LMFDB - Embedded newform 325.2.x.b.93.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(7,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("325.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.4
Root			$-1.83163i$ of defining polynomial
Character	$\chi$	$=$	325.93
Dual form			325.2.x.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58624 - 0.915816i) q^{2} +(0.512942 - 1.91432i) q^{3} +(0.677439 - 1.17336i) q^{4} +(-0.939520 - 3.50634i) q^{6} +(1.76945 - 3.06478i) q^{7} +1.18163i q^{8} +(-0.803451 - 0.463873i) q^{9} +O(q^{10})$	\(q+(1.58624 - 0.915816i) q^{2} +(0.512942 - 1.91432i) q^{3} +(0.677439 - 1.17336i) q^{4} +(-0.939520 - 3.50634i) q^{6} +(1.76945 - 3.06478i) q^{7} +1.18163i q^{8} +(-0.803451 - 0.463873i) q^{9} +(-1.00269 + 3.74209i) q^{11} +(-1.89870 - 1.89870i) q^{12} +(-3.55971 - 0.573112i) q^{13} -6.48197i q^{14} +(2.43703 + 4.22106i) q^{16} +(-1.95684 + 0.524334i) q^{17} -1.69929 q^{18} +(0.518968 - 0.139057i) q^{19} +(-4.95936 - 4.95936i) q^{21} +(1.83656 + 6.85414i) q^{22} +(-0.294095 - 0.0788026i) q^{23} +(2.26202 + 0.606106i) q^{24} +(-6.17142 + 2.35095i) q^{26} +(2.90402 - 2.90402i) q^{27} +(-2.39739 - 4.15240i) q^{28} +(-1.71273 + 0.988843i) q^{29} +(4.13563 - 4.13563i) q^{31} +(5.68479 + 3.28212i) q^{32} +(6.64926 + 3.83895i) q^{33} +(-2.62382 + 2.62382i) q^{34} +(-1.08858 + 0.628491i) q^{36} +(2.70887 + 4.69189i) q^{37} +(0.695857 - 0.695857i) q^{38} +(-2.92305 + 6.52047i) q^{39} +(0.649884 + 0.174136i) q^{41} +(-12.4086 - 3.32487i) q^{42} +(2.28069 + 8.51164i) q^{43} +(3.71155 + 3.71155i) q^{44} +(-0.538675 + 0.144337i) q^{46} -9.75201 q^{47} +(9.33053 - 2.50011i) q^{48} +(-2.76192 - 4.78379i) q^{49} +4.01498i q^{51} +(-3.08395 + 3.78857i) q^{52} +(-3.16254 - 3.16254i) q^{53} +(1.94693 - 7.26602i) q^{54} +(3.62143 + 2.09083i) q^{56} -1.06480i q^{57} +(-1.81120 + 3.13709i) q^{58} +(3.14703 + 11.7449i) q^{59} +(1.44316 - 2.49963i) q^{61} +(2.77263 - 10.3476i) q^{62} +(-2.84334 + 1.64160i) q^{63} +2.27514 q^{64} +14.0631 q^{66} +(1.98310 - 1.14494i) q^{67} +(-0.710408 + 2.65128i) q^{68} +(-0.301707 + 0.522573i) q^{69} +(-1.19607 - 4.46378i) q^{71} +(0.548125 - 0.949380i) q^{72} -14.7546i q^{73} +(8.59382 + 4.96165i) q^{74} +(0.188405 - 0.703137i) q^{76} +(9.69449 + 9.69449i) q^{77} +(1.33490 + 13.0200i) q^{78} -1.59718i q^{79} +(-5.46126 - 9.45918i) q^{81} +(1.19035 - 0.318953i) q^{82} +7.57341 q^{83} +(-9.17877 + 2.45944i) q^{84} +(11.4128 + 11.4128i) q^{86} +(1.01444 + 3.78593i) q^{87} +(-4.42176 - 1.18481i) q^{88} +(4.54423 + 1.21762i) q^{89} +(-8.05520 + 9.89564i) q^{91} +(-0.291695 + 0.291695i) q^{92} +(-5.79560 - 10.0383i) q^{93} +(-15.4690 + 8.93105i) q^{94} +(9.19900 - 9.19900i) q^{96} +(-15.4372 - 8.91268i) q^{97} +(-8.76215 - 5.05883i) q^{98} +(2.54147 - 2.54147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9	$ 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27} - 18 q^{28} - 48 q^{32} - 18 q^{33} + 2 q^{34} + 36 q^{36} + 4 q^{37} + 8 q^{38} + 4 q^{39} + 10 q^{41} - 40 q^{42} - 10 q^{43} - 36 q^{44} + 4 q^{46} + 40 q^{47} + 56 q^{48} + 18 q^{49} + 30 q^{52} + 10 q^{53} - 48 q^{54} - 16 q^{59} - 16 q^{61} + 44 q^{62} + 36 q^{63} + 20 q^{64} - 32 q^{66} - 18 q^{67} - 22 q^{68} - 16 q^{69} - 16 q^{71} - 4 q^{72} + 18 q^{74} - 64 q^{76} + 28 q^{77} - 68 q^{78} - 14 q^{81} - 56 q^{82} - 48 q^{83} - 40 q^{84} + 60 q^{86} + 34 q^{87} - 82 q^{88} - 6 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 48 q^{94} + 56 q^{96} - 66 q^{97} + 30 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	1.58624	−	0.915816i	1.12164	−	0.647580i	0.179822	−	0.983699i	$-0.442448\pi$
$2$	1.58624	−	0.915816i	1.12164	−	0.647580i	0.941819	+	0.336119i	$0.109115\pi$
$3$	0.512942	−	1.91432i	0.296147	−	1.10524i	−0.644155	−	0.764895i	$-0.722791\pi$
$3$	0.512942	−	1.91432i	0.296147	−	1.10524i	0.940302	−	0.340341i	$-0.110542\pi$
$4$	0.677439	−	1.17336i	0.338719	−	0.586679i
$5$		0			0
$5$		0			0
$6$	−0.939520	−	3.50634i	−0.383558	−	1.43146i
$7$	1.76945	−	3.06478i	0.668790	−	1.15838i	−0.309453	−	0.950915i	$-0.600146\pi$
$7$	1.76945	−	3.06478i	0.668790	−	1.15838i	0.978243	−	0.207464i	$-0.0665209\pi$
$8$			1.18163i			0.417769i
$9$	−0.803451	−	0.463873i	−0.267817	−	0.154624i
$10$		0			0
$11$	−1.00269	+	3.74209i	−0.302323	+	1.12828i	0.632903	+	0.774231i	$0.281863\pi$
$11$	−1.00269	+	3.74209i	−0.302323	+	1.12828i	−0.935226	+	0.354053i	$0.884803\pi$
$12$	−1.89870	−	1.89870i	−0.548108	−	0.548108i
$13$	−3.55971	−	0.573112i	−0.987286	−	0.158953i
$13$	−3.55971	−	0.573112i	−0.987286	−	0.158953i
$14$		−	6.48197i		−	1.73238i
$15$		0			0
$16$	2.43703	+	4.22106i	0.609258	+	1.05527i
$17$	−1.95684	+	0.524334i	−0.474603	+	0.127170i	−0.488189	−	0.872738i	$-0.662342\pi$
$17$	−1.95684	+	0.524334i	−0.474603	+	0.127170i	0.0135853	+	0.999908i	$0.495676\pi$
$18$	−1.69929			−0.400526
$19$	0.518968	−	0.139057i	0.119059	−	0.0319019i	−0.198797	−	0.980041i	$-0.563704\pi$
$19$	0.518968	−	0.139057i	0.119059	−	0.0319019i	0.317857	+	0.948139i	$0.397037\pi$
$20$		0			0
$21$	−4.95936	−	4.95936i	−1.08222	−	1.08222i
$22$	1.83656	+	6.85414i	0.391556	+	1.46131i
$23$	−0.294095	−	0.0788026i	−0.0613231	−	0.0164315i	0.228027	−	0.973655i	$-0.426773\pi$
$23$	−0.294095	−	0.0788026i	−0.0613231	−	0.0164315i	−0.289350	+	0.957223i	$0.593439\pi$
$24$	2.26202	+	0.606106i	0.461733	+	0.123721i
$25$		0			0
$26$	−6.17142	+	2.35095i	−1.21032	+	0.461059i
$27$	2.90402	−	2.90402i	0.558879	−	0.558879i
$28$	−2.39739	−	4.15240i	−0.453064	−	0.784730i
$29$	−1.71273	+	0.988843i	−0.318045	+	0.183624i	−0.650521	−	0.759488i	$-0.725449\pi$
$29$	−1.71273	+	0.988843i	−0.318045	+	0.183624i	0.332476	+	0.943112i	$0.392116\pi$
$30$		0			0
$31$	4.13563	−	4.13563i	0.742781	−	0.742781i	−0.230331	−	0.973112i	$-0.573981\pi$
$31$	4.13563	−	4.13563i	0.742781	−	0.742781i	0.973112	+	0.230331i	$0.0739810\pi$
$32$	5.68479	+	3.28212i	1.00494	+	0.580202i
$33$	6.64926	+	3.83895i	1.15749	+	0.668276i
$34$	−2.62382	+	2.62382i	−0.449982	+	0.449982i
$35$		0			0
$36$	−1.08858	+	0.628491i	−0.181430	+	0.104748i
$37$	2.70887	+	4.69189i	0.445335	+	0.771342i	0.998075	−	0.0620109i	$-0.0197514\pi$
$37$	2.70887	+	4.69189i	0.445335	+	0.771342i	−0.552741	+	0.833353i	$0.686418\pi$
$38$	0.695857	−	0.695857i	0.112883	−	0.112883i
$39$	−2.92305	+	6.52047i	−0.468062	+	1.04411i
$40$		0			0
$41$	0.649884	+	0.174136i	0.101495	+	0.0271955i	0.309209	−	0.950994i	$-0.399936\pi$
$41$	0.649884	+	0.174136i	0.101495	+	0.0271955i	−0.207714	+	0.978190i	$0.566602\pi$
$42$	−12.4086	−	3.32487i	−1.91469	−	0.513039i
$43$	2.28069	+	8.51164i	0.347802	+	1.29801i	0.889305	+	0.457314i	$0.151189\pi$
$43$	2.28069	+	8.51164i	0.347802	+	1.29801i	−0.541504	+	0.840698i	$0.682145\pi$
$44$	3.71155	+	3.71155i	0.559538	+	0.559538i
$45$		0			0
$46$	−0.538675	+	0.144337i	−0.0794232	+	0.0212814i
$47$	−9.75201			−1.42248			−0.711238	−	0.702951i	$-0.751865\pi$
$47$	−9.75201			−1.42248			−0.711238	+	0.702951i	$0.751865\pi$
$48$	9.33053	−	2.50011i	1.34675	−	0.360860i
$49$	−2.76192	−	4.78379i	−0.394561	−	0.683399i
$50$		0			0
$51$			4.01498i			0.562209i
$52$	−3.08395	+	3.78857i	−0.427667	+	0.525380i
$53$	−3.16254	−	3.16254i	−0.434409	−	0.434409i	0.455716	−	0.890125i	$-0.349383\pi$
$53$	−3.16254	−	3.16254i	−0.434409	−	0.434409i	−0.890125	+	0.455716i	$0.849383\pi$
$54$	1.94693	−	7.26602i	0.264943	−	0.988781i
$55$		0			0
$56$	3.62143	+	2.09083i	0.483934	+	0.279399i
$57$		−	1.06480i		−	0.141036i
$58$	−1.81120	+	3.13709i	−0.237822	+	0.411919i
$59$	3.14703	+	11.7449i	0.409708	+	1.52905i	0.795203	+	0.606343i	$0.207364\pi$
$59$	3.14703	+	11.7449i	0.409708	+	1.52905i	−0.385495	+	0.922710i	$0.625969\pi$
$60$		0			0
$61$	1.44316	−	2.49963i	0.184778	−	0.320044i	−0.758724	−	0.651412i	$-0.774177\pi$
$61$	1.44316	−	2.49963i	0.184778	−	0.320044i	0.943502	+	0.331368i	$0.107510\pi$
$62$	2.77263	−	10.3476i	0.352124	−	1.31414i
$63$	−2.84334	+	1.64160i	−0.358227	+	0.206822i
$64$	2.27514			0.284392
$65$		0			0
$66$	14.0631			1.73105
$67$	1.98310	−	1.14494i	0.242274	−	0.139877i	−0.373947	−	0.927450i	$-0.621996\pi$
$67$	1.98310	−	1.14494i	0.242274	−	0.139877i	0.616222	+	0.787573i	$0.288663\pi$
$68$	−0.710408	+	2.65128i	−0.0861496	+	0.321515i
$69$	−0.301707	+	0.522573i	−0.0363213	+	0.0629104i
$70$		0			0
$71$	−1.19607	−	4.46378i	−0.141947	−	0.529753i	−0.999872	−	0.0159789i	$-0.994914\pi$
$71$	−1.19607	−	4.46378i	−0.141947	−	0.529753i	0.857925	−	0.513774i	$-0.171753\pi$
$72$	0.548125	−	0.949380i	0.0645972	−	0.111886i
$73$		−	14.7546i		−	1.72690i	−0.504436	−	0.863449i	$-0.668299\pi$
$73$		−	14.7546i		−	1.72690i	0.504436	−	0.863449i	$-0.331701\pi$
$74$	8.59382	+	4.96165i	0.999011	+	0.576780i
$75$		0			0
$76$	0.188405	−	0.703137i	0.0216115	−	0.0806554i
$77$	9.69449	+	9.69449i	1.10479	+	1.10479i
$78$	1.33490	+	13.0200i	0.151147	+	1.47422i
$79$		−	1.59718i		−	0.179696i	−0.995955	−	0.0898482i	$-0.971362\pi$
$79$		−	1.59718i		−	0.179696i	0.995955	−	0.0898482i	$-0.0286382\pi$
$80$		0			0
$81$	−5.46126	−	9.45918i	−0.606807	−	1.05102i
$82$	1.19035	−	0.318953i	0.131452	−	0.0352225i
$83$	7.57341			0.831290			0.415645	−	0.909527i	$-0.363556\pi$
$83$	7.57341			0.831290			0.415645	+	0.909527i	$0.363556\pi$
$84$	−9.17877	+	2.45944i	−1.00149	+	0.268347i
$85$		0			0
$86$	11.4128	+	11.4128i	1.23068	+	1.23068i
$87$	1.01444	+	3.78593i	0.108759	+	0.405895i
$88$	−4.42176	−	1.18481i	−0.471361	−	0.126301i
$89$	4.54423	+	1.21762i	0.481687	+	0.129068i	0.491488	−	0.870884i	$-0.336453\pi$
$89$	4.54423	+	1.21762i	0.481687	+	0.129068i	−0.00980081	+	0.999952i	$0.503120\pi$
$90$		0			0
$91$	−8.05520	+	9.89564i	−0.844415	+	1.03735i
$92$	−0.291695	+	0.291695i	−0.0304113	+	0.0304113i
$93$	−5.79560	−	10.0383i	−0.600976	−	1.04092i
$94$	−15.4690	+	8.93105i	−1.59551	+	0.921167i
$95$		0			0
$96$	9.19900	−	9.19900i	0.938869	−	0.938869i
$97$	−15.4372	−	8.91268i	−1.56741	−	0.904945i	−0.996470	−	0.0839547i	$-0.973245\pi$
$97$	−15.4372	−	8.91268i	−1.56741	−	0.904945i	−0.570942	−	0.820991i	$-0.693422\pi$
$98$	−8.76215	−	5.05883i	−0.885111	−	0.511019i
$99$	2.54147	−	2.54147i	0.255427	−	0.255427i
$100$		0			0
$101$	−3.94379	+	2.27695i	−0.392421	+	0.226565i	−0.683209	−	0.730223i	$-0.739416\pi$
$101$	−3.94379	+	2.27695i	−0.392421	+	0.226565i	0.290787	+	0.956788i	$0.406083\pi$
$102$	3.67698	+	6.36872i	0.364075	+	0.630597i
$103$	−9.79285	+	9.79285i	−0.964918	+	0.964918i	−0.999405	−	0.0344872i	$-0.989020\pi$
$103$	−9.79285	+	9.79285i	−0.964918	+	0.964918i	0.0344872	+	0.999405i	$0.489020\pi$
$104$	0.677205	−	4.20625i	0.0664055	−	0.412457i
$105$		0			0
$106$	−7.91286	−	2.12024i	−0.768565	−	0.205936i
$107$	−6.82933	−	1.82991i	−0.660216	−	0.176904i	−0.0868725	−	0.996219i	$-0.527687\pi$
$107$	−6.82933	−	1.82991i	−0.660216	−	0.176904i	−0.573344	+	0.819315i	$0.694354\pi$
$108$	−1.44016	−	5.37475i	−0.138580	−	0.517186i
$109$	−9.89281	−	9.89281i	−0.947560	−	0.947560i	0.0511324	−	0.998692i	$-0.483717\pi$
$109$	−9.89281	−	9.89281i	−0.947560	−	0.947560i	−0.998692	+	0.0511324i	$0.983717\pi$
$110$		0			0
$111$	10.3713	−	2.77898i	0.984399	−	0.263769i
$112$	17.2488			1.62986
$113$	2.21438	−	0.593341i	0.208311	−	0.0558168i	−0.153154	−	0.988202i	$-0.548943\pi$
$113$	2.21438	−	0.593341i	0.208311	−	0.0558168i	0.361466	+	0.932385i	$0.382277\pi$
$114$	−0.975161	−	1.68903i	−0.0913322	−	0.158192i
$115$		0			0
$116$			2.67952i			0.248787i
$117$	2.59420	+	2.11172i	0.239834	+	0.195229i
$118$	15.7481	+	15.7481i	1.44973	+	1.44973i
$119$	−1.85557	+	6.92507i	−0.170099	+	0.634820i
$120$		0			0
$121$	−3.47160	−	2.00433i	−0.315600	−	0.182212i
$122$		−	5.28668i		−	0.478633i
$123$	0.666705	−	1.15477i	0.0601148	−	0.104122i
$124$	−2.05094	−	7.65421i	−0.184180	−	0.687368i
$125$		0			0
$126$	−3.00681	+	5.20795i	−0.267868	+	0.463961i
$127$	0.332860	−	1.24225i	0.0295366	−	0.110232i	−0.949584	−	0.313513i	$-0.898494\pi$
$127$	0.332860	−	1.24225i	0.0295366	−	0.110232i	0.979120	+	0.203281i	$0.0651606\pi$
$128$	−7.76067	+	4.48062i	−0.685953	+	0.396035i
$129$	17.4639			1.53761
$130$		0			0
$131$	−5.59439			−0.488785			−0.244392	−	0.969676i	$-0.578588\pi$
$131$	−5.59439			−0.488785			−0.244392	+	0.969676i	$0.578588\pi$
$132$	9.00893	−	5.20131i	0.784127	−	0.452716i
$133$	0.492109	−	1.83658i	0.0426713	−	0.159251i
$134$	2.09712	−	3.63231i	0.181163	−	0.313784i
$135$		0			0
$136$	−0.619567	−	2.31226i	−0.0531274	−	0.198274i
$137$	−7.14509	+	12.3757i	−0.610446	+	1.05732i	0.380719	+	0.924691i	$0.375676\pi$
$137$	−7.14509	+	12.3757i	−0.610446	+	1.05732i	−0.991165	+	0.132633i	$0.957657\pi$
$138$			1.10523i			0.0940838i
$139$	−15.0832	−	8.70830i	−1.27934	−	0.738629i	−0.302615	−	0.953113i	$-0.597860\pi$
$139$	−15.0832	−	8.70830i	−1.27934	−	0.738629i	−0.976727	+	0.214484i	$0.931193\pi$
$140$		0			0
$141$	−5.00221	+	18.6685i	−0.421262	+	1.57217i
$142$	−5.98525	−	5.98525i	−0.502271	−	0.502271i
$143$	5.71393	−	12.7461i	0.477823	−	1.06588i
$144$		−	4.52189i		−	0.376824i
$145$		0			0
$146$	−13.5125	−	23.4044i	−1.11830	−	1.93696i
$147$	−10.5744	+	2.83341i	−0.872165	+	0.233696i
$148$	7.34036			0.603374
$149$	12.6828	−	3.39833i	1.03901	−	0.278402i	0.301308	−	0.953527i	$-0.402577\pi$
$149$	12.6828	−	3.39833i	1.03901	−	0.278402i	0.737704	+	0.675124i	$0.235910\pi$
$150$		0			0
$151$	0.765191	+	0.765191i	0.0622704	+	0.0622704i	0.737556	−	0.675286i	$-0.235980\pi$
$151$	0.765191	+	0.765191i	0.0622704	+	0.0622704i	−0.675286	+	0.737556i	$0.735980\pi$
$152$	0.164314	+	0.613227i	0.0133276	+	0.0497392i
$153$	1.81545	+	0.486448i	0.146770	+	0.0393270i
$154$	24.2562	+	6.49942i	1.95462	+	0.523738i
$155$		0			0
$156$	5.67066	+	7.84700i	0.454016	+	0.628263i
$157$	−3.03481	+	3.03481i	−0.242204	+	0.242204i	−0.817762	−	0.575557i	$-0.804785\pi$
$157$	−3.03481	+	3.03481i	−0.242204	+	0.242204i	0.575557	+	0.817762i	$0.304785\pi$
$158$	−1.46272	−	2.53350i	−0.116368	−	0.201555i
$159$	−7.67633	+	4.43193i	−0.608773	+	0.351475i
$160$		0			0
$161$	−0.761901	+	0.761901i	−0.0600462	+	0.0600462i
$162$	−17.3257	−	10.0030i	−1.36124	−	0.785912i
$163$	1.96032	+	1.13179i	0.153544	+	0.0886486i	0.574803	−	0.818292i	$-0.305079\pi$
$163$	1.96032	+	1.13179i	0.153544	+	0.0886486i	−0.421260	+	0.906940i	$0.638412\pi$
$164$	0.644580	−	0.644580i	0.0503333	−	0.0503333i
$165$		0			0
$166$	12.0133	−	6.93585i	0.932409	−	0.538327i
$167$	−0.309785	−	0.536563i	−0.0239719	−	0.0415205i	0.853791	−	0.520617i	$-0.174298\pi$
$167$	−0.309785	−	0.536563i	−0.0239719	−	0.0415205i	−0.877762	+	0.479096i	$0.840965\pi$
$168$	5.86012	−	5.86012i	0.452118	−	0.452118i
$169$	12.3431	+	4.08023i	0.949468	+	0.313864i
$170$		0			0
$171$	−0.481470	−	0.129009i	−0.0368189	−	0.00986560i
$172$	11.5322	+	3.09005i	0.879324	+	0.235614i
$173$	1.71382	+	6.39606i	0.130299	+	0.486283i	0.999973	−	0.00734343i	$-0.00233751\pi$
$173$	1.71382	+	6.39606i	0.130299	+	0.486283i	−0.869674	+	0.493627i	$0.835671\pi$
$174$	5.07636	+	5.07636i	0.384838	+	0.384838i
$175$		0			0
$176$	−18.2392	+	4.88718i	−1.37483	+	0.368385i
$177$	24.0977			1.81130
$178$	8.32336	−	2.23024i	0.623862	−	0.167163i
$179$	−1.09512	−	1.89680i	−0.0818528	−	0.141773i	0.822193	−	0.569209i	$-0.192750\pi$
$179$	−1.09512	−	1.89680i	−0.0818528	−	0.141773i	−0.904046	+	0.427436i	$0.859417\pi$
$180$		0			0
$181$		−	9.59255i		−	0.713009i	−0.934294	−	0.356504i	$-0.883969\pi$
$181$		−	9.59255i		−	0.713009i	0.934294	−	0.356504i	$-0.116031\pi$
$182$	−3.71490	+	23.0739i	−0.275367	+	1.71035i
$183$	−4.04484	−	4.04484i	−0.299003	−	0.299003i
$184$	0.0931154	−	0.347511i	0.00686456	−	0.0256189i
$185$		0			0
$186$	−18.3864	−	10.6154i	−1.34816	−	0.778359i
$187$		−	7.84842i		−	0.573933i
$188$	−6.60639	+	11.4426i	−0.481820	+	0.834537i
$189$	−3.76166	−	14.0387i	−0.273621	−	1.02117i
$190$		0			0
$191$	−1.86557	+	3.23126i	−0.134988	+	0.233806i	−0.925593	−	0.378521i	$-0.876433\pi$
$191$	−1.86557	+	3.23126i	−0.134988	+	0.233806i	0.790605	+	0.612326i	$0.209766\pi$
$192$	1.16701	−	4.35536i	0.0842220	−	0.314321i
$193$	−0.246025	+	0.142043i	−0.0177093	+	0.0102245i	−0.508829	−	0.860868i	$-0.669921\pi$
$193$	−0.246025	+	0.142043i	−0.0177093	+	0.0102245i	0.491119	+	0.871092i	$0.336588\pi$
$194$	−32.6495			−2.34410
$195$		0			0
$196$	−7.48414			−0.534581
$197$	22.3860	−	12.9246i	1.59494	−	0.920838i	0.602496	−	0.798122i	$-0.294173\pi$
$197$	22.3860	−	12.9246i	1.59494	−	0.920838i	0.992442	−	0.122716i	$-0.0391604\pi$
$198$	1.70386	−	6.35890i	0.121088	−	0.451907i
$199$	−2.87625	+	4.98181i	−0.203892	+	0.353151i	−0.949779	−	0.312921i	$-0.898692\pi$
$199$	−2.87625	+	4.98181i	−0.203892	+	0.353151i	0.745887	+	0.666072i	$0.232026\pi$
$200$		0			0
$201$	−1.17458	−	4.38359i	−0.0828484	−	0.309194i
$202$	−4.17053	+	7.22357i	−0.293437	+	0.508248i
$203$			6.99884i			0.491223i
$204$	4.71101	+	2.71990i	0.329836	+	0.190431i
$205$		0			0
$206$	−6.56536	+	24.5023i	−0.457430	+	1.70715i
$207$	0.199737	+	0.199737i	0.0138827	+	0.0138827i
$208$	−6.25598	−	16.4225i	−0.433774	−	1.13869i
$209$			2.08146i			0.143977i
$210$		0			0
$211$	1.61372	+	2.79504i	0.111093	+	0.192418i	0.916211	−	0.400696i	$-0.131232\pi$
$211$	1.61372	+	2.79504i	0.111093	+	0.192418i	−0.805118	+	0.593114i	$0.797898\pi$
$212$	−5.85322	+	1.56837i	−0.402001	+	0.107716i
$213$	−9.15863			−0.627539
$214$	−12.5088	+	3.35173i	−0.855085	+	0.229119i
$215$		0			0
$216$	3.43147	+	3.43147i	0.233482	+	0.233482i
$217$	−5.35700	−	19.9926i	−0.363657	−	1.35719i
$218$	−24.7524	−	6.63238i	−1.67644	−	0.449201i
$219$	−28.2451	−	7.56826i	−1.90863	−	0.511416i
$220$		0			0
$221$	7.26628	−	0.744987i	0.488783	−	0.0501133i
$222$	13.9063	−	13.9063i	0.933331	−	0.933331i
$223$	−3.70762	−	6.42178i	−0.248280	−	0.430034i	0.714768	−	0.699361i	$-0.246532\pi$
$223$	−3.70762	−	6.42178i	−0.248280	−	0.430034i	−0.963049	+	0.269327i	$0.913199\pi$
$224$	20.1179	−	11.6151i	1.34419	−	0.776067i
$225$		0			0
$226$	2.96914	−	2.96914i	0.197504	−	0.197504i
$227$	3.37949	+	1.95115i	0.224305	+	0.129502i	0.607942	−	0.793981i	$-0.291995\pi$
$227$	3.37949	+	1.95115i	0.224305	+	0.129502i	−0.383637	+	0.923484i	$0.625329\pi$
$228$	−1.24939	−	0.721337i	−0.0827430	−	0.0477717i
$229$	12.3946	−	12.3946i	0.819060	−	0.819060i	−0.166912	−	0.985972i	$-0.553379\pi$
$229$	12.3946	−	12.3946i	0.819060	−	0.819060i	0.985972	+	0.166912i	$0.0533795\pi$
$230$		0			0
$231$	23.5311	−	13.5857i	1.54823	−	0.893872i
$232$	−1.16844	−	2.02381i	−0.0767121	−	0.132869i
$233$	−2.88962	+	2.88962i	−0.189305	+	0.189305i	−0.795396	−	0.606090i	$-0.792737\pi$
$233$	−2.88962	+	2.88962i	−0.189305	+	0.189305i	0.606090	+	0.795396i	$0.292737\pi$
$234$	6.04898	+	0.973883i	0.395434	+	0.0636647i
$235$		0			0
$236$	15.9129	+	4.26384i	1.03584	+	0.277552i
$237$	−3.05751	−	0.819258i	−0.198607	−	0.0532165i
$238$	3.39872	+	12.6842i	0.220306	+	0.822193i
$239$	−8.97299	−	8.97299i	−0.580415	−	0.580415i	0.354602	−	0.935017i	$-0.384616\pi$
$239$	−8.97299	−	8.97299i	−0.580415	−	0.580415i	−0.935017	+	0.354602i	$0.884616\pi$
$240$		0			0
$241$	16.9497	−	4.54165i	1.09183	−	0.292554i	0.332394	−	0.943141i	$-0.392144\pi$
$241$	16.9497	−	4.54165i	1.09183	−	0.292554i	0.759432	+	0.650587i	$0.225477\pi$
$242$	−7.34239			−0.471986
$243$	−9.00835	+	2.41378i	−0.577886	+	0.154844i
$244$	−1.95530	−	3.38669i	−0.125176	−	0.216810i
$245$		0			0
$246$		−	2.44232i		−	0.155716i
$247$	−1.92707	+	0.197576i	−0.122617	+	0.0125715i
$248$	4.88677	+	4.88677i	0.310311	+	0.310311i
$249$	3.88472	−	14.4980i	0.246184	−	0.918771i
$250$		0			0
$251$	18.8524	+	10.8845i	1.18996	+	0.687021i	0.958296	−	0.285776i	$-0.0922513\pi$
$251$	18.8524	+	10.8845i	1.18996	+	0.687021i	0.231659	+	0.972797i	$0.425585\pi$
$252$			4.44834i			0.280219i
$253$	0.589774	−	1.02152i	0.0370787	−	0.0642223i
$254$	−0.609678	−	2.27535i	−0.0382546	−	0.142768i
$255$		0			0
$256$	−10.4820	+	18.1554i	−0.655125	+	1.13471i
$257$	−3.31629	+	12.3766i	−0.206864	+	0.772029i	0.782009	+	0.623268i	$0.214195\pi$
$257$	−3.31629	+	12.3766i	−0.206864	+	0.772029i	−0.988873	+	0.148761i	$0.952471\pi$
$258$	27.7019	−	15.9937i	1.72465	−	0.995725i
$259$	19.1728			1.19134
$260$		0			0
$261$	1.83479			0.113571
$262$	−8.87405	+	5.12344i	−0.548241	+	0.316527i
$263$	−4.27179	+	15.9426i	−0.263410	+	0.983060i	0.699806	+	0.714333i	$0.253270\pi$
$263$	−4.27179	+	15.9426i	−0.263410	+	0.983060i	−0.963216	+	0.268727i	$0.913397\pi$
$264$	−4.53621	+	7.85695i	−0.279185	+	0.483562i
$265$		0			0
$266$	−0.901363	−	3.36393i	−0.0552661	−	0.206256i
$267$	4.66185	−	8.07456i	0.285301	−	0.494155i
$268$		−	3.10252i		−	0.189516i
$269$	27.9787	+	16.1535i	1.70589	+	0.984895i	0.939519	+	0.342495i	$0.111272\pi$
$269$	27.9787	+	16.1535i	1.70589	+	0.984895i	0.766370	+	0.642400i	$0.222061\pi$
$270$		0			0
$271$	4.52218	−	16.8770i	0.274703	−	1.02521i	−0.681337	−	0.731970i	$-0.738601\pi$
$271$	4.52218	−	16.8770i	0.274703	−	1.02521i	0.956040	−	0.293236i	$-0.0947321\pi$
$272$	−6.98212	−	6.98212i	−0.423353	−	0.423353i
$273$	14.8116	+	20.4962i	0.896440	+	1.24048i
$274$			26.1743i			1.58125i
$275$		0			0
$276$	0.408777	+	0.708022i	0.0246055	+	0.0426179i
$277$	2.96961	−	0.795705i	0.178427	−	0.0478093i	−0.168499	−	0.985702i	$-0.553892\pi$
$277$	2.96961	−	0.795705i	0.178427	−	0.0478093i	0.346926	+	0.937892i	$0.387225\pi$
$278$	−31.9008			−1.91328
$279$	−5.24118	+	1.40437i	−0.313781	+	0.0840775i
$280$		0			0
$281$	−18.6757	−	18.6757i	−1.11410	−	1.11410i	−0.992590	−	0.121508i	$-0.961227\pi$
$281$	−18.6757	−	18.6757i	−1.11410	−	1.11410i	−0.121508	−	0.992590i	$-0.538773\pi$
$282$	9.16221	+	34.1938i	0.545602	+	2.03621i
$283$	14.8164	+	3.97005i	0.880745	+	0.235995i	0.670728	−	0.741703i	$-0.265982\pi$
$283$	14.8164	+	3.97005i	0.880745	+	0.235995i	0.210016	+	0.977698i	$0.432648\pi$
$284$	−6.04787	−	1.62052i	−0.358875	−	0.0961603i
$285$		0			0
$286$	−2.60944	−	25.4513i	−0.154299	−	1.50497i
$287$	1.68363	−	1.68363i	0.0993814	−	0.0993814i
$288$	−3.04497	−	5.27404i	−0.179427	−	0.310776i
$289$	−11.1681	+	6.44793i	−0.656949	+	0.379290i
$290$		0			0
$291$	−24.9801	+	24.9801i	−1.46436	+	1.46436i
$292$	−17.3125	−	9.99535i	−1.01314	−	0.584934i
$293$	−8.98649	−	5.18835i	−0.524996	−	0.303107i	0.213980	−	0.976838i	$-0.431357\pi$
$293$	−8.98649	−	5.18835i	−0.524996	−	0.303107i	−0.738976	+	0.673731i	$0.764691\pi$
$294$	−14.1787	+	14.1787i	−0.826919	+	0.826919i
$295$		0			0
$296$	−5.54407	+	3.20087i	−0.322243	+	0.186047i
$297$	7.95528	+	13.7790i	0.461612	+	0.799536i
$298$	17.0057	−	17.0057i	0.985111	−	0.985111i
$299$	1.00173	+	0.449064i	0.0579316	+	0.0259701i
$300$		0			0
$301$	30.1219	+	8.07113i	1.73620	+	0.465212i
$302$	1.91455	+	0.513002i	0.110170	+	0.0295200i
$303$	2.33588	+	8.71763i	0.134193	+	0.500814i
$304$	1.85171	+	1.85171i	0.106203	+	0.106203i
$305$		0			0
$306$	3.32524	−	0.890994i	0.190091	−	0.0509347i
$307$	−2.13935			−0.122099			−0.0610496	−	0.998135i	$-0.519445\pi$
$307$	−2.13935			−0.122099			−0.0610496	+	0.998135i	$0.519445\pi$
$308$	17.9425	−	4.80768i	1.02237	−	0.273943i
$309$	13.7235	+	23.7698i	0.780704	+	1.35222i
$310$		0			0
$311$			3.82084i			0.216660i	0.994115	+	0.108330i	$0.0345503\pi$
$311$			3.82084i			0.216660i	−0.994115	+	0.108330i	$0.965450\pi$
$312$	−7.70477	−	3.45395i	−0.436196	−	0.195542i
$313$	−3.04531	−	3.04531i	−0.172131	−	0.172131i	0.615784	−	0.787915i	$-0.288839\pi$
$313$	−3.04531	−	3.04531i	−0.172131	−	0.172131i	−0.787915	+	0.615784i	$0.788839\pi$
$314$	−2.03461	+	7.59327i	−0.114820	+	0.428513i
$315$		0			0
$316$	−1.87406	−	1.08199i	−0.105424	−	0.0608666i
$317$		−	23.1127i		−	1.29814i	−0.760730	−	0.649068i	$-0.775159\pi$
$317$		−	23.1127i		−	1.29814i	0.760730	−	0.649068i	$-0.224841\pi$
$318$	−8.11767	+	14.0602i	−0.455216	+	0.788458i
$319$	−1.98301	−	7.40069i	−0.111027	−	0.414359i
$320$		0			0
$321$	−7.00609	+	12.1349i	−0.391042	+	0.677305i
$322$	−0.510796	+	1.90632i	−0.0284656	+	0.106235i
$323$	−0.942624	+	0.544224i	−0.0524490	+	0.0302814i
$324$	−14.7987			−0.822149
$325$		0			0
$326$	4.14604			0.229628
$327$	−24.0125	+	13.8636i	−1.32789	+	0.766660i
$328$	−0.205764	+	0.767921i	−0.0113614	+	0.0424013i
$329$	−17.2557	+	29.8878i	−0.951338	+	1.64777i
$330$		0			0
$331$	0.516858	+	1.92894i	0.0284091	+	0.106024i	0.978675	−	0.205417i	$-0.0658550\pi$
$331$	0.516858	+	1.92894i	0.0284091	+	0.106024i	−0.950265	+	0.311441i	$0.899188\pi$
$332$	5.13052	−	8.88632i	0.281574	−	0.487700i
$333$		−	5.02628i		−	0.275438i
$334$	−0.982786	−	0.567412i	−0.0537756	−	0.0310474i
$335$		0			0
$336$	8.84765	−	33.0199i	0.482679	−	1.80138i
$337$	−6.12727	−	6.12727i	−0.333773	−	0.333773i	0.520244	−	0.854018i	$-0.325841\pi$
$337$	−6.12727	−	6.12727i	−0.333773	−	0.333773i	−0.854018	+	0.520244i	$0.825841\pi$
$338$	23.3158	−	4.83178i	1.26821	−	0.262814i
$339$		−	4.54338i		−	0.246763i
$340$		0			0
$341$	11.3292	+	19.6227i	0.613508	+	1.06263i
$342$	−0.881876	+	0.236298i	−0.0476864	+	0.0127775i
$343$	5.22396			0.282067
$344$	−10.0576	+	2.69492i	−0.542269	+	0.145301i
$345$		0			0
$346$	8.57614	+	8.57614i	0.461056	+	0.461056i
$347$	8.41384	+	31.4009i	0.451679	+	1.68569i	0.697673	+	0.716417i	$0.254219\pi$
$347$	8.41384	+	31.4009i	0.451679	+	1.68569i	−0.245994	+	0.969271i	$0.579114\pi$
$348$	5.12947	+	1.37444i	0.274969	+	0.0736776i
$349$	6.57321	+	1.76129i	0.351856	+	0.0942795i	0.430418	−	0.902630i	$-0.358366\pi$
$349$	6.57321	+	1.76129i	0.351856	+	0.0942795i	−0.0785620	+	0.996909i	$0.525033\pi$
$350$		0			0
$351$	−12.0018	+	8.67315i	−0.640609	+	0.462938i
$352$	−17.9821	+	17.9821i	−0.958448	+	0.958448i
$353$	13.6631	+	23.6652i	0.727213	+	1.25957i	0.958057	+	0.286579i	$0.0925182\pi$
$353$	13.6631	+	23.6652i	0.727213	+	1.25957i	−0.230843	+	0.972991i	$0.574148\pi$
$354$	38.2248	−	22.0691i	2.03163	−	1.17296i
$355$		0			0
$356$	4.50714	−	4.50714i	0.238878	−	0.238878i
$357$	12.3050	+	7.10431i	0.651251	+	0.376000i
$358$	−3.47423	−	2.00585i	−0.183619	−	0.106012i
$359$	3.89871	−	3.89871i	0.205766	−	0.205766i	−0.596699	−	0.802465i	$-0.703521\pi$
$359$	3.89871	−	3.89871i	0.205766	−	0.205766i	0.802465	+	0.596699i	$0.203521\pi$
$360$		0			0
$361$	−16.2045	+	9.35567i	−0.852868	+	0.492404i
$362$	−8.78501	−	15.2161i	−0.461730	−	0.799740i
$363$	−5.61766	+	5.61766i	−0.294851	+	0.294851i
$364$	6.15423	+	16.1553i	0.322569	+	0.846769i
$365$		0			0
$366$	−10.1204	−	2.71176i	−0.529003	−	0.141746i
$367$	17.4595	+	4.67826i	0.911378	+	0.244203i	0.683896	−	0.729579i	$-0.260284\pi$
$367$	17.4595	+	4.67826i	0.911378	+	0.244203i	0.227482	+	0.973782i	$0.426951\pi$
$368$	−0.384089	−	1.43344i	−0.0200220	−	0.0747232i
$369$	−0.441373	−	0.441373i	−0.0229770	−	0.0229770i
$370$		0			0
$371$	−15.2885	+	4.09653i	−0.793738	+	0.212681i
$372$	−15.7046			−0.814248
$373$	14.9855	−	4.01536i	0.775921	−	0.207907i	0.150936	−	0.988544i	$-0.451771\pi$
$373$	14.9855	−	4.01536i	0.775921	−	0.207907i	0.624986	+	0.780636i	$0.285105\pi$
$374$	−7.18771	−	12.4495i	−0.371668	−	0.643747i
$375$		0			0
$376$		−	11.5232i		−	0.594266i
$377$	6.66353	−	2.53841i	0.343189	−	0.130735i
$378$	−18.8238	−	18.8238i	−0.968191	−	0.968191i
$379$	−5.53029	+	20.6393i	−0.284072	+	1.06017i	0.665443	+	0.746449i	$0.268243\pi$
$379$	−5.53029	+	20.6393i	−0.284072	+	1.06017i	−0.949515	+	0.313722i	$0.898424\pi$
$380$		0			0
$381$	−2.20733	−	1.27440i	−0.113085	−	0.0652897i
$382$			6.83407i			0.349661i
$383$	9.70362	−	16.8072i	0.495832	−	0.858806i	−0.504157	−	0.863612i	$-0.668197\pi$
$383$	9.70362	−	16.8072i	0.495832	−	0.858806i	0.999988	+	0.00480620i	$0.00152987\pi$
$384$	4.59660	+	17.1547i	0.234569	+	0.875424i
$385$		0			0
$386$	−0.260170	+	0.450628i	−0.0132423	+	0.0229364i
$387$	2.11590	−	7.89664i	0.107557	−	0.401409i
$388$	−20.9155	+	12.0756i	−1.06182	+	0.613045i
$389$	−14.8591			−0.753387			−0.376693	−	0.926338i	$-0.622939\pi$
$389$	−14.8591			−0.753387			−0.376693	+	0.926338i	$0.622939\pi$
$390$		0			0
$391$	0.616816			0.0311937
$392$	5.65266	−	3.26357i	0.285503	−	0.164835i
$393$	−2.86960	+	10.7095i	−0.144752	+	0.540222i
$394$	23.6731	−	41.0030i	1.19263	−	2.06570i
$395$		0			0
$396$	−1.26036	−	4.70374i	−0.0633357	−	0.236372i
$397$	2.63889	−	4.57070i	0.132442	−	0.229397i	−0.792175	−	0.610294i	$-0.791051\pi$
$397$	2.63889	−	4.57070i	0.132442	−	0.229397i	0.924617	+	0.380897i	$0.124385\pi$
$398$			10.5365i			0.528145i
$399$	−3.26338	−	1.88411i	−0.163373	−	0.0943236i
$400$		0			0
$401$	7.21557	−	26.9289i	0.360328	−	1.34476i	−0.513317	−	0.858199i	$-0.671583\pi$
$401$	7.21557	−	26.9289i	0.360328	−	1.34476i	0.873645	−	0.486564i	$-0.161750\pi$
$402$	−5.87772	−	5.87772i	−0.293154	−	0.293154i
$403$	−17.0918	+	12.3515i	−0.851404	+	0.615270i
$404$			6.16996i			0.306967i
$405$		0			0
$406$	6.40965	+	11.1018i	0.318106	+	0.550975i
$407$	−20.2737	+	5.43231i	−1.00493	+	0.269270i
$408$	−4.74421			−0.234873
$409$	2.54532	−	0.682016i	0.125858	−	0.0337235i	−0.195340	−	0.980736i	$-0.562581\pi$
$409$	2.54532	−	0.682016i	0.125858	−	0.0337235i	0.321198	+	0.947012i	$0.395914\pi$
$410$		0			0
$411$	20.0260	+	20.0260i	0.987810	+	0.987810i
$412$	4.85646	+	18.1246i	0.239261	+	0.892933i
$413$	41.5640	+	11.1370i	2.04523	+	0.548018i
$414$	0.499753	+	0.133908i	0.0245615	+	0.00658124i
$415$		0			0
$416$	−18.3552	−	14.9414i	−0.899938	−	0.732563i
$417$	−24.4073	+	24.4073i	−1.19523	+	1.19523i
$418$	1.90623	+	3.30169i	0.0932368	+	0.161491i
$419$	17.0348	−	9.83506i	0.832205	−	0.480474i	−0.0224018	−	0.999749i	$-0.507131\pi$
$419$	17.0348	−	9.83506i	0.832205	−	0.480474i	0.854607	+	0.519275i	$0.173798\pi$
$420$		0			0
$421$	10.4427	−	10.4427i	0.508948	−	0.508948i	−0.405256	−	0.914203i	$-0.632817\pi$
$421$	10.4427	−	10.4427i	0.508948	−	0.508948i	0.914203	+	0.405256i	$0.132817\pi$
$422$	5.11948	+	2.95573i	0.249212	+	0.143883i
$423$	7.83526	+	4.52369i	0.380964	+	0.219949i
$424$	3.73695	−	3.73695i	0.181482	−	0.181482i
$425$		0			0
$426$	−14.5278	+	8.38762i	−0.703874	+	0.406382i
$427$	−5.10721	−	8.84594i	−0.247155	−	0.428085i
$428$	−6.77359	+	6.77359i	−0.327414	+	0.327414i
$429$	−21.4693	−	17.4763i	−1.03655	−	0.843765i
$430$		0			0
$431$	16.5486	+	4.43419i	0.797119	+	0.213587i	0.634319	−	0.773072i	$-0.281281\pi$
$431$	16.5486	+	4.43419i	0.797119	+	0.213587i	0.162800	+	0.986659i	$0.447947\pi$
$432$	19.3352	+	5.18086i	0.930267	+	0.249264i
$433$	−2.90826	−	10.8538i	−0.139762	−	0.521599i	−0.999933	−	0.0115927i	$-0.996310\pi$
$433$	−2.90826	−	10.8538i	−0.139762	−	0.521599i	0.860171	−	0.510006i	$-0.170357\pi$
$434$	−26.8070	−	26.8070i	−1.28678	−	1.28678i
$435$		0			0
$436$	−18.3096	+	4.90604i	−0.876870	+	0.234957i
$437$	−0.163584			−0.00782528
$438$	−51.7347	+	13.8623i	−2.47198	+	0.662365i
$439$	2.12218	+	3.67572i	0.101286	+	0.175432i	0.912215	−	0.409712i	$-0.134371\pi$
$439$	2.12218	+	3.67572i	0.101286	+	0.175432i	−0.810929	+	0.585145i	$0.801038\pi$
$440$		0			0
$441$			5.12473i			0.244035i
$442$	10.8438	−	7.83631i	0.515787	−	0.372735i
$443$	−15.1569	−	15.1569i	−0.720126	−	0.720126i	0.248505	−	0.968631i	$-0.420061\pi$
$443$	−15.1569	−	15.1569i	−0.720126	−	0.720126i	−0.968631	+	0.248505i	$0.920061\pi$
$444$	3.76518	−	14.0518i	0.178687	−	0.666870i
$445$		0			0
$446$	−11.7623	−	6.79099i	−0.556963	−	0.321563i
$447$		−	26.0221i		−	1.23080i
$448$	4.02575	−	6.97281i	0.190199	−	0.329434i
$449$	−3.76524	−	14.0521i	−0.177693	−	0.663158i	−0.996077	−	0.0884873i	$-0.971797\pi$
$449$	−3.76524	−	14.0521i	−0.177693	−	0.663158i	0.818385	−	0.574671i	$-0.194870\pi$
$450$		0			0
$451$	−1.30327	+	2.25732i	−0.0613684	+	0.106293i
$452$	0.803904	−	3.00021i	0.0378124	−	0.141118i
$453$	1.85732	−	1.07233i	0.0872646	−	0.0503822i
$454$	7.14758			0.335453
$455$		0			0
$456$	1.25820			0.0589205
$457$	26.2365	−	15.1476i	1.22729	−	0.708576i	0.260828	−	0.965385i	$-0.416004\pi$
$457$	26.2365	−	15.1476i	1.22729	−	0.708576i	0.966462	+	0.256809i	$0.0826711\pi$
$458$	8.30966	−	31.0121i	0.388285	−	1.44910i
$459$	−4.16003	+	7.20538i	−0.194173	+	0.336318i
$460$		0			0
$461$	1.79565	+	6.70146i	0.0836318	+	0.312118i	0.995052	−	0.0993596i	$-0.0316794\pi$
$461$	1.79565	+	6.70146i	0.0836318	+	0.312118i	−0.911420	+	0.411478i	$0.865013\pi$
$462$	24.8840	−	43.1003i	1.15771	−	2.00521i
$463$		−	31.4463i		−	1.46143i	−0.682680	−	0.730717i	$-0.739186\pi$
$463$		−	31.4463i		−	1.46143i	0.682680	−	0.730717i	$-0.260814\pi$
$464$	−8.34794	−	4.81968i	−0.387543	−	0.223748i
$465$		0			0
$466$	−1.93727	+	7.22999i	−0.0897423	+	0.334923i
$467$	3.69622	+	3.69622i	0.171041	+	0.171041i	0.787436	−	0.616396i	$-0.211408\pi$
$467$	3.69622	+	3.69622i	0.171041	+	0.171041i	−0.616396	+	0.787436i	$0.711408\pi$
$468$	4.23522	−	1.61337i	0.195773	−	0.0745780i
$469$		−	8.10369i		−	0.374194i
$470$		0			0
$471$	4.25293	+	7.36630i	0.195965	+	0.339421i
$472$	−13.8781	+	3.71862i	−0.638790	+	0.171163i
$473$	−34.1382			−1.56968
$474$	−5.60024	+	1.50058i	−0.257227	+	0.0689239i
$475$		0			0
$476$	6.86855	+	6.86855i	0.314820	+	0.314820i
$477$	1.07393	+	4.00797i	0.0491720	+	0.183512i
$478$	−22.4509	−	6.01571i	−1.02688	−	0.275152i
$479$	−18.6940	−	5.00904i	−0.854150	−	0.228869i	−0.194928	−	0.980818i	$-0.562447\pi$
$479$	−18.6940	−	5.00904i	−0.854150	−	0.228869i	−0.659222	+	0.751949i	$0.729114\pi$
$480$		0			0
$481$	−6.95380	−	18.2543i	−0.317066	−	0.832323i
$482$	22.7270	−	22.7270i	1.03518	−	1.03518i
$483$	1.06771	+	1.84934i	0.0485827	+	0.0841477i
$484$	−4.70359	+	2.71562i	−0.213800	+	0.123437i
$485$		0			0
$486$	−12.0788	+	12.0788i	−0.547907	+	0.547907i
$487$	20.2327	+	11.6813i	0.916830	+	0.529332i	0.882622	−	0.470083i	$-0.155776\pi$
$487$	20.2327	+	11.6813i	0.916830	+	0.529332i	0.0342077	+	0.999415i	$0.489109\pi$
$488$	2.95363	+	1.70528i	0.133704	+	0.0771943i
$489$	3.17214	−	3.17214i	0.143449	−	0.143449i
$490$		0			0
$491$	18.4624	−	10.6593i	0.833198	−	0.481047i	−0.0217482	−	0.999763i	$-0.506923\pi$
$491$	18.4624	−	10.6593i	0.833198	−	0.481047i	0.854946	+	0.518716i	$0.173590\pi$
$492$	−0.903303	−	1.56457i	−0.0407241	−	0.0705362i
$493$	2.83305	−	2.83305i	0.127594	−	0.127594i
$494$	−2.87585	+	2.07824i	−0.129391	+	0.0935046i
$495$		0			0
$496$	27.5354	+	7.37809i	1.23638	+	0.331286i
$497$	−15.7969	−	4.23276i	−0.708587	−	0.189865i
$498$	−7.11538	−	26.5549i	−0.318848	−	1.18996i
$499$	23.0389	+	23.0389i	1.03136	+	1.03136i	0.999492	+	0.0318687i	$0.0101459\pi$
$499$	23.0389	+	23.0389i	1.03136	+	1.03136i	0.0318687	+	0.999492i	$0.489854\pi$
$500$		0			0
$501$	−1.18606	+	0.317803i	−0.0529891	+	0.0141984i
$502$	39.8727			1.77960
$503$	0.634433	−	0.169996i	0.0282879	−	0.00757973i	−0.244647	−	0.969612i	$-0.578672\pi$
$503$	0.634433	−	0.169996i	0.0282879	−	0.00757973i	0.272935	+	0.962032i	$0.412006\pi$
$504$	−1.93976	−	3.35977i	−0.0864039	−	0.149656i
$505$		0			0
$506$		−	2.16050i		−	0.0960458i
$507$	14.1422	−	21.5357i	0.628075	−	0.956436i
$508$	−1.23211	−	1.23211i	−0.0546662	−	0.0546662i
$509$	8.29035	−	30.9400i	0.367463	−	1.37139i	−0.496587	−	0.867987i	$-0.665414\pi$
$509$	8.29035	−	30.9400i	0.367463	−	1.37139i	0.864050	−	0.503405i	$-0.167920\pi$
$510$		0			0
$511$	−45.2197	−	26.1076i	−2.00040	−	1.15493i
$512$			20.4758i			0.904912i
$513$	1.10327	−	1.91092i	0.0487105	−	0.0843690i
$514$	6.07422	+	22.6693i	0.267923	+	0.999901i
$515$		0			0
$516$	11.8307	−	20.4914i	0.520818	−	0.902084i
$517$	9.77825	−	36.4929i	0.430047	−	1.60496i
$518$	30.4127	−	17.5588i	1.33626	−	0.771489i
$519$	13.1232			0.576046
$520$		0			0
$521$	−23.4746			−1.02844			−0.514220	−	0.857658i	$-0.671919\pi$
$521$	−23.4746			−1.02844			−0.514220	+	0.857658i	$0.671919\pi$
$522$	2.91042	−	1.68033i	0.127386	−	0.0735461i
$523$	−6.40400	+	23.9001i	−0.280027	+	1.04508i	0.672370	+	0.740216i	$0.265277\pi$
$523$	−6.40400	+	23.9001i	−0.280027	+	1.04508i	−0.952397	+	0.304861i	$0.901390\pi$
$524$	−3.78986	+	6.56423i	−0.165561	+	0.286760i
$525$		0			0
$526$	7.82436	+	29.2009i	0.341158	+	1.27322i
$527$	−5.92431	+	10.2612i	−0.258067	+	0.446985i
$528$			37.4226i			1.62861i
$529$	−19.8383	−	11.4536i	−0.862535	−	0.497985i
$530$		0			0
$531$	2.91964	−	10.8963i	0.126702	−	0.472857i
$532$	−1.82159	−	1.82159i	−0.0789759	−	0.0789759i
$533$	−2.21360	−	0.992330i	−0.0958817	−	0.0429826i
$534$		−	17.0776i		−	0.739019i
$535$		0			0
$536$	1.35290	+	2.34329i	0.0584363	+	0.101215i
$537$	−4.19281	+	1.12346i	−0.180933	+	0.0484809i
$538$	59.1745			2.55119
$539$	20.6708	−	5.53871i	0.890353	−	0.238569i
$540$		0			0
$541$	−27.6908	−	27.6908i	−1.19052	−	1.19052i	−0.976922	−	0.213597i	$-0.931482\pi$
$541$	−27.6908	−	27.6908i	−1.19052	−	1.19052i	−0.213597	−	0.976922i	$-0.568518\pi$
$542$	−8.28297	−	30.9125i	−0.355784	−	1.32780i
$543$	−18.3632	−	4.92042i	−0.788042	−	0.211155i
$544$	−12.8452	−	3.44185i	−0.550731	−	0.147568i
$545$		0			0
$546$	42.2655	+	18.9471i	1.80880	+	0.810861i
$547$	−6.53914	+	6.53914i	−0.279593	+	0.279593i	−0.832947	−	0.553353i	$-0.813348\pi$
$547$	−6.53914	+	6.53914i	−0.279593	+	0.279593i	0.553353	+	0.832947i	$0.313348\pi$
$548$	9.68071	+	16.7675i	0.413540	+	0.716272i
$549$	−2.31902	+	1.33889i	−0.0989733	+	0.0571422i
$550$		0			0
$551$	−0.751344	+	0.751344i	−0.0320083	+	0.0320083i
$552$	−0.617486	−	0.356506i	−0.0262820	−	0.0151739i
$553$	−4.89500	−	2.82613i	−0.208156	−	0.120179i
$554$	3.98180	−	3.98180i	0.169170	−	0.169170i
$555$		0			0
$556$	−20.4359	+	11.7987i	−0.866676	+	0.500375i
$557$	8.12429	+	14.0717i	0.344237	+	0.596237i	0.985215	−	0.171323i	$-0.0548042\pi$
$557$	8.12429	+	14.0717i	0.344237	+	0.596237i	−0.640978	+	0.767560i	$0.721471\pi$
$558$	−7.02763	+	7.02763i	−0.297503	+	0.297503i
$559$	−3.24046	−	31.6061i	−0.137057	−	1.33679i
$560$		0			0
$561$	−15.0244	−	4.02578i	−0.634332	−	0.169969i
$562$	−46.7277	−	12.5206i	−1.97109	−	0.528151i
$563$	−8.41827	−	31.4174i	−0.354788	−	1.32409i	−0.880751	−	0.473579i	$-0.842962\pi$
$563$	−8.41827	−	31.4174i	−0.354788	−	1.32409i	0.525964	−	0.850507i	$-0.323705\pi$
$564$	18.5161	+	18.5161i	0.779670	+	0.779670i
$565$		0			0
$566$	27.1382	−	7.27167i	1.14071	−	0.305651i
$567$	−38.6538			−1.62331
$568$	5.27453	−	1.41331i	0.221314	−	0.0593010i
$569$	16.4164	+	28.4341i	0.688212	+	1.19202i	0.972416	+	0.233255i	$0.0749376\pi$
$569$	16.4164	+	28.4341i	0.688212	+	1.19202i	−0.284203	+	0.958764i	$0.591729\pi$
$570$		0			0
$571$			31.7967i			1.33065i	0.746554	+	0.665325i	$0.231707\pi$
$571$			31.7967i			1.33065i	−0.746554	+	0.665325i	$0.768293\pi$
$572$	−11.0849	−	15.3392i	−0.463484	−	0.641364i
$573$	5.22875	+	5.22875i	0.218434	+	0.218434i
$574$	1.12874	−	4.21253i	0.0471129	−	0.175828i
$575$		0			0
$576$	−1.82796	−	1.05538i	−0.0761652	−	0.0439740i
$577$			39.9389i			1.66268i	0.555767	+	0.831338i	$0.312425\pi$
$577$			39.9389i			1.66268i	−0.555767	+	0.831338i	$0.687575\pi$
$578$	−11.8102	+	20.4559i	−0.491241	+	0.850854i
$579$	0.145719	+	0.543832i	0.00605589	+	0.0226009i
$580$		0			0
$581$	13.4008	−	23.2109i	0.555959	−	0.962949i
$582$	−16.7473	+	62.5017i	−0.694197	+	2.59078i
$583$	15.0056	−	8.66348i	0.621468	−	0.358805i
$584$	17.4345			0.721444
$585$		0			0
$586$	−19.0063			−0.785143
$587$	−16.1561	+	9.32773i	−0.666834	+	0.384997i	−0.794876	−	0.606772i	$-0.792464\pi$
$587$	−16.1561	+	9.32773i	−0.666834	+	0.384997i	0.128042	+	0.991769i	$0.459131\pi$
$588$	−3.83892	+	14.3271i	−0.158315	+	0.590838i
$589$	1.57117	−	2.72135i	0.0647389	−	0.112131i
$590$		0			0
$591$	−13.2591	−	49.4837i	−0.545407	−	2.03549i
$592$	−13.2032	+	22.8686i	−0.542647	+	0.939893i
$593$		−	8.65172i		−	0.355284i	−0.984095	−	0.177642i	$-0.943153\pi$
$593$		−	8.65172i		−	0.355284i	0.984095	−	0.177642i	$-0.0568468\pi$
$594$	25.2380	+	14.5712i	1.03553	+	0.597862i
$595$		0			0
$596$	4.60433	−	17.1836i	0.188601	−	0.703867i
$597$	8.06145	+	8.06145i	0.329933	+	0.329933i
$598$	2.00025	−	0.205079i	0.0817962	−	0.00838628i
$599$			35.1779i			1.43733i	0.695356	+	0.718666i	$0.255247\pi$
$599$			35.1779i			1.43733i	−0.695356	+	0.718666i	$0.744753\pi$
$600$		0			0
$601$	20.0384	+	34.7076i	0.817385	+	1.41575i	0.907602	+	0.419831i	$0.137911\pi$
$601$	20.0384	+	34.7076i	0.817385	+	1.41575i	−0.0902170	+	0.995922i	$0.528756\pi$
$602$	55.1722	−	14.7834i	2.24865	−	0.602524i
$603$	−2.12443			−0.0865136
$604$	1.41621	−	0.379473i	0.0576249	−	0.0154405i
$605$		0			0
$606$	11.6890	+	11.6890i	0.474834	+	0.474834i
$607$	−11.1449	−	41.5934i	−0.452358	−	1.68822i	−0.695742	−	0.718292i	$-0.744924\pi$
$607$	−11.1449	−	41.5934i	−0.452358	−	1.68822i	0.243384	−	0.969930i	$-0.421742\pi$
$608$	3.40662	+	0.912802i	0.138157	+	0.0370190i
$609$	13.3981	+	3.59000i	0.542917	+	0.145474i
$610$		0			0
$611$	34.7143	+	5.58899i	1.40439	+	0.226106i
$612$	1.80063	−	1.80063i	0.0727863	−	0.0727863i
$613$	−10.1397	−	17.5625i	−0.409540	−	0.709344i	0.585298	−	0.810818i	$-0.300978\pi$
$613$	−10.1397	−	17.5625i	−0.409540	−	0.709344i	−0.994838	+	0.101474i	$0.967644\pi$
$614$	−3.39352	+	1.95925i	−0.136952	+	0.0790690i
$615$		0			0
$616$	−11.4553	+	11.4553i	−0.461546	+	0.461546i
$617$	−7.50891	−	4.33527i	−0.302297	−	0.174531i	0.341177	−	0.939999i	$-0.389174\pi$
$617$	−7.50891	−	4.33527i	−0.302297	−	0.174531i	−0.643474	+	0.765468i	$0.722508\pi$
$618$	43.5376	+	25.1365i	1.75134	+	1.01114i
$619$	21.3034	−	21.3034i	0.856257	−	0.856257i	−0.134638	−	0.990895i	$-0.542987\pi$
$619$	21.3034	−	21.3034i	0.856257	−	0.856257i	0.990895	+	0.134638i	$0.0429871\pi$
$620$		0			0
$621$	−1.08290	+	0.625215i	−0.0434554	+	0.0250890i
$622$	3.49919	+	6.06077i	0.140305	+	0.243015i
$623$	11.7725	−	11.7725i	0.471657	−	0.471657i
$624$	−34.6468	+	3.55222i	−1.38698	+	0.142203i
$625$		0			0
$626$	−7.61954	−	2.04165i	−0.304538	−	0.0816007i
$627$	3.98458	+	1.06767i	0.159129	+	0.0426385i
$628$	1.50502	+	5.61682i	0.0600569	+	0.224136i
$629$	−7.76093	−	7.76093i	−0.309449	−	0.309449i
$630$		0			0
$631$	−27.4324	+	7.35050i	−1.09207	+	0.292619i	−0.759531	−	0.650472i	$-0.774571\pi$
$631$	−27.4324	+	7.35050i	−1.09207	+	0.292619i	−0.332537	+	0.943090i	$0.607905\pi$
$632$	1.88727			0.0750715
$633$	6.17835	−	1.65548i	0.245567	−	0.0657996i
$634$	−21.1670	−	36.6622i	−0.840647	−	1.45604i
$635$		0			0
$636$			12.0094i			0.476206i
$637$	7.09000	+	18.6118i	0.280916	+	0.737427i
$638$	−9.92320	−	9.92320i	−0.392863	−	0.392863i
$639$	−1.10965	+	4.14125i	−0.0438969	+	0.163825i
$640$		0			0
$641$	14.1756	+	8.18429i	0.559903	+	0.323260i	0.753107	−	0.657899i	$-0.228554\pi$
$641$	14.1756	+	8.18429i	0.559903	+	0.323260i	−0.193204	+	0.981159i	$0.561888\pi$
$642$			25.6652i			1.01292i
$643$	−20.5258	+	35.5518i	−0.809460	+	1.40203i	0.103779	+	0.994600i	$0.466907\pi$
$643$	−20.5258	+	35.5518i	−0.809460	+	1.40203i	−0.913239	+	0.407425i	$0.866427\pi$
$644$	0.377841	+	1.41012i	0.0148890	+	0.0555666i
$645$		0			0
$646$	−0.996819	+	1.72654i	−0.0392193	+	0.0679298i
$647$	−0.733807	+	2.73861i	−0.0288489	+	0.107666i	−0.978849	−	0.204584i	$-0.934416\pi$
$647$	−0.733807	+	2.73861i	−0.0288489	+	0.107666i	0.950000	+	0.312250i	$0.101083\pi$
$648$	11.1772	−	6.45318i	0.439083	−	0.253505i
$649$	−47.1059			−1.84907
$650$		0			0
$651$	−41.0201			−1.60771
$652$	2.65599	−	1.53344i	0.104017	−	0.0600540i
$653$	−0.324978	+	1.21283i	−0.0127174	+	0.0474619i	−0.971993	−	0.235010i	$-0.924488\pi$
$653$	−0.324978	+	1.21283i	−0.0127174	+	0.0474619i	0.959276	+	0.282472i	$0.0911544\pi$
$654$	−25.3930	+	43.9820i	−0.992947	+	1.71983i
$655$		0			0
$656$	0.848749	+	3.16758i	0.0331381	+	0.123673i
$657$	−6.84427	+	11.8546i	−0.267020	+	0.462493i
$658$			63.2122i			2.46427i
$659$	−8.09916	−	4.67605i	−0.315498	−	0.182153i	0.333886	−	0.942613i	$-0.391640\pi$
$659$	−8.09916	−	4.67605i	−0.315498	−	0.182153i	−0.649384	+	0.760460i	$0.724973\pi$
$660$		0			0
$661$	−6.64415	+	24.7963i	−0.258427	+	0.964464i	0.707724	+	0.706489i	$0.249722\pi$
$661$	−6.64415	+	24.7963i	−0.258427	+	0.964464i	−0.966152	+	0.257975i	$0.916945\pi$
$662$	2.58641	+	2.58641i	0.100524	+	0.100524i
$663$	2.30103	−	14.2922i	0.0893647	−	0.555061i
$664$			8.94896i			0.347287i
$665$		0			0
$666$	−4.60315	−	7.97288i	−0.178368	−	0.308943i
$667$	0.581628	−	0.155847i	0.0225207	−	0.00603441i
$668$	−0.839440			−0.0324789
$669$	−14.1952	+	3.80358i	−0.548817	+	0.147055i
$670$		0			0
$671$	7.90679	+	7.90679i	0.305238	+	0.305238i
$672$	−11.9157	−	44.4701i	−0.459660	−	1.71547i
$673$	−39.9267	−	10.6983i	−1.53906	−	0.412390i	−0.613098	−	0.790007i	$-0.710077\pi$
$673$	−39.9267	−	10.6983i	−1.53906	−	0.412390i	−0.925962	+	0.377617i	$0.876744\pi$
$674$	−15.3308	−	4.10787i	−0.590519	−	0.158229i
$675$		0			0
$676$	13.1493	−	11.7188i	0.505740	−	0.450721i
$677$	−15.5322	+	15.5322i	−0.596950	+	0.596950i	−0.939500	−	0.342549i	$-0.888710\pi$
$677$	−15.5322	+	15.5322i	−0.596950	+	0.596950i	0.342549	+	0.939500i	$0.388710\pi$
$678$	−4.16090	−	7.20690i	−0.159799	−	0.276779i
$679$	−54.6308	+	31.5411i	−2.09654	+	1.21044i
$680$		0			0
$681$	5.46862	−	5.46862i	0.209558	−	0.209558i
$682$	35.9415	+	20.7508i	1.37627	+	0.794591i
$683$	−5.76170	−	3.32652i	−0.220465	−	0.127286i	0.385700	−	0.922624i	$-0.373960\pi$
$683$	−5.76170	−	3.32652i	−0.220465	−	0.127286i	−0.606166	+	0.795338i	$0.707293\pi$
$684$	−0.477541	+	0.477541i	−0.0182592	+	0.0182592i
$685$		0			0
$686$	8.28646	−	4.78419i	0.316378	−	0.182661i
$687$	−17.3696	−	30.0851i	−0.662692	−	1.14782i
$688$	−30.3701	+	30.3701i	−1.15785	+	1.15785i
$689$	9.44525	+	13.0702i	0.359835	+	0.497936i
$690$		0			0
$691$	−36.3445	−	9.73848i	−1.38261	−	0.370469i	−0.510542	−	0.859853i	$-0.670555\pi$
$691$	−36.3445	−	9.73848i	−1.38261	−	0.370469i	−0.872069	+	0.489384i	$0.837222\pi$
$692$	8.66588	+	2.32201i	0.329427	+	0.0882698i
$693$	−3.29204	−	12.2861i	−0.125054	−	0.466709i
$694$	42.1038	+	42.1038i	1.59824	+	1.59824i
$695$		0			0
$696$	−4.47356	+	1.19869i	−0.169570	+	0.0454361i
$697$	−1.36302			−0.0516282
$698$	12.0397	−	3.22603i	0.455710	−	0.122107i
$699$	4.04946	+	7.01387i	0.153165	+	0.265289i
$700$		0			0
$701$		−	40.3398i		−	1.52361i	−0.647804	−	0.761807i	$-0.724312\pi$
$701$		−	40.3398i		−	1.52361i	0.647804	−	0.761807i	$-0.275688\pi$
$702$	−11.0947	+	24.7491i	−0.418744	+	0.934096i
$703$	2.05825	+	2.05825i	0.0776285	+	0.0776285i
$704$	−2.28126	+	8.51379i	−0.0859783	+	0.320875i
$705$		0			0
$706$	43.3459	+	25.0258i	1.63134	+	0.941857i
$707$			16.1158i			0.606097i
$708$	16.3247	−	28.2753i	0.613521	−	1.06265i
$709$	11.5415	+	43.0733i	0.433449	+	1.61765i	0.744752	+	0.667341i	$0.232568\pi$
$709$	11.5415	+	43.0733i	0.433449	+	1.61765i	−0.311304	+	0.950311i	$0.600766\pi$
$710$		0			0
$711$	−0.740887	+	1.28325i	−0.0277854	+	0.0481258i
$712$	−1.43878	+	5.36959i	−0.0539204	+	0.201234i
$713$	−1.54217	+	0.890371i	−0.0577546	+	0.0333447i
$714$	26.0250			0.973960
$715$		0			0
$716$	−2.96749			−0.110900
$717$	−21.7798	+	12.5746i	−0.813383	+	0.469607i
$718$	2.61379	−	9.75479i	0.0975457	−	0.364045i
$719$	13.7825	−	23.8720i	0.514001	−	0.890276i	−0.485867	−	0.874033i	$-0.661496\pi$
$719$	13.7825	−	23.8720i	0.514001	−	0.890276i	0.999868	−	0.0162430i	$-0.00517055\pi$
$720$		0			0
$721$	12.6850	+	47.3409i	0.472413	+	1.76307i
$722$	−17.1361	+	29.6807i	−0.637741	+	1.10460i
$723$		−	34.7768i		−	1.29336i
$724$	−11.2555	−	6.49836i	−0.418307	−	0.241510i
$725$		0			0
$726$	−3.76622	+	14.0557i	−0.139777	+	0.521656i
$727$	29.4624	+	29.4624i	1.09270	+	1.09270i	0.995240	+	0.0974593i	$0.0310716\pi$
$727$	29.4624	+	29.4624i	1.09270	+	1.09270i	0.0974593	+	0.995240i	$0.468928\pi$
$728$	−11.6930	−	9.51825i	−0.433370	−	0.352770i
$729$		−	14.2845i		−	0.529057i
$730$		0			0
$731$	−8.92588	−	15.4601i	−0.330135	−	0.571811i
$732$	−7.48617	+	2.00591i	−0.276697	+	0.0741407i
$733$	23.3958			0.864144			0.432072	−	0.901839i	$-0.357783\pi$
$733$	23.3958			0.864144			0.432072	+	0.901839i	$0.357783\pi$
$734$	31.9794	−	8.56885i	1.18038	−	0.316282i
$735$		0			0
$736$	−1.41323	−	1.41323i	−0.0520924	−	0.0520924i
$737$	2.29605	+	8.56897i	0.0845761	+	0.315642i
$738$	−1.10434	−	0.295907i	−0.0406513	−	0.0108925i
$739$	15.5120	+	4.15644i	0.570620	+	0.152897i	0.532581	−	0.846379i	$-0.321222\pi$
$739$	15.5120	+	4.15644i	0.570620	+	0.152897i	0.0380389	+	0.999276i	$0.487889\pi$
$740$		0			0
$741$	−0.610250	+	3.79038i	−0.0224181	+	0.139243i
$742$	−20.4995	+	20.4995i	−0.752561	+	0.752561i
$743$	26.1400	+	45.2759i	0.958985	+	1.66101i	0.724973	+	0.688777i	$0.241852\pi$
$743$	26.1400	+	45.2759i	0.958985	+	1.66101i	0.234011	+	0.972234i	$0.424815\pi$
$744$	11.8615	−	6.84824i	0.434864	−	0.251069i
$745$		0			0
$746$	20.0933	−	20.0933i	0.735669	−	0.735669i
$747$	−6.08487	−	3.51310i	−0.222634	−	0.128538i
$748$	−9.20901	−	5.31682i	−0.336715	−	0.194402i
$749$	−17.6925	+	17.6925i	−0.646468	+	0.646468i
$750$		0			0
$751$	23.7599	−	13.7178i	0.867010	−	0.500569i	0.000656703	−	1.00000i	$-0.499791\pi$
$751$	23.7599	−	13.7178i	0.867010	−	0.500569i	0.866354	+	0.499431i	$0.166458\pi$
$752$	−23.7659	−	41.1638i	−0.866655	−	1.50109i
$753$	30.5066	−	30.5066i	1.11172	−	1.11172i
$754$	8.24524	−	10.1291i	0.300274	−	0.368880i
$755$		0			0
$756$	−19.0207	−	5.09659i	−0.691777	−	0.185361i
$757$	2.32441	+	0.622824i	0.0844821	+	0.0226369i	0.300813	−	0.953683i	$-0.402742\pi$
$757$	2.32441	+	0.622824i	0.0844821	+	0.0226369i	−0.216330	+	0.976320i	$0.569409\pi$
$758$	10.1295	+	37.8037i	0.367919	+	1.37309i
$759$	−1.65300	−	1.65300i	−0.0600000	−	0.0600000i
$760$		0			0
$761$	2.35997	−	0.632352i	0.0855488	−	0.0229227i	−0.215791	−	0.976440i	$-0.569233\pi$
$761$	2.35997	−	0.632352i	0.0855488	−	0.0229227i	0.301340	+	0.953517i	$0.402566\pi$
$762$	−4.66848			−0.169121
$763$	−47.8242	+	12.8144i	−1.73135	+	0.463914i
$764$	2.52761	+	4.37796i	0.0914459	+	0.158389i
$765$		0			0
$766$		−	35.5469i		−	1.28436i
$767$	−4.47139	−	43.6120i	−0.161452	−	1.57474i
$768$	29.3786	+	29.3786i	1.06011	+	1.06011i
$769$	3.50862	−	13.0944i	0.126524	−	0.472195i	−0.873365	−	0.487066i	$-0.838067\pi$
$769$	3.50862	−	13.0944i	0.126524	−	0.472195i	0.999889	+	0.0148712i	$0.00473383\pi$
$770$		0			0
$771$	21.9917	+	12.6969i	0.792011	+	0.457268i
$772$			0.384901i			0.0138529i
$773$	11.2222	−	19.4375i	0.403636	−	0.699118i	−0.590525	−	0.807019i	$-0.701079\pi$
$773$	11.2222	−	19.4375i	0.403636	−	0.699118i	0.994162	+	0.107901i	$0.0344128\pi$
$774$	−3.87555	−	14.4637i	−0.139304	−	0.519888i
$775$		0			0
$776$	10.5315	−	18.2410i	0.378058	−	0.654815i
$777$	9.83454	−	36.7030i	0.352812	−	1.31671i
$778$	−23.5701	+	13.6082i	−0.845030	+	0.487878i
$779$	0.361484			0.0129515
$780$		0			0
$781$	17.9032			0.640626
$782$	0.978419	−	0.564890i	0.0349882	−	0.0202004i
$783$	−2.10217	+	7.84541i	−0.0751255	+	0.280372i
$784$	13.4618	−	23.3165i	0.480778	−	0.832732i
$785$		0			0
$786$	5.25605	+	19.6158i	0.187477	+	0.699674i
$787$	−6.74791	+	11.6877i	−0.240537	+	0.416622i	−0.960867	−	0.277009i	$-0.910657\pi$
$787$	−6.74791	+	11.6877i	−0.240537	+	0.416622i	0.720330	+	0.693631i	$0.243990\pi$
$788$		−	35.0224i		−	1.24762i
$789$	28.3280	+	16.3552i	1.00850	+	0.582260i
$790$		0			0
$791$	2.09978	−	7.83647i	0.0746594	−	0.278633i
$792$	3.00307	+	3.00307i	0.106709	+	0.106709i
$793$	−6.56980	+	8.07086i	−0.233300	+	0.286605i
$794$		−	9.66696i		−	0.343068i
$795$		0			0
$796$	3.89696	+	6.74974i	0.138124	+	0.239238i
$797$	6.06076	−	1.62398i	0.214683	−	0.0575242i	−0.149874	−	0.988705i	$-0.547887\pi$
$797$	6.06076	−	1.62398i	0.214683	−	0.0575242i	0.364558	+	0.931181i	$0.381220\pi$
$798$	−6.90201			−0.244328
$799$	19.0831	−	5.11330i	0.675112	−	0.180896i
$800$		0			0
$801$	−3.08625	−	3.08625i	−0.109047	−	0.109047i
$802$	−13.2163	−	49.3238i	−0.466683	−	1.74168i
$803$	55.2132	+	14.7943i	1.94843	+	0.522081i
$804$	−5.93922	−	1.59141i	−0.209460	−	0.0561247i
$805$		0			0
$806$	−15.8001	+	35.2454i	−0.556534	+	1.24146i
$807$	45.2744	−	45.2744i	1.59374	−	1.59374i
$808$	−2.69050	−	4.66009i	−0.0946516	−	0.163941i
$809$	−18.6872	+	10.7890i	−0.657006	+	0.379322i	−0.791135	−	0.611641i	$-0.790510\pi$
$809$	−18.6872	+	10.7890i	−0.657006	+	0.379322i	0.134130	+	0.990964i	$0.457176\pi$
$810$		0			0
$811$	22.5473	−	22.5473i	0.791743	−	0.791743i	−0.190035	−	0.981777i	$-0.560860\pi$
$811$	22.5473	−	22.5473i	0.791743	−	0.791743i	0.981777	+	0.190035i	$0.0608601\pi$
$812$	8.21215	+	4.74129i	0.288190	+	0.166387i
$813$	−29.9885	−	17.3138i	−1.05174	−	0.607223i
$814$	−27.1839	+	27.1839i	−0.952795	+	0.952795i
$815$		0			0
$816$	−16.9475	+	9.78462i	−0.593280	+	0.342530i
$817$	2.36721	+	4.10012i	0.0828180	+	0.143445i
$818$	3.41289	−	3.41289i	0.119329	−	0.119329i
$819$	11.0623	−	4.21408i	0.386547	−	0.147252i
$820$		0			0
$821$	−17.3216	−	4.64130i	−0.604526	−	0.161982i	−0.0564427	−	0.998406i	$-0.517976\pi$
$821$	−17.3216	−	4.64130i	−0.604526	−	0.161982i	−0.548084	+	0.836423i	$0.684642\pi$
$822$	50.1062	+	13.4259i	1.74765	+	0.468282i
$823$	−0.298185	−	1.11284i	−0.0103941	−	0.0387913i	0.960534	−	0.278162i	$-0.0897254\pi$
$823$	−0.298185	−	1.11284i	−0.0103941	−	0.0387913i	−0.970928	+	0.239371i	$0.923059\pi$
$824$	−11.5715	−	11.5715i	−0.403112	−	0.403112i
$825$		0			0
$826$	76.1300	−	20.3990i	2.64890	−	0.709771i
$827$	4.45029			0.154752			0.0773759	−	0.997002i	$-0.475346\pi$
$827$	4.45029			0.154752			0.0773759	+	0.997002i	$0.475346\pi$
$828$	0.369672	−	0.0990534i	0.0128470	−	0.00344234i
$829$	−14.5637	−	25.2251i	−0.505819	−	0.876103i	−0.999977	−	0.00673181i	$-0.997857\pi$
$829$	−14.5637	−	25.2251i	−0.505819	−	0.876103i	0.494159	−	0.869372i	$-0.335476\pi$
$830$		0			0
$831$		−	6.09295i		−	0.211362i
$832$	−8.09884	−	1.30391i	−0.280777	−	0.0452050i
$833$	7.91294	+	7.91294i	0.274167	+	0.274167i
$834$	−16.3633	+	61.0685i	−0.566613	+	2.11463i
$835$		0			0
$836$	2.44229	+	1.41006i	0.0844685	+	0.0487679i
$837$		−	24.0199i		−	0.830249i
$838$	18.0142	−	31.2015i	0.622291	−	1.07784i
$839$	−8.36719	−	31.2268i	−0.288867	−	1.07807i	−0.945967	−	0.324264i	$-0.894883\pi$
$839$	−8.36719	−	31.2268i	−0.288867	−	1.07807i	0.657099	−	0.753804i	$-0.271783\pi$
$840$		0			0
$841$	−12.5444	+	21.7275i	−0.432565	+	0.749224i
$842$	7.00106	−	26.1283i	0.241273	−	0.900441i
$843$	−45.3309	+	26.1718i	−1.56128	+	0.901405i
$844$	4.37277			0.150517
$845$		0			0
$846$	16.5715			0.569739
$847$	−12.2857	+	7.09313i	−0.422140	+	0.243723i
$848$	5.64207	−	21.0565i	0.193750	−	0.723083i
$849$	15.1999	−	26.3270i	0.521660	−	0.903541i
$850$		0			0
$851$	−0.426931	−	1.59333i	−0.0146350	−	0.0546186i
$852$	−6.20441	+	10.7464i	−0.212560	+	0.368164i
$853$		−	9.24230i		−	0.316450i	−0.987403	−	0.158225i	$-0.949423\pi$
$853$		−	9.24230i		−	0.316450i	0.987403	−	0.158225i	$-0.0505772\pi$
$854$	−16.2025	−	9.35453i	−0.554439	−	0.320105i
$855$		0			0
$856$	2.16228	−	8.06972i	0.0739051	−	0.275817i
$857$	−37.7913	−	37.7913i	−1.29093	−	1.29093i	−0.934214	−	0.356713i	$-0.883897\pi$
$857$	−37.7913	−	37.7913i	−1.29093	−	1.29093i	−0.356713	−	0.934214i	$-0.616103\pi$
$858$	−50.0606	−	8.05973i	−1.70904	−	0.275155i
$859$		−	6.16263i		−	0.210266i	−0.994458	−	0.105133i	$-0.966473\pi$
$859$		−	6.16263i		−	0.210266i	0.994458	−	0.105133i	$-0.0335269\pi$
$860$		0			0
$861$	−2.35941	−	4.08661i	−0.0804083	−	0.139271i
$862$	30.3110	−	8.12181i	1.03240	−	0.276630i
$863$	33.7740			1.14968			0.574840	−	0.818266i	$-0.305064\pi$
$863$	33.7740			1.14968			0.574840	+	0.818266i	$0.305064\pi$
$864$	26.0401	−	6.97742i	0.885902	−	0.237377i
$865$		0			0
$866$	−14.5532	−	14.5532i	−0.494539	−	0.494539i
$867$	6.61482	+	24.6868i	0.224651	+	0.838409i
$868$	−27.0875	−	7.25808i	−0.919410	−	0.246355i
$869$	5.97678	+	1.60147i	0.202748	+	0.0543263i
$870$		0			0
$871$	−7.71545	+	2.93913i	−0.261428	+	0.0995886i
$872$	11.6896	−	11.6896i	0.395861	−	0.395861i
$873$	8.26870	+	14.3218i	0.279853	+	0.484720i
$874$	−0.259484	+	0.149813i	−0.00877716	+	0.00506750i
$875$		0			0
$876$	−28.0146	+	28.0146i	−0.946527	+	0.946527i
$877$	−19.6563	−	11.3486i	−0.663747	−	0.383214i	0.129956	−	0.991520i	$-0.458516\pi$
$877$	−19.6563	−	11.3486i	−0.663747	−	0.383214i	−0.793703	+	0.608305i	$0.791850\pi$
$878$	6.73256	+	3.88705i	0.227213	+	0.131181i
$879$	−14.5417	+	14.5417i	−0.490480	+	0.490480i
$880$		0			0
$881$	−6.78312	+	3.91623i	−0.228529	+	0.131941i	−0.609893	−	0.792484i	$-0.708788\pi$
$881$	−6.78312	+	3.91623i	−0.228529	+	0.131941i	0.381364	+	0.924425i	$0.375454\pi$
$882$	4.69331	+	8.12905i	0.158032	+	0.273719i
$883$	18.9296	−	18.9296i	0.637032	−	0.637032i	−0.312790	−	0.949822i	$-0.601264\pi$
$883$	18.9296	−	18.9296i	0.637032	−	0.637032i	0.949822	+	0.312790i	$0.101264\pi$
$884$	4.04832	−	9.03064i	0.136160	−	0.303733i
$885$		0			0
$886$	−37.9234	−	10.1615i	−1.27406	−	0.341384i
$887$	34.3248	+	9.19729i	1.15251	+	0.308815i	0.783972	−	0.620797i	$-0.213191\pi$
$887$	34.3248	+	9.19729i	1.15251	+	0.308815i	0.368541	+	0.929612i	$0.379857\pi$
$888$	3.28372	+	12.2550i	0.110194	+	0.411251i
$889$	−3.21825	−	3.21825i	−0.107937	−	0.107937i
$890$		0			0
$891$	40.8731	−	10.9519i	1.36930	−	0.366903i
$892$	−10.0467			−0.336389
$893$	−5.06098	+	1.35608i	−0.169359	+	0.0453796i
$894$	−23.8314	−	41.2772i	−0.797042	−	1.38052i
$895$		0			0
$896$			31.7130i			1.05946i
$897$	1.37348	−	1.68730i	0.0458593	−	0.0563372i
$898$	−18.8417	−	18.8417i	−0.628755	−	0.628755i
$899$	−2.99371	+	11.1727i	−0.0998459	+	0.372630i
$900$		0			0
$901$	7.84682	+	4.53036i	0.261415	+	0.150928i
$902$			4.77421i			0.158964i
$903$	30.9015	−	53.5230i	1.02834	−	1.78113i
$904$	0.701108	+	2.61657i	0.0233185	+	0.0870258i
$905$		0			0
$906$	1.96411	−	3.40193i	0.0652530	−	0.113022i
$907$	−12.0355	+	44.9172i	−0.399633	+	1.49145i	0.414109	+	0.910227i	$0.364093\pi$
$907$	−12.0355	+	44.9172i	−0.399633	+	1.49145i	−0.813743	+	0.581225i	$0.802574\pi$
$908$	4.57880	−	2.64357i	0.151953	−	0.0877300i
$909$	4.22485			0.140130
$910$		0			0
$911$	17.7325			0.587504			0.293752	−	0.955882i	$-0.405096\pi$
$911$	17.7325			0.587504			0.293752	+	0.955882i	$0.405096\pi$
$912$	4.49459	−	2.59495i	0.148831	−	0.0859274i
$913$	−7.59379	+	28.3404i	−0.251318	+	0.937931i
$914$	27.7449	−	48.0556i	0.917720	−	1.58954i
$915$		0			0
$916$	−6.14674	−	22.9399i	−0.203094	−	0.757957i
$917$	−9.89902	+	17.1456i	−0.326894	+	0.566198i
$918$			15.2393i			0.502971i
$919$	−42.2580	−	24.3977i	−1.39396	−	0.804806i	−0.400213	−	0.916422i	$-0.631064\pi$
$919$	−42.2580	−	24.3977i	−1.39396	−	0.804806i	−0.993751	+	0.111617i	$0.964397\pi$
$920$		0			0
$921$	−1.09736	+	4.09541i	−0.0361593	+	0.134948i
$922$	8.98564	+	8.98564i	0.295926	+	0.295926i
$923$	1.69940	+	16.5752i	0.0559365	+	0.545581i
$924$		−	36.8139i		−	1.21109i
$925$		0			0
$926$	−28.7990	−	49.8814i	−0.946395	−	1.63920i
$927$	12.4107	−	3.32544i	0.407621	−	0.109222i
$928$	−12.9820			−0.426155
$929$	−10.0330	+	2.68833i	−0.329171	+	0.0882012i	−0.419620	−	0.907700i	$-0.637837\pi$
$929$	−10.0330	+	2.68833i	−0.329171	+	0.0882012i	0.0904485	+	0.995901i	$0.471170\pi$
$930$		0			0
$931$	−2.09857	−	2.09857i	−0.0687778	−	0.0687778i
$932$	1.43302	+	5.34810i	0.0469401	+	0.175183i
$933$	7.31433	+	1.95987i	0.239460	+	0.0641632i
$934$	9.24814	+	2.47803i	0.302608	+	0.0810837i
$935$		0			0
$936$	−2.49527	+	3.06538i	−0.0815604	+	0.100195i
$937$	−5.31856	+	5.31856i	−0.173750	+	0.173750i	−0.788625	−	0.614875i	$-0.789206\pi$
$937$	−5.31856	+	5.31856i	−0.173750	+	0.173750i	0.614875	+	0.788625i	$0.289206\pi$
$938$	−7.42149	−	12.8544i	−0.242320	−	0.419711i
$939$	−7.39178	+	4.26764i	−0.241221	+	0.139269i
$940$		0			0
$941$	−38.9093	+	38.9093i	−1.26841	+	1.26841i	−0.321497	+	0.946911i	$0.604186\pi$
$941$	−38.9093	+	38.9093i	−1.26841	+	1.26841i	−0.946911	+	0.321497i	$0.895814\pi$
$942$	13.4923	+	7.78981i	0.439604	+	0.253806i
$943$	−0.177406	−	0.102425i	−0.00577712	−	0.00333542i
$944$	−41.9064	+	41.9064i	−1.36394	+	1.36394i
$945$		0			0
$946$	−54.1514	+	31.2643i	−1.76061	+	1.01649i
$947$	16.8759	+	29.2298i	0.548392	+	0.949842i	0.998385	+	0.0568101i	$0.0180930\pi$
$947$	16.8759	+	29.2298i	0.548392	+	0.949842i	−0.449993	+	0.893032i	$0.648574\pi$
$948$	−3.03256	+	3.03256i	−0.0984930	+	0.0984930i
$949$	−8.45606	+	52.5222i	−0.274495	+	1.70494i
$950$		0			0
$951$	−44.2451	−	11.8554i	−1.43475	−	0.384439i
$952$	−8.18285	−	2.19259i	−0.265208	−	0.0710622i
$953$	−1.14302	−	4.26581i	−0.0370260	−	0.138183i	0.944939	−	0.327248i	$-0.106121\pi$
$953$	−1.14302	−	4.26581i	−0.0370260	−	0.138183i	−0.981965	+	0.189065i	$0.939454\pi$
$954$	5.37407	+	5.37407i	0.173992	+	0.173992i
$955$		0			0
$956$	−16.6072	+	4.44988i	−0.537115	+	0.143919i
$957$	−15.1845			−0.490845
$958$	−34.2405	+	9.17471i	−1.10626	+	0.296422i
$959$	25.2858	+	43.7963i	0.816520	+	1.41425i
$960$		0			0
$961$		−	3.20686i		−	0.103447i
$962$	−27.7479	−	22.5872i	−0.894630	−	0.728242i
$963$	4.63819	+	4.63819i	0.149463	+	0.149463i
$964$	6.15338	−	22.9647i	0.198187	−	0.739645i
$965$		0			0
$966$	3.38730	+	1.95566i	0.108985	+	0.0629223i
$967$			16.2803i			0.523540i	0.965130	+	0.261770i	$0.0843061\pi$
$967$			16.2803i			0.523540i	−0.965130	+	0.261770i	$0.915694\pi$
$968$	2.36837	−	4.10214i	0.0761223	−	0.131848i
$969$	0.558310	+	2.08364i	0.0179355	+	0.0669363i
$970$		0			0
$971$	−6.40146	+	11.0877i	−0.205433	+	0.355820i	−0.950270	−	0.311426i	$-0.899193\pi$
$971$	−6.40146	+	11.0877i	−0.205433	+	0.355820i	0.744838	+	0.667245i	$0.232527\pi$
$972$	−3.27038	+	12.2052i	−0.104897	+	0.391482i
$973$	−53.3781	+	30.8179i	−1.71122	+	0.987975i
$974$	42.7918			1.37114
$975$		0			0
$976$	14.0681			0.450309
$977$	−13.8986	+	8.02436i	−0.444655	+	0.256722i	−0.705570	−	0.708640i	$-0.749309\pi$
$977$	−13.8986	+	8.02436i	−0.444655	+	0.256722i	0.260915	+	0.965362i	$0.415976\pi$
$978$	2.12668	−	7.93687i	0.0680037	−	0.253793i
$979$	−9.11292	+	15.7840i	−0.291250	+	0.504460i
$980$		0			0
$981$	3.35939	+	12.5374i	0.107257	+	0.400288i
$982$	19.5239	−	33.8164i	0.623033	−	1.07912i
$983$			34.3036i			1.09411i	0.837096	+	0.547057i	$0.184252\pi$
$983$			34.3036i			1.09411i	−0.837096	+	0.547057i	$0.815748\pi$
$984$	1.36450	+	0.787797i	0.0434988	+	0.0251141i
$985$		0			0
$986$	1.89934	−	7.08844i	0.0604874	−	0.225742i
$987$	48.3637	+	48.3637i	1.53943	+	1.53943i
$988$	−1.07364	+	2.39499i	−0.0341572	+	0.0761947i
$989$		−	2.68296i		−	0.0853131i
$990$		0			0
$991$	−11.1772	−	19.3596i	−0.355057	−	0.614977i	0.632071	−	0.774911i	$-0.282205\pi$
$991$	−11.1772	−	19.3596i	−0.355057	−	0.614977i	−0.987128	+	0.159934i	$0.948872\pi$
$992$	37.0838	−	9.93658i	1.17741	−	0.315487i
$993$	3.95773			0.125595
$994$	−28.9341	+	7.75287i	−0.917734	+	0.245906i
$995$		0			0
$996$	−14.3796	−	14.3796i	−0.455637	−	0.455637i
$997$	−3.08118	−	11.4991i	−0.0975820	−	0.364181i	0.899816	−	0.436269i	$-0.143700\pi$
$997$	−3.08118	−	11.4991i	−0.0975820	−	0.364181i	−0.997398	+	0.0720881i	$0.977034\pi$
$998$	57.6445	+	15.4458i	1.82471	+	0.488928i
$999$	21.4920	+	5.75875i	0.679975	+	0.182199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.x.b.93.4		20
5.2	odd	4		325.2.s.b.132.4		20
5.3	odd	4		65.2.o.a.2.2	✓	20
5.4	even	2		65.2.t.a.28.2	yes	20
13.7	odd	12		325.2.s.b.293.4		20
15.8	even	4		585.2.cf.a.262.4		20
15.14	odd	2		585.2.dp.a.28.4		20
65.3	odd	12		845.2.k.e.577.8		20
65.4	even	6		845.2.t.e.188.2		20
65.7	even	12	inner	325.2.x.b.7.4		20
65.8	even	4		845.2.t.f.427.4		20
65.9	even	6		845.2.t.f.188.4		20
65.18	even	4		845.2.t.e.427.2		20
65.19	odd	12		845.2.o.g.488.4		20
65.23	odd	12		845.2.k.d.577.3		20
65.24	odd	12		845.2.k.e.268.8		20
65.28	even	12		845.2.f.d.437.3		20
65.29	even	6		845.2.f.e.408.3		20
65.33	even	12		65.2.t.a.7.2	yes	20
65.34	odd	4		845.2.o.e.258.2		20
65.38	odd	4		845.2.o.g.587.4		20
65.43	odd	12		845.2.o.f.357.4		20
65.44	odd	4		845.2.o.f.258.4		20
65.48	odd	12		845.2.o.e.357.2		20
65.49	even	6		845.2.f.d.408.8		20
65.54	odd	12		845.2.k.d.268.3		20
65.58	even	12		845.2.t.g.657.4		20
65.59	odd	12		65.2.o.a.33.2	yes	20
65.63	even	12		845.2.f.e.437.8		20
65.64	even	2		845.2.t.g.418.4		20
195.59	even	12		585.2.cf.a.163.4		20
195.98	odd	12		585.2.dp.a.397.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	5.3	odd	4
65.2.o.a.33.2	yes	20	65.59	odd	12
65.2.t.a.7.2	yes	20	65.33	even	12
65.2.t.a.28.2	yes	20	5.4	even	2
325.2.s.b.132.4		20	5.2	odd	4
325.2.s.b.293.4		20	13.7	odd	12
325.2.x.b.7.4		20	65.7	even	12	inner
325.2.x.b.93.4		20	1.1	even	1	trivial
585.2.cf.a.163.4		20	195.59	even	12
585.2.cf.a.262.4		20	15.8	even	4
585.2.dp.a.28.4		20	15.14	odd	2
585.2.dp.a.397.4		20	195.98	odd	12
845.2.f.d.408.8		20	65.49	even	6
845.2.f.d.437.3		20	65.28	even	12
845.2.f.e.408.3		20	65.29	even	6
845.2.f.e.437.8		20	65.63	even	12
845.2.k.d.268.3		20	65.54	odd	12
845.2.k.d.577.3		20	65.23	odd	12
845.2.k.e.268.8		20	65.24	odd	12
845.2.k.e.577.8		20	65.3	odd	12
845.2.o.e.258.2		20	65.34	odd	4
845.2.o.e.357.2		20	65.48	odd	12
845.2.o.f.258.4		20	65.44	odd	4
845.2.o.f.357.4		20	65.43	odd	12
845.2.o.g.488.4		20	65.19	odd	12
845.2.o.g.587.4		20	65.38	odd	4
845.2.t.e.188.2		20	65.4	even	6
845.2.t.e.427.2		20	65.18	even	4
845.2.t.f.188.4		20	65.9	even	6
845.2.t.f.427.4		20	65.8	even	4
845.2.t.g.418.4		20	65.64	even	2
845.2.t.g.657.4		20	65.58	even	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58624 - 0.915816i) q^{2} +(0.512942 - 1.91432i) q^{3} +(0.677439 - 1.17336i) q^{4} +(-0.939520 - 3.50634i) q^{6} +(1.76945 - 3.06478i) q^{7} +1.18163i q^{8} +(-0.803451 - 0.463873i) q^{9} +O(q^{10})\)	\(q+(1.58624 - 0.915816i) q^{2} +(0.512942 - 1.91432i) q^{3} +(0.677439 - 1.17336i) q^{4} +(-0.939520 - 3.50634i) q^{6} +(1.76945 - 3.06478i) q^{7} +1.18163i q^{8} +(-0.803451 - 0.463873i) q^{9} +(-1.00269 + 3.74209i) q^{11} +(-1.89870 - 1.89870i) q^{12} +(-3.55971 - 0.573112i) q^{13} -6.48197i q^{14} +(2.43703 + 4.22106i) q^{16} +(-1.95684 + 0.524334i) q^{17} -1.69929 q^{18} +(0.518968 - 0.139057i) q^{19} +(-4.95936 - 4.95936i) q^{21} +(1.83656 + 6.85414i) q^{22} +(-0.294095 - 0.0788026i) q^{23} +(2.26202 + 0.606106i) q^{24} +(-6.17142 + 2.35095i) q^{26} +(2.90402 - 2.90402i) q^{27} +(-2.39739 - 4.15240i) q^{28} +(-1.71273 + 0.988843i) q^{29} +(4.13563 - 4.13563i) q^{31} +(5.68479 + 3.28212i) q^{32} +(6.64926 + 3.83895i) q^{33} +(-2.62382 + 2.62382i) q^{34} +(-1.08858 + 0.628491i) q^{36} +(2.70887 + 4.69189i) q^{37} +(0.695857 - 0.695857i) q^{38} +(-2.92305 + 6.52047i) q^{39} +(0.649884 + 0.174136i) q^{41} +(-12.4086 - 3.32487i) q^{42} +(2.28069 + 8.51164i) q^{43} +(3.71155 + 3.71155i) q^{44} +(-0.538675 + 0.144337i) q^{46} -9.75201 q^{47} +(9.33053 - 2.50011i) q^{48} +(-2.76192 - 4.78379i) q^{49} +4.01498i q^{51} +(-3.08395 + 3.78857i) q^{52} +(-3.16254 - 3.16254i) q^{53} +(1.94693 - 7.26602i) q^{54} +(3.62143 + 2.09083i) q^{56} -1.06480i q^{57} +(-1.81120 + 3.13709i) q^{58} +(3.14703 + 11.7449i) q^{59} +(1.44316 - 2.49963i) q^{61} +(2.77263 - 10.3476i) q^{62} +(-2.84334 + 1.64160i) q^{63} +2.27514 q^{64} +14.0631 q^{66} +(1.98310 - 1.14494i) q^{67} +(-0.710408 + 2.65128i) q^{68} +(-0.301707 + 0.522573i) q^{69} +(-1.19607 - 4.46378i) q^{71} +(0.548125 - 0.949380i) q^{72} -14.7546i q^{73} +(8.59382 + 4.96165i) q^{74} +(0.188405 - 0.703137i) q^{76} +(9.69449 + 9.69449i) q^{77} +(1.33490 + 13.0200i) q^{78} -1.59718i q^{79} +(-5.46126 - 9.45918i) q^{81} +(1.19035 - 0.318953i) q^{82} +7.57341 q^{83} +(-9.17877 + 2.45944i) q^{84} +(11.4128 + 11.4128i) q^{86} +(1.01444 + 3.78593i) q^{87} +(-4.42176 - 1.18481i) q^{88} +(4.54423 + 1.21762i) q^{89} +(-8.05520 + 9.89564i) q^{91} +(-0.291695 + 0.291695i) q^{92} +(-5.79560 - 10.0383i) q^{93} +(-15.4690 + 8.93105i) q^{94} +(9.19900 - 9.19900i) q^{96} +(-15.4372 - 8.91268i) q^{97} +(-8.76215 - 5.05883i) q^{98} +(2.54147 - 2.54147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9	\( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27} - 18 q^{28} - 48 q^{32} - 18 q^{33} + 2 q^{34} + 36 q^{36} + 4 q^{37} + 8 q^{38} + 4 q^{39} + 10 q^{41} - 40 q^{42} - 10 q^{43} - 36 q^{44} + 4 q^{46} + 40 q^{47} + 56 q^{48} + 18 q^{49} + 30 q^{52} + 10 q^{53} - 48 q^{54} - 16 q^{59} - 16 q^{61} + 44 q^{62} + 36 q^{63} + 20 q^{64} - 32 q^{66} - 18 q^{67} - 22 q^{68} - 16 q^{69} - 16 q^{71} - 4 q^{72} + 18 q^{74} - 64 q^{76} + 28 q^{77} - 68 q^{78} - 14 q^{81} - 56 q^{82} - 48 q^{83} - 40 q^{84} + 60 q^{86} + 34 q^{87} - 82 q^{88} - 6 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 48 q^{94} + 56 q^{96} - 66 q^{97} + 30 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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