LMFDB - Embedded newform 196.2.j.a.111.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(27,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("196.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.15
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.145336 - 1.40673i) q^{2} +(-0.0665173 - 0.0834100i) q^{3} +(-1.95776 - 0.408895i) q^{4} +(1.11698 - 0.890758i) q^{5} +(-0.127002 + 0.0814491i) q^{6} +(-1.34404 - 2.27894i) q^{7} +(-0.859735 + 2.69460i) q^{8} +(0.665030 - 2.91369i) q^{9} +O(q^{10})$	\(q+(0.145336 - 1.40673i) q^{2} +(-0.0665173 - 0.0834100i) q^{3} +(-1.95776 - 0.408895i) q^{4} +(1.11698 - 0.890758i) q^{5} +(-0.127002 + 0.0814491i) q^{6} +(-1.34404 - 2.27894i) q^{7} +(-0.859735 + 2.69460i) q^{8} +(0.665030 - 2.91369i) q^{9} +(-1.09072 - 1.70074i) q^{10} +(-1.57408 + 0.359273i) q^{11} +(0.0961186 + 0.190495i) q^{12} +(0.776378 - 0.177203i) q^{13} +(-3.40118 + 1.55948i) q^{14} +(-0.148596 - 0.0339161i) q^{15} +(3.66561 + 1.60103i) q^{16} +(1.17894 - 2.44810i) q^{17} +(-4.00211 - 1.35898i) q^{18} -0.719271 q^{19} +(-2.55099 + 1.28716i) q^{20} +(-0.100684 + 0.263695i) q^{21} +(0.276629 + 2.26651i) q^{22} +(1.19976 + 2.49133i) q^{23} +(0.281944 - 0.107527i) q^{24} +(-0.658421 + 2.88473i) q^{25} +(-0.136441 - 1.11791i) q^{26} +(-0.575627 + 0.277208i) q^{27} +(1.69945 + 5.01117i) q^{28} +(3.80797 + 1.83382i) q^{29} +(-0.0693071 + 0.204105i) q^{30} +7.03624 q^{31} +(2.78496 - 4.92382i) q^{32} +(0.134671 + 0.107396i) q^{33} +(-3.27247 - 2.01425i) q^{34} +(-3.53124 - 1.34830i) q^{35} +(-2.49336 + 5.43236i) q^{36} +(4.28735 + 2.06468i) q^{37} +(-0.104536 + 1.01182i) q^{38} +(-0.0664231 - 0.0529707i) q^{39} +(1.43993 + 3.77561i) q^{40} +(-0.875154 + 0.697912i) q^{41} +(0.356314 + 0.179960i) q^{42} +(4.71379 + 3.75912i) q^{43} +(3.22857 - 0.0597362i) q^{44} +(-1.85257 - 3.84690i) q^{45} +(3.67898 - 1.32566i) q^{46} +(-2.47552 - 10.8460i) q^{47} +(-0.110284 - 0.412245i) q^{48} +(-3.38712 + 6.12596i) q^{49} +(3.96233 + 1.34547i) q^{50} +(-0.282617 + 0.0645054i) q^{51} +(-1.59242 + 0.0294635i) q^{52} +(2.38696 - 1.14950i) q^{53} +(0.306296 + 0.850038i) q^{54} +(-1.43818 + 1.80342i) q^{55} +(7.29634 - 1.66236i) q^{56} +(0.0478440 + 0.0599944i) q^{57} +(3.13312 - 5.09024i) q^{58} +(8.49023 - 10.6464i) q^{59} +(0.277047 + 0.127160i) q^{60} +(-4.31491 + 8.96000i) q^{61} +(1.02262 - 9.89806i) q^{62} +(-7.53394 + 2.40055i) q^{63} +(-6.52171 - 4.63328i) q^{64} +(0.709350 - 0.889497i) q^{65} +(0.170649 - 0.173836i) q^{66} +2.88009i q^{67} +(-3.30910 + 4.31072i) q^{68} +(0.127997 - 0.265788i) q^{69} +(-2.40991 + 4.77153i) q^{70} +(5.12694 + 10.6462i) q^{71} +(7.27947 + 4.29699i) q^{72} +(-12.1165 - 2.76552i) q^{73} +(3.52755 - 5.73106i) q^{74} +(0.284412 - 0.136965i) q^{75} +(1.40816 + 0.294106i) q^{76} +(2.93439 + 3.10435i) q^{77} +(-0.0841689 + 0.0857406i) q^{78} +9.74036i q^{79} +(5.52053 - 1.47686i) q^{80} +(-8.01654 - 3.86056i) q^{81} +(0.854580 + 1.33253i) q^{82} +(-1.87120 + 8.19825i) q^{83} +(0.304939 - 0.475081i) q^{84} +(-0.863816 - 3.78463i) q^{85} +(5.97314 - 6.08468i) q^{86} +(-0.100337 - 0.439603i) q^{87} +(0.385194 - 4.55039i) q^{88} +(-14.2898 - 3.26154i) q^{89} +(-5.68078 + 2.04696i) q^{90} +(-1.44732 - 1.53115i) q^{91} +(-1.33015 - 5.36799i) q^{92} +(-0.468032 - 0.586893i) q^{93} +(-15.6171 + 1.90607i) q^{94} +(-0.803408 + 0.640697i) q^{95} +(-0.595944 + 0.0952258i) q^{96} -1.72514i q^{97} +(8.12528 + 5.65507i) q^{98} +4.82530i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	0.145336	−	1.40673i	0.102768	−	0.994705i
$2$	0.145336	−	1.40673i	0.102768	−	0.994705i
$3$	−0.0665173	−	0.0834100i	−0.0384038	−	0.0481568i	0.762259	−	0.647272i	$-0.224090\pi$
$3$	−0.0665173	−	0.0834100i	−0.0384038	−	0.0481568i	−0.800663	+	0.599116i	$0.795519\pi$
$4$	−1.95776	−	0.408895i	−0.978878	−	0.204447i
$5$	1.11698	−	0.890758i	0.499527	−	0.398359i	−0.341056	−	0.940043i	$-0.610784\pi$
$5$	1.11698	−	0.890758i	0.499527	−	0.398359i	0.840582	+	0.541684i	$0.182213\pi$
$6$	−0.127002	+	0.0814491i	−0.0518485	+	0.0332515i
$7$	−1.34404	−	2.27894i	−0.507999	−	0.861358i
$7$	−1.34404	−	2.27894i	−0.507999	−	0.861358i
$8$	−0.859735	+	2.69460i	−0.303962	+	0.952684i
$9$	0.665030	−	2.91369i	0.221677	−	0.971229i
$10$	−1.09072	−	1.70074i	−0.344915	−	0.537820i
$11$	−1.57408	+	0.359273i	−0.474603	+	0.108325i	−0.453130	−	0.891444i	$-0.649693\pi$
$11$	−1.57408	+	0.359273i	−0.474603	+	0.108325i	−0.0214728	+	0.999769i	$0.506836\pi$
$12$	0.0961186	+	0.190495i	0.0277471	+	0.0549912i
$13$	0.776378	−	0.177203i	0.215329	−	0.0491474i	−0.113496	−	0.993539i	$-0.536205\pi$
$13$	0.776378	−	0.177203i	0.215329	−	0.0491474i	0.328824	+	0.944391i	$0.393348\pi$
$14$	−3.40118	+	1.55948i	−0.909003	+	0.416789i
$15$	−0.148596	−	0.0339161i	−0.0383674	−	0.00875711i
$16$	3.66561	+	1.60103i	0.916402	+	0.400258i
$17$	1.17894	−	2.44810i	0.285936	−	0.593753i	−0.707684	−	0.706529i	$-0.750260\pi$
$17$	1.17894	−	2.44810i	0.285936	−	0.593753i	0.993620	+	0.112776i	$0.0359743\pi$
$18$	−4.00211	−	1.35898i	−0.943306	−	0.320314i
$19$	−0.719271			−0.165012			−0.0825061	−	0.996591i	$-0.526292\pi$
$19$	−0.719271			−0.165012			−0.0825061	+	0.996591i	$0.526292\pi$
$20$	−2.55099	+	1.28716i	−0.570419	+	0.287818i
$21$	−0.100684	+	0.263695i	−0.0219712	+	0.0575430i
$22$	0.276629	+	2.26651i	0.0589776	+	0.483222i
$23$	1.19976	+	2.49133i	0.250167	+	0.519478i	0.987801	−	0.155724i	$-0.0497709\pi$
$23$	1.19976	+	2.49133i	0.250167	+	0.519478i	−0.737633	+	0.675202i	$0.764057\pi$
$24$	0.281944	−	0.107527i	0.0575515	−	0.0219488i
$25$	−0.658421	+	2.88473i	−0.131684	+	0.576946i
$26$	−0.136441	−	1.11791i	−0.0267583	−	0.219239i
$27$	−0.575627	+	0.277208i	−0.110780	+	0.0533486i
$28$	1.69945	+	5.01117i	0.321166	+	0.947023i
$29$	3.80797	+	1.83382i	0.707122	+	0.340532i	0.752641	−	0.658432i	$-0.228780\pi$
$29$	3.80797	+	1.83382i	0.707122	+	0.340532i	−0.0455189	+	0.998963i	$0.514494\pi$
$30$	−0.0693071	+	0.204105i	−0.0126537	+	0.0372643i
$31$	7.03624			1.26375			0.631873	−	0.775072i	$-0.282286\pi$
$31$	7.03624			1.26375			0.631873	+	0.775072i	$0.282286\pi$
$32$	2.78496	−	4.92382i	0.492316	−	0.870417i
$33$	0.134671	+	0.107396i	0.0234431	+	0.0186953i
$34$	−3.27247	−	2.01425i	−0.561224	−	0.345441i
$35$	−3.53124	−	1.34830i	−0.596889	−	0.227905i
$36$	−2.49336	+	5.43236i	−0.415560	+	0.905393i
$37$	4.28735	+	2.06468i	0.704837	+	0.339432i	0.751732	−	0.659468i	$-0.229219\pi$
$37$	4.28735	+	2.06468i	0.704837	+	0.339432i	−0.0468956	+	0.998900i	$0.514933\pi$
$38$	−0.104536	+	1.01182i	−0.0169579	+	0.164138i
$39$	−0.0664231	−	0.0529707i	−0.0106362	−	0.00848210i
$40$	1.43993	+	3.77561i	0.227673	+	0.596977i
$41$	−0.875154	+	0.697912i	−0.136676	+	0.108996i	−0.689442	−	0.724341i	$-0.742144\pi$
$41$	−0.875154	+	0.697912i	−0.136676	+	0.108996i	0.552765	+	0.833337i	$0.313573\pi$
$42$	0.356314	+	0.179960i	0.0549804	+	0.0277684i
$43$	4.71379	+	3.75912i	0.718847	+	0.573261i	0.913122	−	0.407686i	$-0.133664\pi$
$43$	4.71379	+	3.75912i	0.718847	+	0.573261i	−0.194276	+	0.980947i	$0.562236\pi$
$44$	3.22857	−	0.0597362i	0.486725	−	0.00900557i
$45$	−1.85257	−	3.84690i	−0.276165	−	0.573462i
$46$	3.67898	−	1.32566i	0.542437	−	0.195457i
$47$	−2.47552	−	10.8460i	−0.361092	−	1.58205i	−0.750430	−	0.660950i	$-0.770153\pi$
$47$	−2.47552	−	10.8460i	−0.361092	−	1.58205i	0.389338	−	0.921095i	$-0.372704\pi$
$48$	−0.110284	−	0.412245i	−0.0159182	−	0.0595024i
$49$	−3.38712	+	6.12596i	−0.483874	+	0.875138i
$50$	3.96233	+	1.34547i	0.560358	+	0.190278i
$51$	−0.282617	+	0.0645054i	−0.0395742	+	0.00903256i
$52$	−1.59242	+	0.0294635i	−0.220828	+	0.00408585i
$53$	2.38696	−	1.14950i	0.327874	−	0.157896i	−0.262704	−	0.964876i	$-0.584614\pi$
$53$	2.38696	−	1.14950i	0.327874	−	0.157896i	0.590578	+	0.806981i	$0.298900\pi$
$54$	0.306296	+	0.850038i	0.0416816	+	0.115676i
$55$	−1.43818	+	1.80342i	−0.193924	+	0.243174i
$56$	7.29634	−	1.66236i	0.975014	−	0.222142i
$57$	0.0478440	+	0.0599944i	0.00633709	+	0.00794646i
$58$	3.13312	−	5.09024i	0.411398	−	0.668382i
$59$	8.49023	−	10.6464i	1.10533	−	1.38604i	0.190754	−	0.981638i	$-0.438907\pi$
$59$	8.49023	−	10.6464i	1.10533	−	1.38604i	0.914579	−	0.404407i	$-0.132522\pi$
$60$	0.277047	+	0.127160i	0.0357666	+	0.0164163i
$61$	−4.31491	+	8.96000i	−0.552467	+	1.14721i	0.418548	+	0.908195i	$0.362539\pi$
$61$	−4.31491	+	8.96000i	−0.552467	+	1.14721i	−0.971016	+	0.239016i	$0.923175\pi$
$62$	1.02262	−	9.89806i	0.129872	−	1.25706i
$63$	−7.53394	+	2.40055i	−0.949187	+	0.302441i
$64$	−6.52171	−	4.63328i	−0.815214	−	0.579160i
$65$	0.709350	−	0.889497i	0.0879841	−	0.110329i
$66$	0.170649	−	0.173836i	0.0210055	−	0.0213977i
$67$			2.88009i			0.351859i	0.984403	+	0.175929i	$0.0562930\pi$
$67$			2.88009i			0.351859i	−0.984403	+	0.175929i	$0.943707\pi$
$68$	−3.30910	+	4.31072i	−0.401288	+	0.522752i
$69$	0.127997	−	0.265788i	0.0154090	−	0.0319972i
$70$	−2.40991	+	4.77153i	−0.288039	+	0.570307i
$71$	5.12694	+	10.6462i	0.608456	+	1.26347i	0.946610	+	0.322381i	$0.104483\pi$
$71$	5.12694	+	10.6462i	0.608456	+	1.26347i	−0.338154	+	0.941091i	$0.609803\pi$
$72$	7.27947	+	4.29699i	0.857893	+	0.506405i
$73$	−12.1165	−	2.76552i	−1.41813	−	0.323679i	−0.556345	−	0.830951i	$-0.687797\pi$
$73$	−12.1165	−	2.76552i	−1.41813	−	0.323679i	−0.861786	+	0.507272i	$0.830654\pi$
$74$	3.52755	−	5.73106i	0.410069	−	0.666222i
$75$	0.284412	−	0.136965i	0.0328410	−	0.0158154i
$76$	1.40816	+	0.294106i	0.161527	+	0.0337363i
$77$	2.93439	+	3.10435i	0.334404	+	0.353774i
$78$	−0.0841689	+	0.0857406i	−0.00953025	+	0.00970821i
$79$			9.74036i			1.09588i	0.836519	+	0.547938i	$0.184587\pi$
$79$			9.74036i			1.09588i	−0.836519	+	0.547938i	$0.815413\pi$
$80$	5.52053	−	1.47686i	0.617214	−	0.165118i
$81$	−8.01654	−	3.86056i	−0.890727	−	0.428952i
$82$	0.854580	+	1.33253i	0.0943726	+	0.147154i
$83$	−1.87120	+	8.19825i	−0.205391	+	0.899875i	0.762198	+	0.647344i	$0.224120\pi$
$83$	−1.87120	+	8.19825i	−0.205391	+	0.899875i	−0.967589	+	0.252531i	$0.918737\pi$
$84$	0.304939	−	0.475081i	0.0332716	−	0.0518356i
$85$	−0.863816	−	3.78463i	−0.0936940	−	0.410500i
$86$	5.97314	−	6.08468i	0.644100	−	0.656128i
$87$	−0.100337	−	0.439603i	−0.0107572	−	0.0471304i
$88$	0.385194	−	4.55039i	0.0410618	−	0.485073i
$89$	−14.2898	−	3.26154i	−1.51471	−	0.345723i	−0.617233	−	0.786781i	$-0.711746\pi$
$89$	−14.2898	−	3.26154i	−1.51471	−	0.345723i	−0.897479	+	0.441058i	$0.854603\pi$
$90$	−5.68078	+	2.04696i	−0.598806	+	0.215769i
$91$	−1.44732	−	1.53115i	−0.151720	−	0.160508i
$92$	−1.33015	−	5.36799i	−0.138677	−	0.559651i
$93$	−0.468032	−	0.586893i	−0.0485326	−	0.0608580i
$94$	−15.6171	+	1.90607i	−1.61078	+	0.196596i
$95$	−0.803408	+	0.640697i	−0.0824280	+	0.0657341i
$96$	−0.595944	+	0.0952258i	−0.0608233	+	0.00971894i
$97$		−	1.72514i		−	0.175161i	−0.996157	−	0.0875807i	$-0.972086\pi$
$97$		−	1.72514i		−	0.175161i	0.996157	−	0.0875807i	$-0.0279136\pi$
$98$	8.12528	+	5.65507i	0.820777	+	0.571248i
$99$			4.82530i			0.484961i
$100$	2.46858	−	5.37837i	0.246858	−	0.537837i
$101$	2.59652	−	2.07065i	0.258363	−	0.206038i	−0.485738	−	0.874104i	$-0.661449\pi$
$101$	2.59652	−	2.07065i	0.258363	−	0.206038i	0.744102	+	0.668066i	$0.232878\pi$
$102$	0.0496671	+	0.406939i	0.00491778	+	0.0402930i
$103$	−4.75512	−	5.96273i	−0.468536	−	0.587526i	0.490276	−	0.871567i	$-0.336896\pi$
$103$	−4.75512	−	5.96273i	−0.468536	−	0.587526i	−0.958812	+	0.284042i	$0.908325\pi$
$104$	−0.189988	+	2.24438i	−0.0186298	+	0.220079i
$105$	0.122426	+	0.384226i	0.0119476	+	0.0374967i
$106$	−1.27012	−	3.52485i	−0.123365	−	0.342364i
$107$	−15.5330	−	3.54532i	−1.50164	−	0.342739i	−0.608874	−	0.793267i	$-0.708379\pi$
$107$	−15.5330	−	3.54532i	−1.50164	−	0.342739i	−0.892762	+	0.450528i	$0.851236\pi$
$108$	1.24029	−	0.307333i	0.119347	−	0.0295732i
$109$	1.20347	+	5.27275i	0.115272	+	0.505038i	0.999293	+	0.0375916i	$0.0119686\pi$
$109$	1.20347	+	5.27275i	0.115272	+	0.505038i	−0.884022	+	0.467446i	$0.845174\pi$
$110$	2.32790	+	2.28523i	0.221957	+	0.217888i
$111$	−0.112968	−	0.494945i	−0.0107225	−	0.0469781i
$112$	−1.27807	−	10.5055i	−0.120766	−	0.992681i
$113$	2.44897	−	10.7296i	0.230379	−	1.00936i	−0.718947	−	0.695065i	$-0.755375\pi$
$113$	2.44897	−	10.7296i	0.230379	−	1.00936i	0.949326	−	0.314293i	$-0.101767\pi$
$114$	0.0913492	−	0.0585840i	0.00855563	−	0.00548690i
$115$	3.55927	+	1.71406i	0.331904	+	0.159837i
$116$	−6.70523	−	5.14723i	−0.622565	−	0.477908i
$117$		−	2.37997i		−	0.220028i
$118$	−13.7426	−	13.4907i	−1.26511	−	1.24192i
$119$	−7.16363	+	0.603605i	−0.656689	+	0.0553324i
$120$	0.219144	−	0.371248i	0.0200050	−	0.0338902i
$121$	−7.56201	+	3.64167i	−0.687455	+	0.331061i
$122$	11.9772	+	7.37210i	1.08436	+	0.667439i
$123$	0.116426	+	0.0265734i	0.0104978	+	0.00239604i
$124$	−13.7752	−	2.87708i	−1.23705	−	0.258370i
$125$	4.93353	+	10.2446i	0.441268	+	0.916303i
$126$	2.28196	+	10.9471i	0.203293	+	0.975243i
$127$	4.43886	−	9.21738i	0.393885	−	0.817910i	−0.605866	−	0.795567i	$-0.707173\pi$
$127$	4.43886	−	9.21738i	0.393885	−	0.817910i	0.999750	−	0.0223432i	$-0.00711265\pi$
$128$	−7.46559	+	8.50088i	−0.659871	+	0.751379i
$129$		−	0.643224i		−	0.0566327i
$130$	−1.14818	−	1.12714i	−0.100702	−	0.0988565i
$131$	13.0500	−	16.3641i	1.14018	−	1.42974i	0.253513	−	0.967332i	$-0.418414\pi$
$131$	13.0500	−	16.3641i	1.14018	−	1.42974i	0.886667	−	0.462409i	$-0.153015\pi$
$132$	−0.219738	−	0.265321i	−0.0191257	−	0.0230933i
$133$	0.966729	+	1.63918i	0.0838260	+	0.142135i
$134$	4.05149	+	0.418580i	0.349996	+	0.0361598i
$135$	−0.396037	+	0.822379i	−0.0340854	+	0.0707791i
$136$	5.58308	+	5.28150i	0.478745	+	0.452885i
$137$	7.61889	−	9.55379i	0.650926	−	0.816236i	−0.341396	−	0.939920i	$-0.610900\pi$
$137$	7.61889	−	9.55379i	0.650926	−	0.816236i	0.992322	+	0.123684i	$0.0394710\pi$
$138$	−0.355289	−	0.218685i	−0.0302442	−	0.0186157i
$139$	11.6067	+	14.5543i	0.984464	+	1.23448i	0.972103	+	0.234555i	$0.0753633\pi$
$139$	11.6067	+	14.5543i	0.984464	+	1.23448i	0.0123610	+	0.999924i	$0.496065\pi$
$140$	6.36199	+	4.08356i	0.537686	+	0.345123i
$141$	−0.739997	+	0.927927i	−0.0623190	+	0.0781455i
$142$	15.7214	−	5.66493i	1.31931	−	0.475390i
$143$	−1.15842	+	0.557864i	−0.0968717	+	0.0466510i
$144$	7.10265	−	9.61571i	0.591887	−	0.801309i
$145$	5.88689	−	1.34365i	0.488880	−	0.111584i
$146$	−5.65128	+	16.6427i	−0.467704	+	1.37736i
$147$	0.736269	−	0.124963i	0.0607264	−	0.0103068i
$148$	−7.54935	−	5.79522i	−0.620553	−	0.476364i
$149$	2.55312	+	11.1860i	0.209160	+	0.916389i	0.965128	+	0.261780i	$0.0843095\pi$
$149$	2.55312	+	11.1860i	0.209160	+	0.916389i	−0.755968	+	0.654609i	$0.772833\pi$
$150$	−0.151338	−	0.419995i	−0.0123567	−	0.0342925i
$151$	1.30111	+	2.70179i	0.105883	+	0.219869i	0.947178	−	0.320707i	$-0.103921\pi$
$151$	1.30111	+	2.70179i	0.105883	+	0.219869i	−0.841295	+	0.540576i	$0.818206\pi$
$152$	0.618383	−	1.93815i	0.0501575	−	0.157204i
$153$	−6.34898	−	5.06314i	−0.513284	−	0.409331i
$154$	4.79344	−	3.67670i	0.386267	−	0.296277i
$155$	7.85931	−	6.26759i	0.631275	−	0.503425i
$156$	0.108381	+	0.130864i	0.00867741	+	0.0104775i
$157$	16.4784	+	13.1411i	1.31512	+	1.04877i	0.994841	+	0.101451i	$0.0323485\pi$
$157$	16.4784	+	13.1411i	1.31512	+	1.04877i	0.320280	+	0.947323i	$0.396223\pi$
$158$	13.7020	+	1.41562i	1.09007	+	0.112621i
$159$	−0.254653	−	0.122635i	−0.0201953	−	0.00972556i
$160$	−1.27520	−	7.98051i	−0.100814	−	0.630915i
$161$	4.06506	−	6.08262i	0.320372	−	0.479378i
$162$	−6.59585	+	10.7160i	−0.518219	+	0.841929i
$163$	−13.4985	−	10.7647i	−1.05729	−	0.843158i	−0.0692845	−	0.997597i	$-0.522072\pi$
$163$	−13.4985	−	10.7647i	−1.05729	−	0.843158i	−0.988002	+	0.154439i	$0.950643\pi$
$164$	1.99871	−	1.00849i	0.156073	−	0.0787502i
$165$	0.246088			0.0191579
$166$	11.2607	+	3.82376i	0.874003	+	0.296781i
$167$	−3.36001	−	1.61810i	−0.260005	−	0.125212i	0.299341	−	0.954146i	$-0.403233\pi$
$167$	−3.36001	−	1.61810i	−0.260005	−	0.125212i	−0.559346	+	0.828934i	$0.688948\pi$
$168$	−0.623990	−	0.498012i	−0.0481419	−	0.0384225i
$169$	−11.1412	+	5.36533i	−0.857018	+	0.412718i
$170$	−5.44948	+	0.665112i	−0.417956	+	0.0510117i
$171$	−0.478337	+	2.09573i	−0.0365794	+	0.160265i
$172$	−7.69137	−	9.28689i	−0.586461	−	0.708119i
$173$	−6.60475	−	13.7149i	−0.502150	−	1.04272i	−0.985872	−	0.167503i	$-0.946430\pi$
$173$	−6.60475	−	13.7149i	−0.502150	−	1.04272i	0.483722	−	0.875222i	$-0.339285\pi$
$174$	−0.632984	+	0.0772560i	−0.0479864	+	0.00585676i
$175$	7.45906	−	2.37669i	0.563852	−	0.179661i
$176$	−6.34517	−	1.20320i	−0.478285	−	0.0906943i
$177$	−1.45276			−0.109196
$178$	−6.66491	+	19.6278i	−0.499556	+	1.47116i
$179$	−8.81787	+	18.3105i	−0.659079	+	1.36859i	0.256536	+	0.966535i	$0.417419\pi$
$179$	−8.81787	+	18.3105i	−0.659079	+	1.36859i	−0.915615	+	0.402056i	$0.868296\pi$
$180$	2.05390	+	8.28879i	0.153089	+	0.617810i
$181$	13.5674	+	3.09667i	1.00846	+	0.230174i	0.694677	−	0.719322i	$-0.255547\pi$
$181$	13.5674	+	3.09667i	1.00846	+	0.230174i	0.313780	+	0.949496i	$0.398404\pi$
$182$	−2.36426	+	1.81345i	−0.175250	+	0.134422i
$183$	1.03437	−	0.236088i	0.0764628	−	0.0174521i
$184$	−7.74460	+	1.09099i	−0.570940	+	0.0804289i
$185$	6.62800	−	1.51280i	0.487300	−	0.111223i
$186$	−0.893619	+	0.573096i	−0.0655233	+	0.0420214i
$187$	−0.976214	+	4.27707i	−0.0713879	+	0.312771i
$188$	0.411603	+	22.2460i	0.0300192	+	1.62245i
$189$	1.40540	+	0.939242i	0.102228	+	0.0683198i
$190$	0.784521	+	1.22329i	0.0569151	+	0.0887469i
$191$	−0.141184	+	0.112590i	−0.0102157	+	0.00814674i	−0.628584	−	0.777741i	$-0.716365\pi$
$191$	−0.141184	+	0.112590i	−0.0102157	+	0.00814674i	0.618369	+	0.785888i	$0.287794\pi$
$192$	0.0473447	+	0.852169i	0.00341681	+	0.0615000i
$193$	6.69713	+	8.39794i	0.482070	+	0.604497i	0.962080	−	0.272766i	$-0.0879385\pi$
$193$	6.69713	+	8.39794i	0.482070	+	0.604497i	−0.480010	+	0.877263i	$0.659367\pi$
$194$	−2.42680	−	0.250724i	−0.174234	−	0.0180010i
$195$	−0.121377			−0.00869199
$196$	9.13602	−	10.6082i	0.652573	−	0.757726i
$197$	7.38319			0.526031			0.263015	−	0.964792i	$-0.415283\pi$
$197$	7.38319			0.526031			0.263015	+	0.964792i	$0.415283\pi$
$198$	6.78788	+	0.701289i	0.482394	+	0.0498384i
$199$	−4.31796	−	5.41455i	−0.306092	−	0.383827i	0.604865	−	0.796328i	$-0.293227\pi$
$199$	−4.31796	−	5.41455i	−0.306092	−	0.383827i	−0.910957	+	0.412501i	$0.864655\pi$
$200$	−7.20712	−	4.25428i	−0.509620	−	0.300823i
$201$	0.240228	−	0.191576i	0.0169444	−	0.0135127i
$202$	−2.53548	−	3.95353i	−0.178395	−	0.278169i
$203$	−0.938893	−	11.1428i	−0.0658974	−	0.782074i
$204$	0.579670	−	0.0107253i	0.0405850	−	0.000750919i
$205$	−0.355855	+	1.55910i	−0.0248540	+	0.108892i
$206$	−9.07902	+	5.82256i	−0.632565	+	0.405677i
$207$	8.05683	−	1.83892i	0.559988	−	0.127814i
$208$	3.12961	+	0.593449i	0.216999	+	0.0411483i
$209$	1.13219	−	0.258415i	0.0783153	−	0.0178749i
$210$	0.558294	−	0.116379i	0.0385260	−	0.00803089i
$211$	0.796064	+	0.181696i	0.0548033	+	0.0125085i	0.249835	−	0.968289i	$-0.419624\pi$
$211$	0.796064	+	0.181696i	0.0548033	+	0.0125085i	−0.195031	+	0.980797i	$0.562481\pi$
$212$	−5.14310	+	1.27442i	−0.353229	+	0.0875275i
$213$	0.546970	−	1.13579i	0.0374778	−	0.0778234i
$214$	−7.24480	+	21.3355i	−0.495244	+	1.45846i
$215$	8.61366			0.587447
$216$	−0.252076	−	1.78941i	−0.0171516	−	0.121754i
$217$	−9.45698	−	16.0352i	−0.641982	−	1.08854i
$218$	7.59222	−	0.926634i	0.514210	−	0.0627596i
$219$	0.575286	+	1.19459i	0.0388742	+	0.0807231i
$220$	3.55302	−	2.94260i	0.239545	−	0.198390i
$221$	0.481495	−	2.10957i	0.0323889	−	0.141905i
$222$	−0.712671	+	0.0869818i	−0.0478313	+	0.00583784i
$223$	12.2555	−	5.90195i	0.820690	−	0.395223i	0.0240748	−	0.999710i	$-0.492336\pi$
$223$	12.2555	−	5.90195i	0.820690	−	0.395223i	0.796615	+	0.604487i	$0.206622\pi$
$224$	−14.9642	+	0.271062i	−0.999836	+	0.0181111i
$225$	7.96733	+	3.83686i	0.531155	+	0.255791i
$226$	−14.7377	−	5.00442i	−0.980338	−	0.332889i
$227$	4.66017			0.309306			0.154653	−	0.987969i	$-0.450574\pi$
$227$	4.66017			0.309306			0.154653	+	0.987969i	$0.450574\pi$
$228$	−0.0691354	−	0.137018i	−0.00457860	−	0.00907421i
$229$	20.8816	+	16.6525i	1.37990	+	1.10043i	0.983210	+	0.182477i	$0.0584114\pi$
$229$	20.8816	+	16.6525i	1.37990	+	1.10043i	0.396686	+	0.917954i	$0.370160\pi$
$230$	2.92850	−	4.75781i	0.193099	−	0.313721i
$231$	0.0637467	−	0.451250i	0.00419423	−	0.0296901i
$232$	−8.21525	+	8.68434i	−0.539357	+	0.570155i
$233$	−3.40397	−	1.63927i	−0.223001	−	0.107392i	0.319048	−	0.947739i	$-0.396637\pi$
$233$	−3.40397	−	1.63927i	−0.223001	−	0.107392i	−0.542049	+	0.840347i	$0.682351\pi$
$234$	−3.34796	−	0.345895i	−0.218863	−	0.0226118i
$235$	−12.4262	−	9.90958i	−0.810597	−	0.646430i
$236$	−20.9750	+	17.3715i	−1.36536	+	1.13079i
$237$	0.812444	−	0.647903i	0.0527739	−	0.0420858i
$238$	−0.192023	+	10.1650i	−0.0124470	+	0.658898i
$239$	2.80475	+	2.23671i	0.181424	+	0.144681i	0.709991	−	0.704211i	$-0.248699\pi$
$239$	2.80475	+	2.23671i	0.181424	+	0.144681i	−0.528567	+	0.848892i	$0.677270\pi$
$240$	−0.490395	−	0.362231i	−0.0316549	−	0.0233819i
$241$	−0.548789	−	1.13957i	−0.0353506	−	0.0734063i	0.882546	−	0.470227i	$-0.155828\pi$
$241$	−0.548789	−	1.13957i	−0.0353506	−	0.0734063i	−0.917896	+	0.396820i	$0.870114\pi$
$242$	4.02380	+	11.1669i	0.258660	+	0.717838i
$243$	0.637734	+	2.79409i	0.0409106	+	0.179241i
$244$	12.1112	−	15.7771i	0.775342	−	1.01003i
$245$	1.67342	+	9.85965i	0.106911	+	0.629910i
$246$	0.0543023	−	0.159917i	0.00346219	−	0.0101959i
$247$	−0.558427	+	0.127457i	−0.0355318	+	0.00810991i
$248$	−6.04930	+	18.9598i	−0.384131	+	1.20395i
$249$	0.808283	−	0.389249i	0.0512229	−	0.0246676i
$250$	15.1283	−	5.45122i	0.956800	−	0.344765i
$251$	−11.3854	+	14.2769i	−0.718641	+	0.901147i	−0.998260	−	0.0589636i	$-0.981220\pi$
$251$	−11.3854	+	14.2769i	−0.718641	+	0.901147i	0.279619	+	0.960111i	$0.409792\pi$
$252$	15.7312	−	1.61909i	0.990971	−	0.101993i
$253$	−2.78359	−	3.49051i	−0.175003	−	0.219446i
$254$	−12.3212	−	7.58387i	−0.773101	−	0.475854i
$255$	−0.258217	+	0.323794i	−0.0161702	+	0.0202768i
$256$	10.8734	+	11.7375i	0.679587	+	0.733595i
$257$	1.42795	−	2.96517i	0.0890731	−	0.184962i	−0.851673	−	0.524073i	$-0.824412\pi$
$257$	1.42795	−	2.96517i	0.0890731	−	0.184962i	0.940746	+	0.339111i	$0.110126\pi$
$258$	−0.904840	−	0.0934835i	−0.0563329	−	0.00582003i
$259$	−1.05709	−	12.5456i	−0.0656845	−	0.779547i
$260$	−1.75245	+	1.45137i	−0.108682	+	0.0900100i
$261$	7.87559	−	9.87568i	0.487487	−	0.611289i
$262$	−21.1232	−	20.7360i	−1.30500	−	1.28107i
$263$			21.7764i			1.34279i	0.741101	+	0.671394i	$0.234304\pi$
$263$			21.7764i			1.34279i	−0.741101	+	0.671394i	$0.765696\pi$
$264$	−0.405170	+	0.270551i	−0.0249365	+	0.0166512i
$265$	1.64225	−	3.41016i	0.100882	−	0.209484i
$266$	2.44637	−	1.12169i	0.149997	−	0.0687753i
$267$	0.678470	+	1.40886i	0.0415217	+	0.0862207i
$268$	1.17765	−	5.63851i	0.0719366	−	0.344427i
$269$	−26.7443	−	6.10420i	−1.63063	−	0.372180i	−0.693305	−	0.720644i	$-0.743846\pi$
$269$	−26.7443	−	6.10420i	−1.63063	−	0.372180i	−0.937322	+	0.348464i	$0.886703\pi$
$270$	1.09930	+	0.676636i	0.0669015	+	0.0411788i
$271$	−26.7675	+	12.8906i	−1.62601	+	0.783046i	−0.626018	+	0.779809i	$0.715316\pi$
$271$	−26.7675	+	12.8906i	−1.62601	+	0.783046i	−0.999995	+	0.00323725i	$0.998970\pi$
$272$	8.24105	−	7.08627i	0.499687	−	0.429668i
$273$	−0.0314416	+	0.222569i	−0.00190293	+	0.0134705i
$274$	−12.3323	−	12.1062i	−0.745020	−	0.731362i
$275$		−	4.77735i		−	0.288085i
$276$	−0.359266	+	0.468011i	−0.0216253	+	0.0281710i
$277$	3.39397	+	1.63445i	0.203924	+	0.0982045i	0.533058	−	0.846079i	$-0.321043\pi$
$277$	3.39397	+	1.63445i	0.203924	+	0.0982045i	−0.329134	+	0.944283i	$0.606757\pi$
$278$	22.1608	−	14.2121i	1.32911	−	0.852387i
$279$	4.67931	−	20.5014i	0.280143	−	1.22739i
$280$	6.66907	−	8.35609i	0.398553	−	0.499372i
$281$	−5.02418	−	22.0124i	−0.299718	−	1.31315i	−0.870549	−	0.492081i	$-0.836236\pi$
$281$	−5.02418	−	22.0124i	−0.299718	−	1.31315i	0.570832	−	0.821067i	$-0.306621\pi$
$282$	1.19779	+	1.17583i	0.0713274	+	0.0700199i
$283$	−0.731260	−	3.20386i	−0.0434689	−	0.190450i	0.948532	−	0.316682i	$-0.102569\pi$
$283$	−0.731260	−	3.20386i	−0.0434689	−	0.190450i	−0.992001	+	0.126232i	$0.959712\pi$
$284$	−5.68412	−	22.9390i	−0.337290	−	1.36118i
$285$	0.106881	+	0.0243949i	0.00633109	+	0.00144503i
$286$	0.616403	+	1.71065i	0.0364487	+	0.101153i
$287$	2.76674	+	1.05640i	0.163315	+	0.0623574i
$288$	−12.4944	−	11.3890i	−0.736239	−	0.671102i
$289$	5.99602	+	7.51877i	0.352707	+	0.442281i
$290$	−1.03456	−	8.47653i	−0.0607517	−	0.497759i
$291$	−0.143894	+	0.114752i	−0.00843521	+	0.00672686i
$292$	22.5904	+	10.3686i	1.32200	+	0.606775i
$293$		−	17.5913i		−	1.02770i	−0.857881	−	0.513848i	$-0.828219\pi$
$293$		−	17.5913i		−	1.02770i	0.857881	−	0.513848i	$-0.171781\pi$
$294$	−0.0687823	−	1.05389i	−0.00401147	−	0.0614641i
$295$		−	19.4545i		−	1.13269i
$296$	−9.24947	+	9.77762i	−0.537615	+	0.568313i
$297$	0.806490	−	0.643154i	0.0467973	−	0.0373196i
$298$	16.1066	−	1.96582i	0.933032	−	0.113877i
$299$	1.37294	+	1.72161i	0.0793992	+	0.0995634i
$300$	−0.612813	+	0.151850i	−0.0353808	+	0.00876708i
$301$	2.23129	−	15.7949i	0.128609	−	0.910400i
$302$	3.98978	−	1.43764i	0.229586	−	0.0827271i
$303$	−0.345427	−	0.0788414i	−0.0198442	−	0.00452932i
$304$	−2.63657	−	1.15158i	−0.151218	−	0.0660475i
$305$	3.16155	+	13.8516i	0.181030	+	0.793142i
$306$	−8.04518	+	8.19541i	−0.459912	+	0.468501i
$307$	1.48484	+	6.50552i	0.0847444	+	0.371289i	0.999462	−	0.0328047i	$-0.0104439\pi$
$307$	1.48484	+	6.50552i	0.0847444	+	0.371289i	−0.914717	+	0.404094i	$0.867587\pi$
$308$	−4.47546	−	7.27742i	−0.255013	−	0.414669i
$309$	−0.181054	+	0.793250i	−0.0102998	+	0.0451264i
$310$	−7.67454	−	11.9668i	−0.435885	−	0.679668i
$311$	−7.11558	−	3.42668i	−0.403487	−	0.194309i	0.221123	−	0.975246i	$-0.429028\pi$
$311$	−7.11558	−	3.42668i	−0.403487	−	0.194309i	−0.624610	+	0.780937i	$0.714742\pi$
$312$	0.199841	−	0.133443i	0.0113138	−	0.00755471i
$313$		−	1.08255i		−	0.0611892i	−0.999532	−	0.0305946i	$-0.990260\pi$
$313$		−	1.08255i		−	0.0611892i	0.999532	−	0.0305946i	$-0.00974008\pi$
$314$	20.8808	−	21.2707i	1.17837	−	1.20038i
$315$	−6.27692	+	9.39227i	−0.353664	+	0.529194i
$316$	3.98279	−	19.0692i	0.224049	−	1.07273i
$317$	−8.75645	+	4.21689i	−0.491811	+	0.236844i	−0.663316	−	0.748339i	$-0.730851\pi$
$317$	−8.75645	+	4.21689i	−0.491811	+	0.236844i	0.171505	+	0.985183i	$0.445137\pi$
$318$	−0.209523	+	0.340404i	−0.0117495	+	0.0190889i
$319$	−6.65289	−	1.51848i	−0.372490	−	0.0850184i
$320$	−11.4117	+	0.634011i	−0.637935	+	0.0354423i
$321$	0.737501	+	1.53144i	0.0411633	+	0.0854765i
$322$	−7.96579	−	6.60245i	−0.443916	−	0.367940i
$323$	−0.847981	+	1.76085i	−0.0471829	+	0.0979764i
$324$	14.1159	+	10.8360i	0.784215	+	0.601998i
$325$			2.35632i			0.130705i
$326$	−17.1048	+	17.4242i	−0.947349	+	0.965039i
$327$	0.359748	−	0.451110i	0.0198941	−	0.0249465i
$328$	−1.12819	−	2.95821i	−0.0622940	−	0.163340i
$329$	−21.3901	+	20.2189i	−1.17927	+	1.11471i
$330$	0.0357653	−	0.346178i	0.00196882	−	0.0190565i
$331$	0.845301	−	1.75529i	0.0464620	−	0.0964792i	−0.876446	−	0.481501i	$-0.840092\pi$
$331$	0.845301	−	1.75529i	0.0464620	−	0.0964792i	0.922907	+	0.385022i	$0.125806\pi$
$332$	7.01557	−	15.2850i	0.385029	−	0.838876i
$333$	8.86706	−	11.1189i	0.485912	−	0.609314i
$334$	−2.76455	+	4.49144i	−0.151269	+	0.245761i
$335$	2.56546	+	3.21699i	0.140166	+	0.175763i
$336$	−0.791254	+	0.805404i	−0.0431665	+	0.0439384i
$337$	−16.5694	+	20.7774i	−0.902594	+	1.13182i	0.0881546	+	0.996107i	$0.471903\pi$
$337$	−16.5694	+	20.7774i	−0.902594	+	1.13182i	−0.990749	+	0.135710i	$0.956668\pi$
$338$	5.92834	+	16.4524i	0.322459	+	0.894894i
$339$	−1.05786	+	0.509437i	−0.0574549	+	0.0276688i
$340$	0.143626	+	7.76258i	0.00778922	+	0.420985i
$341$	−11.0756	+	2.52793i	−0.599778	+	0.136895i
$342$	2.87860	+	0.977474i	0.155657	+	0.0528557i
$343$	18.5131	−	0.514502i	0.999614	−	0.0277805i
$344$	−14.1819	+	9.46993i	−0.764639	+	0.510584i
$345$	−0.0937838	−	0.410894i	−0.00504915	−	0.0221218i
$346$	−20.2530	+	7.29781i	−1.08881	+	0.392333i
$347$	−1.10899	−	2.30283i	−0.0595335	−	0.123623i	0.869079	−	0.494673i	$-0.164712\pi$
$347$	−1.10899	−	2.30283i	−0.0595335	−	0.123623i	−0.928613	+	0.371050i	$0.878998\pi$
$348$	0.0166829	+	0.901663i	0.000894297	+	0.0483342i
$349$	−20.2733	−	16.1674i	−1.08520	−	0.865421i	−0.0937127	−	0.995599i	$-0.529874\pi$
$349$	−20.2733	−	16.1674i	−1.08520	−	0.865421i	−0.991491	+	0.130179i	$0.958445\pi$
$350$	−2.25928	−	10.8383i	−0.120764	−	0.579330i
$351$	−0.397783	+	0.317221i	−0.0212321	+	0.0169320i
$352$	−2.61475	+	8.75105i	−0.139366	+	0.466432i
$353$	8.69840	+	6.93674i	0.462969	+	0.369205i	0.827019	−	0.562174i	$-0.190035\pi$
$353$	8.69840	+	6.93674i	0.462969	+	0.369205i	−0.364050	+	0.931379i	$0.618606\pi$
$354$	−0.211138	+	2.04364i	−0.0112219	+	0.108618i
$355$	15.2099	+	7.32468i	0.807255	+	0.388754i
$356$	26.6422	+	12.2283i	1.41203	+	0.648099i
$357$	0.526852	+	0.557368i	0.0278839	+	0.0294990i
$358$	24.4763	+	15.0655i	1.29361	+	0.796236i
$359$	9.62380	+	7.67472i	0.507925	+	0.405056i	0.843642	−	0.536906i	$-0.180407\pi$
$359$	9.62380	+	7.67472i	0.507925	+	0.405056i	−0.335717	+	0.941963i	$0.608979\pi$
$360$	11.9586	−	1.68461i	0.630271	−	0.0887870i
$361$	−18.4826			−0.972771
$362$	6.32800	−	18.6356i	0.332592	−	0.979463i
$363$	0.806756	+	0.388513i	0.0423437	+	0.0203917i
$364$	2.20742	+	3.58942i	0.115700	+	0.188137i
$365$	−15.9973	+	7.70387i	−0.837334	+	0.403239i
$366$	−0.181780	−	1.48939i	−0.00950182	−	0.0778515i
$367$	−3.97644	+	17.4219i	−0.207568	+	0.909416i	0.758611	+	0.651544i	$0.225878\pi$
$367$	−3.97644	+	17.4219i	−0.207568	+	0.909416i	−0.966179	+	0.257872i	$0.916979\pi$
$368$	0.409157	+	11.0531i	0.0213288	+	0.576182i
$369$	1.45149	+	3.01406i	0.0755617	+	0.156906i
$370$	−1.16481	−	9.54364i	−0.0605554	−	0.496150i
$371$	−5.82779	−	3.89475i	−0.302564	−	0.202206i
$372$	0.676314	+	1.34037i	0.0350652	+	0.0694949i
$373$	−8.15242			−0.422117			−0.211058	−	0.977473i	$-0.567691\pi$
$373$	−8.15242			−0.422117			−0.211058	+	0.977473i	$0.567691\pi$
$374$	5.87479	+	1.99488i	0.303778	+	0.103153i
$375$	0.526336	−	1.09295i	0.0271799	−	0.0564396i
$376$	31.3538	+	2.65412i	1.61695	+	0.136876i
$377$	3.28138	+	0.748954i	0.169000	+	0.0385731i
$378$	1.52551	−	1.84051i	0.0784638	−	0.0946658i
$379$	−15.7562	+	3.59625i	−0.809341	+	0.184727i	−0.607117	−	0.794613i	$-0.707674\pi$
$379$	−15.7562	+	3.59625i	−0.809341	+	0.184727i	−0.202224	+	0.979339i	$0.564817\pi$
$380$	1.83485	−	0.925818i	0.0941261	−	0.0474935i
$381$	−1.06408	+	0.242870i	−0.0545146	+	0.0124426i
$382$	0.137864	+	0.214970i	0.00705376	+	0.0109988i
$383$	−4.15856	+	18.2198i	−0.212492	+	0.930990i	0.750375	+	0.661013i	$0.229873\pi$
$383$	−4.15856	+	18.2198i	−0.212492	+	0.930990i	−0.962867	+	0.269977i	$0.912984\pi$
$384$	1.20565	+	0.0572496i	0.0615255	+	0.00292151i
$385$	6.04287	+	0.853657i	0.307973	+	0.0435064i
$386$	12.7869	−	8.20051i	0.650837	−	0.417395i
$387$	14.0877	−	11.2346i	0.716119	−	0.571086i
$388$	−0.705401	+	3.37740i	−0.0358113	+	0.171462i
$389$	14.1537	+	17.7482i	0.717622	+	0.899870i	0.998201	−	0.0599614i	$-0.0190978\pi$
$389$	14.1537	+	17.7482i	0.717622	+	0.899870i	−0.280579	+	0.959831i	$0.590526\pi$
$390$	−0.0176404	+	0.170744i	−0.000893257	+	0.00864597i
$391$	7.51348			0.379973
$392$	−13.5950	−	14.3936i	−0.686650	−	0.726988i
$393$	−2.23298			−0.112639
$394$	1.07304	−	10.3861i	0.0540591	−	0.523246i
$395$	8.67631	+	10.8797i	0.436552	+	0.547420i
$396$	1.97304	−	9.44676i	0.0991491	−	0.474718i
$397$	19.0704	−	15.2081i	0.957114	−	0.763273i	−0.0144875	−	0.999895i	$-0.504612\pi$
$397$	19.0704	−	15.2081i	0.957114	−	0.763273i	0.971602	+	0.236622i	$0.0760402\pi$
$398$	−8.24434	+	5.28726i	−0.413251	+	0.265026i
$399$	0.0724195	−	0.189668i	0.00362551	−	0.00949529i
$400$	−7.03206	+	9.52014i	−0.351603	+	0.476007i
$401$	2.23779	−	9.80439i	0.111750	−	0.489608i	−0.887818	−	0.460195i	$-0.847779\pi$
$401$	2.23779	−	9.80439i	0.111750	−	0.489608i	0.999567	−	0.0294122i	$-0.00936354\pi$
$402$	−0.234581	−	0.365778i	−0.0116998	−	0.0182434i
$403$	5.46279	−	1.24685i	0.272121	−	0.0621098i
$404$	−5.93003	+	2.99213i	−0.295030	+	0.148864i
$405$	−12.3931	+	2.82865i	−0.615819	+	0.140557i
$406$	−15.8114	−	0.298688i	−0.784706	−	0.0148236i
$407$	−7.49042	−	1.70964i	−0.371287	−	0.0847437i
$408$	0.0691592	−	0.816996i	0.00342389	−	0.0404473i
$409$	−13.8806	+	28.8234i	−0.686353	+	1.42523i	0.208119	+	0.978104i	$0.433266\pi$
$409$	−13.8806	+	28.8234i	−0.686353	+	1.42523i	−0.894472	+	0.447124i	$0.852448\pi$
$410$	2.14151	+	0.727183i	0.105762	+	0.0359130i
$411$	−1.30367			−0.0643053
$412$	6.87123	+	13.6179i	0.338521	+	0.670907i
$413$	−35.6737	−	5.03951i	−1.75539	−	0.247978i
$414$	−1.41591	−	11.6010i	−0.0695882	−	0.570159i
$415$	5.21258	+	10.8240i	0.255875	+	0.531331i
$416$	1.28966	−	4.31625i	0.0632310	−	0.211622i
$417$	0.441930	−	1.93622i	0.0216414	−	0.0948173i
$418$	−0.198972	−	1.63024i	−0.00973201	−	0.0797376i
$419$	15.1021	−	7.27277i	0.737784	−	0.355298i	−0.0269563	−	0.999637i	$-0.508582\pi$
$419$	15.1021	−	7.27277i	0.737784	−	0.355298i	0.764740	+	0.644339i	$0.222867\pi$
$420$	−0.0825728	−	0.802281i	−0.00402914	−	0.0391473i
$421$	17.0724	+	8.22164i	0.832058	+	0.400698i	0.800887	−	0.598816i	$-0.204362\pi$
$421$	17.0724	+	8.22164i	0.832058	+	0.400698i	0.0311714	+	0.999514i	$0.490076\pi$
$422$	0.371294	−	1.09344i	0.0180743	−	0.0532277i
$423$	−33.2480			−1.61657
$424$	1.04528	+	7.42015i	0.0507635	+	0.360354i
$425$	6.28588	+	5.01282i	0.304910	+	0.243157i
$426$	−1.51826	−	0.934508i	−0.0735598	−	0.0452771i
$427$	26.2187	−	2.20918i	1.26881	−	0.106910i
$428$	28.9602	+	13.2922i	1.39985	+	0.642505i
$429$	0.123586	+	0.0595160i	0.00596680	+	0.00287346i
$430$	1.25187	−	12.1171i	0.0603707	−	0.584337i
$431$	−8.96088	−	7.14607i	−0.431631	−	0.344214i	0.383450	−	0.923562i	$-0.374736\pi$
$431$	−8.96088	−	7.14607i	−0.431631	−	0.344214i	−0.815080	+	0.579348i	$0.803307\pi$
$432$	−2.55384	+	0.0945367i	−0.122872	+	0.00454840i
$433$	12.6715	−	10.1052i	0.608951	−	0.485623i	−0.269791	−	0.962919i	$-0.586955\pi$
$433$	12.6715	−	10.1052i	0.608951	−	0.485623i	0.878742	+	0.477296i	$0.158383\pi$
$434$	−23.9315	+	10.9729i	−1.14875	+	0.526716i
$435$	−0.503654	−	0.401650i	−0.0241483	−	0.0192577i
$436$	−0.200100	−	10.8148i	−0.00958306	−	0.517937i
$437$	−0.862954	−	1.79194i	−0.0412807	−	0.0857202i
$438$	1.76407	−	0.635652i	0.0842908	−	0.0303726i
$439$	6.54949	+	28.6952i	0.312590	+	1.36955i	0.850247	+	0.526383i	$0.176452\pi$
$439$	6.54949	+	28.6952i	0.312590	+	1.36955i	−0.537657	+	0.843164i	$0.680691\pi$
$440$	−3.62305	−	5.42579i	−0.172722	−	0.258664i
$441$	15.5966	+	13.9430i	0.742696	+	0.663950i
$442$	−2.89761	−	0.983927i	−0.137825	−	0.0468007i
$443$	−8.10200	+	1.84923i	−0.384938	+	0.0878595i	−0.410610	−	0.911811i	$-0.634684\pi$
$443$	−8.10200	+	1.84923i	−0.384938	+	0.0878595i	0.0256727	+	0.999670i	$0.491827\pi$
$444$	0.0187831	+	1.01517i	0.000891408	+	0.0481780i
$445$	−18.8666	+	9.08566i	−0.894361	+	0.430701i
$446$	−6.52125	−	18.0979i	−0.308790	−	0.856961i
$447$	0.763194	−	0.957015i	0.0360978	−	0.0452653i
$448$	−1.79352	+	21.0899i	−0.0847358	+	0.996403i
$449$	11.6408	+	14.5971i	0.549362	+	0.688878i	0.976551	−	0.215284i	$-0.0690678\pi$
$449$	11.6408	+	14.5971i	0.549362	+	0.688878i	−0.427190	+	0.904162i	$0.640496\pi$
$450$	6.55535	−	10.6502i	0.309022	−	0.502056i
$451$	1.12682	−	1.41299i	0.0530599	−	0.0665350i
$452$	−9.18177	+	20.0046i	−0.431874	+	0.940937i
$453$	0.138810	−	0.288242i	0.00652186	−	0.0135428i
$454$	0.677289	−	6.55558i	0.0317867	−	0.307669i
$455$	−2.98050	−	0.421047i	−0.139728	−	0.0197390i
$456$	−0.202794	+	0.0773410i	−0.00949670	+	0.00362182i
$457$	−2.70553	+	3.39262i	−0.126559	+	0.158700i	−0.841074	−	0.540920i	$-0.818076\pi$
$457$	−2.70553	+	3.39262i	−0.126559	+	0.158700i	0.714515	+	0.699620i	$0.246648\pi$
$458$	26.4604	−	26.9545i	1.23641	−	1.25950i
$459$			1.73601i			0.0810299i
$460$	−6.26732	−	4.81107i	−0.292215	−	0.224317i
$461$	−7.76722	+	16.1288i	−0.361756	+	0.751193i	−0.999824	−	0.0187870i	$-0.994020\pi$
$461$	−7.76722	+	16.1288i	−0.361756	+	0.751193i	0.638068	+	0.769980i	$0.279734\pi$
$462$	−0.625521	−	0.155257i	−0.0291019	−	0.00722321i
$463$	−16.5200	−	34.3041i	−0.767750	−	1.59425i	−0.803801	−	0.594899i	$-0.797192\pi$
$463$	−16.5200	−	34.3041i	−0.767750	−	1.59425i	0.0360510	−	0.999350i	$-0.488522\pi$
$464$	11.0225	+	12.8187i	0.511707	+	0.595095i
$465$	−1.04556	−	0.238642i	−0.0484867	−	0.0110668i
$466$	−2.80071	+	4.55021i	−0.129741	+	0.210784i
$467$	18.5981	−	8.95636i	0.860616	−	0.414451i	0.0491091	−	0.998793i	$-0.484362\pi$
$467$	18.5981	−	8.95636i	0.860616	−	0.414451i	0.811507	+	0.584342i	$0.198648\pi$
$468$	−0.973158	+	4.65940i	−0.0449842	+	0.215381i
$469$	6.56354	−	3.87095i	0.303076	−	0.178744i
$470$	−15.7460	+	16.0401i	−0.726310	+	0.739873i
$471$		−	2.24858i		−	0.103609i
$472$	21.3884	+	32.0308i	0.984483	+	1.47434i
$473$	−8.77044	−	4.22362i	−0.403265	−	0.194202i
$474$	−0.793344	−	1.23705i	−0.0364395	−	0.0568196i
$475$	0.473583	−	2.07490i	0.0217295	−	0.0952031i
$476$	14.2714	+	1.74746i	0.654130	+	0.0800947i
$477$	−1.76188	−	7.71929i	−0.0806709	−	0.353442i
$478$	3.55407	−	3.62044i	0.162559	−	0.165595i
$479$	−4.94893	−	21.6827i	−0.226123	−	0.990708i	−0.952769	−	0.303696i	$-0.901779\pi$
$479$	−4.94893	−	21.6827i	−0.226123	−	0.990708i	0.726646	−	0.687012i	$-0.241078\pi$
$480$	−0.580831	+	0.637207i	−0.0265112	+	0.0290844i
$481$	3.69448	+	0.843241i	0.168454	+	0.0384485i
$482$	−1.68282	+	0.606375i	−0.0766506	+	0.0276196i
$483$	−0.777748	+	0.0655329i	−0.0353888	+	0.00298185i
$484$	16.2936	−	4.03743i	0.740619	−	0.183520i
$485$	−1.53668	−	1.92694i	−0.0697771	−	0.0874978i
$486$	4.02321	−	0.491035i	0.182496	−	0.0222738i
$487$	32.1640	−	25.6499i	1.45749	−	1.16231i	0.502913	−	0.864337i	$-0.332262\pi$
$487$	32.1640	−	25.6499i	1.45749	−	1.16231i	0.954575	−	0.297970i	$-0.0963097\pi$
$488$	−20.4339	−	19.3302i	−0.925000	−	0.875035i
$489$			1.84195i			0.0832960i
$490$	14.1130	−	0.921090i	0.637562	−	0.0416106i
$491$			20.0236i			0.903652i	0.892106	+	0.451826i	$0.149227\pi$
$491$			20.0236i			0.903652i	−0.892106	+	0.451826i	$0.850773\pi$
$492$	−0.217067	−	0.0996301i	−0.00978615	−	0.00449167i
$493$	8.97876	−	7.16033i	0.404383	−	0.322485i
$494$	0.0981381	+	0.804078i	0.00441544	+	0.0361772i
$495$	4.29818	+	5.38975i	0.193189	+	0.242251i
$496$	25.7921	+	11.2652i	1.15810	+	0.505825i
$497$	17.3712	−	25.9929i	0.779206	−	1.16594i
$498$	−0.430094	−	1.19360i	−0.0192730	−	0.0534867i
$499$	8.49474	+	1.93887i	0.380277	+	0.0867957i	0.408386	−	0.912809i	$-0.366092\pi$
$499$	8.49474	+	1.93887i	0.380277	+	0.0867957i	−0.0281096	+	0.999605i	$0.508949\pi$
$500$	−5.46969	−	22.0737i	−0.244612	−	0.987165i
$501$	0.0885333	+	0.387890i	0.00395538	+	0.0173296i
$502$	18.4289	+	18.0911i	0.822523	+	0.807445i
$503$	−3.39697	−	14.8831i	−0.151463	−	0.663605i	−0.992460	−	0.122565i	$-0.960888\pi$
$503$	−3.39697	−	14.8831i	−0.151463	−	0.663605i	0.840997	−	0.541040i	$-0.181969\pi$
$504$	0.00868105	−	22.3648i	0.000386685	−	0.996206i
$505$	1.05579	−	4.62574i	0.0469822	−	0.205843i
$506$	−5.31474	+	3.40845i	−0.236269	+	0.151524i
$507$	1.18861	+	0.572403i	0.0527879	+	0.0254213i
$508$	−12.4591	+	16.2303i	−0.552785	+	0.720105i
$509$			5.41910i			0.240197i	0.992762	+	0.120099i	$0.0383211\pi$
$509$			5.41910i			0.240197i	−0.992762	+	0.120099i	$0.961679\pi$
$510$	0.417961	+	0.410300i	0.0185076	+	0.0181684i
$511$	9.98263	+	31.3297i	0.441606	+	1.38595i
$512$	18.0918	−	13.5900i	0.799551	−	0.600599i
$513$	0.414032	−	0.199387i	0.0182800	−	0.00880317i
$514$	−3.96365	−	2.43968i	−0.174829	−	0.107610i
$515$	−10.6227	−	2.42456i	−0.468093	−	0.106839i
$516$	−0.263011	+	1.25928i	−0.0115784	+	0.0554365i
$517$	7.79333	+	16.1830i	0.342750	+	0.711728i
$518$	−17.8019	−	0.336290i	−0.782170	−	0.0147757i
$519$	−0.704631	+	1.46318i	−0.0309298	+	0.0642265i
$520$	1.78698	+	2.67615i	0.0783644	+	0.117357i
$521$		−	32.2327i		−	1.41214i	−0.708143	−	0.706069i	$-0.750467\pi$
$521$		−	32.2327i		−	1.41214i	0.708143	−	0.706069i	$-0.249533\pi$
$522$	−12.7478	−	12.5141i	−0.557955	−	0.547727i
$523$	−0.510259	+	0.639845i	−0.0223121	+	0.0279785i	−0.792862	−	0.609401i	$-0.791410\pi$
$523$	−0.510259	+	0.639845i	−0.0223121	+	0.0279785i	0.770550	+	0.637379i	$0.219982\pi$
$524$	−32.2398	+	26.7009i	−1.40840	+	1.16643i
$525$	−0.694396	−	0.464070i	−0.0303059	−	0.0202537i
$526$	30.6334	+	3.16488i	1.33568	+	0.137995i
$527$	8.29534	−	17.2255i	0.361351	−	0.750352i
$528$	0.321705	+	0.609284i	0.0140004	+	0.0265157i
$529$	9.57297	−	12.0041i	0.416216	−	0.521919i
$530$	−4.55848	−	2.80581i	−0.198008	−	0.121877i
$531$	−25.3740	−	31.8181i	−1.10114	−	1.38079i
$532$	−1.22237	−	3.60439i	−0.0529964	−	0.156270i
$533$	−0.555778	+	0.696924i	−0.0240734	+	0.0301871i
$534$	2.08048	−	0.749664i	0.0900313	−	0.0324412i
$535$	−20.5081	+	9.87616i	−0.886640	+	0.426984i
$536$	−7.76068	−	2.47611i	−0.335210	−	0.106952i
$537$	2.11382	−	0.482466i	0.0912181	−	0.0208199i
$538$	−12.4738	+	36.7347i	−0.537785	+	1.58375i
$539$	3.13070	−	10.8597i	0.134849	−	0.467759i
$540$	1.11161	−	1.44808i	0.0478361	−	0.0623154i
$541$	−5.20805	−	22.8180i	−0.223912	−	0.981020i	−0.954502	−	0.298205i	$-0.903612\pi$
$541$	−5.20805	−	22.8180i	−0.223912	−	0.981020i	0.730590	−	0.682816i	$-0.239245\pi$
$542$	14.2432	+	39.5280i	0.611799	+	1.69788i
$543$	−0.644173	−	1.33764i	−0.0276441	−	0.0574036i
$544$	−8.77072	−	12.6228i	−0.376041	−	0.541197i
$545$	6.04099	+	4.81753i	0.258768	+	0.206360i
$546$	0.308524	+	0.0765769i	0.0132036	+	0.00327719i
$547$	−23.6862	+	18.8891i	−1.01275	+	0.807642i	−0.981421	−	0.191868i	$-0.938546\pi$
$547$	−23.6862	+	18.8891i	−1.01275	+	0.807642i	−0.0313296	+	0.999509i	$0.509974\pi$
$548$	−18.8224	+	15.5887i	−0.804054	+	0.665914i
$549$	23.2371	+	18.5310i	0.991735	+	0.790882i
$550$	−6.72042	−	0.694319i	−0.286560	−	0.0296059i
$551$	−2.73896	−	1.31901i	−0.116684	−	0.0561919i
$552$	0.606150	+	0.573408i	0.0257994	+	0.0244059i
$553$	22.1977	−	13.0914i	0.943942	−	0.556704i
$554$	2.79249	−	4.53684i	0.118641	−	0.192752i
$555$	−0.567059	−	0.452215i	−0.0240703	−	0.0191954i
$556$	−16.7718	−	33.2396i	−0.711284	−	1.40967i
$557$	−34.1917			−1.44875			−0.724374	−	0.689407i	$-0.757871\pi$
$557$	−34.1917			−1.44875			−0.724374	+	0.689407i	$0.757871\pi$
$558$	−28.1598	−	9.56209i	−1.19210	−	0.404796i
$559$	4.32582	+	2.08320i	0.182963	+	0.0881101i
$560$	−10.7855	−	10.5960i	−0.455769	−	0.447762i
$561$	0.421686	−	0.203073i	0.0178036	−	0.00857376i
$562$	−31.6956	+	3.86846i	−1.33700	+	0.163181i
$563$	−6.31741	+	27.6784i	−0.266247	+	1.16651i	0.648094	+	0.761560i	$0.275566\pi$
$563$	−6.31741	+	27.6784i	−0.266247	+	1.16651i	−0.914341	+	0.404945i	$0.867291\pi$
$564$	1.82816	−	1.51407i	0.0769793	−	0.0637539i
$565$	−6.82206	−	14.1662i	−0.287006	−	0.595975i
$566$	−4.61323	+	0.563047i	−0.193908	+	0.0236666i
$567$	1.97656	+	23.4580i	0.0830078	+	0.985142i
$568$	−33.0950	+	4.66213i	−1.38864	+	0.195619i
$569$	12.4796			0.523172			0.261586	−	0.965180i	$-0.415754\pi$
$569$	12.4796			0.523172			0.261586	+	0.965180i	$0.415754\pi$
$570$	0.0498506	−	0.146807i	0.00208801	−	0.00614907i
$571$	15.0567	−	31.2657i	0.630105	−	1.30843i	−0.304422	−	0.952537i	$-0.598463\pi$
$571$	15.0567	−	31.2657i	0.630105	−	1.30843i	0.934528	−	0.355890i	$-0.115822\pi$
$572$	2.49600	−	0.618491i	0.104363	−	0.0258604i
$573$	0.0187823	+	0.00428694i	0.000784641	+	0.000179089i
$574$	1.88817	−	3.73851i	0.0788108	−	0.156042i
$575$	−7.97676	+	1.82064i	−0.332654	+	0.0759261i
$576$	−17.8371	+	15.9210i	−0.743211	+	0.663373i
$577$	37.8950	−	8.64930i	1.57759	−	0.360075i	0.658021	−	0.753000i	$-0.271394\pi$
$577$	37.8950	−	8.64930i	1.57759	−	0.360075i	0.919571	+	0.392925i	$0.128537\pi$
$578$	11.4483	−	7.34201i	0.476186	−	0.305388i
$579$	0.254997	−	1.11722i	0.0105973	−	0.0464299i
$580$	−12.0745	+	0.223407i	−0.501367	+	0.00927647i
$581$	21.1983	−	6.75443i	0.879453	−	0.280221i
$582$	0.140511	+	0.219097i	0.00582437	+	0.00908186i
$583$	−3.34427	+	2.66697i	−0.138506	+	0.110455i
$584$	17.8689	−	30.2715i	0.739422	−	1.25264i
$585$	−2.11998	−	2.65837i	−0.0876503	−	0.109910i
$586$	−24.7462	−	2.55665i	−1.02225	−	0.105614i
$587$	−46.5433			−1.92105			−0.960523	−	0.278201i	$-0.910262\pi$
$587$	−46.5433			−1.92105			−0.960523	+	0.278201i	$0.910262\pi$
$588$	−1.49253	−	0.0564099i	−0.0615509	−	0.00232631i
$589$	−5.06097			−0.208533
$590$	−27.3672	−	2.82744i	−1.12669	−	0.116404i
$591$	−0.491110	−	0.615832i	−0.0202016	−	0.0253320i
$592$	12.4101	+	14.4325i	0.510054	+	0.593172i
$593$	3.28269	−	2.61786i	0.134804	−	0.107503i	−0.553766	−	0.832672i	$-0.686810\pi$
$593$	3.28269	−	2.61786i	0.134804	−	0.107503i	0.688571	+	0.725169i	$0.258239\pi$
$594$	−0.787530	−	1.22798i	−0.0323128	−	0.0503848i
$595$	−7.46393	+	7.05527i	−0.305991	+	0.289238i
$596$	−0.424506	−	22.9433i	−0.0173884	−	0.939795i
$597$	−0.164409	+	0.720322i	−0.00672881	+	0.0294808i
$598$	2.62137	−	1.68114i	0.107196	−	0.0687469i
$599$	21.6951	−	4.95177i	0.886438	−	0.202324i	0.245023	−	0.969517i	$-0.421205\pi$
$599$	21.6951	−	4.95177i	0.886438	−	0.202324i	0.641416	+	0.767194i	$0.278347\pi$
$600$	0.124548	+	0.884129i	0.00508466	+	0.0360944i
$601$	−18.7980	+	4.29052i	−0.766786	+	0.175014i	−0.587986	−	0.808871i	$-0.700079\pi$
$601$	−18.7980	+	4.29052i	−0.766786	+	0.175014i	−0.178801	+	0.983885i	$0.557222\pi$
$602$	−21.8947	−	5.43437i	−0.892363	−	0.221488i
$603$	8.39168	+	1.91535i	0.341736	+	0.0779989i
$604$	−1.44251	−	5.82146i	−0.0586951	−	0.236872i
$605$	−5.20273	+	10.8036i	−0.211521	+	0.439228i
$606$	−0.161111	+	0.474462i	−0.00654469	+	0.0192737i
$607$	−34.5050			−1.40052			−0.700258	−	0.713890i	$-0.746932\pi$
$607$	−34.5050			−1.40052			−0.700258	+	0.713890i	$0.746932\pi$
$608$	−2.00314	+	3.54156i	−0.0812381	+	0.143629i
$609$	−0.866972	+	0.819505i	−0.0351315	+	0.0332080i
$610$	19.9449	−	2.43429i	0.807547	−	0.0985616i
$611$	−3.84388	−	7.98190i	−0.155507	−	0.322913i
$612$	10.3594	+	12.5085i	0.418756	+	0.505624i
$613$	10.4992	−	46.0000i	0.424059	−	1.85792i	−0.0837987	−	0.996483i	$-0.526705\pi$
$613$	10.4992	−	46.0000i	0.424059	−	1.85792i	0.507858	−	0.861441i	$-0.330438\pi$
$614$	9.36728	−	1.14328i	0.378033	−	0.0461391i
$615$	0.153715	−	0.0740253i	0.00619839	−	0.00298499i
$616$	−10.8878	+	5.23807i	−0.438681	+	0.211048i
$617$	33.3337	+	16.0527i	1.34196	+	0.646256i	0.960539	−	0.278144i	$-0.0897194\pi$
$617$	33.3337	+	16.0527i	1.34196	+	0.646256i	0.381424	+	0.924400i	$0.375434\pi$
$618$	1.08957	+	0.369981i	0.0438290	+	0.0148828i
$619$	21.7564			0.874465			0.437233	−	0.899348i	$-0.355959\pi$
$619$	21.7564			0.874465			0.437233	+	0.899348i	$0.355959\pi$
$620$	−17.9494	+	9.05677i	−0.720865	+	0.363729i
$621$	−1.38123	−	1.10149i	−0.0554269	−	0.0442015i
$622$	−5.85455	+	9.51165i	−0.234746	+	0.381382i
$623$	11.7731	+	36.9491i	0.471681	+	1.48034i
$624$	−0.158673	−	0.300515i	−0.00635202	−	0.0120302i
$625$	1.30662	+	0.629234i	0.0522647	+	0.0251694i
$626$	−1.52285	−	0.157333i	−0.0608652	−	0.00628828i
$627$	−0.0968646	−	0.0772470i	−0.00386840	−	0.00308495i
$628$	−26.8874	−	32.4650i	−1.07292	−	1.29549i
$629$	10.1091	−	8.06175i	0.403077	−	0.321443i
$630$	12.3001	+	10.1949i	0.490047	+	0.406176i
$631$	−19.7677	−	15.7642i	−0.786941	−	0.627564i	0.145306	−	0.989387i	$-0.453583\pi$
$631$	−19.7677	−	15.7642i	−0.786941	−	0.627564i	−0.932247	+	0.361822i	$0.882155\pi$
$632$	−26.2464	−	8.37413i	−1.04402	−	0.333105i
$633$	−0.0377967	−	0.0784857i	−0.00150228	−	0.00311953i
$634$	4.65938	+	12.9308i	0.185047	+	0.513547i
$635$	−3.25236	−	14.2495i	−0.129066	−	0.565476i
$636$	0.448404	+	0.344215i	0.0177804	+	0.0136490i
$637$	−1.54414	+	5.35628i	−0.0611812	+	0.212223i
$638$	−3.10298	+	9.13810i	−0.122848	+	0.361781i
$639$	34.4293	−	7.85826i	1.36200	−	0.310868i
$640$	−0.766651	+	16.1453i	−0.0303046	+	0.638199i
$641$	21.4306	−	10.3204i	0.846459	−	0.407633i	0.0401968	−	0.999192i	$-0.487202\pi$
$641$	21.4306	−	10.3204i	0.846459	−	0.407633i	0.806262	+	0.591559i	$0.201487\pi$
$642$	2.26150	−	0.814889i	0.0892542	−	0.0321611i
$643$	−6.50045	+	8.15131i	−0.256353	+	0.321456i	−0.893308	−	0.449444i	$-0.851622\pi$
$643$	−6.50045	+	8.15131i	−0.256353	+	0.321456i	0.636956	+	0.770901i	$0.280193\pi$
$644$	−10.4455	+	10.2461i	−0.411612	+	0.403753i
$645$	−0.572957	−	0.718466i	−0.0225602	−	0.0282896i
$646$	2.35379	+	1.44879i	0.0926088	+	0.0570020i
$647$	−2.24435	+	2.81432i	−0.0882344	+	0.110642i	−0.823989	−	0.566606i	$-0.808256\pi$
$647$	−2.24435	+	2.81432i	−0.0882344	+	0.110642i	0.735755	+	0.677248i	$0.236828\pi$
$648$	17.2948	−	18.2823i	0.679403	−	0.718197i
$649$	−9.53932	+	19.8086i	−0.374451	+	0.777556i
$650$	3.31469	+	0.342457i	0.130013	+	0.0134323i
$651$	−0.708440	+	1.85542i	−0.0277660	+	0.0727197i
$652$	22.0252	+	26.5942i	0.862573	+	1.04151i
$653$	−8.82550	+	11.0668i	−0.345369	+	0.433078i	−0.923931	−	0.382560i	$-0.875043\pi$
$653$	−8.82550	+	11.0668i	−0.345369	+	0.433078i	0.578562	+	0.815638i	$0.303614\pi$
$654$	−0.582304	−	0.571630i	−0.0227699	−	0.0223525i
$655$		−	29.9027i		−	1.16839i
$656$	−4.32535	+	1.15712i	−0.168877	+	0.0451781i
$657$	−16.1157	+	33.4646i	−0.628733	+	1.30558i
$658$	25.3338	+	33.0285i	0.987613	+	1.28758i
$659$	12.4421	+	25.8363i	0.484676	+	1.00644i	0.989676	+	0.143321i	$0.0457783\pi$
$659$	12.4421	+	25.8363i	0.484676	+	1.00644i	−0.505000	+	0.863119i	$0.668507\pi$
$660$	−0.481779	−	0.100624i	−0.0187532	−	0.00391678i
$661$	−31.8246	−	7.26375i	−1.23783	−	0.282527i	−0.446986	−	0.894541i	$-0.647502\pi$
$661$	−31.8246	−	7.26375i	−1.23783	−	0.282527i	−0.790847	+	0.612014i	$0.790360\pi$
$662$	−2.34635	−	1.44421i	−0.0911936	−	0.0561309i
$663$	−0.207987	+	0.100161i	−0.00807754	+	0.00388994i
$664$	−20.4823	−	12.0904i	−0.794866	−	0.469200i
$665$	2.53992	+	0.969797i	0.0984939	+	0.0376071i
$666$	−14.3526	−	14.0895i	−0.556152	−	0.545957i
$667$			11.6870i			0.452524i
$668$	5.91644	+	4.54172i	0.228914	+	0.175725i
$669$	−1.30748	−	0.629652i	−0.0505503	−	0.0243437i
$670$	4.89827	−	3.14136i	0.189237	−	0.121361i
$671$	3.57292	−	15.6540i	0.137931	−	0.604315i
$672$	1.01799	+	1.23013i	0.0392696	+	0.0474534i
$673$	−6.73569	−	29.5110i	−0.259642	−	1.13757i	−0.921636	−	0.388056i	$-0.873147\pi$
$673$	−6.73569	−	29.5110i	−0.259642	−	1.13757i	0.661994	−	0.749509i	$-0.269710\pi$
$674$	26.8200	+	26.3283i	1.03307	+	1.01413i
$675$	−0.420664	−	1.84305i	−0.0161914	−	0.0709390i
$676$	24.0057	−	5.94842i	0.923295	−	0.228785i
$677$	−10.1153	−	2.30874i	−0.388761	−	0.0887322i	0.0236726	−	0.999720i	$-0.492464\pi$
$677$	−10.1153	−	2.30874i	−0.388761	−	0.0887322i	−0.412434	+	0.910988i	$0.635321\pi$
$678$	0.562894	+	1.56215i	0.0216178	+	0.0599942i
$679$	−3.93149	+	2.31865i	−0.150877	+	0.0889818i
$680$	10.9407	+	0.926138i	0.419557	+	0.0355158i
$681$	−0.309982	−	0.388705i	−0.0118785	−	0.0148952i
$682$	1.94643	+	15.9477i	0.0745327	+	0.610670i
$683$	−3.43939	+	2.74282i	−0.131605	+	0.104951i	−0.687080	−	0.726582i	$-0.741108\pi$
$683$	−3.43939	+	2.74282i	−0.131605	+	0.104951i	0.555475	+	0.831533i	$0.312536\pi$
$684$	1.79340	−	3.90734i	0.0685724	−	0.149401i
$685$		−	17.4579i		−	0.667034i
$686$	1.96685	−	26.1176i	0.0750948	−	0.997176i
$687$		−	2.84942i		−	0.108712i
$688$	11.2604	+	21.3264i	0.429301	+	0.813062i
$689$	1.64949	−	1.31542i	0.0628404	−	0.0501136i
$690$	−0.591645	+	0.0722106i	−0.0225235	+	0.00274901i
$691$	−21.3276	−	26.7440i	−0.811342	−	1.01739i	−0.999379	−	0.0352288i	$-0.988784\pi$
$691$	−21.3276	−	26.7440i	−0.811342	−	1.01739i	0.188037	−	0.982162i	$-0.439787\pi$
$692$	7.32253	+	29.5511i	0.278361	+	1.12336i
$693$	10.9966	−	6.48540i	0.417725	−	0.246360i
$694$	−3.40063	+	1.22536i	−0.129086	+	0.0465139i
$695$	25.9287	+	5.91806i	0.983532	+	0.224485i
$696$	1.27082	+	0.107575i	0.0481702	+	0.00407764i
$697$	0.676803	+	2.96527i	0.0256357	+	0.112318i
$698$	−25.6895	+	26.1692i	−0.972363	+	0.990520i
$699$	0.0896916	+	0.392965i	0.00339245	+	0.0148633i
$700$	−15.5748	+	1.60300i	−0.588673	+	0.0605878i
$701$	4.50543	−	19.7396i	0.170168	−	0.745554i	−0.815761	−	0.578389i	$-0.803682\pi$
$701$	4.50543	−	19.7396i	0.170168	−	0.745554i	0.985929	−	0.167165i	$-0.0534612\pi$
$702$	0.388431	+	0.605675i	0.0146604	+	0.0228597i
$703$	−3.08377	−	1.48507i	−0.116307	−	0.0560103i
$704$	11.9303	+	4.95007i	0.449640	+	0.186563i
$705$			1.69563i			0.0638611i
$706$	11.0223	−	11.2281i	0.414829	−	0.422575i
$707$	−8.20871	−	3.13426i	−0.308720	−	0.117876i
$708$	2.84416	+	0.594028i	0.106890	+	0.0223249i
$709$	31.4759	−	15.1580i	1.18210	−	0.569270i	0.263578	−	0.964638i	$-0.415097\pi$
$709$	31.4759	−	15.1580i	1.18210	−	0.569270i	0.918523	+	0.395368i	$0.129383\pi$
$710$	12.5144	−	20.3316i	0.469655	−	0.763030i
$711$	28.3804	+	6.47764i	1.06435	+	0.242930i
$712$	21.0740	−	35.7011i	0.789780	−	1.33795i
$713$	8.44180	+	17.5296i	0.316148	+	0.656488i
$714$	0.860634	−	0.660130i	0.0322084	−	0.0247048i
$715$	−0.797001	+	1.65499i	−0.0298062	+	0.0618931i
$716$	24.7503	−	32.2419i	0.924962	−	1.20494i
$717$		−	0.382724i		−	0.0142931i
$718$	12.1949	−	12.4226i	0.455110	−	0.463609i
$719$	−3.26447	+	4.09352i	−0.121744	+	0.152663i	−0.838969	−	0.544180i	$-0.816841\pi$
$719$	−3.26447	+	4.09352i	−0.121744	+	0.152663i	0.717224	+	0.696842i	$0.245412\pi$
$720$	−0.631786	−	17.0672i	−0.0235453	−	0.636059i
$721$	−7.19763	+	18.8508i	−0.268054	+	0.702040i
$722$	−2.68619	+	26.0000i	−0.0999696	+	0.967621i
$723$	−0.0585478	+	0.121576i	−0.00217742	+	0.00452145i
$724$	−25.2954	−	11.6102i	−0.940098	−	0.431488i
$725$	−7.79732	+	9.77753i	−0.289585	+	0.363128i
$726$	0.663782	−	1.07842i	0.0246353	−	0.0400239i
$727$	−23.9283	−	30.0051i	−0.887450	−	1.11283i	−0.992965	−	0.118409i	$-0.962221\pi$
$727$	−23.9283	−	30.0051i	−0.887450	−	1.11283i	0.105515	−	0.994418i	$-0.466351\pi$
$728$	5.37014	−	2.58356i	0.199031	−	0.0957530i
$729$	−16.4522	+	20.6304i	−0.609342	+	0.764090i
$730$	8.51226	+	23.6234i	0.315053	+	0.874341i
$731$	14.7600	−	7.10806i	0.545920	−	0.262901i
$732$	−2.12158	+	0.0392542i	−0.0784158	+	0.00145088i
$733$	−27.7748	+	6.33942i	−1.02589	+	0.234152i	−0.702175	−	0.712004i	$-0.747788\pi$
$733$	−27.7748	+	6.33942i	−1.02589	+	0.234152i	−0.323711	+	0.946156i	$0.604931\pi$
$734$	23.9299	+	8.12578i	0.883270	+	0.299928i
$735$	0.711082	−	0.795418i	0.0262287	−	0.0293394i
$736$	15.6081	+	1.03084i	0.575324	+	0.0379972i
$737$	−1.03474	−	4.53349i	−0.0381151	−	0.166993i
$738$	4.45091	−	1.60380i	0.163840	−	0.0590368i
$739$	−8.26271	−	17.1577i	−0.303949	−	0.631156i	0.691919	−	0.721975i	$-0.256766\pi$
$739$	−8.26271	−	17.1577i	−0.303949	−	0.631156i	−0.995867	+	0.0908195i	$0.971051\pi$
$740$	−13.5946	+	0.251532i	−0.499747	+	0.00924650i
$741$	0.0477762	+	0.0381003i	0.00175510	+	0.00139965i
$742$	−6.32584	+	7.63206i	−0.232229	+	0.280182i
$743$	9.49452	−	7.57163i	0.348320	−	0.277776i	−0.433664	−	0.901075i	$-0.642779\pi$
$743$	9.49452	−	7.57163i	0.348320	−	0.277776i	0.781984	+	0.623299i	$0.214208\pi$
$744$	1.98382	−	0.756584i	0.0727305	−	0.0277377i
$745$	12.8158	+	10.2202i	0.469533	+	0.374440i
$746$	−1.18484	+	11.4682i	−0.0433800	+	0.419882i
$747$	22.6427	+	10.9042i	0.828455	+	0.398963i
$748$	3.66006	−	7.97430i	0.133825	−	0.291569i
$749$	12.7975	+	40.1639i	0.467609	+	1.46756i
$750$	−1.46098	−	0.899254i	−0.0533475	−	0.0328361i
$751$	34.1350	+	27.2217i	1.24560	+	0.993335i	0.999711	+	0.0240379i	$0.00765225\pi$
$751$	34.1350	+	27.2217i	1.24560	+	0.993335i	0.245892	+	0.969297i	$0.420919\pi$
$752$	8.29044	−	43.7204i	0.302321	−	1.59432i
$753$	1.94816			0.0709949
$754$	1.53047	−	4.50716i	0.0557366	−	0.164141i
$755$	3.85996	+	1.85886i	0.140478	+	0.0676507i
$756$	−2.36739	−	2.41347i	−0.0861010	−	0.0877770i
$757$	−25.2466	+	12.1581i	−0.917602	+	0.441894i	−0.832215	−	0.554454i	$-0.812927\pi$
$757$	−25.2466	+	12.1581i	−0.917602	+	0.441894i	−0.0853878	+	0.996348i	$0.527213\pi$
$758$	2.76900	+	22.6873i	0.100574	+	0.824040i
$759$	−0.105987	+	0.464358i	−0.00384707	+	0.0168551i
$760$	−1.03570	−	2.71569i	−0.0375689	−	0.0985085i
$761$	4.39853	+	9.13363i	0.159446	+	0.331094i	0.965352	−	0.260950i	$-0.0840356\pi$
$761$	4.39853	+	9.13363i	0.159446	+	0.331094i	−0.805906	+	0.592044i	$0.798321\pi$
$762$	0.187002	+	1.53217i	0.00677437	+	0.0555047i
$763$	10.3988	−	9.82941i	0.376460	−	0.355849i
$764$	0.322440	−	0.162695i	0.0116655	−	0.00588609i
$765$	−11.6017			−0.419460
$766$	25.0259	+	8.49794i	0.904223	+	0.307043i
$767$	4.70505	−	9.77014i</

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.145336 - 1.40673i) q^{2} +(-0.0665173 - 0.0834100i) q^{3} +(-1.95776 - 0.408895i) q^{4} +(1.11698 - 0.890758i) q^{5} +(-0.127002 + 0.0814491i) q^{6} +(-1.34404 - 2.27894i) q^{7} +(-0.859735 + 2.69460i) q^{8} +(0.665030 - 2.91369i) q^{9} +O(q^{10})\)	\(q+(0.145336 - 1.40673i) q^{2} +(-0.0665173 - 0.0834100i) q^{3} +(-1.95776 - 0.408895i) q^{4} +(1.11698 - 0.890758i) q^{5} +(-0.127002 + 0.0814491i) q^{6} +(-1.34404 - 2.27894i) q^{7} +(-0.859735 + 2.69460i) q^{8} +(0.665030 - 2.91369i) q^{9} +(-1.09072 - 1.70074i) q^{10} +(-1.57408 + 0.359273i) q^{11} +(0.0961186 + 0.190495i) q^{12} +(0.776378 - 0.177203i) q^{13} +(-3.40118 + 1.55948i) q^{14} +(-0.148596 - 0.0339161i) q^{15} +(3.66561 + 1.60103i) q^{16} +(1.17894 - 2.44810i) q^{17} +(-4.00211 - 1.35898i) q^{18} -0.719271 q^{19} +(-2.55099 + 1.28716i) q^{20} +(-0.100684 + 0.263695i) q^{21} +(0.276629 + 2.26651i) q^{22} +(1.19976 + 2.49133i) q^{23} +(0.281944 - 0.107527i) q^{24} +(-0.658421 + 2.88473i) q^{25} +(-0.136441 - 1.11791i) q^{26} +(-0.575627 + 0.277208i) q^{27} +(1.69945 + 5.01117i) q^{28} +(3.80797 + 1.83382i) q^{29} +(-0.0693071 + 0.204105i) q^{30} +7.03624 q^{31} +(2.78496 - 4.92382i) q^{32} +(0.134671 + 0.107396i) q^{33} +(-3.27247 - 2.01425i) q^{34} +(-3.53124 - 1.34830i) q^{35} +(-2.49336 + 5.43236i) q^{36} +(4.28735 + 2.06468i) q^{37} +(-0.104536 + 1.01182i) q^{38} +(-0.0664231 - 0.0529707i) q^{39} +(1.43993 + 3.77561i) q^{40} +(-0.875154 + 0.697912i) q^{41} +(0.356314 + 0.179960i) q^{42} +(4.71379 + 3.75912i) q^{43} +(3.22857 - 0.0597362i) q^{44} +(-1.85257 - 3.84690i) q^{45} +(3.67898 - 1.32566i) q^{46} +(-2.47552 - 10.8460i) q^{47} +(-0.110284 - 0.412245i) q^{48} +(-3.38712 + 6.12596i) q^{49} +(3.96233 + 1.34547i) q^{50} +(-0.282617 + 0.0645054i) q^{51} +(-1.59242 + 0.0294635i) q^{52} +(2.38696 - 1.14950i) q^{53} +(0.306296 + 0.850038i) q^{54} +(-1.43818 + 1.80342i) q^{55} +(7.29634 - 1.66236i) q^{56} +(0.0478440 + 0.0599944i) q^{57} +(3.13312 - 5.09024i) q^{58} +(8.49023 - 10.6464i) q^{59} +(0.277047 + 0.127160i) q^{60} +(-4.31491 + 8.96000i) q^{61} +(1.02262 - 9.89806i) q^{62} +(-7.53394 + 2.40055i) q^{63} +(-6.52171 - 4.63328i) q^{64} +(0.709350 - 0.889497i) q^{65} +(0.170649 - 0.173836i) q^{66} +2.88009i q^{67} +(-3.30910 + 4.31072i) q^{68} +(0.127997 - 0.265788i) q^{69} +(-2.40991 + 4.77153i) q^{70} +(5.12694 + 10.6462i) q^{71} +(7.27947 + 4.29699i) q^{72} +(-12.1165 - 2.76552i) q^{73} +(3.52755 - 5.73106i) q^{74} +(0.284412 - 0.136965i) q^{75} +(1.40816 + 0.294106i) q^{76} +(2.93439 + 3.10435i) q^{77} +(-0.0841689 + 0.0857406i) q^{78} +9.74036i q^{79} +(5.52053 - 1.47686i) q^{80} +(-8.01654 - 3.86056i) q^{81} +(0.854580 + 1.33253i) q^{82} +(-1.87120 + 8.19825i) q^{83} +(0.304939 - 0.475081i) q^{84} +(-0.863816 - 3.78463i) q^{85} +(5.97314 - 6.08468i) q^{86} +(-0.100337 - 0.439603i) q^{87} +(0.385194 - 4.55039i) q^{88} +(-14.2898 - 3.26154i) q^{89} +(-5.68078 + 2.04696i) q^{90} +(-1.44732 - 1.53115i) q^{91} +(-1.33015 - 5.36799i) q^{92} +(-0.468032 - 0.586893i) q^{93} +(-15.6171 + 1.90607i) q^{94} +(-0.803408 + 0.640697i) q^{95} +(-0.595944 + 0.0952258i) q^{96} -1.72514i q^{97} +(8.12528 + 5.65507i) q^{98} +4.82530i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more