LMFDB - Embedded newform 961.2.d.r.388.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			388.1
Character	$\chi$	$=$	961.388
Dual form			961.2.d.r.374.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.01950 + 1.46725i) q^{2} +(-2.00074 - 1.45363i) q^{3} +(1.30751 - 4.02411i) q^{4} -1.14918 q^{5} +6.17333 q^{6} +(0.0819006 - 0.252064i) q^{7} +(1.72110 + 5.29701i) q^{8} +(0.962897 + 2.96349i) q^{9} +(2.32076 - 1.68613i) q^{10} +(0.0901192 - 0.277358i) q^{11} +(-8.46555 + 6.15058i) q^{12} +(3.65972 + 2.65894i) q^{13} +(0.204443 + 0.629212i) q^{14} +(2.29921 + 1.67047i) q^{15} +(-4.40159 - 3.19794i) q^{16} +(-1.69859 - 5.22772i) q^{17} +(-6.29276 - 4.57195i) q^{18} +(-5.62319 + 4.08549i) q^{19} +(-1.50257 + 4.62442i) q^{20} +(-0.530269 + 0.385263i) q^{21} +(0.224959 + 0.692352i) q^{22} +(-0.917019 - 2.82229i) q^{23} +(4.25638 - 13.0998i) q^{24} -3.67939 q^{25} -11.2921 q^{26} +(0.0886486 - 0.272832i) q^{27} +(-0.907248 - 0.659154i) q^{28} +(-2.69176 + 1.95568i) q^{29} -7.09426 q^{30} +2.44197 q^{32} +(-0.583480 + 0.423923i) q^{33} +(11.1007 + 8.06511i) q^{34} +(-0.0941183 + 0.289666i) q^{35} +13.1844 q^{36} +4.07780 q^{37} +(5.36159 - 16.5013i) q^{38} +(-3.45706 - 10.6397i) q^{39} +(-1.97785 - 6.08721i) q^{40} +(-6.06684 + 4.40782i) q^{41} +(0.505599 - 1.55608i) q^{42} +(6.51904 - 4.73636i) q^{43} +(-0.998289 - 0.725299i) q^{44} +(-1.10654 - 3.40558i) q^{45} +(5.99293 + 4.35412i) q^{46} +(-4.46414 - 3.24339i) q^{47} +(4.15784 + 12.7965i) q^{48} +(5.60629 + 4.07321i) q^{49} +(7.43052 - 5.39859i) q^{50} +(-4.20070 + 12.9284i) q^{51} +(15.4850 - 11.2505i) q^{52} +(1.46861 + 4.51991i) q^{53} +(0.221288 + 0.681054i) q^{54} +(-0.103563 + 0.318734i) q^{55} +1.47615 q^{56} +17.1893 q^{57} +(2.56654 - 7.89899i) q^{58} +(1.90331 + 1.38284i) q^{59} +(9.72842 - 7.06811i) q^{60} +10.0530 q^{61} +0.825852 q^{63} +(3.87162 - 2.81290i) q^{64} +(-4.20567 - 3.05560i) q^{65} +(0.556335 - 1.71222i) q^{66} -3.58686 q^{67} -23.2578 q^{68} +(-2.26784 + 6.97969i) q^{69} +(-0.234942 - 0.723076i) q^{70} +(3.36181 + 10.3466i) q^{71} +(-14.0404 + 10.2010i) q^{72} +(0.702814 - 2.16304i) q^{73} +(-8.23510 + 5.98315i) q^{74} +(7.36152 + 5.34845i) q^{75} +(9.08806 + 27.9702i) q^{76} +(-0.0625312 - 0.0454316i) q^{77} +(22.5927 + 16.4145i) q^{78} +(1.17247 + 3.60851i) q^{79} +(5.05821 + 3.67500i) q^{80} +(6.98873 - 5.07761i) q^{81} +(5.78460 - 17.8032i) q^{82} +(2.25988 - 1.64190i) q^{83} +(0.857007 + 2.63760i) q^{84} +(1.95198 + 6.00758i) q^{85} +(-6.21576 + 19.1301i) q^{86} +8.22836 q^{87} +1.62427 q^{88} +(0.989410 - 3.04509i) q^{89} +(7.23150 + 5.25399i) q^{90} +(0.969957 - 0.704715i) q^{91} -12.5562 q^{92} +13.7742 q^{94} +(6.46204 - 4.69495i) q^{95} +(-4.88576 - 3.54971i) q^{96} +(0.623244 - 1.91815i) q^{97} -17.2983 q^{98} +0.908724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{4} + 32 q^{5} - 8 q^{7} - 12 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} + 48 q^{25} + 20 q^{28} + 96 q^{32} + 40 q^{33} - 56 q^{35} + 160 q^{36}+ \cdots + 16 q^{98}+O(q^{100}) $ 48 * q - 16 * q^4 + 32 * q^5 - 8 * q^7 - 12 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 + 48 * q^25 + 20 * q^28 + 96 * q^32 + 40 * q^33 - 56 * q^35 + 160 * q^36 - 36 * q^38 + 16 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 - 48 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 - 32 * q^56 - 40 * q^59 - 32 * q^63 + 28 * q^64 - 24 * q^66 + 64 * q^67 - 24 * q^69 - 12 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 + 104 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 + 256 * q^87 + 44 * q^90 + 64 * q^94 - 40 * q^95 + 8 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.01950	+	1.46725i	−1.42800	+	1.03750i	−0.437617	+	0.899162i	$0.644177\pi$
$2$	−2.01950	+	1.46725i	−1.42800	+	1.03750i	−0.990385	+	0.138342i	$0.955823\pi$
$3$	−2.00074	−	1.45363i	−1.15513	−	0.839251i	−0.165975	−	0.986130i	$-0.553077\pi$
$3$	−2.00074	−	1.45363i	−1.15513	−	0.839251i	−0.989154	+	0.146879i	$0.953077\pi$
$4$	1.30751	−	4.02411i	0.653757	−	2.01206i
$5$	−1.14918			−0.513928			−0.256964	−	0.966421i	$-0.582722\pi$
$5$	−1.14918			−0.513928			−0.256964	+	0.966421i	$0.582722\pi$
$6$	6.17333			2.52025
$7$	0.0819006	−	0.252064i	0.0309555	−	0.0952713i	−0.934385	−	0.356265i	$-0.884050\pi$
$7$	0.0819006	−	0.252064i	0.0309555	−	0.0952713i	0.965341	+	0.260993i	$0.0840501\pi$
$8$	1.72110	+	5.29701i	0.608502	+	1.87278i
$9$	0.962897	+	2.96349i	0.320966	+	0.987830i
$10$	2.32076	−	1.68613i	0.733890	−	0.533202i
$11$	0.0901192	−	0.277358i	0.0271719	−	0.0836267i	−0.936551	−	0.350532i	$-0.886001\pi$
$11$	0.0901192	−	0.277358i	0.0271719	−	0.0836267i	0.963723	+	0.266905i	$0.0860009\pi$
$12$	−8.46555	+	6.15058i	−2.44379	+	1.77552i
$13$	3.65972	+	2.65894i	1.01502	+	0.737458i	0.965257	−	0.261303i	$-0.0841521\pi$
$13$	3.65972	+	2.65894i	1.01502	+	0.737458i	0.0497670	+	0.998761i	$0.484152\pi$
$14$	0.204443	+	0.629212i	0.0546398	+	0.168164i
$15$	2.29921	+	1.67047i	0.593653	+	0.431314i
$16$	−4.40159	−	3.19794i	−1.10040	−	0.799486i
$17$	−1.69859	−	5.22772i	−0.411968	−	1.26791i	−0.914935	−	0.403602i	$-0.867758\pi$
$17$	−1.69859	−	5.22772i	−0.411968	−	1.26791i	0.502967	−	0.864306i	$-0.332242\pi$
$18$	−6.29276	−	4.57195i	−1.48322	−	1.07762i
$19$	−5.62319	+	4.08549i	−1.29005	+	0.937275i	−0.999806	−	0.0196785i	$-0.993736\pi$
$19$	−5.62319	+	4.08549i	−1.29005	+	0.937275i	−0.290242	+	0.956953i	$0.593736\pi$
$20$	−1.50257	+	4.62442i	−0.335984	+	1.03405i
$21$	−0.530269	+	0.385263i	−0.115714	+	0.0840712i
$22$	0.224959	+	0.692352i	0.0479614	+	0.147610i
$23$	−0.917019	−	2.82229i	−0.191212	−	0.588489i	−1.00000		0.000389094i	$-0.999876\pi$
$23$	−0.917019	−	2.82229i	−0.191212	−	0.588489i	0.808788	−	0.588100i	$-0.200124\pi$
$24$	4.25638	−	13.0998i	0.868831	−	2.67399i
$25$	−3.67939			−0.735878
$26$	−11.2921			−2.21457
$27$	0.0886486	−	0.272832i	0.0170604	−	0.0525066i
$28$	−0.907248	−	0.659154i	−0.171454	−	0.124568i
$29$	−2.69176	+	1.95568i	−0.499848	+	0.363161i	−0.808959	−	0.587865i	$-0.799969\pi$
$29$	−2.69176	+	1.95568i	−0.499848	+	0.363161i	0.309111	+	0.951026i	$0.399969\pi$
$30$	−7.09426			−1.29523
$31$		0			0
$31$		0			0
$32$	2.44197			0.431684
$33$	−0.583480	+	0.423923i	−0.101571	+	0.0737956i
$34$	11.1007	+	8.06511i	1.90375	+	1.38316i
$35$	−0.0941183	+	0.289666i	−0.0159089	+	0.0489626i
$36$	13.1844			2.19740
$37$	4.07780			0.670385			0.335193	−	0.942150i	$-0.391199\pi$
$37$	4.07780			0.670385			0.335193	+	0.942150i	$0.391199\pi$
$38$	5.36159	−	16.5013i	0.869764	−	2.67686i
$39$	−3.45706	−	10.6397i	−0.553572	−	1.70372i
$40$	−1.97785	−	6.08721i	−0.312726	−	0.962472i
$41$	−6.06684	+	4.40782i	−0.947481	+	0.688385i	−0.950210	−	0.311611i	$-0.899131\pi$
$41$	−6.06684	+	4.40782i	−0.947481	+	0.688385i	0.00272880	+	0.999996i	$0.499131\pi$
$42$	0.505599	−	1.55608i	0.0780157	−	0.240108i
$43$	6.51904	−	4.73636i	0.994144	−	0.722288i	0.0333192	−	0.999445i	$-0.489392\pi$
$43$	6.51904	−	4.73636i	0.994144	−	0.722288i	0.960825	+	0.277157i	$0.0893922\pi$
$44$	−0.998289	−	0.725299i	−0.150498	−	0.109343i
$45$	−1.10654	−	3.40558i	−0.164953	−	0.507674i
$46$	5.99293	+	4.35412i	0.883610	+	0.641980i
$47$	−4.46414	−	3.24339i	−0.651161	−	0.473096i	0.212505	−	0.977160i	$-0.431838\pi$
$47$	−4.46414	−	3.24339i	−0.651161	−	0.473096i	−0.863667	+	0.504064i	$0.831838\pi$
$48$	4.15784	+	12.7965i	0.600133	+	1.84702i
$49$	5.60629	+	4.07321i	0.800899	+	0.581887i
$50$	7.43052	−	5.39859i	1.05083	−	0.763476i
$51$	−4.20070	+	12.9284i	−0.588216	+	1.81034i
$52$	15.4850	−	11.2505i	2.14739	−	1.56017i
$53$	1.46861	+	4.51991i	0.201729	+	0.620858i	0.999832	+	0.0183366i	$0.00583705\pi$
$53$	1.46861	+	4.51991i	0.201729	+	0.620858i	−0.798103	+	0.602521i	$0.794163\pi$
$54$	0.221288	+	0.681054i	0.0301135	+	0.0926797i
$55$	−0.103563	+	0.318734i	−0.0139644	+	0.0429781i
$56$	1.47615			0.197258
$57$	17.1893			2.27678
$58$	2.56654	−	7.89899i	0.337003	−	1.03719i
$59$	1.90331	+	1.38284i	0.247790	+	0.180030i	0.704747	−	0.709459i	$-0.251061\pi$
$59$	1.90331	+	1.38284i	0.247790	+	0.180030i	−0.456957	+	0.889489i	$0.651061\pi$
$60$	9.72842	−	7.06811i	1.25593	−	0.912489i
$61$	10.0530			1.28716			0.643580	−	0.765379i	$-0.277449\pi$
$61$	10.0530			1.28716			0.643580	+	0.765379i	$0.277449\pi$
$62$		0			0
$63$	0.825852			0.104048
$64$	3.87162	−	2.81290i	0.483953	−	0.351612i
$65$	−4.20567	−	3.05560i	−0.521649	−	0.379000i
$66$	0.556335	−	1.71222i	0.0684802	−	0.210760i
$67$	−3.58686			−0.438204			−0.219102	−	0.975702i	$-0.570313\pi$
$67$	−3.58686			−0.438204			−0.219102	+	0.975702i	$0.570313\pi$
$68$	−23.2578			−2.82043
$69$	−2.26784	+	6.97969i	−0.273016	+	0.840256i
$70$	−0.234942	−	0.723076i	−0.0280809	−	0.0864241i
$71$	3.36181	+	10.3466i	0.398974	+	1.22791i	0.925823	+	0.377956i	$0.123373\pi$
$71$	3.36181	+	10.3466i	0.398974	+	1.22791i	−0.526850	+	0.849958i	$0.676627\pi$
$72$	−14.0404	+	10.2010i	−1.65468	+	1.20219i
$73$	0.702814	−	2.16304i	0.0822582	−	0.253165i	−0.901466	−	0.432850i	$-0.857508\pi$
$73$	0.702814	−	2.16304i	0.0822582	−	0.253165i	0.983724	+	0.179685i	$0.0575080\pi$
$74$	−8.23510	+	5.98315i	−0.957311	+	0.695527i
$75$	7.36152	+	5.34845i	0.850035	+	0.617586i
$76$	9.08806	+	27.9702i	1.04247	+	3.20840i
$77$	−0.0625312	−	0.0454316i	−0.00712610	−	0.00517741i
$78$	22.5927	+	16.4145i	2.55812	+	1.85858i
$79$	1.17247	+	3.60851i	0.131914	+	0.405989i	0.995097	−	0.0989016i	$-0.0315329\pi$
$79$	1.17247	+	3.60851i	0.131914	+	0.405989i	−0.863183	+	0.504890i	$0.831533\pi$
$80$	5.05821	+	3.67500i	0.565525	+	0.410878i
$81$	6.98873	−	5.07761i	0.776526	−	0.564179i
$82$	5.78460	−	17.8032i	0.638802	−	1.96603i
$83$	2.25988	−	1.64190i	0.248054	−	0.180222i	−0.456810	−	0.889564i	$-0.651008\pi$
$83$	2.25988	−	1.64190i	0.248054	−	0.180222i	0.704864	+	0.709342i	$0.251008\pi$
$84$	0.857007	+	2.63760i	0.0935071	+	0.287785i
$85$	1.95198	+	6.00758i	0.211722	+	0.651613i
$86$	−6.21576	+	19.1301i	−0.670262	+	2.06286i
$87$	8.22836			0.882172
$88$	1.62427			0.173148
$89$	0.989410	−	3.04509i	0.104877	−	0.322779i	−0.884824	−	0.465925i	$-0.845722\pi$
$89$	0.989410	−	3.04509i	0.104877	−	0.322779i	0.989702	+	0.143146i	$0.0457217\pi$
$90$	7.23150	+	5.25399i	0.762267	+	0.553819i
$91$	0.969957	−	0.704715i	0.101679	−	0.0738742i
$92$	−12.5562			−1.30908
$93$		0			0
$94$	13.7742			1.42070
$95$	6.46204	−	4.69495i	0.662992	−	0.481692i
$96$	−4.88576	−	3.54971i	−0.498651	−	0.362291i
$97$	0.623244	−	1.91815i	0.0632808	−	0.194758i	−0.914418	−	0.404772i	$-0.867351\pi$
$97$	0.623244	−	1.91815i	0.0632808	−	0.194758i	0.977698	+	0.210014i	$0.0673509\pi$
$98$	−17.2983			−1.74739
$99$	0.908724			0.0913302
$100$	−4.81085	+	14.8063i	−0.481085	+	1.48063i
$101$	3.35653	+	10.3303i	0.333987	+	1.02791i	0.967219	+	0.253944i	$0.0817278\pi$
$101$	3.35653	+	10.3303i	0.333987	+	1.02791i	−0.633232	+	0.773962i	$0.718272\pi$
$102$	−10.4859	−	32.2724i	−1.03826	−	3.19545i
$103$	3.24692	−	2.35903i	0.319929	−	0.232442i	−0.416216	−	0.909266i	$-0.636644\pi$
$103$	3.24692	−	2.35903i	0.319929	−	0.232442i	0.736145	+	0.676824i	$0.236644\pi$
$104$	−7.78569	+	23.9619i	−0.763450	+	2.34966i
$105$	0.609373	−	0.442735i	0.0594687	−	0.0432065i
$106$	−9.59770	−	6.97314i	−0.932211	−	0.677291i
$107$	−5.57886	−	17.1700i	−0.539329	−	1.65988i	−0.734104	−	0.679037i	$-0.762398\pi$
$107$	−5.57886	−	17.1700i	−0.539329	−	1.65988i	0.194775	−	0.980848i	$-0.437602\pi$
$108$	−0.981998	−	0.713463i	−0.0944928	−	0.0686530i
$109$	−0.211472	−	0.153643i	−0.0202553	−	0.0147164i	0.577612	−	0.816312i	$-0.303985\pi$
$109$	−0.211472	−	0.153643i	−0.0202553	−	0.0147164i	−0.597867	+	0.801595i	$0.703985\pi$
$110$	−0.258518	−	0.795636i	−0.0246487	−	0.0758609i
$111$	−8.15862	−	5.92759i	−0.774382	−	0.562621i
$112$	−1.16658	+	0.847569i	−0.110231	+	0.0800878i
$113$	−0.865389	+	2.66339i	−0.0814090	+	0.250551i	−0.983474	−	0.181049i	$-0.942051\pi$
$113$	−0.865389	+	2.66339i	−0.0814090	+	0.250551i	0.902065	+	0.431600i	$0.142051\pi$
$114$	−34.7138	+	25.2211i	−3.25125	+	2.36217i
$115$	1.05382	+	3.24332i	0.0982690	+	0.302441i
$116$	4.35036	+	13.3890i	0.403921	+	1.24314i
$117$	−4.35582	+	13.4058i	−0.402696	+	1.23937i
$118$	−5.87270			−0.540626
$119$	−1.45684			−0.133548
$120$	−4.89134	+	15.0540i	−0.446516	+	1.37424i
$121$	8.83038	+	6.41565i	0.802762	+	0.583241i
$122$	−20.3021	+	14.7503i	−1.83807	+	1.33543i
$123$	18.5455			1.67219
$124$		0			0
$125$	9.97416			0.892116
$126$	−1.66781	+	1.21173i	−0.148580	+	0.107950i
$127$	4.57351	+	3.32285i	0.405834	+	0.294855i	0.771913	−	0.635728i	$-0.219300\pi$
$127$	4.57351	+	3.32285i	0.405834	+	0.294855i	−0.366079	+	0.930584i	$0.619300\pi$
$128$	−5.20073	+	16.0062i	−0.459684	+	1.41476i
$129$	−19.9278			−1.75455
$130$	12.9767			1.13813
$131$	1.96730	−	6.05472i	0.171884	−	0.529003i	−0.827594	−	0.561327i	$-0.810291\pi$
$131$	1.96730	−	6.05472i	0.171884	−	0.529003i	0.999477	+	0.0323242i	$0.0102909\pi$
$132$	0.943006	+	2.90227i	0.0820782	+	0.252611i
$133$	0.569262	+	1.75201i	0.0493613	+	0.151918i
$134$	7.24365	−	5.26282i	0.625756	−	0.454638i
$135$	−0.101873	+	0.313533i	−0.00876783	+	0.0269846i
$136$	24.7678	−	17.9949i	2.12382	−	1.54305i
$137$	2.39702	+	1.74154i	0.204792	+	0.148790i	0.685454	−	0.728116i	$-0.259604\pi$
$137$	2.39702	+	1.74154i	0.204792	+	0.148790i	−0.480662	+	0.876906i	$0.659604\pi$
$138$	−5.66106	−	17.4230i	−0.481902	−	1.48314i
$139$	−10.3605	−	7.52738i	−0.878770	−	0.638464i	0.0541556	−	0.998533i	$-0.482753\pi$
$139$	−10.3605	−	7.52738i	−0.878770	−	0.638464i	−0.932926	+	0.360069i	$0.882753\pi$
$140$	1.04259	+	0.757485i	0.0881149	+	0.0640192i
$141$	4.21693	+	12.9784i	0.355129	+	1.09298i
$142$	−21.9702	−	15.9623i	−1.84370	−	1.33953i
$143$	1.06729	−	0.775432i	0.0892513	−	0.0648449i
$144$	5.23880	−	16.1234i	0.436566	−	1.34361i
$145$	3.09332	−	2.24743i	0.256886	−	0.186639i
$146$	1.75439	+	5.39946i	0.145194	+	0.446862i
$147$	−5.29583	−	16.2989i	−0.436793	−	1.34431i
$148$	5.33177	−	16.4095i	0.438269	−	1.34885i
$149$	17.4535			1.42984			0.714921	−	0.699205i	$-0.246463\pi$
$149$	17.4535			1.42984			0.714921	+	0.699205i	$0.246463\pi$
$150$	−22.7141			−1.85460
$151$	−6.70288	+	20.6294i	−0.545473	+	1.67879i	0.174390	+	0.984677i	$0.444205\pi$
$151$	−6.70288	+	20.6294i	−0.545473	+	1.67879i	−0.719863	+	0.694116i	$0.755795\pi$
$152$	−31.3190	−	22.7546i	−2.54030	−	1.84564i
$153$	13.8567	−	10.0675i	1.12025	−	0.813909i
$154$	0.192941			0.0155477
$155$		0			0
$156$	−47.3356			−3.78988
$157$	11.7569	−	8.54190i	0.938304	−	0.681718i	−0.00970773	−	0.999953i	$-0.503090\pi$
$157$	11.7569	−	8.54190i	0.938304	−	0.681718i	0.948012	+	0.318235i	$0.103090\pi$
$158$	−7.66240	−	5.56706i	−0.609588	−	0.442891i
$159$	3.63195	−	11.1780i	0.288032	−	0.886472i
$160$	−2.80626			−0.221854
$161$	−0.786503			−0.0619852
$162$	−6.66360	+	20.5085i	−0.523542	+	1.61130i
$163$	0.0212089	+	0.0652743i	0.00166121	+	0.00511268i	0.951884	−	0.306460i	$-0.0991444\pi$
$163$	0.0212089	+	0.0652743i	0.00166121	+	0.00511268i	−0.950222	+	0.311572i	$0.899144\pi$
$164$	9.80507	+	30.1769i	0.765648	+	2.35642i
$165$	0.670522	−	0.487163i	0.0522001	−	0.0379256i
$166$	−2.15475	+	6.63163i	−0.167241	+	0.514714i
$167$	3.92909	−	2.85465i	0.304042	−	0.220899i	−0.425294	−	0.905055i	$-0.639829\pi$
$167$	3.92909	−	2.85465i	0.304042	−	0.220899i	0.729336	+	0.684156i	$0.239829\pi$
$168$	−2.95339	−	2.14576i	−0.227859	−	0.165549i
$169$	2.30636	+	7.09824i	0.177412	+	0.546018i
$170$	−12.7566	−	9.26825i	−0.978390	−	0.710842i
$171$	−17.5219	−	12.7304i	−1.33993	−	0.973516i
$172$	−10.5359	−	32.4262i	−0.803355	−	2.47247i
$173$	9.13841	+	6.63945i	0.694781	+	0.504788i	0.878228	−	0.478242i	$-0.158726\pi$
$173$	9.13841	+	6.63945i	0.694781	+	0.504788i	−0.183448	+	0.983029i	$0.558726\pi$
$174$	−16.6172	+	12.0731i	−1.25974	+	0.915257i
$175$	−0.301344	+	0.927442i	−0.0227795	+	0.0701080i
$176$	−1.28364	+	0.932621i	−0.0967582	+	0.0702990i
$177$	−1.79791	−	5.53340i	−0.135139	−	0.415916i
$178$	2.46980	+	7.60127i	0.185120	+	0.569740i
$179$	4.45920	−	13.7240i	0.333296	−	1.02578i	−0.634259	−	0.773120i	$-0.718695\pi$
$179$	4.45920	−	13.7240i	0.333296	−	1.02578i	0.967555	−	0.252659i	$-0.0813052\pi$
$180$	−15.1512			−1.12931
$181$	22.0004			1.63528			0.817639	−	0.575731i	$-0.195282\pi$
$181$	22.0004			1.63528			0.817639	+	0.575731i	$0.195282\pi$
$182$	−0.924833	+	2.84634i	−0.0685532	+	0.210985i
$183$	−20.1135	−	14.6133i	−1.48684	−	1.08025i
$184$	13.3714	−	9.71492i	0.985756	−	0.716194i
$185$	−4.68611			−0.344530
$186$		0			0
$187$	−1.60303			−0.117225
$188$	−18.8887	+	13.7234i	−1.37760	+	1.00088i
$189$	−0.0615108	−	0.0446902i	−0.00447425	−	0.00325074i
$190$	−6.16142	+	18.9629i	−0.446996	+	1.37571i
$191$	21.7663			1.57496			0.787478	−	0.616342i	$-0.211386\pi$
$191$	21.7663			1.57496			0.787478	+	0.616342i	$0.211386\pi$
$192$	−11.8350			−0.854119
$193$	0.683307	−	2.10300i	0.0491855	−	0.151378i	−0.923447	−	0.383726i	$-0.874641\pi$
$193$	0.683307	−	2.10300i	0.0491855	−	0.151378i	0.972633	+	0.232348i	$0.0746408\pi$
$194$	1.55576	+	4.78815i	0.111697	+	0.343769i
$195$	3.97277	+	12.2269i	0.284496	+	0.875589i
$196$	23.7213	−	17.2346i	1.69438	−	1.23104i
$197$	5.37478	−	16.5419i	0.382937	−	1.17856i	−0.555028	−	0.831831i	$-0.687293\pi$
$197$	5.37478	−	16.5419i	0.382937	−	1.17856i	0.937966	−	0.346728i	$-0.112707\pi$
$198$	−1.83517	+	1.33333i	−0.130420	+	0.0947554i
$199$	−9.51393	−	6.91227i	−0.674424	−	0.489998i	0.197079	−	0.980388i	$-0.436854\pi$
$199$	−9.51393	−	6.91227i	−0.674424	−	0.489998i	−0.871503	+	0.490390i	$0.836854\pi$
$200$	−6.33261	−	19.4898i	−0.447783	−	1.37814i
$201$	7.17638	+	5.21394i	0.506183	+	0.367763i
$202$	−21.9357	−	15.9372i	−1.54339	−	1.12134i
$203$	0.272500	+	0.838669i	0.0191257	+	0.0588630i
$204$	46.5330	+	33.8082i	3.25796	+	2.36705i
$205$	6.97188	−	5.06536i	0.486937	−	0.353780i
$206$	−3.09587	+	9.52810i	−0.215699	+	0.663855i
$207$	7.48085	−	5.43516i	0.519955	−	0.377769i
$208$	−7.60544	−	23.4071i	−0.527343	−	1.62299i
$209$	0.626386	+	1.92782i	0.0433280	+	0.133350i
$210$	−0.581024	+	1.78821i	−0.0400944	+	0.123398i
$211$	−7.46501			−0.513912			−0.256956	−	0.966423i	$-0.582720\pi$
$211$	−7.46501			−0.513912			−0.256956	+	0.966423i	$0.582720\pi$
$212$	20.1089			1.38108
$213$	8.31394	−	25.5877i	0.569662	−	1.75324i
$214$	36.4592	+	26.4891i	2.49230	+	1.81076i
$215$	−7.49153	+	5.44292i	−0.510918	+	0.371204i
$216$	1.59777			0.108714
$217$		0			0
$218$	0.652500			0.0441929
$219$	−4.55040	+	3.30606i	−0.307487	+	0.223403i
$220$	1.14721	+	0.833498i	0.0773450	+	0.0561944i
$221$	7.68384	−	23.6484i	0.516871	−	1.59077i
$222$	25.1736			1.68954
$223$	29.1467			1.95181			0.975903	−	0.218206i	$-0.0700206\pi$
$223$	29.1467			1.95181			0.975903	+	0.218206i	$0.0700206\pi$
$224$	0.199999	−	0.615533i	0.0133630	−	0.0411270i
$225$	−3.54287	−	10.9038i	−0.236192	−	0.726923i
$226$	−2.16022	−	6.64846i	−0.143695	−	0.442249i
$227$	−4.81183	+	3.49600i	−0.319372	+	0.232037i	−0.735907	−	0.677082i	$-0.763244\pi$
$227$	−4.81183	+	3.49600i	−0.319372	+	0.232037i	0.416535	+	0.909119i	$0.363244\pi$
$228$	22.4753	−	69.1718i	1.48846	−	4.58101i
$229$	−4.52334	+	3.28640i	−0.298911	+	0.217171i	−0.727124	−	0.686506i	$-0.759143\pi$
$229$	−4.52334	+	3.28640i	−0.298911	+	0.217171i	0.428213	+	0.903678i	$0.359143\pi$
$230$	−6.88695	−	5.00366i	−0.454112	−	0.329932i
$231$	0.0590684	+	0.181794i	0.00388642	+	0.0119612i
$232$	−14.9921	−	10.8924i	−0.984278	−	0.715120i
$233$	21.3413	+	15.5053i	1.39811	+	1.01579i	0.994920	+	0.100673i	$0.0320995\pi$
$233$	21.3413	+	15.5053i	1.39811	+	1.01579i	0.403192	+	0.915115i	$0.367901\pi$
$234$	−10.8732	−	33.4642i	−0.710801	−	2.18762i
$235$	5.13009	+	3.72723i	0.334650	+	0.243137i
$236$	8.05329	−	5.85106i	0.524225	−	0.380872i
$237$	2.89959	−	8.92403i	0.188349	−	0.579678i
$238$	2.94208	−	2.13754i	0.190706	−	0.138556i
$239$	−6.43475	−	19.8041i	−0.416229	−	1.28102i	−0.911147	−	0.412082i	$-0.864802\pi$
$239$	−6.43475	−	19.8041i	−0.416229	−	1.28102i	0.494918	−	0.868940i	$-0.335198\pi$
$240$	−4.77810	−	14.7055i	−0.308425	−	0.949234i
$241$	−4.40677	+	13.5626i	−0.283865	+	0.873646i	0.702872	+	0.711316i	$0.251901\pi$
$241$	−4.40677	+	13.5626i	−0.283865	+	0.873646i	−0.986737	+	0.162329i	$0.948099\pi$
$242$	−27.2463			−1.75146
$243$	−22.2242			−1.42568
$244$	13.1445	−	40.4545i	0.841489	−	2.58984i
$245$	−6.44262	−	4.68084i	−0.411604	−	0.299048i
$246$	−37.4526	+	27.2109i	−2.38789	+	1.73490i
$247$	−31.4424			−2.00063
$248$		0			0
$249$	−6.90815			−0.437786
$250$	−20.1428	+	14.6346i	−1.27394	+	0.925574i
$251$	7.11985	+	5.17288i	0.449401	+	0.326509i	0.789359	−	0.613932i	$-0.210413\pi$
$251$	7.11985	+	5.17288i	0.449401	+	0.326509i	−0.339958	+	0.940441i	$0.610413\pi$
$252$	1.07981	−	3.32332i	0.0680218	−	0.209349i
$253$	−0.865428			−0.0544090
$254$	−14.1117			−0.885445
$255$	4.82735	−	14.8571i	0.302301	−	0.930385i
$256$	−10.0246	−	30.8525i	−0.626537	−	1.92828i
$257$	1.23905	+	3.81341i	0.0772900	+	0.237874i	0.982235	−	0.187654i	$-0.0600883\pi$
$257$	1.23905	+	3.81341i	0.0772900	+	0.237874i	−0.904945	+	0.425528i	$0.860088\pi$
$258$	40.2442	−	29.2391i	2.50549	−	1.82035i
$259$	0.333974	−	1.02787i	0.0207521	−	0.0638685i
$260$	−17.7950	+	12.9288i	−1.10360	+	0.801813i
$261$	−8.38754	−	6.09390i	−0.519175	−	0.377203i
$262$	4.91084	+	15.1140i	0.303393	+	0.933747i
$263$	0.495200	+	0.359784i	0.0305354	+	0.0221852i	0.602948	−	0.797780i	$-0.293993\pi$
$263$	0.495200	+	0.359784i	0.0305354	+	0.0221852i	−0.572413	+	0.819966i	$0.693993\pi$
$264$	−3.24976	−	2.36109i	−0.200009	−	0.145315i
$265$	−1.68769	−	5.19418i	−0.103674	−	0.319076i
$266$	−3.72026	−	2.70293i	−0.228104	−	0.165727i
$267$	−6.40598	+	4.65422i	−0.392040	+	0.284833i
$268$	−4.68986	+	14.4339i	−0.286479	+	0.881691i
$269$	−0.911196	+	0.662023i	−0.0555566	+	0.0403642i	−0.615217	−	0.788358i	$-0.710932\pi$
$269$	−0.911196	+	0.662023i	−0.0555566	+	0.0403642i	0.559660	+	0.828722i	$0.310932\pi$
$270$	−0.254299	−	0.782652i	−0.0154761	−	0.0476307i
$271$	0.0642534	+	0.197752i	0.00390311	+	0.0120125i	0.952989	−	0.303005i	$-0.0979897\pi$
$271$	0.0642534	+	0.197752i	0.00390311	+	0.0120125i	−0.949086	+	0.315017i	$0.897990\pi$
$272$	−9.24145	+	28.4423i	−0.560345	+	1.72456i
$273$	−2.96503			−0.179452
$274$	−7.39606			−0.446813
$275$	−0.331584	+	1.02051i	−0.0199952	+	0.0615390i
$276$	25.1218	+	18.2521i	1.51216	+	1.09865i
$277$	20.1244	−	14.6212i	1.20916	−	0.878503i	0.214002	−	0.976833i	$-0.431350\pi$
$277$	20.1244	−	14.6212i	1.20916	−	0.878503i	0.995154	+	0.0983304i	$0.0313502\pi$
$278$	31.9677			1.91729
$279$		0			0
$280$	−1.69635			−0.101377
$281$	−20.8428	+	15.1432i	−1.24338	+	0.903366i	−0.997819	−	0.0660161i	$-0.978971\pi$
$281$	−20.8428	+	15.1432i	−1.24338	+	0.903366i	−0.245558	+	0.969382i	$0.578971\pi$
$282$	−27.5586	−	20.0225i	−1.64109	−	1.19232i
$283$	−8.27588	+	25.4705i	−0.491950	+	1.51407i	0.329707	+	0.944083i	$0.393050\pi$
$283$	−8.27588	+	25.4705i	−0.491950	+	1.51407i	−0.821657	+	0.569983i	$0.806950\pi$
$284$	46.0315			2.73146
$285$	−19.7536			−1.17010
$286$	−1.01764	+	3.13197i	−0.0601742	+	0.185197i
$287$	0.614174	+	1.89023i	0.0362536	+	0.111577i
$288$	2.35137	+	7.23676i	0.138556	+	0.426430i
$289$	−10.6905	+	7.76713i	−0.628855	+	0.456890i
$290$	−2.94941	+	9.07734i	−0.173195	+	0.533040i
$291$	−4.03522	+	2.93176i	−0.236549	+	0.171863i
$292$	−7.78537	−	5.65640i	−0.455604	−	0.331016i
$293$	6.91047	+	21.2683i	0.403714	+	1.24250i	0.921964	+	0.387275i	$0.126584\pi$
$293$	6.91047	+	21.2683i	0.403714	+	1.24250i	−0.518250	+	0.855229i	$0.673416\pi$
$294$	34.6095	+	25.1453i	2.01847	+	1.46650i
$295$	−2.18724	−	1.58912i	−0.127346	−	0.0925224i
$296$	7.01831	+	21.6001i	0.407931	+	1.25548i
$297$	−0.0676833	−	0.0491748i	−0.00392739	−	0.00285341i
$298$	−35.2472	+	25.6086i	−2.04182	+	1.48347i
$299$	4.14829	−	12.7671i	0.239902	−	0.738341i
$300$	31.1481	−	22.6304i	1.79833	−	1.30657i
$301$	−0.659953	−	2.03113i	−0.0380390	−	0.117072i
$302$	−16.7320	−	51.4958i	−0.962818	−	2.96325i
$303$	8.30087	−	25.5475i	0.476873	−	1.46766i
$304$	37.8161			2.16890
$305$	−11.5527			−0.661507
$306$	−13.2121	+	40.6626i	−0.755285	+	2.32453i
$307$	−5.89598	−	4.28368i	−0.336501	−	0.244483i	0.406683	−	0.913569i	$-0.366685\pi$
$307$	−5.89598	−	4.28368i	−0.336501	−	0.244483i	−0.743184	+	0.669087i	$0.766685\pi$
$308$	−0.264582	+	0.192230i	−0.0150760	+	0.0109533i
$309$	−9.92540			−0.564636
$310$		0			0
$311$	−25.6025			−1.45179			−0.725893	−	0.687808i	$-0.758573\pi$
$311$	−25.6025			−1.45179			−0.725893	+	0.687808i	$0.758573\pi$
$312$	50.4088	−	36.6241i	2.85384	−	2.07343i
$313$	−20.6113	−	14.9750i	−1.16502	−	0.846436i	−0.174615	−	0.984637i	$-0.555868\pi$
$313$	−20.6113	−	14.9750i	−1.16502	−	0.846436i	−0.990404	+	0.138201i	$0.955868\pi$
$314$	−11.2100	+	34.5007i	−0.632615	+	1.94699i
$315$	−0.949050			−0.0534729
$316$	16.0541			0.903112
$317$	−4.39950	+	13.5403i	−0.247101	+	0.760498i	0.748183	+	0.663492i	$0.230926\pi$
$317$	−4.39950	+	13.5403i	−0.247101	+	0.760498i	−0.995284	+	0.0970055i	$0.969074\pi$
$318$	9.06621	+	27.9029i	0.508408	+	1.56472i
$319$	0.299845	+	0.922827i	0.0167881	+	0.0516684i
$320$	−4.44918	+	3.23252i	−0.248717	+	0.180703i
$321$	−13.7968	+	42.4623i	−0.770064	+	2.37001i
$322$	1.58834	−	1.15400i	0.0885149	−	0.0643098i
$323$	30.9092	+	22.4569i	1.71984	+	1.24953i
$324$	−11.2950	−	34.7625i	−0.627501	−	1.93125i
$325$	−13.4655	−	9.78329i	−0.746934	−	0.542679i
$326$	−0.138605	−	0.100703i	−0.00767663	−	0.00557740i
$327$	0.199761	+	0.614801i	0.0110468	+	0.0339986i
$328$	−33.7899	−	24.5498i	−1.86574	−	1.35554i
$329$	−1.18316	+	0.859613i	−0.0652295	+	0.0473920i
$330$	−0.639328	+	1.96765i	−0.0351939	+	0.108316i
$331$	14.1509	−	10.2813i	0.777806	−	0.565109i	−0.126513	−	0.991965i	$-0.540379\pi$
$331$	14.1509	−	10.2813i	0.777806	−	0.565109i	0.904320	+	0.426855i	$0.140379\pi$
$332$	−3.65236	−	11.2408i	−0.200449	−	0.616920i
$333$	3.92650	+	12.0845i	0.215171	+	0.662227i
$334$	−3.74630	+	11.5299i	−0.204988	+	0.630889i
$335$	4.12193			0.225205
$336$	3.56607			0.194545
$337$	−5.07506	+	15.6194i	−0.276456	+	0.850845i	0.712374	+	0.701800i	$0.247620\pi$
$337$	−5.07506	+	15.6194i	−0.276456	+	0.850845i	−0.988830	+	0.149045i	$0.952380\pi$
$338$	−15.0726	−	10.9509i	−0.819841	−	0.595649i
$339$	5.60300	−	4.07082i	0.304313	−	0.221096i
$340$	26.7274			1.44950
$341$		0			0
$342$	54.0640			2.92345
$343$	2.98680	−	2.17004i	0.161272	−	0.117171i
$344$	36.3085	+	26.3797i	1.95762	+	1.42230i
$345$	2.60615	−	8.02090i	0.140310	−	0.431831i
$346$	−28.1967			−1.51587
$347$	26.0876			1.40046			0.700228	−	0.713919i	$-0.253081\pi$
$347$	26.0876			1.40046			0.700228	+	0.713919i	$0.253081\pi$
$348$	10.7587	−	33.1118i	0.576726	−	1.77498i
$349$	3.30519	+	10.1723i	0.176923	+	0.544513i	0.999716	−	0.0238282i	$-0.00758548\pi$
$349$	3.30519	+	10.1723i	0.176923	+	0.544513i	−0.822793	+	0.568341i	$0.807585\pi$
$350$	−0.752227	−	2.31512i	−0.0402082	−	0.123748i
$351$	1.04987	−	0.762778i	0.0560381	−	0.0407141i
$352$	0.220068	−	0.677301i	0.0117297	−	0.0361003i
$353$	11.0361	−	8.01820i	0.587393	−	0.426766i	−0.253989	−	0.967207i	$-0.581743\pi$
$353$	11.0361	−	8.01820i	0.587393	−	0.426766i	0.841382	+	0.540441i	$0.181743\pi$
$354$	11.7498	+	8.53671i	0.624493	+	0.453721i
$355$	−3.86332	−	11.8901i	−0.205044	−	0.631060i
$356$	−10.9601	−	7.96300i	−0.580885	−	0.422038i
$357$	2.91475	+	2.11769i	0.154265	+	0.112080i
$358$	11.1312	+	34.2584i	0.588303	+	1.81061i
$359$	−1.69075	−	1.22840i	−0.0892343	−	0.0648325i	0.542274	−	0.840202i	$-0.317564\pi$
$359$	−1.69075	−	1.22840i	−0.0892343	−	0.0648325i	−0.631508	+	0.775370i	$0.717564\pi$
$360$	16.1349	−	11.7227i	0.850385	−	0.617841i
$361$	9.05774	−	27.8769i	0.476723	−	1.46720i
$362$	−44.4298	+	32.2802i	−2.33518	+	1.69661i
$363$	−8.34138	−	25.6721i	−0.437809	−	1.34744i
$364$	−1.56762	−	4.82464i	−0.0821657	−	0.252880i
$365$	−0.807658	+	2.48572i	−0.0422748	+	0.130108i
$366$	62.0607			3.24397
$367$	−19.9201			−1.03982			−0.519910	−	0.854221i	$-0.674035\pi$
$367$	−19.9201			−1.03982			−0.519910	+	0.854221i	$0.674035\pi$
$368$	−4.98919	+	15.3552i	−0.260080	+	0.800443i
$369$	−18.9043	−	13.7348i	−0.984117	−	0.715003i
$370$	9.46359	−	6.87570i	0.491989	−	0.357451i
$371$	1.25959			0.0653945
$372$		0			0
$373$	10.7238			0.555257			0.277629	−	0.960688i	$-0.410452\pi$
$373$	10.7238			0.555257			0.277629	+	0.960688i	$0.410452\pi$
$374$	3.23731	−	2.35204i	0.167397	−	0.121621i
$375$	−19.9557	−	14.4987i	−1.03051	−	0.748709i
$376$	9.49701	−	29.2288i	0.489771	−	1.50736i
$377$	−15.0511			−0.775174
$378$	0.189793			0.00976189
$379$	4.37371	−	13.4609i	0.224662	−	0.691440i	−0.773663	−	0.633597i	$-0.781578\pi$
$379$	4.37371	−	13.4609i	0.224662	−	0.691440i	0.998326	−	0.0578430i	$-0.0184223\pi$
$380$	−10.4438	−	32.1427i	−0.535755	−	1.64889i
$381$	−4.32025	−	13.2963i	−0.221333	−	0.681193i
$382$	−43.9571	+	31.9367i	−2.24904	+	1.63402i
$383$	−5.51787	+	16.9822i	−0.281950	+	0.867752i	0.705347	+	0.708863i	$0.250791\pi$
$383$	−5.51787	+	16.9822i	−0.281950	+	0.867752i	−0.987296	+	0.158890i	$0.949209\pi$
$384$	33.6723	−	24.4644i	1.71833	−	1.24844i
$385$	0.0718595	+	0.0522090i	0.00366230	+	0.00266082i
$386$	1.70570	+	5.24960i	0.0868177	+	0.267197i
$387$	20.3133	+	14.7585i	1.03258	+	0.750216i
$388$	−6.90394	−	5.01601i	−0.350495	−	0.254649i
$389$	7.25605	+	22.3318i	0.367896	+	1.13227i	0.948147	+	0.317831i	$0.102954\pi$
$389$	7.25605	+	22.3318i	0.367896	+	1.13227i	−0.580251	+	0.814438i	$0.697046\pi$
$390$	−25.9630	−	18.8632i	−1.31469	−	0.955176i
$391$	−13.1965	+	9.58783i	−0.667377	+	0.484878i
$392$	−11.9268	+	36.7070i	−0.602396	+	1.85398i
$393$	−12.7373	+	9.25422i	−0.642514	+	0.466814i
$394$	13.4167	+	41.2924i	0.675925	+	2.08028i
$395$	−1.34738	−	4.14682i	−0.0677941	−	0.208649i
$396$	1.18817	−	3.65681i	0.0597077	−	0.183762i
$397$	−10.1063			−0.507219			−0.253609	−	0.967307i	$-0.581618\pi$
$397$	−10.1063			−0.507219			−0.253609	+	0.967307i	$0.581618\pi$
$398$	29.3554			1.47145
$399$	1.40782	−	4.33281i	0.0704789	−	0.216912i
$400$	16.1952	+	11.7665i	0.809758	+	0.588324i
$401$	−18.5048	+	13.4445i	−0.924085	+	0.671387i	−0.944537	−	0.328404i	$-0.893489\pi$
$401$	−18.5048	+	13.4445i	−0.924085	+	0.671387i	0.0204525	+	0.999791i	$0.493489\pi$
$402$	−22.1428			−1.10438
$403$		0			0
$404$	45.9591			2.28655
$405$	−8.03129	+	5.83508i	−0.399078	+	0.289947i
$406$	−1.78085	−	1.29386i	−0.0883821	−	0.0642134i
$407$	0.367487	−	1.13101i	0.0182157	−	0.0560621i
$408$	−75.7119			−3.74830
$409$	−13.1943			−0.652414			−0.326207	−	0.945298i	$-0.605771\pi$
$409$	−13.1943			−0.652414			−0.326207	+	0.945298i	$0.605771\pi$
$410$	−6.64753	+	20.4590i	−0.328298	+	1.01040i
$411$	−2.26428	−	6.96875i	−0.111689	−	0.343743i
$412$	−5.24760	−	16.1504i	−0.258530	−	0.795675i
$413$	0.504446	−	0.366501i	0.0248221	−	0.0180343i
$414$	−7.13283	+	21.9526i	−0.350559	+	1.07891i
$415$	−2.59700	+	1.88683i	−0.127482	+	0.0926210i
$416$	8.93693	+	6.49306i	0.438169	+	0.318349i
$417$	9.78681	+	30.1207i	0.479262	+	1.47502i
$418$	−4.09358	−	2.97416i	−0.200224	−	0.145471i
$419$	3.60771	+	2.62115i	0.176248	+	0.128052i	0.672412	−	0.740177i	$-0.265258\pi$
$419$	3.60771	+	2.62115i	0.176248	+	0.128052i	−0.496164	+	0.868229i	$0.665258\pi$
$420$	−0.984854	−	3.03107i	−0.0480559	−	0.147901i
$421$	15.6329	+	11.3580i	0.761902	+	0.553554i	0.899493	−	0.436935i	$-0.143936\pi$
$421$	15.6329	+	11.3580i	0.761902	+	0.553554i	−0.137591	+	0.990489i	$0.543936\pi$
$422$	15.0756	−	10.9530i	0.733867	−	0.533186i
$423$	5.31324	−	16.3525i	0.258339	−	0.795085i
$424$	−21.4144	+	15.5585i	−1.03998	+	0.755586i
$425$	6.24977	+	19.2348i	0.303158	+	0.933025i
$426$	20.7536	+	63.8729i	1.00551	+	3.09465i
$427$	0.823350	−	2.53401i	0.0398447	−	0.122629i
$428$	−76.3884			−3.69237
$429$	−3.26256			−0.157518
$430$	7.14301	−	21.9839i	0.344467	−	1.06016i
$431$	8.45043	+	6.13960i	0.407043	+	0.295734i	0.772404	−	0.635132i	$-0.219054\pi$
$431$	8.45043	+	6.13960i	0.407043	+	0.295734i	−0.365361	+	0.930866i	$0.619054\pi$
$432$	−1.26270	+	0.917402i	−0.0607515	+	0.0441385i
$433$	−20.7300			−0.996220			−0.498110	−	0.867114i	$-0.665972\pi$
$433$	−20.7300			−0.996220			−0.498110	+	0.867114i	$0.665972\pi$
$434$		0			0
$435$	−9.45584			−0.453373
$436$	−0.894780	+	0.650096i	−0.0428522	+	0.0311339i
$437$	16.6870	+	12.1238i	0.798248	+	0.579961i
$438$	4.33870	−	13.3532i	0.207311	−	0.638039i
$439$	28.3556			1.35334			0.676669	−	0.736287i	$-0.263423\pi$
$439$	28.3556			1.35334			0.676669	+	0.736287i	$0.263423\pi$
$440$	−1.86658			−0.0889857
$441$	−6.67264	+	20.5363i	−0.317745	+	0.977918i
$442$	19.1807	+	59.0321i	0.912333	+	2.80787i
$443$	−9.02842	−	27.7866i	−0.428953	−	1.32018i	−0.899158	−	0.437625i	$-0.855820\pi$
$443$	−9.02842	−	27.7866i	−0.428953	−	1.32018i	0.470204	−	0.882558i	$-0.344180\pi$
$444$	−34.5208	+	25.0808i	−1.63828	+	1.19028i
$445$	−1.13701	+	3.49935i	−0.0538994	+	0.165885i
$446$	−58.8617	+	42.7655i	−2.78718	+	2.02500i
$447$	−34.9199	−	25.3708i	−1.65165	−	1.20000i
$448$	−0.391942	−	1.20627i	−0.0185175	−	0.0569911i
$449$	−0.943828	−	0.685731i	−0.0445420	−	0.0323616i	0.565292	−	0.824891i	$-0.308764\pi$
$449$	−0.943828	−	0.685731i	−0.0445420	−	0.0323616i	−0.609833	+	0.792530i	$0.708764\pi$
$450$	23.1535	+	16.8220i	1.09147	+	0.792997i
$451$	0.675806	+	2.07992i	0.0318225	+	0.0979394i
$452$	9.58629	+	6.96485i	0.450901	+	0.327599i
$453$	43.3981	−	31.5306i	2.03902	−	1.48144i
$454$	4.58797	−	14.1203i	0.215324	−	0.662699i
$455$	−1.11465	+	0.809843i	−0.0522557	+	0.0379660i
$456$	29.5846	+	91.0521i	1.38543	+	4.26390i
$457$	12.4478	+	38.3105i	0.582285	+	1.79209i	0.609910	+	0.792470i	$0.291205\pi$
$457$	12.4478	+	38.3105i	0.582285	+	1.79209i	−0.0276256	+	0.999618i	$0.508795\pi$
$458$	4.31291	−	13.2738i	0.201529	−	0.620242i
$459$	−1.57687			−0.0736018
$460$	14.4294			0.672772
$461$	−9.06636	+	27.9034i	−0.422262	+	1.29959i	0.483329	+	0.875439i	$0.339428\pi$
$461$	−9.06636	+	27.9034i	−0.422262	+	1.29959i	−0.905591	+	0.424151i	$0.860572\pi$
$462$	−0.386026	−	0.280464i	−0.0179596	−	0.0130484i
$463$	0.517373	−	0.375893i	0.0240444	−	0.0174692i	−0.575698	−	0.817662i	$-0.695270\pi$
$463$	0.517373	−	0.375893i	0.0240444	−	0.0174692i	0.599743	+	0.800193i	$0.295270\pi$
$464$	18.1022			0.840373
$465$		0			0
$466$	−65.8488			−3.05039
$467$	−2.34245	+	1.70189i	−0.108396	+	0.0787541i	−0.640663	−	0.767822i	$-0.721340\pi$
$467$	−2.34245	+	1.70189i	−0.108396	+	0.0787541i	0.532267	+	0.846577i	$0.321340\pi$
$468$	48.2513	+	35.0566i	2.23042	+	1.62049i
$469$	−0.293766	+	0.904117i	−0.0135648	+	0.0417483i
$470$	−15.8290			−0.730136
$471$	−35.9393			−1.65600
$472$	−4.04911	+	12.4619i	−0.186375	+	0.573604i
$473$	−0.726178	−	2.23495i	−0.0333897	−	0.102763i
$474$	7.23808	+	22.2765i	0.332456	+	1.02319i
$475$	20.6899	−	15.0321i	0.949318	−	0.689720i
$476$	−1.90483	+	5.86247i	−0.0873078	+	0.268706i
$477$	−11.9806	+	8.70442i	−0.548554	+	0.398548i
$478$	42.0526	+	30.5530i	1.92344	+	1.39746i
$479$	8.94418	+	27.5274i	0.408670	+	1.25776i	0.917791	+	0.397063i	$0.129970\pi$
$479$	8.94418	+	27.5274i	0.408670	+	1.25776i	−0.509121	+	0.860695i	$0.670030\pi$
$480$	5.61460	+	4.07925i	0.256270	+	0.186191i
$481$	14.9236	+	10.8426i	0.680457	+	0.494381i
$482$	−11.0003	−	33.8556i	−0.501052	−	1.54208i
$483$	1.57359	+	1.14328i	0.0716009	+	0.0520211i
$484$	37.3631	−	27.1459i	1.69832	−	1.23390i
$485$	−0.716218	+	2.20429i	−0.0325218	+	0.100092i
$486$	44.8818	−	32.6085i	2.03588	−	1.47915i
$487$	−0.844612	−	2.59945i	−0.0382730	−	0.117792i	0.930095	−	0.367320i	$-0.119725\pi$
$487$	−0.844612	−	2.59945i	−0.0382730	−	0.117792i	−0.968368	+	0.249528i	$0.919725\pi$
$488$	17.3023	+	53.2511i	0.783239	+	2.41056i
$489$	0.0524508	−	0.161427i	0.00237191	−	0.00729998i
$490$	19.8788			0.898034
$491$	11.4297			0.515817			0.257908	−	0.966169i	$-0.416967\pi$
$491$	11.4297			0.515817			0.257908	+	0.966169i	$0.416967\pi$
$492$	24.2485	−	74.6292i	1.09321	−	3.36454i
$493$	14.7959	+	10.7499i	0.666376	+	0.484150i
$494$	63.4978	−	46.1339i	2.85690	−	2.07566i
$495$	−1.04429			−0.0469372
$496$		0			0
$497$	2.88334			0.129335
$498$	13.9510	−	10.1360i	0.625159	−	0.454205i
$499$	5.19538	+	3.77467i	0.232577	+	0.168977i	0.697970	−	0.716127i	$-0.254087\pi$
$499$	5.19538	+	3.77467i	0.232577	+	0.168977i	−0.465393	+	0.885104i	$0.654087\pi$
$500$	13.0413	−	40.1371i	0.583227	−	1.79499i
$501$	−12.0107			−0.536598
$502$	−21.9684			−0.980500
$503$	−3.87623	+	11.9298i	−0.172833	+	0.531924i	−0.999528	−	0.0307257i	$-0.990218\pi$
$503$	−3.87623	+	11.9298i	−0.172833	+	0.531924i	0.826695	+	0.562650i	$0.190218\pi$
$504$	1.42138	+	4.37455i	0.0633131	+	0.194858i
$505$	−3.85724	−	11.8714i	−0.171645	−	0.528269i
$506$	1.74773	−	1.26980i	0.0776961	−	0.0564495i
$507$	5.70375	−	17.5543i	0.253312	−	0.779615i
$508$	19.3515	−	14.0597i	0.858582	−	0.623797i
$509$	−23.4429	−	17.0322i	−1.03909	−	0.754940i	−0.0689794	−	0.997618i	$-0.521974\pi$
$509$	−23.4429	−	17.0322i	−1.03909	−	0.754940i	−0.970107	+	0.242678i	$0.921974\pi$
$510$	12.0502	+	37.0868i	0.533593	+	1.64223i
$511$	−0.487664	−	0.354308i	−0.0215730	−	0.0156737i
$512$	38.2817	+	27.8133i	1.69183	+	1.22919i
$513$	0.616165	+	1.89636i	0.0272043	+	0.0837263i
$514$	−8.09750	−	5.88318i	−0.357166	−	0.259496i
$515$	−3.73129	+	2.71094i	−0.164420	+	0.119458i
$516$	−26.0559	+	80.1917i	−1.14705	+	3.53024i
$517$	−1.30188	+	0.945874i	−0.0572568	+	0.0415995i
$518$	0.833678	+	2.56580i	0.0366297	+	0.112735i
$519$	−8.63235	−	26.5677i	−0.378918	−	1.16619i
$520$	8.94715	−	27.5365i	0.392358	−	1.20755i
$521$	−12.8122			−0.561314			−0.280657	−	0.959808i	$-0.590552\pi$
$521$	−12.8122			−0.561314			−0.280657	+	0.959808i	$0.590552\pi$
$522$	25.8799			1.13273
$523$	5.92791	−	18.2442i	0.259209	−	0.797764i	−0.733762	−	0.679407i	$-0.762237\pi$
$523$	5.92791	−	18.2442i	0.259209	−	0.797764i	0.992971	−	0.118357i	$-0.0377629\pi$
$524$	−21.7926	−	15.8332i	−0.952014	−	0.691679i
$525$	1.95107	−	1.41753i	0.0851515	−	0.0618662i
$526$	−1.52795			−0.0666218
$527$		0			0
$528$	3.92392			0.170767
$529$	11.4830	−	8.34287i	0.499260	−	0.362733i
$530$	11.0295	+	8.01337i	0.479089	+	0.348079i
$531$	−2.26533	+	6.97197i	−0.0983070	+	0.302558i
$532$	7.79459			0.337938
$533$	−33.9231			−1.46937
$534$	6.10796	−	18.7984i	0.264317	−	0.813485i
$535$	6.41111	+	19.7314i	0.277176	+	0.853061i
$536$	−6.17335	−	18.9996i	−0.266648	−	0.820659i
$537$	−28.8713	+	20.9762i	−1.24589	+	0.905190i
$538$	0.868805	−	2.67391i	0.0374568	−	0.115280i
$539$	1.63497	−	1.18788i	0.0704232	−	0.0511655i
$540$	1.12849	+	0.819896i	0.0485625	+	0.0352827i
$541$	−11.4243	−	35.1604i	−0.491169	−	1.51166i	−0.822842	−	0.568270i	$-0.807613\pi$
$541$	−11.4243	−	35.1604i	−0.491169	−	1.51166i	0.331673	−	0.943394i	$-0.392387\pi$
$542$	−0.419911	−	0.305083i	−0.0180367	−	0.0131044i
$543$	−44.0172	−	31.9804i	−1.88896	−	1.37241i
$544$	−4.14790	−	12.7659i	−0.177840	−	0.547335i
$545$	0.243019	+	0.176563i	0.0104098	+	0.00756314i
$546$	5.98787	−	4.35044i	0.256257	−	0.186182i
$547$	−10.1043	+	31.0979i	−0.432029	+	1.32965i	0.464071	+	0.885798i	$0.346388\pi$
$547$	−10.1043	+	31.0979i	−0.432029	+	1.32965i	−0.896100	+	0.443851i	$0.853612\pi$
$548$	10.1423	−	7.36881i	0.433257	−	0.314780i
$549$	9.68004	+	29.7921i	0.413134	+	1.27150i
$550$	−0.827711	−	2.54743i	−0.0352937	−	0.108623i
$551$	7.14639	−	21.9943i	0.304447	−	0.936990i
$552$	−40.8747			−1.73974
$553$	1.00560			0.0427625
$554$	−19.1881	+	59.0550i	−0.815226	+	2.50901i
$555$	9.37571	+	6.81185i	0.397977	+	0.289147i
$556$	−43.8376	+	31.8499i	−1.85913	+	1.35073i
$557$	28.6262			1.21293			0.606466	−	0.795109i	$-0.292587\pi$
$557$	28.6262			1.21293			0.606466	+	0.795109i	$0.292587\pi$
$558$		0			0
$559$	36.4516			1.54174
$560$	1.34061	−	0.974008i	0.0566510	−	0.0411593i
$561$	3.20724	+	2.33020i	0.135410	+	0.0983811i
$562$	19.8731	−	61.1632i	0.838298	−	2.58001i
$563$	25.7101			1.08355			0.541775	−	0.840523i	$-0.317752\pi$
$563$	25.7101			1.08355			0.541775	+	0.840523i	$0.317752\pi$
$564$	57.7401			2.43130
$565$	0.994486	−	3.06071i	0.0418383	−	0.128765i
$566$	−20.6586	−	63.5805i	−0.868344	−	2.67249i
$567$	−0.707502	−	2.17747i	−0.0297123	−	0.0914450i
$568$	−49.0200	+	35.6151i	−2.05683	+	1.49438i
$569$	7.50317	−	23.0924i	0.314549	−	0.968082i	−0.661391	−	0.750042i	$-0.730033\pi$
$569$	7.50317	−	23.0924i	0.314549	−	0.968082i	0.975940	−	0.218041i	$-0.0699666\pi$
$570$	39.8923	−	28.9835i	1.67091	−	1.21398i
$571$	−10.8708	−	7.89810i	−0.454929	−	0.330525i	0.336610	−	0.941644i	$-0.390720\pi$
$571$	−10.8708	−	7.89810i	−0.454929	−	0.330525i	−0.791539	+	0.611119i	$0.790720\pi$
$572$	−1.72493	−	5.30878i	−0.0721229	−	0.221971i
$573$	−43.5489	−	31.6401i	−1.81928	−	1.32178i
$574$	−4.01377	−	2.91618i	−0.167532	−	0.121719i
$575$	3.37407	+	10.3843i	0.140709	+	0.433056i
$576$	12.0640	+	8.76499i	0.502666	+	0.365208i
$577$	−22.0235	+	16.0010i	−0.916850	+	0.666131i	−0.942738	−	0.333534i	$-0.891759\pi$
$577$	−22.0235	+	16.0010i	−0.916850	+	0.666131i	0.0258878	+	0.999665i	$0.491759\pi$
$578$	10.1932	−	31.3714i	0.423981	−	1.30488i
$579$	−4.42410	+	3.21430i	−0.183859	+	0.133582i
$580$	−4.99934	−	15.3864i	−0.207586	−	0.638885i
$581$	−0.228778	−	0.704107i	−0.00949132	−	0.0292113i
$582$	3.84749	−	11.8414i	0.159484	−	0.490840i
$583$	1.38598			0.0574016
$584$	12.6673			0.524175
$585$	5.00561	−	15.4057i	0.206957	−	0.636947i
$586$	−45.1616	−	32.8118i	−1.86561	−	1.35544i
$587$	−3.42762	+	2.49031i	−0.141473	+	0.102786i	−0.656271	−	0.754526i	$-0.727867\pi$
$587$	−3.42762	+	2.49031i	−0.141473	+	0.102786i	0.514798	+	0.857312i	$0.327867\pi$
$588$	−72.5129			−2.99038
$589$		0			0
$590$	6.74878			0.277843
$591$	−34.7992	+	25.2831i	−1.43145	+	1.04001i
$592$	−17.9488	−	13.0406i	−0.737690	−	0.535963i
$593$	−5.75322	+	17.7066i	−0.236256	+	0.727122i	0.760696	+	0.649108i	$0.224858\pi$
$593$	−5.75322	+	17.7066i	−0.236256	+	0.727122i	−0.996952	+	0.0780138i	$0.975142\pi$
$594$	0.208838			0.00856874
$595$	1.67416			0.0686340
$596$	22.8206	−	70.2346i	0.934769	−	2.87692i
$597$	8.98707	+	27.6594i	0.367816	+	1.13202i
$598$	10.3551	+	31.8697i	0.423452	+	1.30325i
$599$	8.70564	−	6.32502i	0.355703	−	0.258433i	−0.395555	−	0.918442i	$-0.629448\pi$
$599$	8.70564	−	6.32502i	0.355703	−	0.258433i	0.751257	+	0.660009i	$0.229448\pi$
$600$	−15.6609	+	48.1993i	−0.639354	+	1.96773i
$601$	17.1589	−	12.4666i	0.699924	−	0.508525i	−0.179983	−	0.983670i	$-0.557604\pi$
$601$	17.1589	−	12.4666i	0.699924	−	0.508525i	0.879908	+	0.475145i	$0.157604\pi$
$602$	4.31295	+	3.13354i	0.175783	+	0.127714i
$603$	−3.45377	−	10.6296i	−0.140648	−	0.432871i
$604$	74.2507	+	53.9463i	3.02122	+	2.19504i
$605$	−10.1477	−	7.37272i	−0.412562	−	0.299744i
$606$	20.7209	+	63.7725i	0.841731	+	2.59058i
$607$	8.64642	+	6.28199i	0.350947	+	0.254978i	0.749266	−	0.662269i	$-0.230406\pi$
$607$	8.64642	+	6.28199i	0.350947	+	0.254978i	−0.398319	+	0.917247i	$0.630406\pi$
$608$	−13.7317	+	9.97664i	−0.556893	+	0.404606i
$609$	0.673907	−	2.07407i	0.0273081	−	0.0840457i
$610$	23.3307	−	16.9508i	0.944633	−	0.686316i
$611$	−7.71352	−	23.7398i	−0.312056	−	0.960408i
$612$	−22.3949	−	68.9244i	−0.905260	−	2.78610i
$613$	2.29878	−	7.07492i	0.0928469	−	0.285753i	−0.893840	−	0.448387i	$-0.851999\pi$
$613$	2.29878	−	7.07492i	0.0928469	−	0.285753i	0.986687	+	0.162633i	$0.0519988\pi$
$614$	18.1922			0.734176
$615$	−21.3121			−0.859386
$616$	0.133029	−	0.409421i	0.00535989	−	0.0164961i
$617$	−10.8921	−	7.91356i	−0.438499	−	0.318588i	0.346539	−	0.938035i	$-0.387357\pi$
$617$	−10.8921	−	7.91356i	−0.438499	−	0.318588i	−0.785038	+	0.619447i	$0.787357\pi$
$618$	20.0443	−	14.5631i	0.806301	−	0.585812i
$619$	−6.91762			−0.278043			−0.139021	−	0.990289i	$-0.544396\pi$
$619$	−6.91762			−0.278043			−0.139021	+	0.990289i	$0.544396\pi$
$620$		0			0
$621$	−0.851305			−0.0341617
$622$	51.7042	−	37.5653i	2.07315	−	1.50623i
$623$	−0.686525	−	0.498790i	−0.0275050	−	0.0199836i
$624$	−18.8087	+	57.8872i	−0.752950	+	2.31734i
$625$	6.93487			0.277395
$626$	63.5966			2.54183
$627$	1.54909	−	4.76760i	0.0618646	−	0.190400i
$628$	−19.0012	−	58.4798i	−0.758232	−	2.33360i
$629$	−6.92649	−	21.3176i	−0.276177	−	0.849987i
$630$	1.91661	−	1.39250i	0.0763594	−	0.0554783i
$631$	4.20155	−	12.9310i	0.167261	−	0.514776i	−0.831935	−	0.554873i	$-0.812767\pi$
$631$	4.20155	−	12.9310i	0.167261	−	0.514776i	0.999196	+	0.0400970i	$0.0127667\pi$
$632$	−17.0964	+	12.4212i	−0.680057	+	0.494090i
$633$	14.9356	+	10.8513i	0.593635	+	0.431301i
$634$	−10.9822	−	33.7997i	−0.436159	−	1.34236i
$635$	−5.25578	−	3.81855i	−0.208569	−	0.151534i
$636$	−40.2327	−	29.2307i	−1.59533	−	1.15907i
$637$	9.68703	+	29.8136i	0.383814	+	1.18126i
$638$	−1.95956	−	1.42370i	−0.0775796	−	0.0563649i
$639$	−27.4250	+	19.9254i	−1.08491	+	0.788237i
$640$	5.97656	−	18.3940i	0.236244	−	0.727085i
$641$	3.10111	−	2.25309i	0.122486	−	0.0889916i	−0.524855	−	0.851191i	$-0.675881\pi$
$641$	3.10111	−	2.25309i	0.122486	−	0.0889916i	0.647342	+	0.762200i	$0.275881\pi$
$642$	−34.4402	−	105.996i	−1.35925	−	4.18333i
$643$	−2.38860	−	7.35135i	−0.0941972	−	0.289909i	0.892846	−	0.450361i	$-0.148705\pi$
$643$	−2.38860	−	7.35135i	−0.0941972	−	0.289909i	−0.987044	+	0.160452i	$0.948705\pi$
$644$	−1.02836	+	3.16498i	−0.0405232	+	0.124718i
$645$	22.9006			0.901710
$646$	−95.3711			−3.75233
$647$	5.74621	−	17.6850i	0.225907	−	0.695269i	−0.772292	−	0.635268i	$-0.780890\pi$
$647$	5.74621	−	17.6850i	0.225907	−	0.695269i	0.998198	−	0.0600011i	$-0.0191104\pi$
$648$	38.9245	+	28.2803i	1.52910	+	1.11096i
$649$	0.555066	−	0.403279i	0.0217882	−	0.0158301i
$650$	41.5482			1.62965
$651$		0			0
$652$	0.290402			0.0113730
$653$	31.7555	−	23.0717i	1.24269	−	0.902867i	0.244916	−	0.969544i	$-0.421240\pi$
$653$	31.7555	−	23.0717i	1.24269	−	0.902867i	0.997775	+	0.0666771i	$0.0212397\pi$
$654$	−1.30549	−	0.948491i	−0.0510485	−	0.0370889i
$655$	−2.26077	+	6.95795i	−0.0883357	+	0.271869i
$656$	40.7997			1.59296
$657$	7.08689			0.276486
$658$	1.12811	−	3.47198i	0.0439784	−	0.135352i
$659$	4.22762	+	13.0113i	0.164685	+	0.506847i	0.999013	−	0.0444209i	$-0.0141443\pi$
$659$	4.22762	+	13.0113i	0.164685	+	0.506847i	−0.834328	+	0.551268i	$0.814144\pi$
$660$	−1.08368	−	3.33523i	−0.0421823	−	0.129824i
$661$	32.1249	−	23.3401i	1.24952	−	0.907826i	0.251322	−	0.967904i	$-0.419135\pi$
$661$	32.1249	−	23.3401i	1.24952	−	0.907826i	0.998194	+	0.0600775i	$0.0191348\pi$
$662$	−13.4926	+	41.5260i	−0.524405	+	1.61395i
$663$	−49.7493	+	36.1450i	−1.93210	+	1.40376i
$664$	12.5867	+	9.14474i	0.488457	+	0.354885i
$665$	−0.654183	−	2.01337i	−0.0253681	−	0.0780751i
$666$	−25.6606	−	18.6435i	−0.994327	−	0.722421i
$667$	7.98791	+	5.80355i	0.309293	+	0.224715i
$668$	−6.35009	−	19.5436i	−0.245692	−	0.756163i
$669$	−58.3150	−	42.3683i	−2.25459	−	1.63805i
$670$	−8.32424	+	6.04791i	−0.321593	+	0.233651i
$671$	0.905971	−	2.78829i	0.0349746	−	0.107641i
$672$	−1.29490	+	0.940801i	−0.0499519	+	0.0362922i
$673$	7.94454	+	24.4508i	0.306240	+	0.942508i	0.979212	+	0.202841i	$0.0650173\pi$
$673$	7.94454	+	24.4508i	0.306240	+	0.942508i	−0.672972	+	0.739668i	$0.734983\pi$
$674$	−12.6686	−	38.9898i	−0.487975	−	1.50183i
$675$	−0.326173	+	1.00386i	−0.0125544	+	0.0386384i
$676$	31.5797			1.21460
$677$	6.94713			0.267000			0.133500	−	0.991049i	$-0.457378\pi$
$677$	6.94713			0.267000			0.133500	+	0.991049i	$0.457378\pi$
$678$	−5.34233	+	16.4420i	−0.205171	+	0.631452i
$679$	−0.432452	−	0.314195i	−0.0165960	−	0.0120577i
$680$	−28.4626	+	20.6793i	−1.09149	+	0.793016i
$681$	14.7091			0.563654
$682$		0			0
$683$	28.4558			1.08883			0.544415	−	0.838816i	$-0.316752\pi$
$683$	28.4558			1.08883			0.544415	+	0.838816i	$0.316752\pi$
$684$	−74.1385	+	53.8648i	−2.83476	+	2.05957i
$685$	−2.75461	−	2.00134i	−0.105248	−	0.0764672i
$686$	−2.84785	+	8.76477i	−0.108731	+	0.334640i
$687$	13.8272			0.527542
$688$	−43.8407			−1.67141
$689$	−6.64349	+	20.4466i	−0.253097	+	0.778952i
$690$	6.50557	+	20.0221i	0.247663	+	0.762227i
$691$	9.04130	+	27.8263i	0.343947	+	1.05856i	0.962145	+	0.272538i	$0.0878631\pi$
$691$	9.04130	+	27.8263i	0.343947	+	1.05856i	−0.618198	+	0.786023i	$0.712137\pi$
$692$	38.6665	−	28.0928i	1.46988	−	1.06793i
$693$	0.0744251	−	0.229057i	0.00282717	−	0.00870115i
$694$	−52.6839	+	38.2771i	−1.99985	+	1.45298i
$695$	11.9061	+	8.65030i	0.451625	+	0.328124i
$696$	14.1619	+	43.5857i	0.536804	+	1.65211i
$697$	33.3479	+	24.2286i	1.26314	+	0.917726i
$698$	−21.6002	−	15.6935i	−0.817580	−	0.594007i
$699$	−20.1594	−	62.0444i	−0.762500	−	2.34673i
$700$	3.33812	+	2.42529i	0.126169	+	0.0916672i
$701$	6.86101	−	4.98481i	0.259137	−	0.188274i	−0.450630	−	0.892711i	$-0.648800\pi$
$701$	6.86101	−	4.98481i	0.259137	−	0.188274i	0.709766	+	0.704437i	$0.248800\pi$
$702$	−1.00103	+	3.08086i	−0.0377815	+	0.116280i
$703$	−22.9302	+	16.6598i	−0.864829	+	0.628335i
$704$	−0.431273	−	1.32732i	−0.0162542	−	0.0500253i
$705$	−4.84600	−	14.9144i	−0.182511	−	0.561710i
$706$	−10.5227	+	32.3855i	−0.396026	+	1.21884i
$707$	2.87881			0.108269
$708$	−24.6178			−0.925194
$709$	−14.6786	+	45.1759i	−0.551265	+	1.69662i	0.154345	+	0.988017i	$0.450673\pi$
$709$	−14.6786	+	45.1759i	−0.551265	+	1.69662i	−0.705610	+	0.708601i	$0.749327\pi$
$710$	25.2477	+	18.3435i	0.947529	+	0.688420i
$711$	−9.56481	+	6.94924i	−0.358708	+	0.260617i
$712$	17.8328			0.668311
$713$		0			0
$714$	−8.99353			−0.336574
$715$	−1.22651	+	0.891109i	−0.0458687	+	0.0333256i
$716$	−49.3964	−	35.8886i	−1.84603	−	1.34122i
$717$	−15.9135	+	48.9767i	−0.594300	+	1.82907i
$718$	5.21683			0.194691
$719$	−17.6251			−0.657305			−0.328652	−	0.944451i	$-0.606594\pi$
$719$	−17.6251			−0.657305			−0.328652	+	0.944451i	$0.606594\pi$
$720$	−6.02031	+	18.5286i	−0.224364	+	0.690520i
$721$	−0.328701	−	1.01164i	−0.0122415	−	0.0376754i
$722$	22.6103	+	69.5872i	0.841467	+	2.58977i
$723$	28.5318	−	20.7296i	1.06111	−	0.770941i
$724$	28.7658	−	88.5322i	1.06907	−	3.29027i
$725$	9.90405	−	7.19572i	0.367827	−	0.267242i
$726$	54.5129	+	39.6059i	2.02316	+	1.46991i
$727$	−1.23068	−	3.78764i	−0.0456434	−	0.140476i	0.925638	−	0.378411i	$-0.123529\pi$
$727$	−1.23068	−	3.78764i	−0.0456434	−	0.140476i	−0.971281	+	0.237935i	$0.923529\pi$
$728$	5.40228	+	3.92499i	0.200222	+	0.145470i
$729$	23.4988	+	17.0728i	0.870324	+	0.632328i
$730$	−2.01611	−	6.20494i	−0.0746195	−	0.229655i
$731$	−35.8335	−	26.0346i	−1.32535	−	0.962923i
$732$	−85.1045	+	61.8320i	−3.14555	+	2.28538i
$733$	−8.49419	+	26.1424i	−0.313740	+	0.965592i	0.662530	+	0.749035i	$0.269483\pi$
$733$	−8.49419	+	26.1424i	−0.313740	+	0.965592i	−0.976270	+	0.216557i	$0.930517\pi$
$734$	40.2286	−	29.2278i	1.48486	−	1.07882i
$735$	6.08585	+	18.7303i	0.224480	+	0.690878i
$736$	−2.23933	−	6.89196i	−0.0825429	−	0.254041i
$737$	−0.323244	+	0.994844i	−0.0119069	+	0.0366455i
$738$	58.3295			2.14714
$739$	20.5710			0.756716			0.378358	−	0.925659i	$-0.376489\pi$
$739$	20.5710			0.756716			0.378358	+	0.925659i	$0.376489\pi$
$740$	−6.12715	+	18.8574i	−0.225239	+	0.693213i
$741$	62.9081	+	45.7054i	2.31099	+	1.67903i
$742$	−2.54373	+	1.84813i	−0.0933834	+	0.0678470i
$743$	9.45031			0.346698			0.173349	−	0.984860i	$-0.444541\pi$
$743$	9.45031			0.346698			0.173349	+	0.984860i	$0.444541\pi$
$744$		0			0
$745$	−20.0571			−0.734836
$746$	−21.6567	+	15.7345i	−0.792908	+	0.576081i
$747$	7.04179	+	5.11616i	0.257646	+	0.187190i
$748$	−2.09598	+	6.45076i	−0.0766365	+	0.235863i
$749$	−4.78485			−0.174835
$750$	61.5738			2.24836
$751$	3.59167	−	11.0540i	0.131062	−	0.403367i	−0.863895	−	0.503672i	$-0.831982\pi$
$751$	3.59167	−	11.0540i	0.131062	−	0.403367i	0.994957	+	0.100305i	$0.0319819\pi$
$752$	9.27714	+	28.5521i	0.338303	+	1.04119i
$753$	−6.72558	−	20.6992i	−0.245094	−	0.754321i
$754$	30.3958	−	22.0838i	1.10695	−	0.804245i
$755$	7.70280	−	23.7068i	0.280334	−	0.862779i
$756$	−0.260265	+	0.189093i	−0.00946574	+	0.00687726i
$757$	−19.7315	−	14.3358i	−0.717155	−	0.521044i	0.168319	−	0.985733i	$-0.446166\pi$
$757$	−19.7315	−	14.3358i	−0.717155	−	0.521044i	−0.885474	+	0.464689i	$0.846166\pi$
$758$	10.9178	+	33.6016i	0.396553	+	1.22047i
$759$	1.73150	+	1.25801i	0.0628494	+	0.0456628i
$760$	35.9911	+	26.1490i	1.30553	+	0.948525i
$761$	−7.06038	−	21.7296i	−0.255939	−	0.787698i	−0.993643	−	0.112575i	$-0.964090\pi$
$761$	−7.06038	−	21.7296i	−0.255939	−	0.787698i	0.737705	−	0.675124i	$-0.235910\pi$
$762$	28.2338	+	20.5131i	1.02280	+	0.743110i
$763$	−0.0560476	+	0.0407210i	−0.00202906	+	0.00147420i
$764$	28.4598	−	87.5902i	1.02964	−	3.16890i
$765$	−15.9238	+	11.5694i	−0.575728	+	0.418291i
$766$	−13.7739	−	42.3917i	−0.497671	−	1.53168i
$767$	3.28870	+	10.1216i	0.118748	+	0.365469i
$768$	−24.7914	+	76.3000i	−0.894581	+	2.75324i
$769$	−22.9431			−0.827349			−0.413674	−	0.910425i	$-0.635755\pi$
$769$	−22.9431			−0.827349			−0.413674	+	0.910425i	$0.635755\pi$
$770$	−0.221724			−0.00799037
$771$	3.06425	−	9.43078i	0.110356	−	0.339641i
$772$	−7.56929	−	5.49941i	−0.272425	−	0.197928i
$773$	−29.8486	+	21.6863i	−1.07358	+	0.780002i	−0.976552	−	0.215280i	$-0.930934\pi$
$773$	−29.8486	+	21.6863i	−1.07358	+	0.780002i	−0.0970280	+	0.995282i	$0.530934\pi$
$774$	−62.6771			−2.25288
$775$		0			0
$776$	11.2331			0.403246
$777$	−2.16233	+	1.57102i	−0.0775731	+	0.0563601i
$778$	−47.4200	−	34.4526i	−1.70009	−	1.23519i
$779$	16.1069	−	49.5720i	0.577090	−	1.77610i
$780$	54.3970			1.94772
$781$	3.17268			0.113527
$782$	12.5826	−	38.7252i	0.449952	−	1.38481i
$783$	0.294952	+	0.907768i	0.0105407	+	0.0324410i
$784$	−11.6507	−	35.8572i	−0.416097	−	1.28061i
$785$	−13.5108	+	9.81616i	−0.482221	+	0.350354i
$786$	12.1448	−	37.3778i	0.433190	−	1.33322i
$787$	−42.9918	+	31.2353i	−1.53249	+	1.11342i	−0.577657	+	0.816279i	$0.696033\pi$
$787$	−42.9918	+	31.2353i	−1.53249	+	1.11342i	−0.954834	+	0.297140i	$0.903967\pi$
$788$	−59.5387	−	43.2574i	−2.12098	−	1.54098i
$789$	−0.467777	−	1.43967i	−0.0166533	−	0.0512536i
$790$	8.80546	+	6.39754i	0.313284	+	0.227614i
$791$	0.600470	+	0.436267i	0.0213503	+	0.0155119i
$792$	1.56401	+	4.81352i	0.0555746	+	0.171041i
$793$	36.7913	+	26.7304i	1.30650	+	0.949226i
$794$	20.4096	−	14.8284i	0.724309	−	0.526241i
$795$	−4.17375	+	12.8455i	−0.148028	+	0.455583i
$796$	−40.2553	+	29.2472i	−1.42681	+	1.03664i
$797$	−5.21550	−	16.0517i	−0.184743	−	0.568579i	0.815201	−	0.579178i	$-0.196626\pi$
$797$	−5.21550	−	16.0517i	−0.184743	−	0.568579i	−0.999944	+	0.0105987i	$0.996626\pi$
$798$	3.51424	+	10.8157i	0.124403	+	0.382873i
$799$	−9.37277	+	28.8464i	−0.331585	+	1.02051i
$800$	−8.98497			−0.317667
$801$	9.97681			0.352513
$802$	17.6439	−	54.3024i	0.623028	−	1.91748i
$803$	−0.536600	−	0.389863i	−0.0189362	−	0.0137580i
$804$	30.3647	−	22.0612i	1.07088	−	0.778040i
$805$	0.903832			0.0318559
$806$		0			0
$807$	2.78540			0.0980508
$808$	−48.9429	+	35.5591i	−1.72181	+	1.25097i
$809$	2.86187	+	2.07927i	0.100618	+	0.0731033i	0.636957	−	0.770900i	$-0.280193\pi$
$809$	2.86187	+	2.07927i	0.100618	+	0.0731033i	−0.536339	+	0.844003i	$0.680193\pi$
$810$	7.65766	−	23.5679i	0.269063	−	0.828090i
$811$	−11.8457			−0.415957			−0.207979	−	0.978133i	$-0.566688\pi$
$811$	−11.8457			−0.415957			−0.207979	+	0.978133i	$0.566688\pi$
$812$	3.73119			0.130939
$813$	0.158902	−	0.489050i	0.00557294	−	0.0171517i
$814$	0.917336	+	2.82327i	0.0321526	+	0.0989556i
$815$	−0.0243728	−	0.0750118i	−0.000853742	−	0.00262755i
$816$	59.8341	−	43.4720i	2.09461	−	1.52183i
$817$	−17.3075	+	53.2669i	−0.605511	+	1.86357i
$818$	26.6458	−	19.3593i	0.931648	−	0.676882i
$819$	3.02239	+	2.19589i	0.105611	+	0.0767307i
$820$	−11.2678	−	34.6786i	−0.393488	−	1.21103i
$821$	34.9655	+	25.4039i	1.22030	+	0.886603i	0.996125	−	0.0879445i	$-0.0280298\pi$
$821$	34.9655	+	25.4039i	1.22030	+	0.886603i	0.224179	+	0.974548i	$0.428030\pi$
$822$	14.7976	+	10.7511i	0.516127	+	0.374988i
$823$	−8.36589	−	25.7476i	−0.291617	−	0.897504i	−0.984337	−	0.176297i	$-0.943588\pi$
$823$	−8.36589	−	25.7476i	−0.291617	−	0.897504i	0.692720	−	0.721206i	$-0.256412\pi$
$824$	18.0841	+	13.1389i	0.629989	+	0.457714i
$825$	2.14685	−	1.55978i	0.0747438	−	0.0543045i
$826$	−0.480978	+	1.48030i	−0.0167354	+	0.0515061i
$827$	3.55279	−	2.58125i	0.123542	−	0.0897589i	−0.524298	−	0.851535i	$-0.675672\pi$
$827$	3.55279	−	2.58125i	0.123542	−	0.0897589i	0.647841	+	0.761776i	$0.275672\pi$
$828$	−12.0904	−	37.2103i	−0.420169	−	1.29315i
$829$	−4.99416	−	15.3704i	−0.173454	−	0.533837i	0.826105	−	0.563516i	$-0.190552\pi$
$829$	−4.99416	−	15.3704i	−0.173454	−	0.533837i	−0.999559	+	0.0296787i	$0.990552\pi$
$830$	2.47619	−	7.62092i	0.0859497	−	0.264526i
$831$	−61.5174			−2.13402
$832$	21.6484			0.750523
$833$	11.7708	−	36.2268i	0.407834	−	1.25518i
$834$	−63.9591	−	46.4690i	−2.21472	−	1.60909i
$835$	−4.51522	+	3.28050i	−0.156256	+	0.113526i
$836$	8.57677			0.296634
$837$		0			0
$838$	−11.1317			−0.384537
$839$	−38.7928	+	28.1846i	−1.33928	+	0.973042i	−0.339807	+	0.940495i	$0.610362\pi$
$839$	−38.7928	+	28.1846i	−1.33928	+	0.973042i	−0.999470	+	0.0325468i	$0.989638\pi$
$840$	3.39397	+	2.46586i	0.117103	+	0.0850804i
$841$	−5.54059	+	17.0522i	−0.191055	+	0.588006i
$842$	−48.2357			−1.66231
$843$	63.7136			2.19441
$844$	−9.76059	+	30.0400i	−0.335973	+	1.03402i
$845$	−2.65041	−	8.15714i	−0.0911770	−	0.280614i
$846$	13.2631	+	40.8197i	0.455995	+	1.40341i
$847$	2.34037	−	1.70038i	0.0804160	−	0.0584256i
$848$	7.99021	−	24.5913i	0.274385	−	0.844469i
$849$	53.5825	−	38.9300i	1.83895	−	1.33607i
$850$	−40.8437	−	29.6747i	−1.40093	−	1.01783i
$851$	−3.73942	−	11.5087i	−0.128186	−	0.394514i
$852$	−92.0971	−	66.9125i	−3.15520	−	2.29238i
$853$	−26.2469	−	19.0695i	−0.898678	−	0.652928i	0.0394480	−	0.999222i	$-0.487440\pi$
$853$	−26.2469	−	19.0695i	−0.898678	−	0.652928i	−0.938126	+	0.346294i	$0.887440\pi$
$854$	2.05528	+	6.32549i	0.0703301	+	0.216454i
$855$	20.1357	+	14.6295i	0.688627	+	0.500317i
$856$	81.3478	−	59.1026i	2.78041	−	2.02009i
$857$	1.67703	−	5.16138i	0.0572864	−	0.176309i	−0.918319	−	0.395841i	$-0.870453\pi$
$857$	1.67703	−	5.16138i	0.0572864	−	0.176309i	0.975605	+	0.219532i	$0.0704530\pi$
$858$	6.58874	−	4.78700i	0.224936	−	0.163425i
$859$	12.5034	+	38.4814i	0.426609	+	1.31297i	0.901445	+	0.432894i	$0.142507\pi$
$859$	12.5034	+	38.4814i	0.426609	+	1.31297i	−0.474836	+	0.880074i	$0.657493\pi$
$860$	12.1076	+	37.2635i	0.412867	+	1.27067i
$861$	1.51889	−	4.67465i	0.0517635	−	0.159312i
$862$	−26.0740			−0.888083
$863$	−2.36274			−0.0804287			−0.0402144	−	0.999191i	$-0.512804\pi$
$863$	−2.36274			−0.0804287			−0.0402144	+	0.999191i	$0.512804\pi$
$864$	0.216477	−	0.666248i	0.00736470	−	0.0226662i
$865$	−10.5017	−	7.62990i	−0.357067	−	0.259424i
$866$	41.8642	−	30.4161i	1.42260	−	1.03358i
$867$	32.6795			1.10985
$868$		0			0
$869$	1.10651			0.0375358
$870$	19.0961	−	13.8741i	0.647417	−	0.470376i
$871$	−13.1269	−	9.53724i	−0.444788	−	0.323157i
$872$	0.449885	−	1.38460i	0.0152350	−	0.0468886i
$873$	6.28453			0.212699
$874$	−51.4881			−1.74161
$875$	0.816890	−	2.51413i	0.0276159	−	0.0849930i
$876$	7.35424	+	22.6340i	0.248477	+	0.764733i
$877$	−10.3236	−	31.7729i	−0.348604	−	1.07289i	−0.959626	−	0.281280i	$-0.909241\pi$
$877$	−10.3236	−	31.7729i	−0.348604	−	1.07289i	0.611021	−	0.791614i	$-0.290759\pi$
$878$	−57.2641	+	41.6048i	−1.93257	+	1.40409i
$879$	17.0900	−	52.5976i	0.576431	−	1.77407i
$880$	1.47513	−	1.07175i	0.0497268	−	0.0361286i
$881$	37.9288	+	27.5569i	1.27785	+	0.928415i	0.999486	−	0.0320593i	$-0.0102066\pi$
$881$	37.9288	+	27.5569i	1.27785	+	0.928415i	0.278368	+	0.960475i	$0.410207\pi$
$882$	−16.6565	−	51.2634i	−0.560853	−	1.72613i
$883$	25.0137	+	18.1736i	0.841780	+	0.611589i	0.922867	−	0.385118i	$-0.125839\pi$
$883$	25.0137	+	18.1736i	0.841780	+	0.611589i	−0.0810876	+	0.996707i	$0.525839\pi$
$884$	−85.1172	−	61.8413i	−2.86280	−	2.07995i
$885$	2.06612	+	6.35886i	0.0694518	+	0.213751i
$886$	59.0029	+	42.8681i	1.98224	+	1.44018i
$887$	−28.2176	+	20.5013i	−0.947455	+	0.688367i	−0.950204	−	0.311630i	$-0.899125\pi$
$887$	−28.2176	+	20.5013i	−0.947455	+	0.688367i	0.00274837	+	0.999996i	$0.499125\pi$
$888$	17.3567	−	53.4183i	0.582451	−	1.79260i
$889$	1.21215	−	0.880675i	0.0406540	−	0.0295369i
$890$	−2.83824	−	8.73521i	−0.0951381	−	0.292805i
$891$	−0.778499	−	2.39597i	−0.0260807	−	0.0802681i
$892$	38.1097	−	117.289i	1.27601	−	3.92714i
$893$	38.3535			1.28345
$894$	107.746			3.60356
$895$	−5.12441	+	15.7713i	−0.171290	+	0.527177i
$896$	3.60864	+	2.62183i	0.120556	+	0.0875893i
$897$	−26.8582	+	19.5137i	−0.896771	+	0.651542i
$898$	2.91220			0.0971813
$899$		0			0
$900$	−48.5106			−1.61702
$901$	21.1343	−	15.3549i	0.704084	−	0.511547i
$902$	−4.41655	−	3.20881i	−0.147055	−	0.106842i
$903$	−1.63210	+	5.02309i	−0.0543129	+	0.167158i
$904$	−15.5975			−0.518764
$905$	−25.2824			−0.840415
$906$	−41.3791	+	127.352i	−1.37473	+	4.23098i
$907$	−13.5579	−	41.7269i	−0.450182	−	1.38552i	−0.876700	−	0.481038i	$-0.840260\pi$
$907$	−13.5579	−	41.7269i	−0.450182	−	1.38552i	0.426518	−	0.904479i	$-0.359740\pi$
$908$	7.77675	+	23.9344i	0.258081	+	0.794290i
$909$	−27.3818	+	19.8941i	−0.908198	+	0.659845i
$910$	1.06280	−	3.27095i	0.0352314	−	0.108431i
$911$	35.3621	−	25.6921i	1.17160	−	0.851216i	0.180399	−	0.983593i	$-0.442261\pi$
$911$	35.3621	−	25.6921i	1.17160	−	0.851216i	0.991199	+	0.132377i	$0.0422610\pi$
$912$	−75.6603	−	54.9705i	−2.50536	−	1.82025i
$913$	−0.251736	−	0.774763i	−0.00833124	−	0.0256409i
$914$	−81.3495	−	59.1039i	−2.69080	−	1.95498i
$915$	23.1140	+	16.7933i	0.764126	+	0.555170i
$916$	7.31051	+	22.4994i	0.241546	+	0.743403i
$917$	−1.36505	−	0.991770i	−0.0450781	−	0.0327511i
$918$	3.18448	−	2.31366i	0.105104	−	0.0763622i
$919$	−11.1166	+	34.2135i	−0.366704	+	1.12860i	0.582203	+	0.813044i	$0.302191\pi$
$919$	−11.1166	+	34.2135i	−0.366704	+	1.12860i	−0.948907	+	0.315556i	$0.897809\pi$
$920$	−15.3662	+	11.1642i	−0.506608	+	0.368072i
$921$	5.56948	+	17.1411i	0.183521	+	0.564818i
$922$	−22.6318	−	69.6535i	−0.745338	−	2.29392i
$923$	−15.2077	+	46.8045i	−0.500568	+	1.54059i
$924$	0.808792			0.0266073
$925$	−15.0038			−0.493322
$926$	−0.493304	+	1.51823i	−0.0162110	+	0.0498922i
$927$	10.1174	+	7.35073i	0.332299	+	0.241430i
$928$	−6.57321	+	4.77572i	−0.215776	+	0.156771i
$929$	7.67225			0.251719			0.125859	−	0.992048i	$-0.459831\pi$
$929$	7.67225			0.251719			0.125859	+	0.992048i	$0.459831\pi$
$930$		0			0
$931$	−48.1663			−1.57859
$932$	90.2991	−	65.6062i	2.95785	−	2.14900i
$933$	51.2241	+	37.2165i	1.67700	+	1.21841i
$934$	2.23347	−	6.87393i	0.0730815	−	0.224922i
$935$	1.84216			0.0602451
$936$	−78.5077			−2.56611
$937$	13.3194	−	40.9930i	0.435127	−	1.33918i	−0.457830	−	0.889040i	$-0.651373\pi$
$937$	13.3194	−	40.9930i	0.435127	−	1.33918i	0.892957	−	0.450142i	$-0.148627\pi$
$938$	−0.733309	−	2.25689i	−0.0239434	−	0.0736901i
$939$	19.4699	+	59.9222i	0.635376	+	1.95549i
$940$	21.7064	−	15.7706i	0.707986	−	0.514382i
$941$	−11.4255	+	35.1641i	−0.372461	+	1.14632i	0.572715	+	0.819755i	$0.305890\pi$
$941$	−11.4255	+	35.1641i	−0.372461	+	1.14632i	−0.945176	+	0.326562i	$0.894110\pi$
$942$	72.5793	−	52.7320i	2.36476	−	1.71810i
$943$	18.0036	+	13.0804i	0.586277	+	0.425955i
$944$	−3.95536	−	12.1734i	−0.128736	−	0.396209i
$945$	0.0706869	+	0.0513570i	0.00229944	+	0.00167064i
$946$	4.74574	+	3.44798i	0.154297	+	0.112104i
$947$	−18.0782	−	55.6390i	−0.587463	−	1.80802i	−0.589147	−	0.808026i	$-0.700536\pi$
$947$	−18.0782	−	55.6390i	−0.587463	−	1.80802i	0.00168400	−	0.999999i	$-0.499464\pi$
$948$	−32.1201	−	23.3366i	−1.04321	−	0.757937i
$949$	8.32350	−	6.04738i	0.270192	−	0.196306i
$950$	−19.7274	+	60.7146i	−0.640040	+	1.96984i
$951$	28.4848	−	20.6954i	0.923682	−	0.671094i
$952$	−2.50736	−	7.71687i	−0.0812642	−	0.250105i
$953$	16.4513	+	50.6318i	0.532908	+	1.64012i	0.748126	+	0.663557i	$0.230954\pi$
$953$	16.4513	+	50.6318i	0.532908	+	1.64012i	−0.215217	+	0.976566i	$0.569046\pi$
$954$	11.4232	−	35.1571i	0.369841	−	1.13825i
$955$	−25.0134			−0.809414
$956$	−88.1075			−2.84960
$957$	0.741533	−	2.28220i	0.0239703	−	0.0737731i
$958$	−58.4523	−	42.4681i	−1.88851	−	1.37208i
$959$	0.635297	−	0.461571i	0.0205148	−	0.0149049i
$960$	13.6005			0.438956
$961$		0			0
$962$	−46.0470			−1.48462
$963$	45.5112	−	33.0658i	1.46658	−	1.06553i
$964$	48.8156	+	35.4666i	1.57225	+	1.14230i
$965$	−0.785242	+	2.41673i	−0.0252778	+	0.0777971i
$966$	−4.85535			−0.156218
$967$	−12.1008			−0.389134			−0.194567	−	0.980889i	$-0.562330\pi$
$967$	−12.1008			−0.389134			−0.194567	+	0.980889i	$0.562330\pi$
$968$	−18.7858	+	57.8166i	−0.603797	+	1.85830i
$969$	−29.1976	−	89.8609i	−0.937961	−	2.88675i
$970$	−1.78785	−	5.50244i	−0.0574044	−	0.176673i
$971$	−8.63101	+	6.27079i	−0.276982	+	0.201239i	−0.717600	−	0.696455i	$-0.754759\pi$
$971$	−8.63101	+	6.27079i	−0.276982	+	0.201239i	0.440618	+	0.897695i	$0.354759\pi$
$972$	−29.0585	+	89.4327i	−0.932050	+	2.86856i
$973$	−2.74592	+	1.99503i	−0.0880300	+	0.0639576i
$974$	5.51974	+	4.01033i	0.176864	+	0.128499i
$975$	12.7199	+	39.1477i	0.407361	+	1.25373i
$976$	−44.2493	−	32.1490i	−1.41639	−	1.02907i
$977$	38.0219	+	27.6245i	1.21643	+	0.883786i	0.995798	−	0.0915721i	$-0.0291892\pi$
$977$	38.0219	+	27.6245i	1.21643	+	0.883786i	0.220628	+	0.975358i	$0.429189\pi$
$978$	0.130930	+	0.402960i	0.00418667	+	0.0128852i
$979$	−0.755417	−	0.548842i	−0.0241432	−	0.0175411i
$980$	−27.2600	+	19.8056i	−0.870790	+	0.632666i
$981$	0.251695	−	0.774637i	0.00803600	−	0.0247323i
$982$	−23.0823	+	16.7703i	−0.736587	+	0.535162i
$983$	3.55800	+	10.9504i	0.113483	+	0.349264i	0.991628	−	0.129131i	$-0.0412188\pi$
$983$	3.55800	+	10.9504i	0.113483	+	0.349264i	−0.878145	+	0.478395i	$0.841219\pi$
$984$	31.9187	+	98.2357i	1.01753	+	3.13164i
$985$	−6.17658	+	19.0095i	−0.196802	+	0.605695i
$986$	−45.6532			−1.45389
$987$	3.61675			0.115122
$988$	−41.1113	+	126.528i	−1.30793	+	4.02538i
$989$	−19.3455	−	14.0553i	−0.615150	−	0.446933i
$990$	2.10893	−	1.53223i	0.0670263	−	0.0486975i
$991$	−56.6493			−1.79952			−0.899762	−	0.436381i	$-0.856260\pi$
$991$	−56.6493			−1.79952			−0.899762	+	0.436381i	$0.856260\pi$
$992$		0			0
$993$	−43.2575			−1.37274
$994$	−5.82290	+	4.23058i	−0.184691	+	0.134186i
$995$	10.9332	+	7.94343i	0.346606	+	0.251824i
$996$	−9.03249	+	27.7992i	−0.286206	+	0.880850i
$997$	−47.0116			−1.48887			−0.744436	−	0.667693i	$-0.767282\pi$
$997$	−47.0116			−1.48887			−0.744436	+	0.667693i	$0.767282\pi$
$998$	−16.0305			−0.507435
$999$	0.361491	−	1.11255i	0.0114371	−	0.0351996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.r.388.1		48
31.2	even	5	inner	961.2.d.r.374.1		48
31.3	odd	30		961.2.g.v.547.11		96
31.4	even	5	inner	961.2.d.r.628.12		48
31.5	even	3		961.2.g.v.338.1		96
31.6	odd	6		961.2.g.v.235.1		96
31.7	even	15		961.2.g.v.846.11		96
31.8	even	5		961.2.a.k.1.12	yes	12
31.9	even	15		961.2.c.k.521.11		24
31.10	even	15		961.2.g.v.732.2		96
31.11	odd	30		961.2.g.v.448.11		96
31.12	odd	30		961.2.g.v.816.2		96
31.13	odd	30		961.2.g.v.844.12		96
31.14	even	15		961.2.c.k.439.11		24
31.15	odd	10	inner	961.2.d.r.531.11		48
31.16	even	5	inner	961.2.d.r.531.12		48
31.17	odd	30		961.2.c.k.439.12		24
31.18	even	15		961.2.g.v.844.11		96
31.19	even	15		961.2.g.v.816.1		96
31.20	even	15		961.2.g.v.448.12		96
31.21	odd	30		961.2.g.v.732.1		96
31.22	odd	30		961.2.c.k.521.12		24
31.23	odd	10		961.2.a.k.1.11	✓	12
31.24	odd	30		961.2.g.v.846.12		96
31.25	even	3		961.2.g.v.235.2		96
31.26	odd	6		961.2.g.v.338.2		96
31.27	odd	10	inner	961.2.d.r.628.11		48
31.28	even	15		961.2.g.v.547.12		96
31.29	odd	10	inner	961.2.d.r.374.2		48
31.30	odd	2	inner	961.2.d.r.388.2		48
93.8	odd	10		8649.2.a.bp.1.1		12
93.23	even	10		8649.2.a.bp.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.11	✓	12	31.23	odd	10
961.2.a.k.1.12	yes	12	31.8	even	5
961.2.c.k.439.11		24	31.14	even	15
961.2.c.k.439.12		24	31.17	odd	30
961.2.c.k.521.11		24	31.9	even	15
961.2.c.k.521.12		24	31.22	odd	30
961.2.d.r.374.1		48	31.2	even	5	inner
961.2.d.r.374.2		48	31.29	odd	10	inner
961.2.d.r.388.1		48	1.1	even	1	trivial
961.2.d.r.388.2		48	31.30	odd	2	inner
961.2.d.r.531.11		48	31.15	odd	10	inner
961.2.d.r.531.12		48	31.16	even	5	inner
961.2.d.r.628.11		48	31.27	odd	10	inner
961.2.d.r.628.12		48	31.4	even	5	inner
961.2.g.v.235.1		96	31.6	odd	6
961.2.g.v.235.2		96	31.25	even	3
961.2.g.v.338.1		96	31.5	even	3
961.2.g.v.338.2		96	31.26	odd	6
961.2.g.v.448.11		96	31.11	odd	30
961.2.g.v.448.12		96	31.20	even	15
961.2.g.v.547.11		96	31.3	odd	30
961.2.g.v.547.12		96	31.28	even	15
961.2.g.v.732.1		96	31.21	odd	30
961.2.g.v.732.2		96	31.10	even	15
961.2.g.v.816.1		96	31.19	even	15
961.2.g.v.816.2		96	31.12	odd	30
961.2.g.v.844.11		96	31.18	even	15
961.2.g.v.844.12		96	31.13	odd	30
961.2.g.v.846.11		96	31.7	even	15
961.2.g.v.846.12		96	31.24	odd	30
8649.2.a.bp.1.1		12	93.8	odd	10
8649.2.a.bp.1.2		12	93.23	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.01950 + 1.46725i) q^{2} +(-2.00074 - 1.45363i) q^{3} +(1.30751 - 4.02411i) q^{4} -1.14918 q^{5} +6.17333 q^{6} +(0.0819006 - 0.252064i) q^{7} +(1.72110 + 5.29701i) q^{8} +(0.962897 + 2.96349i) q^{9} +(2.32076 - 1.68613i) q^{10} +(0.0901192 - 0.277358i) q^{11} +(-8.46555 + 6.15058i) q^{12} +(3.65972 + 2.65894i) q^{13} +(0.204443 + 0.629212i) q^{14} +(2.29921 + 1.67047i) q^{15} +(-4.40159 - 3.19794i) q^{16} +(-1.69859 - 5.22772i) q^{17} +(-6.29276 - 4.57195i) q^{18} +(-5.62319 + 4.08549i) q^{19} +(-1.50257 + 4.62442i) q^{20} +(-0.530269 + 0.385263i) q^{21} +(0.224959 + 0.692352i) q^{22} +(-0.917019 - 2.82229i) q^{23} +(4.25638 - 13.0998i) q^{24} -3.67939 q^{25} -11.2921 q^{26} +(0.0886486 - 0.272832i) q^{27} +(-0.907248 - 0.659154i) q^{28} +(-2.69176 + 1.95568i) q^{29} -7.09426 q^{30} +2.44197 q^{32} +(-0.583480 + 0.423923i) q^{33} +(11.1007 + 8.06511i) q^{34} +(-0.0941183 + 0.289666i) q^{35} +13.1844 q^{36} +4.07780 q^{37} +(5.36159 - 16.5013i) q^{38} +(-3.45706 - 10.6397i) q^{39} +(-1.97785 - 6.08721i) q^{40} +(-6.06684 + 4.40782i) q^{41} +(0.505599 - 1.55608i) q^{42} +(6.51904 - 4.73636i) q^{43} +(-0.998289 - 0.725299i) q^{44} +(-1.10654 - 3.40558i) q^{45} +(5.99293 + 4.35412i) q^{46} +(-4.46414 - 3.24339i) q^{47} +(4.15784 + 12.7965i) q^{48} +(5.60629 + 4.07321i) q^{49} +(7.43052 - 5.39859i) q^{50} +(-4.20070 + 12.9284i) q^{51} +(15.4850 - 11.2505i) q^{52} +(1.46861 + 4.51991i) q^{53} +(0.221288 + 0.681054i) q^{54} +(-0.103563 + 0.318734i) q^{55} +1.47615 q^{56} +17.1893 q^{57} +(2.56654 - 7.89899i) q^{58} +(1.90331 + 1.38284i) q^{59} +(9.72842 - 7.06811i) q^{60} +10.0530 q^{61} +0.825852 q^{63} +(3.87162 - 2.81290i) q^{64} +(-4.20567 - 3.05560i) q^{65} +(0.556335 - 1.71222i) q^{66} -3.58686 q^{67} -23.2578 q^{68} +(-2.26784 + 6.97969i) q^{69} +(-0.234942 - 0.723076i) q^{70} +(3.36181 + 10.3466i) q^{71} +(-14.0404 + 10.2010i) q^{72} +(0.702814 - 2.16304i) q^{73} +(-8.23510 + 5.98315i) q^{74} +(7.36152 + 5.34845i) q^{75} +(9.08806 + 27.9702i) q^{76} +(-0.0625312 - 0.0454316i) q^{77} +(22.5927 + 16.4145i) q^{78} +(1.17247 + 3.60851i) q^{79} +(5.05821 + 3.67500i) q^{80} +(6.98873 - 5.07761i) q^{81} +(5.78460 - 17.8032i) q^{82} +(2.25988 - 1.64190i) q^{83} +(0.857007 + 2.63760i) q^{84} +(1.95198 + 6.00758i) q^{85} +(-6.21576 + 19.1301i) q^{86} +8.22836 q^{87} +1.62427 q^{88} +(0.989410 - 3.04509i) q^{89} +(7.23150 + 5.25399i) q^{90} +(0.969957 - 0.704715i) q^{91} -12.5562 q^{92} +13.7742 q^{94} +(6.46204 - 4.69495i) q^{95} +(-4.88576 - 3.54971i) q^{96} +(0.623244 - 1.91815i) q^{97} -17.2983 q^{98} +0.908724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{4} + 32 q^{5} - 8 q^{7} - 12 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} + 48 q^{25} + 20 q^{28} + 96 q^{32} + 40 q^{33} - 56 q^{35} + 160 q^{36}+ \cdots + 16 q^{98}+O(q^{100}) \) 48 * q - 16 * q^4 + 32 * q^5 - 8 * q^7 - 12 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 + 48 * q^25 + 20 * q^28 + 96 * q^32 + 40 * q^33 - 56 * q^35 + 160 * q^36 - 36 * q^38 + 16 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 - 48 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 - 32 * q^56 - 40 * q^59 - 32 * q^63 + 28 * q^64 - 24 * q^66 + 64 * q^67 - 24 * q^69 - 12 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 + 104 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 + 256 * q^87 + 44 * q^90 + 64 * q^94 - 40 * q^95 + 8 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more