LMFDB - Embedded newform 625.2.d.q.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$1.20005i$ of defining polynomial
Character	$\chi$	$=$	625.251
Dual form			625.2.d.q.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.405309 - 0.294474i) q^{2} +(-0.955869 + 2.94186i) q^{3} +(-0.540474 + 1.66341i) q^{4} +(0.478880 + 1.47384i) q^{6} -0.0237879 q^{7} +(0.580400 + 1.78629i) q^{8} +(-5.31382 - 3.86071i) q^{9} +O(q^{10})$	\(q+(0.405309 - 0.294474i) q^{2} +(-0.955869 + 2.94186i) q^{3} +(-0.540474 + 1.66341i) q^{4} +(0.478880 + 1.47384i) q^{6} -0.0237879 q^{7} +(0.580400 + 1.78629i) q^{8} +(-5.31382 - 3.86071i) q^{9} +(-2.89894 + 2.10620i) q^{11} +(-4.37689 - 3.18000i) q^{12} +(3.05474 + 2.21940i) q^{13} +(-0.00964144 + 0.00700492i) q^{14} +(-2.06870 - 1.50300i) q^{16} +(1.11958 + 3.44570i) q^{17} -3.29062 q^{18} +(-0.751170 - 2.31186i) q^{19} +(0.0227381 - 0.0699807i) q^{21} +(-0.554744 + 1.70733i) q^{22} +(1.38777 - 1.00828i) q^{23} -5.80980 q^{24} +1.89167 q^{26} +(8.92950 - 6.48766i) q^{27} +(0.0128567 - 0.0395689i) q^{28} +(1.19198 - 3.66855i) q^{29} +(-1.85713 - 5.71565i) q^{31} -5.03748 q^{32} +(-3.42515 - 10.5415i) q^{33} +(1.46845 + 1.06689i) q^{34} +(9.29391 - 6.75242i) q^{36} +(-0.298777 - 0.217074i) q^{37} +(-0.985240 - 0.715819i) q^{38} +(-9.44911 + 6.86518i) q^{39} +(6.31761 + 4.59002i) q^{41} +(-0.0113915 - 0.0350596i) q^{42} -0.174574 q^{43} +(-1.93667 - 5.96047i) q^{44} +(0.265566 - 0.817327i) q^{46} +(-2.41368 + 7.42853i) q^{47} +(6.39902 - 4.64916i) q^{48} -6.99943 q^{49} -11.2070 q^{51} +(-5.34278 + 3.88175i) q^{52} +(2.77245 - 8.53273i) q^{53} +(1.70876 - 5.25902i) q^{54} +(-0.0138065 - 0.0424920i) q^{56} +7.51920 q^{57} +(-0.597171 - 1.83790i) q^{58} +(3.60446 + 2.61879i) q^{59} +(-7.45430 + 5.41587i) q^{61} +(-2.43582 - 1.76973i) q^{62} +(0.126404 + 0.0918382i) q^{63} +(2.09566 - 1.52259i) q^{64} +(-4.49246 - 3.26396i) q^{66} +(1.38250 + 4.25489i) q^{67} -6.33671 q^{68} +(1.63968 + 5.04642i) q^{69} +(-2.99579 + 9.22010i) q^{71} +(3.81221 - 11.7328i) q^{72} +(-3.19875 + 2.32403i) q^{73} -0.185020 q^{74} +4.25156 q^{76} +(0.0689596 - 0.0501021i) q^{77} +(-1.80819 + 5.56504i) q^{78} +(-2.99236 + 9.20955i) q^{79} +(4.46129 + 13.7304i) q^{81} +3.91223 q^{82} +(2.76792 + 8.51877i) q^{83} +(0.104117 + 0.0756454i) q^{84} +(-0.0707566 + 0.0514077i) q^{86} +(9.65298 + 7.01330i) q^{87} +(-5.44483 - 3.95590i) q^{88} +(13.7655 - 10.0012i) q^{89} +(-0.0726659 - 0.0527948i) q^{91} +(0.927119 + 2.85338i) q^{92} +18.5898 q^{93} +(1.20923 + 3.72161i) q^{94} +(4.81518 - 14.8196i) q^{96} +(-0.854239 + 2.62908i) q^{97} +(-2.83693 + 2.06115i) q^{98} +23.5359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.405309	−	0.294474i	0.286597	−	0.208225i	−0.435193	−	0.900337i	$-0.643320\pi$
$2$	0.405309	−	0.294474i	0.286597	−	0.208225i	0.721790	+	0.692113i	$0.243320\pi$
$3$	−0.955869	+	2.94186i	−0.551871	+	1.69848i	0.152195	+	0.988350i	$0.451366\pi$
$3$	−0.955869	+	2.94186i	−0.551871	+	1.69848i	−0.704066	+	0.710134i	$0.748634\pi$
$4$	−0.540474	+	1.66341i	−0.270237	+	0.831704i
$5$		0			0
$5$		0			0
$6$	0.478880	+	1.47384i	0.195502	+	0.601693i
$7$	−0.0237879			−0.00899097			−0.00449549	−	0.999990i	$-0.501431\pi$
$7$	−0.0237879			−0.00899097			−0.00449549	+	0.999990i	$0.501431\pi$
$8$	0.580400	+	1.78629i	0.205202	+	0.631548i
$9$	−5.31382	−	3.86071i	−1.77127	−	1.28690i
$10$		0			0
$11$	−2.89894	+	2.10620i	−0.874063	+	0.635044i	−0.931674	−	0.363295i	$-0.881652\pi$
$11$	−2.89894	+	2.10620i	−0.874063	+	0.635044i	0.0576108	+	0.998339i	$0.481652\pi$
$12$	−4.37689	−	3.18000i	−1.26350	−	0.917986i
$13$	3.05474	+	2.21940i	0.847234	+	0.615551i	0.924382	−	0.381468i	$-0.124582\pi$
$13$	3.05474	+	2.21940i	0.847234	+	0.615551i	−0.0771484	+	0.997020i	$0.524582\pi$
$14$	−0.00964144	+	0.00700492i	−0.00257678	+	0.00187214i
$15$		0			0
$16$	−2.06870	−	1.50300i	−0.517175	−	0.375750i
$17$	1.11958	+	3.44570i	0.271537	+	0.835706i	0.990115	+	0.140259i	$0.0447936\pi$
$17$	1.11958	+	3.44570i	0.271537	+	0.835706i	−0.718577	+	0.695447i	$0.755206\pi$
$18$	−3.29062			−0.775606
$19$	−0.751170	−	2.31186i	−0.172330	−	0.530378i	0.827171	−	0.561950i	$-0.189949\pi$
$19$	−0.751170	−	2.31186i	−0.172330	−	0.530378i	−0.999501	+	0.0315721i	$0.989949\pi$
$20$		0			0
$21$	0.0227381	−	0.0699807i	0.00496186	−	0.0152710i
$22$	−0.554744	+	1.70733i	−0.118272	+	0.364003i
$23$	1.38777	−	1.00828i	0.289371	−	0.210240i	−0.433624	−	0.901094i	$-0.642765\pi$
$23$	1.38777	−	1.00828i	0.289371	−	0.210240i	0.722994	+	0.690854i	$0.242765\pi$
$24$	−5.80980			−1.18592
$25$		0			0
$26$	1.89167			0.370987
$27$	8.92950	−	6.48766i	1.71848	−	1.24855i
$28$	0.0128567	−	0.0395689i	0.00242969	−	0.00747782i
$29$	1.19198	−	3.66855i	0.221346	−	0.681232i	−0.777296	−	0.629135i	$-0.783409\pi$
$29$	1.19198	−	3.66855i	0.221346	−	0.681232i	0.998642	−	0.0520974i	$-0.0165906\pi$
$30$		0			0
$31$	−1.85713	−	5.71565i	−0.333550	−	1.02656i	−0.967432	−	0.253131i	$-0.918540\pi$
$31$	−1.85713	−	5.71565i	−0.333550	−	1.02656i	0.633882	−	0.773430i	$-0.281460\pi$
$32$	−5.03748			−0.890510
$33$	−3.42515	−	10.5415i	−0.596243	−	1.83505i
$34$	1.46845	+	1.06689i	0.251836	+	0.182970i
$35$		0			0
$36$	9.29391	−	6.75242i	1.54899	−	1.12540i
$37$	−0.298777	−	0.217074i	−0.0491186	−	0.0356868i	0.562955	−	0.826488i	$-0.309664\pi$
$37$	−0.298777	−	0.217074i	−0.0491186	−	0.0356868i	−0.612074	+	0.790801i	$0.709664\pi$
$38$	−0.985240	−	0.715819i	−0.159827	−	0.116121i
$39$	−9.44911	+	6.86518i	−1.51307	+	1.09931i
$40$		0			0
$41$	6.31761	+	4.59002i	0.986646	+	0.716840i	0.959184	−	0.282783i	$-0.0912576\pi$
$41$	6.31761	+	4.59002i	0.986646	+	0.716840i	0.0274616	+	0.999623i	$0.491258\pi$
$42$	−0.0113915	−	0.0350596i	−0.00175775	−	0.00540981i
$43$	−0.174574			−0.0266224			−0.0133112	−	0.999911i	$-0.504237\pi$
$43$	−0.174574			−0.0266224			−0.0133112	+	0.999911i	$0.504237\pi$
$44$	−1.93667	−	5.96047i	−0.291964	−	0.898574i
$45$		0			0
$46$	0.265566	−	0.817327i	0.0391555	−	0.120508i
$47$	−2.41368	+	7.42853i	−0.352071	+	1.08356i	0.605618	+	0.795756i	$0.292926\pi$
$47$	−2.41368	+	7.42853i	−0.352071	+	1.08356i	−0.957689	+	0.287807i	$0.907074\pi$
$48$	6.39902	−	4.64916i	0.923619	−	0.671049i
$49$	−6.99943			−0.999919
$50$		0			0
$51$	−11.2070			−1.56929
$52$	−5.34278	+	3.88175i	−0.740910	+	0.538302i
$53$	2.77245	−	8.53273i	0.380826	−	1.17206i	−0.558638	−	0.829412i	$-0.688676\pi$
$53$	2.77245	−	8.53273i	0.380826	−	1.17206i	0.939464	−	0.342649i	$-0.111324\pi$
$54$	1.70876	−	5.25902i	0.232533	−	0.715661i
$55$		0			0
$56$	−0.0138065	−	0.0424920i	−0.00184497	−	0.00567823i
$57$	7.51920			0.995943
$58$	−0.597171	−	1.83790i	−0.0784124	−	0.241328i
$59$	3.60446	+	2.61879i	0.469261	+	0.340938i	0.797153	−	0.603777i	$-0.206338\pi$
$59$	3.60446	+	2.61879i	0.469261	+	0.340938i	−0.327892	+	0.944715i	$0.606338\pi$
$60$		0			0
$61$	−7.45430	+	5.41587i	−0.954426	+	0.693431i	−0.951850	−	0.306566i	$-0.900820\pi$
$61$	−7.45430	+	5.41587i	−0.954426	+	0.693431i	−0.00257641	+	0.999997i	$0.500820\pi$
$62$	−2.43582	−	1.76973i	−0.309350	−	0.224756i
$63$	0.126404	+	0.0918382i	0.0159255	+	0.0115705i
$64$	2.09566	−	1.52259i	0.261958	−	0.190324i
$65$		0			0
$66$	−4.49246	−	3.26396i	−0.552983	−	0.401766i
$67$	1.38250	+	4.25489i	0.168899	+	0.519817i	0.999302	−	0.0373451i	$-0.0118901\pi$
$67$	1.38250	+	4.25489i	0.168899	+	0.519817i	−0.830404	+	0.557162i	$0.811890\pi$
$68$	−6.33671			−0.768439
$69$	1.63968	+	5.04642i	0.197394	+	0.607517i
$70$		0			0
$71$	−2.99579	+	9.22010i	−0.355535	+	1.09422i	0.600164	+	0.799877i	$0.295102\pi$
$71$	−2.99579	+	9.22010i	−0.355535	+	1.09422i	−0.955699	+	0.294347i	$0.904898\pi$
$72$	3.81221	−	11.7328i	0.449273	−	1.38272i
$73$	−3.19875	+	2.32403i	−0.374385	+	0.272007i	−0.759027	−	0.651059i	$-0.774325\pi$
$73$	−3.19875	+	2.32403i	−0.374385	+	0.272007i	0.384642	+	0.923066i	$0.374325\pi$
$74$	−0.185020			−0.0215081
$75$		0			0
$76$	4.25156			0.487687
$77$	0.0689596	−	0.0501021i	0.00785868	−	0.00570967i
$78$	−1.80819	+	5.56504i	−0.204737	+	0.630116i
$79$	−2.99236	+	9.20955i	−0.336667	+	1.03616i	0.629228	+	0.777221i	$0.283371\pi$
$79$	−2.99236	+	9.20955i	−0.336667	+	1.03616i	−0.965895	+	0.258934i	$0.916629\pi$
$80$		0			0
$81$	4.46129	+	13.7304i	0.495699	+	1.52560i
$82$	3.91223			0.432033
$83$	2.76792	+	8.51877i	0.303818	+	0.935057i	0.980115	+	0.198428i	$0.0635836\pi$
$83$	2.76792	+	8.51877i	0.303818	+	0.935057i	−0.676297	+	0.736629i	$0.736416\pi$
$84$	0.104117	+	0.0756454i	0.0113601	+	0.00825359i
$85$		0			0
$86$	−0.0707566	+	0.0514077i	−0.00762988	+	0.00554343i
$87$	9.65298	+	7.01330i	1.03491	+	0.751905i
$88$	−5.44483	−	3.95590i	−0.580421	−	0.421700i
$89$	13.7655	−	10.0012i	1.45914	−	1.06013i	0.475551	−	0.879688i	$-0.342249\pi$
$89$	13.7655	−	10.0012i	1.45914	−	1.06013i	0.983586	−	0.180438i	$-0.0577514\pi$
$90$		0			0
$91$	−0.0726659	−	0.0527948i	−0.00761745	−	0.00553440i
$92$	0.927119	+	2.85338i	0.0966588	+	0.297485i
$93$	18.5898			1.92767
$94$	1.20923	+	3.72161i	0.124722	+	0.383855i
$95$		0			0
$96$	4.81518	−	14.8196i	0.491447	−	1.51252i
$97$	−0.854239	+	2.62908i	−0.0867348	+	0.266942i	−0.985012	−	0.172488i	$-0.944820\pi$
$97$	−0.854239	+	2.62908i	−0.0867348	+	0.266942i	0.898277	+	0.439430i	$0.144820\pi$
$98$	−2.83693	+	2.06115i	−0.286574	+	0.208208i
$99$	23.5359			2.36545
$100$		0			0
$101$	10.3526			1.03012			0.515062	−	0.857153i	$-0.327769\pi$
$101$	10.3526			1.03012			0.515062	+	0.857153i	$0.327769\pi$
$102$	−4.54228	+	3.30016i	−0.449753	+	0.326764i
$103$	−5.65234	+	17.3961i	−0.556941	+	1.71409i	0.133820	+	0.991006i	$0.457276\pi$
$103$	−5.65234	+	17.3961i	−0.556941	+	1.71409i	−0.690761	+	0.723083i	$0.742724\pi$
$104$	−2.19152	+	6.74479i	−0.214896	+	0.661381i
$105$		0			0
$106$	−1.38897	−	4.27481i	−0.134909	−	0.415206i
$107$	−15.8786			−1.53504			−0.767522	−	0.641023i	$-0.778510\pi$
$107$	−15.8786			−1.53504			−0.767522	+	0.641023i	$0.778510\pi$
$108$	5.96546	+	18.3598i	0.574027	+	1.76667i
$109$	−4.82262	−	3.50384i	−0.461924	−	0.335607i	0.332362	−	0.943152i	$-0.392155\pi$
$109$	−4.82262	−	3.50384i	−0.461924	−	0.335607i	−0.794285	+	0.607545i	$0.792155\pi$
$110$		0			0
$111$	0.924194	−	0.671466i	0.0877206	−	0.0637327i
$112$	0.0492100	+	0.0357531i	0.00464991	+	0.00337836i
$113$	1.96454	+	1.42732i	0.184808	+	0.134271i	0.676343	−	0.736587i	$-0.263564\pi$
$113$	1.96454	+	1.42732i	0.184808	+	0.134271i	−0.491535	+	0.870858i	$0.663564\pi$
$114$	3.04760	−	2.21421i	0.285434	−	0.207380i
$115$		0			0
$116$	5.45805	+	3.96551i	0.506767	+	0.368188i
$117$	−7.66387	−	23.5870i	−0.708525	−	2.18062i
$118$	2.23209			0.205480
$119$	−0.0266324	−	0.0819660i	−0.00244139	−	0.00751381i
$120$		0			0
$121$	0.568575	−	1.74989i	0.0516886	−	0.159081i
$122$	−1.42646	+	4.39020i	−0.129146	+	0.397470i
$123$	−19.5420	+	14.1981i	−1.76204	+	1.28020i
$124$	10.5112			0.943932
$125$		0			0
$126$	0.0782768			0.00697345
$127$	−13.8401	+	10.0554i	−1.22811	+	0.892274i	−0.996747	−	0.0805937i	$-0.974318\pi$
$127$	−13.8401	+	10.0554i	−1.22811	+	0.892274i	−0.231363	+	0.972868i	$0.574318\pi$
$128$	3.51436	−	10.8161i	0.310629	−	0.956017i
$129$	0.166870	−	0.513574i	0.0146921	−	0.0452177i
$130$		0			0
$131$	1.48005	+	4.55513i	0.129313	+	0.397983i	0.994662	−	0.103186i	$-0.0329035\pi$
$131$	1.48005	+	4.55513i	0.129313	+	0.397983i	−0.865349	+	0.501169i	$0.832904\pi$
$132$	19.3861			1.68734
$133$	0.0178687	+	0.0549943i	0.00154942	+	0.00476861i
$134$	1.81329	+	1.31743i	0.156645	+	0.113809i
$135$		0			0
$136$	−5.50522	+	3.99977i	−0.472068	+	0.342978i
$137$	10.3638	+	7.52974i	0.885439	+	0.643309i	0.934685	−	0.355478i	$-0.115682\pi$
$137$	10.3638	+	7.52974i	0.885439	+	0.643309i	−0.0492461	+	0.998787i	$0.515682\pi$
$138$	2.15062	+	1.56251i	0.183073	+	0.133010i
$139$	6.42376	−	4.66713i	0.544856	−	0.395861i	−0.281029	−	0.959699i	$-0.590676\pi$
$139$	6.42376	−	4.66713i	0.544856	−	0.395861i	0.825885	+	0.563838i	$0.190676\pi$
$140$		0			0
$141$	−19.5466	−	14.2014i	−1.64612	−	1.19597i
$142$	1.50086	+	4.61917i	0.125949	+	0.387632i
$143$	−13.5300			−1.13144
$144$	5.19004	+	15.9733i	0.432504	+	1.33111i
$145$		0			0
$146$	−0.612115	+	1.88390i	−0.0506590	+	0.155912i
$147$	6.69054	−	20.5914i	0.551827	−	1.69835i
$148$	0.522564	−	0.379665i	0.0429545	−	0.0312082i
$149$	−5.62724			−0.461002			−0.230501	−	0.973072i	$-0.574036\pi$
$149$	−5.62724			−0.461002			−0.230501	+	0.973072i	$0.574036\pi$
$150$		0			0
$151$	−7.36960			−0.599730			−0.299865	−	0.953982i	$-0.596942\pi$
$151$	−7.36960			−0.599730			−0.299865	+	0.953982i	$0.596942\pi$
$152$	3.69367	−	2.68361i	0.299596	−	0.217670i
$153$	7.35365	−	22.6322i	0.594507	−	1.82971i
$154$	0.0131962	−	0.0406137i	0.00106338	−	0.00327274i
$155$		0			0
$156$	−6.31259	−	19.4282i	−0.505412	−	1.55550i
$157$	−8.63091			−0.688822			−0.344411	−	0.938819i	$-0.611921\pi$
$157$	−8.63091			−0.688822			−0.344411	+	0.938819i	$0.611921\pi$
$158$	1.49914	+	4.61389i	0.119265	+	0.367061i
$159$	22.4520	+	16.3123i	1.78056	+	1.29365i
$160$		0			0
$161$	−0.0330122	+	0.0239848i	−0.00260172	+	0.00189026i
$162$	5.85146	+	4.25133i	0.459734	+	0.334016i
$163$	3.84254	+	2.79177i	0.300971	+	0.218668i	0.728012	−	0.685564i	$-0.240444\pi$
$163$	3.84254	+	2.79177i	0.300971	+	0.218668i	−0.427042	+	0.904232i	$0.640444\pi$
$164$	−11.0496	+	8.02798i	−0.862826	+	0.626880i
$165$		0			0
$166$	3.63042	+	2.63765i	0.281775	+	0.204722i
$167$	−5.74670	−	17.6865i	−0.444693	−	1.36862i	−0.882820	−	0.469711i	$-0.844358\pi$
$167$	−5.74670	−	17.6865i	−0.444693	−	1.36862i	0.438127	−	0.898913i	$-0.355642\pi$
$168$	0.138203			0.0106626
$169$	0.388497	+	1.19567i	0.0298844	+	0.0919746i
$170$		0			0
$171$	−4.93386	+	15.1849i	−0.377302	+	1.16122i
$172$	0.0943529	−	0.290388i	0.00719434	−	0.0221419i
$173$	12.7790	−	9.28447i	0.971568	−	0.705885i	0.0157594	−	0.999876i	$-0.494983\pi$
$173$	12.7790	−	9.28447i	0.971568	−	0.705885i	0.955808	+	0.293991i	$0.0949834\pi$
$174$	5.97767			0.453166
$175$		0			0
$176$	9.16266			0.690661
$177$	−11.1495	+	8.10060i	−0.838049	+	0.608878i
$178$	2.63417	−	8.10715i	0.197440	−	0.607657i
$179$	2.89532	−	8.91088i	0.216407	−	0.666031i	−0.782644	−	0.622469i	$-0.786130\pi$
$179$	2.89532	−	8.91088i	0.216407	−	0.666031i	0.999051	−	0.0435615i	$-0.0138704\pi$
$180$		0			0
$181$	−1.80661	−	5.56016i	−0.134284	−	0.413283i	0.861194	−	0.508276i	$-0.169717\pi$
$181$	−1.80661	−	5.56016i	−0.134284	−	0.413283i	−0.995478	+	0.0949930i	$0.969717\pi$
$182$	−0.0449988			−0.00333554
$183$	−8.80740	−	27.1064i	−0.651062	−	2.00376i
$184$	2.60654	+	1.89376i	0.192156	+	0.139610i
$185$		0			0
$186$	7.53462	−	5.47422i	0.552465	−	0.401389i
$187$	−10.5029	−	7.63083i	−0.768051	−	0.558022i
$188$	−11.0521	−	8.02985i	−0.806060	−	0.585637i
$189$	−0.212414	+	0.154328i	−0.0154508	+	0.0112257i
$190$		0			0
$191$	17.7132	+	12.8694i	1.28168	+	0.931196i	0.999602	−	0.0281951i	$-0.00897597\pi$
$191$	17.7132	+	12.8694i	1.28168	+	0.931196i	0.282079	+	0.959391i	$0.408976\pi$
$192$	2.47607	+	7.62055i	0.178695	+	0.549966i
$193$	25.2541			1.81783			0.908916	−	0.416980i	$-0.136911\pi$
$193$	25.2541			1.81783			0.908916	+	0.416980i	$0.136911\pi$
$194$	0.427965	+	1.31714i	0.0307261	+	0.0945651i
$195$		0			0
$196$	3.78301	−	11.6429i	0.270215	−	0.831636i
$197$	−4.46648	+	13.7464i	−0.318224	+	0.979391i	0.656184	+	0.754601i	$0.272170\pi$
$197$	−4.46648	+	13.7464i	−0.318224	+	0.979391i	−0.974407	+	0.224790i	$0.927830\pi$
$198$	9.53930	−	6.93071i	0.677929	−	0.492544i
$199$	−3.77734			−0.267768			−0.133884	−	0.990997i	$-0.542745\pi$
$199$	−3.77734			−0.267768			−0.133884	+	0.990997i	$0.542745\pi$
$200$		0			0
$201$	−13.8388			−0.976112
$202$	4.19601	−	3.04858i	0.295230	−	0.214497i
$203$	−0.0283547	+	0.0872669i	−0.00199011	+	0.00612494i
$204$	6.05707	−	18.6417i	0.424079	−	1.30518i
$205$		0			0
$206$	2.83176	+	8.71526i	0.197298	+	0.607221i
$207$	−11.2670			−0.783113
$208$	−2.98359	−	9.18255i	−0.206875	−	0.636695i
$209$	7.04685	+	5.11984i	0.487441	+	0.354147i
$210$		0			0
$211$	15.2909	−	11.1095i	1.05267	−	0.764810i	0.0799522	−	0.996799i	$-0.474523\pi$
$211$	15.2909	−	11.1095i	1.05267	−	0.764810i	0.972718	+	0.231989i	$0.0745232\pi$
$212$	12.6950	+	9.22343i	0.871894	+	0.633468i
$213$	−24.2607	−	17.6264i	−1.66231	−	1.20774i
$214$	−6.43574	+	4.67584i	−0.439938	+	0.319634i
$215$		0			0
$216$	16.7715	+	12.1852i	1.14116	+	0.829099i
$217$	0.0441771	+	0.135963i	0.00299894	+	0.00922978i
$218$	−2.98644			−0.202267
$219$	−3.77938	−	11.6317i	−0.255387	−	0.786000i
$220$		0			0
$221$	−4.22738	+	13.0105i	−0.284364	+	0.875183i
$222$	0.176855	−	0.544302i	0.0118697	−	0.0365312i
$223$	−9.18686	+	6.67464i	−0.615197	+	0.446967i	−0.851241	−	0.524775i	$-0.824149\pi$
$223$	−9.18686	+	6.67464i	−0.615197	+	0.446967i	0.236043	+	0.971743i	$0.424149\pi$
$224$	0.119831			0.00800655
$225$		0			0
$226$	1.21655			0.0809239
$227$	9.05912	−	6.58183i	0.601275	−	0.436852i	−0.245056	−	0.969509i	$-0.578806\pi$
$227$	9.05912	−	6.58183i	0.601275	−	0.436852i	0.846331	+	0.532657i	$0.178806\pi$
$228$	−4.06393	+	12.5075i	−0.269140	+	0.828329i
$229$	2.98192	−	9.17740i	0.197051	−	0.606459i	−0.802896	−	0.596119i	$-0.796709\pi$
$229$	2.98192	−	9.17740i	0.197051	−	0.606459i	0.999947	−	0.0103402i	$-0.00329146\pi$
$230$		0			0
$231$	0.0814771	+	0.250761i	0.00536080	+	0.0164988i
$232$	7.24491			0.475651
$233$	4.79782	+	14.7662i	0.314315	+	0.967363i	0.976035	+	0.217612i	$0.0698268\pi$
$233$	4.79782	+	14.7662i	0.314315	+	0.967363i	−0.661720	+	0.749751i	$0.730173\pi$
$234$	−10.0520	−	7.30320i	−0.657119	−	0.477425i
$235$		0			0
$236$	−6.30423	+	4.58029i	−0.410371	+	0.298152i
$237$	−24.2329	−	17.6062i	−1.57410	−	1.14365i
$238$	−0.0349312	−	0.0253790i	−0.00226425	−	0.00164508i
$239$	−11.5966	+	8.42544i	−0.750123	+	0.544996i	−0.895865	−	0.444326i	$-0.853443\pi$
$239$	−11.5966	+	8.42544i	−0.750123	+	0.544996i	0.145742	+	0.989323i	$0.453443\pi$
$240$		0			0
$241$	−20.4773	−	14.8777i	−1.31906	−	0.958354i	−0.999943	−	0.0106385i	$-0.996614\pi$
$241$	−20.4773	−	14.8777i	−1.31906	−	0.958354i	−0.319117	−	0.947715i	$-0.603386\pi$
$242$	−0.284850	−	0.876678i	−0.0183109	−	0.0563550i
$243$	−11.5450			−0.740613
$244$	−4.97994	−	15.3267i	−0.318808	−	0.981190i
$245$		0			0
$246$	−3.73958	+	11.5092i	−0.238427	+	0.733802i
$247$	2.83632	−	8.72930i	0.180471	−	0.555432i
$248$	9.13192	−	6.63473i	0.579877	−	0.421305i
$249$	−27.7068			−1.75585
$250$		0			0
$251$	4.23698			0.267436			0.133718	−	0.991019i	$-0.457308\pi$
$251$	4.23698			0.267436			0.133718	+	0.991019i	$0.457308\pi$
$252$	−0.221083	+	0.160626i	−0.0139269	+	0.0101185i
$253$	−1.89944	+	5.84587i	−0.119417	+	0.367526i
$254$	−2.64845	+	8.15110i	−0.166179	+	0.511445i
$255$		0			0
$256$	−0.159715	−	0.491553i	−0.00998220	−	0.0307221i
$257$	20.4007			1.27256			0.636281	−	0.771458i	$-0.280472\pi$
$257$	20.4007			1.27256			0.636281	+	0.771458i	$0.280472\pi$
$258$	−0.0836003	−	0.257295i	−0.00520472	−	0.0160185i
$259$	0.00710727	+	0.00516373i	0.000441624	+	0.000320859i
$260$		0			0
$261$	−20.4972	+	14.8921i	−1.26874	+	0.921796i
$262$	1.94125	+	1.41040i	0.119931	+	0.0871346i
$263$	23.1927	+	16.8505i	1.43012	+	1.03905i	0.989994	+	0.141113i	$0.0450679\pi$
$263$	23.1927	+	16.8505i	1.43012	+	1.03905i	0.440131	+	0.897934i	$0.354932\pi$
$264$	16.8423	−	12.2366i	1.03657	−	0.753112i
$265$		0			0
$266$	0.0234368	+	0.0170278i	0.00143700	+	0.00104404i
$267$	16.2642	+	50.0560i	0.995351	+	3.06338i
$268$	−7.82481			−0.477977
$269$	2.45561	+	7.55759i	0.149721	+	0.460794i	0.997588	−	0.0694152i	$-0.0221133\pi$
$269$	2.45561	+	7.55759i	0.149721	+	0.460794i	−0.847867	+	0.530209i	$0.822113\pi$
$270$		0			0
$271$	2.95262	−	9.08722i	0.179359	−	0.552009i	−0.820447	−	0.571723i	$-0.806275\pi$
$271$	2.95262	−	9.08722i	0.179359	−	0.552009i	0.999806	+	0.0197133i	$0.00627535\pi$
$272$	2.86282	−	8.81085i	0.173584	−	0.534236i
$273$	0.224774	−	0.163308i	0.0136040	−	0.00988385i
$274$	6.41785			0.387717
$275$		0			0
$276$	−9.28045			−0.558618
$277$	13.9073	−	10.1043i	0.835612	−	0.607107i	−0.0855297	−	0.996336i	$-0.527258\pi$
$277$	13.9073	−	10.1043i	0.835612	−	0.607107i	0.921141	+	0.389228i	$0.127258\pi$
$278$	1.22926	−	3.78326i	0.0737259	−	0.226905i
$279$	−12.1981	+	37.5417i	−0.730278	+	2.24757i
$280$		0			0
$281$	8.41089	+	25.8861i	0.501752	+	1.54423i	0.806164	+	0.591692i	$0.201540\pi$
$281$	8.41089	+	25.8861i	0.501752	+	1.54423i	−0.304412	+	0.952540i	$0.598460\pi$
$282$	−12.1043			−0.720803
$283$	1.07507	+	3.30874i	0.0639065	+	0.196684i	0.977912	−	0.209018i	$-0.0670269\pi$
$283$	1.07507	+	3.30874i	0.0639065	+	0.196684i	−0.914005	+	0.405703i	$0.867027\pi$
$284$	−13.7176	−	9.96644i	−0.813991	−	0.591399i
$285$		0			0
$286$	−5.48384	+	3.98424i	−0.324266	+	0.235593i
$287$	−0.150283	−	0.109187i	−0.00887090	−	0.00644509i
$288$	26.7683	+	19.4483i	1.57734	+	1.14600i
$289$	3.13386	−	2.27688i	0.184345	−	0.133934i
$290$		0			0
$291$	−6.91784	−	5.02611i	−0.405531	−	0.294636i
$292$	−2.13696	−	6.57689i	−0.125056	−	0.384883i
$293$	−23.4941			−1.37254			−0.686271	−	0.727346i	$-0.740754\pi$
$293$	−23.4941			−1.37254			−0.686271	+	0.727346i	$0.740754\pi$
$294$	−3.35189	−	10.3161i	−0.195486	−	0.601645i
$295$		0			0
$296$	0.214347	−	0.659691i	0.0124586	−	0.0383438i
$297$	−12.2218	+	37.6147i	−0.709178	+	2.18263i
$298$	−2.28077	+	1.65708i	−0.132122	+	0.0959919i
$299$	6.47706			0.374578
$300$		0			0
$301$	0.00415276			0.000239361
$302$	−2.98696	+	2.17016i	−0.171881	+	0.124879i
$303$	−9.89574	+	30.4560i	−0.568496	+	1.74965i
$304$	−1.92078	+	5.91156i	−0.110164	+	0.339051i
$305$		0			0
$306$	−3.68410	−	11.3385i	−0.210606	−	0.648179i
$307$	−1.11253			−0.0634952			−0.0317476	−	0.999496i	$-0.510107\pi$
$307$	−1.11253			−0.0634952			−0.0317476	+	0.999496i	$0.510107\pi$
$308$	0.0460693	+	0.141787i	0.00262504	+	0.00807905i
$309$	−45.7740	−	33.2568i	−2.60399	−	1.89191i
$310$		0			0
$311$	11.9354	−	8.67154i	0.676792	−	0.491718i	−0.195500	−	0.980704i	$-0.562633\pi$
$311$	11.9354	−	8.67154i	0.676792	−	0.491718i	0.872292	+	0.488986i	$0.162633\pi$
$312$	−17.7474	−	12.8943i	−1.00475	−	0.729994i
$313$	4.00329	+	2.90856i	0.226279	+	0.164402i	0.695149	−	0.718866i	$-0.255339\pi$
$313$	4.00329	+	2.90856i	0.226279	+	0.164402i	−0.468869	+	0.883268i	$0.655339\pi$
$314$	−3.49819	+	2.54158i	−0.197414	+	0.143430i
$315$		0			0
$316$	−13.7019	−	9.95504i	−0.770794	−	0.560015i
$317$	−7.01020	−	21.5752i	−0.393732	−	1.21178i	−0.929944	−	0.367700i	$-0.880145\pi$
$317$	−7.01020	−	21.5752i	−0.393732	−	1.21178i	0.536212	−	0.844083i	$-0.319855\pi$
$318$	13.9036			0.779673
$319$	4.27122	+	13.1455i	0.239142	+	0.736004i
$320$		0			0
$321$	15.1779	−	46.7127i	0.847146	−	2.60725i
$322$	−0.00631724	+	0.0194425i	−0.000352046	+	0.00108349i
$323$	7.12501	−	5.17662i	0.396446	−	0.288035i
$324$	−25.2505			−1.40281
$325$		0			0
$326$	2.37952			0.131789
$327$	14.9176	−	10.8383i	0.824946	−	0.599358i
$328$	−4.53234	+	13.9491i	−0.250257	+	0.770211i
$329$	0.0574162	−	0.176709i	0.00316546	−	0.00974228i
$330$		0			0
$331$	0.535397	+	1.64778i	0.0294281	+	0.0905702i	0.964692	−	0.263381i	$-0.0848378\pi$
$331$	0.535397	+	1.64778i	0.0294281	+	0.0905702i	−0.935264	+	0.353952i	$0.884838\pi$
$332$	−15.6662			−0.859793
$333$	0.749584	+	2.30698i	0.0410770	+	0.126422i
$334$	−7.53741	−	5.47625i	−0.412429	−	0.299647i
$335$		0			0
$336$	−0.152219	+	0.110594i	−0.00830423	+	0.00603338i
$337$	11.3109	+	8.21786i	0.616144	+	0.447655i	0.851573	−	0.524237i	$-0.175649\pi$
$337$	11.3109	+	8.21786i	0.616144	+	0.447655i	−0.235428	+	0.971892i	$0.575649\pi$
$338$	0.509555	+	0.370214i	0.0277161	+	0.0201370i
$339$	−6.07682	+	4.41507i	−0.330048	+	0.239794i
$340$		0			0
$341$	17.4220	+	12.6578i	0.943455	+	0.685460i
$342$	2.47181	+	7.60746i	0.133660	+	0.411364i
$343$	0.333017			0.0179812
$344$	−0.101323	−	0.311840i	−0.00546297	−	0.0168133i
$345$		0			0
$346$	2.44540	−	7.52616i	0.131465	−	0.404609i
$347$	−1.57034	+	4.83301i	−0.0843003	+	0.259450i	−0.984318	−	0.176404i	$-0.943553\pi$
$347$	−1.57034	+	4.83301i	−0.0843003	+	0.259450i	0.900018	+	0.435854i	$0.143553\pi$
$348$	−16.8832	+	12.2663i	−0.905032	+	0.657544i
$349$	−8.88643			−0.475680			−0.237840	−	0.971304i	$-0.576439\pi$
$349$	−8.88643			−0.475680			−0.237840	+	0.971304i	$0.576439\pi$
$350$		0			0
$351$	41.6761			2.22450
$352$	14.6034	−	10.6100i	0.778362	−	0.565513i
$353$	−2.90921	+	8.95362i	−0.154842	+	0.476553i	−0.998145	−	0.0608848i	$-0.980608\pi$
$353$	−2.90921	+	8.95362i	−0.154842	+	0.476553i	0.843303	+	0.537438i	$0.180608\pi$
$354$	−2.13358	+	6.56649i	−0.113399	+	0.349005i
$355$		0			0
$356$	9.19620	+	28.3030i	0.487397	+	1.50005i
$357$	0.266590			0.0141094
$358$	−1.45053	−	4.46426i	−0.0766627	−	0.235943i
$359$	−7.37418	−	5.35765i	−0.389194	−	0.282766i	0.375931	−	0.926648i	$-0.377323\pi$
$359$	−7.37418	−	5.35765i	−0.389194	−	0.282766i	−0.765125	+	0.643882i	$0.777323\pi$
$360$		0			0
$361$	10.5909	−	7.69472i	0.557414	−	0.404985i
$362$	−2.36956	−	1.72158i	−0.124541	−	0.0904844i
$363$	4.60446	+	3.34534i	0.241672	+	0.175585i
$364$	0.127093	−	0.0923387i	0.00666150	−	0.00483986i
$365$		0			0
$366$	−11.5519	−	8.39291i	−0.603825	−	0.438705i
$367$	5.52474	+	17.0034i	0.288389	+	0.887570i	0.985362	+	0.170473i	$0.0545295\pi$
$367$	5.52474	+	17.0034i	0.288389	+	0.887570i	−0.696974	+	0.717097i	$0.745471\pi$
$368$	−4.38633			−0.228653
$369$	−15.8499	−	48.7810i	−0.825113	−	2.53944i
$370$		0			0
$371$	−0.0659507	+	0.202976i	−0.00342399	+	0.0105380i
$372$	−10.0473	+	30.9224i	−0.520929	+	1.60325i
$373$	−2.48687	+	1.80682i	−0.128765	+	0.0935536i	−0.650304	−	0.759674i	$-0.725358\pi$
$373$	−2.48687	+	1.80682i	−0.128765	+	0.0935536i	0.521538	+	0.853228i	$0.325358\pi$
$374$	−6.50402			−0.336315
$375$		0			0
$376$	−14.6704			−0.756567
$377$	11.7832	−	8.56098i	0.606865	−	0.440913i
$378$	−0.0406477	+	0.125101i	−0.00209069	+	0.00643449i
$379$	7.90670	−	24.3343i	0.406140	−	1.24997i	−0.513799	−	0.857910i	$-0.671762\pi$
$379$	7.90670	−	24.3343i	0.406140	−	1.24997i	0.919939	−	0.392060i	$-0.128238\pi$
$380$		0			0
$381$	−16.3523	−	50.3273i	−0.837755	−	2.57835i
$382$	10.9690			0.561224
$383$	0.687652	+	2.11638i	0.0351374	+	0.108142i	0.967087	−	0.254446i	$-0.0818932\pi$
$383$	0.687652	+	2.11638i	0.0351374	+	0.108142i	−0.931950	+	0.362588i	$0.881893\pi$
$384$	28.4602	+	20.6776i	1.45235	+	1.05520i
$385$		0			0
$386$	10.2357	−	7.43669i	0.520985	−	0.378517i
$387$	0.927657	+	0.673982i	0.0471554	+	0.0342604i
$388$	−3.91153	−	2.84189i	−0.198578	−	0.144275i
$389$	−3.75718	+	2.72975i	−0.190496	+	0.138404i	−0.678946	−	0.734189i	$-0.737563\pi$
$389$	−3.75718	+	2.72975i	−0.190496	+	0.138404i	0.488449	+	0.872592i	$0.337563\pi$
$390$		0			0
$391$	5.02794	+	3.65301i	0.254274	+	0.184741i
$392$	−4.06247	−	12.5030i	−0.205186	−	0.631497i
$393$	−14.8153			−0.747333
$394$	2.23766	+	6.88681i	0.112732	+	0.346952i
$395$		0			0
$396$	−12.7205	+	39.1497i	−0.639230	+	1.96735i
$397$	11.7257	−	36.0880i	0.588497	−	1.81121i	0.00374665	−	0.999993i	$-0.498807\pi$
$397$	11.7257	−	36.0880i	0.588497	−	1.81121i	0.584750	−	0.811214i	$-0.301193\pi$
$398$	−1.53099	+	1.11233i	−0.0767415	+	0.0557560i
$399$	−0.178866			−0.00895449
$400$		0			0
$401$	−16.7187			−0.834890			−0.417445	−	0.908702i	$-0.637074\pi$
$401$	−16.7187			−0.834890			−0.417445	+	0.908702i	$0.637074\pi$
$402$	−5.60898	+	4.07516i	−0.279751	+	0.203251i
$403$	7.01227	−	21.5816i	0.349306	−	1.07505i
$404$	−5.59532	+	17.2206i	−0.278377	+	0.856757i
$405$		0			0
$406$	0.0142054	+	0.0437198i	0.000705004	+	0.00216978i
$407$	1.32334			0.0655955
$408$	−6.50452	−	20.0188i	−0.322022	−	0.991081i
$409$	−0.382772	−	0.278100i	−0.0189268	−	0.0137512i	0.578282	−	0.815837i	$-0.303723\pi$
$409$	−0.382772	−	0.278100i	−0.0189268	−	0.0137512i	−0.597208	+	0.802086i	$0.703723\pi$
$410$		0			0
$411$	−32.0579	+	23.2914i	−1.58130	+	1.14888i
$412$	−25.8819	−	18.8043i	−1.27511	−	0.926420i
$413$	−0.0857424	−	0.0622955i	−0.00421911	−	0.00306536i
$414$	−4.56663	+	3.31785i	−0.224438	+	0.163064i
$415$		0			0
$416$	−15.3882	−	11.1802i	−0.754470	−	0.548154i
$417$	7.58979	+	23.3590i	0.371674	+	1.14389i
$418$	4.36381			0.213441
$419$	7.48898	+	23.0487i	0.365861	+	1.12600i	0.949440	+	0.313947i	$0.101651\pi$
$419$	7.48898	+	23.0487i	0.365861	+	1.12600i	−0.583580	+	0.812056i	$0.698349\pi$
$420$		0			0
$421$	−9.68711	+	29.8139i	−0.472121	+	1.45304i	0.377680	+	0.925936i	$0.376722\pi$
$421$	−9.68711	+	29.8139i	−0.472121	+	1.45304i	−0.849801	+	0.527103i	$0.823278\pi$
$422$	2.92609	−	9.00556i	0.142440	−	0.438384i
$423$	41.5052	−	30.1553i	2.01805	−	1.46620i
$424$	16.8510			0.818359
$425$		0			0
$426$	−15.0236			−0.727895
$427$	0.177322	−	0.128832i	0.00858122	−	0.00623462i
$428$	8.58197	−	26.4126i	0.414825	−	1.27670i
$429$	12.9329	−	39.8035i	0.624408	−	1.92173i
$430$		0			0
$431$	−0.618239	−	1.90275i	−0.0297795	−	0.0916520i	0.935062	−	0.354484i	$-0.115343\pi$
$431$	−0.618239	−	1.90275i	−0.0297795	−	0.0916520i	−0.964842	+	0.262832i	$0.915343\pi$
$432$	−28.2234			−1.35790
$433$	−2.18553	−	6.72637i	−0.105030	−	0.323249i	0.884708	−	0.466147i	$-0.154358\pi$
$433$	−2.18553	−	6.72637i	−0.105030	−	0.323249i	−0.989737	+	0.142898i	$0.954358\pi$
$434$	0.0579430	+	0.0420981i	0.00278135	+	0.00202077i
$435$		0			0
$436$	8.43482	−	6.12825i	0.403954	−	0.293490i
$437$	−3.37345	−	2.45096i	−0.161374	−	0.117245i
$438$	−4.95706	−	3.60152i	−0.236858	−	0.172087i
$439$	−10.4865	+	7.61889i	−0.500493	+	0.363630i	−0.809205	−	0.587526i	$-0.800102\pi$
$439$	−10.4865	+	7.61889i	−0.500493	+	0.363630i	0.308712	+	0.951156i	$0.400102\pi$
$440$		0			0
$441$	37.1937	+	27.0228i	1.77113	+	1.28680i
$442$	2.11787	+	6.51814i	0.100737	+	0.310036i
$443$	−21.8687			−1.03901			−0.519506	−	0.854467i	$-0.673884\pi$
$443$	−21.8687			−1.03901			−0.519506	+	0.854467i	$0.673884\pi$
$444$	0.617419	+	1.90022i	0.0293014	+	0.0901804i
$445$		0			0
$446$	−1.75801	+	5.41058i	−0.0832440	+	0.256199i
$447$	5.37890	−	16.5546i	0.254413	−	0.783004i
$448$	−0.0498514	+	0.0362191i	−0.00235526	+	0.00171119i
$449$	0.399626			0.0188595			0.00942976	−	0.999956i	$-0.496998\pi$
$449$	0.399626			0.0188595			0.00942976	+	0.999956i	$0.496998\pi$
$450$		0			0
$451$	−27.9819			−1.31762
$452$	−3.43600	+	2.49640i	−0.161616	+	0.117421i
$453$	7.04437	−	21.6803i	0.330973	−	1.01863i
$454$	1.73356	−	5.33535i	0.0813600	−	0.250400i
$455$		0			0
$456$	4.36415	+	13.4315i	0.204370	+	0.628986i
$457$	35.2247			1.64774			0.823872	−	0.566777i	$-0.191810\pi$
$457$	35.2247			1.64774			0.823872	+	0.566777i	$0.191810\pi$
$458$	−1.49391	−	4.59778i	−0.0698058	−	0.214840i
$459$	32.3518	+	23.5050i	1.51005	+	1.09712i
$460$		0			0
$461$	12.9131	−	9.38194i	0.601425	−	0.436961i	−0.244960	−	0.969533i	$-0.578775\pi$
$461$	12.9131	−	9.38194i	0.601425	−	0.436961i	0.846384	+	0.532573i	$0.178775\pi$
$462$	0.106866	+	0.0776427i	0.00497185	+	0.00361226i
$463$	−24.6614	−	17.9175i	−1.14611	−	0.832699i	−0.158153	−	0.987415i	$-0.550554\pi$
$463$	−24.6614	−	17.9175i	−1.14611	−	0.832699i	−0.987959	+	0.154716i	$0.950554\pi$
$464$	−7.97968	+	5.79757i	−0.370447	+	0.269146i
$465$		0			0
$466$	6.29285	+	4.57202i	0.291511	+	0.211795i
$467$	−2.05390	−	6.32127i	−0.0950434	−	0.292513i	0.892222	−	0.451598i	$-0.149146\pi$
$467$	−2.05390	−	6.32127i	−0.0950434	−	0.292513i	−0.987265	+	0.159084i	$0.949146\pi$
$468$	43.3769			2.00510
$469$	−0.0328867	−	0.101215i	−0.00151857	−	0.00467366i
$470$		0			0
$471$	8.25002	−	25.3910i	0.380141	−	1.16995i
$472$	−2.58589	+	7.95855i	−0.119025	+	0.366322i
$473$	0.506081	−	0.367689i	0.0232696	−	0.0169064i
$474$	−15.0064			−0.689267
$475$		0			0
$476$	0.150737			0.00690902
$477$	−47.6747	+	34.6377i	−2.18288	+	1.58595i
$478$	−2.21914	+	6.82981i	−0.101501	+	0.312388i
$479$	6.87278	−	21.1522i	0.314025	−	0.966471i	−0.662128	−	0.749390i	$-0.730347\pi$
$479$	6.87278	−	21.1522i	0.314025	−	0.966471i	0.976154	−	0.217080i	$-0.0696533\pi$
$480$		0			0
$481$	−0.430912	−	1.32621i	−0.0196479	−	0.0604700i
$482$	−12.6807			−0.577591
$483$	−0.0390045	−	0.120044i	−0.00177477	−	0.00546217i
$484$	2.60349	+	1.89154i	0.118340	+	0.0859792i
$485$		0			0
$486$	−4.67930	+	3.39971i	−0.212257	+	0.154214i
$487$	8.23992	+	5.98665i	0.373386	+	0.271281i	0.758614	−	0.651541i	$-0.225877\pi$
$487$	8.23992	+	5.98665i	0.373386	+	0.271281i	−0.385227	+	0.922822i	$0.625877\pi$
$488$	−14.0008	−	10.1722i	−0.633785	−	0.460472i
$489$	−11.8860	+	8.63565i	−0.537501	+	0.390518i
$490$		0			0
$491$	−5.37191	−	3.90292i	−0.242431	−	0.176136i	0.459935	−	0.887953i	$-0.347873\pi$
$491$	−5.37191	−	3.90292i	−0.242431	−	0.176136i	−0.702366	+	0.711816i	$0.747873\pi$
$492$	−13.0553	−	40.1800i	−0.588577	−	1.81145i
$493$	13.9752			0.629413
$494$	−1.42097	−	4.37329i	−0.0639323	−	0.196763i
$495$		0			0
$496$	−4.74877	+	14.6152i	−0.213226	+	0.656243i
$497$	0.0712635	−	0.219327i	0.00319660	−	0.00983814i
$498$	−11.2298	+	8.15894i	−0.503220	+	0.365611i
$499$	1.08397			0.0485253			0.0242626	−	0.999706i	$-0.492276\pi$
$499$	1.08397			0.0485253			0.0242626	+	0.999706i	$0.492276\pi$
$500$		0			0
$501$	57.5244			2.57000
$502$	1.71729	−	1.24768i	0.0766462	−	0.0556867i
$503$	0.613716	−	1.88882i	0.0273642	−	0.0842184i	−0.936442	−	0.350823i	$-0.885902\pi$
$503$	0.613716	−	1.88882i	0.0273642	−	0.0842184i	0.963806	+	0.266605i	$0.0859018\pi$
$504$	−0.0906843	+	0.279097i	−0.00403940	+	0.0124320i
$505$		0			0
$506$	0.951598	+	2.92872i	0.0423037	+	0.130197i
$507$	−3.88885			−0.172710
$508$	−9.24604	−	28.4564i	−0.410227	−	1.26255i
$509$	−1.86814	−	1.35729i	−0.0828040	−	0.0601607i	0.545613	−	0.838037i	$-0.316297\pi$
$509$	−1.86814	−	1.35729i	−0.0828040	−	0.0601607i	−0.628417	+	0.777877i	$0.716297\pi$
$510$		0			0
$511$	0.0760914	−	0.0552836i	0.00336608	−	0.00244560i
$512$	18.1920	+	13.2172i	0.803979	+	0.584125i
$513$	−21.7062	−	15.7705i	−0.958351	−	0.696283i
$514$	8.26859	−	6.00748i	0.364712	−	0.264979i
$515$		0			0
$516$	0.764094	+	0.555147i	0.0336373	+	0.0244390i
$517$	−8.64889	−	26.6186i	−0.380378	−	1.17068i
$518$	0.00440122			0.000193379
$519$	15.0986	+	46.4687i	0.662755	+	2.03975i
$520$		0			0
$521$	−3.41302	+	10.5042i	−0.149527	+	0.460197i	−0.997565	−	0.0697382i	$-0.977784\pi$
$521$	−3.41302	+	10.5042i	−0.149527	+	0.460197i	0.848038	+	0.529935i	$0.177784\pi$
$522$	−3.92236	+	12.0718i	−0.171677	+	0.528368i
$523$	21.0365	−	15.2839i	0.919861	−	0.668318i	−0.0236286	−	0.999721i	$-0.507522\pi$
$523$	21.0365	−	15.2839i	0.919861	−	0.668318i	0.943489	+	0.331403i	$0.107522\pi$
$524$	−8.37696			−0.365949
$525$		0			0
$526$	14.3623			0.626224
$527$	17.6152	−	12.7982i	0.767332	−	0.557499i
$528$	−8.75830	+	26.9553i	−0.381156	+	1.17308i
$529$	−6.19810	+	19.0758i	−0.269482	+	0.829382i
$530$		0			0
$531$	−9.04302	−	27.8316i	−0.392434	−	1.20779i
$532$	−0.101136			−0.00438478
$533$	9.11161	+	28.0426i	0.394667	+	1.21466i
$534$	21.3322	+	15.4988i	0.923135	+	0.670697i
$535$		0			0
$536$	−6.79805	+	4.93907i	−0.293631	+	0.213336i
$537$	23.4470	+	17.0353i	1.01181	+	0.735126i
$538$	3.22079	+	2.34004i	0.138858	+	0.100886i
$539$	20.2909	−	14.7422i	0.873993	−	0.634993i
$540$		0			0
$541$	0.0147558	+	0.0107207i	0.000634400	+	0.000460919i	0.588102	−	0.808786i	$-0.299875\pi$
$541$	0.0147558	+	0.0107207i	0.000634400	+	0.000460919i	−0.587468	+	0.809247i	$0.699875\pi$
$542$	−1.47923	−	4.55260i	−0.0635384	−	0.195551i
$543$	18.0841			0.776063
$544$	−5.63985	−	17.3577i	−0.241807	−	0.744205i
$545$		0			0
$546$	0.0430130	−	0.132380i	0.00184079	−	0.00566536i
$547$	3.07796	−	9.47298i	0.131604	−	0.405035i	−0.863442	−	0.504447i	$-0.831696\pi$
$547$	3.07796	−	9.47298i	0.131604	−	0.405035i	0.995046	+	0.0994121i	$0.0316962\pi$
$548$	−18.1264	+	13.1696i	−0.774320	+	0.562577i
$549$	60.5199			2.58293
$550$		0			0
$551$	−9.37656			−0.399455
$552$	−8.06268	+	5.85788i	−0.343171	+	0.249328i
$553$	0.0711820	−	0.219076i	0.00302697	−	0.00931604i
$554$	2.66132	−	8.19071i	0.113069	−	0.347990i
$555$		0			0
$556$	4.29147	+	13.2078i	0.181999	+	0.560135i
$557$	34.9291			1.47999			0.739996	−	0.672611i	$-0.234827\pi$
$557$	34.9291			1.47999			0.739996	+	0.672611i	$0.234827\pi$
$558$	6.11109	+	18.8080i	0.258703	+	0.796207i
$559$	−0.533280	−	0.387451i	−0.0225554	−	0.0163874i
$560$		0			0
$561$	32.4883	−	23.6041i	1.37166	−	0.996567i
$562$	11.0318	+	8.01506i	0.465348	+	0.338095i
$563$	12.7775	+	9.28343i	0.538509	+	0.391250i	0.823531	−	0.567271i	$-0.192001\pi$
$563$	12.7775	+	9.28343i	0.538509	+	0.391250i	−0.285022	+	0.958521i	$0.592001\pi$
$564$	34.1871	−	24.8384i	1.43954	−	1.04588i
$565$		0			0
$566$	1.41008	+	1.02448i	0.0592699	+	0.0430621i
$567$	−0.106125	−	0.326618i	−0.00445681	−	0.0137167i
$568$	−18.2085			−0.764012
$569$	−4.49944	−	13.8479i	−0.188627	−	0.580533i	0.811365	−	0.584539i	$-0.198725\pi$
$569$	−4.49944	−	13.8479i	−0.188627	−	0.580533i	−0.999992	+	0.00400651i	$0.998725\pi$
$570$		0			0
$571$	8.53315	−	26.2623i	0.357101	−	1.09904i	−0.597680	−	0.801735i	$-0.703911\pi$
$571$	8.53315	−	26.2623i	0.357101	−	1.09904i	0.954781	−	0.297309i	$-0.0960892\pi$
$572$	7.31263	−	22.5059i	0.305756	−	0.941021i
$573$	−54.7914	+	39.8083i	−2.28895	+	1.66302i
$574$	−0.0930636			−0.00388440
$575$		0			0
$576$	−17.0142			−0.708927
$577$	−21.9664	+	15.9595i	−0.914475	+	0.664405i	−0.942143	−	0.335212i	$-0.891192\pi$
$577$	−21.9664	+	15.9595i	−0.914475	+	0.664405i	0.0276679	+	0.999617i	$0.491192\pi$
$578$	0.599698	−	1.84568i	0.0249442	−	0.0767702i
$579$	−24.1396	+	74.2941i	−1.00321	+	3.08756i
$580$		0			0
$581$	−0.0658429	−	0.202644i	−0.00273162	−	0.00840707i
$582$	−4.28392			−0.177574
$583$	9.93449	+	30.5752i	0.411445	+	1.26630i
$584$	−6.00793	−	4.36502i	−0.248610	−	0.180626i
$585$		0			0
$586$	−9.52239	+	6.91842i	−0.393366	+	0.285797i
$587$	−8.65944	−	6.29145i	−0.357413	−	0.259676i	0.394559	−	0.918871i	$-0.370897\pi$
$587$	−8.65944	−	6.29145i	−0.357413	−	0.259676i	−0.751972	+	0.659195i	$0.770897\pi$
$588$	30.6358	+	22.2582i	1.26340	+	0.917912i
$589$	−11.8188	+	8.58685i	−0.486984	+	0.353815i
$590$		0			0
$591$	−36.1707	−	26.2795i	−1.48786	−	1.08100i
$592$	0.291818	+	0.898122i	0.0119936	+	0.0369126i
$593$	3.84629			0.157948			0.0789740	−	0.996877i	$-0.474836\pi$
$593$	3.84629			0.157948			0.0789740	+	0.996877i	$0.474836\pi$
$594$	6.12297	+	18.8446i	0.251229	+	0.773202i
$595$		0			0
$596$	3.04138	−	9.36039i	0.124580	−	0.383417i
$597$	3.61064	−	11.1124i	0.147774	−	0.454801i
$598$	2.62521	−	1.90733i	0.107353	−	0.0779964i
$599$	46.1423			1.88532			0.942662	−	0.333750i	$-0.108314\pi$
$599$	46.1423			1.88532			0.942662	+	0.333750i	$0.108314\pi$
$600$		0			0
$601$	−13.3119			−0.543005			−0.271503	−	0.962438i	$-0.587521\pi$
$601$	−13.3119			−0.543005			−0.271503	+	0.962438i	$0.587521\pi$
$602$	0.00168315	−	0.00122288i	6.86000e−5	−	4.98408e-5i
$603$	9.08057	−	27.9471i	0.369789	−	1.13809i
$604$	3.98308	−	12.2586i	0.162069	−	0.498797i
$605$		0			0
$606$	4.95766	+	15.2581i	0.201391	+	0.619818i
$607$	−34.0838			−1.38342			−0.691709	−	0.722176i	$-0.743142\pi$
$607$	−34.0838			−1.38342			−0.691709	+	0.722176i	$0.743142\pi$
$608$	3.78401	+	11.6460i	0.153462	+	0.472307i
$609$	−0.229624	−	0.166832i	−0.00930483	−	0.00676035i
$610$		0			0
$611$	−23.8600	+	17.3353i	−0.965274	+	0.701313i
$612$	33.6721	+	24.4642i	1.36111	+	0.988908i
$613$	20.6145	+	14.9773i	0.832612	+	0.604928i	0.920297	−	0.391220i	$-0.127947\pi$
$613$	20.6145	+	14.9773i	0.832612	+	0.604928i	−0.0876853	+	0.996148i	$0.527947\pi$
$614$	−0.450916	+	0.327610i	−0.0181975	+	0.0132213i
$615$		0			0
$616$	0.129521	+	0.0941025i	0.00521855	+	0.00379150i
$617$	8.32657	+	25.6265i	0.335215	+	1.03169i	0.966616	+	0.256229i	$0.0824802\pi$
$617$	8.32657	+	25.6265i	0.335215	+	1.03169i	−0.631401	+	0.775456i	$0.717520\pi$
$618$	−28.3459			−1.14024
$619$	12.1533	+	37.4040i	0.488482	+	1.50339i	0.826873	+	0.562389i	$0.190118\pi$
$619$	12.1533	+	37.4040i	0.488482	+	1.50339i	−0.338391	+	0.941006i	$0.609882\pi$
$620$		0			0
$621$	5.85077	−	18.0068i	0.234783	−	0.722589i
$622$	2.28396	−	7.02931i	0.0915784	−	0.281849i
$623$	−0.327451	+	0.237907i	−0.0131191	+	0.00953156i
$624$	29.8657			1.19559
$625$		0			0
$626$	2.47906			0.0990833
$627$	−21.7977	+	15.8370i	−0.870517	+	0.632468i
$628$	4.66478	−	14.3567i	0.186145	−	0.572896i
$629$	0.413469	−	1.27253i	0.0164861	−	0.0507390i
$630$		0			0
$631$	3.47469	+	10.6940i	0.138325	+	0.425722i	0.996092	−	0.0883169i	$-0.0281488\pi$
$631$	3.47469	+	10.6940i	0.138325	+	0.425722i	−0.857767	+	0.514039i	$0.828149\pi$
$632$	−18.1877			−0.723467
$633$	18.0665	+	55.6030i	0.718080	+	2.21002i
$634$	−9.19463	−	6.68029i	−0.365166	−	0.265308i
$635$		0			0
$636$	−39.2688	+	28.5304i	−1.55711	+	1.13131i
$637$	−21.3815	−	15.5346i	−0.847165	−	0.615501i
$638$	5.60216	+	4.07021i	0.221792	+	0.161141i
$639$	51.5152	−	37.4280i	2.03791	−	1.48063i
$640$		0			0
$641$	−14.1394	−	10.2729i	−0.558473	−	0.405755i	0.272427	−	0.962177i	$-0.412174\pi$
$641$	−14.1394	−	10.2729i	−0.558473	−	0.405755i	−0.830900	+	0.556422i	$0.812174\pi$
$642$	−7.60395	−	23.4026i	−0.300104	−	0.923625i
$643$	8.72320			0.344009			0.172005	−	0.985096i	$-0.444976\pi$
$643$	8.72320			0.344009			0.172005	+	0.985096i	$0.444976\pi$
$644$	−0.0220542	−	0.0678758i	−0.000869057	−	0.00267468i
$645$		0			0
$646$	1.36345	−	4.19626i	0.0536441	−	0.165100i
$647$	−7.74562	+	23.8386i	−0.304512	+	0.937191i	0.675347	+	0.737500i	$0.263994\pi$
$647$	−7.74562	+	23.8386i	−0.304512	+	0.937191i	−0.979859	+	0.199691i	$0.936006\pi$
$648$	−21.9372	+	15.9383i	−0.861773	+	0.626115i
$649$	−15.9648			−0.626674
$650$		0			0
$651$	−0.442212			−0.0173317
$652$	−6.72063	+	4.88283i	−0.263200	+	0.191226i
$653$	−9.26362	+	28.5105i	−0.362514	+	1.11570i	0.589010	+	0.808126i	$0.299518\pi$
$653$	−9.26362	+	28.5105i	−0.362514	+	1.11570i	−0.951523	+	0.307576i	$0.900482\pi$
$654$	2.85465	−	8.78570i	0.111626	−	0.343548i
$655$		0			0
$656$	−6.17046	−	18.9907i	−0.240916	−	0.741464i
$657$	25.9699			1.01318
$658$	−0.0287649	−	0.0885293i	−0.00112137	−	0.00345123i
$659$	3.53218	+	2.56628i	0.137594	+	0.0999680i	0.654453	−	0.756102i	$-0.272899\pi$
$659$	3.53218	+	2.56628i	0.137594	+	0.0999680i	−0.516859	+	0.856071i	$0.672899\pi$
$660$		0			0
$661$	15.7377	−	11.4341i	0.612125	−	0.444735i	−0.238037	−	0.971256i	$-0.576504\pi$
$661$	15.7377	−	11.4341i	0.612125	−	0.444735i	0.850162	+	0.526521i	$0.176504\pi$
$662$	0.702230	+	0.510200i	0.0272929	+	0.0198295i
$663$	−34.2344	−	24.8727i	−1.32955	−	0.965977i
$664$	−13.6105	+	9.88859i	−0.528189	+	0.383752i
$665$		0			0
$666$	0.983160	+	0.714308i	0.0380967	+	0.0276789i
$667$	−2.04471	−	6.29296i	−0.0791714	−	0.243664i
$668$	32.5258			1.25846
$669$	−10.8544	−	33.4065i	−0.419657	−	1.29157i
$670$		0			0
$671$	10.2027	−	31.4006i	0.393869	−	1.21221i
$672$	−0.114543	+	0.352526i	−0.00441858	+	0.0135990i
$673$	−29.3087	+	21.2940i	−1.12977	+	0.820823i	−0.985661	−	0.168740i	$-0.946030\pi$
$673$	−29.3087	+	21.2940i	−1.12977	+	0.820823i	−0.144105	+	0.989562i	$0.546030\pi$
$674$	7.00436			0.269798
$675$		0			0
$676$	−2.19886			−0.0845715
$677$	1.65077	−	1.19936i	0.0634443	−	0.0460950i	−0.555611	−	0.831442i	$-0.687516\pi$
$677$	1.65077	−	1.19936i	0.0634443	−	0.0460950i	0.619055	+	0.785347i	$0.287516\pi$
$678$	−1.16287	+	3.57893i	−0.0446596	+	0.137448i
$679$	0.0203205	−	0.0625402i	0.000779831	−	0.00240007i
$680$		0			0
$681$	10.7035	+	32.9420i	0.410160	+	1.26234i
$682$	10.7887			0.413121
$683$	−4.91662	−	15.1318i	−0.188129	−	0.579003i	0.811859	−	0.583854i	$-0.198456\pi$
$683$	−4.91662	−	15.1318i	−0.188129	−	0.579003i	−0.999988	+	0.00485110i	$0.998456\pi$
$684$	−22.5920	−	16.4140i	−0.863826	−	0.627607i
$685$		0			0
$686$	0.134975	−	0.0980649i	0.00515336	−	0.00374413i
$687$	24.1483	+	17.5448i	0.921316	+	0.669375i
$688$	0.361142	+	0.262385i	0.0137684	+	0.0100033i
$689$	27.4067	−	19.9121i	1.04411	−	0.758591i
$690$		0			0
$691$	3.15651	+	2.29334i	0.120079	+	0.0872427i	0.646204	−	0.763165i	$-0.276356\pi$
$691$	3.15651	+	2.29334i	0.120079	+	0.0872427i	−0.526125	+	0.850407i	$0.676356\pi$
$692$	8.53715	+	26.2747i	0.324534	+	0.998812i
$693$	−0.559869			−0.0212677
$694$	0.786724	+	2.42129i	0.0298636	+	0.0919108i
$695$		0			0
$696$	−6.92518	+	21.3135i	−0.262498	+	0.807887i
$697$	−8.74278	+	26.9075i	−0.331156	+	1.01919i
$698$	−3.60175	+	2.61683i	−0.136328	+	0.0990483i
$699$	−48.0261			−1.81651
$700$		0			0
$701$	30.3587			1.14663			0.573316	−	0.819335i	$-0.305657\pi$
$701$	30.3587			1.14663			0.573316	+	0.819335i	$0.305657\pi$
$702$	16.8917	−	12.2725i	0.637536	−	0.463197i
$703$	−0.277413	+	0.853791i	−0.0104628	+	0.0322013i
$704$	−2.86832	+	8.82779i	−0.108104	+	0.332710i
$705$		0			0
$706$	1.45748	+	4.48567i	0.0548531	+	0.168820i
$707$	−0.246267			−0.00926181
$708$	−7.44857	−	22.9243i	−0.279934	−	0.861550i
$709$	39.2921	+	28.5474i	1.47565	+	1.07212i	0.978928	+	0.204206i	$0.0654614\pi$
$709$	39.2921	+	28.5474i	1.47565	+	1.07212i	0.496717	+	0.867912i	$0.334539\pi$
$710$		0			0
$711$	51.4563	−	37.3852i	1.92976	−	1.40205i
$712$	25.8545	+	18.7844i	0.968939	+	0.703975i
$713$	−8.34023	−	6.05953i	−0.312344	−	0.226931i
$714$	0.108051	−	0.0785038i	0.00404371	−	0.00293793i
$715$		0			0
$716$	13.2576	+	9.63220i	0.495459	+	0.359972i
$717$	−13.7016	−	42.1693i	−0.511697	−	1.57484i
$718$	−4.56651			−0.170421
$719$	1.47166	+	4.52929i	0.0548835	+	0.168914i	0.974741	−	0.223339i	$-0.0716957\pi$
$719$	1.47166	+	4.52929i	0.0548835	+	0.168914i	−0.919857	+	0.392253i	$0.871696\pi$
$720$		0			0
$721$	0.134457	−	0.413816i	0.00500744	−	0.0154113i
$722$	2.02668	−	6.23747i	0.0754251	−	0.232135i
$723$	63.3416	−	46.0204i	2.35570	−	1.71152i
$724$	10.2252			0.380018
$725$		0			0
$726$	2.85135			0.105823
$727$	−2.74007	+	1.99078i	−0.101624	+	0.0738338i	−0.637437	−	0.770503i	$-0.720005\pi$
$727$	−2.74007	+	1.99078i	−0.101624	+	0.0738338i	0.535813	+	0.844337i	$0.320005\pi$
$728$	0.0521315	−	0.160444i	0.00193212	−	0.00594646i
$729$	−2.34834	+	7.22745i	−0.0869756	+	0.267683i
$730$		0			0
$731$	−0.195450	−	0.601532i	−0.00722897	−	0.0222485i
$732$	49.8491			1.84248
$733$	−4.75915	−	14.6472i	−0.175783	−	0.541005i	0.823885	−	0.566757i	$-0.191802\pi$
$733$	−4.75915	−	14.6472i	−0.175783	−	0.541005i	−0.999668	+	0.0257516i	$0.991802\pi$
$734$	7.24628	+	5.26473i	0.267465	+	0.194325i
$735$		0			0
$736$	−6.99089	+	5.07918i	−0.257688	+	0.187221i
$737$	−12.9694	−	9.42285i	−0.477735	−	0.347095i
$738$	−20.7888	−	15.1040i	−0.765248	−	0.555985i
$739$	−8.07775	+	5.86883i	−0.297145	+	0.215888i	−0.726361	−	0.687314i	$-0.758790\pi$
$739$	−8.07775	+	5.86883i	−0.297145	+	0.215888i	0.429216	+	0.903202i	$0.358790\pi$
$740$		0			0
$741$	22.9692	+	16.6881i	0.843796	+	0.613054i
$742$	0.0330406	+	0.101689i	0.00121296	+	0.00373311i
$743$	41.4419			1.52036			0.760178	−	0.649715i	$-0.225112\pi$
$743$	41.4419			1.52036			0.760178	+	0.649715i	$0.225112\pi$
$744$	10.7895	+	33.2068i	0.395563	+	1.21742i
$745$		0			0
$746$	−0.475891	+	1.46464i	−0.0174236	+	0.0536243i
$747$	18.1803	−	55.9533i	0.665184	−	2.04723i
$748$	18.3697	−	13.3464i	0.671665	−	0.487993i
$749$	0.377719			0.0138015
$750$		0			0
$751$	21.1036			0.770082			0.385041	−	0.922900i	$-0.374187\pi$
$751$	21.1036			0.770082			0.385041	+	0.922900i	$0.374187\pi$
$752$	16.1582	−	11.7396i	0.589230	−	0.428101i
$753$	−4.05000	+	12.4646i	−0.147590	+	0.454236i
$754$	2.25484	−	6.93968i	0.0821164	−	0.252728i
$755$		0			0
$756$	−0.141906	−	0.436741i	−0.00516106	−	0.0158841i
$757$	−40.7168			−1.47988			−0.739938	−	0.672675i	$-0.765145\pi$
$757$	−40.7168			−1.47988			−0.739938	+	0.672675i	$0.765145\pi$
$758$	−3.96117	−	12.1912i	−0.143876	−	0.442806i
$759$	−15.3821	−	11.1758i	−0.558336	−	0.405655i
$760$		0			0
$761$	4.10708	−	2.98397i	0.148882	−	0.108169i	−0.510851	−	0.859669i	$-0.670670\pi$
$761$	4.10708	−	2.98397i	0.148882	−	0.108169i	0.659733	+	0.751500i	$0.270670\pi$
$762$	−21.4478	−	15.5828i	−0.776973	−	0.564504i
$763$	0.114720	+	0.0833489i	0.00415314	+	0.00301743i
$764$	−30.9805	+	22.5087i	−1.12084	+	0.814335i
$765$		0			0
$766$	0.901929	+	0.655290i	0.0325880	+	0.0236766i
$767$	5.19855	+	15.9995i	0.187709	+	0.577708i
$768$	1.59875			0.0576899
$769$	−14.4523	−	44.4797i	−0.521164	−	1.60398i	−0.771779	−	0.635891i	$-0.780633\pi$
$769$	−14.4523	−	44.4797i	−0.521164	−	1.60398i	0.250615	−	0.968087i	$-0.419367\pi$
$770$		0			0
$771$	−19.5004	+	60.0161i	−0.702290	+	2.16143i
$772$	−13.6492	+	42.0079i	−0.491245	+	1.51190i
$773$	15.4472	−	11.2231i	0.555598	−	0.403665i	−0.274248	−	0.961659i	$-0.588429\pi$
$773$	15.4472	−	11.2231i	0.555598	−	0.403665i	0.829845	+	0.557994i	$0.188429\pi$
$774$	0.574458			0.0206485
$775$		0			0
$776$	−5.19209			−0.186385
$777$	−0.0219846	+	0.0159727i	−0.000788693	+	0.000573019i
$778$	−0.718977	+	2.21278i	−0.0257766	+	0.0793321i
$779$	5.86589	−	18.0533i	0.210167	−	0.646828i
$780$		0			0
$781$	−10.7348	−	33.0383i	−0.384121	−	1.18220i
$782$	3.11359			0.111342
$783$	−13.1565	−	40.4915i	−0.470174	−	1.44705i
$784$	14.4797	+	10.5201i	0.517133	+	0.375719i
$785$		0			0
$786$	−6.00477	+	4.36272i	−0.214183	+	0.155613i
$787$	−3.25640	−	2.36591i	−0.116078	−	0.0843357i	0.528232	−	0.849100i	$-0.322855\pi$
$787$	−3.25640	−	2.36591i	−0.116078	−	0.0843357i	−0.644310	+	0.764765i	$0.722855\pi$
$788$	−20.4519	−	14.8592i	−0.728568	−	0.529335i
$789$	−71.7410	+	52.1229i	−2.55405	+	1.85562i
$790$		0			0
$791$	−0.0467322	−	0.0339529i	−0.00166161	−	0.00120723i
$792$	13.6602	+	42.0419i	0.485395	+	1.49389i
$793$	−34.7910			−1.23546
$794$	−5.87446	−	18.0797i	−0.208477	−	0.641625i
$795$		0			0
$796$	2.04155	−	6.28325i	0.0723609	−	0.222704i
$797$	4.93953	−	15.2023i	0.174967	−	0.538493i	−0.824665	−	0.565622i	$-0.808636\pi$
$797$	4.93953	−	15.2023i	0.174967	−	0.538493i	0.999632	+	0.0271283i	$0.00863627\pi$
$798$	−0.0724959	+	0.0526714i	−0.00256633	+	0.00186455i
$799$	−28.2988			−1.00114
$800$		0			0
$801$	−111.759			−3.94881
$802$	−6.77622	+	4.92321i	−0.239277	+	0.173845i
$803$	4.37810	−	13.4744i	0.154500	−	0.475502i
$804$	7.47950	−	23.0195i	0.263782	−	0.811836i
$805$		0			0
$806$	−3.51307	−	10.8121i	−0.123743	−	0.380841i
$807$	−24.5806			−0.865279
$808$	6.00866	+	18.4927i	0.211384	+	0.650573i
$809$	23.6245	+	17.1642i	0.830594	+	0.603462i	0.919727	−	0.392558i	$-0.128410\pi$
$809$	23.6245	+	17.1642i	0.830594	+	0.603462i	−0.0891332	+	0.996020i	$0.528410\pi$
$810$		0			0
$811$	−5.75792	+	4.18338i	−0.202188	+	0.146898i	−0.684272	−	0.729227i	$-0.739880\pi$
$811$	−5.75792	+	4.18338i	−0.202188	+	0.146898i	0.482084	+	0.876125i	$0.339880\pi$
$812$	−0.129835	−	0.0943310i	−0.00455633	−	0.00331037i
$813$	23.9110	+	17.3724i	0.838597	+	0.609276i
$814$	0.536361	−	0.389689i	0.0187994	−	0.0136586i
$815$		0			0
$816$	23.1838	+	16.8440i	0.811597	+	0.589659i
$817$	0.131135	+	0.403592i	0.00458784	+	0.0141199i
$818$	−0.237034			−0.00828770
$819$	0.182307	+	0.561084i	0.00637033	+	0.0196059i
$820$		0			0
$821$	−10.0749	+	31.0074i	−0.351617	+	1.08217i	0.606327	+	0.795215i	$0.292642\pi$
$821$	−10.0749	+	31.0074i	−0.351617	+	1.08217i	−0.957945	+	0.286952i	$0.907358\pi$
$822$	−6.13462	+	18.8804i	−0.213970	+	0.658531i
$823$	21.9536	−	15.9502i	0.765253	−	0.555989i	−0.135264	−	0.990810i	$-0.543188\pi$
$823$	21.9536	−	15.9502i	0.765253	−	0.555989i	0.900517	+	0.434821i	$0.143188\pi$
$824$	−34.3551			−1.19681
$825$		0			0
$826$	−0.0530966			−0.00184747
$827$	−44.3529	+	32.2243i	−1.54230	+	1.12055i	−0.593429	+	0.804886i	$0.702226\pi$
$827$	−44.3529	+	32.2243i	−1.54230	+	1.12055i	−0.948872	+	0.315662i	$0.897774\pi$
$828$	6.08954	−	18.7417i	0.211626	−	0.651318i
$829$	0.145846	−	0.448869i	0.00506545	−	0.0155899i	−0.948492	−	0.316802i	$-0.897391\pi$
$829$	0.145846	−	0.448869i	0.00506545	−	0.0155899i	0.953557	+	0.301212i	$0.0973911\pi$
$830$		0			0
$831$	16.4318	+	50.5719i	0.570013	+	1.75432i
$832$	9.78095			0.339093
$833$	−7.83641	−	24.1180i	−0.271515	−	0.835639i
$834$	9.95482	+	7.23260i	0.344707	+	0.250444i
$835$		0			0
$836$	−12.3250	+	8.95464i	−0.426269	+	0.309703i
$837$	−53.6644	−	38.9895i	−1.85491	−	1.34767i
$838$	9.82260	+	7.13653i	0.339316	+	0.246528i
$839$	31.1259	−	22.6143i	1.07458	−	0.780731i	0.0978532	−	0.995201i	$-0.468802\pi$
$839$	31.1259	−	22.6143i	1.07458	−	0.780731i	0.976731	+	0.214470i	$0.0688024\pi$
$840$		0			0
$841$	11.4241	+	8.30008i	0.393934	+	0.286210i
$842$	4.85314	+	14.9364i	0.167250	+	0.514743i
$843$	−84.1929			−2.89976
$844$	10.2153	+	31.4394i	0.351625	+	1.08219i
$845$		0			0
$846$	7.94248	−	24.4444i	0.273068	−	0.840417i
$847$	−0.0135252	+	0.0416263i	−0.000464731	+	0.00143030i
$848$	−18.5601	+	13.4847i	−0.637355	+	0.463065i
$849$	−10.7615			−0.369333
$850$		0			0
$851$	−0.633505			−0.0217163
$852$	42.4321	−	30.8288i	1.45370	−	1.05618i
$853$	11.0795	−	34.0993i	0.379356	−	1.16754i	−0.561136	−	0.827723i	$-0.689636\pi$
$853$	11.0795	−	34.0993i	0.379356	−	1.16754i	0.940492	−	0.339815i	$-0.110364\pi$
$854$	0.0339325	−	0.104434i	0.00116115	−	0.00357364i
$855$		0			0
$856$	−9.21595	−	28.3638i	−0.314995	−	0.969454i
$857$	−0.386299			−0.0131957			−0.00659786	−	0.999978i	$-0.502100\pi$
$857$	−0.386299			−0.0131957			−0.00659786	+	0.999978i	$0.502100\pi$
$858$	−6.47926	−	19.9411i	−0.221198	−	0.680779i
$859$	−18.0321	−	13.1011i	−0.615247	−	0.447003i	0.236011	−	0.971750i	$-0.424160\pi$
$859$	−18.0321	−	13.1011i	−0.615247	−	0.447003i	−0.851258	+	0.524747i	$0.824160\pi$
$860$		0			0
$861$	0.464863	−	0.337743i	0.0158425	−	0.0115102i
$862$	−0.810887	−	0.589144i	−0.0276189	−	0.0200663i
$863$	7.52231	+	5.46528i	0.256062	+	0.186040i	0.708409	−	0.705802i	$-0.249413\pi$
$863$	7.52231	+	5.46528i	0.256062	+	0.186040i	−0.452347	+	0.891842i	$0.649413\pi$
$864$	−44.9822	+	32.6815i	−1.53033	+	1.11185i
$865$		0			0
$866$	−2.86656	−	2.08268i	−0.0974096	−	0.0707722i
$867$	3.70272	+	11.3958i	0.125751	+	0.387021i
$868$	−0.250039			−0.00848686
$869$	−10.7225	−	33.0005i	−0.363736	−	1.11946i
$870$		0			0
$871$	−5.22013	+	16.0659i	−0.176877	+	0.544373i
$872$	3.45982	−	10.6482i	0.117164	−	0.360594i
$873$	14.6894	−	10.6725i	0.497160	−	0.361208i
$874$	−2.08903			−0.0706626
$875$		0			0
$876$	21.3910			0.722734
$877$	23.6060	−	17.1508i	0.797118	−	0.579140i	−0.112949	−	0.993601i	$-0.536030\pi$
$877$	23.6060	−	17.1508i	0.797118	−	0.579140i	0.910067	+	0.414461i	$0.136030\pi$
$878$	−2.00671	+	6.17601i	−0.0677230	+	0.208430i
$879$	22.4573	−	69.1165i	0.757467	−	2.33124i
$880$		0			0
$881$	−12.3835	−	38.1124i	−0.417210	−	1.28404i	−0.910260	−	0.414038i	$-0.864118\pi$
$881$	−12.3835	−	38.1124i	−0.417210	−	1.28404i	0.493050	−	0.870001i	$-0.335882\pi$
$882$	23.0325			0.775543
$883$	−9.52820	−	29.3248i	−0.320650	−	0.986858i	−0.973366	−	0.229256i	$-0.926371\pi$
$883$	−9.52820	−	29.3248i	−0.320650	−	0.986858i	0.652717	−	0.757602i	$-0.273629\pi$
$884$	−19.3570	−	14.0637i	−0.651047	−	0.473014i
$885$		0			0
$886$	−8.86357	+	6.43976i	−0.297777	+	0.216348i
$887$	−31.1899	−	22.6608i	−1.04725	−	0.760875i	−0.0755658	−	0.997141i	$-0.524076\pi$
$887$	−31.1899	−	22.6608i	−1.04725	−	0.760875i	−0.971688	+	0.236266i	$0.924076\pi$
$888$	1.73583	+	1.26116i	0.0582507	+	0.0423216i
$889$	0.329226	−	0.239197i	0.0110419	−	0.00802241i
$890$		0			0
$891$	−41.8521	−	30.4073i	−1.40210	−	1.01868i
$892$	−6.13739	−	18.8889i	−0.205495	−	0.632449i
$893$	18.9868			0.635370
$894$	−2.69477	−	8.29366i	−0.0901267	−	0.277382i
$895$		0			0
$896$	−0.0835993	+	0.257292i	−0.00279286	+	0.00859553i
$897$	−6.19122	+	19.0546i	−0.206719	+	0.636215i
$898$	0.161972	−	0.117680i	0.00540508	−	0.00392702i
$899$	−23.1818			−0.773156
$900$		0			0
$901$	32.5052			1.08291
$902$	−11.3413	+	8.23994i	−0.377624	+	0.274360i
$903$	−0.00396949	+	0.0122168i	−0.000132096	+	0.000406551i
$904$	−1.40939	+	4.33765i	−0.0468755	+	0.144268i
$905$		0			0
$906$	−3.52916	−	10.8616i	−0.117248	−	0.360853i
$907$	4.77670			0.158608			0.0793038	−	0.996850i	$-0.474730\pi$
$907$	4.77670			0.158608			0.0793038	+	0.996850i	$0.474730\pi$
$908$	6.05205	+	18.6263i	0.200844	+	0.618136i
$909$	−55.0119	−	39.9685i	−1.82463	−	1.32567i
$910$		0			0
$911$	9.33054	−	6.77904i	0.309135	−	0.224600i	−0.422390	−	0.906414i	$-0.638809\pi$
$911$	9.33054	−	6.77904i	0.309135	−	0.224600i	0.731525	+	0.681814i	$0.238809\pi$
$912$	−15.5550	−	11.3014i	−0.515077	−	0.374225i
$913$	−25.9663	−	18.8656i	−0.859359	−	0.624361i
$914$	14.2769	−	10.3728i	0.472238	−	0.343101i
$915$		0			0
$916$	13.6541	+	9.92028i	0.451144	+	0.327775i
$917$	−0.0352073	−	0.108357i	−0.00116265	−	0.00357826i
$918$	20.0341			0.661224
$919$	−12.7707	−	39.3041i	−0.421266	−	1.29652i	−0.906525	−	0.422153i	$-0.861274\pi$
$919$	−12.7707	−	39.3041i	−0.421266	−	1.29652i	0.485258	−	0.874371i	$-0.338726\pi$
$920$		0			0
$921$	1.06343	−	3.27290i	0.0350411	−	0.107846i
$922$	2.47107	−	7.60517i	0.0813803	−	0.250463i
$923$	−29.6145	+	21.5162i	−0.974772	+	0.708213i
$924$	−0.461153			−0.0151708
$925$		0			0
$926$	−15.2717			−0.501860
$927$	97.1968	−	70.6176i	3.19236	−	2.31939i
$928$	−6.00460	+	18.4802i	−0.197111	+	0.606644i
$929$	−4.14621	+	12.7607i	−0.136033	+	0.418666i	−0.995749	−	0.0921056i	$-0.970640\pi$
$929$	−4.14621	+	12.7607i	−0.136033	+	0.418666i	0.859716	+	0.510772i	$0.170640\pi$
$930$		0			0
$931$	5.25776	+	16.1817i	0.172316	+	0.530335i
$932$	−27.1552			−0.889499
$933$	14.1018	+	43.4010i	0.461674	+	1.42089i
$934$	−2.69392	−	1.95724i	−0.0881476	−	0.0640430i
$935$		0			0
$936$	37.6850	−	27.3798i	1.23177	−	0.894936i
$937$	33.9729	+	24.6828i	1.10985	+	0.806351i	0.982640	−	0.185525i	$-0.0593985\pi$
$937$	33.9729	+	24.6828i	1.10985	+	0.806351i	0.127208	+	0.991876i	$0.459398\pi$
$938$	−0.0431344	−	0.0313390i	−0.00140839	−	0.00102325i
$939$	−12.3832	+	8.99692i	−0.404111	+	0.293603i
$940$		0			0
$941$	−32.4064	−	23.5446i	−1.05642	−	0.767532i	−0.0829949	−	0.996550i	$-0.526449\pi$
$941$	−32.4064	−	23.5446i	−1.05642	−	0.767532i	−0.973422	+	0.229018i	$0.926449\pi$
$942$	−4.13317	−	12.7206i	−0.134666	−	0.414460i
$943$	13.3954			0.436215
$944$	−3.52050	−	10.8350i	−0.114583	−	0.352649i
$945$		0			0
$946$	0.0968441	−	0.298056i	0.00314867	−	0.00969062i
$947$	−13.5890	+	41.8228i	−0.441585	+	1.35906i	0.444602	+	0.895728i	$0.353345\pi$
$947$	−13.5890	+	41.8228i	−0.441585	+	1.35906i	−0.886186	+	0.463329i	$0.846655\pi$
$948$	42.3836	−	30.7935i	1.37656	−	1.00013i
$949$	−14.9293			−0.484625
$950$		0			0
$951$	70.1721			2.27549
$952$	0.130957	−	0.0951461i	0.00424435	−	0.00308370i
$953$	−12.5514	+	38.6292i	−0.406579	+	1.25132i	0.512990	+	0.858395i	$0.328538\pi$
$953$	−12.5514	+	38.6292i	−0.406579	+	1.25132i	−0.919569	+	0.392928i	$0.871462\pi$
$954$	−9.12308	+	28.0779i	−0.295371	+	0.909057i
$955$		0			0
$956$	−7.74726	−	23.8436i	−0.250564	−	0.771158i
$957$	−42.7548			−1.38207
$958$	−3.44319	−	10.5970i	−0.111244	−	0.342375i
$959$	−0.246533	−	0.179116i	−0.00796095	−	0.00578397i
$960$		0			0
$961$	−4.14019	+	3.00803i	−0.133555	+	0.0970331i
$962$	−0.565188	−	0.410633i	−0.0182224	−	0.0132393i
$963$	84.3760	+	61.3028i	2.71898	+	1.97545i
$964$	35.8150	−	26.0212i	1.15352	−	0.838085i
$965$		0			0
$966$	−0.0511586	−	0.0371689i	−0.00164600	−	0.00119589i
$967$	4.94432	+	15.2171i	0.158999	+	0.489348i	0.998544	−	0.0539419i	$-0.0171786\pi$
$967$	4.94432	+	15.2171i	0.158999	+	0.489348i	−0.839545	+	0.543290i	$0.817179\pi$
$968$	3.45581			0.111074
$969$	8.41833	+	25.9090i	0.270436	+	0.832315i
$970$		0			0
$971$	17.1567	−	52.8028i	0.550583	−	1.69452i	−0.156747	−	0.987639i	$-0.550101\pi$
$971$	17.1567	−	52.8028i	0.550583	−	1.69452i	0.707331	−	0.706883i	$-0.249899\pi$
$972$	6.23978	−	19.2041i	0.200141	−	0.615971i
$973$	−0.152808	+	0.111021i	−0.00489878	+	0.00355917i
$974$	5.10263			0.163499
$975$		0			0
$976$	23.5608			0.754162
$977$	5.11734	−	3.71797i	0.163718	−	0.118948i	−0.502909	−	0.864339i	$-0.667737\pi$
$977$	5.11734	−	3.71797i	0.163718	−	0.118948i	0.666628	+	0.745391i	$0.267737\pi$
$978$	−2.27451	+	7.00021i	−0.0727307	+	0.223842i
$979$	−18.8407	+	57.9858i	−0.602152	+	1.85323i
$980$		0			0
$981$	12.0992	+	37.2375i	0.386298	+	1.18890i
$982$	−3.32659			−0.106156
$983$	−15.0313	−	46.2615i	−0.479423	−	1.47551i	−0.839899	−	0.542743i	$-0.817386\pi$
$983$	−15.0313	−	46.2615i	−0.479423	−	1.47551i	0.360476	−	0.932768i	$-0.382614\pi$
$984$	−36.7041	−	26.6671i	−1.17008	−	0.850115i
$985$		0			0
$986$	5.66429	−	4.11535i	0.180388	−	0.131059i
$987$	0.464971	+	0.337821i	0.0148002	+	0.0107530i
$988$	12.9874	+	9.43591i	0.413185	+	0.300196i
$989$	−0.242270	+	0.176019i	−0.00770373	+	0.00559709i
$990$		0			0
$991$	35.7394	+	25.9662i	1.13530	+	0.824842i	0.986457	−	0.164019i	$-0.0524458\pi$
$991$	35.7394	+	25.9662i	1.13530	+	0.824842i	0.148841	+	0.988861i	$0.452446\pi$
$992$	9.35525	+	28.7925i	0.297029	+	0.914163i
$993$	−5.35931			−0.170073
$994$	−0.0357023	−	0.109880i	−0.00113241	−	0.00348519i
$995$		0			0
$996$	14.9748	−	46.0877i	0.474495	−	1.46035i
$997$	−12.4306	+	38.2574i	−0.393681	+	1.21162i	0.536304	+	0.844025i	$0.319820\pi$
$997$	−12.4306	+	38.2574i	−0.393681	+	1.21162i	−0.929984	+	0.367599i	$0.880180\pi$
$998$	0.439344	−	0.319202i	0.0139072	−	0.0101042i
$999$	−4.07623			−0.128966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.q.251.2		16
5.2	odd	4		625.2.e.j.374.5		32
5.3	odd	4		625.2.e.j.374.4		32
5.4	even	2		625.2.d.m.251.3		16
25.2	odd	20		625.2.e.k.499.5		32
25.3	odd	20		625.2.b.d.624.10		16
25.4	even	10		625.2.a.g.1.4	yes	8
25.6	even	5		625.2.d.p.501.3		16
25.8	odd	20		625.2.e.k.124.5		32
25.9	even	10		625.2.d.m.376.3		16
25.11	even	5		625.2.d.p.126.3		16
25.12	odd	20		625.2.e.j.249.4		32
25.13	odd	20		625.2.e.j.249.5		32
25.14	even	10		625.2.d.n.126.2		16
25.16	even	5	inner	625.2.d.q.376.2		16
25.17	odd	20		625.2.e.k.124.4		32
25.19	even	10		625.2.d.n.501.2		16
25.21	even	5		625.2.a.e.1.5	✓	8
25.22	odd	20		625.2.b.d.624.7		16
25.23	odd	20		625.2.e.k.499.4		32
75.29	odd	10		5625.2.a.s.1.5		8
75.71	odd	10		5625.2.a.be.1.4		8
100.71	odd	10		10000.2.a.bn.1.8		8
100.79	odd	10		10000.2.a.be.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.5	✓	8	25.21	even	5
625.2.a.g.1.4	yes	8	25.4	even	10
625.2.b.d.624.7		16	25.22	odd	20
625.2.b.d.624.10		16	25.3	odd	20
625.2.d.m.251.3		16	5.4	even	2
625.2.d.m.376.3		16	25.9	even	10
625.2.d.n.126.2		16	25.14	even	10
625.2.d.n.501.2		16	25.19	even	10
625.2.d.p.126.3		16	25.11	even	5
625.2.d.p.501.3		16	25.6	even	5
625.2.d.q.251.2		16	1.1	even	1	trivial
625.2.d.q.376.2		16	25.16	even	5	inner
625.2.e.j.249.4		32	25.12	odd	20
625.2.e.j.249.5		32	25.13	odd	20
625.2.e.j.374.4		32	5.3	odd	4
625.2.e.j.374.5		32	5.2	odd	4
625.2.e.k.124.4		32	25.17	odd	20
625.2.e.k.124.5		32	25.8	odd	20
625.2.e.k.499.4		32	25.23	odd	20
625.2.e.k.499.5		32	25.2	odd	20
5625.2.a.s.1.5		8	75.29	odd	10
5625.2.a.be.1.4		8	75.71	odd	10
10000.2.a.be.1.1		8	100.79	odd	10
10000.2.a.bn.1.8		8	100.71	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.405309 - 0.294474i) q^{2} +(-0.955869 + 2.94186i) q^{3} +(-0.540474 + 1.66341i) q^{4} +(0.478880 + 1.47384i) q^{6} -0.0237879 q^{7} +(0.580400 + 1.78629i) q^{8} +(-5.31382 - 3.86071i) q^{9} +O(q^{10})\)	\(q+(0.405309 - 0.294474i) q^{2} +(-0.955869 + 2.94186i) q^{3} +(-0.540474 + 1.66341i) q^{4} +(0.478880 + 1.47384i) q^{6} -0.0237879 q^{7} +(0.580400 + 1.78629i) q^{8} +(-5.31382 - 3.86071i) q^{9} +(-2.89894 + 2.10620i) q^{11} +(-4.37689 - 3.18000i) q^{12} +(3.05474 + 2.21940i) q^{13} +(-0.00964144 + 0.00700492i) q^{14} +(-2.06870 - 1.50300i) q^{16} +(1.11958 + 3.44570i) q^{17} -3.29062 q^{18} +(-0.751170 - 2.31186i) q^{19} +(0.0227381 - 0.0699807i) q^{21} +(-0.554744 + 1.70733i) q^{22} +(1.38777 - 1.00828i) q^{23} -5.80980 q^{24} +1.89167 q^{26} +(8.92950 - 6.48766i) q^{27} +(0.0128567 - 0.0395689i) q^{28} +(1.19198 - 3.66855i) q^{29} +(-1.85713 - 5.71565i) q^{31} -5.03748 q^{32} +(-3.42515 - 10.5415i) q^{33} +(1.46845 + 1.06689i) q^{34} +(9.29391 - 6.75242i) q^{36} +(-0.298777 - 0.217074i) q^{37} +(-0.985240 - 0.715819i) q^{38} +(-9.44911 + 6.86518i) q^{39} +(6.31761 + 4.59002i) q^{41} +(-0.0113915 - 0.0350596i) q^{42} -0.174574 q^{43} +(-1.93667 - 5.96047i) q^{44} +(0.265566 - 0.817327i) q^{46} +(-2.41368 + 7.42853i) q^{47} +(6.39902 - 4.64916i) q^{48} -6.99943 q^{49} -11.2070 q^{51} +(-5.34278 + 3.88175i) q^{52} +(2.77245 - 8.53273i) q^{53} +(1.70876 - 5.25902i) q^{54} +(-0.0138065 - 0.0424920i) q^{56} +7.51920 q^{57} +(-0.597171 - 1.83790i) q^{58} +(3.60446 + 2.61879i) q^{59} +(-7.45430 + 5.41587i) q^{61} +(-2.43582 - 1.76973i) q^{62} +(0.126404 + 0.0918382i) q^{63} +(2.09566 - 1.52259i) q^{64} +(-4.49246 - 3.26396i) q^{66} +(1.38250 + 4.25489i) q^{67} -6.33671 q^{68} +(1.63968 + 5.04642i) q^{69} +(-2.99579 + 9.22010i) q^{71} +(3.81221 - 11.7328i) q^{72} +(-3.19875 + 2.32403i) q^{73} -0.185020 q^{74} +4.25156 q^{76} +(0.0689596 - 0.0501021i) q^{77} +(-1.80819 + 5.56504i) q^{78} +(-2.99236 + 9.20955i) q^{79} +(4.46129 + 13.7304i) q^{81} +3.91223 q^{82} +(2.76792 + 8.51877i) q^{83} +(0.104117 + 0.0756454i) q^{84} +(-0.0707566 + 0.0514077i) q^{86} +(9.65298 + 7.01330i) q^{87} +(-5.44483 - 3.95590i) q^{88} +(13.7655 - 10.0012i) q^{89} +(-0.0726659 - 0.0527948i) q^{91} +(0.927119 + 2.85338i) q^{92} +18.5898 q^{93} +(1.20923 + 3.72161i) q^{94} +(4.81518 - 14.8196i) q^{96} +(-0.854239 + 2.62908i) q^{97} +(-2.83693 + 2.06115i) q^{98} +23.5359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

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