LMFDB - Embedded newform 625.2.h.b.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			274.2
Character	$\chi$	$=$	625.274
Dual form			625.2.h.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618528 - 2.40901i) q^{2} +(-3.26064 + 0.622000i) q^{3} +(-3.66812 + 2.01657i) q^{4} +(3.51519 + 7.47017i) q^{6} +(-0.463359 + 0.637759i) q^{7} +(3.72162 + 3.96312i) q^{8} +(7.45553 - 2.95185i) q^{9} +O(q^{10})$	\(q+(-0.618528 - 2.40901i) q^{2} +(-3.26064 + 0.622000i) q^{3} +(-3.66812 + 2.01657i) q^{4} +(3.51519 + 7.47017i) q^{6} +(-0.463359 + 0.637759i) q^{7} +(3.72162 + 3.96312i) q^{8} +(7.45553 - 2.95185i) q^{9} +(1.00576 - 0.258235i) q^{11} +(10.7061 - 8.85686i) q^{12} +(0.207600 + 0.524337i) q^{13} +(1.82297 + 0.721763i) q^{14} +(2.75944 - 4.34818i) q^{16} +(1.66584 - 3.03015i) q^{17} +(-11.7225 - 16.1346i) q^{18} +(-0.598583 + 3.13788i) q^{19} +(1.11416 - 2.36771i) q^{21} +(-1.24418 - 2.26315i) q^{22} +(3.37563 + 0.212377i) q^{23} +(-14.5999 - 10.6075i) q^{24} +(1.13473 - 0.824427i) q^{26} +(-14.0657 + 8.92634i) q^{27} +(0.413573 - 3.27377i) q^{28} +(-2.01748 - 0.254867i) q^{29} +(-5.56625 - 3.06007i) q^{31} +(-1.84053 - 0.598023i) q^{32} +(-3.11879 + 1.46759i) q^{33} +(-8.33001 - 2.13878i) q^{34} +(-21.3952 + 25.8623i) q^{36} +(4.67893 + 2.96934i) q^{37} +(7.92942 - 0.498877i) q^{38} +(-1.00305 - 1.58055i) q^{39} +(-0.714850 - 11.3622i) q^{41} +(-6.39296 - 1.21952i) q^{42} +(-2.69982 + 0.877225i) q^{43} +(-3.16849 + 2.97541i) q^{44} +(-1.57631 - 8.26328i) q^{46} +(-1.00997 + 1.07551i) q^{47} +(-6.29296 + 15.8942i) q^{48} +(1.97108 + 6.06637i) q^{49} +(-3.54694 + 10.9164i) q^{51} +(-1.81886 - 1.50469i) q^{52} +(-2.80343 - 1.31919i) q^{53} +(30.2036 + 28.3631i) q^{54} +(-4.25196 + 0.537148i) q^{56} -10.6038i q^{57} +(0.633891 + 5.01776i) q^{58} +(-2.27401 - 2.74880i) q^{59} +(0.470039 - 7.47105i) q^{61} +(-3.92885 + 15.3019i) q^{62} +(-1.57202 + 6.12260i) q^{63} +(0.344501 - 5.47569i) q^{64} +(5.46449 + 6.60544i) q^{66} +(-1.70582 - 13.5029i) q^{67} +14.4742i q^{68} +(-11.1388 + 1.40716i) q^{69} +(3.81072 + 3.57851i) q^{71} +(39.4452 + 18.5615i) q^{72} +(-4.81135 - 3.98029i) q^{73} +(4.25911 - 13.1082i) q^{74} +(-4.13207 - 12.7172i) q^{76} +(-0.301335 + 0.761087i) q^{77} +(-3.18714 + 3.39395i) q^{78} +(-1.73061 - 9.07217i) q^{79} +(22.7748 - 21.3870i) q^{81} +(-26.9295 + 8.74992i) q^{82} +(0.187696 + 0.0358049i) q^{83} +(0.687772 + 10.9318i) q^{84} +(3.78315 + 5.96130i) q^{86} +(6.73680 - 0.423843i) q^{87} +(4.76646 + 3.02489i) q^{88} +(1.42021 - 1.71673i) q^{89} +(-0.430594 - 0.110558i) q^{91} +(-12.8105 + 6.02816i) q^{92} +(20.0529 + 6.51558i) q^{93} +(3.21559 + 1.76779i) q^{94} +(6.37326 + 0.805130i) q^{96} +(1.51887 - 12.0231i) q^{97} +(13.3948 - 8.50057i) q^{98} +(6.73619 - 4.89413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	−0.618528	−	2.40901i	−0.437365	−	1.70342i	−0.679920	−	0.733287i	$-0.737985\pi$
$2$	−0.618528	−	2.40901i	−0.437365	−	1.70342i	0.242555	−	0.970138i	$-0.422015\pi$
$3$	−3.26064	+	0.622000i	−1.88253	+	0.359112i	−0.994851	−	0.101352i	$-0.967683\pi$
$3$	−3.26064	+	0.622000i	−1.88253	+	0.359112i	−0.887678	+	0.460464i	$0.847683\pi$
$4$	−3.66812	+	2.01657i	−1.83406	+	1.00828i
$5$		0			0
$5$		0			0
$6$	3.51519	+	7.47017i	1.43507	+	3.04968i
$7$	−0.463359	+	0.637759i	−0.175133	+	0.241050i	−0.887555	−	0.460701i	$-0.847598\pi$
$7$	−0.463359	+	0.637759i	−0.175133	+	0.241050i	0.712422	+	0.701751i	$0.247598\pi$
$8$	3.72162	+	3.96312i	1.31579	+	1.40117i
$9$	7.45553	−	2.95185i	2.48518	−	0.983952i
$10$		0			0
$11$	1.00576	−	0.258235i	0.303247	−	0.0778607i	−0.0940002	−	0.995572i	$-0.529965\pi$
$11$	1.00576	−	0.258235i	0.303247	−	0.0778607i	0.397248	+	0.917711i	$0.369965\pi$
$12$	10.7061	−	8.85686i	3.09059	−	2.55675i
$13$	0.207600	+	0.524337i	0.0575779	+	0.145425i	0.955718	−	0.294285i	$-0.0950814\pi$
$13$	0.207600	+	0.524337i	0.0575779	+	0.145425i	−0.898140	+	0.439710i	$0.855081\pi$
$14$	1.82297	+	0.721763i	0.487208	+	0.192899i
$15$		0			0
$16$	2.75944	−	4.34818i	0.689860	−	1.08705i
$17$	1.66584	−	3.03015i	0.404025	−	0.734919i	−0.593529	−	0.804812i	$-0.702266\pi$
$17$	1.66584	−	3.03015i	0.404025	−	0.734919i	0.997554	+	0.0698933i	$0.0222659\pi$
$18$	−11.7225	−	16.1346i	−2.76302	−	3.80297i
$19$	−0.598583	+	3.13788i	−0.137324	+	0.719880i	0.845303	+	0.534288i	$0.179420\pi$
$19$	−0.598583	+	3.13788i	−0.137324	+	0.719880i	−0.982627	+	0.185592i	$0.940580\pi$
$20$		0			0
$21$	1.11416	−	2.36771i	0.243129	−	0.516676i
$22$	−1.24418	−	2.26315i	−0.265260	−	0.482506i
$23$	3.37563	+	0.212377i	0.703868	+	0.0442836i	0.410691	−	0.911775i	$-0.365287\pi$
$23$	3.37563	+	0.212377i	0.703868	+	0.0442836i	0.293177	+	0.956058i	$0.405287\pi$
$24$	−14.5999	−	10.6075i	−2.98019	−	2.16524i
$25$		0			0
$26$	1.13473	−	0.824427i	0.222538	−	0.161683i
$27$	−14.0657	+	8.92634i	−2.70694	+	1.71788i
$28$	0.413573	−	3.27377i	0.0781580	−	0.618684i
$29$	−2.01748	−	0.254867i	−0.374637	−	0.0473276i	−0.0642393	−	0.997935i	$-0.520462\pi$
$29$	−2.01748	−	0.254867i	−0.374637	−	0.0473276i	−0.310397	+	0.950607i	$0.600462\pi$
$30$		0			0
$31$	−5.56625	−	3.06007i	−0.999729	−	0.549605i	−0.104175	−	0.994559i	$-0.533220\pi$
$31$	−5.56625	−	3.06007i	−0.999729	−	0.549605i	−0.895554	+	0.444954i	$0.853220\pi$
$32$	−1.84053	−	0.598023i	−0.325362	−	0.105717i
$33$	−3.11879	+	1.46759i	−0.542911	+	0.255475i
$34$	−8.33001	−	2.13878i	−1.42859	−	0.366798i
$35$		0			0
$36$	−21.3952	+	25.8623i	−3.56586	+	4.31039i
$37$	4.67893	+	2.96934i	0.769212	+	0.488157i	0.861613	−	0.507565i	$-0.169454\pi$
$37$	4.67893	+	2.96934i	0.769212	+	0.488157i	−0.0924015	+	0.995722i	$0.529454\pi$
$38$	7.92942	−	0.498877i	1.28632	−	0.0809285i
$39$	−1.00305	−	1.58055i	−0.160616	−	0.253090i
$40$		0			0
$41$	−0.714850	−	11.3622i	−0.111641	−	1.77448i	−0.512835	−	0.858487i	$-0.671405\pi$
$41$	−0.714850	−	11.3622i	−0.111641	−	1.77448i	0.401195	−	0.915993i	$-0.368595\pi$
$42$	−6.39296	−	1.21952i	−0.986456	−	0.188176i
$43$	−2.69982	+	0.877225i	−0.411719	+	0.133776i	−0.507551	−	0.861622i	$-0.669449\pi$
$43$	−2.69982	+	0.877225i	−0.411719	+	0.133776i	0.0958317	+	0.995398i	$0.469449\pi$
$44$	−3.16849	+	2.97541i	−0.477668	+	0.448560i
$45$		0			0
$46$	−1.57631	−	8.26328i	−0.232414	−	1.21835i
$47$	−1.00997	+	1.07551i	−0.147319	+	0.156879i	−0.798396	−	0.602133i	$-0.794318\pi$
$47$	−1.00997	+	1.07551i	−0.147319	+	0.156879i	0.651077	+	0.759012i	$0.274318\pi$
$48$	−6.29296	+	15.8942i	−0.908311	+	2.29413i
$49$	1.97108	+	6.06637i	0.281583	+	0.866625i
$50$		0			0
$51$	−3.54694	+	10.9164i	−0.496671	+	1.52860i
$52$	−1.81886	−	1.50469i	−0.252231	−	0.208664i
$53$	−2.80343	−	1.31919i	−0.385081	−	0.181205i	0.223487	−	0.974707i	$-0.428256\pi$
$53$	−2.80343	−	1.31919i	−0.385081	−	0.181205i	−0.608568	+	0.793502i	$0.708256\pi$
$54$	30.2036	+	28.3631i	4.11019	+	3.85973i
$55$		0			0
$56$	−4.25196	+	0.537148i	−0.568192	+	0.0717794i
$57$		−	10.6038i		−	1.40451i
$58$	0.633891	+	5.01776i	0.0832340	+	0.658865i
$59$	−2.27401	−	2.74880i	−0.296051	−	0.357864i	0.601424	−	0.798930i	$-0.294600\pi$
$59$	−2.27401	−	2.74880i	−0.296051	−	0.357864i	−0.897474	+	0.441066i	$0.854600\pi$
$60$		0			0
$61$	0.470039	−	7.47105i	0.0601823	−	0.956570i	−0.845866	−	0.533396i	$-0.820916\pi$
$61$	0.470039	−	7.47105i	0.0601823	−	0.956570i	0.906048	−	0.423174i	$-0.139084\pi$
$62$	−3.92885	+	15.3019i	−0.498965	+	1.94334i
$63$	−1.57202	+	6.12260i	−0.198056	+	0.771375i
$64$	0.344501	−	5.47569i	0.0430626	−	0.684461i
$65$		0			0
$66$	5.46449	+	6.60544i	0.672632	+	0.813073i
$67$	−1.70582	−	13.5029i	−0.208398	−	1.64964i	−0.655525	−	0.755173i	$-0.727553\pi$
$67$	−1.70582	−	13.5029i	−0.208398	−	1.64964i	0.447127	−	0.894471i	$-0.352447\pi$
$68$			14.4742i			1.75526i
$69$	−11.1388	+	1.40716i	−1.34096	+	0.169402i
$70$		0			0
$71$	3.81072	+	3.57851i	0.452249	+	0.424690i	0.876904	−	0.480665i	$-0.159605\pi$
$71$	3.81072	+	3.57851i	0.452249	+	0.424690i	−0.424655	+	0.905355i	$0.639605\pi$
$72$	39.4452	+	18.5615i	4.64866	+	2.18749i
$73$	−4.81135	−	3.98029i	−0.563126	−	0.465858i	0.311778	−	0.950155i	$-0.399076\pi$
$73$	−4.81135	−	3.98029i	−0.563126	−	0.465858i	−0.874904	+	0.484297i	$0.839076\pi$
$74$	4.25911	−	13.1082i	0.495112	−	1.52380i
$75$		0			0
$76$	−4.13207	−	12.7172i	−0.473981	−	1.45876i
$77$	−0.301335	+	0.761087i	−0.0343404	+	0.0867339i
$78$	−3.18714	+	3.39395i	−0.360872	+	0.384290i
$79$	−1.73061	−	9.07217i	−0.194709	−	1.02070i	−0.936659	−	0.350243i	$-0.886099\pi$
$79$	−1.73061	−	9.07217i	−0.194709	−	1.02070i	0.741950	−	0.670455i	$-0.233901\pi$
$80$		0			0
$81$	22.7748	−	21.3870i	2.53054	−	2.37633i
$82$	−26.9295	+	8.74992i	−2.97386	+	0.966267i
$83$	0.187696	+	0.0358049i	0.0206023	+	0.00393010i	0.197672	−	0.980268i	$-0.436662\pi$
$83$	0.187696	+	0.0358049i	0.0206023	+	0.00393010i	−0.177070	+	0.984198i	$0.556662\pi$
$84$	0.687772	+	10.9318i	0.0750420	+	1.19276i
$85$		0			0
$86$	3.78315	+	5.96130i	0.407948	+	0.642823i
$87$	6.73680	−	0.423843i	0.722260	−	0.0454408i
$88$	4.76646	+	3.02489i	0.508107	+	0.322454i
$89$	1.42021	−	1.71673i	0.150542	−	0.181973i	−0.689851	−	0.723951i	$-0.742324\pi$
$89$	1.42021	−	1.71673i	0.150542	−	0.181973i	0.840393	+	0.541977i	$0.182324\pi$
$90$		0			0
$91$	−0.430594	−	0.110558i	−0.0451385	−	0.0115896i
$92$	−12.8105	+	6.02816i	−1.33559	+	0.628480i
$93$	20.0529	+	6.51558i	2.07939	+	0.675634i
$94$	3.21559	+	1.76779i	0.331663	+	0.182333i
$95$		0			0
$96$	6.37326	+	0.805130i	0.650468	+	0.0821732i
$97$	1.51887	−	12.0231i	0.154218	−	1.22076i	−0.705020	−	0.709187i	$-0.749062\pi$
$97$	1.51887	−	12.0231i	0.154218	−	1.22076i	0.859238	−	0.511576i	$-0.170938\pi$
$98$	13.3948	−	8.50057i	1.35307	−	0.858687i
$99$	6.73619	−	4.89413i	0.677013	−	0.491879i
$100$		0			0
$101$	−8.25784	−	5.99967i	−0.821686	−	0.596990i	0.0955088	−	0.995429i	$-0.469552\pi$
$101$	−8.25784	−	5.99967i	−0.821686	−	0.596990i	−0.917195	+	0.398439i	$0.869552\pi$
$102$	28.4915	+	1.79253i	2.82108	+	0.177487i
$103$	−8.16330	−	14.8490i	−0.804353	−	1.46311i	−0.884606	−	0.466339i	$-0.845573\pi$
$103$	−8.16330	−	14.8490i	−0.804353	−	1.46311i	0.0802527	−	0.996775i	$-0.474427\pi$
$104$	−1.30541	+	2.77413i	−0.128006	+	0.272026i
$105$		0			0
$106$	−1.44395	+	7.56944i	−0.140249	+	0.735209i
$107$	8.29283	+	11.4141i	0.801698	+	1.10344i	0.992552	+	0.121824i	$0.0388743\pi$
$107$	8.29283	+	11.4141i	0.801698	+	1.10344i	−0.190854	+	0.981618i	$0.561126\pi$
$108$	33.5940	−	61.1072i	3.23258	−	5.88005i
$109$	0.443460	−	0.698780i	0.0424757	−	0.0669310i	−0.822427	−	0.568871i	$-0.807380\pi$
$109$	0.443460	−	0.698780i	0.0424757	−	0.0669310i	0.864902	+	0.501940i	$0.167380\pi$
$110$		0			0
$111$	−17.1032	−	6.77165i	−1.62337	−	0.642736i
$112$	1.49448	+	3.77463i	0.141215	+	0.356669i
$113$	5.01705	−	4.15047i	0.471965	−	0.390443i	−0.370811	−	0.928708i	$-0.620920\pi$
$113$	5.01705	−	4.15047i	0.471965	−	0.390443i	0.842775	+	0.538265i	$0.180920\pi$
$114$	−25.5446	+	6.55875i	−2.39248	+	0.614283i
$115$		0			0
$116$	7.91432	−	3.13350i	0.734826	−	0.290938i
$117$	3.09554	+	3.29641i	0.286182	+	0.304753i
$118$	−5.21535	+	7.17831i	−0.480111	+	0.660817i
$119$	1.16062	+	2.46645i	0.106394	+	0.226099i
$120$		0			0
$121$	−8.69451	+	4.77985i	−0.790410	+	0.434532i
$122$	−18.2885	+	3.48872i	−1.65577	+	0.315854i
$123$	9.39816	+	36.6034i	0.847403	+	3.30042i
$124$	26.5885			2.38772
$125$		0			0
$126$	15.7217			1.40060
$127$	2.07182	+	8.06920i	0.183844	+	0.716026i	0.991911	+	0.126935i	$0.0405139\pi$
$127$	2.07182	+	8.06920i	0.183844	+	0.716026i	−0.808067	+	0.589091i	$0.799486\pi$
$128$	−17.2060	+	3.28221i	−1.52081	+	0.290110i
$129$	8.25750	−	4.53960i	0.727032	−	0.399689i
$130$		0			0
$131$	4.08655	+	8.68436i	0.357043	+	0.758756i	0.999974	−	0.00716837i	$-0.00228178\pi$
$131$	4.08655	+	8.68436i	0.357043	+	0.758756i	−0.642931	+	0.765924i	$0.722282\pi$
$132$	8.48060	−	11.6725i	0.738141	−	1.01596i
$133$	−1.72385	−	1.83572i	−0.149477	−	0.159177i
$134$	−31.4735	+	12.4612i	−2.71890	+	1.07649i
$135$		0			0
$136$	18.2085	−	4.67514i	1.56136	−	0.400890i
$137$	−1.38806	+	1.14830i	−0.118590	+	0.0981061i	−0.694829	−	0.719175i	$-0.744520\pi$
$137$	−1.38806	+	1.14830i	−0.118590	+	0.0981061i	0.576239	+	0.817281i	$0.304520\pi$
$138$	10.2795	+	25.9631i	0.875051	+	2.21013i
$139$	−8.38439	−	3.31961i	−0.711154	−	0.281566i	−0.0154363	−	0.999881i	$-0.504914\pi$
$139$	−8.38439	−	3.31961i	−0.711154	−	0.281566i	−0.695718	+	0.718315i	$0.744914\pi$
$140$		0			0
$141$	2.62417	−	4.13503i	0.220995	−	0.348232i
$142$	6.26361	−	11.3935i	0.525630	−	0.956118i
$143$	0.344197	+	0.473747i	0.0287832	+	0.0396167i
$144$	7.73790	−	40.5635i	0.644825	−	3.38029i
$145$		0			0
$146$	−6.61260	+	14.0525i	−0.547263	+	1.16299i
$147$	−10.2003	−	18.5542i	−0.841304	−	1.53033i
$148$	−23.1508	−	1.45652i	−1.90298	−	0.119725i
$149$	4.91478	+	3.57079i	0.402634	+	0.292531i	0.770613	−	0.637303i	$-0.219950\pi$
$149$	4.91478	+	3.57079i	0.402634	+	0.292531i	−0.367979	+	0.929834i	$0.619950\pi$
$150$		0			0
$151$	8.84022	−	6.42279i	0.719407	−	0.522680i	−0.166788	−	0.985993i	$-0.553340\pi$
$151$	8.84022	−	6.42279i	0.719407	−	0.522680i	0.886195	+	0.463313i	$0.153340\pi$
$152$	−14.6635	+	9.30575i	−1.18937	+	0.754796i
$153$	3.47516	−	27.5087i	0.280950	−	2.22395i
$154$	2.01985	+	0.255166i	0.162764	+	0.0205619i
$155$		0			0
$156$	6.86657	+	3.77493i	0.549765	+	0.302236i
$157$	−14.1931	−	4.61162i	−1.13273	−	0.368048i	−0.318120	−	0.948051i	$-0.603051\pi$
$157$	−14.1931	−	4.61162i	−1.13273	−	0.368048i	−0.814614	+	0.580003i	$0.803051\pi$
$158$	−20.7845	+	9.78043i	−1.65352	+	0.778089i
$159$	9.96151	+	2.55768i	0.789999	+	0.202837i
$160$		0			0
$161$	−1.69958	+	2.05443i	−0.133945	+	0.161912i
$162$	−65.6083	−	41.6363i	−5.15467	−	3.27125i
$163$	−7.83419	+	0.492885i	−0.613621	+	0.0386057i	−0.366560	−	0.930394i	$-0.619465\pi$
$163$	−7.83419	+	0.492885i	−0.613621	+	0.0386057i	−0.247060	+	0.969000i	$0.579465\pi$
$164$	25.5348	+	40.2364i	1.99393	+	3.14194i
$165$		0			0
$166$	−0.0298409	−	0.474307i	−0.00231610	−	0.0368134i
$167$	9.20316	+	1.75560i	0.712162	+	0.135852i	0.530717	−	0.847549i	$-0.321923\pi$
$167$	9.20316	+	1.75560i	0.712162	+	0.135852i	0.181445	+	0.983401i	$0.441923\pi$
$168$	13.5300	−	4.39616i	1.04386	−	0.339171i
$169$	9.24476	−	8.68141i	0.711135	−	0.667801i
$170$		0			0
$171$	4.79982	+	25.1615i	0.367051	+	1.92415i
$172$	8.13428	−	8.66213i	0.620233	−	0.660481i
$173$	8.18603	−	20.6756i	0.622372	−	1.57193i	−0.185544	−	0.982636i	$-0.559405\pi$
$173$	8.18603	−	20.6756i	0.622372	−	1.57193i	0.807916	−	0.589297i	$-0.200595\pi$
$174$	−5.18794	−	15.9668i	−0.393296	−	1.21044i
$175$		0			0
$176$	1.65248	−	5.08580i	0.124560	−	0.383357i
$177$	9.12446	+	7.54841i	0.685837	+	0.567373i
$178$	−5.01406	−	2.35944i	−0.375820	−	0.176847i
$179$	−4.89894	−	4.60041i	−0.366164	−	0.343851i	0.479524	−	0.877529i	$-0.340809\pi$
$179$	−4.89894	−	4.60041i	−0.366164	−	0.343851i	−0.845688	+	0.533678i	$0.820809\pi$
$180$		0			0
$181$	21.3240	−	2.69385i	1.58500	−	0.200232i	0.717100	−	0.696970i	$-0.245469\pi$
$181$	21.3240	−	2.69385i	1.58500	−	0.200232i	0.867900	+	0.496738i	$0.165469\pi$
$182$			1.10569i			0.0819590i
$183$	3.11437	+	24.6527i	0.230220	+	1.82238i
$184$	11.7211	+	14.1684i	0.864094	+	1.04451i
$185$		0			0
$186$	3.29280	−	52.3376i	0.241440	−	3.83758i
$187$	0.892941	−	3.47777i	0.0652983	−	0.254320i
$188$	1.53585	−	5.98175i	0.112013	−	0.436264i
$189$	0.824598	−	13.1066i	0.0599807	−	0.953365i
$190$		0			0
$191$	−6.43755	−	7.78166i	−0.465805	−	0.563061i	0.484336	−	0.874882i	$-0.339061\pi$
$191$	−6.43755	−	7.78166i	−0.465805	−	0.563061i	−0.950141	+	0.311821i	$0.899061\pi$
$192$	2.28258	+	18.0685i	0.164731	+	1.30398i
$193$		−	15.7585i		−	1.13433i	−0.823606	−	0.567163i	$-0.808041\pi$
$193$		−	15.7585i		−	1.13433i	0.823606	−	0.567163i	$-0.191959\pi$
$194$	−29.9032	+	3.77766i	−2.14693	+	0.271220i
$195$		0			0
$196$	−19.4634	−	18.2774i	−1.39024	−	1.30553i
$197$	14.1591	+	6.66276i	1.00879	+	0.474702i	0.857883	−	0.513846i	$-0.171780\pi$
$197$	14.1591	+	6.66276i	1.00879	+	0.474702i	0.150910	+	0.988547i	$0.451780\pi$
$198$	−15.9565	−	13.2004i	−1.13398	−	0.938110i
$199$	4.36121	−	13.4224i	0.309158	−	0.951490i	−0.668935	−	0.743321i	$-0.733250\pi$
$199$	4.36121	−	13.4224i	0.309158	−	0.951490i	0.978093	−	0.208169i	$-0.0667505\pi$
$200$		0			0
$201$	13.9609	+	42.9671i	0.984723	+	3.03066i
$202$	−9.34555	+	23.6042i	−0.657550	+	1.66078i
$203$	1.09736	−	1.16857i	0.0770197	−	0.0820176i
$204$	−9.00296	−	47.1952i	−0.630333	−	3.30432i
$205$		0			0
$206$	−30.7221	+	28.8499i	−2.14051	+	2.01007i
$207$	25.7941	−	8.38100i	1.79281	−	0.582520i
$208$	2.85277	+	0.544196i	0.197804	+	0.0377332i
$209$	0.208281	+	3.31053i	0.0144071	+	0.228994i
$210$		0			0
$211$	10.2934	+	16.2198i	0.708625	+	1.11661i	0.987702	+	0.156346i	$0.0499714\pi$
$211$	10.2934	+	16.2198i	0.708625	+	1.11661i	−0.279077	+	0.960269i	$0.590029\pi$
$212$	12.9436	−	0.814340i	0.888968	−	0.0559291i
$213$	−14.6512	−	9.29794i	−1.00388	−	0.637084i
$214$	22.3673	−	27.0374i	1.52900	−	1.84824i
$215$		0			0
$216$	−87.7232	−	22.5235i	−5.96881	−	1.53253i
$217$	4.53076	−	2.13202i	0.307568	−	0.144731i
$218$	−1.95766	−	0.636082i	−0.132589	−	0.0430809i
$219$	18.1638	+	9.98563i	1.22740	+	0.674767i
$220$		0			0
$221$	1.93465	+	0.244403i	0.130139	+	0.0164403i
$222$	−5.73412	+	45.3902i	−0.384849	+	3.04639i
$223$	3.95744	−	2.51147i	0.265010	−	0.168180i	−0.396682	−	0.917956i	$-0.629839\pi$
$223$	3.95744	−	2.51147i	0.265010	−	0.168180i	0.661692	+	0.749776i	$0.269839\pi$
$224$	1.23422	−	0.896713i	0.0824647	−	0.0599141i
$225$		0			0
$226$	−13.1017	−	9.51893i	−0.871511	−	0.633190i
$227$	−7.25785	−	0.456625i	−0.481721	−	0.0303073i	−0.179926	−	0.983680i	$-0.557586\pi$
$227$	−7.25785	−	0.456625i	−0.481721	−	0.0303073i	−0.301795	+	0.953373i	$0.597586\pi$
$228$	21.3833	+	38.8961i	1.41614	+	2.57595i
$229$	−6.50796	+	13.8301i	−0.430058	+	0.913920i	0.565932	+	0.824452i	$0.308517\pi$
$229$	−6.50796	+	13.8301i	−0.430058	+	0.913920i	−0.995990	+	0.0894676i	$0.971483\pi$
$230$		0			0
$231$	0.509150	−	2.66906i	0.0334996	−	0.175611i
$232$	−6.49822	−	8.94404i	−0.426629	−	0.587205i
$233$	−7.63001	+	13.8789i	−0.499858	+	0.909239i	0.499227	+	0.866471i	$0.333617\pi$
$233$	−7.63001	+	13.8789i	−0.499858	+	0.909239i	−0.999085	+	0.0427674i	$0.986383\pi$
$234$	6.02640	−	9.49609i	0.393958	−	0.620779i
$235$		0			0
$236$	13.8845	+	5.49725i	0.903802	+	0.357841i
$237$	11.2858	+	28.5046i	0.733089	+	1.85157i
$238$	5.22382	−	4.32152i	0.338610	−	0.280122i
$239$	−7.69706	+	1.97627i	−0.497882	+	0.127834i	−0.489277	−	0.872129i	$-0.662739\pi$
$239$	−7.69706	+	1.97627i	−0.497882	+	0.127834i	−0.00860512	+	0.999963i	$0.502739\pi$
$240$		0			0
$241$	−11.3987	+	4.51307i	−0.734256	+	0.290712i	−0.705340	−	0.708869i	$-0.749206\pi$
$241$	−11.3987	+	4.51307i	−0.734256	+	0.290712i	−0.0289160	+	0.999582i	$0.509206\pi$
$242$	16.8925	+	17.9887i	1.08589	+	1.15635i
$243$	−31.5820	+	43.4689i	−2.02599	+	2.78853i
$244$	13.3417	+	28.3526i	0.854115	+	1.81509i
$245$		0			0
$246$	82.3648	−	45.2804i	5.25139	−	2.88698i
$247$	−1.76958	+	0.337565i	−0.112595	+	0.0214787i
$248$	−8.58803	−	33.4482i	−0.545340	−	2.12396i
$249$	−0.634279			−0.0401958
$250$		0			0
$251$	−6.12354			−0.386514			−0.193257	−	0.981148i	$-0.561905\pi$
$251$	−6.12354			−0.386514			−0.193257	+	0.981148i	$0.561905\pi$
$252$	−6.58029	−	25.6285i	−0.414519	−	1.61444i
$253$	3.44991	−	0.658106i	0.216894	−	0.0413748i
$254$	18.1573	−	9.98204i	1.13929	−	0.626329i
$255$		0			0
$256$	13.8772	+	29.4905i	0.867322	+	1.84315i
$257$	10.4816	−	14.4267i	0.653823	−	0.899910i	−0.345434	−	0.938443i	$-0.612268\pi$
$257$	10.4816	−	14.4267i	0.653823	−	0.899910i	0.999257	+	0.0385326i	$0.0122683\pi$
$258$	−16.0434	−	17.0845i	−0.998819	−	1.06363i
$259$	−4.06175	+	1.60816i	−0.252385	+	0.0999262i
$260$		0			0
$261$	−15.7937	+	4.05514i	−0.977607	+	0.251007i
$262$	18.3930	−	15.2160i	1.13632	−	0.940050i
$263$	−9.06757	−	22.9021i	−0.559131	−	1.41220i	−0.884466	−	0.466604i	$-0.845477\pi$
$263$	−9.06757	−	22.9021i	−0.559131	−	1.41220i	0.325336	−	0.945599i	$-0.394523\pi$
$264$	−17.4232	−	6.89833i	−1.07232	−	0.424563i
$265$		0			0
$266$	−3.35600	+	5.28822i	−0.205770	+	0.324241i
$267$	−3.56297	+	6.48101i	−0.218050	+	0.396632i
$268$	33.4867	+	46.0904i	2.04552	+	2.81542i
$269$	−1.33637	+	7.00550i	−0.0814799	+	0.427133i	0.918050	+	0.396465i	$0.129763\pi$
$269$	−1.33637	+	7.00550i	−0.0814799	+	0.427133i	−0.999530	+	0.0306674i	$0.990237\pi$
$270$		0			0
$271$	10.9628	−	23.2971i	0.665942	−	1.41520i	−0.230958	−	0.972964i	$-0.574186\pi$
$271$	10.9628	−	23.2971i	0.665942	−	1.41520i	0.896900	−	0.442234i	$-0.145814\pi$
$272$	−8.57885	−	15.6049i	−0.520169	−	0.946185i
$273$	1.47278	+	0.0926593i	0.0891366	+	0.00560800i
$274$	3.62482	+	2.63359i	0.218983	+	0.159101i
$275$		0			0
$276$	38.0209	−	27.6238i	2.28859	−	1.66276i
$277$	3.21964	−	2.04324i	0.193449	−	0.122767i	−0.435575	−	0.900153i	$-0.643455\pi$
$277$	3.21964	−	2.04324i	0.193449	−	0.122767i	0.629024	+	0.777386i	$0.283455\pi$
$278$	−2.81099	+	22.2513i	−0.168592	+	1.33455i
$279$	−50.5323	−	6.38371i	−3.02529	−	0.382183i
$280$		0			0
$281$	−6.82242	−	3.75065i	−0.406991	−	0.223745i	0.265089	−	0.964224i	$-0.414599\pi$
$281$	−6.82242	−	3.75065i	−0.406991	−	0.223745i	−0.672080	+	0.740479i	$0.734599\pi$
$282$	−11.5844	−	3.76401i	−0.689843	−	0.224144i
$283$	−2.16893	+	1.02062i	−0.128930	+	0.0606697i	−0.489162	−	0.872193i	$-0.662697\pi$
$283$	−2.16893	+	1.02062i	−0.128930	+	0.0606697i	0.360232	+	0.932863i	$0.382697\pi$
$284$	−21.1945	−	5.44182i	−1.25766	−	0.322912i
$285$		0			0
$286$	0.928364	−	1.12220i	0.0548953	−	0.0663570i
$287$	7.57759	+	4.80888i	0.447291	+	0.283859i
$288$	−15.4874	+	0.974384i	−0.912603	+	0.0574161i
$289$	2.70227	+	4.25810i	0.158957	+	0.250476i
$290$		0			0
$291$	2.52588	+	40.1478i	0.148070	+	2.35350i
$292$	25.6751	+	4.89779i	1.50252	+	0.286622i
$293$	10.5387	−	3.42423i	0.615677	−	0.200046i	0.0154571	−	0.999881i	$-0.495080\pi$
$293$	10.5387	−	3.42423i	0.615677	−	0.200046i	0.600220	+	0.799835i	$0.295080\pi$
$294$	−38.3881	+	36.0488i	−2.23884	+	2.10241i
$295$		0			0
$296$	5.64535	+	29.5939i	0.328129	+	1.72011i
$297$	−11.8416	+	12.6100i	−0.687117	+	0.731705i
$298$	5.56214	−	14.0484i	0.322206	−	0.813800i
$299$	0.589424	+	1.81406i	0.0340873	+	0.104910i
$300$		0			0
$301$	0.691528	−	2.12830i	0.0398590	−	0.122673i
$302$	−20.9405	−	17.3235i	−1.20499	−	0.996853i
$303$	30.6576	+	14.4264i	1.76123	+	0.828774i
$304$	11.9923	+	11.2615i	0.687807	+	0.645894i
$305$		0			0
$306$	−68.4181	+	8.64321i	−3.91120	+	0.494100i
$307$			9.15311i			0.522396i	0.965285	+	0.261198i	$0.0841175\pi$
$307$			9.15311i			0.522396i	−0.965285	+	0.261198i	$0.915882\pi$
$308$	−0.429447	−	3.39942i	−0.0244700	−	0.193700i
$309$	35.8536	+	43.3396i	2.03964	+	2.46550i
$310$		0			0
$311$	−1.68332	+	26.7556i	−0.0954523	+	1.51717i	0.600815	+	0.799388i	$0.294843\pi$
$311$	−1.68332	+	26.7556i	−0.0954523	+	1.51717i	−0.696267	+	0.717782i	$0.745157\pi$
$312$	2.53095	−	9.85738i	0.143287	−	0.558064i
$313$	−6.52893	+	25.4285i	−0.369037	+	1.43730i	0.464860	+	0.885384i	$0.346105\pi$
$313$	−6.52893	+	25.4285i	−0.369037	+	1.43730i	−0.833897	+	0.551920i	$0.813895\pi$
$314$	−2.33059	+	37.0437i	−0.131523	+	2.09050i
$315$		0			0
$316$	24.6427	+	29.7879i	1.38626	+	1.67570i
$317$	−1.58301	−	12.5308i	−0.0889106	−	0.703800i	−0.972064	−	0.234716i	$-0.924584\pi$
$317$	−1.58301	−	12.5308i	−0.0889106	−	0.703800i	0.883153	−	0.469084i	$-0.155416\pi$
$318$		−	25.5793i		−	1.43442i
$319$	−2.09491	+	0.264649i	−0.117293	+	0.0148175i
$320$		0			0
$321$	−34.1395	−	32.0591i	−1.90548	−	1.78936i
$322$	6.00038	+	2.82356i	0.334388	+	0.157351i
$323$	8.51111	+	7.04100i	0.473571	+	0.391772i
$324$	−40.4126	+	124.377i	−2.24514	+	6.90984i
$325$		0			0
$326$	6.03302	+	18.5677i	0.334138	+	1.02837i
$327$	−1.01132	+	2.55430i	−0.0559261	+	0.141253i
$328$	42.3694	−	45.1189i	2.33946	−	2.49127i
$329$	−0.217936	−	1.14246i	−0.0120152	−	0.0629859i
$330$		0			0
$331$	7.72986	−	7.25882i	0.424871	−	0.398981i	−0.442399	−	0.896818i	$-0.645872\pi$
$331$	7.72986	−	7.25882i	0.424871	−	0.398981i	0.867270	+	0.497838i	$0.165872\pi$
$332$	−0.760695	+	0.247165i	−0.0417486	+	0.0135649i
$333$	43.6490	+	8.32650i	2.39195	+	0.456289i
$334$	−1.46317	−	23.2564i	−0.0800609	−	1.27253i
$335$		0			0
$336$	−7.22077	−	11.3781i	−0.393925	−	0.620727i
$337$	−35.3624	+	2.22481i	−1.92631	+	0.121193i	−0.979609	−	0.200915i	$-0.935608\pi$
$337$	−35.3624	+	2.22481i	−1.92631	+	0.121193i	−0.946703	+	0.322108i	$0.895608\pi$
$338$	−26.6317	−	16.9010i	−1.44857	−	0.919293i
$339$	−13.7772	+	16.6538i	−0.748275	+	0.904509i
$340$		0			0
$341$	−6.38852	−	1.64029i	−0.345958	−	0.0888269i
$342$	57.6454	−	27.1259i	3.11711	−	1.46680i
$343$	−10.0303	−	3.25905i	−0.541586	−	0.175972i
$344$	−13.5243	−	7.43502i	−0.729179	−	0.400869i
$345$		0			0
$346$	−54.8708	−	6.93180i	−2.94987	−	0.372656i
$347$	3.75356	−	29.7125i	0.201502	−	1.59505i	−0.489372	−	0.872075i	$-0.662774\pi$
$347$	3.75356	−	29.7125i	0.201502	−	1.59505i	0.690874	−	0.722975i	$-0.257226\pi$
$348$	−23.8567	+	15.1399i	−1.27885	+	0.811584i
$349$	−10.9765	+	7.97493i	−0.587561	+	0.426888i	−0.841442	−	0.540347i	$-0.818293\pi$
$349$	−10.9765	+	7.97493i	−0.587561	+	0.426888i	0.253881	+	0.967235i	$0.418293\pi$
$350$		0			0
$351$	−7.60045	−	5.52205i	−0.405682	−	0.294745i
$352$	−2.00555	−	0.126179i	−0.106896	−	0.00672535i
$353$	11.0371	+	20.0764i	0.587445	+	1.06856i	0.988315	+	0.152424i	$0.0487079\pi$
$353$	11.0371	+	20.0764i	0.587445	+	1.06856i	−0.400870	+	0.916135i	$0.631292\pi$
$354$	12.5404	−	26.6498i	0.666517	−	1.41642i
$355$		0			0
$356$	−1.74758	+	9.16113i	−0.0926215	+	0.485539i
$357$	−5.31850	−	7.32029i	−0.281485	−	0.387431i
$358$	−8.05229	+	14.6471i	−0.425577	+	0.774122i
$359$	10.3356	−	16.2863i	0.545493	−	0.859559i	−0.454013	−	0.890995i	$-0.650008\pi$
$359$	10.3356	−	16.2863i	0.545493	−	0.859559i	0.999506	+	0.0314359i	$0.0100080\pi$
$360$		0			0
$361$	8.17775	+	3.23780i	0.430408	+	0.170410i
$362$	−19.6790	−	49.7034i	−1.03430	−	2.61235i
$363$	25.3766	−	20.9933i	1.33192	−	1.10186i
$364$	1.80242	−	0.462782i	0.0944724	−	0.0242564i
$365$		0			0
$366$	57.4623	−	22.7509i	3.00360	−	1.18921i
$367$	−4.39423	−	4.67937i	−0.229377	−	0.244261i	0.603977	−	0.797002i	$-0.293582\pi$
$367$	−4.39423	−	4.67937i	−0.229377	−	0.244261i	−0.833353	+	0.552741i	$0.813582\pi$
$368$	10.2383	−	14.0918i	0.533709	−	0.734587i
$369$	−38.8692	−	82.6012i	−2.02345	−	4.30005i
$370$		0			0
$371$	2.14032	−	1.17665i	0.111120	−	0.0610888i
$372$	−86.6955	+	16.5381i	−4.49495	+	0.857458i
$373$	1.32347	+	5.15457i	0.0685267	+	0.266894i	0.993610	−	0.112871i	$-0.0360048\pi$
$373$	1.32347	+	5.15457i	0.0685267	+	0.266894i	−0.925083	+	0.379765i	$0.876005\pi$
$374$	−8.93029			−0.461774
$375$		0			0
$376$	−8.02107			−0.413655
$377$	−0.285192	−	1.11075i	−0.0146882	−	0.0572066i
$378$	−32.0839	+	6.12034i	−1.65022	+	0.314796i
$379$	−29.2409	+	16.0753i	−1.50201	+	0.825735i	−0.999251	−	0.0386947i	$-0.987680\pi$
$379$	−29.2409	+	16.0753i	−1.50201	+	0.825735i	−0.502755	+	0.864429i	$0.667680\pi$
$380$		0			0
$381$	−11.7745	−	25.0221i	−0.603225	−	1.28192i
$382$	−14.7643	+	20.3213i	−0.755405	+	1.03973i
$383$	−10.6083	−	11.2967i	−0.542061	−	0.577236i	0.398369	−	0.917225i	$-0.369576\pi$
$383$	−10.6083	−	11.2967i	−0.542061	−	0.577236i	−0.940429	+	0.339990i	$0.889576\pi$
$384$	54.0609	−	21.4042i	2.75878	−	1.09228i
$385$		0			0
$386$	−37.9624	+	9.74710i	−1.93224	+	0.496114i
$387$	−17.5392	+	14.5097i	−0.891566	+	0.737567i
$388$	18.6740	+	47.1652i	0.948029	+	2.39445i
$389$	8.97238	+	3.55241i	0.454917	+	0.180115i	0.584398	−	0.811467i	$-0.301331\pi$
$389$	8.97238	+	3.55241i	0.454917	+	0.180115i	−0.129480	+	0.991582i	$0.541331\pi$
$390$		0			0
$391$	6.26679	−	9.87489i	0.316925	−	0.499395i
$392$	−16.7061	+	30.3884i	−0.843788	+	1.53484i
$393$	−18.7264	−	25.7747i	−0.944623	−	1.30016i
$394$	7.29284	−	38.2304i	0.367408	−	1.92602i
$395$		0			0
$396$	−14.8398	+	31.5362i	−0.745729	+	1.58476i
$397$	4.88630	+	8.88815i	0.245236	+	0.446083i	0.970065	−	0.242846i	$-0.0780810\pi$
$397$	4.88630	+	8.88815i	0.245236	+	0.446083i	−0.724828	+	0.688929i	$0.758081\pi$
$398$	−35.0322	−	2.20404i	−1.75601	−	0.110479i
$399$	6.76268	+	4.91337i	0.338557	+	0.245976i
$400$		0			0
$401$	15.5702	−	11.3124i	0.777537	−	0.564914i	−0.126702	−	0.991941i	$-0.540439\pi$
$401$	15.5702	−	11.3124i	0.777537	−	0.564914i	0.904239	+	0.427027i	$0.140439\pi$
$402$	94.8728	−	60.2081i	4.73182	−	3.00291i
$403$	0.448958	−	3.55387i	0.0223642	−	0.177031i
$404$	42.3895	+	5.35504i	2.10896	+	0.266423i
$405$		0			0
$406$	−3.49384	−	1.92076i	−0.173397	−	0.0953255i
$407$	5.47266	+	1.77818i	0.271270	+	0.0881409i
$408$	−56.4632	+	26.5696i	−2.79535	+	1.31539i
$409$	−24.7135	−	6.34535i	−1.22201	−	0.313758i	−0.418037	−	0.908430i	$-0.637282\pi$
$409$	−24.7135	−	6.34535i	−1.22201	−	0.313758i	−0.803968	+	0.594672i	$0.797282\pi$
$410$		0			0
$411$	3.81171	−	4.60757i	0.188018	−	0.227275i
$412$	59.8879	+	38.0060i	2.95047	+	1.87242i
$413$	2.80676	−	0.176586i	0.138111	−	0.00868923i
$414$	−36.1442	−	56.9542i	−1.77639	−	2.79914i
$415$		0			0
$416$	−0.0685271	−	1.08921i	−0.00335982	−	0.0534027i
$417$	29.4032	+	5.60897i	1.43988	+	0.274672i
$418$	7.84625	−	2.54940i	0.383773	−	0.124695i
$419$	26.8086	−	25.1749i	1.30969	−	1.22988i	0.354084	−	0.935213i	$-0.384793\pi$
$419$	26.8086	−	25.1749i	1.30969	−	1.22988i	0.955601	−	0.294663i	$-0.0952074\pi$
$420$		0			0
$421$	−4.27563	−	22.4137i	−0.208382	−	1.09237i	−0.920627	−	0.390444i	$-0.872322\pi$
$421$	−4.27563	−	22.4137i	−0.208382	−	1.09237i	0.712245	−	0.701931i	$-0.247678\pi$
$422$	32.7068	−	34.8292i	1.59214	−	1.69546i
$423$	−4.35511	+	10.9997i	−0.211752	+	0.534826i
$424$	−5.20517	−	16.0199i	−0.252786	−	0.777994i
$425$		0			0
$426$	−13.3366	+	41.0459i	−0.646161	+	1.98868i
$427$	4.54693	+	3.76155i	0.220041	+	0.182034i
$428$	−53.4364	−	25.1452i	−2.58294	−	1.21544i
$429$	−1.41697	−	1.33063i	−0.0684121	−	0.0642432i
$430$		0			0
$431$	−20.7583	+	2.62238i	−0.999891	+	0.126316i	−0.608202	−	0.793782i	$-0.708109\pi$
$431$	−20.7583	+	2.62238i	−0.999891	+	0.126316i	−0.391689	+	0.920098i	$0.628109\pi$
$432$			85.7917i			4.12766i
$433$	−1.84693	−	14.6200i	−0.0887578	−	0.702590i	−0.972217	−	0.234082i	$-0.924792\pi$
$433$	−1.84693	−	14.6200i	−0.0887578	−	0.702590i	0.883459	−	0.468508i	$-0.155208\pi$
$434$	−7.93844	−	9.59592i	−0.381057	−	0.460619i
$435$		0			0
$436$	−0.217526	+	3.45748i	−0.0104176	+	0.165583i
$437$	−2.68701	+	10.4652i	−0.128537	+	0.500619i
$438$	12.8206	−	49.9331i	0.612594	−	2.38590i
$439$	0.861319	−	13.6903i	0.0411085	−	0.653401i	−0.922485	−	0.386032i	$-0.873846\pi$
$439$	0.861319	−	13.6903i	0.0411085	−	0.653401i	0.963594	−	0.267370i	$-0.0861545\pi$
$440$		0			0
$441$	32.6025	+	39.4097i	1.55250	+	1.87665i
$442$	−0.607865	−	4.81175i	−0.0289132	−	0.228872i
$443$		−	5.72633i		−	0.272066i	−0.990704	−	0.136033i	$-0.956565\pi$
$443$		−	5.72633i		−	0.272066i	0.990704	−	0.136033i	$-0.0434354\pi$
$444$	76.3922	−	9.65058i	3.62541	−	0.457996i
$445$		0			0
$446$	−8.49792	−	7.98008i	−0.402388	−	0.377868i
$447$	−18.2463	−	8.58607i	−0.863022	−	0.406107i
$448$	3.33254	+	2.75692i	0.157448	+	0.130252i
$449$	0.254531	−	0.783366i	0.0120121	−	0.0369693i	−0.944871	−	0.327443i	$-0.893813\pi$
$449$	0.254531	−	0.783366i	0.0120121	−	0.0369693i	0.956883	+	0.290474i	$0.0938130\pi$
$450$		0			0
$451$	−3.65308	−	11.2430i	−0.172017	−	0.529414i
$452$	−10.0335	+	25.3416i	−0.471934	+	1.19197i
$453$	−24.8298	+	26.4410i	−1.16660	+	1.24231i
$454$	3.38917	+	17.7666i	0.159062	+	0.833830i
$455$		0			0
$456$	42.0242	−	39.4633i	1.96796	−	1.84804i
$457$	8.06467	−	2.62037i	0.377250	−	0.122576i	−0.114254	−	0.993452i	$-0.536448\pi$
$457$	8.06467	−	2.62037i	0.377250	−	0.122576i	0.491503	+	0.870876i	$0.336448\pi$
$458$	37.3422	+	7.12340i	1.74489	+	0.332855i
$459$	3.61702	+	57.4909i	0.168828	+	2.68345i
$460$		0			0
$461$	−18.7334	−	29.5191i	−0.872502	−	1.37484i	−0.926497	−	0.376303i	$-0.877195\pi$
$461$	−18.7334	−	29.5191i	−0.872502	−	1.37484i	0.0539945	−	0.998541i	$-0.482805\pi$
$462$	−6.74470	+	0.424340i	−0.313792	+	0.0197421i
$463$	5.58091	+	3.54176i	0.259367	+	0.164599i	0.659152	−	0.752010i	$-0.270915\pi$
$463$	5.58091	+	3.54176i	0.259367	+	0.164599i	−0.399785	+	0.916609i	$0.630915\pi$
$464$	−6.67532	+	8.06908i	−0.309894	+	0.374598i
$465$		0			0
$466$	38.1538	+	9.79623i	1.76744	+	0.453801i
$467$	−13.3371	+	6.27598i	−0.617170	+	0.290418i	−0.708838	−	0.705372i	$-0.750780\pi$
$467$	−13.3371	+	6.27598i	−0.617170	+	0.290418i	0.0916681	+	0.995790i	$0.470780\pi$
$468$	−18.0022	−	5.84928i	−0.832153	−	0.270383i
$469$	9.40201	+	5.16880i	0.434145	+	0.238673i
$470$		0			0
$471$	49.1470	+	6.20871i	2.26457	+	0.286082i
$472$	2.43085	−	19.2422i	0.111889	−	0.885692i
$473$	−2.48884	+	1.57946i	−0.114437	+	0.0726238i
$474$	61.6872	−	44.8184i	2.83339	−	2.05858i
$475$		0			0
$476$	−9.23107	−	6.70676i	−0.423105	−	0.307404i
$477$	−24.7951	−	1.55998i	−1.13529	−	0.0714265i
$478$	9.52169	+	17.3199i	0.435512	+	0.792194i
$479$	−3.28956	+	6.99068i	−0.150304	+	0.319412i	−0.965773	−	0.259388i	$-0.916479\pi$
$479$	−3.28956	+	6.99068i	−0.150304	+	0.319412i	0.815469	+	0.578801i	$0.196479\pi$
$480$		0			0
$481$	−0.585591	+	3.06978i	−0.0267006	+	0.139970i
$482$	17.9224	+	24.6681i	0.816344	+	1.12360i
$483$	4.26384	−	7.75590i	0.194011	−	0.352906i
$484$	22.2536	−	35.0661i	1.01153	−	1.59391i
$485$		0			0
$486$	124.251	+	49.1945i	5.63615	+	2.23151i
$487$	−10.2387	−	25.8600i	−0.463959	−	1.17183i	−0.953914	−	0.300079i	$-0.902987\pi$
$487$	−10.2387	−	25.8600i	−0.463959	−	1.17183i	0.489955	−	0.871748i	$-0.337013\pi$
$488$	31.3580	−	25.9416i	1.41951	−	1.17432i
$489$	25.2379	−	6.47998i	1.14130	−	0.293035i
$490$		0			0
$491$	15.9298	−	6.30707i	0.718904	−	0.284634i	0.0199499	−	0.999801i	$-0.493649\pi$
$491$	15.9298	−	6.30707i	0.718904	−	0.284634i	0.698954	+	0.715167i	$0.253649\pi$
$492$	−108.287	−	115.314i	−4.88194	−	5.19874i
$493$	−4.13308	+	5.68870i	−0.186145	+	0.256206i
$494$	1.90773	+	4.05412i	0.0858327	+	0.182404i
$495$		0			0
$496$	−28.6655	+	15.7590i	−1.28712	+	0.707599i
$497$	−4.04796	+	0.772189i	−0.181576	+	0.0346374i
$498$	0.392319	+	1.52798i	0.0175802	+	0.0684705i
$499$	7.49374			0.335466			0.167733	−	0.985832i	$-0.446355\pi$
$499$	7.49374			0.335466			0.167733	+	0.985832i	$0.446355\pi$
$500$		0			0
$501$	−31.1001			−1.38945
$502$	3.78758	+	14.7516i	0.169048	+	0.658398i
$503$	31.6850	−	6.04424i	1.41276	−	0.269499i	0.576174	−	0.817327i	$-0.304545\pi$
$503$	31.6850	−	6.04424i	1.41276	−	0.269499i	0.836591	+	0.547828i	$0.184545\pi$
$504$	−30.1151	+	16.5559i	−1.34143	+	0.737458i
$505$		0			0
$506$	−3.71925	−	7.90381i	−0.165341	−	0.351367i
$507$	−24.7440	+	34.0571i	−1.09892	+	1.51253i
$508$	−23.8718	−	25.4208i	−1.05914	−	1.12787i
$509$	−21.8917	+	8.66755i	−0.970335	+	0.384183i	−0.799200	−	0.601065i	$-0.794743\pi$
$509$	−21.8917	+	8.66755i	−0.970335	+	0.384183i	−0.171134	+	0.985248i	$0.554743\pi$
$510$		0			0
$511$	4.76785	−	1.22418i	0.210917	−	0.0541544i
$512$	35.4663	−	29.3403i	1.56740	−	1.29667i
$513$	−19.5903	−	49.4796i	−0.864935	−	2.18458i
$514$	−41.2371	−	16.3269i	−1.81889	−	0.720149i
$515$		0			0
$516$	−21.1351	+	33.3036i	−0.930421	+	1.46611i
$517$	−0.738049	+	1.34251i	−0.0324594	+	0.0590434i
$518$	6.38637	+	8.79009i	0.280601	+	0.386214i
$519$	−13.8315	+	72.5072i	−0.607135	+	3.18271i
$520$		0			0
$521$	−6.43758	+	13.6806i	−0.282036	+	0.599356i	−0.994777	−	0.102071i	$-0.967453\pi$
$521$	−6.43758	+	13.6806i	−0.282036	+	0.599356i	0.712742	+	0.701427i	$0.247453\pi$
$522$	19.5377	+	35.5390i	0.855142	+	1.55550i
$523$	−38.1685	−	2.40136i	−1.66899	−	0.105004i	−0.800055	−	0.599926i	$-0.795197\pi$
$523$	−38.1685	−	2.40136i	−1.66899	−	0.105004i	−0.868937	+	0.494922i	$0.835197\pi$
$524$	−32.5025	−	23.6145i	−1.41988	−	1.03160i
$525$		0			0
$526$	−49.5627	+	36.0094i	−2.16104	+	1.57008i
$527$	−18.5450	+	11.7690i	−0.807831	+	0.512665i
$528$	−2.22476	+	17.6108i	−0.0968202	+	0.766411i
$529$	−11.4688	−	1.44885i	−0.498645	−	0.0629935i
$530$		0			0
$531$	−25.0680	−	13.7813i	−1.08786	−	0.598055i
$532$	10.0251	+	3.25737i	0.434645	+	0.141225i
$533$	5.80923	−	2.73362i	0.251626	−	0.118406i
$534$	17.8166	+	4.57452i	0.771000	+	0.197959i
$535$		0			0
$536$	47.1653	−	57.0131i	2.03723	−	2.46259i
$537$	18.8351	+	11.9531i	0.812796	+	0.515816i
$538$	17.7029	−	1.11377i	0.763225	−	0.0480180i
$539$	3.54898	+	5.59230i	0.152865	+	0.240877i
$540$		0			0
$541$	−0.275102	−	4.37262i	−0.0118276	−	0.187994i	−0.999504	−	0.0314854i	$-0.989976\pi$
$541$	−0.275102	−	4.37262i	−0.0118276	−	0.187994i	0.987677	−	0.156508i	$-0.0500238\pi$
$542$	−62.9036	−	11.9995i	−2.70194	−	0.515423i
$543$	−67.8542	+	22.0472i	−2.91190	+	0.946135i
$544$	−4.87812	+	4.58086i	−0.209148	+	0.196403i
$545$		0			0
$546$	−0.687737	−	3.60524i	−0.0294324	−	0.154290i
$547$	18.4117	−	19.6064i	0.787226	−	0.838311i	−0.202796	−	0.979221i	$-0.565003\pi$
$547$	18.4117	−	19.6064i	0.787226	−	0.838311i	0.990022	+	0.140910i	$0.0450029\pi$
$548$	2.77594	−	7.01122i	0.118582	−	0.299505i
$549$	−18.5491	−	57.0882i	−0.791655	−	2.43646i
$550$		0			0
$551$	2.00737	−	6.17806i	0.0855169	−	0.263194i
$552$	−47.0312	−	38.9076i	−2.00178	−	1.65602i
$553$	6.58775	+	3.09996i	0.280140	+	0.131824i
$554$	−6.91362	−	6.49232i	−0.293731	−	0.275832i
$555$		0			0
$556$	37.4492	−	4.73093i	1.58820	−	0.200636i
$557$			9.84523i			0.417156i	0.978006	+	0.208578i	$0.0668835\pi$
$557$			9.84523i			0.417156i	−0.978006	+	0.208578i	$0.933117\pi$
$558$	15.8772	+	125.681i	0.672136	+	5.32050i
$559$	−1.02044	−	1.23351i	−0.0431602	−	0.0521717i
$560$		0			0
$561$	−0.748380	+	11.8952i	−0.0315966	+	0.502214i
$562$	−4.81550	+	18.7551i	−0.203129	+	0.791137i
$563$	3.54726	−	13.8157i	0.149499	−	0.582260i	−0.849045	−	0.528320i	$-0.822822\pi$
$563$	3.54726	−	13.8157i	0.149499	−	0.582260i	0.998544	−	0.0539400i	$-0.0171780\pi$
$564$	−1.28721	+	20.4596i	−0.0542013	+	0.861505i
$565$		0			0
$566$	3.80023	+	4.59369i	0.159736	+	0.193087i
$567$	3.08682	+	24.4347i	0.129634	+	1.02616i
$568$			28.4202i			1.19248i
$569$	26.4864	−	3.34601i	1.11037	−	0.140272i	0.451311	−	0.892367i	$-0.350956\pi$
$569$	26.4864	−	3.34601i	1.11037	−	0.140272i	0.659055	+	0.752095i	$0.270956\pi$
$570$		0			0
$571$	16.4283	+	15.4272i	0.687503	+	0.645609i	0.947409	−	0.320025i	$-0.103691\pi$
$571$	16.4283	+	15.4272i	0.687503	+	0.645609i	−0.259906	+	0.965634i	$0.583691\pi$
$572$	−2.21790	−	1.04366i	−0.0927350	−	0.0436378i
$573$	25.8307	+	21.3690i	1.07909	+	0.892703i
$574$	6.89768	−	21.2289i	0.287904	−	0.886076i
$575$		0			0
$576$	−13.5950	−	41.8411i	−0.566458	−	1.74338i
$577$	6.80093	−	17.1772i	0.283126	−	0.715095i	−0.716716	−	0.697365i	$-0.754356\pi$
$577$	6.80093	−	17.1772i	0.283126	−	0.715095i	0.999843	−	0.0177308i	$-0.00564417\pi$
$578$	8.58635	−	9.14354i	0.357145	−	0.380321i
$579$	9.80181	+	51.3829i	0.407349	+	2.13540i
$580$		0			0
$581$	−0.109806	+	0.103114i	−0.00455550	+	0.00427790i
$582$	95.1539	−	30.9174i	3.94426	−	1.28157i
$583$	−3.16023	−	0.602847i	−0.130884	−	0.0249674i
$584$	−2.13162	−	33.8811i	−0.0882070	−	1.40201i
$585$		0			0
$586$	−14.7675	−	23.2698i	−0.610038	−	0.961267i
$587$	−28.2931	+	1.78005i	−1.16778	+	0.0734705i	−0.634813	−	0.772666i	$-0.718923\pi$
$587$	−28.2931	+	1.78005i	−1.16778	+	0.0734705i	−0.532966	+	0.846136i	$0.678923\pi$
$588$	74.8316	+	47.4896i	3.08600	+	1.95844i
$589$	12.9340	−	15.6345i	0.532937	−	0.644210i
$590$		0			0
$591$	−50.3119	−	12.9179i	−2.06955	−	0.531371i
$592$	25.8225	−	12.1511i	1.06130	−	0.499408i
$593$	39.4502	+	12.8181i	1.62003	+	0.526378i	0.971948	−	0.235196i	$-0.0755732\pi$
$593$	39.4502	+	12.8181i	1.62003	+	0.526378i	0.648078	+	0.761574i	$0.275573\pi$
$594$	37.7019	+	20.7268i	1.54693	+	0.850430i
$595$		0			0
$596$	−25.2287	−	3.18713i	−1.03341	−	0.130550i
$597$	−5.87157	+	46.4783i	−0.240308	+	1.90223i
$598$	4.00551	−	2.54197i	0.163797	−	0.103949i
$599$	−27.7097	+	20.1323i	−1.13219	+	0.822583i	−0.986012	−	0.166675i	$-0.946697\pi$
$599$	−27.7097	+	20.1323i	−1.13219	+	0.822583i	−0.146177	+	0.989258i	$0.546697\pi$
$600$		0			0
$601$	27.0658	+	19.6644i	1.10404	+	0.802130i	0.981714	−	0.190361i	$-0.0609658\pi$
$601$	27.0658	+	19.6644i	1.10404	+	0.802130i	0.122322	+	0.992490i	$0.460966\pi$
$602$	−5.55483	−	0.349480i	−0.226398	−	0.0142437i
$603$	−52.5764	−	95.6362i	−2.14108	−	3.89461i
$604$	−19.4750	+	41.3865i	−0.792426	+	1.68399i
$605$		0			0
$606$	15.7907	−	82.7775i	0.641451	−	3.36261i
$607$	−16.7437	−	23.0458i	−0.679607	−	0.935399i	0.320322	−	0.947309i	$-0.396209\pi$
$607$	−16.7437	−	23.0458i	−0.679607	−	0.935399i	−0.999929	+	0.0119096i	$0.996209\pi$
$608$	2.97823	−	5.41739i	0.120783	−	0.219704i
$609$	−2.85125	+	4.49284i	−0.115538	+	0.182059i
$610$		0			0
$611$	−0.773597	−	0.306289i	−0.0312964	−	0.0123911i
$612$	42.7258	+	107.913i	1.72709	+	4.36213i
$613$	3.71313	−	3.07177i	0.149972	−	0.124068i	−0.559412	−	0.828890i	$-0.688973\pi$
$613$	3.71313	−	3.07177i	0.149972	−	0.124068i	0.709384	+	0.704822i	$0.248973\pi$
$614$	22.0499	−	5.66145i	0.889862	−	0.228478i
$615$		0			0
$616$	−4.13773	+	1.63824i	−0.166714	+	0.0660068i
$617$	15.2887	+	16.2808i	0.615498	+	0.655439i	0.958898	−	0.283750i	$-0.0915786\pi$
$617$	15.2887	+	16.2808i	0.615498	+	0.655439i	−0.343400	+	0.939189i	$0.611579\pi$
$618$	82.2288	−	113.178i	3.30773	−	4.55270i
$619$	8.92369	+	18.9638i	0.358673	+	0.762220i	0.999987	−	0.00505895i	$-0.00161032\pi$
$619$	8.92369	+	18.9638i	0.358673	+	0.762220i	−0.641314	+	0.767279i	$0.721610\pi$
$620$		0			0
$621$	−49.3763	+	27.1448i	−1.98140	+	1.08928i
$622$	65.4956	−	12.4939i	2.62613	−	0.500962i
$623$	0.436797	+	1.70121i	0.0174999	+	0.0681577i
$624$	−9.64034			−0.385923
$625$		0			0
$626$	65.2957			2.60974
$627$	−2.73827	−	10.6649i	−0.109356	−	0.425914i
$628$	61.3617	−	11.7054i	2.44860	−	0.467095i
$629$	16.7919	−	9.23142i	0.669537	−	0.368081i
$630$		0			0
$631$	18.6737	+	39.6835i	0.743386	+	1.57978i	0.813042	+	0.582205i	$0.197810\pi$
$631$	18.6737	+	39.6835i	0.743386	+	1.57978i	−0.0696553	+	0.997571i	$0.522190\pi$
$632$	29.5134	−	40.6218i	1.17398	−	1.61585i
$633$	−43.6516	−	46.4843i	−1.73500	−	1.84758i
$634$	−29.2077	+	11.5641i	−1.15998	+	0.459270i
$635$		0			0
$636$	−41.6977	+	10.7062i	−1.65342	+	0.424527i
$637$	−2.77163	+	2.29289i	−0.109816	+	0.0908477i
$638$	1.93330	+	4.88296i	0.0765402	+	0.193318i
$639$	38.9742	+	15.4310i	1.54180	+	0.610440i
$640$		0			0
$641$	13.4110	−	21.1323i	0.529701	−	0.834675i	−0.469124	−	0.883132i	$-0.655430\pi$
$641$	13.4110	−	21.1323i	0.529701	−	0.834675i	0.998825	+	0.0484569i	$0.0154304\pi$
$642$	−56.1143	+	102.072i	−2.21466	+	4.02844i
$643$	4.15494	+	5.71879i	0.163855	+	0.225527i	0.883047	−	0.469284i	$-0.155488\pi$
$643$	4.15494	+	5.71879i	0.163855	+	0.225527i	−0.719192	+	0.694811i	$0.755488\pi$
$644$	2.09135	−	10.9632i	0.0824106	−	0.432011i
$645$		0			0
$646$	11.6975	−	24.8584i	0.460230	−	0.978039i
$647$	−4.89054	−	8.89586i	−0.192267	−	0.349732i	0.762549	−	0.646931i	$-0.223948\pi$
$647$	−4.89054	−	8.89586i	−0.192267	−	0.349732i	−0.954816	+	0.297198i	$0.903948\pi$
$648$	169.519	+	10.6652i	6.65932	+	0.418969i
$649$	−2.99694	−	2.17740i	−0.117640	−	0.0854705i
$650$		0			0
$651$	−13.4471	+	9.76986i	−0.527032	+	0.382911i
$652$	27.7428	−	17.6061i	1.08649	−	0.689509i
$653$	−1.92930	+	15.2720i	−0.0754993	+	0.597639i	0.908294	+	0.418332i	$0.137385\pi$
$653$	−1.92930	+	15.2720i	−0.0754993	+	0.597639i	−0.983793	+	0.179306i	$0.942615\pi$
$654$	6.77885	+	0.856368i	0.265074	+	0.0334867i
$655$		0			0
$656$	−51.3775	−	28.2450i	−2.00596	−	1.10278i
$657$	−47.6204	−	15.4728i	−1.85785	−	0.603652i
$658$	−2.61739	+	1.23165i	−0.102037	+	0.0480148i
$659$	25.0852	+	6.44078i	0.977180	+	0.250897i	0.703321	−	0.710873i	$-0.251700\pi$
$659$	25.0852	+	6.44078i	0.977180	+	0.250897i	0.273859	+	0.961770i	$0.411700\pi$
$660$		0			0
$661$	−28.1644	+	34.0449i	−1.09547	+	1.32419i	−0.153628	+	0.988129i	$0.549096\pi$
$661$	−28.1644	+	34.0449i	−1.09547	+	1.32419i	−0.941839	+	0.336064i	$0.890904\pi$
$662$	−22.2677	−	14.1315i	−0.865457	−	0.549236i
$663$	−6.46020	+	0.406442i	−0.250893	+	0.0157849i
$664$	0.556634	+	0.877115i	0.0216016	+	0.0340387i
$665$		0			0
$666$	−6.93955	−	110.301i	−0.268902	−	4.27407i
$667$	−6.75615	−	1.28880i	−0.261599	−	0.0499027i
$668$	−37.2986	+	12.1190i	−1.44313	+	0.468900i
$669$	−11.3416	+	10.6505i	−0.438493	+	0.411772i
$670$		0			0
$671$	−1.45654	−	7.63545i	−0.0562291	−	0.294763i
$672$	−3.46658	+	3.69154i	−0.133726	+	0.142404i
$673$	−6.95425	+	17.5644i	−0.268067	+	0.677059i	−0.999991	−	0.00432713i	$-0.998623\pi$
$673$	−6.95425	+	17.5644i	−0.268067	+	0.677059i	0.731924	+	0.681386i	$0.238623\pi$
$674$	27.2322	+	83.8121i	1.04894	+	3.22832i
$675$		0			0
$676$	−16.4043	+	50.4871i	−0.630933	+	1.94181i
$677$	34.8177	+	28.8037i	1.33815	+	1.10702i	0.985206	+	0.171371i	$0.0548198\pi$
$677$	34.8177	+	28.8037i	1.33815	+	1.10702i	0.352945	+	0.935644i	$0.385180\pi$
$678$	48.6406	+	22.8885i	1.86803	+	0.879029i
$679$	6.96407	+	6.53970i	0.267257	+	0.250971i
$680$		0			0
$681$	23.9492	−	3.02549i	0.917737	−	0.115937i
$682$			16.4045i			0.628163i
$683$	−1.23898	−	9.80757i	−0.0474084	−	0.375276i	−0.997913	−	0.0645669i	$-0.979433\pi$
$683$	−1.23898	−	9.80757i	−0.0474084	−	0.375276i	0.950505	−	0.310709i	$-0.100567\pi$
$684$	−68.3462	−	82.6163i	−2.61328	−	3.15891i
$685$		0			0
$686$	−1.64704	+	26.1789i	−0.0628842	+	0.999515i
$687$	12.6178	−	49.1429i	0.481397	−	1.87492i
$688$	−3.63566	+	14.1600i	−0.138608	+	0.539843i
$689$	0.109711	−	1.74381i	0.00417966	−	0.0664338i
$690$		0			0
$691$	12.3817	+	14.9669i	0.471023	+	0.569369i	0.951504	−	0.307636i	$-0.0995378\pi$
$691$	12.3817	+	14.9669i	0.471023	+	0.569369i	−0.480481	+	0.877005i	$0.659538\pi$
$692$	11.6663	+	92.3481i	0.443485	+	3.51055i
$693$			6.56381i			0.249338i
$694$	−73.8993	+	9.33565i	−2.80518	+	0.354376i
$695$		0			0
$696$	26.7515	+	25.1214i	1.01401	+	0.952223i
$697$	−35.6200	−	16.7615i	−1.34920	−	0.634888i
$698$	26.0010	+	21.5099i	0.984151	+	0.814160i
$699$	16.2460	−	50.0000i	0.614479	−	1.89117i
$700$		0			0
$701$	−4.01298	−	12.3507i	−0.151568	−	0.466479i	0.846229	−	0.532820i	$-0.178868\pi$
$701$	−4.01298	−	12.3507i	−0.151568	−	0.466479i	−0.997797	+	0.0663408i	$0.978868\pi$
$702$	−8.60156	+	21.7251i	−0.324645	+	0.819959i
$703$	−12.1182	+	12.9045i	−0.457046	+	0.486704i
$704$	−1.06753	−	5.59618i	−0.0402340	−	0.210914i
$705$		0			0
$706$	41.5374	−	39.0062i	1.56328	−	1.46802i
$707$	7.65269	−	2.48651i	0.287809	−	0.0935149i
$708$	−48.6915	−	9.28840i	−1.82994	−	0.349079i
$709$	−2.19608	−	34.9057i	−0.0824755	−	1.31091i	−0.793857	−	0.608104i	$-0.791930\pi$
$709$	−2.19608	−	34.9057i	−0.0824755	−	1.31091i	0.711382	−	0.702806i	$-0.248070\pi$
$710$		0			0
$711$	−39.6823	−	62.5293i	−1.48820	−	2.34503i
$712$	12.0891	−	0.760581i	0.453058	−	0.0285040i
$713$	−18.1397	−	11.5118i	−0.679339	−	0.431121i
$714$	−14.3450	+	17.3401i	−0.536847	+	0.648937i
$715$		0			0
$716$	27.2470	+	6.99583i	1.01827	+	0.261446i
$717$	23.8681	−	11.2315i	0.891370	−	0.419447i
$718$	−45.6267	−	14.8250i	−1.70277	−	0.553265i
$719$	27.0272	+	14.8583i	1.00794	+	0.554121i	0.898083	−	0.439826i	$-0.144960\pi$
$719$	27.0272	+	14.8583i	1.00794	+	0.554121i	0.109860	+	0.993947i	$0.464960\pi$
$720$		0			0
$721$	13.2526	+	1.67419i	0.493553	+	0.0623502i
$722$	2.74172	−	21.7029i	0.102036	−	0.807699i
$723$	34.3599	−	21.8055i	1.27786	−	0.810954i
$724$	−72.7867	+	52.8826i	−2.70510	+	1.96537i
$725$		0			0
$726$	−66.2692	−	48.1474i	−2.45948	−	1.78692i
$727$	9.26913	+	0.583164i	0.343773	+	0.0216284i	0.233739	−	0.972299i	$-0.424904\pi$
$727$	9.26913	+	0.583164i	0.343773	+	0.0216284i	0.110034	+	0.993928i	$0.464904\pi$
$728$	−1.16435	−	2.11795i	−0.0431538	−	0.0784965i
$729$	36.0325	−	76.5729i	1.33454	−	2.83603i
$730$		0			0
$731$	−1.83934	+	9.64217i	−0.0680306	+	0.356629i
$732$	−61.1377	−	84.1489i	−2.25972	−	3.11023i
$733$	−2.88620	+	5.24998i	−0.106604	+	0.193913i	−0.924229	−	0.381840i	$-0.875291\pi$
$733$	−2.88620	+	5.24998i	−0.106604	+	0.193913i	0.817624	+	0.575752i	$0.195291\pi$
$734$	−8.55469	+	13.4800i	−0.315759	+	0.497557i
$735$		0			0
$736$	−6.08594	−	2.40959i	−0.224331	−	0.0888188i
$737$	−5.20256	−	13.1402i	−0.191639	−	0.484024i
$738$	−174.945	+	144.727i	−6.43982	+	5.32748i
$739$	−13.1162	+	3.36768i	−0.482489	+	0.123882i	−0.482097	−	0.876118i	$-0.660125\pi$
$739$	−13.1162	+	3.36768i	−0.482489	+	0.123882i	−0.000391910		1.00000i	$0.500125\pi$
$740$		0			0
$741$	5.55998	−	2.20135i	0.204251	−	0.0808686i
$742$	−4.15841	−	4.42826i	−0.152660	−	0.162567i
$743$	13.6581	−	18.7987i	0.501066	−	0.689658i	−0.481315	−	0.876548i	$-0.659841\pi$
$743$	13.6581	−	18.7987i	0.501066	−	0.689658i	0.982381	+	0.186890i	$0.0598408\pi$
$744$	48.8072	+	103.721i	1.78936	+	3.80258i
$745$		0			0
$746$	11.5988	−	6.37649i	0.424662	−	0.233460i
$747$	1.50507	−	0.287107i	0.0550675	−	0.0105047i
$748$	3.73775	+	14.5576i	0.136666	+	0.532277i
$749$	−11.1220			−0.406389
$750$		0			0
$751$	45.1704			1.64829			0.824146	−	0.566377i	$-0.191655\pi$
$751$	45.1704			1.64829			0.824146	+	0.566377i	$0.191655\pi$
$752$	1.88955	+	7.35931i	0.0689048	+	0.268366i
$753$	19.9666	−	3.80884i	0.727624	−	0.138802i
$754$	−2.49941	+	1.37406i	−0.0910230	+	0.0500403i
$755$		0			0
$756$	23.4056	+	49.7395i	0.851254	+	1.80901i
$757$	−21.7999	+	30.0050i	−0.792332	+	1.09055i	0.201482	+	0.979492i	$0.435424\pi$
$757$	−21.7999	+	30.0050i	−0.792332	+	1.09055i	−0.993814	+	0.111059i	$0.964576\pi$
$758$	56.8119	+	60.4985i	2.06350	+	2.19741i
$759$	−10.8396	+	4.29169i	−0.393451	+	0.155778i
$760$		0			0
$761$	−6.23285	+	1.60032i	−0.225941	+	0.0580117i	−0.359963	−	0.932967i	$-0.617211\pi$
$761$	−6.23285	+	1.60032i	−0.225941	+	0.0580117i	0.134022	+	0.990978i	$0.457211\pi$
$762$	−52.9954	+	43.8416i	−1.91982	+	1.58821i
$763$	0.240173	+	0.606607i	0.00869483	+	0.0219606i
$764$	39.3059	+	15.5623i	1.42204	+	0.563025i
$765$		0			0
$766$	−20.6523	+	32.5429i	−0.746199	+	1.17582i
$767$	0.969216	−	1.76300i	0.0349964	−	0.0636582i
$768$	−63.5914	−	87.5261i	−2.29466	−	3.15833i
$769$	−2.99673	+	15.7094i	−0.108065	+	0.566495i	0.886531	+	0.462669i	$0.153108\pi$
$769$	−2.99673	+	15.7094i	−0.108065	+	0.566495i	−0.994596	+	0.103825i	$0.966892\pi$
$770$		0			0
$771$	−25.2033	+	53.5596i	−0.907673	+	1.92890i
$772$	31.7782	+	57.8042i	1.14372	+	2.08042i
$773$	8.52249	+	0.536189i	0.306533	+	0.0192854i	0.215312	−	0.976545i	$-0.430923\pi$
$773$	8.52249	+	0.536189i	0.306533	+	0.0192854i	0.0912206	+	0.995831i	$0.470923\pi$
$774$	45.8023	+	33.2773i	1.64633	+	1.19613i
$775$		0			0
$776$	53.3018	−	38.7260i	1.91342	−	1.39018i
$777$	12.2436	−	7.77003i	0.439237	−	0.278748i
$778$	3.00813	−	23.8118i	0.107847	−	0.853693i
$779$	36.0812	+	4.55811i	1.29274	+	0.163311i
$780$		0			0
$781$	4.75676	+	2.61505i	0.170210	+	0.0935738i
$782$	−27.6648	−	8.98885i	−0.989293	−	0.321441i
$783$	30.6522	−	14.4238i	1.09542	−	0.515466i
$784$	31.8168	+	8.16916i	1.13631	+	0.291756i
$785$		0			0
$786$	−50.5086	+	61.0544i	−1.80158	+	2.17774i
$787$	−6.35500	−	4.03301i	−0.226531	−	0.143761i	0.417718	−	0.908577i	$-0.362830\pi$
$787$	−6.35500	−	4.03301i	−0.226531	−	0.143761i	−0.644249	+	0.764816i	$0.722830\pi$
$788$	−65.3731	+	4.11293i	−2.32882	+	0.146517i
$789$	43.8111	+	69.0353i	1.55972	+	2.45772i
$790$		0			0
$791$	0.322301	+	5.12283i	0.0114597	+	0.182147i
$792$	44.4656	+	8.48226i	1.58002	+	0.301404i
$793$	4.01493	−	1.30453i	0.142574	−	0.0463252i
$794$	18.3893	−	17.2687i	0.652612	−	0.612843i
$795$		0			0
$796$	11.0698	+	58.0297i	0.392357	+	2.05681i
$797$	−19.3269	+	20.5811i	−0.684594	+	0.729019i	−0.973588	−	0.228312i	$-0.926679\pi$
$797$	−19.3269	+	20.5811i	−0.684594	+	0.729019i	0.288994	+	0.957331i	$0.406679\pi$
$798$	7.65344	−	19.3304i	0.270929	−	0.684288i
$799$	1.57650	+	4.85197i	0.0557726	+	0.171650i
$800$		0			0
$801$	5.52085	−	16.9914i	0.195069	−	0.600362i
$802$	−36.8822	−	30.5116i	−1.30236	−	1.07740i
$803$	−5.86690	−	2.76076i	−0.207039	−	0.0974249i
$804$	−137.856	−	129.455i	−4.86181	−	4.56554i
$805$		0			0
$806$	−8.83898	+	1.11662i	−0.311340	+	0.0393313i
$807$		−	23.6736i		−	0.833350i
$808$	−6.95511	−	55.0553i	−0.244680	−	1.93684i
$809$	7.95125	+	9.61141i	0.279551	+	0.337919i	0.891536	−	0.452951i	$-0.149629\pi$
$809$	7.95125	+	9.61141i	0.279551	+	0.337919i	−0.611985	+	0.790870i	$0.709629\pi$
$810$		0			0
$811$	2.05459	−	32.6568i	0.0721464	−	1.14673i	−0.780816	−	0.624761i	$-0.785196\pi$
$811$	2.05459	−	32.6568i	0.0721464	−	1.14673i	0.852962	−	0.521973i	$-0.174804\pi$
$812$	−1.66875	+	6.49936i	−0.0585617	+	0.228083i
$813$	−21.2549	+	82.7822i	−0.745441	+	2.90330i
$814$	0.898643	−	14.2835i	0.0314974	−	0.500637i
$815$		0			0
$816$	37.6787	+	45.5458i	1.31902	+	1.59442i
$817$	−1.13656	−	8.99681i	−0.0397633	−	0.314759i
$818$			63.4598i			2.21882i
$819$	−3.53666	+	0.446784i	−0.123581	+	0.0156119i
$820$		0			0
$821$	6.26838	+	5.88640i	0.218768	+	0.205437i	0.786181	−	0.617997i	$-0.212056\pi$
$821$	6.26838	+	5.88640i	0.218768	+	0.205437i	−0.567413	+	0.823434i	$0.692056\pi$
$822$	−13.4573	−	6.33253i	−0.469378	−	0.220872i
$823$	28.4119	+	23.5043i	0.990375	+	0.819310i	0.983544	−	0.180667i	$-0.0578257\pi$
$823$	28.4119	+	23.5043i	0.990375	+	0.819310i	0.00683079	+	0.999977i	$0.497826\pi$
$824$	28.4676	−	87.6144i	0.991717	−	3.05219i
$825$		0			0
$826$	−2.16145	−	6.65227i	−0.0752065	−	0.231462i
$827$	3.60867	−	9.11447i	0.125486	−	0.316941i	−0.853429	−	0.521209i	$-0.825481\pi$
$827$	3.60867	−	9.11447i	0.125486	−	0.316941i	0.978915	+	0.204268i	$0.0654813\pi$
$828$	−77.7149	+	82.7579i	−2.70078	+	2.87604i
$829$	3.95671	+	20.7418i	0.137422	+	0.720393i	0.982575	+	0.185868i	$0.0595096\pi$
$829$	3.95671	+	20.7418i	0.137422	+	0.720393i	−0.845153	+	0.534525i	$0.820490\pi$
$830$		0			0
$831$	−9.22716	+	8.66488i	−0.320087	+	0.300582i
$832$	2.94263	−	0.956117i	0.102017	−	0.0331474i
$833$	21.6655	+	4.13292i	0.750666	+	0.143197i
$834$	−4.67468	−	74.3019i	−0.161871	−	2.57286i
$835$		0			0
$836$	−7.43989	−	11.7234i	−0.257314	−	0.405462i
$837$	105.608	−	6.64431i	3.65036	−	0.229661i
$838$	−77.2285	−	49.0107i	−2.66781	−	1.69305i
$839$	21.3524	−	25.8107i	0.737168	−	0.891083i	−0.260052	−	0.965595i	$-0.583740\pi$
$839$	21.3524	−	25.8107i	0.737168	−	0.891083i	0.997220	+	0.0745113i	$0.0237397\pi$
$840$		0			0
$841$	−24.0836	−	6.18363i	−0.830470	−	0.213229i
$842$	−51.3500	+	24.1635i	−1.76964	+	0.832729i
$843$	24.5783	+	7.98598i	0.846522	+	0.275052i
$844$	−70.4655	−	38.7388i	−2.42552	−	1.33344i
$845$		0			0
$846$	29.1922	+	3.68783i	1.00365	+	0.126790i
$847$	0.980289	−	7.75979i	0.0336831	−	0.266629i
$848$	−13.4720	+	8.54959i	−0.462630	+	0.293594i
$849$	6.43728	−	4.67696i	0.220927	−	0.160513i
$850$		0			0
$851$	15.1637	+	11.0171i	0.519807	+	0.377662i
$852$	72.4923	+	4.56083i	2.48354	+	0.156251i
$853$	21.3979	+	38.9227i	0.732652	+	1.33269i	0.935447	+	0.353467i	$0.114997\pi$
$853$	21.3979	+	38.9227i	0.732652	+	1.33269i	−0.202795	+	0.979221i	$0.565003\pi$
$854$	6.24919	−	13.2802i	0.213843	−	0.454439i
$855$		0			0
$856$	−14.3727	+	75.3444i	−0.491249	+	2.57522i
$857$	18.8965	+	26.0088i	0.645493	+	0.888445i	0.998894	−	0.0470273i	$-0.0149748\pi$
$857$	18.8965	+	26.0088i	0.645493	+	0.888445i	−0.353401	+	0.935472i	$0.614975\pi$
$858$	−2.32905	+	4.23653i	−0.0795124	+	0.144633i
$859$	9.16371	−	14.4397i	0.312662	−	0.492676i	−0.651263	−	0.758852i	$-0.725760\pi$
$859$	9.16371	−	14.4397i	0.312662	−	0.492676i	0.963924	+	0.266176i	$0.0857604\pi$
$860$		0			0
$861$	−27.6989	−	10.9668i	−0.943975	−	0.373746i
$862$	19.1569	+	48.3848i	0.652487	+	1.64799i
$863$	1.51625	−	1.25435i	0.0516138	−	0.0426986i	−0.611259	−	0.791430i	$-0.709337\pi$
$863$	1.51625	−	1.25435i	0.0516138	−	0.0426986i	0.662873	+	0.748732i	$0.269337\pi$
$864$	31.2264	−	8.01757i	1.06234	−	0.272763i
$865$		0			0
$866$	−34.0772	+	13.4921i	−1.15799	+	0.458481i
$867$	−11.4597	−	12.2033i	−0.389190	−	0.414446i
$868$	−12.3200	+	16.9571i	−0.418169	+	0.575560i
$869$	−4.08332	−	8.67750i	−0.138517	−	0.294364i
$870$		0			0
$871$	6.72596	−	3.69763i	0.227900	−	0.125289i
$872$	4.41974	−	0.843110i	0.149671	−	0.0285513i
$873$	−24.1665	−	94.1223i	−0.817912	−	3.18556i
$874$	26.8728			0.908985
$875$		0			0
$876$	−86.7637			−2.93147
$877$	6.26965	+	24.4187i	0.211711	+	0.824561i	0.982313	+	0.187244i	$0.0599556\pi$
$877$	6.26965	+	24.4187i	0.211711	+	0.824561i	−0.770602	+	0.637316i	$0.780044\pi$
$878$	−33.5127	+	6.39289i	−1.13100	+	0.215750i
$879$	−32.2330	+	17.7202i	−1.08719	+	0.597689i
$880$		0			0
$881$	−7.48675	−	15.9102i	−0.252235	−	0.536027i	0.738105	−	0.674686i	$-0.235721\pi$
$881$	−7.48675	−	15.9102i	−0.252235	−	0.536027i	−0.990340	+	0.138659i	$0.955721\pi$
$882$	74.7726	−	102.916i	2.51773	−	3.46535i
$883$	−12.3227	−	13.1224i	−0.414693	−	0.441603i	0.487378	−	0.873191i	$-0.337953\pi$
$883$	−12.3227	−	13.1224i	−0.414693	−	0.441603i	−0.902071	+	0.431588i	$0.857953\pi$
$884$	−7.58938	+	3.00485i	−0.255258	+	0.101064i
$885$		0			0
$886$	−13.7948	+	3.54190i	−0.463444	+	0.118992i
$887$	0.0957476	−	0.0792093i	0.00321489	−	0.00265959i	−0.635815	−	0.771841i	$-0.719336\pi$
$887$	0.0957476	−	0.0792093i	0.00321489	−	0.00265959i	0.639030	+	0.769182i	$0.279336\pi$
$888$	−36.8148	−	92.9837i	−1.23542	−	3.12033i
$889$	−6.10620	−	2.41762i	−0.204795	−	0.0810842i
$890$		0			0
$891$	17.3831	−	27.3914i	0.582356	−	0.917646i
$892$	−9.45182	+	17.1928i	−0.316470	+	0.575657i
$893$	−2.77026	−	3.81294i	−0.0927032	−	0.127595i
$894$	−9.39804	+	49.2662i	−0.314317	+	1.64771i
$895$		0			0
$896$	5.87928	−	12.4941i	0.196413	−	0.417399i
$897$	−3.05024	−	5.54837i	−0.101845	−	0.185255i
$898$	−2.04457	−	0.128633i	−0.0682281	−	0.00429255i
$899$	10.4499	+	7.59229i	0.348523	+	0.253217i
$900$		0			0
$901$	−8.66742	+	6.29725i	−0.288754	+	0.209792i
$902$	−24.8250	+	15.7544i	−0.826583	+	0.524565i
$903$	−0.931017	+	7.36976i	−0.0309823	+	0.245250i
$904$	35.1204	+	4.43673i	1.16809	+	0.147564i
$905$		0			0
$906$	79.0544	+	43.4605i	2.62641	+	1.44388i
$907$	−1.40695	−	0.457146i	−0.0467170	−	0.0151793i	0.285565	−	0.958359i	$-0.407819\pi$
$907$	−1.40695	−	0.457146i	−0.0467170	−	0.0151793i	−0.332282	+	0.943180i	$0.607819\pi$
$908$	27.5435	−	12.9610i	0.914063	−	0.430125i
$909$	−79.2768	−	20.3548i	−2.62945	−	0.675127i
$910$		0			0
$911$	34.6996	−	41.9446i	1.14965	−	1.38969i	0.241834	−	0.970318i	$-0.422251\pi$
$911$	34.6996	−	41.9446i	1.14965	−	1.38969i	0.907815	−	0.419370i	$-0.137749\pi$
$912$	−46.1073	−	29.2606i	−1.52676	−	0.968914i
$913$	0.198023	−	0.0124585i	0.00655360	−	0.000412318i
$914$	−11.3007	−	17.8071i	−0.373794	−	0.589006i
$915$		0			0
$916$	−4.01737	−	63.8542i	−0.132738	−	2.10980i
$917$	−7.43207	−	1.41774i	−0.245428	−	0.0468180i
$918$	136.259	−	44.2731i	4.49721	−	1.46123i
$919$	−8.82636	+	8.28850i	−0.291155	+	0.273412i	−0.816335	−	0.577578i	$-0.803998\pi$
$919$	−8.82636	+	8.28850i	−0.291155	+	0.273412i	0.525181	+	0.850991i	$0.323998\pi$
$920$		0			0
$921$	−5.69323	−	29.8450i	−0.187598	−	0.983425i
$922$	−59.5247	+	63.3873i	−1.96034	+	2.08755i
$923$	−1.08524	+	2.74100i	−0.0357211	+	0.0902212i
$924$	3.51471	+	10.8172i	0.115625	+	0.355858i
$925$		0			0
$926$	5.08016	−	15.6351i	0.166944	−	0.513802i
$927$	−104.694	−	86.6102i	−3.43859	−	2.84465i
$928$	3.56081	+	1.67559i	0.116889	+	0.0550039i
$929$	−15.2833	−	14.3520i	−0.501430	−	0.470874i	0.392071	−	0.919935i	$-0.371759\pi$
$929$	−15.2833	−	14.3520i	−0.501430	−	0.470874i	−0.893501	+	0.449061i	$0.851759\pi$
$930$		0			0
$931$	−20.2154	+	2.55380i	−0.662534	+	0.0836975i
$932$		−	66.2960i		−	2.17160i
$933$	−11.1533	−	88.2873i	−0.365142	−	2.89040i
$934$	23.3683	+	28.2474i	0.764633	+	0.924283i
$935$		0			0
$936$	−1.54367	+	24.5360i	−0.0504565	+	0.801983i
$937$	−5.07137	+	19.7517i	−0.165674	+	0.645259i	0.830434	+	0.557117i	$0.188093\pi$
$937$	−5.07137	+	19.7517i	−0.165674	+	0.645259i	−0.996108	+	0.0881413i	$0.971907\pi$
$938$	6.63627	−	25.8465i	0.216682	−	0.843920i
$939$	5.47194	−	86.9741i	0.178570	−	2.83829i
$940$		0			0
$941$	−20.3352	−	24.5810i	−0.662908	−	0.801318i	0.326698	−	0.945129i	$-0.394064\pi$
$941$	−20.3352	−	24.5810i	−0.662908	−	0.801318i	−0.989605	+	0.143811i	$0.954064\pi$
$942$	−15.4420	−	122.236i	−0.503126	−	3.98265i
$943$		−	38.5065i		−	1.25394i
$944$	−18.2273	+	2.30264i	−0.593247	+	0.0749445i
$945$		0			0
$946$	5.34435	+	5.01868i	0.173760	+	0.163171i
$947$	45.4700	+	21.3965i	1.47758	+	0.695294i	0.984612	−	0.174755i	$-0.0559135\pi$
$947$	45.4700	+	21.3965i	1.47758	+	0.695294i	0.492964	+	0.870050i	$0.335913\pi$
$948$	−98.8789	−	81.7998i	−3.21144	−	2.65673i
$949$	1.08818	−	3.34908i	0.0353239	−	0.108716i
$950$		0			0
$951$	12.9558	+	39.8738i	0.420120	+	1.29300i
$952$	−5.45544	+	13.7789i	−0.176812	+	0.446576i
$953$	14.3314	−	15.2613i	0.464238	−	0.494363i	−0.453663	−	0.891174i	$-0.649883\pi$
$953$	14.3314	−	15.2613i	0.464238	−	0.494363i	0.917901	+	0.396810i	$0.129883\pi$
$954$	11.5785	+	60.6965i	0.374867	+	1.96512i
$955$		0			0
$956$	24.2485	−	22.7708i	0.784252	−	0.736461i
$957$	6.66613	−	2.16596i	0.215486	−	0.0700155i
$958$	18.8753	+	3.60065i	0.609832	+	0.116332i
$959$	−0.0891704	−	1.41732i	−0.00287946	−	0.0457678i
$960$		0			0
$961$	5.00849	+	7.89212i	0.161564	+	0.254584i
$962$	7.75731	−	0.488049i	0.250106	−	0.0157353i
$963$	95.5202	+	60.6190i	3.07810	+	1.95342i
$964$	32.7109	−	39.5407i	1.05355	−	1.27352i
$965$		0			0
$966$	−21.3213	−	5.47438i	−0.686002	−	0.176135i
$967$	4.10340	−	1.93091i	0.131956	−	0.0620940i	−0.358668	−	0.933465i	$-0.616769\pi$
$967$	4.10340	−	1.93091i	0.131956	−	0.0620940i	0.490624	+	0.871371i	$0.336769\pi$
$968$	−51.3008	−	16.6686i	−1.64887	−	0.535750i
$969$	−32.1311	−	17.6642i	−1.03220	−	0.567457i
$970$		0			0
$971$	−15.5189	−	1.96050i	−0.498026	−	0.0629153i	−0.127692	−	0.991814i	$-0.540757\pi$
$971$	−15.5189	−	1.96050i	−0.498026	−	0.0629153i	−0.370334	+	0.928899i	$0.620757\pi$
$972$	28.1887	−	223.136i	0.904152	−	7.15710i
$973$	6.00210	−	3.80905i	0.192418	−	0.122112i
$974$	−55.9639	+	40.6601i	−1.79320	+	1.30284i
$975$		0			0
$976$	−31.1884	−	22.6597i	−0.998317	−	0.725320i
$977$	−9.15641	−	0.576072i	−0.292940	−	0.0184302i	−0.0843591	−	0.996435i	$-0.526884\pi$
$977$	−9.15641	−	0.576072i	−0.292940	−	0.0184302i	−0.208580	+	0.978005i	$0.566884\pi$
$978$	−31.2206	−	56.7901i	−0.998325	−	1.81595i
$979$	0.985063	−	2.09337i	0.0314828	−	0.0669043i
$980$		0			0
$981$	1.24353	−	6.51881i	0.0397028	−	0.208130i
$982$	−25.0468	−	34.4740i	−0.799276	−	1.10011i
$983$	−19.5778	+	35.6119i	−0.624435	+	1.13584i	0.355149	+	0.934810i	$0.384430\pi$
$983$	−19.5778	+	35.6119i	−0.624435	+	1.13584i	−0.979584	+	0.201034i	$0.935570\pi$
$984$	−110.087	+	173.470i	−3.50946	+	5.53002i
$985$		0			0
$986$	16.2605	+	6.43800i	0.517841	+	0.205028i
$987$	1.42122	+	3.58959i	0.0452379	+	0.114258i
$988$	5.81029	−	4.80669i	0.184850	−	0.152921i
$989$	−9.29991	+	2.38781i	−0.295720	+	0.0759280i
$990$		0			0
$991$	−33.4956	+	13.2619i	−1.06402	+	0.421277i	−0.833918	−	0.551888i	$-0.813907\pi$
$991$	−33.4956	+	13.2619i	−1.06402	+	0.421277i	−0.230106	+	0.973165i	$0.573907\pi$
$992$	8.41484	+	8.96089i	0.267171	+	0.284509i
$993$	−20.6893	+	28.4763i	−0.656554	+	0.903669i
$994$	4.36398	+	9.27393i	0.138417	+	0.294151i
$995$		0			0
$996$	2.32661	−	1.27907i	0.0737216	−	0.0405288i
$997$	−7.53095	+	1.43661i	−0.238508	+	0.0454977i	−0.305249	−	0.952273i	$-0.598740\pi$
$997$	−7.53095	+	1.43661i	−0.238508	+	0.0454977i	0.0667415	+	0.997770i	$0.478740\pi$
$998$	−4.63509	−	18.0525i	−0.146721	−	0.571441i
$999$	−92.3177			−2.92080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.b.274.2		440
5.2	odd	4		625.2.g.a.351.10		220
5.3	odd	4		125.2.g.a.21.2	yes	220
5.4	even	2	inner	625.2.h.b.274.21		440
125.6	even	25	inner	625.2.h.b.349.21		440
125.33	odd	100		125.2.g.a.6.2	✓	220
125.92	odd	100		625.2.g.a.276.10		220
125.119	even	50	inner	625.2.h.b.349.2		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.6.2	✓	220	125.33	odd	100
125.2.g.a.21.2	yes	220	5.3	odd	4
625.2.g.a.276.10		220	125.92	odd	100
625.2.g.a.351.10		220	5.2	odd	4
625.2.h.b.274.2		440	1.1	even	1	trivial
625.2.h.b.274.21		440	5.4	even	2	inner
625.2.h.b.349.2		440	125.119	even	50	inner
625.2.h.b.349.21		440	125.6	even	25	inner

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.618528 - 2.40901i) q^{2} +(-3.26064 + 0.622000i) q^{3} +(-3.66812 + 2.01657i) q^{4} +(3.51519 + 7.47017i) q^{6} +(-0.463359 + 0.637759i) q^{7} +(3.72162 + 3.96312i) q^{8} +(7.45553 - 2.95185i) q^{9} +O(q^{10})\)	\(q+(-0.618528 - 2.40901i) q^{2} +(-3.26064 + 0.622000i) q^{3} +(-3.66812 + 2.01657i) q^{4} +(3.51519 + 7.47017i) q^{6} +(-0.463359 + 0.637759i) q^{7} +(3.72162 + 3.96312i) q^{8} +(7.45553 - 2.95185i) q^{9} +(1.00576 - 0.258235i) q^{11} +(10.7061 - 8.85686i) q^{12} +(0.207600 + 0.524337i) q^{13} +(1.82297 + 0.721763i) q^{14} +(2.75944 - 4.34818i) q^{16} +(1.66584 - 3.03015i) q^{17} +(-11.7225 - 16.1346i) q^{18} +(-0.598583 + 3.13788i) q^{19} +(1.11416 - 2.36771i) q^{21} +(-1.24418 - 2.26315i) q^{22} +(3.37563 + 0.212377i) q^{23} +(-14.5999 - 10.6075i) q^{24} +(1.13473 - 0.824427i) q^{26} +(-14.0657 + 8.92634i) q^{27} +(0.413573 - 3.27377i) q^{28} +(-2.01748 - 0.254867i) q^{29} +(-5.56625 - 3.06007i) q^{31} +(-1.84053 - 0.598023i) q^{32} +(-3.11879 + 1.46759i) q^{33} +(-8.33001 - 2.13878i) q^{34} +(-21.3952 + 25.8623i) q^{36} +(4.67893 + 2.96934i) q^{37} +(7.92942 - 0.498877i) q^{38} +(-1.00305 - 1.58055i) q^{39} +(-0.714850 - 11.3622i) q^{41} +(-6.39296 - 1.21952i) q^{42} +(-2.69982 + 0.877225i) q^{43} +(-3.16849 + 2.97541i) q^{44} +(-1.57631 - 8.26328i) q^{46} +(-1.00997 + 1.07551i) q^{47} +(-6.29296 + 15.8942i) q^{48} +(1.97108 + 6.06637i) q^{49} +(-3.54694 + 10.9164i) q^{51} +(-1.81886 - 1.50469i) q^{52} +(-2.80343 - 1.31919i) q^{53} +(30.2036 + 28.3631i) q^{54} +(-4.25196 + 0.537148i) q^{56} -10.6038i q^{57} +(0.633891 + 5.01776i) q^{58} +(-2.27401 - 2.74880i) q^{59} +(0.470039 - 7.47105i) q^{61} +(-3.92885 + 15.3019i) q^{62} +(-1.57202 + 6.12260i) q^{63} +(0.344501 - 5.47569i) q^{64} +(5.46449 + 6.60544i) q^{66} +(-1.70582 - 13.5029i) q^{67} +14.4742i q^{68} +(-11.1388 + 1.40716i) q^{69} +(3.81072 + 3.57851i) q^{71} +(39.4452 + 18.5615i) q^{72} +(-4.81135 - 3.98029i) q^{73} +(4.25911 - 13.1082i) q^{74} +(-4.13207 - 12.7172i) q^{76} +(-0.301335 + 0.761087i) q^{77} +(-3.18714 + 3.39395i) q^{78} +(-1.73061 - 9.07217i) q^{79} +(22.7748 - 21.3870i) q^{81} +(-26.9295 + 8.74992i) q^{82} +(0.187696 + 0.0358049i) q^{83} +(0.687772 + 10.9318i) q^{84} +(3.78315 + 5.96130i) q^{86} +(6.73680 - 0.423843i) q^{87} +(4.76646 + 3.02489i) q^{88} +(1.42021 - 1.71673i) q^{89} +(-0.430594 - 0.110558i) q^{91} +(-12.8105 + 6.02816i) q^{92} +(20.0529 + 6.51558i) q^{93} +(3.21559 + 1.76779i) q^{94} +(6.37326 + 0.805130i) q^{96} +(1.51887 - 12.0231i) q^{97} +(13.3948 - 8.50057i) q^{98} +(6.73619 - 4.89413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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