LMFDB - Embedded newform 128.3.h.a.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

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([4, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.h (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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			79.3
Character	$\chi$	$=$	128.79
Dual form			128.3.h.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.527719 - 1.27403i) q^{3} +(-0.642823 + 1.55191i) q^{5} +(4.95044 - 4.95044i) q^{7} +(5.01930 - 5.01930i) q^{9} +O(q^{10})$	\(q+(-0.527719 - 1.27403i) q^{3} +(-0.642823 + 1.55191i) q^{5} +(4.95044 - 4.95044i) q^{7} +(5.01930 - 5.01930i) q^{9} +(4.27221 - 10.3140i) q^{11} +(1.68327 + 4.06379i) q^{13} +2.31641 q^{15} -28.6469i q^{17} +(-17.5460 + 7.26778i) q^{19} +(-8.91944 - 3.69455i) q^{21} +(24.3334 + 24.3334i) q^{23} +(15.6825 + 15.6825i) q^{25} +(-20.5098 - 8.49542i) q^{27} +(8.57286 - 3.55100i) q^{29} +5.73273i q^{31} -15.3949 q^{33} +(4.50039 + 10.8649i) q^{35} +(-26.1364 + 63.0989i) q^{37} +(4.28908 - 4.28908i) q^{39} +(-14.2561 + 14.2561i) q^{41} +(10.1365 - 24.4717i) q^{43} +(4.56299 + 11.0160i) q^{45} -57.9804 q^{47} -0.0137567i q^{49} +(-36.4969 + 15.1175i) q^{51} +(-46.3830 - 19.2124i) q^{53} +(13.2602 + 13.2602i) q^{55} +(18.5187 + 18.5187i) q^{57} +(27.6347 + 11.4467i) q^{59} +(76.3985 - 31.6453i) q^{61} -49.6955i q^{63} -7.38868 q^{65} +(36.1949 + 87.3821i) q^{67} +(18.1602 - 43.8425i) q^{69} +(5.39666 - 5.39666i) q^{71} +(-25.4031 + 25.4031i) q^{73} +(11.7039 - 28.2558i) q^{75} +(-29.9097 - 72.2084i) q^{77} -50.1674 q^{79} -33.2721i q^{81} +(100.805 - 41.7550i) q^{83} +(44.4574 + 18.4149i) q^{85} +(-9.04814 - 9.04814i) q^{87} +(10.6266 + 10.6266i) q^{89} +(28.4505 + 11.7846i) q^{91} +(7.30366 - 3.02527i) q^{93} -31.9017i q^{95} -14.3055 q^{97} +(-30.3257 - 73.2128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.527719	−	1.27403i	−0.175906	−	0.424676i	0.811194	−	0.584777i	$-0.198818\pi$
$3$	−0.527719	−	1.27403i	−0.175906	−	0.424676i	−0.987101	+	0.160101i	$0.948818\pi$
$4$		0			0
$5$	−0.642823	+	1.55191i	−0.128565	+	0.310382i	−0.975034	−	0.222055i	$-0.928724\pi$
$5$	−0.642823	+	1.55191i	−0.128565	+	0.310382i	0.846470	+	0.532437i	$0.178724\pi$
$6$		0			0
$7$	4.95044	−	4.95044i	0.707206	−	0.707206i	−0.258741	−	0.965947i	$-0.583308\pi$
$7$	4.95044	−	4.95044i	0.707206	−	0.707206i	0.965947	+	0.258741i	$0.0833075\pi$
$8$		0			0
$9$	5.01930	−	5.01930i	0.557700	−	0.557700i
$10$		0			0
$11$	4.27221	−	10.3140i	0.388383	−	0.937640i	−0.601900	−	0.798572i	$-0.705589\pi$
$11$	4.27221	−	10.3140i	0.388383	−	0.937640i	0.990283	−	0.139068i	$-0.0444106\pi$
$12$		0			0
$13$	1.68327	+	4.06379i	0.129483	+	0.312599i	0.975304	−	0.220868i	$-0.0708890\pi$
$13$	1.68327	+	4.06379i	0.129483	+	0.312599i	−0.845821	+	0.533467i	$0.820889\pi$
$14$		0			0
$15$	2.31641			0.154427
$16$		0			0
$17$		−	28.6469i		−	1.68511i	−0.538609	−	0.842556i	$-0.681050\pi$
$17$		−	28.6469i		−	1.68511i	0.538609	−	0.842556i	$-0.318950\pi$
$18$		0			0
$19$	−17.5460	+	7.26778i	−0.923473	+	0.382515i	−0.793199	−	0.608963i	$-0.791586\pi$
$19$	−17.5460	+	7.26778i	−0.923473	+	0.382515i	−0.130274	+	0.991478i	$0.541586\pi$
$20$		0			0
$21$	−8.91944	−	3.69455i	−0.424735	−	0.175931i
$22$		0			0
$23$	24.3334	+	24.3334i	1.05797	+	1.05797i	0.998213	+	0.0597590i	$0.0190332\pi$
$23$	24.3334	+	24.3334i	1.05797	+	1.05797i	0.0597590	+	0.998213i	$0.480967\pi$
$24$		0			0
$25$	15.6825	+	15.6825i	0.627298	+	0.627298i
$26$		0			0
$27$	−20.5098	−	8.49542i	−0.759621	−	0.314645i
$28$		0			0
$29$	8.57286	−	3.55100i	0.295616	−	0.122448i	−0.229946	−	0.973203i	$-0.573855\pi$
$29$	8.57286	−	3.55100i	0.295616	−	0.122448i	0.525562	+	0.850755i	$0.323855\pi$
$30$		0			0
$31$			5.73273i			0.184927i	0.995716	+	0.0924634i	$0.0294741\pi$
$31$			5.73273i			0.184927i	−0.995716	+	0.0924634i	$0.970526\pi$
$32$		0			0
$33$	−15.3949			−0.466512
$34$		0			0
$35$	4.50039	+	10.8649i	0.128583	+	0.310426i
$36$		0			0
$37$	−26.1364	+	63.0989i	−0.706390	+	1.70538i	0.00244114	+	0.999997i	$0.499223\pi$
$37$	−26.1364	+	63.0989i	−0.706390	+	1.70538i	−0.708831	+	0.705379i	$0.750777\pi$
$38$		0			0
$39$	4.28908	−	4.28908i	0.109976	−	0.109976i
$40$		0			0
$41$	−14.2561	+	14.2561i	−0.347711	+	0.347711i	−0.859256	−	0.511545i	$-0.829073\pi$
$41$	−14.2561	+	14.2561i	−0.347711	+	0.347711i	0.511545	+	0.859256i	$0.329073\pi$
$42$		0			0
$43$	10.1365	−	24.4717i	0.235733	−	0.569109i	−0.761100	−	0.648634i	$-0.775340\pi$
$43$	10.1365	−	24.4717i	0.235733	−	0.569109i	0.996833	+	0.0795253i	$0.0253404\pi$
$44$		0			0
$45$	4.56299	+	11.0160i	0.101400	+	0.244801i
$46$		0			0
$47$	−57.9804			−1.23363			−0.616813	−	0.787110i	$-0.711576\pi$
$47$	−57.9804			−1.23363			−0.616813	+	0.787110i	$0.711576\pi$
$48$		0			0
$49$		−	0.0137567i		−	0.000280749i
$50$		0			0
$51$	−36.4969	+	15.1175i	−0.715626	+	0.296422i
$52$		0			0
$53$	−46.3830	−	19.2124i	−0.875150	−	0.362499i	−0.100536	−	0.994933i	$-0.532056\pi$
$53$	−46.3830	−	19.2124i	−0.875150	−	0.362499i	−0.774614	+	0.632434i	$0.782056\pi$
$54$		0			0
$55$	13.2602	+	13.2602i	0.241094	+	0.241094i
$56$		0			0
$57$	18.5187	+	18.5187i	0.324890	+	0.324890i
$58$		0			0
$59$	27.6347	+	11.4467i	0.468384	+	0.194011i	0.604377	−	0.796699i	$-0.293422\pi$
$59$	27.6347	+	11.4467i	0.468384	+	0.194011i	−0.135992	+	0.990710i	$0.543422\pi$
$60$		0			0
$61$	76.3985	−	31.6453i	1.25243	−	0.518775i	0.344855	−	0.938656i	$-0.387928\pi$
$61$	76.3985	−	31.6453i	1.25243	−	0.518775i	0.907579	+	0.419881i	$0.137928\pi$
$62$		0			0
$63$		−	49.6955i		−	0.788818i
$64$		0			0
$65$	−7.38868			−0.113672
$66$		0			0
$67$	36.1949	+	87.3821i	0.540222	+	1.30421i	0.924566	+	0.381021i	$0.124427\pi$
$67$	36.1949	+	87.3821i	0.540222	+	1.30421i	−0.384345	+	0.923190i	$0.625573\pi$
$68$		0			0
$69$	18.1602	−	43.8425i	0.263191	−	0.635399i
$70$		0			0
$71$	5.39666	−	5.39666i	0.0760092	−	0.0760092i	−0.668080	−	0.744089i	$-0.732884\pi$
$71$	5.39666	−	5.39666i	0.0760092	−	0.0760092i	0.744089	+	0.668080i	$0.232884\pi$
$72$		0			0
$73$	−25.4031	+	25.4031i	−0.347988	+	0.347988i	−0.859360	−	0.511372i	$-0.829137\pi$
$73$	−25.4031	+	25.4031i	−0.347988	+	0.347988i	0.511372	+	0.859360i	$0.329137\pi$
$74$		0			0
$75$	11.7039	−	28.2558i	0.156053	−	0.376744i
$76$		0			0
$77$	−29.9097	−	72.2084i	−0.388438	−	0.937771i
$78$		0			0
$79$	−50.1674			−0.635030			−0.317515	−	0.948253i	$-0.602848\pi$
$79$	−50.1674			−0.635030			−0.317515	+	0.948253i	$0.602848\pi$
$80$		0			0
$81$		−	33.2721i		−	0.410767i
$82$		0			0
$83$	100.805	−	41.7550i	1.21452	−	0.503072i	0.318859	−	0.947802i	$-0.396700\pi$
$83$	100.805	−	41.7550i	1.21452	−	0.503072i	0.895665	+	0.444730i	$0.146700\pi$
$84$		0			0
$85$	44.4574	+	18.4149i	0.523029	+	0.216646i
$86$		0			0
$87$	−9.04814	−	9.04814i	−0.104002	−	0.104002i
$88$		0			0
$89$	10.6266	+	10.6266i	0.119400	+	0.119400i	0.764282	−	0.644882i	$-0.223094\pi$
$89$	10.6266	+	10.6266i	0.119400	+	0.119400i	−0.644882	+	0.764282i	$0.723094\pi$
$90$		0			0
$91$	28.4505	+	11.7846i	0.312643	+	0.129501i
$92$		0			0
$93$	7.30366	−	3.02527i	0.0785339	−	0.0325298i
$94$		0			0
$95$		−	31.9017i		−	0.335807i
$96$		0			0
$97$	−14.3055			−0.147479			−0.0737395	−	0.997278i	$-0.523493\pi$
$97$	−14.3055			−0.147479			−0.0737395	+	0.997278i	$0.523493\pi$
$98$		0			0
$99$	−30.3257	−	73.2128i	−0.306321	−	0.739523i
$100$		0			0
$101$	51.6638	−	124.728i	0.511523	−	1.23493i	−0.431474	−	0.902125i	$-0.642006\pi$
$101$	51.6638	−	124.728i	0.511523	−	1.23493i	0.942997	−	0.332801i	$-0.107994\pi$
$102$		0			0
$103$	−4.87593	+	4.87593i	−0.0473392	+	0.0473392i	−0.730380	−	0.683041i	$-0.760657\pi$
$103$	−4.87593	+	4.87593i	−0.0473392	+	0.0473392i	0.683041	+	0.730380i	$0.260657\pi$
$104$		0			0
$105$	11.4672	−	11.4672i	0.109212	−	0.109212i
$106$		0			0
$107$	4.55603	−	10.9992i	0.0425797	−	0.102797i	−0.901159	−	0.433489i	$-0.857282\pi$
$107$	4.55603	−	10.9992i	0.0425797	−	0.102797i	0.943739	+	0.330692i	$0.107282\pi$
$108$		0			0
$109$	11.0098	+	26.5800i	0.101007	+	0.243853i	0.966302	−	0.257410i	$-0.0828690\pi$
$109$	11.0098	+	26.5800i	0.101007	+	0.243853i	−0.865295	+	0.501263i	$0.832869\pi$
$110$		0			0
$111$	94.1824			0.848490
$112$		0			0
$113$			120.275i			1.06438i	0.846624	+	0.532191i	$0.178631\pi$
$113$			120.275i			1.06438i	−0.846624	+	0.532191i	$0.821369\pi$
$114$		0			0
$115$	−53.4052	+	22.1212i	−0.464393	+	0.192358i
$116$		0			0
$117$	28.8462	+	11.9485i	0.246549	+	0.102124i
$118$		0			0
$119$	−141.815	−	141.815i	−1.19172	−	1.19172i
$120$		0			0
$121$	−2.56759	−	2.56759i	−0.0212197	−	0.0212197i
$122$		0			0
$123$	25.6860	+	10.6395i	0.208829	+	0.0864998i
$124$		0			0
$125$	−73.2166	+	30.3273i	−0.585733	+	0.242619i
$126$		0			0
$127$			128.040i			1.00819i	0.863648	+	0.504095i	$0.168174\pi$
$127$			128.040i			1.00819i	−0.863648	+	0.504095i	$0.831826\pi$
$128$		0			0
$129$	−36.5268			−0.283154
$130$		0			0
$131$	−20.1358	−	48.6121i	−0.153708	−	0.371084i	0.828203	−	0.560429i	$-0.189364\pi$
$131$	−20.1358	−	48.6121i	−0.153708	−	0.371084i	−0.981911	+	0.189345i	$0.939364\pi$
$132$		0			0
$133$	−50.8816	+	122.839i	−0.382569	+	0.923602i
$134$		0			0
$135$	26.3683	−	26.3683i	0.195321	−	0.195321i
$136$		0			0
$137$	−1.66083	+	1.66083i	−0.0121228	+	0.0121228i	−0.713142	−	0.701019i	$-0.752729\pi$
$137$	−1.66083	+	1.66083i	−0.0121228	+	0.0121228i	0.701019	+	0.713142i	$0.252729\pi$
$138$		0			0
$139$	−75.6997	+	182.755i	−0.544602	+	1.31479i	0.376843	+	0.926277i	$0.377009\pi$
$139$	−75.6997	+	182.755i	−0.544602	+	1.31479i	−0.921445	+	0.388508i	$0.872991\pi$
$140$		0			0
$141$	30.5974	+	73.8686i	0.217003	+	0.523891i
$142$		0			0
$143$	49.1053			0.343394
$144$		0			0
$145$			15.5870i			0.107496i
$146$		0			0
$147$	−0.0175264	+	0.00725967i	−0.000119227	+	4.93855e-5i
$148$		0			0
$149$	−16.1203	−	6.67724i	−0.108190	−	0.0448137i	0.327932	−	0.944701i	$-0.393648\pi$
$149$	−16.1203	−	6.67724i	−0.108190	−	0.0448137i	−0.436122	+	0.899888i	$0.643648\pi$
$150$		0			0
$151$	127.344	+	127.344i	0.843335	+	0.843335i	0.989291	−	0.145956i	$-0.0466258\pi$
$151$	127.344	+	127.344i	0.843335	+	0.843335i	−0.145956	+	0.989291i	$0.546626\pi$
$152$		0			0
$153$	−143.787	−	143.787i	−0.939787	−	0.939787i
$154$		0			0
$155$	−8.89669	−	3.68513i	−0.0573980	−	0.0237750i
$156$		0			0
$157$	−236.255	+	97.8598i	−1.50481	+	0.623311i	−0.974478	−	0.224482i	$-0.927931\pi$
$157$	−236.255	+	97.8598i	−1.50481	+	0.623311i	−0.530328	+	0.847793i	$0.677931\pi$
$158$		0			0
$159$			69.2319i			0.435421i
$160$		0			0
$161$	240.922			1.49641
$162$		0			0
$163$	−38.0947	−	91.9687i	−0.233710	−	0.564225i	0.762898	−	0.646518i	$-0.223776\pi$
$163$	−38.0947	−	91.9687i	−0.233710	−	0.564225i	−0.996608	+	0.0822932i	$0.973776\pi$
$164$		0			0
$165$	9.89619	−	23.8915i	0.0599769	−	0.144797i
$166$		0			0
$167$	−223.831	+	223.831i	−1.34031	+	1.34031i	−0.444558	+	0.895750i	$0.646639\pi$
$167$	−223.831	+	223.831i	−1.34031	+	1.34031i	−0.895750	+	0.444558i	$0.853361\pi$
$168$		0			0
$169$	105.820	−	105.820i	0.626154	−	0.626154i
$170$		0			0
$171$	−51.5894	+	124.548i	−0.301692	+	0.728350i
$172$		0			0
$173$	13.2654	+	32.0254i	0.0766784	+	0.185118i	0.957571	−	0.288199i	$-0.0930565\pi$
$173$	13.2654	+	32.0254i	0.0766784	+	0.185118i	−0.880892	+	0.473317i	$0.843056\pi$
$174$		0			0
$175$	155.270			0.887259
$176$		0			0
$177$		−	41.2480i		−	0.233039i
$178$		0			0
$179$	13.8305	−	5.72877i	0.0772652	−	0.0320043i	−0.343716	−	0.939074i	$-0.611686\pi$
$179$	13.8305	−	5.72877i	0.0772652	−	0.0320043i	0.420981	+	0.907069i	$0.361686\pi$
$180$		0			0
$181$	153.596	+	63.6217i	0.848599	+	0.351501i	0.764238	−	0.644934i	$-0.223115\pi$
$181$	153.596	+	63.6217i	0.848599	+	0.351501i	0.0843605	+	0.996435i	$0.473115\pi$
$182$		0			0
$183$	−80.6339	−	80.6339i	−0.440623	−	0.440623i
$184$		0			0
$185$	−81.1228	−	81.1228i	−0.438502	−	0.438502i
$186$		0			0
$187$	−295.465	−	122.386i	−1.58003	−	0.654469i
$188$		0			0
$189$	−143.588	+	59.4763i	−0.759727	+	0.314689i
$190$		0			0
$191$		−	2.00135i		−	0.0104783i	−0.999986	−	0.00523914i	$-0.998332\pi$
$191$		−	2.00135i		−	0.0104783i	0.999986	−	0.00523914i	$-0.00166768\pi$
$192$		0			0
$193$	−107.502			−0.557003			−0.278502	−	0.960436i	$-0.589838\pi$
$193$	−107.502			−0.557003			−0.278502	+	0.960436i	$0.589838\pi$
$194$		0			0
$195$	3.89915	+	9.41338i	0.0199956	+	0.0482738i
$196$		0			0
$197$	35.9828	−	86.8701i	0.182654	−	0.440965i	−0.805858	−	0.592109i	$-0.798296\pi$
$197$	35.9828	−	86.8701i	0.182654	−	0.440965i	0.988512	+	0.151144i	$0.0482956\pi$
$198$		0			0
$199$	228.742	−	228.742i	1.14946	−	1.14946i	0.162799	−	0.986659i	$-0.447948\pi$
$199$	228.742	−	228.742i	1.14946	−	1.14946i	0.986659	−	0.162799i	$-0.0520521\pi$
$200$		0			0
$201$	92.2265	−	92.2265i	0.458838	−	0.458838i
$202$		0			0
$203$	24.8605	−	60.0185i	0.122465	−	0.295658i
$204$		0			0
$205$	−12.9601	−	31.2885i	−0.0632200	−	0.152627i
$206$		0			0
$207$	244.273			1.18006
$208$		0			0
$209$			212.019i			1.01445i
$210$		0			0
$211$	244.800	−	101.400i	1.16019	−	0.480567i	0.282252	−	0.959340i	$-0.408918\pi$
$211$	244.800	−	101.400i	1.16019	−	0.480567i	0.877938	+	0.478773i	$0.158918\pi$
$212$		0			0
$213$	−9.72341	−	4.02757i	−0.0456498	−	0.0189088i
$214$		0			0
$215$	31.4619	+	31.4619i	0.146335	+	0.146335i
$216$		0			0
$217$	28.3796	+	28.3796i	0.130781	+	0.130781i
$218$		0			0
$219$	45.7700	+	18.9585i	0.208995	+	0.0865687i
$220$		0			0
$221$	116.415	−	48.2206i	0.526764	−	0.218193i
$222$		0			0
$223$		−	110.575i		−	0.495853i	−0.968779	−	0.247927i	$-0.920251\pi$
$223$		−	110.575i		−	0.495853i	0.968779	−	0.247927i	$-0.0797492\pi$
$224$		0			0
$225$	157.430			0.699689
$226$		0			0
$227$	−153.333	−	370.178i	−0.675475	−	1.63074i	−0.772161	−	0.635427i	$-0.780824\pi$
$227$	−153.333	−	370.178i	−0.675475	−	1.63074i	0.0966861	−	0.995315i	$-0.469176\pi$
$228$		0			0
$229$	−24.0559	+	58.0760i	−0.105047	+	0.253607i	−0.967660	−	0.252258i	$-0.918827\pi$
$229$	−24.0559	+	58.0760i	−0.105047	+	0.253607i	0.862612	+	0.505865i	$0.168827\pi$
$230$		0			0
$231$	−76.2115	+	76.2115i	−0.329920	+	0.329920i
$232$		0			0
$233$	−104.978	+	104.978i	−0.450547	+	0.450547i	−0.895536	−	0.444989i	$-0.853208\pi$
$233$	−104.978	+	104.978i	−0.450547	+	0.450547i	0.444989	+	0.895536i	$0.353208\pi$
$234$		0			0
$235$	37.2711	−	89.9804i	0.158600	−	0.382895i
$236$		0			0
$237$	26.4743	+	63.9146i	0.111706	+	0.269682i
$238$		0			0
$239$	−122.643			−0.513151			−0.256576	−	0.966524i	$-0.582594\pi$
$239$	−122.643			−0.513151			−0.256576	+	0.966524i	$0.582594\pi$
$240$		0			0
$241$		−	188.784i		−	0.783335i	−0.920107	−	0.391668i	$-0.871898\pi$
$241$		−	188.784i		−	0.783335i	0.920107	−	0.391668i	$-0.128102\pi$
$242$		0			0
$243$	−226.977	+	94.0171i	−0.934063	+	0.386902i
$244$		0			0
$245$	0.0213492	+	0.00884311i	8.71395e−5	+	3.60943e-5i
$246$		0			0
$247$	−59.0694	−	59.0694i	−0.239147	−	0.239147i
$248$		0			0
$249$	−106.394	−	106.394i	−0.427285	−	0.427285i
$250$		0			0
$251$	355.365	+	147.197i	1.41580	+	0.586443i	0.953801	−	0.300439i	$-0.0971330\pi$
$251$	355.365	+	147.197i	1.41580	+	0.586443i	0.461997	+	0.886881i	$0.347133\pi$
$252$		0			0
$253$	354.932	−	147.018i	1.40289	−	0.581098i
$254$		0			0
$255$		−	66.3579i		−	0.260227i
$256$		0			0
$257$	84.4316			0.328528			0.164264	−	0.986416i	$-0.447475\pi$
$257$	84.4316			0.328528			0.164264	+	0.986416i	$0.447475\pi$
$258$		0			0
$259$	182.981	+	441.754i	0.706489	+	1.70561i
$260$		0			0
$261$	25.2063	−	60.8533i	0.0965758	−	0.233155i
$262$		0			0
$263$	37.2079	−	37.2079i	0.141475	−	0.141475i	−0.632822	−	0.774297i	$-0.718104\pi$
$263$	37.2079	−	37.2079i	0.141475	−	0.141475i	0.774297	+	0.632822i	$0.218104\pi$
$264$		0			0
$265$	59.6320	−	59.6320i	0.225027	−	0.225027i
$266$		0			0
$267$	7.93072	−	19.1464i	0.0297031	−	0.0717095i
$268$		0			0
$269$	−90.5201	−	218.535i	−0.336506	−	0.812398i	−0.998046	−	0.0624874i	$-0.980097\pi$
$269$	−90.5201	−	218.535i	−0.336506	−	0.812398i	0.661540	−	0.749910i	$-0.269903\pi$
$270$		0			0
$271$	−312.612			−1.15355			−0.576775	−	0.816903i	$-0.695689\pi$
$271$	−312.612			−1.15355			−0.576775	+	0.816903i	$0.695689\pi$
$272$		0			0
$273$		−	42.4657i		−	0.155552i
$274$		0			0
$275$	228.748	−	94.7506i	0.831812	−	0.344548i
$276$		0			0
$277$	−199.434	−	82.6083i	−0.719978	−	0.298225i	−0.00755172	−	0.999971i	$-0.502404\pi$
$277$	−199.434	−	82.6083i	−0.719978	−	0.298225i	−0.712426	+	0.701747i	$0.752404\pi$
$278$		0			0
$279$	28.7743	+	28.7743i	0.103134	+	0.103134i
$280$		0			0
$281$	237.700	+	237.700i	0.845909	+	0.845909i	0.989620	−	0.143711i	$-0.0459036\pi$
$281$	237.700	+	237.700i	0.845909	+	0.845909i	−0.143711	+	0.989620i	$0.545904\pi$
$282$		0			0
$283$	−58.7408	−	24.3312i	−0.207565	−	0.0859761i	0.276479	−	0.961020i	$-0.410832\pi$
$283$	−58.7408	−	24.3312i	−0.207565	−	0.0859761i	−0.484044	+	0.875044i	$0.660832\pi$
$284$		0			0
$285$	−40.6436	+	16.8351i	−0.142609	+	0.0590707i
$286$		0			0
$287$			141.148i			0.491807i
$288$		0			0
$289$	−531.645			−1.83960
$290$		0			0
$291$	7.54927	+	18.2256i	0.0259425	+	0.0626308i
$292$		0			0
$293$	47.5607	−	114.822i	0.162323	−	0.391883i	−0.821701	−	0.569919i	$-0.806974\pi$
$293$	47.5607	−	114.822i	0.162323	−	0.391883i	0.984024	+	0.178036i	$0.0569745\pi$
$294$		0			0
$295$	−35.5284	+	35.5284i	−0.120435	+	0.120435i
$296$		0			0
$297$	−175.244	+	175.244i	−0.590048	+	0.590048i
$298$		0			0
$299$	−57.9258	+	139.845i	−0.193732	+	0.467710i
$300$		0			0
$301$	−70.9655	−	171.326i	−0.235766	−	0.569189i
$302$		0			0
$303$	−186.170			−0.614423
$304$		0			0
$305$			138.906i			0.455429i
$306$		0			0
$307$	−407.254	+	168.690i	−1.32656	+	0.549480i	−0.929673	−	0.368387i	$-0.879910\pi$
$307$	−407.254	+	168.690i	−1.32656	+	0.549480i	−0.396889	+	0.917867i	$0.629910\pi$
$308$		0			0
$309$	8.78520	+	3.63895i	0.0284311	+	0.0117765i
$310$		0			0
$311$	−149.458	−	149.458i	−0.480572	−	0.480572i	0.424742	−	0.905314i	$-0.360365\pi$
$311$	−149.458	−	149.458i	−0.480572	−	0.480572i	−0.905314	+	0.424742i	$0.860365\pi$
$312$		0			0
$313$	295.452	+	295.452i	0.943937	+	0.943937i	0.998510	−	0.0545726i	$-0.0173796\pi$
$313$	295.452	+	295.452i	0.943937	+	0.943937i	−0.0545726	+	0.998510i	$0.517380\pi$
$314$		0			0
$315$	77.1231	+	31.9454i	0.244835	+	0.101414i
$316$		0			0
$317$	−222.852	+	92.3084i	−0.703004	+	0.291194i	−0.705406	−	0.708803i	$-0.749235\pi$
$317$	−222.852	+	92.3084i	−0.703004	+	0.291194i	0.00240221	+	0.999997i	$0.499235\pi$
$318$		0			0
$319$		−	103.591i		−	0.324738i
$320$		0			0
$321$	−16.4176			−0.0511453
$322$		0			0
$323$	208.199	+	502.638i	0.644580	+	1.55615i
$324$		0			0
$325$	−37.3323	+	90.1281i	−0.114868	+	0.277317i
$326$		0			0
$327$	28.0535	−	28.0535i	0.0857906	−	0.0857906i
$328$		0			0
$329$	−287.029	+	287.029i	−0.872427	+	0.872427i
$330$		0			0
$331$	200.624	−	484.350i	0.606115	−	1.46329i	−0.261076	−	0.965318i	$-0.584077\pi$
$331$	200.624	−	484.350i	0.606115	−	1.46329i	0.867192	−	0.497974i	$-0.165923\pi$
$332$		0			0
$333$	185.526	+	447.899i	0.557135	+	1.34504i
$334$		0			0
$335$	−158.876			−0.474257
$336$		0			0
$337$		−	248.089i		−	0.736169i	−0.929792	−	0.368085i	$-0.880014\pi$
$337$		−	248.089i		−	0.736169i	0.929792	−	0.368085i	$-0.119986\pi$
$338$		0			0
$339$	153.234	−	63.4715i	0.452017	−	0.187232i
$340$		0			0
$341$	59.1276	+	24.4914i	0.173395	+	0.0718224i
$342$		0			0
$343$	242.504	+	242.504i	0.707007	+	0.707007i
$344$		0			0
$345$	56.3660	+	56.3660i	0.163380	+	0.163380i
$346$		0			0
$347$	101.462	+	42.0270i	0.292398	+	0.121115i	0.524061	−	0.851681i	$-0.324416\pi$
$347$	101.462	+	42.0270i	0.292398	+	0.121115i	−0.231662	+	0.972796i	$0.574416\pi$
$348$		0			0
$349$	489.895	−	202.921i	1.40371	−	0.581436i	0.452998	−	0.891512i	$-0.350354\pi$
$349$	489.895	−	202.921i	1.40371	−	0.581436i	0.950712	+	0.310076i	$0.100354\pi$
$350$		0			0
$351$		−	97.6474i		−	0.278198i
$352$		0			0
$353$	−185.627			−0.525856			−0.262928	−	0.964815i	$-0.584688\pi$
$353$	−185.627			−0.525856			−0.262928	+	0.964815i	$0.584688\pi$
$354$		0			0
$355$	4.90604	+	11.8442i	0.0138198	+	0.0333640i
$356$		0			0
$357$	−105.838	+	255.514i	−0.296464	+	0.715727i
$358$		0			0
$359$	−222.847	+	222.847i	−0.620743	+	0.620743i	−0.945722	−	0.324978i	$-0.894643\pi$
$359$	−222.847	+	222.847i	−0.620743	+	0.620743i	0.324978	+	0.945722i	$0.394643\pi$
$360$		0			0
$361$	−0.224842	+	0.224842i	−0.000622830	+	0.000622830i
$362$		0			0
$363$	−1.91621	+	4.62614i	−0.00527882	+	0.0127442i
$364$		0			0
$365$	−23.0937	−	55.7530i	−0.0632703	−	0.152748i
$366$		0			0
$367$	−532.771			−1.45169			−0.725846	−	0.687857i	$-0.758552\pi$
$367$	−532.771			−1.45169			−0.725846	+	0.687857i	$0.758552\pi$
$368$		0			0
$369$			143.112i			0.387837i
$370$		0			0
$371$	−324.726	+	134.506i	−0.875273	+	0.362550i
$372$		0			0
$373$	−277.629	−	114.998i	−0.744313	−	0.308305i	−0.0218944	−	0.999760i	$-0.506970\pi$
$373$	−277.629	−	114.998i	−0.744313	−	0.308305i	−0.722419	+	0.691456i	$0.756970\pi$
$374$		0			0
$375$	77.2757	+	77.2757i	0.206068	+	0.206068i
$376$		0			0
$377$	28.8610	+	28.8610i	0.0765543	+	0.0765543i
$378$		0			0
$379$	−306.344	−	126.892i	−0.808296	−	0.334807i	−0.0600223	−	0.998197i	$-0.519117\pi$
$379$	−306.344	−	126.892i	−0.808296	−	0.334807i	−0.748274	+	0.663390i	$0.769117\pi$
$380$		0			0
$381$	163.127	−	67.5692i	0.428154	−	0.177347i
$382$		0			0
$383$		−	163.336i		−	0.426465i	−0.977001	−	0.213233i	$-0.931601\pi$
$383$		−	163.336i		−	0.426465i	0.977001	−	0.213233i	$-0.0683992\pi$
$384$		0			0
$385$	131.288			0.341007
$386$		0			0
$387$	−71.9526	−	173.709i	−0.185924	−	0.448861i
$388$		0			0
$389$	−27.0717	+	65.3568i	−0.0695930	+	0.168012i	−0.954849	−	0.297092i	$-0.903983\pi$
$389$	−27.0717	+	65.3568i	−0.0695930	+	0.168012i	0.885256	+	0.465104i	$0.153983\pi$
$390$		0			0
$391$	697.075	−	697.075i	1.78280	−	1.78280i
$392$		0			0
$393$	−51.3071	+	51.3071i	−0.130552	+	0.130552i
$394$		0			0
$395$	32.2487	−	77.8553i	0.0816423	−	0.197102i
$396$		0			0
$397$	−153.949	−	371.666i	−0.387781	−	0.936187i	−0.990409	−	0.138165i	$-0.955880\pi$
$397$	−153.949	−	371.666i	−0.387781	−	0.936187i	0.602628	−	0.798022i	$-0.294120\pi$
$398$		0			0
$399$	183.352			0.459528
$400$		0			0
$401$		−	287.838i		−	0.717801i	−0.933376	−	0.358900i	$-0.883152\pi$
$401$		−	287.838i		−	0.717801i	0.933376	−	0.358900i	$-0.116848\pi$
$402$		0			0
$403$	−23.2966	+	9.64976i	−0.0578079	+	0.0239448i
$404$		0			0
$405$	51.6353	+	21.3881i	0.127495	+	0.0528100i
$406$		0			0
$407$	539.144	+	539.144i	1.32468	+	1.32468i
$408$		0			0
$409$	−134.641	−	134.641i	−0.329195	−	0.329195i	0.523085	−	0.852280i	$-0.324781\pi$
$409$	−134.641	−	134.641i	−0.329195	−	0.329195i	−0.852280	+	0.523085i	$0.824781\pi$
$410$		0			0
$411$	2.99239	+	1.23949i	0.00728076	+	0.00301579i
$412$		0			0
$413$	193.470	−	80.1378i	0.468450	−	0.194038i
$414$		0			0
$415$			183.282i			0.441644i
$416$		0			0
$417$	272.783			0.654156
$418$		0			0
$419$	−94.1979	−	227.414i	−0.224816	−	0.542754i	0.770716	−	0.637179i	$-0.219899\pi$
$419$	−94.1979	−	227.414i	−0.224816	−	0.542754i	−0.995532	+	0.0944249i	$0.969899\pi$
$420$		0			0
$421$	−151.850	+	366.598i	−0.360689	+	0.870779i	0.634511	+	0.772914i	$0.281202\pi$
$421$	−151.850	+	366.598i	−0.360689	+	0.870779i	−0.995200	+	0.0978656i	$0.968798\pi$
$422$		0			0
$423$	−291.021	+	291.021i	−0.687993	+	0.687993i
$424$		0			0
$425$	449.254	−	449.254i	1.05707	−	1.05707i
$426$		0			0
$427$	221.548	−	534.864i	0.518848	−	1.25261i
$428$		0			0
$429$	−25.9138	−	62.5615i	−0.0604052	−	0.145831i
$430$		0			0
$431$	691.406			1.60419			0.802095	−	0.597196i	$-0.203719\pi$
$431$	691.406			1.60419			0.802095	+	0.597196i	$0.203719\pi$
$432$		0			0
$433$		−	580.011i		−	1.33952i	−0.742579	−	0.669758i	$-0.766398\pi$
$433$		−	580.011i		−	1.33952i	0.742579	−	0.669758i	$-0.233602\pi$
$434$		0			0
$435$	19.8582	−	8.22556i	0.0456511	−	0.0189093i
$436$		0			0
$437$	−603.802	−	250.103i	−1.38170	−	0.572318i
$438$		0			0
$439$	−411.067	−	411.067i	−0.936371	−	0.936371i	0.0617227	−	0.998093i	$-0.480341\pi$
$439$	−411.067	−	411.067i	−0.936371	−	0.936371i	−0.998093	+	0.0617227i	$0.980341\pi$
$440$		0			0
$441$	−0.0690490	−	0.0690490i	−0.000156574	−	0.000156574i
$442$		0			0
$443$	34.4767	+	14.2807i	0.0778256	+	0.0322364i	0.421257	−	0.906941i	$-0.361589\pi$
$443$	34.4767	+	14.2807i	0.0778256	+	0.0322364i	−0.343431	+	0.939178i	$0.611589\pi$
$444$		0			0
$445$	−23.3226	+	9.66052i	−0.0524102	+	0.0217090i
$446$		0			0
$447$			24.0614i			0.0538286i
$448$		0			0
$449$	185.456			0.413043			0.206521	−	0.978442i	$-0.433786\pi$
$449$	185.456			0.413043			0.206521	+	0.978442i	$0.433786\pi$
$450$		0			0
$451$	86.1331	+	207.944i	0.190982	+	0.461073i
$452$		0			0
$453$	95.0375	−	229.441i	0.209796	−	0.506492i
$454$		0			0
$455$	−36.5772	+	36.5772i	−0.0803895	+	0.0803895i
$456$		0			0
$457$	386.211	−	386.211i	0.845100	−	0.845100i	−0.144417	−	0.989517i	$-0.546131\pi$
$457$	386.211	−	386.211i	0.845100	−	0.845100i	0.989517	+	0.144417i	$0.0461306\pi$
$458$		0			0
$459$	−243.367	+	587.541i	−0.530212	+	1.28005i
$460$		0			0
$461$	268.824	+	648.999i	0.583133	+	1.40781i	0.889958	+	0.456042i	$0.150733\pi$
$461$	268.824	+	648.999i	0.583133	+	1.40781i	−0.306826	+	0.951766i	$0.599267\pi$
$462$		0			0
$463$	−49.4705			−0.106848			−0.0534238	−	0.998572i	$-0.517013\pi$
$463$	−49.4705			−0.106848			−0.0534238	+	0.998572i	$0.517013\pi$
$464$		0			0
$465$			13.2793i			0.0285577i
$466$		0			0
$467$	192.753	−	79.8411i	0.412748	−	0.170966i	−0.166640	−	0.986018i	$-0.553292\pi$
$467$	192.753	−	79.8411i	0.412748	−	0.170966i	0.579388	+	0.815052i	$0.303292\pi$
$468$		0			0
$469$	611.761	+	253.400i	1.30439	+	0.540297i
$470$		0			0
$471$	249.352	+	249.352i	0.529410	+	0.529410i
$472$		0			0
$473$	−209.097	−	209.097i	−0.442065	−	0.442065i
$474$		0			0
$475$	−389.141	−	161.187i	−0.819244	−	0.339342i
$476$		0			0
$477$	−329.243	+	136.377i	−0.690237	+	0.285906i
$478$		0			0
$479$		−	256.988i		−	0.536509i	−0.963348	−	0.268254i	$-0.913553\pi$
$479$		−	256.988i		−	0.536509i	0.963348	−	0.268254i	$-0.0864468\pi$
$480$		0			0
$481$	−300.415			−0.624564
$482$		0			0
$483$	−127.139	−	306.941i	−0.263228	−	0.635488i
$484$		0			0
$485$	9.19588	−	22.2008i	0.0189606	−	0.0457749i
$486$		0			0
$487$	10.7898	−	10.7898i	0.0221557	−	0.0221557i	−0.695942	−	0.718098i	$-0.745013\pi$
$487$	10.7898	−	10.7898i	0.0221557	−	0.0221557i	0.718098	+	0.695942i	$0.245013\pi$
$488$		0			0
$489$	−97.0673	+	97.0673i	−0.198502	+	0.198502i
$490$		0			0
$491$	−58.0314	+	140.100i	−0.118190	+	0.285336i	−0.971893	−	0.235425i	$-0.924352\pi$
$491$	−58.0314	+	140.100i	−0.118190	+	0.285336i	0.853702	+	0.520761i	$0.174352\pi$
$492$		0			0
$493$	−101.725	−	245.586i	−0.206339	−	0.498146i
$494$		0			0
$495$	133.114			0.268917
$496$		0			0
$497$		−	53.4317i		−	0.107508i
$498$		0			0
$499$	72.1133	−	29.8703i	0.144516	−	0.0598603i	−0.309253	−	0.950980i	$-0.600079\pi$
$499$	72.1133	−	29.8703i	0.144516	−	0.0598603i	0.453769	+	0.891119i	$0.350079\pi$
$500$		0			0
$501$	403.288	+	167.047i	0.804965	+	0.333428i
$502$		0			0
$503$	−151.600	−	151.600i	−0.301393	−	0.301393i	0.540166	−	0.841559i	$-0.318361\pi$
$503$	−151.600	−	151.600i	−0.301393	−	0.301393i	−0.841559	+	0.540166i	$0.818361\pi$
$504$		0			0
$505$	160.355	+	160.355i	0.317535	+	0.317535i
$506$		0			0
$507$	−190.661	−	78.9744i	−0.376057	−	0.155768i
$508$		0			0
$509$	−562.711	+	233.082i	−1.10552	+	0.457922i	−0.859393	−	0.511315i	$-0.829158\pi$
$509$	−562.711	+	233.082i	−1.10552	+	0.457922i	−0.246128	+	0.969237i	$0.579158\pi$
$510$		0			0
$511$			251.513i			0.492198i
$512$		0			0
$513$	421.607			0.821845
$514$		0			0
$515$	−4.43266	−	10.7014i	−0.00860710	−	0.0207794i
$516$		0			0
$517$	−247.705	+	598.012i	−0.479119	+	1.15670i
$518$		0			0
$519$	33.8009	−	33.8009i	0.0651270	−	0.0651270i
$520$		0			0
$521$	−224.985	+	224.985i	−0.431833	+	0.431833i	−0.889252	−	0.457418i	$-0.848774\pi$
$521$	−224.985	+	224.985i	−0.431833	+	0.431833i	0.457418	+	0.889252i	$0.348774\pi$
$522$		0			0
$523$	9.30771	−	22.4708i	0.0177968	−	0.0429652i	−0.914731	−	0.404063i	$-0.867598\pi$
$523$	9.30771	−	22.4708i	0.0177968	−	0.0429652i	0.932528	+	0.361097i	$0.117598\pi$
$524$		0			0
$525$	−81.9391	−	197.819i	−0.156075	−	0.376797i
$526$		0			0
$527$	164.225			0.311622
$528$		0			0
$529$			655.224i			1.23861i
$530$		0			0
$531$	196.161	−	81.2525i	0.369418	−	0.153018i
$532$		0			0
$533$	−81.9309	−	33.9369i	−0.153717	−	0.0636715i
$534$		0			0
$535$	14.1411	+	14.1411i	0.0264320	+	0.0264320i
$536$		0			0
$537$	−14.5972	−	14.5972i	−0.0271829	−	0.0271829i
$538$		0			0
$539$	−0.141887	−	0.0587715i	−0.000263241	−	0.000109038i
$540$		0			0
$541$	−357.866	+	148.233i	−0.661490	+	0.273998i	−0.688066	−	0.725649i	$-0.741540\pi$
$541$	−357.866	+	148.233i	−0.661490	+	0.273998i	0.0265752	+	0.999647i	$0.491540\pi$
$542$		0			0
$543$		−	229.260i		−	0.422211i
$544$		0			0
$545$	−48.3271			−0.0886735
$546$		0			0
$547$	−187.175	−	451.879i	−0.342184	−	0.826105i	−0.997494	−	0.0707454i	$-0.977462\pi$
$547$	−187.175	−	451.879i	−0.342184	−	0.826105i	0.655311	−	0.755360i	$-0.272538\pi$
$548$		0			0
$549$	224.630	−	542.304i	0.409162	−	0.987804i
$550$		0			0
$551$	−124.611	+	124.611i	−0.226155	+	0.226155i
$552$		0			0
$553$	−248.351	+	248.351i	−0.449097	+	0.449097i
$554$		0			0
$555$	−60.5426	+	146.163i	−0.109086	+	0.263356i
$556$		0			0
$557$	307.716	+	742.891i	0.552452	+	1.33374i	0.915632	+	0.402017i	$0.131691\pi$
$557$	307.716	+	742.891i	0.552452	+	1.33374i	−0.363181	+	0.931719i	$0.618309\pi$
$558$		0			0
$559$	116.510			0.208426
$560$		0			0
$561$			441.016i			0.786125i
$562$		0			0
$563$	−706.303	+	292.560i	−1.25454	+	0.519646i	−0.908228	−	0.418476i	$-0.862565\pi$
$563$	−706.303	+	292.560i	−1.25454	+	0.519646i	−0.346307	+	0.938121i	$0.612565\pi$
$564$		0			0
$565$	−186.656	−	77.3156i	−0.330365	−	0.136842i
$566$		0			0
$567$	−164.712	−	164.712i	−0.290497	−	0.290497i
$568$		0			0
$569$	−552.550	−	552.550i	−0.971089	−	0.971089i	0.0285048	−	0.999594i	$-0.490925\pi$
$569$	−552.550	−	552.550i	−0.971089	−	0.971089i	−0.999594	+	0.0285048i	$0.990925\pi$
$570$		0			0
$571$	476.739	+	197.472i	0.834919	+	0.345835i	0.758848	−	0.651268i	$-0.225763\pi$
$571$	476.739	+	197.472i	0.834919	+	0.345835i	0.0760707	+	0.997102i	$0.475763\pi$
$572$		0			0
$573$	−2.54978	+	1.05615i	−0.00444988	+	0.00184320i
$574$		0			0
$575$			763.214i			1.32733i
$576$		0			0
$577$	−188.090			−0.325980			−0.162990	−	0.986628i	$-0.552114\pi$
$577$	−188.090			−0.325980			−0.162990	+	0.986628i	$0.552114\pi$
$578$		0			0
$579$	56.7307	+	136.960i	0.0979805	+	0.236546i
$580$		0			0
$581$	292.326	−	705.737i	0.503143	−	1.21469i
$582$		0			0
$583$	−396.316	+	396.316i	−0.679787	+	0.679787i
$584$		0			0
$585$	−37.0860	+	37.0860i	−0.0633949	+	0.0633949i
$586$		0			0
$587$	−229.302	+	553.585i	−0.390634	+	0.943075i	0.599167	+	0.800624i	$0.295498\pi$
$587$	−229.302	+	553.585i	−0.390634	+	0.943075i	−0.989802	+	0.142451i	$0.954502\pi$
$588$		0			0
$589$	−41.6642	−	100.586i	−0.0707372	−	0.170775i
$590$		0			0
$591$	−129.664			−0.219397
$592$		0			0
$593$			378.708i			0.638630i	0.947649	+	0.319315i	$0.103453\pi$
$593$			378.708i			0.638630i	−0.947649	+	0.319315i	$0.896547\pi$
$594$		0			0
$595$	311.246	−	128.922i	0.523102	−	0.216676i
$596$		0			0
$597$	−412.135	−	170.712i	−0.690344	−	0.285950i
$598$		0			0
$599$	−745.316	−	745.316i	−1.24427	−	1.24427i	−0.958213	−	0.286055i	$-0.907656\pi$
$599$	−745.316	−	745.316i	−1.24427	−	1.24427i	−0.286055	−	0.958213i	$-0.592344\pi$
$600$		0			0
$601$	130.996	+	130.996i	0.217963	+	0.217963i	0.807640	−	0.589676i	$-0.200745\pi$
$601$	130.996	+	130.996i	0.217963	+	0.217963i	−0.589676	+	0.807640i	$0.700745\pi$
$602$		0			0
$603$	620.270	+	256.924i	1.02864	+	0.426077i
$604$		0			0
$605$	5.63517	−	2.33416i	0.00931433	−	0.00385812i
$606$		0			0
$607$			732.344i			1.20650i	0.797553	+	0.603249i	$0.206127\pi$
$607$			732.344i			1.20650i	−0.797553	+	0.603249i	$0.793873\pi$
$608$		0			0
$609$	−89.5845			−0.147101
$610$		0			0
$611$	−97.5969	−	235.620i	−0.159733	−	0.385630i
$612$		0			0
$613$	208.204	−	502.648i	0.339647	−	0.819981i	−0.658102	−	0.752928i	$-0.728641\pi$
$613$	208.204	−	502.648i	0.339647	−	0.819981i	0.997749	−	0.0670521i	$-0.0213594\pi$
$614$		0			0
$615$	−33.0230	+	33.0230i	−0.0536960	+	0.0536960i
$616$		0			0
$617$	209.834	−	209.834i	0.340087	−	0.340087i	−0.516313	−	0.856400i	$-0.672696\pi$
$617$	209.834	−	209.834i	0.340087	−	0.340087i	0.856400	+	0.516313i	$0.172696\pi$
$618$		0			0
$619$	−175.433	+	423.533i	−0.283414	+	0.684222i	−0.999911	−	0.0133688i	$-0.995744\pi$
$619$	−175.433	+	423.533i	−0.283414	+	0.684222i	0.716497	+	0.697590i	$0.245744\pi$
$620$		0			0
$621$	−292.349	−	705.793i	−0.470772	−	1.13654i
$622$		0			0
$623$	105.213			0.168881
$624$		0			0
$625$			421.338i			0.674141i
$626$		0			0
$627$	270.118	−	111.887i	0.430811	−	0.178448i
$628$		0			0
$629$	1807.59	+	748.727i	2.87375	+	1.19035i
$630$		0			0
$631$	−232.756	−	232.756i	−0.368868	−	0.368868i	0.498196	−	0.867064i	$-0.333996\pi$
$631$	−232.756	−	232.756i	−0.368868	−	0.368868i	−0.867064	+	0.498196i	$0.833996\pi$
$632$		0			0
$633$	−258.372	−	258.372i	−0.408170	−	0.408170i
$634$		0			0
$635$	−198.707	−	82.3071i	−0.312924	−	0.129617i
$636$		0			0
$637$	0.0559042	−	0.0231563i	8.77618e−5	−	3.63521e-5i
$638$		0			0
$639$		−	54.1749i		−	0.0847807i
$640$		0			0
$641$	−123.632			−0.192873			−0.0964366	−	0.995339i	$-0.530744\pi$
$641$	−123.632			−0.192873			−0.0964366	+	0.995339i	$0.530744\pi$
$642$		0			0
$643$	351.513	+	848.628i	0.546677	+	1.31979i	0.919936	+	0.392068i	$0.128240\pi$
$643$	351.513	+	848.628i	0.546677	+	1.31979i	−0.373260	+	0.927727i	$0.621760\pi$
$644$		0			0
$645$	23.4803	−	56.6864i	0.0364035	−	0.0878859i
$646$		0			0
$647$	191.561	−	191.561i	0.296076	−	0.296076i	−0.543399	−	0.839475i	$-0.682863\pi$
$647$	191.561	−	191.561i	0.296076	−	0.296076i	0.839475	+	0.543399i	$0.182863\pi$
$648$		0			0
$649$	236.122	−	236.122i	0.363825	−	0.363825i
$650$		0			0
$651$	21.1799	−	51.1328i	0.0325344	−	0.0785450i
$652$		0			0
$653$	−89.1964	−	215.339i	−0.136595	−	0.329769i	0.840750	−	0.541424i	$-0.182115\pi$
$653$	−89.1964	−	215.339i	−0.136595	−	0.329769i	−0.977344	+	0.211655i	$0.932115\pi$
$654$		0			0
$655$	88.3853			0.134939
$656$		0			0
$657$			255.012i			0.388146i
$658$		0			0
$659$	911.099	−	377.389i	1.38255	−	0.572670i	0.437386	−	0.899274i	$-0.355904\pi$
$659$	911.099	−	377.389i	1.38255	−	0.572670i	0.945161	+	0.326604i	$0.105904\pi$
$660$		0			0
$661$	−496.993	−	205.861i	−0.751880	−	0.311439i	−0.0263718	−	0.999652i	$-0.508395\pi$
$661$	−496.993	−	205.861i	−0.751880	−	0.311439i	−0.725509	+	0.688213i	$0.758395\pi$
$662$		0			0
$663$	−122.869	−	122.869i	−0.185322	−	0.185322i
$664$		0			0
$665$	−157.928	−	157.928i	−0.237485	−	0.237485i
$666$		0			0
$667$	295.014	+	122.199i	0.442300	+	0.183207i
$668$		0			0
$669$	−140.876	+	58.3527i	−0.210577	+	0.0872238i
$670$		0			0
$671$		−	923.172i		−	1.37582i
$672$		0			0
$673$	374.150			0.555944			0.277972	−	0.960589i	$-0.410338\pi$
$673$	374.150			0.555944			0.277972	+	0.960589i	$0.410338\pi$
$674$		0			0
$675$	−188.414	−	454.873i	−0.279132	−	0.673885i
$676$		0			0
$677$	12.3571	−	29.8326i	0.0182527	−	0.0440659i	−0.914490	−	0.404608i	$-0.867408\pi$
$677$	12.3571	−	29.8326i	0.0182527	−	0.0440659i	0.932743	+	0.360542i	$0.117408\pi$
$678$		0			0
$679$	−70.8184	+	70.8184i	−0.104298	+	0.104298i
$680$		0			0
$681$	−390.701	+	390.701i	−0.573716	+	0.573716i
$682$		0			0
$683$	−22.0894	+	53.3285i	−0.0323417	+	0.0780799i	−0.939225	−	0.343302i	$-0.888455\pi$
$683$	−22.0894	+	53.3285i	−0.0323417	+	0.0780799i	0.906883	+	0.421382i	$0.138455\pi$
$684$		0			0
$685$	−1.50984	−	3.64508i	−0.00220415	−	0.00532128i
$686$		0			0
$687$	86.6852			0.126179
$688$		0			0
$689$		−	220.830i		−	0.320508i
$690$		0			0
$691$	622.510	−	257.852i	0.900883	−	0.373158i	0.116323	−	0.993211i	$-0.462889\pi$
$691$	622.510	−	257.852i	0.900883	−	0.373158i	0.784560	+	0.620053i	$0.212889\pi$
$692$		0			0
$693$	−512.562	−	212.310i	−0.739627	−	0.306364i
$694$		0			0
$695$	−234.958	−	234.958i	−0.338069	−	0.338069i
$696$		0			0
$697$	408.394	+	408.394i	0.585932	+	0.585932i
$698$		0			0
$699$	189.143	+	78.3456i	0.270591	+	0.112082i
$700$		0			0
$701$	−34.0835	+	14.1179i	−0.0486213	+	0.0201396i	−0.406862	−	0.913490i	$-0.633377\pi$
$701$	−34.0835	+	14.1179i	−0.0486213	+	0.0201396i	0.358240	+	0.933629i	$0.383377\pi$
$702$		0			0
$703$		−	1297.09i		−	1.84507i
$704$		0			0
$705$	−134.306			−0.190505
$706$		0			0
$707$	−361.698	−	873.215i	−0.511595	−	1.23510i
$708$		0			0
$709$	285.114	−	688.325i	0.402135	−	0.970840i	−0.585012	−	0.811025i	$-0.698910\pi$
$709$	285.114	−	688.325i	0.402135	−	0.970840i	0.987147	−	0.159815i	$-0.0510898\pi$
$710$		0			0
$711$	−251.805	+	251.805i	−0.354156	+	0.354156i
$712$		0			0
$713$	−139.497	+	139.497i	−0.195647	+	0.195647i
$714$		0			0
$715$	−31.5660	+	76.2071i	−0.0441483	+	0.106583i
$716$		0			0
$717$	64.7212	+	156.251i	0.0902666	+	0.217923i
$718$		0			0
$719$	478.037			0.664863			0.332432	−	0.943127i	$-0.392131\pi$
$719$	478.037			0.664863			0.332432	+	0.943127i	$0.392131\pi$
$720$		0			0
$721$			48.2761i			0.0669571i
$722$		0			0
$723$	−240.516	+	99.6249i	−0.332664	+	0.137794i
$724$		0			0
$725$	190.132	+	78.7553i	0.262251	+	0.108628i
$726$		0			0
$727$	408.395	+	408.395i	0.561753	+	0.561753i	0.929805	−	0.368052i	$-0.119975\pi$
$727$	408.395	+	408.395i	0.561753	+	0.561753i	−0.368052	+	0.929805i	$0.619975\pi$
$728$		0			0
$729$	27.8184	+	27.8184i	0.0381597	+	0.0381597i
$730$		0			0
$731$	−701.038	−	290.379i	−0.959012	−	0.397236i
$732$		0			0
$733$	747.573	−	309.655i	1.01988	−	0.422449i	0.190831	−	0.981623i	$-0.438882\pi$
$733$	747.573	−	309.655i	1.01988	−	0.422449i	0.829050	+	0.559174i	$0.188882\pi$
$734$		0			0
$735$		−	0.0318661i		−	4.33552e-5i
$736$		0			0
$737$	1055.89			1.43269
$738$		0			0
$739$	348.876	+	842.261i	0.472092	+	1.13973i	0.963237	+	0.268653i	$0.0865786\pi$
$739$	348.876	+	842.261i	0.472092	+	1.13973i	−0.491145	+	0.871078i	$0.663421\pi$
$740$		0			0
$741$	−44.0840	+	106.428i	−0.0594925	+	0.143628i
$742$		0			0
$743$	345.072	−	345.072i	0.464430	−	0.464430i	−0.435674	−	0.900104i	$-0.643490\pi$
$743$	345.072	−	345.072i	0.464430	−	0.464430i	0.900104	+	0.435674i	$0.143490\pi$
$744$		0			0
$745$	20.7250	−	20.7250i	0.0278187	−	0.0278187i
$746$		0			0
$747$	296.392	−	715.554i	0.396777	−	0.957903i
$748$		0			0
$749$	−31.8967	−	77.0054i	−0.0425857	−	0.102811i
$750$		0			0
$751$	−642.659			−0.855737			−0.427869	−	0.903841i	$-0.640735\pi$
$751$	−642.659			−0.855737			−0.427869	+	0.903841i	$0.640735\pi$
$752$		0			0
$753$		−	530.424i		−	0.704414i
$754$		0			0
$755$	−279.485	+	115.767i	−0.370179	+	0.153333i
$756$		0			0
$757$	241.802	+	100.158i	0.319422	+	0.132309i	0.536633	−	0.843816i	$-0.319696\pi$
$757$	241.802	+	100.158i	0.319422	+	0.132309i	−0.217211	+	0.976125i	$0.569696\pi$
$758$		0			0
$759$	−374.609	−	374.609i	−0.493556	−	0.493556i
$760$		0			0
$761$	−253.025	−	253.025i	−0.332490	−	0.332490i	0.521042	−	0.853531i	$-0.325544\pi$
$761$	−253.025	−	253.025i	−0.332490	−	0.332490i	−0.853531	+	0.521042i	$0.825544\pi$
$762$		0			0
$763$	186.086	+	77.0793i	0.243887	+	0.101021i
$764$		0			0
$765$	315.575	−	130.716i	0.412517	−	0.170870i
$766$		0			0
$767$			131.569i			0.171537i
$768$		0			0
$769$	−1066.22			−1.38650			−0.693248	−	0.720699i	$-0.743821\pi$
$769$	−1066.22			−1.38650			−0.693248	+	0.720699i	$0.743821\pi$
$770$		0			0
$771$	−44.5562	−	107.568i	−0.0577902	−	0.139518i
$772$		0			0
$773$	−497.702	+	1201.56i	−0.643857	+	1.55441i	0.177578	+	0.984107i	$0.443174\pi$
$773$	−497.702	+	1201.56i	−0.643857	+	1.55441i	−0.821435	+	0.570302i	$0.806826\pi$
$774$		0			0
$775$	−89.9033	+	89.9033i	−0.116004	+	0.116004i
$776$		0			0
$777$	466.245	−	466.245i	0.600057	−	0.600057i
$778$		0			0
$779$	146.527	−	353.749i	0.188097	−	0.454106i
$780$		0			0
$781$	−32.6056	−	78.7170i	−0.0417486	−	0.100790i
$782$		0			0
$783$	−205.995			−0.263084
$784$		0			0
$785$		−	429.553i		−	0.547201i
$786$		0			0
$787$	−307.578	+	127.403i	−0.390823	+	0.161884i	−0.569437	−	0.822035i	$-0.692839\pi$
$787$	−307.578	+	127.403i	−0.390823	+	0.161884i	0.178614	+	0.983919i	$0.442839\pi$
$788$		0			0
$789$	−67.0392	−	27.7686i	−0.0849673	−	0.0351946i
$790$		0			0
$791$	595.415	+	595.415i	0.752737	+	0.752737i
$792$		0			0
$793$	257.199	+	257.199i	0.324337	+	0.324337i
$794$		0			0
$795$	−107.442	−	44.5039i	−0.135147	−	0.0559797i
$796$		0			0
$797$	−367.115	+	152.064i	−0.460621	+	0.190795i	−0.600912	−	0.799315i	$-0.705196\pi$
$797$	−367.115	+	152.064i	−0.460621	+	0.190795i	0.140292	+	0.990110i	$0.455196\pi$
$798$		0			0
$799$			1660.96i			2.07880i
$800$		0			0
$801$	106.676			0.133179
$802$		0			0
$803$	153.481	+	370.536i	0.191134	+	0.461439i
$804$		0			0
$805$	−154.870	+	373.889i	−0.192385	+	0.464459i
$806$		0			0
$807$	−230.650	+	230.650i	−0.285812	+	0.285812i
$808$		0			0
$809$	318.547	−	318.547i	0.393754	−	0.393754i	−0.482269	−	0.876023i	$-0.660187\pi$
$809$	318.547	−	318.547i	0.393754	−	0.393754i	0.876023	+	0.482269i	$0.160187\pi$
$810$		0			0
$811$	−187.929	+	453.701i	−0.231725	+	0.559434i	−0.996380	−	0.0850055i	$-0.972909\pi$
$811$	−187.929	+	453.701i	−0.231725	+	0.559434i	0.764655	+	0.644439i	$0.222909\pi$
$812$		0			0
$813$	164.972	+	398.277i	0.202917	+	0.489885i
$814$		0			0
$815$	167.215			0.205172
$816$		0			0
$817$			503.050i			0.615728i
$818$		0			0
$819$	201.952	−	83.6513i	0.246584	−	0.102138i
$820$		0			0
$821$	−1296.86	−	537.177i	−1.57961	−	0.654295i	−0.591257	−	0.806483i	$-0.701368\pi$
$821$	−1296.86	−	537.177i	−1.57961	−	0.654295i	−0.988352	+	0.152188i	$0.951368\pi$
$822$		0			0
$823$	1104.17	+	1104.17i	1.34164	+	1.34164i	0.894426	+	0.447215i	$0.147584\pi$
$823$	1104.17	+	1104.17i	1.34164	+	1.34164i	0.447215	+	0.894426i	$0.352416\pi$
$824$		0			0
$825$	−241.430	−	241.430i	−0.292642	−	0.292642i
$826$		0			0
$827$	−193.766	−	80.2605i	−0.234300	−	0.0970502i	0.262445	−	0.964947i	$-0.415471\pi$
$827$	−193.766	−	80.2605i	−0.234300	−	0.0970502i	−0.496744	+	0.867897i	$0.665471\pi$
$828$		0			0
$829$	−282.707	+	117.101i	−0.341021	+	0.141256i	−0.546620	−	0.837381i	$-0.684086\pi$
$829$	−282.707	+	117.101i	−0.341021	+	0.141256i	0.205599	+	0.978636i	$0.434086\pi$
$830$		0			0
$831$			297.678i			0.358217i
$832$		0			0
$833$	−0.394087			−0.000473093
$834$		0			0
$835$	−203.483	−	491.251i	−0.243692	−	0.588324i
$836$		0			0
$837$	48.7020	−	117.577i	0.0581863	−	0.140474i
$838$		0			0
$839$	922.254	−	922.254i	1.09923	−	1.09923i	0.104729	−	0.994501i	$-0.466603\pi$
$839$	922.254	−	922.254i	1.09923	−	1.09923i	0.994501	−	0.104729i	$-0.0333975\pi$
$840$		0			0
$841$	−533.792	+	533.792i	−0.634711	+	0.634711i
$842$		0			0
$843$	177.398	−	428.276i	0.210436	−	0.508038i
$844$		0			0
$845$	96.1999	+	232.247i	0.113846	+	0.274849i
$846$		0			0
$847$	−25.4214			−0.0300134
$848$		0			0
$849$			87.6775i			0.103271i
$850$		0			0
$851$	−2171.39	+	899.421i	−2.55158	+	1.05690i
$852$		0			0
$853$	319.646	+	132.402i	0.374731	+	0.155219i	0.562097	−	0.827072i	$-0.309995\pi$
$853$	319.646	+	132.402i	0.374731	+	0.155219i	−0.187366	+	0.982290i	$0.559995\pi$
$854$		0			0
$855$	−160.124	−	160.124i	−0.187280	−	0.187280i
$856$		0			0
$857$	−154.384	−	154.384i	−0.180145	−	0.180145i	0.611274	−	0.791419i	$-0.290657\pi$
$857$	−154.384	−	154.384i	−0.180145	−	0.180145i	−0.791419	+	0.611274i	$0.790657\pi$
$858$		0			0
$859$	−598.422	−	247.875i	−0.696650	−	0.288562i	0.00611778	−	0.999981i	$-0.498053\pi$
$859$	−598.422	−	247.875i	−0.696650	−	0.288562i	−0.702768	+	0.711419i	$0.748053\pi$
$860$		0			0
$861$	179.827	−	74.4868i	0.208858	−	0.0865120i
$862$		0			0
$863$		−	687.121i		−	0.796201i	−0.917342	−	0.398101i	$-0.869670\pi$
$863$		−	687.121i		−	0.796201i	0.917342	−	0.398101i	$-0.130330\pi$
$864$		0			0
$865$	−58.2279			−0.0673155
$866$		0			0
$867$	280.559	+	677.330i	0.323598	+	0.781234i
$868$		0			0
$869$	−214.326	+	517.428i	−0.246635	+	0.595429i
$870$		0			0
$871$	−294.176	+	294.176i	−0.337745	+	0.337745i
$872$		0			0
$873$	−71.8034	+	71.8034i	−0.0822491	+	0.0822491i
$874$		0			0
$875$	−212.321	+	512.588i	−0.242653	+	0.585815i
$876$		0			0
$877$	146.136	+	352.804i	0.166632	+	0.402285i	0.985034	−	0.172361i	$-0.0551397\pi$
$877$	146.136	+	352.804i	0.166632	+	0.402285i	−0.818402	+	0.574646i	$0.805140\pi$
$878$		0			0
$879$	−171.385			−0.194977
$880$		0			0
$881$		−	1060.30i		−	1.20352i	−0.798675	−	0.601762i	$-0.794466\pi$
$881$		−	1060.30i		−	1.20352i	0.798675	−	0.601762i	$-0.205534\pi$
$882$		0			0
$883$	−281.886	+	116.761i	−0.319237	+	0.132232i	−0.536547	−	0.843870i	$-0.680272\pi$
$883$	−281.886	+	116.761i	−0.319237	+	0.132232i	0.217310	+	0.976103i	$0.430272\pi$
$884$		0			0
$885$	64.0132	+	26.5151i	0.0723313	+	0.0299606i
$886$		0			0
$887$	934.058	+	934.058i	1.05305	+	1.05305i	0.998511	+	0.0545418i	$0.0173698\pi$
$887$	934.058	+	934.058i	1.05305	+	1.05305i	0.0545418	+	0.998511i	$0.482630\pi$
$888$		0			0
$889$	633.855	+	633.855i	0.712998	+	0.712998i
$890$		0			0
$891$	−343.170	−	142.145i	−0.385151	−	0.159535i
$892$		0			0
$893$	1017.32	−	421.389i	1.13922	−	0.471880i
$894$		0			0
$895$			25.1462i			0.0280964i
$896$		0			0
$897$	208.735			0.232704
$898$		0			0
$899$	20.3569	+	49.1459i	0.0226439	+	0.0546673i
$900$		0			0
$901$	−550.377	+	1328.73i	−0.610851	+	1.47473i
$902$		0			0
$903$	−180.824	+	180.824i	−0.200248	+	0.200248i
$904$		0			0
$905$	−197.470	+	197.470i	−0.218199	+	0.218199i
$906$		0			0
$907$	312.448	−	754.317i	0.344485	−	0.831661i	−0.652765	−	0.757560i	$-0.726391\pi$
$907$	312.448	−	754.317i	0.344485	−	0.831661i	0.997251	−	0.0741012i	$-0.0236088\pi$
$908$		0			0
$909$	−366.729	−	885.362i	−0.403442	−	0.973995i
$910$		0			0
$911$	−678.215			−0.744473			−0.372236	−	0.928138i	$-0.621409\pi$
$911$	−678.215			−0.744473			−0.372236	+	0.928138i	$0.621409\pi$
$912$		0			0
$913$		−	1218.10i		−	1.33417i
$914$		0			0
$915$	176.970	−	73.3034i	0.193410	−	0.0801130i
$916$		0			0
$917$	−340.332	−	140.970i	−0.371137	−	0.153730i
$918$		0			0
$919$	−456.147	−	456.147i	−0.496352	−	0.496352i	0.413949	−	0.910300i	$-0.364149\pi$
$919$	−456.147	−	456.147i	−0.496352	−	0.496352i	−0.910300	+	0.413949i	$0.864149\pi$
$920$		0			0
$921$	429.832	+	429.832i	0.466702	+	0.466702i
$922$		0			0
$923$	31.0149	+	12.8468i	0.0336023	+	0.0139185i
$924$		0			0
$925$	−1399.43	+	579.663i	−1.51290	+	0.626662i
$926$		0			0
$927$			48.9476i			0.0528021i
$928$		0			0
$929$	−1356.05			−1.45969			−0.729845	−	0.683613i	$-0.760408\pi$
$929$	−1356.05			−1.45969			−0.729845	+	0.683613i	$0.760408\pi$
$930$		0			0
$931$	0.0999806	+	0.241375i	0.000107391	+	0.000259264i
$932$		0			0
$933$	−111.542	+	269.285i	−0.119552	+	0.288623i
$934$		0			0
$935$	379.863	−	379.863i	0.406271	−	0.406271i
$936$		0			0
$937$	38.1043	−	38.1043i	0.0406663	−	0.0406663i	−0.686481	−	0.727148i	$-0.740846\pi$
$937$	38.1043	−	38.1043i	0.0406663	−	0.0406663i	0.727148	+	0.686481i	$0.240846\pi$
$938$		0			0
$939$	220.498	−	532.330i	0.234823	−	0.566912i
$940$		0			0
$941$	283.674	+	684.849i	0.301460	+	0.727789i	0.999926	+	0.0121459i	$0.00386625\pi$
$941$	283.674	+	684.849i	0.301460	+	0.727789i	−0.698466	+	0.715643i	$0.746134\pi$
$942$		0			0
$943$	−693.800			−0.735737
$944$		0			0
$945$		−	261.069i		−	0.276264i
$946$		0			0
$947$	187.436	−	77.6384i	0.197926	−	0.0819836i	−0.281519	−	0.959556i	$-0.590838\pi$
$947$	187.436	−	77.6384i	0.197926	−	0.0819836i	0.479445	+	0.877572i	$0.340838\pi$
$948$		0			0
$949$	−145.993	−	60.4723i	−0.153839	−	0.0637222i
$950$		0			0
$951$	235.207	+	235.207i	0.247326	+	0.247326i
$952$		0			0
$953$	960.541	+	960.541i	1.00791	+	1.00791i	0.999968	+	0.00794427i	$0.00252877\pi$
$953$	960.541	+	960.541i	1.00791	+	1.00791i	0.00794427	+	0.999968i	$0.497471\pi$
$954$		0			0
$955$	3.10592	+	1.28652i	0.00325227	+	0.00134714i
$956$		0			0
$957$	−131.978	+	54.6672i	−0.137908	+	0.0571235i
$958$		0			0
$959$			16.4437i			0.0171467i
$960$		0			0
$961$	928.136			0.965802
$962$		0			0
$963$	−32.3404	−	78.0766i	−0.0335830	−	0.0810764i
$964$		0			0
$965$	69.1045	−	166.833i	0.0716109	−	0.172884i
$966$		0			0
$967$	−183.282	+	183.282i	−0.189537	+	0.189537i	−0.795496	−	0.605959i	$-0.792789\pi$
$967$	−183.282	+	183.282i	−0.189537	+	0.189537i	0.605959	+	0.795496i	$0.292789\pi$
$968$		0			0
$969$	530.503	−	530.503i	0.547475	−	0.547475i
$970$		0			0
$971$	344.446	−	831.566i	0.354733	−	0.856401i	−0.641289	−	0.767299i	$-0.721600\pi$
$971$	344.446	−	831.566i	0.354733	−	0.856401i	0.996022	−	0.0891022i	$-0.0283998\pi$
$972$		0			0
$973$	529.972	+	1279.47i	0.544678	+	1.31497i
$974$		0			0
$975$	134.527			0.137976
$976$		0			0
$977$		−	1484.89i		−	1.51985i	−0.650010	−	0.759926i	$-0.725235\pi$
$977$		−	1484.89i		−	1.51985i	0.650010	−	0.759926i	$-0.274765\pi$
$978$		0			0
$979$	155.002	−	64.2040i	0.158327	−	0.0655812i
$980$		0			0
$981$	188.674	+	78.1515i	0.192329	+	0.0796651i
$982$		0			0
$983$	−32.2811	−	32.2811i	−0.0328394	−	0.0328394i	0.690496	−	0.723336i	$-0.257392\pi$
$983$	−32.2811	−	32.2811i	−0.0328394	−	0.0328394i	−0.723336	+	0.690496i	$0.757392\pi$
$984$		0			0
$985$	111.684	+	111.684i	0.113385	+	0.113385i
$986$		0			0
$987$	517.153	+	214.212i	0.523964	+	0.217033i
$988$		0			0
$989$	842.133	−	348.823i	0.851500	−	0.352703i
$990$		0			0
$991$		−	1236.65i		−	1.24789i	−0.781470	−	0.623943i	$-0.785530\pi$
$991$		−	1236.65i		−	1.24789i	0.781470	−	0.623943i	$-0.214470\pi$
$992$		0			0
$993$	−722.948			−0.728044
$994$		0			0
$995$	207.947	+	502.028i	0.208992	+	0.504551i
$996$		0			0
$997$	234.577	−	566.319i	0.235283	−	0.568023i	−0.761501	−	0.648164i	$-0.775537\pi$
$997$	234.577	−	566.319i	0.235283	−	0.568023i	0.996784	+	0.0801409i	$0.0255370\pi$
$998$		0			0
$999$	1072.10	−	1072.10i	1.07318	−	1.07318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.79.3		28
4.3	odd	2		32.3.h.a.11.6	yes	28
8.3	odd	2		256.3.h.b.159.3		28
8.5	even	2		256.3.h.a.159.5		28
12.11	even	2		288.3.u.a.235.2		28
32.3	odd	8	inner	128.3.h.a.47.3		28
32.13	even	8		256.3.h.b.95.3		28
32.19	odd	8		256.3.h.a.95.5		28
32.29	even	8		32.3.h.a.3.6	✓	28
96.29	odd	8		288.3.u.a.163.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.6	✓	28	32.29	even	8
32.3.h.a.11.6	yes	28	4.3	odd	2
128.3.h.a.47.3		28	32.3	odd	8	inner
128.3.h.a.79.3		28	1.1	even	1	trivial
256.3.h.a.95.5		28	32.19	odd	8
256.3.h.a.159.5		28	8.5	even	2
256.3.h.b.95.3		28	32.13	even	8
256.3.h.b.159.3		28	8.3	odd	2
288.3.u.a.163.2		28	96.29	odd	8
288.3.u.a.235.2		28	12.11	even	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.527719 - 1.27403i) q^{3} +(-0.642823 + 1.55191i) q^{5} +(4.95044 - 4.95044i) q^{7} +(5.01930 - 5.01930i) q^{9} +O(q^{10})\)	\(q+(-0.527719 - 1.27403i) q^{3} +(-0.642823 + 1.55191i) q^{5} +(4.95044 - 4.95044i) q^{7} +(5.01930 - 5.01930i) q^{9} +(4.27221 - 10.3140i) q^{11} +(1.68327 + 4.06379i) q^{13} +2.31641 q^{15} -28.6469i q^{17} +(-17.5460 + 7.26778i) q^{19} +(-8.91944 - 3.69455i) q^{21} +(24.3334 + 24.3334i) q^{23} +(15.6825 + 15.6825i) q^{25} +(-20.5098 - 8.49542i) q^{27} +(8.57286 - 3.55100i) q^{29} +5.73273i q^{31} -15.3949 q^{33} +(4.50039 + 10.8649i) q^{35} +(-26.1364 + 63.0989i) q^{37} +(4.28908 - 4.28908i) q^{39} +(-14.2561 + 14.2561i) q^{41} +(10.1365 - 24.4717i) q^{43} +(4.56299 + 11.0160i) q^{45} -57.9804 q^{47} -0.0137567i q^{49} +(-36.4969 + 15.1175i) q^{51} +(-46.3830 - 19.2124i) q^{53} +(13.2602 + 13.2602i) q^{55} +(18.5187 + 18.5187i) q^{57} +(27.6347 + 11.4467i) q^{59} +(76.3985 - 31.6453i) q^{61} -49.6955i q^{63} -7.38868 q^{65} +(36.1949 + 87.3821i) q^{67} +(18.1602 - 43.8425i) q^{69} +(5.39666 - 5.39666i) q^{71} +(-25.4031 + 25.4031i) q^{73} +(11.7039 - 28.2558i) q^{75} +(-29.9097 - 72.2084i) q^{77} -50.1674 q^{79} -33.2721i q^{81} +(100.805 - 41.7550i) q^{83} +(44.4574 + 18.4149i) q^{85} +(-9.04814 - 9.04814i) q^{87} +(10.6266 + 10.6266i) q^{89} +(28.4505 + 11.7846i) q^{91} +(7.30366 - 3.02527i) q^{93} -31.9017i q^{95} -14.3055 q^{97} +(-30.3257 - 73.2128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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