LMFDB - Embedded newform 197.3.c.a.14.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(14,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("197.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			14.13
Character	$\chi$	$=$	197.14
Dual form			197.3.c.a.183.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.770755 + 0.770755i) q^{2} +(4.07862 - 4.07862i) q^{3} +2.81187i q^{4} +(-1.79164 + 1.79164i) q^{5} +6.28722i q^{6} -12.4564i q^{7} +(-5.25028 - 5.25028i) q^{8} -24.2702i q^{9} -2.76183i q^{10} +(-3.64909 + 3.64909i) q^{11} +(11.4686 + 11.4686i) q^{12} +(7.29392 - 7.29392i) q^{13} +(9.60079 + 9.60079i) q^{14} +14.6148i q^{15} -3.15414 q^{16} +(20.8492 + 20.8492i) q^{17} +(18.7064 + 18.7064i) q^{18} -18.2804i q^{19} +(-5.03787 - 5.03787i) q^{20} +(-50.8047 - 50.8047i) q^{21} -5.62510i q^{22} +13.8824 q^{23} -42.8278 q^{24} +18.5800i q^{25} +11.2436i q^{26} +(-62.2814 - 62.2814i) q^{27} +35.0257 q^{28} +16.1967 q^{29} +(-11.2645 - 11.2645i) q^{30} +(-18.8855 + 18.8855i) q^{31} +(23.4322 - 23.4322i) q^{32} +29.7665i q^{33} -32.1392 q^{34} +(22.3173 + 22.3173i) q^{35} +68.2448 q^{36} +3.02209 q^{37} +(14.0897 + 14.0897i) q^{38} -59.4982i q^{39} +18.8133 q^{40} -5.69712i q^{41} +78.3159 q^{42} +29.5375i q^{43} +(-10.2608 - 10.2608i) q^{44} +(43.4836 + 43.4836i) q^{45} +(-10.6999 + 10.6999i) q^{46} +22.9806i q^{47} +(-12.8645 + 12.8645i) q^{48} -106.161 q^{49} +(-14.3206 - 14.3206i) q^{50} +170.072 q^{51} +(20.5096 + 20.5096i) q^{52} -41.2966 q^{53} +96.0073 q^{54} -13.0757i q^{55} +(-65.3994 + 65.3994i) q^{56} +(-74.5589 - 74.5589i) q^{57} +(-12.4837 + 12.4837i) q^{58} +88.3938 q^{59} -41.0951 q^{60} -31.4183 q^{61} -29.1122i q^{62} -302.318 q^{63} +23.5044i q^{64} +26.1362i q^{65} +(-22.9426 - 22.9426i) q^{66} +(16.9321 - 16.9321i) q^{67} +(-58.6254 + 58.6254i) q^{68} +(56.6210 - 56.6210i) q^{69} -34.4024 q^{70} +(41.9412 + 41.9412i) q^{71} +(-127.426 + 127.426i) q^{72} +(-30.0329 + 30.0329i) q^{73} +(-2.32929 + 2.32929i) q^{74} +(75.7808 + 75.7808i) q^{75} +51.4023 q^{76} +(45.4543 + 45.4543i) q^{77} +(45.8585 + 45.8585i) q^{78} +(99.8739 + 99.8739i) q^{79} +(5.65109 - 5.65109i) q^{80} -289.612 q^{81} +(4.39108 + 4.39108i) q^{82} +64.8005i q^{83} +(142.856 - 142.856i) q^{84} -74.7087 q^{85} +(-22.7661 - 22.7661i) q^{86} +(66.0601 - 66.0601i) q^{87} +38.3175 q^{88} +(-91.0809 - 91.0809i) q^{89} -67.0303 q^{90} +(-90.8556 - 90.8556i) q^{91} +39.0356i q^{92} +154.054i q^{93} +(-17.7124 - 17.7124i) q^{94} +(32.7520 + 32.7520i) q^{95} -191.142i q^{96} -43.2796i q^{97} +(81.8238 - 81.8238i) q^{98} +(88.5642 + 88.5642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) $ 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.770755	+	0.770755i	−0.385377	+	0.385377i	−0.873035	−	0.487658i	$-0.837851\pi$
$2$	−0.770755	+	0.770755i	−0.385377	+	0.385377i	0.487658	+	0.873035i	$0.337851\pi$
$3$	4.07862	−	4.07862i	1.35954	−	1.35954i	0.485055	−	0.874484i	$-0.338800\pi$
$3$	4.07862	−	4.07862i	1.35954	−	1.35954i	0.874484	−	0.485055i	$-0.161200\pi$
$4$			2.81187i			0.702969i
$5$	−1.79164	+	1.79164i	−0.358328	+	0.358328i	−0.863197	−	0.504868i	$-0.831541\pi$
$5$	−1.79164	+	1.79164i	−0.358328	+	0.358328i	0.504868	+	0.863197i	$0.331541\pi$
$6$			6.28722i			1.04787i
$7$		−	12.4564i		−	1.77948i	−0.456469	−	0.889739i	$-0.650886\pi$
$7$		−	12.4564i		−	1.77948i	0.456469	−	0.889739i	$-0.349114\pi$
$8$	−5.25028	−	5.25028i	−0.656285	−	0.656285i
$9$		−	24.2702i		−	2.69669i
$10$		−	2.76183i		−	0.276183i
$11$	−3.64909	+	3.64909i	−0.331735	+	0.331735i	−0.853245	−	0.521510i	$-0.825369\pi$
$11$	−3.64909	+	3.64909i	−0.331735	+	0.331735i	0.521510	+	0.853245i	$0.325369\pi$
$12$	11.4686	+	11.4686i	0.955713	+	0.955713i
$13$	7.29392	−	7.29392i	0.561071	−	0.561071i	−0.368541	−	0.929612i	$-0.620142\pi$
$13$	7.29392	−	7.29392i	0.561071	−	0.561071i	0.929612	+	0.368541i	$0.120142\pi$
$14$	9.60079	+	9.60079i	0.685771	+	0.685771i
$15$			14.6148i			0.974323i
$16$	−3.15414			−0.197134
$17$	20.8492	+	20.8492i	1.22642	+	1.22642i	0.965307	+	0.261117i	$0.0840908\pi$
$17$	20.8492	+	20.8492i	1.22642	+	1.22642i	0.261117	+	0.965307i	$0.415909\pi$
$18$	18.7064	+	18.7064i	1.03924	+	1.03924i
$19$		−	18.2804i		−	0.962129i	−0.876685	−	0.481064i	$-0.840250\pi$
$19$		−	18.2804i		−	0.962129i	0.876685	−	0.481064i	$-0.159750\pi$
$20$	−5.03787	−	5.03787i	−0.251894	−	0.251894i
$21$	−50.8047	−	50.8047i	−2.41927	−	2.41927i
$22$		−	5.62510i		−	0.255686i
$23$	13.8824			0.603582			0.301791	−	0.953374i	$-0.402415\pi$
$23$	13.8824			0.603582			0.301791	+	0.953374i	$0.402415\pi$
$24$	−42.8278			−1.78449
$25$			18.5800i			0.743201i
$26$			11.2436i			0.432448i
$27$	−62.2814	−	62.2814i	−2.30672	−	2.30672i
$28$	35.0257			1.25092
$29$	16.1967			0.558507			0.279254	−	0.960217i	$-0.409913\pi$
$29$	16.1967			0.558507			0.279254	+	0.960217i	$0.409913\pi$
$30$	−11.2645	−	11.2645i	−0.375482	−	0.375482i
$31$	−18.8855	+	18.8855i	−0.609211	+	0.609211i	−0.942740	−	0.333529i	$-0.891760\pi$
$31$	−18.8855	+	18.8855i	−0.609211	+	0.609211i	0.333529	+	0.942740i	$0.391760\pi$
$32$	23.4322	−	23.4322i	0.732256	−	0.732256i
$33$			29.7665i			0.902014i
$34$	−32.1392			−0.945272
$35$	22.3173	+	22.3173i	0.637638	+	0.637638i
$36$	68.2448			1.89569
$37$	3.02209			0.0816781			0.0408391	−	0.999166i	$-0.486997\pi$
$37$	3.02209			0.0816781			0.0408391	+	0.999166i	$0.486997\pi$
$38$	14.0897	+	14.0897i	0.370783	+	0.370783i
$39$		−	59.4982i		−	1.52560i
$40$	18.8133			0.470332
$41$		−	5.69712i		−	0.138954i	−0.997584	−	0.0694771i	$-0.977867\pi$
$41$		−	5.69712i		−	0.138954i	0.997584	−	0.0694771i	$-0.0221331\pi$
$42$	78.3159			1.86466
$43$			29.5375i			0.686918i	0.939168	+	0.343459i	$0.111599\pi$
$43$			29.5375i			0.686918i	−0.939168	+	0.343459i	$0.888401\pi$
$44$	−10.2608	−	10.2608i	−0.233199	−	0.233199i
$45$	43.4836	+	43.4836i	0.966301	+	0.966301i
$46$	−10.6999	+	10.6999i	−0.232607	+	0.232607i
$47$			22.9806i			0.488948i	0.969656	+	0.244474i	$0.0786153\pi$
$47$			22.9806i			0.488948i	−0.969656	+	0.244474i	$0.921385\pi$
$48$	−12.8645	+	12.8645i	−0.268011	+	0.268011i
$49$	−106.161			−2.16654
$50$	−14.3206	−	14.3206i	−0.286413	−	0.286413i
$51$	170.072			3.33474
$52$	20.5096	+	20.5096i	0.394415	+	0.394415i
$53$	−41.2966			−0.779180			−0.389590	−	0.920988i	$-0.627383\pi$
$53$	−41.2966			−0.779180			−0.389590	+	0.920988i	$0.627383\pi$
$54$	96.0073			1.77791
$55$		−	13.0757i		−	0.237740i
$56$	−65.3994	+	65.3994i	−1.16785	+	1.16785i
$57$	−74.5589	−	74.5589i	−1.30805	−	1.30805i
$58$	−12.4837	+	12.4837i	−0.215236	+	0.215236i
$59$	88.3938			1.49820			0.749100	−	0.662457i	$-0.230486\pi$
$59$	88.3938			1.49820			0.749100	+	0.662457i	$0.230486\pi$
$60$	−41.0951			−0.684919
$61$	−31.4183			−0.515054			−0.257527	−	0.966271i	$-0.582908\pi$
$61$	−31.4183			−0.515054			−0.257527	+	0.966271i	$0.582908\pi$
$62$		−	29.1122i		−	0.469552i
$63$	−302.318			−4.79870
$64$			23.5044i			0.367256i
$65$			26.1362i			0.402095i
$66$	−22.9426	−	22.9426i	−0.347616	−	0.347616i
$67$	16.9321	−	16.9321i	0.252717	−	0.252717i	−0.569366	−	0.822084i	$-0.692811\pi$
$67$	16.9321	−	16.9321i	0.252717	−	0.252717i	0.822084	+	0.569366i	$0.192811\pi$
$68$	−58.6254	+	58.6254i	−0.862138	+	0.862138i
$69$	56.6210	−	56.6210i	0.820594	−	0.820594i
$70$	−34.4024			−0.491462
$71$	41.9412	+	41.9412i	0.590721	+	0.590721i	0.937826	−	0.347105i	$-0.112835\pi$
$71$	41.9412	+	41.9412i	0.590721	+	0.590721i	−0.347105	+	0.937826i	$0.612835\pi$
$72$	−127.426	+	127.426i	−1.76980	+	1.76980i
$73$	−30.0329	+	30.0329i	−0.411410	+	0.411410i	−0.882230	−	0.470819i	$-0.843958\pi$
$73$	−30.0329	+	30.0329i	−0.411410	+	0.411410i	0.470819	+	0.882230i	$0.343958\pi$
$74$	−2.32929	+	2.32929i	−0.0314769	+	0.0314769i
$75$	75.7808	+	75.7808i	1.01041	+	1.01041i
$76$	51.4023			0.676346
$77$	45.4543	+	45.4543i	0.590316	+	0.590316i
$78$	45.8585	+	45.8585i	0.587930	+	0.587930i
$79$	99.8739	+	99.8739i	1.26423	+	1.26423i	0.949024	+	0.315203i	$0.102072\pi$
$79$	99.8739	+	99.8739i	1.26423	+	1.26423i	0.315203	+	0.949024i	$0.397928\pi$
$80$	5.65109	−	5.65109i	0.0706386	−	0.0706386i
$81$	−289.612			−3.57545
$82$	4.39108	+	4.39108i	0.0535498	+	0.0535498i
$83$			64.8005i			0.780729i	0.920660	+	0.390364i	$0.127651\pi$
$83$			64.8005i			0.780729i	−0.920660	+	0.390364i	$0.872349\pi$
$84$	142.856	−	142.856i	1.70067	−	1.70067i
$85$	−74.7087			−0.878925
$86$	−22.7661	−	22.7661i	−0.264722	−	0.264722i
$87$	66.0601	−	66.0601i	0.759312	−	0.759312i
$88$	38.3175			0.435426
$89$	−91.0809	−	91.0809i	−1.02338	−	1.02338i	−0.999720	−	0.0236614i	$-0.992468\pi$
$89$	−91.0809	−	91.0809i	−1.02338	−	1.02338i	−0.0236614	−	0.999720i	$-0.507532\pi$
$90$	−67.0303			−0.744781
$91$	−90.8556	−	90.8556i	−0.998414	−	0.998414i
$92$			39.0356i			0.424299i
$93$			154.054i			1.65649i
$94$	−17.7124	−	17.7124i	−0.188430	−	0.188430i
$95$	32.7520	+	32.7520i	0.344758	+	0.344758i
$96$		−	191.142i		−	1.99106i
$97$		−	43.2796i		−	0.446181i	−0.974798	−	0.223091i	$-0.928385\pi$
$97$		−	43.2796i		−	0.446181i	0.974798	−	0.223091i	$-0.0716146\pi$
$98$	81.8238	−	81.8238i	0.834937	−	0.834937i
$99$	88.5642	+	88.5642i	0.894587	+	0.894587i
$100$	−52.2447			−0.522447
$101$	24.0889			0.238504			0.119252	−	0.992864i	$-0.461950\pi$
$101$	24.0889			0.238504			0.119252	+	0.992864i	$0.461950\pi$
$102$	−131.084	+	131.084i	−1.28513	+	1.28513i
$103$	56.5935	−	56.5935i	0.549451	−	0.549451i	−0.376831	−	0.926282i	$-0.622986\pi$
$103$	56.5935	−	56.5935i	0.549451	−	0.549451i	0.926282	+	0.376831i	$0.122986\pi$
$104$	−76.5903			−0.736445
$105$	182.048			1.73379
$106$	31.8295	−	31.8295i	0.300278	−	0.300278i
$107$			37.4639i			0.350130i	0.984557	+	0.175065i	$0.0560136\pi$
$107$			37.4639i			0.350130i	−0.984557	+	0.175065i	$0.943986\pi$
$108$	175.127	−	175.127i	1.62155	−	1.62155i
$109$			10.0860i			0.0925321i	0.998929	+	0.0462661i	$0.0147322\pi$
$109$			10.0860i			0.0925321i	−0.998929	+	0.0462661i	$0.985268\pi$
$110$	10.0782	+	10.0782i	0.0916197	+	0.0916197i
$111$	12.3260	−	12.3260i	0.111045	−	0.111045i
$112$			39.2891i			0.350795i
$113$	144.737	+	144.737i	1.28086	+	1.28086i	0.940181	+	0.340677i	$0.110656\pi$
$113$	144.737	+	144.737i	1.28086	+	1.28086i	0.340677	+	0.940181i	$0.389344\pi$
$114$	114.933			1.00819
$115$	−24.8723	+	24.8723i	−0.216281	+	0.216281i
$116$			45.5431i			0.392613i
$117$	−177.025	−	177.025i	−1.51303	−	1.51303i
$118$	−68.1299	+	68.1299i	−0.577372	+	0.577372i
$119$	259.705	−	259.705i	2.18240	−	2.18240i
$120$	76.7321	−	76.7321i	0.639434	−	0.639434i
$121$			94.3683i			0.779903i
$122$	24.2158	−	24.2158i	0.198490	−	0.198490i
$123$	−23.2364	−	23.2364i	−0.188914	−	0.188914i
$124$	−53.1037	−	53.1037i	−0.428256	−	0.428256i
$125$	−78.0798	−	78.0798i	−0.624639	−	0.624639i
$126$	233.013	−	233.013i	1.84931	−	1.84931i
$127$		−	190.593i		−	1.50073i	−0.661023	−	0.750365i	$-0.729878\pi$
$127$		−	190.593i		−	1.50073i	0.661023	−	0.750365i	$-0.270122\pi$
$128$	75.6127	+	75.6127i	0.590724	+	0.590724i
$129$	120.472	+	120.472i	0.933891	+	0.933891i
$130$	−20.1446	−	20.1446i	−0.154958	−	0.154958i
$131$	56.6884	−	56.6884i	0.432736	−	0.432736i	−0.456822	−	0.889558i	$-0.651013\pi$
$131$	56.6884	−	56.6884i	0.432736	−	0.432736i	0.889558	+	0.456822i	$0.151013\pi$
$132$	−83.6995			−0.634087
$133$	−227.708			−1.71209
$134$			26.1009i			0.194783i
$135$	223.172			1.65313
$136$		−	218.929i		−	1.60977i
$137$			176.470i			1.28810i	0.764983	+	0.644050i	$0.222747\pi$
$137$			176.470i			1.28810i	−0.764983	+	0.644050i	$0.777253\pi$
$138$			87.2817i			0.632476i
$139$	111.899	+	111.899i	0.805028	+	0.805028i	0.983877	−	0.178849i	$-0.0572374\pi$
$139$	111.899	+	111.899i	0.805028	+	0.805028i	−0.178849	+	0.983877i	$0.557237\pi$
$140$	−62.7535	+	62.7535i	−0.448240	+	0.448240i
$141$	93.7289	+	93.7289i	0.664744	+	0.664744i
$142$	−64.6527			−0.455301
$143$			53.2323i			0.372254i
$144$			76.5517i			0.531609i
$145$	−29.0187	+	29.0187i	−0.200129	+	0.200129i
$146$		−	46.2961i		−	0.317096i
$147$	−432.989	+	432.989i	−2.94550	+	2.94550i
$148$			8.49774i			0.0574172i
$149$	−64.1689	−	64.1689i	−0.430664	−	0.430664i	0.458190	−	0.888854i	$-0.348498\pi$
$149$	−64.1689	−	64.1689i	−0.430664	−	0.430664i	−0.888854	+	0.458190i	$0.848498\pi$
$150$	−116.817			−0.778779
$151$	−189.569	−	189.569i	−1.25543	−	1.25543i	−0.953253	−	0.302173i	$-0.902288\pi$
$151$	−189.569	−	189.569i	−1.25543	−	1.25543i	−0.302173	−	0.953253i	$-0.597712\pi$
$152$	−95.9775	+	95.9775i	−0.631431	+	0.631431i
$153$	506.015	−	506.015i	3.30729	−	3.30729i
$154$	−70.0682			−0.454989
$155$		−	67.6722i		−	0.436595i
$156$	167.302			1.07245
$157$		−	299.212i		−	1.90581i	−0.303271	−	0.952904i	$-0.598079\pi$
$157$		−	299.212i		−	1.90581i	0.303271	−	0.952904i	$-0.401921\pi$
$158$	−153.957			−0.974409
$159$	−168.433	+	168.433i	−1.05933	+	1.05933i
$160$			83.9643i			0.524777i
$161$		−	172.924i		−	1.07406i
$162$	223.219	−	223.219i	1.37790	−	1.37790i
$163$			82.0498i			0.503373i	0.967809	+	0.251687i	$0.0809852\pi$
$163$			82.0498i			0.503373i	−0.967809	+	0.251687i	$0.919015\pi$
$164$	16.0196			0.0976805
$165$	−53.3308	−	53.3308i	−0.323217	−	0.323217i
$166$	−49.9453	−	49.9453i	−0.300875	−	0.300875i
$167$	−106.878	+	106.878i	−0.639985	+	0.639985i	−0.950552	−	0.310567i	$-0.899481\pi$
$167$	−106.878	+	106.878i	−0.639985	+	0.639985i	0.310567	+	0.950552i	$0.399481\pi$
$168$			533.478i			3.17546i
$169$			62.5974i			0.370399i
$170$	57.5820	−	57.5820i	0.338718	−	0.338718i
$171$	−443.670			−2.59456
$172$	−83.0556			−0.482882
$173$			58.2207i			0.336536i	0.985741	+	0.168268i	$0.0538174\pi$
$173$			58.2207i			0.336536i	−0.985741	+	0.168268i	$0.946183\pi$
$174$			101.832i			0.585243i
$175$	231.439			1.32251
$176$	11.5097	−	11.5097i	0.0653962	−	0.0653962i
$177$	360.525	−	360.525i	2.03686	−	2.03686i
$178$	140.402			0.788776
$179$	−58.9171	+	58.9171i	−0.329146	+	0.329146i	−0.852262	−	0.523116i	$-0.824770\pi$
$179$	−58.9171	+	58.9171i	−0.329146	+	0.329146i	0.523116	+	0.852262i	$0.324770\pi$
$180$	−122.270	+	122.270i	−0.679280	+	0.679280i
$181$		−	252.074i		−	1.39268i	−0.717714	−	0.696338i	$-0.754812\pi$
$181$		−	252.074i		−	1.39268i	0.717714	−	0.696338i	$-0.245188\pi$
$182$	140.055			0.769532
$183$	−128.143	+	128.143i	−0.700235	+	0.700235i
$184$	−72.8865	−	72.8865i	−0.396122	−	0.396122i
$185$	−5.41451	+	5.41451i	−0.0292676	+	0.0292676i
$186$	−118.738	−	118.738i	−0.638374	−	0.638374i
$187$	−152.161			−0.813696
$188$	−64.6185			−0.343715
$189$	−775.799	+	775.799i	−4.10475	+	4.10475i
$190$	−50.4875			−0.265724
$191$	−158.693			−0.830854			−0.415427	−	0.909627i	$-0.636368\pi$
$191$	−158.693			−0.830854			−0.415427	+	0.909627i	$0.636368\pi$
$192$	95.8654	+	95.8654i	0.499299	+	0.499299i
$193$	121.453			0.629292			0.314646	−	0.949209i	$-0.398114\pi$
$193$	121.453			0.629292			0.314646	+	0.949209i	$0.398114\pi$
$194$	33.3579	+	33.3579i	0.171948	+	0.171948i
$195$	106.600	+	106.600i	0.546664	+	0.546664i
$196$		−	298.511i		−	1.52301i
$197$	59.2912	−	187.866i	0.300971	−	0.953633i
$197$	59.2912	−	187.866i	0.300971	−	0.953633i
$198$	−136.522			−0.689507
$199$	217.422	−	217.422i	1.09257	−	1.09257i	0.0973196	−	0.995253i	$-0.468973\pi$
$199$	217.422	−	217.422i	1.09257	−	1.09257i	0.995253	−	0.0973196i	$-0.0310269\pi$
$200$	97.5505	−	97.5505i	0.487752	−	0.487752i
$201$		−	138.119i		−	0.687158i
$202$	−18.5667	+	18.5667i	−0.0919142	+	0.0919142i
$203$		−	201.752i		−	0.993852i
$204$			478.221i			2.34422i
$205$	10.2072	+	10.2072i	0.0497913	+	0.0497913i
$206$			87.2393i			0.423492i
$207$		−	336.929i		−	1.62768i
$208$	−23.0060	+	23.0060i	−0.110606	+	0.110606i
$209$	66.7069	+	66.7069i	0.319172	+	0.319172i
$210$	−140.314	+	140.314i	−0.668162	+	0.668162i
$211$	49.2757	+	49.2757i	0.233534	+	0.233534i	0.814166	−	0.580632i	$-0.197194\pi$
$211$	49.2757	+	49.2757i	0.233534	+	0.233534i	−0.580632	+	0.814166i	$0.697194\pi$
$212$		−	116.121i		−	0.547739i
$213$	342.124			1.60622
$214$	−28.8755	−	28.8755i	−0.134932	−	0.134932i
$215$	−52.9206	−	52.9206i	−0.246142	−	0.246142i
$216$			653.990i			3.02773i
$217$	235.245	+	235.245i	1.08408	+	1.08408i
$218$	−7.77383	−	7.77383i	−0.0356598	−	0.0356598i
$219$			244.986i			1.11866i
$220$	36.7673			0.167124
$221$	304.145			1.37622
$222$			19.0006i			0.0855881i
$223$		−	310.528i		−	1.39250i	−0.717797	−	0.696252i	$-0.754850\pi$
$223$		−	310.528i		−	1.39250i	0.717797	−	0.696252i	$-0.245150\pi$
$224$	−291.880	−	291.880i	−1.30303	−	1.30303i
$225$	450.942			2.00418
$226$	−223.113			−0.987226
$227$	281.201	+	281.201i	1.23877	+	1.23877i	0.960504	+	0.278265i	$0.0897592\pi$
$227$	281.201	+	281.201i	1.23877	+	1.23877i	0.278265	+	0.960504i	$0.410241\pi$
$228$	209.650	−	209.650i	0.919519	−	0.919519i
$229$	−136.786	+	136.786i	−0.597320	+	0.597320i	−0.939599	−	0.342278i	$-0.888801\pi$
$229$	−136.786	+	136.786i	−0.597320	+	0.597320i	0.342278	+	0.939599i	$0.388801\pi$
$230$		−	38.3409i		−	0.166699i
$231$	370.781			1.60511
$232$	−85.0373	−	85.0373i	−0.366540	−	0.366540i
$233$	−222.823			−0.956323			−0.478162	−	0.878272i	$-0.658697\pi$
$233$	−222.823			−0.956323			−0.478162	+	0.878272i	$0.658697\pi$
$234$	272.886			1.16618
$235$	−41.1730	−	41.1730i	−0.175204	−	0.175204i
$236$			248.552i			1.05319i
$237$	814.695			3.43753
$238$			400.338i			1.68209i
$239$	116.614			0.487925			0.243963	−	0.969785i	$-0.421553\pi$
$239$	116.614			0.487925			0.243963	+	0.969785i	$0.421553\pi$
$240$		−	46.0973i		−	0.192072i
$241$	−255.305	−	255.305i	−1.05936	−	1.05936i	−0.998123	−	0.0612340i	$-0.980496\pi$
$241$	−255.305	−	255.305i	−1.05936	−	1.05936i	−0.0612340	−	0.998123i	$-0.519504\pi$
$242$	−72.7348	−	72.7348i	−0.300557	−	0.300557i
$243$	−620.682	+	620.682i	−2.55425	+	2.55425i
$244$		−	88.3442i		−	0.362067i
$245$	190.202	−	190.202i	0.776335	−	0.776335i
$246$	35.8191			0.145606
$247$	−133.336	−	133.336i	−0.539822	−	0.539822i
$248$	198.309			0.799632
$249$	264.296	+	264.296i	1.06143	+	1.06143i
$250$	120.361			0.481443
$251$	−1.35870			−0.00541316			−0.00270658	−	0.999996i	$-0.500862\pi$
$251$	−1.35870			−0.00541316			−0.00270658	+	0.999996i	$0.500862\pi$
$252$		−	850.081i		−	3.37334i
$253$	−50.6581	+	50.6581i	−0.200230	+	0.200230i
$254$	146.900	+	146.900i	0.578348	+	0.578348i
$255$	−304.708	+	304.708i	−1.19493	+	1.19493i
$256$	−210.575			−0.822559
$257$	−340.463			−1.32476			−0.662379	−	0.749169i	$-0.730453\pi$
$257$	−340.463			−1.32476			−0.662379	+	0.749169i	$0.730453\pi$
$258$	−185.709			−0.719801
$259$		−	37.6442i		−	0.145345i
$260$	−73.4917			−0.282660
$261$		−	393.098i		−	1.50612i
$262$			87.3856i			0.333533i
$263$	−9.05544	−	9.05544i	−0.0344313	−	0.0344313i	0.689682	−	0.724113i	$-0.257751\pi$
$263$	−9.05544	−	9.05544i	−0.0344313	−	0.0344313i	−0.724113	+	0.689682i	$0.757751\pi$
$264$	156.282	−	156.282i	0.591979	−	0.591979i
$265$	73.9887	−	73.9887i	0.279202	−	0.279202i
$266$	175.507	−	175.507i	0.659800	−	0.659800i
$267$	−742.968			−2.78265
$268$	47.6108	+	47.6108i	0.177652	+	0.177652i
$269$	−233.819	+	233.819i	−0.869216	+	0.869216i	−0.992386	−	0.123170i	$-0.960694\pi$
$269$	−233.819	+	233.819i	−0.869216	+	0.869216i	0.123170	+	0.992386i	$0.460694\pi$
$270$	−172.011	+	172.011i	−0.637077	+	0.637077i
$271$	−115.273	+	115.273i	−0.425360	+	0.425360i	−0.887044	−	0.461684i	$-0.847245\pi$
$271$	−115.273	+	115.273i	−0.425360	+	0.425360i	0.461684	+	0.887044i	$0.347245\pi$
$272$	−65.7613	−	65.7613i	−0.241770	−	0.241770i
$273$	−741.131			−2.71476
$274$	−136.015	−	136.015i	−0.496405	−	0.496405i
$275$	−67.8002	−	67.8002i	−0.246546	−	0.246546i
$276$	159.211	+	159.211i	0.576852	+	0.576852i
$277$	−247.116	+	247.116i	−0.892115	+	0.892115i	−0.994722	−	0.102607i	$-0.967282\pi$
$277$	−247.116	+	247.116i	−0.892115	+	0.892115i	0.102607	+	0.994722i	$0.467282\pi$
$278$	−172.493			−0.620479
$279$	458.356	+	458.356i	1.64285	+	1.64285i
$280$		−	234.345i		−	0.836945i
$281$	176.735	−	176.735i	0.628949	−	0.628949i	−0.318855	−	0.947804i	$-0.603298\pi$
$281$	176.735	−	176.735i	0.628949	−	0.628949i	0.947804	+	0.318855i	$0.103298\pi$
$282$	−144.484			−0.512355
$283$	385.727	+	385.727i	1.36299	+	1.36299i	0.870075	+	0.492919i	$0.164070\pi$
$283$	385.727	+	385.727i	1.36299	+	1.36299i	0.492919	+	0.870075i	$0.335930\pi$
$284$	−117.933	+	117.933i	−0.415258	+	0.415258i
$285$	267.166			0.937424
$286$	−41.0290	−	41.0290i	−0.143458	−	0.143458i
$287$	−70.9654			−0.247266
$288$	−568.705	−	568.705i	−1.97467	−	1.97467i
$289$			580.379i			2.00823i
$290$		−	44.7326i		−	0.154250i
$291$	−176.521	−	176.521i	−0.606601	−	0.606601i
$292$	−84.4489	−	84.4489i	−0.289208	−	0.289208i
$293$		−	46.1505i		−	0.157510i	−0.996894	−	0.0787551i	$-0.974905\pi$
$293$		−	46.1505i		−	0.157510i	0.996894	−	0.0787551i	$-0.0250945\pi$
$294$		−	667.456i		−	2.27026i
$295$	−158.370	+	158.370i	−0.536848	+	0.536848i
$296$	−15.8668	−	15.8668i	−0.0536042	−	0.0536042i
$297$	454.540			1.53044
$298$	98.9169			0.331936
$299$	101.257	−	101.257i	0.338652	−	0.338652i
$300$	−213.086	+	213.086i	−0.710287	+	0.710287i
$301$	367.929			1.22236
$302$	292.223			0.967626
$303$	98.2495	−	98.2495i	0.324256	−	0.324256i
$304$			57.6591i			0.189668i
$305$	56.2903	−	56.2903i	0.184558	−	0.184558i
$306$			780.027i			2.54911i
$307$	−87.1204	−	87.1204i	−0.283780	−	0.283780i	0.550835	−	0.834614i	$-0.314310\pi$
$307$	−87.1204	−	87.1204i	−0.283780	−	0.283780i	−0.834614	+	0.550835i	$0.814310\pi$
$308$	−127.812	+	127.812i	−0.414974	+	0.414974i
$309$		−	461.646i		−	1.49400i
$310$	52.1587	+	52.1587i	0.168254	+	0.168254i
$311$	−292.031			−0.939005			−0.469503	−	0.882931i	$-0.655567\pi$
$311$	−292.031			−0.939005			−0.469503	+	0.882931i	$0.655567\pi$
$312$	−312.382	+	312.382i	−1.00123	+	1.00123i
$313$			19.1153i			0.0610713i	0.999534	+	0.0305356i	$0.00972131\pi$
$313$			19.1153i			0.0610713i	−0.999534	+	0.0305356i	$0.990279\pi$
$314$	230.619	+	230.619i	0.734455	+	0.734455i
$315$	541.646	−	541.646i	1.71951	−	1.71951i
$316$	−280.833	+	280.833i	−0.888712	+	0.888712i
$317$	−132.398	+	132.398i	−0.417660	+	0.417660i	−0.884396	−	0.466737i	$-0.845430\pi$
$317$	−132.398	+	132.398i	−0.417660	+	0.417660i	0.466737	+	0.884396i	$0.345430\pi$
$318$		−	259.641i		−	0.816480i
$319$	−59.1032	+	59.1032i	−0.185276	+	0.185276i
$320$	−42.1115	−	42.1115i	−0.131598	−	0.131598i
$321$	152.801	+	152.801i	0.476016	+	0.476016i
$322$	133.282	+	133.282i	0.413919	+	0.413919i
$323$	381.133	−	381.133i	1.17998	−	1.17998i
$324$		−	814.352i		−	2.51343i
$325$	135.521	+	135.521i	0.416989	+	0.416989i
$326$	−63.2403	−	63.2403i	−0.193989	−	0.193989i
$327$	41.1369	+	41.1369i	0.125801	+	0.125801i
$328$	−29.9115	+	29.9115i	−0.0911936	+	0.0911936i
$329$	286.254			0.870073
$330$	82.2100			0.249121
$331$			18.3874i			0.0555512i	0.999614	+	0.0277756i	$0.00884239\pi$
$331$			18.3874i			0.0555512i	−0.999614	+	0.0277756i	$0.991158\pi$
$332$	−182.211			−0.548828
$333$		−	73.3468i		−	0.220261i
$334$		−	164.753i		−	0.493271i
$335$			60.6724i			0.181112i
$336$	160.245	+	160.245i	0.476920	+	0.476920i
$337$	−217.224	+	217.224i	−0.644581	+	0.644581i	−0.951678	−	0.307097i	$-0.900642\pi$
$337$	−217.224	+	217.224i	−0.644581	+	0.644581i	0.307097	+	0.951678i	$0.400642\pi$
$338$	−48.2473	−	48.2473i	−0.142743	−	0.142743i
$339$	1180.65			3.48275
$340$		−	210.071i		−	0.617857i
$341$		−	137.830i		−	0.404193i
$342$	341.961	−	341.961i	0.999886	−	0.999886i
$343$			712.014i			2.07584i
$344$	155.080	−	155.080i	0.450814	−	0.450814i
$345$			202.889i			0.588084i
$346$	−44.8739	−	44.8739i	−0.129693	−	0.129693i
$347$	−63.8678			−0.184057			−0.0920286	−	0.995756i	$-0.529335\pi$
$347$	−63.8678			−0.184057			−0.0920286	+	0.995756i	$0.529335\pi$
$348$	185.753	+	185.753i	0.533773	+	0.533773i
$349$	30.8444	−	30.8444i	0.0883793	−	0.0883793i	−0.661535	−	0.749914i	$-0.730095\pi$
$349$	30.8444	−	30.8444i	0.0883793	−	0.0883793i	0.749914	+	0.661535i	$0.230095\pi$
$350$	−178.383	+	178.383i	−0.509666	+	0.509666i
$351$	−908.551			−2.58846
$352$			171.012i			0.485830i
$353$	31.9956			0.0906392			0.0453196	−	0.998973i	$-0.485569\pi$
$353$	31.9956			0.0906392			0.0453196	+	0.998973i	$0.485569\pi$
$354$			555.752i			1.56992i
$355$	−150.287			−0.423344
$356$	256.108	−	256.108i	0.719405	−	0.719405i
$357$		−	2118.47i		−	5.93410i
$358$		−	90.8213i		−	0.253691i
$359$	−304.136	+	304.136i	−0.847176	+	0.847176i	−0.989780	−	0.142604i	$-0.954452\pi$
$359$	−304.136	+	304.136i	−0.847176	+	0.847176i	0.142604	+	0.989780i	$0.454452\pi$
$360$		−	456.602i		−	1.26834i
$361$	26.8253			0.0743084
$362$	194.287	+	194.287i	0.536706	+	0.536706i
$363$	384.892	+	384.892i	1.06031	+	1.06031i
$364$	255.475	−	255.475i	0.701854	−	0.701854i
$365$		−	107.617i		−	0.294840i
$366$		−	197.534i		−	0.539710i
$367$	−40.8840	+	40.8840i	−0.111400	+	0.111400i	−0.760610	−	0.649209i	$-0.775100\pi$
$367$	−40.8840	+	40.8840i	−0.111400	+	0.111400i	0.649209	+	0.760610i	$0.275100\pi$
$368$	−43.7870			−0.118986
$369$	−138.270			−0.374717
$370$		−	8.34651i		−	0.0225581i
$371$			514.404i			1.38653i
$372$	−433.180			−1.16446
$373$	−178.472	+	178.472i	−0.478477	+	0.478477i	−0.904644	−	0.426167i	$-0.859864\pi$
$373$	−178.472	+	178.472i	−0.478477	+	0.478477i	0.426167	+	0.904644i	$0.359864\pi$
$374$	117.279	−	117.279i	0.313580	−	0.313580i
$375$	−636.915			−1.69844
$376$	120.655	−	120.655i	0.320890	−	0.320890i
$377$	118.137	−	118.137i	0.313362	−	0.313362i
$378$		−	1195.90i		−	3.16376i
$379$	261.615			0.690277			0.345138	−	0.938552i	$-0.387832\pi$
$379$	261.615			0.690277			0.345138	+	0.938552i	$0.387832\pi$
$380$	−92.0946	+	92.0946i	−0.242354	+	0.242354i
$381$	−777.355	−	777.355i	−2.04030	−	2.04030i
$382$	122.313	−	122.313i	0.320192	−	0.320192i
$383$	−180.772	−	180.772i	−0.471989	−	0.471989i	0.430569	−	0.902558i	$-0.358313\pi$
$383$	−180.772	−	180.772i	−0.471989	−	0.471989i	−0.902558	+	0.430569i	$0.858313\pi$
$384$	616.790			1.60622
$385$	−162.876			−0.423054
$386$	−93.6107	+	93.6107i	−0.242515	+	0.242515i
$387$	716.881			1.85240
$388$	121.697			0.313651
$389$	45.0851	+	45.0851i	0.115900	+	0.115900i	0.762678	−	0.646778i	$-0.223884\pi$
$389$	45.0851	+	45.0851i	0.115900	+	0.115900i	−0.646778	+	0.762678i	$0.723884\pi$
$390$	−164.324			−0.421344
$391$	289.437	+	289.437i	0.740248	+	0.740248i
$392$	557.374	+	557.374i	1.42187	+	1.42187i
$393$		−	462.420i		−	1.17664i
$394$	99.0995	+	190.497i	0.251521	+	0.483496i
$395$	−357.877			−0.906017
$396$	−249.031	+	249.031i	−0.628867	+	0.628867i
$397$	321.228	−	321.228i	0.809138	−	0.809138i	−0.175365	−	0.984503i	$-0.556111\pi$
$397$	321.228	−	321.228i	0.809138	−	0.809138i	0.984503	+	0.175365i	$0.0561107\pi$
$398$			335.158i			0.842105i
$399$	−928.732	+	928.732i	−2.32765	+	2.32765i
$400$		−	58.6040i		−	0.146510i
$401$			79.9636i			0.199410i	0.995017	+	0.0997052i	$0.0317900\pi$
$401$			79.9636i			0.199410i	−0.995017	+	0.0997052i	$0.968210\pi$
$402$	106.456	+	106.456i	0.264815	+	0.264815i
$403$			275.499i			0.683621i
$404$			67.7351i			0.167661i
$405$	518.880	−	518.880i	1.28119	−	1.28119i
$406$	155.501	+	155.501i	0.383008	+	0.383008i
$407$	−11.0279	+	11.0279i	−0.0270955	+	0.0270955i
$408$	−892.925	−	892.925i	−2.18854	−	2.18854i
$409$		−	153.074i		−	0.374264i	−0.982335	−	0.187132i	$-0.940081\pi$
$409$		−	153.074i		−	0.374264i	0.982335	−	0.187132i	$-0.0599192\pi$
$410$	−15.7345			−0.0383768
$411$	719.752	+	719.752i	1.75122	+	1.75122i
$412$	159.134	+	159.134i	0.386247	+	0.386247i
$413$		−	1101.06i		−	2.66602i
$414$	259.689	+	259.689i	0.627269	+	0.627269i
$415$	−116.099	−	116.099i	−0.279757	−	0.279757i
$416$		−	341.825i		−	0.821695i
$417$	912.785			2.18893
$418$	−102.829			−0.246003
$419$		−	622.087i		−	1.48470i	−0.670015	−	0.742348i	$-0.733712\pi$
$419$		−	622.087i		−	1.48470i	0.670015	−	0.742348i	$-0.266288\pi$
$420$			511.895i			1.21880i
$421$	129.554	+	129.554i	0.307728	+	0.307728i	0.844028	−	0.536299i	$-0.180178\pi$
$421$	129.554	+	129.554i	0.307728	+	0.307728i	−0.536299	+	0.844028i	$0.680178\pi$
$422$	−75.9590			−0.179998
$423$	557.743			1.31854
$424$	216.819	+	216.819i	0.511365	+	0.511365i
$425$	−387.379	+	387.379i	−0.911480	+	0.911480i
$426$	−263.694	+	263.694i	−0.618999	+	0.618999i
$427$			391.357i			0.916527i
$428$	−105.344			−0.246131
$429$	217.114	+	217.114i	0.506094	+	0.506094i
$430$	81.5775			0.189715
$431$	−226.262			−0.524970			−0.262485	−	0.964936i	$-0.584542\pi$
$431$	−226.262			−0.524970			−0.262485	+	0.964936i	$0.584542\pi$
$432$	196.444	+	196.444i	0.454732	+	0.454732i
$433$		−	418.510i		−	0.966535i	−0.875473	−	0.483268i	$-0.839450\pi$
$433$		−	418.510i		−	0.966535i	0.875473	−	0.483268i	$-0.160550\pi$
$434$	−362.632			−0.835557
$435$			236.712i			0.544166i
$436$	−28.3606			−0.0650472
$437$		−	253.776i		−	0.580724i
$438$	−188.824	−	188.824i	−0.431105	−	0.431105i
$439$	114.416	+	114.416i	0.260630	+	0.260630i	0.825310	−	0.564680i	$-0.191000\pi$
$439$	114.416	+	114.416i	0.260630	+	0.260630i	−0.564680	+	0.825310i	$0.691000\pi$
$440$	−68.6512	+	68.6512i	−0.156026	+	0.156026i
$441$			2576.54i			5.84250i
$442$	−234.421	+	234.421i	−0.530365	+	0.530365i
$443$	−280.909			−0.634107			−0.317053	−	0.948408i	$-0.602693\pi$
$443$	−280.909			−0.634107			−0.317053	+	0.948408i	$0.602693\pi$
$444$	34.6590	+	34.6590i	0.0780609	+	0.0780609i
$445$	326.369			0.733413
$446$	239.341	+	239.341i	0.536640	+	0.536640i
$447$	−523.440			−1.17101
$448$	292.779			0.653525
$449$		−	307.464i		−	0.684776i	−0.939559	−	0.342388i	$-0.888764\pi$
$449$		−	307.464i		−	0.684776i	0.939559	−	0.342388i	$-0.111236\pi$
$450$	−347.565	+	347.565i	−0.772367	+	0.772367i
$451$	20.7893	+	20.7893i	0.0460960	+	0.0460960i
$452$	−406.982	+	406.982i	−0.900402	+	0.900402i
$453$	−1546.36			−3.41360
$454$	−433.473			−0.954787
$455$	325.562			0.715520
$456$			782.911i			1.71691i
$457$	−124.373			−0.272151			−0.136076	−	0.990698i	$-0.543449\pi$
$457$	−124.373			−0.272151			−0.136076	+	0.990698i	$0.543449\pi$
$458$		−	210.857i		−	0.460387i
$459$		−	2597.03i		−	5.65803i
$460$	−69.9377	−	69.9377i	−0.152039	−	0.152039i
$461$	−138.002	+	138.002i	−0.299354	+	0.299354i	−0.840761	−	0.541407i	$-0.817892\pi$
$461$	−138.002	+	138.002i	−0.299354	+	0.299354i	0.541407	+	0.840761i	$0.317892\pi$
$462$	−285.781	+	285.781i	−0.618575	+	0.618575i
$463$	520.943	−	520.943i	1.12515	−	1.12515i	0.134192	−	0.990955i	$-0.457156\pi$
$463$	520.943	−	520.943i	1.12515	−	1.12515i	0.990955	−	0.134192i	$-0.0428440\pi$
$464$	−51.0867			−0.110101
$465$	−276.009	−	276.009i	−0.593568	−	0.593568i
$466$	171.742	−	171.742i	0.368545	−	0.368545i
$467$	−458.622	+	458.622i	−0.982061	+	0.982061i	−0.999842	−	0.0177809i	$-0.994340\pi$
$467$	−458.622	+	458.622i	−0.982061	+	0.982061i	0.0177809	+	0.999842i	$0.494340\pi$
$468$	497.772	−	497.772i	1.06362	−	1.06362i
$469$	−210.912	−	210.912i	−0.449705	−	0.449705i
$470$	63.4685			0.135039
$471$	−1220.37	−	1220.37i	−2.59102	−	2.59102i
$472$	−464.093	−	464.093i	−0.983247	−	0.983247i
$473$	−107.785	−	107.785i	−0.227875	−	0.227875i
$474$	−627.930	+	627.930i	−1.32475	+	1.32475i
$475$	339.651			0.715055
$476$	730.258	+	730.258i	1.53416	+	1.53416i
$477$			1002.28i			2.10121i
$478$	−89.8809	+	89.8809i	−0.188035	+	0.188035i
$479$	−37.1360			−0.0775282			−0.0387641	−	0.999248i	$-0.512342\pi$
$479$	−37.1360			−0.0775282			−0.0387641	+	0.999248i	$0.512342\pi$
$480$	342.458	+	342.458i	0.713454	+	0.713454i
$481$	22.0429	−	22.0429i	0.0458272	−	0.0458272i
$482$	393.555			0.816505
$483$	−705.290	−	705.290i	−1.46023	−	1.46023i
$484$	−265.352			−0.548248
$485$	77.5415	+	77.5415i	0.159879	+	0.159879i
$486$		−	956.787i		−	1.96870i
$487$		−	578.917i		−	1.18874i	−0.804191	−	0.594371i	$-0.797401\pi$
$487$		−	578.917i		−	1.18874i	0.804191	−	0.594371i	$-0.202599\pi$
$488$	164.955	+	164.955i	0.338022	+	0.338022i
$489$	334.650	+	334.650i	0.684355	+	0.684355i
$490$			293.198i			0.598363i
$491$			566.666i			1.15411i	0.816707	+	0.577053i	$0.195797\pi$
$491$			566.666i			1.15411i	−0.816707	+	0.577053i	$0.804203\pi$
$492$	65.3378	−	65.3378i	0.132800	−	0.132800i
$493$	337.689	+	337.689i	0.684967	+	0.684967i
$494$	205.539			0.416071
$495$	−317.351			−0.641112
$496$	59.5676	−	59.5676i	0.120096	−	0.120096i
$497$	522.434	−	522.434i	1.05118	−	1.05118i
$498$	−407.415			−0.818103
$499$	−522.976			−1.04805			−0.524024	−	0.851704i	$-0.675570\pi$
$499$	−522.976			−1.04805			−0.524024	+	0.851704i	$0.675570\pi$
$500$	219.551	−	219.551i	0.439101	−	0.439101i
$501$			871.825i			1.74017i
$502$	1.04723	−	1.04723i	0.00208611	−	0.00208611i
$503$			680.317i			1.35252i	0.736664	+	0.676259i	$0.236400\pi$
$503$			680.317i			1.35252i	−0.736664	+	0.676259i	$0.763600\pi$
$504$	1587.26	+	1587.26i	3.14932	+	3.14932i
$505$	−43.1588	+	43.1588i	−0.0854629	+	0.0854629i
$506$		−	78.0899i		−	0.154328i
$507$	255.311	+	255.311i	0.503572	+	0.503572i
$508$	535.923			1.05497
$509$	252.887	−	252.887i	0.496831	−	0.496831i	−0.413619	−	0.910450i	$-0.635735\pi$
$509$	252.887	−	252.887i	0.496831	−	0.496831i	0.910450	+	0.413619i	$0.135735\pi$
$510$		−	469.710i		−	0.921000i
$511$	374.101	+	374.101i	0.732096	+	0.732096i
$512$	−140.149	+	140.149i	−0.273728	+	0.273728i
$513$	−1138.53	+	1138.53i	−2.21936	+	2.21936i
$514$	262.413	−	262.413i	0.510531	−	0.510531i
$515$			202.791i			0.393768i
$516$	−338.752	+	338.752i	−0.656496	+	0.656496i
$517$	−83.8581	−	83.8581i	−0.162201	−	0.162201i
$518$	29.0145	+	29.0145i	0.0560125	+	0.0560125i
$519$	237.460	+	237.460i	0.457533	+	0.457533i
$520$	137.222	−	137.222i	0.263889	−	0.263889i
$521$			755.345i			1.44980i	0.688855	+	0.724899i	$0.258114\pi$
$521$			755.345i			1.44980i	−0.688855	+	0.724899i	$0.741886\pi$
$522$	302.982	+	302.982i	0.580425	+	0.580425i
$523$	669.892	+	669.892i	1.28086	+	1.28086i	0.940177	+	0.340688i	$0.110660\pi$
$523$	669.892	+	669.892i	1.28086	+	1.28086i	0.340688	+	0.940177i	$0.389340\pi$
$524$	159.401	+	159.401i	0.304200	+	0.304200i
$525$	943.953	−	943.953i	1.79801	−	1.79801i
$526$	13.9590			0.0265381
$527$	−787.497			−1.49430
$528$		−	93.8875i		−	0.177817i
$529$	−336.279			−0.635688
$530$			114.054i			0.215197i
$531$		−	2145.34i		−	4.04018i
$532$		−	640.285i		−	1.20354i
$533$	−41.5544	−	41.5544i	−0.0779632	−	0.0779632i
$534$	572.646	−	572.646i	1.07237	−	1.07237i
$535$	−67.1220	−	67.1220i	−0.125462	−	0.125462i
$536$	−177.796			−0.331709
$537$			480.601i			0.894974i
$538$		−	360.434i		−	0.669952i
$539$	387.390	−	387.390i	0.718719	−	0.718719i
$540$			627.531i			1.16210i
$541$	380.352	−	380.352i	0.703054	−	0.703054i	−0.262011	−	0.965065i	$-0.584386\pi$
$541$	380.352	−	380.352i	0.703054	−	0.703054i	0.965065	+	0.262011i	$0.0843858\pi$
$542$		−	177.694i		−	0.327848i
$543$	−1028.11	−	1028.11i	−1.89340	−	1.89340i
$544$	977.086			1.79611
$545$	−18.0705	−	18.0705i	−0.0331569	−	0.0331569i
$546$	571.230	−	571.230i	1.04621	−	1.04621i
$547$	−48.5591	+	48.5591i	−0.0887734	+	0.0887734i	−0.750099	−	0.661326i	$-0.769994\pi$
$547$	−48.5591	+	48.5591i	−0.0887734	+	0.0887734i	0.661326	+	0.750099i	$0.269994\pi$
$548$	−496.211			−0.905494
$549$			762.528i			1.38894i
$550$	104.515			0.190027
$551$		−	296.083i		−	0.537356i
$552$	−594.552			−1.07709
$553$	1244.06	−	1244.06i	2.24967	−	2.24967i
$554$		−	380.931i		−	0.687602i
$555$			44.1674i			0.0795809i
$556$	−314.645	+	314.645i	−0.565909	+	0.565909i
$557$		−	74.4865i		−	0.133728i	−0.997762	−	0.0668640i	$-0.978701\pi$
$557$		−	74.4865i		−	0.133728i	0.997762	−	0.0668640i	$-0.0212994\pi$
$558$	−706.560			−1.26624
$559$	215.444	+	215.444i	0.385409	+	0.385409i
$560$	−70.3920	−	70.3920i	−0.125700	−	0.125700i
$561$	−620.607	+	620.607i	−1.10625	+	1.10625i
$562$			272.438i			0.484765i
$563$			204.532i			0.363289i	0.983364	+	0.181644i	$0.0581420\pi$
$563$			204.532i			0.363289i	−0.983364	+	0.181644i	$0.941858\pi$
$564$	−263.554	+	263.554i	−0.467294	+	0.467294i
$565$	−518.633			−0.917935
$566$	−594.602			−1.05053
$567$			3607.50i			6.36244i
$568$		−	440.406i		−	0.775363i
$569$	−322.772			−0.567262			−0.283631	−	0.958934i	$-0.591539\pi$
$569$	−322.772			−0.567262			−0.283631	+	0.958934i	$0.591539\pi$
$570$	−205.919	+	205.919i	−0.361262	+	0.361262i
$571$	−214.664	+	214.664i	−0.375944	+	0.375944i	−0.869637	−	0.493692i	$-0.835647\pi$
$571$	−214.664	+	214.664i	−0.375944	+	0.375944i	0.493692	+	0.869637i	$0.335647\pi$
$572$	−149.683			−0.261683
$573$	−647.248	+	647.248i	−1.12958	+	1.12958i
$574$	54.6969	−	54.6969i	0.0952907	−	0.0952907i
$575$			257.935i			0.448583i
$576$	570.457			0.990376
$577$	−116.609	+	116.609i	−0.202094	+	0.202094i	−0.800897	−	0.598802i	$-0.795643\pi$
$577$	−116.609	+	116.609i	−0.202094	+	0.202094i	0.598802	+	0.800897i	$0.295643\pi$
$578$	−447.330	−	447.330i	−0.773927	−	0.773927i
$579$	495.361	−	495.361i	0.855546	−	0.855546i
$580$	−81.5970	−	81.5970i	−0.140684	−	0.140684i
$581$	807.177			1.38929
$582$	272.108			0.467540
$583$	150.695	−	150.695i	0.258482	−	0.258482i
$584$	315.363			0.540005
$585$	634.331			1.08433
$586$	35.5707	+	35.5707i	0.0607009	+	0.0607009i
$587$	−769.607			−1.31108			−0.655542	−	0.755158i	$-0.727560\pi$
$587$	−769.607			−1.31108			−0.655542	+	0.755158i	$0.727560\pi$
$588$	−1217.51	−	1217.51i	−2.07060	−	2.07060i
$589$	345.236	+	345.236i	0.586139	+	0.586139i
$590$		−	244.129i		−	0.413778i
$591$	−524.406	−	1008.06i	−0.887320	−	1.70568i
$592$	−9.53210			−0.0161015
$593$	137.438	−	137.438i	0.231767	−	0.231767i	−0.581663	−	0.813430i	$-0.697598\pi$
$593$	137.438	−	137.438i	0.231767	−	0.231767i	0.813430	+	0.581663i	$0.197598\pi$
$594$	−350.339	+	350.339i	−0.589796	+	0.589796i
$595$			930.597i			1.56403i
$596$	180.435	−	180.435i	0.302743	−	0.302743i
$597$		−	1773.56i		−	2.97079i
$598$			156.089i			0.261018i
$599$	−72.5088	−	72.5088i	−0.121050	−	0.121050i	0.643987	−	0.765037i	$-0.277279\pi$
$599$	−72.5088	−	72.5088i	−0.121050	−	0.121050i	−0.765037	+	0.643987i	$0.777279\pi$
$600$		−	795.742i		−	1.32624i
$601$			477.333i			0.794231i	0.917769	+	0.397115i	$0.129989\pi$
$601$			477.333i			0.794231i	−0.917769	+	0.397115i	$0.870011\pi$
$602$	−283.583	+	283.583i	−0.471068	+	0.471068i
$603$	−410.945	−	410.945i	−0.681501	−	0.681501i
$604$	533.045	−	533.045i	0.882525	−	0.882525i
$605$	−169.074	−	169.074i	−0.279462	−	0.279462i
$606$			151.453i			0.249922i
$607$	−1073.67			−1.76882			−0.884410	−	0.466711i	$-0.845439\pi$
$607$	−1073.67			−1.76882			−0.884410	+	0.466711i	$0.845439\pi$
$608$	−428.351	−	428.351i	−0.704525	−	0.704525i
$609$	−822.868	−	822.868i	−1.35118	−	1.35118i
$610$			86.7720i			0.142249i
$611$	167.618	+	167.618i	0.274335	+	0.274335i
$612$	1422.85	+	1422.85i	2.32492	+	2.32492i
$613$			520.153i			0.848536i	0.905537	+	0.424268i	$0.139469\pi$
$613$			520.153i			0.848536i	−0.905537	+	0.424268i	$0.860531\pi$
$614$	134.297			0.218725
$615$	83.2626			0.135386
$616$		−	477.296i		−	0.774831i
$617$			41.7746i			0.0677060i	0.999427	+	0.0338530i	$0.0107778\pi$
$617$			41.7746i			0.0677060i	−0.999427	+	0.0338530i	$0.989222\pi$
$618$	355.816	+	355.816i	0.575754	+	0.575754i
$619$	−454.582			−0.734382			−0.367191	−	0.930146i	$-0.619680\pi$
$619$	−454.582			−0.734382			−0.367191	+	0.930146i	$0.619680\pi$
$620$	190.286			0.306913
$621$	−864.614	−	864.614i	−1.39229	−	1.39229i
$622$	225.084	−	225.084i	0.361871	−	0.361871i
$623$	−1134.54	+	1134.54i	−1.82109	+	1.82109i
$624$			187.666i			0.300746i
$625$	−184.719			−0.295550
$626$	−14.7332	−	14.7332i	−0.0235355	−	0.0235355i
$627$	544.144			0.867853
$628$	841.347			1.33972
$629$	63.0082	+	63.0082i	0.100172	+	0.100172i
$630$			834.953i			1.32532i
$631$	665.119			1.05407			0.527036	−	0.849843i	$-0.323303\pi$
$631$	665.119			1.05407			0.527036	+	0.849843i	$0.323303\pi$
$632$		−	1048.73i		−	1.65939i
$633$	401.954			0.634998
$634$		−	204.093i		−	0.321913i
$635$	341.474	+	341.474i	0.537755	+	0.537755i
$636$	−473.612	−	473.612i	−0.744673	−	0.744673i
$637$	−774.328	+	774.328i	−1.21559	+	1.21559i
$638$		−	91.1081i		−	0.142803i
$639$	1017.92	−	1017.92i	1.59299	−	1.59299i
$640$	−270.942			−0.423347
$641$	10.7337	+	10.7337i	0.0167452	+	0.0167452i	0.715430	−	0.698685i	$-0.246231\pi$
$641$	10.7337	+	10.7337i	0.0167452	+	0.0167452i	−0.698685	+	0.715430i	$0.746231\pi$
$642$	−235.544			−0.366891
$643$	−95.8475	−	95.8475i	−0.149063	−	0.149063i	0.628636	−	0.777699i	$-0.283613\pi$
$643$	−95.8475	−	95.8475i	−0.149063	−	0.149063i	−0.777699	+	0.628636i	$0.783613\pi$
$644$	486.241			0.755032
$645$	−431.685			−0.669280
$646$			587.520i			0.909473i
$647$	142.445	−	142.445i	0.220162	−	0.220162i	−0.588404	−	0.808567i	$-0.700244\pi$
$647$	142.445	−	142.445i	0.220162	−	0.220162i	0.808567	+	0.588404i	$0.200244\pi$
$648$	1520.54	+	1520.54i	2.34652	+	2.34652i
$649$	−322.557	+	322.557i	−0.497006	+	0.497006i
$650$	−208.907			−0.321396
$651$	1918.95			2.94769
$652$	−230.714			−0.353856
$653$		−	446.322i		−	0.683495i	−0.939792	−	0.341747i	$-0.888981\pi$
$653$		−	446.322i		−	0.683495i	0.939792	−	0.341747i	$-0.111019\pi$
$654$	−63.4130			−0.0969617
$655$			203.131i			0.310123i
$656$			17.9695i			0.0273926i
$657$	728.906	+	728.906i	1.10945	+	1.10945i
$658$	−220.632	+	220.632i	−0.335306	+	0.335306i
$659$	206.775	−	206.775i	0.313771	−	0.313771i	−0.532598	−	0.846368i	$-0.678784\pi$
$659$	206.775	−	206.775i	0.313771	−	0.313771i	0.846368	+	0.532598i	$0.178784\pi$
$660$	149.960	−	149.960i	0.227212	−	0.227212i
$661$	−181.862			−0.275132			−0.137566	−	0.990493i	$-0.543928\pi$
$661$	−181.862			−0.275132			−0.137566	+	0.990493i	$0.543928\pi$
$662$	−14.1722	−	14.1722i	−0.0214082	−	0.0214082i
$663$	1240.49	−	1240.49i	1.87103	−	1.87103i
$664$	340.221	−	340.221i	0.512381	−	0.512381i
$665$	407.971	−	407.971i	0.613490	−	0.613490i
$666$	56.5324	+	56.5324i	0.0848835	+	0.0848835i
$667$	224.849			0.337105
$668$	−300.526	−	300.526i	−0.449890	−	0.449890i
$669$	−1266.53	−	1266.53i	−1.89316	−	1.89316i
$670$	−46.7635	−	46.7635i	−0.0697963	−	0.0697963i
$671$	114.648	−	114.648i	0.170861	−	0.170861i
$672$	−2380.93			−3.54305
$673$	−580.202	−	580.202i	−0.862113	−	0.862113i	0.129470	−	0.991583i	$-0.458672\pi$
$673$	−580.202	−	580.202i	−0.862113	−	0.862113i	−0.991583	+	0.129470i	$0.958672\pi$
$674$		−	334.852i		−	0.496814i
$675$	1157.19	−	1157.19i	1.71436	−	1.71436i
$676$	−176.016			−0.260379
$677$	71.3075	+	71.3075i	0.105329	+	0.105329i	0.757807	−	0.652479i	$-0.226271\pi$
$677$	71.3075	+	71.3075i	0.105329	+	0.105329i	−0.652479	+	0.757807i	$0.726271\pi$
$678$	−909.993	+	909.993i	−1.34217	+	1.34217i
$679$	−539.106			−0.793970
$680$	392.242	+	392.242i	0.576826	+	0.576826i
$681$	2293.82			3.36831
$682$	106.233	+	106.233i	0.155767	+	0.155767i
$683$		−	191.450i		−	0.280307i	−0.990130	−	0.140153i	$-0.955240\pi$
$683$		−	191.450i		−	0.280307i	0.990130	−	0.140153i	$-0.0447596\pi$
$684$		−	1247.55i		−	1.82390i
$685$	−316.171	−	316.171i	−0.461563	−	0.461563i
$686$	−548.788	−	548.788i	−0.799982	−	0.799982i
$687$			1115.80i			1.62416i
$688$		−	93.1653i		−	0.135415i
$689$	−301.214	+	301.214i	−0.437175	+	0.437175i
$690$	−156.378	−	156.378i	−0.226634	−	0.226634i
$691$	786.170			1.13773			0.568864	−	0.822432i	$-0.307383\pi$
$691$	786.170			1.13773			0.568864	+	0.822432i	$0.307383\pi$
$692$	−163.709			−0.236574
$693$	1103.19	−	1103.19i	1.59190	−	1.59190i
$694$	49.2264	−	49.2264i	0.0709315	−	0.0709315i
$695$	−400.965			−0.576929
$696$	−693.669			−0.996651
$697$	118.781	−	118.781i	0.170417	−	0.170417i
$698$			47.5469i			0.0681187i
$699$	−908.811	+	908.811i	−1.30016	+	1.30016i
$700$			650.779i			0.929684i
$701$	185.025	+	185.025i	0.263944	+	0.263944i	0.826654	−	0.562710i	$-0.190241\pi$
$701$	185.025	+	185.025i	0.263944	+	0.263944i	−0.562710	+	0.826654i	$0.690241\pi$
$702$	700.270	−	700.270i	0.997535	−	0.997535i
$703$		−	55.2452i		−	0.0785849i
$704$	−85.7696	−	85.7696i	−0.121832	−	0.121832i
$705$	−335.857			−0.476394
$706$	−24.6608	+	24.6608i	−0.0349303	+	0.0349303i
$707$		−	300.060i		−	0.424413i
$708$	1013.75	+	1013.75i	1.43185	+	1.43185i
$709$	−624.792	+	624.792i	−0.881229	+	0.881229i	−0.993660	−	0.112430i	$-0.964136\pi$
$709$	−624.792	+	624.792i	−0.881229	+	0.881229i	0.112430	+	0.993660i	$0.464136\pi$
$710$	115.835	−	115.835i	0.163147	−	0.163147i
$711$	2423.96	−	2423.96i	3.40923	−	3.40923i
$712$			956.402i			1.34326i
$713$	−262.176	+	262.176i	−0.367709	+	0.367709i
$714$	1632.82	+	1632.82i	2.28687	+	2.28687i
$715$	−95.3733	−	95.3733i	−0.133389	−	0.133389i
$716$	−165.668	−	165.668i	−0.231379	−	0.231379i
$717$	475.624	−	475.624i	0.663353	−	0.663353i
$718$		−	468.829i		−	0.652965i
$719$	243.918	+	243.918i	0.339246	+	0.339246i	0.856083	−	0.516838i	$-0.172891\pi$
$719$	243.918	+	243.918i	0.339246	+	0.339246i	−0.516838	+	0.856083i	$0.672891\pi$
$720$	−137.153	−	137.153i	−0.190491	−	0.190491i
$721$	−704.948	−	704.948i	−0.977737	−	0.977737i
$722$	−20.6757	+	20.6757i	−0.0286368	+	0.0286368i
$723$	−2082.58			−2.88048
$724$	708.801			0.979008
$725$			300.935i			0.415083i
$726$	−593.315			−0.817238
$727$			206.541i			0.284101i	0.989859	+	0.142050i	$0.0453695\pi$
$727$			206.541i			0.284101i	−0.989859	+	0.142050i	$0.954631\pi$
$728$			954.036i			1.31049i
$729$			2456.55i			3.36975i
$730$	82.9460	+	82.9460i	0.113625	+	0.113625i
$731$	−615.833	+	615.833i	−0.842452	+	0.842452i
$732$	−360.322	−	360.322i	−0.492243	−	0.492243i
$733$	512.252			0.698843			0.349421	−	0.936966i	$-0.386378\pi$
$733$	512.252			0.698843			0.349421	+	0.936966i	$0.386378\pi$
$734$		−	63.0230i		−	0.0858624i
$735$		−	1551.52i		−	2.11091i
$736$	325.295	−	325.295i	0.441977	−	0.441977i
$737$			123.573i			0.167670i
$738$	106.573	−	106.573i	0.144407	−	0.144407i
$739$			394.248i			0.533489i	0.963767	+	0.266745i	$0.0859480\pi$
$739$			394.248i			0.533489i	−0.963767	+	0.266745i	$0.914052\pi$
$740$	−15.2249	−	15.2249i	−0.0205742	−	0.0205742i
$741$	−1087.65			−1.46782
$742$	−396.479	−	396.479i	−0.534339	−	0.534339i
$743$	328.638	−	328.638i	0.442312	−	0.442312i	−0.450477	−	0.892788i	$-0.648746\pi$
$743$	328.638	−	328.638i	0.442312	−	0.442312i	0.892788	+	0.450477i	$0.148746\pi$
$744$	808.825	−	808.825i	1.08713	−	1.08713i
$745$	229.935			0.308638
$746$		−	275.116i		−	0.368789i
$747$	1572.72			2.10538
$748$		−	427.858i		−	0.572003i
$749$	466.664			0.623049
$750$	490.905	−	490.905i	0.654541	−	0.654541i
$751$		−	787.826i		−	1.04904i	−0.851399	−	0.524518i	$-0.824246\pi$
$751$		−	787.826i		−	1.04904i	0.851399	−	0.524518i	$-0.175754\pi$
$752$		−	72.4839i		−	0.0963882i
$753$	−5.54163	+	5.54163i	−0.00735940	+	0.00735940i
$754$			182.110i			0.241525i
$755$	679.281			0.899710
$756$	−2181.45	−	2181.45i	−2.88551	−	2.88551i
$757$	−722.305	−	722.305i	−0.954168	−	0.954168i	0.0448270	−	0.998995i	$-0.485726\pi$
$757$	−722.305	−	722.305i	−0.954168	−	0.954168i	−0.998995	+	0.0448270i	$0.985726\pi$
$758$	−201.641	+	201.641i	−0.266017	+	0.266017i
$759$			413.230i			0.544440i
$760$		−	343.915i		−	0.452519i
$761$	−346.382	+	346.382i	−0.455166	+	0.455166i	−0.897065	−	0.441899i	$-0.854305\pi$
$761$	−346.382	+	346.382i	−0.455166	+	0.455166i	0.441899	+	0.897065i	$0.354305\pi$
$762$	1198.30			1.57257
$763$	125.635			0.164659
$764$		−	446.225i		−	0.584064i
$765$			1813.20i			2.37019i
$766$	278.661			0.363788
$767$	644.738	−	644.738i	0.840597	−	0.840597i
$768$	−858.856	+	858.856i	−1.11830	+	1.11830i
$769$	−709.265			−0.922321			−0.461161	−	0.887317i	$-0.652567\pi$
$769$	−709.265			−0.922321			−0.461161	+	0.887317i	$0.652567\pi$
$770$	125.537	−	125.537i	0.163035	−	0.163035i
$771$	−1388.62	+	1388.62i	−1.80106	+	1.80106i
$772$			341.511i			0.442372i
$773$	823.941			1.06590			0.532950	−	0.846147i	$-0.321083\pi$
$773$	823.941			1.06590			0.532950	+	0.846147i	$0.321083\pi$
$774$	−552.539	+	552.539i	−0.713875	+	0.713875i
$775$	−350.894	−	350.894i	−0.452766	−	0.452766i
$776$	−227.230	+	227.230i	−0.292822	+	0.292822i
$777$	−153.536	−	153.536i	−0.197602	−	0.197602i
$778$	−69.4991			−0.0893304
$779$	−104.146			−0.133692
$780$	−299.745	+	299.745i	−0.384288	+	0.384288i
$781$	−306.094			−0.391926
$782$	−446.170			−0.570549
$783$	−1008.75	−	1008.75i	−1.28832	−	1.28832i
$784$	334.846			0.427099
$785$	536.081	+	536.081i	0.682906	+	0.682906i
$786$	356.412	+	356.412i	0.453451	+	0.453451i
$787$		−	706.163i		−	0.897284i	−0.893712	−	0.448642i	$-0.851908\pi$
$787$		−	706.163i		−	0.897284i	0.893712	−	0.448642i	$-0.148092\pi$
$788$	528.255	+	166.719i	0.670374	+	0.211573i
$789$	−73.8674			−0.0936215
$790$	275.835	−	275.835i	0.349158	−	0.349158i
$791$	1802.89	−	1802.89i	2.27926	−	2.27926i
$792$		−	929.974i		−	1.17421i
$793$	−229.162	+	229.162i	−0.288982	+	0.288982i
$794$			495.176i			0.623647i
$795$		−	603.543i		−	0.759173i
$796$	611.363	+	611.363i	0.768044	+	0.768044i
$797$			213.284i			0.267609i	0.991008	+	0.133805i	$0.0427194\pi$
$797$			213.284i			0.267609i	−0.991008	+	0.133805i	$0.957281\pi$
$798$		−	1431.65i		−	1.79405i
$799$	−479.127	+	479.127i	−0.599658	+	0.599658i
$800$	435.371	+	435.371i	0.544214	+	0.544214i
$801$	−2210.55	+	2210.55i	−2.75974	+	2.75974i
$802$	−61.6323	−	61.6323i	−0.0768483	−	0.0768483i
$803$		−	219.186i		−	0.272958i
$804$	388.373			0.483051
$805$	309.818	+	309.818i	0.384867	+	0.384867i
$806$	−212.342	−	212.342i	−0.263452	−	0.263452i
$807$			1907.32i			2.36347i
$808$	−126.474	−	126.474i	−0.156527	−	0.156527i
$809$	−348.545	−	348.545i	−0.430834	−	0.430834i	0.458078	−	0.888912i	$-0.348538\pi$
$809$	−348.545	−	348.545i	−0.430834	−	0.430834i	−0.888912	+	0.458078i	$0.848538\pi$
$810$			799.859i			0.987480i
$811$	240.576			0.296641			0.148321	−	0.988939i	$-0.452613\pi$
$811$	240.576			0.296641			0.148321	+	0.988939i	$0.452613\pi$
$812$	567.301			0.698647
$813$			940.306i			1.15659i
$814$		−	16.9996i		−	0.0208840i
$815$	−147.004	−	147.004i	−0.180373	−	0.180373i
$816$	−536.430			−0.657390
$817$	539.958			0.660903
$818$	117.982	+	117.982i	0.144233	+	0.144233i
$819$	−2205.09	+	2205.09i	−2.69241	+	2.69241i
$820$	−28.7014	+	28.7014i	−0.0350017	+	0.0350017i
$821$			733.264i			0.893136i	0.894750	+	0.446568i	$0.147354\pi$
$821$			733.264i			0.893136i	−0.894750	+	0.446568i	$0.852646\pi$
$822$	−1109.50			−1.34976
$823$	940.864	+	940.864i	1.14321	+	1.14321i	0.987859	+	0.155354i	$0.0496519\pi$
$823$	940.864	+	940.864i	1.14321	+	1.14321i	0.155354	+	0.987859i	$0.450348\pi$
$824$	−594.263			−0.721194
$825$	−553.062			−0.670378
$826$	848.651	+	848.651i	1.02742	+	1.02742i
$827$		−	1417.91i		−	1.71452i	−0.514882	−	0.857261i	$-0.672164\pi$
$827$		−	1417.91i		−	1.71452i	0.514882	−	0.857261i	$-0.327836\pi$
$828$	947.401			1.14420
$829$		−	218.636i		−	0.263735i	−0.991267	−	0.131868i	$-0.957903\pi$
$829$		−	218.636i		−	0.263735i	0.991267	−	0.131868i	$-0.0420974\pi$
$830$	178.968			0.215624
$831$			2015.78i			2.42573i
$832$	171.439	+	171.439i	0.206057	+	0.206057i
$833$	−2213.37	−	2213.37i	−2.65710	−	2.65710i
$834$	−703.533	+	703.533i	−0.843565	+	0.843565i
$835$		−	382.973i		−	0.458650i
$836$	−187.572	+	187.572i	−0.224368	+	0.224368i
$837$	2352.43			2.81055
$838$	479.477	+	479.477i	0.572168	+	0.572168i
$839$	−1085.87			−1.29425			−0.647123	−	0.762386i	$-0.724028\pi$
$839$	−1085.87			−1.29425			−0.647123	+	0.762386i	$0.724028\pi$
$840$	−955.802	−	955.802i	−1.13786	−	1.13786i
$841$	−578.667			−0.688070
$842$	−199.708			−0.237183
$843$		−	1441.67i		−	1.71016i
$844$	−138.557	+	138.557i	−0.164167	+	0.164167i
$845$	−112.152	−	112.152i	−0.132725	−	0.132725i
$846$	−429.883	+	429.883i	−0.508136	+	0.508136i
$847$	1175.48			1.38782
$848$	130.255			0.153603
$849$	3146.47			3.70609
$850$		−	597.148i		−	0.702527i
$851$	41.9539			0.0492995
$852$			962.010i			1.12912i
$853$			1226.23i			1.43755i	0.695242	+	0.718776i	$0.255297\pi$
$853$			1226.23i			1.43755i	−0.695242	+	0.718776i	$0.744703\pi$
$854$	−301.640	−	301.640i	−0.353209	−	0.353209i
$855$	794.899	−	794.899i	0.929706	−	0.929706i
$856$	196.696	−	196.696i	0.229785	−	0.229785i
$857$	−1040.63	+	1040.63i	−1.21427	+	1.21427i	−0.244660	+	0.969609i	$0.578676\pi$
$857$	−1040.63	+	1040.63i	−1.21427	+	1.21427i	−0.969609	+	0.244660i	$0.921324\pi$
$858$	−334.683			−0.390074
$859$	−607.045	−	607.045i	−0.706689	−	0.706689i	0.259149	−	0.965837i	$-0.416558\pi$
$859$	−607.045	−	607.045i	−0.706689	−	0.706689i	−0.965837	+	0.259149i	$0.916558\pi$
$860$	148.806	−	148.806i	0.173030	−	0.173030i
$861$	−289.441	+	289.441i	−0.336168	+	0.336168i
$862$	174.392	−	174.392i	0.202311	−	0.202311i
$863$	778.060	+	778.060i	0.901576	+	0.901576i	0.995572	−	0.0939968i	$-0.0299643\pi$
$863$	778.060	+	778.060i	0.901576	+	0.901576i	−0.0939968	+	0.995572i	$0.529964\pi$
$864$	−2918.78			−3.37822
$865$	−104.311	−	104.311i	−0.120590	−	0.120590i
$866$	322.568	+	322.568i	0.372481	+	0.372481i
$867$	2367.14	+	2367.14i	2.73027	+	2.73027i
$868$	−661.479	+	661.479i	−0.762072	+	0.762072i
$869$	−728.897			−0.838777
$870$	−182.447	−	182.447i	−0.209709	−	0.209709i
$871$		−	247.002i		−	0.283585i
$872$	52.9544	−	52.9544i	0.0607275	−	0.0607275i
$873$	−1050.40			−1.20321
$874$	195.599	+	195.599i	0.223798	+	0.223798i
$875$	−972.590	+	972.590i	−1.11153	+	1.11153i
$876$	−688.869			−0.786380
$877$	11.9901	+	11.9901i	0.0136718	+	0.0136718i	0.713910	−	0.700238i	$-0.246923\pi$
$877$	11.9901	+	11.9901i	0.0136718	+	0.0136718i	−0.700238	+	0.713910i	$0.746923\pi$
$878$	−176.374			−0.200881
$879$	−188.230	−	188.230i	−0.214141	−	0.214141i
$880$			41.2426i			0.0468666i
$881$			383.515i			0.435318i	0.976025	+	0.217659i	$0.0698421\pi$
$881$			383.515i			0.435318i	−0.976025	+	0.217659i	$0.930158\pi$
$882$	−1985.88	−	1985.88i	−2.25157	−	2.25157i
$883$	465.265	+	465.265i	0.526914	+	0.526914i	0.919651	−	0.392737i	$-0.128472\pi$
$883$	465.265	+	465.265i	0.526914	+	0.526914i	−0.392737	+	0.919651i	$0.628472\pi$
$884$			855.218i			0.967441i
$885$			1291.86i			1.45973i
$886$	216.512	−	216.512i	0.244370	−	0.244370i
$887$	450.605	+	450.605i	0.508010	+	0.508010i	0.913915	−	0.405905i	$-0.133044\pi$
$887$	450.605	+	450.605i	0.508010	+	0.508010i	−0.405905	+	0.913915i	$0.633044\pi$
$888$	−129.429			−0.145754
$889$	−2374.09			−2.67052
$890$	−251.550	+	251.550i	−0.282641	+	0.282641i
$891$	1056.82	−	1056.82i	1.18610	−	1.18610i
$892$	873.167			0.978887
$893$	420.095			0.470431
$894$	403.444	−	403.444i	0.451280	−	0.451280i
$895$		−	211.117i		−	0.235885i
$896$	941.858	−	941.858i	1.05118	−	1.05118i
$897$		−	825.978i		−	0.920822i
$898$	236.980	+	236.980i	0.263897	+	0.263897i
$899$	−305.883	+	305.883i	−0.340248	+	0.340248i
$900$			1267.99i			1.40888i
$901$	−861.000	−	861.000i	−0.955605	−	0.955605i
$902$	−32.0469			−0.0355287
$903$	1500.64	−	1500.64i	1.66184	−	1.66184i
$904$		−	1519.82i		−	1.68122i
$905$	451.627	+	451.627i	0.499035	+	0.499035i
$906$	1191.87	−	1191.87i	1.31552	−	1.31552i
$907$	22.9175	−	22.9175i	0.0252674	−	0.0252674i	−0.694360	−	0.719628i	$-0.744313\pi$
$907$	22.9175	−	22.9175i	0.0252674	−	0.0252674i	0.719628	+	0.694360i	$0.244313\pi$
$908$	−790.701	+	790.701i	−0.870816	+	0.870816i
$909$		−	584.644i		−	0.643173i
$910$	−250.928	+	250.928i	−0.275745	+	0.275745i
$911$	−678.740	−	678.740i	−0.745049	−	0.745049i	0.228496	−	0.973545i	$-0.426619\pi$
$911$	−678.740	−	678.740i	−0.745049	−	0.745049i	−0.973545	+	0.228496i	$0.926619\pi$
$912$	235.169	+	235.169i	0.257861	+	0.257861i
$913$	−236.463	−	236.463i	−0.258995	−	0.258995i
$914$	95.8612	−	95.8612i	0.104881	−	0.104881i
$915$		−	459.173i		−	0.501828i
$916$	−384.626	−	384.626i	−0.419897	−	0.419897i
$917$	−706.130	−	706.130i	−0.770044	−	0.770044i
$918$	2001.68	+	2001.68i	2.18048	+	2.18048i
$919$	228.047	−	228.047i	0.248147	−	0.248147i	−0.572063	−	0.820210i	$-0.693857\pi$
$919$	228.047	−	228.047i	0.248147	−	0.248147i	0.820210	+	0.572063i	$0.193857\pi$
$920$	261.173			0.283884
$921$	−710.662			−0.771619
$922$		−	212.732i		−	0.230729i
$923$	611.832			0.662873
$924$			1042.59i			1.12835i
$925$			56.1506i			0.0607033i
$926$			803.039i			0.867213i
$927$	−1373.54	−	1373.54i	−1.48170	−	1.48170i
$928$	379.524	−	379.524i	0.408970	−	0.408970i
$929$	−603.793	−	603.793i	−0.649939	−	0.649939i	0.303039	−	0.952978i	$-0.401999\pi$
$929$	−603.793	−	603.793i	−0.649939	−	0.649939i	−0.952978	+	0.303039i	$0.901999\pi$
$930$	425.470			0.457495
$931$			1940.66i			2.08449i
$932$		−	626.551i		−	0.672265i
$933$	−1191.08	+	1191.08i	−1.27661	+	1.27661i
$934$		−	706.971i		−	0.756928i
$935$	272.618	−	272.618i	0.291571	−	0.291571i
$936$			1858.86i			1.98597i
$937$	−196.038	−	196.038i	−0.209219	−	0.209219i	0.594716	−	0.803936i	$-0.297264\pi$
$937$	−196.038	−	196.038i	−0.209219	−	0.209219i	−0.803936	+	0.594716i	$0.797264\pi$
$938$	325.122			0.346612
$939$	77.9640	+	77.9640i	0.0830288	+	0.0830288i
$940$	115.773	−	115.773i	0.123163	−	0.123163i
$941$	507.630	−	507.630i	0.539458	−	0.539458i	−0.383912	−	0.923370i	$-0.625423\pi$
$941$	507.630	−	507.630i	0.539458	−	0.539458i	0.923370	+	0.383912i	$0.125423\pi$
$942$	1881.21			1.99704
$943$		−	79.0897i		−	0.0838703i
$944$	−278.806			−0.295346
$945$		−	2779.91i		−	2.94170i
$946$	166.151			0.175636
$947$	−628.860	+	628.860i	−0.664055	+	0.664055i	−0.956333	−	0.292279i	$-0.905587\pi$
$947$	−628.860	+	628.860i	−0.664055	+	0.664055i	0.292279	+	0.956333i	$0.405587\pi$
$948$			2290.82i			2.41648i
$949$			438.116i			0.461660i
$950$	−261.788	+	261.788i	−0.275566	+	0.275566i
$951$			1080.00i			1.13565i
$952$	−2727.05			−2.86455
$953$	−23.7929	−	23.7929i	−0.0249663	−	0.0249663i	0.694513	−	0.719480i	$-0.255620\pi$
$953$	−23.7929	−	23.7929i	−0.0249663	−	0.0249663i	−0.719480	+	0.694513i	$0.755620\pi$
$954$	−772.509	−	772.509i	−0.809758	−	0.809758i
$955$	284.321	−	284.321i	0.297719	−	0.297719i
$956$			327.904i			0.342996i
$957$			482.119i			0.503781i
$958$	28.6228	−	28.6228i	0.0298776	−	0.0298776i
$959$	2198.17			2.29215
$960$	−343.513			−0.357826
$961$			247.674i			0.257725i
$962$			33.9793i			0.0353215i
$963$	909.258			0.944193
$964$	717.886	−	717.886i	0.744695	−	0.744695i
$965$	−217.601	+	217.601i	−0.225493	+	0.225493i
$966$	1087.21			1.12548
$967$	−709.490	+	709.490i	−0.733703	+	0.733703i	−0.971351	−	0.237649i	$-0.923623\pi$
$967$	−709.490	+	709.490i	−0.733703	+	0.733703i	0.237649	+	0.971351i	$0.423623\pi$
$968$	495.460	−	495.460i	0.511839	−	0.511839i
$969$		−	3108.99i		−	3.20845i
$970$	−119.531			−0.123228
$971$	1115.84	−	1115.84i	1.14917	−	1.14917i	0.162452	−	0.986716i	$-0.448060\pi$
$971$	1115.84	−	1115.84i	1.14917	−	1.14917i	0.986716	−	0.162452i	$-0.0519403\pi$
$972$	−1745.28	−	1745.28i	−1.79556	−	1.79556i
$973$	1393.85	−	1393.85i	1.43253	−	1.43253i
$974$	446.203	+	446.203i	0.458114	+	0.458114i
$975$	1105.48			1.13382
$976$	99.0976			0.101534
$977$	154.028	−	154.028i	0.157654	−	0.157654i	−0.623872	−	0.781526i	$-0.714441\pi$
$977$	154.028	−	154.028i	0.157654	−	0.157654i	0.781526	+	0.623872i	$0.214441\pi$
$978$	−515.866			−0.527470
$979$	664.725			0.678983
$980$	534.824	+	534.824i	0.545739	+	0.545739i
$981$	244.790			0.249531
$982$	−436.760	−	436.760i	−0.444766	−	0.444766i
$983$	−1260.11	−	1260.11i	−1.28191	−	1.28191i	−0.939581	−	0.342326i	$-0.888785\pi$
$983$	−1260.11	−	1260.11i	−1.28191	−	1.28191i	−0.342326	−	0.939581i	$-0.611215\pi$
$984$			243.995i			0.247963i
$985$	230.360	+	442.817i	0.233868	+	0.449560i
$986$	−520.550			−0.527941
$987$	1167.52	−	1167.52i	1.18290	−	1.18290i
$988$	374.924	−	374.924i	0.379478	−	0.379478i
$989$			410.051i			0.414611i
$990$	244.599	−	244.599i	0.247070	−	0.247070i
$991$			1800.56i			1.81691i	0.417980	+	0.908456i	$0.362738\pi$
$991$			1800.56i			1.81691i	−0.417980	+	0.908456i	$0.637262\pi$
$992$			885.059i			0.892197i
$993$	74.9953	+	74.9953i	0.0755240	+	0.0755240i
$994$			805.337i			0.810198i
$995$			779.085i			0.783000i
$996$	−743.168	+	743.168i	−0.746153	+	0.746153i
$997$	−371.170	−	371.170i	−0.372286	−	0.372286i	0.496023	−	0.868309i	$-0.334793\pi$
$997$	−371.170	−	371.170i	−0.372286	−	0.372286i	−0.868309	+	0.496023i	$0.834793\pi$
$998$	403.086	−	403.086i	0.403894	−	0.403894i
$999$	−188.220	−	188.220i	−0.188408	−	0.188408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.3.c.a.14.13	✓	64
197.183	odd	4	inner	197.3.c.a.183.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.3.c.a.14.13	✓	64	1.1	even	1	trivial
197.3.c.a.183.13	yes	64	197.183	odd	4	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.770755 + 0.770755i) q^{2} +(4.07862 - 4.07862i) q^{3} +2.81187i q^{4} +(-1.79164 + 1.79164i) q^{5} +6.28722i q^{6} -12.4564i q^{7} +(-5.25028 - 5.25028i) q^{8} -24.2702i q^{9} -2.76183i q^{10} +(-3.64909 + 3.64909i) q^{11} +(11.4686 + 11.4686i) q^{12} +(7.29392 - 7.29392i) q^{13} +(9.60079 + 9.60079i) q^{14} +14.6148i q^{15} -3.15414 q^{16} +(20.8492 + 20.8492i) q^{17} +(18.7064 + 18.7064i) q^{18} -18.2804i q^{19} +(-5.03787 - 5.03787i) q^{20} +(-50.8047 - 50.8047i) q^{21} -5.62510i q^{22} +13.8824 q^{23} -42.8278 q^{24} +18.5800i q^{25} +11.2436i q^{26} +(-62.2814 - 62.2814i) q^{27} +35.0257 q^{28} +16.1967 q^{29} +(-11.2645 - 11.2645i) q^{30} +(-18.8855 + 18.8855i) q^{31} +(23.4322 - 23.4322i) q^{32} +29.7665i q^{33} -32.1392 q^{34} +(22.3173 + 22.3173i) q^{35} +68.2448 q^{36} +3.02209 q^{37} +(14.0897 + 14.0897i) q^{38} -59.4982i q^{39} +18.8133 q^{40} -5.69712i q^{41} +78.3159 q^{42} +29.5375i q^{43} +(-10.2608 - 10.2608i) q^{44} +(43.4836 + 43.4836i) q^{45} +(-10.6999 + 10.6999i) q^{46} +22.9806i q^{47} +(-12.8645 + 12.8645i) q^{48} -106.161 q^{49} +(-14.3206 - 14.3206i) q^{50} +170.072 q^{51} +(20.5096 + 20.5096i) q^{52} -41.2966 q^{53} +96.0073 q^{54} -13.0757i q^{55} +(-65.3994 + 65.3994i) q^{56} +(-74.5589 - 74.5589i) q^{57} +(-12.4837 + 12.4837i) q^{58} +88.3938 q^{59} -41.0951 q^{60} -31.4183 q^{61} -29.1122i q^{62} -302.318 q^{63} +23.5044i q^{64} +26.1362i q^{65} +(-22.9426 - 22.9426i) q^{66} +(16.9321 - 16.9321i) q^{67} +(-58.6254 + 58.6254i) q^{68} +(56.6210 - 56.6210i) q^{69} -34.4024 q^{70} +(41.9412 + 41.9412i) q^{71} +(-127.426 + 127.426i) q^{72} +(-30.0329 + 30.0329i) q^{73} +(-2.32929 + 2.32929i) q^{74} +(75.7808 + 75.7808i) q^{75} +51.4023 q^{76} +(45.4543 + 45.4543i) q^{77} +(45.8585 + 45.8585i) q^{78} +(99.8739 + 99.8739i) q^{79} +(5.65109 - 5.65109i) q^{80} -289.612 q^{81} +(4.39108 + 4.39108i) q^{82} +64.8005i q^{83} +(142.856 - 142.856i) q^{84} -74.7087 q^{85} +(-22.7661 - 22.7661i) q^{86} +(66.0601 - 66.0601i) q^{87} +38.3175 q^{88} +(-91.0809 - 91.0809i) q^{89} -67.0303 q^{90} +(-90.8556 - 90.8556i) q^{91} +39.0356i q^{92} +154.054i q^{93} +(-17.7124 - 17.7124i) q^{94} +(32.7520 + 32.7520i) q^{95} -191.142i q^{96} -43.2796i q^{97} +(81.8238 - 81.8238i) q^{98} +(88.5642 + 88.5642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) \) 64 * q - 2 * q^2 - 2 * q^3 - 10 * q^5 - 6 * q^8 + 10 * q^11 + 68 * q^12 + 2 * q^13 - 2 * q^14 - 280 * q^16 - 30 * q^17 - 68 * q^18 + 114 * q^20 - 20 * q^21 + 48 * q^23 + 60 * q^24 + 22 * q^27 + 392 * q^28 + 56 * q^29 - 70 * q^30 - 64 * q^31 - 156 * q^32 - 52 * q^34 - 92 * q^35 - 36 * q^36 - 160 * q^37 + 40 * q^38 + 52 * q^40 + 80 * q^42 + 140 * q^44 + 324 * q^45 + 214 * q^46 + 216 * q^48 - 836 * q^49 + 126 * q^50 + 124 * q^51 - 10 * q^52 - 16 * q^53 + 400 * q^54 - 40 * q^56 + 68 * q^57 - 266 * q^58 - 364 * q^59 - 68 * q^60 - 168 * q^61 - 12 * q^63 + 238 * q^66 - 112 * q^67 - 148 * q^68 - 48 * q^69 + 48 * q^70 + 150 * q^71 - 474 * q^72 + 18 * q^73 + 236 * q^74 + 64 * q^75 - 260 * q^76 - 388 * q^77 - 782 * q^78 + 202 * q^79 + 796 * q^80 - 516 * q^81 + 72 * q^82 - 294 * q^84 - 696 * q^85 + 618 * q^86 + 464 * q^87 - 244 * q^88 - 536 * q^89 + 1484 * q^90 + 212 * q^91 + 132 * q^94 + 370 * q^95 - 530 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

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