LMFDB - Embedded newform 430.2.j.a.49.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(49,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("430.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.14
Character	$\chi$	$=$	430.49
Dual form			430.2.j.a.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.66171 - 0.959389i) q^{3} -1.00000 q^{4} +(1.57718 + 1.58509i) q^{5} +(0.959389 - 1.66171i) q^{6} +(-0.863309 + 0.498432i) q^{7} -1.00000i q^{8} +(0.340854 + 0.590377i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.66171 - 0.959389i) q^{3} -1.00000 q^{4} +(1.57718 + 1.58509i) q^{5} +(0.959389 - 1.66171i) q^{6} +(-0.863309 + 0.498432i) q^{7} -1.00000i q^{8} +(0.340854 + 0.590377i) q^{9} +(-1.58509 + 1.57718i) q^{10} +6.30912 q^{11} +(1.66171 + 0.959389i) q^{12} +(-2.37912 + 1.37359i) q^{13} +(-0.498432 - 0.863309i) q^{14} +(-1.10009 - 4.14709i) q^{15} +1.00000 q^{16} +(-5.74209 + 3.31520i) q^{17} +(-0.590377 + 0.340854i) q^{18} +(-1.14110 + 1.97644i) q^{19} +(-1.57718 - 1.58509i) q^{20} +1.91276 q^{21} +6.30912i q^{22} +(7.44138 + 4.29628i) q^{23} +(-0.959389 + 1.66171i) q^{24} +(-0.0250243 + 4.99994i) q^{25} +(-1.37359 - 2.37912i) q^{26} +4.44829i q^{27} +(0.863309 - 0.498432i) q^{28} +(3.00403 + 5.20313i) q^{29} +(4.14709 - 1.10009i) q^{30} +(-2.10893 + 3.65277i) q^{31} +1.00000i q^{32} +(-10.4839 - 6.05290i) q^{33} +(-3.31520 - 5.74209i) q^{34} +(-2.15165 - 0.582308i) q^{35} +(-0.340854 - 0.590377i) q^{36} +(0.618763 + 0.357243i) q^{37} +(-1.97644 - 1.14110i) q^{38} +5.27122 q^{39} +(1.58509 - 1.57718i) q^{40} -2.42725 q^{41} +1.91276i q^{42} +(5.09359 - 4.12981i) q^{43} -6.30912 q^{44} +(-0.398213 + 1.47141i) q^{45} +(-4.29628 + 7.44138i) q^{46} -5.64213i q^{47} +(-1.66171 - 0.959389i) q^{48} +(-3.00313 + 5.20158i) q^{49} +(-4.99994 - 0.0250243i) q^{50} +12.7222 q^{51} +(2.37912 - 1.37359i) q^{52} +(-1.14151 - 0.659053i) q^{53} -4.44829 q^{54} +(9.95061 + 10.0005i) q^{55} +(0.498432 + 0.863309i) q^{56} +(3.79234 - 2.18951i) q^{57} +(-5.20313 + 3.00403i) q^{58} +4.10081 q^{59} +(1.10009 + 4.14709i) q^{60} +(-6.35472 - 11.0067i) q^{61} +(-3.65277 - 2.10893i) q^{62} +(-0.588525 - 0.339785i) q^{63} -1.00000 q^{64} +(-5.92956 - 1.60474i) q^{65} +(6.05290 - 10.4839i) q^{66} +(5.02819 + 2.90302i) q^{67} +(5.74209 - 3.31520i) q^{68} +(-8.24361 - 14.2784i) q^{69} +(0.582308 - 2.15165i) q^{70} +(-6.60669 - 11.4431i) q^{71} +(0.590377 - 0.340854i) q^{72} +(8.16391 - 4.71344i) q^{73} +(-0.357243 + 0.618763i) q^{74} +(4.83847 - 8.28444i) q^{75} +(1.14110 - 1.97644i) q^{76} +(-5.44673 + 3.14467i) q^{77} +5.27122i q^{78} +(5.53111 + 9.58016i) q^{79} +(1.57718 + 1.58509i) q^{80} +(5.29020 - 9.16289i) q^{81} -2.42725i q^{82} +(-9.92118 - 5.72799i) q^{83} -1.91276 q^{84} +(-14.3112 - 3.87308i) q^{85} +(4.12981 + 5.09359i) q^{86} -11.5281i q^{87} -6.30912i q^{88} +(1.39849 - 2.42226i) q^{89} +(-1.47141 - 0.398213i) q^{90} +(1.36928 - 2.37166i) q^{91} +(-7.44138 - 4.29628i) q^{92} +(7.00886 - 4.04657i) q^{93} +5.64213 q^{94} +(-4.93254 + 1.30845i) q^{95} +(0.959389 - 1.66171i) q^{96} +3.30561i q^{97} +(-5.20158 - 3.00313i) q^{98} +(2.15049 + 3.72476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.66171	−	0.959389i	−0.959389	−	0.553903i	−0.0634040	−	0.997988i	$-0.520196\pi$
$3$	−1.66171	−	0.959389i	−0.959389	−	0.553903i	−0.895985	+	0.444084i	$0.853529\pi$
$4$	−1.00000			−0.500000
$5$	1.57718	+	1.58509i	0.705335	+	0.708874i
$5$	1.57718	+	1.58509i	0.705335	+	0.708874i
$6$	0.959389	−	1.66171i	0.391669	−	0.678390i
$7$	−0.863309	+	0.498432i	−0.326300	+	0.188389i	−0.654197	−	0.756324i	$-0.726993\pi$
$7$	−0.863309	+	0.498432i	−0.326300	+	0.188389i	0.327897	+	0.944713i	$0.393660\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.340854	+	0.590377i	0.113618	+	0.196792i
$10$	−1.58509	+	1.57718i	−0.501250	+	0.498747i
$11$	6.30912			1.90227			0.951136	−	0.308771i	$-0.0999177\pi$
$11$	6.30912			1.90227			0.951136	+	0.308771i	$0.0999177\pi$
$12$	1.66171	+	0.959389i	0.479694	+	0.276952i
$13$	−2.37912	+	1.37359i	−0.659850	+	0.380965i	−0.792220	−	0.610236i	$-0.791075\pi$
$13$	−2.37912	+	1.37359i	−0.659850	+	0.380965i	0.132370	+	0.991200i	$0.457741\pi$
$14$	−0.498432	−	0.863309i	−0.133211	−	0.230729i
$15$	−1.10009	−	4.14709i	−0.284043	−	1.07077i
$16$	1.00000			0.250000
$17$	−5.74209	+	3.31520i	−1.39266	+	0.804053i	−0.993609	−	0.112875i	$-0.963994\pi$
$17$	−5.74209	+	3.31520i	−1.39266	+	0.804053i	−0.399052	+	0.916928i	$0.630661\pi$
$18$	−0.590377	+	0.340854i	−0.139153	+	0.0803401i
$19$	−1.14110	+	1.97644i	−0.261785	+	0.453425i	−0.966716	−	0.255850i	$-0.917645\pi$
$19$	−1.14110	+	1.97644i	−0.261785	+	0.453425i	0.704931	+	0.709276i	$0.250978\pi$
$20$	−1.57718	−	1.58509i	−0.352668	−	0.354437i
$21$	1.91276			0.417398
$22$			6.30912i			1.34511i
$23$	7.44138	+	4.29628i	1.55163	+	0.895837i	0.998009	+	0.0630709i	$0.0200894\pi$
$23$	7.44138	+	4.29628i	1.55163	+	0.895837i	0.553626	+	0.832766i	$0.313244\pi$
$24$	−0.959389	+	1.66171i	−0.195834	+	0.339195i
$25$	−0.0250243	+	4.99994i	−0.00500485	+	0.999987i
$26$	−1.37359	−	2.37912i	−0.269383	−	0.466584i
$27$			4.44829i			0.856073i
$28$	0.863309	−	0.498432i	0.163150	−	0.0941947i
$29$	3.00403	+	5.20313i	0.557835	+	0.966198i	0.997677	+	0.0681229i	$0.0217010\pi$
$29$	3.00403	+	5.20313i	0.557835	+	0.966198i	−0.439842	+	0.898075i	$0.644966\pi$
$30$	4.14709	−	1.10009i	0.757151	−	0.200849i
$31$	−2.10893	+	3.65277i	−0.378775	+	0.656057i	−0.990884	−	0.134716i	$-0.956988\pi$
$31$	−2.10893	+	3.65277i	−0.378775	+	0.656057i	0.612109	+	0.790773i	$0.290321\pi$
$32$			1.00000i			0.176777i
$33$	−10.4839	−	6.05290i	−1.82502	−	1.05368i
$34$	−3.31520	−	5.74209i	−0.568551	−	0.984760i
$35$	−2.15165	−	0.582308i	−0.363695	−	0.0984280i
$36$	−0.340854	−	0.590377i	−0.0568090	−	0.0983961i
$37$	0.618763	+	0.357243i	0.101724	+	0.0587304i	0.549999	−	0.835165i	$-0.314628\pi$
$37$	0.618763	+	0.357243i	0.101724	+	0.0587304i	−0.448275	+	0.893896i	$0.647961\pi$
$38$	−1.97644	−	1.14110i	−0.320620	−	0.185110i
$39$	5.27122			0.844070
$40$	1.58509	−	1.57718i	0.250625	−	0.249374i
$41$	−2.42725			−0.379073			−0.189536	−	0.981874i	$-0.560698\pi$
$41$	−2.42725			−0.379073			−0.189536	+	0.981874i	$0.560698\pi$
$42$			1.91276i			0.295145i
$43$	5.09359	−	4.12981i	0.776766	−	0.629790i
$43$	5.09359	−	4.12981i	0.776766	−	0.629790i
$44$	−6.30912			−0.951136
$45$	−0.398213	+	1.47141i	−0.0593621	+	0.219345i
$46$	−4.29628	+	7.44138i	−0.633452	+	1.09717i
$47$		−	5.64213i		−	0.822989i	−0.911412	−	0.411495i	$-0.865007\pi$
$47$		−	5.64213i		−	0.822989i	0.911412	−	0.411495i	$-0.134993\pi$
$48$	−1.66171	−	0.959389i	−0.239847	−	0.138476i
$49$	−3.00313	+	5.20158i	−0.429019	+	0.743082i
$50$	−4.99994	−	0.0250243i	−0.707098	−	0.00353896i
$51$	12.7222			1.78147
$52$	2.37912	−	1.37359i	0.329925	−	0.190482i
$53$	−1.14151	−	0.659053i	−0.156799	−	0.0905279i	0.419548	−	0.907733i	$-0.362189\pi$
$53$	−1.14151	−	0.659053i	−0.156799	−	0.0905279i	−0.576346	+	0.817206i	$0.695522\pi$
$54$	−4.44829			−0.605335
$55$	9.95061	+	10.0005i	1.34174	+	1.34847i
$56$	0.498432	+	0.863309i	0.0666057	+	0.115365i
$57$	3.79234	−	2.18951i	0.502308	−	0.290007i
$58$	−5.20313	+	3.00403i	−0.683205	+	0.394449i
$59$	4.10081			0.533880			0.266940	−	0.963713i	$-0.413987\pi$
$59$	4.10081			0.533880			0.266940	+	0.963713i	$0.413987\pi$
$60$	1.10009	+	4.14709i	0.142021	+	0.535387i
$61$	−6.35472	−	11.0067i	−0.813638	−	1.40926i	−0.910302	−	0.413945i	$-0.864150\pi$
$61$	−6.35472	−	11.0067i	−0.813638	−	1.40926i	0.0966638	−	0.995317i	$-0.469183\pi$
$62$	−3.65277	−	2.10893i	−0.463903	−	0.267834i
$63$	−0.588525	−	0.339785i	−0.0741472	−	0.0428089i
$64$	−1.00000			−0.125000
$65$	−5.92956	−	1.60474i	−0.735471	−	0.199043i
$66$	6.05290	−	10.4839i	0.745061	−	1.29048i
$67$	5.02819	+	2.90302i	0.614291	+	0.354661i	0.774643	−	0.632399i	$-0.217930\pi$
$67$	5.02819	+	2.90302i	0.614291	+	0.354661i	−0.160352	+	0.987060i	$0.551263\pi$
$68$	5.74209	−	3.31520i	0.696330	−	0.402027i
$69$	−8.24361	−	14.2784i	−0.992414	−	1.71891i
$70$	0.582308	−	2.15165i	0.0695991	−	0.257171i
$71$	−6.60669	−	11.4431i	−0.784070	−	1.35805i	−0.929553	−	0.368688i	$-0.879807\pi$
$71$	−6.60669	−	11.4431i	−0.784070	−	1.35805i	0.145484	−	0.989361i	$-0.453526\pi$
$72$	0.590377	−	0.340854i	0.0695766	−	0.0401700i
$73$	8.16391	−	4.71344i	0.955513	−	0.551666i	0.0607241	−	0.998155i	$-0.480659\pi$
$73$	8.16391	−	4.71344i	0.955513	−	0.551666i	0.894789	+	0.446489i	$0.147326\pi$
$74$	−0.357243	+	0.618763i	−0.0415287	+	0.0719298i
$75$	4.83847	−	8.28444i	0.558698	−	0.956605i
$76$	1.14110	−	1.97644i	0.130893	−	0.226713i
$77$	−5.44673	+	3.14467i	−0.620712	+	0.358368i
$78$			5.27122i			0.596848i
$79$	5.53111	+	9.58016i	0.622298	+	1.07785i	0.989057	+	0.147536i	$0.0471342\pi$
$79$	5.53111	+	9.58016i	0.622298	+	1.07785i	−0.366758	+	0.930316i	$0.619532\pi$
$80$	1.57718	+	1.58509i	0.176334	+	0.177219i
$81$	5.29020	−	9.16289i	0.587800	−	1.01810i
$82$		−	2.42725i		−	0.268045i
$83$	−9.92118	−	5.72799i	−1.08899	−	0.628729i	−0.155683	−	0.987807i	$-0.549758\pi$
$83$	−9.92118	−	5.72799i	−1.08899	−	0.628729i	−0.933308	+	0.359078i	$0.883091\pi$
$84$	−1.91276			−0.208699
$85$	−14.3112	−	3.87308i	−1.55226	−	0.420094i
$86$	4.12981	+	5.09359i	0.445329	+	0.549256i
$87$		−	11.5281i		−	1.23595i
$88$		−	6.30912i		−	0.672555i
$89$	1.39849	−	2.42226i	0.148240	−	0.256759i	−0.782337	−	0.622855i	$-0.785973\pi$
$89$	1.39849	−	2.42226i	0.148240	−	0.256759i	0.930577	+	0.366096i	$0.119306\pi$
$90$	−1.47141	−	0.398213i	−0.155101	−	0.0419754i
$91$	1.36928	−	2.37166i	0.143539	−	0.248618i
$92$	−7.44138	−	4.29628i	−0.775817	−	0.447918i
$93$	7.00886	−	4.04657i	0.726785	−	0.419609i
$94$	5.64213			0.581941
$95$	−4.93254	+	1.30845i	−0.506068	+	0.134244i
$96$	0.959389	−	1.66171i	0.0979172	−	0.169598i
$97$			3.30561i			0.335634i	0.985818	+	0.167817i	$0.0536717\pi$
$97$			3.30561i			0.335634i	−0.985818	+	0.167817i	$0.946328\pi$
$98$	−5.20158	−	3.00313i	−0.525439	−	0.303362i
$99$	2.15049	+	3.72476i	0.216133	+	0.374352i
$100$	0.0250243	−	4.99994i	0.00250243	−	0.499994i
$101$	6.13153	+	10.6201i	0.610110	+	1.05674i	0.991221	+	0.132212i	$0.0422080\pi$
$101$	6.13153	+	10.6201i	0.610110	+	1.05674i	−0.381112	+	0.924529i	$0.624459\pi$
$102$			12.7222i			1.25969i
$103$	11.6579	−	6.73067i	1.14868	−	0.663192i	0.200117	−	0.979772i	$-0.435868\pi$
$103$	11.6579	−	6.73067i	1.14868	−	0.663192i	0.948566	+	0.316580i	$0.102534\pi$
$104$	1.37359	+	2.37912i	0.134691	+	0.233292i
$105$	3.01676	+	3.03190i	0.294406	+	0.295883i
$106$	0.659053	−	1.14151i	0.0640129	−	0.110874i
$107$		−	2.00901i		−	0.194219i	−0.995274	−	0.0971093i	$-0.969040\pi$
$107$		−	2.00901i		−	0.194219i	0.995274	−	0.0971093i	$-0.0309597\pi$
$108$		−	4.44829i		−	0.428037i
$109$	−1.64440	+	2.84819i	−0.157505	+	0.272807i	−0.933968	−	0.357356i	$-0.883678\pi$
$109$	−1.64440	+	2.84819i	−0.157505	+	0.272807i	0.776463	+	0.630163i	$0.217012\pi$
$110$	−10.0005	+	9.95061i	−0.953514	+	0.948753i
$111$	−0.685470	−	1.18727i	−0.0650620	−	0.112691i
$112$	−0.863309	+	0.498432i	−0.0815750	+	0.0470974i
$113$			17.4383i			1.64046i	0.572033	+	0.820231i	$0.306155\pi$
$113$			17.4383i			1.64046i	−0.572033	+	0.820231i	$0.693845\pi$
$114$	2.18951	+	3.79234i	0.205066	+	0.355185i
$115$	4.92638	+	18.5713i	0.459387	+	1.73178i
$116$	−3.00403	−	5.20313i	−0.278917	−	0.483099i
$117$	−1.62187	−	0.936386i	−0.149942	−	0.0865689i
$118$			4.10081i			0.377510i
$119$	3.30480	−	5.72408i	0.302950	−	0.524725i
$120$	−4.14709	+	1.10009i	−0.378576	+	0.100424i
$121$	28.8051			2.61864
$122$	11.0067	−	6.35472i	0.996499	−	0.575329i
$123$	4.03338	+	2.32868i	0.363678	+	0.209970i
$124$	2.10893	−	3.65277i	0.189387	−	0.328029i
$125$	−7.96482	+	7.84612i	−0.712395	+	0.701778i
$126$	0.339785	−	0.588525i	0.0302705	−	0.0524300i
$127$		−	16.7375i		−	1.48521i	−0.669728	−	0.742607i	$-0.733589\pi$
$127$		−	16.7375i		−	1.48521i	0.669728	−	0.742607i	$-0.266411\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.4262	+	1.97581i	−1.09406	+	0.173960i
$130$	1.60474	−	5.92956i	0.140745	−	0.520057i
$131$	−3.25552			−0.284436			−0.142218	−	0.989835i	$-0.545423\pi$
$131$	−3.25552			−0.284436			−0.142218	+	0.989835i	$0.545423\pi$
$132$	10.4839	+	6.05290i	0.912510	+	0.526838i
$133$		−	2.27503i		−	0.197270i
$134$	−2.90302	+	5.02819i	−0.250783	+	0.434369i
$135$	−7.05094	+	7.01574i	−0.606848	+	0.603818i
$136$	3.31520	+	5.74209i	0.284276	+	0.492380i
$137$		−	16.4931i		−	1.40910i	−0.709652	−	0.704552i	$-0.751148\pi$
$137$		−	16.4931i		−	1.40910i	0.709652	−	0.704552i	$-0.248852\pi$
$138$	14.2784	−	8.24361i	1.21545	−	0.701743i
$139$	−4.73933	+	8.20876i	−0.401985	+	0.696258i	−0.993965	−	0.109694i	$-0.965013\pi$
$139$	−4.73933	+	8.20876i	−0.401985	+	0.696258i	0.591981	+	0.805952i	$0.298346\pi$
$140$	2.15165	+	0.582308i	0.181848	+	0.0492140i
$141$	−5.41300	+	9.37559i	−0.455857	+	0.789567i
$142$	11.4431	−	6.60669i	0.960285	−	0.554421i
$143$	−15.0102	+	8.66613i	−1.25521	+	0.724699i
$144$	0.340854	+	0.590377i	0.0284045	+	0.0491981i
$145$	−3.50955	+	12.9679i	−0.291452	+	1.07693i
$146$	4.71344	+	8.16391i	0.390087	+	0.675650i
$147$	9.98067	−	5.76234i	0.823192	−	0.475270i
$148$	−0.618763	−	0.357243i	−0.0508620	−	0.0293652i
$149$	2.83928	−	4.91778i	0.232603	−	0.402880i	−0.725970	−	0.687726i	$-0.758609\pi$
$149$	2.83928	−	4.91778i	0.232603	−	0.402880i	0.958573	+	0.284846i	$0.0919424\pi$
$150$	8.28444	+	4.83847i	0.676422	+	0.395059i
$151$	−3.73836			−0.304224			−0.152112	−	0.988363i	$-0.548607\pi$
$151$	−3.73836			−0.304224			−0.152112	+	0.988363i	$0.548607\pi$
$152$	1.97644	+	1.14110i	0.160310	+	0.0925551i
$153$	−3.91443	−	2.26000i	−0.316463	−	0.182710i
$154$	−3.14467	−	5.44673i	−0.253405	−	0.438910i
$155$	−9.11613	+	2.41823i	−0.732225	+	0.194237i
$156$	−5.27122			−0.422035
$157$	12.5507	−	7.24613i	1.00165	−	0.578304i	0.0929157	−	0.995674i	$-0.470381\pi$
$157$	12.5507	−	7.24613i	1.00165	−	0.578304i	0.908737	+	0.417370i	$0.137048\pi$
$158$	−9.58016	+	5.53111i	−0.762157	+	0.440031i
$159$	1.26458	+	2.19031i	0.100287	+	0.173703i
$160$	−1.58509	+	1.57718i	−0.125312	+	0.124687i
$161$	−8.56561			−0.675065
$162$	9.16289	+	5.29020i	0.719905	+	0.415637i
$163$	−6.70706	+	3.87232i	−0.525337	+	0.303304i	−0.739116	−	0.673579i	$-0.764756\pi$
$163$	−6.70706	+	3.87232i	−0.525337	+	0.303304i	0.213778	+	0.976882i	$0.431423\pi$
$164$	2.42725			0.189536
$165$	−6.94063	−	26.1645i	−0.540327	−	2.03690i
$166$	5.72799	−	9.92118i	0.444579	−	0.770033i
$167$	−4.64532	−	2.68198i	−0.359466	−	0.207538i	0.309381	−	0.950938i	$-0.399878\pi$
$167$	−4.64532	−	2.68198i	−0.359466	−	0.207538i	−0.668846	+	0.743401i	$0.733212\pi$
$168$		−	1.91276i		−	0.147573i
$169$	−2.72651	+	4.72246i	−0.209732	+	0.363266i
$170$	3.87308	−	14.3112i	0.297052	−	1.09762i
$171$	−1.55579			−0.118974
$172$	−5.09359	+	4.12981i	−0.388383	+	0.314895i
$173$			0.817995i			0.0621910i	0.999516	+	0.0310955i	$0.00989960\pi$
$173$			0.817995i			0.0621910i	−0.999516	+	0.0310955i	$0.990100\pi$
$174$	11.5281			0.873946
$175$	−2.47052	−	4.32896i	−0.186754	−	0.327239i
$176$	6.30912			0.475568
$177$	−6.81436	−	3.93427i	−0.512199	−	0.295718i
$178$	2.42226	+	1.39849i	0.181556	+	0.104821i
$179$	−7.38076	−	12.7838i	−0.551664	−	0.955510i	−0.998155	−	0.0607216i	$-0.980660\pi$
$179$	−7.38076	−	12.7838i	−0.551664	−	0.955510i	0.446491	−	0.894788i	$-0.352674\pi$
$180$	0.398213	−	1.47141i	0.0296811	−	0.109673i
$181$	−2.09436	−	3.62754i	−0.155673	−	0.269633i	0.777631	−	0.628721i	$-0.216421\pi$
$181$	−2.09436	−	3.62754i	−0.155673	−	0.269633i	−0.933304	+	0.359088i	$0.883088\pi$
$182$	2.37166	+	1.36928i	0.175799	+	0.101498i
$183$			24.3866i			1.80271i
$184$	4.29628	−	7.44138i	0.316726	−	0.548586i
$185$	0.409637	+	1.54423i	0.0301171	+	0.113534i
$186$	4.04657	+	7.00886i	0.296709	+	0.513915i
$187$	−36.2276	+	20.9160i	−2.64922	+	1.52953i
$188$			5.64213i			0.411495i
$189$	−2.21717	−	3.84025i	−0.161275	−	0.279337i
$190$	−1.30845	−	4.93254i	−0.0949249	−	0.357844i
$191$	3.08796	−	5.34851i	0.223437	−	0.387005i	−0.732412	−	0.680862i	$-0.761606\pi$
$191$	3.08796	−	5.34851i	0.223437	−	0.387005i	0.955849	+	0.293857i	$0.0949389\pi$
$192$	1.66171	+	0.959389i	0.119924	+	0.0692379i
$193$			10.2533i			0.738050i	0.929419	+	0.369025i	$0.120308\pi$
$193$			10.2533i			0.738050i	−0.929419	+	0.369025i	$0.879692\pi$
$194$	−3.30561			−0.237329
$195$	8.31365	+	8.35536i	0.595352	+	0.598340i
$196$	3.00313	−	5.20158i	0.214509	−	0.371541i
$197$	−6.09968	+	3.52165i	−0.434584	+	0.250907i	−0.701298	−	0.712869i	$-0.747396\pi$
$197$	−6.09968	+	3.52165i	−0.434584	+	0.250907i	0.266714	+	0.963776i	$0.414062\pi$
$198$	−3.72476	+	2.15049i	−0.264707	+	0.152829i
$199$	21.0013			1.48874			0.744371	−	0.667766i	$-0.232749\pi$
$199$	21.0013			1.48874			0.744371	+	0.667766i	$0.232749\pi$
$200$	4.99994	+	0.0250243i	0.353549	+	0.00176948i
$201$	−5.57026	−	9.64797i	−0.392896	−	0.680515i
$202$	−10.6201	+	6.13153i	−0.747229	+	0.431413i
$203$	−5.18682	−	2.99461i	−0.364043	−	0.210180i
$204$	−12.7222			−0.890736
$205$	−3.82820	−	3.84741i	−0.267373	−	0.268715i
$206$	6.73067	+	11.6579i	0.468948	+	0.812241i
$207$			5.85762i			0.407133i
$208$	−2.37912	+	1.37359i	−0.164963	+	0.0952412i
$209$	−7.19931	+	12.4696i	−0.497987	+	0.862539i
$210$	−3.03190	+	3.01676i	−0.209221	+	0.208176i
$211$	−23.9641			−1.64975			−0.824877	−	0.565312i	$-0.808756\pi$
$211$	−23.9641			−1.64975			−0.824877	+	0.565312i	$0.808756\pi$
$212$	1.14151	+	0.659053i	0.0783994	+	0.0452639i
$213$			25.3535i			1.73720i
$214$	2.00901			0.137333
$215$	14.5796	+	1.56037i	0.994322	+	0.106416i
$216$	4.44829			0.302668
$217$		−	4.20463i		−	0.285429i
$218$	−2.84819	−	1.64440i	−0.192904	−	0.111373i
$219$	−18.0881			−1.22228
$220$	−9.95061	−	10.0005i	−0.670870	−	0.674236i
$221$	9.10742	−	15.7745i	0.612632	−	1.06111i
$222$	1.18727	−	0.685470i	0.0796843	−	0.0460058i
$223$		−	18.2644i		−	1.22307i	−0.791217	−	0.611536i	$-0.790552\pi$
$223$		−	18.2644i		−	1.22307i	0.791217	−	0.611536i	$-0.209448\pi$
$224$	−0.498432	−	0.863309i	−0.0333029	−	0.0576823i
$225$	−2.96038	+	1.68948i	−0.197358	+	0.112632i
$226$	−17.4383			−1.15998
$227$	0.719556	+	0.415436i	0.0477586	+	0.0275734i	0.523689	−	0.851909i	$-0.324555\pi$
$227$	0.719556	+	0.415436i	0.0477586	+	0.0275734i	−0.475931	+	0.879483i	$0.657889\pi$
$228$	−3.79234	+	2.18951i	−0.251154	+	0.145004i
$229$	−11.4207	−	19.7812i	−0.754699	−	1.30718i	−0.945524	−	0.325553i	$-0.894449\pi$
$229$	−11.4207	−	19.7812i	−0.754699	−	1.30718i	0.190824	−	0.981624i	$-0.438884\pi$
$230$	−18.5713	+	4.92638i	−1.22455	+	0.324836i
$231$	12.0678			0.794006
$232$	5.20313	−	3.00403i	0.341603	−	0.197224i
$233$	−3.83756	+	2.21562i	−0.251407	+	0.145150i	−0.620408	−	0.784279i	$-0.713033\pi$
$233$	−3.83756	+	2.21562i	−0.251407	+	0.145150i	0.369001	+	0.929429i	$0.379700\pi$
$234$	0.936386	−	1.62187i	0.0612135	−	0.106025i
$235$	8.94329	−	8.89864i	0.583396	−	0.580483i
$236$	−4.10081			−0.266940
$237$		−	21.2259i		−	1.37877i
$238$	5.72408	+	3.30480i	0.371037	+	0.214218i
$239$	3.86183	−	6.68888i	0.249801	−	0.432668i	−0.713670	−	0.700482i	$-0.752968\pi$
$239$	3.86183	−	6.68888i	0.249801	−	0.432668i	0.963470	+	0.267815i	$0.0863016\pi$
$240$	−1.10009	−	4.14709i	−0.0710107	−	0.267693i
$241$	−1.17716	−	2.03890i	−0.0758274	−	0.131337i	0.825618	−	0.564229i	$-0.190826\pi$
$241$	−1.17716	−	2.03890i	−0.0758274	−	0.131337i	−0.901446	+	0.432892i	$0.857493\pi$
$242$			28.8051i			1.85166i
$243$	−6.02457	+	3.47829i	−0.386476	+	0.223132i
$244$	6.35472	+	11.0067i	0.406819	+	0.704631i
$245$	−12.9814	+	3.44357i	−0.829354	+	0.220002i
$246$	−2.32868	+	4.03338i	−0.148471	+	0.257159i
$247$		−	6.26958i		−	0.398924i
$248$	3.65277	+	2.10893i	0.231951	+	0.133917i
$249$	10.9907	+	19.0365i	0.696510	+	1.20639i
$250$	−7.84612	−	7.96482i	−0.496232	−	0.503740i
$251$	9.70270	+	16.8056i	0.612429	+	1.06076i	0.990830	+	0.135116i	$0.0431407\pi$
$251$	9.70270	+	16.8056i	0.612429	+	1.06076i	−0.378401	+	0.925642i	$0.623526\pi$
$252$	0.588525	+	0.339785i	0.0370736	+	0.0214044i
$253$	46.9486	+	27.1058i	2.95163	+	1.70413i
$254$	16.7375			1.05020
$255$	20.0652	+	20.1659i	1.25653	+	1.26284i
$256$	1.00000			0.0625000
$257$		−	9.79361i		−	0.610909i	−0.952207	−	0.305454i	$-0.901192\pi$
$257$		−	9.79361i		−	0.610909i	0.952207	−	0.305454i	$-0.0988083\pi$
$258$	−1.97581	−	12.4262i	−0.123008	−	0.773619i
$259$	−0.712246			−0.0442568
$260$	5.92956	+	1.60474i	0.367736	+	0.0995214i
$261$	−2.04787	+	3.54702i	−0.126760	+	0.219555i
$262$		−	3.25552i		−	0.201127i
$263$	9.27806	+	5.35669i	0.572110	+	0.330308i	0.757992	−	0.652264i	$-0.226181\pi$
$263$	9.27806	+	5.35669i	0.572110	+	0.330308i	−0.185882	+	0.982572i	$0.559514\pi$
$264$	−6.05290	+	10.4839i	−0.372531	+	0.645242i
$265$	−0.755710	−	2.84884i	−0.0464229	−	0.175003i
$266$	2.27503			0.139491
$267$	−4.64778	+	2.68340i	−0.284440	+	0.164221i
$268$	−5.02819	−	2.90302i	−0.307145	−	0.177330i
$269$	−24.3081			−1.48209			−0.741046	−	0.671455i	$-0.765670\pi$
$269$	−24.3081			−1.48209			−0.741046	+	0.671455i	$0.765670\pi$
$270$	−7.01574	−	7.05094i	−0.426964	−	0.429106i
$271$	7.45800	+	12.9176i	0.453041	+	0.784690i	0.998573	−	0.0533996i	$-0.0170057\pi$
$271$	7.45800	+	12.9176i	0.453041	+	0.784690i	−0.545532	+	0.838090i	$0.683672\pi$
$272$	−5.74209	+	3.31520i	−0.348165	+	0.201013i
$273$	−4.55069	+	2.62734i	−0.275420	+	0.159014i
$274$	16.4931			0.996387
$275$	−0.157881	+	31.5452i	−0.00952059	+	1.90225i
$276$	8.24361	+	14.2784i	0.496207	+	0.859456i
$277$	−4.75828	−	2.74719i	−0.285897	−	0.165063i	0.350193	−	0.936678i	$-0.386116\pi$
$277$	−4.75828	−	2.74719i	−0.285897	−	0.165063i	−0.636090	+	0.771615i	$0.719449\pi$
$278$	−8.20876	−	4.73933i	−0.492328	−	0.284246i
$279$	−2.87535			−0.172143
$280$	−0.582308	+	2.15165i	−0.0347996	+	0.128586i
$281$	0.555222	−	0.961672i	0.0331217	−	0.0573685i	−0.848989	−	0.528410i	$-0.822788\pi$
$281$	0.555222	−	0.961672i	0.0331217	−	0.0573685i	0.882111	+	0.471041i	$0.156122\pi$
$282$	−9.37559	−	5.41300i	−0.558308	−	0.322339i
$283$	7.37044	−	4.25533i	0.438127	−	0.252953i	−0.264676	−	0.964337i	$-0.585265\pi$
$283$	7.37044	−	4.25533i	0.438127	−	0.252953i	0.702803	+	0.711385i	$0.251932\pi$
$284$	6.60669	+	11.4431i	0.392035	+	0.679024i
$285$	9.45176	+	2.55796i	0.559874	+	0.151520i
$286$	−8.66613	−	15.0102i	−0.512439	−	0.887571i
$287$	2.09547	−	1.20982i	0.123691	−	0.0714133i
$288$	−0.590377	+	0.340854i	−0.0347883	+	0.0200850i
$289$	13.4810	−	23.3499i	0.793003	−	1.37352i
$290$	−12.9679	−	3.50955i	−0.761503	−	0.206088i
$291$	3.17137	−	5.49297i	0.185909	−	0.322003i
$292$	−8.16391	+	4.71344i	−0.477757	+	0.275833i
$293$		−	7.82979i		−	0.457421i	−0.973494	−	0.228711i	$-0.926549\pi$
$293$		−	7.82979i		−	0.457421i	0.973494	−	0.228711i	$-0.0734510\pi$
$294$	5.76234	+	9.98067i	0.336067	+	0.582084i
$295$	6.46771	+	6.50016i	0.376564	+	0.378454i
$296$	0.357243	−	0.618763i	0.0207643	−	0.0359649i
$297$			28.0648i			1.62848i
$298$	4.91778	+	2.83928i	0.284879	+	0.164475i
$299$	−23.6053			−1.36513
$300$	−4.83847	+	8.28444i	−0.279349	+	0.478302i
$301$	−2.33892	+	6.10411i	−0.134813	+	0.351835i
$302$		−	3.73836i		−	0.215119i
$303$		−	23.5301i		−	1.35177i
$304$	−1.14110	+	1.97644i	−0.0654463	+	0.113356i
$305$	7.42409	−	27.4323i	0.425102	−	1.57077i
$306$	2.26000	−	3.91443i	0.129195	−	0.223773i
$307$	9.11133	+	5.26043i	0.520011	+	0.300229i	0.736939	−	0.675959i	$-0.236270\pi$
$307$	9.11133	+	5.26043i	0.520011	+	0.300229i	−0.216928	+	0.976188i	$0.569604\pi$
$308$	5.44673	−	3.14467i	0.310356	−	0.179184i
$309$	−25.8293			−1.46938
$310$	−2.41823	−	9.11613i	−0.137346	−	0.517761i
$311$	10.3506	−	17.9278i	0.586929	−	1.01659i	−0.407703	−	0.913115i	$-0.633670\pi$
$311$	10.3506	−	17.9278i	0.586929	−	1.01659i	0.994632	−	0.103477i	$-0.0329967\pi$
$312$		−	5.27122i		−	0.298424i
$313$	25.5345	+	14.7424i	1.44330	+	0.833288i	0.998068	−	0.0621292i	$-0.0197891\pi$
$313$	25.5345	+	14.7424i	1.44330	+	0.833288i	0.445229	+	0.895417i	$0.353122\pi$
$314$	7.24613	+	12.5507i	0.408923	+	0.708275i
$315$	−0.389618	−	1.46877i	−0.0219525	−	0.0827556i
$316$	−5.53111	−	9.58016i	−0.311149	−	0.538926i
$317$		−	1.23963i		−	0.0696245i	−0.999394	−	0.0348123i	$-0.988917\pi$
$317$		−	1.23963i		−	0.0696245i	0.999394	−	0.0348123i	$-0.0110833\pi$
$318$	−2.19031	+	1.26458i	−0.122826	+	0.0709139i
$319$	18.9528	+	32.8272i	1.06115	+	1.83797i
$320$	−1.57718	−	1.58509i	−0.0881669	−	0.0886093i
$321$	−1.92743	+	3.33840i	−0.107578	+	0.186331i
$322$		−	8.56561i		−	0.477343i
$323$		−	15.1318i		−	0.841957i
$324$	−5.29020	+	9.16289i	−0.293900	+	0.509050i
$325$	−6.80832	−	11.9298i	−0.377657	−	0.661748i
$326$	−3.87232	−	6.70706i	−0.214468	−	0.371470i
$327$	5.46504	−	3.15524i	0.302217	−	0.174485i
$328$			2.42725i			0.134022i
$329$	2.81222	+	4.87090i	0.155043	+	0.268542i
$330$	26.1645	−	6.94063i	1.44031	−	0.382069i
$331$	1.83031	+	3.17018i	0.100603	+	0.174249i	0.911933	−	0.410339i	$-0.134590\pi$
$331$	1.83031	+	3.17018i	0.100603	+	0.174249i	−0.811330	+	0.584588i	$0.801256\pi$
$332$	9.92118	+	5.72799i	0.544495	+	0.314365i
$333$			0.487071i			0.0266913i
$334$	2.68198	−	4.64532i	0.146751	−	0.254181i
$335$	3.32878	+	12.5487i	0.181871	+	0.685609i
$336$	1.91276			0.104350
$337$	−4.82802	+	2.78746i	−0.262999	+	0.151842i	−0.625702	−	0.780062i	$-0.715187\pi$
$337$	−4.82802	+	2.78746i	−0.262999	+	0.151842i	0.362703	+	0.931905i	$0.381854\pi$
$338$	−4.72246	−	2.72651i	−0.256868	−	0.148303i
$339$	16.7302	−	28.9775i	0.908657	−	1.57384i
$340$	14.3112	+	3.87308i	0.776132	+	0.210047i
$341$	−13.3055	+	23.0458i	−0.720533	+	1.24800i
$342$		−	1.55579i		−	0.0841274i
$343$		−	12.9655i		−	0.700070i
$344$	−4.12981	−	5.09359i	−0.222664	−	0.274628i
$345$	9.63085	−	35.5864i	0.518507	−	1.91591i
$346$	−0.817995			−0.0439757
$347$	−11.5244	−	6.65360i	−0.618661	−	0.357184i	0.157686	−	0.987489i	$-0.449596\pi$
$347$	−11.5244	−	6.65360i	−0.618661	−	0.357184i	−0.776348	+	0.630305i	$0.782930\pi$
$348$			11.5281i			0.617973i
$349$	2.71845	−	4.70850i	0.145515	−	0.252040i	−0.784050	−	0.620698i	$-0.786849\pi$
$349$	2.71845	−	4.70850i	0.145515	−	0.252040i	0.929565	+	0.368658i	$0.120183\pi$
$350$	4.32896	−	2.47052i	0.231393	−	0.132055i
$351$	−6.11011	−	10.5830i	−0.326134	−	0.564880i
$352$			6.30912i			0.336277i
$353$	10.7741	−	6.22041i	0.573445	−	0.331079i	−0.185079	−	0.982724i	$-0.559254\pi$
$353$	10.7741	−	6.22041i	0.573445	−	0.331079i	0.758524	+	0.651645i	$0.225921\pi$
$354$	3.93427	−	6.81436i	0.209104	−	0.362179i
$355$	7.71846	−	28.5200i	0.409654	−	1.51369i
$356$	−1.39849	+	2.42226i	−0.0741200	+	0.128380i
$357$	−10.9832	+	6.34117i	−0.581294	+	0.335610i
$358$	12.7838	−	7.38076i	0.675647	−	0.390085i
$359$	−1.59546	−	2.76341i	−0.0842050	−	0.145847i	0.820847	−	0.571148i	$-0.193502\pi$
$359$	−1.59546	−	2.76341i	−0.0842050	−	0.145847i	−0.905052	+	0.425301i	$0.860168\pi$
$360$	1.47141	+	0.398213i	0.0775503	+	0.0209877i
$361$	6.89580	+	11.9439i	0.362937	+	0.628625i
$362$	3.62754	−	2.09436i	0.190659	−	0.110077i
$363$	−47.8657	−	27.6353i	−2.51230	−	1.45047i
$364$	−1.36928	+	2.37166i	−0.0717697	+	0.124309i
$365$	20.3472	+	5.50661i	1.06502	+	0.288229i
$366$	−24.3866			−1.27471
$367$	26.2004	+	15.1268i	1.36765	+	0.789613i	0.990628	−	0.136591i	$-0.0436147\pi$
$367$	26.2004	+	15.1268i	1.36765	+	0.789613i	0.377022	+	0.926204i	$0.376948\pi$
$368$	7.44138	+	4.29628i	0.387909	+	0.223959i
$369$	−0.827338	−	1.43299i	−0.0430695	−	0.0745985i
$370$	−1.54423	+	0.409637i	−0.0802808	+	0.0212960i
$371$	1.31397			0.0682180
$372$	−7.00886	+	4.04657i	−0.363392	+	0.209805i
$373$	−29.0459	+	16.7697i	−1.50394	+	0.868301i	−0.503951	+	0.863732i	$0.668121\pi$
$373$	−29.0459	+	16.7697i	−1.50394	+	0.868301i	−0.999990	+	0.00456841i	$0.998546\pi$
$374$	−20.9160	−	36.2276i	−1.08154	−	1.87328i
$375$	20.7627	−	5.39662i	1.07218	−	0.278680i
$376$	−5.64213			−0.290971
$377$	−14.2939	−	8.25260i	−0.736174	−	0.425030i
$378$	3.84025	−	2.21717i	0.197521	−	0.114039i
$379$	37.6956			1.93629			0.968145	−	0.250389i	$-0.0805584\pi$
$379$	37.6956			1.93629			0.968145	+	0.250389i	$0.0805584\pi$
$380$	4.93254	−	1.30845i	0.253034	−	0.0671220i
$381$	−16.0578	+	27.8129i	−0.822665	+	1.42490i
$382$	5.34851	+	3.08796i	0.273654	+	0.157994i
$383$		−	1.65236i		−	0.0844316i	−0.999109	−	0.0422158i	$-0.986558\pi$
$383$		−	1.65236i		−	0.0844316i	0.999109	−	0.0422158i	$-0.0134417\pi$
$384$	−0.959389	+	1.66171i	−0.0489586	+	0.0847988i
$385$	−13.5750	−	3.67385i	−0.691848	−	0.187237i
$386$	−10.2533			−0.521880
$387$	4.17431	+	1.59948i	0.212192	+	0.0813059i
$388$		−	3.30561i		−	0.167817i
$389$	−0.410501			−0.0208132			−0.0104066	−	0.999946i	$-0.503313\pi$
$389$	−0.410501			−0.0208132			−0.0104066	+	0.999946i	$0.503313\pi$
$390$	−8.35536	+	8.31365i	−0.423090	+	0.420978i
$391$	−56.9721			−2.88120
$392$	5.20158	+	3.00313i	0.262719	+	0.151681i
$393$	5.40973	+	3.12331i	0.272885	+	0.157550i
$394$	−3.52165	−	6.09968i	−0.177418	−	0.307297i
$395$	−6.46188	+	23.8769i	−0.325133	+	1.20138i
$396$	−2.15049	−	3.72476i	−0.108066	−	0.187176i
$397$	0.753818	+	0.435217i	0.0378331	+	0.0218429i	0.518797	−	0.854897i	$-0.326380\pi$
$397$	0.753818	+	0.435217i	0.0378331	+	0.0218429i	−0.480964	+	0.876740i	$0.659713\pi$
$398$			21.0013i			1.05270i
$399$	−2.18264	+	3.78045i	−0.109269	+	0.189259i
$400$	−0.0250243	+	4.99994i	−0.00125121	+	0.249997i
$401$	11.6931	+	20.2530i	0.583923	+	1.01138i	0.995009	+	0.0997880i	$0.0318165\pi$
$401$	11.6931	+	20.2530i	0.583923	+	1.01138i	−0.411085	+	0.911597i	$0.634850\pi$
$402$	9.64797	−	5.57026i	0.481197	−	0.277819i
$403$		−	11.5872i		−	0.577199i
$404$	−6.13153	−	10.6201i	−0.305055	−	0.528370i
$405$	22.8676	−	6.06606i	1.13630	−	0.301425i
$406$	2.99461	−	5.18682i	0.148620	−	0.257417i
$407$	3.90386	+	2.25389i	0.193507	+	0.111721i
$408$		−	12.7222i		−	0.629845i
$409$	13.5812			0.671545			0.335772	−	0.941943i	$-0.391003\pi$
$409$	13.5812			0.671545			0.335772	+	0.941943i	$0.391003\pi$
$410$	3.84741	−	3.82820i	0.190010	−	0.189061i
$411$	−15.8233	+	27.4068i	−0.780508	+	1.35188i
$412$	−11.6579	+	6.73067i	−0.574341	+	0.331596i
$413$	−3.54027	+	2.04397i	−0.174205	+	0.100577i
$414$	−5.85762			−0.287886
$415$	−6.56806	−	24.7600i	−0.322414	−	1.21542i
$416$	−1.37359	−	2.37912i	−0.0673457	−	0.116646i
$417$	15.7508	−	9.09372i	0.771319	−	0.445321i
$418$	−12.4696	−	7.19931i	−0.609907	−	0.352130i
$419$	−14.5466			−0.710648			−0.355324	−	0.934743i	$-0.615629\pi$
$419$	−14.5466			−0.710648			−0.355324	+	0.934743i	$0.615629\pi$
$420$	−3.01676	−	3.03190i	−0.147203	−	0.147941i
$421$	−6.35799	−	11.0124i	−0.309869	−	0.536709i	0.668464	−	0.743744i	$-0.266952\pi$
$421$	−6.35799	−	11.0124i	−0.309869	−	0.536709i	−0.978334	+	0.207035i	$0.933619\pi$
$422$		−	23.9641i		−	1.16655i
$423$	3.33098	−	1.92314i	0.161958	−	0.0935064i
$424$	−0.659053	+	1.14151i	−0.0320064	+	0.0554368i
$425$	−16.4321	−	28.7930i	−0.797073	−	1.39667i
$426$	−25.3535			−1.22838
$427$	10.9722	+	6.33478i	0.530980	+	0.306562i
$428$			2.00901i			0.0971093i
$429$	33.2568			1.60565
$430$	−1.56037	+	14.5796i	−0.0752476	+	0.703092i
$431$	29.0476			1.39917			0.699586	−	0.714549i	$-0.253368\pi$
$431$	29.0476			1.39917			0.699586	+	0.714549i	$0.253368\pi$
$432$			4.44829i			0.214018i
$433$	9.56834	+	5.52428i	0.459825	+	0.265480i	0.711971	−	0.702209i	$-0.247803\pi$
$433$	9.56834	+	5.52428i	0.459825	+	0.265480i	−0.252146	+	0.967689i	$0.581136\pi$
$434$	4.20463			0.201829
$435$	18.2731	−	18.1819i	0.876130	−	0.871756i
$436$	1.64440	−	2.84819i	0.0787526	−	0.136403i
$437$	−16.9826	+	9.80493i	−0.812390	+	0.469034i
$438$		−	18.0881i		−	0.864281i
$439$	0.815471	+	1.41244i	0.0389203	+	0.0674119i	0.884829	−	0.465915i	$-0.154275\pi$
$439$	0.815471	+	1.41244i	0.0389203	+	0.0674119i	−0.845909	+	0.533327i	$0.820941\pi$
$440$	10.0005	−	9.95061i	0.476757	−	0.474377i
$441$	−4.09452			−0.194977
$442$	15.7745	+	9.10742i	0.750317	+	0.433196i
$443$	3.72043	−	2.14799i	0.176763	−	0.102054i	−0.409008	−	0.912531i	$-0.634125\pi$
$443$	3.72043	−	2.14799i	0.176763	−	0.102054i	0.585771	+	0.810477i	$0.300792\pi$
$444$	0.685470	+	1.18727i	0.0325310	+	0.0563453i
$445$	6.04517	−	1.60360i	0.286569	−	0.0760178i
$446$	18.2644			0.864842
$447$	−9.43612	+	5.44795i	−0.446313	+	0.257679i
$448$	0.863309	−	0.498432i	0.0407875	−	0.0235487i
$449$	1.65246	−	2.86214i	0.0779842	−	0.135073i	−0.824396	−	0.566014i	$-0.808485\pi$
$449$	1.65246	−	2.86214i	0.0779842	−	0.135073i	0.902380	+	0.430941i	$0.141818\pi$
$450$	−1.68948	−	2.96038i	−0.0796426	−	0.139553i
$451$	−15.3138			−0.721100
$452$		−	17.4383i		−	0.820231i
$453$	6.21208	+	3.58654i	0.291869	+	0.168511i
$454$	−0.415436	+	0.719556i	−0.0194974	+	0.0337704i
$455$	5.91889	−	1.57010i	0.277482	−	0.0736073i
$456$	−2.18951	−	3.79234i	−0.102533	−	0.177593i
$457$		−	16.6561i		−	0.779138i	−0.920997	−	0.389569i	$-0.872624\pi$
$457$		−	16.6561i		−	0.779138i	0.920997	−	0.389569i	$-0.127376\pi$
$458$	19.7812	−	11.4207i	0.924314	−	0.533653i
$459$	−14.7469	−	25.5425i	−0.688328	−	1.19222i
$460$	−4.92638	−	18.5713i	−0.229693	−	0.865889i
$461$	11.7487	−	20.3494i	0.547193	−	0.947766i	−0.451272	−	0.892386i	$-0.649030\pi$
$461$	11.7487	−	20.3494i	0.547193	−	0.947766i	0.998465	−	0.0553799i	$-0.0176370\pi$
$462$			12.0678i			0.561447i
$463$	−22.9933	−	13.2752i	−1.06859	−	0.616950i	−0.140794	−	0.990039i	$-0.544965\pi$
$463$	−22.9933	−	13.2752i	−1.06859	−	0.616950i	−0.927796	+	0.373089i	$0.878299\pi$
$464$	3.00403	+	5.20313i	0.139459	+	0.241549i
$465$	17.4684	+	4.72752i	0.810077	+	0.219234i
$466$	−2.21562	−	3.83756i	−0.102636	−	0.177771i
$467$	11.2211	+	6.47852i	0.519252	+	0.299790i	0.736629	−	0.676298i	$-0.236417\pi$
$467$	11.2211	+	6.47852i	0.519252	+	0.299790i	−0.217377	+	0.976088i	$0.569750\pi$
$468$	1.62187	+	0.936386i	0.0749709	+	0.0432845i
$469$	−5.78784			−0.267257
$470$	8.89864	+	8.94329i	0.410464	+	0.412523i
$471$	−27.8074			−1.28130
$472$		−	4.10081i		−	0.188755i
$473$	32.1361	−	26.0555i	1.47762	−	1.19803i
$474$	21.2259			0.974939
$475$	−9.85350	−	5.75486i	−0.452109	−	0.264051i
$476$	−3.30480	+	5.72408i	−0.151475	+	0.262363i
$477$		−	0.898563i		−	0.0411424i
$478$	6.68888	+	3.86183i	0.305942	+	0.176636i
$479$	−4.08771	+	7.08012i	−0.186772	+	0.323499i	−0.944172	−	0.329452i	$-0.893136\pi$
$479$	−4.08771	+	7.08012i	−0.186772	+	0.323499i	0.757400	+	0.652951i	$0.226469\pi$
$480$	4.14709	−	1.10009i	0.189288	−	0.0502122i
$481$	−1.96282			−0.0894969
$482$	2.03890	−	1.17716i	0.0928692	−	0.0536181i
$483$	14.2336	+	8.21775i	0.647650	+	0.373921i
$484$	−28.8051			−1.30932
$485$	−5.23969	+	5.21353i	−0.237922	+	0.236734i
$486$	−3.47829	−	6.02457i	−0.157778	−	0.273280i
$487$	−34.8661	+	20.1299i	−1.57993	+	0.912175i	−0.585066	+	0.810985i	$0.698932\pi$
$487$	−34.8661	+	20.1299i	−1.57993	+	0.912175i	−0.994867	+	0.101190i	$0.967735\pi$
$488$	−11.0067	+	6.35472i	−0.498249	+	0.287664i
$489$	14.8602			0.672004
$490$	−3.44357	−	12.9814i	−0.155565	−	0.586442i
$491$	−10.7013	−	18.5352i	−0.482943	−	0.836482i	0.516865	−	0.856067i	$-0.327099\pi$
$491$	−10.7013	−	18.5352i	−0.482943	−	0.836482i	−0.999808	+	0.0195847i	$0.993766\pi$
$492$	−4.03338	−	2.32868i	−0.181839	−	0.104985i
$493$	−34.4988	−	19.9179i	−1.55375	−	0.897057i
$494$	6.26958			0.282082
$495$	−2.51238	+	9.28333i	−0.112923	+	0.417255i
$496$	−2.10893	+	3.65277i	−0.0946937	+	0.164014i
$497$	11.4072	+	6.58597i	0.511684	+	0.295421i
$498$	−19.0365	+	10.9907i	−0.853047	+	0.492507i
$499$	1.15659	+	2.00327i	0.0517760	+	0.0896787i	0.890752	−	0.454490i	$-0.150178\pi$
$499$	1.15659	+	2.00327i	0.0517760	+	0.0896787i	−0.838976	+	0.544169i	$0.816845\pi$
$500$	7.96482	−	7.84612i	0.356198	−	0.350889i
$501$	5.14612	+	8.91334i	0.229912	+	0.398219i
$502$	−16.8056	+	9.70270i	−0.750069	+	0.433053i
$503$	26.5460	−	15.3263i	1.18363	−	0.683368i	0.226777	−	0.973947i	$-0.427181\pi$
$503$	26.5460	−	15.3263i	1.18363	−	0.683368i	0.956851	+	0.290579i	$0.0938479\pi$
$504$	−0.339785	+	0.588525i	−0.0151352	+	0.0262150i
$505$	−7.16334	+	26.4688i	−0.318764	+	1.17785i
$506$	−27.1058	+	46.9486i	−1.20500	+	2.08712i
$507$	9.06136	−	5.23158i	0.402429	−	0.232342i
$508$			16.7375i			0.742607i
$509$	−20.6488	−	35.7648i	−0.915243	−	1.58525i	−0.806544	−	0.591174i	$-0.798665\pi$
$509$	−20.6488	−	35.7648i	−0.915243	−	1.58525i	−0.108699	−	0.994075i	$-0.534668\pi$
$510$	−20.1659	+	20.0652i	−0.892962	+	0.888504i
$511$	−4.69865	+	8.13830i	−0.207856	+	0.360017i
$512$			1.00000i			0.0441942i
$513$	−8.79175	−	5.07592i	−0.388165	−	0.224107i
$514$	9.79361			0.431978
$515$	29.0552	+	7.86331i	1.28033	+	0.346499i
$516$	12.4262	−	1.97581i	0.547032	−	0.0869801i
$517$		−	35.5969i		−	1.56555i
$518$		−	0.712246i		−	0.0312943i
$519$	0.784776	−	1.35927i	0.0344478	−	0.0596654i
$520$	−1.60474	+	5.92956i	−0.0703723	+	0.260028i
$521$	−14.9052	+	25.8165i	−0.653007	+	1.13104i	0.329383	+	0.944196i	$0.393159\pi$
$521$	−14.9052	+	25.8165i	−0.653007	+	1.13104i	−0.982390	+	0.186844i	$0.940174\pi$
$522$	−3.54702	−	2.04787i	−0.155249	−	0.0896330i
$523$	−11.9870	+	6.92067i	−0.524153	+	0.302620i	−0.738632	−	0.674109i	$-0.764528\pi$
$523$	−11.9870	+	6.92067i	−0.524153	+	0.302620i	0.214479	+	0.976729i	$0.431195\pi$
$524$	3.25552			0.142218
$525$	−0.0478654	+	9.56368i	−0.00208902	+	0.417393i
$526$	−5.35669	+	9.27806i	−0.233563	+	0.404543i
$527$		−	27.9661i		−	1.21822i
$528$	−10.4839	−	6.05290i	−0.456255	−	0.263419i
$529$	25.4161	+	44.0219i	1.10505	+	1.91400i
$530$	2.84884	−	0.755710i	0.123746	−	0.0328259i
$531$	1.39778	+	2.42102i	0.0606584	+	0.105063i
$532$			2.27503i			0.0986352i
$533$	5.77472	−	3.33404i	0.250131	−	0.144413i
$534$	−2.68340	−	4.64778i	−0.116122	−	0.201129i
$535$	3.18447	−	3.16857i	0.137677	−	0.136989i
$536$	2.90302	−	5.02819i	0.125392	−	0.217185i
$537$			28.3241i			1.22227i
$538$		−	24.3081i		−	1.04800i
$539$	−18.9471	+	32.8174i	−0.816111	+	1.41355i
$540$	7.05094	−	7.01574i	0.303424	−	0.301909i
$541$	−6.39981	−	11.0848i	−0.275149	−	0.476573i	0.695023	−	0.718987i	$-0.255394\pi$
$541$	−6.39981	−	11.0848i	−0.275149	−	0.476573i	−0.970173	+	0.242414i	$0.922061\pi$
$542$	−12.9176	+	7.45800i	−0.554860	+	0.320348i
$543$			8.03723i			0.344911i
$544$	−3.31520	−	5.74209i	−0.142138	−	0.246190i
$545$	−7.10815	+	1.88557i	−0.304480	+	0.0807690i
$546$	−2.62734	−	4.55069i	−0.112440	−	0.194752i
$547$	14.1905	+	8.19289i	0.606742	+	0.350303i	0.771689	−	0.636000i	$-0.219412\pi$
$547$	14.1905	+	8.19289i	0.606742	+	0.350303i	−0.164947	+	0.986302i	$0.552745\pi$
$548$			16.4931i			0.704552i
$549$	4.33206	−	7.50335i	0.184888	−	0.320235i
$550$	−31.5452	−	0.157881i	−1.34509	−	0.00673208i
$551$	−13.7115			−0.584131
$552$	−14.2784	+	8.24361i	−0.607727	+	0.350871i
$553$	−9.55011	−	5.51376i	−0.406112	−	0.234469i
$554$	2.74719	−	4.75828i	0.116717	−	0.202160i
$555$	0.800822	−	2.95907i	0.0339930	−	0.125605i
$556$	4.73933	−	8.20876i	0.200992	−	0.348129i
$557$			27.8203i			1.17878i	0.807847	+	0.589392i	$0.200633\pi$
$557$			27.8203i			1.17878i	−0.807847	+	0.589392i	$0.799367\pi$
$558$		−	2.87535i		−	0.121723i
$559$	−6.44563	+	16.8218i	−0.272621	+	0.711487i
$560$	−2.15165	−	0.582308i	−0.0909238	−	0.0246070i
$561$	80.2663			3.38884
$562$	0.961672	+	0.555222i	0.0405657	+	0.0234206i
$563$			3.87180i			0.163177i	0.996666	+	0.0815885i	$0.0259993\pi$
$563$			3.87180i			0.163177i	−0.996666	+	0.0815885i	$0.974001\pi$
$564$	5.41300	−	9.37559i	0.227928	−	0.394783i
$565$	−27.6414	+	27.5034i	−1.16288	+	1.15707i
$566$	4.25533	+	7.37044i	0.178865	+	0.309803i
$567$			10.5472i			0.442941i
$568$	−11.4431	+	6.60669i	−0.480143	+	0.277210i
$569$	19.2800	−	33.3940i	0.808260	−	1.39995i	−0.105808	−	0.994387i	$-0.533743\pi$
$569$	19.2800	−	33.3940i	0.808260	−	1.39995i	0.914068	−	0.405561i	$-0.132924\pi$
$570$	−2.55796	+	9.45176i	−0.107141	+	0.395891i
$571$	9.75978	−	16.9044i	0.408434	−	0.707428i	−0.586280	−	0.810108i	$-0.699408\pi$
$571$	9.75978	−	16.9044i	0.408434	−	0.707428i	0.994714	+	0.102680i	$0.0327417\pi$
$572$	15.0102	−	8.66613i	0.627607	−	0.362349i
$573$	−10.2626	+	5.92512i	−0.428726	+	0.247525i
$574$	1.20982	+	2.09547i	0.0504968	+	0.0874631i
$575$	−21.6674	+	37.0989i	−0.903591	+	1.54713i
$576$	−0.340854	−	0.590377i	−0.0142023	−	0.0245990i
$577$	−10.0666	+	5.81197i	−0.419079	+	0.241955i	−0.694683	−	0.719316i	$-0.744455\pi$
$577$	−10.0666	+	5.81197i	−0.419079	+	0.241955i	0.275604	+	0.961271i	$0.411122\pi$
$578$	23.3499	+	13.4810i	0.971226	+	0.560738i
$579$	9.83692	−	17.0380i	0.408808	−	0.708077i
$580$	3.50955	−	12.9679i	0.145726	−	0.538464i
$581$	11.4201			0.473784
$582$	5.49297	+	3.17137i	0.227691	+	0.131457i
$583$	−7.20195	−	4.15805i	−0.298274	−	0.172209i
$584$	−4.71344	−	8.16391i	−0.195043	−	0.337825i
$585$	−1.07372	−	4.04765i	−0.0443927	−	0.167350i
$586$	7.82979			0.323446
$587$	36.7265	−	21.2041i	1.51587	−	0.875186i	0.516040	−	0.856565i	$-0.327406\pi$
$587$	36.7265	−	21.2041i	1.51587	−	0.875186i	0.999827	−	0.0186214i	$-0.00592772\pi$
$588$	−9.98067	+	5.76234i	−0.411596	+	0.237635i
$589$	−4.81298	−	8.33632i	−0.198315	−	0.343492i
$590$	−6.50016	+	6.46771i	−0.267607	+	0.266271i
$591$	13.5145			0.555914
$592$	0.618763	+	0.357243i	0.0254310	+	0.0146826i
$593$	7.28764	−	4.20752i	0.299268	−	0.172782i	−0.342846	−	0.939392i	$-0.611391\pi$
$593$	7.28764	−	4.20752i	0.299268	−	0.172782i	0.642114	+	0.766609i	$0.278058\pi$
$594$	−28.0648			−1.15151
$595$	14.2854	−	3.78948i	0.585646	−	0.155354i
$596$	−2.83928	+	4.91778i	−0.116301	+	0.201440i
$597$	−34.8981	−	20.1484i	−1.42828	−	0.824620i
$598$		−	23.6053i		−	0.965291i
$599$	−0.207163	+	0.358816i	−0.00846443	+	0.0146608i	−0.870227	−	0.492652i	$-0.836028\pi$
$599$	−0.207163	+	0.358816i	−0.00846443	+	0.0146608i	0.861762	+	0.507313i	$0.169361\pi$
$600$	−8.28444	−	4.83847i	−0.338211	−	0.197530i
$601$	−9.04393			−0.368909			−0.184455	−	0.982841i	$-0.559052\pi$
$601$	−9.04393			−0.368909			−0.184455	+	0.982841i	$0.559052\pi$
$602$	−6.10411	−	2.33892i	−0.248785	−	0.0953272i
$603$			3.95803i			0.161183i
$604$	3.73836			0.152112
$605$	45.4307	+	45.6586i	1.84702	+	1.85629i
$606$	23.5301			0.955844
$607$	−6.22957	−	3.59665i	−0.252851	−	0.145983i	0.368218	−	0.929739i	$-0.379968\pi$
$607$	−6.22957	−	3.59665i	−0.252851	−	0.145983i	−0.621069	+	0.783756i	$0.713301\pi$
$608$	−1.97644	−	1.14110i	−0.0801550	−	0.0462775i
$609$	5.74599	+	9.95235i	0.232839	+	0.403289i
$610$	27.4323	+	7.42409i	1.11070	+	0.300593i
$611$	7.74996	+	13.4233i	0.313530	+	0.543050i
$612$	3.91443	+	2.26000i	0.158231	+	0.0913549i
$613$			30.8828i			1.24734i	0.781687	+	0.623671i	$0.214360\pi$
$613$			30.8828i			1.24734i	−0.781687	+	0.623671i	$0.785640\pi$
$614$	−5.26043	+	9.11133i	−0.212294	+	0.367703i
$615$	2.67020	+	10.0660i	0.107673	+	0.405901i
$616$	3.14467	+	5.44673i	0.126702	+	0.219455i
$617$	13.7378	−	7.93152i	0.553063	−	0.319311i	−0.197293	−	0.980344i	$-0.563215\pi$
$617$	13.7378	−	7.93152i	0.553063	−	0.319311i	0.750356	+	0.661033i	$0.229882\pi$
$618$		−	25.8293i		−	1.03901i
$619$	14.4907	+	25.0986i	0.582430	+	1.00880i	0.995190	+	0.0979588i	$0.0312314\pi$
$619$	14.4907	+	25.0986i	0.582430	+	1.00880i	−0.412760	+	0.910840i	$0.635435\pi$
$620$	9.11613	−	2.41823i	0.366113	−	0.0971183i
$621$	−19.1111	+	33.1014i	−0.766902	+	1.32831i
$622$	17.9278	+	10.3506i	0.718839	+	0.415022i
$623$			2.78821i			0.111707i
$624$	5.27122			0.211018
$625$	−24.9987	−	0.250239i	−0.999950	−	0.0100096i
$626$	−14.7424	+	25.5345i	−0.589223	+	1.02056i
$627$	23.9263	−	13.8139i	0.955526	−	0.551673i
$628$	−12.5507	+	7.24613i	−0.500826	+	0.289152i
$629$	−4.73733			−0.188890
$630$	1.46877	−	0.389618i	0.0585171	−	0.0155228i
$631$	12.8991	+	22.3419i	0.513505	+	0.889417i	0.999877	+	0.0156656i	$0.00498671\pi$
$631$	12.8991	+	22.3419i	0.513505	+	0.889417i	−0.486372	+	0.873752i	$0.661680\pi$
$632$	9.58016	−	5.53111i	0.381078	−	0.220016i
$633$	39.8213	+	22.9909i	1.58276	+	0.913804i
$634$	1.23963			0.0492320
$635$	26.5305	−	26.3980i	1.05283	−	1.04757i
$636$	−1.26458	−	2.19031i	−0.0501437	−	0.0868514i
$637$		−	16.5003i		−	0.653764i
$638$	−32.8272	+	18.9528i	−1.29964	+	0.750349i
$639$	4.50383	−	7.80087i	0.178169	−	0.308598i
$640$	1.58509	−	1.57718i	0.0626562	−	0.0623434i
$641$	−29.7873			−1.17653			−0.588263	−	0.808670i	$-0.700188\pi$
$641$	−29.7873			−1.17653			−0.588263	+	0.808670i	$0.700188\pi$
$642$	−3.33840	−	1.92743i	−0.131756	−	0.0760694i
$643$			0.756238i			0.0298231i	0.999889	+	0.0149116i	$0.00474667\pi$
$643$			0.756238i			0.0298231i	−0.999889	+	0.0149116i	$0.995253\pi$
$644$	8.56561			0.337532
$645$	−22.7301	−	16.5804i	−0.894997	−	0.652853i
$646$	15.1318			0.595353
$647$		−	18.0395i		−	0.709207i	−0.935017	−	0.354603i	$-0.884616\pi$
$647$		−	18.0395i		−	0.709207i	0.935017	−	0.354603i	$-0.115384\pi$
$648$	−9.16289	−	5.29020i	−0.359952	−	0.207819i
$649$	25.8725			1.01559
$650$	11.9298	−	6.80832i	0.467927	−	0.267044i
$651$	−4.03387	+	6.98688i	−0.158100	+	0.273837i
$652$	6.70706	−	3.87232i	0.262669	−	0.151652i
$653$			7.90049i			0.309170i	0.987979	+	0.154585i	$0.0494041\pi$
$653$			7.90049i			0.309170i	−0.987979	+	0.154585i	$0.950596\pi$
$654$	3.15524	+	5.46504i	0.123380	+	0.213700i
$655$	−5.13453	−	5.16030i	−0.200623	−	0.201629i
$656$	−2.42725			−0.0947682
$657$	5.56540	+	3.21319i	0.217127	+	0.125358i
$658$	−4.87090	+	2.81222i	−0.189888	+	0.109632i
$659$	12.5263	+	21.6962i	0.487955	+	0.845164i	0.999904	−	0.0138525i	$-0.00440952\pi$
$659$	12.5263	+	21.6962i	0.487955	+	0.845164i	−0.511949	+	0.859016i	$0.671076\pi$
$660$	6.94063	+	26.1645i	0.270164	+	1.01845i
$661$	22.6102			0.879435			0.439717	−	0.898136i	$-0.355079\pi$
$661$	22.6102			0.879435			0.439717	+	0.898136i	$0.355079\pi$
$662$	−3.17018	+	1.83031i	−0.123213	+	0.0711369i
$663$	−30.2678	+	17.4751i	−1.17550	+	0.678677i
$664$	−5.72799	+	9.92118i	−0.222289	+	0.385016i
$665$	3.60613	−	3.58813i	0.139840	−	0.139142i
$666$	−0.487071			−0.0188736
$667$			51.6247i			1.99891i
$668$	4.64532	+	2.68198i	0.179733	+	0.103769i
$669$	−17.5226	+	30.3501i	−0.677463	+	1.17340i
$670$	−12.5487	+	3.32878i	−0.484799	+	0.128602i
$671$	−40.0927	−	69.4426i	−1.54776	−	2.68080i
$672$			1.91276i			0.0737863i
$673$	−19.4600	+	11.2352i	−0.750128	+	0.433087i	−0.825740	−	0.564051i	$-0.809242\pi$
$673$	−19.4600	+	11.2352i	−0.750128	+	0.433087i	0.0756123	+	0.997137i	$0.475909\pi$
$674$	−2.78746	−	4.82802i	−0.107369	−	0.185968i
$675$	−22.2412	−	0.111315i	−0.856062	−	0.00428452i
$676$	2.72651	−	4.72246i	0.104866	−	0.181633i
$677$		−	7.90493i		−	0.303811i	−0.988395	−	0.151906i	$-0.951459\pi$
$677$		−	7.90493i		−	0.303811i	0.988395	−	0.151906i	$-0.0485410\pi$
$678$	28.9775	+	16.7302i	1.11287	+	0.642518i
$679$	−1.64762	−	2.85376i	−0.0632299	−	0.109517i
$680$	−3.87308	+	14.3112i	−0.148526	+	0.548809i
$681$	−0.797129	−	1.38067i	−0.0305460	−	0.0529073i
$682$	−23.0458	−	13.3055i	−0.882469	−	0.509494i
$683$	−24.7836	−	14.3088i	−0.948318	−	0.547512i	−0.0557599	−	0.998444i	$-0.517758\pi$
$683$	−24.7836	−	14.3088i	−0.948318	−	0.547512i	−0.892558	+	0.450933i	$0.851091\pi$
$684$	1.55579			0.0594871
$685$	26.1431	−	26.0126i	0.998877	−	0.993891i
$686$	12.9655			0.495024
$687$			43.8275i			1.67212i
$688$	5.09359	−	4.12981i	0.194191	−	0.157447i
$689$	3.62107			0.137952
$690$	35.5864	+	9.63085i	1.35475	+	0.366640i
$691$	16.4718	−	28.5300i	0.626618	−	1.08533i	−0.361608	−	0.932330i	$-0.617772\pi$
$691$	16.4718	−	28.5300i	0.626618	−	1.08533i	0.988226	−	0.153003i	$-0.0488945\pi$
$692$		−	0.817995i		−	0.0310955i
$693$	−3.71308	−	2.14375i	−0.141048	−	0.0814342i
$694$	6.65360	−	11.5244i	0.252567	−	0.437459i
$695$	−20.4864	+	5.43440i	−0.777093	+	0.206139i
$696$	−11.5281			−0.436973
$697$	13.9375	−	8.04681i	0.527920	−	0.304795i
$698$	4.70850	+	2.71845i	0.178219	+	0.102895i
$699$	8.50255			0.321596
$700$	2.47052	+	4.32896i	0.0933770	+	0.163619i
$701$	−21.6920	−	37.5716i	−0.819294	−	1.41906i	−0.906203	−	0.422843i	$-0.861032\pi$
$701$	−21.6920	−	37.5716i	−0.819294	−	1.41906i	0.0869091	−	0.996216i	$-0.472301\pi$
$702$	10.5830	−	6.11011i	0.399430	−	0.230611i
$703$	−1.41214	+	0.815297i	−0.0532597	+	0.0307495i
$704$	−6.30912			−0.237784
$705$	−23.3984	+	6.20687i	−0.881235	+	0.233764i
$706$	6.22041	+	10.7741i	0.234108	+	0.405487i
$707$	−10.5868	−	6.11229i	−0.398158	−	0.229876i
$708$	6.81436	+	3.93427i	0.256099	+	0.147859i
$709$	26.0811			0.979498			0.489749	−	0.871863i	$-0.337088\pi$
$709$	26.0811			0.979498			0.489749	+	0.871863i	$0.337088\pi$
$710$	28.5200	+	7.71846i	1.07034	+	0.289669i
$711$	−3.77060	+	6.53087i	−0.141409	+	0.244927i
$712$	−2.42226	−	1.39849i	−0.0907781	−	0.0524107i
$713$	−31.3867	+	18.1211i	−1.17544	+	0.678641i
$714$	−6.34117	−	10.9832i	−0.237312	−	0.411037i
$715$	−37.4103	−	10.1245i	−1.39907	−	0.378634i
$716$	7.38076	+	12.7838i	0.275832	+	0.477755i
$717$	−12.8345	+	7.40999i	−0.479312	+	0.276731i
$718$	2.76341	−	1.59546i	0.103130	−	0.0595420i
$719$	6.13416	−	10.6247i	0.228766	−	0.396234i	−0.728677	−	0.684858i	$-0.759864\pi$
$719$	6.13416	−	10.6247i	0.228766	−	0.396234i	0.957443	+	0.288624i	$0.0931977\pi$
$720$	−0.398213	+	1.47141i	−0.0148405	+	0.0548363i
$721$	−6.70956	+	11.6213i	−0.249877	+	0.432800i
$722$	−11.9439	+	6.89580i	−0.444505	+	0.256635i
$723$			4.51741i			0.168004i
$724$	2.09436	+	3.62754i	0.0778364	+	0.134817i
$725$	−26.0905	+	14.8898i	−0.968978	+	0.552992i
$726$	27.6353	−	47.8657i	1.02564	−	1.77646i
$727$		−	14.7683i		−	0.547726i	−0.961769	−	0.273863i	$-0.911699\pi$
$727$		−	14.7683i		−	0.547726i	0.961769	−	0.273863i	$-0.0883015\pi$
$728$	−2.37166	−	1.36928i	−0.0878996	−	0.0507489i
$729$	−18.3931			−0.681225
$730$	−5.50661	+	20.3472i	−0.203809	+	0.753082i
$731$	−15.5567	+	40.6000i	−0.575387	+	1.50164i
$732$		−	24.3866i		−	0.901354i
$733$		−	8.70977i		−	0.321703i	−0.986979	−	0.160851i	$-0.948576\pi$
$733$		−	8.70977i		−	0.321703i	0.986979	−	0.160851i	$-0.0514240\pi$
$734$	−15.1268	+	26.2004i	−0.558341	+	0.967074i
$735$	24.8751	+	6.73203i	0.917533	+	0.248315i
$736$	−4.29628	+	7.44138i	−0.158363	+	0.274293i
$737$	31.7234	+	18.3155i	1.16855	+	0.674662i
$738$	1.43299	−	0.827338i	0.0527491	−	0.0304547i
$739$	8.66547			0.318764			0.159382	−	0.987217i	$-0.449050\pi$
$739$	8.66547			0.318764			0.159382	+	0.987217i	$0.449050\pi$
$740$	−0.409637	−	1.54423i	−0.0150585	−	0.0567671i
$741$	−6.01496	+	10.4182i	−0.220965	+	0.382723i
$742$			1.31397i			0.0482374i
$743$	−27.5705	−	15.9178i	−1.01146	−	0.583969i	−0.0998443	−	0.995003i	$-0.531834\pi$
$743$	−27.5705	−	15.9178i	−1.01146	−	0.583969i	−0.911620	+	0.411034i	$0.865168\pi$
$744$	−4.04657	−	7.00886i	−0.148354	−	0.256957i
$745$	12.2732	−	3.25569i	0.449654	−	0.119279i
$746$	−16.7697	−	29.0459i	−0.613981	−	1.06345i
$747$		−	7.80964i		−	0.285740i
$748$	36.2276	−	20.9160i	1.32461	−	0.764764i
$749$	1.00136	+	1.73440i	0.0365888	+	0.0633736i
$750$	5.39662	+	20.7627i	0.197057	+	0.758147i
$751$	−8.98679	+	15.5656i	−0.327933	+	0.567996i	−0.982101	−	0.188353i	$-0.939685\pi$
$751$	−8.98679	+	15.5656i	−0.327933	+	0.567996i	0.654169	+	0.756349i	$0.273019\pi$
$752$		−	5.64213i		−	0.205747i
$753$		−	37.2346i		−	1.35691i
$754$	8.25260	−	14.2939i	0.300542	−	0.520554i
$755$	−5.89606	−	5.92564i	−0.214580	−	0.215656i
$756$	2.21717	+	3.84025i	0.0806376	+	0.139668i
$757$	2.98682	−	1.72444i	0.108558	−	0.0626760i	−0.444738	−	0.895661i	$-0.646703\pi$
$757$	2.98682	−	1.72444i	0.108558	−	0.0626760i	0.553296	+	0.832985i	$0.313370\pi$
$758$			37.6956i			1.36916i
$759$	−52.0100	−	90.0839i	−1.88784	−	3.26984i
$760$	1.30845	+	4.93254i	0.0474624	+	0.178922i
$761$	9.58432	+	16.6005i	0.347431	+	0.601768i	0.985792	−	0.167969i	$-0.0537207\pi$
$761$	9.58432	+	16.6005i	0.347431	+	0.601768i	−0.638361	+	0.769737i	$0.720387\pi$
$762$	−27.8129	−	16.0578i	−1.00755	−	0.581712i
$763$		−	3.27849i		−	0.118689i
$764$	−3.08796	+	5.34851i	−0.111719	+	0.193502i
$765$	−2.59145	−	9.76914i	−0.0936940	−	0.353204i
$766$	1.65236			0.0597021
$767$	−9.75634	+	5.63282i	−0.352281	+	0.203389i
$768$	−1.66171	−	0.959389i	−0.0599618	−	0.0346190i
$769$	18.4569	−	31.9684i	0.665574	−	1.15281i	−0.313555	−	0.949570i	$-0.601520\pi$
$769$	18.4569	−	31.9684i	0.665574	−	1.15281i	0.979129	−	0.203239i	$-0.0651467\pi$
$770$	3.67385	−	13.5750i	0.132396	−	0.489210i
$771$	−9.39588	+	16.2741i	−0.338384	+	0.586099i
$772$		−	10.2533i		−	0.369025i
$773$			35.1311i			1.26358i	0.775141	+	0.631788i	$0.217679\pi$
$773$			35.1311i			1.26358i	−0.775141	+	0.631788i	$0.782321\pi$
$774$	−1.59948	+	4.17431i	−0.0574920	+	0.150043i
$775$	−18.2109	−	10.6359i	−0.654153	−	0.382054i
$776$	3.30561			0.118664
$777$	1.18355	+	0.683320i	0.0424595	+	0.0245140i
$778$		−	0.410501i		−	0.0147172i
$779$	2.76972	−	4.79730i	0.0992356	−	0.171881i
$780$	−8.31365	−	8.35536i	−0.297676	−	0.299170i
$781$	−41.6824	−	72.1961i	−1.49151	−	2.58338i
$782$		−	56.9721i		−	2.03732i
$783$	−23.1450	+	13.3628i	−0.827136	+	0.477547i
$784$	−3.00313	+	5.20158i	−0.107255	+	0.185771i
$785$	31.2804	+	8.46551i	1.11645	+	0.302147i
$786$	−3.12331	+	5.40973i	−0.111405	+	0.192959i
$787$	0.582205	−	0.336136i	0.0207534	−	0.0119820i	−0.489587	−	0.871954i	$-0.662853\pi$
$787$	0.582205	−	0.336136i	0.0207534	−	0.0119820i	0.510341	+	0.859972i	$0.329519\pi$
$788$	6.09968	−	3.52165i	0.217292	−	0.125454i
$789$	−10.2783	−	17.8025i	−0.365917	−	0.633787i
$790$	−23.8769	−	6.46188i	−0.849503	−	0.229904i
$791$	−8.69182	−	15.0547i	−0.309046	−	0.535283i
$792$	3.72476	−	2.15049i	0.132354	−	0.0764144i
$793$	30.2373	+	17.4575i	1.07376	+	0.619935i
$794$	−0.435217	+	0.753818i	−0.0154453	+	0.0267520i
$795$	−1.47738	+	5.45897i	−0.0523972	+	0.193610i
$796$	−21.0013			−0.744371
$797$	−3.13087	−	1.80761i	−0.110901	−	0.0640288i	0.443523	−	0.896263i	$-0.353728\pi$
$797$	−3.13087	−	1.80761i	−0.110901	−	0.0640288i	−0.554425	+	0.832234i	$0.687062\pi$
$798$	−3.78045	−	2.18264i	−0.133826	−	0.0772647i
$799$	18.7048	+	32.3976i	0.661727	+	1.14615i
$800$	−4.99994	−	0.0250243i	−0.176774	−	0.000884741i
$801$	1.90673			0.0673709
$802$	−20.2530	+	11.6931i	−0.715157	+	0.412896i
$803$	51.5071	−	29.7377i	1.81765	−	1.04942i
$804$	5.57026	+	9.64797i	0.196448	+	0.340258i
$805$	−13.5095	−	13.5773i	−0.476147	−	0.478536i
$806$	11.5872			0.408142
$807$	40.3930	+	23.3209i	1.42190	+	0.820936i
$808$	10.6201	−	6.13153i	0.373614	−	0.215706i
$809$	−3.16443			−0.111256			−0.0556278	−	0.998452i	$-0.517716\pi$
$809$	−3.16443			−0.111256			−0.0556278	+	0.998452i	$0.517716\pi$
$810$	6.06606	+	22.8676i	0.213140	+	0.803486i
$811$	−20.3753	+	35.2911i	−0.715474	+	1.23924i	0.247302	+	0.968939i	$0.420456\pi$
$811$	−20.3753	+	35.2911i	−0.715474	+	1.23924i	−0.962776	+	0.270300i	$0.912877\pi$
$812$	5.18682	+	2.99461i	0.182022	+	0.105090i
$813$		−	28.6205i		−	1.00376i
$814$	−2.25389	+	3.90386i	−0.0789989	+	0.136830i
$815$	−16.7162	−	4.52396i	−0.585543	−	0.158467i
$816$	12.7222			0.445368
$817$	2.35002	+	14.7797i	0.0822169	+	0.517075i
$818$			13.5812i			0.474854i
$819$	1.86690			0.0652347
$820$	3.82820	+	3.84741i	0.133687	+	0.134357i
$821$	−3.21995			−0.112377			−0.0561884	−	0.998420i	$-0.517895\pi$
$821$	−3.21995			−0.112377			−0.0561884	+	0.998420i	$0.517895\pi$
$822$	−27.4068	−	15.8233i	−0.955923	−	0.551902i
$823$	18.0786	+	10.4377i	0.630181	+	0.363835i	0.780822	−	0.624753i	$-0.214800\pi$
$823$	18.0786	+	10.4377i	0.630181	+	0.363835i	−0.150641	+	0.988589i	$0.548134\pi$
$824$	−6.73067	−	11.6579i	−0.234474	−	0.406121i
$825$	30.5265	−	52.2676i	1.06280	−	1.81972i
$826$	−2.04397	−	3.54027i	−0.0711190	−	0.123182i
$827$	13.0702	+	7.54607i	0.454494	+	0.262402i	0.709726	−	0.704477i	$-0.248819\pi$
$827$	13.0702	+	7.54607i	0.454494	+	0.262402i	−0.255232	+	0.966880i	$0.582152\pi$
$828$		−	5.85762i		−	0.203566i
$829$	−27.7174	+	48.0079i	−0.962663	+	1.66738i	−0.246898	+	0.969042i	$0.579411\pi$
$829$	−27.7174	+	48.0079i	−0.962663	+	1.66738i	−0.715766	+	0.698340i	$0.753922\pi$
$830$	24.7600	−	6.56806i	0.859433	−	0.227981i
$831$	5.27125	+	9.13008i	0.182858	+	0.316719i
$832$	2.37912	−	1.37359i	0.0824813	−	0.0476206i
$833$		−	39.8239i		−	1.37982i
$834$	9.09372	+	15.7508i	0.314890	+	0.545405i
$835$	−3.07532	−	11.5932i	−0.106426	−	0.401199i
$836$	7.19931	−	12.4696i	0.248993	−	0.431269i
$837$	−16.2486	−	9.38112i	−0.561633	−	0.324259i
$838$		−	14.5466i		−	0.502504i
$839$	2.07782			0.0717342			0.0358671	−	0.999357i	$-0.488581\pi$
$839$	2.07782			0.0717342			0.0358671	+	0.999357i	$0.488581\pi$
$840$	3.03190	−	3.01676i	0.104610	−	0.104088i
$841$	−3.54841	+	6.14602i	−0.122359	+	0.211932i
$842$	11.0124	−	6.35799i	0.379511	−	0.219111i
$843$	−1.84523	+	1.06535i	−0.0635533	+	0.0366925i
$844$	23.9641			0.824877
$845$	−11.7857	+	3.12639i	−0.405441	+	0.107551i
$846$	1.92314	+	3.33098i	0.0661190	+	0.114522i
$847$	−24.8677	+	14.3574i	−0.854463	+	0.493325i
$848$	−1.14151	−	0.659053i	−0.0391997	−	0.0226320i
$849$	−16.3301			−0.560446
$850$	28.7930	−	16.4321i	0.987593	−	0.563616i
$851$	3.06964	+	5.31676i	0.105226	+	0.182256i
$852$		−	25.3535i		−	0.868598i
$853$	8.94179	−	5.16255i	0.306161	−	0.176762i	−0.339046	−	0.940770i	$-0.610104\pi$
$853$	8.94179	−	5.16255i	0.306161	−	0.176762i	0.645207	+	0.764008i	$0.276771\pi$
$854$	−6.33478	+	10.9722i	−0.216772	+	0.375460i
$855$	−2.45375	−	2.46607i	−0.0839166	−	0.0843377i
$856$	−2.00901			−0.0686667
$857$	28.1454	+	16.2497i	0.961428	+	0.555081i	0.896612	−	0.442817i	$-0.146021\pi$
$857$	28.1454	+	16.2497i	0.961428	+	0.555081i	0.0648157	+	0.997897i	$0.479354\pi$
$858$			33.2568i			1.13537i
$859$	−53.7808			−1.83498			−0.917488	−	0.397763i	$-0.869787\pi$
$859$	−53.7808			−1.83498			−0.917488	+	0.397763i	$0.869787\pi$
$860$	−14.5796	−	1.56037i	−0.497161	−	0.0532081i
$861$	−4.64274			−0.158224
$862$			29.0476i			0.989364i
$863$	9.61921	+	5.55366i	0.327442	+	0.189049i	0.654705	−	0.755885i	$-0.272793\pi$
$863$	9.61921	+	5.55366i	0.327442	+	0.189049i	−0.327263	+	0.944933i	$0.606126\pi$
$864$	−4.44829			−0.151334
$865$	−1.29660	+	1.29012i	−0.0440856	+	0.0438655i
$866$	−5.52428	+	9.56834i	−0.187723	+	0.325145i
$867$	−44.8032	+	25.8671i	−1.52160	+	0.878494i
$868$			4.20463i			0.142714i
$869$	34.8965	+	60.4424i	1.18378	+	2.05037i
$870$	18.1819	+	18.2731i	0.616425	+	0.619518i
$871$	−15.9502			−0.540453
$872$	2.84819	+	1.64440i	0.0964518	+	0.0556865i
$873$	−1.95155	+	1.12673i	−0.0660501	+	0.0381341i
$874$	−9.80493	−	16.9826i	−0.331657	−	0.574447i
$875$	2.96535	−	10.7435i	0.100247	−	0.363198i
$876$	18.0881			0.611139
$877$	−2.26405	+	1.30715i	−0.0764514	+	0.0441392i	−0.537738	−	0.843112i	$-0.680721\pi$
$877$	−2.26405	+	1.30715i	−0.0764514	+	0.0441392i	0.461287	+	0.887251i	$0.347388\pi$
$878$	−1.41244	+	0.815471i	−0.0476674	+	0.0275208i
$879$	−7.51181	+	13.0108i	−0.253367	+	0.438845i
$880$	9.95061	+	10.0005i	0.335435	+	0.337118i
$881$	49.6244			1.67189			0.835945	−	0.548813i	$-0.184920\pi$
$881$	49.6244			1.67189			0.835945	+	0.548813i	$0.184920\pi$
$882$		−	4.09452i		−	0.137870i
$883$	22.9381	+	13.2433i	0.771928	+	0.445673i	0.833562	−	0.552426i	$-0.186298\pi$
$883$	22.9381	+	13.2433i	0.771928	+	0.445673i	−0.0616337	+	0.998099i	$0.519631\pi$
$884$	−9.10742	+	15.7745i	−0.306316	+	0.530555i
$885$	−4.51128	−	17.0064i	−0.151645	−	0.571665i
$886$	2.14799	+	3.72043i	0.0721633	+	0.124990i
$887$		−	18.5306i		−	0.622198i	−0.950378	−	0.311099i	$-0.899303\pi$
$887$		−	18.5306i		−	0.622198i	0.950378	−	0.311099i	$-0.100697\pi$
$888$	−1.18727	+	0.685470i	−0.0398422	+	0.0230029i
$889$	8.34250	+	14.4496i	0.279799	+	0.484625i
$890$	1.60360	+	6.04517i	0.0537527	+	0.202635i
$891$	33.3765	−	57.8098i	1.11816	−	1.93670i
$892$			18.2644i			0.611536i
$893$	11.1513	+	6.43821i	0.373164	+	0.215446i
$894$	−5.44795	−	9.43612i	−0.182207	−	0.315591i
$895$	8.62279	−	31.8616i	0.288228	−	1.06501i
$896$	0.498432	+	0.863309i	0.0166514	+	0.0288411i
$897$	39.2251	+	22.6466i	1.30969	+	0.756149i
$898$	2.86214	+	1.65246i	0.0955108	+	0.0551432i
$899$	−25.3412			−0.845175
$900$	2.96038	−	1.68948i	0.0986792	−	0.0563159i
$901$	8.73956			0.291157
$902$		−	15.3138i		−	0.509894i
$903$	9.74282	−	7.89933i	0.324221	−	0.262873i
$904$	17.4383			0.579991
$905$	2.44680	−	9.04103i	0.0813345	−	0.300534i
$906$	−3.58654	+	6.21208i	−0.119155	+	0.206382i
$907$		−	26.3405i		−	0.874623i	−0.899310	−	0.437312i	$-0.855931\pi$
$907$		−	26.3405i		−	0.874623i	0.899310	−	0.437312i	$-0.144069\pi$
$908$	−0.719556	−	0.415436i	−0.0238793	−	0.0137867i
$909$	−4.17991	+	7.23982i	−0.138639	+	0.240130i
$910$	1.57010	+	5.91889i	0.0520483	+	0.196209i
$911$	29.1788			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$911$	29.1788			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$912$	3.79234	−	2.18951i	0.125577	−	0.0725019i
$913$	−62.5939	−	36.1386i	−2.07156	−	1.19601i
$914$	16.6561			0.550934
$915$	−38.6549	+	38.4620i	−1.27789	+	1.27151i
$916$	11.4207	+	19.7812i	0.377350	+	0.653589i
$917$	2.81052	−	1.62266i	0.0928116	−	0.0535848i
$918$	25.5425	−	14.7469i	0.843027	−	0.486722i
$919$	−33.0962			−1.09174			−0.545871	−	0.837869i	$-0.683801\pi$
$919$	−33.0962			−1.09174			−0.545871	+	0.837869i	$0.683801\pi$
$920$	18.5713	−	4.92638i	0.612276	−	0.162418i
$921$	−10.0936	−	17.4826i	−0.332595	−	0.576072i
$922$	20.3494	+	11.7487i	0.670172	+	0.386924i
$923$	31.4363	+	18.1497i	1.03474	+	0.597406i
$924$	−12.0678			−0.397003
$925$	−1.80168	+	3.08484i	−0.0592388	+	0.101429i
$926$	13.2752	−	22.9933i	0.436250	−	0.755607i
$927$	7.94726	+	4.58835i	0.261022	+	0.150701i
$928$	−5.20313	+	3.00403i	−0.170801	+	0.0986122i
$929$	5.84908	+	10.1309i	0.191902	+	0.332384i	0.945881	−	0.324515i	$-0.105201\pi$
$929$	5.84908	+	10.1309i	0.191902	+	0.332384i	−0.753978	+	0.656899i	$0.771868\pi$
$930$	−4.72752	+	17.4684i	−0.155022	+	0.572811i
$931$	−6.85372	−	11.8710i	−0.224622	−	0.389056i
$932$	3.83756	−	2.21562i	0.125703	−	0.0725749i
$933$	−34.3994	+	19.8605i	−1.12619	+	0.650204i
$934$	−6.47852	+	11.2211i	−0.211984	+	0.367167i
$935$	−90.2910	−	24.4357i	−2.95283	−	0.799134i
$936$	−0.936386	+	1.62187i	−0.0306067	+	0.0530124i
$937$	17.4791	−	10.0916i	0.571017	−	0.329677i	−0.186539	−	0.982448i	$-0.559727\pi$
$937$	17.4791	−	10.0916i	0.571017	−	0.329677i	0.757555	+	0.652771i	$0.226394\pi$
$938$		−	5.78784i		−	0.188980i
$939$	−28.2873	−	48.9951i	−0.923122	−	1.59889i
$940$	−8.94329	+	8.89864i	−0.291698	+	0.290242i
$941$	12.6337	−	21.8823i	0.411848	−	0.713342i	−0.583244	−	0.812297i	$-0.698217\pi$
$941$	12.6337	−	21.8823i	0.411848	−	0.713342i	0.995092	+	0.0989550i	$0.0315500\pi$
$942$		−	27.8074i		−	0.906015i
$943$	−18.0621	−	10.4281i	−0.588182	−	0.339587i
$944$	4.10081			0.133470
$945$	2.59027	−	9.57116i	0.0842616	−	0.311350i
$946$	26.0555	+	32.1361i	0.847137	+	1.04484i
$947$			35.8652i			1.16546i	0.812664	+	0.582732i	$0.198016\pi$
$947$			35.8652i			1.16546i	−0.812664	+	0.582732i	$0.801984\pi$
$948$			21.2259i			0.689386i
$949$	−12.9486	+	22.4277i	−0.420330	+	0.728034i
$950$	5.75486	−	9.85350i	0.186712	−	0.319690i
$951$	−1.18929	+	2.05991i	−0.0385653	+	0.0667970i
$952$	−5.72408	−	3.30480i	−0.185518	−	0.107109i
$953$	21.4925	−	12.4087i	0.696210	−	0.401957i	−0.109724	−	0.993962i	$-0.534997\pi$
$953$	21.4925	−	12.4087i	0.696210	−	0.401957i	0.805934	+	0.592005i	$0.201663\pi$
$954$	0.898563			0.0290921
$955$	13.3481	−	3.54085i	0.431936	−	0.114579i
$956$	−3.86183	+	6.68888i	−0.124900	+	0.216334i
$957$		−	72.7325i		−	2.35111i
$958$	−7.08012	−	4.08771i	−0.228748	−	0.132068i
$959$	8.22071	+	14.2387i	0.265460	+	0.459791i
$960$	1.10009	+	4.14709i	0.0355054	+	0.133847i
$961$	6.60483	+	11.4399i	0.213059	+	0.369029i
$962$		−	1.96282i		−	0.0632838i
$963$	1.18607	−	0.684781i	0.0382207	−	0.0220667i
$964$	1.17716	+	2.03890i	0.0379137	+	0.0656685i
$965$	−16.2524	+	16.1713i	−0.523184	+	0.520572i
$966$	−8.21775	+	14.2336i	−0.264402	+	0.457958i
$967$			3.27120i			0.105195i	0.998616	+	0.0525973i	$0.0167500\pi$
$967$			3.27120i			0.105195i	−0.998616	+	0.0525973i	$0.983250\pi$
$968$		−	28.8051i		−	0.925830i
$969$	−14.5173	+	25.1447i	−0.466363	+	0.807764i
$970$	−5.21353	−	5.23969i	−0.167396	−	0.168236i
$971$	−18.7712	−	32.5127i	−0.602398	−	1.04338i	−0.992457	−	0.122594i	$-0.960879\pi$
$971$	−18.7712	−	32.5127i	−0.602398	−	1.04338i	0.390059	−	0.920790i	$-0.372455\pi$
$972$	6.02457	−	3.47829i	0.193238	−	0.111566i
$973$		−	9.44893i		−	0.302919i
$974$	−20.1299	−	34.8661i	−0.645005	−	1.11718i
$975$	−0.131908	+	26.3558i	−0.00422445	+	0.844060i
$976$	−6.35472	−	11.0067i	−0.203409	−	0.352316i
$977$	−21.0463	−	12.1511i	−0.673331	−	0.388748i	0.124006	−	0.992281i	$-0.460426\pi$
$977$	−21.0463	−	12.1511i	−0.673331	−	0.388748i	−0.797338	+	0.603533i	$0.793759\pi$
$978$			14.8602i			0.475178i
$979$	8.82327	−	15.2823i	0.281993	−	0.488426i
$980$	12.9814	−	3.44357i	0.414677	−	0.110001i
$981$	−2.24200			−0.0715817
$982$	18.5352	−	10.7013i	0.591482	−	0.341492i
$983$	−34.7620	−	20.0698i	−1.10873	−	0.640128i	−0.170233	−	0.985404i	$-0.554452\pi$
$983$	−34.7620	−	20.0698i	−1.10873	−	0.640128i	−0.938501	+	0.345276i	$0.887785\pi$
$984$	2.32868	−	4.03338i	0.0742355	−	0.128580i
$985$	−15.2024	−	4.11428i	−0.484389	−	0.131092i
$986$	19.9179	−	34.4988i	0.634315	−	1.09867i
$987$		−	10.7920i		−	0.343514i
$988$			6.26958i			0.199462i
$989$	55.6462	−	8.84795i	1.76945	−	0.281349i
$990$	−9.28333	−	2.51238i	−0.295044	−	0.0798486i
$991$	42.1623			1.33933			0.669664	−	0.742664i	$-0.266438\pi$
$991$	42.1623			1.33933			0.669664	+	0.742664i	$0.266438\pi$
$992$	−3.65277	−	2.10893i	−0.115976	−	0.0669586i
$993$		−	7.02390i		−	0.222897i
$994$	−6.58597	+	11.4072i	−0.208894	+	0.361815i
$995$	33.1228	+	33.2890i	1.05006	+	1.05533i
$996$	−10.9907	−	19.0365i	−0.348255	−	0.603196i
$997$			41.1031i			1.30175i	0.759185	+	0.650875i	$0.225598\pi$
$997$			41.1031i			1.30175i	−0.759185	+	0.650875i	$0.774402\pi$
$998$	−2.00327	+	1.15659i	−0.0634124	+	0.0366112i
$999$	−1.58912	+	2.75244i	−0.0502775	+	0.0870833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.j.a.49.14	yes	44
5.4	even	2	inner	430.2.j.a.49.9	✓	44
43.36	even	3	inner	430.2.j.a.79.20	yes	44
215.79	even	6	inner	430.2.j.a.79.3	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.j.a.49.9	✓	44	5.4	even	2	inner
430.2.j.a.49.14	yes	44	1.1	even	1	trivial
430.2.j.a.79.3	yes	44	215.79	even	6	inner
430.2.j.a.79.20	yes	44	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.66171 - 0.959389i) q^{3} -1.00000 q^{4} +(1.57718 + 1.58509i) q^{5} +(0.959389 - 1.66171i) q^{6} +(-0.863309 + 0.498432i) q^{7} -1.00000i q^{8} +(0.340854 + 0.590377i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.66171 - 0.959389i) q^{3} -1.00000 q^{4} +(1.57718 + 1.58509i) q^{5} +(0.959389 - 1.66171i) q^{6} +(-0.863309 + 0.498432i) q^{7} -1.00000i q^{8} +(0.340854 + 0.590377i) q^{9} +(-1.58509 + 1.57718i) q^{10} +6.30912 q^{11} +(1.66171 + 0.959389i) q^{12} +(-2.37912 + 1.37359i) q^{13} +(-0.498432 - 0.863309i) q^{14} +(-1.10009 - 4.14709i) q^{15} +1.00000 q^{16} +(-5.74209 + 3.31520i) q^{17} +(-0.590377 + 0.340854i) q^{18} +(-1.14110 + 1.97644i) q^{19} +(-1.57718 - 1.58509i) q^{20} +1.91276 q^{21} +6.30912i q^{22} +(7.44138 + 4.29628i) q^{23} +(-0.959389 + 1.66171i) q^{24} +(-0.0250243 + 4.99994i) q^{25} +(-1.37359 - 2.37912i) q^{26} +4.44829i q^{27} +(0.863309 - 0.498432i) q^{28} +(3.00403 + 5.20313i) q^{29} +(4.14709 - 1.10009i) q^{30} +(-2.10893 + 3.65277i) q^{31} +1.00000i q^{32} +(-10.4839 - 6.05290i) q^{33} +(-3.31520 - 5.74209i) q^{34} +(-2.15165 - 0.582308i) q^{35} +(-0.340854 - 0.590377i) q^{36} +(0.618763 + 0.357243i) q^{37} +(-1.97644 - 1.14110i) q^{38} +5.27122 q^{39} +(1.58509 - 1.57718i) q^{40} -2.42725 q^{41} +1.91276i q^{42} +(5.09359 - 4.12981i) q^{43} -6.30912 q^{44} +(-0.398213 + 1.47141i) q^{45} +(-4.29628 + 7.44138i) q^{46} -5.64213i q^{47} +(-1.66171 - 0.959389i) q^{48} +(-3.00313 + 5.20158i) q^{49} +(-4.99994 - 0.0250243i) q^{50} +12.7222 q^{51} +(2.37912 - 1.37359i) q^{52} +(-1.14151 - 0.659053i) q^{53} -4.44829 q^{54} +(9.95061 + 10.0005i) q^{55} +(0.498432 + 0.863309i) q^{56} +(3.79234 - 2.18951i) q^{57} +(-5.20313 + 3.00403i) q^{58} +4.10081 q^{59} +(1.10009 + 4.14709i) q^{60} +(-6.35472 - 11.0067i) q^{61} +(-3.65277 - 2.10893i) q^{62} +(-0.588525 - 0.339785i) q^{63} -1.00000 q^{64} +(-5.92956 - 1.60474i) q^{65} +(6.05290 - 10.4839i) q^{66} +(5.02819 + 2.90302i) q^{67} +(5.74209 - 3.31520i) q^{68} +(-8.24361 - 14.2784i) q^{69} +(0.582308 - 2.15165i) q^{70} +(-6.60669 - 11.4431i) q^{71} +(0.590377 - 0.340854i) q^{72} +(8.16391 - 4.71344i) q^{73} +(-0.357243 + 0.618763i) q^{74} +(4.83847 - 8.28444i) q^{75} +(1.14110 - 1.97644i) q^{76} +(-5.44673 + 3.14467i) q^{77} +5.27122i q^{78} +(5.53111 + 9.58016i) q^{79} +(1.57718 + 1.58509i) q^{80} +(5.29020 - 9.16289i) q^{81} -2.42725i q^{82} +(-9.92118 - 5.72799i) q^{83} -1.91276 q^{84} +(-14.3112 - 3.87308i) q^{85} +(4.12981 + 5.09359i) q^{86} -11.5281i q^{87} -6.30912i q^{88} +(1.39849 - 2.42226i) q^{89} +(-1.47141 - 0.398213i) q^{90} +(1.36928 - 2.37166i) q^{91} +(-7.44138 - 4.29628i) q^{92} +(7.00886 - 4.04657i) q^{93} +5.64213 q^{94} +(-4.93254 + 1.30845i) q^{95} +(0.959389 - 1.66171i) q^{96} +3.30561i q^{97} +(-5.20158 - 3.00313i) q^{98} +(2.15049 + 3.72476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

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