LMFDB - Embedded newform 875.2.h.d.176.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(176,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("875.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.h (of order $5$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			176.3
Character	$\chi$	$=$	875.176
Dual form			875.2.h.d.701.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72620 + 1.25416i) q^{2} +(0.523784 - 1.61204i) q^{3} +(0.788824 - 2.42775i) q^{4} +(1.11760 + 3.43962i) q^{6} -1.00000 q^{7} +(0.364416 + 1.12156i) q^{8} +(0.102725 + 0.0746342i) q^{9} +O(q^{10})$	\(q+(-1.72620 + 1.25416i) q^{2} +(0.523784 - 1.61204i) q^{3} +(0.788824 - 2.42775i) q^{4} +(1.11760 + 3.43962i) q^{6} -1.00000 q^{7} +(0.364416 + 1.12156i) q^{8} +(0.102725 + 0.0746342i) q^{9} +(-1.67312 + 1.21559i) q^{11} +(-3.50046 - 2.54323i) q^{12} +(-1.52101 - 1.10508i) q^{13} +(1.72620 - 1.25416i) q^{14} +(2.09467 + 1.52187i) q^{16} +(0.774264 + 2.38294i) q^{17} -0.270928 q^{18} +(1.88247 + 5.79366i) q^{19} +(-0.523784 + 1.61204i) q^{21} +(1.36360 - 4.19672i) q^{22} +(-4.59409 + 3.33780i) q^{23} +1.99887 q^{24} +4.01152 q^{26} +(4.28797 - 3.11539i) q^{27} +(-0.788824 + 2.42775i) q^{28} +(1.74293 - 5.36417i) q^{29} +(0.895341 + 2.75558i) q^{31} -7.88304 q^{32} +(1.08323 + 3.33385i) q^{33} +(-4.32512 - 3.14238i) q^{34} +(0.262226 - 0.190518i) q^{36} +(0.389864 + 0.283253i) q^{37} +(-10.5157 - 7.64010i) q^{38} +(-2.57812 + 1.87311i) q^{39} +(5.31332 + 3.86036i) q^{41} +(-1.11760 - 3.43962i) q^{42} +10.9911 q^{43} +(1.63136 + 5.02081i) q^{44} +(3.74419 - 11.5234i) q^{46} +(1.68511 - 5.18622i) q^{47} +(3.55047 - 2.57957i) q^{48} +1.00000 q^{49} +4.24694 q^{51} +(-3.88267 + 2.82093i) q^{52} +(-3.25150 + 10.0071i) q^{53} +(-3.49470 + 10.7556i) q^{54} +(-0.364416 - 1.12156i) q^{56} +10.3256 q^{57} +(3.71889 + 11.4456i) q^{58} +(1.18719 + 0.862546i) q^{59} +(5.87272 - 4.26678i) q^{61} +(-5.00147 - 3.63378i) q^{62} +(-0.102725 - 0.0746342i) q^{63} +(9.41838 - 6.84285i) q^{64} +(-6.05105 - 4.39634i) q^{66} +(3.72006 + 11.4492i) q^{67} +6.39594 q^{68} +(2.97436 + 9.15415i) q^{69} +(-0.0938043 + 0.288700i) q^{71} +(-0.0462718 + 0.142410i) q^{72} +(10.7250 - 7.79217i) q^{73} -1.02823 q^{74} +15.5505 q^{76} +(1.67312 - 1.21559i) q^{77} +(2.10117 - 6.46674i) q^{78} +(0.595259 - 1.83202i) q^{79} +(-2.65846 - 8.18189i) q^{81} -14.0134 q^{82} +(5.54095 + 17.0533i) q^{83} +(3.50046 + 2.54323i) q^{84} +(-18.9728 + 13.7845i) q^{86} +(-7.73435 - 5.61933i) q^{87} +(-1.97307 - 1.43352i) q^{88} +(-4.18602 + 3.04132i) q^{89} +(1.52101 + 1.10508i) q^{91} +(4.47943 + 13.7863i) q^{92} +4.91107 q^{93} +(3.59552 + 11.0659i) q^{94} +(-4.12901 + 12.7078i) q^{96} +(-2.74159 + 8.43774i) q^{97} +(-1.72620 + 1.25416i) q^{98} -0.262596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.72620	+	1.25416i	−1.22061	+	0.886824i	−0.996151	−	0.0876592i	$-0.972061\pi$
$2$	−1.72620	+	1.25416i	−1.22061	+	0.886824i	−0.224459	+	0.974484i	$0.572061\pi$
$3$	0.523784	−	1.61204i	0.302407	−	0.930712i	−0.678226	−	0.734854i	$-0.737251\pi$
$3$	0.523784	−	1.61204i	0.302407	−	0.930712i	0.980632	−	0.195858i	$-0.0627493\pi$
$4$	0.788824	−	2.42775i	0.394412	−	1.21388i
$5$		0			0
$5$		0			0
$6$	1.11760	+	3.43962i	0.456258	+	1.40422i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.364416	+	1.12156i	0.128840	+	0.396530i
$9$	0.102725	+	0.0746342i	0.0342417	+	0.0248781i
$10$		0			0
$11$	−1.67312	+	1.21559i	−0.504465	+	0.366515i	−0.810720	−	0.585434i	$-0.800924\pi$
$11$	−1.67312	+	1.21559i	−0.504465	+	0.366515i	0.306255	+	0.951949i	$0.400924\pi$
$12$	−3.50046	−	2.54323i	−1.01050	−	0.734168i
$13$	−1.52101	−	1.10508i	−0.421853	−	0.306494i	0.356530	−	0.934284i	$-0.383960\pi$
$13$	−1.52101	−	1.10508i	−0.421853	−	0.306494i	−0.778383	+	0.627790i	$0.783960\pi$
$14$	1.72620	−	1.25416i	0.461347	−	0.335188i
$15$		0			0
$16$	2.09467	+	1.52187i	0.523668	+	0.380467i
$17$	0.774264	+	2.38294i	0.187787	+	0.577948i	0.999985	−	0.00543333i	$-0.00172949\pi$
$17$	0.774264	+	2.38294i	0.187787	+	0.577948i	−0.812199	+	0.583381i	$0.801729\pi$
$18$	−0.270928			−0.0638583
$19$	1.88247	+	5.79366i	0.431869	+	1.32916i	0.896261	+	0.443527i	$0.146273\pi$
$19$	1.88247	+	5.79366i	0.431869	+	1.32916i	−0.464392	+	0.885630i	$0.653727\pi$
$20$		0			0
$21$	−0.523784	+	1.61204i	−0.114299	+	0.351776i
$22$	1.36360	−	4.19672i	0.290720	−	0.894743i
$23$	−4.59409	+	3.33780i	−0.957935	+	0.695980i	−0.952670	−	0.304006i	$-0.901676\pi$
$23$	−4.59409	+	3.33780i	−0.957935	+	0.695980i	−0.00526439	+	0.999986i	$0.501676\pi$
$24$	1.99887			0.408017
$25$		0			0
$26$	4.01152			0.786725
$27$	4.28797	−	3.11539i	0.825220	−	0.599558i
$28$	−0.788824	+	2.42775i	−0.149074	+	0.458802i
$29$	1.74293	−	5.36417i	0.323653	−	0.996102i	−0.648392	−	0.761307i	$-0.724558\pi$
$29$	1.74293	−	5.36417i	0.323653	−	0.996102i	0.972045	−	0.234795i	$-0.0754419\pi$
$30$		0			0
$31$	0.895341	+	2.75558i	0.160808	+	0.494916i	0.998703	−	0.0509153i	$-0.0162139\pi$
$31$	0.895341	+	2.75558i	0.160808	+	0.494916i	−0.837895	+	0.545832i	$0.816214\pi$
$32$	−7.88304			−1.39354
$33$	1.08323	+	3.33385i	0.188566	+	0.580348i
$34$	−4.32512	−	3.14238i	−0.741752	−	0.538914i
$35$		0			0
$36$	0.262226	−	0.190518i	0.0437043	−	0.0317530i
$37$	0.389864	+	0.283253i	0.0640933	+	0.0465665i	0.619371	−	0.785099i	$-0.287388\pi$
$37$	0.389864	+	0.283253i	0.0640933	+	0.0465665i	−0.555277	+	0.831665i	$0.687388\pi$
$38$	−10.5157	−	7.64010i	−1.70587	−	1.23939i
$39$	−2.57812	+	1.87311i	−0.412829	+	0.299938i
$40$		0			0
$41$	5.31332	+	3.86036i	0.829802	+	0.602886i	0.919503	−	0.393082i	$-0.128591\pi$
$41$	5.31332	+	3.86036i	0.829802	+	0.602886i	−0.0897014	+	0.995969i	$0.528591\pi$
$42$	−1.11760	−	3.43962i	−0.172449	−	0.530744i
$43$	10.9911			1.67612			0.838060	−	0.545578i	$-0.183690\pi$
$43$	10.9911			1.67612			0.838060	+	0.545578i	$0.183690\pi$
$44$	1.63136	+	5.02081i	0.245937	+	0.756915i
$45$		0			0
$46$	3.74419	−	11.5234i	0.552051	−	1.69904i
$47$	1.68511	−	5.18622i	0.245798	−	0.756488i	−0.749706	−	0.661771i	$-0.769805\pi$
$47$	1.68511	−	5.18622i	0.245798	−	0.756488i	0.995504	−	0.0947176i	$-0.0301948\pi$
$48$	3.55047	−	2.57957i	0.512466	−	0.372329i
$49$	1.00000			0.142857
$50$		0			0
$51$	4.24694			0.594691
$52$	−3.88267	+	2.82093i	−0.538430	+	0.391192i
$53$	−3.25150	+	10.0071i	−0.446628	+	1.37458i	0.434061	+	0.900883i	$0.357080\pi$
$53$	−3.25150	+	10.0071i	−0.446628	+	1.37458i	−0.880689	+	0.473695i	$0.842920\pi$
$54$	−3.49470	+	10.7556i	−0.475569	+	1.46365i
$55$		0			0
$56$	−0.364416	−	1.12156i	−0.0486971	−	0.149874i
$57$	10.3256			1.36766
$58$	3.71889	+	11.4456i	0.488314	+	1.50287i
$59$	1.18719	+	0.862546i	0.154559	+	0.112294i	0.662377	−	0.749171i	$-0.269548\pi$
$59$	1.18719	+	0.862546i	0.154559	+	0.112294i	−0.507818	+	0.861465i	$0.669548\pi$
$60$		0			0
$61$	5.87272	−	4.26678i	0.751924	−	0.546305i	−0.144498	−	0.989505i	$-0.546157\pi$
$61$	5.87272	−	4.26678i	0.751924	−	0.546305i	0.896423	+	0.443200i	$0.146157\pi$
$62$	−5.00147	−	3.63378i	−0.635188	−	0.461491i
$63$	−0.102725	−	0.0746342i	−0.0129422	−	0.00940303i
$64$	9.41838	−	6.84285i	1.17730	−	0.855356i
$65$		0			0
$66$	−6.05105	−	4.39634i	−0.744833	−	0.541153i
$67$	3.72006	+	11.4492i	0.454477	+	1.39874i	0.871748	+	0.489955i	$0.162987\pi$
$67$	3.72006	+	11.4492i	0.454477	+	1.39874i	−0.417270	+	0.908782i	$0.637013\pi$
$68$	6.39594			0.775622
$69$	2.97436	+	9.15415i	0.358071	+	1.10203i
$70$		0			0
$71$	−0.0938043	+	0.288700i	−0.0111325	+	0.0342624i	−0.956468	−	0.291836i	$-0.905734\pi$
$71$	−0.0938043	+	0.288700i	−0.0111325	+	0.0342624i	0.945336	+	0.326098i	$0.105734\pi$
$72$	−0.0462718	+	0.142410i	−0.00545318	+	0.0167832i
$73$	10.7250	−	7.79217i	1.25527	−	0.912004i	0.256751	−	0.966478i	$-0.417348\pi$
$73$	10.7250	−	7.79217i	1.25527	−	0.912004i	0.998515	+	0.0544732i	$0.0173479\pi$
$74$	−1.02823			−0.119529
$75$		0			0
$76$	15.5505			1.78376
$77$	1.67312	−	1.21559i	0.190670	−	0.138530i
$78$	2.10117	−	6.46674i	0.237911	−	0.732214i
$79$	0.595259	−	1.83202i	0.0669718	−	0.206118i	−0.911970	−	0.410256i	$-0.865439\pi$
$79$	0.595259	−	1.83202i	0.0669718	−	0.206118i	0.978942	+	0.204138i	$0.0654392\pi$
$80$		0			0
$81$	−2.65846	−	8.18189i	−0.295384	−	0.909099i
$82$	−14.0134			−1.54752
$83$	5.54095	+	17.0533i	0.608198	+	1.87184i	0.473100	+	0.881009i	$0.343135\pi$
$83$	5.54095	+	17.0533i	0.608198	+	1.87184i	0.135098	+	0.990832i	$0.456865\pi$
$84$	3.50046	+	2.54323i	0.381932	+	0.277490i
$85$		0			0
$86$	−18.9728	+	13.7845i	−2.04589	+	1.48642i
$87$	−7.73435	−	5.61933i	−0.829209	−	0.602456i
$88$	−1.97307	−	1.43352i	−0.210330	−	0.152813i
$89$	−4.18602	+	3.04132i	−0.443718	+	0.322380i	−0.787110	−	0.616812i	$-0.788424\pi$
$89$	−4.18602	+	3.04132i	−0.443718	+	0.322380i	0.343393	+	0.939192i	$0.388424\pi$
$90$		0			0
$91$	1.52101	+	1.10508i	0.159446	+	0.115844i
$92$	4.47943	+	13.7863i	0.467012	+	1.43732i
$93$	4.91107			0.509254
$94$	3.59552	+	11.0659i	0.370849	+	1.14136i
$95$		0			0
$96$	−4.12901	+	12.7078i	−0.421415	+	1.29698i
$97$	−2.74159	+	8.43774i	−0.278366	+	0.856723i	0.709943	+	0.704259i	$0.248721\pi$
$97$	−2.74159	+	8.43774i	−0.278366	+	0.856723i	−0.988309	+	0.152464i	$0.951279\pi$
$98$	−1.72620	+	1.25416i	−0.174373	+	0.126689i
$99$	−0.262596			−0.0263919
$100$		0			0
$101$	−8.59159			−0.854895			−0.427447	−	0.904040i	$-0.640587\pi$
$101$	−8.59159			−0.854895			−0.427447	+	0.904040i	$0.640587\pi$
$102$	−7.33108	+	5.32634i	−0.725885	+	0.527386i
$103$	−3.91608	+	12.0524i	−0.385863	+	1.18756i	0.549990	+	0.835171i	$0.314631\pi$
$103$	−3.91608	+	12.0524i	−0.385863	+	1.18756i	−0.935853	+	0.352392i	$0.885369\pi$
$104$	0.685129	−	2.10861i	0.0671824	−	0.206766i
$105$		0			0
$106$	−6.93773	−	21.3521i	−0.673852	−	2.07390i
$107$	−1.20139			−0.116143			−0.0580714	−	0.998312i	$-0.518495\pi$
$107$	−1.20139			−0.116143			−0.0580714	+	0.998312i	$0.518495\pi$
$108$	−4.18094	−	12.8676i	−0.402312	−	1.23819i
$109$	−5.14722	−	3.73967i	−0.493014	−	0.358196i	0.313328	−	0.949645i	$-0.398556\pi$
$109$	−5.14722	−	3.73967i	−0.493014	−	0.358196i	−0.806342	+	0.591449i	$0.798556\pi$
$110$		0			0
$111$	0.660820	−	0.480113i	0.0627222	−	0.0455704i
$112$	−2.09467	−	1.52187i	−0.197928	−	0.143803i
$113$	−8.47352	−	6.15637i	−0.797121	−	0.579143i	0.112947	−	0.993601i	$-0.463971\pi$
$113$	−8.47352	−	6.15637i	−0.797121	−	0.579143i	−0.910068	+	0.414458i	$0.863971\pi$
$114$	−17.8241	+	12.9500i	−1.66938	+	1.21288i
$115$		0			0
$116$	−11.6480	−	8.46278i	−1.08149	−	0.785749i
$117$	−0.0737696	−	0.227039i	−0.00682000	−	0.0209898i
$118$	−3.13110			−0.288242
$119$	−0.774264	−	2.38294i	−0.0709766	−	0.218444i
$120$		0			0
$121$	−2.07752	+	6.39396i	−0.188866	+	0.581269i
$122$	−4.78628	+	14.7306i	−0.433329	+	1.33365i
$123$	9.00608	−	6.54330i	0.812051	−	0.589990i
$124$	7.39612			0.664191
$125$		0			0
$126$	0.270928			0.0241362
$127$	13.6996	−	9.95332i	1.21564	−	0.883214i	0.219910	−	0.975520i	$-0.429424\pi$
$127$	13.6996	−	9.95332i	1.21564	−	0.883214i	0.995731	+	0.0923059i	$0.0294238\pi$
$128$	−2.80401	+	8.62985i	−0.247842	+	0.762778i
$129$	5.75694	−	17.7180i	0.506870	−	1.55999i
$130$		0			0
$131$	1.85455	+	5.70773i	0.162033	+	0.498687i	0.998805	−	0.0488643i	$-0.0155602\pi$
$131$	1.85455	+	5.70773i	0.162033	+	0.498687i	−0.836772	+	0.547551i	$0.815560\pi$
$132$	8.94823			0.778843
$133$	−1.88247	−	5.79366i	−0.163231	−	0.502374i
$134$	−20.7806	−	15.0980i	−1.79517	−	1.30427i
$135$		0			0
$136$	−2.39044	+	1.73676i	−0.204979	+	0.148926i
$137$	12.1317	+	8.81422i	1.03648	+	0.753050i	0.969596	−	0.244711i	$-0.0786931\pi$
$137$	12.1317	+	8.81422i	1.03648	+	0.753050i	0.0668877	+	0.997761i	$0.478693\pi$
$138$	−16.6151	−	12.0716i	−1.41437	−	1.02760i
$139$	−16.3214	+	11.8582i	−1.38436	+	1.00580i	−0.387907	+	0.921698i	$0.626802\pi$
$139$	−16.3214	+	11.8582i	−1.38436	+	1.00580i	−0.996457	+	0.0841011i	$0.973198\pi$
$140$		0			0
$141$	−7.47777	−	5.43292i	−0.629742	−	0.457534i
$142$	−0.200151	−	0.616000i	−0.0167963	−	0.0516936i
$143$	3.88817			0.325145
$144$	0.101592	+	0.312669i	0.00846602	+	0.0260557i
$145$		0			0
$146$	−8.74090	+	26.9017i	−0.723402	+	2.22640i
$147$	0.523784	−	1.61204i	0.0432010	−	0.132959i
$148$	0.995202	−	0.723056i	0.0818051	−	0.0594349i
$149$	−10.3764			−0.850071			−0.425035	−	0.905177i	$-0.639738\pi$
$149$	−10.3764			−0.850071			−0.425035	+	0.905177i	$0.639738\pi$
$150$		0			0
$151$	17.3336			1.41059			0.705294	−	0.708915i	$-0.250815\pi$
$151$	17.3336			1.41059			0.705294	+	0.708915i	$0.250815\pi$
$152$	−5.81191	+	4.22260i	−0.471408	+	0.342498i
$153$	−0.0983124	+	0.302575i	−0.00794809	+	0.0244617i
$154$	−1.36360	+	4.19672i	−0.109882	+	0.338181i
$155$		0			0
$156$	2.51377	+	7.73658i	0.201263	+	0.619422i
$157$	12.3970			0.989385			0.494692	−	0.869068i	$-0.335281\pi$
$157$	12.3970			0.989385			0.494692	+	0.869068i	$0.335281\pi$
$158$	1.27010	+	3.90898i	0.101044	+	0.310982i
$159$	14.4287	+	10.4831i	1.14427	+	0.831364i
$160$		0			0
$161$	4.59409	−	3.33780i	0.362065	−	0.263056i
$162$	14.8504	+	10.7895i	1.16676	+	0.847701i
$163$	7.54214	+	5.47969i	0.590746	+	0.429202i	0.842582	−	0.538568i	$-0.181034\pi$
$163$	7.54214	+	5.47969i	0.590746	+	0.429202i	−0.251836	+	0.967770i	$0.581034\pi$
$164$	13.5633	−	9.85429i	1.05911	−	0.769491i
$165$		0			0
$166$	−30.9523	−	22.4882i	−2.40237	−	1.74542i
$167$	−2.61722	−	8.05497i	−0.202526	−	0.623312i	−0.999806	−	0.0197018i	$-0.993728\pi$
$167$	−2.61722	−	8.05497i	−0.202526	−	0.623312i	0.797280	−	0.603610i	$-0.206272\pi$
$168$	−1.99887			−0.154216
$169$	−2.92494	−	9.00205i	−0.224996	−	0.692465i
$170$		0			0
$171$	−0.239028	+	0.735652i	−0.0182789	+	0.0562567i
$172$	8.67001	−	26.6836i	0.661082	−	2.03460i
$173$	−16.2250	+	11.7882i	−1.23356	+	0.896237i	−0.997152	−	0.0754156i	$-0.975972\pi$
$173$	−16.2250	+	11.7882i	−1.23356	+	0.896237i	−0.236413	+	0.971653i	$0.575972\pi$
$174$	20.3986			1.54641
$175$		0			0
$176$	−5.35461			−0.403619
$177$	2.01229	−	1.46202i	0.151253	−	0.109892i
$178$	3.41162	−	10.4999i	0.255712	−	0.786999i
$179$	2.92849	−	9.01297i	0.218886	−	0.673661i	−0.779969	−	0.625818i	$-0.784765\pi$
$179$	2.92849	−	9.01297i	0.218886	−	0.673661i	0.998855	−	0.0478432i	$-0.0152348\pi$
$180$		0			0
$181$	−5.00456	−	15.4024i	−0.371986	−	1.14485i	−0.945490	−	0.325652i	$-0.894416\pi$
$181$	−5.00456	−	15.4024i	−0.371986	−	1.14485i	0.573504	−	0.819203i	$-0.305584\pi$
$182$	−4.01152			−0.297354
$183$	−3.80219	−	11.7019i	−0.281066	−	0.865031i
$184$	−5.41769	−	3.93618i	−0.399397	−	0.290179i
$185$		0			0
$186$	−8.47749	+	6.15926i	−0.621600	+	0.451619i
$187$	−4.19212	−	3.04575i	−0.306558	−	0.222728i
$188$	−11.2616	−	8.18204i	−0.821337	−	0.596736i
$189$	−4.28797	+	3.11539i	−0.311904	+	0.226611i
$190$		0			0
$191$	21.7871	+	15.8293i	1.57646	+	1.14537i	0.920616	+	0.390470i	$0.127687\pi$
$191$	21.7871	+	15.8293i	1.57646	+	1.14537i	0.655845	+	0.754896i	$0.272313\pi$
$192$	−6.09776	−	18.7670i	−0.440068	−	1.35439i
$193$	−8.82966			−0.635573			−0.317786	−	0.948162i	$-0.602939\pi$
$193$	−8.82966			−0.635573			−0.317786	+	0.948162i	$0.602939\pi$
$194$	−5.84974	−	18.0036i	−0.419987	−	1.29259i
$195$		0			0
$196$	0.788824	−	2.42775i	0.0563446	−	0.173411i
$197$	−3.98586	+	12.2672i	−0.283981	+	0.874002i	0.702722	+	0.711465i	$0.251968\pi$
$197$	−3.98586	+	12.2672i	−0.283981	+	0.874002i	−0.986702	+	0.162538i	$0.948032\pi$
$198$	0.453295	−	0.329338i	0.0322142	−	0.0234050i
$199$	−2.72762			−0.193356			−0.0966778	−	0.995316i	$-0.530822\pi$
$199$	−2.72762			−0.193356			−0.0966778	+	0.995316i	$0.530822\pi$
$200$		0			0
$201$	20.4050			1.43926
$202$	14.8308	−	10.7752i	1.04349	−	0.758142i
$203$	−1.74293	+	5.36417i	−0.122329	+	0.376491i
$204$	3.35009	−	10.3105i	0.234553	−	0.721881i
$205$		0			0
$206$	−8.35575	−	25.7163i	−0.582172	−	1.79174i
$207$	−0.721044			−0.0501160
$208$	−1.50424	−	4.62957i	−0.104300	−	0.321003i
$209$	−10.1923	−	7.40516i	−0.705018	−	0.512226i
$210$		0			0
$211$	12.6936	−	9.22244i	0.873864	−	0.634899i	−0.0577572	−	0.998331i	$-0.518395\pi$
$211$	12.6936	−	9.22244i	0.873864	−	0.634899i	0.931621	+	0.363432i	$0.118395\pi$
$212$	21.7298	+	15.7877i	1.49241	+	1.08430i
$213$	0.416263	+	0.302433i	0.0285219	+	0.0207223i
$214$	2.07384	−	1.50673i	0.141765	−	0.102998i
$215$		0			0
$216$	5.05669	+	3.67390i	0.344064	+	0.249977i
$217$	−0.895341	−	2.75558i	−0.0607797	−	0.187061i
$218$	13.5753			0.919435
$219$	−6.94371	−	21.3705i	−0.469213	−	1.44409i
$220$		0			0
$221$	1.45567	−	4.48011i	0.0979193	−	0.301365i
$222$	−0.538569	+	1.65755i	−0.0361464	+	0.111247i
$223$	−4.75072	+	3.45160i	−0.318132	+	0.231136i	−0.735378	−	0.677657i	$-0.762995\pi$
$223$	−4.75072	+	3.45160i	−0.318132	+	0.231136i	0.417246	+	0.908794i	$0.362995\pi$
$224$	7.88304			0.526708
$225$		0			0
$226$	22.3481			1.48657
$227$	1.23012	−	0.893737i	0.0816462	−	0.0593194i	−0.546213	−	0.837646i	$-0.683931\pi$
$227$	1.23012	−	0.893737i	0.0816462	−	0.0593194i	0.627860	+	0.778327i	$0.283931\pi$
$228$	8.14510	−	25.0680i	0.539422	−	1.66017i
$229$	6.62526	−	20.3905i	0.437810	−	1.34744i	−0.452370	−	0.891830i	$-0.649421\pi$
$229$	6.62526	−	20.3905i	0.437810	−	1.34744i	0.890180	−	0.455609i	$-0.150579\pi$
$230$		0			0
$231$	−1.08323	−	3.33385i	−0.0712714	−	0.219351i
$232$	6.65137			0.436684
$233$	−6.40710	−	19.7190i	−0.419743	−	1.29184i	−0.907939	−	0.419103i	$-0.862345\pi$
$233$	−6.40710	−	19.7190i	−0.419743	−	1.29184i	0.488196	−	0.872734i	$-0.337655\pi$
$234$	0.412085	+	0.299397i	0.0269388	+	0.0195722i
$235$		0			0
$236$	3.03053	−	2.20181i	0.197271	−	0.143326i
$237$	−2.64150	−	1.91916i	−0.171584	−	0.124663i
$238$	4.32512	+	3.14238i	0.280356	+	0.203690i
$239$	13.7831	−	10.0140i	0.891558	−	0.647754i	−0.0447261	−	0.998999i	$-0.514242\pi$
$239$	13.7831	−	10.0140i	0.891558	−	0.647754i	0.936284	+	0.351245i	$0.114242\pi$
$240$		0			0
$241$	−4.92123	−	3.57549i	−0.317004	−	0.230317i	0.417892	−	0.908497i	$-0.362769\pi$
$241$	−4.92123	−	3.57549i	−0.317004	−	0.230317i	−0.734896	+	0.678180i	$0.762769\pi$
$242$	−4.43282	−	13.6428i	−0.284952	−	0.876993i
$243$	1.31867			0.0845926
$244$	−5.72614	−	17.6232i	−0.366578	−	1.12821i
$245$		0			0
$246$	−7.33998	+	22.5901i	−0.467980	+	1.44029i
$247$	3.53919	−	10.8925i	0.225194	−	0.693074i
$248$	−2.76426	+	2.00835i	−0.175530	+	0.127530i
$249$	30.3928			1.92607
$250$		0			0
$251$	−19.1633			−1.20958			−0.604788	−	0.796387i	$-0.706742\pi$
$251$	−19.1633			−1.20958			−0.604788	+	0.796387i	$0.706742\pi$
$252$	−0.262226	+	0.190518i	−0.0165187	+	0.0120015i
$253$	3.62906	−	11.1691i	0.228157	−	0.702195i
$254$	−11.1652	+	34.3629i	−0.700566	+	2.15612i
$255$		0			0
$256$	1.21208	+	3.73039i	0.0757549	+	0.233150i
$257$	−15.6052			−0.973424			−0.486712	−	0.873563i	$-0.661804\pi$
$257$	−15.6052			−0.973424			−0.486712	+	0.873563i	$0.661804\pi$
$258$	12.2836	+	37.8050i	0.764743	+	2.35364i
$259$	−0.389864	−	0.283253i	−0.0242250	−	0.0176005i
$260$		0			0
$261$	0.579393	−	0.420954i	0.0358636	−	0.0260564i
$262$	−10.3597	−	7.52679i	−0.640027	−	0.465007i
$263$	−18.0983	−	13.1492i	−1.11599	−	0.810814i	−0.132393	−	0.991197i	$-0.542266\pi$
$263$	−18.0983	−	13.1492i	−1.11599	−	0.810814i	−0.983596	+	0.180383i	$0.942266\pi$
$264$	−3.34435	+	2.42981i	−0.205830	+	0.149544i
$265$		0			0
$266$	10.5157	+	7.64010i	0.644759	+	0.468445i
$267$	2.71017	+	8.34104i	0.165860	+	0.510463i
$268$	30.7302			1.87714
$269$	0.320389	+	0.986055i	0.0195344	+	0.0601208i	0.960349	−	0.278802i	$-0.0899374\pi$
$269$	0.320389	+	0.986055i	0.0195344	+	0.0601208i	−0.940814	+	0.338923i	$0.889937\pi$
$270$		0			0
$271$	−5.39177	+	16.5941i	−0.327526	+	1.00802i	0.642761	+	0.766067i	$0.277789\pi$
$271$	−5.39177	+	16.5941i	−0.327526	+	1.00802i	−0.970287	+	0.241956i	$0.922211\pi$
$272$	−2.00469	+	6.16981i	−0.121552	+	0.374099i
$273$	2.57812	−	1.87311i	0.156035	−	0.113366i
$274$	−31.9963			−1.93296
$275$		0			0
$276$	24.5703			1.47896
$277$	18.2016	−	13.2242i	1.09363	−	0.794565i	0.113618	−	0.993525i	$-0.463756\pi$
$277$	18.2016	−	13.2242i	1.09363	−	0.794565i	0.980008	+	0.198959i	$0.0637561\pi$
$278$	13.3020	−	40.9393i	0.797800	−	2.45538i
$279$	−0.113686	+	0.349890i	−0.00680622	+	0.0209474i
$280$		0			0
$281$	0.378929	+	1.16622i	0.0226050	+	0.0695711i	0.961723	−	0.274025i	$-0.0883550\pi$
$281$	0.378929	+	1.16622i	0.0226050	+	0.0695711i	−0.939118	+	0.343596i	$0.888355\pi$
$282$	19.7219			1.17442
$283$	−1.76710	−	5.43858i	−0.105043	−	0.323290i	0.884697	−	0.466166i	$-0.154365\pi$
$283$	−1.76710	−	5.43858i	−0.105043	−	0.323290i	−0.989741	+	0.142876i	$0.954365\pi$
$284$	0.626897	+	0.455467i	0.0371995	+	0.0270270i
$285$		0			0
$286$	−6.71176	+	4.87638i	−0.396875	+	0.288346i
$287$	−5.31332	−	3.86036i	−0.313636	−	0.227870i
$288$	−0.809787	−	0.588345i	−0.0477172	−	0.0346686i
$289$	8.67438	−	6.30230i	0.510257	−	0.370724i
$290$		0			0
$291$	12.1660	+	8.83910i	0.713183	+	0.518157i
$292$	−10.4573	−	32.1843i	−0.611968	−	1.88344i
$293$	−3.57430			−0.208813			−0.104406	−	0.994535i	$-0.533294\pi$
$293$	−3.57430			−0.208813			−0.104406	+	0.994535i	$0.533294\pi$
$294$	1.11760	+	3.43962i	0.0651797	+	0.200602i
$295$		0			0
$296$	−0.175611	+	0.540476i	−0.0102072	+	0.0314145i
$297$	−3.38724	+	10.4249i	−0.196548	+	0.604911i
$298$	17.9118	−	13.0137i	1.03760	−	0.753864i
$299$	10.6762			0.617422
$300$		0			0
$301$	−10.9911			−0.633514
$302$	−29.9213	+	21.7391i	−1.72178	+	1.25094i
$303$	−4.50013	+	13.8500i	−0.258526	+	0.795661i
$304$	−4.87402	+	15.0007i	−0.279544	+	0.860349i
$305$		0			0
$306$	−0.209770	−	0.645604i	−0.0119917	−	0.0369067i
$307$	−19.9639			−1.13940			−0.569700	−	0.821853i	$-0.692941\pi$
$307$	−19.9639			−1.13940			−0.569700	+	0.821853i	$0.692941\pi$
$308$	−1.63136	−	5.02081i	−0.0929553	−	0.286087i
$309$	17.3779	+	12.6258i	0.988592	+	0.718254i
$310$		0			0
$311$	−10.2321	+	7.43403i	−0.580207	+	0.421545i	−0.838799	−	0.544442i	$-0.816742\pi$
$311$	−10.2321	+	7.43403i	−0.580207	+	0.421545i	0.258592	+	0.965987i	$0.416742\pi$
$312$	−3.04031	−	2.20891i	−0.172123	−	0.125055i
$313$	−9.59261	−	6.96944i	−0.542206	−	0.393936i	0.282697	−	0.959209i	$-0.408771\pi$
$313$	−9.59261	−	6.96944i	−0.542206	−	0.393936i	−0.824904	+	0.565273i	$0.808771\pi$
$314$	−21.3997	+	15.5478i	−1.20765	+	0.877411i
$315$		0			0
$316$	−3.97813	−	2.89028i	−0.223787	−	0.162591i
$317$	2.88420	+	8.87665i	0.161993	+	0.498562i	0.998802	−	0.0489321i	$-0.0155818\pi$
$317$	2.88420	+	8.87665i	0.161993	+	0.498562i	−0.836809	+	0.547494i	$0.815582\pi$
$318$	−38.0544			−2.13398
$319$	3.60453	+	11.0936i	0.201815	+	0.621122i
$320$		0			0
$321$	−0.629268	+	1.93669i	−0.0351223	+	0.108095i
$322$	−3.74419	+	11.5234i	−0.208656	+	0.642177i
$323$	−12.3484	+	8.97164i	−0.687084	+	0.499195i
$324$	−21.9607			−1.22004
$325$		0			0
$326$	−19.8917			−1.10170
$327$	−8.72454	+	6.33875i	−0.482468	+	0.350534i
$328$	−2.39335	+	7.36596i	−0.132150	+	0.406717i
$329$	−1.68511	+	5.18622i	−0.0929029	+	0.285926i
$330$		0			0
$331$	0.629302	+	1.93679i	0.0345896	+	0.106456i	0.966861	−	0.255305i	$-0.0821758\pi$
$331$	0.629302	+	1.93679i	0.0345896	+	0.106456i	−0.932271	+	0.361761i	$0.882176\pi$
$332$	45.7720			2.51206
$333$	0.0189085	+	0.0581944i	0.00103618	+	0.00318903i
$334$	14.6201	+	10.6221i	0.799974	+	0.581215i
$335$		0			0
$336$	−3.55047	+	2.57957i	−0.193694	+	0.140727i
$337$	−15.7709	−	11.4582i	−0.859096	−	0.624170i	0.0685426	−	0.997648i	$-0.478165\pi$
$337$	−15.7709	−	11.4582i	−0.859096	−	0.624170i	−0.927639	+	0.373478i	$0.878165\pi$
$338$	16.3390	+	11.8710i	0.888727	+	0.645698i
$339$	−14.3626	+	10.4350i	−0.780070	+	0.566754i
$340$		0			0
$341$	−4.84767	−	3.52204i	−0.262516	−	0.190729i
$342$	−0.510014	−	1.56966i	−0.0275784	−	0.0848776i
$343$	−1.00000			−0.0539949
$344$	4.00531	+	12.3271i	0.215952	+	0.664632i
$345$		0			0
$346$	13.2234	−	40.6975i	0.710895	−	2.18791i
$347$	6.01074	−	18.4992i	0.322674	−	0.993087i	−0.649806	−	0.760100i	$-0.725150\pi$
$347$	6.01074	−	18.4992i	0.322674	−	0.993087i	0.972480	−	0.232987i	$-0.0748500\pi$
$348$	−19.7434	+	14.3444i	−1.05836	+	0.768941i
$349$	−10.4238			−0.557973			−0.278987	−	0.960295i	$-0.589999\pi$
$349$	−10.4238			−0.557973			−0.278987	+	0.960295i	$0.589999\pi$
$350$		0			0
$351$	−9.96482			−0.531883
$352$	13.1893	−	9.58257i	0.702991	−	0.510753i
$353$	−1.97864	+	6.08963i	−0.105312	+	0.324118i	−0.989804	−	0.142439i	$-0.954506\pi$
$353$	−1.97864	+	6.08963i	−0.105312	+	0.324118i	0.884491	+	0.466557i	$0.154506\pi$
$354$	−1.64002	+	5.04747i	−0.0871662	+	0.268270i
$355$		0			0
$356$	4.08154	+	12.5617i	0.216321	+	0.665768i
$357$	−4.24694			−0.224772
$358$	6.24853	+	19.2310i	0.330245	+	1.01639i
$359$	12.2002	+	8.86397i	0.643902	+	0.467822i	0.861189	−	0.508286i	$-0.169721\pi$
$359$	12.2002	+	8.86397i	0.643902	+	0.467822i	−0.217287	+	0.976108i	$0.569721\pi$
$360$		0			0
$361$	−14.6515	+	10.6449i	−0.771129	+	0.560258i
$362$	27.9560	+	20.3112i	1.46933	+	1.06753i
$363$	9.21915	+	6.69810i	0.483880	+	0.351559i
$364$	3.88267	−	2.82093i	0.203507	−	0.147857i
$365$		0			0
$366$	21.2394	+	15.4313i	1.11020	+	0.806609i
$367$	0.242546	+	0.746479i	0.0126608	+	0.0389659i	0.957187	−	0.289469i	$-0.0934788\pi$
$367$	0.242546	+	0.746479i	0.0126608	+	0.0389659i	−0.944527	+	0.328435i	$0.893479\pi$
$368$	−14.7028			−0.766437
$369$	0.257698	+	0.793112i	0.0134152	+	0.0412878i
$370$		0			0
$371$	3.25150	−	10.0071i	0.168809	−	0.519542i
$372$	3.87397	−	11.9228i	0.200856	−	0.618171i
$373$	−20.7534	+	15.0783i	−1.07457	+	0.780723i	−0.976729	−	0.214479i	$-0.931195\pi$
$373$	−20.7534	+	15.0783i	−1.07457	+	0.780723i	−0.0978438	+	0.995202i	$0.531195\pi$
$374$	11.0563			0.571708
$375$		0			0
$376$	6.43072			0.331639
$377$	−8.57886	+	6.23291i	−0.441834	+	0.321011i
$378$	3.49470	−	10.7556i	0.179748	−	0.553208i
$379$	−6.65026	+	20.4674i	−0.341601	+	1.05134i	0.621777	+	0.783194i	$0.286411\pi$
$379$	−6.65026	+	20.4674i	−0.341601	+	1.05134i	−0.963378	+	0.268146i	$0.913589\pi$
$380$		0			0
$381$	−8.86954	−	27.2977i	−0.454401	−	1.39850i
$382$	−57.4614			−2.93998
$383$	4.03595	+	12.4214i	0.206227	+	0.634703i	0.999661	+	0.0260457i	$0.00829154\pi$
$383$	4.03595	+	12.4214i	0.206227	+	0.634703i	−0.793433	+	0.608657i	$0.791708\pi$
$384$	12.4430	+	9.04035i	0.634978	+	0.461338i
$385$		0			0
$386$	15.2418	−	11.0738i	0.775786	−	0.563641i
$387$	1.12906	+	0.820309i	0.0573933	+	0.0416987i
$388$	18.3221	+	13.3118i	0.930164	+	0.675804i
$389$	24.3911	−	17.7212i	1.23668	−	0.898499i	0.239306	−	0.970944i	$-0.423080\pi$
$389$	24.3911	−	17.7212i	1.23668	−	0.898499i	0.997372	+	0.0724447i	$0.0230801\pi$
$390$		0			0
$391$	−11.5108	−	8.36310i	−0.582127	−	0.422940i
$392$	0.364416	+	1.12156i	0.0184058	+	0.0566471i
$393$	10.1725			0.513134
$394$	−8.50464	−	26.1746i	−0.428457	−	1.31866i
$395$		0			0
$396$	−0.207142	+	0.637519i	−0.0104093	+	0.0320365i
$397$	−4.15004	+	12.7725i	−0.208285	+	0.641034i	0.791278	+	0.611457i	$0.209416\pi$
$397$	−4.15004	+	12.7725i	−0.208285	+	0.641034i	−0.999562	+	0.0295772i	$0.990584\pi$
$398$	4.70842	−	3.42087i	0.236012	−	0.171473i
$399$	−10.3256			−0.516928
$400$		0			0
$401$	−21.3013			−1.06373			−0.531867	−	0.846828i	$-0.678510\pi$
$401$	−21.3013			−1.06373			−0.531867	+	0.846828i	$0.678510\pi$
$402$	−35.2232	+	25.5911i	−1.75677	+	1.27637i
$403$	1.68331	−	5.18069i	0.0838516	−	0.258069i
$404$	−6.77725	+	20.8582i	−0.337181	+	1.03774i
$405$		0			0
$406$	−3.71889	−	11.4456i	−0.184565	−	0.568033i
$407$	−0.996609			−0.0494001
$408$	1.54765	+	4.76318i	0.0766202	+	0.235813i
$409$	−3.89603	−	2.83063i	−0.192646	−	0.139966i	0.487281	−	0.873245i	$-0.337989\pi$
$409$	−3.89603	−	2.83063i	−0.192646	−	0.139966i	−0.679927	+	0.733280i	$0.737989\pi$
$410$		0			0
$411$	20.5633	−	14.9401i	1.01431	−	0.736941i
$412$	26.1712	+	19.0145i	1.28936	+	0.936778i
$413$	−1.18719	−	0.862546i	−0.0584179	−	0.0424431i
$414$	1.24467	−	0.904303i	0.0611720	−	0.0444441i
$415$		0			0
$416$	11.9902	+	8.71140i	0.587868	+	0.427111i
$417$	10.5670	+	32.5219i	0.517469	+	1.59261i
$418$	26.8813			1.31481
$419$	6.82925	+	21.0183i	0.333631	+	1.02681i	0.967393	+	0.253281i	$0.0815098\pi$
$419$	6.82925	+	21.0183i	0.333631	+	1.02681i	−0.633762	+	0.773528i	$0.718490\pi$
$420$		0			0
$421$	−9.61511	+	29.5923i	−0.468612	+	1.44224i	0.385772	+	0.922594i	$0.373935\pi$
$421$	−9.61511	+	29.5923i	−0.468612	+	1.44224i	−0.854383	+	0.519644i	$0.826065\pi$
$422$	−10.3453	+	31.8396i	−0.503602	+	1.54993i
$423$	0.560173	−	0.406989i	0.0272365	−	0.0197885i
$424$	−12.4084			−0.602605
$425$		0			0
$426$	−1.09785			−0.0531911
$427$	−5.87272	+	4.26678i	−0.284201	+	0.206484i
$428$	−0.947685	+	2.91668i	−0.0458081	+	0.140983i
$429$	2.03656	−	6.26788i	0.0983260	−	0.302616i
$430$		0			0
$431$	−1.30812	−	4.02599i	−0.0630101	−	0.193925i	0.914596	−	0.404369i	$-0.132509\pi$
$431$	−1.30812	−	4.02599i	−0.0630101	−	0.193925i	−0.977606	+	0.210444i	$0.932509\pi$
$432$	13.7231			0.660254
$433$	6.72345	+	20.6927i	0.323109	+	0.994426i	0.972287	+	0.233790i	$0.0751128\pi$
$433$	6.72345	+	20.6927i	0.323109	+	0.994426i	−0.649179	+	0.760636i	$0.724887\pi$
$434$	5.00147	+	3.63378i	0.240078	+	0.174427i
$435$		0			0
$436$	−13.1393	+	9.54623i	−0.629256	+	0.457181i
$437$	−27.9864	−	20.3333i	−1.33877	−	0.972673i
$438$	38.7883	+	28.1814i	1.85338	+	1.34656i
$439$	4.91237	−	3.56905i	0.234455	−	0.170341i	−0.464354	−	0.885649i	$-0.653714\pi$
$439$	4.91237	−	3.56905i	0.234455	−	0.170341i	0.698809	+	0.715308i	$0.253714\pi$
$440$		0			0
$441$	0.102725	+	0.0746342i	0.00489168	+	0.00355401i
$442$	3.10598	+	9.55922i	0.147736	+	0.454686i
$443$	−6.79775			−0.322971			−0.161485	−	0.986875i	$-0.551628\pi$
$443$	−6.79775			−0.322971			−0.161485	+	0.986875i	$0.551628\pi$
$444$	−0.644326	−	1.98303i	−0.0305783	−	0.0941105i
$445$		0			0
$446$	3.87185	−	11.9163i	0.183337	−	0.564254i
$447$	−5.43501	+	16.7272i	−0.257067	+	0.791171i
$448$	−9.41838	+	6.84285i	−0.444976	+	0.323294i
$449$	−25.9097			−1.22275			−0.611376	−	0.791340i	$-0.709384\pi$
$449$	−25.9097			−1.22275			−0.611376	+	0.791340i	$0.709384\pi$
$450$		0			0
$451$	−13.5824			−0.639573
$452$	−21.6303	+	15.7153i	−1.01740	+	0.739185i
$453$	9.07905	−	27.9425i	0.426571	−	1.31285i
$454$	−1.00255	+	3.08554i	−0.0470522	+	0.144812i
$455$		0			0
$456$	3.76282	+	11.5808i	0.176210	+	0.542319i
$457$	24.0284			1.12400			0.562000	−	0.827137i	$-0.310032\pi$
$457$	24.0284			1.12400			0.562000	+	0.827137i	$0.310032\pi$
$458$	14.1363	+	43.5072i	0.660548	+	2.03296i
$459$	10.7438	+	7.80584i	0.501478	+	0.364345i
$460$		0			0
$461$	31.9285	−	23.1974i	1.48706	−	1.08041i	0.511863	−	0.859067i	$-0.328955\pi$
$461$	31.9285	−	23.1974i	1.48706	−	1.08041i	0.975196	−	0.221344i	$-0.0710445\pi$
$462$	6.05105	+	4.39634i	0.281520	+	0.204536i
$463$	24.1966	+	17.5798i	1.12451	+	0.817005i	0.984887	−	0.173200i	$-0.0554106\pi$
$463$	24.1966	+	17.5798i	1.12451	+	0.817005i	0.139624	+	0.990205i	$0.455411\pi$
$464$	11.8144	−	8.58368i	0.548471	−	0.398488i
$465$		0			0
$466$	35.7908	+	26.0035i	1.65797	+	1.20459i
$467$	−0.399907	−	1.23079i	−0.0185055	−	0.0569540i	0.941377	−	0.337355i	$-0.109532\pi$
$467$	−0.399907	−	1.23079i	−0.0185055	−	0.0569540i	−0.959883	+	0.280401i	$0.909532\pi$
$468$	−0.609386			−0.0281689
$469$	−3.72006	−	11.4492i	−0.171776	−	0.528673i
$470$		0			0
$471$	6.49332	−	19.9844i	0.299197	−	0.920832i
$472$	−0.534762	+	1.64583i	−0.0246144	+	0.0757554i
$473$	−18.3894	+	13.3606i	−0.845544	+	0.614323i
$474$	6.96670			0.319991
$475$		0			0
$476$	−6.39594			−0.293157
$477$	−1.08088	+	0.785307i	−0.0494902	+	0.0359567i
$478$	−11.2333	+	34.5725i	−0.513799	+	1.58131i
$479$	4.95435	−	15.2479i	0.226370	−	0.696695i	−0.771780	−	0.635890i	$-0.780633\pi$
$479$	4.95435	−	15.2479i	0.226370	−	0.696695i	0.998150	−	0.0608053i	$-0.0193669\pi$
$480$		0			0
$481$	−0.279971	−	0.861663i	−0.0127656	−	0.0392884i
$482$	12.9793			0.591190
$483$	−2.97436	−	9.15415i	−0.135338	−	0.416528i
$484$	13.8841	+	10.0874i	0.631097	+	0.458519i
$485$		0			0
$486$	−2.27629	+	1.65382i	−0.103254	+	0.0750187i
$487$	−4.56291	−	3.31515i	−0.206765	−	0.150224i	0.479584	−	0.877496i	$-0.340788\pi$
$487$	−4.56291	−	3.31515i	−0.206765	−	0.150224i	−0.686349	+	0.727272i	$0.740788\pi$
$488$	6.92554	+	5.03170i	0.313504	+	0.227774i
$489$	12.7839	−	9.28807i	0.578110	−	0.420021i
$490$		0			0
$491$	2.92339	+	2.12397i	0.131931	+	0.0958533i	0.651793	−	0.758397i	$-0.274017\pi$
$491$	2.92339	+	2.12397i	0.131931	+	0.0958533i	−0.519863	+	0.854250i	$0.674017\pi$
$492$	−8.78130	−	27.0260i	−0.395891	−	1.21843i
$493$	14.1320			0.636472
$494$	7.55159	+	23.2414i	0.339762	+	1.04568i
$495$		0			0
$496$	−2.31818	+	7.13462i	−0.104089	+	0.320354i
$497$	0.0938043	−	0.288700i	0.00420770	−	0.0129500i
$498$	−52.4642	+	38.1175i	−2.35098	+	1.70808i
$499$	−14.4978			−0.649010			−0.324505	−	0.945884i	$-0.605198\pi$
$499$	−14.4978			−0.649010			−0.324505	+	0.945884i	$0.605198\pi$
$500$		0			0
$501$	−14.3558			−0.641369
$502$	33.0797	−	24.0338i	1.47642	−	1.07268i
$503$	9.03770	−	27.8152i	0.402971	−	1.24022i	−0.519607	−	0.854406i	$-0.673922\pi$
$503$	9.03770	−	27.8152i	0.402971	−	1.24022i	0.922578	−	0.385811i	$-0.126078\pi$
$504$	0.0462718	−	0.142410i	0.00206111	−	0.00634344i
$505$		0			0
$506$	7.74333	+	23.8315i	0.344233	+	1.05944i
$507$	−16.0437			−0.712526
$508$	−13.3576	−	41.1106i	−0.592649	−	1.82399i
$509$	−16.4484	−	11.9505i	−0.729064	−	0.529696i	0.160203	−	0.987084i	$-0.448785\pi$
$509$	−16.4484	−	11.9505i	−0.729064	−	0.529696i	−0.889267	+	0.457388i	$0.848785\pi$
$510$		0			0
$511$	−10.7250	+	7.79217i	−0.474446	+	0.344705i
$512$	−21.4528	−	15.5864i	−0.948088	−	0.688826i
$513$	26.1215	+	18.9784i	1.15329	+	0.837916i
$514$	26.9377	−	19.5714i	1.18817	−	0.863256i
$515$		0			0
$516$	−38.4738	−	27.9528i	−1.69371	−	1.23055i
$517$	3.48495	+	10.7256i	0.153268	+	0.471710i
$518$	1.02823			0.0451778
$519$	10.5046	+	32.3298i	0.461101	+	1.41912i
$520$		0			0
$521$	2.99346	−	9.21291i	0.131146	−	0.403625i	−0.863825	−	0.503792i	$-0.831938\pi$
$521$	2.99346	−	9.21291i	0.131146	−	0.403625i	0.994971	+	0.100167i	$0.0319377\pi$
$522$	−0.472207	+	1.45330i	−0.0206679	+	0.0636093i
$523$	−21.9086	+	15.9175i	−0.957995	+	0.696024i	−0.952684	−	0.303962i	$-0.901691\pi$
$523$	−21.9086	+	15.9175i	−0.957995	+	0.696024i	−0.00531106	+	0.999986i	$0.501691\pi$
$524$	15.3199			0.669252
$525$		0			0
$526$	47.7325			2.08124
$527$	−5.87314	+	4.26709i	−0.255838	+	0.185877i
$528$	−2.80466	+	8.63185i	−0.122057	+	0.375653i
$529$	2.85736	−	8.79406i	0.124233	−	0.382350i
$530$		0			0
$531$	0.0575792	+	0.177210i	0.00249872	+	0.00769028i
$532$	−15.5505			−0.674200
$533$	−3.81563	−	11.7433i	−0.165273	−	0.508659i
$534$	−15.1393	−	10.9993i	−0.655141	−	0.475988i
$535$		0			0
$536$	−11.4852	+	8.34450i	−0.496086	+	0.360428i
$537$	−12.9954	−	9.44170i	−0.560792	−	0.407439i
$538$	−1.78973	−	1.30031i	−0.0771605	−	0.0560604i
$539$	−1.67312	+	1.21559i	−0.0720664	+	0.0523593i
$540$		0			0
$541$	−29.3632	−	21.3336i	−1.26242	−	0.917203i	−0.263548	−	0.964646i	$-0.584893\pi$
$541$	−29.3632	−	21.3336i	−1.26242	−	0.917203i	−0.998874	+	0.0474430i	$0.984893\pi$
$542$	−11.5044	−	35.4070i	−0.494157	−	1.52086i
$543$	−27.4507			−1.17802
$544$	−6.10355	−	18.7848i	−0.261688	−	0.805392i
$545$		0			0
$546$	−2.10117	+	6.46674i	−0.0899218	+	0.276751i
$547$	13.1975	−	40.6179i	0.564286	−	1.73669i	−0.105776	−	0.994390i	$-0.533733\pi$
$547$	13.1975	−	40.6179i	0.564286	−	1.73669i	0.670062	−	0.742305i	$-0.266267\pi$
$548$	30.9685	−	22.5000i	1.32291	−	0.961151i
$549$	0.921724			0.0393382
$550$		0			0
$551$	34.3592			1.46375
$552$	−9.18299	+	6.67183i	−0.390854	+	0.283972i
$553$	−0.595259	+	1.83202i	−0.0253130	+	0.0779053i
$554$	−14.8343	+	45.6553i	−0.630249	+	1.93971i
$555$		0			0
$556$	15.9140	+	48.9784i	0.674906	+	2.07715i
$557$	29.3580			1.24394			0.621969	−	0.783042i	$-0.286333\pi$
$557$	29.3580			1.24394			0.621969	+	0.783042i	$0.286333\pi$
$558$	−0.242573	−	0.746562i	−0.0102689	−	0.0316045i
$559$	−16.7175	−	12.1460i	−0.707077	−	0.513721i
$560$		0			0
$561$	−7.10564	+	5.16255i	−0.300000	+	0.217963i
$562$	−2.11674	−	1.53790i	−0.0892893	−	0.0648725i
$563$	5.37077	+	3.90209i	0.226351	+	0.164454i	0.695181	−	0.718835i	$-0.255324\pi$
$563$	5.37077	+	3.90209i	0.226351	+	0.164454i	−0.468830	+	0.883288i	$0.655324\pi$
$564$	−19.0884	+	13.8686i	−0.803768	+	0.583971i
$565$		0			0
$566$	9.87122	+	7.17186i	0.414918	+	0.301456i
$567$	2.65846	+	8.18189i	0.111645	+	0.343607i
$568$	−0.357977			−0.0150204
$569$	−0.896734	−	2.75986i	−0.0375931	−	0.115700i	0.930499	−	0.366295i	$-0.119374\pi$
$569$	−0.896734	−	2.75986i	−0.0375931	−	0.115700i	−0.968092	+	0.250595i	$0.919374\pi$
$570$		0			0
$571$	2.79136	−	8.59091i	0.116815	−	0.359519i	−0.875507	−	0.483206i	$-0.839472\pi$
$571$	2.79136	−	8.59091i	0.116815	−	0.359519i	0.992321	+	0.123688i	$0.0394721\pi$
$572$	3.06708	−	9.43950i	0.128241	−	0.394685i
$573$	36.9292	−	26.8306i	1.54274	−	1.12086i
$574$	14.0134			0.584907
$575$		0			0
$576$	1.47822			0.0615923
$577$	11.9486	−	8.68114i	0.497425	−	0.361401i	−0.310607	−	0.950538i	$-0.600532\pi$
$577$	11.9486	−	8.68114i	0.497425	−	0.361401i	0.808033	+	0.589138i	$0.200532\pi$
$578$	−7.06963	+	21.7581i	−0.294058	+	0.905017i
$579$	−4.62483	+	14.2338i	−0.192201	+	0.591535i
$580$		0			0
$581$	−5.54095	−	17.0533i	−0.229877	−	0.707489i
$582$	−32.0866			−1.33003
$583$	−6.72439	−	20.6955i	−0.278496	−	0.857122i
$584$	12.6477	+	9.18910i	0.523366	+	0.380248i
$585$		0			0
$586$	6.16996	−	4.48274i	0.254879	−	0.185180i
$587$	−12.1222	−	8.80727i	−0.500336	−	0.363515i	0.308810	−	0.951124i	$-0.400069\pi$
$587$	−12.1222	−	8.80727i	−0.500336	−	0.363515i	−0.809145	+	0.587609i	$0.800069\pi$
$588$	−3.50046	−	2.54323i	−0.144357	−	0.104881i
$589$	−14.2794	+	10.3746i	−0.588373	+	0.427478i
$590$		0			0
$591$	17.6875	+	12.8507i	0.727567	+	0.528608i
$592$	0.385564	+	1.18664i	0.0158466	+	0.0487708i
$593$	38.4718			1.57985			0.789924	−	0.613205i	$-0.210120\pi$
$593$	38.4718			1.57985			0.789924	+	0.613205i	$0.210120\pi$
$594$	−7.22736	−	22.2435i	−0.296542	−	0.912663i
$595$		0			0
$596$	−8.18518	+	25.1914i	−0.335278	+	1.03188i
$597$	−1.42868	+	4.39703i	−0.0584721	+	0.179958i
$598$	−18.4293	+	13.3897i	−0.753631	+	0.547545i
$599$	−26.7785			−1.09414			−0.547070	−	0.837087i	$-0.684257\pi$
$599$	−26.7785			−1.09414			−0.547070	+	0.837087i	$0.684257\pi$
$600$		0			0
$601$	−6.15561			−0.251093			−0.125546	−	0.992088i	$-0.540068\pi$
$601$	−6.15561			−0.251093			−0.125546	+	0.992088i	$0.540068\pi$
$602$	18.9728	−	13.7845i	0.773273	−	0.561816i
$603$	−0.472356	+	1.45376i	−0.0192358	+	0.0592017i
$604$	13.6732	−	42.0816i	0.556353	−	1.71228i
$605$		0			0
$606$	−9.60195	−	29.5518i	−0.390052	−	1.20046i
$607$	5.96735			0.242207			0.121104	−	0.992640i	$-0.461357\pi$
$607$	5.96735			0.242207			0.121104	+	0.992640i	$0.461357\pi$
$608$	−14.8396	−	45.6717i	−0.601826	−	1.85223i
$609$	7.73435	+	5.61933i	0.313412	+	0.227707i
$610$		0			0
$611$	−8.29427	+	6.02614i	−0.335550	+	0.243791i
$612$	0.657024	+	0.477356i	0.0265586	+	0.0192960i
$613$	−12.0679	−	8.76786i	−0.487419	−	0.354130i	0.316772	−	0.948502i	$-0.397401\pi$
$613$	−12.0679	−	8.76786i	−0.487419	−	0.354130i	−0.804191	+	0.594371i	$0.797401\pi$
$614$	34.4617	−	25.0379i	1.39076	−	1.01045i
$615$		0			0
$616$	1.97307	+	1.43352i	0.0794971	+	0.0577580i
$617$	4.70134	+	14.4692i	0.189269	+	0.582510i	0.999996	−	0.00291491i	$-0.000927845\pi$
$617$	4.70134	+	14.4692i	0.189269	+	0.582510i	−0.810727	+	0.585425i	$0.800928\pi$
$618$	−45.8324			−1.84365
$619$	11.0539	+	34.0205i	0.444295	+	1.36740i	0.883255	+	0.468892i	$0.155347\pi$
$619$	11.0539	+	34.0205i	0.444295	+	1.36740i	−0.438961	+	0.898506i	$0.644653\pi$
$620$		0			0
$621$	−9.30076	+	28.6248i	−0.373227	+	1.14867i
$622$	8.33915	−	25.6653i	0.334370	−	1.02908i
$623$	4.18602	−	3.04132i	0.167709	−	0.121848i
$624$	−8.25094			−0.330302
$625$		0			0
$626$	25.2996			1.01117
$627$	−17.2760	+	12.5518i	−0.689937	+	0.501269i
$628$	9.77902	−	30.0967i	0.390225	−	1.20099i
$629$	−0.373117	+	1.14833i	−0.0148771	+	0.0457871i
$630$		0			0
$631$	12.0622	+	37.1237i	0.480190	+	1.47787i	0.838829	+	0.544395i	$0.183241\pi$
$631$	12.0622	+	37.1237i	0.480190	+	1.47787i	−0.358639	+	0.933476i	$0.616759\pi$
$632$	2.27163			0.0903606
$633$	−8.21825	−	25.2932i	−0.326646	−	1.00531i
$634$	−16.1114	−	11.7056i	−0.639867	−	0.464891i
$635$		0			0
$636$	36.8321	−	26.7601i	1.46049	−	1.06111i
$637$	−1.52101	−	1.10508i	−0.0602647	−	0.0437849i
$638$	−20.1353	−	14.6291i	−0.797163	−	0.579173i
$639$	−0.0311830	+	0.0226558i	−0.00123358	+	0.000896248i
$640$		0			0
$641$	31.6838	+	23.0196i	1.25143	+	0.909220i	0.998304	−	0.0582120i	$-0.0185399\pi$
$641$	31.6838	+	23.0196i	1.25143	+	0.909220i	0.253130	+	0.967432i	$0.418540\pi$
$642$	−1.34267	−	4.13232i	−0.0529910	−	0.163090i
$643$	−26.9293			−1.06199			−0.530994	−	0.847376i	$-0.678181\pi$
$643$	−26.9293			−1.06199			−0.530994	+	0.847376i	$0.678181\pi$
$644$	−4.47943	−	13.7863i	−0.176514	−	0.543254i
$645$		0			0
$646$	10.0640	−	30.9737i	0.395962	−	1.21865i
$647$	4.35458	−	13.4020i	0.171196	−	0.526888i	−0.828243	−	0.560369i	$-0.810659\pi$
$647$	4.35458	−	13.4020i	0.171196	−	0.526888i	0.999439	+	0.0334813i	$0.0106594\pi$
$648$	8.20766	−	5.96322i	0.322428	−	0.234257i
$649$	−3.03482			−0.119127
$650$		0			0
$651$	−4.91107			−0.192480
$652$	19.2527	−	13.9879i	0.753996	−	0.547810i
$653$	8.98789	−	27.6619i	0.351724	−	1.08249i	−0.606162	−	0.795342i	$-0.707291\pi$
$653$	8.98789	−	27.6619i	0.351724	−	1.08249i	0.957885	−	0.287152i	$-0.0927085\pi$
$654$	7.11052	−	21.8839i	0.278043	−	0.855729i
$655$		0			0
$656$	5.25472	+	16.1724i	0.205162	+	0.631425i
$657$	1.68329			0.0656714
$658$	−3.59552	−	11.0659i	−0.140168	−	0.431392i
$659$	16.7357	+	12.1592i	0.651931	+	0.473655i	0.863928	−	0.503615i	$-0.167997\pi$
$659$	16.7357	+	12.1592i	0.651931	+	0.473655i	−0.211998	+	0.977270i	$0.567997\pi$
$660$		0			0
$661$	−23.1609	+	16.8274i	−0.900854	+	0.654509i	−0.938685	−	0.344775i	$-0.887955\pi$
$661$	−23.1609	+	16.8274i	−0.900854	+	0.654509i	0.0378310	+	0.999284i	$0.487955\pi$
$662$	−3.51535	−	2.55405i	−0.136628	−	0.0992660i
$663$	−6.45965	−	4.69321i	−0.250872	−	0.182269i
$664$	−17.1070	+	12.4290i	−0.663880	+	0.482337i
$665$		0			0
$666$	−0.105625	−	0.0767410i	−0.00409288	−	0.00297365i
$667$	9.89740	+	30.4611i	0.383229	+	1.17946i
$668$	−21.6200			−0.836502
$669$	3.07577	+	9.46625i	0.118916	+	0.365987i
$670$		0			0
$671$	−4.63909	+	14.2777i	−0.179090	+	0.551183i
$672$	4.12901	−	12.7078i	0.159280	−	0.490213i
$673$	30.1882	−	21.9330i	1.16367	−	0.845455i	0.173432	−	0.984846i	$-0.444514\pi$
$673$	30.1882	−	21.9330i	1.16367	−	0.845455i	0.990237	+	0.139391i	$0.0445143\pi$
$674$	41.5942			1.60215
$675$		0			0
$676$	−24.1620			−0.929308
$677$	−13.5835	+	9.86900i	−0.522057	+	0.379296i	−0.817378	−	0.576102i	$-0.804573\pi$
$677$	−13.5835	+	9.86900i	−0.522057	+	0.379296i	0.295321	+	0.955398i	$0.404573\pi$
$678$	11.7056	−	36.0260i	0.449549	−	1.38357i
$679$	2.74159	−	8.43774i	0.105212	−	0.323811i
$680$		0			0
$681$	−0.796422	−	2.45114i	−0.0305190	−	0.0939277i
$682$	12.7853			0.489573
$683$	5.13393	+	15.8006i	0.196444	+	0.604593i	0.999957	+	0.00930526i	$0.00296200\pi$
$683$	5.13393	+	15.8006i	0.196444	+	0.604593i	−0.803512	+	0.595288i	$0.797038\pi$
$684$	1.59743	+	1.16060i	0.0610792	+	0.0443766i
$685$		0			0
$686$	1.72620	−	1.25416i	0.0659067	−	0.0478840i
$687$	−29.4001	−	21.3604i	−1.12168	−	0.814950i
$688$	23.0227	+	16.7269i	0.877731	+	0.637709i
$689$	16.0042	−	11.6277i	0.609712	−	0.442982i
$690$		0			0
$691$	−26.2524	−	19.0735i	−0.998687	−	0.725589i	−0.0368808	−	0.999320i	$-0.511742\pi$
$691$	−26.2524	−	19.0735i	−0.998687	−	0.725589i	−0.961806	+	0.273731i	$0.911742\pi$
$692$	15.8200	+	48.6891i	0.601388	+	1.85088i
$693$	0.262596			0.00997521
$694$	12.8251	+	39.4717i	0.486836	+	1.49833i
$695$		0			0
$696$	3.48388	−	10.7223i	0.132056	−	0.406427i
$697$	−5.08508	+	15.6503i	−0.192611	+	0.592796i
$698$	17.9936	−	13.0731i	0.681067	−	0.494824i
$699$	−35.1438			−1.32926
$700$		0			0
$701$	−0.758935			−0.0286646			−0.0143323	−	0.999897i	$-0.504562\pi$
$701$	−0.758935			−0.0286646			−0.0143323	+	0.999897i	$0.504562\pi$
$702$	17.2013	−	12.4975i	0.649221	−	0.471687i
$703$	−0.907161	+	2.79196i	−0.0342142	+	0.105301i
$704$	−7.43995	+	22.8978i	−0.280404	+	0.862994i
$705$		0			0
$706$	−4.22183	−	12.9935i	−0.158891	−	0.489015i
$707$	8.59159			0.323120
$708$	−1.96207	−	6.03862i	−0.0737389	−	0.226945i
$709$	18.2828	+	13.2832i	0.686625	+	0.498862i	0.875549	−	0.483129i	$-0.160500\pi$
$709$	18.2828	+	13.2832i	0.686625	+	0.498862i	−0.188924	+	0.981992i	$0.560500\pi$
$710$		0			0
$711$	0.197879	−	0.143768i	0.00742105	−	0.00539171i
$712$	−4.93647	−	3.58655i	−0.185002	−	0.134412i
$713$	−13.3109	−	9.67090i	−0.498495	−	0.362178i
$714$	7.33108	−	5.32634i	0.274359	−	0.199333i
$715$		0			0
$716$	−19.5712	−	14.2193i	−0.731410	−	0.531400i
$717$	−8.92365	−	27.4642i	−0.333260	−	1.02567i
$718$	−32.1768			−1.20083
$719$	−3.36609	−	10.3598i	−0.125534	−	0.386354i	0.868464	−	0.495752i	$-0.165108\pi$
$719$	−3.36609	−	10.3598i	−0.125534	−	0.386354i	−0.993998	+	0.109398i	$0.965108\pi$
$720$		0			0
$721$	3.91608	−	12.0524i	0.145842	−	0.448857i
$722$	11.9410	−	36.7505i	0.444397	−	1.36771i
$723$	−8.34149	+	6.06045i	−0.310223	+	0.225390i
$724$	−41.3410			−1.53643
$725$		0			0
$726$	−24.3146			−0.902399
$727$	9.27971	−	6.74211i	0.344166	−	0.250051i	−0.402252	−	0.915529i	$-0.631772\pi$
$727$	9.27971	−	6.74211i	0.344166	−	0.250051i	0.746417	+	0.665478i	$0.231772\pi$
$728$	−0.685129	+	2.10861i	−0.0253926	+	0.0781503i
$729$	8.66607	−	26.6714i	0.320966	−	0.987831i
$730$		0			0
$731$	8.50998	+	26.1910i	0.314753	+	0.968710i
$732$	−31.4086			−1.16090
$733$	5.38923	+	16.5863i	0.199056	+	0.612631i	0.999905	+	0.0137649i	$0.00438164\pi$
$733$	5.38923	+	16.5863i	0.199056	+	0.612631i	−0.800850	+	0.598866i	$0.795618\pi$
$734$	−1.35489	−	0.984383i	−0.0500098	−	0.0363342i
$735$		0			0
$736$	36.2154	−	26.3120i	1.33492	−	0.969875i
$737$	−20.1416	−	14.6337i	−0.741926	−	0.539041i
$738$	−1.43953	−	1.04588i	−0.0529897	−	0.0384993i
$739$	11.3465	−	8.24371i	0.417388	−	0.303250i	−0.359198	−	0.933261i	$-0.616950\pi$
$739$	11.3465	−	8.24371i	0.417388	−	0.303250i	0.776586	+	0.630011i	$0.216950\pi$
$740$		0			0
$741$	−15.7054	−	11.4106i	−0.576953	−	0.419181i
$742$	6.93773	+	21.3521i	0.254692	+	0.783862i
$743$	0.956607			0.0350945			0.0175473	−	0.999846i	$-0.494414\pi$
$743$	0.956607			0.0350945			0.0175473	+	0.999846i	$0.494414\pi$
$744$	1.78967	+	5.50803i	0.0656124	+	0.201934i
$745$		0			0
$746$	16.9141	−	52.0562i	0.619269	−	1.90591i
$747$	−0.703564	+	2.16535i	−0.0257421	+	0.0792259i
$748$	−10.7012	+	7.77486i	−0.391274	+	0.284277i
$749$	1.20139			0.0438978
$750$		0			0
$751$	1.86740			0.0681425			0.0340713	−	0.999419i	$-0.489153\pi$
$751$	1.86740			0.0681425			0.0340713	+	0.999419i	$0.489153\pi$
$752$	11.4225	−	8.29893i	0.416536	−	0.302631i
$753$	−10.0374	+	30.8920i	−0.365784	+	1.12577i
$754$	6.99179	−	21.5185i	0.254626	−	0.783658i
$755$		0			0
$756$	4.18094	+	12.8676i	0.152059	+	0.467991i
$757$	−13.4048			−0.487207			−0.243604	−	0.969875i	$-0.578330\pi$
$757$	−13.4048			−0.487207			−0.243604	+	0.969875i	$0.578330\pi$
$758$	−14.1897	−	43.6714i	−0.515393	−	1.58622i
$759$	−16.1042	−	11.7004i	−0.584545	−	0.424697i
$760$		0			0
$761$	30.2833	−	22.0021i	1.09777	−	0.797574i	0.117073	−	0.993123i	$-0.462649\pi$
$761$	30.2833	−	22.0021i	1.09777	−	0.797574i	0.980694	+	0.195549i	$0.0626488\pi$
$762$	49.5462	+	35.9974i	1.79487	+	1.30405i
$763$	5.14722	+	3.73967i	0.186342	+	0.135385i
$764$	55.6157	−	40.4072i	2.01211	−	1.46188i
$765$		0			0
$766$	−22.5453	−	16.3801i	−0.814593	−	0.591837i
$767$	−0.852553	−	2.62389i	−0.0307839	−	0.0947431i
$768$	6.64841			0.239904
$769$	−13.7573	−	42.3406i	−0.496101	−	1.52684i	−0.815235	−	0.579131i	$-0.803392\pi$
$769$	−13.7573	−	42.3406i	−0.496101	−	1.52684i	0.319134	−	0.947710i	$-0.396608\pi$
$770$		0			0
$771$	−8.17374	+	25.1562i	−0.294370	+	0.905977i
$772$	−6.96505	+	21.4362i	−0.250678	+	0.771506i
$773$	25.4464	−	18.4879i	0.915242	−	0.664962i	−0.0270929	−	0.999633i	$-0.508625\pi$
$773$	25.4464	−	18.4879i	0.915242	−	0.664962i	0.942335	+	0.334670i	$0.108625\pi$
$774$	−2.97778			−0.107034
$775$		0			0
$776$	−10.4625			−0.375581
$777$	−0.660820	+	0.480113i	−0.0237068	+	0.0172240i
$778$	−19.8788	+	61.1807i	−0.712690	+	2.19343i
$779$	−12.3634	+	38.0506i	−0.442964	+	1.36330i
$780$		0			0
$781$	−0.193996	−	0.597058i	−0.00694171	−	0.0213644i
$782$	30.3587			1.08562
$783$	−9.23789	−	28.4313i	−0.330135	−	1.01605i
$784$	2.09467	+	1.52187i	0.0748097	+	0.0543525i
$785$		0			0
$786$	−17.5598	+	12.7579i	−0.626336	+	0.455060i
$787$	17.6207	+	12.8022i	0.628110	+	0.456349i	0.855745	−	0.517398i	$-0.173099\pi$
$787$	17.6207	+	12.8022i	0.628110	+	0.456349i	−0.227635	+	0.973747i	$0.573099\pi$
$788$	26.6376	+	19.3533i	0.948925	+	0.689434i
$789$	−30.6766	+	22.2879i	−1.09212	+	0.793469i
$790$		0			0
$791$	8.47352	+	6.15637i	0.301284	+	0.218895i
$792$	−0.0956942	−	0.294517i	−0.00340035	−	0.0104652i
$793$	−13.6476			−0.484641
$794$	−8.85495	−	27.2527i	−0.314250	−	0.967163i
$795$		0			0
$796$	−2.15161	+	6.62198i	−0.0762618	+	0.234710i
$797$	14.5187	−	44.6841i	0.514280	−	1.58279i	−0.270307	−	0.962774i	$-0.587125\pi$
$797$	14.5187	−	44.6841i	0.514280	−	1.58279i	0.784588	−	0.620018i	$-0.212875\pi$
$798$	17.8241	−	12.9500i	0.630967	−	0.458424i
$799$	13.6632			0.483368
$800$		0			0
$801$	−0.656997			−0.0232138
$802$	36.7703	−	26.7152i	1.29840	−	0.943346i
$803$	−8.47211	+	26.0745i	−0.298974	+	0.920148i
$804$	16.0960	−	49.5383i	0.567661	−	1.74708i
$805$		0			0
$806$	3.59168	+	11.0541i	0.126512	+	0.389363i
$807$	1.75738			0.0618625
$808$	−3.13091	−	9.63594i	−0.110145	−	0.338991i
$809$	−3.76306	−	2.73402i	−0.132302	−	0.0961231i	0.519666	−	0.854370i	$-0.326056\pi$
$809$	−3.76306	−	2.73402i	−0.132302	−	0.0961231i	−0.651968	+	0.758246i	$0.726056\pi$
$810$		0			0
$811$	−35.2103	+	25.5818i	−1.23640	+	0.898298i	−0.997353	−	0.0727097i	$-0.976835\pi$
$811$	−35.2103	+	25.5818i	−1.23640	+	0.898298i	−0.239048	+	0.971008i	$0.576835\pi$
$812$	11.6480	+	8.46278i	0.408765	+	0.296985i
$813$	23.9263	+	17.3835i	0.839133	+	0.609666i
$814$	1.72035	−	1.24991i	0.0602982	−	0.0438092i
$815$		0			0
$816$	8.89595	+	6.46329i	0.311421	+	0.226260i
$817$	20.6904	+	63.6784i	0.723865	+	2.22783i
$818$	10.2754			0.359270
$819$	0.0737696	+	0.227039i	0.00257772	+	0.00793340i
$820$		0			0
$821$	5.56659	−	17.1322i	0.194275	−	0.597918i	−0.805709	−	0.592312i	$-0.798215\pi$
$821$	5.56659	−	17.1322i	0.194275	−	0.597918i	0.999984	−	0.00560649i	$-0.00178461\pi$
$822$	−16.7591	+	51.5793i	−0.584541	+	1.79903i
$823$	27.2781	−	19.8187i	0.950854	−	0.690836i	−0.000154582	−	1.00000i	$-0.500049\pi$
$823$	27.2781	−	19.8187i	0.950854	−	0.690836i	0.951009	+	0.309164i	$0.100049\pi$
$824$	−14.9446			−0.520619
$825$		0			0
$826$	3.13110			0.108945
$827$	−15.8723	+	11.5319i	−0.551933	+	0.401003i	−0.828498	−	0.559992i	$-0.810804\pi$
$827$	−15.8723	+	11.5319i	−0.551933	+	0.401003i	0.276564	+	0.960995i	$0.410804\pi$
$828$	−0.568777	+	1.75051i	−0.0197664	+	0.0608346i
$829$	−15.4344	+	47.5021i	−0.536058	+	1.64982i	0.205293	+	0.978700i	$0.434185\pi$
$829$	−15.4344	+	47.5021i	−0.536058	+	1.64982i	−0.741352	+	0.671117i	$0.765815\pi$
$830$		0			0
$831$	−11.7843	−	36.2683i	−0.408792	−	1.25813i
$832$	−21.8874			−0.758808
$833$	0.774264	+	2.38294i	0.0268267	+	0.0825639i
$834$	−59.0285	−	42.8867i	−2.04399	−	1.48504i
$835$		0			0
$836$	−26.0179	+	18.9031i	−0.899846	+	0.653777i
$837$	12.4239	+	9.02649i	0.429433	+	0.312001i
$838$	−38.1489	−	27.7168i	−1.31783	−	0.957461i
$839$	−0.371702	+	0.270057i	−0.0128326	+	0.00932342i	−0.594183	−	0.804330i	$-0.702525\pi$
$839$	−0.371702	+	0.270057i	−0.0128326	+	0.00932342i	0.581350	+	0.813653i	$0.302525\pi$
$840$		0			0
$841$	−2.27507	−	1.65294i	−0.0784507	−	0.0569978i
$842$	−20.5158	−	63.1411i	−0.707020	−	2.17599i
$843$	2.07848			0.0715866
$844$	−12.3768	−	38.0918i	−0.426026	−	1.31117i
$845$		0			0
$846$	−0.456542	+	1.40509i	−0.0156962	+	0.0483080i
$847$	2.07752	−	6.39396i	0.0713845	−	0.219699i
$848$	−22.0403	+	16.0132i	−0.756867	+	0.549896i
$849$	−9.69279			−0.332656
$850$		0			0
$851$	−2.73651			−0.0938065
$852$	1.06259	−	0.772017i	0.0364037	−	0.0264489i
$853$	2.83026	−	8.71063i	0.0969061	−	0.298246i	−0.890840	−	0.454318i	$-0.849883\pi$
$853$	2.83026	−	8.71063i	0.0969061	−	0.298246i	0.987746	+	0.156072i	$0.0498830\pi$
$854$	4.78628	−	14.7306i	0.163783	−	0.504072i
$855$		0			0
$856$	−0.437805	−	1.34743i	−0.0149639	−	0.0460541i
$857$	37.3998			1.27755			0.638777	−	0.769392i	$-0.279441\pi$
$857$	37.3998			1.27755			0.638777	+	0.769392i	$0.279441\pi$
$858$	4.34541	+	13.3738i	0.148350	+	0.456574i
$859$	−0.300466	−	0.218301i	−0.0102518	−	0.00744834i	0.582648	−	0.812725i	$-0.302017\pi$
$859$	−0.300466	−	0.218301i	−0.0102518	−	0.00744834i	−0.592899	+	0.805277i	$0.702017\pi$
$860$		0			0
$861$	−9.00608	+	6.54330i	−0.306927	+	0.222995i
$862$	7.30732	+	5.30908i	0.248888	+	0.180828i
$863$	2.09090	+	1.51913i	0.0711751	+	0.0517118i	0.622804	−	0.782378i	$-0.285993\pi$
$863$	2.09090	+	1.51913i	0.0711751	+	0.0517118i	−0.551629	+	0.834090i	$0.685993\pi$
$864$	−33.8022	+	24.5588i	−1.14998	+	0.835506i
$865$		0			0
$866$	−37.5579	−	27.2874i	−1.27627	−	0.927265i
$867$	−5.61607	−	17.2845i	−0.190732	−	0.587012i
$868$	−7.39612			−0.251041
$869$	1.23105	+	3.78878i	0.0417604	+	0.128525i
$870$		0			0
$871$	6.99399	−	21.5253i	0.236982	−	0.729357i
$872$	2.31853	−	7.13569i	0.0785152	−	0.241645i
$873$	−0.911375	+	0.662152i	−0.0308454	+	0.0224105i
$874$	73.8113			2.49670
$875$		0			0
$876$	−57.3597			−1.93801
$877$	−3.64451	+	2.64789i	−0.123066	+	0.0894129i	−0.647616	−	0.761967i	$-0.724234\pi$
$877$	−3.64451	+	2.64789i	−0.123066	+	0.0894129i	0.524550	+	0.851380i	$0.324234\pi$
$878$	−4.00359	+	12.3218i	−0.135115	+	0.415840i
$879$	−1.87216	+	5.76191i	−0.0631463	+	0.194344i
$880$		0			0
$881$	6.55682	+	20.1798i	0.220905	+	0.679876i	0.998682	+	0.0513347i	$0.0163475\pi$
$881$	6.55682	+	20.1798i	0.220905	+	0.679876i	−0.777777	+	0.628541i	$0.783652\pi$
$882$	−0.270928			−0.00912261
$883$	13.4294	+	41.3314i	0.451934	+	1.39091i	0.874697	+	0.484670i	$0.161060\pi$
$883$	13.4294	+	41.3314i	0.451934	+	1.39091i	−0.422763	+	0.906240i	$0.638940\pi$
$884$	−9.72831	−	7.06803i	−0.327199	−	0.237724i
$885$		0			0
$886$	11.7343	−	8.52546i	0.394221	−	0.286418i
$887$	11.5626	+	8.40070i	0.388233	+	0.282068i	0.764731	−	0.644349i	$-0.222872\pi$
$887$	11.5626	+	8.40070i	0.388233	+	0.282068i	−0.376498	+	0.926417i	$0.622872\pi$
$888$	0.779287	+	0.566185i	0.0261512	+	0.0189999i
$889$	−13.6996	+	9.95332i	−0.459469	+	0.333824i
$890$		0			0
$891$	14.3938	+	10.4577i	0.482209	+	0.350346i
$892$	4.63215	+	14.2563i	0.155096	+	0.477336i
$893$	33.2194			1.11164
$894$	−11.5967	−	35.6910i	−0.387852	−	1.19368i
$895$		0			0
$896$	2.80401	−	8.62985i	0.0936753	−	0.288303i
$897$	5.59203	−	17.2105i	0.186712	−	0.574642i
$898$	44.7253	−	32.4948i	1.49250	−	1.08437i
$899$	16.3419			0.545033
$900$		0			0
$901$	−26.3638			−0.878305
$902$	23.4461	−	17.0346i	0.780668	−	0.567189i
$903$	−5.75694	+	17.7180i	−0.191579	+	0.589619i
$904$	3.81683	−	11.7470i	0.126946	−	0.390699i
$905$		0			0
$906$	19.3720	+	59.6209i	0.643592	+	1.98077i
$907$	−17.3448			−0.575926			−0.287963	−	0.957641i	$-0.592978\pi$
$907$	−17.3448			−0.575926			−0.287963	+	0.957641i	$0.592978\pi$
$908$	−1.19942	−	3.69144i	−0.0398042	−	0.122505i
$909$	−0.882573	−	0.641227i	−0.0292731	−	0.0212681i
$910$		0			0
$911$	−22.5384	+	16.3751i	−0.746732	+	0.542532i	−0.894812	−	0.446443i	$-0.852691\pi$
$911$	−22.5384	+	16.3751i	−0.746732	+	0.542532i	0.148080	+	0.988975i	$0.452691\pi$
$912$	21.6288	+	15.7142i	0.716201	+	0.520351i
$913$	−30.0005	−	21.7966i	−0.992872	−	0.721364i
$914$	−41.4778	+	30.1354i	−1.37196	+	0.996791i
$915$		0			0
$916$	−44.2768	−	32.1690i	−1.46295	−	1.06289i
$917$	−1.85455	−	5.70773i	−0.0612428	−	0.188486i
$918$	−28.3357			−0.935219
$919$	−7.90356	−	24.3247i	−0.260714	−	0.802397i	−0.992650	−	0.121022i	$-0.961383\pi$
$919$	−7.90356	−	24.3247i	−0.260714	−	0.802397i	0.731935	−	0.681374i	$-0.238617\pi$
$920$		0			0
$921$	−10.4568	+	32.1826i	−0.344562	+	1.06045i
$922$	−26.0218	+	80.0869i	−0.856982	+	2.63752i
$923$	0.461714	−	0.335455i	0.0151975	−	0.0110416i
$924$	−8.94823			−0.294375
$925$		0			0
$926$	−63.8161			−2.09713
$927$	−1.30181	+	0.945817i	−0.0427569	+	0.0310647i
$928$	−13.7396	+	42.2860i	−0.451023	+	1.38811i
$929$	3.76544	−	11.5888i	0.123540	−	0.380217i	−0.870092	−	0.492889i	$-0.835941\pi$
$929$	3.76544	−	11.5888i	0.123540	−	0.380217i	0.993632	+	0.112672i	$0.0359409\pi$
$930$		0			0
$931$	1.88247	+	5.79366i	0.0616956	+	0.189879i
$932$	−52.9270			−1.73368
$933$	6.62457	+	20.3883i	0.216879	+	0.667484i
$934$	2.23392	+	1.62304i	0.0730962	+	0.0531075i
$935$		0			0
$936$	0.227755	−	0.165473i	0.00744439	−	0.00540867i
$937$	−0.702550	−	0.510433i	−0.0229513	−	0.0166751i	0.576250	−	0.817273i	$-0.304515\pi$
$937$	−0.702550	−	0.510433i	−0.0229513	−	0.0166751i	−0.599202	+	0.800598i	$0.704515\pi$
$938$	20.7806	+	15.0980i	0.678512	+	0.492968i
$939$	−16.2595	+	11.8132i	−0.530608	+	0.385509i
$940$		0			0
$941$	16.9561	+	12.3193i	0.552753	+	0.401599i	0.828800	−	0.559546i	$-0.189024\pi$
$941$	16.9561	+	12.3193i	0.552753	+	0.401599i	−0.276046	+	0.961144i	$0.589024\pi$
$942$	13.8548	+	42.6408i	0.451415	+	1.38931i
$943$	−37.2950			−1.21449
$944$	1.17410	+	3.61350i	0.0382136	+	0.117610i
$945$		0			0
$946$	14.9874	−	46.1264i	0.487281	−	1.49970i
$947$	−10.7736	+	33.1576i	−0.350094	+	1.07748i	0.608706	+	0.793396i	$0.291689\pi$
$947$	−10.7736	+	33.1576i	−0.350094	+	1.07748i	−0.958800	+	0.284082i	$0.908311\pi$
$948$	−6.74293	+	4.89902i	−0.219000	+	0.159113i
$949$	−24.9238			−0.809062
$950$		0			0
$951$	15.8202			0.513006
$952$	2.39044	−	1.73676i	0.0774748	−	0.0562887i
$953$	17.0035	−	52.3315i	0.550799	−	1.69518i	−0.155989	−	0.987759i	$-0.549857\pi$
$953$	17.0035	−	52.3315i	0.550799	−	1.69518i	0.706788	−	0.707425i	$-0.250143\pi$
$954$	0.880921	−	2.71120i	0.0285209	−	0.0877782i
$955$		0			0
$956$	−13.4391	−	41.3614i	−0.434652	−	1.33772i
$957$	19.7713			0.639116
$958$	10.5711	+	32.5345i	0.341537	+	1.05114i
$959$	−12.1317	−	8.81422i	−0.391754	−	0.284626i
$960$		0			0
$961$	18.2880	−	13.2870i	0.589934	−	0.428612i
$962$	1.56395	+	1.13628i	0.0504237	+	0.0366350i
$963$	−0.123413	−	0.0896648i	−0.00397693	−	0.00288941i
$964$	−12.5624	+	9.12710i	−0.404607	+	0.293964i
$965$		0			0
$966$	16.6151	+	12.0716i	0.534583	+	0.388397i
$967$	7.12411	+	21.9258i	0.229096	+	0.705085i	0.997850	+	0.0655402i	$0.0208770\pi$
$967$	7.12411	+	21.9258i	0.229096	+	0.705085i	−0.768754	+	0.639545i	$0.779123\pi$
$968$	−7.92826			−0.254824
$969$	7.99476	+	24.6053i	0.256829	+	0.790437i
$970$		0			0
$971$	4.38503	−	13.4957i	0.140722	−	0.433098i	−0.855714	−	0.517449i	$-0.826882\pi$
$971$	4.38503	−	13.4957i	0.140722	−	0.433098i	0.996436	+	0.0843509i	$0.0268817\pi$
$972$	1.04020	−	3.20140i	0.0333643	−	0.102685i
$973$	16.3214	−	11.8582i	0.523241	−	0.380157i
$974$	12.0342			0.385601
$975$		0			0
$976$	18.7949			0.601610
$977$	15.7123	−	11.4157i	0.502681	−	0.365219i	−0.307359	−	0.951594i	$-0.599445\pi$
$977$	15.7123	−	11.4157i	0.502681	−	0.365219i	0.810040	+	0.586375i	$0.199445\pi$
$978$	−10.4189	+	32.0662i	−0.333161	+	1.02536i
$979$	3.30671	−	10.1770i	0.105683	−	0.325258i
$980$		0			0
$981$	−0.249642	−	0.768318i	−0.00797044	−	0.0245305i
$982$	−7.71015			−0.246041
$983$	−8.30507	−	25.5604i	−0.264890	−	0.815249i	−0.991719	−	0.128430i	$-0.959006\pi$
$983$	−8.30507	−	25.5604i	−0.264890	−	0.815249i	0.726828	−	0.686819i	$-0.240994\pi$
$984$	10.6206	+	7.71634i	0.338573	+	0.245988i
$985$		0			0
$986$	−24.3947	+	17.7238i	−0.776884	+	0.564439i
$987$	7.47777	+	5.43292i	0.238020	+	0.172932i
$988$	−23.6525	−	17.1846i	−0.752487	−	0.546714i
$989$	−50.4939	+	36.6860i	−1.60561	+	1.16655i
$990$		0			0
$991$	22.7620	+	16.5376i	0.723058	+	0.525333i	0.887360	−	0.461078i	$-0.152537\pi$
$991$	22.7620	+	16.5376i	0.723058	+	0.525333i	−0.164302	+	0.986410i	$0.552537\pi$
$992$	−7.05801	−	21.7223i	−0.224092	−	0.689684i
$993$	3.45181			0.109540
$994$	0.200151	+	0.616000i	0.00634839	+	0.0195383i
$995$		0			0
$996$	23.9746	−	73.7863i	0.759665	−	2.33801i
$997$	3.64196	−	11.2088i	0.115342	−	0.354986i	−0.876676	−	0.481081i	$-0.840244\pi$
$997$	3.64196	−	11.2088i	0.115342	−	0.354986i	0.992018	+	0.126095i	$0.0402444\pi$
$998$	25.0261	−	18.1825i	0.792188	−	0.575558i
$999$	2.55417			0.0808103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.h.d.176.3		56
5.2	odd	4		875.2.n.c.449.3		56
5.3	odd	4		175.2.n.a.64.12	✓	56
5.4	even	2		875.2.h.e.176.12		56
25.4	even	10		4375.2.a.o.1.5		28
25.9	even	10		875.2.h.e.701.12		56
25.12	odd	20		175.2.n.a.134.12	yes	56
25.13	odd	20		875.2.n.c.799.3		56
25.16	even	5	inner	875.2.h.d.701.3		56
25.21	even	5		4375.2.a.p.1.24		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.12	✓	56	5.3	odd	4
175.2.n.a.134.12	yes	56	25.12	odd	20
875.2.h.d.176.3		56	1.1	even	1	trivial
875.2.h.d.701.3		56	25.16	even	5	inner
875.2.h.e.176.12		56	5.4	even	2
875.2.h.e.701.12		56	25.9	even	10
875.2.n.c.449.3		56	5.2	odd	4
875.2.n.c.799.3		56	25.13	odd	20
4375.2.a.o.1.5		28	25.4	even	10
4375.2.a.p.1.24		28	25.21	even	5

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.h (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72620 + 1.25416i) q^{2} +(0.523784 - 1.61204i) q^{3} +(0.788824 - 2.42775i) q^{4} +(1.11760 + 3.43962i) q^{6} -1.00000 q^{7} +(0.364416 + 1.12156i) q^{8} +(0.102725 + 0.0746342i) q^{9} +O(q^{10})\)	\(q+(-1.72620 + 1.25416i) q^{2} +(0.523784 - 1.61204i) q^{3} +(0.788824 - 2.42775i) q^{4} +(1.11760 + 3.43962i) q^{6} -1.00000 q^{7} +(0.364416 + 1.12156i) q^{8} +(0.102725 + 0.0746342i) q^{9} +(-1.67312 + 1.21559i) q^{11} +(-3.50046 - 2.54323i) q^{12} +(-1.52101 - 1.10508i) q^{13} +(1.72620 - 1.25416i) q^{14} +(2.09467 + 1.52187i) q^{16} +(0.774264 + 2.38294i) q^{17} -0.270928 q^{18} +(1.88247 + 5.79366i) q^{19} +(-0.523784 + 1.61204i) q^{21} +(1.36360 - 4.19672i) q^{22} +(-4.59409 + 3.33780i) q^{23} +1.99887 q^{24} +4.01152 q^{26} +(4.28797 - 3.11539i) q^{27} +(-0.788824 + 2.42775i) q^{28} +(1.74293 - 5.36417i) q^{29} +(0.895341 + 2.75558i) q^{31} -7.88304 q^{32} +(1.08323 + 3.33385i) q^{33} +(-4.32512 - 3.14238i) q^{34} +(0.262226 - 0.190518i) q^{36} +(0.389864 + 0.283253i) q^{37} +(-10.5157 - 7.64010i) q^{38} +(-2.57812 + 1.87311i) q^{39} +(5.31332 + 3.86036i) q^{41} +(-1.11760 - 3.43962i) q^{42} +10.9911 q^{43} +(1.63136 + 5.02081i) q^{44} +(3.74419 - 11.5234i) q^{46} +(1.68511 - 5.18622i) q^{47} +(3.55047 - 2.57957i) q^{48} +1.00000 q^{49} +4.24694 q^{51} +(-3.88267 + 2.82093i) q^{52} +(-3.25150 + 10.0071i) q^{53} +(-3.49470 + 10.7556i) q^{54} +(-0.364416 - 1.12156i) q^{56} +10.3256 q^{57} +(3.71889 + 11.4456i) q^{58} +(1.18719 + 0.862546i) q^{59} +(5.87272 - 4.26678i) q^{61} +(-5.00147 - 3.63378i) q^{62} +(-0.102725 - 0.0746342i) q^{63} +(9.41838 - 6.84285i) q^{64} +(-6.05105 - 4.39634i) q^{66} +(3.72006 + 11.4492i) q^{67} +6.39594 q^{68} +(2.97436 + 9.15415i) q^{69} +(-0.0938043 + 0.288700i) q^{71} +(-0.0462718 + 0.142410i) q^{72} +(10.7250 - 7.79217i) q^{73} -1.02823 q^{74} +15.5505 q^{76} +(1.67312 - 1.21559i) q^{77} +(2.10117 - 6.46674i) q^{78} +(0.595259 - 1.83202i) q^{79} +(-2.65846 - 8.18189i) q^{81} -14.0134 q^{82} +(5.54095 + 17.0533i) q^{83} +(3.50046 + 2.54323i) q^{84} +(-18.9728 + 13.7845i) q^{86} +(-7.73435 - 5.61933i) q^{87} +(-1.97307 - 1.43352i) q^{88} +(-4.18602 + 3.04132i) q^{89} +(1.52101 + 1.10508i) q^{91} +(4.47943 + 13.7863i) q^{92} +4.91107 q^{93} +(3.59552 + 11.0659i) q^{94} +(-4.12901 + 12.7078i) q^{96} +(-2.74159 + 8.43774i) q^{97} +(-1.72620 + 1.25416i) q^{98} -0.262596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more