LMFDB - Embedded newform 950.2.l.i.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 $ x^18 + 24x^16 - 12x^15 + 393x^14 - 222x^13 + 3518x^12 - 2478x^11 + 22809x^10 - 12862x^9 + 77397x^8 - 24822x^7 + 178501x^6 - 39408x^5 + 132588x^4 + 45584x^3 + 50640x^2 + 1824x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.2
Root			$-0.288205 - 0.499186i$ of defining polynomial
Character	$\chi$	$=$	950.101
Dual form			950.2.l.i.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.541649 + 0.197144i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.541649 - 0.197144i) q^{6} +(-2.43209 + 4.21251i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.04362 - 1.71480i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.541649 + 0.197144i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.541649 - 0.197144i) q^{6} +(-2.43209 + 4.21251i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.04362 - 1.71480i) q^{9} +(2.68454 + 4.64975i) q^{11} +(0.288205 - 0.499186i) q^{12} +(-3.62457 + 1.31923i) q^{13} +(0.844657 + 4.79029i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-1.07407 + 0.901248i) q^{17} -2.66775 q^{18} +(4.35299 + 0.226908i) q^{19} +(-2.14781 + 1.80223i) q^{21} +(5.04528 + 1.83633i) q^{22} +(-0.927092 + 5.25780i) q^{23} +(-0.100093 - 0.567654i) q^{24} +(-1.92859 + 3.34042i) q^{26} +(-1.63348 - 2.82926i) q^{27} +(3.72618 + 3.12664i) q^{28} +(-2.78364 - 2.33575i) q^{29} +(-4.10189 + 7.10468i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.537405 + 3.04777i) q^{33} +(-0.243471 + 1.38079i) q^{34} +(-2.04362 + 1.71480i) q^{36} +10.4594 q^{37} +(3.48044 - 2.62423i) q^{38} -2.22332 q^{39} +(1.79322 + 0.652678i) q^{41} +(-0.486869 + 2.76117i) q^{42} +(-0.256764 - 1.45618i) q^{43} +(5.04528 - 1.83633i) q^{44} +(2.66945 + 4.62363i) q^{46} +(2.39030 + 2.00570i) q^{47} +(-0.441556 - 0.370510i) q^{48} +(-8.33016 - 14.4283i) q^{49} +(-0.759442 + 0.276414i) q^{51} +(0.669793 + 3.79858i) q^{52} +(0.312568 - 1.77266i) q^{53} +(-3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(2.31306 + 0.981070i) q^{57} -3.63378 q^{58} +(-5.61133 + 4.70846i) q^{59} +(1.40916 - 7.99176i) q^{61} +(1.42457 + 8.07914i) q^{62} +(12.1939 - 4.43820i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.37075 + 1.98929i) q^{66} +(-6.46916 - 5.42827i) q^{67} +(0.701047 + 1.21425i) q^{68} +(-1.53870 + 2.66511i) q^{69} +(1.04647 + 5.93485i) q^{71} +(-0.463250 + 2.62722i) q^{72} +(-1.19931 - 0.436515i) q^{73} +(8.01234 - 6.72316i) q^{74} +(0.979350 - 4.24746i) q^{76} -26.1162 q^{77} +(-1.70316 + 1.42912i) q^{78} +(15.6290 + 5.68848i) q^{79} +(1.06275 + 6.02717i) q^{81} +(1.79322 - 0.652678i) q^{82} +(7.23049 - 12.5236i) q^{83} +(1.40188 + 2.42814i) q^{84} +(-1.13271 - 0.950453i) q^{86} +(-1.04727 - 1.81393i) q^{87} +(2.68454 - 4.64975i) q^{88} +(-9.02905 + 3.28630i) q^{89} +(3.25800 - 18.4770i) q^{91} +(5.01693 + 1.82601i) q^{92} +(-3.62243 + 3.03958i) q^{93} +3.12031 q^{94} -0.576411 q^{96} +(4.65687 - 3.90758i) q^{97} +(-15.6556 - 5.69817i) q^{98} +(2.48722 - 14.1057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 9 * q^8 - 18 * q^9	$ 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) $ 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.541649	+	0.197144i	0.312721	+	0.113821i	0.493613	−	0.869682i	$-0.335676\pi$
$3$	0.541649	+	0.197144i	0.312721	+	0.113821i	−0.180892	+	0.983503i	$0.557898\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	0.541649	−	0.197144i	0.221127	−	0.0804837i
$7$	−2.43209	+	4.21251i	−0.919245	+	1.59218i	−0.118681	+	0.992932i	$0.537866\pi$
$7$	−2.43209	+	4.21251i	−0.919245	+	1.59218i	−0.800564	+	0.599247i	$0.795467\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.04362	−	1.71480i	−0.681205	−	0.571599i
$10$		0			0
$11$	2.68454	+	4.64975i	0.809418	+	1.40195i	0.913268	+	0.407360i	$0.133550\pi$
$11$	2.68454	+	4.64975i	0.809418	+	1.40195i	−0.103850	+	0.994593i	$0.533116\pi$
$12$	0.288205	−	0.499186i	0.0831977	−	0.144103i
$13$	−3.62457	+	1.31923i	−1.00527	+	0.365890i	−0.791616	−	0.611019i	$-0.790760\pi$
$13$	−3.62457	+	1.31923i	−1.00527	+	0.365890i	−0.213658	+	0.976909i	$0.568538\pi$
$14$	0.844657	+	4.79029i	0.225744	+	1.28026i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.07407	+	0.901248i	−0.260499	+	0.218585i	−0.763678	−	0.645598i	$-0.776608\pi$
$17$	−1.07407	+	0.901248i	−0.260499	+	0.218585i	0.503178	+	0.864183i	$0.332164\pi$
$18$	−2.66775			−0.628795
$19$	4.35299	+	0.226908i	0.998644	+	0.0520563i
$19$	4.35299	+	0.226908i	0.998644	+	0.0520563i
$20$		0			0
$21$	−2.14781	+	1.80223i	−0.468691	+	0.393278i
$22$	5.04528	+	1.83633i	1.07566	+	0.391507i
$23$	−0.927092	+	5.25780i	−0.193312	+	1.09633i	0.721490	+	0.692425i	$0.243457\pi$
$23$	−0.927092	+	5.25780i	−0.193312	+	1.09633i	−0.914802	+	0.403902i	$0.867654\pi$
$24$	−0.100093	−	0.567654i	−0.0204313	−	0.115872i
$25$		0			0
$26$	−1.92859	+	3.34042i	−0.378228	+	0.655110i
$27$	−1.63348	−	2.82926i	−0.314363	−	0.544492i
$28$	3.72618	+	3.12664i	0.704183	+	0.590879i
$29$	−2.78364	−	2.33575i	−0.516908	−	0.433738i	0.346644	−	0.937997i	$-0.387321\pi$
$29$	−2.78364	−	2.33575i	−0.516908	−	0.433738i	−0.863552	+	0.504259i	$0.831766\pi$
$30$		0			0
$31$	−4.10189	+	7.10468i	−0.736721	+	1.27604i	0.217244	+	0.976117i	$0.430293\pi$
$31$	−4.10189	+	7.10468i	−0.736721	+	1.27604i	−0.953964	+	0.299920i	$0.903040\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.537405	+	3.04777i	0.0935501	+	0.530549i
$34$	−0.243471	+	1.38079i	−0.0417549	+	0.236804i
$35$		0			0
$36$	−2.04362	+	1.71480i	−0.340603	+	0.285800i
$37$	10.4594			1.71951			0.859755	−	0.510706i	$-0.170616\pi$
$37$	10.4594			1.71951			0.859755	+	0.510706i	$0.170616\pi$
$38$	3.48044	−	2.62423i	0.564601	−	0.425706i
$39$	−2.22332			−0.356016
$40$		0			0
$41$	1.79322	+	0.652678i	0.280054	+	0.101931i	0.478228	−	0.878236i	$-0.341279\pi$
$41$	1.79322	+	0.652678i	0.280054	+	0.101931i	−0.198175	+	0.980167i	$0.563501\pi$
$42$	−0.486869	+	2.76117i	−0.0751256	+	0.426058i
$43$	−0.256764	−	1.45618i	−0.0391561	−	0.222065i	0.958950	−	0.283574i	$-0.0915200\pi$
$43$	−0.256764	−	1.45618i	−0.0391561	−	0.222065i	−0.998107	+	0.0615084i	$0.980409\pi$
$44$	5.04528	−	1.83633i	0.760604	−	0.276837i
$45$		0			0
$46$	2.66945	+	4.62363i	0.393590	+	0.681717i
$47$	2.39030	+	2.00570i	0.348661	+	0.292561i	0.800252	−	0.599664i	$-0.204699\pi$
$47$	2.39030	+	2.00570i	0.348661	+	0.292561i	−0.451591	+	0.892225i	$0.649143\pi$
$48$	−0.441556	−	0.370510i	−0.0637331	−	0.0534785i
$49$	−8.33016	−	14.4283i	−1.19002	−	2.06118i
$50$		0			0
$51$	−0.759442	+	0.276414i	−0.106343	+	0.0387058i
$52$	0.669793	+	3.79858i	0.0928835	+	0.526769i
$53$	0.312568	−	1.77266i	0.0429346	−	0.243494i	−0.955786	−	0.294063i	$-0.904992\pi$
$53$	0.312568	−	1.77266i	0.0429346	−	0.243494i	0.998721	+	0.0505691i	$0.0161035\pi$
$54$	−3.06993	−	1.11736i	−0.417765	−	0.152054i
$55$		0			0
$56$	4.86419			0.650004
$57$	2.31306	+	0.981070i	0.306372	+	0.129946i
$58$	−3.63378			−0.477139
$59$	−5.61133	+	4.70846i	−0.730532	+	0.612990i	−0.930277	−	0.366859i	$-0.880433\pi$
$59$	−5.61133	+	4.70846i	−0.730532	+	0.612990i	0.199744	+	0.979848i	$0.435989\pi$
$60$		0			0
$61$	1.40916	−	7.99176i	0.180425	−	1.02324i	−0.751269	−	0.659996i	$-0.770558\pi$
$61$	1.40916	−	7.99176i	0.180425	−	1.02324i	0.931694	−	0.363244i	$-0.118331\pi$
$62$	1.42457	+	8.07914i	0.180921	+	1.02605i
$63$	12.1939	−	4.43820i	1.53628	−	0.559161i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	2.37075	+	1.98929i	0.291819	+	0.244865i
$67$	−6.46916	−	5.42827i	−0.790334	−	0.663169i	0.155494	−	0.987837i	$-0.450303\pi$
$67$	−6.46916	−	5.42827i	−0.790334	−	0.663169i	−0.945828	+	0.324668i	$0.894747\pi$
$68$	0.701047	+	1.21425i	0.0850144	+	0.147249i
$69$	−1.53870	+	2.66511i	−0.185238	+	0.320842i
$70$		0			0
$71$	1.04647	+	5.93485i	0.124194	+	0.704337i	0.981783	+	0.190003i	$0.0608498\pi$
$71$	1.04647	+	5.93485i	0.124194	+	0.704337i	−0.857590	+	0.514334i	$0.828039\pi$
$72$	−0.463250	+	2.62722i	−0.0545945	+	0.309621i
$73$	−1.19931	−	0.436515i	−0.140369	−	0.0510902i	0.270880	−	0.962613i	$-0.412685\pi$
$73$	−1.19931	−	0.436515i	−0.140369	−	0.0510902i	−0.411249	+	0.911523i	$0.634907\pi$
$74$	8.01234	−	6.72316i	0.931416	−	0.781551i
$75$		0			0
$76$	0.979350	−	4.24746i	0.112339	−	0.487217i
$77$	−26.1162			−2.97621
$78$	−1.70316	+	1.42912i	−0.192845	+	0.161816i
$79$	15.6290	+	5.68848i	1.75840	+	0.640004i	0.999931	−	0.0117101i	$-0.00372754\pi$
$79$	15.6290	+	5.68848i	1.75840	+	0.640004i	0.758465	+	0.651714i	$0.225950\pi$
$80$		0			0
$81$	1.06275	+	6.02717i	0.118084	+	0.669685i
$82$	1.79322	−	0.652678i	0.198028	−	0.0720762i
$83$	7.23049	−	12.5236i	0.793649	−	1.37464i	−0.130044	−	0.991508i	$-0.541512\pi$
$83$	7.23049	−	12.5236i	0.793649	−	1.37464i	0.923693	−	0.383133i	$-0.125155\pi$
$84$	1.40188	+	2.42814i	0.152958	+	0.264931i
$85$		0			0
$86$	−1.13271	−	0.950453i	−0.122143	−	0.102490i
$87$	−1.04727	−	1.81393i	−0.112280	−	0.194474i
$88$	2.68454	−	4.64975i	0.286172	−	0.495665i
$89$	−9.02905	+	3.28630i	−0.957077	+	0.348348i	−0.772887	−	0.634543i	$-0.781188\pi$
$89$	−9.02905	+	3.28630i	−0.957077	+	0.348348i	−0.184190	+	0.982891i	$0.558966\pi$
$90$		0			0
$91$	3.25800	−	18.4770i	0.341531	−	1.93692i
$92$	5.01693	+	1.82601i	0.523051	+	0.190375i
$93$	−3.62243	+	3.03958i	−0.375628	+	0.315189i
$94$	3.12031			0.321836
$95$		0			0
$96$	−0.576411			−0.0588297
$97$	4.65687	−	3.90758i	0.472834	−	0.396755i	−0.374993	−	0.927028i	$-0.622355\pi$
$97$	4.65687	−	3.90758i	0.472834	−	0.396755i	0.847827	+	0.530273i	$0.177911\pi$
$98$	−15.6556	−	5.69817i	−1.58145	−	0.575602i
$99$	2.48722	−	14.1057i	0.249975	−	1.41768i
$100$		0			0
$101$	−1.17995	+	0.429466i	−0.117409	+	0.0427335i	−0.400057	−	0.916490i	$-0.631010\pi$
$101$	−1.17995	+	0.429466i	−0.117409	+	0.0427335i	0.282647	+	0.959224i	$0.408787\pi$
$102$	−0.404091	+	0.699906i	−0.0400109	+	0.0693010i
$103$	3.68352	+	6.38005i	0.362948	+	0.628645i	0.988445	−	0.151582i	$-0.0484368\pi$
$103$	3.68352	+	6.38005i	0.362948	+	0.628645i	−0.625496	+	0.780227i	$0.715103\pi$
$104$	2.95477	+	2.47935i	0.289739	+	0.243120i
$105$		0			0
$106$	−0.900005	−	1.55885i	−0.0874162	−	0.151409i
$107$	−4.36539	+	7.56108i	−0.422018	+	0.730957i	−0.996137	−	0.0878153i	$-0.972011\pi$
$107$	−4.36539	+	7.56108i	−0.422018	+	0.730957i	0.574119	+	0.818772i	$0.305345\pi$
$108$	−3.06993	+	1.11736i	−0.295404	+	0.107518i
$109$	1.41173	+	8.00630i	0.135219	+	0.766865i	0.974707	+	0.223487i	$0.0717439\pi$
$109$	1.41173	+	8.00630i	0.135219	+	0.766865i	−0.839488	+	0.543378i	$0.817145\pi$
$110$		0			0
$111$	5.66531	+	2.06200i	0.537727	+	0.195717i
$112$	3.72618	−	3.12664i	0.352091	−	0.295440i
$113$	4.48210			0.421640			0.210820	−	0.977525i	$-0.432387\pi$
$113$	4.48210			0.421640			0.210820	+	0.977525i	$0.432387\pi$
$114$	2.40253	−	0.735261i	0.225017	−	0.0688635i
$115$		0			0
$116$	−2.78364	+	2.33575i	−0.258454	+	0.216869i
$117$	9.66944	+	3.51939i	0.893940	+	0.325368i
$118$	−1.27198	+	7.21378i	−0.117096	+	0.664082i
$119$	−1.18429	−	6.71643i	−0.108564	−	0.615694i
$120$		0			0
$121$	−8.91346	+	15.4386i	−0.810314	+	1.40351i
$122$	−4.05753	−	7.02784i	−0.367351	−	0.636271i
$123$	0.842623	+	0.707045i	0.0759768	+	0.0637521i
$124$	6.28445	+	5.27328i	0.564361	+	0.473555i
$125$		0			0
$126$	6.48822	−	11.2379i	0.578017	−	1.00115i
$127$	−0.130789	+	0.0476033i	−0.0116057	+	0.00422411i	−0.347816	−	0.937563i	$-0.613077\pi$
$127$	−0.130789	+	0.0476033i	−0.0116057	+	0.00422411i	0.336211	+	0.941787i	$0.390855\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	0.148001	−	0.839357i	0.0130308	−	0.0739013i
$130$		0			0
$131$	9.52200	−	7.98991i	0.831941	−	0.698082i	−0.123795	−	0.992308i	$-0.539506\pi$
$131$	9.52200	−	7.98991i	0.831941	−	0.698082i	0.955736	+	0.294226i	$0.0950620\pi$
$132$	3.09479			0.269367
$133$	−11.5427	+	17.7851i	−1.00088	+	1.54217i
$134$	−8.44489			−0.729528
$135$		0			0
$136$	1.31754	+	0.479544i	0.112978	+	0.0411206i
$137$	2.49734	−	14.1631i	0.213362	−	1.21004i	−0.670364	−	0.742032i	$-0.733862\pi$
$137$	2.49734	−	14.1631i	0.213362	−	1.21004i	0.883726	−	0.468004i	$-0.155027\pi$
$138$	0.534386	+	3.03065i	0.0454899	+	0.257986i
$139$	−16.7746	+	6.10544i	−1.42280	+	0.517857i	−0.934859	−	0.355020i	$-0.884474\pi$
$139$	−16.7746	+	6.10544i	−1.42280	+	0.517857i	−0.487941	+	0.872877i	$0.662252\pi$
$140$		0			0
$141$	0.899291	+	1.55762i	0.0757340	+	0.131175i
$142$	4.61650	+	3.87370i	0.387408	+	0.325074i
$143$	−15.8644	−	13.3118i	−1.32665	−	1.11319i
$144$	1.33388	+	2.31034i	0.111156	+	0.192528i
$145$		0			0
$146$	−1.19931	+	0.436515i	−0.0992559	+	0.0361262i
$147$	−1.66758	−	9.45729i	−0.137539	−	0.780024i
$148$	1.81625	−	10.3005i	0.149295	−	0.846694i
$149$	2.71250	+	0.987271i	0.222217	+	0.0808804i	0.450729	−	0.892661i	$-0.351164\pi$
$149$	2.71250	+	0.987271i	0.222217	+	0.0808804i	−0.228512	+	0.973541i	$0.573386\pi$
$150$		0			0
$151$	2.01805			0.164226			0.0821132	−	0.996623i	$-0.473833\pi$
$151$	2.01805			0.164226			0.0821132	+	0.996623i	$0.473833\pi$
$152$	−1.97999	−	3.88325i	−0.160598	−	0.314973i
$153$	3.74044			0.302396
$154$	−20.0061	+	16.7871i	−1.61214	+	1.35275i
$155$		0			0
$156$	−0.386076	+	2.18954i	−0.0309108	+	0.175304i
$157$	1.91697	+	10.8717i	0.152991	+	0.867655i	0.960600	+	0.277936i	$0.0896504\pi$
$157$	1.91697	+	10.8717i	0.152991	+	0.867655i	−0.807609	+	0.589719i	$0.799239\pi$
$158$	15.6290	−	5.68848i	1.24337	−	0.452551i
$159$	0.518772	−	0.898540i	0.0411413	−	0.0712589i
$160$		0			0
$161$	−19.8938	−	16.6928i	−1.56785	−	1.31558i
$162$	4.68830	+	3.93395i	0.368348	+	0.309081i
$163$	−2.96434	−	5.13439i	−0.232185	−	0.402157i	0.726266	−	0.687414i	$-0.241254\pi$
$163$	−2.96434	−	5.13439i	−0.232185	−	0.402157i	−0.958451	+	0.285257i	$0.907921\pi$
$164$	0.954151	−	1.65264i	0.0745067	−	0.129049i
$165$		0			0
$166$	−2.51112	−	14.2413i	−0.194901	−	1.10534i
$167$	−1.25507	+	7.11784i	−0.0971200	+	0.550795i	0.896957	+	0.442118i	$0.145773\pi$
$167$	−1.25507	+	7.11784i	−0.0971200	+	0.550795i	−0.994077	+	0.108677i	$0.965339\pi$
$168$	2.63468	+	0.958946i	0.203270	+	0.0739843i
$169$	1.43852	−	1.20707i	0.110656	−	0.0928512i
$170$		0			0
$171$	−8.50673	−	7.92821i	−0.650526	−	0.606285i
$172$	−1.47864			−0.112745
$173$	3.95167	−	3.31585i	0.300440	−	0.252099i	−0.480087	−	0.877221i	$-0.659395\pi$
$173$	3.95167	−	3.31585i	0.300440	−	0.252099i	0.780528	+	0.625121i	$0.214951\pi$
$174$	−1.96823	−	0.716378i	−0.149211	−	0.0543085i
$175$		0			0
$176$	−0.932329	−	5.28750i	−0.0702770	−	0.398560i
$177$	−3.96761	+	1.44409i	−0.298224	+	0.108545i
$178$	−4.80426	+	8.32122i	−0.360094	+	0.623701i
$179$	−4.09186	−	7.08730i	−0.305840	−	0.529730i	0.671608	−	0.740906i	$-0.265604\pi$
$179$	−4.09186	−	7.08730i	−0.305840	−	0.529730i	−0.977448	+	0.211177i	$0.932270\pi$
$180$		0			0
$181$	−2.62934	−	2.20628i	−0.195437	−	0.163991i	0.539818	−	0.841782i	$-0.318493\pi$
$181$	−2.62934	−	2.20628i	−0.195437	−	0.163991i	−0.735255	+	0.677791i	$0.762938\pi$
$182$	−9.38103	−	16.2484i	−0.695368	−	1.20441i
$183$	2.33880	−	4.05092i	0.172889	−	0.299453i
$184$	5.01693	−	1.82601i	0.369853	−	0.134616i
$185$		0			0
$186$	−0.821137	+	4.65690i	−0.0602087	+	0.341461i
$187$	−7.07395	−	2.57471i	−0.517298	−	0.188281i
$188$	2.39030	−	2.00570i	0.174330	−	0.146281i
$189$	15.8911			1.15591
$190$		0			0
$191$	3.77584			0.273210			0.136605	−	0.990626i	$-0.456381\pi$
$191$	3.77584			0.273210			0.136605	+	0.990626i	$0.456381\pi$
$192$	−0.441556	+	0.370510i	−0.0318666	+	0.0267392i
$193$	11.4435	+	4.16508i	0.823718	+	0.299809i	0.719278	−	0.694722i	$-0.244473\pi$
$193$	11.4435	+	4.16508i	0.823718	+	0.299809i	0.104440	+	0.994531i	$0.466695\pi$
$194$	1.05563	−	5.98676i	0.0757896	−	0.429824i
$195$		0			0
$196$	−15.6556	+	5.69817i	−1.11826	+	0.407012i
$197$	3.60118	−	6.23743i	0.256574	−	0.444399i	−0.708748	−	0.705462i	$-0.750740\pi$
$197$	3.60118	−	6.23743i	0.256574	−	0.444399i	0.965322	+	0.261063i	$0.0840731\pi$
$198$	−7.16167	−	12.4044i	−0.508958	−	0.881541i
$199$	4.47147	+	3.75201i	0.316974	+	0.265973i	0.787367	−	0.616484i	$-0.211443\pi$
$199$	4.47147	+	3.75201i	0.316974	+	0.265973i	−0.470393	+	0.882457i	$0.655888\pi$
$200$		0			0
$201$	−2.43386	−	4.21557i	−0.171671	−	0.297344i
$202$	−0.627838	+	1.08745i	−0.0441745	+	0.0765125i
$203$	16.6094	−	6.04534i	1.16575	−	0.424299i
$204$	0.140339	+	0.795903i	0.00982571	+	0.0557244i
$205$		0			0
$206$	6.92276	+	2.51968i	0.482332	+	0.175554i
$207$	10.9107	−	9.15514i	0.758344	−	0.636327i
$208$	3.85718			0.267448
$209$	10.6307	+	20.8495i	0.735340	+	1.44219i
$210$		0			0
$211$	8.17443	−	6.85916i	0.562751	−	0.472204i	−0.316481	−	0.948599i	$-0.602501\pi$
$211$	8.17443	−	6.85916i	0.562751	−	0.472204i	0.879231	+	0.476395i	$0.158057\pi$
$212$	−1.69146	−	0.615640i	−0.116170	−	0.0422823i
$213$	−0.603199	+	3.42091i	−0.0413305	+	0.234397i
$214$	1.51608	+	8.59814i	0.103637	+	0.587757i
$215$		0			0
$216$	−1.63348	+	2.82926i	−0.111144	+	0.192507i
$217$	−19.9523	−	34.5585i	−1.35445	−	2.34598i
$218$	6.22780	+	5.22574i	0.421800	+	0.353932i
$219$	−0.563551	−	0.472875i	−0.0380812	−	0.0319539i
$220$		0			0
$221$	2.70407	−	4.68358i	0.181895	−	0.315052i
$222$	5.66531	−	2.06200i	0.380231	−	0.138393i
$223$	0.0172725	+	0.0979573i	0.00115665	+	0.00655971i	0.985381	−	0.170367i	$-0.0544954\pi$
$223$	0.0172725	+	0.0979573i	0.00115665	+	0.00655971i	−0.984224	+	0.176927i	$0.943384\pi$
$224$	0.844657	−	4.79029i	0.0564360	−	0.320065i
$225$		0			0
$226$	3.43349	−	2.88104i	0.228392	−	0.191644i
$227$	13.8262			0.917680			0.458840	−	0.888519i	$-0.348265\pi$
$227$	13.8262			0.917680			0.458840	+	0.888519i	$0.348265\pi$
$228$	1.36782	−	2.10756i	0.0905864	−	0.139576i
$229$	15.5752			1.02924			0.514619	−	0.857419i	$-0.327934\pi$
$229$	15.5752			1.02924			0.514619	+	0.857419i	$0.327934\pi$
$230$		0			0
$231$	−14.1458	−	5.14865i	−0.930725	−	0.338756i
$232$	−0.630999	+	3.57857i	−0.0414271	+	0.234945i
$233$	2.64658	+	15.0095i	0.173384	+	0.983307i	0.939993	+	0.341193i	$0.110831\pi$
$233$	2.64658	+	15.0095i	0.173384	+	0.983307i	−0.766610	+	0.642113i	$0.778058\pi$
$234$	9.66944	−	3.51939i	0.632111	−	0.230070i
$235$		0			0
$236$	3.66253	+	6.34369i	0.238411	+	0.412939i
$237$	7.34396	+	6.16232i	0.477042	+	0.400285i
$238$	−5.22446	−	4.38384i	−0.338651	−	0.284162i
$239$	−8.41167	−	14.5694i	−0.544106	−	0.942419i	−0.998663	−	0.0517011i	$-0.983536\pi$
$239$	−8.41167	−	14.5694i	−0.544106	−	0.942419i	0.454557	−	0.890718i	$-0.349798\pi$
$240$		0			0
$241$	8.55776	−	3.11477i	0.551254	−	0.200640i	−0.0513496	−	0.998681i	$-0.516352\pi$
$241$	8.55776	−	3.11477i	0.551254	−	0.200640i	0.602604	+	0.798041i	$0.294130\pi$
$242$	3.09561	+	17.5561i	0.198993	+	1.12855i
$243$	−2.31448	+	13.1261i	−0.148474	+	0.842039i
$244$	−7.62565	−	2.77551i	−0.488182	−	0.177684i
$245$		0			0
$246$	1.09997			0.0701313
$247$	−16.0770	+	4.92017i	−1.02296	+	0.313063i
$248$	8.20377			0.520940
$249$	6.38533	−	5.35793i	0.404654	−	0.339545i
$250$		0			0
$251$	2.91829	−	16.5504i	0.184201	−	1.04465i	−0.742777	−	0.669539i	$-0.766492\pi$
$251$	2.91829	−	16.5504i	0.184201	−	1.04465i	0.926978	−	0.375116i	$-0.122397\pi$
$252$	−2.25334	−	12.7793i	−0.141947	−	0.805020i
$253$	−26.9363	+	9.80400i	−1.69347	+	0.616372i
$254$	−0.0695914	+	0.120536i	−0.00436655	+	0.00756309i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	7.58176	+	6.36185i	0.472937	+	0.396841i	0.847865	−	0.530213i	$-0.177888\pi$
$257$	7.58176	+	6.36185i	0.472937	+	0.396841i	−0.374927	+	0.927054i	$0.622332\pi$
$258$	−0.426153	−	0.738118i	−0.0265311	−	0.0459532i
$259$	−25.4382	+	44.0602i	−1.58065	+	2.73777i
$260$		0			0
$261$	1.68335	+	9.54674i	0.104197	+	0.590929i
$262$	2.15846	−	12.2412i	0.133350	−	0.756267i
$263$	−21.0609	−	7.66554i	−1.29867	−	0.472677i	−0.402107	−	0.915593i	$-0.631722\pi$
$263$	−21.0609	−	7.66554i	−1.29867	−	0.472677i	−0.896564	+	0.442915i	$0.853944\pi$
$264$	2.37075	−	1.98929i	0.145909	−	0.122432i
$265$		0			0
$266$	2.58983	+	21.0437i	0.158793	+	1.29027i
$267$	−5.53845			−0.338948
$268$	−6.46916	+	5.42827i	−0.395167	+	0.331584i
$269$	−7.02217	−	2.55586i	−0.428149	−	0.155834i	0.118952	−	0.992900i	$-0.462047\pi$
$269$	−7.02217	−	2.55586i	−0.428149	−	0.155834i	−0.547101	+	0.837066i	$0.684269\pi$
$270$		0			0
$271$	−1.84950	−	10.4890i	−0.112349	−	0.637163i	−0.988029	−	0.154271i	$-0.950697\pi$
$271$	−1.84950	−	10.4890i	−0.112349	−	0.637163i	0.875680	−	0.482893i	$-0.160414\pi$
$272$	1.31754	−	0.479544i	0.0798874	−	0.0290766i
$273$	5.40733	−	9.36576i	0.327266	−	0.566842i
$274$	−7.19080	−	12.4548i	−0.434412	−	0.752424i
$275$		0			0
$276$	2.35743	+	1.97812i	0.141900	+	0.119069i
$277$	−1.16317	−	2.01467i	−0.0698880	−	0.121050i	0.828964	−	0.559302i	$-0.188931\pi$
$277$	−1.16317	−	2.01467i	−0.0698880	−	0.121050i	−0.898852	+	0.438253i	$0.855598\pi$
$278$	−8.92555	+	15.4595i	−0.535319	+	0.927200i
$279$	20.5658	−	7.48532i	1.23124	−	0.448135i
$280$		0			0
$281$	−2.96472	+	16.8137i	−0.176860	+	1.00302i	0.759115	+	0.650957i	$0.225632\pi$
$281$	−2.96472	+	16.8137i	−0.176860	+	1.00302i	−0.935975	+	0.352067i	$0.885479\pi$
$282$	1.69011	+	0.615151i	0.100645	+	0.0366317i
$283$	−6.48680	+	5.44307i	−0.385600	+	0.323557i	−0.814896	−	0.579607i	$-0.803206\pi$
$283$	−6.48680	+	5.44307i	−0.385600	+	0.323557i	0.429296	+	0.903164i	$0.358762\pi$
$284$	6.02641			0.357601
$285$		0			0
$286$	−20.7095			−1.22458
$287$	−7.11069	+	5.96658i	−0.419731	+	0.352196i
$288$	2.50687	+	0.912424i	0.147718	+	0.0537651i
$289$	−2.61065	+	14.8057i	−0.153568	+	0.870925i
$290$		0			0
$291$	3.29275	−	1.19846i	0.193024	−	0.0702551i
$292$	−0.638142	+	1.10529i	−0.0373444	+	0.0646824i
$293$	−1.29622	−	2.24512i	−0.0757260	−	0.131161i	0.825676	−	0.564145i	$-0.190794\pi$
$293$	−1.29622	−	2.24512i	−0.0757260	−	0.131161i	−0.901402	+	0.432984i	$0.857461\pi$
$294$	−7.35647	−	6.17281i	−0.429038	−	0.360006i
$295$		0			0
$296$	−5.22969	−	9.05808i	−0.303969	−	0.526490i
$297$	8.77025	−	15.1905i	0.508901	−	0.881443i
$298$	2.71250	−	0.987271i	0.157131	−	0.0571911i
$299$	−3.57596	−	20.2803i	−0.206803	−	1.17284i
$300$		0			0
$301$	6.75864	+	2.45994i	0.389562	+	0.141789i
$302$	1.54591	−	1.29718i	0.0889573	−	0.0746441i
$303$	−0.723785			−0.0415804
$304$	−4.01286	−	1.70203i	−0.230154	−	0.0976183i
$305$		0			0
$306$	2.86534	−	2.40431i	0.163801	−	0.137445i
$307$	−3.87311	−	1.40970i	−0.221050	−	0.0804557i	0.229121	−	0.973398i	$-0.426415\pi$
$307$	−3.87311	−	1.40970i	−0.221050	−	0.0804557i	−0.450171	+	0.892942i	$0.648637\pi$
$308$	−4.53502	+	25.7194i	−0.258407	+	1.46550i
$309$	0.737387	+	4.18193i	0.0419485	+	0.237902i
$310$		0			0
$311$	−1.24153	+	2.15040i	−0.0704008	+	0.121938i	−0.899077	−	0.437791i	$-0.855761\pi$
$311$	−1.24153	+	2.15040i	−0.0704008	+	0.121938i	0.828676	+	0.559728i	$0.189094\pi$
$312$	1.11166	+	1.92545i	0.0629354	+	0.109007i
$313$	−4.12243	−	3.45913i	−0.233014	−	0.195522i	0.518803	−	0.854894i	$-0.326378\pi$
$313$	−4.12243	−	3.45913i	−0.233014	−	0.195522i	−0.751817	+	0.659372i	$0.770822\pi$
$314$	8.45667	+	7.09599i	0.477238	+	0.400450i
$315$		0			0
$316$	8.31600	−	14.4037i	0.467812	−	0.810273i
$317$	18.2914	−	6.65753i	1.02735	−	0.373924i	0.227278	−	0.973830i	$-0.427017\pi$
$317$	18.2914	−	6.65753i	1.02735	−	0.373924i	0.800071	+	0.599906i	$0.204795\pi$
$318$	−0.180168	−	1.02178i	−0.0101033	−	0.0572987i
$319$	3.38788	−	19.2136i	0.189685	−	1.07576i
$320$		0			0
$321$	−3.85513	+	3.23484i	−0.215172	+	0.180551i
$322$	−25.9695			−1.44722
$323$	−4.87990	+	3.67941i	−0.271525	+	0.204728i
$324$	6.12015			0.340008
$325$		0			0
$326$	−5.57114	−	2.02773i	−0.308557	−	0.112306i
$327$	−0.813735	+	4.61492i	−0.0449996	+	0.255206i
$328$	−0.331373	−	1.87931i	−0.0182970	−	0.103768i
$329$	−14.2625	+	5.19111i	−0.786315	+	0.286195i
$330$		0			0
$331$	9.35511	+	16.2035i	0.514203	+	0.890626i	0.999864	+	0.0164787i	$0.00524557\pi$
$331$	9.35511	+	16.2035i	0.514203	+	0.890626i	−0.485661	+	0.874147i	$0.661421\pi$
$332$	−11.0778	−	9.29534i	−0.607971	−	0.510148i
$333$	−21.3749	−	17.9357i	−1.17134	−	0.982870i
$334$	3.61382	+	6.25932i	0.197739	+	0.342495i
$335$		0			0
$336$	2.63468	−	0.958946i	0.143734	−	0.0523148i
$337$	4.35808	+	24.7159i	0.237400	+	1.34636i	0.837501	+	0.546436i	$0.184016\pi$
$337$	4.35808	+	24.7159i	0.237400	+	1.34636i	−0.600101	+	0.799924i	$0.704873\pi$
$338$	0.326087	−	1.84933i	0.0177368	−	0.100590i
$339$	2.42772	+	0.883619i	0.131856	+	0.0479916i
$340$		0			0
$341$	−44.0466			−2.38526
$342$	−11.6127	−	0.605335i	−0.627942	−	0.0327328i
$343$	46.9896			2.53720
$344$	−1.13271	+	0.950453i	−0.0610714	+	0.0512450i
$345$		0			0
$346$	0.895772	−	5.08018i	0.0481570	−	0.273112i
$347$	−3.95111	−	22.4078i	−0.212107	−	1.20292i	−0.885857	−	0.463957i	$-0.846429\pi$
$347$	−3.95111	−	22.4078i	−0.212107	−	1.20292i	0.673751	−	0.738958i	$-0.264682\pi$
$348$	−1.96823	+	0.716378i	−0.105508	+	0.0384019i
$349$	−6.58190	+	11.4002i	−0.352321	+	0.610238i	−0.986656	−	0.162820i	$-0.947941\pi$
$349$	−6.58190	+	11.4002i	−0.352321	+	0.610238i	0.634335	+	0.773059i	$0.281274\pi$
$350$		0			0
$351$	9.65310	+	8.09992i	0.515245	+	0.432341i
$352$	−4.11295	−	3.45117i	−0.219221	−	0.183948i
$353$	−6.15281	−	10.6570i	−0.327481	−	0.567213i	0.654530	−	0.756036i	$-0.272866\pi$
$353$	−6.15281	−	10.6570i	−0.327481	−	0.567213i	−0.982011	+	0.188822i	$0.939533\pi$
$354$	−2.11112	+	3.65657i	−0.112205	+	0.194345i
$355$		0			0
$356$	1.66850	+	9.46254i	0.0884304	+	0.501513i
$357$	0.682636	−	3.87142i	0.0361290	−	0.204897i
$358$	−7.69017	−	2.79899i	−0.406438	−	0.147931i
$359$	9.62244	−	8.07418i	0.507853	−	0.426139i	−0.352520	−	0.935804i	$-0.614675\pi$
$359$	9.62244	−	8.07418i	0.507853	−	0.426139i	0.860373	+	0.509665i	$0.170231\pi$
$360$		0			0
$361$	18.8970	+	1.97546i	0.994580	+	0.103972i
$362$	−3.43236			−0.180401
$363$	−7.87158	+	6.60504i	−0.413151	+	0.346675i
$364$	−17.6306	−	6.41700i	−0.924093	−	0.336342i
$365$		0			0
$366$	−0.812257	−	4.60654i	−0.0424574	−	0.240788i
$367$	2.52261	−	0.918156i	0.131679	−	0.0479274i	−0.275340	−	0.961347i	$-0.588790\pi$
$367$	2.52261	−	0.918156i	0.131679	−	0.0479274i	0.407019	+	0.913420i	$0.366568\pi$
$368$	2.66945	−	4.62363i	0.139155	−	0.241023i
$369$	−2.54544	−	4.40883i	−0.132510	−	0.229514i
$370$		0			0
$371$	6.70717	+	5.62798i	0.348219	+	0.292190i
$372$	2.36437	+	4.09521i	0.122587	+	0.212327i
$373$	−9.27119	+	16.0582i	−0.480044	+	0.831461i	−0.999738	−	0.0228917i	$-0.992713\pi$
$373$	−9.27119	+	16.0582i	−0.480044	+	0.831461i	0.519694	+	0.854353i	$0.326046\pi$
$374$	−7.07395	+	2.57471i	−0.365785	+	0.133135i
$375$		0			0
$376$	0.541837	−	3.07291i	0.0279431	−	0.158473i
$377$	13.1709	+	4.79381i	0.678334	+	0.246894i
$378$	12.1733	−	10.2146i	0.626125	−	0.525381i
$379$	11.5855			0.595108			0.297554	−	0.954705i	$-0.403829\pi$
$379$	11.5855			0.595108			0.297554	+	0.954705i	$0.403829\pi$
$380$		0			0
$381$	−0.0802265			−0.00411013
$382$	2.89246	−	2.42706i	0.147991	−	0.124179i
$383$	27.3254	+	9.94564i	1.39626	+	0.508199i	0.927067	−	0.374895i	$-0.122321\pi$
$383$	27.3254	+	9.94564i	1.39626	+	0.508199i	0.469197	+	0.883094i	$0.344543\pi$
$384$	−0.100093	+	0.567654i	−0.00510783	+	0.0289680i
$385$		0			0
$386$	11.4435	−	4.16508i	0.582457	−	0.211997i
$387$	−1.97233	+	3.41617i	−0.100259	+	0.173654i
$388$	−3.03956	−	5.26467i	−0.154310	−	0.267273i
$389$	22.8144	+	19.1436i	1.15674	+	0.970618i	0.999856	−	0.0169993i	$-0.00541131\pi$
$389$	22.8144	+	19.1436i	1.15674	+	0.970618i	0.156882	+	0.987617i	$0.449856\pi$
$390$		0			0
$391$	−3.74282	−	6.48276i	−0.189283	−	0.327847i
$392$	−8.33016	+	14.4283i	−0.420737	+	0.728737i
$393$	6.73274	−	2.45052i	0.339622	−	0.123612i
$394$	−1.25068	−	7.09294i	−0.0630082	−	0.357337i
$395$		0			0
$396$	−13.4595	−	4.89887i	−0.676367	−	0.246178i
$397$	−4.80307	+	4.03025i	−0.241059	+	0.202273i	−0.755311	−	0.655367i	$-0.772514\pi$
$397$	−4.80307	+	4.03025i	−0.241059	+	0.202273i	0.514252	+	0.857639i	$0.328070\pi$
$398$	5.83709			0.292587
$399$	−9.75834	+	7.35772i	−0.488528	+	0.368347i
$400$		0			0
$401$	7.58485	−	6.36445i	0.378769	−	0.317825i	−0.433450	−	0.901178i	$-0.642704\pi$
$401$	7.58485	−	6.36445i	0.378769	−	0.317825i	0.812219	+	0.583353i	$0.198259\pi$
$402$	−4.57417	−	1.66486i	−0.228139	−	0.0830357i
$403$	5.49483	−	31.1627i	0.273717	−	1.55233i
$404$	0.218046	+	1.23660i	0.0108482	+	0.0615231i
$405$		0			0
$406$	8.83769	−	15.3073i	0.438607	−	0.759690i
$407$	28.0786	+	48.6335i	1.39180	+	2.41067i
$408$	0.619103	+	0.519489i	0.0306502	+	0.0257185i
$409$	−23.4859	−	19.7070i	−1.16130	−	0.974449i	−0.161380	−	0.986892i	$-0.551595\pi$
$409$	−23.4859	−	19.7070i	−1.16130	−	0.974449i	−0.999923	+	0.0124433i	$0.996039\pi$
$410$		0			0
$411$	4.14486	−	7.17910i	0.204451	−	0.354119i
$412$	6.92276	−	2.51968i	0.341060	−	0.124136i
$413$	−6.18717	−	35.0892i	−0.304451	−	1.72663i
$414$	2.47325	−	14.0265i	0.121554	−	0.689365i
$415$		0			0
$416$	2.95477	−	2.47935i	0.144870	−	0.121560i
$417$	−10.2896			−0.503882
$418$	21.5454	+	9.13834i	1.05382	+	0.446971i
$419$	17.9296			0.875916			0.437958	−	0.898995i	$-0.355702\pi$
$419$	17.9296			0.875916			0.437958	+	0.898995i	$0.355702\pi$
$420$		0			0
$421$	30.2850	+	11.0228i	1.47600	+	0.537220i	0.949723	−	0.313093i	$-0.101365\pi$
$421$	30.2850	+	11.0228i	1.47600	+	0.537220i	0.526278	+	0.850313i	$0.323587\pi$
$422$	1.85299	−	10.5088i	0.0902022	−	0.511562i
$423$	−1.44549	−	8.19775i	−0.0702819	−	0.398588i
$424$	−1.69146	+	0.615640i	−0.0821444	+	0.0298981i
$425$		0			0
$426$	1.73684	+	3.00830i	0.0841503	+	0.145753i
$427$	30.2382	+	25.3728i	1.46333	+	1.22788i
$428$	6.68816	+	5.61204i	0.323285	+	0.271268i
$429$	−5.96858	−	10.3379i	−0.288166	−	0.499118i
$430$		0			0
$431$	1.30703	−	0.475720i	0.0629575	−	0.0229146i	−0.310349	−	0.950623i	$-0.600446\pi$
$431$	1.30703	−	0.475720i	0.0629575	−	0.0229146i	0.373307	+	0.927708i	$0.378224\pi$
$432$	0.567300	+	3.21732i	0.0272942	+	0.154793i
$433$	−5.77441	+	32.7483i	−0.277500	+	1.57378i	0.453406	+	0.891304i	$0.350209\pi$
$433$	−5.77441	+	32.7483i	−0.277500	+	1.57378i	−0.730906	+	0.682478i	$0.760902\pi$
$434$	−37.4981	−	13.6482i	−1.79997	−	0.655135i
$435$		0			0
$436$	8.12981			0.389347
$437$	−5.22866	+	22.6768i	−0.250121	+	1.08478i
$438$	−0.735663			−0.0351513
$439$	−27.6648	+	23.2135i	−1.32037	+	1.10792i	−0.334141	+	0.942523i	$0.608446\pi$
$439$	−27.6648	+	23.2135i	−1.32037	+	1.10792i	−0.986227	+	0.165397i	$0.947109\pi$
$440$		0			0
$441$	−7.71789	+	43.7704i	−0.367519	+	2.08430i
$442$	−0.939112	−	5.32597i	−0.0446690	−	0.253330i
$443$	30.0586	−	10.9404i	1.42813	−	0.519795i	0.491732	−	0.870746i	$-0.336364\pi$
$443$	30.0586	−	10.9404i	1.42813	−	0.519795i	0.936394	+	0.350951i	$0.114142\pi$
$444$	3.01445	−	5.22118i	0.143059	−	0.247786i
$445$		0			0
$446$	0.0761973	+	0.0639371i	0.00360805	+	0.00302751i
$447$	1.27459	+	1.06951i	0.0602860	+	0.0505860i
$448$	−2.43209	−	4.21251i	−0.114906	−	0.199022i
$449$	1.09116	−	1.88995i	0.0514951	−	0.0891922i	−0.839129	−	0.543933i	$-0.816935\pi$
$449$	1.09116	−	1.88995i	0.0514951	−	0.0891922i	0.890624	+	0.454741i	$0.150268\pi$
$450$		0			0
$451$	1.77917	+	10.0902i	0.0837777	+	0.475127i
$452$	0.778308	−	4.41400i	0.0366085	−	0.207617i
$453$	1.09307	+	0.397846i	0.0513570	+	0.0186924i
$454$	10.5915	−	8.88734i	0.497084	−	0.417103i
$455$		0			0
$456$	−0.306897	−	2.49370i	−0.0143718	−	0.116778i
$457$	37.2037			1.74031			0.870157	−	0.492774i	$-0.164017\pi$
$457$	37.2037			1.74031			0.870157	+	0.492774i	$0.164017\pi$
$458$	11.9313	−	10.0115i	0.557512	−	0.467808i
$459$	4.30433	+	1.56665i	0.200909	+	0.0731248i
$460$		0			0
$461$	−0.847556	−	4.80673i	−0.0394746	−	0.223872i	0.958688	−	0.284459i	$-0.0918138\pi$
$461$	−0.847556	−	4.80673i	−0.0394746	−	0.223872i	−0.998163	+	0.0605870i	$0.980703\pi$
$462$	−14.1458	+	5.14865i	−0.658122	+	0.239537i
$463$	−10.1113	+	17.5133i	−0.469913	+	0.813914i	−0.999408	−	0.0343994i	$-0.989048\pi$
$463$	−10.1113	+	17.5133i	−0.469913	+	0.813914i	0.529495	+	0.848313i	$0.322381\pi$
$464$	1.81689	+	3.14694i	0.0843470	+	0.146093i
$465$		0			0
$466$	11.6753	+	9.79677i	0.540850	+	0.453827i
$467$	19.5063	+	33.7859i	0.902644	+	1.56342i	0.824049	+	0.566518i	$0.191710\pi$
$467$	19.5063	+	33.7859i	0.902644	+	1.56342i	0.0785944	+	0.996907i	$0.474957\pi$
$468$	5.14500	−	8.91140i	0.237828	−	0.411930i
$469$	38.6003	−	14.0493i	1.78239	−	0.648739i
$470$		0			0
$471$	−1.10496	+	6.26656i	−0.0509140	+	0.288748i
$472$	6.88331	+	2.50532i	0.316830	+	0.115317i
$473$	6.08158	−	5.10305i	0.279631	−	0.234639i
$474$	9.58686			0.440339
$475$		0			0
$476$	−6.82004			−0.312596
$477$	−3.67853	+	3.08665i	−0.168428	+	0.141328i
$478$	−15.8088	−	5.75392i	−0.723076	−	0.263178i
$479$	−5.39865	+	30.6172i	−0.246670	+	1.39894i	0.569911	+	0.821707i	$0.306978\pi$
$479$	−5.39865	+	30.6172i	−0.246670	+	1.39894i	−0.816581	+	0.577231i	$0.804133\pi$
$480$		0			0
$481$	−37.9107	+	13.7984i	−1.72858	+	0.629151i
$482$	4.55349	−	7.88688i	0.207406	−	0.359237i
$483$	−7.48453	−	12.9636i	−0.340558	−	0.589864i
$484$	13.6562	+	11.4589i	0.620737	+	0.520860i
$485$		0			0
$486$	6.66429	+	11.5429i	0.302298	+	0.523596i
$487$	−13.9870	+	24.2263i	−0.633813	+	1.09780i	0.352952	+	0.935641i	$0.385178\pi$
$487$	−13.9870	+	24.2263i	−0.633813	+	1.09780i	−0.986765	+	0.162155i	$0.948155\pi$
$488$	−7.62565	+	2.77551i	−0.345197	+	0.125641i
$489$	−0.593418	−	3.36544i	−0.0268353	−	0.152191i
$490$		0			0
$491$	−2.79400	−	1.01693i	−0.126091	−	0.0458935i	0.278204	−	0.960522i	$-0.410261\pi$
$491$	−2.79400	−	1.01693i	−0.126091	−	0.0458935i	−0.404295	+	0.914629i	$0.632483\pi$
$492$	0.842623	−	0.707045i	0.0379884	−	0.0318760i
$493$	5.09490			0.229463
$494$	−9.15311	+	14.1032i	−0.411818	+	0.634533i
$495$		0			0
$496$	6.28445	−	5.27328i	0.282180	−	0.236777i
$497$	−27.5458	−	10.0258i	−1.23560	−	0.449720i
$498$	1.44744	−	8.20883i	0.0648612	−	0.367846i
$499$	3.20155	+	18.1569i	0.143321	+	0.812815i	0.968700	+	0.248235i	$0.0798506\pi$
$499$	3.20155	+	18.1569i	0.143321	+	0.812815i	−0.825379	+	0.564580i	$0.809038\pi$
$500$		0			0
$501$	−2.08304	+	3.60794i	−0.0930636	+	0.161191i
$502$	−8.40288	−	14.5542i	−0.375039	−	0.649586i
$503$	−2.50412	−	2.10120i	−0.111653	−	0.0936881i	0.585252	−	0.810852i	$-0.300996\pi$
$503$	−2.50412	−	2.10120i	−0.111653	−	0.0936881i	−0.696905	+	0.717163i	$0.745440\pi$
$504$	−9.94053	−	8.34110i	−0.442786	−	0.371542i
$505$		0			0
$506$	−14.3325	+	24.8246i	−0.637157	+	1.10359i
$507$	1.01714	−	0.370209i	0.0451728	−	0.0164416i
$508$	0.0241688	+	0.137068i	0.00107232	+	0.00608142i
$509$	6.53272	−	37.0489i	0.289558	−	1.64216i	−0.398978	−	0.916960i	$-0.630635\pi$
$509$	6.53272	−	37.0489i	0.289558	−	1.64216i	0.688536	−	0.725202i	$-0.258254\pi$
$510$		0			0
$511$	4.75567	−	3.99048i	0.210378	−	0.176528i
$512$	1.00000			0.0441942
$513$	−6.46852	−	12.6864i	−0.285592	−	0.560118i
$514$	9.89728			0.436550
$515$		0			0
$516$	−0.800905	−	0.291506i	−0.0352579	−	0.0128328i
$517$	−2.90916	+	16.4987i	−0.127945	+	0.725610i
$518$	8.83459	+	50.1034i	0.388169	+	2.20142i
$519$	2.79412	−	1.01698i	0.122648	−	0.0446403i
$520$		0			0
$521$	−15.7203	−	27.2284i	−0.688719	−	1.19290i	−0.972252	−	0.233934i	$-0.924840\pi$
$521$	−15.7203	−	27.2284i	−0.688719	−	1.19290i	0.283533	−	0.958962i	$-0.408493\pi$
$522$	7.42605	+	6.23119i	0.325029	+	0.272732i
$523$	−3.43679	−	2.88381i	−0.150280	−	0.126100i	0.564548	−	0.825400i	$-0.309051\pi$
$523$	−3.43679	−	2.88381i	−0.150280	−	0.126100i	−0.714828	+	0.699300i	$0.753495\pi$
$524$	−6.21505	−	10.7648i	−0.271506	−	0.470261i
$525$		0			0
$526$	−21.0609	+	7.66554i	−0.918299	+	0.334233i
$527$	−1.99738	−	11.3277i	−0.0870073	−	0.493443i
$528$	0.537405	−	3.04777i	0.0233875	−	0.132637i
$529$	−5.17201	−	1.88246i	−0.224870	−	0.0818460i
$530$		0			0
$531$	19.5415			0.848027
$532$	15.5106	+	14.4557i	0.672469	+	0.626735i
$533$	−7.36067			−0.318826
$534$	−4.24270	+	3.56005i	−0.183599	+	0.154058i
$535$		0			0
$536$	−1.46644	+	8.31660i	−0.0633406	+	0.359222i
$537$	−0.819129	−	4.64551i	−0.0353480	−	0.200469i
$538$	−7.02217	+	2.55586i	−0.302747	+	0.110191i
$539$	44.7252	−	77.4664i	1.92645	−	3.33671i
$540$		0			0
$541$	17.0269	+	14.2873i	0.732045	+	0.614259i	0.930688	−	0.365813i	$-0.119209\pi$
$541$	17.0269	+	14.2873i	0.732045	+	0.614259i	−0.198643	+	0.980072i	$0.563653\pi$
$542$	−8.15902	−	6.84623i	−0.350460	−	0.294071i
$543$	−0.989225	−	1.71339i	−0.0424517	−	0.0735285i
$544$	0.701047	−	1.21425i	0.0300571	−	0.0520605i
$545$		0			0
$546$	−1.87794	−	10.6504i	−0.0803686	−	0.455793i
$547$	5.00894	−	28.4071i	0.214167	−	1.21460i	−0.668180	−	0.744000i	$-0.732926\pi$
$547$	5.00894	−	28.4071i	0.214167	−	1.21460i	0.882347	−	0.470600i	$-0.155962\pi$
$548$	−13.5143	−	4.91880i	−0.577302	−	0.210121i
$549$	−16.5840	+	13.9157i	−0.707790	+	0.593906i
$550$		0			0
$551$	−11.5871	−	10.7991i	−0.493629	−	0.460058i
$552$	3.07740			0.130983
$553$	−61.9739	+	52.0023i	−2.63540	+	2.21136i
$554$	−2.18604	−	0.795654i	−0.0928760	−	0.0338041i
$555$		0			0
$556$	3.09981	+	17.5799i	0.131461	+	0.745554i
$557$	−26.3406	+	9.58721i	−1.11609	+	0.406223i	−0.833223	−	0.552937i	$-0.813507\pi$
$557$	−26.3406	+	9.58721i	−1.11609	+	0.406223i	−0.282865	+	0.959160i	$0.591285\pi$
$558$	10.9428	−	18.9535i	0.463246	−	0.802366i
$559$	2.85170	+	4.93929i	0.120614	+	0.208910i
$560$		0			0
$561$	−3.32401	−	2.78917i	−0.140340	−	0.117759i
$562$	8.53656	+	14.7858i	0.360093	+	0.623699i
$563$	−3.28614	+	5.69177i	−0.138494	+	0.239879i	−0.926927	−	0.375242i	$-0.877560\pi$
$563$	−3.28614	+	5.69177i	−0.138494	+	0.239879i	0.788432	+	0.615121i	$0.210893\pi$
$564$	1.69011	−	0.615151i	0.0711666	−	0.0259025i
$565$		0			0
$566$	−1.47044	+	8.33927i	−0.0618071	+	0.350526i
$567$	−27.9742	−	10.1818i	−1.17481	−	0.427595i
$568$	4.61650	−	3.87370i	0.193704	−	0.162537i
$569$	3.90032			0.163510			0.0817549	−	0.996652i	$-0.473948\pi$
$569$	3.90032			0.163510			0.0817549	+	0.996652i	$0.473948\pi$
$570$		0			0
$571$	18.1559			0.759802			0.379901	−	0.925027i	$-0.375958\pi$
$571$	18.1559			0.759802			0.379901	+	0.925027i	$0.375958\pi$
$572$	−15.8644	+	13.3118i	−0.663323	+	0.556594i
$573$	2.04518	+	0.744385i	0.0854386	+	0.0310971i
$574$	−1.61186	+	9.14132i	−0.0672778	+	0.381551i
$575$		0			0
$576$	2.50687	−	0.912424i	0.104453	−	0.0380177i
$577$	7.00915	−	12.1402i	0.291795	−	0.505403i	−0.682439	−	0.730942i	$-0.739081\pi$
$577$	7.00915	−	12.1402i	0.291795	−	0.505403i	0.974234	+	0.225539i	$0.0724142\pi$
$578$	7.51707	+	13.0199i	0.312669	+	0.541558i
$579$	5.37721	+	4.51202i	0.223469	+	0.187513i
$580$		0			0
$581$	35.1705	+	60.9170i	1.45912	+	2.52726i
$582$	1.75203	−	3.03461i	0.0726241	−	0.125789i
$583$	9.08155	−	3.30541i	0.376119	−	0.136896i
$584$	0.221624	+	1.25689i	0.00917088	+	0.0520106i
$585$		0			0
$586$	−2.43610	−	0.886667i	−0.100634	−	0.0366279i
$587$	5.83061	−	4.89246i	0.240655	−	0.201933i	−0.514481	−	0.857502i	$-0.672015\pi$
$587$	5.83061	−	4.89246i	0.240655	−	0.201933i	0.755136	+	0.655568i	$0.227571\pi$
$588$	−9.60319			−0.396029
$589$	−19.4676	+	29.9958i	−0.802148	+	1.23596i
$590$		0			0
$591$	3.18025	−	2.66855i	0.130818	−	0.109769i
$592$	−9.82860	−	3.57732i	−0.403953	−	0.147027i
$593$	1.63620	−	9.27933i	0.0671905	−	0.381056i	−0.932606	−	0.360896i	$-0.882471\pi$
$593$	1.63620	−	9.27933i	0.0671905	−	0.381056i	0.999797	−	0.0201608i	$-0.00641780\pi$
$594$	−3.04587	−	17.2740i	−0.124974	−	0.708761i
$595$		0			0
$596$	1.44329	−	2.49986i	0.0591196	−	0.102398i
$597$	1.68228	+	2.91380i	0.0688512	+	0.119254i
$598$	−15.7753	−	13.2370i	−0.645099	−	0.541302i
$599$	10.7502	+	9.02053i	0.439243	+	0.368569i	0.835426	−	0.549603i	$-0.185221\pi$
$599$	10.7502	+	9.02053i	0.439243	+	0.368569i	−0.396183	+	0.918172i	$0.629665\pi$
$600$		0			0
$601$	6.78599	−	11.7537i	0.276806	−	0.479443i	−0.693783	−	0.720184i	$-0.744057\pi$
$601$	6.78599	−	11.7537i	0.276806	−	0.479443i	0.970589	+	0.240742i	$0.0773906\pi$
$602$	6.75864	−	2.45994i	0.275462	−	0.100260i
$603$	3.91210	+	22.1866i	0.159313	+	0.903508i
$604$	0.350430	−	1.98739i	0.0142588	−	0.0808657i
$605$		0			0
$606$	−0.554451	+	0.465240i	−0.0225231	+	0.0188991i
$607$	−2.07689			−0.0842984			−0.0421492	−	0.999111i	$-0.513420\pi$
$607$	−2.07689			−0.0842984			−0.0421492	+	0.999111i	$0.513420\pi$
$608$	−4.16808	+	1.27559i	−0.169038	+	0.0517318i
$609$	10.1883			0.412850
$610$		0			0
$611$	−11.3098	−	4.11642i	−0.457545	−	0.166533i
$612$	0.649520	−	3.68361i	0.0262553	−	0.148901i
$613$	2.86849	+	16.2680i	0.115857	+	0.657059i	0.986322	+	0.164828i	$0.0527071\pi$
$613$	2.86849	+	16.2680i	0.115857	+	0.657059i	−0.870465	+	0.492230i	$0.836182\pi$
$614$	−3.87311	+	1.40970i	−0.156306	+	0.0568908i
$615$		0			0
$616$	13.0581	+	22.6173i	0.526125	+	0.911275i
$617$	−17.5283	−	14.7080i	−0.705661	−	0.592120i	0.217717	−	0.976012i	$-0.430139\pi$
$617$	−17.5283	−	14.7080i	−0.705661	−	0.592120i	−0.923378	+	0.383892i	$0.874583\pi$
$618$	3.25297	+	2.72956i	0.130853	+	0.109799i
$619$	6.66514	+	11.5444i	0.267895	+	0.464007i	0.968318	−	0.249721i	$-0.0803388\pi$
$619$	6.66514	+	11.5444i	0.267895	+	0.464007i	−0.700423	+	0.713728i	$0.747005\pi$
$620$		0			0
$621$	16.3901	−	5.96550i	0.657711	−	0.239387i
$622$	0.431179	+	2.44534i	0.0172887	+	0.0980492i
$623$	8.11590	−	46.0276i	0.325157	−	1.84406i
$624$	2.08924	+	0.760421i	0.0836365	+	0.0304412i
$625$		0			0
$626$	−5.38145			−0.215086
$627$	1.64775	+	13.3889i	0.0658048	+	0.534700i
$628$	11.0394			0.440520
$629$	−11.2341	+	9.42649i	−0.447931	+	0.375859i
$630$		0			0
$631$	1.51546	−	8.59462i	0.0603297	−	0.342147i	−0.939670	−	0.342081i	$-0.888868\pi$
$631$	1.51546	−	8.59462i	0.0603297	−	0.342147i	1.00000		6.52024e-5i	$-2.07546e-5\pi$
$632$	−2.88812	−	16.3793i	−0.114883	−	0.651534i
$633$	5.77991	−	2.10372i	0.229731	−	0.0836152i
$634$	9.73266	−	16.8575i	0.386533	−	0.669495i
$635$		0			0
$636$	−0.794805	−	0.666921i	−0.0315161	−	0.0264451i
$637$	49.2275	+	41.3068i	1.95046	+	1.63663i
$638$	−9.75501	−	16.8962i	−0.386204	−	0.668926i
$639$	8.03848	−	13.9230i	0.317997	−	0.550787i
$640$		0			0
$641$	−0.151753	−	0.860632i	−0.00599387	−	0.0339929i	0.981664	−	0.190619i	$-0.0610494\pi$
$641$	−0.151753	−	0.860632i	−0.00599387	−	0.0339929i	−0.987658	+	0.156626i	$0.949938\pi$
$642$	−0.873887	+	4.95606i	−0.0344896	+	0.195600i
$643$	−17.8620	−	6.50122i	−0.704407	−	0.256383i	−0.0351158	−	0.999383i	$-0.511180\pi$
$643$	−17.8620	−	6.50122i	−0.704407	−	0.256383i	−0.669291	+	0.743000i	$0.733402\pi$
$644$	−19.8938	+	16.6928i	−0.783924	+	0.657790i
$645$		0			0
$646$	−1.37314	+	5.95533i	−0.0540255	+	0.234309i
$647$	−14.4175			−0.566810			−0.283405	−	0.959000i	$-0.591464\pi$
$647$	−14.4175			−0.566810			−0.283405	+	0.959000i	$0.591464\pi$
$648$	4.68830	−	3.93395i	0.184174	−	0.154540i
$649$	−36.9570	−	13.4512i	−1.45069	−	0.528007i
$650$		0			0
$651$	−3.99417	−	22.6520i	−0.156544	−	0.887804i
$652$	−5.57114	+	2.02773i	−0.218183	+	0.0794121i
$653$	5.23384	−	9.06528i	0.204816	−	0.354752i	−0.745258	−	0.666776i	$-0.767674\pi$
$653$	5.23384	−	9.06528i	0.204816	−	0.354752i	0.950074	+	0.312024i	$0.101007\pi$
$654$	2.34306	+	4.05829i	0.0916207	+	0.158692i
$655$		0			0
$656$	−1.46184	−	1.22663i	−0.0570755	−	0.0478920i
$657$	1.70240	+	2.94865i	0.0664171	+	0.115038i
$658$	−7.58889	+	13.1444i	−0.295846	+	0.512420i
$659$	−5.20991	+	1.89625i	−0.202949	+	0.0738675i	−0.441495	−	0.897264i	$-0.645552\pi$
$659$	−5.20991	+	1.89625i	−0.202949	+	0.0738675i	0.238545	+	0.971131i	$0.423329\pi$
$660$		0			0
$661$	5.00125	−	28.3635i	0.194526	−	1.10321i	−0.718566	−	0.695459i	$-0.755201\pi$
$661$	5.00125	−	28.3635i	0.194526	−	1.10321i	0.913092	−	0.407753i	$-0.133688\pi$
$662$	17.5818	+	6.39927i	0.683338	+	0.248715i
$663$	2.38799	−	2.00376i	0.0927420	−	0.0778198i
$664$	−14.4610			−0.561195
$665$		0			0
$666$	−27.9030			−1.08122
$667$	14.8616	−	12.4703i	0.575443	−	0.482854i
$668$	6.79176	+	2.47200i	0.262781	+	0.0956445i
$669$	−0.00995606	+	0.0564636i	−0.000384924	+	0.00218301i
$670$		0			0
$671$	40.9427	−	14.9019i	1.58057	−	0.575282i
$672$	1.40188	−	2.42814i	0.0540789	−	0.0936674i
$673$	19.9705	+	34.5899i	0.769807	+	1.33334i	0.937668	+	0.347533i	$0.112981\pi$
$673$	19.9705	+	34.5899i	0.769807	+	1.33334i	−0.167861	+	0.985811i	$0.553686\pi$
$674$	19.2255	+	16.1322i	0.740540	+	0.621387i
$675$		0			0
$676$	−0.938930	−	1.62627i	−0.0361127	−	0.0625490i
$677$	7.29022	−	12.6270i	0.280186	−	0.485296i	−0.691245	−	0.722621i	$-0.742937\pi$
$677$	7.29022	−	12.6270i	0.280186	−	0.485296i	0.971430	+	0.237325i	$0.0762706\pi$
$678$	2.42772	−	0.883619i	0.0932361	−	0.0339352i
$679$	5.13477	+	29.1207i	0.197054	+	1.11755i
$680$		0			0
$681$	7.48897	+	2.72576i	0.286978	+	0.104451i
$682$	−33.7417	+	28.3126i	−1.29204	+	1.08415i
$683$	26.6159			1.01843			0.509214	−	0.860640i	$-0.329936\pi$
$683$	26.6159			1.01843			0.509214	+	0.860640i	$0.329936\pi$
$684$	−9.28494	+	7.00078i	−0.355018	+	0.267681i
$685$		0			0
$686$	35.9961	−	30.2043i	1.37434	−	1.15321i
$687$	8.43628	+	3.07056i	0.321864	+	0.117149i
$688$	−0.256764	+	1.45618i	−0.00978902	+	0.0555163i
$689$	1.20563	+	6.83749i	0.0459310	+	0.260488i
$690$		0			0
$691$	−18.6248	+	32.2591i	−0.708521	+	1.22719i	0.256885	+	0.966442i	$0.417304\pi$
$691$	−18.6248	+	32.2591i	−0.708521	+	1.22719i	−0.965406	+	0.260752i	$0.916029\pi$
$692$	−2.57927	−	4.46743i	−0.0980492	−	0.169826i
$693$	53.3714	+	44.7839i	2.02741	+	1.70120i
$694$	−17.4302	−	14.6257i	−0.661642	−	0.555183i
$695$		0			0
$696$	−1.04727	+	1.81393i	−0.0396968	+	0.0687569i
$697$	−2.51426	+	0.915115i	−0.0952344	+	0.0346625i
$698$	2.28587	+	12.9638i	0.0865215	+	0.490688i
$699$	−1.52552	+	8.65165i	−0.0577004	+	0.327235i
$700$		0			0
$701$	−30.3425	+	25.4604i	−1.14602	+	0.961626i	−0.999619	−	0.0275989i	$-0.991214\pi$
$701$	−30.3425	+	25.4604i	−1.14602	+	0.961626i	−0.146402	+	0.989225i	$0.546769\pi$
$702$	12.6012			0.475603
$703$	45.5295	+	2.37332i	1.71718	+	0.0895114i
$704$	−5.36907			−0.202354
$705$		0			0
$706$	−11.5635	−	4.20877i	−0.435198	−	0.158399i
$707$	1.06062	−	6.01505i	0.0398886	−	0.226219i
$708$	0.733185	+	4.15810i	0.0275548	+	0.156271i
$709$	34.4453	−	12.5371i	1.29362	−	0.470839i	0.398707	−	0.917079i	$-0.369459\pi$
$709$	34.4453	−	12.5371i	1.29362	−	0.470839i	0.894914	+	0.446239i	$0.147237\pi$
$710$		0			0
$711$	−22.1850	−	38.4256i	−0.832003	−	1.44107i
$712$	7.36055	+	6.17623i	0.275848	+	0.231464i
$713$	−33.5521	−	28.1536i	−1.25654	−	1.05436i
$714$	−1.96557	−	3.40447i	−0.0735597	−	0.127409i
$715$		0			0
$716$	−7.69017	+	2.79899i	−0.287395	+	0.104603i
$717$	−1.68389	−	9.54983i	−0.0628861	−	0.356645i
$718$	2.18123	−	12.3704i	0.0814028	−	0.461658i
$719$	−10.3333	−	3.76101i	−0.385367	−	0.140262i	0.142069	−	0.989857i	$-0.454624\pi$
$719$	−10.3333	−	3.76101i	−0.385367	−	0.140262i	−0.527436	+	0.849595i	$0.676847\pi$
$720$		0			0
$721$	−35.8347			−1.33455
$722$	15.7458	−	10.6335i	0.585997	−	0.395737i
$723$	5.24936			0.195226
$724$	−2.62934	+	2.20628i	−0.0977187	+	0.0819957i
$725$		0			0
$726$	−1.78434	+	10.1195i	−0.0662232	+	0.375570i
$727$	−7.88597	−	44.7236i	−0.292475	−	1.65871i	−0.677293	−	0.735714i	$-0.736847\pi$
$727$	−7.88597	−	44.7236i	−0.292475	−	1.65871i	0.384818	−	0.922992i	$-0.374264\pi$
$728$	−17.6306	+	6.41700i	−0.653432	+	0.237830i
$729$	5.33885	−	9.24717i	0.197735	−	0.342488i
$730$		0			0
$731$	1.58816	+	1.33262i	0.0587402	+	0.0492889i
$732$	−3.58325	−	3.00670i	−0.132441	−	0.111131i
$733$	−13.5168	−	23.4118i	−0.499255	−	0.864735i	0.500744	−	0.865595i	$-0.333060\pi$
$733$	−13.5168	−	23.4118i	−0.499255	−	0.864735i	−1.00000		0.000859816i	$0.999726\pi$
$734$	1.34225	−	2.32485i	0.0495435	−	0.0858119i
$735$		0			0
$736$	−0.927092	−	5.25780i	−0.0341731	−	0.193805i
$737$	7.87342	−	44.6524i	0.290021	−	1.64479i
$738$	−4.78386	−	1.74118i	−0.176096	−	0.0640938i
$739$	−0.964167	+	0.809032i	−0.0354675	+	0.0297607i	−0.660349	−	0.750959i	$-0.729592\pi$
$739$	−0.964167	+	0.809032i	−0.0354675	+	0.0297607i	0.624882	+	0.780720i	$0.285147\pi$
$740$		0			0
$741$	−9.67809	−	0.504490i	−0.355534	−	0.0185329i
$742$	8.75559			0.321428
$743$	−40.0045	+	33.5678i	−1.46762	+	1.23148i	−0.549315	+	0.835615i	$0.685111\pi$
$743$	−40.0045	+	33.5678i	−1.46762	+	1.23148i	−0.918308	+	0.395867i	$0.870444\pi$
$744$	4.44356	+	1.61733i	0.162909	+	0.0592940i
$745$		0			0
$746$	3.21985	+	18.2607i	0.117887	+	0.668571i
$747$	−36.2517	+	13.1945i	−1.32638	+	0.482763i
$748$	−3.76397	+	6.51938i	−0.137624	+	0.238372i
$749$	−21.2341	−	36.7785i	−0.775876	−	1.34386i
$750$		0			0
$751$	0.810409	+	0.680014i	0.0295723	+	0.0248141i	0.657454	−	0.753495i	$-0.271633\pi$
$751$	0.810409	+	0.680014i	0.0295723	+	0.0248141i	−0.627882	+	0.778309i	$0.716078\pi$
$752$	−1.56016	−	2.70227i	−0.0568931	−	0.0985417i
$753$	4.84351	−	8.38920i	0.176507	−	0.305720i
$754$	13.1709	−	4.79381i	0.479655	−	0.174580i
$755$		0			0
$756$	2.75945	−	15.6496i	0.100360	−	0.569172i
$757$	1.73900	+	0.632944i	0.0632050	+	0.0230047i	0.373429	−	0.927659i	$-0.378182\pi$
$757$	1.73900	+	0.632944i	0.0632050	+	0.0230047i	−0.310224	+	0.950663i	$0.600404\pi$
$758$	8.87503	−	7.44703i	0.322355	−	0.270488i
$759$	−16.5228			−0.599739
$760$		0			0
$761$	−31.8442			−1.15435			−0.577176	−	0.816620i	$-0.695845\pi$
$761$	−31.8442			−1.15435			−0.577176	+	0.816620i	$0.695845\pi$
$762$	−0.0614570	+	0.0515686i	−0.00222635	+	0.00186813i
$763$	−37.1601	−	13.5252i	−1.34529	−	0.489644i
$764$	0.655668	−	3.71848i	0.0237212	−	0.134530i
$765$		0			0
$766$	27.3254	−	9.94564i	0.987308	−	0.359351i
$767$	14.1271	−	24.4688i	0.510099	−	0.883517i
$768$	0.288205	+	0.499186i	0.0103997	+	0.0180128i
$769$	0.0929228	+	0.0779715i	0.00335088	+	0.00281172i	0.644462	−	0.764637i	$-0.277082\pi$
$769$	0.0929228	+	0.0779715i	0.00335088	+	0.00281172i	−0.641111	+	0.767448i	$0.721526\pi$
$770$		0			0
$771$	2.85245	+	4.94059i	0.102728	+	0.177931i
$772$	6.08894	−	10.5463i	0.219146	−	0.379571i
$773$	−32.7308	+	11.9131i	−1.17725	+	0.428483i	−0.855229	−	0.518251i	$-0.826583\pi$
$773$	−32.7308	+	11.9131i	−1.17725	+	0.428483i	−0.322018	+	0.946734i	$0.604361\pi$
$774$	0.684981	+	3.88472i	0.0246211	+	0.139633i
$775$		0			0
$776$	−5.71250	−	2.07918i	−0.205067	−	0.0746382i
$777$	−22.4648	+	18.8502i	−0.805919	+	0.676246i
$778$	29.7821			1.06774
$779$	7.65776	+	3.24800i	0.274368	+	0.116372i
$780$		0			0
$781$	−24.7863	+	20.7982i	−0.886923	+	0.744217i
$782$	−7.03421	−	2.56024i	−0.251543	−	0.0915541i
$783$	−2.06144	+	11.6910i	−0.0736700	+	0.417803i
$784$	2.89303	+	16.4072i	0.103323	+	0.585972i
$785$		0			0
$786$	3.58242	−	6.20493i	0.127781	−	0.221323i
$787$	9.58626	+	16.6039i	0.341713	+	0.591865i	0.984751	−	0.173970i	$-0.0556595\pi$
$787$	9.58626	+	16.6039i	0.341713	+	0.591865i	−0.643038	+	0.765834i	$0.722326\pi$
$788$	−5.51733	−	4.62959i	−0.196547	−	0.164922i
$789$	−9.89640	−	8.30406i	−0.352321	−	0.295632i
$790$		0			0
$791$	−10.9009	+	18.8809i	−0.387591	+	0.671327i
$792$	−13.4595	+	4.89887i	−0.478264	+	0.174074i
$793$	5.43540	+	30.8257i	0.193017	+	1.09465i
$794$	−1.08877	+	6.17471i	−0.0386389	+	0.219132i
$795$		0			0
$796$	4.47147	−	3.75201i	0.158487	−	0.132986i
$797$	22.4041			0.793593			0.396796	−	0.917907i	$-0.370122\pi$
$797$	22.4041			0.793593			0.396796	+	0.917907i	$0.370122\pi$
$798$	−2.74587	+	11.9089i	−0.0972028	+	0.421570i
$799$	−4.37497			−0.154775
$800$		0			0
$801$	24.0872	+	8.76704i	0.851081	+	0.309768i
$802$	1.71935	−	9.75090i	0.0607122	−	0.344316i
$803$	−1.18992	−	6.74835i	−0.0419912	−	0.238144i
$804$	−4.57417	+	1.66486i	−0.161318	+	0.0587151i
$805$		0			0
$806$	−15.8217	−	27.4040i	−0.557297	−	0.965266i
$807$	−3.29968	−	2.76876i	−0.116154	−	0.0974649i
$808$	0.961904	+	0.807133i	0.0338396	+	0.0283948i
$809$	−22.7973	−	39.4861i	−0.801511	−	1.38826i	−0.918621	−	0.395139i	$-0.870696\pi$
$809$	−22.7973	−	39.4861i	−0.801511	−	1.38826i	0.117110	−	0.993119i	$-0.462637\pi$
$810$		0			0
$811$	−35.6230	+	12.9657i	−1.25089	+	0.455288i	−0.880704	−	0.473667i	$-0.842930\pi$
$811$	−35.6230	+	12.9657i	−1.25089	+	0.455288i	−0.370191	+	0.928956i	$0.620708\pi$
$812$	−3.06930	−	17.4069i	−0.107711	−	0.610861i
$813$	1.06607	−	6.04599i	0.0373888	−	0.212042i
$814$	52.7704	+	19.2069i	1.84960	+	0.673200i
$815$		0			0
$816$	0.808181			0.0282920
$817$	−0.787270	−	6.39699i	−0.0275431	−	0.223802i
$818$	−30.6587			−1.07196
$819$	−38.3424	+	32.1731i	−1.33979	+	1.12422i
$820$		0			0
$821$	9.63416	−	54.6380i	0.336235	−	1.90688i	−0.0784541	−	0.996918i	$-0.524998\pi$
$821$	9.63416	−	54.6380i	0.336235	−	1.90688i	0.414689	−	0.909963i	$-0.363890\pi$
$822$	−1.43949	−	8.16377i	−0.0502081	−	0.284744i
$823$	−6.02255	+	2.19203i	−0.209933	+	0.0764094i	−0.444846	−	0.895607i	$-0.646742\pi$
$823$	−6.02255	+	2.19203i	−0.209933	+	0.0764094i	0.234913	+	0.972016i	$0.424519\pi$
$824$	3.68352	−	6.38005i	0.128322	−	0.222260i
$825$		0			0
$826$	−27.2945	−	22.9028i	−0.949699	−	0.796892i
$827$	−3.36481	−	2.82341i	−0.117006	−	0.0981796i	0.582407	−	0.812897i	$-0.302111\pi$
$827$	−3.36481	−	2.82341i	−0.117006	−	0.0981796i	−0.699413	+	0.714717i	$0.746555\pi$
$828$	−7.12144	−	12.3347i	−0.247487	−	0.428660i
$829$	−25.0469	+	43.3826i	−0.869916	+	1.50674i	−0.00783422	+	0.999969i	$0.502494\pi$
$829$	−25.0469	+	43.3826i	−0.869916	+	1.50674i	−0.862082	+	0.506769i	$0.830840\pi$
$830$		0			0
$831$	−0.232849	−	1.32055i	−0.00807745	−	0.0458095i
$832$	0.669793	−	3.79858i	0.0232209	−	0.131692i
$833$	21.9506	+	7.98936i	0.760543	+	0.276815i
$834$	−7.88227	+	6.61401i	−0.272941	+	0.229024i
$835$		0			0
$836$	22.3787	−	6.84871i	0.773984	−	0.236868i
$837$	26.8013			0.926390
$838$	13.7348	−	11.5249i	0.474462	−	0.398121i
$839$	−28.3895	−	10.3329i	−0.980115	−	0.356733i	−0.198230	−	0.980156i	$-0.563519\pi$
$839$	−28.3895	−	10.3329i	−0.980115	−	0.356733i	−0.781885	+	0.623423i	$0.785742\pi$
$840$		0			0
$841$	−2.74289	−	15.5557i	−0.0945823	−	0.536403i
$842$	30.2850	−	11.0228i	1.04369	−	0.379872i
$843$	−4.92056	+	8.52266i	−0.169473	+	0.293536i
$844$	−5.33548	−	9.24132i	−0.183655	−	0.318099i
$845$		0			0
$846$	−6.37672	−	5.35070i	−0.219236	−	0.183961i
$847$	−43.3567	−	75.0961i	−1.48975	−	2.58033i
$848$	−0.900005	+	1.55885i	−0.0309063	+	0.0535313i
$849$	−4.58664	+	1.66940i	−0.157413	+	0.0572937i
$850$		0			0
$851$	−9.69680	+	54.9933i	−0.332402	+	1.88515i
$852$	3.26420	+	1.18807i	0.111830	+	0.0407026i
$853$	9.07579	−	7.61549i	0.310749	−	0.260750i	−0.474052	−	0.880497i	$-0.657209\pi$
$853$	9.07579	−	7.61549i	0.310749	−	0.260750i	0.784802	+	0.619747i	$0.212765\pi$
$854$	39.4731			1.35074
$855$		0			0
$856$	8.73078			0.298412
$857$	−36.4650	+	30.5978i	−1.24562	+	1.04520i	−0.248558	+	0.968617i	$0.579957\pi$
$857$	−36.4650	+	30.5978i	−1.24562	+	1.04520i	−0.997063	+	0.0765828i	$0.975599\pi$
$858$	−11.2173	−	4.08275i	−0.382951	−	0.139383i
$859$	1.97498	−	11.2007i	0.0673853	−	0.382161i	−0.932400	−	0.361429i	$-0.882289\pi$
$859$	1.97498	−	11.2007i	0.0673853	−	0.382161i	0.999785	−	0.0207325i	$-0.00659983\pi$
$860$		0			0
$861$	−5.02777	+	1.82996i	−0.171346	+	0.0623648i
$862$	0.695457	−	1.20457i	0.0236873	−	0.0410277i
$863$	−24.4357	−	42.3239i	−0.831801	−	1.44072i	−0.896608	−	0.442825i	$-0.853976\pi$
$863$	−24.4357	−	42.3239i	−0.831801	−	1.44072i	0.0648068	−	0.997898i	$-0.479357\pi$
$864$	2.50263	+	2.09996i	0.0851412	+	0.0714420i
$865$		0			0
$866$	16.6267	+	28.7984i	0.565000	+	0.978608i
$867$	−4.33292	+	7.50483i	−0.147154	+	0.254878i
$868$	−37.4981	+	13.6482i	−1.27277	+	0.463250i
$869$	15.5065	+	87.9417i	0.526022	+	2.98322i
$870$		0			0
$871$	30.6091	+	11.1408i	1.03715	+	0.377491i
$872$	6.22780	−	5.22574i	0.210900	−	0.176966i
$873$	−16.2176			−0.548882
$874$	10.5710	+	20.7323i	0.357568	+	0.701282i
$875$		0			0
$876$	−0.563551	+	0.472875i	−0.0190406	+	0.0159770i
$877$	−27.7048	−	10.0837i	−0.935524	−	0.340503i	−0.171127	−	0.985249i	$-0.554741\pi$
$877$	−27.7048	−	10.0837i	−0.935524	−	0.340503i	−0.764397	+	0.644746i	$0.776963\pi$
$878$	−6.27110	+	35.5652i	−0.211639	+	1.20027i
$879$	−0.259484	−	1.47161i	−0.00875218	−	0.0496361i
$880$		0			0
$881$	20.8616	−	36.1334i	0.702846	−	1.21736i	−0.264618	−	0.964353i	$-0.585246\pi$
$881$	20.8616	−	36.1334i	0.702846	−	1.21736i	0.967463	−	0.253011i	$-0.0814209\pi$
$882$	22.2228	+	38.4910i	0.748280	+	1.29606i
$883$	−4.53603	−	3.80618i	−0.152650	−	0.128088i	0.563264	−	0.826277i	$-0.309545\pi$
$883$	−4.53603	−	3.80618i	−0.152650	−	0.128088i	−0.715914	+	0.698189i	$0.753990\pi$
$884$	−4.14287	−	3.47628i	−0.139340	−	0.116920i
$885$		0			0
$886$	15.9938	−	27.7021i	0.537323	−	0.930672i
$887$	−12.9931	+	4.72909i	−0.436265	+	0.158787i	−0.550810	−	0.834631i	$-0.685681\pi$
$887$	−12.9931	+	4.72909i	−0.436265	+	0.158787i	0.114545	+	0.993418i	$0.463459\pi$
$888$	−1.04691	−	5.93730i	−0.0351319	−	0.199243i
$889$	0.117562	−	0.666726i	0.00394290	−	0.0223613i
$890$		0			0
$891$	−25.1718	+	21.1217i	−0.843288	+	0.707603i
$892$	0.0994685			0.00333045
$893$	9.94983	+	9.27316i	0.332958	+	0.310315i
$894$	1.66386			0.0556478
$895$		0			0
$896$	−4.57084	−	1.66365i	−0.152701	−	0.0555787i
$897$	2.06122	−	11.6898i	0.0688222	−	0.390310i
$898$	−0.378957	−	2.14917i	−0.0126459	−	0.0717187i
$899$	28.0129	−	10.1959i	0.934282	−	0.340051i
$900$		0			0
$901$	1.26189	+	2.18566i	0.0420397	+	0.0728149i
$902$	7.84875	+	6.58588i	0.261335	+	0.219286i
$903$	3.17585	+	2.66485i	0.105686	+	0.0886807i
$904$	−2.24105	−	3.88161i	−0.0745362	−	0.129100i
$905$		0			0
$906$	1.09307	−	0.397846i	0.0363149	−	0.0132175i
$907$	−1.45100	−	8.22903i	−0.0481797	−	0.273240i	0.951195	−	0.308589i	$-0.0998569\pi$
$907$	−1.45100	−	8.22903i	−0.0481797	−	0.273240i	−0.999375	+	0.0353489i	$0.988746\pi$
$908$	2.40090	−	13.6162i	0.0796767	−	0.451869i
$909$	3.14781	+	1.14571i	0.104406	+	0.0380008i
$910$		0			0
$911$	39.5762			1.31122			0.655609	−	0.755101i	$-0.272412\pi$
$911$	39.5762			1.31122			0.655609	+	0.755101i	$0.272412\pi$
$912$	−1.83802	−	1.71302i	−0.0608628	−	0.0567237i
$913$	77.6420			2.56958
$914$	28.4997	−	23.9141i	0.942685	−	0.791007i
$915$		0			0
$916$	2.70460	−	15.3386i	0.0893626	−	0.506800i
$917$	10.4992	+	59.5437i	0.346713	+	1.96631i
$918$	4.30433	−	1.56665i	0.142064	−	0.0517071i
$919$	19.0623	−	33.0169i	0.628807	−	1.08913i	−0.358984	−	0.933344i	$-0.616877\pi$
$919$	19.0623	−	33.0169i	0.628807	−	1.08913i	0.987791	−	0.155782i	$-0.0497899\pi$
$920$		0			0
$921$	−1.81995	−	1.52712i	−0.0599695	−	0.0503204i
$922$	−3.73897	−	3.13737i	−0.123136	−	0.103324i
$923$	−11.6225	−	20.1307i	−0.382559	−	0.662611i
$924$	−7.52682	+	13.0368i	−0.247614	+	0.428880i
$925$		0			0
$926$	3.51163	+	19.9154i	0.115399	+	0.654462i
$927$	3.41279	−	19.3549i	0.112091	−	0.635697i
$928$	3.41464	+	1.24283i	0.112091	+	0.0407977i
$929$	29.3240	−	24.6058i	0.962090	−	0.807289i	−0.0192022	−	0.999816i	$-0.506113\pi$
$929$	29.3240	−	24.6058i	0.962090	−	0.807289i	0.981292	+	0.192527i	$0.0616682\pi$
$930$		0			0
$931$	−32.9872	−	64.6962i	−1.08111	−	2.12033i
$932$	15.2411			0.499238
$933$	−1.09641	+	0.919999i	−0.0358949	+	0.0301194i
$934$	36.6598	+	13.3431i	1.19955	+	0.436599i
$935$		0			0
$936$	−1.78684	−	10.1337i	−0.0584047	−	0.331230i
$937$	1.77169	−	0.644843i	0.0578787	−	0.0210661i	−0.312919	−	0.949780i	$-0.601307\pi$
$937$	1.77169	−	0.644843i	0.0578787	−	0.0210661i	0.370797	+	0.928714i	$0.379084\pi$
$938$	20.5388	−	35.5742i	0.670615	−	1.16154i
$939$	−1.55096	−	2.68635i	−0.0506138	−	0.0876656i
$940$		0			0
$941$	−11.3282	−	9.50548i	−0.369288	−	0.309870i	0.439192	−	0.898393i	$-0.355265\pi$
$941$	−11.3282	−	9.50548i	−0.369288	−	0.309870i	−0.808480	+	0.588524i	$0.799709\pi$
$942$	3.18161	+	5.51072i	0.103663	+	0.179549i
$943$	−5.09413	+	8.82329i	−0.165888	+	0.287326i
$944$	6.88331	−	2.50532i	0.224033	−	0.0815412i
$945$		0			0
$946$	1.37858	−	7.81833i	0.0448216	−	0.254196i
$947$	−5.33767	−	1.94275i	−0.173451	−	0.0631310i	0.253835	−	0.967248i	$-0.418308\pi$
$947$	−5.33767	−	1.94275i	−0.173451	−	0.0631310i	−0.427286	+	0.904117i	$0.640530\pi$
$948$	7.34396	−	6.16232i	0.238521	−	0.200143i
$949$	4.92286			0.159803
$950$		0			0
$951$	11.2200			0.363834
$952$	−5.22446	+	4.38384i	−0.169326	+	0.142081i
$953$	−12.0998	−	4.40396i	−0.391950	−	0.142658i	0.138524	−	0.990359i	$-0.455764\pi$
$953$	−12.0998	−	4.40396i	−0.391950	−	0.142658i	−0.530475	+	0.847701i	$0.677986\pi$
$954$	−0.833855	+	4.72902i	−0.0269970	+	0.153108i
$955$		0			0
$956$	−15.8088	+	5.75392i	−0.511292	+	0.186095i
$957$	5.62289	−	9.73913i	0.181762	−	0.314821i
$958$	15.5448	+	26.9244i	0.502229	+	0.869886i
$959$	53.5885	+	44.9661i	1.73046	+	1.45203i
$960$		0			0
$961$	−18.1509	−	31.4384i	−0.585514	−	1.01414i
$962$	−20.1719	+	34.9387i	−0.650367	+	1.12647i
$963$	21.8869	−	7.96618i	0.705295	−	0.256706i
$964$	−1.58141	−	8.96862i	−0.0509338	−	0.288860i
$965$		0			0
$966$	−14.0663	−	5.11972i	−0.452577	−	0.164724i
$967$	37.3576	−	31.3467i	1.20134	−	1.00804i	0.201747	−	0.979438i	$-0.435338\pi$
$967$	37.3576	−	31.3467i	1.20134	−	1.00804i	0.999591	−	0.0286047i	$-0.00910640\pi$
$968$	17.8269			0.572979
$969$	−3.36856	+	1.03090i	−0.108214	+	0.0331174i
$970$		0			0
$971$	22.9752	−	19.2784i	0.737308	−	0.618675i	−0.194805	−	0.980842i	$-0.562407\pi$
$971$	22.9752	−	19.2784i	0.737308	−	0.618675i	0.932113	+	0.362167i	$0.117963\pi$
$972$	12.5248	+	4.55864i	0.401732	+	0.146218i
$973$	15.0781	−	85.5120i	0.483381	−	2.74139i
$974$	4.85765	+	27.5491i	0.155649	+	0.882730i
$975$		0			0
$976$	−4.05753	+	7.02784i	−0.129878	+	0.224956i
$977$	−26.8514	−	46.5081i	−0.859054	−	1.48792i	−0.872833	−	0.488019i	$-0.837720\pi$
$977$	−26.8514	−	46.5081i	−0.859054	−	1.48792i	0.0137792	−	0.999905i	$-0.495614\pi$
$978$	−2.61785	−	2.19664i	−0.0837096	−	0.0702407i
$979$	−39.5193	−	33.1606i	−1.26304	−	1.05982i
$980$		0			0
$981$	10.8442	−	18.7826i	0.346227	−	0.599683i
$982$	−2.79400	+	1.01693i	−0.0891600	+	0.0324516i
$983$	10.0589	+	57.0469i	0.320829	+	1.81951i	0.537495	+	0.843267i	$0.319371\pi$
$983$	10.0589	+	57.0469i	0.320829	+	1.81951i	−0.216665	+	0.976246i	$0.569518\pi$
$984$	0.191007	−	1.08326i	0.00608908	−	0.0345329i
$985$		0			0
$986$	3.90292	−	3.27494i	0.124294	−	0.104295i
$987$	−8.74864			−0.278472
$988$	2.05367	+	16.6872i	0.0653360	+	0.530890i
$989$	7.89434			0.251025
$990$		0			0
$991$	6.56906	+	2.39094i	0.208673	+	0.0759508i	0.444242	−	0.895907i	$-0.353473\pi$
$991$	6.56906	+	2.39094i	0.208673	+	0.0759508i	−0.235569	+	0.971858i	$0.575695\pi$
$992$	1.42457	−	8.07914i	0.0452302	−	0.256513i
$993$	1.87275	+	10.6209i	0.0594301	+	0.337045i
$994$	−27.5458	+	10.0258i	−0.873698	+	0.318000i
$995$		0			0
$996$	−4.16773	−	7.21872i	−0.132060	−	0.228734i
$997$	−29.0837	−	24.4042i	−0.921091	−	0.772887i	0.0531052	−	0.998589i	$-0.483088\pi$
$997$	−29.0837	−	24.4042i	−0.921091	−	0.772887i	−0.974196	+	0.225702i	$0.927533\pi$
$998$	14.1236	+	11.8511i	0.447074	+	0.375140i
$999$	−17.0851	−	29.5923i	−0.540550	−	0.936260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.i.101.2		18
5.2	odd	4		950.2.u.g.899.5		36
5.3	odd	4		950.2.u.g.899.2		36
5.4	even	2		190.2.k.d.101.2	✓	18
19.16	even	9	inner	950.2.l.i.301.2		18
95.4	even	18		3610.2.a.bi.1.6		9
95.34	odd	18		3610.2.a.bj.1.4		9
95.54	even	18		190.2.k.d.111.2	yes	18
95.73	odd	36		950.2.u.g.149.5		36
95.92	odd	36		950.2.u.g.149.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.2	✓	18	5.4	even	2
190.2.k.d.111.2	yes	18	95.54	even	18
950.2.l.i.101.2		18	1.1	even	1	trivial
950.2.l.i.301.2		18	19.16	even	9	inner
950.2.u.g.149.2		36	95.92	odd	36
950.2.u.g.149.5		36	95.73	odd	36
950.2.u.g.899.2		36	5.3	odd	4
950.2.u.g.899.5		36	5.2	odd	4
3610.2.a.bi.1.6		9	95.4	even	18
3610.2.a.bj.1.4		9	95.34	odd	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.541649 + 0.197144i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.541649 - 0.197144i) q^{6} +(-2.43209 + 4.21251i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.04362 - 1.71480i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.541649 + 0.197144i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.541649 - 0.197144i) q^{6} +(-2.43209 + 4.21251i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.04362 - 1.71480i) q^{9} +(2.68454 + 4.64975i) q^{11} +(0.288205 - 0.499186i) q^{12} +(-3.62457 + 1.31923i) q^{13} +(0.844657 + 4.79029i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-1.07407 + 0.901248i) q^{17} -2.66775 q^{18} +(4.35299 + 0.226908i) q^{19} +(-2.14781 + 1.80223i) q^{21} +(5.04528 + 1.83633i) q^{22} +(-0.927092 + 5.25780i) q^{23} +(-0.100093 - 0.567654i) q^{24} +(-1.92859 + 3.34042i) q^{26} +(-1.63348 - 2.82926i) q^{27} +(3.72618 + 3.12664i) q^{28} +(-2.78364 - 2.33575i) q^{29} +(-4.10189 + 7.10468i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.537405 + 3.04777i) q^{33} +(-0.243471 + 1.38079i) q^{34} +(-2.04362 + 1.71480i) q^{36} +10.4594 q^{37} +(3.48044 - 2.62423i) q^{38} -2.22332 q^{39} +(1.79322 + 0.652678i) q^{41} +(-0.486869 + 2.76117i) q^{42} +(-0.256764 - 1.45618i) q^{43} +(5.04528 - 1.83633i) q^{44} +(2.66945 + 4.62363i) q^{46} +(2.39030 + 2.00570i) q^{47} +(-0.441556 - 0.370510i) q^{48} +(-8.33016 - 14.4283i) q^{49} +(-0.759442 + 0.276414i) q^{51} +(0.669793 + 3.79858i) q^{52} +(0.312568 - 1.77266i) q^{53} +(-3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(2.31306 + 0.981070i) q^{57} -3.63378 q^{58} +(-5.61133 + 4.70846i) q^{59} +(1.40916 - 7.99176i) q^{61} +(1.42457 + 8.07914i) q^{62} +(12.1939 - 4.43820i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.37075 + 1.98929i) q^{66} +(-6.46916 - 5.42827i) q^{67} +(0.701047 + 1.21425i) q^{68} +(-1.53870 + 2.66511i) q^{69} +(1.04647 + 5.93485i) q^{71} +(-0.463250 + 2.62722i) q^{72} +(-1.19931 - 0.436515i) q^{73} +(8.01234 - 6.72316i) q^{74} +(0.979350 - 4.24746i) q^{76} -26.1162 q^{77} +(-1.70316 + 1.42912i) q^{78} +(15.6290 + 5.68848i) q^{79} +(1.06275 + 6.02717i) q^{81} +(1.79322 - 0.652678i) q^{82} +(7.23049 - 12.5236i) q^{83} +(1.40188 + 2.42814i) q^{84} +(-1.13271 - 0.950453i) q^{86} +(-1.04727 - 1.81393i) q^{87} +(2.68454 - 4.64975i) q^{88} +(-9.02905 + 3.28630i) q^{89} +(3.25800 - 18.4770i) q^{91} +(5.01693 + 1.82601i) q^{92} +(-3.62243 + 3.03958i) q^{93} +3.12031 q^{94} -0.576411 q^{96} +(4.65687 - 3.90758i) q^{97} +(-15.6556 - 5.69817i) q^{98} +(2.48722 - 14.1057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 9 * q^8 - 18 * q^9	\( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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