LMFDB - Embedded newform 875.2.n.b.274.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(99,875)]

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([9, 0]))

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

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

chi := DirichletCharacter("875.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.n (of order $10$, 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 $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			274.5
Character	$\chi$	$=$	875.274
Dual form			875.2.n.b.99.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41293 - 0.459090i) q^{2} +(1.82328 - 2.50953i) q^{3} +(0.167580 + 0.121754i) q^{4} +(-3.72827 + 2.70875i) q^{6} -1.00000i q^{7} +(1.56560 + 2.15486i) q^{8} +(-2.04634 - 6.29798i) q^{9} +O(q^{10})$	\(q+(-1.41293 - 0.459090i) q^{2} +(1.82328 - 2.50953i) q^{3} +(0.167580 + 0.121754i) q^{4} +(-3.72827 + 2.70875i) q^{6} -1.00000i q^{7} +(1.56560 + 2.15486i) q^{8} +(-2.04634 - 6.29798i) q^{9} +(1.87462 - 5.76947i) q^{11} +(0.611092 - 0.198556i) q^{12} +(3.03120 - 0.984896i) q^{13} +(-0.459090 + 1.41293i) q^{14} +(-1.35083 - 4.15742i) q^{16} +(1.80106 + 2.47895i) q^{17} +9.83807i q^{18} +(-1.24098 + 0.901624i) q^{19} +(-2.50953 - 1.82328i) q^{21} +(-5.29741 + 7.29126i) q^{22} +(-0.430310 - 0.139816i) q^{23} +8.26220 q^{24} -4.73503 q^{26} +(-10.6856 - 3.47197i) q^{27} +(0.121754 - 0.167580i) q^{28} +(2.38495 + 1.73277i) q^{29} +(-0.913571 + 0.663748i) q^{31} +1.16721i q^{32} +(-11.0607 - 15.2238i) q^{33} +(-1.40672 - 4.32943i) q^{34} +(0.423880 - 1.30457i) q^{36} +(3.90332 - 1.26826i) q^{37} +(2.16735 - 0.704213i) q^{38} +(3.05510 - 9.40262i) q^{39} +(-2.45117 - 7.54393i) q^{41} +(2.70875 + 3.72827i) q^{42} +3.03187i q^{43} +(1.01661 - 0.738608i) q^{44} +(0.543810 + 0.395101i) q^{46} +(-3.40439 + 4.68574i) q^{47} +(-12.8961 - 4.19020i) q^{48} -1.00000 q^{49} +9.50482 q^{51} +(0.627885 + 0.204012i) q^{52} +(-2.36682 + 3.25765i) q^{53} +(13.5041 + 9.81132i) q^{54} +(2.15486 - 1.56560i) q^{56} +4.75819i q^{57} +(-2.57428 - 3.54319i) q^{58} +(-2.23176 - 6.86866i) q^{59} +(-4.33740 + 13.3491i) q^{61} +(1.59553 - 0.518420i) q^{62} +(-6.29798 + 2.04634i) q^{63} +(-2.16581 + 6.66567i) q^{64} +(8.63897 + 26.5880i) q^{66} +(5.76618 + 7.93647i) q^{67} +0.634710i q^{68} +(-1.13545 + 0.824951i) q^{69} +(-5.06836 - 3.68238i) q^{71} +(10.3675 - 14.2697i) q^{72} +(-2.41296 - 0.784018i) q^{73} -6.09737 q^{74} -0.317741 q^{76} +(-5.76947 - 1.87462i) q^{77} +(-8.63329 + 11.8827i) q^{78} +(2.78358 + 2.02239i) q^{79} +(-12.1238 + 8.80843i) q^{81} +11.7844i q^{82} +(10.5319 + 14.4959i) q^{83} +(-0.198556 - 0.611092i) q^{84} +(1.39190 - 4.28383i) q^{86} +(8.69687 - 2.82578i) q^{87} +(15.3673 - 4.99314i) q^{88} +(0.615208 - 1.89341i) q^{89} +(-0.984896 - 3.03120i) q^{91} +(-0.0550883 - 0.0758225i) q^{92} +3.50283i q^{93} +(6.96134 - 5.05771i) q^{94} +(2.92914 + 2.12814i) q^{96} +(-3.46922 + 4.77497i) q^{97} +(1.41293 + 0.459090i) q^{98} -40.1721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 30 q^{6} + 10 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 30 * q^6 + 10 * q^9	$ 56 q + 12 q^{4} - 30 q^{6} + 10 q^{9} - 16 q^{11} + 12 q^{14} + 32 q^{16} - 44 q^{19} - 8 q^{21} - 76 q^{24} - 16 q^{26} + 74 q^{29} - 2 q^{31} + 20 q^{34} - 82 q^{36} - 48 q^{39} + 20 q^{41} - 130 q^{44} + 52 q^{46} - 56 q^{49} + 4 q^{51} + 28 q^{54} + 4 q^{56} + 38 q^{59} - 96 q^{61} + 40 q^{64} + 182 q^{66} - 62 q^{69} + 24 q^{71} - 140 q^{74} - 12 q^{76} + 144 q^{79} - 20 q^{81} - 16 q^{84} - 120 q^{86} - 6 q^{89} + 16 q^{91} - 24 q^{94} + 44 q^{96} - 124 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 30 * q^6 + 10 * q^9 - 16 * q^11 + 12 * q^14 + 32 * q^16 - 44 * q^19 - 8 * q^21 - 76 * q^24 - 16 * q^26 + 74 * q^29 - 2 * q^31 + 20 * q^34 - 82 * q^36 - 48 * q^39 + 20 * q^41 - 130 * q^44 + 52 * q^46 - 56 * q^49 + 4 * q^51 + 28 * q^54 + 4 * q^56 + 38 * q^59 - 96 * q^61 + 40 * q^64 + 182 * q^66 - 62 * q^69 + 24 * q^71 - 140 * q^74 - 12 * q^76 + 144 * q^79 - 20 * q^81 - 16 * q^84 - 120 * q^86 - 6 * q^89 + 16 * q^91 - 24 * q^94 + 44 * q^96 - 124 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−1.41293	−	0.459090i	−0.999094	−	0.324625i	−0.236591	−	0.971609i	$-0.576030\pi$
$2$	−1.41293	−	0.459090i	−0.999094	−	0.324625i	−0.762503	+	0.646984i	$0.776030\pi$
$3$	1.82328	−	2.50953i	1.05267	−	1.44888i	0.166201	−	0.986092i	$-0.446850\pi$
$3$	1.82328	−	2.50953i	1.05267	−	1.44888i	0.886470	−	0.462786i	$-0.153150\pi$
$4$	0.167580	+	0.121754i	0.0837902	+	0.0608772i
$5$		0			0
$5$		0			0
$6$	−3.72827	+	2.70875i	−1.52206	+	1.10584i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.56560	+	2.15486i	0.553522	+	0.761858i
$9$	−2.04634	−	6.29798i	−0.682113	−	2.09933i
$10$		0			0
$11$	1.87462	−	5.76947i	0.565218	−	1.73956i	−0.102086	−	0.994776i	$-0.532552\pi$
$11$	1.87462	−	5.76947i	0.565218	−	1.73956i	0.667303	−	0.744786i	$-0.267448\pi$
$12$	0.611092	−	0.198556i	0.176407	−	0.0573182i
$13$	3.03120	−	0.984896i	0.840703	−	0.273161i	0.143156	−	0.989700i	$-0.454275\pi$
$13$	3.03120	−	0.984896i	0.840703	−	0.273161i	0.697547	+	0.716539i	$0.254275\pi$
$14$	−0.459090	+	1.41293i	−0.122697	+	0.377622i
$15$		0			0
$16$	−1.35083	−	4.15742i	−0.337707	−	1.03936i
$17$	1.80106	+	2.47895i	0.436821	+	0.601233i	0.969502	−	0.245084i	$-0.0788154\pi$
$17$	1.80106	+	2.47895i	0.436821	+	0.601233i	−0.532681	+	0.846316i	$0.678815\pi$
$18$			9.83807i			2.31886i
$19$	−1.24098	+	0.901624i	−0.284700	+	0.206847i	−0.720965	−	0.692972i	$-0.756301\pi$
$19$	−1.24098	+	0.901624i	−0.284700	+	0.206847i	0.436265	+	0.899818i	$0.356301\pi$
$20$		0			0
$21$	−2.50953	−	1.82328i	−0.547624	−	0.397872i
$22$	−5.29741	+	7.29126i	−1.12941	+	1.55450i
$23$	−0.430310	−	0.139816i	−0.0897257	−	0.0291537i	0.263810	−	0.964575i	$-0.415021\pi$
$23$	−0.430310	−	0.139816i	−0.0897257	−	0.0291537i	−0.353536	+	0.935421i	$0.615021\pi$
$24$	8.26220			1.68652
$25$		0			0
$26$	−4.73503			−0.928616
$27$	−10.6856	−	3.47197i	−2.05645	−	0.668181i
$28$	0.121754	−	0.167580i	0.0230094	−	0.0316697i
$29$	2.38495	+	1.73277i	0.442874	+	0.321767i	0.786776	−	0.617239i	$-0.211749\pi$
$29$	2.38495	+	1.73277i	0.442874	+	0.321767i	−0.343902	+	0.939006i	$0.611749\pi$
$30$		0			0
$31$	−0.913571	+	0.663748i	−0.164082	+	0.119213i	−0.666796	−	0.745240i	$-0.732335\pi$
$31$	−0.913571	+	0.663748i	−0.164082	+	0.119213i	0.502714	+	0.864453i	$0.332335\pi$
$32$			1.16721i			0.206335i
$33$	−11.0607	−	15.2238i	−1.92542	−	2.65012i
$34$	−1.40672	−	4.32943i	−0.241250	−	0.742491i
$35$		0			0
$36$	0.423880	−	1.30457i	0.0706467	−	0.217428i
$37$	3.90332	−	1.26826i	0.641701	−	0.208501i	0.0299497	−	0.999551i	$-0.490465\pi$
$37$	3.90332	−	1.26826i	0.641701	−	0.208501i	0.611751	+	0.791050i	$0.290465\pi$
$38$	2.16735	−	0.704213i	0.351590	−	0.114238i
$39$	3.05510	−	9.40262i	0.489207	−	1.50562i
$40$		0			0
$41$	−2.45117	−	7.54393i	−0.382809	−	1.17816i	−0.938057	−	0.346480i	$-0.887377\pi$
$41$	−2.45117	−	7.54393i	−0.382809	−	1.17816i	0.555248	−	0.831685i	$-0.312623\pi$
$42$	2.70875	+	3.72827i	0.417969	+	0.575285i
$43$			3.03187i			0.462356i	0.972911	+	0.231178i	$0.0742580\pi$
$43$			3.03187i			0.462356i	−0.972911	+	0.231178i	$0.925742\pi$
$44$	1.01661	−	0.738608i	0.153259	−	0.111349i
$45$		0			0
$46$	0.543810	+	0.395101i	0.0801804	+	0.0582545i
$47$	−3.40439	+	4.68574i	−0.496581	+	0.683485i	−0.981585	−	0.191027i	$-0.938818\pi$
$47$	−3.40439	+	4.68574i	−0.496581	+	0.683485i	0.485004	+	0.874512i	$0.338818\pi$
$48$	−12.8961	−	4.19020i	−1.86139	−	0.604804i
$49$	−1.00000			−0.142857
$50$		0			0
$51$	9.50482			1.33094
$52$	0.627885	+	0.204012i	0.0870719	+	0.0282914i
$53$	−2.36682	+	3.25765i	−0.325108	+	0.447473i	−0.940018	−	0.341125i	$-0.889192\pi$
$53$	−2.36682	+	3.25765i	−0.325108	+	0.447473i	0.614910	+	0.788597i	$0.289192\pi$
$54$	13.5041	+	9.81132i	1.83768	+	1.33515i
$55$		0			0
$56$	2.15486	−	1.56560i	0.287955	−	0.209212i
$57$			4.75819i			0.630237i
$58$	−2.57428	−	3.54319i	−0.338019	−	0.465244i
$59$	−2.23176	−	6.86866i	−0.290551	−	0.894223i	−0.984680	−	0.174373i	$-0.944210\pi$
$59$	−2.23176	−	6.86866i	−0.290551	−	0.894223i	0.694129	−	0.719851i	$-0.255790\pi$
$60$		0			0
$61$	−4.33740	+	13.3491i	−0.555347	+	1.70918i	0.139680	+	0.990197i	$0.455393\pi$
$61$	−4.33740	+	13.3491i	−0.555347	+	1.70918i	−0.695026	+	0.718984i	$0.744607\pi$
$62$	1.59553	−	0.518420i	0.202633	−	0.0658394i
$63$	−6.29798	+	2.04634i	−0.793471	+	0.257814i
$64$	−2.16581	+	6.66567i	−0.270726	+	0.833208i
$65$		0			0
$66$	8.63897	+	26.5880i	1.06338	+	3.27276i
$67$	5.76618	+	7.93647i	0.704451	+	0.969594i	0.999899	+	0.0142352i	$0.00453135\pi$
$67$	5.76618	+	7.93647i	0.704451	+	0.969594i	−0.295447	+	0.955359i	$0.595469\pi$
$68$			0.634710i			0.0769698i
$69$	−1.13545	+	0.824951i	−0.136692	+	0.0993124i
$70$		0			0
$71$	−5.06836	−	3.68238i	−0.601504	−	0.437018i	0.244908	−	0.969546i	$-0.421242\pi$
$71$	−5.06836	−	3.68238i	−0.601504	−	0.437018i	−0.846412	+	0.532528i	$0.821242\pi$
$72$	10.3675	−	14.2697i	1.22182	−	1.68170i
$73$	−2.41296	−	0.784018i	−0.282416	−	0.0917624i	0.164384	−	0.986396i	$-0.447436\pi$
$73$	−2.41296	−	0.784018i	−0.282416	−	0.0917624i	−0.446800	+	0.894634i	$0.647436\pi$
$74$	−6.09737			−0.708805
$75$		0			0
$76$	−0.317741			−0.0364473
$77$	−5.76947	−	1.87462i	−0.657493	−	0.213632i
$78$	−8.63329	+	11.8827i	−0.977527	+	1.34545i
$79$	2.78358	+	2.02239i	0.313178	+	0.227537i	0.733259	−	0.679950i	$-0.237998\pi$
$79$	2.78358	+	2.02239i	0.313178	+	0.227537i	−0.420081	+	0.907487i	$0.637998\pi$
$80$		0			0
$81$	−12.1238	+	8.80843i	−1.34708	+	0.978714i
$82$			11.7844i			1.30137i
$83$	10.5319	+	14.4959i	1.15602	+	1.59113i	0.724928	+	0.688825i	$0.241873\pi$
$83$	10.5319	+	14.4959i	1.15602	+	1.59113i	0.431097	+	0.902306i	$0.358127\pi$
$84$	−0.198556	−	0.611092i	−0.0216642	−	0.0666756i
$85$		0			0
$86$	1.39190	−	4.28383i	0.150093	−	0.461937i
$87$	8.69687	−	2.82578i	0.932402	−	0.302956i
$88$	15.3673	−	4.99314i	1.63816	−	0.532270i
$89$	0.615208	−	1.89341i	0.0652119	−	0.200702i	−0.913142	−	0.407643i	$-0.866351\pi$
$89$	0.615208	−	1.89341i	0.0652119	−	0.200702i	0.978353	+	0.206941i	$0.0663509\pi$
$90$		0			0
$91$	−0.984896	−	3.03120i	−0.103245	−	0.317756i
$92$	−0.0550883	−	0.0758225i	−0.00574335	−	0.00790504i
$93$			3.50283i			0.363227i
$94$	6.96134	−	5.05771i	0.718007	−	0.521663i
$95$		0			0
$96$	2.92914	+	2.12814i	0.298954	+	0.217203i
$97$	−3.46922	+	4.77497i	−0.352246	+	0.484825i	−0.947968	−	0.318366i	$-0.896866\pi$
$97$	−3.46922	+	4.77497i	−0.352246	+	0.484825i	0.595722	+	0.803191i	$0.296866\pi$
$98$	1.41293	+	0.459090i	0.142728	+	0.0463750i
$99$	−40.1721			−4.03745
$100$		0			0
$101$	−8.61324			−0.857049			−0.428525	−	0.903530i	$-0.640966\pi$
$101$	−8.61324			−0.857049			−0.428525	+	0.903530i	$0.640966\pi$
$102$	−13.4297	−	4.36356i	−1.32974	−	0.432057i
$103$	1.83760	−	2.52924i	0.181064	−	0.249213i	−0.708831	−	0.705378i	$-0.750777\pi$
$103$	1.83760	−	2.52924i	0.181064	−	0.249213i	0.889895	+	0.456165i	$0.150777\pi$
$104$	6.86794	+	4.98985i	0.673457	+	0.489295i
$105$		0			0
$106$	4.83971	−	3.51626i	0.470074	−	0.341529i
$107$		−	12.7809i		−	1.23558i	−0.786344	−	0.617789i	$-0.788029\pi$
$107$		−	12.7809i		−	1.23558i	0.786344	−	0.617789i	$-0.211971\pi$
$108$	−1.36797	−	1.88286i	−0.131633	−	0.181178i
$109$	4.34008	+	13.3574i	0.415704	+	1.27941i	0.911619	+	0.411036i	$0.134833\pi$
$109$	4.34008	+	13.3574i	0.415704	+	1.27941i	−0.495915	+	0.868371i	$0.665167\pi$
$110$		0			0
$111$	3.93409	−	12.1079i	0.373407	−	1.14923i
$112$	−4.15742	+	1.35083i	−0.392840	+	0.127641i
$113$	1.73980	−	0.565296i	0.163667	−	0.0531786i	−0.226037	−	0.974119i	$-0.572577\pi$
$113$	1.73980	−	0.565296i	0.163667	−	0.0531786i	0.389704	+	0.920940i	$0.372577\pi$
$114$	2.18443	−	6.72300i	0.204591	−	0.629666i
$115$		0			0
$116$	0.188699	+	0.580756i	0.0175203	+	0.0539219i
$117$	−12.4057	−	17.0750i	−1.14691	−	1.57858i
$118$			10.7295i			0.987733i
$119$	2.47895	−	1.80106i	0.227245	−	0.165103i
$120$		0			0
$121$	−20.8735	−	15.1655i	−1.89759	−	1.37868i
$122$	12.2569	−	16.8702i	1.10969	−	1.52735i
$123$	−23.4009	−	7.60341i	−2.10999	−	0.685577i
$124$	−0.233911			−0.0210058
$125$		0			0
$126$	9.83807			0.876445
$127$	10.6291	+	3.45362i	0.943183	+	0.306459i	0.739943	−	0.672670i	$-0.234853\pi$
$127$	10.6291	+	3.45362i	0.943183	+	0.306459i	0.203241	+	0.979129i	$0.434853\pi$
$128$	7.49241	−	10.3124i	0.662241	−	0.911497i
$129$	7.60857	+	5.52795i	0.669898	+	0.486709i
$130$		0			0
$131$	7.71872	−	5.60798i	0.674388	−	0.489972i	−0.197103	−	0.980383i	$-0.563153\pi$
$131$	7.71872	−	5.60798i	0.674388	−	0.489972i	0.871491	+	0.490411i	$0.163153\pi$
$132$		−	3.89790i		−	0.339268i
$133$	0.901624	+	1.24098i	0.0781807	+	0.107607i
$134$	−4.50368	−	13.8609i	−0.389058	−	1.19740i
$135$		0			0
$136$	−2.52205	+	7.76206i	−0.216264	+	0.665591i
$137$	−10.4578	+	3.39795i	−0.893470	+	0.290306i	−0.719539	−	0.694452i	$-0.755647\pi$
$137$	−10.4578	+	3.39795i	−0.893470	+	0.290306i	−0.173931	+	0.984758i	$0.555647\pi$
$138$	1.98304	−	0.644328i	0.168807	−	0.0548488i
$139$	3.09341	−	9.52052i	0.262379	−	0.807520i	−0.729906	−	0.683547i	$-0.760436\pi$
$139$	3.09341	−	9.52052i	0.262379	−	0.807520i	0.992286	−	0.123973i	$-0.0395637\pi$
$140$		0			0
$141$	5.55184	+	17.0868i	0.467550	+	1.43897i
$142$	5.47071	+	7.52979i	0.459092	+	0.631886i
$143$		−	19.3347i		−	1.61685i
$144$	−23.4191	+	17.0150i	−1.95159	+	1.41792i
$145$		0			0
$146$	3.04941	+	2.21553i	0.252371	+	0.183358i
$147$	−1.82328	+	2.50953i	−0.150382	+	0.206983i
$148$	0.808536	+	0.262709i	0.0664613	+	0.0215946i
$149$	5.00195			0.409776			0.204888	−	0.978785i	$-0.434317\pi$
$149$	5.00195			0.409776			0.204888	+	0.978785i	$0.434317\pi$
$150$		0			0
$151$	9.77589			0.795550			0.397775	−	0.917483i	$-0.369782\pi$
$151$	9.77589			0.795550			0.397775	+	0.917483i	$0.369782\pi$
$152$	−3.88575	−	1.26256i	−0.315176	−	0.102407i
$153$	11.9268	−	16.4158i	0.964222	−	1.32714i
$154$	7.29126	+	5.29741i	0.587546	+	0.426877i
$155$		0			0
$156$	1.65678	−	1.20372i	0.132649	−	0.0963751i
$157$			0.0856625i			0.00683662i	0.999994	+	0.00341831i	$0.00108808\pi$
$157$			0.0856625i			0.00683662i	−0.999994	+	0.00341831i	$0.998912\pi$
$158$	−3.00456	−	4.13542i	−0.239030	−	0.328996i
$159$	3.85979	+	11.8792i	0.306101	+	0.942083i
$160$		0			0
$161$	−0.139816	+	0.430310i	−0.0110190	+	0.0339131i
$162$	21.1739	−	6.87982i	1.66358	−	0.540530i
$163$	3.68755	−	1.19816i	0.288832	−	0.0938471i	−0.161018	−	0.986952i	$-0.551478\pi$
$163$	3.68755	−	1.19816i	0.288832	−	0.0938471i	0.449849	+	0.893104i	$0.351478\pi$
$164$	0.507738	−	1.56266i	0.0396477	−	0.122023i
$165$		0			0
$166$	−8.22592	−	25.3168i	−0.638456	−	1.96496i
$167$	−7.44423	−	10.2461i	−0.576052	−	0.792867i	0.417204	−	0.908813i	$-0.363010\pi$
$167$	−7.44423	−	10.2461i	−0.576052	−	0.792867i	−0.993256	+	0.115946i	$0.963010\pi$
$168$		−	8.26220i		−	0.637443i
$169$	−2.29908	+	1.67038i	−0.176853	+	0.128491i
$170$		0			0
$171$	8.21787	+	5.97063i	0.628436	+	0.456586i
$172$	−0.369144	+	0.508083i	−0.0281469	+	0.0387409i
$173$	8.58556	+	2.78962i	0.652748	+	0.212091i	0.616625	−	0.787257i	$-0.288499\pi$
$173$	8.58556	+	2.78962i	0.652748	+	0.212091i	0.0361225	+	0.999347i	$0.488499\pi$
$174$	−13.5854			−1.02990
$175$		0			0
$176$	−26.5184			−1.99890
$177$	−21.3062	−	6.92281i	−1.60147	−	0.520351i
$178$	−1.73849	+	2.39283i	−0.130306	+	0.179350i
$179$	−19.5030	−	14.1697i	−1.45772	−	1.05910i	−0.983950	−	0.178446i	$-0.942893\pi$
$179$	−19.5030	−	14.1697i	−1.45772	−	1.05910i	−0.473770	−	0.880649i	$-0.657107\pi$
$180$		0			0
$181$	11.5854	−	8.41729i	0.861137	−	0.625652i	−0.0670572	−	0.997749i	$-0.521361\pi$
$181$	11.5854	−	8.41729i	0.861137	−	0.625652i	0.928194	+	0.372097i	$0.121361\pi$
$182$			4.73503i			0.350984i
$183$	25.5918	+	35.2240i	1.89180	+	2.60383i
$184$	−0.372407	−	1.14615i	−0.0274542	−	0.0844954i
$185$		0			0
$186$	1.60811	−	4.94926i	0.117913	−	0.362898i
$187$	17.6785	−	5.74409i	1.29278	−	0.420050i
$188$	−1.14102	+	0.370739i	−0.0832173	+	0.0270389i
$189$	−3.47197	+	10.6856i	−0.252549	+	0.777265i
$190$		0			0
$191$	5.00598	+	15.4068i	0.362220	+	1.11480i	0.951704	+	0.307018i	$0.0993313\pi$
$191$	5.00598	+	15.4068i	0.362220	+	1.11480i	−0.589484	+	0.807780i	$0.700669\pi$
$192$	12.7788	+	17.5885i	0.922231	+	1.26934i
$193$			10.9768i			0.790127i	0.918654	+	0.395064i	$0.129277\pi$
$193$			10.9768i			0.790127i	−0.918654	+	0.395064i	$0.870723\pi$
$194$	7.09392	−	5.15403i	0.509314	−	0.370038i
$195$		0			0
$196$	−0.167580	−	0.121754i	−0.0119700	−	0.00869674i
$197$	9.83630	−	13.5385i	0.700807	−	0.964578i	−0.299139	−	0.954210i	$-0.596699\pi$
$197$	9.83630	−	13.5385i	0.700807	−	0.964578i	0.999946	−	0.0103689i	$-0.00330058\pi$
$198$	56.7605	+	18.4426i	4.03379	+	1.31066i
$199$	−3.87252			−0.274515			−0.137258	−	0.990535i	$-0.543829\pi$
$199$	−3.87252			−0.274515			−0.137258	+	0.990535i	$0.543829\pi$
$200$		0			0
$201$	30.4302			2.14638
$202$	12.1699	+	3.95425i	0.856273	+	0.278220i
$203$	1.73277	−	2.38495i	0.121617	−	0.167391i
$204$	1.59282	+	1.15725i	0.111520	+	0.0810239i
$205$		0			0
$206$	−3.75755	+	2.73002i	−0.261801	+	0.190209i
$207$			2.99619i			0.208250i
$208$	−8.18926	−	11.2715i	−0.567823	−	0.781541i
$209$	2.87554	+	8.84999i	0.198905	+	0.612167i
$210$		0			0
$211$	3.59777	−	11.0728i	0.247681	−	0.762284i	−0.747503	−	0.664258i	$-0.768747\pi$
$211$	3.59777	−	11.0728i	0.247681	−	0.762284i	0.995184	−	0.0980252i	$-0.0312526\pi$
$212$	−0.793266	+	0.257748i	−0.0544817	+	0.0177022i
$213$	−18.4821	+	6.00519i	−1.26637	+	0.411469i
$214$	−5.86759	+	18.0586i	−0.401100	+	1.23446i
$215$		0			0
$216$	−9.24778	−	28.4617i	−0.629231	−	1.93658i
$217$	0.663748	+	0.913571i	0.0450582	+	0.0620172i
$218$		−	20.8656i		−	1.41320i
$219$	−6.36702	+	4.62591i	−0.430243	+	0.312590i
$220$		0			0
$221$	7.90087	+	5.74032i	0.531470	+	0.386135i
$222$	−11.1172	+	15.3015i	−0.746138	+	1.02697i
$223$	19.8950	+	6.46428i	1.33227	+	0.432880i	0.886691	−	0.462363i	$-0.152998\pi$
$223$	19.8950	+	6.46428i	1.33227	+	0.432880i	0.445578	+	0.895243i	$0.352998\pi$
$224$	1.16721			0.0779872
$225$		0			0
$226$	−2.71775			−0.180782
$227$	−0.931212	−	0.302569i	−0.0618067	−	0.0200822i	0.277950	−	0.960595i	$-0.410345\pi$
$227$	−0.931212	−	0.302569i	−0.0618067	−	0.0200822i	−0.339757	+	0.940513i	$0.610345\pi$
$228$	−0.579330	+	0.797379i	−0.0383671	+	0.0528077i
$229$	5.22726	+	3.79782i	0.345427	+	0.250967i	0.746948	−	0.664882i	$-0.231518\pi$
$229$	5.22726	+	3.79782i	0.345427	+	0.250967i	−0.401521	+	0.915850i	$0.631518\pi$
$230$		0			0
$231$	−15.2238	+	11.0607i	−1.00165	+	0.727742i
$232$			7.85205i			0.515512i
$233$	−9.70227	−	13.3540i	−0.635617	−	0.874851i	0.362756	−	0.931884i	$-0.381836\pi$
$233$	−9.70227	−	13.3540i	−0.635617	−	0.874851i	−0.998372	+	0.0570332i	$0.981836\pi$
$234$	9.68947	+	29.8211i	0.633421	+	1.94947i
$235$		0			0
$236$	0.462289	−	1.42278i	0.0300925	−	0.0926151i
$237$	10.1505	−	3.29810i	0.659346	−	0.214235i
$238$	−4.32943	+	1.40672i	−0.280635	+	0.0911839i
$239$	6.80639	−	20.9479i	0.440269	−	1.35501i	−0.447321	−	0.894374i	$-0.647622\pi$
$239$	6.80639	−	20.9479i	0.440269	−	1.35501i	0.887590	−	0.460635i	$-0.152378\pi$
$240$		0			0
$241$	4.66948	+	14.3712i	0.300787	+	0.925728i	0.981216	+	0.192914i	$0.0617938\pi$
$241$	4.66948	+	14.3712i	0.300787	+	0.925728i	−0.680428	+	0.732815i	$0.738206\pi$
$242$	22.5305	+	31.0105i	1.44831	+	1.99343i
$243$			12.7786i			0.819745i
$244$	−2.35218	+	1.70896i	−0.150583	+	0.109405i
$245$		0			0
$246$	29.5732	+	21.4862i	1.88552	+	1.36991i
$247$	−2.87365	+	3.95524i	−0.182846	+	0.251666i
$248$	−2.86057	−	0.929455i	−0.181646	−	0.0590204i
$249$	55.5804			3.52227
$250$		0			0
$251$	20.9803			1.32427			0.662133	−	0.749386i	$-0.269651\pi$
$251$	20.9803			1.32427			0.662133	+	0.749386i	$0.269651\pi$
$252$	−1.30457	−	0.423880i	−0.0821801	−	0.0267019i
$253$	−1.61333	+	2.22056i	−0.101429	+	0.139605i
$254$	−13.4327	−	9.75945i	−0.842845	−	0.612362i
$255$		0			0
$256$	−3.98028	+	2.89184i	−0.248767	+	0.180740i
$257$		−	19.5669i		−	1.22055i	−0.792189	−	0.610276i	$-0.791058\pi$
$257$		−	19.5669i		−	1.22055i	0.792189	−	0.610276i	$-0.208942\pi$
$258$	−8.21257	−	11.3036i	−0.511293	−	0.703734i
$259$	−1.26826	−	3.90332i	−0.0788061	−	0.242540i
$260$		0			0
$261$	6.03253	−	18.5662i	0.373404	−	1.14922i
$262$	−13.4806	+	4.38011i	−0.832834	+	0.270604i
$263$	10.8414	−	3.52257i	0.668507	−	0.217211i	0.0449505	−	0.998989i	$-0.485687\pi$
$263$	10.8414	−	3.52257i	0.668507	−	0.217211i	0.623557	+	0.781778i	$0.285687\pi$
$264$	15.4885	−	47.6686i	0.953248	−	2.93380i
$265$		0			0
$266$	−0.704213	−	2.16735i	−0.0431781	−	0.132888i
$267$	−3.62988	−	4.99611i	−0.222145	−	0.305757i
$268$			2.03206i			0.124128i
$269$	−24.5956	+	17.8697i	−1.49962	+	1.08954i	−0.529088	+	0.848567i	$0.677466\pi$
$269$	−24.5956	+	17.8697i	−1.49962	+	1.08954i	−0.970532	+	0.240971i	$0.922534\pi$
$270$		0			0
$271$	13.2225	+	9.60671i	0.803210	+	0.583566i	0.911854	−	0.410515i	$-0.134651\pi$
$271$	13.2225	+	9.60671i	0.803210	+	0.583566i	−0.108644	+	0.994081i	$0.534651\pi$
$272$	7.87310	−	10.8364i	0.477377	−	0.657053i
$273$	−9.40262	−	3.05510i	−0.569072	−	0.184903i
$274$	16.3361			0.986901
$275$		0			0
$276$	−0.290720			−0.0174993
$277$	−3.14150	−	1.02073i	−0.188754	−	0.0613300i	0.213115	−	0.977027i	$-0.431639\pi$
$277$	−3.14150	−	1.02073i	−0.188754	−	0.0613300i	−0.401869	+	0.915697i	$0.631639\pi$
$278$	−8.74155	+	12.0317i	−0.524283	+	0.721614i
$279$	6.04975	+	4.39540i	0.362189	+	0.263146i
$280$		0			0
$281$	14.7592	−	10.7232i	0.880461	−	0.639692i	−0.0529123	−	0.998599i	$-0.516850\pi$
$281$	14.7592	−	10.7232i	0.880461	−	0.639692i	0.933373	+	0.358907i	$0.116850\pi$
$282$		−	26.6913i		−	1.58944i
$283$	4.04657	+	5.56963i	0.240544	+	0.331080i	0.912172	−	0.409809i	$-0.134405\pi$
$283$	4.04657	+	5.56963i	0.240544	+	0.331080i	−0.671628	+	0.740889i	$0.734405\pi$
$284$	−0.401013	−	1.23419i	−0.0237957	−	0.0732357i
$285$		0			0
$286$	−8.87636	+	27.3186i	−0.524870	+	1.61538i
$287$	−7.54393	+	2.45117i	−0.445304	+	0.144688i
$288$	7.35104	−	2.38850i	0.433164	−	0.140744i
$289$	2.35193	−	7.23851i	0.138349	−	0.425794i
$290$		0			0
$291$	5.65758	+	17.4122i	0.331653	+	1.02072i
$292$	−0.308907	−	0.425174i	−0.0180774	−	0.0248815i
$293$		−	12.3481i		−	0.721383i	−0.932685	−	0.360692i	$-0.882541\pi$
$293$		−	12.3481i		−	0.721383i	0.932685	−	0.360692i	$-0.117459\pi$
$294$	3.72827	−	2.70875i	0.217437	−	0.157977i
$295$		0			0
$296$	8.84395	+	6.42550i	0.514044	+	0.373475i
$297$	−40.0629	+	55.1418i	−2.32468	+	3.19965i
$298$	−7.06742	−	2.29634i	−0.409405	−	0.133024i
$299$	−1.44206			−0.0833963
$300$		0			0
$301$	3.03187			0.174754
$302$	−13.8127	−	4.48801i	−0.794830	−	0.258256i
$303$	−15.7043	+	21.6152i	−0.902191	+	1.24176i
$304$	5.42478	+	3.94134i	0.311133	+	0.226051i
$305$		0			0
$306$	−24.3880	+	17.7190i	−1.39417	+	1.01292i
$307$			1.98074i			0.113047i	0.998401	+	0.0565234i	$0.0180016\pi$
$307$			1.98074i			0.113047i	−0.998401	+	0.0565234i	$0.981998\pi$
$308$	−0.738608	−	1.01661i	−0.0420861	−	0.0579266i
$309$	−2.99674	−	9.22302i	−0.170479	−	0.524679i
$310$		0			0
$311$	5.30403	−	16.3241i	0.300764	−	0.925657i	−0.680460	−	0.732785i	$-0.738220\pi$
$311$	5.30403	−	16.3241i	0.300764	−	0.925657i	0.981224	−	0.192872i	$-0.0617801\pi$
$312$	25.0444	−	8.13741i	1.41786	−	0.460690i
$313$	−9.18681	+	2.98498i	−0.519269	+	0.168721i	−0.556914	−	0.830570i	$-0.688015\pi$
$313$	−9.18681	+	2.98498i	−0.519269	+	0.168721i	0.0376444	+	0.999291i	$0.488015\pi$
$314$	0.0393268	−	0.121035i	0.00221934	−	0.00683042i
$315$		0			0
$316$	0.220239	+	0.677827i	0.0123894	+	0.0381308i
$317$	−2.72664	−	3.75290i	−0.153143	−	0.210784i	0.725551	−	0.688168i	$-0.241585\pi$
$317$	−2.72664	−	3.75290i	−0.153143	−	0.210784i	−0.878695	+	0.477384i	$0.841585\pi$
$318$		−	18.5565i		−	1.04060i
$319$	14.4680	−	10.5116i	0.810054	−	0.588539i
$320$		0			0
$321$	−32.0741	−	23.3032i	−1.79020	−	1.30066i
$322$	0.395101	−	0.543810i	0.0220181	−	0.0303054i
$323$	−4.47015	−	1.45244i	−0.248726	−	0.0808160i
$324$	−3.10417			−0.172454
$325$		0			0
$326$	−5.76033			−0.319035
$327$	41.4340	+	13.4627i	2.29130	+	0.744490i
$328$	12.4186	−	17.0927i	0.685701	−	0.943786i
$329$	4.68574	+	3.40439i	0.258333	+	0.187690i
$330$		0			0
$331$	−3.63545	+	2.64131i	−0.199822	+	0.145179i	−0.683197	−	0.730234i	$-0.739411\pi$
$331$	−3.63545	+	2.64131i	−0.199822	+	0.145179i	0.483375	+	0.875414i	$0.339411\pi$
$332$			3.71153i			0.203697i
$333$	−15.9750	−	21.9877i	−0.875425	−	1.20492i
$334$	5.81431	+	17.8946i	0.318145	+	0.979150i
$335$		0			0
$336$	−4.19020	+	12.8961i	−0.228594	+	0.703541i
$337$	−21.0769	+	6.84830i	−1.14813	+	0.373050i	−0.820439	−	0.571734i	$-0.806271\pi$
$337$	−21.0769	+	6.84830i	−1.14813	+	0.373050i	−0.327692	+	0.944785i	$0.606271\pi$
$338$	4.01531	−	1.30465i	0.218404	−	0.0709637i
$339$	1.75352	−	5.39678i	0.0952382	−	0.293113i
$340$		0			0
$341$	2.11688	+	6.51510i	0.114636	+	0.352812i
$342$	−8.87024	−	12.2088i	−0.479648	−	0.660179i
$343$			1.00000i			0.0539949i
$344$	−6.53326	+	4.74669i	−0.352250	+	0.255924i
$345$		0			0
$346$	−10.8501	−	7.88308i	−0.583306	−	0.423797i
$347$	−5.33043	+	7.33671i	−0.286152	+	0.393855i	−0.927760	−	0.373178i	$-0.878268\pi$
$347$	−5.33043	+	7.33671i	−0.286152	+	0.393855i	0.641607	+	0.767033i	$0.278268\pi$
$348$	1.80148	+	0.585335i	0.0965693	+	0.0313773i
$349$	−12.1902			−0.652527			−0.326263	−	0.945279i	$-0.605790\pi$
$349$	−12.1902			−0.652527			−0.326263	+	0.945279i	$0.605790\pi$
$350$		0			0
$351$	−35.8098			−1.91138
$352$	6.73416	+	2.18806i	0.358932	+	0.116624i
$353$	−12.3358	+	16.9787i	−0.656566	+	0.903686i	−0.999362	−	0.0357244i	$-0.988626\pi$
$353$	−12.3358	+	16.9787i	−0.656566	+	0.903686i	0.342796	+	0.939410i	$0.388626\pi$
$354$	26.9261	+	19.5629i	1.43110	+	1.03976i
$355$		0			0
$356$	0.333628	−	0.242395i	0.0176823	−	0.0128469i
$357$		−	9.50482i		−	0.503049i
$358$	21.0512	+	28.9745i	1.11259	+	1.53135i
$359$	−4.53244	−	13.9494i	−0.239213	−	0.736222i	−0.996535	−	0.0831797i	$-0.973492\pi$
$359$	−4.53244	−	13.9494i	−0.239213	−	0.736222i	0.757322	−	0.653042i	$-0.226508\pi$
$360$		0			0
$361$	−5.14422	+	15.8323i	−0.270748	+	0.833278i
$362$	−20.2337	+	6.57432i	−1.06346	+	0.345539i
$363$	−76.1163	+	24.7317i	−3.99507	+	1.29808i
$364$	0.204012	−	0.627885i	0.0106931	−	0.0329101i
$365$		0			0
$366$	−19.9884	−	61.5181i	−1.04481	−	3.21560i
$367$	12.9988	+	17.8913i	0.678531	+	0.933918i	0.999915	−	0.0130309i	$-0.00414797\pi$
$367$	12.9988	+	17.8913i	0.678531	+	0.933918i	−0.321384	+	0.946949i	$0.604148\pi$
$368$			1.97785i			0.103102i
$369$	−42.4956	+	30.8749i	−2.21223	+	1.60728i
$370$		0			0
$371$	3.25765	+	2.36682i	0.169129	+	0.122879i
$372$	−0.426485	+	0.587006i	−0.0221122	+	0.0304349i
$373$	−29.1989	−	9.48730i	−1.51186	−	0.491234i	−0.568411	−	0.822745i	$-0.692442\pi$
$373$	−29.1989	−	9.48730i	−1.51186	−	0.491234i	−0.943451	+	0.331511i	$0.892442\pi$
$374$	−27.6156			−1.42797
$375$		0			0
$376$	−15.4270			−0.795587
$377$	8.93586	+	2.90344i	0.460220	+	0.149535i
$378$	9.81132	−	13.5041i	0.504640	−	0.694577i
$379$	29.1010	+	21.1431i	1.49482	+	1.08605i	0.972390	+	0.233364i	$0.0749732\pi$
$379$	29.1010	+	21.1431i	1.49482	+	1.08605i	0.522427	+	0.852684i	$0.325027\pi$
$380$		0			0
$381$	28.0468	−	20.3772i	1.43688	−	1.04396i
$382$		−	24.0670i		−	1.23137i
$383$	−0.851390	−	1.17184i	−0.0435040	−	0.0598781i	0.786711	−	0.617322i	$-0.211782\pi$
$383$	−0.851390	−	1.17184i	−0.0435040	−	0.0598781i	−0.830215	+	0.557444i	$0.811782\pi$
$384$	−12.2186	−	37.6048i	−0.623525	−	1.91901i
$385$		0			0
$386$	5.03933	−	15.5095i	0.256495	−	0.789411i
$387$	19.0947	−	6.20424i	0.970637	−	0.315379i
$388$	−1.16275	+	0.377800i	−0.0590296	+	0.0191799i
$389$	0.0148511	−	0.0457069i	0.000752980	−	0.00231743i	−0.950679	−	0.310175i	$-0.899612\pi$
$389$	0.0148511	−	0.0457069i	0.000752980	−	0.00231743i	0.951432	+	0.307858i	$0.0996122\pi$
$390$		0			0
$391$	−0.428417	−	1.31853i	−0.0216660	−	0.0666810i
$392$	−1.56560	−	2.15486i	−0.0790746	−	0.108837i
$393$		−	29.5953i		−	1.49288i
$394$	−20.1134	+	14.6132i	−1.01330	+	0.736205i
$395$		0			0
$396$	−6.73206	−	4.89113i	−0.338299	−	0.245789i
$397$	3.25999	−	4.48699i	0.163614	−	0.225196i	−0.719336	−	0.694662i	$-0.755554\pi$
$397$	3.25999	−	4.48699i	0.163614	−	0.225196i	0.882950	+	0.469467i	$0.155554\pi$
$398$	5.47160	+	1.77783i	0.274267	+	0.0891146i
$399$	4.75819			0.238207
$400$		0			0
$401$	−3.14714			−0.157161			−0.0785804	−	0.996908i	$-0.525039\pi$
$401$	−3.14714			−0.157161			−0.0785804	+	0.996908i	$0.525039\pi$
$402$	−42.9958	−	13.9702i	−2.14443	−	0.696769i
$403$	−2.11549	+	2.91172i	−0.105380	+	0.145043i
$404$	−1.44341	−	1.04870i	−0.0718123	−	0.0521747i
$405$		0			0
$406$	−3.54319	+	2.57428i	−0.175846	+	0.127759i
$407$		−	24.8976i		−	1.23413i
$408$	14.8807	+	20.4815i	0.736705	+	1.01399i
$409$	−2.97325	−	9.15073i	−0.147018	−	0.452475i	0.850247	−	0.526384i	$-0.176453\pi$
$409$	−2.97325	−	9.15073i	−0.147018	−	0.452475i	−0.997265	+	0.0739092i	$0.976453\pi$
$410$		0			0
$411$	−10.5403	+	32.4396i	−0.519912	+	1.60013i
$412$	0.615891	−	0.200115i	0.0303428	−	0.00985897i
$413$	−6.86866	+	2.23176i	−0.337985	+	0.109818i
$414$	1.37552	−	4.23342i	0.0676031	−	0.208061i
$415$		0			0
$416$	1.14958	+	3.53803i	0.0563626	+	0.173466i
$417$	−18.2519	−	25.1216i	−0.893799	−	1.23021i
$418$		−	13.8246i		−	0.676182i
$419$	−13.7056	+	9.95770i	−0.669563	+	0.486466i	−0.869879	−	0.493266i	$-0.835803\pi$
$419$	−13.7056	+	9.95770i	−0.669563	+	0.486466i	0.200316	+	0.979731i	$0.435803\pi$
$420$		0			0
$421$	−1.08741	−	0.790051i	−0.0529972	−	0.0385047i	0.560971	−	0.827835i	$-0.310428\pi$
$421$	−1.08741	−	0.790051i	−0.0529972	−	0.0385047i	−0.613968	+	0.789331i	$0.710428\pi$
$422$	−10.1668	+	13.9934i	−0.494913	+	0.681190i
$423$	36.4772	+	11.8522i	1.77358	+	0.576272i
$424$	−10.7253			−0.520865
$425$		0			0
$426$	28.8709			1.39880
$427$	13.3491	+	4.33740i	0.646010	+	0.209901i
$428$	1.55613	−	2.14183i	0.0752185	−	0.103529i
$429$	−48.5210	−	35.2526i	−2.34262	−	1.70201i
$430$		0			0
$431$	27.4499	−	19.9435i	1.32222	−	0.960647i	0.322315	−	0.946632i	$-0.395539\pi$
$431$	27.4499	−	19.9435i	1.32222	−	0.960647i	0.999902	−	0.0140142i	$-0.00446101\pi$
$432$			49.1147i			2.36303i
$433$	9.54314	+	13.1350i	0.458614	+	0.631228i	0.974221	−	0.225597i	$-0.0724334\pi$
$433$	9.54314	+	13.1350i	0.458614	+	0.631228i	−0.515607	+	0.856825i	$0.672433\pi$
$434$	−0.518420	−	1.59553i	−0.0248850	−	0.0765881i
$435$		0			0
$436$	−0.899008	+	2.76686i	−0.0430547	+	0.132509i
$437$	0.660067	−	0.214469i	0.0315753	−	0.0102594i
$438$	11.1199	−	3.61307i	0.531328	−	0.172639i
$439$	1.25090	−	3.84987i	0.0597021	−	0.183744i	−0.916758	−	0.399444i	$-0.869203\pi$
$439$	1.25090	−	3.84987i	0.0597021	−	0.183744i	0.976460	+	0.215700i	$0.0692032\pi$
$440$		0			0
$441$	2.04634	+	6.29798i	0.0974447	+	0.299904i
$442$	−8.52807	−	11.7379i	−0.405639	−	0.558314i
$443$			18.1315i			0.861456i	0.902482	+	0.430728i	$0.141743\pi$
$443$			18.1315i			0.861456i	−0.902482	+	0.430728i	$0.858257\pi$
$444$	2.13346	−	1.55005i	0.101250	−	0.0735622i
$445$		0			0
$446$	−25.1426	−	18.2672i	−1.19054	−	0.864976i
$447$	9.11996	−	12.5525i	0.431359	−	0.593715i
$448$	6.66567	+	2.16581i	0.314923	+	0.102325i
$449$	29.2576			1.38075			0.690377	−	0.723450i	$-0.257445\pi$
$449$	29.2576			1.38075			0.690377	+	0.723450i	$0.257445\pi$
$450$		0			0
$451$	−48.1195			−2.26586
$452$	0.360384	+	0.117096i	0.0169511	+	0.00550773i
$453$	17.8242	−	24.5329i	0.837453	−	1.15265i
$454$	1.17683	+	0.855019i	0.0552315	+	0.0401280i
$455$		0			0
$456$	−10.2532	+	7.44940i	−0.480151	+	0.348850i
$457$		−	19.9217i		−	0.931900i	−0.884811	−	0.465950i	$-0.845713\pi$
$457$		−	19.9217i		−	0.931900i	0.884811	−	0.465950i	$-0.154287\pi$
$458$	−5.64222	−	7.76585i	−0.263644	−	0.362874i
$459$	−10.6386	−	32.7423i	−0.496568	−	1.52828i
$460$		0			0
$461$	−9.96893	+	30.6812i	−0.464299	+	1.42897i	0.395563	+	0.918439i	$0.370550\pi$
$461$	−9.96893	+	30.6812i	−0.464299	+	1.42897i	−0.859862	+	0.510527i	$0.829450\pi$
$462$	26.5880	−	8.63897i	1.23699	−	0.401921i
$463$	29.0613	−	9.44259i	1.35059	−	0.438835i	0.457702	−	0.889106i	$-0.348673\pi$
$463$	29.0613	−	9.44259i	1.35059	−	0.438835i	0.892892	+	0.450271i	$0.148673\pi$
$464$	3.98219	−	12.2559i	0.184869	−	0.568967i
$465$		0			0
$466$	7.57795	+	23.3225i	0.351042	+	1.08040i
$467$	−6.64478	−	9.14575i	−0.307484	−	0.423215i	0.627111	−	0.778930i	$-0.284237\pi$
$467$	−6.64478	−	9.14575i	−0.307484	−	0.423215i	−0.934594	+	0.355715i	$0.884237\pi$
$468$		−	4.37188i		−	0.202090i
$469$	7.93647	−	5.76618i	0.366472	−	0.266258i
$470$		0			0
$471$	0.214973	+	0.156187i	0.00990542	+	0.00719671i
$472$	11.3070	−	15.5627i	0.520445	−	0.716331i
$473$	17.4923	+	5.68360i	0.804297	+	0.261332i
$474$	−15.8561			−0.728295
$475$		0			0
$476$	0.634710			0.0290919
$477$	25.3599	+	8.23994i	1.16115	+	0.377281i
$478$	−19.2339	+	26.4733i	−0.879740	+	1.21086i
$479$	−11.3304	−	8.23205i	−0.517701	−	0.376132i	0.298036	−	0.954555i	$-0.403668\pi$
$479$	−11.3304	−	8.23205i	−0.517701	−	0.376132i	−0.815737	+	0.578423i	$0.803668\pi$
$480$		0			0
$481$	10.5826	−	7.68872i	0.482526	−	0.350575i
$482$		−	22.4492i		−	1.02253i
$483$	0.824951	+	1.13545i	0.0375366	+	0.0516646i
$484$	−1.65152	−	5.08287i	−0.0750692	−	0.231039i
$485$		0			0
$486$	5.86650	−	18.0552i	0.266110	−	0.819002i
$487$	2.29236	−	0.744834i	0.103877	−	0.0337517i	−0.256617	−	0.966513i	$-0.582608\pi$
$487$	2.29236	−	0.744834i	0.103877	−	0.0337517i	0.360494	+	0.932761i	$0.382608\pi$
$488$	−35.5561	+	11.5529i	−1.60955	+	0.522974i
$489$	3.71663	−	11.4386i	0.168072	−	0.517272i
$490$		0			0
$491$	11.7101	+	36.0400i	0.528470	+	1.62646i	0.757350	+	0.653009i	$0.226494\pi$
$491$	11.7101	+	36.0400i	0.528470	+	1.62646i	−0.228880	+	0.973455i	$0.573506\pi$
$492$	−2.99579	−	4.12334i	−0.135060	−	0.185895i
$493$			9.03298i			0.406825i
$494$	5.87608	−	4.26922i	0.264377	−	0.192081i
$495$		0			0
$496$	3.99356	+	2.90149i	0.179316	+	0.130281i
$497$	−3.68238	+	5.06836i	−0.165177	+	0.227347i
$498$	−78.5314	−	25.5164i	−3.51908	−	1.14342i
$499$	−3.80005			−0.170113			−0.0850567	−	0.996376i	$-0.527107\pi$
$499$	−3.80005			−0.170113			−0.0850567	+	0.996376i	$0.527107\pi$
$500$		0			0
$501$	−39.2858			−1.75516
$502$	−29.6438	−	9.63185i	−1.32307	−	0.429890i
$503$	7.43059	−	10.2273i	0.331314	−	0.456014i	−0.610566	−	0.791966i	$-0.709058\pi$
$503$	7.43059	−	10.2273i	0.331314	−	0.456014i	0.941879	+	0.335952i	$0.109058\pi$
$504$	−14.2697	−	10.3675i	−0.635621	−	0.461806i
$505$		0			0
$506$	3.29896	−	2.39684i	0.146657	−	0.106552i
$507$			8.81520i			0.391497i
$508$	1.36074	+	1.87290i	0.0603732	+	0.0830966i
$509$	13.4003	+	41.2420i	0.593959	+	1.82802i	0.559840	+	0.828601i	$0.310863\pi$
$509$	13.4003	+	41.2420i	0.593959	+	1.82802i	0.0341196	+	0.999418i	$0.489137\pi$
$510$		0			0
$511$	−0.784018	+	2.41296i	−0.0346829	+	0.106743i
$512$	−17.2945	+	5.61931i	−0.764314	+	0.248341i
$513$	16.3911	−	5.32578i	0.723683	−	0.235139i
$514$	−8.98298	+	27.6468i	−0.396222	+	1.21945i
$515$		0			0
$516$	0.601996	+	1.85275i	0.0265014	+	0.0815629i
$517$	20.6523	+	28.4255i	0.908288	+	1.25015i
$518$			6.09737i			0.267903i
$519$	22.6545	−	16.4595i	0.994422	−	0.722490i
$520$		0			0
$521$	−1.45390	−	1.05632i	−0.0636963	−	0.0462781i	0.555481	−	0.831529i	$-0.312534\pi$
$521$	−1.45390	−	1.05632i	−0.0636963	−	0.0462781i	−0.619178	+	0.785251i	$0.712534\pi$
$522$	−17.0471	+	23.4633i	−0.746132	+	1.02696i
$523$	−15.4373	−	5.01588i	−0.675026	−	0.219329i	−0.0486094	−	0.998818i	$-0.515479\pi$
$523$	−15.4373	−	5.01588i	−0.675026	−	0.219329i	−0.626416	+	0.779489i	$0.715479\pi$
$524$	1.97630			0.0863352
$525$		0			0
$526$	−16.9353			−0.738414
$527$	−3.29079	−	1.06924i	−0.143349	−	0.0465769i
$528$	−48.3505	+	66.5488i	−2.10419	+	2.89616i
$529$	−18.4418	−	13.3987i	−0.801816	−	0.582554i
$530$		0			0
$531$	−38.6917	+	28.1112i	−1.67908	+	1.21992i
$532$			0.317741i			0.0137758i
$533$	−14.8600	−	20.4530i	−0.643657	−	0.885918i
$534$	2.83512	+	8.72560i	0.122688	+	0.377594i
$535$		0			0
$536$	−8.07446	+	24.8506i	−0.348763	+	1.07338i
$537$	−71.1187	+	23.1079i	−3.06900	+	0.997178i
$538$	42.9557	−	13.9572i	1.85195	−	0.601736i
$539$	−1.87462	+	5.76947i	−0.0807454	+	0.248509i
$540$		0			0
$541$	−10.2758	−	31.6256i	−0.441790	−	1.35969i	−0.885966	−	0.463751i	$-0.846503\pi$
$541$	−10.2758	−	31.6256i	−0.441790	−	1.35969i	0.444175	−	0.895940i	$-0.353497\pi$
$542$	−14.2722	−	19.6439i	−0.613042	−	0.843780i
$543$		−	44.4210i		−	1.90629i
$544$	−2.89344	+	2.10221i	−0.124055	+	0.0901314i
$545$		0			0
$546$	11.8827	+	8.63329i	0.508533	+	0.369471i
$547$	−0.426714	+	0.587322i	−0.0182450	+	0.0251121i	−0.818042	−	0.575158i	$-0.804940\pi$
$547$	−0.426714	+	0.587322i	−0.0182450	+	0.0251121i	0.799797	+	0.600270i	$0.204940\pi$
$548$	−2.16624	−	0.703853i	−0.0925371	−	0.0300671i
$549$	92.9483			3.96694
$550$		0			0
$551$	−4.52198			−0.192643
$552$	−3.55530	−	1.15519i	−0.151324	−	0.0491681i
$553$	2.02239	−	2.78358i	0.0860009	−	0.118370i
$554$	3.97011	+	2.88446i	0.168674	+	0.122549i
$555$		0			0
$556$	1.67756	−	1.21882i	0.0711444	−	0.0516894i
$557$			1.47906i			0.0626698i	0.999509	+	0.0313349i	$0.00997584\pi$
$557$			1.47906i			0.0626698i	−0.999509	+	0.0313349i	$0.990024\pi$
$558$	−6.53000	−	8.98778i	−0.276437	−	0.380483i
$559$	2.98608	+	9.19020i	0.126298	+	0.388704i
$560$		0			0
$561$	17.8179	−	54.8378i	0.752272	−	2.31525i
$562$	−25.7767	+	8.37535i	−1.08732	+	0.353293i
$563$	−27.1495	+	8.82141i	−1.14422	+	0.371778i	−0.818962	−	0.573848i	$-0.805450\pi$
$563$	−27.1495	+	8.82141i	−1.14422	+	0.371778i	−0.325254	+	0.945627i	$0.605450\pi$
$564$	−1.15001	+	3.53938i	−0.0484243	+	0.149035i
$565$		0			0
$566$	−3.16058	−	9.72725i	−0.132849	−	0.408867i
$567$	8.80843	+	12.1238i	0.369919	+	0.509150i
$568$		−	16.6867i		−	0.700160i
$569$	18.8462	−	13.6926i	0.790074	−	0.574023i	−0.117911	−	0.993024i	$-0.537620\pi$
$569$	18.8462	−	13.6926i	0.790074	−	0.574023i	0.907986	+	0.419002i	$0.137620\pi$
$570$		0			0
$571$	−13.8094	−	10.0331i	−0.577907	−	0.419874i	0.260062	−	0.965592i	$-0.416257\pi$
$571$	−13.8094	−	10.0331i	−0.577907	−	0.419874i	−0.837969	+	0.545718i	$0.816257\pi$
$572$	2.35409	−	3.24012i	0.0984292	−	0.135476i
$573$	47.7912	+	15.5283i	1.99651	+	0.648704i
$574$	11.7844			0.491870
$575$		0			0
$576$	46.4122			1.93384
$577$	36.2491	+	11.7780i	1.50907	+	0.490326i	0.942647	−	0.333790i	$-0.108328\pi$
$577$	36.2491	+	11.7780i	1.50907	+	0.490326i	0.566421	+	0.824116i	$0.308328\pi$
$578$	−6.64624	+	9.14777i	−0.276447	+	0.380497i
$579$	27.5466	+	20.0138i	1.14480	+	0.831744i
$580$		0			0
$581$	14.4959	−	10.5319i	0.601391	−	0.436936i
$582$		−	27.1996i		−	1.12746i
$583$	14.3580	+	19.7621i	0.594649	+	0.818465i
$584$	−2.08827	−	6.42704i	−0.0864134	−	0.265953i
$585$		0			0
$586$	−5.66888	+	17.4470i	−0.234179	+	0.720729i
$587$	−5.16075	+	1.67683i	−0.213007	+	0.0692101i	−0.413577	−	0.910469i	$-0.635721\pi$
$587$	−5.16075	+	1.67683i	−0.213007	+	0.0692101i	0.200570	+	0.979679i	$0.435721\pi$
$588$	−0.611092	+	0.198556i	−0.0252010	+	0.00818831i
$589$	0.535271	−	1.64739i	0.0220555	−	0.0678797i
$590$		0			0
$591$	−16.0409	−	49.3690i	−0.659836	−	2.03077i
$592$	−10.5454	−	14.5145i	−0.433414	−	0.596543i
$593$			34.6559i			1.42315i	0.702611	+	0.711574i	$0.252017\pi$
$593$			34.6559i			1.42315i	−0.702611	+	0.711574i	$0.747983\pi$
$594$	81.9212	−	59.5192i	3.36127	−	2.44210i
$595$		0			0
$596$	0.838229	+	0.609009i	0.0343352	+	0.0249460i
$597$	−7.06068	+	9.71819i	−0.288974	+	0.397739i
$598$	2.03753	+	0.662033i	0.0833208	+	0.0270726i
$599$	−11.7104			−0.478476			−0.239238	−	0.970961i	$-0.576898\pi$
$599$	−11.7104			−0.478476			−0.239238	+	0.970961i	$0.576898\pi$
$600$		0			0
$601$	−3.86935			−0.157834			−0.0789170	−	0.996881i	$-0.525146\pi$
$601$	−3.86935			−0.157834			−0.0789170	+	0.996881i	$0.525146\pi$
$602$	−4.28383	−	1.39190i	−0.174596	−	0.0567296i
$603$	38.1842	−	52.5560i	1.55498	−	2.14025i
$604$	1.63825	+	1.19026i	0.0666593	+	0.0484308i
$605$		0			0
$606$	32.1125	−	23.3311i	1.30448	−	0.947760i
$607$			21.5901i			0.876316i	0.898898	+	0.438158i	$0.144369\pi$
$607$			21.5901i			0.876316i	−0.898898	+	0.438158i	$0.855631\pi$
$608$	−1.05238	−	1.44848i	−0.0426797	−	0.0587435i
$609$	−2.82578	−	8.69687i	−0.114507	−	0.352415i
$610$		0			0
$611$	−5.70441	+	17.5564i	−0.230776	+	0.710254i
$612$	3.99739	−	1.29883i	0.161585	−	0.0525021i
$613$	−12.0634	+	3.91962i	−0.487234	+	0.158312i	−0.542324	−	0.840169i	$-0.682455\pi$
$613$	−12.0634	+	3.91962i	−0.487234	+	0.158312i	0.0550898	+	0.998481i	$0.482455\pi$
$614$	0.909337	−	2.79865i	0.0366979	−	0.112944i
$615$		0			0
$616$	−4.99314	−	15.3673i	−0.201179	−	0.619166i
$617$	27.2970	+	37.5711i	1.09893	+	1.51255i	0.836789	+	0.547526i	$0.184430\pi$
$617$	27.2970	+	37.5711i	1.09893	+	1.51255i	0.262146	+	0.965028i	$0.415570\pi$
$618$			14.4073i			0.579545i
$619$	−5.59826	+	4.06737i	−0.225013	+	0.163481i	−0.694580	−	0.719415i	$-0.744410\pi$
$619$	−5.59826	+	4.06737i	−0.225013	+	0.163481i	0.469567	+	0.882897i	$0.344410\pi$
$620$		0			0
$621$	4.11269	+	2.98804i	0.165037	+	0.119906i
$622$	−14.9885	+	20.6299i	−0.600983	+	0.827183i
$623$	−1.89341	−	0.615208i	−0.0758580	−	0.0246478i
$624$	−43.2176			−1.73009
$625$		0			0
$626$	14.3507			0.573570
$627$	27.4522	+	8.91977i	1.09634	+	0.356221i
$628$	−0.0104298	+	0.0143554i	−0.000416194	+	0.000572842i
$629$	10.1741	+	7.39189i	0.405666	+	0.294734i
$630$		0			0
$631$	8.02227	−	5.82852i	0.319361	−	0.232030i	−0.416542	−	0.909117i	$-0.636758\pi$
$631$	8.02227	−	5.82852i	0.319361	−	0.232030i	0.735903	+	0.677087i	$0.236758\pi$
$632$			9.16448i			0.364544i
$633$	−21.2278	−	29.2176i	−0.843729	−	1.16129i
$634$	2.12964	+	6.55436i	0.0845789	+	0.260307i
$635$		0			0
$636$	−0.799520	+	2.46067i	−0.0317030	+	0.0975719i
$637$	−3.03120	+	0.984896i	−0.120100	+	0.0390230i
$638$	−25.2681	+	8.21011i	−1.00037	+	0.325042i
$639$	−12.8200	+	39.4558i	−0.507151	+	1.56085i
$640$		0			0
$641$	−2.46654	−	7.59123i	−0.0974225	−	0.299836i	0.890455	−	0.455071i	$-0.150386\pi$
$641$	−2.46654	−	7.59123i	−0.0974225	−	0.299836i	−0.987877	+	0.155236i	$0.950386\pi$
$642$	34.6203	+	47.6507i	1.36635	+	1.88062i
$643$			36.4821i			1.43871i	0.694641	+	0.719356i	$0.255563\pi$
$643$			36.4821i			1.43871i	−0.694641	+	0.719356i	$0.744437\pi$
$644$	−0.0758225	+	0.0550883i	−0.00298782	+	0.00217078i
$645$		0			0
$646$	5.64922	+	4.10440i	0.222266	+	0.161486i
$647$	−27.3706	+	37.6725i	−1.07605	+	1.48106i	−0.212256	+	0.977214i	$0.568081\pi$
$647$	−27.3706	+	37.6725i	−1.07605	+	1.48106i	−0.863795	+	0.503843i	$0.831919\pi$
$648$	−37.9618	−	12.3345i	−1.49128	−	0.484547i
$649$	−43.8122			−1.71978
$650$		0			0
$651$	3.50283			0.137287
$652$	0.763843	+	0.248188i	0.0299144	+	0.00971978i
$653$	26.9223	−	37.0553i	1.05355	−	1.45009i	0.167860	−	0.985811i	$-0.446314\pi$
$653$	26.9223	−	37.0553i	1.05355	−	1.45009i	0.885690	−	0.464277i	$-0.153686\pi$
$654$	−52.3628	−	38.0438i	−2.04755	−	1.48763i
$655$		0			0
$656$	−28.0522	+	20.3811i	−1.09526	+	0.795749i
$657$			16.8011i			0.655475i
$658$	−5.05771	−	6.96134i	−0.197170	−	0.271381i
$659$	12.0854	+	37.1951i	0.470781	+	1.44892i	0.851564	+	0.524251i	$0.175655\pi$
$659$	12.0854	+	37.1951i	0.470781	+	1.44892i	−0.380782	+	0.924665i	$0.624345\pi$
$660$		0			0
$661$	3.79585	−	11.6824i	0.147641	−	0.454394i	−0.849700	−	0.527267i	$-0.823217\pi$
$661$	3.79585	−	11.6824i	0.147641	−	0.454394i	0.997341	+	0.0728732i	$0.0232168\pi$
$662$	6.34923	−	2.06299i	0.246770	−	0.0801804i
$663$	28.8110	−	9.36126i	1.11893	−	0.363561i
$664$	−14.7479	+	45.3894i	−0.572330	+	1.76145i
$665$		0			0
$666$	12.4773	+	38.4011i	0.483485	+	1.48801i
$667$	−0.783999	−	1.07908i	−0.0303565	−	0.0417822i
$668$		−	2.62341i		−	0.101503i
$669$	52.4965	−	38.1409i	2.02963	−	1.47461i
$670$		0			0
$671$	68.8865	+	50.0490i	2.65933	+	1.93212i
$672$	2.12814	−	2.92914i	0.0820949	−	0.112994i
$673$	−47.1398	−	15.3166i	−1.81711	−	0.590413i	−0.999901	−	0.0140655i	$-0.995523\pi$
$673$	−47.1398	−	15.3166i	−1.81711	−	0.590413i	−0.817204	−	0.576348i	$-0.804477\pi$
$674$	32.9242			1.26819
$675$		0			0
$676$	−0.588658			−0.0226407
$677$	36.1845	+	11.7570i	1.39068	+	0.451860i	0.906166	−	0.422922i	$-0.138996\pi$
$677$	36.1845	+	11.7570i	1.39068	+	0.451860i	0.484516	+	0.874782i	$0.338996\pi$
$678$	−4.95521	+	6.82026i	−0.190304	+	0.261931i
$679$	4.77497	+	3.46922i	0.183247	+	0.133137i
$680$		0			0
$681$	−2.45717	+	1.78524i	−0.0941588	+	0.0684104i
$682$		−	10.1772i		−	0.389706i
$683$	20.9049	+	28.7731i	0.799903	+	1.10097i	0.992804	+	0.119754i	$0.0382105\pi$
$683$	20.9049	+	28.7731i	0.799903	+	1.10097i	−0.192901	+	0.981218i	$0.561790\pi$
$684$	0.650204	+	2.00112i	0.0248612	+	0.0765149i
$685$		0			0
$686$	0.459090	−	1.41293i	0.0175281	−	0.0539460i
$687$	19.0615	−	6.19346i	0.727242	−	0.236295i
$688$	12.6048	−	4.09554i	0.480553	−	0.156141i
$689$	−3.96586	+	12.2056i	−0.151087	+	0.464998i
$690$		0			0
$691$	1.11438	+	3.42969i	0.0423928	+	0.130472i	0.970013	−	0.243053i	$-0.0781490\pi$
$691$	1.11438	+	3.42969i	0.0423928	+	0.130472i	−0.927620	+	0.373525i	$0.878149\pi$
$692$	1.09912	+	1.51281i	0.0417824	+	0.0575086i
$693$			40.1721i			1.52601i
$694$	10.8997	−	7.91912i	0.413748	−	0.300606i
$695$		0			0
$696$	19.7050	+	14.3165i	0.746914	+	0.542665i
$697$	14.2863	−	19.6634i	0.541132	−	0.744804i
$698$	17.2239	+	5.59640i	0.651936	+	0.211827i
$699$	−51.2023			−1.93665
$700$		0			0
$701$	−14.5633			−0.550048			−0.275024	−	0.961437i	$-0.588686\pi$
$701$	−14.5633			−0.550048			−0.275024	+	0.961437i	$0.588686\pi$
$702$	50.5968	+	16.4399i	1.90965	+	0.620484i
$703$	−3.70044	+	5.09321i	−0.139565	+	0.192094i
$704$	34.3973	+	24.9911i	1.29640	+	0.941888i
$705$		0			0
$706$	25.2243	−	18.3266i	0.949330	−	0.689729i
$707$			8.61324i			0.323934i
$708$	−2.72763	−	3.75425i	−0.102510	−	0.141094i
$709$	−0.328661	−	1.01151i	−0.0123431	−	0.0379882i	0.944695	−	0.327949i	$-0.106358\pi$
$709$	−0.328661	−	1.01151i	−0.0123431	−	0.0379882i	−0.957038	+	0.289961i	$0.906358\pi$
$710$		0			0
$711$	7.04083	−	21.6695i	0.264052	−	0.812668i
$712$	5.04321	−	1.63864i	0.189002	−	0.0614105i
$713$	0.485921	−	0.157885i	0.0181979	−	0.00591285i
$714$	−4.36356	+	13.4297i	−0.163302	+	0.502593i
$715$		0			0
$716$	−1.54309	−	4.74914i	−0.0576679	−	0.177484i
$717$	−40.1595	−	55.2748i	−1.49978	−	2.06427i
$718$			21.7904i			0.813209i
$719$	22.5531	−	16.3858i	0.841089	−	0.611087i	−0.0815860	−	0.996666i	$-0.525999\pi$
$719$	22.5531	−	16.3858i	0.841089	−	0.611087i	0.922675	+	0.385580i	$0.125999\pi$
$720$		0			0
$721$	−2.52924	−	1.83760i	−0.0941937	−	0.0684358i
$722$	14.5369	−	20.0083i	0.541006	−	0.744631i
$723$	44.5786	+	14.4845i	1.65790	+	0.538683i
$724$	2.96633			0.110243
$725$		0			0
$726$	118.901			4.41284
$727$	−23.2952	−	7.56907i	−0.863971	−	0.280721i	−0.156685	−	0.987649i	$-0.550081\pi$
$727$	−23.2952	−	7.56907i	−0.863971	−	0.280721i	−0.707286	+	0.706928i	$0.750081\pi$
$728$	4.98985	−	6.86794i	0.184936	−	0.254543i
$729$	−4.30312	−	3.12640i	−0.159375	−	0.115793i
$730$		0			0
$731$	−7.51585	+	5.46058i	−0.277984	+	0.201967i
$732$			9.01877i			0.333343i
$733$	0.530531	+	0.730214i	0.0195956	+	0.0269711i	0.818702	−	0.574218i	$-0.194694\pi$
$733$	0.530531	+	0.730214i	0.0195956	+	0.0269711i	−0.799107	+	0.601189i	$0.794694\pi$
$734$	−10.1527	−	31.2468i	−0.374743	−	1.15334i
$735$		0			0
$736$	0.163194	−	0.502260i	0.00601541	−	0.0185135i
$737$	56.5986	−	18.3900i	2.08484	−	0.677405i
$738$	74.2178	−	24.1148i	2.73199	−	0.887679i
$739$	−11.2221	+	34.5379i	−0.412810	+	1.27050i	0.501385	+	0.865224i	$0.332824\pi$
$739$	−11.2221	+	34.5379i	−0.412810	+	1.27050i	−0.914195	+	0.405274i	$0.867176\pi$
$740$		0			0
$741$	4.68632	+	14.4230i	0.172156	+	0.529842i
$742$	−3.51626	−	4.83971i	−0.129086	−	0.177671i
$743$			41.5345i			1.52375i	0.647723	+	0.761876i	$0.275722\pi$
$743$			41.5345i			1.52375i	−0.647723	+	0.761876i	$0.724278\pi$
$744$	−7.54811	+	5.48402i	−0.276727	+	0.201054i
$745$		0			0
$746$	36.9006	+	26.8098i	1.35103	+	0.981578i
$747$	69.7431	−	95.9931i	2.55176	−	3.51220i
$748$	3.66194	+	1.18984i	0.133894	+	0.0435047i
$749$	−12.7809			−0.467005
$750$		0			0
$751$	−20.1947			−0.736916			−0.368458	−	0.929644i	$-0.620114\pi$
$751$	−20.1947			−0.736916			−0.368458	+	0.929644i	$0.620114\pi$
$752$	24.0793	+	7.82385i	0.878083	+	0.285306i
$753$	38.2530	−	52.6507i	1.39402	−	1.91870i
$754$	−11.2928	−	8.20472i	−0.411260	−	0.298798i
$755$		0			0
$756$	−1.88286	+	1.36797i	−0.0684788	+	0.0497528i
$757$			35.1781i			1.27857i	0.768969	+	0.639286i	$0.220770\pi$
$757$			35.1781i			1.27857i	−0.768969	+	0.639286i	$0.779230\pi$
$758$	−31.4111	−	43.2337i	−1.14090	−	1.57032i
$759$	2.63100	+	8.09740i	0.0954994	+	0.293917i
$760$		0			0
$761$	4.54431	−	13.9859i	0.164731	−	0.506990i	−0.834285	−	0.551333i	$-0.814119\pi$
$761$	4.54431	−	13.9859i	0.164731	−	0.506990i	0.999016	+	0.0443428i	$0.0141194\pi$
$762$	−48.9833	+	15.9156i	−1.77448	+	0.576562i
$763$	13.3574	−	4.34008i	0.483570	−	0.157122i
$764$	−1.03694	+	3.19138i	−0.0375153	+	0.115460i
$765$		0			0
$766$	0.664978	+	2.04659i	0.0240266	+	0.0739464i
$767$	−13.5298	−	18.6222i	−0.488534	−	0.672409i
$768$			15.2613i			0.550693i
$769$	−19.9219	+	14.4741i	−0.718403	+	0.521950i	−0.885873	−	0.463927i	$-0.846440\pi$
$769$	−19.9219	+	14.4741i	−0.718403	+	0.521950i	0.167471	+	0.985877i	$0.446440\pi$
$770$		0			0
$771$	−49.1038	−	35.6760i	−1.76843	−	1.28484i
$772$	−1.33647	+	1.83950i	−0.0481007	+	0.0662050i
$773$	−3.92805	−	1.27630i	−0.141282	−	0.0459054i	0.237522	−	0.971382i	$-0.423665\pi$
$773$	−3.92805	−	1.27630i	−0.141282	−	0.0459054i	−0.378805	+	0.925477i	$0.623665\pi$
$774$	−29.8278			−1.07214
$775$		0			0
$776$	−15.7208			−0.564344
$777$	−12.1079	−	3.93409i	−0.434368	−	0.141135i
$778$	−0.0419671	+	0.0577628i	−0.00150459	+	0.00207090i
$779$	9.84365	+	7.15183i	0.352685	+	0.256241i
$780$		0			0
$781$	−30.7466	+	22.3387i	−1.10020	+	0.799343i
$782$			2.05968i			0.0736539i
$783$	−19.4686	−	26.7962i	−0.695750	−	0.957618i
$784$	1.35083	+	4.15742i	0.0482439	+	0.148479i
$785$		0			0
$786$	−13.5869	+	41.8161i	−0.484628	+	1.49153i
$787$	−8.19872	+	2.66392i	−0.292253	+	0.0949586i	−0.451474	−	0.892284i	$-0.649102\pi$
$787$	−8.19872	+	2.66392i	−0.292253	+	0.0949586i	0.159221	+	0.987243i	$0.449102\pi$
$788$	3.29674	−	1.07118i	0.117442	−	0.0381591i
$789$	10.9268	−	33.6294i	0.389006	−	1.19724i
$790$		0			0
$791$	−0.565296	−	1.73980i	−0.0200996	−	0.0618603i
$792$	−62.8933	−	86.5653i	−2.23482	−	3.07596i
$793$			44.7357i			1.58861i
$794$	−6.66607	+	4.84319i	−0.236570	+	0.171878i
$795$		0			0
$796$	−0.648958	−	0.471496i	−0.0230017	−	0.0167117i
$797$	24.2443	−	33.3694i	0.858777	−	1.18201i	−0.123082	−	0.992396i	$-0.539278\pi$
$797$	24.2443	−	33.3694i	0.858777	−	1.18201i	0.981860	−	0.189609i	$-0.0607220\pi$
$798$	−6.72300	−	2.18443i	−0.237991	−	0.0773281i
$799$	−17.7472			−0.627850
$800$		0			0
$801$	−13.1836			−0.465820
$802$	4.44670	+	1.44482i	0.157018	+	0.0510184i
$803$	−9.04674	+	12.4518i	−0.319253	+	0.439414i
$804$	5.09950	+	3.70501i	0.179846	+	0.130665i
$805$		0			0
$806$	4.32579	−	3.14287i	0.152369	−	0.110703i
$807$			94.3049i			3.31969i
$808$	−13.4849	−	18.5603i	−0.474395	−	0.652949i
$809$	−1.49942	−	4.61474i	−0.0527168	−	0.162246i	0.921232	−	0.389014i	$-0.127184\pi$
$809$	−1.49942	−	4.61474i	−0.0527168	−	0.162246i	−0.973949	+	0.226768i	$0.927184\pi$
$810$		0			0
$811$	5.88322	−	18.1067i	0.206588	−	0.635811i	−0.793057	−	0.609148i	$-0.791512\pi$
$811$	5.88322	−	18.1067i	0.206588	−	0.635811i	0.999644	−	0.0266637i	$-0.00848833\pi$
$812$	0.580756	−	0.188699i	0.0203806	−	0.00662204i
$813$	48.2167	−	15.6665i	1.69103	−	0.549450i
$814$	−11.4302	+	35.1786i	−0.400629	+	1.23301i
$815$		0			0
$816$	−12.8394	−	39.5156i	−0.449469	−	1.38332i
$817$	−2.73361	−	3.76249i	−0.0956369	−	0.131633i
$818$			14.2944i			0.499791i
$819$	−17.0750	+	12.4057i	−0.596648	+	0.433490i
$820$		0			0
$821$	0.896336	+	0.651226i	0.0312823	+	0.0227279i	0.603317	−	0.797502i	$-0.293846\pi$
$821$	0.896336	+	0.651226i	0.0312823	+	0.0227279i	−0.572034	+	0.820230i	$0.693846\pi$
$822$	29.7853	−	40.9960i	1.03888	−	1.42990i
$823$	−9.77872	−	3.17730i	−0.340865	−	0.110754i	0.133582	−	0.991038i	$-0.457352\pi$
$823$	−9.77872	−	3.17730i	−0.340865	−	0.110754i	−0.474447	+	0.880284i	$0.657352\pi$
$824$	8.32709			0.290088
$825$		0			0
$826$	10.7295			0.373328
$827$	−42.8841	−	13.9339i	−1.49122	−	0.484528i	−0.553780	−	0.832663i	$-0.686815\pi$
$827$	−42.8841	−	13.9339i	−1.49122	−	0.484528i	−0.937445	+	0.348135i	$0.886815\pi$
$828$	−0.364799	+	0.502103i	−0.0126777	+	0.0174493i
$829$	−1.48372	−	1.07799i	−0.0515319	−	0.0374401i	0.561721	−	0.827327i	$-0.310139\pi$
$829$	−1.48372	−	1.07799i	−0.0515319	−	0.0374401i	−0.613253	+	0.789887i	$0.710139\pi$
$830$		0			0
$831$	−8.28939	+	6.02260i	−0.287556	+	0.208922i
$832$			22.3380i			0.774432i
$833$	−1.80106	−	2.47895i	−0.0624030	−	0.0858904i
$834$	14.2556	+	43.8743i	0.493632	+	1.51924i
$835$		0			0
$836$	−0.595641	+	1.83320i	−0.0206007	+	0.0634024i
$837$	12.0666	−	3.92067i	0.417082	−	0.135518i
$838$	23.9366	−	7.77746i	0.826875	−	0.268668i
$839$	−2.21596	+	6.82004i	−0.0765036	+	0.235454i	−0.981994	−	0.188913i	$-0.939503\pi$
$839$	−2.21596	+	6.82004i	−0.0765036	+	0.235454i	0.905490	+	0.424367i	$0.139503\pi$
$840$		0			0
$841$	−6.27599	−	19.3155i	−0.216413	−	0.666052i
$842$	1.17373	+	1.61551i	0.0404496	+	0.0556741i
$843$		−	56.5901i		−	1.94907i
$844$	1.95108	−	1.41754i	0.0671589	−	0.0487938i
$845$		0			0
$846$	−46.0986	−	33.4926i	−1.58490	−	1.15150i
$847$	−15.1655	+	20.8735i	−0.521091	+	0.717220i
$848$	16.7406	+	5.43935i	0.574875	+	0.186788i
$849$	21.3552			0.732908
$850$		0			0
$851$	−1.85696			−0.0636557
$852$	−3.82840	−	1.24392i	−0.131159	−	0.0426160i
$853$	−15.9584	+	21.9649i	−0.546406	+	0.752063i	−0.989519	−	0.144403i	$-0.953874\pi$
$853$	−15.9584	+	21.9649i	−0.546406	+	0.752063i	0.443113	+	0.896466i	$0.353874\pi$
$854$	−16.8702	−	12.2569i	−0.577285	−	0.419422i
$855$		0			0
$856$	27.5411	−	20.0098i	0.941335	−	0.683920i
$857$		−	27.1198i		−	0.926394i	−0.886255	−	0.463197i	$-0.846702\pi$
$857$		−	27.1198i		−	0.926394i	0.886255	−	0.463197i	$-0.153298\pi$
$858$	52.3728	+	72.0850i	1.78798	+	2.46094i
$859$	−13.7841	−	42.4230i	−0.470306	−	1.44745i	−0.852185	−	0.523240i	$-0.824723\pi$
$859$	−13.7841	−	42.4230i	−0.470306	−	1.44745i	0.381879	−	0.924212i	$-0.375277\pi$
$860$		0			0
$861$	−7.60341	+	23.4009i	−0.259124	+	0.797501i
$862$	−47.9408	+	15.5769i	−1.63287	+	0.530551i
$863$	−39.3313	+	12.7795i	−1.33885	+	0.435020i	−0.888929	−	0.458046i	$-0.848550\pi$
$863$	−39.3313	+	12.7795i	−1.33885	+	0.435020i	−0.449926	+	0.893066i	$0.648550\pi$
$864$	4.05251	−	12.4723i	0.137869	−	0.424317i
$865$		0			0
$866$	−7.45367	−	22.9400i	−0.253286	−	0.779534i
$867$	−13.8770	−	19.1001i	−0.471288	−	0.648672i
$868$			0.233911i			0.00793945i
$869$	16.8863	−	12.2686i	0.572828	−	0.416184i
$870$		0			0
$871$	25.2950	+	18.3779i	0.857090	+	0.622712i
$872$	−21.9885	+	30.2646i	−0.744624	+	1.02489i
$873$	37.1719	+	12.0779i	1.25808	+	0.408774i
$874$	−1.03109			−0.0348771
$875$		0			0
$876$	−1.63021			−0.0550798
$877$	−35.7142	−	11.6042i	−1.20598	−	0.391847i	−0.364024	−	0.931390i	$-0.618597\pi$
$877$	−35.7142	−	11.6042i	−1.20598	−	0.391847i	−0.841959	+	0.539542i	$0.818597\pi$
$878$	−3.53487	+	4.86533i	−0.119296	+	0.164197i
$879$	−30.9879	−	22.5140i	−1.04520	−	0.759379i
$880$		0			0
$881$	−42.9348	+	31.1940i	−1.44651	+	1.05095i	−0.459880	+	0.887981i	$0.652108\pi$
$881$	−42.9348	+	31.1940i	−1.44651	+	1.05095i	−0.986631	+	0.162971i	$0.947892\pi$
$882$		−	9.83807i		−	0.331265i
$883$	−13.2737	−	18.2696i	−0.446694	−	0.614821i	0.524989	−	0.851109i	$-0.324069\pi$
$883$	−13.2737	−	18.2696i	−0.446694	−	0.614821i	−0.971683	+	0.236287i	$0.924069\pi$
$884$	0.625123	+	1.92393i	0.0210252	+	0.0647088i
$885$		0			0
$886$	8.32400	−	25.6186i	0.279650	−	0.860675i
$887$	−31.6943	+	10.2981i	−1.06419	+	0.345777i	−0.788223	−	0.615390i	$-0.788999\pi$
$887$	−31.6943	+	10.2981i	−1.06419	+	0.345777i	−0.275969	+	0.961167i	$0.588999\pi$
$888$	32.2500	−	10.4787i	1.08224	−	0.351641i
$889$	3.45362	−	10.6291i	0.115831	−	0.356490i
$890$		0			0
$891$	28.0926	+	86.4601i	0.941137	+	2.89652i
$892$	2.54696	+	3.50559i	0.0852786	+	0.117376i
$893$		−	8.88438i		−	0.297304i
$894$	−18.6486	+	13.5490i	−0.623703	+	0.453147i
$895$		0			0
$896$	−10.3124	−	7.49241i	−0.344514	−	0.250304i
$897$	−2.62927	+	3.61888i	−0.0877889	+	0.120831i
$898$	−41.3391	−	13.4319i	−1.37950	−	0.448227i
$899$	−3.32894			−0.111027
$900$		0			0
$901$	−12.3383			−0.411049
$902$	67.9896	+	22.0912i	2.26381	+	0.735556i
$903$	5.52795	−	7.60857i	0.183959	−	0.253197i
$904$	3.94196	+	2.86400i	0.131108	+	0.0952554i
$905$		0			0
$906$	−36.4471	+	26.4804i	−1.21088	+	0.879752i
$907$		−	44.1113i		−	1.46469i	−0.680932	−	0.732347i	$-0.738425\pi$
$907$		−	44.1113i		−	1.46469i	0.680932	−	0.732347i	$-0.261575\pi$
$908$	−0.119214	−	0.164084i	−0.00395625	−	0.00544531i
$909$	17.6256	+	54.2460i	0.584604	+	1.79923i
$910$		0			0
$911$	17.4185	−	53.6085i	0.577100	−	1.77613i	−0.0518160	−	0.998657i	$-0.516501\pi$
$911$	17.4185	−	53.6085i	0.577100	−	1.77613i	0.628916	−	0.777474i	$-0.283499\pi$
$912$	19.7818	−	6.42750i	0.655041	−	0.212836i
$913$	103.377	−	33.5892i	3.42128	−	1.11164i
$914$	−9.14586	+	28.1481i	−0.302518	+	0.931055i
$915$		0			0
$916$	0.413585	+	1.27288i	0.0136652	+	0.0420572i
$917$	−5.60798	−	7.71872i	−0.185192	−	0.254895i
$918$			51.1467i			1.68809i
$919$	−9.15281	+	6.64991i	−0.301923	+	0.219360i	−0.728423	−	0.685127i	$-0.759747\pi$
$919$	−9.15281	+	6.64991i	−0.301923	+	0.219360i	0.426500	+	0.904488i	$0.359747\pi$
$920$		0			0
$921$	4.97073	+	3.61144i	0.163791	+	0.119001i
$922$	28.1708	−	38.7738i	0.927757	−	1.27695i
$923$	−18.9900	−	6.17021i	−0.625062	−	0.203095i
$924$	−3.89790			−0.128231
$925$		0			0
$926$	−45.3967			−1.49183
$927$	−19.6894	−	6.39749i	−0.646686	−	0.210121i
$928$	−2.02250	+	2.78373i	−0.0663918	+	0.0913804i
$929$	−28.9782	−	21.0539i	−0.950745	−	0.690757i	0.000237801	−	1.00000i	$-0.499924\pi$
$929$	−28.9782	−	21.0539i	−0.950745	−	0.690757i	−0.950983	+	0.309243i	$0.899924\pi$
$930$		0			0
$931$	1.24098	−	0.901624i	0.0406714	−	0.0295495i
$932$		−	3.41917i		−	0.111999i
$933$	−31.2952	−	43.0741i	−1.02456	−	1.41018i
$934$	5.18990	+	15.9729i	0.169819	+	0.522649i
$935$		0			0
$936$	17.3719	−	53.4651i	0.567817	−	1.74756i
$937$	48.3373	−	15.7057i	1.57911	−	0.513084i	0.617283	−	0.786741i	$-0.288233\pi$
$937$	48.3373	−	15.7057i	1.57911	−	0.513084i	0.961827	+	0.273657i	$0.0882334\pi$
$938$	−13.8609	+	4.50368i	−0.452574	+	0.147050i
$939$	−9.25924	+	28.4970i	−0.302164	+	0.929965i
$940$		0			0
$941$	3.88216	+	11.9481i	0.126555	+	0.389496i	0.994181	−	0.107721i	$-0.0343554\pi$
$941$	3.88216	+	11.9481i	0.126555	+	0.389496i	−0.867626	+	0.497217i	$0.834355\pi$
$942$	−0.232038	−	0.319373i	−0.00756021	−	0.0104057i
$943$			3.58894i			0.116872i
$944$	−25.5412	+	18.5568i	−0.831295	+	0.603971i
$945$		0			0
$946$	−22.1062	−	16.0611i	−0.718733	−	0.522190i
$947$	14.9939	−	20.6373i	0.487236	−	0.670623i	−0.492639	−	0.870234i	$-0.663968\pi$
$947$	14.9939	−	20.6373i	0.487236	−	0.670623i	0.979875	+	0.199611i	$0.0639677\pi$
$948$	2.10259	+	0.683171i	0.0682888	+	0.0221884i
$949$	−8.08633			−0.262493
$950$		0			0
$951$	−14.3894			−0.466610
$952$	7.76206	+	2.52205i	0.251570	+	0.0817400i
$953$	−7.36077	+	10.1312i	−0.238439	+	0.328183i	−0.911420	−	0.411476i	$-0.865013\pi$
$953$	−7.36077	+	10.1312i	−0.238439	+	0.328183i	0.672982	+	0.739659i	$0.265013\pi$
$954$	−32.0490	−	23.2850i	−1.03762	−	0.753878i
$955$		0			0
$956$	3.69112	−	2.68176i	0.119379	−	0.0867342i
$957$		−	55.4736i		−	1.79321i
$958$	12.2299	+	16.8330i	0.395130	+	0.543850i
$959$	3.39795	+	10.4578i	0.109725	+	0.337700i
$960$		0			0
$961$	−9.18548	+	28.2700i	−0.296306	+	0.911935i
$962$	−18.4823	+	6.00527i	−0.595894	+	0.193618i
$963$	−80.4940	+	26.1541i	−2.59388	+	0.842803i
$964$	−0.967239	+	2.97686i	−0.0311527	+	0.0958781i
$965$		0			0
$966$	−0.644328	−	1.98304i	−0.0207309	−	0.0638031i
$967$	33.0486	+	45.4875i	1.06277	+	1.46278i	0.877186	+	0.480151i	$0.159418\pi$
$967$	33.0486	+	45.4875i	1.06277	+	1.46278i	0.185586	+	0.982628i	$0.440582\pi$
$968$		−	68.7223i		−	2.20882i
$969$	−11.7953	+	8.56978i	−0.378919	+	0.275301i
$970$		0			0
$971$	−8.84079	−	6.42321i	−0.283714	−	0.206131i	0.436822	−	0.899548i	$-0.356104\pi$
$971$	−8.84079	−	6.42321i	−0.283714	−	0.206131i	−0.720536	+	0.693418i	$0.756104\pi$
$972$	−1.55584	+	2.14144i	−0.0499037	+	0.0686866i
$973$	−9.52052	−	3.09341i	−0.305214	−	0.0991700i
$974$	−3.58090			−0.114739
$975$		0			0
$976$	61.3571			1.96399
$977$	−33.8381	−	10.9947i	−1.08258	−	0.351750i	−0.287202	−	0.957870i	$-0.592725\pi$
$977$	−33.8381	−	10.9947i	−1.08258	−	0.351750i	−0.795373	+	0.606120i	$0.792725\pi$
$978$	−10.5027	+	14.4557i	−0.335839	+	0.462243i
$979$	−9.77073	−	7.09885i	−0.312274	−	0.226880i
$980$		0			0
$981$	75.2434	−	54.6675i	2.40234	−	1.74540i
$982$		−	56.2981i		−	1.79654i
$983$	3.53843	+	4.87023i	0.112858	+	0.155336i	0.861709	−	0.507402i	$-0.169394\pi$
$983$	3.53843	+	4.87023i	0.112858	+	0.155336i	−0.748851	+	0.662738i	$0.769394\pi$
$984$	−20.2521	−	62.3295i	−0.645613	−	1.98699i
$985$		0			0
$986$	4.14695	−	12.7630i	0.132066	−	0.406457i
$987$	17.0868	−	5.55184i	0.543879	−	0.176717i
$988$	−0.963134	+	0.312941i	−0.0306414	+	0.00995599i
$989$	0.423904	−	1.30464i	0.0134794	−	0.0414853i
$990$		0			0
$991$	10.3209	+	31.7645i	0.327854	+	1.00903i	0.970136	+	0.242563i	$0.0779881\pi$
$991$	10.3209	+	31.7645i	0.327854	+	1.00903i	−0.642281	+	0.766469i	$0.722012\pi$
$992$	−0.774731	−	1.06633i	−0.0245977	−	0.0338559i
$993$			13.9391i			0.442344i
$994$	7.52979	−	5.47071i	0.238830	−	0.173520i
$995$		0			0
$996$	9.31420	+	6.76716i	0.295132	+	0.214426i
$997$	17.9932	−	24.7655i	0.569850	−	0.784332i	−0.422687	−	0.906276i	$-0.638913\pi$
$997$	17.9932	−	24.7655i	0.569850	−	0.784332i	0.992537	+	0.121944i	$0.0389129\pi$
$998$	5.36921	+	1.74456i	0.169959	+	0.0552231i
$999$	−46.1127			−1.45894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.n.b.274.5		56
5.2	odd	4		875.2.h.b.351.6		28
5.3	odd	4		175.2.h.b.71.2	✓	28
5.4	even	2	inner	875.2.n.b.274.10		56
25.6	even	5	inner	875.2.n.b.99.10		56
25.8	odd	20		175.2.h.b.106.2	yes	28
25.12	odd	20		4375.2.a.h.1.11		14
25.13	odd	20		4375.2.a.g.1.4		14
25.17	odd	20		875.2.h.b.526.6		28
25.19	even	10	inner	875.2.n.b.99.5		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.h.b.71.2	✓	28	5.3	odd	4
175.2.h.b.106.2	yes	28	25.8	odd	20
875.2.h.b.351.6		28	5.2	odd	4
875.2.h.b.526.6		28	25.17	odd	20
875.2.n.b.99.5		56	25.19	even	10	inner
875.2.n.b.99.10		56	25.6	even	5	inner
875.2.n.b.274.5		56	1.1	even	1	trivial
875.2.n.b.274.10		56	5.4	even	2	inner
4375.2.a.g.1.4		14	25.13	odd	20
4375.2.a.h.1.11		14	25.12	odd	20

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.n (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41293 - 0.459090i) q^{2} +(1.82328 - 2.50953i) q^{3} +(0.167580 + 0.121754i) q^{4} +(-3.72827 + 2.70875i) q^{6} -1.00000i q^{7} +(1.56560 + 2.15486i) q^{8} +(-2.04634 - 6.29798i) q^{9} +O(q^{10})\)	\(q+(-1.41293 - 0.459090i) q^{2} +(1.82328 - 2.50953i) q^{3} +(0.167580 + 0.121754i) q^{4} +(-3.72827 + 2.70875i) q^{6} -1.00000i q^{7} +(1.56560 + 2.15486i) q^{8} +(-2.04634 - 6.29798i) q^{9} +(1.87462 - 5.76947i) q^{11} +(0.611092 - 0.198556i) q^{12} +(3.03120 - 0.984896i) q^{13} +(-0.459090 + 1.41293i) q^{14} +(-1.35083 - 4.15742i) q^{16} +(1.80106 + 2.47895i) q^{17} +9.83807i q^{18} +(-1.24098 + 0.901624i) q^{19} +(-2.50953 - 1.82328i) q^{21} +(-5.29741 + 7.29126i) q^{22} +(-0.430310 - 0.139816i) q^{23} +8.26220 q^{24} -4.73503 q^{26} +(-10.6856 - 3.47197i) q^{27} +(0.121754 - 0.167580i) q^{28} +(2.38495 + 1.73277i) q^{29} +(-0.913571 + 0.663748i) q^{31} +1.16721i q^{32} +(-11.0607 - 15.2238i) q^{33} +(-1.40672 - 4.32943i) q^{34} +(0.423880 - 1.30457i) q^{36} +(3.90332 - 1.26826i) q^{37} +(2.16735 - 0.704213i) q^{38} +(3.05510 - 9.40262i) q^{39} +(-2.45117 - 7.54393i) q^{41} +(2.70875 + 3.72827i) q^{42} +3.03187i q^{43} +(1.01661 - 0.738608i) q^{44} +(0.543810 + 0.395101i) q^{46} +(-3.40439 + 4.68574i) q^{47} +(-12.8961 - 4.19020i) q^{48} -1.00000 q^{49} +9.50482 q^{51} +(0.627885 + 0.204012i) q^{52} +(-2.36682 + 3.25765i) q^{53} +(13.5041 + 9.81132i) q^{54} +(2.15486 - 1.56560i) q^{56} +4.75819i q^{57} +(-2.57428 - 3.54319i) q^{58} +(-2.23176 - 6.86866i) q^{59} +(-4.33740 + 13.3491i) q^{61} +(1.59553 - 0.518420i) q^{62} +(-6.29798 + 2.04634i) q^{63} +(-2.16581 + 6.66567i) q^{64} +(8.63897 + 26.5880i) q^{66} +(5.76618 + 7.93647i) q^{67} +0.634710i q^{68} +(-1.13545 + 0.824951i) q^{69} +(-5.06836 - 3.68238i) q^{71} +(10.3675 - 14.2697i) q^{72} +(-2.41296 - 0.784018i) q^{73} -6.09737 q^{74} -0.317741 q^{76} +(-5.76947 - 1.87462i) q^{77} +(-8.63329 + 11.8827i) q^{78} +(2.78358 + 2.02239i) q^{79} +(-12.1238 + 8.80843i) q^{81} +11.7844i q^{82} +(10.5319 + 14.4959i) q^{83} +(-0.198556 - 0.611092i) q^{84} +(1.39190 - 4.28383i) q^{86} +(8.69687 - 2.82578i) q^{87} +(15.3673 - 4.99314i) q^{88} +(0.615208 - 1.89341i) q^{89} +(-0.984896 - 3.03120i) q^{91} +(-0.0550883 - 0.0758225i) q^{92} +3.50283i q^{93} +(6.96134 - 5.05771i) q^{94} +(2.92914 + 2.12814i) q^{96} +(-3.46922 + 4.77497i) q^{97} +(1.41293 + 0.459090i) q^{98} -40.1721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 30 q^{6} + 10 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 30 * q^6 + 10 * q^9	\( 56 q + 12 q^{4} - 30 q^{6} + 10 q^{9} - 16 q^{11} + 12 q^{14} + 32 q^{16} - 44 q^{19} - 8 q^{21} - 76 q^{24} - 16 q^{26} + 74 q^{29} - 2 q^{31} + 20 q^{34} - 82 q^{36} - 48 q^{39} + 20 q^{41} - 130 q^{44} + 52 q^{46} - 56 q^{49} + 4 q^{51} + 28 q^{54} + 4 q^{56} + 38 q^{59} - 96 q^{61} + 40 q^{64} + 182 q^{66} - 62 q^{69} + 24 q^{71} - 140 q^{74} - 12 q^{76} + 144 q^{79} - 20 q^{81} - 16 q^{84} - 120 q^{86} - 6 q^{89} + 16 q^{91} - 24 q^{94} + 44 q^{96} - 124 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 30 * q^6 + 10 * q^9 - 16 * q^11 + 12 * q^14 + 32 * q^16 - 44 * q^19 - 8 * q^21 - 76 * q^24 - 16 * q^26 + 74 * q^29 - 2 * q^31 + 20 * q^34 - 82 * q^36 - 48 * q^39 + 20 * q^41 - 130 * q^44 + 52 * q^46 - 56 * q^49 + 4 * q^51 + 28 * q^54 + 4 * q^56 + 38 * q^59 - 96 * q^61 + 40 * q^64 + 182 * q^66 - 62 * q^69 + 24 * q^71 - 140 * q^74 - 12 * q^76 + 144 * q^79 - 20 * q^81 - 16 * q^84 - 120 * q^86 - 6 * q^89 + 16 * q^91 - 24 * q^94 + 44 * q^96 - 124 * q^99

Introduction

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