LMFDB - Embedded newform 961.2.c.k.439.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(439,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("961.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.12
Character	$\chi$	$=$	961.439
Dual form			961.2.c.k.521.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.49624 q^{2} +(1.23653 - 2.14173i) q^{3} +4.23120 q^{4} +(0.574589 + 0.995217i) q^{5} +(3.08667 - 5.34626i) q^{6} +(-0.132518 + 0.229528i) q^{7} +5.56961 q^{8} +(-1.55800 - 2.69853i) q^{9} +(1.43431 + 2.48430i) q^{10} +(0.145816 + 0.252560i) q^{11} +(5.23200 - 9.06208i) q^{12} +(-2.26183 - 3.91761i) q^{13} +(-0.330796 + 0.572956i) q^{14} +2.84198 q^{15} +5.44066 q^{16} +(-2.74837 + 4.76032i) q^{17} +(-3.88914 - 6.73618i) q^{18} +(-3.47532 + 6.01943i) q^{19} +(2.43120 + 4.21096i) q^{20} +(0.327724 + 0.567635i) q^{21} +(0.363991 + 0.630451i) q^{22} +2.96754 q^{23} +(6.88697 - 11.9286i) q^{24} +(1.83970 - 3.18645i) q^{25} +(-5.64607 - 9.77928i) q^{26} -0.286873 q^{27} +(-0.560710 + 0.971178i) q^{28} -3.32720 q^{29} +7.09426 q^{30} +2.44197 q^{32} +0.721221 q^{33} +(-6.86059 + 11.8829i) q^{34} -0.304573 q^{35} +(-6.59221 - 11.4180i) q^{36} +(2.03890 - 3.53147i) q^{37} +(-8.67523 + 15.0259i) q^{38} -11.1873 q^{39} +(3.20024 + 5.54297i) q^{40} +(-3.74951 - 6.49435i) q^{41} +(0.818077 + 1.41695i) q^{42} +(-4.02899 + 6.97841i) q^{43} +(0.616976 + 1.06863i) q^{44} +(1.79042 - 3.10110i) q^{45} +7.40767 q^{46} +5.51798 q^{47} +(6.72753 - 11.6524i) q^{48} +(3.46488 + 6.00134i) q^{49} +(4.59232 - 7.95413i) q^{50} +(6.79688 + 11.7725i) q^{51} +(-9.57027 - 16.5762i) q^{52} +(2.37626 + 4.11580i) q^{53} -0.716103 q^{54} +(-0.167568 + 0.290237i) q^{55} +(-0.738073 + 1.27838i) q^{56} +(8.59466 + 14.8864i) q^{57} -8.30549 q^{58} +(1.17631 - 2.03743i) q^{59} +12.0250 q^{60} -10.0530 q^{61} +0.825852 q^{63} -4.78559 q^{64} +(2.59925 - 4.50203i) q^{65} +1.80034 q^{66} +(1.79343 + 3.10631i) q^{67} +(-11.6289 + 20.1419i) q^{68} +(3.66944 - 6.35566i) q^{69} -0.760287 q^{70} +(-5.43953 - 9.42153i) q^{71} +(-8.67745 - 15.0298i) q^{72} +(1.13718 + 1.96965i) q^{73} +(5.08957 - 8.81540i) q^{74} +(-4.54967 - 7.88025i) q^{75} +(-14.7048 + 25.4694i) q^{76} -0.0772929 q^{77} -27.9261 q^{78} +(1.89710 - 3.28588i) q^{79} +(3.12614 + 5.41464i) q^{80} +(4.31927 - 7.48120i) q^{81} +(-9.35967 - 16.2114i) q^{82} +(-1.39668 - 2.41913i) q^{83} +(1.38667 + 2.40178i) q^{84} -6.31674 q^{85} +(-10.0573 + 17.4198i) q^{86} +(-4.11418 + 7.12597i) q^{87} +(0.812137 + 1.40666i) q^{88} -3.20180 q^{89} +(4.46931 - 7.74107i) q^{90} +1.19893 q^{91} +12.5562 q^{92} +13.7742 q^{94} -7.98753 q^{95} +(3.01956 - 5.23004i) q^{96} +2.01686 q^{97} +(8.64916 + 14.9808i) q^{98} +(0.454362 - 0.786978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 32 q^{4} - 8 q^{5} - 8 q^{7} + 24 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} - 32 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} - 12 q^{25} + 20 q^{28} + 48 q^{32} - 80 q^{33} + 112 q^{35} - 40 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) $ 24 * q + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.49624			1.76511			0.882553	−	0.470213i	$-0.155823\pi$
$2$	2.49624			1.76511			0.882553	+	0.470213i	$0.155823\pi$
$3$	1.23653	−	2.14173i	0.713909	−	1.23653i	−0.249469	−	0.968383i	$-0.580256\pi$
$3$	1.23653	−	2.14173i	0.713909	−	1.23653i	0.963379	−	0.268145i	$-0.0864105\pi$
$4$	4.23120			2.11560
$5$	0.574589	+	0.995217i	0.256964	+	0.445075i	0.965427	−	0.260673i	$-0.0839445\pi$
$5$	0.574589	+	0.995217i	0.256964	+	0.445075i	−0.708463	+	0.705748i	$0.750611\pi$
$6$	3.08667	−	5.34626i	1.26013	−	2.18260i
$7$	−0.132518	+	0.229528i	−0.0500871	+	0.0867534i	−0.889982	−	0.455996i	$-0.849283\pi$
$7$	−0.132518	+	0.229528i	−0.0500871	+	0.0867534i	0.839895	+	0.542749i	$0.182617\pi$
$8$	5.56961			1.96915
$9$	−1.55800	−	2.69853i	−0.519333	−	0.899512i
$10$	1.43431	+	2.48430i	0.453569	+	0.785604i
$11$	0.145816	+	0.252560i	0.0439651	+	0.0761499i	0.887171	−	0.461442i	$-0.152668\pi$
$11$	0.145816	+	0.252560i	0.0439651	+	0.0761499i	−0.843205	+	0.537591i	$0.819334\pi$
$12$	5.23200	−	9.06208i	1.51035	−	2.61600i
$13$	−2.26183	−	3.91761i	−0.627319	−	1.08655i	−0.988087	−	0.153893i	$-0.950819\pi$
$13$	−2.26183	−	3.91761i	−0.627319	−	1.08655i	0.360768	−	0.932656i	$-0.382515\pi$
$14$	−0.330796	+	0.572956i	−0.0884090	+	0.153129i
$15$	2.84198			0.733796
$16$	5.44066			1.36017
$17$	−2.74837	+	4.76032i	−0.666578	+	1.15455i	0.312276	+	0.949991i	$0.398909\pi$
$17$	−2.74837	+	4.76032i	−0.666578	+	1.15455i	−0.978855	+	0.204556i	$0.934425\pi$
$18$	−3.88914	−	6.73618i	−0.916678	−	1.58773i
$19$	−3.47532	+	6.01943i	−0.797294	+	1.38095i	0.124079	+	0.992272i	$0.460402\pi$
$19$	−3.47532	+	6.01943i	−0.797294	+	1.38095i	−0.921373	+	0.388681i	$0.872931\pi$
$20$	2.43120	+	4.21096i	0.543633	+	0.941600i
$21$	0.327724	+	0.567635i	0.0715153	+	0.123868i
$22$	0.363991	+	0.630451i	0.0776031	+	0.134413i
$23$	2.96754			0.618774			0.309387	−	0.950936i	$-0.399876\pi$
$23$	2.96754			0.618774			0.309387	+	0.950936i	$0.399876\pi$
$24$	6.88697	−	11.9286i	1.40580	−	2.43491i
$25$	1.83970	−	3.18645i	0.367939	−	0.637289i
$26$	−5.64607	−	9.77928i	−1.10729	−	1.91787i
$27$	−0.286873			−0.0552087
$28$	−0.560710	+	0.971178i	−0.105964	+	0.183535i
$29$	−3.32720			−0.617846			−0.308923	−	0.951087i	$-0.599969\pi$
$29$	−3.32720			−0.617846			−0.308923	+	0.951087i	$0.599969\pi$
$30$	7.09426			1.29523
$31$		0			0
$31$		0			0
$32$	2.44197			0.431684
$33$	0.721221			0.125548
$34$	−6.86059	+	11.8829i	−1.17658	+	2.03790i
$35$	−0.304573			−0.0514823
$36$	−6.59221	−	11.4180i	−1.09870	−	1.90301i
$37$	2.03890	−	3.53147i	0.335193	−	0.580571i	−0.648329	−	0.761360i	$-0.724532\pi$
$37$	2.03890	−	3.53147i	0.335193	−	0.580571i	0.983522	+	0.180789i	$0.0578652\pi$
$38$	−8.67523	+	15.0259i	−1.40731	+	2.43753i
$39$	−11.1873			−1.79140
$40$	3.20024	+	5.54297i	0.506002	+	0.876421i
$41$	−3.74951	−	6.49435i	−0.585575	−	1.01425i	−0.994803	−	0.101814i	$-0.967535\pi$
$41$	−3.74951	−	6.49435i	−0.585575	−	1.01425i	0.409228	−	0.912432i	$-0.365798\pi$
$42$	0.818077	+	1.41695i	0.126232	+	0.218640i
$43$	−4.02899	+	6.97841i	−0.614415	+	1.06420i	0.376072	+	0.926590i	$0.377274\pi$
$43$	−4.02899	+	6.97841i	−0.614415	+	1.06420i	−0.990487	+	0.137607i	$0.956059\pi$
$44$	0.616976	+	1.06863i	0.0930127	+	0.161103i
$45$	1.79042	−	3.10110i	0.266900	−	0.462284i
$46$	7.40767			1.09220
$47$	5.51798			0.804880			0.402440	−	0.915446i	$-0.368162\pi$
$47$	5.51798			0.804880			0.402440	+	0.915446i	$0.368162\pi$
$48$	6.72753	−	11.6524i	0.971035	−	1.68188i
$49$	3.46488	+	6.00134i	0.494983	+	0.857335i
$50$	4.59232	−	7.95413i	0.649452	−	1.12488i
$51$	6.79688	+	11.7725i	0.951753	+	1.64849i
$52$	−9.57027	−	16.5762i	−1.32716	−	2.29870i
$53$	2.37626	+	4.11580i	0.326404	+	0.565349i	0.981796	−	0.189941i	$-0.0608296\pi$
$53$	2.37626	+	4.11580i	0.326404	+	0.565349i	−0.655391	+	0.755289i	$0.727496\pi$
$54$	−0.716103			−0.0974492
$55$	−0.167568	+	0.290237i	−0.0225949	+	0.0391355i
$56$	−0.738073	+	1.27838i	−0.0986292	+	0.170831i
$57$	8.59466	+	14.8864i	1.13839	+	1.97175i
$58$	−8.30549			−1.09056
$59$	1.17631	−	2.03743i	0.153143	−	0.265251i	−0.779239	−	0.626727i	$-0.784394\pi$
$59$	1.17631	−	2.03743i	0.153143	−	0.265251i	0.932381	+	0.361477i	$0.117727\pi$
$60$	12.0250			1.55242
$61$	−10.0530			−1.28716			−0.643580	−	0.765379i	$-0.722551\pi$
$61$	−10.0530			−1.28716			−0.643580	+	0.765379i	$0.722551\pi$
$62$		0			0
$63$	0.825852			0.104048
$64$	−4.78559			−0.598199
$65$	2.59925	−	4.50203i	0.322397	−	0.558408i
$66$	1.80034			0.221606
$67$	1.79343	+	3.10631i	0.219102	+	0.379496i	0.954534	−	0.298103i	$-0.0963539\pi$
$67$	1.79343	+	3.10631i	0.219102	+	0.379496i	−0.735432	+	0.677599i	$0.763021\pi$
$68$	−11.6289	+	20.1419i	−1.41021	+	2.44256i
$69$	3.66944	−	6.35566i	0.441749	−	0.765131i
$70$	−0.760287			−0.0908717
$71$	−5.43953	−	9.42153i	−0.645553	−	1.11813i	−0.984174	−	0.177207i	$-0.943294\pi$
$71$	−5.43953	−	9.42153i	−0.645553	−	1.11813i	0.338621	−	0.940923i	$-0.390040\pi$
$72$	−8.67745	−	15.0298i	−1.02265	−	1.77128i
$73$	1.13718	+	1.96965i	0.133096	+	0.230530i	0.924869	−	0.380287i	$-0.124175\pi$
$73$	1.13718	+	1.96965i	0.133096	+	0.230530i	−0.791772	+	0.610816i	$0.790841\pi$
$74$	5.08957	−	8.81540i	0.591651	−	1.02477i
$75$	−4.54967	−	7.88025i	−0.525350	−	0.909933i
$76$	−14.7048	+	25.4694i	−1.68675	+	2.92155i
$77$	−0.0772929			−0.00880834
$78$	−27.9261			−3.16201
$79$	1.89710	−	3.28588i	0.213441	−	0.369690i	−0.739348	−	0.673323i	$-0.764866\pi$
$79$	1.89710	−	3.28588i	0.213441	−	0.369690i	0.952789	+	0.303633i	$0.0981996\pi$
$80$	3.12614	+	5.41464i	0.349514	+	0.605375i
$81$	4.31927	−	7.48120i	0.479919	−	0.831244i
$82$	−9.35967	−	16.2114i	−1.03360	−	1.79025i
$83$	−1.39668	−	2.41913i	−0.153306	−	0.265534i	0.779135	−	0.626856i	$-0.215659\pi$
$83$	−1.39668	−	2.41913i	−0.153306	−	0.265534i	−0.932441	+	0.361323i	$0.882325\pi$
$84$	1.38667	+	2.40178i	0.151298	+	0.262055i
$85$	−6.31674			−0.685147
$86$	−10.0573	+	17.4198i	−1.08451	+	1.87842i
$87$	−4.11418	+	7.12597i	−0.441086	+	0.763984i
$88$	0.812137	+	1.40666i	0.0865741	+	0.149951i
$89$	−3.20180			−0.339390			−0.169695	−	0.985497i	$-0.554278\pi$
$89$	−3.20180			−0.339390			−0.169695	+	0.985497i	$0.554278\pi$
$90$	4.46931	−	7.74107i	0.471107	−	0.815981i
$91$	1.19893			0.125682
$92$	12.5562			1.30908
$93$		0			0
$94$	13.7742			1.42070
$95$	−7.98753			−0.819503
$96$	3.01956	−	5.23004i	0.308183	−	0.533789i
$97$	2.01686			0.204781			0.102391	−	0.994744i	$-0.467351\pi$
$97$	2.01686			0.204781			0.102391	+	0.994744i	$0.467351\pi$
$98$	8.64916	+	14.9808i	0.873697	+	1.51329i
$99$	0.454362	−	0.786978i	0.0456651	−	0.0790943i
$100$	7.78412	−	13.4825i	0.778412	−	1.34825i
$101$	10.8619			1.08080			0.540402	−	0.841407i	$-0.318272\pi$
$101$	10.8619			1.08080			0.540402	+	0.841407i	$0.318272\pi$
$102$	16.9666	+	29.3871i	1.67995	+	2.90975i
$103$	2.00671	+	3.47572i	0.197727	+	0.342473i	0.947791	−	0.318892i	$-0.103311\pi$
$103$	2.00671	+	3.47572i	0.197727	+	0.342473i	−0.750064	+	0.661365i	$0.769977\pi$
$104$	−12.5975	−	21.8195i	−1.23529	−	2.13958i
$105$	−0.376613	+	0.652313i	−0.0367537	+	0.0636593i
$106$	5.93171	+	10.2740i	0.576138	+	0.997901i
$107$	9.02679	−	15.6349i	0.872653	−	1.51148i	0.0134107	−	0.999910i	$-0.495731\pi$
$107$	9.02679	−	15.6349i	0.872653	−	1.51148i	0.859242	−	0.511569i	$-0.170936\pi$
$108$	−1.21382			−0.116800
$109$	0.261393			0.0250370			0.0125185	−	0.999922i	$-0.496015\pi$
$109$	0.261393			0.0250370			0.0125185	+	0.999922i	$0.496015\pi$
$110$	−0.418290	+	0.724500i	−0.0398824	+	0.0690784i
$111$	−5.04231	−	8.73353i	−0.478594	−	0.828950i
$112$	−0.720986	+	1.24878i	−0.0681267	+	0.117999i
$113$	1.40023	+	2.42527i	0.131722	+	0.228150i	0.924341	−	0.381568i	$-0.124616\pi$
$113$	1.40023	+	2.42527i	0.131722	+	0.228150i	−0.792618	+	0.609718i	$0.791283\pi$
$114$	21.4543	+	37.1600i	2.00938	+	3.48035i
$115$	1.70511	+	2.95334i	0.159003	+	0.275401i
$116$	−14.0781			−1.30712
$117$	−7.04787	+	12.2073i	−0.651575	+	1.12856i
$118$	2.93635	−	5.08591i	0.270313	−	0.468196i
$119$	−0.728418	−	1.26166i	−0.0667739	−	0.115656i
$120$	15.8287			1.44496
$121$	5.45748	−	9.45262i	0.496134	−	0.859330i
$122$	−25.0948			−2.27197
$123$	−18.5455			−1.67219
$124$		0			0
$125$	9.97416			0.892116
$126$	2.06152			0.183655
$127$	−2.82659	+	4.89579i	−0.250819	+	0.434431i	−0.963752	−	0.266801i	$-0.914033\pi$
$127$	−2.82659	+	4.89579i	−0.250819	+	0.434431i	0.712932	+	0.701233i	$0.247367\pi$
$128$	−16.8299			−1.48757
$129$	9.96390	+	17.2580i	0.877273	+	1.51948i
$130$	6.48834	−	11.2381i	0.569065	−	0.985649i
$131$	−3.18315	+	5.51338i	−0.278113	+	0.481707i	−0.970916	−	0.239421i	$-0.923042\pi$
$131$	−3.18315	+	5.51338i	−0.278113	+	0.481707i	0.692802	+	0.721127i	$0.256376\pi$
$132$	3.05163			0.265611
$133$	−0.921085	−	1.59537i	−0.0798682	−	0.138336i
$134$	4.47682	+	7.75408i	0.386738	+	0.669851i
$135$	−0.164834	−	0.285501i	−0.0141866	−	0.0245720i
$136$	−15.3074	+	26.5131i	−1.31260	+	2.27348i
$137$	−1.48144	−	2.56593i	−0.126568	−	0.219223i	0.795777	−	0.605590i	$-0.207063\pi$
$137$	−1.48144	−	2.56593i	−0.126568	−	0.219223i	−0.922345	+	0.386368i	$0.873730\pi$
$138$	9.15979	−	15.8652i	0.779733	−	1.35054i
$139$	−12.8063			−1.08622			−0.543110	−	0.839662i	$-0.682753\pi$
$139$	−12.8063			−1.08622			−0.543110	+	0.839662i	$0.682753\pi$
$140$	−1.28871			−0.108916
$141$	6.82313	−	11.8180i	0.574611	−	0.995256i
$142$	−13.5783	−	23.5184i	−1.13947	−	1.97362i
$143$	0.659622	−	1.14250i	0.0551604	−	0.0955405i
$144$	−8.47655	−	14.6818i	−0.706379	−	1.22349i
$145$	−1.91177	−	3.31129i	−0.158764	−	0.274988i
$146$	2.83866	+	4.91671i	0.234929	+	0.406910i
$147$	17.1377			1.41349
$148$	8.62699	−	14.9424i	0.709134	−	1.22826i
$149$	−8.72673	+	15.1151i	−0.714921	+	1.23828i	0.248069	+	0.968742i	$0.420204\pi$
$149$	−8.72673	+	15.1151i	−0.714921	+	1.23828i	−0.962990	+	0.269537i	$0.913129\pi$
$150$	−11.3570	−	19.6710i	−0.927299	−	1.60613i
$151$	21.6910			1.76519			0.882594	−	0.470136i	$-0.155795\pi$
$151$	21.6910			1.76519			0.882594	+	0.470136i	$0.155795\pi$
$152$	−19.3562	+	33.5259i	−1.56999	+	2.71931i
$153$	17.1279			1.38471
$154$	−0.192941			−0.0155477
$155$		0			0
$156$	−47.3356			−3.78988
$157$	−14.5323			−1.15981			−0.579904	−	0.814685i	$-0.696910\pi$
$157$	−14.5323			−1.15981			−0.579904	+	0.814685i	$0.696910\pi$
$158$	4.73562	−	8.20234i	0.376746	−	0.652543i
$159$	11.7532			0.932092
$160$	1.40313	+	2.43029i	0.110927	+	0.192131i
$161$	−0.393252	+	0.681132i	−0.0309926	+	0.0536807i
$162$	10.7819	−	18.6749i	0.847109	−	1.46724i
$163$	0.0686335			0.00537579			0.00268789	−	0.999996i	$-0.499144\pi$
$163$	0.0686335			0.00537579			0.00268789	+	0.999996i	$0.499144\pi$
$164$	−15.8649	−	27.4789i	−1.23884	−	2.14574i
$165$	0.414406	+	0.717772i	0.0322614	+	0.0558784i
$166$	−3.48645	−	6.03871i	−0.270601	−	0.468695i
$167$	−2.42831	+	4.20595i	−0.187908	+	0.325466i	−0.944553	−	0.328360i	$-0.893504\pi$
$167$	−2.42831	+	4.20595i	−0.187908	+	0.325466i	0.756644	+	0.653827i	$0.226837\pi$
$168$	1.82530	+	3.16150i	0.140825	+	0.243915i
$169$	−3.73177	+	6.46361i	−0.287059	+	0.497201i
$170$	−15.7681			−1.20936
$171$	21.6582			1.65624
$172$	−17.0475	+	29.5271i	−1.29986	+	2.25142i
$173$	5.64785	+	9.78236i	0.429398	+	0.743739i	0.996820	−	0.0796881i	$-0.0253924\pi$
$173$	5.64785	+	9.78236i	0.429398	+	0.743739i	−0.567422	+	0.823427i	$0.692059\pi$
$174$	−10.2700	+	17.7881i	−0.778564	+	1.34851i
$175$	0.487585	+	0.844522i	0.0368580	+	0.0638399i
$176$	0.793335	+	1.37410i	0.0597999	+	0.103576i
$177$	−2.90908	−	5.03868i	−0.218660	−	0.378730i
$178$	−7.99245			−0.599060
$179$	7.21513	−	12.4970i	0.539284	−	0.934068i	−0.459658	−	0.888096i	$-0.652028\pi$
$179$	7.21513	−	12.4970i	0.539284	−	0.934068i	0.998943	−	0.0459721i	$-0.0146385\pi$
$180$	7.57562	−	13.1214i	0.564653	−	0.978009i
$181$	11.0002	+	19.0529i	0.817639	+	1.41619i	0.907417	+	0.420231i	$0.138051\pi$
$181$	11.0002	+	19.0529i	0.817639	+	1.41619i	−0.0897781	+	0.995962i	$0.528616\pi$
$182$	2.99282			0.221843
$183$	−12.4309	+	21.5309i	−0.918915	+	1.59161i
$184$	16.5280			1.21846
$185$	4.68611			0.344530
$186$		0			0
$187$	−1.60303			−0.117225
$188$	23.3477			1.70280
$189$	0.0380158	−	0.0658453i	0.00276524	−	0.00478954i
$190$	−19.9388			−1.44651
$191$	−10.8832	−	18.8502i	−0.787478	−	1.36395i	−0.927507	−	0.373805i	$-0.878053\pi$
$191$	−10.8832	−	18.8502i	−0.787478	−	1.36395i	0.140029	−	0.990147i	$-0.455280\pi$
$192$	−5.91751	+	10.2494i	−0.427060	+	0.739689i
$193$	−1.10561	+	1.91498i	−0.0795839	+	0.137843i	−0.903070	−	0.429492i	$-0.858692\pi$
$193$	−1.10561	+	1.91498i	−0.0795839	+	0.137843i	0.823487	+	0.567336i	$0.192026\pi$
$194$	5.03456			0.361460
$195$	−6.42808	−	11.1338i	−0.460324	−	0.797305i
$196$	14.6606	+	25.3929i	1.04719	+	1.81378i
$197$	8.69658	+	15.0629i	0.619605	+	1.07319i	0.989558	+	0.144137i	$0.0460407\pi$
$197$	8.69658	+	15.0629i	0.619605	+	1.07319i	−0.369952	+	0.929051i	$0.620626\pi$
$198$	1.13420	−	1.96448i	0.0806038	−	0.139610i
$199$	5.87993	+	10.1843i	0.416817	+	0.721949i	0.995617	−	0.0935208i	$-0.0298122\pi$
$199$	5.87993	+	10.1843i	0.416817	+	0.721949i	−0.578800	+	0.815469i	$0.696479\pi$
$200$	10.2464	−	17.7473i	0.724529	−	1.25492i
$201$	8.87049			0.625676
$202$	27.1140			1.90773
$203$	0.440914	−	0.763686i	0.0309461	−	0.0536002i
$204$	28.7590	+	49.8120i	2.01353	+	3.48754i
$205$	4.30886	−	7.46316i	0.300944	−	0.521249i
$206$	5.00922	+	8.67623i	0.349009	+	0.604501i
$207$	−4.62342	−	8.00800i	−0.321350	−	0.556594i
$208$	−12.3059	−	21.3144i	−0.853258	−	1.47789i
$209$	−2.02703			−0.140212
$210$	−0.940116	+	1.62833i	−0.0648742	+	0.112365i
$211$	3.73250	−	6.46488i	0.256956	−	0.445061i	−0.708469	−	0.705742i	$-0.750614\pi$
$211$	3.73250	−	6.46488i	0.256956	−	0.445061i	0.965425	+	0.260681i	$0.0839471\pi$
$212$	10.0544	+	17.4148i	0.690541	+	1.19605i
$213$	−26.9045			−1.84347
$214$	22.5330	−	39.0283i	1.54033	−	2.66792i
$215$	−9.26004			−0.631530
$216$	−1.59777			−0.108714
$217$		0			0
$218$	0.652500			0.0441929
$219$	5.62460			0.380075
$220$	−0.709015	+	1.22805i	−0.0478018	+	0.0827952i
$221$	24.8654			1.67263
$222$	−12.5868	−	21.8010i	−0.844770	−	1.46318i
$223$	14.5733	−	25.2418i	0.975903	−	1.69031i	0.298979	−	0.954260i	$-0.403354\pi$
$223$	14.5733	−	25.2418i	0.975903	−	1.69031i	0.676924	−	0.736053i	$-0.263313\pi$
$224$	−0.323605	+	0.560500i	−0.0216218	+	0.0374500i
$225$	−11.4650			−0.764332
$226$	3.49530	+	6.05405i	0.232504	+	0.402709i
$227$	−2.97387	−	5.15090i	−0.197383	−	0.341877i	0.750296	−	0.661102i	$-0.229911\pi$
$227$	−2.97387	−	5.15090i	−0.197383	−	0.341877i	−0.947679	+	0.319225i	$0.896578\pi$
$228$	36.3657	+	62.9873i	2.40838	+	4.17144i
$229$	2.79558	−	4.84209i	0.184737	−	0.319974i	−0.758751	−	0.651381i	$-0.774190\pi$
$229$	2.79558	−	4.84209i	0.184737	−	0.319974i	0.943488	+	0.331407i	$0.107523\pi$
$230$	4.25637	+	7.37224i	0.280657	+	0.486111i
$231$	−0.0955747	+	0.165540i	−0.00628836	+	0.0108918i
$232$	−18.5312			−1.21663
$233$	−26.3792			−1.72816			−0.864081	−	0.503353i	$-0.832099\pi$
$233$	−26.3792			−1.72816			−0.864081	+	0.503353i	$0.832099\pi$
$234$	−17.5931	+	30.4722i	−1.15010	+	1.99203i
$235$	3.17057	+	5.49158i	0.206825	+	0.358231i
$236$	4.97721	−	8.62078i	0.323989	−	0.561165i
$237$	−4.69164	−	8.12616i	−0.304755	−	0.527851i
$238$	−1.81830	−	3.14939i	−0.117863	−	0.204145i
$239$	−10.4116	−	18.0335i	−0.673473	−	1.16649i	−0.976913	−	0.213639i	$-0.931468\pi$
$239$	−10.4116	−	18.0335i	−0.673473	−	1.16649i	0.303440	−	0.952851i	$-0.401865\pi$
$240$	15.4623			0.998084
$241$	−7.13030	+	12.3500i	−0.459303	+	0.795536i	−0.998924	−	0.0463719i	$-0.985234\pi$
$241$	−7.13030	+	12.3500i	−0.459303	+	0.795536i	0.539621	+	0.841908i	$0.318567\pi$
$242$	13.6232	−	23.5960i	0.875730	−	1.51681i
$243$	−11.1121	−	19.2467i	−0.712842	−	1.23468i
$244$	−42.5364			−2.72312
$245$	−3.98176	+	6.89661i	−0.254385	+	0.440608i
$246$	−46.2940			−2.95160
$247$	31.4424			2.00063
$248$		0			0
$249$	−6.90815			−0.437786
$250$	24.8979			1.57468
$251$	−4.40031	+	7.62156i	−0.277745	+	0.481069i	−0.970824	−	0.239793i	$-0.922920\pi$
$251$	−4.40031	+	7.62156i	−0.277745	+	0.481069i	0.693079	+	0.720862i	$0.256254\pi$
$252$	3.49434			0.220123
$253$	0.432714	+	0.749482i	0.0272045	+	0.0471196i
$254$	−7.05583	+	12.2211i	−0.442722	+	0.766818i
$255$	−7.81082	+	13.5287i	−0.489133	+	0.847202i
$256$	−32.4403			−2.02752
$257$	−2.00483	−	3.47247i	−0.125058	−	0.216607i	0.796698	−	0.604378i	$-0.206578\pi$
$257$	−2.00483	−	3.47247i	−0.125058	−	0.216607i	−0.921756	+	0.387771i	$0.873245\pi$
$258$	24.8723	+	43.0800i	1.54848	+	2.68205i
$259$	0.540381	+	0.935967i	0.0335776	+	0.0581582i
$260$	10.9979	−	19.0490i	0.682063	−	1.18137i
$261$	5.18378	+	8.97857i	0.320868	+	0.555760i
$262$	−7.94591	+	13.7627i	−0.490900	+	0.850263i
$263$	0.612101			0.0377438			0.0188719	−	0.999822i	$-0.493993\pi$
$263$	0.612101			0.0377438			0.0188719	+	0.999822i	$0.493993\pi$
$264$	4.01692			0.247224
$265$	−2.73074	+	4.72979i	−0.167748	+	0.290548i
$266$	−2.29925	−	3.98241i	−0.140976	−	0.244177i
$267$	−3.95911	+	6.85738i	−0.242294	+	0.419665i
$268$	7.58835	+	13.1434i	0.463532	+	0.802862i
$269$	0.563150	+	0.975404i	0.0343359	+	0.0594715i	0.882683	−	0.469969i	$-0.155735\pi$
$269$	0.563150	+	0.975404i	0.0343359	+	0.0594715i	−0.848347	+	0.529441i	$0.822402\pi$
$270$	−0.411465	−	0.712677i	−0.0250409	−	0.0433722i
$271$	−0.207928			−0.0126307			−0.00631537	−	0.999980i	$-0.502010\pi$
$271$	−0.207928			−0.0126307			−0.00631537	+	0.999980i	$0.502010\pi$
$272$	−14.9530	+	25.8993i	−0.906657	+	1.57038i
$273$	1.48251	−	2.56779i	0.0897258	−	0.155410i
$274$	−3.69803	−	6.40518i	−0.223406	−	0.386951i
$275$	1.07303			0.0647060
$276$	15.5261	−	26.8921i	0.934564	−	1.61871i
$277$	24.8751			1.49460			0.747299	−	0.664488i	$-0.231350\pi$
$277$	24.8751			1.49460			0.747299	+	0.664488i	$0.231350\pi$
$278$	−31.9677			−1.91729
$279$		0			0
$280$	−1.69635			−0.101377
$281$	25.7631			1.53690			0.768449	−	0.639911i	$-0.221029\pi$
$281$	25.7631			1.53690			0.768449	+	0.639911i	$0.221029\pi$
$282$	17.0322	−	29.5006i	1.01425	−	1.75673i
$283$	−26.7813			−1.59198			−0.795992	−	0.605308i	$-0.793050\pi$
$283$	−26.7813			−1.59198			−0.795992	+	0.605308i	$0.793050\pi$
$284$	−23.0157	−	39.8644i	−1.36573	−	2.36552i
$285$	−9.87679	+	17.1071i	−0.585051	+	1.01334i
$286$	1.64657	−	2.85195i	0.0973639	−	0.168639i
$287$	1.98751			0.117319
$288$	−3.80459	−	6.58974i	−0.224188	−	0.388304i
$289$	−6.60711	−	11.4439i	−0.388654	−	0.673168i
$290$	−4.77224	−	8.26577i	−0.280236	−	0.485382i
$291$	2.49390	−	4.31957i	0.146195	−	0.253217i
$292$	4.81162	+	8.33398i	0.281579	+	0.487709i
$293$	−11.1814	+	19.3667i	−0.653223	+	1.13142i	0.329113	+	0.944291i	$0.393250\pi$
$293$	−11.1814	+	19.3667i	−0.653223	+	1.13142i	−0.982336	+	0.187125i	$0.940083\pi$
$294$	42.7797			2.49496
$295$	2.70358			0.157409
$296$	11.3559	−	19.6689i	0.660046	−	1.14323i
$297$	−0.0418306	−	0.0724527i	−0.00242726	−	0.00420413i
$298$	−21.7840	+	37.7310i	−1.26191	+	2.18570i
$299$	−6.71207	−	11.6256i	−0.388169	−	0.672328i
$300$	−19.2506	−	33.3429i	−1.11143	−	1.92506i
$301$	−1.06783	−	1.84953i	−0.0615485	−	0.106605i
$302$	54.1459			3.11574
$303$	13.4311	−	23.2633i	0.771596	−	1.33644i
$304$	−18.9081	+	32.7497i	−1.08445	+	1.87833i
$305$	−5.77636	−	10.0050i	−0.330754	−	0.572882i
$306$	42.7552			2.44415
$307$	−3.64392	+	6.31145i	−0.207969	+	0.360213i	−0.951075	−	0.308961i	$-0.900019\pi$
$307$	−3.64392	+	6.31145i	−0.207969	+	0.360213i	0.743105	+	0.669174i	$0.233352\pi$
$308$	−0.327042			−0.0186349
$309$	9.92540			0.564636
$310$		0			0
$311$	−25.6025			−1.45179			−0.725893	−	0.687808i	$-0.758573\pi$
$311$	−25.6025			−1.45179			−0.725893	+	0.687808i	$0.758573\pi$
$312$	−62.3087			−3.52754
$313$	12.7385	−	22.0637i	0.720022	−	1.24711i	−0.240969	−	0.970533i	$-0.577465\pi$
$313$	12.7385	−	22.0637i	0.720022	−	1.24711i	0.960991	−	0.276581i	$-0.0892014\pi$
$314$	−36.2762			−2.04718
$315$	0.474525	+	0.821902i	0.0267365	+	0.0463089i
$316$	8.02703	−	13.9032i	0.451556	−	0.782118i
$317$	7.11854	−	12.3297i	0.399817	−	0.692504i	−0.593886	−	0.804549i	$-0.702407\pi$
$317$	7.11854	−	12.3297i	0.399817	−	0.692504i	0.993703	+	0.112045i	$0.0357402\pi$
$318$	29.3389			1.64524
$319$	−0.485159	−	0.840320i	−0.0271637	−	0.0470489i
$320$	−2.74975	−	4.76270i	−0.153715	−	0.266243i
$321$	−22.3237	−	38.6659i	−1.24599	−	2.15812i
$322$	−0.981650	+	1.70027i	−0.0547052	+	0.0947522i
$323$	−19.1030	−	33.0873i	−1.06292	−	1.84103i
$324$	18.2757	−	31.6545i	1.01532	−	1.75858i
$325$	−16.6443			−0.923261
$326$	0.171325			0.00948884
$327$	0.323220	−	0.559834i	0.0178741	−	0.0309589i
$328$	−20.8833	−	36.1710i	−1.15309	−	1.99721i
$329$	−0.731231	+	1.26653i	−0.0403141	+	0.0698260i
$330$	1.03445	+	1.79173i	0.0569449	+	0.0986314i
$331$	−8.74577	−	15.1481i	−0.480711	−	0.832616i	0.519044	−	0.854747i	$-0.326288\pi$
$331$	−8.74577	−	15.1481i	−0.480711	−	0.832616i	−0.999755	+	0.0221319i	$0.992955\pi$
$332$	−5.90965	−	10.2358i	−0.324334	−	0.561763i
$333$	−12.7064			−0.696307
$334$	−6.06164	+	10.4991i	−0.331678	+	0.574483i
$335$	−2.06097	+	3.56970i	−0.112603	+	0.195034i
$336$	1.78304	+	3.08831i	0.0972726	+	0.168481i
$337$	16.4232			0.894631			0.447316	−	0.894376i	$-0.352380\pi$
$337$	16.4232			0.894631			0.447316	+	0.894376i	$0.352380\pi$
$338$	−9.31537	+	16.1347i	−0.506689	+	0.877612i
$339$	6.92569			0.376152
$340$	−26.7274			−1.44950
$341$		0			0
$342$	54.0640			2.92345
$343$	−3.69188			−0.199343
$344$	−22.4399	+	38.8670i	−1.20988	+	2.09557i
$345$	8.43368			0.454054
$346$	14.0984	+	24.4191i	0.757933	+	1.31278i
$347$	13.0438	−	22.5925i	0.700228	−	1.21283i	−0.268158	−	0.963375i	$-0.586415\pi$
$347$	13.0438	−	22.5925i	0.700228	−	1.21283i	0.968386	−	0.249456i	$-0.0802519\pi$
$348$	−17.4079	+	30.1514i	−0.933162	+	1.61628i
$349$	10.6958			0.572535			0.286267	−	0.958150i	$-0.407585\pi$
$349$	10.6958			0.572535			0.286267	+	0.958150i	$0.407585\pi$
$350$	1.21713	+	2.10813i	0.0650583	+	0.112684i
$351$	0.648858	+	1.12385i	0.0346335	+	0.0599869i
$352$	0.356078	+	0.616745i	0.0189790	+	0.0328726i
$353$	−6.82069	+	11.8138i	−0.363029	+	0.628784i	−0.988458	−	0.151497i	$-0.951591\pi$
$353$	−6.82069	+	11.8138i	−0.363029	+	0.628784i	0.625429	+	0.780281i	$0.284924\pi$
$354$	−7.26176	−	12.5777i	−0.385958	−	0.668499i
$355$	6.25098	−	10.8270i	0.331768	−	0.574638i
$356$	−13.5475			−0.718014
$357$	−3.60283			−0.190682
$358$	18.0107	−	31.1954i	0.951894	−	1.64873i
$359$	−1.04494	−	1.80989i	−0.0551498	−	0.0955223i	0.837132	−	0.547000i	$-0.184230\pi$
$359$	−1.04494	−	1.80989i	−0.0551498	−	0.0955223i	−0.892282	+	0.451478i	$0.850897\pi$
$360$	9.97193	−	17.2719i	0.525567	−	0.910309i
$361$	−14.6557	−	25.3845i	−0.771354	−	1.33602i
$362$	27.4591	+	47.5606i	1.44322	+	2.49973i
$363$	−13.4966	−	23.3769i	−0.708390	−	1.22697i
$364$	5.07293			0.265894
$365$	−1.30682	+	2.26348i	−0.0684020	+	0.118476i
$366$	−31.0304	+	53.7462i	−1.62198	+	2.80936i
$367$	−9.96005	−	17.2513i	−0.519910	−	0.900511i	−0.999732	−	0.0231450i	$-0.992632\pi$
$367$	−9.96005	−	17.2513i	−0.519910	−	0.900511i	0.479822	−	0.877366i	$-0.340701\pi$
$368$	16.1454			0.841635
$369$	−11.6835	+	20.2364i	−0.608218	+	1.05346i
$370$	11.6976			0.608132
$371$	−1.25959			−0.0653945
$372$		0			0
$373$	10.7238			0.555257			0.277629	−	0.960688i	$-0.410452\pi$
$373$	10.7238			0.555257			0.277629	+	0.960688i	$0.410452\pi$
$374$	−4.00153			−0.206914
$375$	12.3333	−	21.3619i	0.636890	−	1.10313i
$376$	30.7330			1.58493
$377$	7.52557	+	13.0347i	0.387587	+	0.671320i
$378$	0.0948964	−	0.164365i	0.00488095	−	0.00845405i
$379$	−7.07681	+	12.2574i	−0.363512	+	0.629620i	−0.988536	−	0.150985i	$-0.951756\pi$
$379$	−7.07681	+	12.2574i	−0.363512	+	0.629620i	0.625025	+	0.780605i	$0.285089\pi$
$380$	−33.7968			−1.73374
$381$	6.99030	+	12.1076i	0.358124	+	0.620289i
$382$	−27.1670	−	47.0546i	−1.38998	−	2.40752i
$383$	−8.92810	−	15.4639i	−0.456204	−	0.790169i	0.542552	−	0.840022i	$-0.317458\pi$
$383$	−8.92810	−	15.4639i	−0.456204	−	0.790169i	−0.998757	+	0.0498529i	$0.984125\pi$
$384$	−20.8106	+	36.0451i	−1.06199	+	1.83942i
$385$	−0.0444116	−	0.0769232i	−0.00226343	−	0.00392037i
$386$	−2.75988	+	4.78025i	−0.140474	+	0.243308i
$387$	25.1086			1.27634
$388$	8.53374			0.433235
$389$	11.7405	−	20.3352i	0.595269	−	1.03104i	−0.398240	−	0.917281i	$-0.630379\pi$
$389$	11.7405	−	20.3352i	0.595269	−	1.03104i	0.993509	−	0.113754i	$-0.0362877\pi$
$390$	−16.0460	−	27.7925i	−0.812521	−	1.40733i
$391$	−8.15590	+	14.1264i	−0.412461	+	0.714404i
$392$	19.2980	+	33.4251i	0.974697	+	1.68822i
$393$	7.87211	+	13.6349i	0.397096	+	0.687790i
$394$	21.7087	+	37.6006i	1.09367	+	1.89429i
$395$	4.36022			0.219386
$396$	1.92250	−	3.32986i	0.0966092	−	0.167332i
$397$	5.05313	−	8.75228i	0.253609	−	0.439264i	−0.710907	−	0.703286i	$-0.751716\pi$
$397$	5.05313	−	8.75228i	0.253609	−	0.439264i	0.964517	+	0.264021i	$0.0850489\pi$
$398$	14.6777	+	25.4225i	0.735727	+	1.27432i
$399$	−4.55579			−0.228075
$400$	10.0092	−	17.3364i	0.500458	−	0.866819i
$401$	−22.8732			−1.14223			−0.571116	−	0.820869i	$-0.693489\pi$
$401$	−22.8732			−1.14223			−0.571116	+	0.820869i	$0.693489\pi$
$402$	22.1428			1.10438
$403$		0			0
$404$	45.9591			2.28655
$405$	9.92722			0.493288
$406$	1.10063	−	1.90634i	0.0546232	−	0.0946101i
$407$	1.18921			0.0589472
$408$	37.8560	+	65.5684i	1.87415	+	3.24612i
$409$	−6.59713	+	11.4266i	−0.326207	+	0.565007i	−0.981756	−	0.190146i	$-0.939104\pi$
$409$	−6.59713	+	11.4266i	−0.326207	+	0.565007i	0.655549	+	0.755153i	$0.272437\pi$
$410$	10.7559	−	18.6298i	0.531197	−	0.920061i
$411$	−7.32738			−0.361433
$412$	8.49079	+	14.7065i	0.418311	+	0.724536i
$413$	0.311765	+	0.539992i	0.0153409	+	0.0265713i
$414$	−11.5412	−	19.9899i	−0.567217	−	0.982448i
$415$	1.60504	−	2.78001i	0.0787882	−	0.136465i
$416$	−5.52333	−	9.56668i	−0.270803	−	0.469045i
$417$	−15.8354	+	27.4277i	−0.775462	+	1.34314i
$418$	−5.05994			−0.247490
$419$	−4.45937			−0.217855			−0.108927	−	0.994050i	$-0.534742\pi$
$419$	−4.45937			−0.217855			−0.108927	+	0.994050i	$0.534742\pi$
$420$	−1.59353	+	2.76007i	−0.0777561	+	0.134678i
$421$	9.66167	+	16.7345i	0.470881	+	0.815590i	0.999445	−	0.0333033i	$-0.0106027\pi$
$421$	9.66167	+	16.7345i	0.470881	+	0.815590i	−0.528564	+	0.848893i	$0.677269\pi$
$422$	9.31721	−	16.1379i	0.453555	−	0.785580i
$423$	−8.59701	−	14.8905i	−0.418001	−	0.723999i
$424$	13.2348	+	22.9234i	0.642740	+	1.11326i
$425$	10.1123	+	17.5151i	0.490521	+	0.849606i
$426$	−67.1600			−3.25391
$427$	1.33221	−	2.30745i	0.0644700	−	0.111665i
$428$	38.1942	−	66.1543i	1.84619	−	3.19769i
$429$	−1.63128	−	2.82546i	−0.0787590	−	0.136415i
$430$	−23.1153			−1.11472
$431$	5.22265	−	9.04590i	0.251566	−	0.435726i	−0.712391	−	0.701783i	$-0.752388\pi$
$431$	5.22265	−	9.04590i	0.251566	−	0.435726i	0.963957	+	0.266057i	$0.0857210\pi$
$432$	−1.56078			−0.0750930
$433$	20.7300			0.996220			0.498110	−	0.867114i	$-0.334028\pi$
$433$	20.7300			0.996220			0.498110	+	0.867114i	$0.334028\pi$
$434$		0			0
$435$	−9.45584			−0.453373
$436$	1.10601			0.0529682
$437$	−10.3131	+	17.8629i	−0.493345	+	0.854498i
$438$	14.0403			0.670873
$439$	−14.1778	−	24.5567i	−0.676669	−	1.17203i	−0.975978	−	0.217869i	$-0.930089\pi$
$439$	−14.1778	−	24.5567i	−0.676669	−	1.17203i	0.299309	−	0.954156i	$-0.403244\pi$
$440$	−0.933290	+	1.61651i	−0.0444929	+	0.0770639i
$441$	10.7966	−	18.7002i	0.514122	−	0.890485i
$442$	62.0700			2.95237
$443$	14.6083	+	25.3023i	0.694061	+	1.20215i	0.970496	+	0.241116i	$0.0775136\pi$
$443$	14.6083	+	25.3023i	0.694061	+	1.20215i	−0.276435	+	0.961033i	$0.589153\pi$
$444$	−21.3350	−	36.9533i	−1.01251	−	1.75373i
$445$	−1.83972	−	3.18649i	−0.0872110	−	0.151054i
$446$	36.3785	−	63.0094i	1.72257	−	2.98358i
$447$	21.5817	+	37.3806i	1.02078	+	1.76804i
$448$	0.634176	−	1.09843i	0.0299620	−	0.0518957i
$449$	−1.16663			−0.0550569			−0.0275285	−	0.999621i	$-0.508764\pi$
$449$	−1.16663			−0.0550569			−0.0275285	+	0.999621i	$0.508764\pi$
$450$	−28.6193			−1.34913
$451$	1.09348	−	1.89396i	0.0514898	−	0.0891830i
$452$	5.92465	+	10.2618i	0.278672	+	0.482674i
$453$	26.8215	−	46.4562i	1.26018	−	2.18270i
$454$	−7.42349	−	12.8579i	−0.348402	−	0.603449i
$455$	0.688894	+	1.19320i	0.0322958	+	0.0559380i
$456$	47.8689	+	82.9114i	2.24167	+	3.88268i
$457$	−40.2820			−1.88431			−0.942157	−	0.335173i	$-0.891205\pi$
$457$	−40.2820			−1.88431			−0.942157	+	0.335173i	$0.891205\pi$
$458$	6.97843	−	12.0870i	0.326081	−	0.564788i
$459$	0.788433	−	1.36561i	0.0368009	−	0.0637411i
$460$	7.21468	+	12.4962i	0.336386	+	0.582638i
$461$	29.3394			1.36647			0.683235	−	0.730199i	$-0.260572\pi$
$461$	29.3394			1.36647			0.683235	+	0.730199i	$0.260572\pi$
$462$	−0.238577	+	0.413228i	−0.0110996	+	0.0192251i
$463$	0.639508			0.0297205			0.0148602	−	0.999890i	$-0.495270\pi$
$463$	0.639508			0.0297205			0.0148602	+	0.999890i	$0.495270\pi$
$464$	−18.1022			−0.840373
$465$		0			0
$466$	−65.8488			−3.05039
$467$	2.89543			0.133984			0.0669922	−	0.997753i	$-0.478660\pi$
$467$	2.89543			0.133984			0.0669922	+	0.997753i	$0.478660\pi$
$468$	−29.8209	+	51.6514i	−1.37847	+	2.38759i
$469$	−0.950645			−0.0438967
$470$	7.91449	+	13.7083i	0.365068	+	0.632317i
$471$	−17.9696	+	31.1243i	−0.827998	+	1.43413i
$472$	6.55159	−	11.3477i	0.301561	−	0.522320i
$473$	−2.34996			−0.108051
$474$	−11.7115	−	20.2848i	−0.537925	−	0.931713i
$475$	12.7871	+	22.1479i	0.586711	+	1.01621i
$476$	−3.08208	−	5.33832i	−0.141267	−	0.244682i
$477$	7.40442	−	12.8248i	0.339025	−	0.587209i
$478$	−25.9899	−	45.0159i	−1.18875	−	2.05898i
$479$	−14.4720	+	25.0662i	−0.661242	+	1.14531i	0.319047	+	0.947739i	$0.396637\pi$
$479$	−14.4720	+	25.0662i	−0.661242	+	1.14531i	−0.980290	+	0.197566i	$0.936696\pi$
$480$	6.94003			0.316768
$481$	−18.4466			−0.841091
$482$	−17.7989	+	30.8286i	−0.810718	+	1.40421i
$483$	0.972533	+	1.68448i	0.0442518	+	0.0766463i
$484$	23.0917	−	39.9960i	1.04962	−	1.81800i
$485$	1.15887	+	2.00721i	0.0526214	+	0.0911429i
$486$	−27.7385	−	48.0444i	−1.25824	−	2.17934i
$487$	−1.36661	−	2.36704i	−0.0619271	−	0.107261i	0.833400	−	0.552671i	$-0.186391\pi$
$487$	−1.36661	−	2.36704i	−0.0619271	−	0.107261i	−0.895327	+	0.445410i	$0.853058\pi$
$488$	−55.9915			−2.53462
$489$	0.0848672	−	0.146994i	0.00383783	−	0.00664731i
$490$	−9.93942	+	17.2156i	−0.449017	+	0.777721i
$491$	5.71487	+	9.89845i	0.257908	+	0.446711i	0.965681	−	0.259729i	$-0.0836334\pi$
$491$	5.71487	+	9.89845i	0.257908	+	0.446711i	−0.707773	+	0.706440i	$0.750300\pi$
$492$	−78.4697			−3.53769
$493$	9.14440	−	15.8386i	0.411843	−	0.713333i
$494$	78.4876			3.53133
$495$	1.04429			0.0469372
$496$		0			0
$497$	2.88334			0.129335
$498$	−17.2444			−0.772739
$499$	−3.21092	+	5.56148i	−0.143741	+	0.248966i	−0.928902	−	0.370325i	$-0.879246\pi$
$499$	−3.21092	+	5.56148i	−0.143741	+	0.248966i	0.785162	+	0.619291i	$0.212580\pi$
$500$	42.2027			1.88736
$501$	6.00534	+	10.4016i	0.268299	+	0.464707i
$502$	−10.9842	+	19.0252i	−0.490250	+	0.849138i
$503$	6.27188	−	10.8632i	0.279649	−	0.484367i	−0.691648	−	0.722234i	$-0.743115\pi$
$503$	6.27188	−	10.8632i	0.279649	−	0.484367i	0.971298	+	0.237868i	$0.0764485\pi$
$504$	4.59967			0.204886
$505$	6.24115	+	10.8100i	0.277728	+	0.481038i
$506$	1.08016	+	1.87089i	0.0480188	+	0.0831710i
$507$	9.22886	+	15.9849i	0.409868	+	0.709912i
$508$	−11.9599	+	20.7151i	−0.530633	+	0.919083i
$509$	14.4885	+	25.0948i	0.642191	+	1.11231i	0.984943	+	0.172881i	$0.0553076\pi$
$509$	14.4885	+	25.0948i	0.642191	+	1.11231i	−0.342752	+	0.939426i	$0.611359\pi$
$510$	−19.4977	+	33.7709i	−0.863371	+	1.49540i
$511$	−0.602785			−0.0266657
$512$	−47.3188			−2.09122
$513$	0.996975	−	1.72681i	0.0440175	−	0.0762406i
$514$	−5.00453	−	8.66810i	−0.220740	−	0.382334i
$515$	−2.30606	+	3.99422i	−0.101617	+	0.176006i
$516$	42.1593	+	73.0220i	1.85596	+	3.21462i
$517$	0.804609	+	1.39362i	0.0353866	+	0.0612915i
$518$	1.34892	+	2.33640i	0.0592681	+	0.102655i
$519$	27.9349			1.22621
$520$	14.4768	−	25.0745i	0.634849	−	1.09959i
$521$	6.40611	−	11.0957i	0.280657	−	0.486112i	−0.690890	−	0.722960i	$-0.742781\pi$
$521$	6.40611	−	11.0957i	0.280657	−	0.486112i	0.971547	+	0.236848i	$0.0761144\pi$
$522$	12.9400	+	22.4127i	0.566366	+	0.980975i
$523$	−19.1831			−0.838819			−0.419410	−	0.907797i	$-0.637763\pi$
$523$	−19.1831			−0.838819			−0.419410	+	0.907797i	$0.637763\pi$
$524$	−13.4686	+	23.3282i	−0.588377	+	1.01910i
$525$	2.41165			0.105253
$526$	1.52795			0.0666218
$527$		0			0
$528$	3.92392			0.170767
$529$	−14.1937			−0.617119
$530$	−6.81658	+	11.8067i	−0.296093	+	0.512849i
$531$	−7.33077			−0.318128
$532$	−3.89730	−	6.75032i	−0.168969	−	0.292663i
$533$	−16.9615	+	29.3782i	−0.734685	+	1.27251i
$534$	−9.88289	+	17.1177i	−0.427674	+	0.740754i
$535$	20.7468			0.896961
$536$	9.98869	+	17.3009i	0.431446	+	0.747286i
$537$	−17.8434	−	30.9057i	−0.770000	−	1.33368i
$538$	1.40576	+	2.43484i	0.0606064	+	0.104973i
$539$	−1.01047	+	1.75018i	−0.0435240	+	0.0753857i
$540$	−0.697445	−	1.20801i	−0.0300133	−	0.0519845i
$541$	18.4849	−	32.0168i	0.794729	−	1.37651i	−0.128282	−	0.991738i	$-0.540946\pi$
$541$	18.4849	−	32.0168i	0.794729	−	1.37651i	0.923011	−	0.384773i	$-0.125720\pi$
$542$	−0.519038			−0.0222946
$543$	54.4082			2.33488
$544$	−6.71145	+	11.6246i	−0.287751	+	0.498399i
$545$	0.150194	+	0.260143i	0.00643360	+	0.0111433i
$546$	3.70071	−	6.40981i	0.158376	−	0.274315i
$547$	16.3491	+	28.3175i	0.699038	+	1.21077i	0.968800	+	0.247842i	$0.0797215\pi$
$547$	16.3491	+	28.3175i	0.699038	+	1.21077i	−0.269762	+	0.962927i	$0.586945\pi$
$548$	−6.26828	−	10.8570i	−0.267768	−	0.463787i
$549$	15.6626	+	27.1285i	0.668465	+	1.15781i
$550$	2.67853			0.114213
$551$	11.5631	−	20.0279i	0.492605	−	0.853217i
$552$	20.4373	−	35.3985i	0.869871	−	1.50666i
$553$	0.502801	+	0.870876i	0.0213813	+	0.0370334i
$554$	62.0941			2.63813
$555$	5.79450	−	10.0364i	0.245963	−	0.426020i
$556$	−54.1862			−2.29801
$557$	−28.6262			−1.21293			−0.606466	−	0.795109i	$-0.707413\pi$
$557$	−28.6262			−1.21293			−0.606466	+	0.795109i	$0.707413\pi$
$558$		0			0
$559$	36.4516			1.54174
$560$	−1.65708			−0.0700245
$561$	−1.98219	+	3.43325i	−0.0836879	+	0.144952i
$562$	64.3108			2.71279
$563$	−12.8550	−	22.2656i	−0.541775	−	0.938382i	−0.998802	−	0.0489294i	$-0.984419\pi$
$563$	−12.8550	−	22.2656i	−0.541775	−	0.938382i	0.457027	−	0.889453i	$-0.348914\pi$
$564$	28.8700	−	50.0044i	1.21565	−	2.10556i
$565$	−1.60911	+	2.78706i	−0.0676959	+	0.117253i
$566$	−66.8525			−2.81002
$567$	1.14476	+	1.98279i	0.0480755	+	0.0832692i
$568$	−30.2960	−	52.4743i	−1.27119	−	2.20177i
$569$	12.1404	+	21.0277i	0.508951	+	0.881529i	0.999946	+	0.0103668i	$0.00329992\pi$
$569$	12.1404	+	21.0277i	0.508951	+	0.881529i	−0.490995	+	0.871162i	$0.663367\pi$
$570$	−24.6548	+	42.7034i	−1.03268	+	1.78865i
$571$	6.71853	+	11.6368i	0.281162	+	0.486986i	0.971671	−	0.236337i	$-0.0759470\pi$
$571$	6.71853	+	11.6368i	0.281162	+	0.486986i	−0.690509	+	0.723323i	$0.742614\pi$
$572$	2.79099	−	4.83414i	0.116697	−	0.202126i
$573$	−53.8293			−2.24875
$574$	4.96130			0.207081
$575$	5.45936	−	9.45589i	0.227671	−	0.394338i
$576$	7.45594	+	12.9141i	0.310664	+	0.538086i
$577$	−13.6113	+	23.5754i	−0.566645	+	0.981457i	0.430250	+	0.902710i	$0.358425\pi$
$577$	−13.6113	+	23.5754i	−0.566645	+	0.981457i	−0.996895	+	0.0787475i	$0.974908\pi$
$578$	−16.4929	−	28.5666i	−0.686015	−	1.18821i
$579$	2.73425	+	4.73585i	0.113631	+	0.196815i
$580$	−8.08910	−	14.0107i	−0.335882	−	0.581764i
$581$	0.740342			0.0307146
$582$	6.22537	−	10.7827i	0.258050	−	0.446956i
$583$	−0.692992	+	1.20030i	−0.0287008	+	0.0497113i
$584$	6.33363	+	10.9702i	0.262088	+	0.453949i
$585$	−16.1985			−0.669726
$586$	−27.9114	+	48.3439i	−1.15301	+	1.99707i
$587$	−4.23677			−0.174870			−0.0874351	−	0.996170i	$-0.527867\pi$
$587$	−4.23677			−0.174870			−0.0874351	+	0.996170i	$0.527867\pi$
$588$	72.5129			2.99038
$589$		0			0
$590$	6.74878			0.277843
$591$	43.0142			1.76937
$592$	11.0930	−	19.2136i	0.455918	−	0.789673i
$593$	−18.6178			−0.764541			−0.382271	−	0.924050i	$-0.624858\pi$
$593$	−18.6178			−0.764541			−0.382271	+	0.924050i	$0.624858\pi$
$594$	−0.104419	−	0.180859i	−0.00428437	−	0.00742074i
$595$	0.837081	−	1.44987i	0.0343170	−	0.0594388i
$596$	−36.9245	+	63.9552i	−1.51249	+	2.61971i
$597$	29.0828			1.19028
$598$	−16.7549	−	29.0204i	−0.685159	−	1.18673i
$599$	5.38038	+	9.31909i	0.219836	+	0.380768i	0.954758	−	0.297385i	$-0.0961143\pi$
$599$	5.38038	+	9.31909i	0.219836	+	0.380768i	−0.734921	+	0.678152i	$0.762781\pi$
$600$	−25.3399	−	43.8899i	−1.03450	−	1.79180i
$601$	−10.6048	+	18.3680i	−0.432577	+	0.749245i	−0.997094	−	0.0761758i	$-0.975729\pi$
$601$	−10.6048	+	18.3680i	−0.432577	+	0.749245i	0.564517	+	0.825421i	$0.309062\pi$
$602$	−2.66555	−	4.61686i	−0.108640	−	0.188169i
$603$	5.58832	−	9.67925i	0.227574	−	0.394170i
$604$	91.7789			3.73443
$605$	12.5432			0.509954
$606$	33.5272	−	58.0708i	1.36195	−	2.35897i
$607$	5.34378	+	9.25570i	0.216897	+	0.375677i	0.953858	−	0.300259i	$-0.0970730\pi$
$607$	5.34378	+	9.25570i	0.216897	+	0.375677i	−0.736960	+	0.675936i	$0.763740\pi$
$608$	−8.48664	+	14.6993i	−0.344179	+	0.596135i
$609$	−1.09040	−	1.88864i	−0.0441854	−	0.0765314i
$610$	−14.4192	−	24.9747i	−0.583815	−	1.01120i
$611$	−12.4807	−	21.6173i	−0.504916	−	0.874541i
$612$	72.4714			2.92948
$613$	3.71950	−	6.44237i	0.150229	−	0.260205i	−0.781082	−	0.624428i	$-0.785332\pi$
$613$	3.71950	−	6.44237i	0.150229	−	0.260205i	0.931312	+	0.364223i	$0.118665\pi$
$614$	−9.09608	+	15.7549i	−0.367088	+	0.635815i
$615$	−10.6560	−	18.4568i	−0.429693	−	0.744250i
$616$	−0.430491			−0.0173450
$617$	−6.73168	+	11.6596i	−0.271007	+	0.469398i	−0.969120	−	0.246590i	$-0.920690\pi$
$617$	−6.73168	+	11.6596i	−0.271007	+	0.469398i	0.698113	+	0.715988i	$0.254023\pi$
$618$	24.7762			0.996643
$619$	6.91762			0.278043			0.139021	−	0.990289i	$-0.455604\pi$
$619$	6.91762			0.278043			0.139021	+	0.990289i	$0.455604\pi$
$620$		0			0
$621$	−0.851305			−0.0341617
$622$	−63.9099			−2.56256
$623$	0.424296	−	0.734902i	0.0169991	−	0.0294432i
$624$	−60.8662			−2.43660
$625$	−3.46743	−	6.00577i	−0.138697	−	0.240231i
$626$	31.7983	−	55.0762i	1.27091	−	2.20129i
$627$	−2.50648	+	4.34134i	−0.100099	+	0.173377i
$628$	−61.4893			−2.45369
$629$	11.2073	+	19.4116i	0.446864	+	0.773992i
$630$	1.18453	+	2.05166i	0.0471927	+	0.0817402i
$631$	6.79825	+	11.7749i	0.270634	+	0.468752i	0.969024	−	0.246965i	$-0.0794334\pi$
$631$	6.79825	+	11.7749i	0.270634	+	0.468752i	−0.698390	+	0.715717i	$0.746100\pi$
$632$	10.5661	−	18.3011i	0.420298	−	0.727978i
$633$	−9.23068	−	15.9880i	−0.366887	−	0.635466i
$634$	17.7696	−	30.7778i	0.705720	−	1.22234i
$635$	−6.49650			−0.257806
$636$	49.7303			1.97193
$637$	15.6739	−	27.1481i	0.621024	−	1.07565i
$638$	−1.21107	−	2.09764i	−0.0479468	−	0.0830463i
$639$	−16.9496	+	29.3575i	−0.670514	+	1.16136i
$640$	−9.67028	−	16.7494i	−0.382251	−	0.662079i
$641$	−1.91659	−	3.31963i	−0.0757008	−	0.131118i	0.825690	−	0.564124i	$-0.190786\pi$
$641$	−1.91659	−	3.31963i	−0.0757008	−	0.131118i	−0.901391	+	0.433006i	$0.857453\pi$
$642$	−55.7254	−	96.5192i	−2.19931	−	3.80931i
$643$	7.72967			0.304828			0.152414	−	0.988317i	$-0.451295\pi$
$643$	7.72967			0.304828			0.152414	+	0.988317i	$0.451295\pi$
$644$	−1.66393	+	2.88201i	−0.0655679	+	0.113567i
$645$	−11.4503	+	19.8325i	−0.450855	+	0.780904i
$646$	−47.6855	−	82.5938i	−1.87616	−	3.24961i
$647$	−18.5951			−0.731049			−0.365525	−	0.930802i	$-0.619110\pi$
$647$	−18.5951			−0.731049			−0.365525	+	0.930802i	$0.619110\pi$
$648$	24.0567	−	41.6674i	0.945035	−	1.63685i
$649$	0.686099			0.0269317
$650$	−41.5482			−1.62965
$651$		0			0
$652$	0.290402			0.0113730
$653$	−39.2520			−1.53605			−0.768025	−	0.640420i	$-0.778760\pi$
$653$	−39.2520			−1.53605			−0.768025	+	0.640420i	$0.778760\pi$
$654$	0.806834	−	1.39748i	0.0315497	−	0.0546457i
$655$	−7.31602			−0.285860
$656$	−20.3998	−	35.3336i	−0.796480	−	1.37954i
$657$	3.54344	−	6.13742i	0.138243	−	0.239444i
$658$	−1.82533	+	3.16156i	−0.0711586	+	0.123250i
$659$	13.6809			0.532930			0.266465	−	0.963845i	$-0.414144\pi$
$659$	13.6809			0.532930			0.266465	+	0.963845i	$0.414144\pi$
$660$	1.75343	+	3.03704i	0.0682523	+	0.118216i
$661$	19.8543	+	34.3887i	0.772243	+	1.33756i	0.936331	+	0.351118i	$0.114199\pi$
$661$	19.8543	+	34.3887i	0.772243	+	1.33756i	−0.164088	+	0.986446i	$0.552468\pi$
$662$	−21.8315	−	37.8133i	−0.848506	−	1.46965i
$663$	30.7468	−	53.2550i	1.19411	−	2.06825i
$664$	−7.77898	−	13.4736i	−0.301883	−	0.522877i
$665$	1.05849	−	1.83336i	0.0410465	−	0.0710946i
$666$	−31.7182			−1.22906
$667$	−9.87360			−0.382307
$668$	−10.2747	+	17.7962i	−0.397539	+	0.688557i
$669$	−36.0407	−	62.4242i	−1.39341	−	2.41346i
$670$	−5.14466	+	8.91082i	−0.198756	+	0.344255i
$671$	−1.46589	−	2.53900i	−0.0565901	−	0.0980170i
$672$	0.800293	+	1.38615i	0.0308720	+	0.0534718i
$673$	12.8545	+	22.2647i	0.495506	+	0.858241i	0.999987	−	0.00518156i	$-0.00164935\pi$
$673$	12.8545	+	22.2647i	0.495506	+	0.858241i	−0.504481	+	0.863423i	$0.668316\pi$
$674$	40.9963			1.57912
$675$	−0.527758	+	0.914104i	−0.0203134	+	0.0351839i
$676$	−15.7899	+	27.3488i	−0.607302	+	1.05188i
$677$	3.47357	+	6.01639i	0.133500	+	0.231229i	0.925023	−	0.379910i	$-0.124045\pi$
$677$	3.47357	+	6.01639i	0.133500	+	0.231229i	−0.791523	+	0.611139i	$0.790712\pi$
$678$	17.2882			0.663948
$679$	−0.267270	+	0.462925i	−0.0102569	+	0.0177654i
$680$	−35.1818			−1.34916
$681$	−14.7091			−0.563654
$682$		0			0
$683$	28.4558			1.08883			0.544415	−	0.838816i	$-0.316752\pi$
$683$	28.4558			1.08883			0.544415	+	0.838816i	$0.316752\pi$
$684$	91.6402			3.50395
$685$	1.70244	−	2.94871i	0.0650469	−	0.112665i
$686$	−9.21582			−0.351862
$687$	−6.91362	−	11.9747i	−0.263771	−	0.456865i
$688$	−21.9204	+	37.9672i	−0.835706	+	1.44749i
$689$	10.7494	−	18.6185i	0.409519	−	0.709308i
$690$	21.0525			0.801453
$691$	−14.6291	−	25.3384i	−0.556518	−	0.963918i	−0.997784	−	0.0665414i	$-0.978804\pi$
$691$	−14.6291	−	25.3384i	−0.556518	−	0.963918i	0.441265	−	0.897377i	$-0.354530\pi$
$692$	23.8972	+	41.3911i	0.908435	+	1.57346i
$693$	0.120422	+	0.208577i	0.00457446	+	0.00792320i
$694$	32.5604	−	56.3964i	1.23598	−	2.14078i
$695$	−7.35838	−	12.7451i	−0.279119	−	0.483449i
$696$	−22.9144	+	39.6888i	−0.868567	+	1.50440i
$697$	41.2202			1.56133
$698$	26.6993			1.01058
$699$	−32.6187	+	56.4972i	−1.23375	+	2.13692i
$700$	2.06307	+	3.57334i	0.0779768	+	0.135060i
$701$	4.24034	−	7.34448i	0.160155	−	0.277397i	−0.774769	−	0.632244i	$-0.782134\pi$
$701$	4.24034	−	7.34448i	0.160155	−	0.277397i	0.934924	+	0.354847i	$0.115467\pi$
$702$	1.61970	+	2.80541i	0.0611318	+	0.105883i
$703$	14.1717	+	24.5460i	0.534494	+	0.925771i
$704$	−0.697815	−	1.20865i	−0.0262999	−	0.0455527i
$705$	15.6820			0.590617
$706$	−17.0261	+	29.4900i	−0.640784	+	1.10987i
$707$	−1.43940	+	2.49312i	−0.0541343	+	0.0937634i
$708$	−12.3089	−	21.3197i	−0.462597	−	0.801242i
$709$	47.5008			1.78393			0.891965	−	0.452105i	$-0.149327\pi$
$709$	47.5008			1.78393			0.891965	+	0.452105i	$0.149327\pi$
$710$	15.6039	−	27.0268i	0.585605	−	1.01430i
$711$	−11.8228			−0.443388
$712$	−17.8328			−0.668311
$713$		0			0
$714$	−8.99353			−0.336574
$715$	1.51605			0.0566969
$716$	30.5287	−	52.8772i	1.14091	−	1.97611i
$717$	−51.4971			−1.92319
$718$	−2.60842	−	4.51791i	−0.0973453	−	0.168607i
$719$	−8.81254	+	15.2638i	−0.328652	+	0.569243i	−0.982245	−	0.187604i	$-0.939928\pi$
$719$	−8.81254	+	15.2638i	−0.328652	+	0.569243i	0.653592	+	0.756847i	$0.273261\pi$
$720$	9.74107	−	16.8720i	0.363028	−	0.628783i
$721$	−1.06370			−0.0396142
$722$	−36.5842	−	63.3657i	−1.36152	−	2.35823i
$723$	17.6336	+	30.5423i	0.655801	+	1.13588i
$724$	46.5441	+	80.6168i	1.72980	+	2.99610i
$725$	−6.12104	+	10.6020i	−0.227330	+	0.393747i
$726$	−33.6908	−	58.3542i	−1.25038	−	2.16573i
$727$	1.99128	−	3.44900i	0.0738526	−	0.127916i	−0.826734	−	0.562593i	$-0.809804\pi$
$727$	1.99128	−	3.44900i	0.0738526	−	0.127916i	0.900587	+	0.434676i	$0.143137\pi$
$728$	6.67759			0.247488
$729$	−29.0461			−1.07578
$730$	−3.26213	+	5.65017i	−0.120737	+	0.209122i
$731$	−22.1463	−	38.3586i	−0.819111	−	1.41874i
$732$	−52.5974	+	91.1015i	−1.94406	+	3.36721i
$733$	13.7439	+	23.8051i	0.507642	+	0.879261i	0.999961	+	0.00884661i	$0.00281600\pi$
$733$	13.7439	+	23.8051i	0.507642	+	0.879261i	−0.492319	+	0.870415i	$0.663851\pi$
$734$	−24.8626	−	43.0634i	−0.917697	−	1.58950i
$735$	9.84711	+	17.0557i	0.363216	+	0.629109i
$736$	7.24664			0.267115
$737$	−0.523020	+	0.905898i	−0.0192657	+	0.0333692i
$738$	−29.1647	+	50.5148i	−1.07357	+	1.85948i
$739$	10.2855	+	17.8150i	0.378358	+	0.655335i	0.990823	−	0.135162i	$-0.0431555\pi$
$739$	10.2855	+	17.8150i	0.378358	+	0.655335i	−0.612466	+	0.790497i	$0.709822\pi$
$740$	19.8279			0.728887
$741$	38.8794	−	67.3410i	1.42827	−	2.47383i
$742$	−3.14423			−0.115428
$743$	−9.45031			−0.346698			−0.173349	−	0.984860i	$-0.555459\pi$
$743$	−9.45031			−0.346698			−0.173349	+	0.984860i	$0.555459\pi$
$744$		0			0
$745$	−20.0571			−0.734836
$746$	26.7691			0.980088
$747$	−4.35206	+	7.53800i	−0.159234	+	0.275801i
$748$	−6.78273			−0.248001
$749$	2.39242	+	4.14380i	0.0874173	+	0.151411i
$750$	30.7869	−	53.3245i	1.12418	−	1.94713i
$751$	−5.81144	+	10.0657i	−0.212063	+	0.367303i	−0.952360	−	0.304976i	$-0.901351\pi$
$751$	−5.81144	+	10.0657i	−0.212063	+	0.367303i	0.740297	+	0.672280i	$0.234685\pi$
$752$	30.0215			1.09477
$753$	10.8822	+	18.8485i	0.396570	+	0.686879i
$754$	18.7856	+	32.5377i	0.684132	+	1.18495i
$755$	12.4634	+	21.5872i	0.453590	+	0.785640i
$756$	0.160852	−	0.278605i	0.00585015	−	0.0101328i
$757$	12.1948	+	21.1219i	0.443226	+	0.767690i	0.997927	−	0.0643599i	$-0.0205006\pi$
$757$	12.1948	+	21.1219i	0.443226	+	0.767690i	−0.554701	+	0.832050i	$0.687167\pi$
$758$	−17.6654	+	30.5974i	−0.641637	+	1.11135i
$759$	2.14025			0.0776862
$760$	−44.4874			−1.61373
$761$	−11.4239	+	19.7868i	−0.414117	+	0.717273i	−0.995335	−	0.0964754i	$-0.969243\pi$
$761$	−11.4239	+	19.7868i	−0.414117	+	0.717273i	0.581218	+	0.813748i	$0.302576\pi$
$762$	17.4495	+	30.2234i	0.632127	+	1.09488i
$763$	−0.0346393	+	0.0599971i	−0.00125403	+	0.00217204i
$764$	−46.0489	−	79.7590i	−1.66599	−	2.88558i
$765$	9.84148	+	17.0459i	0.355819	+	0.616297i
$766$	−22.2866	−	38.6016i	−0.805249	−	1.39473i
$767$	−10.6425			−0.384277
$768$	−40.1133	+	69.4782i	−1.44746	+	2.50708i
$769$	11.4715	−	19.8693i	0.413674	−	0.716505i	−0.581614	−	0.813465i	$-0.697579\pi$
$769$	11.4715	−	19.8693i	0.413674	−	0.716505i	0.995288	+	0.0969600i	$0.0309119\pi$
$770$	−0.110862	−	0.192019i	−0.00399519	−	0.00691987i
$771$	−9.91611			−0.357120
$772$	−4.67808	+	8.10267i	−0.168368	+	0.291621i
$773$	−36.8949			−1.32702			−0.663509	−	0.748168i	$-0.730934\pi$
$773$	−36.8949			−1.32702			−0.663509	+	0.748168i	$0.730934\pi$
$774$	62.6771			2.25288
$775$		0			0
$776$	11.2331			0.403246
$777$	2.67278			0.0958856
$778$	29.3072	−	50.7615i	1.05071	−	1.81989i
$779$	52.1231			1.86750
$780$	−27.1985	−	47.1092i	−0.973862	−	1.68678i
$781$	1.58634	−	2.74762i	0.0567636	−	0.0983175i
$782$	−20.3591	+	35.2629i	−0.728038	+	1.26100i
$783$	0.954484			0.0341105
$784$	18.8512	+	32.6513i	0.673258	+	1.16612i
$785$	−8.35013	−	14.4628i	−0.298029	−	0.516201i
$786$	19.6507	+	34.0359i	0.700916	+	1.21402i
$787$	26.5704	−	46.0212i	0.947132	−	1.64048i	0.195705	−	0.980663i	$-0.437300\pi$
$787$	26.5704	−	46.0212i	0.947132	−	1.64048i	0.751426	−	0.659817i	$-0.229366\pi$
$788$	36.7970	+	63.7342i	1.31084	+	2.27044i
$789$	0.756880	−	1.31095i	0.0269456	−	0.0466712i
$790$	10.8841			0.387240
$791$	−0.742222			−0.0263904
$792$	2.53062	−	4.38316i	0.0899217	−	0.155749i
$793$	22.7383	+	39.3838i	0.807460	+	1.39856i
$794$	12.6138	−	21.8478i	0.447648	−	0.775348i
$795$	6.75328	+	11.6970i	0.239514	+	0.414851i
$796$	24.8792	+	43.0920i	0.881819	+	1.52736i
$797$	−8.43886	−	14.6165i	−0.298920	−	0.517744i	0.676969	−	0.736011i	$-0.263293\pi$
$797$	−8.43886	−	14.6165i	−0.298920	−	0.517744i	−0.975889	+	0.218267i	$0.929960\pi$
$798$	−11.3723			−0.402576
$799$	−15.1655	+	26.2673i	−0.536515	+	0.929272i
$800$	4.49248	−	7.78121i	0.158833	−	0.275107i
$801$	4.98840	+	8.64017i	0.176257	+	0.305285i
$802$	−57.0969			−2.01616
$803$	−0.331637	+	0.574412i	−0.0117032	+	0.0202706i
$804$	37.5328			1.32368
$805$	−0.903832			−0.0318559
$806$		0			0
$807$	2.78540			0.0980508
$808$	60.4968			2.12827
$809$	−1.76873	+	3.06354i	−0.0621854	+	0.107708i	−0.895442	−	0.445178i	$-0.853140\pi$
$809$	−1.76873	+	3.06354i	−0.0621854	+	0.107708i	0.833257	+	0.552886i	$0.186474\pi$
$810$	24.7807			0.870705
$811$	5.92283	+	10.2586i	0.207979	+	0.360230i	0.951078	−	0.308952i	$-0.0999782\pi$
$811$	5.92283	+	10.2586i	0.207979	+	0.360230i	−0.743099	+	0.669181i	$0.766645\pi$
$812$	1.86560	−	3.23131i	0.0654696	−	0.113397i
$813$	−0.257109	+	0.445326i	−0.00901720	+	0.0156183i
$814$	2.96856			0.104048
$815$	0.0394360	+	0.0683052i	0.00138138	+	0.00239263i
$816$	36.9795	+	64.0504i	1.29454	+	2.24221i
$817$	−28.0041	−	48.5044i	−0.979738	−	1.69696i
$818$	−16.4680	+	28.5234i	−0.575790	+	0.997298i
$819$	−1.86794	−	3.23536i	−0.0652710	−	0.113053i
$820$	18.2316	−	31.5781i	0.636676	−	1.10276i
$821$	43.2198			1.50838			0.754190	−	0.656656i	$-0.228030\pi$
$821$	43.2198			1.50838			0.754190	+	0.656656i	$0.228030\pi$
$822$	−18.2909			−0.637967
$823$	−13.5363	+	23.4456i	−0.471846	+	0.817261i	−0.999481	−	0.0322103i	$-0.989745\pi$
$823$	−13.5363	+	23.4456i	−0.471846	+	0.817261i	0.527635	+	0.849471i	$0.323079\pi$
$824$	11.1766	+	19.3584i	0.389355	+	0.674382i
$825$	1.32683	−	2.29813i	0.0461942	−	0.0800107i
$826$	0.778238	+	1.34795i	0.0270784	+	0.0469011i
$827$	−2.19574	−	3.80314i	−0.0763534	−	0.132248i	0.825321	−	0.564664i	$-0.190994\pi$
$827$	−2.19574	−	3.80314i	−0.0763534	−	0.132248i	−0.901674	+	0.432416i	$0.857661\pi$
$828$	−19.5626	−	33.8835i	−0.679848	−	1.17753i
$829$	16.1614			0.561310			0.280655	−	0.959809i	$-0.409448\pi$
$829$	16.1614			0.561310			0.280655	+	0.959809i	$0.409448\pi$
$830$	4.00655	−	6.93955i	0.139070	−	0.240875i
$831$	30.7587	−	53.2756i	1.06701	−	1.84811i
$832$	10.8242	+	18.7481i	0.375261	+	0.649972i
$833$	−38.0911			−1.31978
$834$	−39.5289	+	68.4661i	−1.36877	+	2.37079i
$835$	−5.58112			−0.193142
$836$	−8.57677			−0.296634
$837$		0			0
$838$	−11.1317			−0.384537
$839$	47.9506			1.65544			0.827719	−	0.561143i	$-0.189638\pi$
$839$	47.9506			1.65544			0.827719	+	0.561143i	$0.189638\pi$
$840$	−2.09759	+	3.63313i	−0.0723737	+	0.125355i
$841$	−17.9297			−0.618266
$842$	24.1178	+	41.7733i	0.831155	+	1.43960i
$843$	31.8568	−	55.1776i	1.09721	−	1.90042i
$844$	15.7930	−	27.3542i	0.543617	−	0.941571i
$845$	−8.57692			−0.295055
$846$	−21.4602	−	37.1701i	−0.737816	−	1.27793i
$847$	1.44643	+	2.50528i	0.0496998	+	0.0860826i
$848$	12.9284	+	22.3927i	0.443964	+	0.768968i
$849$	−33.1158	+	57.3583i	−1.13653	+	1.96853i
$850$	25.2428	+	43.7218i	0.865821	+	1.49965i
$851$	6.05050	−	10.4798i	0.207409	−	0.359242i
$852$	−113.838			−3.90004
$853$	32.4430			1.11083			0.555414	−	0.831574i	$-0.312560\pi$
$853$	32.4430			1.11083			0.555414	+	0.831574i	$0.312560\pi$
$854$	3.32551	−	5.75995i	0.113796	−	0.197101i
$855$	12.4446	+	21.5546i	0.425595	+	0.737152i
$856$	50.2757	−	87.0801i	1.71839	−	2.97634i
$857$	−2.71350	−	4.69992i	−0.0926913	−	0.160546i	0.815951	−	0.578120i	$-0.196214\pi$
$857$	−2.71350	−	4.69992i	−0.0926913	−	0.160546i	−0.908643	+	0.417574i	$0.862880\pi$
$858$	−4.07206	−	7.05302i	−0.139018	−	0.240786i
$859$	20.2309	+	35.0409i	0.690268	+	1.19558i	0.971750	+	0.236013i	$0.0758408\pi$
$859$	20.2309	+	35.0409i	0.690268	+	1.19558i	−0.281482	+	0.959567i	$0.590826\pi$
$860$	−39.1811			−1.33606
$861$	2.45761	−	4.25671i	0.0837552	−	0.145068i
$862$	13.0370	−	22.5807i	0.444041	−	0.769102i
$863$	−1.18137	−	2.04620i	−0.0402144	−	0.0696533i	0.845218	−	0.534422i	$-0.179471\pi$
$863$	−1.18137	−	2.04620i	−0.0402144	−	0.0696533i	−0.885432	+	0.464769i	$0.846137\pi$
$864$	−0.700535			−0.0238327
$865$	−6.49038	+	11.2417i	−0.220680	+	0.382228i
$866$	51.7470			1.75843
$867$	−32.6795			−1.10985
$868$		0			0
$869$	1.10651			0.0375358
$870$	−23.6040			−0.800252
$871$	8.11286	−	14.0519i	0.274894	−	0.476130i
$872$	1.45586			0.0493016
$873$	−3.14227	−	5.44257i	−0.106350	−	0.184203i
$874$	−25.7441	+	44.5900i	−0.870806	+	1.50828i
$875$	−1.32176	+	2.28935i	−0.0446835	+	0.0773941i
$876$	23.7988			0.804088
$877$	16.7040	+	28.9322i	0.564054	+	0.976970i	0.997137	+	0.0756157i	$0.0240922\pi$
$877$	16.7040	+	28.9322i	0.564054	+	0.976970i	−0.433083	+	0.901354i	$0.642574\pi$
$878$	−35.3911	−	61.2992i	−1.19439	−	2.06875i
$879$	27.6522	+	47.8950i	0.932685	+	1.61546i
$880$	−0.911683	+	1.57908i	−0.0307328	+	0.0532308i
$881$	−23.4413	−	40.6015i	−0.789757	−	1.36790i	−0.926116	−	0.377240i	$-0.876873\pi$
$881$	−23.4413	−	40.6015i	−0.789757	−	1.36790i	0.136358	−	0.990660i	$-0.456460\pi$
$882$	26.9508	−	46.6801i	0.907480	−	1.57180i
$883$	30.9187			1.04050			0.520248	−	0.854015i	$-0.325839\pi$
$883$	30.9187			1.04050			0.520248	+	0.854015i	$0.325839\pi$
$884$	105.211			3.53862
$885$	3.34305	−	5.79033i	0.112375	−	0.194640i
$886$	36.4658	+	63.1606i	1.22509	+	2.12192i
$887$	−17.4395	+	30.2060i	−0.585560	+	1.01422i	0.409246	+	0.912424i	$0.365792\pi$
$887$	−17.4395	+	30.2060i	−0.585560	+	1.01422i	−0.994805	+	0.101795i	$0.967542\pi$
$888$	−28.0837	−	48.6423i	−0.942426	−	1.63233i
$889$	−0.749147	−	1.29756i	−0.0251256	−	0.0435188i
$890$	−4.59237	−	7.95422i	−0.153937	−	0.266626i
$891$	2.51927			0.0843989
$892$	61.6627	−	106.803i	2.06462	−	3.57603i
$893$	−19.1767	+	33.2151i	−0.641725	+	1.11150i
$894$	53.8730	+	93.3107i	1.80178	+	3.12078i
$895$	16.5829			0.554307
$896$	2.23026	−	3.86293i	0.0745079	−	0.129051i
$897$	−33.1986			−1.10847
$898$	−2.91220			−0.0971813
$899$		0			0
$900$	−48.5106			−1.61702
$901$	−26.1234			−0.870296
$902$	2.72958	−	4.72777i	0.0908850	−	0.157417i
$903$	−5.28158			−0.175760
$904$	7.79873	+	13.5078i	0.259382	+	0.449263i
$905$	−12.6412	+	21.8952i	−0.420208	+	0.727821i
$906$	66.9528	−	115.966i	2.22436	−	3.85270i
$907$	−43.8742			−1.45682			−0.728410	−	0.685142i	$-0.759740\pi$
$907$	−43.8742			−1.45682			−0.728410	+	0.685142i	$0.759740\pi$
$908$	−12.5831	−	21.7945i	−0.417583	−	0.723275i
$909$	−16.9229	−	29.3113i	−0.561297	−	0.972196i
$910$	1.71964	+	2.97851i	0.0570056	+	0.0987366i
$911$	−21.8550	+	37.8539i	−0.724088	+	1.25416i	0.235261	+	0.971932i	$0.424406\pi$
$911$	−21.8550	+	37.8539i	−0.724088	+	1.25416i	−0.959348	+	0.282225i	$0.908928\pi$
$912$	46.7607	+	80.9919i	1.54840	+	2.68191i
$913$	0.407317	−	0.705494i	0.0134802	−	0.0233484i
$914$	−100.553			−3.32601
$915$	−28.5705			−0.944512
$916$	11.8287	−	20.4878i	0.390830	−	0.676937i
$917$	−0.843650	−	1.46124i	−0.0278598	−	0.0482545i
$918$	1.96812	−	3.40888i	0.0649575	−	0.112510i
$919$	17.9871	+	31.1546i	0.593340	+	1.02769i	0.993779	+	0.111371i	$0.0355243\pi$
$919$	17.9871	+	31.1546i	0.593340	+	1.02769i	−0.400439	+	0.916323i	$0.631142\pi$
$920$	9.49681	+	16.4490i	0.313101	+	0.542306i
$921$	9.01160	+	15.6086i	0.296942	+	0.514319i
$922$	73.2380			2.41197
$923$	−24.6066	+	42.6199i	−0.809936	+	1.40285i
$924$	−0.404396	+	0.700434i	−0.0133037	+	0.0230426i
$925$	−7.50190	−	12.9937i	−0.246661	−	0.427229i
$926$	1.59636			0.0524598
$927$	6.25290	−	10.8303i	0.205372	−	0.355715i
$928$	−8.12493			−0.266714
$929$	−7.67225			−0.251719			−0.125859	−	0.992048i	$-0.540169\pi$
$929$	−7.67225			−0.251719			−0.125859	+	0.992048i	$0.540169\pi$
$930$		0			0
$931$	−48.1663			−1.57859
$932$	−111.616			−3.65610
$933$	−31.6582	+	54.8336i	−1.03644	+	1.79517i
$934$	7.22768			0.236497
$935$	−0.921081	−	1.59536i	−0.0301226	−	0.0521738i
$936$	−39.2539	+	67.9897i	−1.28305	+	2.22231i
$937$	−21.5513	+	37.3279i	−0.704050	+	1.21945i	0.262984	+	0.964800i	$0.415293\pi$
$937$	−21.5513	+	37.3279i	−0.704050	+	1.21945i	−0.967033	+	0.254650i	$0.918040\pi$
$938$	−2.37304			−0.0774824
$939$	−31.5030	−	54.5647i	−1.02806	−	1.78065i
$940$	13.4153	+	23.2360i	0.437559	+	0.757875i
$941$	−18.4869	−	32.0202i	−0.602655	−	1.04383i	−0.992417	−	0.122913i	$-0.960776\pi$
$941$	−18.4869	−	32.0202i	−0.602655	−	1.04383i	0.389763	−	0.920915i	$-0.372557\pi$
$942$	−44.8565	+	77.6937i	−1.46150	+	2.53140i
$943$	−11.1268	−	19.2722i	−0.362339	−	0.627589i
$944$	6.39991	−	11.0850i	0.208299	−	0.360785i
$945$	0.0873738			0.00284227
$946$	−5.86606			−0.190722
$947$	−29.2512	+	50.6645i	−0.950535	+	1.64637i	−0.206264	+	0.978496i	$0.566131\pi$
$947$	−29.2512	+	50.6645i	−0.950535	+	1.64637i	−0.744271	+	0.667878i	$0.767203\pi$
$948$	−19.8513	−	34.3834i	−0.644740	−	1.11672i
$949$	5.14421	−	8.91003i	0.166988	−	0.289232i
$950$	31.9196	+	55.2863i	1.03561	+	1.79372i
$951$	−17.6046	−	30.4920i	−0.570867	−	0.988770i
$952$	−4.05700	−	7.02693i	−0.131488	−	0.227744i
$953$	−53.2374			−1.72453			−0.862264	−	0.506459i	$-0.830954\pi$
$953$	−53.2374			−1.72453			−0.862264	+	0.506459i	$0.830954\pi$
$954$	18.4832	−	32.0138i	0.598415	−	1.03649i
$955$	12.5067	−	21.6622i	0.404707	−	0.700973i
$956$	−44.0537	−	76.3033i	−1.42480	−	2.46783i
$957$	−2.39965			−0.0775697
$958$	−36.1255	+	62.5713i	−1.16716	+	2.02159i
$959$	0.785271			0.0253577
$960$	−13.6005			−0.438956
$961$		0			0
$962$	−46.0470			−1.48462
$963$	−56.2550			−1.81279
$964$	−30.1697	+	52.2555i	−0.971701	+	1.68304i
$965$	−2.54110			−0.0818008
$966$	2.42767	+	4.20485i	0.0781091	+	0.135289i
$967$	−6.05038	+	10.4796i	−0.194567	+	0.337000i	−0.946759	−	0.321945i	$-0.895664\pi$
$967$	−6.05038	+	10.4796i	−0.194567	+	0.337000i	0.752191	+	0.658945i	$0.228997\pi$
$968$	30.3960	−	52.6474i	0.976965	−	1.69215i
$969$	−94.4854			−3.03531
$970$	2.89280	+	5.01048i	0.0928823	+	0.160877i
$971$	−5.33426	−	9.23920i	−0.171184	−	0.296500i	0.767650	−	0.640870i	$-0.221426\pi$
$971$	−5.33426	−	9.23920i	−0.171184	−	0.296500i	−0.938834	+	0.344369i	$0.888093\pi$
$972$	−47.0176	−	81.4368i	−1.50809	−	2.61209i
$973$	1.69707	−	2.93941i	0.0544056	−	0.0942332i
$974$	−3.41139	−	5.90869i	−0.109308	−	0.189327i
$975$	−20.5812	+	35.6476i	−0.659125	+	1.14164i
$976$	−54.6952			−1.75075
$977$	−46.9976			−1.50359			−0.751793	−	0.659399i	$-0.770811\pi$
$977$	−46.9976			−1.50359			−0.751793	+	0.659399i	$0.770811\pi$
$978$	0.211849	−	0.366932i	0.00677417	−	0.0117332i
$979$	−0.466873	−	0.808648i	−0.0149213	−	0.0258445i
$980$	−16.8476	+	29.1810i	−0.538178	+	0.932151i
$981$	−0.407251	−	0.705379i	−0.0130025	−	0.0225210i
$982$	14.2657	+	24.7089i	0.455236	+	0.788492i
$983$	5.75697	+	9.97137i	0.183619	+	0.318037i	0.943110	−	0.332480i	$-0.107885\pi$
$983$	5.75697	+	9.97137i	0.183619	+	0.318037i	−0.759491	+	0.650517i	$0.774552\pi$
$984$	−103.291			−3.29280
$985$	−9.99391	+	17.3100i	−0.318432	+	0.551541i
$986$	22.8266	−	39.5368i	0.726947	−	1.25911i
$987$	1.80837	+	3.13220i	0.0575612	+	0.0996989i
$988$	133.039			4.23254
$989$	−11.9562	+	20.7087i	−0.380184	+	0.658498i
$990$	2.60679			0.0828491
$991$	56.6493			1.79952			0.899762	−	0.436381i	$-0.143740\pi$
$991$	56.6493			1.79952			0.899762	+	0.436381i	$0.143740\pi$
$992$		0			0
$993$	−43.2575			−1.37274
$994$	7.19750			0.228291
$995$	−6.75709	+	11.7036i	−0.214214	+	0.371030i
$996$	−29.2298			−0.926181
$997$	23.5058	+	40.7133i	0.744436	+	1.28940i	0.950458	+	0.310854i	$0.100615\pi$
$997$	23.5058	+	40.7133i	0.744436	+	1.28940i	−0.206021	+	0.978548i	$0.566052\pi$
$998$	−8.01523	+	13.8828i	−0.253718	+	0.439452i
$999$	−0.584904	+	1.01308i	−0.0185055	+	0.0320526i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.11	✓	12	31.5	even	3
961.2.a.k.1.12	yes	12	31.26	odd	6
961.2.c.k.439.11		24	31.30	odd	2	inner
961.2.c.k.439.12		24	1.1	even	1	trivial
961.2.c.k.521.11		24	31.6	odd	6	inner
961.2.c.k.521.12		24	31.25	even	3	inner
961.2.d.r.374.1		48	31.22	odd	30
961.2.d.r.374.2		48	31.9	even	15
961.2.d.r.388.1		48	31.11	odd	30
961.2.d.r.388.2		48	31.20	even	15
961.2.d.r.531.11		48	31.10	even	15
961.2.d.r.531.12		48	31.21	odd	30
961.2.d.r.628.11		48	31.18	even	15
961.2.d.r.628.12		48	31.13	odd	30
961.2.g.v.235.1		96	31.4	even	5
961.2.g.v.235.2		96	31.27	odd	10
961.2.g.v.338.1		96	31.24	odd	30
961.2.g.v.338.2		96	31.7	even	15
961.2.g.v.448.11		96	31.28	even	15
961.2.g.v.448.12		96	31.3	odd	30
961.2.g.v.547.11		96	31.2	even	5
961.2.g.v.547.12		96	31.29	odd	10
961.2.g.v.732.1		96	31.14	even	15
961.2.g.v.732.2		96	31.17	odd	30
961.2.g.v.816.1		96	31.23	odd	10
961.2.g.v.816.2		96	31.8	even	5
961.2.g.v.844.11		96	31.12	odd	30
961.2.g.v.844.12		96	31.19	even	15
961.2.g.v.846.11		96	31.15	odd	10
961.2.g.v.846.12		96	31.16	even	5
8649.2.a.bp.1.1		12	93.26	even	6
8649.2.a.bp.1.2		12	93.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.49624 q^{2} +(1.23653 - 2.14173i) q^{3} +4.23120 q^{4} +(0.574589 + 0.995217i) q^{5} +(3.08667 - 5.34626i) q^{6} +(-0.132518 + 0.229528i) q^{7} +5.56961 q^{8} +(-1.55800 - 2.69853i) q^{9} +(1.43431 + 2.48430i) q^{10} +(0.145816 + 0.252560i) q^{11} +(5.23200 - 9.06208i) q^{12} +(-2.26183 - 3.91761i) q^{13} +(-0.330796 + 0.572956i) q^{14} +2.84198 q^{15} +5.44066 q^{16} +(-2.74837 + 4.76032i) q^{17} +(-3.88914 - 6.73618i) q^{18} +(-3.47532 + 6.01943i) q^{19} +(2.43120 + 4.21096i) q^{20} +(0.327724 + 0.567635i) q^{21} +(0.363991 + 0.630451i) q^{22} +2.96754 q^{23} +(6.88697 - 11.9286i) q^{24} +(1.83970 - 3.18645i) q^{25} +(-5.64607 - 9.77928i) q^{26} -0.286873 q^{27} +(-0.560710 + 0.971178i) q^{28} -3.32720 q^{29} +7.09426 q^{30} +2.44197 q^{32} +0.721221 q^{33} +(-6.86059 + 11.8829i) q^{34} -0.304573 q^{35} +(-6.59221 - 11.4180i) q^{36} +(2.03890 - 3.53147i) q^{37} +(-8.67523 + 15.0259i) q^{38} -11.1873 q^{39} +(3.20024 + 5.54297i) q^{40} +(-3.74951 - 6.49435i) q^{41} +(0.818077 + 1.41695i) q^{42} +(-4.02899 + 6.97841i) q^{43} +(0.616976 + 1.06863i) q^{44} +(1.79042 - 3.10110i) q^{45} +7.40767 q^{46} +5.51798 q^{47} +(6.72753 - 11.6524i) q^{48} +(3.46488 + 6.00134i) q^{49} +(4.59232 - 7.95413i) q^{50} +(6.79688 + 11.7725i) q^{51} +(-9.57027 - 16.5762i) q^{52} +(2.37626 + 4.11580i) q^{53} -0.716103 q^{54} +(-0.167568 + 0.290237i) q^{55} +(-0.738073 + 1.27838i) q^{56} +(8.59466 + 14.8864i) q^{57} -8.30549 q^{58} +(1.17631 - 2.03743i) q^{59} +12.0250 q^{60} -10.0530 q^{61} +0.825852 q^{63} -4.78559 q^{64} +(2.59925 - 4.50203i) q^{65} +1.80034 q^{66} +(1.79343 + 3.10631i) q^{67} +(-11.6289 + 20.1419i) q^{68} +(3.66944 - 6.35566i) q^{69} -0.760287 q^{70} +(-5.43953 - 9.42153i) q^{71} +(-8.67745 - 15.0298i) q^{72} +(1.13718 + 1.96965i) q^{73} +(5.08957 - 8.81540i) q^{74} +(-4.54967 - 7.88025i) q^{75} +(-14.7048 + 25.4694i) q^{76} -0.0772929 q^{77} -27.9261 q^{78} +(1.89710 - 3.28588i) q^{79} +(3.12614 + 5.41464i) q^{80} +(4.31927 - 7.48120i) q^{81} +(-9.35967 - 16.2114i) q^{82} +(-1.39668 - 2.41913i) q^{83} +(1.38667 + 2.40178i) q^{84} -6.31674 q^{85} +(-10.0573 + 17.4198i) q^{86} +(-4.11418 + 7.12597i) q^{87} +(0.812137 + 1.40666i) q^{88} -3.20180 q^{89} +(4.46931 - 7.74107i) q^{90} +1.19893 q^{91} +12.5562 q^{92} +13.7742 q^{94} -7.98753 q^{95} +(3.01956 - 5.23004i) q^{96} +2.01686 q^{97} +(8.64916 + 14.9808i) q^{98} +(0.454362 - 0.786978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 32 q^{4} - 8 q^{5} - 8 q^{7} + 24 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} - 32 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} - 12 q^{25} + 20 q^{28} + 48 q^{32} - 80 q^{33} + 112 q^{35} - 40 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) \) 24 * q + 32 * q^4 - 8 * q^5 - 8 * q^7 + 24 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 - 32 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 - 12 * q^25 + 20 * q^28 + 48 * q^32 - 80 * q^33 + 112 * q^35 - 40 * q^36 - 36 * q^38 - 32 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 + 96 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 + 8 * q^56 - 40 * q^59 - 16 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 24 * q^69 + 24 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 - 208 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 - 64 * q^87 + 44 * q^90 + 32 * q^94 + 80 * q^95 - 16 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

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