LMFDB - Embedded newform 425.2.k.a.171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			171.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	425.171
Dual form			425.2.k.a.256.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.118034 + 0.363271i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-0.309017 + 0.224514i) q^{6} +4.61803 q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.618034 - 1.90211i) q^{9} +0.854102 q^{10} +(1.00000 - 3.07768i) q^{11} +(0.572949 + 1.76336i) q^{12} +(-0.572949 - 1.76336i) q^{13} +(-0.545085 + 1.67760i) q^{14} +(0.690983 - 2.12663i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.809017 + 0.587785i) q^{17} +0.763932 q^{18} +(-3.92705 + 2.85317i) q^{19} +(1.28115 - 3.94298i) q^{20} +(3.73607 + 2.71441i) q^{21} +(1.00000 + 0.726543i) q^{22} +(0.690983 - 2.12663i) q^{23} -1.47214 q^{24} +(-4.04508 + 2.93893i) q^{25} +0.708204 q^{26} +(1.54508 - 4.75528i) q^{27} +(6.92705 + 5.03280i) q^{28} +(5.16312 + 3.75123i) q^{29} +(0.690983 + 0.502029i) q^{30} +(-8.28115 + 6.01661i) q^{31} -4.14590 q^{32} +(2.61803 - 1.90211i) q^{33} +(-0.118034 - 0.363271i) q^{34} +(-3.19098 - 9.82084i) q^{35} +(1.14590 - 3.52671i) q^{36} +(3.07295 + 9.45756i) q^{37} +(-0.572949 - 1.76336i) q^{38} +(0.572949 - 1.76336i) q^{39} +(2.66312 + 1.93487i) q^{40} +(0.763932 + 2.35114i) q^{41} +(-1.42705 + 1.03681i) q^{42} -6.85410 q^{43} +(4.85410 - 3.52671i) q^{44} +(-3.61803 + 2.62866i) q^{45} +(0.690983 + 0.502029i) q^{46} +(-2.11803 - 1.53884i) q^{47} +(-0.972136 + 2.99193i) q^{48} +14.3262 q^{49} +(-0.590170 - 1.81636i) q^{50} -1.00000 q^{51} +(1.06231 - 3.26944i) q^{52} +(-3.04508 - 2.21238i) q^{53} +(1.54508 + 1.12257i) q^{54} -7.23607 q^{55} +(-5.50000 + 3.99598i) q^{56} -4.85410 q^{57} +(-1.97214 + 1.43284i) q^{58} +(3.59017 + 11.0494i) q^{59} +(3.35410 - 2.43690i) q^{60} +(-1.54508 + 4.75528i) q^{61} +(-1.20820 - 3.71847i) q^{62} +(-2.85410 - 8.78402i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(-3.35410 + 2.43690i) q^{65} +(0.381966 + 1.17557i) q^{66} +(12.4721 - 9.06154i) q^{67} -1.85410 q^{68} +(1.80902 - 1.31433i) q^{69} +3.94427 q^{70} +(-6.35410 - 4.61653i) q^{71} +(2.38197 + 1.73060i) q^{72} +(2.78115 - 8.55951i) q^{73} -3.79837 q^{74} -5.00000 q^{75} -9.00000 q^{76} +(4.61803 - 14.2128i) q^{77} +(0.572949 + 0.416272i) q^{78} +(-1.69098 - 1.22857i) q^{79} +(5.69098 - 4.13474i) q^{80} +(-0.809017 + 0.587785i) q^{81} -0.944272 q^{82} +(-4.80902 + 3.49396i) q^{83} +(2.64590 + 8.14324i) q^{84} +(1.80902 + 1.31433i) q^{85} +(0.809017 - 2.48990i) q^{86} +(1.97214 + 6.06961i) q^{87} +(1.47214 + 4.53077i) q^{88} +(0.381966 - 1.17557i) q^{89} +(-0.527864 - 1.62460i) q^{90} +(-2.64590 - 8.14324i) q^{91} +(3.35410 - 2.43690i) q^{92} -10.2361 q^{93} +(0.809017 - 0.587785i) q^{94} +(8.78115 + 6.37988i) q^{95} +(-3.35410 - 2.43690i) q^{96} +(-6.59017 - 4.78804i) q^{97} +(-1.69098 + 5.20431i) q^{98} -6.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + q^{6} + 14 q^{7} - 7 q^{8} + 2 q^{9} - 10 q^{10} + 4 q^{11} + 9 q^{12} - 9 q^{13} + 9 q^{14} + 5 q^{15} - 14 q^{16} - q^{17} + 12 q^{18} - 9 q^{19} - 15 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + q^6 + 14 * q^7 - 7 * q^8 + 2 * q^9 - 10 * q^10 + 4 * q^11 + 9 * q^12 - 9 * q^13 + 9 * q^14 + 5 * q^15 - 14 * q^16 - q^17 + 12 * q^18 - 9 * q^19 - 15 * q^20 + 6 * q^21 + 4 * q^22 + 5 * q^23 + 12 * q^24 - 5 * q^25 - 24 * q^26 - 5 * q^27 + 21 * q^28 + 5 * q^29 + 5 * q^30 - 13 * q^31 - 30 * q^32 + 6 * q^33 + 4 * q^34 - 15 * q^35 + 18 * q^36 + 19 * q^37 - 9 * q^38 + 9 * q^39 - 5 * q^40 + 12 * q^41 + q^42 - 14 * q^43 + 6 * q^44 - 10 * q^45 + 5 * q^46 - 4 * q^47 + 14 * q^48 + 26 * q^49 + 20 * q^50 - 4 * q^51 - 36 * q^52 - q^53 - 5 * q^54 - 20 * q^55 - 22 * q^56 - 6 * q^57 + 10 * q^58 - 8 * q^59 + 5 * q^61 + 22 * q^62 + 2 * q^63 - 17 * q^64 + 6 * q^66 + 32 * q^67 + 6 * q^68 + 5 * q^69 - 20 * q^70 - 12 * q^71 + 14 * q^72 - 9 * q^73 + 34 * q^74 - 20 * q^75 - 36 * q^76 + 14 * q^77 + 9 * q^78 - 9 * q^79 + 25 * q^80 - q^81 + 32 * q^82 - 17 * q^83 + 24 * q^84 + 5 * q^85 + q^86 - 10 * q^87 - 12 * q^88 + 6 * q^89 - 20 * q^90 - 24 * q^91 - 32 * q^93 + q^94 + 15 * q^95 - 4 * q^97 - 9 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	−0.984076	−	0.177750i	$-0.943118\pi$
$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	0.900613	+	0.434622i	$0.143118\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i	0.796305	−	0.604896i	$-0.206785\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i	−0.329218	+	0.944254i	$0.606785\pi$
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$5$	−0.690983	−	2.12663i	−0.309017	−	0.951057i
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$	4.61803			1.74545			0.872726	−	0.488210i	$-0.162350\pi$
$7$	4.61803			1.74545			0.872726	+	0.488210i	$0.162350\pi$
$8$	−1.19098	+	0.865300i	−0.421076	+	0.305930i
$9$	−0.618034	−	1.90211i	−0.206011	−	0.634038i
$10$	0.854102			0.270091
$11$	1.00000	−	3.07768i	0.301511	−	0.927957i	−0.679445	−	0.733727i	$-0.737779\pi$
$11$	1.00000	−	3.07768i	0.301511	−	0.927957i	0.980956	−	0.194230i	$-0.0622207\pi$
$12$	0.572949	+	1.76336i	0.165396	+	0.509037i
$13$	−0.572949	−	1.76336i	−0.158907	−	0.489067i	0.839628	−	0.543161i	$-0.182773\pi$
$13$	−0.572949	−	1.76336i	−0.158907	−	0.489067i	−0.998536	+	0.0540944i	$0.982773\pi$
$14$	−0.545085	+	1.67760i	−0.145680	+	0.448357i
$15$	0.690983	−	2.12663i	0.178411	−	0.549093i
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$18$	0.763932			0.180061
$19$	−3.92705	+	2.85317i	−0.900927	+	0.654562i	−0.938704	−	0.344724i	$-0.887972\pi$
$19$	−3.92705	+	2.85317i	−0.900927	+	0.654562i	0.0377767	+	0.999286i	$0.487972\pi$
$20$	1.28115	−	3.94298i	0.286475	−	0.881678i
$21$	3.73607	+	2.71441i	0.815277	+	0.592333i
$22$	1.00000	+	0.726543i	0.213201	+	0.154899i
$23$	0.690983	−	2.12663i	0.144080	−	0.443432i	−0.852812	−	0.522219i	$-0.825104\pi$
$23$	0.690983	−	2.12663i	0.144080	−	0.443432i	0.996892	+	0.0787863i	$0.0251045\pi$
$24$	−1.47214			−0.300498
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	0.708204			0.138890
$27$	1.54508	−	4.75528i	0.297352	−	0.915155i
$28$	6.92705	+	5.03280i	1.30909	+	0.951109i
$29$	5.16312	+	3.75123i	0.958767	+	0.696585i	0.952864	−	0.303397i	$-0.0981210\pi$
$29$	5.16312	+	3.75123i	0.958767	+	0.696585i	0.00590304	+	0.999983i	$0.498121\pi$
$30$	0.690983	+	0.502029i	0.126156	+	0.0916575i
$31$	−8.28115	+	6.01661i	−1.48734	+	1.08062i	−0.512241	+	0.858842i	$0.671184\pi$
$31$	−8.28115	+	6.01661i	−1.48734	+	1.08062i	−0.975098	+	0.221773i	$0.928816\pi$
$32$	−4.14590			−0.732898
$33$	2.61803	−	1.90211i	0.455741	−	0.331115i
$34$	−0.118034	−	0.363271i	−0.0202427	−	0.0623005i
$35$	−3.19098	−	9.82084i	−0.539375	−	1.66002i
$36$	1.14590	−	3.52671i	0.190983	−	0.587785i
$37$	3.07295	+	9.45756i	0.505190	+	1.55481i	0.800451	+	0.599398i	$0.204593\pi$
$37$	3.07295	+	9.45756i	0.505190	+	1.55481i	−0.295262	+	0.955416i	$0.595407\pi$
$38$	−0.572949	−	1.76336i	−0.0929446	−	0.286054i
$39$	0.572949	−	1.76336i	0.0917453	−	0.282363i
$40$	2.66312	+	1.93487i	0.421076	+	0.305930i
$41$	0.763932	+	2.35114i	0.119306	+	0.367187i	0.992821	−	0.119611i	$-0.0381648\pi$
$41$	0.763932	+	2.35114i	0.119306	+	0.367187i	−0.873515	+	0.486798i	$0.838165\pi$
$42$	−1.42705	+	1.03681i	−0.220199	+	0.159984i
$43$	−6.85410			−1.04524			−0.522620	−	0.852566i	$-0.675045\pi$
$43$	−6.85410			−1.04524			−0.522620	+	0.852566i	$0.675045\pi$
$44$	4.85410	−	3.52671i	0.731783	−	0.531672i
$45$	−3.61803	+	2.62866i	−0.539345	+	0.391857i
$46$	0.690983	+	0.502029i	0.101880	+	0.0740201i
$47$	−2.11803	−	1.53884i	−0.308947	−	0.224463i	0.422498	−	0.906364i	$-0.361154\pi$
$47$	−2.11803	−	1.53884i	−0.308947	−	0.224463i	−0.731445	+	0.681901i	$0.761154\pi$
$48$	−0.972136	+	2.99193i	−0.140316	+	0.431847i
$49$	14.3262			2.04661
$50$	−0.590170	−	1.81636i	−0.0834626	−	0.256872i
$51$	−1.00000			−0.140028
$52$	1.06231	−	3.26944i	0.147315	−	0.453390i
$53$	−3.04508	−	2.21238i	−0.418275	−	0.303894i	0.358669	−	0.933465i	$-0.383231\pi$
$53$	−3.04508	−	2.21238i	−0.418275	−	0.303894i	−0.776943	+	0.629571i	$0.783231\pi$
$54$	1.54508	+	1.12257i	0.210259	+	0.152762i
$55$	−7.23607			−0.975711
$56$	−5.50000	+	3.99598i	−0.734968	+	0.533986i
$57$	−4.85410			−0.642942
$58$	−1.97214	+	1.43284i	−0.258954	+	0.188141i
$59$	3.59017	+	11.0494i	0.467400	+	1.43851i	0.855939	+	0.517078i	$0.172980\pi$
$59$	3.59017	+	11.0494i	0.467400	+	1.43851i	−0.388538	+	0.921433i	$0.627020\pi$
$60$	3.35410	−	2.43690i	0.433013	−	0.314602i
$61$	−1.54508	+	4.75528i	−0.197828	+	0.608852i	0.802104	+	0.597184i	$0.203714\pi$
$61$	−1.54508	+	4.75528i	−0.197828	+	0.608852i	−0.999932	+	0.0116673i	$0.996286\pi$
$62$	−1.20820	−	3.71847i	−0.153442	−	0.472246i
$63$	−2.85410	−	8.78402i	−0.359583	−	1.10668i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	−3.35410	+	2.43690i	−0.416025	+	0.302260i
$66$	0.381966	+	1.17557i	0.0470168	+	0.144703i
$67$	12.4721	−	9.06154i	1.52371	−	1.10704i	0.564106	−	0.825702i	$-0.309221\pi$
$67$	12.4721	−	9.06154i	1.52371	−	1.10704i	0.959608	−	0.281341i	$-0.0907790\pi$
$68$	−1.85410			−0.224843
$69$	1.80902	−	1.31433i	0.217780	−	0.158226i
$70$	3.94427			0.471431
$71$	−6.35410	−	4.61653i	−0.754093	−	0.547881i	0.143000	−	0.989723i	$-0.454325\pi$
$71$	−6.35410	−	4.61653i	−0.754093	−	0.547881i	−0.897093	+	0.441842i	$0.854325\pi$
$72$	2.38197	+	1.73060i	0.280717	+	0.203953i
$73$	2.78115	−	8.55951i	0.325509	−	1.00181i	−0.645701	−	0.763590i	$-0.723435\pi$
$73$	2.78115	−	8.55951i	0.325509	−	1.00181i	0.971210	−	0.238224i	$-0.0765653\pi$
$74$	−3.79837			−0.441552
$75$	−5.00000			−0.577350
$76$	−9.00000			−1.03237
$77$	4.61803	−	14.2128i	0.526274	−	1.61970i
$78$	0.572949	+	0.416272i	0.0648737	+	0.0471335i
$79$	−1.69098	−	1.22857i	−0.190250	−	0.138225i	0.488583	−	0.872518i	$-0.337514\pi$
$79$	−1.69098	−	1.22857i	−0.190250	−	0.138225i	−0.678833	+	0.734293i	$0.737514\pi$
$80$	5.69098	−	4.13474i	0.636271	−	0.462278i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−0.944272			−0.104277
$83$	−4.80902	+	3.49396i	−0.527858	+	0.383511i	−0.819556	−	0.572999i	$-0.805780\pi$
$83$	−4.80902	+	3.49396i	−0.527858	+	0.383511i	0.291698	+	0.956511i	$0.405780\pi$
$84$	2.64590	+	8.14324i	0.288691	+	0.888500i
$85$	1.80902	+	1.31433i	0.196215	+	0.142559i
$86$	0.809017	−	2.48990i	0.0872385	−	0.268493i
$87$	1.97214	+	6.06961i	0.211435	+	0.650731i
$88$	1.47214	+	4.53077i	0.156930	+	0.482982i
$89$	0.381966	−	1.17557i	0.0404883	−	0.124610i	−0.928769	−	0.370658i	$-0.879132\pi$
$89$	0.381966	−	1.17557i	0.0404883	−	0.124610i	0.969258	+	0.246048i	$0.0791321\pi$
$90$	−0.527864	−	1.62460i	−0.0556418	−	0.171248i
$91$	−2.64590	−	8.14324i	−0.277365	−	0.853643i
$92$	3.35410	−	2.43690i	0.349689	−	0.254064i
$93$	−10.2361			−1.06143
$94$	0.809017	−	0.587785i	0.0834437	−	0.0606254i
$95$	8.78115	+	6.37988i	0.900927	+	0.654562i
$96$	−3.35410	−	2.43690i	−0.342327	−	0.248715i
$97$	−6.59017	−	4.78804i	−0.669130	−	0.486152i	0.200604	−	0.979672i	$-0.435710\pi$
$97$	−6.59017	−	4.78804i	−0.669130	−	0.486152i	−0.869734	+	0.493521i	$0.835710\pi$
$98$	−1.69098	+	5.20431i	−0.170815	+	0.525715i
$99$	−6.47214			−0.650474
$100$	−9.27051			−0.927051
$101$	−7.76393			−0.772540			−0.386270	−	0.922386i	$-0.626237\pi$
$101$	−7.76393			−0.772540			−0.386270	+	0.922386i	$0.626237\pi$
$102$	0.118034	−	0.363271i	0.0116871	−	0.0359692i
$103$	−1.07295	−	0.779543i	−0.105721	−	0.0768107i	0.533669	−	0.845694i	$-0.320813\pi$
$103$	−1.07295	−	0.779543i	−0.105721	−	0.0768107i	−0.639390	+	0.768883i	$0.720813\pi$
$104$	2.20820	+	1.60435i	0.216532	+	0.157320i
$105$	3.19098	−	9.82084i	0.311408	−	0.958415i
$106$	1.16312	−	0.845055i	0.112972	−	0.0820790i
$107$	−0.0557281			−0.00538744			−0.00269372	−	0.999996i	$-0.500857\pi$
$107$	−0.0557281			−0.00538744			−0.00269372	+	0.999996i	$0.500857\pi$
$108$	7.50000	−	5.44907i	0.721688	−	0.524337i
$109$	−1.76393	−	5.42882i	−0.168954	−	0.519987i	0.830352	−	0.557239i	$-0.188139\pi$
$109$	−1.76393	−	5.42882i	−0.168954	−	0.519987i	−0.999306	+	0.0372524i	$0.988139\pi$
$110$	0.854102	−	2.62866i	0.0814354	−	0.250632i
$111$	−3.07295	+	9.45756i	−0.291671	+	0.897672i
$112$	4.48936	+	13.8168i	0.424204	+	1.30557i
$113$	−2.26393	−	6.96767i	−0.212973	−	0.655463i	−0.999291	−	0.0376416i	$-0.988015\pi$
$113$	−2.26393	−	6.96767i	−0.212973	−	0.655463i	0.786318	−	0.617821i	$-0.211985\pi$
$114$	0.572949	−	1.76336i	0.0536616	−	0.165153i
$115$	−5.00000			−0.466252
$116$	3.65654	+	11.2537i	0.339501	+	1.04488i
$117$	−3.00000	+	2.17963i	−0.277350	+	0.201507i
$118$	−4.43769			−0.408523
$119$	−3.73607	+	2.71441i	−0.342485	+	0.248830i
$120$	1.01722	+	3.13068i	0.0928591	+	0.285791i
$121$	0.427051	+	0.310271i	0.0388228	+	0.0282064i
$122$	−1.54508	−	1.12257i	−0.139885	−	0.101633i
$123$	−0.763932	+	2.35114i	−0.0688814	+	0.211995i
$124$	−18.9787			−1.70434
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$	3.52786			0.314287
$127$	2.29180	−	7.05342i	0.203364	−	0.625890i	−0.796413	−	0.604754i	$-0.793272\pi$
$127$	2.29180	−	7.05342i	0.203364	−	0.625890i	0.999777	−	0.0211364i	$-0.00672843\pi$
$128$	−8.16312	−	5.93085i	−0.721525	−	0.524218i
$129$	−5.54508	−	4.02874i	−0.488218	−	0.354711i
$130$	−0.489357	−	1.50609i	−0.0429194	−	0.132092i
$131$	−16.4443	+	11.9475i	−1.43674	+	1.04385i	−0.448032	+	0.894018i	$0.647875\pi$
$131$	−16.4443	+	11.9475i	−1.43674	+	1.04385i	−0.988711	+	0.149837i	$0.952125\pi$
$132$	6.00000			0.522233
$133$	−18.1353	+	13.1760i	−1.57253	+	1.14251i
$134$	1.81966	+	5.60034i	0.157195	+	0.483796i
$135$	−11.1803			−0.962250
$136$	0.454915	−	1.40008i	0.0390086	−	0.120056i
$137$	−1.36475	−	4.20025i	−0.116598	−	0.358852i	0.875679	−	0.482894i	$-0.160414\pi$
$137$	−1.36475	−	4.20025i	−0.116598	−	0.358852i	−0.992277	+	0.124042i	$0.960414\pi$
$138$	0.263932	+	0.812299i	0.0224674	+	0.0691475i
$139$	1.30902	−	4.02874i	0.111029	−	0.341713i	−0.880069	−	0.474846i	$-0.842504\pi$
$139$	1.30902	−	4.02874i	0.111029	−	0.341713i	0.991098	+	0.133133i	$0.0425037\pi$
$140$	5.91641	−	18.2088i	0.500028	−	1.53893i
$141$	−0.809017	−	2.48990i	−0.0681315	−	0.209687i
$142$	2.42705	−	1.76336i	0.203674	−	0.147978i
$143$	−6.00000			−0.501745
$144$	5.09017	−	3.69822i	0.424181	−	0.308185i
$145$	4.40983	−	13.5721i	0.366216	−	1.12710i
$146$	2.78115	+	2.02063i	0.230170	+	0.167228i
$147$	11.5902	+	8.42075i	0.955941	+	0.694532i
$148$	−5.69756	+	17.5353i	−0.468337	+	1.44139i
$149$	−15.1803			−1.24362			−0.621811	−	0.783167i	$-0.713603\pi$
$149$	−15.1803			−1.24362			−0.621811	+	0.783167i	$0.713603\pi$
$150$	0.590170	−	1.81636i	0.0481872	−	0.148305i
$151$	11.1459			0.907040			0.453520	−	0.891246i	$-0.350168\pi$
$151$	11.1459			0.907040			0.453520	+	0.891246i	$0.350168\pi$
$152$	2.20820	−	6.79615i	0.179109	−	0.551241i
$153$	1.61803	+	1.17557i	0.130810	+	0.0950392i
$154$	4.61803	+	3.35520i	0.372132	+	0.270370i
$155$	18.5172	+	13.4535i	1.48734	+	1.08062i
$156$	2.78115	−	2.02063i	0.222670	−	0.161780i
$157$	21.0000			1.67598			0.837991	−	0.545684i	$-0.183730\pi$
$157$	21.0000			1.67598			0.837991	+	0.545684i	$0.183730\pi$
$158$	0.645898	−	0.469272i	0.0513849	−	0.0373333i
$159$	−1.16312	−	3.57971i	−0.0922413	−	0.283890i
$160$	2.86475	+	8.81678i	0.226478	+	0.697028i
$161$	3.19098	−	9.82084i	0.251485	−	0.773990i
$162$	−0.118034	−	0.363271i	−0.00927363	−	0.0285413i
$163$	−3.60081	−	11.0822i	−0.282037	−	0.868022i	−0.987271	−	0.159047i	$-0.949158\pi$
$163$	−3.60081	−	11.0822i	−0.282037	−	0.868022i	0.705234	−	0.708975i	$-0.250842\pi$
$164$	−1.41641	+	4.35926i	−0.110603	+	0.340401i
$165$	−5.85410	−	4.25325i	−0.455741	−	0.331115i
$166$	−0.701626	−	2.15938i	−0.0544567	−	0.167601i
$167$	16.2533	−	11.8087i	1.25772	−	0.913785i	0.259074	−	0.965857i	$-0.416583\pi$
$167$	16.2533	−	11.8087i	1.25772	−	0.913785i	0.998643	+	0.0520724i	$0.0165827\pi$
$168$	−6.79837			−0.524506
$169$	7.73607	−	5.62058i	0.595082	−	0.432352i
$170$	−0.690983	+	0.502029i	−0.0529960	+	0.0385038i
$171$	7.85410	+	5.70634i	0.600618	+	0.436375i
$172$	−10.2812	−	7.46969i	−0.783931	−	0.569559i
$173$	−1.92705	+	5.93085i	−0.146511	+	0.450914i	−0.997202	−	0.0747513i	$-0.976184\pi$
$173$	−1.92705	+	5.93085i	−0.146511	+	0.450914i	0.850691	+	0.525666i	$0.176184\pi$
$174$	−2.43769			−0.184801
$175$	−18.6803	+	13.5721i	−1.41210	+	1.02595i
$176$	10.1803			0.767372
$177$	−3.59017	+	11.0494i	−0.269854	+	0.830524i
$178$	0.381966	+	0.277515i	0.0286296	+	0.0208006i
$179$	21.2254	+	15.4212i	1.58646	+	1.15263i	0.908778	+	0.417280i	$0.137017\pi$
$179$	21.2254	+	15.4212i	1.58646	+	1.15263i	0.677685	+	0.735352i	$0.262983\pi$
$180$	−8.29180			−0.618034
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	−0.412899	−	0.910777i	$-0.635484\pi$
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	0.738608	+	0.674136i	$0.235484\pi$
$182$	3.27051			0.242426
$183$	−4.04508	+	2.93893i	−0.299021	+	0.217252i
$184$	1.01722	+	3.13068i	0.0749905	+	0.230797i
$185$	17.9894	−	13.0700i	1.32260	−	0.960928i
$186$	1.20820	−	3.71847i	0.0885898	−	0.272651i
$187$	1.00000	+	3.07768i	0.0731272	+	0.225063i
$188$	−1.50000	−	4.61653i	−0.109399	−	0.336695i
$189$	7.13525	−	21.9601i	0.519013	−	1.59736i
$190$	−3.35410	+	2.43690i	−0.243332	+	0.176791i
$191$	−6.38197	−	19.6417i	−0.461783	−	1.42122i	−0.862984	−	0.505231i	$-0.831407\pi$
$191$	−6.38197	−	19.6417i	−0.461783	−	1.42122i	0.401201	−	0.915990i	$-0.368593\pi$
$192$	−3.80902	+	2.76741i	−0.274892	+	0.199721i
$193$	22.9443			1.65156			0.825782	−	0.563989i	$-0.190734\pi$
$193$	22.9443			1.65156			0.825782	+	0.563989i	$0.190734\pi$
$194$	2.51722	−	1.82887i	0.180726	−	0.131305i
$195$	−4.14590			−0.296894
$196$	21.4894	+	15.6129i	1.53495	+	1.11521i
$197$	1.76393	+	1.28157i	0.125675	+	0.0913082i	0.648847	−	0.760919i	$-0.275252\pi$
$197$	1.76393	+	1.28157i	0.125675	+	0.0913082i	−0.523172	+	0.852227i	$0.675252\pi$
$198$	0.763932	−	2.35114i	0.0542903	−	0.167088i
$199$	10.3262			0.732008			0.366004	−	0.930613i	$-0.380726\pi$
$199$	10.3262			0.732008			0.366004	+	0.930613i	$0.380726\pi$
$200$	2.27458	−	7.00042i	0.160837	−	0.495005i
$201$	15.4164			1.08739
$202$	0.916408	−	2.82041i	0.0644782	−	0.198444i
$203$	23.8435	+	17.3233i	1.67348	+	1.21586i
$204$	−1.50000	−	1.08981i	−0.105021	−	0.0763022i
$205$	4.47214	−	3.24920i	0.312348	−	0.226934i
$206$	0.409830	−	0.297759i	0.0285542	−	0.0207459i
$207$	−4.47214			−0.310835
$208$	4.71885	−	3.42844i	0.327193	−	0.237720i
$209$	4.85410	+	14.9394i	0.335765	+	1.03338i
$210$	3.19098	+	2.31838i	0.220199	+	0.159984i
$211$	−6.54508	+	20.1437i	−0.450582	+	1.38675i	0.425662	+	0.904882i	$0.360041\pi$
$211$	−6.54508	+	20.1437i	−0.450582	+	1.38675i	−0.876244	+	0.481867i	$0.839959\pi$
$212$	−2.15654	−	6.63715i	−0.148112	−	0.455841i
$213$	−2.42705	−	7.46969i	−0.166299	−	0.511815i
$214$	0.00657781	−	0.0202444i	0.000449650	−	0.00138388i
$215$	4.73607	+	14.5761i	0.322997	+	0.994083i
$216$	2.27458	+	7.00042i	0.154765	+	0.476318i
$217$	−38.2426	+	27.7849i	−2.59608	+	1.88616i
$218$	2.18034			0.147671
$219$	7.28115	−	5.29007i	0.492015	−	0.357470i
$220$	−10.8541	−	7.88597i	−0.731783	−	0.531672i
$221$	1.50000	+	1.08981i	0.100901	+	0.0733088i
$222$	−3.07295	−	2.23263i	−0.206243	−	0.149844i
$223$	3.00000	−	9.23305i	0.200895	−	0.618291i	−0.798962	−	0.601381i	$-0.794617\pi$
$223$	3.00000	−	9.23305i	0.200895	−	0.618291i	0.999857	−	0.0169095i	$-0.00538272\pi$
$224$	−19.1459			−1.27924
$225$	8.09017	+	5.87785i	0.539345	+	0.391857i
$226$	2.79837			0.186145
$227$	−4.14590	+	12.7598i	−0.275173	+	0.846895i	0.714001	+	0.700145i	$0.246881\pi$
$227$	−4.14590	+	12.7598i	−0.275173	+	0.846895i	−0.989174	+	0.146750i	$0.953119\pi$
$228$	−7.28115	−	5.29007i	−0.482206	−	0.350343i
$229$	−4.85410	−	3.52671i	−0.320768	−	0.233052i	0.415735	−	0.909486i	$-0.363524\pi$
$229$	−4.85410	−	3.52671i	−0.320768	−	0.233052i	−0.736503	+	0.676434i	$0.763524\pi$
$230$	0.590170	−	1.81636i	0.0389147	−	0.119767i
$231$	12.0902	−	8.78402i	0.795475	−	0.577946i
$232$	−9.39512			−0.616820
$233$	−6.61803	+	4.80828i	−0.433562	+	0.315001i	−0.783072	−	0.621932i	$-0.786348\pi$
$233$	−6.61803	+	4.80828i	−0.433562	+	0.315001i	0.349510	+	0.936933i	$0.386348\pi$
$234$	−0.437694	−	1.34708i	−0.0286130	−	0.0880616i
$235$	−1.80902	+	5.56758i	−0.118007	+	0.363189i
$236$	−6.65654	+	20.4867i	−0.433304	+	1.33357i
$237$	−0.645898	−	1.98787i	−0.0419556	−	0.129126i
$238$	−0.545085	−	1.67760i	−0.0353326	−	0.108743i
$239$	0.454915	−	1.40008i	0.0294260	−	0.0905639i	−0.935265	−	0.353949i	$-0.884839\pi$
$239$	0.454915	−	1.40008i	0.0294260	−	0.0905639i	0.964691	+	0.263385i	$0.0848388\pi$
$240$	7.03444			0.454071
$241$	−4.07295	−	12.5352i	−0.262362	−	0.807466i	−0.992289	−	0.123942i	$-0.960446\pi$
$241$	−4.07295	−	12.5352i	−0.262362	−	0.807466i	0.729928	−	0.683524i	$-0.239554\pi$
$242$	−0.163119	+	0.118513i	−0.0104857	+	0.00761830i
$243$	−16.0000			−1.02640
$244$	−7.50000	+	5.44907i	−0.480138	+	0.348841i
$245$	−9.89919	−	30.4666i	−0.632436	−	1.94644i
$246$	−0.763932	−	0.555029i	−0.0487065	−	0.0353874i
$247$	7.28115	+	5.29007i	0.463289	+	0.336599i
$248$	4.65654	−	14.3314i	0.295691	−	0.910042i
$249$	−5.94427			−0.376703
$250$	−3.45492	+	2.51014i	−0.218508	+	0.158755i
$251$	−23.6525			−1.49293			−0.746466	−	0.665424i	$-0.768251\pi$
$251$	−23.6525			−1.49293			−0.746466	+	0.665424i	$0.768251\pi$
$252$	5.29180	−	16.2865i	0.333352	−	1.02595i
$253$	−5.85410	−	4.25325i	−0.368044	−	0.267400i
$254$	2.29180	+	1.66509i	0.143800	+	0.104477i
$255$	0.690983	+	2.12663i	0.0432710	+	0.133175i
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	4.85410			0.302791			0.151395	−	0.988473i	$-0.451623\pi$
$257$	4.85410			0.302791			0.151395	+	0.988473i	$0.451623\pi$
$258$	2.11803	−	1.53884i	0.131863	−	0.0958041i
$259$	14.1910	+	43.6754i	0.881785	+	2.71385i
$260$	−7.68692			−0.476722
$261$	3.94427	−	12.1392i	0.244144	−	0.751399i
$262$	−2.39919	−	7.38394i	−0.148222	−	0.456181i
$263$	2.28115	+	7.02067i	0.140662	+	0.432913i	0.996428	−	0.0844506i	$-0.0269135\pi$
$263$	2.28115	+	7.02067i	0.140662	+	0.432913i	−0.855766	+	0.517363i	$0.826914\pi$
$264$	−1.47214	+	4.53077i	−0.0906037	+	0.278850i
$265$	−2.60081	+	8.00448i	−0.159767	+	0.491711i
$266$	−2.64590	−	8.14324i	−0.162230	−	0.499294i
$267$	1.00000	−	0.726543i	0.0611990	−	0.0444637i
$268$	28.5836			1.74602
$269$	10.8541	−	7.88597i	0.661786	−	0.480816i	−0.205479	−	0.978661i	$-0.565875\pi$
$269$	10.8541	−	7.88597i	0.661786	−	0.480816i	0.867266	+	0.497846i	$0.165875\pi$
$270$	1.31966	−	4.06150i	0.0803120	−	0.247175i
$271$	12.8541	+	9.33905i	0.780831	+	0.567307i	0.905228	−	0.424926i	$-0.139700\pi$
$271$	12.8541	+	9.33905i	0.780831	+	0.567307i	−0.124397	+	0.992232i	$0.539700\pi$
$272$	−2.54508	−	1.84911i	−0.154318	−	0.112119i
$273$	2.64590	−	8.14324i	0.160137	−	0.492851i
$274$	1.68692			0.101910
$275$	5.00000	+	15.3884i	0.301511	+	0.927957i
$276$	4.14590			0.249554
$277$	−5.48936	+	16.8945i	−0.329823	+	1.01509i	0.639393	+	0.768880i	$0.279186\pi$
$277$	−5.48936	+	16.8945i	−0.329823	+	1.01509i	−0.969216	+	0.246212i	$0.920814\pi$
$278$	1.30902	+	0.951057i	0.0785096	+	0.0570406i
$279$	16.5623	+	12.0332i	0.991559	+	0.720410i
$280$	12.2984	+	8.93529i	0.734968	+	0.533986i
$281$	6.92705	−	5.03280i	0.413233	−	0.300232i	−0.361676	−	0.932304i	$-0.617795\pi$
$281$	6.92705	−	5.03280i	0.413233	−	0.300232i	0.774909	+	0.632072i	$0.217795\pi$
$282$	1.00000			0.0595491
$283$	−2.35410	+	1.71036i	−0.139937	+	0.101670i	−0.655551	−	0.755151i	$-0.727564\pi$
$283$	−2.35410	+	1.71036i	−0.139937	+	0.101670i	0.515614	+	0.856821i	$0.327564\pi$
$284$	−4.50000	−	13.8496i	−0.267026	−	0.821821i
$285$	3.35410	+	10.3229i	0.198680	+	0.611474i
$286$	0.708204	−	2.17963i	0.0418770	−	0.128884i
$287$	3.52786	+	10.8576i	0.208243	+	0.640907i
$288$	2.56231	+	7.88597i	0.150985	+	0.464685i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	4.40983	+	3.20393i	0.258954	+	0.188141i
$291$	−2.51722	−	7.74721i	−0.147562	−	0.454149i
$292$	13.5000	−	9.80832i	0.790028	−	0.573989i
$293$	−2.94427			−0.172006			−0.0860031	−	0.996295i	$-0.527409\pi$
$293$	−2.94427			−0.172006			−0.0860031	+	0.996295i	$0.527409\pi$
$294$	−4.42705	+	3.21644i	−0.258191	+	0.187587i
$295$	21.0172	−	15.2699i	1.22367	−	0.889048i
$296$	−11.8435	−	8.60478i	−0.688387	−	0.500142i
$297$	−13.0902	−	9.51057i	−0.759569	−	0.551859i
$298$	1.79180	−	5.51458i	0.103796	−	0.319451i
$299$	−4.14590			−0.239763
$300$	−7.50000	−	5.44907i	−0.433013	−	0.314602i
$301$	−31.6525			−1.82442
$302$	−1.31559	+	4.04898i	−0.0757040	+	0.232993i
$303$	−6.28115	−	4.56352i	−0.360843	−	0.262168i
$304$	−12.3541	−	8.97578i	−0.708556	−	0.514796i
$305$	11.1803			0.640184
$306$	−0.618034	+	0.449028i	−0.0353307	+	0.0256692i
$307$	−1.05573			−0.0602536			−0.0301268	−	0.999546i	$-0.509591\pi$
$307$	−1.05573			−0.0602536			−0.0301268	+	0.999546i	$0.509591\pi$
$308$	22.4164	−	16.2865i	1.27729	−	0.928008i
$309$	−0.409830	−	1.26133i	−0.0233144	−	0.0717544i
$310$	−7.07295	+	5.13880i	−0.401717	+	0.291864i
$311$	1.84346	−	5.67358i	0.104533	−	0.321719i	−0.885088	−	0.465424i	$-0.845902\pi$
$311$	1.84346	−	5.67358i	0.104533	−	0.321719i	0.989621	+	0.143705i	$0.0459017\pi$
$312$	0.843459	+	2.59590i	0.0477515	+	0.146964i
$313$	4.14590	+	12.7598i	0.234340	+	0.721224i	0.997208	+	0.0746704i	$0.0237905\pi$
$313$	4.14590	+	12.7598i	0.234340	+	0.721224i	−0.762868	+	0.646554i	$0.776210\pi$
$314$	−2.47871	+	7.62870i	−0.139882	+	0.430512i
$315$	−16.7082	+	12.1392i	−0.941401	+	0.683968i
$316$	−1.19756	−	3.68571i	−0.0673681	−	0.207338i
$317$	−7.19098	+	5.22455i	−0.403886	+	0.293440i	−0.771122	−	0.636688i	$-0.780304\pi$
$317$	−7.19098	+	5.22455i	−0.403886	+	0.293440i	0.367236	+	0.930128i	$0.380304\pi$
$318$	1.43769			0.0806219
$319$	16.7082	−	12.1392i	0.935480	−	0.679666i
$320$	10.5279			0.588525
$321$	−0.0450850	−	0.0327561i	−0.00251640	−	0.00182827i
$322$	3.19098	+	2.31838i	0.177827	+	0.129199i
$323$	1.50000	−	4.61653i	0.0834622	−	0.256870i
$324$	−1.85410			−0.103006
$325$	7.50000	+	5.44907i	0.416025	+	0.302260i
$326$	4.45085			0.246510
$327$	1.76393	−	5.42882i	0.0975457	−	0.300215i
$328$	−2.94427	−	2.13914i	−0.162570	−	0.118114i
$329$	−9.78115	−	7.10642i	−0.539252	−	0.391790i
$330$	2.23607	−	1.62460i	0.123091	−	0.0894312i
$331$	14.0902	−	10.2371i	0.774466	−	0.562682i	−0.128847	−	0.991664i	$-0.541128\pi$
$331$	14.0902	−	10.2371i	0.774466	−	0.562682i	0.903313	+	0.428982i	$0.141128\pi$
$332$	−11.0213			−0.604872
$333$	16.0902	−	11.6902i	0.881736	−	0.640619i
$334$	2.37132	+	7.29818i	0.129753	+	0.399339i
$335$	−27.8885	−	20.2622i	−1.52371	−	1.10704i
$336$	−4.48936	+	13.8168i	−0.244914	+	0.753769i
$337$	−4.42705	−	13.6251i	−0.241157	−	0.742204i	−0.996245	−	0.0865809i	$-0.972406\pi$
$337$	−4.42705	−	13.6251i	−0.241157	−	0.742204i	0.755088	−	0.655623i	$-0.227594\pi$
$338$	1.12868	+	3.47371i	0.0613919	+	0.188945i
$339$	2.26393	−	6.96767i	0.122960	−	0.378432i
$340$	1.28115	+	3.94298i	0.0694803	+	0.213838i
$341$	10.2361	+	31.5034i	0.554314	+	1.70600i
$342$	−3.00000	+	2.17963i	−0.162221	+	0.117861i
$343$	33.8328			1.82680
$344$	8.16312	−	5.93085i	0.440126	−	0.319770i
$345$	−4.04508	−	2.93893i	−0.217780	−	0.158226i
$346$	−1.92705	−	1.40008i	−0.103599	−	0.0752690i
$347$	−7.30902	−	5.31031i	−0.392369	−	0.285072i	0.374057	−	0.927406i	$-0.377966\pi$
$347$	−7.30902	−	5.31031i	−0.392369	−	0.285072i	−0.766425	+	0.642333i	$0.777966\pi$
$348$	−3.65654	+	11.2537i	−0.196011	+	0.603260i
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$	−2.72542	−	8.38800i	−0.145680	−	0.448357i
$351$	−9.27051			−0.494823
$352$	−4.14590	+	12.7598i	−0.220977	+	0.680098i
$353$	−20.2082	−	14.6821i	−1.07557	−	0.781450i	−0.0986683	−	0.995120i	$-0.531458\pi$
$353$	−20.2082	−	14.6821i	−1.07557	−	0.781450i	−0.976906	+	0.213670i	$0.931458\pi$
$354$	−3.59017	−	2.60841i	−0.190815	−	0.138635i
$355$	−5.42705	+	16.7027i	−0.288038	+	0.886490i
$356$	1.85410	−	1.34708i	0.0982672	−	0.0713953i
$357$	−4.61803			−0.244412
$358$	−8.10739	+	5.89036i	−0.428489	+	0.311315i
$359$	−10.7533	−	33.0952i	−0.567537	−	1.74670i	−0.660291	−	0.751010i	$-0.729567\pi$
$359$	−10.7533	−	33.0952i	−0.567537	−	1.74670i	0.0927541	−	0.995689i	$-0.470433\pi$
$360$	2.03444	−	6.26137i	0.107225	−	0.330003i
$361$	1.40983	−	4.33901i	0.0742016	−	0.228369i
$362$	0.639320	+	1.96763i	0.0336019	+	0.103416i
$363$	0.163119	+	0.502029i	0.00856153	+	0.0263497i
$364$	4.90576	−	15.0984i	0.257132	−	0.791371i
$365$	−20.1246			−1.05337
$366$	−0.590170	−	1.81636i	−0.0308487	−	0.0949425i
$367$	−27.3885	+	19.8989i	−1.42967	+	1.03872i	−0.439592	+	0.898197i	$0.644877\pi$
$367$	−27.3885	+	19.8989i	−1.42967	+	1.03872i	−0.990078	+	0.140519i	$0.955123\pi$
$368$	7.03444			0.366696
$369$	4.00000	−	2.90617i	0.208232	−	0.151289i
$370$	2.62461	+	8.07772i	0.136447	+	0.419941i
$371$	−14.0623	−	10.2169i	−0.730079	−	0.530433i
$372$	−15.3541	−	11.1554i	−0.796073	−	0.578381i
$373$	4.06231	−	12.5025i	0.210338	−	0.647354i	−0.789114	−	0.614247i	$-0.789460\pi$
$373$	4.06231	−	12.5025i	0.210338	−	0.647354i	0.999452	−	0.0331072i	$-0.0105403\pi$
$374$	−1.23607			−0.0639156
$375$	3.45492	+	10.6331i	0.178411	+	0.549093i
$376$	3.85410			0.198760
$377$	3.65654	−	11.2537i	0.188321	−	0.579594i
$378$	7.13525	+	5.18407i	0.366998	+	0.266640i
$379$	−18.5172	−	13.4535i	−0.951166	−	0.691062i	−8.34488e−5	−	1.00000i	$-0.500027\pi$
$379$	−18.5172	−	13.4535i	−0.951166	−	0.691062i	−0.951082	+	0.308938i	$0.900027\pi$
$380$	6.21885	+	19.1396i	0.319020	+	0.981843i
$381$	6.00000	−	4.35926i	0.307389	−	0.223331i
$382$	7.88854			0.403613
$383$	−13.3713	+	9.71483i	−0.683243	+	0.496405i	−0.874432	−	0.485148i	$-0.838766\pi$
$383$	−13.3713	+	9.71483i	−0.683243	+	0.496405i	0.191189	+	0.981553i	$0.438766\pi$
$384$	−3.11803	−	9.59632i	−0.159117	−	0.489710i
$385$	−33.4164			−1.70306
$386$	−2.70820	+	8.33499i	−0.137844	+	0.424240i
$387$	4.23607	+	13.0373i	0.215331	+	0.662722i
$388$	−4.66718	−	14.3641i	−0.236940	−	0.729228i
$389$	7.21885	−	22.2173i	0.366010	−	1.12646i	−0.583336	−	0.812231i	$-0.698253\pi$
$389$	7.21885	−	22.2173i	0.366010	−	1.12646i	0.949346	−	0.314232i	$-0.101747\pi$
$390$	0.489357	−	1.50609i	0.0247795	−	0.0762636i
$391$	0.690983	+	2.12663i	0.0349445	+	0.107548i
$392$	−17.0623	+	12.3965i	−0.861777	+	0.626117i
$393$	−20.3262			−1.02532
$394$	−0.673762	+	0.489517i	−0.0339436	+	0.0246615i
$395$	−1.44427	+	4.44501i	−0.0726692	+	0.223653i
$396$	−9.70820	−	7.05342i	−0.487856	−	0.354448i
$397$	−4.78115	−	3.47371i	−0.239959	−	0.174341i	0.461306	−	0.887241i	$-0.347381\pi$
$397$	−4.78115	−	3.47371i	−0.239959	−	0.174341i	−0.701265	+	0.712901i	$0.747381\pi$
$398$	−1.21885	+	3.75123i	−0.0610953	+	0.188032i
$399$	−22.4164			−1.12222
$400$	−12.7254	−	9.24556i	−0.636271	−	0.462278i
$401$	3.76393			0.187962			0.0939809	−	0.995574i	$-0.470041\pi$
$401$	3.76393			0.187962			0.0939809	+	0.995574i	$0.470041\pi$
$402$	−1.81966	+	5.60034i	−0.0907564	+	0.279319i
$403$	15.3541	+	11.1554i	0.764842	+	0.555690i
$404$	−11.6459	−	8.46124i	−0.579405	−	0.420962i
$405$	1.80902	+	1.31433i	0.0898908	+	0.0653095i
$406$	−9.10739	+	6.61691i	−0.451992	+	0.328392i
$407$	32.1803			1.59512
$408$	1.19098	−	0.865300i	0.0589624	−	0.0428387i
$409$	4.36475	+	13.4333i	0.215823	+	0.664234i	0.999094	+	0.0425542i	$0.0135495\pi$
$409$	4.36475	+	13.4333i	0.215823	+	0.664234i	−0.783271	+	0.621680i	$0.786450\pi$
$410$	0.652476	+	2.00811i	0.0322235	+	0.0991737i
$411$	1.36475	−	4.20025i	0.0673179	−	0.207183i
$412$	−0.759867	−	2.33863i	−0.0374359	−	0.115216i
$413$	16.5795	+	51.0265i	0.815825	+	2.51085i
$414$	0.527864	−	1.62460i	0.0259431	−	0.0798447i
$415$	10.7533	+	7.81272i	0.527858	+	0.383511i
$416$	2.37539	+	7.31069i	0.116463	+	0.358436i
$417$	3.42705	−	2.48990i	0.167823	−	0.121931i
$418$	−6.00000			−0.293470
$419$	−30.4615	+	22.1316i	−1.48814	+	1.08120i	−0.513323	+	0.858195i	$0.671586\pi$
$419$	−30.4615	+	22.1316i	−1.48814	+	1.08120i	−0.974818	+	0.223003i	$0.928414\pi$
$420$	15.4894	−	11.2537i	0.755803	−	0.549123i
$421$	−2.23607	−	1.62460i	−0.108979	−	0.0791781i	0.531961	−	0.846769i	$-0.321455\pi$
$421$	−2.23607	−	1.62460i	−0.108979	−	0.0791781i	−0.640940	+	0.767591i	$0.721455\pi$
$422$	−6.54508	−	4.75528i	−0.318610	−	0.231484i
$423$	−1.61803	+	4.97980i	−0.0786715	+	0.242126i
$424$	5.54102			0.269096
$425$	1.54508	−	4.75528i	0.0749476	−	0.230665i
$426$	3.00000			0.145350
$427$	−7.13525	+	21.9601i	−0.345299	+	1.06272i
$428$	−0.0835921	−	0.0607332i	−0.00404058	−	0.00293565i
$429$	−4.85410	−	3.52671i	−0.234358	−	0.170271i
$430$	−5.85410			−0.282310
$431$	25.3713	−	18.4333i	1.22209	−	0.887903i	0.225821	−	0.974169i	$-0.427493\pi$
$431$	25.3713	−	18.4333i	1.22209	−	0.887903i	0.996272	+	0.0862657i	$0.0274934\pi$
$432$	15.7295			0.756785
$433$	−6.92705	+	5.03280i	−0.332893	+	0.241861i	−0.741657	−	0.670779i	$-0.765960\pi$
$433$	−6.92705	+	5.03280i	−0.332893	+	0.241861i	0.408764	+	0.912640i	$0.365960\pi$
$434$	−5.57953	−	17.1720i	−0.267826	−	0.824283i
$435$	11.5451	−	8.38800i	0.553544	−	0.402174i
$436$	3.27051	−	10.0656i	0.156629	−	0.482055i
$437$	3.35410	+	10.3229i	0.160448	+	0.493810i
$438$	1.06231	+	3.26944i	0.0507589	+	0.156220i
$439$	−2.57295	+	7.91872i	−0.122800	+	0.377940i	−0.993494	−	0.113886i	$-0.963670\pi$
$439$	−2.57295	+	7.91872i	−0.122800	+	0.377940i	0.870694	+	0.491826i	$0.163670\pi$
$440$	8.61803	−	6.26137i	0.410849	−	0.298499i
$441$	−8.85410	−	27.2501i	−0.421624	−	1.29762i
$442$	−0.572949	+	0.416272i	−0.0272524	+	0.0198000i
$443$	5.47214			0.259989			0.129995	−	0.991515i	$-0.458504\pi$
$443$	5.47214			0.259989			0.129995	+	0.991515i	$0.458504\pi$
$444$	−14.9164	+	10.8374i	−0.707901	+	0.514320i
$445$	−2.76393			−0.131023
$446$	3.00000	+	2.17963i	0.142054	+	0.103208i
$447$	−12.2812	−	8.92278i	−0.580879	−	0.422033i
$448$	−6.71885	+	20.6785i	−0.317436	+	0.976967i
$449$	−22.0902			−1.04250			−0.521250	−	0.853404i	$-0.674534\pi$
$449$	−22.0902			−1.04250			−0.521250	+	0.853404i	$0.674534\pi$
$450$	−3.09017	+	2.24514i	−0.145672	+	0.105837i
$451$	8.00000			0.376705
$452$	4.19756	−	12.9188i	0.197437	−	0.607648i
$453$	9.01722	+	6.55139i	0.423666	+	0.307811i
$454$	−4.14590	−	3.01217i	−0.194577	−	0.141368i
$455$	−15.4894	+	11.2537i	−0.726152	+	0.527580i
$456$	5.78115	−	4.20025i	0.270727	−	0.196695i
$457$	24.8328			1.16163			0.580815	−	0.814036i	$-0.302734\pi$
$457$	24.8328			1.16163			0.580815	+	0.814036i	$0.302734\pi$
$458$	1.85410	−	1.34708i	0.0866365	−	0.0629451i
$459$	1.54508	+	4.75528i	0.0721184	+	0.221958i
$460$	−7.50000	−	5.44907i	−0.349689	−	0.254064i
$461$	−1.39919	+	4.30625i	−0.0651666	+	0.200562i	−0.978338	−	0.207013i	$-0.933626\pi$
$461$	−1.39919	+	4.30625i	−0.0651666	+	0.200562i	0.913172	+	0.407576i	$0.133626\pi$
$462$	1.76393	+	5.42882i	0.0820655	+	0.252572i
$463$	−6.98278	−	21.4908i	−0.324517	−	0.998761i	−0.971658	−	0.236391i	$-0.924035\pi$
$463$	−6.98278	−	21.4908i	−0.324517	−	0.998761i	0.647141	−	0.762371i	$-0.275965\pi$
$464$	−6.20414	+	19.0944i	−0.288020	+	0.886434i
$465$	7.07295	+	21.7683i	0.328000	+	1.00948i
$466$	−0.965558	−	2.97168i	−0.0447286	−	0.137661i
$467$	−4.11803	+	2.99193i	−0.190560	+	0.138450i	−0.678975	−	0.734162i	$-0.737575\pi$
$467$	−4.11803	+	2.99193i	−0.190560	+	0.138450i	0.488415	+	0.872612i	$0.337575\pi$
$468$	−6.87539			−0.317815
$469$	57.5967	−	41.8465i	2.65957	−	1.93229i
$470$	−1.80902	−	1.31433i	−0.0834437	−	0.0606254i
$471$	16.9894	+	12.3435i	0.782828	+	0.568758i
$472$	−13.8369	−	10.0531i	−0.636894	−	0.462731i
$473$	−6.85410	+	21.0948i	−0.315152	+	0.969938i
$474$	0.798374			0.0366705
$475$	7.50000	−	23.0826i	0.344124	−	1.05910i
$476$	−8.56231			−0.392453
$477$	−2.32624	+	7.15942i	−0.106511	+	0.327808i
$478$	0.454915	+	0.330515i	0.0208073	+	0.0151174i
$479$	−0.781153	−	0.567541i	−0.0356918	−	0.0259316i	0.569796	−	0.821786i	$-0.307022\pi$
$479$	−0.781153	−	0.567541i	−0.0356918	−	0.0259316i	−0.605488	+	0.795854i	$0.707022\pi$
$480$	−2.86475	+	8.81678i	−0.130757	+	0.402429i
$481$	14.9164	−	10.8374i	0.680130	−	0.494143i
$482$	5.03444			0.229313
$483$	8.35410	−	6.06961i	0.380125	−	0.276177i
$484$	0.302439	+	0.930812i	0.0137472	+	0.0423096i
$485$	−5.62868	+	17.3233i	−0.255585	+	0.786610i
$486$	1.88854	−	5.81234i	0.0856661	−	0.263653i
$487$	6.92705	+	21.3193i	0.313895	+	0.966068i	0.976207	+	0.216841i	$0.0695752\pi$
$487$	6.92705	+	21.3193i	0.313895	+	0.966068i	−0.662312	+	0.749228i	$0.730425\pi$
$488$	−2.27458	−	7.00042i	−0.102965	−	0.316894i
$489$	3.60081	−	11.0822i	0.162834	−	0.501153i
$490$	12.2361			0.552769
$491$	4.30902	+	13.2618i	0.194463	+	0.598496i	0.999982	+	0.00592659i	$0.00188650\pi$
$491$	4.30902	+	13.2618i	0.194463	+	0.598496i	−0.805519	+	0.592570i	$0.798113\pi$
$492$	−3.70820	+	2.69417i	−0.167179	+	0.121462i
$493$	−6.38197			−0.287429
$494$	−2.78115	+	2.02063i	−0.125130	+	0.0909123i
$495$	4.47214	+	13.7638i	0.201008	+	0.618638i
$496$	−26.0517	−	18.9276i	−1.16975	−	0.849876i
$497$	−29.3435	−	21.3193i	−1.31623	−	0.956300i
$498$	0.701626	−	2.15938i	0.0314406	−	0.0967643i
$499$	−22.3262			−0.999460			−0.499730	−	0.866181i	$-0.666567\pi$
$499$	−22.3262			−0.999460			−0.499730	+	0.866181i	$0.666567\pi$
$500$	6.40576	+	19.7149i	0.286475	+	0.881678i
$501$	20.0902			0.897563
$502$	2.79180	−	8.59226i	0.124604	−	0.383492i
$503$	22.5623	+	16.3925i	1.00600	+	0.730904i	0.963367	−	0.268186i	$-0.0864243\pi$
$503$	22.5623	+	16.3925i	1.00600	+	0.730904i	0.0426364	+	0.999091i	$0.486424\pi$
$504$	11.0000	+	7.99197i	0.489979	+	0.355991i
$505$	5.36475	+	16.5110i	0.238728	+	0.734729i
$506$	2.23607	−	1.62460i	0.0994053	−	0.0722222i
$507$	9.56231			0.424677
$508$	11.1246	−	8.08250i	0.493575	−	0.358603i
$509$	−2.13525	−	6.57164i	−0.0946435	−	0.291283i	0.892517	−	0.451014i	$-0.148937\pi$
$509$	−2.13525	−	6.57164i	−0.0946435	−	0.291283i	−0.987161	+	0.159731i	$0.948937\pi$
$510$	−0.854102			−0.0378203
$511$	12.8435	−	39.5281i	0.568161	−	1.74862i
$512$	−6.89261	−	21.2133i	−0.304613	−	0.937503i
$513$	7.50000	+	23.0826i	0.331133	+	1.01912i
$514$	−0.572949	+	1.76336i	−0.0252717	+	0.0777783i
$515$	−0.916408	+	2.82041i	−0.0403818	+	0.124282i
$516$	−3.92705	−	12.0862i	−0.172879	−	0.532066i
$517$	−6.85410	+	4.97980i	−0.301443	+	0.219011i
$518$	−17.5410			−0.770708
$519$	−5.04508	+	3.66547i	−0.221455	+	0.160896i
$520$	1.88603	−	5.80461i	0.0827079	−	0.254549i
$521$	−1.89919	−	1.37984i	−0.0832049	−	0.0604519i	0.545405	−	0.838173i	$-0.316376\pi$
$521$	−1.89919	−	1.37984i	−0.0832049	−	0.0604519i	−0.628610	+	0.777721i	$0.716376\pi$
$522$	3.94427	+	2.86568i	0.172636	+	0.125427i
$523$	4.40983	−	13.5721i	0.192828	−	0.593465i	−0.807167	−	0.590324i	$-0.799000\pi$
$523$	4.40983	−	13.5721i	0.192828	−	0.593465i	0.999995	−	0.00314118i	$-0.000999871\pi$
$524$	−37.6869			−1.64636
$525$	−23.0902			−1.00774
$526$	−2.81966			−0.122943
$527$	3.16312	−	9.73508i	0.137788	−	0.424067i
$528$	8.23607	+	5.98385i	0.358429	+	0.260414i
$529$	14.5623	+	10.5801i	0.633144	+	0.460006i
$530$	−2.60081	−	1.88960i	−0.112972	−	0.0820790i
$531$	18.7984	−	13.6578i	0.815780	−	0.592699i
$532$	−41.5623			−1.80195
$533$	3.70820	−	2.69417i	0.160620	−	0.116697i
$534$	0.145898	+	0.449028i	0.00631363	+	0.0194313i
$535$	0.0385072	+	0.118513i	0.00166481	+	0.00512376i
$536$	−7.01316	+	21.5843i	−0.302922	+	0.932299i
$537$	8.10739	+	24.9520i	0.349860	+	1.07676i
$538$	1.58359	+	4.87380i	0.0682735	+	0.210124i
$539$	14.3262	−	44.0916i	0.617075	−	1.89916i
$540$	−16.7705	−	12.1845i	−0.721688	−	0.524337i
$541$	−7.67376	−	23.6174i	−0.329921	−	1.01539i	−0.969170	−	0.246392i	$-0.920755\pi$
$541$	−7.67376	−	23.6174i	−0.329921	−	1.01539i	0.639249	−	0.769000i	$-0.279245\pi$
$542$	−4.90983	+	3.56720i	−0.210895	+	0.153224i
$543$	5.41641			0.232440
$544$	3.35410	−	2.43690i	0.143806	−	0.104481i
$545$	−10.3262	+	7.50245i	−0.442327	+	0.321370i
$546$	2.64590	+	1.92236i	0.113234	+	0.0822693i
$547$	27.9894	+	20.3355i	1.19674	+	0.869481i	0.993960	−	0.109743i	$-0.0350029\pi$
$547$	27.9894	+	20.3355i	1.19674	+	0.869481i	0.202779	+	0.979225i	$0.435003\pi$
$548$	2.53038	−	7.78770i	0.108092	−	0.332674i
$549$	10.0000			0.426790
$550$	−6.18034			−0.263531
$551$	−30.9787			−1.31974
$552$	−1.01722	+	3.13068i	−0.0432958	+	0.133251i
$553$	−7.80902	−	5.67358i	−0.332073	−	0.241265i
$554$	−5.48936	−	3.98825i	−0.233220	−	0.169445i
$555$	22.2361			0.943869
$556$	6.35410	−	4.61653i	0.269474	−	0.195784i
$557$	44.8328			1.89963			0.949814	−	0.312816i	$-0.101272\pi$
$557$	44.8328			1.89963			0.949814	+	0.312816i	$0.101272\pi$
$558$	−6.32624	+	4.59628i	−0.267811	+	0.194576i
$559$	3.92705	+	12.0862i	0.166097	+	0.511193i
$560$	26.2812	−	19.0944i	1.11058	−	0.806885i
$561$	−1.00000	+	3.07768i	−0.0422200	+	0.129940i
$562$	1.01064	+	3.11044i	0.0426314	+	0.131206i
$563$	−3.13525	−	9.64932i	−0.132135	−	0.406670i	0.862998	−	0.505207i	$-0.168584\pi$
$563$	−3.13525	−	9.64932i	−0.132135	−	0.406670i	−0.995133	+	0.0985366i	$0.968584\pi$
$564$	1.50000	−	4.61653i	0.0631614	−	0.194391i
$565$	−13.2533	+	9.62908i	−0.557570	+	0.405098i
$566$	−0.343459	−	1.05706i	−0.0144367	−	0.0444314i
$567$	−3.73607	+	2.71441i	−0.156900	+	0.113995i
$568$	11.5623			0.485144
$569$	−34.2254	+	24.8662i	−1.43480	+	1.04245i	−0.445708	+	0.895178i	$0.647048\pi$
$569$	−34.2254	+	24.8662i	−1.43480	+	1.04245i	−0.989097	+	0.147268i	$0.952952\pi$
$570$	−4.14590			−0.173653
$571$	−1.71885	−	1.24882i	−0.0719315	−	0.0522613i	0.551238	−	0.834348i	$-0.314155\pi$
$571$	−1.71885	−	1.24882i	−0.0719315	−	0.0522613i	−0.623170	+	0.782086i	$0.714155\pi$
$572$	−9.00000	−	6.53888i	−0.376309	−	0.273404i
$573$	6.38197	−	19.6417i	0.266610	−	0.820543i
$574$	−4.36068			−0.182011
$575$	3.45492	+	10.6331i	0.144080	+	0.443432i
$576$	9.41641			0.392350
$577$	5.65248	−	17.3965i	0.235316	−	0.724227i	−0.761764	−	0.647855i	$-0.775666\pi$
$577$	5.65248	−	17.3965i	0.235316	−	0.724227i	0.997079	−	0.0763722i	$-0.0243337\pi$
$578$	0.309017	+	0.224514i	0.0128534	+	0.00933855i
$579$	18.5623	+	13.4863i	0.771423	+	0.560472i
$580$	21.4058	−	15.5522i	0.888826	−	0.645770i
$581$	−22.2082	+	16.1352i	−0.921352	+	0.669401i
$582$	3.11146			0.128974
$583$	−9.85410	+	7.15942i	−0.408115	+	0.296513i
$584$	4.09424	+	12.6008i	0.169421	+	0.521423i
$585$	6.70820	+	4.87380i	0.277350	+	0.201507i
$586$	0.347524	−	1.06957i	0.0143561	−	0.0441835i
$587$	3.98278	+	12.2577i	0.164387	+	0.505931i	0.998991	−	0.0449200i	$-0.0143033\pi$
$587$	3.98278	+	12.2577i	0.164387	+	0.505931i	−0.834604	+	0.550851i	$0.814303\pi$
$588$	8.20820	+	25.2623i	0.338501	+	1.04180i
$589$	15.3541	−	47.2551i	0.632655	−	1.94711i
$590$	3.06637	+	9.43732i	0.126241	+	0.388528i
$591$	0.673762	+	2.07363i	0.0277149	+	0.0852976i
$592$	−25.3090	+	18.3881i	−1.04019	+	0.755745i
$593$	37.0902			1.52311			0.761555	−	0.648100i	$-0.224436\pi$
$593$	37.0902			1.52311			0.761555	+	0.648100i	$0.224436\pi$
$594$	5.00000	−	3.63271i	0.205152	−	0.149052i
$595$	8.35410	+	6.06961i	0.342485	+	0.248830i
$596$	−22.7705	−	16.5437i	−0.932716	−	0.677658i
$597$	8.35410	+	6.06961i	0.341911	+	0.248413i
$598$	0.489357	−	1.50609i	0.0200113	−	0.0615884i
$599$	−12.8197			−0.523797			−0.261899	−	0.965095i	$-0.584349\pi$
$599$	−12.8197			−0.523797			−0.261899	+	0.965095i	$0.584349\pi$
$600$	5.95492	−	4.32650i	0.243108	−	0.176629i
$601$	27.8541			1.13619			0.568096	−	0.822962i	$-0.307680\pi$
$601$	27.8541			1.13619			0.568096	+	0.822962i	$0.307680\pi$
$602$	3.73607	−	11.4984i	0.152271	−	0.468641i
$603$	−24.9443	−	18.1231i	−1.01581	−	0.738029i
$604$	16.7188	+	12.1470i	0.680280	+	0.494253i
$605$	0.364745	−	1.12257i	0.0148290	−	0.0456390i
$606$	2.39919	−	1.74311i	0.0974603	−	0.0708091i
$607$	−30.6180			−1.24275			−0.621374	−	0.783514i	$-0.713425\pi$
$607$	−30.6180			−1.24275			−0.621374	+	0.783514i	$0.713425\pi$
$608$	16.2812	−	11.8290i	0.660288	−	0.479727i
$609$	9.10739	+	28.0297i	0.369050	+	1.13582i
$610$	−1.31966	+	4.06150i	−0.0534315	+	0.164445i
$611$	−1.50000	+	4.61653i	−0.0606835	+	0.186765i
$612$	1.14590	+	3.52671i	0.0463202	+	0.142559i
$613$	−8.60739	−	26.4908i	−0.347649	−	1.06995i	−0.960150	−	0.279485i	$-0.909836\pi$
$613$	−8.60739	−	26.4908i	−0.347649	−	1.06995i	0.612501	−	0.790470i	$-0.290164\pi$
$614$	0.124612	−	0.383516i	0.00502892	−	0.0154774i
$615$	5.52786			0.222905
$616$	6.79837	+	20.9232i	0.273914	+	0.843021i
$617$	25.8992	−	18.8169i	1.04266	−	0.757538i	0.0718586	−	0.997415i	$-0.477107\pi$
$617$	25.8992	−	18.8169i	1.04266	−	0.757538i	0.970803	+	0.239877i	$0.0771070\pi$
$618$	0.506578			0.0203775
$619$	−24.8435	+	18.0498i	−0.998543	+	0.725484i	−0.961775	−	0.273840i	$-0.911706\pi$
$619$	−24.8435	+	18.0498i	−0.998543	+	0.725484i	−0.0367676	+	0.999324i	$0.511706\pi$
$620$	13.1140	+	40.3606i	0.526670	+	1.62092i
$621$	−9.04508	−	6.57164i	−0.362967	−	0.263711i
$622$	1.84346	+	1.33935i	0.0739160	+	0.0537031i
$623$	1.76393	−	5.42882i	0.0706704	−	0.217501i
$624$	5.83282			0.233500
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	−5.12461			−0.204821
$627$	−4.85410	+	14.9394i	−0.193854	+	0.596622i
$628$	31.5000	+	22.8861i	1.25699	+	0.913254i
$629$	−8.04508	−	5.84510i	−0.320779	−	0.233059i
$630$	−2.43769	−	7.50245i	−0.0971201	−	0.298905i
$631$	−9.80902	+	7.12667i	−0.390491	+	0.283708i	−0.765657	−	0.643250i	$-0.777586\pi$
$631$	−9.80902	+	7.12667i	−0.390491	+	0.283708i	0.375166	+	0.926958i	$0.377586\pi$
$632$	3.07701			0.122397
$633$	−17.1353	+	12.4495i	−0.681065	+	0.494823i
$634$	−1.04915	−	3.22895i	−0.0416671	−	0.128238i
$635$	−16.5836			−0.658100
$636$	2.15654	−	6.63715i	0.0855124	−	0.263180i
$637$	−8.20820	−	25.2623i	−0.325221	−	1.00093i
$638$	2.43769	+	7.50245i	0.0965092	+	0.297025i
$639$	−4.85410	+	14.9394i	−0.192025	+	0.590993i
$640$	−6.97214	+	21.4580i	−0.275598	+	0.848203i
$641$	9.28115	+	28.5645i	0.366584	+	1.12823i	0.948984	+	0.315326i	$0.102114\pi$
$641$	9.28115	+	28.5645i	0.366584	+	1.12823i	−0.582400	+	0.812902i	$0.697886\pi$
$642$	0.0172209	−	0.0125117i	0.000679656	−	0.000493799i
$643$	−5.70820			−0.225110			−0.112555	−	0.993646i	$-0.535903\pi$
$643$	−5.70820			−0.225110			−0.112555	+	0.993646i	$0.535903\pi$
$644$	15.4894	−	11.2537i	0.610366	−	0.443457i
$645$	−4.73607	+	14.5761i	−0.186482	+	0.573934i
$646$	1.50000	+	1.08981i	0.0590167	+	0.0428782i
$647$	4.52786	+	3.28969i	0.178009	+	0.129331i	0.673222	−	0.739441i	$-0.264910\pi$
$647$	4.52786	+	3.28969i	0.178009	+	0.129331i	−0.495213	+	0.868772i	$0.664910\pi$
$648$	0.454915	−	1.40008i	0.0178708	−	0.0550005i
$649$	37.5967			1.47580
$650$	−2.86475	+	2.08136i	−0.112365	+	0.0816376i
$651$	−47.2705			−1.85268
$652$	6.67627	−	20.5475i	0.261463	−	0.804701i
$653$	7.88197	+	5.72658i	0.308445	+	0.224099i	0.731229	−	0.682132i	$-0.238947\pi$
$653$	7.88197	+	5.72658i	0.308445	+	0.224099i	−0.422784	+	0.906231i	$0.638947\pi$
$654$	1.76393	+	1.28157i	0.0689752	+	0.0501134i
$655$	36.7705	+	26.7153i	1.43674	+	1.04385i
$656$	−6.29180	+	4.57126i	−0.245653	+	0.178478i
$657$	−18.0000			−0.702247
$658$	3.73607	−	2.71441i	0.145647	−	0.105819i
$659$	10.3607	+	31.8869i	0.403595	+	1.24214i	0.922063	+	0.387040i	$0.126502\pi$
$659$	10.3607	+	31.8869i	0.403595	+	1.24214i	−0.518468	+	0.855097i	$0.673498\pi$
$660$	−4.14590	−	12.7598i	−0.161379	−	0.496673i
$661$	14.7361	−	45.3530i	0.573167	−	1.76403i	−0.0691723	−	0.997605i	$-0.522036\pi$
$661$	14.7361	−	45.3530i	0.573167	−	1.76403i	0.642339	−	0.766421i	$-0.277964\pi$
$662$	2.05573	+	6.32688i	0.0798981	+	0.245901i
$663$	0.572949	+	1.76336i	0.0222515	+	0.0684831i
$664$	2.70414	−	8.32248i	0.104941	−	0.322975i
$665$	40.5517	+	29.4625i	1.57253	+	1.14251i
$666$	2.34752	+	7.22494i	0.0909647	+	0.279961i
$667$	11.5451	−	8.38800i	0.447027	−	0.324784i
$668$	37.2492			1.44122
$669$	7.85410	−	5.70634i	0.303657	−	0.220620i
$670$	10.6525	−	7.73948i	0.411541	−	0.299002i
$671$	13.0902	+	9.51057i	0.505340	+	0.367151i
$672$	−15.4894	−	11.2537i	−0.597515	−	0.434120i
$673$	−6.41641	+	19.7477i	−0.247334	+	0.761217i	0.747909	+	0.663801i	$0.231058\pi$
$673$	−6.41641	+	19.7477i	−0.247334	+	0.761217i	−0.995244	+	0.0974160i	$0.968942\pi$
$674$	5.47214			0.210779
$675$	7.72542	+	23.7764i	0.297352	+	0.915155i
$676$	17.7295			0.681903
$677$	14.7533	−	45.4060i	0.567015	−	1.74509i	−0.0948726	−	0.995489i	$-0.530244\pi$
$677$	14.7533	−	45.4060i	0.567015	−	1.74509i	0.661888	−	0.749603i	$-0.269756\pi$
$678$	2.26393	+	1.64484i	0.0869458	+	0.0631698i
$679$	−30.4336	−	22.1113i	−1.16794	−	0.848555i
$680$	−3.29180			−0.126235
$681$	−10.8541	+	7.88597i	−0.415930	+	0.302191i
$682$	−12.6525			−0.484488
$683$	36.7877	−	26.7279i	1.40764	−	1.02271i	0.413984	−	0.910284i	$-0.364137\pi$
$683$	36.7877	−	26.7279i	1.40764	−	1.02271i	0.993660	−	0.112428i	$-0.0358629\pi$
$684$	5.56231	+	17.1190i	0.212680	+	0.654562i
$685$	−7.98936	+	5.80461i	−0.305258	+	0.221783i
$686$	−3.99342	+	12.2905i	−0.152470	+	0.469253i
$687$	−1.85410	−	5.70634i	−0.0707384	−	0.217710i
$688$	−6.66312	−	20.5070i	−0.254029	−	0.781821i
$689$	−2.15654	+	6.63715i	−0.0821577	+	0.252855i
$690$	1.54508	−	1.12257i	0.0588204	−	0.0427355i
$691$	1.77051	+	5.44907i	0.0673534	+	0.207292i	0.979069	−	0.203530i	$-0.0652415\pi$
$691$	1.77051	+	5.44907i	0.0673534	+	0.207292i	−0.911715	+	0.410823i	$0.865242\pi$
$692$	−9.35410	+	6.79615i	−0.355590	+	0.258351i
$693$	−29.8885			−1.13537
$694$	2.79180	−	2.02836i	0.105975	−	0.0769954i
$695$	−9.47214			−0.359299
$696$	−7.60081	−	5.52231i	−0.288108	−	0.209323i
$697$	−2.00000	−	1.45309i	−0.0757554	−	0.0550395i
$698$	0.708204	−	2.17963i	0.0268059	−	0.0825001i
$699$	−8.18034			−0.309409
$700$	−42.8115			−1.61812
$701$	42.3607			1.59994			0.799970	−	0.600039i	$-0.204848\pi$
$701$	42.3607			1.59994			0.799970	+	0.600039i	$0.204848\pi$
$702$	1.09424	−	3.36771i	0.0412992	−	0.127106i
$703$	−39.0517	−	28.3727i	−1.47286	−	1.07010i
$704$	12.3262	+	8.95554i	0.464563	+	0.337524i
$705$	−4.73607	+	3.44095i	−0.178371	+	0.129594i
$706$	7.71885	−	5.60807i	0.290503	−	0.211063i
$707$	−35.8541			−1.34843
$708$	−17.4271	+	12.6615i	−0.654949	+	0.475848i
$709$	−3.39919	−	10.4616i	−0.127659	−	0.392894i	0.866717	−	0.498800i	$-0.166226\pi$
$709$	−3.39919	−	10.4616i	−0.127659	−	0.392894i	−0.994376	+	0.105906i	$0.966226\pi$
$710$	−5.42705	−	3.94298i	−0.203674	−	0.147978i
$711$	−1.29180	+	3.97574i	−0.0484461	+	0.149102i
$712$	0.562306	+	1.73060i	0.0210733	+	0.0648570i
$713$	7.07295	+	21.7683i	0.264884	+	0.815229i
$714$	0.545085	−	1.67760i	0.0203993	−	0.0627826i
$715$	4.14590	+	12.7598i	0.155048	+	0.477188i
$716$	15.0319	+	46.2635i	0.561770	+	1.72895i
$717$	1.19098	−	0.865300i	0.0444781	−	0.0323152i
$718$	13.2918			0.496045
$719$	12.7533	−	9.26581i	0.475617	−	0.345556i	−0.324009	−	0.946054i	$-0.605031\pi$
$719$	12.7533	−	9.26581i	0.475617	−	0.345556i	0.799626	+	0.600498i	$0.205031\pi$
$720$	−11.3820	−	8.26948i	−0.424181	−	0.308185i
$721$	−4.95492	−	3.59996i	−0.184531	−	0.134069i
$722$	1.40983	+	1.02430i	0.0524684	+	0.0381206i
$723$	4.07295	−	12.5352i	0.151475	−	0.466191i
$724$	10.0426			0.373229
$725$	−31.9098			−1.18510
$726$	−0.201626			−0.00748305
$727$	7.20820	−	22.1846i	0.267337	−	0.822780i	−0.723808	−	0.690001i	$-0.757610\pi$
$727$	7.20820	−	22.1846i	0.267337	−	0.822780i	0.991146	−	0.132779i	$-0.0423900\pi$
$728$	10.1976	+	7.40896i	0.377947	+	0.274594i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	2.37539	−	7.31069i	0.0879171	−	0.270581i
$731$	5.54508	−	4.02874i	0.205092	−	0.149008i
$732$	−9.27051			−0.342648
$733$	−23.5795	+	17.1315i	−0.870930	+	0.632767i	−0.930836	−	0.365437i	$-0.880920\pi$
$733$	−23.5795	+	17.1315i	−0.870930	+	0.632767i	0.0599066	+	0.998204i	$0.480920\pi$
$734$	−3.99593	−	12.2982i	−0.147493	−	0.453936i
$735$	9.89919	−	30.4666i	0.365137	−	1.12378i
$736$	−2.86475	+	8.81678i	−0.105596	+	0.324991i
$737$	−15.4164	−	47.4468i	−0.567871	−	1.74773i
$738$	0.583592	+	1.79611i	0.0214823	+	0.0661158i
$739$	−9.62461	+	29.6215i	−0.354047	+	1.08964i	0.602513	+	0.798109i	$0.294166\pi$
$739$	−9.62461	+	29.6215i	−0.354047	+	1.08964i	−0.956560	+	0.291536i	$0.905834\pi$
$740$	41.2279			1.51557
$741$	2.78115	+	8.55951i	0.102168	+	0.314441i
$742$	5.37132	−	3.90249i	0.197187	−	0.143265i
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$	12.1910	−	8.85727i	0.446943	−	0.324723i
$745$	10.4894	+	32.2829i	0.384300	+	1.18275i
$746$	4.06231	+	2.95144i	0.148732	+	0.108060i
$747$	9.61803	+	6.98791i	0.351905	+	0.255674i
$748$	−1.85410	+	5.70634i	−0.0677927	+	0.208644i
$749$	−0.257354			−0.00940352
$750$	−4.27051			−0.155937
$751$	8.52786			0.311186			0.155593	−	0.987821i	$-0.450271\pi$
$751$	8.52786			0.311186			0.155593	+	0.987821i	$0.450271\pi$
$752$	2.54508	−	7.83297i	0.0928097	−	0.285639i
$753$	−19.1353	−	13.9026i	−0.697327	−	0.506638i
$754$	3.65654	+	2.65663i	0.133163	+	0.0967489i
$755$	−7.70163	−	23.7032i	−0.280291	−	0.862647i
$756$	34.6353	−	25.1640i	1.25967	−	0.915205i
$757$	−29.3607			−1.06713			−0.533566	−	0.845758i	$-0.679148\pi$
$757$	−29.3607			−1.06713			−0.533566	+	0.845758i	$0.679148\pi$
$758$	7.07295	−	5.13880i	0.256901	−	0.186650i
$759$	−2.23607	−	6.88191i	−0.0811641	−	0.249797i
$760$	−15.9787			−0.579609
$761$	5.40983	−	16.6497i	0.196106	−	0.603553i	−0.803856	−	0.594824i	$-0.797222\pi$
$761$	5.40983	−	16.6497i	0.196106	−	0.603553i	0.999962	−	0.00872845i	$-0.00277839\pi$
$762$	0.875388	+	2.69417i	0.0317120	+	0.0975994i
$763$	−8.14590	−	25.0705i	−0.294901	−	0.907613i
$764$	11.8328	−	36.4177i	0.428096	−	1.31754i
$765$	1.38197	−	4.25325i	0.0499651	−	0.153777i
$766$	−1.95085	−	6.00410i	−0.0704871	−	0.216937i
$767$	17.4271	−	12.6615i	0.629254	−	0.457180i
$768$	−5.56231			−0.200712
$769$	−7.85410	+	5.70634i	−0.283226	+	0.205776i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118034 + 0.363271i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(-0.690983 - 2.12663i) q^{5} +(-0.309017 + 0.224514i) q^{6} +4.61803 q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.618034 - 1.90211i) q^{9} +0.854102 q^{10} +(1.00000 - 3.07768i) q^{11} +(0.572949 + 1.76336i) q^{12} +(-0.572949 - 1.76336i) q^{13} +(-0.545085 + 1.67760i) q^{14} +(0.690983 - 2.12663i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-0.809017 + 0.587785i) q^{17} +0.763932 q^{18} +(-3.92705 + 2.85317i) q^{19} +(1.28115 - 3.94298i) q^{20} +(3.73607 + 2.71441i) q^{21} +(1.00000 + 0.726543i) q^{22} +(0.690983 - 2.12663i) q^{23} -1.47214 q^{24} +(-4.04508 + 2.93893i) q^{25} +0.708204 q^{26} +(1.54508 - 4.75528i) q^{27} +(6.92705 + 5.03280i) q^{28} +(5.16312 + 3.75123i) q^{29} +(0.690983 + 0.502029i) q^{30} +(-8.28115 + 6.01661i) q^{31} -4.14590 q^{32} +(2.61803 - 1.90211i) q^{33} +(-0.118034 - 0.363271i) q^{34} +(-3.19098 - 9.82084i) q^{35} +(1.14590 - 3.52671i) q^{36} +(3.07295 + 9.45756i) q^{37} +(-0.572949 - 1.76336i) q^{38} +(0.572949 - 1.76336i) q^{39} +(2.66312 + 1.93487i) q^{40} +(0.763932 + 2.35114i) q^{41} +(-1.42705 + 1.03681i) q^{42} -6.85410 q^{43} +(4.85410 - 3.52671i) q^{44} +(-3.61803 + 2.62866i) q^{45} +(0.690983 + 0.502029i) q^{46} +(-2.11803 - 1.53884i) q^{47} +(-0.972136 + 2.99193i) q^{48} +14.3262 q^{49} +(-0.590170 - 1.81636i) q^{50} -1.00000 q^{51} +(1.06231 - 3.26944i) q^{52} +(-3.04508 - 2.21238i) q^{53} +(1.54508 + 1.12257i) q^{54} -7.23607 q^{55} +(-5.50000 + 3.99598i) q^{56} -4.85410 q^{57} +(-1.97214 + 1.43284i) q^{58} +(3.59017 + 11.0494i) q^{59} +(3.35410 - 2.43690i) q^{60} +(-1.54508 + 4.75528i) q^{61} +(-1.20820 - 3.71847i) q^{62} +(-2.85410 - 8.78402i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(-3.35410 + 2.43690i) q^{65} +(0.381966 + 1.17557i) q^{66} +(12.4721 - 9.06154i) q^{67} -1.85410 q^{68} +(1.80902 - 1.31433i) q^{69} +3.94427 q^{70} +(-6.35410 - 4.61653i) q^{71} +(2.38197 + 1.73060i) q^{72} +(2.78115 - 8.55951i) q^{73} -3.79837 q^{74} -5.00000 q^{75} -9.00000 q^{76} +(4.61803 - 14.2128i) q^{77} +(0.572949 + 0.416272i) q^{78} +(-1.69098 - 1.22857i) q^{79} +(5.69098 - 4.13474i) q^{80} +(-0.809017 + 0.587785i) q^{81} -0.944272 q^{82} +(-4.80902 + 3.49396i) q^{83} +(2.64590 + 8.14324i) q^{84} +(1.80902 + 1.31433i) q^{85} +(0.809017 - 2.48990i) q^{86} +(1.97214 + 6.06961i) q^{87} +(1.47214 + 4.53077i) q^{88} +(0.381966 - 1.17557i) q^{89} +(-0.527864 - 1.62460i) q^{90} +(-2.64590 - 8.14324i) q^{91} +(3.35410 - 2.43690i) q^{92} -10.2361 q^{93} +(0.809017 - 0.587785i) q^{94} +(8.78115 + 6.37988i) q^{95} +(-3.35410 - 2.43690i) q^{96} +(-6.59017 - 4.78804i) q^{97} +(-1.69098 + 5.20431i) q^{98} -6.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + q^{6} + 14 q^{7} - 7 q^{8} + 2 q^{9} - 10 q^{10} + 4 q^{11} + 9 q^{12} - 9 q^{13} + 9 q^{14} + 5 q^{15} - 14 q^{16} - q^{17} + 12 q^{18} - 9 q^{19} - 15 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + q^6 + 14 * q^7 - 7 * q^8 + 2 * q^9 - 10 * q^10 + 4 * q^11 + 9 * q^12 - 9 * q^13 + 9 * q^14 + 5 * q^15 - 14 * q^16 - q^17 + 12 * q^18 - 9 * q^19 - 15 * q^20 + 6 * q^21 + 4 * q^22 + 5 * q^23 + 12 * q^24 - 5 * q^25 - 24 * q^26 - 5 * q^27 + 21 * q^28 + 5 * q^29 + 5 * q^30 - 13 * q^31 - 30 * q^32 + 6 * q^33 + 4 * q^34 - 15 * q^35 + 18 * q^36 + 19 * q^37 - 9 * q^38 + 9 * q^39 - 5 * q^40 + 12 * q^41 + q^42 - 14 * q^43 + 6 * q^44 - 10 * q^45 + 5 * q^46 - 4 * q^47 + 14 * q^48 + 26 * q^49 + 20 * q^50 - 4 * q^51 - 36 * q^52 - q^53 - 5 * q^54 - 20 * q^55 - 22 * q^56 - 6 * q^57 + 10 * q^58 - 8 * q^59 + 5 * q^61 + 22 * q^62 + 2 * q^63 - 17 * q^64 + 6 * q^66 + 32 * q^67 + 6 * q^68 + 5 * q^69 - 20 * q^70 - 12 * q^71 + 14 * q^72 - 9 * q^73 + 34 * q^74 - 20 * q^75 - 36 * q^76 + 14 * q^77 + 9 * q^78 - 9 * q^79 + 25 * q^80 - q^81 + 32 * q^82 - 17 * q^83 + 24 * q^84 + 5 * q^85 + q^86 - 10 * q^87 - 12 * q^88 + 6 * q^89 - 20 * q^90 - 24 * q^91 - 32 * q^93 + q^94 + 15 * q^95 - 4 * q^97 - 9 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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