LMFDB - Embedded newform 350.2.m.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	350.169
Dual form			350.2.m.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-0.840443 - 1.15677i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.82116 - 1.29744i) q^{5} +(1.15677 + 0.840443i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.295277 - 0.908768i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.840443 - 1.15677i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.82116 - 1.29744i) q^{5} +(1.15677 + 0.840443i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.295277 - 0.908768i) q^{9} +(2.13296 + 0.671171i) q^{10} +(0.927971 + 2.85600i) q^{11} +(-1.35987 - 0.441847i) q^{12} +(-3.36414 - 1.09308i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.0297410 + 3.19710i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.72835 + 3.75525i) q^{17} +0.955535i q^{18} +(-2.22874 - 1.61927i) q^{19} +(-2.23597 + 0.0208001i) q^{20} +(-1.15677 + 0.840443i) q^{21} +(-1.76511 - 2.42946i) q^{22} +(-1.93301 + 0.628073i) q^{23} +1.42985 q^{24} +(1.63328 + 4.72572i) q^{25} +3.53727 q^{26} +(-5.37900 + 1.74774i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-1.50674 + 1.09471i) q^{29} +(-1.01624 - 3.03143i) q^{30} +(-1.15513 - 0.839252i) q^{31} +1.00000i q^{32} +(2.52383 - 3.47376i) q^{33} +(1.43438 - 4.41457i) q^{34} +(-1.29744 + 1.82116i) q^{35} +(-0.295277 - 0.908768i) q^{36} +(-3.41641 - 1.11006i) q^{37} +(2.62004 + 0.851302i) q^{38} +(1.56293 + 4.81021i) q^{39} +(2.12011 - 0.710735i) q^{40} +(-3.34004 + 10.2796i) q^{41} +(0.840443 - 1.15677i) q^{42} -11.6349i q^{43} +(2.42946 + 1.76511i) q^{44} +(-1.71682 + 1.27191i) q^{45} +(1.64432 - 1.19467i) q^{46} +(-4.40064 - 6.05697i) q^{47} +(-1.35987 + 0.441847i) q^{48} -1.00000 q^{49} +(-3.01367 - 3.98971i) q^{50} +6.63700 q^{51} +(-3.36414 + 1.09308i) q^{52} +(2.59481 + 3.57145i) q^{53} +(4.57565 - 3.32440i) q^{54} +(2.01551 - 6.40524i) q^{55} +(0.809017 + 0.587785i) q^{56} +3.93905i q^{57} +(1.09471 - 1.50674i) q^{58} +(2.07763 - 6.39429i) q^{59} +(1.90327 + 2.56903i) q^{60} +(-0.905043 - 2.78544i) q^{61} +(1.35794 + 0.441221i) q^{62} +(-0.908768 - 0.295277i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(4.70845 + 6.35546i) q^{65} +(-1.32686 + 4.08365i) q^{66} +(-4.60456 + 6.33764i) q^{67} +4.64175i q^{68} +(2.35112 + 1.70819i) q^{69} +(0.671171 - 2.13296i) q^{70} +(6.12891 - 4.45291i) q^{71} +(0.561650 + 0.773044i) q^{72} +(8.08779 - 2.62788i) q^{73} +3.59223 q^{74} +(4.09389 - 5.86103i) q^{75} -2.75487 q^{76} +(2.85600 - 0.927971i) q^{77} +(-2.97287 - 4.09181i) q^{78} +(2.86380 - 2.08067i) q^{79} +(-1.79671 + 1.33110i) q^{80} +(4.22335 + 3.06844i) q^{81} -10.8086i q^{82} +(4.64162 - 6.38864i) q^{83} +(-0.441847 + 1.35987i) q^{84} +(9.84101 - 3.29906i) q^{85} +(3.59537 + 11.0654i) q^{86} +(2.53265 + 0.822909i) q^{87} +(-2.85600 - 0.927971i) q^{88} +(-0.728789 - 2.24298i) q^{89} +(1.23975 - 1.74019i) q^{90} +(-1.09308 + 3.36414i) q^{91} +(-1.19467 + 1.64432i) q^{92} +2.04157i q^{93} +(6.05697 + 4.40064i) q^{94} +(1.95798 + 5.84063i) q^{95} +(1.15677 - 0.840443i) q^{96} +(9.87603 + 13.5932i) q^{97} +(0.951057 - 0.309017i) q^{98} +2.86945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	−0.840443	−	1.15677i	−0.485230	−	0.667862i	0.494269	−	0.869309i	$-0.335436\pi$
$3$	−0.840443	−	1.15677i	−0.485230	−	0.667862i	−0.979499	+	0.201447i	$0.935436\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−1.82116	−	1.29744i	−0.814450	−	0.580234i
$5$	−1.82116	−	1.29744i	−0.814450	−	0.580234i
$6$	1.15677	+	0.840443i	0.472250	+	0.343110i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.295277	−	0.908768i	0.0984256	−	0.302923i
$10$	2.13296	+	0.671171i	0.674502	+	0.212243i
$11$	0.927971	+	2.85600i	0.279794	+	0.861117i	0.987911	+	0.155022i	$0.0495449\pi$
$11$	0.927971	+	2.85600i	0.279794	+	0.861117i	−0.708117	+	0.706095i	$0.750455\pi$
$12$	−1.35987	−	0.441847i	−0.392560	−	0.127550i
$13$	−3.36414	−	1.09308i	−0.933045	−	0.303165i	−0.197238	−	0.980356i	$-0.563197\pi$
$13$	−3.36414	−	1.09308i	−0.933045	−	0.303165i	−0.735807	+	0.677191i	$0.763197\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	0.0297410	+	3.19710i	0.00767909	+	0.825487i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.72835	+	3.75525i	−0.661723	+	0.910783i	−0.999537	−	0.0304297i	$-0.990312\pi$
$17$	−2.72835	+	3.75525i	−0.661723	+	0.910783i	0.337814	+	0.941213i	$0.390312\pi$
$18$			0.955535i			0.225222i
$19$	−2.22874	−	1.61927i	−0.511308	−	0.371487i	0.302012	−	0.953304i	$-0.402342\pi$
$19$	−2.22874	−	1.61927i	−0.511308	−	0.371487i	−0.813319	+	0.581817i	$0.802342\pi$
$20$	−2.23597	+	0.0208001i	−0.499978	+	0.00465104i
$21$	−1.15677	+	0.840443i	−0.252428	+	0.183400i
$22$	−1.76511	−	2.42946i	−0.376322	−	0.517963i
$23$	−1.93301	+	0.628073i	−0.403060	+	0.130962i	−0.503530	−	0.863978i	$-0.667966\pi$
$23$	−1.93301	+	0.628073i	−0.403060	+	0.130962i	0.100469	+	0.994940i	$0.467966\pi$
$24$	1.42985			0.291866
$25$	1.63328	+	4.72572i	0.326656	+	0.945143i
$26$	3.53727			0.693715
$27$	−5.37900	+	1.74774i	−1.03519	+	0.336353i
$28$	−0.587785	−	0.809017i	−0.111081	−	0.152890i
$29$	−1.50674	+	1.09471i	−0.279794	+	0.203282i	−0.718828	−	0.695188i	$-0.755321\pi$
$29$	−1.50674	+	1.09471i	−0.279794	+	0.203282i	0.439034	+	0.898471i	$0.355321\pi$
$30$	−1.01624	−	3.03143i	−0.185540	−	0.553461i
$31$	−1.15513	−	0.839252i	−0.207468	−	0.150734i	0.479200	−	0.877706i	$-0.340927\pi$
$31$	−1.15513	−	0.839252i	−0.207468	−	0.150734i	−0.686667	+	0.726972i	$0.740927\pi$
$32$			1.00000i			0.176777i
$33$	2.52383	−	3.47376i	0.439343	−	0.604704i
$34$	1.43438	−	4.41457i	0.245994	−	0.757092i
$35$	−1.29744	+	1.82116i	−0.219308	+	0.307833i
$36$	−0.295277	−	0.908768i	−0.0492128	−	0.151461i
$37$	−3.41641	−	1.11006i	−0.561654	−	0.182493i	0.0144111	−	0.999896i	$-0.495413\pi$
$37$	−3.41641	−	1.11006i	−0.561654	−	0.182493i	−0.576065	+	0.817404i	$0.695413\pi$
$38$	2.62004	+	0.851302i	0.425026	+	0.138099i
$39$	1.56293	+	4.81021i	0.250269	+	0.770250i
$40$	2.12011	−	0.710735i	0.335218	−	0.112377i
$41$	−3.34004	+	10.2796i	−0.521627	+	1.60540i	0.249263	+	0.968436i	$0.419812\pi$
$41$	−3.34004	+	10.2796i	−0.521627	+	1.60540i	−0.770890	+	0.636968i	$0.780188\pi$
$42$	0.840443	−	1.15677i	0.129683	−	0.178494i
$43$		−	11.6349i		−	1.77430i	−0.461483	−	0.887149i	$-0.652682\pi$
$43$		−	11.6349i		−	1.77430i	0.461483	−	0.887149i	$-0.347318\pi$
$44$	2.42946	+	1.76511i	0.366255	+	0.266100i
$45$	−1.71682	+	1.27191i	−0.255929	+	0.189605i
$46$	1.64432	−	1.19467i	0.242441	−	0.176144i
$47$	−4.40064	−	6.05697i	−0.641900	−	0.883499i	0.356815	−	0.934175i	$-0.383863\pi$
$47$	−4.40064	−	6.05697i	−0.641900	−	0.883499i	−0.998715	+	0.0506756i	$0.983863\pi$
$48$	−1.35987	+	0.441847i	−0.196280	+	0.0637752i
$49$	−1.00000			−0.142857
$50$	−3.01367	−	3.98971i	−0.426197	−	0.564230i
$51$	6.63700			0.929365
$52$	−3.36414	+	1.09308i	−0.466523	+	0.151582i
$53$	2.59481	+	3.57145i	0.356425	+	0.490577i	0.949148	−	0.314829i	$-0.101947\pi$
$53$	2.59481	+	3.57145i	0.356425	+	0.490577i	−0.592723	+	0.805406i	$0.701947\pi$
$54$	4.57565	−	3.32440i	0.622667	−	0.452394i
$55$	2.01551	−	6.40524i	0.271772	−	0.863682i
$56$	0.809017	+	0.587785i	0.108109	+	0.0785461i
$57$			3.93905i			0.521740i
$58$	1.09471	−	1.50674i	0.143742	−	0.197844i
$59$	2.07763	−	6.39429i	0.270485	−	0.832466i	−0.719894	−	0.694084i	$-0.755810\pi$
$59$	2.07763	−	6.39429i	0.270485	−	0.832466i	0.990379	−	0.138382i	$-0.0441903\pi$
$60$	1.90327	+	2.56903i	0.245711	+	0.331660i
$61$	−0.905043	−	2.78544i	−0.115879	−	0.356639i	0.876250	−	0.481856i	$-0.160037\pi$
$61$	−0.905043	−	2.78544i	−0.115879	−	0.356639i	−0.992129	+	0.125217i	$0.960037\pi$
$62$	1.35794	+	0.441221i	0.172458	+	0.0560351i
$63$	−0.908768	−	0.295277i	−0.114494	−	0.0372014i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	4.70845	+	6.35546i	0.584012	+	0.788297i
$66$	−1.32686	+	4.08365i	−0.163325	+	0.502662i
$67$	−4.60456	+	6.33764i	−0.562537	+	0.774266i	−0.991646	−	0.128987i	$-0.958827\pi$
$67$	−4.60456	+	6.33764i	−0.562537	+	0.774266i	0.429109	+	0.903253i	$0.358827\pi$
$68$			4.64175i			0.562895i
$69$	2.35112	+	1.70819i	0.283042	+	0.205642i
$70$	0.671171	−	2.13296i	0.0802203	−	0.254938i
$71$	6.12891	−	4.45291i	0.727367	−	0.528463i	−0.161362	−	0.986895i	$-0.551589\pi$
$71$	6.12891	−	4.45291i	0.727367	−	0.528463i	0.888730	+	0.458432i	$0.151589\pi$
$72$	0.561650	+	0.773044i	0.0661910	+	0.0911042i
$73$	8.08779	−	2.62788i	0.946604	−	0.307570i	0.205269	−	0.978706i	$-0.434193\pi$
$73$	8.08779	−	2.62788i	0.946604	−	0.307570i	0.741335	+	0.671135i	$0.234193\pi$
$74$	3.59223			0.417588
$75$	4.09389	−	5.86103i	0.472722	−	0.676773i
$76$	−2.75487			−0.316006
$77$	2.85600	−	0.927971i	0.325472	−	0.105752i
$78$	−2.97287	−	4.09181i	−0.336612	−	0.463306i
$79$	2.86380	−	2.08067i	0.322203	−	0.234094i	−0.414912	−	0.909862i	$-0.636188\pi$
$79$	2.86380	−	2.08067i	0.322203	−	0.234094i	0.737115	+	0.675768i	$0.236188\pi$
$80$	−1.79671	+	1.33110i	−0.200879	+	0.148821i
$81$	4.22335	+	3.06844i	0.469261	+	0.340938i
$82$		−	10.8086i		−	1.19361i
$83$	4.64162	−	6.38864i	0.509484	−	0.701244i	−0.474348	−	0.880337i	$-0.657316\pi$
$83$	4.64162	−	6.38864i	0.509484	−	0.701244i	0.983832	+	0.179093i	$0.0573162\pi$
$84$	−0.441847	+	1.35987i	−0.0482095	+	0.148374i
$85$	9.84101	−	3.29906i	1.06741	−	0.357833i
$86$	3.59537	+	11.0654i	0.387698	+	1.19321i
$87$	2.53265	+	0.822909i	0.271529	+	0.0882251i
$88$	−2.85600	−	0.927971i	−0.304451	−	0.0989221i
$89$	−0.728789	−	2.24298i	−0.0772515	−	0.237756i	0.904972	−	0.425471i	$-0.139892\pi$
$89$	−0.728789	−	2.24298i	−0.0772515	−	0.237756i	−0.982223	+	0.187716i	$0.939892\pi$
$90$	1.23975	−	1.74019i	0.130681	−	0.183432i
$91$	−1.09308	+	3.36414i	−0.114586	+	0.352658i
$92$	−1.19467	+	1.64432i	−0.124552	+	0.171432i
$93$			2.04157i			0.211701i
$94$	6.05697	+	4.40064i	0.624728	+	0.453892i
$95$	1.95798	+	5.84063i	0.200885	+	0.599236i
$96$	1.15677	−	0.840443i	0.118062	−	0.0857774i
$97$	9.87603	+	13.5932i	1.00276	+	1.38018i	0.923617	+	0.383316i	$0.125218\pi$
$97$	9.87603	+	13.5932i	1.00276	+	1.38018i	0.0791415	+	0.996863i	$0.474782\pi$
$98$	0.951057	−	0.309017i	0.0960712	−	0.0312154i
$99$	2.86945			0.288391
$100$	4.09906	+	2.86317i	0.409906	+	0.286317i
$101$	−11.2520			−1.11962			−0.559808	−	0.828623i	$-0.689125\pi$
$101$	−11.2520			−1.11962			−0.559808	+	0.828623i	$0.689125\pi$
$102$	−6.31216	+	2.05094i	−0.624997	+	0.203074i
$103$	−7.57248	−	10.4226i	−0.746138	−	1.02697i	−0.998242	−	0.0592709i	$-0.981122\pi$
$103$	−7.57248	−	10.4226i	−0.746138	−	1.02697i	0.252104	−	0.967700i	$-0.418878\pi$
$104$	2.86171	−	2.07915i	0.280614	−	0.203878i
$105$	3.19710	−	0.0297410i	0.312005	−	0.00290242i
$106$	−3.57145	−	2.59481i	−0.346890	−	0.252030i
$107$			5.18712i			0.501458i	0.968057	+	0.250729i	$0.0806703\pi$
$107$			5.18712i			0.501458i	−0.968057	+	0.250729i	$0.919330\pi$
$108$	−3.32440	+	4.57565i	−0.319891	+	0.440292i
$109$	3.67615	−	11.3140i	0.352112	−	1.08369i	−0.605554	−	0.795804i	$-0.707048\pi$
$109$	3.67615	−	11.3140i	0.352112	−	1.08369i	0.957665	−	0.287884i	$-0.0929516\pi$
$110$	0.0624623	+	6.71457i	0.00595554	+	0.640209i
$111$	1.58722	+	4.88495i	0.150652	+	0.463659i
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	−19.0454	−	6.18823i	−1.79164	−	0.582139i	−0.792042	−	0.610467i	$-0.790982\pi$
$113$	−19.0454	−	6.18823i	−1.79164	−	0.582139i	−0.999599	+	0.0283275i	$0.990982\pi$
$114$	−1.21723	−	3.74626i	−0.114004	−	0.350869i
$115$	4.33522	+	1.36415i	0.404261	+	0.127207i
$116$	−0.575522	+	1.77127i	−0.0534359	+	0.164459i
$117$	−1.98671	+	2.73447i	−0.183671	+	0.252801i
$118$			6.72336i			0.618935i
$119$	3.75525	+	2.72835i	0.344244	+	0.250108i
$120$	−2.60399	−	1.85515i	−0.237711	−	0.169351i
$121$	1.60357	−	1.16506i	0.145779	−	0.105915i
$122$	1.72149	+	2.36943i	0.155857	+	0.214518i
$123$	14.6983	−	4.77575i	1.32530	−	0.430615i
$124$	−1.42782			−0.128222
$125$	3.15687	−	10.7254i	0.282359	−	0.959309i
$126$	0.955535			0.0851259
$127$	13.5371	−	4.39845i	1.20122	−	0.390300i	0.361010	−	0.932562i	$-0.382432\pi$
$127$	13.5371	−	4.39845i	1.20122	−	0.390300i	0.840209	+	0.542262i	$0.182432\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−13.4589	+	9.77844i	−1.18499	+	0.860943i
$130$	−6.44195	−	4.58941i	−0.564996	−	0.402517i
$131$	−13.6515	−	9.91837i	−1.19273	−	0.866572i	−0.199184	−	0.979962i	$-0.563829\pi$
$131$	−13.6515	−	9.91837i	−1.19273	−	0.866572i	−0.993551	+	0.113390i	$0.963829\pi$
$132$		−	4.29380i		−	0.373727i
$133$	−1.61927	+	2.22874i	−0.140409	+	0.193256i
$134$	2.42076	−	7.45034i	0.209122	−	0.643611i
$135$	12.0636	+	3.79602i	1.03827	+	0.326709i
$136$	−1.43438	−	4.41457i	−0.122997	−	0.378546i
$137$	−2.66013	−	0.864329i	−0.227270	−	0.0738446i	0.193168	−	0.981166i	$-0.438124\pi$
$137$	−2.66013	−	0.864329i	−0.227270	−	0.0738446i	−0.420438	+	0.907321i	$0.638124\pi$
$138$	−2.76391	−	0.898048i	−0.235280	−	0.0764470i
$139$	0.550656	+	1.69474i	0.0467060	+	0.143746i	0.971690	−	0.236260i	$-0.0759218\pi$
$139$	0.550656	+	1.69474i	0.0467060	+	0.143746i	−0.924984	+	0.380006i	$0.875922\pi$
$140$	0.0208001	+	2.23597i	0.00175793	+	0.188974i
$141$	−3.30803	+	10.1811i	−0.278587	+	0.857401i
$142$	−4.45291	+	6.12891i	−0.373680	+	0.514326i
$143$		−	10.6223i		−	0.888285i
$144$	−0.773044	−	0.561650i	−0.0644204	−	0.0468041i
$145$	4.16434	−	0.0387387i	0.345829	−	0.00321707i
$146$	−6.87989	+	4.99853i	−0.569383	+	0.413681i
$147$	0.840443	+	1.15677i	0.0693186	+	0.0954089i
$148$	−3.41641	+	1.11006i	−0.280827	+	0.0912463i
$149$	−20.9526			−1.71650			−0.858251	−	0.513230i	$-0.828449\pi$
$149$	−20.9526			−1.71650			−0.858251	+	0.513230i	$0.828449\pi$
$150$	−2.08236	+	6.83925i	−0.170024	+	0.558423i
$151$	−17.5233			−1.42602			−0.713012	−	0.701152i	$-0.752669\pi$
$151$	−17.5233			−1.42602			−0.713012	+	0.701152i	$0.752669\pi$
$152$	2.62004	−	0.851302i	0.212513	−	0.0690497i
$153$	2.60704	+	3.58828i	0.210766	+	0.290095i
$154$	−2.42946	+	1.76511i	−0.195772	+	0.142236i
$155$	1.01480	+	3.02713i	0.0815109	+	0.243145i
$156$	4.09181	+	2.97287i	0.327607	+	0.238020i
$157$		−	0.0664729i		−	0.00530511i	−0.999996	−	0.00265256i	$-0.999156\pi$
$157$		−	0.0664729i		−	0.00530511i	0.999996	−	0.00265256i	$-0.000844336\pi$
$158$	−2.08067	+	2.86380i	−0.165529	+	0.227832i
$159$	1.95056	−	6.00321i	0.154689	−	0.476085i
$160$	1.29744	−	1.82116i	0.102572	−	0.143976i
$161$	0.628073	+	1.93301i	0.0494991	+	0.152342i
$162$	−4.96484	−	1.61318i	−0.390075	−	0.126743i
$163$	−19.3153	−	6.27591i	−1.51289	−	0.491567i	−0.569142	−	0.822239i	$-0.692724\pi$
$163$	−19.3153	−	6.27591i	−1.51289	−	0.491567i	−0.943746	+	0.330673i	$0.892724\pi$
$164$	3.34004	+	10.2796i	0.260814	+	0.802702i
$165$	−9.10332	+	3.05176i	−0.708693	+	0.237579i
$166$	−2.44024	+	7.51030i	−0.189400	+	0.582912i
$167$	0.199330	−	0.274354i	0.0154246	−	0.0212301i	−0.801235	−	0.598350i	$-0.795823\pi$
$167$	0.199330	−	0.274354i	0.0154246	−	0.0212301i	0.816660	+	0.577120i	$0.195823\pi$
$168$		−	1.42985i		−	0.110315i
$169$	−0.394584	−	0.286682i	−0.0303526	−	0.0220525i
$170$	−8.33989	+	6.17863i	−0.639640	+	0.473879i
$171$	−2.12964	+	1.54727i	−0.162858	+	0.118323i
$172$	−6.83879	−	9.41279i	−0.521453	−	0.717719i
$173$	16.8727	−	5.48226i	1.28281	−	0.416809i	0.413238	−	0.910623i	$-0.364398\pi$
$173$	16.8727	−	5.48226i	1.28281	−	0.416809i	0.869567	+	0.493814i	$0.164398\pi$
$174$	−2.66299			−0.201881
$175$	4.72572	−	1.63328i	0.357231	−	0.123465i
$176$	3.00298			0.226358
$177$	−9.14287	+	2.97070i	−0.687220	+	0.223291i
$178$	1.38624	+	1.90800i	0.103903	+	0.143010i
$179$	4.29763	−	3.12241i	0.321220	−	0.233380i	−0.415476	−	0.909604i	$-0.636385\pi$
$179$	4.29763	−	3.12241i	0.321220	−	0.233380i	0.736696	+	0.676224i	$0.236385\pi$
$180$	−0.641328	+	2.03812i	−0.0478017	+	0.151913i
$181$	−15.3045	−	11.1194i	−1.13758	−	0.826499i	−0.150798	−	0.988565i	$-0.548184\pi$
$181$	−15.3045	−	11.1194i	−1.13758	−	0.826499i	−0.986780	+	0.162066i	$0.948184\pi$
$182$		−	3.53727i		−	0.262200i
$183$	−2.46147	+	3.38793i	−0.181957	+	0.250443i
$184$	0.628073	−	1.93301i	0.0463021	−	0.142503i
$185$	4.78161	+	6.45420i	0.351551	+	0.474522i
$186$	−0.630879	−	1.94164i	−0.0462583	−	0.142368i
$187$	−13.2568	−	4.30741i	−0.969437	−	0.314989i
$188$	−7.12039	−	2.31356i	−0.519308	−	0.168733i
$189$	1.74774	+	5.37900i	0.127130	+	0.391265i
$190$	−3.66701	−	4.94971i	−0.266033	−	0.359090i
$191$	1.00627	−	3.09699i	0.0728113	−	0.224090i	−0.908028	−	0.418910i	$-0.862412\pi$
$191$	1.00627	−	3.09699i	0.0728113	−	0.224090i	0.980839	+	0.194820i	$0.0624122\pi$
$192$	−0.840443	+	1.15677i	−0.0606538	+	0.0834828i
$193$			24.3410i			1.75210i	0.482216	+	0.876052i	$0.339832\pi$
$193$			24.3410i			1.75210i	−0.482216	+	0.876052i	$0.660168\pi$
$194$	−13.5932	−	9.87603i	−0.975934	−	0.709058i
$195$	3.39462	−	10.7880i	0.243094	−	0.772545i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	1.56974	+	2.16056i	0.111839	+	0.153933i	0.861267	−	0.508153i	$-0.169671\pi$
$197$	1.56974	+	2.16056i	0.111839	+	0.153933i	−0.749428	+	0.662086i	$0.769671\pi$
$198$	−2.72901	+	0.886709i	−0.193942	+	0.0630157i
$199$	16.9618			1.20239			0.601194	−	0.799103i	$-0.294692\pi$
$199$	16.9618			1.20239			0.601194	+	0.799103i	$0.294692\pi$
$200$	−4.78320	−	1.45635i	−0.338224	−	0.102980i
$201$	11.2011			0.790063
$202$	10.7013	−	3.47706i	0.752940	−	0.244645i
$203$	1.09471	+	1.50674i	0.0768334	+	0.105752i
$204$	5.36944	−	3.90113i	0.375936	−	0.273134i
$205$	19.4200	−	14.3873i	1.35635	−	1.00485i
$206$	10.4226	+	7.57248i	0.726178	+	0.527599i
$207$			1.94211i			0.134986i
$208$	−2.07915	+	2.86171i	−0.144163	+	0.198424i
$209$	2.55644	−	7.86792i	0.176833	−	0.544235i
$210$	−3.03143	+	1.01624i	−0.209189	+	0.0701274i
$211$	−3.26706	−	10.0550i	−0.224914	−	0.692213i	−0.998300	−	0.0582788i	$-0.981439\pi$
$211$	−3.26706	−	10.0550i	−0.224914	−	0.692213i	0.773387	−	0.633935i	$-0.218561\pi$
$212$	4.19849	+	1.36417i	0.288354	+	0.0936918i
$213$	−10.3020	−	3.34732i	−0.705881	−	0.229355i
$214$	−1.60291	−	4.93325i	−0.109573	−	0.337230i
$215$	−15.0956	+	21.1890i	−1.02951	+	1.44508i
$216$	1.74774	−	5.37900i	0.118919	−	0.365994i
$217$	−0.839252	+	1.15513i	−0.0569721	+	0.0784154i
$218$			11.8963i			0.805718i
$219$	−9.83719	−	7.14714i	−0.664736	−	0.482959i
$220$	−2.13432	−	6.36664i	−0.143896	−	0.429239i
$221$	13.2833	−	9.65091i	0.893534	−	0.649191i
$222$	−3.01906	−	4.15538i	−0.202626	−	0.278891i
$223$	4.75051	−	1.54353i	0.318118	−	0.103363i	−0.145606	−	0.989343i	$-0.546513\pi$
$223$	4.75051	−	1.54353i	0.318118	−	0.103363i	0.463723	+	0.885980i	$0.346513\pi$
$224$	1.00000			0.0668153
$225$	4.77685	−	0.0888809i	0.318457	−	0.00592539i
$226$	20.0255			1.33208
$227$	24.7646	−	8.04651i	1.64369	−	0.534066i	0.666328	−	0.745659i	$-0.267865\pi$
$227$	24.7646	−	8.04651i	1.64369	−	0.534066i	0.977358	+	0.211593i	$0.0678653\pi$
$228$	2.31531	+	3.18676i	0.153335	+	0.211048i
$229$	−11.0807	+	8.05061i	−0.732235	+	0.532000i	−0.890270	−	0.455434i	$-0.849484\pi$
$229$	−11.0807	+	8.05061i	−0.732235	+	0.532000i	0.158035	+	0.987434i	$0.449484\pi$
$230$	−4.54458	+	0.0422759i	−0.299661	+	0.00278759i
$231$	−3.47376	−	2.52383i	−0.228557	−	0.166056i
$232$		−	1.86243i		−	0.122274i
$233$	−8.94822	+	12.3162i	−0.586218	+	0.806859i	−0.994360	−	0.106059i	$-0.966177\pi$
$233$	−8.94822	+	12.3162i	−0.586218	+	0.806859i	0.408142	+	0.912918i	$0.366177\pi$
$234$	1.04447	−	3.21456i	0.0682793	−	0.210142i
$235$	0.155727	+	16.7403i	0.0101585	+	1.09202i
$236$	−2.07763	−	6.39429i	−0.135242	−	0.416233i
$237$	−4.81372	−	1.56407i	−0.312685	−	0.101598i
$238$	−4.41457	−	1.43438i	−0.286154	−	0.0929770i
$239$	6.50199	+	20.0111i	0.420579	+	1.29441i	0.907165	+	0.420775i	$0.138242\pi$
$239$	6.50199	+	20.0111i	0.420579	+	1.29441i	−0.486586	+	0.873633i	$0.661758\pi$
$240$	3.04981	+	0.959672i	0.196865	+	0.0619466i
$241$	−1.40903	+	4.33654i	−0.0907635	+	0.279341i	−0.986126	−	0.165996i	$-0.946916\pi$
$241$	−1.40903	+	4.33654i	−0.0907635	+	0.279341i	0.895363	+	0.445337i	$0.146916\pi$
$242$	−1.16506	+	1.60357i	−0.0748930	+	0.103081i
$243$			9.50314i			0.609627i
$244$	−2.36943	−	1.72149i	−0.151687	−	0.110207i
$245$	1.82116	+	1.29744i	0.116350	+	0.0828906i
$246$	−12.5031	+	9.08403i	−0.797168	+	0.579176i
$247$	5.72780	+	7.88365i	0.364451	+	0.501624i
$248$	1.35794	−	0.441221i	0.0862292	−	0.0280176i
$249$	−11.2912			−0.715552
$250$	0.311966	+	11.1760i	0.0197304	+	0.706831i
$251$	−19.7398			−1.24596			−0.622982	−	0.782236i	$-0.714079\pi$
$251$	−19.7398			−1.24596			−0.622982	+	0.782236i	$0.714079\pi$
$252$	−0.908768	+	0.295277i	−0.0572470	+	0.0186007i
$253$	−3.58755	−	4.93784i	−0.225548	−	0.310440i
$254$	−11.5153	+	8.36636i	−0.722534	+	0.524952i
$255$	−12.0871	−	8.61113i	−0.756921	−	0.539250i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$		−	16.1788i		−	1.00921i	−0.863352	−	0.504603i	$-0.831639\pi$
$257$		−	16.1788i		−	1.00921i	0.863352	−	0.504603i	$-0.168361\pi$
$258$	9.77844	−	13.4589i	0.608779	−	0.837912i
$259$	−1.11006	+	3.41641i	−0.0689757	+	0.212285i
$260$	7.54486	+	2.37411i	0.467912	+	0.147236i
$261$	0.549932	+	1.69252i	0.0340399	+	0.104764i
$262$	16.0483	+	5.21440i	0.991465	+	0.322147i
$263$	15.2031	+	4.93977i	0.937461	+	0.304600i	0.737610	−	0.675227i	$-0.235954\pi$
$263$	15.2031	+	4.93977i	0.937461	+	0.304600i	0.199851	+	0.979826i	$0.435954\pi$
$264$	1.32686	+	4.08365i	0.0816624	+	0.251331i
$265$	−0.0918233	−	9.87082i	−0.00564066	−	0.606360i
$266$	0.851302	−	2.62004i	0.0521967	−	0.160645i
$267$	−1.98211	+	2.72814i	−0.121303	+	0.166960i
$268$			7.83375i			0.478522i
$269$	−5.44417	−	3.95542i	−0.331937	−	0.241166i	0.409315	−	0.912393i	$-0.365768\pi$
$269$	−5.44417	−	3.95542i	−0.331937	−	0.241166i	−0.741252	+	0.671227i	$0.765768\pi$
$270$	−12.6462	+	0.117642i	−0.769625	+	0.00715943i
$271$	14.3455	−	10.4226i	0.871428	−	0.633129i	−0.0595420	−	0.998226i	$-0.518964\pi$
$271$	14.3455	−	10.4226i	0.871428	−	0.633129i	0.930970	+	0.365097i	$0.118964\pi$
$272$	2.72835	+	3.75525i	0.165431	+	0.227696i
$273$	4.81021	−	1.56293i	0.291127	−	0.0945930i
$274$	2.79703			0.168975
$275$	−11.9810	+	9.04999i	−0.722482	+	0.545735i
$276$	2.90615			0.174929
$277$	−1.10227	+	0.358149i	−0.0662290	+	0.0215191i	−0.341944	−	0.939720i	$-0.611085\pi$
$277$	−1.10227	+	0.358149i	−0.0662290	+	0.0215191i	0.275715	+	0.961239i	$0.411085\pi$
$278$	−1.04741	−	1.44164i	−0.0628194	−	0.0864635i
$279$	−1.10377	+	0.801935i	−0.0660809	+	0.0480106i
$280$	−0.710735	−	2.12011i	−0.0424746	−	0.126701i
$281$	18.1357	+	13.1764i	1.08189	+	0.786037i	0.978011	−	0.208553i	$-0.0668755\pi$
$281$	18.1357	+	13.1764i	1.08189	+	0.786037i	0.103876	+	0.994590i	$0.466876\pi$
$282$		−	10.7050i		−	0.637474i
$283$	−2.30076	+	3.16673i	−0.136766	+	0.188242i	−0.871906	−	0.489673i	$-0.837116\pi$
$283$	−2.30076	+	3.16673i	−0.136766	+	0.188242i	0.735140	+	0.677915i	$0.237116\pi$
$284$	2.34103	−	7.20496i	0.138915	−	0.427536i
$285$	5.11069	−	7.17366i	0.302731	−	0.424931i
$286$	3.28248	+	10.1024i	0.194097	+	0.597370i
$287$	10.2796	+	3.34004i	0.606786	+	0.197157i
$288$	0.908768	+	0.295277i	0.0535497	+	0.0173993i
$289$	−1.40474	−	4.32336i	−0.0826320	−	0.254315i
$290$	−3.94855	+	1.32369i	−0.231867	+	0.0777300i
$291$	7.42396	−	22.8486i	0.435200	−	1.33941i
$292$	4.99853	−	6.87989i	0.292517	−	0.402615i
$293$			15.3892i			0.899044i	0.893269	+	0.449522i	$0.148406\pi$
$293$			15.3892i			0.899044i	−0.893269	+	0.449522i	$0.851594\pi$
$294$	−1.15677	−	0.840443i	−0.0674643	−	0.0490157i
$295$	−12.0799	+	8.94945i	−0.703322	+	0.521057i
$296$	2.90617	−	2.11146i	0.168918	−	0.122726i
$297$	−9.98311	−	13.7406i	−0.579279	−	0.797309i
$298$	19.9271	−	6.47470i	1.15434	−	0.375069i
$299$	7.18945			0.415777
$300$	−0.133000	−	7.14800i	−0.00767876	−	0.412690i
$301$	−11.6349			−0.670622
$302$	16.6656	−	5.41499i	0.958999	−	0.311598i
$303$	9.45667	+	13.0160i	0.543271	+	0.747749i
$304$	−2.22874	+	1.61927i	−0.127827	+	0.0928717i
$305$	−1.96571	+	6.24698i	−0.112556	+	0.357701i
$306$	−3.58828	−	2.60704i	−0.205128	−	0.149034i
$307$			21.6566i			1.23601i	0.786174	+	0.618005i	$0.212059\pi$
$307$			21.6566i			1.23601i	−0.786174	+	0.618005i	$0.787941\pi$
$308$	1.76511	−	2.42946i	0.100576	−	0.138431i
$309$	−5.69235	+	17.5192i	−0.323826	+	0.996635i
$310$	−1.90057	−	2.56538i	−0.107945	−	0.145704i
$311$	−3.53297	−	10.8734i	−0.200336	−	0.616572i	−0.999873	−	0.0159543i	$-0.994921\pi$
$311$	−3.53297	−	10.8734i	−0.200336	−	0.616572i	0.799536	−	0.600618i	$-0.205079\pi$
$312$	−4.81021	−	1.56293i	−0.272325	−	0.0884836i
$313$	29.7375	+	9.66231i	1.68086	+	0.546146i	0.985079	−	0.172103i	$-0.0550562\pi$
$313$	29.7375	+	9.66231i	1.68086	+	0.546146i	0.695786	+	0.718249i	$0.255056\pi$
$314$	0.0205412	+	0.0632195i	0.00115921	+	0.00356768i
$315$	1.27191	+	1.71682i	0.0716641	+	0.0967320i
$316$	1.09387	−	3.36660i	0.0615352	−	0.189386i
$317$	12.8449	−	17.6795i	0.721441	−	0.992979i	−0.278033	−	0.960571i	$-0.589683\pi$
$317$	12.8449	−	17.6795i	0.721441	−	0.992979i	0.999475	−	0.0324074i	$-0.0103174\pi$
$318$			6.31215i			0.353968i
$319$	−4.52470	−	3.28738i	−0.253334	−	0.184058i
$320$	−0.671171	+	2.13296i	−0.0375196	+	0.119236i
$321$	6.00031	−	4.35948i	0.334905	−	0.243323i
$322$	−1.19467	−	1.64432i	−0.0665761	−	0.0916341i
$323$	12.1616	−	3.95153i	0.676688	−	0.219869i
$324$	5.22035			0.290019
$325$	−0.329026	−	17.6833i	−0.0182511	−	0.980892i
$326$	20.3093			1.12483
$327$	−16.1773	+	5.25634i	−0.894609	+	0.290676i
$328$	−6.35314	−	8.74435i	−0.350794	−	0.482826i
$329$	−6.05697	+	4.40064i	−0.333931	+	0.242615i
$330$	7.71473	−	5.71547i	0.424682	−	0.314626i
$331$	−2.63109	−	1.91160i	−0.144618	−	0.105071i	0.513124	−	0.858315i	$-0.328488\pi$
$331$	−2.63109	−	1.91160i	−0.144618	−	0.105071i	−0.657742	+	0.753244i	$0.728488\pi$
$332$		−	7.89679i		−	0.433393i
$333$	−2.01757	+	2.77695i	−0.110562	+	0.152176i
$334$	−0.104794	+	0.322522i	−0.00573406	+	0.0176476i
$335$	16.6084	−	5.56772i	0.907413	−	0.304197i
$336$	0.441847	+	1.35987i	0.0241047	+	0.0741868i
$337$	1.68353	+	0.547012i	0.0917077	+	0.0297976i	0.354511	−	0.935052i	$-0.384647\pi$
$337$	1.68353	+	0.547012i	0.0917077	+	0.0297976i	−0.262804	+	0.964849i	$0.584647\pi$
$338$	0.463861	+	0.150718i	0.0252307	+	0.00819796i
$339$	8.84822	+	27.2320i	0.480569	+	1.47904i
$340$	6.02241	−	8.45339i	0.326611	−	0.458450i
$341$	1.32498	−	4.07786i	0.0717515	−	0.220828i
$342$	1.54727	−	2.12964i	0.0836669	−	0.115158i
$343$			1.00000i			0.0539949i
$344$	9.41279	+	6.83879i	0.507504	+	0.368723i
$345$	−2.06550	−	6.16134i	−0.111203	−	0.331715i
$346$	−14.3527	+	10.4279i	−0.771609	+	0.560606i
$347$	0.166651	+	0.229376i	0.00894631	+	0.0123135i	0.813467	−	0.581611i	$-0.197578\pi$
$347$	0.166651	+	0.229376i	0.00894631	+	0.0123135i	−0.804520	+	0.593925i	$0.797578\pi$
$348$	2.53265	−	0.822909i	0.135764	−	0.0441125i
$349$	17.2183			0.921675			0.460837	−	0.887485i	$-0.347549\pi$
$349$	17.2183			0.921675			0.460837	+	0.887485i	$0.347549\pi$
$350$	−3.98971	+	3.01367i	−0.213259	+	0.161087i
$351$	20.0061			1.06785
$352$	−2.85600	+	0.927971i	−0.152225	+	0.0494610i
$353$	−13.6194	−	18.7455i	−0.724889	−	0.997725i	−0.999347	−	0.0361255i	$-0.988498\pi$
$353$	−13.6194	−	18.7455i	−0.724889	−	0.997725i	0.274458	−	0.961599i	$-0.411502\pi$
$354$	7.77739	−	5.65060i	0.413364	−	0.300326i
$355$	−16.9391	+	0.157576i	−0.899037	+	0.00836328i
$356$	−1.90800	−	1.38624i	−0.101124	−	0.0734706i
$357$		−	6.63700i		−	0.351267i
$358$	−3.12241	+	4.29763i	−0.165024	+	0.227137i
$359$	6.86199	−	21.1190i	0.362162	−	1.11462i	−0.589578	−	0.807712i	$-0.700706\pi$
$359$	6.86199	−	21.1190i	0.362162	−	1.11462i	0.951739	−	0.306908i	$-0.0992942\pi$
$360$	−0.0198752	−	2.13655i	−0.00104752	−	0.112606i
$361$	−3.52609	−	10.8522i	−0.185584	−	0.571168i
$362$	17.9916	+	5.84582i	0.945616	+	0.307249i
$363$	−2.69542	−	0.875795i	−0.141473	−	0.0459673i
$364$	1.09308	+	3.36414i	0.0572928	+	0.176329i
$365$	−18.1387	−	5.70764i	−0.949424	−	0.298752i
$366$	1.29407	−	3.98275i	0.0676423	−	0.208182i
$367$	11.2975	−	15.5497i	0.589724	−	0.811686i	−0.404995	−	0.914319i	$-0.632727\pi$
$367$	11.2975	−	15.5497i	0.589724	−	0.811686i	0.994719	+	0.102633i	$0.0327267\pi$
$368$			2.03249i			0.105951i
$369$	8.35554	+	6.07065i	0.434972	+	0.316026i
$370$	−6.54204	−	4.66071i	−0.340104	−	0.242299i
$371$	3.57145	−	2.59481i	0.185421	−	0.134716i
$372$	1.20000	+	1.65166i	0.0622172	+	0.0856347i
$373$	13.4492	−	4.36991i	0.696373	−	0.226265i	0.0606235	−	0.998161i	$-0.480691\pi$
$373$	13.4492	−	4.36991i	0.696373	−	0.226265i	0.635750	+	0.771895i	$0.280691\pi$
$374$	13.9391			0.720772
$375$	−15.0600	+	5.36231i	−0.777695	+	0.276909i
$376$	7.48682			0.386103
$377$	6.26547	−	2.03578i	0.322688	−	0.104848i
$378$	−3.32440	−	4.57565i	−0.170989	−	0.235346i
$379$	−13.8670	+	10.0750i	−0.712302	+	0.517518i	−0.883916	−	0.467647i	$-0.845102\pi$
$379$	−13.8670	+	10.0750i	−0.712302	+	0.517518i	0.171613	+	0.985164i	$0.445102\pi$
$380$	5.01708	+	3.57429i	0.257371	+	0.183357i
$381$	−16.4651	−	11.9626i	−0.843534	−	0.612864i
$382$			3.25637i			0.166610i
$383$	−0.0295074	+	0.0406135i	−0.00150776	+	0.00207525i	−0.809770	−	0.586747i	$-0.800408\pi$
$383$	−0.0295074	+	0.0406135i	−0.00150776	+	0.00207525i	0.808262	+	0.588822i	$0.200408\pi$
$384$	0.441847	−	1.35987i	0.0225479	−	0.0693954i
$385$	−6.40524	−	2.01551i	−0.326441	−	0.102720i
$386$	−7.52179	−	23.1497i	−0.382849	−	1.17829i
$387$	−10.5734	−	3.43550i	−0.537475	−	0.174636i
$388$	15.9798	+	5.19214i	0.811249	+	0.263591i
$389$	−9.39856	−	28.9258i	−0.476526	−	1.46660i	−0.843889	−	0.536518i	$-0.819739\pi$
$389$	−9.39856	−	28.9258i	−0.476526	−	1.46660i	0.367363	−	0.930077i	$-0.380261\pi$
$390$	0.105202	+	11.3090i	0.00532710	+	0.572653i
$391$	2.91536	−	8.97255i	0.147436	−	0.453761i
$392$	0.587785	−	0.809017i	0.0296876	−	0.0408615i
$393$			24.1275i			1.21707i
$394$	−2.16056	−	1.56974i	−0.108847	−	0.0790822i
$395$	−7.91501	+	0.0736293i	−0.398247	+	0.00370469i
$396$	2.32144	−	1.68662i	0.116657	−	0.0847559i
$397$	12.3365	+	16.9798i	0.619152	+	0.852190i	0.997291	−	0.0735593i	$-0.0234358\pi$
$397$	12.3365	+	16.9798i	0.619152	+	0.852190i	−0.378139	+	0.925749i	$0.623436\pi$
$398$	−16.1316	+	5.24148i	−0.808604	+	0.262731i
$399$	3.93905			0.197199
$400$	4.99913	−	0.0930169i	0.249957	−	0.00465084i
$401$	6.97933			0.348531			0.174266	−	0.984699i	$-0.444245\pi$
$401$	6.97933			0.348531			0.174266	+	0.984699i	$0.444245\pi$
$402$	−10.6529	+	3.46132i	−0.531316	+	0.172635i
$403$	2.96866	+	4.08601i	0.147879	+	0.203539i
$404$	−9.10306	+	6.61376i	−0.452894	+	0.329047i
$405$	−3.71028	−	11.0677i	−0.184365	−	0.549958i
$406$	−1.50674	−	1.09471i	−0.0747781	−	0.0543294i
$407$		−	10.7874i		−	0.534710i
$408$	−3.90113	+	5.36944i	−0.193135	+	0.265827i
$409$	0.637909	−	1.96328i	0.0315426	−	0.0970780i	−0.934046	−	0.357153i	$-0.883747\pi$
$409$	0.637909	−	1.96328i	0.0315426	−	0.0970780i	0.965588	+	0.260075i	$0.0837474\pi$
$410$	−14.0236	+	19.6843i	−0.692574	+	0.972136i
$411$	1.23586	+	3.80358i	0.0609604	+	0.187617i
$412$	−12.2525	−	3.98109i	−0.603638	−	0.196134i
$413$	−6.39429	−	2.07763i	−0.314643	−	0.102234i
$414$	−0.600146	−	1.84706i	−0.0294956	−	0.0907780i
$415$	−16.7421	+	5.61253i	−0.821835	+	0.275508i
$416$	1.09308	−	3.36414i	0.0535925	−	0.164941i
$417$	1.49764	−	2.06132i	0.0733395	−	0.100943i
$418$			8.27282i			0.404637i
$419$	−7.78119	−	5.65337i	−0.380136	−	0.276185i	0.381265	−	0.924466i	$-0.375488\pi$
$419$	−7.78119	−	5.65337i	−0.380136	−	0.276185i	−0.761402	+	0.648281i	$0.775488\pi$
$420$	2.56903	−	1.90327i	0.125356	−	0.0928700i
$421$	−12.5821	+	9.14145i	−0.613216	+	0.445527i	−0.850545	−	0.525902i	$-0.823728\pi$
$421$	−12.5821	+	9.14145i	−0.613216	+	0.445527i	0.237330	+	0.971429i	$0.423728\pi$
$422$	6.21432	+	8.55328i	0.302508	+	0.416367i
$423$	−6.80379	+	2.21068i	−0.330811	+	0.107487i
$424$	−4.41456			−0.214390
$425$	−22.2024	−	6.76003i	−1.07698	−	0.327910i
$426$	10.8322			0.524820
$427$	−2.78544	+	0.905043i	−0.134797	+	0.0437981i
$428$	3.04891	+	4.19647i	0.147375	+	0.202844i
$429$	−12.2876	+	8.92748i	−0.593252	+	0.431023i
$430$	7.80898	−	24.8167i	0.376582	−	1.19677i
$431$	21.1993	+	15.4022i	1.02113	+	0.741897i	0.966515	−	0.256610i	$-0.0826058\pi$
$431$	21.1993	+	15.4022i	1.02113	+	0.741897i	0.0546184	+	0.998507i	$0.482606\pi$
$432$			5.65581i			0.272115i
$433$	−7.43189	+	10.2291i	−0.357154	+	0.491580i	−0.949353	−	0.314212i	$-0.898260\pi$
$433$	−7.43189	+	10.2291i	−0.357154	+	0.491580i	0.592199	+	0.805792i	$0.298260\pi$
$434$	0.441221	−	1.35794i	0.0211793	−	0.0651831i
$435$	−3.54470	−	4.78463i	−0.169955	−	0.229405i
$436$	−3.67615	−	11.3140i	−0.176056	−	0.541844i
$437$	5.32519	+	1.73026i	0.254739	+	0.0827696i
$438$	11.5643	+	3.75747i	0.552564	+	0.179539i
$439$	9.73441	+	29.9594i	0.464598	+	1.42989i	0.859487	+	0.511157i	$0.170783\pi$
$439$	9.73441	+	29.9594i	0.464598	+	1.42989i	−0.394889	+	0.918729i	$0.629217\pi$
$440$	3.99726	+	5.39549i	0.190562	+	0.257220i
$441$	−0.295277	+	0.908768i	−0.0140608	+	0.0432747i
$442$	−9.65091	+	13.2833i	−0.459047	+	0.631824i
$443$		−	1.92028i		−	0.0912353i	−0.998959	−	0.0456176i	$-0.985474\pi$
$443$		−	1.92028i		−	0.0912353i	0.998959	−	0.0456176i	$-0.0145256\pi$
$444$	4.15538	+	3.01906i	0.197206	+	0.143278i
$445$	−1.58290	+	5.03040i	−0.0750366	+	0.238464i
$446$	−4.04102	+	2.93598i	−0.191348	+	0.139022i
$447$	17.6095	+	24.2373i	0.832899	+	1.14639i
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	−31.6018			−1.49138			−0.745691	−	0.666292i	$-0.767881\pi$
$449$	−31.6018			−1.49138			−0.745691	+	0.666292i	$0.767881\pi$
$450$	−4.51559	+	1.56066i	−0.212867	+	0.0735702i
$451$	−32.4580			−1.52839
$452$	−19.0454	+	6.18823i	−0.895820	+	0.291070i
$453$	14.7273	+	20.2704i	0.691950	+	0.952387i
$454$	−21.0660	+	15.3054i	−0.988678	+	0.718317i
$455$	6.35546	−	4.70845i	0.297948	−	0.220736i
$456$	−3.18676	−	2.31531i	−0.149234	−	0.108425i
$457$			39.6499i			1.85474i	0.374140	+	0.927372i	$0.377938\pi$
$457$			39.6499i			1.85474i	−0.374140	+	0.927372i	$0.622062\pi$
$458$	8.05061	−	11.0807i	0.376181	−	0.517768i
$459$	8.11258	−	24.9680i	0.378663	−	1.16540i
$460$	4.30909	−	1.44456i	0.200912	−	0.0673529i
$461$	13.0741	+	40.2378i	0.608920	+	1.87406i	0.467187	+	0.884158i	$0.345267\pi$
$461$	13.0741	+	40.2378i	0.608920	+	1.87406i	0.141733	+	0.989905i	$0.454733\pi$
$462$	4.08365	+	1.32686i	0.189989	+	0.0617310i
$463$	−39.6527	−	12.8839i	−1.84282	−	0.598768i	−0.997965	−	0.0637703i	$-0.979688\pi$
$463$	−39.6527	−	12.8839i	−1.84282	−	0.598768i	−0.844854	−	0.534998i	$-0.820312\pi$
$464$	0.575522	+	1.77127i	0.0267179	+	0.0822294i
$465$	2.64882	−	3.71803i	0.122836	−	0.172419i
$466$	4.70436	−	14.4785i	0.217925	−	0.670705i
$467$	−19.1912	+	26.4144i	−0.888061	+	1.22231i	0.0860613	+	0.996290i	$0.472572\pi$
$467$	−19.1912	+	26.4144i	−0.888061	+	1.22231i	−0.974122	+	0.226021i	$0.927428\pi$
$468$			3.37999i			0.156240i
$469$	6.33764	+	4.60456i	0.292645	+	0.212619i
$470$	−5.32115	−	15.8729i	−0.245446	−	0.732161i
$471$	−0.0768939	+	0.0558667i	−0.00354308	+	0.00257420i
$472$	3.95189	+	5.43931i	0.181901	+	0.250365i
$473$	33.2292	−	10.7968i	1.52788	−	0.496438i
$474$	5.06145			0.232480
$475$	4.01207	−	13.1771i	0.184086	−	0.604607i
$476$	4.64175			0.212754
$477$	4.01181	−	1.30352i	0.183688	−	0.0596839i
$478$	−12.3675	−	17.0224i	−0.565677	−	0.778588i
$479$	−24.6253	+	17.8914i	−1.12516	+	0.817477i	−0.984983	−	0.172650i	$-0.944767\pi$
$479$	−24.6253	+	17.8914i	−1.12516	+	0.817477i	−0.140177	+	0.990126i	$0.544767\pi$
$480$	−3.19710	+	0.0297410i	−0.145927	+	0.00135748i
$481$	10.2799	+	7.46879i	0.468724	+	0.340548i
$482$		−	4.55971i		−	0.207689i
$483$	1.70819	−	2.35112i	0.0777253	−	0.106980i
$484$	0.612509	−	1.88511i	0.0278413	−	0.0856868i
$485$	−0.349486	−	37.5690i	−0.0158693	−	1.70592i
$486$	−2.93663	−	9.03802i	−0.133208	−	0.409973i
$487$	−29.3318	−	9.53047i	−1.32915	−	0.431867i	−0.443522	−	0.896264i	$-0.646271\pi$
$487$	−29.3318	−	9.53047i	−1.32915	−	0.431867i	−0.885627	+	0.464397i	$0.846271\pi$
$488$	2.78544	+	0.905043i	0.126091	+	0.0409694i
$489$	8.97359	+	27.6179i	0.405800	+	1.24892i
$490$	−2.13296	−	0.671171i	−0.0963574	−	0.0303204i
$491$	1.14784	−	3.53269i	0.0518012	−	0.159428i	−0.921809	−	0.387644i	$-0.873289\pi$
$491$	1.14784	−	3.53269i	0.0518012	−	0.159428i	0.973611	+	0.228216i	$0.0732891\pi$
$492$	9.08403	−	12.5031i	0.409540	−	0.563683i
$493$		−	8.64493i		−	0.389348i
$494$	−7.88365	−	5.72780i	−0.354702	−	0.257706i
$495$	−5.22574	−	3.72295i	−0.234880	−	0.167334i
$496$	−1.15513	+	0.839252i	−0.0518669	+	0.0376835i
$497$	−4.45291	−	6.12891i	−0.199740	−	0.274919i
$498$	10.7386	−	3.48918i	0.481207	−	0.156354i
$499$	38.2044			1.71026			0.855132	−	0.518411i	$-0.173476\pi$
$499$	38.2044			1.71026			0.855132	+	0.518411i	$0.173476\pi$
$500$	−3.75027	−	10.5326i	−0.167717	−	0.471032i
$501$	−0.484889			−0.0216633
$502$	18.7737	−	6.09993i	0.837909	−	0.272253i
$503$	−25.7549	−	35.4486i	−1.14836	−	1.58058i	−0.747250	−	0.664544i	$-0.768626\pi$
$503$	−25.7549	−	35.4486i	−1.14836	−	1.58058i	−0.401106	−	0.916032i	$-0.631374\pi$
$504$	0.773044	−	0.561650i	0.0344341	−	0.0250179i
$505$	20.4917	+	14.5988i	0.911870	+	0.649639i
$506$	4.93784	+	3.58755i	0.219514	+	0.159486i
$507$			0.697383i			0.0309719i
$508$	8.36636	−	11.5153i	0.371197	−	0.510909i
$509$	−2.32628	+	7.15954i	−0.103110	+	0.317341i	−0.989282	−	0.146015i	$-0.953355\pi$
$509$	−2.32628	+	7.15954i	−0.103110	+	0.317341i	0.886172	+	0.463357i	$0.153355\pi$
$510$	14.1565	+	4.45456i	0.626859	+	0.197251i
$511$	−2.62788	−	8.08779i	−0.116251	−	0.357783i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	14.8185	+	4.81481i	0.654251	+	0.212579i
$514$	4.99952	+	15.3869i	0.220520	+	0.678689i
$515$	0.267969	+	28.8062i	0.0118081	+	1.26935i
$516$	−5.14083	+	15.8218i	−0.226312	+	0.696518i
$517$	13.2150	−	18.1889i	0.581197	−	0.799949i
$518$		−	3.59223i		−	0.157833i
$519$	−20.5222	−	14.9103i	−0.900827	−	0.654489i
$520$	−7.90923	+	0.0735756i	−0.346843	+	0.00322650i
$521$	0.0386179	−	0.0280576i	0.00169188	−	0.00122922i	−0.586939	−	0.809631i	$-0.699667\pi$
$521$	0.0386179	−	0.0280576i	0.00169188	−	0.00122922i	0.588631	+	0.808402i	$0.299667\pi$
$522$	−1.04603	−	1.43974i	−0.0457836	−	0.0630157i
$523$	−3.33435	+	1.08340i	−0.145801	+	0.0473736i	−0.381008	−	0.924572i	$-0.624423\pi$
$523$	−3.33435	+	1.08340i	−0.145801	+	0.0473736i	0.235207	+	0.971945i	$0.424423\pi$
$524$	−16.8741			−0.737150
$525$	−5.86103	−	4.09389i	−0.255796	−	0.178672i
$526$	−15.9854			−0.696999
$527$	6.30321	−	2.04804i	0.274572	−	0.0892139i
$528$	−2.52383	−	3.47376i	−0.109836	−	0.151176i
$529$	−15.2653	+	11.0909i	−0.663710	+	0.482214i
$530$	3.13758	+	9.35934i	0.136288	+	0.406544i
$531$	−5.19746	−	3.77617i	−0.225550	−	0.163872i
$532$			2.75487i			0.119439i
$533$	22.4728	−	30.9311i	0.973404	−	1.33978i
$534$	1.04206	−	3.20712i	0.0450943	−	0.138786i
$535$	6.73000	−	9.44660i	0.290963	−	0.408412i
$536$	−2.42076	−	7.45034i	−0.104561	−	0.321806i
$537$	−7.22382	−	2.34716i	−0.311731	−	0.101288i
$538$	6.40000	+	2.07949i	0.275924	+	0.0896530i
$539$	−0.927971	−	2.85600i	−0.0399706	−	0.123017i
$540$	11.9909	−	4.01979i	0.516008	−	0.172984i
$541$	7.69457	−	23.6815i	0.330816	−	1.01815i	−0.637931	−	0.770093i	$-0.720210\pi$
$541$	7.69457	−	23.6815i	0.330816	−	1.01815i	0.968747	−	0.248052i	$-0.0797904\pi$
$542$	−10.4226	+	14.3455i	−0.447690	+	0.616192i
$543$			27.0491i			1.16079i
$544$	−3.75525	−	2.72835i	−0.161005	−	0.116977i
$545$	−21.3742	+	15.8351i	−0.915570	+	0.678302i
$546$	−4.09181	+	2.97287i	−0.175113	+	0.127227i
$547$	9.33711	+	12.8514i	0.399226	+	0.549487i	0.960549	−	0.278109i	$-0.0897077\pi$
$547$	9.33711	+	12.8514i	0.399226	+	0.549487i	−0.561324	+	0.827596i	$0.689708\pi$
$548$	−2.66013	+	0.864329i	−0.113635	+	0.0369223i
$549$	−2.79855			−0.119439
$550$	8.59802	−	12.3094i	0.366621	−	0.524874i
$551$	5.13075			0.218577
$552$	−2.76391	+	0.898048i	−0.117640	+	0.0382235i
$553$	−2.08067	−	2.86380i	−0.0884792	−	0.121781i
$554$	0.937647	−	0.681240i	0.0398368	−	0.0289431i
$555$	3.44736	−	10.9556i	0.146332	−	0.465040i
$556$	1.44164	+	1.04741i	0.0611390	+	0.0444200i
$557$		−	34.8339i		−	1.47596i	−0.674822	−	0.737981i	$-0.735779\pi$
$557$		−	34.8339i		−	1.47596i	0.674822	−	0.737981i	$-0.264221\pi$
$558$	0.801935	−	1.10377i	0.0339486	−	0.0467263i
$559$	−12.7178	+	39.1413i	−0.537905	+	1.65550i
$560$	1.33110	+	1.79671i	0.0562492	+	0.0759250i
$561$	6.15894	+	18.9553i	0.260031	+	0.800292i
$562$	−21.3198	−	6.92723i	−0.899323	−	0.292208i
$563$	−6.70657	−	2.17910i	−0.282648	−	0.0918380i	0.164262	−	0.986417i	$-0.447476\pi$
$563$	−6.70657	−	2.17910i	−0.282648	−	0.0918380i	−0.446910	+	0.894579i	$0.647476\pi$
$564$	3.30803	+	10.1811i	0.139293	+	0.428701i
$565$	26.6559	+	35.9801i	1.12142	+	1.51369i
$566$	1.20958	−	3.72271i	0.0508425	−	0.156477i
$567$	3.06844	−	4.22335i	0.128862	−	0.177364i
$568$			7.57575i			0.317871i
$569$	−12.1681	−	8.84066i	−0.510115	−	0.370620i	0.302752	−	0.953069i	$-0.402094\pi$
$569$	−12.1681	−	8.84066i	−0.510115	−	0.370620i	−0.812867	+	0.582449i	$0.802094\pi$
$570$	−2.64377	+	8.40184i	−0.110736	+	0.351914i
$571$	25.9876	−	18.8811i	1.08755	−	0.790148i	0.108563	−	0.994090i	$-0.465375\pi$
$571$	25.9876	−	18.8811i	1.08755	−	0.790148i	0.978983	+	0.203941i	$0.0653751\pi$
$572$	−6.24365	−	8.59365i	−0.261060	−	0.359319i
$573$	−4.42822	+	1.43882i	−0.184992	+	0.0601074i
$574$	−10.8086			−0.451143
$575$	−6.12524	−	8.10903i	−0.255440	−	0.338170i
$576$	−0.955535			−0.0398140
$577$	17.2660	−	5.61006i	0.718793	−	0.233550i	0.0732932	−	0.997310i	$-0.476649\pi$
$577$	17.2660	−	5.61006i	0.718793	−	0.233550i	0.645500	+	0.763760i	$0.276649\pi$
$578$	2.67198	+	3.67767i	0.111140	+	0.152971i
$579$	28.1570	−	20.4573i	1.17016	−	0.850174i
$580$	3.34625	−	2.47908i	0.138945	−	0.102938i
$581$	−6.38864	−	4.64162i	−0.265045	−	0.192567i
$582$			24.0245i			0.995846i
$583$	−7.79216	+	10.7250i	−0.322718	+	0.444184i
$584$	−2.62788	+	8.08779i	−0.108743	+	0.334675i
$585$	7.16593	−	2.40227i	0.296275	−	0.0993218i
$586$	−4.75551	−	14.6360i	−0.196448	−	0.604606i
$587$	30.6926	+	9.97263i	1.26682	+	0.411615i	0.863920	−	0.503629i	$-0.168002\pi$
$587$	30.6926	+	9.97263i	1.26682	+	0.411615i	0.402900	+	0.915244i	$0.368002\pi$
$588$	1.35987	+	0.441847i	0.0560799	+	0.0182215i
$589$	1.21551	+	3.74095i	0.0500841	+	0.154143i
$590$	8.72318	−	12.2443i	0.359128	−	0.504092i
$591$	1.17999	−	3.63165i	0.0485385	−	0.149386i
$592$	−2.11146	+	2.90617i	−0.0867804	+	0.119443i
$593$			20.1612i			0.827922i	0.910295	+	0.413961i	$0.135855\pi$
$593$			20.1612i			0.827922i	−0.910295	+	0.413961i	$0.864145\pi$
$594$	13.7406	+	9.98311i	0.563783	+	0.409612i
$595$	−3.29906	−	9.84101i	−0.135248	−	0.403442i
$596$	−16.9510	+	12.3156i	−0.694340	+	0.504467i
$597$	−14.2554	−	19.6209i	−0.583435	−	0.803029i
$598$	−6.83757	+	2.22166i	−0.279609	+	0.0908505i
$599$	−15.9996			−0.653728			−0.326864	−	0.945071i	$-0.605992\pi$
$599$	−15.9996			−0.653728			−0.326864	+	0.945071i	$0.605992\pi$
$600$	2.33534	+	6.75705i	0.0953400	+	0.275856i
$601$	−34.3490			−1.40112			−0.700562	−	0.713591i	$-0.747067\pi$
$601$	−34.3490			−1.40112			−0.700562	+	0.713591i	$0.747067\pi$
$602$	11.0654	−	3.59537i	0.450992	−	0.146536i
$603$	4.39982	+	6.05584i	0.179175	+	0.246613i
$604$	−14.1766	+	10.2999i	−0.576839	+	0.419098i
$605$	−4.43197	+	0.0412283i	−0.180185	+	0.00167617i
$606$	−13.0160	−	9.45667i	−0.528738	−	0.384151i
$607$			1.52675i			0.0619688i	0.999520	+	0.0309844i	$0.00986421\pi$
$607$			1.52675i			0.0619688i	−0.999520	+	0.0309844i	$0.990136\pi$
$608$	1.61927	−	2.22874i	0.0656702	−	0.0903873i
$609$	0.822909	−	2.53265i	0.0333460	−	0.102628i
$610$	−0.0609189	−	6.54867i	−0.00246654	−	0.265148i
$611$	8.18367	+	25.1867i	0.331076	+	1.01895i
$612$	4.21827	+	1.37060i	0.170514	+	0.0554032i
$613$	−27.9484	−	9.08099i	−1.12883	−	0.366778i	−0.315696	−	0.948860i	$-0.602238\pi$
$613$	−27.9484	−	9.08099i	−1.12883	−	0.366778i	−0.813129	+	0.582083i	$0.802238\pi$
$614$	−6.69227	−	20.5967i	−0.270078	−	0.831215i
$615$	−32.9642	−	10.3727i	−1.32925	−	0.418269i
$616$	−0.927971	+	2.85600i	−0.0373890	+	0.115072i
$617$	18.0527	−	24.8474i	0.726773	−	1.00032i	−0.272498	−	0.962156i	$-0.587850\pi$
$617$	18.0527	−	24.8474i	0.726773	−	1.00032i	0.999272	−	0.0381616i	$-0.0121502\pi$
$618$		−	18.4208i		−	0.740994i
$619$	14.0406	+	10.2011i	0.564339	+	0.410017i	0.833045	−	0.553206i	$-0.186596\pi$
$619$	14.0406	+	10.2011i	0.564339	+	0.410017i	−0.268705	+	0.963222i	$0.586596\pi$
$620$	2.60030	+	1.85252i	0.104430	+	0.0743988i
$621$	9.29994	−	6.75680i	0.373194	−	0.271141i
$622$	6.72011	+	9.24944i	0.269452	+	0.370869i
$623$	−2.24298	+	0.728789i	−0.0898632	+	0.0291983i
$624$	5.05776			0.202472
$625$	−19.6648	+	15.4369i	−0.786591	+	0.617474i
$626$	−31.2679			−1.24972
$627$	−11.2499	+	3.65532i	−0.449279	+	0.145980i
$628$	−0.0390718	−	0.0537777i	−0.00155913	−	0.00214596i
$629$	13.4897	−	9.80086i	0.537871	−	0.390786i
$630$	−1.74019	−	1.23975i	−0.0693307	−	0.0493929i
$631$	−9.16483	−	6.65864i	−0.364846	−	0.265076i	0.390224	−	0.920720i	$-0.372397\pi$
$631$	−9.16483	−	6.65864i	−0.364846	−	0.265076i	−0.755071	+	0.655644i	$0.772397\pi$
$632$			3.53985i			0.140808i
$633$	−8.88553	+	12.2299i	−0.353168	+	0.486094i
$634$	−6.75296	+	20.7835i	−0.268194	+	0.825417i
$635$	−30.3599	−	9.55325i	−1.20480	−	0.379109i
$636$	−1.95056	−	6.00321i	−0.0773447	−	0.238043i
$637$	3.36414	+	1.09308i	0.133292	+	0.0433092i
$638$	5.31910	+	1.72828i	0.210585	+	0.0684233i
$639$	−2.23694	−	6.88460i	−0.0884920	−	0.272350i
$640$	−0.0208001	−	2.23597i	−0.000822196	−	0.0883845i
$641$	4.10846	−	12.6445i	0.162274	−	0.499429i	−0.836551	−	0.547889i	$-0.815431\pi$
$641$	4.10846	−	12.6445i	0.162274	−	0.499429i	0.998825	+	0.0484605i	$0.0154315\pi$
$642$	−4.35948	+	6.00031i	−0.172055	+	0.236813i
$643$			21.7954i			0.859528i	0.902941	+	0.429764i	$0.141403\pi$
$643$			21.7954i			0.859528i	−0.902941	+	0.429764i	$0.858597\pi$
$644$	1.64432	+	1.19467i	0.0647951	+	0.0470764i
$645$	37.1978	−	0.346032i	1.46466	−	0.0136250i
$646$	−10.3452	+	7.51626i	−0.407028	+	0.295723i
$647$	−3.31723	−	4.56578i	−0.130414	−	0.179499i	0.738816	−	0.673907i	$-0.235385\pi$
$647$	−3.31723	−	4.56578i	−0.130414	−	0.179499i	−0.869230	+	0.494408i	$0.835385\pi$
$648$	−4.96484	+	1.61318i	−0.195037	+	0.0633715i
$649$	20.1901			0.792531
$650$	5.77736	+	16.7161i	0.226607	+	0.655660i
$651$	2.04157			0.0800153
$652$	−19.3153	+	6.27591i	−0.756444	+	0.245783i
$653$	−9.47118	−	13.0360i	−0.370636	−	0.510137i	0.582438	−	0.812875i	$-0.302099\pi$
$653$	−9.47118	−	13.0360i	−0.370636	−	0.510137i	−0.953074	+	0.302739i	$0.902099\pi$
$654$	13.7613	−	9.99815i	0.538108	−	0.390959i
$655$	11.9930	+	35.7750i	0.468607	+	1.39784i
$656$	8.74435	+	6.35314i	0.341409	+	0.248049i
$657$		−	8.12588i		−	0.317021i
$658$	4.40064	−	6.05697i	0.171555	−	0.236125i
$659$	−6.46826	+	19.9073i	−0.251968	+	0.775477i	0.742444	+	0.669908i	$0.233666\pi$
$659$	−6.46826	+	19.9073i	−0.251968	+	0.775477i	−0.994412	+	0.105569i	$0.966334\pi$
$660$	−5.57096	+	7.81972i	−0.216849	+	0.304382i
$661$	14.3127	+	44.0499i	0.556698	+	1.71334i	0.691415	+	0.722457i	$0.256987\pi$
$661$	14.3127	+	44.0499i	0.556698	+	1.71334i	−0.134717	+	0.990884i	$0.543013\pi$
$662$	3.09303	+	1.00499i	0.120214	+	0.0390599i
$663$	−22.3278	−	7.25474i	−0.867140	−	0.281751i
$664$	2.44024	+	7.51030i	0.0946998	+	0.291456i
$665$	5.84063	−	1.95798i	0.226490	−	0.0759274i
$666$	1.06070	−	3.26450i	0.0411013	−	0.126497i
$667$	2.22498	−	3.06242i	0.0861515	−	0.118577i
$668$		−	0.339120i		−	0.0131209i
$669$	−5.77805	−	4.19800i	−0.223392	−	0.162304i
$670$	−14.0750	+	10.4275i	−0.543765	+	0.402849i
$671$	7.11536	−	5.16961i	0.274685	−	0.199571i
$672$	−0.840443	−	1.15677i	−0.0324208	−	0.0446234i
$673$	36.5634	−	11.8802i	1.40942	−	0.457947i	0.497193	−	0.867640i	$-0.334364\pi$
$673$	36.5634	−	11.8802i	1.40942	−	0.457947i	0.912224	+	0.409692i	$0.134364\pi$
$674$	−1.77017			−0.0681843
$675$	−17.0448	−	22.5651i	−0.656053	−	0.868530i
$676$	−0.487733			−0.0187589
$677$	1.28612	−	0.417887i	0.0494298	−	0.0160607i	−0.284198	−	0.958766i	$-0.591727\pi$
$677$	1.28612	−	0.417887i	0.0494298	−	0.0160607i	0.333628	+	0.942705i	$0.391727\pi$
$678$	−16.8303	−	23.1649i	−0.646364	−	0.889644i
$679$	13.5932	−	9.87603i	0.521659	−	0.379007i
$680$	−3.11541	+	9.90068i	−0.119470	+	0.379674i
$681$	−30.1212	−	21.8844i	−1.15425	−	0.838610i
$682$			4.28771i			0.164185i
$683$	20.0870	−	27.6474i	0.768609	−	1.05790i	−0.227840	−	0.973699i	$-0.573166\pi$
$683$	20.0870	−	27.6474i	0.768609	−	1.05790i	0.996449	−	0.0842011i	$-0.0268338\pi$
$684$	−0.813450	+	2.50354i	−0.0311030	+	0.0957253i
$685$	3.72312	+	5.02546i	0.142253	+	0.192013i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	18.6254	+	6.05177i	0.710605	+	0.230889i
$688$	−11.0654	−	3.59537i	−0.421865	−	0.137072i
$689$	−4.82545	−	14.8512i	−0.183835	−	0.565786i
$690$	3.86837	+	5.22151i	0.147266	+	0.198779i
$691$	−3.38546	+	10.4194i	−0.128789	+	0.396372i	−0.994572	−	0.104047i	$-0.966821\pi$
$691$	−3.38546	+	10.4194i	−0.128789	+	0.396372i	0.865783	+	0.500419i	$0.166821\pi$
$692$	10.4279	−	14.3527i	0.396409	−	0.545610i
$693$		−	2.86945i		−	0.109001i
$694$	−0.229376	−	0.166651i	−0.00870698	−	0.00632599i
$695$	1.19600	−	3.80085i	0.0453668	−	0.144175i
$696$	−2.15440	+	1.56527i	−0.0816625	+	0.0593312i
$697$	−29.4897	−	40.5891i	−1.11700	−	1.53742i
$698$	−16.3756	+	5.32075i	−0.619825	+	0.201393i
$699$	21.7675			0.823321
$700$	2.86317	−	4.09906i	0.108217	−	0.154930i
$701$	26.1778			0.988721			0.494361	−	0.869257i	$-0.335402\pi$
$701$	26.1778			0.988721			0.494361	+	0.869257i	$0.335402\pi$
$702$	−19.0270	+	6.18223i	−0.718126	+	0.233333i
$703$	5.81680	+	8.00613i	0.219385	+	0.301957i
$704$	2.42946	−	1.76511i	0.0915637	−	0.0665249i
$705$	19.2338	−	14.2494i	0.724388	−	0.536665i
$706$	18.7455	+	13.6194i	0.705498	+	0.512574i
$707$			11.2520i			0.423175i
$708$	−5.65060	+	7.77739i	−0.212363	+	0.292292i
$709$	14.3734	−	44.2368i	0.539805	−	1.66135i	−0.193228	−	0.981154i	$-0.561896\pi$
$709$	14.3734	−	44.2368i	0.539805	−	1.66135i	0.733032	−	0.680194i	$-0.238104\pi$
$710$	16.0614	−	5.38435i	0.602773	−	0.202071i
$711$	−1.04524	−	3.21690i	−0.0391994	−	0.120643i
$712$	2.24298	+	0.728789i	0.0840593	+	0.0273125i
$713$	2.75999	+	0.896775i	0.103362	+	0.0335845i
$714$	2.05094	+	6.31216i	0.0767547	+	0.236227i
$715$	−13.7819	+	19.3450i	−0.515413	+	0.723463i
$716$	1.64155	−	5.05216i	0.0613475	−	0.188808i
$717$	17.6837	−	24.3395i	0.660409	−	0.908974i
$718$			22.2059i			0.828715i
$719$	−25.6331	−	18.6236i	−0.955954	−	0.694541i	−0.00374659	−	0.999993i	$-0.501193\pi$
$719$	−25.6331	−	18.6236i	−0.955954	−	0.694541i	−0.952208	+	0.305452i	$0.901193\pi$
$720$	0.679133	+	2.02584i	0.0253098	+	0.0754985i
$721$	−10.4226	+	7.57248i	−0.388159	+	0.282014i
$722$	6.70703	+	9.23143i	0.249610	+	0.343558i
$723$	6.20059	−	2.01470i	0.230603	−	0.0749273i
$724$	−18.9175			−0.703062
$725$	−7.63420	−	5.33244i	−0.283527	−	0.198042i
$726$	2.83413			0.105185
$727$	−8.77025	+	2.84963i	−0.325271	+	0.105687i	−0.467101	−	0.884204i	$-0.654701\pi$
$727$	−8.77025	+	2.84963i	−0.325271	+	0.105687i	0.141830	+	0.989891i	$0.454701\pi$
$728$	−2.07915	−	2.86171i	−0.0770586	−	0.106062i
$729$	23.6630	−	17.1922i	0.876408	−	0.636747i
$730$	19.0147	−	0.176884i	0.703766	−	0.00654678i
$731$	43.6918	+	31.7440i	1.61600	+	1.17409i
$732$			4.18771i			0.154782i
$733$	−5.36313	+	7.38171i	−0.198092	+	0.272650i	−0.896494	−	0.443055i	$-0.853895\pi$
$733$	−5.36313	+	7.38171i	−0.198092	+	0.272650i	0.698403	+	0.715705i	$0.253895\pi$
$734$	−5.93944	+	18.2797i	−0.219229	+	0.674717i
$735$	−0.0297410	−	3.19710i	−0.00109701	−	0.117927i
$736$	−0.628073	−	1.93301i	−0.0231511	−	0.0712517i
$737$	−22.3732	−	7.26950i	−0.824128	−	0.267775i
$738$	−9.82252	−	3.19153i	−0.361572	−	0.117482i
$739$	−7.56837	−	23.2930i	−0.278407	−	0.856849i	−0.988298	−	0.152537i	$-0.951256\pi$
$739$	−7.56837	−	23.2930i	−0.278407	−	0.856849i	0.709891	−	0.704312i	$-0.248744\pi$
$740$	7.66208	+	2.41100i	0.281664	+	0.0886301i
$741$	4.30568	−	13.2515i	0.158173	−	0.486807i
$742$	−2.59481	+	3.57145i	−0.0952585	+	0.131112i
$743$		−	25.5222i		−	0.936319i	−0.883644	−	0.468160i	$-0.844917\pi$
$743$		−	25.5222i		−	0.936319i	0.883644	−	0.468160i	$-0.155083\pi$
$744$	−1.65166	−	1.20000i	−0.0605529	−	0.0439942i
$745$	38.1581	+	27.1848i	1.39800	+	0.995973i
$746$	−11.4406	+	8.31206i	−0.418869	+	0.304326i
$747$	−4.43523	−	6.10457i	−0.162277	−	0.223355i
$748$	−13.2568	+	4.30741i	−0.484718	+	0.157495i
$749$	5.18712			0.189533
$750$	12.6659	−	9.75366i	0.462492	−	0.356153i
$751$	36.3796			1.32751			0.663756	−	0.747949i	$-0.268961\pi$
$751$	36.3796			1.32751			0.663756	+	0.747949i	$0.268961\pi$
$752$	−7.12039	+	2.31356i	−0.259654	+	0.0843667i
$753$	16.5902	+	22.8344i	0.604580	+	0.832133i
$754$	−5.32973	+	3.87228i	−0.194097	+	0.141020i
$755$	31.9128	+	22.7355i	1.16142	+	0.827428i
$756$	4.57565	+	3.32440i	0.166415	+	0.120907i
$757$		−	5.55876i		−	0.202037i	−0.994885	−	0.101018i	$-0.967790\pi$
$757$		−	5.55876i		−	0.202037i	0.994885	−	0.101018i	$-0.0322101\pi$
$758$	10.0750	−	13.8670i	0.365940	−	0.503674i
$759$	−2.69682	+	8.29996i	−0.0978884	+	0.301269i
$760$	−5.87604	−	1.84899i	−0.213146	−	0.0670699i
$761$	−1.44368	−	4.44319i	−0.0523333	−	0.161065i	0.921474	−	0.388440i	$-0.126986\pi$
$761$	−1.44368	−	4.44319i	−0.0523333	−	0.161065i	−0.973807	+	0.227374i	$0.926986\pi$
$762$	19.3559	+	6.28912i	0.701191	+	0.227831i
$763$	−11.3140	−	3.67615i	−0.409596	−	0.133086i
$764$	−1.00627	−	3.09699i	−0.0364057	−	0.112045i
$765$	−0.0922559	−	9.91733i	−0.00333552	−	0.358562i
$766$	0.0155130	−	0.0477440i	0.000560506	−	0.00172506i
$767$	−13.9789	+	19.2403i	−0.504749	+	0.694727i
$768$			1.42985i			0.0515952i
$769$	7.37212	+	5.35616i	0.265846	+	0.193148i	0.712720	−	0.701449i	$-0.247463\pi$
$769$	7.37212	+	5.35616i	0.265846	+	0.193148i	−0.446875	+	0.894597i	$0.647463\pi$
$770$	6.71457	−	0.0624623i	0.241976	−	0.00225098i
$771$	−18.7152	+	13.5974i	−0.674010	+	0.489697i
$772$	14.3073	+	19.6923i	0.514931	+	0.708741i
$773$	−11.6667	+	3.79075i	−0.419623	+	0.136344i	−0.511215	−	0.859453i	$-0.670804\pi$
$773$	−11.6667	+	3.79075i	−0.419623	+	0.136344i	0.0915921	+	0.995797i	$0.470804\pi$
$774$	11.1175			0.399611
$775$	2.07941	−	6.82956i	0.0746947	−	0.245325i
$776$	−16.8021			−0.603160
$777$	4.88495	−	1.58722i	0.175246	−	0.0569410i
$778$	17.8771	+	24.6057i	0.640926	+	0.882158i
$779$	24.0896	−	17.5021i	0.863098	−	0.627078i
$780$	−3.59472	−	10.7230i	−0.128712	−	0.383944i
$781$	18.4050	+	13.3720i	0.658582	+	0.478488i
$782$			9.43429i			0.337370i
$783$	6.19146	−	8.52182i	0.221265	−	0.304545i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	−0.0862448	+	0.121058i	−0.00307821	+	0.00432075i
$786$	−7.45579	−	22.9466i	−0.265939	−	0.818477i
$787$	36.6341	+	11.9031i	1.30587	+	0.424301i	0.877618	−	0.479360i	$-0.159131\pi$
$787$	36.6341	+	11.9031i	1.30587	+	0.424301i	0.428247	+	0.903662i	$0.359131\pi$
$788$	2.53989	+	0.825259i	0.0904797	+	0.0293986i
$789$	−7.06313	−	21.7381i	−0.251454	−	0.773896i
$790$	7.50487	−	2.51590i	0.267011	−	0.0895116i
$791$	−6.18823	+	19.0454i	−0.220028	+	0.677176i
$792$	−1.68662	+	2.32144i	−0.0599315	+	0.0824886i
$793$			10.3599i			0.367890i
$794$	−16.9798	−	12.3365i	−0.602589	−	0.437807i
$795$	−11.3411	+	8.40209i	−0.402228	+	0.297991i
$796$	13.7224	−	9.96988i	0.486376	−	0.353373i
$797$	−21.9565	−	30.2205i	−0.777739	−	1.07047i	−0.995528	−	0.0944694i	$-0.969885\pi$
$797$	−21.9565	−	30.2205i	−0.777739	−	1.07047i	0.217789	−	0.975996i	$-0.430115\pi$
$798$	−3.74626	+	1.21723i	−0.132616	+	0.0430896i
$799$	34.7520			1.22944
$800$	−4.72572	+	1.63328i	−0.167079	+	0.0577452i
$801$	−2.25355			−0.0796251
$802$	−6.63774	+	2.15673i	−0.234387	+	0.0761568i
$803$	15.0105	+	20.6601i	0.529708	+	0.729081i
$804$	9.06186	−	6.58382i	0.319587	−	0.232194i
$805$	1.36415	−	4.33522i	0.0480798	−	0.152796i
$806$	−4.08601	−	2.96866i	−0.143924	−	0.104567i
$807$			9.62196i			0.338709i
$808$	6.61376	−	9.10306i	0.232671	−	0.320244i
$809$	13.9730	−	43.0046i	0.491266	−	1.51196i	−0.331431	−	0.943480i	$-0.607531\pi$
$809$	13.9730	−	43.0046i	0.491266	−	1.51196i	0.822696	−	0.568481i	$-0.192469\pi$
$810$	6.94880	+	9.37946i	0.244156	+	0.329561i
$811$	1.97262	+	6.07109i	0.0692679	+	0.213185i	0.979698	−	0.200478i	$-0.0642494\pi$
$811$	1.97262	+	6.07109i	0.0692679	+	0.213185i	−0.910430	+	0.413662i	$0.864249\pi$
$812$	1.77127	+	0.575522i	0.0621596	+	0.0201969i
$813$	−24.1132	−	7.83485i	−0.845686	−	0.274780i
$814$	3.33348	+	10.2594i	0.116839	+	0.359592i
$815$	27.0336	+	36.4899i	0.946947	+	1.27819i
$816$	2.05094	−	6.31216i	0.0717974	−	0.220970i
$817$	−18.8400	+	25.9310i	−0.659128	+	0.907212i
$818$			2.06432i			0.0721771i
$819$	2.73447	+	1.98671i	0.0955500	+	0.0694211i
$820$	7.25443	−	23.0544i	0.253336	−	0.805093i
$821$	−38.3929	+	27.8941i	−1.33992	+	0.973511i	−0.340476	+	0.940253i	$0.610588\pi$
$821$	−38.3929	+	27.8941i	−1.33992	+	0.973511i	−0.999447	+	0.0332581i	$0.989412\pi$
$822$	−2.35074	−	3.23552i	−0.0819916	−	0.112852i
$823$	−38.5735	+	12.5333i	−1.34459	+	0.436883i	−0.890868	−	0.454262i	$-0.849903\pi$
$823$	−38.5735	+	12.5333i	−1.34459	+	0.436883i	−0.453719	+	0.891145i	$0.649903\pi$
$824$	12.8831			0.448803
$825$	20.5381	+	6.25329i	0.715046	+	0.217712i
$826$	6.72336			0.233936
$827$	−18.6839	+	6.07077i	−0.649703	+	0.211101i	−0.615283	−	0.788306i	$-0.710958\pi$
$827$	−18.6839	+	6.07077i	−0.649703	+	0.211101i	−0.0344199	+	0.999407i	$0.510958\pi$
$828$	1.14155	+	1.57120i	0.0396714	+	0.0546030i
$829$	4.71482	−	3.42552i	0.163753	−	0.118973i	−0.502891	−	0.864350i	$-0.667730\pi$
$829$	4.71482	−	3.42552i	0.163753	−	0.118973i	0.666644	+	0.745377i	$0.267730\pi$
$830$	14.1883	−	10.5114i	0.492482	−	0.364856i
$831$	1.34069	+	0.974070i	0.0465081	+	0.0337901i
$832$			3.53727i			0.122633i
$833$	2.72835	−	3.75525i	0.0945318	−	0.130112i
$834$	−0.787354	+	2.42323i	−0.0272638	+	0.0839094i
$835$	−0.718970	+	0.241024i	−0.0248810	+	0.00834099i
$836$	−2.55644	−	7.86792i	−0.0884164	−	0.272118i
$837$	7.68024	+	2.49546i	0.265468	+	0.0862558i
$838$	9.14734	+	2.97215i	0.315990	+	0.102671i
$839$	1.15396	+	3.55152i	0.0398391	+	0.122612i	0.968998	−	0.247068i	$-0.0794672\pi$
$839$	1.15396	+	3.55152i	0.0398391	+	0.122612i	−0.929159	+	0.369680i	$0.879467\pi$
$840$	−1.85515	+	2.60399i	−0.0640086	+	0.0898461i
$841$	−7.88962	+	24.2818i	−0.272056	+	0.837302i
$842$	9.14145	−	12.5821i	0.315035	−	0.433609i
$843$		−	32.0529i		−	1.10396i
$844$	−8.55328	−	6.21432i	−0.294416	−	0.213906i
$845$	0.346649	+	1.03405i	0.0119251	+	0.0355722i
$846$	5.78765	−	4.20497i	0.198983	−	0.144570i
$847$	−1.16506	−	1.60357i	−0.0400320	−	0.0550993i
$848$	4.19849	−	1.36417i	0.144177	−	0.0468459i
$849$	5.59684			0.192083
$850$	23.2047	−	0.431761i	0.795916	−	0.0148093i
$851$	7.30115			0.250280
$852$	−10.3020	+	3.34732i	−0.352941	+	0.114677i
$853$	−17.0858	−	23.5165i	−0.585006	−	0.805191i	0.409227	−	0.912432i	$-0.365798\pi$
$853$	−17.0858	−	23.5165i	−0.585006	−	0.805191i	−0.994233	+	0.107241i	$0.965798\pi$
$854$	2.36943	−	1.72149i	0.0810803	−	0.0589083i
$855$	5.88592	−	0.0547537i	0.201294	−	0.00187254i
$856$	−4.19647	−	3.04891i	−0.143432	−	0.104210i
$857$		−	7.42102i		−	0.253497i	−0.991935	−	0.126749i	$-0.959546\pi$
$857$		−	7.42102i		−	0.253497i	0.991935	−	0.126749i	$-0.0404541\pi$
$858$	8.92748	−	12.2876i	0.304779	−	0.419492i
$859$	7.10394	−	21.8637i	0.242383	−	0.745979i	−0.753673	−	0.657250i	$-0.771720\pi$
$859$	7.10394	−	21.8637i	0.242383	−	0.745979i	0.996056	−	0.0887288i	$-0.0282804\pi$
$860$	0.242006	+	26.0152i	0.00825234	+	0.887111i
$861$	−4.77575	−	14.6983i	−0.162757	−	0.500915i
$862$	−24.9212	−	8.09740i	−0.848821	−	0.275799i
$863$	15.3370	+	4.98329i	0.522077	+	0.169633i	0.558188	−	0.829715i	$-0.311497\pi$
$863$	15.3370	+	4.98329i	0.522077	+	0.169633i	−0.0361107	+	0.999348i	$0.511497\pi$
$864$	−1.74774	−	5.37900i	−0.0594594	−	0.182997i
$865$	−37.8408	−	11.9072i	−1.28663	−	0.404858i
$866$	3.90718	−	12.0251i	0.132771	−	0.408628i
$867$	−3.82053	+	5.25850i	−0.129752	+	0.178588i
$868$			1.42782i			0.0484634i
$869$	8.59993	+	6.24822i	0.291733	+	0.211956i
$870$	4.84974	+	3.45508i	0.164422	+	0.117138i
$871$	22.4179	−	16.2876i	0.759602	−	0.551883i
$872$	6.99246	+	9.62429i	0.236794	+	0.325920i
$873$	15.2692	−	4.96127i	0.516785	−	0.167914i
$874$	−5.59924			−0.189397
$875$	−10.7254	−	3.15687i	−0.362585	−	0.106722i
$876$	−12.1594			−0.410829
$877$	−1.41953	+	0.461235i	−0.0479343	+	0.0155748i	−0.332886	−	0.942967i	$-0.608022\pi$
$877$	−1.41953	+	0.461235i	−0.0479343	+	0.0155748i	0.284952	+	0.958542i	$0.408022\pi$
$878$	−18.5159	−	25.4850i	−0.624883	−	0.860078i
$879$	17.8017	−	12.9337i	0.600437	−	0.436243i
$880$	−5.46892	−	3.89619i	−0.184357	−	0.131341i
$881$	26.4459	+	19.2141i	0.890986	+	0.647339i	0.936135	−	0.351641i	$-0.114376\pi$
$881$	26.4459	+	19.2141i	0.890986	+	0.647339i	−0.0451489	+	0.998980i	$0.514376\pi$
$882$		−	0.955535i		−	0.0321745i
$883$	−28.9284	+	39.8165i	−0.973517	+	1.33993i	−0.0332671	+	0.999446i	$0.510591\pi$
$883$	−28.9284	+	39.8165i	−0.973517	+	1.33993i	−0.940250	+	0.340485i	$0.889409\pi$
$884$	5.07379	−	15.6155i	0.170650	−	0.525206i
$885$	20.5050	+	6.45222i	0.689267	+	0.216889i
$886$	0.593399	+	1.82630i	0.0199356	+	0.0613556i
$887$	−15.5583	−	5.05521i	−0.522398	−	0.169737i	0.0359352	−	0.999354i	$-0.488559\pi$
$887$	−15.5583	−	5.05521i	−0.522398	−	0.169737i	−0.558333	+	0.829617i	$0.688559\pi$
$888$	−4.88495	−	1.58722i	−0.163928	−	0.0532635i
$889$	−4.39845	−	13.5371i	−0.147519	−	0.454018i
$890$	−0.0490552	−	5.27334i	−0.00164433	−	0.176763i
$891$	−4.84433	+	14.9093i	−0.162291	+	0.499481i
$892$	2.93598	−	4.04102i	0.0983037	−	0.135304i
$893$			20.6252i			0.690197i
$894$	−24.2373	−	17.6095i	−0.810618	−	0.588948i
$895$	−11.8778	+	0.110493i	−0.397032	+	0.00369339i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−6.04233	−	8.31655i	−0.201747	−	0.277681i
$898$	30.0551	−	9.76550i	1.00295	−	0.325879i
$899$	2.65921			0.0886897
$900$	3.81231	−	2.87967i	0.127077	−	0.0959889i
$901$	−20.4913			−0.682663
$902$	30.8694	−	10.0301i	1.02784	−	0.333965i
$903$	9.77844	+	13.4589i	0.325406	+	0.447883i
$904$	16.2010	−	11.7707i	0.538837	−	0.391488i
$905$	13.4453	+	40.1070i	0.446937	+	1.33320i
$906$	−20.2704	−	14.7273i	−0.673440	−	0.489282i
$907$		−	5.25971i		−	0.174646i	−0.996180	−	0.0873228i	$-0.972169\pi$
$907$		−	5.25971i		−	0.174646i	0.996180	−	0.0873228i	$-0.0278312\pi$
$908$	15.3054	−	21.0660i	0.507927	−	0.699101i
$909$	−3.32245	+	10.2255i	−0.110199	+	0.339157i
$910$	−4.58941	+	6.44195i	−0.152137	+	0.213549i
$911$	12.9960	+	39.9976i	0.430577	+	1.32518i	0.897552	+	0.440908i	$0.145344\pi$
$911$	12.9960	+	39.9976i	0.430577	+	1.32518i	−0.466976	+	0.884270i	$0.654656\pi$
$912$	3.74626	+	1.21723i	0.124051	+	0.0403066i
$913$	22.5533	+	7.32800i	0.746404	+	0.242521i
$914$	−12.2525	−	37.7093i	−0.405277	−	1.24731i
$915$	8.87840	−	2.97635i	0.293511	−	0.0983952i
$916$	−4.23246	+	13.0262i	−0.139844	+	0.430397i
$917$	−9.91837	+	13.6515i	−0.327534	+	0.450811i
$918$			26.2529i			0.866474i
$919$	4.95998	+	3.60364i	0.163615	+	0.118873i	0.666580	−	0.745434i	$-0.267758\pi$
$919$	4.95998	+	3.60364i	0.163615	+	0.118873i	−0.502965	+	0.864307i	$0.667758\pi$
$920$	−3.65179	+	2.70544i	−0.120396	+	0.0891957i
$921$	25.0518	−	18.2012i	0.825484	−	0.599749i
$922$	−24.8684	−	34.2284i	−0.818996	−	1.12725i
$923$	−25.4859	+	8.28087i	−0.838878	+	0.272568i
$924$	−4.29380			−0.141256
$925$	−0.334138	−	17.9580i	−0.0109864	−	0.590456i
$926$	41.6933			1.37013
$927$	−11.7077	+	3.80407i	−0.384532	+	0.124942i
$928$	−1.09471	−	1.50674i	−0.0359356	−	0.0494610i
$929$	10.1238	−	7.35534i	0.332150	−	0.241321i	−0.409193	−	0.912448i	$-0.634190\pi$
$929$	10.1238	−	7.35534i	0.332150	−	0.241321i	0.741342	+	0.671127i	$0.234190\pi$
$930$	−1.37024	+	4.35458i	−0.0449319	+	0.142792i
$931$	2.22874	+	1.61927i	0.0730440	+	0.0530695i
$932$			15.2236i			0.498667i
$933$	−9.60874	+	13.2253i	−0.314576	+	0.432977i
$934$	10.0894	−	31.0520i	0.330135	−	1.01605i
$935$	18.5543	+	25.0445i	0.606790	+	0.819043i
$936$	−1.04447	−	3.21456i	−0.0341397	−	0.105071i
$937$	−39.8593	−	12.9511i	−1.30215	−	0.423093i	−0.425818	−	0.904809i	$-0.640014\pi$
$937$	−39.8593	−	12.9511i	−1.30215	−	0.423093i	−0.876327	+	0.481716i	$0.840014\pi$
$938$	−7.45034	−	2.42076i	−0.243262	−	0.0790407i
$939$	−13.8156	−	42.5202i	−0.450856	−	1.38759i
$940$	9.96570	+	13.4517i	0.325045	+	0.438745i
$941$	−10.1275	+	31.1693i	−0.330148	+	1.01609i	0.638915	+	0.769277i	$0.279384\pi$
$941$	−10.1275	+	31.1693i	−0.330148	+	1.01609i	−0.969063	+	0.246813i	$0.920616\pi$
$942$	0.0558667	−	0.0768939i	0.00182023	−	0.00250534i
$943$		−	21.9684i		−	0.715388i
$944$	−5.43931	−	3.95189i	−0.177035	−	0.128623i
$945$	3.79602	−	12.0636i	0.123484	−	0.392430i
$946$	−28.2664	+	20.5368i	−0.919020	+	0.667707i
$947$	10.2420	+	14.0969i	0.332820	+	0.458087i	0.942327	−	0.334693i	$-0.108633\pi$
$947$	10.2420	+	14.0969i	0.332820	+	0.458087i	−0.609507	+	0.792780i	$0.708633\pi$
$948$	−4.81372	+	1.56407i	−0.156343	+	0.0507988i
$949$	−30.0810			−0.976469
$950$	0.256250	+	13.7720i	0.00831383	+	0.446822i
$951$	−31.2465			−1.01324
$952$	−4.41457	+	1.43438i	−0.143077	+	0.0464885i
$953$	−9.94444	−	13.6873i	−0.322132	−	0.443377i	0.616985	−	0.786975i	$-0.288354\pi$
$953$	−9.94444	−	13.6873i	−0.322132	−	0.443377i	−0.939117	+	0.343599i	$0.888354\pi$
$954$	−3.41265	+	2.47943i	−0.110489	+	0.0802747i
$955$	−5.85075	+	4.33454i	−0.189326	+	0.140263i
$956$	17.0224	+	12.3675i	0.550545	+	0.399994i
$957$			7.99690i			0.258503i
$958$	17.8914	−	24.6253i	0.578043	−	0.795608i
$959$	−0.864329	+	2.66013i	−0.0279106	+	0.0859001i
$960$	3.03143	−	1.01624i	0.0978390	−	0.0327991i
$961$	−8.94954	−	27.5439i	−0.288695	−	0.888512i
$962$	−12.0848	−	3.92658i	−0.389628	−	0.126598i
$963$	4.71389	+	1.53164i	0.151903	+	0.0493563i
$964$	1.40903	+	4.33654i	0.0453817	+	0.139671i
$965$	31.5811	−	44.3290i	1.01663	−	1.42700i
$966$	−0.898048	+	2.76391i	−0.0288942	+	0.0889273i
$967$	22.9732	−	31.6199i	0.738767	−	1.01683i	−0.259921	−	0.965630i	$-0.583697\pi$
$967$	22.9732	−	31.6199i	0.738767	−	1.01683i	0.998689	−	0.0511961i	$-0.0163034\pi$
$968$			1.98212i			0.0637078i
$969$	−14.7921	−	10.7471i	−0.475192	−	0.345247i
$970$	11.9418	+	35.6223i	0.383430	+	1.14376i
$971$	−25.1254	+	18.2547i	−0.806313	+	0.585821i	−0.912759	−	0.408498i	$-0.866053\pi$
$971$	−25.1254	+	18.2547i	−0.806313	+	0.585821i	0.106446	+	0.994318i	$0.466053\pi$
$972$	5.58581	+	7.68820i	0.179165	+	0.246599i
$973$	1.69474	−	0.550656i	0.0543310	−	0.0176532i
$974$	30.8412			0.988217
$975$	−20.1790	+	15.2424i	−0.646245	+	0.488148i
$976$	−2.92878			−0.0937480
$977$	−28.4578	+	9.24651i	−0.910447	+	0.295822i	−0.726542	−	0.687122i	$-0.758874\pi$
$977$	−28.4578	+	9.24651i	−0.910447	+	0.295822i	−0.183905	+	0.982944i	$0.558874\pi$
$978$	−17.0688	−	23.4932i	−0.545799	−	0.751229i
$979$	5.72967	−	4.16285i	0.183121	−	0.133045i
$980$	2.23597	−	0.0208001i	0.0714255	−	0.000664435i
$981$	−9.19635	−	6.68154i	−0.293617	−	0.213325i
$982$			3.71449i			0.118534i
$983$	−10.4031	+	14.3186i	−0.331807	+	0.456694i	−0.942026	−	0.335539i	$-0.891082\pi$
$983$	−10.4031	+	14.3186i	−0.331807	+	0.456694i	0.610219	+	0.792233i	$0.291082\pi$
$984$	−4.77575	+	14.6983i	−0.152246	+	0.468563i
$985$	−0.0555486	−	5.97137i	−0.00176993	−	0.190264i
$986$	2.67143	+	8.22181i	0.0850756	+	0.261836i
$987$	10.1811	+	3.30803i	0.324067	+	0.105296i
$988$	9.26778	+	3.01128i	0.294847	+	0.0958017i
$989$	7.30753	+	22.4903i	0.232366	+	0.715149i
$990$	6.12043	+	1.92589i	0.194520	+	0.0612089i
$991$	−2.01881	+	6.21326i	−0.0641296	+	0.197371i	−0.977987	−	0.208664i	$-0.933089\pi$
$991$	−2.01881	+	6.21326i	−0.0641296	+	0.197371i	0.913858	+	0.406034i	$0.133089\pi$
$992$	0.839252	−	1.15513i	0.0266463	−	0.0366755i
$993$			4.65016i			0.147568i
$994$	6.12891	+	4.45291i	0.194397	+	0.141238i
$995$	−30.8902	−	22.0069i	−0.979285	−	0.697667i
$996$	−9.13478	+	6.63681i	−0.289447	+	0.210295i
$997$	−15.6397	−	21.5262i	−0.495315	−	0.681743i	0.486042	−	0.873935i	$-0.338440\pi$
$997$	−15.6397	−	21.5262i	−0.495315	−	0.681743i	−0.981357	+	0.192193i	$0.938440\pi$
$998$	−36.3345	+	11.8058i	−1.15015	+	0.373706i
$999$	20.3170			0.642800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.169.1	yes	24
25.2	odd	20		8750.2.a.z.1.8		12
25.4	even	10	inner	350.2.m.a.29.1	✓	24
25.23	odd	20		8750.2.a.bb.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.29.1	✓	24	25.4	even	10	inner
350.2.m.a.169.1	yes	24	1.1	even	1	trivial
8750.2.a.z.1.8		12	25.2	odd	20
8750.2.a.bb.1.5		12	25.23	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.840443 - 1.15677i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.82116 - 1.29744i) q^{5} +(1.15677 + 0.840443i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.295277 - 0.908768i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.840443 - 1.15677i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.82116 - 1.29744i) q^{5} +(1.15677 + 0.840443i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.295277 - 0.908768i) q^{9} +(2.13296 + 0.671171i) q^{10} +(0.927971 + 2.85600i) q^{11} +(-1.35987 - 0.441847i) q^{12} +(-3.36414 - 1.09308i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.0297410 + 3.19710i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.72835 + 3.75525i) q^{17} +0.955535i q^{18} +(-2.22874 - 1.61927i) q^{19} +(-2.23597 + 0.0208001i) q^{20} +(-1.15677 + 0.840443i) q^{21} +(-1.76511 - 2.42946i) q^{22} +(-1.93301 + 0.628073i) q^{23} +1.42985 q^{24} +(1.63328 + 4.72572i) q^{25} +3.53727 q^{26} +(-5.37900 + 1.74774i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-1.50674 + 1.09471i) q^{29} +(-1.01624 - 3.03143i) q^{30} +(-1.15513 - 0.839252i) q^{31} +1.00000i q^{32} +(2.52383 - 3.47376i) q^{33} +(1.43438 - 4.41457i) q^{34} +(-1.29744 + 1.82116i) q^{35} +(-0.295277 - 0.908768i) q^{36} +(-3.41641 - 1.11006i) q^{37} +(2.62004 + 0.851302i) q^{38} +(1.56293 + 4.81021i) q^{39} +(2.12011 - 0.710735i) q^{40} +(-3.34004 + 10.2796i) q^{41} +(0.840443 - 1.15677i) q^{42} -11.6349i q^{43} +(2.42946 + 1.76511i) q^{44} +(-1.71682 + 1.27191i) q^{45} +(1.64432 - 1.19467i) q^{46} +(-4.40064 - 6.05697i) q^{47} +(-1.35987 + 0.441847i) q^{48} -1.00000 q^{49} +(-3.01367 - 3.98971i) q^{50} +6.63700 q^{51} +(-3.36414 + 1.09308i) q^{52} +(2.59481 + 3.57145i) q^{53} +(4.57565 - 3.32440i) q^{54} +(2.01551 - 6.40524i) q^{55} +(0.809017 + 0.587785i) q^{56} +3.93905i q^{57} +(1.09471 - 1.50674i) q^{58} +(2.07763 - 6.39429i) q^{59} +(1.90327 + 2.56903i) q^{60} +(-0.905043 - 2.78544i) q^{61} +(1.35794 + 0.441221i) q^{62} +(-0.908768 - 0.295277i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(4.70845 + 6.35546i) q^{65} +(-1.32686 + 4.08365i) q^{66} +(-4.60456 + 6.33764i) q^{67} +4.64175i q^{68} +(2.35112 + 1.70819i) q^{69} +(0.671171 - 2.13296i) q^{70} +(6.12891 - 4.45291i) q^{71} +(0.561650 + 0.773044i) q^{72} +(8.08779 - 2.62788i) q^{73} +3.59223 q^{74} +(4.09389 - 5.86103i) q^{75} -2.75487 q^{76} +(2.85600 - 0.927971i) q^{77} +(-2.97287 - 4.09181i) q^{78} +(2.86380 - 2.08067i) q^{79} +(-1.79671 + 1.33110i) q^{80} +(4.22335 + 3.06844i) q^{81} -10.8086i q^{82} +(4.64162 - 6.38864i) q^{83} +(-0.441847 + 1.35987i) q^{84} +(9.84101 - 3.29906i) q^{85} +(3.59537 + 11.0654i) q^{86} +(2.53265 + 0.822909i) q^{87} +(-2.85600 - 0.927971i) q^{88} +(-0.728789 - 2.24298i) q^{89} +(1.23975 - 1.74019i) q^{90} +(-1.09308 + 3.36414i) q^{91} +(-1.19467 + 1.64432i) q^{92} +2.04157i q^{93} +(6.05697 + 4.40064i) q^{94} +(1.95798 + 5.84063i) q^{95} +(1.15677 - 0.840443i) q^{96} +(9.87603 + 13.5932i) q^{97} +(0.951057 - 0.309017i) q^{98} +2.86945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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