LMFDB - Embedded newform 76.5.j.a.53.2

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			53.2
Character	$\chi$	$=$	76.53
Dual form			76.5.j.a.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.79937 + 1.37524i) q^{3} +(0.638039 - 0.535378i) q^{5} +(23.1636 - 40.1206i) q^{7} +(-17.1762 + 6.25164i) q^{9} +O(q^{10})$	\(q+(-7.79937 + 1.37524i) q^{3} +(0.638039 - 0.535378i) q^{5} +(23.1636 - 40.1206i) q^{7} +(-17.1762 + 6.25164i) q^{9} +(95.5660 + 165.525i) q^{11} +(208.358 + 36.7391i) q^{13} +(-4.24003 + 5.05307i) q^{15} +(504.579 + 183.652i) q^{17} +(130.825 - 336.461i) q^{19} +(-125.486 + 344.771i) q^{21} +(-238.506 - 200.131i) q^{23} +(-108.410 + 614.822i) q^{25} +(680.917 - 393.128i) q^{27} +(67.5830 + 185.683i) q^{29} +(-677.986 - 391.435i) q^{31} +(-972.991 - 1159.57i) q^{33} +(-6.70040 - 37.9998i) q^{35} +1109.80i q^{37} -1675.58 q^{39} +(1014.78 - 178.934i) q^{41} +(867.530 - 727.944i) q^{43} +(-7.61212 + 13.1846i) q^{45} +(-1488.89 + 541.910i) q^{47} +(127.391 + 220.647i) q^{49} +(-4187.96 - 738.451i) q^{51} +(623.443 - 742.990i) q^{53} +(149.593 + 54.4476i) q^{55} +(-557.642 + 2804.10i) q^{57} +(1659.58 - 4559.66i) q^{59} +(-3868.03 - 3245.67i) q^{61} +(-147.045 + 833.932i) q^{63} +(152.610 - 88.1093i) q^{65} +(-70.2062 - 192.890i) q^{67} +(2135.43 + 1232.89i) q^{69} +(3442.94 + 4103.13i) q^{71} +(1418.98 + 8047.43i) q^{73} -4944.31i q^{75} +8854.63 q^{77} +(5647.18 - 995.751i) q^{79} +(-3635.90 + 3050.88i) q^{81} +(-2389.76 + 4139.18i) q^{83} +(420.264 - 152.964i) q^{85} +(-782.463 - 1355.27i) q^{87} +(11031.2 + 1945.10i) q^{89} +(6300.32 - 7508.43i) q^{91} +(5826.18 + 2120.56i) q^{93} +(-96.6620 - 284.716i) q^{95} +(613.294 - 1685.01i) q^{97} +(-2676.27 - 2245.66i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−7.79937	+	1.37524i	−0.866597	+	0.152804i	−0.589235	−	0.807961i	$-0.700571\pi$
$3$	−7.79937	+	1.37524i	−0.866597	+	0.152804i	−0.277361	+	0.960766i	$0.589460\pi$
$4$		0			0
$5$	0.638039	−	0.535378i	0.0255216	−	0.0214151i	−0.629938	−	0.776646i	$-0.716920\pi$
$5$	0.638039	−	0.535378i	0.0255216	−	0.0214151i	0.655459	+	0.755231i	$0.272475\pi$
$6$		0			0
$7$	23.1636	−	40.1206i	0.472728	−	0.818788i	−0.526785	−	0.849998i	$-0.676603\pi$
$7$	23.1636	−	40.1206i	0.472728	−	0.818788i	0.999513	+	0.0312103i	$0.00993616\pi$
$8$		0			0
$9$	−17.1762	+	6.25164i	−0.212052	+	0.0771807i
$10$		0			0
$11$	95.5660	+	165.525i	0.789802	+	1.36798i	0.926088	+	0.377307i	$0.123150\pi$
$11$	95.5660	+	165.525i	0.789802	+	1.36798i	−0.136286	+	0.990669i	$0.543517\pi$
$12$		0			0
$13$	208.358	+	36.7391i	1.23289	+	0.217391i	0.751864	−	0.659318i	$-0.229155\pi$
$13$	208.358	+	36.7391i	1.23289	+	0.217391i	0.481021	+	0.876709i	$0.340266\pi$
$14$		0			0
$15$	−4.24003	+	5.05307i	−0.0188446	+	0.0224581i
$16$		0			0
$17$	504.579	+	183.652i	1.74595	+	0.635473i	0.999549	−	0.0300258i	$-0.00955895\pi$
$17$	504.579	+	183.652i	1.74595	+	0.635473i	0.746399	+	0.665499i	$0.231781\pi$
$18$		0			0
$19$	130.825	−	336.461i	0.362397	−	0.932024i
$19$	130.825	−	336.461i	0.362397	−	0.932024i
$20$		0			0
$21$	−125.486	+	344.771i	−0.284550	+	0.781794i
$22$		0			0
$23$	−238.506	−	200.131i	−0.450863	−	0.378319i	0.388893	−	0.921283i	$-0.372858\pi$
$23$	−238.506	−	200.131i	−0.450863	−	0.378319i	−0.839756	+	0.542964i	$0.817302\pi$
$24$		0			0
$25$	−108.410	+	614.822i	−0.173455	+	0.983715i
$26$		0			0
$27$	680.917	−	393.128i	0.934042	−	0.539270i
$28$		0			0
$29$	67.5830	+	185.683i	0.0803603	+	0.220788i	0.973366	−	0.229258i	$-0.0736299\pi$
$29$	67.5830	+	185.683i	0.0803603	+	0.220788i	−0.893005	+	0.450046i	$0.851408\pi$
$30$		0			0
$31$	−677.986	−	391.435i	−0.705500	−	0.407321i	0.103892	−	0.994589i	$-0.466870\pi$
$31$	−677.986	−	391.435i	−0.705500	−	0.407321i	−0.809393	+	0.587268i	$0.800204\pi$
$32$		0			0
$33$	−972.991	−	1159.57i	−0.893472	−	1.06480i
$34$		0			0
$35$	−6.70040	−	37.9998i	−0.00546971	−	0.0310203i
$36$		0			0
$37$			1109.80i			0.810665i	0.914169	+	0.405332i	$0.132844\pi$
$37$			1109.80i			0.810665i	−0.914169	+	0.405332i	$0.867156\pi$
$38$		0			0
$39$	−1675.58			−1.10163
$40$		0			0
$41$	1014.78	−	178.934i	0.603679	−	0.106445i	0.136549	−	0.990633i	$-0.456399\pi$
$41$	1014.78	−	178.934i	0.603679	−	0.106445i	0.467130	+	0.884188i	$0.345288\pi$
$42$		0			0
$43$	867.530	−	727.944i	0.469189	−	0.393696i	−0.377310	−	0.926087i	$-0.623151\pi$
$43$	867.530	−	727.944i	0.469189	−	0.393696i	0.846498	+	0.532391i	$0.178706\pi$
$44$		0			0
$45$	−7.61212	+	13.1846i	−0.00375907	+	0.00651090i
$46$		0			0
$47$	−1488.89	+	541.910i	−0.674009	+	0.245319i	−0.656273	−	0.754524i	$-0.727868\pi$
$47$	−1488.89	+	541.910i	−0.674009	+	0.245319i	−0.0177359	+	0.999843i	$0.505646\pi$
$48$		0			0
$49$	127.391	+	220.647i	0.0530574	+	0.0918981i
$50$		0			0
$51$	−4187.96	−	738.451i	−1.61014	−	0.283910i
$52$		0			0
$53$	623.443	−	742.990i	0.221945	−	0.264504i	−0.643570	−	0.765388i	$-0.722547\pi$
$53$	623.443	−	742.990i	0.221945	−	0.264504i	0.865514	+	0.500884i	$0.166992\pi$
$54$		0			0
$55$	149.593	+	54.4476i	0.0494524	+	0.0179992i
$56$		0			0
$57$	−557.642	+	2804.10i	−0.171635	+	0.863064i
$58$		0			0
$59$	1659.58	−	4559.66i	0.476754	−	1.30987i	−0.435480	−	0.900199i	$-0.643421\pi$
$59$	1659.58	−	4559.66i	0.476754	−	1.30987i	0.912233	−	0.409671i	$-0.134357\pi$
$60$		0			0
$61$	−3868.03	−	3245.67i	−1.03951	−	0.872257i	−0.0475625	−	0.998868i	$-0.515145\pi$
$61$	−3868.03	−	3245.67i	−1.03951	−	0.872257i	−0.991952	+	0.126612i	$0.959590\pi$
$62$		0			0
$63$	−147.045	+	833.932i	−0.0370483	+	0.210111i
$64$		0			0
$65$	152.610	−	88.1093i	0.0361206	−	0.0208543i
$66$		0			0
$67$	−70.2062	−	192.890i	−0.0156396	−	0.0429695i	0.931627	−	0.363415i	$-0.118389\pi$
$67$	−70.2062	−	192.890i	−0.0156396	−	0.0429695i	−0.947267	+	0.320446i	$0.896167\pi$
$68$		0			0
$69$	2135.43	+	1232.89i	0.448525	+	0.258956i
$70$		0			0
$71$	3442.94	+	4103.13i	0.682987	+	0.813953i	0.990489	−	0.137595i	$-0.0439373\pi$
$71$	3442.94	+	4103.13i	0.682987	+	0.813953i	−0.307501	+	0.951548i	$0.599493\pi$
$72$		0			0
$73$	1418.98	+	8047.43i	0.266275	+	1.51012i	0.765380	+	0.643578i	$0.222551\pi$
$73$	1418.98	+	8047.43i	0.266275	+	1.51012i	−0.499106	+	0.866541i	$0.666338\pi$
$74$		0			0
$75$		−	4944.31i		−	0.878988i
$76$		0			0
$77$	8854.63			1.49344
$78$		0			0
$79$	5647.18	−	995.751i	0.904852	−	0.159550i	0.298187	−	0.954507i	$-0.403618\pi$
$79$	5647.18	−	995.751i	0.904852	−	0.159550i	0.606665	+	0.794957i	$0.292507\pi$
$80$		0			0
$81$	−3635.90	+	3050.88i	−0.554169	+	0.465003i
$82$		0			0
$83$	−2389.76	+	4139.18i	−0.346894	+	0.600839i	−0.985696	−	0.168533i	$-0.946097\pi$
$83$	−2389.76	+	4139.18i	−0.346894	+	0.600839i	0.638802	+	0.769371i	$0.279430\pi$
$84$		0			0
$85$	420.264	−	152.964i	0.0581681	−	0.0211714i
$86$		0			0
$87$	−782.463	−	1355.27i	−0.103377	−	0.179055i
$88$		0			0
$89$	11031.2	+	1945.10i	1.39265	+	0.245562i	0.819121	−	0.573621i	$-0.194462\pi$
$89$	11031.2	+	1945.10i	1.39265	+	0.245562i	0.573532	+	0.819183i	$0.305573\pi$
$90$		0			0
$91$	6300.32	−	7508.43i	0.760816	−	0.906705i
$92$		0			0
$93$	5826.18	+	2120.56i	0.673624	+	0.245179i
$94$		0			0
$95$	−96.6620	−	284.716i	−0.0107105	−	0.0315475i
$96$		0			0
$97$	613.294	−	1685.01i	0.0651816	−	0.179085i	−0.902826	−	0.430006i	$-0.858511\pi$
$97$	613.294	−	1685.01i	0.0651816	−	0.179085i	0.968007	+	0.250921i	$0.0807335\pi$
$98$		0			0
$99$	−2676.27	−	2245.66i	−0.273061	−	0.229125i
$100$		0			0
$101$	−2527.79	+	14335.8i	−0.247798	+	1.40533i	0.566105	+	0.824333i	$0.308450\pi$
$101$	−2527.79	+	14335.8i	−0.247798	+	1.40533i	−0.813903	+	0.581000i	$0.802661\pi$
$102$		0			0
$103$	−16876.4	+	9743.57i	−1.59076	+	0.918425i	−0.597582	+	0.801808i	$0.703872\pi$
$103$	−16876.4	+	9743.57i	−1.59076	+	0.918425i	−0.993177	+	0.116618i	$0.962795\pi$
$104$		0			0
$105$	104.518	+	287.160i	0.00948007	+	0.0260463i
$106$		0			0
$107$	−3946.18	−	2278.33i	−0.344675	−	0.198998i	0.317663	−	0.948204i	$-0.397102\pi$
$107$	−3946.18	−	2278.33i	−0.344675	−	0.198998i	−0.662337	+	0.749206i	$0.730435\pi$
$108$		0			0
$109$	−8297.49	−	9888.56i	−0.698383	−	0.832300i	0.293959	−	0.955818i	$-0.405027\pi$
$109$	−8297.49	−	9888.56i	−0.698383	−	0.832300i	−0.992342	+	0.123517i	$0.960582\pi$
$110$		0			0
$111$	−1526.24	−	8655.74i	−0.123873	−	0.702519i
$112$		0			0
$113$		−	17919.3i		−	1.40334i	−0.712500	−	0.701672i	$-0.752437\pi$
$113$		−	17919.3i		−	1.40334i	0.712500	−	0.701672i	$-0.247563\pi$
$114$		0			0
$115$	−259.322			−0.0196085
$116$		0			0
$117$	−3808.48	+	671.538i	−0.278215	+	0.0490567i
$118$		0			0
$119$	19056.1	−	15990.0i	1.34568	−	1.12916i
$120$		0			0
$121$	−10945.2	+	18957.7i	−0.747574	+	1.29484i
$122$		0			0
$123$	−7668.60	+	2791.14i	−0.506881	+	0.184490i
$124$		0			0
$125$	520.274	+	901.141i	0.0332976	+	0.0576731i
$126$		0			0
$127$	−29312.4	−	5168.57i	−1.81737	−	0.320452i	−0.841744	−	0.539876i	$-0.818471\pi$
$127$	−29312.4	−	5168.57i	−1.81737	−	0.320452i	−0.975629	+	0.219424i	$0.929582\pi$
$128$		0			0
$129$	−5765.09	+	6870.56i	−0.346439	+	0.412870i
$130$		0			0
$131$	16507.9	+	6008.38i	0.961942	+	0.350118i	0.774794	−	0.632213i	$-0.217853\pi$
$131$	16507.9	+	6008.38i	0.961942	+	0.350118i	0.187148	+	0.982332i	$0.440076\pi$
$132$		0			0
$133$	−10468.6	−	13042.5i	−0.591815	−	0.737320i
$134$		0			0
$135$	223.980	−	615.379i	0.0122897	−	0.0337657i
$136$		0			0
$137$	−5277.66	−	4428.48i	−0.281190	−	0.235947i	0.491274	−	0.871005i	$-0.336531\pi$
$137$	−5277.66	−	4428.48i	−0.281190	−	0.235947i	−0.772464	+	0.635059i	$0.780976\pi$
$138$		0			0
$139$	−390.360	+	2213.84i	−0.0202039	+	0.114582i	−0.993242	−	0.116063i	$-0.962973\pi$
$139$	−390.360	+	2213.84i	−0.0202039	+	0.114582i	0.973038	+	0.230645i	$0.0740836\pi$
$140$		0			0
$141$	10867.1	−	6274.13i	0.546608	−	0.315584i
$142$		0			0
$143$	13830.7	+	37999.5i	0.676349	+	1.85825i
$144$		0			0
$145$	142.531	+	82.2904i	0.00677913	+	0.00391393i
$146$		0			0
$147$	−1297.01	−	1545.72i	−0.0600218	−	0.0715312i
$148$		0			0
$149$	−3144.64	−	17834.2i	−0.141644	−	0.803304i	−0.970001	−	0.243103i	$-0.921835\pi$
$149$	−3144.64	−	17834.2i	−0.141644	−	0.803304i	0.828356	−	0.560201i	$-0.189276\pi$
$150$		0			0
$151$		−	12669.8i		−	0.555668i	−0.960629	−	0.277834i	$-0.910383\pi$
$151$		−	12669.8i		−	0.555668i	0.960629	−	0.277834i	$-0.0896166\pi$
$152$		0			0
$153$	−9814.89			−0.419278
$154$		0			0
$155$	−642.148	+	113.228i	−0.0267283	+	0.00471292i
$156$		0			0
$157$	12674.1	−	10634.8i	0.514183	−	0.431451i	−0.348415	−	0.937340i	$-0.613280\pi$
$157$	12674.1	−	10634.8i	0.514183	−	0.431451i	0.862598	+	0.505889i	$0.168836\pi$
$158$		0			0
$159$	−3840.67	+	6652.24i	−0.151919	+	0.263132i
$160$		0			0
$161$	−13554.0	+	4933.27i	−0.522898	+	0.190319i
$162$		0			0
$163$	−5938.09	−	10285.1i	−0.223497	−	0.387108i	0.732370	−	0.680906i	$-0.238414\pi$
$163$	−5938.09	−	10285.1i	−0.223497	−	0.387108i	−0.955867	+	0.293798i	$0.905081\pi$
$164$		0			0
$165$	−1241.61	−	218.930i	−0.0456056	−	0.00804150i
$166$		0			0
$167$	−9815.28	+	11697.4i	−0.351941	+	0.419427i	−0.912750	−	0.408518i	$-0.866046\pi$
$167$	−9815.28	+	11697.4i	−0.351941	+	0.419427i	0.560809	+	0.827945i	$0.310490\pi$
$168$		0			0
$169$	15224.6	+	5541.30i	0.533056	+	0.194016i
$170$		0			0
$171$	−143.659	+	6597.00i	−0.00491292	+	0.225608i
$172$		0			0
$173$	11914.5	−	32734.8i	0.398092	−	1.09375i	−0.565120	−	0.825009i	$-0.691170\pi$
$173$	11914.5	−	32734.8i	0.398092	−	1.09375i	0.963212	−	0.268741i	$-0.0866076\pi$
$174$		0			0
$175$	22155.9	+	18591.0i	0.723457	+	0.607052i
$176$		0			0
$177$	−6673.05	+	37844.8i	−0.212999	+	1.20798i
$178$		0			0
$179$	27682.7	−	15982.6i	0.863978	−	0.498818i	−0.00136433	−	0.999999i	$-0.500434\pi$
$179$	27682.7	−	15982.6i	0.863978	−	0.498818i	0.865342	+	0.501181i	$0.167101\pi$
$180$		0			0
$181$	−19495.0	−	53562.1i	−0.595068	−	1.63494i	−0.760965	−	0.648793i	$-0.775274\pi$
$181$	−19495.0	−	53562.1i	−0.595068	−	1.63494i	0.165897	−	0.986143i	$-0.446948\pi$
$182$		0			0
$183$	34631.8	+	19994.7i	1.03412	+	0.597052i
$184$		0			0
$185$	594.163	+	708.096i	0.0173605	+	0.0206894i
$186$		0			0
$187$	17821.6	+	101071.i	0.509640	+	2.89031i
$188$		0			0
$189$		−	36425.1i		−	1.01971i
$190$		0			0
$191$	50921.9			1.39585			0.697924	−	0.716172i	$-0.254107\pi$
$191$	50921.9			1.39585			0.697924	+	0.716172i	$0.254107\pi$
$192$		0			0
$193$	7155.09	−	1261.64i	0.192088	−	0.0338703i	−0.0767763	−	0.997048i	$-0.524463\pi$
$193$	7155.09	−	1261.64i	0.192088	−	0.0338703i	0.268864	+	0.963178i	$0.413352\pi$
$194$		0			0
$195$	−1069.09	+	897.071i	−0.0281154	+	0.0235916i
$196$		0			0
$197$	−6657.78	+	11531.6i	−0.171552	+	0.297137i	−0.938963	−	0.344019i	$-0.888212\pi$
$197$	−6657.78	+	11531.6i	−0.171552	+	0.297137i	0.767410	+	0.641156i	$0.221545\pi$
$198$		0			0
$199$	−27819.3	+	10125.4i	−0.702491	+	0.255686i	−0.668474	−	0.743736i	$-0.733052\pi$
$199$	−27819.3	+	10125.4i	−0.702491	+	0.255686i	−0.0340168	+	0.999421i	$0.510830\pi$
$200$		0			0
$201$	812.834	+	1407.87i	0.0201191	+	0.0348474i
$202$		0			0
$203$	9015.18	+	1589.62i	0.218767	+	0.0385746i
$204$		0			0
$205$	551.675	−	657.461i	0.0131273	−	0.0156445i
$206$		0			0
$207$	5347.78	+	1946.43i	0.124805	+	0.0454254i
$208$		0			0
$209$	68195.2	−	10499.3i	1.56121	−	0.240363i
$210$		0			0
$211$	−16.0715	+	44.1560i	−0.000360986	+	0.000991801i	−0.939873	−	0.341524i	$-0.889057\pi$
$211$	−16.0715	+	44.1560i	−0.000360986	+	0.000991801i	0.939512	+	0.342516i	$0.111279\pi$
$212$		0			0
$213$	−32495.5	−	27267.0i	−0.716250	−	0.601005i
$214$		0			0
$215$	163.792	−	928.913i	0.00354337	−	0.0200955i
$216$		0			0
$217$	−31409.2	+	18134.1i	−0.667019	+	0.385103i
$218$		0			0
$219$	−22134.3	−	60813.4i	−0.461506	−	1.26798i
$220$		0			0
$221$	98385.7	+	56803.0i	2.01441	+	1.16302i
$222$		0			0
$223$	−15121.7	−	18021.4i	−0.304082	−	0.362391i	0.592265	−	0.805743i	$-0.298234\pi$
$223$	−15121.7	−	18021.4i	−0.304082	−	0.362391i	−0.896348	+	0.443352i	$0.853789\pi$
$224$		0			0
$225$	−1981.57	−	11238.1i	−0.0391422	−	0.221986i
$226$		0			0
$227$			9051.77i			0.175664i	0.996135	+	0.0878318i	$0.0279938\pi$
$227$			9051.77i			0.175664i	−0.996135	+	0.0878318i	$0.972006\pi$
$228$		0			0
$229$	−17379.0			−0.331401			−0.165700	−	0.986176i	$-0.552988\pi$
$229$	−17379.0			−0.331401			−0.165700	+	0.986176i	$0.552988\pi$
$230$		0			0
$231$	−69060.5	+	12177.2i	−1.29421	+	0.228205i
$232$		0			0
$233$	−52913.9	+	44400.0i	−0.974670	+	0.817845i	−0.983277	−	0.182118i	$-0.941705\pi$
$233$	−52913.9	+	44400.0i	−0.974670	+	0.817845i	0.00860682	+	0.999963i	$0.497260\pi$
$234$		0			0
$235$	−659.840	+	1142.88i	−0.0119482	+	0.0206949i
$236$		0			0
$237$	−42675.1	+	15532.5i	−0.759762	+	0.276531i
$238$		0			0
$239$	−47309.5	−	81942.5i	−0.828233	−	1.43454i	−0.899423	−	0.437079i	$-0.856013\pi$
$239$	−47309.5	−	81942.5i	−0.828233	−	1.43454i	0.0711902	−	0.997463i	$-0.477320\pi$
$240$		0			0
$241$	−105764.	−	18649.1i	−1.82098	−	0.321088i	−0.844314	−	0.535849i	$-0.819992\pi$
$241$	−105764.	−	18649.1i	−1.82098	−	0.321088i	−0.976667	+	0.214761i	$0.931103\pi$
$242$		0			0
$243$	−16775.0	+	19991.6i	−0.284086	+	0.338560i
$244$		0			0
$245$	199.410	+	72.5793i	0.00332212	+	0.00120915i
$246$		0			0
$247$	39619.7	−	65297.7i	0.649408	−	1.07030i
$248$		0			0
$249$	12946.2	−	35569.5i	0.208807	−	0.573692i
$250$		0			0
$251$	−4024.48	−	3376.94i	−0.0638796	−	0.0536013i	0.610289	−	0.792179i	$-0.291053\pi$
$251$	−4024.48	−	3376.94i	−0.0638796	−	0.0536013i	−0.674168	+	0.738578i	$0.735498\pi$
$252$		0			0
$253$	10333.6	−	58604.5i	0.161439	−	0.915566i
$254$		0			0
$255$	−3067.44	+	1770.98i	−0.0471732	+	0.0272354i
$256$		0			0
$257$	6106.37	+	16777.1i	0.0924521	+	0.254010i	0.977296	−	0.211877i	$-0.0679576\pi$
$257$	6106.37	+	16777.1i	0.0924521	+	0.254010i	−0.884844	+	0.465887i	$0.845735\pi$
$258$		0			0
$259$	44525.9	+	25707.0i	0.663763	+	0.383224i
$260$		0			0
$261$	−2321.64	−	2766.83i	−0.0340812	−	0.0406164i
$262$		0			0
$263$	−817.509	−	4636.32i	−0.0118190	−	0.0670289i	0.978328	−	0.207062i	$-0.0663902\pi$
$263$	−817.509	−	4636.32i	−0.0118190	−	0.0670289i	−0.990147	+	0.140033i	$0.955279\pi$
$264$		0			0
$265$		−	807.835i		−	0.0115035i
$266$		0			0
$267$	−88711.4			−1.24439
$268$		0			0
$269$	7559.50	−	1332.94i	0.104469	−	0.0184208i	−0.121169	−	0.992632i	$-0.538664\pi$
$269$	7559.50	−	1332.94i	0.104469	−	0.0184208i	0.225638	+	0.974211i	$0.427553\pi$
$270$		0			0
$271$	52245.4	−	43839.1i	0.711392	−	0.596929i	−0.213597	−	0.976922i	$-0.568518\pi$
$271$	52245.4	−	43839.1i	0.711392	−	0.596929i	0.924989	+	0.379993i	$0.124074\pi$
$272$		0			0
$273$	−38812.6	+	67225.4i	−0.520772	+	0.902004i
$274$		0			0
$275$	−112129.	+	40811.5i	−1.48269	+	0.539657i
$276$		0			0
$277$	−31305.4	−	54222.6i	−0.408000	−	0.706677i	0.586665	−	0.809829i	$-0.300440\pi$
$277$	−31305.4	−	54222.6i	−0.408000	−	0.706677i	−0.994666	+	0.103153i	$0.967107\pi$
$278$		0			0
$279$	14092.4	+	2484.86i	0.181040	+	0.0319223i
$280$		0			0
$281$	−67625.0	+	80592.3i	−0.856435	+	1.02066i	0.143086	+	0.989710i	$0.454298\pi$
$281$	−67625.0	+	80592.3i	−0.856435	+	1.02066i	−0.999521	+	0.0309495i	$0.990147\pi$
$282$		0			0
$283$	125903.	+	45824.9i	1.57204	+	0.572175i	0.973453	−	0.228885i	$-0.0735081\pi$
$283$	125903.	+	45824.9i	1.57204	+	0.572175i	0.598584	+	0.801060i	$0.295730\pi$
$284$		0			0
$285$	1145.46	+	2087.67i	0.0141022	+	0.0257023i
$286$		0			0
$287$	16327.2	−	44858.6i	0.198220	−	0.544605i
$288$		0			0
$289$	156891.	+	131647.i	1.87846	+	1.57622i
$290$		0			0
$291$	−2466.01	+	13985.5i	−0.0291212	+	0.165155i
$292$		0			0
$293$	100485.	−	58014.9i	1.17048	−	0.675779i	0.216689	−	0.976241i	$-0.430474\pi$
$293$	100485.	−	58014.9i	1.17048	−	0.675779i	0.953794	+	0.300462i	$0.0971409\pi$
$294$		0			0
$295$	−1382.27	−	3797.74i	−0.0158835	−	0.0436397i
$296$		0			0
$297$	130145.	+	75139.3i	1.47542	+	0.851832i
$298$		0			0
$299$	−42342.0	−	50461.3i	−0.473619	−	0.564437i
$300$		0			0
$301$	−9110.40	−	51667.7i	−0.100555	−	0.570277i
$302$		0			0
$303$		−	115287.i		−	1.25572i
$304$		0			0
$305$	−4205.62			−0.0452095
$306$		0			0
$307$	−136092.	+	23996.7i	−1.44396	+	0.254610i	−0.840080	−	0.542462i	$-0.817492\pi$
$307$	−136092.	+	23996.7i	−1.44396	+	0.254610i	−0.603884	+	0.797072i	$0.706381\pi$
$308$		0			0
$309$	118225.	−	99202.8i	1.23821	−	1.03898i
$310$		0			0
$311$	−57568.9	+	99712.2i	−0.595205	+	1.03093i	0.398313	+	0.917250i	$0.369596\pi$
$311$	−57568.9	+	99712.2i	−0.595205	+	1.03093i	−0.993518	+	0.113676i	$0.963737\pi$
$312$		0			0
$313$	−49771.9	+	18115.5i	−0.508037	+	0.184910i	−0.583305	−	0.812253i	$-0.698241\pi$
$313$	−49771.9	+	18115.5i	−0.508037	+	0.184910i	0.0752683	+	0.997163i	$0.476019\pi$
$314$		0			0
$315$	352.649	+	610.806i	0.00355403	+	0.00615576i
$316$		0			0
$317$	−46437.0	−	8188.09i	−0.462110	−	0.0814825i	−0.0622538	−	0.998060i	$-0.519829\pi$
$317$	−46437.0	−	8188.09i	−0.462110	−	0.0814825i	−0.399856	+	0.916578i	$0.630940\pi$
$318$		0			0
$319$	−24276.5	+	28931.7i	−0.238564	+	0.284310i
$320$		0			0
$321$	33911.0	+	12342.6i	0.329102	+	0.119783i
$322$		0			0
$323$	127803.	−	145745.i	1.22500	−	1.39697i
$324$		0			0
$325$	−45176.0	+	124120.i	−0.427701	+	1.17510i
$326$		0			0
$327$	78314.3	+	65713.5i	0.732395	+	0.614553i
$328$		0			0
$329$	−12746.3	+	72287.6i	−0.117758	+	0.667840i
$330$		0			0
$331$	30281.9	−	17483.2i	0.276393	−	0.159575i	−0.355396	−	0.934716i	$-0.615654\pi$
$331$	30281.9	−	17483.2i	0.276393	−	0.159575i	0.631789	+	0.775140i	$0.282321\pi$
$332$		0			0
$333$	−6938.07	−	19062.2i	−0.0625677	−	0.171903i
$334$		0			0
$335$	−148.063	−	85.4844i	−0.00131934	−	0.000761724i
$336$		0			0
$337$	31733.6	+	37818.6i	0.279421	+	0.333001i	0.887442	−	0.460920i	$-0.152481\pi$
$337$	31733.6	+	37818.6i	0.279421	+	0.333001i	−0.608020	+	0.793921i	$0.708036\pi$
$338$		0			0
$339$	24643.3	+	139759.i	0.214437	+	1.21613i
$340$		0			0
$341$		−	149632.i		−	1.28681i
$342$		0			0
$343$	123035.			1.04578
$344$		0			0
$345$	2022.55	−	356.630i	0.0169926	−	0.00299626i
$346$		0			0
$347$	−33446.4	+	28064.9i	−0.277774	+	0.233080i	−0.771022	−	0.636809i	$-0.780254\pi$
$347$	−33446.4	+	28064.9i	−0.277774	+	0.233080i	0.493248	+	0.869889i	$0.335810\pi$
$348$		0			0
$349$	28848.8	−	49967.6i	0.236852	−	0.410239i	−0.722957	−	0.690893i	$-0.757218\pi$
$349$	28848.8	−	49967.6i	0.236852	−	0.410239i	0.959809	+	0.280653i	$0.0905511\pi$
$350$		0			0
$351$	156317.	−	56894.9i	1.26880	−	0.461805i
$352$		0			0
$353$	39122.8	+	67762.7i	0.313965	+	0.543803i	0.979217	−	0.202816i	$-0.0650093\pi$
$353$	39122.8	+	67762.7i	0.313965	+	0.543803i	−0.665252	+	0.746619i	$0.731676\pi$
$354$		0			0
$355$	4393.46	+	774.686i	0.0348618	+	0.00614708i
$356$		0			0
$357$	−126636.	+	150918.i	−0.993618	+	1.18415i
$358$		0			0
$359$	−136903.	−	49828.5i	−1.06224	−	0.386624i	−0.248971	−	0.968511i	$-0.580092\pi$
$359$	−136903.	−	49828.5i	−1.06224	−	0.386624i	−0.813270	+	0.581887i	$0.802315\pi$
$360$		0			0
$361$	−96090.4	−	88035.2i	−0.737336	−	0.675526i
$362$		0			0
$363$	59294.5	−	162910.i	0.449988	−	1.23633i
$364$		0			0
$365$	5213.78	+	4374.88i	0.0391352	+	0.0328383i
$366$		0			0
$367$	−30340.5	+	172069.i	−0.225263	+	1.27753i	0.636918	+	0.770931i	$0.280209\pi$
$367$	−30340.5	+	172069.i	−0.225263	+	1.27753i	−0.862181	+	0.506600i	$0.830902\pi$
$368$		0			0
$369$	−16311.6	+	9417.48i	−0.119796	+	0.0691643i
$370$		0			0
$371$	−15368.0	−	42223.3i	−0.111653	−	0.306764i
$372$		0			0
$373$	193882.	+	111938.i	1.39354	+	0.804561i	0.993705	−	0.112025i	$-0.0357337\pi$
$373$	193882.	+	111938.i	1.39354	+	0.804561i	0.399836	+	0.916587i	$0.369067\pi$
$374$		0			0
$375$	−5297.10	−	6312.83i	−0.0376682	−	0.0448913i
$376$		0			0
$377$	7259.62	+	41171.4i	0.0510777	+	0.289676i
$378$		0			0
$379$		−	194659.i		−	1.35518i	−0.735440	−	0.677590i	$-0.763024\pi$
$379$		−	194659.i		−	1.35518i	0.735440	−	0.677590i	$-0.236976\pi$
$380$		0			0
$381$	235726.			1.62390
$382$		0			0
$383$	−223241.	+	39363.5i	−1.52187	+	0.268347i	−0.871167	−	0.490987i	$-0.836636\pi$
$383$	−223241.	+	39363.5i	−1.52187	+	0.268347i	−0.650702	+	0.759333i	$0.725525\pi$
$384$		0			0
$385$	5649.60	−	4740.58i	0.0381150	−	0.0319823i
$386$		0			0
$387$	−10350.0	+	17926.8i	−0.0691068	+	0.119696i
$388$		0			0
$389$	−237179.	+	86325.9i	−1.56739	+	0.570482i	−0.972414	−	0.233263i	$-0.925060\pi$
$389$	−237179.	+	86325.9i	−1.56739	+	0.570482i	−0.594973	+	0.803745i	$0.702837\pi$
$390$		0			0
$391$	−83591.0	−	144784.i	−0.546771	−	0.947036i
$392$		0			0
$393$	−137014.	−	24159.3i	−0.887115	−	0.156422i
$394$		0			0
$395$	3070.02	−	3658.71i	0.0196765	−	0.0234495i
$396$		0			0
$397$	169678.	+	61757.6i	1.07657	+	0.391841i	0.818631	−	0.574320i	$-0.194733\pi$
$397$	169678.	+	61757.6i	1.07657	+	0.391841i	0.257942	+	0.966160i	$0.416956\pi$
$398$		0			0
$399$	99585.0	+	87326.0i	0.625530	+	0.548527i
$400$		0			0
$401$	24795.4	−	68124.8i	0.154199	−	0.423659i	−0.838406	−	0.545046i	$-0.816512\pi$
$401$	24795.4	−	68124.8i	0.154199	−	0.423659i	0.992605	+	0.121387i	$0.0387343\pi$
$402$		0			0
$403$	−126883.	−	106467.i	−0.781253	−	0.655549i
$404$		0			0
$405$	−686.470	+	3893.17i	−0.00418516	+	0.0237352i
$406$		0			0
$407$	−183700.	+	106059.i	−1.10897	+	0.640264i
$408$		0			0
$409$	−50355.5	−	138351.i	−0.301024	−	0.827056i	−0.994323	−	0.106406i	$-0.966066\pi$
$409$	−50355.5	−	138351.i	−0.301024	−	0.827056i	0.693299	−	0.720650i	$-0.256157\pi$
$410$		0			0
$411$	47252.6	+	27281.3i	0.279732	+	0.161503i
$412$		0			0
$413$	−144494.	−	172202.i	−0.847131	−	1.00957i
$414$		0			0
$415$	691.269	+	3920.38i	0.00401376	+	0.0227631i
$416$		0			0
$417$		−	17803.4i		−	0.102384i
$418$		0			0
$419$	−118436.			−0.674617			−0.337309	−	0.941394i	$-0.609517\pi$
$419$	−118436.			−0.674617			−0.337309	+	0.941394i	$0.609517\pi$
$420$		0			0
$421$	−3817.47	+	673.122i	−0.0215383	+	0.00379778i	−0.184407	−	0.982850i	$-0.559036\pi$
$421$	−3817.47	+	673.122i	−0.0215383	+	0.00379778i	0.162869	+	0.986648i	$0.447925\pi$
$422$		0			0
$423$	22185.6	−	18615.9i	0.123991	−	0.104041i
$424$		0			0
$425$	−167614.	+	290316.i	−0.927968	+	1.60729i
$426$		0			0
$427$	−219816.	+	80006.5i	−1.20560	+	0.438803i
$428$		0			0
$429$	−160129.	−	277351.i	−0.870072	−	1.50701i
$430$		0			0
$431$	−52442.0	−	9246.94i	−0.282309	−	0.0497787i	0.0307006	−	0.999529i	$-0.490226\pi$
$431$	−52442.0	−	9246.94i	−0.282309	−	0.0497787i	−0.313010	+	0.949750i	$0.601337\pi$
$432$		0			0
$433$	168576.	−	200901.i	0.899127	−	1.07154i	−0.0979547	−	0.995191i	$-0.531230\pi$
$433$	168576.	−	200901.i	0.899127	−	1.07154i	0.997081	−	0.0763465i	$-0.0243255\pi$
$434$		0			0
$435$	−1224.82	−	445.799i	−0.00647284	−	0.00235592i
$436$		0			0
$437$	−98538.7	+	54065.8i	−0.515993	+	0.283113i
$438$		0			0
$439$	47629.2	−	130860.i	0.247141	−	0.679014i	−0.752647	−	0.658424i	$-0.771223\pi$
$439$	47629.2	−	130860.i	0.247141	−	0.679014i	0.999788	−	0.0205899i	$-0.00655444\pi$
$440$		0			0
$441$	−3567.50	−	2993.49i	−0.0183437	−	0.0153922i
$442$		0			0
$443$	51518.8	−	292178.i	0.262518	−	1.48881i	−0.513494	−	0.858093i	$-0.671649\pi$
$443$	51518.8	−	292178.i	0.262518	−	1.48881i	0.776012	−	0.630718i	$-0.217240\pi$
$444$		0			0
$445$	8079.70	−	4664.82i	0.0408014	−	0.0235567i
$446$		0			0
$447$	49052.4	+	134770.i	0.245497	+	0.674497i
$448$		0			0
$449$	95659.2	+	55228.9i	0.474498	+	0.273951i	0.718121	−	0.695919i	$-0.245003\pi$
$449$	95659.2	+	55228.9i	0.474498	+	0.273951i	−0.243623	+	0.969870i	$0.578336\pi$
$450$		0			0
$451$	126597.	+	150872.i	0.622401	+	0.741749i
$452$		0			0
$453$	17424.0	+	98816.4i	0.0849085	+	0.481540i
$454$		0			0
$455$		−	8163.73i		−	0.0394335i
$456$		0			0
$457$	−197803.			−0.947110			−0.473555	−	0.880764i	$-0.657030\pi$
$457$	−197803.			−0.947110			−0.473555	+	0.880764i	$0.657030\pi$
$458$		0			0
$459$	415775.	−	73312.3i	1.97348	−	0.347978i
$460$		0			0
$461$	29644.6	−	24874.8i	0.139490	−	0.117046i	−0.570373	−	0.821386i	$-0.693201\pi$
$461$	29644.6	−	24874.8i	0.139490	−	0.117046i	0.709863	+	0.704340i	$0.248757\pi$
$462$		0			0
$463$	−60072.0	+	104048.i	−0.280227	+	0.485368i	−0.971441	−	0.237283i	$-0.923743\pi$
$463$	−60072.0	+	104048.i	−0.280227	+	0.485368i	0.691213	+	0.722651i	$0.257076\pi$
$464$		0			0
$465$	4852.63	−	1766.21i	0.0224425	−	0.00816840i
$466$		0			0
$467$	71703.3	+	124194.i	0.328780	+	0.569464i	0.982270	−	0.187471i	$-0.0600292\pi$
$467$	71703.3	+	124194.i	0.328780	+	0.569464i	−0.653490	+	0.756935i	$0.726696\pi$
$468$		0			0
$469$	−9365.09	−	1651.32i	−0.0425762	−	0.00750732i
$470$		0			0
$471$	−84224.5	+	100375.i	−0.379662	+	0.452463i
$472$		0			0
$473$	203399.	+	74031.3i	0.909133	+	0.330897i
$474$		0			0
$475$	192680.	+	116910.i	0.853986	+	0.518160i
$476$		0			0
$477$	−6063.49	+	16659.3i	−0.0266493	+	0.0732184i
$478$		0			0
$479$	−120222.	−	100878.i	−0.523979	−	0.439671i	0.342037	−	0.939686i	$-0.388883\pi$
$479$	−120222.	−	100878.i	−0.523979	−	0.439671i	−0.866016	+	0.500016i	$0.833328\pi$
$480$		0			0
$481$	−40773.0	+	231235.i	−0.176231	+	0.999457i
$482$		0			0
$483$	98928.5	−	57116.4i	0.424060	−	0.244831i
$484$		0			0
$485$	−510.813	−	1403.45i	−0.00217159	−	0.00596641i
$486$		0			0
$487$	134338.	+	77560.2i	0.566424	+	0.327025i	0.755720	−	0.654895i	$-0.227287\pi$
$487$	134338.	+	77560.2i	0.566424	+	0.327025i	−0.189296	+	0.981920i	$0.560621\pi$
$488$		0			0
$489$	60457.8	+	72050.8i	0.252833	+	0.301315i
$490$		0			0
$491$	27722.8	+	157224.i	0.114994	+	0.652163i	0.986753	+	0.162228i	$0.0518681\pi$
$491$	27722.8	+	157224.i	0.114994	+	0.652163i	−0.871759	+	0.489934i	$0.837021\pi$
$492$		0			0
$493$			106103.i			0.436551i
$494$		0			0
$495$	−2909.84			−0.0118757
$496$		0			0
$497$	244371.	−	43089.3i	0.989322	−	0.174444i
$498$		0			0
$499$	211495.	−	177466.i	0.849375	−	0.712710i	−0.110277	−	0.993901i	$-0.535174\pi$
$499$	211495.	−	177466.i	0.849375	−	0.712710i	0.959652	+	0.281190i	$0.0907293\pi$
$500$		0			0
$501$	60466.2	−	104731.i	0.240900	−	0.417252i
$502$		0			0
$503$	−58971.7	+	21463.9i	−0.233081	+	0.0848347i	−0.455920	−	0.890021i	$-0.650690\pi$
$503$	−58971.7	+	21463.9i	−0.233081	+	0.0848347i	0.222839	+	0.974855i	$0.428468\pi$
$504$		0			0
$505$	6062.25	+	10500.1i	0.0237712	+	0.0411729i
$506$		0			0
$507$	−126363.	−	22281.2i	−0.491591	−	0.0866807i
$508$		0			0
$509$	266313.	−	317380.i	1.02792	−	1.22502i	0.0538991	−	0.998546i	$-0.482835\pi$
$509$	266313.	−	317380.i	1.02792	−	1.22502i	0.974017	−	0.226476i	$-0.0727205\pi$
$510$		0			0
$511$	355736.	+	129477.i	1.36234	+	0.495852i
$512$		0			0
$513$	−43190.7	−	280533.i	−0.164118	−	1.06598i
$514$		0			0
$515$	−5551.28	+	15252.0i	−0.0209305	+	0.0575060i
$516$		0			0
$517$	−231987.	−	194660.i	−0.867924	−	0.728275i
$518$		0			0
$519$	−47907.4	+	271696.i	−0.177856	+	1.00867i
$520$		0			0
$521$	−126272.	+	72903.2i	−0.465191	+	0.268578i	−0.714225	−	0.699917i	$-0.753221\pi$
$521$	−126272.	+	72903.2i	−0.465191	+	0.268578i	0.249033	+	0.968495i	$0.419887\pi$
$522$		0			0
$523$	161926.	+	444889.i	0.591990	+	1.62648i	0.766807	+	0.641877i	$0.221844\pi$
$523$	161926.	+	444889.i	0.591990	+	1.62648i	−0.174818	+	0.984601i	$0.555934\pi$
$524$		0			0
$525$	−198369.	−	114528.i	−0.719705	−	0.415522i
$526$		0			0
$527$	−270210.	−	322023.i	−0.972925	−	1.15949i
$528$		0			0
$529$	−31760.9	−	180125.i	−0.113496	−	0.643668i
$530$		0			0
$531$			88692.8i			0.314557i
$532$		0			0
$533$	218012.			0.767408
$534$		0			0
$535$	−3737.59	+	659.037i	−0.0130582	+	0.00230251i
$536$		0			0
$537$	−193928.	+	162725.i	−0.672499	+	0.564294i
$538$		0			0
$539$	−24348.5	+	42172.8i	−0.0838096	+	0.145163i
$540$		0			0
$541$	128104.	−	46625.9i	0.437690	−	0.159306i	−0.113771	−	0.993507i	$-0.536293\pi$
$541$	128104.	−	46625.9i	0.437690	−	0.159306i	0.551461	+	0.834201i	$0.314071\pi$
$542$		0			0
$543$	225710.	+	390940.i	0.765509	+	1.32590i
$544$		0			0
$545$	−10588.2	−	1866.99i	−0.0356477	−	0.00628564i
$546$		0			0
$547$	−207771.	+	247611.i	−0.694400	+	0.827554i	−0.991880	−	0.127174i	$-0.959409\pi$
$547$	−207771.	+	247611.i	−0.694400	+	0.827554i	0.297481	+	0.954728i	$0.403854\pi$
$548$		0			0
$549$	86729.0	+	31566.8i	0.287753	+	0.104733i
$550$		0			0
$551$	71316.5	+	1553.02i	0.234902	+	0.00511532i
$552$		0			0
$553$	90859.2	−	249634.i	0.297111	−	0.816306i
$554$		0			0
$555$	−5607.90	−	4705.59i	−0.0182060	−	0.0152766i
$556$		0			0
$557$	−94444.8	+	535623.i	−0.304416	+	1.72643i	0.321825	+	0.946799i	$0.395704\pi$
$557$	−94444.8	+	535623.i	−0.304416	+	1.72643i	−0.626241	+	0.779630i	$0.715407\pi$
$558$		0			0
$559$	207500.	−	119800.i	0.664042	−	0.383385i
$560$		0			0
$561$	−277995.	−	763784.i	−0.883305	−	2.42686i
$562$		0			0
$563$	−364078.	−	210201.i	−1.14862	−	0.663158i	−0.200072	−	0.979781i	$-0.564118\pi$
$563$	−364078.	−	210201.i	−1.14862	−	0.663158i	−0.948552	+	0.316623i	$0.897451\pi$
$564$		0			0
$565$	−9593.61	−	11433.2i	−0.0300528	−	0.0358155i
$566$		0			0
$567$	38182.6	+	216544.i	0.118768	+	0.673566i
$568$		0			0
$569$		−	311903.i		−	0.963374i	−0.876343	−	0.481687i	$-0.840024\pi$
$569$		−	311903.i		−	0.963374i	0.876343	−	0.481687i	$-0.159976\pi$
$570$		0			0
$571$	−4647.72			−0.0142550			−0.00712751	−	0.999975i	$-0.502269\pi$
$571$	−4647.72			−0.0142550			−0.00712751	+	0.999975i	$0.502269\pi$
$572$		0			0
$573$	−397159.	+	70029.8i	−1.20964	+	0.213292i
$574$		0			0
$575$	148901.	−	124943.i	0.450362	−	0.377899i
$576$		0			0
$577$	92600.9	−	160390.i	0.278140	−	0.481753i	−0.692782	−	0.721147i	$-0.743615\pi$
$577$	92600.9	−	160390.i	0.278140	−	0.481753i	0.970923	+	0.239394i	$0.0769487\pi$
$578$		0			0
$579$	−54070.1	+	19679.9i	−0.161287	+	0.0587038i
$580$		0			0
$581$	110711.	+	191757.i	0.327973	+	0.568066i
$582$		0			0
$583$	182564.	+	32190.9i	0.537127	+	0.0947100i
$584$		0			0
$585$	−2070.43	+	2467.45i	−0.00604992	+	0.00721001i
$586$		0			0
$587$	−177355.	−	64551.9i	−0.514715	−	0.187341i	0.0715858	−	0.997434i	$-0.477194\pi$
$587$	−177355.	−	64551.9i	−0.514715	−	0.187341i	−0.586301	+	0.810094i	$0.699416\pi$
$588$		0			0
$589$	−220400.	+	176906.i	−0.635304	+	0.509931i
$590$		0			0
$591$	36067.7	−	99095.3i	0.103263	−	0.283712i
$592$		0			0
$593$	131397.	+	110255.i	0.373659	+	0.313537i	0.810207	−	0.586144i	$-0.199355\pi$
$593$	131397.	+	110255.i	0.373659	+	0.313537i	−0.436548	+	0.899681i	$0.643799\pi$
$594$		0			0
$595$	3597.86	−	20404.5i	0.0101627	−	0.0576357i
$596$		0			0
$597$	203048.	−	117230.i	0.569706	−	0.328920i
$598$		0			0
$599$	136137.	+	374034.i	0.379423	+	1.04246i	0.971596	+	0.236645i	$0.0760477\pi$
$599$	136137.	+	374034.i	0.379423	+	1.04246i	−0.592174	+	0.805810i	$0.701730\pi$
$600$		0			0
$601$	−376812.	−	217553.i	−1.04322	−	0.602304i	−0.122477	−	0.992471i	$-0.539084\pi$
$601$	−376812.	−	217553.i	−1.04322	−	0.602304i	−0.920744	+	0.390168i	$0.872417\pi$
$602$		0			0
$603$	2411.76	+	2874.22i	0.00663283	+	0.00790470i
$604$		0			0
$605$	3166.05	+	17955.6i	0.00864983	+	0.0490556i
$606$		0			0
$607$		−	48561.9i		−	0.131801i	−0.997826	−	0.0659005i	$-0.979008\pi$
$607$		−	48561.9i		−	0.131801i	0.997826	−	0.0659005i	$-0.0209920\pi$
$608$		0			0
$609$	−72498.8			−0.195477
$610$		0			0
$611$	−330130.	+	58210.8i	−0.884306	+	0.155927i
$612$		0			0
$613$	−265441.	+	222732.i	−0.706395	+	0.592736i	−0.923585	−	0.383394i	$-0.874755\pi$
$613$	−265441.	+	222732.i	−0.706395	+	0.592736i	0.217190	+	0.976129i	$0.430311\pi$
$614$		0			0
$615$	−3398.55	+	5886.47i	−0.00898553	+	0.0155634i
$616$		0			0
$617$	380855.	−	138620.i	1.00044	−	0.364129i	0.210683	−	0.977554i	$-0.432431\pi$
$617$	380855.	−	138620.i	1.00044	−	0.364129i	0.789753	+	0.613426i	$0.210209\pi$
$618$		0			0
$619$	−163814.	−	283734.i	−0.427533	−	0.740508i	0.569120	−	0.822254i	$-0.307284\pi$
$619$	−163814.	−	283734.i	−0.427533	−	0.740508i	−0.996653	+	0.0817457i	$0.973950\pi$
$620$		0			0
$621$	−241080.	−	42508.9i	−0.625141	−	0.110229i
$622$		0			0
$623$	333561.	−	397523.i	0.859409	−	1.02420i
$624$		0			0
$625$	−365846.	−	133157.i	−0.936565	−	0.340882i
$626$		0			0
$627$	−517440.	+	175672.i	−1.31621	+	0.446857i
$628$		0			0
$629$	−203817.	+	559982.i	−0.515156	+	1.41538i
$630$		0			0
$631$	−270104.	−	226644.i	−0.678379	−	0.569228i	0.237153	−	0.971472i	$-0.423786\pi$
$631$	−270104.	−	226644.i	−0.678379	−	0.569228i	−0.915532	+	0.402244i	$0.868230\pi$
$632$		0			0
$633$	64.6222	−	366.491i	0.000161278	−	0.000914652i
$634$		0			0
$635$	−21469.6	+	12395.5i	−0.0532448	+	0.0307409i
$636$		0			0
$637$	18436.5	+	50653.8i	0.0454359	+	0.124834i
$638$		0			0
$639$	−84788.0	−	48952.4i	−0.207650	−	0.119887i
$640$		0			0
$641$	284607.	+	339181.i	0.692675	+	0.825498i	0.991676	−	0.128755i	$-0.0410981\pi$
$641$	284607.	+	339181.i	0.692675	+	0.825498i	−0.299002	+	0.954253i	$0.596654\pi$
$642$		0			0
$643$	−68762.6	−	389972.i	−0.166315	−	0.943217i	−0.947699	−	0.319166i	$-0.896597\pi$
$643$	−68762.6	−	389972.i	−0.166315	−	0.943217i	0.781384	−	0.624050i	$-0.214514\pi$
$644$		0			0
$645$			7470.19i			0.0179561i
$646$		0			0
$647$	−129762.			−0.309983			−0.154992	−	0.987916i	$-0.549535\pi$
$647$	−129762.			−0.309983			−0.154992	+	0.987916i	$0.549535\pi$
$648$		0			0
$649$	913338.	−	161046.i	2.16841	−	0.382350i
$650$		0			0
$651$	220034.	−	184630.i	0.519191	−	0.435653i
$652$		0			0
$653$	126553.	−	219197.i	0.296788	−	0.514052i	−0.678611	−	0.734498i	$-0.737418\pi$
$653$	126553.	−	219197.i	0.296788	−	0.514052i	0.975399	+	0.220445i	$0.0707511\pi$
$654$		0			0
$655$	13749.4	−	5004.39i	0.0320481	−	0.0116646i
$656$		0			0
$657$	−74682.3	−	129354.i	−0.173016	−	0.299673i
$658$		0			0
$659$	156021.	+	27510.7i	0.359263	+	0.0633477i	0.350366	−	0.936613i	$-0.386057\pi$
$659$	156021.	+	27510.7i	0.359263	+	0.0633477i	0.00889634	+	0.999960i	$0.497168\pi$
$660$		0			0
$661$	−434961.	+	518366.i	−0.995513	+	1.18641i	−0.0130570	+	0.999915i	$0.504156\pi$
$661$	−434961.	+	518366.i	−0.995513	+	1.18641i	−0.982456	+	0.186492i	$0.940288\pi$
$662$		0			0
$663$	−845464.	−	307724.i	−1.92339	−	0.700058i
$664$		0			0
$665$	−13662.0	−	2716.93i	−0.0308938	−	0.00614377i
$666$		0			0
$667$	21041.8	−	57812.0i	0.0472968	−	0.129947i
$668$		0			0
$669$	142723.	+	119759.i	0.318892	+	0.267582i
$670$		0			0
$671$	167587.	−	950433.i	0.372216	−	2.11094i
$672$		0			0
$673$	−706065.	+	407647.i	−1.55889	+	0.900024i	−0.561523	+	0.827461i	$0.689785\pi$
$673$	−706065.	+	407647.i	−1.55889	+	0.900024i	−0.997364	+	0.0725630i	$0.976882\pi$
$674$		0			0
$675$	167885.	+	461261.i	0.368473	+	1.01237i
$676$		0			0
$677$	316533.	+	182751.i	0.690624	+	0.398732i	0.803846	−	0.594838i	$-0.202784\pi$
$677$	316533.	+	182751.i	0.690624	+	0.398732i	−0.113221	+	0.993570i	$0.536117\pi$
$678$		0			0
$679$	−53397.6	−	63636.8i	−0.115820	−	0.138028i
$680$		0			0
$681$	−12448.3	−	70598.1i	−0.0268422	−	0.152229i
$682$		0			0
$683$			125776.i			0.269623i	0.990871	+	0.134811i	$0.0430428\pi$
$683$			125776.i			0.269623i	−0.990871	+	0.134811i	$0.956957\pi$
$684$		0			0
$685$	−5738.27			−0.0122292
$686$		0			0
$687$	135545.	−	23900.3i	0.287191	−	0.0506395i
$688$		0			0
$689$	157196.	−	131903.i	0.331133	−	0.277854i
$690$		0			0
$691$	−289348.	+	501166.i	−0.605989	+	1.04960i	0.385905	+	0.922538i	$0.373889\pi$
$691$	−289348.	+	501166.i	−0.605989	+	1.04960i	−0.991894	+	0.127065i	$0.959444\pi$
$692$		0			0
$693$	−152089.	+	55355.9i	−0.316688	+	0.115265i
$694$		0			0
$695$	936.177	+	1621.51i	0.00193815	+	0.00335698i
$696$		0			0
$697$	544901.	+	96080.7i	1.12164	+	0.197775i
$698$		0			0
$699$	351634.	−	419061.i	0.719675	−	0.857676i
$700$		0			0
$701$	733783.	+	267075.i	1.49325	+	0.543498i	0.954302	−	0.298843i	$-0.0966007\pi$
$701$	733783.	+	267075.i	1.49325	+	0.543498i	0.538945	+	0.842341i	$0.318823\pi$
$702$		0			0
$703$	373404.	+	145190.i	0.755559	+	0.293783i
$704$		0			0
$705$	3574.61	−	9821.16i	0.00719201	−	0.0197599i
$706$		0			0
$707$	516609.	+	433486.i	1.03353	+	0.867234i
$708$		0			0
$709$	157506.	−	893259.i	0.313331	−	1.77699i	−0.268096	−	0.963392i	$-0.586394\pi$
$709$	157506.	−	893259.i	0.313331	−	1.77699i	0.581427	−	0.813598i	$-0.302494\pi$
$710$		0			0
$711$	−90772.3	+	52407.4i	−0.179562	+	0.103670i
$712$		0			0
$713$	83365.7	+	229045.i	0.163987	+	0.450550i
$714$		0			0
$715$	29168.6	+	16840.5i	0.0570563	+	0.0329415i
$716$		0			0
$717$	481675.	+	574038.i	0.936948	+	1.11661i
$718$		0			0
$719$	−36072.2	−	204576.i	−0.0697775	−	0.395728i	−0.999615	−	0.0277566i	$-0.991164\pi$
$719$	−36072.2	−	204576.i	−0.0697775	−	0.395728i	0.929837	−	0.367971i	$-0.119947\pi$
$720$		0			0
$721$			902787.i			1.73666i
$722$		0			0
$723$	850542.			1.62712
$724$		0			0
$725$	−121488.	+	21421.7i	−0.231131	+	0.0407547i
$726$		0			0
$727$	−505469.	+	424139.i	−0.956370	+	0.802489i	−0.980359	−	0.197223i	$-0.936808\pi$
$727$	−505469.	+	424139.i	−0.956370	+	0.802489i	0.0239891	+	0.999712i	$0.492363\pi$
$728$		0			0
$729$	295567.	−	511938.i	0.556162	−	0.963301i
$730$		0			0
$731$	571425.	−	207982.i	1.06936	−	0.389216i
$732$		0			0
$733$	235776.	+	408377.i	0.438826	+	0.760069i	0.997599	−	0.0692514i	$-0.0220611\pi$
$733$	235776.	+	408377.i	0.438826	+	0.760069i	−0.558773	+	0.829321i	$0.688728\pi$
$734$		0			0
$735$	−1655.09	−	291.836i	−0.00306370	−	0.000540213i
$736$		0			0
$737$	25218.8	−	30054.6i	0.0464290	−	0.0553320i
$738$		0			0
$739$	−559014.	−	203465.i	−1.02361	−	0.372563i	−0.224965	−	0.974367i	$-0.572227\pi$
$739$	−559014.	−	203465.i	−1.02361	−	0.372563i	−0.798644	+	0.601804i	$0.794449\pi$
$740$		0			0
$741$	−219209.	+	563768.i	−0.399229	+	1.02675i
$742$		0			0
$743$	−115197.	+	316500.i	−0.208671	+	0.573319i	−0.999237	−	0.0390578i	$-0.987564\pi$
$743$	−115197.	+	316500.i	−0.208671	+	0.573319i	0.790566	+	0.612377i	$0.209787\pi$
$744$		0			0
$745$	−11554.4	−	9695.31i	−0.0208178	−	0.0174682i
$746$		0			0
$747$	15170.4	−	86035.4i	0.0271866	−	0.154183i
$748$		0			0
$749$	−182816.	+	105549.i	−0.325874	+	0.188144i
$750$		0			0
$751$	−163368.	−	448849.i	−0.289659	−	0.795831i	−0.996114	−	0.0880731i	$-0.971929\pi$
$751$	−163368.	−	448849.i	−0.289659	−	0.795831i	0.706455	−	0.707758i	$-0.250293\pi$
$752$		0			0
$753$	36032.5	+	20803.4i	0.0635483	+	0.0366896i
$754$		0			0
$755$	−6783.13	−	8083.82i	−0.0118997	−	0.0141815i
$756$		0			0
$757$	−126507.	−	717459.i	−0.220762	−	1.25200i	−0.870623	−	0.491950i	$-0.836284\pi$
$757$	−126507.	−	717459.i	−0.220762	−	1.25200i	0.649861	−	0.760053i	$-0.274827\pi$
$758$		0			0
$759$			471289.i			0.818095i
$760$		0			0
$761$	−307163.			−0.530396			−0.265198	−	0.964194i	$-0.585437\pi$
$761$	−307163.			−0.530396			−0.265198	+	0.964194i	$0.585437\pi$
$762$		0			0
$763$	−588935.	+	103845.i	−1.01162	+	0.178376i
$764$		0			0
$765$	−6262.28	+	5254.68i	−0.0107006	+	0.00897891i
$766$		0			0
$767$	513304.	−	889068.i	0.872537	−	1.51128i
$768$		0			0
$769$	968775.	−	352605.i	1.63821	−	0.596261i	0.651488	−	0.758659i	$-0.274145\pi$
$769$	968775.	−	352605.i	1.63821	−	0.596261i	0.986725	+	0.162398i	$0.0519229\pi$
$770$		0			0
$771$	−70698.3	−	122453.i	−0.118932	−	0.205997i
$772$		0			0
$773$	1.03440e6	+	182393.i	1.73113	+	0.305245i	0.948391	−	0.317103i	$-0.102710\pi$
$773$	1.03440e6	+	182393.i	1.73113	+	0.305245i	0.782740	+	0.622348i	$0.213821\pi$
$774$		0			0
$775$	314163.	−	374405.i	0.523060	−	0.623359i
$776$		0			0
$777$	−382627.	−	139265.i	−0.633773	−	0.230674i
$778$		0			0
$779$	72555.5	−	364844.i	0.119563	−	0.601219i
$780$		0			0
$781$	−350144.	+	962013.i	−0.574044	+	1.57717i
$782$		0			0
$783$	119015.	+	99865.8i	0.194124	+	0.162890i
$784$		0			0
$785$	2392.91	−	13570.9i	0.00388318	−	0.0220226i
$786$		0			0
$787$	−152033.	+	87776.2i	−0.245464	+	0.141719i	−0.617686	−	0.786425i	$-0.711930\pi$
$787$	−152033.	+	87776.2i	−0.245464	+	0.141719i	0.372221	+	0.928144i	$0.378596\pi$
$788$		0			0
$789$	12752.1	+	35036.1i	0.0204846	+	0.0562810i
$790$		0			0
$791$	−718933.	−	415076.i	−1.14904	−	0.663399i
$792$		0			0
$793$	−686692.	−	818368.i	−1.09198	−	1.30137i
$794$		0			0
$795$	1110.97	+	6300.60i	0.00175779	+	0.00996891i
$796$		0			0
$797$			616704.i			0.970868i	0.874273	+	0.485434i	$0.161338\pi$
$797$			616704.i			0.970868i	−0.874273	+	0.485434i	$0.838662\pi$
$798$		0			0
$799$	−850783.			−1.33268
$800$		0			0
$801$	−201635.	+	35553.6i	−0.314268	+	0.0554139i
$802$		0			0
$803$	−1.19645e6	+	1.00394e6i	−1.85550	+	1.55695i
$804$		0			0
$805$	−6006.84	+	10404.2i	−0.00926946	+	0.0160552i
$806$		0			0
$807$	−57126.2	+	20792.2i	−0.0877180	+	0.0319267i
$808$		0			0
$809$	−51993.1	−	90054.7i	−0.0794417	−	0.137597i	0.823567	−	0.567218i	$-0.191980\pi$
$809$	−51993.1	−	90054.7i	−0.0794417	−	0.137597i	−0.903009	+	0.429621i	$0.858647\pi$
$810$		0			0
$811$	773819.	+	136445.i	1.17652	+	0.207452i	0.727523	−	0.686084i	$-0.240672\pi$
$811$	773819.	+	136445.i	1.17652	+	0.207452i	0.448993	+	0.893535i	$0.351783\pi$
$812$		0			0
$813$	−347192.	+	413767.i	−0.525277	+	0.626000i
$814$		0			0
$815$	−9295.14	−	3383.16i	−0.0139940	−	0.00509339i
$816$		0			0
$817$	−131429.	−	387123.i	−0.196901	−	0.579969i
$818$		0			0
$819$	−61275.8	+	168354.i	−0.0913526	+	0.250989i
$820$		0			0
$821$	−712467.	−	597831.i	−1.05701	−	0.886936i	−0.0631958	−	0.998001i	$-0.520129\pi$
$821$	−712467.	−	597831.i	−1.05701	−	0.886936i	−0.993813	+	0.111065i	$0.964574\pi$
$822$		0			0
$823$	24772.4	−	140491.i	0.0365736	−	0.207419i	−0.961045	−	0.276392i	$-0.910861\pi$
$823$	24772.4	−	140491.i	0.0365736	−	0.207419i	0.997619	+	0.0689730i	$0.0219722\pi$
$824$		0			0
$825$	818408.	−	472508.i	1.20244	−	0.694227i
$826$		0			0
$827$	−225103.	−	618464.i	−0.329131	−	0.904281i	−0.988332	−	0.152314i	$-0.951327\pi$
$827$	−225103.	−	618464.i	−0.329131	−	0.904281i	0.659201	−	0.751967i	$-0.270895\pi$
$828$		0			0
$829$	−416484.	−	240457.i	−0.606024	−	0.349888i	0.165384	−	0.986229i	$-0.447114\pi$
$829$	−416484.	−	240457.i	−0.606024	−	0.349888i	−0.771408	+	0.636341i	$0.780447\pi$
$830$		0			0
$831$	318732.	+	379850.i	0.461555	+	0.550060i
$832$		0			0
$833$	23756.4	+	134730.i	0.0342367	+	0.194166i
$834$		0			0
$835$			12718.3i			0.0182413i
$836$		0			0
$837$	−615536.			−0.878623
$838$		0			0
$839$	−162087.	+	28580.4i	−0.230264	+	0.0406017i	−0.287589	−	0.957754i	$-0.592854\pi$
$839$	−162087.	+	28580.4i	−0.230264	+	0.0406017i	0.0573256	+	0.998356i	$0.481743\pi$
$840$		0			0
$841$	511898.	−	429533.i	0.723755	−	0.607302i
$842$		0			0
$843$	416598.	−	721570.i	0.586223	−	1.01537i
$844$		0			0
$845$	12680.6	−	4615.36i	0.0177593	−	0.00646386i
$846$		0			0
$847$	507063.	+	878258.i	0.706797	+	1.22421i
$848$		0			0
$849$	−1.04498e6	−	184259.i	−1.44975	−	0.255631i
$850$		0			0
$851$	222105.	−	264694.i	0.306690	−	0.365498i
$852$		0			0
$853$	−989647.	−	360202.i	−1.36014	−	0.495049i	−0.444039	−	0.896007i	$-0.646455\pi$
$853$	−989647.	−	360202.i	−1.36014	−	0.495049i	−0.916096	+	0.400959i	$0.868677\pi$
$854$		0			0
$855$	3440.23	+	4286.06i	0.00470604	+	0.00586308i
$856$		0			0
$857$	−101250.	+	278182.i	−0.137858	+	0.378762i	−0.989340	−	0.145621i	$-0.953482\pi$
$857$	−101250.	+	278182.i	−0.137858	+	0.378762i	0.851482	+	0.524383i	$0.175704\pi$
$858$		0			0
$859$	620070.	+	520301.i	0.840339	+	0.705128i	0.957640	−	0.287968i	$-0.0929797\pi$
$859$	620070.	+	520301.i	0.840339	+	0.705128i	−0.117301	+	0.993096i	$0.537424\pi$
$860$		0			0
$861$	−65650.5	+	372322.i	−0.0885587	+	0.502242i
$862$		0			0
$863$	966368.	−	557933.i	1.29754	−	0.749135i	0.317562	−	0.948238i	$-0.397136\pi$
$863$	966368.	−	557933.i	1.29754	−	0.749135i	0.979979	+	0.199102i	$0.0638027\pi$
$864$		0			0
$865$	−9923.60	−	27264.9i	−0.0132629	−	0.0364394i
$866$		0			0
$867$	−1.40470e6	−	811003.i	−1.86872	−	1.07891i
$868$		0			0
$869$	704501.	+	839591.i	0.932915	+	1.11180i
$870$		0			0
$871$	−7541.40	−	42769.4i	−0.00994067	−	0.0563763i
$872$		0			0
$873$			32776.2i			0.0430062i
$874$		0			0
$875$	48205.8			0.0629627
$876$		0			0
$877$	453527.	−	79969.1i	0.589664	−	0.103974i	0.129148	−	0.991625i	$-0.458776\pi$
$877$	453527.	−	79969.1i	0.589664	−	0.103974i	0.460515	+	0.887652i	$0.347665\pi$
$878$		0			0
$879$	−703934.	+	590670.i	−0.911074	+	0.764482i
$880$		0			0
$881$	653425.	−	1.13177e6i	0.841868	−	1.45816i	−0.0464448	−	0.998921i	$-0.514789\pi$
$881$	653425.	−	1.13177e6i	0.841868	−	1.45816i	0.888313	−	0.459238i	$-0.151878\pi$
$882$		0			0
$883$	−138215.	+	50306.2i	−0.177269	+	0.0645208i	−0.429130	−	0.903243i	$-0.641180\pi$
$883$	−138215.	+	50306.2i	−0.177269	+	0.0645208i	0.251861	+	0.967764i	$0.418958\pi$
$884$		0			0
$885$	16003.6	+	27719.1i	0.0204330	+	0.0353909i
$886$		0			0
$887$	161952.	+	28556.5i	0.205844	+	0.0362959i	0.275619	−	0.961267i	$-0.411117\pi$
$887$	161952.	+	28556.5i	0.205844	+	0.0362959i	−0.0697751	+	0.997563i	$0.522228\pi$
$888$		0			0
$889$	−886349.	+	1.05631e6i	−1.12150	+	1.33656i
$890$		0			0
$891$	−852466.	−	310272.i	−1.07380	−	0.390830i
$892$		0			0
$893$	−12452.8	+	571847.i	−0.0156157	+	0.717095i
$894$		0			0
$895$	9105.91	−	25018.3i	0.0113678	−	0.0312328i
$896$		0			0
$897$	399637.	+	335336.i	0.496685	+	0.416768i
$898$		0			0
$899$	26862.5	−	152345.i	0.0332374	−	0.188498i
$900$		0			0
$901$	451028.	−	260401.i	0.555589	−	0.320769i
$902$		0			0
$903$	142111.	+	390446.i	0.174282	+	0.478835i
$904$		0			0
$905$	−41114.6	−	23737.5i	−0.0501994	−	0.0289827i
$906$		0			0
$907$	−289245.	−	344709.i	−0.351602	−	0.419023i	0.561036	−	0.827791i	$-0.310403\pi$
$907$	−289245.	−	344709.i	−0.351602	−	0.419023i	−0.912638	+	0.408768i	$0.865958\pi$
$908$		0			0
$909$	−46204.4	−	262038.i	−0.0559185	−	0.317129i
$910$		0			0
$911$			1.42304e6i			1.71467i	0.514757	+	0.857336i	$0.327882\pi$
$911$			1.42304e6i			1.71467i	−0.514757	+	0.857336i	$0.672118\pi$
$912$		0			0
$913$	−913518.			−1.09591
$914$		0			0
$915$	32801.2	−	5783.73i	0.0391784	−	0.00690822i
$916$		0			0
$917$	623443.	−	523131.i	0.741409	−	0.622116i
$918$		0			0
$919$	−92255.4	+	159791.i	−0.109235	+	0.189200i	−0.915460	−	0.402408i	$-0.868173\pi$
$919$	−92255.4	+	159791.i	−0.109235	+	0.189200i	0.806226	+	0.591608i	$0.201507\pi$
$920$		0			0
$921$	1.02843e6	−	374319.i	1.21243	−	0.441288i
$922$		0			0
$923$	566617.	+	981410.i	0.665099	+	1.15199i
$924$		0			0
$925$	−682329.	−	120313.i	−0.797463	−	0.140614i
$926$		0			0
$927$	228959.	−	272863.i	0.266439	−	0.317530i
$928$		0			0
$929$	82033.9	+	29857.9i	0.0950522	+	0.0345962i	0.389109	−	0.921192i	$-0.372783\pi$
$929$	82033.9	+	29857.9i	0.0950522	+	0.0345962i	−0.294056	+	0.955788i	$0.595005\pi$
$930$		0			0
$931$	90905.1	−	13995.7i	0.104879	−	0.0161471i
$932$		0			0
$933$	311873.	−	856863.i	0.358273	−	0.984347i
$934$		0			0
$935$	65482.3	+	54946.2i	0.0749033	+	0.0628513i
$936$		0			0
$937$	229447.	−	1.30126e6i	0.261339	−	1.48212i	−0.517924	−	0.855427i	$-0.673295\pi$
$937$	229447.	−	1.30126e6i	0.261339	−	1.48212i	0.779262	−	0.626698i	$-0.215594\pi$
$938$		0			0
$939$	363276.	−	209738.i	0.412008	−	0.237873i
$940$		0			0
$941$	−365226.	−	1.00345e6i	−0.412460	−	1.13323i	−0.955878	−	0.293763i	$-0.905092\pi$
$941$	−365226.	−	1.00345e6i	−0.412460	−	1.13323i	0.543418	−	0.839462i	$-0.317130\pi$
$942$		0			0
$943$	−277843.	−	160413.i	−0.312447	−	0.180391i
$944$		0			0
$945$	−19501.2	−	23240.6i	−0.0218372	−	0.0260246i
$946$		0			0
$947$	−119571.	−	678120.i	−0.133329	−	0.756148i	−0.976009	−	0.217732i	$-0.930134\pi$
$947$	−119571.	−	678120.i	−0.133329	−	0.756148i	0.842679	−	0.538416i	$-0.180977\pi$
$948$		0			0
$949$			1.72888e6i			1.91969i
$950$		0			0
$951$	373440.			0.412914
$952$		0			0
$953$	929117.	−	163828.i	1.02302	−	0.180386i	0.363123	−	0.931741i	$-0.381711\pi$
$953$	929117.	−	163828.i	1.02302	−	0.180386i	0.659898	+	0.751355i	$0.270599\pi$
$954$		0			0
$955$	32490.2	−	27262.5i	0.0356242	−	0.0298923i
$956$		0			0
$957$	149554.	−	259035.i	0.163295	−	0.282836i
$958$		0			0
$959$	−299923.	+	109163.i	−0.326117	+	0.118697i
$960$		0			0
$961$	−155317.	−	269018.i	−0.168180	−	0.291296i
$962$		0			0
$963$	82023.8	+	14463.0i	0.0884479	+	0.0155957i
$964$		0			0
$965$	3889.78	−	4635.65i	0.00417705	−	0.00497802i
$966$		0			0
$967$	701607.	+	255364.i	0.750310	+	0.273091i	0.688736	−	0.725012i	$-0.258166\pi$
$967$	701607.	+	255364.i	0.750310	+	0.273091i	0.0615741	+	0.998103i	$0.480388\pi$
$968$		0			0
$969$	−796352.	+	1.31248e6i	−0.848120	+	1.39780i
$970$		0			0
$971$	−422780.	+	1.16158e6i	−0.448410	+	1.23200i	0.485420	+	0.874281i	$0.338667\pi$
$971$	−422780.	+	1.16158e6i	−0.448410	+	1.23200i	−0.933830	+	0.357716i	$0.883556\pi$
$972$		0			0
$973$	79778.4	+	66942.1i	0.0842675	+	0.0707088i
$974$		0			0
$975$	181649.	−	1.03019e6i	0.191084	−	1.08369i
$976$		0			0
$977$	−1.18840e6	+	686121.i	−1.24501	+	0.718806i	−0.970110	−	0.242667i	$-0.921978\pi$
$977$	−1.18840e6	+	686121.i	−1.24501	+	0.718806i	−0.274899	+	0.961473i	$0.588644\pi$
$978$		0			0
$979$	732245.	+	2.01183e6i	0.763996	+	2.09906i
$980$		0			0
$981$	204339.	+	117975.i	0.212331	+	0.122589i
$982$		0			0
$983$	29587.7	+	35261.2i	0.0306199	+	0.0364914i	0.781137	−	0.624360i	$-0.214640\pi$
$983$	29587.7	+	35261.2i	0.0306199	+	0.0364914i	−0.750517	+	0.660851i	$0.770196\pi$
$984$		0			0
$985$	1925.85	+	10922.0i	0.00198495	+	0.0112572i
$986$		0			0
$987$		−	581327.i		−	0.596741i
$988$		0			0
$989$	−352595.			−0.360482
$990$		0			0
$991$	656367.	−	115735.i	0.668343	−	0.117847i	0.170826	−	0.985301i	$-0.445356\pi$
$991$	656367.	−	115735.i	0.668343	−	0.117847i	0.497517	+	0.867454i	$0.334245\pi$
$992$		0			0
$993$	−212136.	+	178003.i	−0.215137	+	0.180522i
$994$		0			0
$995$	−12328.9	+	21354.3i	−0.0124531	+	0.0215694i
$996$		0			0
$997$	1.73997e6	−	633296.i	1.75045	−	0.637113i	0.750730	−	0.660609i	$-0.229702\pi$
$997$	1.73997e6	−	633296.i	1.75045	−	0.637113i	0.999724	+	0.0234964i	$0.00747981\pi$
$998$		0			0
$999$	436293.	+	755682.i	0.437167	+	0.757195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.53.2	yes	42
19.14	odd	18	inner	76.5.j.a.33.2	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.2	✓	42	19.14	odd	18	inner
76.5.j.a.53.2	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)

\(f(q)\)	\(=\)	\(q+(-7.79937 + 1.37524i) q^{3} +(0.638039 - 0.535378i) q^{5} +(23.1636 - 40.1206i) q^{7} +(-17.1762 + 6.25164i) q^{9} +O(q^{10})\)	\(q+(-7.79937 + 1.37524i) q^{3} +(0.638039 - 0.535378i) q^{5} +(23.1636 - 40.1206i) q^{7} +(-17.1762 + 6.25164i) q^{9} +(95.5660 + 165.525i) q^{11} +(208.358 + 36.7391i) q^{13} +(-4.24003 + 5.05307i) q^{15} +(504.579 + 183.652i) q^{17} +(130.825 - 336.461i) q^{19} +(-125.486 + 344.771i) q^{21} +(-238.506 - 200.131i) q^{23} +(-108.410 + 614.822i) q^{25} +(680.917 - 393.128i) q^{27} +(67.5830 + 185.683i) q^{29} +(-677.986 - 391.435i) q^{31} +(-972.991 - 1159.57i) q^{33} +(-6.70040 - 37.9998i) q^{35} +1109.80i q^{37} -1675.58 q^{39} +(1014.78 - 178.934i) q^{41} +(867.530 - 727.944i) q^{43} +(-7.61212 + 13.1846i) q^{45} +(-1488.89 + 541.910i) q^{47} +(127.391 + 220.647i) q^{49} +(-4187.96 - 738.451i) q^{51} +(623.443 - 742.990i) q^{53} +(149.593 + 54.4476i) q^{55} +(-557.642 + 2804.10i) q^{57} +(1659.58 - 4559.66i) q^{59} +(-3868.03 - 3245.67i) q^{61} +(-147.045 + 833.932i) q^{63} +(152.610 - 88.1093i) q^{65} +(-70.2062 - 192.890i) q^{67} +(2135.43 + 1232.89i) q^{69} +(3442.94 + 4103.13i) q^{71} +(1418.98 + 8047.43i) q^{73} -4944.31i q^{75} +8854.63 q^{77} +(5647.18 - 995.751i) q^{79} +(-3635.90 + 3050.88i) q^{81} +(-2389.76 + 4139.18i) q^{83} +(420.264 - 152.964i) q^{85} +(-782.463 - 1355.27i) q^{87} +(11031.2 + 1945.10i) q^{89} +(6300.32 - 7508.43i) q^{91} +(5826.18 + 2120.56i) q^{93} +(-96.6620 - 284.716i) q^{95} +(613.294 - 1685.01i) q^{97} +(-2676.27 - 2245.66i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 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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