LMFDB - Embedded newform 950.2.u.f.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.3
Character	$\chi$	$=$	950.99
Dual form			950.2.u.f.499.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(-0.402740 + 0.0710139i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.0710139 + 0.402740i) q^{6} +(1.99244 + 1.15033i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.66192 + 0.968860i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(-0.402740 + 0.0710139i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.0710139 + 0.402740i) q^{6} +(1.99244 + 1.15033i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.66192 + 0.968860i) q^{9} +(1.32398 + 2.29321i) q^{11} +(0.354164 + 0.204476i) q^{12} +(-5.02221 - 0.885551i) q^{13} +(1.76241 - 1.47884i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.955698 + 2.62576i) q^{17} +2.83276i q^{18} +(1.11951 + 4.21268i) q^{19} +(-0.884124 - 0.321795i) q^{21} +(2.60774 - 0.459814i) q^{22} +(0.751910 - 0.896091i) q^{23} +(0.313276 - 0.262870i) q^{24} +(-2.54984 + 4.41645i) q^{26} +(2.06575 - 1.19266i) q^{27} +(-0.786875 - 2.16192i) q^{28} +(-4.18479 + 1.52314i) q^{29} +(-4.11588 + 7.12891i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-0.696070 - 0.829544i) q^{33} +(2.14054 + 1.79613i) q^{34} +(2.66192 + 0.968860i) q^{36} -2.99954i q^{37} +(4.34152 + 0.388831i) q^{38} +2.08553 q^{39} +(1.97511 + 11.2014i) q^{41} +(-0.604776 + 0.720744i) q^{42} +(0.990646 + 1.18061i) q^{43} +(0.459814 - 2.60774i) q^{44} +(-0.584882 - 1.01305i) q^{46} +(-3.61169 - 9.92304i) q^{47} +(-0.139870 - 0.384290i) q^{48} +(-0.853462 - 1.47824i) q^{49} +(0.198432 - 1.12537i) q^{51} +(3.27801 + 3.90658i) q^{52} +(-2.72428 + 3.24667i) q^{53} +(-0.414207 - 2.34908i) q^{54} -2.30067 q^{56} +(-0.750029 - 1.61712i) q^{57} +4.45336i q^{58} +(10.5415 + 3.83681i) q^{59} +(2.53595 + 2.12792i) q^{61} +(5.29127 + 6.30589i) q^{62} +(-6.41823 - 1.13171i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.01759 + 0.370371i) q^{66} +(2.88116 + 7.91593i) q^{67} +(2.41991 - 1.39714i) q^{68} +(-0.239189 + 0.414288i) q^{69} +(-0.239189 + 0.200703i) q^{71} +(1.82086 - 2.17002i) q^{72} +(15.1155 - 2.66528i) q^{73} +(-2.81865 - 1.02590i) q^{74} +(1.85027 - 3.94671i) q^{76} +6.09209i q^{77} +(0.713293 - 1.95976i) q^{78} +(1.52957 + 8.67461i) q^{79} +(5.76279 - 4.83556i) q^{81} +(11.2014 + 1.97511i) q^{82} +(-1.53755 - 0.887706i) q^{83} +(0.470432 + 0.814813i) q^{84} +(1.44823 - 0.527112i) q^{86} +(1.57722 - 0.910608i) q^{87} +(-2.29321 - 1.32398i) q^{88} +(-1.12686 + 6.39074i) q^{89} +(-8.98775 - 7.54162i) q^{91} +(-1.15199 + 0.203127i) q^{92} +(1.15138 - 3.16338i) q^{93} -10.5599 q^{94} -0.408953 q^{96} +(0.896300 - 2.46256i) q^{97} +(-1.68099 + 0.296404i) q^{98} +(-5.74613 - 4.82158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	−0.402740	+	0.0710139i	−0.232522	+	0.0409999i	−0.288695	−	0.957421i	$-0.593221\pi$
$3$	−0.402740	+	0.0710139i	−0.232522	+	0.0409999i	0.0561729	+	0.998421i	$0.482110\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.0710139	+	0.402740i	−0.0289913	+	0.164418i
$7$	1.99244	+	1.15033i	0.753071	+	0.434786i	0.826802	−	0.562493i	$-0.190158\pi$
$7$	1.99244	+	1.15033i	0.753071	+	0.434786i	−0.0737317	+	0.997278i	$0.523491\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.66192	+	0.968860i	−0.887307	+	0.322953i
$10$		0			0
$11$	1.32398	+	2.29321i	0.399196	+	0.691427i	0.993627	−	0.112719i	$-0.0359561\pi$
$11$	1.32398	+	2.29321i	0.399196	+	0.691427i	−0.594431	+	0.804147i	$0.702623\pi$
$12$	0.354164	+	0.204476i	0.102238	+	0.0590273i
$13$	−5.02221	−	0.885551i	−1.39291	−	0.245608i	−0.573683	−	0.819077i	$-0.694486\pi$
$13$	−5.02221	−	0.885551i	−1.39291	−	0.245608i	−0.819227	+	0.573470i	$0.805597\pi$
$14$	1.76241	−	1.47884i	0.471025	−	0.395237i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.955698	+	2.62576i	−0.231791	+	0.636840i	−0.999994	−	0.00336552i	$-0.998929\pi$
$17$	−0.955698	+	2.62576i	−0.231791	+	0.636840i	0.768203	+	0.640206i	$0.221151\pi$
$18$			2.83276i			0.667687i
$19$	1.11951	+	4.21268i	0.256832	+	0.966456i
$19$	1.11951	+	4.21268i	0.256832	+	0.966456i
$20$		0			0
$21$	−0.884124	−	0.321795i	−0.192932	−	0.0702214i
$22$	2.60774	−	0.459814i	0.555971	−	0.0980327i
$23$	0.751910	−	0.896091i	0.156784	−	0.186848i	−0.681934	−	0.731413i	$-0.738861\pi$
$23$	0.751910	−	0.896091i	0.156784	−	0.186848i	0.838718	+	0.544566i	$0.183305\pi$
$24$	0.313276	−	0.262870i	0.0639472	−	0.0536581i
$25$		0			0
$26$	−2.54984	+	4.41645i	−0.500065	+	0.866138i
$27$	2.06575	−	1.19266i	0.397554	−	0.229528i
$28$	−0.786875	−	2.16192i	−0.148705	−	0.408565i
$29$	−4.18479	+	1.52314i	−0.777096	+	0.282840i	−0.699961	−	0.714181i	$-0.746799\pi$
$29$	−4.18479	+	1.52314i	−0.777096	+	0.282840i	−0.0771351	+	0.997021i	$0.524577\pi$
$30$		0			0
$31$	−4.11588	+	7.12891i	−0.739233	+	1.28039i	0.213608	+	0.976919i	$0.431479\pi$
$31$	−4.11588	+	7.12891i	−0.739233	+	1.28039i	−0.952841	+	0.303470i	$0.901855\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−0.696070	−	0.829544i	−0.121170	−	0.144405i
$34$	2.14054	+	1.79613i	0.367099	+	0.308033i
$35$		0			0
$36$	2.66192	+	0.968860i	0.443654	+	0.161477i
$37$		−	2.99954i		−	0.493122i	−0.969127	−	0.246561i	$-0.920699\pi$
$37$		−	2.99954i		−	0.493122i	0.969127	−	0.246561i	$-0.0793006\pi$
$38$	4.34152	+	0.388831i	0.704288	+	0.0630767i
$39$	2.08553			0.333952
$40$		0			0
$41$	1.97511	+	11.2014i	0.308460	+	1.74936i	0.606753	+	0.794890i	$0.292472\pi$
$41$	1.97511	+	11.2014i	0.308460	+	1.74936i	−0.298293	+	0.954474i	$0.596417\pi$
$42$	−0.604776	+	0.720744i	−0.0933190	+	0.111213i
$43$	0.990646	+	1.18061i	0.151072	+	0.180041i	0.836273	−	0.548314i	$-0.184730\pi$
$43$	0.990646	+	1.18061i	0.151072	+	0.180041i	−0.685201	+	0.728354i	$0.740286\pi$
$44$	0.459814	−	2.60774i	0.0693196	−	0.393131i
$45$		0			0
$46$	−0.584882	−	1.01305i	−0.0862361	−	0.149365i
$47$	−3.61169	−	9.92304i	−0.526819	−	1.44742i	−0.862795	−	0.505553i	$-0.831288\pi$
$47$	−3.61169	−	9.92304i	−0.526819	−	1.44742i	0.335976	−	0.941871i	$-0.390934\pi$
$48$	−0.139870	−	0.384290i	−0.0201885	−	0.0554675i
$49$	−0.853462	−	1.47824i	−0.121923	−	0.211177i
$50$		0			0
$51$	0.198432	−	1.12537i	0.0277861	−	0.157583i
$52$	3.27801	+	3.90658i	0.454579	+	0.541746i
$53$	−2.72428	+	3.24667i	−0.374208	+	0.445964i	−0.919977	−	0.391972i	$-0.871793\pi$
$53$	−2.72428	+	3.24667i	−0.374208	+	0.445964i	0.545769	+	0.837936i	$0.316238\pi$
$54$	−0.414207	−	2.34908i	−0.0563664	−	0.319670i
$55$		0			0
$56$	−2.30067			−0.307440
$57$	−0.750029	−	1.61712i	−0.0993438	−	0.214192i
$58$			4.45336i			0.584755i
$59$	10.5415	+	3.83681i	1.37239	+	0.499510i	0.919863	−	0.392239i	$-0.128300\pi$
$59$	10.5415	+	3.83681i	1.37239	+	0.499510i	0.452529	+	0.891749i	$0.350522\pi$
$60$		0			0
$61$	2.53595	+	2.12792i	0.324695	+	0.272452i	0.790534	−	0.612418i	$-0.209803\pi$
$61$	2.53595	+	2.12792i	0.324695	+	0.272452i	−0.465839	+	0.884870i	$0.654247\pi$
$62$	5.29127	+	6.30589i	0.671992	+	0.800849i
$63$	−6.41823	−	1.13171i	−0.808620	−	0.142582i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−1.01759	+	0.370371i	−0.125256	+	0.0455895i
$67$	2.88116	+	7.91593i	0.351990	+	0.967084i	0.981730	+	0.190279i	$0.0609391\pi$
$67$	2.88116	+	7.91593i	0.351990	+	0.967084i	−0.629740	+	0.776806i	$0.716839\pi$
$68$	2.41991	−	1.39714i	0.293458	−	0.169428i
$69$	−0.239189	+	0.414288i	−0.0287950	+	0.0498744i
$70$		0			0
$71$	−0.239189	+	0.200703i	−0.0283865	+	0.0238191i	−0.656871	−	0.754003i	$-0.728120\pi$
$71$	−0.239189	+	0.200703i	−0.0283865	+	0.0238191i	0.628484	+	0.777823i	$0.283676\pi$
$72$	1.82086	−	2.17002i	0.214591	−	0.255739i
$73$	15.1155	−	2.66528i	1.76914	−	0.311947i	0.808242	−	0.588851i	$-0.200419\pi$
$73$	15.1155	−	2.66528i	1.76914	−	0.311947i	0.960898	+	0.276904i	$0.0893084\pi$
$74$	−2.81865	−	1.02590i	−0.327661	−	0.119259i
$75$		0			0
$76$	1.85027	−	3.94671i	0.212240	−	0.452718i
$77$			6.09209i			0.694258i
$78$	0.713293	−	1.95976i	0.0807645	−	0.221899i
$79$	1.52957	+	8.67461i	0.172090	+	0.975970i	0.941450	+	0.337154i	$0.109464\pi$
$79$	1.52957	+	8.67461i	0.172090	+	0.975970i	−0.769360	+	0.638816i	$0.779425\pi$
$80$		0			0
$81$	5.76279	−	4.83556i	0.640310	−	0.537284i
$82$	11.2014	+	1.97511i	1.23699	+	0.218114i
$83$	−1.53755	−	0.887706i	−0.168768	−	0.0974384i	0.413237	−	0.910624i	$-0.364398\pi$
$83$	−1.53755	−	0.887706i	−0.168768	−	0.0974384i	−0.582005	+	0.813185i	$0.697732\pi$
$84$	0.470432	+	0.814813i	0.0513284	+	0.0889034i
$85$		0			0
$86$	1.44823	−	0.527112i	0.156166	−	0.0568399i
$87$	1.57722	−	0.910608i	0.169096	−	0.0976274i
$88$	−2.29321	−	1.32398i	−0.244456	−	0.141137i
$89$	−1.12686	+	6.39074i	−0.119447	+	0.677417i	0.865005	+	0.501763i	$0.167315\pi$
$89$	−1.12686	+	6.39074i	−0.119447	+	0.677417i	−0.984452	+	0.175654i	$0.943796\pi$
$90$		0			0
$91$	−8.98775	−	7.54162i	−0.942173	−	0.790577i
$92$	−1.15199	+	0.203127i	−0.120104	+	0.0211775i
$93$	1.15138	−	3.16338i	0.119392	−	0.328027i
$94$	−10.5599			−1.08917
$95$		0			0
$96$	−0.408953			−0.0417386
$97$	0.896300	−	2.46256i	0.0910055	−	0.250035i	−0.885837	−	0.463997i	$-0.846415\pi$
$97$	0.896300	−	2.46256i	0.0910055	−	0.250035i	0.976842	+	0.213962i	$0.0686369\pi$
$98$	−1.68099	+	0.296404i	−0.169806	+	0.0299413i
$99$	−5.74613	−	4.82158i	−0.577508	−	0.484587i
$100$		0			0
$101$	1.69635	−	9.62050i	0.168794	−	0.957276i	−0.776273	−	0.630397i	$-0.782892\pi$
$101$	1.69635	−	9.62050i	0.168794	−	0.957276i	0.945066	−	0.326879i	$-0.105997\pi$
$102$	−0.989630	−	0.571363i	−0.0979880	−	0.0565734i
$103$	−0.430950	+	0.248809i	−0.0424628	+	0.0245159i	−0.521081	−	0.853507i	$-0.674471\pi$
$103$	−0.430950	+	0.248809i	−0.0424628	+	0.0245159i	0.478618	+	0.878023i	$0.341138\pi$
$104$	4.79213	−	1.74419i	0.469907	−	0.171032i
$105$		0			0
$106$	2.11911	+	3.67041i	0.205826	+	0.356502i
$107$	−16.6780	−	9.62904i	−1.61232	−	0.930874i	−0.988831	−	0.149044i	$-0.952380\pi$
$107$	−16.6780	−	9.62904i	−1.61232	−	0.930874i	−0.623491	−	0.781831i	$-0.714286\pi$
$108$	−2.34908	−	0.414207i	−0.226041	−	0.0398571i
$109$	−8.91741	+	7.48260i	−0.854133	+	0.716703i	−0.960696	−	0.277603i	$-0.910460\pi$
$109$	−8.91741	+	7.48260i	−0.854133	+	0.716703i	0.106563	+	0.994306i	$0.466016\pi$
$110$		0			0
$111$	0.213009	+	1.20804i	0.0202180	+	0.114662i
$112$	−0.786875	+	2.16192i	−0.0743527	+	0.204282i
$113$			9.87717i			0.929166i	0.885530	+	0.464583i	$0.153796\pi$
$113$			9.87717i			0.929166i	−0.885530	+	0.464583i	$0.846204\pi$
$114$	−1.77612	+	0.151711i	−0.166349	+	0.0142090i
$115$		0			0
$116$	4.18479	+	1.52314i	0.388548	+	0.141420i
$117$	14.2267	−	2.50855i	1.31526	−	0.231916i
$118$	7.21084	−	8.59355i	0.663812	−	0.791100i
$119$	−4.92467	+	4.13229i	−0.451444	+	0.378806i
$120$		0			0
$121$	1.99414	−	3.45395i	0.181285	−	0.313996i
$122$	2.86693	−	1.65522i	0.259560	−	0.149857i
$123$	−1.59091	−	4.37099i	−0.143448	−	0.394119i
$124$	7.73532	−	2.81543i	0.694652	−	0.252833i
$125$		0			0
$126$	−3.25862	+	5.64409i	−0.290301	+	0.502816i
$127$	−8.29089	−	1.46191i	−0.735697	−	0.129723i	−0.206769	−	0.978390i	$-0.566295\pi$
$127$	−8.29089	−	1.46191i	−0.735697	−	0.129723i	−0.528928	+	0.848667i	$0.677406\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	−0.482812	−	0.405127i	−0.0425092	−	0.0356695i
$130$		0			0
$131$	−16.0131	−	5.82829i	−1.39907	−	0.509220i	−0.471169	−	0.882043i	$-0.656168\pi$
$131$	−16.0131	−	5.82829i	−1.39907	−	0.509220i	−0.927903	+	0.372823i	$0.878390\pi$
$132$			1.08289i			0.0942537i
$133$	−2.61545	+	9.68132i	−0.226788	+	0.839477i
$134$	8.42395			0.727719
$135$		0			0
$136$	−0.485221	−	2.75182i	−0.0416073	−	0.235967i
$137$	−7.53983	+	8.98562i	−0.644171	+	0.767694i	−0.985023	−	0.172424i	$-0.944840\pi$
$137$	−7.53983	+	8.98562i	−0.644171	+	0.767694i	0.340851	+	0.940117i	$0.389285\pi$
$138$	0.307496	+	0.366459i	0.0261758	+	0.0311951i
$139$	2.24940	−	12.7570i	0.190792	−	1.08203i	−0.727494	−	0.686114i	$-0.759315\pi$
$139$	2.24940	−	12.7570i	0.190792	−	1.08203i	0.918286	−	0.395919i	$-0.129574\pi$
$140$		0			0
$141$	2.15925	+	3.73992i	0.181841	+	0.314958i
$142$	0.106792	+	0.293409i	0.00896179	+	0.0246223i
$143$	−4.61857	−	12.6894i	−0.386224	−	1.06114i
$144$	−1.41638	−	2.45324i	−0.118032	−	0.204437i
$145$		0			0
$146$	2.66528	−	15.1155i	0.220580	−	1.25097i
$147$	0.448699	+	0.534738i	0.0370080	+	0.0441045i
$148$	−1.92807	+	2.29778i	−0.158486	+	0.188877i
$149$	−2.84467	−	16.1329i	−0.233044	−	1.32166i	−0.846693	−	0.532081i	$-0.821410\pi$
$149$	−2.84467	−	16.1329i	−0.233044	−	1.32166i	0.613649	−	0.789579i	$-0.289701\pi$
$150$		0			0
$151$	3.71278			0.302141			0.151071	−	0.988523i	$-0.451728\pi$
$151$	3.71278			0.302141			0.151071	+	0.988523i	$0.451728\pi$
$152$	−3.07586	−	3.08854i	−0.249485	−	0.250514i
$153$		−	7.91550i		−	0.639931i
$154$	5.72469	+	2.08362i	0.461309	+	0.167903i
$155$		0			0
$156$	−1.59761	−	1.34055i	−0.127911	−	0.107330i
$157$	−3.18002	−	3.78981i	−0.253794	−	0.302459i	0.624072	−	0.781367i	$-0.285477\pi$
$157$	−3.18002	−	3.78981i	−0.253794	−	0.302459i	−0.877865	+	0.478908i	$0.841033\pi$
$158$	8.67461	+	1.52957i	0.690115	+	0.121686i
$159$	0.866617	−	1.50102i	0.0687272	−	0.119039i
$160$		0			0
$161$	2.52894	−	0.920458i	0.199308	−	0.0725422i
$162$	−2.57295	−	7.06911i	−0.202150	−	0.555402i
$163$	6.98012	−	4.02997i	0.546725	−	0.315652i	−0.201075	−	0.979576i	$-0.564443\pi$
$163$	6.98012	−	4.02997i	0.546725	−	0.315652i	0.747800	+	0.663924i	$0.231110\pi$
$164$	5.68710	−	9.85035i	0.444088	−	0.769183i
$165$		0			0
$166$	−1.36004	+	1.14121i	−0.105560	+	0.0885753i
$167$	1.16138	−	1.38408i	0.0898705	−	0.107104i	−0.719235	−	0.694767i	$-0.755508\pi$
$167$	1.16138	−	1.38408i	0.0898705	−	0.107104i	0.809106	+	0.587663i	$0.199952\pi$
$168$	0.926571	−	0.163379i	0.0714865	−	0.0126050i
$169$	12.2224	+	4.44857i	0.940181	+	0.342198i
$170$		0			0
$171$	−7.06154	−	10.1292i	−0.540009	−	0.774598i
$172$		−	1.54117i		−	0.117513i
$173$	−7.03447	+	19.3270i	−0.534820	+	1.46941i	0.318451	+	0.947939i	$0.396838\pi$
$173$	−7.03447	+	19.3270i	−0.534820	+	1.46941i	−0.853271	+	0.521468i	$0.825385\pi$
$174$	−0.316251	−	1.79355i	−0.0239749	−	0.135968i
$175$		0			0
$176$	−2.02846	+	1.70208i	−0.152901	+	0.128299i
$177$	−4.51797	−	0.796640i	−0.339591	−	0.0598791i
$178$	5.61992	+	3.24466i	0.421231	+	0.243198i
$179$	−7.78778	−	13.4888i	−0.582086	−	1.00820i	−0.995232	−	0.0975373i	$-0.968903\pi$
$179$	−7.78778	−	13.4888i	−0.582086	−	1.00820i	0.413146	−	0.910665i	$-0.364430\pi$
$180$		0			0
$181$	6.41314	−	2.33419i	0.476685	−	0.173499i	−0.0924934	−	0.995713i	$-0.529484\pi$
$181$	6.41314	−	2.33419i	0.476685	−	0.173499i	0.569178	+	0.822214i	$0.307261\pi$
$182$	−10.1608	+	5.86634i	−0.753169	+	0.434842i
$183$	−1.17244	−	0.676909i	−0.0866693	−	0.0500385i
$184$	−0.203127	+	1.15199i	−0.0149747	+	0.0849260i
$185$		0			0
$186$	−2.57881	−	2.16388i	−0.189088	−	0.158663i
$187$	−7.28673	+	1.28485i	−0.532859	+	0.0939574i
$188$	−3.61169	+	9.92304i	−0.263410	+	0.723712i
$189$	5.48784			0.399181
$190$		0			0
$191$	−3.27667			−0.237091			−0.118546	−	0.992949i	$-0.537823\pi$
$191$	−3.27667			−0.237091			−0.118546	+	0.992949i	$0.537823\pi$
$192$	−0.139870	+	0.384290i	−0.0100943	+	0.0277337i
$193$	23.3109	−	4.11035i	1.67796	−	0.295869i	0.748045	−	0.663648i	$-0.230993\pi$
$193$	23.3109	−	4.11035i	1.67796	−	0.295869i	0.929913	+	0.367779i	$0.119882\pi$
$194$	−2.00750	−	1.68449i	−0.144130	−	0.120940i
$195$		0			0
$196$	−0.296404	+	1.68099i	−0.0211717	+	0.120071i
$197$	−5.96227	−	3.44232i	−0.424794	−	0.245255i	0.272332	−	0.962203i	$-0.412205\pi$
$197$	−5.96227	−	3.44232i	−0.424794	−	0.245255i	−0.697126	+	0.716948i	$0.745538\pi$
$198$	−6.49609	+	3.75052i	−0.461657	+	0.266538i
$199$	−17.8456	+	6.49525i	−1.26504	+	0.460436i	−0.885456	−	0.464722i	$-0.846154\pi$
$199$	−17.8456	+	6.49525i	−1.26504	+	0.460436i	−0.379581	+	0.925158i	$0.623932\pi$
$200$		0			0
$201$	−1.72250	−	2.98346i	−0.121496	−	0.210437i
$202$	−8.46013	−	4.88446i	−0.595252	−	0.343669i
$203$	−10.0901	−	1.77915i	−0.708183	−	0.124872i
$204$	−0.875379	+	0.734531i	−0.0612888	+	0.0514274i
$205$		0			0
$206$	0.0864105	+	0.490058i	0.00602050	+	0.0341440i
$207$	−1.13334	+	3.11382i	−0.0787724	+	0.216425i
$208$		−	5.09968i		−	0.353599i
$209$	−8.17834	+	8.14478i	−0.565708	+	0.563386i
$210$		0			0
$211$	11.5977	+	4.22122i	0.798419	+	0.290601i	0.708831	−	0.705378i	$-0.249223\pi$
$211$	11.5977	+	4.22122i	0.798419	+	0.290601i	0.0895880	+	0.995979i	$0.471445\pi$
$212$	4.17384	−	0.735960i	0.286660	−	0.0505459i
$213$	0.0820782	−	0.0978170i	0.00562391	−	0.00670231i
$214$	−14.7525	+	12.3789i	−1.00846	+	0.846201i
$215$		0			0
$216$	−1.19266	+	2.06575i	−0.0811503	+	0.140556i
$217$	−16.4013	+	9.46927i	−1.11339	+	0.642816i
$218$	3.98141	+	10.9388i	0.269655	+	0.740871i
$219$	−5.89836	+	2.14683i	−0.398574	+	0.145069i
$220$		0			0
$221$	7.12496	−	12.3408i	0.479277	−	0.830131i
$222$	1.20804	+	0.213009i	0.0810781	+	0.0142963i
$223$	−3.07863	−	3.66897i	−0.206161	−	0.245693i	0.653050	−	0.757315i	$-0.273489\pi$
$223$	−3.07863	−	3.66897i	−0.206161	−	0.245693i	−0.859210	+	0.511622i	$0.829045\pi$
$224$	1.76241	+	1.47884i	0.117756	+	0.0988092i
$225$		0			0
$226$	9.28150	+	3.37819i	0.617396	+	0.224714i
$227$		−	4.24421i		−	0.281698i	−0.990031	−	0.140849i	$-0.955017\pi$
$227$		−	4.24421i		−	0.281698i	0.990031	−	0.140849i	$-0.0449832\pi$
$228$	−0.464906	+	1.72089i	−0.0307892	+	0.113969i
$229$	28.8958			1.90949			0.954745	−	0.297425i	$-0.0961278\pi$
$229$	28.8958			1.90949			0.954745	+	0.297425i	$0.0961278\pi$
$230$		0			0
$231$	−0.432623	−	2.45353i	−0.0284645	−	0.161430i
$232$	2.86257	−	3.41147i	0.187937	−	0.223974i
$233$	−8.75986	−	10.4396i	−0.573877	−	0.683920i	0.398545	−	0.917149i	$-0.369515\pi$
$233$	−8.75986	−	10.4396i	−0.573877	−	0.683920i	−0.972422	+	0.233229i	$0.925071\pi$
$234$	2.50855	−	14.2267i	0.163989	−	0.930028i
$235$		0			0
$236$	−5.60904	−	9.71514i	−0.365117	−	0.632402i
$237$	−1.23204	−	3.38499i	−0.0800293	−	0.219879i
$238$	2.19875	+	6.04100i	0.142524	+	0.391580i
$239$	7.44355	+	12.8926i	0.481483	+	0.833954i	0.999774	−	0.0212507i	$-0.00676481\pi$
$239$	7.44355	+	12.8926i	0.481483	+	0.833954i	−0.518291	+	0.855205i	$0.673431\pi$
$240$		0			0
$241$	2.01439	−	11.4242i	0.129759	−	0.735897i	−0.848609	−	0.529021i	$-0.822559\pi$
$241$	2.01439	−	11.4242i	0.129759	−	0.735897i	0.978367	−	0.206876i	$-0.0663297\pi$
$242$	−2.56362	−	3.05520i	−0.164796	−	0.196396i
$243$	−6.57728	+	7.83850i	−0.421933	+	0.502840i
$244$	−0.574854	−	3.26016i	−0.0368012	−	0.208710i
$245$		0			0
$246$	−4.65151			−0.296569
$247$	−1.89185	−	22.1483i	−0.120375	−	1.40927i
$248$		−	8.23175i		−	0.522717i
$249$	0.682273	+	0.248327i	0.0432373	+	0.0157371i
$250$		0			0
$251$	16.1409	+	13.5438i	1.01880	+	0.854879i	0.989477	−	0.144691i	$-0.0462188\pi$
$251$	16.1409	+	13.5438i	1.01880	+	0.854879i	0.0293281	+	0.999570i	$0.490663\pi$
$252$	4.18920	+	4.99249i	0.263895	+	0.314498i
$253$	3.05044	+	0.537874i	0.191779	+	0.0338159i
$254$	−4.20939	+	7.29088i	−0.264121	+	0.457471i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	9.47920	+	26.0439i	0.591296	+	1.62457i	0.768102	+	0.640327i	$0.221201\pi$
$257$	9.47920	+	26.0439i	0.591296	+	1.62457i	−0.176806	+	0.984246i	$0.556577\pi$
$258$	−0.545827	+	0.315133i	−0.0339817	+	0.0196193i
$259$	3.45048	−	5.97640i	0.214402	−	0.371356i
$260$		0			0
$261$	9.66388	−	8.10896i	0.598179	−	0.501932i
$262$	−10.9536	+	13.0540i	−0.676716	+	0.806479i
$263$	−8.86847	+	1.56375i	−0.546853	+	0.0964250i	−0.440248	−	0.897876i	$-0.645109\pi$
$263$	−8.86847	+	1.56375i	−0.546853	+	0.0964250i	−0.106606	+	0.994301i	$0.533998\pi$
$264$	1.01759	+	0.370371i	0.0626281	+	0.0227948i
$265$		0			0
$266$	8.20293	+	5.76892i	0.502954	+	0.353715i
$267$		−	2.65383i		−	0.162412i
$268$	2.88116	−	7.91593i	0.175995	−	0.483542i
$269$	−1.29149	−	7.32442i	−0.0787437	−	0.446578i	−0.998532	−	0.0541630i	$-0.982751\pi$
$269$	−1.29149	−	7.32442i	−0.0787437	−	0.446578i	0.919788	−	0.392415i	$-0.128360\pi$
$270$		0			0
$271$	−14.3191	+	12.0152i	−0.869824	+	0.729869i	−0.964061	−	0.265681i	$-0.914403\pi$
$271$	−14.3191	+	12.0152i	−0.869824	+	0.729869i	0.0942373	+	0.995550i	$0.469959\pi$
$272$	−2.75182	−	0.485221i	−0.166854	−	0.0294208i
$273$	4.15529	+	2.39906i	0.251489	+	0.145197i
$274$	5.86495	+	10.1584i	0.354315	+	0.613691i
$275$		0			0
$276$	0.449528	−	0.163615i	0.0270584	−	0.00984846i
$277$	3.37548	−	1.94884i	0.202813	−	0.117094i	−0.395154	−	0.918615i	$-0.629309\pi$
$277$	3.37548	−	1.94884i	0.202813	−	0.117094i	0.597967	+	0.801521i	$0.295975\pi$
$278$	−11.2183	−	6.47689i	−0.672829	−	0.388458i
$279$	4.04923	−	22.9643i	0.242421	−	1.37484i
$280$		0			0
$281$	−4.50354	−	3.77891i	−0.268658	−	0.225431i	0.498499	−	0.866890i	$-0.333885\pi$
$281$	−4.50354	−	3.77891i	−0.268658	−	0.225431i	−0.767157	+	0.641459i	$0.778329\pi$
$282$	4.25288	−	0.749898i	0.253256	−	0.0446558i
$283$	6.38923	−	17.5543i	0.379800	−	1.04349i	−0.591639	−	0.806203i	$-0.701519\pi$
$283$	6.38923	−	17.5543i	0.379800	−	1.04349i	0.971439	−	0.237289i	$-0.0762589\pi$
$284$	0.312239			0.0185280
$285$		0			0
$286$	−13.5038			−0.798495
$287$	−8.95007	+	24.5901i	−0.528306	+	1.45151i
$288$	−2.78972	+	0.491903i	−0.164386	+	0.0289857i
$289$	7.04150	+	5.90852i	0.414206	+	0.347560i
$290$		0			0
$291$	−0.186099	+	1.05542i	−0.0109093	+	0.0618700i
$292$	−13.2924	−	7.67436i	−0.777877	−	0.449108i
$293$	−9.17131	+	5.29506i	−0.535794	+	0.309341i	−0.743373	−	0.668878i	$-0.766775\pi$
$293$	−9.17131	+	5.29506i	−0.535794	+	0.309341i	0.207579	+	0.978218i	$0.433442\pi$
$294$	0.655953	−	0.238748i	0.0382560	−	0.0139240i
$295$		0			0
$296$	1.49977	+	2.59768i	0.0871725	+	0.150987i
$297$	5.47003	+	3.15813i	0.317404	+	0.183253i
$298$	−16.1329	−	2.84467i	−0.934555	−	0.164787i
$299$	−4.56978	+	3.83450i	−0.264277	+	0.221755i
$300$		0			0
$301$	0.615709	+	3.49186i	0.0354889	+	0.201267i
$302$	1.26984	−	3.48887i	0.0730713	−	0.200762i
$303$			3.99502i			0.229508i
$304$	−3.95428	+	1.83402i	−0.226794	+	0.105188i
$305$		0			0
$306$	−7.43814	−	2.70726i	−0.425210	−	0.154764i
$307$	4.63123	−	0.816611i	0.264318	−	0.0466065i	−0.0399183	−	0.999203i	$-0.512710\pi$
$307$	4.63123	−	0.816611i	0.264318	−	0.0466065i	0.304237	+	0.952596i	$0.401599\pi$
$308$	3.91592	−	4.66681i	0.223130	−	0.265916i
$309$	0.155892	−	0.130809i	0.00886838	−	0.00744145i
$310$		0			0
$311$	6.81200	−	11.7987i	0.386273	−	0.669045i	−0.605672	−	0.795715i	$-0.707096\pi$
$311$	6.81200	−	11.7987i	0.386273	−	0.669045i	0.991945	+	0.126670i	$0.0404289\pi$
$312$	−1.80612	+	1.04276i	−0.102251	+	0.0590349i
$313$	10.5708	+	29.0431i	0.597498	+	1.64161i	0.756242	+	0.654292i	$0.227033\pi$
$313$	10.5708	+	29.0431i	0.597498	+	1.64161i	−0.158744	+	0.987320i	$0.550744\pi$
$314$	−4.64889	+	1.69206i	−0.262352	+	0.0954882i
$315$		0			0
$316$	4.40421	−	7.62832i	0.247756	−	0.429127i
$317$	8.02529	+	1.41507i	0.450745	+	0.0794785i	0.394412	−	0.918934i	$-0.370948\pi$
$317$	8.02529	+	1.41507i	0.450745	+	0.0794785i	0.0563326	+	0.998412i	$0.482059\pi$
$318$	−1.11410	−	1.32773i	−0.0624757	−	0.0744556i
$319$	−9.03346	−	7.57998i	−0.505777	−	0.424397i
$320$		0			0
$321$	7.40069	+	2.69363i	0.413066	+	0.150344i
$322$		−	2.69124i		−	0.149977i
$323$	−12.1314	−	1.08650i	−0.675010	−	0.0604545i
$324$	−7.52279			−0.417933
$325$		0			0
$326$	−1.39960	−	7.93750i	−0.0775164	−	0.439617i
$327$	3.06003	−	3.64680i	0.169220	−	0.201669i
$328$	−7.31119	−	8.71314i	−0.403693	−	0.481103i
$329$	4.21874	−	23.9257i	0.232587	−	1.31907i
$330$		0			0
$331$	−0.314743	−	0.545150i	−0.0172998	−	0.0299642i	0.857246	−	0.514907i	$-0.172174\pi$
$331$	−0.314743	−	0.545150i	−0.0172998	−	0.0299642i	−0.874546	+	0.484943i	$0.838840\pi$
$332$	0.607227	+	1.66834i	0.0333259	+	0.0915621i
$333$	2.90614	+	7.98455i	0.159255	+	0.437551i
$334$	−0.903396	−	1.56473i	−0.0494316	−	0.0856181i
$335$		0			0
$336$	0.163379	−	0.926571i	0.00891308	−	0.0505486i
$337$	−9.91232	−	11.8130i	−0.539958	−	0.643497i	0.425220	−	0.905090i	$-0.360197\pi$
$337$	−9.91232	−	11.8130i	−0.539958	−	0.643497i	−0.965178	+	0.261593i	$0.915752\pi$
$338$	8.36059	−	9.96376i	0.454756	−	0.541957i
$339$	−0.701416	−	3.97793i	−0.0380957	−	0.216051i
$340$		0			0
$341$	−21.7974			−1.18040
$342$	−11.9335	+	3.17129i	−0.645290	+	0.171484i
$343$		−	20.0317i		−	1.08161i
$344$	−1.44823	−	0.527112i	−0.0780832	−	0.0284200i
$345$		0			0
$346$	15.7555	+	13.2205i	0.847023	+	0.710737i
$347$	9.87631	+	11.7701i	0.530188	+	0.631854i	0.962958	−	0.269651i	$-0.0869082\pi$
$347$	9.87631	+	11.7701i	0.530188	+	0.631854i	−0.432770	+	0.901504i	$0.642464\pi$
$348$	−1.79355	−	0.316251i	−0.0961442	−	0.0169528i
$349$	−17.7797	+	30.7954i	−0.951727	+	1.64844i	−0.210041	+	0.977693i	$0.567360\pi$
$349$	−17.7797	+	30.7954i	−0.951727	+	1.64844i	−0.741686	+	0.670747i	$0.765974\pi$
$350$		0			0
$351$	−11.4308	+	4.16047i	−0.610130	+	0.222069i
$352$	0.905657	+	2.48827i	0.0482717	+	0.132625i
$353$	−17.0172	+	9.82488i	−0.905734	+	0.522926i	−0.879056	−	0.476718i	$-0.841826\pi$
$353$	−17.0172	+	9.82488i	−0.905734	+	0.522926i	−0.0266780	+	0.999644i	$0.508493\pi$
$354$	−2.29383	+	3.97303i	−0.121916	+	0.211164i
$355$		0			0
$356$	4.97111	−	4.17126i	0.263468	−	0.221076i
$357$	1.68991	−	2.01396i	0.0894396	−	0.106590i
$358$	−15.3389	+	2.70467i	−0.810687	+	0.142946i
$359$	18.3084	+	6.66371i	0.966280	+	0.351697i	0.776491	−	0.630128i	$-0.216998\pi$
$359$	18.3084	+	6.66371i	0.966280	+	0.351697i	0.189789	+	0.981825i	$0.439220\pi$
$360$		0			0
$361$	−16.4934	+	9.43225i	−0.868074	+	0.496434i
$362$		−	6.82472i		−	0.358699i
$363$	−0.557841	+	1.53266i	−0.0292791	+	0.0804436i
$364$	2.03736	+	11.5544i	0.106787	+	0.605617i
$365$		0			0
$366$	−1.03708	+	0.870217i	−0.0542093	+	0.0454870i
$367$	21.0908	+	3.71888i	1.10093	+	0.194124i	0.694454	−	0.719537i	$-0.255646\pi$
$367$	21.0908	+	3.71888i	1.10093	+	0.194124i	0.406477	+	0.913661i	$0.366757\pi$
$368$	1.01305	+	0.584882i	0.0528086	+	0.0304891i
$369$	−16.1102	−	27.9036i	−0.838662	−	1.45261i
$370$		0			0
$371$	−9.16271	+	3.33495i	−0.475704	+	0.173142i
$372$	−2.91539	+	1.68320i	−0.151156	+	0.0872698i
$373$	12.4952	+	7.21408i	0.646975	+	0.373531i	0.787296	−	0.616575i	$-0.211480\pi$
$373$	12.4952	+	7.21408i	0.646975	+	0.373531i	−0.140321	+	0.990106i	$0.544814\pi$
$374$	−1.28485	+	7.28673i	−0.0664379	+	0.376788i
$375$		0			0
$376$	8.08934	+	6.78776i	0.417176	+	0.350052i
$377$	22.3657	−	3.94368i	1.15189	−	0.203110i
$378$	1.87695	−	5.15688i	0.0965399	−	0.265241i
$379$	8.16356			0.419334			0.209667	−	0.977773i	$-0.432762\pi$
$379$	8.16356			0.419334			0.209667	+	0.977773i	$0.432762\pi$
$380$		0			0
$381$	3.44289			0.176384
$382$	−1.12069	+	3.07906i	−0.0573393	+	0.157538i
$383$	27.0262	−	4.76545i	1.38098	−	0.243503i	0.566673	−	0.823943i	$-0.308230\pi$
$383$	27.0262	−	4.76545i	1.38098	−	0.243503i	0.814303	+	0.580440i	$0.197119\pi$
$384$	0.313276	+	0.262870i	0.0159868	+	0.0134145i
$385$		0			0
$386$	4.11035	−	23.3109i	0.209211	−	1.18650i
$387$	−3.78086	−	2.18288i	−0.192192	−	0.110962i
$388$	−2.26951	+	1.31030i	−0.115217	+	0.0665205i
$389$	−14.8341	+	5.39919i	−0.752121	+	0.273750i	−0.689498	−	0.724288i	$-0.742169\pi$
$389$	−14.8341	+	5.39919i	−0.752121	+	0.273750i	−0.0626229	+	0.998037i	$0.519947\pi$
$390$		0			0
$391$	1.63432	+	2.83073i	0.0826512	+	0.143156i
$392$	1.47824	+	0.853462i	0.0746623	+	0.0431063i
$393$	6.86300	+	1.21013i	0.346193	+	0.0610431i
$394$	−5.27393	+	4.42536i	−0.265697	+	0.222946i
$395$		0			0
$396$	1.30254	+	7.38709i	0.0654552	+	0.371215i
$397$	13.0598	−	35.8815i	0.655452	−	1.80084i	0.0589010	−	0.998264i	$-0.481240\pi$
$397$	13.0598	−	35.8815i	0.655452	−	1.80084i	0.596551	−	0.802575i	$-0.296537\pi$
$398$			18.9908i			0.951925i
$399$	0.365838	−	4.08479i	0.0183148	−	0.204495i
$400$		0			0
$401$	15.1995	+	5.53217i	0.759028	+	0.276264i	0.692399	−	0.721514i	$-0.256554\pi$
$401$	15.1995	+	5.53217i	0.759028	+	0.276264i	0.0666283	+	0.997778i	$0.478776\pi$
$402$	−3.39266	+	0.598218i	−0.169211	+	0.0298364i
$403$	26.9838	−	32.1580i	1.34416	−	1.60191i
$404$	−7.48342	+	6.27934i	−0.372314	+	0.312409i
$405$		0			0
$406$	−5.12286	+	8.87305i	−0.254243	+	0.440362i
$407$	6.87857	−	3.97134i	0.340958	−	0.196852i
$408$	0.390836	+	1.07381i	0.0193492	+	0.0531616i
$409$	29.6569	−	10.7942i	1.46644	−	0.533740i	0.519307	−	0.854587i	$-0.326190\pi$
$409$	29.6569	−	10.7942i	1.46644	−	0.533740i	0.947131	+	0.320848i	$0.103968\pi$
$410$		0			0
$411$	2.39849	−	4.15430i	0.118309	−	0.204917i
$412$	0.490058	+	0.0864105i	0.0241434	+	0.00425714i
$413$	16.5898	+	19.7709i	0.816329	+	0.972863i
$414$	2.53841	+	2.12998i	0.124756	+	0.104683i
$415$		0			0
$416$	−4.79213	−	1.74419i	−0.234954	−	0.0855162i
$417$			5.29748i			0.259419i
$418$	4.85643	+	10.4708i	0.237536	+	0.512144i
$419$	15.0026			0.732925			0.366463	−	0.930433i	$-0.380569\pi$
$419$	15.0026			0.732925			0.366463	+	0.930433i	$0.380569\pi$
$420$		0			0
$421$	−0.407466	−	2.31085i	−0.0198587	−	0.112624i	0.973267	−	0.229676i	$-0.0737667\pi$
$421$	−0.407466	−	2.31085i	−0.0198587	−	0.112624i	−0.993126	+	0.117052i	$0.962656\pi$
$422$	7.93330	−	9.45454i	0.386187	−	0.460240i
$423$	19.2281	+	22.9151i	0.934901	+	1.11417i
$424$	0.735960	−	4.17384i	0.0357414	−	0.202699i
$425$		0			0
$426$	−0.0638455	−	0.110584i	−0.00309333	−	0.00535780i
$427$	2.60491	+	7.15693i	0.126060	+	0.346348i
$428$	6.58665	+	18.0967i	0.318378	+	0.874736i
$429$	2.76120	+	4.78255i	0.133312	+	0.230904i
$430$		0			0
$431$	−6.04701	+	34.2943i	−0.291274	+	1.65190i	0.390697	+	0.920519i	$0.372234\pi$
$431$	−6.04701	+	34.2943i	−0.291274	+	1.65190i	−0.681971	+	0.731379i	$0.738877\pi$
$432$	1.53326	+	1.82726i	0.0737688	+	0.0879142i
$433$	2.82901	−	3.37149i	0.135954	−	0.162023i	−0.693772	−	0.720195i	$-0.744052\pi$
$433$	2.82901	−	3.37149i	0.135954	−	0.162023i	0.829726	+	0.558171i	$0.188497\pi$
$434$	3.28864	+	18.6508i	0.157860	+	0.895268i
$435$		0			0
$436$	11.6409			0.557496
$437$	4.61672	+	2.16438i	0.220847	+	0.103536i
$438$			6.27690i			0.299922i
$439$	2.39398	+	0.871336i	0.114258	+	0.0415866i	0.398517	−	0.917161i	$-0.369525\pi$
$439$	2.39398	+	0.871336i	0.114258	+	0.0415866i	−0.284258	+	0.958748i	$0.591747\pi$
$440$		0			0
$441$	3.70405	+	3.10807i	0.176384	+	0.148003i
$442$	−9.15967	−	10.9161i	−0.435681	−	0.519224i
$443$	−39.3402	−	6.93673i	−1.86911	−	0.329574i	−0.879791	−	0.475361i	$-0.842318\pi$
$443$	−39.3402	−	6.93673i	−1.86911	−	0.329574i	−0.989316	+	0.145787i	$0.953429\pi$
$444$	0.613336	−	1.06233i	0.0291076	−	0.0504159i
$445$		0			0
$446$	−4.50066	+	1.63811i	−0.213112	+	0.0775666i
$447$	2.29132	+	6.29536i	0.108376	+	0.297760i
$448$	1.99244	−	1.15033i	0.0941338	−	0.0543482i
$449$	12.4299	−	21.5293i	0.586605	−	1.01603i	−0.408068	−	0.912952i	$-0.633797\pi$
$449$	12.4299	−	21.5293i	0.586605	−	1.01603i	0.994673	−	0.103079i	$-0.0328694\pi$
$450$		0			0
$451$	−23.0721	+	19.3598i	−1.08642	+	0.911617i
$452$	6.34892	−	7.56635i	0.298628	−	0.355891i
$453$	−1.49528	+	0.263659i	−0.0702545	+	0.0123878i
$454$	−3.98825	−	1.45160i	−0.187178	−	0.0681272i
$455$		0			0
$456$	1.45810	+	1.02545i	0.0682819	+	0.0480210i
$457$			37.9539i			1.77541i	0.460416	+	0.887703i	$0.347700\pi$
$457$			37.9539i			1.77541i	−0.460416	+	0.887703i	$0.652300\pi$
$458$	9.88296	−	27.1532i	0.461800	−	1.26879i
$459$	1.15741	+	6.56399i	0.0540232	+	0.306381i
$460$		0			0
$461$	1.29024	−	1.08264i	0.0600927	−	0.0504238i	−0.612247	−	0.790667i	$-0.709734\pi$
$461$	1.29024	−	1.08264i	0.0600927	−	0.0504238i	0.672339	+	0.740243i	$0.265290\pi$
$462$	−2.45353	−	0.432623i	−0.114148	−	0.0201275i
$463$	7.60068	+	4.38825i	0.353233	+	0.203939i	0.666108	−	0.745855i	$-0.267959\pi$
$463$	7.60068	+	4.38825i	0.353233	+	0.203939i	−0.312875	+	0.949794i	$0.601292\pi$
$464$	−2.22668	−	3.85673i	−0.103371	−	0.179044i
$465$		0			0
$466$	−12.8061	+	4.66102i	−0.593229	+	0.215918i
$467$	0.452589	−	0.261302i	0.0209433	−	0.0120916i	−0.489492	−	0.872008i	$-0.662818\pi$
$467$	0.452589	−	0.261302i	0.0209433	−	0.0120916i	0.510435	+	0.859916i	$0.329484\pi$
$468$	−12.5107	−	7.22308i	−0.578309	−	0.333887i
$469$	−3.36543	+	19.0863i	−0.155401	+	0.881323i
$470$		0			0
$471$	1.54985	+	1.30048i	0.0714134	+	0.0599230i
$472$	−11.0477	+	1.94800i	−0.508509	+	0.0896639i
$473$	−1.39577	+	3.83486i	−0.0641777	+	0.176327i
$474$	−3.60223			−0.165456
$475$		0			0
$476$	6.42870			0.294659
$477$	4.10625	−	11.2818i	0.188012	−	0.516559i
$478$	14.6609	−	2.58512i	0.670576	−	0.118241i
$479$	5.31590	+	4.46057i	0.242890	+	0.203809i	0.756103	−	0.654452i	$-0.227101\pi$
$479$	5.31590	+	4.46057i	0.242890	+	0.203809i	−0.513214	+	0.858261i	$0.671545\pi$
$480$		0			0
$481$	−2.65625	+	15.0643i	−0.121114	+	0.686874i
$482$	−10.0463	−	5.80022i	−0.457595	−	0.264193i
$483$	−0.953139	+	0.550295i	−0.0433693	+	0.0250393i
$484$	−3.74776	+	1.36407i	−0.170353	+	0.0620033i
$485$		0			0
$486$	5.11622	+	8.86155i	0.232076	+	0.401968i
$487$	35.6711	+	20.5947i	1.61641	+	0.933236i	0.987838	+	0.155486i	$0.0496943\pi$
$487$	35.6711	+	20.5947i	1.61641	+	0.933236i	0.628574	+	0.777750i	$0.283639\pi$
$488$	−3.26016	−	0.574854i	−0.147580	−	0.0260224i
$489$	−2.52499	+	2.11872i	−0.114184	+	0.0958117i
$490$		0			0
$491$	−3.65055	−	20.7033i	−0.164747	−	0.934327i	−0.949325	−	0.314297i	$-0.898231\pi$
$491$	−3.65055	−	20.7033i	−0.164747	−	0.934327i	0.784578	−	0.620030i	$-0.212880\pi$
$492$	−1.59091	+	4.37099i	−0.0717238	+	0.197059i
$493$		−	12.4439i		−	0.560446i
$494$	−21.4597	−	5.79743i	−0.965517	−	0.260839i
$495$		0			0
$496$	−7.73532	−	2.81543i	−0.347326	−	0.126416i
$497$	−0.707445	+	0.124742i	−0.0317333	+	0.00559543i
$498$	0.466702	−	0.556194i	0.0209134	−	0.0249236i
$499$	−17.9199	+	15.0366i	−0.802203	+	0.673128i	−0.948733	−	0.316078i	$-0.897634\pi$
$499$	−17.9199	+	15.0366i	−0.802203	+	0.673128i	0.146530	+	0.989206i	$0.453190\pi$
$500$		0			0
$501$	−0.369446	+	0.639900i	−0.0165056	+	0.0285886i
$502$	18.2476	−	10.5352i	0.814428	−	0.470210i
$503$	−8.06613	−	22.1615i	−0.359651	−	0.988132i	−0.979151	−	0.203136i	$-0.934887\pi$
$503$	−8.06613	−	22.1615i	−0.359651	−	0.988132i	0.619500	−	0.784997i	$-0.287335\pi$
$504$	6.12420	−	2.22903i	0.272794	−	0.0992887i
$505$		0			0
$506$	1.54875	−	2.68251i	0.0688502	−	0.119252i
$507$	−5.23834	−	0.923661i	−0.232643	−	0.0410212i
$508$	5.41149	+	6.44916i	0.240096	+	0.286135i
$509$	2.07742	+	1.74316i	0.0920801	+	0.0772644i	0.687666	−	0.726027i	$-0.258635\pi$
$509$	2.07742	+	1.74316i	0.0920801	+	0.0772644i	−0.595586	+	0.803292i	$0.703080\pi$
$510$		0			0
$511$	33.1827	+	12.0775i	1.46792	+	0.534278i
$512$			1.00000i			0.0441942i
$513$	7.33692	+	7.36716i	0.323933	+	0.325268i
$514$	27.7153			1.22247
$515$		0			0
$516$	0.109445	+	0.620691i	0.00481803	+	0.0273244i
$517$	17.9737	−	21.4203i	0.790485	−	0.942063i
$518$	−4.43585	−	5.28644i	−0.194900	−	0.232273i
$519$	1.46057	−	8.28331i	0.0641120	−	0.363597i
$520$		0			0
$521$	8.92779	+	15.4634i	0.391134	+	0.677464i	0.992599	−	0.121435i	$-0.0387496\pi$
$521$	8.92779	+	15.4634i	0.391134	+	0.677464i	−0.601466	+	0.798899i	$0.705416\pi$
$522$	−4.31469	−	11.8545i	−0.188849	−	0.518857i
$523$	3.60971	+	9.91759i	0.157841	+	0.433666i	0.993254	−	0.115957i	$-0.0369936\pi$
$523$	3.60971	+	9.91759i	0.157841	+	0.433666i	−0.835413	+	0.549623i	$0.814771\pi$
$524$	8.52039	+	14.7578i	0.372215	+	0.644695i
$525$		0			0
$526$	−1.56375	+	8.86847i	−0.0681828	+	0.386684i
$527$	−14.7853	−	17.6204i	−0.644056	−	0.767556i
$528$	0.696070	−	0.829544i	0.0302926	−	0.0361013i
$529$	3.75630	+	21.3030i	0.163317	+	0.926218i
$530$		0			0
$531$	−31.7781			−1.37905
$532$	8.22658	−	5.73514i	0.356667	−	0.248650i
$533$		−	58.0048i		−	2.51247i
$534$	−2.49378	−	0.907662i	−0.107916	−	0.0392784i
$535$		0			0
$536$	−6.45312	−	5.41481i	−0.278732	−	0.233884i
$537$	4.09434	+	4.87945i	0.176684	+	0.210564i
$538$	−7.32442	−	1.29149i	−0.315778	−	0.0556802i
$539$	2.25994	−	3.91433i	0.0973424	−	0.168602i
$540$		0			0
$541$	3.45906	−	1.25899i	0.148717	−	0.0541284i	−0.266589	−	0.963810i	$-0.585897\pi$
$541$	3.45906	−	1.25899i	0.148717	−	0.0541284i	0.415306	+	0.909682i	$0.363675\pi$
$542$	6.39313	+	17.5650i	0.274608	+	0.754481i
$543$	−2.41707	+	1.39549i	−0.103726	+	0.0598864i
$544$	−1.39714	+	2.41991i	−0.0599018	+	0.103753i
$545$		0			0
$546$	3.67557	−	3.08417i	0.157300	−	0.131990i
$547$	3.55531	−	4.23706i	0.152014	−	0.181164i	−0.684663	−	0.728860i	$-0.740051\pi$
$547$	3.55531	−	4.23706i	0.152014	−	0.181164i	0.836677	+	0.547696i	$0.184495\pi$
$548$	11.5517	−	2.03688i	0.493464	−	0.0870110i
$549$	−8.81216	−	3.20736i	−0.376094	−	0.136887i
$550$		0			0
$551$	−11.1014	−	15.9240i	−0.472936	−	0.678387i
$552$		−	0.478378i		−	0.0203611i
$553$	−6.93113	+	19.0431i	−0.294742	+	0.809796i
$554$	−0.676824	−	3.83846i	−0.0287555	−	0.163080i
$555$		0			0
$556$	−9.92317	+	8.32653i	−0.420836	+	0.353123i
$557$	9.59001	+	1.69098i	0.406342	+	0.0716490i	0.373084	−	0.927798i	$-0.378300\pi$
$557$	9.59001	+	1.69098i	0.406342	+	0.0716490i	0.0332583	+	0.999447i	$0.489412\pi$
$558$	−20.1945	−	11.6593i	−0.854900	−	0.493577i
$559$	−3.92974	−	6.80651i	−0.166210	−	0.287885i
$560$		0			0
$561$	2.84342	−	1.03492i	0.120049	−	0.0436943i
$562$	−5.09132	+	2.93947i	−0.214764	+	0.123994i
$563$	−29.5542	−	17.0631i	−1.24556	−	0.719125i	−0.275340	−	0.961347i	$-0.588790\pi$
$563$	−29.5542	−	17.0631i	−1.24556	−	0.719125i	−0.970221	+	0.242223i	$0.922124\pi$
$564$	0.749898	−	4.25288i	0.0315764	−	0.179079i
$565$		0			0
$566$	−14.3104	−	12.0078i	−0.601509	−	0.504726i
$567$	17.0445	−	3.00541i	0.715802	−	0.126215i
$568$	0.106792	−	0.293409i	0.00448090	−	0.0123112i
$569$	−31.8304			−1.33440			−0.667199	−	0.744880i	$-0.732507\pi$
$569$	−31.8304			−1.33440			−0.667199	+	0.744880i	$0.732507\pi$
$570$		0			0
$571$	27.6840			1.15854			0.579270	−	0.815136i	$-0.303338\pi$
$571$	27.6840			1.15854			0.579270	+	0.815136i	$0.303338\pi$
$572$	−4.61857	+	12.6894i	−0.193112	+	0.530571i
$573$	1.31964	−	0.232689i	0.0551289	−	0.00972071i
$574$	20.0461	+	16.8206i	0.836706	+	0.702080i
$575$		0			0
$576$	−0.491903	+	2.78972i	−0.0204960	+	0.116238i
$577$	30.8319	+	17.8008i	1.28355	+	0.741057i	0.977495	−	0.210957i	$-0.0676581\pi$
$577$	30.8319	+	17.8008i	1.28355	+	0.741057i	0.306053	+	0.952014i	$0.400991\pi$
$578$	7.96053	−	4.59601i	0.331114	−	0.191169i
$579$	−9.09635	+	3.31080i	−0.378031	+	0.137592i
$580$		0			0
$581$	−2.04232	−	3.53740i	−0.0847296	−	0.146756i
$582$	0.928123	+	0.535852i	0.0384719	+	0.0222118i
$583$	−11.0522	−	1.94880i	−0.457734	−	0.0807109i
$584$	−11.7578	+	9.86596i	−0.486541	+	0.408256i
$585$		0			0
$586$	1.83896	+	10.4292i	0.0759665	+	0.430828i
$587$	0.285977	−	0.785714i	0.0118035	−	0.0324299i	−0.933651	−	0.358184i	$-0.883396\pi$
$587$	0.285977	−	0.785714i	0.0118035	−	0.0324299i	0.945454	+	0.325754i	$0.105618\pi$
$588$		−	0.698051i		−	0.0287871i
$589$	−34.6396	−	9.35803i	−1.42730	−	0.385591i
$590$		0			0
$591$	2.64569	+	0.962954i	0.108829	+	0.0396106i
$592$	2.95397	−	0.520865i	0.121408	−	0.0214074i
$593$	−11.1190	+	13.2512i	−0.456604	+	0.544160i	−0.944400	−	0.328798i	$-0.893357\pi$
$593$	−11.1190	+	13.2512i	−0.456604	+	0.544160i	0.487796	+	0.872958i	$0.337801\pi$
$594$	4.83853	−	4.06001i	0.198527	−	0.166584i
$595$		0			0
$596$	−8.19090	+	14.1871i	−0.335512	+	0.581124i
$597$	6.72586	−	3.88318i	0.275271	−	0.158928i
$598$	2.04030	+	5.60566i	0.0834339	+	0.229233i
$599$	−0.980251	+	0.356782i	−0.0400520	+	0.0145777i	−0.361968	−	0.932190i	$-0.617895\pi$
$599$	−0.980251	+	0.356782i	−0.0400520	+	0.0145777i	0.321916	+	0.946768i	$0.395673\pi$
$600$		0			0
$601$	21.9915	−	38.0903i	0.897051	−	1.55374i	0.0658048	−	0.997833i	$-0.479039\pi$
$601$	21.9915	−	38.0903i	0.897051	−	1.55374i	0.831246	−	0.555905i	$-0.187628\pi$
$602$	3.49186	+	0.615709i	0.142317	+	0.0250944i
$603$	−15.3389	−	18.2801i	−0.624646	−	0.744425i
$604$	−2.84415	−	2.38653i	−0.115727	−	0.0971064i
$605$		0			0
$606$	3.75409	+	1.36638i	0.152500	+	0.0555053i
$607$			35.1548i			1.42689i	0.700711	+	0.713445i	$0.252866\pi$
$607$			35.1548i			1.42689i	−0.700711	+	0.713445i	$0.747134\pi$
$608$	0.370973	+	4.34308i	0.0150450	+	0.176135i
$609$	4.19001			0.169788
$610$		0			0
$611$	9.35131	+	53.0339i	0.378313	+	2.14552i
$612$	−5.08799	+	6.06363i	−0.205670	+	0.245108i
$613$	28.5514	+	34.0263i	1.15318	+	1.37431i	0.915181	+	0.403044i	$0.132048\pi$
$613$	28.5514	+	34.0263i	1.15318	+	1.37431i	0.238001	+	0.971265i	$0.423508\pi$
$614$	0.816611	−	4.63123i	0.0329557	−	0.186901i
$615$		0			0
$616$	−3.04605	−	5.27591i	−0.122729	−	0.212572i
$617$	1.41711	+	3.89348i	0.0570508	+	0.156746i	0.964944	−	0.262456i	$-0.0845324\pi$
$617$	1.41711	+	3.89348i	0.0570508	+	0.156746i	−0.907893	+	0.419201i	$0.862310\pi$
$618$	−0.0696019	−	0.191230i	−0.00279980	−	0.00769238i
$619$	22.9770	+	39.7973i	0.923523	+	1.59959i	0.793920	+	0.608022i	$0.208037\pi$
$619$	22.9770	+	39.7973i	0.923523	+	1.59959i	0.129603	+	0.991566i	$0.458630\pi$
$620$		0			0
$621$	0.484524	−	2.74787i	0.0194433	−	0.110268i
$622$	−8.75734	−	10.4366i	−0.351137	−	0.418469i
$623$	−9.59668	+	11.4369i	−0.384483	+	0.458209i
$624$	0.362148	+	2.05385i	0.0144975	+	0.0822196i
$625$		0			0
$626$	30.9070			1.23529
$627$	2.71535	−	3.86100i	0.108441	−	0.154194i
$628$			4.94724i			0.197416i
$629$	7.87608	+	2.86666i	0.314040	+	0.114301i
$630$		0			0
$631$	−13.6051	−	11.4160i	−0.541609	−	0.454464i	0.330479	−	0.943813i	$-0.392790\pi$
$631$	−13.6051	−	11.4160i	−0.541609	−	0.454464i	−0.872088	+	0.489350i	$0.837234\pi$
$632$	−5.66195	−	6.74765i	−0.225220	−	0.268407i
$633$	−4.97063	−	0.876455i	−0.197565	−	0.0348360i
$634$	4.07454	−	7.05732i	0.161821	−	0.280282i
$635$		0			0
$636$	−1.62871	+	0.592801i	−0.0645824	+	0.0235061i
$637$	2.97721	+	8.17981i	0.117961	+	0.324096i
$638$	−10.2125	+	5.89618i	−0.404316	+	0.233432i
$639$	0.442249	−	0.765998i	0.0174951	−	0.0303024i
$640$		0			0
$641$	−2.62235	+	2.20041i	−0.103577	+	0.0869110i	−0.693105	−	0.720836i	$-0.743758\pi$
$641$	−2.62235	+	2.20041i	−0.103577	+	0.0869110i	0.589529	+	0.807747i	$0.299313\pi$
$642$	5.06237	−	6.03309i	0.199796	−	0.238107i
$643$	40.2653	−	7.09985i	1.58791	−	0.279991i	0.691216	−	0.722648i	$-0.257075\pi$
$643$	40.2653	−	7.09985i	1.58791	−	0.279991i	0.896691	+	0.442657i	$0.145964\pi$
$644$	−2.52894	−	0.920458i	−0.0996541	−	0.0362711i
$645$		0			0
$646$	−5.17016	+	11.0282i	−0.203417	+	0.433898i
$647$		−	27.9797i		−	1.10000i	−0.835166	−	0.549998i	$-0.814629\pi$
$647$		−	27.9797i		−	1.10000i	0.835166	−	0.549998i	$-0.185371\pi$
$648$	−2.57295	+	7.06911i	−0.101075	+	0.277701i
$649$	5.15823	+	29.2538i	0.202478	+	1.14831i
$650$		0			0
$651$	5.93299	−	4.97837i	0.232532	−	0.195118i
$652$	−7.93750	−	1.39960i	−0.310856	−	0.0548124i
$653$	13.2980	+	7.67760i	0.520391	+	0.300448i	0.737095	−	0.675790i	$-0.236197\pi$
$653$	13.2980	+	7.67760i	0.520391	+	0.300448i	−0.216704	+	0.976237i	$0.569531\pi$
$654$	−2.38028	−	4.12277i	−0.0930763	−	0.161213i
$655$		0			0
$656$	−10.6883	+	3.89021i	−0.417306	+	0.151887i
$657$	−37.6541	+	21.7396i	−1.46903	+	0.848142i
$658$	−21.0399	−	12.1474i	−0.820221	−	0.473555i
$659$	8.57081	−	48.6075i	0.333871	−	1.89348i	−0.104229	−	0.994553i	$-0.533238\pi$
$659$	8.57081	−	48.6075i	0.333871	−	1.89348i	0.438101	−	0.898926i	$-0.355651\pi$
$660$		0			0
$661$	30.0511	+	25.2159i	1.16885	+	0.980785i	0.999988	−	0.00485448i	$-0.00154524\pi$
$661$	30.0511	+	25.2159i	1.16885	+	0.980785i	0.168865	+	0.985639i	$0.445990\pi$
$662$	−0.619922	+	0.109309i	−0.0240940	+	0.00424841i
$663$	−1.99314	+	5.47610i	−0.0774070	+	0.212674i
$664$	1.77541			0.0688993
$665$		0			0
$666$	8.49698			0.329251
$667$	−1.78171	+	4.89522i	−0.0689882	+	0.189544i
$668$	−1.77934	+	0.313746i	−0.0688448	+	0.0121392i
$669$	1.50044	+	1.25902i	0.0580102	+	0.0486764i
$670$		0			0
$671$	−1.52219	+	8.63278i	−0.0587636	+	0.333265i
$672$	−0.814813	−	0.470432i	−0.0314321	−	0.0181473i
$673$	−37.1086	+	21.4246i	−1.43043	+	0.825859i	−0.997153	−	0.0754013i	$-0.975976\pi$
$673$	−37.1086	+	21.4246i	−1.43043	+	0.825859i	−0.433277	+	0.901261i	$0.642643\pi$
$674$	−14.4908	+	5.27423i	−0.558166	+	0.203156i
$675$		0			0
$676$	−6.50338	−	11.2642i	−0.250130	−	0.433238i
$677$	−0.888611	−	0.513040i	−0.0341521	−	0.0197177i	0.482827	−	0.875716i	$-0.339610\pi$
$677$	−0.888611	−	0.513040i	−0.0341521	−	0.0197177i	−0.516979	+	0.855998i	$0.672943\pi$
$678$	−3.97793	−	0.701416i	−0.152771	−	0.0269377i
$679$	4.61859	−	3.87546i	0.177245	−	0.148727i
$680$		0			0
$681$	0.301398	+	1.70931i	0.0115496	+	0.0655010i
$682$	−7.45515	+	20.4828i	−0.285472	+	0.784329i
$683$			44.8988i			1.71800i	0.511972	+	0.859002i	$0.328915\pi$
$683$			44.8988i			1.71800i	−0.511972	+	0.859002i	$0.671085\pi$
$684$	−1.10146	+	12.2985i	−0.0421155	+	0.470244i
$685$		0			0
$686$	−18.8237	−	6.85126i	−0.718692	−	0.261582i
$687$	−11.6375	+	2.05201i	−0.443998	+	0.0782889i
$688$	−0.990646	+	1.18061i	−0.0377680	+	0.0450102i
$689$	16.5570	−	13.8930i	0.630771	−	0.529279i
$690$		0			0
$691$	0.745705	−	1.29160i	0.0283680	−	0.0491348i	−0.851493	−	0.524366i	$-0.824302\pi$
$691$	0.745705	−	1.29160i	0.0283680	−	0.0491348i	0.879861	+	0.475231i	$0.157636\pi$
$692$	17.8119	−	10.2837i	0.677107	−	0.390928i
$693$	−5.90238	−	16.2167i	−0.224213	−	0.616020i
$694$	14.4382	−	5.25508i	0.548067	−	0.199480i
$695$		0			0
$696$	−0.910608	+	1.57722i	−0.0345165	+	0.0597843i
$697$	−31.2998	−	5.51900i	−1.18556	−	0.209047i
$698$	22.8572	+	27.2401i	0.865157	+	1.03105i
$699$	4.26930	+	3.58237i	0.161480	+	0.135498i
$700$		0			0
$701$	−16.7716	−	6.10435i	−0.633453	−	0.230558i	0.00528040	−	0.999986i	$-0.498319\pi$
$701$	−16.7716	−	6.10435i	−0.633453	−	0.230558i	−0.638734	+	0.769428i	$0.720541\pi$
$702$			12.1644i			0.459115i
$703$	12.6361	−	3.35801i	0.476581	−	0.126650i
$704$	2.64797			0.0997989
$705$		0			0
$706$	3.41215	+	19.3512i	0.128418	+	0.728294i
$707$	14.4467	−	17.2169i	0.543323	−	0.647507i
$708$	2.94889	+	3.51436i	0.110826	+	0.132078i
$709$	4.94285	−	28.0323i	0.185632	−	1.05277i	−0.739508	−	0.673148i	$-0.764942\pi$
$709$	4.94285	−	28.0323i	0.185632	−	1.05277i	0.925140	−	0.379626i	$-0.123947\pi$
$710$		0			0
$711$	−12.4761	−	21.6092i	−0.467889	−	0.810408i
$712$	−2.21948	−	6.09797i	−0.0831785	−	0.228531i
$713$	3.29338	+	9.04849i	0.123338	+	0.338869i
$714$	−1.31452	−	2.27681i	−0.0491946	−	0.0852075i
$715$		0			0
$716$	−2.70467	+	15.3389i	−0.101078	+	0.573243i
$717$	−3.91337	−	4.66377i	−0.146148	−	0.174172i
$718$	12.5237	−	14.9251i	0.467379	−	0.557001i
$719$	0.0102041	+	0.0578704i	0.000380549	+	0.00215820i	0.984997	−	0.172569i	$-0.0552068\pi$
$719$	0.0102041	+	0.0578704i	0.000380549	+	0.00215820i	−0.984617	+	0.174727i	$0.944096\pi$
$720$		0			0
$721$	−1.14485			−0.0426366
$722$	3.22234	+	18.7248i	0.119923	+	0.696863i
$723$			4.74403i			0.176432i
$724$	−6.41314	−	2.33419i	−0.238342	−	0.0867495i
$725$		0			0
$726$	1.24943	+	1.04840i	0.0463708	+	0.0389097i
$727$	−19.9079	−	23.7254i	−0.738345	−	0.879925i	0.257930	−	0.966164i	$-0.416960\pi$
$727$	−19.9079	−	23.7254i	−0.738345	−	0.879925i	−0.996275	+	0.0862385i	$0.972515\pi$
$728$	11.5544	+	2.03736i	0.428236	+	0.0755095i
$729$	−9.19189	+	15.9208i	−0.340440	+	0.589660i
$730$		0			0
$731$	−4.04675	+	1.47289i	−0.149674	+	0.0544770i
$732$	0.463033	+	1.27217i	0.0171142	+	0.0470209i
$733$	11.7529	−	6.78551i	0.434102	−	0.250629i	−0.266991	−	0.963699i	$-0.586029\pi$
$733$	11.7529	−	6.78551i	0.434102	−	0.250629i	0.701092	+	0.713070i	$0.252696\pi$
$734$	10.7081	−	18.5470i	0.395243	−	0.684580i
$735$		0			0
$736$	0.896091	−	0.751910i	0.0330304	−	0.0277158i
$737$	−14.3382	+	17.0876i	−0.528156	+	0.629431i
$738$	−31.7309	+	5.59501i	−1.16803	+	0.205955i
$739$	−15.2620	−	5.55490i	−0.561420	−	0.204340i	0.0456930	−	0.998956i	$-0.485450\pi$
$739$	−15.2620	−	5.55490i	−0.561420	−	0.204340i	−0.607113	+	0.794615i	$0.707673\pi$
$740$		0			0
$741$	2.33476	+	8.78568i	0.0857697	+	0.322750i
$742$			9.75075i			0.357961i
$743$	10.4981	−	28.8433i	0.385138	−	1.05816i	−0.584024	−	0.811736i	$-0.698523\pi$
$743$	10.4981	−	28.8433i	0.385138	−	1.05816i	0.969163	−	0.246422i	$-0.0792550\pi$
$744$	0.584569	+	3.31525i	0.0214313	+	0.121543i
$745$		0			0
$746$	11.0526	−	9.27425i	0.404665	−	0.339554i
$747$	4.95290	+	0.873331i	0.181217	+	0.0319535i
$748$	6.40785	+	3.69957i	0.234294	+	0.135270i
$749$	−22.1532	−	38.3705i	−0.809461	−	1.40203i
$750$		0			0
$751$	−32.6013	+	11.8659i	−1.18964	+	0.432992i	−0.859596	−	0.510974i	$-0.829285\pi$
$751$	−32.6013	+	11.8659i	−1.18964	+	0.432992i	−0.330041	+	0.943967i	$0.607063\pi$
$752$	9.14512	−	5.27994i	0.333488	−	0.192540i
$753$	−7.46239	−	4.30841i	−0.271944	−	0.157007i
$754$	3.94368	−	22.3657i	0.143620	−	0.814511i
$755$		0			0
$756$	−4.20393	−	3.52751i	−0.152895	−	0.128294i
$757$	−15.4528	+	2.72475i	−0.561642	+	0.0990326i	−0.447259	−	0.894404i	$-0.647600\pi$
$757$	−15.4528	+	2.72475i	−0.561642	+	0.0990326i	−0.114382	+	0.993437i	$0.536489\pi$
$758$	2.79210	−	7.67124i	0.101414	−	0.278632i
$759$	−1.26673			−0.0459793
$760$		0			0
$761$	19.4434			0.704822			0.352411	−	0.935845i	$-0.385362\pi$
$761$	19.4434			0.704822			0.352411	+	0.935845i	$0.385362\pi$
$762$	1.17754	−	3.23525i	0.0426576	−	0.117201i
$763$	−26.3749	+	4.65060i	−0.954835	+	0.168363i
$764$	2.51007	+	2.10620i	0.0908112	+	0.0761996i
$765$		0			0
$766$	4.76545	−	27.0262i	0.172183	−	0.976497i
$767$	−49.5441	−	28.6043i	−1.78894	−	1.03284i
$768$	0.354164	−	0.204476i	0.0127798	−	0.00737841i
$769$	37.7602	−	13.7436i	1.36167	−	0.495607i	0.445098	−	0.895482i	$-0.353169\pi$
$769$	37.7602	−	13.7436i	1.36167	−	0.495607i	0.916570	+	0.399875i	$0.130946\pi$
$770$		0			0
$771$	−5.66713	−	9.81576i	−0.204097	−	0.353506i
$772$	−20.4993	−	11.8353i	−0.737786	−	0.425961i
$773$	−30.4187	−	5.36365i	−1.09409	−	0.192917i	−0.402650	−	0.915354i	$-0.631911\pi$
$773$	−30.4187	−	5.36365i	−1.09409	−	0.192917i	−0.691436	+	0.722437i	$0.743022\pi$
$774$	−3.34437	+	2.80626i	−0.120211	+	0.100869i
$775$		0			0
$776$	0.455063	+	2.58079i	0.0163358	+	0.0926451i
$777$	−0.965237	+	2.65197i	−0.0346277	+	0.0951388i
$778$			15.7862i			0.565961i
$779$	−44.9768	+	20.8605i	−1.61146	+	0.747407i
$780$		0			0
$781$	−0.776936	−	0.282782i	−0.0278010	−	0.0101187i
$782$	3.21898	−	0.567594i	0.115111	−	0.0202971i
$783$	−6.82814	+	8.13747i	−0.244018	+	0.290809i
$784$	1.30758	−	1.09719i	0.0466993	−	0.0391853i
$785$		0			0
$786$	3.48444	−	6.03522i	0.124286	−	0.215269i
$787$	−20.0345	+	11.5669i	−0.714154	+	0.412317i	−0.812597	−	0.582825i	$-0.801947\pi$
$787$	−20.0345	+	11.5669i	−0.714154	+	0.412317i	0.0984430	+	0.995143i	$0.468614\pi$
$788$	2.35468	+	6.46944i	0.0838821	+	0.230464i
$789$	3.46064	−	1.25957i	0.123202	−	0.0448419i
$790$		0			0
$791$	−11.3620	+	19.6796i	−0.403988	+	0.699727i
$792$	7.38709	+	1.30254i	0.262489	+	0.0462838i
$793$	−10.8517	−	12.9325i	−0.385355	−	0.459248i
$794$	−29.2508	−	24.5444i	−1.03807	−	0.871047i
$795$		0			0
$796$	17.8456	+	6.49525i	0.632519	+	0.230218i
$797$		−	12.1286i		−	0.429618i	−0.976656	−	0.214809i	$-0.931087\pi$
$797$		−	12.1286i		−	0.429618i	0.976656	−	0.214809i	$-0.0689128\pi$
$798$	−3.71332	−	1.74085i	−0.131450	−	0.0616256i
$799$	29.5072			1.04389
$800$		0			0
$801$	−3.19212	−	18.1034i	−0.112788	−	0.639652i
$802$	10.3971	−	12.3908i	0.367134	−	0.437533i
$803$	26.1247	+	31.1342i	0.921922	+	1.09870i
$804$	−0.598218	+	3.39266i	−0.0210975	+	0.119650i
$805$		0			0
$806$	−20.9897	−	36.3552i	−0.739329	−	1.28056i
$807$	1.04027	+	2.85812i	0.0366193	+	0.100611i
$808$	3.34116	+	9.17977i	0.117542	+	0.322943i
$809$	−2.77035	−	4.79839i	−0.0974005	−	0.168703i	0.813207	−	0.581974i	$-0.197719\pi$
$809$	−2.77035	−	4.79839i	−0.0974005	−	0.168703i	−0.910608	+	0.413271i	$0.864386\pi$
$810$		0			0
$811$	3.82958	−	21.7186i	0.134475	−	0.762644i	−0.840749	−	0.541424i	$-0.817885\pi$
$811$	3.82958	−	21.7186i	0.134475	−	0.762644i	0.975224	−	0.221219i	$-0.0710036\pi$
$812$	6.58582	+	7.84867i	0.231117	+	0.275434i
$813$	4.91363	−	5.85584i	0.172329	−	0.205373i
$814$	−1.37923	−	7.82202i	−0.0483421	−	0.274162i
$815$		0			0
$816$	1.14273			0.0400034
$817$	−3.86448	+	5.49497i	−0.135201	+	0.192245i
$818$		−	31.5602i		−	1.10348i
$819$	31.2315	+	11.3673i	1.09132	+	0.397207i
$820$		0			0
$821$	−27.6363	−	23.1896i	−0.964512	−	0.809322i	0.0171690	−	0.999853i	$-0.494535\pi$
$821$	−27.6363	−	23.1896i	−0.964512	−	0.809322i	−0.981681	+	0.190531i	$0.938979\pi$
$822$	−3.08344	−	3.67470i	−0.107547	−	0.128170i
$823$	−36.6265	−	6.45824i	−1.27672	−	0.225120i	−0.506133	−	0.862456i	$-0.668925\pi$
$823$	−36.6265	−	6.45824i	−1.27672	−	0.225120i	−0.770586	+	0.637336i	$0.780037\pi$
$824$	0.248809	−	0.430950i	0.00866767	−	0.0150129i
$825$		0			0
$826$	24.2526	−	8.82723i	0.843856	−	0.307139i
$827$	−17.0533	−	46.8534i	−0.593000	−	1.62925i	−0.764908	−	0.644140i	$-0.777215\pi$
$827$	−17.0533	−	46.8534i	−0.593000	−	1.62925i	0.171908	−	0.985113i	$-0.445007\pi$
$828$	2.86971	−	1.65683i	0.0997294	−	0.0575788i
$829$	2.41813	−	4.18832i	0.0839851	−	0.145466i	−0.820973	−	0.570967i	$-0.806569\pi$
$829$	2.41813	−	4.18832i	0.0839851	−	0.145466i	0.904958	+	0.425500i	$0.139902\pi$
$830$		0			0
$831$	−1.22105	+	1.02458i	−0.0423577	+	0.0355423i
$832$	−3.27801	+	3.90658i	−0.113645	+	0.135436i
$833$	4.69715	−	0.828235i	0.162747	−	0.0286966i
$834$	4.97800	+	1.81185i	0.172374	+	0.0627391i
$835$		0			0
$836$	11.5003	−	0.982325i	0.397747	−	0.0339744i
$837$			19.6354i			0.678698i
$838$	5.13119	−	14.0978i	0.177254	−	0.487002i
$839$	1.26744	+	7.18802i	0.0437570	+	0.248158i	0.998838	−	0.0481853i	$-0.0153438\pi$
$839$	1.26744	+	7.18802i	0.0437570	+	0.248158i	−0.955081	+	0.296343i	$0.904233\pi$
$840$		0			0
$841$	−7.02276	+	5.89279i	−0.242164	+	0.203200i
$842$	−2.31085	−	0.407466i	−0.0796372	−	0.0140422i
$843$	2.08211	+	1.20211i	0.0717116	+	0.0414027i
$844$	−6.17101	−	10.6885i	−0.212415	−	0.367914i
$845$		0			0
$846$	28.1096	−	10.2310i	0.966427	−	0.351751i
$847$	7.94640	−	4.58786i	0.273042	−	0.157641i
$848$	−3.67041	−	2.11911i	−0.126042	−	0.0727706i
$849$	−1.32660	+	7.52352i	−0.0455288	+	0.258207i
$850$		0			0
$851$	−2.68786	−	2.25539i	−0.0921388	−	0.0773136i
$852$	−0.125751	+	0.0221733i	−0.00430816	+	0.000759646i
$853$	11.7656	−	32.3257i	0.402846	−	1.10681i	−0.558027	−	0.829823i	$-0.688441\pi$
$853$	11.7656	−	32.3257i	0.402846	−	1.10681i	0.960873	−	0.276989i	$-0.0893364\pi$
$854$	7.61625			0.260623
$855$		0			0
$856$	19.2581			0.658228
$857$	−9.05674	+	24.8832i	−0.309372	+	0.849993i	0.683407	+	0.730038i	$0.260498\pi$
$857$	−9.05674	+	24.8832i	−0.309372	+	0.849993i	−0.992779	+	0.119956i	$0.961725\pi$
$858$	5.43851	−	0.958956i	0.185668	−	0.0327382i
$859$	21.2971	+	17.8704i	0.726649	+	0.609731i	0.929216	−	0.369538i	$-0.120484\pi$
$859$	21.2971	+	17.8704i	0.726649	+	0.609731i	−0.202567	+	0.979268i	$0.564928\pi$
$860$		0			0
$861$	1.85831	−	10.5390i	0.0633311	−	0.359168i
$862$	30.1579	+	17.4117i	1.02718	+	0.593044i
$863$	−37.5517	+	21.6805i	−1.27827	+	0.738012i	−0.976531	−	0.215378i	$-0.930902\pi$
$863$	−37.5517	+	21.6805i	−1.27827	+	0.738012i	−0.301743	+	0.953389i	$0.597568\pi$
$864$	2.24147	−	0.815828i	0.0762564	−	0.0277550i
$865$		0			0
$866$	−2.20058	−	3.81152i	−0.0747788	−	0.129521i
$867$	−3.25548	−	1.87955i	−0.110562	−	0.0638329i
$868$	18.6508	+	3.28864i	0.633050	+	0.111624i
$869$	−17.8675	+	14.9926i	−0.606115	+	0.508591i
$870$		0			0
$871$	−7.45984	−	42.3068i	−0.252767	−	1.43351i
$872$	3.98141	−	10.9388i	0.134827	−	0.370435i
$873$			7.42354i			0.251249i
$874$	3.61286	−	3.59803i	0.122207	−	0.121705i
$875$		0			0
$876$	5.89836	+	2.14683i	0.199287	+	0.0725345i
$877$	−18.4197	+	3.24789i	−0.621988	+	0.109673i	−0.475757	−	0.879577i	$-0.657826\pi$
$877$	−18.4197	+	3.24789i	−0.621988	+	0.109673i	−0.146232	+	0.989250i	$0.546715\pi$
$878$	1.63758	−	1.95159i	0.0552655	−	0.0658629i
$879$	3.31763	−	2.78382i	0.111901	−	0.0938960i
$880$		0			0
$881$	−6.40305	+	11.0904i	−0.215724	+	0.373646i	−0.953496	−	0.301404i	$-0.902545\pi$
$881$	−6.40305	+	11.0904i	−0.215724	+	0.373646i	0.737772	+	0.675050i	$0.235878\pi$
$882$	4.18749	−	2.41765i	0.141000	−	0.0814065i
$883$	−7.75990	−	21.3201i	−0.261141	−	0.717480i	−0.999091	−	0.0426245i	$-0.986428\pi$
$883$	−7.75990	−	21.3201i	−0.261141	−	0.717480i	0.737950	−	0.674856i	$-0.235794\pi$
$884$	−13.3905	+	4.87376i	−0.450373	+	0.163922i
$885$		0			0
$886$	−19.9735	+	34.5951i	−0.671023	+	1.16225i
$887$	−0.815912	−	0.143867i	−0.0273956	−	0.00483059i	0.159934	−	0.987128i	$-0.448872\pi$
$887$	−0.815912	−	0.143867i	−0.0273956	−	0.00483059i	−0.187329	+	0.982297i	$0.559983\pi$
$888$	−0.788489	−	0.939685i	−0.0264600	−	0.0315338i
$889$	−14.8374	−	12.4501i	−0.497630	−	0.417561i
$890$		0			0
$891$	18.7188	+	6.81307i	0.627102	+	0.228246i
$892$			4.78950i			0.160364i
$893$	37.7593	−	26.3238i	1.26357	−	0.880893i
$894$	6.69938			0.224061
$895$		0			0
$896$	−0.399507	−	2.26572i	−0.0133466	−	0.0756923i
$897$	1.56813	−	1.86882i	0.0523583	−	0.0623982i
$898$	−15.9796	−	19.0438i	−0.533247	−	0.635499i
$899$	6.36577	−	36.1021i	0.212310	−	1.20407i
$900$		0			0
$901$	−5.92138	−	10.2561i	−0.197270	−	0.341681i
$902$	10.3011	+	28.3021i	0.342990	+	0.942357i
$903$	−0.495941	−	1.36259i	−0.0165039	−	0.0453440i
$904$	−4.93858	−	8.55388i	−0.164255	−	0.284498i
$905$		0			0
$906$	−0.263659	+	1.49528i	−0.00875947	+	0.0496774i
$907$	−4.35194	−	5.18644i	−0.144504	−	0.172213i	0.688938	−	0.724820i	$-0.258077\pi$
$907$	−4.35194	−	5.18644i	−0.144504	−	0.172213i	−0.833442	+	0.552608i	$0.813633\pi$
$908$	−2.72812	+	3.25125i	−0.0905360	+	0.107897i
$909$	4.80536	+	27.2525i	0.159384	+	0.903910i
$910$		0			0
$911$	26.0838			0.864196			0.432098	−	0.901827i	$-0.357773\pi$
$911$	26.0838			0.864196			0.432098	+	0.901827i	$0.357773\pi$
$912$	1.46231	−	1.01944i	0.0484218	−	0.0337571i
$913$		−	4.70123i		−	0.155588i
$914$	35.6650	+	12.9810i	1.17969	+	0.429373i
$915$		0			0
$916$	−22.1355	−	18.5739i	−0.731377	−	0.613698i
$917$	−25.2006	−	30.0329i	−0.832198	−	0.991775i
$918$	6.56399	+	1.15741i	0.216644	+	0.0382002i
$919$	−29.5834	+	51.2400i	−0.975867	+	1.69025i	−0.298823	+	0.954309i	$0.596594\pi$
$919$	−29.5834	+	51.2400i	−0.975867	+	1.69025i	−0.677044	+	0.735942i	$0.736739\pi$
$920$		0			0
$921$	−1.80719	+	0.657764i	−0.0595490	+	0.0216741i
$922$	−0.576063	−	1.58272i	−0.0189716	−	0.0521241i
$923$	1.37899	−	0.796160i	0.0453900	−	0.0262059i
$924$	−1.24569	+	2.15760i	−0.0409801	+	0.0709797i
$925$		0			0
$926$	6.72319	−	5.64143i	0.220938	−	0.185389i
$927$	0.906094	−	1.07984i	0.0297600	−	0.0354666i
$928$	−4.38571	+	0.773318i	−0.143968	+	0.0253854i
$929$	35.9741	+	13.0935i	1.18027	+	0.429583i	0.856297	−	0.516483i	$-0.172759\pi$
$929$	35.9741	+	13.0935i	1.18027	+	0.429583i	0.323973	+	0.946066i	$0.394981\pi$
$930$		0			0
$931$	5.27190	−	5.25026i	0.172779	−	0.172070i
$932$			13.6279i			0.446397i
$933$	−1.90559	+	5.23557i	−0.0623862	+	0.171405i
$934$	−0.0907494	−	0.514665i	−0.00296941	−	0.0168404i
$935$		0			0
$936$	−11.0664	+	9.28582i	−0.361717	+	0.303516i
$937$	−3.84349	−	0.677711i	−0.125561	−	0.0221398i	0.110514	−	0.993875i	$-0.464750\pi$
$937$	−3.84349	−	0.677711i	−0.125561	−	0.0221398i	−0.236076	+	0.971735i	$0.575861\pi$
$938$	16.7842	+	9.69036i	0.548024	+	0.316402i
$939$	−6.31975	−	10.9461i	−0.206237	−	0.357213i
$940$		0			0
$941$	23.6727	−	8.61616i	0.771708	−	0.280879i	0.0739975	−	0.997258i	$-0.476424\pi$
$941$	23.6727	−	8.61616i	0.771708	−	0.280879i	0.697711	+	0.716380i	$0.254202\pi$
$942$	1.75213	−	1.01159i	0.0570875	−	0.0329595i
$943$	11.5226	+	6.65256i	0.375227	+	0.216637i
$944$	−1.94800	+	11.0477i	−0.0634020	+	0.359570i
$945$		0			0
$946$	3.12620	+	2.62320i	0.101642	+	0.0852874i
$947$	20.2726	−	3.57460i	0.658770	−	0.116159i	0.165738	−	0.986170i	$-0.447000\pi$
$947$	20.2726	−	3.57460i	0.658770	−	0.116159i	0.493032	+	0.870011i	$0.335888\pi$
$948$	−1.23204	+	3.38499i	−0.0400147	+	0.109939i
$949$	−78.2736			−2.54087
$950$		0			0
$951$	−3.33259			−0.108067
$952$	2.19875	−	6.04100i	0.0712618	−	0.195790i
$953$	39.4790	−	6.96122i	1.27885	−	0.225496i	0.507359	−	0.861735i	$-0.330622\pi$
$953$	39.4790	−	6.96122i	1.27885	−	0.225496i	0.771492	+	0.636239i	$0.219511\pi$
$954$	−9.19702	−	7.71722i	−0.297765	−	0.249854i
$955$		0			0
$956$	2.58512	−	14.6609i	0.0836087	−	0.474169i
$957$	4.17642	+	2.41126i	0.135004	+	0.0779449i
$958$	6.00971	−	3.46971i	0.194165	−	0.112101i
$959$	−25.3591	+	9.22996i	−0.818889	+	0.298051i
$960$		0			0
$961$	−18.3809	−	31.8366i	−0.592931	−	1.02699i
$962$	13.2473	+	7.64836i	0.427112	+	0.246593i
$963$	53.7247	+	9.47311i	1.73125	+	0.305267i
$964$	−8.88645	+	7.45662i	−0.286213	+	0.240161i
$965$		0			0
$966$	0.191115	+	1.08387i	0.00614904	+	0.0348729i
$967$	−21.0917	+	57.9491i	−0.678264	+	1.86352i	−0.217275	+	0.976110i	$0.569717\pi$
$967$	−21.0917	+	57.9491i	−0.678264	+	1.86352i	−0.460989	+	0.887406i	$0.652505\pi$
$968$			3.98828i			0.128188i
$969$	4.96296	−	0.423921i	0.159433	−	0.0136183i
$970$		0			0
$971$	19.4401	+	7.07561i	0.623862	+	0.227067i	0.634558	−	0.772876i	$-0.281182\pi$
$971$	19.4401	+	7.07561i	0.623862	+	0.227067i	−0.0106954	+	0.999943i	$0.503405\pi$
$972$	10.0770	−	1.77684i	0.323219	−	0.0569923i
$973$	19.1566	−	22.8299i	0.614132	−	0.731894i
$974$	31.5529	−	26.4761i	1.01102	−	0.848348i
$975$		0			0
$976$	−1.65522	+	2.86693i	−0.0529825	+	0.0917683i
$977$	−9.13528	+	5.27426i	−0.292264	+	0.168738i	−0.638962	−	0.769238i	$-0.720636\pi$
$977$	−9.13528	+	5.27426i	−0.292264	+	0.168738i	0.346699	+	0.937977i	$0.387303\pi$
$978$	1.12735	+	3.09736i	0.0360485	+	0.0990426i
$979$	−16.1472	+	5.87710i	−0.516067	+	0.187833i
$980$		0			0
$981$	16.4879	−	28.5578i	0.526417	−	0.911781i
$982$	−20.7033	−	3.65055i	−0.660669	−	0.116494i
$983$	15.5294	+	18.5072i	0.495312	+	0.590290i	0.954560	−	0.298018i	$-0.0963257\pi$
$983$	15.5294	+	18.5072i	0.495312	+	0.590290i	−0.459248	+	0.888308i	$0.651881\pi$
$984$	3.56326	+	2.98993i	0.113593	+	0.0953156i
$985$		0			0
$986$	−11.6935	−	4.25607i	−0.372396	−	0.135541i
$987$			9.93542i			0.316248i
$988$	−12.7874	+	18.1827i	−0.406823	+	0.578468i
$989$	1.80281			0.0573259
$990$		0			0
$991$	−5.95262	−	33.7590i	−0.189091	−	1.07239i	−0.920585	−	0.390542i	$-0.872288\pi$
$991$	−5.95262	−	33.7590i	−0.189091	−	1.07239i	0.731494	−	0.681848i	$-0.238824\pi$
$992$	−5.29127	+	6.30589i	−0.167998	+	0.200212i
$993$	0.165473	+	0.197203i	0.00525112	+	0.00625804i
$994$	−0.124742	+	0.707445i	−0.00395657	+	0.0224388i
$995$		0			0
$996$	−0.363030	−	0.628786i	−0.0115030	−	0.0199238i
$997$	−14.4521	−	39.7067i	−0.457701	−	1.25752i	−0.927192	−	0.374587i	$-0.877785\pi$
$997$	−14.4521	−	39.7067i	−0.457701	−	1.25752i	0.469490	−	0.882938i	$-0.344438\pi$
$998$	8.00078	+	21.9820i	0.253260	+	0.695827i
$999$	−3.57744	−	6.19631i	−0.113185	−	0.196042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.99.3		24
5.2	odd	4		950.2.l.g.251.2		12
5.3	odd	4		190.2.k.c.61.1	✓	12
5.4	even	2	inner	950.2.u.f.99.2		24
19.5	even	9	inner	950.2.u.f.499.2		24
95.24	even	18	inner	950.2.u.f.499.3		24
95.28	odd	36		3610.2.a.bf.1.3		6
95.43	odd	36		190.2.k.c.81.1	yes	12
95.48	even	36		3610.2.a.bd.1.4		6
95.62	odd	36		950.2.l.g.651.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.61.1	✓	12	5.3	odd	4
190.2.k.c.81.1	yes	12	95.43	odd	36
950.2.l.g.251.2		12	5.2	odd	4
950.2.l.g.651.2		12	95.62	odd	36
950.2.u.f.99.2		24	5.4	even	2	inner
950.2.u.f.99.3		24	1.1	even	1	trivial
950.2.u.f.499.2		24	19.5	even	9	inner
950.2.u.f.499.3		24	95.24	even	18	inner
3610.2.a.bd.1.4		6	95.48	even	36
3610.2.a.bf.1.3		6	95.28	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.402740 + 0.0710139i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.0710139 + 0.402740i) q^{6} +(1.99244 + 1.15033i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.66192 + 0.968860i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.402740 + 0.0710139i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.0710139 + 0.402740i) q^{6} +(1.99244 + 1.15033i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.66192 + 0.968860i) q^{9} +(1.32398 + 2.29321i) q^{11} +(0.354164 + 0.204476i) q^{12} +(-5.02221 - 0.885551i) q^{13} +(1.76241 - 1.47884i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.955698 + 2.62576i) q^{17} +2.83276i q^{18} +(1.11951 + 4.21268i) q^{19} +(-0.884124 - 0.321795i) q^{21} +(2.60774 - 0.459814i) q^{22} +(0.751910 - 0.896091i) q^{23} +(0.313276 - 0.262870i) q^{24} +(-2.54984 + 4.41645i) q^{26} +(2.06575 - 1.19266i) q^{27} +(-0.786875 - 2.16192i) q^{28} +(-4.18479 + 1.52314i) q^{29} +(-4.11588 + 7.12891i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-0.696070 - 0.829544i) q^{33} +(2.14054 + 1.79613i) q^{34} +(2.66192 + 0.968860i) q^{36} -2.99954i q^{37} +(4.34152 + 0.388831i) q^{38} +2.08553 q^{39} +(1.97511 + 11.2014i) q^{41} +(-0.604776 + 0.720744i) q^{42} +(0.990646 + 1.18061i) q^{43} +(0.459814 - 2.60774i) q^{44} +(-0.584882 - 1.01305i) q^{46} +(-3.61169 - 9.92304i) q^{47} +(-0.139870 - 0.384290i) q^{48} +(-0.853462 - 1.47824i) q^{49} +(0.198432 - 1.12537i) q^{51} +(3.27801 + 3.90658i) q^{52} +(-2.72428 + 3.24667i) q^{53} +(-0.414207 - 2.34908i) q^{54} -2.30067 q^{56} +(-0.750029 - 1.61712i) q^{57} +4.45336i q^{58} +(10.5415 + 3.83681i) q^{59} +(2.53595 + 2.12792i) q^{61} +(5.29127 + 6.30589i) q^{62} +(-6.41823 - 1.13171i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.01759 + 0.370371i) q^{66} +(2.88116 + 7.91593i) q^{67} +(2.41991 - 1.39714i) q^{68} +(-0.239189 + 0.414288i) q^{69} +(-0.239189 + 0.200703i) q^{71} +(1.82086 - 2.17002i) q^{72} +(15.1155 - 2.66528i) q^{73} +(-2.81865 - 1.02590i) q^{74} +(1.85027 - 3.94671i) q^{76} +6.09209i q^{77} +(0.713293 - 1.95976i) q^{78} +(1.52957 + 8.67461i) q^{79} +(5.76279 - 4.83556i) q^{81} +(11.2014 + 1.97511i) q^{82} +(-1.53755 - 0.887706i) q^{83} +(0.470432 + 0.814813i) q^{84} +(1.44823 - 0.527112i) q^{86} +(1.57722 - 0.910608i) q^{87} +(-2.29321 - 1.32398i) q^{88} +(-1.12686 + 6.39074i) q^{89} +(-8.98775 - 7.54162i) q^{91} +(-1.15199 + 0.203127i) q^{92} +(1.15138 - 3.16338i) q^{93} -10.5599 q^{94} -0.408953 q^{96} +(0.896300 - 2.46256i) q^{97} +(-1.68099 + 0.296404i) q^{98} +(-5.74613 - 4.82158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

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