LMFDB - Embedded newform 370.2.c.b.369.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(369,370)]

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([1, 1]))

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

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

chi := DirichletCharacter("370.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.c (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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
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			369.4
Root			$-0.987983i$ of defining polynomial
Character	$\chi$	$=$	370.369
Dual form			370.2.c.b.369.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -0.987983i q^{3} +1.00000 q^{4} +(1.85396 + 1.25013i) q^{5} -0.987983i q^{6} +4.78937i q^{7} +1.00000 q^{8} +2.02389 q^{9} +(1.85396 + 1.25013i) q^{10} -5.98732 q^{11} -0.987983i q^{12} +3.49410 q^{13} +4.78937i q^{14} +(1.23510 - 1.83168i) q^{15} +1.00000 q^{16} -4.96343 q^{17} +2.02389 q^{18} -7.33092i q^{19} +(1.85396 + 1.25013i) q^{20} +4.73182 q^{21} -5.98732 q^{22} +1.74873 q^{23} -0.987983i q^{24} +(1.87436 + 4.63538i) q^{25} +3.49410 q^{26} -4.96352i q^{27} +4.78937i q^{28} -7.85004i q^{29} +(1.23510 - 1.83168i) q^{30} -3.24097i q^{31} +1.00000 q^{32} +5.91537i q^{33} -4.96343 q^{34} +(-5.98732 + 8.87932i) q^{35} +2.02389 q^{36} +(3.96343 - 4.61424i) q^{37} -7.33092i q^{38} -3.45211i q^{39} +(1.85396 + 1.25013i) q^{40} -0.530665 q^{41} +4.73182 q^{42} -1.76838 q^{43} -5.98732 q^{44} +(3.75222 + 2.53012i) q^{45} +1.74873 q^{46} +4.30638i q^{47} -0.987983i q^{48} -15.9381 q^{49} +(1.87436 + 4.63538i) q^{50} +4.90379i q^{51} +3.49410 q^{52} +3.66238i q^{53} -4.96352i q^{54} +(-11.1003 - 7.48491i) q^{55} +4.78937i q^{56} -7.24283 q^{57} -7.85004i q^{58} +2.15110i q^{59} +(1.23510 - 1.83168i) q^{60} +3.06584i q^{61} -3.24097i q^{62} +9.69316i q^{63} +1.00000 q^{64} +(6.47793 + 4.36807i) q^{65} +5.91537i q^{66} +3.79622i q^{67} -4.96343 q^{68} -1.72772i q^{69} +(-5.98732 + 8.87932i) q^{70} -8.47719 q^{71} +2.02389 q^{72} -9.05445i q^{73} +(3.96343 - 4.61424i) q^{74} +(4.57968 - 1.85184i) q^{75} -7.33092i q^{76} -28.6755i q^{77} -3.45211i q^{78} +5.56622i q^{79} +(1.85396 + 1.25013i) q^{80} +1.16780 q^{81} -0.530665 q^{82} +3.77680i q^{83} +4.73182 q^{84} +(-9.20203 - 6.20492i) q^{85} -1.76838 q^{86} -7.75571 q^{87} -5.98732 q^{88} +8.45791i q^{89} +(3.75222 + 2.53012i) q^{90} +16.7345i q^{91} +1.74873 q^{92} -3.20203 q^{93} +4.30638i q^{94} +(9.16459 - 13.5913i) q^{95} -0.987983i q^{96} -3.64747 q^{97} -15.9381 q^{98} -12.1177 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8} - 8 q^{9} + 3 q^{10} + 2 q^{13} + 10 q^{15} + 10 q^{16} - 18 q^{17} - 8 q^{18} + 3 q^{20} - 12 q^{21} - 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} + 10 q^{32}+ \cdots - 82 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8 - 8 * q^9 + 3 * q^10 + 2 * q^13 + 10 * q^15 + 10 * q^16 - 18 * q^17 - 8 * q^18 + 3 * q^20 - 12 * q^21 - 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 + 10 * q^32 - 18 * q^34 - 8 * q^36 + 8 * q^37 + 3 * q^40 - 4 * q^41 - 12 * q^42 + 10 * q^43 - 20 * q^45 - 10 * q^46 - 8 * q^49 + 5 * q^50 + 2 * q^52 - 5 * q^55 - 12 * q^57 + 10 * q^60 + 10 * q^64 + 2 * q^65 - 18 * q^68 - 20 * q^71 - 8 * q^72 + 8 * q^74 + 25 * q^75 + 3 * q^80 + 58 * q^81 - 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 + 10 * q^87 - 20 * q^90 - 10 * q^92 + 32 * q^93 + 2 * q^95 - 2 * q^97 - 8 * q^98 - 82 * q^99

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	0.987983i		−	0.570412i	−0.958466	−	0.285206i	$-0.907938\pi$
$3$		−	0.987983i		−	0.570412i	0.958466	−	0.285206i	$-0.0920621\pi$
$4$	1.00000			0.500000
$5$	1.85396	+	1.25013i	0.829118	+	0.559074i
$5$	1.85396	+	1.25013i	0.829118	+	0.559074i
$6$		−	0.987983i		−	0.403342i
$7$			4.78937i			1.81021i	0.425186	+	0.905106i	$0.360209\pi$
$7$			4.78937i			1.81021i	−0.425186	+	0.905106i	$0.639791\pi$
$8$	1.00000			0.353553
$9$	2.02389			0.674630
$10$	1.85396	+	1.25013i	0.586275	+	0.395325i
$11$	−5.98732			−1.80525			−0.902623	−	0.430432i	$-0.858361\pi$
$11$	−5.98732			−1.80525			−0.902623	+	0.430432i	$0.858361\pi$
$12$		−	0.987983i		−	0.285206i
$13$	3.49410			0.969088			0.484544	−	0.874767i	$-0.338985\pi$
$13$	3.49410			0.969088			0.484544	+	0.874767i	$0.338985\pi$
$14$			4.78937i			1.28001i
$15$	1.23510	−	1.83168i	0.318903	−	0.472939i
$16$	1.00000			0.250000
$17$	−4.96343			−1.20381			−0.601905	−	0.798568i	$-0.705591\pi$
$17$	−4.96343			−1.20381			−0.601905	+	0.798568i	$0.705591\pi$
$18$	2.02389			0.477035
$19$		−	7.33092i		−	1.68183i	−0.541168	−	0.840915i	$-0.682018\pi$
$19$		−	7.33092i		−	1.68183i	0.541168	−	0.840915i	$-0.317982\pi$
$20$	1.85396	+	1.25013i	0.414559	+	0.279537i
$21$	4.73182			1.03257
$22$	−5.98732			−1.27650
$23$	1.74873			0.364635			0.182318	−	0.983240i	$-0.441640\pi$
$23$	1.74873			0.364635			0.182318	+	0.983240i	$0.441640\pi$
$24$		−	0.987983i		−	0.201671i
$25$	1.87436	+	4.63538i	0.374873	+	0.927076i
$26$	3.49410			0.685249
$27$		−	4.96352i		−	0.955229i
$28$			4.78937i			0.905106i
$29$		−	7.85004i		−	1.45772i	−0.684665	−	0.728858i	$-0.740051\pi$
$29$		−	7.85004i		−	1.45772i	0.684665	−	0.728858i	$-0.259949\pi$
$30$	1.23510	−	1.83168i	0.225498	−	0.334418i
$31$		−	3.24097i		−	0.582096i	−0.956708	−	0.291048i	$-0.905996\pi$
$31$		−	3.24097i		−	0.582096i	0.956708	−	0.291048i	$-0.0940039\pi$
$32$	1.00000			0.176777
$33$			5.91537i			1.02973i
$34$	−4.96343			−0.851222
$35$	−5.98732	+	8.87932i	−1.01204	+	1.50088i
$36$	2.02389			0.337315
$37$	3.96343	−	4.61424i	0.651584	−	0.758576i
$37$	3.96343	−	4.61424i	0.651584	−	0.758576i
$38$		−	7.33092i		−	1.18923i
$39$		−	3.45211i		−	0.552780i
$40$	1.85396	+	1.25013i	0.293137	+	0.197662i
$41$	−0.530665			−0.0828760			−0.0414380	−	0.999141i	$-0.513194\pi$
$41$	−0.530665			−0.0828760			−0.0414380	+	0.999141i	$0.513194\pi$
$42$	4.73182			0.730135
$43$	−1.76838			−0.269676			−0.134838	−	0.990868i	$-0.543051\pi$
$43$	−1.76838			−0.269676			−0.134838	+	0.990868i	$0.543051\pi$
$44$	−5.98732			−0.902623
$45$	3.75222	+	2.53012i	0.559348	+	0.377168i
$46$	1.74873			0.257836
$47$			4.30638i			0.628150i	0.949398	+	0.314075i	$0.101694\pi$
$47$			4.30638i			0.628150i	−0.949398	+	0.314075i	$0.898306\pi$
$48$		−	0.987983i		−	0.142603i
$49$	−15.9381			−2.27687
$50$	1.87436	+	4.63538i	0.265075	+	0.655542i
$51$			4.90379i			0.686668i
$52$	3.49410			0.484544
$53$			3.66238i			0.503067i	0.967849	+	0.251534i	$0.0809349\pi$
$53$			3.66238i			0.503067i	−0.967849	+	0.251534i	$0.919065\pi$
$54$		−	4.96352i		−	0.675449i
$55$	−11.1003	−	7.48491i	−1.49676	−	1.00927i
$56$			4.78937i			0.640007i
$57$	−7.24283			−0.959336
$58$		−	7.85004i		−	1.03076i
$59$			2.15110i			0.280049i	0.990148	+	0.140025i	$0.0447182\pi$
$59$			2.15110i			0.280049i	−0.990148	+	0.140025i	$0.955282\pi$
$60$	1.23510	−	1.83168i	0.159451	−	0.236470i
$61$			3.06584i			0.392541i	0.980550	+	0.196270i	$0.0628830\pi$
$61$			3.06584i			0.392541i	−0.980550	+	0.196270i	$0.937117\pi$
$62$		−	3.24097i		−	0.411604i
$63$			9.69316i			1.22122i
$64$	1.00000			0.125000
$65$	6.47793	+	4.36807i	0.803489	+	0.541792i
$66$			5.91537i			0.728132i
$67$			3.79622i			0.463782i	0.972742	+	0.231891i	$0.0744912\pi$
$67$			3.79622i			0.463782i	−0.972742	+	0.231891i	$0.925509\pi$
$68$	−4.96343			−0.601905
$69$		−	1.72772i		−	0.207992i
$70$	−5.98732	+	8.87932i	−0.715622	+	1.06128i
$71$	−8.47719			−1.00606			−0.503028	−	0.864270i	$-0.667781\pi$
$71$	−8.47719			−1.00606			−0.503028	+	0.864270i	$0.667781\pi$
$72$	2.02389			0.238518
$73$		−	9.05445i		−	1.05974i	−0.848078	−	0.529872i	$-0.822240\pi$
$73$		−	9.05445i		−	1.05974i	0.848078	−	0.529872i	$-0.177760\pi$
$74$	3.96343	−	4.61424i	0.460740	−	0.536394i
$75$	4.57968	−	1.85184i	0.528816	−	0.213832i
$76$		−	7.33092i		−	0.840915i
$77$		−	28.6755i		−	3.26788i
$78$		−	3.45211i		−	0.390874i
$79$			5.56622i			0.626248i	0.949712	+	0.313124i	$0.101376\pi$
$79$			5.56622i			0.626248i	−0.949712	+	0.313124i	$0.898624\pi$
$80$	1.85396	+	1.25013i	0.207279	+	0.139768i
$81$	1.16780			0.129755
$82$	−0.530665			−0.0586022
$83$			3.77680i			0.414558i	0.978282	+	0.207279i	$0.0664607\pi$
$83$			3.77680i			0.414558i	−0.978282	+	0.207279i	$0.933539\pi$
$84$	4.73182			0.516284
$85$	−9.20203	−	6.20492i	−0.998100	−	0.673018i
$86$	−1.76838			−0.190690
$87$	−7.75571			−0.831499
$88$	−5.98732			−0.638251
$89$			8.45791i			0.896537i	0.893899	+	0.448268i	$0.147959\pi$
$89$			8.45791i			0.896537i	−0.893899	+	0.448268i	$0.852041\pi$
$90$	3.75222	+	2.53012i	0.395519	+	0.266698i
$91$			16.7345i			1.75426i
$92$	1.74873			0.182318
$93$	−3.20203			−0.332035
$94$			4.30638i			0.444169i
$95$	9.16459	−	13.5913i	0.940267	−	1.39443i
$96$		−	0.987983i		−	0.100836i
$97$	−3.64747			−0.370345			−0.185172	−	0.982706i	$-0.559284\pi$
$97$	−3.64747			−0.370345			−0.185172	+	0.982706i	$0.559284\pi$
$98$	−15.9381			−1.60999
$99$	−12.1177			−1.21787
$100$	1.87436	+	4.63538i	0.187436	+	0.463538i
$101$	2.30416			0.229272			0.114636	−	0.993408i	$-0.463430\pi$
$101$	2.30416			0.229272			0.114636	+	0.993408i	$0.463430\pi$
$102$			4.90379i			0.485547i
$103$	11.1716			1.10077			0.550383	−	0.834912i	$-0.314482\pi$
$103$	11.1716			1.10077			0.550383	+	0.834912i	$0.314482\pi$
$104$	3.49410			0.342625
$105$	8.77262	+	5.91537i	0.856120	+	0.577281i
$106$			3.66238i			0.355722i
$107$		−	6.51807i		−	0.630126i	−0.949071	−	0.315063i	$-0.897974\pi$
$107$		−	6.51807i		−	0.630126i	0.949071	−	0.315063i	$-0.102026\pi$
$108$		−	4.96352i		−	0.477615i
$109$			1.33812i			0.128169i	0.997944	+	0.0640846i	$0.0204127\pi$
$109$			1.33812i			0.128169i	−0.997944	+	0.0640846i	$0.979587\pi$
$110$	−11.1003	−	7.48491i	−1.05837	−	0.713659i
$111$	−4.55879	−	3.91580i	−0.432701	−	0.371672i
$112$			4.78937i			0.452553i
$113$	1.39109			0.130863			0.0654315	−	0.997857i	$-0.479158\pi$
$113$	1.39109			0.130863			0.0654315	+	0.997857i	$0.479158\pi$
$114$	−7.24283			−0.678353
$115$	3.24208	+	2.18613i	0.302326	+	0.203858i
$116$		−	7.85004i		−	0.728858i
$117$	7.07167			0.653776
$118$			2.15110i			0.198025i
$119$		−	23.7717i		−	2.17915i
$120$	1.23510	−	1.83168i	0.112749	−	0.167209i
$121$	24.8480			2.25891
$122$			3.06584i			0.277568i
$123$			0.524288i			0.0472735i
$124$		−	3.24097i		−	0.291048i
$125$	−2.31981	+	10.9370i	−0.207490	+	0.978237i
$126$			9.69316i			0.863535i
$127$			7.51024i			0.666426i	0.942852	+	0.333213i	$0.108133\pi$
$127$			7.51024i			0.666426i	−0.942852	+	0.333213i	$0.891867\pi$
$128$	1.00000			0.0883883
$129$			1.74713i			0.153827i
$130$	6.47793	+	4.36807i	0.568152	+	0.383105i
$131$		−	6.19975i		−	0.541675i	−0.962625	−	0.270837i	$-0.912699\pi$
$131$		−	6.19975i		−	0.541675i	0.962625	−	0.270837i	$-0.0873006\pi$
$132$			5.91537i			0.514867i
$133$	35.1105			3.04447
$134$			3.79622i			0.327943i
$135$	6.20503	−	9.20218i	0.534044	−	0.791998i
$136$	−4.96343			−0.425611
$137$			8.97186i			0.766518i	0.923641	+	0.383259i	$0.125198\pi$
$137$			8.97186i			0.766518i	−0.923641	+	0.383259i	$0.874802\pi$
$138$		−	1.72772i		−	0.147073i
$139$	5.04168			0.427629			0.213815	−	0.976874i	$-0.431411\pi$
$139$	5.04168			0.427629			0.213815	+	0.976874i	$0.431411\pi$
$140$	−5.98732	+	8.87932i	−0.506021	+	0.750440i
$141$	4.25463			0.358305
$142$	−8.47719			−0.711390
$143$	−20.9203			−1.74944
$144$	2.02389			0.168657
$145$	9.81355	−	14.5537i	0.814971	−	1.20862i
$146$		−	9.05445i		−	0.749352i
$147$			15.7466i			1.29875i
$148$	3.96343	−	4.61424i	0.325792	−	0.379288i
$149$	−21.6451			−1.77324			−0.886619	−	0.462500i	$-0.846952\pi$
$149$	−21.6451			−1.77324			−0.886619	+	0.462500i	$0.846952\pi$
$150$	4.57968	−	1.85184i	0.373929	−	0.151202i
$151$	6.47544			0.526964			0.263482	−	0.964664i	$-0.415129\pi$
$151$	6.47544			0.526964			0.263482	+	0.964664i	$0.415129\pi$
$152$		−	7.33092i		−	0.594616i
$153$	−10.0454			−0.812126
$154$		−	28.6755i		−	2.31074i
$155$	4.05163	−	6.00865i	0.325435	−	0.482626i
$156$		−	3.45211i		−	0.276390i
$157$			13.1689i			1.05099i	0.850797	+	0.525495i	$0.176120\pi$
$157$			13.1689i			1.05099i	−0.850797	+	0.525495i	$0.823880\pi$
$158$			5.56622i			0.442825i
$159$	3.61837			0.286956
$160$	1.85396	+	1.25013i	0.146569	+	0.0988312i
$161$			8.37532i			0.660067i
$162$	1.16780			0.0917509
$163$	−18.7651			−1.46979			−0.734896	−	0.678180i	$-0.762769\pi$
$163$	−18.7651			−1.46979			−0.734896	+	0.678180i	$0.762769\pi$
$164$	−0.530665			−0.0414380
$165$	−7.39497	+	10.9669i	−0.575697	+	0.853771i
$166$			3.77680i			0.293136i
$167$	−7.19692			−0.556914			−0.278457	−	0.960449i	$-0.589823\pi$
$167$	−7.19692			−0.556914			−0.278457	+	0.960449i	$0.589823\pi$
$168$	4.73182			0.365068
$169$	−0.791278			−0.0608676
$170$	−9.20203	−	6.20492i	−0.705763	−	0.475896i
$171$		−	14.8370i		−	1.13461i
$172$	−1.76838			−0.134838
$173$			9.79406i			0.744629i	0.928107	+	0.372314i	$0.121436\pi$
$173$			9.79406i			0.744629i	−0.928107	+	0.372314i	$0.878564\pi$
$174$	−7.75571			−0.587959
$175$	−22.2006	+	8.97703i	−1.67820	+	0.678600i
$176$	−5.98732			−0.451311
$177$	2.12525			0.159743
$178$			8.45791i			0.633947i
$179$		−	11.2829i		−	0.843320i	−0.906754	−	0.421660i	$-0.861448\pi$
$179$		−	11.2829i		−	0.843320i	0.906754	−	0.421660i	$-0.138552\pi$
$180$	3.75222	+	2.53012i	0.279674	+	0.188584i
$181$	1.82697			0.135798			0.0678989	−	0.997692i	$-0.478370\pi$
$181$	1.82697			0.135798			0.0678989	+	0.997692i	$0.478370\pi$
$182$			16.7345i			1.24045i
$183$	3.02900			0.223910
$184$	1.74873			0.128918
$185$	13.1164	−	3.59984i	0.964340	−	0.264665i
$186$	−3.20203			−0.234784
$187$	29.7177			2.17317
$188$			4.30638i			0.314075i
$189$	23.7721			1.72917
$190$	9.16459	−	13.5913i	0.664869	−	0.986014i
$191$			23.8204i			1.72358i	0.507264	+	0.861791i	$0.330657\pi$
$191$			23.8204i			1.72358i	−0.507264	+	0.861791i	$0.669343\pi$
$192$		−	0.987983i		−	0.0713015i
$193$	−8.40405			−0.604937			−0.302468	−	0.953159i	$-0.597811\pi$
$193$	−8.40405			−0.604937			−0.302468	+	0.953159i	$0.597811\pi$
$194$	−3.64747			−0.261873
$195$	4.31558	−	6.40009i	0.309045	−	0.458320i
$196$	−15.9381			−1.13843
$197$		−	4.22797i		−	0.301230i	−0.988592	−	0.150615i	$-0.951875\pi$
$197$		−	4.22797i		−	0.301230i	0.988592	−	0.150615i	$-0.0481254\pi$
$198$	−12.1177			−0.861166
$199$		−	17.7545i		−	1.25858i	−0.777170	−	0.629290i	$-0.783346\pi$
$199$		−	17.7545i		−	1.25858i	0.777170	−	0.629290i	$-0.216654\pi$
$200$	1.87436	+	4.63538i	0.132538	+	0.327771i
$201$	3.75060			0.264547
$202$	2.30416			0.162120
$203$	37.5968			2.63878
$204$			4.90379i			0.343334i
$205$	−0.983834	−	0.663399i	−0.0687139	−	0.0463338i
$206$	11.1716			0.778360
$207$	3.53924			0.245994
$208$	3.49410			0.242272
$209$			43.8926i			3.03611i
$210$	8.77262	+	5.91537i	0.605368	+	0.408200i
$211$	4.57321			0.314833			0.157417	−	0.987532i	$-0.449683\pi$
$211$	4.57321			0.314833			0.157417	+	0.987532i	$0.449683\pi$
$212$			3.66238i			0.251534i
$213$			8.37532i			0.573867i
$214$		−	6.51807i		−	0.445566i
$215$	−3.27852	−	2.21071i	−0.223593	−	0.150769i
$216$		−	4.96352i		−	0.337725i
$217$	15.5222			1.05372
$218$			1.33812i			0.0906293i
$219$	−8.94565			−0.604491
$220$	−11.1003	−	7.48491i	−0.748381	−	0.504633i
$221$	−17.3427			−1.16660
$222$	−4.55879	−	3.91580i	−0.305966	−	0.262812i
$223$			20.3205i			1.36076i	0.732860	+	0.680380i	$0.238185\pi$
$223$			20.3205i			1.36076i	−0.732860	+	0.680380i	$0.761815\pi$
$224$			4.78937i			0.320003i
$225$	3.79351	+	9.38150i	0.252900	+	0.625433i
$226$	1.39109			0.0925341
$227$	5.74303			0.381178			0.190589	−	0.981670i	$-0.438960\pi$
$227$	5.74303			0.381178			0.190589	+	0.981670i	$0.438960\pi$
$228$	−7.24283			−0.479668
$229$	23.4383			1.54885			0.774423	−	0.632669i	$-0.218040\pi$
$229$	23.4383			1.54885			0.774423	+	0.632669i	$0.218040\pi$
$230$	3.24208	+	2.18613i	0.213777	+	0.144149i
$231$	−28.3309			−1.86404
$232$		−	7.85004i		−	0.515380i
$233$		−	17.2961i		−	1.13310i	−0.824027	−	0.566551i	$-0.808277\pi$
$233$		−	17.2961i		−	1.13310i	0.824027	−	0.566551i	$-0.191723\pi$
$234$	7.07167			0.462289
$235$	−5.38352	+	7.98388i	−0.351182	+	0.520811i
$236$			2.15110i			0.140025i
$237$	5.49933			0.357220
$238$		−	23.7717i		−	1.54089i
$239$		−	3.68796i		−	0.238554i	−0.992861	−	0.119277i	$-0.961942\pi$
$239$		−	3.68796i		−	0.238554i	0.992861	−	0.119277i	$-0.0380577\pi$
$240$	1.23510	−	1.83168i	0.0797256	−	0.118235i
$241$		−	11.3613i		−	0.731844i	−0.930646	−	0.365922i	$-0.880754\pi$
$241$		−	11.3613i		−	0.731844i	0.930646	−	0.365922i	$-0.119246\pi$
$242$	24.8480			1.59729
$243$		−	16.0443i		−	1.02924i
$244$			3.06584i			0.196270i
$245$	−29.5486	−	19.9246i	−1.88779	−	1.27294i
$246$			0.524288i			0.0334274i
$247$		−	25.6150i		−	1.62984i
$248$		−	3.24097i		−	0.205802i
$249$	3.73141			0.236469
$250$	−2.31981	+	10.9370i	−0.146718	+	0.691718i
$251$		−	12.8260i		−	0.809567i	−0.914412	−	0.404784i	$-0.867347\pi$
$251$		−	12.8260i		−	0.809567i	0.914412	−	0.404784i	$-0.132653\pi$
$252$			9.69316i			0.610612i
$253$	−10.4702			−0.658256
$254$			7.51024i			0.471234i
$255$	−6.13036	+	9.09145i	−0.383898	+	0.569328i
$256$	1.00000			0.0625000
$257$	−14.0268			−0.874965			−0.437483	−	0.899227i	$-0.644130\pi$
$257$	−14.0268			−0.874965			−0.437483	+	0.899227i	$0.644130\pi$
$258$			1.74713i			0.108772i
$259$	22.0993	+	18.9824i	1.37318	+	1.17951i
$260$	6.47793	+	4.36807i	0.401744	+	0.270896i
$261$		−	15.8876i		−	0.983419i
$262$		−	6.19975i		−	0.383022i
$263$			3.57182i			0.220248i	0.993918	+	0.110124i	$0.0351248\pi$
$263$			3.57182i			0.220248i	−0.993918	+	0.110124i	$0.964875\pi$
$264$			5.91537i			0.364066i
$265$	−4.57844	+	6.78993i	−0.281252	+	0.417102i
$266$	35.1105			2.15276
$267$	8.35627			0.511396
$268$			3.79622i			0.231891i
$269$	−0.458895			−0.0279793			−0.0139897	−	0.999902i	$-0.504453\pi$
$269$	−0.458895			−0.0279793			−0.0139897	+	0.999902i	$0.504453\pi$
$270$	6.20503	−	9.20218i	0.377626	−	0.560027i
$271$	28.8897			1.75492			0.877462	−	0.479645i	$-0.159235\pi$
$271$	28.8897			1.75492			0.877462	+	0.479645i	$0.159235\pi$
$272$	−4.96343			−0.300952
$273$	16.5334			1.00065
$274$			8.97186i			0.542010i
$275$	−11.2224	−	27.7535i	−0.676738	−	1.67360i
$276$		−	1.72772i		−	0.103996i
$277$	−22.4482			−1.34878			−0.674391	−	0.738374i	$-0.735594\pi$
$277$	−22.4482			−1.34878			−0.674391	+	0.738374i	$0.735594\pi$
$278$	5.04168			0.302380
$279$		−	6.55937i		−	0.392699i
$280$	−5.98732	+	8.87932i	−0.357811	+	0.530641i
$281$		−	6.04908i		−	0.360858i	−0.983588	−	0.180429i	$-0.942251\pi$
$281$		−	6.04908i		−	0.360858i	0.983588	−	0.180429i	$-0.0577486\pi$
$282$	4.25463			0.253360
$283$	−10.8317			−0.643878			−0.321939	−	0.946760i	$-0.604335\pi$
$283$	−10.8317			−0.643878			−0.321939	+	0.946760i	$0.604335\pi$
$284$	−8.47719			−0.503028
$285$	−13.4279	−	9.05445i	−0.795403	−	0.536340i
$286$	−20.9203			−1.23704
$287$		−	2.54155i		−	0.150023i
$288$	2.02389			0.119259
$289$	7.63567			0.449157
$290$	9.81355	−	14.5537i	0.576271	−	0.854622i
$291$			3.60364i			0.211249i
$292$		−	9.05445i		−	0.529872i
$293$			23.3144i			1.36204i	0.732264	+	0.681021i	$0.238464\pi$
$293$			23.3144i			1.36204i	−0.732264	+	0.681021i	$0.761536\pi$
$294$			15.7466i			0.918357i
$295$	−2.68915	+	3.98806i	−0.156568	+	0.232194i
$296$	3.96343	−	4.61424i	0.230370	−	0.268197i
$297$			29.7182i			1.72442i
$298$	−21.6451			−1.25387
$299$	6.11023			0.353364
$300$	4.57968	−	1.85184i	0.264408	−	0.106916i
$301$		−	8.46945i		−	0.488171i
$302$	6.47544			0.372620
$303$		−	2.27647i		−	0.130780i
$304$		−	7.33092i		−	0.420457i
$305$	−3.83269	+	5.68396i	−0.219459	+	0.325462i
$306$	−10.0454			−0.574260
$307$			14.2651i			0.814153i	0.913394	+	0.407077i	$0.133452\pi$
$307$			14.2651i			0.814153i	−0.913394	+	0.407077i	$0.866548\pi$
$308$		−	28.6755i		−	1.63394i
$309$		−	11.0373i		−	0.627891i
$310$	4.05163	−	6.00865i	0.230117	−	0.341268i
$311$		−	22.5322i		−	1.27768i	−0.769339	−	0.638841i	$-0.779414\pi$
$311$		−	22.5322i		−	1.27768i	0.769339	−	0.638841i	$-0.220586\pi$
$312$		−	3.45211i		−	0.195437i
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$			13.1689i			0.743162i
$315$	−12.1177	+	17.9708i	−0.682754	+	1.01254i
$316$			5.56622i			0.313124i
$317$		−	12.3877i		−	0.695764i	−0.937538	−	0.347882i	$-0.886901\pi$
$317$		−	12.3877i		−	0.695764i	0.937538	−	0.347882i	$-0.113099\pi$
$318$	3.61837			0.202908
$319$			47.0007i			2.63154i
$320$	1.85396	+	1.25013i	0.103640	+	0.0698842i
$321$	−6.43975			−0.359432
$322$			8.37532i			0.466738i
$323$			36.3865i			2.02460i
$324$	1.16780			0.0648777
$325$	6.54921	+	16.1965i	0.363285	+	0.898419i
$326$	−18.7651			−1.03930
$327$	1.32204			0.0731092
$328$	−0.530665			−0.0293011
$329$	−20.6249			−1.13709
$330$	−7.39497	+	10.9669i	−0.407080	+	0.603707i
$331$			19.0068i			1.04471i	0.852728	+	0.522355i	$0.174946\pi$
$331$			19.0068i			1.04471i	−0.852728	+	0.522355i	$0.825054\pi$
$332$			3.77680i			0.207279i
$333$	8.02155	−	9.33871i	0.439578	−	0.511758i
$334$	−7.19692			−0.393798
$335$	−4.74575	+	7.03805i	−0.259288	+	0.384530i
$336$	4.73182			0.258142
$337$		−	25.1046i		−	1.36753i	−0.729701	−	0.683766i	$-0.760341\pi$
$337$		−	25.1046i		−	1.36753i	0.729701	−	0.683766i	$-0.239659\pi$
$338$	−0.791278			−0.0430399
$339$		−	1.37438i		−	0.0746459i
$340$	−9.20203	−	6.20492i	−0.499050	−	0.336509i
$341$			19.4047i			1.05083i
$342$		−	14.8370i		−	0.802292i
$343$		−	42.8078i		−	2.31140i
$344$	−1.76838			−0.0953449
$345$	2.15986	−	3.20312i	0.116283	−	0.172450i
$346$			9.79406i			0.526532i
$347$	−30.4282			−1.63347			−0.816736	−	0.577011i	$-0.804219\pi$
$347$	−30.4282			−1.63347			−0.816736	+	0.577011i	$0.804219\pi$
$348$	−7.75571			−0.415750
$349$	15.1341			0.810111			0.405056	−	0.914292i	$-0.367252\pi$
$349$	15.1341			0.810111			0.405056	+	0.914292i	$0.367252\pi$
$350$	−22.2006	+	8.97703i	−1.18667	+	0.479842i
$351$		−	17.3430i		−	0.925702i
$352$	−5.98732			−0.319125
$353$	10.1331			0.539332			0.269666	−	0.962954i	$-0.413087\pi$
$353$	10.1331			0.539332			0.269666	+	0.962954i	$0.413087\pi$
$354$	2.12525			0.112956
$355$	−15.7164	−	10.5976i	−0.834140	−	0.562460i
$356$			8.45791i			0.448268i
$357$	−23.4861			−1.24301
$358$		−	11.2829i		−	0.596317i
$359$	−26.3685			−1.39168			−0.695838	−	0.718199i	$-0.744967\pi$
$359$	−26.3685			−1.39168			−0.695838	+	0.718199i	$0.744967\pi$
$360$	3.75222	+	2.53012i	0.197759	+	0.133349i
$361$	−34.7424			−1.82855
$362$	1.82697			0.0960235
$363$		−	24.5494i		−	1.28851i
$364$			16.7345i			0.877128i
$365$	11.3192	−	16.7866i	0.592475	−	0.878653i
$366$	3.02900			0.158328
$367$			2.21157i			0.115443i	0.998333	+	0.0577215i	$0.0183835\pi$
$367$			2.21157i			0.115443i	−0.998333	+	0.0577215i	$0.981616\pi$
$368$	1.74873			0.0911588
$369$	−1.07401			−0.0559106
$370$	13.1164	−	3.59984i	0.681892	−	0.187147i
$371$	−17.5405			−0.910658
$372$	−3.20203			−0.166017
$373$			6.08275i			0.314953i	0.987523	+	0.157476i	$0.0503358\pi$
$373$			6.08275i			0.314953i	−0.987523	+	0.157476i	$0.949664\pi$
$374$	29.7177			1.53666
$375$	10.8056	+	2.29193i	0.557998	+	0.118355i
$376$			4.30638i			0.222085i
$377$		−	27.4288i		−	1.41266i
$378$	23.7721			1.22271
$379$	−20.0919			−1.03205			−0.516025	−	0.856574i	$-0.672589\pi$
$379$	−20.0919			−1.03205			−0.516025	+	0.856574i	$0.672589\pi$
$380$	9.16459	−	13.5913i	0.470133	−	0.697217i
$381$	7.41999			0.380138
$382$			23.8204i			1.21876i
$383$	−11.5368			−0.589501			−0.294751	−	0.955574i	$-0.595237\pi$
$383$	−11.5368			−0.589501			−0.294751	+	0.955574i	$0.595237\pi$
$384$		−	0.987983i		−	0.0504178i
$385$	35.8480	−	53.1634i	1.82698	−	2.70946i
$386$	−8.40405			−0.427755
$387$	−3.57901			−0.181932
$388$	−3.64747			−0.185172
$389$		−	8.55057i		−	0.433531i	−0.976224	−	0.216766i	$-0.930449\pi$
$389$		−	8.55057i		−	0.433531i	0.976224	−	0.216766i	$-0.0695507\pi$
$390$	4.31558	−	6.40009i	0.218528	−	0.324081i
$391$	−8.67970			−0.438951
$392$	−15.9381			−0.804995
$393$	−6.12525			−0.308978
$394$		−	4.22797i		−	0.213002i
$395$	−6.95848	+	10.3196i	−0.350119	+	0.519234i
$396$	−12.1177			−0.608936
$397$			9.84444i			0.494078i	0.969006	+	0.247039i	$0.0794576\pi$
$397$			9.84444i			0.494078i	−0.969006	+	0.247039i	$0.920542\pi$
$398$		−	17.7545i		−	0.889951i
$399$		−	34.6886i		−	1.73660i
$400$	1.87436	+	4.63538i	0.0937182	+	0.231769i
$401$			31.0959i			1.55285i	0.630207	+	0.776427i	$0.282970\pi$
$401$			31.0959i			1.55285i	−0.630207	+	0.776427i	$0.717030\pi$
$402$	3.75060			0.187063
$403$		−	11.3243i		−	0.564102i
$404$	2.30416			0.114636
$405$	2.16506	+	1.45990i	0.107582	+	0.0725428i
$406$	37.5968			1.86590
$407$	−23.7304	+	27.6269i	−1.17627	+	1.36942i
$408$			4.90379i			0.242774i
$409$		−	38.3150i		−	1.89455i	−0.320417	−	0.947277i	$-0.603823\pi$
$409$		−	38.3150i		−	1.89455i	0.320417	−	0.947277i	$-0.396177\pi$
$410$	−0.983834	−	0.663399i	−0.0485881	−	0.0327629i
$411$	8.86404			0.437231
$412$	11.1716			0.550383
$413$	−10.3024			−0.506948
$414$	3.53924			0.173944
$415$	−4.72148	+	7.00205i	−0.231768	+	0.343717i
$416$	3.49410			0.171312
$417$		−	4.98109i		−	0.243925i
$418$			43.8926i			2.14686i
$419$	29.0183			1.41764			0.708819	−	0.705391i	$-0.249228\pi$
$419$	29.0183			1.41764			0.708819	+	0.705391i	$0.249228\pi$
$420$	8.77262	+	5.91537i	0.428060	+	0.288641i
$421$			23.6443i			1.15235i	0.817326	+	0.576175i	$0.195455\pi$
$421$			23.6443i			1.15235i	−0.817326	+	0.576175i	$0.804545\pi$
$422$	4.57321			0.222621
$423$			8.71564i			0.423769i
$424$			3.66238i			0.177861i
$425$	−9.30328	−	23.0074i	−0.451276	−	1.11602i
$426$			8.37532i			0.405785i
$427$	−14.6834			−0.710582
$428$		−	6.51807i		−	0.315063i
$429$			20.6689i			0.997904i
$430$	−3.27852	−	2.21071i	−0.158104	−	0.106610i
$431$		−	32.1126i		−	1.54681i	−0.633912	−	0.773406i	$-0.718552\pi$
$431$		−	32.1126i		−	1.54681i	0.633912	−	0.773406i	$-0.281448\pi$
$432$		−	4.96352i		−	0.238807i
$433$			13.0575i			0.627504i	0.949505	+	0.313752i	$0.101586\pi$
$433$			13.0575i			0.627504i	−0.949505	+	0.313752i	$0.898414\pi$
$434$	15.5222			0.745091
$435$	−14.3788	−	9.69562i	−0.689411	−	0.464869i
$436$			1.33812i			0.0640846i
$437$		−	12.8198i		−	0.613254i
$438$	−8.94565			−0.427440
$439$			28.0499i			1.33875i	0.742924	+	0.669375i	$0.233438\pi$
$439$			28.0499i			1.33875i	−0.742924	+	0.669375i	$0.766562\pi$
$440$	−11.1003	−	7.48491i	−0.529185	−	0.356829i
$441$	−32.2569			−1.53604
$442$	−17.3427			−0.824909
$443$		−	6.79629i		−	0.322902i	−0.986881	−	0.161451i	$-0.948383\pi$
$443$		−	6.79629i		−	0.322902i	0.986881	−	0.161451i	$-0.0516173\pi$
$444$	−4.55879	−	3.91580i	−0.216351	−	0.185836i
$445$	−10.5735	+	15.6807i	−0.501230	+	0.743335i
$446$			20.3205i			0.962203i
$447$			21.3850i			1.01148i
$448$			4.78937i			0.226277i
$449$			17.3278i			0.817747i	0.912591	+	0.408874i	$0.134078\pi$
$449$			17.3278i			0.817747i	−0.912591	+	0.408874i	$0.865922\pi$
$450$	3.79351	+	9.38150i	0.178828	+	0.442248i
$451$	3.17726			0.149611
$452$	1.39109			0.0654315
$453$		−	6.39762i		−	0.300587i
$454$	5.74303			0.269534
$455$	−20.9203	+	31.0252i	−0.980758	+	1.45448i
$456$	−7.24283			−0.339176
$457$	−3.20960			−0.150139			−0.0750693	−	0.997178i	$-0.523918\pi$
$457$	−3.20960			−0.150139			−0.0750693	+	0.997178i	$0.523918\pi$
$458$	23.4383			1.09520
$459$			24.6361i			1.14991i
$460$	3.24208	+	2.18613i	0.151163	+	0.101929i
$461$		−	34.0347i		−	1.58515i	−0.609773	−	0.792576i	$-0.708739\pi$
$461$		−	34.0347i		−	1.58515i	0.609773	−	0.792576i	$-0.291261\pi$
$462$	−28.3309			−1.31807
$463$	−26.0543			−1.21085			−0.605423	−	0.795904i	$-0.706996\pi$
$463$	−26.0543			−1.21085			−0.605423	+	0.795904i	$0.706996\pi$
$464$		−	7.85004i		−	0.364429i
$465$	−5.93644	−	4.00294i	−0.275296	−	0.185632i
$466$		−	17.2961i		−	0.801224i
$467$	20.3289			0.940710			0.470355	−	0.882477i	$-0.344126\pi$
$467$	20.3289			0.940710			0.470355	+	0.882477i	$0.344126\pi$
$468$	7.07167			0.326888
$469$	−18.1815			−0.839544
$470$	−5.38352	+	7.98388i	−0.248323	+	0.368269i
$471$	13.0106			0.599498
$472$			2.15110i			0.0990123i
$473$	10.5879			0.486832
$474$	5.49933			0.252593
$475$	33.9816	−	13.7408i	1.55918	−	0.630472i
$476$		−	23.7717i		−	1.08958i
$477$			7.41226i			0.339384i
$478$		−	3.68796i		−	0.168683i
$479$			6.22972i			0.284643i	0.989820	+	0.142322i	$0.0454567\pi$
$479$			6.22972i			0.284643i	−0.989820	+	0.142322i	$0.954543\pi$
$480$	1.23510	−	1.83168i	0.0563745	−	0.0836046i
$481$	13.8486	−	16.1226i	0.631443	−	0.735127i
$482$		−	11.3613i		−	0.517492i
$483$	8.27467			0.376511
$484$	24.8480			1.12946
$485$	−6.76228	−	4.55980i	−0.307059	−	0.207050i
$486$		−	16.0443i		−	0.727785i
$487$	30.5352			1.38368			0.691841	−	0.722050i	$-0.256800\pi$
$487$	30.5352			1.38368			0.691841	+	0.722050i	$0.256800\pi$
$488$			3.06584i			0.138784i
$489$			18.5396i			0.838387i
$490$	−29.5486	−	19.9246i	−1.33487	−	0.900103i
$491$	24.5944			1.10993			0.554965	−	0.831874i	$-0.312732\pi$
$491$	24.5944			1.10993			0.554965	+	0.831874i	$0.312732\pi$
$492$			0.524288i			0.0236367i
$493$			38.9632i			1.75481i
$494$		−	25.6150i		−	1.15247i
$495$	−22.4657	−	15.1486i	−1.00976	−	0.680881i
$496$		−	3.24097i		−	0.145524i
$497$		−	40.6004i		−	1.82118i
$498$	3.73141			0.167209
$499$			33.5739i			1.50297i	0.659747	+	0.751487i	$0.270663\pi$
$499$			33.5739i			1.50297i	−0.659747	+	0.751487i	$0.729337\pi$
$500$	−2.31981	+	10.9370i	−0.103745	+	0.489119i
$501$			7.11043i			0.317671i
$502$		−	12.8260i		−	0.572451i
$503$	1.77931			0.0793357			0.0396679	−	0.999213i	$-0.487370\pi$
$503$	1.77931			0.0793357			0.0396679	+	0.999213i	$0.487370\pi$
$504$			9.69316i			0.431768i
$505$	4.27183	+	2.88049i	0.190094	+	0.128180i
$506$	−10.4702			−0.465458
$507$			0.781770i			0.0347196i
$508$			7.51024i			0.333213i
$509$	29.5114			1.30807			0.654035	−	0.756464i	$-0.273075\pi$
$509$	29.5114			1.30807			0.654035	+	0.756464i	$0.273075\pi$
$510$	−6.13036	+	9.09145i	−0.271457	+	0.402576i
$511$	43.3651			1.91836
$512$	1.00000			0.0441942
$513$	−36.3872			−1.60653
$514$	−14.0268			−0.618694
$515$	20.7117	+	13.9659i	0.912665	+	0.615410i
$516$			1.74713i			0.0769133i
$517$		−	25.7837i		−	1.13397i
$518$	22.0993	+	18.9824i	0.970988	+	0.834037i
$519$	9.67637			0.424745
$520$	6.47793	+	4.36807i	0.284076	+	0.191552i
$521$	29.2841			1.28296			0.641481	−	0.767139i	$-0.278320\pi$
$521$	29.2841			1.28296			0.641481	+	0.767139i	$0.278320\pi$
$522$		−	15.8876i		−	0.695382i
$523$	29.9729			1.31062			0.655312	−	0.755359i	$-0.272537\pi$
$523$	29.9729			1.31062			0.655312	+	0.755359i	$0.272537\pi$
$524$		−	6.19975i		−	0.270837i
$525$	8.86915	+	21.9338i	0.387082	+	0.957269i
$526$			3.57182i			0.155739i
$527$			16.0864i			0.700732i
$528$			5.91537i			0.257434i
$529$	−19.9419			−0.867041
$530$	−4.57844	+	6.78993i	−0.198875	+	0.294936i
$531$			4.35359i			0.188930i
$532$	35.1105			1.52223
$533$	−1.85420			−0.0803141
$534$	8.35627			0.361611
$535$	8.14842	−	12.0843i	0.352287	−	0.522449i
$536$			3.79622i			0.163972i
$537$	−11.1473			−0.481040
$538$	−0.458895			−0.0197844
$539$	95.4264			4.11031
$540$	6.20503	−	9.20218i	0.267022	−	0.395999i
$541$			18.7155i			0.804644i	0.915498	+	0.402322i	$0.131797\pi$
$541$			18.7155i			0.804644i	−0.915498	+	0.402322i	$0.868203\pi$
$542$	28.8897			1.24092
$543$		−	1.80502i		−	0.0774607i
$544$	−4.96343			−0.212805
$545$	−1.67283	+	2.48084i	−0.0716560	+	0.106267i
$546$	16.5334			0.707566
$547$	32.4792			1.38871			0.694355	−	0.719633i	$-0.255690\pi$
$547$	32.4792			1.38871			0.694355	+	0.719633i	$0.255690\pi$
$548$			8.97186i			0.383259i
$549$			6.20492i			0.264820i
$550$	−11.2224	−	27.7535i	−0.478526	−	1.18341i
$551$	−57.5480			−2.45163
$552$		−	1.72772i		−	0.0735364i
$553$	−26.6587			−1.13364
$554$	−22.4482			−0.953733
$555$	−3.55658	−	12.9588i	−0.150968	−	0.550072i
$556$	5.04168			0.213815
$557$	16.0158			0.678612			0.339306	−	0.940676i	$-0.389808\pi$
$557$	16.0158			0.678612			0.339306	+	0.940676i	$0.389808\pi$
$558$		−	6.55937i		−	0.277680i
$559$	−6.17891			−0.261340
$560$	−5.98732	+	8.87932i	−0.253011	+	0.375220i
$561$		−	29.3606i		−	1.23960i
$562$		−	6.04908i		−	0.255165i
$563$	15.3069			0.645109			0.322554	−	0.946551i	$-0.395458\pi$
$563$	15.3069			0.645109			0.322554	+	0.946551i	$0.395458\pi$
$564$	4.25463			0.179152
$565$	2.57904	+	1.73904i	0.108501	+	0.0731621i
$566$	−10.8317			−0.455291
$567$			5.59302i			0.234885i
$568$	−8.47719			−0.355695
$569$		−	26.6494i		−	1.11720i	−0.829437	−	0.558601i	$-0.811338\pi$
$569$		−	26.6494i		−	1.11720i	0.829437	−	0.558601i	$-0.188662\pi$
$570$	−13.4279	−	9.05445i	−0.562435	−	0.379249i
$571$	23.1683			0.969564			0.484782	−	0.874635i	$-0.338899\pi$
$571$	23.1683			0.969564			0.484782	+	0.874635i	$0.338899\pi$
$572$	−20.9203			−0.874721
$573$	23.5341			0.983152
$574$		−	2.54155i		−	0.106082i
$575$	3.27776	+	8.10603i	0.136692	+	0.338045i
$576$	2.02389			0.0843287
$577$	3.54110			0.147418			0.0737091	−	0.997280i	$-0.476516\pi$
$577$	3.54110			0.147418			0.0737091	+	0.997280i	$0.476516\pi$
$578$	7.63567			0.317602
$579$			8.30306i			0.345063i
$580$	9.81355	−	14.5537i	0.407485	−	0.604309i
$581$	−18.0885			−0.750437
$582$			3.60364i			0.149376i
$583$		−	21.9279i		−	0.908160i
$584$		−	9.05445i		−	0.374676i
$585$	13.1106	+	8.84048i	0.542057	+	0.365509i
$586$			23.3144i			0.963109i
$587$	−12.0976			−0.499320			−0.249660	−	0.968334i	$-0.580319\pi$
$587$	−12.0976			−0.499320			−0.249660	+	0.968334i	$0.580319\pi$
$588$			15.7466i			0.649377i
$589$	−23.7593			−0.978986
$590$	−2.68915	+	3.98806i	−0.110710	+	0.164186i
$591$	−4.17716			−0.171825
$592$	3.96343	−	4.61424i	0.162896	−	0.189644i
$593$			17.2007i			0.706348i	0.935558	+	0.353174i	$0.114898\pi$
$593$			17.2007i			0.706348i	−0.935558	+	0.353174i	$0.885102\pi$
$594$			29.7182i			1.21935i
$595$	29.7177	−	44.0719i	1.21831	−	1.80677i
$596$	−21.6451			−0.886619
$597$	−17.5411			−0.717910
$598$	6.11023			0.249866
$599$	2.41919			0.0988454			0.0494227	−	0.998778i	$-0.484262\pi$
$599$	2.41919			0.0988454			0.0494227	+	0.998778i	$0.484262\pi$
$600$	4.57968	−	1.85184i	0.186965	−	0.0756011i
$601$	−39.0483			−1.59281			−0.796407	−	0.604761i	$-0.793269\pi$
$601$	−39.0483			−1.59281			−0.796407	+	0.604761i	$0.793269\pi$
$602$		−	8.46945i		−	0.345189i
$603$			7.68313i			0.312881i
$604$	6.47544			0.263482
$605$	46.0674	+	31.0632i	1.87290	+	1.26290i
$606$		−	2.27647i		−	0.0924752i
$607$	38.0508			1.54443			0.772217	−	0.635359i	$-0.219148\pi$
$607$	38.0508			1.54443			0.772217	+	0.635359i	$0.219148\pi$
$608$		−	7.33092i		−	0.297308i
$609$		−	37.1450i		−	1.50519i
$610$	−3.83269	+	5.68396i	−0.155181	+	0.230137i
$611$			15.0469i			0.608733i
$612$	−10.0454			−0.406063
$613$			7.12176i			0.287645i	0.989603	+	0.143823i	$0.0459395\pi$
$613$			7.12176i			0.287645i	−0.989603	+	0.143823i	$0.954061\pi$
$614$			14.2651i			0.575693i
$615$	−0.655427	+	0.972011i	−0.0264294	+	0.0391953i
$616$		−	28.6755i		−	1.15537i
$617$			42.6678i			1.71774i	0.512192	+	0.858871i	$0.328834\pi$
$617$			42.6678i			1.71774i	−0.512192	+	0.858871i	$0.671166\pi$
$618$		−	11.0373i		−	0.443986i
$619$	−6.30429			−0.253391			−0.126695	−	0.991942i	$-0.540437\pi$
$619$	−6.30429			−0.253391			−0.126695	+	0.991942i	$0.540437\pi$
$620$	4.05163	−	6.00865i	0.162717	−	0.241313i
$621$		−	8.67985i		−	0.348310i
$622$		−	22.5322i		−	0.903458i
$623$	−40.5081			−1.62292
$624$		−	3.45211i		−	0.138195i
$625$	−17.9735	+	17.3768i	−0.718941	+	0.695072i
$626$	10.0000			0.399680
$627$	43.3651			1.73184
$628$			13.1689i			0.525495i
$629$	−19.6722	+	22.9025i	−0.784383	+	0.913181i
$630$	−12.1177	+	17.9708i	−0.482780	+	0.715973i
$631$			32.6385i			1.29932i	0.760225	+	0.649660i	$0.225089\pi$
$631$			32.6385i			1.29932i	−0.760225	+	0.649660i	$0.774911\pi$
$632$			5.56622i			0.221412i
$633$		−	4.51826i		−	0.179585i
$634$		−	12.3877i		−	0.491979i
$635$	−9.38875	+	13.9237i	−0.372581	+	0.552546i
$636$	3.61837			0.143478
$637$	−55.6892			−2.20649
$638$			47.0007i			1.86078i
$639$	−17.1569			−0.678716
$640$	1.85396	+	1.25013i	0.0732844	+	0.0494156i
$641$	−12.1721			−0.480767			−0.240384	−	0.970678i	$-0.577273\pi$
$641$	−12.1721			−0.480767			−0.240384	+	0.970678i	$0.577273\pi$
$642$	−6.43975			−0.254156
$643$	−10.0853			−0.397727			−0.198864	−	0.980027i	$-0.563725\pi$
$643$	−10.0853			−0.397727			−0.198864	+	0.980027i	$0.563725\pi$
$644$			8.37532i			0.330034i
$645$	−2.18414	+	3.23912i	−0.0860004	+	0.127540i
$646$			36.3865i			1.43161i
$647$	38.5061			1.51383			0.756916	−	0.653512i	$-0.226705\pi$
$647$	38.5061			1.51383			0.756916	+	0.653512i	$0.226705\pi$
$648$	1.16780			0.0458754
$649$		−	12.8793i		−	0.505558i
$650$	6.54921	+	16.1965i	0.256881	+	0.635278i
$651$		−	15.3357i		−	0.601053i
$652$	−18.7651			−0.734896
$653$	2.20349			0.0862293			0.0431146	−	0.999070i	$-0.486272\pi$
$653$	2.20349			0.0862293			0.0431146	+	0.999070i	$0.486272\pi$
$654$	1.32204			0.0516960
$655$	7.75048	−	11.4941i	0.302836	−	0.449112i
$656$	−0.530665			−0.0207190
$657$		−	18.3252i		−	0.714935i
$658$	−20.6249			−0.804041
$659$	−20.4048			−0.794859			−0.397430	−	0.917633i	$-0.630098\pi$
$659$	−20.4048			−0.794859			−0.397430	+	0.917633i	$0.630098\pi$
$660$	−7.39497	+	10.9669i	−0.287849	+	0.426886i
$661$			27.0306i			1.05137i	0.850680	+	0.525684i	$0.176191\pi$
$661$			27.0306i			1.05137i	−0.850680	+	0.525684i	$0.823809\pi$
$662$			19.0068i			0.738721i
$663$			17.1343i			0.665442i
$664$			3.77680i			0.146568i
$665$	65.0936	+	43.8926i	2.52422	+	1.70208i
$666$	8.02155	−	9.33871i	0.310829	−	0.361868i
$667$		−	13.7276i		−	0.531535i
$668$	−7.19692			−0.278457
$669$	20.0763			0.776194
$670$	−4.74575	+	7.03805i	−0.183344	+	0.271904i
$671$		−	18.3562i		−	0.708632i
$672$	4.73182			0.182534
$673$			11.6776i			0.450139i	0.974343	+	0.225070i	$0.0722609\pi$
$673$			11.6776i			0.450139i	−0.974343	+	0.225070i	$0.927739\pi$
$674$		−	25.1046i		−	0.966991i
$675$	23.0078	−	9.30344i	0.885570	−	0.358090i
$676$	−0.791278			−0.0304338
$677$			37.2578i			1.43193i	0.698135	+	0.715966i	$0.254014\pi$
$677$			37.2578i			1.43193i	−0.698135	+	0.715966i	$0.745986\pi$
$678$		−	1.37438i		−	0.0527826i
$679$		−	17.4691i		−	0.670402i
$680$	−9.20203	−	6.20492i	−0.352882	−	0.237948i
$681$		−	5.67402i		−	0.217429i
$682$			19.4047i			0.743046i
$683$	46.3018			1.77169			0.885845	−	0.463981i	$-0.153580\pi$
$683$	46.3018			1.77169			0.885845	+	0.463981i	$0.153580\pi$
$684$		−	14.8370i		−	0.567306i
$685$	−11.2160	+	16.6335i	−0.428540	+	0.635533i
$686$		−	42.8078i		−	1.63441i
$687$		−	23.1566i		−	0.883480i
$688$	−1.76838			−0.0674190
$689$			12.7967i			0.487516i
$690$	2.15986	−	3.20312i	0.0822246	−	0.121941i
$691$	29.7037			1.12998			0.564991	−	0.825097i	$-0.308879\pi$
$691$	29.7037			1.12998			0.564991	+	0.825097i	$0.308879\pi$
$692$			9.79406i			0.372314i
$693$		−	58.0361i		−	2.20461i
$694$	−30.4282			−1.15504
$695$	9.34708	+	6.30273i	0.354555	+	0.239076i
$696$	−7.75571			−0.293979
$697$	2.63392			0.0997669
$698$	15.1341			0.572835
$699$	−17.0882			−0.646336
$700$	−22.2006	+	8.97703i	−0.839102	+	0.339300i
$701$		−	45.9214i		−	1.73443i	−0.497936	−	0.867214i	$-0.665909\pi$
$701$		−	45.9214i		−	1.73443i	0.497936	−	0.867214i	$-0.334091\pi$
$702$		−	17.3430i		−	0.654570i
$703$	−33.8266	−	29.0556i	−1.27580	−	1.09585i
$704$	−5.98732			−0.225656
$705$	7.88793	+	5.31883i	0.297077	+	0.200319i
$706$	10.1331			0.381365
$707$			11.0355i			0.415031i
$708$	2.12525			0.0798717
$709$		−	52.6575i		−	1.97759i	−0.149266	−	0.988797i	$-0.547691\pi$
$709$		−	52.6575i		−	1.97759i	0.149266	−	0.988797i	$-0.452309\pi$
$710$	−15.7164	−	10.5976i	−0.589826	−	0.397719i
$711$			11.2654i			0.422486i
$712$			8.45791i			0.316974i
$713$		−	5.66759i		−	0.212253i
$714$	−23.4861			−0.878944
$715$	−38.7855	−	26.1530i	−1.45049	−	0.978068i
$716$		−	11.2829i		−	0.421660i
$717$	−3.64364			−0.136074
$718$	−26.3685			−0.984063
$719$	−13.3494			−0.497850			−0.248925	−	0.968523i	$-0.580077\pi$
$719$	−13.3494			−0.497850			−0.248925	+	0.968523i	$0.580077\pi$
$720$	3.75222	+	2.53012i	0.139837	+	0.0942920i
$721$			53.5048i			1.99262i
$722$	−34.7424			−1.29298
$723$	−11.2247			−0.417453
$724$	1.82697			0.0678989
$725$	36.3879	−	14.7138i	1.35141	−	0.546458i
$726$		−	24.5494i		−	0.911115i
$727$	−13.1733			−0.488571			−0.244286	−	0.969703i	$-0.578553\pi$
$727$	−13.1733			−0.488571			−0.244286	+	0.969703i	$0.578553\pi$
$728$			16.7345i			0.620223i
$729$	−12.3481			−0.457338
$730$	11.3192	−	16.7866i	0.418943	−	0.621301i
$731$	8.77726			0.324639
$732$	3.02900			0.111955
$733$		−	32.3264i		−	1.19400i	−0.802241	−	0.597001i	$-0.796359\pi$
$733$		−	32.3264i		−	1.19400i	0.802241	−	0.597001i	$-0.203641\pi$
$734$			2.21157i			0.0816305i
$735$	−19.6852	+	29.1935i	−0.726099	+	1.07682i
$736$	1.74873			0.0644590
$737$		−	22.7292i		−	0.837240i
$738$	−1.07401			−0.0395348
$739$	6.94169			0.255354			0.127677	−	0.991816i	$-0.459248\pi$
$739$	6.94169			0.255354			0.127677	+	0.991816i	$0.459248\pi$
$740$	13.1164	−	3.59984i	0.482170	−	0.132333i
$741$	−25.3072			−0.929681
$742$	−17.5405			−0.643933
$743$		−	36.0784i		−	1.32359i	−0.749685	−	0.661795i	$-0.769795\pi$
$743$		−	36.0784i		−	1.32359i	0.749685	−	0.661795i	$-0.230205\pi$
$744$	−3.20203			−0.117392
$745$	−40.1293	−	27.0592i	−1.47022	−	0.991371i
$746$			6.08275i			0.222705i
$747$			7.64382i			0.279673i
$748$	29.7177			1.08659
$749$	31.2175			1.14066
$750$	10.8056	+	2.29193i	0.394564	+	0.0836896i
$751$	−29.9052			−1.09126			−0.545629	−	0.838027i	$-0.683709\pi$
$751$	−29.9052			−1.09126			−0.545629	+	0.838027i	$0.683709\pi$
$752$			4.30638i			0.157038i
$753$	−12.6718			−0.461787
$754$		−	27.4288i		−	0.998898i
$755$	12.0052	+	8.09512i	0.436915	+	0.294612i
$756$	23.7721			0.864584
$757$	−24.9464			−0.906693			−0.453347	−	0.891334i	$-0.649770\pi$
$757$	−24.9464			−0.906693			−0.453347	+	0.891334i	$0.649770\pi$
$758$	−20.0919			−0.729769
$759$			10.3444i			0.375477i
$760$	9.16459	−	13.5913i	0.332434	−	0.493007i
$761$	11.7647			0.426469			0.213235	−	0.977001i	$-0.431600\pi$
$761$	11.7647			0.426469			0.213235	+	0.977001i	$0.431600\pi$
$762$	7.41999			0.268798
$763$	−6.40878			−0.232013
$764$			23.8204i			0.861791i
$765$	−18.6239	−	12.5581i	−0.673348	−	0.454038i
$766$	−11.5368			−0.416840
$767$			7.51615i			0.271392i
$768$		−	0.987983i		−	0.0356508i
$769$			26.7939i			0.966214i	0.875561	+	0.483107i	$0.160492\pi$
$769$			26.7939i			0.966214i	−0.875561	+	0.483107i	$0.839508\pi$
$770$	35.8480	−	53.1634i	1.29187	−	1.91587i
$771$			13.8582i			0.499091i
$772$	−8.40405			−0.302468
$773$			2.77358i			0.0997589i	0.998755	+	0.0498794i	$0.0158837\pi$
$773$			2.77358i			0.0997589i	−0.998755	+	0.0498794i	$0.984116\pi$
$774$	−3.57901			−0.128645
$775$	15.0231	−	6.07477i	0.539647	−	0.218212i
$776$	−3.64747			−0.130937
$777$	18.7542	−	21.8337i	0.672805	−	0.783281i
$778$		−	8.55057i		−	0.306553i
$779$			3.89026i			0.139383i
$780$	4.31558	−	6.40009i	0.154522	−	0.229160i
$781$	50.7556			1.81618
$782$	−8.67970			−0.310386
$783$	−38.9638			−1.39245
$784$	−15.9381			−0.569217
$785$	−16.4628	+	24.4146i	−0.587581	+	0.871395i
$786$	−6.12525			−0.218480
$787$		−	28.0910i		−	1.00134i	−0.865639	−	0.500669i	$-0.833088\pi$
$787$		−	28.0910i		−	1.00134i	0.865639	−	0.500669i	$-0.166912\pi$
$788$		−	4.22797i		−	0.150615i
$789$	3.52890			0.125632
$790$	−6.95848	+	10.3196i	−0.247572	+	0.367154i
$791$			6.66246i			0.236890i
$792$	−12.1177			−0.430583
$793$			10.7123i			0.380407i
$794$			9.84444i			0.349366i
$795$	6.70833	+	4.52343i	0.237920	+	0.160429i
$796$		−	17.7545i		−	0.629290i
$797$	−1.36472			−0.0483407			−0.0241704	−	0.999708i	$-0.507694\pi$
$797$	−1.36472			−0.0483407			−0.0241704	+	0.999708i	$0.507694\pi$
$798$		−	34.6886i		−	1.22796i
$799$		−	21.3744i		−	0.756173i
$800$	1.87436	+	4.63538i	0.0662688	+	0.163885i
$801$			17.1179i			0.604831i
$802$			31.0959i			1.09803i
$803$			54.2119i			1.91310i
$804$	3.75060			0.132273
$805$	−10.4702	+	15.5275i	−0.369026	+	0.547274i
$806$		−	11.3243i		−	0.398881i
$807$			0.453381i			0.0159598i
$808$	2.30416			0.0810600
$809$			0.636644i			0.0223832i	0.999937	+	0.0111916i	$0.00356247\pi$
$809$			0.636644i			0.0223832i	−0.999937	+	0.0111916i	$0.996438\pi$
$810$	2.16506	+	1.45990i	0.0760723	+	0.0512955i
$811$	11.3776			0.399521			0.199760	−	0.979845i	$-0.435984\pi$
$811$	11.3776			0.399521			0.199760	+	0.979845i	$0.435984\pi$
$812$	37.5968			1.31939
$813$		−	28.5425i		−	1.00103i
$814$	−23.7304	+	27.6269i	−0.831748	+	0.968324i
$815$	−34.7897	−	23.4587i	−1.21863	−	0.821722i
$816$			4.90379i			0.171667i
$817$			12.9639i			0.453549i
$818$		−	38.3150i		−	1.33965i
$819$			33.8688i			1.18347i
$820$	−0.983834	−	0.663399i	−0.0343570	−	0.0231669i
$821$	−26.1807			−0.913711			−0.456856	−	0.889541i	$-0.651024\pi$
$821$	−26.1807			−0.913711			−0.456856	+	0.889541i	$0.651024\pi$
$822$	8.86404			0.309169
$823$		−	21.7020i		−	0.756485i	−0.925707	−	0.378242i	$-0.876529\pi$
$823$		−	21.7020i		−	0.756485i	0.925707	−	0.378242i	$-0.123471\pi$
$824$	11.1716			0.389180
$825$	−27.4200	+	11.0876i	−0.954642	+	0.386020i
$826$	−10.3024			−0.358467
$827$	−7.90798			−0.274988			−0.137494	−	0.990503i	$-0.543905\pi$
$827$	−7.90798			−0.274988			−0.137494	+	0.990503i	$0.543905\pi$
$828$	3.53924			0.122997
$829$		−	21.7391i		−	0.755030i	−0.926003	−	0.377515i	$-0.876779\pi$
$829$		−	21.7391i		−	0.755030i	0.926003	−	0.377515i	$-0.123221\pi$
$830$	−4.72148	+	7.00205i	−0.163885	+	0.243045i
$831$			22.1785i			0.769362i
$832$	3.49410			0.121136
$833$	79.1076			2.74092
$834$		−	4.98109i		−	0.172481i
$835$	−13.3428	−	8.99706i	−0.461748	−	0.311356i
$836$			43.8926i			1.51806i
$837$	−16.0866			−0.556035
$838$	29.0183			1.00242
$839$	11.3258			0.391011			0.195506	−	0.980703i	$-0.437365\pi$
$839$	11.3258			0.391011			0.195506	+	0.980703i	$0.437365\pi$
$840$	8.77262	+	5.91537i	0.302684	+	0.204100i
$841$	−32.6231			−1.12494
$842$			23.6443i			0.814835i
$843$	−5.97639			−0.205838
$844$	4.57321			0.157417
$845$	−1.46700	−	0.989199i	−0.0504664	−	0.0340295i
$846$			8.71564i			0.299650i
$847$			119.006i			4.08911i
$848$			3.66238i			0.125767i
$849$			10.7015i			0.367276i
$850$	−9.30328	−	23.0074i	−0.319100	−	0.789147i
$851$	6.93097	−	8.06906i	0.237591	−	0.276604i
$852$			8.37532i			0.286934i
$853$	−48.1277			−1.64786			−0.823930	−	0.566691i	$-0.808223\pi$
$853$	−48.1277			−1.64786			−0.823930	+	0.566691i	$0.808223\pi$
$854$	−14.6834			−0.502457
$855$	18.5481	−	27.5072i	0.634332	−	0.940727i
$856$		−	6.51807i		−	0.222783i
$857$	−40.0486			−1.36803			−0.684017	−	0.729466i	$-0.739769\pi$
$857$	−40.0486			−1.36803			−0.684017	+	0.729466i	$0.739769\pi$
$858$			20.6689i			0.705624i
$859$		−	7.66509i		−	0.261530i	−0.991413	−	0.130765i	$-0.958257\pi$
$859$		−	7.66509i		−	0.261530i	0.991413	−	0.130765i	$-0.0417433\pi$
$860$	−3.27852	−	2.21071i	−0.111797	−	0.0753844i
$861$	−2.51101			−0.0855750
$862$		−	32.1126i		−	1.09376i
$863$		−	50.9196i		−	1.73332i	−0.498896	−	0.866662i	$-0.666261\pi$
$863$		−	50.9196i		−	1.73332i	0.498896	−	0.866662i	$-0.333739\pi$
$864$		−	4.96352i		−	0.168862i
$865$	−12.2438	+	18.1578i	−0.416302	+	0.617385i
$866$			13.0575i			0.443712i
$867$		−	7.54391i		−	0.256205i
$868$	15.5222			0.526859
$869$		−	33.3267i		−	1.13053i
$870$	−14.3788	−	9.69562i	−0.487487	−	0.328712i
$871$			13.2644i			0.449446i
$872$			1.33812i			0.0453146i
$873$	−7.38208			−0.249846
$874$		−	12.8198i		−	0.433636i
$875$	−52.3815	−	11.1104i	−1.77082	−	0.375601i
$876$	−8.94565			−0.302245
$877$		−	2.50813i		−	0.0846937i	−0.999103	−	0.0423468i	$-0.986517\pi$
$877$		−	2.50813i		−	0.0846937i	0.999103	−	0.0423468i	$-0.0134834\pi$
$878$			28.0499i			0.946640i
$879$	23.0342			0.776925
$880$	−11.1003	−	7.48491i	−0.374190	−	0.252316i
$881$	24.0074			0.808829			0.404414	−	0.914576i	$-0.367475\pi$
$881$	24.0074			0.808829			0.404414	+	0.914576i	$0.367475\pi$
$882$	−32.2569			−1.08615
$883$	34.7959			1.17098			0.585488	−	0.810681i	$-0.300903\pi$
$883$	34.7959			1.17098			0.585488	+	0.810681i	$0.300903\pi$
$884$	−17.3427			−0.583299
$885$	3.94014	+	2.65683i	0.132446	+	0.0893084i
$886$		−	6.79629i		−	0.228326i
$887$			0.672248i			0.0225719i	0.999936	+	0.0112859i	$0.00359250\pi$
$887$			0.672248i			0.0225719i	−0.999936	+	0.0112859i	$0.996408\pi$
$888$	−4.55879	−	3.91580i	−0.152983	−	0.131406i
$889$	−35.9693			−1.20637
$890$	−10.5735	+	15.6807i	−0.354423	+	0.525617i
$891$	−6.99198			−0.234240
$892$			20.3205i			0.680380i
$893$	31.5698			1.05644
$894$			21.3850i			0.715222i
$895$	14.1050	−	20.9180i	0.471478	−	0.699212i
$896$			4.78937i			0.160002i
$897$		−	6.03681i		−	0.201563i
$898$			17.3278i			0.578235i
$899$	−25.4418			−0.848531
$900$	3.79351	+	9.38150i	0.126450	+	0.312717i
$901$		−	18.1780i		−	0.605597i
$902$	3.17726			0.105791
$903$	−8.36767			−0.278459
$904$	1.39109			0.0462671
$905$	3.38714	+	2.28395i	0.112592	+	0.0759210i
$906$		−	6.39762i		−	0.212547i
$907$	36.6618			1.21734			0.608668	−	0.793425i	$-0.291704\pi$
$907$	36.6618			1.21734			0.608668	+	0.793425i	$0.291704\pi$
$908$	5.74303			0.190589
$909$	4.66336			0.154674
$910$	−20.9203	+	31.0252i	−0.693501	+	1.02848i
$911$		−	20.5358i		−	0.680381i	−0.940356	−	0.340191i	$-0.889508\pi$
$911$		−	20.5358i		−	0.680381i	0.940356	−	0.340191i	$-0.110492\pi$
$912$	−7.24283			−0.239834
$913$		−	22.6129i		−	0.748378i
$914$	−3.20960			−0.106164
$915$	5.61565	+	3.78663i	0.185648	+	0.125182i
$916$	23.4383			0.774423
$917$	29.6929			0.980546
$918$			24.6361i			0.813112i
$919$		−	42.3926i		−	1.39840i	−0.714925	−	0.699202i	$-0.753539\pi$
$919$		−	42.3926i		−	1.39840i	0.714925	−	0.699202i	$-0.246461\pi$
$920$	3.24208	+	2.18613i	0.106888	+	0.0720747i
$921$	14.0937			0.464403
$922$		−	34.0347i		−	1.12087i
$923$	−29.6201			−0.974958
$924$	−28.3309			−0.932019
$925$	28.8177	+	9.72326i	0.947519	+	0.319699i
$926$	−26.0543			−0.856197
$927$	22.6100			0.742610
$928$		−	7.85004i		−	0.257690i
$929$	1.22700			0.0402565			0.0201282	−	0.999797i	$-0.493593\pi$
$929$	1.22700			0.0402565			0.0201282	+	0.999797i	$0.493593\pi$
$930$	−5.93644	−	4.00294i	−0.194664	−	0.131262i
$931$			116.841i			3.82930i
$932$		−	17.2961i		−	0.566551i
$933$	−22.2614			−0.728806
$934$	20.3289			0.665183
$935$	55.0955	+	37.1509i	1.80182	+	1.21496i
$936$	7.07167			0.231145
$937$		−	31.9456i		−	1.04362i	−0.853063	−	0.521808i	$-0.825258\pi$
$937$		−	31.9456i		−	1.04362i	0.853063	−	0.521808i	$-0.174742\pi$
$938$	−18.1815			−0.593647
$939$		−	9.87983i		−	0.322416i
$940$	−5.38352	+	7.98388i	−0.175591	+	0.260405i
$941$	6.72808			0.219329			0.109665	−	0.993969i	$-0.465022\pi$
$941$	6.72808			0.219329			0.109665	+	0.993969i	$0.465022\pi$
$942$	13.0106			0.423909
$943$	−0.927990			−0.0302195
$944$			2.15110i			0.0700123i
$945$	44.0727	+	29.7182i	1.43368	+	0.966732i
$946$	10.5879			0.344242
$947$	3.77013			0.122513			0.0612564	−	0.998122i	$-0.480489\pi$
$947$	3.77013			0.122513			0.0612564	+	0.998122i	$0.480489\pi$
$948$	5.49933			0.178610
$949$		−	31.6372i		−	1.02699i
$950$	33.9816	−	13.7408i	1.10251	−	0.445811i
$951$	−12.2389			−0.396872
$952$		−	23.7717i		−	0.770446i
$953$			13.7237i			0.444553i	0.974984	+	0.222276i	$0.0713487\pi$
$953$			13.7237i			0.444553i	−0.974984	+	0.222276i	$0.928651\pi$
$954$			7.41226i			0.239981i
$955$	−29.7785	+	44.1621i	−0.963610	+	1.42905i
$956$		−	3.68796i		−	0.119277i
$957$	46.4359			1.50106
$958$			6.22972i			0.201273i
$959$	−42.9696			−1.38756
$960$	1.23510	−	1.83168i	0.0398628	−	0.0591174i
$961$	20.4961			0.661164
$962$	13.8486	−	16.1226i	0.446498	−	0.519814i
$963$		−	13.1919i		−	0.425102i
$964$		−	11.3613i		−	0.365922i
$965$	−15.5808	−	10.5061i	−0.501564	−	0.338204i
$966$	8.27467			0.266233
$967$	−43.7304			−1.40627			−0.703137	−	0.711055i	$-0.748218\pi$
$967$	−43.7304			−1.40627			−0.703137	+	0.711055i	$0.748218\pi$
$968$	24.8480			0.798646
$969$	35.9493			1.15486
$970$	−6.76228	−	4.55980i	−0.217124	−	0.146406i
$971$	36.2807			1.16430			0.582151	−	0.813081i	$-0.302211\pi$
$971$	36.2807			1.16430			0.582151	+	0.813081i	$0.302211\pi$
$972$		−	16.0443i		−	0.514622i
$973$			24.1465i			0.774100i
$974$	30.5352			0.978410
$975$	16.0018	−	6.47051i	0.512469	−	0.207222i
$976$			3.06584i			0.0981351i
$977$	−29.6513			−0.948628			−0.474314	−	0.880356i	$-0.657304\pi$
$977$	−29.6513			−0.948628			−0.474314	+	0.880356i	$0.657304\pi$
$978$			18.5396i			0.592829i
$979$		−	50.6402i		−	1.61847i
$980$	−29.5486	−	19.9246i	−0.943896	−	0.636469i
$981$			2.70822i			0.0864667i
$982$	24.5944			0.784839
$983$			42.0082i			1.33985i	0.742427	+	0.669927i	$0.233675\pi$
$983$			42.0082i			1.33985i	−0.742427	+	0.669927i	$0.766325\pi$
$984$			0.524288i			0.0167137i
$985$	5.28550	−	7.83850i	0.168410	−	0.249755i
$986$			38.9632i			1.24084i
$987$			20.3770i			0.648607i
$988$		−	25.6150i		−	0.814921i
$989$	−3.09243			−0.0983334
$990$	−22.4657	−	15.1486i	−0.714008	−	0.481455i
$991$		−	20.7399i		−	0.658824i	−0.944186	−	0.329412i	$-0.893149\pi$
$991$		−	20.7399i		−	0.658824i	0.944186	−	0.329412i	$-0.106851\pi$
$992$		−	3.24097i		−	0.102901i
$993$	18.7784			0.595915
$994$		−	40.6004i		−	1.28777i
$995$	22.1953	−	32.9161i	0.703639	−	1.04351i
$996$	3.73141			0.118234
$997$	−16.0224			−0.507435			−0.253718	−	0.967278i	$-0.581653\pi$
$997$	−16.0224			−0.507435			−0.253718	+	0.967278i	$0.581653\pi$
$998$			33.5739i			1.06276i
$999$	−22.9029	−	19.6726i	−0.724614	−	0.622413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.c.b.369.4	yes	10
3.2	odd	2		3330.2.e.c.739.1		10
5.2	odd	4		1850.2.d.i.1701.14		20
5.3	odd	4		1850.2.d.i.1701.7		20
5.4	even	2		370.2.c.a.369.7	yes	10
15.14	odd	2		3330.2.e.d.739.9		10
37.36	even	2		370.2.c.a.369.4	✓	10
111.110	odd	2		3330.2.e.d.739.10		10
185.73	odd	4		1850.2.d.i.1701.17		20
185.147	odd	4		1850.2.d.i.1701.4		20
185.184	even	2	inner	370.2.c.b.369.7	yes	10
555.554	odd	2		3330.2.e.c.739.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.4	✓	10	37.36	even	2
370.2.c.a.369.7	yes	10	5.4	even	2
370.2.c.b.369.4	yes	10	1.1	even	1	trivial
370.2.c.b.369.7	yes	10	185.184	even	2	inner
1850.2.d.i.1701.4		20	185.147	odd	4
1850.2.d.i.1701.7		20	5.3	odd	4
1850.2.d.i.1701.14		20	5.2	odd	4
1850.2.d.i.1701.17		20	185.73	odd	4
3330.2.e.c.739.1		10	3.2	odd	2
3330.2.e.c.739.2		10	555.554	odd	2
3330.2.e.d.739.9		10	15.14	odd	2
3330.2.e.d.739.10		10	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.987983i q^{3} +1.00000 q^{4} +(1.85396 + 1.25013i) q^{5} -0.987983i q^{6} +4.78937i q^{7} +1.00000 q^{8} +2.02389 q^{9} +(1.85396 + 1.25013i) q^{10} -5.98732 q^{11} -0.987983i q^{12} +3.49410 q^{13} +4.78937i q^{14} +(1.23510 - 1.83168i) q^{15} +1.00000 q^{16} -4.96343 q^{17} +2.02389 q^{18} -7.33092i q^{19} +(1.85396 + 1.25013i) q^{20} +4.73182 q^{21} -5.98732 q^{22} +1.74873 q^{23} -0.987983i q^{24} +(1.87436 + 4.63538i) q^{25} +3.49410 q^{26} -4.96352i q^{27} +4.78937i q^{28} -7.85004i q^{29} +(1.23510 - 1.83168i) q^{30} -3.24097i q^{31} +1.00000 q^{32} +5.91537i q^{33} -4.96343 q^{34} +(-5.98732 + 8.87932i) q^{35} +2.02389 q^{36} +(3.96343 - 4.61424i) q^{37} -7.33092i q^{38} -3.45211i q^{39} +(1.85396 + 1.25013i) q^{40} -0.530665 q^{41} +4.73182 q^{42} -1.76838 q^{43} -5.98732 q^{44} +(3.75222 + 2.53012i) q^{45} +1.74873 q^{46} +4.30638i q^{47} -0.987983i q^{48} -15.9381 q^{49} +(1.87436 + 4.63538i) q^{50} +4.90379i q^{51} +3.49410 q^{52} +3.66238i q^{53} -4.96352i q^{54} +(-11.1003 - 7.48491i) q^{55} +4.78937i q^{56} -7.24283 q^{57} -7.85004i q^{58} +2.15110i q^{59} +(1.23510 - 1.83168i) q^{60} +3.06584i q^{61} -3.24097i q^{62} +9.69316i q^{63} +1.00000 q^{64} +(6.47793 + 4.36807i) q^{65} +5.91537i q^{66} +3.79622i q^{67} -4.96343 q^{68} -1.72772i q^{69} +(-5.98732 + 8.87932i) q^{70} -8.47719 q^{71} +2.02389 q^{72} -9.05445i q^{73} +(3.96343 - 4.61424i) q^{74} +(4.57968 - 1.85184i) q^{75} -7.33092i q^{76} -28.6755i q^{77} -3.45211i q^{78} +5.56622i q^{79} +(1.85396 + 1.25013i) q^{80} +1.16780 q^{81} -0.530665 q^{82} +3.77680i q^{83} +4.73182 q^{84} +(-9.20203 - 6.20492i) q^{85} -1.76838 q^{86} -7.75571 q^{87} -5.98732 q^{88} +8.45791i q^{89} +(3.75222 + 2.53012i) q^{90} +16.7345i q^{91} +1.74873 q^{92} -3.20203 q^{93} +4.30638i q^{94} +(9.16459 - 13.5913i) q^{95} -0.987983i q^{96} -3.64747 q^{97} -15.9381 q^{98} -12.1177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8} - 8 q^{9} + 3 q^{10} + 2 q^{13} + 10 q^{15} + 10 q^{16} - 18 q^{17} - 8 q^{18} + 3 q^{20} - 12 q^{21} - 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} + 10 q^{32}+ \cdots - 82 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8 - 8 * q^9 + 3 * q^10 + 2 * q^13 + 10 * q^15 + 10 * q^16 - 18 * q^17 - 8 * q^18 + 3 * q^20 - 12 * q^21 - 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 + 10 * q^32 - 18 * q^34 - 8 * q^36 + 8 * q^37 + 3 * q^40 - 4 * q^41 - 12 * q^42 + 10 * q^43 - 20 * q^45 - 10 * q^46 - 8 * q^49 + 5 * q^50 + 2 * q^52 - 5 * q^55 - 12 * q^57 + 10 * q^60 + 10 * q^64 + 2 * q^65 - 18 * q^68 - 20 * q^71 - 8 * q^72 + 8 * q^74 + 25 * q^75 + 3 * q^80 + 58 * q^81 - 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 + 10 * q^87 - 20 * q^90 - 10 * q^92 + 32 * q^93 + 2 * q^95 - 2 * q^97 - 8 * q^98 - 82 * q^99

Introduction

L-functions

Modular forms

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Database

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