LMFDB - Embedded newform 92.5.f.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(5,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("92.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.f (of order $22$, degree $10$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	92.5
Dual form			92.5.f.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.5723 - 12.2011i) q^{3} +(-24.5957 - 3.53633i) q^{5} +(14.8856 - 6.79802i) q^{7} +(-25.5654 - 177.811i) q^{9} +O(q^{10})$	\(q+(10.5723 - 12.2011i) q^{3} +(-24.5957 - 3.53633i) q^{5} +(14.8856 - 6.79802i) q^{7} +(-25.5654 - 177.811i) q^{9} +(-21.9521 - 74.7621i) q^{11} +(11.8188 - 25.8795i) q^{13} +(-303.180 + 262.707i) q^{15} +(-89.1503 - 138.721i) q^{17} +(-285.244 + 443.848i) q^{19} +(74.4316 - 253.491i) q^{21} +(524.777 - 66.7096i) q^{23} +(-7.24015 - 2.12590i) q^{25} +(-1339.68 - 860.958i) q^{27} +(1006.38 - 646.763i) q^{29} +(-702.489 - 810.715i) q^{31} +(-1144.26 - 522.568i) q^{33} +(-390.161 + 114.562i) q^{35} +(1998.19 - 287.296i) q^{37} +(-190.806 - 417.807i) q^{39} +(41.9672 - 291.888i) q^{41} +(1887.85 + 1635.83i) q^{43} +4463.80i q^{45} +4207.33 q^{47} +(-1396.95 + 1612.17i) q^{49} +(-2635.06 - 378.865i) q^{51} +(-504.747 + 230.510i) q^{53} +(275.545 + 1916.46i) q^{55} +(2399.74 + 8172.77i) q^{57} +(789.929 - 1729.70i) q^{59} +(-2094.56 + 1814.95i) q^{61} +(-1589.32 - 2473.03i) q^{63} +(-382.209 + 594.729i) q^{65} +(2199.71 - 7491.52i) q^{67} +(4734.17 - 7108.12i) q^{69} +(2887.18 + 847.751i) q^{71} +(3635.24 + 2336.23i) q^{73} +(-102.483 + 65.8620i) q^{75} +(-835.005 - 963.647i) q^{77} +(-2021.77 - 923.312i) q^{79} +(-10706.6 + 3143.76i) q^{81} +(-3685.57 + 529.905i) q^{83} +(1702.15 + 3727.19i) q^{85} +(2748.57 - 19116.7i) q^{87} +(6102.84 + 5288.14i) q^{89} -465.575i q^{91} -17318.5 q^{93} +(8585.36 - 9908.04i) q^{95} +(-1075.38 - 154.616i) q^{97} +(-12732.3 + 5814.67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 10 q^{3} - 318 q^{9}+O(q^{10}) $ 80 * q + 10 * q^3 - 318 * q^9	$ 80 q + 10 q^{3} - 318 q^{9} + 2 q^{13} + 1463 q^{15} - 495 q^{17} - 957 q^{19} - 1353 q^{21} + 1614 q^{23} + 1890 q^{25} + 4723 q^{27} - 1617 q^{29} - 3271 q^{31} - 6655 q^{33} - 5280 q^{35} + 3520 q^{37} + 6138 q^{39} + 11370 q^{41} + 7216 q^{43} - 270 q^{47} - 14512 q^{49} - 17424 q^{51} - 7392 q^{53} + 5746 q^{55} + 18381 q^{57} + 11772 q^{59} - 22484 q^{61} - 27775 q^{63} - 27951 q^{65} - 2926 q^{67} + 15769 q^{69} + 19779 q^{71} + 24400 q^{73} + 2809 q^{75} + 19839 q^{77} + 21604 q^{79} + 22224 q^{81} - 11253 q^{83} - 25594 q^{85} + 45506 q^{87} + 7656 q^{89} + 7970 q^{93} - 22437 q^{95} + 32439 q^{97} - 48477 q^{99}+O(q^{100}) $ 80 * q + 10 * q^3 - 318 * q^9 + 2 * q^13 + 1463 * q^15 - 495 * q^17 - 957 * q^19 - 1353 * q^21 + 1614 * q^23 + 1890 * q^25 + 4723 * q^27 - 1617 * q^29 - 3271 * q^31 - 6655 * q^33 - 5280 * q^35 + 3520 * q^37 + 6138 * q^39 + 11370 * q^41 + 7216 * q^43 - 270 * q^47 - 14512 * q^49 - 17424 * q^51 - 7392 * q^53 + 5746 * q^55 + 18381 * q^57 + 11772 * q^59 - 22484 * q^61 - 27775 * q^63 - 27951 * q^65 - 2926 * q^67 + 15769 * q^69 + 19779 * q^71 + 24400 * q^73 + 2809 * q^75 + 19839 * q^77 + 21604 * q^79 + 22224 * q^81 - 11253 * q^83 - 25594 * q^85 + 45506 * q^87 + 7656 * q^89 + 7970 * q^93 - 22437 * q^95 + 32439 * q^97 - 48477 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$

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
$3$	10.5723	−	12.2011i	1.17470	−	1.35568i	0.253144	−	0.967428i	$-0.418535\pi$
$3$	10.5723	−	12.2011i	1.17470	−	1.35568i	0.921555	−	0.388247i	$-0.126919\pi$
$4$		0			0
$5$	−24.5957	−	3.53633i	−0.983828	−	0.141453i	−0.368418	−	0.929660i	$-0.620100\pi$
$5$	−24.5957	−	3.53633i	−0.983828	−	0.141453i	−0.615410	+	0.788207i	$0.711010\pi$
$6$		0			0
$7$	14.8856	−	6.79802i	0.303787	−	0.138735i	−0.257689	−	0.966228i	$-0.582961\pi$
$7$	14.8856	−	6.79802i	0.303787	−	0.138735i	0.561476	+	0.827493i	$0.310234\pi$
$8$		0			0
$9$	−25.5654	−	177.811i	−0.315622	−	2.19520i
$10$		0			0
$11$	−21.9521	−	74.7621i	−0.181423	−	0.617869i	−0.999109	−	0.0422048i	$-0.986562\pi$
$11$	−21.9521	−	74.7621i	−0.181423	−	0.617869i	0.817686	−	0.575664i	$-0.195256\pi$
$12$		0			0
$13$	11.8188	−	25.8795i	0.0699335	−	0.153133i	−0.871437	−	0.490507i	$-0.836811\pi$
$13$	11.8188	−	25.8795i	0.0699335	−	0.153133i	0.941371	+	0.337374i	$0.109539\pi$
$14$		0			0
$15$	−303.180	+	262.707i	−1.34747	+	1.16759i
$16$		0			0
$17$	−89.1503	−	138.721i	−0.308478	−	0.480002i	0.652053	−	0.758173i	$-0.273908\pi$
$17$	−89.1503	−	138.721i	−0.308478	−	0.480002i	−0.960531	+	0.278172i	$0.910272\pi$
$18$		0			0
$19$	−285.244	+	443.848i	−0.790149	+	1.22950i	0.179201	+	0.983812i	$0.442649\pi$
$19$	−285.244	+	443.848i	−0.790149	+	1.22950i	−0.969350	+	0.245683i	$0.920988\pi$
$20$		0			0
$21$	74.4316	−	253.491i	0.168779	−	0.574809i
$22$		0			0
$23$	524.777	−	66.7096i	0.992017	−	0.126105i
$23$	524.777	−	66.7096i	0.992017	−	0.126105i
$24$		0			0
$25$	−7.24015	−	2.12590i	−0.0115842	−	0.00340144i
$26$		0			0
$27$	−1339.68	−	860.958i	−1.83769	−	1.18101i
$28$		0			0
$29$	1006.38	−	646.763i	1.19665	−	0.769040i	0.218277	−	0.975887i	$-0.429956\pi$
$29$	1006.38	−	646.763i	1.19665	−	0.769040i	0.978373	+	0.206847i	$0.0663201\pi$
$30$		0			0
$31$	−702.489	−	810.715i	−0.730998	−	0.843617i	0.261586	−	0.965180i	$-0.415755\pi$
$31$	−702.489	−	810.715i	−0.730998	−	0.843617i	−0.992584	+	0.121564i	$0.961209\pi$
$32$		0			0
$33$	−1144.26	−	522.568i	−1.05075	−	0.479860i
$34$		0			0
$35$	−390.161	+	114.562i	−0.318499	+	0.0935198i
$36$		0			0
$37$	1998.19	−	287.296i	1.45960	−	0.209858i	0.633655	−	0.773616i	$-0.281554\pi$
$37$	1998.19	−	287.296i	1.45960	−	0.209858i	0.825940	+	0.563757i	$0.190645\pi$
$38$		0			0
$39$	−190.806	−	417.807i	−0.125448	−	0.274693i
$40$		0			0
$41$	41.9672	−	291.888i	0.0249656	−	0.173640i	−0.973524	−	0.228586i	$-0.926590\pi$
$41$	41.9672	−	291.888i	0.0249656	−	0.173640i	0.998489	+	0.0549465i	$0.0174988\pi$
$42$		0			0
$43$	1887.85	+	1635.83i	1.02101	+	0.884711i	0.993376	−	0.114907i	$-0.0366570\pi$
$43$	1887.85	+	1635.83i	1.02101	+	0.884711i	0.0276348	+	0.999618i	$0.491202\pi$
$44$		0			0
$45$			4463.80i			2.20435i
$46$		0			0
$47$	4207.33			1.90463			0.952315	−	0.305117i	$-0.0986956\pi$
$47$	4207.33			1.90463			0.952315	+	0.305117i	$0.0986956\pi$
$48$		0			0
$49$	−1396.95	+	1612.17i	−0.581821	+	0.671458i
$50$		0			0
$51$	−2635.06	−	378.865i	−1.01310	−	0.145661i
$52$		0			0
$53$	−504.747	+	230.510i	−0.179689	+	0.0820613i	−0.503228	−	0.864153i	$-0.667855\pi$
$53$	−504.747	+	230.510i	−0.179689	+	0.0820613i	0.323539	+	0.946215i	$0.395127\pi$
$54$		0			0
$55$	275.545	+	1916.46i	0.0910892	+	0.633539i
$56$		0			0
$57$	2399.74	+	8172.77i	0.738610	+	2.51547i
$58$		0			0
$59$	789.929	−	1729.70i	0.226926	−	0.496898i	−0.761582	−	0.648069i	$-0.775577\pi$
$59$	789.929	−	1729.70i	0.226926	−	0.496898i	0.988508	+	0.151170i	$0.0483042\pi$
$60$		0			0
$61$	−2094.56	+	1814.95i	−0.562903	+	0.487758i	−0.889206	−	0.457507i	$-0.848742\pi$
$61$	−2094.56	+	1814.95i	−0.562903	+	0.487758i	0.326303	+	0.945265i	$0.394197\pi$
$62$		0			0
$63$	−1589.32	−	2473.03i	−0.400434	−	0.623087i
$64$		0			0
$65$	−382.209	+	594.729i	−0.0904637	+	0.140764i
$66$		0			0
$67$	2199.71	−	7491.52i	0.490022	−	1.66886i	−0.228647	−	0.973509i	$-0.573430\pi$
$67$	2199.71	−	7491.52i	0.490022	−	1.66886i	0.718669	−	0.695352i	$-0.244752\pi$
$68$		0			0
$69$	4734.17	−	7108.12i	0.994364	−	1.49299i
$70$		0			0
$71$	2887.18	+	847.751i	0.572739	+	0.168171i	0.555261	−	0.831676i	$-0.312618\pi$
$71$	2887.18	+	847.751i	0.572739	+	0.168171i	0.0174775	+	0.999847i	$0.494436\pi$
$72$		0			0
$73$	3635.24	+	2336.23i	0.682162	+	0.438399i	0.835292	−	0.549807i	$-0.185299\pi$
$73$	3635.24	+	2336.23i	0.682162	+	0.438399i	−0.153130	+	0.988206i	$0.548935\pi$
$74$		0			0
$75$	−102.483	+	65.8620i	−0.0182192	+	0.0117088i
$76$		0			0
$77$	−835.005	−	963.647i	−0.140834	−	0.162531i
$78$		0			0
$79$	−2021.77	−	923.312i	−0.323950	−	0.147943i	0.246801	−	0.969066i	$-0.420621\pi$
$79$	−2021.77	−	923.312i	−0.323950	−	0.147943i	−0.570751	+	0.821123i	$0.693348\pi$
$80$		0			0
$81$	−10706.6	+	3143.76i	−1.63186	+	0.479158i
$82$		0			0
$83$	−3685.57	+	529.905i	−0.534994	+	0.0769205i	−0.404516	−	0.914531i	$-0.632560\pi$
$83$	−3685.57	+	529.905i	−0.534994	+	0.0769205i	−0.130477	+	0.991451i	$0.541651\pi$
$84$		0			0
$85$	1702.15	+	3727.19i	0.235592	+	0.515874i
$86$		0			0
$87$	2748.57	−	19116.7i	0.363135	−	2.52566i
$88$		0			0
$89$	6102.84	+	5288.14i	0.770463	+	0.667610i	0.948629	−	0.316390i	$-0.102471\pi$
$89$	6102.84	+	5288.14i	0.770463	+	0.667610i	−0.178166	+	0.984000i	$0.557016\pi$
$90$		0			0
$91$		−	465.575i		−	0.0562221i
$92$		0			0
$93$	−17318.5			−2.00237
$94$		0			0
$95$	8585.36	−	9908.04i	0.951287	−	1.09784i
$96$		0			0
$97$	−1075.38	−	154.616i	−0.114293	−	0.0164328i	0.0849311	−	0.996387i	$-0.472933\pi$
$97$	−1075.38	−	154.616i	−0.114293	−	0.0164328i	−0.199224	+	0.979954i	$0.563842\pi$
$98$		0			0
$99$	−12732.3	+	5814.67i	−1.29909	+	0.593273i
$100$		0			0
$101$	−651.083	−	4528.38i	−0.0638254	−	0.443915i	−0.996527	−	0.0832670i	$-0.973465\pi$
$101$	−651.083	−	4528.38i	−0.0638254	−	0.443915i	0.932702	−	0.360648i	$-0.117445\pi$
$102$		0			0
$103$	4875.10	+	16603.1i	0.459525	+	1.56500i	0.785030	+	0.619458i	$0.212648\pi$
$103$	4875.10	+	16603.1i	0.459525	+	1.56500i	−0.325505	+	0.945540i	$0.605534\pi$
$104$		0			0
$105$	−2727.12	+	5971.57i	−0.247358	+	0.541639i
$106$		0			0
$107$	−13228.0	+	11462.2i	−1.15539	+	1.00115i	−0.155477	+	0.987839i	$0.549692\pi$
$107$	−13228.0	+	11462.2i	−1.15539	+	1.00115i	−0.999911	+	0.0133107i	$0.995763\pi$
$108$		0			0
$109$	−4008.41	−	6237.20i	−0.337380	−	0.524973i	0.630565	−	0.776136i	$-0.282823\pi$
$109$	−4008.41	−	6237.20i	−0.337380	−	0.524973i	−0.967945	+	0.251164i	$0.919187\pi$
$110$		0			0
$111$	17620.1	−	27417.4i	1.43009	−	2.22526i
$112$		0			0
$113$	−2698.78	+	9191.20i	−0.211354	+	0.719806i	0.783759	+	0.621065i	$0.213300\pi$
$113$	−2698.78	+	9191.20i	−0.211354	+	0.719806i	−0.995113	+	0.0987410i	$0.968518\pi$
$114$		0			0
$115$	−13143.2	−	215.014i	−0.993812	−	0.0162581i
$116$		0			0
$117$	−4903.82	−	1439.89i	−0.358231	−	0.105186i
$118$		0			0
$119$	−2270.08	−	1458.89i	−0.160305	−	0.103022i
$120$		0			0
$121$	7209.31	−	4633.14i	0.492406	−	0.316450i
$122$		0			0
$123$	−3117.66	−	3597.97i	−0.206072	−	0.237820i
$124$		0			0
$125$	14297.5	+	6529.45i	0.915040	+	0.417885i
$126$		0			0
$127$	−10266.7	+	3014.57i	−0.636535	+	0.186904i	−0.584049	−	0.811718i	$-0.698533\pi$
$127$	−10266.7	+	3014.57i	−0.636535	+	0.186904i	−0.0524857	+	0.998622i	$0.516714\pi$
$128$		0			0
$129$	39917.8	−	5739.32i	2.39876	−	0.344890i
$130$		0			0
$131$	−13917.0	−	30474.1i	−0.810969	−	1.77577i	−0.603189	−	0.797598i	$-0.706104\pi$
$131$	−13917.0	−	30474.1i	−0.810969	−	1.77577i	−0.207780	−	0.978176i	$-0.566624\pi$
$132$		0			0
$133$	−1228.73	+	8546.03i	−0.0694631	+	0.483127i
$134$		0			0
$135$	29905.6	+	25913.4i	1.64091	+	1.42186i
$136$		0			0
$137$		−	23419.8i		−	1.24779i	−0.781509	−	0.623895i	$-0.785549\pi$
$137$		−	23419.8i		−	1.24779i	0.781509	−	0.623895i	$-0.214451\pi$
$138$		0			0
$139$	−36674.3			−1.89816			−0.949080	−	0.315036i	$-0.897984\pi$
$139$	−36674.3			−1.89816			−0.949080	+	0.315036i	$0.897984\pi$
$140$		0			0
$141$	44481.1	−	51333.9i	2.23737	−	2.58206i
$142$		0			0
$143$	−2194.25	−	315.486i	−0.107304	−	0.0154279i
$144$		0			0
$145$	−27039.9	+	12348.7i	−1.28608	+	0.587334i
$146$		0			0
$147$	4901.21	+	34088.7i	0.226813	+	1.57752i
$148$		0			0
$149$	5667.65	+	19302.2i	0.255288	+	0.869431i	0.983009	+	0.183558i	$0.0587614\pi$
$149$	5667.65	+	19302.2i	0.255288	+	0.869431i	−0.727721	+	0.685873i	$0.759420\pi$
$150$		0			0
$151$	−9215.92	+	20180.0i	−0.404189	+	0.885051i	0.592639	+	0.805468i	$0.298086\pi$
$151$	−9215.92	+	20180.0i	−0.404189	+	0.885051i	−0.996828	+	0.0795826i	$0.974641\pi$
$152$		0			0
$153$	−22386.9	+	19398.4i	−0.956338	+	0.828672i
$154$		0			0
$155$	14411.3	+	22424.3i	0.599844	+	0.933376i
$156$		0			0
$157$	−10171.3	+	15826.8i	−0.412645	+	0.642088i	−0.983907	−	0.178680i	$-0.942817\pi$
$157$	−10171.3	+	15826.8i	−0.412645	+	0.642088i	0.571262	+	0.820767i	$0.306454\pi$
$158$		0			0
$159$	−2523.86	+	8595.49i	−0.0998324	+	0.339998i
$160$		0			0
$161$	7358.12	−	4560.45i	0.283867	−	0.175937i
$162$		0			0
$163$	−13548.8	−	3978.29i	−0.509949	−	0.149734i	0.0166285	−	0.999862i	$-0.494707\pi$
$163$	−13548.8	−	3978.29i	−0.509949	−	0.149734i	−0.526577	+	0.850127i	$0.676525\pi$
$164$		0			0
$165$	26296.0	+	16899.4i	0.965877	+	0.620731i
$166$		0			0
$167$	23504.2	−	15105.2i	0.842776	−	0.541619i	−0.0465379	−	0.998917i	$-0.514819\pi$
$167$	23504.2	−	15105.2i	0.842776	−	0.541619i	0.889314	+	0.457297i	$0.151182\pi$
$168$		0			0
$169$	18173.4	+	20973.2i	0.636302	+	0.734331i
$170$		0			0
$171$	86213.6	+	39372.4i	2.94838	+	1.34648i
$172$		0			0
$173$	−38802.0	+	11393.3i	−1.29647	+	0.380678i	−0.855947	−	0.517064i	$-0.827025\pi$
$173$	−38802.0	+	11393.3i	−1.29647	+	0.380678i	−0.440523	+	0.897741i	$0.645207\pi$
$174$		0			0
$175$	−122.226	+	17.5734i	−0.00399104	+	0.000573825i
$176$		0			0
$177$	−12752.9	−	27924.9i	−0.407063	−	0.891344i
$178$		0			0
$179$	6129.12	−	42629.0i	0.191290	−	1.33045i	−0.637309	−	0.770608i	$-0.719953\pi$
$179$	6129.12	−	42629.0i	0.191290	−	1.33045i	0.828599	−	0.559842i	$-0.189138\pi$
$180$		0			0
$181$	8869.37	+	7685.35i	0.270730	+	0.234588i	0.779635	−	0.626234i	$-0.215404\pi$
$181$	8869.37	+	7685.35i	0.270730	+	0.234588i	−0.508906	+	0.860822i	$0.669950\pi$
$182$		0			0
$183$			44744.1i			1.33608i
$184$		0			0
$185$	−50162.8			−1.46568
$186$		0			0
$187$	−8414.00	+	9710.27i	−0.240613	+	0.277682i
$188$		0			0
$189$	−25794.7	−	3708.71i	−0.722115	−	0.103824i
$190$		0			0
$191$	20399.2	−	9316.01i	0.559173	−	0.255366i	−0.115719	−	0.993282i	$-0.536917\pi$
$191$	20399.2	−	9316.01i	0.559173	−	0.255366i	0.674893	+	0.737916i	$0.264190\pi$
$192$		0			0
$193$	1328.94	+	9242.95i	0.0356771	+	0.248140i	0.999853	−	0.0171226i	$-0.00545056\pi$
$193$	1328.94	+	9242.95i	0.0356771	+	0.248140i	−0.964176	+	0.265262i	$0.914541\pi$
$194$		0			0
$195$	3215.51	+	10951.0i	0.0845630	+	0.287995i
$196$		0			0
$197$	29012.8	−	63529.2i	0.747580	−	1.63697i	−0.0230879	−	0.999733i	$-0.507350\pi$
$197$	29012.8	−	63529.2i	0.747580	−	1.63697i	0.770667	−	0.637237i	$-0.219923\pi$
$198$		0			0
$199$	−35714.5	+	30946.8i	−0.901859	+	0.781466i	−0.976449	−	0.215749i	$-0.930781\pi$
$199$	−35714.5	+	30946.8i	−0.901859	+	0.781466i	0.0745895	+	0.997214i	$0.476235\pi$
$200$		0			0
$201$	−68148.7	−	106041.i	−1.68681	−	2.62472i
$202$		0			0
$203$	10583.9	−	16468.8i	0.256834	−	0.399642i
$204$		0			0
$205$	−2064.42	+	7030.79i	−0.0491237	+	0.167300i
$206$		0			0
$207$	−25277.9	−	91605.9i	−0.589929	−	2.13788i
$208$		0			0
$209$	39444.7	+	11582.0i	0.903018	+	0.265150i
$210$		0			0
$211$	−26493.6	−	17026.4i	−0.595081	−	0.382435i	0.208156	−	0.978096i	$-0.433254\pi$
$211$	−26493.6	−	17026.4i	−0.595081	−	0.382435i	−0.803236	+	0.595661i	$0.796890\pi$
$212$		0			0
$213$	40867.6	−	26264.0i	0.900782	−	0.578897i
$214$		0			0
$215$	−40648.1	−	46910.5i	−0.879354	−	1.01483i
$216$		0			0
$217$	−15968.2	−	7292.44i	−0.339107	−	0.154865i
$218$		0			0
$219$	66937.4	−	19654.6i	1.39566	−	0.409803i
$220$		0			0
$221$	−4643.66	+	667.658i	−0.0950771	+	0.0136700i
$222$		0			0
$223$	11262.3	+	24661.1i	0.226474	+	0.495909i	0.988422	−	0.151729i	$-0.0484841\pi$
$223$	11262.3	+	24661.1i	0.226474	+	0.495909i	−0.761948	+	0.647638i	$0.775757\pi$
$224$		0			0
$225$	−192.912	+	1341.73i	−0.00381060	+	0.0265033i
$226$		0			0
$227$	16415.1	+	14223.8i	0.318561	+	0.276035i	0.799432	−	0.600757i	$-0.205134\pi$
$227$	16415.1	+	14223.8i	0.318561	+	0.276035i	−0.480871	+	0.876792i	$0.659679\pi$
$228$		0			0
$229$			1660.19i			0.0316582i	0.999875	+	0.0158291i	$0.00503877\pi$
$229$			1660.19i			0.0316582i	−0.999875	+	0.0158291i	$0.994961\pi$
$230$		0			0
$231$	−20585.4			−0.385777
$232$		0			0
$233$	−53645.3	+	61910.0i	−0.988143	+	1.14038i	0.00195492	+	0.999998i	$0.499378\pi$
$233$	−53645.3	+	61910.0i	−0.988143	+	1.14038i	−0.990098	+	0.140380i	$0.955168\pi$
$234$		0			0
$235$	−103482.	−	14878.5i	−1.87383	−	0.269416i
$236$		0			0
$237$	−32640.2	+	14906.3i	−0.581107	+	0.265383i
$238$		0			0
$239$	7178.78	+	49929.5i	0.125677	+	0.874101i	0.950945	+	0.309360i	$0.100115\pi$
$239$	7178.78	+	49929.5i	0.125677	+	0.874101i	−0.825268	+	0.564741i	$0.808976\pi$
$240$		0			0
$241$	19360.3	+	65935.0i	0.333332	+	1.13523i	0.940257	+	0.340466i	$0.110585\pi$
$241$	19360.3	+	65935.0i	0.333332	+	1.13523i	−0.606925	+	0.794759i	$0.707597\pi$
$242$		0			0
$243$	−21252.0	+	46535.5i	−0.359905	+	0.788082i
$244$		0			0
$245$	40060.2	−	34712.4i	0.667392	−	0.578298i
$246$		0			0
$247$	8115.33	+	12627.7i	0.133019	+	0.206981i
$248$		0			0
$249$	−32499.5	+	50570.3i	−0.524178	+	0.815636i
$250$		0			0
$251$	−1754.68	+	5975.89i	−0.0278516	+	0.0948539i	−0.972246	−	0.233961i	$-0.924831\pi$
$251$	−1754.68	+	5975.89i	−0.0278516	+	0.0948539i	0.944394	+	0.328815i	$0.106649\pi$
$252$		0			0
$253$	−16507.3	−	37769.0i	−0.257891	−	0.590058i
$254$		0			0
$255$	63471.4	+	18636.9i	0.976108	+	0.286611i
$256$		0			0
$257$	81029.1	+	52074.3i	1.22680	+	0.788419i	0.983390	−	0.181504i	$-0.0580965\pi$
$257$	81029.1	+	52074.3i	1.22680	+	0.788419i	0.243413	+	0.969923i	$0.421733\pi$
$258$		0			0
$259$	27791.1	−	17860.3i	0.414292	−	0.266249i
$260$		0			0
$261$	−140730.	−	162412.i	−2.06589	−	2.38416i
$262$		0			0
$263$	−31125.7	−	14214.6i	−0.449995	−	0.205506i	0.177509	−	0.984119i	$-0.443196\pi$
$263$	−31125.7	−	14214.6i	−0.449995	−	0.205506i	−0.627504	+	0.778613i	$0.715923\pi$
$264$		0			0
$265$	13229.8	−	3884.61i	0.188391	−	0.0553166i
$266$		0			0
$267$	129042.	−	18553.4i	1.81013	−	0.260257i
$268$		0			0
$269$	7996.03	+	17508.9i	0.110502	+	0.241965i	0.956802	−	0.290742i	$-0.0939020\pi$
$269$	7996.03	+	17508.9i	0.110502	+	0.241965i	−0.846300	+	0.532707i	$0.821175\pi$
$270$		0			0
$271$	−3142.30	+	21855.2i	−0.0427867	+	0.297588i	0.957181	+	0.289492i	$0.0934862\pi$
$271$	−3142.30	+	21855.2i	−0.0427867	+	0.297588i	−0.999967	+	0.00809625i	$0.997423\pi$
$272$		0			0
$273$	−5680.52	−	4922.20i	−0.0762190	−	0.0660441i
$274$		0			0
$275$			587.957i			0.00777463i
$276$		0			0
$277$	63972.1			0.833740			0.416870	−	0.908966i	$-0.363127\pi$
$277$	63972.1			0.833740			0.416870	+	0.908966i	$0.363127\pi$
$278$		0			0
$279$	−126195.	+	145637.i	−1.62119	+	1.87095i
$280$		0			0
$281$	33253.7	+	4781.16i	0.421141	+	0.0605509i	0.349628	−	0.936889i	$-0.386308\pi$
$281$	33253.7	+	4781.16i	0.421141	+	0.0605509i	0.0715131	+	0.997440i	$0.477217\pi$
$282$		0			0
$283$	59074.5	−	26978.4i	0.737611	−	0.336856i	−0.0109337	−	0.999940i	$-0.503480\pi$
$283$	59074.5	−	26978.4i	0.737611	−	0.336856i	0.748544	+	0.663085i	$0.230753\pi$
$284$		0			0
$285$	−30121.8	−	209501.i	−0.370843	−	2.57927i
$286$		0			0
$287$	−1359.55	−	4630.22i	−0.0165057	−	0.0562131i
$288$		0			0
$289$	23400.3	−	51239.4i	0.280172	−	0.613492i
$290$		0			0
$291$	−13255.7	+	11486.1i	−0.156537	+	0.135640i
$292$		0			0
$293$	−6573.28	−	10228.2i	−0.0765679	−	0.119142i	0.800858	−	0.598855i	$-0.204377\pi$
$293$	−6573.28	−	10228.2i	−0.0765679	−	0.119142i	−0.877426	+	0.479713i	$0.840741\pi$
$294$		0			0
$295$	−25545.6	+	39749.8i	−0.293544	+	0.456763i
$296$		0			0
$297$	−34958.3	+	119057.i	−0.396312	+	1.34971i
$298$		0			0
$299$	4475.81	−	14369.4i	0.0500644	−	0.160730i
$300$		0			0
$301$	39222.1	+	11516.7i	0.432911	+	0.127114i
$302$		0			0
$303$	−62134.6	−	39931.5i	−0.676781	−	0.434941i
$304$		0			0
$305$	57935.5	−	37232.9i	0.622795	−	0.400246i
$306$		0			0
$307$	104875.	+	121033.i	1.11275	+	1.28418i	0.954969	+	0.296705i	$0.0958877\pi$
$307$	104875.	+	121033.i	1.11275	+	1.28418i	0.157778	+	0.987475i	$0.449567\pi$
$308$		0			0
$309$	254116.	+	116051.i	2.66143	+	1.21544i
$310$		0			0
$311$	36919.4	−	10840.5i	0.381710	−	0.112080i	−0.0852479	−	0.996360i	$-0.527168\pi$
$311$	36919.4	−	10840.5i	0.381710	−	0.112080i	0.466958	+	0.884280i	$0.345350\pi$
$312$		0			0
$313$	48090.9	−	6914.43i	0.490879	−	0.0705778i	0.107569	−	0.994198i	$-0.465693\pi$
$313$	48090.9	−	6914.43i	0.490879	−	0.0705778i	0.383310	+	0.923620i	$0.374784\pi$
$314$		0			0
$315$	30345.0	+	66446.3i	0.305820	+	0.669653i
$316$		0			0
$317$	8580.08	−	59675.7i	0.0853833	−	0.593854i	−0.901544	−	0.432687i	$-0.857565\pi$
$317$	8580.08	−	59675.7i	0.0853833	−	0.593854i	0.986927	−	0.161166i	$-0.0515255\pi$
$318$		0			0
$319$	−70445.6	−	61041.5i	−0.692265	−	0.599851i
$320$		0			0
$321$			282578.i			2.74238i
$322$		0			0
$323$	87000.4			0.833904
$324$		0			0
$325$	−140.587	+	162.246i	−0.00133100	+	0.00153605i
$326$		0			0
$327$	−118479.	−	17034.7i	−1.10801	−	0.159308i
$328$		0			0
$329$	62628.5	−	28601.5i	0.578602	−	0.264239i
$330$		0			0
$331$	−14461.9	−	100585.i	−0.131999	−	0.918070i	−0.942945	−	0.332949i	$-0.891956\pi$
$331$	−14461.9	−	100585.i	−0.131999	−	0.918070i	0.810946	−	0.585121i	$-0.198953\pi$
$332$		0			0
$333$	−102169.	−	347955.i	−0.921362	−	3.13787i
$334$		0			0
$335$	−80595.8	+	176480.i	−0.718163	+	1.57256i
$336$		0			0
$337$	−63572.3	+	55085.7i	−0.559768	+	0.485042i	−0.888182	−	0.459492i	$-0.848031\pi$
$337$	−63572.3	+	55085.7i	−0.559768	+	0.485042i	0.328414	+	0.944534i	$0.393486\pi$
$338$		0			0
$339$	83610.3	+	130100.i	0.727546	+	1.13208i
$340$		0			0
$341$	−45189.7	+	70316.5i	−0.388625	+	0.604712i
$342$		0			0
$343$	−20904.4	+	71194.0i	−0.177685	+	0.605139i
$344$		0			0
$345$	−141577.	+	158088.i	−1.18947	+	1.32819i
$346$		0			0
$347$	−151562.	−	44502.5i	−1.25872	−	0.369594i	−0.416704	−	0.909042i	$-0.636815\pi$
$347$	−151562.	−	44502.5i	−1.25872	−	0.369594i	−0.842019	+	0.539448i	$0.818633\pi$
$348$		0			0
$349$	199636.	+	128298.i	1.63903	+	1.05334i	0.941622	+	0.336673i	$0.109302\pi$
$349$	199636.	+	128298.i	1.63903	+	1.05334i	0.697412	+	0.716670i	$0.254335\pi$
$350$		0			0
$351$	−38114.5	+	24494.7i	−0.309368	+	0.198819i
$352$		0			0
$353$	61660.4	+	71159.9i	0.494831	+	0.571066i	0.947150	−	0.320791i	$-0.103949\pi$
$353$	61660.4	+	71159.9i	0.494831	+	0.571066i	−0.452319	+	0.891856i	$0.649403\pi$
$354$		0			0
$355$	−68014.2	−	31061.0i	−0.539688	−	0.246467i
$356$		0			0
$357$	−41800.0	+	12273.6i	−0.327974	+	0.0963019i
$358$		0			0
$359$	−29134.3	+	4188.87i	−0.226056	+	0.0325019i	−0.254412	−	0.967096i	$-0.581882\pi$
$359$	−29134.3	+	4188.87i	−0.226056	+	0.0325019i	0.0283562	+	0.999598i	$0.490973\pi$
$360$		0			0
$361$	−61499.7	−	134666.i	−0.471909	−	1.03334i
$362$		0			0
$363$	19689.6	−	136944.i	0.149425	−	1.03928i
$364$		0			0
$365$	−81149.6	−	70316.6i	−0.609117	−	0.527803i
$366$		0			0
$367$		−	136008.i		−	1.00979i	−0.863180	−	0.504896i	$-0.831531\pi$
$367$		−	136008.i		−	1.00979i	0.863180	−	0.504896i	$-0.168469\pi$
$368$		0			0
$369$	−52974.0			−0.389054
$370$		0			0
$371$	−5946.44	+	6862.56i	−0.0432025	+	0.0498584i
$372$		0			0
$373$	144593.	+	20789.3i	1.03927	+	0.149424i	0.640761	−	0.767740i	$-0.278619\pi$
$373$	144593.	+	20789.3i	1.03927	+	0.149424i	0.398509	+	0.917165i	$0.369528\pi$
$374$		0			0
$375$	230824.	−	105414.i	1.64141	−	0.749608i
$376$		0			0
$377$	−4843.69	−	33688.6i	−0.0340795	−	0.237028i
$378$		0			0
$379$	−51232.2	−	174481.i	−0.356668	−	1.21470i	−0.921135	−	0.389244i	$-0.872736\pi$
$379$	−51232.2	−	174481.i	−0.356668	−	1.21470i	0.564467	−	0.825456i	$-0.309082\pi$
$380$		0			0
$381$	−71761.4	+	157135.i	−0.494357	+	1.08249i
$382$		0			0
$383$	150860.	−	130721.i	1.02843	−	0.891142i	0.0343106	−	0.999411i	$-0.489076\pi$
$383$	150860.	−	130721.i	1.02843	−	0.891142i	0.994122	+	0.108270i	$0.0345310\pi$
$384$		0			0
$385$	17129.8	+	26654.4i	0.115566	+	0.179824i
$386$		0			0
$387$	242606.	−	377502.i	1.61987	−	2.52056i
$388$		0			0
$389$	−10727.9	+	36535.7i	−0.0708947	+	0.241445i	−0.987315	−	0.158771i	$-0.949247\pi$
$389$	−10727.9	+	36535.7i	−0.0708947	+	0.241445i	0.916421	+	0.400216i	$0.131065\pi$
$390$		0			0
$391$	−56038.0	−	66850.1i	−0.366546	−	0.437269i
$392$		0			0
$393$	−518951.	−	152378.i	−3.36002	−	0.986590i
$394$		0			0
$395$	46461.8	+	29859.2i	0.297784	+	0.191374i
$396$		0			0
$397$	−146344.	+	94049.4i	−0.928524	+	0.596726i	−0.915119	−	0.403184i	$-0.867903\pi$
$397$	−146344.	+	94049.4i	−0.928524	+	0.596726i	−0.0134049	+	0.999910i	$0.504267\pi$
$398$		0			0
$399$	91280.2	+	105343.i	0.573365	+	0.661698i
$400$		0			0
$401$	−21307.2	−	9730.67i	−0.132507	−	0.0605137i	0.348058	−	0.937473i	$-0.386841\pi$
$401$	−21307.2	−	9730.67i	−0.132507	−	0.0605137i	−0.480565	+	0.876959i	$0.659568\pi$
$402$		0			0
$403$	−29283.5	+	8598.40i	−0.180307	+	0.0529429i
$404$		0			0
$405$	274455.	−	39460.7i	1.67325	−	0.240577i
$406$		0			0
$407$	−65343.3	−	143082.i	−0.394469	−	0.863766i
$408$		0			0
$409$	−24870.8	+	172981.i	−0.148677	+	1.03407i	0.769712	+	0.638392i	$0.220400\pi$
$409$	−24870.8	+	172981.i	−0.148677	+	1.03407i	−0.918389	+	0.395680i	$0.870509\pi$
$410$		0			0
$411$	−285746.	−	247601.i	−1.69160	−	1.46578i
$412$		0			0
$413$		−	31117.6i		−	0.182434i
$414$		0			0
$415$	92523.1			0.537222
$416$		0			0
$417$	−387732.	+	447467.i	−2.22977	+	2.57329i
$418$		0			0
$419$	−34535.3	−	4965.43i	−0.196714	−	0.0282832i	0.0432535	−	0.999064i	$-0.486228\pi$
$419$	−34535.3	−	4965.43i	−0.196714	−	0.0282832i	−0.239967	+	0.970781i	$0.577137\pi$
$420$		0			0
$421$	281383.	−	128503.i	1.58757	−	0.725020i	0.590916	−	0.806733i	$-0.298766\pi$
$421$	281383.	−	128503.i	1.58757	−	0.725020i	0.996656	+	0.0817132i	$0.0260391\pi$
$422$		0			0
$423$	−107562.	−	748111.i	−0.601144	−	4.18105i
$424$		0			0
$425$	350.555	+	1193.88i	0.00194079	+	0.00660972i
$426$		0			0
$427$	−18840.7	+	41255.4i	−0.103334	+	0.226269i
$428$		0			0
$429$	−27047.6	+	23436.8i	−0.146965	+	0.127346i
$430$		0			0
$431$	36092.0	+	56160.3i	0.194293	+	0.302326i	0.924707	−	0.380678i	$-0.124310\pi$
$431$	36092.0	+	56160.3i	0.194293	+	0.302326i	−0.730415	+	0.683004i	$0.760673\pi$
$432$		0			0
$433$	168046.	−	261484.i	0.896296	−	1.39466i	−0.0224216	−	0.999749i	$-0.507138\pi$
$433$	168046.	−	261484.i	0.896296	−	1.39466i	0.918718	−	0.394915i	$-0.129226\pi$
$434$		0			0
$435$	−135206.	+	460470.i	−0.714525	+	2.43345i
$436$		0			0
$437$	−120080.	+	251950.i	−0.628795	+	1.31932i
$438$		0			0
$439$	−79946.4	−	23474.4i	−0.414830	−	0.121805i	0.0676561	−	0.997709i	$-0.478448\pi$
$439$	−79946.4	−	23474.4i	−0.414830	−	0.121805i	−0.482486	+	0.875904i	$0.660266\pi$
$440$		0			0
$441$	322376.	+	207178.i	1.65762	+	1.06529i
$442$		0			0
$443$	−29021.1	+	18650.7i	−0.147879	+	0.0950359i	−0.612488	−	0.790480i	$-0.709831\pi$
$443$	−29021.1	+	18650.7i	−0.147879	+	0.0950359i	0.464609	+	0.885516i	$0.346195\pi$
$444$		0			0
$445$	−131403.	−	151647.i	−0.663568	−	0.765798i
$446$		0			0
$447$	295428.	+	134918.i	1.47855	+	0.675232i
$448$		0			0
$449$	−99796.2	+	29302.8i	−0.495018	+	0.145350i	−0.519707	−	0.854345i	$-0.673959\pi$
$449$	−99796.2	+	29302.8i	−0.495018	+	0.145350i	0.0246885	+	0.999695i	$0.492141\pi$
$450$		0			0
$451$	−22743.4	+	3270.01i	−0.111816	+	0.0160767i
$452$		0			0
$453$	148785.	+	325794.i	0.725041	+	1.58762i
$454$		0			0
$455$	−1646.43	+	11451.2i	−0.00795280	+	0.0553129i
$456$		0			0
$457$	145.420	+	126.007i	0.000696290	+	0.000603339i	0.655209	−	0.755448i	$-0.272581\pi$
$457$	145.420	+	126.007i	0.000696290	+	0.000603339i	−0.654513	+	0.756051i	$0.727126\pi$
$458$		0			0
$459$			262595.i			1.24641i
$460$		0			0
$461$	−77848.0			−0.366307			−0.183154	−	0.983084i	$-0.558631\pi$
$461$	−77848.0			−0.366307			−0.183154	+	0.983084i	$0.558631\pi$
$462$		0			0
$463$	−65727.0	+	75853.0i	−0.306607	+	0.353843i	−0.888052	−	0.459742i	$-0.847942\pi$
$463$	−65727.0	+	75853.0i	−0.306607	+	0.353843i	0.581446	+	0.813585i	$0.302487\pi$
$464$		0			0
$465$	425961.	+	61244.0i	1.96999	+	0.283242i
$466$		0			0
$467$	−286018.	+	130620.i	−1.31147	+	0.598930i	−0.943644	−	0.330963i	$-0.892626\pi$
$467$	−286018.	+	130620.i	−1.31147	+	0.598930i	−0.367830	+	0.929893i	$0.619899\pi$
$468$		0			0
$469$	−18183.5	−	126469.i	−0.0826671	−	0.574962i
$470$		0			0
$471$	85570.6	+	291427.i	0.385729	+	1.31367i
$472$		0			0
$473$	80855.9	−	177050.i	0.361401	−	0.791358i
$474$		0			0
$475$	3008.78	−	2607.12i	0.0133353	−	0.0115551i
$476$		0			0
$477$	53891.4	+	83856.7i	0.236855	+	0.368554i
$478$		0			0
$479$	−56154.0	+	87377.3i	−0.244743	+	0.380827i	−0.941792	−	0.336196i	$-0.890859\pi$
$479$	−56154.0	+	87377.3i	−0.244743	+	0.380827i	0.697049	+	0.717023i	$0.254496\pi$
$480$		0			0
$481$	16181.0	−	55107.5i	0.0699385	−	0.238189i
$482$		0			0
$483$	22149.7	−	137991.i	0.0949454	−	0.591504i
$484$		0			0
$485$	25902.9	+	7605.79i	0.110120	+	0.0323341i
$486$		0			0
$487$	87729.5	+	56380.3i	0.369903	+	0.237722i	0.712364	−	0.701810i	$-0.247624\pi$
$487$	87729.5	+	56380.3i	0.369903	+	0.237722i	−0.342462	+	0.939532i	$0.611261\pi$
$488$		0			0
$489$	−191782.	+	123251.i	−0.802028	+	0.515432i
$490$		0			0
$491$	106407.	+	122801.i	0.441377	+	0.509376i	0.932230	−	0.361867i	$-0.117860\pi$
$491$	106407.	+	122801.i	0.441377	+	0.509376i	−0.490853	+	0.871242i	$0.663315\pi$
$492$		0			0
$493$	−179439.	−	81946.8i	−0.738281	−	0.337162i
$494$		0			0
$495$	333723.	−	97990.0i	1.36200	−	0.399919i
$496$		0			0
$497$	48740.3	−	7007.80i	0.197322	−	0.0283706i
$498$		0			0
$499$	133211.	+	291692.i	0.534982	+	1.17145i	0.963450	+	0.267890i	$0.0863264\pi$
$499$	133211.	+	291692.i	0.534982	+	1.17145i	−0.428467	+	0.903557i	$0.640946\pi$
$500$		0			0
$501$	64193.2	−	446473.i	0.255749	−	1.77877i
$502$		0			0
$503$	−197069.	−	170761.i	−0.778901	−	0.674922i	0.171765	−	0.985138i	$-0.445053\pi$
$503$	−197069.	−	170761.i	−0.778901	−	0.674922i	−0.950666	+	0.310216i	$0.899599\pi$
$504$		0			0
$505$			113681.i			0.445765i
$506$		0			0
$507$	448031.			1.74298
$508$		0			0
$509$	−117954.	+	136126.i	−0.455278	+	0.525419i	−0.936258	−	0.351313i	$-0.885735\pi$
$509$	−117954.	+	136126.i	−0.455278	+	0.525419i	0.480980	+	0.876731i	$0.340281\pi$
$510$		0			0
$511$	69994.4	+	10063.7i	0.268053	+	0.0385403i
$512$		0			0
$513$	764268.	−	349030.i	2.90410	−	1.32626i
$514$		0			0
$515$	−61192.6	−	425604.i	−0.230720	−	1.60469i
$516$		0			0
$517$	−92359.8	−	314549.i	−0.345543	−	1.17681i
$518$		0			0
$519$	−271216.	+	593880.i	−1.00689	+	2.20477i
$520$		0			0
$521$	−220261.	+	190857.i	−0.811451	+	0.703127i	−0.958216	−	0.286045i	$-0.907659\pi$
$521$	−220261.	+	190857.i	−0.811451	+	0.703127i	0.146765	+	0.989171i	$0.453114\pi$
$522$		0			0
$523$	−202404.	−	314947.i	−0.739974	−	1.15142i	−0.983391	−	0.181500i	$-0.941905\pi$
$523$	−202404.	−	314947.i	−0.739974	−	1.15142i	0.243417	−	0.969922i	$-0.421732\pi$
$524$		0			0
$525$	−1077.79	+	1677.08i	−0.00391035	+	0.00608463i
$526$		0			0
$527$	−49835.8	+	169725.i	−0.179440	+	0.611118i
$528$		0			0
$529$	270941.	−	70015.3i	0.968195	−	0.250197i
$530$		0			0
$531$	−327756.	−	96237.8i	−1.16242	−	0.341316i
$532$		0			0
$533$	−7057.92	−	4535.85i	−0.0248440	−	0.0159663i
$534$		0			0
$535$	365887.	−	235141.i	1.27832	−	0.821526i
$536$		0			0
$537$	−455321.	−	525468.i	−1.57895	−	1.82221i
$538$		0			0
$539$	151195.	+	69048.6i	0.520428	+	0.237672i
$540$		0			0
$541$	−176311.	+	51769.7i	−0.602401	+	0.176881i	−0.568692	−	0.822551i	$-0.692550\pi$
$541$	−176311.	+	51769.7i	−0.602401	+	0.176881i	−0.0337092	+	0.999432i	$0.510732\pi$
$542$		0			0
$543$	187539.	−	26964.1i	0.636052	−	0.0914504i
$544$		0			0
$545$	76532.8	+	167583.i	0.257664	+	0.564206i
$546$		0			0
$547$	21432.1	−	149063.i	0.0716292	−	0.498192i	−0.922151	−	0.386831i	$-0.873570\pi$
$547$	21432.1	−	149063.i	0.0716292	−	0.498192i	0.993780	−	0.111361i	$-0.0355211\pi$
$548$		0			0
$549$	376267.	+	326037.i	1.24839	+	1.08174i
$550$		0			0
$551$			631166.i			2.07893i
$552$		0			0
$553$	−36371.9			−0.118937
$554$		0			0
$555$	−530336.	+	612040.i	−1.72173	+	1.98698i
$556$		0			0
$557$	−434943.	−	62535.3i	−1.40191	−	0.201565i	−0.600477	−	0.799642i	$-0.705022\pi$
$557$	−434943.	−	62535.3i	−1.40191	−	0.201565i	−0.801438	+	0.598077i	$0.795932\pi$
$558$		0			0
$559$	64646.5	−	29523.1i	0.206881	−	0.0944796i
$560$		0			0
$561$	29520.5	+	205320.i	0.0937991	+	0.652387i
$562$		0			0
$563$	44333.1	+	150985.i	0.139866	+	0.476339i	0.999396	−	0.0347454i	$-0.0110620\pi$
$563$	44333.1	+	150985.i	0.139866	+	0.476339i	−0.859530	+	0.511085i	$0.829244\pi$
$564$		0			0
$565$	98881.5	−	216520.i	0.309755	−	0.678269i
$566$		0			0
$567$	−138003.	+	119581.i	−0.429263	+	0.371959i
$568$		0			0
$569$	−111021.	−	172753.i	−0.342912	−	0.533581i	0.626373	−	0.779524i	$-0.284539\pi$
$569$	−111021.	−	172753.i	−0.342912	−	0.533581i	−0.969284	+	0.245943i	$0.920903\pi$
$570$		0			0
$571$	−232271.	+	361421.i	−0.712398	+	1.10851i	0.276658	+	0.960969i	$0.410773\pi$
$571$	−232271.	+	361421.i	−0.712398	+	1.10851i	−0.989055	+	0.147544i	$0.952863\pi$
$572$		0			0
$573$	102001.	−	347384.i	0.310667	−	1.05804i
$574$		0			0
$575$	−3941.28	−	632.635i	−0.0119207	−	0.00191345i
$576$		0			0
$577$	115747.	+	33986.3i	0.347662	+	0.102083i	0.450901	−	0.892574i	$-0.351103\pi$
$577$	115747.	+	33986.3i	0.347662	+	0.102083i	−0.103240	+	0.994657i	$0.532921\pi$
$578$		0			0
$579$	126824.	+	81504.8i	0.378307	+	0.243123i
$580$		0			0
$581$	−51259.6	+	32942.5i	−0.151853	+	0.0975898i
$582$		0			0
$583$	28313.7	+	32675.8i	0.0833029	+	0.0961366i
$584$		0			0
$585$	115521.	+	52756.7i	0.337559	+	0.154158i
$586$		0			0
$587$	97011.4	−	28485.1i	0.281544	−	0.0826688i	−0.137912	−	0.990445i	$-0.544039\pi$
$587$	97011.4	−	28485.1i	0.281544	−	0.0826688i	0.419456	+	0.907776i	$0.362221\pi$
$588$		0			0
$589$	560215.	−	80546.7i	1.61482	−	0.232176i
$590$		0			0
$591$	−468393.	−	1.02564e6i	−1.34102	−	2.93642i
$592$		0			0
$593$	−12339.8	+	85825.1i	−0.0350912	+	0.244065i	−0.999816	−	0.0191968i	$-0.993889\pi$
$593$	−12339.8	+	85825.1i	−0.0350912	+	0.244065i	0.964725	+	0.263261i	$0.0847982\pi$
$594$		0			0
$595$	50675.0	+	43910.2i	0.143140	+	0.124031i
$596$		0			0
$597$			762935.i			2.14062i
$598$		0			0
$599$	529996.			1.47713			0.738565	−	0.674182i	$-0.235504\pi$
$599$	529996.			1.47713			0.738565	+	0.674182i	$0.235504\pi$
$600$		0			0
$601$	132421.	−	152822.i	0.366614	−	0.423095i	−0.542231	−	0.840230i	$-0.682420\pi$
$601$	132421.	−	152822.i	0.366614	−	0.423095i	0.908845	+	0.417134i	$0.136966\pi$
$602$		0			0
$603$	−1.38831e6	−	199609.i	−3.81815	−	0.548967i
$604$		0			0
$605$	−193702.	+	88461.0i	−0.529206	+	0.241680i
$606$		0			0
$607$	−39868.7	−	277293.i	−0.108207	−	0.752596i	−0.969607	−	0.244668i	$-0.921321\pi$
$607$	−39868.7	−	277293.i	−0.108207	−	0.752596i	0.861400	−	0.507927i	$-0.169588\pi$
$608$		0			0
$609$	−89041.8	−	303248.i	−0.240082	−	0.817643i
$610$		0			0
$611$	49725.4	−	108883.i	0.133197	−	0.291662i
$612$		0			0
$613$	472201.	−	409164.i	1.25662	−	1.08887i	0.264400	−	0.964413i	$-0.414826\pi$
$613$	472201.	−	409164.i	1.25662	−	1.08887i	0.992225	−	0.124459i	$-0.0397194\pi$
$614$		0			0
$615$	63957.5	+	99519.8i	0.169099	+	0.263123i
$616$		0			0
$617$	−98718.1	+	153608.i	−0.259314	+	0.403501i	−0.946360	−	0.323113i	$-0.895271\pi$
$617$	−98718.1	+	153608.i	−0.259314	+	0.403501i	0.687046	+	0.726614i	$0.258907\pi$
$618$		0			0
$619$	−187975.	+	640183.i	−0.490589	+	1.67079i	0.226658	+	0.973974i	$0.427220\pi$
$619$	−187975.	+	640183.i	−0.490589	+	1.67079i	−0.717247	+	0.696819i	$0.754598\pi$
$620$		0			0
$621$	−760465.	−	362441.i	−1.97195	−	0.939841i
$622$		0			0
$623$	126793.	+	37229.8i	0.326678	+	0.0959213i
$624$		0			0
$625$	−324599.	−	208607.i	−0.830974	−	0.534035i
$626$		0			0
$627$	558334.	−	358820.i	1.42023	−	0.912728i
$628$		0			0
$629$	−217993.	−	251577.i	−0.550986	−	0.635872i
$630$		0			0
$631$	29782.9	+	13601.4i	0.0748011	+	0.0341605i	0.452464	−	0.891783i	$-0.350545\pi$
$631$	29782.9	+	13601.4i	0.0748011	+	0.0341605i	−0.377663	+	0.925943i	$0.623272\pi$
$632$		0			0
$633$	−487839.	+	143242.i	−1.21750	+	0.357490i
$634$		0			0
$635$	263177.	−	37839.1i	0.652679	−	0.0938411i
$636$		0			0
$637$	25211.9	+	55206.3i	0.0621336	+	0.136054i
$638$		0			0
$639$	76928.0	−	535046.i	0.188401	−	1.31036i
$640$		0			0
$641$	−40230.7	−	34860.1i	−0.0979132	−	0.0848422i	0.604529	−	0.796583i	$-0.293361\pi$
$641$	−40230.7	−	34860.1i	−0.0979132	−	0.0848422i	−0.702442	+	0.711741i	$0.747907\pi$
$642$		0			0
$643$		−	730688.i		−	1.76730i	−0.468148	−	0.883650i	$-0.655079\pi$
$643$		−	730688.i		−	1.76730i	0.468148	−	0.883650i	$-0.344921\pi$
$644$		0			0
$645$	−1.00210e6			−2.40876
$646$		0			0
$647$	462152.	−	533352.i	1.10402	−	1.27411i	0.145412	−	0.989371i	$-0.453549\pi$
$647$	462152.	−	533352.i	1.10402	−	1.27411i	0.958607	−	0.284734i	$-0.0919053\pi$
$648$		0			0
$649$	−146657.	−	21086.1i	−0.348187	−	0.0500618i
$650$		0			0
$651$	−257796.	+	117732.i	−0.608296	+	0.277799i
$652$		0			0
$653$	−2911.50	−	20249.9i	−0.00682794	−	0.0474894i	0.986123	−	0.166019i	$-0.0530912\pi$
$653$	−2911.50	−	20249.9i	−0.00682794	−	0.0474894i	−0.992951	+	0.118529i	$0.962182\pi$
$654$		0			0
$655$	234533.	+	798746.i	0.546665	+	1.86177i
$656$		0			0
$657$	322471.	−	706114.i	0.747069	−	1.63585i
$658$		0			0
$659$	−6185.73	+	5359.96i	−0.0142436	+	0.0123422i	−0.661953	−	0.749545i	$-0.730272\pi$
$659$	−6185.73	+	5359.96i	−0.0142436	+	0.0123422i	0.647710	+	0.761887i	$0.275727\pi$
$660$		0			0
$661$	−34873.3	−	54264.0i	−0.0798161	−	0.124196i	0.799050	−	0.601264i	$-0.205336\pi$
$661$	−34873.3	−	54264.0i	−0.0798161	−	0.124196i	−0.878867	+	0.477068i	$0.841700\pi$
$662$		0			0
$663$	−40948.0	+	63716.4i	−0.0931550	+	0.144952i
$664$		0			0
$665$	60443.1	−	205850.i	0.136680	−	0.465488i
$666$		0			0
$667$	484981.	−	406542.i	1.09012	−	0.913805i
$668$		0			0
$669$	419960.	+	123312.i	0.938331	+	0.275519i
$670$		0			0
$671$	181670.	+	116752.i	0.403494	+	0.259310i
$672$		0			0
$673$	322695.	−	207384.i	0.712464	−	0.457873i	−0.133544	−	0.991043i	$-0.542636\pi$
$673$	322695.	−	207384.i	0.712464	−	0.457873i	0.846008	+	0.533170i	$0.178999\pi$
$674$		0			0
$675$	7869.14	+	9081.47i	0.0172711	+	0.0199319i
$676$		0			0
$677$	345941.	+	157986.i	0.754787	+	0.344699i	0.755368	−	0.655300i	$-0.227458\pi$
$677$	345941.	+	157986.i	0.754787	+	0.344699i	−0.000581829		1.00000i	$0.500185\pi$
$678$		0			0
$679$	−17058.7	+	5008.89i	−0.0370005	+	0.0108643i
$680$		0			0
$681$	347092.	−	49904.2i	0.748428	−	0.107608i
$682$		0			0
$683$	138605.	+	303502.i	0.297123	+	0.650609i	0.998036	−	0.0626378i	$-0.0199513\pi$
$683$	138605.	+	303502.i	0.297123	+	0.650609i	−0.700913	+	0.713246i	$0.747224\pi$
$684$		0			0
$685$	−82819.9	+	576025.i	−0.176504	+	1.22761i
$686$		0			0
$687$	20256.1	+	17552.0i	0.0429183	+	0.0371889i
$688$		0			0
$689$			15786.9i			0.0332552i
$690$		0			0
$691$	−453392.			−0.949550			−0.474775	−	0.880107i	$-0.657471\pi$
$691$	−453392.			−0.949550			−0.474775	+	0.880107i	$0.657471\pi$
$692$		0			0
$693$	−150000.	+	173109.i	−0.312338	+	0.360457i
$694$		0			0
$695$	902031.	+	129693.i	1.86746	+	0.268501i
$696$		0			0
$697$	−44232.3	+	20200.2i	−0.0910487	+	0.0415805i
$698$		0			0
$699$	188215.	+	1.30906e6i	0.385211	+	2.67920i
$700$		0			0
$701$	−147821.	−	503433.i	−0.300816	−	1.02448i	−0.961725	−	0.274018i	$-0.911647\pi$
$701$	−147821.	−	503433.i	−0.300816	−	1.02448i	0.660909	−	0.750466i	$-0.270171\pi$
$702$		0			0
$703$	−442455.	+	968840.i	−0.895278	+	1.96039i
$704$		0			0
$705$	−1.27558e6	+	1.10529e6i	−2.56643	+	2.22382i
$706$		0			0
$707$	−40475.8	−	62981.5i	−0.0809760	−	0.126001i
$708$		0			0
$709$	62345.0	−	97010.7i	0.124025	−	0.192987i	−0.773689	−	0.633566i	$-0.781591\pi$
$709$	62345.0	−	97010.7i	0.124025	−	0.192987i	0.897714	+	0.440579i	$0.145227\pi$
$710$		0			0
$711$	−112488.	+	383099.i	−0.222519	+	0.757830i
$712$		0			0
$713$	−422733.	−	378582.i	−0.831547	−	0.744699i
$714$		0			0
$715$	52853.5	+	15519.2i	0.103386	+	0.0303569i
$716$		0			0
$717$	685090.	+	440281.i	1.33263	+	0.856429i
$718$		0			0
$719$	13023.3	−	8369.60i	0.0251921	−	0.0161900i	−0.527984	−	0.849254i	$-0.677052\pi$
$719$	13023.3	−	8369.60i	0.0251921	−	0.0161900i	0.553176	+	0.833064i	$0.313416\pi$
$720$		0			0
$721$	185437.	+	214005.i	0.356718	+	0.411674i
$722$		0			0
$723$	1.00916e6	+	460868.i	1.93056	+	0.881658i
$724$		0			0
$725$	−8661.31	+	2543.19i	−0.0164781	+	0.00483841i
$726$		0			0
$727$	−554431.	+	79715.2i	−1.04901	+	0.150825i	−0.645196	−	0.764017i	$-0.723224\pi$
$727$	−554431.	+	79715.2i	−1.04901	+	0.150825i	−0.403812	+	0.914842i	$0.632315\pi$
$728$		0			0
$729$	−32373.0	−	70886.9i	−0.0609154	−	0.133386i
$730$		0			0
$731$	58621.0	−	407718.i	0.109703	−	0.763001i
$732$		0			0
$733$	720481.	+	624300.i	1.34096	+	1.16194i	0.972659	+	0.232237i	$0.0746044\pi$
$733$	720481.	+	624300.i	1.34096	+	1.16194i	0.368297	+	0.929708i	$0.379941\pi$
$734$		0			0
$735$		−	855767.i		−	1.58409i
$736$		0			0
$737$	−608370.			−1.12004
$738$		0			0
$739$	186114.	−	214787.i	0.340793	−	0.393296i	−0.559321	−	0.828951i	$-0.688938\pi$
$739$	186114.	−	214787.i	0.340793	−	0.393296i	0.900113	+	0.435656i	$0.143483\pi$
$740$		0			0
$741$	239869.	+	34488.0i	0.436856	+	0.0628104i
$742$		0			0
$743$	−722126.	+	329784.i	−1.30808	+	0.597382i	−0.942752	−	0.333495i	$-0.891772\pi$
$743$	−722126.	+	329784.i	−1.30808	+	0.597382i	−0.365332	+	0.930877i	$0.619045\pi$
$744$		0			0
$745$	−71140.7	−	494795.i	−0.128176	−	0.891482i
$746$		0			0
$747$	188446.	+	641789.i	0.337712	+	1.15014i
$748$		0			0
$749$	−118987.	+	260546.i	−0.212098	+	0.464430i
$750$		0			0
$751$	−84791.1	+	73471.9i	−0.150339	+	0.130269i	−0.726783	−	0.686867i	$-0.758985\pi$
$751$	−84791.1	+	73471.9i	−0.150339	+	0.130269i	0.576444	+	0.817137i	$0.304440\pi$
$752$		0			0
$753$	54361.3	+	84587.9i	0.0958739	+	0.149183i
$754$		0			0
$755$	298035.	−	463752.i	0.522846	−	0.813564i
$756$		0			0
$757$	−72669.7	+	247490.i	−0.126812	+	0.431883i	−0.998284	−	0.0585631i	$-0.981348\pi$
$757$	−72669.7	+	247490.i	−0.126812	+	0.431883i	0.871471	+	0.490446i	$0.163166\pi$
$758$		0			0
$759$	−635343.	−	197898.i	−1.10287	−	0.343525i
$760$		0			0
$761$	930267.	+	273151.i	1.60634	+	0.471665i	0.957303	−	0.289088i	$-0.0933520\pi$
$761$	930267.	+	273151.i	1.60634	+	0.471665i	0.649041	+	0.760753i	$0.275170\pi$
$762$		0			0
$763$	−102068.	−	65595.2i	−0.175324	−	0.112674i
$764$		0			0
$765$	619221.	−	397949.i	1.05809	−	0.679994i
$766$		0			0
$767$	−35427.8	−	40885.9i	−0.0602218	−	0.0694997i
$768$		0			0
$769$	894997.	+	408731.i	1.51345	+	0.691170i	0.987248	−	0.159188i	$-0.0508876\pi$
$769$	894997.	+	408731.i	1.51345	+	0.691170i	0.526204	+	0.850358i	$0.323615\pi$
$770$		0			0
$771$	1.49203e6	−	438099.i	2.50997	−	0.736992i
$772$		0			0
$773$	−24059.0	+	3459.16i	−0.0402641	+	0.00578910i	−0.162417	−	0.986722i	$-0.551929\pi$
$773$	−24059.0	+	3459.16i	−0.0402641	+	0.00578910i	0.122153	+	0.992511i	$0.461020\pi$
$774$		0			0
$775$	3362.62	+	7363.12i	0.00559854	+	0.0122591i
$776$		0			0
$777$	75901.4	−	527906.i	0.125721	−	0.874409i
$778$		0			0
$779$	117583.	+	101886.i	0.193763	+	0.167896i
$780$		0			0
$781$		−	234461.i		−	0.384387i
$782$		0			0
$783$	−1.90506e6			−3.10732
$784$		0			0
$785$	306139.	−	353303.i	0.496797	−	0.573334i
$786$		0			0
$787$	−599573.	−	86205.6i	−0.968038	−	0.139183i	−0.359880	−	0.932999i	$-0.617182\pi$
$787$	−599573.	−	86205.6i	−0.968038	−	0.139183i	−0.608158	+	0.793816i	$0.708091\pi$
$788$		0			0
$789$	−502504.	+	229486.i	−0.807208	+	0.368639i
$790$		0			0
$791$	22309.0	+	155163.i	0.0356556	+	0.247990i
$792$		0			0
$793$	22214.8	+	75656.7i	0.0353261	+	0.120310i
$794$		0			0
$795$	92472.6	−	202487.i	0.146312	−	0.320378i
$796$		0			0
$797$	−58835.1	+	50980.9i	−0.0926232	+	0.0802585i	−0.699942	−	0.714200i	$-0.746791\pi$
$797$	−58835.1	+	50980.9i	−0.0926232	+	0.0802585i	0.607318	+	0.794459i	$0.292245\pi$
$798$		0			0
$799$	−375084.	−	583643.i	−0.587537	−	0.914226i
$800$		0			0
$801$	784270.	−	1.22035e6i	1.22236	−	1.90204i
$802$		0			0
$803$	94860.0	−	323064.i	0.147113	−	0.501022i
$804$		0			0
$805$	−197105.	+	86146.8i	−0.304163	+	0.132938i
$806$		0			0
$807$	298163.	+	87548.7i	0.457833	+	0.134432i
$808$		0			0
$809$	791114.	+	508418.i	1.20877	+	0.776826i	0.980451	−	0.196761i	$-0.0630424\pi$
$809$	791114.	+	508418.i	1.20877	+	0.776826i	0.228314	+	0.973588i	$0.426679\pi$
$810$		0			0
$811$	−497913.	+	319990.i	−0.757028	+	0.486513i	−0.861338	−	0.508032i	$-0.830373\pi$
$811$	−497913.	+	319990.i	−0.757028	+	0.486513i	0.104310	+	0.994545i	$0.466737\pi$
$812$		0			0
$813$	233435.	+	269399.i	0.353171	+	0.407581i
$814$		0			0
$815$	319174.	+	145762.i	0.480521	+	0.219447i
$816$		0			0
$817$	−1.26456e6	+	371308.i	−1.89450	+	0.556275i
$818$		0			0
$819$	−82784.6	+	11902.6i	−0.123419	+	0.0177450i
$820$		0			0
$821$	−427464.	−	936015.i	−0.634180	−	1.38866i	−0.904743	−	0.425959i	$-0.859937\pi$
$821$	−427464.	−	936015.i	−0.634180	−	1.38866i	0.270562	−	0.962703i	$-0.412790\pi$
$822$		0			0
$823$	−163828.	+	1.13945e6i	−0.241873	+	1.68226i	0.400834	+	0.916151i	$0.368720\pi$
$823$	−163828.	+	1.13945e6i	−0.241873	+	1.68226i	−0.642707	+	0.766112i	$0.722189\pi$
$824$		0			0
$825$	7173.71	+	6216.05i	0.0105399	+	0.00913286i
$826$		0			0
$827$		−	789112.i		−	1.15379i	−0.816817	−	0.576896i	$-0.804264\pi$
$827$		−	789112.i		−	1.15379i	0.816817	−	0.576896i	$-0.195736\pi$
$828$		0			0
$829$	−400589.			−0.582894			−0.291447	−	0.956587i	$-0.594137\pi$
$829$	−400589.			−0.582894			−0.291447	+	0.956587i	$0.594137\pi$
$830$		0			0
$831$	676332.	−	780528.i	0.979394	−	1.13028i
$832$		0			0
$833$	348180.	+	50060.7i	0.501780	+	0.0721451i
$834$		0			0
$835$	−631519.	+	288405.i	−0.905760	+	0.413647i
$836$		0			0
$837$	243116.	+	1.69091e6i	0.347027	+	2.41362i
$838$		0			0
$839$	165190.	+	562587.i	0.234672	+	0.799219i	0.989654	+	0.143474i	$0.0458272\pi$
$839$	165190.	+	562587.i	0.234672	+	0.799219i	−0.754982	+	0.655745i	$0.772355\pi$
$840$		0			0
$841$	300689.	−	658417.i	0.425133	−	0.930912i
$842$		0			0
$843$	409903.	−	355183.i	0.576801	−	0.499801i
$844$		0			0
$845$	−372820.	−	580119.i	−0.522138	−	0.812463i
$846$		0			0
$847$	75818.6	−	117976.i	0.105684	−	0.164447i
$848$		0			0
$849$	295387.	−	1.00600e6i	0.409804	−	1.39566i
$850$		0			0
$851$	1.02944e6	−	284064.i	1.42148	−	0.392245i
$852$		0			0
$853$	−769903.	−	226064.i	−1.05813	−	0.310694i	−0.294031	−	0.955796i	$-0.594997\pi$
$853$	−769903.	−	226064.i	−1.05813	−	0.310694i	−0.764097	+	0.645102i	$0.776815\pi$
$854$		0			0
$855$	−1.98125e6	−	1.27327e6i	−2.71024	−	1.74176i
$856$		0			0
$857$	−544023.	+	349622.i	−0.740722	+	0.476033i	−0.855789	−	0.517324i	$-0.826928\pi$
$857$	−544023.	+	349622.i	−0.740722	+	0.476033i	0.115067	+	0.993358i	$0.463292\pi$
$858$		0			0
$859$	66622.0	+	76885.9i	0.0902883	+	0.104198i	0.799096	−	0.601204i	$-0.205312\pi$
$859$	66622.0	+	76885.9i	0.0902883	+	0.104198i	−0.708807	+	0.705402i	$0.750767\pi$
$860$		0			0
$861$	−70867.3	−	32364.0i	−0.0955960	−	0.0436572i
$862$		0			0
$863$	−451329.	+	132522.i	−0.605999	+	0.177937i	−0.570315	−	0.821426i	$-0.693179\pi$
$863$	−451329.	+	132522.i	−0.605999	+	0.177937i	−0.0356834	+	0.999363i	$0.511361\pi$
$864$		0			0
$865$	994654.	−	143010.i	1.32935	−	0.191132i
$866$		0			0
$867$	−377782.	−	827227.i	−0.502577	−	1.10049i
$868$		0			0
$869$	−24646.6	+	171421.i	−0.0326375	+	0.226999i
$870$		0			0
$871$	−167879.	−	145468.i	−0.221289	−	0.191748i
$872$		0			0
$873$			195168.i			0.256082i
$874$		0			0
$875$	257214.			0.335953
$876$		0			0
$877$	84819.4	−	97886.8i	0.110280	−	0.127270i	−0.697926	−	0.716170i	$-0.745894\pi$
$877$	84819.4	−	97886.8i	0.110280	−	0.127270i	0.808206	+	0.588900i	$0.200439\pi$
$878$		0			0
$879$	−194290.	−	27934.7i	−0.251462	−	0.0361548i
$880$		0			0
$881$	−1.22652e6	+	560132.i	−1.58024	+	0.721670i	−0.995953	−	0.0898791i	$-0.971352\pi$
$881$	−1.22652e6	+	560132.i	−1.58024	+	0.721670i	−0.584284	+	0.811549i	$0.698625\pi$
$882$		0			0
$883$	47576.5	+	330902.i	0.0610199	+	0.424403i	0.997318	+	0.0731953i	$0.0233196\pi$
$883$	47576.5	+	330902.i	0.0610199	+	0.424403i	−0.936298	+	0.351207i	$0.885771\pi$
$884$		0			0
$885$	214914.	+	731931.i	0.274397	+	0.934510i
$886$		0			0
$887$	−190354.	+	416817.i	−0.241944	+	0.529783i	−0.991180	−	0.132520i	$-0.957693\pi$
$887$	−190354.	+	416817.i	−0.241944	+	0.529783i	0.749237	+	0.662302i	$0.230421\pi$
$888$		0			0
$889$	−132332.	+	114667.i	−0.167441	+	0.145089i
$890$		0			0
$891$	470068.	+	731440.i	0.592114	+	0.921347i
$892$		0			0
$893$	−1.20011e6	+	1.86741e6i	−1.50494	+	2.34173i
$894$		0			0
$895$	−301500.	+	1.02681e6i	−0.376393	+	1.28188i
$896$		0			0
$897$	−128002.	−	206527.i	−0.159087	−	0.256680i
$898$		0			0
$899$	−1.23131e6	−	361546.i	−1.52352	−	0.447347i
$900$		0			0
$901$	76974.9	+	49468.7i	0.0948199	+	0.0609370i
$902$		0			0
$903$	555184.	−	356795.i	0.680866	−	0.437566i
$904$		0			0
$905$	−190970.	−	220392.i	−0.233168	−	0.269090i
$906$		0			0
$907$	−1.11152e6	−	507616.i	−1.35115	−	0.617051i	−0.397401	−	0.917645i	$-0.630088\pi$
$907$	−1.11152e6	−	507616.i	−1.35115	−	0.617051i	−0.953752	+	0.300594i	$0.902815\pi$
$908$		0			0
$909$	−788552.	+	231540.i	−0.954339	+	0.280219i
$910$		0			0
$911$	217783.	−	31312.4i	0.262414	−	0.0377294i	−0.00985203	−	0.999951i	$-0.503136\pi$
$911$	217783.	−	31312.4i	0.262414	−	0.0377294i	0.272266	+	0.962222i	$0.412227\pi$
$912$		0			0
$913$	120523.	+	263909.i	0.144587	+	0.316601i
$914$		0			0
$915$	158230.	−	1.10051e6i	0.188993	−	1.31448i
$916$		0			0
$917$	−414326.	−	359016.i	−0.492724	−	0.426948i
$918$		0			0
$919$			1.03938e6i			1.23067i	0.788265	+	0.615336i	$0.210980\pi$
$919$			1.03938e6i			1.23067i	−0.788265	+	0.615336i	$0.789020\pi$
$920$		0			0
$921$	2.58550e6			3.04807
$922$		0			0
$923$	56062.2	−	64699.3i	0.0658062	−	0.0759444i
$924$		0			0
$925$	−15077.9	−	2167.88i	−0.0176221	−	0.00253368i
$926$		0			0
$927$	2.82758e6	−	1.29131e6i	3.29045	−	1.50270i
$928$		0			0
$929$	−66222.1	−	460585.i	−0.0767312	−	0.533677i	−0.991541	−	0.129793i	$-0.958569\pi$
$929$	−66222.1	−	460585.i	−0.0767312	−	0.533677i	0.914810	−	0.403884i	$-0.132340\pi$
$930$		0			0
$931$	−317086.	−	1.07990e6i	−0.365829	−	1.24590i
$932$		0			0
$933$	258057.	−	565065.i	0.296450	−	0.649135i
$934$		0			0
$935$	241287.	−	209076.i	0.276001	−	0.239156i
$936$		0			0
$937$	−57061.4	−	88789.3i	−0.0649925	−	0.101130i	0.807236	−	0.590228i	$-0.200962\pi$
$937$	−57061.4	−	88789.3i	−0.0649925	−	0.101130i	−0.872229	+	0.489098i	$0.837326\pi$
$938$		0			0
$939$	424068.	−	659863.i	0.480955	−	0.748381i
$940$		0			0
$941$	218400.	−	743802.i	0.246645	−	0.839997i	−0.739364	−	0.673306i	$-0.764874\pi$
$941$	218400.	−	743802.i	0.246645	−	0.839997i	0.986009	−	0.166691i	$-0.0533082\pi$
$942$		0			0
$943$	2551.67	−	155976.i	0.00286946	−	0.175402i
$944$		0			0
$945$	621323.	+	182437.i	0.695750	+	0.204291i
$946$		0			0
$947$	581283.	+	373568.i	0.648169	+	0.416553i	0.822997	−	0.568046i	$-0.192301\pi$
$947$	581283.	+	373568.i	0.648169	+	0.416553i	−0.174828	+	0.984599i	$0.555937\pi$
$948$		0			0
$949$	103424.	−	66466.9i	0.114839	−	0.0738028i
$950$		0			0
$951$	−637398.	−	735596.i	−0.704773	−	0.813352i
$952$		0			0
$953$	84076.8	+	38396.6i	0.0925743	+	0.0422773i	0.461164	−	0.887315i	$-0.347432\pi$
$953$	84076.8	+	38396.6i	0.0925743	+	0.0422773i	−0.368590	+	0.929592i	$0.620159\pi$
$954$		0			0
$955$	−534677.	+	156995.i	−0.586253	+	0.172139i
$956$		0			0
$957$	−1.48954e6	+	214164.i	−1.62641	+	0.233842i
$958$		0			0
$959$	−159208.	−	348617.i	−0.173112	−	0.379063i
$960$		0			0
$961$	−32338.1	+	224916.i	−0.0350161	+	0.243542i
$962$		0			0
$963$	2.37628e6	+	2.05906e6i	2.56239	+	2.22033i
$964$		0			0
$965$		−	232036.i		−	0.249173i
$966$		0			0
$967$	−550633.			−0.588856			−0.294428	−	0.955674i	$-0.595129\pi$
$967$	−550633.			−0.588856			−0.294428	+	0.955674i	$0.595129\pi$
$968$		0			0
$969$	919794.	−	1.06150e6i	0.979587	−	1.13050i
$970$		0			0
$971$	−1.78352e6	−	256431.i	−1.89164	−	0.271977i	−0.903860	−	0.427828i	$-0.859279\pi$
$971$	−1.78352e6	−	256431.i	−1.89164	−	0.271977i	−0.987781	+	0.155851i	$0.950188\pi$
$972$		0			0
$973$	−545919.	+	249313.i	−0.576637	+	0.263341i
$974$		0			0
$975$	493.249	+	3430.62i	0.000518868	+	0.00360881i
$976$		0			0
$977$	−38575.1	−	131375.i	−0.0404127	−	0.137633i	0.936816	−	0.349824i	$-0.113758\pi$
$977$	−38575.1	−	131375.i	−0.0404127	−	0.137633i	−0.977228	+	0.212190i	$0.931940\pi$
$978$		0			0
$979$	261382.	−	572347.i	0.272716	−	0.597165i
$980$		0			0
$981$	−1.00657e6	+	872197.i	−1.04594	+	0.906310i
$982$		0			0
$983$	−263429.	−	409904.i	−0.272620	−	0.424205i	0.677766	−	0.735277i	$-0.262948\pi$
$983$	−263429.	−	409904.i	−0.272620	−	0.424205i	−0.950386	+	0.311073i	$0.899312\pi$
$984$		0			0
$985$	−938251.	+	1.45995e6i	−0.967044	+	1.50475i
$986$		0			0
$987$	313158.	−	1.06652e6i	0.321462	−	1.09480i
$988$		0			0
$989$	1.09983e6	+	732509.i	1.12443	+	0.748894i
$990$		0			0
$991$	1.44653e6	+	424739.i	1.47292	+	0.432489i	0.917048	−	0.398777i	$-0.130565\pi$
$991$	1.44653e6	+	424739.i	1.47292	+	0.432489i	0.555875	+	0.831266i	$0.312383\pi$
$992$		0			0
$993$	−1.38014e6	−	886961.i	−1.39966	−	0.899510i
$994$		0			0
$995$	987862.	−	634861.i	0.997815	−	0.641257i
$996$		0			0
$997$	915746.	+	1.05683e6i	0.921265	+	1.06320i	0.997811	+	0.0661305i	$0.0210654\pi$
$997$	915746.	+	1.05683e6i	0.921265	+	1.06320i	−0.0765459	+	0.997066i	$0.524389\pi$
$998$		0			0
$999$	−2.92427e6	−	1.33547e6i	−2.93013	−	1.33815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.f.a.5.8	✓	80
23.14	odd	22	inner	92.5.f.a.37.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.f.a.5.8	✓	80	1.1	even	1	trivial
92.5.f.a.37.8	yes	80	23.14	odd	22	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(10.5723 - 12.2011i) q^{3} +(-24.5957 - 3.53633i) q^{5} +(14.8856 - 6.79802i) q^{7} +(-25.5654 - 177.811i) q^{9} +O(q^{10})\)	\(q+(10.5723 - 12.2011i) q^{3} +(-24.5957 - 3.53633i) q^{5} +(14.8856 - 6.79802i) q^{7} +(-25.5654 - 177.811i) q^{9} +(-21.9521 - 74.7621i) q^{11} +(11.8188 - 25.8795i) q^{13} +(-303.180 + 262.707i) q^{15} +(-89.1503 - 138.721i) q^{17} +(-285.244 + 443.848i) q^{19} +(74.4316 - 253.491i) q^{21} +(524.777 - 66.7096i) q^{23} +(-7.24015 - 2.12590i) q^{25} +(-1339.68 - 860.958i) q^{27} +(1006.38 - 646.763i) q^{29} +(-702.489 - 810.715i) q^{31} +(-1144.26 - 522.568i) q^{33} +(-390.161 + 114.562i) q^{35} +(1998.19 - 287.296i) q^{37} +(-190.806 - 417.807i) q^{39} +(41.9672 - 291.888i) q^{41} +(1887.85 + 1635.83i) q^{43} +4463.80i q^{45} +4207.33 q^{47} +(-1396.95 + 1612.17i) q^{49} +(-2635.06 - 378.865i) q^{51} +(-504.747 + 230.510i) q^{53} +(275.545 + 1916.46i) q^{55} +(2399.74 + 8172.77i) q^{57} +(789.929 - 1729.70i) q^{59} +(-2094.56 + 1814.95i) q^{61} +(-1589.32 - 2473.03i) q^{63} +(-382.209 + 594.729i) q^{65} +(2199.71 - 7491.52i) q^{67} +(4734.17 - 7108.12i) q^{69} +(2887.18 + 847.751i) q^{71} +(3635.24 + 2336.23i) q^{73} +(-102.483 + 65.8620i) q^{75} +(-835.005 - 963.647i) q^{77} +(-2021.77 - 923.312i) q^{79} +(-10706.6 + 3143.76i) q^{81} +(-3685.57 + 529.905i) q^{83} +(1702.15 + 3727.19i) q^{85} +(2748.57 - 19116.7i) q^{87} +(6102.84 + 5288.14i) q^{89} -465.575i q^{91} -17318.5 q^{93} +(8585.36 - 9908.04i) q^{95} +(-1075.38 - 154.616i) q^{97} +(-12732.3 + 5814.67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 10 q^{3} - 318 q^{9}+O(q^{10}) \) 80 * q + 10 * q^3 - 318 * q^9	\( 80 q + 10 q^{3} - 318 q^{9} + 2 q^{13} + 1463 q^{15} - 495 q^{17} - 957 q^{19} - 1353 q^{21} + 1614 q^{23} + 1890 q^{25} + 4723 q^{27} - 1617 q^{29} - 3271 q^{31} - 6655 q^{33} - 5280 q^{35} + 3520 q^{37} + 6138 q^{39} + 11370 q^{41} + 7216 q^{43} - 270 q^{47} - 14512 q^{49} - 17424 q^{51} - 7392 q^{53} + 5746 q^{55} + 18381 q^{57} + 11772 q^{59} - 22484 q^{61} - 27775 q^{63} - 27951 q^{65} - 2926 q^{67} + 15769 q^{69} + 19779 q^{71} + 24400 q^{73} + 2809 q^{75} + 19839 q^{77} + 21604 q^{79} + 22224 q^{81} - 11253 q^{83} - 25594 q^{85} + 45506 q^{87} + 7656 q^{89} + 7970 q^{93} - 22437 q^{95} + 32439 q^{97} - 48477 q^{99}+O(q^{100}) \) 80 * q + 10 * q^3 - 318 * q^9 + 2 * q^13 + 1463 * q^15 - 495 * q^17 - 957 * q^19 - 1353 * q^21 + 1614 * q^23 + 1890 * q^25 + 4723 * q^27 - 1617 * q^29 - 3271 * q^31 - 6655 * q^33 - 5280 * q^35 + 3520 * q^37 + 6138 * q^39 + 11370 * q^41 + 7216 * q^43 - 270 * q^47 - 14512 * q^49 - 17424 * q^51 - 7392 * q^53 + 5746 * q^55 + 18381 * q^57 + 11772 * q^59 - 22484 * q^61 - 27775 * q^63 - 27951 * q^65 - 2926 * q^67 + 15769 * q^69 + 19779 * q^71 + 24400 * q^73 + 2809 * q^75 + 19839 * q^77 + 21604 * q^79 + 22224 * q^81 - 11253 * q^83 - 25594 * q^85 + 45506 * q^87 + 7656 * q^89 + 7970 * q^93 - 22437 * q^95 + 32439 * q^97 - 48477 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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