LMFDB - Embedded newform 76.5.j.a.13.6

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			13.6
Character	$\chi$	$=$	76.13
Dual form			76.5.j.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.28951 - 9.03787i) q^{3} +(7.51461 + 42.6175i) q^{5} +(-18.8739 + 32.6905i) q^{7} +(-8.81253 - 7.39459i) q^{9} +O(q^{10})$	\(q+(3.28951 - 9.03787i) q^{3} +(7.51461 + 42.6175i) q^{5} +(-18.8739 + 32.6905i) q^{7} +(-8.81253 - 7.39459i) q^{9} +(103.948 + 180.042i) q^{11} +(-76.3894 - 209.878i) q^{13} +(409.891 + 72.2748i) q^{15} +(361.904 - 303.674i) q^{17} +(-54.7631 + 356.822i) q^{19} +(233.366 + 278.115i) q^{21} +(-61.0806 + 346.405i) q^{23} +(-1172.47 + 426.745i) q^{25} +(578.857 - 334.203i) q^{27} +(-524.525 + 625.105i) q^{29} +(162.613 + 93.8845i) q^{31} +(1969.14 - 347.212i) q^{33} +(-1535.02 - 558.700i) q^{35} -914.694i q^{37} -2148.13 q^{39} +(819.137 - 2250.56i) q^{41} +(-232.697 - 1319.69i) q^{43} +(248.916 - 431.135i) q^{45} +(670.959 + 563.001i) q^{47} +(488.055 + 845.336i) q^{49} +(-1554.07 - 4269.78i) q^{51} +(-4531.29 - 798.988i) q^{53} +(-6891.83 + 5782.93i) q^{55} +(3044.77 + 1668.71i) q^{57} +(2507.79 + 2988.66i) q^{59} +(173.586 - 984.457i) q^{61} +(408.059 - 148.521i) q^{63} +(8370.44 - 4832.68i) q^{65} +(1694.50 - 2019.42i) q^{67} +(2929.84 + 1691.54i) q^{69} +(-2943.73 + 519.059i) q^{71} +(455.176 + 165.670i) q^{73} +12000.4i q^{75} -7847.56 q^{77} +(847.785 - 2329.27i) q^{79} +(-1278.13 - 7248.66i) q^{81} +(1815.81 - 3145.08i) q^{83} +(15661.4 + 13141.5i) q^{85} +(3924.18 + 6796.88i) q^{87} +(-2615.57 - 7186.22i) q^{89} +(8302.78 + 1464.00i) q^{91} +(1383.43 - 1160.84i) q^{93} +(-15618.4 + 347.516i) q^{95} +(125.731 + 149.840i) q^{97} +(415.299 - 2355.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	3.28951	−	9.03787i	0.365502	−	1.00421i	−0.611550	−	0.791206i	$-0.709454\pi$
$3$	3.28951	−	9.03787i	0.365502	−	1.00421i	0.977052	−	0.213002i	$-0.0683240\pi$
$4$		0			0
$5$	7.51461	+	42.6175i	0.300585	+	1.70470i	0.643594	+	0.765367i	$0.277443\pi$
$5$	7.51461	+	42.6175i	0.300585	+	1.70470i	−0.343009	+	0.939332i	$0.611446\pi$
$6$		0			0
$7$	−18.8739	+	32.6905i	−0.385181	+	0.667153i	−0.991794	−	0.127844i	$-0.959194\pi$
$7$	−18.8739	+	32.6905i	−0.385181	+	0.667153i	0.606613	+	0.794997i	$0.292528\pi$
$8$		0			0
$9$	−8.81253	−	7.39459i	−0.108797	−	0.0912912i
$10$		0			0
$11$	103.948	+	180.042i	0.859070	+	1.48795i	0.872817	+	0.488048i	$0.162291\pi$
$11$	103.948	+	180.042i	0.859070	+	1.48795i	−0.0137466	+	0.999906i	$0.504376\pi$
$12$		0			0
$13$	−76.3894	−	209.878i	−0.452008	−	1.24188i	−0.931309	−	0.364231i	$-0.881332\pi$
$13$	−76.3894	−	209.878i	−0.452008	−	1.24188i	0.479300	−	0.877651i	$-0.340890\pi$
$14$		0			0
$15$	409.891	+	72.2748i	1.82174	+	0.321221i
$16$		0			0
$17$	361.904	−	303.674i	1.25226	−	1.05077i	0.255802	−	0.966729i	$-0.417660\pi$
$17$	361.904	−	303.674i	1.25226	−	1.05077i	0.996462	−	0.0840453i	$-0.0267841\pi$
$18$		0			0
$19$	−54.7631	+	356.822i	−0.151698	+	0.988427i
$19$	−54.7631	+	356.822i	−0.151698	+	0.988427i
$20$		0			0
$21$	233.366	+	278.115i	0.529175	+	0.630647i
$22$		0			0
$23$	−61.0806	+	346.405i	−0.115464	+	0.654831i	0.871055	+	0.491186i	$0.163436\pi$
$23$	−61.0806	+	346.405i	−0.115464	+	0.654831i	−0.986519	+	0.163645i	$0.947675\pi$
$24$		0			0
$25$	−1172.47	+	426.745i	−1.87596	+	0.682792i
$26$		0			0
$27$	578.857	−	334.203i	0.794042	−	0.458440i
$28$		0			0
$29$	−524.525	+	625.105i	−0.623692	+	0.743287i	−0.981701	−	0.190431i	$-0.939011\pi$
$29$	−524.525	+	625.105i	−0.623692	+	0.743287i	0.358009	+	0.933718i	$0.383456\pi$
$30$		0			0
$31$	162.613	+	93.8845i	0.169212	+	0.0976946i	0.582214	−	0.813035i	$-0.302187\pi$
$31$	162.613	+	93.8845i	0.169212	+	0.0976946i	−0.413002	+	0.910730i	$0.635520\pi$
$32$		0			0
$33$	1969.14	−	347.212i	1.80821	−	0.318835i
$34$		0			0
$35$	−1535.02	−	558.700i	−1.25307	−	0.456082i
$36$		0			0
$37$		−	914.694i		−	0.668148i	−0.942547	−	0.334074i	$-0.891577\pi$
$37$		−	914.694i		−	0.668148i	0.942547	−	0.334074i	$-0.108423\pi$
$38$		0			0
$39$	−2148.13			−1.41232
$40$		0			0
$41$	819.137	−	2250.56i	0.487292	−	1.33882i	−0.415832	−	0.909442i	$-0.636509\pi$
$41$	819.137	−	2250.56i	0.487292	−	1.33882i	0.903123	−	0.429381i	$-0.141268\pi$
$42$		0			0
$43$	−232.697	−	1319.69i	−0.125850	−	0.713733i	−0.980799	−	0.195020i	$-0.937523\pi$
$43$	−232.697	−	1319.69i	−0.125850	−	0.713733i	0.854949	−	0.518712i	$-0.173588\pi$
$44$		0			0
$45$	248.916	−	431.135i	0.122921	−	0.212906i
$46$		0			0
$47$	670.959	+	563.001i	0.303739	+	0.254867i	0.781898	−	0.623406i	$-0.214252\pi$
$47$	670.959	+	563.001i	0.303739	+	0.254867i	−0.478160	+	0.878273i	$0.658696\pi$
$48$		0			0
$49$	488.055	+	845.336i	0.203272	+	0.352077i
$50$		0			0
$51$	−1554.07	−	4269.78i	−0.597491	−	1.64159i
$52$		0			0
$53$	−4531.29	−	798.988i	−1.61313	−	0.284439i	−0.706930	−	0.707283i	$-0.749920\pi$
$53$	−4531.29	−	798.988i	−1.61313	−	0.284439i	−0.906202	+	0.422845i	$0.861032\pi$
$54$		0			0
$55$	−6891.83	+	5782.93i	−2.27829	+	1.91171i
$56$		0			0
$57$	3044.77	+	1668.71i	0.937140	+	0.513608i
$58$		0			0
$59$	2507.79	+	2988.66i	0.720421	+	0.858565i	0.994672	−	0.103094i	$-0.0328741\pi$
$59$	2507.79	+	2988.66i	0.720421	+	0.858565i	−0.274250	+	0.961658i	$0.588430\pi$
$60$		0			0
$61$	173.586	−	984.457i	0.0466504	−	0.264568i	−0.952558	−	0.304358i	$-0.901558\pi$
$61$	173.586	−	984.457i	0.0466504	−	0.264568i	0.999208	+	0.0397906i	$0.0126691\pi$
$62$		0			0
$63$	408.059	−	148.521i	0.102812	−	0.0374203i
$64$		0			0
$65$	8370.44	−	4832.68i	1.98117	−	1.14383i
$66$		0			0
$67$	1694.50	−	2019.42i	0.377477	−	0.449860i	−0.543539	−	0.839384i	$-0.682916\pi$
$67$	1694.50	−	2019.42i	0.377477	−	0.449860i	0.921016	+	0.389524i	$0.127360\pi$
$68$		0			0
$69$	2929.84	+	1691.54i	0.615384	+	0.355292i
$70$		0			0
$71$	−2943.73	+	519.059i	−0.583958	+	0.102968i	−0.457819	−	0.889045i	$-0.651369\pi$
$71$	−2943.73	+	519.059i	−0.583958	+	0.102968i	−0.126138	+	0.992013i	$0.540258\pi$
$72$		0			0
$73$	455.176	+	165.670i	0.0854148	+	0.0310885i	0.384374	−	0.923177i	$-0.374417\pi$
$73$	455.176	+	165.670i	0.0854148	+	0.0310885i	−0.298959	+	0.954266i	$0.596639\pi$
$74$		0			0
$75$			12000.4i			2.13341i
$76$		0			0
$77$	−7847.56			−1.32359
$78$		0			0
$79$	847.785	−	2329.27i	0.135841	−	0.373221i	−0.853056	−	0.521819i	$-0.825254\pi$
$79$	847.785	−	2329.27i	0.135841	−	0.373221i	0.988898	+	0.148598i	$0.0474760\pi$
$80$		0			0
$81$	−1278.13	−	7248.66i	−0.194808	−	1.10481i
$82$		0			0
$83$	1815.81	−	3145.08i	0.263581	−	0.456536i	−0.703610	−	0.710587i	$-0.748430\pi$
$83$	1815.81	−	3145.08i	0.263581	−	0.456536i	0.967191	+	0.254051i	$0.0817630\pi$
$84$		0			0
$85$	15661.4	+	13141.5i	2.16767	+	1.81889i
$86$		0			0
$87$	3924.18	+	6796.88i	0.518454	+	0.897989i
$88$		0			0
$89$	−2615.57	−	7186.22i	−0.330207	−	0.907236i	−0.988057	−	0.154087i	$-0.950756\pi$
$89$	−2615.57	−	7186.22i	−0.330207	−	0.907236i	0.657850	−	0.753149i	$-0.271466\pi$
$90$		0			0
$91$	8302.78	+	1464.00i	1.00263	+	0.176791i
$92$		0			0
$93$	1383.43	−	1160.84i	0.159953	−	0.134216i
$94$		0			0
$95$	−15618.4	+	347.516i	−1.73057	+	0.0385059i
$96$		0			0
$97$	125.731	+	149.840i	0.0133628	+	0.0159252i	0.772684	−	0.634790i	$-0.218914\pi$
$97$	125.731	+	149.840i	0.0133628	+	0.0159252i	−0.759322	+	0.650715i	$0.774469\pi$
$98$		0			0
$99$	415.299	−	2355.28i	0.0423731	−	0.240310i
$100$		0			0
$101$	5764.46	−	2098.09i	0.565088	−	0.205675i	−0.0436498	−	0.999047i	$-0.513899\pi$
$101$	5764.46	−	2098.09i	0.565088	−	0.205675i	0.608737	+	0.793372i	$0.291676\pi$
$102$		0			0
$103$	10806.4	−	6239.10i	1.01861	−	0.588095i	0.104909	−	0.994482i	$-0.466545\pi$
$103$	10806.4	−	6239.10i	1.01861	−	0.588095i	0.913701	+	0.406387i	$0.133212\pi$
$104$		0			0
$105$	−10098.9	+	12035.4i	−0.916001	+	1.09165i
$106$		0			0
$107$	−1213.06	−	700.358i	−0.105953	−	0.0611720i	0.446087	−	0.894990i	$-0.352817\pi$
$107$	−1213.06	−	700.358i	−0.105953	−	0.0611720i	−0.552040	+	0.833818i	$0.686150\pi$
$108$		0			0
$109$	11058.0	−	1949.82i	0.930727	−	0.164112i	0.312326	−	0.949975i	$-0.398892\pi$
$109$	11058.0	−	1949.82i	0.930727	−	0.164112i	0.618401	+	0.785863i	$0.287781\pi$
$110$		0			0
$111$	−8266.88	−	3008.90i	−0.670959	−	0.244209i
$112$		0			0
$113$		−	5242.34i		−	0.410552i	−0.978704	−	0.205276i	$-0.934191\pi$
$113$		−	5242.34i		−	0.410552i	0.978704	−	0.205276i	$-0.0658092\pi$
$114$		0			0
$115$	−15221.9			−1.15100
$116$		0			0
$117$	−878.778	+	2414.42i	−0.0641960	+	0.176377i
$118$		0			0
$119$	3096.71	+	17562.3i	0.218679	+	1.24019i
$120$		0			0
$121$	−14289.7	+	24750.4i	−0.976004	+	1.69049i
$122$		0			0
$123$	−17645.7	−	14806.5i	−1.16635	−	0.978684i
$124$		0			0
$125$	−13474.1	−	23337.8i	−0.862340	−	1.49362i
$126$		0			0
$127$	−2155.34	−	5921.76i	−0.133632	−	0.367150i	0.854771	−	0.519005i	$-0.173697\pi$
$127$	−2155.34	−	5921.76i	−0.133632	−	0.367150i	−0.988403	+	0.151855i	$0.951475\pi$
$128$		0			0
$129$	−12692.7	−	2238.06i	−0.762734	−	0.134491i
$130$		0			0
$131$	21564.8	−	18095.0i	1.25662	−	1.05443i	0.260583	−	0.965451i	$-0.416085\pi$
$131$	21564.8	−	18095.0i	1.25662	−	1.05443i	0.996034	−	0.0889757i	$-0.0283594\pi$
$132$		0			0
$133$	−10631.1	−	8524.84i	−0.601000	−	0.481929i
$134$		0			0
$135$	18592.8	+	22158.0i	1.02018	+	1.21580i
$136$		0			0
$137$	4797.81	−	27209.7i	0.255624	−	1.44972i	−0.538842	−	0.842407i	$-0.681138\pi$
$137$	4797.81	−	27209.7i	0.255624	−	1.44972i	0.794466	−	0.607309i	$-0.207751\pi$
$138$		0			0
$139$	−7874.43	+	2866.06i	−0.407558	+	0.148339i	−0.537660	−	0.843162i	$-0.680692\pi$
$139$	−7874.43	+	2866.06i	−0.407558	+	0.148339i	0.130102	+	0.991501i	$0.458469\pi$
$140$		0			0
$141$	7295.46	−	4212.03i	0.366956	−	0.211862i
$142$		0			0
$143$	29846.5	−	35569.6i	1.45956	−	1.73943i
$144$		0			0
$145$	−30582.0	−	17656.5i	−1.45455	−	0.839787i
$146$		0			0
$147$	9245.50	−	1630.23i	0.427854	−	0.0754422i
$148$		0			0
$149$	11813.3	+	4299.70i	0.532108	+	0.193671i	0.594079	−	0.804407i	$-0.297517\pi$
$149$	11813.3	+	4299.70i	0.532108	+	0.193671i	−0.0619716	+	0.998078i	$0.519739\pi$
$150$		0			0
$151$		−	1094.46i		−	0.0480005i	−0.999712	−	0.0240002i	$-0.992360\pi$
$151$		−	1094.46i		−	0.0480005i	0.999712	−	0.0240002i	$-0.00764025\pi$
$152$		0			0
$153$	−5434.83			−0.232169
$154$		0			0
$155$	−2779.15	+	7635.65i	−0.115677	+	0.317821i
$156$		0			0
$157$	2873.20	+	16294.7i	0.116565	+	0.661071i	0.985964	+	0.166960i	$0.0533951\pi$
$157$	2873.20	+	16294.7i	0.116565	+	0.661071i	−0.869399	+	0.494111i	$0.835494\pi$
$158$		0			0
$159$	−22126.9	+	38324.9i	−0.875238	+	1.51596i
$160$		0			0
$161$	−10171.3	−	8534.76i	−0.392397	−	0.329261i
$162$		0			0
$163$	8971.48	+	15539.1i	0.337667	+	0.584857i	0.983993	−	0.178204i	$-0.0570288\pi$
$163$	8971.48	+	15539.1i	0.337667	+	0.584857i	−0.646326	+	0.763061i	$0.723695\pi$
$164$		0			0
$165$	29594.6	+	81310.4i	1.08704	+	2.98661i
$166$		0			0
$167$	−31190.3	−	5499.70i	−1.11837	−	0.197199i	−0.416247	−	0.909252i	$-0.636655\pi$
$167$	−31190.3	−	5499.70i	−1.11837	−	0.197199i	−0.702127	+	0.712052i	$0.747766\pi$
$168$		0			0
$169$	−16334.5	+	13706.3i	−0.571915	+	0.479894i
$170$		0			0
$171$	3121.15	−	2739.55i	0.106739	−	0.0936888i
$172$		0			0
$173$	715.042	+	852.154i	0.0238913	+	0.0284725i	0.777858	−	0.628440i	$-0.216306\pi$
$173$	715.042	+	852.154i	0.0238913	+	0.0284725i	−0.753967	+	0.656913i	$0.771862\pi$
$174$		0			0
$175$	8178.58	−	46383.0i	0.267056	−	1.51455i
$176$		0			0
$177$	35260.5	−	12833.8i	1.12549	−	0.409646i
$178$		0			0
$179$	−18126.2	+	10465.1i	−0.565718	+	0.326617i	−0.755437	−	0.655221i	$-0.772575\pi$
$179$	−18126.2	+	10465.1i	−0.565718	+	0.326617i	0.189719	+	0.981838i	$0.439242\pi$
$180$		0			0
$181$	−21860.1	+	26051.8i	−0.667259	+	0.795209i	−0.988408	−	0.151820i	$-0.951487\pi$
$181$	−21860.1	+	26051.8i	−0.667259	+	0.795209i	0.321149	+	0.947029i	$0.395931\pi$
$182$		0			0
$183$	−8326.37	−	4807.23i	−0.248630	−	0.143547i
$184$		0			0
$185$	38982.0	−	6873.57i	1.13899	−	0.200835i
$186$		0			0
$187$	92293.2	+	33592.0i	2.63929	+	0.960622i
$188$		0			0
$189$			25230.8i			0.706330i
$190$		0			0
$191$	42570.4			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$191$	42570.4			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$192$		0			0
$193$	−15357.1	+	42193.2i	−0.412281	+	1.13273i	0.543693	+	0.839284i	$0.317025\pi$
$193$	−15357.1	+	42193.2i	−0.412281	+	1.13273i	−0.955975	+	0.293449i	$0.905197\pi$
$194$		0			0
$195$	−16142.4	−	91548.1i	−0.424521	−	2.40758i
$196$		0			0
$197$	7105.29	−	12306.7i	0.183083	−	0.317110i	−0.759846	−	0.650104i	$-0.774725\pi$
$197$	7105.29	−	12306.7i	0.183083	−	0.317110i	0.942929	+	0.332994i	$0.108059\pi$
$198$		0			0
$199$	−22313.5	−	18723.2i	−0.563457	−	0.472797i	0.316010	−	0.948756i	$-0.397657\pi$
$199$	−22313.5	−	18723.2i	−0.563457	−	0.472797i	−0.879467	+	0.475959i	$0.842101\pi$
$200$		0			0
$201$	−12677.2	−	21957.6i	−0.313784	−	0.543490i
$202$		0			0
$203$	−10535.2	−	28945.1i	−0.255652	−	0.702398i
$204$		0			0
$205$	102069.	+	17997.5i	2.42876	+	0.428256i
$206$		0			0
$207$	3099.80	−	2601.04i	0.0723424	−	0.0607025i
$208$		0			0
$209$	−69935.6	+	27231.1i	−1.60105	+	0.623408i
$210$		0			0
$211$	19420.0	+	23143.9i	0.436200	+	0.519843i	0.938700	−	0.344734i	$-0.112031\pi$
$211$	19420.0	+	23143.9i	0.436200	+	0.519843i	−0.502501	+	0.864577i	$0.667587\pi$
$212$		0			0
$213$	−4992.26	+	28312.5i	−0.110037	+	0.624049i
$214$		0			0
$215$	54493.3	−	19833.9i	1.17887	−	0.429074i
$216$		0			0
$217$	−6138.26	+	3543.92i	−0.130354	+	0.0752601i
$218$		0			0
$219$	2994.61	−	3568.84i	0.0624385	−	0.0744113i
$220$		0			0
$221$	−91380.1	−	52758.3i	−1.87097	−	1.08021i
$222$		0			0
$223$	−80813.3	+	14249.6i	−1.62507	+	0.286544i	−0.910653	−	0.413171i	$-0.864421\pi$
$223$	−80813.3	+	14249.6i	−1.62507	+	0.286544i	−0.714421	+	0.699716i	$0.753310\pi$
$224$		0			0
$225$	13488.1	+	4909.25i	0.266431	+	0.0969728i
$226$		0			0
$227$			47803.2i			0.927695i	0.885915	+	0.463847i	$0.153531\pi$
$227$			47803.2i			0.927695i	−0.885915	+	0.463847i	$0.846469\pi$
$228$		0			0
$229$	32706.7			0.623686			0.311843	−	0.950134i	$-0.399054\pi$
$229$	32706.7			0.623686			0.311843	+	0.950134i	$0.399054\pi$
$230$		0			0
$231$	−25814.7	+	70925.2i	−0.483774	+	1.32916i
$232$		0			0
$233$	−8373.17	−	47486.6i	−0.154233	−	0.874701i	−0.959483	−	0.281765i	$-0.909080\pi$
$233$	−8373.17	−	47486.6i	−0.154233	−	0.874701i	0.805250	−	0.592935i	$-0.202031\pi$
$234$		0			0
$235$	−18951.7	+	32825.3i	−0.343172	+	0.594392i
$236$		0			0
$237$	−18262.8	−	15324.3i	−0.325141	−	0.272826i
$238$		0			0
$239$	−39420.4	−	68278.1i	−0.690121	−	1.19532i	−0.971798	−	0.235815i	$-0.924224\pi$
$239$	−39420.4	−	68278.1i	−0.690121	−	1.19532i	0.281677	−	0.959509i	$-0.409109\pi$
$240$		0			0
$241$	−30298.5	−	83244.4i	−0.521659	−	1.43325i	−0.868672	−	0.495387i	$-0.835026\pi$
$241$	−30298.5	−	83244.4i	−0.521659	−	1.43325i	0.347013	−	0.937860i	$-0.387196\pi$
$242$		0			0
$243$	−16398.5	−	2891.49i	−0.277709	−	0.0489677i
$244$		0			0
$245$	−32358.5	+	27152.0i	−0.539084	+	0.452346i
$246$		0			0
$247$	79072.5	−	15763.9i	1.29608	−	0.258386i
$248$		0			0
$249$	−22451.6	−	26756.8i	−0.362117	−	0.431555i
$250$		0			0
$251$	−16099.8	+	91306.6i	−0.255548	+	1.44929i	0.539112	+	0.842234i	$0.318760\pi$
$251$	−16099.8	+	91306.6i	−0.255548	+	1.44929i	−0.794661	+	0.607054i	$0.792351\pi$
$252$		0			0
$253$	−68716.8	+	25010.9i	−1.07355	+	0.390740i
$254$		0			0
$255$	170289.	−	98316.5i	2.61883	−	1.51198i
$256$		0			0
$257$	−57015.0	+	67947.8i	−0.863223	+	1.02875i	0.136053	+	0.990702i	$0.456558\pi$
$257$	−57015.0	+	67947.8i	−0.863223	+	1.02875i	−0.999276	+	0.0380473i	$0.987886\pi$
$258$		0			0
$259$	29901.8	+	17263.8i	0.445756	+	0.257358i
$260$		0			0
$261$	9244.78	−	1630.10i	0.135711	−	0.0239295i
$262$		0			0
$263$	61111.7	+	22242.9i	0.883513	+	0.321573i	0.743627	−	0.668595i	$-0.233104\pi$
$263$	61111.7	+	22242.9i	0.883513	+	0.321573i	0.139887	+	0.990168i	$0.455326\pi$
$264$		0			0
$265$		−	199116.i		−	2.83540i
$266$		0			0
$267$	−73552.0			−1.03174
$268$		0			0
$269$	−16485.4	+	45293.3i	−0.227822	+	0.625936i	−0.999955	−	0.00952562i	$-0.996968\pi$
$269$	−16485.4	+	45293.3i	−0.227822	+	0.625936i	0.772133	+	0.635461i	$0.219190\pi$
$270$		0			0
$271$	3910.58	+	22178.0i	0.0532479	+	0.301984i	0.999788	−	0.0206031i	$-0.00655864\pi$
$271$	3910.58	+	22178.0i	0.0532479	+	0.301984i	−0.946540	+	0.322587i	$0.895448\pi$
$272$		0			0
$273$	40543.6	−	70223.5i	0.543997	−	0.942231i
$274$		0			0
$275$	−198708.	−	166736.i	−2.62754	−	2.20477i
$276$		0			0
$277$	−6433.92	−	11143.9i	−0.0838525	−	0.145237i	0.821049	−	0.570858i	$-0.193389\pi$
$277$	−6433.92	−	11143.9i	−0.0838525	−	0.145237i	−0.904902	+	0.425621i	$0.860056\pi$
$278$		0			0
$279$	−738.791	−	2029.81i	−0.00949103	−	0.0260764i
$280$		0			0
$281$	86611.2	+	15271.9i	1.09689	+	0.193411i	0.692671	−	0.721254i	$-0.256434\pi$
$281$	86611.2	+	15271.9i	1.09689	+	0.193411i	0.404215	+	0.914664i	$0.367545\pi$
$282$		0			0
$283$	−89003.0	+	74682.4i	−1.11130	+	0.932493i	−0.998133	−	0.0610832i	$-0.980544\pi$
$283$	−89003.0	+	74682.4i	−1.11130	+	0.932493i	−0.113169	+	0.993576i	$0.536100\pi$
$284$		0			0
$285$	−48236.1	+	142300.i	−0.593858	+	1.75192i
$286$		0			0
$287$	58111.7	+	69254.8i	0.705504	+	0.840787i
$288$		0			0
$289$	24253.7	−	137550.i	0.290391	−	1.64689i
$290$		0			0
$291$	1767.83	−	643.437i	0.0208763	−	0.00759837i
$292$		0			0
$293$	64975.6	−	37513.7i	0.756859	−	0.436973i	−0.0713079	−	0.997454i	$-0.522717\pi$
$293$	64975.6	−	37513.7i	0.756859	−	0.436973i	0.828167	+	0.560482i	$0.189384\pi$
$294$		0			0
$295$	−108524.	+	129334.i	−1.24705	+	1.48617i
$296$		0			0
$297$	120341.	+	69479.1i	1.36428	+	0.787665i
$298$		0			0
$299$	77368.8	−	13642.2i	0.865413	−	0.152596i
$300$		0			0
$301$	47533.3	+	17300.7i	0.524644	+	0.190955i
$302$		0			0
$303$		−	59000.1i		−	0.642640i
$304$		0			0
$305$	43259.5			0.465031
$306$		0			0
$307$	−36832.6	+	101197.i	−0.390801	+	1.07372i	0.575836	+	0.817565i	$0.304677\pi$
$307$	−36832.6	+	101197.i	−0.390801	+	1.07372i	−0.966637	+	0.256151i	$0.917545\pi$
$308$		0			0
$309$	−20840.2	−	118191.i	−0.218265	−	1.23785i
$310$		0			0
$311$	33480.2	−	57989.4i	0.346152	−	0.599553i	−0.639410	−	0.768866i	$-0.720821\pi$
$311$	33480.2	−	57989.4i	0.346152	−	0.599553i	0.985562	+	0.169313i	$0.0541548\pi$
$312$		0			0
$313$	34053.8	+	28574.5i	0.347597	+	0.291669i	0.799824	−	0.600234i	$-0.204926\pi$
$313$	34053.8	+	28574.5i	0.347597	+	0.291669i	−0.452227	+	0.891903i	$0.649370\pi$
$314$		0			0
$315$	9396.01	+	16274.4i	0.0946940	+	0.164015i
$316$		0			0
$317$	35448.9	+	97395.0i	0.352764	+	0.969211i	0.981478	+	0.191574i	$0.0613593\pi$
$317$	35448.9	+	97395.0i	0.352764	+	0.969211i	−0.628714	+	0.777636i	$0.716418\pi$
$318$		0			0
$319$	−167068.	−	29458.7i	−1.64177	−	0.289489i
$320$		0			0
$321$	−10320.1	+	8659.60i	−0.100155	+	0.0840403i
$322$		0			0
$323$	88538.5	+	145766.i	0.848647	+	1.39717i
$324$		0			0
$325$	179129.	+	213478.i	1.69590	+	2.02109i
$326$		0			0
$327$	18753.1	−	106354.i	0.175379	−	0.994626i
$328$		0			0
$329$	−31068.4	+	11308.0i	−0.287029	+	0.104470i
$330$		0			0
$331$	59041.4	−	34087.6i	0.538891	−	0.311129i	−0.205739	−	0.978607i	$-0.565960\pi$
$331$	59041.4	−	34087.6i	0.538891	−	0.311129i	0.744629	+	0.667478i	$0.232626\pi$
$332$		0			0
$333$	−6763.78	+	8060.76i	−0.0609960	+	0.0726922i
$334$		0			0
$335$	98796.2	+	57040.0i	0.880340	+	0.508265i
$336$		0			0
$337$	74850.9	−	13198.2i	0.659079	−	0.116213i	0.165902	−	0.986142i	$-0.446947\pi$
$337$	74850.9	−	13198.2i	0.659079	−	0.116213i	0.493177	+	0.869929i	$0.335835\pi$
$338$		0			0
$339$	−47379.5	−	17244.7i	−0.412279	−	0.150057i
$340$		0			0
$341$			39036.2i			0.335706i
$342$		0			0
$343$	−127478.			−1.08355
$344$		0			0
$345$	−50072.8	+	137574.i	−0.420691	+	1.15584i
$346$		0			0
$347$	7554.18	+	42841.9i	0.0627377	+	0.355803i	0.999975	+	0.00711023i	$0.00226328\pi$
$347$	7554.18	+	42841.9i	0.0627377	+	0.355803i	−0.937237	+	0.348693i	$0.886626\pi$
$348$		0			0
$349$	78844.4	−	136562.i	0.647321	−	1.12119i	−0.336439	−	0.941705i	$-0.609223\pi$
$349$	78844.4	−	136562.i	0.647321	−	1.12119i	0.983760	−	0.179488i	$-0.0574441\pi$
$350$		0			0
$351$	−114360.	−	95959.7i	−0.928242	−	0.778888i
$352$		0			0
$353$	−19855.9	−	34391.5i	−0.159346	−	0.275995i	0.775287	−	0.631609i	$-0.217605\pi$
$353$	−19855.9	−	34391.5i	−0.159346	−	0.275995i	−0.934633	+	0.355614i	$0.884272\pi$
$354$		0			0
$355$	−44242.0	−	121554.i	−0.351057	−	0.964522i
$356$		0			0
$357$	168913.	+	29783.9i	1.32534	+	0.233692i
$358$		0			0
$359$	−113432.	+	95180.6i	−0.880128	+	0.738515i	−0.966205	−	0.257773i	$-0.917011\pi$
$359$	−113432.	+	95180.6i	−0.880128	+	0.738515i	0.0860774	+	0.996288i	$0.472567\pi$
$360$		0			0
$361$	−124323.	−	39081.3i	−0.953975	−	0.299885i
$362$		0			0
$363$	176685.	+	210565.i	1.34087	+	1.59799i
$364$		0			0
$365$	−3639.99	+	20643.4i	−0.0273221	+	0.154951i
$366$		0			0
$367$	9866.08	−	3590.96i	0.0732508	−	0.0266611i	−0.305135	−	0.952309i	$-0.598702\pi$
$367$	9866.08	−	3590.96i	0.0732508	−	0.0266611i	0.378386	+	0.925648i	$0.376479\pi$
$368$		0			0
$369$	−23860.6	+	13775.9i	−0.175238	+	0.101174i
$370$		0			0
$371$	111642.	−	133050.i	0.811112	−	0.966645i
$372$		0			0
$373$	−88926.0	−	51341.5i	−0.639162	−	0.369021i	0.145129	−	0.989413i	$-0.453640\pi$
$373$	−88926.0	−	51341.5i	−0.639162	−	0.369021i	−0.784292	+	0.620392i	$0.786973\pi$
$374$		0			0
$375$	−255247.	+	45006.9i	−1.81509	+	0.320049i
$376$		0			0
$377$	171264.	+	62335.0i	1.20499	+	0.438580i
$378$		0			0
$379$		−	193364.i		−	1.34616i	−0.739570	−	0.673080i	$-0.764971\pi$
$379$		−	193364.i		−	1.34616i	0.739570	−	0.673080i	$-0.235029\pi$
$380$		0			0
$381$	−60610.1			−0.417537
$382$		0			0
$383$	−31138.5	+	85552.4i	−0.212276	+	0.583223i	−0.999438	−	0.0335230i	$-0.989327\pi$
$383$	−31138.5	+	85552.4i	−0.212276	+	0.583223i	0.787162	+	0.616746i	$0.211550\pi$
$384$		0			0
$385$	−58971.4	−	334443.i	−0.397850	−	2.25632i
$386$		0			0
$387$	−7707.93	+	13350.5i	−0.0514654	+	0.0891407i
$388$		0			0
$389$	22260.3	+	18678.6i	0.147107	+	0.123437i	0.713371	−	0.700787i	$-0.247167\pi$
$389$	22260.3	+	18678.6i	0.147107	+	0.123437i	−0.566264	+	0.824224i	$0.691612\pi$
$390$		0			0
$391$	83088.9	+	143914.i	0.543488	+	0.941348i
$392$		0			0
$393$	−92602.7	−	254424.i	−0.599568	−	1.64730i
$394$		0			0
$395$	105638.	+	18626.9i	0.677061	+	0.119384i
$396$		0			0
$397$	211925.	−	177826.i	1.34462	−	1.12827i	0.364212	−	0.931316i	$-0.381338\pi$
$397$	211925.	−	177826.i	1.34462	−	1.12827i	0.980412	−	0.196957i	$-0.0631061\pi$
$398$		0			0
$399$	−112018.	+	68039.8i	−0.703623	+	0.427383i
$400$		0			0
$401$	−187594.	−	223565.i	−1.16662	−	1.39032i	−0.905140	−	0.425114i	$-0.860234\pi$
$401$	−187594.	−	223565.i	−1.16662	−	1.39032i	−0.261479	−	0.965209i	$-0.584210\pi$
$402$		0			0
$403$	7282.41	−	41300.6i	0.0448400	−	0.254300i
$404$		0			0
$405$	299315.	−	108942.i	1.82481	−	0.664177i
$406$		0			0
$407$	164684.	−	95080.2i	0.994172	−	0.573986i
$408$		0			0
$409$	−184229.	+	219556.i	−1.10131	+	1.31250i	−0.155483	+	0.987839i	$0.549693\pi$
$409$	−184229.	+	219556.i	−1.10131	+	1.31250i	−0.945832	+	0.324658i	$0.894751\pi$
$410$		0			0
$411$	−230135.	−	132869.i	−1.36238	−	0.786573i
$412$		0			0
$413$	−145032.	+	25573.1i	−0.850286	+	0.149928i
$414$		0			0
$415$	147680.	+	53751.3i	0.857485	+	0.312099i
$416$		0			0
$417$			80596.0i			0.463491i
$418$		0			0
$419$	−87412.0			−0.497901			−0.248951	−	0.968516i	$-0.580086\pi$
$419$	−87412.0			−0.497901			−0.248951	+	0.968516i	$0.580086\pi$
$420$		0			0
$421$	−97498.4	+	267875.i	−0.550090	+	1.51136i	0.283499	+	0.958973i	$0.408505\pi$
$421$	−97498.4	+	267875.i	−0.550090	+	1.51136i	−0.833588	+	0.552386i	$0.813717\pi$
$422$		0			0
$423$	−1749.68	−	9922.92i	−0.00977862	−	0.0554573i
$424$		0			0
$425$	−294732.	+	510490.i	−1.63173	+	2.82624i
$426$		0			0
$427$	28906.1	+	24255.1i	0.158538	+	0.133029i
$428$		0			0
$429$	−223293.	−	386755.i	−1.21328	−	2.10146i
$430$		0			0
$431$	102913.	+	282752.i	0.554010	+	1.52213i	0.828188	+	0.560451i	$0.189372\pi$
$431$	102913.	+	282752.i	0.554010	+	1.52213i	−0.274178	+	0.961679i	$0.588406\pi$
$432$		0			0
$433$	−260545.	−	45941.1i	−1.38966	−	0.245034i	−0.571769	−	0.820414i	$-0.693743\pi$
$433$	−260545.	−	45941.1i	−1.38966	−	0.245034i	−0.817886	+	0.575381i	$0.804854\pi$
$434$		0			0
$435$	−260177.	+	218315.i	−1.37496	+	1.15373i
$436$		0			0
$437$	−120260.	−	40765.1i	−0.629737	−	0.213465i
$438$		0			0
$439$	−132702.	−	158148.i	−0.688570	−	0.820605i	0.302612	−	0.953114i	$-0.402141\pi$
$439$	−132702.	−	158148.i	−0.688570	−	0.820605i	−0.991182	+	0.132509i	$0.957697\pi$
$440$		0			0
$441$	1949.91	−	11058.5i	0.0100262	−	0.0568616i
$442$		0			0
$443$	64757.2	−	23569.7i	0.329975	−	0.120101i	−0.171720	−	0.985146i	$-0.554932\pi$
$443$	64757.2	−	23569.7i	0.329975	−	0.120101i	0.501695	+	0.865045i	$0.332710\pi$
$444$		0			0
$445$	286603.	−	165471.i	1.44731	−	0.835605i
$446$		0			0
$447$	77720.2	−	92623.3i	0.388972	−	0.463559i
$448$		0			0
$449$	−217623.	−	125644.i	−1.07947	−	0.623233i	−0.148718	−	0.988880i	$-0.547515\pi$
$449$	−217623.	−	125644.i	−1.07947	−	0.623233i	−0.930754	+	0.365646i	$0.880848\pi$
$450$		0			0
$451$	490344.	−	86460.8i	2.41072	−	0.425076i
$452$		0			0
$453$	−9891.57	−	3600.24i	−0.0482024	−	0.0175442i
$454$		0			0
$455$			364845.i			1.76232i
$456$		0			0
$457$	358067.			1.71448			0.857238	−	0.514921i	$-0.172179\pi$
$457$	358067.			1.71448			0.857238	+	0.514921i	$0.172179\pi$
$458$		0			0
$459$	108002.	−	296733.i	0.512633	−	1.40845i
$460$		0			0
$461$	54042.7	+	306491.i	0.254293	+	1.44217i	0.797880	+	0.602817i	$0.205955\pi$
$461$	54042.7	+	306491.i	0.254293	+	1.44217i	−0.543586	+	0.839353i	$0.682934\pi$
$462$		0			0
$463$	5432.68	−	9409.69i	0.0253427	−	0.0438948i	−0.853076	−	0.521787i	$-0.825266\pi$
$463$	5432.68	−	9409.69i	0.0253427	−	0.0438948i	0.878419	+	0.477892i	$0.158599\pi$
$464$		0			0
$465$	59867.9	+	50235.2i	0.276878	+	0.232328i
$466$		0			0
$467$	−109600.	−	189833.i	−0.502547	−	0.870437i	−0.999996	−	0.00294375i	$-0.999063\pi$
$467$	−109600.	−	189833.i	−0.502547	−	0.870437i	0.497448	−	0.867494i	$-0.334270\pi$
$468$		0			0
$469$	34034.2	+	93508.2i	0.154728	+	0.425113i
$470$		0			0
$471$	156721.	+	27634.2i	0.706457	+	0.124567i
$472$		0			0
$473$	213412.	−	179074.i	0.953887	−	0.800406i
$474$		0			0
$475$	−88063.9	−	441734.i	−0.390311	−	1.95782i
$476$		0			0
$477$	34023.9	+	40548.1i	0.149537	+	0.178211i
$478$		0			0
$479$	53014.1	−	300658.i	0.231058	−	1.31039i	−0.619701	−	0.784838i	$-0.712746\pi$
$479$	53014.1	−	300658.i	0.231058	−	1.31039i	0.850759	−	0.525556i	$-0.176143\pi$
$480$		0			0
$481$	−191974.	+	69872.9i	−0.829761	+	0.302008i
$482$		0			0
$483$	−110595.	+	63851.9i	−0.474068	+	0.273703i
$484$		0			0
$485$	−5440.99	+	6484.32i	−0.0231310	+	0.0275665i
$486$		0			0
$487$	−4289.91	−	2476.78i	−0.0180880	−	0.0104431i	0.490929	−	0.871200i	$-0.336658\pi$
$487$	−4289.91	−	2476.78i	−0.0180880	−	0.0104431i	−0.509017	+	0.860757i	$0.669991\pi$
$488$		0			0
$489$	169952.	−	29967.1i	0.710735	−	0.125322i
$490$		0			0
$491$	184130.	+	67017.8i	0.763768	+	0.277989i	0.694387	−	0.719601i	$-0.255675\pi$
$491$	184130.	+	67017.8i	0.763768	+	0.277989i	0.0693808	+	0.997590i	$0.477898\pi$
$492$		0			0
$493$			385513.i			1.58615i
$494$		0			0
$495$	103497.			0.422393
$496$		0			0
$497$	38591.3	−	106029.i	0.156234	−	0.429250i
$498$		0			0
$499$	176.716	+	1002.21i	0.000709701	+	0.00402492i	0.985161	−	0.171635i	$-0.0549051\pi$
$499$	176.716	+	1002.21i	0.000709701	+	0.00402492i	−0.984451	+	0.175660i	$0.943794\pi$
$500$		0			0
$501$	−152307.	+	263803.i	−0.606797	+	1.05100i
$502$		0			0
$503$	−114887.	−	96401.4i	−0.454081	−	0.381020i	0.386866	−	0.922136i	$-0.373557\pi$
$503$	−114887.	−	96401.4i	−0.454081	−	0.381020i	−0.840948	+	0.541116i	$0.818002\pi$
$504$		0			0
$505$	132733.	+	229900.i	0.520471	+	0.901482i
$506$		0			0
$507$	70142.8	+	192716.i	0.272877	+	0.749724i
$508$		0			0
$509$	140606.	+	24792.6i	0.542709	+	0.0956943i	0.438281	−	0.898838i	$-0.355588\pi$
$509$	140606.	+	24792.6i	0.542709	+	0.0956943i	0.104428	+	0.994532i	$0.466699\pi$
$510$		0			0
$511$	−14006.8	+	11753.1i	−0.0536409	+	0.0450101i
$512$		0			0
$513$	87551.1	+	224851.i	0.332680	+	0.854397i
$514$		0			0
$515$	347101.	+	413659.i	1.30870	+	1.55965i
$516$		0			0
$517$	−31619.6	+	179324.i	−0.118297	+	0.670898i
$518$		0			0
$519$	10053.8	−	3659.28i	0.0373246	−	0.0135851i
$520$		0			0
$521$	−105137.	+	60701.1i	−0.387331	+	0.223625i	−0.681003	−	0.732281i	$-0.738456\pi$
$521$	−105137.	+	60701.1i	−0.387331	+	0.223625i	0.293672	+	0.955906i	$0.405123\pi$
$522$		0			0
$523$	38925.4	−	46389.5i	0.142308	−	0.169596i	−0.690182	−	0.723635i	$-0.742470\pi$
$523$	38925.4	−	46389.5i	0.142308	−	0.169596i	0.832491	+	0.554039i	$0.186914\pi$
$524$		0			0
$525$	−392300.	−	226495.i	−1.42331	−	0.821749i
$526$		0			0
$527$	87360.5	−	15404.0i	0.314553	−	0.0554642i
$528$		0			0
$529$	146699.	+	53393.9i	0.524221	+	0.190801i
$530$		0			0
$531$		−	44881.7i		−	0.159177i
$532$		0			0
$533$	−534917.			−1.88292
$534$		0			0
$535$	20731.8	−	56960.3i	0.0724320	−	0.199005i
$536$		0			0
$537$	34956.3	+	198247.i	0.121221	+	0.687477i
$538$		0			0
$539$	−101464.	+	175741.i	−0.349249	+	0.604917i
$540$		0			0
$541$	−322743.	−	270814.i	−1.10271	−	0.925286i	−0.105109	−	0.994461i	$-0.533519\pi$
$541$	−322743.	−	270814.i	−1.10271	−	0.925286i	−0.997605	+	0.0691745i	$0.977963\pi$
$542$		0			0
$543$	163544.	+	283266.i	0.554670	+	0.960717i
$544$		0			0
$545$	166193.	+	456610.i	0.559524	+	1.53728i
$546$		0			0
$547$	−329113.	−	58031.6i	−1.09994	−	0.193950i	−0.405925	−	0.913906i	$-0.633051\pi$
$547$	−329113.	−	58031.6i	−1.09994	−	0.193950i	−0.694019	+	0.719956i	$0.744162\pi$
$548$		0			0
$549$	−8809.38	+	7391.95i	−0.0292281	+	0.0245253i
$550$		0			0
$551$	−194327.	−	221395.i	−0.640072	−	0.729229i
$552$		0			0
$553$	60144.0	+	71676.8i	0.196672	+	0.234384i
$554$		0			0
$555$	66109.3	−	374924.i	0.214623	−	1.21719i
$556$		0			0
$557$	371939.	−	135375.i	1.19884	−	0.436342i	0.336021	−	0.941855i	$-0.390919\pi$
$557$	371939.	−	135375.i	1.19884	−	0.436342i	0.862819	+	0.505512i	$0.168697\pi$
$558$		0			0
$559$	−259199.	+	149648.i	−0.829487	+	0.478904i
$560$		0			0
$561$	607200.	−	723632.i	1.92933	−	2.29928i
$562$		0			0
$563$	267894.	+	154669.i	0.845175	+	0.487962i	0.859020	−	0.511942i	$-0.171074\pi$
$563$	267894.	+	154669.i	0.845175	+	0.487962i	−0.0138446	+	0.999904i	$0.504407\pi$
$564$		0			0
$565$	223415.	−	39394.1i	0.699867	−	0.123406i
$566$		0			0
$567$	261085.	+	95027.3i	0.812113	+	0.295585i
$568$		0			0
$569$		−	282436.i		−	0.872360i	−0.899859	−	0.436180i	$-0.856331\pi$
$569$		−	282436.i		−	0.872360i	0.899859	−	0.436180i	$-0.143669\pi$
$570$		0			0
$571$	−162080.			−0.497114			−0.248557	−	0.968617i	$-0.579956\pi$
$571$	−162080.			−0.497114			−0.248557	+	0.968617i	$0.579956\pi$
$572$		0			0
$573$	140036.	−	384746.i	0.426511	−	1.17183i
$574$		0			0
$575$	−76211.5	−	432217.i	−0.230507	−	1.30727i
$576$		0			0
$577$	−320896.	+	555808.i	−0.963857	+	1.66945i	−0.251202	+	0.967935i	$0.580826\pi$
$577$	−320896.	+	555808.i	−0.963857	+	1.66945i	−0.712655	+	0.701515i	$0.752507\pi$
$578$		0			0
$579$	330819.	+	277590.i	0.986810	+	0.828032i
$580$		0			0
$581$	68542.7	+	118719.i	0.203053	+	0.351698i
$582$		0			0
$583$	−327164.	−	898877.i	−0.962562	−	2.64462i
$584$		0			0
$585$	−109500.	−	19307.9i	−0.319966	−	0.0564186i
$586$		0			0
$587$	342332.	−	287251.i	0.993509	−	0.833653i	0.00743718	−	0.999972i	$-0.497633\pi$
$587$	342332.	−	287251.i	0.993509	−	0.833653i	0.986072	+	0.166319i	$0.0531882\pi$
$588$		0			0
$589$	−42405.2	+	52882.4i	−0.122233	+	0.152434i
$590$		0			0
$591$	−87853.5	−	104700.i	−0.251527	−	0.299758i
$592$		0			0
$593$	−4325.64	+	24531.9i	−0.0123010	+	0.0697625i	−0.990340	−	0.138658i	$-0.955721\pi$
$593$	−4325.64	+	24531.9i	−0.0123010	+	0.0697625i	0.978039	+	0.208420i	$0.0668322\pi$
$594$		0			0
$595$	−725192.	+	263948.i	−2.04842	+	0.745564i
$596$		0			0
$597$	−242619.	+	140076.i	−0.680731	+	0.393020i
$598$		0			0
$599$	−362000.	+	431415.i	−1.00892	+	1.20238i	−0.0296996	+	0.999559i	$0.509455\pi$
$599$	−362000.	+	431415.i	−1.00892	+	1.20238i	−0.979216	+	0.202820i	$0.934989\pi$
$600$		0			0
$601$	−108967.	−	62911.9i	−0.301679	−	0.174174i	0.341518	−	0.939875i	$-0.389059\pi$
$601$	−108967.	−	62911.9i	−0.301679	−	0.174174i	−0.643197	+	0.765701i	$0.722392\pi$
$602$		0			0
$603$	−29865.6	+	5266.11i	−0.0821365	+	0.0144829i
$604$		0			0
$605$	−1.16218e6	−	423000.i	−3.17514	−	1.15566i
$606$		0			0
$607$			421927.i			1.14514i	0.819855	+	0.572571i	$0.194054\pi$
$607$			421927.i			1.14514i	−0.819855	+	0.572571i	$0.805946\pi$
$608$		0			0
$609$	−296258.			−0.798794
$610$		0			0
$611$	66907.5	−	183827.i	0.179222	−	0.492410i
$612$		0			0
$613$	−11873.9	−	67340.2i	−0.0315989	−	0.179206i	0.964924	−	0.262531i	$-0.0845572\pi$
$613$	−11873.9	−	67340.2i	−0.0315989	−	0.179206i	−0.996522	+	0.0833248i	$0.973446\pi$
$614$		0			0
$615$	498415.	−	863281.i	1.31777	−	2.28245i
$616$		0			0
$617$	260713.	+	218764.i	0.684845	+	0.574653i	0.917417	−	0.397926i	$-0.130270\pi$
$617$	260713.	+	218764.i	0.684845	+	0.574653i	−0.232573	+	0.972579i	$0.574714\pi$
$618$		0			0
$619$	−68974.6	−	119468.i	−0.180015	−	0.311795i	0.761871	−	0.647729i	$-0.224281\pi$
$619$	−68974.6	−	119468.i	−0.180015	−	0.311795i	−0.941885	+	0.335935i	$0.890948\pi$
$620$		0			0
$621$	80412.8	+	220932.i	0.208517	+	0.572897i
$622$		0			0
$623$	284287.	+	50127.4i	0.732454	+	0.129151i
$624$		0			0
$625$	295964.	−	248344.i	0.757669	−	0.635760i
$626$		0			0
$627$	16056.9	+	721645.i	0.0408439	+	1.83565i
$628$		0			0
$629$	−277769.	−	331032.i	−0.702072	−	0.836697i
$630$		0			0
$631$	14222.2	−	80658.1i	0.0357197	−	0.202577i	−0.961725	−	0.274016i	$-0.911648\pi$
$631$	14222.2	−	80658.1i	0.0357197	−	0.202577i	0.997445	+	0.0714390i	$0.0227591\pi$
$632$		0			0
$633$	273054.	−	99383.6i	0.681462	−	0.248032i
$634$		0			0
$635$	236174.	−	136355.i	0.585713	−	0.338161i
$636$		0			0
$637$	140135.	−	167007.i	0.345357	−	0.411581i
$638$		0			0
$639$	29779.9	+	17193.5i	0.0729327	+	0.0421077i
$640$		0			0
$641$	−583030.	+	102804.i	−1.41897	+	0.250204i	−0.829917	−	0.557887i	$-0.811612\pi$
$641$	−583030.	+	102804.i	−1.41897	+	0.250204i	−0.589058	+	0.808091i	$0.700501\pi$
$642$		0			0
$643$	−640784.	−	233226.i	−1.54985	−	0.564100i	−0.581468	−	0.813569i	$-0.697522\pi$
$643$	−640784.	−	233226.i	−1.54985	−	0.564100i	−0.968383	+	0.249470i	$0.919744\pi$
$644$		0			0
$645$		−	557747.i		−	1.34066i
$646$		0			0
$647$	21537.2			0.0514493			0.0257247	−	0.999669i	$-0.491811\pi$
$647$	21537.2			0.0514493			0.0257247	+	0.999669i	$0.491811\pi$
$648$		0			0
$649$	−277408.	+	762172.i	−0.658612	+	1.80952i
$650$		0			0
$651$	11837.6	+	67134.5i	0.0279321	+	0.158411i
$652$		0			0
$653$	220827.	−	382483.i	0.517876	−	0.896987i	−0.481909	−	0.876221i	$-0.660056\pi$
$653$	220827.	−	382483.i	0.517876	−	0.896987i	0.999784	−	0.0207656i	$-0.00661036\pi$
$654$		0			0
$655$	933216.	+	783061.i	2.17520	+	1.82521i
$656$		0			0
$657$	−2786.18	−	4825.81i	−0.00645474	−	0.0111799i
$658$		0			0
$659$	40628.8	+	111627.i	0.0935542	+	0.257038i	0.977640	−	0.210287i	$-0.0674399\pi$
$659$	40628.8	+	111627.i	0.0935542	+	0.257038i	−0.884085	+	0.467325i	$0.845218\pi$
$660$		0			0
$661$	−258721.	−	45619.5i	−0.592146	−	0.104411i	−0.130458	−	0.991454i	$-0.541645\pi$
$661$	−258721.	−	45619.5i	−0.592146	−	0.104411i	−0.461688	+	0.887043i	$0.652756\pi$
$662$		0			0
$663$	−777419.	+	652332.i	−1.76859	+	1.48403i
$664$		0			0
$665$	283419.	−	517131.i	0.640893	−	1.16939i
$666$		0			0
$667$	−184501.	−	219880.i	−0.414713	−	0.494236i
$668$		0			0
$669$	−137051.	+	777254.i	−0.306217	+	1.73664i
$670$		0			0
$671$	195288.	−	71078.9i	0.433740	−	0.157869i
$672$		0			0
$673$	577163.	−	333225.i	1.27429	−	0.735712i	0.298497	−	0.954410i	$-0.403515\pi$
$673$	577163.	−	333225.i	1.27429	−	0.735712i	0.975792	+	0.218699i	$0.0701813\pi$
$674$		0			0
$675$	−536074.	+	638868.i	−1.17657	+	1.40218i
$676$		0			0
$677$	58995.1	+	34060.8i	0.128718	+	0.0743153i	0.562976	−	0.826473i	$-0.309656\pi$
$677$	58995.1	+	34060.8i	0.128718	+	0.0743153i	−0.434258	+	0.900788i	$0.642990\pi$
$678$		0			0
$679$	−7271.37	+	1282.14i	−0.0157716	+	0.00278097i
$680$		0			0
$681$	432039.	+	157249.i	0.931598	+	0.339074i
$682$		0			0
$683$		−	573992.i		−	1.23045i	−0.788351	−	0.615225i	$-0.789065\pi$
$683$		−	573992.i		−	1.23045i	0.788351	−	0.615225i	$-0.210935\pi$
$684$		0			0
$685$	1.19566e6			2.54817
$686$		0			0
$687$	107589.	−	295599.i	0.227958	−	0.626310i
$688$		0			0
$689$	178452.	+	1.01205e6i	0.375909	+	2.13189i
$690$		0			0
$691$	102921.	−	178264.i	0.215549	−	0.373342i	−0.737893	−	0.674917i	$-0.764179\pi$
$691$	102921.	−	178264.i	0.215549	−	0.373342i	0.953442	+	0.301576i	$0.0975126\pi$
$692$		0			0
$693$	69156.8	+	58029.5i	0.144002	+	0.120832i
$694$		0			0
$695$	−181317.	−	314051.i	−0.375379	−	0.650176i
$696$		0			0
$697$	−386987.	−	1.06324e6i	−0.796583	−	2.18859i
$698$		0			0
$699$	−456722.	−	80532.3i	−0.934754	−	0.164822i
$700$		0			0
$701$	−360259.	+	302293.i	−0.733127	+	0.615167i	−0.930982	−	0.365065i	$-0.881047\pi$
$701$	−360259.	+	302293.i	−0.733127	+	0.615167i	0.197855	+	0.980231i	$0.436602\pi$
$702$		0			0
$703$	326383.	+	50091.4i	0.660415	+	0.101357i
$704$		0			0
$705$	234329.	+	279262.i	0.471463	+	0.561868i
$706$		0			0
$707$	−40210.0	+	228042.i	−0.0804442	+	0.456222i
$708$		0			0
$709$	−173573.	+	63175.4i	−0.345295	+	0.125677i	−0.508845	−	0.860858i	$-0.669928\pi$
$709$	−173573.	+	63175.4i	−0.345295	+	0.125677i	0.163551	+	0.986535i	$0.447705\pi$
$710$		0			0
$711$	−24695.1	+	14257.7i	−0.0488508	+	0.0282040i
$712$		0			0
$713$	−42454.6	+	50595.4i	−0.0835114	+	0.0995250i
$714$		0			0
$715$	1.74017e6	+	1.00469e6i	3.40393	+	1.96526i
$716$		0			0
$717$	−746762.	+	131674.i	−1.45259	+	0.256131i
$718$		0			0
$719$	−117349.	−	42711.4i	−0.226997	−	0.0826201i	0.226018	−	0.974123i	$-0.427429\pi$
$719$	−117349.	−	42711.4i	−0.226997	−	0.0826201i	−0.453015	+	0.891503i	$0.649651\pi$
$720$		0			0
$721$			471023.i			0.906091i
$722$		0			0
$723$	−852019.			−1.62994
$724$		0			0
$725$	348231.	−	956757.i	0.662508	−	1.82023i
$726$		0			0
$727$	8299.90	+	47071.1i	0.0157038	+	0.0890605i	0.991652	−	0.128940i	$-0.0411576\pi$
$727$	8299.90	+	47071.1i	0.0157038	+	0.0890605i	−0.975949	+	0.218001i	$0.930046\pi$
$728$		0			0
$729$	218023.	−	377628.i	0.410250	−	0.710573i
$730$		0			0
$731$	−484970.	−	406938.i	−0.907570	−	0.761542i
$732$		0			0
$733$	379709.	+	657676.i	0.706713	+	1.22406i	0.966070	+	0.258282i	$0.0831563\pi$
$733$	379709.	+	657676.i	0.706713	+	1.22406i	−0.259356	+	0.965782i	$0.583510\pi$
$734$		0			0
$735$	138953.	+	381769.i	0.257213	+	0.706686i
$736$		0			0
$737$	539720.	+	95167.2i	0.993651	+	0.175207i
$738$		0			0
$739$	257352.	−	215944.i	0.471236	−	0.395414i	−0.376009	−	0.926616i	$-0.622704\pi$
$739$	257352.	−	215944.i	0.471236	−	0.395414i	0.847245	+	0.531202i	$0.178259\pi$
$740$		0			0
$741$	117638.	−	766502.i	0.214246	−	1.39597i
$742$		0			0
$743$	−469418.	−	559431.i	−0.850320	−	1.01337i	−0.999698	−	0.0245920i	$-0.992171\pi$
$743$	−469418.	−	559431.i	−0.850320	−	1.01337i	0.149377	−	0.988780i	$-0.452273\pi$
$744$		0			0
$745$	−94469.7	+	535765.i	−0.170208	+	0.965298i
$746$		0			0
$747$	−39258.4	+	14288.9i	−0.0703545	+	0.0256069i
$748$		0			0
$749$	45790.1	−	26436.9i	0.0816221	−	0.0471245i
$750$		0			0
$751$	38755.9	−	46187.5i	0.0687160	−	0.0818925i	−0.730591	−	0.682815i	$-0.760756\pi$
$751$	38755.9	−	46187.5i	0.0687160	−	0.0818925i	0.799307	+	0.600922i	$0.205200\pi$
$752$		0			0
$753$	772256.	+	445862.i	1.36198	+	0.786341i
$754$		0			0
$755$	46643.1	−	8224.43i	0.0818264	−	0.0144282i
$756$		0			0
$757$	614099.	+	223514.i	1.07163	+	0.390043i	0.816788	−	0.576938i	$-0.195753\pi$
$757$	614099.	+	223514.i	1.07163	+	0.390043i	0.254847	+	0.966981i	$0.417975\pi$
$758$		0			0
$759$			703327.i			1.22088i
$760$		0			0
$761$	149877.			0.258800			0.129400	−	0.991592i	$-0.458695\pi$
$761$	149877.			0.258800			0.129400	+	0.991592i	$0.458695\pi$
$762$		0			0
$763$	−144966.	+	398291.i	−0.249010	+	0.684150i
$764$		0			0
$765$	−40840.7	−	231619.i	−0.0697863	−	0.395778i
$766$		0			0
$767$	435687.	−	754632.i	0.740600	−	1.28276i
$768$		0			0
$769$	−264461.	−	221909.i	−0.447208	−	0.375252i	0.391191	−	0.920310i	$-0.372063\pi$
$769$	−264461.	−	221909.i	−0.447208	−	0.375252i	−0.838398	+	0.545058i	$0.816508\pi$
$770$		0			0
$771$	426552.	+	738809.i	0.717568	+	1.24286i
$772$		0			0
$773$	−257582.	−	707701.i	−0.431079	−	1.18438i	−0.945151	−	0.326633i	$-0.894086\pi$
$773$	−257582.	−	707701.i	−0.431079	−	1.18438i	0.514072	−	0.857747i	$-0.328136\pi$
$774$		0			0
$775$	−230724.	−	40682.8i	−0.384139	−	0.0677341i
$776$		0			0
$777$	254390.	−	213459.i	0.421365	−	0.353567i
$778$		0			0
$779$	758192.	+	415534.i	1.24941	+	0.684749i
$780$		0			0
$781$	−399446.	−	476041.i	−0.654872	−	0.780446i
$782$		0			0
$783$	−94712.9	+	537144.i	−0.154485	+	0.876127i
$784$		0			0
$785$	−672850.	+	244897.i	−1.09189	+	0.397415i
$786$		0			0
$787$	−982271.	+	567114.i	−1.58592	+	0.915632i	−0.591952	+	0.805973i	$0.701643\pi$
$787$	−982271.	+	567114.i	−1.58592	+	0.915632i	−0.993969	+	0.109659i	$0.965024\pi$
$788$		0			0
$789$	402056.	−	479152.i	0.645851	−	0.769695i
$790$		0			0
$791$	171374.	+	98943.1i	0.273901	+	0.158137i
$792$		0			0
$793$	−219876.	+	38770.1i	−0.349648	+	0.0616524i
$794$		0			0
$795$	−1.79959e6	−	654996.i	−2.84733	−	1.03634i
$796$		0			0
$797$		−	199812.i		−	0.314561i	−0.987554	−	0.157281i	$-0.949727\pi$
$797$		−	199812.i		−	0.314561i	0.987554	−	0.157281i	$-0.0502728\pi$
$798$		0			0
$799$	413792.			0.648169
$800$		0			0
$801$	−30089.3	+	82669.8i	−0.0468973	+	0.128849i
$802$		0			0
$803$	17486.7	+	99171.9i	0.0271192	+	0.153800i
$804$		0			0
$805$	287297.	−	497612.i	0.443342	−	0.767890i
$806$		0			0
$807$	355126.	+	297986.i	0.545300	+	0.457561i
$808$		0			0
$809$	−265478.	−	459821.i	−0.405631	−	0.702573i	0.588764	−	0.808305i	$-0.299615\pi$
$809$	−265478.	−	459821.i	−0.405631	−	0.702573i	−0.994395	+	0.105732i	$0.966282\pi$
$810$		0			0
$811$	264099.	+	725607.i	0.401537	+	1.10321i	0.961526	+	0.274714i	$0.0885832\pi$
$811$	264099.	+	725607.i	0.401537	+	1.10321i	−0.559989	+	0.828500i	$0.689195\pi$
$812$		0			0
$813$	213306.	+	37611.5i	0.322717	+	0.0569036i
$814$		0			0
$815$	−594818.	+	499112.i	−0.895507	+	0.751420i
$816$		0			0
$817$	483638.	−	10761.2i	0.724564	−	0.0161219i
$818$		0			0
$819$	−62342.7	−	74297.2i	−0.0929433	−	0.110766i
$820$		0			0
$821$	60839.6	−	345039.i	0.0902610	−	0.511895i	−0.905836	−	0.423629i	$-0.860756\pi$
$821$	60839.6	−	345039.i	0.0902610	−	0.511895i	0.996097	−	0.0882667i	$-0.0281328\pi$
$822$		0			0
$823$	−1.20647e6	+	439118.i	−1.78121	+	0.648308i	−0.781509	+	0.623894i	$0.785550\pi$
$823$	−1.20647e6	+	439118.i	−1.78121	+	0.648308i	−0.999702	+	0.0244135i	$0.992228\pi$
$824$		0			0
$825$	−2.16059e6	+	1.24742e6i	−3.17442	+	1.83275i
$826$		0			0
$827$	−111442.	+	132811.i	−0.162943	+	0.194188i	−0.841338	−	0.540509i	$-0.818232\pi$
$827$	−111442.	+	132811.i	−0.162943	+	0.194188i	0.678395	+	0.734698i	$0.262676\pi$
$828$		0			0
$829$	−308829.	−	178302.i	−0.449375	−	0.259447i	0.258191	−	0.966094i	$-0.416873\pi$
$829$	−308829.	−	178302.i	−0.449375	−	0.259447i	−0.707566	+	0.706647i	$0.750207\pi$
$830$		0			0
$831$	−121881.	+	21491.0i	−0.176496	+	0.0311210i
$832$		0			0
$833$	433336.	+	157721.i	0.624503	+	0.227300i
$834$		0			0
$835$		−	1.37058e6i		−	1.96577i
$836$		0			0
$837$	125506.			0.179148
$838$		0			0
$839$	309925.	−	851512.i	0.440284	−	1.20967i	−0.499022	−	0.866589i	$-0.666307\pi$
$839$	309925.	−	851512.i	0.440284	−	1.20967i	0.939306	−	0.343080i	$-0.111470\pi$
$840$		0			0
$841$	7188.83	+	40769.9i	0.0101640	+	0.0576431i
$842$		0			0
$843$	422934.	−	732543.i	0.595138	−	1.03081i
$844$		0			0
$845$	−706873.	−	593137.i	−0.989984	−	0.830695i
$846$		0			0
$847$	−539402.	−	934272.i	−0.751876	−	1.30229i
$848$		0			0
$849$	382193.	+	1.05007e6i	0.530234	+	1.45680i
$850$		0			0
$851$	316855.	+	55870.1i	0.437524	+	0.0771472i
$852$		0			0
$853$	618755.	−	519197.i	0.850395	−	0.713566i	−0.109482	−	0.993989i	$-0.534919\pi$
$853$	618755.	−	519197.i	0.850395	−	0.713566i	0.959877	+	0.280423i	$0.0904746\pi$
$854$		0			0
$855$	140207.	+	112429.i	0.191795	+	0.153796i
$856$		0			0
$857$	−236051.	−	281314.i	−0.321398	−	0.383027i	0.581020	−	0.813890i	$-0.302654\pi$
$857$	−236051.	−	281314.i	−0.321398	−	0.383027i	−0.902418	+	0.430862i	$0.858209\pi$
$858$		0			0
$859$	23909.4	−	135597.i	0.0324028	−	0.183766i	−0.964311	−	0.264774i	$-0.914703\pi$
$859$	23909.4	−	135597.i	0.0324028	−	0.183766i	0.996713	+	0.0810079i	$0.0258139\pi$
$860$		0			0
$861$	817074.	−	297391.i	1.10219	−	0.401163i
$862$		0			0
$863$	272435.	−	157291.i	0.365799	−	0.211194i	−0.305823	−	0.952088i	$-0.598932\pi$
$863$	272435.	−	157291.i	0.365799	−	0.211194i	0.671621	+	0.740895i	$0.265598\pi$
$864$		0			0
$865$	−30943.4	+	36876.9i	−0.0413557	+	0.0492859i
$866$		0			0
$867$	−1.16337e6	−	671673.i	−1.54768	−	0.893552i
$868$		0			0
$869$	507492.	−	89484.6i	0.672032	−	0.118497i
$870$		0			0
$871$	−553274.	−	201375.i	−0.729296	−	0.265442i
$872$		0			0
$873$		−	2250.20i		−	0.00295252i
$874$		0			0
$875$	1.01723e6			1.32863
$876$		0			0
$877$	54111.4	−	148670.i	0.0703541	−	0.193296i	−0.899532	−	0.436854i	$-0.856092\pi$
$877$	54111.4	−	148670.i	0.0703541	−	0.193296i	0.969886	+	0.243558i	$0.0783147\pi$
$878$		0			0
$879$	−125305.	−	710642.i	−0.162178	−	0.919758i
$880$		0			0
$881$	−251115.	+	434943.i	−0.323534	+	0.560378i	−0.981215	−	0.192919i	$-0.938204\pi$
$881$	−251115.	+	434943.i	−0.323534	+	0.560378i	0.657680	+	0.753297i	$0.271538\pi$
$882$		0			0
$883$	123938.	+	103997.i	0.158959	+	0.133382i	0.718798	−	0.695219i	$-0.244693\pi$
$883$	123938.	+	103997.i	0.158959	+	0.133382i	−0.559839	+	0.828601i	$0.689137\pi$
$884$		0			0
$885$	811913.	+	1.40627e6i	1.03663	+	1.79549i
$886$		0			0
$887$	−105807.	−	290703.i	−0.134483	−	0.369490i	0.854111	−	0.520090i	$-0.174102\pi$
$887$	−105807.	−	290703.i	−0.134483	−	0.369490i	−0.988595	+	0.150600i	$0.951879\pi$
$888$		0			0
$889$	234265.	+	41307.2i	0.296417	+	0.0522664i
$890$		0			0
$891$	1.17221e6	−	983598.i	1.47655	−	1.23897i
$892$		0			0
$893$	−237635.	+	208581.i	−0.297994	+	0.261561i
$894$		0			0
$895$	−582209.	−	693850.i	−0.726830	−	0.866203i
$896$		0			0
$897$	131209.	−	744125.i	0.163072	−	0.924829i
$898$		0			0
$899$	−143982.	+	52405.2i	−0.178151	+	0.0648418i
$900$		0			0
$901$	−1.88252e6	+	1.08688e6i	−2.31895	+	1.33885i
$902$		0			0
$903$	312723.	−	372688.i	0.383516	−	0.457057i
$904$		0			0
$905$	−1.27453e6	−	735853.i	−1.55616	−	0.898449i
$906$		0			0
$907$	161004.	−	28389.3i	0.195714	−	0.0345096i	−0.0749319	−	0.997189i	$-0.523874\pi$
$907$	161004.	−	28389.3i	0.195714	−	0.0345096i	0.270646	+	0.962679i	$0.412763\pi$
$908$		0			0
$909$	−66313.9	−	24136.3i	−0.0802559	−	0.0292108i
$910$		0			0
$911$		−	900368.i		−	1.08488i	−0.840093	−	0.542442i	$-0.817500\pi$
$911$		−	900368.i		−	1.08488i	0.840093	−	0.542442i	$-0.182500\pi$
$912$		0			0
$913$	754996.			0.905739
$914$		0			0
$915$	142303.	−	390974.i	0.169970	−	0.466987i
$916$		0			0
$917$	184524.	+	1.04649e6i	0.219439	+	1.24450i
$918$		0			0
$919$	−722969.	+	1.25222e6i	−0.856030	+	1.48269i	0.0196571	+	0.999807i	$0.493743\pi$
$919$	−722969.	+	1.25222e6i	−0.856030	+	1.48269i	−0.875687	+	0.482880i	$0.839591\pi$
$920$		0			0
$921$	793441.	+	665776.i	0.935396	+	0.784890i
$922$		0			0
$923$	333809.	+	578174.i	0.391827	+	0.678665i
$924$		0			0
$925$	390341.	+	1.07245e6i	0.456206	+	1.25342i
$926$		0			0
$927$	−141367.	−	24926.9i	−0.164509	−	0.0290074i
$928$		0			0
$929$	776900.	−	651896.i	0.900188	−	0.755348i	−0.0700387	−	0.997544i	$-0.522312\pi$
$929$	776900.	−	651896.i	0.900188	−	0.755348i	0.970227	+	0.242196i	$0.0778678\pi$
$930$		0			0
$931$	−328362.	+	127856.i	−0.378838	+	0.147510i
$932$		0			0
$933$	−413967.	−	493346.i	−0.475556	−	0.566746i
$934$		0			0
$935$	−738058.	+	4.18574e6i	−0.844243	+	4.78794i
$936$		0			0
$937$	−382818.	+	139334.i	−0.436027	+	0.158701i	−0.550701	−	0.834702i	$-0.685640\pi$
$937$	−382818.	+	139334.i	−0.436027	+	0.158701i	0.114675	+	0.993403i	$0.463417\pi$
$938$		0			0
$939$	370273.	−	213777.i	0.419943	−	0.242454i
$940$		0			0
$941$	388427.	−	462909.i	0.438662	−	0.522777i	−0.500738	−	0.865599i	$-0.666938\pi$
$941$	388427.	−	462909.i	0.438662	−	0.522777i	0.939401	+	0.342821i	$0.111383\pi$
$942$		0			0
$943$	729573.	+	421219.i	0.820438	+	0.473680i
$944$		0			0
$945$	−1.07527e6	+	189600.i	−1.20408	+	0.212312i
$946$		0			0
$947$	−433842.	−	157906.i	−0.483762	−	0.176075i	0.0886142	−	0.996066i	$-0.471756\pi$
$947$	−433842.	−	157906.i	−0.483762	−	0.176075i	−0.572376	+	0.819991i	$0.693978\pi$
$948$		0			0
$949$		−	108187.i		−	0.120127i
$950$		0			0
$951$	996853.			1.10222
$952$		0			0
$953$	280335.	−	770214.i	0.308668	−	0.848059i	−0.684249	−	0.729249i	$-0.739870\pi$
$953$	280335.	−	770214.i	0.308668	−	0.848059i	0.992917	−	0.118810i	$-0.0379080\pi$
$954$		0			0
$955$	319900.	+	1.81424e6i	0.350758	+	1.98925i
$956$		0			0
$957$	−815817.	+	1.41304e6i	−0.890777	+	1.54287i
$958$		0			0
$959$	798946.	+	670395.i	0.868721	+	0.728943i
$960$		0			0
$961$	−444132.	−	769259.i	−0.480912	−	0.832963i
$962$		0			0
$963$	5511.22	+	15142.0i	0.00594286	+	0.0163279i
$964$		0			0
$965$	−1.91357e6	−	337414.i	−2.05489	−	0.362333i
$966$		0			0
$967$	−679472.	+	570145.i	−0.726639	+	0.609723i	−0.929213	−	0.369544i	$-0.879514\pi$
$967$	−679472.	+	570145.i	−0.726639	+	0.609723i	0.202574	+	0.979267i	$0.435069\pi$
$968$		0			0
$969$	1.60866e6	−	320702.i	1.71323	−	0.341549i
$970$		0			0
$971$	−96323.4	−	114794.i	−0.102163	−	0.121753i	0.712540	−	0.701631i	$-0.247545\pi$
$971$	−96323.4	−	114794.i	−0.102163	−	0.121753i	−0.814703	+	0.579878i	$0.803100\pi$
$972$		0			0
$973$	54928.1	−	311513.i	0.0580188	−	0.329041i
$974$		0			0
$975$	2.51863e6	−	916706.i	2.64945	−	0.964319i
$976$		0			0
$977$	−1.01163e6	+	584064.i	−1.05982	+	0.611887i	−0.925383	−	0.379035i	$-0.876256\pi$
$977$	−1.01163e6	+	584064.i	−1.05982	+	0.611887i	−0.134438	+	0.990922i	$0.542923\pi$
$978$		0			0
$979$	1.02194e6	−	1.21790e6i	1.06625	−	1.27071i
$980$		0			0
$981$	−111867.	−	64586.2i	−0.116242	−	0.0671123i
$982$		0			0
$983$	314368.	−	55431.6i	0.325336	−	0.0573654i	−0.00859514	−	0.999963i	$-0.502736\pi$
$983$	314368.	−	55431.6i	0.325336	−	0.0573654i	0.333931	+	0.942598i	$0.391625\pi$
$984$		0			0
$985$	577875.	+	210329.i	0.595609	+	0.216784i
$986$		0			0
$987$			317989.i			0.326421i
$988$		0			0
$989$	471362.			0.481905
$990$		0			0
$991$	−150707.	+	414063.i	−0.153456	+	0.421618i	−0.992469	−	0.122493i	$-0.960911\pi$
$991$	−150707.	+	414063.i	−0.153456	+	0.421618i	0.839013	+	0.544112i	$0.183133\pi$
$992$		0			0
$993$	−113861.	−	645740.i	−0.115472	−	0.654876i
$994$		0			0
$995$	630260.	−	1.09164e6i	0.636610	−	1.10264i
$996$		0			0
$997$	−934386.	−	784043.i	−0.940018	−	0.788769i	0.0375705	−	0.999294i	$-0.488038\pi$
$997$	−934386.	−	784043.i	−0.940018	−	0.788769i	−0.977588	+	0.210525i	$0.932483\pi$
$998$		0			0
$999$	−305693.	−	529477.i	−0.306306	−	0.530537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.13.6	✓	42
19.3	odd	18	inner	76.5.j.a.41.6	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.13.6	✓	42	1.1	even	1	trivial
76.5.j.a.41.6	yes	42	19.3	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)

\(f(q)\)	\(=\)	\(q+(3.28951 - 9.03787i) q^{3} +(7.51461 + 42.6175i) q^{5} +(-18.8739 + 32.6905i) q^{7} +(-8.81253 - 7.39459i) q^{9} +O(q^{10})\)	\(q+(3.28951 - 9.03787i) q^{3} +(7.51461 + 42.6175i) q^{5} +(-18.8739 + 32.6905i) q^{7} +(-8.81253 - 7.39459i) q^{9} +(103.948 + 180.042i) q^{11} +(-76.3894 - 209.878i) q^{13} +(409.891 + 72.2748i) q^{15} +(361.904 - 303.674i) q^{17} +(-54.7631 + 356.822i) q^{19} +(233.366 + 278.115i) q^{21} +(-61.0806 + 346.405i) q^{23} +(-1172.47 + 426.745i) q^{25} +(578.857 - 334.203i) q^{27} +(-524.525 + 625.105i) q^{29} +(162.613 + 93.8845i) q^{31} +(1969.14 - 347.212i) q^{33} +(-1535.02 - 558.700i) q^{35} -914.694i q^{37} -2148.13 q^{39} +(819.137 - 2250.56i) q^{41} +(-232.697 - 1319.69i) q^{43} +(248.916 - 431.135i) q^{45} +(670.959 + 563.001i) q^{47} +(488.055 + 845.336i) q^{49} +(-1554.07 - 4269.78i) q^{51} +(-4531.29 - 798.988i) q^{53} +(-6891.83 + 5782.93i) q^{55} +(3044.77 + 1668.71i) q^{57} +(2507.79 + 2988.66i) q^{59} +(173.586 - 984.457i) q^{61} +(408.059 - 148.521i) q^{63} +(8370.44 - 4832.68i) q^{65} +(1694.50 - 2019.42i) q^{67} +(2929.84 + 1691.54i) q^{69} +(-2943.73 + 519.059i) q^{71} +(455.176 + 165.670i) q^{73} +12000.4i q^{75} -7847.56 q^{77} +(847.785 - 2329.27i) q^{79} +(-1278.13 - 7248.66i) q^{81} +(1815.81 - 3145.08i) q^{83} +(15661.4 + 13141.5i) q^{85} +(3924.18 + 6796.88i) q^{87} +(-2615.57 - 7186.22i) q^{89} +(8302.78 + 1464.00i) q^{91} +(1383.43 - 1160.84i) q^{93} +(-15618.4 + 347.516i) q^{95} +(125.731 + 149.840i) q^{97} +(415.299 - 2355.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 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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