LMFDB - Embedded newform 418.2.n.d.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	418.49
Dual form			418.2.n.d.273.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(2.21549 - 0.986399i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.36163 + 1.51224i) q^{5} +(2.37216 - 0.504218i) q^{6} +(-1.11442 + 0.809676i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.92802 - 2.14128i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(2.21549 - 0.986399i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.36163 + 1.51224i) q^{5} +(2.37216 - 0.504218i) q^{6} +(-1.11442 + 0.809676i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.92802 - 2.14128i) q^{9} +(1.01746 + 1.76229i) q^{10} +(-2.99104 - 1.43308i) q^{11} +2.42515 q^{12} +(-0.182811 + 0.203032i) q^{13} +(-1.25841 + 0.560281i) q^{14} +(4.50835 + 2.00725i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.850181 - 0.944222i) q^{17} +(2.33108 - 1.69363i) q^{18} +(-4.34969 + 0.283151i) q^{19} +(0.628825 + 1.93533i) q^{20} +(-1.67033 + 2.89310i) q^{21} +(-2.62772 - 2.02363i) q^{22} +(-1.18988 - 2.06093i) q^{23} +(2.37216 + 0.504218i) q^{24} +(0.0897997 - 0.854387i) q^{25} +(-0.221028 + 0.160587i) q^{26} +(-0.0888984 + 0.273601i) q^{27} +(-1.34740 + 0.286399i) q^{28} +(-0.803851 - 0.357898i) q^{29} +(3.99250 + 2.90072i) q^{30} +(-1.22700 - 3.77632i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-8.04019 - 0.224609i) q^{33} +(-0.635288 - 1.10035i) q^{34} +(-2.74186 - 0.582800i) q^{35} +(2.63227 - 1.17196i) q^{36} +(8.20532 - 5.96151i) q^{37} +(-4.31351 - 0.627388i) q^{38} +(-0.204745 + 0.630139i) q^{39} +(0.212707 + 2.02377i) q^{40} +(5.63662 - 2.50959i) q^{41} +(-2.23534 + 2.48259i) q^{42} +(-2.90706 + 5.03517i) q^{43} +(-2.14956 - 2.52574i) q^{44} +5.86338 q^{45} +(-0.735386 - 2.26329i) q^{46} +(0.591810 - 5.63070i) q^{47} +(2.21549 + 0.986399i) q^{48} +(-1.57675 + 4.85275i) q^{49} +(0.265474 - 0.817046i) q^{50} +(-2.81495 - 1.25330i) q^{51} +(-0.249586 + 0.111123i) q^{52} +(2.68955 - 2.98705i) q^{53} +(-0.143841 + 0.249139i) q^{54} +(-1.90552 - 6.47449i) q^{55} -1.37750 q^{56} +(-9.35740 + 4.91785i) q^{57} +(-0.711874 - 0.517207i) q^{58} +(1.55433 + 14.7885i) q^{59} +(3.30216 + 3.66742i) q^{60} +(-2.60335 + 0.553360i) q^{61} +(-0.415046 - 3.94890i) q^{62} +(-0.414885 + 3.94736i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.555953 q^{65} +(-7.81780 - 1.89135i) q^{66} +(-0.197999 - 0.342945i) q^{67} +(-0.392630 - 1.20839i) q^{68} +(-4.66907 - 3.39228i) q^{69} +(-2.56077 - 1.14013i) q^{70} +(6.67036 + 7.40818i) q^{71} +(2.81841 - 0.599072i) q^{72} +(-0.236350 - 2.24872i) q^{73} +(9.26548 - 4.12526i) q^{74} +(-0.643816 - 1.98146i) q^{75} +(-4.08881 - 1.51051i) q^{76} +(4.49361 - 0.824717i) q^{77} +(-0.331284 + 0.573800i) q^{78} +(1.51409 + 0.321831i) q^{79} +(-0.212707 + 2.02377i) q^{80} +(0.976484 + 9.29062i) q^{81} +(6.03522 - 1.28283i) q^{82} +(-4.85141 + 14.9311i) q^{83} +(-2.70265 + 1.96359i) q^{84} +(0.270261 - 2.57136i) q^{85} +(-3.89040 + 4.32073i) q^{86} -2.13395 q^{87} +(-1.57746 - 2.91747i) q^{88} +(-4.30860 - 7.46271i) q^{89} +(5.73525 + 1.21906i) q^{90} +(0.0393385 - 0.374281i) q^{91} +(-0.248753 - 2.36672i) q^{92} +(-6.44336 - 7.15608i) q^{93} +(1.74957 - 5.38461i) q^{94} +(-6.35086 - 6.19224i) q^{95} +(1.96199 + 1.42547i) q^{96} +(4.45168 + 0.946234i) q^{97} +(-2.55124 + 4.41888i) q^{98} +(-8.83538 + 3.64165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	2.21549	−	0.986399i	1.27911	−	0.569498i	0.349121	−	0.937078i	$-0.386480\pi$
$3$	2.21549	−	0.986399i	1.27911	−	0.569498i	0.929992	+	0.367580i	$0.119813\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	1.36163	+	1.51224i	0.608939	+	0.676295i	0.966225	−	0.257700i	$-0.0829646\pi$
$5$	1.36163	+	1.51224i	0.608939	+	0.676295i	−0.357286	+	0.933995i	$0.616298\pi$
$6$	2.37216	−	0.504218i	0.968430	−	0.205846i
$7$	−1.11442	+	0.809676i	−0.421213	+	0.306029i	−0.778126	−	0.628109i	$-0.783829\pi$
$7$	−1.11442	+	0.809676i	−0.421213	+	0.306029i	0.356913	+	0.934138i	$0.383829\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.92802	−	2.14128i	0.642672	−	0.713760i
$10$	1.01746	+	1.76229i	0.321749	+	0.557286i
$11$	−2.99104	−	1.43308i	−0.901831	−	0.432089i
$11$	−2.99104	−	1.43308i	−0.901831	−	0.432089i
$12$	2.42515			0.700082
$13$	−0.182811	+	0.203032i	−0.0507025	+	0.0563109i	−0.767963	−	0.640495i	$-0.778729\pi$
$13$	−0.182811	+	0.203032i	−0.0507025	+	0.0563109i	0.717260	+	0.696806i	$0.245396\pi$
$14$	−1.25841	+	0.560281i	−0.336325	+	0.149741i
$15$	4.50835	+	2.00725i	1.16405	+	0.518269i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.850181	−	0.944222i	−0.206199	−	0.229007i	0.631171	−	0.775644i	$-0.282575\pi$
$17$	−0.850181	−	0.944222i	−0.206199	−	0.229007i	−0.837370	+	0.546636i	$0.815908\pi$
$18$	2.33108	−	1.69363i	0.549441	−	0.399193i
$19$	−4.34969	+	0.283151i	−0.997888	+	0.0649593i
$19$	−4.34969	+	0.283151i	−0.997888	+	0.0649593i
$20$	0.628825	+	1.93533i	0.140610	+	0.432752i
$21$	−1.67033	+	2.89310i	−0.364496	+	0.631325i
$22$	−2.62772	−	2.02363i	−0.560232	−	0.431440i
$23$	−1.18988	−	2.06093i	−0.248107	−	0.429734i	0.714894	−	0.699233i	$-0.246475\pi$
$23$	−1.18988	−	2.06093i	−0.248107	−	0.429734i	−0.963001	+	0.269499i	$0.913142\pi$
$24$	2.37216	+	0.504218i	0.484215	+	0.102923i
$25$	0.0897997	−	0.854387i	0.0179599	−	0.170877i
$26$	−0.221028	+	0.160587i	−0.0433472	+	0.0314936i
$27$	−0.0888984	+	0.273601i	−0.0171085	+	0.0526546i
$28$	−1.34740	+	0.286399i	−0.254635	+	0.0541244i
$29$	−0.803851	−	0.357898i	−0.149271	−	0.0664599i	0.330741	−	0.943721i	$-0.392701\pi$
$29$	−0.803851	−	0.357898i	−0.149271	−	0.0664599i	−0.480013	+	0.877262i	$0.659368\pi$
$30$	3.99250	+	2.90072i	0.728927	+	0.529597i
$31$	−1.22700	−	3.77632i	−0.220376	−	0.678246i	−0.998728	−	0.0504189i	$-0.983944\pi$
$31$	−1.22700	−	3.77632i	−0.220376	−	0.678246i	0.778353	−	0.627827i	$-0.216056\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−8.04019	−	0.224609i	−1.39962	−	0.0390994i
$34$	−0.635288	−	1.10035i	−0.108951	−	0.188709i
$35$	−2.74186	−	0.582800i	−0.463459	−	0.0985112i
$36$	2.63227	−	1.17196i	0.438711	−	0.195327i
$37$	8.20532	−	5.96151i	1.34895	−	0.980066i	0.349882	−	0.936794i	$-0.386222\pi$
$37$	8.20532	−	5.96151i	1.34895	−	0.980066i	0.999063	−	0.0432726i	$-0.0137784\pi$
$38$	−4.31351	−	0.627388i	−0.699744	−	0.101776i
$39$	−0.204745	+	0.630139i	−0.0327854	+	0.100903i
$40$	0.212707	+	2.02377i	0.0336320	+	0.319987i
$41$	5.63662	−	2.50959i	0.880292	−	0.391931i	0.0837305	−	0.996488i	$-0.473317\pi$
$41$	5.63662	−	2.50959i	0.880292	−	0.391931i	0.796562	+	0.604557i	$0.206650\pi$
$42$	−2.23534	+	2.48259i	−0.344920	+	0.383073i
$43$	−2.90706	+	5.03517i	−0.443322	+	0.767856i	−0.997934	−	0.0642531i	$-0.979533\pi$
$43$	−2.90706	+	5.03517i	−0.443322	+	0.767856i	0.554612	+	0.832109i	$0.312867\pi$
$44$	−2.14956	−	2.52574i	−0.324059	−	0.380770i
$45$	5.86338			0.874060
$46$	−0.735386	−	2.26329i	−0.108427	−	0.333703i
$47$	0.591810	−	5.63070i	0.0863244	−	0.821322i	−0.862615	−	0.505862i	$-0.831175\pi$
$47$	0.591810	−	5.63070i	0.0863244	−	0.821322i	0.948939	−	0.315460i	$-0.102159\pi$
$48$	2.21549	+	0.986399i	0.319778	+	0.142374i
$49$	−1.57675	+	4.85275i	−0.225251	+	0.693250i
$50$	0.265474	−	0.817046i	0.0375437	−	0.115548i
$51$	−2.81495	−	1.25330i	−0.394171	−	0.175496i
$52$	−0.249586	+	0.111123i	−0.0346114	+	0.0154100i
$53$	2.68955	−	2.98705i	0.369439	−	0.410303i	−0.529547	−	0.848280i	$-0.677638\pi$
$53$	2.68955	−	2.98705i	0.369439	−	0.410303i	0.898986	+	0.437977i	$0.144305\pi$
$54$	−0.143841	+	0.249139i	−0.0195742	+	0.0339036i
$55$	−1.90552	−	6.47449i	−0.256941	−	0.873019i
$56$	−1.37750			−0.184077
$57$	−9.35740	+	4.91785i	−1.23942	+	0.651385i
$58$	−0.711874	−	0.517207i	−0.0934737	−	0.0679126i
$59$	1.55433	+	14.7885i	0.202357	+	1.92529i	0.350947	+	0.936395i	$0.385860\pi$
$59$	1.55433	+	14.7885i	0.202357	+	1.92529i	−0.148591	+	0.988899i	$0.547474\pi$
$60$	3.30216	+	3.66742i	0.426307	+	0.473462i
$61$	−2.60335	+	0.553360i	−0.333325	+	0.0708505i	−0.371534	−	0.928419i	$-0.621168\pi$
$61$	−2.60335	+	0.553360i	−0.333325	+	0.0708505i	0.0382089	+	0.999270i	$0.487835\pi$
$62$	−0.415046	−	3.94890i	−0.0527109	−	0.501511i
$63$	−0.414885	+	3.94736i	−0.0522705	+	0.497321i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.555953			−0.0689575
$66$	−7.81780	−	1.89135i	−0.962304	−	0.232809i
$67$	−0.197999	−	0.342945i	−0.0241895	−	0.0418974i	0.853677	−	0.520802i	$-0.174367\pi$
$67$	−0.197999	−	0.342945i	−0.0241895	−	0.0418974i	−0.877867	+	0.478905i	$0.841034\pi$
$68$	−0.392630	−	1.20839i	−0.0476133	−	0.146539i
$69$	−4.66907	−	3.39228i	−0.562090	−	0.408382i
$70$	−2.56077	−	1.14013i	−0.306071	−	0.136271i
$71$	6.67036	+	7.40818i	0.791626	+	0.879190i	0.994996	−	0.0999123i	$-0.0318562\pi$
$71$	6.67036	+	7.40818i	0.791626	+	0.879190i	−0.203370	+	0.979102i	$0.565190\pi$
$72$	2.81841	−	0.599072i	0.332153	−	0.0706013i
$73$	−0.236350	−	2.24872i	−0.0276627	−	0.263193i	−0.999608	−	0.0279873i	$-0.991090\pi$
$73$	−0.236350	−	2.24872i	−0.0276627	−	0.263193i	0.971946	−	0.235206i	$-0.0755765\pi$
$74$	9.26548	−	4.12526i	1.07709	−	0.479551i
$75$	−0.643816	−	1.98146i	−0.0743415	−	0.228800i
$76$	−4.08881	−	1.51051i	−0.469019	−	0.173267i
$77$	4.49361	−	0.824717i	0.512094	−	0.0939852i
$78$	−0.331284	+	0.573800i	−0.0375105	+	0.0649701i
$79$	1.51409	+	0.321831i	0.170349	+	0.0362088i	0.292296	−	0.956328i	$-0.405581\pi$
$79$	1.51409	+	0.321831i	0.170349	+	0.0362088i	−0.121947	+	0.992537i	$0.538914\pi$
$80$	−0.212707	+	2.02377i	−0.0237814	+	0.226265i
$81$	0.976484	+	9.29062i	0.108498	+	1.03229i
$82$	6.03522	−	1.28283i	0.666479	−	0.141664i
$83$	−4.85141	+	14.9311i	−0.532511	+	1.63890i	0.216455	+	0.976293i	$0.430551\pi$
$83$	−4.85141	+	14.9311i	−0.532511	+	1.63890i	−0.748966	+	0.662609i	$0.769449\pi$
$84$	−2.70265	+	1.96359i	−0.294883	+	0.214245i
$85$	0.270261	−	2.57136i	0.0293139	−	0.278903i
$86$	−3.89040	+	4.32073i	−0.419513	+	0.465916i
$87$	−2.13395			−0.228784
$88$	−1.57746	−	2.91747i	−0.168158	−	0.311003i
$89$	−4.30860	−	7.46271i	−0.456710	−	0.791046i	0.542074	−	0.840331i	$-0.317639\pi$
$89$	−4.30860	−	7.46271i	−0.456710	−	0.791046i	−0.998785	+	0.0492849i	$0.984306\pi$
$90$	5.73525	+	1.21906i	0.604548	+	0.128501i
$91$	0.0393385	−	0.374281i	0.00412380	−	0.0392353i
$92$	−0.248753	−	2.36672i	−0.0259343	−	0.246748i
$93$	−6.44336	−	7.15608i	−0.668145	−	0.742051i
$94$	1.74957	−	5.38461i	0.180454	−	0.555380i
$95$	−6.35086	−	6.19224i	−0.651584	−	0.635310i
$96$	1.96199	+	1.42547i	0.200245	+	0.145486i
$97$	4.45168	+	0.946234i	0.452000	+	0.0960755i	0.428286	−	0.903643i	$-0.359118\pi$
$97$	4.45168	+	0.946234i	0.452000	+	0.0960755i	0.0237138	+	0.999719i	$0.492451\pi$
$98$	−2.55124	+	4.41888i	−0.257714	+	0.446374i
$99$	−8.83538	+	3.64165i	−0.887989	+	0.365999i
$100$	0.429547	−	0.743996i	0.0429547	−	0.0743996i
$101$	2.70640	−	3.00576i	0.269297	−	0.299085i	−0.593295	−	0.804985i	$-0.702173\pi$
$101$	2.70640	−	3.00576i	0.269297	−	0.299085i	0.862592	+	0.505901i	$0.168840\pi$
$102$	−2.49286	−	1.81117i	−0.246830	−	0.179332i
$103$	−6.27721	+	4.56066i	−0.618512	+	0.449376i	−0.852402	−	0.522888i	$-0.824855\pi$
$103$	−6.27721	+	4.56066i	−0.618512	+	0.449376i	0.233889	+	0.972263i	$0.424855\pi$
$104$	−0.267236	+	0.0568028i	−0.0262046	+	0.00556997i
$105$	−6.64943	+	1.41338i	−0.648918	+	0.137932i
$106$	3.25182	−	2.36259i	0.315845	−	0.229475i
$107$	−0.552491	−	0.401408i	−0.0534113	−	0.0388056i	0.560759	−	0.827979i	$-0.310509\pi$
$107$	−0.552491	−	0.401408i	−0.0534113	−	0.0388056i	−0.614171	+	0.789173i	$0.710509\pi$
$108$	−0.192496	+	0.213789i	−0.0185230	+	0.0205719i
$109$	−5.66719	+	9.81585i	−0.542818	+	0.940188i	0.455923	+	0.890019i	$0.349309\pi$
$109$	−5.66719	+	9.81585i	−0.542818	+	0.940188i	−0.998741	+	0.0501689i	$0.984024\pi$
$110$	−0.517761	−	6.72918i	−0.0493665	−	0.641602i
$111$	12.2984	−	21.3014i	1.16731	−	2.02184i
$112$	−1.34740	−	0.286399i	−0.127318	−	0.0270622i
$113$	1.49627	+	1.08710i	0.140757	+	0.102266i	0.655935	−	0.754817i	$-0.272274\pi$
$113$	1.49627	+	1.08710i	0.140757	+	0.102266i	−0.515179	+	0.857083i	$0.672274\pi$
$114$	−10.1754	+	2.86487i	−0.953013	+	0.268320i
$115$	1.49645	−	4.60561i	0.139545	−	0.429475i
$116$	−0.588785	−	0.653912i	−0.0546673	−	0.0607142i
$117$	0.0822858	+	0.782897i	0.00760733	+	0.0723789i
$118$	−1.55433	+	14.7885i	−0.143088	+	1.36139i
$119$	1.71198	+	0.363892i	0.156937	+	0.0333579i
$120$	2.46750	+	4.27384i	0.225251	+	0.390146i
$121$	6.89259	+	8.57276i	0.626599	+	0.779342i
$122$	−2.66151			−0.240962
$123$	10.0124	−	11.1199i	0.902789	−	1.00265i
$124$	0.415046	−	3.94890i	0.0372723	−	0.354622i
$125$	9.64574	−	7.00804i	0.862742	−	0.626819i
$126$	−1.22652	+	3.77484i	−0.109267	+	0.336290i
$127$	−18.7041	+	3.97568i	−1.65972	+	0.352785i	−0.939920	−	0.341395i	$-0.889101\pi$
$127$	−18.7041	+	3.97568i	−1.65972	+	0.352785i	−0.719802	+	0.694180i	$0.755767\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−1.47386	+	14.0229i	−0.129767	+	1.23465i
$130$	−0.543804	−	0.115589i	−0.0476948	−	0.0101378i
$131$	9.98978	−	17.3028i	0.872811	−	1.51175i	0.0137347	−	0.999906i	$-0.495628\pi$
$131$	9.98978	−	17.3028i	0.872811	−	1.51175i	0.859076	−	0.511847i	$-0.171039\pi$
$132$	−7.25372	−	3.47543i	−0.631356	−	0.302497i
$133$	4.61814	−	3.83739i	0.400444	−	0.332744i
$134$	−0.122370	−	0.376617i	−0.0105712	−	0.0325348i
$135$	−0.534798	+	0.238107i	−0.0460281	+	0.0204930i
$136$	−0.132811	−	1.26362i	−0.0113885	−	0.108354i
$137$	2.47269	−	0.525586i	0.211256	−	0.0449039i	−0.101068	−	0.994880i	$-0.532226\pi$
$137$	2.47269	−	0.525586i	0.211256	−	0.0449039i	0.312324	+	0.949976i	$0.398893\pi$
$138$	−3.86174	−	4.28890i	−0.328733	−	0.365095i
$139$	−7.11023	−	3.16568i	−0.603082	−	0.268509i	0.0823995	−	0.996599i	$-0.473742\pi$
$139$	−7.11023	−	3.16568i	−0.603082	−	0.268509i	−0.685482	+	0.728090i	$0.740408\pi$
$140$	−2.26777	−	1.64763i	−0.191661	−	0.139250i
$141$	−4.24297	−	13.0585i	−0.357322	−	1.09973i
$142$	4.98435	+	8.63314i	0.418277	+	0.724477i
$143$	0.837753	−	0.345294i	0.0700564	−	0.0288749i
$144$	2.88138			0.240115
$145$	−0.553319	−	1.70294i	−0.0459507	−	0.141422i
$146$	0.236350	−	2.24872i	0.0195605	−	0.186106i
$147$	1.29347	+	12.3065i	0.106683	+	1.01502i
$148$	9.92069	−	2.10871i	0.815476	−	0.173335i
$149$	−0.832973	−	0.925110i	−0.0682398	−	0.0757880i	0.708058	−	0.706154i	$-0.249571\pi$
$149$	−0.832973	−	0.925110i	−0.0682398	−	0.0757880i	−0.776298	+	0.630366i	$0.782905\pi$
$150$	−0.217778	−	2.07202i	−0.0177815	−	0.169180i
$151$	3.89163	+	2.82743i	0.316696	+	0.230093i	0.734764	−	0.678322i	$-0.237293\pi$
$151$	3.89163	+	2.82743i	0.316696	+	0.230093i	−0.418068	+	0.908416i	$0.637293\pi$
$152$	−3.68541	−	2.32761i	−0.298926	−	0.188794i
$153$	−3.66101			−0.295975
$154$	4.56688	+	0.127579i	0.368010	+	0.0102806i
$155$	4.03999	−	6.99746i	0.324499	−	0.562049i
$156$	−0.443344	+	0.492383i	−0.0354959	+	0.0394222i
$157$	−8.88539	+	3.95603i	−0.709131	+	0.315726i	−0.729418	−	0.684069i	$-0.760209\pi$
$157$	−8.88539	+	3.95603i	−0.709131	+	0.315726i	0.0202864	+	0.999794i	$0.493542\pi$
$158$	1.41410	+	0.629596i	0.112499	+	0.0500880i
$159$	3.01225	−	9.27076i	0.238887	−	0.735219i
$160$	−0.628825	+	1.93533i	−0.0497130	+	0.153001i
$161$	2.99472	+	1.33333i	0.236017	+	0.105082i
$162$	−0.976484	+	9.29062i	−0.0767198	+	0.729940i
$163$	−5.53828	−	17.0451i	−0.433792	−	1.33507i	−0.894320	−	0.447428i	$-0.852340\pi$
$163$	−5.53828	−	17.0451i	−0.433792	−	1.33507i	0.460528	−	0.887645i	$-0.347660\pi$
$164$	6.17005			0.481800
$165$	−10.6081	−	12.4645i	−0.825839	−	0.970364i
$166$	−7.84974	+	13.5962i	−0.609258	+	1.05527i
$167$	2.77904	−	3.08644i	0.215049	−	0.238836i	−0.625963	−	0.779853i	$-0.715294\pi$
$167$	2.77904	−	3.08644i	0.215049	−	0.238836i	0.841012	+	0.541017i	$0.181961\pi$
$168$	−3.05184	+	1.35877i	−0.235455	+	0.104831i
$169$	1.35107	+	12.8546i	0.103928	+	0.988812i
$170$	0.798970	−	2.45898i	0.0612782	−	0.188595i
$171$	−7.77998	+	9.85983i	−0.594950	+	0.754000i
$172$	−4.70372	+	3.41745i	−0.358655	+	0.260578i
$173$	−5.12412	+	2.28140i	−0.389579	+	0.173452i	−0.592173	−	0.805811i	$-0.701730\pi$
$173$	−5.12412	+	2.28140i	−0.389579	+	0.173452i	0.202593	+	0.979263i	$0.435063\pi$
$174$	−2.08732	−	0.443674i	−0.158239	−	0.0336348i
$175$	0.591702	+	1.02486i	0.0447285	+	0.0774720i
$176$	−0.936410	−	3.18169i	−0.0705846	−	0.239829i
$177$	18.0309	+	31.2305i	1.35529	+	2.34743i
$178$	−2.66286	−	8.19544i	−0.199590	−	0.614274i
$179$	−5.20024	−	3.77819i	−0.388684	−	0.282396i	0.376232	−	0.926526i	$-0.377220\pi$
$179$	−5.20024	−	3.77819i	−0.388684	−	0.282396i	−0.764916	+	0.644130i	$0.777220\pi$
$180$	5.35646	+	2.38485i	0.399247	+	0.177756i
$181$	−3.73104	+	0.793058i	−0.277326	+	0.0589475i	−0.344475	−	0.938795i	$-0.611943\pi$
$181$	−3.73104	+	0.793058i	−0.277326	+	0.0589475i	0.0671488	+	0.997743i	$0.478610\pi$
$182$	0.116296	−	0.357923i	0.00862045	−	0.0265310i
$183$	−5.22187	+	3.79391i	−0.386011	+	0.280454i
$184$	0.248753	−	2.36672i	0.0183383	−	0.174477i
$185$	20.1878	+	4.29106i	1.48424	+	0.315485i
$186$	−4.81473	−	8.33935i	−0.353033	−	0.611471i
$187$	1.18978	+	4.04258i	0.0870054	+	0.295622i
$188$	2.83086	−	4.90319i	0.206461	−	0.357602i
$189$	−0.122458	−	0.376887i	−0.00890750	−	0.0274145i
$190$	−4.92464	−	7.37734i	−0.357271	−	0.535209i
$191$	8.37509	−	6.08486i	0.606000	−	0.440285i	−0.242004	−	0.970275i	$-0.577805\pi$
$191$	8.37509	−	6.08486i	0.606000	−	0.440285i	0.848004	+	0.529991i	$0.177805\pi$
$192$	1.62275	+	1.80224i	0.117112	+	0.130066i
$193$	5.92469	+	6.58004i	0.426469	+	0.473642i	0.917635	−	0.397424i	$-0.130096\pi$
$193$	5.92469	+	6.58004i	0.426469	+	0.473642i	−0.491166	+	0.871066i	$0.663429\pi$
$194$	4.15767	+	1.85111i	0.298503	+	0.132902i
$195$	−1.23171	+	0.548392i	−0.0882045	+	0.0392712i
$196$	−3.41423	+	3.79188i	−0.243873	+	0.270849i
$197$	24.0831			1.71585			0.857924	−	0.513777i	$-0.171754\pi$
$197$	24.0831			1.71585			0.857924	+	0.513777i	$0.171754\pi$
$198$	−9.39945	+	1.72509i	−0.667990	+	0.122597i
$199$	6.87894	+	11.9147i	0.487635	+	0.844609i	0.999899	−	0.0142195i	$-0.00452635\pi$
$199$	6.87894	+	11.9147i	0.487635	+	0.844609i	−0.512264	+	0.858828i	$0.671193\pi$
$200$	0.574845	−	0.638431i	0.0406477	−	0.0451439i
$201$	−0.776946	−	0.564484i	−0.0548015	−	0.0398156i
$202$	3.27219	−	2.37739i	0.230231	−	0.167272i
$203$	1.18561	−	0.252010i	0.0832137	−	0.0176876i
$204$	−2.06182	−	2.28988i	−0.144356	−	0.160324i
$205$	11.4701	+	5.10681i	0.801105	+	0.356675i
$206$	−7.08826	+	3.15590i	−0.493862	+	0.219882i
$207$	−6.70714	−	1.42565i	−0.466179	−	0.0990893i
$208$	−0.273206			−0.0189434
$209$	13.4159	+	5.38652i	0.927995	+	0.372594i
$210$	−6.79798			−0.469105
$211$	4.42218	+	0.939963i	0.304435	+	0.0647097i	0.357596	−	0.933876i	$-0.383596\pi$
$211$	4.42218	+	0.939963i	0.304435	+	0.0647097i	−0.0531611	+	0.998586i	$0.516930\pi$
$212$	3.67197	−	1.63487i	0.252192	−	0.112283i
$213$	22.0855	+	9.83311i	1.51328	+	0.673754i
$214$	−0.456960	−	0.507506i	−0.0312372	−	0.0346924i
$215$	−11.5727	+	2.45986i	−0.789253	+	0.167761i
$216$	−0.232739	+	0.169095i	−0.0158359	+	0.0115054i
$217$	4.42499	+	3.21494i	0.300388	+	0.218245i
$218$	−7.58417	+	8.42308i	−0.513665	+	0.570483i
$219$	−2.74177	−	4.74889i	−0.185272	−	0.320900i
$220$	0.892629	−	6.68978i	0.0601811	−	0.451025i
$221$	0.347129			0.0233504
$222$	16.4584	−	18.2789i	1.10462	−	1.22680i
$223$	8.99519	−	4.00491i	0.602362	−	0.268189i	−0.0828155	−	0.996565i	$-0.526391\pi$
$223$	8.99519	−	4.00491i	0.602362	−	0.268189i	0.685178	+	0.728376i	$0.259725\pi$
$224$	−1.25841	−	0.560281i	−0.0840812	−	0.0374354i
$225$	−1.65635	−	1.83956i	−0.110423	−	0.122637i
$226$	1.23755	+	1.37444i	0.0823204	+	0.0914261i
$227$	8.38076	−	6.08898i	0.556251	−	0.404140i	−0.273834	−	0.961777i	$-0.588292\pi$
$227$	8.38076	−	6.08898i	0.556251	−	0.404140i	0.830085	+	0.557637i	$0.188292\pi$
$228$	−10.5487	+	0.686685i	−0.698603	+	0.0454768i
$229$	4.79177	+	14.7476i	0.316649	+	0.974546i	0.975070	+	0.221896i	$0.0712246\pi$
$229$	4.79177	+	14.7476i	0.316649	+	0.974546i	−0.658421	+	0.752650i	$0.728775\pi$
$230$	2.42131	−	4.19384i	0.159657	−	0.276533i
$231$	9.14204	−	6.25964i	0.601502	−	0.411854i
$232$	−0.439962	−	0.762037i	−0.0288850	−	0.0500302i
$233$	12.1440	+	2.58129i	0.795581	+	0.169106i	0.587733	−	0.809055i	$-0.300021\pi$
$233$	12.1440	+	2.58129i	0.795581	+	0.169106i	0.207848	+	0.978161i	$0.433354\pi$
$234$	−0.0822858	+	0.782897i	−0.00537919	+	0.0511796i
$235$	9.32080	−	6.77196i	0.608022	−	0.441754i
$236$	−4.59506	+	14.1421i	−0.299113	+	0.920575i
$237$	3.67191	−	0.780490i	0.238516	−	0.0506982i
$238$	1.59891	+	0.711880i	0.103642	+	0.0461443i
$239$	−19.9167	−	14.4703i	−1.28830	−	0.936008i	−0.288535	−	0.957469i	$-0.593168\pi$
$239$	−19.9167	−	14.4703i	−1.28830	−	0.936008i	−0.999770	+	0.0214612i	$0.993168\pi$
$240$	1.52500	+	4.69346i	0.0984383	+	0.302962i
$241$	−0.312490	−	0.541249i	−0.0201293	−	0.0348649i	0.855785	−	0.517331i	$-0.173074\pi$
$241$	−0.312490	−	0.541249i	−0.0201293	−	0.0348649i	−0.875915	+	0.482466i	$0.839741\pi$
$242$	4.95959	+	9.81848i	0.318815	+	0.631156i
$243$	10.8961	+	18.8727i	0.698987	+	1.21068i
$244$	−2.60335	−	0.553360i	−0.166663	−	0.0354252i
$245$	−9.48548	+	4.22321i	−0.606005	+	0.269811i
$246$	12.1056	−	8.79522i	0.771824	−	0.560763i
$247$	0.737681	−	0.934889i	0.0469375	−	0.0594855i
$248$	1.22700	−	3.77632i	0.0779145	−	0.239796i
$249$	3.97978	+	37.8651i	0.252209	+	2.39960i
$250$	10.8920	−	4.84944i	0.688872	−	0.306705i
$251$	6.73237	−	7.47705i	0.424943	−	0.471947i	−0.492213	−	0.870475i	$-0.663812\pi$
$251$	6.73237	−	7.47705i	0.424943	−	0.471947i	0.917156	+	0.398527i	$0.130479\pi$
$252$	−1.98455	+	3.43735i	−0.125015	+	0.216533i
$253$	0.605500	+	7.86951i	0.0380675	+	0.494752i
$254$	−19.1220			−1.19982
$255$	−1.93763	−	5.96340i	−0.121339	−	0.373443i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	13.2412	+	5.89538i	0.825965	+	0.367743i	0.775785	−	0.630997i	$-0.217354\pi$
$257$	13.2412	+	5.89538i	0.825965	+	0.367743i	0.0501798	+	0.998740i	$0.484021\pi$
$258$	−4.35718	+	13.4100i	−0.271266	+	0.834871i
$259$	−4.31731	+	13.2873i	−0.268264	+	0.825633i
$260$	−0.507888	−	0.226127i	−0.0314979	−	0.0140238i
$261$	−2.31620	+	1.03124i	−0.143369	+	0.0638320i
$262$	13.3689	−	14.8477i	0.825936	−	0.917294i
$263$	12.2633	−	21.2406i	0.756185	−	1.30975i	−0.188598	−	0.982054i	$-0.560394\pi$
$263$	12.2633	−	21.2406i	0.756185	−	1.30975i	0.944783	−	0.327697i	$-0.106273\pi$
$264$	−6.37263	−	4.90762i	−0.392208	−	0.302043i
$265$	8.17932			0.502452
$266$	5.31506	−	2.79337i	0.325887	−	0.171273i
$267$	−16.9069	−	12.2836i	−1.03468	−	0.751741i
$268$	−0.0413931	−	0.393829i	−0.00252849	−	0.0240569i
$269$	−11.9212	−	13.2398i	−0.726848	−	0.807247i	0.260557	−	0.965458i	$-0.416094\pi$
$269$	−11.9212	−	13.2398i	−0.726848	−	0.807247i	−0.987405	+	0.158212i	$0.949427\pi$
$270$	−0.572617	+	0.121713i	−0.0348483	+	0.00740724i
$271$	−2.85946	−	27.2059i	−0.173700	−	1.65264i	−0.640264	−	0.768155i	$-0.721175\pi$
$271$	−2.85946	−	27.2059i	−0.173700	−	1.65264i	0.466565	−	0.884487i	$-0.345492\pi$
$272$	0.132811	−	1.26362i	0.00805287	−	0.0766179i
$273$	−0.282036	−	0.868019i	−0.0170696	−	0.0525349i
$274$	2.52793			0.152718
$275$	−1.49300	+	2.42681i	−0.0900310	+	0.146342i
$276$	−2.88564	−	4.99808i	−0.173695	−	0.300849i
$277$	−2.45734	−	7.56292i	−0.147647	−	0.454412i	0.849695	−	0.527275i	$-0.176786\pi$
$277$	−2.45734	−	7.56292i	−0.147647	−	0.454412i	−0.997342	+	0.0728633i	$0.976786\pi$
$278$	−6.29668	−	4.57480i	−0.377650	−	0.274378i
$279$	−10.4518	−	4.65345i	−0.625734	−	0.278595i
$280$	−1.87565	−	2.08312i	−0.112091	−	0.124490i
$281$	−25.3771	+	5.39406i	−1.51387	+	0.321783i	−0.888621	−	0.458643i	$-0.848336\pi$
$281$	−25.3771	+	5.39406i	−1.51387	+	0.321783i	−0.625249	+	0.780426i	$0.715002\pi$
$282$	−1.43523	−	13.6553i	−0.0854668	−	0.813162i
$283$	−10.5700	+	4.70606i	−0.628320	+	0.279746i	−0.696090	−	0.717955i	$-0.745078\pi$
$283$	−10.5700	+	4.70606i	−0.628320	+	0.279746i	0.0677694	+	0.997701i	$0.478412\pi$
$284$	3.08050	+	9.48079i	0.182794	+	0.562581i
$285$	−20.1783	−	7.45436i	−1.19526	−	0.441558i
$286$	0.891237	−	0.163570i	0.0526999	−	0.00967207i
$287$	−4.24963	+	7.36058i	−0.250848	+	0.434481i
$288$	2.81841	+	0.599072i	0.166076	+	0.0353006i
$289$	1.60824	−	15.3014i	0.0946022	−	0.900080i
$290$	−0.187166	−	1.78077i	−0.0109908	−	0.104570i
$291$	10.7960	−	2.29476i	0.632874	−	0.134521i
$292$	0.698722	−	2.15044i	0.0408896	−	0.125845i
$293$	21.8070	−	15.8437i	1.27398	−	0.925599i	0.274624	−	0.961552i	$-0.411447\pi$
$293$	21.8070	−	15.8437i	1.27398	−	0.925599i	0.999353	+	0.0359530i	$0.0114467\pi$
$294$	−1.29347	+	12.3065i	−0.0754366	+	0.717731i
$295$	−20.2473	+	22.4869i	−1.17884	+	1.30924i
$296$	10.1423			0.589511
$297$	0.657990	−	0.690953i	0.0381804	−	0.0400932i
$298$	−0.622429	−	1.07808i	−0.0360563	−	0.0624514i
$299$	0.635957	+	0.135177i	0.0367784	+	0.00781748i
$300$	0.217778	−	2.07202i	0.0125734	−	0.119628i
$301$	−0.837165	−	7.96509i	−0.0482534	−	0.459100i
$302$	3.21873	+	3.57476i	0.185217	+	0.205704i
$303$	3.03112	−	9.32883i	0.174133	−	0.535927i
$304$	−3.12093	−	3.04299i	−0.178998	−	0.174527i
$305$	−4.38161	−	3.18343i	−0.250890	−	0.182283i
$306$	−3.58100	−	0.761166i	−0.204712	−	0.0435130i
$307$	7.87162	−	13.6341i	0.449257	−	0.778136i	−0.549081	−	0.835769i	$-0.685022\pi$
$307$	7.87162	−	13.6341i	0.449257	−	0.778136i	0.998338	+	0.0576330i	$0.0183553\pi$
$308$	4.44056	+	1.07430i	0.253024	+	0.0612139i
$309$	−9.40847	+	16.2959i	−0.535229	+	0.927044i
$310$	5.40656	−	6.00459i	0.307072	−	0.341038i
$311$	18.9093	+	13.7384i	1.07225	+	0.779032i	0.976314	−	0.216356i	$-0.0694173\pi$
$311$	18.9093	+	13.7384i	1.07225	+	0.779032i	0.0959307	+	0.995388i	$0.469417\pi$
$312$	−0.536028	+	0.389447i	−0.0303466	+	0.0220481i
$313$	−27.2168	+	5.78511i	−1.53838	+	0.326994i	−0.897629	−	0.440752i	$-0.854712\pi$
$313$	−27.2168	+	5.78511i	−1.53838	+	0.326994i	−0.640755	+	0.767745i	$0.721379\pi$
$314$	−9.51373	+	2.02220i	−0.536891	+	0.114120i
$315$	−6.53429	+	4.74744i	−0.368165	+	0.267488i
$316$	1.25229	+	0.909845i	0.0704470	+	0.0511828i
$317$	12.7862	−	14.2005i	0.718146	−	0.797582i	−0.268008	−	0.963417i	$-0.586365\pi$
$317$	12.7862	−	14.2005i	0.718146	−	0.797582i	0.986154	+	0.165835i	$0.0530319\pi$
$318$	4.87393	−	8.44189i	0.273316	−	0.473397i
$319$	1.89145	+	2.22246i	0.105901	+	0.124434i
$320$	−1.01746	+	1.76229i	−0.0568778	+	0.0985152i
$321$	−1.61999	−	0.344339i	−0.0904188	−	0.0192191i
$322$	2.65206	+	1.92684i	0.147794	+	0.107378i
$323$	3.96538	+	3.86634i	0.220640	+	0.215129i
$324$	−2.88678	+	8.88458i	−0.160376	+	0.493588i
$325$	0.157051	+	0.174423i	0.00871164	+	0.00967526i
$326$	−1.87339	−	17.8241i	−0.103757	−	0.987184i
$327$	−2.87324	+	27.3370i	−0.158890	+	1.51174i
$328$	6.03522	+	1.28283i	0.333239	+	0.0708322i
$329$	3.89952	+	6.75416i	0.214987	+	0.372369i
$330$	−7.78475	−	14.3977i	−0.428537	−	0.792568i
$331$	−27.7117			−1.52317			−0.761586	−	0.648063i	$-0.775579\pi$
$331$	−27.7117			−1.52317			−0.761586	+	0.648063i	$0.775579\pi$
$332$	−10.5050	+	11.6670i	−0.576537	+	0.640309i
$333$	3.05473	−	29.0638i	0.167398	−	1.59268i
$334$	3.36002	−	2.44120i	0.183852	−	0.133576i
$335$	0.249014	−	0.766386i	0.0136051	−	0.0418721i
$336$	−3.26766	+	0.694562i	−0.178265	+	0.0378915i
$337$	0.891055	+	8.47783i	0.0485389	+	0.461817i	0.991614	+	0.129236i	$0.0412526\pi$
$337$	0.891055	+	8.47783i	0.0485389	+	0.461817i	−0.943075	+	0.332580i	$0.892081\pi$
$338$	−1.35107	+	12.8546i	−0.0734884	+	0.699195i
$339$	4.38728	+	0.932544i	0.238284	+	0.0506488i
$340$	1.29276	−	2.23913i	0.0701098	−	0.121434i
$341$	−1.74175	+	13.0535i	−0.0943210	+	0.706886i
$342$	−9.65994	+	8.02682i	−0.522350	+	0.434041i
$343$	−5.15169	−	15.8553i	−0.278165	−	0.856104i
$344$	−5.31146	+	2.36481i	−0.286375	+	0.127502i
$345$	−1.22759	−	11.6798i	−0.0660915	−	0.628818i
$346$	−5.48647	+	1.16619i	−0.294955	+	0.0626945i
$347$	15.8785	+	17.6349i	0.852405	+	0.946691i	0.999097	−	0.0424909i	$-0.0135294\pi$
$347$	15.8785	+	17.6349i	0.852405	+	0.946691i	−0.146692	+	0.989182i	$0.546863\pi$
$348$	−1.94946	−	0.867957i	−0.104502	−	0.0465274i
$349$	10.0036	+	7.26802i	0.535479	+	0.389048i	0.822403	−	0.568905i	$-0.192633\pi$
$349$	10.0036	+	7.26802i	0.535479	+	0.389048i	−0.286924	+	0.957953i	$0.592633\pi$
$350$	0.365692	+	1.12548i	0.0195471	+	0.0601597i
$351$	−0.0392982	−	0.0680664i	−0.00209758	−	0.00363312i
$352$	−0.254438	−	3.30685i	−0.0135616	−	0.176256i
$353$	7.91121			0.421071			0.210536	−	0.977586i	$-0.432479\pi$
$353$	7.91121			0.421071			0.210536	+	0.977586i	$0.432479\pi$
$354$	11.1437	+	34.2969i	0.592283	+	1.82286i
$355$	−2.12041	+	20.1744i	−0.112540	+	1.07075i
$356$	−0.900742	−	8.56999i	−0.0477392	−	0.454209i
$357$	4.15181	−	0.882494i	0.219737	−	0.0467065i
$358$	−4.30107	−	4.77682i	−0.227319	−	0.252463i
$359$	−1.17747	−	11.2028i	−0.0621443	−	0.591264i	−0.980638	−	0.195828i	$-0.937260\pi$
$359$	−1.17747	−	11.2028i	−0.0621443	−	0.591264i	0.918494	−	0.395435i	$-0.129406\pi$
$360$	4.74357	+	3.44641i	0.250008	+	0.181642i
$361$	18.8397	−	2.46324i	0.991561	−	0.129644i
$362$	−3.81440			−0.200480
$363$	23.7266	+	12.1940i	1.24532	+	0.640020i
$364$	0.188171	−	0.325922i	0.00986285	−	0.0170830i
$365$	3.07879	−	3.41935i	0.161151	−	0.178977i
$366$	−5.89655	+	2.62532i	−0.308218	+	0.137227i
$367$	−30.6178	−	13.6319i	−1.59823	−	0.711580i	−0.602018	−	0.798483i	$-0.705636\pi$
$367$	−30.6178	−	13.6319i	−1.59823	−	0.711580i	−0.996217	+	0.0869027i	$0.972303\pi$
$368$	0.735386	−	2.26329i	0.0383347	−	0.117982i
$369$	5.49378	−	16.9081i	0.285995	−	0.880201i
$370$	18.8545	+	8.39457i	0.980200	+	0.436413i
$371$	−0.578758	+	5.50651i	−0.0300476	+	0.285884i
$372$	−2.97566	−	9.15815i	−0.154281	−	0.474828i
$373$	−18.6113			−0.963659			−0.481829	−	0.876265i	$-0.660027\pi$
$373$	−18.6113			−0.963659			−0.481829	+	0.876265i	$0.660027\pi$
$374$	0.323282	+	4.20160i	0.0167165	+	0.217260i
$375$	14.4573	−	25.0408i	0.746572	−	1.29310i
$376$	3.78843	−	4.20747i	0.195373	−	0.216984i
$377$	0.219617	−	0.0977799i	0.0113109	−	0.00503592i
$378$	−0.0414228	−	0.394111i	−0.00213056	−	0.0202709i
$379$	1.97413	−	6.07576i	0.101404	−	0.312091i	−0.887465	−	0.460874i	$-0.847536\pi$
$379$	1.97413	−	6.07576i	0.101404	−	0.312091i	0.988870	+	0.148784i	$0.0475358\pi$
$380$	−3.28319	−	8.24002i	−0.168424	−	0.422704i
$381$	−37.5172	+	27.2578i	−1.92206	+	1.39646i
$382$	9.45718	−	4.21061i	0.483872	−	0.215434i
$383$	−7.51196	−	1.59672i	−0.383843	−	0.0815884i	0.0119486	−	0.999929i	$-0.496197\pi$
$383$	−7.51196	−	1.59672i	−0.383843	−	0.0815884i	−0.395792	+	0.918340i	$0.629530\pi$
$384$	1.21258	+	2.10025i	0.0618791	+	0.107178i
$385$	7.36580	+	5.67247i	0.375396	+	0.289096i
$386$	4.42716	+	7.66806i	0.225336	+	0.390294i
$387$	5.17685	+	15.9327i	0.263154	+	0.809905i
$388$	3.68195	+	2.67509i	0.186922	+	0.135807i
$389$	−0.798609	−	0.355563i	−0.0404911	−	0.0180278i	0.386391	−	0.922335i	$-0.373721\pi$
$389$	−0.798609	−	0.355563i	−0.0404911	−	0.0180278i	−0.426882	+	0.904307i	$0.640388\pi$
$390$	−1.31881	+	0.280322i	−0.0667805	+	0.0141946i
$391$	−0.934364	+	2.87568i	−0.0472528	+	0.145429i
$392$	−4.12800	+	2.99916i	−0.208495	+	0.151481i
$393$	5.06477	−	48.1881i	0.255484	−	2.43077i
$394$	23.5568	+	5.00715i	1.18677	+	0.252257i
$395$	1.57495	+	2.72789i	0.0792443	+	0.137255i
$396$	−9.55272	−	0.266862i	−0.480042	−	0.0134103i
$397$	−11.1867	+	19.3758i	−0.561442	+	0.972446i	0.435929	+	0.899981i	$0.356420\pi$
$397$	−11.1867	+	19.3758i	−0.561442	+	0.972446i	−0.997371	+	0.0724649i	$0.976913\pi$
$398$	4.25142	+	13.0845i	0.213104	+	0.655868i
$399$	6.44624	−	13.0570i	0.322716	−	0.653669i
$400$	0.695021	−	0.504962i	0.0347510	−	0.0252481i
$401$	−19.3529	−	21.4935i	−0.966436	−	1.07334i	−0.997272	−	0.0738119i	$-0.976484\pi$
$401$	−19.3529	−	21.4935i	−0.966436	−	1.07334i	0.0308357	−	0.999524i	$-0.490183\pi$
$402$	−0.642605	−	0.713685i	−0.0320502	−	0.0355954i
$403$	0.991020	+	0.441231i	0.0493662	+	0.0219793i
$404$	3.69497	−	1.64511i	0.183832	−	0.0818472i
$405$	−12.7201	+	14.1271i	−0.632065	+	0.701979i
$406$	1.21210			0.0601555
$407$	−33.0857	+	6.07225i	−1.64000	+	0.300990i
$408$	−1.54067	−	2.66852i	−0.0762746	−	0.132111i
$409$	−5.49859	+	6.10681i	−0.271888	+	0.301962i	−0.863590	−	0.504194i	$-0.831789\pi$
$409$	−5.49859	+	6.10681i	−0.271888	+	0.301962i	0.591702	+	0.806157i	$0.298456\pi$
$410$	10.1577	+	7.37998i	0.501652	+	0.364471i
$411$	4.95978	−	3.60349i	0.244648	−	0.177747i
$412$	−7.58951	+	1.61320i	−0.373908	+	0.0794767i
$413$	−13.7061	−	15.2221i	−0.674431	−	0.749031i
$414$	−6.26417	−	2.78899i	−0.307867	−	0.137071i
$415$	−29.1852	+	12.9941i	−1.43265	+	0.637856i
$416$	−0.267236	−	0.0568028i	−0.0131023	−	0.00278498i
$417$	−18.8753			−0.924326
$418$	12.0028	+	8.05813i	0.587075	+	0.394136i
$419$	−39.5049			−1.92994			−0.964971	−	0.262358i	$-0.915500\pi$
$419$	−39.5049			−1.92994			−0.964971	+	0.262358i	$0.915500\pi$
$420$	−6.64943	−	1.41338i	−0.324459	−	0.0689659i
$421$	12.4070	−	5.52397i	0.604682	−	0.269222i	−0.0814749	−	0.996675i	$-0.525963\pi$
$421$	12.4070	−	5.52397i	0.604682	−	0.269222i	0.686157	+	0.727454i	$0.259296\pi$
$422$	4.13011	+	1.83884i	0.201051	+	0.0895136i
$423$	−10.9159	−	12.1233i	−0.530748	−	0.589456i
$424$	3.93164	−	0.835696i	0.190937	−	0.0405850i
$425$	−0.883077	+	0.641593i	−0.0428355	+	0.0311218i
$426$	19.5585	+	14.2101i	0.947612	+	0.688480i
$427$	2.45320	−	2.72455i	0.118719	−	0.131850i
$428$	−0.341458	−	0.591423i	−0.0165050	−	0.0285875i
$429$	1.51543	−	1.59135i	0.0731659	−	0.0768313i
$430$	−11.8313			−0.570554
$431$	16.0602	−	17.8366i	0.773591	−	0.859160i	−0.219608	−	0.975588i	$-0.570478\pi$
$431$	16.0602	−	17.8366i	0.773591	−	0.859160i	0.993199	+	0.116428i	$0.0371445\pi$
$432$	−0.262810	+	0.117011i	−0.0126445	+	0.00562967i
$433$	−32.7319	−	14.5732i	−1.57299	−	0.700341i	−0.579578	−	0.814917i	$-0.696783\pi$
$433$	−32.7319	−	14.5732i	−1.57299	−	0.700341i	−0.993415	+	0.114575i	$0.963449\pi$
$434$	3.65987	+	4.06470i	0.175679	+	0.195112i
$435$	−2.90565	−	3.22705i	−0.139315	−	0.154725i
$436$	−9.16970	+	6.66218i	−0.439149	+	0.319060i
$437$	5.75917	+	8.62751i	0.275498	+	0.412710i
$438$	−1.69451	−	5.21516i	−0.0809667	−	0.249190i
$439$	−16.7767	+	29.0580i	−0.800706	+	1.38686i	0.118446	+	0.992961i	$0.462209\pi$
$439$	−16.7767	+	29.0580i	−0.800706	+	1.38686i	−0.919152	+	0.393903i	$0.871124\pi$
$440$	2.26401	−	6.35801i	0.107932	−	0.303106i
$441$	7.35109	+	12.7325i	0.350052	+	0.606307i
$442$	0.339544	+	0.0721722i	0.0161504	+	0.00343288i
$443$	2.21361	−	21.0611i	0.105172	−	1.00064i	−0.806920	−	0.590660i	$-0.798867\pi$
$443$	2.21361	−	21.0611i	0.105172	−	1.00064i	0.912092	−	0.409985i	$-0.134466\pi$
$444$	19.8992	−	14.4576i	0.944372	−	0.686127i
$445$	5.41871	−	16.6771i	0.256872	−	0.790569i
$446$	9.63129	−	2.04719i	0.456055	−	0.0969374i
$447$	−2.75797	−	1.22793i	−0.130448	−	0.0580790i
$448$	−1.11442	−	0.809676i	−0.0526516	−	0.0382536i
$449$	−5.49081	−	16.8990i	−0.259127	−	0.797512i	−0.992988	−	0.118212i	$-0.962284\pi$
$449$	−5.49081	−	16.8990i	−0.259127	−	0.797512i	0.733861	−	0.679300i	$-0.237716\pi$
$450$	−1.23769	−	2.14373i	−0.0583450	−	0.101057i
$451$	−20.4558	−	0.571447i	−0.963224	−	0.0269084i
$452$	0.924743	+	1.60170i	0.0434962	+	0.0753377i
$453$	11.4108	+	2.42545i	0.536128	+	0.113958i
$454$	9.46359	−	4.21346i	0.444148	−	0.197748i
$455$	0.619568	−	0.450142i	0.0290458	−	0.0211030i
$456$	−10.4609	−	1.52151i	−0.489878	−	0.0712514i
$457$	−11.5739	+	35.6208i	−0.541404	+	1.66627i	0.187985	+	0.982172i	$0.439804\pi$
$457$	−11.5739	+	35.6208i	−0.541404	+	1.66627i	−0.729390	+	0.684099i	$0.760196\pi$
$458$	1.62087	+	15.4215i	0.0757383	+	0.720602i
$459$	0.333920	−	0.148671i	0.0155861	−	0.00693936i
$460$	3.24035	−	3.59877i	0.151082	−	0.167794i
$461$	5.71961	−	9.90665i	0.266389	−	0.461399i	−0.701538	−	0.712632i	$-0.747503\pi$
$461$	5.71961	−	9.90665i	0.266389	−	0.461399i	0.967926	+	0.251234i	$0.0808362\pi$
$462$	10.2437	−	4.22212i	0.476581	−	0.196431i
$463$	14.2778			0.663546			0.331773	−	0.943359i	$-0.392353\pi$
$463$	14.2778			0.663546			0.331773	+	0.943359i	$0.392353\pi$
$464$	−0.271912	−	0.836858i	−0.0126232	−	0.0388502i
$465$	2.04825	−	19.4878i	0.0949855	−	0.903727i
$466$	11.3420	+	5.04977i	0.525406	+	0.233926i
$467$	−13.0585	+	40.1899i	−0.604275	+	1.85977i	−0.102572	+	0.994726i	$0.532707\pi$
$467$	−13.0585	+	40.1899i	−0.604275	+	1.85977i	−0.501702	+	0.865040i	$0.667293\pi$
$468$	−0.243261	+	0.748681i	−0.0112448	+	0.0346078i
$469$	0.498329	+	0.221871i	0.0230107	+	0.0102450i
$470$	10.5251	−	4.68607i	0.485486	−	0.216152i
$471$	−15.7833	+	17.5291i	−0.727254	+	0.807697i
$472$	−7.43496	+	12.8777i	−0.342222	+	0.592746i
$473$	15.9109	−	10.8943i	0.731583	−	0.500922i
$474$	3.75395			0.172425
$475$	−0.148680	+	3.74175i	−0.00682192	+	0.171683i
$476$	1.41596	+	1.02876i	0.0649004	+	0.0471529i
$477$	−1.21061	−	11.5182i	−0.0554300	−	0.527381i
$478$	−16.4729	−	18.2950i	−0.753454	−	0.836796i
$479$	34.6228	−	7.35931i	1.58196	−	0.336256i	0.668666	−	0.743562i	$-0.266865\pi$
$479$	34.6228	−	7.35931i	1.58196	−	0.336256i	0.913291	+	0.407307i	$0.133532\pi$
$480$	0.515848	+	4.90797i	0.0235451	+	0.224017i
$481$	−0.289643	+	2.75577i	−0.0132066	+	0.125652i
$482$	−0.193130	−	0.594392i	−0.00879682	−	0.0270738i
$483$	7.94997			0.361736
$484$	2.80983	+	10.6351i	0.127720	+	0.483413i
$485$	4.63060	+	8.02044i	0.210265	+	0.364189i
$486$	6.73418	+	20.7257i	0.305469	+	0.940136i
$487$	−23.6554	−	17.1867i	−1.07193	−	0.778803i	−0.0956718	−	0.995413i	$-0.530500\pi$
$487$	−23.6554	−	17.1867i	−1.07193	−	0.778803i	−0.976258	+	0.216610i	$0.930500\pi$
$488$	−2.43141	−	1.08254i	−0.110065	−	0.0490041i
$489$	−29.0833	−	32.3002i	−1.31519	−	1.46067i
$490$	−10.1563	+	2.15878i	−0.458813	+	0.0975237i
$491$	−1.72592	−	16.4210i	−0.0778895	−	0.741069i	−0.961863	−	0.273532i	$-0.911808\pi$
$491$	−1.72592	−	16.4210i	−0.0778895	−	0.741069i	0.883973	−	0.467537i	$-0.154859\pi$
$492$	13.6697	−	6.08613i	0.616277	−	0.274384i
$493$	0.345485	+	1.06329i	0.0155598	+	0.0478883i
$494$	0.915935	−	0.761087i	0.0412099	−	0.0342429i
$495$	−17.5376	−	8.40266i	−0.788255	−	0.377672i
$496$	1.98533	−	3.43869i	0.0891438	−	0.154402i
$497$	−13.4318	−	2.85503i	−0.602500	−	0.128065i
$498$	−3.97978	+	37.8651i	−0.178338	+	1.69678i
$499$	1.03606	+	9.85741i	0.0463802	+	0.441278i	0.992928	+	0.118716i	$0.0378777\pi$
$499$	1.03606	+	9.85741i	0.0463802	+	0.441278i	−0.946548	+	0.322563i	$0.895456\pi$
$500$	11.6623	−	2.47889i	0.521552	−	0.110859i
$501$	3.11247	−	9.57921i	0.139055	−	0.427968i
$502$	8.13982	−	5.91392i	0.363298	−	0.263951i
$503$	−2.55649	+	24.3233i	−0.113988	+	1.08452i	0.776688	+	0.629885i	$0.216898\pi$
$503$	−2.55649	+	24.3233i	−0.113988	+	1.08452i	−0.890676	+	0.454638i	$0.849769\pi$
$504$	−2.65585	+	2.94962i	−0.118301	+	0.131387i
$505$	8.23055			0.366255
$506$	−1.04389	+	7.82343i	−0.0464068	+	0.347794i
$507$	15.6730	+	27.1464i	0.696062	+	1.20562i
$508$	−18.7041	−	3.97568i	−0.829861	−	0.176392i
$509$	−0.550834	+	5.24083i	−0.0244153	+	0.232296i	0.975509	+	0.219961i	$0.0705930\pi$
$509$	−0.550834	+	5.24083i	−0.0244153	+	0.232296i	−0.999924	+	0.0123348i	$0.996074\pi$
$510$	−0.655424	−	6.23594i	−0.0290227	−	0.276132i
$511$	2.08413	+	2.31466i	0.0921966	+	0.102395i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	0.309210	−	1.21525i	0.0136520	−	0.0536547i
$514$	11.7262	+	8.51955i	0.517219	+	0.375781i
$515$	−15.4441	−	3.28274i	−0.680547	−	0.144655i
$516$	−7.05006	+	12.2111i	−0.310362	+	0.537562i
$517$	−9.83934	+	15.9935i	−0.432734	+	0.703394i
$518$	−6.98555	+	12.0993i	−0.306927	+	0.531614i
$519$	−9.10205	+	10.1088i	−0.399536	+	0.443729i
$520$	−0.449776	−	0.326781i	−0.0197240	−	0.0143303i
$521$	−13.7495	+	9.98962i	−0.602378	+	0.437653i	−0.846722	−	0.532035i	$-0.821427\pi$
$521$	−13.7495	+	9.98962i	−0.602378	+	0.437653i	0.244344	+	0.969689i	$0.421427\pi$
$522$	−2.47999	+	0.527138i	−0.108546	+	0.0230722i
$523$	24.4291	−	5.19256i	1.06821	−	0.227055i	0.359924	−	0.932982i	$-0.382803\pi$
$523$	24.4291	−	5.19256i	1.06821	−	0.227055i	0.708285	+	0.705927i	$0.249469\pi$
$524$	16.1638	−	11.7437i	0.706119	−	0.513025i
$525$	2.32183	+	1.68691i	0.101333	+	0.0736227i
$526$	16.4115	−	18.2268i	0.715573	−	0.794725i
$527$	−2.52251	+	4.36911i	−0.109882	+	0.190322i
$528$	−5.21302	−	6.12532i	−0.226868	−	0.266570i
$529$	8.66837	−	15.0141i	0.376886	−	0.652785i
$530$	8.00058	+	1.70058i	0.347523	+	0.0738683i
$531$	34.6630	+	25.1842i	1.50425	+	1.09290i
$532$	5.77969	−	1.62727i	0.250581	−	0.0705510i
$533$	−0.520909	+	1.60319i	−0.0225631	+	0.0694419i
$534$	−13.9835	−	15.5303i	−0.605126	−	0.672060i
$535$	−0.145261	−	1.38207i	−0.00628019	−	0.0597520i
$536$	0.0413931	−	0.393829i	0.00178791	−	0.0170108i
$537$	−15.2479	−	3.24104i	−0.657995	−	0.139861i
$538$	−8.90797	−	15.4291i	−0.384050	−	0.665194i
$539$	11.6705	−	12.2551i	0.502683	−	0.527866i
$540$	−0.585409			−0.0251920
$541$	10.1296	−	11.2501i	0.435507	−	0.483680i	−0.484940	−	0.874548i	$-0.661158\pi$
$541$	10.1296	−	11.2501i	0.435507	−	0.483680i	0.920447	+	0.390868i	$0.127825\pi$
$542$	2.85946	−	27.2059i	0.122824	−	1.16859i
$543$	−7.48382	+	5.43731i	−0.321161	+	0.233337i
$544$	0.392630	−	1.20839i	0.0168339	−	0.0518093i
$545$	−22.5605	+	4.79539i	−0.966388	+	0.205412i
$546$	−0.0954020	−	0.907689i	−0.00408283	−	0.0388455i
$547$	−2.71140	+	25.7972i	−0.115931	+	1.10301i	0.769631	+	0.638489i	$0.220440\pi$
$547$	−2.71140	+	25.7972i	−0.115931	+	1.10301i	−0.885562	+	0.464521i	$0.846227\pi$
$548$	2.47269	+	0.525586i	0.105628	+	0.0224519i
$549$	−3.83441	+	6.64139i	−0.163649	+	0.283448i
$550$	−1.96493	+	2.06337i	−0.0837850	+	0.0879823i
$551$	3.59785	+	1.32913i	0.153273	+	0.0566230i
$552$	−1.78343	−	5.48882i	−0.0759076	−	0.233620i
$553$	−1.94792	+	0.867271i	−0.0828341	+	0.0368801i
$554$	−0.831223	−	7.90856i	−0.0353153	−	0.336003i
$555$	48.9586	−	10.4065i	2.07818	−	0.441730i
$556$	−5.20792	−	5.78398i	−0.220865	−	0.245296i
$557$	6.68681	+	2.97716i	0.283329	+	0.126146i	0.543481	−	0.839421i	$-0.317106\pi$
$557$	6.68681	+	2.97716i	0.283329	+	0.126146i	−0.260152	+	0.965568i	$0.583773\pi$
$558$	−9.25592	−	6.72482i	−0.391834	−	0.284684i
$559$	−0.490858	−	1.51071i	−0.0207611	−	0.0638961i
$560$	−1.40156	−	2.42757i	−0.0592266	−	0.102583i
$561$	6.62354	+	7.78268i	0.279646	+	0.328585i
$562$	−25.9440			−1.09438
$563$	−1.20271	−	3.70156i	−0.0506882	−	0.156002i	0.922508	−	0.385977i	$-0.126136\pi$
$563$	−1.20271	−	3.70156i	−0.0506882	−	0.156002i	−0.973197	+	0.229975i	$0.926136\pi$
$564$	1.43523	−	13.6553i	0.0604341	−	0.574992i
$565$	0.393399	+	3.74294i	0.0165504	+	0.157467i
$566$	−11.3174	+	2.40560i	−0.475708	+	0.101115i
$567$	−8.61062	−	9.56306i	−0.361612	−	0.401611i
$568$	1.04201	+	9.91408i	0.0437219	+	0.415986i
$569$	−35.5342	−	25.8171i	−1.48967	−	1.08231i	−0.974277	−	0.225354i	$-0.927646\pi$
$569$	−35.5342	−	25.8171i	−1.48967	−	1.08231i	−0.515393	−	0.856954i	$-0.672354\pi$
$570$	−18.1875	−	11.4868i	−0.761790	−	0.481128i
$571$	−0.983949			−0.0411770			−0.0205885	−	0.999788i	$-0.506554\pi$
$571$	−0.983949			−0.0411770			−0.0205885	+	0.999788i	$0.506554\pi$
$572$	0.905769	+	0.0253033i	0.0378721	+	0.00105799i
$573$	12.5528	−	21.7421i	0.524401	−	0.908290i
$574$	−5.68712	+	6.31619i	−0.237376	+	0.263633i
$575$	−1.86768	+	0.831547i	−0.0778878	+	0.0346779i
$576$	2.63227	+	1.17196i	0.109678	+	0.0488317i
$577$	7.54893	−	23.2332i	0.314266	−	0.967212i	−0.661789	−	0.749690i	$-0.730203\pi$
$577$	7.54893	−	23.2332i	0.314266	−	0.967212i	0.976055	−	0.217522i	$-0.0697974\pi$
$578$	4.75442	−	14.6326i	0.197758	−	0.608636i
$579$	19.6166	+	8.73389i	0.815240	+	0.362968i
$580$	0.187166	−	1.78077i	0.00777166	−	0.0739424i
$581$	−6.68283	−	20.5676i	−0.277251	−	0.853290i
$582$	11.0372			0.457507
$583$	−12.3252	+	5.08004i	−0.510459	+	0.210394i
$584$	1.13056	−	1.95818i	0.0467827	−	0.0810300i
$585$	−1.07189	+	1.19045i	−0.0443171	+	0.0492191i
$586$	24.6245	−	10.9635i	1.01723	−	0.452900i
$587$	1.18032	+	11.2300i	0.0487169	+	0.463510i	0.991500	+	0.130105i	$0.0415313\pi$
$587$	1.18032	+	11.2300i	0.0487169	+	0.463510i	−0.942783	+	0.333406i	$0.891802\pi$
$588$	−3.82387	+	11.7687i	−0.157694	+	0.485332i
$589$	6.40634	+	16.0784i	0.263969	+	0.662498i
$590$	−24.4802	+	17.7859i	−1.00783	+	0.732233i
$591$	53.3558	−	23.7555i	2.19476	−	0.977172i
$592$	9.92069	+	2.10871i	0.407738	+	0.0866674i
$593$	10.7596	+	18.6363i	0.441846	+	0.765299i	0.997827	−	0.0658959i	$-0.0209905\pi$
$593$	10.7596	+	18.6363i	0.441846	+	0.765299i	−0.555981	+	0.831195i	$0.687657\pi$
$594$	0.787268	−	0.539050i	0.0323020	−	0.0221175i
$595$	1.78078	+	3.08441i	0.0730050	+	0.126448i
$596$	−0.384682	−	1.18393i	−0.0157572	−	0.0484957i
$597$	26.9928	+	19.6114i	1.10474	+	0.802643i
$598$	0.593955	+	0.264446i	0.0242886	+	0.0108140i
$599$	44.4921	−	9.45709i	1.81790	−	0.386406i	0.832139	−	0.554568i	$-0.187116\pi$
$599$	44.4921	−	9.45709i	1.81790	−	0.386406i	0.985759	+	0.168162i	$0.0537831\pi$
$600$	0.643816	−	1.98146i	0.0262837	−	0.0808929i
$601$	−7.86077	+	5.71118i	−0.320648	+	0.232964i	−0.736452	−	0.676490i	$-0.763500\pi$
$601$	−7.86077	+	5.71118i	−0.320648	+	0.232964i	0.415804	+	0.909454i	$0.363500\pi$
$602$	0.837165	−	7.96509i	0.0341203	−	0.324633i
$603$	−1.11609	−	0.237232i	−0.0454506	−	0.00966082i
$604$	2.40516	+	4.16586i	0.0978645	+	0.169506i
$605$	−3.57895	+	22.0962i	−0.145505	+	0.898337i
$606$	4.90445	−	8.49476i	0.199230	−	0.345076i
$607$	−11.4928	−	35.3713i	−0.466480	−	1.43568i	−0.857112	−	0.515130i	$-0.827744\pi$
$607$	−11.4928	−	35.3713i	−0.466480	−	1.43568i	0.390632	−	0.920547i	$-0.372256\pi$
$608$	−2.42006	−	3.62537i	−0.0981465	−	0.147028i
$609$	2.37813	−	1.72781i	0.0963667	−	0.0700145i
$610$	−3.62399	−	4.02485i	−0.146731	−	0.162961i
$611$	1.03502	+	1.14951i	0.0418725	+	0.0465041i
$612$	−3.34450	−	1.48907i	−0.135193	−	0.0601919i
$613$	5.12129	−	2.28015i	0.206847	−	0.0920942i	−0.300698	−	0.953719i	$-0.597220\pi$
$613$	5.12129	−	2.28015i	0.206847	−	0.0920942i	0.507545	+	0.861625i	$0.330553\pi$
$614$	10.5343	−	11.6995i	0.425129	−	0.472154i
$615$	30.4492			1.22783
$616$	4.12016	+	1.97407i	0.166006	+	0.0795375i
$617$	0.731509	+	1.26701i	0.0294494	+	0.0510079i	0.880375	−	0.474279i	$-0.157291\pi$
$617$	0.731509	+	1.26701i	0.0294494	+	0.0510079i	−0.850925	+	0.525287i	$0.823958\pi$
$618$	−12.5910	+	13.9837i	−0.506484	+	0.562507i
$619$	28.0924	+	20.4103i	1.12913	+	0.820360i	0.985568	−	0.169281i	$-0.0541447\pi$
$619$	28.0924	+	20.4103i	1.12913	+	0.820360i	0.143561	+	0.989641i	$0.454145\pi$
$620$	6.53683	−	4.74929i	0.262526	−	0.190736i
$621$	0.669652	−	0.142339i	0.0268722	−	0.00571187i
$622$	15.6397	+	17.3696i	0.627094	+	0.696458i
$623$	10.8440	+	4.82805i	0.434455	+	0.193432i
$624$	−0.605285	+	0.269490i	−0.0242308	+	0.0107882i
$625$	19.5302	+	4.15127i	0.781207	+	0.166051i
$626$	−27.8248			−1.11210
$627$	35.0360	−	1.29961i	1.39920	−	0.0519014i
$628$	−9.72627			−0.388120
$629$	−12.6050	−	2.67927i	−0.502594	−	0.106830i
$630$	−7.37854	+	3.28514i	−0.293968	+	0.130883i
$631$	−19.0433	−	8.47861i	−0.758101	−	0.337528i	−0.00897835	−	0.999960i	$-0.502858\pi$
$631$	−19.0433	−	8.47861i	−0.758101	−	0.337528i	−0.749123	+	0.662431i	$0.769525\pi$
$632$	1.03576	+	1.15033i	0.0412004	+	0.0457576i
$633$	10.7245	−	2.27956i	0.426259	−	0.0906042i
$634$	15.4593	−	11.2318i	0.613966	−	0.446073i
$635$	−31.4803	−	22.8717i	−1.24926	−	0.907637i
$636$	6.52259	−	7.24406i	0.258637	−	0.287246i
$637$	−0.697015	−	1.20727i	−0.0276167	−	0.0478336i
$638$	1.38804	+	2.56715i	0.0549532	+	0.101635i
$639$	28.7236			1.13629
$640$	−1.36163	+	1.51224i	−0.0538231	+	0.0597766i
$641$	−33.1843	+	14.7746i	−1.31070	+	0.583562i	−0.938721	−	0.344679i	$-0.887988\pi$
$641$	−33.1843	+	14.7746i	−1.31070	+	0.583562i	−0.371981	+	0.928240i	$0.621321\pi$
$642$	−1.51299	−	0.673628i	−0.0597131	−	0.0265860i
$643$	26.6757	+	29.6264i	1.05199	+	1.16835i	0.985345	+	0.170573i	$0.0545618\pi$
$643$	26.6757	+	29.6264i	1.05199	+	1.16835i	0.0666417	+	0.997777i	$0.478772\pi$
$644$	2.19350	+	2.43612i	0.0864358	+	0.0959967i
$645$	−23.2128	+	16.8651i	−0.914005	+	0.664063i
$646$	3.07487	+	4.60631i	0.120979	+	0.181233i
$647$	13.2575	+	40.8023i	0.521206	+	1.60411i	0.771699	+	0.635987i	$0.219407\pi$
$647$	13.2575	+	40.8023i	0.521206	+	1.60411i	−0.250494	+	0.968118i	$0.580593\pi$
$648$	−4.67090	+	8.09024i	−0.183490	+	0.317814i
$649$	16.5439	−	46.4603i	0.649406	−	1.82373i
$650$	0.117355	+	0.203264i	0.00460303	+	0.00797269i
$651$	12.9747	+	2.75787i	0.508520	+	0.108089i
$652$	1.87339	−	17.8241i	0.0733675	−	0.698045i
$653$	−5.60514	+	4.07237i	−0.219346	+	0.159364i	−0.692032	−	0.721867i	$-0.743284\pi$
$653$	−5.60514	+	4.07237i	−0.219346	+	0.159364i	0.472686	+	0.881231i	$0.343284\pi$
$654$	−8.49414	+	26.1423i	−0.332147	+	1.02224i
$655$	39.7684	−	8.45303i	1.55388	−	0.330287i
$656$	5.63662	+	2.50959i	0.220073	+	0.0979828i
$657$	−5.27083	−	3.82949i	−0.205635	−	0.149402i
$658$	2.41003	+	7.41732i	0.0939529	+	0.289157i
$659$	19.6505	+	34.0357i	0.765476	+	1.32584i	0.939994	+	0.341190i	$0.110830\pi$
$659$	19.6505	+	34.0357i	0.765476	+	1.32584i	−0.174518	+	0.984654i	$0.555837\pi$
$660$	−4.62119	−	15.7016i	−0.179879	−	0.611185i
$661$	−17.9700	−	31.1249i	−0.698951	−	1.21062i	−0.968830	−	0.247725i	$-0.920317\pi$
$661$	−17.9700	−	31.1249i	−0.698951	−	1.21062i	0.269879	−	0.962894i	$-0.413016\pi$
$662$	−27.1061	−	5.76159i	−1.05351	−	0.223930i
$663$	0.769061	−	0.342408i	0.0298678	−	0.0132980i
$664$	−12.7012	+	9.22793i	−0.492900	+	0.358113i
$665$	12.0913	+	1.75864i	0.468879	+	0.0681971i
$666$	9.03067	−	27.7935i	0.349931	−	1.07698i
$667$	0.218884	+	2.08254i	0.00847521	+	0.0806362i
$668$	3.79415	−	1.68926i	0.146800	−	0.0653595i
$669$	15.9783	−	17.7457i	0.617756	−	0.686088i
$670$	0.402913	−	0.697866i	0.0155659	−	0.0269609i
$671$	8.57973	+	2.07568i	0.331217	+	0.0801309i
$672$	−3.34066			−0.128869
$673$	8.03822	+	24.7391i	0.309851	+	0.953622i	0.977822	+	0.209436i	$0.0671626\pi$
$673$	8.03822	+	24.7391i	0.309851	+	0.953622i	−0.667972	+	0.744187i	$0.732837\pi$
$674$	−0.891055	+	8.47783i	−0.0343222	+	0.326554i
$675$	0.225778	+	0.100523i	0.00869021	+	0.00386913i
$676$	−3.99416	+	12.2927i	−0.153621	+	0.472798i
$677$	−12.4701	+	38.3789i	−0.479263	+	1.47502i	0.360857	+	0.932621i	$0.382484\pi$
$677$	−12.4701	+	38.3789i	−0.479263	+	1.47502i	−0.840120	+	0.542400i	$0.817516\pi$
$678$	4.09752	+	1.82433i	0.157364	+	0.0700630i
$679$	−5.72720	+	2.54992i	−0.219790	+	0.0978568i
$680$	1.73005	−	1.92142i	0.0663445	−	0.0736830i
$681$	12.5613	−	21.7568i	0.481351	−	0.833724i
$682$	−4.41766	+	12.4061i	−0.169161	+	0.475054i
$683$	7.21040			0.275898			0.137949	−	0.990439i	$-0.455949\pi$
$683$	7.21040			0.275898			0.137949	+	0.990439i	$0.455949\pi$
$684$	−11.1177	+	5.84300i	−0.425096	+	0.223413i
$685$	4.16170	+	3.02365i	0.159010	+	0.115528i
$686$	−1.74262	−	16.5799i	−0.0665334	−	0.633023i
$687$	25.1631	+	27.9464i	0.960032	+	1.06622i
$688$	−5.68706	+	1.20882i	−0.216817	+	0.0460859i
$689$	0.114787	+	1.09213i	0.00437305	+	0.0416068i
$690$	1.22759	−	11.6798i	0.0467337	−	0.444642i
$691$	5.42353	+	16.6919i	0.206321	+	0.634990i	0.999657	+	0.0262055i	$0.00834242\pi$
$691$	5.42353	+	16.6919i	0.206321	+	0.634990i	−0.793336	+	0.608784i	$0.791658\pi$
$692$	−5.60904			−0.213224
$693$	6.89781	−	11.2121i	0.262026	−	0.425914i
$694$	11.8651	+	20.5509i	0.450391	+	0.780100i
$695$	−4.89422	−	15.0629i	−0.185648	−	0.571367i
$696$	−1.72641	−	1.25431i	−0.0654392	−	0.0475444i
$697$	−7.16175	−	3.18862i	−0.271271	−	0.120778i
$698$	8.27386	+	9.18906i	0.313170	+	0.347811i
$699$	29.4511	−	6.26003i	1.11394	−	0.236776i
$700$	0.123699	+	1.17692i	0.00467540	+	0.0444834i
$701$	−3.49097	+	1.55428i	−0.131852	+	0.0587044i	−0.471602	−	0.881811i	$-0.656324\pi$
$701$	−3.49097	+	1.55428i	−0.131852	+	0.0587044i	0.339750	+	0.940516i	$0.389658\pi$
$702$	−0.0242876	−	0.0747495i	−0.000916676	−	0.00282124i
$703$	−34.0026	+	28.2541i	−1.28243	+	1.06562i
$704$	0.438655	−	3.28749i	0.0165324	−	0.123902i
$705$	13.9703	−	24.1972i	0.526151	−	0.911320i
$706$	7.73834	+	1.64483i	0.291236	+	0.0619041i
$707$	−0.582383	+	5.54100i	−0.0219028	+	0.208391i
$708$	3.76949	+	35.8643i	0.141666	+	1.34786i
$709$	2.43316	−	0.517185i	0.0913793	−	0.0194233i	−0.161995	−	0.986792i	$-0.551793\pi$
$709$	2.43316	−	0.517185i	0.0913793	−	0.0194233i	0.253374	+	0.967368i	$0.418460\pi$
$710$	−6.26857	+	19.2927i	−0.235255	+	0.724041i
$711$	3.60833	−	2.62161i	0.135323	−	0.0983179i
$712$	0.900742	−	8.56999i	0.0337567	−	0.321174i
$713$	−6.32275	+	7.02213i	−0.236789	+	0.262981i
$714$	4.24456			0.158849
$715$	1.66288	+	0.796723i	0.0621880	+	0.0297958i
$716$	−3.21392	−	5.56668i	−0.120110	−	0.208037i
$717$	−58.3988	−	12.4130i	−2.18094	−	0.463574i
$718$	1.17747	−	11.2028i	0.0439427	−	0.418087i
$719$	1.14040	+	10.8502i	0.0425299	+	0.404645i	0.994989	+	0.0999799i	$0.0318778\pi$
$719$	1.14040	+	10.8502i	0.0425299	+	0.404645i	−0.952460	+	0.304665i	$0.901455\pi$
$720$	3.92336	+	4.35734i	0.146215	+	0.162388i
$721$	3.30282	−	10.1650i	0.123003	−	0.378565i
$722$	18.9401	+	1.50757i	0.704877	+	0.0561060i
$723$	−1.22621	−	0.890892i	−0.0456031	−	0.0331326i
$724$	−3.73104	−	0.793058i	−0.138663	−	0.0294738i
$725$	−0.377969	+	0.654661i	−0.0140374	+	0.0243135i
$726$	20.6729	+	16.8606i	0.767242	+	0.625755i
$727$	10.4767	−	18.1461i	0.388558	−	0.673003i	−0.603698	−	0.797213i	$-0.706307\pi$
$727$	10.4767	−	18.1461i	0.388558	−	0.673003i	0.992256	+	0.124211i	$0.0396399\pi$
$728$	0.251822	−	0.279677i	0.00933316	−	0.0103655i
$729$	20.0832	+	14.5913i	0.743823	+	0.540419i
$730$	3.72244	−	2.70451i	0.137774	−	0.100098i
$731$	7.22584	−	1.53590i	0.267257	−	0.0568073i
$732$	−6.31353	+	1.34198i	−0.233355	+	0.0496011i
$733$	22.7603	−	16.5363i	0.840672	−	0.610784i	−0.0818865	−	0.996642i	$-0.526094\pi$
$733$	22.7603	−	16.5363i	0.840672	−	0.610784i	0.922558	+	0.385858i	$0.126094\pi$
$734$	−27.1145	−	19.6998i	−1.00081	−	0.727133i
$735$	−16.8492	+	18.7129i	−0.621493	+	0.690238i
$736$	1.18988	−	2.06093i	0.0438596	−	0.0759670i
$737$	0.100757	+	1.30951i	0.00371143	+	0.0482363i
$738$	8.88912	−	15.3964i	0.327213	−	0.566749i
$739$	−3.06019	−	0.650463i	−0.112571	−	0.0239277i	0.151282	−	0.988491i	$-0.451660\pi$
$739$	−3.06019	−	0.650463i	−0.112571	−	0.0239277i	−0.263853	+	0.964563i	$0.584993\pi$
$740$	16.6972	+	12.1312i	0.613800	+	0.445952i
$741$	0.712151	−	2.79888i	0.0261615	−	0.102820i
$742$	−1.71098	+	5.26585i	−0.0628120	+	0.193315i
$743$	−24.3614	−	27.0561i	−0.893734	−	0.992592i	0.106265	−	0.994338i	$-0.466111\pi$
$743$	−24.3614	−	27.0561i	−0.893734	−	0.992592i	−0.999998	+	0.00174601i	$0.999444\pi$
$744$	−1.00655	−	9.57670i	−0.0369020	−	0.351099i
$745$	0.264790	−	2.51931i	0.00970117	−	0.0923005i
$746$	−18.2046	−	3.86951i	−0.666519	−	0.141673i
$747$	22.6181	+	39.1756i	0.827552	+	1.43336i
$748$	−0.557345	+	4.17700i	−0.0203785	+	0.152726i
$749$	0.940720			0.0343731
$750$	19.3477	−	21.4878i	0.706477	−	0.784622i
$751$	3.49586	−	33.2609i	0.127566	−	1.21371i	−0.724128	−	0.689666i	$-0.757757\pi$
$751$	3.49586	−	33.2609i	0.127566	−	1.21371i	0.851693	−	0.524040i	$-0.175576\pi$
$752$	4.58042	−	3.32787i	0.167031	−	0.121355i
$753$	7.54013	−	23.2061i	0.274778	−	0.845679i
$754$	0.235148	−	0.0499822i	0.00856357	−	0.00182024i
$755$	1.02319	+	9.73500i	0.0372377	+	0.354293i
$756$	0.0414228	−	0.394111i	0.00150653	−	0.0143337i
$757$	10.8476	+	2.30574i	0.394264	+	0.0838034i	0.400778	−	0.916175i	$-0.368740\pi$
$757$	10.8476	+	2.30574i	0.394264	+	0.0838034i	−0.00651364	+	0.999979i	$0.502073\pi$
$758$	3.19422	−	5.53254i	0.116019	−	0.200951i
$759$	9.10396	+	16.8375i	0.330453	+	0.611164i
$760$	−1.49825	−	8.74257i	−0.0543471	−	0.317126i
$761$	−8.64035	−	26.5923i	−0.313213	−	0.963969i	−0.976484	−	0.215590i	$-0.930833\pi$
$761$	−8.64035	−	26.5923i	−0.313213	−	0.963969i	0.663271	−	0.748379i	$-0.269167\pi$
$762$	−42.3645	+	18.8619i	−1.53471	+	0.683295i
$763$	−1.63202	−	15.5276i	−0.0590830	−	0.562137i
$764$	10.1260	−	2.15234i	0.366344	−	0.0778689i
$765$	−4.98493	−	5.53633i	−0.180231	−	0.200166i
$766$	−7.01583	−	3.12365i	−0.253492	−	0.112862i
$767$	−3.28668	−	2.38791i	−0.118675	−	0.0862224i
$768$	0.749414	+	2.30646i	0.0270422	+	0.0832272i
$769$	17.9033	+	31.0095i	0.645611	+	1.11823i	0.984160	+	0.177282i	$0.0567305\pi$
$769$	17.9033	+	31.0095i	0.645611	+	1.11823i	−0.338549	+	0.940949i	$0.609936\pi$
$770$	6.02547	+	7.07994i	0.217143	+	0.255143i
$771$	35.1510			1.26593
$772$	2.73613	+	8.42096i	0.0984756	+	0.303077i
$773$	−5.53753	+	52.6861i	−0.199171	+	1.89499i	0.202625	+	0.979256i	$0.435053\pi$
$773$	−5.53753	+	52.6861i	−0.199171	+	1.89499i	−0.401796	+	0.915729i	$0.631614\pi$
$774$	1.75113	+	16.6609i	0.0629430	+	0.598863i
$775$	−3.33662	+	0.709220i	−0.119855	+	0.0254759i
$776$	3.04530	+	3.38215i	0.109320	+	0.121412i
$777$	3.54164	+	33.6965i	0.127056	+	1.20885i
$778$	−0.707231	−	0.513834i	−0.0253555	−	0.0184218i
$779$	−23.8070	+	12.5119i	−0.852973	+	0.448287i
$780$	−1.34827			−0.0482759
$781$	−9.33479	−	31.7173i	−0.334025	−	1.13493i
$782$	−1.51183	+	2.61857i	−0.0540630	+	0.0936399i
$783$	0.169382	−	0.188118i	0.00605323	−	0.00672280i
$784$	−4.66135	+	2.07537i	−0.166477	+	0.0741202i
$785$	−18.0811	−	8.05021i	−0.645341	−	0.287324i
$786$	14.9730	−	46.0820i	0.534068	−	1.64369i
$787$	−10.3004	+	31.7013i	−0.367169	+	1.13003i	0.581443	+	0.813587i	$0.302488\pi$
$787$	−10.3004	+	31.7013i	−0.367169	+	1.13003i	−0.948612	+	0.316442i	$0.897512\pi$
$788$	22.0010	+	9.79547i	0.783753	+	0.348949i
$789$	6.21742	−	59.1548i	0.221346	−	2.10597i
$790$	0.973372	+	2.99573i	0.0346310	+	0.106583i
$791$	−2.54767			−0.0905849
$792$	−9.28848	−	2.24715i	−0.330052	−	0.0798491i
$793$	0.363571	−	0.629723i	0.0129108	−	0.0223621i
$794$	−14.9707	+	16.6266i	−0.531289	+	0.590056i
$795$	18.1212	−	8.06807i	0.642692	−	0.286145i
$796$	1.43809	+	13.6825i	0.0509717	+	0.484964i
$797$	−8.47753	+	26.0912i	−0.300290	+	0.924196i	0.681104	+	0.732187i	$0.261500\pi$
$797$	−8.47753	+	26.0912i	−0.300290	+	0.924196i	−0.981393	+	0.192009i	$0.938500\pi$
$798$	9.02008	−	11.4315i	0.319307	−	0.404669i
$799$	−5.81977	+	4.22831i	−0.205889	+	0.149587i
$800$	0.784821	−	0.349425i	0.0277476	−	0.0123540i
$801$	−24.2868	−	5.16232i	−0.858132	−	0.182402i
$802$	−14.4612	−	25.0475i	−0.510643	−	0.884460i
$803$	−2.51566	+	7.06472i	−0.0887757	+	0.249309i
$804$	−0.480179	−	0.831694i	−0.0169346	−	0.0293316i
$805$	2.06137	+	6.34425i	0.0726538	+	0.223605i
$806$	0.877627	+	0.637634i	0.0309131	+	0.0224597i
$807$	−39.4710	−	17.5736i	−1.38945	−	0.618621i
$808$	3.95627	−	0.840930i	0.139181	−	0.0295838i
$809$	6.07482	−	18.6964i	0.213579	−	0.657329i	−0.785672	−	0.618643i	$-0.787683\pi$
$809$	6.07482	−	18.6964i	0.213579	−	0.657329i	0.999251	−	0.0386863i	$-0.0123173\pi$
$810$	−15.3793	+	11.1737i	−0.540373	+	0.392604i
$811$	0.0474571	−	0.451524i	0.00166645	−	0.0158552i	−0.993657	−	0.112453i	$-0.964129\pi$
$811$	0.0474571	−	0.451524i	0.00166645	−	0.0158552i	0.995324	+	0.0965976i	$0.0307960\pi$
$812$	1.18561	+	0.252010i	0.0416069	+	0.00884381i
$813$	−33.1710	−	57.4539i	−1.16336	−	2.01499i
$814$	−33.6252	−	0.939344i	−1.17856	−	0.0329240i
$815$	18.2352	−	31.5843i	0.638751	−	1.10635i
$816$	−0.952187	−	2.93053i	−0.0333332	−	0.102589i
$817$	11.2191	−	22.7246i	0.392506	−	0.795032i
$818$	−6.64811	+	4.83014i	−0.232446	+	0.168882i
$819$	−0.725595	−	0.805855i	−0.0253543	−	0.0281588i
$820$	8.40132	+	9.33061i	0.293387	+	0.325839i
$821$	−18.9292	−	8.42784i	−0.660635	−	0.294134i	0.0489000	−	0.998804i	$-0.484428\pi$
$821$	−18.9292	−	8.42784i	−0.660635	−	0.294134i	−0.709535	+	0.704670i	$0.751095\pi$
$822$	5.60060	−	2.49355i	0.195343	−	0.0869725i
$823$	−27.5016	+	30.5436i	−0.958644	+	1.06468i	0.0392119	+	0.999231i	$0.487515\pi$
$823$	−27.5016	+	30.5436i	−0.958644	+	1.06468i	−0.997856	+	0.0654510i	$0.979151\pi$
$824$	−7.75906			−0.270300
$825$	−0.913909	+	6.84926i	−0.0318182	+	0.238461i
$826$	−10.2417	−	17.7391i	−0.356354	−	0.617223i
$827$	−32.5761	+	36.1794i	−1.13278	+	1.25808i	−0.170697	+	0.985324i	$0.554602\pi$
$827$	−32.5761	+	36.1794i	−1.13278	+	1.25808i	−0.962083	+	0.272756i	$0.912065\pi$
$828$	−5.54742	−	4.03043i	−0.192786	−	0.140067i
$829$	−15.8669	+	11.5280i	−0.551081	+	0.400383i	−0.828184	−	0.560457i	$-0.810626\pi$
$829$	−15.8669	+	11.5280i	−0.551081	+	0.400383i	0.277103	+	0.960840i	$0.410626\pi$
$830$	−31.2491	+	6.64220i	−1.08467	+	0.230554i
$831$	−12.9043	−	14.3316i	−0.447644	−	0.497159i
$832$	−0.249586	−	0.111123i	−0.00865285	−	0.00385250i
$833$	5.92260	−	2.63691i	0.205206	−	0.0913635i
$834$	−18.4628	−	3.92439i	−0.639314	−	0.135890i
$835$	8.45146			0.292475
$836$	10.0651	+	10.3776i	0.348109	+	0.358915i
$837$	1.14228			0.0394831
$838$	−38.6416	−	8.21353i	−1.33485	−	0.283732i
$839$	−33.2107	+	14.7863i	−1.14656	+	0.510481i	−0.889961	−	0.456037i	$-0.849269\pi$
$839$	−33.2107	+	14.7863i	−1.14656	+	0.510481i	−0.256599	+	0.966518i	$0.582602\pi$
$840$	−6.21027	−	2.76499i	−0.214275	−	0.0954012i
$841$	−18.8867	−	20.9758i	−0.651266	−	0.723304i
$842$	13.2844	−	2.82369i	0.457811	−	0.0973107i
$843$	−50.9019	+	36.9824i	−1.75316	+	1.27374i
$844$	3.65754	+	2.65736i	0.125898	+	0.0914701i
$845$	−17.5995	+	19.5463i	−0.605442	+	0.672412i
$846$	−8.15676	−	14.1279i	−0.280435	−	0.485728i
$847$	−14.6224	−	3.97293i	−0.502433	−	0.136511i
$848$	4.01948			0.138029
$849$	−18.7756	+	20.8524i	−0.644378	+	0.715654i
$850$	−0.997174	+	0.443970i	−0.0342028	+	0.0152281i
$851$	−22.0496	−	9.81712i	−0.755851	−	0.336526i
$852$	16.1767	+	17.9660i	0.554203	+	0.615505i
$853$	10.9705	+	12.1840i	0.375624	+	0.417172i	0.901083	−	0.433646i	$-0.142773\pi$
$853$	10.9705	+	12.1840i	0.375624	+	0.417172i	−0.525460	+	0.850819i	$0.676107\pi$
$854$	2.96605	−	2.15496i	0.101496	−	0.0737414i
$855$	−25.5039	+	1.66022i	−0.872214	+	0.0567784i
$856$	−0.211033	−	0.649492i	−0.00721295	−	0.0221992i
$857$	−14.8152	+	25.6608i	−0.506079	+	0.876555i	0.493896	+	0.869521i	$0.335572\pi$
$857$	−14.8152	+	25.6608i	−0.506079	+	0.876555i	−0.999975	+	0.00703387i	$0.997761\pi$
$858$	1.81318	−	1.24150i	0.0619009	−	0.0423842i
$859$	−19.2488	−	33.3398i	−0.656760	−	1.13754i	−0.981450	−	0.191720i	$-0.938593\pi$
$859$	−19.2488	−	33.3398i	−0.656760	−	1.13754i	0.324690	−	0.945821i	$-0.394740\pi$
$860$	−11.5727	−	2.45986i	−0.394627	−	0.0838805i
$861$	−2.15454	+	20.4991i	−0.0734267	+	0.698608i
$862$	19.4177	−	14.1078i	0.661368	−	0.480512i
$863$	6.87902	−	21.1715i	0.234165	−	0.720685i	−0.763066	−	0.646320i	$-0.776307\pi$
$863$	6.87902	−	21.1715i	0.234165	−	0.720685i	0.997231	−	0.0743648i	$-0.0236929\pi$
$864$	−0.281395	+	0.0598123i	−0.00957325	+	0.00203486i
$865$	−10.4272	−	4.64248i	−0.354535	−	0.157849i
$866$	−28.9867	−	21.0600i	−0.985007	−	0.715649i
$867$	−11.5302	−	35.4863i	−0.391587	−	1.20518i
$868$	2.73480	+	4.73680i	0.0928250	+	0.160778i
$869$	−4.06750	−	3.13242i	−0.137981	−	0.106260i
$870$	−2.17122	−	3.76065i	−0.0736111	−	0.127498i
$871$	0.105825	+	0.0224938i	0.00358574	+	0.000762174i
$872$	−10.3545	+	4.61010i	−0.350646	+	0.156118i
$873$	10.6091	−	7.70794i	0.359063	−	0.260874i
$874$	3.83956	+	9.63637i	0.129875	+	0.325955i
$875$	−5.07520	+	15.6199i	−0.171573	+	0.528048i
$876$	−0.573186	−	5.45350i	−0.0193662	−	0.184257i
$877$	43.1023	−	19.1904i	1.45546	−	0.648013i	0.481856	−	0.876250i	$-0.339963\pi$
$877$	43.1023	−	19.1904i	1.45546	−	0.648013i	0.973606	+	0.228237i	$0.0732961\pi$
$878$	−22.4516	+	24.9350i	−0.757703	+	0.841515i
$879$	32.6849	−	56.6119i	1.10243	−	1.90947i
$880$	3.53644	−	5.74836i	0.119213	−	0.193777i
$881$	−28.4846			−0.959671			−0.479835	−	0.877358i	$-0.659304\pi$
$881$	−28.4846			−0.959671			−0.479835	+	0.877358i	$0.659304\pi$
$882$	4.54322	+	13.9826i	0.152978	+	0.470819i
$883$	−4.15518	+	39.5339i	−0.139833	+	1.33042i	0.669385	+	0.742915i	$0.266557\pi$
$883$	−4.15518	+	39.5339i	−0.139833	+	1.33042i	−0.809219	+	0.587508i	$0.800109\pi$
$884$	0.317118	+	0.141190i	0.0106658	+	0.00474874i
$885$	−22.6766	+	69.7915i	−0.762266	+	2.34601i
$886$	6.54410	−	20.1407i	0.219853	−	0.676639i
$887$	3.32354	+	1.47973i	0.111593	+	0.0496846i	0.461774	−	0.886998i	$-0.347213\pi$
$887$	3.32354	+	1.47973i	0.111593	+	0.0496846i	−0.350181	+	0.936682i	$0.613880\pi$
$888$	22.4702	−	10.0044i	0.754051	−	0.335725i
$889$	17.6253	−	19.5749i	0.591134	−	0.656520i
$890$	8.76766	−	15.1860i	0.293893	−	0.509037i
$891$	10.3935	−	29.1880i	0.348194	−	0.977834i
$892$	9.84646			0.329684
$893$	−0.979854	+	24.6594i	−0.0327896	+	0.825195i
$894$	−2.44240	−	1.77451i	−0.0816861	−	0.0593484i
$895$	−1.36725	−	13.0085i	−0.0457021	−	0.434827i
$896$	−0.921730	−	1.02368i	−0.0307928	−	0.0341989i
$897$	1.54229	−	0.327825i	0.0514957	−	0.0109458i
$898$	−1.85733	−	17.6713i	−0.0619798	−	0.589699i
$899$	−0.365210	+	3.47474i	−0.0121804	+	0.115889i
$900$	−0.764931	−	2.35422i	−0.0254977	−	0.0784739i
$901$	−5.10705			−0.170140
$902$	−19.8899	−	4.81195i	−0.662263	−	0.160220i
$903$	−9.71149	−	16.8208i	−0.323178	−	0.559761i
$904$	0.571523	+	1.75897i	0.0190086	+	0.0585023i
$905$	−6.27959	−	4.56239i	−0.208741	−	0.151659i
$906$	10.6572	+	4.74489i	0.354062	+	0.157639i
$907$	−17.2658	−	19.1757i	−0.573303	−	0.636717i	0.384848	−	0.922980i	$-0.374254\pi$
$907$	−17.2658	−	19.1757i	−0.573303	−	0.636717i	−0.958151	+	0.286263i	$0.907587\pi$
$908$	10.1328	−	2.15380i	0.336269	−	0.0714763i
$909$	−1.21819	−	11.5903i	−0.0404049	−	0.384427i
$910$	0.699618	−	0.311490i	0.0231921	−	0.0103258i
$911$	0.0347428	+	0.106927i	0.00115108	+	0.00354266i	0.951630	−	0.307245i	$-0.0994072\pi$
$911$	0.0347428	+	0.106927i	0.00115108	+	0.00354266i	−0.950479	+	0.310788i	$0.899407\pi$
$912$	−9.91600	−	3.66322i	−0.328351	−	0.121301i
$913$	35.9081	−	37.7070i	1.18839	−	1.24792i
$914$	−18.7270	+	32.4360i	−0.619433	+	1.07289i
$915$	−12.8475	−	2.73083i	−0.424727	−	0.0902785i
$916$	−1.62087	+	15.4215i	−0.0535551	+	0.509542i
$917$	2.87682	+	27.3712i	0.0950011	+	0.903875i
$918$	0.357534	−	0.0759961i	0.0118004	−	0.00250824i
$919$	18.3957	−	56.6161i	0.606818	−	1.86759i	0.123041	−	0.992402i	$-0.460735\pi$
$919$	18.3957	−	56.6161i	0.606818	−	1.86759i	0.483777	−	0.875192i	$-0.339265\pi$
$920$	3.91777	−	2.84642i	0.129165	−	0.0938438i
$921$	3.99088	−	37.9707i	0.131504	−	1.25118i
$922$	7.65433	−	8.50099i	0.252082	−	0.279965i
$923$	−2.72351			−0.0896454
$924$	10.8977	−	2.00007i	0.358508	−	0.0657973i
$925$	−4.35660	−	7.54586i	−0.143244	−	0.248106i
$926$	13.9658	+	2.96852i	0.458945	+	0.0975518i
$927$	−2.33692	+	22.2343i	−0.0767545	+	0.730271i
$928$	−0.0919772	−	0.875105i	−0.00301930	−	0.0287267i
$929$	18.8911	+	20.9807i	0.619797	+	0.688354i	0.968538	−	0.248865i	$-0.0800575\pi$
$929$	18.8911	+	20.9807i	0.619797	+	0.688354i	−0.348741	+	0.937219i	$0.613391\pi$
$930$	6.05524	−	18.6361i	0.198559	−	0.611103i
$931$	5.48433	−	21.5544i	0.179742	−	0.706418i
$932$	10.0442	+	7.29754i	0.329009	+	0.239039i
$933$	55.4448	+	11.7851i	1.81518	+	0.385828i
$934$	−21.1291	+	36.5966i	−0.691364	+	1.19748i
$935$	−4.49331	+	7.30372i	−0.146947	+	0.238857i
$936$	−0.393605	+	0.681744i	−0.0128654	+	0.0222835i
$937$	−18.0649	+	20.0631i	−0.590155	+	0.655434i	−0.962060	−	0.272837i	$-0.912038\pi$
$937$	−18.0649	+	20.0631i	−0.590155	+	0.655434i	0.371905	+	0.928271i	$0.378705\pi$
$938$	0.441310	+	0.320631i	0.0144093	+	0.0104690i
$939$	−54.5921	+	39.6635i	−1.78155	+	1.29437i
$940$	11.2694	−	2.39538i	0.367567	−	0.0781287i
$941$	25.8101	−	5.48611i	0.841385	−	0.178842i	0.232993	−	0.972478i	$-0.425148\pi$
$941$	25.8101	−	5.48611i	0.841385	−	0.178842i	0.608392	+	0.793636i	$0.291815\pi$
$942$	−19.0829	+	13.8645i	−0.621753	+	0.451730i
$943$	−11.8790	−	8.63059i	−0.386833	−	0.281051i
$944$	−9.94992	+	11.0505i	−0.323842	+	0.359663i
$945$	0.403202	−	0.698366i	0.0131162	−	0.0227178i
$946$	17.8283	−	7.34821i	0.579647	−	0.238911i
$947$	−4.75252	+	8.23161i	−0.154436	+	0.267491i	−0.932854	−	0.360256i	$-0.882689\pi$
$947$	−4.75252	+	8.23161i	−0.154436	+	0.267491i	0.778417	+	0.627747i	$0.216023\pi$
$948$	3.67191	+	0.780490i	0.119258	+	0.0253491i
$949$	0.499770	+	0.363104i	0.0162232	+	0.0117869i
$950$	−0.923384	+	3.62907i	−0.0299585	+	0.117743i
$951$	14.3203	−	44.0735i	0.464369	−	1.42918i
$952$	1.17113	+	1.30067i	0.0379565	+	0.0421549i
$953$	2.46409	+	23.4442i	0.0798197	+	0.759434i	0.959088	+	0.283107i	$0.0913652\pi$
$953$	2.46409	+	23.4442i	0.0798197	+	0.759434i	−0.879269	+	0.476326i	$0.841968\pi$
$954$	1.21061	−	11.5182i	0.0391949	−	0.372915i
$955$	20.6055	+	4.37984i	0.666779	+	0.141728i
$956$	−12.3092	−	21.3202i	−0.398108	−	0.689543i
$957$	6.38273	+	3.05812i	0.206324	+	0.0988549i
$958$	35.3963			1.14360
$959$	−2.33007	+	2.58780i	−0.0752419	+	0.0835646i
$960$	−0.515848	+	4.90797i	−0.0166489	+	0.158404i
$961$	12.3245	−	8.95427i	0.397564	−	0.288847i
$962$	−0.856269	+	2.63533i	−0.0276072	+	0.0849663i
$963$	−1.92474	+	0.409116i	−0.0620238	+	0.0131836i
$964$	−0.0653283	−	0.621557i	−0.00210408	−	0.0200190i
$965$	−1.88338	+	17.9191i	−0.0606281	+	0.576838i
$966$	7.77624	+	1.65289i	0.250196	+	0.0531809i
$967$	−2.57699	+	4.46348i	−0.0828705	+	0.143536i	−0.904482	−	0.426512i	$-0.859742\pi$
$967$	−2.57699	+	4.46348i	−0.0828705	+	0.143536i	0.821611	+	0.570048i	$0.193075\pi$
$968$	0.537277	+	10.9869i	0.0172687	+	0.353131i
$969$	12.5990	+	4.65439i	0.404739	+	0.149521i
$970$	2.86187	+	8.80793i	0.0918891	+	0.282806i
$971$	6.90684	−	3.07512i	0.221651	−	0.0986854i	−0.292907	−	0.956141i	$-0.594623\pi$
$971$	6.90684	−	3.07512i	0.221651	−	0.0986854i	0.514558	+	0.857456i	$0.327956\pi$
$972$	2.27791	+	21.6729i	0.0730641	+	0.695158i
$973$	10.4870	−	2.22908i	0.336198	−	0.0714610i
$974$	−19.5652	−	21.7293i	−0.626909	−	0.696253i
$975$	0.519996	+	0.231517i	0.0166532	+	0.00741449i
$976$	−2.15321	−	1.56440i	−0.0689226	−	0.0500752i
$977$	−12.8851	−	39.6564i	−0.412232	−	1.26872i	−0.914703	−	0.404126i	$-0.867576\pi$
$977$	−12.8851	−	39.6564i	−0.412232	−	1.26872i	0.502471	−	0.864594i	$-0.332424\pi$
$978$	−21.7321	−	37.6411i	−0.694917	−	1.20363i
$979$	2.19254	+	28.4958i	0.0700738	+	0.910729i
$980$	−10.3832			−0.331678
$981$	10.0921	+	31.0602i	0.322215	+	0.991675i
$982$	1.72592	−	16.4210i	0.0550762	−	0.524015i
$983$	0.960150	+	9.13522i	0.0306240	+	0.291368i	0.999106	+	0.0422833i	$0.0134632\pi$
$983$	0.960150	+	9.13522i	0.0306240	+	0.291368i	−0.968482	+	0.249085i	$0.919870\pi$
$984$	14.6363	−	3.11105i	0.466590	−	0.0991767i
$985$	32.7922	+	36.4194i	1.04485	+	1.16042i
$986$	0.116864	+	1.11189i	0.00372171	+	0.0354097i
$987$	15.3016	+	11.1173i	0.487056	+	0.353867i
$988$	1.05416	−	0.554021i	0.0335373	−	0.0176258i
$989$	13.8362			0.439965
$990$	−15.4073	−	11.8653i	−0.489677	−	0.377104i
$991$	−1.41751	+	2.45520i	−0.0450288	+	0.0779921i	−0.887661	−	0.460497i	$-0.847671\pi$
$991$	−1.41751	+	2.45520i	−0.0450288	+	0.0779921i	0.842633	+	0.538489i	$0.181005\pi$
$992$	2.65689	−	2.95077i	0.0843562	−	0.0936871i
$993$	−61.3950	+	27.3348i	−1.94831	+	0.867444i
$994$	−12.5447	−	5.58527i	−0.397895	−	0.177154i
$995$	−8.65130	+	26.6260i	−0.274265	+	0.844100i
$996$	−11.7654	+	36.2102i	−0.372802	+	1.14737i
$997$	−33.6745	−	14.9928i	−1.06648	−	0.474828i	−0.202984	−	0.979182i	$-0.565064\pi$
$997$	−33.6745	−	14.9928i	−1.06648	−	0.474828i	−0.863497	+	0.504354i	$0.831731\pi$
$998$	−1.03606	+	9.85741i	−0.0327958	+	0.312031i
$999$	0.901637	+	2.77495i	0.0285265	+	0.0877957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.49.8	✓	64
11.9	even	5	inner	418.2.n.d.163.1	yes	64
19.7	even	3	inner	418.2.n.d.159.1	yes	64
209.64	even	15	inner	418.2.n.d.273.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.8	✓	64	1.1	even	1	trivial
418.2.n.d.159.1	yes	64	19.7	even	3	inner
418.2.n.d.163.1	yes	64	11.9	even	5	inner
418.2.n.d.273.8	yes	64	209.64	even	15	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(2.21549 - 0.986399i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.36163 + 1.51224i) q^{5} +(2.37216 - 0.504218i) q^{6} +(-1.11442 + 0.809676i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.92802 - 2.14128i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(2.21549 - 0.986399i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.36163 + 1.51224i) q^{5} +(2.37216 - 0.504218i) q^{6} +(-1.11442 + 0.809676i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.92802 - 2.14128i) q^{9} +(1.01746 + 1.76229i) q^{10} +(-2.99104 - 1.43308i) q^{11} +2.42515 q^{12} +(-0.182811 + 0.203032i) q^{13} +(-1.25841 + 0.560281i) q^{14} +(4.50835 + 2.00725i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.850181 - 0.944222i) q^{17} +(2.33108 - 1.69363i) q^{18} +(-4.34969 + 0.283151i) q^{19} +(0.628825 + 1.93533i) q^{20} +(-1.67033 + 2.89310i) q^{21} +(-2.62772 - 2.02363i) q^{22} +(-1.18988 - 2.06093i) q^{23} +(2.37216 + 0.504218i) q^{24} +(0.0897997 - 0.854387i) q^{25} +(-0.221028 + 0.160587i) q^{26} +(-0.0888984 + 0.273601i) q^{27} +(-1.34740 + 0.286399i) q^{28} +(-0.803851 - 0.357898i) q^{29} +(3.99250 + 2.90072i) q^{30} +(-1.22700 - 3.77632i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-8.04019 - 0.224609i) q^{33} +(-0.635288 - 1.10035i) q^{34} +(-2.74186 - 0.582800i) q^{35} +(2.63227 - 1.17196i) q^{36} +(8.20532 - 5.96151i) q^{37} +(-4.31351 - 0.627388i) q^{38} +(-0.204745 + 0.630139i) q^{39} +(0.212707 + 2.02377i) q^{40} +(5.63662 - 2.50959i) q^{41} +(-2.23534 + 2.48259i) q^{42} +(-2.90706 + 5.03517i) q^{43} +(-2.14956 - 2.52574i) q^{44} +5.86338 q^{45} +(-0.735386 - 2.26329i) q^{46} +(0.591810 - 5.63070i) q^{47} +(2.21549 + 0.986399i) q^{48} +(-1.57675 + 4.85275i) q^{49} +(0.265474 - 0.817046i) q^{50} +(-2.81495 - 1.25330i) q^{51} +(-0.249586 + 0.111123i) q^{52} +(2.68955 - 2.98705i) q^{53} +(-0.143841 + 0.249139i) q^{54} +(-1.90552 - 6.47449i) q^{55} -1.37750 q^{56} +(-9.35740 + 4.91785i) q^{57} +(-0.711874 - 0.517207i) q^{58} +(1.55433 + 14.7885i) q^{59} +(3.30216 + 3.66742i) q^{60} +(-2.60335 + 0.553360i) q^{61} +(-0.415046 - 3.94890i) q^{62} +(-0.414885 + 3.94736i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.555953 q^{65} +(-7.81780 - 1.89135i) q^{66} +(-0.197999 - 0.342945i) q^{67} +(-0.392630 - 1.20839i) q^{68} +(-4.66907 - 3.39228i) q^{69} +(-2.56077 - 1.14013i) q^{70} +(6.67036 + 7.40818i) q^{71} +(2.81841 - 0.599072i) q^{72} +(-0.236350 - 2.24872i) q^{73} +(9.26548 - 4.12526i) q^{74} +(-0.643816 - 1.98146i) q^{75} +(-4.08881 - 1.51051i) q^{76} +(4.49361 - 0.824717i) q^{77} +(-0.331284 + 0.573800i) q^{78} +(1.51409 + 0.321831i) q^{79} +(-0.212707 + 2.02377i) q^{80} +(0.976484 + 9.29062i) q^{81} +(6.03522 - 1.28283i) q^{82} +(-4.85141 + 14.9311i) q^{83} +(-2.70265 + 1.96359i) q^{84} +(0.270261 - 2.57136i) q^{85} +(-3.89040 + 4.32073i) q^{86} -2.13395 q^{87} +(-1.57746 - 2.91747i) q^{88} +(-4.30860 - 7.46271i) q^{89} +(5.73525 + 1.21906i) q^{90} +(0.0393385 - 0.374281i) q^{91} +(-0.248753 - 2.36672i) q^{92} +(-6.44336 - 7.15608i) q^{93} +(1.74957 - 5.38461i) q^{94} +(-6.35086 - 6.19224i) q^{95} +(1.96199 + 1.42547i) q^{96} +(4.45168 + 0.946234i) q^{97} +(-2.55124 + 4.41888i) q^{98} +(-8.83538 + 3.64165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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