LMFDB - Embedded newform 128.4.g.a.81.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, not 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.10
Character	$\chi$	$=$	128.81
Dual form			128.4.g.a.49.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.06585 + 2.51256i) q^{3} +(-2.91165 - 7.02935i) q^{5} +(13.3899 - 13.3899i) q^{7} +(11.3897 + 11.3897i) q^{9} +O(q^{10})$	\(q+(6.06585 + 2.51256i) q^{3} +(-2.91165 - 7.02935i) q^{5} +(13.3899 - 13.3899i) q^{7} +(11.3897 + 11.3897i) q^{9} +(49.6279 - 20.5565i) q^{11} +(8.74801 - 21.1196i) q^{13} -49.9547i q^{15} +77.7412i q^{17} +(-53.3229 + 128.733i) q^{19} +(114.864 - 47.5784i) q^{21} +(35.5116 + 35.5116i) q^{23} +(47.4543 - 47.4543i) q^{25} +(-27.3680 - 66.0722i) q^{27} +(-245.435 - 101.662i) q^{29} +202.613 q^{31} +352.685 q^{33} +(-133.110 - 55.1358i) q^{35} +(36.3055 + 87.6493i) q^{37} +(106.128 - 106.128i) q^{39} +(-36.8088 - 36.8088i) q^{41} +(-185.642 + 76.8954i) q^{43} +(46.8995 - 113.225i) q^{45} -82.9731i q^{47} -15.5815i q^{49} +(-195.329 + 471.567i) q^{51} +(-534.758 + 221.504i) q^{53} +(-288.998 - 288.998i) q^{55} +(-646.898 + 646.898i) q^{57} +(-75.7461 - 182.867i) q^{59} +(-472.240 - 195.608i) q^{61} +305.016 q^{63} -173.928 q^{65} +(102.750 + 42.5604i) q^{67} +(126.183 + 304.633i) q^{69} +(-520.392 + 520.392i) q^{71} +(244.389 + 244.389i) q^{73} +(407.082 - 168.619i) q^{75} +(389.264 - 939.766i) q^{77} +774.758i q^{79} -904.451i q^{81} +(23.9166 - 57.7397i) q^{83} +(546.470 - 226.355i) q^{85} +(-1233.34 - 1233.34i) q^{87} +(-351.137 + 351.137i) q^{89} +(-165.654 - 399.925i) q^{91} +(1229.02 + 509.078i) q^{93} +1060.17 q^{95} +1302.03 q^{97} +(799.382 + 331.115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	6.06585	+	2.51256i	1.16737	+	0.483542i	0.880324	−	0.474373i	$-0.157325\pi$
$3$	6.06585	+	2.51256i	1.16737	+	0.483542i	0.287050	+	0.957916i	$0.407325\pi$
$4$		0			0
$5$	−2.91165	−	7.02935i	−0.260426	−	0.628724i	0.738539	−	0.674211i	$-0.235516\pi$
$5$	−2.91165	−	7.02935i	−0.260426	−	0.628724i	−0.998965	+	0.0454866i	$0.985516\pi$
$6$		0			0
$7$	13.3899	−	13.3899i	0.722989	−	0.722989i	−0.246224	−	0.969213i	$-0.579190\pi$
$7$	13.3899	−	13.3899i	0.722989	−	0.722989i	0.969213	+	0.246224i	$0.0791898\pi$
$8$		0			0
$9$	11.3897	+	11.3897i	0.421842	+	0.421842i
$10$		0			0
$11$	49.6279	−	20.5565i	1.36031	−	0.563457i	0.421164	−	0.906985i	$-0.361622\pi$
$11$	49.6279	−	20.5565i	1.36031	−	0.563457i	0.939143	+	0.343527i	$0.111622\pi$
$12$		0			0
$13$	8.74801	−	21.1196i	0.186635	−	0.450578i	−0.802672	−	0.596420i	$-0.796589\pi$
$13$	8.74801	−	21.1196i	0.186635	−	0.450578i	0.989308	+	0.145842i	$0.0465892\pi$
$14$		0			0
$15$		−	49.9547i		−	0.859884i
$16$		0			0
$17$			77.7412i			1.10912i	0.832144	+	0.554559i	$0.187113\pi$
$17$			77.7412i			1.10912i	−0.832144	+	0.554559i	$0.812887\pi$
$18$		0			0
$19$	−53.3229	+	128.733i	−0.643848	+	1.55439i	0.177599	+	0.984103i	$0.443167\pi$
$19$	−53.3229	+	128.733i	−0.643848	+	1.55439i	−0.821447	+	0.570284i	$0.806833\pi$
$20$		0			0
$21$	114.864	−	47.5784i	1.19359	−	0.494403i
$22$		0			0
$23$	35.5116	+	35.5116i	0.321943	+	0.321943i	0.849512	−	0.527569i	$-0.176897\pi$
$23$	35.5116	+	35.5116i	0.321943	+	0.321943i	−0.527569	+	0.849512i	$0.676897\pi$
$24$		0			0
$25$	47.4543	−	47.4543i	0.379634	−	0.379634i
$26$		0			0
$27$	−27.3680	−	66.0722i	−0.195073	−	0.470948i
$28$		0			0
$29$	−245.435	−	101.662i	−1.57159	−	0.650973i	−0.584535	−	0.811368i	$-0.698723\pi$
$29$	−245.435	−	101.662i	−1.57159	−	0.650973i	−0.987053	+	0.160395i	$0.948723\pi$
$30$		0			0
$31$	202.613			1.17389			0.586943	−	0.809629i	$-0.300331\pi$
$31$	202.613			1.17389			0.586943	+	0.809629i	$0.300331\pi$
$32$		0			0
$33$	352.685			1.86044
$34$		0			0
$35$	−133.110	−	55.1358i	−0.642846	−	0.266276i
$36$		0			0
$37$	36.3055	+	87.6493i	0.161313	+	0.389445i	0.983783	−	0.179365i	$-0.0574042\pi$
$37$	36.3055	+	87.6493i	0.161313	+	0.389445i	−0.822469	+	0.568809i	$0.807404\pi$
$38$		0			0
$39$	106.128	−	106.128i	0.435747	−	0.435747i
$40$		0			0
$41$	−36.8088	−	36.8088i	−0.140209	−	0.140209i	0.633518	−	0.773728i	$-0.281610\pi$
$41$	−36.8088	−	36.8088i	−0.140209	−	0.140209i	−0.773728	+	0.633518i	$0.781610\pi$
$42$		0			0
$43$	−185.642	+	76.8954i	−0.658375	+	0.272708i	−0.686754	−	0.726889i	$-0.740965\pi$
$43$	−185.642	+	76.8954i	−0.658375	+	0.272708i	0.0283797	+	0.999597i	$0.490965\pi$
$44$		0			0
$45$	46.8995	−	113.225i	0.155364	−	0.375081i
$46$		0			0
$47$		−	82.9731i		−	0.257508i	−0.991677	−	0.128754i	$-0.958902\pi$
$47$		−	82.9731i		−	0.257508i	0.991677	−	0.128754i	$-0.0410977\pi$
$48$		0			0
$49$		−	15.5815i		−	0.0454271i
$50$		0			0
$51$	−195.329	+	471.567i	−0.536305	+	1.29476i
$52$		0			0
$53$	−534.758	+	221.504i	−1.38594	+	0.574074i	−0.946062	−	0.323984i	$-0.894978\pi$
$53$	−534.758	+	221.504i	−1.38594	+	0.574074i	−0.439876	+	0.898059i	$0.644978\pi$
$54$		0			0
$55$	−288.998	−	288.998i	−0.708519	−	0.708519i
$56$		0			0
$57$	−646.898	+	646.898i	−1.50322	+	1.50322i
$58$		0			0
$59$	−75.7461	−	182.867i	−0.167141	−	0.403513i	0.818010	−	0.575204i	$-0.195077\pi$
$59$	−75.7461	−	182.867i	−0.167141	−	0.403513i	−0.985151	+	0.171690i	$0.945077\pi$
$60$		0			0
$61$	−472.240	−	195.608i	−0.991216	−	0.410575i	−0.172647	−	0.984984i	$-0.555232\pi$
$61$	−472.240	−	195.608i	−0.991216	−	0.410575i	−0.818569	+	0.574409i	$0.805232\pi$
$62$		0			0
$63$	305.016			0.609975
$64$		0			0
$65$	−173.928			−0.331894
$66$		0			0
$67$	102.750	+	42.5604i	0.187357	+	0.0776057i	0.474389	−	0.880315i	$-0.342669\pi$
$67$	102.750	+	42.5604i	0.187357	+	0.0776057i	−0.287033	+	0.957921i	$0.592669\pi$
$68$		0			0
$69$	126.183	+	304.633i	0.220155	+	0.531500i
$70$		0			0
$71$	−520.392	+	520.392i	−0.869847	+	0.869847i	−0.992455	−	0.122608i	$-0.960874\pi$
$71$	−520.392	+	520.392i	−0.869847	+	0.869847i	0.122608	+	0.992455i	$0.460874\pi$
$72$		0			0
$73$	244.389	+	244.389i	0.391829	+	0.391829i	0.875339	−	0.483510i	$-0.160638\pi$
$73$	244.389	+	244.389i	0.391829	+	0.391829i	−0.483510	+	0.875339i	$0.660638\pi$
$74$		0			0
$75$	407.082	−	168.619i	0.626744	−	0.259606i
$76$		0			0
$77$	389.264	−	939.766i	0.576113	−	1.39086i
$78$		0			0
$79$			774.758i			1.10338i	0.834049	+	0.551690i	$0.186017\pi$
$79$			774.758i			1.10338i	−0.834049	+	0.551690i	$0.813983\pi$
$80$		0			0
$81$		−	904.451i		−	1.24067i
$82$		0			0
$83$	23.9166	−	57.7397i	0.0316287	−	0.0763585i	−0.907276	−	0.420536i	$-0.861842\pi$
$83$	23.9166	−	57.7397i	0.0316287	−	0.0763585i	0.938905	+	0.344177i	$0.111842\pi$
$84$		0			0
$85$	546.470	−	226.355i	0.697330	−	0.288843i
$86$		0			0
$87$	−1233.34	−	1233.34i	−1.51986	−	1.51986i
$88$		0			0
$89$	−351.137	+	351.137i	−0.418207	+	0.418207i	−0.884585	−	0.466378i	$-0.845559\pi$
$89$	−351.137	+	351.137i	−0.418207	+	0.418207i	0.466378	+	0.884585i	$0.345559\pi$
$90$		0			0
$91$	−165.654	−	399.925i	−0.190827	−	0.460698i
$92$		0			0
$93$	1229.02	+	509.078i	1.37036	+	0.567623i
$94$		0			0
$95$	1060.17			1.14496
$96$		0			0
$97$	1302.03			1.36290			0.681452	−	0.731863i	$-0.261349\pi$
$97$	1302.03			1.36290			0.681452	+	0.731863i	$0.261349\pi$
$98$		0			0
$99$	799.382	+	331.115i	0.811525	+	0.336145i
$100$		0			0
$101$	255.210	+	616.132i	0.251429	+	0.607004i	0.998320	−	0.0579428i	$-0.0184541\pi$
$101$	255.210	+	616.132i	0.251429	+	0.607004i	−0.746891	+	0.664947i	$0.768454\pi$
$102$		0			0
$103$	−119.916	+	119.916i	−0.114715	+	0.114715i	−0.762134	−	0.647419i	$-0.775848\pi$
$103$	−119.916	+	119.916i	−0.114715	+	0.114715i	0.647419	+	0.762134i	$0.275848\pi$
$104$		0			0
$105$	−668.891	−	668.891i	−0.621687	−	0.621687i
$106$		0			0
$107$	659.373	−	273.121i	0.595738	−	0.246763i	−0.0643789	−	0.997926i	$-0.520507\pi$
$107$	659.373	−	273.121i	0.595738	−	0.246763i	0.660117	+	0.751163i	$0.270507\pi$
$108$		0			0
$109$	−471.995	+	1139.50i	−0.414761	+	1.00132i	0.569081	+	0.822281i	$0.307299\pi$
$109$	−471.995	+	1139.50i	−0.414761	+	1.00132i	−0.983842	+	0.179040i	$0.942701\pi$
$110$		0			0
$111$			622.887i			0.532629i
$112$		0			0
$113$		−	832.434i		−	0.692998i	−0.938050	−	0.346499i	$-0.887370\pi$
$113$		−	832.434i		−	0.692998i	0.938050	−	0.346499i	$-0.112630\pi$
$114$		0			0
$115$	146.226	−	353.021i	0.118571	−	0.286255i
$116$		0			0
$117$	340.184	−	140.909i	0.268803	−	0.111342i
$118$		0			0
$119$	1040.95	+	1040.95i	0.801880	+	0.801880i
$120$		0			0
$121$	1099.20	−	1099.20i	0.825843	−	0.825843i
$122$		0			0
$123$	−130.793	−	315.761i	−0.0958795	−	0.231473i
$124$		0			0
$125$	−1350.41	−	559.359i	−0.966276	−	0.400245i
$126$		0			0
$127$	−187.556			−0.131046			−0.0655232	−	0.997851i	$-0.520872\pi$
$127$	−187.556			−0.131046			−0.0655232	+	0.997851i	$0.520872\pi$
$128$		0			0
$129$	−1319.28			−0.900435
$130$		0			0
$131$	−1001.26	−	414.737i	−0.667793	−	0.276609i	0.0229207	−	0.999737i	$-0.492703\pi$
$131$	−1001.26	−	414.737i	−0.667793	−	0.276609i	−0.690714	+	0.723128i	$0.742703\pi$
$132$		0			0
$133$	1009.74	+	2437.72i	0.658310	+	1.58930i
$134$		0			0
$135$	−384.759	+	384.759i	−0.245294	+	0.245294i
$136$		0			0
$137$	−1273.38	−	1273.38i	−0.794101	−	0.794101i	0.188057	−	0.982158i	$-0.439781\pi$
$137$	−1273.38	−	1273.38i	−0.794101	−	0.794101i	−0.982158	+	0.188057i	$0.939781\pi$
$138$		0			0
$139$	2129.20	−	881.945i	1.29926	−	0.538170i	0.377525	−	0.925999i	$-0.376775\pi$
$139$	2129.20	−	881.945i	1.29926	−	0.538170i	0.921731	+	0.387830i	$0.126775\pi$
$140$		0			0
$141$	208.475	−	503.302i	0.124516	−	0.300608i
$142$		0			0
$143$		−	1227.95i		−	0.718085i
$144$		0			0
$145$			2021.25i			1.15763i
$146$		0			0
$147$	39.1494	−	94.5150i	0.0219659	−	0.0530304i
$148$		0			0
$149$	139.146	−	57.6361i	0.0765051	−	0.0316895i	−0.344103	−	0.938932i	$-0.611817\pi$
$149$	139.146	−	57.6361i	0.0765051	−	0.0316895i	0.420608	+	0.907243i	$0.361817\pi$
$150$		0			0
$151$	2027.42	+	2027.42i	1.09264	+	1.09264i	0.995245	+	0.0973988i	$0.0310522\pi$
$151$	2027.42	+	2027.42i	1.09264	+	1.09264i	0.0973988	+	0.995245i	$0.468948\pi$
$152$		0			0
$153$	−885.452	+	885.452i	−0.467873	+	0.467873i
$154$		0			0
$155$	−589.940	−	1424.24i	−0.305710	−	0.738050i
$156$		0			0
$157$	816.713	+	338.294i	0.415164	+	0.171967i	0.580481	−	0.814274i	$-0.302865\pi$
$157$	816.713	+	338.294i	0.415164	+	0.171967i	−0.165317	+	0.986241i	$0.552865\pi$
$158$		0			0
$159$	−3800.31			−1.89550
$160$		0			0
$161$	950.997			0.465522
$162$		0			0
$163$	953.491	+	394.949i	0.458179	+	0.189784i	0.599821	−	0.800134i	$-0.295238\pi$
$163$	953.491	+	394.949i	0.458179	+	0.189784i	−0.141642	+	0.989918i	$0.545238\pi$
$164$		0			0
$165$	−1026.90	−	2479.15i	−0.484508	−	1.16971i
$166$		0			0
$167$	896.156	−	896.156i	0.415249	−	0.415249i	−0.468313	−	0.883563i	$-0.655138\pi$
$167$	896.156	−	896.156i	0.415249	−	0.415249i	0.883563	+	0.468313i	$0.155138\pi$
$168$		0			0
$169$	1184.01	+	1184.01i	0.538919	+	0.538919i
$170$		0			0
$171$	−2073.57	+	858.900i	−0.927308	+	0.384104i
$172$		0			0
$173$	−268.247	+	647.606i	−0.117887	+	0.284604i	−0.971798	−	0.235815i	$-0.924224\pi$
$173$	−268.247	+	647.606i	−0.117887	+	0.284604i	0.853911	+	0.520419i	$0.174224\pi$
$174$		0			0
$175$		−	1270.82i		−	0.548943i
$176$		0			0
$177$		−	1299.56i		−	0.551870i
$178$		0			0
$179$	−842.440	+	2033.83i	−0.351770	+	0.849249i	0.644631	+	0.764494i	$0.277011\pi$
$179$	−842.440	+	2033.83i	−0.351770	+	0.849249i	−0.996402	+	0.0847553i	$0.972989\pi$
$180$		0			0
$181$	1394.35	−	577.557i	0.572602	−	0.237180i	−0.0775438	−	0.996989i	$-0.524708\pi$
$181$	1394.35	−	577.557i	0.572602	−	0.237180i	0.650146	+	0.759809i	$0.274708\pi$
$182$		0			0
$183$	−2373.06	−	2373.06i	−0.958589	−	0.958589i
$184$		0			0
$185$	510.408	−	510.408i	0.202843	−	0.202843i
$186$		0			0
$187$	1598.09	+	3858.13i	0.624941	+	1.50874i
$188$		0			0
$189$	−1251.16	−	518.247i	−0.481526	−	0.199455i
$190$		0			0
$191$	−779.721			−0.295386			−0.147693	−	0.989033i	$-0.547185\pi$
$191$	−779.721			−0.295386			−0.147693	+	0.989033i	$0.547185\pi$
$192$		0			0
$193$	−4175.15			−1.55717			−0.778585	−	0.627539i	$-0.784062\pi$
$193$	−4175.15			−1.55717			−0.778585	+	0.627539i	$0.784062\pi$
$194$		0			0
$195$	−1055.02	−	437.004i	−0.387444	−	0.160485i
$196$		0			0
$197$	−1793.41	−	4329.67i	−0.648604	−	1.56587i	−0.814778	−	0.579773i	$-0.803141\pi$
$197$	−1793.41	−	4329.67i	−0.648604	−	1.56587i	0.166174	−	0.986096i	$-0.446859\pi$
$198$		0			0
$199$	−1333.84	+	1333.84i	−0.475144	+	0.475144i	−0.903575	−	0.428431i	$-0.859067\pi$
$199$	−1333.84	+	1333.84i	−0.475144	+	0.475144i	0.428431	+	0.903575i	$0.359067\pi$
$200$		0			0
$201$	516.330	+	516.330i	0.181190	+	0.181190i
$202$		0			0
$203$	−4647.61	+	1925.10i	−1.60689	+	0.665595i
$204$		0			0
$205$	−151.568	+	365.917i	−0.0516388	+	0.124667i
$206$		0			0
$207$			808.935i			0.271618i
$208$		0			0
$209$			7484.88i			2.47722i
$210$		0			0
$211$	1172.83	−	2831.46i	0.382658	−	0.923818i	−0.608792	−	0.793330i	$-0.708346\pi$
$211$	1172.83	−	2831.46i	0.382658	−	0.923818i	0.991450	−	0.130488i	$-0.0416544\pi$
$212$		0			0
$213$	−4464.13	+	1849.11i	−1.43604	+	0.594829i
$214$		0			0
$215$	1081.05	+	1081.05i	0.342916	+	0.342916i
$216$		0			0
$217$	2712.98	−	2712.98i	0.848707	−	0.848707i
$218$		0			0
$219$	868.385	+	2096.47i	0.267945	+	0.646877i
$220$		0			0
$221$	1641.86	+	680.080i	0.499744	+	0.207001i
$222$		0			0
$223$	2462.13			0.739356			0.369678	−	0.929160i	$-0.379468\pi$
$223$	2462.13			0.739356			0.369678	+	0.929160i	$0.379468\pi$
$224$		0			0
$225$	1080.98			0.320291
$226$		0			0
$227$	−2912.19	−	1206.27i	−0.851494	−	0.352700i	−0.0861187	−	0.996285i	$-0.527446\pi$
$227$	−2912.19	−	1206.27i	−0.851494	−	0.352700i	−0.765375	+	0.643585i	$0.777446\pi$
$228$		0			0
$229$	−578.212	−	1395.93i	−0.166853	−	0.402819i	0.818232	−	0.574889i	$-0.194955\pi$
$229$	−578.212	−	1395.93i	−0.166853	−	0.402819i	−0.985085	+	0.172070i	$0.944955\pi$
$230$		0			0
$231$	4722.43	−	4722.43i	1.34508	−	1.34508i
$232$		0			0
$233$	3037.56	+	3037.56i	0.854065	+	0.854065i	0.990631	−	0.136566i	$-0.0436067\pi$
$233$	3037.56	+	3037.56i	0.854065	+	0.854065i	−0.136566	+	0.990631i	$0.543607\pi$
$234$		0			0
$235$	−583.247	+	241.589i	−0.161901	+	0.0670618i
$236$		0			0
$237$	−1946.62	+	4699.57i	−0.533531	+	1.28806i
$238$		0			0
$239$		−	68.1814i		−	0.0184531i	−0.999957	−	0.00922654i	$-0.997063\pi$
$239$		−	68.1814i		−	0.0184531i	0.999957	−	0.00922654i	$-0.00293694\pi$
$240$		0			0
$241$		−	6115.20i		−	1.63450i	−0.576282	−	0.817251i	$-0.695497\pi$
$241$		−	6115.20i		−	1.63450i	0.576282	−	0.817251i	$-0.304503\pi$
$242$		0			0
$243$	1533.55	−	3702.32i	0.404845	−	0.977382i
$244$		0			0
$245$	−109.528	+	45.3679i	−0.0285611	+	0.0118304i
$246$		0			0
$247$	2252.31	+	2252.31i	0.580207	+	0.580207i
$248$		0			0
$249$	290.149	−	290.149i	0.0738451	−	0.0738451i
$250$		0			0
$251$	−183.755	−	443.623i	−0.0462092	−	0.111559i	0.899090	−	0.437765i	$-0.144230\pi$
$251$	−183.755	−	443.623i	−0.0462092	−	0.111559i	−0.945299	+	0.326206i	$0.894230\pi$
$252$		0			0
$253$	2492.36	+	1032.37i	0.619341	+	0.256540i
$254$		0			0
$255$	3883.54			0.953712
$256$		0			0
$257$	−26.1354			−0.00634350			−0.00317175	−	0.999995i	$-0.501010\pi$
$257$	−26.1354			−0.00634350			−0.00317175	+	0.999995i	$0.501010\pi$
$258$		0			0
$259$	1659.75	+	687.490i	0.398192	+	0.164937i
$260$		0			0
$261$	−1637.53	−	3953.34i	−0.388354	−	0.937570i
$262$		0			0
$263$	2404.98	−	2404.98i	0.563869	−	0.563869i	−0.366535	−	0.930404i	$-0.619456\pi$
$263$	2404.98	−	2404.98i	0.563869	−	0.563869i	0.930404	+	0.366535i	$0.119456\pi$
$264$		0			0
$265$	3114.06	+	3114.06i	0.721869	+	0.721869i
$266$		0			0
$267$	−3012.20	+	1247.69i	−0.690425	+	0.285983i
$268$		0			0
$269$	3217.65	−	7768.09i	0.729306	−	1.76070i	0.0844104	−	0.996431i	$-0.473099\pi$
$269$	3217.65	−	7768.09i	0.729306	−	1.76070i	0.644896	−	0.764270i	$-0.276901\pi$
$270$		0			0
$271$		−	4099.60i		−	0.918941i	−0.888193	−	0.459471i	$-0.848039\pi$
$271$		−	4099.60i		−	0.918941i	0.888193	−	0.459471i	$-0.151961\pi$
$272$		0			0
$273$		−	2842.10i		−	0.630080i
$274$		0			0
$275$	1379.56	−	3330.55i	0.302511	−	0.730327i
$276$		0			0
$277$	−62.6281	+	25.9414i	−0.0135847	+	0.00562696i	−0.389465	−	0.921041i	$-0.627340\pi$
$277$	−62.6281	+	25.9414i	−0.0135847	+	0.00562696i	0.375881	+	0.926668i	$0.377340\pi$
$278$		0			0
$279$	2307.71	+	2307.71i	0.495194	+	0.495194i
$280$		0			0
$281$	371.515	−	371.515i	0.0788709	−	0.0788709i	−0.666571	−	0.745442i	$-0.732239\pi$
$281$	371.515	−	371.515i	0.0788709	−	0.0788709i	0.745442	+	0.666571i	$0.232239\pi$
$282$		0			0
$283$	1150.78	+	2778.24i	0.241721	+	0.583566i	0.997454	−	0.0713139i	$-0.0227192\pi$
$283$	1150.78	+	2778.24i	0.241721	+	0.583566i	−0.755733	+	0.654880i	$0.772719\pi$
$284$		0			0
$285$	6430.82	+	2663.73i	1.33659	+	0.553634i
$286$		0			0
$287$	−985.737			−0.202739
$288$		0			0
$289$	−1130.69			−0.230143
$290$		0			0
$291$	7897.95	+	3271.44i	1.59102	+	0.659021i
$292$		0			0
$293$	1547.04	+	3734.89i	0.308461	+	0.744691i	0.999755	+	0.0221175i	$0.00704081\pi$
$293$	1547.04	+	3734.89i	0.308461	+	0.744691i	−0.691294	+	0.722573i	$0.742959\pi$
$294$		0			0
$295$	−1064.89	+	1064.89i	−0.210171	+	0.210171i
$296$		0			0
$297$	−2716.43	−	2716.43i	−0.530718	−	0.530718i
$298$		0			0
$299$	1060.64	−	439.333i	0.205146	−	0.0849743i
$300$		0			0
$301$	−1456.11	+	3515.36i	−0.278833	+	0.673163i
$302$		0			0
$303$			4378.60i			0.830178i
$304$		0			0
$305$			3889.09i			0.730126i
$306$		0			0
$307$	−2115.16	+	5106.46i	−0.393221	+	0.949319i	0.596013	+	0.802975i	$0.296751\pi$
$307$	−2115.16	+	5106.46i	−0.393221	+	0.949319i	−0.989234	+	0.146344i	$0.953249\pi$
$308$		0			0
$309$	−1028.69	+	426.097i	−0.189386	+	0.0784461i
$310$		0			0
$311$	−3571.19	−	3571.19i	−0.651137	−	0.651137i	0.302130	−	0.953267i	$-0.402302\pi$
$311$	−3571.19	−	3571.19i	−0.651137	−	0.651137i	−0.953267	+	0.302130i	$0.902302\pi$
$312$		0			0
$313$	−304.665	+	304.665i	−0.0550182	+	0.0550182i	−0.734081	−	0.679062i	$-0.762387\pi$
$313$	−304.665	+	304.665i	−0.0550182	+	0.0550182i	0.679062	+	0.734081i	$0.262387\pi$
$314$		0			0
$315$	−888.101	−	2144.07i	−0.158853	−	0.383506i
$316$		0			0
$317$	−6782.93	−	2809.58i	−1.20179	−	0.497798i	−0.310213	−	0.950667i	$-0.600400\pi$
$317$	−6782.93	−	2809.58i	−1.20179	−	0.497798i	−0.891577	+	0.452869i	$0.850400\pi$
$318$		0			0
$319$	−14270.2			−2.50464
$320$		0			0
$321$	4685.89			0.814770
$322$		0			0
$323$	−10007.8	−	4145.39i	−1.72400	−	0.714104i
$324$		0			0
$325$	−587.083	−	1417.34i	−0.100202	−	0.241908i
$326$		0			0
$327$	−5726.10	+	5726.10i	−0.968362	+	0.968362i
$328$		0			0
$329$	−1111.01	−	1111.01i	−0.186175	−	0.186175i
$330$		0			0
$331$	3670.23	−	1520.26i	0.609468	−	0.252450i	−0.0565331	−	0.998401i	$-0.518005\pi$
$331$	3670.23	−	1520.26i	0.609468	−	0.252450i	0.666001	+	0.745951i	$0.268005\pi$
$332$		0			0
$333$	−584.792	+	1411.81i	−0.0962354	+	0.232333i
$334$		0			0
$335$		−	846.186i		−	0.138006i
$336$		0			0
$337$			5082.79i			0.821593i	0.911727	+	0.410797i	$0.134749\pi$
$337$			5082.79i			0.821593i	−0.911727	+	0.410797i	$0.865251\pi$
$338$		0			0
$339$	2091.54	−	5049.42i	0.335094	−	0.808988i
$340$		0			0
$341$	10055.3	−	4165.03i	1.59684	−	0.661434i
$342$		0			0
$343$	4384.12	+	4384.12i	0.690146	+	0.690146i
$344$		0			0
$345$	1773.97	−	1773.97i	0.276833	−	0.276833i
$346$		0			0
$347$	1154.04	+	2786.09i	0.178536	+	0.431023i	0.987660	−	0.156615i	$-0.0500580\pi$
$347$	1154.04	+	2786.09i	0.178536	+	0.431023i	−0.809124	+	0.587638i	$0.800058\pi$
$348$		0			0
$349$	−2241.53	−	928.474i	−0.343801	−	0.142407i	0.204100	−	0.978950i	$-0.434573\pi$
$349$	−2241.53	−	928.474i	−0.343801	−	0.142407i	−0.547901	+	0.836543i	$0.684573\pi$
$350$		0			0
$351$	−1634.83			−0.248606
$352$		0			0
$353$	−8284.27			−1.24908			−0.624542	−	0.780991i	$-0.714715\pi$
$353$	−8284.27			−1.24908			−0.624542	+	0.780991i	$0.714715\pi$
$354$		0			0
$355$	5173.22	+	2142.82i	0.773425	+	0.320363i
$356$		0			0
$357$	3698.80	+	8929.70i	0.548351	+	1.32384i
$358$		0			0
$359$	−1889.18	+	1889.18i	−0.277736	+	0.277736i	−0.832205	−	0.554469i	$-0.812922\pi$
$359$	−1889.18	+	1889.18i	−0.277736	+	0.277736i	0.554469	+	0.832205i	$0.312922\pi$
$360$		0			0
$361$	−8878.78	−	8878.78i	−1.29447	−	1.29447i
$362$		0			0
$363$	9429.36	−	3905.77i	1.36340	−	0.564738i
$364$		0			0
$365$	1006.32	−	2429.47i	0.144310	−	0.348395i
$366$		0			0
$367$		−	7429.67i		−	1.05675i	−0.849012	−	0.528373i	$-0.822802\pi$
$367$		−	7429.67i		−	1.05675i	0.849012	−	0.528373i	$-0.177198\pi$
$368$		0			0
$369$		−	838.486i		−	0.118292i
$370$		0			0
$371$	−4194.46	+	10126.3i	−0.586969	+	1.41707i
$372$		0			0
$373$	1661.51	−	688.219i	0.230642	−	0.0955351i	−0.264369	−	0.964421i	$-0.585164\pi$
$373$	1661.51	−	688.219i	0.230642	−	0.0955351i	0.495012	+	0.868886i	$0.335164\pi$
$374$		0			0
$375$	−6785.98	−	6785.98i	−0.934471	−	0.934471i
$376$		0			0
$377$	−4294.13	+	4294.13i	−0.586628	+	0.586628i
$378$		0			0
$379$	−3773.37	−	9109.72i	−0.511412	−	1.23466i	−0.943062	−	0.332616i	$-0.892069\pi$
$379$	−3773.37	−	9109.72i	−0.511412	−	1.23466i	0.431651	−	0.902041i	$-0.357931\pi$
$380$		0			0
$381$	−1137.69	−	471.245i	−0.152980	−	0.0633664i
$382$		0			0
$383$	13137.5			1.75273			0.876366	−	0.481646i	$-0.159961\pi$
$383$	13137.5			1.75273			0.876366	+	0.481646i	$0.159961\pi$
$384$		0			0
$385$	−7739.35			−1.02450
$386$		0			0
$387$	−2990.23	−	1238.59i	−0.392770	−	0.162691i
$388$		0			0
$389$	1767.36	+	4266.78i	0.230357	+	0.556130i	0.996219	−	0.0868742i	$-0.0276878\pi$
$389$	1767.36	+	4266.78i	0.230357	+	0.556130i	−0.765863	+	0.643004i	$0.777688\pi$
$390$		0			0
$391$	−2760.71	+	2760.71i	−0.357072	+	0.357072i
$392$		0			0
$393$	−5031.47	−	5031.47i	−0.645812	−	0.645812i
$394$		0			0
$395$	5446.04	−	2255.83i	0.693722	−	0.287349i
$396$		0			0
$397$	−5649.54	+	13639.2i	−0.714212	+	1.72426i	−0.0250151	+	0.999687i	$0.507963\pi$
$397$	−5649.54	+	13639.2i	−0.714212	+	1.72426i	−0.689197	+	0.724574i	$0.742037\pi$
$398$		0			0
$399$			17323.9i			2.17363i
$400$		0			0
$401$		−	5422.25i		−	0.675247i	−0.941281	−	0.337624i	$-0.890377\pi$
$401$		−	5422.25i		−	0.675247i	0.941281	−	0.337624i	$-0.109623\pi$
$402$		0			0
$403$	1772.46	−	4279.11i	0.219089	−	0.528927i
$404$		0			0
$405$	−6357.70	+	2633.45i	−0.780042	+	0.323104i
$406$		0			0
$407$	3603.53	+	3603.53i	0.438871	+	0.438871i
$408$		0			0
$409$	−2622.89	+	2622.89i	−0.317099	+	0.317099i	−0.847652	−	0.530553i	$-0.821984\pi$
$409$	−2622.89	+	2622.89i	−0.317099	+	0.317099i	0.530553	+	0.847652i	$0.321984\pi$
$410$		0			0
$411$	−4524.68	−	10923.5i	−0.543031	−	1.31099i
$412$		0			0
$413$	−3462.82	−	1434.35i	−0.412577	−	0.170895i
$414$		0			0
$415$	−475.509			−0.0562454
$416$		0			0
$417$	15131.4			1.77695
$418$		0			0
$419$	1293.33	+	535.717i	0.150796	+	0.0624617i	0.456805	−	0.889567i	$-0.348994\pi$
$419$	1293.33	+	535.717i	0.150796	+	0.0624617i	−0.306009	+	0.952029i	$0.598994\pi$
$420$		0			0
$421$	−871.790	−	2104.69i	−0.100923	−	0.243649i	0.865351	−	0.501166i	$-0.167096\pi$
$421$	−871.790	−	2104.69i	−0.100923	−	0.243649i	−0.966274	+	0.257517i	$0.917096\pi$
$422$		0			0
$423$	945.041	−	945.041i	0.108628	−	0.108628i
$424$		0			0
$425$	3689.15	+	3689.15i	0.421059	+	0.421059i
$426$		0			0
$427$	−8942.46	+	3704.09i	−1.01348	+	0.419797i
$428$		0			0
$429$	3085.29	−	7448.55i	0.347224	−	0.838274i
$430$		0			0
$431$			5681.29i			0.634938i	0.948269	+	0.317469i	$0.102833\pi$
$431$			5681.29i			0.634938i	−0.948269	+	0.317469i	$0.897167\pi$
$432$		0			0
$433$		−	9616.41i		−	1.06729i	−0.845710	−	0.533643i	$-0.820822\pi$
$433$		−	9616.41i		−	1.06729i	0.845710	−	0.533643i	$-0.179178\pi$
$434$		0			0
$435$	−5078.51	+	12260.6i	−0.559761	+	1.35138i
$436$		0			0
$437$	−6465.09	+	2677.93i	−0.707705	+	0.293141i
$438$		0			0
$439$	−10175.7	−	10175.7i	−1.10629	−	1.10629i	−0.993634	−	0.112657i	$-0.964064\pi$
$439$	−10175.7	−	10175.7i	−1.10629	−	1.10629i	−0.112657	−	0.993634i	$-0.535936\pi$
$440$		0			0
$441$	177.469	−	177.469i	0.0191630	−	0.0191630i
$442$		0			0
$443$	−925.474	−	2234.29i	−0.0992564	−	0.239626i	0.866449	−	0.499265i	$-0.166397\pi$
$443$	−925.474	−	2234.29i	−0.0992564	−	0.239626i	−0.965706	+	0.259639i	$0.916397\pi$
$444$		0			0
$445$	3490.65	+	1445.88i	0.371849	+	0.154025i
$446$		0			0
$447$	988.852			0.104633
$448$		0			0
$449$	8501.56			0.893571			0.446785	−	0.894641i	$-0.352569\pi$
$449$	8501.56			0.893571			0.446785	+	0.894641i	$0.352569\pi$
$450$		0			0
$451$	−2583.41	−	1070.08i	−0.269729	−	0.111726i
$452$		0			0
$453$	7204.03	+	17392.1i	0.747185	+	1.80386i
$454$		0			0
$455$	−2328.89	+	2328.89i	−0.239956	+	0.239956i
$456$		0			0
$457$	7829.53	+	7829.53i	0.801422	+	0.801422i	0.983318	−	0.181895i	$-0.0582232\pi$
$457$	7829.53	+	7829.53i	0.801422	+	0.801422i	−0.181895	+	0.983318i	$0.558223\pi$
$458$		0			0
$459$	5136.53	−	2127.62i	0.522337	−	0.216359i
$460$		0			0
$461$	4138.96	−	9992.34i	0.418158	−	1.00952i	−0.564723	−	0.825280i	$-0.691017\pi$
$461$	4138.96	−	9992.34i	0.418158	−	1.00952i	0.982881	−	0.184241i	$-0.0589828\pi$
$462$		0			0
$463$		−	13379.7i		−	1.34300i	−0.741004	−	0.671501i	$-0.765650\pi$
$463$		−	13379.7i		−	1.34300i	0.741004	−	0.671501i	$-0.234350\pi$
$464$		0			0
$465$		−	10121.5i		−	1.00940i
$466$		0			0
$467$	−2256.68	+	5448.12i	−0.223612	+	0.539848i	−0.995375	−	0.0960626i	$-0.969375\pi$
$467$	−2256.68	+	5448.12i	−0.223612	+	0.539848i	0.771763	+	0.635910i	$0.219375\pi$
$468$		0			0
$469$	1945.70	−	805.934i	0.191565	−	0.0793488i
$470$		0			0
$471$	4104.08	+	4104.08i	0.401499	+	0.401499i
$472$		0			0
$473$	−7632.31	+	7632.31i	−0.741932	+	0.741932i
$474$		0			0
$475$	3578.53	+	8639.33i	0.345672	+	0.834525i
$476$		0			0
$477$	−8613.63	−	3567.88i	−0.826816	−	0.342478i
$478$		0			0
$479$	15500.6			1.47858			0.739289	−	0.673389i	$-0.235162\pi$
$479$	15500.6			1.47858			0.739289	+	0.673389i	$0.235162\pi$
$480$		0			0
$481$	2168.71			0.205582
$482$		0			0
$483$	5768.61	+	2389.44i	0.543438	+	0.225100i
$484$		0			0
$485$	−3791.07	−	9152.46i	−0.354936	−	0.856891i
$486$		0			0
$487$	3384.07	−	3384.07i	0.314880	−	0.314880i	−0.531917	−	0.846797i	$-0.678528\pi$
$487$	3384.07	−	3384.07i	0.314880	−	0.314880i	0.846797	+	0.531917i	$0.178528\pi$
$488$		0			0
$489$	4791.40	+	4791.40i	0.443098	+	0.443098i
$490$		0			0
$491$	5913.07	−	2449.27i	0.543489	−	0.225121i	−0.0940105	−	0.995571i	$-0.529969\pi$
$491$	5913.07	−	2449.27i	0.543489	−	0.225121i	0.637500	+	0.770451i	$0.279969\pi$
$492$		0			0
$493$	7903.35	−	19080.4i	0.722006	−	1.74308i
$494$		0			0
$495$		−	6583.23i		−	0.597766i
$496$		0			0
$497$			13936.0i			1.25778i
$498$		0			0
$499$	5163.06	−	12464.7i	0.463187	−	1.11823i	−0.503894	−	0.863765i	$-0.668100\pi$
$499$	5163.06	−	12464.7i	0.463187	−	1.11823i	0.967081	−	0.254467i	$-0.0819001\pi$
$500$		0			0
$501$	7687.60	−	3184.31i	0.685542	−	0.283961i
$502$		0			0
$503$	−6921.39	−	6921.39i	−0.613537	−	0.613537i	0.330329	−	0.943866i	$-0.392840\pi$
$503$	−6921.39	−	6921.39i	−0.613537	−	0.613537i	−0.943866	+	0.330329i	$0.892840\pi$
$504$		0			0
$505$	3587.93	−	3587.93i	0.316160	−	0.316160i
$506$		0			0
$507$	4207.12	+	10156.9i	0.368530	+	0.889710i
$508$		0			0
$509$	14532.1	+	6019.39i	1.26547	+	0.524174i	0.911584	−	0.411115i	$-0.134860\pi$
$509$	14532.1	+	6019.39i	1.26547	+	0.524174i	0.353885	+	0.935289i	$0.384860\pi$
$510$		0			0
$511$	6544.71			0.566577
$512$		0			0
$513$	9965.00			0.857633
$514$		0			0
$515$	1192.09	+	493.779i	0.101999	+	0.0422495i
$516$		0			0
$517$	−1705.64	−	4117.78i	−0.145095	−	0.350290i
$518$		0			0
$519$	−3254.29	+	3254.29i	−0.275236	+	0.275236i
$520$		0			0
$521$	−6505.72	−	6505.72i	−0.547065	−	0.547065i	0.378526	−	0.925591i	$-0.376431\pi$
$521$	−6505.72	−	6505.72i	−0.547065	−	0.547065i	−0.925591	+	0.378526i	$0.876431\pi$
$522$		0			0
$523$	−18929.1	+	7840.67i	−1.58262	+	0.655543i	−0.988826	−	0.149075i	$-0.952370\pi$
$523$	−18929.1	+	7840.67i	−1.58262	+	0.655543i	−0.593794	+	0.804617i	$0.702370\pi$
$524$		0			0
$525$	3193.01	−	7708.61i	0.265437	−	0.640822i
$526$		0			0
$527$			15751.4i			1.30198i
$528$		0			0
$529$		−	9644.85i		−	0.792706i
$530$		0			0
$531$	1220.08	−	2945.54i	0.0997119	−	0.240726i
$532$		0			0
$533$	−1099.39	+	455.382i	−0.0893431	+	0.0370071i
$534$		0			0
$535$	−3839.73	−	3839.73i	−0.310292	−	0.310292i
$536$		0			0
$537$	−10220.2	+	10220.2i	−0.821295	+	0.821295i
$538$		0			0
$539$	−320.301	−	773.276i	−0.0255962	−	0.0617947i
$540$		0			0
$541$	−14495.4	−	6004.19i	−1.15195	−	0.477154i	−0.276765	−	0.960938i	$-0.589262\pi$
$541$	−14495.4	−	6004.19i	−1.15195	−	0.477154i	−0.875188	+	0.483783i	$0.839262\pi$
$542$		0			0
$543$	9909.05			0.783127
$544$		0			0
$545$	9384.21			0.737569
$546$		0			0
$547$	17281.4	+	7158.21i	1.35082	+	0.559530i	0.936522	−	0.350609i	$-0.114025\pi$
$547$	17281.4	+	7158.21i	1.35082	+	0.559530i	0.414303	+	0.910139i	$0.364025\pi$
$548$		0			0
$549$	−3150.76	−	7606.62i	−0.244939	−	0.591334i
$550$		0			0
$551$	26174.6	−	26174.6i	2.02373	−	2.02373i
$552$		0			0
$553$	10374.0	+	10374.0i	0.797732	+	0.797732i
$554$		0			0
$555$	4378.49	−	1813.63i	0.334877	−	0.138711i
$556$		0			0
$557$	−3341.04	+	8065.99i	−0.254155	+	0.613585i	−0.998531	−	0.0541753i	$-0.982747\pi$
$557$	−3341.04	+	8065.99i	−0.254155	+	0.613585i	0.744376	+	0.667761i	$0.232747\pi$
$558$		0			0
$559$			4593.35i			0.347546i
$560$		0			0
$561$			27418.1i			2.06345i
$562$		0			0
$563$	−4945.85	+	11940.3i	−0.370236	+	0.893828i	0.623474	+	0.781844i	$0.285721\pi$
$563$	−4945.85	+	11940.3i	−0.370236	+	0.893828i	−0.993710	+	0.111984i	$0.964279\pi$
$564$		0			0
$565$	−5851.47	+	2423.76i	−0.435705	+	0.180475i
$566$		0			0
$567$	−12110.6	−	12110.6i	−0.896994	−	0.896994i
$568$		0			0
$569$	−8205.09	+	8205.09i	−0.604526	+	0.604526i	−0.941510	−	0.336984i	$-0.890593\pi$
$569$	−8205.09	+	8205.09i	−0.604526	+	0.604526i	0.336984	+	0.941510i	$0.390593\pi$
$570$		0			0
$571$	−4078.90	−	9847.33i	−0.298943	−	0.721712i	−0.999963	−	0.00857103i	$-0.997272\pi$
$571$	−4078.90	−	9847.33i	−0.298943	−	0.721712i	0.701020	−	0.713141i	$-0.252728\pi$
$572$		0			0
$573$	−4729.67	−	1959.09i	−0.344825	−	0.142831i
$574$		0			0
$575$	3370.35			0.244441
$576$		0			0
$577$	−4675.49			−0.337337			−0.168668	−	0.985673i	$-0.553947\pi$
$577$	−4675.49			−0.337337			−0.168668	+	0.985673i	$0.553947\pi$
$578$		0			0
$579$	−25325.8	−	10490.3i	−1.81780	−	0.752958i
$580$		0			0
$581$	−452.890	−	1093.37i	−0.0323391	−	0.0780736i
$582$		0			0
$583$	−21985.6	+	21985.6i	−1.56183	+	1.56183i
$584$		0			0
$585$	−1980.99	−	1980.99i	−0.140007	−	0.140007i
$586$		0			0
$587$	−3400.03	+	1408.34i	−0.239070	+	0.0990260i	−0.499002	−	0.866601i	$-0.666300\pi$
$587$	−3400.03	+	1408.34i	−0.239070	+	0.0990260i	0.259932	+	0.965627i	$0.416300\pi$
$588$		0			0
$589$	−10803.9	+	26083.0i	−0.755804	+	1.82467i
$590$		0			0
$591$		−	30769.2i		−	2.14158i
$592$		0			0
$593$		−	15975.1i		−	1.10627i	−0.833090	−	0.553137i	$-0.813431\pi$
$593$		−	15975.1i		−	1.10627i	0.833090	−	0.553137i	$-0.186569\pi$
$594$		0			0
$595$	4286.32	−	10348.1i	0.295331	−	0.712993i
$596$		0			0
$597$	−11442.3	+	4739.54i	−0.784422	+	0.324918i
$598$		0			0
$599$	14655.9	+	14655.9i	0.999707	+	0.999707i	1.00000		0.000292806i	$-9.32030e-5\pi$
$599$	14655.9	+	14655.9i	0.999707	+	0.999707i	−0.000292806		1.00000i	$0.500093\pi$
$600$		0			0
$601$	12665.9	−	12665.9i	0.859656	−	0.859656i	−0.131641	−	0.991297i	$-0.542025\pi$
$601$	12665.9	−	12665.9i	0.859656	−	0.859656i	0.991297	+	0.131641i	$0.0420247\pi$
$602$		0			0
$603$	685.542	+	1655.05i	0.0462976	+	0.111772i
$604$		0			0
$605$	−10927.1	−	4526.16i	−0.734299	−	0.304156i
$606$		0			0
$607$	−18257.0			−1.22080			−0.610402	−	0.792092i	$-0.708992\pi$
$607$	−18257.0			−1.22080			−0.610402	+	0.792092i	$0.708992\pi$
$608$		0			0
$609$	−33028.7			−2.19768
$610$		0			0
$611$	−1752.35	−	725.849i	−0.116027	−	0.0480601i
$612$		0			0
$613$	−2056.78	−	4965.49i	−0.135518	−	0.327169i	0.841523	−	0.540221i	$-0.181659\pi$
$613$	−2056.78	−	4965.49i	−0.135518	−	0.327169i	−0.977041	+	0.213053i	$0.931659\pi$
$614$		0			0
$615$	−1838.77	+	1838.77i	−0.120564	+	0.120564i
$616$		0			0
$617$	2198.69	+	2198.69i	0.143462	+	0.143462i	0.775190	−	0.631728i	$-0.217654\pi$
$617$	2198.69	+	2198.69i	0.143462	+	0.143462i	−0.631728	+	0.775190i	$0.717654\pi$
$618$		0			0
$619$	−14373.8	+	5953.83i	−0.933331	+	0.386598i	−0.796941	−	0.604057i	$-0.793550\pi$
$619$	−14373.8	+	5953.83i	−0.933331	+	0.386598i	−0.136390	+	0.990655i	$0.543550\pi$
$620$		0			0
$621$	1374.45	−	3318.21i	0.0888159	−	0.214421i
$622$		0			0
$623$			9403.41i			0.604719i
$624$		0			0
$625$			2732.38i			0.174872i
$626$		0			0
$627$	−18806.2	+	45402.2i	−1.19784	+	2.89185i
$628$		0			0
$629$	−6813.96	+	2822.43i	−0.431940	+	0.178915i
$630$		0			0
$631$	21029.2	+	21029.2i	1.32672	+	1.32672i	0.908216	+	0.418502i	$0.137445\pi$
$631$	21029.2	+	21029.2i	1.32672	+	1.32672i	0.418502	+	0.908216i	$0.362555\pi$
$632$		0			0
$633$	14228.4	−	14228.4i	0.893410	−	0.893410i
$634$		0			0
$635$	546.098	+	1318.40i	0.0341279	+	0.0823921i
$636$		0			0
$637$	−329.074	−	136.307i	−0.0204684	−	0.00847830i
$638$		0			0
$639$	−11854.3			−0.733876
$640$		0			0
$641$	22576.4			1.39113			0.695564	−	0.718464i	$-0.255155\pi$
$641$	22576.4			1.39113			0.695564	+	0.718464i	$0.255155\pi$
$642$		0			0
$643$	−15365.6	−	6364.66i	−0.942398	−	0.390354i	−0.142029	−	0.989862i	$-0.545363\pi$
$643$	−15365.6	−	6364.66i	−0.942398	−	0.390354i	−0.800368	+	0.599509i	$0.795363\pi$
$644$		0			0
$645$	3841.29	+	9273.69i	0.234497	+	0.566126i
$646$		0			0
$647$	2866.06	−	2866.06i	0.174152	−	0.174152i	−0.614649	−	0.788801i	$-0.710702\pi$
$647$	2866.06	−	2866.06i	0.174152	−	0.174152i	0.788801	+	0.614649i	$0.210702\pi$
$648$		0			0
$649$	−7518.24	−	7518.24i	−0.454725	−	0.454725i
$650$		0			0
$651$	23273.1	−	9640.03i	1.40114	−	0.580373i
$652$		0			0
$653$	−1656.18	+	3998.36i	−0.0992514	+	0.239614i	−0.965704	−	0.259645i	$-0.916394\pi$
$653$	−1656.18	+	3998.36i	−0.0992514	+	0.239614i	0.866453	+	0.499259i	$0.166394\pi$
$654$		0			0
$655$			8245.81i			0.491894i
$656$		0			0
$657$			5567.05i			0.330580i
$658$		0			0
$659$	7707.07	−	18606.5i	0.455576	−	1.09986i	−0.514594	−	0.857434i	$-0.672057\pi$
$659$	7707.07	−	18606.5i	0.455576	−	1.09986i	0.970170	−	0.242424i	$-0.0779426\pi$
$660$		0			0
$661$	25591.1	−	10600.2i	1.50587	−	0.623751i	0.531168	−	0.847267i	$-0.321753\pi$
$661$	25591.1	−	10600.2i	1.50587	−	0.623751i	0.974700	+	0.223515i	$0.0717533\pi$
$662$		0			0
$663$	8250.53	+	8250.53i	0.483294	+	0.483294i
$664$		0			0
$665$	14195.6	−	14195.6i	0.827791	−	0.827791i
$666$		0			0
$667$	−5105.58	−	12326.0i	−0.296385	−	0.715537i
$668$		0			0
$669$	14934.9	+	6186.24i	0.863105	+	0.357510i
$670$		0			0
$671$	−27457.3			−1.57970
$672$		0			0
$673$	−32715.5			−1.87383			−0.936917	−	0.349553i	$-0.886333\pi$
$673$	−32715.5			−1.87383			−0.936917	+	0.349553i	$0.886333\pi$
$674$		0			0
$675$	−4434.14	−	1836.68i	−0.252844	−	0.104732i
$676$		0			0
$677$	−249.757	−	602.967i	−0.0141786	−	0.0342303i	0.916632	−	0.399733i	$-0.130897\pi$
$677$	−249.757	−	602.967i	−0.0141786	−	0.0342303i	−0.930810	+	0.365503i	$0.880897\pi$
$678$		0			0
$679$	17434.2	−	17434.2i	0.985365	−	0.985365i
$680$		0			0
$681$	−14634.1	−	14634.1i	−0.823466	−	0.823466i
$682$		0			0
$683$	1024.16	−	424.220i	0.0573767	−	0.0237662i	−0.353811	−	0.935317i	$-0.615114\pi$
$683$	1024.16	−	424.220i	0.0573767	−	0.0237662i	0.411187	+	0.911551i	$0.365114\pi$
$684$		0			0
$685$	−5243.38	+	12658.6i	−0.292466	+	0.706075i
$686$		0			0
$687$		−	9920.29i		−	0.550921i
$688$		0			0
$689$			13231.6i			0.731615i
$690$		0			0
$691$	6429.36	−	15521.9i	0.353957	−	0.854528i	−0.642166	−	0.766565i	$-0.721964\pi$
$691$	6429.36	−	15521.9i	0.353957	−	0.854528i	0.996124	−	0.0879632i	$-0.0280358\pi$
$692$		0			0
$693$	15137.3	−	6270.08i	0.829753	−	0.343695i
$694$		0			0
$695$	−12399.0	−	12399.0i	−0.676721	−	0.676721i
$696$		0			0
$697$	2861.56	−	2861.56i	0.155508	−	0.155508i
$698$		0			0
$699$	10793.3	+	26057.4i	0.584037	+	1.40999i
$700$		0			0
$701$	20337.8	+	8424.21i	1.09579	+	0.453892i	0.856023	−	0.516938i	$-0.172928\pi$
$701$	20337.8	+	8424.21i	1.09579	+	0.453892i	0.239769	+	0.970830i	$0.422928\pi$
$702$		0			0
$703$	−13219.3			−0.709209
$704$		0			0
$705$	−4144.90			−0.221427
$706$		0			0
$707$	11667.2	+	4832.72i	0.620638	+	0.257077i
$708$		0			0
$709$	−11697.5	−	28240.4i	−0.619620	−	1.49589i	−0.852146	−	0.523304i	$-0.824699\pi$
$709$	−11697.5	−	28240.4i	−0.619620	−	1.49589i	0.232527	−	0.972590i	$-0.425301\pi$
$710$		0			0
$711$	−8824.29	+	8824.29i	−0.465452	+	0.465452i
$712$		0			0
$713$	7195.13	+	7195.13i	0.377924	+	0.377924i
$714$		0			0
$715$	−8631.68	+	3575.36i	−0.451478	+	0.187008i
$716$		0			0
$717$	171.310	−	413.578i	0.00892284	−	0.0215416i
$718$		0			0
$719$		−	2930.75i		−	0.152015i	−0.997107	−	0.0760074i	$-0.975783\pi$
$719$		−	2930.75i		−	0.152015i	0.997107	−	0.0760074i	$-0.0242173\pi$
$720$		0			0
$721$			3211.34i			0.165876i
$722$		0			0
$723$	15364.8	−	37093.9i	0.790350	−	1.90807i
$724$		0			0
$725$	−16471.2	+	6822.61i	−0.843760	+	0.349497i
$726$		0			0
$727$	11618.1	+	11618.1i	0.592696	+	0.592696i	0.938359	−	0.345663i	$-0.112346\pi$
$727$	11618.1	+	11618.1i	0.592696	+	0.592696i	−0.345663	+	0.938359i	$0.612346\pi$
$728$		0			0
$729$	1336.91	−	1336.91i	0.0679218	−	0.0679218i
$730$		0			0
$731$	−5977.94	−	14432.0i	−0.302465	−	0.730215i
$732$		0			0
$733$	8786.76	+	3639.59i	0.442764	+	0.183399i	0.592917	−	0.805264i	$-0.297976\pi$
$733$	8786.76	+	3639.59i	0.442764	+	0.183399i	−0.150152	+	0.988663i	$0.547976\pi$
$734$		0			0
$735$	−778.369			−0.0390620
$736$		0			0
$737$	5974.15			0.298590
$738$		0			0
$739$	30367.3	+	12578.6i	1.51161	+	0.626130i	0.975890	−	0.218265i	$-0.0700397\pi$
$739$	30367.3	+	12578.6i	1.51161	+	0.626130i	0.535721	+	0.844395i	$0.320040\pi$
$740$		0			0
$741$	8003.13	+	19321.3i	0.396764	+	0.957874i
$742$		0			0
$743$	−28118.1	+	28118.1i	−1.38836	+	1.38836i	−0.559596	+	0.828765i	$0.689044\pi$
$743$	−28118.1	+	28118.1i	−1.38836	+	1.38836i	−0.828765	+	0.559596i	$0.810956\pi$
$744$		0			0
$745$	−810.288	−	810.288i	−0.0398479	−	0.0398479i
$746$		0			0
$747$	930.043	−	385.236i	0.0455535	−	0.0188689i
$748$		0			0
$749$	5171.89	−	12486.1i	0.252305	−	0.609119i
$750$		0			0
$751$			2199.78i			0.106886i	0.998571	+	0.0534428i	$0.0170195\pi$
$751$			2199.78i			0.106886i	−0.998571	+	0.0534428i	$0.982981\pi$
$752$		0			0
$753$		−	3152.65i		−	0.152575i
$754$		0			0
$755$	8348.32	−	20154.6i	0.402419	−	0.971525i
$756$		0			0
$757$	1609.12	−	666.518i	0.0772581	−	0.0320013i	−0.343720	−	0.939072i	$-0.611687\pi$
$757$	1609.12	−	666.518i	0.0772581	−	0.0320013i	0.420978	+	0.907071i	$0.361687\pi$
$758$		0			0
$759$	12524.4	+	12524.4i	0.598955	+	0.598955i
$760$		0			0
$761$	−13159.3	+	13159.3i	−0.626837	+	0.626837i	−0.947271	−	0.320434i	$-0.896171\pi$
$761$	−13159.3	+	13159.3i	−0.626837	+	0.626837i	0.320434	+	0.947271i	$0.396171\pi$
$762$		0			0
$763$	8937.81	+	21577.8i	0.424077	+	1.02381i
$764$		0			0
$765$	8802.28	+	3646.02i	0.416009	+	0.172317i
$766$		0			0
$767$	−4524.70			−0.213008
$768$		0			0
$769$	−13781.4			−0.646253			−0.323127	−	0.946356i	$-0.604734\pi$
$769$	−13781.4			−0.646253			−0.323127	+	0.946356i	$0.604734\pi$
$770$		0			0
$771$	−158.533	−	65.6667i	−0.00740524	−	0.00306735i
$772$		0			0
$773$	−904.546	−	2183.77i	−0.0420883	−	0.101610i	0.901437	−	0.432909i	$-0.142513\pi$
$773$	−904.546	−	2183.77i	−0.0420883	−	0.101610i	−0.943526	+	0.331299i	$0.892513\pi$
$774$		0			0
$775$	9614.87	−	9614.87i	0.445647	−	0.445647i
$776$		0			0
$777$	8340.43	+	8340.43i	0.385085	+	0.385085i
$778$		0			0
$779$	6701.26	−	2775.75i	0.308213	−	0.127666i
$780$		0			0
$781$	−15128.5	+	36523.4i	−0.693137	+	1.67338i
$782$		0			0
$783$			18998.7i			0.867124i
$784$		0			0
$785$		−	6725.96i		−	0.305809i
$786$		0			0
$787$	7363.51	−	17777.1i	0.333521	−	0.805190i	−0.664787	−	0.747033i	$-0.731478\pi$
$787$	7363.51	−	17777.1i	0.333521	−	0.805190i	0.998307	−	0.0581569i	$-0.0185224\pi$
$788$		0			0
$789$	20630.9	−	8545.61i	0.930901	−	0.385592i
$790$		0			0
$791$	−11146.2	−	11146.2i	−0.501030	−	0.501030i
$792$		0			0
$793$	−8262.32	+	8262.32i	−0.369992	+	0.369992i
$794$		0			0
$795$	11065.2	+	26713.7i	0.493637	+	1.19175i
$796$		0			0
$797$	−2646.36	−	1096.16i	−0.117615	−	0.0487177i	0.323100	−	0.946365i	$-0.395275\pi$
$797$	−2646.36	−	1096.16i	−0.117615	−	0.0487177i	−0.440715	+	0.897647i	$0.645275\pi$
$798$		0			0
$799$	6450.42			0.285607
$800$		0			0
$801$	−7998.71			−0.352835
$802$		0			0
$803$	17152.3	+	7104.71i	0.753787	+	0.312229i
$804$		0			0
$805$	−2768.97	−	6684.89i	−0.121234	−	0.292685i
$806$		0			0
$807$	39035.6	−	39035.6i	1.70275	−	1.70275i
$808$		0			0
$809$	−25414.2	−	25414.2i	−1.10447	−	1.10447i	−0.993864	−	0.110607i	$-0.964720\pi$
$809$	−25414.2	−	25414.2i	−1.10447	−	1.10447i	−0.110607	−	0.993864i	$-0.535280\pi$
$810$		0			0
$811$	−3623.77	+	1501.01i	−0.156902	+	0.0649910i	−0.459752	−	0.888047i	$-0.652062\pi$
$811$	−3623.77	+	1501.01i	−0.156902	+	0.0649910i	0.302850	+	0.953038i	$0.402062\pi$
$812$		0			0
$813$	10300.5	−	24867.6i	0.444347	−	1.07275i
$814$		0			0
$815$		−	7852.38i		−	0.337493i
$816$		0			0
$817$		−	27998.5i		−	1.19895i
$818$		0			0
$819$	2668.28	−	6441.80i	0.113843	−	0.274841i
$820$		0			0
$821$	−12700.5	+	5260.71i	−0.539890	+	0.223630i	−0.635929	−	0.771748i	$-0.719383\pi$
$821$	−12700.5	+	5260.71i	−0.539890	+	0.223630i	0.0960388	+	0.995378i	$0.469383\pi$
$822$		0			0
$823$	−12604.5	−	12604.5i	−0.533857	−	0.533857i	0.387861	−	0.921718i	$-0.373214\pi$
$823$	−12604.5	−	12604.5i	−0.533857	−	0.533857i	−0.921718	+	0.387861i	$0.873214\pi$
$824$		0			0
$825$	16736.4	−	16736.4i	0.706287	−	0.706287i
$826$		0			0
$827$	759.345	+	1833.22i	0.0319287	+	0.0770826i	0.939040	−	0.343809i	$-0.111717\pi$
$827$	759.345	+	1833.22i	0.0319287	+	0.0770826i	−0.907111	+	0.420892i	$0.861717\pi$
$828$		0			0
$829$	33918.6	+	14049.5i	1.42104	+	0.588614i	0.955122	−	0.296214i	$-0.0957241\pi$
$829$	33918.6	+	14049.5i	1.42104	+	0.588614i	0.465918	+	0.884828i	$0.345724\pi$
$830$		0			0
$831$	−445.072			−0.0185793
$832$		0			0
$833$	1211.32			0.0503840
$834$		0			0
$835$	−8908.70	−	3690.10i	−0.369219	−	0.152936i
$836$		0			0
$837$	−5545.12	−	13387.1i	−0.228993	−	0.552839i
$838$		0			0
$839$	−23682.3	+	23682.3i	−0.974498	+	0.974498i	−0.999683	−	0.0251848i	$-0.991983\pi$
$839$	−23682.3	+	23682.3i	−0.974498	+	0.974498i	0.0251848	+	0.999683i	$0.491983\pi$
$840$		0			0
$841$	32657.3	+	32657.3i	1.33902	+	1.33902i
$842$		0			0
$843$	3187.01	−	1320.10i	0.130209	−	0.0539344i
$844$		0			0
$845$	4875.38	−	11770.2i	0.198483	−	0.479180i
$846$		0			0
$847$		−	29436.4i		−	1.19415i
$848$		0			0
$849$			19743.8i			0.798122i
$850$		0			0
$851$	−1823.30	+	4401.83i	−0.0734452	+	0.177312i
$852$		0			0
$853$	−22116.2	+	9160.83i	−0.887742	+	0.367715i	−0.779495	−	0.626409i	$-0.784524\pi$
$853$	−22116.2	+	9160.83i	−0.887742	+	0.367715i	−0.108248	+	0.994124i	$0.534524\pi$
$854$		0			0
$855$	12075.0	+	12075.0i	0.482991	+	0.482991i
$856$		0			0
$857$	28853.3	−	28853.3i	1.15007	−	1.15007i	0.163530	−	0.986538i	$-0.447712\pi$
$857$	28853.3	−	28853.3i	1.15007	−	1.15007i	0.986538	−	0.163530i	$-0.0522880\pi$
$858$		0			0
$859$	−4841.92	−	11689.4i	−0.192321	−	0.464305i	0.798076	−	0.602557i	$-0.205851\pi$
$859$	−4841.92	−	11689.4i	−0.192321	−	0.464305i	−0.990397	+	0.138252i	$0.955851\pi$
$860$		0			0
$861$	−5979.33	−	2476.72i	−0.236673	−	0.0980330i
$862$		0			0
$863$	17390.7			0.685965			0.342982	−	0.939342i	$-0.388563\pi$
$863$	17390.7			0.685965			0.342982	+	0.939342i	$0.388563\pi$
$864$		0			0
$865$	5333.29			0.209639
$866$		0			0
$867$	−6858.61	−	2840.93i	−0.268663	−	0.111284i
$868$		0			0
$869$	15926.3	+	38449.6i	0.621708	+	1.50094i
$870$		0			0
$871$	1797.71	−	1797.71i	0.0699348	−	0.0699348i
$872$		0			0
$873$	14829.8	+	14829.8i	0.574930	+	0.574930i
$874$		0			0
$875$	−25571.7	+	10592.2i	−0.987980	+	0.409235i
$876$		0			0
$877$	596.594	−	1440.31i	0.0229710	−	0.0554569i	−0.911978	−	0.410239i	$-0.865445\pi$
$877$	596.594	−	1440.31i	0.0229710	−	0.0554569i	0.934949	+	0.354783i	$0.115445\pi$
$878$		0			0
$879$			26542.3i			1.01849i
$880$		0			0
$881$		−	33644.4i		−	1.28662i	−0.765607	−	0.643308i	$-0.777561\pi$
$881$		−	33644.4i		−	1.28662i	0.765607	−	0.643308i	$-0.222439\pi$
$882$		0			0
$883$	−4327.10	+	10446.6i	−0.164913	+	0.398136i	−0.984635	−	0.174626i	$-0.944128\pi$
$883$	−4327.10	+	10446.6i	−0.164913	+	0.398136i	0.819721	+	0.572763i	$0.194128\pi$
$884$		0			0
$885$	−9135.08	+	3783.87i	−0.346974	+	0.143721i
$886$		0			0
$887$	−13569.1	−	13569.1i	−0.513647	−	0.513647i	0.401995	−	0.915642i	$-0.368317\pi$
$887$	−13569.1	−	13569.1i	−0.513647	−	0.513647i	−0.915642	+	0.401995i	$0.868317\pi$
$888$		0			0
$889$	−2511.36	+	2511.36i	−0.0947451	+	0.0947451i
$890$		0			0
$891$	−18592.4	−	44886.0i	−0.699067	−	1.68770i
$892$		0			0
$893$	10681.4	+	4424.37i	0.400267	+	0.165796i
$894$		0			0
$895$	16749.4			0.625554
$896$		0			0
$897$	7537.56			0.280571
$898$		0			0
$899$	−49728.3	−	20598.2i	−1.84486	−	0.764168i
$900$		0			0
$901$	−17220.0	−	41572.8i	−0.636716	−	1.53717i
$902$		0			0
$903$	−17665.1	+	17665.1i	−0.651005	+	0.651005i
$904$		0			0
$905$	−8119.71	−	8119.71i	−0.298241	−	0.298241i
$906$		0			0
$907$	−23791.9	+	9854.94i	−0.871001	+	0.360780i	−0.773000	−	0.634406i	$-0.781245\pi$
$907$	−23791.9	+	9854.94i	−0.871001	+	0.360780i	−0.0980007	+	0.995186i	$0.531245\pi$
$908$		0			0
$909$	−4110.80	+	9924.36i	−0.149996	+	0.362123i
$910$		0			0
$911$			42220.1i			1.53547i	0.640767	+	0.767736i	$0.278617\pi$
$911$			42220.1i			1.53547i	−0.640767	+	0.767736i	$0.721383\pi$
$912$		0			0
$913$		−	3357.14i		−	0.121692i
$914$		0			0
$915$	−9771.56	+	23590.6i	−0.353047	+	0.852330i
$916$		0			0
$917$	−18960.2	+	7853.57i	−0.682792	+	0.282822i
$918$		0			0
$919$	29324.7	+	29324.7i	1.05259	+	1.05259i	0.998538	+	0.0540546i	$0.0172145\pi$
$919$	29324.7	+	29324.7i	1.05259	+	1.05259i	0.0540546	+	0.998538i	$0.482786\pi$
$920$		0			0
$921$	−25660.6	+	25660.6i	−0.918072	+	0.918072i
$922$		0			0
$923$	6438.05	+	15542.8i	0.229589	+	0.554278i
$924$		0			0
$925$	5882.18	+	2436.48i	0.209086	+	0.0866065i
$926$		0			0
$927$	−2731.63			−0.0967836
$928$		0			0
$929$	−12957.9			−0.457625			−0.228812	−	0.973471i	$-0.573484\pi$
$929$	−12957.9			−0.457625			−0.228812	+	0.973471i	$0.573484\pi$
$930$		0			0
$931$	2005.85	+	830.850i	0.0706112	+	0.0292481i
$932$		0			0
$933$	−12689.5	−	30635.1i	−0.445268	−	1.07497i
$934$		0			0
$935$	22467.1	−	22467.1i	0.785831	−	0.785831i
$936$		0			0
$937$	30016.0	+	30016.0i	1.04651	+	1.04651i	0.998864	+	0.0476462i	$0.0151720\pi$
$937$	30016.0	+	30016.0i	1.04651	+	1.04651i	0.0476462	+	0.998864i	$0.484828\pi$
$938$		0			0
$939$	−2613.54	+	1082.56i	−0.0908304	+	0.0376232i
$940$		0			0
$941$	−15045.0	+	36321.8i	−0.521203	+	1.25830i	0.415953	+	0.909386i	$0.363448\pi$
$941$	−15045.0	+	36321.8i	−0.521203	+	1.25830i	−0.937156	+	0.348910i	$0.886552\pi$
$942$		0			0
$943$		−	2614.28i		−	0.0902786i
$944$		0			0
$945$			10303.8i			0.354690i
$946$		0			0
$947$	−12223.9	+	29511.1i	−0.419454	+	1.01265i	0.563052	+	0.826421i	$0.309627\pi$
$947$	−12223.9	+	29511.1i	−0.419454	+	1.01265i	−0.982506	+	0.186230i	$0.940373\pi$
$948$		0			0
$949$	7299.30	−	3023.47i	0.249679	−	0.103420i
$950$		0			0
$951$	−34085.0	−	34085.0i	−1.16223	−	1.16223i
$952$		0			0
$953$	−26512.6	+	26512.6i	−0.901183	+	0.901183i	−0.995539	−	0.0943555i	$-0.969921\pi$
$953$	−26512.6	+	26512.6i	−0.901183	+	0.901183i	0.0943555	+	0.995539i	$0.469921\pi$
$954$		0			0
$955$	2270.28	+	5480.93i	0.0769261	+	0.185716i
$956$		0			0
$957$	−86561.1	−	35854.8i	−2.92385	−	1.21110i
$958$		0			0
$959$	−34100.9			−1.14825
$960$		0			0
$961$	11261.2			0.378007
$962$		0			0
$963$	10620.9	+	4399.31i	0.355402	+	0.147213i
$964$		0			0
$965$	12156.6	+	29348.6i	0.405528	+	0.979031i
$966$		0			0
$967$	−2114.28	+	2114.28i	−0.0703109	+	0.0703109i	−0.741388	−	0.671077i	$-0.765832\pi$
$967$	−2114.28	+	2114.28i	−0.0703109	+	0.0703109i	0.671077	+	0.741388i	$0.265832\pi$
$968$		0			0
$969$	−50290.6	−	50290.6i	−1.66725	−	1.66725i
$970$		0			0
$971$	9687.75	−	4012.80i	0.320180	−	0.132623i	−0.216805	−	0.976215i	$-0.569563\pi$
$971$	9687.75	−	4012.80i	0.320180	−	0.132623i	0.536984	+	0.843592i	$0.319563\pi$
$972$		0			0
$973$	16700.7	−	40319.1i	0.550257	−	1.32844i
$974$		0			0
$975$		−	10072.5i		−	0.330849i
$976$		0			0
$977$			29819.0i			0.976453i	0.872717	+	0.488226i	$0.162356\pi$
$977$			29819.0i			0.976453i	−0.872717	+	0.488226i	$0.837644\pi$
$978$		0			0
$979$	−10208.0	+	24644.3i	−0.333248	+	0.804532i
$980$		0			0
$981$	−18354.5	+	7602.67i	−0.597363	+	0.247436i
$982$		0			0
$983$	−30424.5	−	30424.5i	−0.987174	−	0.987174i	0.0127444	−	0.999919i	$-0.495943\pi$
$983$	−30424.5	−	30424.5i	−0.987174	−	0.987174i	−0.999919	+	0.0127444i	$0.995943\pi$
$984$		0			0
$985$	−25213.0	+	25213.0i	−0.815587	+	0.815587i
$986$		0			0
$987$	−3947.73	−	9530.66i	−0.127313	−	0.307360i
$988$		0			0
$989$	−9323.11	−	3861.76i	−0.299755	−	0.124163i
$990$		0			0
$991$	23803.1			0.762999			0.381499	−	0.924369i	$-0.375408\pi$
$991$	23803.1			0.762999			0.381499	+	0.924369i	$0.375408\pi$
$992$		0			0
$993$	26082.8			0.833547
$994$		0			0
$995$	13259.7	+	5492.36i	0.422474	+	0.174995i
$996$		0			0
$997$	2498.66	+	6032.29i	0.0793714	+	0.191619i	0.958584	−	0.284810i	$-0.0919306\pi$
$997$	2498.66	+	6032.29i	0.0793714	+	0.191619i	−0.879213	+	0.476430i	$0.841931\pi$
$998$		0			0
$999$	4797.57	−	4797.57i	0.151940	−	0.151940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.81.10		44
4.3	odd	2		32.4.g.a.29.5	yes	44
8.3	odd	2		256.4.g.b.161.10		44
8.5	even	2		256.4.g.a.161.2		44
32.5	even	8		256.4.g.a.97.2		44
32.11	odd	8		32.4.g.a.21.5	✓	44
32.21	even	8	inner	128.4.g.a.49.10		44
32.27	odd	8		256.4.g.b.97.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.5	✓	44	32.11	odd	8
32.4.g.a.29.5	yes	44	4.3	odd	2
128.4.g.a.49.10		44	32.21	even	8	inner
128.4.g.a.81.10		44	1.1	even	1	trivial
256.4.g.a.97.2		44	32.5	even	8
256.4.g.a.161.2		44	8.5	even	2
256.4.g.b.97.10		44	32.27	odd	8
256.4.g.b.161.10		44	8.3	odd	2

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.06585 + 2.51256i) q^{3} +(-2.91165 - 7.02935i) q^{5} +(13.3899 - 13.3899i) q^{7} +(11.3897 + 11.3897i) q^{9} +O(q^{10})\)	\(q+(6.06585 + 2.51256i) q^{3} +(-2.91165 - 7.02935i) q^{5} +(13.3899 - 13.3899i) q^{7} +(11.3897 + 11.3897i) q^{9} +(49.6279 - 20.5565i) q^{11} +(8.74801 - 21.1196i) q^{13} -49.9547i q^{15} +77.7412i q^{17} +(-53.3229 + 128.733i) q^{19} +(114.864 - 47.5784i) q^{21} +(35.5116 + 35.5116i) q^{23} +(47.4543 - 47.4543i) q^{25} +(-27.3680 - 66.0722i) q^{27} +(-245.435 - 101.662i) q^{29} +202.613 q^{31} +352.685 q^{33} +(-133.110 - 55.1358i) q^{35} +(36.3055 + 87.6493i) q^{37} +(106.128 - 106.128i) q^{39} +(-36.8088 - 36.8088i) q^{41} +(-185.642 + 76.8954i) q^{43} +(46.8995 - 113.225i) q^{45} -82.9731i q^{47} -15.5815i q^{49} +(-195.329 + 471.567i) q^{51} +(-534.758 + 221.504i) q^{53} +(-288.998 - 288.998i) q^{55} +(-646.898 + 646.898i) q^{57} +(-75.7461 - 182.867i) q^{59} +(-472.240 - 195.608i) q^{61} +305.016 q^{63} -173.928 q^{65} +(102.750 + 42.5604i) q^{67} +(126.183 + 304.633i) q^{69} +(-520.392 + 520.392i) q^{71} +(244.389 + 244.389i) q^{73} +(407.082 - 168.619i) q^{75} +(389.264 - 939.766i) q^{77} +774.758i q^{79} -904.451i q^{81} +(23.9166 - 57.7397i) q^{83} +(546.470 - 226.355i) q^{85} +(-1233.34 - 1233.34i) q^{87} +(-351.137 + 351.137i) q^{89} +(-165.654 - 399.925i) q^{91} +(1229.02 + 509.078i) q^{93} +1060.17 q^{95} +1302.03 q^{97} +(799.382 + 331.115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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