LMFDB - Embedded newform 349.2.c.a.122.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(122,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("349.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.c (of order $3$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			122.4
Character	$\chi$	$=$	349.122
Dual form			349.2.c.a.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19066 + 2.06228i) q^{2} +(0.388808 + 0.673436i) q^{3} +(-1.83534 - 3.17890i) q^{4} +(-0.996293 - 1.72563i) q^{5} -1.85175 q^{6} +(0.620144 - 1.07412i) q^{7} +3.97841 q^{8} +(1.19766 - 2.07440i) q^{9} +O(q^{10})$	\(q+(-1.19066 + 2.06228i) q^{2} +(0.388808 + 0.673436i) q^{3} +(-1.83534 - 3.17890i) q^{4} +(-0.996293 - 1.72563i) q^{5} -1.85175 q^{6} +(0.620144 - 1.07412i) q^{7} +3.97841 q^{8} +(1.19766 - 2.07440i) q^{9} +4.74498 q^{10} +4.95989 q^{11} +(1.42719 - 2.47196i) q^{12} +(-2.77192 + 4.80111i) q^{13} +(1.47676 + 2.55782i) q^{14} +(0.774734 - 1.34188i) q^{15} +(-1.06625 + 1.84681i) q^{16} +0.515940 q^{17} +(2.85200 + 4.93981i) q^{18} +(3.21239 + 5.56402i) q^{19} +(-3.65707 + 6.33423i) q^{20} +0.964468 q^{21} +(-5.90554 + 10.2287i) q^{22} +(4.00386 - 6.93489i) q^{23} +(1.54684 + 2.67920i) q^{24} +(0.514800 - 0.891661i) q^{25} +(-6.60083 - 11.4330i) q^{26} +4.19548 q^{27} -4.55269 q^{28} +(-3.11668 - 5.39826i) q^{29} +(1.84489 + 3.19544i) q^{30} +4.56346 q^{31} +(1.43932 + 2.49297i) q^{32} +(1.92845 + 3.34017i) q^{33} +(-0.614309 + 1.06401i) q^{34} -2.47138 q^{35} -8.79242 q^{36} -7.62211 q^{37} -15.2994 q^{38} -4.31099 q^{39} +(-3.96366 - 6.86526i) q^{40} +10.7818 q^{41} +(-1.14835 + 1.98901i) q^{42} +(0.0154122 + 0.0266947i) q^{43} +(-9.10307 - 15.7670i) q^{44} -4.77287 q^{45} +(9.53447 + 16.5142i) q^{46} -11.2307 q^{47} -1.65827 q^{48} +(2.73084 + 4.72996i) q^{49} +(1.22590 + 2.12333i) q^{50} +(0.200602 + 0.347452i) q^{51} +20.3497 q^{52} +8.52029 q^{53} +(-4.99539 + 8.65227i) q^{54} +(-4.94150 - 8.55894i) q^{55} +(2.46719 - 4.27329i) q^{56} +(-2.49800 + 4.32667i) q^{57} +14.8436 q^{58} +(-0.178598 - 0.309341i) q^{59} -5.68759 q^{60} +0.800087 q^{61} +(-5.43353 + 9.41115i) q^{62} +(-1.48544 - 2.57286i) q^{63} -11.1200 q^{64} +11.0466 q^{65} -9.18449 q^{66} -12.4746 q^{67} +(-0.946924 - 1.64012i) q^{68} +6.22694 q^{69} +(2.94257 - 5.09668i) q^{70} +(1.34055 - 2.32190i) q^{71} +(4.76477 - 8.25282i) q^{72} +(-0.0413693 - 0.0716538i) q^{73} +(9.07533 - 15.7189i) q^{74} +0.800635 q^{75} +(11.7916 - 20.4237i) q^{76} +(3.07585 - 5.32752i) q^{77} +(5.13292 - 8.89047i) q^{78} +15.4559 q^{79} +4.24921 q^{80} +(-1.96173 - 3.39782i) q^{81} +(-12.8374 + 22.2351i) q^{82} +(0.478106 - 0.828105i) q^{83} +(-1.77012 - 3.06595i) q^{84} +(-0.514027 - 0.890321i) q^{85} -0.0734026 q^{86} +(2.42358 - 4.19777i) q^{87} +19.7325 q^{88} +(0.150073 + 0.259935i) q^{89} +(5.68286 - 9.84300i) q^{90} +(3.43798 + 5.95476i) q^{91} -29.3938 q^{92} +(1.77431 + 3.07320i) q^{93} +(13.3719 - 23.1609i) q^{94} +(6.40095 - 11.0868i) q^{95} +(-1.11924 + 1.93858i) q^{96} +(-1.88342 + 3.26218i) q^{97} -13.0060 q^{98} +(5.94024 - 10.2888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.19066	+	2.06228i	−0.841923	+	1.45825i	0.0463437	+	0.998926i	$0.485243\pi$
$2$	−1.19066	+	2.06228i	−0.841923	+	1.45825i	−0.888267	+	0.459328i	$0.848090\pi$
$3$	0.388808	+	0.673436i	0.224479	+	0.388808i	0.956163	−	0.292835i	$-0.0945988\pi$
$3$	0.388808	+	0.673436i	0.224479	+	0.388808i	−0.731684	+	0.681644i	$0.761265\pi$
$4$	−1.83534	−	3.17890i	−0.917669	−	1.58945i
$5$	−0.996293	−	1.72563i	−0.445556	−	0.771725i	0.552535	−	0.833490i	$-0.313661\pi$
$5$	−0.996293	−	1.72563i	−0.445556	−	0.771725i	−0.998091	+	0.0617645i	$0.980327\pi$
$6$	−1.85175			−0.755975
$7$	0.620144	−	1.07412i	0.234392	−	0.405979i	−0.724704	−	0.689061i	$-0.758023\pi$
$7$	0.620144	−	1.07412i	0.234392	−	0.405979i	0.959096	+	0.283081i	$0.0913566\pi$
$8$	3.97841			1.40658
$9$	1.19766	−	2.07440i	0.399219	−	0.691467i
$10$	4.74498			1.50049
$11$	4.95989			1.49546			0.747732	−	0.664001i	$-0.231143\pi$
$11$	4.95989			1.49546			0.747732	+	0.664001i	$0.231143\pi$
$12$	1.42719	−	2.47196i	0.411994	−	0.713594i
$13$	−2.77192	+	4.80111i	−0.768794	+	1.33159i	0.169424	+	0.985543i	$0.445809\pi$
$13$	−2.77192	+	4.80111i	−0.768794	+	1.33159i	−0.938217	+	0.346046i	$0.887524\pi$
$14$	1.47676	+	2.55782i	0.394681	+	0.683607i
$15$	0.774734	−	1.34188i	0.200035	−	0.346471i
$16$	−1.06625	+	1.84681i	−0.266564	+	0.461702i
$17$	0.515940			0.125134			0.0625669	−	0.998041i	$-0.480071\pi$
$17$	0.515940			0.125134			0.0625669	+	0.998041i	$0.480071\pi$
$18$	2.85200	+	4.93981i	0.672223	+	1.16432i
$19$	3.21239	+	5.56402i	0.736972	+	1.27647i	0.953853	+	0.300275i	$0.0970783\pi$
$19$	3.21239	+	5.56402i	0.736972	+	1.27647i	−0.216881	+	0.976198i	$0.569588\pi$
$20$	−3.65707	+	6.33423i	−0.817745	+	1.41638i
$21$	0.964468			0.210464
$22$	−5.90554	+	10.2287i	−1.25906	+	2.18076i
$23$	4.00386	−	6.93489i	0.834863	−	1.44603i	−0.0592786	−	0.998241i	$-0.518880\pi$
$23$	4.00386	−	6.93489i	0.834863	−	1.44603i	0.894142	−	0.447784i	$-0.147787\pi$
$24$	1.54684	+	2.67920i	0.315747	+	0.546890i
$25$	0.514800	−	0.891661i	0.102960	−	0.178332i
$26$	−6.60083	−	11.4330i	−1.29453	−	2.24219i
$27$	4.19548			0.807421
$28$	−4.55269			−0.860378
$29$	−3.11668	−	5.39826i	−0.578754	−	1.00243i	−0.995623	−	0.0934643i	$-0.970206\pi$
$29$	−3.11668	−	5.39826i	−0.578754	−	1.00243i	0.416869	−	0.908967i	$-0.363127\pi$
$30$	1.84489	+	3.19544i	0.336829	+	0.583405i
$31$	4.56346			0.819622			0.409811	−	0.912170i	$-0.365595\pi$
$31$	4.56346			0.819622			0.409811	+	0.912170i	$0.365595\pi$
$32$	1.43932	+	2.49297i	0.254438	+	0.440700i
$33$	1.92845	+	3.34017i	0.335699	+	0.581448i
$34$	−0.614309	+	1.06401i	−0.105353	+	0.182477i
$35$	−2.47138			−0.417739
$36$	−8.79242			−1.46540
$37$	−7.62211			−1.25307			−0.626534	−	0.779394i	$-0.715527\pi$
$37$	−7.62211			−1.25307			−0.626534	+	0.779394i	$0.715527\pi$
$38$	−15.2994			−2.48189
$39$	−4.31099			−0.690311
$40$	−3.96366	−	6.86526i	−0.626710	−	1.08549i
$41$	10.7818			1.68383			0.841917	−	0.539607i	$-0.181427\pi$
$41$	10.7818			1.68383			0.841917	+	0.539607i	$0.181427\pi$
$42$	−1.14835	+	1.98901i	−0.177195	+	0.306910i
$43$	0.0154122	+	0.0266947i	0.00235034	+	0.00407090i	0.867198	−	0.497963i	$-0.165919\pi$
$43$	0.0154122	+	0.0266947i	0.00235034	+	0.00407090i	−0.864848	+	0.502034i	$0.832585\pi$
$44$	−9.10307	−	15.7670i	−1.37234	−	2.37696i
$45$	−4.77287			−0.711497
$46$	9.53447	+	16.5142i	1.40578	+	2.43488i
$47$	−11.2307			−1.63817			−0.819083	−	0.573675i	$-0.805517\pi$
$47$	−11.2307			−1.63817			−0.819083	+	0.573675i	$0.805517\pi$
$48$	−1.65827			−0.239351
$49$	2.73084	+	4.72996i	0.390120	+	0.675708i
$50$	1.22590	+	2.12333i	0.173369	+	0.300284i
$51$	0.200602	+	0.347452i	0.0280899	+	0.0486531i
$52$	20.3497			2.82199
$53$	8.52029			1.17035			0.585176	−	0.810906i	$-0.301025\pi$
$53$	8.52029			1.17035			0.585176	+	0.810906i	$0.301025\pi$
$54$	−4.99539	+	8.65227i	−0.679787	+	1.17742i
$55$	−4.94150	−	8.55894i	−0.666312	−	1.15409i
$56$	2.46719	−	4.27329i	0.329692	−	0.571043i
$57$	−2.49800	+	4.32667i	−0.330869	+	0.573081i
$58$	14.8436			1.94906
$59$	−0.178598	−	0.309341i	−0.0232515	−	0.0402727i	0.854166	−	0.520001i	$-0.174069\pi$
$59$	−0.178598	−	0.309341i	−0.0232515	−	0.0402727i	−0.877417	+	0.479728i	$0.840735\pi$
$60$	−5.68759			−0.734265
$61$	0.800087			0.102441			0.0512203	−	0.998687i	$-0.483689\pi$
$61$	0.800087			0.102441			0.0512203	+	0.998687i	$0.483689\pi$
$62$	−5.43353	+	9.41115i	−0.690059	+	1.19522i
$63$	−1.48544	−	2.57286i	−0.187148	−	0.324149i
$64$	−11.1200			−1.39000
$65$	11.0466			1.37016
$66$	−9.18449			−1.13053
$67$	−12.4746			−1.52401			−0.762006	−	0.647570i	$-0.775785\pi$
$67$	−12.4746			−1.52401			−0.762006	+	0.647570i	$0.775785\pi$
$68$	−0.946924	−	1.64012i	−0.114831	−	0.198894i
$69$	6.22694			0.749635
$70$	2.94257	−	5.09668i	0.351704	−	0.609170i
$71$	1.34055	−	2.32190i	0.159094	−	0.275559i	−0.775448	−	0.631411i	$-0.782476\pi$
$71$	1.34055	−	2.32190i	0.159094	−	0.275559i	0.934542	+	0.355852i	$0.115809\pi$
$72$	4.76477	−	8.25282i	0.561533	−	0.972604i
$73$	−0.0413693	−	0.0716538i	−0.00484191	−	0.00838644i	0.863594	−	0.504187i	$-0.168208\pi$
$73$	−0.0413693	−	0.0716538i	−0.00484191	−	0.00838644i	−0.868436	+	0.495801i	$0.834875\pi$
$74$	9.07533	−	15.7189i	1.05499	−	1.82729i
$75$	0.800635			0.0924493
$76$	11.7916	−	20.4237i	1.35259	−	2.34276i
$77$	3.07585	−	5.32752i	0.350525	−	0.607127i
$78$	5.13292	−	8.89047i	0.581188	−	1.00665i
$79$	15.4559			1.73892			0.869460	−	0.494003i	$-0.164467\pi$
$79$	15.4559			1.73892			0.869460	+	0.494003i	$0.164467\pi$
$80$	4.24921			0.475076
$81$	−1.96173	−	3.39782i	−0.217970	−	0.377535i
$82$	−12.8374	+	22.2351i	−1.41766	+	2.45546i
$83$	0.478106	−	0.828105i	0.0524790	−	0.0908963i	−0.838593	−	0.544759i	$-0.816621\pi$
$83$	0.478106	−	0.828105i	0.0524790	−	0.0908963i	0.891072	+	0.453863i	$0.149954\pi$
$84$	−1.77012	−	3.06595i	−0.193136	−	0.334522i
$85$	−0.514027	−	0.890321i	−0.0557541	−	0.0965689i
$86$	−0.0734026			−0.00791521
$87$	2.42358	−	4.19777i	0.259836	−	0.450048i
$88$	19.7325			2.10349
$89$	0.150073	+	0.259935i	0.0159077	+	0.0275530i	0.873870	−	0.486160i	$-0.161603\pi$
$89$	0.150073	+	0.259935i	0.0159077	+	0.0275530i	−0.857962	+	0.513713i	$0.828270\pi$
$90$	5.68286	−	9.84300i	0.599026	−	1.03754i
$91$	3.43798	+	5.95476i	0.360399	+	0.624229i
$92$	−29.3938			−3.06451
$93$	1.77431	+	3.07320i	0.183988	+	0.318676i
$94$	13.3719	−	23.1609i	1.37921	−	2.38886i
$95$	6.40095	−	11.0868i	0.656724	−	1.13748i
$96$	−1.11924	+	1.93858i	−0.114232	+	0.197855i
$97$	−1.88342	+	3.26218i	−0.191232	+	0.331224i	−0.945659	−	0.325160i	$-0.894582\pi$
$97$	−1.88342	+	3.26218i	−0.191232	+	0.331224i	0.754427	+	0.656385i	$0.227915\pi$
$98$	−13.0060			−1.31381
$99$	5.94024	−	10.2888i	0.597017	−	1.03406i
$100$	−3.77933			−0.377933
$101$	−17.0725			−1.69878			−0.849388	−	0.527768i	$-0.823029\pi$
$101$	−17.0725			−1.69878			−0.849388	+	0.527768i	$0.823029\pi$
$102$	−0.955393			−0.0945980
$103$	9.35397			0.921674			0.460837	−	0.887485i	$-0.347549\pi$
$103$	9.35397			0.921674			0.460837	+	0.887485i	$0.347549\pi$
$104$	−11.0279	+	19.1008i	−1.08137	+	1.87299i
$105$	−0.960893	−	1.66432i	−0.0937735	−	0.162421i
$106$	−10.1448	+	17.5712i	−0.985346	+	1.70667i
$107$	−0.791686	+	1.37124i	−0.0765352	+	0.132563i	−0.901753	−	0.432252i	$-0.857719\pi$
$107$	−0.791686	+	1.37124i	−0.0765352	+	0.132563i	0.825218	+	0.564815i	$0.191052\pi$
$108$	−7.70013	−	13.3370i	−0.740945	−	1.28335i
$109$	4.39408	+	7.61077i	0.420876	+	0.728979i	0.996025	−	0.0890694i	$-0.0283893\pi$
$109$	4.39408	+	7.61077i	0.420876	+	0.728979i	−0.575149	+	0.818049i	$0.695056\pi$
$110$	23.5346			2.24393
$111$	−2.96354	−	5.13300i	−0.281287	−	0.487203i
$112$	1.32246	+	2.29057i	0.124961	+	0.216439i
$113$	3.85166	−	6.67127i	0.362334	−	0.627580i	−0.626011	−	0.779814i	$-0.715313\pi$
$113$	3.85166	−	6.67127i	0.362334	−	0.627580i	0.988344	+	0.152234i	$0.0486467\pi$
$114$	−5.94854	−	10.3032i	−0.557132	−	0.964981i
$115$	−15.9561			−1.48791
$116$	−11.4403	+	19.8152i	−1.06221	+	1.83980i
$117$	6.63963	+	11.5002i	0.613834	+	1.06319i
$118$	0.850597			0.0783038
$119$	0.319957	−	0.554182i	0.0293304	−	0.0508018i
$120$	3.08221	−	5.33854i	0.281366	−	0.487340i
$121$	13.6005			1.23641
$122$	−0.952631	+	1.65000i	−0.0862471	+	0.149384i
$123$	4.19205	+	7.26085i	0.377985	+	0.654689i
$124$	−8.37550	−	14.5068i	−0.752142	−	1.30275i
$125$	−12.0145			−1.07461
$126$	7.07460			0.630256
$127$	−20.2213			−1.79435			−0.897175	−	0.441675i	$-0.854384\pi$
$127$	−20.2213			−1.79435			−0.897175	+	0.441675i	$0.854384\pi$
$128$	10.3615	−	17.9466i	0.915832	−	1.58627i
$129$	−0.0119848	+	0.0207582i	−0.00105520	+	0.00182766i
$130$	−13.1527	+	22.7812i	−1.15357	+	1.99804i
$131$	−6.52778			−0.570334			−0.285167	−	0.958478i	$-0.592049\pi$
$131$	−6.52778			−0.570334			−0.285167	+	0.958478i	$0.592049\pi$
$132$	7.07870	−	12.2607i	0.616122	−	1.06715i
$133$	7.96856			0.690962
$134$	14.8530	−	25.7261i	1.28310	−	2.22240i
$135$	−4.17993	−	7.23985i	−0.359751	−	0.623107i
$136$	2.05262			0.176011
$137$	3.47044	+	6.01098i	0.296500	+	0.513553i	0.975333	−	0.220740i	$-0.0708473\pi$
$137$	3.47044	+	6.01098i	0.296500	+	0.513553i	−0.678833	+	0.734293i	$0.737514\pi$
$138$	−7.41416	+	12.8417i	−0.631135	+	1.09316i
$139$	−17.8196			−1.51144			−0.755718	−	0.654897i	$-0.772712\pi$
$139$	−17.8196			−1.51144			−0.755718	+	0.654897i	$0.772712\pi$
$140$	4.53582	+	7.85627i	0.383347	+	0.663976i
$141$	−4.36659	−	7.56315i	−0.367733	−	0.636932i
$142$	3.19228	+	5.52918i	0.267890	+	0.463999i
$143$	−13.7484	+	23.8130i	−1.14970	+	1.99134i
$144$	2.55401	+	4.42368i	0.212834	+	0.368640i
$145$	−6.21026	+	10.7565i	−0.515734	+	0.893278i
$146$	0.197027			0.0163061
$147$	−2.12355	+	3.67809i	−0.175147	+	0.303364i
$148$	13.9891	+	24.2299i	1.14990	+	1.99169i
$149$	1.66157	−	2.87792i	0.136121	−	0.235768i	−0.789904	−	0.613230i	$-0.789870\pi$
$149$	1.66157	−	2.87792i	0.136121	−	0.235768i	0.926025	+	0.377462i	$0.123203\pi$
$150$	−0.953283	+	1.65113i	−0.0778352	+	0.134815i
$151$	−0.338442	−	0.586199i	−0.0275420	−	0.0477042i	0.851926	−	0.523662i	$-0.175435\pi$
$151$	−0.338442	−	0.586199i	−0.0275420	−	0.0477042i	−0.879468	+	0.475958i	$0.842101\pi$
$152$	12.7802	+	22.1359i	1.03661	+	1.79546i
$153$	0.617919	−	1.07027i	0.0499558	−	0.0865259i
$154$	7.32457	+	12.6865i	0.590230	+	1.02231i
$155$	−4.54655	−	7.87485i	−0.365188	−	0.632523i
$156$	7.91212	+	13.7042i	0.633477	+	1.09721i
$157$	−1.65413	−	2.86503i	−0.132014	−	0.228654i	0.792439	−	0.609951i	$-0.208811\pi$
$157$	−1.65413	−	2.86503i	−0.132014	−	0.228654i	−0.924453	+	0.381297i	$0.875478\pi$
$158$	−18.4027	+	31.8744i	−1.46404	+	2.53579i
$159$	3.31276	+	5.73787i	0.262719	+	0.455042i
$160$	2.86797	−	4.96746i	0.226733	−	0.392713i
$161$	−4.96594	−	8.60126i	−0.391371	−	0.677875i
$162$	9.34301			0.734056
$163$	3.68949			0.288983			0.144492	−	0.989506i	$-0.453845\pi$
$163$	3.68949			0.288983			0.144492	+	0.989506i	$0.453845\pi$
$164$	−19.7882	−	34.2742i	−1.54520	−	2.67637i
$165$	3.84259	−	6.65557i	0.299146	−	0.518135i
$166$	1.13852	+	1.97198i	0.0883666	+	0.153055i
$167$	1.83031			0.141634			0.0708168	−	0.997489i	$-0.477439\pi$
$167$	1.83031			0.141634			0.0708168	+	0.997489i	$0.477439\pi$
$168$	3.83705			0.296035
$169$	−8.86713	−	15.3583i	−0.682087	−	1.18141i
$170$	2.44813			0.187763
$171$	15.3893			1.17685
$172$	0.0565731	−	0.0979876i	0.00431366	−	0.00747148i
$173$	−4.43051	+	7.67386i	−0.336845	+	0.583433i	−0.983838	−	0.179063i	$-0.942693\pi$
$173$	−4.43051	+	7.67386i	−0.336845	+	0.583433i	0.646992	+	0.762497i	$0.276027\pi$
$174$	5.77133	+	9.99623i	0.437523	+	0.757812i
$175$	−0.638501	−	1.10592i	−0.0482661	−	0.0835994i
$176$	−5.28851	+	9.15996i	−0.398636	+	0.690458i
$177$	0.138881	−	0.240548i	0.0104389	−	0.0180807i
$178$	−0.714744			−0.0535724
$179$	−18.4981			−1.38261			−0.691305	−	0.722563i	$-0.742964\pi$
$179$	−18.4981			−1.38261			−0.691305	+	0.722563i	$0.742964\pi$
$180$	8.75982	+	15.1725i	0.652919	+	1.13089i
$181$	9.32504			0.693125			0.346562	−	0.938027i	$-0.387349\pi$
$181$	9.32504			0.693125			0.346562	+	0.938027i	$0.387349\pi$
$182$	−16.3739			−1.21371
$183$	0.311080	+	0.538807i	0.0229957	+	0.0398298i
$184$	15.9290	−	27.5899i	1.17430	−	2.03395i
$185$	7.59385	+	13.1529i	0.558311	+	0.967023i
$186$	−8.45040			−0.619614
$187$	2.55901			0.187133
$188$	20.6121	+	35.7013i	1.50329	+	2.60378i
$189$	2.60180	−	4.50646i	0.189253	−	0.327796i
$190$	15.2427	+	26.4011i	1.10582	+	1.91534i
$191$	2.44681	−	4.23799i	0.177045	−	0.306650i	−0.763822	−	0.645427i	$-0.776680\pi$
$191$	2.44681	−	4.23799i	0.177045	−	0.306650i	0.940867	+	0.338776i	$0.110013\pi$
$192$	−4.32354	−	7.48858i	−0.312024	−	0.540442i
$193$	−3.05688	−	5.29468i	−0.220039	−	0.381119i	0.734780	−	0.678305i	$-0.237285\pi$
$193$	−3.05688	−	5.29468i	−0.220039	−	0.381119i	−0.954820	+	0.297186i	$0.903952\pi$
$194$	−4.48502	−	7.76829i	−0.322006	−	0.557731i
$195$	4.29501	+	7.43917i	0.307572	+	0.532730i
$196$	10.0240	−	17.3621i	0.716003	−	1.24015i
$197$	10.8904	+	18.8628i	0.775911	+	1.34392i	0.934281	+	0.356537i	$0.116043\pi$
$197$	10.8904	+	18.8628i	0.775911	+	1.34392i	−0.158370	+	0.987380i	$0.550624\pi$
$198$	14.1456	+	24.5009i	1.00528	+	1.74120i
$199$	−8.19403	+	14.1925i	−0.580859	+	1.00608i	0.414519	+	0.910041i	$0.363950\pi$
$199$	−8.19403	+	14.1925i	−0.580859	+	1.00608i	−0.995378	+	0.0960367i	$0.969383\pi$
$200$	2.04809	−	3.54739i	0.144822	−	0.250838i
$201$	−4.85022	−	8.40082i	−0.342108	−	0.592548i
$202$	20.3275	−	35.2083i	1.43024	−	2.47725i
$203$	−7.73117			−0.542622
$204$	0.736344	−	1.27538i	0.0515544	−	0.0892948i
$205$	−10.7418	−	18.6054i	−0.750242	−	1.29946i
$206$	−11.1374	+	19.2905i	−0.775978	+	1.34403i
$207$	−9.59050	−	16.6112i	−0.666586	−	1.15456i
$208$	−5.91115	−	10.2384i	−0.409865	−	0.709907i
$209$	15.9331	+	27.5969i	1.10211	+	1.90892i
$210$	4.57638			0.315800
$211$	−6.96145	+	12.0576i	−0.479246	+	0.830079i	−0.999717	−	0.0238010i	$-0.992423\pi$
$211$	−6.96145	+	12.0576i	−0.479246	+	0.830079i	0.520471	+	0.853880i	$0.325757\pi$
$212$	−15.6376	−	27.0851i	−1.07400	−	1.86022i
$213$	2.08487			0.142853
$214$	−1.88526	−	3.26536i	−0.128873	−	0.223215i
$215$	0.0307101	−	0.0531915i	0.00209441	−	0.00362763i
$216$	16.6914			1.13570
$217$	2.83000	−	4.90171i	0.192113	−	0.332750i
$218$	−20.9274			−1.41738
$219$	0.0321695	−	0.0557191i	0.00217381	−	0.00376515i
$220$	−18.1387	+	31.4171i	−1.22291	+	2.11814i
$221$	−1.43015	+	2.47709i	−0.0962021	+	0.166627i
$222$	14.1143			0.947287
$223$	−17.2864			−1.15758			−0.578791	−	0.815476i	$-0.696475\pi$
$223$	−17.2864			−1.15758			−0.578791	+	0.815476i	$0.696475\pi$
$224$	3.57034			0.238553
$225$	−1.23311	−	2.13581i	−0.0822072	−	0.142387i
$226$	9.17203	+	15.8864i	0.610114	+	1.05675i
$227$	2.75056	−	4.76411i	0.182561	−	0.316205i	−0.760191	−	0.649700i	$-0.774895\pi$
$227$	2.75056	−	4.76411i	0.182561	−	0.316205i	0.942752	+	0.333495i	$0.108228\pi$
$228$	18.3387			1.21451
$229$	3.09389	−	5.35877i	0.204450	−	0.354118i	−0.745507	−	0.666497i	$-0.767793\pi$
$229$	3.09389	−	5.35877i	0.204450	−	0.354118i	0.949957	+	0.312380i	$0.101126\pi$
$230$	18.9983	−	32.9059i	1.25271	−	2.16975i
$231$	4.78366			0.314741
$232$	−12.3994	−	21.4765i	−0.814064	−	1.41000i
$233$	−13.0198	+	22.5510i	−0.852958	+	1.47737i	0.0255677	+	0.999673i	$0.491861\pi$
$233$	−13.0198	+	22.5510i	−0.852958	+	1.47737i	−0.878526	+	0.477694i	$0.841473\pi$
$234$	−31.6221			−2.06720
$235$	11.1891	+	19.3800i	0.729894	+	1.26421i
$236$	−0.655575	+	1.13549i	−0.0426743	+	0.0739141i
$237$	6.00937	+	10.4085i	0.390350	+	0.676107i
$238$	0.761919	+	1.31968i	0.0493879	+	0.0855423i
$239$	−1.06656			−0.0689900			−0.0344950	−	0.999405i	$-0.510982\pi$
$239$	−1.06656			−0.0689900			−0.0344950	+	0.999405i	$0.510982\pi$
$240$	1.65213	+	2.86157i	0.106644	+	0.184713i
$241$	−0.878667	−	1.52190i	−0.0565999	−	0.0980339i	0.836337	−	0.548215i	$-0.184693\pi$
$241$	−0.878667	−	1.52190i	−0.0565999	−	0.0980339i	−0.892937	+	0.450182i	$0.851359\pi$
$242$	−16.1936	+	28.0481i	−1.04096	+	1.80300i
$243$	7.81870	−	13.5424i	0.501570	−	0.868744i
$244$	−1.46843	−	2.54340i	−0.0940066	−	0.162824i
$245$	5.44144	−	9.42485i	0.347641	−	0.602132i
$246$	−19.9652			−1.27294
$247$	−35.6180			−2.26632
$248$	18.1553			1.15286
$249$	0.743567			0.0471216
$250$	14.3052	−	24.7773i	0.904738	−	1.56705i
$251$	9.73640			0.614556			0.307278	−	0.951620i	$-0.400582\pi$
$251$	9.73640			0.614556			0.307278	+	0.951620i	$0.400582\pi$
$252$	−5.45256	+	9.44412i	−0.343479	+	0.594923i
$253$	19.8587	−	34.3963i	1.24851	−	2.16248i
$254$	24.0767	−	41.7020i	1.51070	−	2.61662i
$255$	0.399716	−	0.692329i	0.0250312	−	0.0433553i
$256$	13.5540	+	23.4761i	0.847122	+	1.46726i
$257$	6.47999			0.404211			0.202105	−	0.979364i	$-0.435222\pi$
$257$	6.47999			0.404211			0.202105	+	0.979364i	$0.435222\pi$
$258$	−0.0285395	−	0.0494319i	−0.00177679	−	0.00307750i
$259$	−4.72680	+	8.18707i	−0.293709	+	0.508719i
$260$	−20.2742	−	35.1160i	−1.25735	−	2.17780i
$261$	−14.9309			−0.924198
$262$	7.77235	−	13.4621i	0.480178	−	0.831692i
$263$	−3.90988			−0.241094			−0.120547	−	0.992708i	$-0.538465\pi$
$263$	−3.90988			−0.241094			−0.120547	+	0.992708i	$0.538465\pi$
$264$	7.67215	+	13.2886i	0.472188	+	0.817854i
$265$	−8.48871	−	14.7029i	−0.521457	−	0.903190i
$266$	−9.48784	+	16.4334i	−0.581737	+	1.00760i
$267$	−0.116699	+	0.202129i	−0.00714189	+	0.0123701i
$268$	22.8951	+	39.6554i	1.39854	+	2.42234i
$269$	−26.3433			−1.60618			−0.803090	−	0.595857i	$-0.796812\pi$
$269$	−26.3433			−1.60618			−0.803090	+	0.595857i	$0.796812\pi$
$270$	19.9075			1.21153
$271$	−2.66764	+	4.62049i	−0.162048	+	0.280675i	−0.935603	−	0.353054i	$-0.885143\pi$
$271$	−2.66764	+	4.62049i	−0.162048	+	0.280675i	0.773555	+	0.633729i	$0.218477\pi$
$272$	−0.550123	+	0.952842i	−0.0333561	+	0.0577745i
$273$	−2.67343	+	4.63052i	−0.161804	+	0.280252i
$274$	−16.5284			−0.998520
$275$	2.55335	−	4.42254i	0.153973	−	0.266689i
$276$	−11.4285	−	19.7948i	−0.687917	−	1.19151i
$277$	2.96863	−	5.14182i	0.178368	−	0.308942i	−0.762954	−	0.646453i	$-0.776252\pi$
$277$	2.96863	−	5.14182i	0.178368	−	0.308942i	0.941322	+	0.337511i	$0.109585\pi$
$278$	21.2170	−	36.7490i	1.27251	−	2.20406i
$279$	5.46546	−	9.46646i	0.327209	−	0.566742i
$280$	−9.83216			−0.587584
$281$	−0.966924	−	1.67476i	−0.0576819	−	0.0999079i	0.835743	−	0.549121i	$-0.185038\pi$
$281$	−0.966924	−	1.67476i	−0.0576819	−	0.0999079i	−0.893424	+	0.449214i	$0.851704\pi$
$282$	20.7965			1.23841
$283$	17.1910			1.02190			0.510949	−	0.859611i	$-0.329294\pi$
$283$	17.1910			1.02190			0.510949	+	0.859611i	$0.329294\pi$
$284$	−9.84145			−0.583982
$285$	9.95497			0.589682
$286$	−32.7394	−	56.7063i	−1.93592	−	3.35312i
$287$	6.68627	−	11.5810i	0.394678	−	0.683602i
$288$	6.89524			0.406306
$289$	−16.7338			−0.984342
$290$	−14.7886	−	25.6146i	−0.868417	−	1.50414i
$291$	−2.92916			−0.171710
$292$	−0.151853	+	0.263018i	−0.00888654	+	0.0153919i
$293$	8.51477	−	14.7480i	0.497438	−	0.861588i	−0.502558	−	0.864544i	$-0.667608\pi$
$293$	8.51477	−	14.7480i	0.497438	−	0.861588i	0.999996	+	0.00295588i	$0.000940886\pi$
$294$	−5.05684	−	8.75871i	−0.294921	−	0.510818i
$295$	−0.355872	+	0.616388i	−0.0207197	+	0.0358875i
$296$	−30.3239			−1.76254
$297$	20.8091			1.20747
$298$	3.95672	+	6.85324i	0.229207	+	0.396998i
$299$	22.1968	+	38.4460i	1.28367	+	2.22339i
$300$	−1.46943	−	2.54514i	−0.0848379	−	0.146943i
$301$	0.0382311			0.00220360
$302$	1.61188			0.0927531
$303$	−6.63793	−	11.4972i	−0.381339	−	0.660498i
$304$	−13.7009			−0.785800
$305$	−0.797121	−	1.38065i	−0.0456430	−	0.0790560i
$306$	1.47146	+	2.54865i	0.0841178	+	0.145696i
$307$	−10.9426	+	18.9532i	−0.624529	+	1.08172i	0.364103	+	0.931359i	$0.381376\pi$
$307$	−10.9426	+	18.9532i	−0.624529	+	1.08172i	−0.988632	+	0.150357i	$0.951958\pi$
$308$	−22.5809			−1.28666
$309$	3.63690	+	6.29929i	0.206896	+	0.358354i
$310$	21.6536			1.22984
$311$	−4.96051			−0.281285			−0.140642	−	0.990060i	$-0.544917\pi$
$311$	−4.96051			−0.281285			−0.140642	+	0.990060i	$0.544917\pi$
$312$	−17.1509			−0.970977
$313$	27.7556			1.56884			0.784419	−	0.620231i	$-0.212961\pi$
$313$	27.7556			1.56884			0.784419	+	0.620231i	$0.212961\pi$
$314$	7.87800			0.444581
$315$	−2.95986	+	5.12664i	−0.166769	+	0.288853i
$316$	−28.3667	−	49.1326i	−1.59575	−	2.76393i
$317$	8.53420	+	14.7817i	0.479328	+	0.830221i	0.999719	−	0.0237075i	$-0.00754703\pi$
$317$	8.53420	+	14.7817i	0.479328	+	0.830221i	−0.520391	+	0.853928i	$0.674214\pi$
$318$	−15.7775			−0.884756
$319$	−15.4584	−	26.7748i	−0.865505	−	1.49910i
$320$	11.0788	+	19.1890i	0.619321	+	1.07270i
$321$	−1.23126			−0.0687220
$322$	23.6510			1.31802
$323$	1.65740	+	2.87070i	0.0922201	+	0.159730i
$324$	−7.20088	+	12.4723i	−0.400049	+	0.692905i
$325$	2.85398	+	4.94323i	0.158310	+	0.274201i
$326$	−4.39292	+	7.60877i	−0.243302	+	0.421411i
$327$	−3.41691	+	5.91826i	−0.188955	+	0.327280i
$328$	42.8944			2.36845
$329$	−6.96465	+	12.0631i	−0.383974	+	0.665062i
$330$	9.15044	+	15.8490i	0.503715	+	0.872460i
$331$	2.71577	+	4.70385i	0.149272	+	0.258547i	0.930959	−	0.365125i	$-0.118974\pi$
$331$	2.71577	+	4.70385i	0.149272	+	0.258547i	−0.781687	+	0.623671i	$0.785640\pi$
$332$	−3.50995			−0.192633
$333$	−9.12867	+	15.8113i	−0.500248	+	0.866455i
$334$	−2.17927	+	3.77461i	−0.119245	+	0.206538i
$335$	12.4283	+	21.5265i	0.679032	+	1.17612i
$336$	−1.02837	+	1.78119i	−0.0561021	+	0.0971717i
$337$	6.33596	−	10.9742i	0.345142	−	0.597803i	−0.640238	−	0.768177i	$-0.721164\pi$
$337$	6.33596	−	10.9742i	0.345142	−	0.597803i	0.985380	+	0.170374i	$0.0544975\pi$
$338$	42.2309			2.29706
$339$	5.99023			0.325345
$340$	−1.88683	+	3.26808i	−0.102328	+	0.177237i
$341$	22.6343			1.22572
$342$	−18.3235	+	31.7372i	−0.990819	+	1.71615i
$343$	15.4561			0.834550
$344$	0.0613160	+	0.106202i	0.00330594	+	0.00572605i
$345$	−6.20386	−	10.7454i	−0.334004	−	0.578513i
$346$	−10.5504	−	18.2739i	−0.567196	−	0.982412i
$347$	11.0843	−	19.1985i	0.595035	−	1.03063i	−0.398507	−	0.917165i	$-0.630471\pi$
$347$	11.0843	−	19.1985i	0.595035	−	1.03063i	0.993542	−	0.113466i	$-0.0361952\pi$
$348$	−17.7924			−0.953772
$349$	−5.79143	+	17.7612i	−0.310008	+	0.950734i
$349$	−5.79143	+	17.7612i	−0.310008	+	0.950734i
$350$	3.04095			0.162545
$351$	−11.6296	+	20.1430i	−0.620740	+	1.07515i
$352$	7.13886	+	12.3649i	0.380503	+	0.659050i
$353$	−3.14677	−	5.45036i	−0.167486	−	0.290094i	0.770050	−	0.637984i	$-0.220231\pi$
$353$	−3.14677	−	5.45036i	−0.167486	−	0.290094i	−0.937535	+	0.347890i	$0.886898\pi$
$354$	0.330719	+	0.572822i	0.0175775	+	0.0304452i
$355$	−5.34232			−0.283541
$356$	0.550870	−	0.954135i	0.0291961	−	0.0505691i
$357$	0.497608			0.0263362
$358$	22.0249	−	38.1482i	1.16405	−	2.01620i
$359$	−6.09611			−0.321740			−0.160870	−	0.986976i	$-0.551430\pi$
$359$	−6.09611			−0.321740			−0.160870	+	0.986976i	$0.551430\pi$
$360$	−18.9884			−1.00078
$361$	−11.1388	+	19.2930i	−0.586255	+	1.01542i
$362$	−11.1029	+	19.2309i	−0.583558	+	1.01075i
$363$	5.28799	+	9.15907i	0.277547	+	0.480726i
$364$	12.6197	−	21.8580i	0.661453	−	1.14567i
$365$	−0.0824319	+	0.142776i	−0.00431468	+	0.00747325i
$366$	−1.48156			−0.0774425
$367$	−17.6536	−	30.5769i	−0.921510	−	1.59610i	−0.797080	−	0.603874i	$-0.793623\pi$
$367$	−17.6536	−	30.5769i	−0.921510	−	1.59610i	−0.124430	−	0.992228i	$-0.539710\pi$
$368$	8.53827	+	14.7887i	0.445088	+	0.770916i
$369$	12.9129	−	22.3658i	0.672218	−	1.16432i
$370$	−36.1668			−1.88022
$371$	5.28381	−	9.15182i	0.274322	−	0.475139i
$372$	6.51293	−	11.2807i	0.337679	−	0.584878i
$373$	10.6879	+	18.5120i	0.553399	+	0.958515i	0.998026	+	0.0627992i	$0.0200028\pi$
$373$	10.6879	+	18.5120i	0.553399	+	0.958515i	−0.444627	+	0.895716i	$0.646664\pi$
$374$	−3.04690	+	5.27739i	−0.157552	+	0.272887i
$375$	−4.67134	−	8.09099i	−0.241227	−	0.417817i
$376$	−44.6803			−2.30421
$377$	34.5569			1.77977
$378$	6.19572	+	10.7313i	0.318674	+	0.551959i
$379$	−4.41677	−	7.65007i	−0.226874	−	0.392958i	0.730006	−	0.683441i	$-0.239517\pi$
$379$	−4.41677	−	7.65007i	−0.226874	−	0.392958i	−0.956880	+	0.290483i	$0.906184\pi$
$380$	−46.9917			−2.41062
$381$	−7.86221	−	13.6177i	−0.402793	−	0.697658i
$382$	5.82662	+	10.0920i	0.298116	+	0.516352i
$383$	0.837659	−	1.45087i	0.0428024	−	0.0741359i	−0.843831	−	0.536610i	$-0.819705\pi$
$383$	0.837659	−	1.45087i	0.0428024	−	0.0741359i	0.886633	+	0.462474i	$0.153038\pi$
$384$	16.1145			0.822338
$385$	−12.2578			−0.624714
$386$	14.5588			0.741025
$387$	0.0738340			0.00375319
$388$	13.8269			0.701952
$389$	13.9206	+	24.1112i	0.705802	+	1.22248i	0.966401	+	0.257038i	$0.0827465\pi$
$389$	13.9206	+	24.1112i	0.705802	+	1.22248i	−0.260599	+	0.965447i	$0.583920\pi$
$390$	−20.4556			−1.03581
$391$	2.06575	−	3.57799i	0.104470	−	0.180947i
$392$	10.8644	+	18.8177i	0.548736	+	0.950438i
$393$	−2.53805	−	4.39604i	−0.128028	−	0.221751i
$394$	−51.8671			−2.61303
$395$	−15.3986	−	26.6711i	−0.774786	−	1.34197i
$396$	−43.6094			−2.19146
$397$	18.5438			0.930686			0.465343	−	0.885130i	$-0.345931\pi$
$397$	18.5438			0.930686			0.465343	+	0.885130i	$0.345931\pi$
$398$	−19.5126	−	33.7968i	−0.978077	−	1.69408i
$399$	3.09824	+	5.36631i	0.155106	+	0.268652i
$400$	1.09782	+	1.90147i	0.0548908	+	0.0950737i
$401$	6.81277			0.340213			0.170107	−	0.985426i	$-0.445589\pi$
$401$	6.81277			0.340213			0.170107	+	0.985426i	$0.445589\pi$
$402$	23.0998			1.15211
$403$	−12.6496	+	21.9097i	−0.630120	+	1.09140i
$404$	31.3338	+	54.2717i	1.55891	+	2.70012i
$405$	−3.90892	+	6.77044i	−0.194236	+	0.336426i
$406$	9.20519	−	15.9439i	0.456846	−	0.791280i
$407$	−37.8048			−1.87392
$408$	0.798076	+	1.38231i	0.0395106	+	0.0684344i
$409$	−17.1164			−0.846353			−0.423176	−	0.906047i	$-0.639085\pi$
$409$	−17.1164			−0.846353			−0.423176	+	0.906047i	$0.639085\pi$
$410$	51.1594			2.52658
$411$	−2.69867	+	4.67424i	−0.133116	+	0.230563i
$412$	−17.1677	−	29.7353i	−0.845791	−	1.46495i
$413$	−0.443026			−0.0217999
$414$	45.6761			2.24486
$415$	−1.90534			−0.0935293
$416$	−15.9587			−0.782441
$417$	−6.92840	−	12.0003i	−0.339285	−	0.587659i
$418$	−75.8835			−3.71158
$419$	−2.58183	+	4.47186i	−0.126131	+	0.218464i	−0.922174	−	0.386775i	$-0.873589\pi$
$419$	−2.58183	+	4.47186i	−0.126131	+	0.218464i	0.796044	+	0.605239i	$0.206922\pi$
$420$	−3.52713	+	6.10916i	−0.172106	+	0.298097i
$421$	−14.0341	+	24.3078i	−0.683982	+	1.18469i	0.289773	+	0.957095i	$0.406420\pi$
$421$	−14.0341	+	24.3078i	−0.683982	+	1.18469i	−0.973756	+	0.227596i	$0.926913\pi$
$422$	−16.5774	−	28.7130i	−0.806977	−	1.39772i
$423$	−13.4505	+	23.2970i	−0.653987	+	1.13274i
$424$	33.8972			1.64619
$425$	0.265606	−	0.460043i	0.0128838	−	0.0223154i
$426$	−2.48237	+	4.29958i	−0.120271	+	0.208316i
$427$	0.496169	−	0.859390i	0.0240113	−	0.0415888i
$428$	5.81204			0.280936
$429$	−21.3820			−1.03233
$430$	0.0731305	+	0.126666i	0.00352667	+	0.00610837i
$431$	−11.1208	+	19.2618i	−0.535671	+	0.927810i	0.463459	+	0.886118i	$0.346608\pi$
$431$	−11.1208	+	19.2618i	−0.535671	+	0.927810i	−0.999131	+	0.0416918i	$0.986725\pi$
$432$	−4.47345	+	7.74825i	−0.215229	+	0.372788i
$433$	10.1837	+	17.6388i	0.489400	+	0.847665i	0.999926	−	0.0121972i	$-0.00388257\pi$
$433$	10.1837	+	17.6388i	0.489400	+	0.847665i	−0.510526	+	0.859862i	$0.670549\pi$
$434$	6.73914	+	11.6725i	0.323489	+	0.560300i
$435$	−9.65840			−0.463085
$436$	16.1292	−	27.9367i	0.772450	−	1.33792i
$437$	51.4478			2.46108
$438$	0.0766057	+	0.132685i	0.00366036	+	0.00633993i
$439$	−5.65719	+	9.79855i	−0.270003	+	0.467659i	−0.968862	−	0.247600i	$-0.920358\pi$
$439$	−5.65719	+	9.79855i	−0.270003	+	0.467659i	0.698859	+	0.715259i	$0.253691\pi$
$440$	−19.6593	−	34.0510i	−0.937222	−	1.62332i
$441$	13.0824			0.622974
$442$	−3.40563	−	5.89873i	−0.161989	−	0.280574i
$443$	7.13505	−	12.3583i	0.338997	−	0.587159i	−0.645248	−	0.763973i	$-0.723246\pi$
$443$	7.13505	−	12.3583i	0.338997	−	0.587159i	0.984244	+	0.176814i	$0.0565792\pi$
$444$	−10.8782	+	18.8416i	−0.516256	+	0.894182i
$445$	0.299034	−	0.517942i	0.0141756	−	0.0245528i
$446$	20.5822	−	35.6494i	0.974595	−	1.68805i
$447$	2.58412			0.122225
$448$	−6.89598	+	11.9442i	−0.325805	+	0.564310i
$449$	−23.1615			−1.09306			−0.546529	−	0.837440i	$-0.684051\pi$
$449$	−23.1615			−1.09306			−0.546529	+	0.837440i	$0.684051\pi$
$450$	5.87285			0.276849
$451$	53.4765			2.51811
$452$	−28.2764			−1.33001
$453$	0.263178	−	0.455838i	0.0123652	−	0.0214171i
$454$	6.54996	+	11.3449i	0.307405	+	0.532441i
$455$	6.85048	−	11.8654i	0.321155	−	0.556258i
$456$	−9.93808	+	17.2133i	−0.465393	+	0.806085i
$457$	5.63897	+	9.76697i	0.263780	+	0.456880i	0.967243	−	0.253852i	$-0.0816975\pi$
$457$	5.63897	+	9.76697i	0.263780	+	0.456880i	−0.703464	+	0.710731i	$0.748364\pi$
$458$	7.36754	+	12.7609i	0.344262	+	0.596280i
$459$	2.16462			0.101036
$460$	29.2848	+	50.7228i	1.36541	+	2.36496i
$461$	17.0727	+	29.5707i	0.795153	+	1.37724i	0.922742	+	0.385418i	$0.125943\pi$
$461$	17.0727	+	29.5707i	0.795153	+	1.37724i	−0.127590	+	0.991827i	$0.540724\pi$
$462$	−5.69570	+	9.86525i	−0.264988	+	0.458973i
$463$	14.8033	+	25.6400i	0.687966	+	1.19159i	0.972495	+	0.232925i	$0.0748296\pi$
$463$	14.8033	+	25.6400i	0.687966	+	1.19159i	−0.284528	+	0.958668i	$0.591837\pi$
$464$	13.2927			0.617099
$465$	3.53547	−	6.12361i	0.163953	−	0.283976i
$466$	−31.0044	−	53.7012i	−1.43625	−	2.48766i
$467$	−1.00459			−0.0464868			−0.0232434	−	0.999730i	$-0.507399\pi$
$467$	−1.00459			−0.0464868			−0.0232434	+	0.999730i	$0.507399\pi$
$468$	24.3719	−	42.2134i	1.12659	−	1.95132i
$469$	−7.73603	+	13.3992i	−0.357217	+	0.618718i
$470$	−53.2895			−2.45806
$471$	1.28628	−	2.22790i	0.0592685	−	0.102656i
$472$	−0.710536	−	1.23068i	−0.0327051	−	0.0566468i
$473$	0.0764428	+	0.132403i	0.00351484	+	0.00608788i
$474$	−28.6204			−1.31458
$475$	6.61495			0.303515
$476$	−2.34892			−0.107662
$477$	10.2044	−	17.6745i	0.467227	−	0.809260i
$478$	1.26991	−	2.19955i	0.0580843	−	0.100605i
$479$	6.68567	−	11.5799i	0.305476	−	0.529100i	−0.671891	−	0.740650i	$-0.734518\pi$
$479$	6.68567	−	11.5799i	0.305476	−	0.529100i	0.977367	+	0.211550i	$0.0678511\pi$
$480$	4.46036			0.203586
$481$	21.1279	−	36.5946i	0.963350	−	1.66857i
$482$	4.18477			0.190611
$483$	3.86160	−	6.68848i	0.175709	−	0.304337i
$484$	−24.9615	−	43.2346i	−1.13461	−	1.96521i
$485$	7.50576			0.340819
$486$	18.6188	+	32.2487i	0.844566	+	1.46283i
$487$	−2.02508	+	3.50755i	−0.0917652	+	0.158942i	−0.908254	−	0.418419i	$-0.862584\pi$
$487$	−2.02508	+	3.50755i	−0.0917652	+	0.158942i	0.816489	+	0.577361i	$0.195918\pi$
$488$	3.18307			0.144091
$489$	1.43450	+	2.48463i	0.0648705	+	0.112359i
$490$	12.9578	+	22.4436i	0.585374	+	1.01390i
$491$	−6.17030	−	10.6873i	−0.278462	−	0.482310i	0.692541	−	0.721378i	$-0.256491\pi$
$491$	−6.17030	−	10.6873i	−0.278462	−	0.482310i	−0.971003	+	0.239069i	$0.923158\pi$
$492$	15.3877	−	26.6522i	0.693729	−	1.20157i
$493$	−1.60802	−	2.78518i	−0.0724217	−	0.125438i
$494$	42.4089	−	73.4543i	1.90806	−	3.30486i
$495$	−23.6729			−1.06402
$496$	−4.86581	+	8.42784i	−0.218482	+	0.378421i
$497$	−1.66267	−	2.87982i	−0.0745808	−	0.129178i
$498$	−0.885334	+	1.53344i	−0.0396728	+	0.0687153i
$499$	−3.44310	+	5.96362i	−0.154134	+	0.266968i	−0.932743	−	0.360541i	$-0.882592\pi$
$499$	−3.44310	+	5.96362i	−0.154134	+	0.266968i	0.778609	+	0.627509i	$0.215925\pi$
$500$	22.0507	+	38.1929i	0.986136	+	1.70804i
$501$	0.711639	+	1.23260i	0.0317937	+	0.0550683i
$502$	−11.5927	+	20.0792i	−0.517409	+	0.896178i
$503$	−0.0792331	−	0.137236i	−0.00353283	−	0.00611904i	0.864254	−	0.503056i	$-0.167791\pi$
$503$	−0.0792331	−	0.137236i	−0.00353283	−	0.00611904i	−0.867786	+	0.496937i	$0.834458\pi$
$504$	−5.90968	−	10.2359i	−0.263238	−	0.455942i
$505$	17.0092	+	29.4608i	0.756900	+	1.31099i
$506$	47.2899	+	81.9086i	2.10229	+	3.64128i
$507$	6.89523	−	11.9429i	0.306228	−	0.530402i
$508$	37.1129	+	64.2815i	1.64662	+	2.85203i
$509$	9.14678	−	15.8427i	0.405424	−	0.702215i	−0.588947	−	0.808172i	$-0.700457\pi$
$509$	9.14678	−	15.8427i	0.405424	−	0.702215i	0.994371	+	0.105957i	$0.0337905\pi$
$510$	0.951851	+	1.64865i	0.0421487	+	0.0730036i
$511$	−0.102620			−0.00453963
$512$	−23.1067			−1.02118
$513$	13.4775	+	23.3437i	0.595047	+	1.03065i
$514$	−7.71546	+	13.3636i	−0.340315	+	0.589442i
$515$	−9.31929	−	16.1415i	−0.410657	−	0.711279i
$516$	0.0879844			0.00387330
$517$	−55.7030			−2.44982
$518$	−11.2560	−	19.4960i	−0.494561	−	0.856605i
$519$	−6.89047			−0.302458
$520$	43.9479			1.92724
$521$	−8.11496	+	14.0555i	−0.355523	+	0.615784i	−0.987207	−	0.159442i	$-0.949031\pi$
$521$	−8.11496	+	14.0555i	−0.355523	+	0.615784i	0.631684	+	0.775226i	$0.282364\pi$
$522$	17.7776	−	30.7917i	0.778103	−	1.34771i
$523$	−12.1262	−	21.0031i	−0.530240	−	0.918402i	−0.999378	−	0.0352773i	$-0.988769\pi$
$523$	−12.1262	−	21.0031i	−0.530240	−	0.918402i	0.469138	−	0.883125i	$-0.344565\pi$
$524$	11.9807	+	20.7511i	0.523378	+	0.906518i
$525$	0.496509	−	0.859978i	0.0216694	−	0.0375325i
$526$	4.65534	−	8.06328i	0.202982	−	0.351576i
$527$	2.35447			0.102562
$528$	−8.22486			−0.357941
$529$	−20.5618	−	35.6142i	−0.893993	−	1.54844i
$530$	40.4286			1.75611
$531$	−0.855596			−0.0371297
$532$	−14.6250	−	25.3313i	−0.634075	−	1.09825i
$533$	−29.8863	+	51.7647i	−1.29452	+	2.24218i
$534$	−0.277898	−	0.481334i	−0.0120258	−	0.0208294i
$535$	3.15500			0.136403
$536$	−49.6290			−2.14365
$537$	−7.19220	−	12.4573i	−0.310366	−	0.537570i
$538$	31.3659	−	54.3274i	1.35228	−	2.34222i
$539$	13.5447	+	23.4601i	0.583411	+	1.01050i
$540$	−15.3432	+	26.5752i	−0.660265	+	1.14361i
$541$	−18.1045	−	31.3580i	−0.778375	−	1.34819i	−0.932878	−	0.360193i	$-0.882711\pi$
$541$	−18.1045	−	31.3580i	−0.778375	−	1.34819i	0.154503	−	0.987992i	$-0.450622\pi$
$542$	−6.35250	−	11.0029i	−0.272863	−	0.472613i
$543$	3.62565	+	6.27981i	0.155592	+	0.269492i
$544$	0.742602	+	1.28622i	0.0318388	+	0.0551464i
$545$	8.75558	−	15.1651i	0.375048	−	0.649602i
$546$	−6.36629	−	11.0267i	−0.272452	−	0.471901i
$547$	20.1385	+	34.8810i	0.861062	+	1.49140i	0.870905	+	0.491451i	$0.163533\pi$
$547$	20.1385	+	34.8810i	0.861062	+	1.49140i	−0.00984381	+	0.999952i	$0.503133\pi$
$548$	12.7389	−	22.0644i	0.544177	−	0.942543i
$549$	0.958229	−	1.65970i	0.0408962	−	0.0708343i
$550$	6.08035	+	10.5315i	0.259267	+	0.449063i
$551$	20.0240	−	34.6826i	0.853050	−	1.47753i
$552$	24.7733			1.05442
$553$	9.58486	−	16.6015i	0.407590	−	0.705966i
$554$	7.06926	+	12.2443i	0.300344	+	0.520211i
$555$	−5.90511	+	10.2279i	−0.250658	+	0.434152i
$556$	32.7049	+	56.6466i	1.38700	+	2.40235i
$557$	−8.23696	−	14.2668i	−0.349011	−	0.604505i	0.637063	−	0.770812i	$-0.280149\pi$
$557$	−8.23696	−	14.2668i	−0.349011	−	0.604505i	−0.986074	+	0.166307i	$0.946816\pi$
$558$	13.0150	+	22.5426i	0.550969	+	0.954306i
$559$	−0.170886			−0.00722769
$560$	2.63512	−	4.56416i	0.111354	−	0.192871i
$561$	0.994962	+	1.72333i	0.0420073	+	0.0727588i
$562$	4.60511			0.194255
$563$	−7.84715	−	13.5917i	−0.330718	−	0.572820i	0.651935	−	0.758275i	$-0.273958\pi$
$563$	−7.84715	−	13.5917i	−0.330718	−	0.572820i	−0.982653	+	0.185455i	$0.940624\pi$
$564$	−16.0283	+	27.7619i	−0.674914	+	1.16899i
$565$	−15.3495			−0.645760
$566$	−20.4686	+	35.4526i	−0.860359	+	1.49019i
$567$	−4.86622			−0.204362
$568$	5.33326	−	9.23747i	0.223779	−	0.387596i
$569$	21.8342	−	37.8180i	0.915338	−	1.58541i	0.108933	−	0.994049i	$-0.465257\pi$
$569$	21.8342	−	37.8180i	0.915338	−	1.58541i	0.806405	−	0.591363i	$-0.201410\pi$
$570$	−11.8530	+	20.5300i	−0.496467	+	0.859906i
$571$	−29.1754			−1.22095			−0.610476	−	0.792035i	$-0.709022\pi$
$571$	−29.1754			−1.22095			−0.610476	+	0.792035i	$0.709022\pi$
$572$	100.932			4.22018
$573$	3.80535			0.158971
$574$	15.9221	+	27.5779i	0.664577	+	1.15108i
$575$	−4.12238	−	7.14017i	−0.171915	−	0.297766i
$576$	−13.3179	+	23.0673i	−0.554913	+	0.961137i
$577$	−15.4069			−0.641396			−0.320698	−	0.947182i	$-0.603917\pi$
$577$	−15.4069			−0.641396			−0.320698	+	0.947182i	$0.603917\pi$
$578$	19.9243	−	34.5098i	0.828740	−	1.43542i
$579$	2.37708	−	4.11723i	0.0987882	−	0.171106i
$580$	45.5917			1.89309
$581$	−0.592989	−	1.02709i	−0.0246013	−	0.0426108i
$582$	3.48763	−	6.04075i	0.144567	−	0.250397i
$583$	42.2597			1.75022
$584$	−0.164584	−	0.285068i	−0.00681054	−	0.0117962i
$585$	13.2300	−	22.9151i	0.546994	−	0.947422i
$586$	20.2764	+	35.1197i	0.837609	+	1.45078i
$587$	−19.7188	−	34.1539i	−0.813881	−	1.40968i	−0.910128	−	0.414326i	$-0.864017\pi$
$587$	−19.7188	−	34.1539i	−0.813881	−	1.40968i	0.0962471	−	0.995357i	$-0.469316\pi$
$588$	15.5897			0.642909
$589$	14.6596	+	25.3912i	0.604039	+	1.04623i
$590$	−0.847444	−	1.46782i	−0.0348887	−	0.0604290i
$591$	−8.46857	+	14.6680i	−0.348351	+	0.603361i
$592$	8.12711	−	14.0766i	0.334022	−	0.578543i
$593$	4.54885	+	7.87884i	0.186799	+	0.323545i	0.944181	−	0.329426i	$-0.106855\pi$
$593$	4.54885	+	7.87884i	0.186799	+	0.323545i	−0.757382	+	0.652972i	$0.773522\pi$
$594$	−24.7766	+	42.9143i	−1.01660	+	1.76080i
$595$	−1.27508			−0.0522733
$596$	−12.1982			−0.499656
$597$	−12.7436			−0.521562
$598$	−105.715			−4.32302
$599$	8.39454	−	14.5398i	0.342992	−	0.594079i	−0.641995	−	0.766709i	$-0.721893\pi$
$599$	8.39454	−	14.5398i	0.342992	−	0.594079i	0.984987	+	0.172630i	$0.0552264\pi$
$600$	3.18525			0.130037
$601$	−4.44989	+	7.70743i	−0.181515	+	0.314393i	−0.942397	−	0.334498i	$-0.891433\pi$
$601$	−4.44989	+	7.70743i	−0.181515	+	0.314393i	0.760882	+	0.648890i	$0.224767\pi$
$602$	−0.0455202	+	0.0788433i	−0.00185526	+	0.00321341i
$603$	−14.9403	+	25.8773i	−0.608414	+	1.05380i
$604$	−1.24231	+	2.15175i	−0.0505489	+	0.0875533i
$605$	−13.5501	−	23.4694i	−0.550890	−	0.954169i
$606$	31.6140			1.28423
$607$	−12.4764	−	21.6097i	−0.506400	−	0.877111i	−0.999973	−	0.00740627i	$-0.997642\pi$
$607$	−12.4764	−	21.6097i	−0.506400	−	0.877111i	0.493572	−	0.869705i	$-0.335691\pi$
$608$	−9.24730	+	16.0168i	−0.375027	+	0.649566i
$609$	−3.00594	−	5.20644i	−0.121807	−	0.210976i
$610$	3.79640			0.153712
$611$	31.1307	−	53.9199i	1.25941	−	2.18136i
$612$	−4.53636			−0.183371
$613$	−12.3798	−	21.4425i	−0.500016	−	0.866053i	−1.00000		1.83678e-5i	$-0.999994\pi$
$613$	−12.3798	−	21.4425i	−0.500016	−	0.866053i	0.499984	−	0.866035i	$-0.333339\pi$
$614$	−26.0579	−	45.1336i	−1.05161	−	1.82144i
$615$	8.35302	−	14.4679i	0.336826	−	0.583401i
$616$	12.2370	−	21.1951i	0.493042	−	0.853973i
$617$	12.3670	+	21.4202i	0.497876	+	0.862346i	0.999997	−	0.00245110i	$-0.000780209\pi$
$617$	12.3670	+	21.4202i	0.497876	+	0.862346i	−0.502121	+	0.864797i	$0.667447\pi$
$618$	−17.3212			−0.696762
$619$	7.69988			0.309484			0.154742	−	0.987955i	$-0.450545\pi$
$619$	7.69988			0.309484			0.154742	+	0.987955i	$0.450545\pi$
$620$	−16.6889	+	28.9060i	−0.670242	+	1.16089i
$621$	16.7981	−	29.0952i	0.674086	−	1.16755i
$622$	5.90627	−	10.2300i	0.236820	−	0.410184i
$623$	0.372268			0.0149146
$624$	4.59661	−	7.96156i	0.184012	−	0.318718i
$625$	9.39596	+	16.2743i	0.375838	+	0.650971i
$626$	−33.0474	+	57.2399i	−1.32084	+	2.28776i
$627$	−12.3898	+	21.4598i	−0.494802	+	0.857022i
$628$	−6.07176	+	10.5166i	−0.242290	+	0.419658i
$629$	−3.93255			−0.156801
$630$	−7.04838	−	12.2081i	−0.280814	−	0.486384i
$631$	−11.3002			−0.449855			−0.224927	−	0.974376i	$-0.572214\pi$
$631$	−11.3002			−0.449855			−0.224927	+	0.974376i	$0.572214\pi$
$632$	61.4898			2.44593
$633$	−10.8267			−0.430322
$634$	−40.6453			−1.61423
$635$	20.1463	+	34.8945i	0.799483	+	1.38475i
$636$	12.1601	−	21.0619i	0.482178	−	0.835157i
$637$	−30.2788			−1.19969
$638$	73.6228			2.91475
$639$	−3.21104	−	5.56168i	−0.127027	−	0.220017i
$640$	−41.2922			−1.63222
$641$	−11.0797	+	19.1906i	−0.437621	+	0.757982i	−0.997505	−	0.0705890i	$-0.977512\pi$
$641$	−11.0797	+	19.1906i	−0.437621	+	0.757982i	0.559885	+	0.828571i	$0.310845\pi$
$642$	1.46601	−	2.53920i	0.0578586	−	0.100214i
$643$	19.1698	+	33.2031i	0.755983	+	1.30940i	0.944884	+	0.327405i	$0.106174\pi$
$643$	19.1698	+	33.2031i	0.755983	+	1.30940i	−0.188901	+	0.981996i	$0.560493\pi$
$644$	−18.2284	+	31.5725i	−0.718298	+	1.24413i
$645$	0.0477614			0.00188060
$646$	−7.89358			−0.310569
$647$	19.9441	+	34.5442i	0.784084	+	1.35807i	0.929545	+	0.368709i	$0.120200\pi$
$647$	19.9441	+	34.5442i	0.784084	+	1.35807i	−0.145461	+	0.989364i	$0.546467\pi$
$648$	−7.80457	−	13.5179i	−0.306592	−	0.531034i
$649$	−0.885826	−	1.53430i	−0.0347717	−	0.0602264i
$650$	−13.5925			−0.533140
$651$	4.40132			0.172501
$652$	−6.77146	−	11.7285i	−0.265191	−	0.459324i
$653$	−14.7288			−0.576381			−0.288191	−	0.957573i	$-0.593054\pi$
$653$	−14.7288			−0.576381			−0.288191	+	0.957573i	$0.593054\pi$
$654$	−8.13674	−	14.0933i	−0.318172	−	0.551090i
$655$	6.50358	+	11.2645i	0.254116	+	0.440141i
$656$	−11.4961	+	19.9119i	−0.448849	+	0.777429i
$657$	−0.198185			−0.00773193
$658$	−16.5850	−	28.7261i	−0.646553	−	1.11986i
$659$	−46.7544			−1.82129			−0.910647	−	0.413186i	$-0.864416\pi$
$659$	−46.7544			−1.82129			−0.910647	+	0.413186i	$0.864416\pi$
$660$	−28.2098			−1.09807
$661$	45.3733			1.76482			0.882408	−	0.470484i	$-0.155921\pi$
$661$	45.3733			1.76482			0.882408	+	0.470484i	$0.155921\pi$
$662$	−12.9342			−0.502702
$663$	−2.22421			−0.0863812
$664$	1.90210	−	3.29454i	0.0738159	−	0.127853i
$665$	−7.93903	−	13.7508i	−0.307862	−	0.533233i
$666$	−21.7383	−	37.6518i	−0.842341	−	1.45898i
$667$	−49.9151			−1.93272
$668$	−3.35924	−	5.81837i	−0.129973	−	0.225119i
$669$	−6.72109	−	11.6413i	−0.259852	−	0.450077i
$670$	−59.1916			−2.28677
$671$	3.96834			0.153196
$672$	1.38818	+	2.40439i	0.0535501	+	0.0927515i
$673$	−1.19741	+	2.07397i	−0.0461567	+	0.0799457i	−0.888181	−	0.459494i	$-0.848031\pi$
$673$	−1.19741	+	2.07397i	−0.0461567	+	0.0799457i	0.842024	+	0.539440i	$0.181364\pi$
$674$	15.0879	+	26.1331i	0.581166	+	1.00661i
$675$	2.15984	−	3.74095i	0.0831322	−	0.143989i
$676$	−32.5484	+	56.3754i	−1.25186	+	2.16829i
$677$	−13.5537			−0.520911			−0.260455	−	0.965486i	$-0.583873\pi$
$677$	−13.5537			−0.520911			−0.260455	+	0.965486i	$0.583873\pi$
$678$	−7.13232	+	12.3535i	−0.273915	+	0.474435i
$679$	2.33598	+	4.04604i	0.0896468	+	0.155273i
$680$	−2.04501	−	3.54206i	−0.0784226	−	0.135832i
$681$	4.27776			0.163924
$682$	−26.9497	+	46.6783i	−1.03196	+	1.78740i
$683$	5.99845	−	10.3896i	0.229524	−	0.397548i	−0.728143	−	0.685425i	$-0.759616\pi$
$683$	5.99845	−	10.3896i	0.229524	−	0.397548i	0.957667	+	0.287878i	$0.0929496\pi$
$684$	−28.2446	−	48.9211i	−1.07996	−	1.87055i
$685$	6.91515	−	11.9774i	0.264214	−	0.457633i
$686$	−18.4029	+	31.8748i	−0.702627	+	1.21699i
$687$	4.81172			0.183579
$688$	−0.0657333			−0.00250606
$689$	−23.6176	+	40.9069i	−0.899759	+	1.55843i
$690$	29.5467			1.12482
$691$	10.2326	−	17.7235i	0.389268	−	0.674232i	−0.603083	−	0.797678i	$-0.706061\pi$
$691$	10.2326	−	17.7235i	0.389268	−	0.674232i	0.992351	+	0.123446i	$0.0393946\pi$
$692$	32.5259			1.23645
$693$	−7.36761	−	12.7611i	−0.279872	−	0.484753i
$694$	26.3952	+	45.7178i	1.00195	+	1.73542i
$695$	17.7535	+	30.7500i	0.673429	+	1.16641i
$696$	9.64201	−	16.7005i	0.365480	−	0.633029i
$697$	5.56276			0.210705
$698$	−29.7329	−	33.0911i	−1.12541	−	1.25252i
$699$	−20.2489			−0.765883
$700$	−2.34373	+	4.05946i	−0.0885846	+	0.153433i
$701$	−12.4030	−	21.4827i	−0.468457	−	0.811391i	0.530893	−	0.847439i	$-0.321856\pi$
$701$	−12.4030	−	21.4827i	−0.468457	−	0.811391i	−0.999350	+	0.0360479i	$0.988523\pi$
$702$	−27.6937	−	47.9669i	−1.04523	−	1.81039i
$703$	−24.4852	−	42.4095i	−0.923475	−	1.59951i
$704$	−55.1538			−2.07869
$705$	−8.70080	+	15.0702i	−0.327691	+	0.567578i
$706$	14.9869			0.564040
$707$	−10.5874	+	18.3379i	−0.398180	+	0.689669i
$708$	−1.01957			−0.0383179
$709$	13.7874			0.517797			0.258898	−	0.965905i	$-0.416641\pi$
$709$	13.7874			0.517797			0.258898	+	0.965905i	$0.416641\pi$
$710$	6.36088	−	11.0174i	0.238720	−	0.413475i
$711$	18.5108	−	32.0617i	0.694210	−	1.20241i
$712$	0.597053	+	1.03413i	0.0223755	+	0.0387555i
$713$	18.2715	−	31.6471i	0.684273	−	1.18519i
$714$	−0.592481	+	1.02621i	−0.0221730	+	0.0384048i
$715$	54.7899			2.04903
$716$	33.9502	+	58.8035i	1.26878	+	2.19759i
$717$	−0.414687	−	0.718260i	−0.0154868	−	0.0268239i
$718$	7.25839	−	12.5719i	0.270881	−	0.469179i
$719$	2.84872			0.106239			0.0531196	−	0.998588i	$-0.483084\pi$
$719$	2.84872			0.106239			0.0531196	+	0.998588i	$0.483084\pi$
$720$	5.08909	−	8.81456i	0.189659	−	0.328499i
$721$	5.80080	−	10.0473i	0.216033	−	0.374181i
$722$	−26.5251	−	45.9429i	−0.987163	−	1.70982i
$723$	0.683266	−	1.18345i	0.0254109	−	0.0440130i
$724$	−17.1146	−	29.6433i	−0.636059	−	1.10169i
$725$	−6.41788			−0.238354
$726$	−25.1848			−0.934694
$727$	−5.43884	−	9.42035i	−0.201715	−	0.349381i	0.747366	−	0.664413i	$-0.231318\pi$
$727$	−5.43884	−	9.42035i	−0.201715	−	0.349381i	−0.949081	+	0.315031i	$0.897985\pi$
$728$	13.6777	+	23.6905i	0.506930	+	0.878028i
$729$	0.389511			0.0144263
$730$	−0.196297	−	0.339996i	−0.00726526	−	0.0125838i
$731$	0.00795176	+	0.0137729i	0.000294107	+	0.000509408i
$732$	1.14188	−	1.97779i	0.0422049	−	0.0731011i
$733$	−26.8829			−0.992944			−0.496472	−	0.868053i	$-0.665372\pi$
$733$	−26.8829			−0.992944			−0.496472	+	0.868053i	$0.665372\pi$
$734$	84.0776			3.10336
$735$	8.46271			0.312152
$736$	23.0513			0.849684
$737$	−61.8725			−2.27910
$738$	30.7497	+	53.2600i	1.13191	+	1.96053i
$739$	−2.61604			−0.0962326			−0.0481163	−	0.998842i	$-0.515322\pi$
$739$	−2.61604			−0.0962326			−0.0481163	+	0.998842i	$0.515322\pi$
$740$	27.8746	−	48.2802i	1.02469	−	1.77481i
$741$	−13.8486	−	23.9864i	−0.508739	−	0.881163i
$742$	12.5824	+	21.7934i	0.461915	+	0.800061i
$743$	−46.2601			−1.69712			−0.848560	−	0.529100i	$-0.822530\pi$
$743$	−46.2601			−1.69712			−0.848560	+	0.529100i	$0.822530\pi$
$744$	7.05894	+	12.2264i	0.258793	+	0.448243i
$745$	−6.62163			−0.242598
$746$	−50.9026			−1.86368
$747$	−1.14521	−	1.98357i	−0.0419012	−	0.0725750i
$748$	−4.69664	−	8.13482i	−0.171726	−	0.297438i
$749$	0.981918	+	1.70073i	0.0358785	+	0.0621434i
$750$	22.2479			0.812377
$751$	44.2869			1.61605			0.808025	−	0.589148i	$-0.200536\pi$
$751$	44.2869			1.61605			0.808025	+	0.589148i	$0.200536\pi$
$752$	11.9748	−	20.7409i	0.436676	−	0.756344i
$753$	3.78559	+	6.55683i	0.137955	+	0.238944i
$754$	−41.1454	+	71.2660i	−1.49843	+	2.59535i
$755$	−0.674375	+	1.16805i	−0.0245430	+	0.0425098i
$756$	−19.1008			−0.694688
$757$	−7.29656	−	12.6380i	−0.265198	−	0.459337i	0.702417	−	0.711765i	$-0.252104\pi$
$757$	−7.29656	−	12.6380i	−0.265198	−	0.459337i	−0.967616	+	0.252429i	$0.918771\pi$
$758$	21.0355			0.764042
$759$	30.8849			1.12105
$760$	25.4656	−	44.1078i	0.923735	−	1.59996i
$761$	13.5404	+	23.4527i	0.490840	+	0.850161i	0.999944	−	0.0105444i	$-0.00335645\pi$
$761$	13.5404	+	23.4527i	0.490840	+	0.850161i	−0.509104	+	0.860705i	$0.670023\pi$
$762$	37.4448			1.35648
$763$	10.8998			0.394601
$764$	−17.9629			−0.649873
$765$	−2.46251			−0.0890323
$766$	1.99473	+	3.45498i	0.0720726	+	0.124833i
$767$	1.98024			0.0715023
$768$	−10.5398	+	18.2554i	−0.380321	+	0.658736i
$769$	9.86930	−	17.0941i	0.355896	−	0.616430i	−0.631375	−	0.775478i	$-0.717509\pi$
$769$	9.86930	−	17.0941i	0.355896	−	0.616430i	0.987271	+	0.159048i	$0.0508423\pi$
$770$	14.5948	−	25.2790i	0.525961	−	0.910991i
$771$	2.51947	+	4.36386i	0.0907367	+	0.157161i
$772$	−11.2208	+	19.4351i	−0.403847	+	0.699483i
$773$	−34.4040			−1.23743			−0.618713	−	0.785617i	$-0.712346\pi$
$773$	−34.4040			−1.23743			−0.618713	+	0.785617i	$0.712346\pi$
$774$	−0.0879111	+	0.152267i	−0.00315990	+	0.00547311i
$775$	2.34927	−	4.06906i	0.0843884	−	0.146165i
$776$	−7.49302	+	12.9783i	−0.268984	+	0.465894i
$777$	−7.35128			−0.263726
$778$	−66.2987			−2.37692
$779$	34.6353	+	59.9901i	1.24094	+	2.14937i
$780$	15.7656	−	27.3068i	0.564498	−	0.977740i
$781$	6.64898	−	11.5164i	0.237919	−	0.412088i
$782$	4.91921	+	8.52033i	0.175911	+	0.304686i
$783$	−13.0760	−	22.6483i	−0.467298	−	0.809384i
$784$	−11.6471			−0.415968
$785$	−3.29599	+	5.70882i	−0.117639	+	0.203757i
$786$	12.0878			0.431158
$787$	17.2873	+	29.9424i	0.616225	+	1.06733i	0.990168	+	0.139881i	$0.0446720\pi$
$787$	17.2873	+	29.9424i	0.616225	+	1.06733i	−0.373944	+	0.927451i	$0.621995\pi$
$788$	39.9752	−	69.2391i	1.42406	−	2.46654i
$789$	−1.52020	−	2.63306i	−0.0541204	−	0.0937393i
$790$	73.3378			2.60924
$791$	−4.77717	−	8.27430i	−0.169857	−	0.294200i
$792$	23.6327	−	40.9331i	0.839752	−	1.45449i
$793$	−2.21778	+	3.84131i	−0.0787557	+	0.136409i
$794$	−22.0793	+	38.2425i	−0.783566	+	1.35718i
$795$	6.60096	−	11.4332i	0.234112	−	0.405494i
$796$	60.1552			2.13215
$797$	−3.22019	+	5.57753i	−0.114065	+	0.197566i	−0.917406	−	0.397953i	$-0.869721\pi$
$797$	−3.22019	+	5.57753i	−0.114065	+	0.197566i	0.803341	+	0.595520i	$0.203054\pi$
$798$	−14.7558			−0.522350
$799$	−5.79437			−0.204990
$800$	2.96385			0.104788
$801$	0.718945			0.0254027
$802$	−8.11168	+	14.0498i	−0.286433	+	0.496117i
$803$	−0.205187	−	0.355395i	−0.00724090	−	0.0125416i
$804$	−17.8036	+	30.8367i	−0.627884	+	1.08753i
$805$	−9.89507	+	17.1388i	−0.348755	+	0.604062i
$806$	−30.1227	−	52.1740i	−1.06103	−	1.83775i
$807$	−10.2425	−	17.7405i	−0.360553	−	0.624496i
$808$	−67.9214			−2.38947
$809$	−3.92601	−	6.80006i	−0.138031	−	0.239077i	0.788720	−	0.614753i	$-0.210744\pi$
$809$	−3.92601	−	6.80006i	−0.138031	−	0.239077i	−0.926751	+	0.375675i	$0.877411\pi$
$810$	−9.30838	−	16.1226i	−0.327063	−	0.566490i
$811$	2.94924	−	5.10823i	0.103562	−	0.179374i	−0.809588	−	0.586999i	$-0.800309\pi$
$811$	2.94924	−	5.10823i	0.103562	−	0.179374i	0.913150	+	0.407624i	$0.133643\pi$
$812$	14.1893	+	24.5766i	0.497947	+	0.862470i
$813$	−4.14880			−0.145505
$814$	45.0127	−	77.9642i	1.57769	−	2.73264i
$815$	−3.67581	−	6.36669i	−0.128758	−	0.223016i
$816$	−0.855570			−0.0299509
$817$	−0.0990198	+	0.171507i	−0.00346426	+	0.00600028i
$818$	20.3798	−	35.2989i	0.712564	−	1.23420i
$819$	16.4701			0.575512
$820$	−39.4298	+	68.2944i	−1.37695	+	2.38494i
$821$	−5.24852	−	9.09069i	−0.183174	−	0.317267i	0.759785	−	0.650174i	$-0.225304\pi$
$821$	−5.24852	−	9.09069i	−0.183174	−	0.317267i	−0.942960	+	0.332906i	$0.891971\pi$
$822$	−6.42639	−	11.1308i	−0.224146	−	0.388233i
$823$	−23.2008			−0.808729			−0.404365	−	0.914598i	$-0.632507\pi$
$823$	−23.2008			−0.808729			−0.404365	+	0.914598i	$0.632507\pi$
$824$	37.2139			1.29641
$825$	3.97106			0.138255
$826$	0.527492	−	0.913644i	0.0183538	−	0.0317897i
$827$	6.10370	−	10.5719i	0.212247	−	0.367622i	−0.740171	−	0.672419i	$-0.765255\pi$
$827$	6.10370	−	10.5719i	0.212247	−	0.367622i	0.952417	+	0.304797i	$0.0985887\pi$
$828$	−35.2036	+	60.9745i	−1.22341	+	2.11901i
$829$	46.9891			1.63200			0.815999	−	0.578053i	$-0.196187\pi$
$829$	46.9891			1.63200			0.815999	+	0.578053i	$0.196187\pi$
$830$	2.26861	−	3.92934i	0.0787445	−	0.136389i
$831$	4.61691			0.160159
$832$	30.8237	−	53.3883i	1.06862	−	1.85090i
$833$	1.40895	+	2.44037i	0.0488173	+	0.0845540i
$834$	32.9974			1.14261
$835$	−1.82352	−	3.15844i	−0.0631057	−	0.109302i
$836$	58.4852	−	101.299i	2.02275	−	3.50351i
$837$	19.1459			0.661781
$838$	−6.14815	−	10.6489i	−0.212384	−	0.367861i
$839$	11.6002	+	20.0921i	0.400482	+	0.693655i	0.993784	−	0.111325i	$-0.0355095\pi$
$839$	11.6002	+	20.0921i	0.400482	+	0.693655i	−0.593302	+	0.804980i	$0.702176\pi$
$840$	−3.82283	−	6.62133i	−0.131900	−	0.228458i
$841$	−4.92744	+	8.53458i	−0.169912	+	0.294296i
$842$	−33.4198	−	57.8847i	−1.15172	−	1.99484i
$843$	0.751896	−	1.30232i	0.0258967	−	0.0448544i
$844$	51.1065			1.75916
$845$	−17.6685	+	30.6028i	−0.607816	+	1.05277i
$846$	−32.0300	−	55.4775i	−1.10121	−	1.90736i
$847$	8.43427	−	14.6086i	0.289805	−	0.501957i
$848$	−9.08480	+	15.7353i	−0.311973	+	0.540354i
$849$	6.68399	+	11.5770i	0.229394	+	0.397322i
$850$	0.632493	+	1.09551i	0.0216943	+	0.0375757i
$851$	−30.5179	+	52.8585i	−1.04614	+	1.81197i
$852$	−3.82644	−	6.62758i	−0.131092	−	0.227057i
$853$	19.3615	+	33.5351i	0.662925	+	1.14822i	0.979844	+	0.199767i	$0.0640184\pi$
$853$	19.3615	+	33.5351i	0.662925	+	1.14822i	−0.316919	+	0.948453i	$0.602648\pi$
$854$	1.18154	+	2.04648i	0.0404313	+	0.0700291i
$855$	−15.3323	−	26.5563i	−0.524353	−	0.908206i
$856$	−3.14965	+	5.45536i	−0.107653	+	0.186460i
$857$	22.7341	+	39.3766i	0.776582	+	1.34508i	0.933901	+	0.357532i	$0.116382\pi$
$857$	22.7341	+	39.3766i	0.776582	+	1.34508i	−0.157319	+	0.987548i	$0.550285\pi$
$858$	25.4587	−	44.0958i	0.869146	−	1.50540i
$859$	9.38645	+	16.2578i	0.320261	+	0.554709i	0.980542	−	0.196310i	$-0.0628959\pi$
$859$	9.38645	+	16.2578i	0.320261	+	0.554709i	−0.660280	+	0.751019i	$0.729563\pi$
$860$	−0.225454			−0.00768791
$861$	10.3987			0.354387
$862$	−26.4822	−	45.8686i	−0.901988	−	1.56229i
$863$	23.6557	−	40.9728i	0.805248	−	1.39473i	−0.110875	−	0.993834i	$-0.535365\pi$
$863$	23.6557	−	40.9728i	0.805248	−	1.39473i	0.916123	−	0.400897i	$-0.131301\pi$
$864$	6.03864	+	10.4592i	0.205439	+	0.355830i
$865$	17.6563			0.600333
$866$	−48.5015			−1.64815
$867$	−6.50624	−	11.2691i	−0.220964	−	0.382720i
$868$	−20.7761			−0.705185
$869$	76.6594			2.60049
$870$	11.4999	−	19.9183i	0.389882	−	0.675295i
$871$	34.5786	−	59.8919i	1.17165	−	2.02936i
$872$	17.4814	+	30.2788i	0.591997	+	1.02537i
$873$	4.51138	+	7.81394i	0.152687	+	0.264462i
$874$	−61.2568	+	106.100i	−2.07204	+	3.58888i
$875$	−7.45072	+	12.9050i	−0.251880	+	0.436269i
$876$	−0.236167			−0.00797935
$877$	47.3075			1.59746			0.798731	−	0.601689i	$-0.205505\pi$
$877$	47.3075			1.59746			0.798731	+	0.601689i	$0.205505\pi$
$878$	−13.4716	−	23.3335i	−0.454644	−	0.787466i
$879$	13.2424			0.446657
$880$	21.0756			0.710458
$881$	−24.8450	−	43.0328i	−0.837049	−	1.44981i	−0.892351	−	0.451342i	$-0.850945\pi$
$881$	−24.8450	−	43.0328i	−0.837049	−	1.44981i	0.0553014	−	0.998470i	$-0.482388\pi$
$882$	−15.5767	+	26.9797i	−0.524496	+	0.908454i
$883$	−23.1091	−	40.0262i	−0.777684	−	1.34699i	−0.933273	−	0.359167i	$-0.883061\pi$
$883$	−23.1091	−	40.0262i	−0.777684	−	1.34699i	0.155589	−	0.987822i	$-0.450272\pi$
$884$	10.4992			0.353127
$885$	−0.553463			−0.0186045
$886$	16.9908	+	29.4290i	0.570818	+	0.988686i
$887$	12.5207	−	21.6865i	0.420404	−	0.728161i	−0.575575	−	0.817749i	$-0.695222\pi$
$887$	12.5207	−	21.6865i	0.420404	−	0.728161i	0.995979	+	0.0895882i	$0.0285551\pi$
$888$	−11.7902	−	20.4212i	−0.395652	−	0.685290i
$889$	−12.5401	+	21.7201i	−0.420582	+	0.728469i
$890$	0.712095	+	1.23338i	0.0238695	+	0.0413431i
$891$	−9.72997	−	16.8528i	−0.325966	−	0.564590i
$892$	31.7264	+	54.9517i	1.06228	+	1.83992i
$893$	−36.0773	−	62.4878i	−1.20728	−	2.09107i
$894$	−3.07681	+	5.32919i	−0.102904	+	0.178235i
$895$	18.4295	+	31.9208i	0.616030	+	1.06700i
$896$	−12.8512	−	22.2589i	−0.429328	−	0.743618i
$897$	−17.2606	+	29.8962i	−0.576315	+	0.998207i
$898$	27.5774	−	47.7655i	0.920270	−	1.59396i
$899$	−14.2229	−	24.6347i	−0.474360	−	0.821615i
$900$	−4.52634	+	7.83985i	−0.150878	+	0.261328i
$901$	4.39596			0.146451
$902$	−63.6723	+	110.284i	−2.12006	+	3.67205i
$903$	0.0148646	+	0.0257462i	0.000494662	+	0.000856779i
$904$	15.3235	−	26.5411i	0.509652	−	0.882742i
$905$	−9.29047	−	16.0916i	−0.308826	−	0.534902i
$906$	0.626711	+	1.08550i	0.0208211	+	0.0360632i
$907$	8.04753	+	13.9387i	0.267214	+	0.462828i	0.968141	−	0.250404i	$-0.0805636\pi$
$907$	8.04753	+	13.9387i	0.267214	+	0.462828i	−0.700927	+	0.713233i	$0.747230\pi$
$908$	−20.1928			−0.670123
$909$	−20.4470	+	35.4152i	−0.678184	+	1.17465i
$910$	16.3132	+	28.2552i	0.540776	+	0.936652i
$911$	−47.0027			−1.55727			−0.778635	−	0.627477i	$-0.784088\pi$
$911$	−47.0027			−1.55727			−0.778635	+	0.627477i	$0.784088\pi$
$912$	−5.32702	−	9.22666i	−0.176395	−	0.305525i
$913$	2.37136	−	4.10731i	0.0784804	−	0.135932i
$914$	−26.8563			−0.888329
$915$	0.619854	−	1.07362i	0.0204918	−	0.0354928i
$916$	−22.7133			−0.750470
$917$	−4.04816	+	7.01162i	−0.133682	+	0.231544i
$918$	−2.57732	+	4.46405i	−0.0850643	+	0.147336i
$919$	17.1618	−	29.7252i	0.566117	−	0.980543i	−0.430828	−	0.902434i	$-0.641778\pi$
$919$	17.1618	−	29.7252i	0.566117	−	0.980543i	0.996945	−	0.0781089i	$-0.0248882\pi$
$920$	−63.4798			−2.09287
$921$	−17.0183			−0.560773
$922$	−81.3108			−2.67783
$923$	7.43181	+	12.8723i	0.244621	+	0.423696i
$924$	−8.77962	−	15.2068i	−0.288828	−	0.500266i
$925$	−3.92387	+	6.79633i	−0.129016	+	0.223462i
$926$	−70.5026			−2.31686
$927$	11.2028	−	19.4039i	0.367949	−	0.637307i
$928$	8.97181	−	15.5396i	0.294514	−	0.510113i
$929$	8.81432			0.289188			0.144594	−	0.989491i	$-0.453812\pi$
$929$	8.81432			0.289188			0.144594	+	0.989491i	$0.453812\pi$
$930$	8.41908	+	14.5823i	0.276072	+	0.478172i
$931$	−17.5450	+	30.3889i	−0.575016	+	0.995956i
$932$	95.5833			3.13093
$933$	−1.92869	−	3.34058i	−0.0631424	−	0.109366i
$934$	1.19612	−	2.07174i	0.0391383	−	0.0677895i
$935$	−2.54952	−	4.41590i	−0.0833782	−	0.144415i
$936$	26.4152	+	45.7524i	0.863407	+	1.49546i
$937$	−12.2121			−0.398953			−0.199476	−	0.979903i	$-0.563924\pi$
$937$	−12.2121			−0.398953			−0.199476	+	0.979903i	$0.563924\pi$
$938$	−18.4220	−	31.9078i	−0.601498	−	1.04183i
$939$	10.7916	+	18.6916i	0.352171	+	0.609977i
$940$	41.0714	−	71.1378i	1.33960	−	2.32026i
$941$	−2.44254	+	4.23061i	−0.0796246	+	0.137914i	−0.903088	−	0.429455i	$-0.858706\pi$
$941$	−2.44254	+	4.23061i	−0.0796246	+	0.137914i	0.823463	+	0.567369i	$0.192039\pi$
$942$	3.06303	+	5.30533i	0.0997990	+	0.172857i
$943$	43.1689	−	74.7706i	1.40577	−	2.43487i
$944$	0.761723			0.0247920
$945$	−10.3686			−0.337292
$946$	−0.364069			−0.0118369
$947$	32.3777			1.05213			0.526067	−	0.850443i	$-0.323666\pi$
$947$	32.3777			1.05213			0.526067	+	0.850443i	$0.323666\pi$
$948$	22.0584	−	38.2063i	0.716425	−	1.24088i
$949$	0.458691			0.0148897
$950$	−7.87615	+	13.6419i	−0.255536	+	0.442601i
$951$	−6.63633	+	11.4945i	−0.215198	+	0.372733i
$952$	1.27292	−	2.20476i	0.0412556	−	0.0714568i
$953$	−22.9863	+	39.8135i	−0.744600	+	1.28969i	0.205781	+	0.978598i	$0.434027\pi$
$953$	−22.9863	+	39.8135i	−0.744600	+	1.28969i	−0.950381	+	0.311087i	$0.899307\pi$
$954$	24.2999	+	42.0886i	0.786738	+	1.36267i
$955$	−9.75094			−0.315533
$956$	1.95750	+	3.39049i	0.0633100	+	0.109656i
$957$	12.0207	−	20.8205i	0.388574	−	0.673031i
$958$	15.9207	+	27.5755i	0.514374	+	0.890922i
$959$	8.60869			0.277989
$960$	−8.61502	+	14.9216i	−0.278048	+	0.481594i
$961$	−10.1748			−0.328219
$962$	50.3123	+	87.1434i	1.62213	+	2.80962i
$963$	1.89634	+	3.28455i	0.0611085	+	0.105843i
$964$	−3.22530	+	5.58638i	−0.103880	+	0.179925i
$965$	−6.09111	+	10.5501i	−0.196080	+	0.339620i
$966$	9.19569	+	15.9274i	0.295867	+	0.512456i
$967$	9.63870			0.309960			0.154980	−	0.987918i	$-0.450469\pi$
$967$	9.63870			0.309960			0.154980	+	0.987918i	$0.450469\pi$
$968$	54.1084			1.73911
$969$	−1.28882	+	2.23230i	−0.0414029	+	0.0717119i
$970$	−8.93680	+	15.4790i	−0.286943	+	0.497000i
$971$	9.49202	−	16.4407i	0.304613	−	0.527606i	−0.672562	−	0.740041i	$-0.734806\pi$
$971$	9.49202	−	16.4407i	0.304613	−	0.527606i	0.977175	+	0.212435i	$0.0681394\pi$
$972$	−57.3998			−1.84110
$973$	−11.0507	+	19.1404i	−0.354269	+	0.613612i
$974$	−4.82236	−	8.35258i	−0.154519	−	0.267634i
$975$	−2.21930	+	3.84394i	−0.0710744	+	0.123105i
$976$	−0.853096	+	1.47761i	−0.0273069	+	0.0472970i
$977$	−22.2579	+	38.5518i	−0.712093	+	1.23338i	0.251977	+	0.967733i	$0.418919\pi$
$977$	−22.2579	+	38.5518i	−0.712093	+	1.23338i	−0.964070	+	0.265649i	$0.914414\pi$
$978$	−6.83202			−0.218464
$979$	0.744347	+	1.28925i	0.0237894	+	0.0412045i
$980$	−39.9475			−1.27608
$981$	21.0504			0.672087
$982$	29.3869			0.937773
$983$	13.8901			0.443025			0.221512	−	0.975158i	$-0.428901\pi$
$983$	13.8901			0.443025			0.221512	+	0.975158i	$0.428901\pi$
$984$	16.6777	+	28.8866i	0.531666	+	0.920872i
$985$	21.7001	−	37.5857i	0.691423	−	1.19758i
$986$	7.65842			0.243894
$987$	−10.8317			−0.344775
$988$	65.3710	+	113.226i	2.07973	+	3.60220i
$989$	0.246833			0.00784884
$990$	28.1863	−	48.8202i	0.895821	−	1.55161i
$991$	16.9763	−	29.4039i	0.539271	−	0.934045i	−0.459672	−	0.888089i	$-0.652033\pi$
$991$	16.9763	−	29.4039i	0.539271	−	0.934045i	0.998943	−	0.0459564i	$-0.0146335\pi$
$992$	6.56828	+	11.3766i	0.208543	+	0.361207i
$993$	−2.11183	+	3.65779i	−0.0670167	+	0.116076i
$994$	7.91868			0.251165
$995$	32.6546			1.03522
$996$	−1.36470	−	2.36372i	−0.0432421	−	0.0748974i
$997$	−1.73636	−	3.00747i	−0.0549912	−	0.0952476i	0.837219	−	0.546867i	$-0.184180\pi$
$997$	−1.73636	−	3.00747i	−0.0549912	−	0.0952476i	−0.892211	+	0.451620i	$0.850846\pi$
$998$	−8.19911	−	14.2013i	−0.259538	−	0.449534i
$999$	−31.9784			−1.01175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.c.a.122.4	✓	56
349.226	even	3	inner	349.2.c.a.226.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.c.a.122.4	✓	56	1.1	even	1	trivial
349.2.c.a.226.4	yes	56	349.226	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19066 + 2.06228i) q^{2} +(0.388808 + 0.673436i) q^{3} +(-1.83534 - 3.17890i) q^{4} +(-0.996293 - 1.72563i) q^{5} -1.85175 q^{6} +(0.620144 - 1.07412i) q^{7} +3.97841 q^{8} +(1.19766 - 2.07440i) q^{9} +O(q^{10})\)	\(q+(-1.19066 + 2.06228i) q^{2} +(0.388808 + 0.673436i) q^{3} +(-1.83534 - 3.17890i) q^{4} +(-0.996293 - 1.72563i) q^{5} -1.85175 q^{6} +(0.620144 - 1.07412i) q^{7} +3.97841 q^{8} +(1.19766 - 2.07440i) q^{9} +4.74498 q^{10} +4.95989 q^{11} +(1.42719 - 2.47196i) q^{12} +(-2.77192 + 4.80111i) q^{13} +(1.47676 + 2.55782i) q^{14} +(0.774734 - 1.34188i) q^{15} +(-1.06625 + 1.84681i) q^{16} +0.515940 q^{17} +(2.85200 + 4.93981i) q^{18} +(3.21239 + 5.56402i) q^{19} +(-3.65707 + 6.33423i) q^{20} +0.964468 q^{21} +(-5.90554 + 10.2287i) q^{22} +(4.00386 - 6.93489i) q^{23} +(1.54684 + 2.67920i) q^{24} +(0.514800 - 0.891661i) q^{25} +(-6.60083 - 11.4330i) q^{26} +4.19548 q^{27} -4.55269 q^{28} +(-3.11668 - 5.39826i) q^{29} +(1.84489 + 3.19544i) q^{30} +4.56346 q^{31} +(1.43932 + 2.49297i) q^{32} +(1.92845 + 3.34017i) q^{33} +(-0.614309 + 1.06401i) q^{34} -2.47138 q^{35} -8.79242 q^{36} -7.62211 q^{37} -15.2994 q^{38} -4.31099 q^{39} +(-3.96366 - 6.86526i) q^{40} +10.7818 q^{41} +(-1.14835 + 1.98901i) q^{42} +(0.0154122 + 0.0266947i) q^{43} +(-9.10307 - 15.7670i) q^{44} -4.77287 q^{45} +(9.53447 + 16.5142i) q^{46} -11.2307 q^{47} -1.65827 q^{48} +(2.73084 + 4.72996i) q^{49} +(1.22590 + 2.12333i) q^{50} +(0.200602 + 0.347452i) q^{51} +20.3497 q^{52} +8.52029 q^{53} +(-4.99539 + 8.65227i) q^{54} +(-4.94150 - 8.55894i) q^{55} +(2.46719 - 4.27329i) q^{56} +(-2.49800 + 4.32667i) q^{57} +14.8436 q^{58} +(-0.178598 - 0.309341i) q^{59} -5.68759 q^{60} +0.800087 q^{61} +(-5.43353 + 9.41115i) q^{62} +(-1.48544 - 2.57286i) q^{63} -11.1200 q^{64} +11.0466 q^{65} -9.18449 q^{66} -12.4746 q^{67} +(-0.946924 - 1.64012i) q^{68} +6.22694 q^{69} +(2.94257 - 5.09668i) q^{70} +(1.34055 - 2.32190i) q^{71} +(4.76477 - 8.25282i) q^{72} +(-0.0413693 - 0.0716538i) q^{73} +(9.07533 - 15.7189i) q^{74} +0.800635 q^{75} +(11.7916 - 20.4237i) q^{76} +(3.07585 - 5.32752i) q^{77} +(5.13292 - 8.89047i) q^{78} +15.4559 q^{79} +4.24921 q^{80} +(-1.96173 - 3.39782i) q^{81} +(-12.8374 + 22.2351i) q^{82} +(0.478106 - 0.828105i) q^{83} +(-1.77012 - 3.06595i) q^{84} +(-0.514027 - 0.890321i) q^{85} -0.0734026 q^{86} +(2.42358 - 4.19777i) q^{87} +19.7325 q^{88} +(0.150073 + 0.259935i) q^{89} +(5.68286 - 9.84300i) q^{90} +(3.43798 + 5.95476i) q^{91} -29.3938 q^{92} +(1.77431 + 3.07320i) q^{93} +(13.3719 - 23.1609i) q^{94} +(6.40095 - 11.0868i) q^{95} +(-1.11924 + 1.93858i) q^{96} +(-1.88342 + 3.26218i) q^{97} -13.0060 q^{98} +(5.94024 - 10.2888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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