LMFDB - Embedded newform 76.5.j.a.33.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			33.7
Character	$\chi$	$=$	76.33
Dual form			76.5.j.a.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.9907 + 2.64326i) q^{3} +(1.74782 + 1.46659i) q^{5} +(22.6416 + 39.2164i) q^{7} +(141.618 + 51.5447i) q^{9} +O(q^{10})$	\(q+(14.9907 + 2.64326i) q^{3} +(1.74782 + 1.46659i) q^{5} +(22.6416 + 39.2164i) q^{7} +(141.618 + 51.5447i) q^{9} +(51.9608 - 89.9988i) q^{11} +(-220.896 + 38.9500i) q^{13} +(22.3243 + 26.6051i) q^{15} +(-69.3454 + 25.2397i) q^{17} +(340.990 + 118.520i) q^{19} +(235.753 + 647.727i) q^{21} +(547.158 - 459.120i) q^{23} +(-107.626 - 610.378i) q^{25} +(918.911 + 530.533i) q^{27} +(-295.925 + 813.048i) q^{29} +(-723.951 + 417.974i) q^{31} +(1016.82 - 1211.79i) q^{33} +(-17.9411 + 101.749i) q^{35} -603.379i q^{37} -3414.34 q^{39} +(-1040.36 - 183.444i) q^{41} +(-2617.31 - 2196.19i) q^{43} +(171.927 + 297.786i) q^{45} +(-1022.17 - 372.038i) q^{47} +(175.216 - 303.482i) q^{49} +(-1106.25 + 195.061i) q^{51} +(-1040.77 - 1240.34i) q^{53} +(222.810 - 81.0960i) q^{55} +(4798.38 + 2678.01i) q^{57} +(-653.388 - 1795.17i) q^{59} +(2687.88 - 2255.40i) q^{61} +(1185.06 + 6720.80i) q^{63} +(-443.210 - 255.888i) q^{65} +(-1445.83 + 3972.38i) q^{67} +(9415.82 - 5436.23i) q^{69} +(-3642.09 + 4340.47i) q^{71} +(-337.943 + 1916.57i) q^{73} -9434.45i q^{75} +4705.90 q^{77} +(-6050.83 - 1066.92i) q^{79} +(3021.46 + 2535.30i) q^{81} +(3629.32 + 6286.16i) q^{83} +(-158.219 - 57.5872i) q^{85} +(-6585.21 + 11405.9i) q^{87} +(10477.3 - 1847.43i) q^{89} +(-6528.93 - 7780.87i) q^{91} +(-11957.3 + 4352.11i) q^{93} +(422.168 + 707.244i) q^{95} +(-4970.62 - 13656.7i) q^{97} +(11997.5 - 10067.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

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
$3$	14.9907	+	2.64326i	1.66563	+	0.293695i	0.925494	−	0.378763i	$-0.123651\pi$
$3$	14.9907	+	2.64326i	1.66563	+	0.293695i	0.740135	+	0.672459i	$0.234762\pi$
$4$		0			0
$5$	1.74782	+	1.46659i	0.0699127	+	0.0586637i	0.677074	−	0.735915i	$-0.263248\pi$
$5$	1.74782	+	1.46659i	0.0699127	+	0.0586637i	−0.607162	+	0.794578i	$0.707692\pi$
$6$		0			0
$7$	22.6416	+	39.2164i	0.462074	+	0.800335i	0.999064	−	0.0432534i	$-0.0137723\pi$
$7$	22.6416	+	39.2164i	0.462074	+	0.800335i	−0.536991	+	0.843588i	$0.680439\pi$
$8$		0			0
$9$	141.618	+	51.5447i	1.74837	+	0.636354i
$10$		0			0
$11$	51.9608	−	89.9988i	0.429428	−	0.743791i	−0.567394	−	0.823446i	$-0.692048\pi$
$11$	51.9608	−	89.9988i	0.429428	−	0.743791i	0.996823	+	0.0796549i	$0.0253818\pi$
$12$		0			0
$13$	−220.896	+	38.9500i	−1.30708	+	0.230473i	−0.783440	−	0.621467i	$-0.786537\pi$
$13$	−220.896	+	38.9500i	−1.30708	+	0.230473i	−0.523639	+	0.851940i	$0.675426\pi$
$14$		0			0
$15$	22.3243	+	26.6051i	0.0992193	+	0.118245i
$16$		0			0
$17$	−69.3454	+	25.2397i	−0.239950	+	0.0873345i	−0.459196	−	0.888335i	$-0.651862\pi$
$17$	−69.3454	+	25.2397i	−0.239950	+	0.0873345i	0.219246	+	0.975670i	$0.429640\pi$
$18$		0			0
$19$	340.990	+	118.520i	0.944570	+	0.328309i
$19$	340.990	+	118.520i	0.944570	+	0.328309i
$20$		0			0
$21$	235.753	+	647.727i	0.534588	+	1.46877i
$22$		0			0
$23$	547.158	−	459.120i	1.03432	−	0.867901i	0.0429653	−	0.999077i	$-0.486320\pi$
$23$	547.158	−	459.120i	1.03432	−	0.867901i	0.991359	+	0.131175i	$0.0418751\pi$
$24$		0			0
$25$	−107.626	−	610.378i	−0.172202	−	0.976605i
$26$		0			0
$27$	918.911	+	530.533i	1.26051	+	0.727755i
$28$		0			0
$29$	−295.925	+	813.048i	−0.351873	+	0.966763i	0.629895	+	0.776680i	$0.283098\pi$
$29$	−295.925	+	813.048i	−0.351873	+	0.966763i	−0.981768	+	0.190083i	$0.939124\pi$
$30$		0			0
$31$	−723.951	+	417.974i	−0.753331	+	0.434936i	−0.826896	−	0.562354i	$-0.809896\pi$
$31$	−723.951	+	417.974i	−0.753331	+	0.434936i	0.0735650	+	0.997290i	$0.476562\pi$
$32$		0			0
$33$	1016.82	−	1211.79i	0.933716	−	1.11276i
$34$		0			0
$35$	−17.9411	+	101.749i	−0.0146458	+	0.0830605i
$36$		0			0
$37$		−	603.379i		−	0.440744i	−0.975416	−	0.220372i	$-0.929273\pi$
$37$		−	603.379i		−	0.440744i	0.975416	−	0.220372i	$-0.0707272\pi$
$38$		0			0
$39$	−3414.34			−2.24480
$40$		0			0
$41$	−1040.36	−	183.444i	−0.618894	−	0.109128i	−0.144594	−	0.989491i	$-0.546188\pi$
$41$	−1040.36	−	183.444i	−0.618894	−	0.109128i	−0.474300	+	0.880363i	$0.657299\pi$
$42$		0			0
$43$	−2617.31	−	2196.19i	−1.41553	−	1.18777i	−0.953685	−	0.300808i	$-0.902744\pi$
$43$	−2617.31	−	2196.19i	−1.41553	−	1.18777i	−0.461844	−	0.886961i	$-0.652812\pi$
$44$		0			0
$45$	171.927	+	297.786i	0.0849022	+	0.147055i
$46$		0			0
$47$	−1022.17	−	372.038i	−0.462728	−	0.168419i	0.100128	−	0.994975i	$-0.468075\pi$
$47$	−1022.17	−	372.038i	−0.462728	−	0.168419i	−0.562855	+	0.826555i	$0.690297\pi$
$48$		0			0
$49$	175.216	−	303.482i	0.0729761	−	0.126398i
$50$		0			0
$51$	−1106.25	+	195.061i	−0.425317	+	0.0749948i
$52$		0			0
$53$	−1040.77	−	1240.34i	−0.370512	−	0.441559i	0.548284	−	0.836292i	$-0.315281\pi$
$53$	−1040.77	−	1240.34i	−0.370512	−	0.441559i	−0.918796	+	0.394734i	$0.870837\pi$
$54$		0			0
$55$	222.810	−	81.0960i	0.0736560	−	0.0268086i
$56$		0			0
$57$	4798.38	+	2678.01i	1.47688	+	0.824257i
$58$		0			0
$59$	−653.388	−	1795.17i	−0.187701	−	0.515705i	0.809772	−	0.586744i	$-0.199591\pi$
$59$	−653.388	−	1795.17i	−0.187701	−	0.515705i	−0.997474	+	0.0710395i	$0.977368\pi$
$60$		0			0
$61$	2687.88	−	2255.40i	0.722355	−	0.606128i	−0.205680	−	0.978619i	$-0.565941\pi$
$61$	2687.88	−	2255.40i	0.722355	−	0.606128i	0.928036	+	0.372491i	$0.121496\pi$
$62$		0			0
$63$	1185.06	+	6720.80i	0.298578	+	1.69332i
$64$		0			0
$65$	−443.210	−	255.888i	−0.104902	−	0.0605651i
$66$		0			0
$67$	−1445.83	+	3972.38i	−0.322082	+	0.884914i	0.667967	+	0.744191i	$0.267165\pi$
$67$	−1445.83	+	3972.38i	−0.322082	+	0.884914i	−0.990049	+	0.140723i	$0.955057\pi$
$68$		0			0
$69$	9415.82	−	5436.23i	1.97770	−	1.14182i
$70$		0			0
$71$	−3642.09	+	4340.47i	−0.722493	+	0.861033i	−0.994870	−	0.101157i	$-0.967746\pi$
$71$	−3642.09	+	4340.47i	−0.722493	+	0.861033i	0.272378	+	0.962190i	$0.412190\pi$
$72$		0			0
$73$	−337.943	+	1916.57i	−0.0634159	+	0.359649i	0.936543	+	0.350553i	$0.114007\pi$
$73$	−337.943	+	1916.57i	−0.0634159	+	0.359649i	−0.999959	+	0.00909602i	$0.997105\pi$
$74$		0			0
$75$		−	9434.45i		−	1.67724i
$76$		0			0
$77$	4705.90			0.793710
$78$		0			0
$79$	−6050.83	−	1066.92i	−0.969529	−	0.170954i	−0.333611	−	0.942711i	$-0.608267\pi$
$79$	−6050.83	−	1066.92i	−0.969529	−	0.170954i	−0.635918	+	0.771757i	$0.719378\pi$
$80$		0			0
$81$	3021.46	+	2535.30i	0.460518	+	0.386420i
$82$		0			0
$83$	3629.32	+	6286.16i	0.526828	+	0.912493i	0.999511	+	0.0312603i	$0.00995207\pi$
$83$	3629.32	+	6286.16i	0.526828	+	0.912493i	−0.472683	+	0.881232i	$0.656715\pi$
$84$		0			0
$85$	−158.219	−	57.5872i	−0.0218989	−	0.00797054i
$86$		0			0
$87$	−6585.21	+	11405.9i	−0.870023	+	1.50692i
$88$		0			0
$89$	10477.3	−	1847.43i	1.32272	−	0.233232i	0.532697	−	0.846306i	$-0.321178\pi$
$89$	10477.3	−	1847.43i	1.32272	−	0.233232i	0.790025	+	0.613074i	$0.210067\pi$
$90$		0			0
$91$	−6528.93	−	7780.87i	−0.788423	−	0.939605i
$92$		0			0
$93$	−11957.3	+	4352.11i	−1.38251	+	0.503192i
$94$		0			0
$95$	422.168	+	707.244i	0.0467776	+	0.0783650i
$96$		0			0
$97$	−4970.62	−	13656.7i	−0.528284	−	1.45145i	−0.861090	−	0.508452i	$-0.830218\pi$
$97$	−4970.62	−	13656.7i	−0.528284	−	1.45145i	0.332807	−	0.942995i	$-0.392004\pi$
$98$		0			0
$99$	11997.5	−	10067.1i	1.22411	−	1.02715i
$100$		0			0
$101$	3332.38	+	18898.8i	0.326672	+	1.85265i	0.497659	+	0.867373i	$0.334193\pi$
$101$	3332.38	+	18898.8i	0.326672	+	1.85265i	−0.170987	+	0.985273i	$0.554696\pi$
$102$		0			0
$103$	16336.7	+	9432.00i	1.53989	+	0.889056i	0.998844	+	0.0480638i	$0.0153051\pi$
$103$	16336.7	+	9432.00i	1.53989	+	0.889056i	0.541047	+	0.840993i	$0.318028\pi$
$104$		0			0
$105$	−537.898	+	1477.86i	−0.0487890	+	0.134047i
$106$		0			0
$107$	19063.0	−	11006.0i	1.66503	−	0.961307i	0.694777	−	0.719225i	$-0.255503\pi$
$107$	19063.0	−	11006.0i	1.66503	−	0.961307i	0.970256	−	0.242082i	$-0.0778301\pi$
$108$		0			0
$109$	2125.72	−	2533.33i	0.178918	−	0.213226i	−0.669131	−	0.743145i	$-0.733333\pi$
$109$	2125.72	−	2533.33i	0.178918	−	0.213226i	0.848048	+	0.529919i	$0.177778\pi$
$110$		0			0
$111$	1594.89	−	9045.04i	0.129444	−	0.734116i
$112$		0			0
$113$			22240.3i			1.74174i	0.491512	+	0.870871i	$0.336444\pi$
$113$			22240.3i			1.74174i	−0.491512	+	0.870871i	$0.663556\pi$
$114$		0			0
$115$	1629.67			0.123227
$116$		0			0
$117$	−33290.5	−	5870.02i	−2.43192	−	0.428813i
$118$		0			0
$119$	−2559.90	−	2148.01i	−0.180771	−	0.151685i
$120$		0			0
$121$	1920.65	+	3326.66i	0.131183	+	0.227216i
$122$		0			0
$123$	−15110.8	−	5499.88i	−0.998796	−	0.363532i
$124$		0			0
$125$	1420.07	−	2459.63i	0.0908845	−	0.157416i
$126$		0			0
$127$	−18978.7	+	3346.45i	−1.17668	+	0.207480i	−0.727594	−	0.686008i	$-0.759361\pi$
$127$	−18978.7	+	3346.45i	−1.17668	+	0.207480i	−0.449086	+	0.893489i	$0.648250\pi$
$128$		0			0
$129$	−33430.1	−	39840.5i	−2.00890	−	2.39412i
$130$		0			0
$131$	−8075.04	+	2939.07i	−0.470546	+	0.171265i	−0.566400	−	0.824131i	$-0.691664\pi$
$131$	−8075.04	+	2939.07i	−0.470546	+	0.171265i	0.0958537	+	0.995395i	$0.469442\pi$
$132$		0			0
$133$	3072.64	+	16055.9i	0.173703	+	0.907676i
$134$		0			0
$135$	828.012	+	2274.94i	0.0454327	+	0.124825i
$136$		0			0
$137$	27262.3	−	22875.8i	1.45252	−	1.21881i	0.521800	−	0.853068i	$-0.325261\pi$
$137$	27262.3	−	22875.8i	1.45252	−	1.21881i	0.930718	−	0.365739i	$-0.119184\pi$
$138$		0			0
$139$	−1315.13	−	7458.49i	−0.0680675	−	0.386030i	−0.999742	−	0.0227348i	$-0.992763\pi$
$139$	−1315.13	−	7458.49i	−0.0680675	−	0.386030i	0.931674	−	0.363295i	$-0.118348\pi$
$140$		0			0
$141$	−14339.5	−	8278.94i	−0.721269	−	0.416425i
$142$		0			0
$143$	−7972.50	+	21904.3i	−0.389872	+	1.07117i
$144$		0			0
$145$	−1709.63	+	987.057i	−0.0813143	+	0.0469468i
$146$		0			0
$147$	3428.78	−	4086.26i	0.158674	−	0.189100i
$148$		0			0
$149$	−3595.41	+	20390.6i	−0.161948	+	0.918452i	0.790208	+	0.612839i	$0.209973\pi$
$149$	−3595.41	+	20390.6i	−0.161948	+	0.918452i	−0.952156	+	0.305613i	$0.901139\pi$
$150$		0			0
$151$		−	15854.9i		−	0.695359i	−0.937613	−	0.347679i	$-0.886970\pi$
$151$		−	15854.9i		−	0.695359i	0.937613	−	0.347679i	$-0.113030\pi$
$152$		0			0
$153$	−11121.5			−0.475096
$154$		0			0
$155$	−1878.33	−	331.201i	−0.0781824	−	0.0137857i
$156$		0			0
$157$	153.155	+	128.512i	0.00621343	+	0.00521369i	0.645889	−	0.763431i	$-0.276487\pi$
$157$	153.155	+	128.512i	0.00621343	+	0.00521369i	−0.639676	+	0.768645i	$0.720931\pi$
$158$		0			0
$159$	−12323.3	−	21344.5i	−0.487451	−	0.844290i
$160$		0			0
$161$	30393.6	+	11062.3i	1.17255	+	0.426772i
$162$		0			0
$163$	−4690.34	+	8123.92i	−0.176534	+	0.305767i	−0.940691	−	0.339264i	$-0.889822\pi$
$163$	−4690.34	+	8123.92i	−0.176534	+	0.305767i	0.764157	+	0.645031i	$0.223155\pi$
$164$		0			0
$165$	3554.42	−	626.740i	0.130557	−	0.0230207i
$166$		0			0
$167$	32828.4	+	39123.3i	1.17711	+	1.40282i	0.896525	+	0.442994i	$0.146084\pi$
$167$	32828.4	+	39123.3i	1.17711	+	1.40282i	0.280584	+	0.959830i	$0.409472\pi$
$168$		0			0
$169$	20439.5	−	7439.38i	0.715645	−	0.260474i
$170$		0			0
$171$	42181.2	+	34360.7i	1.44254	+	1.17509i
$172$		0			0
$173$	12496.4	+	34333.7i	0.417536	+	1.14717i	0.953095	+	0.302673i	$0.0978789\pi$
$173$	12496.4	+	34333.7i	0.417536	+	1.14717i	−0.535558	+	0.844498i	$0.679899\pi$
$174$		0			0
$175$	21500.0	−	18040.7i	0.702041	−	0.589083i
$176$		0			0
$177$	−5049.62	−	28637.8i	−0.161180	−	0.914099i
$178$		0			0
$179$	18153.5	+	10480.9i	0.566570	+	0.327110i	0.755778	−	0.654827i	$-0.227259\pi$
$179$	18153.5	+	10480.9i	0.566570	+	0.327110i	−0.189208	+	0.981937i	$0.560592\pi$
$180$		0			0
$181$	1559.86	−	4285.68i	0.0476133	−	0.130816i	−0.913607	−	0.406599i	$-0.866715\pi$
$181$	1559.86	−	4285.68i	0.0476133	−	0.130816i	0.961220	+	0.275782i	$0.0889369\pi$
$182$		0			0
$183$	46254.8	−	26705.2i	1.38119	−	0.797432i
$184$		0			0
$185$	884.911	−	1054.60i	0.0258557	−	0.0308136i
$186$		0			0
$187$	−1331.71	+	7552.48i	−0.0380825	+	0.215976i
$188$		0			0
$189$			48048.5i			1.34511i
$190$		0			0
$191$	−30053.3			−0.823806			−0.411903	−	0.911228i	$-0.635136\pi$
$191$	−30053.3			−0.823806			−0.411903	+	0.911228i	$0.635136\pi$
$192$		0			0
$193$	2660.50	+	469.117i	0.0714246	+	0.0125941i	0.209246	−	0.977863i	$-0.432899\pi$
$193$	2660.50	+	469.117i	0.0714246	+	0.0125941i	−0.137822	+	0.990457i	$0.544010\pi$
$194$		0			0
$195$	−5967.64	−	5007.44i	−0.156940	−	0.131688i
$196$		0			0
$197$	−21955.7	−	38028.4i	−0.565738	−	0.979886i	−0.996981	−	0.0776504i	$-0.975258\pi$
$197$	−21955.7	−	38028.4i	−0.565738	−	0.979886i	0.431243	−	0.902236i	$-0.358075\pi$
$198$		0			0
$199$	−66862.0	−	24335.8i	−1.68839	−	0.614524i	−0.693969	−	0.720005i	$-0.744140\pi$
$199$	−66862.0	−	24335.8i	−1.68839	−	0.614524i	−0.994421	+	0.105481i	$0.966362\pi$
$200$		0			0
$201$	−32173.9	+	55726.9i	−0.796365	+	1.37934i
$202$		0			0
$203$	−38585.0	+	6803.58i	−0.936325	+	0.165099i
$204$		0			0
$205$	−1549.32	−	1846.41i	−0.0368667	−	0.0439360i
$206$		0			0
$207$	101152.	−	36816.5i	2.36067	−	0.859214i
$208$		0			0
$209$	28384.7	−	24530.3i	0.649819	−	0.561578i
$210$		0			0
$211$	5157.13	+	14169.1i	0.115836	+	0.318256i	0.984039	−	0.177952i	$-0.0569473\pi$
$211$	5157.13	+	14169.1i	0.115836	+	0.318256i	−0.868203	+	0.496209i	$0.834725\pi$
$212$		0			0
$213$	−66070.2	+	55439.5i	−1.45629	+	1.22197i
$214$		0			0
$215$	−1353.67	−	7677.06i	−0.0292844	−	0.166080i
$216$		0			0
$217$	−32782.8	−	18927.2i	−0.696189	−	0.401945i
$218$		0			0
$219$	−10132.0	+	27837.4i	−0.211255	+	0.580417i
$220$		0			0
$221$	14335.1	−	8276.36i	0.293505	−	0.169455i
$222$		0			0
$223$	7463.74	−	8894.94i	0.150088	−	0.178868i	−0.685762	−	0.727826i	$-0.740531\pi$
$223$	7463.74	−	8894.94i	0.150088	−	0.178868i	0.835850	+	0.548958i	$0.184975\pi$
$224$		0			0
$225$	16220.0	−	91988.0i	0.320394	−	1.81705i
$226$		0			0
$227$			47690.9i			0.925515i	0.886485	+	0.462757i	$0.153140\pi$
$227$			47690.9i			0.925515i	−0.886485	+	0.462757i	$0.846860\pi$
$228$		0			0
$229$	19081.8			0.363872			0.181936	−	0.983310i	$-0.441764\pi$
$229$	19081.8			0.363872			0.181936	+	0.983310i	$0.441764\pi$
$230$		0			0
$231$	70544.6	+	12438.9i	1.32203	+	0.233109i
$232$		0			0
$233$	43461.8	+	36468.8i	0.800564	+	0.671753i	0.948336	−	0.317269i	$-0.102766\pi$
$233$	43461.8	+	36468.8i	0.800564	+	0.671753i	−0.147772	+	0.989021i	$0.547210\pi$
$234$		0			0
$235$	−1240.93	−	2149.35i	−0.0224705	−	0.0389200i
$236$		0			0
$237$	−87885.7	−	31987.8i	−1.56467	−	0.569492i
$238$		0			0
$239$	39853.0	−	69027.3i	0.697694	−	1.20844i	−0.271571	−	0.962419i	$-0.587543\pi$
$239$	39853.0	−	69027.3i	0.697694	−	1.20844i	0.969264	−	0.246022i	$-0.0791236\pi$
$240$		0			0
$241$	−29149.5	+	5139.84i	−0.501876	+	0.0884943i	−0.418854	−	0.908053i	$-0.637568\pi$
$241$	−29149.5	+	5139.84i	−0.501876	+	0.0884943i	−0.0830218	+	0.996548i	$0.526457\pi$
$242$		0			0
$243$	−16653.1	−	19846.4i	−0.282022	−	0.336101i
$244$		0			0
$245$	751.329	−	273.462i	0.0125169	−	0.00455579i
$246$		0			0
$247$	−79939.8	−	12899.0i	−1.31029	−	0.211428i
$248$		0			0
$249$	37789.9	+	103827.i	0.609505	+	1.67460i
$250$		0			0
$251$	−84937.6	+	71271.1i	−1.34819	+	1.13127i	−0.368756	+	0.929526i	$0.620216\pi$
$251$	−84937.6	+	71271.1i	−1.34819	+	1.13127i	−0.979438	+	0.201743i	$0.935339\pi$
$252$		0			0
$253$	−12889.5	−	73099.7i	−0.201369	−	1.14202i
$254$		0			0
$255$	−2219.60	−	1281.48i	−0.0341345	−	0.0197076i
$256$		0			0
$257$	19104.6	−	52489.5i	0.289249	−	0.794705i	−0.706923	−	0.707290i	$-0.749917\pi$
$257$	19104.6	−	52489.5i	0.289249	−	0.794705i	0.996172	−	0.0874145i	$-0.0278604\pi$
$258$		0			0
$259$	23662.4	−	13661.5i	0.352743	−	0.203656i
$260$		0			0
$261$	−83816.6	+	99888.7i	−1.23041	+	1.46634i
$262$		0			0
$263$	17609.9	−	99870.8i	0.254593	−	1.44387i	−0.542524	−	0.840040i	$-0.682531\pi$
$263$	17609.9	−	99870.8i	0.254593	−	1.44387i	0.797116	−	0.603826i	$-0.206358\pi$
$264$		0			0
$265$		−	3694.27i		−	0.0526062i
$266$		0			0
$267$	161945.			2.27166
$268$		0			0
$269$	−41529.3	−	7322.74i	−0.573919	−	0.101197i	−0.120847	−	0.992671i	$-0.538561\pi$
$269$	−41529.3	−	7322.74i	−0.573919	−	0.101197i	−0.453072	+	0.891474i	$0.649672\pi$
$270$		0			0
$271$	31060.4	+	26062.8i	0.422930	+	0.354880i	0.829276	−	0.558839i	$-0.188753\pi$
$271$	31060.4	+	26062.8i	0.422930	+	0.354880i	−0.406346	+	0.913719i	$0.633197\pi$
$272$		0			0
$273$	−77306.0	−	133898.i	−1.03726	−	1.79659i
$274$		0			0
$275$	−60525.6	−	22029.5i	−0.800339	−	0.291299i
$276$		0			0
$277$	−48837.0	+	84588.2i	−0.636487	+	1.10243i	0.349711	+	0.936858i	$0.386280\pi$
$277$	−48837.0	+	84588.2i	−0.636487	+	1.10243i	−0.986198	+	0.165570i	$0.947054\pi$
$278$		0			0
$279$	−124069.	+	21876.7i	−1.59387	+	0.281043i
$280$		0			0
$281$	2277.32	+	2714.00i	0.0288411	+	0.0343714i	0.780272	−	0.625440i	$-0.215081\pi$
$281$	2277.32	+	2714.00i	0.0288411	+	0.0343714i	−0.751431	+	0.659812i	$0.770636\pi$
$282$		0			0
$283$	−12326.9	+	4486.61i	−0.153915	+	0.0560203i	−0.417829	−	0.908526i	$-0.637209\pi$
$283$	−12326.9	+	4486.61i	−0.153915	+	0.0560203i	0.263914	+	0.964546i	$0.414987\pi$
$284$		0			0
$285$	4459.14	+	11717.9i	0.0548987	+	0.144265i
$286$		0			0
$287$	−16361.4	−	44952.6i	−0.198636	−	0.545747i
$288$		0			0
$289$	−59809.0	+	50185.8i	−0.716096	+	0.600876i
$290$		0			0
$291$	−38414.8	−	217861.i	−0.453641	−	2.57273i
$292$		0			0
$293$	71409.0	+	41228.0i	0.831797	+	0.480238i	0.854468	−	0.519505i	$-0.173883\pi$
$293$	71409.0	+	41228.0i	0.831797	+	0.480238i	−0.0226704	+	0.999743i	$0.507217\pi$
$294$		0			0
$295$	1490.78	−	4095.88i	0.0171305	−	0.0470655i
$296$		0			0
$297$	95494.7	−	55133.9i	1.08260	−	0.625037i
$298$		0			0
$299$	−102982.	+	122730.i	−1.15192	+	1.37280i
$300$		0			0
$301$	26866.4	−	152367.i	0.296535	−	1.68173i
$302$		0			0
$303$			292114.i			3.18176i
$304$		0			0
$305$	8005.69			0.0860595
$306$		0			0
$307$	67311.4	+	11868.8i	0.714187	+	0.125930i	0.518924	−	0.854821i	$-0.326333\pi$
$307$	67311.4	+	11868.8i	0.714187	+	0.125930i	0.195263	+	0.980751i	$0.437444\pi$
$308$		0			0
$309$	219967.	+	184574.i	2.30377	+	1.93310i
$310$		0			0
$311$	−39321.7	−	68107.2i	−0.406548	−	0.704162i	0.587952	−	0.808896i	$-0.299934\pi$
$311$	−39321.7	−	68107.2i	−0.406548	−	0.704162i	−0.994500	+	0.104734i	$0.966601\pi$
$312$		0			0
$313$	54369.8	+	19789.0i	0.554970	+	0.201992i	0.604253	−	0.796792i	$-0.293472\pi$
$313$	54369.8	+	19789.0i	0.554970	+	0.201992i	−0.0492835	+	0.998785i	$0.515694\pi$
$314$		0			0
$315$	−7785.41	+	13484.7i	−0.0784622	+	0.135900i
$316$		0			0
$317$	20211.3	−	3563.80i	0.201130	−	0.0354646i	−0.0721755	−	0.997392i	$-0.522994\pi$
$317$	20211.3	−	3563.80i	0.201130	−	0.0354646i	0.273305	+	0.961927i	$0.411883\pi$
$318$		0			0
$319$	57796.8	+	68879.5i	0.567966	+	0.676875i
$320$		0			0
$321$	314858.	−	114599.i	3.05566	−	1.11217i
$322$		0			0
$323$	−26637.5	+	387.671i	−0.255322	+	0.00371585i
$324$		0			0
$325$	47548.4	+	130638.i	0.450163	+	1.23681i
$326$		0			0
$327$	38562.2	−	32357.5i	0.360634	−	0.302608i
$328$		0			0
$329$	−8553.48	−	48509.2i	−0.0790226	−	0.448159i
$330$		0			0
$331$	−74022.2	−	42736.8i	−0.675626	−	0.390073i	0.122579	−	0.992459i	$-0.460883\pi$
$331$	−74022.2	−	42736.8i	−0.675626	−	0.390073i	−0.798205	+	0.602386i	$0.794217\pi$
$332$		0			0
$333$	31101.0	−	85449.2i	0.280469	−	0.770583i
$334$		0			0
$335$	−8352.91	+	4822.55i	−0.0744300	+	0.0429722i
$336$		0			0
$337$	106192.	−	126555.i	0.935043	−	1.11434i	−0.0582025	−	0.998305i	$-0.518537\pi$
$337$	106192.	−	126555.i	0.935043	−	1.11434i	0.993245	−	0.116036i	$-0.0370187\pi$
$338$		0			0
$339$	−58786.8	+	333397.i	−0.511541	+	2.90109i
$340$		0			0
$341$			86873.0i			0.747095i
$342$		0			0
$343$	124594.			1.05903
$344$		0			0
$345$	24429.9	+	4307.65i	0.205250	+	0.0361911i
$346$		0			0
$347$	−78074.5	−	65512.3i	−0.648411	−	0.544081i	0.258178	−	0.966097i	$-0.416878\pi$
$347$	−78074.5	−	65512.3i	−0.648411	−	0.544081i	−0.906588	+	0.422016i	$0.861322\pi$
$348$		0			0
$349$	15832.1	+	27422.1i	0.129984	+	0.225138i	0.923670	−	0.383189i	$-0.125174\pi$
$349$	15832.1	+	27422.1i	0.129984	+	0.225138i	−0.793686	+	0.608327i	$0.791841\pi$
$350$		0			0
$351$	−223648.	−	81401.3i	−1.81531	−	0.660720i
$352$		0			0
$353$	24201.5	−	41918.2i	0.194219	−	0.336397i	−0.752425	−	0.658678i	$-0.771116\pi$
$353$	24201.5	−	41918.2i	0.194219	−	0.336397i	0.946644	+	0.322280i	$0.104449\pi$
$354$		0			0
$355$	−12731.4	+	2244.89i	−0.101023	+	0.0178131i
$356$		0			0
$357$	−32696.8	−	38966.6i	−0.256548	−	0.305743i
$358$		0			0
$359$	−5651.88	+	2057.12i	−0.0438535	+	0.0159614i	−0.363854	−	0.931456i	$-0.618539\pi$
$359$	−5651.88	+	2057.12i	−0.0438535	+	0.0159614i	0.320000	+	0.947417i	$0.396317\pi$
$360$		0			0
$361$	102227.	+	80828.0i	0.784426	+	0.620223i
$362$		0			0
$363$	19998.6	+	54945.6i	0.151770	+	0.416984i
$364$		0			0
$365$	−3401.49	+	2854.19i	−0.0255320	+	0.0214239i
$366$		0			0
$367$	1654.48	+	9383.00i	0.0122837	+	0.0696642i	0.990333	−	0.138707i	$-0.0442948\pi$
$367$	1654.48	+	9383.00i	0.0122837	+	0.0696642i	−0.978050	+	0.208372i	$0.933184\pi$
$368$		0			0
$369$	−137878.	−	79603.9i	−1.01261	−	0.584631i
$370$		0			0
$371$	25077.0	−	68898.4i	0.182191	−	0.500566i
$372$		0			0
$373$	−102897.	+	59407.9i	−0.739583	+	0.426998i	−0.821918	−	0.569606i	$-0.807096\pi$
$373$	−102897.	+	59407.9i	−0.739583	+	0.426998i	0.0823346	+	0.996605i	$0.473762\pi$
$374$		0			0
$375$	27789.2	−	33117.9i	0.197612	−	0.235505i
$376$		0			0
$377$	33700.6	−	191126.i	0.237113	−	1.34473i
$378$		0			0
$379$			198715.i			1.38341i	0.722178	+	0.691707i	$0.243141\pi$
$379$			198715.i			1.38341i	−0.722178	+	0.691707i	$0.756859\pi$
$380$		0			0
$381$	−293348.			−2.02085
$382$		0			0
$383$	−105698.	−	18637.4i	−0.720557	−	0.127054i	−0.198668	−	0.980067i	$-0.563662\pi$
$383$	−105698.	−	18637.4i	−0.720557	−	0.127054i	−0.521889	+	0.853013i	$0.674773\pi$
$384$		0			0
$385$	8225.06	+	6901.64i	0.0554904	+	0.0465619i
$386$		0			0
$387$	−257456.	−	445927.i	−1.71902	−	2.97744i
$388$		0			0
$389$	−62934.1	−	22906.1i	−0.415898	−	0.151375i	0.125591	−	0.992082i	$-0.459917\pi$
$389$	−62934.1	−	22906.1i	−0.415898	−	0.151375i	−0.541489	+	0.840708i	$0.682139\pi$
$390$		0			0
$391$	−26354.9	+	45647.9i	−0.172388	+	0.298585i
$392$		0			0
$393$	−128819.	+	22714.2i	−0.834054	+	0.147066i
$394$		0			0
$395$	−9011.00	−	10738.9i	−0.0577536	−	0.0688280i
$396$		0			0
$397$	75943.7	−	27641.3i	0.481849	−	0.175379i	−0.0896634	−	0.995972i	$-0.528579\pi$
$397$	75943.7	−	27641.3i	0.481849	−	0.175379i	0.571512	+	0.820593i	$0.306357\pi$
$398$		0			0
$399$	3621.07	+	248810.i	0.0227453	+	1.56287i
$400$		0			0
$401$	59805.6	+	164315.i	0.371923	+	1.02185i	0.974617	+	0.223878i	$0.0718719\pi$
$401$	59805.6	+	164315.i	0.371923	+	1.02185i	−0.602694	+	0.797973i	$0.705906\pi$
$402$		0			0
$403$	143638.	−	120527.i	0.884423	−	0.742119i
$404$		0			0
$405$	1562.70	+	8862.49i	0.00952719	+	0.0540314i
$406$		0			0
$407$	−54303.3	−	31352.1i	−0.327822	−	0.189268i
$408$		0			0
$409$	−73359.1	+	201552.i	−0.438538	+	1.20487i	0.501905	+	0.864923i	$0.332633\pi$
$409$	−73359.1	+	201552.i	−0.438538	+	1.20487i	−0.940443	+	0.339951i	$0.889590\pi$
$410$		0			0
$411$	469146.	−	270862.i	2.77731	−	1.60348i
$412$		0			0
$413$	55606.3	−	66269.0i	0.326005	−	0.388517i
$414$		0			0
$415$	−2875.86	+	16309.8i	−0.0166983	+	0.0947005i
$416$		0			0
$417$		−	115284.i		−	0.662974i
$418$		0			0
$419$	55056.9			0.313606			0.156803	−	0.987630i	$-0.449881\pi$
$419$	55056.9			0.313606			0.156803	+	0.987630i	$0.449881\pi$
$420$		0			0
$421$	−118222.	−	20845.8i	−0.667015	−	0.117613i	−0.170120	−	0.985423i	$-0.554416\pi$
$421$	−118222.	−	20845.8i	−0.667015	−	0.117613i	−0.496895	+	0.867811i	$0.665527\pi$
$422$		0			0
$423$	−125580.	−	105374.i	−0.701844	−	0.588917i
$424$		0			0
$425$	22869.1	+	39610.5i	0.126611	+	0.219297i
$426$		0			0
$427$	149307.	+	54343.2i	0.818887	+	0.298050i
$428$		0			0
$429$	−177412.	+	307286.i	−0.963979	+	1.66966i
$430$		0			0
$431$	−50451.8	+	8896.02i	−0.271595	+	0.0478896i	−0.307787	−	0.951455i	$-0.599588\pi$
$431$	−50451.8	+	8896.02i	−0.271595	+	0.0478896i	0.0361916	+	0.999345i	$0.488477\pi$
$432$		0			0
$433$	−98086.0	−	116894.i	−0.523156	−	0.623473i	0.438168	−	0.898893i	$-0.355628\pi$
$433$	−98086.0	−	116894.i	−0.523156	−	0.623473i	−0.961324	+	0.275420i	$0.911183\pi$
$434$		0			0
$435$	−28237.6	+	10277.6i	−0.149227	+	0.0543144i
$436$		0			0
$437$	240990.	−	91706.2i	1.26193	−	0.480215i
$438$		0			0
$439$	1574.10	+	4324.80i	0.00816776	+	0.0224407i	0.943710	−	0.330775i	$-0.107310\pi$
$439$	1574.10	+	4324.80i	0.00816776	+	0.0224407i	−0.935542	+	0.353216i	$0.885088\pi$
$440$		0			0
$441$	40456.5	−	33947.1i	0.208023	−	0.174552i
$442$		0			0
$443$	−19737.6	−	111938.i	−0.100574	−	0.570386i	−0.992896	−	0.118986i	$-0.962036\pi$
$443$	−19737.6	−	111938.i	−0.100574	−	0.570386i	0.892321	−	0.451401i	$-0.149075\pi$
$444$		0			0
$445$	21021.8	+	12136.9i	0.106157	+	0.0612900i
$446$		0			0
$447$	−107795.	+	296164.i	−0.539490	+	1.48224i
$448$		0			0
$449$	−143782.	+	83012.8i	−0.713203	+	0.411768i	−0.812246	−	0.583315i	$-0.801755\pi$
$449$	−143782.	+	83012.8i	−0.713203	+	0.411768i	0.0990431	+	0.995083i	$0.468422\pi$
$450$		0			0
$451$	−70567.6	+	84099.2i	−0.346939	+	0.413465i
$452$		0			0
$453$	41908.5	−	237675.i	0.204224	−	1.15821i
$454$		0			0
$455$		−	23174.8i		−	0.111942i
$456$		0			0
$457$	24060.3			0.115205			0.0576023	−	0.998340i	$-0.481654\pi$
$457$	24060.3			0.115205			0.0576023	+	0.998340i	$0.481654\pi$
$458$		0			0
$459$	−77112.8	−	13597.1i	−0.366017	−	0.0645386i
$460$		0			0
$461$	−57941.6	−	48618.7i	−0.272639	−	0.228771i	0.496209	−	0.868203i	$-0.334725\pi$
$461$	−57941.6	−	48618.7i	−0.272639	−	0.228771i	−0.768848	+	0.639432i	$0.779170\pi$
$462$		0			0
$463$	90196.5	+	156225.i	0.420754	+	0.728767i	0.996013	−	0.0892042i	$-0.0284324\pi$
$463$	90196.5	+	156225.i	0.420754	+	0.728767i	−0.575260	+	0.817971i	$0.695099\pi$
$464$		0			0
$465$	−27282.0	−	9929.83i	−0.126174	−	0.0459236i
$466$		0			0
$467$	42977.3	−	74438.9i	0.197063	−	0.341324i	−0.750512	−	0.660857i	$-0.770193\pi$
$467$	42977.3	−	74438.9i	0.197063	−	0.341324i	0.947575	+	0.319534i	$0.103526\pi$
$468$		0			0
$469$	−188518.	+	33240.9i	−0.857053	+	0.151122i
$470$		0			0
$471$	1956.20	+	2331.31i	0.00881803	+	0.0105089i
$472$		0			0
$473$	−333652.	+	121439.i	−1.49132	+	0.542796i
$474$		0			0
$475$	35642.4	−	220889.i	0.157972	−	0.979008i
$476$		0			0
$477$	−83458.4	−	229300.i	−0.366803	−	1.00778i
$478$		0			0
$479$	252890.	−	212200.i	1.10220	−	0.924857i	0.104631	−	0.994511i	$-0.466634\pi$
$479$	252890.	−	212200.i	1.10220	−	0.924857i	0.997571	+	0.0696541i	$0.0221895\pi$
$480$		0			0
$481$	23501.6	+	133284.i	0.101580	+	0.576088i
$482$		0			0
$483$	426379.	+	246170.i	1.82768	+	1.05521i
$484$		0			0
$485$	11341.0	−	31159.2i	0.0482136	−	0.132466i
$486$		0			0
$487$	383052.	−	221155.i	1.61510	−	0.932480i	0.626941	−	0.779067i	$-0.284307\pi$
$487$	383052.	−	221155.i	1.61510	−	0.932480i	0.988162	−	0.153413i	$-0.0490265\pi$
$488$		0			0
$489$	−91784.9	+	109385.i	−0.383843	+	0.457446i
$490$		0			0
$491$	−25947.9	+	147158.i	−0.107631	+	0.610408i	0.882505	+	0.470302i	$0.155855\pi$
$491$	−25947.9	+	147158.i	−0.107631	+	0.610408i	−0.990137	+	0.140105i	$0.955256\pi$
$492$		0			0
$493$		−	63850.2i		−	0.262705i
$494$		0			0
$495$	35733.9			0.145838
$496$		0			0
$497$	−252680.	−	44554.4i	−1.02296	−	0.180375i
$498$		0			0
$499$	81269.1	+	68192.9i	0.326381	+	0.273866i	0.791223	−	0.611528i	$-0.209445\pi$
$499$	81269.1	+	68192.9i	0.326381	+	0.273866i	−0.464843	+	0.885393i	$0.653889\pi$
$500$		0			0
$501$	388706.	+	673258.i	1.54862	+	2.68229i
$502$		0			0
$503$	−377464.	−	137385.i	−1.49190	−	0.543006i	−0.537949	−	0.842977i	$-0.680801\pi$
$503$	−377464.	−	137385.i	−1.49190	−	0.543006i	−0.953948	+	0.299971i	$0.903023\pi$
$504$		0			0
$505$	−21892.5	+	37919.0i	−0.0858446	+	0.148687i
$506$		0			0
$507$	326066.	−	57494.3i	1.26850	−	0.223671i
$508$		0			0
$509$	−303927.	−	362206.i	−1.17310	−	1.39804i	−0.899908	−	0.436080i	$-0.856366\pi$
$509$	−303927.	−	362206.i	−1.17310	−	1.39804i	−0.273188	−	0.961961i	$-0.588078\pi$
$510$		0			0
$511$	−82812.7	+	30141.3i	−0.317143	+	0.115431i
$512$		0			0
$513$	250461.	+	289816.i	0.951710	+	1.10125i
$514$		0			0
$515$	14720.7	+	40444.7i	0.0555026	+	0.152492i
$516$		0			0
$517$	−86595.5	+	72662.2i	−0.323977	+	0.271849i
$518$		0			0
$519$	96577.0	+	547716.i	0.358541	+	2.03339i
$520$		0			0
$521$	190978.	+	110261.i	0.703569	+	0.406206i	0.808675	−	0.588255i	$-0.200185\pi$
$521$	190978.	+	110261.i	0.703569	+	0.406206i	−0.105106	+	0.994461i	$0.533518\pi$
$522$		0			0
$523$	−52251.1	+	143559.i	−0.191026	+	0.524839i	−0.997820	−	0.0659933i	$-0.978978\pi$
$523$	−52251.1	+	143559.i	−0.191026	+	0.524839i	0.806794	+	0.590833i	$0.201201\pi$
$524$		0			0
$525$	369985.	−	213611.i	1.34235	−	0.775006i
$526$		0			0
$527$	39653.2	−	47256.9i	0.142777	−	0.170155i
$528$		0			0
$529$	39996.6	−	226832.i	0.142926	−	0.810575i
$530$		0			0
$531$		−	287906.i		−	1.02109i
$532$		0			0
$533$	236957.			0.834094
$534$		0			0
$535$	49459.9	+	8721.11i	0.172801	+	0.0304694i
$536$		0			0
$537$	244429.	+	205100.i	0.847625	+	0.711242i
$538$		0			0
$539$	−18208.7	−	31538.4i	−0.0626759	−	0.108558i
$540$		0			0
$541$	46433.1	+	16900.3i	0.158647	+	0.0577430i	0.420123	−	0.907467i	$-0.361987\pi$
$541$	46433.1	+	16900.3i	0.158647	+	0.0577430i	−0.261476	+	0.965210i	$0.584209\pi$
$542$		0			0
$543$	34711.4	−	60122.0i	0.117726	−	0.203908i
$544$		0			0
$545$	7430.74	−	1310.24i	0.0250172	−	0.00441121i
$546$		0			0
$547$	−250370.	−	298379.i	−0.836773	−	0.997227i	−0.999944	−	0.0106295i	$-0.996616\pi$
$547$	−250370.	−	298379.i	−0.836773	−	0.997227i	0.163170	−	0.986598i	$-0.447828\pi$
$548$		0			0
$549$	496906.	−	180859.i	1.64866	−	0.600061i
$550$		0			0
$551$	−197270.	+	242168.i	−0.649766	+	0.797652i
$552$		0			0
$553$	−95159.5	−	261449.i	−0.311173	−	0.854941i
$554$		0			0
$555$	16053.0	−	13470.0i	0.0521158	−	0.0437303i
$556$		0			0
$557$	39569.2	+	224408.i	0.127540	+	0.723316i	0.979767	+	0.200143i	$0.0641406\pi$
$557$	39569.2	+	224408.i	0.127540	+	0.723316i	−0.852227	+	0.523173i	$0.824748\pi$
$558$		0			0
$559$	663696.	+	383185.i	2.12396	+	1.22627i
$560$		0			0
$561$	−39926.3	+	109697.i	−0.126862	+	0.348552i
$562$		0			0
$563$	55165.1	−	31849.6i	0.174040	−	0.100482i	−0.410450	−	0.911883i	$-0.634628\pi$
$563$	55165.1	−	31849.6i	0.174040	−	0.100482i	0.584489	+	0.811401i	$0.301295\pi$
$564$		0			0
$565$	−32617.5	+	38872.0i	−0.102177	+	0.121770i
$566$		0			0
$567$	−31014.9	+	175894.i	−0.0964726	+	0.547123i
$568$		0			0
$569$		−	158917.i		−	0.490848i	−0.969416	−	0.245424i	$-0.921073\pi$
$569$		−	158917.i		−	0.490848i	0.969416	−	0.245424i	$-0.0789271\pi$
$570$		0			0
$571$	−529437.			−1.62384			−0.811918	−	0.583772i	$-0.801576\pi$
$571$	−529437.			−1.62384			−0.811918	+	0.583772i	$0.801576\pi$
$572$		0			0
$573$	−450518.	−	79438.5i	−1.37216	−	0.241948i
$574$		0			0
$575$	−339125.	−	284560.i	−1.02571	−	0.860672i
$576$		0			0
$577$	−178205.	−	308660.i	−0.535264	−	0.927104i	−0.999151	−	0.0412098i	$-0.986879\pi$
$577$	−178205.	−	308660.i	−0.535264	−	0.927104i	0.463887	−	0.885895i	$-0.346455\pi$
$578$		0			0
$579$	38642.6	+	14064.7i	0.115268	+	0.0419541i
$580$		0			0
$581$	−164347.	+	284658.i	−0.486866	+	0.843277i
$582$		0			0
$583$	−165708.	+	29218.8i	−0.487536	+	0.0859657i
$584$		0			0
$585$	−49576.8	−	59083.4i	−0.144866	−	0.172645i
$586$		0			0
$587$	−486773.	+	177171.i	−1.41270	+	0.514181i	−0.931922	−	0.362660i	$-0.881869\pi$
$587$	−486773.	+	177171.i	−1.41270	+	0.514181i	−0.480780	+	0.876841i	$0.659646\pi$
$588$		0			0
$589$	−296398.	+	56722.2i	−0.854368	+	0.163502i
$590$		0			0
$591$	−228612.	−	628105.i	−0.654521	−	1.79828i
$592$		0			0
$593$	246993.	−	207252.i	0.702385	−	0.589371i	−0.220066	−	0.975485i	$-0.570627\pi$
$593$	246993.	−	207252.i	0.702385	−	0.589371i	0.922451	+	0.386114i	$0.126183\pi$
$594$		0			0
$595$	−1323.98	−	7508.67i	−0.00373979	−	0.0212094i
$596$		0			0
$597$	−937979.	−	541542.i	−2.63175	−	1.51944i
$598$		0			0
$599$	73922.5	−	203100.i	0.206026	−	0.566053i	−0.793044	−	0.609165i	$-0.791505\pi$
$599$	73922.5	−	203100.i	0.206026	−	0.566053i	0.999070	+	0.0431116i	$0.0137271\pi$
$600$		0			0
$601$	−289330.	+	167045.i	−0.801022	+	0.462470i	−0.843828	−	0.536613i	$-0.819703\pi$
$601$	−289330.	+	167045.i	−0.801022	+	0.462470i	0.0428067	+	0.999083i	$0.486370\pi$
$602$		0			0
$603$	−409510.	+	488035.i	−1.12624	+	1.34220i
$604$		0			0
$605$	−1521.92	+	8631.21i	−0.00415795	+	0.0235809i
$606$		0			0
$607$		−	313650.i		−	0.851271i	−0.904895	−	0.425636i	$-0.860051\pi$
$607$		−	313650.i		−	0.851271i	0.904895	−	0.425636i	$-0.139949\pi$
$608$		0			0
$609$	−596399.			−1.60806
$610$		0			0
$611$	240284.	+	42368.5i	0.643638	+	0.113491i
$612$		0			0
$613$	59956.8	+	50309.7i	0.159557	+	0.133885i	0.719071	−	0.694937i	$-0.244568\pi$
$613$	59956.8	+	50309.7i	0.159557	+	0.133885i	−0.559514	+	0.828821i	$0.689012\pi$
$614$		0			0
$615$	−18344.8	−	31774.2i	−0.0485024	−	0.0840086i
$616$		0			0
$617$	360615.	+	131253.i	0.947269	+	0.344778i	0.769032	−	0.639210i	$-0.220738\pi$
$617$	360615.	+	131253.i	0.947269	+	0.344778i	0.178237	+	0.983988i	$0.442961\pi$
$618$		0			0
$619$	267081.	−	462598.i	0.697046	−	1.20732i	−0.272440	−	0.962173i	$-0.587831\pi$
$619$	267081.	−	462598.i	0.697046	−	1.20732i	0.969486	−	0.245146i	$-0.0788360\pi$
$620$		0			0
$621$	746367.	−	131605.i	1.93539	−	0.341262i
$622$		0			0
$623$	309672.	+	369053.i	0.797859	+	0.950851i
$624$		0			0
$625$	−357921.	+	130272.i	−0.916277	+	0.333498i
$626$		0			0
$627$	490346.	−	292697.i	1.24729	−	0.744531i
$628$		0			0
$629$	15229.1	+	41841.6i	0.0384922	+	0.105756i
$630$		0			0
$631$	307667.	−	258163.i	0.772720	−	0.648389i	−0.168684	−	0.985670i	$-0.553952\pi$
$631$	307667.	−	258163.i	0.772720	−	0.648389i	0.941404	+	0.337281i	$0.109507\pi$
$632$		0			0
$633$	39856.2	+	226036.i	0.0994691	+	0.564117i
$634$		0			0
$635$	−38079.1	−	21985.0i	−0.0944364	−	0.0545229i
$636$		0			0
$637$	−26883.8	+	73862.7i	−0.0662541	+	0.182032i
$638$		0			0
$639$	−739512.	+	426958.i	−1.81111	+	1.04564i
$640$		0			0
$641$	322528.	−	384374.i	0.784967	−	0.935487i	−0.214179	−	0.976794i	$-0.568708\pi$
$641$	322528.	−	384374.i	0.784967	−	0.935487i	0.999146	+	0.0413071i	$0.0131522\pi$
$642$		0			0
$643$	−94880.3	+	538093.i	−0.229485	+	1.30147i	0.624438	+	0.781074i	$0.285328\pi$
$643$	−94880.3	+	538093.i	−0.229485	+	1.30147i	−0.853923	+	0.520399i	$0.825783\pi$
$644$		0			0
$645$		−	118662.i		−	0.285229i
$646$		0			0
$647$	761998.			1.82031			0.910155	−	0.414268i	$-0.135962\pi$
$647$	761998.			1.82031			0.910155	+	0.414268i	$0.135962\pi$
$648$		0			0
$649$	−195513.	−	34474.3i	−0.464181	−	0.0818476i
$650$		0			0
$651$	−441407.	−	370384.i	−1.04154	−	0.873958i
$652$		0			0
$653$	168084.	+	291130.i	0.394185	+	0.682748i	0.992997	−	0.118141i	$-0.0376936\pi$
$653$	168084.	+	291130.i	0.394185	+	0.682748i	−0.598812	+	0.800890i	$0.704360\pi$
$654$		0			0
$655$	−18424.1	−	6705.83i	−0.0429442	−	0.0156304i
$656$		0			0
$657$	−146648.	+	254002.i	−0.339739	+	0.588445i
$658$		0			0
$659$	−446874.	+	78796.0i	−1.02900	+	0.181440i	−0.662565	−	0.749004i	$-0.730532\pi$
$659$	−446874.	+	78796.0i	−1.02900	+	0.181440i	−0.366433	+	0.930444i	$0.619421\pi$
$660$		0			0
$661$	−57916.7	−	69022.4i	−0.132556	−	0.157975i	0.695683	−	0.718349i	$-0.255102\pi$
$661$	−57916.7	−	69022.4i	−0.132556	−	0.157975i	−0.828240	+	0.560374i	$0.810657\pi$
$662$		0			0
$663$	236769.	−	86176.7i	0.538638	−	0.196048i
$664$		0			0
$665$	−18177.0	+	32569.0i	−0.0411036	+	0.0736481i
$666$		0			0
$667$	211369.	+	580730.i	0.475104	+	1.30534i
$668$		0			0
$669$	135398.	−	113612.i	0.302524	−	0.253848i
$670$		0			0
$671$	−63318.8	−	359099.i	−0.140633	−	0.797570i
$672$		0			0
$673$	−182103.	−	105137.i	−0.402056	−	0.232127i	0.285315	−	0.958434i	$-0.407902\pi$
$673$	−182103.	−	105137.i	−0.402056	−	0.232127i	−0.687371	+	0.726307i	$0.741235\pi$
$674$		0			0
$675$	224927.	−	617982.i	0.493667	−	1.35634i
$676$		0			0
$677$	197145.	−	113821.i	0.430138	−	0.248340i	−0.269268	−	0.963065i	$-0.586782\pi$
$677$	197145.	−	113821.i	0.430138	−	0.248340i	0.699405	+	0.714725i	$0.253448\pi$
$678$		0			0
$679$	423023.	−	504139.i	0.917538	−	1.09348i
$680$		0			0
$681$	−126059.	+	714917.i	−0.271819	+	1.54156i
$682$		0			0
$683$			517412.i			1.10916i	0.832130	+	0.554581i	$0.187121\pi$
$683$			517412.i			1.10916i	−0.832130	+	0.554581i	$0.812879\pi$
$684$		0			0
$685$	81199.0			0.173049
$686$		0			0
$687$	286049.	+	50438.2i	0.606076	+	0.106868i
$688$		0			0
$689$	278213.	+	233448.i	0.586056	+	0.491759i
$690$		0			0
$691$	151640.	+	262647.i	0.317582	+	0.550069i	0.979983	−	0.199081i	$-0.0637957\pi$
$691$	151640.	+	262647.i	0.317582	+	0.550069i	−0.662401	+	0.749150i	$0.730462\pi$
$692$		0			0
$693$	666440.	+	242564.i	1.38770	+	0.505080i
$694$		0			0
$695$	8639.96	−	14964.8i	0.0178872	−	0.0309815i
$696$		0			0
$697$	76774.3	−	13537.4i	0.158034	−	0.0278656i
$698$		0			0
$699$	555125.	+	661572.i	1.13615	+	1.35401i
$700$		0			0
$701$	−161694.	+	58851.8i	−0.329047	+	0.119763i	−0.501261	−	0.865296i	$-0.667130\pi$
$701$	−161694.	+	58851.8i	−0.329047	+	0.119763i	0.172214	+	0.985060i	$0.444908\pi$
$702$		0			0
$703$	71512.3	−	205746.i	0.144701	−	0.416314i
$704$		0			0
$705$	−12921.1	−	35500.3i	−0.0259968	−	0.0714257i
$706$		0			0
$707$	−665694.	+	558584.i	−1.33179	+	1.11751i
$708$		0			0
$709$	−153332.	−	869587.i	−0.305028	−	1.72990i	−0.623374	−	0.781924i	$-0.714239\pi$
$709$	−153332.	−	869587.i	−0.305028	−	1.72990i	0.318347	−	0.947974i	$-0.396872\pi$
$710$		0			0
$711$	−801911.	−	462983.i	−1.58631	−	0.915854i
$712$		0			0
$713$	−204216.	+	561078.i	−0.401708	+	1.10368i
$714$		0			0
$715$	−46059.1	+	26592.2i	−0.0900956	+	0.0520167i
$716$		0			0
$717$	779879.	−	929424.i	1.51701	−	1.80790i
$718$		0			0
$719$	82145.5	−	465870.i	0.158901	−	0.901171i	−0.796232	−	0.604992i	$-0.793176\pi$
$719$	82145.5	−	465870.i	0.158901	−	0.901171i	0.955132	−	0.296179i	$-0.0957125\pi$
$720$		0			0
$721$			854222.i			1.64324i
$722$		0			0
$723$	−450556.			−0.861929
$724$		0			0
$725$	528116.	+	93121.1i	1.00474	+	0.177163i
$726$		0			0
$727$	−333613.	−	279935.i	−0.631210	−	0.529648i	0.270094	−	0.962834i	$-0.412945\pi$
$727$	−333613.	−	279935.i	−0.631210	−	0.529648i	−0.901305	+	0.433185i	$0.857390\pi$
$728$		0			0
$729$	−356923.	−	618210.i	−0.671614	−	1.16327i
$730$		0			0
$731$	236930.	+	86235.3i	0.443389	+	0.161380i
$732$		0			0
$733$	298467.	−	516959.i	0.555505	−	0.962162i	−0.442359	−	0.896838i	$-0.645858\pi$
$733$	298467.	−	516959.i	0.555505	−	0.962162i	0.997864	−	0.0653246i	$-0.0208083\pi$
$734$		0			0
$735$	11985.7	−	2113.41i	0.0221866	−	0.00391209i
$736$		0			0
$737$	282383.	+	336531.i	0.519880	+	0.619569i
$738$		0			0
$739$	−581638.	+	211699.i	−1.06504	+	0.387641i	−0.814318	−	0.580419i	$-0.802889\pi$
$739$	−581638.	+	211699.i	−1.06504	+	0.387641i	−0.250718	+	0.968060i	$0.580667\pi$
$740$		0			0
$741$	−1.16425e6	−	404666.i	−2.12037	−	0.736988i
$742$		0			0
$743$	212892.	+	584915.i	0.385639	+	1.05953i	0.968944	+	0.247281i	$0.0795370\pi$
$743$	212892.	+	584915.i	0.385639	+	1.05953i	−0.583305	+	0.812253i	$0.698241\pi$
$744$		0			0
$745$	−36188.8	+	30366.0i	−0.0652020	+	0.0547110i
$746$		0			0
$747$	189958.	+	1.07730e6i	0.340421	+	1.93062i
$748$		0			0
$749$	863232.	+	498387.i	1.53874	+	0.888389i
$750$		0			0
$751$	60368.6	−	165861.i	0.107036	−	0.294080i	−0.874599	−	0.484847i	$-0.838875\pi$
$751$	60368.6	−	165861.i	0.107036	−	0.294080i	0.981635	+	0.190767i	$0.0610975\pi$
$752$		0			0
$753$	−1.46166e6	+	843889.i	−2.57784	+	1.48832i
$754$		0			0
$755$	23252.6	−	27711.4i	0.0407923	−	0.0486144i
$756$		0			0
$757$	48880.6	−	277216.i	0.0852992	−	0.483756i	−0.911992	−	0.410207i	$-0.865456\pi$
$757$	48880.6	−	277216.i	0.0852992	−	0.483756i	0.997292	−	0.0735486i	$-0.0234324\pi$
$758$		0			0
$759$		−	1.12988e6i		−	1.96133i
$760$		0			0
$761$	877643.			1.51547			0.757737	−	0.652560i	$-0.226305\pi$
$761$	877643.			1.51547			0.757737	+	0.652560i	$0.226305\pi$
$762$		0			0
$763$	147478.	+	26004.4i	0.253325	+	0.0446680i
$764$		0			0
$765$	−19438.4	−	16310.7i	−0.0332152	−	0.0278709i
$766$		0			0
$767$	214253.	+	371097.i	0.364196	+	0.630807i
$768$		0			0
$769$	802513.	+	292091.i	1.35706	+	0.493930i	0.915145	−	0.403126i	$-0.132076\pi$
$769$	802513.	+	292091.i	1.35706	+	0.493930i	0.441917	+	0.897056i	$0.354298\pi$
$770$		0			0
$771$	425134.	−	736353.i	0.715182	−	1.23873i
$772$		0			0
$773$	772475.	−	136208.i	1.29278	−	0.227953i	0.515384	−	0.856960i	$-0.327649\pi$
$773$	772475.	−	136208.i	1.29278	−	0.227953i	0.777400	+	0.629007i	$0.216538\pi$
$774$		0			0
$775$	333038.	+	396899.i	0.554486	+	0.660810i
$776$		0			0
$777$	390825.	−	142249.i	0.647352	−	0.235617i
$778$		0			0
$779$	−333011.	−	185856.i	−0.548761	−	0.306267i
$780$		0			0
$781$	201391.	+	553318.i	0.330170	+	0.907136i
$782$		0			0
$783$	−703278.	+	590120.i	−1.14711	+	0.962536i
$784$		0			0
$785$	79.2117	+	449.232i	0.000128543	+	0.000729006i
$786$		0			0
$787$	70058.3	+	40448.2i	0.113112	+	0.0653054i	0.555489	−	0.831524i	$-0.312531\pi$
$787$	70058.3	+	40448.2i	0.113112	+	0.0653054i	−0.442377	+	0.896829i	$0.645865\pi$
$788$		0			0
$789$	527968.	−	1.45058e6i	0.848113	−	2.33017i
$790$		0			0
$791$	−872185.	+	503556.i	−1.39398	+	0.804813i
$792$		0			0
$793$	−505896.	+	602903.i	−0.804479	+	0.958741i
$794$		0			0
$795$	9764.90	−	55379.5i	0.0154502	−	0.0876223i
$796$		0			0
$797$		−	217329.i		−	0.342138i	−0.985259	−	0.171069i	$-0.945278\pi$
$797$		−	217329.i		−	0.342138i	0.985259	−	0.171069i	$-0.0547220\pi$
$798$		0			0
$799$	80272.6			0.125740
$800$		0			0
$801$	1.57900e6	+	278420.i	2.46102	+	0.433945i
$802$		0			0
$803$	154929.	+	130001.i	0.240272	+	0.201612i
$804$		0			0
$805$	36898.4	+	63909.9i	0.0569398	+	0.0986226i
$806$		0			0
$807$	−603196.	−	219545.i	−0.926214	−	0.337114i
$808$		0			0
$809$	132242.	−	229051.i	0.202057	−	0.349973i	−0.747134	−	0.664673i	$-0.768571\pi$
$809$	132242.	−	229051.i	0.202057	−	0.349973i	0.949191	+	0.314700i	$0.101904\pi$
$810$		0			0
$811$	26180.5	−	4616.33i	0.0398049	−	0.00701868i	−0.153710	−	0.988116i	$-0.549122\pi$
$811$	26180.5	−	4616.33i	0.0398049	−	0.00701868i	0.193515	+	0.981097i	$0.438011\pi$
$812$		0			0
$813$	396725.	+	472799.i	0.600218	+	0.715312i
$814$		0			0
$815$	−20112.3	+	7320.29i	−0.0302794	+	0.0110208i
$816$		0			0
$817$	−632185.	−	1.05908e6i	−0.947110	−	1.58666i
$818$		0			0
$819$	−523550.	−	1.43844e6i	−0.780531	−	2.14449i
$820$		0			0
$821$	−209659.	+	175925.i	−0.311049	+	0.261001i	−0.784925	−	0.619590i	$-0.787299\pi$
$821$	−209659.	+	175925.i	−0.311049	+	0.261001i	0.473877	+	0.880591i	$0.342854\pi$
$822$		0			0
$823$	−111480.	−	632237.i	−0.164588	−	0.933427i	−0.949488	−	0.313804i	$-0.898397\pi$
$823$	−111480.	−	632237.i	−0.164588	−	0.933427i	0.784900	−	0.619623i	$-0.212715\pi$
$824$		0			0
$825$	−849089.	−	490222.i	−1.24751	−	0.720252i
$826$		0			0
$827$	−209840.	+	576530.i	−0.306815	+	0.842968i	0.686457	+	0.727170i	$0.259165\pi$
$827$	−209840.	+	576530.i	−0.306815	+	0.842968i	−0.993273	+	0.115798i	$0.963057\pi$
$828$		0			0
$829$	20876.8	−	12053.2i	0.0303777	−	0.0175386i	−0.484734	−	0.874661i	$-0.661084\pi$
$829$	20876.8	−	12053.2i	0.0303777	−	0.0175386i	0.515112	+	0.857123i	$0.327750\pi$
$830$		0			0
$831$	−955687.	+	1.13894e6i	−1.38393	+	1.64930i
$832$		0			0
$833$	−4490.60	+	25467.5i	−0.00647165	+	0.0367025i
$834$		0			0
$835$			116526.i			0.167129i
$836$		0			0
$837$	−886996.			−1.26611
$838$		0			0
$839$	−158732.	−	27988.7i	−0.225496	−	0.0397611i	0.0597582	−	0.998213i	$-0.480967\pi$
$839$	−158732.	−	27988.7i	−0.225496	−	0.0397611i	−0.285255	+	0.958452i	$0.592078\pi$
$840$		0			0
$841$	−31666.3	−	26571.2i	−0.0447719	−	0.0375681i
$842$		0			0
$843$	26964.7	+	46704.2i	0.0379438	+	0.0657205i
$844$		0			0
$845$	46635.1	+	16973.8i	0.0653130	+	0.0237720i
$846$		0			0
$847$	−86973.2	+	150642.i	−0.121232	+	0.209981i
$848$		0			0
$849$	−196647.	+	34674.2i	−0.272817	+	0.0481051i
$850$		0			0
$851$	−277023.	−	330143.i	−0.382522	−	0.455873i
$852$		0			0
$853$	−177828.	+	64724.0i	−0.244400	+	0.0889543i	−0.461316	−	0.887236i	$-0.652622\pi$
$853$	−177828.	+	64724.0i	−0.244400	+	0.0889543i	0.216916	+	0.976190i	$0.430400\pi$
$854$		0			0
$855$	23331.8	+	121919.i	0.0319166	+	0.166778i
$856$		0			0
$857$	−305096.	−	838245.i	−0.415408	−	1.14133i	−0.954274	−	0.298933i	$-0.903369\pi$
$857$	−305096.	−	838245.i	−0.415408	−	1.14133i	0.538866	−	0.842392i	$-0.318853\pi$
$858$		0			0
$859$	−745497.	+	625546.i	−1.01032	+	0.847760i	−0.988381	−	0.151999i	$-0.951429\pi$
$859$	−745497.	+	625546.i	−1.01032	+	0.847760i	−0.0219409	+	0.999759i	$0.506985\pi$
$860$		0			0
$861$	−126447.	−	717117.i	−0.170570	−	0.967350i
$862$		0			0
$863$	8871.54	+	5121.99i	0.0119118	+	0.00687728i	0.505944	−	0.862566i	$-0.331144\pi$
$863$	8871.54	+	5121.99i	0.0119118	+	0.00687728i	−0.494032	+	0.869444i	$0.664478\pi$
$864$		0			0
$865$	−28512.0	+	78336.2i	−0.0381062	+	0.104696i
$866$		0			0
$867$	−1.02923e6	+	594227.i	−1.36922	+	0.790522i
$868$		0			0
$869$	−410428.	+	489129.i	−0.543497	+	0.647715i
$870$		0			0
$871$	164654.	−	933799.i	0.217038	−	1.23088i
$872$		0			0
$873$		−	2.19024e6i		−	2.87384i
$874$		0			0
$875$	128611.			0.167981
$876$		0			0
$877$	731216.	+	128933.i	0.950706	+	0.167635i	0.627433	−	0.778671i	$-0.284106\pi$
$877$	731216.	+	128933.i	0.950706	+	0.167635i	0.323273	+	0.946306i	$0.395217\pi$
$878$		0			0
$879$	961491.	+	806787.i	1.24442	+	1.04419i
$880$		0			0
$881$	428429.	+	742061.i	0.551985	+	0.956066i	0.998131	+	0.0611060i	$0.0194628\pi$
$881$	428429.	+	742061.i	0.551985	+	0.956066i	−0.446146	+	0.894960i	$0.647204\pi$
$882$		0			0
$883$	−652614.	−	237532.i	−0.837018	−	0.304650i	−0.112282	−	0.993676i	$-0.535816\pi$
$883$	−652614.	−	237532.i	−0.837018	−	0.304650i	−0.724736	+	0.689027i	$0.758038\pi$
$884$		0			0
$885$	33174.2	−	57459.4i	0.0423559	−	0.0733626i
$886$		0			0
$887$	−114060.	+	20111.9i	−0.144973	+	0.0255627i	−0.245664	−	0.969355i	$-0.579006\pi$
$887$	−114060.	+	20111.9i	−0.144973	+	0.0255627i	0.100691	+	0.994918i	$0.467895\pi$
$888$		0			0
$889$	−560943.	−	668506.i	−0.709766	−	0.845867i
$890$		0			0
$891$	385171.	−	140191.i	0.485175	−	0.176589i
$892$		0			0
$893$	−304454.	−	248008.i	−0.381785	−	0.311002i
$894$		0			0
$895$	16357.7	+	44942.5i	0.0204210	+	0.0561062i
$896$		0			0
$897$	−1.86818e6	+	1.56759e6i	−2.32185	+	1.94826i
$898$		0			0
$899$	−125597.	−	712296.i	−0.155403	−	0.881335i
$900$		0			0
$901$	103478.	+	59743.2i	0.127467	+	0.0735934i
$902$		0			0
$903$	805489.	−	2.21306e6i	0.987834	−	2.71405i
$904$		0			0
$905$	9011.69	−	5202.90i	0.0110029	−	0.00635256i
$906$		0			0
$907$	559305.	−	666554.i	0.679883	−	0.810253i	−0.310210	−	0.950668i	$-0.600399\pi$
$907$	559305.	−	666554.i	0.679883	−	0.810253i	0.990093	+	0.140415i	$0.0448437\pi$
$908$		0			0
$909$	−502211.	+	2.84818e6i	−0.607797	+	3.44699i
$910$		0			0
$911$			363042.i			0.437442i	0.975787	+	0.218721i	$0.0701884\pi$
$911$			363042.i			0.437442i	−0.975787	+	0.218721i	$0.929812\pi$
$912$		0			0
$913$	754329.			0.904939
$914$		0			0
$915$	120011.	+	21161.1i	0.143343	+	0.0252753i
$916$		0			0
$917$	−298092.	−	250129.i	−0.354496	−	0.297457i
$918$		0			0
$919$	190974.	+	330777.i	0.226123	+	0.391656i	0.956656	−	0.291221i	$-0.0940617\pi$
$919$	190974.	+	330777.i	0.226123	+	0.391656i	−0.730533	+	0.682877i	$0.760728\pi$
$920$		0			0
$921$	977669.	+	355843.i	1.15258	+	0.419506i
$922$		0			0
$923$	635462.	−	1.10065e6i	0.745910	−	1.29195i
$924$		0			0
$925$	−368289.	+	64939.3i	−0.430433	+	0.0758970i
$926$		0			0
$927$	1.82740e6	+	2.17781e6i	2.12654	+	2.53431i
$928$		0			0
$929$	938767.	−	341683.i	1.08774	−	0.395906i	0.264959	−	0.964260i	$-0.414642\pi$
$929$	938767.	−	341683.i	1.08774	−	0.395906i	0.822785	+	0.568353i	$0.192419\pi$
$930$		0			0
$931$	95715.3	−	82717.8i	0.110429	−	0.0954333i
$932$		0			0
$933$	−409434.	−	1.12491e6i	−0.470349	−	1.29227i
$934$		0			0
$935$	−13404.0	+	11247.3i	−0.0153324	+	0.0128654i
$936$		0			0
$937$	194823.	+	1.10490e6i	0.221902	+	1.25847i	0.868519	+	0.495655i	$0.165072\pi$
$937$	194823.	+	1.10490e6i	0.221902	+	1.25847i	−0.646617	+	0.762815i	$0.723817\pi$
$938$		0			0
$939$	762732.	+	440363.i	0.865049	+	0.499436i
$940$		0			0
$941$	−365334.	+	1.00375e6i	−0.412582	+	1.13356i	0.543230	+	0.839584i	$0.317201\pi$
$941$	−365334.	+	1.00375e6i	−0.412582	+	1.13356i	−0.955813	+	0.293977i	$0.905021\pi$
$942$		0			0
$943$	−653464.	+	377277.i	−0.734849	+	0.424265i
$944$		0			0
$945$	−70467.6	+	83980.0i	−0.0789089	+	0.0940399i
$946$		0			0
$947$	292348.	−	1.65799e6i	0.325987	−	1.84877i	−0.176657	−	0.984273i	$-0.556528\pi$
$947$	292348.	−	1.65799e6i	0.325987	−	1.84877i	0.502644	−	0.864493i	$-0.332361\pi$
$948$		0			0
$949$		−	436527.i		−	0.484706i
$950$		0			0
$951$	312401.			0.345423
$952$		0			0
$953$	11284.1	+	1989.69i	0.0124246	+	0.00219079i	0.179857	−	0.983693i	$-0.442436\pi$
$953$	11284.1	+	1989.69i	0.0124246	+	0.00219079i	−0.167432	+	0.985884i	$0.553548\pi$
$954$		0			0
$955$	−52527.6	−	44075.9i	−0.0575945	−	0.0483275i
$956$		0			0
$957$	684345.	+	1.18532e6i	0.747225	+	1.29423i
$958$		0			0
$959$	1.51437e6	+	551185.i	1.64662	+	0.599322i
$960$		0			0
$961$	−112357.	+	194607.i	−0.121661	+	0.210723i
$962$		0			0
$963$	3.26696e6	−	576052.i	3.52282	−	0.621169i
$964$		0			0
$965$	3962.06	+	4721.79i	0.00425467	+	0.00507052i
$966$		0			0
$967$	−1.39440e6	+	507520.i	−1.49120	+	0.542751i	−0.953764	−	0.300556i	$-0.902828\pi$
$967$	−1.39440e6	+	507520.i	−1.49120	+	0.542751i	−0.537432	+	0.843307i	$0.680605\pi$
$968$		0			0
$969$	−400338.	−	64598.3i	−0.426363	−	0.0687976i
$970$		0			0
$971$	427600.	+	1.17482e6i	0.453523	+	1.24604i	0.930229	+	0.366981i	$0.119608\pi$
$971$	427600.	+	1.17482e6i	0.453523	+	1.24604i	−0.476706	+	0.879063i	$0.658169\pi$
$972$		0			0
$973$	262718.	−	220447.i	0.277501	−	0.232851i
$974$		0			0
$975$	367472.	+	2.08404e6i	0.386558	+	2.19228i
$976$		0			0
$977$	36995.9	+	21359.6i	0.0387583	+	0.0223771i	0.519254	−	0.854620i	$-0.326210\pi$
$977$	36995.9	+	21359.6i	0.0387583	+	0.0223771i	−0.480496	+	0.876997i	$0.659543\pi$
$978$		0			0
$979$	378142.	−	1.03894e6i	0.394539	−	1.08399i
$980$		0			0
$981$	431620.	−	249196.i	0.448501	−	0.258942i
$982$		0			0
$983$	398552.	−	474975.i	0.412456	−	0.491546i	−0.519320	−	0.854580i	$-0.673815\pi$
$983$	398552.	−	474975.i	0.412456	−	0.491546i	0.931776	+	0.363034i	$0.118259\pi$
$984$		0			0
$985$	17397.6	−	98666.8i	0.0179315	−	0.101695i
$986$		0			0
$987$		−	749794.i		−	0.769675i
$988$		0			0
$989$	−2.44039e6			−2.49498
$990$		0			0
$991$	−782007.	−	137889.i	−0.796276	−	0.140405i	−0.239313	−	0.970942i	$-0.576922\pi$
$991$	−782007.	−	137889.i	−0.796276	−	0.140405i	−0.556963	+	0.830538i	$0.688033\pi$
$992$		0			0
$993$	−996677.	−	836312.i	−1.01078	−	0.848144i
$994$		0			0
$995$	−81171.8	−	140594.i	−0.0819897	−	0.142010i
$996$		0			0
$997$	−422163.	−	153655.i	−0.424707	−	0.154581i	0.120819	−	0.992675i	$-0.461448\pi$
$997$	−422163.	−	153655.i	−0.424707	−	0.154581i	−0.545526	+	0.838094i	$0.683670\pi$
$998$		0			0
$999$	320113.	−	554451.i	0.320754	−	0.555562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.33.7	✓	42
19.15	odd	18	inner	76.5.j.a.53.7	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.7	✓	42	1.1	even	1	trivial
76.5.j.a.53.7	yes	42	19.15	odd	18	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(14.9907 + 2.64326i) q^{3} +(1.74782 + 1.46659i) q^{5} +(22.6416 + 39.2164i) q^{7} +(141.618 + 51.5447i) q^{9} +O(q^{10})\)	\(q+(14.9907 + 2.64326i) q^{3} +(1.74782 + 1.46659i) q^{5} +(22.6416 + 39.2164i) q^{7} +(141.618 + 51.5447i) q^{9} +(51.9608 - 89.9988i) q^{11} +(-220.896 + 38.9500i) q^{13} +(22.3243 + 26.6051i) q^{15} +(-69.3454 + 25.2397i) q^{17} +(340.990 + 118.520i) q^{19} +(235.753 + 647.727i) q^{21} +(547.158 - 459.120i) q^{23} +(-107.626 - 610.378i) q^{25} +(918.911 + 530.533i) q^{27} +(-295.925 + 813.048i) q^{29} +(-723.951 + 417.974i) q^{31} +(1016.82 - 1211.79i) q^{33} +(-17.9411 + 101.749i) q^{35} -603.379i q^{37} -3414.34 q^{39} +(-1040.36 - 183.444i) q^{41} +(-2617.31 - 2196.19i) q^{43} +(171.927 + 297.786i) q^{45} +(-1022.17 - 372.038i) q^{47} +(175.216 - 303.482i) q^{49} +(-1106.25 + 195.061i) q^{51} +(-1040.77 - 1240.34i) q^{53} +(222.810 - 81.0960i) q^{55} +(4798.38 + 2678.01i) q^{57} +(-653.388 - 1795.17i) q^{59} +(2687.88 - 2255.40i) q^{61} +(1185.06 + 6720.80i) q^{63} +(-443.210 - 255.888i) q^{65} +(-1445.83 + 3972.38i) q^{67} +(9415.82 - 5436.23i) q^{69} +(-3642.09 + 4340.47i) q^{71} +(-337.943 + 1916.57i) q^{73} -9434.45i q^{75} +4705.90 q^{77} +(-6050.83 - 1066.92i) q^{79} +(3021.46 + 2535.30i) q^{81} +(3629.32 + 6286.16i) q^{83} +(-158.219 - 57.5872i) q^{85} +(-6585.21 + 11405.9i) q^{87} +(10477.3 - 1847.43i) q^{89} +(-6528.93 - 7780.87i) q^{91} +(-11957.3 + 4352.11i) q^{93} +(422.168 + 707.244i) q^{95} +(-4970.62 - 13656.7i) q^{97} +(11997.5 - 10067.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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