LMFDB - Embedded newform 429.2.b.b.298.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(298,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("429.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.b (of order $2$, degree $1$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 $ x^14 + 23x^12 + 201x^10 + 835x^8 + 1695x^6 + 1565x^4 + 511x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			298.7
Root			$-0.409068i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.b.298.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.409068i q^{2} +1.00000 q^{3} +1.83266 q^{4} -4.13953i q^{5} -0.409068i q^{6} +5.18273i q^{7} -1.56782i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.409068i q^{2} +1.00000 q^{3} +1.83266 q^{4} -4.13953i q^{5} -0.409068i q^{6} +5.18273i q^{7} -1.56782i q^{8} +1.00000 q^{9} -1.69335 q^{10} +1.00000i q^{11} +1.83266 q^{12} +(2.62060 - 2.47638i) q^{13} +2.12009 q^{14} -4.13953i q^{15} +3.02398 q^{16} +0.488730 q^{17} -0.409068i q^{18} +0.446180i q^{19} -7.58636i q^{20} +5.18273i q^{21} +0.409068 q^{22} -5.50882 q^{23} -1.56782i q^{24} -12.1357 q^{25} +(-1.01301 - 1.07200i) q^{26} +1.00000 q^{27} +9.49821i q^{28} -6.58571 q^{29} -1.69335 q^{30} -1.52580i q^{31} -4.37265i q^{32} +1.00000i q^{33} -0.199924i q^{34} +21.4541 q^{35} +1.83266 q^{36} -7.87139i q^{37} +0.182518 q^{38} +(2.62060 - 2.47638i) q^{39} -6.49004 q^{40} +8.78563i q^{41} +2.12009 q^{42} +4.57514 q^{43} +1.83266i q^{44} -4.13953i q^{45} +2.25348i q^{46} +5.42082i q^{47} +3.02398 q^{48} -19.8607 q^{49} +4.96433i q^{50} +0.488730 q^{51} +(4.80268 - 4.53837i) q^{52} +8.66677 q^{53} -0.409068i q^{54} +4.13953 q^{55} +8.12559 q^{56} +0.446180i q^{57} +2.69400i q^{58} +5.60493i q^{59} -7.58636i q^{60} -0.855775 q^{61} -0.624155 q^{62} +5.18273i q^{63} +4.25925 q^{64} +(-10.2510 - 10.8481i) q^{65} +0.409068 q^{66} +3.87464i q^{67} +0.895677 q^{68} -5.50882 q^{69} -8.77618i q^{70} +8.49886i q^{71} -1.56782i q^{72} +5.95291i q^{73} -3.21993 q^{74} -12.1357 q^{75} +0.817698i q^{76} -5.18273 q^{77} +(-1.01301 - 1.07200i) q^{78} -8.91459 q^{79} -12.5179i q^{80} +1.00000 q^{81} +3.59392 q^{82} -0.457495i q^{83} +9.49821i q^{84} -2.02311i q^{85} -1.87154i q^{86} -6.58571 q^{87} +1.56782 q^{88} -4.68461i q^{89} -1.69335 q^{90} +(12.8344 + 13.5819i) q^{91} -10.0958 q^{92} -1.52580i q^{93} +2.21748 q^{94} +1.84697 q^{95} -4.37265i q^{96} +2.06057i q^{97} +8.12439i q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9} - 18 q^{12} + 16 q^{14} + 34 q^{16} + 4 q^{17} + 6 q^{22} - 8 q^{23} - 26 q^{25} - 6 q^{26} + 14 q^{27} - 24 q^{29} - 8 q^{35} - 18 q^{36} - 32 q^{38} - 20 q^{40} + 16 q^{42} + 32 q^{43} + 34 q^{48} - 46 q^{49} + 4 q^{51} + 4 q^{52} + 20 q^{53} + 12 q^{55} - 32 q^{56} - 20 q^{61} + 72 q^{62} - 58 q^{64} + 12 q^{65} + 6 q^{66} - 20 q^{68} - 8 q^{69} - 26 q^{75} - 12 q^{77} - 6 q^{78} + 12 q^{79} + 14 q^{81} + 20 q^{82} - 24 q^{87} - 30 q^{88} + 16 q^{91} - 24 q^{92} + 64 q^{94} - 36 q^{95}+O(q^{100}) $ 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9 - 18 * q^12 + 16 * q^14 + 34 * q^16 + 4 * q^17 + 6 * q^22 - 8 * q^23 - 26 * q^25 - 6 * q^26 + 14 * q^27 - 24 * q^29 - 8 * q^35 - 18 * q^36 - 32 * q^38 - 20 * q^40 + 16 * q^42 + 32 * q^43 + 34 * q^48 - 46 * q^49 + 4 * q^51 + 4 * q^52 + 20 * q^53 + 12 * q^55 - 32 * q^56 - 20 * q^61 + 72 * q^62 - 58 * q^64 + 12 * q^65 + 6 * q^66 - 20 * q^68 - 8 * q^69 - 26 * q^75 - 12 * q^77 - 6 * q^78 + 12 * q^79 + 14 * q^81 + 20 * q^82 - 24 * q^87 - 30 * q^88 + 16 * q^91 - 24 * q^92 + 64 * q^94 - 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	0.409068i		−	0.289255i	−0.989486	−	0.144627i	$-0.953802\pi$
$2$		−	0.409068i		−	0.289255i	0.989486	−	0.144627i	$-0.0461984\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.83266			0.916332
$5$		−	4.13953i		−	1.85125i	−0.378437	−	0.925627i	$-0.623538\pi$
$5$		−	4.13953i		−	1.85125i	0.378437	−	0.925627i	$-0.376462\pi$
$6$		−	0.409068i		−	0.167001i
$7$			5.18273i			1.95889i	0.201714	+	0.979445i	$0.435349\pi$
$7$			5.18273i			1.95889i	−0.201714	+	0.979445i	$0.564651\pi$
$8$		−	1.56782i		−	0.554308i
$9$	1.00000			0.333333
$10$	−1.69335			−0.535484
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	1.83266			0.529044
$13$	2.62060	−	2.47638i	0.726824	−	0.686823i
$13$	2.62060	−	2.47638i	0.726824	−	0.686823i
$14$	2.12009			0.566618
$15$		−	4.13953i		−	1.06882i
$16$	3.02398			0.755995
$17$	0.488730			0.118534			0.0592672	−	0.998242i	$-0.481124\pi$
$17$	0.488730			0.118534			0.0592672	+	0.998242i	$0.481124\pi$
$18$		−	0.409068i		−	0.0964183i
$19$			0.446180i			0.102361i	0.998689	+	0.0511803i	$0.0162983\pi$
$19$			0.446180i			0.102361i	−0.998689	+	0.0511803i	$0.983702\pi$
$20$		−	7.58636i		−	1.69636i
$21$			5.18273i			1.13097i
$22$	0.409068			0.0872136
$23$	−5.50882			−1.14867			−0.574334	−	0.818621i	$-0.694739\pi$
$23$	−5.50882			−1.14867			−0.574334	+	0.818621i	$0.694739\pi$
$24$		−	1.56782i		−	0.320030i
$25$	−12.1357			−2.42714
$26$	−1.01301	−	1.07200i	−0.198667	−	0.210237i
$27$	1.00000			0.192450
$28$			9.49821i			1.79499i
$29$	−6.58571			−1.22294			−0.611468	−	0.791269i	$-0.709421\pi$
$29$	−6.58571			−1.22294			−0.611468	+	0.791269i	$0.709421\pi$
$30$	−1.69335			−0.309162
$31$		−	1.52580i		−	0.274041i	−0.990568	−	0.137021i	$-0.956247\pi$
$31$		−	1.52580i		−	0.274041i	0.990568	−	0.137021i	$-0.0437527\pi$
$32$		−	4.37265i		−	0.772983i
$33$			1.00000i			0.174078i
$34$		−	0.199924i		−	0.0342866i
$35$	21.4541			3.62640
$36$	1.83266			0.305444
$37$		−	7.87139i		−	1.29405i	−0.762470	−	0.647024i	$-0.776013\pi$
$37$		−	7.87139i		−	1.29405i	0.762470	−	0.647024i	$-0.223987\pi$
$38$	0.182518			0.0296083
$39$	2.62060	−	2.47638i	0.419632	−	0.396538i
$40$	−6.49004			−1.02617
$41$			8.78563i			1.37209i	0.727561	+	0.686043i	$0.240654\pi$
$41$			8.78563i			1.37209i	−0.727561	+	0.686043i	$0.759346\pi$
$42$	2.12009			0.327137
$43$	4.57514			0.697702			0.348851	−	0.937178i	$-0.386572\pi$
$43$	4.57514			0.697702			0.348851	+	0.937178i	$0.386572\pi$
$44$			1.83266i			0.276284i
$45$		−	4.13953i		−	0.617085i
$46$			2.25348i			0.332258i
$47$			5.42082i			0.790708i	0.918529	+	0.395354i	$0.129378\pi$
$47$			5.42082i			0.790708i	−0.918529	+	0.395354i	$0.870622\pi$
$48$	3.02398			0.436474
$49$	−19.8607			−2.83725
$50$			4.96433i			0.702062i
$51$	0.488730			0.0684359
$52$	4.80268	−	4.53837i	0.666012	−	0.629358i
$53$	8.66677			1.19047			0.595236	−	0.803551i	$-0.297059\pi$
$53$	8.66677			1.19047			0.595236	+	0.803551i	$0.297059\pi$
$54$		−	0.409068i		−	0.0556671i
$55$	4.13953			0.558174
$56$	8.12559			1.08583
$57$			0.446180i			0.0590980i
$58$			2.69400i			0.353740i
$59$			5.60493i			0.729700i	0.931066	+	0.364850i	$0.118880\pi$
$59$			5.60493i			0.729700i	−0.931066	+	0.364850i	$0.881120\pi$
$60$		−	7.58636i		−	0.979395i
$61$	−0.855775			−0.109571			−0.0547854	−	0.998498i	$-0.517447\pi$
$61$	−0.855775			−0.109571			−0.0547854	+	0.998498i	$0.517447\pi$
$62$	−0.624155			−0.0792678
$63$			5.18273i			0.652963i
$64$	4.25925			0.532406
$65$	−10.2510	−	10.8481i	−1.27148	−	1.34554i
$66$	0.409068			0.0503528
$67$			3.87464i			0.473363i	0.971587	+	0.236681i	$0.0760598\pi$
$67$			3.87464i			0.473363i	−0.971587	+	0.236681i	$0.923940\pi$
$68$	0.895677			0.108617
$69$	−5.50882			−0.663184
$70$		−	8.77618i		−	1.04895i
$71$			8.49886i			1.00863i	0.863520	+	0.504315i	$0.168255\pi$
$71$			8.49886i			1.00863i	−0.863520	+	0.504315i	$0.831745\pi$
$72$		−	1.56782i		−	0.184769i
$73$			5.95291i			0.696735i	0.937358	+	0.348368i	$0.113264\pi$
$73$			5.95291i			0.696735i	−0.937358	+	0.348368i	$0.886736\pi$
$74$	−3.21993			−0.374310
$75$	−12.1357			−1.40131
$76$			0.817698i			0.0937963i
$77$	−5.18273			−0.590627
$78$	−1.01301	−	1.07200i	−0.114700	−	0.121381i
$79$	−8.91459			−1.00297			−0.501485	−	0.865166i	$-0.667213\pi$
$79$	−8.91459			−1.00297			−0.501485	+	0.865166i	$0.667213\pi$
$80$		−	12.5179i		−	1.39954i
$81$	1.00000			0.111111
$82$	3.59392			0.396882
$83$		−	0.457495i		−	0.0502166i	−0.999685	−	0.0251083i	$-0.992007\pi$
$83$		−	0.457495i		−	0.0502166i	0.999685	−	0.0251083i	$-0.00799306\pi$
$84$			9.49821i			1.03634i
$85$		−	2.02311i		−	0.219437i
$86$		−	1.87154i		−	0.201814i
$87$	−6.58571			−0.706062
$88$	1.56782			0.167130
$89$		−	4.68461i		−	0.496568i	−0.968687	−	0.248284i	$-0.920133\pi$
$89$		−	4.68461i		−	0.496568i	0.968687	−	0.248284i	$-0.0798666\pi$
$90$	−1.69335			−0.178495
$91$	12.8344	+	13.5819i	1.34541	+	1.42377i
$92$	−10.0958			−1.05256
$93$		−	1.52580i		−	0.158218i
$94$	2.21748			0.228716
$95$	1.84697			0.189496
$96$		−	4.37265i		−	0.446282i
$97$			2.06057i			0.209219i	0.994513	+	0.104609i	$0.0333592\pi$
$97$			2.06057i			0.209219i	−0.994513	+	0.104609i	$0.966641\pi$
$98$			8.12439i			0.820687i
$99$			1.00000i			0.100504i
$100$	−22.2407			−2.22407
$101$	−3.86561			−0.384642			−0.192321	−	0.981332i	$-0.561602\pi$
$101$	−3.86561			−0.384642			−0.192321	+	0.981332i	$0.561602\pi$
$102$		−	0.199924i		−	0.0197954i
$103$	−0.350877			−0.0345730			−0.0172865	−	0.999851i	$-0.505503\pi$
$103$	−0.350877			−0.0345730			−0.0172865	+	0.999851i	$0.505503\pi$
$104$	−3.88251	−	4.10863i	−0.380712	−	0.402885i
$105$	21.4541			2.09370
$106$		−	3.54530i		−	0.344350i
$107$	−12.5796			−1.21612			−0.608060	−	0.793891i	$-0.708052\pi$
$107$	−12.5796			−1.21612			−0.608060	+	0.793891i	$0.708052\pi$
$108$	1.83266			0.176348
$109$			4.61460i			0.441999i	0.975274	+	0.220999i	$0.0709319\pi$
$109$			4.61460i			0.441999i	−0.975274	+	0.220999i	$0.929068\pi$
$110$		−	1.69335i		−	0.161455i
$111$		−	7.87139i		−	0.747119i
$112$			15.6725i			1.48091i
$113$	2.22602			0.209407			0.104703	−	0.994504i	$-0.466611\pi$
$113$	2.22602			0.209407			0.104703	+	0.994504i	$0.466611\pi$
$114$	0.182518			0.0170944
$115$			22.8039i			2.12648i
$116$	−12.0694			−1.12061
$117$	2.62060	−	2.47638i	0.242275	−	0.228941i
$118$	2.29280			0.211069
$119$			2.53296i			0.232196i
$120$	−6.49004			−0.592457
$121$	−1.00000			−0.0909091
$122$			0.350070i			0.0316939i
$123$			8.78563i			0.792174i
$124$		−	2.79627i		−	0.251113i
$125$			29.5385i			2.64200i
$126$	2.12009			0.188873
$127$	18.2528			1.61967			0.809836	−	0.586656i	$-0.199556\pi$
$127$	18.2528			1.61967			0.809836	+	0.586656i	$0.199556\pi$
$128$		−	10.4876i		−	0.926985i
$129$	4.57514			0.402818
$130$	−4.43760	+	4.19337i	−0.389203	+	0.367783i
$131$	3.18466			0.278245			0.139122	−	0.990275i	$-0.455572\pi$
$131$	3.18466			0.278245			0.139122	+	0.990275i	$0.455572\pi$
$132$			1.83266i			0.159513i
$133$	−2.31243			−0.200513
$134$	1.58499			0.136922
$135$		−	4.13953i		−	0.356274i
$136$		−	0.766241i		−	0.0657046i
$137$		−	5.11813i		−	0.437271i	−0.975807	−	0.218635i	$-0.929839\pi$
$137$		−	5.11813i		−	0.437271i	0.975807	−	0.218635i	$-0.0701606\pi$
$138$			2.25348i			0.191829i
$139$	−10.7714			−0.913617			−0.456809	−	0.889565i	$-0.651008\pi$
$139$	−10.7714			−0.913617			−0.456809	+	0.889565i	$0.651008\pi$
$140$	39.3181			3.32299
$141$			5.42082i			0.456515i
$142$	3.47661			0.291751
$143$	2.47638	+	2.62060i	0.207085	+	0.219146i
$144$	3.02398			0.251998
$145$			27.2617i			2.26396i
$146$	2.43514			0.201534
$147$	−19.8607			−1.63809
$148$		−	14.4256i		−	1.18578i
$149$		−	4.42220i		−	0.362281i	−0.983457	−	0.181140i	$-0.942021\pi$
$149$		−	4.42220i		−	0.362281i	0.983457	−	0.181140i	$-0.0579788\pi$
$150$			4.96433i			0.405336i
$151$		−	4.64014i		−	0.377609i	−0.982015	−	0.188805i	$-0.939539\pi$
$151$		−	4.64014i		−	0.377609i	0.982015	−	0.188805i	$-0.0604613\pi$
$152$	0.699530			0.0567394
$153$	0.488730			0.0395115
$154$			2.12009i			0.170842i
$155$	−6.31608			−0.507320
$156$	4.80268	−	4.53837i	0.384522	−	0.363360i
$157$	10.8227			0.863745			0.431873	−	0.901935i	$-0.357853\pi$
$157$	10.8227			0.863745			0.431873	+	0.901935i	$0.357853\pi$
$158$			3.64667i			0.290114i
$159$	8.66677			0.687319
$160$	−18.1007			−1.43099
$161$		−	28.5508i		−	2.25011i
$162$		−	0.409068i		−	0.0321394i
$163$		−	24.4714i		−	1.91675i	−0.285519	−	0.958373i	$-0.592166\pi$
$163$		−	24.4714i		−	1.91675i	0.285519	−	0.958373i	$-0.407834\pi$
$164$			16.1011i			1.25729i
$165$	4.13953			0.322262
$166$	−0.187147			−0.0145254
$167$		−	1.26722i		−	0.0980603i	−0.998797	−	0.0490302i	$-0.984387\pi$
$167$		−	1.26722i		−	0.0980603i	0.998797	−	0.0490302i	$-0.0156130\pi$
$168$	8.12559			0.626903
$169$	0.735113	−	12.9792i	0.0565471	−	0.998400i
$170$	−0.827590			−0.0634733
$171$			0.446180i			0.0341202i
$172$	8.38469			0.639326
$173$	−3.24638			−0.246818			−0.123409	−	0.992356i	$-0.539383\pi$
$173$	−3.24638			−0.246818			−0.123409	+	0.992356i	$0.539383\pi$
$174$			2.69400i			0.204232i
$175$		−	62.8961i		−	4.75450i
$176$			3.02398i			0.227941i
$177$			5.60493i			0.421292i
$178$	−1.91633			−0.143635
$179$	16.5303			1.23553			0.617765	−	0.786363i	$-0.288038\pi$
$179$	16.5303			1.23553			0.617765	+	0.786363i	$0.288038\pi$
$180$		−	7.58636i		−	0.565454i
$181$	−12.2065			−0.907303			−0.453651	−	0.891179i	$-0.649879\pi$
$181$	−12.2065			−0.907303			−0.453651	+	0.891179i	$0.649879\pi$
$182$	5.55592	−	5.25014i	0.411832	−	0.389167i
$183$	−0.855775			−0.0632607
$184$			8.63684i			0.636717i
$185$	−32.5838			−2.39561
$186$	−0.624155			−0.0457653
$187$			0.488730i			0.0357395i
$188$			9.93454i			0.724551i
$189$			5.18273i			0.376988i
$190$		−	0.755539i		−	0.0548125i
$191$	−17.4410			−1.26199			−0.630995	−	0.775787i	$-0.717353\pi$
$191$	−17.4410			−1.26199			−0.630995	+	0.775787i	$0.717353\pi$
$192$	4.25925			0.307385
$193$		−	0.941498i		−	0.0677705i	−0.999426	−	0.0338852i	$-0.989212\pi$
$193$		−	0.941498i		−	0.0677705i	0.999426	−	0.0338852i	$-0.0107881\pi$
$194$	0.842912			0.0605175
$195$	−10.2510	−	10.8481i	−0.734092	−	0.776846i
$196$	−36.3980			−2.59986
$197$		−	16.7419i		−	1.19281i	−0.802684	−	0.596404i	$-0.796596\pi$
$197$		−	16.7419i		−	1.19281i	0.802684	−	0.596404i	$-0.203404\pi$
$198$	0.409068			0.0290712
$199$	−13.1573			−0.932693			−0.466347	−	0.884602i	$-0.654430\pi$
$199$	−13.1573			−0.932693			−0.466347	+	0.884602i	$0.654430\pi$
$200$			19.0266i			1.34538i
$201$			3.87464i			0.273296i
$202$			1.58130i			0.111260i
$203$		−	34.1320i		−	2.39560i
$204$	0.895677			0.0627100
$205$	36.3684			2.54008
$206$			0.143533i			0.0100004i
$207$	−5.50882			−0.382890
$208$	7.92465	−	7.48852i	0.549476	−	0.519235i
$209$	−0.446180			−0.0308629
$210$		−	8.77618i		−	0.605614i
$211$	13.5657			0.933898			0.466949	−	0.884284i	$-0.345353\pi$
$211$	13.5657			0.933898			0.466949	+	0.884284i	$0.345353\pi$
$212$	15.8833			1.09087
$213$			8.49886i			0.582332i
$214$			5.14593i			0.351768i
$215$		−	18.9389i		−	1.29162i
$216$		−	1.56782i		−	0.106677i
$217$	7.90780			0.536816
$218$	1.88769			0.127850
$219$			5.95291i			0.402260i
$220$	7.58636			0.511473
$221$	1.28077	−	1.21028i	0.0861537	−	0.0814122i
$222$	−3.21993			−0.216108
$223$		−	11.8725i		−	0.795044i	−0.917593	−	0.397522i	$-0.869870\pi$
$223$		−	11.8725i		−	0.795044i	0.917593	−	0.397522i	$-0.130130\pi$
$224$	22.6623			1.51419
$225$	−12.1357			−0.809047
$226$		−	0.910595i		−	0.0605719i
$227$			13.0255i			0.864532i	0.901746	+	0.432266i	$0.142286\pi$
$227$			13.0255i			0.864532i	−0.901746	+	0.432266i	$0.857714\pi$
$228$			0.817698i			0.0541533i
$229$			6.45867i			0.426801i	0.976965	+	0.213401i	$0.0684540\pi$
$229$			6.45867i			0.426801i	−0.976965	+	0.213401i	$0.931546\pi$
$230$	9.32836			0.615094
$231$	−5.18273			−0.340999
$232$			10.3252i			0.677883i
$233$	13.2616			0.868795			0.434397	−	0.900721i	$-0.356961\pi$
$233$	13.2616			0.868795			0.434397	+	0.900721i	$0.356961\pi$
$234$	−1.01301	−	1.07200i	−0.0662223	−	0.0700791i
$235$	22.4396			1.46380
$236$			10.2720i			0.668647i
$237$	−8.91459			−0.579065
$238$	1.03615			0.0671637
$239$		−	0.426040i		−	0.0275583i	−0.999905	−	0.0137791i	$-0.995614\pi$
$239$		−	0.426040i		−	0.0275583i	0.999905	−	0.0137791i	$-0.00438617\pi$
$240$		−	12.5179i		−	0.808024i
$241$			12.9860i			0.836503i	0.908331	+	0.418251i	$0.137357\pi$
$241$			12.9860i			0.836503i	−0.908331	+	0.418251i	$0.862643\pi$
$242$			0.409068i			0.0262959i
$243$	1.00000			0.0641500
$244$	−1.56835			−0.100403
$245$			82.2141i			5.25246i
$246$	3.59392			0.229140
$247$	1.10491	+	1.16926i	0.0703037	+	0.0743982i
$248$	−2.39218			−0.151903
$249$		−	0.457495i		−	0.0289926i
$250$	12.0832			0.764211
$251$	−4.37202			−0.275959			−0.137980	−	0.990435i	$-0.544061\pi$
$251$	−4.37202			−0.275959			−0.137980	+	0.990435i	$0.544061\pi$
$252$			9.49821i			0.598331i
$253$		−	5.50882i		−	0.346337i
$254$		−	7.46663i		−	0.468498i
$255$		−	2.02311i		−	0.126692i
$256$	4.22834			0.264271
$257$	11.2798			0.703614			0.351807	−	0.936073i	$-0.385567\pi$
$257$	11.2798			0.703614			0.351807	+	0.936073i	$0.385567\pi$
$258$		−	1.87154i		−	0.116517i
$259$	40.7953			2.53490
$260$	−18.7867	−	19.8808i	−1.16510	−	1.23296i
$261$	−6.58571			−0.407645
$262$		−	1.30274i		−	0.0804836i
$263$	−0.914614			−0.0563975			−0.0281988	−	0.999602i	$-0.508977\pi$
$263$	−0.914614			−0.0563975			−0.0281988	+	0.999602i	$0.508977\pi$
$264$	1.56782			0.0964927
$265$		−	35.8763i		−	2.20387i
$266$			0.945942i			0.0579994i
$267$		−	4.68461i		−	0.286694i
$268$			7.10091i			0.433757i
$269$	13.1384			0.801064			0.400532	−	0.916283i	$-0.368825\pi$
$269$	13.1384			0.801064			0.400532	+	0.916283i	$0.368825\pi$
$270$	−1.69335			−0.103054
$271$		−	12.3173i		−	0.748224i	−0.927384	−	0.374112i	$-0.877948\pi$
$271$		−	12.3173i		−	0.748224i	0.927384	−	0.374112i	$-0.122052\pi$
$272$	1.47791			0.0896115
$273$	12.8344	+	13.5819i	0.776773	+	0.822013i
$274$	−2.09366			−0.126483
$275$		−	12.1357i		−	0.731810i
$276$	−10.0958			−0.607697
$277$	20.1395			1.21006			0.605031	−	0.796202i	$-0.293161\pi$
$277$	20.1395			1.21006			0.605031	+	0.796202i	$0.293161\pi$
$278$			4.40623i			0.264268i
$279$		−	1.52580i		−	0.0913471i
$280$		−	33.6361i		−	2.01014i
$281$		−	6.66666i		−	0.397699i	−0.980030	−	0.198850i	$-0.936279\pi$
$281$		−	6.66666i		−	0.397699i	0.980030	−	0.198850i	$-0.0637206\pi$
$282$	2.21748			0.132049
$283$	−27.5589			−1.63820			−0.819102	−	0.573647i	$-0.805528\pi$
$283$	−27.5589			−1.63820			−0.819102	+	0.573647i	$0.805528\pi$
$284$			15.5755i			0.924239i
$285$	1.84697			0.109405
$286$	1.07200	−	1.01301i	0.0633890	−	0.0599004i
$287$	−45.5336			−2.68776
$288$		−	4.37265i		−	0.257661i
$289$	−16.7611			−0.985950
$290$	11.1519			0.654863
$291$			2.06057i			0.120793i
$292$			10.9097i			0.638440i
$293$		−	13.8127i		−	0.806945i	−0.914992	−	0.403472i	$-0.867803\pi$
$293$		−	13.8127i		−	0.806945i	0.914992	−	0.403472i	$-0.132197\pi$
$294$			8.12439i			0.473824i
$295$	23.2018			1.35086
$296$	−12.3409			−0.717301
$297$			1.00000i			0.0580259i
$298$	−1.80898			−0.104791
$299$	−14.4364	+	13.6419i	−0.834880	+	0.788933i
$300$	−22.2407			−1.28406
$301$			23.7117i			1.36672i
$302$	−1.89813			−0.109225
$303$	−3.86561			−0.222073
$304$			1.34924i			0.0773842i
$305$			3.54251i			0.202843i
$306$		−	0.199924i		−	0.0114289i
$307$			21.0868i			1.20349i	0.798690	+	0.601743i	$0.205527\pi$
$307$			21.0868i			1.20349i	−0.798690	+	0.601743i	$0.794473\pi$
$308$	−9.49821			−0.541210
$309$	−0.350877			−0.0199607
$310$			2.58371i			0.146745i
$311$	29.7858			1.68900			0.844498	−	0.535558i	$-0.179899\pi$
$311$	29.7858			1.68900			0.844498	+	0.535558i	$0.179899\pi$
$312$	−3.88251	−	4.10863i	−0.219804	−	0.232606i
$313$	26.3709			1.49057			0.745287	−	0.666744i	$-0.232312\pi$
$313$	26.3709			1.49057			0.745287	+	0.666744i	$0.232312\pi$
$314$		−	4.42722i		−	0.249842i
$315$	21.4541			1.20880
$316$	−16.3374			−0.919053
$317$		−	24.5073i		−	1.37647i	−0.725490	−	0.688233i	$-0.758387\pi$
$317$		−	24.5073i		−	1.37647i	0.725490	−	0.688233i	$-0.241613\pi$
$318$		−	3.54530i		−	0.198810i
$319$		−	6.58571i		−	0.368729i
$320$		−	17.6313i		−	0.985619i
$321$	−12.5796			−0.702127
$322$	−11.6792			−0.650857
$323$			0.218061i			0.0121333i
$324$	1.83266			0.101815
$325$	−31.8029	+	30.0526i	−1.76410	+	1.66702i
$326$	−10.0105			−0.554428
$327$			4.61460i			0.255188i
$328$	13.7743			0.760558
$329$	−28.0947			−1.54891
$330$		−	1.69335i		−	0.0932158i
$331$		−	10.4965i		−	0.576939i	−0.957489	−	0.288469i	$-0.906854\pi$
$331$		−	10.4965i		−	0.576939i	0.957489	−	0.288469i	$-0.0931464\pi$
$332$		−	0.838434i		−	0.0460150i
$333$		−	7.87139i		−	0.431349i
$334$	−0.518379			−0.0283644
$335$	16.0392			0.876315
$336$			15.6725i			0.855004i
$337$	−21.9103			−1.19353			−0.596765	−	0.802416i	$-0.703547\pi$
$337$	−21.9103			−1.19353			−0.596765	+	0.802416i	$0.703547\pi$
$338$	−5.30938	−	0.300711i	−0.288792	−	0.0163565i
$339$	2.22602			0.120901
$340$		−	3.70768i		−	0.201077i
$341$	1.52580			0.0826266
$342$	0.182518			0.00986944
$343$		−	66.6537i		−	3.59896i
$344$		−	7.17299i		−	0.386742i
$345$			22.8039i			1.22772i
$346$			1.32799i			0.0713933i
$347$	−16.4119			−0.881036			−0.440518	−	0.897744i	$-0.645205\pi$
$347$	−16.4119			−0.881036			−0.440518	+	0.897744i	$0.645205\pi$
$348$	−12.0694			−0.646987
$349$		−	25.0915i		−	1.34312i	−0.740951	−	0.671559i	$-0.765625\pi$
$349$		−	25.0915i		−	1.34312i	0.740951	−	0.671559i	$-0.234375\pi$
$350$	−25.7288			−1.37526
$351$	2.62060	−	2.47638i	0.139877	−	0.132179i
$352$	4.37265			0.233063
$353$		−	9.19662i		−	0.489486i	−0.969588	−	0.244743i	$-0.921296\pi$
$353$		−	9.19662i		−	0.489486i	0.969588	−	0.244743i	$-0.0787037\pi$
$354$	2.29280			0.121861
$355$	35.1813			1.86723
$356$		−	8.58532i		−	0.455021i
$357$			2.53296i			0.134058i
$358$		−	6.76200i		−	0.357383i
$359$			22.6236i			1.19403i	0.802231	+	0.597013i	$0.203646\pi$
$359$			22.6236i			1.19403i	−0.802231	+	0.597013i	$0.796354\pi$
$360$	−6.49004			−0.342055
$361$	18.8009			0.989522
$362$			4.99329i			0.262442i
$363$	−1.00000			−0.0524864
$364$	23.5211	+	24.8910i	1.23284	+	1.30464i
$365$	24.6422			1.28983
$366$			0.350070i			0.0182985i
$367$	−13.9344			−0.727371			−0.363685	−	0.931522i	$-0.618482\pi$
$367$	−13.9344			−0.727371			−0.363685	+	0.931522i	$0.618482\pi$
$368$	−16.6586			−0.868388
$369$			8.78563i			0.457362i
$370$			13.3290i			0.692942i
$371$			44.9175i			2.33200i
$372$		−	2.79627i		−	0.144980i
$373$	20.5104			1.06199			0.530995	−	0.847375i	$-0.321818\pi$
$373$	20.5104			1.06199			0.530995	+	0.847375i	$0.321818\pi$
$374$	0.199924			0.0103378
$375$			29.5385i			1.52536i
$376$	8.49887			0.438296
$377$	−17.2585	+	16.3087i	−0.888859	+	0.839941i
$378$	2.12009			0.109046
$379$			2.32811i			0.119587i	0.998211	+	0.0597934i	$0.0190442\pi$
$379$			2.32811i			0.119587i	−0.998211	+	0.0597934i	$0.980956\pi$
$380$	3.38488			0.173641
$381$	18.2528			0.935118
$382$			7.13457i			0.365037i
$383$		−	27.2203i		−	1.39089i	−0.718578	−	0.695447i	$-0.755207\pi$
$383$		−	27.2203i		−	1.39089i	0.718578	−	0.695447i	$-0.244793\pi$
$384$		−	10.4876i		−	0.535195i
$385$			21.4541i			1.09340i
$386$	−0.385137			−0.0196029
$387$	4.57514			0.232567
$388$			3.77632i			0.191714i
$389$	24.9318			1.26409			0.632047	−	0.774930i	$-0.282215\pi$
$389$	24.9318			1.26409			0.632047	+	0.774930i	$0.282215\pi$
$390$	−4.43760	+	4.19337i	−0.224706	+	0.212340i
$391$	−2.69233			−0.136157
$392$			31.1381i			1.57271i
$393$	3.18466			0.160645
$394$	−6.84856			−0.345026
$395$			36.9022i			1.85675i
$396$			1.83266i			0.0920948i
$397$		−	31.3269i		−	1.57225i	−0.618066	−	0.786126i	$-0.712084\pi$
$397$		−	31.3269i		−	1.57225i	0.618066	−	0.786126i	$-0.287916\pi$
$398$			5.38222i			0.269786i
$399$	−2.31243			−0.115766
$400$	−36.6981			−1.83491
$401$			8.94790i			0.446837i	0.974723	+	0.223418i	$0.0717216\pi$
$401$			8.94790i			0.446837i	−0.974723	+	0.223418i	$0.928278\pi$
$402$	1.58499			0.0790522
$403$	−3.77845	−	3.99851i	−0.188218	−	0.199180i
$404$	−7.08435			−0.352460
$405$		−	4.13953i		−	0.205695i
$406$	−13.9623			−0.692937
$407$	7.87139			0.390170
$408$		−	0.766241i		−	0.0379346i
$409$			30.0934i			1.48802i	0.668166	+	0.744012i	$0.267079\pi$
$409$			30.0934i			1.48802i	−0.668166	+	0.744012i	$0.732921\pi$
$410$		−	14.8771i		−	0.734730i
$411$		−	5.11813i		−	0.252459i
$412$	−0.643040			−0.0316803
$413$	−29.0489			−1.42940
$414$			2.25348i			0.110753i
$415$	−1.89381			−0.0929636
$416$	−10.8283	−	11.4590i	−0.530903	−	0.561823i
$417$	−10.7714			−0.527477
$418$			0.182518i			0.00892725i
$419$	32.6525			1.59518			0.797588	−	0.603202i	$-0.206109\pi$
$419$	32.6525			1.59518			0.797588	+	0.603202i	$0.206109\pi$
$420$	39.3181			1.91853
$421$			28.3956i			1.38392i	0.721938	+	0.691958i	$0.243252\pi$
$421$			28.3956i			1.38392i	−0.721938	+	0.691958i	$0.756748\pi$
$422$		−	5.54928i		−	0.270135i
$423$			5.42082i			0.263569i
$424$		−	13.5879i		−	0.659888i
$425$	−5.93108			−0.287700
$426$	3.47661			0.168442
$427$		−	4.43525i		−	0.214637i
$428$	−23.0542			−1.11437
$429$	2.47638	+	2.62060i	0.119561	+	0.126524i
$430$	−7.74731			−0.373608
$431$		−	14.1585i		−	0.681992i	−0.940065	−	0.340996i	$-0.889236\pi$
$431$		−	14.1585i		−	0.681992i	0.940065	−	0.340996i	$-0.110764\pi$
$432$	3.02398			0.145491
$433$	−15.5980			−0.749590			−0.374795	−	0.927108i	$-0.622287\pi$
$433$	−15.5980			−0.749590			−0.374795	+	0.927108i	$0.622287\pi$
$434$		−	3.23483i		−	0.155277i
$435$			27.2617i			1.30710i
$436$			8.45701i			0.405017i
$437$		−	2.45793i		−	0.117579i
$438$	2.43514			0.116356
$439$	−16.0616			−0.766579			−0.383289	−	0.923628i	$-0.625209\pi$
$439$	−16.0616			−0.766579			−0.383289	+	0.923628i	$0.625209\pi$
$440$		−	6.49004i		−	0.309400i
$441$	−19.8607			−0.945749
$442$	−0.495087	−	0.523921i	−0.0235489	−	0.0249204i
$443$	−8.20834			−0.389990			−0.194995	−	0.980804i	$-0.562469\pi$
$443$	−8.20834			−0.389990			−0.194995	+	0.980804i	$0.562469\pi$
$444$		−	14.4256i		−	0.684609i
$445$	−19.3921			−0.919273
$446$	−4.85668			−0.229970
$447$		−	4.42220i		−	0.209163i
$448$			22.0746i			1.04292i
$449$			10.4304i			0.492242i	0.969239	+	0.246121i	$0.0791561\pi$
$449$			10.4304i			0.492242i	−0.969239	+	0.246121i	$0.920844\pi$
$450$			4.96433i			0.234021i
$451$	−8.78563			−0.413699
$452$	4.07955			0.191886
$453$		−	4.64014i		−	0.218013i
$454$	5.32831			0.250070
$455$	56.2226	−	53.1284i	2.63576	−	2.49070i
$456$	0.699530			0.0327585
$457$			18.1240i			0.847807i	0.905707	+	0.423904i	$0.139340\pi$
$457$			18.1240i			0.847807i	−0.905707	+	0.423904i	$0.860660\pi$
$458$	2.64204			0.123454
$459$	0.488730			0.0228120
$460$			41.7919i			1.94856i
$461$		−	28.6242i		−	1.33316i	−0.745432	−	0.666581i	$-0.767757\pi$
$461$		−	28.6242i		−	1.33316i	0.745432	−	0.666581i	$-0.232243\pi$
$462$			2.12009i			0.0986356i
$463$		−	9.44955i		−	0.439158i	−0.975595	−	0.219579i	$-0.929532\pi$
$463$		−	9.44955i		−	0.439158i	0.975595	−	0.219579i	$-0.0704683\pi$
$464$	−19.9151			−0.924534
$465$	−6.31608			−0.292901
$466$		−	5.42489i		−	0.251303i
$467$	−19.1423			−0.885800			−0.442900	−	0.896571i	$-0.646050\pi$
$467$	−19.1423			−0.885800			−0.442900	+	0.896571i	$0.646050\pi$
$468$	4.80268	−	4.53837i	0.222004	−	0.209786i
$469$	−20.0812			−0.927265
$470$		−	9.17934i		−	0.423412i
$471$	10.8227			0.498683
$472$	8.78753			0.404479
$473$			4.57514i			0.210365i
$474$			3.64667i			0.167497i
$475$		−	5.41471i		−	0.248444i
$476$			4.64206i			0.212768i
$477$	8.66677			0.396824
$478$	−0.174280			−0.00797136
$479$			11.5433i			0.527428i	0.964601	+	0.263714i	$0.0849476\pi$
$479$			11.5433i			0.527428i	−0.964601	+	0.263714i	$0.915052\pi$
$480$	−18.1007			−0.826182
$481$	−19.4925	−	20.6278i	−0.888783	−	0.940546i
$482$	5.31216			0.241962
$483$		−	28.5508i		−	1.29910i
$484$	−1.83266			−0.0833029
$485$	8.52977			0.387317
$486$		−	0.409068i		−	0.0185557i
$487$		−	34.7318i		−	1.57385i	−0.617051	−	0.786923i	$-0.711673\pi$
$487$		−	34.7318i		−	1.57385i	0.617051	−	0.786923i	$-0.288327\pi$
$488$			1.34170i			0.0607360i
$489$		−	24.4714i		−	1.10663i
$490$	33.6311			1.51930
$491$	−19.9935			−0.902295			−0.451148	−	0.892449i	$-0.648985\pi$
$491$	−19.9935			−0.902295			−0.451148	+	0.892449i	$0.648985\pi$
$492$			16.1011i			0.725894i
$493$	−3.21863			−0.144960
$494$	0.478307	−	0.451983i	0.0215200	−	0.0203357i
$495$	4.13953			0.186058
$496$		−	4.61398i		−	0.207174i
$497$	−44.0473			−1.97579
$498$	−0.187147			−0.00838624
$499$			10.3565i			0.463623i	0.972761	+	0.231811i	$0.0744652\pi$
$499$			10.3565i			0.463623i	−0.972761	+	0.231811i	$0.925535\pi$
$500$			54.1340i			2.42095i
$501$		−	1.26722i		−	0.0566151i
$502$			1.78845i			0.0798226i
$503$	41.2438			1.83897			0.919486	−	0.393124i	$-0.128606\pi$
$503$	41.2438			1.83897			0.919486	+	0.393124i	$0.128606\pi$
$504$	8.12559			0.361943
$505$			16.0018i			0.712070i
$506$	−2.25348			−0.100180
$507$	0.735113	−	12.9792i	0.0326475	−	0.576426i
$508$	33.4512			1.48416
$509$		−	9.47338i		−	0.419900i	−0.977712	−	0.209950i	$-0.932670\pi$
$509$		−	9.47338i		−	0.419900i	0.977712	−	0.209950i	$-0.0673301\pi$
$510$	−0.827590			−0.0366463
$511$	−30.8523			−1.36483
$512$		−	22.7049i		−	1.00343i
$513$			0.446180i			0.0196993i
$514$		−	4.61420i		−	0.203524i
$515$			1.45247i			0.0640033i
$516$	8.38469			0.369115
$517$	−5.42082			−0.238407
$518$		−	16.6881i		−	0.733231i
$519$	−3.24638			−0.142500
$520$	−17.0078	+	16.0718i	−0.745842	+	0.704794i
$521$	−6.47023			−0.283466			−0.141733	−	0.989905i	$-0.545267\pi$
$521$	−6.47023			−0.283466			−0.141733	+	0.989905i	$0.545267\pi$
$522$			2.69400i			0.117913i
$523$	16.1999			0.708372			0.354186	−	0.935175i	$-0.384758\pi$
$523$	16.1999			0.708372			0.354186	+	0.935175i	$0.384758\pi$
$524$	5.83640			0.254964
$525$		−	62.8961i		−	2.74501i
$526$			0.374140i			0.0163133i
$527$		−	0.745703i		−	0.0324833i
$528$			3.02398i			0.131602i
$529$	7.34712			0.319440
$530$	−14.6759			−0.637479
$531$			5.60493i			0.243233i
$532$	−4.23791			−0.183737
$533$	21.7565	+	23.0237i	0.942380	+	0.997265i
$534$	−1.91633			−0.0829275
$535$			52.0738i			2.25135i
$536$	6.07474			0.262389
$537$	16.5303			0.713334
$538$		−	5.37451i		−	0.231712i
$539$		−	19.8607i		−	0.855462i
$540$		−	7.58636i		−	0.326465i
$541$		−	6.65767i		−	0.286236i	−0.989706	−	0.143118i	$-0.954287\pi$
$541$		−	6.65767i		−	0.286236i	0.989706	−	0.143118i	$-0.0457128\pi$
$542$	−5.03862			−0.216427
$543$	−12.2065			−0.523832
$544$		−	2.13705i		−	0.0916251i
$545$	19.1023			0.818252
$546$	5.55592	−	5.25014i	0.237771	−	0.224685i
$547$	2.06963			0.0884912			0.0442456	−	0.999021i	$-0.485912\pi$
$547$	2.06963			0.0884912			0.0442456	+	0.999021i	$0.485912\pi$
$548$		−	9.37980i		−	0.400685i
$549$	−0.855775			−0.0365236
$550$	−4.96433			−0.211680
$551$		−	2.93841i		−	0.125181i
$552$			8.63684i			0.367608i
$553$		−	46.2020i		−	1.96471i
$554$		−	8.23841i		−	0.350016i
$555$	−32.5838			−1.38311
$556$	−19.7403			−0.837176
$557$			12.3459i			0.523111i	0.965188	+	0.261556i	$0.0842355\pi$
$557$			12.3459i			0.523111i	−0.965188	+	0.261556i	$0.915764\pi$
$558$	−0.624155			−0.0264226
$559$	11.9896	−	11.3298i	0.507107	−	0.479198i
$560$	64.8767			2.74154
$561$			0.488730i			0.0206342i
$562$	−2.72712			−0.115037
$563$	3.72355			0.156929			0.0784645	−	0.996917i	$-0.474998\pi$
$563$	3.72355			0.156929			0.0784645	+	0.996917i	$0.474998\pi$
$564$			9.93454i			0.418320i
$565$		−	9.21469i		−	0.387665i
$566$			11.2735i			0.473859i
$567$			5.18273i			0.217654i
$568$	13.3247			0.559091
$569$	−27.2092			−1.14067			−0.570334	−	0.821413i	$-0.693186\pi$
$569$	−27.2092			−1.14067			−0.570334	+	0.821413i	$0.693186\pi$
$570$		−	0.755539i		−	0.0316460i
$571$	−31.1102			−1.30192			−0.650961	−	0.759112i	$-0.725634\pi$
$571$	−31.1102			−1.30192			−0.650961	+	0.759112i	$0.725634\pi$
$572$	4.53837	+	4.80268i	0.189759	+	0.200810i
$573$	−17.4410			−0.728610
$574$			18.6263i			0.777448i
$575$	66.8534			2.78798
$576$	4.25925			0.177469
$577$			5.53948i			0.230611i	0.993330	+	0.115306i	$0.0367848\pi$
$577$			5.53948i			0.230611i	−0.993330	+	0.115306i	$0.963215\pi$
$578$			6.85645i			0.285191i
$579$		−	0.941498i		−	0.0391273i
$580$			49.9616i			2.07454i
$581$	2.37107			0.0983687
$582$	0.842912			0.0349398
$583$			8.66677i			0.358941i
$584$	9.33309			0.386206
$585$	−10.2510	−	10.8481i	−0.423828	−	0.448512i
$586$	−5.65032			−0.233413
$587$			27.8516i			1.14956i	0.818308	+	0.574780i	$0.194912\pi$
$587$			27.8516i			1.14956i	−0.818308	+	0.574780i	$0.805088\pi$
$588$	−36.3980			−1.50103
$589$	0.680780			0.0280511
$590$		−	9.49111i		−	0.390743i
$591$		−	16.7419i		−	0.688668i
$592$		−	23.8029i		−	0.978294i
$593$		−	0.298235i		−	0.0122470i	−0.999981	−	0.00612351i	$-0.998051\pi$
$593$		−	0.298235i		−	0.0122470i	0.999981	−	0.00612351i	$-0.00194919\pi$
$594$	0.409068			0.0167843
$595$	10.4852			0.429853
$596$		−	8.10440i		−	0.331969i
$597$	−13.1573			−0.538491
$598$	5.58048	+	5.90548i	0.228203	+	0.241493i
$599$	22.8194			0.932375			0.466188	−	0.884686i	$-0.345627\pi$
$599$	22.8194			0.932375			0.466188	+	0.884686i	$0.345627\pi$
$600$			19.0266i			0.776758i
$601$	−2.27297			−0.0927164			−0.0463582	−	0.998925i	$-0.514762\pi$
$601$	−2.27297			−0.0927164			−0.0463582	+	0.998925i	$0.514762\pi$
$602$	9.69971			0.395331
$603$			3.87464i			0.157788i
$604$		−	8.50381i		−	0.346015i
$605$			4.13953i			0.168296i
$606$			1.58130i			0.0642358i
$607$	−4.31576			−0.175171			−0.0875857	−	0.996157i	$-0.527915\pi$
$607$	−4.31576			−0.175171			−0.0875857	+	0.996157i	$0.527915\pi$
$608$	1.95099			0.0791231
$609$		−	34.1320i		−	1.38310i
$610$	1.44913			0.0586734
$611$	13.4240	+	14.2058i	0.543077	+	0.574706i
$612$	0.895677			0.0362056
$613$		−	11.3555i		−	0.458646i	−0.973350	−	0.229323i	$-0.926349\pi$
$613$		−	11.3555i		−	0.458646i	0.973350	−	0.229323i	$-0.0736512\pi$
$614$	8.62593			0.348114
$615$	36.3684			1.46651
$616$			8.12559i			0.327390i
$617$			23.6846i			0.953507i	0.879037	+	0.476753i	$0.158186\pi$
$617$			23.6846i			0.953507i	−0.879037	+	0.476753i	$0.841814\pi$
$618$			0.143533i			0.00577373i
$619$		−	27.4080i		−	1.10162i	−0.834631	−	0.550810i	$-0.814319\pi$
$619$		−	27.4080i		−	1.10162i	0.834631	−	0.550810i	$-0.185681\pi$
$620$	−11.5753			−0.464873
$621$	−5.50882			−0.221061
$622$		−	12.1844i		−	0.488550i
$623$	24.2791			0.972721
$624$	7.92465	−	7.48852i	0.317240	−	0.299781i
$625$	61.5968			2.46387
$626$		−	10.7875i		−	0.431156i
$627$	−0.446180			−0.0178187
$628$	19.8344			0.791477
$629$		−	3.84698i		−	0.153389i
$630$		−	8.77618i		−	0.349651i
$631$			42.3930i			1.68764i	0.536627	+	0.843819i	$0.319698\pi$
$631$			42.3930i			1.68764i	−0.536627	+	0.843819i	$0.680302\pi$
$632$			13.9765i			0.555954i
$633$	13.5657			0.539186
$634$	−10.0251			−0.398149
$635$		−	75.5579i		−	2.99842i
$636$	15.8833			0.629812
$637$	−52.0471	+	49.1826i	−2.06218	+	1.94869i
$638$	−2.69400			−0.106657
$639$			8.49886i			0.336210i
$640$	−43.4139			−1.71608
$641$	−18.4040			−0.726916			−0.363458	−	0.931611i	$-0.618404\pi$
$641$	−18.4040			−0.726916			−0.363458	+	0.931611i	$0.618404\pi$
$642$			5.14593i			0.203094i
$643$		−	0.572048i		−	0.0225594i	−0.999936	−	0.0112797i	$-0.996409\pi$
$643$		−	0.572048i		−	0.0225594i	0.999936	−	0.0112797i	$-0.00359051\pi$
$644$		−	52.3239i		−	2.06185i
$645$		−	18.9389i		−	0.745719i
$646$	0.0892020			0.00350961
$647$	−16.2324			−0.638163			−0.319082	−	0.947727i	$-0.603374\pi$
$647$	−16.2324			−0.638163			−0.319082	+	0.947727i	$0.603374\pi$
$648$		−	1.56782i		−	0.0615898i
$649$	−5.60493			−0.220013
$650$	12.2936	+	13.0095i	0.482193	+	0.510276i
$651$	7.90780			0.309931
$652$		−	44.8478i		−	1.75638i
$653$	−2.56096			−0.100218			−0.0501090	−	0.998744i	$-0.515957\pi$
$653$	−2.56096			−0.100218			−0.0501090	+	0.998744i	$0.515957\pi$
$654$	1.88769			0.0738144
$655$		−	13.1830i		−	0.515102i
$656$			26.5676i			1.03729i
$657$			5.95291i			0.232245i
$658$			11.4926i			0.448029i
$659$	−37.8432			−1.47416			−0.737082	−	0.675804i	$-0.763797\pi$
$659$	−37.8432			−1.47416			−0.737082	+	0.675804i	$0.763797\pi$
$660$	7.58636			0.295299
$661$			33.9955i			1.32227i	0.750267	+	0.661135i	$0.229925\pi$
$661$			33.9955i			1.32227i	−0.750267	+	0.661135i	$0.770075\pi$
$662$	−4.29378			−0.166882
$663$	1.28077	−	1.21028i	0.0497409	−	0.0470034i
$664$	−0.717270			−0.0278355
$665$			9.57238i			0.371201i
$666$	−3.21993			−0.124770
$667$	36.2795			1.40475
$668$		−	2.32238i		−	0.0898558i
$669$		−	11.8725i		−	0.459019i
$670$		−	6.56112i		−	0.253478i
$671$		−	0.855775i		−	0.0330368i
$672$	22.6623			0.874217
$673$	34.7689			1.34024			0.670122	−	0.742251i	$-0.266242\pi$
$673$	34.7689			1.34024			0.670122	+	0.742251i	$0.266242\pi$
$674$			8.96280i			0.345234i
$675$	−12.1357			−0.467103
$676$	1.34721	−	23.7865i	0.0518159	−	0.914865i
$677$	−31.6215			−1.21531			−0.607656	−	0.794201i	$-0.707890\pi$
$677$	−31.6215			−1.21531			−0.607656	+	0.794201i	$0.707890\pi$
$678$		−	0.910595i		−	0.0349712i
$679$	−10.6794			−0.409836
$680$	−3.17188			−0.121636
$681$			13.0255i			0.499138i
$682$		−	0.624155i		−	0.0239001i
$683$			29.1127i			1.11397i	0.830523	+	0.556984i	$0.188041\pi$
$683$			29.1127i			1.11397i	−0.830523	+	0.556984i	$0.811959\pi$
$684$			0.817698i			0.0312654i
$685$	−21.1866			−0.809500
$686$	−27.2659			−1.04102
$687$			6.45867i			0.246414i
$688$	13.8351			0.527459
$689$	22.7122	−	21.4622i	0.865264	−	0.817644i
$690$	9.32836			0.355125
$691$			6.72289i			0.255751i	0.991790	+	0.127875i	$0.0408158\pi$
$691$			6.72289i			0.255751i	−0.991790	+	0.127875i	$0.959184\pi$
$692$	−5.94953			−0.226167
$693$	−5.18273			−0.196876
$694$			6.71357i			0.254844i
$695$			44.5885i			1.69134i
$696$			10.3252i			0.391376i
$697$			4.29380i			0.162639i
$698$	−10.2641			−0.388503
$699$	13.2616			0.501599
$700$		−	115.267i		−	4.35670i
$701$	33.5332			1.26653			0.633265	−	0.773935i	$-0.281714\pi$
$701$	33.5332			1.26653			0.633265	+	0.773935i	$0.281714\pi$
$702$	−1.01301	−	1.07200i	−0.0382335	−	0.0404602i
$703$	3.51205			0.132460
$704$			4.25925i			0.160526i
$705$	22.4396			0.845126
$706$	−3.76204			−0.141586
$707$		−	20.0344i		−	0.753471i
$708$			10.2720i			0.386044i
$709$		−	40.1123i		−	1.50645i	−0.657764	−	0.753224i	$-0.728498\pi$
$709$		−	40.1123i		−	1.50645i	0.657764	−	0.753224i	$-0.271502\pi$
$710$		−	14.3915i		−	0.540105i
$711$	−8.91459			−0.334323
$712$	−7.34463			−0.275252
$713$			8.40535i			0.314783i
$714$	1.03615			0.0387770
$715$	10.8481	−	10.2510i	0.405694	−	0.383367i
$716$	30.2944			1.13216
$717$		−	0.426040i		−	0.0159108i
$718$	9.25458			0.345378
$719$	−7.15141			−0.266703			−0.133351	−	0.991069i	$-0.542574\pi$
$719$	−7.15141			−0.266703			−0.133351	+	0.991069i	$0.542574\pi$
$720$		−	12.5179i		−	0.466513i
$721$		−	1.81850i		−	0.0677246i
$722$		−	7.69086i		−	0.286224i
$723$			12.9860i			0.482955i
$724$	−22.3704			−0.831390
$725$	79.9222			2.96824
$726$			0.409068i			0.0151819i
$727$	38.2917			1.42016			0.710081	−	0.704120i	$-0.248658\pi$
$727$	38.2917			1.42016			0.710081	+	0.704120i	$0.248658\pi$
$728$	21.2940	−	20.1220i	0.789206	−	0.745772i
$729$	1.00000			0.0370370
$730$		−	10.0804i		−	0.373091i
$731$	2.23601			0.0827017
$732$	−1.56835			−0.0579678
$733$			35.4025i			1.30762i	0.756658	+	0.653811i	$0.226831\pi$
$733$			35.4025i			1.30762i	−0.756658	+	0.653811i	$0.773169\pi$
$734$			5.70013i			0.210395i
$735$			82.2141i			3.03251i
$736$			24.0882i			0.887902i
$737$	−3.87464			−0.142724
$738$	3.59392			0.132294
$739$			2.87016i			0.105580i	0.998606	+	0.0527902i	$0.0168115\pi$
$739$			2.87016i			0.105580i	−0.998606	+	0.0527902i	$0.983189\pi$
$740$	−59.7152			−2.19517
$741$	1.10491	+	1.16926i	0.0405899	+	0.0429538i
$742$	18.3743			0.674543
$743$		−	23.1129i		−	0.847930i	−0.905679	−	0.423965i	$-0.860638\pi$
$743$		−	23.1129i		−	0.847930i	0.905679	−	0.423965i	$-0.139362\pi$
$744$	−2.39218			−0.0877014
$745$	−18.3058			−0.670673
$746$		−	8.39016i		−	0.307185i
$747$		−	0.457495i		−	0.0167389i
$748$			0.895677i			0.0327492i
$749$		−	65.1969i		−	2.38224i
$750$	12.0832			0.441218
$751$	37.5587			1.37054			0.685268	−	0.728291i	$-0.259685\pi$
$751$	37.5587			1.37054			0.685268	+	0.728291i	$0.259685\pi$
$752$			16.3925i			0.597771i
$753$	−4.37202			−0.159325
$754$	6.67137	+	7.05991i	0.242957	+	0.257107i
$755$	−19.2080			−0.699050
$756$			9.49821i			0.345446i
$757$	−47.4259			−1.72372			−0.861862	−	0.507143i	$-0.830702\pi$
$757$	−47.4259			−1.72372			−0.861862	+	0.507143i	$0.830702\pi$
$758$	0.952354			0.0345910
$759$		−	5.50882i		−	0.199958i
$760$		−	2.89572i		−	0.105039i
$761$			23.0592i			0.835895i	0.908471	+	0.417947i	$0.137250\pi$
$761$			23.0592i			0.835895i	−0.908471	+	0.417947i	$0.862750\pi$
$762$		−	7.46663i		−	0.270487i
$763$	−23.9163			−0.865826
$764$	−31.9636			−1.15640
$765$		−	2.02311i		−	0.0731458i
$766$	−11.1350			−0.402323
$767$	13.8799	+	14.6883i	0.501175	+	0.530364i
$768$	4.22834			0.152577
$769$			40.2536i			1.45158i	0.687915	+	0.725792i	$0.258526\pi$
$769$			40.2536i			1.45158i	−0.687915	+	0.725792i	$0.741474\pi$
$770$	8.77618			0.316272
$771$	11.2798			0.406232
$772$		−	1.72545i		−	0.0621003i
$773$		−	25.6183i		−	0.921426i	−0.887549	−	0.460713i	$-0.847594\pi$
$773$		−	25.6183i		−	0.921426i	0.887549	−	0.460713i	$-0.152406\pi$
$774$		−	1.87154i		−	0.0672712i
$775$			18.5166i			0.665137i
$776$	3.23060			0.115972
$777$	40.7953			1.46352
$778$		−	10.1988i		−	0.365645i
$779$	−3.91997			−0.140448
$780$	−18.7867	−	19.8808i	−0.672672	−	0.711848i
$781$	−8.49886			−0.304113
$782$			1.10134i			0.0393840i
$783$	−6.58571			−0.235354
$784$	−60.0585			−2.14495
$785$		−	44.8009i		−	1.59901i
$786$		−	1.30274i		−	0.0464673i
$787$			23.3425i			0.832070i	0.909349	+	0.416035i	$0.136581\pi$
$787$			23.3425i			0.832070i	−0.909349	+	0.416035i	$0.863419\pi$
$788$		−	30.6822i		−	1.09301i
$789$	−0.914614			−0.0325611
$790$	15.0955			0.537074
$791$			11.5369i			0.410204i
$792$	1.56782			0.0557101
$793$	−2.24265	+	2.11922i	−0.0796387	+	0.0752558i
$794$	−12.8148			−0.454781
$795$		−	35.8763i		−	1.27240i
$796$	−24.1128			−0.854656
$797$	49.4116			1.75025			0.875125	−	0.483897i	$-0.160779\pi$
$797$	49.4116			1.75025			0.875125	+	0.483897i	$0.160779\pi$
$798$			0.945942i			0.0334860i
$799$			2.64932i			0.0937261i
$800$			53.0652i			1.87614i
$801$		−	4.68461i		−	0.165523i
$802$	3.66030			0.129250
$803$	−5.95291			−0.210074
$804$			7.10091i			0.250430i
$805$	−118.187			−4.16553
$806$	−1.63566	+	1.54564i	−0.0576137	+	0.0544430i
$807$	13.1384			0.462495
$808$			6.06058i			0.213210i
$809$	22.7489			0.799810			0.399905	−	0.916556i	$-0.369043\pi$
$809$	22.7489			0.799810			0.399905	+	0.916556i	$0.369043\pi$
$810$	−1.69335			−0.0594982
$811$			23.4289i			0.822701i	0.911477	+	0.411350i	$0.134943\pi$
$811$			23.4289i			0.822701i	−0.911477	+	0.411350i	$0.865057\pi$
$812$		−	62.5524i		−	2.19516i
$813$		−	12.3173i		−	0.431987i
$814$		−	3.21993i		−	0.112859i
$815$	−101.300			−3.54838
$816$	1.47791			0.0517372
$817$			2.04133i			0.0714173i
$818$	12.3103			0.430418
$819$	12.8344	+	13.5819i	0.448470	+	0.474589i
$820$	66.6510			2.32755
$821$			6.75303i			0.235682i	0.993032	+	0.117841i	$0.0375973\pi$
$821$			6.75303i			0.235682i	−0.993032	+	0.117841i	$0.962403\pi$
$822$	−2.09366			−0.0730248
$823$	36.4194			1.26950			0.634751	−	0.772717i	$-0.281103\pi$
$823$	36.4194			1.26950			0.634751	+	0.772717i	$0.281103\pi$
$824$			0.550113i			0.0191641i
$825$		−	12.1357i		−	0.422511i
$826$			11.8830i			0.413461i
$827$		−	49.2124i		−	1.71128i	−0.517569	−	0.855642i	$-0.673163\pi$
$827$		−	49.2124i		−	1.71128i	0.517569	−	0.855642i	$-0.326837\pi$
$828$	−10.0958			−0.350854
$829$	−2.84332			−0.0987525			−0.0493762	−	0.998780i	$-0.515723\pi$
$829$	−2.84332			−0.0987525			−0.0493762	+	0.998780i	$0.515723\pi$
$830$			0.774699i			0.0268902i
$831$	20.1395			0.698630
$832$	11.1618	−	10.5475i	0.386966	−	0.365669i
$833$	−9.70653			−0.336311
$834$			4.40623i			0.152575i
$835$	−5.24569			−0.181535
$836$	−0.817698			−0.0282807
$837$		−	1.52580i		−	0.0527393i
$838$		−	13.3571i		−	0.461413i
$839$			8.15579i			0.281569i	0.990040	+	0.140785i	$0.0449625\pi$
$839$			8.15579i			0.281569i	−0.990040	+	0.140785i	$0.955038\pi$
$840$		−	33.6361i		−	1.16056i
$841$	14.3716			0.495571
$842$	11.6157			0.400304
$843$		−	6.66666i		−	0.229612i
$844$	24.8613			0.855761
$845$	−53.7278	−	3.04302i	−1.84829	−	0.104683i
$846$	2.21748			0.0762387
$847$		−	5.18273i		−	0.178081i
$848$	26.2081			0.899991
$849$	−27.5589			−0.945818
$850$			2.42622i			0.0832185i
$851$			43.3621i			1.48643i
$852$			15.5755i			0.533609i
$853$			12.7020i			0.434910i	0.976070	+	0.217455i	$0.0697755\pi$
$853$			12.7020i			0.434910i	−0.976070	+	0.217455i	$0.930225\pi$
$854$	−1.81432			−0.0620848
$855$	1.84697			0.0631652
$856$			19.7226i			0.674105i
$857$	50.4563			1.72355			0.861777	−	0.507287i	$-0.169352\pi$
$857$	50.4563			1.72355			0.861777	+	0.507287i	$0.169352\pi$
$858$	1.07200	−	1.01301i	0.0365976	−	0.0345835i
$859$	−8.22512			−0.280637			−0.140319	−	0.990106i	$-0.544813\pi$
$859$	−8.22512			−0.280637			−0.140319	+	0.990106i	$0.544813\pi$
$860$		−	34.7087i		−	1.18356i
$861$	−45.5336			−1.55178
$862$	−5.79180			−0.197269
$863$			15.2200i			0.518094i	0.965865	+	0.259047i	$0.0834084\pi$
$863$			15.2200i			0.518094i	−0.965865	+	0.259047i	$0.916592\pi$
$864$		−	4.37265i		−	0.148761i
$865$			13.4385i			0.456923i
$866$			6.38063i			0.216823i
$867$	−16.7611			−0.569238
$868$	14.4923			0.491902
$869$		−	8.91459i		−	0.302407i
$870$	11.1519			0.378085
$871$	9.59507	+	10.1539i	0.325117	+	0.344052i
$872$	7.23487			0.245003
$873$			2.06057i			0.0697396i
$874$	−1.00546			−0.0340102
$875$	−153.090			−5.17538
$876$			10.9097i			0.368604i
$877$			16.0542i			0.542113i	0.962563	+	0.271057i	$0.0873731\pi$
$877$			16.0542i			0.542113i	−0.962563	+	0.271057i	$0.912627\pi$
$878$			6.57029i			0.221737i
$879$		−	13.8127i		−	0.465890i
$880$	12.5179			0.421977
$881$	−51.9810			−1.75128			−0.875642	−	0.482961i	$-0.839561\pi$
$881$	−51.9810			−1.75128			−0.875642	+	0.482961i	$0.839561\pi$
$882$			8.12439i			0.273562i
$883$	21.5188			0.724164			0.362082	−	0.932146i	$-0.382066\pi$
$883$	21.5188			0.724164			0.362082	+	0.932146i	$0.382066\pi$
$884$	2.34721	−	2.21803i	0.0789453	−	0.0746006i
$885$	23.2018			0.779919
$886$			3.35777i			0.112806i
$887$	−18.2083			−0.611376			−0.305688	−	0.952132i	$-0.598887\pi$
$887$	−18.2083			−0.611376			−0.305688	+	0.952132i	$0.598887\pi$
$888$	−12.3409			−0.414134
$889$			94.5993i			3.17276i
$890$			7.93269i			0.265904i
$891$			1.00000i			0.0335013i
$892$		−	21.7584i		−	0.728524i
$893$	−2.41866			−0.0809374
$894$	−1.80898			−0.0605014
$895$		−	68.4275i		−	2.28728i
$896$	54.3546			1.81586
$897$	−14.4364	+	13.6419i	−0.482018	+	0.455491i
$898$	4.26676			0.142384
$899$			10.0485i			0.335135i
$900$	−22.2407			−0.741355
$901$	4.23571			0.141112
$902$			3.59392i			0.119665i
$903$			23.7117i			0.789077i
$904$		−	3.49000i		−	0.116076i
$905$			50.5292i			1.67965i
$906$	−1.89813			−0.0630612
$907$	6.58414			0.218623			0.109311	−	0.994008i	$-0.465135\pi$
$907$	6.58414			0.218623			0.109311	+	0.994008i	$0.465135\pi$
$908$			23.8713i			0.792198i
$909$	−3.86561			−0.128214
$910$	−21.7331	−	22.9989i	−0.720446	−	0.762405i
$911$	−51.4764			−1.70549			−0.852745	−	0.522328i	$-0.825064\pi$
$911$	−51.4764			−1.70549			−0.852745	+	0.522328i	$0.825064\pi$
$912$			1.34924i			0.0446778i
$913$	0.457495			0.0151409
$914$	7.41397			0.245232
$915$			3.54251i			0.117112i
$916$			11.8366i			0.391091i
$917$			16.5052i			0.545051i
$918$		−	0.199924i		−	0.00659847i
$919$	−31.1301			−1.02689			−0.513443	−	0.858123i	$-0.671630\pi$
$919$	−31.1301			−1.02689			−0.513443	+	0.858123i	$0.671630\pi$
$920$	35.7525			1.17872
$921$			21.0868i			0.694833i
$922$	−11.7093			−0.385624
$923$	21.0464	+	22.2721i	0.692750	+	0.733096i
$924$	−9.49821			−0.312468
$925$			95.5248i			3.14084i
$926$	−3.86551			−0.127029
$927$	−0.350877			−0.0115243
$928$			28.7970i			0.945309i
$929$		−	54.5430i		−	1.78950i	−0.446569	−	0.894749i	$-0.647354\pi$
$929$		−	54.5430i		−	1.78950i	0.446569	−	0.894749i	$-0.352646\pi$
$930$			2.58371i			0.0847231i
$931$		−	8.86146i		−	0.290423i
$932$	24.3040			0.796104
$933$	29.7858			0.975142
$934$			7.83051i			0.256222i
$935$	2.02311			0.0661628
$936$	−3.88251	−	4.10863i	−0.126904	−	0.134295i
$937$	−36.4863			−1.19195			−0.595977	−	0.803001i	$-0.703235\pi$
$937$	−36.4863			−1.19195			−0.595977	+	0.803001i	$0.703235\pi$
$938$			8.21459i			0.268216i
$939$	26.3709			0.860583
$940$	41.1243			1.34133
$941$		−	6.77293i		−	0.220791i	−0.993888	−	0.110396i	$-0.964788\pi$
$941$		−	6.77293i		−	0.220791i	0.993888	−	0.110396i	$-0.0352118\pi$
$942$		−	4.42722i		−	0.144247i
$943$		−	48.3985i		−	1.57607i
$944$			16.9492i			0.551650i
$945$	21.4541			0.697901
$946$	1.87154			0.0608491
$947$		−	4.44833i		−	0.144551i	−0.997385	−	0.0722756i	$-0.976974\pi$
$947$		−	4.44833i		−	0.144551i	0.997385	−	0.0722756i	$-0.0230261\pi$
$948$	−16.3374			−0.530616
$949$	14.7416	+	15.6002i	0.478534	+	0.506404i
$950$	−2.21498			−0.0718636
$951$		−	24.5073i		−	0.794703i
$952$	3.97122			0.128708
$953$	52.2252			1.69174			0.845870	−	0.533389i	$-0.179082\pi$
$953$	52.2252			1.69174			0.845870	+	0.533389i	$0.179082\pi$
$954$		−	3.54530i		−	0.114783i
$955$			72.1977i			2.33626i
$956$		−	0.780789i		−	0.0252525i
$957$		−	6.58571i		−	0.212886i
$958$	4.72201			0.152561
$959$	26.5259			0.856565
$960$		−	17.6313i		−	0.569047i
$961$	28.6719			0.924901
$962$	−8.43816	+	7.97377i	−0.272057	+	0.257085i
$963$	−12.5796			−0.405373
$964$			23.7990i			0.766514i
$965$	−3.89736			−0.125460
$966$	−11.6792			−0.375772
$967$		−	24.6459i		−	0.792559i	−0.918130	−	0.396279i	$-0.870301\pi$
$967$		−	24.6459i		−	0.792559i	0.918130	−	0.396279i	$-0.129699\pi$
$968$			1.56782i			0.0503917i
$969$			0.218061i			0.00700514i
$970$		−	3.48926i		−	0.112033i
$971$	16.6242			0.533495			0.266748	−	0.963766i	$-0.414051\pi$
$971$	16.6242			0.533495			0.266748	+	0.963766i	$0.414051\pi$
$972$	1.83266			0.0587827
$973$		−	55.8252i		−	1.78967i
$974$	−14.2077			−0.455243
$975$	−31.8029	+	30.0526i	−1.01851	+	0.962453i
$976$	−2.58785			−0.0828350
$977$			11.6096i			0.371425i	0.982604	+	0.185712i	$0.0594593\pi$
$977$			11.6096i			0.371425i	−0.982604	+	0.185712i	$0.940541\pi$
$978$	−10.0105			−0.320099
$979$	4.68461			0.149721
$980$			150.671i			4.81300i
$981$			4.61460i			0.147333i
$982$			8.17871i			0.260993i
$983$			58.4986i			1.86582i	0.360114	+	0.932908i	$0.382738\pi$
$983$			58.4986i			1.86582i	−0.360114	+	0.932908i	$0.617262\pi$
$984$	13.7743			0.439108
$985$	−69.3034			−2.20819
$986$			1.31664i			0.0419304i
$987$	−28.0947			−0.894263
$988$	2.02493	+	2.14286i	0.0644215	+	0.0681735i
$989$	−25.2036			−0.801429
$990$		−	1.69335i		−	0.0538182i
$991$	24.4396			0.776350			0.388175	−	0.921586i	$-0.373106\pi$
$991$	24.4396			0.776350			0.388175	+	0.921586i	$0.373106\pi$
$992$	−6.67178			−0.211829
$993$		−	10.4965i		−	0.333096i
$994$			18.0184i			0.571508i
$995$			54.4649i			1.72665i
$996$		−	0.838434i		−	0.0265668i
$997$	−36.4681			−1.15496			−0.577478	−	0.816406i	$-0.695963\pi$
$997$	−36.4681			−1.15496			−0.577478	+	0.816406i	$0.695963\pi$
$998$	4.23653			0.134105
$999$		−	7.87139i		−	0.249040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.b.298.7	✓	14
3.2	odd	2		1287.2.b.c.298.8		14
13.5	odd	4		5577.2.a.x.1.4		7
13.8	odd	4		5577.2.a.y.1.4		7
13.12	even	2	inner	429.2.b.b.298.8	yes	14
39.38	odd	2		1287.2.b.c.298.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.7	✓	14	1.1	even	1	trivial
429.2.b.b.298.8	yes	14	13.12	even	2	inner
1287.2.b.c.298.7		14	39.38	odd	2
1287.2.b.c.298.8		14	3.2	odd	2
5577.2.a.x.1.4		7	13.5	odd	4
5577.2.a.y.1.4		7	13.8	odd	4

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.409068i q^{2} +1.00000 q^{3} +1.83266 q^{4} -4.13953i q^{5} -0.409068i q^{6} +5.18273i q^{7} -1.56782i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.409068i q^{2} +1.00000 q^{3} +1.83266 q^{4} -4.13953i q^{5} -0.409068i q^{6} +5.18273i q^{7} -1.56782i q^{8} +1.00000 q^{9} -1.69335 q^{10} +1.00000i q^{11} +1.83266 q^{12} +(2.62060 - 2.47638i) q^{13} +2.12009 q^{14} -4.13953i q^{15} +3.02398 q^{16} +0.488730 q^{17} -0.409068i q^{18} +0.446180i q^{19} -7.58636i q^{20} +5.18273i q^{21} +0.409068 q^{22} -5.50882 q^{23} -1.56782i q^{24} -12.1357 q^{25} +(-1.01301 - 1.07200i) q^{26} +1.00000 q^{27} +9.49821i q^{28} -6.58571 q^{29} -1.69335 q^{30} -1.52580i q^{31} -4.37265i q^{32} +1.00000i q^{33} -0.199924i q^{34} +21.4541 q^{35} +1.83266 q^{36} -7.87139i q^{37} +0.182518 q^{38} +(2.62060 - 2.47638i) q^{39} -6.49004 q^{40} +8.78563i q^{41} +2.12009 q^{42} +4.57514 q^{43} +1.83266i q^{44} -4.13953i q^{45} +2.25348i q^{46} +5.42082i q^{47} +3.02398 q^{48} -19.8607 q^{49} +4.96433i q^{50} +0.488730 q^{51} +(4.80268 - 4.53837i) q^{52} +8.66677 q^{53} -0.409068i q^{54} +4.13953 q^{55} +8.12559 q^{56} +0.446180i q^{57} +2.69400i q^{58} +5.60493i q^{59} -7.58636i q^{60} -0.855775 q^{61} -0.624155 q^{62} +5.18273i q^{63} +4.25925 q^{64} +(-10.2510 - 10.8481i) q^{65} +0.409068 q^{66} +3.87464i q^{67} +0.895677 q^{68} -5.50882 q^{69} -8.77618i q^{70} +8.49886i q^{71} -1.56782i q^{72} +5.95291i q^{73} -3.21993 q^{74} -12.1357 q^{75} +0.817698i q^{76} -5.18273 q^{77} +(-1.01301 - 1.07200i) q^{78} -8.91459 q^{79} -12.5179i q^{80} +1.00000 q^{81} +3.59392 q^{82} -0.457495i q^{83} +9.49821i q^{84} -2.02311i q^{85} -1.87154i q^{86} -6.58571 q^{87} +1.56782 q^{88} -4.68461i q^{89} -1.69335 q^{90} +(12.8344 + 13.5819i) q^{91} -10.0958 q^{92} -1.52580i q^{93} +2.21748 q^{94} +1.84697 q^{95} -4.37265i q^{96} +2.06057i q^{97} +8.12439i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9} - 18 q^{12} + 16 q^{14} + 34 q^{16} + 4 q^{17} + 6 q^{22} - 8 q^{23} - 26 q^{25} - 6 q^{26} + 14 q^{27} - 24 q^{29} - 8 q^{35} - 18 q^{36} - 32 q^{38} - 20 q^{40} + 16 q^{42} + 32 q^{43} + 34 q^{48} - 46 q^{49} + 4 q^{51} + 4 q^{52} + 20 q^{53} + 12 q^{55} - 32 q^{56} - 20 q^{61} + 72 q^{62} - 58 q^{64} + 12 q^{65} + 6 q^{66} - 20 q^{68} - 8 q^{69} - 26 q^{75} - 12 q^{77} - 6 q^{78} + 12 q^{79} + 14 q^{81} + 20 q^{82} - 24 q^{87} - 30 q^{88} + 16 q^{91} - 24 q^{92} + 64 q^{94} - 36 q^{95}+O(q^{100}) \) 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9 - 18 * q^12 + 16 * q^14 + 34 * q^16 + 4 * q^17 + 6 * q^22 - 8 * q^23 - 26 * q^25 - 6 * q^26 + 14 * q^27 - 24 * q^29 - 8 * q^35 - 18 * q^36 - 32 * q^38 - 20 * q^40 + 16 * q^42 + 32 * q^43 + 34 * q^48 - 46 * q^49 + 4 * q^51 + 4 * q^52 + 20 * q^53 + 12 * q^55 - 32 * q^56 - 20 * q^61 + 72 * q^62 - 58 * q^64 + 12 * q^65 + 6 * q^66 - 20 * q^68 - 8 * q^69 - 26 * q^75 - 12 * q^77 - 6 * q^78 + 12 * q^79 + 14 * q^81 + 20 * q^82 - 24 * q^87 - 30 * q^88 + 16 * q^91 - 24 * q^92 + 64 * q^94 - 36 * q^95

Introduction

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