LMFDB - Embedded newform 370.2.d.c.221.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(221,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("370.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.d (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			221.5
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	370.221
Dual form			370.2.d.c.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.14637 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.14637i q^{6} -0.342923 q^{7} -1.00000i q^{8} -1.68585 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.14637 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.14637i q^{6} -0.342923 q^{7} -1.00000i q^{8} -1.68585 q^{9} +1.00000 q^{10} +1.19656 q^{11} +1.14637 q^{12} -4.68585i q^{13} -0.342923i q^{14} +1.14637i q^{15} +1.00000 q^{16} -4.17513i q^{17} -1.68585i q^{18} -3.14637i q^{19} +1.00000i q^{20} +0.393115 q^{21} +1.19656i q^{22} -4.68585i q^{23} +1.14637i q^{24} -1.00000 q^{25} +4.68585 q^{26} +5.37169 q^{27} +0.342923 q^{28} +0.803442i q^{29} -1.14637 q^{30} +4.63565i q^{31} +1.00000i q^{32} -1.37169 q^{33} +4.17513 q^{34} +0.342923i q^{35} +1.68585 q^{36} +(-3.19656 - 5.17513i) q^{37} +3.14637 q^{38} +5.37169i q^{39} -1.00000 q^{40} +3.78202 q^{41} +0.393115i q^{42} -1.19656i q^{43} -1.19656 q^{44} +1.68585i q^{45} +4.68585 q^{46} +3.83221 q^{47} -1.14637 q^{48} -6.88240 q^{49} -1.00000i q^{50} +4.78623i q^{51} +4.68585i q^{52} -11.1537 q^{53} +5.37169i q^{54} -1.19656i q^{55} +0.342923i q^{56} +3.60688i q^{57} -0.803442 q^{58} +0.167788i q^{59} -1.14637i q^{60} +2.17513i q^{61} -4.63565 q^{62} +0.578116 q^{63} -1.00000 q^{64} -4.68585 q^{65} -1.37169i q^{66} -1.24675 q^{67} +4.17513i q^{68} +5.37169i q^{69} -0.342923 q^{70} +0.685846 q^{71} +1.68585i q^{72} -11.9572 q^{73} +(5.17513 - 3.19656i) q^{74} +1.14637 q^{75} +3.14637i q^{76} -0.410327 q^{77} -5.37169 q^{78} +5.14637i q^{79} -1.00000i q^{80} -1.10038 q^{81} +3.78202i q^{82} +4.22533 q^{83} -0.393115 q^{84} -4.17513 q^{85} +1.19656 q^{86} -0.921039i q^{87} -1.19656i q^{88} -4.58546i q^{89} -1.68585 q^{90} +1.60688i q^{91} +4.68585i q^{92} -5.31415i q^{93} +3.83221i q^{94} -3.14637 q^{95} -1.14637i q^{96} -4.21798i q^{97} -6.88240i q^{98} -2.01721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 - 6 * q^4 + 10 * q^7 + 14 * q^9	$ 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9} + 6 q^{10} - 2 q^{11} + 4 q^{12} + 6 q^{16} - 16 q^{21} - 6 q^{25} + 4 q^{26} - 16 q^{27} - 10 q^{28} - 4 q^{30} + 40 q^{33} - 14 q^{34} - 14 q^{36} - 10 q^{37} + 16 q^{38} - 6 q^{40} + 2 q^{41} + 2 q^{44} + 4 q^{46} - 4 q^{47} - 4 q^{48} - 8 q^{49} + 2 q^{53} - 14 q^{58} - 10 q^{62} + 58 q^{63} - 6 q^{64} - 4 q^{65} + 8 q^{67} + 10 q^{70} - 20 q^{71} - 12 q^{73} - 8 q^{74} + 4 q^{75} - 30 q^{77} + 16 q^{78} + 6 q^{81} - 20 q^{83} + 16 q^{84} + 14 q^{85} - 2 q^{86} + 14 q^{90} - 16 q^{95} - 58 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 - 6 * q^4 + 10 * q^7 + 14 * q^9 + 6 * q^10 - 2 * q^11 + 4 * q^12 + 6 * q^16 - 16 * q^21 - 6 * q^25 + 4 * q^26 - 16 * q^27 - 10 * q^28 - 4 * q^30 + 40 * q^33 - 14 * q^34 - 14 * q^36 - 10 * q^37 + 16 * q^38 - 6 * q^40 + 2 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 - 4 * q^48 - 8 * q^49 + 2 * q^53 - 14 * q^58 - 10 * q^62 + 58 * q^63 - 6 * q^64 - 4 * q^65 + 8 * q^67 + 10 * q^70 - 20 * q^71 - 12 * q^73 - 8 * q^74 + 4 * q^75 - 30 * q^77 + 16 * q^78 + 6 * q^81 - 20 * q^83 + 16 * q^84 + 14 * q^85 - 2 * q^86 + 14 * q^90 - 16 * q^95 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.14637			−0.661854			−0.330927	−	0.943656i	$-0.607361\pi$
$3$	−1.14637			−0.661854			−0.330927	+	0.943656i	$0.607361\pi$
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	1.14637i		−	0.468002i
$7$	−0.342923			−0.129613			−0.0648064	−	0.997898i	$-0.520643\pi$
$7$	−0.342923			−0.129613			−0.0648064	+	0.997898i	$0.520643\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.68585			−0.561949
$10$	1.00000			0.316228
$11$	1.19656			0.360776			0.180388	−	0.983596i	$-0.442265\pi$
$11$	1.19656			0.360776			0.180388	+	0.983596i	$0.442265\pi$
$12$	1.14637			0.330927
$13$		−	4.68585i		−	1.29962i	−0.760097	−	0.649810i	$-0.774848\pi$
$13$		−	4.68585i		−	1.29962i	0.760097	−	0.649810i	$-0.225152\pi$
$14$		−	0.342923i		−	0.0916500i
$15$			1.14637i			0.295990i
$16$	1.00000			0.250000
$17$		−	4.17513i		−	1.01262i	−0.862352	−	0.506309i	$-0.831009\pi$
$17$		−	4.17513i		−	1.01262i	0.862352	−	0.506309i	$-0.168991\pi$
$18$		−	1.68585i		−	0.397358i
$19$		−	3.14637i		−	0.721826i	−0.932600	−	0.360913i	$-0.882465\pi$
$19$		−	3.14637i		−	0.721826i	0.932600	−	0.360913i	$-0.117535\pi$
$20$			1.00000i			0.223607i
$21$	0.393115			0.0857848
$22$			1.19656i			0.255107i
$23$		−	4.68585i		−	0.977066i	−0.872545	−	0.488533i	$-0.837532\pi$
$23$		−	4.68585i		−	0.977066i	0.872545	−	0.488533i	$-0.162468\pi$
$24$			1.14637i			0.234001i
$25$	−1.00000			−0.200000
$26$	4.68585			0.918970
$27$	5.37169			1.03378
$28$	0.342923			0.0648064
$29$			0.803442i			0.149196i	0.997214	+	0.0745978i	$0.0237673\pi$
$29$			0.803442i			0.149196i	−0.997214	+	0.0745978i	$0.976233\pi$
$30$	−1.14637			−0.209297
$31$			4.63565i			0.832588i	0.909230	+	0.416294i	$0.136671\pi$
$31$			4.63565i			0.832588i	−0.909230	+	0.416294i	$0.863329\pi$
$32$			1.00000i			0.176777i
$33$	−1.37169			−0.238781
$34$	4.17513			0.716030
$35$			0.342923i			0.0579646i
$36$	1.68585			0.280974
$37$	−3.19656	−	5.17513i	−0.525511	−	0.850787i
$37$	−3.19656	−	5.17513i	−0.525511	−	0.850787i
$38$	3.14637			0.510408
$39$			5.37169i			0.860159i
$40$	−1.00000			−0.158114
$41$	3.78202			0.590652			0.295326	−	0.955397i	$-0.404572\pi$
$41$	3.78202			0.590652			0.295326	+	0.955397i	$0.404572\pi$
$42$			0.393115i			0.0606590i
$43$		−	1.19656i		−	0.182473i	−0.995829	−	0.0912367i	$-0.970918\pi$
$43$		−	1.19656i		−	0.182473i	0.995829	−	0.0912367i	$-0.0290820\pi$
$44$	−1.19656			−0.180388
$45$			1.68585i			0.251311i
$46$	4.68585			0.690890
$47$	3.83221			0.558986			0.279493	−	0.960148i	$-0.409834\pi$
$47$	3.83221			0.558986			0.279493	+	0.960148i	$0.409834\pi$
$48$	−1.14637			−0.165464
$49$	−6.88240			−0.983201
$50$		−	1.00000i		−	0.141421i
$51$			4.78623i			0.670206i
$52$			4.68585i			0.649810i
$53$	−11.1537			−1.53208			−0.766040	−	0.642793i	$-0.777776\pi$
$53$	−11.1537			−1.53208			−0.766040	+	0.642793i	$0.777776\pi$
$54$			5.37169i			0.730995i
$55$		−	1.19656i		−	0.161344i
$56$			0.342923i			0.0458250i
$57$			3.60688i			0.477744i
$58$	−0.803442			−0.105497
$59$			0.167788i			0.0218442i	0.999940	+	0.0109221i	$0.00347668\pi$
$59$			0.167788i			0.0218442i	−0.999940	+	0.0109221i	$0.996523\pi$
$60$		−	1.14637i		−	0.147995i
$61$			2.17513i			0.278497i	0.990257	+	0.139249i	$0.0444688\pi$
$61$			2.17513i			0.278497i	−0.990257	+	0.139249i	$0.955531\pi$
$62$	−4.63565			−0.588729
$63$	0.578116			0.0728357
$64$	−1.00000			−0.125000
$65$	−4.68585			−0.581208
$66$		−	1.37169i		−	0.168844i
$67$	−1.24675			−0.152315			−0.0761574	−	0.997096i	$-0.524265\pi$
$67$	−1.24675			−0.152315			−0.0761574	+	0.997096i	$0.524265\pi$
$68$			4.17513i			0.506309i
$69$			5.37169i			0.646676i
$70$	−0.342923			−0.0409871
$71$	0.685846			0.0813950			0.0406975	−	0.999172i	$-0.487042\pi$
$71$	0.685846			0.0813950			0.0406975	+	0.999172i	$0.487042\pi$
$72$			1.68585i			0.198679i
$73$	−11.9572			−1.39948			−0.699740	−	0.714398i	$-0.746701\pi$
$73$	−11.9572			−1.39948			−0.699740	+	0.714398i	$0.746701\pi$
$74$	5.17513	−	3.19656i	0.601597	−	0.371592i
$75$	1.14637			0.132371
$76$			3.14637i			0.360913i
$77$	−0.410327			−0.0467611
$78$	−5.37169			−0.608224
$79$			5.14637i			0.579011i	0.957176	+	0.289506i	$0.0934909\pi$
$79$			5.14637i			0.579011i	−0.957176	+	0.289506i	$0.906509\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−1.10038			−0.122265
$82$			3.78202i			0.417654i
$83$	4.22533			0.463790			0.231895	−	0.972741i	$-0.425507\pi$
$83$	4.22533			0.463790			0.231895	+	0.972741i	$0.425507\pi$
$84$	−0.393115			−0.0428924
$85$	−4.17513			−0.452857
$86$	1.19656			0.129028
$87$		−	0.921039i		−	0.0987457i
$88$		−	1.19656i		−	0.127553i
$89$		−	4.58546i		−	0.486058i	−0.970019	−	0.243029i	$-0.921859\pi$
$89$		−	4.58546i		−	0.486058i	0.970019	−	0.243029i	$-0.0781410\pi$
$90$	−1.68585			−0.177704
$91$			1.60688i			0.168447i
$92$			4.68585i			0.488533i
$93$		−	5.31415i		−	0.551052i
$94$			3.83221i			0.395262i
$95$	−3.14637			−0.322810
$96$		−	1.14637i		−	0.117000i
$97$		−	4.21798i		−	0.428271i	−0.976804	−	0.214136i	$-0.931307\pi$
$97$		−	4.21798i		−	0.428271i	0.976804	−	0.214136i	$-0.0686934\pi$
$98$		−	6.88240i		−	0.695228i
$99$	−2.01721			−0.202737
$100$	1.00000			0.100000
$101$	9.95715			0.990774			0.495387	−	0.868672i	$-0.335026\pi$
$101$	9.95715			0.990774			0.495387	+	0.868672i	$0.335026\pi$
$102$	−4.78623			−0.473907
$103$			10.6430i			1.04869i	0.851507	+	0.524343i	$0.175689\pi$
$103$			10.6430i			1.04869i	−0.851507	+	0.524343i	$0.824311\pi$
$104$	−4.68585			−0.459485
$105$		−	0.393115i		−	0.0383641i
$106$		−	11.1537i		−	1.08334i
$107$	17.8322			1.72390			0.861952	−	0.506989i	$-0.169242\pi$
$107$	17.8322			1.72390			0.861952	+	0.506989i	$0.169242\pi$
$108$	−5.37169			−0.516891
$109$		−	0.217980i		−	0.0208787i	−0.999946	−	0.0104394i	$-0.996677\pi$
$109$		−	0.217980i		−	0.0208787i	0.999946	−	0.0104394i	$-0.00332302\pi$
$110$	1.19656			0.114087
$111$	3.66442	+	5.93260i	0.347812	+	0.563097i
$112$	−0.342923			−0.0324032
$113$		−	13.5468i		−	1.27438i	−0.770707	−	0.637189i	$-0.780097\pi$
$113$		−	13.5468i		−	1.27438i	0.770707	−	0.637189i	$-0.219903\pi$
$114$	−3.60688			−0.337816
$115$	−4.68585			−0.436957
$116$		−	0.803442i		−	0.0745978i
$117$			7.89962i			0.730320i
$118$	−0.167788			−0.0154462
$119$			1.43175i			0.131248i
$120$	1.14637			0.104648
$121$	−9.56825			−0.869841
$122$	−2.17513			−0.196927
$123$	−4.33558			−0.390926
$124$		−	4.63565i		−	0.416294i
$125$			1.00000i			0.0894427i
$126$			0.578116i			0.0515026i
$127$	−12.4177			−1.10189			−0.550945	−	0.834541i	$-0.685733\pi$
$127$	−12.4177			−1.10189			−0.550945	+	0.834541i	$0.685733\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			1.37169i			0.120771i
$130$		−	4.68585i		−	0.410976i
$131$			18.9112i			1.65228i	0.563467	+	0.826138i	$0.309467\pi$
$131$			18.9112i			1.65228i	−0.563467	+	0.826138i	$0.690533\pi$
$132$	1.37169			0.119390
$133$			1.07896i			0.0935578i
$134$		−	1.24675i		−	0.107703i
$135$		−	5.37169i		−	0.462322i
$136$	−4.17513			−0.358015
$137$	18.3503			1.56777			0.783885	−	0.620906i	$-0.213235\pi$
$137$	18.3503			1.56777			0.783885	+	0.620906i	$0.213235\pi$
$138$	−5.37169			−0.457269
$139$	19.7392			1.67425			0.837127	−	0.547008i	$-0.184233\pi$
$139$	19.7392			1.67425			0.837127	+	0.547008i	$0.184233\pi$
$140$		−	0.342923i		−	0.0289823i
$141$	−4.39312			−0.369967
$142$			0.685846i			0.0575549i
$143$		−	5.60688i		−	0.468871i
$144$	−1.68585			−0.140487
$145$	0.803442			0.0667223
$146$		−	11.9572i		−	0.989581i
$147$	7.88975			0.650736
$148$	3.19656	+	5.17513i	0.262755	+	0.425393i
$149$	18.9786			1.55479			0.777393	−	0.629015i	$-0.216542\pi$
$149$	18.9786			1.55479			0.777393	+	0.629015i	$0.216542\pi$
$150$			1.14637i			0.0936004i
$151$	−8.68585			−0.706844			−0.353422	−	0.935464i	$-0.614982\pi$
$151$	−8.68585			−0.706844			−0.353422	+	0.935464i	$0.614982\pi$
$152$	−3.14637			−0.255204
$153$			7.03863i			0.569040i
$154$		−	0.410327i		−	0.0330651i
$155$	4.63565			0.372345
$156$		−	5.37169i		−	0.430080i
$157$	−6.36748			−0.508180			−0.254090	−	0.967181i	$-0.581776\pi$
$157$	−6.36748			−0.508180			−0.254090	+	0.967181i	$0.581776\pi$
$158$	−5.14637			−0.409423
$159$	12.7862			1.01401
$160$	1.00000			0.0790569
$161$			1.60688i			0.126640i
$162$		−	1.10038i		−	0.0864543i
$163$			1.53213i			0.120006i	0.998198	+	0.0600030i	$0.0191110\pi$
$163$			1.53213i			0.120006i	−0.998198	+	0.0600030i	$0.980889\pi$
$164$	−3.78202			−0.295326
$165$			1.37169i			0.106786i
$166$			4.22533i			0.327949i
$167$		−	13.8568i		−	1.07227i	−0.844133	−	0.536135i	$-0.819884\pi$
$167$		−	13.8568i		−	1.07227i	0.844133	−	0.536135i	$-0.180116\pi$
$168$		−	0.393115i		−	0.0303295i
$169$	−8.95715			−0.689012
$170$		−	4.17513i		−	0.320218i
$171$			5.30429i			0.405629i
$172$			1.19656i			0.0912367i
$173$	9.19656			0.699201			0.349601	−	0.936899i	$-0.386317\pi$
$173$	9.19656			0.699201			0.349601	+	0.936899i	$0.386317\pi$
$174$	0.921039			0.0698238
$175$	0.342923			0.0259225
$176$	1.19656			0.0901939
$177$		−	0.192347i		−	0.0144577i
$178$	4.58546			0.343695
$179$		−	22.4752i		−	1.67988i	−0.542682	−	0.839938i	$-0.682591\pi$
$179$		−	22.4752i		−	1.67988i	0.542682	−	0.839938i	$-0.317409\pi$
$180$		−	1.68585i		−	0.125656i
$181$	7.41454			0.551118			0.275559	−	0.961284i	$-0.411137\pi$
$181$	7.41454			0.551118			0.275559	+	0.961284i	$0.411137\pi$
$182$	−1.60688			−0.119110
$183$		−	2.49350i		−	0.184325i
$184$	−4.68585			−0.345445
$185$	−5.17513	+	3.19656i	−0.380483	+	0.235016i
$186$	5.31415			0.389653
$187$		−	4.99579i		−	0.365328i
$188$	−3.83221			−0.279493
$189$	−1.84208			−0.133991
$190$		−	3.14637i		−	0.228261i
$191$		−	1.32150i		−	0.0956204i	−0.998856	−	0.0478102i	$-0.984776\pi$
$191$		−	1.32150i		−	0.0956204i	0.998856	−	0.0478102i	$-0.0152243\pi$
$192$	1.14637			0.0827318
$193$			12.7434i			0.917289i	0.888620	+	0.458644i	$0.151665\pi$
$193$			12.7434i			0.917289i	−0.888620	+	0.458644i	$0.848335\pi$
$194$	4.21798			0.302833
$195$	5.37169			0.384675
$196$	6.88240			0.491600
$197$	10.3931			0.740479			0.370239	−	0.928936i	$-0.379276\pi$
$197$	10.3931			0.740479			0.370239	+	0.928936i	$0.379276\pi$
$198$		−	2.01721i		−	0.143357i
$199$		−	8.47521i		−	0.600792i	−0.953815	−	0.300396i	$-0.902881\pi$
$199$		−	8.47521i		−	0.600792i	0.953815	−	0.300396i	$-0.0971188\pi$
$200$			1.00000i			0.0707107i
$201$	1.42923			0.100810
$202$			9.95715i			0.700583i
$203$		−	0.275519i		−	0.0193376i
$204$		−	4.78623i		−	0.335103i
$205$		−	3.78202i		−	0.264148i
$206$	−10.6430			−0.741533
$207$			7.89962i			0.549061i
$208$		−	4.68585i		−	0.324905i
$209$		−	3.76481i		−	0.260417i
$210$	0.393115			0.0271275
$211$	12.6602			0.871565			0.435782	−	0.900052i	$-0.356472\pi$
$211$	12.6602			0.871565			0.435782	+	0.900052i	$0.356472\pi$
$212$	11.1537			0.766040
$213$	−0.786230			−0.0538716
$214$			17.8322i			1.21898i
$215$	−1.19656			−0.0816046
$216$		−	5.37169i		−	0.365497i
$217$		−	1.58967i		−	0.107914i
$218$	0.217980			0.0147635
$219$	13.7073			0.926251
$220$			1.19656i			0.0806719i
$221$	−19.5640			−1.31602
$222$	−5.93260	+	3.66442i	−0.398170	+	0.245940i
$223$	20.5928			1.37900			0.689498	−	0.724287i	$-0.257831\pi$
$223$	20.5928			1.37900			0.689498	+	0.724287i	$0.257831\pi$
$224$		−	0.342923i		−	0.0229125i
$225$	1.68585			0.112390
$226$	13.5468			0.901122
$227$			17.1966i			1.14138i	0.821167	+	0.570688i	$0.193323\pi$
$227$			17.1966i			1.14138i	−0.821167	+	0.570688i	$0.806677\pi$
$228$		−	3.60688i		−	0.238872i
$229$	−4.04285			−0.267159			−0.133579	−	0.991038i	$-0.542647\pi$
$229$	−4.04285			−0.267159			−0.133579	+	0.991038i	$0.542647\pi$
$230$		−	4.68585i		−	0.308976i
$231$	0.470385			0.0309491
$232$	0.803442			0.0527486
$233$	3.80765			0.249448			0.124724	−	0.992191i	$-0.460196\pi$
$233$	3.80765			0.249448			0.124724	+	0.992191i	$0.460196\pi$
$234$	−7.89962			−0.516414
$235$		−	3.83221i		−	0.249986i
$236$		−	0.167788i		−	0.0109221i
$237$		−	5.89962i		−	0.383221i
$238$	−1.43175			−0.0928066
$239$		−	21.3215i		−	1.37917i	−0.724203	−	0.689587i	$-0.757792\pi$
$239$		−	21.3215i		−	1.37917i	0.724203	−	0.689587i	$-0.242208\pi$
$240$			1.14637i			0.0739976i
$241$		−	21.3717i		−	1.37667i	−0.725392	−	0.688336i	$-0.758342\pi$
$241$		−	21.3717i		−	1.37667i	0.725392	−	0.688336i	$-0.241658\pi$
$242$		−	9.56825i		−	0.615070i
$243$	−14.8536			−0.952861
$244$		−	2.17513i		−	0.139249i
$245$			6.88240i			0.439701i
$246$		−	4.33558i		−	0.276426i
$247$	−14.7434			−0.938099
$248$	4.63565			0.294364
$249$	−4.84377			−0.306961
$250$	−1.00000			−0.0632456
$251$			10.1249i			0.639081i	0.947573	+	0.319540i	$0.103528\pi$
$251$			10.1249i			0.639081i	−0.947573	+	0.319540i	$0.896472\pi$
$252$	−0.578116			−0.0364179
$253$		−	5.60688i		−	0.352502i
$254$		−	12.4177i		−	0.779154i
$255$	4.78623			0.299725
$256$	1.00000			0.0625000
$257$		−	30.3074i		−	1.89053i	−0.326311	−	0.945263i	$-0.605806\pi$
$257$		−	30.3074i		−	1.89053i	0.326311	−	0.945263i	$-0.394194\pi$
$258$	−1.37169			−0.0853978
$259$	1.09617	+	1.77467i	0.0681129	+	0.110273i
$260$	4.68585			0.290604
$261$		−	1.35448i		−	0.0838402i
$262$	−18.9112			−1.16834
$263$	−12.3429			−0.761097			−0.380549	−	0.924761i	$-0.624265\pi$
$263$	−12.3429			−0.761097			−0.380549	+	0.924761i	$0.624265\pi$
$264$			1.37169i			0.0844218i
$265$			11.1537i			0.685167i
$266$	−1.07896			−0.0661554
$267$			5.25662i			0.321700i
$268$	1.24675			0.0761574
$269$	−13.3717			−0.815286			−0.407643	−	0.913141i	$-0.633649\pi$
$269$	−13.3717			−0.815286			−0.407643	+	0.913141i	$0.633649\pi$
$270$	5.37169			0.326911
$271$	−20.2499			−1.23009			−0.615046	−	0.788491i	$-0.710863\pi$
$271$	−20.2499			−1.23009			−0.615046	+	0.788491i	$0.710863\pi$
$272$		−	4.17513i		−	0.253155i
$273$		−	1.84208i		−	0.111488i
$274$			18.3503i			1.10858i
$275$	−1.19656			−0.0721551
$276$		−	5.37169i		−	0.323338i
$277$			7.46365i			0.448448i	0.974538	+	0.224224i	$0.0719847\pi$
$277$			7.46365i			0.448448i	−0.974538	+	0.224224i	$0.928015\pi$
$278$			19.7392i			1.18388i
$279$		−	7.81500i		−	0.467872i
$280$	0.342923			0.0204936
$281$			4.93573i			0.294441i	0.989104	+	0.147221i	$0.0470327\pi$
$281$			4.93573i			0.294441i	−0.989104	+	0.147221i	$0.952967\pi$
$282$		−	4.39312i		−	0.261606i
$283$			13.0361i			0.774917i	0.921887	+	0.387458i	$0.126647\pi$
$283$			13.0361i			0.774917i	−0.921887	+	0.387458i	$0.873353\pi$
$284$	−0.685846			−0.0406975
$285$	3.60688			0.213653
$286$	5.60688			0.331542
$287$	−1.29694			−0.0765561
$288$		−	1.68585i		−	0.0993394i
$289$	−0.431750			−0.0253971
$290$			0.803442i			0.0471798i
$291$			4.83535i			0.283453i
$292$	11.9572			0.699740
$293$	23.3545			1.36438			0.682192	−	0.731173i	$-0.261027\pi$
$293$	23.3545			1.36438			0.682192	+	0.731173i	$0.261027\pi$
$294$			7.88975i			0.460140i
$295$	0.167788			0.00976902
$296$	−5.17513	+	3.19656i	−0.300799	+	0.185796i
$297$	6.42754			0.372964
$298$			18.9786i			1.09940i
$299$	−21.9572			−1.26982
$300$	−1.14637			−0.0661854
$301$			0.410327i			0.0236509i
$302$		−	8.68585i		−	0.499814i
$303$	−11.4145			−0.655748
$304$		−	3.14637i		−	0.180456i
$305$	2.17513			0.124548
$306$	−7.03863			−0.402372
$307$	10.2682			0.586036			0.293018	−	0.956107i	$-0.405340\pi$
$307$	10.2682			0.586036			0.293018	+	0.956107i	$0.405340\pi$
$308$	0.410327			0.0233806
$309$		−	12.2008i		−	0.694077i
$310$			4.63565i			0.263287i
$311$			8.98592i			0.509545i	0.967001	+	0.254772i	$0.0820006\pi$
$311$			8.98592i			0.509545i	−0.967001	+	0.254772i	$0.917999\pi$
$312$	5.37169			0.304112
$313$		−	3.17092i		−	0.179231i	−0.995976	−	0.0896156i	$-0.971436\pi$
$313$		−	3.17092i		−	0.179231i	0.995976	−	0.0896156i	$-0.0285639\pi$
$314$		−	6.36748i		−	0.359338i
$315$		−	0.578116i		−	0.0325731i
$316$		−	5.14637i		−	0.289506i
$317$	−12.1751			−0.683824			−0.341912	−	0.939732i	$-0.611074\pi$
$317$	−12.1751			−0.683824			−0.341912	+	0.939732i	$0.611074\pi$
$318$			12.7862i			0.717016i
$319$			0.961365i			0.0538261i
$320$			1.00000i			0.0559017i
$321$	−20.4422			−1.14097
$322$	−1.60688			−0.0895482
$323$	−13.1365			−0.730934
$324$	1.10038			0.0611325
$325$			4.68585i			0.259924i
$326$	−1.53213			−0.0848571
$327$			0.249885i			0.0138187i
$328$		−	3.78202i		−	0.208827i
$329$	−1.31415			−0.0724516
$330$	−1.37169			−0.0755092
$331$			13.8898i			0.763450i	0.924276	+	0.381725i	$0.124670\pi$
$331$			13.8898i			0.763450i	−0.924276	+	0.381725i	$0.875330\pi$
$332$	−4.22533			−0.231895
$333$	5.38890	+	8.72448i	0.295310	+	0.478099i
$334$	13.8568			0.758209
$335$			1.24675i			0.0681172i
$336$	0.393115			0.0214462
$337$	−23.1365			−1.26033			−0.630163	−	0.776463i	$-0.717012\pi$
$337$	−23.1365			−1.26033			−0.630163	+	0.776463i	$0.717012\pi$
$338$		−	8.95715i		−	0.487205i
$339$			15.5296i			0.843453i
$340$	4.17513			0.226428
$341$			5.54683i			0.300378i
$342$	−5.30429			−0.286823
$343$	4.76060			0.257048
$344$	−1.19656			−0.0645141
$345$	5.37169			0.289202
$346$			9.19656i			0.494410i
$347$			13.1709i			0.707052i	0.935425	+	0.353526i	$0.115017\pi$
$347$			13.1709i			0.707052i	−0.935425	+	0.353526i	$0.884983\pi$
$348$			0.921039i			0.0493729i
$349$	−9.60688			−0.514245			−0.257122	−	0.966379i	$-0.582774\pi$
$349$	−9.60688			−0.514245			−0.257122	+	0.966379i	$0.582774\pi$
$350$			0.342923i			0.0183300i
$351$		−	25.1709i		−	1.34352i
$352$			1.19656i			0.0637767i
$353$			15.3973i			0.819517i	0.912194	+	0.409758i	$0.134387\pi$
$353$			15.3973i			0.819517i	−0.912194	+	0.409758i	$0.865613\pi$
$354$	0.192347			0.0102231
$355$		−	0.685846i		−	0.0364009i
$356$			4.58546i			0.243029i
$357$		−	1.64131i		−	0.0868673i
$358$	22.4752			1.18785
$359$	−7.32885			−0.386802			−0.193401	−	0.981120i	$-0.561952\pi$
$359$	−7.32885			−0.386802			−0.193401	+	0.981120i	$0.561952\pi$
$360$	1.68585			0.0888519
$361$	9.10038			0.478968
$362$			7.41454i			0.389699i
$363$	10.9687			0.575708
$364$		−	1.60688i		−	0.0842236i
$365$			11.9572i			0.625866i
$366$	2.49350			0.130337
$367$	−28.7079			−1.49854			−0.749270	−	0.662265i	$-0.769595\pi$
$367$	−28.7079			−1.49854			−0.749270	+	0.662265i	$0.769595\pi$
$368$		−	4.68585i		−	0.244267i
$369$	−6.37590			−0.331916
$370$	−3.19656	−	5.17513i	−0.166181	−	0.269042i
$371$	3.82487			0.198577
$372$			5.31415i			0.275526i
$373$	2.97858			0.154225			0.0771124	−	0.997022i	$-0.475430\pi$
$373$	2.97858			0.154225			0.0771124	+	0.997022i	$0.475430\pi$
$374$	4.99579			0.258326
$375$		−	1.14637i		−	0.0591981i
$376$		−	3.83221i		−	0.197631i
$377$	3.76481			0.193897
$378$		−	1.84208i		−	0.0947462i
$379$	20.4507			1.05048			0.525240	−	0.850954i	$-0.323976\pi$
$379$	20.4507			1.05048			0.525240	+	0.850954i	$0.323976\pi$
$380$	3.14637			0.161405
$381$	14.2352			0.729291
$382$	1.32150			0.0676138
$383$			27.3435i			1.39719i	0.715518	+	0.698595i	$0.246191\pi$
$383$			27.3435i			1.39719i	−0.715518	+	0.698595i	$0.753809\pi$
$384$			1.14637i			0.0585002i
$385$			0.410327i			0.0209122i
$386$	−12.7434			−0.648621
$387$			2.01721i			0.102541i
$388$			4.21798i			0.214136i
$389$			20.1323i			1.02075i	0.859953	+	0.510374i	$0.170493\pi$
$389$			20.1323i			1.02075i	−0.859953	+	0.510374i	$0.829507\pi$
$390$			5.37169i			0.272006i
$391$	−19.5640			−0.989396
$392$			6.88240i			0.347614i
$393$		−	21.6791i		−	1.09357i
$394$			10.3931i			0.523598i
$395$	5.14637			0.258942
$396$	2.01721			0.101369
$397$	4.23519			0.212558			0.106279	−	0.994336i	$-0.466106\pi$
$397$	4.23519			0.212558			0.106279	+	0.994336i	$0.466106\pi$
$398$	8.47521			0.424824
$399$		−	1.23688i		−	0.0619217i
$400$	−1.00000			−0.0500000
$401$			1.02142i			0.0510074i	0.999675	+	0.0255037i	$0.00811896\pi$
$401$			1.02142i			0.0510074i	−0.999675	+	0.0255037i	$0.991881\pi$
$402$			1.42923i			0.0712836i
$403$	21.7220			1.08205
$404$	−9.95715			−0.495387
$405$			1.10038i			0.0546785i
$406$	0.275519			0.0136738
$407$	−3.82487	−	6.19235i	−0.189592	−	0.306943i
$408$	4.78623			0.236954
$409$			32.7005i			1.61694i	0.588539	+	0.808469i	$0.299703\pi$
$409$			32.7005i			1.61694i	−0.588539	+	0.808469i	$0.700297\pi$
$410$	3.78202			0.186781
$411$	−21.0361			−1.03764
$412$		−	10.6430i		−	0.524343i
$413$		−	0.0575385i		−	0.00283128i
$414$	−7.89962			−0.388245
$415$		−	4.22533i		−	0.207413i
$416$	4.68585			0.229743
$417$	−22.6283			−1.10811
$418$	3.76481			0.184143
$419$	1.50650			0.0735974			0.0367987	−	0.999323i	$-0.488284\pi$
$419$	1.50650			0.0735974			0.0367987	+	0.999323i	$0.488284\pi$
$420$			0.393115i			0.0191821i
$421$		−	25.3288i		−	1.23445i	−0.786786	−	0.617226i	$-0.788256\pi$
$421$		−	25.3288i		−	1.23445i	0.786786	−	0.617226i	$-0.211744\pi$
$422$			12.6602i			0.616290i
$423$	−6.46052			−0.314121
$424$			11.1537i			0.541672i
$425$			4.17513i			0.202524i
$426$		−	0.786230i		−	0.0380930i
$427$		−	0.745904i		−	0.0360968i
$428$	−17.8322			−0.861952
$429$			6.42754i			0.310325i
$430$		−	1.19656i		−	0.0577031i
$431$		−	32.5008i		−	1.56551i	−0.622330	−	0.782755i	$-0.713814\pi$
$431$		−	32.5008i		−	1.56551i	0.622330	−	0.782755i	$-0.286186\pi$
$432$	5.37169			0.258446
$433$	32.7434			1.57355			0.786773	−	0.617242i	$-0.211750\pi$
$433$	32.7434			1.57355			0.786773	+	0.617242i	$0.211750\pi$
$434$	1.58967			0.0763067
$435$	−0.921039			−0.0441604
$436$			0.217980i			0.0104394i
$437$	−14.7434			−0.705272
$438$			13.7073i			0.654959i
$439$			2.32823i			0.111120i	0.998455	+	0.0555602i	$0.0176945\pi$
$439$			2.32823i			0.111120i	−0.998455	+	0.0555602i	$0.982306\pi$
$440$	−1.19656			−0.0570436
$441$	11.6027			0.552508
$442$		−	19.5640i		−	0.930566i
$443$	25.2614			1.20021			0.600104	−	0.799922i	$-0.295126\pi$
$443$	25.2614			1.20021			0.600104	+	0.799922i	$0.295126\pi$
$444$	−3.66442	−	5.93260i	−0.173906	−	0.281549i
$445$	−4.58546			−0.217372
$446$			20.5928i			0.975098i
$447$	−21.7564			−1.02904
$448$	0.342923			0.0162016
$449$			33.6363i			1.58739i	0.608313	+	0.793697i	$0.291846\pi$
$449$			33.6363i			1.58739i	−0.608313	+	0.793697i	$0.708154\pi$
$450$			1.68585i			0.0794716i
$451$	4.52540			0.213093
$452$			13.5468i			0.637189i
$453$	9.95715			0.467828
$454$	−17.1966			−0.807074
$455$	1.60688			0.0753319
$456$	3.60688			0.168908
$457$		−	27.7476i		−	1.29798i	−0.760798	−	0.648989i	$-0.775192\pi$
$457$		−	27.7476i		−	1.29798i	0.760798	−	0.648989i	$-0.224808\pi$
$458$		−	4.04285i		−	0.188910i
$459$		−	22.4275i		−	1.04683i
$460$	4.68585			0.218479
$461$		−	24.3675i		−	1.13491i	−0.823406	−	0.567453i	$-0.807929\pi$
$461$		−	24.3675i		−	1.13491i	0.823406	−	0.567453i	$-0.192071\pi$
$462$			0.470385i			0.0218843i
$463$		−	11.6644i		−	0.542092i	−0.962566	−	0.271046i	$-0.912630\pi$
$463$		−	11.6644i		−	0.542092i	0.962566	−	0.271046i	$-0.0873695\pi$
$464$			0.803442i			0.0372989i
$465$	−5.31415			−0.246438
$466$			3.80765i			0.176386i
$467$		−	14.8181i		−	0.685702i	−0.939390	−	0.342851i	$-0.888607\pi$
$467$		−	14.8181i		−	0.685702i	0.939390	−	0.342851i	$-0.111393\pi$
$468$		−	7.89962i		−	0.365160i
$469$	0.427539			0.0197419
$470$	3.83221			0.176767
$471$	7.29946			0.336341
$472$	0.167788			0.00772308
$473$		−	1.43175i		−	0.0658319i
$474$	5.89962			0.270978
$475$			3.14637i			0.144365i
$476$		−	1.43175i		−	0.0656242i
$477$	18.8034			0.860950
$478$	21.3215			0.975223
$479$			5.98171i			0.273311i	0.990619	+	0.136656i	$0.0436354\pi$
$479$			5.98171i			0.273311i	−0.990619	+	0.136656i	$0.956365\pi$
$480$	−1.14637			−0.0523242
$481$	−24.2499	+	14.9786i	−1.10570	+	0.682964i
$482$	21.3717			0.973454
$483$		−	1.84208i		−	0.0838174i
$484$	9.56825			0.434920
$485$	−4.21798			−0.191529
$486$		−	14.8536i		−	0.673775i
$487$		−	4.53635i		−	0.205561i	−0.994704	−	0.102781i	$-0.967226\pi$
$487$		−	4.53635i		−	0.205561i	0.994704	−	0.102781i	$-0.0327740\pi$
$488$	2.17513			0.0984637
$489$		−	1.75639i		−	0.0794265i
$490$	−6.88240			−0.310915
$491$	−33.0361			−1.49090			−0.745450	−	0.666562i	$-0.767765\pi$
$491$	−33.0361			−1.49090			−0.745450	+	0.666562i	$0.767765\pi$
$492$	4.33558			0.195463
$493$	3.35448			0.151078
$494$		−	14.7434i		−	0.663336i
$495$			2.01721i			0.0906669i
$496$			4.63565i			0.208147i
$497$	−0.235192			−0.0105498
$498$		−	4.84377i		−	0.217054i
$499$		−	23.9817i		−	1.07357i	−0.843719	−	0.536784i	$-0.819639\pi$
$499$		−	23.9817i		−	1.07357i	0.843719	−	0.536784i	$-0.180361\pi$
$500$		−	1.00000i		−	0.0447214i
$501$			15.8849i			0.709686i
$502$	−10.1249			−0.451898
$503$		−	15.5296i		−	0.692431i	−0.938155	−	0.346216i	$-0.887467\pi$
$503$		−	15.5296i		−	0.692431i	0.938155	−	0.346216i	$-0.112533\pi$
$504$		−	0.578116i		−	0.0257513i
$505$		−	9.95715i		−	0.443088i
$506$	5.60688			0.249256
$507$	10.2682			0.456026
$508$	12.4177			0.550945
$509$	5.56404			0.246622			0.123311	−	0.992368i	$-0.460649\pi$
$509$	5.56404			0.246622			0.123311	+	0.992368i	$0.460649\pi$
$510$			4.78623i			0.211938i
$511$	4.10038			0.181390
$512$			1.00000i			0.0441942i
$513$		−	16.9013i		−	0.746211i
$514$	30.3074			1.33680
$515$	10.6430			0.468987
$516$		−	1.37169i		−	0.0603854i
$517$	4.58546			0.201668
$518$	−1.77467	+	1.09617i	−0.0779747	+	0.0481631i
$519$	−10.5426			−0.462769
$520$			4.68585i			0.205488i
$521$	−4.12602			−0.180764			−0.0903821	−	0.995907i	$-0.528809\pi$
$521$	−4.12602			−0.180764			−0.0903821	+	0.995907i	$0.528809\pi$
$522$	1.35448			0.0592840
$523$			40.2499i			1.76000i	0.474969	+	0.880002i	$0.342459\pi$
$523$			40.2499i			1.76000i	−0.474969	+	0.880002i	$0.657541\pi$
$524$		−	18.9112i		−	0.826138i
$525$	−0.393115			−0.0171570
$526$		−	12.3429i		−	0.538177i
$527$	19.3545			0.843094
$528$	−1.37169			−0.0596952
$529$	1.04285			0.0453411
$530$	−11.1537			−0.484486
$531$		−	0.282865i		−	0.0122753i
$532$		−	1.07896i		−	0.0467789i
$533$		−	17.7220i		−	0.767623i
$534$	−5.25662			−0.227476
$535$		−	17.8322i		−	0.770954i
$536$			1.24675i			0.0538514i
$537$			25.7648i			1.11183i
$538$		−	13.3717i		−	0.576495i
$539$	−8.23519			−0.354715
$540$			5.37169i			0.231161i
$541$		−	30.1151i		−	1.29475i	−0.762172	−	0.647374i	$-0.775867\pi$
$541$		−	30.1151i		−	1.29475i	0.762172	−	0.647374i	$-0.224133\pi$
$542$		−	20.2499i		−	0.869807i
$543$	−8.49977			−0.364760
$544$	4.17513			0.179007
$545$	−0.217980			−0.00933726
$546$	1.84208			0.0788336
$547$		−	39.1684i		−	1.67472i	−0.546652	−	0.837360i	$-0.684098\pi$
$547$		−	39.1684i		−	1.67472i	0.546652	−	0.837360i	$-0.315902\pi$
$548$	−18.3503			−0.783885
$549$		−	3.66694i		−	0.156501i
$550$		−	1.19656i		−	0.0510214i
$551$	2.52792			0.107693
$552$	5.37169			0.228634
$553$		−	1.76481i		−	0.0750472i
$554$	−7.46365			−0.317100
$555$	5.93260	−	3.66442i	0.251825	−	0.155546i
$556$	−19.7392			−0.837127
$557$		−	11.6644i		−	0.494237i	−0.968985	−	0.247119i	$-0.920516\pi$
$557$		−	11.6644i		−	0.494237i	0.968985	−	0.247119i	$-0.0794838\pi$
$558$	7.81500			0.330835
$559$	−5.60688			−0.237146
$560$			0.342923i			0.0144911i
$561$			5.72700i			0.241794i
$562$	−4.93573			−0.208201
$563$		−	7.63879i		−	0.321937i	−0.986960	−	0.160968i	$-0.948538\pi$
$563$		−	7.63879i		−	0.321937i	0.986960	−	0.160968i	$-0.0514617\pi$
$564$	4.39312			0.184984
$565$	−13.5468			−0.569919
$566$	−13.0361			−0.547949
$567$	0.377347			0.0158471
$568$		−	0.685846i		−	0.0287775i
$569$		−	4.38469i		−	0.183816i	−0.995768	−	0.0919080i	$-0.970703\pi$
$569$		−	4.38469i		−	0.183816i	0.995768	−	0.0919080i	$-0.0292966\pi$
$570$			3.60688i			0.151076i
$571$	−3.58967			−0.150223			−0.0751116	−	0.997175i	$-0.523931\pi$
$571$	−3.58967			−0.150223			−0.0751116	+	0.997175i	$0.523931\pi$
$572$			5.60688i			0.234436i
$573$			1.51492i			0.0632868i
$574$		−	1.29694i		−	0.0541333i
$575$			4.68585i			0.195413i
$576$	1.68585			0.0702436
$577$			0.149501i			0.00622381i	0.999995	+	0.00311191i	$0.000990552\pi$
$577$			0.149501i			0.00622381i	−0.999995	+	0.00311191i	$0.999009\pi$
$578$		−	0.431750i		−	0.0179584i
$579$		−	14.6086i		−	0.607112i
$580$	−0.803442			−0.0333611
$581$	−1.44896			−0.0601131
$582$	−4.83535			−0.200432
$583$	−13.3461			−0.552737
$584$			11.9572i			0.494791i
$585$	7.89962			0.326609
$586$			23.3545i			0.964765i
$587$			21.1109i			0.871339i	0.900107	+	0.435669i	$0.143488\pi$
$587$			21.1109i			0.871339i	−0.900107	+	0.435669i	$0.856512\pi$
$588$	−7.88975			−0.325368
$589$	14.5855			0.600983
$590$			0.167788i			0.00690774i
$591$	−11.9143			−0.490089
$592$	−3.19656	−	5.17513i	−0.131378	−	0.212697i
$593$	31.0214			1.27390			0.636949	−	0.770906i	$-0.280196\pi$
$593$	31.0214			1.27390			0.636949	+	0.770906i	$0.280196\pi$
$594$			6.42754i			0.263725i
$595$	1.43175			0.0586960
$596$	−18.9786			−0.777393
$597$			9.71569i			0.397637i
$598$		−	21.9572i		−	0.897895i
$599$	−40.7152			−1.66358			−0.831790	−	0.555091i	$-0.812683\pi$
$599$	−40.7152			−1.66358			−0.831790	+	0.555091i	$0.812683\pi$
$600$		−	1.14637i		−	0.0468002i
$601$	45.2113			1.84421			0.922103	−	0.386945i	$-0.126470\pi$
$601$	45.2113			1.84421			0.922103	+	0.386945i	$0.126470\pi$
$602$	−0.410327			−0.0167237
$603$	2.10183			0.0855931
$604$	8.68585			0.353422
$605$			9.56825i			0.389005i
$606$		−	11.4145i		−	0.463684i
$607$			0.0491168i			0.00199359i	1.00000		0.000996796i	$0.000317290\pi$
$607$			0.0491168i			0.00199359i	−1.00000		0.000996796i	$0.999683\pi$
$608$	3.14637			0.127602
$609$			0.315845i			0.0127987i
$610$			2.17513i			0.0880686i
$611$		−	17.9572i		−	0.726469i
$612$		−	7.03863i		−	0.284520i
$613$	−17.1966			−0.694562			−0.347281	−	0.937761i	$-0.612895\pi$
$613$	−17.1966			−0.694562			−0.347281	+	0.937761i	$0.612895\pi$
$614$			10.2682i			0.414390i
$615$			4.33558i			0.174827i
$616$			0.410327i			0.0165326i
$617$	39.0508			1.57213			0.786063	−	0.618146i	$-0.212116\pi$
$617$	39.0508			1.57213			0.786063	+	0.618146i	$0.212116\pi$
$618$	12.2008			0.490787
$619$	45.7623			1.83934			0.919671	−	0.392690i	$-0.128456\pi$
$619$	45.7623			1.83934			0.919671	+	0.392690i	$0.128456\pi$
$620$	−4.63565			−0.186172
$621$		−	25.1709i		−	1.01007i
$622$	−8.98592			−0.360303
$623$			1.57246i			0.0629993i
$624$			5.37169i			0.215040i
$625$	1.00000			0.0400000
$626$	3.17092			0.126736
$627$			4.31585i			0.172358i
$628$	6.36748			0.254090
$629$	−21.6069	+	13.3461i	−0.861523	+	0.532142i
$630$	0.578116			0.0230327
$631$		−	32.9002i		−	1.30974i	−0.755743	−	0.654869i	$-0.772724\pi$
$631$		−	32.9002i		−	1.30974i	0.755743	−	0.654869i	$-0.227276\pi$
$632$	5.14637			0.204711
$633$	−14.5132			−0.576849
$634$		−	12.1751i		−	0.483536i
$635$			12.4177i			0.492780i
$636$	−12.7862			−0.507007
$637$			32.2499i			1.27779i
$638$	−0.961365			−0.0380608
$639$	−1.15623			−0.0457398
$640$	−1.00000			−0.0395285
$641$	13.5321			0.534487			0.267244	−	0.963629i	$-0.413887\pi$
$641$	13.5321			0.534487			0.267244	+	0.963629i	$0.413887\pi$
$642$		−	20.4422i		−	0.806791i
$643$			21.3116i			0.840449i	0.907420	+	0.420224i	$0.138049\pi$
$643$			21.3116i			0.840449i	−0.907420	+	0.420224i	$0.861951\pi$
$644$		−	1.60688i		−	0.0633201i
$645$	1.37169			0.0540103
$646$		−	13.1365i		−	0.516849i
$647$			39.4783i			1.55205i	0.630700	+	0.776027i	$0.282768\pi$
$647$			39.4783i			1.55205i	−0.630700	+	0.776027i	$0.717232\pi$
$648$			1.10038i			0.0432272i
$649$			0.200768i			0.00788085i
$650$	−4.68585			−0.183794
$651$			1.82235i			0.0714234i
$652$		−	1.53213i		−	0.0600030i
$653$		−	2.00000i		−	0.0782660i	−0.999234	−	0.0391330i	$-0.987540\pi$
$653$		−	2.00000i		−	0.0782660i	0.999234	−	0.0391330i	$-0.0124596\pi$
$654$	−0.249885			−0.00977129
$655$	18.9112			0.738921
$656$	3.78202			0.147663
$657$	20.1579			0.786435
$658$		−	1.31415i		−	0.0512311i
$659$	0.585462			0.0228064			0.0114032	−	0.999935i	$-0.496370\pi$
$659$	0.585462			0.0228064			0.0114032	+	0.999935i	$0.496370\pi$
$660$		−	1.37169i		−	0.0533931i
$661$			24.5682i			0.955594i	0.878470	+	0.477797i	$0.158565\pi$
$661$			24.5682i			0.955594i	−0.878470	+	0.477797i	$0.841435\pi$
$662$	−13.8898			−0.539840
$663$	22.4275			0.871013
$664$		−	4.22533i		−	0.163974i
$665$	1.07896			0.0418403
$666$	−8.72448	+	5.38890i	−0.338067	+	0.208816i
$667$	3.76481			0.145774
$668$			13.8568i			0.536135i
$669$	−23.6069			−0.912695
$670$	−1.24675			−0.0481661
$671$			2.60267i			0.100475i
$672$			0.393115i			0.0151647i
$673$	−36.6577			−1.41305			−0.706525	−	0.707688i	$-0.749738\pi$
$673$	−36.6577			−1.41305			−0.706525	+	0.707688i	$0.749738\pi$
$674$		−	23.1365i		−	0.891185i
$675$	−5.37169			−0.206757
$676$	8.95715			0.344506
$677$	20.2646			0.778831			0.389416	−	0.921062i	$-0.372677\pi$
$677$	20.2646			0.778831			0.389416	+	0.921062i	$0.372677\pi$
$678$	−15.5296			−0.596411
$679$			1.44644i			0.0555094i
$680$			4.17513i			0.160109i
$681$		−	19.7135i		−	0.755425i
$682$	−5.54683			−0.212399
$683$			7.15371i			0.273729i	0.990590	+	0.136865i	$0.0437025\pi$
$683$			7.15371i			0.273729i	−0.990590	+	0.136865i	$0.956297\pi$
$684$		−	5.30429i		−	0.202815i
$685$		−	18.3503i		−	0.701128i
$686$			4.76060i			0.181760i
$687$	4.63458			0.176820
$688$		−	1.19656i		−	0.0456183i
$689$			52.2646i			1.99112i
$690$			5.37169i			0.204497i
$691$	6.38217			0.242789			0.121395	−	0.992604i	$-0.461263\pi$
$691$	6.38217			0.242789			0.121395	+	0.992604i	$0.461263\pi$
$692$	−9.19656			−0.349601
$693$	0.691749			0.0262774
$694$	−13.1709			−0.499961
$695$		−	19.7392i		−	0.748750i
$696$	−0.921039			−0.0349119
$697$		−	15.7904i		−	0.598106i
$698$		−	9.60688i		−	0.363626i
$699$	−4.36496			−0.165098
$700$	−0.342923			−0.0129613
$701$			24.7434i			0.934545i	0.884113	+	0.467272i	$0.154763\pi$
$701$			24.7434i			0.934545i	−0.884113	+	0.467272i	$0.845237\pi$
$702$	25.1709			0.950015
$703$	−16.2829	+	10.0575i	−0.614120	+	0.379327i
$704$	−1.19656			−0.0450970
$705$			4.39312i			0.165454i
$706$	−15.3973			−0.579486
$707$	−3.41454			−0.128417
$708$			0.192347i			0.00722883i
$709$			0.0684794i			0.00257180i	0.999999	+	0.00128590i	$0.000409314\pi$
$709$			0.0684794i			0.00257180i	−0.999999	+	0.00128590i	$0.999591\pi$
$710$	0.685846			0.0257393
$711$		−	8.67598i		−	0.325375i
$712$	−4.58546			−0.171847
$713$	21.7220			0.813494
$714$	1.64131			0.0614244
$715$	−5.60688			−0.209686
$716$			22.4752i			0.839938i
$717$			24.4422i			0.912812i
$718$		−	7.32885i		−	0.273510i
$719$	−12.4507			−0.464331			−0.232166	−	0.972676i	$-0.574581\pi$
$719$	−12.4507			−0.464331			−0.232166	+	0.972676i	$0.574581\pi$
$720$			1.68585i			0.0628278i
$721$		−	3.64973i		−	0.135923i
$722$			9.10038i			0.338681i
$723$			24.4998i			0.911156i
$724$	−7.41454			−0.275559
$725$		−	0.803442i		−	0.0298391i
$726$			10.9687i			0.407087i
$727$			1.94246i			0.0720419i	0.999351	+	0.0360210i	$0.0114683\pi$
$727$			1.94246i			0.0720419i	−0.999351	+	0.0360210i	$0.988532\pi$
$728$	1.60688			0.0595551
$729$	20.3288			0.752920
$730$	−11.9572			−0.442554
$731$	−4.99579			−0.184776
$732$			2.49350i			0.0921624i
$733$	−23.7392			−0.876826			−0.438413	−	0.898774i	$-0.644459\pi$
$733$	−23.7392			−0.876826			−0.438413	+	0.898774i	$0.644459\pi$
$734$		−	28.7079i		−	1.05963i
$735$		−	7.88975i		−	0.291018i
$736$	4.68585			0.172723
$737$	−1.49181			−0.0549514
$738$		−	6.37590i		−	0.234700i
$739$	38.4826			1.41560			0.707802	−	0.706411i	$-0.249687\pi$
$739$	38.4826			1.41560			0.707802	+	0.706411i	$0.249687\pi$
$740$	5.17513	−	3.19656i	0.190242	−	0.117508i
$741$	16.9013			0.620885
$742$			3.82487i			0.140415i
$743$	−29.5798			−1.08518			−0.542589	−	0.839998i	$-0.682556\pi$
$743$	−29.5798			−1.08518			−0.542589	+	0.839998i	$0.682556\pi$
$744$	−5.31415			−0.194826
$745$		−	18.9786i		−	0.695321i
$746$			2.97858i			0.109053i
$747$	−7.12325			−0.260626
$748$			4.99579i			0.182664i
$749$	−6.11508			−0.223440
$750$	1.14637			0.0418593
$751$	52.4653			1.91449			0.957244	−	0.289282i	$-0.0934166\pi$
$751$	52.4653			1.91449			0.957244	+	0.289282i	$0.0934166\pi$
$752$	3.83221			0.139746
$753$		−	11.6069i		−	0.422978i
$754$			3.76481i			0.137106i
$755$			8.68585i			0.316110i
$756$	1.84208			0.0669957
$757$			31.1365i			1.13168i	0.824517	+	0.565838i	$0.191447\pi$
$757$			31.1365i			1.13168i	−0.824517	+	0.565838i	$0.808553\pi$
$758$			20.4507i			0.742801i
$759$			6.42754i			0.233305i
$760$			3.14637i			0.114131i
$761$	31.2259			1.13194			0.565970	−	0.824426i	$-0.308502\pi$
$761$	31.2259			1.13194			0.565970	+	0.824426i	$0.308502\pi$
$762$			14.2352i			0.515687i
$763$			0.0747505i			0.00270615i
$764$			1.32150i			0.0478102i
$765$	7.03863			0.254482
$766$	−27.3435			−0.987962
$767$	0.786230			0.0283891
$768$	−1.14637			−0.0413659
$769$			20.4998i			0.739241i	0.929183	+	0.369620i	$0.120512\pi$
$769$			20.4998i			0.739241i	−0.929183	+	0.369620i	$0.879488\pi$
$770$	−0.410327			−0.0147872
$771$			34.7434i			1.25125i
$772$		−	12.7434i		−	0.458644i
$773$	16.1239			0.579935			0.289968	−	0.957036i	$-0.406355\pi$
$773$	16.1239			0.579935			0.289968	+	0.957036i	$0.406355\pi$
$774$	−2.01721			−0.0725072
$775$		−	4.63565i		−	0.166518i
$776$	−4.21798			−0.151417
$777$	−1.25662	−	2.03442i	−0.0450808	−	0.0729846i
$778$	−20.1323			−0.721778
$779$		−	11.8996i		−	0.426348i
$780$	−5.37169			−0.192337
$781$	0.820654			0.0293653
$782$		−	19.5640i		−	0.699609i
$783$			4.31585i			0.154236i
$784$	−6.88240			−0.245800
$785$			6.36748i			0.227265i
$786$	21.6791			0.773268
$787$	−53.6974			−1.91411			−0.957053	−	0.289913i	$-0.906373\pi$
$787$	−53.6974			−1.91411			−0.957053	+	0.289913i	$0.906373\pi$
$788$	−10.3931			−0.370239
$789$	14.1495			0.503736
$790$			5.14637i			0.183099i
$791$			4.64552i			0.165176i
$792$			2.01721i			0.0716785i
$793$	10.1923			0.361941
$794$			4.23519i			0.150301i
$795$		−	12.7862i		−	0.453481i
$796$			8.47521i			0.300396i
$797$		−	12.0491i		−	0.426802i	−0.976965	−	0.213401i	$-0.931546\pi$
$797$		−	12.0491i		−	0.426802i	0.976965	−	0.213401i	$-0.0684540\pi$
$798$	1.23688			0.0437852
$799$		−	16.0000i		−	0.566039i
$800$		−	1.00000i		−	0.0353553i
$801$			7.73038i			0.273140i
$802$	−1.02142			−0.0360677
$803$	−14.3074			−0.504898
$804$	−1.42923			−0.0504051
$805$	1.60688			0.0566352
$806$			21.7220i			0.765123i
$807$	15.3288			0.539601
$808$		−	9.95715i		−	0.350291i
$809$			25.1365i			0.883752i	0.897076	+	0.441876i	$0.145687\pi$
$809$			25.1365i			0.883752i	−0.897076	+	0.441876i	$0.854313\pi$
$810$	−1.10038			−0.0386636
$811$	−2.62831			−0.0922924			−0.0461462	−	0.998935i	$-0.514694\pi$
$811$	−2.62831			−0.0922924			−0.0461462	+	0.998935i	$0.514694\pi$
$812$			0.275519i			0.00966882i
$813$	23.2138			0.814142
$814$	6.19235	−	3.82487i	0.217042	−	0.134061i
$815$	1.53213			0.0536683
$816$			4.78623i			0.167552i
$817$	−3.76481			−0.131714
$818$	−32.7005			−1.14335
$819$		−	2.70896i		−	0.0946587i
$820$			3.78202i			0.132074i
$821$	14.8207			0.517244			0.258622	−	0.965979i	$-0.416732\pi$
$821$	14.8207			0.517244			0.258622	+	0.965979i	$0.416732\pi$
$822$		−	21.0361i		−	0.733719i
$823$	−51.9473			−1.81077			−0.905384	−	0.424593i	$-0.860417\pi$
$823$	−51.9473			−1.81077			−0.905384	+	0.424593i	$0.860417\pi$
$824$	10.6430			0.370766
$825$	1.37169			0.0477562
$826$	0.0575385			0.00200202
$827$		−	11.3889i		−	0.396031i	−0.980199	−	0.198016i	$-0.936550\pi$
$827$		−	11.3889i		−	0.396031i	0.980199	−	0.198016i	$-0.0634496\pi$
$828$		−	7.89962i		−	0.274531i
$829$		−	47.2259i		−	1.64022i	−0.572202	−	0.820112i	$-0.693911\pi$
$829$		−	47.2259i		−	1.64022i	0.572202	−	0.820112i	$-0.306089\pi$
$830$	4.22533			0.146663
$831$		−	8.55608i		−	0.296807i
$832$			4.68585i			0.162452i
$833$			28.7350i			0.995607i
$834$		−	22.6283i		−	0.783554i
$835$	−13.8568			−0.479533
$836$			3.76481i			0.130209i
$837$			24.9013i			0.860715i
$838$			1.50650i			0.0520412i
$839$	53.4355			1.84480			0.922399	−	0.386238i	$-0.126226\pi$
$839$	53.4355			1.84480			0.922399	+	0.386238i	$0.126226\pi$
$840$	−0.393115			−0.0135638
$841$	28.3545			0.977741
$842$	25.3288			0.872890
$843$		−	5.65815i		−	0.194877i
$844$	−12.6602			−0.435782
$845$			8.95715i			0.308135i
$846$		−	6.46052i		−	0.222117i
$847$	3.28117			0.112742
$848$	−11.1537			−0.383020
$849$		−	14.9442i		−	0.512882i
$850$	−4.17513			−0.143206
$851$	−24.2499	+	14.9786i	−0.831275	+	0.513459i
$852$	0.786230			0.0269358
$853$		−	23.5725i		−	0.807106i	−0.914956	−	0.403553i	$-0.867775\pi$
$853$		−	23.5725i		−	0.807106i	0.914956	−	0.403553i	$-0.132225\pi$
$854$	0.745904			0.0255243
$855$	5.30429			0.181403
$856$		−	17.8322i		−	0.609492i
$857$			42.9101i			1.46578i	0.680347	+	0.732891i	$0.261829\pi$
$857$			42.9101i			1.46578i	−0.680347	+	0.732891i	$0.738171\pi$
$858$	−6.42754			−0.219433
$859$			42.0905i			1.43611i	0.695986	+	0.718055i	$0.254967\pi$
$859$			42.0905i			1.43611i	−0.695986	+	0.718055i	$0.745033\pi$
$860$	1.19656			0.0408023
$861$	1.48677			0.0506690
$862$	32.5008			1.10698
$863$	−30.2144			−1.02851			−0.514255	−	0.857637i	$-0.671931\pi$
$863$	−30.2144			−1.02851			−0.514255	+	0.857637i	$0.671931\pi$
$864$			5.37169i			0.182749i
$865$		−	9.19656i		−	0.312692i
$866$			32.7434i			1.11267i
$867$	0.494943			0.0168092
$868$			1.58967i			0.0539570i
$869$			6.15792i			0.208893i
$870$		−	0.921039i		−	0.0312261i
$871$			5.84208i			0.197951i
$872$	−0.217980			−0.00738175
$873$			7.11087i			0.240666i
$874$		−	14.7434i		−	0.498702i
$875$		−	0.342923i		−	0.0115929i
$876$	−13.7073			−0.463126
$877$	−44.5548			−1.50451			−0.752254	−	0.658873i	$-0.771033\pi$
$877$	−44.5548			−1.50451			−0.752254	+	0.658873i	$0.771033\pi$
$878$	−2.32823			−0.0785740
$879$	−26.7728			−0.903023
$880$		−	1.19656i		−	0.0403359i
$881$	−31.9891			−1.07774			−0.538869	−	0.842389i	$-0.681148\pi$
$881$	−31.9891			−1.07774			−0.538869	+	0.842389i	$0.681148\pi$
$882$			11.6027i			0.390682i
$883$			0.375903i			0.0126501i	0.999980	+	0.00632507i	$0.00201335\pi$
$883$			0.375903i			0.0126501i	−0.999980	+	0.00632507i	$0.997987\pi$
$884$	19.5640			0.658010
$885$	−0.192347			−0.00646567
$886$			25.2614i			0.848675i
$887$	−52.5731			−1.76523			−0.882616	−	0.470095i	$-0.844219\pi$
$887$	−52.5731			−1.76523			−0.882616	+	0.470095i	$0.844219\pi$
$888$	5.93260	−	3.66442i	0.199085	−	0.122970i
$889$	4.25831			0.142819
$890$		−	4.58546i		−	0.153705i
$891$	−1.31667			−0.0441102
$892$	−20.5928			−0.689498
$893$		−	12.0575i		−	0.403490i
$894$		−	21.7564i		−	0.727642i
$895$	−22.4752			−0.751263
$896$			0.342923i			0.0114563i
$897$	25.1709			0.840433
$898$	−33.6363			−1.12246
$899$	−3.72448			−0.124218
$900$	−1.68585			−0.0561949
$901$			46.5682i			1.55141i
$902$			4.52540i			0.150679i
$903$		−	0.470385i		−	0.0156534i
$904$	−13.5468			−0.450561
$905$		−	7.41454i		−	0.246468i
$906$			9.95715i			0.330804i
$907$		−	42.2562i		−	1.40309i	−0.712624	−	0.701546i	$-0.752493\pi$
$907$		−	42.2562i		−	1.40309i	0.712624	−	0.701546i	$-0.247507\pi$
$908$		−	17.1966i		−	0.570688i
$909$	−16.7862			−0.556764
$910$			1.60688i			0.0532677i
$911$			27.6399i			0.915750i	0.889017	+	0.457875i	$0.151389\pi$
$911$			27.6399i			0.915750i	−0.889017	+	0.457875i	$0.848611\pi$
$912$			3.60688i			0.119436i
$913$	5.05585			0.167324
$914$	27.7476			0.917809
$915$	−2.49350			−0.0824325
$916$	4.04285			0.133579
$917$		−	6.48508i		−	0.214156i
$918$	22.4275			0.740219
$919$		−	53.3106i		−	1.75855i	−0.476312	−	0.879277i	$-0.658027\pi$
$919$		−	53.3106i		−	1.75855i	0.476312	−	0.879277i	$-0.341973\pi$
$920$			4.68585i			0.154488i
$921$	−11.7711			−0.387870
$922$	24.3675			0.802500
$923$		−	3.21377i		−	0.105783i
$924$	−0.470385			−0.0154745
$925$	3.19656	+	5.17513i	0.105102	+	0.170157i
$926$	11.6644			0.383317
$927$		−	17.9425i		−	0.589308i
$928$	−0.803442			−0.0263743
$929$	−44.0122			−1.44399			−0.721996	−	0.691897i	$-0.756775\pi$
$929$	−44.0122			−1.44399			−0.721996	+	0.691897i	$0.756775\pi$
$930$		−	5.31415i		−	0.174258i
$931$			21.6546i			0.709699i
$932$	−3.80765			−0.124724
$933$		−	10.3012i		−	0.337245i
$934$	14.8181			0.484864
$935$	−4.99579			−0.163380
$936$	7.89962			0.258207
$937$	−13.7648			−0.449677			−0.224838	−	0.974396i	$-0.572185\pi$
$937$	−13.7648			−0.449677			−0.224838	+	0.974396i	$0.572185\pi$
$938$			0.427539i			0.0139597i
$939$			3.63504i			0.118625i
$940$			3.83221i			0.124993i
$941$	−5.57246			−0.181657			−0.0908285	−	0.995867i	$-0.528952\pi$
$941$	−5.57246			−0.181657			−0.0908285	+	0.995867i	$0.528952\pi$
$942$			7.29946i			0.237829i
$943$		−	17.7220i		−	0.577106i
$944$			0.167788i			0.00546105i
$945$			1.84208i			0.0599228i
$946$	1.43175			0.0465502
$947$			1.53213i			0.0497877i	0.999690	+	0.0248938i	$0.00792477\pi$
$947$			1.53213i			0.0497877i	−0.999690	+	0.0248938i	$0.992075\pi$
$948$			5.89962i			0.191611i
$949$			56.0294i			1.81879i
$950$	−3.14637			−0.102082
$951$	13.9572			0.452592
$952$	1.43175			0.0464033
$953$	−40.5426			−1.31330			−0.656652	−	0.754194i	$-0.728028\pi$
$953$	−40.5426			−1.31330			−0.656652	+	0.754194i	$0.728028\pi$
$954$			18.8034i			0.608784i
$955$	−1.32150			−0.0427627
$956$			21.3215i			0.689587i
$957$		−	1.10208i		−	0.0356251i
$958$	−5.98171			−0.193260
$959$	−6.29273			−0.203203
$960$		−	1.14637i		−	0.0369988i
$961$	9.51071			0.306797
$962$	−14.9786	−	24.2499i	−0.482929	−	0.781848i
$963$	−30.0624			−0.968746
$964$			21.3717i			0.688336i
$965$	12.7434			0.410224
$966$	1.84208			0.0592679
$967$			23.1793i			0.745398i	0.927952	+	0.372699i	$0.121568\pi$
$967$			23.1793i			0.745398i	−0.927952	+	0.372699i	$0.878432\pi$
$968$			9.56825i			0.307535i
$969$	15.0592			0.483772
$970$		−	4.21798i		−	0.135431i
$971$	46.0319			1.47723			0.738617	−	0.674125i	$-0.235479\pi$
$971$	46.0319			1.47723			0.738617	+	0.674125i	$0.235479\pi$
$972$	14.8536			0.476431
$973$	−6.76902			−0.217005
$974$	4.53635			0.145354
$975$		−	5.37169i		−	0.172032i
$976$			2.17513i			0.0696244i
$977$		−	14.2608i		−	0.456244i	−0.973633	−	0.228122i	$-0.926741\pi$
$977$		−	14.2608i		−	0.456244i	0.973633	−	0.228122i	$-0.0732585\pi$
$978$	1.75639			0.0561630
$979$		−	5.48677i		−	0.175358i
$980$		−	6.88240i		−	0.219850i
$981$			0.367482i			0.0117328i
$982$		−	33.0361i		−	1.05422i
$983$	−34.9368			−1.11431			−0.557156	−	0.830408i	$-0.688107\pi$
$983$	−34.9368			−1.11431			−0.557156	+	0.830408i	$0.688107\pi$
$984$			4.33558i			0.138213i
$985$		−	10.3931i		−	0.331152i
$986$			3.35448i			0.106828i
$987$	1.50650			0.0479524
$988$	14.7434			0.469050
$989$	−5.60688			−0.178289
$990$	−2.01721			−0.0641112
$991$		−	11.4647i		−	0.364189i	−0.983281	−	0.182095i	$-0.941712\pi$
$991$		−	11.4647i		−	0.364189i	0.983281	−	0.182095i	$-0.0582877\pi$
$992$	−4.63565			−0.147182
$993$		−	15.9227i		−	0.505293i
$994$		−	0.235192i		−	0.00745985i
$995$	−8.47521			−0.268682
$996$	4.84377			0.153481
$997$		−	45.4783i		−	1.44031i	−0.693811	−	0.720157i	$-0.744070\pi$
$997$		−	45.4783i		−	1.44031i	0.693811	−	0.720157i	$-0.255930\pi$
$998$	23.9817			0.759128
$999$	−17.1709	−	27.7992i	−0.543264	−	0.879529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.d.c.221.5	yes	6
3.2	odd	2		3330.2.h.n.2071.1		6
4.3	odd	2		2960.2.p.g.961.3		6
5.2	odd	4		1850.2.c.i.1849.4		6
5.3	odd	4		1850.2.c.j.1849.3		6
5.4	even	2		1850.2.d.f.1701.2		6
37.36	even	2	inner	370.2.d.c.221.2	✓	6
111.110	odd	2		3330.2.h.n.2071.4		6
148.147	odd	2		2960.2.p.g.961.4		6
185.73	odd	4		1850.2.c.i.1849.3		6
185.147	odd	4		1850.2.c.j.1849.4		6
185.184	even	2		1850.2.d.f.1701.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.d.c.221.2	✓	6	37.36	even	2	inner
370.2.d.c.221.5	yes	6	1.1	even	1	trivial
1850.2.c.i.1849.3		6	185.73	odd	4
1850.2.c.i.1849.4		6	5.2	odd	4
1850.2.c.j.1849.3		6	5.3	odd	4
1850.2.c.j.1849.4		6	185.147	odd	4
1850.2.d.f.1701.2		6	5.4	even	2
1850.2.d.f.1701.5		6	185.184	even	2
2960.2.p.g.961.3		6	4.3	odd	2
2960.2.p.g.961.4		6	148.147	odd	2
3330.2.h.n.2071.1		6	3.2	odd	2
3330.2.h.n.2071.4		6	111.110	odd	2

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.14637 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.14637i q^{6} -0.342923 q^{7} -1.00000i q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.14637 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.14637i q^{6} -0.342923 q^{7} -1.00000i q^{8} -1.68585 q^{9} +1.00000 q^{10} +1.19656 q^{11} +1.14637 q^{12} -4.68585i q^{13} -0.342923i q^{14} +1.14637i q^{15} +1.00000 q^{16} -4.17513i q^{17} -1.68585i q^{18} -3.14637i q^{19} +1.00000i q^{20} +0.393115 q^{21} +1.19656i q^{22} -4.68585i q^{23} +1.14637i q^{24} -1.00000 q^{25} +4.68585 q^{26} +5.37169 q^{27} +0.342923 q^{28} +0.803442i q^{29} -1.14637 q^{30} +4.63565i q^{31} +1.00000i q^{32} -1.37169 q^{33} +4.17513 q^{34} +0.342923i q^{35} +1.68585 q^{36} +(-3.19656 - 5.17513i) q^{37} +3.14637 q^{38} +5.37169i q^{39} -1.00000 q^{40} +3.78202 q^{41} +0.393115i q^{42} -1.19656i q^{43} -1.19656 q^{44} +1.68585i q^{45} +4.68585 q^{46} +3.83221 q^{47} -1.14637 q^{48} -6.88240 q^{49} -1.00000i q^{50} +4.78623i q^{51} +4.68585i q^{52} -11.1537 q^{53} +5.37169i q^{54} -1.19656i q^{55} +0.342923i q^{56} +3.60688i q^{57} -0.803442 q^{58} +0.167788i q^{59} -1.14637i q^{60} +2.17513i q^{61} -4.63565 q^{62} +0.578116 q^{63} -1.00000 q^{64} -4.68585 q^{65} -1.37169i q^{66} -1.24675 q^{67} +4.17513i q^{68} +5.37169i q^{69} -0.342923 q^{70} +0.685846 q^{71} +1.68585i q^{72} -11.9572 q^{73} +(5.17513 - 3.19656i) q^{74} +1.14637 q^{75} +3.14637i q^{76} -0.410327 q^{77} -5.37169 q^{78} +5.14637i q^{79} -1.00000i q^{80} -1.10038 q^{81} +3.78202i q^{82} +4.22533 q^{83} -0.393115 q^{84} -4.17513 q^{85} +1.19656 q^{86} -0.921039i q^{87} -1.19656i q^{88} -4.58546i q^{89} -1.68585 q^{90} +1.60688i q^{91} +4.68585i q^{92} -5.31415i q^{93} +3.83221i q^{94} -3.14637 q^{95} -1.14637i q^{96} -4.21798i q^{97} -6.88240i q^{98} -2.01721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 - 6 * q^4 + 10 * q^7 + 14 * q^9	\( 6 q - 4 q^{3} - 6 q^{4} + 10 q^{7} + 14 q^{9} + 6 q^{10} - 2 q^{11} + 4 q^{12} + 6 q^{16} - 16 q^{21} - 6 q^{25} + 4 q^{26} - 16 q^{27} - 10 q^{28} - 4 q^{30} + 40 q^{33} - 14 q^{34} - 14 q^{36} - 10 q^{37} + 16 q^{38} - 6 q^{40} + 2 q^{41} + 2 q^{44} + 4 q^{46} - 4 q^{47} - 4 q^{48} - 8 q^{49} + 2 q^{53} - 14 q^{58} - 10 q^{62} + 58 q^{63} - 6 q^{64} - 4 q^{65} + 8 q^{67} + 10 q^{70} - 20 q^{71} - 12 q^{73} - 8 q^{74} + 4 q^{75} - 30 q^{77} + 16 q^{78} + 6 q^{81} - 20 q^{83} + 16 q^{84} + 14 q^{85} - 2 q^{86} + 14 q^{90} - 16 q^{95} - 58 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 - 6 * q^4 + 10 * q^7 + 14 * q^9 + 6 * q^10 - 2 * q^11 + 4 * q^12 + 6 * q^16 - 16 * q^21 - 6 * q^25 + 4 * q^26 - 16 * q^27 - 10 * q^28 - 4 * q^30 + 40 * q^33 - 14 * q^34 - 14 * q^36 - 10 * q^37 + 16 * q^38 - 6 * q^40 + 2 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 - 4 * q^48 - 8 * q^49 + 2 * q^53 - 14 * q^58 - 10 * q^62 + 58 * q^63 - 6 * q^64 - 4 * q^65 + 8 * q^67 + 10 * q^70 - 20 * q^71 - 12 * q^73 - 8 * q^74 + 4 * q^75 - 30 * q^77 + 16 * q^78 + 6 * q^81 - 20 * q^83 + 16 * q^84 + 14 * q^85 - 2 * q^86 + 14 * q^90 - 16 * q^95 - 58 * q^99

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