$	−1.22227e6	+	444869.i	−0.191708	+	0.0697759i
$528$		0			0
$529$	4.31584e6	+	3.62142e6i	0.670543	+	0.562652i
$530$		0			0
$531$	−9.49507e6			−1.46138
$532$		0			0
$533$	7.41864e6			1.13111
$534$		0			0
$535$	564341.	+	473538.i	0.0852426	+	0.0715271i
$536$		0			0
$537$	86979.5	−	31658.0i	0.0130161	−	0.00473748i
$538$		0			0
$539$	2.23553e6	+	3.87206e6i	0.331443	+	0.574077i
$540$		0			0
$541$	123319.	+	699379.i	0.0181150	+	0.102735i	0.992525	−	0.122044i	$-0.0389450\pi$
$541$	123319.	+	699379.i	0.0181150	+	0.102735i	−0.974410	+	0.224779i	$0.927834\pi$
$542$		0			0
$543$	322853.	−	559198.i	0.0469900	−	0.0813891i
$544$		0			0
$545$	468867.	−	393426.i	0.0676174	−	0.0567377i
$546$		0			0
$547$	−9.91073e6	−	3.60721e6i	−1.41624	−	0.515470i	−0.483287	−	0.875462i	$-0.660557\pi$
$547$	−9.91073e6	−	3.60721e6i	−1.41624	−	0.515470i	−0.932955	+	0.359992i	$0.882779\pi$
$548$		0			0
$549$	−1.11394e6	+	6.31749e6i	−0.157737	+	0.894569i
$550$		0			0
$551$	−9.67045e6	+	1.68868e6i	−1.35696	+	0.236956i
$552$		0			0
$553$	−500082.	+	2.83610e6i	−0.0695390	+	0.394375i
$554$		0			0
$555$	−45594.0	−	16594.9i	−0.00628312	−	0.00228687i
$556$		0			0
$557$	3.55158e6	−	2.98013e6i	0.485046	−	0.407002i	−0.367201	−	0.930142i	$-0.619684\pi$
$557$	3.55158e6	−	2.98013e6i	0.485046	−	0.407002i	0.852247	+	0.523139i	$0.175239\pi$
$558$		0			0
$559$	−5.10464e6	+	8.84149e6i	−0.690932	+	1.19673i
$560$		0			0
$561$	54928.9	+	311517.i	0.00736874	+	0.0417902i
$562$		0			0
$563$	5.83893e6	+	1.01133e7i	0.776358	+	1.34469i	0.934028	+	0.357199i	$0.116268\pi$
$563$	5.83893e6	+	1.01133e7i	0.776358	+	1.34469i	−0.157670	+	0.987492i	$0.550398\pi$
$564$		0			0
$565$	1.77290e6	−	645282.i	0.233648	−	0.0850410i
$566$		0			0
$567$	−3.73423e6	−	3.13339e6i	−0.487802	−	0.409315i
$568$		0			0
$569$	−852301.			−0.110360			−0.0551801	−	0.998476i	$-0.517573\pi$
$569$	−852301.			−0.110360			−0.0551801	+	0.998476i	$0.517573\pi$
$570$		0			0
$571$	−2.00050e6			−0.256772			−0.128386	−	0.991724i	$-0.540980\pi$
$571$	−2.00050e6			−0.256772			−0.128386	+	0.991724i	$0.540980\pi$
$572$		0			0
$573$	89819.1	+	75367.2i	0.0114283	+	0.00958949i
$574$		0			0
$575$	9.62505e6	−	3.50323e6i	1.21404	−	0.441875i
$576$		0			0
$577$	−7.36330e6	−	1.27536e7i	−0.920732	−	1.59475i	−0.798285	−	0.602279i	$-0.794259\pi$
$577$	−7.36330e6	−	1.27536e7i	−0.920732	−	1.59475i	−0.122447	−	0.992475i	$-0.539074\pi$
$578$		0			0
$579$	−7701.89	−	43679.6i	−0.000954775	−	0.00541480i
$580$		0			0
$581$	170977.	−	296140.i	0.0210134	−	0.0363963i
$582$		0			0
$583$	−7.14680e6	+	5.99688e6i	−0.870844	+	0.730725i
$584$		0			0
$585$	−1.46504e6	−	533230.i	−0.176994	−	0.0644207i
$586$		0			0
$587$	−138545.	+	785729.i	−0.0165957	+	0.0941191i	−0.991981	−	0.126390i	$-0.959661\pi$
$587$	−138545.	+	785729.i	−0.0165957	+	0.0941191i	0.975385	+	0.220509i	$0.0707719\pi$
$588$		0			0
$589$	−2.22695e6	+	1.28082e6i	−0.264498	+	0.152125i
$590$		0			0
$591$	−30268.4	+	171661.i	−0.00356469	+	0.0202163i
$592$		0			0
$593$	1.02179e7	+	3.71902e6i	1.19323	+	0.434302i	0.860858	−	0.508845i	$-0.169927\pi$
$593$	1.02179e7	+	3.71902e6i	1.19323	+	0.434302i	0.332376	+	0.943147i	$0.392150\pi$
$594$		0			0
$595$	676304.	−	567486.i	0.0783158	−	0.0657147i
$596$		0			0
$597$	346716.	−	600529.i	0.0398142	−	0.0689602i
$598$		0			0
$599$	1.27275e6	+	7.21814e6i	0.144936	+	0.821975i	0.967418	+	0.253183i	$0.0814776\pi$
$599$	1.27275e6	+	7.21814e6i	0.144936	+	0.821975i	−0.822482	+	0.568791i	$0.807411\pi$
$600$		0			0
$601$	−1.14394e6	−	1.98137e6i	−0.129187	−	0.223758i	0.794175	−	0.607689i	$-0.207903\pi$
$601$	−1.14394e6	−	1.98137e6i	−0.129187	−	0.223758i	−0.923362	+	0.383931i	$0.874570\pi$
$602$		0			0
$603$	950555.	−	345974.i	0.106459	−	0.0387480i
$604$		0			0
$605$	453466.	+	380503.i	0.0503682	+	0.0422639i
$606$		0			0
$607$	1.03568e7			1.14091			0.570457	−	0.821328i	$-0.306766\pi$
$607$	1.03568e7			1.14091			0.570457	+	0.821328i	$0.306766\pi$
$608$		0			0
$609$	455299.			0.0497455
$610$		0			0
$611$	−2.05363e6	−	1.72320e6i	−0.222545	−	0.186738i
$612$		0			0
$613$	8.70279e6	−	3.16756e6i	0.935422	−	0.340466i	0.171065	−	0.985260i	$-0.445279\pi$
$613$	8.70279e6	−	3.16756e6i	0.935422	−	0.340466i	0.764356	+	0.644794i	$0.223057\pi$
$614$		0			0
$615$	−89221.5	−	154536.i	−0.00951222	−	0.0164756i
$616$		0			0
$617$	−2.75913e6	−	1.56478e7i	−0.291782	−	1.65478i	−0.679999	−	0.733213i	$-0.738020\pi$
$617$	−2.75913e6	−	1.56478e7i	−0.291782	−	1.65478i	0.388217	−	0.921568i	$-0.373091\pi$
$618$		0			0
$619$	−4.67692e6	+	8.10067e6i	−0.490607	+	0.849756i	−0.999942	−	0.0108125i	$-0.996558\pi$
$619$	−4.67692e6	+	8.10067e6i	−0.490607	+	0.849756i	0.509335	+	0.860569i	$0.329892\pi$
$620$		0			0
$621$	1.13087e6	−	948913.i	0.117675	−	0.0987410i
$622$		0			0
$623$	−8.26364e6	−	3.00772e6i	−0.853004	−	0.310468i
$624$		0			0
$625$	1.41341e6	−	8.01583e6i	0.144733	−	0.820821i
$626$		0			0
$627$	212711.	+	587438.i	0.0216083	+	0.0596751i
$628$		0			0
$629$	576519.	−	3.26960e6i	0.0581015	−	0.329510i
$630$		0			0
$631$	−3.12872e6	−	1.13876e6i	−0.312819	−	0.113857i	0.180840	−	0.983513i	$-0.442119\pi$
$631$	−3.12872e6	−	1.13876e6i	−0.312819	−	0.113857i	−0.493659	+	0.869656i	$0.664341\pi$
$632$		0			0
$633$	−81412.1	+	68312.9i	−0.00807569	+	0.00677631i
$634$		0			0
$635$	−2.12884e6	+	3.68725e6i	−0.209512	+	0.362885i
$636$		0			0
$637$	828899.	+	4.70092e6i	0.0809381	+	0.459023i
$638$		0			0
$639$	−4.53877e6	−	7.86137e6i	−0.439730	−	0.761634i
$640$		0			0
$641$	6.25377e6	−	2.27619e6i	0.601169	−	0.218808i	−0.0234657	−	0.999725i	$-0.507470\pi$
$641$	6.25377e6	−	2.27619e6i	0.601169	−	0.218808i	0.624635	+	0.780917i	$0.285248\pi$
$642$		0			0
$643$	−2.00596e6	−	1.68320e6i	−0.191335	−	0.160549i	0.542088	−	0.840322i	$-0.317634\pi$
$643$	−2.00596e6	−	1.68320e6i	−0.191335	−	0.160549i	−0.733423	+	0.679773i	$0.762078\pi$
$644$		0			0
$645$	245567.			0.0232418
$646$		0			0
$647$	9.59789e6			0.901395			0.450698	−	0.892677i	$-0.351175\pi$
$647$	9.59789e6			0.901395			0.450698	+	0.892677i	$0.351175\pi$
$648$		0			0
$649$	1.36145e7	+	1.14239e7i	1.26879	+	1.06464i
$650$		0			0
$651$	111964.	−	40751.6i	0.0103544	−	0.00376870i
$652$		0			0
$653$	−3.49070e6	−	6.04607e6i	−0.320354	−	0.554869i	0.660207	−	0.751083i	$-0.270468\pi$
$653$	−3.49070e6	−	6.04607e6i	−0.320354	−	0.554869i	−0.980561	+	0.196215i	$0.937135\pi$
$654$		0			0
$655$	−194116.	−	1.10089e6i	−0.0176790	−	0.100263i
$656$		0			0
$657$	3.84268e6	−	6.65571e6i	0.347312	−	0.601563i
$658$		0			0
$659$	−1.71116e6	+	1.43584e6i	−0.153489	+	0.128793i	−0.716298	−	0.697794i	$-0.754165\pi$
$659$	−1.71116e6	+	1.43584e6i	−0.153489	+	0.128793i	0.562809	+	0.826587i	$0.309721\pi$
$660$		0			0
$661$	1.34270e7	+	4.88703e6i	1.19530	+	0.435052i	0.861580	−	0.507621i	$-0.169475\pi$
$661$	1.34270e7	+	4.88703e6i	1.19530	+	0.435052i	0.333716	+	0.942674i	$0.391697\pi$
$662$		0			0
$663$	−58643.6	+	332585.i	−0.00518128	+	0.0293845i
$664$		0			0
$665$	1.12304e6	−	1.33390e6i	0.0984783	−	0.116969i
$666$		0			0
$667$	3.76369e6	−	2.13450e7i	0.327567	−	1.85772i
$668$		0			0
$669$	−12137.1	−	4417.56i	−0.00104846	−	0.000381607i
$670$		0			0
$671$	9.19804e6	−	7.71807e6i	0.788659	−	0.661763i
$672$		0			0
$673$	−485113.	+	840241.i	−0.0412862	+	0.0715099i	−0.885930	−	0.463819i	$-0.846479\pi$
$673$	−485113.	+	840241.i	−0.0412862	+	0.0715099i	0.844644	+	0.535329i	$0.179812\pi$
$674$		0			0
$675$	−217535.	−	1.23370e6i	−0.0183768	−	0.104220i
$676$		0			0
$677$	−1.42427e6	−	2.46691e6i	−0.119432	−	0.206862i	0.800111	−	0.599852i	$-0.204774\pi$
$677$	−1.42427e6	−	2.46691e6i	−0.119432	−	0.206862i	−0.919543	+	0.392990i	$0.871441\pi$
$678$		0			0
$679$	−7.46107e6	+	2.71561e6i	−0.621050	+	0.226044i
$680$		0			0
$681$	750174.	+	629471.i	0.0619861	+	0.0520125i
$682$		0			0
$683$	2.98511e6			0.244855			0.122428	−	0.992477i	$-0.460932\pi$
$683$	2.98511e6			0.244855			0.122428	+	0.992477i	$0.460932\pi$
$684$		0			0
$685$	−93642.6			−0.00762513
$686$		0			0
$687$	−568096.	−	476689.i	−0.0459229	−	0.0385339i
$688$		0			0
$689$	−9.35975e6	+	3.40667e6i	−0.751132	+	0.273390i
$690$		0			0
$691$	−2.89550e6	−	5.01515e6i	−0.230690	−	0.399566i	0.727322	−	0.686297i	$-0.240765\pi$
$691$	−2.89550e6	−	5.01515e6i	−0.230690	−	0.399566i	−0.958011	+	0.286731i	$0.907432\pi$
$692$		0			0
$693$	1.58945e6	+	9.01422e6i	0.125723	+	0.713009i
$694$		0			0
$695$	−1.31352e6	+	2.27508e6i	−0.103151	+	0.178663i
$696$		0			0
$697$	9.35352e6	−	7.84854e6i	0.729278	−	0.611937i
$698$		0			0
$699$	−268839.	−	97849.2i	−0.0208113	−	0.00757468i
$700$		0			0
$701$	−460849.	+	2.61361e6i	−0.0354213	+	0.200884i	−0.997383	−	0.0723007i	$-0.976966\pi$
$701$	−460849.	+	2.61361e6i	−0.0354213	+	0.200884i	0.961962	+	0.273185i	$0.0880770\pi$
$702$		0			0
$703$	10843.0	−	6.55735e6i	0.000827489	−	0.500426i
$704$		0			0
$705$	−11197.3	+	63503.0i	−0.000848477	+	0.00481195i
$706$		0			0
$707$	−3.77220e6	−	1.37297e6i	−0.283822	−	0.103303i
$708$		0			0
$709$	−4.91587e6	+	4.12491e6i	−0.367270	+	0.308176i	−0.807680	−	0.589621i	$-0.799277\pi$
$709$	−4.91587e6	+	4.12491e6i	−0.367270	+	0.308176i	0.440411	+	0.897796i	$0.354833\pi$
$710$		0			0
$711$	4.18517e6	−	7.24892e6i	0.310484	−	0.537774i
$712$		0			0
$713$	−984941.	−	5.58588e6i	−0.0725582	−	0.411498i
$714$		0			0
$715$	1.45909e6	+	2.52721e6i	0.106737	+	0.184874i
$716$		0			0
$717$	630495.	−	229481.i	0.0458019	−	0.0166705i
$718$		0			0
$719$	5.48585e6	+	4.60318e6i	0.395751	+	0.332074i	0.818848	−	0.574010i	$-0.194613\pi$
$719$	5.48585e6	+	4.60318e6i	0.395751	+	0.332074i	−0.423098	+	0.906084i	$0.639057\pi$
$720$		0			0
$721$	−7.94777e6			−0.569387
$722$		0			0
$723$	1.02725e6			0.0730852
$724$		0			0
$725$	−1.40896e7	−	1.18226e7i	−0.995527	−	0.835346i
$726$		0			0
$727$	5.77797e6	−	2.10301e6i	0.405452	−	0.147572i	−0.131240	−	0.991351i	$-0.541896\pi$
$727$	5.77797e6	−	2.10301e6i	0.405452	−	0.147572i	0.536692	+	0.843778i	$0.319674\pi$
$728$		0			0
$729$	7.03897e6	+	1.21919e7i	0.490558	+	0.849671i
$730$		0			0
$731$	2.91784e6	+	1.65479e7i	0.201961	+	1.14538i
$732$		0			0
$733$	−1.93293e6	+	3.34793e6i	−0.132879	+	0.230153i	−0.924785	−	0.380490i	$-0.875755\pi$
$733$	−1.93293e6	+	3.34793e6i	−0.132879	+	0.230153i	0.791906	+	0.610643i	$0.209089\pi$
$734$		0			0
$735$	87955.0	−	73803.0i	0.00600540	−	0.00503913i
$736$		0			0
$737$	−1.77920e6	−	647577.i	−0.120658	−	0.0439160i
$738$		0			0
$739$	−3.36659e6	+	1.90929e7i	−0.226766	+	1.28606i	0.632513	+	0.774550i	$0.282024\pi$
$739$	−3.36659e6	+	1.90929e7i	−0.226766	+	1.28606i	−0.859279	+	0.511507i	$0.829088\pi$
$740$		0			0
$741$	−1102.95	+	667015.i	−7.37925e−5	+	0.0446262i
$742$		0			0
$743$	−3.66700e6	+	2.07966e7i	−0.243691	+	1.38204i	0.579823	+	0.814743i	$0.303122\pi$
$743$	−3.66700e6	+	2.07966e7i	−0.243691	+	1.38204i	−0.823514	+	0.567297i	$0.807989\pi$
$744$		0			0
$745$	951900.	+	346463.i	0.0628349	+	0.0228700i
$746$		0			0
$747$	−761366.	+	638862.i	−0.0499220	+	0.0418895i
$748$		0			0
$749$	2.30883e6	−	3.99901e6i	0.150379	−	0.260464i
$750$		0			0
$751$	−418537.	−	2.37364e6i	−0.0270791	−	0.153573i	0.968270	−	0.249906i	$-0.0803998\pi$
$751$	−418537.	−	2.37364e6i	−0.0270791	−	0.153573i	−0.995349	+	0.0963329i	$0.969289\pi$
$752$		0			0
$753$	−120699.	−	209058.i	−0.00775743	−	0.0134363i
$754$		0			0
$755$	−3.99625e6	+	1.45452e6i	−0.255144	+	0.0928648i
$756$		0			0
$757$	−1.35256e7	−	1.13493e7i	−0.857862	−	0.719832i	0.103644	−	0.994614i	$-0.466950\pi$
$757$	−1.35256e7	−	1.13493e7i	−0.857862	−	0.719832i	−0.961506	+	0.274782i	$0.911394\pi$
$758$		0			0
$759$	−1.37940e6			−0.0869132
$760$		0			0
$761$	−1.69543e7			−1.06125			−0.530627	−	0.847605i	$-0.678043\pi$
$761$	−1.69543e7			−1.06125			−0.530627	+	0.847605i	$0.678043\pi$
$762$		0			0
$763$	−2.93889e6	−	2.46602e6i	−0.182756	−	0.153351i
$764$		0			0
$765$	−2.41127e6	+	877630.i	−0.148968	+	0.0542198i
$766$		0			0
$767$	9.48717e6	+	1.64323e7i	0.582302	+	1.00858i
$768$		0			0
$769$	1.33596e6	+	7.57660e6i	0.0814661	+	0.462017i	0.998063	+	0.0622055i	$0.0198134\pi$
$769$	1.33596e6	+	7.57660e6i	0.0814661	+	0.462017i	−0.916597	+	0.399812i	$0.869075\pi$
$770$		0			0
$771$	−231169.	+	400396.i	−0.0140053	+	0.0242579i
$772$		0			0
$773$	−1.79085e7	+	1.50270e7i	−1.07798	+	0.904534i	−0.995752	−	0.0920795i	$-0.970649\pi$
$773$	−1.79085e7	+	1.50270e7i	−1.07798	+	0.904534i	−0.0822298	+	0.996613i	$0.526204\pi$
$774$		0			0
$775$	−4.52299e6	−	1.64623e6i	−0.270503	−	0.0984549i
$776$		0			0
$777$	−52811.2	+	299507.i	−0.00313815	+	0.0177973i
$778$		0			0
$779$	1.55320e7	−	1.84483e7i	0.917032	−	1.08921i
$780$		0			0
$781$	−2.95044e6	+	1.67328e7i	−0.173085	+	0.981612i
$782$		0			0
$783$	−2.49099e6	−	906645.i	−0.145200	−	0.0528485i
$784$		0			0
$785$	−5.40783e6	+	4.53771e6i	−0.313220	+	0.262823i
$786$		0			0
$787$	1.70353e6	−	2.95059e6i	0.0980419	−	0.169814i	−0.812832	−	0.582498i	$-0.802075\pi$
$787$	1.70353e6	−	2.95059e6i	0.0980419	−	0.169814i	0.910874	+	0.412684i	$0.135409\pi$
$788$		0			0
$789$	−55157.6	−	312815.i	−0.00315437	−	0.0178893i
$790$		0			0
$791$	−5.91292e6	−	1.02415e7i	−0.336016	−	0.581998i
$792$		0			0
$793$	1.20461e7	−	4.38443e6i	0.680244	−	0.247588i
$794$		0			0
$795$	183530.	+	154000.i	0.0102989	+	0.00864178i
$796$		0			0
$797$	−1.80191e7			−1.00482			−0.502408	−	0.864631i	$-0.667552\pi$
$797$	−1.80191e7			−1.00482			−0.502408	+	0.864631i	$0.667552\pi$
$798$		0			0
$799$	−4.41229e6			−0.244510
$800$		0			0
$801$	1.95799e7	+	1.64295e7i	1.07828	+	0.904781i
$802$		0			0
$803$	−1.35175e7	+	4.91998e6i	−0.739791	+	0.269262i
$804$		0			0
$805$	1.92494e6	+	3.33410e6i	0.104695	+	0.181338i
$806$		0			0
$807$	−104051.	−	590101.i	−0.00562421	−	0.0318965i
$808$		0			0
$809$	6.50160e6	−	1.12611e7i	0.349260	−	0.604936i	−0.636858	−	0.770981i	$-0.719766\pi$
$809$	6.50160e6	−	1.12611e7i	0.349260	−	0.604936i	0.986118	+	0.166045i	$0.0530997\pi$
$810$		0			0
$811$	1.90637e7	−	1.59963e7i	1.01778	−	0.854021i	0.0284352	−	0.999596i	$-0.490948\pi$
$811$	1.90637e7	−	1.59963e7i	1.01778	−	0.854021i	0.989347	+	0.145575i	$0.0465031\pi$
$812$		0			0
$813$	−653838.	−	237978.i	−0.0346932	−	0.0126273i
$814$		0			0
$815$	735159.	−	4.16929e6i	0.0387692	−	0.219871i
$816$		0			0
$817$	1.12993e7	+	3.12049e7i	0.592236	+	1.63557i
$818$		0			0
$819$	−1.69694e6	+	9.62385e6i	−0.0884011	+	0.501348i
$820$		0			0
$821$	−3.40894e7	−	1.24075e7i	−1.76507	−	0.642432i	−0.765069	−	0.643948i	$-0.777295\pi$
$821$	−3.40894e7	−	1.24075e7i	−1.76507	−	0.642432i	−0.999999	+	0.00151586i	$0.999517\pi$
$822$		0			0
$823$	−1.18333e7	+	9.92935e6i	−0.608986	+	0.511000i	−0.894320	−	0.447428i	$-0.852340\pi$
$823$	−1.18333e7	+	9.92935e6i	−0.608986	+	0.511000i	0.285334	+	0.958428i	$0.407896\pi$
$824$		0			0
$825$	−585275.	+	1.01373e6i	−0.0299382	+	0.0518544i
$826$		0			0
$827$	−1.82459e6	−	1.03478e7i	−0.0927689	−	0.526119i	−0.995408	−	0.0957209i	$-0.969484\pi$
$827$	−1.82459e6	−	1.03478e7i	−0.0927689	−	0.526119i	0.902639	−	0.430398i	$-0.141627\pi$
$828$		0			0
$829$	5.30578e6	+	9.18988e6i	0.268141	+	0.464434i	0.968382	−	0.249473i	$-0.0802574\pi$
$829$	5.30578e6	+	9.18988e6i	0.268141	+	0.464434i	−0.700241	+	0.713907i	$0.746924\pi$
$830$		0			0
$831$	−1.79869e6	+	654668.i	−0.0903551	+	0.0328866i
$832$		0			0
$833$	6.01841e6	+	5.05005e6i	0.300517	+	0.252164i
$834$		0			0
$835$	6.01046e6			0.298326
$836$		0			0
$837$	−693716.			−0.0342269
$838$		0			0
$839$	−5.24644e6	−	4.40228e6i	−0.257312	−	0.215910i	0.505001	−	0.863118i	$-0.331492\pi$
$839$	−5.24644e6	−	4.40228e6i	−0.257312	−	0.215910i	−0.762313	+	0.647208i	$0.775936\pi$
$840$		0			0
$841$	−1.72985e7	+	6.29613e6i	−0.843370	+	0.306962i
$842$		0			0
$843$	1.11827e6	+	1.93690e6i	0.0541974	+	0.0938726i
$844$		0			0
$845$	−316258.	−	1.79359e6i	−0.0152370	−	0.0864134i
$846$		0			0
$847$	1.85522e6	−	3.21333e6i	0.0888559	−	0.153903i
$848$		0			0
$849$	890379.	−	747116.i	0.0423941	−	0.0355729i
$850$		0			0
$851$	1.36047e7	+	4.95171e6i	0.643970	+	0.234386i
$852$		0			0
$853$	1.34155e6	−	7.60830e6i	0.0631297	−	0.358026i	−0.936836	−	0.349768i	$-0.886260\pi$
$853$	1.34155e6	−	7.60830e6i	0.0631297	−	0.358026i	0.999966	−	0.00825789i	$-0.00262860\pi$
$854$		0			0
$855$	−4.39329e6	+	2.52679e6i	−0.205530	+	0.118210i
$856$		0			0
$857$	3.69656e6	−	2.09642e7i	0.171928	−	0.975049i	−0.769703	−	0.638402i	$-0.779596\pi$
$857$	3.69656e6	−	2.09642e7i	0.171928	−	0.975049i	0.941631	−	0.336648i	$-0.109293\pi$
$858$		0			0
$859$	3.26915e7	+	1.18988e7i	1.51165	+	0.550197i	0.959048	−	0.283245i	$-0.0914108\pi$
$859$	3.26915e7	+	1.18988e7i	1.51165	+	0.550197i	0.552607	+	0.833442i	$0.313633\pi$
$860$		0			0
$861$	−856816.	+	718954.i	−0.0393894	+	0.0330517i
$862$		0			0
$863$	2.10284e7	−	3.64223e7i	0.961125	−	1.66472i	0.241441	−	0.970415i	$-0.422380\pi$
$863$	2.10284e7	−	3.64223e7i	0.961125	−	1.66472i	0.719684	−	0.694302i	$-0.244287\pi$
$864$		0			0
$865$	872870.	+	4.95029e6i	0.0396652	+	0.224952i
$866$		0			0
$867$	−343758.	−	595406.i	−0.0155312	−	0.0269008i
$868$		0			0
$869$	−1.47223e7	+	5.35849e6i	−0.661344	+	0.240710i
$870$		0			0
$871$	−1.54851e6	−	1.29935e6i	−0.0691621	−	0.0580339i
$872$		0			0
$873$	2.30774e7			1.02483
$874$		0			0
$875$	6.72988e6			0.297158
$876$		0			0
$877$	−1.92190e7	−	1.61266e7i	−0.843783	−	0.708018i	0.114628	−	0.993408i	$-0.463432\pi$
$877$	−1.92190e7	−	1.61266e7i	−0.843783	−	0.708018i	−0.958411	+	0.285390i	$0.907877\pi$
$878$		0			0
$879$	923298.	−	336053.i	0.0403060	−	0.0146702i
$880$		0			0
$881$	−6.19478e6	−	1.07297e7i	−0.268897	−	0.465744i	0.699680	−	0.714456i	$-0.253326\pi$
$881$	−6.19478e6	−	1.07297e7i	−0.268897	−	0.465744i	−0.968577	+	0.248713i	$0.919993\pi$
$882$		0			0
$883$	−6.13995e6	−	3.48214e7i	−0.265010	−	1.50295i	−0.769005	−	0.639242i	$-0.779248\pi$
$883$	−6.13995e6	−	3.48214e7i	−0.265010	−	1.50295i	0.503995	−	0.863707i	$-0.331863\pi$
$884$		0			0
$885$	228198.	−	395251.i	0.00979386	−	0.0169635i
$886$		0			0
$887$	8.06446e6	−	6.76688e6i	0.344165	−	0.288788i	−0.454277	−	0.890860i	$-0.650102\pi$
$887$	8.06446e6	−	6.76688e6i	0.344165	−	0.288788i	0.798442	+	0.602072i	$0.205658\pi$
$888$		0			0
$889$	2.50780e7	+	9.12763e6i	1.06424	+	0.387350i
$890$		0			0
$891$	4.60509e6	−	2.61167e7i	0.194332	−	1.10211i
$892$		0			0
$893$	−8.58474e6	+	1.49909e6i	−0.360245	+	0.0629069i
$894$		0			0
$895$	244050.	−	1.38408e6i	0.0101841	−	0.0577567i
$896$		0			0
$897$	−1.38387e6	−	503689.i	−0.0574269	−	0.0209017i
$898$		0			0
$899$	−7.80227e6	+	6.54688e6i	−0.321975	+	0.270169i
$900$		0			0
$901$	−8.19681e6	+	1.41973e7i	−0.336382	+	0.582631i
$902$		0			0
$903$	−267285.	−	1.51585e6i	−0.0109082	−	0.0618637i
$904$		0			0
$905$	−4.90211e6	−	8.49069e6i	−0.198958	−	0.344605i
$906$		0			0
$907$	−5.47395e6	+	1.99235e6i	−0.220944	+	0.0804171i	−0.450120	−	0.892968i	$-0.648619\pi$
$907$	−5.47395e6	+	1.99235e6i	−0.220944	+	0.0804171i	0.229176	+	0.973385i	$0.426397\pi$
$908$		0			0
$909$	8.93789e6	+	7.49978e6i	0.358778	+	0.301050i
$910$		0			0
$911$	3.64512e7			1.45518			0.727588	−	0.686015i	$-0.240641\pi$
$911$	3.64512e7			1.45518			0.727588	+	0.686015i	$0.240641\pi$
$912$		0			0
$913$	1.86032e6			0.0738602
$914$		0			0
$915$	−236206.	−	198200.i	−0.00932692	−	0.00782621i
$916$		0			0
$917$	−6.58431e6	+	2.39649e6i	−0.258575	+	0.0941137i
$918$		0			0
$919$	−2.86733e6	−	4.96636e6i	−0.111993	−	0.193977i	0.804581	−	0.593843i	$-0.202390\pi$
$919$	−2.86733e6	−	4.96636e6i	−0.111993	−	0.193977i	−0.916574	+	0.399866i	$0.869057\pi$
$920$		0			0
$921$	−277485.	−	1.57370e6i	−0.0107793	−	0.0611325i
$922$		0			0
$923$	−9.06998e6	+	1.57097e7i	−0.350431	+	0.606964i
$924$		0			0
$925$	9.41147e6	−	7.89716e6i	0.361662	−	0.303471i
$926$		0			0
$927$	2.17072e7	+	7.90077e6i	0.829667	+	0.301974i
$928$		0			0
$929$	8.07472e6	−	4.57940e7i	0.306964	−	1.74088i	−0.307147	−	0.951662i	$-0.599374\pi$
$929$	8.07472e6	−	4.57940e7i	0.306964	−	1.74088i	0.614111	−	0.789220i	$-0.289515\pi$
$930$		0			0
$931$	1.34254e7	+	7.78081e6i	0.507638	+	0.294205i
$932$		0			0
$933$	−264515.	+	1.50014e6i	−0.00994826	+	0.0564194i
$934$		0			0
$935$	4.51330e6	+	1.64271e6i	0.168836	+	0.0614512i
$936$		0			0
$937$	1.29149e7	−	1.08369e7i	0.480554	−	0.403233i	−0.370072	−	0.929003i	$-0.620667\pi$
$937$	1.29149e7	−	1.08369e7i	0.480554	−	0.403233i	0.850627	+	0.525770i	$0.176223\pi$
$938$		0			0
$939$	−175723.	+	304361.i	−0.00650375	+	0.0112648i
$940$		0			0
$941$	1.62796e6	+	9.23260e6i	0.0599334	+	0.339899i	0.999999	−	0.00109334i	$-0.000348022\pi$
$941$	1.62796e6	+	9.23260e6i	0.0599334	+	0.339899i	−0.940066	+	0.340993i	$0.889237\pi$
$942$		0			0
$943$	2.66226e7	+	4.61118e7i	0.974926	+	1.68862i
$944$		0			0
$945$	442461.	−	161043.i	0.0161174	−	0.00586626i
$946$		0			0
$947$	−2.87458e7	−	2.41206e7i	−1.04160	−	0.874002i	−0.0494103	−	0.998779i	$-0.515734\pi$
$947$	−2.87458e7	−	2.41206e7i	−1.04160	−	0.874002i	−0.992185	+	0.124776i	$0.960179\pi$
$948$		0			0
$949$	−1.53579e7			−0.553563
$950$		0			0
$951$	−987854.			−0.0354194
$952$		0			0
$953$	−1.38381e7	−	1.16115e7i	−0.493564	−	0.414149i	0.361738	−	0.932280i	$-0.382184\pi$
$953$	−1.38381e7	−	1.16115e7i	−0.493564	−	0.414149i	−0.855301	+	0.518131i	$0.826628\pi$
$954$		0			0
$955$	1.67293e6	−	608897.i	0.0593567	−	0.0216041i
$956$		0			0
$957$	1.23847e6	+	2.14510e6i	0.0437126	+	0.0757125i
$958$		0			0
$959$	101924.	+	578041.i	0.00357875	+	0.0202961i
$960$		0			0
$961$	1.29819e7	−	2.24853e7i	0.453449	−	0.785398i
$962$		0			0
$963$	−1.02813e7	+	8.62702e6i	−0.357258	+	0.299775i
$964$		0			0
$965$	−632835.	−	230333.i	−0.0218762	−	0.00796229i
$966$		0			0
$967$	9.00850e6	−	5.10897e7i	0.309803	−	1.75698i	−0.290182	−	0.956972i	$-0.593716\pi$
$967$	9.00850e6	−	5.10897e7i	0.309803	−	1.75698i	0.599985	−	0.800011i	$-0.295173\pi$
$968$		0			0
$969$	704276.	+	842148.i	0.0240954	+	0.0288124i
$970$		0			0
$971$	−7.03723e6	+	3.99101e7i	−0.239527	+	1.35842i	0.593341	+	0.804951i	$0.297809\pi$
$971$	−7.03723e6	+	3.99101e7i	−0.239527	+	1.35842i	−0.832868	+	0.553472i	$0.813303\pi$
$972$		0			0
$973$	1.54734e7	+	5.63186e6i	0.523967	+	0.190708i
$974$		0			0
$975$	−957336.	+	803300.i	−0.0322517	+	0.0270624i
$976$		0			0
$977$	−1.23856e7	+	2.14525e7i	−0.415126	+	0.719020i	−0.995442	−	0.0953718i	$-0.969596\pi$
$977$	−1.23856e7	+	2.14525e7i	−0.415126	+	0.719020i	0.580315	+	0.814392i	$0.302929\pi$
$978$		0			0
$979$	−8.30761e6	−	4.71148e7i	−0.277025	−	1.57109i
$980$		0			0
$981$	5.57534e6	+	9.65678e6i	0.184969	+	0.320376i
$982$		0			0
$983$	−4.04138e7	+	1.47094e7i	−1.33397	+	0.485525i	−0.907908	−	0.419169i	$-0.862321\pi$
$983$	−4.04138e7	+	1.47094e7i	−1.33397	+	0.485525i	−0.426061	+	0.904694i	$0.640099\pi$
$984$		0			0
$985$	2.02746e6	+	1.70124e6i	0.0665826	+	0.0558694i
$986$		0			0
$987$	404182.			0.0132064
$988$		0			0
$989$	−7.32742e7			−2.38210
$990$		0			0
$991$	−1.14765e7	−	9.62993e6i	−0.371215	−	0.311486i	0.438027	−	0.898962i	$-0.355677\pi$
$991$	−1.14765e7	−	9.62993e6i	−0.371215	−	0.311486i	−0.809242	+	0.587475i	$0.800122\pi$
$992$		0			0
$993$	2.44227e6	−	888914.i	0.0785996	−	0.0286079i
$994$		0			0
$995$	−5.26443e6	−	9.11826e6i	−0.168575	−	0.291981i
$996$		0			0
$997$	7.89584e6	+	4.47795e7i	0.251571	+	1.42673i	0.804724	+	0.593649i	$0.202313\pi$
$997$	7.89584e6	+	4.47795e7i	0.251571	+	1.42673i	−0.553153	+	0.833080i	$0.686576\pi$
$998$		0			0
$999$	885350.	−	1.53347e6i	0.0280673	−	0.0486141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.17.4	yes	48
19.9	even	9	inner	76.6.i.a.9.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.9.4	✓	48	19.9	even	9	inner
76.6.i.a.17.4	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.670817 - 0.562882i) q^{3} +(-12.4943 + 4.54757i) q^{5} +(41.6708 + 72.1759i) q^{7} +(-42.0633 - 238.553i) q^{9} +O(q^{10})\)	\(q+(-0.670817 - 0.562882i) q^{3} +(-12.4943 + 4.54757i) q^{5} +(41.6708 + 72.1759i) q^{7} +(-42.0633 - 238.553i) q^{9} +(-226.700 + 392.656i) q^{11} +(-370.814 + 311.150i) q^{13} +(10.9412 + 3.98225i) q^{15} +(-138.347 + 784.604i) q^{17} +(-2.60199 + 1573.56i) q^{19} +(12.6731 - 71.8725i) q^{21} +(-3264.71 - 1188.26i) q^{23} +(-2258.46 + 1895.07i) q^{25} +(-212.457 + 367.986i) q^{27} +(1083.32 + 6143.80i) q^{29} +(816.303 + 1413.88i) q^{31} +(373.093 - 135.795i) q^{33} +(-848.873 - 712.289i) q^{35} -4167.20 q^{37} +423.889 q^{39} +(-11740.2 - 9851.22i) q^{41} +(19818.8 - 7213.47i) q^{43} +(1610.39 + 2789.28i) q^{45} +(961.691 + 5454.02i) q^{47} +(4930.59 - 8540.04i) q^{49} +(534.444 - 448.452i) q^{51} +(19335.8 + 7037.65i) q^{53} +(1046.84 - 5936.91i) q^{55} +(887.474 - 1054.11i) q^{57} +(6806.67 - 38602.6i) q^{59} +(-24885.4 - 9057.56i) q^{61} +(15465.0 - 12976.7i) q^{63} +(3218.10 - 5573.91i) q^{65} +(725.150 + 4112.53i) q^{67} +(1521.17 + 2634.75i) q^{69} +(35214.4 - 12817.0i) q^{71} +(24304.4 + 20393.8i) q^{73} +2581.72 q^{75} -37787.1 q^{77} +(26470.6 + 22211.4i) q^{79} +(-54963.2 + 20005.0i) q^{81} +(-2051.52 - 3553.34i) q^{83} +(-1839.49 - 10432.2i) q^{85} +(2731.53 - 4731.14i) q^{87} +(-80831.0 + 67825.2i) q^{89} +(-37909.6 - 13798.0i) q^{91} +(248.257 - 1407.94i) q^{93} +(-7123.36 - 19672.4i) q^{95} +(-16543.4 + 93822.2i) q^{97} +(103205. + 37563.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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