LMFDB - Embedded newform 225.2.q.a.16.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.8
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27611 + 0.568159i) q^{2} +(-0.563301 + 1.63789i) q^{3} +(-0.0326201 + 0.0362283i) q^{4} +(0.323231 - 2.21258i) q^{5} +(-0.211752 - 2.41017i) q^{6} +(2.19012 - 3.79340i) q^{7} +(0.884357 - 2.72177i) q^{8} +(-2.36538 - 1.84525i) q^{9} +O(q^{10})$	\(q+(-1.27611 + 0.568159i) q^{2} +(-0.563301 + 1.63789i) q^{3} +(-0.0326201 + 0.0362283i) q^{4} +(0.323231 - 2.21258i) q^{5} +(-0.211752 - 2.41017i) q^{6} +(2.19012 - 3.79340i) q^{7} +(0.884357 - 2.72177i) q^{8} +(-2.36538 - 1.84525i) q^{9} +(0.844622 + 3.00714i) q^{10} +(-1.20545 + 0.536699i) q^{11} +(-0.0409631 - 0.0738356i) q^{12} +(4.27610 + 1.90384i) q^{13} +(-0.639572 + 6.08512i) q^{14} +(3.44190 + 1.77577i) q^{15} +(0.407674 + 3.87876i) q^{16} +(0.180345 - 0.555045i) q^{17} +(4.06688 + 1.01082i) q^{18} +(-0.359390 + 1.10609i) q^{19} +(0.0696142 + 0.0838847i) q^{20} +(4.97949 + 5.72401i) q^{21} +(1.23335 - 1.36977i) q^{22} +(0.762156 - 7.25143i) q^{23} +(3.95981 + 2.98166i) q^{24} +(-4.79104 - 1.43035i) q^{25} -6.53844 q^{26} +(4.35475 - 2.83481i) q^{27} +(0.0659865 + 0.203085i) q^{28} +(-7.11401 - 1.51213i) q^{29} +(-5.40114 - 0.310522i) q^{30} +(9.81763 - 2.08680i) q^{31} +(0.137855 + 0.238771i) q^{32} +(-0.200027 - 2.27671i) q^{33} +(0.0852144 + 0.810761i) q^{34} +(-7.68530 - 6.07197i) q^{35} +(0.144009 - 0.0255015i) q^{36} +(-1.53428 + 1.11472i) q^{37} +(-0.169815 - 1.61568i) q^{38} +(-5.52702 + 5.93135i) q^{39} +(-5.73629 - 2.83647i) q^{40} +(5.09540 + 2.26862i) q^{41} +(-9.60650 - 4.47530i) q^{42} +(3.67658 - 6.36802i) q^{43} +(0.0198781 - 0.0611784i) q^{44} +(-4.84734 + 4.63717i) q^{45} +(3.14737 + 9.68661i) q^{46} +(6.33736 + 1.34705i) q^{47} +(-6.58263 - 1.51718i) q^{48} +(-6.09327 - 10.5539i) q^{49} +(6.92654 - 0.896798i) q^{50} +(0.807516 + 0.608044i) q^{51} +(-0.208460 + 0.0928122i) q^{52} +(2.92352 + 8.99768i) q^{53} +(-3.94650 + 6.09171i) q^{54} +(0.797854 + 2.84063i) q^{55} +(-8.38793 - 9.31574i) q^{56} +(-1.60921 - 1.21170i) q^{57} +(9.93736 - 2.11225i) q^{58} +(0.108208 + 0.0481772i) q^{59} +(-0.176608 + 0.0667683i) q^{60} +(-6.61228 + 2.94398i) q^{61} +(-11.3427 + 8.24095i) q^{62} +(-12.1803 + 4.93153i) q^{63} +(-6.62211 - 4.81124i) q^{64} +(5.59457 - 8.84584i) q^{65} +(1.54879 + 2.79168i) q^{66} +(-9.14471 + 1.94377i) q^{67} +(0.0142255 + 0.0246392i) q^{68} +(11.4477 + 5.33306i) q^{69} +(13.2571 + 3.38200i) q^{70} +(-0.489945 - 1.50790i) q^{71} +(-7.11420 + 4.80617i) q^{72} +(-7.83289 - 5.69093i) q^{73} +(1.32456 - 2.29421i) q^{74} +(5.04156 - 7.04150i) q^{75} +(-0.0283484 - 0.0491008i) q^{76} +(-0.604158 + 5.74818i) q^{77} +(3.68311 - 10.7093i) q^{78} +(2.18684 + 0.464828i) q^{79} +(8.71385 + 0.351721i) q^{80} +(2.19008 + 8.72946i) q^{81} -7.79120 q^{82} +(-0.603180 - 0.669900i) q^{83} +(-0.369802 - 0.00631949i) q^{84} +(-1.16979 - 0.578436i) q^{85} +(-1.07365 + 10.2151i) q^{86} +(6.48404 - 10.8002i) q^{87} +(0.394728 + 3.75558i) q^{88} +(6.73704 + 4.89475i) q^{89} +(3.55107 - 8.67157i) q^{90} +(16.5872 - 12.0513i) q^{91} +(0.237845 + 0.264154i) q^{92} +(-2.11232 + 17.2557i) q^{93} +(-8.85247 + 1.88165i) q^{94} +(2.33115 + 1.15270i) q^{95} +(-0.468735 + 0.0912911i) q^{96} +(-1.97015 - 0.418768i) q^{97} +(13.7719 + 10.0059i) q^{98} +(3.84169 + 0.954853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.27611	+	0.568159i	−0.902343	+	0.401749i	−0.804844	−	0.593487i	$-0.797751\pi$
$2$	−1.27611	+	0.568159i	−0.902343	+	0.401749i	−0.0974991	+	0.995236i	$0.531084\pi$
$3$	−0.563301	+	1.63789i	−0.325222	+	0.945638i
$3$	−0.563301	+	1.63789i	−0.325222	+	0.945638i
$4$	−0.0326201	+	0.0362283i	−0.0163100	+	0.0181141i
$5$	0.323231	−	2.21258i	0.144553	−	0.989497i
$5$	0.323231	−	2.21258i	0.144553	−	0.989497i
$6$	−0.211752	−	2.41017i	−0.0864472	−	0.983947i
$7$	2.19012	−	3.79340i	0.827788	−	1.43377i	−0.0719810	−	0.997406i	$-0.522932\pi$
$7$	2.19012	−	3.79340i	0.827788	−	1.43377i	0.899769	−	0.436366i	$-0.143735\pi$
$8$	0.884357	−	2.72177i	0.312668	−	0.962292i
$9$	−2.36538	−	1.84525i	−0.788461	−	0.615084i
$10$	0.844622	+	3.00714i	0.267093	+	0.950940i
$11$	−1.20545	+	0.536699i	−0.363456	+	0.161821i	−0.580336	−	0.814377i	$-0.697079\pi$
$11$	−1.20545	+	0.536699i	−0.363456	+	0.161821i	0.216880	+	0.976198i	$0.430412\pi$
$12$	−0.0409631	−	0.0738356i	−0.0118250	−	0.0213145i
$13$	4.27610	+	1.90384i	1.18598	+	0.528031i	0.902392	−	0.430917i	$-0.141810\pi$
$13$	4.27610	+	1.90384i	1.18598	+	0.528031i	0.283584	+	0.958947i	$0.408476\pi$
$14$	−0.639572	+	6.08512i	−0.170933	+	1.62632i
$15$	3.44190	+	1.77577i	0.888694	+	0.458501i
$16$	0.407674	+	3.87876i	0.101918	+	0.969690i
$17$	0.180345	−	0.555045i	0.0437401	−	0.134618i	−0.926802	−	0.375551i	$-0.877453\pi$
$17$	0.180345	−	0.555045i	0.0437401	−	0.134618i	0.970542	+	0.240933i	$0.0774534\pi$
$18$	4.06688	+	1.01082i	0.958572	+	0.238253i
$19$	−0.359390	+	1.10609i	−0.0824498	+	0.253754i	−0.983780	−	0.179378i	$-0.942592\pi$
$19$	−0.359390	+	1.10609i	−0.0824498	+	0.253754i	0.901331	+	0.433132i	$0.142592\pi$
$20$	0.0696142	+	0.0838847i	0.0155662	+	0.0187572i
$21$	4.97949	+	5.72401i	1.08661	+	1.24908i
$22$	1.23335	−	1.36977i	0.262950	−	0.292036i
$23$	0.762156	−	7.25143i	0.158920	−	1.51203i	−0.566696	−	0.823927i	$-0.691778\pi$
$23$	0.762156	−	7.25143i	0.158920	−	1.51203i	0.725616	−	0.688100i	$-0.241555\pi$
$24$	3.95981	+	2.98166i	0.808293	+	0.608629i
$25$	−4.79104	−	1.43035i	−0.958209	−	0.286070i
$26$	−6.53844			−1.28229
$27$	4.35475	−	2.83481i	0.838072	−	0.545560i
$28$	0.0659865	+	0.203085i	0.0124703	+	0.0383795i
$29$	−7.11401	−	1.51213i	−1.32104	−	0.280795i	−0.507171	−	0.861845i	$-0.669309\pi$
$29$	−7.11401	−	1.51213i	−1.32104	−	0.280795i	−0.813868	+	0.581050i	$0.802642\pi$
$30$	−5.40114	−	0.310522i	−0.986109	−	0.0566933i
$31$	9.81763	−	2.08680i	1.76330	−	0.374801i	0.791602	−	0.611037i	$-0.209247\pi$
$31$	9.81763	−	2.08680i	1.76330	−	0.374801i	0.971696	+	0.236236i	$0.0759139\pi$
$32$	0.137855	+	0.238771i	0.0243695	+	0.0422092i
$33$	−0.200027	−	2.27671i	−0.0348202	−	0.396325i
$34$	0.0852144	+	0.810761i	0.0146142	+	0.139044i
$35$	−7.68530	−	6.07197i	−1.29905	−	1.02635i
$36$	0.144009	−	0.0255015i	0.0240016	−	0.00425025i
$37$	−1.53428	+	1.11472i	−0.252234	+	0.183259i	−0.706716	−	0.707497i	$-0.749824\pi$
$37$	−1.53428	+	1.11472i	−0.252234	+	0.183259i	0.454482	+	0.890756i	$0.349824\pi$
$38$	−0.169815	−	1.61568i	−0.0275476	−	0.262097i
$39$	−5.52702	+	5.93135i	−0.885031	+	0.949777i
$40$	−5.73629	−	2.83647i	−0.906988	−	0.448486i
$41$	5.09540	+	2.26862i	0.795767	+	0.354298i	0.764016	−	0.645197i	$-0.223225\pi$
$41$	5.09540	+	2.26862i	0.795767	+	0.354298i	0.0317513	+	0.999496i	$0.489892\pi$
$42$	−9.60650	−	4.47530i	−1.48232	−	0.690554i
$43$	3.67658	−	6.36802i	0.560673	−	0.971114i	−0.436765	−	0.899576i	$-0.643876\pi$
$43$	3.67658	−	6.36802i	0.560673	−	0.971114i	0.997438	−	0.0715380i	$-0.0227907\pi$
$44$	0.0198781	−	0.0611784i	0.00299673	−	0.00922299i
$45$	−4.84734	+	4.63717i	−0.722599	+	0.691268i
$46$	3.14737	+	9.68661i	0.464055	+	1.42821i
$47$	6.33736	+	1.34705i	0.924398	+	0.196487i	0.645435	−	0.763815i	$-0.276676\pi$
$47$	6.33736	+	1.34705i	0.924398	+	0.196487i	0.278963	+	0.960302i	$0.410009\pi$
$48$	−6.58263	−	1.51718i	−0.950121	−	0.218986i
$49$	−6.09327	−	10.5539i	−0.870467	−	1.50769i
$50$	6.92654	−	0.896798i	0.979561	−	0.126826i
$51$	0.807516	+	0.608044i	0.113075	+	0.0851431i
$52$	−0.208460	+	0.0928122i	−0.0289081	+	0.0128707i
$53$	2.92352	+	8.99768i	0.401577	+	1.23593i	0.923720	+	0.383068i	$0.125133\pi$
$53$	2.92352	+	8.99768i	0.401577	+	1.23593i	−0.522143	+	0.852858i	$0.674867\pi$
$54$	−3.94650	+	6.09171i	−0.537050	+	0.828977i
$55$	0.797854	+	2.84063i	0.107583	+	0.383030i
$56$	−8.38793	−	9.31574i	−1.12088	−	1.24487i
$57$	−1.60921	−	1.21170i	−0.213145	−	0.160494i
$58$	9.93736	−	2.11225i	1.30484	−	0.277352i
$59$	0.108208	+	0.0481772i	0.0140874	+	0.00627214i	0.413768	−	0.910382i	$-0.364212\pi$
$59$	0.108208	+	0.0481772i	0.0140874	+	0.00627214i	−0.399681	+	0.916654i	$0.630879\pi$
$60$	−0.176608	+	0.0667683i	−0.0228000	+	0.00861975i
$61$	−6.61228	+	2.94398i	−0.846615	+	0.376937i	−0.783744	−	0.621084i	$-0.786693\pi$
$61$	−6.61228	+	2.94398i	−0.846615	+	0.376937i	−0.0628715	+	0.998022i	$0.520026\pi$
$62$	−11.3427	+	8.24095i	−1.44052	+	1.04660i
$63$	−12.1803	+	4.93153i	−1.53457	+	0.621314i
$64$	−6.62211	−	4.81124i	−0.827764	−	0.601406i
$65$	5.59457	−	8.84584i	0.693921	−	1.09719i
$66$	1.54879	+	2.79168i	0.190643	+	0.343632i
$67$	−9.14471	+	1.94377i	−1.11720	+	0.237469i	−0.729275	−	0.684220i	$-0.760143\pi$
$67$	−9.14471	+	1.94377i	−1.11720	+	0.237469i	−0.387929	+	0.921689i	$0.626809\pi$
$68$	0.0142255	+	0.0246392i	0.00172509	+	0.00298794i
$69$	11.4477	+	5.33306i	1.37815	+	0.642026i
$70$	13.2571	+	3.38200i	1.58453	+	0.404227i
$71$	−0.489945	−	1.50790i	−0.0581458	−	0.178954i	0.917765	−	0.397123i	$-0.129992\pi$
$71$	−0.489945	−	1.50790i	−0.0581458	−	0.178954i	−0.975911	+	0.218169i	$0.929992\pi$
$72$	−7.11420	+	4.80617i	−0.838417	+	0.566413i
$73$	−7.83289	−	5.69093i	−0.916771	−	0.666073i	0.0259473	−	0.999663i	$-0.491740\pi$
$73$	−7.83289	−	5.69093i	−0.916771	−	0.666073i	−0.942718	+	0.333590i	$0.891740\pi$
$74$	1.32456	−	2.29421i	0.153977	−	0.266697i
$75$	5.04156	−	7.04150i	0.582149	−	0.813082i
$76$	−0.0283484	−	0.0491008i	−0.00325178	−	0.00563225i
$77$	−0.604158	+	5.74818i	−0.0688502	+	0.655066i
$78$	3.68311	−	10.7093i	0.417030	−	1.21258i
$79$	2.18684	+	0.464828i	0.246039	+	0.0522972i	0.329280	−	0.944232i	$-0.393194\pi$
$79$	2.18684	+	0.464828i	0.246039	+	0.0522972i	−0.0832412	+	0.996529i	$0.526527\pi$
$80$	8.71385	+	0.351721i	0.974238	+	0.0393236i
$81$	2.19008	+	8.72946i	0.243343	+	0.969940i
$82$	−7.79120			−0.860394
$83$	−0.603180	−	0.669900i	−0.0662077	−	0.0735310i	0.709131	−	0.705077i	$-0.249087\pi$
$83$	−0.603180	−	0.669900i	−0.0662077	−	0.0735310i	−0.775339	+	0.631546i	$0.782421\pi$
$84$	−0.369802	−	0.00631949i	−0.0403487	−	0.000689513i
$85$	−1.16979	−	0.578436i	−0.126882	−	0.0627402i
$86$	−1.07365	+	10.2151i	−0.115775	+	1.10153i
$87$	6.48404	−	10.8002i	0.695162	−	1.15790i
$88$	0.394728	+	3.75558i	0.0420781	+	0.400346i
$89$	6.73704	+	4.89475i	0.714125	+	0.518842i	0.884502	−	0.466537i	$-0.154499\pi$
$89$	6.73704	+	4.89475i	0.714125	+	0.518842i	−0.170377	+	0.985379i	$0.554499\pi$
$90$	3.55107	−	8.67157i	0.374316	−	0.914064i
$91$	16.5872	−	12.0513i	1.73881	−	1.26332i
$92$	0.237845	+	0.264154i	0.0247971	+	0.0275399i
$93$	−2.11232	+	17.2557i	−0.219038	+	1.78933i
$94$	−8.85247	+	1.88165i	−0.913063	+	0.194077i
$95$	2.33115	+	1.15270i	0.239171	+	0.118265i
$96$	−0.468735	+	0.0912911i	−0.0478401	+	0.00931736i
$97$	−1.97015	−	0.418768i	−0.200038	−	0.0425194i	0.106803	−	0.994280i	$-0.465939\pi$
$97$	−1.97015	−	0.418768i	−0.200038	−	0.0425194i	−0.306841	+	0.951761i	$0.599272\pi$
$98$	13.7719	+	10.0059i	1.39117	+	1.01075i
$99$	3.84169	+	0.954853i	0.386104	+	0.0959663i
$100$	0.208103	−	0.126913i	0.0208103	−	0.0126913i
$101$	−2.39536	+	4.14889i	−0.238348	+	0.412830i	−0.960240	−	0.279175i	$-0.909939\pi$
$101$	−2.39536	+	4.14889i	−0.238348	+	0.412830i	0.721893	+	0.692005i	$0.243272\pi$
$102$	−1.37594	−	0.317130i	−0.136238	−	0.0314006i
$103$	3.16455	−	3.51459i	0.311812	−	0.346303i	−0.566785	−	0.823866i	$-0.691813\pi$
$103$	3.16455	−	3.51459i	0.311812	−	0.346303i	0.878598	+	0.477563i	$0.158480\pi$
$104$	8.96342	−	9.95489i	0.878936	−	0.976157i
$105$	14.2744	−	9.16735i	1.39304	−	0.894642i
$106$	−8.84283	−	9.82096i	−0.858892	−	0.953896i
$107$	−5.47406			−0.529197			−0.264599	−	0.964359i	$-0.585239\pi$
$107$	−5.47406			−0.529197			−0.264599	+	0.964359i	$0.585239\pi$
$108$	−0.0393519	+	0.250237i	−0.00378664	+	0.0240791i
$109$	2.34618	−	1.70460i	0.224723	−	0.163271i	−0.469727	−	0.882812i	$-0.655648\pi$
$109$	2.34618	−	1.70460i	0.224723	−	0.163271i	0.694450	+	0.719541i	$0.255648\pi$
$110$	−2.63207	−	3.17163i	−0.250958	−	0.302403i
$111$	−0.961529	−	3.14091i	−0.0912643	−	0.298122i
$112$	15.6065	+	6.94848i	1.47468	+	0.656570i
$113$	2.67568	+	1.19129i	0.251707	+	0.112067i	0.528712	−	0.848801i	$-0.322675\pi$
$113$	2.67568	+	1.19129i	0.251707	+	0.112067i	−0.277005	+	0.960869i	$0.589342\pi$
$114$	2.74196	+	0.631975i	0.256808	+	0.0591898i
$115$	−15.7980	−	4.03022i	−1.47317	−	0.375820i
$116$	0.286841	−	0.208403i	0.0266326	−	0.0193497i
$117$	−6.60154	−	12.3938i	−0.610313	−	1.14581i
$118$	−0.165457			−0.0152315
$119$	−1.71053	−	1.89974i	−0.156804	−	0.174149i
$120$	7.87710	−	7.79765i	0.719077	−	0.711824i
$121$	−6.19538	+	6.88067i	−0.563217	+	0.625515i
$122$	6.76532	−	7.51365i	0.612503	−	0.680254i
$123$	−6.58599	+	7.06780i	−0.593839	+	0.637282i
$124$	−0.244651	+	0.423747i	−0.0219703	+	0.0380536i
$125$	−4.71338	+	10.1382i	−0.421577	+	0.906793i
$126$	12.7414	−	13.2135i	1.13510	−	1.17715i
$127$	3.62814	+	2.63599i	0.321945	+	0.233907i	0.737005	−	0.675887i	$-0.236239\pi$
$127$	3.62814	+	2.63599i	0.321945	+	0.233907i	−0.415060	+	0.909794i	$0.636239\pi$
$128$	10.6447	+	2.26260i	0.940867	+	0.199987i
$129$	8.35911	+	9.60895i	0.735979	+	0.846021i
$130$	−2.11342	+	14.4668i	−0.185359	+	1.26882i
$131$	−4.66950	+	0.992533i	−0.407976	+	0.0867180i	−0.407328	−	0.913282i	$-0.633540\pi$
$131$	−4.66950	+	0.992533i	−0.407976	+	0.0867180i	−0.000647887		1.00000i	$0.500206\pi$
$132$	0.0890063	+	0.0670200i	0.00774700	+	0.00583334i
$133$	3.40873	+	3.78578i	0.295575	+	0.328269i
$134$	10.5652	−	7.67610i	0.912698	−	0.663114i
$135$	−4.86467	−	10.5515i	−0.418684	−	0.908132i
$136$	−1.35122	−	0.981717i	−0.115866	−	0.0841815i
$137$	0.873169	+	8.30765i	0.0745999	+	0.709771i	0.966348	+	0.257238i	$0.0828126\pi$
$137$	0.873169	+	8.30765i	0.0745999	+	0.709771i	−0.891748	+	0.452532i	$0.850521\pi$
$138$	−17.6385	−	0.301422i	−1.50149	−	0.0256587i
$139$	−0.631147	+	6.00496i	−0.0535332	+	0.509334i	0.934596	+	0.355710i	$0.115761\pi$
$139$	−0.631147	+	6.00496i	−0.0535332	+	0.509334i	−0.988129	+	0.153624i	$0.950906\pi$
$140$	0.470672	−	0.0803571i	0.0397791	−	0.00679141i
$141$	−5.77616	+	9.62112i	−0.486440	+	0.810244i
$142$	1.48195	+	1.64587i	0.124362	+	0.138118i
$143$	−6.17639			−0.516496
$144$	6.19298	−	9.92701i	0.516082	−	0.827251i
$145$	−5.64518	+	15.2516i	−0.468807	+	1.26657i
$146$	13.2290	+	2.81190i	1.09484	+	0.232715i
$147$	20.7184	−	4.03513i	1.70883	−	0.332812i
$148$	0.00966396	−	0.0919465i	0.000794373	−	0.00755795i
$149$	0.670873	+	1.16199i	0.0549600	+	0.0951936i	0.892196	−	0.451647i	$-0.149164\pi$
$149$	0.670873	+	1.16199i	0.0549600	+	0.0951936i	−0.837236	+	0.546841i	$0.815830\pi$
$150$	−2.43287	+	11.8501i	−0.198643	+	0.967557i
$151$	−1.42269	+	2.46416i	−0.115777	+	0.200531i	−0.918090	−	0.396372i	$-0.870269\pi$
$151$	−1.42269	+	2.46416i	−0.115777	+	0.200531i	0.802313	+	0.596903i	$0.203602\pi$
$152$	2.69269	+	1.95636i	0.218406	+	0.158681i
$153$	−1.45078	+	0.980113i	−0.117289	+	0.0792375i
$154$	−2.49491	−	7.67854i	−0.201046	−	0.618754i
$155$	−1.44386	−	22.3968i	−0.115974	−	1.79896i
$156$	−0.0345909	−	0.393715i	−0.00276949	−	0.0315225i
$157$	6.35992	+	11.0157i	0.507577	+	0.879149i	0.999962	+	0.00877142i	$0.00279207\pi$
$157$	6.35992	+	11.0157i	0.507577	+	0.879149i	−0.492384	+	0.870378i	$0.663875\pi$
$158$	−3.05474	+	0.649305i	−0.243022	+	0.0516559i
$159$	−16.3841	−	0.279984i	−1.29934	−	0.0222042i
$160$	0.572860	−	0.227837i	0.0452886	−	0.0180121i
$161$	−25.8384	−	18.7727i	−2.03635	−	1.47949i
$162$	−7.75450	−	9.89540i	−0.609251	−	0.777456i
$163$	13.8750	−	10.0808i	1.08677	−	0.789587i	0.107922	−	0.994159i	$-0.465580\pi$
$163$	13.8750	−	10.0808i	1.08677	−	0.789587i	0.978851	+	0.204572i	$0.0655803\pi$
$164$	−0.248400	+	0.110595i	−0.0193968	+	0.00863601i
$165$	−5.10207	−	0.293328i	−0.397196	−	0.0228356i
$166$	1.15033	+	0.512161i	0.0892830	+	0.0397514i
$167$	−12.8472	+	2.73077i	−0.994150	+	0.211313i	−0.676139	−	0.736774i	$-0.736348\pi$
$167$	−12.8472	+	2.73077i	−0.994150	+	0.211313i	−0.318011	+	0.948087i	$0.603015\pi$
$168$	19.9831	−	8.49096i	1.54173	−	0.655092i
$169$	5.96170	+	6.62114i	0.458592	+	0.509318i
$170$	1.82142	+	0.0735188i	0.139697	+	0.00563863i
$171$	2.89111	−	1.95316i	0.221089	−	0.149362i
$172$	0.110772	+	0.340921i	0.00844629	+	0.0259950i
$173$	9.19344	−	4.09318i	0.698964	−	0.311199i	−0.0263151	−	0.999654i	$-0.508377\pi$
$173$	9.19344	−	4.09318i	0.698964	−	0.311199i	0.725279	+	0.688455i	$0.241711\pi$
$174$	−2.13808	+	17.4662i	−0.162088	+	1.32411i
$175$	−15.9189	+	15.0417i	−1.20335	+	1.13705i
$176$	−2.57315	−	4.45683i	−0.193959	−	0.335947i
$177$	−0.139863	+	0.150094i	−0.0105127	+	0.0112818i
$178$	−11.3782	−	2.41850i	−0.852830	−	0.181275i
$179$	6.70590	+	20.6386i	0.501222	+	1.54260i	0.807030	+	0.590510i	$0.201073\pi$
$179$	6.70590	+	20.6386i	0.501222	+	1.54260i	−0.305808	+	0.952093i	$0.598927\pi$
$180$	−0.00987591	−	0.326875i	−0.000736107	−	0.0243639i
$181$	−3.44592	+	10.6055i	−0.256133	+	0.788297i	0.737471	+	0.675379i	$0.236020\pi$
$181$	−3.44592	+	10.6055i	−0.256133	+	0.788297i	−0.993604	+	0.112918i	$0.963980\pi$
$182$	−14.3200	+	24.8029i	−1.06147	+	1.83852i
$183$	−1.09721	−	12.4885i	−0.0811084	−	0.923180i
$184$	−19.0627	−	8.48727i	−1.40532	−	0.625690i
$185$	1.97048	+	3.75503i	0.144873	+	0.276075i
$186$	−7.10844	−	23.2202i	−0.521216	−	1.70259i
$187$	0.0804960	+	0.765868i	0.00588645	+	0.0560058i
$188$	−0.255526	+	0.185651i	−0.0186362	+	0.0135400i
$189$	−1.21615	−	22.7279i	−0.0884621	−	1.65321i
$190$	−3.62971	−	0.146508i	−0.263327	−	0.0106288i
$191$	−0.745267	−	7.09074i	−0.0539256	−	0.513068i	−0.987829	−	0.155543i	$-0.950287\pi$
$191$	−0.745267	−	7.09074i	−0.0539256	−	0.513068i	0.933904	−	0.357525i	$-0.116379\pi$
$192$	11.6105	−	8.13613i	0.837919	−	0.587174i
$193$	−6.86581	−	11.8919i	−0.494212	−	0.856000i	0.505766	−	0.862671i	$-0.331210\pi$
$193$	−6.86581	−	11.8919i	−0.494212	−	0.856000i	−0.999978	+	0.00667102i	$0.997877\pi$
$194$	2.75204	−	0.584964i	0.197585	−	0.0419980i
$195$	11.3371	+	14.1462i	0.811867	+	1.01303i
$196$	0.581111	+	0.123519i	0.0415079	+	0.00882278i
$197$	2.96275	+	9.11841i	0.211087	+	0.649660i	0.999408	+	0.0343956i	$0.0109506\pi$
$197$	2.96275	+	9.11841i	0.211087	+	0.649660i	−0.788321	+	0.615264i	$0.789049\pi$
$198$	−5.44491	+	0.964196i	−0.386953	+	0.0685224i
$199$	−8.78106			−0.622473			−0.311236	−	0.950333i	$-0.600743\pi$
$199$	−8.78106			−0.622473			−0.311236	+	0.950333i	$0.600743\pi$
$200$	−8.13008	+	11.7752i	−0.574883	+	0.832632i
$201$	1.96754	−	16.0730i	0.138780	−	1.13370i
$202$	0.699508	−	6.65537i	0.0492172	−	0.468270i
$203$	−21.3167	+	23.6746i	−1.49614	+	1.66163i
$204$	−0.0483696	+	0.00942048i	−0.00338655	+	0.000659566i
$205$	6.66649	−	10.5407i	0.465608	−	0.736194i
$206$	−2.04146	+	6.28295i	−0.142235	+	0.437754i
$207$	−15.1835	+	15.7460i	−1.05533	+	1.09443i
$208$	−5.64129	+	17.3621i	−0.391153	+	1.20384i
$209$	−0.160412	−	1.52622i	−0.0110959	−	0.105571i
$210$	−13.0071	+	19.8086i	−0.897575	+	1.36692i
$211$	−0.707483	+	6.73125i	−0.0487051	+	0.463399i	0.942803	+	0.333351i	$0.108180\pi$
$211$	−0.707483	+	6.73125i	−0.0487051	+	0.463399i	−0.991508	+	0.130047i	$0.958487\pi$
$212$	−0.421336	−	0.187591i	−0.0289375	−	0.0128838i
$213$	2.74576	+	0.0469218i	0.188136	+	0.00321503i
$214$	6.98548	−	3.11014i	0.477518	−	0.212604i
$215$	−12.9014	−	10.1931i	−0.879867	−	0.695161i
$216$	−3.86456	−	14.3596i	−0.262950	−	0.977048i
$217$	13.5857	−	41.8126i	0.922259	−	2.83842i
$218$	−2.02549	+	3.50825i	−0.137184	+	0.237609i
$219$	13.7334	−	9.62373i	0.928018	−	0.650312i
$220$	−0.128937	−	0.0637566i	−0.00869293	−	0.00429847i
$221$	1.82789	−	2.03008i	0.122957	−	0.136558i
$222$	3.01155	+	3.46183i	0.202122	+	0.232343i
$223$	−13.7113	+	6.10468i	−0.918179	+	0.408800i	−0.810736	−	0.585411i	$-0.800933\pi$
$223$	−13.7113	+	6.10468i	−0.918179	+	0.408800i	−0.107443	+	0.994211i	$0.534266\pi$
$224$	1.20767			0.0806912
$225$	8.69330	+	12.2240i	0.579554	+	0.814934i
$226$	−4.09130			−0.272149
$227$	25.4887	−	11.3483i	1.69174	−	0.753212i	0.692239	−	0.721669i	$-0.256625\pi$
$227$	25.4887	−	11.3483i	1.69174	−	0.753212i	0.999502	−	0.0315432i	$-0.0100422\pi$
$228$	0.0963905	−	0.0187730i	0.00638362	−	0.00124328i
$229$	11.4319	−	12.6965i	0.755444	−	0.839006i	−0.235696	−	0.971827i	$-0.575737\pi$
$229$	11.4319	−	12.6965i	0.755444	−	0.839006i	0.991140	+	0.132821i	$0.0424036\pi$
$230$	22.4498	−	3.83281i	1.48029	−	0.252728i
$231$	−9.07458	−	4.22750i	−0.597063	−	0.278149i
$232$	−10.4070	+	18.0255i	−0.683253	+	1.18343i
$233$	0.407967	−	1.25559i	0.0267268	−	0.0822566i	−0.936803	−	0.349856i	$-0.886230\pi$
$233$	0.407967	−	1.25559i	0.0267268	−	0.0822566i	0.963530	+	0.267600i	$0.0862304\pi$
$234$	15.4659	+	12.0651i	1.01104	+	0.788718i
$235$	5.02888	−	13.5865i	0.328048	−	0.886287i
$236$	−0.00527512	+	0.00234864i	−0.000343381	+	0.000152883i
$237$	−1.99319	+	3.31998i	−0.129472	+	0.215656i
$238$	3.26217	+	1.45241i	0.211455	+	0.0941460i
$239$	−0.172902	+	1.64505i	−0.0111841	+	0.106410i	−0.998690	−	0.0511739i	$-0.983704\pi$
$239$	−0.172902	+	1.64505i	−0.0111841	+	0.106410i	0.987506	+	0.157584i	$0.0503704\pi$
$240$	−5.48460	+	14.0742i	−0.354029	+	0.908487i
$241$	2.46128	+	23.4175i	0.158545	+	1.50846i	0.727511	+	0.686096i	$0.240677\pi$
$241$	2.46128	+	23.4175i	0.158545	+	1.50846i	−0.568966	+	0.822361i	$0.692656\pi$
$242$	3.99665	−	12.3004i	0.256914	−	0.790701i
$243$	−15.5316	−	1.33019i	−0.996353	−	0.0853319i
$244$	0.109038	−	0.335584i	0.00698044	−	0.0214836i
$245$	−25.3208	+	10.0705i	−1.61769	+	0.643383i
$246$	4.38879	−	12.7611i	0.279819	−	0.813621i
$247$	−3.64261	+	4.04552i	−0.231773	+	0.257410i
$248$	3.00249	−	28.5668i	0.190659	−	1.81399i
$249$	1.43700	−	0.610590i	0.0910659	−	0.0386945i
$250$	0.254630	−	15.6154i	0.0161042	−	0.987606i
$251$	2.38514			0.150549			0.0752744	−	0.997163i	$-0.476017\pi$
$251$	2.38514			0.150549			0.0752744	+	0.997163i	$0.476017\pi$
$252$	0.218661	−	0.602137i	0.0137743	−	0.0379311i
$253$	2.97310	+	9.15025i	0.186917	+	0.575271i
$254$	−6.12755	−	1.30245i	−0.384477	−	0.0817230i
$255$	1.60636	−	1.59016i	0.100594	−	0.0995796i
$256$	1.14375	−	0.243111i	0.0714841	−	0.0151944i
$257$	2.09112	+	3.62192i	0.130440	+	0.225929i	0.923846	−	0.382764i	$-0.125028\pi$
$257$	2.09112	+	3.62192i	0.130440	+	0.225929i	−0.793406	+	0.608693i	$0.791694\pi$
$258$	−16.1265	−	7.51273i	−1.00399	−	0.467722i
$259$	0.868319	+	8.26151i	0.0539547	+	0.513345i
$260$	0.137974	+	0.491234i	0.00855679	+	0.0304650i
$261$	14.0371	+	16.7039i	0.868875	+	1.03395i
$262$	5.39486	−	3.91960i	0.333296	−	0.242153i
$263$	1.73040	+	16.4637i	0.106701	+	1.01519i	0.908581	+	0.417708i	$0.137167\pi$
$263$	1.73040	+	16.4637i	0.106701	+	1.01519i	−0.801880	+	0.597485i	$0.796167\pi$
$264$	−6.37359	−	1.46900i	−0.392267	−	0.0904108i
$265$	20.8531	−	3.56021i	1.28099	−	0.218702i
$266$	−6.50083	−	2.89436i	−0.398591	−	0.177464i
$267$	−11.8121	+	8.27733i	−0.722886	+	0.506565i
$268$	0.227882	−	0.394703i	0.0139201	−	0.0241103i
$269$	−2.06909	+	6.36801i	−0.126155	+	0.388264i	−0.994110	−	0.108379i	$-0.965434\pi$
$269$	−2.06909	+	6.36801i	−0.126155	+	0.388264i	0.867955	+	0.496643i	$0.165434\pi$
$270$	12.2028	+	10.7010i	0.742638	+	0.651241i
$271$	5.24382	+	16.1388i	0.318539	+	0.980363i	0.974273	+	0.225371i	$0.0723594\pi$
$271$	5.24382	+	16.1388i	0.318539	+	0.980363i	−0.655734	+	0.754992i	$0.727641\pi$
$272$	2.22641	+	0.473238i	0.134996	+	0.0286943i
$273$	10.3952	+	33.9566i	0.629144	+	2.05515i
$274$	−5.83432	−	10.1053i	−0.352464	−	0.610486i
$275$	6.54301	−	0.847141i	0.394558	−	0.0510845i
$276$	−0.566634	+	0.240767i	−0.0341073	+	0.0144924i
$277$	24.5133	−	10.9140i	1.47286	−	0.655761i	0.495747	−	0.868467i	$-0.334894\pi$
$277$	24.5133	−	10.9140i	1.47286	−	0.655761i	0.977116	+	0.212706i	$0.0682278\pi$
$278$	−2.60636	−	8.02156i	−0.156319	−	0.481101i
$279$	−27.0731	−	13.1799i	−1.62083	−	0.789061i
$280$	−23.3231	+	15.5479i	−1.39382	+	0.929162i
$281$	−3.17901	−	3.53065i	−0.189644	−	0.210621i	0.640823	−	0.767688i	$-0.278593\pi$
$281$	−3.17901	−	3.53065i	−0.189644	−	0.210621i	−0.830467	+	0.557067i	$0.811926\pi$
$282$	1.90466	−	15.5593i	0.113421	−	0.926545i
$283$	−5.72020	+	1.21587i	−0.340030	+	0.0722757i	−0.374762	−	0.927121i	$-0.622276\pi$
$283$	−5.72020	+	1.21587i	−0.340030	+	0.0722757i	0.0347318	+	0.999397i	$0.488942\pi$
$284$	0.0706105	+	0.0314378i	0.00418996	+	0.00186549i
$285$	−3.20114	+	3.16885i	−0.189619	+	0.187707i
$286$	7.88173	−	3.50917i	0.466057	−	0.207502i
$287$	19.7653	−	14.3603i	1.16671	−	0.847664i
$288$	0.114514	−	0.819163i	0.00674781	−	0.0482696i
$289$	13.4777	+	9.79215i	0.792808	+	0.576009i
$290$	−1.46147	−	22.6700i	−0.0858206	−	1.33123i
$291$	1.79568	−	2.99100i	0.105265	−	0.175335i
$292$	0.461682	−	0.0981336i	0.0270179	−	0.00574283i
$293$	4.72283	+	8.18018i	0.275911	+	0.477891i	0.970364	−	0.241646i	$-0.0776873\pi$
$293$	4.72283	+	8.18018i	0.275911	+	0.477891i	−0.694454	+	0.719537i	$0.744354\pi$
$294$	−24.1463	+	16.9206i	−1.40824	+	0.986830i
$295$	0.141572	−	0.223846i	0.00824265	−	0.0130328i
$296$	1.67716	+	5.16177i	0.0974829	+	0.300022i
$297$	−3.72797	+	5.75440i	−0.216319	+	0.333904i
$298$	−1.51630	−	1.10165i	−0.0878367	−	0.0638171i
$299$	17.0646	−	29.5568i	0.986872	−	1.70931i
$300$	0.0906453	+	0.412341i	0.00523341	+	0.0238065i
$301$	−16.1043	−	27.8935i	−0.928237	−	1.60775i
$302$	0.415461	−	3.95285i	0.0239071	−	0.227461i
$303$	−5.44613	−	6.26042i	−0.312872	−	0.359652i
$304$	−4.43677	−	0.943064i	−0.254466	−	0.0540884i
$305$	4.37650	+	15.5818i	0.250598	+	0.892211i
$306$	1.29449	−	2.07500i	0.0740013	−	0.118620i
$307$	6.59126			0.376183			0.188091	−	0.982152i	$-0.439770\pi$
$307$	6.59126			0.376183			0.188091	+	0.982152i	$0.439770\pi$
$308$	−0.188539	−	0.209394i	−0.0107430	−	0.0119313i
$309$	3.97392	+	7.16296i	0.226069	+	0.407487i
$310$	14.5675	+	27.7604i	0.827377	+	1.57668i
$311$	1.57285	−	14.9647i	0.0891882	−	0.848569i	−0.854882	−	0.518823i	$-0.826370\pi$
$311$	1.57285	−	14.9647i	0.0891882	−	0.848569i	0.944070	−	0.329746i	$-0.106963\pi$
$312$	11.2559	+	20.2887i	0.637242	+	1.14862i
$313$	−2.55089	−	24.2701i	−0.144185	−	1.37183i	−0.792228	−	0.610225i	$-0.791079\pi$
$313$	−2.55089	−	24.2701i	−0.144185	−	1.37183i	0.648044	−	0.761603i	$-0.275587\pi$
$314$	−14.3746	−	10.4438i	−0.811206	−	0.589376i
$315$	6.97437	+	28.5439i	0.392961	+	1.60826i
$316$	−0.0881749	+	0.0640628i	−0.00496023	+	0.00360382i
$317$	8.89733	+	9.88149i	0.499724	+	0.555000i	0.939252	−	0.343229i	$-0.111521\pi$
$317$	8.89733	+	9.88149i	0.499724	+	0.555000i	−0.439528	+	0.898229i	$0.644854\pi$
$318$	21.0669	−	8.95145i	1.18137	−	0.501973i
$319$	9.38712	−	1.99529i	0.525578	−	0.111715i
$320$	−12.7857	+	13.0968i	−0.714745	+	0.732135i
$321$	3.08354	−	8.96592i	0.172107	−	0.500429i
$322$	43.6384	+	9.27562i	2.43187	+	0.516910i
$323$	0.549115	+	0.398956i	0.0305536	+	0.0221985i
$324$	−0.387694	−	0.205413i	−0.0215386	−	0.0114118i
$325$	−17.7638	−	15.2377i	−0.985359	−	0.845235i
$326$	−11.9785	+	20.7473i	−0.663427	+	1.14909i
$327$	1.47035	+	4.80300i	0.0813103	+	0.265606i
$328$	10.6808	−	11.8622i	0.589749	−	0.654983i
$329$	18.9895	−	21.0899i	1.04692	−	1.16273i
$330$	6.67744	−	2.52447i	0.367581	−	0.138968i
$331$	3.89678	+	4.32781i	0.214186	+	0.237878i	0.840658	−	0.541566i	$-0.182168\pi$
$331$	3.89678	+	4.32781i	0.214186	+	0.237878i	−0.626472	+	0.779444i	$0.715502\pi$
$332$	0.0439451			0.00241180
$333$	5.68609	+	0.194394i	0.311596	+	0.0106527i
$334$	14.8429	−	10.7840i	0.812169	−	0.590075i
$335$	1.34490	+	20.8617i	0.0734796	+	1.13980i
$336$	−20.1721	+	21.6478i	−1.10048	+	1.18098i
$337$	−14.1703	−	6.30902i	−0.771905	−	0.343674i	−0.0172975	−	0.999850i	$-0.505506\pi$
$337$	−14.1703	−	6.30902i	−0.771905	−	0.343674i	−0.754608	+	0.656176i	$0.772173\pi$
$338$	−11.3696	−	5.06208i	−0.618426	−	0.275341i
$339$	−3.45842	+	3.71143i	−0.187836	+	0.201577i
$340$	0.0591144	−	0.0235109i	0.00320593	−	0.00127506i
$341$	−10.7146	+	7.78464i	−0.580230	+	0.421562i
$342$	−2.57966	+	4.13505i	−0.139492	+	0.223598i
$343$	−22.7183			−1.22667
$344$	−14.0809	−	15.6384i	−0.759190	−	0.843166i
$345$	15.5001	−	23.6053i	0.834498	−	1.27086i
$346$	−9.40622	+	10.4467i	−0.505682	+	0.561616i
$347$	−12.8606	+	14.2832i	−0.690396	+	0.766762i	−0.981816	−	0.189833i	$-0.939205\pi$
$347$	−12.8606	+	14.2832i	−0.690396	+	0.766762i	0.291421	+	0.956595i	$0.405872\pi$
$348$	0.179763	+	0.587209i	0.00963630	+	0.0314777i
$349$	−13.3541	+	23.1300i	−0.714829	+	1.23812i	0.248197	+	0.968710i	$0.420162\pi$
$349$	−13.3541	+	23.1300i	−0.714829	+	1.23812i	−0.963026	+	0.269410i	$0.913171\pi$
$350$	11.7681	−	28.2393i	0.629029	−	1.50945i
$351$	24.0184	−	3.83118i	1.28201	−	0.204493i
$352$	−0.294325	−	0.213839i	−0.0156876	−	0.0113977i
$353$	−34.5987	−	7.35419i	−1.84150	−	0.391424i	−0.850580	−	0.525845i	$-0.823749\pi$
$353$	−34.5987	−	7.35419i	−1.84150	−	0.391424i	−0.990924	+	0.134421i	$0.957082\pi$
$354$	0.0932020	−	0.271001i	0.00495363	−	0.0144035i
$355$	−3.49471	+	0.596646i	−0.185480	+	0.0316667i
$356$	−0.397091	+	0.0844043i	−0.0210458	+	0.00447342i
$357$	4.07511	−	1.73154i	0.215678	−	0.0916430i
$358$	−20.2835	−	22.5271i	−1.07201	−	1.19059i
$359$	17.3365	−	12.5957i	0.914987	−	0.664777i	−0.0272839	−	0.999628i	$-0.508686\pi$
$359$	17.3365	−	12.5957i	0.914987	−	0.664777i	0.942271	+	0.334850i	$0.108686\pi$
$360$	8.33453	+	17.2943i	0.439268	+	0.911488i
$361$	14.2771	+	10.3729i	0.751424	+	0.545941i
$362$	−1.62822	−	15.4915i	−0.0855775	−	0.814216i
$363$	−7.77993	−	14.0233i	−0.408341	−	0.736030i
$364$	−0.104478	+	0.994041i	−0.00547613	+	0.0521019i
$365$	−15.1235	+	15.4914i	−0.791599	+	0.810859i
$366$	8.49564	+	15.3133i	0.444074	+	0.800440i
$367$	5.29000	+	5.87514i	0.276136	+	0.306680i	0.865221	−	0.501391i	$-0.167178\pi$
$367$	5.29000	+	5.87514i	0.276136	+	0.306680i	−0.589085	+	0.808071i	$0.700512\pi$
$368$	28.4372			1.48239
$369$	−7.86640	−	14.7684i	−0.409508	−	0.768814i
$370$	−4.64799	−	3.67227i	−0.241638	−	0.190912i
$371$	40.5347	+	8.61591i	2.10446	+	0.447316i
$372$	−0.556241	−	0.639409i	−0.0288397	−	0.0331518i
$373$	3.46082	−	32.9275i	0.179194	−	1.70492i	−0.422639	−	0.906298i	$-0.638896\pi$
$373$	3.46082	−	32.9275i	0.179194	−	1.70492i	0.601833	−	0.798622i	$-0.294437\pi$
$374$	−0.537856	−	0.931594i	−0.0278119	−	0.0481716i
$375$	−13.9503	−	13.4309i	−0.720391	−	0.693568i
$376$	9.27084	−	16.0576i	0.478107	−	0.828106i
$377$	−27.5414	−	20.0100i	−1.41845	−	1.03057i
$378$	14.4650	+	28.3122i	0.743999	+	1.45622i
$379$	−2.01655	−	6.20630i	−0.103583	−	0.318796i	0.885812	−	0.464044i	$-0.153602\pi$
$379$	−2.01655	−	6.20630i	−0.103583	−	0.318796i	−0.989395	+	0.145248i	$0.953602\pi$
$380$	−0.117803	+	0.0468522i	−0.00604315	+	0.00240347i
$381$	−6.36121	+	4.45764i	−0.325895	+	0.228372i
$382$	4.97971	+	8.62511i	0.254784	+	0.441299i
$383$	6.39088	−	1.35842i	0.326559	−	0.0694122i	−0.0417152	−	0.999130i	$-0.513282\pi$
$383$	6.39088	−	1.35842i	0.326559	−	0.0694122i	0.368274	+	0.929717i	$0.379949\pi$
$384$	−9.70206	+	16.1603i	−0.495106	+	0.824679i
$385$	12.5230	+	3.19474i	0.638233	+	0.162819i
$386$	15.5180	+	11.2745i	0.789845	+	0.573856i
$387$	−20.4471	+	8.27859i	−1.03939	+	0.420825i
$388$	0.0794376	−	0.0577148i	0.00403283	−	0.00293002i
$389$	−7.39899	+	3.29424i	−0.375144	+	0.167025i	−0.585643	−	0.810569i	$-0.699158\pi$
$389$	−7.39899	+	3.29424i	−0.375144	+	0.167025i	0.210499	+	0.977594i	$0.432491\pi$
$390$	−22.5046	−	11.6107i	−1.13957	−	0.587933i
$391$	−3.88742	−	1.73079i	−0.196595	−	0.0875299i
$392$	−34.1138	+	7.25112i	−1.72301	+	0.366237i
$393$	1.00467	−	8.20724i	0.0506790	−	0.414000i
$394$	−8.96149	−	9.95274i	−0.451473	−	0.501412i
$395$	1.73533	−	4.68833i	0.0873137	−	0.235895i
$396$	−0.159909	+	0.108030i	−0.00803572	+	0.00542873i
$397$	−6.12281	−	18.8441i	−0.307295	−	0.945757i	−0.978811	−	0.204766i	$-0.934357\pi$
$397$	−6.12281	−	18.8441i	−0.307295	−	0.945757i	0.671516	−	0.740990i	$-0.265643\pi$
$398$	11.2056	−	4.98904i	0.561684	−	0.250078i
$399$	−8.12085	+	3.45061i	−0.406551	+	0.172746i
$400$	3.59479	−	19.1664i	0.179740	−	0.958321i
$401$	14.5828	+	25.2582i	0.728231	+	1.26133i	0.957630	+	0.288000i	$0.0929905\pi$
$401$	14.5828	+	25.2582i	0.728231	+	1.26133i	−0.229399	+	0.973332i	$0.573676\pi$
$402$	6.62122	+	21.6287i	0.330236	+	1.07874i
$403$	45.9541	+	9.76784i	2.28914	+	0.486571i
$404$	−0.0721702	−	0.222117i	−0.00359060	−	0.0110507i
$405$	20.0226	−	2.02411i	0.994929	−	0.100579i
$406$	13.7514	−	42.3225i	0.682471	−	2.10043i
$407$	1.25122	−	2.16718i	0.0620207	−	0.107423i
$408$	2.36909	−	1.66015i	0.117287	−	0.0821895i
$409$	11.2935	+	5.02818i	0.558426	+	0.248627i	0.666487	−	0.745517i	$-0.267797\pi$
$409$	11.2935	+	5.02818i	0.558426	+	0.248627i	−0.108060	+	0.994144i	$0.534464\pi$
$410$	−2.51835	+	17.2387i	−0.124373	+	0.851357i
$411$	−14.0989	−	3.24955i	−0.695447	−	0.160288i
$412$	0.0240996	+	0.229292i	0.00118730	+	0.0112964i
$413$	0.419744	−	0.304962i	0.0206542	−	0.0150062i
$414$	10.4295	−	28.7203i	0.512582	−	1.41152i
$415$	−1.67717	+	1.11805i	−0.0823293	+	0.0548831i
$416$	0.134897	+	1.28346i	0.00661389	+	0.0629269i
$417$	−9.47996	−	4.41635i	−0.464235	−	0.216270i
$418$	1.07183	+	1.85647i	0.0524252	+	0.0908030i
$419$	−7.15571	+	1.52099i	−0.349579	+	0.0743053i	−0.379355	−	0.925251i	$-0.623854\pi$
$419$	−7.15571	+	1.52099i	−0.349579	+	0.0743053i	0.0297757	+	0.999557i	$0.490521\pi$
$420$	−0.133514	+	0.816176i	−0.00651481	+	0.0398253i
$421$	−18.7647	−	3.98857i	−0.914537	−	0.194391i	−0.273474	−	0.961879i	$-0.588173\pi$
$421$	−18.7647	−	3.98857i	−0.914537	−	0.194391i	−0.641063	+	0.767488i	$0.721506\pi$
$422$	−2.92160	−	8.99175i	−0.142221	−	0.437712i
$423$	−12.5046	−	14.8803i	−0.607996	−	0.723505i
$424$	27.0751			1.31488
$425$	−1.65795	+	2.40129i	−0.0804224	+	0.116480i
$426$	−3.53054	+	1.50015i	−0.171055	+	0.0726825i
$427$	−3.31401	+	31.5307i	−0.160376	+	1.52588i
$428$	0.178564	−	0.198316i	0.00863123	−	0.00958595i
$429$	3.47917	−	10.1163i	0.167976	−	0.488418i
$430$	22.2548	+	5.67740i	1.07322	+	0.273788i
$431$	11.4223	−	35.1542i	0.550192	−	1.69332i	−0.158123	−	0.987419i	$-0.550544\pi$
$431$	11.4223	−	35.1542i	0.550192	−	1.69332i	0.708315	−	0.705897i	$-0.249456\pi$
$432$	12.7709	+	15.7353i	0.614439	+	0.757067i
$433$	−10.1680	+	31.2939i	−0.488643	+	1.50389i	0.337992	+	0.941149i	$0.390252\pi$
$433$	−10.1680	+	31.2939i	−0.488643	+	1.50389i	−0.826635	+	0.562739i	$0.809748\pi$
$434$	6.41936	+	61.0761i	0.308139	+	2.93175i
$435$	−21.8005	−	17.8374i	−1.04525	−	0.855239i
$436$	−0.0147779	+	0.140602i	−0.000707733	+	0.00673363i
$437$	7.74681	+	3.44910i	0.370580	+	0.164993i
$438$	−12.0575	+	20.0837i	−0.576128	+	0.959634i
$439$	28.8487	−	12.8443i	1.37687	−	0.613023i	0.421068	−	0.907029i	$-0.361655\pi$
$439$	28.8487	−	12.8443i	1.37687	−	0.613023i	0.955804	+	0.294006i	$0.0949886\pi$
$440$	8.43713	+	0.340551i	0.402224	+	0.0162352i
$441$	−5.06160	+	36.2075i	−0.241029	+	1.72417i
$442$	−1.17918	+	3.62913i	−0.0560877	+	0.172620i
$443$	−19.3550	+	33.5238i	−0.919583	+	1.59276i	−0.119533	+	0.992830i	$0.538140\pi$
$443$	−19.3550	+	33.5238i	−0.919583	+	1.59276i	−0.800050	+	0.599933i	$0.795194\pi$
$444$	0.145155	+	0.0676221i	0.00688874	+	0.00320920i
$445$	13.0076	−	13.3241i	0.616622	−	0.631624i
$446$	14.0287	−	15.5804i	0.664278	−	0.737755i
$447$	−2.28111	+	0.444270i	−0.107893	+	0.0210132i
$448$	−32.7542	+	14.5831i	−1.54749	+	0.688988i
$449$	−17.6894			−0.834813			−0.417407	−	0.908720i	$-0.637061\pi$
$449$	−17.6894			−0.834813			−0.417407	+	0.908720i	$0.637061\pi$
$450$	−18.0388	−	10.6600i	−0.850355	−	0.502515i
$451$	−7.35979			−0.346559
$452$	−0.130439	+	0.0580754i	−0.00613535	+	0.00273164i
$453$	−3.23464	−	3.71827i	−0.151976	−	0.174700i
$454$	−26.0786	+	28.9632i	−1.22393	+	1.35931i
$455$	−21.3030	−	40.5959i	−0.998702	−	1.90317i
$456$	−4.72110	+	3.30833i	−0.221086	+	0.154927i
$457$	−9.10167	+	15.7645i	−0.425758	+	0.737434i	−0.996491	−	0.0837013i	$-0.973326\pi$
$457$	−9.10167	+	15.7645i	−0.425758	+	0.737434i	0.570733	+	0.821136i	$0.306659\pi$
$458$	−7.37476	+	22.6972i	−0.344600	+	1.06057i
$459$	−0.788092	−	2.92833i	−0.0367850	−	0.136683i
$460$	0.661341	−	0.440869i	0.0308352	−	0.0205556i
$461$	−3.15453	+	1.40449i	−0.146921	+	0.0654136i	−0.478880	−	0.877880i	$-0.658957\pi$
$461$	−3.15453	+	1.40449i	−0.146921	+	0.0654136i	0.331959	+	0.943294i	$0.392290\pi$
$462$	13.9820	+	0.238936i	0.650502	+	0.0111163i
$463$	13.0433	+	5.80726i	0.606175	+	0.269886i	0.686786	−	0.726859i	$-0.259021\pi$
$463$	13.0433	+	5.80726i	0.606175	+	0.269886i	−0.0806119	+	0.996746i	$0.525687\pi$
$464$	2.96499	−	28.2100i	0.137646	−	1.30962i
$465$	37.4969	+	10.2513i	1.73888	+	0.475391i
$466$	0.192767	+	1.83406i	0.00892978	+	0.0849611i
$467$	6.91811	−	21.2917i	0.320132	−	0.985264i	−0.653459	−	0.756962i	$-0.726683\pi$
$467$	6.91811	−	21.2917i	0.320132	−	0.985264i	0.973590	−	0.228302i	$-0.0733173\pi$
$468$	0.664349	+	0.165124i	0.0307095	+	0.00763286i
$469$	−12.6545	+	38.9467i	−0.584332	+	1.79839i
$470$	1.30192	+	20.1950i	0.0600531	+	0.931527i
$471$	−21.6251	+	4.21171i	−0.996432	+	0.194065i
$472$	0.226822	−	0.251911i	0.0104403	−	0.0115951i
$473$	−1.01420	+	9.64952i	−0.0466332	+	0.443685i
$474$	0.657246	−	5.36909i	0.0301883	−	0.246610i
$475$	3.30395	−	4.78527i	0.151596	−	0.219563i
$476$	0.124622			0.00571204
$477$	9.68774	−	26.6776i	0.443571	−	1.22148i
$478$	−0.714011	−	2.19750i	−0.0326581	−	0.100511i
$479$	29.0035	+	6.16489i	1.32520	+	0.281681i	0.815544	−	0.578695i	$-0.196438\pi$
$479$	29.0035	+	6.16489i	1.32520	+	0.281681i	0.509660	+	0.860376i	$0.329771\pi$
$480$	0.0504794	+	1.06662i	0.00230406	+	0.0486845i
$481$	−8.68297	+	1.84562i	−0.395909	+	0.0841531i
$482$	−16.4457	−	28.4849i	−0.749083	−	1.29745i
$483$	45.3024	−	31.7458i	2.06133	−	1.44448i
$484$	−0.0471809	−	0.448896i	−0.00214459	−	0.0204044i
$485$	−1.56337	+	4.22375i	−0.0709889	+	0.191791i
$486$	20.5757	−	7.12695i	0.933334	−	0.323285i
$487$	−19.1564	+	13.9180i	−0.868061	+	0.630683i	−0.930066	−	0.367393i	$-0.880250\pi$
$487$	−19.1564	+	13.9180i	−0.868061	+	0.630683i	0.0620051	+	0.998076i	$0.480250\pi$
$488$	2.16521	+	20.6006i	0.0980147	+	0.932547i
$489$	8.69543	+	28.4043i	0.393221	+	1.28449i
$490$	26.5904	−	27.2373i	1.20123	−	1.23046i
$491$	−19.4291	−	8.65038i	−0.876822	−	0.390386i	−0.0815717	−	0.996667i	$-0.525994\pi$
$491$	−19.4291	−	8.65038i	−0.876822	−	0.390386i	−0.795250	+	0.606281i	$0.792661\pi$
$492$	−0.0412185	−	0.469151i	−0.00185827	−	0.0211510i
$493$	−2.12228	+	3.67589i	−0.0955826	+	0.165554i
$494$	2.34985	−	7.23209i	0.105725	−	0.325387i
$495$	3.35444	−	8.19141i	0.150771	−	0.368177i
$496$	12.0966	+	37.2295i	0.543153	+	1.67165i
$497$	−6.79310	−	1.44392i	−0.304712	−	0.0647685i
$498$	−1.48685	+	1.59562i	−0.0666272	+	0.0715014i
$499$	9.71305	+	16.8235i	0.434816	+	0.753123i	0.997281	−	0.0736982i	$-0.0234802\pi$
$499$	9.71305	+	16.8235i	0.434816	+	0.753123i	−0.562465	+	0.826821i	$0.690147\pi$
$500$	−0.213540	−	0.501468i	−0.00954982	−	0.0224263i
$501$	2.76416	−	22.5806i	0.123494	−	1.00883i
$502$	−3.04369	+	1.35514i	−0.135847	+	0.0604828i
$503$	−13.4070	−	41.2624i	−0.597787	−	1.83980i	−0.540334	−	0.841450i	$-0.681702\pi$
$503$	−13.4070	−	41.2624i	−0.597787	−	1.83980i	−0.0574525	−	0.998348i	$-0.518298\pi$
$504$	2.65078	+	37.5131i	0.118075	+	1.67097i
$505$	8.40551	+	6.64099i	0.374040	+	0.295520i
$506$	−8.99278	−	9.98750i	−0.399778	−	0.443998i
$507$	−14.2029	+	6.03493i	−0.630775	+	0.268021i
$508$	−0.213848	+	0.0454547i	−0.00948795	+	0.00201673i
$509$	−30.2872	−	13.4847i	−1.34245	−	0.597699i	−0.395322	−	0.918543i	$-0.629367\pi$
$509$	−30.2872	−	13.4847i	−1.34245	−	0.597699i	−0.947132	+	0.320843i	$0.896034\pi$
$510$	−1.14642	+	2.94188i	−0.0507645	+	0.130269i
$511$	−38.7430	+	17.2495i	−1.71389	+	0.763073i
$512$	−18.9297	+	13.7532i	−0.836581	+	0.607812i
$513$	1.57050	+	5.83554i	0.0693393	+	0.257646i
$514$	−4.72631	−	3.43387i	−0.208469	−	0.151461i
$515$	−6.75344	−	8.13785i	−0.297592	−	0.358597i
$516$	−0.620790	−	0.0106086i	−0.0273288	−	0.000467016i
$517$	−8.36230	+	1.77746i	−0.367773	+	0.0781727i
$518$	−5.80191	−	10.0492i	−0.254921	−	0.441537i
$519$	1.52552	+	17.3636i	0.0669629	+	0.762176i
$520$	−19.1288	−	23.0500i	−0.838852	−	1.01081i
$521$	−3.32016	−	10.2184i	−0.145459	−	0.447676i	0.851611	−	0.524175i	$-0.175626\pi$
$521$	−3.32016	−	10.2184i	−0.145459	−	0.447676i	−0.997070	+	0.0764982i	$0.975626\pi$
$522$	−27.4033	−	13.3407i	−1.19941	−	0.583905i
$523$	25.5685	+	18.5766i	1.11803	+	0.812297i	0.983909	−	0.178668i	$-0.0571787\pi$
$523$	25.5685	+	18.5766i	1.11803	+	0.812297i	0.134122	+	0.990965i	$0.457179\pi$
$524$	0.116362	−	0.201545i	0.00508329	−	0.00880451i
$525$	−15.6696	−	34.5464i	−0.683878	−	1.50773i
$526$	−11.5622	−	20.0262i	−0.504134	−	0.873185i
$527$	0.612292	−	5.82557i	0.0266719	−	0.253766i
$528$	8.74928	−	1.70401i	0.380763	−	0.0741576i
$529$	−29.5049	−	6.27146i	−1.28282	−	0.272672i
$530$	−24.5880	+	16.3911i	−1.06803	+	0.711982i
$531$	−0.167054	−	0.313628i	−0.00724952	−	0.0136103i
$532$	−0.248346			−0.0107671
$533$	17.4693	+	19.4016i	0.756680	+	0.840379i
$534$	10.3706	−	17.2739i	0.448779	−	0.747514i
$535$	−1.76938	+	12.1118i	−0.0764971	+	0.523639i
$536$	−2.79670	+	26.6088i	−0.120799	+	1.14933i
$537$	−37.5813	−	0.642220i	−1.62175	−	0.0277138i
$538$	−0.977661	−	9.30183i	−0.0421500	−	0.401030i
$539$	13.0094	+	9.45185i	0.560353	+	0.407120i
$540$	0.540950	+	0.167954i	0.0232788	+	0.00722757i
$541$	−7.53845	+	5.47700i	−0.324103	+	0.235475i	−0.737924	−	0.674883i	$-0.764194\pi$
$541$	−7.53845	+	5.47700i	−0.324103	+	0.235475i	0.413821	+	0.910358i	$0.364194\pi$
$542$	−15.8611	−	17.6155i	−0.681291	−	0.756651i
$543$	−15.4295	−	11.6181i	−0.662143	−	0.498581i
$544$	0.157390	−	0.0334544i	0.00674806	−	0.00143434i
$545$	−3.01321	−	5.74210i	−0.129072	−	0.245965i
$546$	−32.5581	−	37.4261i	−1.39336	−	1.60169i
$547$	−41.2188	−	8.76133i	−1.76239	−	0.374608i	−0.790948	−	0.611884i	$-0.790412\pi$
$547$	−41.2188	−	8.76133i	−1.76239	−	0.374608i	−0.971442	+	0.237276i	$0.923745\pi$
$548$	−0.329455	−	0.239363i	−0.0140736	−	0.0102251i
$549$	21.0730	+	5.23769i	0.899372	+	0.223539i
$550$	−7.86826	+	4.79851i	−0.335504	+	0.204609i
$551$	4.22926	−	7.32529i	0.180172	−	0.312068i
$552$	24.6393	−	26.4418i	1.04872	−	1.12544i
$553$	6.55274	−	7.27755i	0.278651	−	0.309473i
$554$	−25.0807	+	27.8549i	−1.06558	+	1.18344i
$555$	−7.26031	+	1.11223i	−0.308183	+	0.0472113i
$556$	−0.196961	−	0.218748i	−0.00835302	−	0.00927697i
$557$	21.0827			0.893303			0.446651	−	0.894708i	$-0.352616\pi$
$557$	21.0827			0.893303			0.446651	+	0.894708i	$0.352616\pi$
$558$	42.0365	+	1.43713i	1.77955	+	0.0608384i
$559$	27.8451	−	20.2306i	1.17772	−	0.855665i
$560$	20.4186	−	32.2848i	0.862844	−	1.36428i
$561$	−1.29975	−	0.299571i	−0.0548756	−	0.0126479i
$562$	6.06273	+	2.69930i	0.255741	+	0.113863i
$563$	37.4859	+	16.6898i	1.57984	+	0.703391i	0.994237	−	0.107204i	$-0.0341899\pi$
$563$	37.4859	+	16.6898i	1.57984	+	0.703391i	0.585606	+	0.810596i	$0.300857\pi$
$564$	−0.160138	−	0.523102i	−0.00674301	−	0.0220266i
$565$	3.50069	−	5.53511i	0.147275	−	0.232864i
$566$	6.60877	−	4.80155i	0.277787	−	0.201824i
$567$	37.9109	+	10.8107i	1.59211	+	0.454008i
$568$	−4.53744			−0.190387
$569$	−19.5221	−	21.6815i	−0.818408	−	0.908935i	0.178779	−	0.983889i	$-0.442785\pi$
$569$	−19.5221	−	21.6815i	−0.818408	−	0.908935i	−0.997187	+	0.0749548i	$0.976119\pi$
$570$	2.28458	−	5.86255i	0.0956906	−	0.245555i
$571$	19.5128	−	21.6712i	0.816586	−	0.906910i	−0.180471	−	0.983580i	$-0.557762\pi$
$571$	19.5128	−	21.6712i	0.816586	−	0.906910i	0.997057	+	0.0766699i	$0.0244288\pi$
$572$	0.201474	−	0.223760i	0.00842407	−	0.00935588i
$573$	12.0337	+	2.77355i	0.502714	+	0.115867i
$574$	−17.0637	+	29.5552i	−0.712224	+	1.23361i
$575$	−14.0236	+	33.6518i	−0.584824	+	1.40338i
$576$	6.78587	+	23.5999i	0.282745	+	0.983329i
$577$	−30.4784	−	22.1438i	−1.26883	−	0.921860i	−0.269677	−	0.962951i	$-0.586917\pi$
$577$	−30.4784	−	22.1438i	−1.26883	−	0.921860i	−0.999155	+	0.0410905i	$0.986917\pi$
$578$	−22.7625	−	4.83832i	−0.946796	−	0.201248i
$579$	23.3452	−	4.54672i	0.970194	−	0.188955i
$580$	−0.368392	−	0.702023i	−0.0152966	−	0.0291499i
$581$	−3.86224	+	0.820944i	−0.160233	+	0.0340585i
$582$	−0.592119	+	4.83706i	−0.0245441	+	0.200503i
$583$	−8.35319	−	9.27716i	−0.345954	−	0.384221i
$584$	−22.4165	+	16.2865i	−0.927601	+	0.673942i
$585$	−29.5561	+	10.6004i	−1.22200	+	0.438273i
$586$	−10.6745	−	7.75546i	−0.440958	−	0.320375i
$587$	−0.713188	−	6.78553i	−0.0294364	−	0.280069i	−0.999332	−	0.0365473i	$-0.988364\pi$
$587$	−0.713188	−	6.78553i	−0.0294364	−	0.280069i	0.969896	−	0.243521i	$-0.0783026\pi$
$588$	−0.529651	+	0.882219i	−0.0218424	+	0.0363821i
$589$	−1.22017	+	11.6091i	−0.0502763	+	0.478347i
$590$	−0.0534807	+	0.366087i	−0.00220177	+	0.0150716i
$591$	−16.6039	−	0.283741i	−0.682993	−	0.0116715i
$592$	−4.94921	−	5.49665i	−0.203411	−	0.225911i
$593$	7.55029			0.310053			0.155027	−	0.987910i	$-0.450454\pi$
$593$	7.55029			0.310053			0.155027	+	0.987910i	$0.450454\pi$
$594$	1.48787	−	9.46131i	0.0610482	−	0.388202i
$595$	−4.75623	+	3.17064i	−0.194986	+	0.129984i
$596$	−0.0639806	−	0.0135995i	−0.00262075	−	0.000557058i
$597$	4.94638	−	14.3824i	0.202442	−	0.588634i
$598$	−4.98331	+	47.4130i	−0.203783	+	1.93886i
$599$	11.9085	+	20.6261i	0.486568	+	0.842760i	0.999881	−	0.0154411i	$-0.00491526\pi$
$599$	11.9085	+	20.6261i	0.486568	+	0.842760i	−0.513313	+	0.858202i	$0.671582\pi$
$600$	−14.7068	−	19.9492i	−0.600403	−	0.814421i
$601$	−4.31568	+	7.47497i	−0.176040	+	0.304911i	−0.940521	−	0.339736i	$-0.889662\pi$
$601$	−4.31568	+	7.47497i	−0.176040	+	0.304911i	0.764481	+	0.644647i	$0.222996\pi$
$602$	36.3987	+	26.4452i	1.48350	+	1.07783i
$603$	25.2175	+	12.2765i	1.02694	+	0.499940i
$604$	−0.0428643	−	0.131923i	−0.00174412	−	0.00536786i
$605$	13.2215	+	15.9318i	0.537531	+	0.647721i
$606$	10.5067	+	4.89469i	0.426807	+	0.198833i
$607$	−15.7006	−	27.1942i	−0.637268	−	1.10378i	−0.986030	−	0.166569i	$-0.946731\pi$
$607$	−15.7006	−	27.1942i	−0.637268	−	1.10378i	0.348762	−	0.937211i	$-0.386602\pi$
$608$	−0.313646	+	0.0666675i	−0.0127200	+	0.00270373i
$609$	−26.7687	−	48.2503i	−1.08472	−	1.95520i
$610$	−14.4378	−	17.3975i	−0.584570	−	0.704403i
$611$	24.5346	+	17.8254i	0.992563	+	0.721139i
$612$	0.0118169	−	0.0845308i	0.000477670	−	0.00341695i
$613$	28.7507	−	20.8886i	1.16123	−	0.843681i	0.171295	−	0.985220i	$-0.445205\pi$
$613$	28.7507	−	20.8886i	1.16123	−	0.843681i	0.989933	+	0.141538i	$0.0452048\pi$
$614$	−8.41114	+	3.74488i	−0.339446	+	0.151131i
$615$	13.5093	+	16.8566i	0.544747	+	0.679723i
$616$	15.1109	+	6.72782i	0.608837	+	0.271072i
$617$	42.6070	−	9.05640i	1.71529	−	0.364597i	0.757674	−	0.652634i	$-0.226336\pi$
$617$	42.6070	−	9.05640i	1.71529	−	0.364597i	0.957619	+	0.288037i	$0.0930026\pi$
$618$	−9.14085	−	6.88288i	−0.367699	−	0.276870i
$619$	11.7244	+	13.0213i	0.471244	+	0.523370i	0.931169	−	0.364588i	$-0.118790\pi$
$619$	11.7244	+	13.0213i	0.471244	+	0.523370i	−0.459924	+	0.887958i	$0.652124\pi$
$620$	0.858497	+	0.678278i	0.0344781	+	0.0272403i
$621$	−17.2374	−	33.7387i	−0.691715	−	1.35389i
$622$	6.49519	+	19.9901i	0.260433	+	0.801531i
$623$	33.3227	−	14.8362i	1.33505	−	0.594401i
$624$	−25.2595	−	19.0199i	−1.01119	−	0.761406i
$625$	20.9082	+	13.7057i	0.836328	+	0.548229i
$626$	17.0445	+	29.5219i	0.681235	+	1.17993i
$627$	2.59014	+	0.596981i	0.103440	+	0.0238411i
$628$	−0.606541	−	0.128924i	−0.0242036	−	0.00514464i
$629$	0.342020	+	1.05263i	0.0136372	+	0.0419710i
$630$	−25.1175	−	32.4624i	−1.00070	−	1.29333i
$631$	−2.00653	+	6.17548i	−0.0798788	+	0.245842i	−0.983019	−	0.183504i	$-0.941256\pi$
$631$	−2.00653	+	6.17548i	−0.0798788	+	0.245842i	0.903140	+	0.429346i	$0.141256\pi$
$632$	3.19911	−	5.54102i	0.127254	−	0.220410i
$633$	−10.6265	−	4.95050i	−0.422367	−	0.196765i
$634$	−16.9682	−	7.55473i	−0.673893	−	0.300037i
$635$	7.00508	−	7.17552i	0.277988	−	0.284752i
$636$	0.544592	−	0.584433i	0.0215945	−	0.0231743i
$637$	−5.96256	−	56.7299i	−0.236245	−	2.24772i
$638$	−10.8453	+	7.87958i	−0.429370	+	0.311955i
$639$	−1.62354	+	4.47083i	−0.0642263	+	0.176863i
$640$	8.44688	−	22.8209i	0.333892	−	0.902076i
$641$	0.984425	+	9.36618i	0.0388825	+	0.369942i	0.996610	+	0.0822663i	$0.0262158\pi$
$641$	0.984425	+	9.36618i	0.0388825	+	0.369942i	−0.957728	+	0.287676i	$0.907118\pi$
$642$	1.15914	+	13.1934i	0.0457477	+	0.520702i
$643$	5.52063	+	9.56201i	0.217712	+	0.377089i	0.954108	−	0.299462i	$-0.0968072\pi$
$643$	5.52063	+	9.56201i	0.217712	+	0.377089i	−0.736396	+	0.676551i	$0.763474\pi$
$644$	1.52295	−	0.323713i	0.0600127	−	0.0127561i
$645$	23.9625	−	15.3893i	0.943523	−	0.605954i
$646$	−0.927400	−	0.197125i	−0.0364880	−	0.00775577i
$647$	8.41216	+	25.8900i	0.330716	+	1.01784i	0.968794	+	0.247868i	$0.0797299\pi$
$647$	8.41216	+	25.8900i	0.330716	+	1.01784i	−0.638078	+	0.769972i	$0.720270\pi$
$648$	25.6964	+	1.75906i	1.00945	+	0.0691022i
$649$	−0.156295			−0.00613513
$650$	31.3259	+	9.35224i	1.22870	+	0.366825i
$651$	60.8316	+	45.8050i	2.38418	+	1.79524i
$652$	−0.0873945	+	0.831503i	−0.00342263	+	0.0325642i
$653$	1.12352	−	1.24780i	0.0439669	−	0.0488302i	−0.720760	−	0.693184i	$-0.756207\pi$
$653$	1.12352	−	1.24780i	0.0439669	−	0.0488302i	0.764727	+	0.644354i	$0.222874\pi$
$654$	−4.60518	−	5.29374i	−0.180077	−	0.207002i
$655$	0.686736	+	10.6525i	0.0268330	+	0.416227i
$656$	−6.72215	+	20.6887i	−0.262456	+	0.807757i
$657$	8.02660	+	27.9149i	0.313147	+	1.08906i
$658$	−12.2501	+	37.7020i	−0.477560	+	1.46978i
$659$	1.71958	+	16.3607i	0.0669852	+	0.637322i	0.975580	+	0.219643i	$0.0704894\pi$
$659$	1.71958	+	16.3607i	0.0669852	+	0.637322i	−0.908595	+	0.417678i	$0.862844\pi$
$660$	0.177057	−	0.175271i	0.00689193	−	0.00682241i
$661$	0.647069	−	6.15645i	0.0251681	−	0.239458i	−0.974705	−	0.223497i	$-0.928253\pi$
$661$	0.647069	−	6.15645i	0.0251681	−	0.239458i	0.999873	−	0.0159610i	$-0.00508074\pi$
$662$	−7.43158	−	3.30875i	−0.288837	−	0.128598i
$663$	2.29540	+	4.13744i	0.0891459	+	0.160685i
$664$	−2.35674	+	1.04929i	−0.0914593	+	0.0407203i
$665$	9.47816	−	6.31843i	0.367547	−	0.245018i
$666$	−7.36650	+	2.98254i	−0.285446	+	0.115571i
$667$	−16.3871	+	50.4343i	−0.634510	+	1.95282i
$668$	0.320147	−	0.554511i	0.0123869	−	0.0214547i
$669$	−2.27520	−	25.8965i	−0.0879644	−	1.00122i
$670$	−13.5690	−	25.8576i	−0.524216	−	0.998968i
$671$	6.39071	−	7.09761i	0.246711	−	0.274000i
$672$	−0.680284	+	1.97804i	−0.0262425	+	0.0763046i
$673$	5.10668	−	2.27364i	0.196848	−	0.0876423i	−0.305945	−	0.952049i	$-0.598972\pi$
$673$	5.10668	−	2.27364i	0.196848	−	0.0876423i	0.502793	+	0.864407i	$0.332306\pi$
$674$	21.6673			0.834594
$675$	−24.9186	+	7.35290i	−0.959116	+	0.283013i
$676$	−0.434344			−0.0167055
$677$	−10.9525	+	4.87636i	−0.420938	+	0.187414i	−0.606264	−	0.795263i	$-0.707333\pi$
$677$	−10.9525	+	4.87636i	−0.420938	+	0.187414i	0.185326	+	0.982677i	$0.440666\pi$
$678$	2.30463	−	6.70110i	0.0885088	−	0.257354i
$679$	−5.90342	+	6.55641i	−0.226552	+	0.251612i
$680$	−2.60888	+	2.67236i	−0.100046	+	0.102480i
$681$	4.22948	+	48.1402i	0.162074	+	1.84474i
$682$	9.25009	−	16.0216i	0.354204	−	0.613500i
$683$	5.37897	−	16.5548i	0.205821	−	0.633450i	−0.793858	−	0.608103i	$-0.791931\pi$
$683$	5.37897	−	16.5548i	0.205821	−	0.633450i	0.999679	−	0.0253475i	$-0.00806923\pi$
$684$	−0.0235486	+	0.168452i	−0.000900404	+	0.00644093i
$685$	18.6636	+	0.753327i	0.713100	+	0.0287832i
$686$	28.9910	−	12.9076i	1.10688	−	0.492815i
$687$	14.3558	+	25.8762i	0.547708	+	0.987240i
$688$	26.1988	+	11.6645i	0.998822	+	0.444704i
$689$	−4.62888	+	44.0409i	−0.176346	+	1.67782i
$690$	−6.36824	+	38.9293i	−0.242435	+	1.48201i
$691$	0.0730737	+	0.695250i	0.00277985	+	0.0264485i	0.995824	−	0.0912950i	$-0.0291006\pi$
$691$	0.0730737	+	0.695250i	0.00277985	+	0.0264485i	−0.993044	+	0.117743i	$0.962434\pi$
$692$	−0.151602	+	0.466582i	−0.00576303	+	0.0177368i
$693$	12.0359	−	12.4818i	0.457206	−	0.474145i
$694$	8.29642	−	25.5338i	0.314928	−	0.969248i
$695$	13.0825	+	3.33745i	0.496246	+	0.126597i
$696$	−23.6615	−	27.1993i	−0.896886	−	1.03099i
$697$	2.17812	−	2.41904i	0.0825020	−	0.0916278i
$698$	3.89974	−	37.1035i	0.147607	−	1.40439i
$699$	1.82672	+	1.37548i	0.0690928	+	0.0520255i
$700$	−0.0256611	−	1.06738i	−0.000969897	−	0.0403430i
$701$	17.1962			0.649492			0.324746	−	0.945801i	$-0.394721\pi$
$701$	17.1962			0.649492			0.324746	+	0.945801i	$0.394721\pi$
$702$	−28.4732	+	18.5352i	−1.07465	+	0.699568i
$703$	−0.681574	−	2.09767i	−0.0257060	−	0.0791150i
$704$	10.5648	+	2.24561i	0.398175	+	0.0846348i
$705$	19.4205	+	15.8901i	0.731418	+	0.598454i
$706$	48.3300	−	10.2729i	1.81892	−	0.386624i
$707$	10.4923	+	18.1732i	0.394603	+	0.683472i
$708$	−0.000875332	−	0.00996307i	−3.28970e−5	−	0.000374435i
$709$	1.91637	+	18.2330i	0.0719708	+	0.684756i	0.969715	+	0.244239i	$0.0785382\pi$
$709$	1.91637	+	18.2330i	0.0719708	+	0.684756i	−0.897744	+	0.440517i	$0.854795\pi$
$710$	4.12063	−	2.74693i	0.154644	−	0.103091i
$711$	−4.31500	−	5.13478i	−0.161825	−	0.192569i
$712$	19.2803	−	14.0080i	0.722561	−	0.524971i
$713$	−7.64973	−	72.7823i	−0.286484	−	2.72572i
$714$	−4.21648	+	4.52495i	−0.157798	+	0.169342i
$715$	−1.99640	+	13.6658i	−0.0746611	+	0.511071i
$716$	−0.966449	−	0.430291i	−0.0361179	−	0.0160807i
$717$	−2.59703	−	1.20986i	−0.0969877	−	0.0451829i
$718$	−14.9669	+	25.9234i	−0.558559	+	0.967452i
$719$	−2.37768	+	7.31774i	−0.0886724	+	0.272906i	−0.985553	−	0.169367i	$-0.945828\pi$
$719$	−2.37768	+	7.31774i	−0.0886724	+	0.272906i	0.896881	+	0.442273i	$0.145828\pi$
$720$	−19.9626	−	16.9112i	−0.743961	−	0.630243i
$721$	−6.40150	−	19.7018i	−0.238404	−	0.733733i
$722$	−24.1125	−	5.12526i	−0.897373	−	0.190743i
$723$	−39.7419	−	9.15981i	−1.47802	−	0.340657i
$724$	−0.271811	−	0.470790i	−0.0101018	−	0.0174968i
$725$	31.9207	+	17.4202i	1.18550	+	0.646970i
$726$	17.8955	+	13.4749i	0.664163	+	0.500101i
$727$	29.7328	−	13.2379i	1.10273	−	0.490967i	0.227062	−	0.973880i	$-0.427088\pi$
$727$	29.7328	−	13.2379i	1.10273	−	0.490967i	0.875668	+	0.482913i	$0.160421\pi$
$728$	−18.1319	−	55.8043i	−0.672013	−	2.06824i
$729$	10.9277	−	24.6898i	0.404729	−	0.914437i
$730$	10.4976	−	28.3613i	0.388532	−	1.04970i
$731$	−2.87149	−	3.18911i	−0.106206	−	0.117953i
$732$	0.488230	+	0.367627i	0.0180455	+	0.0135879i
$733$	−28.4887	+	6.05545i	−1.05225	+	0.223663i	−0.701400	−	0.712767i	$-0.747442\pi$
$733$	−28.4887	+	6.05545i	−1.05225	+	0.223663i	−0.350853	+	0.936431i	$0.614108\pi$
$734$	−10.0886	−	4.49174i	−0.372377	−	0.165793i
$735$	−2.23122	−	47.1455i	−0.0822999	−	1.73899i
$736$	1.83650	−	0.817662i	0.0676943	−	0.0301394i
$737$	9.98024	−	7.25107i	0.367627	−	0.267096i
$738$	18.4292	+	14.3767i	0.678387	+	0.529215i
$739$	−11.3734	−	8.26328i	−0.418378	−	0.303970i	0.358607	−	0.933489i	$-0.383252\pi$
$739$	−11.3734	−	8.26328i	−0.418378	−	0.303970i	−0.776985	+	0.629519i	$0.783252\pi$
$740$	−0.200315	−	0.0511022i	−0.00736374	−	0.00187855i
$741$	−4.57425	−	8.24504i	−0.168039	−	0.302889i
$742$	−56.6218	+	12.0353i	−2.07865	+	0.441831i
$743$	−14.8798	−	25.7725i	−0.545886	−	0.945503i	−0.998551	−	0.0538219i	$-0.982860\pi$
$743$	−14.8798	−	25.7725i	−0.545886	−	0.945503i	0.452664	−	0.891681i	$-0.350474\pi$
$744$	45.0981	+	21.0095i	1.65338	+	0.770245i
$745$	2.78784	−	1.10877i	0.102138	−	0.0406223i
$746$	14.2917	+	43.9852i	0.523255	+	1.61041i
$747$	0.190619	+	2.69759i	0.00697439	+	0.0986997i
$748$	−0.0303719	−	0.0220665i	−0.00111051	−	0.000806830i
$749$	−11.9889	+	20.7653i	−0.438063	+	0.758748i
$750$	25.4330	+	9.21324i	0.928680	+	0.336420i
$751$	−15.3394	−	26.5687i	−0.559744	−	0.969505i	−0.997517	−	0.0704197i	$-0.977566\pi$
$751$	−15.3394	−	26.5687i	−0.559744	−	0.969505i	0.437773	−	0.899085i	$-0.355767\pi$
$752$	−2.64129	+	25.1302i	−0.0963181	+	0.916405i
$753$	−1.34355	+	3.90660i	−0.0489618	+	0.142365i
$754$	46.5145	+	9.88697i	1.69396	+	0.360062i
$755$	4.99231	+	3.94430i	0.181689	+	0.143548i
$756$	0.863064	+	0.697327i	0.0313893	+	0.0253615i
$757$	−12.3530			−0.448977			−0.224488	−	0.974477i	$-0.572071\pi$
$757$	−12.3530			−0.448977			−0.224488	+	0.974477i	$0.572071\pi$
$758$	6.09950	+	6.77418i	0.221544	+	0.246049i
$759$	−16.6619	−	0.284732i	−0.604788	−	0.0103351i
$760$	5.19896	−	5.32545i	0.188586	−	0.193174i
$761$	2.22064	−	21.1280i	0.0804982	−	0.765889i	−0.877589	−	0.479413i	$-0.840850\pi$
$761$	2.22064	−	21.1280i	0.0804982	−	0.765889i	0.958087	−	0.286476i	$-0.0924838\pi$
$762$	5.58493	−	9.30259i	0.202321	−	0.336997i
$763$	−1.32781	−	12.6333i	−0.0480701	−	0.457356i
$764$	0.281196	+	0.204301i	0.0101733	+	0.00739135i
$765$	1.69964	+	3.52678i	0.0614507	+	0.127511i
$766$	−7.38364	+	5.36453i	−0.266782	+	0.193828i
$767$	0.370985	+	0.412021i	0.0133955	+	0.0148772i
$768$	−0.246084	+	2.01028i	−0.00887979	+	0.0725396i
$769$	9.20733	−	1.95708i	0.332025	−	0.0705740i	−0.0388830	−	0.999244i	$-0.512380\pi$
$769$	9.20733	−	1.95708i	0.332025	−	0.0705740i	0.370908	+	0.928670i	$0.379047\pi$
$770$	−17.7958	+	3.03825i	−0.641317	+	0.109491i
$771$	−7.11024	+	1.38479i	−0.256069	+	0.0498721i
$772$	0.654787	+	0.139179i	0.0235663	+	0.00500917i
$773$	14.6694	+	10.6580i	0.527622	+	0.383340i	0.819468	−	0.573125i	$-0.194269\pi$
$773$	14.6694	+	10.6580i	0.527622	+	0.383340i	−0.291845	+	0.956466i	$0.594269\pi$
$774$	21.3891	−	22.1816i	0.768816	−	0.797300i
$775$	−50.0215	−	4.04467i	−1.79683	−	0.145289i
$776$	−2.88210	+	4.99195i	−0.103461	+	0.179201i
$777$	−14.0206	−	3.23150i	−0.502986	−	0.115929i
$778$	7.57024	−	8.40760i	0.271406	−	0.301427i
$779$	−4.34053	+	4.82064i	−0.155516	+	0.172717i
$780$	−0.882309	−	0.0507256i	−0.0315917	−	0.00181627i
$781$	1.39989	+	1.55473i	0.0500920	+	0.0556328i
$782$	5.94412			0.212561
$783$	−35.2663	+	13.5819i	−1.26032	+	0.485379i
$784$	38.4518	−	27.9369i	1.37328	−	0.997745i
$785$	26.4289	−	10.5112i	0.943287	−	0.375162i
$786$	3.38095	+	11.0441i	0.120594	+	0.393931i
$787$	−18.9135	−	8.42085i	−0.674195	−	0.300171i	0.0409357	−	0.999162i	$-0.486966\pi$
$787$	−18.9135	−	8.42085i	−0.674195	−	0.300171i	−0.715131	+	0.698991i	$0.753633\pi$
$788$	−0.426989	−	0.190108i	−0.0152109	−	0.00677231i
$789$	−27.9405	−	6.43979i	−0.994707	−	0.229263i
$790$	0.449256	+	6.96874i	0.0159838	+	0.247937i
$791$	10.3791	−	7.54087i	0.369039	−	0.268123i
$792$	5.99632	−	9.61177i	0.213070	−	0.341539i
$793$	−33.8796			−1.20310
$794$	18.5198	+	20.5683i	0.657242	+	0.729941i
$795$	−5.91531	+	36.1606i	−0.209795	+	1.28248i
$796$	0.286439	−	0.318123i	0.0101526	−	0.0112756i
$797$	13.3956	−	14.8773i	0.474497	−	0.526982i	−0.457616	−	0.889150i	$-0.651297\pi$
$797$	13.3956	−	14.8773i	0.474497	−	0.526982i	0.932113	+	0.362168i	$0.117963\pi$
$798$	8.40257	−	9.01727i	0.297448	−	0.319208i
$799$	1.89058	−	3.27459i	0.0668840	−	0.115847i
$800$	−0.318942	−	1.34114i	−0.0112763	−	0.0474166i
$801$	−6.90364	−	24.0095i	−0.243928	−	0.848334i
$802$	−32.9599	−	23.9467i	−1.16385	−	0.845589i
$803$	12.4964	+	2.65620i	0.440990	+	0.0937353i
$804$	0.518115	+	0.595583i	0.0182725	+	0.0210046i
$805$	−49.8878	+	51.1016i	−1.75832	+	1.80110i
$806$	−64.1919	+	13.6444i	−2.26106	+	0.480604i
$807$	−9.26459	−	6.97606i	−0.326129	−	0.245569i
$808$	9.17398	+	10.1887i	0.322739	+	0.358438i
$809$	−4.72327	+	3.43166i	−0.166061	+	0.120651i	−0.667712	−	0.744420i	$-0.732726\pi$
$809$	−4.72327	+	3.43166i	−0.166061	+	0.120651i	0.501651	+	0.865070i	$0.332726\pi$
$810$	−24.4009	+	13.9590i	−0.857360	+	0.490468i
$811$	7.21895	+	5.24487i	0.253492	+	0.184172i	0.707273	−	0.706941i	$-0.249925\pi$
$811$	7.21895	+	5.24487i	0.253492	+	0.184172i	−0.453781	+	0.891113i	$0.649925\pi$
$812$	−0.162337	−	1.54453i	−0.00569691	−	0.0542025i
$813$	−29.3875	−	0.502197i	−1.03066	−	0.0176128i
$814$	−0.365389	+	3.47644i	−0.0128069	+	0.121849i
$815$	−17.8197	−	33.9580i	−0.624198	−	1.18950i
$816$	−2.02925	+	3.38004i	−0.0710380	+	0.118325i
$817$	5.72227	+	6.35522i	0.200197	+	0.222341i
$818$	−17.2685			−0.603778
$819$	−61.4729	−	2.10161i	−2.14804	−	0.0734362i
$820$	0.164410	+	0.585354i	0.00574144	+	0.0204414i
$821$	0.988521	+	0.210117i	0.0344996	+	0.00733312i	0.225129	−	0.974329i	$-0.427720\pi$
$821$	0.988521	+	0.210117i	0.0344996	+	0.00733312i	−0.190630	+	0.981662i	$0.561053\pi$
$822$	19.8379	−	3.86364i	0.691928	−	0.134760i
$823$	−3.98839	+	37.9470i	−0.139027	+	1.32275i	0.673223	+	0.739440i	$0.264910\pi$
$823$	−3.98839	+	37.9470i	−0.139027	+	1.32275i	−0.812249	+	0.583310i	$0.801757\pi$
$824$	−6.76732	−	11.7213i	−0.235751	−	0.408332i
$825$	−2.29816	+	11.1939i	−0.0800116	+	0.389723i
$826$	−0.362371	+	0.627644i	−0.0126085	+	0.0218385i
$827$	−17.3951	−	12.6383i	−0.604889	−	0.439477i	0.242722	−	0.970096i	$-0.421960\pi$
$827$	−17.3951	−	12.6383i	−0.604889	−	0.439477i	−0.847611	+	0.530619i	$0.821960\pi$
$828$	−0.0751646	−	1.06371i	−0.00261215	−	0.0369665i
$829$	−9.35263	−	28.7844i	−0.324830	−	0.999725i	−0.971517	−	0.236969i	$-0.923846\pi$
$829$	−9.35263	−	28.7844i	−0.324830	−	0.999725i	0.646687	−	0.762756i	$-0.276154\pi$
$830$	1.50502	−	2.37966i	0.0522400	−	0.0825991i
$831$	4.06764	+	46.2981i	0.141105	+	1.60606i
$832$	−19.1569	−	33.1808i	−0.664147	−	1.15034i
$833$	−6.95676	+	1.47871i	−0.241038	+	0.0512341i
$834$	14.6066	+	0.249610i	0.505786	+	0.00864328i
$835$	1.88942	+	29.3083i	0.0653862	+	1.01425i
$836$	0.0605248	+	0.0439738i	0.00209329	+	0.00152087i
$837$	36.8376	−	36.9186i	1.27329	−	1.27609i
$838$	8.26727	−	6.00653i	0.285588	−	0.207492i
$839$	−42.6213	+	18.9762i	−1.47145	+	0.655133i	−0.976838	−	0.213980i	$-0.931357\pi$
$839$	−42.6213	+	18.9762i	−1.47145	+	0.655133i	−0.494614	+	0.869113i	$0.664691\pi$
$840$	−12.3278	−	46.9588i	−0.425350	−	1.62023i
$841$	21.8298	+	9.71926i	0.752752	+	0.335147i
$842$	26.2119	−	5.57152i	0.903322	−	0.192007i
$843$	7.57357	−	3.21806i	0.260848	−	0.110836i
$844$	−0.220783	−	0.245205i	−0.00759968	−	0.00844030i
$845$	16.5768	−	11.0506i	0.570260	−	0.380152i
$846$	24.4116	+	11.8842i	0.839289	+	0.408588i
$847$	12.5325	+	38.5711i	0.430622	+	1.32532i
$848$	−33.7080	+	15.0078i	−1.15754	+	0.515368i
$849$	1.23074	−	10.0540i	0.0422387	−	0.345051i
$850$	0.751405	−	4.00628i	0.0257730	−	0.137414i
$851$	6.91394	+	11.9753i	0.237007	+	0.410508i
$852$	−0.0912667	+	0.0979435i	−0.00312675	+	0.00335549i
$853$	−37.6833	−	8.00983i	−1.29025	−	0.274251i	−0.488844	−	0.872371i	$-0.662581\pi$
$853$	−37.6833	−	8.00983i	−1.29025	−	0.274251i	−0.801407	+	0.598120i	$0.795915\pi$
$854$	−13.6854	−	42.1194i	−0.468305	−	1.44130i
$855$	−3.38703	−	7.02814i	−0.115834	−	0.240357i
$856$	−4.84103	+	14.8991i	−0.165463	+	0.509242i
$857$	12.2887	−	21.2847i	0.419775	−	0.727071i	−0.576142	−	0.817350i	$-0.695442\pi$
$857$	12.2887	−	21.2847i	0.419775	−	0.727071i	0.995917	+	0.0902786i	$0.0287757\pi$
$858$	1.30786	+	14.8861i	0.0446497	+	0.508205i
$859$	−19.4528	−	8.66093i	−0.663720	−	0.295507i	0.0470908	−	0.998891i	$-0.485005\pi$
$859$	−19.4528	−	8.66093i	−0.663720	−	0.295507i	−0.710810	+	0.703384i	$0.751672\pi$
$860$	0.790121	−	0.134896i	0.0269429	−	0.00459992i
$861$	12.3869	+	40.4627i	0.422144	+	1.37896i
$862$	5.39711	+	51.3501i	0.183826	+	1.74899i
$863$	−35.2998	+	25.6468i	−1.20162	+	0.873027i	−0.994443	−	0.105276i	$-0.966427\pi$
$863$	−35.2998	+	25.6468i	−1.20162	+	0.873027i	−0.207176	+	0.978304i	$0.566427\pi$
$864$	1.27719	+	0.648997i	0.0434510	+	0.0220793i
$865$	−6.08490	−	21.6643i	−0.206893	−	0.736608i
$866$	−4.80445	−	45.7113i	−0.163262	−	1.55333i
$867$	−23.6305	+	16.5592i	−0.802534	+	0.562379i
$868$	1.07163	+	1.85612i	0.0363735	+	0.0630007i
$869$	−2.88559	+	0.613352i	−0.0978871	+	0.0208065i
$870$	37.9542	+	10.3763i	1.28677	+	0.351789i
$871$	−42.8043	−	9.09834i	−1.45037	−	0.308285i
$872$	−2.56467	−	7.89325i	−0.0868507	−	0.267299i
$873$	3.88742	+	4.62596i	0.131569	+	0.156565i
$874$	−11.8454			−0.400676
$875$	28.1356	+	40.0837i	0.951157	+	1.35508i
$876$	−0.0993338	+	0.811465i	−0.00335618	+	0.0274168i
$877$	−4.13435	+	39.3358i	−0.139607	+	1.32827i	0.670464	+	0.741942i	$0.266095\pi$
$877$	−4.13435	+	39.3358i	−0.139607	+	1.32827i	−0.810071	+	0.586332i	$0.800572\pi$
$878$	−29.5164	+	32.7813i	−0.996129	+	1.10631i
$879$	−16.0586	+	3.12758i	−0.541644	+	0.105491i
$880$	−10.6928	+	4.25273i	−0.360455	+	0.143360i
$881$	0.704221	−	2.16737i	0.0237258	−	0.0730206i	−0.938493	−	0.345299i	$-0.887777\pi$
$881$	0.704221	−	2.16737i	0.0237258	−	0.0730206i	0.962218	+	0.272279i	$0.0877773\pi$
$882$	−14.1125	−	49.0805i	−0.475192	−	1.65262i
$883$	6.87966	−	21.1734i	0.231519	−	0.712542i	−0.766045	−	0.642787i	$-0.777778\pi$
$883$	6.87966	−	21.1734i	0.231519	−	0.712542i	0.997564	−	0.0697555i	$-0.0222219\pi$
$884$	0.0139203	+	0.132443i	0.000468190	+	0.00445453i
$885$	0.286888	+	0.357973i	0.00964365	+	0.0120331i
$886$	5.65215	−	53.7766i	0.189888	−	1.80666i
$887$	18.4661	+	8.22166i	0.620033	+	0.276056i	0.692617	−	0.721306i	$-0.256458\pi$
$887$	18.4661	+	8.22166i	0.620033	+	0.276056i	−0.0725839	+	0.997362i	$0.523125\pi$
$888$	−9.39916	−	0.160621i	−0.315415	−	0.00539007i
$889$	17.9455	−	7.98983i	0.601871	−	0.267970i
$890$	−9.02891	+	24.3934i	−0.302650	+	0.817669i
$891$	−7.32512	−	9.34748i	−0.245401	−	0.313152i
$892$	0.226103	−	0.695873i	0.00757049	−	0.0232996i
$893$	−3.76754	+	6.52557i	−0.126076	+	0.218370i
$894$	2.65852	−	1.86297i	0.0889143	−	0.0623070i
$895$	47.8322	−	8.16632i	1.59885	−	0.272970i
$896$	31.8961	−	35.4242i	1.06557	−	1.18344i
$897$	38.7983	+	44.5994i	1.29544	+	1.48913i
$898$	22.5735	−	10.0504i	0.753288	−	0.335385i
$899$	−72.9982			−2.43463
$900$	−0.726431	−	0.0838048i	−0.0242144	−	0.00279349i
$901$	5.52136			0.183943
$902$	9.39187	−	4.18153i	0.312715	−	0.139230i
$903$	54.7581	−	10.6647i	1.82223	−	0.354899i
$904$	5.60868	−	6.22907i	0.186542	−	0.207176i
$905$	22.3516	+	11.0524i	0.742993	+	0.367394i
$906$	6.24031	+	2.90712i	0.207320	+	0.0965827i
$907$	14.1331	−	24.4792i	0.469281	−	0.812819i	−0.530102	−	0.847934i	$-0.677846\pi$
$907$	14.1331	−	24.4792i	0.469281	−	0.812819i	0.999383	+	0.0351150i	$0.0111798\pi$
$908$	−0.420313	+	1.29359i	−0.0139486	+	0.0429293i
$909$	13.3217	−	5.39367i	0.441853	−	0.178897i
$910$	50.2499	+	39.7012i	1.66577	+	1.31608i
$911$	−20.8237	+	9.27132i	−0.689921	+	0.307172i	−0.721585	−	0.692326i	$-0.756586\pi$
$911$	−20.8237	+	9.27132i	−0.689921	+	0.307172i	0.0316642	+	0.999499i	$0.489919\pi$
$912$	4.04387	−	6.73572i	0.133906	−	0.223042i
$913$	1.08664	+	0.483802i	0.0359624	+	0.0160115i
$914$	2.65792	−	25.2884i	0.0879162	−	0.836467i
$915$	−27.9866	−	1.60900i	−0.925208	−	0.0531920i
$916$	0.0870599	+	0.828319i	0.00287654	+	0.0273684i
$917$	−6.46170	+	19.8871i	−0.213384	+	0.656729i
$918$	2.66944	+	3.28910i	0.0881048	+	0.108556i
$919$	2.81038	−	8.64946i	0.0927059	−	0.285320i	−0.893943	−	0.448180i	$-0.852072\pi$
$919$	2.81038	−	8.64946i	0.0927059	−	0.285320i	0.986649	+	0.162861i	$0.0520722\pi$
$920$	−24.9404	+	39.4345i	−0.822262	+	1.30012i
$921$	−3.71286	+	10.7958i	−0.122343	+	0.355733i
$922$	3.22755	−	3.58455i	0.106294	−	0.118051i
$923$	0.775742	−	7.38069i	0.0255338	−	0.242938i
$924$	0.449168	−	0.190855i	0.0147766	−	0.00627866i
$925$	8.94523	−	3.14611i	0.294117	−	0.103444i
$926$	−19.9441			−0.655404
$927$	−13.9707	+	2.47396i	−0.458857	+	0.0812554i
$928$	−0.619647	−	1.90708i	−0.0203409	−	0.0626028i
$929$	−34.8214	−	7.40152i	−1.14245	−	0.242836i	−0.402452	−	0.915441i	$-0.631842\pi$
$929$	−34.8214	−	7.40152i	−1.14245	−	0.242836i	−0.740001	+	0.672605i	$0.765175\pi$
$930$	−53.6744	+	8.22252i	−1.76005	+	0.269627i
$931$	13.8634	−	2.94675i	0.454354	−	0.0965758i
$932$	0.0321800	+	0.0557375i	0.00105409	+	0.00182574i
$933$	23.6245	+	11.0058i	0.773433	+	0.360313i
$934$	3.26886	+	31.1011i	0.106960	+	1.01766i
$935$	1.72057	+	0.0694480i	0.0562685	+	0.00227119i
$936$	−39.5712	+	7.00735i	−1.29343	+	0.229043i
$937$	−38.6879	+	28.1084i	−1.26388	+	0.918261i	−0.998941	−	0.0460048i	$-0.985351\pi$
$937$	−38.6879	+	28.1084i	−1.26388	+	0.918261i	−0.264937	+	0.964266i	$0.585351\pi$
$938$	−5.97936	−	56.8898i	−0.195233	−	1.85752i
$939$	41.1888	+	9.49329i	1.34414	+	0.309802i
$940$	0.328174	+	0.625381i	0.0107038	+	0.0203977i
$941$	−15.5165	−	6.90840i	−0.505824	−	0.225207i	0.137927	−	0.990442i	$-0.455956\pi$
$941$	−15.5165	−	6.90840i	−0.505824	−	0.225207i	−0.643751	+	0.765235i	$0.722623\pi$
$942$	25.2030	−	17.6611i	0.821158	−	0.575429i
$943$	20.3342	−	35.2199i	0.662172	−	1.14692i
$944$	−0.142754	+	0.439352i	−0.00464625	+	0.0142997i
$945$	−50.6805	−	4.65551i	−1.64864	−	0.151444i
$946$	−4.18822	−	12.8900i	−0.136171	−	0.419091i
$947$	10.5494	+	2.24233i	0.342808	+	0.0728661i	0.376099	−	0.926580i	$-0.377265\pi$
$947$	10.5494	+	2.24233i	0.342808	+	0.0728661i	−0.0332907	+	0.999446i	$0.510599\pi$
$948$	−0.0552590	−	0.180508i	−0.00179473	−	0.00586262i
$949$	−22.6596	−	39.2476i	−0.735561	−	1.27403i
$950$	−1.49739	+	7.98368i	−0.0485818	+	0.259025i
$951$	−21.1967	+	9.00662i	−0.687350	+	0.292060i
$952$	−6.68338	+	2.97563i	−0.216610	+	0.0964408i
$953$	11.1268	+	34.2446i	0.360431	+	1.10929i	0.952793	+	0.303620i	$0.0981954\pi$
$953$	11.1268	+	34.2446i	0.360431	+	1.10929i	−0.592362	+	0.805672i	$0.701805\pi$
$954$	2.79454	+	39.5476i	0.0904766	+	1.28040i
$955$	−15.9297	−	0.642979i	−0.515474	−	0.0208063i
$956$	−0.0539574	−	0.0599257i	−0.00174511	−	0.00193814i
$957$	−2.01970	+	16.4990i	−0.0652875	+	0.533338i
$958$	−40.5142	+	8.61156i	−1.30895	+	0.278227i
$959$	33.4266	+	14.8825i	1.07940	+	0.480581i
$960$	−14.2490	−	28.3191i	−0.459884	−	0.913996i
$961$	63.7111	−	28.3660i	2.05520	−	0.915033i
$962$	10.0318	−	7.28852i	0.323438	−	0.234991i
$963$	12.9483	+	10.1010i	0.417252	+	0.325501i
$964$	−0.928664	−	0.674714i	−0.0299103	−	0.0217311i
$965$	−28.5311	+	11.3473i	−0.918449	+	0.365284i
$966$	−39.7740	+	66.2500i	−1.27971	+	2.13156i
$967$	45.8900	−	9.75423i	1.47572	−	0.313675i	0.601373	−	0.798969i	$-0.294621\pi$
$967$	45.8900	−	9.75423i	1.47572	−	0.313675i	0.874351	+	0.485294i	$0.161287\pi$
$968$	13.2487	+	22.9474i	0.425829	+	0.737557i
$969$	−0.962764	+	0.674660i	−0.0309284	+	0.0216732i
$970$	−0.404738	−	6.27820i	−0.0129954	−	0.201581i
$971$	−9.01662	−	27.7503i	−0.289357	−	0.890549i	−0.985059	−	0.172218i	$-0.944906\pi$
$971$	−9.01662	−	27.7503i	−0.289357	−	0.890549i	0.695702	−	0.718331i	$-0.255094\pi$
$972$	0.554833	−	0.519292i	0.0177963	−	0.0166563i
$973$	21.3970	+	15.5458i	0.685955	+	0.498375i
$974$	16.5380	−	28.6447i	0.529912	−	0.917835i
$975$	34.9641	−	20.5118i	1.11975	−	0.656904i
$976$	−14.1146	−	24.4472i	−0.451798	−	0.782537i
$977$	0.0846304	−	0.805204i	0.00270756	−	0.0257608i	−0.993085	−	0.117400i	$-0.962544\pi$
$977$	0.0846304	−	0.805204i	0.00270756	−	0.0257608i	0.995792	+	0.0916393i	$0.0292107\pi$
$978$	−27.2344	−	31.3065i	−0.870861	−	1.00107i
$979$	−10.7481	−	2.28459i	−0.343512	−	0.0730158i
$980$	0.461129	−	1.24583i	0.0147302	−	0.0397966i
$981$	−8.69504	−	0.297263i	−0.277611	−	0.00949087i
$982$	29.7084			0.948032
$983$	−40.7538	−	45.2617i	−1.29985	−	1.44363i	−0.826702	−	0.562640i	$-0.809786\pi$
$983$	−40.7538	−	45.2617i	−1.29985	−	1.44363i	−0.473144	−	0.880985i	$-0.656881\pi$
$984$	13.4126	+	24.1760i	0.427577	+	0.770704i
$985$	21.1329	−	3.60798i	0.673350	−	0.114960i
$986$	0.619760	−	5.89662i	0.0197372	−	0.187787i
$987$	23.8463	+	42.9827i	0.759035	+	1.36815i
$988$	−0.0277402	−	0.263931i	−0.000882534	−	0.00839675i
$989$	−43.3751	−	31.5138i	−1.37925	−	1.00208i
$990$	0.373402	+	12.3590i	0.0118675	+	0.392794i
$991$	33.3687	−	24.2438i	1.05999	−	0.770129i	0.0859046	−	0.996303i	$-0.472622\pi$
$991$	33.3687	−	24.2438i	1.05999	−	0.770129i	0.974087	+	0.226175i	$0.0726220\pi$
$992$	1.85167	+	2.05649i	0.0587907	+	0.0652937i
$993$	−9.28355	+	3.94464i	−0.294604	+	0.125180i
$994$	9.48908	−	2.01697i	0.300975	−	0.0639743i
$995$	−2.83831	+	19.4288i	−0.0899803	+	0.615935i
$996$	−0.0247543	+	0.0719774i	−0.000784371	+	0.00228069i
$997$	−0.911404	−	0.193725i	−0.0288645	−	0.00613533i	0.193457	−	0.981109i	$-0.438030\pi$
$997$	−0.911404	−	0.193725i	−0.0288645	−	0.00613533i	−0.222321	+	0.974973i	$0.571363\pi$
$998$	−21.9533	−	15.9500i	−0.694919	−	0.504888i
$999$	−3.52138	+	9.20371i	−0.111412	+	0.291193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.8	✓	224
3.2	odd	2		675.2.r.a.316.21		224
9.4	even	3	inner	225.2.q.a.166.21	yes	224
9.5	odd	6		675.2.r.a.91.8		224
25.11	even	5	inner	225.2.q.a.61.21	yes	224
75.11	odd	10		675.2.r.a.586.8		224
225.86	odd	30		675.2.r.a.361.21		224
225.211	even	15	inner	225.2.q.a.211.8	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.8	✓	224	1.1	even	1	trivial
225.2.q.a.61.21	yes	224	25.11	even	5	inner
225.2.q.a.166.21	yes	224	9.4	even	3	inner
225.2.q.a.211.8	yes	224	225.211	even	15	inner
675.2.r.a.91.8		224	9.5	odd	6
675.2.r.a.316.21		224	3.2	odd	2
675.2.r.a.361.21		224	225.86	odd	30
675.2.r.a.586.8		224	75.11	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27611 + 0.568159i) q^{2} +(-0.563301 + 1.63789i) q^{3} +(-0.0326201 + 0.0362283i) q^{4} +(0.323231 - 2.21258i) q^{5} +(-0.211752 - 2.41017i) q^{6} +(2.19012 - 3.79340i) q^{7} +(0.884357 - 2.72177i) q^{8} +(-2.36538 - 1.84525i) q^{9} +O(q^{10})\)	\(q+(-1.27611 + 0.568159i) q^{2} +(-0.563301 + 1.63789i) q^{3} +(-0.0326201 + 0.0362283i) q^{4} +(0.323231 - 2.21258i) q^{5} +(-0.211752 - 2.41017i) q^{6} +(2.19012 - 3.79340i) q^{7} +(0.884357 - 2.72177i) q^{8} +(-2.36538 - 1.84525i) q^{9} +(0.844622 + 3.00714i) q^{10} +(-1.20545 + 0.536699i) q^{11} +(-0.0409631 - 0.0738356i) q^{12} +(4.27610 + 1.90384i) q^{13} +(-0.639572 + 6.08512i) q^{14} +(3.44190 + 1.77577i) q^{15} +(0.407674 + 3.87876i) q^{16} +(0.180345 - 0.555045i) q^{17} +(4.06688 + 1.01082i) q^{18} +(-0.359390 + 1.10609i) q^{19} +(0.0696142 + 0.0838847i) q^{20} +(4.97949 + 5.72401i) q^{21} +(1.23335 - 1.36977i) q^{22} +(0.762156 - 7.25143i) q^{23} +(3.95981 + 2.98166i) q^{24} +(-4.79104 - 1.43035i) q^{25} -6.53844 q^{26} +(4.35475 - 2.83481i) q^{27} +(0.0659865 + 0.203085i) q^{28} +(-7.11401 - 1.51213i) q^{29} +(-5.40114 - 0.310522i) q^{30} +(9.81763 - 2.08680i) q^{31} +(0.137855 + 0.238771i) q^{32} +(-0.200027 - 2.27671i) q^{33} +(0.0852144 + 0.810761i) q^{34} +(-7.68530 - 6.07197i) q^{35} +(0.144009 - 0.0255015i) q^{36} +(-1.53428 + 1.11472i) q^{37} +(-0.169815 - 1.61568i) q^{38} +(-5.52702 + 5.93135i) q^{39} +(-5.73629 - 2.83647i) q^{40} +(5.09540 + 2.26862i) q^{41} +(-9.60650 - 4.47530i) q^{42} +(3.67658 - 6.36802i) q^{43} +(0.0198781 - 0.0611784i) q^{44} +(-4.84734 + 4.63717i) q^{45} +(3.14737 + 9.68661i) q^{46} +(6.33736 + 1.34705i) q^{47} +(-6.58263 - 1.51718i) q^{48} +(-6.09327 - 10.5539i) q^{49} +(6.92654 - 0.896798i) q^{50} +(0.807516 + 0.608044i) q^{51} +(-0.208460 + 0.0928122i) q^{52} +(2.92352 + 8.99768i) q^{53} +(-3.94650 + 6.09171i) q^{54} +(0.797854 + 2.84063i) q^{55} +(-8.38793 - 9.31574i) q^{56} +(-1.60921 - 1.21170i) q^{57} +(9.93736 - 2.11225i) q^{58} +(0.108208 + 0.0481772i) q^{59} +(-0.176608 + 0.0667683i) q^{60} +(-6.61228 + 2.94398i) q^{61} +(-11.3427 + 8.24095i) q^{62} +(-12.1803 + 4.93153i) q^{63} +(-6.62211 - 4.81124i) q^{64} +(5.59457 - 8.84584i) q^{65} +(1.54879 + 2.79168i) q^{66} +(-9.14471 + 1.94377i) q^{67} +(0.0142255 + 0.0246392i) q^{68} +(11.4477 + 5.33306i) q^{69} +(13.2571 + 3.38200i) q^{70} +(-0.489945 - 1.50790i) q^{71} +(-7.11420 + 4.80617i) q^{72} +(-7.83289 - 5.69093i) q^{73} +(1.32456 - 2.29421i) q^{74} +(5.04156 - 7.04150i) q^{75} +(-0.0283484 - 0.0491008i) q^{76} +(-0.604158 + 5.74818i) q^{77} +(3.68311 - 10.7093i) q^{78} +(2.18684 + 0.464828i) q^{79} +(8.71385 + 0.351721i) q^{80} +(2.19008 + 8.72946i) q^{81} -7.79120 q^{82} +(-0.603180 - 0.669900i) q^{83} +(-0.369802 - 0.00631949i) q^{84} +(-1.16979 - 0.578436i) q^{85} +(-1.07365 + 10.2151i) q^{86} +(6.48404 - 10.8002i) q^{87} +(0.394728 + 3.75558i) q^{88} +(6.73704 + 4.89475i) q^{89} +(3.55107 - 8.67157i) q^{90} +(16.5872 - 12.0513i) q^{91} +(0.237845 + 0.264154i) q^{92} +(-2.11232 + 17.2557i) q^{93} +(-8.85247 + 1.88165i) q^{94} +(2.33115 + 1.15270i) q^{95} +(-0.468735 + 0.0912911i) q^{96} +(-1.97015 - 0.418768i) q^{97} +(13.7719 + 10.0059i) q^{98} +(3.84169 + 0.954853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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