LMFDB - Embedded newform 197.3.i.a.2.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(2,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(196))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("197.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.i (of order $196$, degree $84$, 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:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$2688$
Relative dimension:	$32$ over $\Q(\zeta_{196})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{196}]$

Embedding invariants

Embedding label			2.18
Character	$\chi$	$=$	197.2
Dual form			197.3.i.a.99.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.648427 + 0.0103942i) q^{2} +(0.725334 - 0.177830i) q^{3} +(-3.57760 - 0.114727i) q^{4} +(-0.578637 - 3.98330i) q^{5} +(0.472175 - 0.107771i) q^{6} +(-3.67258 + 3.79224i) q^{7} +(-4.90966 - 0.236266i) q^{8} +(-7.48491 + 3.90487i) q^{9} +O(q^{10})$	\(q+(0.648427 + 0.0103942i) q^{2} +(0.725334 - 0.177830i) q^{3} +(-3.57760 - 0.114727i) q^{4} +(-0.578637 - 3.98330i) q^{5} +(0.472175 - 0.107771i) q^{6} +(-3.67258 + 3.79224i) q^{7} +(-4.90966 - 0.236266i) q^{8} +(-7.48491 + 3.90487i) q^{9} +(-0.333801 - 2.58889i) q^{10} +(2.03040 + 1.01819i) q^{11} +(-2.61535 + 0.552990i) q^{12} +(-11.4049 - 4.83152i) q^{13} +(-2.42082 + 2.42082i) q^{14} +(-1.12806 - 2.78632i) q^{15} +(11.1072 + 0.713107i) q^{16} +(-22.8525 + 15.4024i) q^{17} +(-4.89400 + 2.45422i) q^{18} +(-1.79818 + 1.43400i) q^{19} +(1.61314 + 14.3170i) q^{20} +(-1.98947 + 3.40374i) q^{21} +(1.30598 + 0.681329i) q^{22} +(12.2108 - 33.1808i) q^{23} +(-3.60316 + 0.701715i) q^{24} +(8.43485 - 2.50342i) q^{25} +(-7.34504 - 3.25143i) q^{26} +(-9.78210 + 8.60181i) q^{27} +(13.5741 - 13.1458i) q^{28} +(-46.4871 - 30.2597i) q^{29} +(-0.702501 - 1.81845i) q^{30} +(-10.0812 + 12.2339i) q^{31} +(26.7931 + 2.15188i) q^{32} +(1.65378 + 0.377465i) q^{33} +(-14.9783 + 9.74979i) q^{34} +(17.2307 + 12.4346i) q^{35} +(27.2260 - 13.1113i) q^{36} +(53.8918 - 3.45997i) q^{37} +(-1.18089 + 0.911154i) q^{38} +(-9.13157 - 1.47632i) q^{39} +(1.89979 + 19.6934i) q^{40} +(-2.73458 + 14.0415i) q^{41} +(-1.32541 + 2.18640i) q^{42} +(2.91808 + 8.78879i) q^{43} +(-7.14712 - 3.87563i) q^{44} +(19.8853 + 27.5551i) q^{45} +(8.26272 - 21.3884i) q^{46} +(-30.1171 - 53.4760i) q^{47} +(8.18326 - 1.45796i) q^{48} +(0.677285 + 21.1202i) q^{49} +(5.49540 - 1.53561i) q^{50} +(-13.8367 + 15.2358i) q^{51} +(40.2479 + 18.5937i) q^{52} +(12.1729 + 27.4989i) q^{53} +(-6.43239 + 5.47597i) q^{54} +(2.88091 - 8.67684i) q^{55} +(18.9271 - 17.7509i) q^{56} +(-1.04927 + 1.35990i) q^{57} +(-29.8289 - 20.1044i) q^{58} +(-0.708082 - 0.0912970i) q^{59} +(3.71607 + 10.0978i) q^{60} +(8.89638 + 14.6755i) q^{61} +(-6.66407 + 7.82799i) q^{62} +(12.6807 - 42.7255i) q^{63} +(-26.9636 - 2.60115i) q^{64} +(-12.6461 + 48.2249i) q^{65} +(1.06843 + 0.261948i) q^{66} +(-119.601 - 33.4207i) q^{67} +(83.5242 - 52.4817i) q^{68} +(2.95638 - 26.2386i) q^{69} +(11.0436 + 8.24206i) q^{70} +(24.2249 + 7.61437i) q^{71} +(37.6709 - 17.4032i) q^{72} +(31.5192 + 27.7162i) q^{73} +(34.9809 - 1.68337i) q^{74} +(5.67290 - 3.31579i) q^{75} +(6.59768 - 4.92397i) q^{76} +(-11.3180 + 3.96035i) q^{77} +(-5.90581 - 1.05220i) q^{78} +(7.26402 - 50.0050i) q^{79} +(-3.58653 - 44.6560i) q^{80} +(37.9040 - 54.3383i) q^{81} +(-1.91912 + 9.07644i) q^{82} +(111.487 + 88.9076i) q^{83} +(7.50802 - 11.9489i) q^{84} +(74.5756 + 82.1161i) q^{85} +(1.80081 + 5.72922i) q^{86} +(-39.0998 - 13.6816i) q^{87} +(-9.72799 - 5.47870i) q^{88} +(41.2304 + 50.0347i) q^{89} +(12.6078 + 18.0742i) q^{90} +(60.2077 - 25.5061i) q^{91} +(-47.4921 + 117.306i) q^{92} +(-5.13666 + 10.6664i) q^{93} +(-18.9729 - 34.9884i) q^{94} +(6.75255 + 6.33292i) q^{95} +(19.8166 - 3.20379i) q^{96} +(-33.4133 - 127.419i) q^{97} +(0.219641 + 13.7020i) q^{98} +(-19.1732 + 0.307345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9}+O(q^{10}) $ 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9} - 84 q^{10} - 140 q^{11} - 140 q^{12} - 84 q^{13} - 28 q^{14} - 84 q^{15} + 112 q^{16} - 84 q^{17} - 210 q^{18} - 98 q^{19} - 84 q^{20} - 84 q^{21} - 84 q^{22} - 84 q^{23} - 308 q^{24} - 84 q^{25} + 70 q^{26} - 126 q^{27} - 910 q^{28} - 294 q^{29} + 70 q^{30} - 84 q^{31} - 84 q^{32} - 98 q^{33} - 84 q^{34} - 84 q^{35} + 2198 q^{36} + 126 q^{37} - 140 q^{38} - 84 q^{39} + 476 q^{40} + 28 q^{41} - 588 q^{42} - 84 q^{43} - 84 q^{44} - 966 q^{45} - 448 q^{46} + 266 q^{47} - 1428 q^{48} + 756 q^{49} - 84 q^{50} - 84 q^{51} + 126 q^{52} - 84 q^{53} - 588 q^{54} - 84 q^{55} - 84 q^{56} - 672 q^{57} + 532 q^{58} + 616 q^{59} - 378 q^{60} - 364 q^{61} - 854 q^{62} + 1036 q^{63} - 1428 q^{64} + 28 q^{65} + 406 q^{66} - 84 q^{67} - 966 q^{68} - 504 q^{69} - 84 q^{70} + 434 q^{71} - 532 q^{72} - 84 q^{73} + 546 q^{74} - 84 q^{75} - 308 q^{76} + 700 q^{77} + 2310 q^{78} - 1400 q^{79} - 84 q^{80} - 700 q^{81} - 84 q^{82} - 98 q^{83} - 588 q^{84} + 1666 q^{85} - 84 q^{86} - 84 q^{87} + 420 q^{88} + 868 q^{89} - 1890 q^{90} + 1260 q^{91} + 924 q^{92} - 98 q^{93} - 420 q^{94} - 1834 q^{95} + 364 q^{96} + 504 q^{97} - 980 q^{98} + 630 q^{99}+O(q^{100}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9 - 84 * q^10 - 140 * q^11 - 140 * q^12 - 84 * q^13 - 28 * q^14 - 84 * q^15 + 112 * q^16 - 84 * q^17 - 210 * q^18 - 98 * q^19 - 84 * q^20 - 84 * q^21 - 84 * q^22 - 84 * q^23 - 308 * q^24 - 84 * q^25 + 70 * q^26 - 126 * q^27 - 910 * q^28 - 294 * q^29 + 70 * q^30 - 84 * q^31 - 84 * q^32 - 98 * q^33 - 84 * q^34 - 84 * q^35 + 2198 * q^36 + 126 * q^37 - 140 * q^38 - 84 * q^39 + 476 * q^40 + 28 * q^41 - 588 * q^42 - 84 * q^43 - 84 * q^44 - 966 * q^45 - 448 * q^46 + 266 * q^47 - 1428 * q^48 + 756 * q^49 - 84 * q^50 - 84 * q^51 + 126 * q^52 - 84 * q^53 - 588 * q^54 - 84 * q^55 - 84 * q^56 - 672 * q^57 + 532 * q^58 + 616 * q^59 - 378 * q^60 - 364 * q^61 - 854 * q^62 + 1036 * q^63 - 1428 * q^64 + 28 * q^65 + 406 * q^66 - 84 * q^67 - 966 * q^68 - 504 * q^69 - 84 * q^70 + 434 * q^71 - 532 * q^72 - 84 * q^73 + 546 * q^74 - 84 * q^75 - 308 * q^76 + 700 * q^77 + 2310 * q^78 - 1400 * q^79 - 84 * q^80 - 700 * q^81 - 84 * q^82 - 98 * q^83 - 588 * q^84 + 1666 * q^85 - 84 * q^86 - 84 * q^87 + 420 * q^88 + 868 * q^89 - 1890 * q^90 + 1260 * q^91 + 924 * q^92 - 98 * q^93 - 420 * q^94 - 1834 * q^95 + 364 * q^96 + 504 * q^97 - 980 * q^98 + 630 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{196}\right)$

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 $

$2$	0.648427	+	0.0103942i	0.324214	+	0.00519711i	0.177923	−	0.984044i	$-0.443062\pi$
$2$	0.648427	+	0.0103942i	0.324214	+	0.00519711i	0.146291	+	0.989242i	$0.453266\pi$
$3$	0.725334	−	0.177830i	0.241778	−	0.0592768i	−0.115378	−	0.993322i	$-0.536808\pi$
$3$	0.725334	−	0.177830i	0.241778	−	0.0592768i	0.357156	+	0.934045i	$0.383747\pi$
$4$	−3.57760	−	0.114727i	−0.894399	−	0.0286816i
$5$	−0.578637	−	3.98330i	−0.115727	−	0.796660i	−0.963771	−	0.266733i	$-0.914056\pi$
$5$	−0.578637	−	3.98330i	−0.115727	−	0.796660i	0.848043	−	0.529927i	$-0.177781\pi$
$6$	0.472175	−	0.107771i	0.0786958	−	0.0179618i
$7$	−3.67258	+	3.79224i	−0.524654	+	0.541748i	−0.927649	−	0.373454i	$-0.878173\pi$
$7$	−3.67258	+	3.79224i	−0.524654	+	0.541748i	0.402995	+	0.915202i	$0.367969\pi$
$8$	−4.90966	−	0.236266i	−0.613708	−	0.0295333i
$9$	−7.48491	+	3.90487i	−0.831656	+	0.433875i
$10$	−0.333801	−	2.58889i	−0.0333801	−	0.258889i
$11$	2.03040	+	1.01819i	0.184581	+	0.0925631i	0.538164	−	0.842840i	$-0.319118\pi$
$11$	2.03040	+	1.01819i	0.184581	+	0.0925631i	−0.353582	+	0.935403i	$0.615037\pi$
$12$	−2.61535	+	0.552990i	−0.217946	+	0.0460825i
$13$	−11.4049	−	4.83152i	−0.877301	−	0.371655i	−0.0956830	−	0.995412i	$-0.530504\pi$
$13$	−11.4049	−	4.83152i	−0.877301	−	0.371655i	−0.781618	+	0.623757i	$0.785606\pi$
$14$	−2.42082	+	2.42082i	−0.172915	+	0.172915i
$15$	−1.12806	−	2.78632i	−0.0752038	−	0.185755i
$16$	11.1072	+	0.713107i	0.694201	+	0.0445692i
$17$	−22.8525	+	15.4024i	−1.34427	+	0.906023i	−0.999467	−	0.0326534i	$-0.989604\pi$
$17$	−22.8525	+	15.4024i	−1.34427	+	0.906023i	−0.344800	+	0.938676i	$0.612053\pi$
$18$	−4.89400	+	2.45422i	−0.271889	+	0.136346i
$19$	−1.79818	+	1.43400i	−0.0946410	+	0.0754737i	−0.669667	−	0.742661i	$-0.733563\pi$
$19$	−1.79818	+	1.43400i	−0.0946410	+	0.0754737i	0.575026	+	0.818135i	$0.304992\pi$
$20$	1.61314	+	14.3170i	0.0806570	+	0.715851i
$21$	−1.98947	+	3.40374i	−0.0947367	+	0.162083i
$22$	1.30598	+	0.681329i	0.0593627	+	0.0309695i
$23$	12.2108	−	33.1808i	0.530905	−	1.44264i	−0.334897	−	0.942255i	$-0.608701\pi$
$23$	12.2108	−	33.1808i	0.530905	−	1.44264i	0.865802	−	0.500386i	$-0.166809\pi$
$24$	−3.60316	+	0.701715i	−0.150132	+	0.0292381i
$25$	8.43485	−	2.50342i	0.337394	−	0.100137i
$26$	−7.34504	−	3.25143i	−0.282501	−	0.125055i
$27$	−9.78210	+	8.60181i	−0.362300	+	0.318586i
$28$	13.5741	−	13.1458i	0.484788	−	0.469491i
$29$	−46.4871	−	30.2597i	−1.60300	−	1.04344i	−0.960929	−	0.276796i	$-0.910727\pi$
$29$	−46.4871	−	30.2597i	−1.60300	−	1.04344i	−0.642074	−	0.766643i	$-0.721926\pi$
$30$	−0.702501	−	1.81845i	−0.0234167	−	0.0606151i
$31$	−10.0812	+	12.2339i	−0.325199	+	0.394641i	−0.908685	−	0.417482i	$-0.862913\pi$
$31$	−10.0812	+	12.2339i	−0.325199	+	0.394641i	0.583486	+	0.812123i	$0.301688\pi$
$32$	26.7931	+	2.15188i	0.837283	+	0.0672462i
$33$	1.65378	+	0.377465i	0.0501146	+	0.0114383i
$34$	−14.9783	+	9.74979i	−0.440538	+	0.286759i
$35$	17.2307	+	12.4346i	0.492306	+	0.355276i
$36$	27.2260	−	13.1113i	0.756277	−	0.364204i
$37$	53.8918	−	3.45997i	1.45654	−	0.0935127i	0.684464	−	0.729047i	$-0.260036\pi$
$37$	53.8918	−	3.45997i	1.45654	−	0.0935127i	0.772073	+	0.635534i	$0.219220\pi$
$38$	−1.18089	+	0.911154i	−0.0310761	+	0.0239777i
$39$	−9.13157	−	1.47632i	−0.234143	−	0.0378544i
$40$	1.89979	+	19.6934i	0.0474949	+	0.492334i
$41$	−2.73458	+	14.0415i	−0.0666970	+	0.342475i	−0.999856	−	0.0169898i	$-0.994592\pi$
$41$	−2.73458	+	14.0415i	−0.0666970	+	0.342475i	0.933159	+	0.359465i	$0.117041\pi$
$42$	−1.32541	+	2.18640i	−0.0315573	+	0.0520570i
$43$	2.91808	+	8.78879i	0.0678623	+	0.204390i	0.977469	−	0.211081i	$-0.0676983\pi$
$43$	2.91808	+	8.78879i	0.0678623	+	0.204390i	−0.909606	+	0.415471i	$0.863617\pi$
$44$	−7.14712	−	3.87563i	−0.162435	−	0.0880824i
$45$	19.8853	+	27.5551i	0.441896	+	0.612336i
$46$	8.26272	−	21.3884i	0.179624	−	0.464965i
$47$	−30.1171	−	53.4760i	−0.640790	−	1.13779i	−0.980362	−	0.197208i	$-0.936813\pi$
$47$	−30.1171	−	53.4760i	−0.640790	−	1.13779i	0.339572	−	0.940580i	$-0.389718\pi$
$48$	8.18326	−	1.45796i	0.170485	−	0.0303742i
$49$	0.677285	+	21.1202i	0.0138221	+	0.431025i
$50$	5.49540	−	1.53561i	0.109908	−	0.0307122i
$51$	−13.8367	+	15.2358i	−0.271308	+	0.298740i
$52$	40.2479	+	18.5937i	0.773998	+	0.357570i
$53$	12.1729	+	27.4989i	0.229678	+	0.518846i	0.991680	−	0.128728i	$-0.0410895\pi$
$53$	12.1729	+	27.4989i	0.229678	+	0.518846i	−0.762002	+	0.647575i	$0.775783\pi$
$54$	−6.43239	+	5.47597i	−0.119118	+	0.101407i
$55$	2.88091	−	8.67684i	0.0523802	−	0.157761i
$56$	18.9271	−	17.7509i	0.337984	−	0.316980i
$57$	−1.04927	+	1.35990i	−0.0184083	+	0.0238579i
$58$	−29.8289	−	20.1044i	−0.514292	−	0.346628i
$59$	−0.708082	−	0.0912970i	−0.0120014	−	0.00154741i	0.121874	−	0.992546i	$-0.461110\pi$
$59$	−0.708082	−	0.0912970i	−0.0120014	−	0.00154741i	−0.133876	+	0.990998i	$0.542742\pi$
$60$	3.71607	+	10.0978i	0.0619345	+	0.168296i
$61$	8.89638	+	14.6755i	0.145842	+	0.240582i	0.919561	−	0.392947i	$-0.128544\pi$
$61$	8.89638	+	14.6755i	0.145842	+	0.240582i	−0.773719	+	0.633529i	$0.781606\pi$
$62$	−6.66407	+	7.82799i	−0.107485	+	0.126258i
$63$	12.6807	−	42.7255i	0.201281	−	0.678182i
$64$	−26.9636	−	2.60115i	−0.421307	−	0.0406430i
$65$	−12.6461	+	48.2249i	−0.194555	+	0.741921i
$66$	1.06843	+	0.261948i	0.0161884	+	0.00396891i
$67$	−119.601	−	33.4207i	−1.78509	−	0.498816i	−0.791428	−	0.611263i	$-0.790662\pi$
$67$	−119.601	−	33.4207i	−1.78509	−	0.498816i	−0.993658	+	0.112446i	$0.964131\pi$
$68$	83.5242	−	52.4817i	1.22830	−	0.771790i
$69$	2.95638	−	26.2386i	0.0428461	−	0.380269i
$70$	11.0436	+	8.24206i	0.157766	+	0.117744i
$71$	24.2249	+	7.61437i	0.341196	+	0.107245i	0.465621	−	0.884984i	$-0.345831\pi$
$71$	24.2249	+	7.61437i	0.341196	+	0.107245i	−0.124425	+	0.992229i	$0.539709\pi$
$72$	37.6709	−	17.4032i	0.523208	−	0.241711i
$73$	31.5192	+	27.7162i	0.431770	+	0.379674i	0.848359	−	0.529421i	$-0.177591\pi$
$73$	31.5192	+	27.7162i	0.431770	+	0.379674i	−0.416589	+	0.909095i	$0.636774\pi$
$74$	34.9809	−	1.68337i	0.472715	−	0.0227483i
$75$	5.67290	−	3.31579i	0.0756387	−	0.0442105i
$76$	6.59768	−	4.92397i	0.0868115	−	0.0647891i
$77$	−11.3180	+	3.96035i	−0.146987	+	0.0514331i
$78$	−5.90581	−	1.05220i	−0.0757155	−	0.0134898i
$79$	7.26402	−	50.0050i	0.0919496	−	0.632975i	−0.891666	−	0.452695i	$-0.850463\pi$
$79$	7.26402	−	50.0050i	0.0919496	−	0.632975i	0.983615	−	0.180280i	$-0.0577005\pi$
$80$	−3.58653	−	44.6560i	−0.0448317	−	0.558200i
$81$	37.9040	−	54.3383i	0.467951	−	0.670843i
$82$	−1.91912	+	9.07644i	−0.0234039	+	0.110688i
$83$	111.487	+	88.9076i	1.34321	+	1.07118i	0.990800	+	0.135332i	$0.0432100\pi$
$83$	111.487	+	88.9076i	1.34321	+	1.07118i	0.352412	+	0.935845i	$0.385361\pi$
$84$	7.50802	−	11.9489i	0.0893812	−	0.142249i
$85$	74.5756	+	82.1161i	0.877361	+	0.966071i
$86$	1.80081	+	5.72922i	0.0209396	+	0.0666188i
$87$	−39.0998	−	13.6816i	−0.449423	−	0.157260i
$88$	−9.72799	−	5.47870i	−0.110545	−	0.0622580i
$89$	41.2304	+	50.0347i	0.463263	+	0.562187i	0.950357	−	0.311163i	$-0.100718\pi$
$89$	41.2304	+	50.0347i	0.463263	+	0.562187i	−0.487093	+	0.873350i	$0.661943\pi$
$90$	12.6078	+	18.0742i	0.140086	+	0.200824i
$91$	60.2077	−	25.5061i	0.661623	−	0.280286i
$92$	−47.4921	+	117.306i	−0.516218	+	1.27507i
$93$	−5.13666	+	10.6664i	−0.0552329	+	0.114692i
$94$	−18.9729	−	34.9884i	−0.201840	−	0.372216i
$95$	6.75255	+	6.33292i	0.0710794	+	0.0666623i
$96$	19.8166	−	3.20379i	0.206423	−	0.0333728i
$97$	−33.4133	−	127.419i	−0.344467	−	1.31360i	−0.882354	−	0.470586i	$-0.844043\pi$
$97$	−33.4133	−	127.419i	−0.344467	−	1.31360i	0.537887	−	0.843017i	$-0.319223\pi$
$98$	0.219641	+	13.7020i	0.00224124	+	0.139816i
$99$	−19.1732	+	0.307345i	−0.193669	+	0.00310450i
$100$	−30.4637	+	7.98852i	−0.304637	+	0.0798852i
$101$	−21.5174	−	133.093i	−0.213044	−	1.31775i	−0.841648	−	0.540026i	$-0.818414\pi$
$101$	−21.5174	−	133.093i	−0.213044	−	1.31775i	0.628604	−	0.777725i	$-0.283627\pi$
$102$	−9.13046	+	9.73545i	−0.0895143	+	0.0954456i
$103$	−139.568	+	75.6826i	−1.35503	+	0.734782i	−0.981250	−	0.192737i	$-0.938264\pi$
$103$	−139.568	+	75.6826i	−1.35503	+	0.734782i	−0.373776	+	0.927519i	$0.621937\pi$
$104$	54.8528	+	26.4157i	0.527430	+	0.253997i
$105$	14.7093	+	5.95513i	0.140088	+	0.0567155i
$106$	7.60743	+	17.9575i	0.0717682	+	0.169411i
$107$	−118.422	+	82.6064i	−1.10675	+	0.772022i	−0.975647	−	0.219346i	$-0.929607\pi$
$107$	−118.422	+	82.6064i	−1.10675	+	0.772022i	−0.131105	+	0.991369i	$0.541852\pi$
$108$	35.9832	−	29.6515i	0.333178	−	0.274551i
$109$	−73.6493	+	130.772i	−0.675681	+	1.19974i	0.294102	+	0.955774i	$0.404979\pi$
$109$	−73.6493	+	130.772i	−0.675681	+	1.19974i	−0.969784	+	0.243967i	$0.921551\pi$
$110$	1.95825	−	5.59635i	0.0178023	−	0.0508759i
$111$	38.4743	−	12.0932i	0.346615	−	0.108948i
$112$	−43.4964	+	39.5023i	−0.388361	+	0.352699i
$113$	−139.399	−	87.5905i	−1.23362	−	0.775137i	−0.252327	−	0.967642i	$-0.581196\pi$
$113$	−139.399	−	87.5905i	−1.23362	−	0.775137i	−0.981296	+	0.192505i	$0.938339\pi$
$114$	−0.694511	+	0.870890i	−0.00609221	+	0.00763938i
$115$	−139.234	−	29.4397i	−1.21073	−	0.255998i
$116$	162.840	+	113.590i	1.40380	+	0.979227i
$117$	104.231	−	8.37130i	0.890865	−	0.0715496i
$118$	−0.458190	−	0.0665594i	−0.00388297	−	0.000564063i
$119$	25.5182	−	143.229i	0.214439	−	1.20360i
$120$	4.88006	+	13.9464i	0.0406672	+	0.116220i
$121$	−69.2856	−	92.8364i	−0.572608	−	0.767243i
$122$	5.61611	+	9.60847i	0.0460337	+	0.0787579i
$123$	0.513520	+	10.6710i	0.00417496	+	0.0867565i
$124$	37.4699	−	42.6113i	0.302177	−	0.343639i
$125$	−57.0546	−	123.501i	−0.456437	−	0.988004i
$126$	8.66661	−	27.5726i	0.0687826	−	0.218830i
$127$	−87.9343	+	117.824i	−0.692396	+	0.927748i	−0.999715	−	0.0238584i	$-0.992405\pi$
$127$	−87.9343	+	117.824i	−0.692396	+	0.927748i	0.307319	+	0.951607i	$0.400568\pi$
$128$	−124.298	−	14.0050i	−0.971080	−	0.109414i
$129$	3.67950	+	5.85589i	0.0285232	+	0.0453945i
$130$	−8.70131	+	31.1389i	−0.0669331	+	0.239530i
$131$	−1.36004	+	5.54735i	−0.0103820	+	0.0423462i	−0.976196	−	0.216889i	$-0.930409\pi$
$131$	−1.36004	+	5.54735i	−0.0103820	+	0.0423462i	0.965814	+	0.259235i	$0.0834704\pi$
$132$	−5.87326	−	1.54015i	−0.0444944	−	0.0116678i
$133$	1.16588	−	12.0856i	0.00876604	−	0.0908692i
$134$	−77.2050	−	22.9140i	−0.576157	−	0.171000i
$135$	39.9239	+	33.9877i	0.295732	+	0.251761i
$136$	115.837	−	70.2212i	0.851744	−	0.516332i
$137$	36.4837	−	13.4263i	0.266305	−	0.0980025i	−0.208719	−	0.977976i	$-0.566929\pi$
$137$	36.4837	−	13.4263i	0.266305	−	0.0980025i	0.475023	+	0.879973i	$0.342440\pi$
$138$	2.18973	−	16.9831i	0.0158676	−	0.123066i
$139$	−59.3437	+	88.0483i	−0.426933	+	0.633441i	−0.979836	−	0.199805i	$-0.935969\pi$
$139$	−59.3437	+	88.0483i	−0.426933	+	0.633441i	0.552902	+	0.833246i	$0.313520\pi$
$140$	−60.2179	−	46.4629i	−0.430128	−	0.331878i
$141$	−31.3547	−	33.4322i	−0.222373	−	0.237108i
$142$	15.6289	+	5.18916i	0.110063	+	0.0365434i
$143$	−18.2371	−	21.4223i	−0.127532	−	0.149806i
$144$	−85.9211	+	38.0347i	−0.596674	+	0.264130i
$145$	−93.6344	+	202.681i	−0.645754	+	1.39780i
$146$	20.1498	+	18.2996i	0.138013	+	0.125339i
$147$	4.24708	+	15.1988i	0.0288917	+	0.103393i
$148$	−193.200	+	6.19555i	−1.30541	+	0.0418618i
$149$	12.2163	+	68.5678i	0.0819886	+	0.460186i	0.998225	+	0.0595492i	$0.0189663\pi$
$149$	12.2163	+	68.5678i	0.0819886	+	0.460186i	−0.916237	+	0.400637i	$0.868789\pi$
$150$	3.71293	−	2.09108i	0.0247528	−	0.0139405i
$151$	−198.223	−	76.5770i	−1.31273	−	0.507133i	−0.400310	−	0.916380i	$-0.631098\pi$
$151$	−198.223	−	76.5770i	−1.31273	−	0.507133i	−0.912424	+	0.409247i	$0.865791\pi$
$152$	9.16726	−	6.61560i	0.0603109	−	0.0435237i
$153$	110.905	−	204.522i	0.724868	−	1.33674i
$154$	−7.38008	+	2.45035i	−0.0479226	+	0.0159114i
$155$	54.5645	+	33.0773i	0.352029	+	0.213402i
$156$	32.4997	+	6.32931i	0.208331	+	0.0405725i
$157$	23.5436	−	2.27122i	0.149959	−	0.0144664i	−0.0207705	−	0.999784i	$-0.506612\pi$
$157$	23.5436	−	2.27122i	0.149959	−	0.0144664i	0.170730	+	0.985318i	$0.445387\pi$
$158$	5.22995	−	32.3491i	0.0331010	−	0.204741i
$159$	13.7196	+	17.7811i	0.0862866	+	0.111831i
$160$	−6.93190	−	107.970i	−0.0433244	−	0.674812i
$161$	80.9841	+	168.165i	0.503007	+	1.04450i
$162$	25.1428	−	34.8404i	0.155202	−	0.215064i
$163$	45.3623	+	69.6886i	0.278296	+	0.427538i	0.949515	−	0.313722i	$-0.101576\pi$
$163$	45.3623	+	69.6886i	0.278296	+	0.427538i	−0.671219	+	0.741259i	$0.734229\pi$
$164$	11.3941	−	49.9210i	0.0694764	−	0.304396i
$165$	0.546615	−	6.80592i	0.00331282	−	0.0412480i
$166$	71.3668	+	58.8089i	0.429921	+	0.354271i
$167$	113.569	−	43.8738i	0.680054	−	0.262717i	0.00445885	−	0.999990i	$-0.498581\pi$
$167$	113.569	−	43.8738i	0.680054	−	0.262717i	0.675595	+	0.737273i	$0.263887\pi$
$168$	10.5718	−	16.2411i	0.0629274	−	0.0966735i
$169$	−10.8417	−	11.1950i	−0.0641522	−	0.0662424i
$170$	47.5033	+	54.0214i	0.279431	+	0.317773i
$171$	7.85962	−	17.7550i	0.0459627	−	0.103831i
$172$	−9.43140	−	31.7775i	−0.0548337	−	0.184753i
$173$	28.0727	+	144.147i	0.162270	+	0.833220i	0.969895	+	0.243524i	$0.0783035\pi$
$173$	28.0727	+	144.147i	0.162270	+	0.833220i	−0.807625	+	0.589696i	$0.799247\pi$
$174$	−25.2111	−	9.27793i	−0.144892	−	0.0533214i
$175$	−21.4841	+	41.1809i	−0.122766	+	0.235320i
$176$	21.8260	+	12.7572i	0.124011	+	0.0724841i
$177$	−0.529831	+	0.0596976i	−0.00299340	+	0.000337275i
$178$	26.2149	+	32.8724i	0.147274	+	0.184676i
$179$	3.64113	+	7.26084i	0.0203415	+	0.0405633i	0.903840	−	0.427872i	$-0.140736\pi$
$179$	3.64113	+	7.26084i	0.0203415	+	0.0405633i	−0.883498	+	0.468435i	$0.844818\pi$
$180$	−67.9803	−	100.862i	−0.377668	−	0.560347i
$181$	−21.2618	+	331.170i	−0.117469	+	1.82967i	0.339982	+	0.940432i	$0.389579\pi$
$181$	−21.2618	+	331.170i	−0.117469	+	1.82967i	−0.457451	+	0.889235i	$0.651237\pi$
$182$	39.3054	−	15.9130i	0.215964	−	0.0874341i
$183$	9.06260	+	9.06260i	0.0495224	+	0.0495224i
$184$	−67.7905	+	160.021i	−0.368426	+	0.869680i
$185$	−44.9659	−	212.665i	−0.243059	−	1.14954i
$186$	−3.44162	+	6.86298i	−0.0185033	+	0.0368978i
$187$	−62.0823	+	8.00463i	−0.331991	+	0.0428055i
$188$	101.612	+	194.771i	0.540488	+	1.03602i
$189$	3.30540	−	68.6869i	0.0174889	−	0.363423i
$190$	4.31271	+	4.17662i	0.0226985	+	0.0219822i
$191$	−75.2820	−	329.832i	−0.394146	−	1.72687i	−0.649805	−	0.760101i	$-0.725149\pi$
$191$	−75.2820	−	329.832i	−0.394146	−	1.72687i	0.255658	−	0.966767i	$-0.417708\pi$
$192$	−20.0202	+	2.90825i	−0.104272	+	0.0151472i
$193$	0.490969	−	15.3102i	0.00254388	−	0.0793275i	−0.997427	−	0.0716901i	$-0.977161\pi$
$193$	0.490969	−	15.3102i	0.00254388	−	0.0793275i	0.999971	−	0.00763743i	$-0.00243109\pi$
$194$	−20.3417	−	82.9696i	−0.104854	−	0.427678i
$195$	−0.596762	+	37.2280i	−0.00306032	+	0.190913i
$196$		−	75.6374i		−	0.385905i
$197$	152.676	−	124.495i	0.775004	−	0.631956i
$197$	152.676	−	124.495i	0.775004	−	0.631956i
$198$	−12.4356			−0.0628063
$199$	−142.442	−	2.28333i	−0.715788	−	0.0114740i	−0.342928	−	0.939362i	$-0.611419\pi$
$199$	−142.442	−	2.28333i	−0.715788	−	0.0114740i	−0.372860	+	0.927888i	$0.621623\pi$
$200$	−42.0037	+	10.2981i	−0.210019	+	0.0514903i
$201$	−92.6937	−	2.97251i	−0.461163	−	0.0147886i
$202$	−12.5691	−	86.5247i	−0.0622232	−	0.428340i
$203$	285.479	−	65.1588i	1.40630	−	0.320979i
$204$	51.2501	−	52.9199i	0.251226	−	0.259411i
$205$	57.5137	+	2.76771i	0.280555	+	0.0135010i
$206$	−91.2861	+	47.6239i	−0.443137	+	0.231184i
$207$	38.1697	+	296.037i	0.184395	+	1.43013i
$208$	−123.232	−	61.7976i	−0.592459	−	0.297104i
$209$	−5.11111	+	1.08069i	−0.0244551	+	0.00517078i
$210$	9.47600	+	4.01436i	0.0451238	+	0.0191160i
$211$	49.5000	−	49.5000i	0.234597	−	0.234597i	−0.580011	−	0.814608i	$-0.696952\pi$
$211$	49.5000	−	49.5000i	0.234597	−	0.234597i	0.814608	+	0.580011i	$0.196952\pi$
$212$	−40.3950	−	99.7763i	−0.190542	−	0.470643i
$213$	18.9252	+	1.21504i	0.0888508	+	0.00570441i
$214$	−77.6469	+	52.3333i	−0.362836	+	0.244548i
$215$	33.3199	−	16.7091i	0.154976	−	0.0777168i
$216$	50.0591	−	39.9208i	0.231755	−	0.184819i
$217$	−9.36989	−	83.1601i	−0.0431792	−	0.383226i
$218$	−49.1154	+	84.0304i	−0.225300	+	0.385461i
$219$	27.7908	+	14.4984i	0.126898	+	0.0662029i
$220$	−11.3022	+	30.7117i	−0.0513736	+	0.139599i
$221$	335.048	−	65.2506i	1.51606	−	0.295252i
$222$	25.0735	−	7.44168i	0.112944	−	0.0335211i
$223$	258.748	+	114.540i	1.16031	+	0.513633i	0.893035	−	0.449988i	$-0.148572\pi$
$223$	258.748	+	114.540i	1.16031	+	0.513633i	0.267272	+	0.963621i	$0.413878\pi$
$224$	−106.560	+	93.7028i	−0.475715	+	0.418316i
$225$	−53.3585	+	51.6749i	−0.237149	+	0.229666i
$226$	−89.4799	−	58.2450i	−0.395929	−	0.257721i
$227$	−65.6532	−	169.946i	−0.289221	−	0.748661i	−0.999020	−	0.0442564i	$-0.985908\pi$
$227$	−65.6532	−	169.946i	−0.289221	−	0.748661i	0.709799	−	0.704404i	$-0.248786\pi$
$228$	3.90989	−	4.74479i	0.0171486	−	0.0208105i
$229$	275.081	+	22.0931i	1.20123	+	0.0964762i	0.664506	−	0.747283i	$-0.268642\pi$
$229$	275.081	+	22.0931i	1.20123	+	0.0964762i	0.536722	+	0.843759i	$0.319663\pi$
$230$	−89.9774	−	20.5368i	−0.391206	−	0.0892902i
$231$	−7.50508	+	4.88526i	−0.0324895	+	0.0211483i
$232$	221.086	+	159.548i	0.952959	+	0.687708i
$233$	310.347	−	149.455i	1.33196	−	0.641440i	0.373759	−	0.927526i	$-0.378069\pi$
$233$	310.347	−	149.455i	1.33196	−	0.641440i	0.958204	+	0.286086i	$0.0923543\pi$
$234$	67.6734	−	4.34477i	0.289202	−	0.0185674i
$235$	−195.584	+	150.909i	−0.832273	+	0.642165i
$236$	2.52276	+	0.407860i	0.0106896	+	0.00172822i
$237$	−3.62357	−	37.5621i	−0.0152893	−	0.158490i
$238$	18.0354	−	92.6081i	0.0757791	−	0.389110i
$239$	−94.6025	+	156.057i	−0.395826	+	0.652957i	−0.988281	−	0.152647i	$-0.951220\pi$
$239$	−94.6025	+	156.057i	−0.395826	+	0.652957i	0.592455	+	0.805604i	$0.298159\pi$
$240$	−10.5426	−	31.7527i	−0.0439276	−	0.132303i
$241$	−36.7177	−	19.9107i	−0.152356	−	0.0826170i	0.398718	−	0.917074i	$-0.369455\pi$
$241$	−36.7177	−	19.9107i	−0.152356	−	0.0826170i	−0.551074	+	0.834457i	$0.685782\pi$
$242$	−43.9617	−	60.9178i	−0.181660	−	0.251726i
$243$	60.0773	−	155.513i	0.247232	−	0.639969i
$244$	−30.1440	−	53.5237i	−0.123541	−	0.219359i
$245$	83.7364	−	14.9188i	0.341781	−	0.0608930i
$246$	0.222063	+	6.92473i	0.000902694	+	0.0281493i
$247$	27.4365	−	7.66673i	0.111079	−	0.0310394i
$248$	52.3856	−	57.6823i	0.211232	−	0.232590i
$249$	96.6756	+	44.6620i	0.388255	+	0.179366i
$250$	−35.7120	−	80.6741i	−0.142848	−	0.322696i
$251$	−185.791	+	158.167i	−0.740205	+	0.630146i	−0.936609	−	0.350377i	$-0.886053\pi$
$251$	−185.791	+	158.167i	−0.740205	+	0.630146i	0.196404	+	0.980523i	$0.437074\pi$
$252$	−50.2682	+	151.400i	−0.199477	+	0.600793i
$253$	58.5773	−	54.9371i	0.231531	−	0.217143i
$254$	−58.2437	+	75.4863i	−0.229306	+	0.297190i
$255$	68.6950	+	46.2998i	0.269392	+	0.181568i
$256$	27.0129	+	3.48293i	0.105519	+	0.0136052i
$257$	11.7687	+	31.9793i	0.0457925	+	0.124433i	0.959300	−	0.282389i	$-0.0911268\pi$
$257$	11.7687	+	31.9793i	0.0457925	+	0.124433i	−0.913508	+	0.406822i	$0.866637\pi$
$258$	2.32502	+	3.83536i	0.00901170	+	0.0148657i
$259$	−184.801	+	217.078i	−0.713517	+	0.838138i
$260$	50.7751	−	171.078i	0.195289	−	0.657994i
$261$	466.112	+	44.9652i	1.78587	+	0.172281i
$262$	−0.939550	+	3.58291i	−0.00358607	+	0.0136752i
$263$	48.3862	+	11.8629i	0.183978	+	0.0451060i	0.329037	−	0.944317i	$-0.393276\pi$
$263$	48.3862	+	11.8629i	0.183978	+	0.0451060i	−0.145059	+	0.989423i	$0.546337\pi$
$264$	−8.03032	−	2.24396i	−0.0304179	−	0.00849984i
$265$	102.492	−	64.4003i	0.386764	−	0.243020i
$266$	0.881611	−	7.82451i	0.00331433	−	0.0294155i
$267$	38.8035	+	28.9598i	0.145332	+	0.108464i
$268$	424.049	+	133.287i	1.58227	+	0.497340i
$269$	63.4738	−	29.3235i	0.235962	−	0.109009i	−0.297849	−	0.954613i	$-0.596269\pi$
$269$	63.4738	−	29.3235i	0.235962	−	0.109009i	0.533812	+	0.845603i	$0.320759\pi$
$270$	25.5344	+	22.4535i	0.0945720	+	0.0831612i
$271$	309.565	−	14.8971i	1.14231	−	0.0549709i	0.531720	−	0.846920i	$-0.321546\pi$
$271$	309.565	−	14.8971i	1.14231	−	0.0549709i	0.610587	+	0.791949i	$0.290934\pi$
$272$	−264.812	+	154.781i	−0.973572	+	0.569049i
$273$	39.1349	−	29.2072i	0.143351	−	0.106986i
$274$	23.7966	−	8.32679i	0.0868489	−	0.0303897i
$275$	19.6750	+	3.50538i	0.0715456	+	0.0127468i
$276$	−13.5870	+	93.5319i	−0.0492282	+	0.338884i
$277$	−3.39484	−	42.2692i	−0.0122557	−	0.152596i	0.987738	−	0.156120i	$-0.0498987\pi$
$277$	−3.39484	−	42.2692i	−0.0122557	−	0.152596i	−0.999994	+	0.00352380i	$0.998878\pi$
$278$	−39.3953	+	56.4761i	−0.141710	+	0.203151i
$279$	27.6849	−	130.935i	0.0992291	−	0.469301i
$280$	−81.6590	−	65.1209i	−0.291639	−	0.232575i
$281$	−96.6828	+	153.870i	−0.344067	+	0.547579i	−0.973271	−	0.229661i	$-0.926238\pi$
$281$	−96.6828	+	153.870i	−0.344067	+	0.547579i	0.629204	+	0.777240i	$0.283381\pi$
$282$	−19.9837	−	22.0043i	−0.0708642	−	0.0780294i
$283$	−68.3302	−	217.391i	−0.241450	−	0.768165i	−0.993976	−	0.109602i	$-0.965042\pi$
$283$	−68.3302	−	217.391i	−0.241450	−	0.768165i	0.752526	−	0.658563i	$-0.228835\pi$
$284$	−85.7933	−	30.0204i	−0.302089	−	0.105706i
$285$	6.02404	+	3.39267i	0.0211370	+	0.0119041i
$286$	−11.6027	−	14.0804i	−0.0405691	−	0.0492321i
$287$	−43.2056	−	61.9385i	−0.150542	−	0.215814i
$288$	−208.946	+	88.5169i	−0.725509	+	0.307350i
$289$	176.553	−	436.088i	0.610909	−	1.50896i
$290$	−62.8218	+	130.451i	−0.216627	+	0.449830i
$291$	−46.8949	−	86.4798i	−0.161151	−	0.297181i
$292$	−109.583	−	102.773i	−0.375285	−	0.351964i
$293$	245.040	−	39.6162i	0.836315	−	0.135209i	0.273583	−	0.961848i	$-0.411791\pi$
$293$	245.040	−	39.6162i	0.836315	−	0.135209i	0.562732	+	0.826639i	$0.309750\pi$
$294$	2.59594	+	9.89945i	0.00882974	+	0.0336716i
$295$	0.0460592	+	2.87333i	0.000156133	+	0.00974010i
$296$	−265.408	+	4.25447i	−0.896649	+	0.0143732i
$297$	−28.6199	+	7.50501i	−0.0963632	+	0.0252694i
$298$	7.20867	+	44.5882i	0.0241902	+	0.149625i
$299$	−299.577	+	319.427i	−1.00193	+	1.06832i
$300$	−20.6757	+	11.2117i	−0.0689191	+	0.0373724i
$301$	−44.0461	−	21.2115i	−0.146332	−	0.0704700i
$302$	−127.737	−	51.7150i	−0.422970	−	0.171242i
$303$	−39.2753	−	92.7104i	−0.129621	−	0.305975i
$304$	−20.9954	+	14.6455i	−0.0690637	+	0.0481759i
$305$	53.3092	−	43.9287i	0.174784	−	0.144029i
$306$	74.0395	−	131.465i	0.241959	−	0.429623i
$307$	−88.2512	+	252.207i	−0.287463	+	0.821523i	0.706087	+	0.708126i	$0.250459\pi$
$307$	−88.2512	+	252.207i	−0.287463	+	0.821523i	−0.993550	+	0.113397i	$0.963827\pi$
$308$	40.9457	−	12.8700i	0.132940	−	0.0417859i
$309$	−87.7745	+	79.7145i	−0.284060	+	0.257976i
$310$	35.0373	+	22.0154i	0.113024	+	0.0710174i
$311$	351.459	−	440.716i	1.13009	−	1.41709i	0.234558	−	0.972102i	$-0.424636\pi$
$311$	351.459	−	440.716i	1.13009	−	1.41709i	0.895535	−	0.444990i	$-0.146793\pi$
$312$	44.4841	+	9.40571i	0.142577	+	0.0301465i
$313$	103.566	+	72.2429i	0.330880	+	0.230808i	0.725797	−	0.687909i	$-0.241471\pi$
$313$	103.566	+	72.2429i	0.330880	+	0.230808i	−0.394916	+	0.918717i	$0.629226\pi$
$314$	15.2899	−	1.22801i	0.0486940	−	0.00391085i
$315$	−177.526	−	25.7885i	−0.563574	−	0.0818681i
$316$	−31.7246	+	178.064i	−0.100394	+	0.563495i
$317$	−9.49745	−	27.1421i	−0.0299604	−	0.0856219i	0.927932	−	0.372750i	$-0.121585\pi$
$317$	−9.49745	−	27.1421i	−0.0299604	−	0.0856219i	−0.957892	+	0.287128i	$0.907299\pi$
$318$	8.71132	+	11.6724i	0.0273941	+	0.0367056i
$319$	−63.5769	−	108.772i	−0.199301	−	0.340978i
$320$	5.24101	+	108.909i	0.0163782	+	0.340342i
$321$	−71.2059	+	80.9763i	−0.221825	+	0.252263i
$322$	50.7643	+	109.885i	0.157653	+	0.341257i
$323$	19.0059	−	60.4668i	0.0588419	−	0.187204i
$324$	−141.839	+	190.052i	−0.437776	+	0.586579i
$325$	−108.294	−	12.2018i	−0.333212	−	0.0375440i
$326$	28.6898	+	45.6595i	0.0880054	+	0.140060i
$327$	−30.1651	+	107.950i	−0.0922481	+	0.330123i
$328$	16.7434	−	68.2927i	0.0510468	−	0.208210i
$329$	313.401	+	82.1835i	0.952588	+	0.249798i
$330$	0.425183	−	4.40746i	0.00128843	−	0.0133559i
$331$	−562.411	−	166.921i	−1.69913	−	0.504292i	−0.717735	−	0.696316i	$-0.754821\pi$
$331$	−562.411	−	166.921i	−1.69913	−	0.504292i	−0.981390	+	0.192024i	$0.938495\pi$
$332$	−388.654	−	330.866i	−1.17064	−	0.996584i
$333$	−389.865	+	236.338i	−1.17076	+	0.709725i
$334$	74.0972	−	27.2685i	0.221848	−	0.0816421i
$335$	−63.9191	+	495.744i	−0.190803	+	1.47983i
$336$	−24.5247	+	36.3873i	−0.0729902	+	0.108296i
$337$	112.485	+	86.7916i	0.333785	+	0.257542i	0.764045	−	0.645163i	$-0.223211\pi$
$337$	112.485	+	86.7916i	0.333785	+	0.257542i	−0.430260	+	0.902705i	$0.641578\pi$
$338$	−6.91370	−	7.37181i	−0.0204547	−	0.0218101i
$339$	−116.687	−	38.7429i	−0.344211	−	0.114286i
$340$	−257.381	−	302.334i	−0.757002	−	0.889217i
$341$	−32.9252	+	14.5750i	−0.0965549	+	0.0427420i
$342$	5.28094	−	11.4311i	0.0154413	−	0.0334244i
$343$	−274.072	−	248.905i	−0.799045	−	0.725672i
$344$	−12.2503	−	43.8394i	−0.0356113	−	0.127440i
$345$	−106.227	+	3.40649i	−0.307904	+	0.00987387i
$346$	16.7048	+	93.7607i	0.0482797	+	0.270985i
$347$	80.6030	−	45.3947i	0.232285	−	0.130821i	−0.370196	−	0.928954i	$-0.620709\pi$
$347$	80.6030	−	45.3947i	0.232285	−	0.130821i	0.602481	+	0.798133i	$0.294179\pi$
$348$	138.313	+	53.4330i	0.397453	+	0.153543i
$349$	−495.510	+	357.588i	−1.41980	+	1.02461i	−0.427073	+	0.904217i	$0.640455\pi$
$349$	−495.510	+	357.588i	−1.41980	+	1.02461i	−0.992727	+	0.120390i	$0.961586\pi$
$350$	−14.3589	+	26.4795i	−0.0410254	+	0.0756558i
$351$	153.124	−	50.8406i	0.436250	−	0.144845i
$352$	52.2095	+	31.6497i	0.148322	+	0.0899140i
$353$	102.142	+	19.8921i	0.289353	+	0.0563514i	0.333747	−	0.942663i	$-0.391687\pi$
$353$	102.142	+	19.8921i	0.289353	+	0.0563514i	−0.0443944	+	0.999014i	$0.514136\pi$
$354$	−0.344177	+	0.0332024i	−0.000972252	+	9.37920e-5i
$355$	16.3129	−	100.901i	0.0459518	−	0.284228i
$356$	−141.766	−	183.734i	−0.398218	−	0.516107i
$357$	−6.96122	−	108.427i	−0.0194992	−	0.303716i
$358$	2.28554	+	4.74597i	0.00638419	+	0.0132569i
$359$	104.062	−	144.199i	0.289867	−	0.401669i	−0.640700	−	0.767791i	$-0.721356\pi$
$359$	104.062	−	144.199i	0.289867	−	0.401669i	0.930567	+	0.366122i	$0.119315\pi$
$360$	−91.1198	−	139.984i	−0.253111	−	0.388846i
$361$	−79.1530	+	346.792i	−0.219260	+	0.960642i
$362$	−17.2290	+	214.518i	−0.0475939	+	0.592592i
$363$	−66.7643	−	55.0163i	−0.183924	−	0.151560i
$364$	−218.325	+	84.3429i	−0.599794	+	0.231711i
$365$	92.1637	−	141.588i	0.252503	−	0.387913i
$366$	5.78224	+	5.97063i	0.0157985	+	0.0163132i
$367$	−474.723	−	539.862i	−1.29352	−	1.47101i	−0.798315	−	0.602240i	$-0.794275\pi$
$367$	−474.723	−	539.862i	−1.29352	−	1.47101i	−0.495209	−	0.868774i	$-0.664908\pi$
$368$	159.290	−	359.838i	0.432852	−	0.977821i
$369$	−34.3621	−	115.777i	−0.0931222	−	0.313760i
$370$	−26.9466	−	138.365i	−0.0728287	−	0.373960i
$371$	−148.988	−	54.8290i	−0.401586	−	0.147787i
$372$	19.6006	−	37.5707i	0.0526898	−	0.100997i
$373$	−268.191	−	156.757i	−0.719012	−	0.420260i	0.0992825	−	0.995059i	$-0.468345\pi$
$373$	−268.191	−	156.757i	−0.719012	−	0.420260i	−0.818294	+	0.574800i	$0.805080\pi$
$374$	−40.3391	+	4.54512i	−0.107858	+	0.0121527i
$375$	−63.3458	−	79.4331i	−0.168922	−	0.211822i
$376$	135.230	+	269.665i	0.359655	+	0.717194i
$377$	383.981	+	569.713i	1.01852	+	1.51117i
$378$	2.85726	−	44.5041i	0.00755888	−	0.117736i
$379$	−24.6547	+	9.98159i	−0.0650520	+	0.0263366i	−0.407562	−	0.913178i	$-0.633621\pi$
$379$	−24.6547	+	9.98159i	−0.0650520	+	0.0263366i	0.342510	+	0.939514i	$0.388723\pi$
$380$	−23.4313	−	23.4313i	−0.0616614	−	0.0616614i
$381$	−42.8291	+	101.099i	−0.112412	+	0.265352i
$382$	−45.3865	−	214.654i	−0.118813	−	0.561923i
$383$	−151.945	+	302.995i	−0.396722	+	0.791110i	−0.999979	−	0.00643725i	$-0.997951\pi$
$383$	−151.945	+	302.995i	−0.396722	+	0.791110i	0.603257	+	0.797547i	$0.293869\pi$
$384$	−92.6483	+	11.9457i	−0.241272	+	0.0311085i
$385$	22.3243	+	42.7915i	0.0579851	+	0.111147i
$386$	0.477495	−	9.92245i	0.00123703	−	0.0257058i
$387$	−56.1606	−	54.3886i	−0.145118	−	0.140539i
$388$	104.921	+	459.689i	0.270415	+	1.18476i
$389$	155.959	−	22.6555i	0.400922	−	0.0582404i	0.0596845	−	0.998217i	$-0.480991\pi$
$389$	155.959	−	22.6555i	0.400922	−	0.0582404i	0.341238	+	0.939977i	$0.389154\pi$
$390$	−0.773913	+	24.1334i	−0.00198439	+	0.0618806i
$391$	232.015	+	946.340i	0.593388	+	2.42031i
$392$	1.66476	−	103.853i	0.00424683	−	0.264932i
$393$			4.26554i			0.0108538i
$394$	100.293	−	79.1392i	0.254551	−	0.200861i
$395$	−203.388			−0.514907
$396$	68.6294	+	1.10012i	0.173307	+	0.00277809i
$397$	474.240	−	116.270i	1.19456	−	0.292871i	0.409511	−	0.912305i	$-0.365699\pi$
$397$	474.240	−	116.270i	1.19456	−	0.292871i	0.785048	+	0.619434i	$0.212638\pi$
$398$	−92.3394	−	2.96114i	−0.232009	−	0.00744006i
$399$	−1.30353	−	8.97343i	−0.00326700	−	0.0224898i
$400$	95.4729	−	21.7911i	0.238682	−	0.0544777i
$401$	299.886	−	309.657i	0.747845	−	0.772211i	−0.231840	−	0.972754i	$-0.574475\pi$
$401$	299.886	−	309.657i	0.747845	−	0.772211i	0.979685	+	0.200543i	$0.0642705\pi$
$402$	−60.0742	−	2.89093i	−0.149438	−	0.00719138i
$403$	174.083	−	90.8190i	0.431968	−	0.225357i
$404$	61.7114	+	478.621i	0.152751	+	1.18471i
$405$	−238.378	−	119.541i	−0.588588	−	0.295163i
$406$	185.790	−	39.2834i	0.457611	−	0.0967572i
$407$	112.945	+	47.8473i	0.277505	+	0.117561i
$408$	71.5332	−	71.5332i	0.175327	−	0.175327i
$409$	−28.3945	−	70.1351i	−0.0694243	−	0.171479i	0.888231	−	0.459398i	$-0.151935\pi$
$409$	−28.3945	−	70.1351i	−0.0694243	−	0.171479i	−0.957655	+	0.287918i	$0.907037\pi$
$410$	37.2647	+	2.39247i	0.0908894	+	0.00583529i
$411$	24.0753	−	16.2265i	0.0585773	−	0.0394805i
$412$	508.000	−	254.749i	1.23301	−	0.618324i
$413$	2.94670	−	2.34992i	0.00713488	−	0.00568988i
$414$	21.6732	+	192.355i	0.0523507	+	0.464625i
$415$	289.635	−	495.530i	0.697917	−	1.19405i
$416$	−295.176	−	153.993i	−0.709558	−	0.370176i
$417$	−27.3864	+	74.4176i	−0.0656747	+	0.178459i
$418$	−3.32541	+	0.647624i	−0.00795553	+	0.00154934i
$419$	−564.742	+	167.613i	−1.34783	+	0.400030i	−0.876278	−	0.481806i	$-0.839981\pi$
$419$	−564.742	+	167.613i	−1.34783	+	0.400030i	−0.471556	+	0.881836i	$0.656307\pi$
$420$	−51.9406	−	22.9926i	−0.123668	−	0.0547442i
$421$	−327.081	+	287.616i	−0.776914	+	0.683173i	−0.953594	−	0.301095i	$-0.902648\pi$
$421$	−327.081	+	287.616i	−0.776914	+	0.683173i	0.176680	+	0.984268i	$0.443464\pi$
$422$	32.6117	−	31.5826i	0.0772788	−	0.0748404i
$423$	434.241	+	282.660i	1.02657	+	0.668226i
$424$	−53.2679	−	137.886i	−0.125632	−	0.325203i
$425$	−154.199	+	187.126i	−0.362821	+	0.440297i
$426$	12.2590	+	0.984577i	0.0287770	+	0.00231121i
$427$	−88.3257	−	20.1598i	−0.206852	−	0.0472126i
$428$	433.145	−	281.946i	1.01202	−	0.658752i
$429$	−17.0375	−	12.2952i	−0.0397145	−	0.0286602i
$430$	21.7792	−	10.4883i	0.0506493	−	0.0243914i
$431$	−350.333	+	22.4921i	−0.812837	+	0.0521858i	−0.464935	−	0.885345i	$-0.653922\pi$
$431$	−350.333	+	22.4921i	−0.812837	+	0.0521858i	−0.347902	+	0.937531i	$0.613106\pi$
$432$	−114.786	+	88.5665i	−0.265708	+	0.205015i
$433$	552.366	+	89.3023i	1.27567	+	0.206241i	0.759649	−	0.650334i	$-0.225371\pi$
$433$	552.366	+	89.3023i	1.27567	+	0.206241i	0.516024	+	0.856574i	$0.327412\pi$
$434$	−5.21130	−	54.0206i	−0.0120076	−	0.124471i
$435$	−31.8733	+	163.663i	−0.0732720	+	0.376236i
$436$	278.490	−	459.399i	0.638739	−	1.05367i
$437$	25.6240	+	77.1753i	0.0586360	+	0.176602i
$438$	17.8696	+	9.69003i	0.0407981	+	0.0221234i
$439$	−34.7658	−	48.1750i	−0.0791932	−	0.109738i	0.769442	−	0.638717i	$-0.220534\pi$
$439$	−34.7658	−	48.1750i	−0.0791932	−	0.109738i	−0.848635	+	0.528979i	$0.822575\pi$
$440$	−16.1943	+	41.9197i	−0.0368053	+	0.0952720i
$441$	−87.5413	−	155.438i	−0.198506	−	0.352468i
$442$	217.933	−	38.8277i	0.493060	−	0.0878455i
$443$	−21.5564	−	672.207i	−0.0486600	−	1.51740i	−0.674983	−	0.737833i	$-0.735849\pi$
$443$	−21.5564	−	672.207i	−0.0486600	−	1.51740i	0.626323	−	0.779564i	$-0.284559\pi$
$444$	−139.033	+	38.8507i	−0.313137	+	0.0875016i
$445$	175.446	−	193.185i	0.394260	−	0.434124i
$446$	166.589	+	76.9604i	0.373518	+	0.172557i
$447$	21.0543	+	47.5621i	0.0471014	+	0.106403i
$448$	108.890	−	92.6996i	0.243059	−	0.206919i
$449$	−138.347	+	416.678i	−0.308122	+	0.928013i	0.673831	+	0.738886i	$0.264648\pi$
$449$	−138.347	+	416.678i	−0.308122	+	0.928013i	−0.981953	+	0.189128i	$0.939434\pi$
$450$	−35.1362	+	32.9528i	−0.0780805	+	0.0732283i
$451$	−19.8492	+	25.7254i	−0.0440116	+	0.0570408i
$452$	488.666	+	329.356i	1.08112	+	0.728664i
$453$	−157.395	−	20.2939i	−0.347451	−	0.0447989i
$454$	−40.8049	−	110.880i	−0.0898785	−	0.244229i
$455$	−136.437	−	225.067i	−0.299861	−	0.494652i
$456$	5.47287	−	6.42874i	0.0120019	−	0.0140981i
$457$	−79.4721	+	267.768i	−0.173900	+	0.585925i	0.825857	+	0.563879i	$0.190692\pi$
$457$	−79.4721	+	267.768i	−0.173900	+	0.585925i	−0.999757	+	0.0220463i	$0.992982\pi$
$458$	178.140	+	17.1850i	0.388953	+	0.0375218i
$459$	91.0573	−	347.241i	0.198382	−	0.756516i
$460$	494.747	+	121.297i	1.07554	+	0.263690i
$461$	357.951	+	100.024i	0.776467	+	0.216972i	0.634525	−	0.772903i	$-0.281196\pi$
$461$	357.951	+	100.024i	0.776467	+	0.216972i	0.141942	+	0.989875i	$0.454665\pi$
$462$	−4.91727	+	3.08973i	−0.0106435	+	0.00668772i
$463$	21.0416	−	186.750i	0.0454463	−	0.403347i	−0.950309	−	0.311308i	$-0.899233\pi$
$463$	21.0416	−	186.750i	0.0454463	−	0.403347i	0.995755	−	0.0920392i	$-0.0293385\pi$
$464$	−494.764	−	369.252i	−1.06630	−	0.795801i
$465$	45.4597	+	14.2889i	0.0977627	+	0.0307288i
$466$	202.791	−	93.6851i	0.435174	−	0.201041i
$467$	−2.34928	−	2.06582i	−0.00503057	−	0.00442359i	0.657830	−	0.753166i	$-0.271474\pi$
$467$	−2.34928	−	2.06582i	−0.00503057	−	0.00442359i	−0.662861	+	0.748742i	$0.730658\pi$
$468$	−373.858	+	17.9910i	−0.798841	+	0.0384424i
$469$	565.982	−	330.814i	1.20679	−	0.705361i
$470$	−128.391	+	95.8204i	−0.273172	+	0.203873i
$471$	16.6731	−	5.83417i	0.0353994	−	0.0123868i
$472$	3.45487	+	0.615533i	0.00731964	+	0.00130410i
$473$	−3.02384	+	20.8159i	−0.00639289	+	0.0440082i
$474$	−1.95919	−	24.3939i	−0.00413332	−	0.0514640i
$475$	−11.5775	+	16.5972i	−0.0243736	+	0.0349414i
$476$	−107.726	+	509.487i	−0.226315	+	1.07035i
$477$	−198.493	−	158.293i	−0.416127	−	0.331851i
$478$	−62.9649	+	100.208i	−0.131726	+	0.209640i
$479$	−168.508	−	185.546i	−0.351791	−	0.387361i	0.538597	−	0.842564i	$-0.318955\pi$
$479$	−168.508	−	185.546i	−0.351791	−	0.387361i	−0.890388	+	0.455203i	$0.849567\pi$
$480$	−24.2283	−	77.0816i	−0.0504756	−	0.160587i
$481$	−631.349	−	220.919i	−1.31258	−	0.459290i
$482$	−23.6018	−	13.2923i	−0.0489664	−	0.0275774i
$483$	88.6454	+	107.575i	0.183531	+	0.222722i
$484$	237.225	+	340.080i	0.490134	+	0.702644i
$485$	−488.216	+	206.825i	−1.00663	+	0.426443i
$486$	40.5722	−	100.214i	0.0834818	−	0.206202i
$487$	−53.0728	+	110.207i	−0.108979	+	0.226297i	−0.948325	−	0.317300i	$-0.897224\pi$
$487$	−53.0728	+	110.207i	−0.108979	+	0.226297i	0.839346	+	0.543597i	$0.182938\pi$
$488$	−40.2109	−	74.1537i	−0.0823994	−	0.151954i
$489$	45.2956	+	42.4807i	0.0926289	+	0.0868727i
$490$	54.4520	−	8.80337i	0.111127	−	0.0179661i
$491$	−42.5768	−	162.364i	−0.0867145	−	0.330680i	0.909702	−	0.415262i	$-0.136310\pi$
$491$	−42.5768	−	162.364i	−0.0867145	−	0.330680i	−0.996417	+	0.0845816i	$0.973045\pi$
$492$	−0.612913	−	38.2356i	−0.00124576	−	0.0777146i
$493$	1528.42	−	24.5004i	3.10024	−	0.0496966i
$494$	17.8702	−	4.68613i	0.0361746	−	0.00948610i
$495$	12.3186	+	76.1949i	0.0248861	+	0.153929i
$496$	−120.698	+	128.695i	−0.243342	+	0.259467i
$497$	−117.843	+	63.9022i	−0.237109	+	0.128576i
$498$	62.2228	+	29.9649i	0.124945	+	0.0601705i
$499$	−310.977	−	125.901i	−0.623200	−	0.252306i	0.0418270	−	0.999125i	$-0.486682\pi$
$499$	−310.977	−	125.901i	−0.623200	−	0.252306i	−0.665027	+	0.746819i	$0.731580\pi$
$500$	189.949	+	448.380i	0.379899	+	0.896761i
$501$	74.5734	−	52.0192i	0.148849	−	0.103831i
$502$	−122.116	+	100.628i	−0.243259	+	0.200455i
$503$	−123.690	+	219.624i	−0.245905	+	0.436629i	−0.966478	−	0.256750i	$-0.917348\pi$
$503$	−123.690	+	219.624i	−0.245905	+	0.436629i	0.720573	+	0.693379i	$0.243879\pi$
$504$	−72.3525	+	206.772i	−0.143557	+	0.410261i
$505$	−517.698	+	162.723i	−1.02514	+	0.322224i
$506$	38.5541	−	35.0138i	0.0761939	−	0.0691973i
$507$	−9.85467	−	6.19210i	−0.0194372	−	0.0122132i
$508$	328.111	−	411.438i	0.645888	−	0.809918i
$509$	−216.002	−	45.6714i	−0.424365	−	0.0897277i	−0.0102396	−	0.999948i	$-0.503259\pi$
$509$	−216.002	−	45.6714i	−0.424365	−	0.0897277i	−0.414125	+	0.910220i	$0.635912\pi$
$510$	44.0624	+	30.7361i	0.0863969	+	0.0602668i
$511$	−220.863	+	17.7386i	−0.432218	+	0.0347134i
$512$	512.622	+	74.4664i	1.00121	+	0.145442i
$513$	5.25497	−	29.4951i	0.0102436	−	0.0574954i
$514$	7.29872	+	20.8585i	0.0141998	+	0.0405808i
$515$	382.225	+	512.147i	0.742185	+	0.994460i
$516$	−12.4919	−	21.3721i	−0.0242092	−	0.0414188i
$517$	−6.70073	−	139.243i	−0.0129608	−	0.269328i
$518$	−122.086	+	138.838i	−0.235688	+	0.268027i
$519$	45.9958	+	99.5627i	0.0886239	+	0.191836i
$520$	73.4817	−	233.780i	0.141311	−	0.449577i
$521$	256.993	−	344.347i	0.493268	−	0.660935i	−0.483472	−	0.875360i	$-0.660624\pi$
$521$	256.993	−	344.347i	0.493268	−	0.660935i	0.976740	+	0.214425i	$0.0687878\pi$
$522$	301.772	+	34.0016i	0.578108	+	0.0651371i
$523$	399.175	+	635.284i	0.763241	+	1.21469i	0.971598	+	0.236639i	$0.0760458\pi$
$523$	399.175	+	635.284i	0.763241	+	1.21469i	−0.208356	+	0.978053i	$0.566811\pi$
$524$	5.50212	−	19.6901i	0.0105002	−	0.0375766i
$525$	−8.25991	+	33.6905i	−0.0157332	+	0.0641723i
$526$	31.2516	+	8.19514i	0.0594137	+	0.0155801i
$527$	41.9494	−	434.849i	0.0796003	−	0.825141i
$528$	18.0997	+	5.37191i	0.0342798	+	0.0101741i
$529$	−549.053	−	467.416i	−1.03791	−	0.883584i
$530$	67.1283	−	40.6936i	0.126657	−	0.0767803i
$531$	5.65643	−	2.08162i	0.0106524	−	0.00392018i
$532$	−5.55760	+	43.1036i	−0.0104466	+	0.0810219i
$533$	99.0292	−	146.930i	0.185796	−	0.275665i
$534$	24.8602	+	19.1817i	0.0465548	+	0.0359207i
$535$	397.569	+	423.913i	0.743120	+	0.792360i
$536$	579.303	+	192.342i	1.08079	+	0.358847i
$537$	3.93224	+	4.61903i	0.00732260	+	0.00860154i
$538$	41.4629	−	18.3544i	0.0770687	−	0.0341160i
$539$	−20.1294	+	43.5721i	−0.0373458	+	0.0808387i
$540$	−138.932	−	126.175i	−0.257282	−	0.233657i
$541$	−154.519	−	552.967i	−0.285617	−	1.02212i	−0.959135	−	0.282950i	$-0.908687\pi$
$541$	−154.519	−	552.967i	−0.285617	−	1.02212i	0.673518	−	0.739171i	$-0.264782\pi$
$542$	200.885	−	6.44200i	0.370637	−	0.0118856i
$543$	43.4701	+	243.990i	0.0800555	+	0.449336i
$544$	−645.434	+	363.501i	−1.18646	+	0.668201i
$545$	563.519	+	217.698i	1.03398	+	0.399445i
$546$	25.6797	−	18.5319i	0.0470325	−	0.0339413i
$547$	233.594	−	430.775i	0.427045	−	0.787523i	−0.572429	−	0.819955i	$-0.693999\pi$
$547$	233.594	−	430.775i	0.427045	−	0.787523i	0.999474	+	0.0324317i	$0.0103251\pi$
$548$	−132.064	+	43.8484i	−0.240993	+	0.0800153i
$549$	−123.895	−	75.1056i	−0.225673	−	0.136804i
$550$	12.7214	+	2.47749i	0.0231298	+	0.00450453i
$551$	126.985	−	12.2500i	0.230462	−	0.0222324i
$552$	−20.7141	+	128.124i	−0.0375255	+	0.232109i
$553$	162.953	+	211.194i	0.294671	+	0.381906i
$554$	−1.76195	−	27.4438i	−0.00318042	−	0.0495375i
$555$	−70.4337	−	146.257i	−0.126908	−	0.263526i
$556$	222.409	−	308.193i	0.400017	−	0.554304i
$557$	−127.564	−	195.973i	−0.229020	−	0.351836i	0.704907	−	0.709300i	$-0.250989\pi$
$557$	−127.564	−	195.973i	−0.229020	−	0.351836i	−0.933927	+	0.357463i	$0.883642\pi$
$558$	19.3126	−	84.6141i	0.0346104	−	0.151638i
$559$	9.18271	−	114.334i	0.0164270	−	0.204533i
$560$	182.518	+	150.402i	0.325925	+	0.268574i
$561$	−43.6070	+	16.8462i	−0.0777308	+	0.0300288i
$562$	−64.2911	+	98.7684i	−0.114397	+	0.175744i
$563$	−160.024	−	165.238i	−0.284234	−	0.293495i	0.561083	−	0.827759i	$-0.310385\pi$
$563$	−160.024	−	165.238i	−0.284234	−	0.293495i	−0.845318	+	0.534264i	$0.820589\pi$
$564$	108.339	+	123.204i	0.192090	+	0.218447i
$565$	−268.237	+	605.953i	−0.474756	+	1.07248i
$566$	−42.0476	−	141.672i	−0.0742890	−	0.250304i
$567$	66.8582	+	343.303i	0.117916	+	0.605472i
$568$	−117.137	−	43.1075i	−0.206227	−	0.0758935i
$569$	−240.900	+	461.760i	−0.423374	+	0.811529i	−0.999985	−	0.00548981i	$-0.998253\pi$
$569$	−240.900	+	461.760i	−0.423374	+	0.811529i	0.576611	+	0.817019i	$0.304375\pi$
$570$	3.87088	+	2.26252i	0.00679103	+	0.00396933i
$571$	−731.400	+	82.4090i	−1.28091	+	0.144324i	−0.726063	−	0.687628i	$-0.758652\pi$
$571$	−731.400	+	82.4090i	−1.28091	+	0.144324i	−0.554847	+	0.831952i	$0.687223\pi$
$572$	62.7872	+	78.7326i	0.109768	+	0.137644i
$573$	−113.259	−	225.851i	−0.197659	−	0.394155i
$574$	−27.3719	−	40.6117i	−0.0476862	−	0.0707521i
$575$	19.9311	−	310.443i	0.0346628	−	0.539902i
$576$	211.978	−	85.8202i	0.368017	−	0.148993i
$577$	393.072	+	393.072i	0.681234	+	0.681234i	0.960278	−	0.279044i	$-0.0900175\pi$
$577$	393.072	+	393.072i	0.681234	+	0.681234i	−0.279044	+	0.960278i	$0.590017\pi$
$578$	119.014	−	280.936i	0.205907	−	0.486049i
$579$	−2.36651	−	11.1923i	−0.00408723	−	0.0193304i
$580$	358.239	−	714.369i	0.617653	−	1.23167i
$581$	−746.602	+	96.2637i	−1.28503	+	0.165686i
$582$	−29.5090	−	56.5633i	−0.0507028	−	0.0971878i
$583$	−3.28331	+	68.2280i	−0.00563176	+	0.117029i
$584$	−148.200	−	143.524i	−0.253768	−	0.245760i
$585$	−93.6575	−	410.340i	−0.160098	−	0.701436i
$586$	159.303	−	23.1412i	0.271847	−	0.0394902i
$587$	30.7381	−	958.526i	0.0523647	−	1.63292i	−0.550327	−	0.834949i	$-0.685497\pi$
$587$	30.7381	−	958.526i	0.0523647	−	1.63292i	0.602692	−	0.797974i	$-0.294095\pi$
$588$	−13.4506	−	54.8624i	−0.0228752	−	0.0933034i
$589$	0.584372	−	36.4551i	0.000992143	−	0.0618932i
$590$			1.86362i			0.00315868i
$591$	88.6019	−	117.451i	0.149919	−	0.198733i
$592$	601.056			1.01530
$593$	−1013.63	−	16.2484i	−1.70932	−	0.0274003i	−0.846342	−	0.532640i	$-0.821200\pi$
$593$	−1013.63	−	16.2484i	−1.70932	−	0.0274003i	−0.862979	+	0.505239i	$0.831404\pi$
$594$	−18.6359	+	4.56897i	−0.0313736	+	0.00769187i
$595$	−585.289	−	18.7691i	−0.983678	−	0.0315446i
$596$	−35.8384	−	246.709i	−0.0601316	−	0.413942i
$597$	−103.724	+	23.6743i	−0.173742	+	0.0396555i
$598$	−197.574	+	204.011i	−0.330391	+	0.341156i
$599$	−651.214	−	31.3382i	−1.08717	−	0.0523175i	−0.503258	−	0.864136i	$-0.667866\pi$
$599$	−651.214	−	31.3382i	−1.08717	−	0.0523175i	−0.583910	+	0.811819i	$0.698478\pi$
$600$	−28.6354	+	14.9391i	−0.0477257	+	0.0248985i
$601$	−121.767	−	944.401i	−0.202607	−	1.57138i	−0.706561	−	0.707652i	$-0.749755\pi$
$601$	−121.767	−	944.401i	−0.202607	−	1.57138i	0.503954	−	0.863730i	$-0.331878\pi$
$602$	−28.3402	−	14.2119i	−0.0470767	−	0.0236078i
$603$	1025.70	−	216.875i	1.70100	−	0.359660i
$604$	700.375	+	296.703i	1.15956	+	0.491230i
$605$	−329.704	+	329.704i	−0.544965	+	0.544965i
$606$	−24.5035	−	60.5241i	−0.0404348	−	0.0998748i
$607$	768.750	+	49.3554i	1.26647	+	0.0813103i	0.682756	−	0.730646i	$-0.260781\pi$
$607$	768.750	+	49.3554i	1.26647	+	0.0813103i	0.583718	+	0.811957i	$0.301597\pi$
$608$	−51.2645	+	34.5518i	−0.0843167	+	0.0568286i
$609$	195.481	−	98.0289i	0.320987	−	0.160967i
$610$	35.0237	−	27.9305i	0.0574159	−	0.0457877i
$611$	85.1133	+	755.401i	0.139302	+	1.23634i
$612$	−420.236	+	718.972i	−0.686661	+	1.17479i
$613$	−765.529	−	399.376i	−1.24882	−	0.651510i	−0.296044	−	0.955174i	$-0.595667\pi$
$613$	−765.529	−	399.376i	−1.24882	−	0.651510i	−0.952779	+	0.303664i	$0.901790\pi$
$614$	−59.8460	+	162.621i	−0.0974690	+	0.264855i
$615$	42.2088	−	8.22017i	0.0686322	−	0.0133661i
$616$	56.5033	−	16.7699i	0.0917262	−	0.0272239i
$617$	278.769	+	123.403i	0.451814	+	0.200005i	0.618143	−	0.786066i	$-0.287885\pi$
$617$	278.769	+	123.403i	0.451814	+	0.200005i	−0.166329	+	0.986070i	$0.553191\pi$
$618$	−57.7440	+	50.7767i	−0.0934368	+	0.0821629i
$619$	−136.797	+	132.481i	−0.220997	+	0.214024i	−0.797901	−	0.602788i	$-0.794057\pi$
$619$	−136.797	+	132.481i	−0.220997	+	0.214024i	0.576904	+	0.816812i	$0.304261\pi$
$620$	−191.415	−	124.597i	−0.308734	−	0.200963i
$621$	165.967	+	429.613i	0.267258	+	0.691808i
$622$	232.476	−	282.119i	0.373756	−	0.453567i
$623$	−341.165	−	27.4006i	−0.547617	−	0.0439817i
$624$	−100.374	−	22.9096i	−0.160855	−	0.0367141i
$625$	−274.577	+	178.730i	−0.439324	+	0.285968i
$626$	66.4038	+	47.9207i	0.106076	+	0.0765507i
$627$	−3.51508	+	1.69277i	−0.00560619	+	0.00269980i
$628$	−84.4901	+	5.42445i	−0.134538	+	0.00863765i
$629$	−1178.27	+	909.132i	−1.87325	+	1.44536i
$630$	−114.845	−	18.5672i	−0.182293	−	0.0294717i
$631$	30.9358	+	320.682i	0.0490266	+	0.508212i	0.986911	+	0.161265i	$0.0515573\pi$
$631$	30.9358	+	320.682i	0.0490266	+	0.508212i	−0.937885	+	0.346947i	$0.887218\pi$
$632$	−47.4784	+	243.791i	−0.0751240	+	0.385746i
$633$	27.1014	−	44.7067i	0.0428143	−	0.0706266i
$634$	−5.87628	−	17.6984i	−0.00926858	−	0.0279155i
$635$	520.210	+	282.091i	0.819229	+	0.444238i
$636$	−47.0431	−	65.1877i	−0.0739672	−	0.102496i
$637$	94.3184	−	244.147i	0.148067	−	0.383276i
$638$	−40.0944	−	71.1916i	−0.0628438	−	0.111586i
$639$	−211.054	+	37.6023i	−0.330288	+	0.0588455i
$640$	16.1373	+	503.221i	0.0252146	+	0.786283i
$641$	377.683	−	105.538i	0.589209	−	0.164646i	0.0383788	−	0.999263i	$-0.487781\pi$
$641$	377.683	−	105.538i	0.589209	−	0.164646i	0.550830	+	0.834617i	$0.314311\pi$
$642$	−47.0135	+	51.7671i	−0.0732298	+	0.0806341i
$643$	358.318	+	165.535i	0.557260	+	0.257442i	0.677775	−	0.735269i	$-0.262944\pi$
$643$	358.318	+	165.535i	0.557260	+	0.257442i	−0.120515	+	0.992712i	$0.538455\pi$
$644$	−270.435	−	610.918i	−0.419931	−	0.948631i
$645$	21.1966	−	18.0450i	0.0328630	−	0.0279767i
$646$	12.9525	−	39.0108i	0.0200503	−	0.0603882i
$647$	454.986	−	426.712i	0.703224	−	0.659523i	−0.247739	−	0.968827i	$-0.579688\pi$
$647$	454.986	−	426.712i	0.703224	−	0.659523i	0.950963	+	0.309303i	$0.100096\pi$
$648$	−198.934	+	257.827i	−0.306997	+	0.397881i
$649$	−1.34473	−	0.906334i	−0.00207200	−	0.00139651i
$650$	−70.0940	−	9.03762i	−0.107837	−	0.0139040i
$651$	−21.5847	−	58.6526i	−0.0331562	−	0.0900961i
$652$	−154.293	−	254.522i	−0.236645	−	0.390371i
$653$	445.649	−	523.484i	0.682464	−	0.801660i	−0.306175	−	0.951975i	$-0.599049\pi$
$653$	445.649	−	523.484i	0.682464	−	0.801660i	0.988638	+	0.150315i	$0.0480287\pi$
$654$	−20.6819	+	69.6843i	−0.0316238	+	0.106551i
$655$	22.8837	+	2.20756i	0.0349370	+	0.00337033i
$656$	−40.3866	+	154.012i	−0.0615649	+	0.234774i
$657$	−344.147	−	84.3746i	−0.523816	−	0.128424i
$658$	202.364	+	56.5476i	0.307544	+	0.0859386i
$659$	−795.963	+	500.137i	−1.20783	+	0.758933i	−0.976829	−	0.214020i	$-0.931344\pi$
$659$	−795.963	+	500.137i	−1.20783	+	0.758933i	−0.231005	+	0.972952i	$0.574202\pi$
$660$	−2.73639	+	24.2861i	−0.00414604	+	0.0367972i
$661$	164.665	+	122.893i	0.249115	+	0.185919i	0.715400	−	0.698715i	$-0.246245\pi$
$661$	164.665	+	122.893i	0.249115	+	0.185919i	−0.466285	+	0.884635i	$0.654408\pi$
$662$	−362.947	−	114.082i	−0.548259	−	0.172329i
$663$	231.418	−	106.910i	0.349047	−	0.161252i
$664$	−526.356	−	462.847i	−0.792704	−	0.697058i
$665$	−48.8152	+	2.34912i	−0.0734063	+	0.00353251i
$666$	−255.255	+	149.196i	−0.383266	+	0.224018i
$667$	−1571.69	+	1172.98i	−2.35635	+	1.75859i
$668$	−411.337	+	143.933i	−0.615775	+	0.215469i
$669$	208.048	+	37.0666i	0.310983	+	0.0554059i
$670$	−46.5998	+	320.789i	−0.0695519	+	0.478790i
$671$	3.12066	+	38.8553i	0.00465075	+	0.0579066i
$672$	−60.6284	+	86.9154i	−0.0902209	+	0.129338i
$673$	60.2611	−	285.003i	0.0895409	−	0.423482i	−0.910411	−	0.413704i	$-0.864235\pi$
$673$	60.2611	−	285.003i	0.0895409	−	0.423482i	0.999952	−	0.00977723i	$-0.00311224\pi$
$674$	72.0365	+	57.4472i	0.106879	+	0.0852332i
$675$	−60.9766	+	97.0437i	−0.0903357	+	0.143768i
$676$	37.5029	+	41.2949i	0.0554777	+	0.0610871i
$677$	79.4020	+	252.615i	0.117285	+	0.373139i	0.994205	−	0.107497i	$-0.0342835\pi$
$677$	79.4020	+	252.615i	0.117285	+	0.373139i	−0.876920	+	0.480636i	$0.840406\pi$
$678$	−75.2606	−	26.3348i	−0.111004	−	0.0388419i
$679$	605.918	+	341.247i	0.892368	+	0.502572i
$680$	−346.740	−	420.782i	−0.509912	−	0.618797i
$681$	−77.8421	−	111.592i	−0.114306	−	0.163866i
$682$	−21.5011	+	9.10861i	−0.0315266	+	0.0133557i
$683$	346.974	−	857.031i	0.508014	−	1.25480i	−0.428299	−	0.903637i	$-0.640887\pi$
$683$	346.974	−	857.031i	0.508014	−	1.25480i	0.936313	−	0.351167i	$-0.114215\pi$
$684$	−30.1555	+	62.6186i	−0.0440870	+	0.0915476i
$685$	−74.5920	−	137.557i	−0.108893	−	0.200813i
$686$	−175.129	−	164.246i	−0.255290	−	0.239425i
$687$	203.454	−	32.8929i	0.296149	−	0.0478791i
$688$	26.1444	+	99.6999i	0.0380006	+	0.144913i
$689$	−5.97011	−	372.436i	−0.00866490	−	0.540546i
$690$	−68.9157	+	1.10471i	−0.0998779	+	0.00160103i
$691$	−766.952	+	201.119i	−1.10992	+	0.291054i	−0.762714	−	0.646736i	$-0.776134\pi$
$691$	−766.952	+	201.119i	−1.10992	+	0.291054i	−0.347202	+	0.937790i	$0.612868\pi$
$692$	−83.8951	−	518.921i	−0.121236	−	0.749886i
$693$	69.2497	−	73.8383i	0.0999274	−	0.106549i
$694$	52.7370	−	28.5974i	0.0759899	−	0.0412066i
$695$	385.061	+	185.436i	0.554045	+	0.266814i
$696$	188.734	+	76.4099i	0.271170	+	0.109784i
$697$	−153.780	−	363.002i	−0.220632	−	0.520806i
$698$	−325.019	+	226.719i	−0.465643	+	0.324813i
$699$	198.528	−	163.594i	0.284017	−	0.234041i
$700$	81.5859	−	144.864i	0.116551	−	0.206949i
$701$	−117.348	+	335.362i	−0.167401	+	0.478405i	−0.996771	−	0.0802945i	$-0.974414\pi$
$701$	−117.348	+	335.362i	−0.167401	+	0.478405i	0.829370	+	0.558700i	$0.188700\pi$
$702$	99.8181	−	31.3748i	0.142191	−	0.0446935i
$703$	−91.9456	+	83.5026i	−0.130790	+	0.118780i
$704$	−52.0984	−	32.7356i	−0.0740034	−	0.0464994i
$705$	−115.028	+	144.240i	−0.163160	+	0.204596i
$706$	66.0246	+	13.9602i	0.0935192	+	0.0197737i
$707$	583.744	+	407.195i	0.825664	+	0.575947i
$708$	1.90237	−	0.152788i	0.00268696	−	0.000215803i
$709$	1255.50	+	182.382i	1.77081	+	0.257238i	0.949617	−	0.313413i	$-0.101472\pi$
$709$	1255.50	+	182.382i	1.77081	+	0.257238i	0.821193	+	0.570651i	$0.193309\pi$
$710$	11.6265	−	65.2574i	0.0163754	−	0.0919118i
$711$	140.893	+	402.648i	0.198161	+	0.566312i
$712$	−190.606	−	255.395i	−0.267705	−	0.358700i
$713$	282.830	+	483.886i	0.396676	+	0.678663i
$714$	−3.38683	−	70.3791i	−0.00474346	−	0.0985701i
$715$	−74.7788	+	85.0395i	−0.104586	+	0.118936i
$716$	−12.1935	−	26.3941i	−0.0170300	−	0.0368632i
$717$	−40.8668	+	130.016i	−0.0569969	+	0.181334i
$718$	68.9756	−	92.4210i	0.0960663	−	0.128720i
$719$	27.9325	+	3.14724i	0.0388491	+	0.00437725i	0.131368	−	0.991334i	$-0.458063\pi$
$719$	27.9325	+	3.14724i	0.0388491	+	0.00437725i	−0.0925185	+	0.995711i	$0.529492\pi$
$720$	201.221	+	320.241i	0.279473	+	0.444779i
$721$	225.567	−	807.224i	0.312853	−	1.11959i
$722$	−54.9296	+	224.046i	−0.0760797	+	0.310314i
$723$	−30.1733	−	7.91238i	−0.0417335	−	0.0109438i
$724$	114.060	−	1182.35i	0.157542	−	1.63308i
$725$	−467.864	−	138.860i	−0.645330	−	0.191531i
$726$	−42.7199	−	36.3680i	−0.0588429	−	0.0500937i
$727$	29.3582	−	17.7971i	0.0403827	−	0.0244802i	−0.498057	−	0.867144i	$-0.665953\pi$
$727$	29.3582	−	17.7971i	0.0403827	−	0.0244802i	0.538439	+	0.842664i	$0.319014\pi$
$728$	−301.626	+	111.001i	−0.414321	+	0.152474i
$729$	−60.3281	+	467.893i	−0.0827546	+	0.641828i
$730$	61.2331	−	90.8516i	0.0838810	−	0.124454i
$731$	−202.054	−	155.901i	−0.276407	−	0.213270i
$732$	−31.3826	−	33.4620i	−0.0428724	−	0.0457132i
$733$	695.782	+	231.016i	0.949226	+	0.315165i	0.747488	−	0.664275i	$-0.231260\pi$
$733$	695.782	+	231.016i	0.949226	+	0.315165i	0.201737	+	0.979440i	$0.435341\pi$
$734$	−302.212	−	354.995i	−0.411733	−	0.483645i
$735$	58.0838	−	25.7120i	0.0790256	−	0.0349823i
$736$	398.566	−	862.738i	0.541530	−	1.17220i
$737$	−208.808	−	189.634i	−0.283322	−	0.257305i
$738$	−21.0779	−	75.4303i	−0.0285608	−	0.102209i
$739$	−36.9801	+	1.18588i	−0.0500408	+	0.00160471i	−0.0570619	−	0.998371i	$-0.518173\pi$
$739$	−36.9801	+	1.18588i	−0.0500408	+	0.00160471i	0.00702115	+	0.999975i	$0.497765\pi$
$740$	136.472	+	765.989i	0.184421	+	1.03512i
$741$	18.5372	−	10.4400i	0.0250165	−	0.0140890i
$742$	−96.0381	−	37.1013i	−0.129431	−	0.0500017i
$743$	603.214	−	435.313i	0.811863	−	0.585885i	−0.100656	−	0.994921i	$-0.532094\pi$
$743$	603.214	−	435.313i	0.811863	−	0.585885i	0.912518	+	0.409036i	$0.134135\pi$
$744$	27.7394	−	51.1547i	0.0372841	−	0.0687563i
$745$	266.057	−	88.3371i	0.357124	−	0.118573i
$746$	−172.273	−	104.433i	−0.230929	−	0.139991i
$747$	−1181.64	−	230.124i	−1.58185	−	0.308065i
$748$	223.024	−	21.5148i	0.298160	−	0.0287631i
$749$	121.653	−	752.464i	0.162420	−	1.00463i
$750$	−40.2495	−	52.1650i	−0.0536660	−	0.0695533i
$751$	34.6249	+	539.311i	0.0461051	+	0.718123i	0.954165	+	0.299282i	$0.0967473\pi$
$751$	34.6249	+	539.311i	0.0461051	+	0.718123i	−0.908060	+	0.418841i	$0.862436\pi$
$752$	−296.384	−	615.447i	−0.394127	−	0.818413i
$753$	−106.634	+	147.763i	−0.141612	+	0.196232i
$754$	243.062	+	373.408i	0.322363	+	0.495237i
$755$	−190.330	+	833.891i	−0.252093	+	1.10449i
$756$	−19.7056	+	245.355i	−0.0260656	+	0.324543i
$757$	−452.166	−	372.602i	−0.597313	−	0.492208i	0.287734	−	0.957710i	$-0.407098\pi$
$757$	−452.166	−	372.602i	−0.597313	−	0.492208i	−0.885047	+	0.465502i	$0.845874\pi$
$758$	−16.0905	+	6.21606i	−0.0212276	+	0.00820061i
$759$	32.7186	−	50.2646i	0.0431075	−	0.0662247i
$760$	−31.6564	−	32.6879i	−0.0416532	−	0.0430104i
$761$	53.5848	+	60.9373i	0.0704136	+	0.0800753i	0.785097	−	0.619373i	$-0.212613\pi$
$761$	53.5848	+	60.9373i	0.0704136	+	0.0800753i	−0.714684	+	0.699448i	$0.753429\pi$
$762$	−28.8224	+	65.1103i	−0.0378247	+	0.0854465i
$763$	−225.435	−	759.565i	−0.295459	−	0.995498i
$764$	231.488	+	1188.64i	0.302995	+	1.55581i
$765$	−878.845	−	323.423i	−1.14882	−	0.422775i

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.i (of order \(196\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(0.648427 + 0.0103942i) q^{2} +(0.725334 - 0.177830i) q^{3} +(-3.57760 - 0.114727i) q^{4} +(-0.578637 - 3.98330i) q^{5} +(0.472175 - 0.107771i) q^{6} +(-3.67258 + 3.79224i) q^{7} +(-4.90966 - 0.236266i) q^{8} +(-7.48491 + 3.90487i) q^{9} +O(q^{10})\)	\(q+(0.648427 + 0.0103942i) q^{2} +(0.725334 - 0.177830i) q^{3} +(-3.57760 - 0.114727i) q^{4} +(-0.578637 - 3.98330i) q^{5} +(0.472175 - 0.107771i) q^{6} +(-3.67258 + 3.79224i) q^{7} +(-4.90966 - 0.236266i) q^{8} +(-7.48491 + 3.90487i) q^{9} +(-0.333801 - 2.58889i) q^{10} +(2.03040 + 1.01819i) q^{11} +(-2.61535 + 0.552990i) q^{12} +(-11.4049 - 4.83152i) q^{13} +(-2.42082 + 2.42082i) q^{14} +(-1.12806 - 2.78632i) q^{15} +(11.1072 + 0.713107i) q^{16} +(-22.8525 + 15.4024i) q^{17} +(-4.89400 + 2.45422i) q^{18} +(-1.79818 + 1.43400i) q^{19} +(1.61314 + 14.3170i) q^{20} +(-1.98947 + 3.40374i) q^{21} +(1.30598 + 0.681329i) q^{22} +(12.2108 - 33.1808i) q^{23} +(-3.60316 + 0.701715i) q^{24} +(8.43485 - 2.50342i) q^{25} +(-7.34504 - 3.25143i) q^{26} +(-9.78210 + 8.60181i) q^{27} +(13.5741 - 13.1458i) q^{28} +(-46.4871 - 30.2597i) q^{29} +(-0.702501 - 1.81845i) q^{30} +(-10.0812 + 12.2339i) q^{31} +(26.7931 + 2.15188i) q^{32} +(1.65378 + 0.377465i) q^{33} +(-14.9783 + 9.74979i) q^{34} +(17.2307 + 12.4346i) q^{35} +(27.2260 - 13.1113i) q^{36} +(53.8918 - 3.45997i) q^{37} +(-1.18089 + 0.911154i) q^{38} +(-9.13157 - 1.47632i) q^{39} +(1.89979 + 19.6934i) q^{40} +(-2.73458 + 14.0415i) q^{41} +(-1.32541 + 2.18640i) q^{42} +(2.91808 + 8.78879i) q^{43} +(-7.14712 - 3.87563i) q^{44} +(19.8853 + 27.5551i) q^{45} +(8.26272 - 21.3884i) q^{46} +(-30.1171 - 53.4760i) q^{47} +(8.18326 - 1.45796i) q^{48} +(0.677285 + 21.1202i) q^{49} +(5.49540 - 1.53561i) q^{50} +(-13.8367 + 15.2358i) q^{51} +(40.2479 + 18.5937i) q^{52} +(12.1729 + 27.4989i) q^{53} +(-6.43239 + 5.47597i) q^{54} +(2.88091 - 8.67684i) q^{55} +(18.9271 - 17.7509i) q^{56} +(-1.04927 + 1.35990i) q^{57} +(-29.8289 - 20.1044i) q^{58} +(-0.708082 - 0.0912970i) q^{59} +(3.71607 + 10.0978i) q^{60} +(8.89638 + 14.6755i) q^{61} +(-6.66407 + 7.82799i) q^{62} +(12.6807 - 42.7255i) q^{63} +(-26.9636 - 2.60115i) q^{64} +(-12.6461 + 48.2249i) q^{65} +(1.06843 + 0.261948i) q^{66} +(-119.601 - 33.4207i) q^{67} +(83.5242 - 52.4817i) q^{68} +(2.95638 - 26.2386i) q^{69} +(11.0436 + 8.24206i) q^{70} +(24.2249 + 7.61437i) q^{71} +(37.6709 - 17.4032i) q^{72} +(31.5192 + 27.7162i) q^{73} +(34.9809 - 1.68337i) q^{74} +(5.67290 - 3.31579i) q^{75} +(6.59768 - 4.92397i) q^{76} +(-11.3180 + 3.96035i) q^{77} +(-5.90581 - 1.05220i) q^{78} +(7.26402 - 50.0050i) q^{79} +(-3.58653 - 44.6560i) q^{80} +(37.9040 - 54.3383i) q^{81} +(-1.91912 + 9.07644i) q^{82} +(111.487 + 88.9076i) q^{83} +(7.50802 - 11.9489i) q^{84} +(74.5756 + 82.1161i) q^{85} +(1.80081 + 5.72922i) q^{86} +(-39.0998 - 13.6816i) q^{87} +(-9.72799 - 5.47870i) q^{88} +(41.2304 + 50.0347i) q^{89} +(12.6078 + 18.0742i) q^{90} +(60.2077 - 25.5061i) q^{91} +(-47.4921 + 117.306i) q^{92} +(-5.13666 + 10.6664i) q^{93} +(-18.9729 - 34.9884i) q^{94} +(6.75255 + 6.33292i) q^{95} +(19.8166 - 3.20379i) q^{96} +(-33.4133 - 127.419i) q^{97} +(0.219641 + 13.7020i) q^{98} +(-19.1732 + 0.307345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9}+O(q^{10}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9} - 84 q^{10} - 140 q^{11} - 140 q^{12} - 84 q^{13} - 28 q^{14} - 84 q^{15} + 112 q^{16} - 84 q^{17} - 210 q^{18} - 98 q^{19} - 84 q^{20} - 84 q^{21} - 84 q^{22} - 84 q^{23} - 308 q^{24} - 84 q^{25} + 70 q^{26} - 126 q^{27} - 910 q^{28} - 294 q^{29} + 70 q^{30} - 84 q^{31} - 84 q^{32} - 98 q^{33} - 84 q^{34} - 84 q^{35} + 2198 q^{36} + 126 q^{37} - 140 q^{38} - 84 q^{39} + 476 q^{40} + 28 q^{41} - 588 q^{42} - 84 q^{43} - 84 q^{44} - 966 q^{45} - 448 q^{46} + 266 q^{47} - 1428 q^{48} + 756 q^{49} - 84 q^{50} - 84 q^{51} + 126 q^{52} - 84 q^{53} - 588 q^{54} - 84 q^{55} - 84 q^{56} - 672 q^{57} + 532 q^{58} + 616 q^{59} - 378 q^{60} - 364 q^{61} - 854 q^{62} + 1036 q^{63} - 1428 q^{64} + 28 q^{65} + 406 q^{66} - 84 q^{67} - 966 q^{68} - 504 q^{69} - 84 q^{70} + 434 q^{71} - 532 q^{72} - 84 q^{73} + 546 q^{74} - 84 q^{75} - 308 q^{76} + 700 q^{77} + 2310 q^{78} - 1400 q^{79} - 84 q^{80} - 700 q^{81} - 84 q^{82} - 98 q^{83} - 588 q^{84} + 1666 q^{85} - 84 q^{86} - 84 q^{87} + 420 q^{88} + 868 q^{89} - 1890 q^{90} + 1260 q^{91} + 924 q^{92} - 98 q^{93} - 420 q^{94} - 1834 q^{95} + 364 q^{96} + 504 q^{97} - 980 q^{98} + 630 q^{99}+O(q^{100}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9 - 84 * q^10 - 140 * q^11 - 140 * q^12 - 84 * q^13 - 28 * q^14 - 84 * q^15 + 112 * q^16 - 84 * q^17 - 210 * q^18 - 98 * q^19 - 84 * q^20 - 84 * q^21 - 84 * q^22 - 84 * q^23 - 308 * q^24 - 84 * q^25 + 70 * q^26 - 126 * q^27 - 910 * q^28 - 294 * q^29 + 70 * q^30 - 84 * q^31 - 84 * q^32 - 98 * q^33 - 84 * q^34 - 84 * q^35 + 2198 * q^36 + 126 * q^37 - 140 * q^38 - 84 * q^39 + 476 * q^40 + 28 * q^41 - 588 * q^42 - 84 * q^43 - 84 * q^44 - 966 * q^45 - 448 * q^46 + 266 * q^47 - 1428 * q^48 + 756 * q^49 - 84 * q^50 - 84 * q^51 + 126 * q^52 - 84 * q^53 - 588 * q^54 - 84 * q^55 - 84 * q^56 - 672 * q^57 + 532 * q^58 + 616 * q^59 - 378 * q^60 - 364 * q^61 - 854 * q^62 + 1036 * q^63 - 1428 * q^64 + 28 * q^65 + 406 * q^66 - 84 * q^67 - 966 * q^68 - 504 * q^69 - 84 * q^70 + 434 * q^71 - 532 * q^72 - 84 * q^73 + 546 * q^74 - 84 * q^75 - 308 * q^76 + 700 * q^77 + 2310 * q^78 - 1400 * q^79 - 84 * q^80 - 700 * q^81 - 84 * q^82 - 98 * q^83 - 588 * q^84 + 1666 * q^85 - 84 * q^86 - 84 * q^87 + 420 * q^88 + 868 * q^89 - 1890 * q^90 + 1260 * q^91 + 924 * q^92 - 98 * q^93 - 420 * q^94 - 1834 * q^95 + 364 * q^96 + 504 * q^97 - 980 * q^98 + 630 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more