LMFDB - Embedded newform 300.2.w.a.103.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.20
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.611319 + 1.27526i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.25258 + 1.55918i) q^{4} +(-0.726283 - 2.11483i) q^{5} +(0.803287 + 1.16393i) q^{6} +(3.39156 + 3.39156i) q^{7} +(-2.75409 - 0.644208i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(0.611319 + 1.27526i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.25258 + 1.55918i) q^{4} +(-0.726283 - 2.11483i) q^{5} +(0.803287 + 1.16393i) q^{6} +(3.39156 + 3.39156i) q^{7} +(-2.75409 - 0.644208i) q^{8} +(0.951057 - 0.309017i) q^{9} +(2.25297 - 2.21904i) q^{10} +(2.54925 + 0.828300i) q^{11} +(-0.993248 + 1.73593i) q^{12} +(-1.36403 + 2.67705i) q^{13} +(-2.25180 + 6.39845i) q^{14} +(-1.04817 - 1.97518i) q^{15} +(-0.862092 - 3.90600i) q^{16} +(0.0551663 - 0.348307i) q^{17} +(0.975476 + 1.02394i) q^{18} +(0.0301061 - 0.0218734i) q^{19} +(4.20713 + 1.51659i) q^{20} +(3.88036 + 2.81925i) q^{21} +(0.502103 + 3.75731i) q^{22} +(-0.826275 - 1.62166i) q^{23} +(-2.82096 - 0.205443i) q^{24} +(-3.94503 + 3.07193i) q^{25} +(-4.24780 - 0.102957i) q^{26} +(0.891007 - 0.453990i) q^{27} +(-9.53626 + 1.03986i) q^{28} +(3.43571 - 4.72885i) q^{29} +(1.87810 - 2.54416i) q^{30} +(-3.91117 - 5.38327i) q^{31} +(4.45415 - 3.48720i) q^{32} +(2.64744 + 0.419313i) q^{33} +(0.477906 - 0.142575i) q^{34} +(4.70935 - 9.63581i) q^{35} +(-0.709460 + 1.86994i) q^{36} +(-8.36414 - 4.26174i) q^{37} +(0.0462987 + 0.0250216i) q^{38} +(-0.928450 + 2.85748i) q^{39} +(0.637856 + 6.29231i) q^{40} +(-2.14293 - 6.59526i) q^{41} +(-1.22314 + 6.67193i) q^{42} +(3.96315 - 3.96315i) q^{43} +(-4.48460 + 2.93723i) q^{44} +(-1.34426 - 1.78689i) q^{45} +(1.56292 - 2.04506i) q^{46} +(1.79499 + 11.3331i) q^{47} +(-1.46251 - 3.72304i) q^{48} +16.0054i q^{49} +(-6.32918 - 3.15300i) q^{50} -0.352648i q^{51} +(-2.46546 - 5.47999i) q^{52} +(-0.934134 - 5.89789i) q^{53} +(1.12365 + 0.858733i) q^{54} +(-0.0997595 - 5.99281i) q^{55} +(-7.15578 - 11.5255i) q^{56} +(0.0263137 - 0.0263137i) q^{57} +(8.13084 + 1.49059i) q^{58} +(-3.53381 - 10.8759i) q^{59} +(4.39258 + 0.839774i) q^{60} +(-1.26478 + 3.89259i) q^{61} +(4.47410 - 8.27866i) q^{62} +(4.27362 + 2.17752i) q^{63} +(7.16999 + 3.54841i) q^{64} +(6.65219 + 0.940388i) q^{65} +(1.08369 + 3.63250i) q^{66} +(8.89404 + 1.40868i) q^{67} +(0.473973 + 0.522296i) q^{68} +(-1.06979 - 1.47243i) q^{69} +(15.1671 + 0.115090i) q^{70} +(-9.59181 + 13.2020i) q^{71} +(-2.81836 + 0.238382i) q^{72} +(4.09605 - 2.08704i) q^{73} +(0.321677 - 13.2717i) q^{74} +(-3.41590 + 3.65125i) q^{75} +(-0.00360574 + 0.0743391i) q^{76} +(5.83669 + 11.4552i) q^{77} +(-4.21161 + 0.562813i) q^{78} +(-1.31184 - 0.953110i) q^{79} +(-7.63440 + 4.66004i) q^{80} +(0.809017 - 0.587785i) q^{81} +(7.10066 - 6.76460i) q^{82} +(0.977173 - 6.16963i) q^{83} +(-9.25618 + 2.51886i) q^{84} +(-0.776676 + 0.136302i) q^{85} +(7.47680 + 2.63130i) q^{86} +(2.65366 - 5.20810i) q^{87} +(-6.48725 - 3.92346i) q^{88} +(-13.2764 - 4.31376i) q^{89} +(1.45698 - 2.80664i) q^{90} +(-13.7056 + 4.45321i) q^{91} +(3.56343 + 0.742940i) q^{92} +(-4.70515 - 4.70515i) q^{93} +(-13.3554 + 9.21725i) q^{94} +(-0.0681241 - 0.0477831i) q^{95} +(3.85379 - 4.14105i) q^{96} +(8.89748 - 1.40922i) q^{97} +(-20.4110 + 9.78438i) q^{98} +2.68044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.611319	+	1.27526i	0.432268	+	0.901745i
$2$	0.611319	+	1.27526i	0.432268	+	0.901745i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$4$	−1.25258	+	1.55918i	−0.626289	+	0.779591i
$5$	−0.726283	−	2.11483i	−0.324804	−	0.945781i
$5$	−0.726283	−	2.11483i	−0.324804	−	0.945781i
$6$	0.803287	+	1.16393i	0.327941	+	0.475172i
$7$	3.39156	+	3.39156i	1.28189	+	1.28189i	0.939591	+	0.342298i	$0.111205\pi$
$7$	3.39156	+	3.39156i	1.28189	+	1.28189i	0.342298	+	0.939591i	$0.388795\pi$
$8$	−2.75409	−	0.644208i	−0.973717	−	0.227762i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	2.25297	−	2.21904i	0.712452	−	0.701721i
$11$	2.54925	+	0.828300i	0.768627	+	0.249742i	0.666977	−	0.745078i	$-0.267588\pi$
$11$	2.54925	+	0.828300i	0.768627	+	0.249742i	0.101650	+	0.994820i	$0.467588\pi$
$12$	−0.993248	+	1.73593i	−0.286726	+	0.501120i
$13$	−1.36403	+	2.67705i	−0.378313	+	0.742481i	−0.999140	−	0.0414664i	$-0.986797\pi$
$13$	−1.36403	+	2.67705i	−0.378313	+	0.742481i	0.620827	+	0.783948i	$0.286797\pi$
$14$	−2.25180	+	6.39845i	−0.601819	+	1.71006i
$15$	−1.04817	−	1.97518i	−0.270637	−	0.509989i
$16$	−0.862092	−	3.90600i	−0.215523	−	0.976499i
$17$	0.0551663	−	0.348307i	0.0133798	−	0.0844767i	−0.980095	−	0.198530i	$-0.936383\pi$
$17$	0.0551663	−	0.348307i	0.0133798	−	0.0844767i	0.993475	+	0.114053i	$0.0363834\pi$
$18$	0.975476	+	1.02394i	0.229922	+	0.241344i
$19$	0.0301061	−	0.0218734i	0.00690682	−	0.00501810i	−0.584326	−	0.811519i	$-0.698641\pi$
$19$	0.0301061	−	0.0218734i	0.00690682	−	0.00501810i	0.591233	+	0.806501i	$0.298641\pi$
$20$	4.20713	+	1.51659i	0.940743	+	0.339119i
$21$	3.88036	+	2.81925i	0.846765	+	0.615210i
$22$	0.502103	+	3.75731i	0.107049	+	0.801061i
$23$	−0.826275	−	1.62166i	−0.172290	−	0.338139i	0.788674	−	0.614812i	$-0.210768\pi$
$23$	−0.826275	−	1.62166i	−0.172290	−	0.338139i	−0.960964	+	0.276673i	$0.910768\pi$
$24$	−2.82096	−	0.205443i	−0.575825	−	0.0419358i
$25$	−3.94503	+	3.07193i	−0.789005	+	0.614387i
$26$	−4.24780	−	0.102957i	−0.833062	−	0.0201915i
$27$	0.891007	−	0.453990i	0.171474	−	0.0873705i
$28$	−9.53626	+	1.03986i	−1.80218	+	0.196515i
$29$	3.43571	−	4.72885i	0.637996	−	0.878126i	−0.360511	−	0.932755i	$-0.617398\pi$
$29$	3.43571	−	4.72885i	0.637996	−	0.878126i	0.998507	+	0.0546290i	$0.0173976\pi$
$30$	1.87810	−	2.54416i	0.342892	−	0.464498i
$31$	−3.91117	−	5.38327i	−0.702467	−	0.966864i	−0.999926	−	0.0121289i	$-0.996139\pi$
$31$	−3.91117	−	5.38327i	−0.702467	−	0.966864i	0.297459	−	0.954735i	$-0.403861\pi$
$32$	4.45415	−	3.48720i	0.787390	−	0.616456i
$33$	2.64744	+	0.419313i	0.460859	+	0.0729930i
$34$	0.477906	−	0.142575i	0.0819602	−	0.0244514i
$35$	4.70935	−	9.63581i	0.796025	−	1.62875i
$36$	−0.709460	+	1.86994i	−0.118243	+	0.311656i
$37$	−8.36414	−	4.26174i	−1.37506	−	0.700626i	−0.398759	−	0.917056i	$-0.630559\pi$
$37$	−8.36414	−	4.26174i	−1.37506	−	0.700626i	−0.976298	+	0.216430i	$0.930559\pi$
$38$	0.0462987	+	0.0250216i	0.00751065	+	0.00405903i
$39$	−0.928450	+	2.85748i	−0.148671	+	0.457562i
$40$	0.637856	+	6.29231i	0.100854	+	0.994901i
$41$	−2.14293	−	6.59526i	−0.334669	−	1.03001i	−0.966885	−	0.255214i	$-0.917854\pi$
$41$	−2.14293	−	6.59526i	−0.334669	−	1.03001i	0.632215	−	0.774793i	$-0.282146\pi$
$42$	−1.22314	+	6.67193i	−0.188734	+	1.02950i
$43$	3.96315	−	3.96315i	0.604375	−	0.604375i	−0.337095	−	0.941470i	$-0.609445\pi$
$43$	3.96315	−	3.96315i	0.604375	−	0.604375i	0.941470	+	0.337095i	$0.109445\pi$
$44$	−4.48460	+	2.93723i	−0.676079	+	0.442803i
$45$	−1.34426	−	1.78689i	−0.200390	−	0.266374i
$46$	1.56292	−	2.04506i	0.230440	−	0.301528i
$47$	1.79499	+	11.3331i	0.261827	+	1.65311i	0.671594	+	0.740919i	$0.265610\pi$
$47$	1.79499	+	11.3331i	0.261827	+	1.65311i	−0.409767	+	0.912190i	$0.634390\pi$
$48$	−1.46251	−	3.72304i	−0.211095	−	0.537375i
$49$			16.0054i			2.28648i
$50$	−6.32918	−	3.15300i	−0.895082	−	0.445902i
$51$		−	0.352648i		−	0.0493806i
$52$	−2.46546	−	5.47999i	−0.341898	−	0.759938i
$53$	−0.934134	−	5.89789i	−0.128313	−	0.810138i	−0.964960	−	0.262396i	$-0.915487\pi$
$53$	−0.934134	−	5.89789i	−0.128313	−	0.810138i	0.836647	−	0.547742i	$-0.184513\pi$
$54$	1.12365	+	0.858733i	0.152909	+	0.116859i
$55$	−0.0997595	−	5.99281i	−0.0134516	−	0.808070i
$56$	−7.15578	−	11.5255i	−0.956232	−	1.54016i
$57$	0.0263137	−	0.0263137i	0.00348534	−	0.00348534i
$58$	8.13084	+	1.49059i	1.06763	+	0.195724i
$59$	−3.53381	−	10.8759i	−0.460063	−	1.41593i	−0.865087	−	0.501622i	$-0.832737\pi$
$59$	−3.53381	−	10.8759i	−0.460063	−	1.41593i	0.405024	−	0.914306i	$-0.367263\pi$
$60$	4.39258	+	0.839774i	0.567080	+	0.108414i
$61$	−1.26478	+	3.89259i	−0.161938	+	0.498395i	−0.998798	−	0.0490230i	$-0.984389\pi$
$61$	−1.26478	+	3.89259i	−0.161938	+	0.498395i	0.836859	+	0.547418i	$0.184389\pi$
$62$	4.47410	−	8.27866i	0.568211	−	1.05139i
$63$	4.27362	+	2.17752i	0.538425	+	0.274341i
$64$	7.16999	+	3.54841i	0.896249	+	0.443551i
$65$	6.65219	+	0.940388i	0.825103	+	0.116641i
$66$	1.08369	+	3.63250i	0.133394	+	0.447130i
$67$	8.89404	+	1.40868i	1.08658	+	0.172097i	0.673932	−	0.738793i	$-0.264604\pi$
$67$	8.89404	+	1.40868i	1.08658	+	0.172097i	0.412648	+	0.910891i	$0.364604\pi$
$68$	0.473973	+	0.522296i	0.0574776	+	0.0633377i
$69$	−1.06979	−	1.47243i	−0.128787	−	0.177260i
$70$	15.1671	+	0.115090i	1.81281	+	0.0137559i
$71$	−9.59181	+	13.2020i	−1.13834	+	1.56679i	−0.367172	+	0.930153i	$0.619674\pi$
$71$	−9.59181	+	13.2020i	−1.13834	+	1.56679i	−0.771165	+	0.636635i	$0.780326\pi$
$72$	−2.81836	+	0.238382i	−0.332147	+	0.0280935i
$73$	4.09605	−	2.08704i	0.479406	−	0.244270i	−0.197550	−	0.980293i	$-0.563299\pi$
$73$	4.09605	−	2.08704i	0.479406	−	0.244270i	0.676956	+	0.736023i	$0.263299\pi$
$74$	0.321677	−	13.2717i	0.0373942	−	1.54281i
$75$	−3.41590	+	3.65125i	−0.394434	+	0.421610i
$76$	−0.00360574	+	0.0743391i	−0.000413607	+	0.00852728i
$77$	5.83669	+	11.4552i	0.665153	+	1.30544i
$78$	−4.21161	+	0.562813i	−0.476871	+	0.0637260i
$79$	−1.31184	−	0.953110i	−0.147594	−	0.107233i	0.511538	−	0.859261i	$-0.329076\pi$
$79$	−1.31184	−	0.953110i	−0.147594	−	0.107233i	−0.659132	+	0.752028i	$0.729076\pi$
$80$	−7.63440	+	4.66004i	−0.853552	+	0.521008i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	7.10066	−	6.76460i	0.784137	−	0.747025i
$83$	0.977173	−	6.16963i	0.107259	−	0.677205i	−0.874205	−	0.485557i	$-0.838617\pi$
$83$	0.977173	−	6.16963i	0.107259	−	0.677205i	0.981464	−	0.191648i	$-0.0613832\pi$
$84$	−9.25618	+	2.51886i	−1.00993	+	0.274830i
$85$	−0.776676	+	0.136302i	−0.0842423	+	0.0147840i
$86$	7.47680	+	2.63130i	0.806244	+	0.283741i
$87$	2.65366	−	5.20810i	0.284502	−	0.558367i
$88$	−6.48725	−	3.92346i	−0.691543	−	0.418242i
$89$	−13.2764	−	4.31376i	−1.40729	−	0.457257i	−0.495751	−	0.868465i	$-0.665107\pi$
$89$	−13.2764	−	4.31376i	−1.40729	−	0.457257i	−0.911542	+	0.411207i	$0.865107\pi$
$90$	1.45698	−	2.80664i	0.153579	−	0.295845i
$91$	−13.7056	+	4.45321i	−1.43673	+	0.466823i
$92$	3.56343	+	0.742940i	0.371513	+	0.0774568i
$93$	−4.70515	−	4.70515i	−0.487901	−	0.487901i
$94$	−13.3554	+	9.21725i	−1.37750	+	0.950687i
$95$	−0.0681241	−	0.0477831i	−0.00698939	−	0.00490245i
$96$	3.85379	−	4.14105i	0.393326	−	0.422644i
$97$	8.89748	−	1.40922i	0.903402	−	0.143085i	0.312584	−	0.949890i	$-0.398805\pi$
$97$	8.89748	−	1.40922i	0.903402	−	0.143085i	0.590818	+	0.806805i	$0.298805\pi$
$98$	−20.4110	+	9.78438i	−2.06182	+	0.988372i
$99$	2.68044			0.269394
$100$	0.151754	−	9.99885i	0.0151754	−	0.999885i
$101$	−2.30442			−0.229298			−0.114649	−	0.993406i	$-0.536574\pi$
$101$	−2.30442			−0.229298			−0.114649	+	0.993406i	$0.536574\pi$
$102$	0.449718	−	0.215580i	0.0445288	−	0.0213456i
$103$	4.48812	−	0.710848i	0.442227	−	0.0700419i	0.0686497	−	0.997641i	$-0.478131\pi$
$103$	4.48812	−	0.710848i	0.442227	−	0.0700419i	0.373578	+	0.927599i	$0.378131\pi$
$104$	5.48123	−	6.49412i	0.537479	−	0.636801i
$105$	3.14399	−	10.2539i	0.306822	−	1.00068i
$106$	6.95029	−	4.79676i	0.675072	−	0.465902i
$107$	6.74496	+	6.74496i	0.652060	+	0.652060i	0.953489	−	0.301429i	$-0.0974636\pi$
$107$	6.74496	+	6.74496i	0.652060	+	0.652060i	−0.301429	+	0.953489i	$0.597464\pi$
$108$	−0.408203	+	1.95790i	−0.0392793	+	0.188399i
$109$	0.913063	−	0.296672i	0.0874556	−	0.0284161i	−0.264962	−	0.964259i	$-0.585360\pi$
$109$	0.913063	−	0.296672i	0.0874556	−	0.0284161i	0.352418	+	0.935843i	$0.385360\pi$
$110$	7.58141	−	3.79073i	0.722859	−	0.361432i
$111$	−8.92785	−	2.90083i	−0.847394	−	0.275335i
$112$	10.3236	−	16.1713i	0.975487	−	1.52804i
$113$	0.881591	−	1.73022i	0.0829331	−	0.162765i	−0.845816	−	0.533475i	$-0.820886\pi$
$113$	0.881591	−	1.73022i	0.0829331	−	0.162765i	0.928749	+	0.370710i	$0.120886\pi$
$114$	0.0496430	+	0.0174708i	0.00464949	+	0.00163629i
$115$	−2.82942	+	2.92521i	−0.263845	+	0.272778i
$116$	3.06964	+	11.2802i	0.285009	+	1.04734i
$117$	−0.470012	+	2.96754i	−0.0434526	+	0.274349i
$118$	11.7094	−	11.1552i	1.07794	−	1.02692i
$119$	1.36840	−	0.994203i	0.125441	−	0.0911384i
$120$	1.61434	+	6.11506i	0.147368	+	0.558226i
$121$	−3.08661	−	2.24255i	−0.280601	−	0.203868i
$122$	−5.73725	+	0.766690i	−0.519426	+	0.0694128i
$123$	−3.14827	−	6.17883i	−0.283870	−	0.557127i
$124$	13.2925	+	0.644741i	1.19371	+	0.0578994i
$125$	9.36183	+	6.11197i	0.837347	+	0.546671i
$126$	−0.164359	+	6.78113i	−0.0146423	+	0.604111i
$127$	−14.5964	+	7.43723i	−1.29522	+	0.659948i	−0.959419	−	0.281985i	$-0.909007\pi$
$127$	−14.5964	+	7.43723i	−1.29522	+	0.659948i	−0.335801	+	0.941933i	$0.609007\pi$
$128$	−0.141997	+	11.3128i	−0.0125509	+	0.999921i
$129$	3.29439	−	4.53433i	0.290054	−	0.399226i
$130$	2.86737	+	9.05815i	0.251485	+	0.794453i
$131$	−6.08229	−	8.37156i	−0.531412	−	0.731426i	0.455933	−	0.890014i	$-0.349306\pi$
$131$	−6.08229	−	8.37156i	−0.531412	−	0.731426i	−0.987345	+	0.158588i	$0.949306\pi$
$132$	−3.96991	+	3.60261i	−0.345536	+	0.313567i
$133$	0.176292	+	0.0279219i	0.0152864	+	0.00242113i
$134$	3.64066	+	12.2034i	0.314505	+	1.05421i
$135$	−1.60724	−	1.55460i	−0.138329	−	0.133799i
$136$	−0.376315	+	0.923728i	−0.0322687	+	0.0792090i
$137$	6.62679	+	3.37652i	0.566165	+	0.288475i	0.713550	−	0.700604i	$-0.247086\pi$
$137$	6.62679	+	3.37652i	0.566165	+	0.288475i	−0.147386	+	0.989079i	$0.547086\pi$
$138$	1.22376	−	2.26438i	0.104173	−	0.192757i
$139$	−1.52421	+	4.69104i	−0.129282	+	0.397889i	−0.994657	−	0.103236i	$-0.967080\pi$
$139$	−1.52421	+	4.69104i	−0.129282	+	0.397889i	0.865375	+	0.501125i	$0.167080\pi$
$140$	9.12515	+	19.4123i	0.771216	+	1.64064i
$141$	3.54579	+	10.9128i	0.298609	+	0.919025i
$142$	−22.6996	−	4.16143i	−1.90491	−	0.349219i
$143$	−5.69465	+	5.69465i	−0.476210	+	0.476210i
$144$	−2.02692	−	3.44842i	−0.168910	−	0.287368i
$145$	−12.4960	−	3.83147i	−1.03774	−	0.318186i
$146$	5.16551	+	3.94768i	0.427501	+	0.326712i
$147$	2.50379	+	15.8083i	0.206509	+	1.30385i
$148$	17.1216	−	7.70304i	1.40739	−	0.633186i
$149$		−	4.51885i		−	0.370199i	−0.982720	−	0.185099i	$-0.940739\pi$
$149$		−	4.51885i		−	0.370199i	0.982720	−	0.185099i	$-0.0592607\pi$
$150$	−6.74450	−	2.12408i	−0.550686	−	0.173431i
$151$			23.1084i			1.88053i	0.340438	+	0.940267i	$0.389425\pi$
$151$			23.1084i			1.88053i	−0.340438	+	0.940267i	$0.610575\pi$
$152$	−0.0970060	+	0.0408466i	−0.00786822	+	0.00331310i
$153$	−0.0551663	−	0.348307i	−0.00445993	−	0.0281589i
$154$	−11.0402	+	14.4461i	−0.889647	+	1.16410i
$155$	−8.54409	+	12.1813i	−0.686277	+	0.978422i
$156$	−3.29237	−	5.02684i	−0.263600	−	0.402469i
$157$	−2.93743	+	2.93743i	−0.234433	+	0.234433i	−0.814540	−	0.580107i	$-0.803011\pi$
$157$	−2.93743	+	2.93743i	−0.234433	+	0.234433i	0.580107	+	0.814540i	$0.303011\pi$
$158$	0.413509	−	2.25560i	0.0328970	−	0.179446i
$159$	−1.84527	−	5.67915i	−0.146339	−	0.450386i
$160$	−10.6098	−	6.88708i	−0.838779	−	0.544471i
$161$	2.69758	−	8.30231i	0.212599	−	0.654314i
$162$	1.24415	+	0.672383i	0.0977494	+	0.0528274i
$163$	16.0221	+	8.16368i	1.25495	+	0.639429i	0.949795	−	0.312874i	$-0.101292\pi$
$163$	16.0221	+	8.16368i	1.25495	+	0.639429i	0.305155	+	0.952303i	$0.401292\pi$
$164$	12.9674	+	4.91987i	1.01258	+	0.384177i
$165$	−1.03601	−	5.90342i	−0.0806535	−	0.459581i
$166$	8.46525	−	2.52546i	0.657031	−	0.196014i
$167$	−10.4908	−	1.66158i	−0.811801	−	0.128577i	−0.263287	−	0.964718i	$-0.584807\pi$
$167$	−10.4908	−	1.66158i	−0.811801	−	0.128577i	−0.548515	+	0.836141i	$0.684807\pi$
$168$	−8.87067	−	10.2642i	−0.684387	−	0.791901i
$169$	2.33516	+	3.21407i	0.179627	+	0.247236i
$170$	−0.648617	−	0.907141i	−0.0497466	−	0.0695745i
$171$	0.0218734	−	0.0301061i	0.00167270	−	0.00230227i
$172$	1.21511	+	11.1434i	0.0926513	+	0.849679i
$173$	−4.09233	+	2.08515i	−0.311134	+	0.158531i	−0.602584	−	0.798055i	$-0.705862\pi$
$173$	−4.09233	+	2.08515i	−0.311134	+	0.158531i	0.291450	+	0.956586i	$0.405862\pi$
$174$	8.26391	+	0.200298i	0.626486	+	0.0151846i
$175$	−23.7984	−	2.96114i	−1.79899	−	0.223841i
$176$	1.03765	−	10.6714i	0.0782160	−	0.804388i
$177$	−5.19167	−	10.1892i	−0.390230	−	0.765870i
$178$	−2.61493	−	19.5679i	−0.195998	−	1.46668i
$179$	9.71609	+	7.05915i	0.726214	+	0.527626i	0.888364	−	0.459141i	$-0.151843\pi$
$179$	9.71609	+	7.05915i	0.726214	+	0.527626i	−0.162149	+	0.986766i	$0.551843\pi$
$180$	4.46987	+	0.142284i	0.333165	+	0.0106052i
$181$	−15.7632	+	11.4527i	−1.17167	+	0.851269i	−0.991208	−	0.132313i	$-0.957760\pi$
$181$	−15.7632	+	11.4527i	−1.17167	+	0.851269i	−0.180463	+	0.983582i	$0.557760\pi$
$182$	−14.0575	−	14.7559i	−1.04201	−	1.09378i
$183$	−0.640272	+	4.04252i	−0.0473303	+	0.298832i
$184$	1.23095	+	4.99848i	0.0907468	+	0.368492i
$185$	−2.93813	+	20.7840i	−0.216016	+	1.52807i
$186$	3.12395	−	8.87664i	0.229059	−	0.650867i
$187$	0.429135	−	0.842225i	0.0313815	−	0.0615896i
$188$	−19.9188	−	11.3969i	−1.45273	−	0.831207i
$189$	4.56164	+	1.48217i	0.331810	+	0.107812i
$190$	0.0192904	−	0.116087i	0.00139947	−	0.00842182i
$191$	−7.51089	+	2.44043i	−0.543469	+	0.176584i	−0.567870	−	0.823119i	$-0.692232\pi$
$191$	−7.51089	+	2.44043i	−0.543469	+	0.176584i	0.0244009	+	0.999702i	$0.492232\pi$
$192$	7.63681	+	2.38309i	0.551139	+	0.171985i
$193$	12.4322	+	12.4322i	0.894893	+	0.894893i	0.994979	−	0.100086i	$-0.0319118\pi$
$193$	12.4322	+	12.4322i	0.894893	+	0.894893i	−0.100086	+	0.994979i	$0.531912\pi$
$194$	7.23632	+	10.4851i	0.519537	+	0.752788i
$195$	6.71740	−	0.111821i	0.481043	−	0.00800770i
$196$	−24.9553	−	20.0480i	−1.78252	−	1.43200i
$197$	−5.51782	+	0.873937i	−0.393128	+	0.0622654i	−0.349869	−	0.936798i	$-0.613774\pi$
$197$	−5.51782	+	0.873937i	−0.393128	+	0.0622654i	−0.0432589	+	0.999064i	$0.513774\pi$
$198$	1.63860	+	3.41826i	0.116450	+	0.242925i
$199$	18.0700			1.28095			0.640476	−	0.767978i	$-0.278737\pi$
$199$	18.0700			1.28095			0.640476	+	0.767978i	$0.278737\pi$
$200$	12.8439	−	5.91896i	0.908201	−	0.418533i
$201$	9.00490			0.635157
$202$	−1.40873	−	2.93873i	−0.0991181	−	0.206768i
$203$	27.6906	−	4.38576i	1.94350	−	0.307820i
$204$	0.549842	+	0.441720i	0.0384967	+	0.0309266i
$205$	−12.3915	+	9.32197i	−0.865459	+	0.651074i
$206$	3.65019	+	5.28896i	0.254321	+	0.368500i
$207$	−1.28695	−	1.28695i	−0.0894495	−	0.0894495i
$208$	11.6325	+	3.02002i	0.806567	+	0.209401i
$209$	0.0948657	−	0.0308237i	0.00656200	−	0.00213212i
$210$	14.9984	−	2.25898i	1.03499	−	0.155885i
$211$	7.52169	+	2.44395i	0.517815	+	0.168248i	0.556253	−	0.831013i	$-0.312238\pi$
$211$	7.52169	+	2.44395i	0.517815	+	0.168248i	−0.0384386	+	0.999261i	$0.512238\pi$
$212$	10.3660	+	5.93109i	0.711937	+	0.407349i
$213$	−7.40847	+	14.5399i	−0.507620	+	0.996260i
$214$	−4.47826	+	12.7249i	−0.306127	+	0.869856i
$215$	−11.2598	−	5.50303i	−0.767910	−	0.375303i
$216$	−2.74637	+	0.676336i	−0.186867	+	0.0460188i
$217$	4.99270	−	31.5227i	0.338927	−	2.13990i
$218$	0.936507	+	0.983032i	0.0634283	+	0.0665794i
$219$	3.71913	−	2.70211i	0.251316	−	0.182592i
$220$	9.46883	+	7.35092i	0.638388	+	0.495599i
$221$	0.857187	+	0.622783i	0.0576607	+	0.0418929i
$222$	−1.75844	−	13.1587i	−0.118019	−	0.883152i
$223$	−9.58505	−	18.8117i	−0.641862	−	1.25973i	−0.951142	−	0.308754i	$-0.900088\pi$
$223$	−9.58505	−	18.8117i	−0.641862	−	1.25973i	0.309280	−	0.950971i	$-0.399912\pi$
$224$	26.9336	+	3.27947i	1.79957	+	0.219119i
$225$	−2.80266	+	4.14066i	−0.186844	+	0.276044i
$226$	2.74541	+	0.0665426i	0.182622	+	0.00442634i
$227$	3.75568	−	1.91361i	0.249273	−	0.127011i	−0.324890	−	0.945752i	$-0.605327\pi$
$227$	3.75568	−	1.91361i	0.249273	−	0.127011i	0.574163	+	0.818741i	$0.305327\pi$
$228$	0.00806785	+	0.0739879i	0.000534306	+	0.00489997i
$229$	9.56819	−	13.1695i	0.632284	−	0.870264i	−0.365891	−	0.930658i	$-0.619236\pi$
$229$	9.56819	−	13.1695i	0.632284	−	0.870264i	0.998175	+	0.0603935i	$0.0192355\pi$
$230$	−5.46009	−	1.82001i	−0.360028	−	0.120008i
$231$	7.55682	+	10.4011i	0.497202	+	0.684340i
$232$	−12.5086	+	10.8104i	−0.821231	+	0.709735i
$233$	−3.96847	−	0.628543i	−0.259983	−	0.0411772i	0.0250823	−	0.999685i	$-0.492015\pi$
$233$	−3.96847	−	0.628543i	−0.259983	−	0.0411772i	−0.285065	+	0.958508i	$0.592015\pi$
$234$	−4.07171	+	1.21472i	−0.266176	+	0.0794090i
$235$	22.6640	−	12.0272i	1.47844	−	0.784567i
$236$	21.3839	+	8.11313i	1.39198	+	0.528120i
$237$	−1.44479	−	0.736158i	−0.0938493	−	0.0478186i
$238$	2.10440	+	1.13730i	0.136408	+	0.0737199i
$239$	−0.935034	+	2.87774i	−0.0604823	+	0.186145i	−0.976733	−	0.214461i	$-0.931201\pi$
$239$	−0.935034	+	2.87774i	−0.0604823	+	0.186145i	0.916250	+	0.400606i	$0.131201\pi$
$240$	−6.81142	+	5.79695i	−0.439675	+	0.374191i
$241$	−5.19805	−	15.9980i	−0.334836	−	1.03052i	−0.966803	−	0.255524i	$-0.917752\pi$
$241$	−5.19805	−	15.9980i	−0.334836	−	1.03052i	0.631967	−	0.774995i	$-0.282248\pi$
$242$	0.972938	−	5.30715i	0.0625428	−	0.341156i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−4.48502	−	6.84780i	−0.287124	−	0.438385i
$245$	33.8487	−	11.6244i	2.16251	−	0.742658i
$246$	5.95503	−	7.79211i	0.379679	−	0.496807i
$247$	0.0174907	+	0.110432i	0.00111290	+	0.00702660i
$248$	7.30377	+	17.3456i	0.463790	+	1.10145i
$249$		−	6.24653i		−	0.395858i
$250$	−2.07129	+	15.6751i	−0.131000	+	0.991382i
$251$		−	5.01058i		−	0.316265i	−0.987418	−	0.158132i	$-0.949453\pi$
$251$		−	5.01058i		−	0.316265i	0.987418	−	0.158132i	$-0.0505473\pi$
$252$	−8.74818	+	3.93583i	−0.551084	+	0.247934i
$253$	−0.763160	−	4.81841i	−0.0479795	−	0.302931i
$254$	−18.4075	−	14.0677i	−1.15499	−	0.882685i
$255$	−0.745792	+	0.256123i	−0.0467033	+	0.0160390i
$256$	−14.5136	+	6.73465i	−0.907100	+	0.420916i
$257$	−8.87423	+	8.87423i	−0.553559	+	0.553559i	−0.927466	−	0.373907i	$-0.878018\pi$
$257$	−8.87423	+	8.87423i	−0.553559	+	0.553559i	0.373907	+	0.927466i	$0.378018\pi$
$258$	7.79637	+	1.42928i	0.485381	+	0.0889829i
$259$	−13.9135	−	42.8215i	−0.864545	−	2.66080i
$260$	−9.79863	+	9.19406i	−0.607685	+	0.570191i
$261$	1.80626	−	5.55910i	0.111805	−	0.344100i
$262$	6.95770	−	12.8742i	0.429848	−	0.795370i
$263$	13.9737	+	7.11993i	0.861652	+	0.439034i	0.828217	−	0.560407i	$-0.189355\pi$
$263$	13.9737	+	7.11993i	0.861652	+	0.439034i	0.0334351	+	0.999441i	$0.489355\pi$
$264$	−7.02114	−	2.86032i	−0.432122	−	0.176041i
$265$	−11.7946	+	6.25908i	−0.724537	+	0.384492i
$266$	0.0721628	+	0.241887i	0.00442459	+	0.0148311i
$267$	−13.7877	−	2.18376i	−0.843796	−	0.133644i
$268$	−13.3369	+	12.1029i	−0.814679	+	0.739305i
$269$	−6.69890	−	9.22024i	−0.408439	−	0.562168i	0.554398	−	0.832252i	$-0.312949\pi$
$269$	−6.69890	−	9.22024i	−0.408439	−	0.562168i	−0.962837	+	0.270084i	$0.912949\pi$
$270$	0.999990	−	3.00000i	0.0608575	−	0.182574i
$271$	14.5904	−	20.0820i	0.886305	−	1.21989i	−0.0883300	−	0.996091i	$-0.528153\pi$
$271$	14.5904	−	20.0820i	0.886305	−	1.21989i	0.974635	−	0.223802i	$-0.0718470\pi$
$272$	−1.40804	+	0.0847928i	−0.0853751	+	0.00514132i
$273$	−12.8402	+	6.54241i	−0.777124	+	0.395965i
$274$	−0.254860	+	10.5150i	−0.0153966	+	0.635235i
$275$	−12.6013	+	4.56345i	−0.759889	+	0.275186i
$276$	3.63578	+	0.176350i	0.218848	+	0.0106150i
$277$	−6.27732	−	12.3199i	−0.377168	−	0.740233i	0.621914	−	0.783086i	$-0.286355\pi$
$277$	−6.27732	−	12.3199i	−0.377168	−	0.740233i	−0.999081	+	0.0428524i	$0.986355\pi$
$278$	−6.91408	+	0.923955i	−0.414679	+	0.0554151i
$279$	−5.38327	−	3.91117i	−0.322288	−	0.234156i
$280$	−19.1774	+	23.5041i	−1.14607	+	1.40464i
$281$	−0.275686	+	0.200297i	−0.0164460	+	0.0119487i	−0.595978	−	0.803001i	$-0.703235\pi$
$281$	−0.275686	+	0.200297i	−0.0164460	+	0.0119487i	0.579532	+	0.814950i	$0.303235\pi$
$282$	−11.7491	+	11.1930i	−0.699648	+	0.666534i
$283$	−1.04683	+	6.60944i	−0.0622278	+	0.392891i	0.936841	+	0.349754i	$0.113735\pi$
$283$	−1.04683	+	6.60944i	−0.0622278	+	0.392891i	−0.999069	+	0.0431363i	$0.986265\pi$
$284$	−8.56980	−	31.4919i	−0.508524	−	1.86870i
$285$	−0.0747604	−	0.0365379i	−0.00442842	−	0.00216432i
$286$	−10.7434	−	3.78092i	−0.635271	−	0.223570i
$287$	15.1004	−	29.6361i	0.891346	−	1.74936i
$288$	3.15854	−	4.69293i	0.186119	−	0.276534i
$289$	16.0497	+	5.21486i	0.944099	+	0.306756i
$290$	−2.75294	−	18.2779i	−0.161658	−	1.07332i
$291$	8.56748	−	2.78374i	0.502235	−	0.163186i
$292$	−1.87655	+	9.00066i	−0.109817	+	0.526724i
$293$	8.69276	+	8.69276i	0.507837	+	0.507837i	0.913862	−	0.406025i	$-0.133086\pi$
$293$	8.69276	+	8.69276i	0.507837	+	0.507837i	−0.406025	+	0.913862i	$0.633086\pi$
$294$	−18.6291	+	12.8569i	−1.08647	+	0.749830i
$295$	−20.4342	+	15.3724i	−1.18973	+	0.895017i
$296$	20.2901	+	17.1255i	1.17934	+	0.995397i
$297$	2.64744	−	0.419313i	0.153620	−	0.0243310i
$298$	5.76272	−	2.76246i	0.333825	−	0.160025i
$299$	5.46832			0.316241
$300$	−1.41428	−	9.89949i	−0.0816534	−	0.571547i
$301$	26.8825			1.54948
$302$	−29.4692	+	14.1266i	−1.69576	+	0.812894i
$303$	−2.27604	+	0.360490i	−0.130755	+	0.0207096i
$304$	−0.111392	−	0.0987376i	−0.00638875	−	0.00566299i
$305$	9.15076	−	0.152328i	0.523971	−	0.00872230i
$306$	0.410457	−	0.283278i	0.0234643	−	0.0161939i
$307$	−8.92000	−	8.92000i	−0.509091	−	0.509091i	0.405156	−	0.914248i	$-0.367217\pi$
$307$	−8.92000	−	8.92000i	−0.509091	−	0.509091i	−0.914248	+	0.405156i	$0.867217\pi$
$308$	−25.1716	−	5.24803i	−1.43428	−	0.299034i
$309$	4.32166	−	1.40419i	0.245851	−	0.0798817i
$310$	−20.7574	−	3.44931i	−1.17894	−	0.195908i
$311$	2.46111	+	0.799664i	0.139557	+	0.0453448i	0.377963	−	0.925821i	$-0.376625\pi$
$311$	2.46111	+	0.799664i	0.139557	+	0.0453448i	−0.238406	+	0.971166i	$0.576625\pi$
$312$	4.39784	−	7.27162i	0.248979	−	0.411675i
$313$	−3.76802	+	7.39517i	−0.212981	+	0.417999i	−0.972638	−	0.232325i	$-0.925367\pi$
$313$	−3.76802	+	7.39517i	−0.212981	+	0.417999i	0.759657	+	0.650324i	$0.225367\pi$
$314$	−5.54170	−	1.95029i	−0.312736	−	0.110061i
$315$	1.50122	−	10.6195i	0.0845844	−	0.598339i
$316$	3.12926	−	0.851556i	0.176035	−	0.0479038i
$317$	−4.41319	+	27.8638i	−0.247869	+	1.56498i	0.478754	+	0.877949i	$0.341088\pi$
$317$	−4.41319	+	27.8638i	−0.247869	+	1.56498i	−0.726624	+	0.687036i	$0.758912\pi$
$318$	6.11435	−	5.82497i	0.342876	−	0.326648i
$319$	12.6754	−	9.20921i	0.709686	−	0.515617i
$320$	2.29684	−	17.7405i	0.128397	−	0.991723i
$321$	7.71706	+	5.60677i	0.430724	+	0.312939i
$322$	12.2367	−	1.63523i	0.681924	−	0.0911280i
$323$	−0.00595780	−	0.0116928i	−0.000331501	−	0.000650607i
$324$	−0.0968940	+	1.99765i	−0.00538300	+	0.110981i
$325$	−2.84261	−	14.7513i	−0.157680	−	0.818252i
$326$	−0.616196	+	25.4230i	−0.0341279	+	1.40805i
$327$	0.855412	−	0.435854i	0.0473044	−	0.0241028i
$328$	1.65310	+	19.5444i	0.0912770	+	1.07916i
$329$	−32.3492	+	44.5249i	−1.78347	+	2.45474i
$330$	6.89507	−	4.93006i	0.379561	−	0.271391i
$331$	1.20304	+	1.65584i	0.0661251	+	0.0910134i	0.840799	−	0.541348i	$-0.182086\pi$
$331$	1.20304	+	1.65584i	0.0661251	+	0.0910134i	−0.774674	+	0.632361i	$0.782086\pi$
$332$	8.39558	+	9.25154i	0.460768	+	0.507744i
$333$	−9.27172	−	1.46850i	−0.508087	−	0.0804731i
$334$	−4.29427	−	14.3942i	−0.234972	−	0.787618i
$335$	−3.48048	−	19.8325i	−0.190159	−	1.08356i
$336$	7.66674	−	17.5871i	0.418255	−	0.959456i
$337$	11.0019	+	5.60576i	0.599313	+	0.305365i	0.727202	−	0.686423i	$-0.240820\pi$
$337$	11.0019	+	5.60576i	0.599313	+	0.305365i	−0.127890	+	0.991788i	$0.540820\pi$
$338$	−2.67125	+	4.94275i	−0.145297	+	0.268850i
$339$	0.600071	−	1.84683i	0.0325914	−	0.100306i
$340$	0.760329	−	1.38171i	0.0412346	−	0.0749336i
$341$	−5.51158	−	16.9629i	−0.298469	−	0.918593i
$342$	0.0517648	+	0.00948983i	0.00279912	+	0.000513151i
$343$	−30.5423	+	30.5423i	−1.64913	+	1.64913i
$344$	−13.4680	+	8.36177i	−0.726144	+	0.450836i
$345$	−2.33698	+	3.33182i	−0.125819	+	0.179379i
$346$	−5.16082	−	3.94410i	−0.277448	−	0.212036i
$347$	2.22959	+	14.0770i	0.119690	+	0.755695i	0.972402	+	0.233313i	$0.0749567\pi$
$347$	2.22959	+	14.0770i	0.119690	+	0.755695i	−0.852711	+	0.522382i	$0.825043\pi$
$348$	4.79645	+	10.6611i	0.257117	+	0.571494i
$349$		−	18.7834i		−	1.00545i	−0.864445	−	0.502727i	$-0.832330\pi$
$349$		−	18.7834i		−	1.00545i	0.864445	−	0.502727i	$-0.167670\pi$
$350$	−10.7722	−	32.1594i	−0.575799	−	1.71899i
$351$			3.00453i			0.160370i
$352$	14.2432	−	5.20036i	0.759164	−	0.277180i
$353$	−1.30877	−	8.26323i	−0.0696586	−	0.439807i	−0.997726	−	0.0673957i	$-0.978531\pi$
$353$	−1.30877	−	8.26323i	−0.0696586	−	0.439807i	0.928068	−	0.372412i	$-0.121469\pi$
$354$	9.82016	−	12.8496i	0.521936	−	0.682949i
$355$	34.8863	+	10.6967i	1.85158	+	0.567720i
$356$	23.3556	−	15.2970i	1.23785	−	0.810737i
$357$	1.19603	−	1.19603i	0.0633005	−	0.0633005i
$358$	−3.06263	+	16.7059i	−0.161865	+	0.882936i
$359$	−6.27998	−	19.3278i	−0.331445	−	1.02008i	−0.968447	−	0.249220i	$-0.919826\pi$
$359$	−6.27998	−	19.3278i	−0.331445	−	1.02008i	0.637002	−	0.770862i	$-0.280174\pi$
$360$	2.55107	+	5.78723i	0.134453	+	0.305014i
$361$	−5.87089	+	18.0688i	−0.308994	+	0.950987i
$362$	−24.2415	−	13.1010i	−1.27410	−	0.688573i
$363$	−3.39942	−	1.73209i	−0.178423	−	0.0909112i
$364$	10.2240	−	26.9475i	0.535881	−	1.41243i
$365$	−7.38863	−	7.14667i	−0.386738	−	0.374074i
$366$	−5.54668	+	1.65475i	−0.289929	+	0.0864954i
$367$	29.5302	+	4.67713i	1.54147	+	0.244144i	0.868560	−	0.495584i	$-0.165046\pi$
$367$	29.5302	+	4.67713i	1.54147	+	0.244144i	0.672905	+	0.739729i	$0.265046\pi$
$368$	−5.62186	+	4.62544i	−0.293059	+	0.241118i
$369$	−4.07610	−	5.61026i	−0.212193	−	0.292059i
$370$	−28.3011	+	8.95876i	−1.47131	+	0.465744i
$371$	16.8349	−	23.1712i	0.874024	−	1.20299i
$372$	13.2298	−	1.44261i	0.685931	−	0.0747958i
$373$	22.6709	−	11.5514i	1.17386	−	0.598110i	0.245354	−	0.969434i	$-0.421096\pi$
$373$	22.6709	−	11.5514i	1.17386	−	0.598110i	0.928504	+	0.371324i	$0.121096\pi$
$374$	1.33639	+	0.0323912i	0.0691033	+	0.00167491i
$375$	10.2027	+	4.57221i	0.526865	+	0.236108i
$376$	2.35733	−	32.3688i	0.121570	−	1.66929i
$377$	7.97299	+	15.6479i	0.410630	+	0.805907i
$378$	0.898467	+	6.72336i	0.0462122	+	0.345812i
$379$	7.12172	+	5.17423i	0.365818	+	0.265783i	0.755475	−	0.655178i	$-0.227406\pi$
$379$	7.12172	+	5.17423i	0.365818	+	0.265783i	−0.389656	+	0.920960i	$0.627406\pi$
$380$	0.159833	−	0.0463657i	0.00819928	−	0.00237851i
$381$	−13.2532	+	9.62905i	−0.678984	+	0.493311i
$382$	−7.70374	−	8.08645i	−0.394157	−	0.413739i
$383$	−2.70392	+	17.0719i	−0.138164	+	0.872332i	0.817083	+	0.576521i	$0.195590\pi$
$383$	−2.70392	+	17.0719i	−0.138164	+	0.872332i	−0.955246	+	0.295811i	$0.904410\pi$
$384$	1.62947	+	11.1958i	0.0831533	+	0.571331i
$385$	19.9866	−	20.6633i	1.01861	−	1.05310i
$386$	−8.25429	+	23.4544i	−0.420132	+	1.19380i
$387$	2.54450	−	4.99386i	0.129344	−	0.253852i
$388$	−8.94756	+	15.6379i	−0.454244	+	0.793896i
$389$	−1.60757	−	0.522332i	−0.0815072	−	0.0264833i	0.267980	−	0.963425i	$-0.413644\pi$
$389$	−1.60757	−	0.522332i	−0.0815072	−	0.0264833i	−0.349487	+	0.936941i	$0.613644\pi$
$390$	4.24907	+	8.49808i	0.215160	+	0.430317i
$391$	−0.610416	+	0.198336i	−0.0308701	+	0.0100303i
$392$	10.3108	−	44.0802i	0.520774	−	2.22639i
$393$	−7.31701	−	7.31701i	−0.369094	−	0.369094i
$394$	−4.48764	−	6.50240i	−0.226084	−	0.327586i
$395$	−1.06290	+	3.46655i	−0.0534801	+	0.174421i
$396$	−3.35746	+	4.17929i	−0.168719	+	0.210017i
$397$	24.6975	−	3.91170i	1.23953	−	0.196322i	0.497962	−	0.867199i	$-0.334082\pi$
$397$	24.6975	−	3.91170i	1.23953	−	0.196322i	0.741569	+	0.670876i	$0.234082\pi$
$398$	11.0466	+	23.0440i	0.553714	+	1.15509i
$399$	0.178489			0.00893564
$400$	15.3999	+	12.7610i	0.769997	+	0.638048i
$401$	−34.9493			−1.74529			−0.872644	−	0.488358i	$-0.837596\pi$
$401$	−34.9493			−1.74529			−0.872644	+	0.488358i	$0.837596\pi$
$402$	5.50487	+	11.4836i	0.274558	+	0.572750i
$403$	19.7463	−	3.12750i	0.983631	−	0.155792i
$404$	2.88646	−	3.59300i	0.143607	−	0.178759i
$405$	−1.83064	−	1.28404i	−0.0909654	−	0.0638043i
$406$	22.5208	+	32.6317i	1.11769	+	1.61948i
$407$	−17.7923	−	17.7923i	−0.881930	−	0.881930i
$408$	−0.227179	+	0.971224i	−0.0112470	+	0.0480828i
$409$	−9.56258	+	3.10707i	−0.472839	+	0.153635i	−0.535736	−	0.844385i	$-0.679966\pi$
$409$	−9.56258	+	3.10707i	−0.472839	+	0.153635i	0.0628973	+	0.998020i	$0.479966\pi$
$410$	−19.4631	−	10.1037i	−0.961213	−	0.498986i
$411$	7.07340	+	2.29829i	0.348905	+	0.113366i
$412$	−4.51338	+	7.88818i	−0.222358	+	0.388623i
$413$	24.9013	−	48.8716i	1.22531	−	2.40481i
$414$	0.854462	−	2.42794i	0.0419945	−	0.119327i
$415$	−13.7574	+	2.41434i	−0.675326	+	0.118515i
$416$	3.25984	+	16.6806i	0.159827	+	0.817835i
$417$	−0.771606	+	4.87173i	−0.0377857	+	0.238570i
$418$	0.0973015	+	0.102135i	0.00475917	+	0.00499561i
$419$	−8.26609	+	6.00566i	−0.403825	+	0.293396i	−0.771097	−	0.636718i	$-0.780292\pi$
$419$	−8.26609	+	6.00566i	−0.403825	+	0.293396i	0.367272	+	0.930113i	$0.380292\pi$
$420$	12.0496	+	17.7459i	0.587959	+	0.865909i
$421$	−20.6955	−	15.0362i	−1.00864	−	0.732817i	−0.0447139	−	0.999000i	$-0.514238\pi$
$421$	−20.6955	−	15.0362i	−1.00864	−	0.732817i	−0.963923	+	0.266182i	$0.914238\pi$
$422$	1.48148	+	11.0861i	0.0721175	+	0.539665i
$423$	5.20928	+	10.2238i	0.253284	+	0.497097i
$424$	−1.22678	+	16.8451i	−0.0595778	+	0.818070i
$425$	0.852342	+	1.54355i	0.0413447	+	0.0748729i
$426$	−23.0711	−	0.559192i	−1.11780	−	0.0270929i
$427$	−17.4915	+	8.91238i	−0.846474	+	0.431300i
$428$	−18.9652	+	2.06802i	−0.916718	+	0.0999615i
$429$	−4.73370	+	6.51538i	−0.228545	+	0.314565i
$430$	0.134486	−	17.7232i	0.00648551	−	0.854691i
$431$	17.6050	+	24.2312i	0.848003	+	1.16718i	0.984299	+	0.176508i	$0.0564801\pi$
$431$	17.6050	+	24.2312i	0.848003	+	1.16718i	−0.136296	+	0.990668i	$0.543520\pi$
$432$	−2.54141	−	3.08889i	−0.122274	−	0.148614i
$433$	−18.5450	−	2.93724i	−0.891215	−	0.141155i	−0.305999	−	0.952032i	$-0.598990\pi$
$433$	−18.5450	−	2.93724i	−0.891215	−	0.141155i	−0.585216	+	0.810877i	$0.698990\pi$
$434$	43.2517	−	12.9034i	2.07615	−	0.619383i
$435$	−12.9416	−	1.82949i	−0.620500	−	0.0877171i
$436$	−0.681118	+	1.79524i	−0.0326196	+	0.0859762i
$437$	−0.0603471	−	0.0307484i	−0.00288679	−	0.00147089i
$438$	5.71947	+	3.09101i	0.273287	+	0.147694i
$439$	−10.6931	+	32.9099i	−0.510353	+	1.57070i	0.281229	+	0.959641i	$0.409258\pi$
$439$	−10.6931	+	32.9099i	−0.510353	+	1.57070i	−0.791582	+	0.611063i	$0.790742\pi$
$440$	−3.58587	+	16.5690i	−0.170950	+	0.789895i
$441$	4.94593	+	15.2220i	0.235521	+	0.724858i
$442$	−0.270196	+	1.47386i	−0.0128519	+	0.0701042i
$443$	−16.6791	+	16.6791i	−0.792447	+	0.792447i	−0.981891	−	0.189445i	$-0.939331\pi$
$443$	−16.6791	+	16.6791i	−0.792447	+	0.792447i	0.189445	+	0.981891i	$0.439331\pi$
$444$	15.7058	−	10.2866i	0.745363	−	0.488181i
$445$	0.519543	+	31.2103i	0.0246287	+	1.47951i
$446$	18.1303	−	23.7234i	0.858495	−	1.12333i
$447$	−0.706904	−	4.46322i	−0.0334354	−	0.211103i
$448$	12.2828	+	36.3521i	0.580309	+	1.71748i
$449$		−	17.2460i		−	0.813887i	−0.913453	−	0.406943i	$-0.866595\pi$
$449$		−	17.2460i		−	0.813887i	0.913453	−	0.406943i	$-0.133405\pi$
$450$	−6.99374	−	1.04286i	−0.329688	−	0.0491609i
$451$		−	18.5879i		−	0.875272i
$452$	1.59346	+	3.54180i	0.0749502	+	0.166592i
$453$	3.61495	+	22.8239i	0.169845	+	1.07236i
$454$	4.73627	+	3.61964i	0.222284	+	0.169878i
$455$	19.3719	+	25.7507i	0.908170	+	1.20721i
$456$	−0.0894218	+	0.0555188i	−0.00418756	+	0.00259991i
$457$	14.6247	−	14.6247i	0.684114	−	0.684114i	−0.276811	−	0.960925i	$-0.589277\pi$
$457$	14.6247	−	14.6247i	0.684114	−	0.684114i	0.960925	+	0.276811i	$0.0892774\pi$
$458$	22.6437	+	4.15119i	1.05807	+	0.193972i
$459$	−0.108974	−	0.335388i	−0.00508648	−	0.0156546i
$460$	−1.01687	−	8.07564i	−0.0474117	−	0.376529i
$461$	2.25667	−	6.94532i	0.105104	−	0.323476i	−0.884651	−	0.466254i	$-0.845603\pi$
$461$	2.25667	−	6.94532i	0.105104	−	0.323476i	0.989755	+	0.142778i	$0.0456034\pi$
$462$	−8.64445	+	15.9953i	−0.402176	+	0.744168i
$463$	−4.74359	−	2.41698i	−0.220453	−	0.112327i	0.340276	−	0.940325i	$-0.389479\pi$
$463$	−4.74359	−	2.41698i	−0.220453	−	0.112327i	−0.560730	+	0.827999i	$0.689479\pi$
$464$	−21.4328	−	9.34317i	−0.994992	−	0.433746i
$465$	−6.53333	+	13.3679i	−0.302976	+	0.619920i
$466$	−1.62444	−	5.44507i	−0.0752508	−	0.252238i
$467$	−3.91689	−	0.620374i	−0.181252	−	0.0287075i	0.0651486	−	0.997876i	$-0.479248\pi$
$467$	−3.91689	−	0.620374i	−0.181252	−	0.0287075i	−0.246401	+	0.969168i	$0.579248\pi$
$468$	−4.03820	−	4.44991i	−0.186666	−	0.205697i
$469$	25.3871	+	34.9423i	1.17227	+	1.61348i
$470$	29.1927	+	21.5501i	1.34656	+	0.994032i
$471$	−2.44175	+	3.36079i	−0.112510	+	0.154857i
$472$	2.72605	+	32.2298i	0.125476	+	1.48350i
$473$	13.3857	−	6.82037i	0.615477	−	0.313601i
$474$	0.0555653	−	2.29251i	0.00255220	−	0.105299i
$475$	−0.0515759	+	0.178775i	−0.00236646	+	0.00820277i
$476$	−0.163890	+	3.37891i	−0.00751190	+	0.154872i
$477$	−2.71096	−	5.32057i	−0.124126	−	0.243612i
$478$	−4.24147	+	0.566803i	−0.194000	+	0.0259250i
$479$	7.13723	+	5.18550i	0.326108	+	0.236932i	0.738778	−	0.673949i	$-0.235403\pi$
$479$	7.13723	+	5.18550i	0.326108	+	0.236932i	−0.412669	+	0.910881i	$0.635403\pi$
$480$	−11.5566	−	5.14255i	−0.527483	−	0.234724i
$481$	22.8178	−	16.5781i	1.04040	−	0.755898i
$482$	17.2239	−	16.4087i	0.784527	−	0.747397i
$483$	1.36560	−	8.62209i	0.0621372	−	0.392319i
$484$	7.36277	−	2.00361i	0.334671	−	0.0910731i
$485$	−9.44236	−	17.7932i	−0.428755	−	0.807946i
$486$	1.33401	+	0.469478i	0.0605121	+	0.0212959i
$487$	−3.40456	+	6.68183i	−0.154275	+	0.302782i	−0.955189	−	0.295998i	$-0.904348\pi$
$487$	−3.40456	+	6.68183i	−0.154275	+	0.302782i	0.800913	+	0.598780i	$0.204348\pi$
$488$	5.99095	−	9.90575i	0.271198	−	0.448412i
$489$	17.1019	+	5.55676i	0.773377	+	0.251285i
$490$	35.5165	+	36.0596i	1.60447	+	1.62901i
$491$	22.0491	−	7.16420i	0.995063	−	0.323316i	0.234172	−	0.972195i	$-0.424762\pi$
$491$	22.0491	−	7.16420i	0.995063	−	0.323316i	0.760891	+	0.648880i	$0.224762\pi$
$492$	13.5774	+	2.83075i	0.612116	+	0.127620i
$493$	−1.45755	−	1.45755i	−0.0656450	−	0.0656450i
$494$	−0.130137	+	0.0898141i	−0.00585513	+	0.00404093i
$495$	−1.94676	−	5.66867i	−0.0875002	−	0.254788i
$496$	−17.6552	+	19.9179i	−0.792743	+	0.894340i
$497$	−77.3065	+	12.2442i	−3.46767	+	0.549225i
$498$	7.96596	−	3.81862i	0.356963	−	0.171117i
$499$	−30.1851			−1.35127			−0.675636	−	0.737235i	$-0.736131\pi$
$499$	−30.1851			−1.35127			−0.675636	+	0.737235i	$0.736131\pi$
$500$	−21.2561	+	6.94106i	−0.950602	+	0.310414i
$501$	−10.6216			−0.474536
$502$	6.38979	−	3.06306i	0.285190	−	0.136711i
$503$	−26.9819	+	4.27351i	−1.20306	+	0.190546i	−0.725607	−	0.688110i	$-0.758441\pi$
$503$	−26.9819	+	4.27351i	−1.20306	+	0.190546i	−0.477455	+	0.878656i	$0.658441\pi$
$504$	−10.3671	−	8.75017i	−0.461789	−	0.389763i
$505$	1.67366	+	4.87345i	0.0744768	+	0.216866i
$506$	5.67819	−	3.91881i	0.252426	−	0.174212i
$507$	2.80920	+	2.80920i	0.124761	+	0.124761i
$508$	6.68714	−	32.0741i	0.296694	−	1.42306i
$509$	−29.0971	+	9.45423i	−1.28971	+	0.419051i	−0.871989	−	0.489526i	$-0.837170\pi$
$509$	−29.0971	+	9.45423i	−1.28971	+	0.419051i	−0.417718	+	0.908577i	$0.637170\pi$
$510$	−0.782539	−	0.794506i	−0.0346514	−	0.0351813i
$511$	20.9703	+	6.81367i	0.927672	+	0.301419i
$512$	−17.4609	−	14.3916i	−0.771669	−	0.636025i
$513$	0.0168945	−	0.0331572i	0.000745909	−	0.00146393i
$514$	−16.7419	−	5.89197i	−0.738455	−	0.259884i
$515$	−4.76297	−	8.97534i	−0.209881	−	0.395501i
$516$	2.94337	+	10.8162i	0.129575	+	0.476155i
$517$	−4.81137	+	30.3778i	−0.211604	+	1.33601i
$518$	46.1029	−	43.9210i	2.02565	−	1.92978i
$519$	−3.71576	+	2.69966i	−0.163104	+	0.118502i
$520$	−17.7149	−	6.87531i	−0.776850	−	0.301502i
$521$	28.5539	+	20.7457i	1.25097	+	0.908883i	0.998278	−	0.0586631i	$-0.0186838\pi$
$521$	28.5539	+	20.7457i	1.25097	+	0.908883i	0.252693	+	0.967547i	$0.418684\pi$
$522$	8.19350	−	1.09493i	0.358620	−	0.0479237i
$523$	−4.66469	−	9.15497i	−0.203973	−	0.400319i	0.766247	−	0.642546i	$-0.222122\pi$
$523$	−4.66469	−	9.15497i	−0.203973	−	0.400319i	−0.970219	+	0.242227i	$0.922122\pi$
$524$	20.6713	+	1.00264i	0.903031	+	0.0438006i
$525$	−23.9687	+	0.798212i	−1.04608	+	0.0348368i
$526$	−0.537413	+	22.1726i	−0.0234323	+	0.966771i
$527$	−2.09079	+	1.06531i	−0.0910764	+	0.0464057i
$528$	−0.644500	−	10.7024i	−0.0280483	−	0.465760i
$529$	11.5720	−	15.9275i	0.503131	−	0.692501i
$530$	−15.1922	−	11.2149i	−0.659908	−	0.487144i
$531$	−6.72170	−	9.25163i	−0.291697	−	0.401487i
$532$	−0.264355	+	0.239896i	−0.0114612	+	0.0104008i
$533$	20.5789	+	3.25938i	0.891371	+	0.141179i
$534$	−5.64384	−	18.9179i	−0.244233	−	0.818659i
$535$	9.36570	−	19.1632i	0.404914	−	0.828497i
$536$	−23.5875	−	9.60923i	−1.01882	−	0.415056i
$537$	10.7008	+	5.45231i	0.461772	+	0.235285i
$538$	7.66305	−	14.1793i	0.330377	−	0.611315i
$539$	−13.2573	+	40.8016i	−0.571031	+	1.75745i
$540$	4.43710	−	0.558710i	0.190942	−	0.0240431i
$541$	5.83972	+	17.9728i	0.251069	+	0.772711i	0.994579	+	0.103986i	$0.0331597\pi$
$541$	5.83972	+	17.9728i	0.251069	+	0.772711i	−0.743510	+	0.668725i	$0.766840\pi$
$542$	34.5292	+	6.33009i	1.48315	+	0.271901i
$543$	−13.7776	+	13.7776i	−0.591252	+	0.591252i
$544$	−0.968895	−	1.74379i	−0.0415410	−	0.0747642i
$545$	−1.29055	−	1.71551i	−0.0552813	−	0.0734843i
$546$	−16.1927	−	12.3751i	−0.692985	−	0.529606i
$547$	−4.20606	−	26.5560i	−0.179838	−	1.13545i	−0.898136	−	0.439718i	$-0.855079\pi$
$547$	−4.20606	−	26.5560i	−0.179838	−	1.13545i	0.718298	−	0.695736i	$-0.244921\pi$
$548$	−13.5652	+	6.10301i	−0.579475	+	0.260708i
$549$			4.09291i			0.174681i
$550$	−13.5230	−	13.2803i	−0.576623	−	0.566272i
$551$		−	0.217518i		−	0.00926659i
$552$	1.99773	+	4.74437i	0.0850290	+	0.201934i
$553$	−1.21667	−	7.68173i	−0.0517379	−	0.326660i
$554$	11.8737	−	15.5366i	0.504465	−	0.660088i
$555$	0.349373	+	20.9877i	0.0148301	+	0.890879i
$556$	−5.40499	−	8.25243i	−0.229223	−	0.349981i
$557$	27.7402	−	27.7402i	1.17539	−	1.17539i	0.194483	−	0.980906i	$-0.437697\pi$
$557$	27.7402	−	27.7402i	1.17539	−	1.17539i	0.980906	−	0.194483i	$-0.0623029\pi$
$558$	1.69687	−	9.25604i	0.0718343	−	0.391840i
$559$	5.20373	+	16.0154i	0.220094	+	0.677380i
$560$	−41.6973	−	10.0877i	−1.76203	−	0.426284i
$561$	0.292099	−	0.898987i	0.0123324	−	0.0379553i
$562$	−0.423963	−	0.229126i	−0.0178838	−	0.00966508i
$563$	−11.2472	−	5.73075i	−0.474014	−	0.241522i	0.200628	−	0.979668i	$-0.435702\pi$
$563$	−11.2472	−	5.73075i	−0.474014	−	0.241522i	−0.674642	+	0.738145i	$0.735702\pi$
$564$	−21.4564	−	8.14064i	−0.903479	−	0.342783i
$565$	−4.29941	−	0.607786i	−0.180877	−	0.0255698i
$566$	−9.06871	+	2.70549i	−0.381186	+	0.113720i
$567$	4.73734	+	0.750321i	0.198950	+	0.0315105i
$568$	34.9215	−	30.1803i	1.46527	−	1.26634i
$569$	−7.12484	−	9.80651i	−0.298689	−	0.411110i	0.633123	−	0.774051i	$-0.281773\pi$
$569$	−7.12484	−	9.80651i	−0.298689	−	0.411110i	−0.931812	+	0.362941i	$0.881773\pi$
$570$	0.000892935	−	0.117675i	3.74009e−5	−	0.00492887i
$571$	−8.14919	+	11.2164i	−0.341033	+	0.469391i	−0.944743	−	0.327813i	$-0.893689\pi$
$571$	−8.14919	+	11.2164i	−0.341033	+	0.469391i	0.603710	+	0.797204i	$0.293689\pi$
$572$	−1.74599	−	16.0120i	−0.0730036	−	0.669495i
$573$	−7.03665	+	3.58535i	−0.293960	+	0.149780i
$574$	47.0249	+	1.13978i	1.96278	+	0.0475733i
$575$	8.24130	+	3.85921i	0.343686	+	0.160940i
$576$	7.91559	+	1.15909i	0.329816	+	0.0482954i
$577$	−6.88925	−	13.5209i	−0.286803	−	0.562883i	0.701988	−	0.712189i	$-0.252296\pi$
$577$	−6.88925	−	13.5209i	−0.286803	−	0.562883i	−0.988791	+	0.149306i	$0.952296\pi$
$578$	3.16117	+	23.6555i	0.131487	+	0.983938i
$579$	14.2240	+	10.3344i	0.591130	+	0.429481i
$580$	21.6262	−	14.6844i	0.897980	−	0.609735i
$581$	24.2388	−	17.6105i	1.00560	−	0.730608i
$582$	8.78746	+	9.22402i	0.364252	+	0.382348i
$583$	2.50389	−	15.8089i	0.103700	−	0.654739i
$584$	−12.6254	+	3.10918i	−0.522441	+	0.128659i
$585$	6.61720	−	1.16128i	0.273588	−	0.0480129i
$586$	−5.77149	+	16.3996i	−0.238418	+	0.677461i
$587$	−14.2971	+	28.0597i	−0.590106	+	1.15815i	0.382121	+	0.924112i	$0.375194\pi$
$587$	−14.2971	+	28.0597i	−0.590106	+	1.15815i	−0.972228	+	0.234037i	$0.924806\pi$
$588$	−27.7842	−	15.8973i	−1.14580	−	0.655594i
$589$	−0.235501	−	0.0765188i	−0.00970364	−	0.00315290i
$590$	−32.0957	−	16.6615i	−1.32136	−	0.685945i
$591$	−5.31317	+	1.72635i	−0.218555	+	0.0710127i
$592$	−9.43569	+	36.3443i	−0.387805	+	1.49374i
$593$	−11.4197	−	11.4197i	−0.468950	−	0.468950i	0.432624	−	0.901574i	$-0.357588\pi$
$593$	−11.4197	−	11.4197i	−0.468950	−	0.468950i	−0.901574	+	0.432624i	$0.857588\pi$
$594$	2.15316	+	3.11984i	0.0883452	+	0.128008i
$595$	−3.09642	−	2.17187i	−0.126941	−	0.0890379i
$596$	7.04571	+	5.66022i	0.288604	+	0.231852i
$597$	17.8476	−	2.82678i	0.730453	−	0.115692i
$598$	3.34289	+	6.97354i	0.136701	+	0.285169i
$599$	2.22321			0.0908378			0.0454189	−	0.998968i	$-0.485538\pi$
$599$	2.22321			0.0908378			0.0454189	+	0.998968i	$0.485538\pi$
$600$	11.7598	−	7.85531i	0.480094	−	0.320692i
$601$	25.3987			1.03603			0.518017	−	0.855370i	$-0.326670\pi$
$601$	25.3987			1.03603			0.518017	+	0.855370i	$0.326670\pi$
$602$	16.4338	+	34.2822i	0.669792	+	1.39724i
$603$	8.89404	−	1.40868i	0.362193	−	0.0573658i
$604$	−36.0302	−	28.9451i	−1.46605	−	1.17776i
$605$	−2.50087	+	8.15639i	−0.101675	+	0.331604i
$606$	−1.85111	−	2.68218i	−0.0751961	−	0.108956i
$607$	−26.4929	−	26.4929i	−1.07531	−	1.07531i	−0.996923	−	0.0783895i	$-0.975022\pi$
$607$	−26.4929	−	26.4929i	−1.07531	−	1.07531i	−0.0783895	−	0.996923i	$-0.524978\pi$
$608$	0.0578204	−	0.202413i	0.00234493	−	0.00820895i
$609$	26.6636	−	8.66354i	1.08046	−	0.351064i
$610$	5.78829	+	11.5765i	0.234361	+	0.468718i
$611$	−32.7879	−	10.6534i	−1.32646	−	0.430992i
$612$	0.612173	+	0.350267i	0.0247456	+	0.0141587i
$613$	−20.4288	+	40.0938i	−0.825111	+	1.61937i	−0.0406662	+	0.999173i	$0.512948\pi$
$613$	−20.4288	+	40.0938i	−0.825111	+	1.61937i	−0.784445	+	0.620199i	$0.787052\pi$
$614$	5.92236	−	16.8283i	0.239007	−	0.679135i
$615$	−10.7807	+	11.1457i	−0.434718	+	0.449436i
$616$	−8.69526	−	35.3085i	−0.350342	−	1.42262i
$617$	1.08266	−	6.83563i	0.0435862	−	0.275192i	−0.956264	−	0.292505i	$-0.905511\pi$
$617$	1.08266	−	6.83563i	0.0435862	−	0.275192i	0.999850	+	0.0173129i	$0.00551115\pi$
$618$	4.43262	+	4.65283i	0.178306	+	0.187164i
$619$	−21.2578	+	15.4447i	−0.854425	+	0.620776i	−0.926362	−	0.376633i	$-0.877082\pi$
$619$	−21.2578	+	15.4447i	−0.854425	+	0.620776i	0.0719377	+	0.997409i	$0.477082\pi$
$620$	−8.29064	−	28.5798i	−0.332960	−	1.14779i
$621$	−1.47243	−	1.06979i	−0.0590867	−	0.0429290i
$622$	0.484744	+	3.62741i	0.0194365	+	0.145446i
$623$	−30.3973	−	59.6580i	−1.21784	−	2.39015i
$624$	11.9617	+	1.16312i	0.478851	+	0.0465619i
$625$	6.12644	−	24.2377i	0.245058	−	0.969508i
$626$	−11.7342	−	0.284411i	−0.468994	−	0.0113673i
$627$	0.0888759	−	0.0452845i	0.00354936	−	0.00180849i
$628$	−0.900624	−	8.25936i	−0.0359388	−	0.329584i
$629$	−1.94581	+	2.67818i	−0.0775846	+	0.106786i
$630$	14.4603	−	4.57743i	0.576113	−	0.182369i
$631$	−8.12239	−	11.1795i	−0.323347	−	0.445049i	0.616138	−	0.787638i	$-0.288696\pi$
$631$	−8.12239	−	11.1795i	−0.323347	−	0.445049i	−0.939485	+	0.342589i	$0.888696\pi$
$632$	2.99893	+	3.47005i	0.119291	+	0.138031i
$633$	7.81141	+	1.23721i	0.310476	+	0.0491745i
$634$	−38.2314	+	11.4057i	−1.51836	+	0.452977i
$635$	26.3296	+	25.4674i	1.04486	+	1.01064i
$636$	11.1662	+	4.23648i	0.442767	+	0.167987i
$637$	−42.8473	−	21.8318i	−1.69767	−	0.865006i
$638$	19.4928	+	10.5347i	0.771729	+	0.417071i
$639$	−5.04271	+	15.5199i	−0.199487	+	0.613956i
$640$	24.0278	−	7.91601i	0.949784	−	0.312908i
$641$	−4.52717	−	13.9332i	−0.178813	−	0.550328i	0.820975	−	0.570965i	$-0.193431\pi$
$641$	−4.52717	−	13.9332i	−0.178813	−	0.550328i	−0.999787	+	0.0206365i	$0.993431\pi$
$642$	−2.43251	+	13.2688i	−0.0960036	+	0.523677i
$643$	−7.98979	+	7.98979i	−0.315087	+	0.315087i	−0.846876	−	0.531790i	$-0.821520\pi$
$643$	−7.98979	+	7.98979i	−0.315087	+	0.315087i	0.531790	+	0.846876i	$0.321520\pi$
$644$	9.56587	+	14.6053i	0.376948	+	0.575530i
$645$	−11.9820	−	3.67386i	−0.471791	−	0.144658i
$646$	0.0112693	−	0.0147458i	0.000443385	−	0.000580166i
$647$	−1.32584	−	8.37100i	−0.0521240	−	0.329098i	−0.999947	−	0.0103008i	$-0.996721\pi$
$647$	−1.32584	−	8.37100i	−0.0521240	−	0.329098i	0.947823	−	0.318797i	$-0.103279\pi$
$648$	−2.60676	+	1.09764i	−0.102403	+	0.0431192i
$649$		−	30.6525i		−	1.20322i
$650$	17.0739	−	12.6428i	0.669695	−	0.495891i
$651$		−	31.9156i		−	1.25087i
$652$	−32.7976	+	14.7557i	−1.28445	+	0.577879i
$653$	2.70934	+	17.1061i	0.106025	+	0.669413i	0.982259	+	0.187528i	$0.0600476\pi$
$653$	2.70934	+	17.1061i	0.106025	+	0.669413i	−0.876235	+	0.481885i	$0.839952\pi$
$654$	1.07876	+	0.824428i	0.0421827	+	0.0322377i
$655$	−13.2870	+	18.9431i	−0.519165	+	0.740170i
$656$	−23.9137	+	14.0560i	−0.933671	+	0.548794i
$657$	3.25064	−	3.25064i	0.126820	−	0.126820i
$658$	−76.5565	−	14.0348i	−2.98448	−	0.547133i
$659$	−5.39595	−	16.6070i	−0.210196	−	0.646917i	−0.999460	−	0.0328630i	$-0.989538\pi$
$659$	−5.39595	−	16.6070i	−0.210196	−	0.646917i	0.789264	−	0.614054i	$-0.210462\pi$
$660$	10.5022	+	5.77917i	0.408797	+	0.224954i
$661$	0.873558	−	2.68854i	0.0339775	−	0.104572i	−0.932629	−	0.360836i	$-0.882492\pi$
$661$	0.873558	−	2.68854i	0.0339775	−	0.104572i	0.966607	+	0.256264i	$0.0824915\pi$
$662$	−1.37619	+	2.54644i	−0.0534872	+	0.0989701i
$663$	0.944059	+	0.481022i	0.0366642	+	0.0186813i
$664$	−6.66575	+	16.3622i	−0.258681	+	0.634976i
$665$	−0.0689877	−	0.393107i	−0.00267523	−	0.0152440i
$666$	−3.79526	−	12.7216i	−0.147063	−	0.492951i
$667$	−10.5074	−	1.66421i	−0.406849	−	0.0644385i
$668$	15.7312	−	14.2758i	0.608660	−	0.552347i
$669$	−12.4098	−	17.0807i	−0.479792	−	0.660377i
$670$	23.1639	−	16.5625i	0.894900	−	0.639865i
$671$	−6.44847	+	8.87555i	−0.248940	+	0.342637i
$672$	27.1150	−	0.974247i	1.04598	−	0.0375824i
$673$	−30.3795	+	15.4791i	−1.17104	+	0.596677i	−0.927723	−	0.373269i	$-0.878237\pi$
$673$	−30.3795	+	15.4791i	−1.17104	+	0.596677i	−0.243321	+	0.969946i	$0.578237\pi$
$674$	−0.423123	+	17.4572i	−0.0162981	+	0.672427i
$675$	−2.12041	+	4.52812i	−0.0816148	+	0.174287i
$676$	−7.93628	−	0.384941i	−0.305242	−	0.0148054i
$677$	9.43439	+	18.5160i	0.362593	+	0.711629i	0.998174	−	0.0604054i	$-0.0192393\pi$
$677$	9.43439	+	18.5160i	0.362593	+	0.711629i	−0.635581	+	0.772034i	$0.719239\pi$
$678$	2.72202	−	0.363754i	0.104539	−	0.0139699i
$679$	34.9558	+	25.3969i	1.34148	+	0.974643i
$680$	2.22684	+	0.124954i	0.0853954	+	0.00479177i
$681$	3.41008	−	2.47757i	0.130675	−	0.0949407i
$682$	18.2628	−	17.3984i	0.699318	−	0.666221i
$683$	3.51625	−	22.2008i	0.134546	−	0.849488i	−0.824423	−	0.565975i	$-0.808500\pi$
$683$	3.51625	−	22.2008i	0.134546	−	0.849488i	0.958968	−	0.283513i	$-0.0915001\pi$
$684$	0.0195428	+	0.0718149i	0.000747237	+	0.00274591i
$685$	2.32784	−	16.4668i	0.0889421	−	0.629166i
$686$	−57.6204	−	20.2783i	−2.19996	−	0.774229i
$687$	7.39023	−	14.5041i	0.281955	−	0.553368i
$688$	−18.8967	−	12.0635i	−0.720428	−	0.459915i
$689$	17.0632	+	5.54416i	0.650055	+	0.211216i
$690$	−5.67758	−	0.943456i	−0.216142	−	0.0359168i
$691$	5.65723	−	1.83814i	0.215211	−	0.0699263i	−0.199427	−	0.979913i	$-0.563908\pi$
$691$	5.65723	−	1.83814i	0.215211	−	0.0699263i	0.414638	+	0.909986i	$0.363908\pi$
$692$	1.87485	−	8.99250i	0.0712709	−	0.341843i
$693$	9.09086	+	9.09086i	0.345333	+	0.345333i
$694$	−16.5889	+	11.4489i	−0.629707	+	0.434593i
$695$	11.0278	−	0.183574i	0.418307	−	0.00696337i
$696$	−10.6635	+	12.6340i	−0.404199	+	0.478892i
$697$	−2.41539	+	0.382560i	−0.0914894	+	0.0144905i
$698$	23.9538	−	11.4827i	0.906663	−	0.434625i
$699$	−4.01793			−0.151972
$700$	34.4264	−	33.3970i	1.30120	−	1.26229i
$701$	−2.92229			−0.110374			−0.0551868	−	0.998476i	$-0.517575\pi$
$701$	−2.92229			−0.110374			−0.0551868	+	0.998476i	$0.517575\pi$
$702$	−3.83156	+	1.83672i	−0.144613	+	0.0693227i
$703$	−0.345031	+	0.0546475i	−0.0130131	+	0.00206107i
$704$	15.3389	+	14.9847i	0.578108	+	0.564756i
$705$	20.5035	−	15.4245i	0.772208	−	0.580922i
$706$	9.73769	−	6.72048i	0.366483	−	0.252929i
$707$	−7.81557	−	7.81557i	−0.293935	−	0.293935i
$708$	22.3898	+	4.66806i	0.841462	+	0.175436i
$709$	−17.0212	+	5.53052i	−0.639244	+	0.207703i	−0.610666	−	0.791889i	$-0.709098\pi$
$709$	−17.0212	+	5.53052i	−0.639244	+	0.207703i	−0.0285783	+	0.999592i	$0.509098\pi$
$710$	7.68564	+	51.0283i	0.288437	+	1.91506i
$711$	−1.54216	−	0.501079i	−0.0578357	−	0.0187919i
$712$	33.7853	+	20.4332i	1.26616	+	0.765767i
$713$	−5.49811	+	10.7906i	−0.205906	+	0.404113i
$714$	2.25640	+	0.794093i	0.0844437	+	0.0297182i
$715$	16.1792	+	7.90729i	0.605066	+	0.295716i
$716$	−23.1767	+	6.30700i	−0.866153	+	0.235704i
$717$	−0.473345	+	2.98858i	−0.0176774	+	0.111611i
$718$	20.8089	−	19.8241i	0.776582	−	0.739827i
$719$	22.8599	−	16.6087i	0.852530	−	0.619399i	−0.0733124	−	0.997309i	$-0.523357\pi$
$719$	22.8599	−	16.6087i	0.852530	−	0.619399i	0.925842	+	0.377910i	$0.123357\pi$
$720$	−5.82071	+	6.79112i	−0.216925	+	0.253090i
$721$	17.6326	+	12.8108i	0.656673	+	0.477101i
$722$	−26.6314	+	3.55885i	−0.991117	+	0.132447i
$723$	−7.63669	−	14.9878i	−0.284011	−	0.557404i
$724$	1.88792	−	38.9231i	0.0701641	−	1.44656i
$725$	0.972751	+	29.2097i	0.0361271	+	1.08482i
$726$	0.130738	−	5.39401i	0.00485216	−	0.200190i
$727$	30.9208	−	15.7550i	1.14679	−	0.584319i	0.225904	−	0.974150i	$-0.427466\pi$
$727$	30.9208	−	15.7550i	1.14679	−	0.584319i	0.920887	+	0.389831i	$0.127466\pi$
$728$	40.6152	−	3.43529i	1.50530	−	0.127320i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	4.59705	−	13.7913i	0.170145	−	0.510440i
$731$	−1.16176	−	1.59902i	−0.0429692	−	0.0591420i
$732$	−5.50103	−	6.06188i	−0.203324	−	0.224053i
$733$	−18.5838	−	2.94338i	−0.686407	−	0.108716i	−0.196517	−	0.980500i	$-0.562963\pi$
$733$	−18.5838	−	2.94338i	−0.686407	−	0.108716i	−0.489890	+	0.871784i	$0.662963\pi$
$734$	12.0878	+	40.5179i	0.446170	+	1.49554i
$735$	31.6135	−	16.7764i	1.16608	−	0.618808i
$736$	−9.33539	−	4.34171i	−0.344107	−	0.160038i
$737$	21.5063	+	10.9580i	0.792194	+	0.403643i
$738$	4.66276	−	8.62774i	0.171638	−	0.317592i
$739$	−8.48650	+	26.1188i	−0.312181	+	0.960794i	0.664718	+	0.747094i	$0.268552\pi$
$739$	−8.48650	+	26.1188i	−0.312181	+	0.960794i	−0.976899	+	0.213700i	$0.931448\pi$
$740$	−28.7258	−	30.6147i	−1.05598	−	1.12542i
$741$	0.0345507	+	0.106336i	0.00126925	+	0.00390635i
$742$	39.8408	+	7.30386i	1.46260	+	0.268133i
$743$	−24.4972	+	24.4972i	−0.898716	+	0.898716i	−0.995323	−	0.0966068i	$-0.969201\pi$
$743$	−24.4972	+	24.4972i	−0.898716	+	0.898716i	0.0966068	+	0.995323i	$0.469201\pi$
$744$	9.92730	+	15.9895i	0.363952	+	0.586203i
$745$	−9.55661	+	3.28197i	−0.350127	+	0.120242i
$746$	28.5902	+	21.8498i	1.04676	+	0.799977i
$747$	−0.977173	−	6.16963i	−0.0357529	−	0.225735i
$748$	0.775656	+	1.72405i	0.0283608	+	0.0630376i
$749$			45.7519i			1.67174i
$750$	0.406340	+	15.8062i	0.0148374	+	0.577160i
$751$		−	20.0362i		−	0.731131i	−0.930786	−	0.365565i	$-0.880876\pi$
$751$		−	20.0362i		−	0.731131i	0.930786	−	0.365565i	$-0.119124\pi$
$752$	42.7198	−	16.7815i	1.55783	−	0.611957i
$753$	−0.783827	−	4.94889i	−0.0285642	−	0.180348i
$754$	−15.0811	+	19.7335i	−0.549221	+	0.718651i
$755$	48.8703	−	16.7832i	1.77857	−	0.610804i
$756$	−8.02478	+	5.25589i	−0.291858	+	0.191155i
$757$	−21.6448	+	21.6448i	−0.786693	+	0.786693i	−0.980951	−	0.194257i	$-0.937770\pi$
$757$	−21.6448	+	21.6448i	−0.786693	+	0.786693i	0.194257	+	0.980951i	$0.437770\pi$
$758$	−2.24486	+	12.2452i	−0.0815368	+	0.444764i
$759$	−1.50753	−	4.63970i	−0.0547199	−	0.168410i
$760$	0.156838	+	0.175485i	0.00568910	+	0.00636551i
$761$	−10.0218	+	30.8439i	−0.363289	+	1.11809i	0.587756	+	0.809038i	$0.300011\pi$
$761$	−10.0218	+	30.8439i	−0.363289	+	1.11809i	−0.951045	+	0.309051i	$0.899989\pi$
$762$	−20.3815	−	11.0149i	−0.738344	−	0.399029i
$763$	4.10289	+	2.09053i	0.148535	+	0.0756822i
$764$	5.60290	−	14.7677i	0.202706	−	0.534276i
$765$	−0.696543	+	0.369637i	−0.0251836	+	0.0133642i
$766$	−23.4240	+	6.98815i	−0.846345	+	0.252492i
$767$	33.9357	+	5.37489i	1.22535	+	0.194076i
$768$	−13.2814	+	8.92216i	−0.479250	+	0.321951i
$769$	12.5344	+	17.2521i	0.452001	+	0.622126i	0.972826	−	0.231537i	$-0.0743756\pi$
$769$	12.5344	+	17.2521i	0.452001	+	0.622126i	−0.520825	+	0.853664i	$0.674376\pi$
$770$	38.5693	+	12.8563i	1.38994	+	0.463309i
$771$	−7.37674	+	10.1532i	−0.265667	+	0.365659i
$772$	−34.9565	+	3.81175i	−1.25811	+	0.137188i
$773$	34.3860	−	17.5205i	1.23678	−	0.630169i	0.291541	−	0.956558i	$-0.405832\pi$
$773$	34.3860	−	17.5205i	1.23678	−	0.630169i	0.945236	+	0.326389i	$0.105832\pi$
$774$	7.92398	+	0.192059i	0.284821	+	0.00690342i
$775$	31.9667	+	9.22226i	1.14828	+	0.331273i
$776$	−25.4123	−	1.85071i	−0.912247	−	0.0664365i
$777$	−20.4410	−	40.1177i	−0.733317	−	1.43921i
$778$	−0.316630	−	2.36939i	−0.0113517	−	0.0849466i
$779$	−0.208776	−	0.151685i	−0.00748018	−	0.00543467i
$780$	−8.23972	+	10.6137i	−0.295029	+	0.380032i
$781$	−35.3871	+	25.7102i	−1.26625	+	0.919984i
$782$	−0.626089	−	0.657193i	−0.0223889	−	0.0235012i
$783$	0.914388	−	5.77322i	0.0326776	−	0.206318i
$784$	62.5169	−	13.7981i	2.23275	−	0.492789i
$785$	8.34559	+	4.07877i	0.297867	+	0.145578i
$786$	4.85807	−	13.8041i	0.173282	−	0.492377i
$787$	3.16858	−	6.21869i	0.112948	−	0.221672i	−0.827612	−	0.561300i	$-0.810301\pi$
$787$	3.16858	−	6.21869i	0.112948	−	0.221672i	0.940560	+	0.339628i	$0.110301\pi$
$788$	5.54888	−	9.69795i	0.197671	−	0.345475i
$789$	14.9154	+	4.84631i	0.531003	+	0.172533i
$790$	−5.07053	+	0.763699i	−0.180401	+	0.0271712i
$791$	8.85811	−	2.87818i	0.314958	−	0.102336i
$792$	−7.38216	−	1.72676i	−0.262313	−	0.0613577i
$793$	−8.69548	−	8.69548i	−0.308786	−	0.308786i
$794$	20.0865	+	29.1044i	0.712842	+	1.03288i
$795$	−10.6703	+	8.02710i	−0.378435	+	0.284692i
$796$	−22.6342	+	28.1745i	−0.802247	+	0.998618i
$797$	18.1235	−	2.87048i	0.641967	−	0.101678i	0.173041	−	0.984915i	$-0.444641\pi$
$797$	18.1235	−	2.87048i	0.641967	−	0.101678i	0.468927	+	0.883237i	$0.344641\pi$
$798$	0.109114	+	0.227620i	0.00386259	+	0.00805767i
$799$	4.04643			0.143153
$800$	−6.85928	+	27.4399i	−0.242512	+	0.970148i
$801$	−13.9596			−0.493239
$802$	−21.3652	−	44.5695i	−0.754431	−	1.57380i
$803$	12.1705	−	1.92762i	0.429489	−	0.0680243i
$804$	−11.2794	+	14.0403i	−0.397792	+	0.495162i
$805$	−19.5172	+	0.324894i	−0.687891	+	0.0114510i
$806$	16.0596	+	23.2697i	0.565676	+	0.819641i
$807$	−8.05879	−	8.05879i	−0.283683	−	0.283683i
$808$	6.34656	+	1.48452i	0.223271	+	0.0522253i
$809$	12.5468	−	4.07670i	0.441122	−	0.143329i	−0.0800314	−	0.996792i	$-0.525502\pi$
$809$	12.5468	−	4.07670i	0.441122	−	0.143329i	0.521153	+	0.853463i	$0.325502\pi$
$810$	0.518375	−	3.11950i	0.0182138	−	0.109608i
$811$	−25.4347	−	8.26423i	−0.893133	−	0.290196i	−0.173733	−	0.984793i	$-0.555583\pi$
$811$	−25.4347	−	8.26423i	−0.893133	−	0.290196i	−0.719400	+	0.694596i	$0.755583\pi$
$812$	−27.8465	+	48.6682i	−0.977220	+	1.70792i
$813$	11.2693	−	22.1172i	0.395230	−	0.775683i
$814$	11.8130	−	33.5665i	0.414046	−	1.17651i
$815$	5.62821	−	39.8132i	0.197147	−	1.39460i
$816$	−1.37744	+	0.304015i	−0.0482201	+	0.0106427i
$817$	0.0326276	−	0.206003i	0.00114150	−	0.00720713i
$818$	−9.80811	−	10.2954i	−0.342932	−	0.359969i
$819$	−11.6587	+	8.47051i	−0.407387	+	0.295984i
$820$	0.986690	−	30.9971i	0.0344567	−	1.08246i
$821$	−40.6822	−	29.5573i	−1.41982	−	1.03156i	−0.991802	−	0.127786i	$-0.959213\pi$
$821$	−40.6822	−	29.5573i	−1.41982	−	1.03156i	−0.428015	−	0.903772i	$-0.640787\pi$
$822$	1.39319	+	10.4254i	0.0485930	+	0.363628i
$823$	−11.6026	−	22.7713i	−0.404440	−	0.793757i	0.595515	−	0.803345i	$-0.296948\pi$
$823$	−11.6026	−	22.7713i	−0.404440	−	0.793757i	−0.999954	+	0.00958732i	$0.996948\pi$
$824$	−12.8186	−	0.933544i	−0.446557	−	0.0325215i
$825$	−11.7323	+	6.47855i	−0.408466	+	0.225554i
$826$	77.5466	+	1.87955i	2.69819	+	0.0653980i
$827$	−25.9636	+	13.2291i	−0.902842	+	0.460021i	−0.842832	−	0.538177i	$-0.819113\pi$
$827$	−25.9636	+	13.2291i	−0.902842	+	0.460021i	−0.0600101	+	0.998198i	$0.519113\pi$
$828$	3.61860	−	0.394583i	0.125755	−	0.0137127i
$829$	20.8622	−	28.7143i	0.724573	−	0.997289i	−0.274786	−	0.961505i	$-0.588607\pi$
$829$	20.8622	−	28.7143i	0.724573	−	0.997289i	0.999360	−	0.0357841i	$-0.0113929\pi$
$830$	−11.4891	−	16.0684i	−0.398792	−	0.557742i
$831$	−8.12730	−	11.1863i	−0.281933	−	0.388047i
$832$	−19.2794	+	14.3543i	−0.668391	+	0.497647i
$833$	5.57478	+	0.882958i	0.193155	+	0.0305927i
$834$	−6.68442	+	1.99418i	−0.231463	+	0.0690528i
$835$	4.10533	+	23.3930i	0.142071	+	0.809549i
$836$	−0.0707670	+	0.186522i	−0.00244753	+	0.00645100i
$837$	−5.92883	−	3.02089i	−0.204930	−	0.104417i
$838$	−12.7120	−	6.87004i	−0.439129	−	0.237322i
$839$	−7.35139	+	22.6253i	−0.253798	+	0.781110i	0.740266	+	0.672314i	$0.234700\pi$
$839$	−7.35139	+	22.6253i	−0.253798	+	0.781110i	−0.994064	+	0.108796i	$0.965300\pi$
$840$	−15.2645	+	26.2147i	−0.526674	+	0.904493i
$841$	−1.59644	−	4.91333i	−0.0550496	−	0.169425i
$842$	6.52348	−	35.5840i	0.224814	−	1.22631i
$843$	−0.240958	+	0.240958i	−0.00829904	+	0.00829904i
$844$	−13.2321	+	8.66645i	−0.455467	+	0.298311i
$845$	5.10123	−	7.27279i	0.175488	−	0.250192i
$846$	−9.85346	+	12.8932i	−0.338769	+	0.443276i
$847$	−2.86267	−	18.0742i	−0.0983625	−	0.621036i
$848$	−22.2318	+	8.73325i	−0.763444	+	0.299901i
$849$			6.69183i			0.229663i
$850$	−1.44737	+	2.03056i	−0.0496444	+	0.0696475i
$851$			17.0851i			0.585671i
$852$	−13.3907	−	29.7636i	−0.458758	−	1.01968i
$853$	0.988144	+	6.23890i	0.0338334	+	0.213616i	0.998813	−	0.0487092i	$-0.0155108\pi$
$853$	0.988144	+	6.23890i	0.0338334	+	0.213616i	−0.964980	+	0.262325i	$0.915511\pi$
$854$	−22.0585	−	16.8580i	−0.754827	−	0.576867i
$855$	−0.0795557	−	0.0243930i	−0.00272075	−	0.000834221i
$856$	−14.2310	−	22.9214i	−0.486407	−	0.783436i
$857$	−10.6659	+	10.6659i	−0.364342	+	0.364342i	−0.865409	−	0.501067i	$-0.832941\pi$
$857$	−10.6659	+	10.6659i	−0.364342	+	0.364342i	0.501067	+	0.865409i	$0.332941\pi$
$858$	−11.2026	−	2.05373i	−0.382451	−	0.0701131i
$859$	5.00278	+	15.3970i	0.170693	+	0.525338i	0.999411	−	0.0343286i	$-0.0109293\pi$
$859$	5.00278	+	15.3970i	0.170693	+	0.525338i	−0.828718	+	0.559666i	$0.810929\pi$
$860$	22.6840	−	10.6630i	0.773517	−	0.363607i
$861$	10.2783	−	31.6335i	0.350285	−	1.07807i
$862$	−20.1388	+	37.2640i	−0.685931	+	1.26922i
$863$	25.6142	+	13.0511i	0.871916	+	0.444264i	0.831894	−	0.554935i	$-0.187257\pi$
$863$	25.6142	+	13.0511i	0.871916	+	0.444264i	0.0400228	+	0.999199i	$0.487257\pi$
$864$	2.38552	−	5.12926i	0.0811570	−	0.174501i
$865$	7.38193	+	7.14018i	0.250993	+	0.242773i
$866$	−7.59115	−	25.4453i	−0.257958	−	0.864666i
$867$	16.6679	+	2.63993i	0.566071	+	0.0896568i
$868$	42.8958	+	47.2692i	1.45598	+	1.60442i
$869$	−2.55475	−	3.51631i	−0.0866640	−	0.119283i
$870$	−5.57834	−	17.6223i	−0.189124	−	0.597450i
$871$	−15.9028	+	21.8884i	−0.538846	+	0.741658i
$872$	−2.70577	+	0.228859i	−0.0916291	+	0.00775013i
$873$	8.02653	−	4.08972i	0.271657	−	0.138416i
$874$	0.00232089	−	0.0957553i	7.85053e−5	−	0.00323897i
$875$	11.0221	+	52.4803i	0.372615	+	1.77416i
$876$	−0.445431	+	9.18340i	−0.0150497	+	0.310278i
$877$	13.9377	+	27.3543i	0.470643	+	0.923689i	0.997288	+	0.0736037i	$0.0234500\pi$
$877$	13.9377	+	27.3543i	0.470643	+	0.923689i	−0.526644	+	0.850086i	$0.676550\pi$
$878$	−48.5056	+	6.48198i	−1.63698	+	0.218756i
$879$	9.94559	+	7.22589i	0.335456	+	0.243723i
$880$	−23.3219	+	5.55601i	−0.786180	+	0.187293i
$881$	2.53464	−	1.84152i	0.0853941	−	0.0620424i	−0.544269	−	0.838911i	$-0.683193\pi$
$881$	2.53464	−	1.84152i	0.0853941	−	0.0620424i	0.629663	+	0.776868i	$0.283193\pi$
$882$	−16.3885	+	15.6129i	−0.551829	+	0.525712i
$883$	−1.35062	+	8.52750i	−0.0454521	+	0.286973i	−0.999936	−	0.0112883i	$-0.996407\pi$
$883$	−1.35062	+	8.52750i	−0.0454521	+	0.286973i	0.954484	+	0.298262i	$0.0964068\pi$
$884$	−2.04473	+	0.556425i	−0.0687716	+	0.0187146i
$885$	−17.7779	+	18.3798i	−0.597597	+	0.617830i
$886$	−31.4664	−	11.0739i	−1.05713	−	0.372036i
$887$	9.92825	−	19.4853i	0.333358	−	0.654252i	−0.662104	−	0.749412i	$-0.730336\pi$
$887$	9.92825	−	19.4853i	0.333358	−	0.654252i	0.995462	+	0.0951599i	$0.0303362\pi$
$888$	22.7193	+	13.7405i	0.762411	+	0.461102i
$889$	−74.7284	−	24.2807i	−2.50631	−	0.814349i
$890$	−39.4837	+	19.7420i	−1.32350	+	0.661753i
$891$	2.54925	−	0.828300i	0.0854030	−	0.0277491i
$892$	41.3369	+	8.61833i	1.38406	+	0.288563i
$893$	0.301935	+	0.301935i	0.0101039	+	0.0101039i
$894$	5.25962	−	3.62994i	0.175908	−	0.121403i
$895$	7.87228	−	25.6748i	0.263141	−	0.858215i
$896$	−38.8497	+	37.8865i	−1.29788	+	1.26570i
$897$	5.40100	−	0.855434i	0.180334	−	0.0285621i
$898$	21.9931	−	10.5428i	0.733919	−	0.351817i
$899$	−38.8944			−1.29720
$900$	−2.94549	−	9.55636i	−0.0981829	−	0.318545i
$901$	−2.10581			−0.0701546
$902$	23.7045	−	11.3632i	0.789272	−	0.378352i
$903$	26.5516	−	4.20536i	0.883581	−	0.139945i
$904$	−3.54260	+	4.19725i	−0.117825	+	0.139598i
$905$	35.6690	+	25.0187i	1.18568	+	0.831649i
$906$	−26.8965	+	18.5627i	−0.893577	+	0.616703i
$907$	34.7662	+	34.7662i	1.15439	+	1.15439i	0.985663	+	0.168729i	$0.0539662\pi$
$907$	34.7662	+	34.7662i	1.15439	+	1.15439i	0.168729	+	0.985663i	$0.446034\pi$
$908$	−1.72061	+	8.25273i	−0.0571005	+	0.273877i
$909$	−2.19163	+	0.712104i	−0.0726918	+	0.0236190i
$910$	−20.9964	+	40.4461i	−0.696025	+	1.34078i
$911$	15.1798	+	4.93221i	0.502928	+	0.163411i	0.549484	−	0.835504i	$-0.314824\pi$
$911$	15.1798	+	4.93221i	0.502928	+	0.163411i	−0.0465554	+	0.998916i	$0.514824\pi$
$912$	−0.125466	−	0.0800965i	−0.00415460	−	0.00265226i
$913$	7.60136	−	14.9185i	0.251568	−	0.493731i
$914$	27.5906	+	9.70994i	0.912617	+	0.321176i
$915$	9.01427	−	1.58195i	0.298003	−	0.0522976i
$916$	8.54870	+	31.4144i	0.282457	+	1.03796i
$917$	7.76418	−	49.0211i	0.256396	−	1.61882i
$918$	0.361090	−	0.344000i	0.0119177	−	0.0113537i
$919$	20.3943	−	14.8173i	0.672747	−	0.488779i	−0.198197	−	0.980162i	$-0.563508\pi$
$919$	20.3943	−	14.8173i	0.672747	−	0.488779i	0.870944	+	0.491383i	$0.163508\pi$
$920$	9.67692	−	6.23356i	0.319038	−	0.205514i
$921$	−10.2056	−	7.41479i	−0.336285	−	0.244326i
$922$	10.2366	−	1.36796i	0.337126	−	0.0450514i
$923$	−22.2590	−	43.6857i	−0.732662	−	1.43793i
$924$	−25.6827	−	1.24571i	−0.844897	−	0.0409808i
$925$	46.0886	−	8.88141i	1.51538	−	0.292019i
$926$	0.182434	−	7.52686i	0.00599515	−	0.247348i
$927$	4.04879	−	2.06296i	0.132980	−	0.0677565i
$928$	−1.18728	−	33.0440i	−0.0389743	−	1.08472i
$929$	6.69493	−	9.21478i	0.219654	−	0.302327i	−0.684942	−	0.728597i	$-0.740173\pi$
$929$	6.69493	−	9.21478i	0.219654	−	0.302327i	0.904596	+	0.426270i	$0.140173\pi$
$930$	−21.0415	−	0.159665i	−0.689977	−	0.00523563i
$931$	0.350092	+	0.481860i	0.0114738	+	0.0157923i
$932$	5.95083	−	5.40026i	0.194926	−	0.176891i
$933$	2.55591	+	0.404816i	0.0836767	+	0.0132531i
$934$	−1.60333	−	5.37430i	−0.0524625	−	0.175852i
$935$	−2.09284	−	0.295854i	−0.0684431	−	0.00967547i
$936$	3.20617	−	7.87007i	0.104797	−	0.257241i
$937$	40.0127	+	20.3875i	1.30716	+	0.666030i	0.962137	−	0.272565i	$-0.0878721\pi$
$937$	40.0127	+	20.3875i	1.30716	+	0.666030i	0.345020	+	0.938595i	$0.387872\pi$
$938$	−29.0409	+	53.7360i	−0.948220	+	1.75454i
$939$	−2.56478	+	7.89357i	−0.0836983	+	0.257597i
$940$	−9.63592	+	50.4023i	−0.314289	+	1.64394i
$941$	−1.59956	−	4.92295i	−0.0521443	−	0.160484i	0.921593	−	0.388157i	$-0.126888\pi$
$941$	−1.59956	−	4.92295i	−0.0521443	−	0.160484i	−0.973738	+	0.227673i	$0.926888\pi$
$942$	−5.77857	−	1.05936i	−0.188276	−	0.0345158i
$943$	−8.92460	+	8.92460i	−0.290625	+	0.290625i
$944$	−39.4349	+	23.1791i	−1.28350	+	0.754416i
$945$	−0.178510	−	10.7236i	−0.00580694	−	0.348838i
$946$	16.8807	+	12.9009i	0.548839	+	0.419444i
$947$	−2.98118	−	18.8224i	−0.0968752	−	0.611646i	−0.987586	−	0.157076i	$-0.949793\pi$
$947$	−2.98118	−	18.8224i	−0.0968752	−	0.611646i	0.890711	−	0.454569i	$-0.150207\pi$
$948$	2.95752	−	1.33060i	0.0960557	−	0.0432157i
$949$			13.8121i			0.448360i
$950$	−0.259514	+	0.0435159i	−0.00841975	+	0.00141184i
$951$			28.2111i			0.914807i
$952$	−4.40917	+	1.85659i	−0.142902	+	0.0601723i
$953$	−2.74989	−	17.3621i	−0.0890776	−	0.562414i	−0.991350	−	0.131247i	$-0.958102\pi$
$953$	−2.74989	−	17.3621i	−0.0890776	−	0.562414i	0.902272	−	0.431167i	$-0.141898\pi$
$954$	5.12784	−	6.70975i	0.166020	−	0.217236i
$955$	10.6161	+	14.1118i	0.343530	+	0.456648i
$956$	−3.31571	−	5.06248i	−0.107238	−	0.163732i
$957$	11.0787	−	11.0787i	0.358123	−	0.358123i
$958$	−2.24974	+	12.2718i	−0.0726859	+	0.396485i
$959$	11.0235	+	33.9268i	0.355967	+	1.09555i
$960$	−0.506657	−	17.8814i	−0.0163523	−	0.577119i
$961$	−4.10277	+	12.6270i	−0.132348	+	0.407324i
$962$	35.0904	+	18.9642i	1.13136	+	0.611430i
$963$	8.49914	+	4.33053i	0.273881	+	0.139549i
$964$	31.4547	+	11.9340i	1.01309	+	0.384368i
$965$	17.2628	−	35.3214i	0.555708	−	1.13704i
$966$	11.8302	−	3.52934i	0.380631	−	0.113555i
$967$	12.9879	+	2.05708i	0.417663	+	0.0661513i	0.361729	−	0.932283i	$-0.382186\pi$
$967$	12.9879	+	2.05708i	0.417663	+	0.0661513i	0.0559338	+	0.998434i	$0.482186\pi$
$968$	7.05612	+	8.16461i	0.226792	+	0.262420i
$969$	−0.00771361	−	0.0106169i	−0.000247797	−	0.000341063i
$970$	16.9186	−	22.9188i	0.543225	−	0.735877i
$971$	21.5179	−	29.6169i	0.690543	−	0.950451i	−0.309457	−	0.950914i	$-0.600147\pi$
$971$	21.5179	−	29.6169i	0.690543	−	0.950451i	1.00000		0.000462355i	$0.000147172\pi$
$972$	0.216801	+	1.98821i	0.00695388	+	0.0637720i
$973$	−21.0794	+	10.7405i	−0.675775	+	0.344325i
$974$	−10.6023	−	0.256977i	−0.339721	−	0.00823406i
$975$	−5.11522	−	14.1250i	−0.163818	−	0.452361i
$976$	16.2948	+	1.58445i	0.521584	+	0.0507170i
$977$	14.9130	+	29.2685i	0.477110	+	0.936381i	0.996638	+	0.0819281i	$0.0261078\pi$
$977$	14.9130	+	29.2685i	0.477110	+	0.936381i	−0.519528	+	0.854453i	$0.673892\pi$
$978$	3.36842	+	25.2064i	0.107710	+	0.806012i
$979$	−30.2717	−	21.9937i	−0.967487	−	0.702920i
$980$	−24.2735	+	67.3367i	−0.775389	+	2.15099i
$981$	0.776698	−	0.564304i	0.0247981	−	0.0180168i
$982$	22.6153	+	23.7388i	0.721682	+	0.757535i
$983$	−6.39812	+	40.3961i	−0.204068	+	1.28844i	0.646639	+	0.762796i	$0.276174\pi$
$983$	−6.39812	+	40.3961i	−0.204068	+	1.28844i	−0.850707	+	0.525640i	$0.823826\pi$
$984$	4.69017	+	19.0452i	0.149517	+	0.607139i
$985$	5.85573	+	11.0345i	0.186579	+	0.351589i
$986$	0.967732	−	2.74979i	0.0308189	−	0.0875712i
$987$	−24.9857	+	49.0373i	−0.795305	+	1.56087i
$988$	−0.194091	−	0.111053i	−0.00617487	−	0.00353308i
$989$	−9.70152	−	3.15222i	−0.308490	−	0.100235i
$990$	6.03895	−	5.94799i	0.191930	−	0.189039i
$991$	52.3225	−	17.0006i	1.66208	−	0.540043i	0.680774	−	0.732494i	$-0.261644\pi$
$991$	52.3225	−	17.0006i	1.66208	−	0.540043i	0.981307	+	0.192451i	$0.0616436\pi$
$992$	−36.1935	−	10.3388i	−1.14914	−	0.328258i
$993$	1.44726	+	1.44726i	0.0459274	+	0.0459274i
$994$	−62.8734	−	91.1009i	−1.99422	−	2.88955i
$995$	−13.1240	−	38.2151i	−0.416058	−	1.21150i
$996$	9.73948	+	7.82428i	0.308607	+	0.247922i
$997$	33.8775	−	5.36566i	1.07291	−	0.169932i	0.405106	−	0.914270i	$-0.367235\pi$
$997$	33.8775	−	5.36566i	1.07291	−	0.169932i	0.667804	+	0.744337i	$0.267235\pi$
$998$	−18.4527	−	38.4939i	−0.584111	−	1.21850i
$999$	−9.38730			−0.297001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.20	yes	240
3.2	odd	2		900.2.bj.f.703.11		240
4.3	odd	2	inner	300.2.w.a.103.21	yes	240
12.11	even	2		900.2.bj.f.703.10		240
25.17	odd	20	inner	300.2.w.a.67.21	yes	240
75.17	even	20		900.2.bj.f.667.10		240
100.67	even	20	inner	300.2.w.a.67.20	✓	240
300.167	odd	20		900.2.bj.f.667.11		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.20	✓	240	100.67	even	20	inner
300.2.w.a.67.21	yes	240	25.17	odd	20	inner
300.2.w.a.103.20	yes	240	1.1	even	1	trivial
300.2.w.a.103.21	yes	240	4.3	odd	2	inner
900.2.bj.f.667.10		240	75.17	even	20
900.2.bj.f.667.11		240	300.167	odd	20
900.2.bj.f.703.10		240	12.11	even	2
900.2.bj.f.703.11		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.611319 + 1.27526i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.25258 + 1.55918i) q^{4} +(-0.726283 - 2.11483i) q^{5} +(0.803287 + 1.16393i) q^{6} +(3.39156 + 3.39156i) q^{7} +(-2.75409 - 0.644208i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(0.611319 + 1.27526i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-1.25258 + 1.55918i) q^{4} +(-0.726283 - 2.11483i) q^{5} +(0.803287 + 1.16393i) q^{6} +(3.39156 + 3.39156i) q^{7} +(-2.75409 - 0.644208i) q^{8} +(0.951057 - 0.309017i) q^{9} +(2.25297 - 2.21904i) q^{10} +(2.54925 + 0.828300i) q^{11} +(-0.993248 + 1.73593i) q^{12} +(-1.36403 + 2.67705i) q^{13} +(-2.25180 + 6.39845i) q^{14} +(-1.04817 - 1.97518i) q^{15} +(-0.862092 - 3.90600i) q^{16} +(0.0551663 - 0.348307i) q^{17} +(0.975476 + 1.02394i) q^{18} +(0.0301061 - 0.0218734i) q^{19} +(4.20713 + 1.51659i) q^{20} +(3.88036 + 2.81925i) q^{21} +(0.502103 + 3.75731i) q^{22} +(-0.826275 - 1.62166i) q^{23} +(-2.82096 - 0.205443i) q^{24} +(-3.94503 + 3.07193i) q^{25} +(-4.24780 - 0.102957i) q^{26} +(0.891007 - 0.453990i) q^{27} +(-9.53626 + 1.03986i) q^{28} +(3.43571 - 4.72885i) q^{29} +(1.87810 - 2.54416i) q^{30} +(-3.91117 - 5.38327i) q^{31} +(4.45415 - 3.48720i) q^{32} +(2.64744 + 0.419313i) q^{33} +(0.477906 - 0.142575i) q^{34} +(4.70935 - 9.63581i) q^{35} +(-0.709460 + 1.86994i) q^{36} +(-8.36414 - 4.26174i) q^{37} +(0.0462987 + 0.0250216i) q^{38} +(-0.928450 + 2.85748i) q^{39} +(0.637856 + 6.29231i) q^{40} +(-2.14293 - 6.59526i) q^{41} +(-1.22314 + 6.67193i) q^{42} +(3.96315 - 3.96315i) q^{43} +(-4.48460 + 2.93723i) q^{44} +(-1.34426 - 1.78689i) q^{45} +(1.56292 - 2.04506i) q^{46} +(1.79499 + 11.3331i) q^{47} +(-1.46251 - 3.72304i) q^{48} +16.0054i q^{49} +(-6.32918 - 3.15300i) q^{50} -0.352648i q^{51} +(-2.46546 - 5.47999i) q^{52} +(-0.934134 - 5.89789i) q^{53} +(1.12365 + 0.858733i) q^{54} +(-0.0997595 - 5.99281i) q^{55} +(-7.15578 - 11.5255i) q^{56} +(0.0263137 - 0.0263137i) q^{57} +(8.13084 + 1.49059i) q^{58} +(-3.53381 - 10.8759i) q^{59} +(4.39258 + 0.839774i) q^{60} +(-1.26478 + 3.89259i) q^{61} +(4.47410 - 8.27866i) q^{62} +(4.27362 + 2.17752i) q^{63} +(7.16999 + 3.54841i) q^{64} +(6.65219 + 0.940388i) q^{65} +(1.08369 + 3.63250i) q^{66} +(8.89404 + 1.40868i) q^{67} +(0.473973 + 0.522296i) q^{68} +(-1.06979 - 1.47243i) q^{69} +(15.1671 + 0.115090i) q^{70} +(-9.59181 + 13.2020i) q^{71} +(-2.81836 + 0.238382i) q^{72} +(4.09605 - 2.08704i) q^{73} +(0.321677 - 13.2717i) q^{74} +(-3.41590 + 3.65125i) q^{75} +(-0.00360574 + 0.0743391i) q^{76} +(5.83669 + 11.4552i) q^{77} +(-4.21161 + 0.562813i) q^{78} +(-1.31184 - 0.953110i) q^{79} +(-7.63440 + 4.66004i) q^{80} +(0.809017 - 0.587785i) q^{81} +(7.10066 - 6.76460i) q^{82} +(0.977173 - 6.16963i) q^{83} +(-9.25618 + 2.51886i) q^{84} +(-0.776676 + 0.136302i) q^{85} +(7.47680 + 2.63130i) q^{86} +(2.65366 - 5.20810i) q^{87} +(-6.48725 - 3.92346i) q^{88} +(-13.2764 - 4.31376i) q^{89} +(1.45698 - 2.80664i) q^{90} +(-13.7056 + 4.45321i) q^{91} +(3.56343 + 0.742940i) q^{92} +(-4.70515 - 4.70515i) q^{93} +(-13.3554 + 9.21725i) q^{94} +(-0.0681241 - 0.0477831i) q^{95} +(3.85379 - 4.14105i) q^{96} +(8.89748 - 1.40922i) q^{97} +(-20.4110 + 9.78438i) q^{98} +2.68044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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