LMFDB - Embedded newform 349.2.h.a.17.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(17,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([43]))

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

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

chi := DirichletCharacter("349.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.h (of order $58$, degree $28$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$784$
Relative dimension:	$28$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			17.15
Character	$\chi$	$=$	349.17
Dual form			349.2.h.a.308.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.100044 - 0.105615i) q^{2} +(-1.65632 - 1.94997i) q^{3} +(0.107132 + 1.97593i) q^{4} +(-0.547752 + 0.416391i) q^{5} +(-0.371651 - 0.0201504i) q^{6} +(1.05893 - 1.75995i) q^{7} +(0.441159 + 0.374724i) q^{8} +(-0.573647 + 3.49909i) q^{9} +O(q^{10})$	\(q+(0.100044 - 0.105615i) q^{2} +(-1.65632 - 1.94997i) q^{3} +(0.107132 + 1.97593i) q^{4} +(-0.547752 + 0.416391i) q^{5} +(-0.371651 - 0.0201504i) q^{6} +(1.05893 - 1.75995i) q^{7} +(0.441159 + 0.374724i) q^{8} +(-0.573647 + 3.49909i) q^{9} +(-0.0108222 + 0.0995082i) q^{10} +(1.17925 - 5.35737i) q^{11} +(3.67558 - 3.48169i) q^{12} +(-1.73721 + 0.482333i) q^{13} +(-0.0799382 - 0.287911i) q^{14} +(1.71921 + 0.378426i) q^{15} +(-3.85076 + 0.418796i) q^{16} +(-5.06630 - 5.96451i) q^{17} +(0.312167 + 0.410648i) q^{18} +(-0.632560 - 1.58761i) q^{19} +(-0.881442 - 1.03771i) q^{20} +(-5.18579 + 0.850168i) q^{21} +(-0.447842 - 0.660518i) q^{22} +(-1.25024 - 4.50296i) q^{23} -1.48091i q^{24} +(-1.21099 + 4.36159i) q^{25} +(-0.122855 + 0.231730i) q^{26} +(1.19653 - 0.719930i) q^{27} +(3.59100 + 1.90383i) q^{28} +(7.06721 + 6.69441i) q^{29} +(0.211963 - 0.143715i) q^{30} +(1.69814 - 3.20302i) q^{31} +(-1.04159 + 1.37019i) q^{32} +(-12.3999 + 6.57403i) q^{33} +(-1.13679 - 0.0616352i) q^{34} +(0.152797 + 1.40495i) q^{35} +(-6.97543 - 0.758624i) q^{36} +(-2.80522 - 10.1035i) q^{37} +(-0.230959 - 0.0920224i) q^{38} +(3.81791 + 2.58861i) q^{39} +(-0.397677 - 0.0215614i) q^{40} +(2.24937 - 2.64816i) q^{41} +(-0.429016 + 0.632752i) q^{42} +(0.853958 - 3.87957i) q^{43} +(10.7121 + 1.75617i) q^{44} +(-1.14277 - 2.15550i) q^{45} +(-0.600659 - 0.318449i) q^{46} +(-0.0715414 + 0.212327i) q^{47} +(7.19474 + 6.81522i) q^{48} +(1.30275 + 2.45725i) q^{49} +(0.339497 + 0.564249i) q^{50} +(-3.23921 + 19.7583i) q^{51} +(-1.13917 - 3.38093i) q^{52} +(2.69379 - 5.82253i) q^{53} +(0.0436704 - 0.198396i) q^{54} +(1.58482 + 3.42554i) q^{55} +(1.12665 - 0.379614i) q^{56} +(-2.04807 + 3.86306i) q^{57} +(1.41406 - 0.0766682i) q^{58} +(4.40265 - 3.73964i) q^{59} +(-0.563562 + 3.43758i) q^{60} +(-3.83054 - 4.04385i) q^{61} +(-0.168399 - 0.499791i) q^{62} +(5.55079 + 4.71488i) q^{63} +(-1.21281 - 7.39779i) q^{64} +(0.750720 - 0.987556i) q^{65} +(-0.546221 + 1.96731i) q^{66} +(-4.66737 + 11.7142i) q^{67} +(11.2427 - 10.6497i) q^{68} +(-6.70985 + 9.89629i) q^{69} +(0.163670 + 0.124419i) q^{70} +(8.13504 + 6.90996i) q^{71} +(-1.56426 + 1.32870i) q^{72} +(10.4050 + 6.26046i) q^{73} +(-1.34772 - 0.714518i) q^{74} +(10.5108 - 4.86280i) q^{75} +(3.06924 - 1.41998i) q^{76} +(-8.17999 - 7.74850i) q^{77} +(0.655355 - 0.144254i) q^{78} +(3.59180 + 7.76354i) q^{79} +(1.93488 - 1.83282i) q^{80} +(6.69488 + 2.25577i) q^{81} +(-0.0546501 - 0.502499i) q^{82} +(-6.28474 + 4.77753i) q^{83} +(-2.23544 - 10.1557i) q^{84} +(5.25865 + 1.15752i) q^{85} +(-0.324308 - 0.478318i) q^{86} +(1.34836 - 24.8690i) q^{87} +(2.52777 - 1.92156i) q^{88} +(-3.54588 - 2.40416i) q^{89} +(-0.341980 - 0.0949503i) q^{90} +(-0.990695 + 3.56816i) q^{91} +(8.76362 - 2.95281i) q^{92} +(-9.05847 + 1.99392i) q^{93} +(0.0152677 + 0.0287979i) q^{94} +(1.00755 + 0.606223i) q^{95} +(4.39706 - 0.238402i) q^{96} +(-6.86681 + 9.03314i) q^{97} +(0.389855 + 0.108243i) q^{98} +(18.0695 + 7.19953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 784 q - 29 q^{2} - 25 q^{3} + 3 q^{4} - 21 q^{5} - 29 q^{6} - 29 q^{7} + 58 q^{8} - 57 q^{9}+O(q^{10}) $ 784 * q - 29 * q^2 - 25 * q^3 + 3 * q^4 - 21 * q^5 - 29 * q^6 - 29 * q^7 + 58 * q^8 - 57 * q^9	\( 784 q - 29 q^{2} - 25 q^{3} + 3 q^{4} - 21 q^{5} - 29 q^{6} - 29 q^{7} + 58 q^{8} - 57 q^{9} - 29 q^{10} - 29 q^{11} - 37 q^{12} - 29 q^{13} - 33 q^{14} - 37 q^{15} - 57 q^{16} - 21 q^{17} - 145 q^{18} + 43 q^{19} - 35 q^{20} - 145 q^{21} - 17 q^{22} - 13 q^{23} - 45 q^{25} + 7 q^{26} - 43 q^{27} - 29 q^{28} - 13 q^{29} - 29 q^{30} - 53 q^{31} - 29 q^{32} - 29 q^{33} - 29 q^{34} - 87 q^{35} + 33 q^{36} + 150 q^{37} - 29 q^{38} - 29 q^{39} - 29 q^{40} - 91 q^{41} + 145 q^{42} - 29 q^{43} - 145 q^{44} + 23 q^{45} - 29 q^{46} - 29 q^{47} + 111 q^{48} + 19 q^{49} + 348 q^{50} + 61 q^{51} - 145 q^{52} - 29 q^{53} - 29 q^{54} - 145 q^{55} + 9 q^{56} - 23 q^{57} - 29 q^{58} - 29 q^{59} + 405 q^{60} - 174 q^{61} - 29 q^{62} - 29 q^{63} - 210 q^{64} - 29 q^{65} + 244 q^{66} - 75 q^{67} - 77 q^{68} - 103 q^{69} - 115 q^{70} - 29 q^{71} - 203 q^{72} - 79 q^{73} + 87 q^{74} + 7 q^{75} - 105 q^{76} + 39 q^{77} + 233 q^{78} - 29 q^{79} + 99 q^{80} + 207 q^{81} - 29 q^{82} + 93 q^{83} - 435 q^{84} + 126 q^{85} - 147 q^{86} + 115 q^{87} - 139 q^{88} - 435 q^{89} - 29 q^{90} - 57 q^{91} - 47 q^{92} - 99 q^{93} - 51 q^{94} + 233 q^{95} + 609 q^{96} - 29 q^{97} + 377 q^{98} - 29 q^{99}+O(q^{100}) \) 784 * q - 29 * q^2 - 25 * q^3 + 3 * q^4 - 21 * q^5 - 29 * q^6 - 29 * q^7 + 58 * q^8 - 57 * q^9 - 29 * q^10 - 29 * q^11 - 37 * q^12 - 29 * q^13 - 33 * q^14 - 37 * q^15 - 57 * q^16 - 21 * q^17 - 145 * q^18 + 43 * q^19 - 35 * q^20 - 145 * q^21 - 17 * q^22 - 13 * q^23 - 45 * q^25 + 7 * q^26 - 43 * q^27 - 29 * q^28 - 13 * q^29 - 29 * q^30 - 53 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 87 * q^35 + 33 * q^36 + 150 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91 * q^41 + 145 * q^42 - 29 * q^43 - 145 * q^44 + 23 * q^45 - 29 * q^46 - 29 * q^47 + 111 * q^48 + 19 * q^49 + 348 * q^50 + 61 * q^51 - 145 * q^52 - 29 * q^53 - 29 * q^54 - 145 * q^55 + 9 * q^56 - 23 * q^57 - 29 * q^58 - 29 * q^59 + 405 * q^60 - 174 * q^61 - 29 * q^62 - 29 * q^63 - 210 * q^64 - 29 * q^65 + 244 * q^66 - 75 * q^67 - 77 * q^68 - 103 * q^69 - 115 * q^70 - 29 * q^71 - 203 * q^72 - 79 * q^73 + 87 * q^74 + 7 * q^75 - 105 * q^76 + 39 * q^77 + 233 * q^78 - 29 * q^79 + 99 * q^80 + 207 * q^81 - 29 * q^82 + 93 * q^83 - 435 * q^84 + 126 * q^85 - 147 * q^86 + 115 * q^87 - 139 * q^88 - 435 * q^89 - 29 * q^90 - 57 * q^91 - 47 * q^92 - 99 * q^93 - 51 * q^94 + 233 * q^95 + 609 * q^96 - 29 * q^97 + 377 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{43}{58}\right)$

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 $

$2$	0.100044	−	0.105615i	0.0707417	−	0.0746811i	−0.689664	−	0.724130i	$-0.742242\pi$
$2$	0.100044	−	0.105615i	0.0707417	−	0.0746811i	0.760405	+	0.649449i	$0.225000\pi$
$3$	−1.65632	−	1.94997i	−0.956278	−	1.12582i	−0.991972	−	0.126455i	$-0.959640\pi$
$3$	−1.65632	−	1.94997i	−0.956278	−	1.12582i	0.0356941	−	0.999363i	$-0.488636\pi$
$4$	0.107132	+	1.97593i	0.0535660	+	0.987967i
$5$	−0.547752	+	0.416391i	−0.244962	+	0.186216i	−0.720450	−	0.693507i	$-0.756065\pi$
$5$	−0.547752	+	0.416391i	−0.244962	+	0.186216i	0.475488	+	0.879722i	$0.342272\pi$
$6$	−0.371651	−	0.0201504i	−0.151726	−	0.00822635i
$7$	1.05893	−	1.75995i	0.400238	−	0.665200i	−0.589553	−	0.807730i	$-0.700696\pi$
$7$	1.05893	−	1.75995i	0.400238	−	0.665200i	0.989791	+	0.142530i	$0.0455236\pi$
$8$	0.441159	+	0.374724i	0.155973	+	0.132485i
$9$	−0.573647	+	3.49909i	−0.191216	+	1.16636i
$10$	−0.0108222	+	0.0995082i	−0.00342227	+	0.0314673i
$11$	1.17925	−	5.35737i	0.355556	−	1.61531i	−0.371297	−	0.928514i	$-0.621087\pi$
$11$	1.17925	−	5.35737i	0.355556	−	1.61531i	0.726853	−	0.686793i	$-0.240982\pi$
$12$	3.67558	−	3.48169i	1.06105	−	1.00508i
$13$	−1.73721	+	0.482333i	−0.481815	+	0.133775i	−0.499939	−	0.866061i	$-0.666644\pi$
$13$	−1.73721	+	0.482333i	−0.481815	+	0.133775i	0.0181245	+	0.999836i	$0.494230\pi$
$14$	−0.0799382	−	0.287911i	−0.0213644	−	0.0769476i
$15$	1.71921	+	0.378426i	0.443897	+	0.0977091i
$16$	−3.85076	+	0.418796i	−0.962690	+	0.104699i
$17$	−5.06630	−	5.96451i	−1.22876	−	1.44661i	−0.854636	−	0.519227i	$-0.826220\pi$
$17$	−5.06630	−	5.96451i	−1.22876	−	1.44661i	−0.374123	−	0.927379i	$-0.622056\pi$
$18$	0.312167	+	0.410648i	0.0735784	+	0.0967907i
$19$	−0.632560	−	1.58761i	−0.145119	−	0.364222i	0.838392	−	0.545067i	$-0.183496\pi$
$19$	−0.632560	−	1.58761i	−0.145119	−	0.364222i	−0.983512	+	0.180846i	$0.942117\pi$
$20$	−0.881442	−	1.03771i	−0.197097	−	0.232040i
$21$	−5.18579	+	0.850168i	−1.13163	+	0.185522i
$22$	−0.447842	−	0.660518i	−0.0954803	−	0.140823i
$23$	−1.25024	−	4.50296i	−0.260693	−	0.938932i	−0.971792	−	0.235840i	$-0.924216\pi$
$23$	−1.25024	−	4.50296i	−0.260693	−	0.938932i	0.711099	−	0.703092i	$-0.248198\pi$
$24$		−	1.48091i		−	0.302290i
$25$	−1.21099	+	4.36159i	−0.242198	+	0.872318i
$26$	−0.122855	+	0.231730i	−0.0240939	+	0.0454459i
$27$	1.19653	−	0.719930i	0.230273	−	0.138551i
$28$	3.59100	+	1.90383i	0.678635	+	0.359790i
$29$	7.06721	+	6.69441i	1.31235	+	1.24312i	0.950440	+	0.310907i	$0.100633\pi$
$29$	7.06721	+	6.69441i	1.31235	+	1.24312i	0.361907	+	0.932214i	$0.382126\pi$
$30$	0.211963	−	0.143715i	0.0386990	−	0.0262386i
$31$	1.69814	−	3.20302i	0.304994	−	0.575280i	−0.682881	−	0.730530i	$-0.739273\pi$
$31$	1.69814	−	3.20302i	0.304994	−	0.575280i	0.987875	+	0.155249i	$0.0496181\pi$
$32$	−1.04159	+	1.37019i	−0.184130	+	0.242218i
$33$	−12.3999	+	6.57403i	−2.15855	+	1.14439i
$34$	−1.13679	−	0.0616352i	−0.194959	−	0.0105703i
$35$	0.152797	+	1.40495i	0.0258274	+	0.237479i
$36$	−6.97543	−	0.758624i	−1.16257	−	0.126437i
$37$	−2.80522	−	10.1035i	−0.461175	−	1.66100i	−0.719153	−	0.694851i	$-0.755470\pi$
$37$	−2.80522	−	10.1035i	−0.461175	−	1.66100i	0.257978	−	0.966151i	$-0.416944\pi$
$38$	−0.230959	−	0.0920224i	−0.0374665	−	0.0149280i
$39$	3.81791	+	2.58861i	0.611355	+	0.414509i
$40$	−0.397677	−	0.0215614i	−0.0628783	−	0.00340916i
$41$	2.24937	−	2.64816i	0.351292	−	0.413573i	−0.557927	−	0.829890i	$-0.688403\pi$
$41$	2.24937	−	2.64816i	0.351292	−	0.413573i	0.909220	+	0.416316i	$0.136679\pi$
$42$	−0.429016	+	0.632752i	−0.0661986	+	0.0976357i
$43$	0.853958	−	3.87957i	0.130227	−	0.591629i	−0.865629	−	0.500686i	$-0.833081\pi$
$43$	0.853958	−	3.87957i	0.130227	−	0.591629i	0.995856	−	0.0909425i	$-0.0289879\pi$
$44$	10.7121	+	1.75617i	1.61492	+	0.264752i
$45$	−1.14277	−	2.15550i	−0.170354	−	0.321322i
$46$	−0.600659	−	0.318449i	−0.0885624	−	0.0469528i
$47$	−0.0715414	+	0.212327i	−0.0104354	+	0.0309711i	−0.952744	−	0.303773i	$-0.901753\pi$
$47$	−0.0715414	+	0.212327i	−0.0104354	+	0.0309711i	0.942309	+	0.334744i	$0.108650\pi$
$48$	7.19474	+	6.81522i	1.03847	+	0.983693i
$49$	1.30275	+	2.45725i	0.186107	+	0.351036i
$50$	0.339497	+	0.564249i	0.0480122	+	0.0797969i
$51$	−3.23921	+	19.7583i	−0.453580	+	2.76672i
$52$	−1.13917	−	3.38093i	−0.157974	−	0.468851i
$53$	2.69379	−	5.82253i	0.370020	−	0.799786i	−0.629716	−	0.776825i	$-0.716829\pi$
$53$	2.69379	−	5.82253i	0.370020	−	0.799786i	0.999736	−	0.0229604i	$-0.00730915\pi$
$54$	0.0436704	−	0.198396i	0.00594278	−	0.0269983i
$55$	1.58482	+	3.42554i	0.213698	+	0.461900i
$56$	1.12665	−	0.379614i	0.150555	−	0.0507280i
$57$	−2.04807	+	3.86306i	−0.271273	+	0.511675i
$58$	1.41406	−	0.0766682i	0.185675	−	0.0100670i
$59$	4.40265	−	3.73964i	0.573176	−	0.486860i	−0.313288	−	0.949658i	$-0.601430\pi$
$59$	4.40265	−	3.73964i	0.573176	−	0.486860i	0.886464	+	0.462798i	$0.153155\pi$
$60$	−0.563562	+	3.43758i	−0.0727556	+	0.443790i
$61$	−3.83054	−	4.04385i	−0.490450	−	0.517762i	0.433045	−	0.901372i	$-0.357439\pi$
$61$	−3.83054	−	4.04385i	−0.490450	−	0.517762i	−0.923495	+	0.383610i	$0.874681\pi$
$62$	−0.168399	−	0.499791i	−0.0213867	−	0.0634736i
$63$	5.55079	+	4.71488i	0.699334	+	0.594019i
$64$	−1.21281	−	7.39779i	−0.151601	−	0.924724i
$65$	0.750720	−	0.987556i	0.0931154	−	0.122491i
$66$	−0.546221	+	1.96731i	−0.0672352	+	0.242159i
$67$	−4.66737	+	11.7142i	−0.570211	+	1.43112i	0.307323	+	0.951605i	$0.400567\pi$
$67$	−4.66737	+	11.7142i	−0.570211	+	1.43112i	−0.877534	+	0.479515i	$0.840813\pi$
$68$	11.2427	−	10.6497i	1.36338	−	1.29146i
$69$	−6.70985	+	9.89629i	−0.807772	+	1.19137i
$70$	0.163670	+	0.124419i	0.0195623	+	0.0148709i
$71$	8.13504	+	6.90996i	0.965451	+	0.820062i	0.983708	−	0.179772i	$-0.0575359\pi$
$71$	8.13504	+	6.90996i	0.965451	+	0.820062i	−0.0182572	+	0.999833i	$0.505812\pi$
$72$	−1.56426	+	1.32870i	−0.184350	+	0.156588i
$73$	10.4050	+	6.26046i	1.21781	+	0.732731i	0.971633	−	0.236494i	$-0.0759983\pi$
$73$	10.4050	+	6.26046i	1.21781	+	0.732731i	0.246176	+	0.969225i	$0.420826\pi$
$74$	−1.34772	−	0.714518i	−0.156670	−	0.0830610i
$75$	10.5108	−	4.86280i	1.21368	−	0.561508i
$76$	3.06924	−	1.41998i	0.352066	−	0.162883i
$77$	−8.17999	−	7.74850i	−0.932196	−	0.883023i
$78$	0.655355	−	0.144254i	0.0742043	−	0.0163336i
$79$	3.59180	+	7.76354i	0.404109	+	0.873467i	0.997640	+	0.0686561i	$0.0218711\pi$
$79$	3.59180	+	7.76354i	0.404109	+	0.873467i	−0.593532	+	0.804811i	$0.702267\pi$
$80$	1.93488	−	1.83282i	0.216326	−	0.204915i
$81$	6.69488	+	2.25577i	0.743876	+	0.250641i
$82$	−0.0546501	−	0.502499i	−0.00603509	−	0.0554918i
$83$	−6.28474	+	4.77753i	−0.689839	+	0.524402i	−0.890343	−	0.455291i	$-0.849535\pi$
$83$	−6.28474	+	4.77753i	−0.689839	+	0.524402i	0.200503	+	0.979693i	$0.435742\pi$
$84$	−2.23544	−	10.1557i	−0.243907	−	1.10808i
$85$	5.25865	+	1.15752i	0.570380	+	0.125550i
$86$	−0.324308	−	0.478318i	−0.0349710	−	0.0515783i
$87$	1.34836	−	24.8690i	0.144559	−	2.66623i
$88$	2.52777	−	1.92156i	0.269461	−	0.204839i
$89$	−3.54588	−	2.40416i	−0.375862	−	0.254841i	0.358599	−	0.933492i	$-0.383255\pi$
$89$	−3.54588	−	2.40416i	−0.375862	−	0.254841i	−0.734461	+	0.678651i	$0.762565\pi$
$90$	−0.341980	−	0.0949503i	−0.0360479	−	0.0100086i
$91$	−0.990695	+	3.56816i	−0.103853	+	0.374045i
$92$	8.76362	−	2.95281i	0.913670	−	0.307851i
$93$	−9.05847	+	1.99392i	−0.939320	+	0.206760i
$94$	0.0152677	+	0.0287979i	0.00157474	+	0.00297028i
$95$	1.00755	+	0.606223i	0.103373	+	0.0621972i
$96$	4.39706	−	0.238402i	0.448773	−	0.0243318i
$97$	−6.86681	+	9.03314i	−0.697219	+	0.917176i	−0.999349	−	0.0360908i	$-0.988509\pi$
$97$	−6.86681	+	9.03314i	−0.697219	+	0.917176i	0.302129	+	0.953267i	$0.402303\pi$
$98$	0.389855	+	0.108243i	0.0393813	+	0.0109342i
$99$	18.0695	+	7.19953i	1.81605	+	0.723580i
$100$	−8.74796	−	1.92557i	−0.874796	−	0.192557i
$101$	−14.8596	+	5.92060i	−1.47858	+	0.589121i	−0.963426	−	0.267974i	$-0.913646\pi$
$101$	−14.8596	+	5.92060i	−1.47858	+	0.589121i	−0.515157	+	0.857096i	$0.672266\pi$
$102$	1.76271	+	2.31881i	0.174534	+	0.229596i
$103$	−2.86528	+	3.02484i	−0.282324	+	0.298046i	−0.851698	−	0.524032i	$-0.824427\pi$
$103$	−2.86528	+	3.02484i	−0.282324	+	0.298046i	0.569374	+	0.822079i	$0.307186\pi$
$104$	−0.947126	−	0.438187i	−0.0928734	−	0.0429678i
$105$	2.48653	−	2.62500i	0.242660	−	0.256173i
$106$	−0.345449	−	0.867013i	−0.0335530	−	0.0842117i
$107$	14.7492	−	5.87660i	1.42585	−	0.568112i	0.475621	−	0.879650i	$-0.342223\pi$
$107$	14.7492	−	5.87660i	1.42585	−	0.568112i	0.950234	+	0.311538i	$0.100844\pi$
$108$	1.55072	+	2.28714i	0.149218	+	0.220080i
$109$	−6.33039	−	0.688471i	−0.606341	−	0.0659436i	−0.200202	−	0.979755i	$-0.564160\pi$
$109$	−6.33039	−	0.688471i	−0.606341	−	0.0659436i	−0.406139	+	0.913811i	$0.633125\pi$
$110$	0.520340	+	0.175323i	0.0496125	+	0.0167164i
$111$	−15.0552	+	22.2047i	−1.42897	+	2.10758i
$112$	−3.34062	+	7.22064i	−0.315659	+	0.682286i
$113$	−0.595805	−	0.628983i	−0.0560486	−	0.0591698i	0.697368	−	0.716713i	$-0.254354\pi$
$113$	−0.595805	−	0.628983i	−0.0560486	−	0.0591698i	−0.753417	+	0.657543i	$0.771596\pi$
$114$	0.203101	+	0.602782i	0.0190222	+	0.0564557i
$115$	2.55981	+	1.94592i	0.238704	+	0.181458i
$116$	−12.4706	+	14.6815i	−1.15787	+	1.36315i
$117$	−0.691184	−	6.35533i	−0.0639000	−	0.587551i
$118$	0.0454955	−	0.839114i	0.00418820	−	0.0772467i
$119$	−15.8621	+	2.60046i	−1.45408	+	0.238384i
$120$	0.616638	+	0.811173i	0.0562911	+	0.0740496i
$121$	−17.3275	−	8.01654i	−1.57522	−	0.728776i
$122$	−0.810313			−0.0733623
$123$	−8.88953			−0.801542
$124$	6.51089	+	3.01226i	0.584695	+	0.270509i
$125$	−2.42617	−	6.08923i	−0.217003	−	0.544638i
$126$	1.05328	−	0.114552i	0.0938341	−	0.0102051i
$127$	1.35120	+	6.13857i	0.119900	+	0.544710i	0.997825	+	0.0659132i	$0.0209960\pi$
$127$	1.35120	+	6.13857i	0.119900	+	0.544710i	−0.877926	+	0.478797i	$0.841073\pi$
$128$	−3.75180	−	2.54379i	−0.331616	−	0.224841i
$129$	−8.97949	+	4.76062i	−0.790600	+	0.419149i
$130$	−0.0291958	−	0.178086i	−0.00256064	−	0.0156192i
$131$	6.10006	−	5.18144i	0.532965	−	0.452704i	−0.340044	−	0.940410i	$-0.610442\pi$
$131$	6.10006	−	5.18144i	0.532965	−	0.452704i	0.873008	+	0.487705i	$0.162166\pi$
$132$	−14.3183	−	23.7972i	−1.24625	−	2.07128i
$133$	−3.46395	−	0.567886i	−0.300363	−	0.0492420i
$134$	0.770256	+	1.66488i	0.0665400	+	0.143824i
$135$	−0.355632	+	0.892569i	−0.0306079	+	0.0768201i
$136$		−	4.52976i		−	0.388424i
$137$	15.8609	+	6.31955i	1.35509	+	0.539915i	0.930772	−	0.365600i	$-0.119136\pi$
$137$	15.8609	+	6.31955i	1.35509	+	0.539915i	0.424313	+	0.905516i	$0.360516\pi$
$138$	0.373918	+	1.69872i	0.0318300	+	0.144605i
$139$	−0.100840	−	1.85989i	−0.00855315	−	0.157753i	−0.999690	−	0.0249070i	$-0.992071\pi$
$139$	−0.100840	−	1.85989i	−0.00855315	−	0.157753i	0.991137	−	0.132846i	$-0.0424117\pi$
$140$	−2.75971	+	0.452432i	−0.233238	+	0.0382375i
$141$	0.532528	−	0.212179i	0.0448470	−	0.0178687i
$142$	1.54366	−	0.167883i	0.129541	−	0.0140884i
$143$	0.535442	+	9.87565i	0.0447759	+	0.825843i
$144$	0.743574	−	13.7144i	0.0619645	−	1.14287i
$145$	−6.65857	−	0.724163i	−0.552964	−	0.0601385i
$146$	1.70215	−	0.472600i	0.140871	−	0.0391126i
$147$	2.63380	−	6.61033i	0.217232	−	0.545211i
$148$	19.6633	−	6.62533i	1.61631	−	0.544599i
$149$	13.5737	−	9.20322i	1.11200	−	0.753957i	0.140288	−	0.990111i	$-0.455197\pi$
$149$	13.5737	−	9.20322i	1.11200	−	0.753957i	0.971716	+	0.236154i	$0.0758869\pi$
$150$	0.537954	−	1.59659i	0.0439237	−	0.130361i
$151$	−4.26452	+	1.97298i	−0.347041	+	0.160558i	−0.585664	−	0.810554i	$-0.699166\pi$
$151$	−4.26452	+	1.97298i	−0.347041	+	0.160558i	0.238623	+	0.971112i	$0.423304\pi$
$152$	0.315854	−	0.937422i	0.0256192	−	0.0760350i
$153$	23.7766	−	14.3059i	1.92223	−	1.15657i
$154$	−1.63671	+	0.0887401i	−0.131890	+	0.00715088i
$155$	0.403551	+	2.46155i	0.0324140	+	0.197717i
$156$	−4.70590	+	7.82127i	−0.376774	+	0.626203i
$157$	15.5821	−	18.3447i	1.24359	−	1.46407i	0.409617	−	0.912258i	$-0.365662\pi$
$157$	15.5821	−	18.3447i	1.24359	−	1.46407i	0.833971	−	0.551808i	$-0.186062\pi$
$158$	1.17928	+	0.397347i	0.0938188	+	0.0316112i
$159$	−15.8156	+	4.39117i	−1.25426	+	0.348242i
$160$		−	1.18424i		−	0.0936222i
$161$	−9.24892	−	2.56795i	−0.728917	−	0.202383i
$162$	0.908025	−	0.481404i	0.0713412	−	0.0378227i
$163$	4.27933	−	7.11231i	0.335183	−	0.557079i	−0.642729	−	0.766093i	$-0.722198\pi$
$163$	4.27933	−	7.11231i	0.335183	−	0.557079i	0.977913	+	0.209015i	$0.0670256\pi$
$164$	5.47357	+	4.16090i	0.427414	+	0.324912i
$165$	4.05473	−	8.76416i	0.315661	−	0.682289i
$166$	−0.124170	+	1.14173i	−0.00963747	+	0.0886151i
$167$	0.591213	+	0.982603i	0.0457494	+	0.0760361i	0.878888	−	0.477028i	$-0.158286\pi$
$167$	0.591213	+	0.982603i	0.0457494	+	0.0760361i	−0.833139	+	0.553064i	$0.813458\pi$
$168$	−2.60634	−	1.56818i	−0.201083	−	0.120988i
$169$	−8.35390	+	5.02638i	−0.642608	+	0.386644i
$170$	0.648346	−	0.439590i	0.0497259	−	0.0337150i
$171$	5.91804	−	1.30266i	0.452564	−	0.0996169i
$172$	7.75726	+	1.27174i	0.591486	+	0.0969691i
$173$	1.98230	−	18.2269i	0.150711	−	1.38577i	−0.637542	−	0.770416i	$-0.720049\pi$
$173$	1.98230	−	18.2269i	0.150711	−	1.38577i	0.788253	−	0.615351i	$-0.210986\pi$
$174$	−2.49164	−	2.63039i	−0.188891	−	0.199410i
$175$	6.39385	+	6.74991i	0.483330	+	0.510245i
$176$	−2.29735	+	21.1238i	−0.173170	+	1.59227i
$177$	−14.5844	−	2.39099i	−1.09623	−	0.179718i
$178$	−0.608659	+	0.133976i	−0.0456209	+	0.0100419i
$179$	17.1742	−	11.6444i	1.28366	−	0.870343i	0.287490	−	0.957784i	$-0.407179\pi$
$179$	17.1742	−	11.6444i	1.28366	−	0.870343i	0.996170	+	0.0874412i	$0.0278690\pi$
$180$	4.13669	−	2.48897i	0.308331	−	0.185517i
$181$	0.838421	+	0.504461i	0.0623194	+	0.0374963i	0.546373	−	0.837542i	$-0.316008\pi$
$181$	0.838421	+	0.504461i	0.0623194	+	0.0374963i	−0.484053	+	0.875039i	$0.660836\pi$
$182$	0.277738	+	0.461605i	0.0205873	+	0.0342164i
$183$	−1.54079	+	14.1674i	−0.113899	+	1.04728i
$184$	1.13581	−	2.45502i	0.0837332	−	0.180986i
$185$	5.74356	+	4.36614i	0.422275	+	0.321005i
$186$	−0.695656	+	1.15619i	−0.0510080	+	0.0847760i
$187$	−37.9285	+	20.1084i	−2.77361	+	1.47047i
$188$	−0.427209	−	0.118614i	−0.0311574	−	0.00865082i
$189$		−	2.86820i		−	0.208631i
$190$	0.164825	−	0.0457636i	0.0119577	−	0.00332004i
$191$	−2.86664	−	0.965882i	−0.207422	−	0.0698888i	0.213672	−	0.976905i	$-0.431457\pi$
$191$	−2.86664	−	0.965882i	−0.207422	−	0.0698888i	−0.421095	+	0.907017i	$0.638354\pi$
$192$	−12.4167	+	14.6181i	−0.896099	+	1.05497i
$193$	−7.14377	+	11.8730i	−0.514220	+	0.854640i	−0.999809	−	0.0195475i	$-0.993777\pi$
$193$	−7.14377	+	11.8730i	−0.514220	+	0.854640i	0.485589	+	0.874187i	$0.338605\pi$
$194$	0.267053	+	1.62895i	0.0191733	+	0.116952i
$195$	−3.16914	+	0.171826i	−0.226947	+	0.0123047i
$196$	−4.71580	+	2.83740i	−0.336843	+	0.202672i
$197$	2.50985	−	7.44898i	0.178820	−	0.530718i	−0.820333	−	0.571887i	$-0.806212\pi$
$197$	2.50985	−	7.44898i	0.178820	−	0.530718i	0.999152	+	0.0411691i	$0.0131082\pi$
$198$	2.56812	−	1.18814i	0.182508	−	0.0844372i
$199$	5.39758	−	16.0195i	0.382625	−	1.13559i	−0.567408	−	0.823437i	$-0.692054\pi$
$199$	5.39758	−	16.0195i	0.382625	−	1.13559i	0.950032	−	0.312152i	$-0.101050\pi$
$200$	−2.16863	+	1.47037i	−0.153345	+	0.103971i
$201$	30.5731	−	10.3013i	2.15646	−	0.726596i
$202$	−0.861305	+	2.16171i	−0.0606012	+	0.152098i
$203$	19.2655	−	5.34905i	1.35218	−	0.375430i
$204$	−39.3882	−	4.28372i	−2.75772	−	0.299920i
$205$	−0.129428	+	2.38715i	−0.00903962	+	0.166726i
$206$	0.0328148	+	0.605233i	0.00228631	+	0.0421686i
$207$	16.4735	−	1.79160i	1.14499	−	0.124525i
$208$	6.48757	−	2.58488i	0.449832	−	0.179229i
$209$	−9.25134	+	1.51668i	−0.639928	+	0.104911i
$210$	−0.0284771	−	0.525230i	−0.00196511	−	0.0362443i
$211$	−0.325865	−	1.48042i	−0.0224335	−	0.101916i	0.964073	−	0.265636i	$-0.0855819\pi$
$211$	−0.325865	−	1.48042i	−0.0224335	−	0.101916i	−0.986507	+	0.163719i	$0.947651\pi$
$212$	11.7935	+	4.69897i	0.809983	+	0.322727i
$213$		−	27.3082i		−	1.87113i
$214$	0.854905	−	2.14565i	0.0584401	−	0.146674i
$215$	1.14766	+	2.48062i	0.0782697	+	0.169177i
$216$	0.797636	+	0.130766i	0.0542723	+	0.00889749i
$217$	−3.83897	−	6.38042i	−0.260606	−	0.433131i
$218$	−0.706029	+	0.599706i	−0.0478183	+	0.0406172i
$219$	−5.02625	−	30.6587i	−0.339642	−	2.07173i
$220$	−6.59886	+	3.49849i	−0.444895	+	0.235868i
$221$	11.6781	+	7.91795i	0.785554	+	0.532619i
$222$	0.838974	+	3.81150i	0.0563083	+	0.255811i
$223$	12.0348	−	1.30886i	0.805907	−	0.0876476i	0.304114	−	0.952636i	$-0.401640\pi$
$223$	12.0348	−	1.30886i	0.805907	−	0.0876476i	0.501793	+	0.864988i	$0.332674\pi$
$224$	1.30850	+	3.28410i	0.0874281	+	0.219428i
$225$	−14.5669	−	6.73938i	−0.971128	−	0.449292i
$226$	−0.126037			−0.00838383
$227$	−12.7824			−0.848395			−0.424197	−	0.905570i	$-0.639444\pi$
$227$	−12.7824			−0.848395			−0.424197	+	0.905570i	$0.639444\pi$
$228$	−7.85257	−	3.63299i	−0.520049	−	0.240600i
$229$	3.67119	+	4.82937i	0.242599	+	0.319133i	0.901237	−	0.433326i	$-0.142660\pi$
$229$	3.67119	+	4.82937i	0.242599	+	0.319133i	−0.658638	+	0.752460i	$0.728867\pi$
$230$	0.461612	−	0.0756774i	0.0304378	−	0.00499002i
$231$	−1.56066	+	28.7848i	−0.102684	+	1.89390i
$232$	0.609205	+	5.60155i	0.0399963	+	0.367760i
$233$	−9.50492	+	11.1901i	−0.622688	+	0.733085i	−0.979579	−	0.201061i	$-0.935561\pi$
$233$	−9.50492	+	11.1901i	−0.622688	+	0.733085i	0.356891	+	0.934146i	$0.383837\pi$
$234$	−0.740367	−	0.562813i	−0.0483993	−	0.0367922i
$235$	−0.0492241	−	0.146092i	−0.00321103	−	0.00952999i
$236$	7.86096	+	8.29871i	0.511705	+	0.540200i
$237$	9.18953	−	19.8628i	0.596924	−	1.29023i
$238$	−1.31226	+	1.93544i	−0.0850612	+	0.125456i
$239$	−19.4491	−	6.55316i	−1.25806	−	0.423889i	−0.390213	−	0.920725i	$-0.627598\pi$
$239$	−19.4491	−	6.55316i	−1.25806	−	0.423889i	−0.867844	+	0.496836i	$0.834495\pi$
$240$	−6.77873	−	0.737232i	−0.437565	−	0.0475881i
$241$	−5.88458	−	8.67910i	−0.379059	−	0.559070i	0.589527	−	0.807749i	$-0.299314\pi$
$241$	−5.88458	−	8.67910i	−0.379059	−	0.559070i	−0.968586	+	0.248679i	$0.920004\pi$
$242$	−2.58017	+	1.02803i	−0.165860	+	0.0660846i
$243$	−8.24080	−	20.6828i	−0.528648	−	1.32681i
$244$	7.58001	−	8.00212i	0.485261	−	0.512283i
$245$	−1.73676	−	0.803511i	−0.110958	−	0.0513344i
$246$	−0.889342	+	0.938867i	−0.0567024	+	0.0598600i
$247$	1.86464	+	2.45290i	0.118644	+	0.156074i
$248$	1.94940	−	0.776711i	0.123787	−	0.0493212i
$249$	19.7256	+	4.34194i	1.25006	+	0.275159i
$250$	−0.885838	−	0.352950i	−0.0560253	−	0.0223225i
$251$	7.63765	+	2.12058i	0.482084	+	0.133850i	0.500064	−	0.865988i	$-0.333310\pi$
$251$	7.63765	+	2.12058i	0.482084	+	0.133850i	−0.0179800	+	0.999838i	$0.505724\pi$
$252$	−8.72163	+	11.4731i	−0.549411	+	0.722738i
$253$	−25.5984	+	1.38790i	−1.60936	+	0.0872567i
$254$	0.783505	+	0.471419i	0.0491615	+	0.0295795i
$255$	−6.45289	−	12.1714i	−0.404096	−	0.762205i
$256$	13.9986	−	3.08132i	0.874910	−	0.192582i
$257$	16.7542	−	5.64514i	1.04510	−	0.352134i	0.256177	−	0.966630i	$-0.417537\pi$
$257$	16.7542	−	5.64514i	1.04510	−	0.352134i	0.788920	+	0.614496i	$0.210641\pi$
$258$	−0.395549	+	1.42464i	−0.0246258	+	0.0886942i
$259$	−20.7522	−	5.76182i	−1.28948	−	0.358022i
$260$	2.03177	+	1.37758i	0.126005	+	0.0854336i
$261$	−27.4784	+	20.8886i	−1.70087	+	1.29297i
$262$	0.0630359	−	1.16263i	0.00389437	−	0.0718275i
$263$	−2.90858	−	4.28983i	−0.179351	−	0.264522i	0.727378	−	0.686237i	$-0.240739\pi$
$263$	−2.90858	−	4.28983i	−0.179351	−	0.264522i	−0.906729	+	0.421715i	$0.861428\pi$
$264$	−7.93379	−	1.74636i	−0.488291	−	0.107481i
$265$	0.948917	+	4.31097i	0.0582915	+	0.264821i
$266$	−0.406524	+	0.309032i	−0.0249256	+	0.0189479i
$267$	1.18506	+	10.8964i	0.0725244	+	0.666851i
$268$	−23.6466	−	7.96746i	−1.44444	−	0.486690i
$269$	1.14659	−	1.08611i	0.0699088	−	0.0662212i	−0.651947	−	0.758264i	$-0.726048\pi$
$269$	1.14659	−	1.08611i	0.0699088	−	0.0662212i	0.721856	+	0.692043i	$0.243289\pi$
$270$	0.0586899	+	0.126856i	0.00357175	+	0.00772021i
$271$	3.64940	−	0.803293i	0.221685	−	0.0487966i	−0.102739	−	0.994708i	$-0.532761\pi$
$271$	3.64940	−	0.803293i	0.221685	−	0.0487966i	0.324424	+	0.945912i	$0.394830\pi$
$272$	22.0070	+	20.8462i	1.33437	+	1.26398i
$273$	8.59873	−	3.97820i	0.520419	−	0.240771i
$274$	2.25422	−	1.04291i	0.136182	−	0.0630047i
$275$	21.9386	+	11.6311i	1.32295	+	0.701382i
$276$	−20.2733	−	12.1980i	−1.22031	−	0.734235i
$277$	−13.1067	+	11.1329i	−0.787503	+	0.668911i	−0.948051	−	0.318117i	$-0.896949\pi$
$277$	−13.1067	+	11.1329i	−0.787503	+	0.668911i	0.160549	+	0.987028i	$0.448674\pi$
$278$	−0.206520	−	0.175420i	−0.0123863	−	0.0105210i
$279$	10.2335	+	7.77934i	0.612666	+	0.465737i
$280$	−0.459059	+	0.677062i	−0.0274340	+	0.0404622i
$281$	−11.3878	+	10.7871i	−0.679338	+	0.643504i	−0.947457	−	0.319882i	$-0.896357\pi$
$281$	−11.3878	+	10.7871i	−0.679338	+	0.643504i	0.268119	+	0.963386i	$0.413598\pi$
$282$	0.0308669	−	0.0774702i	0.00183810	−	0.00461328i
$283$	2.60182	−	9.37091i	0.154662	−	0.557043i	−0.845087	−	0.534629i	$-0.820451\pi$
$283$	2.60182	−	9.37091i	0.154662	−	0.557043i	0.999749	−	0.0224133i	$-0.00713498\pi$
$284$	−12.7821	+	16.8146i	−0.758479	+	0.997762i
$285$	−0.486710	−	2.96880i	−0.0288302	−	0.175856i
$286$	1.09658	+	0.931447i	0.0648424	+	0.0550776i
$287$	−2.27872	−	6.76300i	−0.134509	−	0.399207i
$288$	−4.19693	−	4.43064i	−0.247306	−	0.261078i
$289$	−7.15769	+	43.6600i	−0.421041	+	2.56823i
$290$	−0.742631	+	0.630797i	−0.0436088	+	0.0370417i
$291$	28.9880	−	1.57169i	1.69931	−	0.0921338i
$292$	−11.2556	+	21.2302i	−0.658681	+	1.24240i
$293$	7.14183	−	2.40636i	0.417230	−	0.140581i	−0.102853	−	0.994697i	$-0.532797\pi$
$293$	7.14183	−	2.40636i	0.417230	−	0.140581i	0.520084	+	0.854115i	$0.325901\pi$
$294$	−0.434655	−	0.939491i	−0.0253496	−	0.0547922i
$295$	−0.854409	+	3.88162i	−0.0497456	+	0.225997i
$296$	2.54847	−	5.50842i	0.148127	−	0.320171i
$297$	−2.44592	−	7.25924i	−0.141927	−	0.421224i
$298$	0.385970	−	2.35432i	0.0223587	−	0.136382i
$299$	4.34386	+	7.21954i	0.251212	+	0.417517i
$300$	10.7346	+	20.2477i	0.619764	+	1.16900i
$301$	−5.92358	−	5.61112i	−0.341430	−	0.323419i
$302$	−0.218263	+	0.647781i	−0.0125596	+	0.0372756i
$303$	36.1573	+	19.1694i	2.07718	+	1.10125i
$304$	3.10072	+	5.84858i	0.177839	+	0.335439i
$305$	3.78201	+	0.620029i	0.216557	+	0.0355028i
$306$	0.867786	−	3.94239i	0.0496080	−	0.225371i
$307$	13.0482	−	19.2447i	0.744702	−	1.09835i	−0.246902	−	0.969040i	$-0.579413\pi$
$307$	13.0482	−	19.2447i	0.744702	−	1.09835i	0.991604	−	0.129313i	$-0.0412770\pi$
$308$	14.4342	−	16.9932i	0.822464	−	0.968279i
$309$	10.6442	+	0.577111i	0.605527	+	0.0328307i
$310$	0.300350	+	0.203642i	0.0170587	+	0.0115661i
$311$	−14.8447	−	5.91468i	−0.841768	−	0.335391i	−0.0909133	−	0.995859i	$-0.528979\pi$
$311$	−14.8447	−	5.91468i	−0.841768	−	0.335391i	−0.750854	+	0.660468i	$0.770358\pi$
$312$	0.714293	+	2.57265i	0.0404389	+	0.145648i
$313$	5.39356	+	0.586585i	0.304862	+	0.0331558i	0.259272	−	0.965804i	$-0.416518\pi$
$313$	5.39356	+	0.586585i	0.304862	+	0.0331558i	0.0455906	+	0.998960i	$0.485483\pi$
$314$	−0.378579	−	3.48098i	−0.0213645	−	0.196443i
$315$	−5.00369	−	0.271292i	−0.281926	−	0.0152856i
$316$	−14.9555	+	7.92888i	−0.841310	+	0.446034i
$317$	−3.51292	+	4.62117i	−0.197305	+	0.259551i	−0.884097	−	0.467304i	$-0.845225\pi$
$317$	−3.51292	+	4.62117i	−0.197305	+	0.259551i	0.686791	+	0.726855i	$0.259019\pi$
$318$	−1.11848	+	2.10967i	−0.0627210	+	0.118304i
$319$	44.1984	−	29.9673i	2.47464	−	1.67785i
$320$	3.74469	+	3.54716i	0.209335	+	0.198292i
$321$	−35.8886	−	19.0269i	−2.00310	−	1.06198i
$322$	−1.19651	+	0.719918i	−0.0666790	+	0.0401194i
$323$	−6.26455	+	11.8162i	−0.348569	+	0.657471i
$324$	−3.74001	+	13.4703i	−0.207779	+	0.748351i
$325$		−	8.16109i		−	0.452696i
$326$	−0.323045	−	1.16350i	−0.0178918	−	0.0644405i
$327$	9.14266	+	13.4844i	0.505590	+	0.745690i
$328$	1.98466	−	0.325368i	0.109584	−	0.0179655i
$329$	0.297929	+	0.350749i	0.0164254	+	0.0193374i
$330$	−0.519976	−	1.30504i	−0.0286237	−	0.0718401i
$331$	3.44319	+	4.52944i	0.189255	+	0.248961i	0.880928	−	0.473250i	$-0.156919\pi$
$331$	3.44319	+	4.52944i	0.189255	+	0.248961i	−0.691673	+	0.722211i	$0.743126\pi$
$332$	−10.1134	−	11.9064i	−0.555044	−	0.653449i
$333$	36.9622	−	4.01988i	2.02552	−	0.220288i
$334$	0.162925	+	0.0358625i	0.00891485	+	0.00196231i
$335$	−2.32113	−	8.35995i	−0.126817	−	0.456753i
$336$	19.6132	−	5.44558i	1.06999	−	0.297081i
$337$	5.77532	−	5.47067i	0.314602	−	0.298007i	−0.514062	−	0.857753i	$-0.671860\pi$
$337$	5.77532	−	5.47067i	0.314602	−	0.298007i	0.828664	+	0.559746i	$0.189101\pi$
$338$	−0.304896	+	1.38516i	−0.0165841	+	0.0753425i
$339$	−0.239656	+	2.20360i	−0.0130163	+	0.119683i
$340$	−1.72381	+	10.5147i	−0.0934865	+	0.570242i
$341$	−15.1573	−	12.8747i	−0.820812	−	0.697204i
$342$	0.454483	−	0.755357i	0.0245757	−	0.0408451i
$343$	20.0608	+	1.08767i	1.08318	+	0.0587285i
$344$	1.83050	−	1.39151i	0.0986939	−	0.0750251i
$345$	−0.445385	−	8.21464i	−0.0239787	−	0.442261i
$346$	−1.72672	−	2.03285i	−0.0928290	−	0.109287i
$347$	0.668399	−	0.705620i	0.0358815	−	0.0378797i	−0.707808	−	0.706405i	$-0.750316\pi$
$347$	0.668399	−	0.705620i	0.0358815	−	0.0378797i	0.743689	+	0.668526i	$0.233074\pi$
$348$	49.2839			2.64190
$349$	−1.87751	+	18.5870i	−0.100501	+	0.994937i
$349$	−1.87751	+	18.5870i	−0.100501	+	0.994937i
$350$	1.35256			0.0722972
$351$	−1.73138	+	1.82780i	−0.0924142	+	0.0975605i
$352$	6.11234	+	7.19600i	0.325789	+	0.383548i
$353$	−0.301314	−	5.55740i	−0.0160373	−	0.295791i	−0.995539	−	0.0943536i	$-0.969922\pi$
$353$	−0.301314	−	5.55740i	−0.0160373	−	0.295791i	0.979501	−	0.201437i	$-0.0645612\pi$
$354$	−1.71161	+	1.30113i	−0.0909708	+	0.0691542i
$355$	−7.33323	−	0.397596i	−0.389207	−	0.0211022i
$356$	4.37059	−	7.26398i	0.231641	−	0.384990i
$357$	31.3436	+	26.6235i	1.65888	+	1.40907i
$358$	0.488350	−	2.97880i	0.0258101	−	0.157435i
$359$	0.0924275	−	0.849856i	0.00487813	−	0.0448537i	−0.991446	−	0.130518i	$-0.958336\pi$
$359$	0.0924275	−	0.849856i	0.00487813	−	0.0448537i	0.996324	+	0.0856647i	$0.0273014\pi$
$360$	0.303572	−	1.37914i	0.0159996	−	0.0726871i
$361$	11.6736	−	11.0578i	0.614398	−	0.581988i
$362$	0.137158	−	0.0380816i	0.00720884	−	0.00200153i
$363$	13.0678	+	47.0661i	0.685883	+	2.47033i
$364$	−7.15659	−	1.57528i	−0.375107	−	0.0825673i
$365$	−8.30614	+	0.903347i	−0.434763	+	0.0472834i
$366$	1.34214	+	1.58009i	0.0701548	+	0.0825926i
$367$	7.28252	+	9.57999i	0.380145	+	0.500072i	0.945881	−	0.324515i	$-0.105201\pi$
$367$	7.28252	+	9.57999i	0.380145	+	0.500072i	−0.565736	+	0.824586i	$0.691408\pi$
$368$	6.70020	+	16.8162i	0.349272	+	0.876607i
$369$	7.97582	+	9.38986i	0.415204	+	0.488816i
$370$	1.03574	−	0.169801i	0.0538454	−	0.00882751i
$371$	−7.39485	−	10.9066i	−0.383922	−	0.566242i
$372$	−4.91031	−	17.6853i	−0.254588	−	0.916942i
$373$		−	2.16780i		−	0.112244i	−0.998424	−	0.0561222i	$-0.982126\pi$
$373$		−	2.16780i		−	0.112244i	0.998424	−	0.0561222i	$-0.0178736\pi$
$374$	−1.67076	+	6.01754i	−0.0863931	+	0.311160i
$375$	−7.85532	+	14.8167i	−0.405647	+	0.765131i
$376$	−0.111125	+	0.0668619i	−0.00573085	+	0.00344814i
$377$	−15.5061	−	8.22083i	−0.798607	−	0.423394i
$378$	−0.302925	−	0.286946i	−0.0155808	−	0.0147589i
$379$	22.9609	−	15.5679i	1.17942	−	0.799667i	0.195928	−	0.980618i	$-0.437228\pi$
$379$	22.9609	−	15.5679i	1.17942	−	0.799667i	0.983492	+	0.180951i	$0.0579176\pi$
$380$	−1.08992	+	2.05580i	−0.0559115	+	0.105460i
$381$	9.73203	−	12.8023i	0.498587	−	0.655880i
$382$	−0.388801	+	0.206129i	−0.0198928	+	0.0105465i
$383$	−7.08329	−	0.384045i	−0.361939	−	0.0196238i	−0.127727	−	0.991809i	$-0.540768\pi$
$383$	−7.08329	−	0.384045i	−0.361939	−	0.0196238i	−0.234212	+	0.972186i	$0.575251\pi$
$384$	1.25388	+	11.5292i	0.0639869	+	0.588349i
$385$	7.70701	+	0.838188i	0.392786	+	0.0427180i
$386$	0.539280	+	1.94231i	0.0274487	+	0.0988611i
$387$	13.0851	+	5.21358i	0.665153	+	0.265021i
$388$	−18.5845	−	12.6006i	−0.943487	−	0.639700i
$389$	10.0304	+	0.543831i	0.508560	+	0.0275733i	0.306634	−	0.951827i	$-0.400797\pi$
$389$	10.0304	+	0.543831i	0.508560	+	0.0275733i	0.201926	+	0.979401i	$0.435280\pi$
$390$	−0.298906	+	0.351899i	−0.0151357	+	0.0178191i
$391$	−20.5239	+	30.2704i	−1.03794	+	1.53084i
$392$	−0.346070	+	1.57221i	−0.0174791	+	0.0794086i
$393$	−20.2073	−	3.31282i	−1.01933	−	0.167110i
$394$	−0.535629	−	1.01030i	−0.0269846	−	0.0508983i
$395$	−5.20008	−	2.75691i	−0.261645	−	0.138715i
$396$	−12.2900	+	36.4754i	−0.617595	+	1.83296i
$397$	3.07418	+	2.91202i	0.154289	+	0.146150i	0.760950	−	0.648810i	$-0.224733\pi$
$397$	3.07418	+	2.91202i	0.154289	+	0.146150i	−0.606662	+	0.794960i	$0.707492\pi$
$398$	−1.15190	−	2.17271i	−0.0577395	−	0.108908i
$399$	4.63006	+	7.69521i	0.231793	+	0.385243i
$400$	2.83662	−	17.3026i	0.141831	−	0.865130i
$401$	1.84067	+	5.46291i	0.0919186	+	0.272805i	0.983744	−	0.179574i	$-0.0574720\pi$
$401$	1.84067	+	5.46291i	0.0919186	+	0.272805i	−0.891826	+	0.452379i	$0.850575\pi$
$402$	1.97068	−	4.25956i	0.0982887	−	0.212447i
$403$	−1.40509	+	6.38338i	−0.0699924	+	0.317979i
$404$	−13.2906	−	28.7273i	−0.661234	−	1.42923i
$405$	−4.60642	+	1.55208i	−0.228895	+	0.0771236i
$406$	1.36246	−	2.56987i	0.0676177	−	0.127540i
$407$	−57.4361	+	3.11410i	−2.84700	+	0.154360i
$408$	−8.83292	+	7.50275i	−0.437295	+	0.371441i
$409$	−3.00082	+	18.3042i	−0.148381	+	0.905085i	0.802754	+	0.596310i	$0.203367\pi$
$409$	−3.00082	+	18.3042i	−0.148381	+	0.905085i	−0.951135	+	0.308775i	$0.900081\pi$
$410$	0.239171	+	0.252489i	0.0118118	+	0.0124696i
$411$	−13.9478	−	41.3955i	−0.687992	−	2.04189i
$412$	−6.28385	−	5.33755i	−0.309583	−	0.262962i
$413$	−1.91951	−	11.7085i	−0.0944528	−	0.576137i
$414$	1.45885	−	1.91908i	0.0716986	−	0.0943178i
$415$	1.45316	−	5.23381i	0.0713328	−	0.256918i
$416$	1.14858	−	2.88271i	0.0563135	−	0.141336i
$417$	−3.45971	+	3.27721i	−0.169423	+	0.160486i
$418$	−0.765355	+	1.12881i	−0.0374347	+	0.0552121i
$419$	−24.5722	−	18.6793i	−1.20043	−	0.912544i	−0.202658	−	0.979250i	$-0.564958\pi$
$419$	−24.5722	−	18.6793i	−1.20043	−	0.912544i	−0.997773	+	0.0667061i	$0.978751\pi$
$420$	5.45321	+	4.63200i	0.266089	+	0.226018i
$421$	−13.2472	+	11.2523i	−0.645631	+	0.548404i	−0.909264	−	0.416219i	$-0.863355\pi$
$421$	−13.2472	+	11.2523i	−0.645631	+	0.548404i	0.263633	+	0.964623i	$0.415079\pi$
$422$	−0.188956	−	0.113691i	−0.00919821	−	0.00553438i
$423$	−0.701913	−	0.372131i	−0.0341282	−	0.0180936i
$424$	3.37023	−	1.55923i	0.163673	−	0.0757231i
$425$	32.1500	−	14.8742i	1.55950	−	0.721504i
$426$	−2.88416	−	2.73202i	−0.139738	−	0.132367i
$427$	−11.1733	+	2.45942i	−0.540712	+	0.119020i
$428$	13.1919	+	28.5138i	0.637654	+	1.37827i
$429$	18.3704	−	17.4014i	0.886931	−	0.840145i
$430$	0.376807	+	0.126961i	0.0181713	+	0.00612261i
$431$	−4.09432	−	37.6466i	−0.197216	−	1.81337i	−0.506319	−	0.862346i	$-0.668994\pi$
$431$	−4.09432	−	37.6466i	−0.197216	−	1.81337i	0.309103	−	0.951029i	$-0.399971\pi$
$432$	−4.30606	+	3.27338i	−0.207175	+	0.157491i
$433$	3.94511	+	17.9228i	0.189590	+	0.861316i	0.971334	+	0.237717i	$0.0763991\pi$
$433$	3.94511	+	17.9228i	0.189590	+	0.861316i	−0.781744	+	0.623599i	$0.785670\pi$
$434$	−1.05793	−	0.232869i	−0.0507824	−	0.0111781i
$435$	9.61664	+	14.1835i	0.461083	+	0.680046i
$436$	0.682186	−	12.5822i	0.0326708	−	0.602577i
$437$	−6.35808	+	4.83328i	−0.304148	+	0.231207i
$438$	−3.74087	−	2.53637i	−0.178746	−	0.121193i
$439$	26.8649	+	7.45899i	1.28219	+	0.355998i	0.840814	−	0.541324i	$-0.182077\pi$
$439$	26.8649	+	7.45899i	1.28219	+	0.355998i	0.441376	+	0.897322i	$0.354491\pi$
$440$	−0.584472	+	2.10508i	−0.0278636	+	0.100356i
$441$	−9.34546	+	3.14885i	−0.445022	+	0.149945i
$442$	2.00458	−	0.441240i	0.0953479	−	0.0209877i
$443$	4.86547	+	9.17726i	0.231166	+	0.436025i	0.971774	−	0.235912i	$-0.0758076\pi$
$443$	4.86547	+	9.17726i	0.231166	+	0.436025i	−0.740609	+	0.671936i	$0.765463\pi$
$444$	−45.4880	−	27.3692i	−2.15876	−	1.29889i
$445$	2.94333	−	0.159583i	0.139527	−	0.00756495i
$446$	1.06577	−	1.40199i	0.0504656	−	0.0663863i
$447$	−40.4285	−	11.2249i	−1.91220	−	0.530921i
$448$	−14.3041	−	5.69926i	−0.675803	−	0.269265i
$449$	23.8278	+	5.24490i	1.12450	+	0.247522i	0.738023	−	0.674775i	$-0.235759\pi$
$449$	23.8278	+	5.24490i	1.12450	+	0.247522i	0.386481	+	0.922297i	$0.373691\pi$
$450$	−2.16911	+	0.864253i	−0.102253	+	0.0407413i
$451$	−11.5346	−	15.1735i	−0.543144	−	0.714494i
$452$	1.17900	−	1.24465i	0.0554555	−	0.0585436i
$453$	10.9107	+	5.04781i	0.512628	+	0.237167i
$454$	−1.27880	+	1.35001i	−0.0600169	+	0.0633591i
$455$	−0.943093	−	2.36699i	−0.0442129	−	0.110966i
$456$	−2.35110	+	0.936766i	−0.110101	+	0.0438681i
$457$	11.3222	+	16.6989i	0.529628	+	0.781143i	0.994556	−	0.104206i	$-0.0332300\pi$
$457$	11.3222	+	16.6989i	0.529628	+	0.781143i	−0.464928	+	0.885349i	$0.653920\pi$
$458$	0.877333	+	0.0954157i	0.0409951	+	0.00445849i
$459$	−10.3560	−	3.48935i	−0.483378	−	0.162869i
$460$	−3.57077	+	5.26649i	−0.166488	+	0.245552i
$461$	−4.17543	+	9.02504i	−0.194469	+	0.420338i	−0.980140	−	0.198306i	$-0.936456\pi$
$461$	−4.17543	+	9.02504i	−0.194469	+	0.420338i	0.785671	+	0.618645i	$0.212318\pi$
$462$	2.88397	+	3.04457i	0.134174	+	0.141646i
$463$	5.03175	+	14.9337i	0.233845	+	0.694027i	0.998755	+	0.0498899i	$0.0158870\pi$
$463$	5.03175	+	14.9337i	0.233845	+	0.694027i	−0.764910	+	0.644138i	$0.777216\pi$
$464$	−30.0177	−	22.8189i	−1.39354	−	1.05934i
$465$	4.13155	−	4.86404i	0.191596	−	0.225564i
$466$	0.230929	+	2.12336i	0.0106976	+	0.0983627i
$467$	−2.22489	+	41.0357i	−0.102956	+	1.89890i	0.257731	+	0.966217i	$0.417025\pi$
$467$	−2.22489	+	41.0357i	−0.102956	+	1.89890i	−0.360686	+	0.932687i	$0.617458\pi$
$468$	12.4837	−	2.04659i	0.577058	−	0.0946039i
$469$	15.6741	+	20.6189i	0.723762	+	0.952093i
$470$	−0.0203541	−	0.00941680i	−0.000938864	−	0.000434365i
$471$	−61.5807			−2.83749
$472$	3.34360			0.153902
$473$	−19.7773	−	9.14993i	−0.909359	−	0.420714i
$474$	−1.17846	−	2.95771i	−0.0541284	−	0.135852i
$475$	7.69051	−	0.836394i	0.352865	−	0.0383764i
$476$	−6.83769	−	31.0639i	−0.313405	−	1.42381i
$477$	18.8283	+	12.7659i	0.862087	+	0.584510i
$478$	−2.63787	+	1.39851i	−0.120654	+	0.0639665i
$479$	3.77724	+	23.0402i	0.172587	+	1.05273i	0.921018	+	0.389520i	$0.127359\pi$
$479$	3.77724	+	23.0402i	0.172587	+	1.05273i	−0.748431	+	0.663212i	$0.769193\pi$
$480$	−2.30923	+	1.96148i	−0.105402	+	0.0895289i
$481$	9.74649	+	16.1988i	0.444402	+	0.738601i
$482$	−1.50536	−	0.246791i	−0.0685672	−	0.0112410i
$483$	10.3118	+	22.2885i	0.469202	+	1.01416i
$484$	13.9838	−	35.0967i	0.635628	−	1.59531i
$485$		−	7.80720i		−	0.354507i
$486$	−3.00886	−	1.19884i	−0.136485	−	0.0543805i
$487$	−6.37578	−	28.9655i	−0.288914	−	1.31255i	−0.867707	−	0.497076i	$-0.834407\pi$
$487$	−6.37578	−	28.9655i	−0.288914	−	1.31255i	0.578793	−	0.815474i	$-0.303524\pi$
$488$	−0.174549	−	3.21938i	−0.00790148	−	0.145734i
$489$	−20.9568	+	3.43569i	−0.947698	+	0.155367i
$490$	−0.258615	+	0.103042i	−0.0116830	+	0.00465495i
$491$	−3.51512	+	0.382292i	−0.158635	+	0.0172526i	−0.187092	−	0.982342i	$-0.559906\pi$
$491$	−3.51512	+	0.382292i	−0.158635	+	0.0172526i	0.0284568	+	0.999595i	$0.490941\pi$
$492$	−0.952353	−	17.5651i	−0.0429354	−	0.791897i
$493$	4.12431	−	76.0684i	0.185749	−	3.42595i
$494$	0.445609	+	0.0484629i	0.0200489	+	0.00218045i
$495$	−12.8954	+	3.58039i	−0.579605	+	0.160927i
$496$	−5.19770	+	13.0453i	−0.233384	+	0.585749i
$497$	20.7756	−	7.00013i	0.931915	−	0.313999i
$498$	2.43200	−	1.64894i	0.108981	−	0.0738906i
$499$	−6.59310	+	19.5676i	−0.295148	+	0.875968i	0.692793	+	0.721136i	$0.256380\pi$
$499$	−6.59310	+	19.5676i	−0.295148	+	0.875968i	−0.987941	+	0.154831i	$0.950517\pi$
$500$	11.7720	−	5.44631i	0.526460	−	0.243566i
$501$	0.936811	−	2.78036i	0.0418536	−	0.124217i
$502$	0.988065	−	0.594499i	0.0440995	−	0.0265338i
$503$	16.1501	−	0.875636i	0.720099	−	0.0390427i	0.309553	−	0.950882i	$-0.399821\pi$
$503$	16.1501	−	0.875636i	0.720099	−	0.0390427i	0.410547	+	0.911840i	$0.365338\pi$
$504$	0.682002	+	4.16003i	0.0303788	+	0.185302i
$505$	5.67409	−	9.43041i	0.252494	−	0.419648i
$506$	−2.41438	+	2.84242i	−0.107332	+	0.126361i
$507$	23.6381	+	7.96459i	1.04980	+	0.353720i
$508$	−11.9847	+	3.32753i	−0.531733	+	0.147635i
$509$		−	13.3254i		−	0.590638i	−0.955399	−	0.295319i	$-0.904574\pi$
$509$		−	13.3254i		−	0.590638i	0.955399	−	0.295319i	$-0.0954259\pi$
$510$	−1.93106	−	0.536156i	−0.0855087	−	0.0237414i
$511$	22.0362	−	11.6829i	0.974826	−	0.516820i
$512$	5.74891	−	9.55476i	0.254068	−	0.422265i
$513$	−1.89984	−	1.44422i	−0.0838802	−	0.0637641i
$514$	1.07994	−	2.33425i	0.0476341	−	0.102960i
$515$	0.309950	−	2.84994i	0.0136580	−	0.125583i
$516$	−10.3687	−	17.2329i	−0.456455	−	0.758635i
$517$	1.05315	+	0.633660i	0.0463175	+	0.0278683i
$518$	−2.68466	+	1.61531i	−0.117957	+	0.0709726i
$519$	−38.8253	+	26.3242i	−1.70424	+	1.15551i
$520$	0.701248	−	0.154356i	0.0307517	−	0.00676897i
$521$	−31.8950	−	5.22893i	−1.39735	−	0.229083i	−0.584421	−	0.811451i	$-0.698678\pi$
$521$	−31.8950	−	5.22893i	−1.39735	−	0.229083i	−0.812926	+	0.582367i	$0.802127\pi$
$522$	−0.542903	+	4.99191i	−0.0237622	+	0.218490i
$523$	−22.1889	−	23.4245i	−0.970251	−	1.02428i	−0.999695	−	0.0247151i	$-0.992132\pi$
$523$	−22.1889	−	23.4245i	−0.970251	−	1.02428i	0.0294436	−	0.999566i	$-0.490626\pi$
$524$	10.8917	+	11.4982i	0.475806	+	0.502302i
$525$	2.57186	−	23.6479i	0.112245	−	1.03208i
$526$	−0.744056	−	0.121982i	−0.0324424	−	0.00531866i
$527$	−27.7077	+	6.09893i	−1.20697	+	0.265674i
$528$	44.9960	−	30.5081i	1.95820	−	1.32769i
$529$	0.994153	−	0.598162i	0.0432240	−	0.0260070i
$530$	0.550237	+	0.331066i	0.0239008	+	0.0143806i
$531$	10.5598	+	17.5505i	0.458256	+	0.761627i
$532$	0.751005	−	6.90538i	0.0325602	−	0.299386i
$533$	−2.63032	+	5.68535i	−0.113932	+	0.246260i
$534$	1.26938	+	0.964961i	0.0549316	+	0.0417580i
$535$	−5.63192	+	9.36033i	−0.243489	+	0.404682i
$536$	−6.44865	+	3.41886i	−0.278539	+	0.147672i
$537$	−51.1523	−	14.2024i	−2.20738	−	0.612877i
$538$		−	0.229756i		−	0.00990546i
$539$	14.7007	−	4.08162i	0.633202	−	0.175808i
$540$	−1.80176	−	0.607082i	−0.0775353	−	0.0261247i
$541$	20.6915	−	24.3599i	0.889597	−	1.04731i	−0.108983	−	0.994044i	$-0.534759\pi$
$541$	20.6915	−	24.3599i	0.889597	−	1.04731i	0.998580	−	0.0532710i	$-0.0169647\pi$
$542$	0.280260	−	0.465795i	0.0120382	−	0.0200076i
$543$	−0.405010	−	2.47045i	−0.0173806	−	0.106017i
$544$	13.4496	−	0.729215i	0.576646	−	0.0312648i
$545$	3.75416	−	2.25880i	0.160810	−	0.0967564i
$546$	0.440093	−	1.30615i	0.0188342	−	0.0558980i
$547$	−21.8223	+	10.0961i	−0.933056	+	0.431678i	−0.826695	−	0.562650i	$-0.809782\pi$
$547$	−21.8223	+	10.0961i	−0.933056	+	0.431678i	−0.106361	+	0.994328i	$0.533920\pi$
$548$	−10.7878	+	32.0171i	−0.460832	+	1.36770i
$549$	16.3472	−	11.0837i	0.697681	−	0.473039i
$550$	3.42324	−	1.15342i	0.145968	−	0.0491822i
$551$	6.15766	−	15.4546i	0.262325	−	0.658386i
$552$	−6.66849	+	1.85150i	−0.283830	+	0.0788050i
$553$	17.4669	+	1.89964i	0.742770	+	0.0807811i
$554$	−0.135440	+	2.49804i	−0.00575428	+	0.106131i
$555$	−0.999328	−	18.4315i	−0.0424191	−	0.782375i
$556$	3.66421	−	0.398507i	0.155397	−	0.0169005i
$557$	−27.9582	+	11.1396i	−1.18463	+	0.471998i	−0.877456	−	0.479656i	$-0.840761\pi$
$557$	−27.9582	+	11.1396i	−1.18463	+	0.471998i	−0.307170	+	0.951655i	$0.599382\pi$
$558$	1.84542	−	0.302541i	0.0781227	−	0.0128076i
$559$	0.387743	+	7.15151i	0.0163998	+	0.302477i
$560$	−1.17677	−	5.34613i	−0.0497277	−	0.225915i
$561$	102.033	+	40.6536i	4.30783	+	1.71639i
$562$			2.28190i			0.0962563i
$563$	13.1117	−	32.9079i	0.552593	−	1.38690i	−0.341864	−	0.939749i	$-0.611058\pi$
$563$	13.1117	−	32.9079i	0.552593	−	1.38690i	0.894457	−	0.447154i	$-0.147562\pi$
$564$	0.476302	+	1.02951i	0.0200559	+	0.0433502i
$565$	0.588256	+	0.0964397i	0.0247481	+	0.00405725i
$566$	−0.729412	−	1.21229i	−0.0306595	−	0.0509565i
$567$	11.0595	−	9.39399i	0.464453	−	0.394510i
$568$	0.999517	+	6.09678i	0.0419388	+	0.255815i
$569$	21.7040	−	11.5068i	0.909881	−	0.482388i	0.0534036	−	0.998573i	$-0.482993\pi$
$569$	21.7040	−	11.5068i	0.909881	−	0.482388i	0.856477	+	0.516185i	$0.172648\pi$
$570$	−0.362242	−	0.245606i	−0.0151726	−	0.0102873i
$571$	1.61457	+	7.33508i	0.0675677	+	0.306963i	0.998269	−	0.0588175i	$-0.0187330\pi$
$571$	1.61457	+	7.33508i	0.0675677	+	0.306963i	−0.930701	+	0.365781i	$0.880802\pi$
$572$	−19.4563	+	2.11600i	−0.813508	+	0.0884743i
$573$	2.86463	+	7.18968i	0.119672	+	0.300353i
$574$	−0.942247	−	0.435930i	−0.0393286	−	0.0181954i
$575$	21.1541			0.882187
$576$	26.5813			1.10755
$577$	−0.620636	−	0.287137i	−0.0258374	−	0.0119537i	0.406928	−	0.913460i	$-0.366600\pi$
$577$	−0.620636	−	0.287137i	−0.0258374	−	0.0119537i	−0.432765	+	0.901507i	$0.642462\pi$
$578$	3.89507	+	5.12387i	0.162013	+	0.213125i
$579$	34.9845	−	5.73541i	1.45391	−	0.238356i
$580$	0.717553	−	13.2345i	0.0297948	−	0.549532i
$581$	1.75315	+	16.1199i	0.0727328	+	0.668767i
$582$	2.73408	−	3.21881i	0.113331	−	0.133424i
$583$	−28.0168	−	21.2978i	−1.16034	−	0.882065i
$584$	2.24430	+	6.66085i	0.0928698	+	0.275628i
$585$	3.02490	+	3.19335i	0.125064	+	0.132029i
$586$	0.460348	−	0.995026i	0.0190168	−	0.0411042i
$587$	13.7790	−	20.3224i	0.568719	−	0.838797i	−0.429205	−	0.903207i	$-0.641206\pi$
$587$	13.7790	−	20.3224i	0.568719	−	0.838797i	0.997924	+	0.0644099i	$0.0205165\pi$
$588$	13.3437	+	4.49603i	0.550287	+	0.185413i
$589$	−6.15931	−	0.669866i	−0.253790	−	0.0276013i
$590$	0.324479	+	0.478571i	0.0133586	+	0.0197024i
$591$	−18.6824	+	7.44376i	−0.768493	+	0.306195i
$592$	15.0335	+	37.7313i	0.617874	+	1.55075i
$593$	−15.3371	+	16.1912i	−0.629819	+	0.664892i	−0.960316	−	0.278915i	$-0.910025\pi$
$593$	−15.3371	+	16.1912i	−0.629819	+	0.664892i	0.330497	+	0.943807i	$0.392784\pi$
$594$	−1.01138	−	0.467916i	−0.0414976	−	0.0191988i
$595$	7.60571	−	8.02925i	0.311804	−	0.329167i
$596$	19.6391	+	25.8349i	0.804451	+	1.05824i
$597$	−40.1777	+	16.0082i	−1.64436	+	0.655174i
$598$	1.19707	+	0.263495i	0.0489518	+	0.0107751i
$599$	−18.8871	−	7.52530i	−0.771705	−	0.307475i	−0.0491524	−	0.998791i	$-0.515652\pi$
$599$	−18.8871	−	7.52530i	−0.771705	−	0.307475i	−0.722553	+	0.691316i	$0.757031\pi$
$600$	6.45913	+	1.79337i	0.263693	+	0.0732140i
$601$	19.9459	−	26.2384i	0.813612	−	1.07029i	−0.182588	−	0.983190i	$-0.558447\pi$
$601$	19.9459	−	26.2384i	0.813612	−	1.07029i	0.996200	−	0.0870984i	$-0.0277595\pi$
$602$	−1.18524	+	0.0642616i	−0.0483066	+	0.00261911i
$603$	−38.3117	−	23.0514i	−1.56017	−	0.938725i
$604$	−4.35534	−	8.21504i	−0.177216	−	0.334265i
$605$	12.8292	−	2.82391i	0.521580	−	0.114808i
$606$	5.64188	−	1.90097i	0.229186	−	0.0772217i
$607$	0.297627	−	1.07195i	0.0120803	−	0.0435093i	−0.957264	−	0.289215i	$-0.906606\pi$
$607$	0.297627	−	1.07195i	0.0120803	−	0.0435093i	0.969345	+	0.245705i	$0.0790196\pi$
$608$	2.83420	+	0.786912i	0.114942	+	0.0319135i
$609$	−42.3404	−	28.7075i	−1.71572	−	1.16329i
$610$	0.443851	−	0.337407i	0.0179710	−	0.0136612i
$611$	0.0218697	−	0.403363i	0.000884755	−	0.0163183i
$612$	30.8148	+	45.4485i	1.24562	+	1.83715i
$613$	−20.5103	−	4.51466i	−0.828404	−	0.182346i	−0.219523	−	0.975607i	$-0.570450\pi$
$613$	−20.5103	−	4.51466i	−0.828404	−	0.182346i	−0.608881	+	0.793262i	$0.708381\pi$
$614$	−0.727134	−	3.30340i	−0.0293447	−	0.133314i
$615$	4.86926	−	3.70151i	0.196347	−	0.149259i
$616$	−0.705129	−	6.48355i	−0.0284105	−	0.261230i
$617$	−26.0581	−	8.78000i	−1.04906	−	0.353470i	−0.258601	−	0.965984i	$-0.583261\pi$
$617$	−26.0581	−	8.78000i	−1.04906	−	0.353470i	−0.790459	+	0.612515i	$0.790158\pi$
$618$	1.12584	−	1.06645i	0.0452878	−	0.0428989i
$619$	4.02899	+	8.70852i	0.161939	+	0.350025i	0.971511	−	0.236996i	$-0.0761628\pi$
$619$	4.02899	+	8.70852i	0.161939	+	0.350025i	−0.809572	+	0.587021i	$0.800301\pi$
$620$	−4.82063	+	1.06110i	−0.193601	+	0.0426149i
$621$	−4.73777	−	4.48786i	−0.190120	−	0.180091i
$622$	−2.10980	+	0.976099i	−0.0845954	+	0.0391380i
$623$	−7.98605	+	3.69474i	−0.319954	+	0.148027i
$624$	−15.7860	−	8.36919i	−0.631944	−	0.335036i
$625$	−15.5287	−	9.34334i	−0.621150	−	0.373734i
$626$	0.601545	−	0.510957i	0.0240426	−	0.0204219i
$627$	18.2807	+	15.5278i	0.730060	+	0.620119i
$628$	37.9172	+	28.8239i	1.51306	+	1.15020i
$629$	−46.0503	+	67.9190i	−1.83614	+	2.70811i
$630$	−0.529241	+	0.501324i	−0.0210855	+	0.0199732i
$631$	1.40524	−	3.52690i	0.0559419	−	0.140404i	−0.898349	−	0.439282i	$-0.855233\pi$
$631$	1.40524	−	3.52690i	0.0559419	−	0.140404i	0.954291	+	0.298878i	$0.0966124\pi$
$632$	−1.32463	+	4.77089i	−0.0526910	+	0.189776i
$633$	−2.34704	+	3.08748i	−0.0932866	+	0.122716i
$634$	0.136619	+	0.833337i	0.00542582	+	0.0330960i
$635$	−3.29617	−	2.79979i	−0.130804	−	0.111106i
$636$	−10.3710	−	30.7801i	−0.411237	−	1.22051i
$637$	−3.44836	−	3.64039i	−0.136629	−	0.144238i
$638$	1.25679	−	7.66606i	0.0497567	−	0.303502i
$639$	−28.8452	+	24.5014i	−1.14110	+	0.969259i
$640$	3.11427	−	0.168851i	0.123102	−	0.00667441i
$641$	10.1523	−	19.1494i	0.400993	−	0.756354i	−0.597987	−	0.801506i	$-0.704032\pi$
$641$	10.1523	−	19.1494i	0.400993	−	0.756354i	0.998980	+	0.0451522i	$0.0143773\pi$
$642$	−5.59996	+	1.88685i	−0.221013	+	0.0744679i
$643$	17.7074	+	38.2740i	0.698313	+	1.50938i	0.853277	+	0.521458i	$0.174612\pi$
$643$	17.7074	+	38.2740i	0.698313	+	1.50938i	−0.154964	+	0.987920i	$0.549526\pi$
$644$	4.08325	−	18.5504i	0.160902	−	0.730987i
$645$	2.93626	−	6.34662i	0.115615	−	0.249898i
$646$	0.621238	+	1.84377i	0.0244423	+	0.0725421i
$647$	−1.14753	+	6.99961i	−0.0451139	+	0.275183i	−0.999744	−	0.0226103i	$-0.992802\pi$
$647$	−1.14753	+	6.99961i	−0.0451139	+	0.275183i	0.954630	+	0.297793i	$0.0962506\pi$
$648$	2.10822	+	3.50388i	0.0828186	+	0.137646i
$649$	−14.8428	−	27.9966i	−0.582633	−	1.09896i
$650$	−0.861933	−	0.816467i	−0.0338078	−	0.0320245i
$651$	−6.08307	+	18.0539i	−0.238414	+	0.707589i
$652$	14.5119	+	7.69372i	0.568330	+	0.301310i
$653$	9.20742	+	17.3670i	0.360314	+	0.679624i	0.995707	−	0.0925649i	$-0.0295066\pi$
$653$	9.20742	+	17.3670i	0.360314	+	0.679624i	−0.635393	+	0.772189i	$0.719162\pi$
$654$	2.33882	+	0.383431i	0.0914552	+	0.0149933i
$655$	−1.18382	+	5.37815i	−0.0462557	+	0.210142i
$656$	−7.55275	+	11.1395i	−0.294885	+	0.434923i
$657$	−27.8747	+	32.8166i	−1.08750	+	1.28030i
$658$	0.0668504	+	0.00362452i	0.00260610	+	0.000141299i
$659$	8.51456	+	5.77302i	0.331680	+	0.224885i	0.715647	−	0.698462i	$-0.246132\pi$
$659$	8.51456	+	5.77302i	0.331680	+	0.224885i	−0.383967	+	0.923347i	$0.625442\pi$
$660$	17.7518	+	7.07296i	0.690988	+	0.275315i
$661$	−10.3135	−	37.1458i	−0.401148	−	1.44480i	−0.838197	−	0.545367i	$-0.816390\pi$
$661$	−10.3135	−	37.1458i	−0.401148	−	1.44480i	0.437049	−	0.899438i	$-0.356024\pi$
$662$	0.822847	+	0.0894901i	0.0319809	+	0.00347813i
$663$	−3.90291	−	35.8867i	−0.151576	−	1.39372i
$664$	−4.56282	−	0.247389i	−0.177072	−	0.00960056i
$665$	2.13385	−	1.13130i	0.0827471	−	0.0438698i
$666$	3.27328	−	4.30593i	0.126837	−	0.166851i
$667$	21.3090	−	40.1930i	0.825087	−	1.55628i
$668$	−1.87822	+	1.27347i	−0.0726706	+	0.0492719i
$669$	−22.4857	−	21.2996i	−0.869346	−	0.823488i
$670$	−1.11515	−	0.591215i	−0.0430820	−	0.0228406i
$671$	−26.1816	+	15.7529i	−1.01073	+	0.608135i
$672$	4.23660	−	7.99108i	0.163430	−	0.308262i
$673$	5.40047	−	19.4507i	0.208173	−	0.749770i	−0.783545	−	0.621335i	$-0.786591\pi$
$673$	5.40047	−	19.4507i	0.208173	−	0.749770i	0.991718	−	0.128435i	$-0.0409955\pi$
$674$		−	1.15727i		−	0.0445763i
$675$	1.69105	+	6.09062i	0.0650886	+	0.234428i
$676$	−10.8268	−	15.9683i	−0.416414	−	0.614164i
$677$	4.46904	−	0.732662i	0.171759	−	0.0281585i	−0.0752886	−	0.997162i	$-0.523988\pi$
$677$	4.46904	−	0.732662i	0.171759	−	0.0281585i	0.247048	+	0.969003i	$0.420540\pi$
$678$	0.208757	+	0.245768i	0.00801728	+	0.00943867i
$679$	8.62644	+	21.6507i	0.331052	+	0.830879i
$680$	1.88615	+	2.48119i	0.0723306	+	0.0951492i
$681$	21.1717	+	24.9253i	0.811302	+	0.955138i
$682$	−2.87615	+	0.312800i	−0.110134	+	0.0119777i
$683$	1.23638	+	0.272148i	0.0473089	+	0.0104135i	0.238562	−	0.971127i	$-0.423324\pi$
$683$	1.23638	+	0.272148i	0.0473089	+	0.0104135i	−0.191253	+	0.981541i	$0.561255\pi$
$684$	3.20798	+	11.5541i	0.122660	+	0.441783i
$685$	−11.3192	+	3.14277i	−0.432485	+	0.120079i
$686$	2.12184	−	2.00991i	0.0810121	−	0.0767388i
$687$	3.33646	−	15.1577i	0.127294	−	0.578303i
$688$	−1.66364	+	15.2969i	−0.0634257	+	0.583190i
$689$	−1.87127	+	11.4142i	−0.0712897	+	0.434848i
$690$	−0.912147	−	0.774785i	−0.0347249	−	0.0294956i
$691$	10.9118	−	18.1356i	0.415106	−	0.689911i	−0.576800	−	0.816885i	$-0.695699\pi$
$691$	10.9118	−	18.1356i	0.415106	−	0.689911i	0.991906	+	0.126974i	$0.0405265\pi$
$692$	36.2276	+	1.96420i	1.37717	+	0.0746678i
$693$	31.8051	−	24.1776i	1.20818	−	0.918432i
$694$	−0.00765488	−	0.141186i	−0.000290575	−	0.00535934i
$695$	0.829674	+	0.976768i	0.0314713	+	0.0370509i
$696$	9.91384	−	10.4659i	0.375783	−	0.396709i
$697$	−27.1910			−1.02993
$698$	1.77523	+	2.05780i	0.0671934	+	0.0778890i
$699$	37.5635			1.42078
$700$	−12.6524	+	13.3570i	−0.478215	+	0.504846i
$701$	−8.82436	−	10.3888i	−0.333291	−	0.392381i	0.569833	−	0.821761i	$-0.307008\pi$
$701$	−8.82436	−	10.3888i	−0.333291	−	0.392381i	−0.903124	+	0.429380i	$0.858732\pi$
$702$	0.0198287	+	0.365719i	0.000748387	+	0.0138032i
$703$	−14.2659	+	10.8446i	−0.538048	+	0.409013i
$704$	−41.0629	−	2.22637i	−1.54762	−	0.0839094i
$705$	−0.203345	+	0.337961i	−0.00765840	+	0.0127284i
$706$	−0.617090	−	0.524161i	−0.0232245	−	0.0197271i
$707$	−5.31526	+	32.4217i	−0.199901	+	1.21934i
$708$	3.16199	−	29.0740i	0.118835	−	1.09267i
$709$	−5.19264	+	23.5904i	−0.195014	+	0.885955i	0.772872	+	0.634563i	$0.218820\pi$
$709$	−5.19264	+	23.5904i	−0.195014	+	0.885955i	−0.967885	+	0.251393i	$0.919111\pi$
$710$	−0.775637	+	0.734722i	−0.0291091	+	0.0275736i
$711$	−29.2258	+	8.11449i	−1.09605	+	0.304317i
$712$	−0.663398	−	2.38934i	−0.0248619	−	0.0895444i
$713$	−16.5462	−	3.64209i	−0.619659	−	0.136397i
$714$	5.94758	−	0.646838i	0.222583	−	0.0242073i
$715$	−4.40542	−	5.18646i	−0.164753	−	0.193963i
$716$	24.8485	+	32.6876i	0.928631	+	1.22159i
$717$	19.4355	+	48.7794i	0.725831	+	1.82170i
$718$	−0.0805108	−	0.0947846i	−0.00300464	−	0.00353733i
$719$	30.1863	−	4.94879i	1.12576	−	0.184559i	0.429996	−	0.902831i	$-0.358515\pi$
$719$	30.1863	−	4.94879i	1.12576	−	0.184559i	0.695763	+	0.718272i	$0.255067\pi$
$720$	5.30326	+	7.82172i	0.197641	+	0.291498i
$721$	2.28945	+	8.24585i	0.0852636	+	0.307092i
$722$		−	2.33917i		−	0.0870547i
$723$	−7.17726	+	25.8502i	−0.266925	+	0.961378i
$724$	−0.906961	+	1.71071i	−0.0337069	+	0.0635780i
$725$	−37.7566	+	22.7174i	−1.40225	+	0.843703i
$726$	6.27824	+	3.32851i	0.233007	+	0.123533i
$727$	−14.0590	−	13.3174i	−0.521420	−	0.493915i	0.381118	−	0.924526i	$-0.375539\pi$
$727$	−14.0590	−	13.3174i	−0.521420	−	0.493915i	−0.902537	+	0.430612i	$0.858298\pi$
$728$	−1.77413	+	1.20289i	−0.0657536	+	0.0445821i
$729$	−16.7541	+	31.6016i	−0.620522	+	1.17043i
$730$	−0.735571	+	0.967627i	−0.0272247	+	0.0358135i
$731$	−27.4661	+	14.5616i	−1.01587	+	0.538581i
$732$	−28.1589	−	1.52673i	−1.04078	−	0.0564296i
$733$	5.31017	+	48.8262i	0.196135	+	1.80344i	0.516655	+	0.856194i	$0.327177\pi$
$733$	5.31017	+	48.8262i	0.196135	+	1.80344i	−0.320519	+	0.947242i	$0.603857\pi$
$734$	1.74036	+	0.189276i	0.0642380	+	0.00698630i
$735$	1.30981	+	4.71751i	0.0483131	+	0.174008i
$736$	7.47218	+	2.97719i	0.275428	+	0.109741i
$737$	57.2535	+	38.8188i	2.10896	+	1.42991i
$738$	1.78964	+	0.0970315i	0.0658776	+	0.00357178i
$739$	32.6704	−	38.4626i	1.20180	−	1.41487i	0.317301	−	0.948325i	$-0.397223\pi$
$739$	32.6704	−	38.4626i	1.20180	−	1.41487i	0.884498	−	0.466543i	$-0.154501\pi$
$740$	−8.01189	+	11.8167i	−0.294523	+	0.434389i
$741$	1.69463	−	7.69879i	0.0622539	−	0.282822i
$742$	−1.89171	−	0.310130i	−0.0694468	−	0.0113852i
$743$	−3.35932	−	6.33636i	−0.123242	−	0.232458i	0.814213	−	0.580567i	$-0.197169\pi$
$743$	−3.35932	−	6.33636i	−0.123242	−	0.232458i	−0.937454	+	0.348108i	$0.886824\pi$
$744$	−4.74340	−	2.51479i	−0.173901	−	0.0921967i
$745$	−3.60291	+	10.6931i	−0.132000	+	0.391763i
$746$	−0.228952	−	0.216875i	−0.00838254	−	0.00794036i
$747$	−13.1118	−	24.7315i	−0.479736	−	0.904877i
$748$	−43.7963	−	72.7900i	−1.60135	−	2.66147i
$749$	5.27577	−	32.1807i	0.192772	−	1.17586i
$750$	0.778990	+	2.31196i	0.0284447	+	0.0844208i
$751$	13.2821	−	28.7087i	0.484670	−	1.04760i	−0.498832	−	0.866699i	$-0.666238\pi$
$751$	13.2821	−	28.7087i	0.484670	−	1.04760i	0.983502	−	0.180898i	$-0.0579004\pi$
$752$	0.186567	−	0.847583i	0.00680341	−	0.0309082i
$753$	−8.51533	−	18.4056i	−0.310316	−	0.670737i
$754$	−2.41954	+	0.815237i	−0.0881143	+	0.0296892i
$755$	1.51437	−	2.85641i	0.0551136	−	0.103955i
$756$	5.66737	−	0.307276i	0.206120	−	0.0111755i
$757$	26.4638	−	22.4786i	0.961844	−	0.816998i	−0.0213105	−	0.999773i	$-0.506784\pi$
$757$	26.4638	−	22.4786i	0.961844	−	0.816998i	0.983155	+	0.182775i	$0.0585080\pi$
$758$	0.652894	−	3.98248i	0.0237142	−	0.144650i
$759$	45.1055	+	47.6173i	1.63723	+	1.72840i
$760$	0.217324	+	0.644994i	0.00788316	+	0.0233964i
$761$	−12.7122	−	10.7979i	−0.460818	−	0.391422i	0.386686	−	0.922211i	$-0.373620\pi$
$761$	−12.7122	−	10.7979i	−0.460818	−	0.391422i	−0.847504	+	0.530789i	$0.821896\pi$
$762$	−0.378482	−	2.30864i	−0.0137109	−	0.0836331i
$763$	−7.91511	+	10.4121i	−0.286546	+	0.376945i
$764$	1.60141	−	5.76776i	0.0579370	−	0.208670i
$765$	−7.06686	+	17.7365i	−0.255503	+	0.641264i
$766$	−0.749200	+	0.709680i	−0.0270697	+	0.0256418i
$767$	−5.84456	+	8.62008i	−0.211035	+	0.311253i
$768$	−29.1946	−	22.1932i	−1.05347	−	0.800827i
$769$	29.4994	+	25.0570i	1.06378	+	0.903580i	0.995564	−	0.0940908i	$-0.0299944\pi$
$769$	29.4994	+	25.0570i	1.06378	+	0.903580i	0.0682130	+	0.997671i	$0.478270\pi$
$770$	0.859564	−	0.730120i	0.0309765	−	0.0263117i
$771$	−38.7582	−	23.3200i	−1.39584	−	0.839850i
$772$	−24.2257	−	12.8436i	−0.871901	−	0.462252i
$773$	11.6253	−	5.37844i	0.418134	−	0.193449i	−0.199530	−	0.979892i	$-0.563941\pi$
$773$	11.6253	−	5.37844i	0.418134	−	0.193449i	0.617663	+	0.786443i	$0.288079\pi$
$774$	1.85972	−	0.860396i	0.0668461	−	0.0309263i
$775$	11.9139	+	11.2854i	0.427958	+	0.405384i
$776$	−6.41429	+	1.41189i	−0.230260	+	0.0506840i
$777$	23.1369	+	50.0097i	0.830033	+	1.79409i
$778$	1.06091	−	1.00495i	0.0380356	−	0.0360292i
$779$	−5.62710	−	1.89599i	−0.201612	−	0.0679309i
$780$	−0.679034	−	6.24361i	−0.0243133	−	0.223557i
$781$	46.6124	−	35.4338i	1.66792	−	1.26792i
$782$	1.14373	+	5.19600i	0.0408996	+	0.185809i
$783$	13.2757	+	2.92219i	0.474433	+	0.104431i
$784$	−6.04567	−	8.91670i	−0.215917	−	0.318453i
$785$	−0.896588	+	16.5366i	−0.0320006	+	0.590216i
$786$	−2.37150	+	1.80277i	−0.0845887	+	0.0643027i
$787$	24.5632	+	16.6543i	0.875585	+	0.593662i	0.914051	−	0.405598i	$-0.132937\pi$
$787$	24.5632	+	16.6543i	0.875585	+	0.593662i	−0.0384662	+	0.999260i	$0.512247\pi$
$788$	14.9876	+	4.16128i	0.533910	+	0.148239i
$789$	−3.54752	+	12.7770i	−0.126295	+	0.454873i
$790$	−0.811407	+	0.273395i	−0.0288686	+	0.00972695i
$791$	−1.73790	+	0.382540i	−0.0617925	+	0.0136016i
$792$	5.27367	+	9.94719i	0.187392	+	0.353458i
$793$	8.60492	+	5.17741i	0.305570	+	0.183855i
$794$	0.615106	−	0.0333501i	0.0218293	−	0.00118355i
$795$	6.83457	−	8.99072i	0.242397	−	0.318868i
$796$	32.2317	+	8.94907i	1.14242	+	0.317192i
$797$	0.281651	+	0.112220i	0.00997657	+	0.00397503i	0.375121	−	0.926976i	$-0.377601\pi$
$797$	0.281651	+	0.112220i	0.00997657	+	0.00397503i	−0.365145	+	0.930951i	$0.618980\pi$
$798$	1.27594	+	0.280855i	0.0451677	+	0.00994217i
$799$	1.62888	−	0.649005i	0.0576256	−	0.0229601i
$800$	−4.71487	−	6.20230i	−0.166696	−	0.219285i
$801$	10.4465	−	11.0282i	0.369108	−	0.389662i
$802$	0.761113	+	0.352128i	0.0268758	+	0.0124341i
$803$	45.8096	−	48.3606i	1.61659	−	1.70661i
$804$	23.6300	+	59.3069i	0.833366	+	2.09159i
$805$	6.13539	−	2.44456i	0.216244	−	0.0861595i
$806$	0.533610	+	0.787017i	0.0187956	+	0.0277215i
$807$	−4.01700	−	0.436876i	−0.141405	−	0.0153787i
$808$	−8.77402	−	2.95631i	−0.308669	−	0.104003i
$809$	−0.272866	+	0.402447i	−0.00959345	+	0.0141493i	−0.832455	−	0.554092i	$-0.813066\pi$
$809$	−0.272866	+	0.402447i	−0.00959345	+	0.0141493i	0.822862	+	0.568241i	$0.192376\pi$
$810$	−0.296921	+	0.641783i	−0.0104327	+	0.0225500i
$811$	37.5809	+	39.6736i	1.31964	+	1.39313i	0.864435	+	0.502744i	$0.167676\pi$
$811$	37.5809	+	39.6736i	1.31964	+	1.39313i	0.455207	+	0.890385i	$0.349565\pi$
$812$	12.6333	+	37.4944i	0.443343	+	1.31579i
$813$	−7.61098	−	5.78571i	−0.266929	−	0.202914i
$814$	−5.41724	+	6.37766i	−0.189874	+	0.223537i
$815$	0.617482	+	5.67766i	0.0216295	+	0.198880i
$816$	4.19874	−	77.4411i	0.146985	−	2.71098i
$817$	−6.69941	+	1.09831i	−0.234383	+	0.0384251i
$818$	1.63299	+	2.14816i	0.0570960	+	0.0751085i
$819$	−11.9170	−	5.51340i	−0.416414	−	0.192654i
$820$	−4.73072			−0.165204
$821$	−32.9652			−1.15049			−0.575246	−	0.817980i	$-0.695094\pi$
$821$	−32.9652			−1.15049			−0.575246	+	0.817980i	$0.695094\pi$
$822$	−5.76737	−	2.66827i	−0.201160	−	0.0930666i
$823$	−14.1867	−	35.6060i	−0.494518	−	1.24115i	−0.938552	−	0.345137i	$-0.887832\pi$
$823$	−14.1867	−	35.6060i	−0.494518	−	1.24115i	0.444034	−	0.896010i	$-0.353547\pi$
$824$	−2.39752	+	0.260746i	−0.0835217	+	0.00908353i
$825$	−13.6570	−	62.0446i	−0.475477	−	2.16011i
$826$	−1.42863	−	0.968633i	−0.0497083	−	0.0337030i
$827$	−2.17564	+	1.15345i	−0.0756545	+	0.0401095i	−0.505806	−	0.862647i	$-0.668805\pi$
$827$	−2.17564	+	1.15345i	−0.0756545	+	0.0401095i	0.430152	+	0.902757i	$0.358460\pi$
$828$	5.30492	+	32.3586i	0.184359	+	1.12454i
$829$	−7.72936	+	6.56537i	−0.268452	+	0.228025i	−0.771494	−	0.636237i	$-0.780490\pi$
$829$	−7.72936	+	6.56537i	−0.268452	+	0.228025i	0.503042	+	0.864262i	$0.332214\pi$
$830$	−0.407389	−	0.677086i	−0.0141407	−	0.0235020i
$831$	43.4177	+	7.11797i	1.50614	+	0.246920i
$832$	5.67510	+	12.2665i	0.196749	+	0.425265i
$833$	8.05616	−	20.2194i	0.279129	−	0.700562i
$834$			0.693261i			0.0240057i
$835$	−0.732985	−	0.292048i	−0.0253660	−	0.0101067i
$836$	−3.98797	−	18.1176i	−0.137927	−	0.626609i
$837$	−0.274078	−	5.05506i	−0.00947351	−	0.174729i
$838$	−4.43111	+	0.726444i	−0.153070	+	0.0250946i
$839$	−35.0530	+	13.9664i	−1.21017	+	0.482174i	−0.885937	−	0.463805i	$-0.846484\pi$
$839$	−35.0530	+	13.9664i	−1.21017	+	0.482174i	−0.324228	+	0.945979i	$0.605104\pi$
$840$	2.08060	−	0.226279i	0.0717876	−	0.00780738i
$841$	3.56021	+	65.6641i	0.122766	+	2.26428i
$842$	−0.136892	+	2.52483i	−0.00471762	+	0.0870114i
$843$	39.8964	+	4.33899i	1.37410	+	0.149443i
$844$	2.89030	−	0.802489i	0.0994884	−	0.0276228i
$845$	2.48293	−	6.23169i	0.0854155	−	0.214377i
$846$	−0.109525	+	0.0369032i	−0.00376554	+	0.00126876i
$847$	−32.4573	+	22.0066i	−1.11525	+	0.756155i
$848$	−7.93469	+	23.5493i	−0.272478	+	0.808687i
$849$	−22.5825	+	10.4478i	−0.775029	+	0.358566i
$850$	1.64547	−	4.88359i	0.0564393	−	0.167506i
$851$	−41.9884	+	25.2636i	−1.43934	+	0.866024i
$852$	53.9593	−	2.92559i	1.84861	−	0.100229i
$853$	2.63544	+	16.0755i	0.0902356	+	0.550413i	0.992793	+	0.119843i	$0.0382392\pi$
$853$	2.63544	+	16.0755i	0.0902356	+	0.550413i	−0.902557	+	0.430570i	$0.858313\pi$
$854$	−0.858065	+	1.42611i	−0.0293624	+	0.0488006i
$855$	−2.69921	+	3.17775i	−0.0923110	+	0.108677i
$856$	8.70883	+	2.93434i	0.297662	+	0.100294i
$857$	1.99519	−	0.553963i	0.0681545	−	0.0189230i	−0.233284	−	0.972409i	$-0.574947\pi$
$857$	1.99519	−	0.553963i	0.0681545	−	0.0189230i	0.301438	+	0.953486i	$0.402533\pi$
$858$		−	3.68109i		−	0.125670i
$859$	−37.1824	−	10.3237i	−1.26865	−	0.352238i	−0.432945	−	0.901420i	$-0.642526\pi$
$859$	−37.1824	−	10.3237i	−1.26865	−	0.352238i	−0.835703	+	0.549182i	$0.814939\pi$
$860$	−4.77860	+	2.53345i	−0.162949	+	0.0863900i
$861$	−9.41338	+	15.6452i	−0.320807	+	0.533186i
$862$	−4.38566	−	3.33389i	−0.149376	−	0.113553i
$863$	−4.21411	+	9.10866i	−0.143450	+	0.310062i	−0.965961	−	0.258687i	$-0.916710\pi$
$863$	−4.21411	+	9.10866i	−0.143450	+	0.310062i	0.822511	+	0.568749i	$0.192572\pi$
$864$	−0.259858	+	2.38936i	−0.00884056	+	0.0812876i
$865$	6.50371	+	10.8093i	0.221133	+	0.367526i
$866$	2.28760	+	1.37641i	0.0777359	+	0.0467722i
$867$	96.9913	−	58.3577i	3.29400	−	1.98193i
$868$	12.1960	−	8.26910i	0.413960	−	0.280672i
$869$	45.8278	−	10.0875i	1.55460	−	0.342194i
$870$	2.46007	+	0.403309i	0.0834043	+	0.0136734i
$871$	2.45804	−	22.6013i	0.0832874	−	0.765815i
$872$	−2.53472	−	2.67587i	−0.0858365	−	0.0906164i
$873$	−27.6686	−	29.2094i	−0.936442	−	0.988590i
$874$	−0.125619	+	1.15505i	−0.00424913	+	0.0390701i
$875$	−13.2859	−	2.17812i	−0.449146	−	0.0736337i
$876$	60.0412	−	13.2161i	2.02860	−	0.446530i
$877$	−34.7781	+	23.5802i	−1.17437	+	0.796245i	−0.982698	−	0.185213i	$-0.940703\pi$
$877$	−34.7781	+	23.5802i	−1.17437	+	0.796245i	−0.191676	+	0.981458i	$0.561392\pi$
$878$	3.47545	−	2.09111i	0.117291	−	0.0705714i
$879$	−16.5215	−	9.94067i	−0.557257	−	0.335290i
$880$	−7.53738	−	12.5272i	−0.254085	−	0.422292i
$881$	−4.87440	+	44.8194i	−0.164223	+	1.51000i	0.564637	+	0.825339i	$0.309016\pi$
$881$	−4.87440	+	44.8194i	−0.164223	+	1.51000i	−0.728860	+	0.684663i	$0.759949\pi$
$882$	−0.602390	+	1.30204i	−0.0202835	+	0.0438421i
$883$	0.539798	+	0.410344i	0.0181656	+	0.0138092i	0.614218	−	0.789137i	$-0.289472\pi$
$883$	0.539798	+	0.410344i	0.0181656	+	0.0138092i	−0.596052	+	0.802946i	$0.703265\pi$
$884$	−14.3942	+	23.9234i	−0.484131	+	0.804632i
$885$	8.98424	−	4.76314i	0.302002	−	0.160111i
$886$	1.45602	+	0.404261i	0.0489159	+	0.0135814i
$887$			23.2755i			0.781515i	0.920494	+	0.390757i	$0.127787\pi$
$887$			23.2755i			0.781515i	−0.920494	+	0.390757i	$0.872213\pi$
$888$	−14.9624	+	4.15428i	−0.502104	+	0.139409i
$889$	12.2344	+	4.12226i	0.410330	+	0.138256i
$890$	0.277608	−	0.326825i	0.00930544	−	0.0109552i
$891$	19.9799	−	33.2068i	0.669352	−	1.11247i
$892$	3.87553	+	23.6397i	0.129762	+	0.791514i
$893$	0.382347	−	0.0207302i	0.0127947	−	0.000693711i
$894$	−5.23014	+	3.14687i	−0.174922	+	0.105247i
$895$	−4.55859	+	13.5294i	−0.152377	+	0.452238i
$896$	−8.44984	+	3.90931i	−0.282289	+	0.130601i
$897$	6.88309	−	20.4283i	0.229820	−	0.682081i
$898$	2.93777	−	1.99185i	0.0980345	−	0.0664691i
$899$	33.4434	−	11.2684i	1.11540	−	0.375822i
$900$	11.7560	−	29.5053i	0.391866	−	0.983510i
$901$	−48.3761	+	13.4316i	−1.61164	+	0.447470i
$902$	−2.75652	−	0.299790i	−0.0917821	−	0.00998191i
$903$	−1.13016	+	20.8447i	−0.0376095	+	0.693667i
$904$	−0.0271495	−	0.500744i	−0.000902980	−	0.0166545i
$905$	−0.669300	+	0.0727908i	−0.0222483	+	0.00241965i
$906$	1.62467	−	0.647328i	0.0539760	−	0.0215060i
$907$	17.7853	−	2.91575i	0.590550	−	0.0968158i	0.140905	−	0.990023i	$-0.454999\pi$
$907$	17.7853	−	2.91575i	0.590550	−	0.0968158i	0.449645	+	0.893207i	$0.351550\pi$
$908$	−1.36940	−	25.2571i	−0.0454451	−	0.838186i
$909$	−12.1926	−	55.3913i	−0.404402	−	1.83721i
$910$	−0.344340	−	0.137198i	−0.0114148	−	0.00454805i
$911$			0.701520i			0.0232424i	0.999932	+	0.0116212i	$0.00369922\pi$
$911$			0.701520i			0.0232424i	−0.999932	+	0.0116212i	$0.996301\pi$
$912$	6.26878	−	15.7335i	0.207580	−	0.520987i
$913$	18.1838	+	39.3035i	0.601794	+	1.30076i
$914$	2.89637	+	0.474836i	0.0958034	+	0.0157062i
$915$	−5.05519	−	8.40179i	−0.167119	−	0.277754i
$916$	−9.14921	+	7.77141i	−0.302298	+	0.256775i
$917$	−2.65956	−	16.2226i	−0.0878265	−	0.535718i
$918$	−1.40459	+	0.744664i	−0.0463582	+	0.0245776i
$919$	40.2006	+	27.2567i	1.32610	+	0.899116i	0.998948	−	0.0458571i	$-0.0146019\pi$
$919$	40.2006	+	27.2567i	1.32610	+	0.899116i	0.327149	+	0.944973i	$0.393912\pi$
$920$	0.400102	+	1.81768i	0.0131910	+	0.0599272i
$921$	−59.1387	+	6.43172i	−1.94869	+	0.211933i
$922$	0.535454	+	1.34389i	0.0176342	+	0.0442586i
$923$	−17.4651	−	8.08024i	−0.574872	−	0.265964i
$924$	−57.0440			−1.87661
$925$	47.4644			1.56062
$926$	2.08062	+	0.962596i	0.0683733	+	0.0316329i
$927$	−8.94053	−	11.7611i	−0.293646	−	0.386284i
$928$	−16.5338	+	2.71058i	−0.542749	+	0.0889792i
$929$	0.118028	−	2.17690i	0.00387237	−	0.0714216i	−0.995958	−	0.0898151i	$-0.971372\pi$
$929$	0.118028	−	2.17690i	0.00387237	−	0.0714216i	0.999831	+	0.0183935i	$0.00585515\pi$
$930$	−0.100379	−	0.922971i	−0.00329156	−	0.0302654i
$931$	3.07708	−	3.62261i	0.100847	−	0.118726i
$932$	−23.1291	−	17.5823i	−0.757619	−	0.575927i
$933$	13.0542	+	38.7435i	0.427375	+	1.26840i
$934$	4.11140	+	4.34035i	0.134529	+	0.142020i
$935$	12.4025	−	26.8075i	0.405604	−	0.876699i
$936$	2.07657	−	3.06272i	0.0678749	−	0.100108i
$937$	−24.6819	−	8.31631i	−0.806324	−	0.271682i	−0.114197	−	0.993458i	$-0.536430\pi$
$937$	−24.6819	−	8.31631i	−0.806324	−	0.271682i	−0.692127	+	0.721776i	$0.743326\pi$
$938$	3.74576	+	0.407376i	0.122303	+	0.0133013i
$939$	−7.78966	−	11.4889i	−0.254206	−	0.374925i
$940$	0.283395	−	0.112915i	0.00924332	−	0.00368287i
$941$	−9.14368	−	22.9489i	−0.298075	−	0.748113i	−0.999379	−	0.0352496i	$-0.988777\pi$
$941$	−9.14368	−	22.9489i	−0.298075	−	0.748113i	0.701303	−	0.712863i	$-0.252602\pi$
$942$	−6.16077	+	6.50384i	−0.200729	+	0.211907i
$943$	−14.7368	−	6.81798i	−0.479897	−	0.222024i
$944$	−15.3874	+	16.2443i	−0.500817	+	0.528707i
$945$	1.19429	+	1.57106i	0.0388503	+	0.0511067i
$946$	−2.94496	+	1.17338i	−0.0957490	+	0.0381499i
$947$	−52.4712	−	11.5498i	−1.70509	−	0.375318i	−0.747679	−	0.664060i	$-0.768832\pi$
$947$	−52.4712	−	11.5498i	−1.70509	−	0.375318i	−0.957407	+	0.288743i	$0.906763\pi$
$948$	40.2322	+	16.0300i	1.30668	+	0.520629i
$949$	−21.0952	−	5.85705i	−0.684779	−	0.190128i
$950$	0.681053	−	0.895910i	0.0220963	−	0.0290672i
$951$	14.8297	−	0.804043i	0.480886	−	0.0260729i
$952$	−7.97217	−	4.79670i	−0.258380	−	0.155462i
$953$	14.9053	+	28.1144i	0.482830	+	0.910714i	0.998543	+	0.0539527i	$0.0171820\pi$
$953$	14.9053	+	28.1144i	0.482830	+	0.910714i	−0.515714	+	0.856761i	$0.672473\pi$
$954$	3.23192	−	0.711400i	0.104637	−	0.0230324i
$955$	1.97239	−	0.664576i	0.0638251	−	0.0215052i
$956$	10.8650	−	39.1322i	0.351399	−	1.26563i
$957$	−131.642	−	36.5503i	−4.25539	−	1.18150i
$958$	2.81128	+	1.90609i	0.0908282	+	0.0615831i
$959$	27.9176	−	21.2224i	0.901508	−	0.685308i
$960$	0.714452	−	13.1773i	0.0230588	−	0.425295i
$961$	10.0211	+	14.7800i	0.323261	+	0.476775i
$962$	2.68591	+	0.591214i	0.0865973	+	0.0190615i
$963$	12.1020	+	54.9797i	0.389980	+	1.77170i
$964$	16.5189	−	12.5573i	0.532038	−	0.404445i
$965$	−1.03080	−	9.47808i	−0.0331827	−	0.305110i
$966$	3.38563	+	1.14075i	0.108931	+	0.0367031i
$967$	20.5371	−	19.4537i	0.660427	−	0.625590i	−0.282232	−	0.959346i	$-0.591075\pi$
$967$	20.5371	−	19.4537i	0.660427	−	0.625590i	0.942659	+	0.333756i	$0.108316\pi$
$968$	−4.64018	−	10.0296i	−0.149141	−	0.322363i
$969$	33.4174	−	7.35573i	1.07352	−	0.236300i
$970$	−0.824557	−	0.781062i	−0.0264749	−	0.0250784i
$971$	−29.7141	+	13.7472i	−0.953571	+	0.441169i	−0.834066	−	0.551665i	$-0.813993\pi$
$971$	−29.7141	+	13.7472i	−0.953571	+	0.441169i	−0.119505	+	0.992834i	$0.538131\pi$
$972$	39.9851	−	18.4991i	1.28252	−	0.593358i
$973$	−3.38010	−	1.79201i	−0.108361	−	0.0574493i
$974$	−3.69704	−	2.22444i	−0.118461	−	0.0712756i
$975$	−15.9139	+	13.5174i	−0.509653	+	0.432903i
$976$	16.4440	+	13.9677i	0.526361	+	0.447095i
$977$	5.53512	+	4.20769i	0.177084	+	0.134616i	0.689962	−	0.723846i	$-0.257627\pi$
$977$	5.53512	+	4.20769i	0.177084	+	0.134616i	−0.512877	+	0.858462i	$0.671420\pi$
$978$	−1.73374	+	2.55707i	−0.0554387	+	0.0817660i
$979$	−17.0615	+	16.1615i	−0.545286	+	0.516523i
$980$	1.40162	−	3.51781i	0.0447732	−	0.112372i
$981$	6.04043	−	21.7557i	0.192856	−	0.694605i
$982$	−0.311290	+	0.409495i	−0.00993367	+	0.0130675i
$983$	−3.57819	−	21.8260i	−0.114126	−	0.696140i	−0.980467	−	0.196686i	$-0.936982\pi$
$983$	−3.57819	−	21.8260i	−0.114126	−	0.696140i	0.866340	−	0.499455i	$-0.166466\pi$
$984$	−3.92169	−	3.33112i	−0.125019	−	0.106192i
$985$	1.72691	+	5.12527i	0.0550238	+	0.163305i
$986$	−7.62135	−	8.04576i	−0.242713	−	0.256229i
$987$	0.190485	−	1.16191i	0.00606321	−	0.0369839i
$988$	−4.64700	+	3.94720i	−0.147841	+	0.125577i
$989$	−18.5372	+	1.00506i	−0.589449	+	0.0319590i
$990$	−0.911963	+	1.72014i	−0.0289841	+	0.0546698i
$991$	3.66017	−	1.23325i	0.116269	−	0.0391756i	−0.260566	−	0.965456i	$-0.583909\pi$
$991$	3.66017	−	1.23325i	0.116269	−	0.0391756i	0.376835	+	0.926281i	$0.377012\pi$
$992$	2.62000	+	5.66303i	0.0831850	+	0.179801i
$993$	3.12926	−	14.2164i	0.0993040	−	0.451142i
$994$	1.33916	−	2.89454i	0.0424755	−	0.0918092i
$995$	3.71381	+	11.0222i	0.117736	+	0.349427i
$996$	−6.46613	+	39.4417i	−0.204887	+	1.24976i
$997$	1.95444	+	3.24830i	0.0618976	+	0.102875i	0.886261	−	0.463187i	$-0.153294\pi$
$997$	1.95444	+	3.24830i	0.0618976	+	0.102875i	−0.824363	+	0.566061i	$0.808466\pi$
$998$	1.40704	+	2.65395i	0.0445390	+	0.0840094i
$999$	−10.6303	−	10.0696i	−0.336329	−	0.318588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.h.a.17.15	✓	784
349.308	even	58	inner	349.2.h.a.308.15	yes	784

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.h.a.17.15	✓	784	1.1	even	1	trivial
349.2.h.a.308.15	yes	784	349.308	even	58	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.h (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.100044 - 0.105615i) q^{2} +(-1.65632 - 1.94997i) q^{3} +(0.107132 + 1.97593i) q^{4} +(-0.547752 + 0.416391i) q^{5} +(-0.371651 - 0.0201504i) q^{6} +(1.05893 - 1.75995i) q^{7} +(0.441159 + 0.374724i) q^{8} +(-0.573647 + 3.49909i) q^{9} +O(q^{10})\)	\(q+(0.100044 - 0.105615i) q^{2} +(-1.65632 - 1.94997i) q^{3} +(0.107132 + 1.97593i) q^{4} +(-0.547752 + 0.416391i) q^{5} +(-0.371651 - 0.0201504i) q^{6} +(1.05893 - 1.75995i) q^{7} +(0.441159 + 0.374724i) q^{8} +(-0.573647 + 3.49909i) q^{9} +(-0.0108222 + 0.0995082i) q^{10} +(1.17925 - 5.35737i) q^{11} +(3.67558 - 3.48169i) q^{12} +(-1.73721 + 0.482333i) q^{13} +(-0.0799382 - 0.287911i) q^{14} +(1.71921 + 0.378426i) q^{15} +(-3.85076 + 0.418796i) q^{16} +(-5.06630 - 5.96451i) q^{17} +(0.312167 + 0.410648i) q^{18} +(-0.632560 - 1.58761i) q^{19} +(-0.881442 - 1.03771i) q^{20} +(-5.18579 + 0.850168i) q^{21} +(-0.447842 - 0.660518i) q^{22} +(-1.25024 - 4.50296i) q^{23} -1.48091i q^{24} +(-1.21099 + 4.36159i) q^{25} +(-0.122855 + 0.231730i) q^{26} +(1.19653 - 0.719930i) q^{27} +(3.59100 + 1.90383i) q^{28} +(7.06721 + 6.69441i) q^{29} +(0.211963 - 0.143715i) q^{30} +(1.69814 - 3.20302i) q^{31} +(-1.04159 + 1.37019i) q^{32} +(-12.3999 + 6.57403i) q^{33} +(-1.13679 - 0.0616352i) q^{34} +(0.152797 + 1.40495i) q^{35} +(-6.97543 - 0.758624i) q^{36} +(-2.80522 - 10.1035i) q^{37} +(-0.230959 - 0.0920224i) q^{38} +(3.81791 + 2.58861i) q^{39} +(-0.397677 - 0.0215614i) q^{40} +(2.24937 - 2.64816i) q^{41} +(-0.429016 + 0.632752i) q^{42} +(0.853958 - 3.87957i) q^{43} +(10.7121 + 1.75617i) q^{44} +(-1.14277 - 2.15550i) q^{45} +(-0.600659 - 0.318449i) q^{46} +(-0.0715414 + 0.212327i) q^{47} +(7.19474 + 6.81522i) q^{48} +(1.30275 + 2.45725i) q^{49} +(0.339497 + 0.564249i) q^{50} +(-3.23921 + 19.7583i) q^{51} +(-1.13917 - 3.38093i) q^{52} +(2.69379 - 5.82253i) q^{53} +(0.0436704 - 0.198396i) q^{54} +(1.58482 + 3.42554i) q^{55} +(1.12665 - 0.379614i) q^{56} +(-2.04807 + 3.86306i) q^{57} +(1.41406 - 0.0766682i) q^{58} +(4.40265 - 3.73964i) q^{59} +(-0.563562 + 3.43758i) q^{60} +(-3.83054 - 4.04385i) q^{61} +(-0.168399 - 0.499791i) q^{62} +(5.55079 + 4.71488i) q^{63} +(-1.21281 - 7.39779i) q^{64} +(0.750720 - 0.987556i) q^{65} +(-0.546221 + 1.96731i) q^{66} +(-4.66737 + 11.7142i) q^{67} +(11.2427 - 10.6497i) q^{68} +(-6.70985 + 9.89629i) q^{69} +(0.163670 + 0.124419i) q^{70} +(8.13504 + 6.90996i) q^{71} +(-1.56426 + 1.32870i) q^{72} +(10.4050 + 6.26046i) q^{73} +(-1.34772 - 0.714518i) q^{74} +(10.5108 - 4.86280i) q^{75} +(3.06924 - 1.41998i) q^{76} +(-8.17999 - 7.74850i) q^{77} +(0.655355 - 0.144254i) q^{78} +(3.59180 + 7.76354i) q^{79} +(1.93488 - 1.83282i) q^{80} +(6.69488 + 2.25577i) q^{81} +(-0.0546501 - 0.502499i) q^{82} +(-6.28474 + 4.77753i) q^{83} +(-2.23544 - 10.1557i) q^{84} +(5.25865 + 1.15752i) q^{85} +(-0.324308 - 0.478318i) q^{86} +(1.34836 - 24.8690i) q^{87} +(2.52777 - 1.92156i) q^{88} +(-3.54588 - 2.40416i) q^{89} +(-0.341980 - 0.0949503i) q^{90} +(-0.990695 + 3.56816i) q^{91} +(8.76362 - 2.95281i) q^{92} +(-9.05847 + 1.99392i) q^{93} +(0.0152677 + 0.0287979i) q^{94} +(1.00755 + 0.606223i) q^{95} +(4.39706 - 0.238402i) q^{96} +(-6.86681 + 9.03314i) q^{97} +(0.389855 + 0.108243i) q^{98} +(18.0695 + 7.19953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 784 q - 29 q^{2} - 25 q^{3} + 3 q^{4} - 21 q^{5} - 29 q^{6} - 29 q^{7} + 58 q^{8} - 57 q^{9}+O(q^{10}) \) 784 * q - 29 * q^2 - 25 * q^3 + 3 * q^4 - 21 * q^5 - 29 * q^6 - 29 * q^7 + 58 * q^8 - 57 * q^9	\( 784 q - 29 q^{2} - 25 q^{3} + 3 q^{4} - 21 q^{5} - 29 q^{6} - 29 q^{7} + 58 q^{8} - 57 q^{9} - 29 q^{10} - 29 q^{11} - 37 q^{12} - 29 q^{13} - 33 q^{14} - 37 q^{15} - 57 q^{16} - 21 q^{17} - 145 q^{18} + 43 q^{19} - 35 q^{20} - 145 q^{21} - 17 q^{22} - 13 q^{23} - 45 q^{25} + 7 q^{26} - 43 q^{27} - 29 q^{28} - 13 q^{29} - 29 q^{30} - 53 q^{31} - 29 q^{32} - 29 q^{33} - 29 q^{34} - 87 q^{35} + 33 q^{36} + 150 q^{37} - 29 q^{38} - 29 q^{39} - 29 q^{40} - 91 q^{41} + 145 q^{42} - 29 q^{43} - 145 q^{44} + 23 q^{45} - 29 q^{46} - 29 q^{47} + 111 q^{48} + 19 q^{49} + 348 q^{50} + 61 q^{51} - 145 q^{52} - 29 q^{53} - 29 q^{54} - 145 q^{55} + 9 q^{56} - 23 q^{57} - 29 q^{58} - 29 q^{59} + 405 q^{60} - 174 q^{61} - 29 q^{62} - 29 q^{63} - 210 q^{64} - 29 q^{65} + 244 q^{66} - 75 q^{67} - 77 q^{68} - 103 q^{69} - 115 q^{70} - 29 q^{71} - 203 q^{72} - 79 q^{73} + 87 q^{74} + 7 q^{75} - 105 q^{76} + 39 q^{77} + 233 q^{78} - 29 q^{79} + 99 q^{80} + 207 q^{81} - 29 q^{82} + 93 q^{83} - 435 q^{84} + 126 q^{85} - 147 q^{86} + 115 q^{87} - 139 q^{88} - 435 q^{89} - 29 q^{90} - 57 q^{91} - 47 q^{92} - 99 q^{93} - 51 q^{94} + 233 q^{95} + 609 q^{96} - 29 q^{97} + 377 q^{98} - 29 q^{99}+O(q^{100}) \) 784 * q - 29 * q^2 - 25 * q^3 + 3 * q^4 - 21 * q^5 - 29 * q^6 - 29 * q^7 + 58 * q^8 - 57 * q^9 - 29 * q^10 - 29 * q^11 - 37 * q^12 - 29 * q^13 - 33 * q^14 - 37 * q^15 - 57 * q^16 - 21 * q^17 - 145 * q^18 + 43 * q^19 - 35 * q^20 - 145 * q^21 - 17 * q^22 - 13 * q^23 - 45 * q^25 + 7 * q^26 - 43 * q^27 - 29 * q^28 - 13 * q^29 - 29 * q^30 - 53 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 87 * q^35 + 33 * q^36 + 150 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91 * q^41 + 145 * q^42 - 29 * q^43 - 145 * q^44 + 23 * q^45 - 29 * q^46 - 29 * q^47 + 111 * q^48 + 19 * q^49 + 348 * q^50 + 61 * q^51 - 145 * q^52 - 29 * q^53 - 29 * q^54 - 145 * q^55 + 9 * q^56 - 23 * q^57 - 29 * q^58 - 29 * q^59 + 405 * q^60 - 174 * q^61 - 29 * q^62 - 29 * q^63 - 210 * q^64 - 29 * q^65 + 244 * q^66 - 75 * q^67 - 77 * q^68 - 103 * q^69 - 115 * q^70 - 29 * q^71 - 203 * q^72 - 79 * q^73 + 87 * q^74 + 7 * q^75 - 105 * q^76 + 39 * q^77 + 233 * q^78 - 29 * q^79 + 99 * q^80 + 207 * q^81 - 29 * q^82 + 93 * q^83 - 435 * q^84 + 126 * q^85 - 147 * q^86 + 115 * q^87 - 139 * q^88 - 435 * q^89 - 29 * q^90 - 57 * q^91 - 47 * q^92 - 99 * q^93 - 51 * q^94 + 233 * q^95 + 609 * q^96 - 29 * q^97 + 377 * q^98 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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