LMFDB - Embedded newform 76.5.j.a.53.5

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			53.5
Character	$\chi$	$=$	76.53
Dual form			76.5.j.a.33.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.99890 - 1.05777i) q^{3} +(34.0076 - 28.5357i) q^{5} +(-4.84547 + 8.39260i) q^{7} +(-41.2471 + 15.0127i) q^{9} +O(q^{10})$	\(q+(5.99890 - 1.05777i) q^{3} +(34.0076 - 28.5357i) q^{5} +(-4.84547 + 8.39260i) q^{7} +(-41.2471 + 15.0127i) q^{9} +(-85.0973 - 147.393i) q^{11} +(264.067 + 46.5622i) q^{13} +(173.824 - 207.155i) q^{15} +(-15.8843 - 5.78142i) q^{17} +(360.996 + 1.73039i) q^{19} +(-20.1901 + 55.4718i) q^{21} +(-237.410 - 199.211i) q^{23} +(233.696 - 1325.36i) q^{25} +(-658.861 + 380.393i) q^{27} +(408.729 + 1122.97i) q^{29} +(591.769 + 341.658i) q^{31} +(-666.398 - 794.182i) q^{33} +(74.7064 + 423.681i) q^{35} +75.0731i q^{37} +1633.37 q^{39} +(-1640.73 + 289.305i) q^{41} +(-1655.38 + 1389.03i) q^{43} +(-974.316 + 1687.56i) q^{45} +(-3586.36 + 1305.33i) q^{47} +(1153.54 + 1997.99i) q^{49} +(-101.404 - 17.8802i) q^{51} +(1513.80 - 1804.08i) q^{53} +(-7099.91 - 2584.16i) q^{55} +(2167.41 - 371.470i) q^{57} +(-101.845 + 279.818i) q^{59} +(4809.33 + 4035.51i) q^{61} +(73.8660 - 418.915i) q^{63} +(10309.0 - 5951.89i) q^{65} +(1482.85 + 4074.08i) q^{67} +(-1634.92 - 943.922i) q^{69} +(-2209.37 - 2633.02i) q^{71} +(-32.0162 - 181.573i) q^{73} -8197.89i q^{75} +1649.35 q^{77} +(-6939.21 + 1223.57i) q^{79} +(-826.450 + 693.474i) q^{81} +(1291.84 - 2237.54i) q^{83} +(-705.164 + 256.659i) q^{85} +(3639.77 + 6304.26i) q^{87} +(-4599.38 - 810.995i) q^{89} +(-1670.31 + 1990.60i) q^{91} +(3911.36 + 1423.62i) q^{93} +(12326.0 - 10242.4i) q^{95} +(3641.95 - 10006.2i) q^{97} +(5722.79 + 4801.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

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
$3$	5.99890	−	1.05777i	0.666545	−	0.117530i	0.169870	−	0.985467i	$-0.445665\pi$
$3$	5.99890	−	1.05777i	0.666545	−	0.117530i	0.496675	+	0.867937i	$0.334554\pi$
$4$		0			0
$5$	34.0076	−	28.5357i	1.36030	−	1.14143i	0.384414	−	0.923161i	$-0.374403\pi$
$5$	34.0076	−	28.5357i	1.36030	−	1.14143i	0.975889	−	0.218269i	$-0.0700410\pi$
$6$		0			0
$7$	−4.84547	+	8.39260i	−0.0988872	+	0.171278i	−0.911224	−	0.411911i	$-0.864862\pi$
$7$	−4.84547	+	8.39260i	−0.0988872	+	0.171278i	0.812337	+	0.583188i	$0.198195\pi$
$8$		0			0
$9$	−41.2471	+	15.0127i	−0.509224	+	0.185342i
$10$		0			0
$11$	−85.0973	−	147.393i	−0.703283	−	1.21812i	−0.967308	−	0.253606i	$-0.918383\pi$
$11$	−85.0973	−	147.393i	−0.703283	−	1.21812i	0.264025	−	0.964516i	$-0.414950\pi$
$12$		0			0
$13$	264.067	+	46.5622i	1.56253	+	0.275516i	0.886983	−	0.461803i	$-0.152797\pi$
$13$	264.067	+	46.5622i	1.56253	+	0.275516i	0.675545	+	0.737319i	$0.263908\pi$
$14$		0			0
$15$	173.824	−	207.155i	0.772551	−	0.920690i
$16$		0			0
$17$	−15.8843	−	5.78142i	−0.0549631	−	0.0200049i	0.314392	−	0.949293i	$-0.398199\pi$
$17$	−15.8843	−	5.78142i	−0.0549631	−	0.0200049i	−0.369355	+	0.929288i	$0.620421\pi$
$18$		0			0
$19$	360.996	+	1.73039i	0.999989	+	0.00479331i
$19$	360.996	+	1.73039i	0.999989	+	0.00479331i
$20$		0			0
$21$	−20.1901	+	55.4718i	−0.0457825	+	0.125786i
$22$		0			0
$23$	−237.410	−	199.211i	−0.448791	−	0.376580i	0.390196	−	0.920732i	$-0.372407\pi$
$23$	−237.410	−	199.211i	−0.448791	−	0.376580i	−0.838987	+	0.544152i	$0.816852\pi$
$24$		0			0
$25$	233.696	−	1325.36i	0.373914	−	2.12057i
$26$		0			0
$27$	−658.861	+	380.393i	−0.903787	+	0.521802i
$28$		0			0
$29$	408.729	+	1122.97i	0.486003	+	1.33528i	0.904271	+	0.426959i	$0.140415\pi$
$29$	408.729	+	1122.97i	0.486003	+	1.33528i	−0.418268	+	0.908324i	$0.637363\pi$
$30$		0			0
$31$	591.769	+	341.658i	0.615785	+	0.355523i	0.775226	−	0.631684i	$-0.217636\pi$
$31$	591.769	+	341.658i	0.615785	+	0.355523i	−0.159441	+	0.987207i	$0.550969\pi$
$32$		0			0
$33$	−666.398	−	794.182i	−0.611935	−	0.729276i
$34$		0			0
$35$	74.7064	+	423.681i	0.0609848	+	0.345862i
$36$		0			0
$37$			75.0731i			0.0548379i	0.999624	+	0.0274190i	$0.00872882\pi$
$37$			75.0731i			0.0548379i	−0.999624	+	0.0274190i	$0.991271\pi$
$38$		0			0
$39$	1633.37			1.07388
$40$		0			0
$41$	−1640.73	+	289.305i	−0.976043	+	0.172103i	−0.638849	−	0.769332i	$-0.720589\pi$
$41$	−1640.73	+	289.305i	−0.976043	+	0.172103i	−0.337194	+	0.941435i	$0.609478\pi$
$42$		0			0
$43$	−1655.38	+	1389.03i	−0.895283	+	0.751232i	−0.969263	−	0.246028i	$-0.920875\pi$
$43$	−1655.38	+	1389.03i	−0.895283	+	0.751232i	0.0739793	+	0.997260i	$0.476430\pi$
$44$		0			0
$45$	−974.316	+	1687.56i	−0.481144	+	0.833365i
$46$		0			0
$47$	−3586.36	+	1305.33i	−1.62352	+	0.590914i	−0.984049	−	0.177899i	$-0.943070\pi$
$47$	−3586.36	+	1305.33i	−1.62352	+	0.590914i	−0.639474	+	0.768813i	$0.720848\pi$
$48$		0			0
$49$	1153.54	+	1997.99i	0.480443	+	0.832151i
$50$		0			0
$51$	−101.404	−	17.8802i	−0.0389865	−	0.00687437i
$52$		0			0
$53$	1513.80	−	1804.08i	0.538911	−	0.642249i	−0.426033	−	0.904708i	$-0.640089\pi$
$53$	1513.80	−	1804.08i	0.538911	−	0.642249i	0.964943	+	0.262459i	$0.0845335\pi$
$54$		0			0
$55$	−7099.91	−	2584.16i	−2.34708	−	0.854267i
$56$		0			0
$57$	2167.41	−	371.470i	0.667100	−	0.114334i
$58$		0			0
$59$	−101.845	+	279.818i	−0.0292575	+	0.0803844i	−0.953461	−	0.301515i	$-0.902508\pi$
$59$	−101.845	+	279.818i	−0.0292575	+	0.0803844i	0.924204	+	0.381899i	$0.124730\pi$
$60$		0			0
$61$	4809.33	+	4035.51i	1.29248	+	1.08452i	0.991392	+	0.130928i	$0.0417956\pi$
$61$	4809.33	+	4035.51i	1.29248	+	1.08452i	0.301092	+	0.953595i	$0.402649\pi$
$62$		0			0
$63$	73.8660	−	418.915i	0.0186107	−	0.105547i
$64$		0			0
$65$	10309.0	−	5951.89i	2.43999	−	1.40873i
$66$		0			0
$67$	1482.85	+	4074.08i	0.330329	+	0.907571i	0.988026	+	0.154288i	$0.0493084\pi$
$67$	1482.85	+	4074.08i	0.330329	+	0.907571i	−0.657697	+	0.753282i	$0.728469\pi$
$68$		0			0
$69$	−1634.92	−	943.922i	−0.343398	−	0.198261i
$70$		0			0
$71$	−2209.37	−	2633.02i	−0.438280	−	0.522321i	0.501012	−	0.865440i	$-0.332961\pi$
$71$	−2209.37	−	2633.02i	−0.438280	−	0.522321i	−0.939292	+	0.343119i	$0.888517\pi$
$72$		0			0
$73$	−32.0162	−	181.573i	−0.00600793	−	0.0340726i	0.981656	−	0.190659i	$-0.0610623\pi$
$73$	−32.0162	−	181.573i	−0.00600793	−	0.0340726i	−0.987664	+	0.156586i	$0.949951\pi$
$74$		0			0
$75$		−	8197.89i		−	1.45740i
$76$		0			0
$77$	1649.35			0.278183
$78$		0			0
$79$	−6939.21	+	1223.57i	−1.11187	+	0.196053i	−0.699271	−	0.714857i	$-0.746492\pi$
$79$	−6939.21	+	1223.57i	−1.11187	+	0.196053i	−0.412604	+	0.910911i	$0.635381\pi$
$80$		0			0
$81$	−826.450	+	693.474i	−0.125964	+	0.105696i
$82$		0			0
$83$	1291.84	−	2237.54i	0.187523	−	0.324799i	−0.756901	−	0.653530i	$-0.773288\pi$
$83$	1291.84	−	2237.54i	0.187523	−	0.324799i	0.944424	+	0.328731i	$0.106621\pi$
$84$		0			0
$85$	−705.164	+	256.659i	−0.0976006	+	0.0355237i
$86$		0			0
$87$	3639.77	+	6304.26i	0.480878	+	0.832906i
$88$		0			0
$89$	−4599.38	−	810.995i	−0.580656	−	0.102385i	−0.124397	−	0.992232i	$-0.539700\pi$
$89$	−4599.38	−	810.995i	−0.580656	−	0.102385i	−0.456259	+	0.889847i	$0.650811\pi$
$90$		0			0
$91$	−1670.31	+	1990.60i	−0.201704	+	0.240381i
$92$		0			0
$93$	3911.36	+	1423.62i	0.452233	+	0.164599i
$94$		0			0
$95$	12326.0	−	10242.4i	1.36576	−	1.13490i
$96$		0			0
$97$	3641.95	−	10006.2i	0.387071	−	1.06347i	−0.581242	−	0.813731i	$-0.697433\pi$
$97$	3641.95	−	10006.2i	0.387071	−	1.06347i	0.968313	−	0.249739i	$-0.0803447\pi$
$98$		0			0
$99$	5722.79	+	4801.99i	0.583898	+	0.489949i
$100$		0			0
$101$	2097.95	−	11898.1i	0.205662	−	1.16637i	−0.690733	−	0.723109i	$-0.742712\pi$
$101$	2097.95	−	11898.1i	0.205662	−	1.16637i	0.896395	−	0.443256i	$-0.146177\pi$
$102$		0			0
$103$	−5400.66	+	3118.07i	−0.509064	+	0.293908i	−0.732449	−	0.680822i	$-0.761623\pi$
$103$	−5400.66	+	3118.07i	−0.509064	+	0.293908i	0.223385	+	0.974730i	$0.428289\pi$
$104$		0			0
$105$	896.313	+	2462.60i	0.0812982	+	0.223365i
$106$		0			0
$107$	5330.34	+	3077.47i	0.465573	+	0.268798i	0.714385	−	0.699753i	$-0.246707\pi$
$107$	5330.34	+	3077.47i	0.465573	+	0.268798i	−0.248812	+	0.968552i	$0.580040\pi$
$108$		0			0
$109$	−270.618	−	322.510i	−0.0227774	−	0.0271451i	0.754535	−	0.656259i	$-0.227862\pi$
$109$	−270.618	−	322.510i	−0.0227774	−	0.0271451i	−0.777313	+	0.629114i	$0.783418\pi$
$110$		0			0
$111$	79.4100	+	450.356i	0.00644509	+	0.0365519i
$112$		0			0
$113$			19914.1i			1.55957i	0.626050	+	0.779783i	$0.284671\pi$
$113$			19914.1i			1.55957i	−0.626050	+	0.779783i	$0.715329\pi$
$114$		0			0
$115$	−13758.4			−1.04033
$116$		0			0
$117$	−11591.0	+	2043.81i	−0.846741	+	0.149303i
$118$		0			0
$119$	125.488	−	105.297i	0.00886154	−	0.00743571i
$120$		0			0
$121$	−7162.58	+	12406.0i	−0.489214	+	0.847344i
$122$		0			0
$123$	−9536.55	+	3471.02i	−0.630349	+	0.229428i
$124$		0			0
$125$	−15999.6	−	27712.1i	−1.02397	−	1.77357i
$126$		0			0
$127$	14420.3	+	2542.69i	0.894061	+	0.157647i	0.601758	−	0.798679i	$-0.294467\pi$
$127$	14420.3	+	2542.69i	0.894061	+	0.157647i	0.292303	+	0.956326i	$0.405578\pi$
$128$		0			0
$129$	−8461.19	+	10083.7i	−0.508454	+	0.605952i
$130$		0			0
$131$	6312.69	+	2297.63i	0.367851	+	0.133887i	0.519330	−	0.854574i	$-0.326181\pi$
$131$	6312.69	+	2297.63i	0.367851	+	0.133887i	−0.151479	+	0.988460i	$0.548404\pi$
$132$		0			0
$133$	−1763.72	+	3021.31i	−0.0997070	+	0.170802i
$134$		0			0
$135$	−11551.4	+	31737.3i	−0.633824	+	1.74142i
$136$		0			0
$137$	−5133.97	−	4307.92i	−0.273535	−	0.229523i	0.495693	−	0.868498i	$-0.334914\pi$
$137$	−5133.97	−	4307.92i	−0.273535	−	0.229523i	−0.769227	+	0.638975i	$0.779359\pi$
$138$		0			0
$139$	−3028.64	+	17176.3i	−0.156754	+	0.888995i	0.800411	+	0.599452i	$0.204615\pi$
$139$	−3028.64	+	17176.3i	−0.156754	+	0.888995i	−0.957165	+	0.289543i	$0.906497\pi$
$140$		0			0
$141$	−20133.5	+	11624.1i	−1.01270	+	0.584683i
$142$		0			0
$143$	−15608.5	−	42883.9i	−0.763288	−	2.09712i
$144$		0			0
$145$	45944.7	+	26526.2i	2.18524	+	1.26165i
$146$		0			0
$147$	9033.41	+	10765.6i	0.418039	+	0.498200i
$148$		0			0
$149$	1299.35	+	7368.96i	0.0585265	+	0.331920i	0.999986	−	0.00520451i	$-0.00165666\pi$
$149$	1299.35	+	7368.96i	0.0585265	+	0.331920i	−0.941460	+	0.337125i	$0.890546\pi$
$150$		0			0
$151$		−	30535.0i		−	1.33919i	−0.742724	−	0.669597i	$-0.766467\pi$
$151$		−	30535.0i		−	1.33919i	0.742724	−	0.669597i	$-0.233533\pi$
$152$		0			0
$153$	741.978			0.0316963
$154$		0			0
$155$	29874.1	−	5267.61i	1.24346	−	0.219255i
$156$		0			0
$157$	−148.150	+	124.312i	−0.00601037	+	0.00504330i	−0.645788	−	0.763517i	$-0.723471\pi$
$157$	−148.150	+	124.312i	−0.00601037	+	0.00504330i	0.639777	+	0.768560i	$0.279027\pi$
$158$		0			0
$159$	7172.84	−	12423.7i	0.283725	−	0.491425i
$160$		0			0
$161$	2822.26	−	1027.22i	0.108879	−	0.0396289i
$162$		0			0
$163$	−16074.0	−	27841.0i	−0.604992	−	1.04788i	−0.992053	−	0.125822i	$-0.959843\pi$
$163$	−16074.0	−	27841.0i	−0.604992	−	1.04788i	0.387061	−	0.922054i	$-0.373490\pi$
$164$		0			0
$165$	−45325.1	−	7992.04i	−1.66483	−	0.293555i
$166$		0			0
$167$	−21991.2	+	26208.1i	−0.788526	+	0.939728i	−0.999285	−	0.0378096i	$-0.987962\pi$
$167$	−21991.2	+	26208.1i	−0.788526	+	0.939728i	0.210759	+	0.977538i	$0.432406\pi$
$168$		0			0
$169$	40724.9	+	14822.6i	1.42589	+	0.518982i
$170$		0			0
$171$	−14916.0	+	5348.16i	−0.510107	+	0.182899i
$172$		0			0
$173$	16667.4	−	45793.2i	0.556897	−	1.53006i	−0.267216	−	0.963637i	$-0.586104\pi$
$173$	16667.4	−	45793.2i	0.556897	−	1.53006i	0.824113	−	0.566426i	$-0.191674\pi$
$174$		0			0
$175$	9990.83	+	8383.30i	0.326231	+	0.273741i
$176$		0			0
$177$	−314.978	+	1786.33i	−0.0100539	+	0.0570184i
$178$		0			0
$179$	26330.6	−	15202.0i	0.821779	−	0.474455i	−0.0292503	−	0.999572i	$-0.509312\pi$
$179$	26330.6	−	15202.0i	0.821779	−	0.474455i	0.851030	+	0.525118i	$0.175979\pi$
$180$		0			0
$181$	−14950.0	−	41074.7i	−0.456334	−	1.25377i	−0.928195	−	0.372095i	$-0.878640\pi$
$181$	−14950.0	−	41074.7i	−0.456334	−	1.25377i	0.471861	−	0.881673i	$-0.343583\pi$
$182$		0			0
$183$	33119.4	+	19121.5i	0.988962	+	0.570978i
$184$		0			0
$185$	2142.27	+	2553.05i	0.0625936	+	0.0745962i
$186$		0			0
$187$	499.573	+	2833.22i	0.0142862	+	0.0810208i
$188$		0			0
$189$		−	7372.74i		−	0.206398i
$190$		0			0
$191$	45410.8			1.24478			0.622390	−	0.782708i	$-0.286162\pi$
$191$	45410.8			1.24478			0.622390	+	0.782708i	$0.286162\pi$
$192$		0			0
$193$	−34192.0	+	6028.97i	−0.917930	+	0.161856i	−0.612602	−	0.790392i	$-0.709877\pi$
$193$	−34192.0	+	6028.97i	−0.917930	+	0.161856i	−0.305328	+	0.952247i	$0.598766\pi$
$194$		0			0
$195$	55546.8	−	46609.3i	1.46080	−	1.22575i
$196$		0			0
$197$	13673.8	−	23683.7i	0.352336	−	0.610264i	−0.634322	−	0.773069i	$-0.718721\pi$
$197$	13673.8	−	23683.7i	0.352336	−	0.610264i	0.986658	+	0.162805i	$0.0520541\pi$
$198$		0			0
$199$	15225.8	−	5541.74i	0.384480	−	0.139939i	−0.142546	−	0.989788i	$-0.545529\pi$
$199$	15225.8	−	5541.74i	0.384480	−	0.139939i	0.527027	+	0.849849i	$0.323307\pi$
$200$		0			0
$201$	13204.9	+	22871.5i	0.326845	+	0.566113i
$202$		0			0
$203$	−11405.1	−	2011.03i	−0.276763	−	0.0488009i
$204$		0			0
$205$	−47541.7	+	56657.9i	−1.13127	+	1.34820i
$206$		0			0
$207$	12783.2	+	4652.70i	0.298331	+	0.108584i
$208$		0			0
$209$	−30464.7	−	53355.4i	−0.697436	−	1.22148i
$210$		0			0
$211$	4693.81	−	12896.1i	0.105429	−	0.289664i	−0.875750	−	0.482766i	$-0.839632\pi$
$211$	4693.81	−	12896.1i	0.105429	−	0.289664i	0.981179	+	0.193101i	$0.0618546\pi$
$212$		0			0
$213$	−16038.9	−	13458.2i	−0.353521	−	0.296640i
$214$		0			0
$215$	−16658.5	+	94474.9i	−0.360378	+	2.04381i
$216$		0			0
$217$	−5734.80	+	3310.99i	−0.121786	+	0.0703134i
$218$		0			0
$219$	−384.125	−	1055.37i	−0.00800910	−	0.0220048i
$220$		0			0
$221$	−3925.33	−	2266.29i	−0.0803696	−	0.0464014i
$222$		0			0
$223$	−13224.5	−	15760.4i	−0.265932	−	0.316925i	0.616510	−	0.787347i	$-0.288546\pi$
$223$	−13224.5	−	15760.4i	−0.265932	−	0.316925i	−0.882441	+	0.470422i	$0.844102\pi$
$224$		0			0
$225$	10257.9	+	58175.6i	0.202626	+	1.14915i
$226$		0			0
$227$		−	61891.8i		−	1.20111i	−0.799585	−	0.600553i	$-0.794947\pi$
$227$		−	61891.8i		−	1.20111i	0.799585	−	0.600553i	$-0.205053\pi$
$228$		0			0
$229$	−63028.4			−1.20189			−0.600946	−	0.799290i	$-0.705209\pi$
$229$	−63028.4			−1.20189			−0.600946	+	0.799290i	$0.705209\pi$
$230$		0			0
$231$	9894.26	−	1744.63i	0.185421	−	0.0326948i
$232$		0			0
$233$	41194.0	−	34565.9i	0.758791	−	0.636701i	−0.179021	−	0.983845i	$-0.557293\pi$
$233$	41194.0	−	34565.9i	0.758791	−	0.636701i	0.937812	+	0.347144i	$0.112849\pi$
$234$		0			0
$235$	−84714.9	+	146731.i	−1.53400	+	2.65696i
$236$		0			0
$237$	−40333.4	+	14680.2i	−0.718072	+	0.261357i
$238$		0			0
$239$	−56098.7	−	97165.8i	−0.982103	−	1.70105i	−0.654163	−	0.756354i	$-0.726979\pi$
$239$	−56098.7	−	97165.8i	−0.982103	−	1.70105i	−0.327940	−	0.944699i	$-0.606354\pi$
$240$		0			0
$241$	−31255.5	−	5511.18i	−0.538136	−	0.0948879i	−0.102027	−	0.994782i	$-0.532533\pi$
$241$	−31255.5	−	5511.18i	−0.538136	−	0.0948879i	−0.436109	+	0.899894i	$0.643644\pi$
$242$		0			0
$243$	35386.7	−	42172.2i	0.599277	−	0.714191i
$244$		0			0
$245$	96243.4	+	35029.8i	1.60339	+	0.583586i
$246$		0			0
$247$	95246.6	+	17265.7i	1.56119	+	0.283002i
$248$		0			0
$249$	5382.85	−	14789.2i	0.0868187	−	0.238532i
$250$		0			0
$251$	30001.7	+	25174.4i	0.476210	+	0.399588i	0.849054	−	0.528306i	$-0.177173\pi$
$251$	30001.7	+	25174.4i	0.476210	+	0.399588i	−0.372844	+	0.927894i	$0.621617\pi$
$252$		0			0
$253$	−9159.28	+	51944.9i	−0.143094	+	0.811524i
$254$		0			0
$255$	−3958.73	+	2285.57i	−0.0608801	+	0.0351491i
$256$		0			0
$257$	42439.4	+	116601.i	0.642545	+	1.76538i	0.643582	+	0.765377i	$0.277448\pi$
$257$	42439.4	+	116601.i	0.642545	+	1.76538i	−0.00103757	+	0.999999i	$0.500330\pi$
$258$		0			0
$259$	−630.059	−	363.765i	−0.00939251	−	0.00542277i
$260$		0			0
$261$	−33717.8	−	40183.3i	−0.494969	−	0.589881i
$262$		0			0
$263$	1435.20	+	8139.42i	0.0207492	+	0.117674i	0.993423	−	0.114501i	$-0.0365268\pi$
$263$	1435.20	+	8139.42i	0.0207492	+	0.117674i	−0.972674	+	0.232175i	$0.925416\pi$
$264$		0			0
$265$		−	104550.i		−	1.48878i
$266$		0			0
$267$	−28449.1			−0.399067
$268$		0			0
$269$	−69892.5	+	12323.9i	−0.965886	+	0.170312i	−0.634278	−	0.773105i	$-0.718702\pi$
$269$	−69892.5	+	12323.9i	−0.965886	+	0.170312i	−0.331608	+	0.943417i	$0.607591\pi$
$270$		0			0
$271$	−40886.7	+	34308.0i	−0.556728	+	0.467151i	−0.877212	−	0.480104i	$-0.840599\pi$
$271$	−40886.7	+	34308.0i	−0.556728	+	0.467151i	0.320483	+	0.947254i	$0.396155\pi$
$272$		0			0
$273$	−7914.43	+	13708.2i	−0.106193	+	0.183931i
$274$		0			0
$275$	−215235.	+	78339.1i	−2.84608	+	1.03589i
$276$		0			0
$277$	57325.0	+	99289.9i	0.747110	+	1.29403i	0.949202	+	0.314667i	$0.101893\pi$
$277$	57325.0	+	99289.9i	0.747110	+	1.29403i	−0.202092	+	0.979367i	$0.564774\pi$
$278$		0			0
$279$	−29538.0	−	5208.35i	−0.379466	−	0.0669101i
$280$		0			0
$281$	20703.8	−	24673.8i	0.262203	−	0.312481i	−0.618841	−	0.785517i	$-0.712397\pi$
$281$	20703.8	−	24673.8i	0.262203	−	0.312481i	0.881043	+	0.473036i	$0.156842\pi$
$282$		0			0
$283$	6274.15	+	2283.60i	0.0783397	+	0.0285133i	0.380893	−	0.924619i	$-0.375617\pi$
$283$	6274.15	+	2283.60i	0.0783397	+	0.0285133i	−0.302553	+	0.953133i	$0.597839\pi$
$284$		0			0
$285$	63108.2	−	74481.4i	0.776955	−	0.916976i
$286$		0			0
$287$	5522.08	−	15171.8i	0.0670408	−	0.184193i
$288$		0			0
$289$	−63761.9	−	53502.6i	−0.763424	−	0.640589i
$290$		0			0
$291$	11263.5	−	63878.5i	0.133011	−	0.754342i
$292$		0			0
$293$	−84869.8	+	48999.6i	−0.988594	+	0.570765i	−0.904854	−	0.425723i	$-0.860020\pi$
$293$	−84869.8	+	48999.6i	−0.988594	+	0.570765i	−0.0837402	+	0.996488i	$0.526687\pi$
$294$		0			0
$295$	4521.30	+	12422.2i	0.0519540	+	0.142743i
$296$		0			0
$297$	112134.	+	64740.9i	1.27124	+	0.733949i
$298$		0			0
$299$	−53416.6	−	63659.4i	−0.597494	−	0.712066i
$300$		0			0
$301$	−3636.47	−	20623.4i	−0.0401372	−	0.227629i
$302$		0			0
$303$		−	73594.6i		−	0.801606i
$304$		0			0
$305$	278710.			2.99608
$306$		0			0
$307$	87461.7	−	15421.9i	0.927986	−	0.163629i	0.310826	−	0.950467i	$-0.399394\pi$
$307$	87461.7	−	15421.9i	0.927986	−	0.163629i	0.617160	+	0.786838i	$0.288283\pi$
$308$		0			0
$309$	−29099.8	+	24417.7i	−0.304771	+	0.255733i
$310$		0			0
$311$	−90523.7	+	156792.i	−0.935926	+	1.62107i	−0.162950	+	0.986634i	$0.552101\pi$
$311$	−90523.7	+	156792.i	−0.935926	+	1.62107i	−0.772975	+	0.634436i	$0.781232\pi$
$312$		0			0
$313$	−6780.13	+	2467.77i	−0.0692069	+	0.0251893i	−0.376392	−	0.926461i	$-0.622835\pi$
$313$	−6780.13	+	2467.77i	−0.0692069	+	0.0251893i	0.307185	+	0.951650i	$0.400613\pi$
$314$		0			0
$315$	−9442.04	−	16354.1i	−0.0951579	−	0.164818i
$316$		0			0
$317$	−46575.8	−	8212.58i	−0.463492	−	0.0817261i	−0.0629743	−	0.998015i	$-0.520059\pi$
$317$	−46575.8	−	8212.58i	−0.463492	−	0.0817261i	−0.400518	+	0.916289i	$0.631170\pi$
$318$		0			0
$319$	130736.	−	155806.i	1.28474	−	1.53109i
$320$		0			0
$321$	35231.4	+	12823.2i	0.341917	+	0.124448i
$322$		0			0
$323$	−5724.17	−	2114.56i	−0.0548665	−	0.0202681i
$324$		0			0
$325$	123423.	−	339102.i	1.16850	−	3.21043i
$326$		0			0
$327$	−1964.55	−	1648.46i	−0.0183725	−	0.0154164i
$328$		0			0
$329$	6422.50	−	36423.8i	0.0593352	−	0.336507i
$330$		0			0
$331$	154909.	−	89437.0i	1.41391	−	0.816321i	0.418156	−	0.908375i	$-0.362677\pi$
$331$	154909.	−	89437.0i	1.41391	−	0.816321i	0.995754	+	0.0920539i	$0.0293432\pi$
$332$		0			0
$333$	−1127.05	−	3096.55i	−0.0101638	−	0.0279248i
$334$		0			0
$335$	166685.	+	96235.6i	1.48528	+	0.857524i
$336$		0			0
$337$	22317.6	+	26597.1i	0.196511	+	0.234193i	0.855298	−	0.518137i	$-0.173374\pi$
$337$	22317.6	+	26597.1i	0.196511	+	0.234193i	−0.658786	+	0.752330i	$0.728930\pi$
$338$		0			0
$339$	21064.5	+	119463.i	0.183296	+	1.03952i
$340$		0			0
$341$		−	116297.i		−	1.00013i
$342$		0			0
$343$	−45625.8			−0.387813
$344$		0			0
$345$	−82535.2	+	14553.2i	−0.693427	+	0.122270i
$346$		0			0
$347$	36360.0	−	30509.7i	0.301971	−	0.253384i	−0.479193	−	0.877709i	$-0.659071\pi$
$347$	36360.0	−	30509.7i	0.301971	−	0.253384i	0.781164	+	0.624326i	$0.214626\pi$
$348$		0			0
$349$	−71440.1	+	123738.i	−0.586531	+	1.01590i	0.408151	+	0.912914i	$0.366174\pi$
$349$	−71440.1	+	123738.i	−0.586531	+	1.01590i	−0.994683	+	0.102988i	$0.967160\pi$
$350$		0			0
$351$	−191695.	+	69771.4i	−1.55596	+	0.566322i
$352$		0			0
$353$	−37596.6	−	65119.2i	−0.301716	−	0.522588i	0.674808	−	0.737993i	$-0.264226\pi$
$353$	−37596.6	−	65119.2i	−0.301716	−	0.522588i	−0.976525	+	0.215405i	$0.930893\pi$
$354$		0			0
$355$	−150270.	−	26496.7i	−1.19239	−	0.210250i
$356$		0			0
$357$	641.412	−	764.405i	0.00503269	−	0.00599773i
$358$		0			0
$359$	−160872.	−	58552.6i	−1.24822	−	0.454316i	−0.368421	−	0.929659i	$-0.620102\pi$
$359$	−160872.	−	58552.6i	−1.24822	−	0.454316i	−0.879800	+	0.475343i	$0.842324\pi$
$360$		0			0
$361$	130315.	+	1249.32i	0.999954	+	0.00958651i
$362$		0			0
$363$	−29845.0	+	81998.5i	−0.226495	+	0.622290i
$364$		0			0
$365$	−6270.12	−	5261.25i	−0.0470641	−	0.0394915i
$366$		0			0
$367$	−36058.3	+	204497.i	−0.267716	+	1.51829i	0.493474	+	0.869761i	$0.335727\pi$
$367$	−36058.3	+	204497.i	−0.267716	+	1.51829i	−0.761189	+	0.648530i	$0.775384\pi$
$368$		0			0
$369$	63332.1	−	36564.8i	0.465126	−	0.268541i
$370$		0			0
$371$	7805.82	+	21446.3i	0.0567115	+	0.155813i
$372$		0			0
$373$	−10398.5	−	6003.57i	−0.0747399	−	0.0431511i	0.462164	−	0.886794i	$-0.347073\pi$
$373$	−10398.5	−	6003.57i	−0.0747399	−	0.0431511i	−0.536904	+	0.843643i	$0.680406\pi$
$374$		0			0
$375$	−125293.	−	149318.i	−0.890971	−	1.06182i
$376$		0			0
$377$	55643.8	+	315572.i	0.391502	+	2.22032i
$378$		0			0
$379$		−	229462.i		−	1.59747i	−0.601685	−	0.798733i	$-0.705504\pi$
$379$		−	229462.i		−	1.59747i	0.601685	−	0.798733i	$-0.294496\pi$
$380$		0			0
$381$	89195.6			0.614460
$382$		0			0
$383$	−21536.6	+	3797.49i	−0.146818	+	0.0258880i	−0.246574	−	0.969124i	$-0.579305\pi$
$383$	−21536.6	+	3797.49i	−0.146818	+	0.0258880i	0.0997560	+	0.995012i	$0.468194\pi$
$384$		0			0
$385$	56090.2	−	47065.3i	0.378413	−	0.317526i
$386$		0			0
$387$	47426.6	−	82145.2i	0.316665	−	0.548479i
$388$		0			0
$389$	−31439.8	+	11443.2i	−0.207769	+	0.0756218i	−0.443808	−	0.896122i	$-0.646373\pi$
$389$	−31439.8	+	11443.2i	−0.207769	+	0.0756218i	0.236039	+	0.971744i	$0.424151\pi$
$390$		0			0
$391$	2619.38	+	4536.90i	0.0171335	+	0.0296760i
$392$		0			0
$393$	40299.6	+	7105.90i	0.260925	+	0.0460081i
$394$		0			0
$395$	−201070.	+	239626.i	−1.28870	+	1.53582i
$396$		0			0
$397$	116394.	+	42364.1i	0.738500	+	0.268792i	0.683759	−	0.729708i	$-0.260344\pi$
$397$	116394.	+	42364.1i	0.738500	+	0.268792i	0.0547419	+	0.998501i	$0.482566\pi$
$398$		0			0
$399$	−7384.52	+	19990.2i	−0.0463849	+	0.125565i
$400$		0			0
$401$	−63858.8	+	175450.i	−0.397129	+	1.09110i	0.566547	+	0.824029i	$0.308279\pi$
$401$	−63858.8	+	175450.i	−0.397129	+	1.09110i	−0.963676	+	0.267074i	$0.913943\pi$
$402$		0			0
$403$	140358.	+	117775.i	0.864228	+	0.725174i
$404$		0			0
$405$	−8316.76	+	47166.7i	−0.0507042	+	0.287558i
$406$		0			0
$407$	11065.2	−	6388.52i	0.0667993	−	0.0385666i
$408$		0			0
$409$	−27376.4	−	75216.0i	−0.163655	−	0.449639i	0.830575	−	0.556907i	$-0.188012\pi$
$409$	−27376.4	−	75216.0i	−0.163655	−	0.449639i	−0.994230	+	0.107268i	$0.965790\pi$
$410$		0			0
$411$	−35355.0	−	20412.2i	−0.209299	−	0.120839i
$412$		0			0
$413$	−1854.91	−	2210.60i	−0.0108749	−	0.0129601i
$414$		0			0
$415$	−19917.4	−	112957.i	−0.115647	−	0.655869i
$416$		0			0
$417$			106242.i			0.610978i
$418$		0			0
$419$	−111338.			−0.634182			−0.317091	−	0.948395i	$-0.602706\pi$
$419$	−111338.			−0.634182			−0.317091	+	0.948395i	$0.602706\pi$
$420$		0			0
$421$	−199288.	+	35139.9i	−1.12439	+	0.198260i	−0.704768	−	0.709438i	$-0.748949\pi$
$421$	−199288.	+	35139.9i	−1.12439	+	0.198260i	−0.419623	+	0.907699i	$0.637838\pi$
$422$		0			0
$423$	128331.	−	107682.i	0.717215	−	0.601815i
$424$		0			0
$425$	−11374.6	+	19701.3i	−0.0629733	+	0.109073i
$426$		0			0
$427$	−57171.9	+	20808.9i	−0.313565	+	0.114128i
$428$		0			0
$429$	−138995.	−	240746.i	−0.755239	−	1.30811i
$430$		0			0
$431$	−132451.	−	23354.7i	−0.713020	−	0.125725i	−0.194640	−	0.980875i	$-0.562354\pi$
$431$	−132451.	−	23354.7i	−0.713020	−	0.125725i	−0.518381	+	0.855150i	$0.673465\pi$
$432$		0			0
$433$	−222724.	+	265433.i	−1.18793	+	1.41572i	−0.301126	+	0.953585i	$0.597362\pi$
$433$	−222724.	+	265433.i	−1.18793	+	1.41572i	−0.886808	+	0.462139i	$0.847082\pi$
$434$		0			0
$435$	303676.	+	110529.i	1.60484	+	0.584115i
$436$		0			0
$437$	−85359.4	−	72325.1i	−0.446981	−	0.378727i
$438$		0			0
$439$	73917.7	−	203087.i	0.383547	−	1.05379i	−0.586304	−	0.810091i	$-0.699418\pi$
$439$	73917.7	−	203087.i	0.383547	−	1.05379i	0.969851	−	0.243697i	$-0.0783602\pi$
$440$		0			0
$441$	−77575.7	−	65093.7i	−0.398886	−	0.334705i
$442$		0			0
$443$	−17227.7	+	97702.9i	−0.0877847	+	0.497852i	0.908936	+	0.416935i	$0.136896\pi$
$443$	−17227.7	+	97702.9i	−0.0877847	+	0.497852i	−0.996721	+	0.0809164i	$0.974215\pi$
$444$		0			0
$445$	−179556.	+	103667.i	−0.906734	+	0.523503i
$446$		0			0
$447$	15589.3	+	42831.3i	0.0780211	+	0.214361i
$448$		0			0
$449$	202057.	+	116658.i	1.00226	+	0.578656i	0.908917	−	0.416978i	$-0.136911\pi$
$449$	202057.	+	116658.i	1.00226	+	0.578656i	0.0933451	+	0.995634i	$0.470244\pi$
$450$		0			0
$451$	182263.	+	217212.i	0.896076	+	1.06790i
$452$		0			0
$453$	−32298.9	−	183176.i	−0.157395	−	0.892633i
$454$		0			0
$455$			115359.i			0.557222i
$456$		0			0
$457$	−364349.			−1.74456			−0.872278	−	0.489010i	$-0.837358\pi$
$457$	−364349.			−1.74456			−0.872278	+	0.489010i	$0.837358\pi$
$458$		0			0
$459$	12664.8	−	2233.14i	0.0601135	−	0.0105996i
$460$		0			0
$461$	207772.	−	174341.i	0.977654	−	0.820349i	−0.00607982	−	0.999982i	$-0.501935\pi$
$461$	207772.	−	174341.i	0.977654	−	0.820349i	0.983734	+	0.179632i	$0.0574908\pi$
$462$		0			0
$463$	35131.9	−	60850.3i	0.163885	−	0.283858i	−0.772374	−	0.635169i	$-0.780931\pi$
$463$	35131.9	−	60850.3i	0.163885	−	0.283858i	0.936259	+	0.351311i	$0.114264\pi$
$464$		0			0
$465$	173640.	−	63199.7i	0.803052	−	0.292287i
$466$		0			0
$467$	127963.	+	221638.i	0.586746	+	1.01627i	0.994655	+	0.103251i	$0.0329244\pi$
$467$	127963.	+	221638.i	0.586746	+	1.01627i	−0.407910	+	0.913022i	$0.633742\pi$
$468$		0			0
$469$	−41377.3	−	7295.93i	−0.188112	−	0.0331692i
$470$		0			0
$471$	−757.241	+	902.445i	−0.00341344	+	0.00406798i
$472$		0			0
$473$	345601.	+	125788.i	1.54473	+	0.562236i
$474$		0			0
$475$	86656.8	−	478044.i	0.384074	−	2.11876i
$476$		0			0
$477$	−35355.8	+	97139.3i	−0.155390	+	0.426931i
$478$		0			0
$479$	−113005.	−	94822.4i	−0.492523	−	0.413276i	0.362407	−	0.932020i	$-0.381955\pi$
$479$	−113005.	−	94822.4i	−0.492523	−	0.413276i	−0.854929	+	0.518744i	$0.826400\pi$
$480$		0			0
$481$	−3495.57	+	19824.3i	−0.0151087	+	0.0856858i
$482$		0			0
$483$	15843.9	−	9147.49i	0.0679154	−	0.0392110i
$484$		0			0
$485$	−161680.	−	444212.i	−0.687341	−	1.88846i
$486$		0			0
$487$	315135.	+	181943.i	1.32874	+	0.767147i	0.985104	−	0.171958i	$-0.0550092\pi$
$487$	315135.	+	181943.i	1.32874	+	0.767147i	0.343632	+	0.939104i	$0.388343\pi$
$488$		0			0
$489$	−125876.	−	150013.i	−0.526411	−	0.627352i
$490$		0			0
$491$	−17094.6	−	96948.4i	−0.0709082	−	0.402140i	−0.999517	−	0.0310799i	$-0.990105\pi$
$491$	−17094.6	−	96948.4i	−0.0709082	−	0.402140i	0.928609	−	0.371060i	$-0.121006\pi$
$492$		0			0
$493$		−	20200.7i		−	0.0831137i
$494$		0			0
$495$	331646.			1.35352
$496$		0			0
$497$	32803.3	−	5784.11i	0.132802	−	0.0234166i
$498$		0			0
$499$	−238014.	+	199717.i	−0.955875	+	0.802075i	−0.980277	−	0.197628i	$-0.936676\pi$
$499$	−238014.	+	199717.i	−0.955875	+	0.802075i	0.0244018	+	0.999702i	$0.492232\pi$
$500$		0			0
$501$	−104201.	+	180481.i	−0.415142	+	0.719046i
$502$		0			0
$503$	181510.	−	66064.1i	0.717403	−	0.261113i	0.0425803	−	0.999093i	$-0.486442\pi$
$503$	181510.	−	66064.1i	0.717403	−	0.261113i	0.674823	+	0.737980i	$0.264220\pi$
$504$		0			0
$505$	−268175.	−	464492.i	−1.05156	−	1.82136i
$506$		0			0
$507$	259984.	+	45842.1i	1.01142	+	0.178340i
$508$		0			0
$509$	−77548.5	+	92418.7i	−0.299321	+	0.356717i	−0.894652	−	0.446763i	$-0.852577\pi$
$509$	−77548.5	+	92418.7i	−0.299321	+	0.356717i	0.595331	+	0.803481i	$0.297021\pi$
$510$		0			0
$511$	1679.00	+	611.108i	0.00642999	+	0.00234032i
$512$		0			0
$513$	−238504.	+	136180.i	−0.906278	+	0.517463i
$514$		0			0
$515$	−94686.8	+	260150.i	−0.357006	+	0.980865i
$516$		0			0
$517$	497585.	+	417524.i	1.86160	+	1.56207i
$518$		0			0
$519$	51547.3	−	292339.i	0.191369	−	1.08531i
$520$		0			0
$521$	121685.	−	70254.9i	0.448293	−	0.258822i	−0.258816	−	0.965927i	$-0.583332\pi$
$521$	121685.	−	70254.9i	0.448293	−	0.258822i	0.707109	+	0.707105i	$0.249999\pi$
$522$		0			0
$523$	−158548.	−	435608.i	−0.579639	−	1.59255i	−0.788790	−	0.614663i	$-0.789292\pi$
$523$	−158548.	−	435608.i	−0.579639	−	1.59255i	0.209150	−	0.977883i	$-0.432930\pi$
$524$		0			0
$525$	68801.6	+	39722.6i	0.249620	+	0.144118i
$526$		0			0
$527$	−7424.58	−	8848.27i	−0.0267332	−	0.0318594i
$528$		0			0
$529$	−31915.2	−	181000.i	−0.114048	−	0.646796i
$530$		0			0
$531$		−	13070.7i		−	0.0463563i
$532$		0			0
$533$	−446733.			−1.57251
$534$		0			0
$535$	269090.	−	47447.8i	0.940134	−	0.165771i
$536$		0			0
$537$	141875.	−	119047.i	0.491990	−	0.412829i
$538$		0			0
$539$	196327.	−	340048.i	0.675774	−	1.17048i
$540$		0			0
$541$	118888.	−	43271.7i	0.406204	−	0.147846i	−0.130834	−	0.991404i	$-0.541765\pi$
$541$	118888.	−	43271.7i	0.406204	−	0.147846i	0.537038	+	0.843558i	$0.319543\pi$
$542$		0			0
$543$	−133131.	−	230589.i	−0.451522	−	0.782059i
$544$		0			0
$545$	−18406.1	−	3245.50i	−0.0619683	−	0.0109267i
$546$		0			0
$547$	155955.	−	185860.i	0.521225	−	0.621172i	−0.439645	−	0.898172i	$-0.644896\pi$
$547$	155955.	−	185860.i	0.521225	−	0.621172i	0.960870	+	0.277000i	$0.0893402\pi$
$548$		0			0
$549$	−258955.	−	94252.0i	−0.859172	−	0.312713i
$550$		0			0
$551$	145606.	+	406096.i	0.479597	+	1.33760i
$552$		0			0
$553$	23354.8	−	64166.8i	0.0763706	−	0.209826i
$554$		0			0
$555$	15551.8	+	13049.5i	0.0504887	+	0.0423651i
$556$		0			0
$557$	−29312.5	+	166240.i	−0.0944806	+	0.535826i	0.900425	+	0.435012i	$0.143256\pi$
$557$	−29312.5	+	166240.i	−0.0944806	+	0.535826i	−0.994905	+	0.100814i	$0.967855\pi$
$558$		0			0
$559$	−501808.	+	289719.i	−1.60588	+	0.927156i
$560$		0			0
$561$	5993.78	+	16467.8i	0.0190447	+	0.0523250i
$562$		0			0
$563$	197080.	+	113784.i	0.621765	+	0.358976i	0.777556	−	0.628814i	$-0.216459\pi$
$563$	197080.	+	113784.i	0.621765	+	0.358976i	−0.155791	+	0.987790i	$0.549793\pi$
$564$		0			0
$565$	568264.	+	677230.i	1.78013	+	2.12148i
$566$		0			0
$567$	−1815.51	−	10296.3i	−0.00564719	−	0.0320268i
$568$		0			0
$569$		−	89793.2i		−	0.277344i	−0.990338	−	0.138672i	$-0.955717\pi$
$569$		−	89793.2i		−	0.277344i	0.990338	−	0.138672i	$-0.0442834\pi$
$570$		0			0
$571$	326526.			1.00149			0.500744	−	0.865595i	$-0.333060\pi$
$571$	326526.			1.00149			0.500744	+	0.865595i	$0.333060\pi$
$572$		0			0
$573$	272415.	−	48034.1i	0.829701	−	0.146299i
$574$		0			0
$575$	−319508.	+	268099.i	−0.966375	+	0.810885i
$576$		0			0
$577$	94275.3	−	163290.i	0.283169	−	0.490464i	−0.688994	−	0.724767i	$-0.741947\pi$
$577$	94275.3	−	163290.i	0.283169	−	0.490464i	0.972164	+	0.234303i	$0.0752808\pi$
$578$		0			0
$579$	−198737.	+	72334.4i	−0.592818	+	0.215768i
$580$		0			0
$581$	12519.2	+	21683.9i	0.0370872	+	0.0642369i
$582$		0			0
$583$	−394728.	−	69601.2i	−1.16134	−	0.204776i
$584$		0			0
$585$	−335861.	+	400264.i	−0.981405	+	1.16959i
$586$		0			0
$587$	−277682.	−	101068.i	−0.805882	−	0.293317i	−0.0939604	−	0.995576i	$-0.529953\pi$
$587$	−277682.	−	101068.i	−0.805882	−	0.293317i	−0.711922	+	0.702259i	$0.752175\pi$
$588$		0			0
$589$	213035.	+	124361.i	0.614073	+	0.358471i
$590$		0			0
$591$	56975.9	−	156540.i	0.163123	−	0.448178i
$592$		0			0
$593$	−268160.	−	225013.i	−0.762579	−	0.639880i	0.176218	−	0.984351i	$-0.443614\pi$
$593$	−268160.	−	225013.i	−0.762579	−	0.639880i	−0.938797	+	0.344471i	$0.888058\pi$
$594$		0			0
$595$	1262.82	−	7161.80i	0.00356703	−	0.0202296i
$596$		0			0
$597$	85476.2	−	49349.7i	0.239826	−	0.138464i
$598$		0			0
$599$	−4488.71	−	12332.6i	−0.0125103	−	0.0343718i	0.933280	−	0.359149i	$-0.116933\pi$
$599$	−4488.71	−	12332.6i	−0.0125103	−	0.0343718i	−0.945791	+	0.324777i	$0.894711\pi$
$600$		0			0
$601$	−560770.	−	323761.i	−1.55252	−	0.896345i	−0.997936	−	0.0642139i	$-0.979546\pi$
$601$	−560770.	−	323761.i	−1.55252	−	0.896345i	−0.554579	−	0.832131i	$-0.687121\pi$
$602$		0			0
$603$	−122326.	−	145783.i	−0.336423	−	0.400933i
$604$		0			0
$605$	110431.	+	626286.i	0.301704	+	1.71105i
$606$		0			0
$607$			142197.i			0.385933i	0.981205	+	0.192966i	$0.0618108\pi$
$607$			142197.i			0.385933i	−0.981205	+	0.192966i	$0.938189\pi$
$608$		0			0
$609$	−70545.6			−0.190211
$610$		0			0
$611$	−1.00782e6	+	177706.i	−2.69960	+	0.476013i
$612$		0			0
$613$	−162636.	+	136468.i	−0.432809	+	0.363170i	−0.833011	−	0.553257i	$-0.813385\pi$
$613$	−162636.	+	136468.i	−0.432809	+	0.363170i	0.400201	+	0.916427i	$0.368940\pi$
$614$		0			0
$615$	−225267.	+	390173.i	−0.595589	+	1.03159i
$616$		0			0
$617$	−66186.4	+	24089.9i	−0.173859	+	0.0632796i	−0.427483	−	0.904023i	$-0.640600\pi$
$617$	−66186.4	+	24089.9i	−0.173859	+	0.0632796i	0.253624	+	0.967303i	$0.418377\pi$
$618$		0			0
$619$	358449.	+	620852.i	0.935505	+	1.62034i	0.773731	+	0.633514i	$0.218388\pi$
$619$	358449.	+	620852.i	0.935505	+	1.62034i	0.161773	+	0.986828i	$0.448279\pi$
$620$		0			0
$621$	232199.	+	40942.9i	0.602111	+	0.106168i
$622$		0			0
$623$	29092.5	−	34671.1i	0.0749558	−	0.0893288i
$624$		0			0
$625$	−544490.	−	198178.i	−1.39390	−	0.507337i
$626$		0			0
$627$	−239193.	−	287849.i	−0.608433	−	0.732201i
$628$		0			0
$629$	434.029	−	1192.49i	0.00109703	−	0.00301406i
$630$		0			0
$631$	18387.5	+	15428.9i	0.0461810	+	0.0387504i	0.665586	−	0.746321i	$-0.268182\pi$
$631$	18387.5	+	15428.9i	0.0461810	+	0.0387504i	−0.619405	+	0.785072i	$0.712626\pi$
$632$		0			0
$633$	14516.6	−	82327.7i	0.0362291	−	0.205465i
$634$		0			0
$635$	562957.	−	325023.i	1.39614	−	0.806060i
$636$		0			0
$637$	211582.	+	581316.i	0.521434	+	1.43263i
$638$		0			0
$639$	130659.	+	75436.0i	0.319991	+	0.184747i
$640$		0			0
$641$	−346608.	−	413071.i	−0.843573	−	1.00533i	−0.999845	−	0.0176168i	$-0.994392\pi$
$641$	−346608.	−	413071.i	−0.843573	−	1.00533i	0.156272	−	0.987714i	$-0.450052\pi$
$642$		0			0
$643$	17369.9	+	98509.7i	0.0420123	+	0.238263i	0.998582	−	0.0532413i	$-0.0169552\pi$
$643$	17369.9	+	98509.7i	0.0420123	+	0.238263i	−0.956569	+	0.291505i	$0.905844\pi$
$644$		0			0
$645$			584367.i			1.40464i
$646$		0			0
$647$	364992.			0.871915			0.435958	−	0.899967i	$-0.356410\pi$
$647$	364992.			0.871915			0.435958	+	0.899967i	$0.356410\pi$
$648$		0			0
$649$	49909.9	−	8800.47i	0.118494	−	0.0208937i
$650$		0			0
$651$	−30900.3	+	25928.4i	−0.0729122	+	0.0611806i
$652$		0			0
$653$	323834.	−	560897.i	0.759444	−	1.31540i	−0.183690	−	0.982984i	$-0.558804\pi$
$653$	323834.	−	560897.i	0.759444	−	1.31540i	0.943134	−	0.332412i	$-0.107862\pi$
$654$		0			0
$655$	280244.	−	102000.i	0.653211	−	0.237749i
$656$		0			0
$657$	4046.49	+	7008.72i	0.00937448	+	0.0162371i
$658$		0			0
$659$	326976.	+	57654.6i	0.752912	+	0.132759i	0.536916	−	0.843635i	$-0.319589\pi$
$659$	326976.	+	57654.6i	0.752912	+	0.132759i	0.215996	+	0.976394i	$0.430700\pi$
$660$		0			0
$661$	458466.	−	546379.i	1.04931	−	1.25052i	0.0820794	−	0.996626i	$-0.473844\pi$
$661$	458466.	−	546379.i	1.04931	−	1.25052i	0.967232	−	0.253895i	$-0.0817117\pi$
$662$		0			0
$663$	−25944.9	−	9443.17i	−0.0590235	−	0.0214828i
$664$		0			0
$665$	26235.6	+	153076.i	0.0593263	+	0.346151i
$666$		0			0
$667$	126672.	−	348028.i	0.284727	−	0.782282i
$668$		0			0
$669$	−96003.4	−	80556.4i	−0.214504	−	0.179990i
$670$		0			0
$671$	185544.	−	1.05227e6i	0.412099	−	2.33713i
$672$		0			0
$673$	65371.3	−	37742.1i	0.144330	−	0.0833290i	−0.426096	−	0.904678i	$-0.640111\pi$
$673$	65371.3	−	37742.1i	0.144330	−	0.0833290i	0.570426	+	0.821349i	$0.306778\pi$
$674$		0			0
$675$	350184.	+	962123.i	0.768579	+	2.11165i
$676$		0			0
$677$	−204572.	−	118110.i	−0.446344	−	0.257697i	0.259941	−	0.965624i	$-0.416297\pi$
$677$	−204572.	−	118110.i	−0.446344	−	0.257697i	−0.706285	+	0.707928i	$0.749630\pi$
$678$		0			0
$679$	66331.0	+	79050.2i	0.143872	+	0.171460i
$680$		0			0
$681$	−65467.2	−	371283.i	−0.141166	−	0.800591i
$682$		0			0
$683$		−	94053.5i		−	0.201620i	−0.994906	−	0.100810i	$-0.967857\pi$
$683$		−	94053.5i		−	0.201620i	0.994906	−	0.100810i	$-0.0321434\pi$
$684$		0			0
$685$	−297524.			−0.634074
$686$		0			0
$687$	−378101.	+	66669.4i	−0.801114	+	0.141258i
$688$		0			0
$689$	483747.	−	405912.i	1.01901	−	0.855053i
$690$		0			0
$691$	−203613.	+	352668.i	−0.426431	+	0.738600i	−0.996553	−	0.0829599i	$-0.973563\pi$
$691$	−203613.	+	352668.i	−0.426431	+	0.738600i	0.570122	+	0.821560i	$0.306896\pi$
$692$		0			0
$693$	−68030.8	+	24761.2i	−0.141657	+	0.0515590i
$694$		0			0
$695$	387141.	+	670548.i	0.801493	+	1.38823i
$696$		0			0
$697$	27734.4	+	4890.33i	0.0570892	+	0.0100664i
$698$		0			0
$699$	210556.	−	250931.i	0.430936	−	0.513570i
$700$		0			0
$701$	−196445.	−	71500.1i	−0.399765	−	0.145503i	0.134310	−	0.990939i	$-0.457118\pi$
$701$	−196445.	−	71500.1i	−0.399765	−	0.145503i	−0.534076	+	0.845437i	$0.679340\pi$
$702$		0			0
$703$	−129.905	+	27101.1i	−0.000262855	+	0.0548373i
$704$		0			0
$705$	−352990.	+	969831.i	−0.710205	+	1.95127i
$706$		0			0
$707$	89690.4	+	75259.2i	0.179435	+	0.150564i
$708$		0			0
$709$	−60558.2	+	343442.i	−0.120470	+	0.683221i	0.863425	+	0.504477i	$0.168315\pi$
$709$	−60558.2	+	343442.i	−0.120470	+	0.683221i	−0.983896	+	0.178744i	$0.942796\pi$
$710$		0			0
$711$	267853.	−	154645.i	0.529856	−	0.305913i
$712$		0			0
$713$	−72430.1	−	199000.i	−0.142475	−	0.391448i
$714$		0			0
$715$	−1.75453e6	−	1.01298e6i	−3.43201	−	1.98147i
$716$		0			0
$717$	−439310.	−	523549.i	−0.854540	−	1.01840i
$718$		0			0
$719$	−74932.9	−	424966.i	−0.144949	−	0.822046i	−0.967408	−	0.253222i	$-0.918510\pi$
$719$	−74932.9	−	424966.i	−0.144949	−	0.822046i	0.822459	−	0.568824i	$-0.192601\pi$
$720$		0			0
$721$		−	60434.1i		−	0.116255i
$722$		0			0
$723$	−193328.			−0.369844
$724$		0			0
$725$	1.58386e6	−	279277.i	3.01329	−	0.531324i
$726$		0			0
$727$	−671227.	+	563226.i	−1.26999	+	1.06565i	−0.275448	+	0.961316i	$0.588826\pi$
$727$	−671227.	+	563226.i	−1.26999	+	1.06565i	−0.994542	+	0.104332i	$0.966729\pi$
$728$		0			0
$729$	211367.	−	366098.i	0.397723	−	0.688877i
$730$		0			0
$731$	34325.1	−	12493.3i	0.0642359	−	0.0233799i
$732$		0			0
$733$	3877.58	+	6716.17i	0.00721694	+	0.0125001i	0.869611	−	0.493737i	$-0.164369\pi$
$733$	3877.58	+	6716.17i	0.00721694	+	0.0125001i	−0.862394	+	0.506237i	$0.831036\pi$
$734$		0			0
$735$	614408.	+	108337.i	1.13732	+	0.200540i
$736$		0			0
$737$	474305.	−	565254.i	0.873217	−	1.04066i
$738$		0			0
$739$	176124.	+	64103.8i	0.322500	+	0.117380i	0.498197	−	0.867064i	$-0.333996\pi$
$739$	176124.	+	64103.8i	0.322500	+	0.117380i	−0.175697	+	0.984444i	$0.556218\pi$
$740$		0			0
$741$	589638.	+	2826.35i	1.07386	+	0.00514742i
$742$		0			0
$743$	22018.8	−	60496.3i	0.0398857	−	0.109585i	−0.918151	−	0.396231i	$-0.870318\pi$
$743$	22018.8	−	60496.3i	0.0398857	−	0.109585i	0.958037	+	0.286646i	$0.0925403\pi$
$744$		0			0
$745$	254466.	+	213523.i	0.458478	+	0.384708i
$746$		0			0
$747$	−19693.3	+	111686.i	−0.0352921	+	0.200151i
$748$		0			0
$749$	−51656.0	+	29823.6i	−0.0920783	+	0.0531614i
$750$		0			0
$751$	243557.	+	669168.i	0.431838	+	1.18647i	0.944683	+	0.327984i	$0.106369\pi$
$751$	243557.	+	669168.i	0.431838	+	1.18647i	−0.512845	+	0.858481i	$0.671408\pi$
$752$		0			0
$753$	206606.	+	119284.i	0.364379	+	0.210374i
$754$		0			0
$755$	−871338.	−	1.03842e6i	−1.52860	−	1.82171i
$756$		0			0
$757$	−73762.8	−	418329.i	−0.128720	−	0.730006i	−0.979029	−	0.203722i	$-0.934696\pi$
$757$	−73762.8	−	418329.i	−0.128720	−	0.730006i	0.850309	−	0.526284i	$-0.176415\pi$
$758$		0			0
$759$			321301.i			0.557735i
$760$		0			0
$761$	507568.			0.876446			0.438223	−	0.898866i	$-0.355608\pi$
$761$	507568.			0.876446			0.438223	+	0.898866i	$0.355608\pi$
$762$		0			0
$763$	4017.98	−	708.477i	0.00690173	−	0.00121696i
$764$		0			0
$765$	25232.9	−	21172.9i	0.0431165	−	0.0361791i
$766$		0			0
$767$	−39923.0	+	69148.6i	−0.0678629	+	0.117542i
$768$		0			0
$769$	−274196.	+	99799.1i	−0.463669	+	0.168762i	−0.563282	−	0.826264i	$-0.690462\pi$
$769$	−274196.	+	99799.1i	−0.463669	+	0.168762i	0.0996132	+	0.995026i	$0.468239\pi$
$770$		0			0
$771$	377927.	+	654589.i	0.635769	+	1.10118i
$772$		0			0
$773$	725809.	+	127980.i	1.21468	+	0.214181i	0.744036	−	0.668140i	$-0.232909\pi$
$773$	725809.	+	127980.i	1.21468	+	0.214181i	0.470648	+	0.882321i	$0.344020\pi$
$774$		0			0
$775$	591113.	−	704461.i	0.984164	−	1.17288i
$776$		0			0
$777$	−4164.44	−	1515.73i	−0.00689786	−	0.00251062i
$778$		0			0
$779$	−592797.	+	101599.i	−0.976857	+	0.167422i
$780$		0			0
$781$	−200077.	+	549708.i	−0.328017	+	0.901218i
$782$		0			0
$783$	−696467.	−	584405.i	−1.13600	−	0.953214i
$784$		0			0
$785$	−1490.86	+	8455.11i	−0.00241935	+	0.0137208i
$786$		0			0
$787$	539768.	−	311635.i	0.871481	−	0.503150i	0.00364072	−	0.999993i	$-0.498841\pi$
$787$	539768.	−	311635.i	0.871481	−	0.503150i	0.867840	+	0.496844i	$0.165508\pi$
$788$		0			0
$789$	17219.2	+	47309.5i	0.0276605	+	0.0759966i
$790$		0			0
$791$	−167131.	−	96493.2i	−0.267119	−	0.154221i
$792$		0			0
$793$	1.08209e6	+	1.28958e6i	1.72074	+	2.05070i
$794$		0			0
$795$	−110589.	−	627183.i	−0.174976	−	0.992339i
$796$		0			0
$797$		−	368595.i		−	0.580273i	−0.956985	−	0.290136i	$-0.906299\pi$
$797$		−	368595.i		−	0.580273i	0.956985	−	0.290136i	$-0.0937007\pi$
$798$		0			0
$799$	64513.6			0.101055
$800$		0			0
$801$	201886.	−	35598.0i	0.314660	−	0.0554831i
$802$		0			0
$803$	−24038.1	+	20170.3i	−0.0372794	+	0.0312811i
$804$		0			0
$805$	66665.8	−	115469.i	0.102875	−	0.178185i
$806$		0			0
$807$	−406242.	+	147860.i	−0.623790	+	0.227041i
$808$		0			0
$809$	154219.	+	267115.i	0.235635	+	0.408132i	0.959457	−	0.281855i	$-0.0909496\pi$
$809$	154219.	+	267115.i	0.235635	+	0.408132i	−0.723822	+	0.689987i	$0.757616\pi$
$810$		0			0
$811$	−1.13723e6	−	200524.i	−1.72904	−	0.304876i	−0.781355	−	0.624087i	$-0.785471\pi$
$811$	−1.13723e6	−	200524.i	−1.72904	−	0.304876i	−0.947684	+	0.319210i	$0.896582\pi$
$812$		0			0
$813$	−208985.	+	249059.i	−0.316180	+	0.376809i
$814$		0			0
$815$	−1.34110e6	−	488122.i	−2.01905	−	0.734874i
$816$		0			0
$817$	−599989.	+	498569.i	−0.898874	+	0.746932i
$818$		0			0
$819$	39011.2	−	107182.i	0.0581595	−	0.159792i
$820$		0			0
$821$	−625093.	−	524515.i	−0.927381	−	0.778165i	0.0479647	−	0.998849i	$-0.484726\pi$
$821$	−625093.	−	524515.i	−0.927381	−	0.778165i	−0.975345	+	0.220684i	$0.929171\pi$
$822$		0			0
$823$	89388.5	−	506947.i	0.131972	−	0.748451i	−0.844949	−	0.534848i	$-0.820369\pi$
$823$	89388.5	−	506947.i	0.131972	−	0.748451i	0.976921	−	0.213603i	$-0.0685199\pi$
$824$		0			0
$825$	−1.20831e6	+	697618.i	−1.77529	+	1.02497i
$826$		0			0
$827$	415278.	+	1.14097e6i	0.607194	+	1.66825i	0.736327	+	0.676626i	$0.236558\pi$
$827$	415278.	+	1.14097e6i	0.607194	+	1.66825i	−0.129133	+	0.991627i	$0.541219\pi$
$828$		0			0
$829$	−115870.	−	66897.5i	−0.168601	−	0.0973421i	0.413325	−	0.910584i	$-0.364367\pi$
$829$	−115870.	−	66897.5i	−0.168601	−	0.0973421i	−0.581926	+	0.813242i	$0.697701\pi$
$830$		0			0
$831$	448913.	+	534994.i	0.650070	+	0.774723i
$832$		0			0
$833$	−6772.00	−	38405.9i	−0.00975948	−	0.0553488i
$834$		0			0
$835$			1.51881e6i			2.17836i
$836$		0			0
$837$	−519858.			−0.742051
$838$		0			0
$839$	−415852.	+	73325.9i	−0.590765	+	0.104168i	−0.461036	−	0.887382i	$-0.652522\pi$
$839$	−415852.	+	73325.9i	−0.590765	+	0.104168i	−0.129729	+	0.991549i	$0.541411\pi$
$840$		0			0
$841$	−552200.	+	463351.i	−0.780736	+	0.655115i
$842$		0			0
$843$	98100.8	−	169916.i	0.138044	−	0.239099i
$844$		0			0
$845$	1.80793e6	−	658033.i	2.53203	−	0.921582i
$846$		0			0
$847$	−69412.2	−	120225.i	−0.0967540	−	0.167583i
$848$		0			0
$849$	40053.5	+	7062.51i	0.0555681	+	0.00979815i
$850$		0			0
$851$	14955.4	−	17823.1i	0.0206509	−	0.0246108i
$852$		0			0
$853$	241698.	+	87970.8i	0.332181	+	0.120904i	0.502726	−	0.864446i	$-0.332331\pi$
$853$	241698.	+	87970.8i	0.332181	+	0.120904i	−0.170545	+	0.985350i	$0.554553\pi$
$854$		0			0
$855$	−354644.	+	607518.i	−0.485133	+	0.831049i
$856$		0			0
$857$	112992.	−	310444.i	0.153847	−	0.422690i	−0.838694	−	0.544603i	$-0.816681\pi$
$857$	112992.	−	310444.i	0.153847	−	0.422690i	0.992541	+	0.121913i	$0.0389027\pi$
$858$		0			0
$859$	341166.	+	286272.i	0.462358	+	0.387965i	0.843998	−	0.536346i	$-0.180196\pi$
$859$	341166.	+	286272.i	0.462358	+	0.387965i	−0.381639	+	0.924311i	$0.624640\pi$
$860$		0			0
$861$	17078.2	−	96855.2i	0.0230375	−	0.130652i
$862$		0			0
$863$	−1.03497e6	+	597541.i	−1.38965	+	0.802317i	−0.993276	−	0.115771i	$-0.963066\pi$
$863$	−1.03497e6	+	597541.i	−1.38965	+	0.802317i	−0.396377	+	0.918088i	$0.629733\pi$
$864$		0			0
$865$	−739927.	−	2.03293e6i	−0.988910	−	2.71701i
$866$		0			0
$867$	−439095.	−	253512.i	−0.584144	−	0.337256i
$868$		0			0
$869$	770853.	+	918667.i	1.02078	+	1.21652i
$870$		0			0
$871$	201873.	+	1.14488e6i	0.266098	+	1.50912i
$872$		0			0
$873$			467402.i			0.613285i
$874$		0			0
$875$	310102.			0.405031
$876$		0			0
$877$	−213220.	+	37596.4i	−0.277222	+	0.0488818i	−0.310531	−	0.950563i	$-0.600507\pi$
$877$	−213220.	+	37596.4i	−0.277222	+	0.0488818i	0.0333083	+	0.999445i	$0.489396\pi$
$878$		0			0
$879$	−457295.	+	383716.i	−0.591860	+	0.496630i
$880$		0			0
$881$	86083.0	−	149100.i	0.110909	−	0.192099i	−0.805228	−	0.592965i	$-0.797957\pi$
$881$	86083.0	−	149100.i	0.110909	−	0.192099i	0.916137	+	0.400866i	$0.131291\pi$
$882$		0			0
$883$	1.34505e6	−	489560.i	1.72512	−	0.627891i	0.726852	−	0.686794i	$-0.240982\pi$
$883$	1.34505e6	−	489560.i	1.72512	−	0.627891i	0.998264	+	0.0589029i	$0.0187602\pi$
$884$		0			0
$885$	40262.6	+	69736.9i	0.0514062	+	0.0890381i
$886$		0			0
$887$	1.15864e6	+	204299.i	1.47265	+	0.259668i	0.851638	−	0.524131i	$-0.175610\pi$
$887$	1.15864e6	+	204299.i	1.47265	+	0.259668i	0.621015	+	0.783799i	$0.286721\pi$
$888$		0			0
$889$	−91213.0	+	108703.i	−0.115413	+	0.137543i
$890$		0			0
$891$	172542.	+	62800.0i	0.217339	+	0.0791051i
$892$		0			0
$893$	−1.29692e6	+	465012.i	−1.62634	+	0.583125i
$894$		0			0
$895$	461641.	−	1.26835e6i	0.576312	−	1.58341i
$896$		0			0
$897$	−387778.	−	325384.i	−0.481946	−	0.404400i
$898$		0			0
$899$	−141800.	+	804186.i	−0.175451	+	0.995032i
$900$		0			0
$901$	−34475.8	+	19904.6i	−0.0424683	+	0.0245191i
$902$		0			0
$903$	−43629.6	−	119871.i	−0.0535064	−	0.147008i
$904$		0			0
$905$	−1.68051e6	−	970242.i	−2.05184	−	1.18463i
$906$		0			0
$907$	−75848.0	−	90392.1i	−0.0921997	−	0.109879i	0.717972	−	0.696072i	$-0.245071\pi$
$907$	−75848.0	−	90392.1i	−0.0921997	−	0.109879i	−0.810172	+	0.586193i	$0.800626\pi$
$908$		0			0
$909$	92088.2	+	522258.i	0.111449	+	0.632059i
$910$		0			0
$911$		−	173199.i		−	0.208693i	−0.994541	−	0.104347i	$-0.966725\pi$
$911$		−	173199.i		−	0.208693i	0.994541	−	0.104347i	$-0.0332752\pi$
$912$		0			0
$913$	−439729.			−0.527526
$914$		0			0
$915$	1.67195e6	−	294811.i	1.99702	−	0.352128i
$916$		0			0
$917$	−49871.1	+	41846.8i	−0.0593075	+	0.0497649i
$918$		0			0
$919$	456516.	−	790709.i	0.540536	−	0.936236i	−0.458337	−	0.888778i	$-0.651555\pi$
$919$	456516.	−	790709.i	0.540536	−	0.936236i	0.998873	−	0.0474578i	$-0.0151119\pi$
$920$		0			0
$921$	508362.	−	185029.i	0.599313	−	0.218132i
$922$		0			0
$923$	−460822.	−	798168.i	−0.540916	−	0.936895i
$924$		0			0
$925$	99498.7	+	17544.3i	0.116288	+	0.0205047i
$926$		0			0
$927$	175951.	−	209690.i	0.204754	−	0.244016i
$928$		0			0
$929$	207140.	+	75392.8i	0.240012	+	0.0873572i	0.459226	−	0.888320i	$-0.348127\pi$
$929$	207140.	+	75392.8i	0.240012	+	0.0873572i	−0.219214	+	0.975677i	$0.570349\pi$
$930$		0			0
$931$	412967.	+	723264.i	0.476448	+	0.834444i
$932$		0			0
$933$	−377193.	+	1.03633e6i	−0.433312	+	1.19052i
$934$		0			0
$935$	97837.2	+	82095.2i	0.111913	+	0.0939062i
$936$		0			0
$937$	−134743.	+	764167.i	−0.153472	+	0.870380i	0.806698	+	0.590963i	$0.201252\pi$
$937$	−134743.	+	764167.i	−0.153472	+	0.870380i	−0.960170	+	0.279417i	$0.909859\pi$
$938$		0			0
$939$	−38063.0	+	21975.7i	−0.0431690	+	0.0249236i
$940$		0			0
$941$	−280991.	−	772016.i	−0.317331	−	0.871860i	−0.991124	−	0.132940i	$-0.957558\pi$
$941$	−280991.	−	772016.i	−0.317331	−	0.871860i	0.673793	−	0.738920i	$-0.264664\pi$
$942$		0			0
$943$	447158.	+	258167.i	0.502849	+	0.290320i
$944$		0			0
$945$	−210387.	−	250729.i	−0.235589	−	0.280764i
$946$		0			0
$947$	−134460.	−	762563.i	−0.149932	−	0.850307i	−0.963274	−	0.268521i	$-0.913465\pi$
$947$	−134460.	−	762563.i	−0.149932	−	0.850307i	0.813342	−	0.581786i	$-0.197646\pi$
$948$		0			0
$949$		−	49438.2i		−	0.0548947i
$950$		0			0
$951$	−288091.			−0.318543
$952$		0			0
$953$	285949.	−	50420.6i	0.314850	−	0.0555165i	−0.0139904	−	0.999902i	$-0.504453\pi$
$953$	285949.	−	50420.6i	0.314850	−	0.0555165i	0.328840	+	0.944386i	$0.393342\pi$
$954$		0			0
$955$	1.54431e6	−	1.29583e6i	1.69328	−	1.42083i
$956$		0			0
$957$	619469.	−	1.07295e6i	0.676387	−	1.17154i
$958$		0			0
$959$	61031.1	−	22213.5i	0.0663612	−	0.0241535i
$960$		0			0
$961$	−228300.	−	395427.i	−0.247206	−	0.428174i
$962$		0			0
$963$	−266063.	−	46914.0i	−0.286900	−	0.0505883i
$964$		0			0
$965$	−990745.	+	1.18072e6i	−1.06392	+	1.26793i
$966$		0			0
$967$	−729456.	−	265500.i	−0.780093	−	0.283931i	−0.0788815	−	0.996884i	$-0.525135\pi$
$967$	−729456.	−	265500.i	−0.780093	−	0.283931i	−0.701211	+	0.712953i	$0.747357\pi$
$968$		0			0
$969$	−36575.5	−	6630.16i	−0.0389531	−	0.00706117i
$970$		0			0
$971$	−363405.	+	998447.i	−0.385436	+	1.05898i	0.583597	+	0.812044i	$0.301645\pi$
$971$	−363405.	+	998447.i	−0.385436	+	1.05898i	−0.969033	+	0.246933i	$0.920577\pi$
$972$		0			0
$973$	−129478.	−	108645.i	−0.136764	−	0.114759i
$974$		0			0
$975$	381711.	−	2.16479e6i	0.401537	−	2.27723i
$976$		0			0
$977$	550212.	−	317665.i	0.576423	−	0.332798i	−0.183288	−	0.983059i	$-0.558674\pi$
$977$	550212.	−	317665.i	0.576423	−	0.332798i	0.759711	+	0.650261i	$0.225341\pi$
$978$		0			0
$979$	271860.	+	746929.i	0.283648	+	0.779316i
$980$		0			0
$981$	16004.0	+	9239.91i	0.0166299	+	0.00960129i
$982$		0			0
$983$	1.08183e6	+	1.28928e6i	1.11957	+	1.33426i	0.936302	+	0.351195i	$0.114225\pi$
$983$	1.08183e6	+	1.28928e6i	1.11957	+	1.33426i	0.183272	+	0.983062i	$0.441331\pi$
$984$		0			0
$985$	−210820.	−	1.19562e6i	−0.217290	−	1.23231i
$986$		0			0
$987$		−	225297.i		−	0.231270i
$988$		0			0
$989$	669714.			0.684694
$990$		0			0
$991$	1.13891e6	−	200820.i	1.15969	−	0.204485i	0.439488	−	0.898249i	$-0.355160\pi$
$991$	1.13891e6	−	200820.i	1.15969	−	0.204485i	0.720202	+	0.693764i	$0.244049\pi$
$992$		0			0
$993$	834683.	−	700382.i	0.846492	−	0.710291i
$994$		0			0
$995$	359655.	−	622940.i	0.363279	−	0.629217i
$996$		0			0
$997$	992263.	−	361154.i	0.998244	−	0.363331i	0.209337	−	0.977844i	$-0.432870\pi$
$997$	992263.	−	361154.i	0.998244	−	0.363331i	0.788907	+	0.614513i	$0.210647\pi$
$998$		0			0
$999$	−28557.3	−	49462.7i	−0.0286145	−	0.0495618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.53.5	yes	42
19.14	odd	18	inner	76.5.j.a.33.5	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.5	✓	42	19.14	odd	18	inner
76.5.j.a.53.5	yes	42	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(5.99890 - 1.05777i) q^{3} +(34.0076 - 28.5357i) q^{5} +(-4.84547 + 8.39260i) q^{7} +(-41.2471 + 15.0127i) q^{9} +O(q^{10})\)	\(q+(5.99890 - 1.05777i) q^{3} +(34.0076 - 28.5357i) q^{5} +(-4.84547 + 8.39260i) q^{7} +(-41.2471 + 15.0127i) q^{9} +(-85.0973 - 147.393i) q^{11} +(264.067 + 46.5622i) q^{13} +(173.824 - 207.155i) q^{15} +(-15.8843 - 5.78142i) q^{17} +(360.996 + 1.73039i) q^{19} +(-20.1901 + 55.4718i) q^{21} +(-237.410 - 199.211i) q^{23} +(233.696 - 1325.36i) q^{25} +(-658.861 + 380.393i) q^{27} +(408.729 + 1122.97i) q^{29} +(591.769 + 341.658i) q^{31} +(-666.398 - 794.182i) q^{33} +(74.7064 + 423.681i) q^{35} +75.0731i q^{37} +1633.37 q^{39} +(-1640.73 + 289.305i) q^{41} +(-1655.38 + 1389.03i) q^{43} +(-974.316 + 1687.56i) q^{45} +(-3586.36 + 1305.33i) q^{47} +(1153.54 + 1997.99i) q^{49} +(-101.404 - 17.8802i) q^{51} +(1513.80 - 1804.08i) q^{53} +(-7099.91 - 2584.16i) q^{55} +(2167.41 - 371.470i) q^{57} +(-101.845 + 279.818i) q^{59} +(4809.33 + 4035.51i) q^{61} +(73.8660 - 418.915i) q^{63} +(10309.0 - 5951.89i) q^{65} +(1482.85 + 4074.08i) q^{67} +(-1634.92 - 943.922i) q^{69} +(-2209.37 - 2633.02i) q^{71} +(-32.0162 - 181.573i) q^{73} -8197.89i q^{75} +1649.35 q^{77} +(-6939.21 + 1223.57i) q^{79} +(-826.450 + 693.474i) q^{81} +(1291.84 - 2237.54i) q^{83} +(-705.164 + 256.659i) q^{85} +(3639.77 + 6304.26i) q^{87} +(-4599.38 - 810.995i) q^{89} +(-1670.31 + 1990.60i) q^{91} +(3911.36 + 1423.62i) q^{93} +(12326.0 - 10242.4i) q^{95} +(3641.95 - 10006.2i) q^{97} +(5722.79 + 4801.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more