LMFDB - Embedded newform 403.2.l.c.25.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.18
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0456796i q^{2} +(-1.38907 - 2.40594i) q^{3} +1.99791 q^{4} +(1.25901 + 0.726890i) q^{5} +(0.109902 - 0.0634522i) q^{6} +(3.37083 - 1.94615i) q^{7} +0.182623i q^{8} +(-2.35904 + 4.08597i) q^{9} +O(q^{10})$	\(q+0.0456796i q^{2} +(-1.38907 - 2.40594i) q^{3} +1.99791 q^{4} +(1.25901 + 0.726890i) q^{5} +(0.109902 - 0.0634522i) q^{6} +(3.37083 - 1.94615i) q^{7} +0.182623i q^{8} +(-2.35904 + 4.08597i) q^{9} +(-0.0332040 + 0.0575110i) q^{10} +(4.61476 + 2.66433i) q^{11} +(-2.77524 - 4.80686i) q^{12} +(-2.43729 + 2.65700i) q^{13} +(0.0888992 + 0.153978i) q^{14} -4.03881i q^{15} +3.98748 q^{16} +(-0.180975 - 0.313457i) q^{17} +(-0.186645 - 0.107760i) q^{18} +(-1.92657 + 1.11231i) q^{19} +(2.51539 + 1.45226i) q^{20} +(-9.36464 - 5.40668i) q^{21} +(-0.121706 + 0.210800i) q^{22} +0.428612 q^{23} +(0.439380 - 0.253676i) q^{24} +(-1.44326 - 2.49980i) q^{25} +(-0.121370 - 0.111334i) q^{26} +4.77305 q^{27} +(6.73462 - 3.88823i) q^{28} -7.70065 q^{29} +0.184491 q^{30} +(-5.49130 - 0.919550i) q^{31} +0.547392i q^{32} -14.8038i q^{33} +(0.0143186 - 0.00826685i) q^{34} +5.65854 q^{35} +(-4.71315 + 8.16342i) q^{36} +(5.16646 - 2.98286i) q^{37} +(-0.0508098 - 0.0880051i) q^{38} +(9.77814 + 2.17322i) q^{39} +(-0.132747 + 0.229924i) q^{40} +(1.59673 + 0.921870i) q^{41} +(0.246975 - 0.427773i) q^{42} +(-4.68376 - 8.11250i) q^{43} +(9.21989 + 5.32311i) q^{44} +(-5.94010 + 3.42952i) q^{45} +0.0195788i q^{46} +3.48799i q^{47} +(-5.53890 - 9.59366i) q^{48} +(4.07498 - 7.05808i) q^{49} +(0.114190 - 0.0659276i) q^{50} +(-0.502774 + 0.870829i) q^{51} +(-4.86949 + 5.30845i) q^{52} +(-2.49130 + 4.31506i) q^{53} +0.218031i q^{54} +(3.87335 + 6.70884i) q^{55} +(0.355411 + 0.615590i) q^{56} +(5.35230 + 3.09015i) q^{57} -0.351763i q^{58} +(-12.0997 + 6.98577i) q^{59} -8.06918i q^{60} -11.3454 q^{61} +(0.0420047 - 0.250840i) q^{62} +18.3641i q^{63} +7.94996 q^{64} +(-4.99991 + 1.57354i) q^{65} +0.676231 q^{66} +(9.07912 + 5.24183i) q^{67} +(-0.361572 - 0.626261i) q^{68} +(-0.595372 - 1.03122i) q^{69} +0.258480i q^{70} +(1.24196 + 0.717045i) q^{71} +(-0.746192 - 0.430814i) q^{72} +(-11.8818 - 6.85998i) q^{73} +(0.136256 + 0.236002i) q^{74} +(-4.00959 + 6.94481i) q^{75} +(-3.84913 + 2.22230i) q^{76} +20.7407 q^{77} +(-0.0992717 + 0.446661i) q^{78} +(-1.88892 - 3.27171i) q^{79} +(5.02028 + 2.89846i) q^{80} +(0.447000 + 0.774227i) q^{81} +(-0.0421106 + 0.0729377i) q^{82} +(10.3146 + 5.95513i) q^{83} +(-18.7097 - 10.8021i) q^{84} -0.526195i q^{85} +(0.370576 - 0.213952i) q^{86} +(10.6968 + 18.5273i) q^{87} +(-0.486568 + 0.842761i) q^{88} +16.5238i q^{89} +(-0.156659 - 0.271341i) q^{90} +(-3.04477 + 13.6996i) q^{91} +0.856329 q^{92} +(5.41543 + 14.4891i) q^{93} -0.159330 q^{94} -3.23410 q^{95} +(1.31699 - 0.760367i) q^{96} -14.3360i q^{97} +(0.322410 + 0.186143i) q^{98} +(-21.7728 + 12.5705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$			0.0456796i			0.0323003i	0.999870	+	0.0161502i	$0.00514098\pi$
$2$			0.0456796i			0.0323003i	−0.999870	+	0.0161502i	$0.994859\pi$
$3$	−1.38907	−	2.40594i	−0.801981	−	1.38907i	−0.918311	−	0.395860i	$-0.870446\pi$
$3$	−1.38907	−	2.40594i	−0.801981	−	1.38907i	0.116330	−	0.993211i	$-0.462887\pi$
$4$	1.99791			0.998957
$5$	1.25901	+	0.726890i	0.563046	+	0.325075i	0.754367	−	0.656453i	$-0.227944\pi$
$5$	1.25901	+	0.726890i	0.563046	+	0.325075i	−0.191321	+	0.981528i	$0.561277\pi$
$6$	0.109902	−	0.0634522i	0.0448675	−	0.0259042i
$7$	3.37083	−	1.94615i	1.27405	−	0.735575i	0.298305	−	0.954471i	$-0.403579\pi$
$7$	3.37083	−	1.94615i	1.27405	−	0.735575i	0.975748	+	0.218896i	$0.0702455\pi$
$8$			0.182623i			0.0645670i
$9$	−2.35904	+	4.08597i	−0.786346	+	1.36199i
$10$	−0.0332040	+	0.0575110i	−0.0105000	+	0.0181866i
$11$	4.61476	+	2.66433i	1.39140	+	0.803327i	0.993471	−	0.114088i	$-0.0363946\pi$
$11$	4.61476	+	2.66433i	1.39140	+	0.803327i	0.397932	+	0.917415i	$0.369728\pi$
$12$	−2.77524	−	4.80686i	−0.801144	−	1.38762i
$13$	−2.43729	+	2.65700i	−0.675982	+	0.736918i
$13$	−2.43729	+	2.65700i	−0.675982	+	0.736918i
$14$	0.0888992	+	0.153978i	0.0237593	+	0.0411523i
$15$		−	4.03881i		−	1.04282i
$16$	3.98748			0.996871
$17$	−0.180975	−	0.313457i	−0.0438928	−	0.0760246i	0.843244	−	0.537530i	$-0.180643\pi$
$17$	−0.180975	−	0.313457i	−0.0438928	−	0.0760246i	−0.887137	+	0.461506i	$0.847309\pi$
$18$	−0.186645	−	0.107760i	−0.0439927	−	0.0253992i
$19$	−1.92657	+	1.11231i	−0.441986	+	0.255181i	−0.704440	−	0.709764i	$-0.748802\pi$
$19$	−1.92657	+	1.11231i	−0.441986	+	0.255181i	0.262453	+	0.964945i	$0.415468\pi$
$20$	2.51539	+	1.45226i	0.562459	+	0.324736i
$21$	−9.36464	−	5.40668i	−2.04353	−	1.17983i
$22$	−0.121706	+	0.210800i	−0.0259477	+	0.0449428i
$23$	0.428612			0.0893718			0.0446859	−	0.999001i	$-0.485771\pi$
$23$	0.428612			0.0893718			0.0446859	+	0.999001i	$0.485771\pi$
$24$	0.439380	−	0.253676i	0.0896881	−	0.0517814i
$25$	−1.44326	−	2.49980i	−0.288653	−	0.499961i
$26$	−0.121370	−	0.111334i	−0.0238027	−	0.0218345i
$27$	4.77305			0.918575
$28$	6.73462	−	3.88823i	1.27272	−	0.734807i
$29$	−7.70065			−1.42998			−0.714988	−	0.699137i	$-0.753568\pi$
$29$	−7.70065			−1.42998			−0.714988	+	0.699137i	$0.753568\pi$
$30$	0.184491			0.0336833
$31$	−5.49130	−	0.919550i	−0.986267	−	0.165156i
$31$	−5.49130	−	0.919550i	−0.986267	−	0.165156i
$32$			0.547392i			0.0967662i
$33$		−	14.8038i		−	2.57701i
$34$	0.0143186	−	0.00826685i	0.00245562	−	0.00141775i
$35$	5.65854			0.956468
$36$	−4.71315	+	8.16342i	−0.785525	+	1.36057i
$37$	5.16646	−	2.98286i	0.849361	−	0.490379i	−0.0110742	−	0.999939i	$-0.503525\pi$
$37$	5.16646	−	2.98286i	0.849361	−	0.490379i	0.860435	+	0.509560i	$0.170192\pi$
$38$	−0.0508098	−	0.0880051i	−0.00824243	−	0.0142763i
$39$	9.77814	+	2.17322i	1.56576	+	0.347994i
$40$	−0.132747	+	0.229924i	−0.0209891	+	0.0363542i
$41$	1.59673	+	0.921870i	0.249367	+	0.143972i	0.619474	−	0.785017i	$-0.287346\pi$
$41$	1.59673	+	0.921870i	0.249367	+	0.143972i	−0.370108	+	0.928989i	$0.620679\pi$
$42$	0.246975	−	0.427773i	0.0381090	−	0.0660067i
$43$	−4.68376	−	8.11250i	−0.714266	−	1.23715i	−0.963242	−	0.268636i	$-0.913427\pi$
$43$	−4.68376	−	8.11250i	−0.714266	−	1.23715i	0.248976	−	0.968510i	$-0.419906\pi$
$44$	9.21989	+	5.32311i	1.38995	+	0.802489i
$45$	−5.94010	+	3.42952i	−0.885498	+	0.511243i
$46$			0.0195788i			0.00288674i
$47$			3.48799i			0.508776i	0.967102	+	0.254388i	$0.0818741\pi$
$47$			3.48799i			0.508776i	−0.967102	+	0.254388i	$0.918126\pi$
$48$	−5.53890	−	9.59366i	−0.799471	−	1.38472i
$49$	4.07498	−	7.05808i	0.582140	−	1.00830i
$50$	0.114190	−	0.0659276i	0.0161489	−	0.00932357i
$51$	−0.502774	+	0.870829i	−0.0704024	+	0.121941i
$52$	−4.86949	+	5.30845i	−0.675277	+	0.736149i
$53$	−2.49130	+	4.31506i	−0.342206	+	0.592719i	−0.984842	−	0.173453i	$-0.944507\pi$
$53$	−2.49130	+	4.31506i	−0.342206	+	0.592719i	0.642636	+	0.766172i	$0.277841\pi$
$54$			0.218031i			0.0296703i
$55$	3.87335	+	6.70884i	0.522283	+	0.904620i
$56$	0.355411	+	0.615590i	0.0474938	+	0.0822617i
$57$	5.35230	+	3.09015i	0.708929	+	0.409300i
$58$		−	0.351763i		−	0.0461887i
$59$	−12.0997	+	6.98577i	−1.57525	+	0.909470i	−0.579738	+	0.814803i	$0.696845\pi$
$59$	−12.0997	+	6.98577i	−1.57525	+	0.909470i	−0.995509	+	0.0946669i	$0.969821\pi$
$60$		−	8.06918i		−	1.04173i
$61$	−11.3454			−1.45263			−0.726314	−	0.687363i	$-0.758768\pi$
$61$	−11.3454			−1.45263			−0.726314	+	0.687363i	$0.758768\pi$
$62$	0.0420047	−	0.250840i	0.00533460	−	0.0318568i
$63$			18.3641i			2.31366i
$64$	7.94996			0.993746
$65$	−4.99991	+	1.57354i	−0.620163	+	0.195174i
$66$	0.676231			0.0832383
$67$	9.07912	+	5.24183i	1.10919	+	0.640392i	0.938620	−	0.344954i	$-0.112105\pi$
$67$	9.07912	+	5.24183i	1.10919	+	0.640392i	0.170571	+	0.985345i	$0.445439\pi$
$68$	−0.361572	−	0.626261i	−0.0438470	−	0.0759453i
$69$	−0.595372	−	1.03122i	−0.0716744	−	0.124144i
$70$			0.258480i			0.0308942i
$71$	1.24196	+	0.717045i	0.147393	+	0.0850976i	0.571883	−	0.820335i	$-0.306213\pi$
$71$	1.24196	+	0.717045i	0.147393	+	0.0850976i	−0.424490	+	0.905433i	$0.639546\pi$
$72$	−0.746192	−	0.430814i	−0.0879396	−	0.0507719i
$73$	−11.8818	−	6.85998i	−1.39066	−	0.802900i	−0.397275	−	0.917700i	$-0.630044\pi$
$73$	−11.8818	−	6.85998i	−1.39066	−	0.802900i	−0.993389	+	0.114800i	$0.963377\pi$
$74$	0.136256	+	0.236002i	0.0158394	+	0.0274346i
$75$	−4.00959	+	6.94481i	−0.462987	+	0.801918i
$76$	−3.84913	+	2.22230i	−0.441525	+	0.254915i
$77$	20.7407			2.36363
$78$	−0.0992717	+	0.446661i	−0.0112403	+	0.0505744i
$79$	−1.88892	−	3.27171i	−0.212520	−	0.368096i	0.739982	−	0.672626i	$-0.234834\pi$
$79$	−1.88892	−	3.27171i	−0.212520	−	0.368096i	−0.952503	+	0.304530i	$0.901500\pi$
$80$	5.02028	+	2.89846i	0.561285	+	0.324058i
$81$	0.447000	+	0.774227i	0.0496667	+	0.0860252i
$82$	−0.0421106	+	0.0729377i	−0.00465034	+	0.00805463i
$83$	10.3146	+	5.95513i	1.13217	+	0.653660i	0.944480	−	0.328567i	$-0.106566\pi$
$83$	10.3146	+	5.95513i	1.13217	+	0.653660i	0.187692	+	0.982228i	$0.439899\pi$
$84$	−18.7097	−	10.8021i	−2.04140	−	1.17860i
$85$		−	0.526195i		−	0.0570738i
$86$	0.370576	−	0.213952i	0.0399602	−	0.0230710i
$87$	10.6968	+	18.5273i	1.14681	+	1.98634i
$88$	−0.486568	+	0.842761i	−0.0518684	+	0.0898386i
$89$			16.5238i			1.75152i	0.482747	+	0.875760i	$0.339639\pi$
$89$			16.5238i			1.75152i	−0.482747	+	0.875760i	$0.660361\pi$
$90$	−0.156659	−	0.271341i	−0.0165133	−	0.0286019i
$91$	−3.04477	+	13.6996i	−0.319179	+	1.43611i
$92$	0.856329			0.0892785
$93$	5.41543	+	14.4891i	0.561554	+	1.50245i
$94$	−0.159330			−0.0164336
$95$	−3.23410			−0.331812
$96$	1.31699	−	0.760367i	0.134415	−	0.0776046i
$97$		−	14.3360i		−	1.45560i	−0.685788	−	0.727802i	$-0.740542\pi$
$97$		−	14.3360i		−	1.45560i	0.685788	−	0.727802i	$-0.259458\pi$
$98$	0.322410	+	0.186143i	0.0325683	+	0.0188033i
$99$	−21.7728	+	12.5705i	−2.18825	+	1.26338i
$100$	−2.88351	−	4.99439i	−0.288351	−	0.499439i
$101$	12.5359			1.24737			0.623683	−	0.781677i	$-0.285636\pi$
$101$	12.5359			1.24737			0.623683	+	0.781677i	$0.285636\pi$
$102$	−0.0397791	−	0.0229665i	−0.00393872	−	0.00227402i
$103$	−2.67855	+	4.63938i	−0.263925	+	0.457131i	−0.967281	−	0.253706i	$-0.918350\pi$
$103$	−2.67855	+	4.63938i	−0.263925	+	0.457131i	0.703356	+	0.710837i	$0.251684\pi$
$104$	−0.485228	−	0.445105i	−0.0475805	−	0.0436461i
$105$	−7.86011	−	13.6141i	−0.767069	−	1.32860i
$106$	−0.197110	−	0.113801i	−0.0191450	−	0.0110534i
$107$	−5.65905	−	9.80176i	−0.547081	−	0.947571i	−0.998473	−	0.0552458i	$-0.982406\pi$
$107$	−5.65905	−	9.80176i	−0.547081	−	0.947571i	0.451392	−	0.892326i	$-0.350928\pi$
$108$	9.53615			0.917616
$109$			3.50754i			0.335962i	0.985790	+	0.167981i	$0.0537247\pi$
$109$			3.50754i			0.335962i	−0.985790	+	0.167981i	$0.946275\pi$
$110$	−0.306457	+	0.176933i	−0.0292195	+	0.0168699i
$111$	−14.3532	−	8.28680i	−1.36234	−	0.786549i
$112$	13.4411	−	7.76023i	1.27007	−	0.733273i
$113$	6.52165	−	11.2958i	0.613505	−	1.06262i	−0.377140	−	0.926156i	$-0.623092\pi$
$113$	6.52165	−	11.2958i	0.613505	−	1.06262i	0.990645	−	0.136466i	$-0.0435743\pi$
$114$	−0.141157	+	0.244491i	−0.0132205	+	0.0228986i
$115$	0.539627	+	0.311554i	0.0503204	+	0.0290525i
$116$	−15.3852			−1.42848
$117$	−5.10675	−	16.2266i	−0.472119	−	1.50015i
$118$	−0.319107	−	0.552709i	−0.0293762	−	0.0508810i
$119$	−1.22007	−	0.704407i	−0.111844	−	0.0645729i
$120$	0.737579			0.0673314
$121$	8.69734	+	15.0642i	0.790668	+	1.36948i
$122$		−	0.518253i		−	0.0469204i
$123$		−	5.12217i		−	0.461851i
$124$	−10.9712	−	1.83718i	−0.985238	−	0.164984i
$125$		−	11.4653i		−	1.02548i
$126$	−0.838866			−0.0747321
$127$	0.152041	+	0.263343i	0.0134915	+	0.0233679i	0.872692	−	0.488271i	$-0.162372\pi$
$127$	0.152041	+	0.263343i	0.0134915	+	0.0233679i	−0.859201	+	0.511638i	$0.829039\pi$
$128$			1.45794i			0.128865i
$129$	−13.0121	+	22.5377i	−1.14566	+	1.98433i
$130$	−0.0718788	−	0.228394i	−0.00630418	−	0.0200315i
$131$	−2.18790	−	3.78955i	−0.191158	−	0.331095i	0.754477	−	0.656327i	$-0.227891\pi$
$131$	−2.18790	−	3.78955i	−0.191158	−	0.331095i	−0.945634	+	0.325232i	$0.894557\pi$
$132$		−	29.5767i		−	2.57432i
$133$	−4.32943	+	7.49880i	−0.375409	+	0.650228i
$134$	−0.239445	+	0.414730i	−0.0206849	+	0.0358272i
$135$	6.00932	+	3.46948i	0.517200	+	0.298606i
$136$	0.0572445	−	0.0330501i	0.00490868	−	0.00283403i
$137$	−5.51009	−	3.18125i	−0.470759	−	0.271793i	0.245799	−	0.969321i	$-0.420950\pi$
$137$	−5.51009	−	3.18125i	−0.470759	−	0.271793i	−0.716557	+	0.697528i	$0.754283\pi$
$138$	0.0471055	−	0.0271964i	0.00400988	−	0.00231511i
$139$	5.18457			0.439749			0.219875	−	0.975528i	$-0.429435\pi$
$139$	5.18457			0.439749			0.219875	+	0.975528i	$0.429435\pi$
$140$	11.3053			0.955470
$141$	8.39191	−	4.84507i	0.706726	−	0.408029i
$142$	−0.0327543	+	0.0567321i	−0.00274868	+	0.00476085i
$143$	−18.3266	+	5.76765i	−1.53255	+	0.482315i
$144$	−9.40662	+	16.2928i	−0.783885	+	1.35773i
$145$	−9.69520	−	5.59753i	−0.805143	−	0.464849i
$146$	0.313361	−	0.542757i	0.0259339	−	0.0449189i
$147$	−22.6418			−1.86746
$148$	10.3221	−	5.95949i	0.848475	−	0.489867i
$149$	13.3000	−	7.67878i	1.08958	−	0.629070i	0.156116	−	0.987739i	$-0.450103\pi$
$149$	13.3000	−	7.67878i	1.08958	−	0.629070i	0.933465	+	0.358669i	$0.116769\pi$
$150$	−0.317236	−	0.183156i	−0.0259022	−	0.0149546i
$151$			0.418901i			0.0340897i	0.999855	+	0.0170449i	$0.00542581\pi$
$151$			0.418901i			0.0340897i	−0.999855	+	0.0170449i	$0.994574\pi$
$152$	−0.203133	−	0.351837i	−0.0164763	−	0.0285377i
$153$	1.70770			0.138060
$154$			0.947428i			0.0763459i
$155$	−6.24520	−	5.14930i	−0.501626	−	0.413601i
$156$	19.5359	+	4.34191i	1.56412	+	0.347631i
$157$	2.15899			0.172306			0.0861530	−	0.996282i	$-0.472543\pi$
$157$	2.15899			0.172306			0.0861530	+	0.996282i	$0.472543\pi$
$158$	0.149450	−	0.0862851i	0.0118896	−	0.00686447i
$159$	13.8424			1.09777
$160$	−0.397894	+	0.689173i	−0.0314563	+	0.0544839i
$161$	1.44478	−	0.834142i	0.113864	−	0.0657396i
$162$	−0.0353663	+	0.0204188i	−0.00277864	+	0.00160425i
$163$			15.3206i			1.20000i	0.800000	+	0.600000i	$0.204833\pi$
$163$			15.3206i			1.20000i	−0.800000	+	0.600000i	$0.795167\pi$
$164$	3.19012	+	1.84182i	0.249107	+	0.143822i
$165$	10.7607	−	18.6381i	0.837721	−	1.45098i
$166$	−0.272028	+	0.471166i	−0.0211134	+	0.0365696i
$167$	17.2091	−	9.93568i	1.33168	−	0.768846i	0.346123	−	0.938189i	$-0.387498\pi$
$167$	17.2091	−	9.93568i	1.33168	−	0.768846i	0.985557	+	0.169344i	$0.0541648\pi$
$168$	0.987383	−	1.71020i	0.0761783	−	0.131945i
$169$	−1.11925	−	12.9517i	−0.0860958	−	0.996287i
$170$	0.0240363			0.00184350
$171$		−	10.4959i		−	0.802642i
$172$	−9.35774	−	16.2081i	−0.713521	−	1.23585i
$173$	−1.91073	+	3.30947i	−0.145270	+	0.251615i	−0.929474	−	0.368889i	$-0.879738\pi$
$173$	−1.91073	+	3.30947i	−0.145270	+	0.251615i	0.784204	+	0.620503i	$0.213072\pi$
$174$	−0.846320	+	0.488623i	−0.0641594	+	0.0370424i
$175$	−9.72998	−	5.61760i	−0.735517	−	0.424651i
$176$	18.4013	+	10.6240i	1.38705	+	0.800813i
$177$	33.6147	+	19.4075i	2.52664	+	1.45875i
$178$	−0.754800			−0.0565747
$179$	3.03131	+	5.25038i	0.226571	+	0.392432i	0.956790	−	0.290781i	$-0.0939152\pi$
$179$	3.03131	+	5.25038i	0.226571	+	0.392432i	−0.730219	+	0.683213i	$0.760582\pi$
$180$	−11.8678	+	6.85188i	−0.884574	+	0.510709i
$181$	3.55562	−	6.15851i	0.264287	−	0.457758i	−0.703090	−	0.711101i	$-0.748197\pi$
$181$	3.55562	−	6.15851i	0.264287	−	0.457758i	0.967377	+	0.253343i	$0.0815301\pi$
$182$	−0.625792	−	0.139084i	−0.0463868	−	0.0103096i
$183$	15.7596	+	27.2964i	1.16498	+	2.01780i
$184$			0.0782744i			0.00577046i
$185$	8.67284			0.637640
$186$	−0.661855	+	0.247374i	−0.0485296	+	0.0181384i
$187$		−	1.92871i		−	0.141041i
$188$			6.96871i			0.508245i
$189$	16.0891	−	9.28907i	1.17031	−	0.675680i
$190$		−	0.147732i		−	0.0107176i
$191$	−5.02568	+	8.70473i	−0.363645	+	0.629852i	−0.988558	−	0.150843i	$-0.951801\pi$
$191$	−5.02568	+	8.70473i	−0.363645	+	0.629852i	0.624912	+	0.780695i	$0.285135\pi$
$192$	−11.0431	−	19.1272i	−0.796965	−	1.38038i
$193$	0.620882	−	0.358467i	0.0446921	−	0.0258030i	−0.477487	−	0.878639i	$-0.658452\pi$
$193$	0.620882	−	0.358467i	0.0446921	−	0.0258030i	0.522180	+	0.852836i	$0.325119\pi$
$194$	0.654864			0.0470165
$195$	10.7311	+	9.84374i	0.768469	+	0.704925i
$196$	8.14146	−	14.1014i	0.581533	−	1.00724i
$197$	−4.76127	−	2.74892i	−0.339227	−	0.195853i	0.320703	−	0.947180i	$-0.396081\pi$
$197$	−4.76127	−	2.74892i	−0.339227	−	0.195853i	−0.659930	+	0.751327i	$0.729414\pi$
$198$	−0.574216	−	0.994571i	−0.0408078	−	0.0706811i
$199$	7.59611	−	13.1569i	0.538474	−	0.932665i	−0.460512	−	0.887653i	$-0.652334\pi$
$199$	7.59611	−	13.1569i	0.538474	−	0.932665i	0.998986	−	0.0450113i	$-0.0143324\pi$
$200$	0.456522	−	0.263573i	0.0322810	−	0.0186374i
$201$		−	29.1251i		−	2.05433i
$202$			0.572633i			0.0402903i
$203$	−25.9576	+	14.9866i	−1.82186	+	1.05185i
$204$	−1.00450	+	1.73984i	−0.0703289	+	0.121813i
$205$	1.34020	+	2.32129i	0.0936033	+	0.162126i
$206$	−0.211925	−	0.122355i	−0.0147655	−	0.00852486i
$207$	−1.01111	+	1.75130i	−0.0702771	+	0.121723i
$208$	−9.71865	+	10.5947i	−0.673867	+	0.734612i
$209$	−11.8542			−0.819975
$210$	0.621887	−	0.359047i	0.0429143	−	0.0247766i
$211$	11.4894	+	19.9002i	0.790962	+	1.36999i	0.925372	+	0.379060i	$0.123753\pi$
$211$	11.4894	+	19.9002i	0.790962	+	1.36999i	−0.134410	+	0.990926i	$0.542914\pi$
$212$	−4.97740	+	8.62111i	−0.341849	+	0.592100i
$213$		−	3.98411i		−	0.272986i
$214$	0.447740	−	0.258503i	0.0306069	−	0.0176709i
$215$		−	13.6183i		−	0.928760i
$216$			0.871669i			0.0593096i
$217$	−20.2998	+	7.58725i	−1.37804	+	0.515056i
$218$	−0.160223			−0.0108517
$219$			38.1160i			2.57564i
$220$	7.73862	+	13.4037i	0.521738	+	0.903677i
$221$	1.27394	+	0.283137i	0.0856947	+	0.0190459i
$222$	0.378538	−	0.655646i	0.0254058	−	0.0440041i
$223$	0.675531	−	0.390018i	0.0452369	−	0.0261175i	−0.477211	−	0.878789i	$-0.658352\pi$
$223$	0.675531	−	0.390018i	0.0452369	−	0.0261175i	0.522448	+	0.852671i	$0.325019\pi$
$224$	1.06531	+	1.84517i	0.0711788	+	0.123285i
$225$	13.6188			0.907923
$226$	0.515988	+	0.297906i	0.0343230	+	0.0198164i
$227$	3.25775	+	1.88086i	0.216225	+	0.124837i	0.604201	−	0.796832i	$-0.293492\pi$
$227$	3.25775	+	1.88086i	0.216225	+	0.124837i	−0.387976	+	0.921669i	$0.626826\pi$
$228$	10.6934	+	6.17385i	0.708189	+	0.408873i
$229$	−2.54141	+	1.46728i	−0.167941	+	0.0969608i	−0.581615	−	0.813464i	$-0.697579\pi$
$229$	−2.54141	+	1.46728i	−0.167941	+	0.0969608i	0.413674	+	0.910425i	$0.364245\pi$
$230$	−0.0142316	+	0.0246499i	−0.000938406	+	0.00162537i
$231$	−28.8104	−	49.9010i	−1.89558	−	3.28325i
$232$		−	1.40632i		−	0.0923292i
$233$	−9.22280			−0.604205			−0.302103	−	0.953275i	$-0.597689\pi$
$233$	−9.22280			−0.604205			−0.302103	+	0.953275i	$0.597689\pi$
$234$	0.741226	−	0.233274i	0.0484555	−	0.0152496i
$235$	−2.53539	+	4.39142i	−0.165390	+	0.286465i
$236$	−24.1742	+	13.9570i	−1.57360	+	0.908521i
$237$	−5.24769	+	9.08927i	−0.340874	+	0.590411i
$238$	0.0321770	−	0.0557322i	0.00208573	−	0.00361258i
$239$	−5.22248	−	3.01520i	−0.337814	−	0.195037i	0.321491	−	0.946913i	$-0.395816\pi$
$239$	−5.22248	−	3.01520i	−0.337814	−	0.195037i	−0.659305	+	0.751876i	$0.729149\pi$
$240$		−	16.1047i		−	1.03955i
$241$	−7.07505	+	4.08478i	−0.455744	+	0.263124i	−0.710253	−	0.703946i	$-0.751420\pi$
$241$	−7.07505	+	4.08478i	−0.455744	+	0.263124i	0.254509	+	0.967070i	$0.418086\pi$
$242$	−0.688128	+	0.397291i	−0.0442345	+	0.0255388i
$243$	8.40141	−	14.5517i	0.538951	−	0.933490i
$244$	−22.6671			−1.45111
$245$	10.2609	−	5.92413i	0.655544	−	0.378479i
$246$	0.233979			0.0149179
$247$	1.74022	−	7.82991i	0.110728	−	0.498206i
$248$	0.167931	−	1.00284i	0.0106636	−	0.0636803i
$249$		−	33.0884i		−	2.09689i
$250$	0.523728			0.0331235
$251$	13.8774	+	24.0364i	0.875934	+	1.51716i	0.855765	+	0.517365i	$0.173087\pi$
$251$	13.8774	+	24.0364i	0.875934	+	1.51716i	0.0201694	+	0.999797i	$0.493579\pi$
$252$			36.6900i			2.31125i
$253$	1.97794	+	1.14196i	0.124352	+	0.0717947i
$254$	−0.0120294	+	0.00694518i	−0.000754792	+	0.000435779i
$255$	−1.26599	+	0.730922i	−0.0792796	+	0.0457721i
$256$	15.8333			0.989583
$257$	−4.00758	+	6.94133i	−0.249986	+	0.432988i	−0.963522	−	0.267630i	$-0.913759\pi$
$257$	−4.00758	+	6.94133i	−0.249986	+	0.432988i	0.713536	+	0.700619i	$0.247093\pi$
$258$	−1.02951	−	0.594389i	−0.0640946	−	0.0370050i
$259$	11.6102	−	20.1094i	0.721421	−	1.24954i
$260$	−9.98939	+	3.14380i	−0.619516	+	0.194970i
$261$	18.1661	−	31.4647i	1.12445	−	1.94761i
$262$	0.173105	−	0.0999422i	0.0106945	−	0.00617445i
$263$	2.00561			0.123671			0.0618355	−	0.998086i	$-0.480305\pi$
$263$	2.00561			0.123671			0.0618355	+	0.998086i	$0.480305\pi$
$264$	2.70351			0.166390
$265$	−6.27314	+	3.62180i	−0.385356	+	0.222485i
$266$	−0.342542	−	0.197767i	−0.0210026	−	0.0121258i
$267$	39.7553	−	22.9527i	2.43298	−	1.40468i
$268$	18.1393	+	10.4727i	1.10803	+	0.639724i
$269$	−6.12969	+	10.6169i	−0.373734	+	0.647326i	−0.990137	−	0.140105i	$-0.955256\pi$
$269$	−6.12969	+	10.6169i	−0.373734	+	0.647326i	0.616403	+	0.787431i	$0.288589\pi$
$270$	−0.158485	+	0.274503i	−0.00964506	+	0.0167057i
$271$		−	15.2475i		−	0.926219i	−0.886301	−	0.463110i	$-0.846734\pi$
$271$		−	15.2475i		−	0.926219i	0.886301	−	0.463110i	$-0.153266\pi$
$272$	−0.721634	−	1.24991i	−0.0437555	−	0.0757867i
$273$	37.1898	−	11.7042i	2.25083	−	0.708368i
$274$	0.145318	−	0.251698i	0.00877899	−	0.0152057i
$275$		−	15.3813i		−	0.927529i
$276$	−1.18950	−	2.06028i	−0.0715996	−	0.124014i
$277$	−5.74669			−0.345285			−0.172643	−	0.984985i	$-0.555231\pi$
$277$	−5.74669			−0.345285			−0.172643	+	0.984985i	$0.555231\pi$
$278$			0.236829i			0.0142040i
$279$	16.7114	−	20.2681i	1.00049	−	1.21342i
$280$			1.03338i			0.0617562i
$281$		−	23.5073i		−	1.40233i	−0.713000	−	0.701164i	$-0.752664\pi$
$281$		−	23.5073i		−	1.40233i	0.713000	−	0.701164i	$-0.247336\pi$
$282$	0.221321	+	0.383339i	0.0131795	+	0.0228275i
$283$	−6.94506			−0.412841			−0.206420	−	0.978463i	$-0.566181\pi$
$283$	−6.94506			−0.412841			−0.206420	+	0.978463i	$0.566181\pi$
$284$	2.48132	+	1.43259i	0.147240	+	0.0850088i
$285$	4.49240	+	7.78106i	0.266107	+	0.460910i
$286$	−0.263464	−	0.837152i	−0.0155789	−	0.0495019i
$287$	7.17638			0.423608
$288$	−2.23663	−	1.29132i	−0.131795	−	0.0760917i
$289$	8.43450	−	14.6090i	0.496147	−	0.859352i
$290$	0.255693	−	0.442873i	0.0150148	−	0.0260064i
$291$	−34.4917	+	19.9138i	−2.02194	+	1.16737i
$292$	−23.7389	−	13.7056i	−1.38921	−	0.802062i
$293$	−11.2418	+	6.49047i	−0.656754	+	0.379177i	−0.791039	−	0.611766i	$-0.790460\pi$
$293$	−11.2418	+	6.49047i	−0.656754	+	0.379177i	0.134285	+	0.990943i	$0.457126\pi$
$294$		−	1.03427i		−	0.0603196i
$295$	−20.3115			−1.18258
$296$	0.544738	+	0.943514i	0.0316623	+	0.0548407i
$297$	22.0265	+	12.7170i	1.27811	+	0.737915i
$298$	0.350763	+	0.607540i	0.0203192	+	0.0351938i
$299$	−1.04465	+	1.13882i	−0.0604137	+	0.0658596i
$300$	−8.01081	+	13.8751i	−0.462504	+	0.801081i
$301$	−31.5763	−	18.2306i	−1.82003	−	1.05079i
$302$	−0.0191352			−0.00110111
$303$	−17.4132	−	30.1606i	−1.00036	−	1.73268i
$304$	−7.68218	+	4.43531i	−0.440604	+	0.254383i
$305$	−14.2840	−	8.24685i	−0.817898	−	0.472213i
$306$			0.0780072i			0.00445937i
$307$	13.7200	−	7.92122i	0.783040	−	0.452088i	−0.0544669	−	0.998516i	$-0.517346\pi$
$307$	13.7200	−	7.92122i	0.783040	−	0.452088i	0.837506	+	0.546427i	$0.184013\pi$
$308$	41.4382			2.36116
$309$	14.8828			0.846651
$310$	0.235218	−	0.285278i	0.0133595	−	0.0162027i
$311$	−20.1613			−1.14325			−0.571623	−	0.820517i	$-0.693686\pi$
$311$	−20.1613			−1.14325			−0.571623	+	0.820517i	$0.693686\pi$
$312$	−0.396880	+	1.78571i	−0.0224689	+	0.101096i
$313$	7.60195	+	13.1670i	0.429688	+	0.744241i	0.996845	−	0.0793685i	$-0.0252904\pi$
$313$	7.60195	+	13.1670i	0.429688	+	0.744241i	−0.567158	+	0.823609i	$0.691957\pi$
$314$			0.0986217i			0.00556554i
$315$	−13.3487	+	23.1206i	−0.752114	+	1.30270i
$316$	−3.77390	−	6.53659i	−0.212299	−	0.367712i
$317$	−4.85475	+	2.80289i	−0.272670	+	0.157426i	−0.630100	−	0.776514i	$-0.716986\pi$
$317$	−4.85475	+	2.80289i	−0.272670	+	0.157426i	0.357431	+	0.933940i	$0.383653\pi$
$318$			0.632313i			0.0354584i
$319$	−35.5367	−	20.5171i	−1.98967	−	1.14874i
$320$	10.0091	+	5.77875i	0.559525	+	0.323042i
$321$	−15.7216	+	27.2307i	−0.877496	+	1.51987i
$322$	0.0381033	+	0.0659968i	0.00212341	+	0.00367786i
$323$	0.697323	+	0.402599i	0.0388001	+	0.0224012i
$324$	0.893067	+	1.54684i	0.0496149	+	0.0859355i
$325$	10.1596	+	2.25800i	0.563554	+	0.125251i
$326$	−0.699837			−0.0387604
$327$	8.43895	−	4.87223i	0.466675	−	0.269435i
$328$	−0.168355	+	0.291599i	−0.00929583	+	0.0161009i
$329$	6.78815	+	11.7574i	0.374243	+	0.648208i
$330$	0.851381	+	0.491545i	0.0468670	+	0.0270587i
$331$	16.1012	+	9.29600i	0.884999	+	0.510955i	0.872304	−	0.488965i	$-0.162625\pi$
$331$	16.1012	+	9.29600i	0.884999	+	0.510955i	0.0126958	+	0.999919i	$0.495959\pi$
$332$	20.6077	+	11.8978i	1.13099	+	0.652978i
$333$			28.1467i			1.54243i
$334$	0.453857	+	0.786104i	0.0248340	+	0.0430137i
$335$	7.62047	+	13.1990i	0.416351	+	0.721141i
$336$	−37.3413	−	21.5590i	−2.03714	−	1.17614i
$337$	−1.60605			−0.0874871			−0.0437435	−	0.999043i	$-0.513928\pi$
$337$	−1.60605			−0.0874871			−0.0437435	+	0.999043i	$0.513928\pi$
$338$	0.591629	−	0.0511267i	0.0321804	−	0.00278092i
$339$	−36.2361			−1.96808
$340$		−	1.05129i		−	0.0570143i
$341$	−22.8911	−	18.8742i	−1.23962	−	1.02209i
$342$	0.479448			0.0259256
$343$		−	4.47601i		−	0.241682i
$344$	1.48153	−	0.855361i	0.0798787	−	0.0461180i
$345$		−	1.73108i		−	0.0931982i
$346$	−0.151175	−	0.0872811i	−0.00812723	−	0.00469226i
$347$	0.940923	+	1.62973i	0.0505114	+	0.0874883i	0.890176	−	0.455618i	$-0.150582\pi$
$347$	0.940923	+	1.62973i	0.0505114	+	0.0874883i	−0.839664	+	0.543106i	$0.817248\pi$
$348$	21.3712	+	37.0160i	1.14562	+	1.98427i
$349$			23.6256i			1.26465i	0.774704	+	0.632324i	$0.217899\pi$
$349$			23.6256i			1.26465i	−0.774704	+	0.632324i	$0.782101\pi$
$350$	0.256610	−	0.444461i	0.0137164	−	0.0237574i
$351$	−11.6333	+	12.6820i	−0.620940	+	0.676914i
$352$	−1.45844	+	2.52609i	−0.0777349	+	0.134641i
$353$	−17.0288	+	9.83158i	−0.906352	+	0.523282i	−0.879256	−	0.476350i	$-0.841959\pi$
$353$	−17.0288	+	9.83158i	−0.906352	+	0.523282i	−0.0270963	+	0.999633i	$0.508626\pi$
$354$	−0.886524	+	1.53550i	−0.0471182	+	0.0816112i
$355$	1.04243	+	1.80553i	0.0553262	+	0.0958278i
$356$			33.0131i			1.74969i
$357$			3.91389i			0.207145i
$358$	−0.239835	+	0.138469i	−0.0126757	+	0.00731831i
$359$	6.07359	+	3.50659i	0.320552	+	0.185071i	0.651638	−	0.758530i	$-0.274082\pi$
$359$	6.07359	+	3.50659i	0.320552	+	0.185071i	−0.331087	+	0.943600i	$0.607415\pi$
$360$	−0.626309	−	1.08480i	−0.0330094	−	0.0571739i
$361$	−7.02554	+	12.1686i	−0.369765	+	0.640452i
$362$	0.281318	+	0.162419i	0.0147857	+	0.00853655i
$363$	24.1625	−	41.8506i	1.26820	−	2.19659i
$364$	−6.08319	+	27.3706i	−0.318846	+	1.43461i
$365$	−9.97290	−	17.2736i	−0.522005	−	0.904140i
$366$	−1.24689	+	0.719890i	−0.0651758	+	0.0376292i
$367$	13.1443	−	22.7666i	0.686126	−	1.18841i	−0.286955	−	0.957944i	$-0.592643\pi$
$367$	13.1443	−	22.7666i	0.686126	−	1.18841i	0.973081	−	0.230462i	$-0.0740236\pi$
$368$	1.70908			0.0890921
$369$	−7.53347	+	4.34945i	−0.392177	+	0.226423i
$370$			0.396171i			0.0205960i
$371$			19.3937i			1.00687i
$372$	10.8196	+	28.9479i	0.560968	+	1.50088i
$373$	−0.891291			−0.0461493			−0.0230747	−	0.999734i	$-0.507346\pi$
$373$	−0.891291			−0.0461493			−0.0230747	+	0.999734i	$0.507346\pi$
$374$	0.0881025			0.00455567
$375$	−27.5848	+	15.9261i	−1.42447	+	0.822419i
$376$	−0.636988			−0.0328501
$377$	18.7687	−	20.4606i	0.966638	−	1.05377i
$378$	0.424321	+	0.734945i	0.0218247	+	0.0378015i
$379$	−6.00363	+	3.46620i	−0.308386	+	0.178046i	−0.646204	−	0.763165i	$-0.723644\pi$
$379$	−6.00363	+	3.46620i	−0.308386	+	0.178046i	0.337818	+	0.941211i	$0.390311\pi$
$380$	−6.46145			−0.331466
$381$	0.422392	−	0.731605i	0.0216398	−	0.0374813i
$382$	−0.397628	−	0.229571i	−0.0203444	−	0.0117459i
$383$	−1.27372	−	0.735384i	−0.0650841	−	0.0375763i	0.467105	−	0.884202i	$-0.345297\pi$
$383$	−1.27372	−	0.735384i	−0.0650841	−	0.0375763i	−0.532189	+	0.846626i	$0.678630\pi$
$384$	3.50771	−	2.02518i	0.179002	−	0.103347i
$385$	26.1128	+	15.0762i	1.33083	+	0.768356i
$386$	0.0163746	+	0.0283616i	0.000833445	+	0.00144357i
$387$	44.1966			2.24664
$388$		−	28.6422i		−	1.45408i
$389$	−15.4827	−	26.8168i	−0.785002	−	1.35966i	−0.928998	−	0.370085i	$-0.879329\pi$
$389$	−15.4827	−	26.8168i	−0.785002	−	1.35966i	0.143996	−	0.989578i	$-0.454005\pi$
$390$	−0.449658	+	0.490191i	−0.0227693	+	0.0248218i
$391$	−0.0775679	−	0.134352i	−0.00392278	−	0.00679445i
$392$	1.28897	+	0.744185i	0.0651027	+	0.0375870i
$393$	−6.07829	+	10.5279i	−0.306609	+	0.531063i
$394$	0.125570	−	0.217493i	0.00632610	−	0.0109571i
$395$		−	5.49215i		−	0.276340i
$396$	−43.5001	+	25.1148i	−2.18596	+	1.26207i
$397$	−11.8136	+	6.82056i	−0.592906	+	0.342314i	−0.766246	−	0.642548i	$-0.777877\pi$
$397$	−11.8136	+	6.82056i	−0.592906	+	0.342314i	0.173340	+	0.984862i	$0.444544\pi$
$398$	0.600999	+	0.346987i	0.0301254	+	0.0173929i
$399$	24.0556			1.20428
$400$	−5.75499	−	9.96793i	−0.287749	−	0.498397i
$401$			18.9283i			0.945235i	0.881268	+	0.472617i	$0.156691\pi$
$401$			18.9283i			0.945235i	−0.881268	+	0.472617i	$0.843309\pi$
$402$	1.33042			0.0663554
$403$	15.8271	−	12.3492i	0.788406	−	0.615155i
$404$	25.0456			1.24607
$405$			1.29968i			0.0645816i
$406$	−0.684582	−	1.18573i	−0.0339752	−	0.0588468i
$407$	31.7893			1.57574
$408$	−0.159033	−	0.0918180i	−0.00787333	−	0.00454567i
$409$	23.6452	−	13.6515i	1.16918	−	0.675025i	0.215691	−	0.976462i	$-0.430799\pi$
$409$	23.6452	−	13.6515i	1.16918	−	0.675025i	0.953486	+	0.301436i	$0.0974661\pi$
$410$	−0.106035	+	0.0612196i	−0.00523672	+	0.00302342i
$411$			17.6759i			0.871890i
$412$	−5.35150	+	9.26907i	−0.263650	+	0.456654i
$413$	−27.1907	+	47.0956i	−1.33797	+	2.31742i
$414$	−0.0799984	−	0.0461871i	−0.00393171	−	0.00226997i
$415$	8.65745	+	14.9951i	0.424977	+	0.736082i
$416$	−1.45442	−	1.33415i	−0.0713088	−	0.0654123i
$417$	−7.20173	−	12.4738i	−0.352670	−	0.610843i
$418$		−	0.541496i		−	0.0264855i
$419$	−7.67420			−0.374909			−0.187455	−	0.982273i	$-0.560024\pi$
$419$	−7.67420			−0.374909			−0.187455	+	0.982273i	$0.560024\pi$
$420$	−15.7038	−	27.1998i	−0.766268	−	1.32722i
$421$	−9.77317	−	5.64254i	−0.476315	−	0.275001i	0.242564	−	0.970135i	$-0.422011\pi$
$421$	−9.77317	−	5.64254i	−0.476315	−	0.275001i	−0.718880	+	0.695135i	$0.755345\pi$
$422$	−0.909032	+	0.524830i	−0.0442510	+	0.0255483i
$423$	−14.2518	−	8.22831i	−0.692948	−	0.400074i
$424$	−0.788028	−	0.454968i	−0.0382700	−	0.0220952i
$425$	−0.522388	+	0.904803i	−0.0253395	+	0.0438894i
$426$	0.181992			0.00881755
$427$	−38.2434	+	22.0798i	−1.85073	+	1.06852i
$428$	−11.3063	−	19.5831i	−0.546510	−	0.946583i
$429$	39.3336	+	36.0811i	1.89904	+	1.74201i
$430$	0.622078			0.0299993
$431$	9.75404	−	5.63150i	0.469836	−	0.271260i	−0.246335	−	0.969185i	$-0.579226\pi$
$431$	9.75404	−	5.63150i	0.469836	−	0.271260i	0.716171	+	0.697925i	$0.245893\pi$
$432$	19.0325			0.915701
$433$	2.41491			0.116053			0.0580267	−	0.998315i	$-0.481519\pi$
$433$	2.41491			0.116053			0.0580267	+	0.998315i	$0.481519\pi$
$434$	−0.346582	−	0.927287i	−0.0166365	−	0.0445112i
$435$			31.1014i			1.49120i
$436$			7.00777i			0.335611i
$437$	−0.825753	+	0.476749i	−0.0395011	+	0.0228060i
$438$	−1.74112			−0.0831940
$439$	7.81146	−	13.5298i	0.372821	−	0.645744i	−0.617178	−	0.786824i	$-0.711724\pi$
$439$	7.81146	−	13.5298i	0.372821	−	0.645744i	0.989998	+	0.141079i	$0.0450573\pi$
$440$	−1.22519	+	0.707363i	−0.0584086	+	0.0337222i
$441$	19.2261	+	33.3005i	0.915527	+	1.58574i
$442$	−0.0129336	+	0.0581931i	−0.000615188	+	0.00276797i
$443$	−5.53076	+	9.57956i	−0.262774	+	0.455138i	−0.966978	−	0.254859i	$-0.917971\pi$
$443$	−5.53076	+	9.57956i	−0.262774	+	0.455138i	0.704204	+	0.709998i	$0.251304\pi$
$444$	−28.6764	−	16.5563i	−1.36092	−	0.785728i
$445$	−12.0110	+	20.8036i	−0.569375	+	0.986187i
$446$	0.0178159	+	0.0308580i	0.000843605	+	0.00146117i
$447$	−36.9494	−	21.3327i	−1.74765	−	1.00900i
$448$	26.7980	−	15.4718i	1.26608	−	0.730974i
$449$			10.7069i			0.505290i	0.967559	+	0.252645i	$0.0813005\pi$
$449$			10.7069i			0.505290i	−0.967559	+	0.252645i	$0.918700\pi$
$450$			0.622103i			0.0293262i
$451$	4.91234	+	8.50842i	0.231313	+	0.400646i
$452$	13.0297	−	22.5681i	0.612865	−	1.06151i
$453$	1.00785	−	0.581884i	0.0473530	−	0.0273393i
$454$	−0.0859170	+	0.148813i	−0.00403229	+	0.00698412i
$455$	−13.7915	+	15.0347i	−0.646555	+	0.704838i
$456$	−0.564332	+	0.977452i	−0.0264273	+	0.0457734i
$457$			20.3654i			0.952653i	0.879268	+	0.476327i	$0.158032\pi$
$457$			20.3654i			0.952653i	−0.879268	+	0.476327i	$0.841968\pi$
$458$	−0.0670249	−	0.116091i	−0.00313187	−	0.00542455i
$459$	−0.863802	−	1.49615i	−0.0403188	−	0.0698343i
$460$	1.07813	+	0.622457i	0.0502679	+	0.0290222i
$461$		−	19.4786i		−	0.907209i	−0.891203	−	0.453604i	$-0.850138\pi$
$461$		−	19.4786i		−	0.907209i	0.891203	−	0.453604i	$-0.149862\pi$
$462$	2.27946	−	1.31605i	0.106050	−	0.0612280i
$463$			3.83752i			0.178345i	0.996016	+	0.0891723i	$0.0284222\pi$
$463$			3.83752i			0.178345i	−0.996016	+	0.0891723i	$0.971578\pi$
$464$	−30.7062			−1.42550
$465$	−3.71389	+	22.1783i	−0.172227	+	1.02849i
$466$		−	0.421293i		−	0.0195160i
$467$	20.8281			0.963809			0.481905	−	0.876224i	$-0.339945\pi$
$467$	20.8281			0.963809			0.481905	+	0.876224i	$0.339945\pi$
$468$	−10.2028	−	32.4194i	−0.471627	−	1.49859i
$469$	40.8055			1.88422
$470$	−0.200598	−	0.115815i	−0.00925290	−	0.00534217i
$471$	−2.99899	−	5.19440i	−0.138186	−	0.239345i
$472$	−1.27576	−	2.20968i	−0.0587217	−	0.101709i
$473$		−	49.9164i		−	2.29516i
$474$	−0.415194	−	0.239712i	−0.0190705	−	0.0110103i
$475$	5.56110	+	3.21071i	0.255161	+	0.147317i
$476$	−2.43759	−	1.40734i	−0.111727	−	0.0645055i
$477$	−11.7541	−	20.3588i	−0.538185	−	0.932163i
$478$	0.137733	−	0.238561i	0.00629976	−	0.0109115i
$479$	10.8953	−	6.29038i	0.497817	−	0.287415i	−0.229994	−	0.973192i	$-0.573871\pi$
$479$	10.8953	−	6.29038i	0.497817	−	0.287415i	0.727812	+	0.685777i	$0.240537\pi$
$480$	2.21081			0.100909
$481$	−4.66672	+	20.9973i	−0.212784	+	0.957397i
$482$	−0.186591	−	0.323185i	−0.00849899	−	0.0147207i
$483$	−4.01379	−	2.31737i	−0.182634	−	0.105444i
$484$	17.3765	+	30.0970i	0.789843	+	1.36805i
$485$	10.4207	−	18.0492i	0.473180	−	0.819572i
$486$	0.664714	+	0.383773i	0.0301520	+	0.0174083i
$487$	21.1166	+	12.1917i	0.956884	+	0.552457i	0.895213	−	0.445639i	$-0.147024\pi$
$487$	21.1166	+	12.1917i	0.956884	+	0.552457i	0.0616713	+	0.998097i	$0.480357\pi$
$488$		−	2.07193i		−	0.0937918i
$489$	36.8604	−	21.2814i	1.66689	−	0.962377i
$490$	0.270612	+	0.468713i	0.0122250	+	0.0211743i
$491$	7.47672	−	12.9501i	0.337420	−	0.584428i	−0.646527	−	0.762891i	$-0.723779\pi$
$491$	7.47672	−	12.9501i	0.337420	−	0.584428i	0.983947	+	0.178463i	$0.0571125\pi$
$492$		−	10.2337i		−	0.461369i
$493$	1.39362	+	2.41383i	0.0627657	+	0.108713i
$494$	0.357667	+	0.0794925i	0.0160922	+	0.00357654i
$495$	−36.5495			−1.64278
$496$	−21.8965	−	3.66669i	−0.983182	−	0.164639i
$497$	5.58190			0.250383
$498$	1.51146			0.0677303
$499$	36.5626	−	21.1094i	1.63677	−	0.944988i	0.654831	−	0.755776i	$-0.272740\pi$
$499$	36.5626	−	21.1094i	1.63677	−	0.944988i	0.981936	−	0.189212i	$-0.0605934\pi$
$500$		−	22.9066i		−	1.02441i
$501$	−47.8093	−	27.6027i	−2.13596	−	1.23320i
$502$	−1.09797	+	0.633914i	−0.0490048	+	0.0282930i
$503$	−9.96985	−	17.2683i	−0.444534	−	0.769955i	0.553486	−	0.832859i	$-0.313297\pi$
$503$	−9.96985	−	17.2683i	−0.444534	−	0.769955i	−0.998020	+	0.0629034i	$0.979964\pi$
$504$	−3.35371			−0.149386
$505$	15.7828	+	9.11220i	0.702325	+	0.405488i
$506$	−0.0521645	+	0.0903515i	−0.00231899	+	0.00401661i
$507$	−29.6064	+	20.6837i	−1.31487	+	0.918596i
$508$	0.303765	+	0.526137i	0.0134774	+	0.0233436i
$509$	19.4167	+	11.2103i	0.860631	+	0.496886i	0.864224	−	0.503108i	$-0.167810\pi$
$509$	19.4167	+	11.2103i	0.860631	+	0.496886i	−0.00359246	+	0.999994i	$0.501144\pi$
$510$	−0.0333882	−	0.0578301i	−0.00147845	−	0.00256076i
$511$	−53.4021			−2.36237
$512$			3.63913i			0.160828i
$513$	−9.19564	+	5.30911i	−0.405998	+	0.234403i
$514$	−0.317077	−	0.183065i	−0.0139857	−	0.00807463i
$515$	−6.74463	+	3.89401i	−0.297204	+	0.171591i
$516$	−25.9971	+	45.0284i	−1.14446	+	1.98226i
$517$	−9.29318	+	16.0963i	−0.408714	+	0.707913i
$518$	0.918588	+	0.530347i	0.0403605	+	0.0233021i
$519$	10.6165			0.466014
$520$	−0.287365	−	0.913099i	−0.0126018	−	0.0400420i
$521$	−21.6959	−	37.5784i	−0.950514	−	1.64634i	−0.744314	−	0.667829i	$-0.767224\pi$
$521$	−21.6959	−	37.5784i	−0.950514	−	1.64634i	−0.206200	−	0.978510i	$-0.566110\pi$
$522$	1.43729	+	0.829821i	0.0629085	+	0.0363203i
$523$	34.3881			1.50369			0.751844	−	0.659341i	$-0.229165\pi$
$523$	34.3881			1.50369			0.751844	+	0.659341i	$0.229165\pi$
$524$	−4.37123	−	7.57119i	−0.190958	−	0.330749i
$525$			31.2130i			1.36225i
$526$			0.0916152i			0.00399461i
$527$	0.705548	+	1.88771i	0.0307341	+	0.0822298i
$528$		−	59.0299i		−	2.56895i
$529$	−22.8163			−0.992013
$530$	−0.165442	−	0.286554i	−0.00718635	−	0.0124471i
$531$		−	65.9187i		−	2.86063i
$532$	−8.64983	+	14.9819i	−0.375018	+	0.649550i
$533$	−6.34109	+	1.99563i	−0.274663	+	0.0864403i
$534$	1.04847	+	1.81600i	0.0453718	+	0.0785862i
$535$		−	16.4540i		−	0.711369i
$536$	−0.957279	+	1.65806i	−0.0413482	+	0.0716171i
$537$	8.42141	−	14.5863i	0.363411	−	0.629446i
$538$	−0.484977	−	0.280002i	−0.0209088	−	0.0120717i
$539$	37.6101	−	21.7142i	1.61998	−	0.935298i
$540$	12.0061	+	6.93173i	0.516661	+	0.298294i
$541$	22.7855	−	13.1552i	0.979624	−	0.565586i	0.0774674	−	0.996995i	$-0.475317\pi$
$541$	22.7855	−	13.1552i	0.979624	−	0.565586i	0.902157	+	0.431409i	$0.141983\pi$
$542$	0.696499			0.0299172
$543$	−19.7560			−0.847812
$544$	0.171584	−	0.0990642i	0.00735661	−	0.00424734i
$545$	−2.54960	+	4.41603i	−0.109213	+	0.189162i
$546$	0.534641	+	1.69882i	0.0228805	+	0.0727026i
$547$	6.17850	−	10.7015i	0.264174	−	0.457562i	−0.703173	−	0.711019i	$-0.748234\pi$
$547$	6.17850	−	10.7015i	0.264174	−	0.457562i	0.967347	+	0.253456i	$0.0815675\pi$
$548$	−11.0087	−	6.35586i	−0.470268	−	0.271509i
$549$	26.7642	−	46.3570i	1.14227	−	1.97847i
$550$	0.702612			0.0299595
$551$	14.8359	−	8.56550i	0.632030	−	0.364903i
$552$	0.188324	−	0.108729i	0.00801558	−	0.00462780i
$553$	−12.7345	−	7.35224i	−0.541524	−	0.312649i
$554$		−	0.262507i		−	0.0111528i
$555$	−12.0472	−	20.8663i	−0.511375	−	0.885727i
$556$	10.3583			0.439291
$557$			38.0150i			1.61075i	0.592766	+	0.805375i	$0.298036\pi$
$557$			38.0150i			1.61075i	−0.592766	+	0.805375i	$0.701964\pi$
$558$	0.925836	+	0.763372i	0.0391938	+	0.0323161i
$559$	32.9706	+	7.32780i	1.39451	+	0.309933i
$560$	22.5633			0.953475
$561$	−4.64036	+	2.67911i	−0.195916	+	0.113112i
$562$	1.07380			0.0452957
$563$	−15.3956	+	26.6660i	−0.648848	+	1.12384i	0.334550	+	0.942378i	$0.391416\pi$
$563$	−15.3956	+	26.6660i	−0.648848	+	1.12384i	−0.983398	+	0.181460i	$0.941918\pi$
$564$	16.7663	−	9.68003i	0.705989	−	0.407603i
$565$	16.4216	−	9.48104i	0.690864	−	0.398870i
$566$		−	0.317247i		−	0.0133349i
$567$	3.01352	+	1.73986i	0.126556	+	0.0730671i
$568$	−0.130949	+	0.226810i	−0.00549449	+	0.00951674i
$569$	13.0541	−	22.6104i	0.547257	−	0.947876i	−0.451204	−	0.892421i	$-0.649005\pi$
$569$	13.0541	−	22.6104i	0.547257	−	0.947876i	0.998461	−	0.0554558i	$-0.0176612\pi$
$570$	−0.355435	+	0.205211i	−0.0148876	+	0.00859533i
$571$	−11.8892	+	20.5926i	−0.497546	+	0.861775i	−0.999996	−	0.00283159i	$-0.999099\pi$
$571$	−11.8892	+	20.5926i	−0.497546	+	0.861775i	0.502450	+	0.864606i	$0.332432\pi$
$572$	−36.6150	+	11.5233i	−1.53095	+	0.481812i
$573$	27.9241			1.16655
$574$			0.327814i			0.0136827i
$575$	−0.618600	−	1.07145i	−0.0257974	−	0.0446824i
$576$	−18.7543	+	32.4833i	−0.781428	+	1.35347i
$577$	24.8238	−	14.3320i	1.03343	−	0.596649i	0.115462	−	0.993312i	$-0.463165\pi$
$577$	24.8238	−	14.3320i	1.03343	−	0.596649i	0.917964	+	0.396663i	$0.129832\pi$
$578$	0.667332	+	0.385284i	0.0277573	+	0.0160257i
$579$	−1.72490	−	0.995871i	−0.0716844	−	0.0413870i
$580$	−19.3702	−	11.1834i	−0.804303	−	0.464364i
$581$	46.3582			1.92326
$582$	−0.909652	−	1.57556i	−0.0377063	−	0.0653092i
$583$	−22.9935	+	13.2753i	−0.952293	+	0.549807i
$584$	1.25279	−	2.16990i	0.0518408	−	0.0897909i
$585$	5.36553	−	24.1416i	0.221837	−	0.998130i
$586$	−0.296482	−	0.513521i	−0.0122475	−	0.0212134i
$587$		−	16.9101i		−	0.697956i	−0.937131	−	0.348978i	$-0.886529\pi$
$587$		−	16.9101i		−	0.697956i	0.937131	−	0.348978i	$-0.113471\pi$
$588$	−45.2363			−1.86551
$589$	11.6022	−	4.33644i	0.478062	−	0.178680i
$590$		−	0.927822i		−	0.0381978i
$591$			15.2738i			0.628280i
$592$	20.6012	−	11.8941i	0.846704	−	0.488845i
$593$		−	18.8997i		−	0.776118i	−0.921635	−	0.388059i	$-0.873146\pi$
$593$		−	18.8997i		−	0.776118i	0.921635	−	0.388059i	$-0.126854\pi$
$594$	−0.580907	+	1.00616i	−0.0238349	+	0.0412833i
$595$	−1.02405	−	1.77371i	−0.0419821	−	0.0727151i
$596$	26.5723	−	15.3415i	1.08844	−	0.628414i
$597$	−42.2062			−1.72738
$598$	−0.0520208	−	0.0477192i	−0.00212729	−	0.00195138i
$599$	−15.6563	+	27.1175i	−0.639700	+	1.10799i	0.345799	+	0.938309i	$0.387608\pi$
$599$	−15.6563	+	27.1175i	−0.639700	+	1.10799i	−0.985499	+	0.169684i	$0.945725\pi$
$600$	−1.26828	−	0.732243i	−0.0517774	−	0.0298937i
$601$	−12.1642	−	21.0691i	−0.496189	−	0.859425i	0.503801	−	0.863820i	$-0.331934\pi$
$601$	−12.1642	−	21.0691i	−0.496189	−	0.859425i	−0.999990	+	0.00439478i	$0.998601\pi$
$602$	0.832764	−	1.44239i	0.0339409	−	0.0587874i
$603$	−42.8360	+	24.7314i	−1.74442	+	1.00714i
$604$			0.836929i			0.0340541i
$605$			25.2880i			1.02810i
$606$	1.37772	−	0.795429i	0.0559662	−	0.0323121i
$607$	19.0218	−	32.9467i	0.772070	−	1.33727i	−0.164356	−	0.986401i	$-0.552555\pi$
$607$	19.0218	−	32.9467i	0.772070	−	1.33727i	0.936426	−	0.350864i	$-0.114112\pi$
$608$	−0.608869	−	1.05459i	−0.0246929	−	0.0427694i
$609$	72.1138	+	41.6349i	2.92220	+	1.68713i
$610$	0.376713	−	0.652485i	0.0152526	−	0.0264184i
$611$	−9.26758	−	8.50125i	−0.374926	−	0.343924i
$612$	3.41185			0.137916
$613$	−5.56881	+	3.21516i	−0.224922	+	0.129859i	−0.608227	−	0.793763i	$-0.708119\pi$
$613$	−5.56881	+	3.21516i	−0.224922	+	0.129859i	0.383305	+	0.923622i	$0.374786\pi$
$614$	0.361838	+	0.626722i	0.0146026	+	0.0252924i
$615$	3.72326	−	6.44887i	0.150136	−	0.260043i
$616$			3.78774i			0.152612i
$617$	−29.9548	+	17.2944i	−1.20593	+	0.696246i	−0.961869	−	0.273512i	$-0.911815\pi$
$617$	−29.9548	+	17.2944i	−1.20593	+	0.696246i	−0.244066	+	0.969759i	$0.578481\pi$
$618$			0.679838i			0.0273471i
$619$			13.3254i			0.535592i	0.963476	+	0.267796i	$0.0862953\pi$
$619$			13.3254i			0.535592i	−0.963476	+	0.267796i	$0.913705\pi$
$620$	−12.4774	−	10.2878i	−0.501103	−	0.413170i
$621$	2.04579			0.0820946
$622$		−	0.920962i		−	0.0369272i
$623$	32.1578	+	55.6989i	1.28837	+	2.23153i
$624$	38.9902	+	8.66568i	1.56086	+	0.346905i
$625$	1.11767	−	1.93587i	0.0447070	−	0.0774347i
$626$	−0.601461	+	0.347254i	−0.0240392	+	0.0138790i
$627$	16.4664	+	28.5206i	0.657604	+	1.13900i
$628$	4.31347			0.172126
$629$	−1.87000	−	1.07964i	−0.0745617	−	0.0430482i
$630$	−1.05614	−	0.609763i	−0.0420776	−	0.0242935i
$631$	15.0213	+	8.67253i	0.597987	+	0.345248i	0.768249	−	0.640151i	$-0.221128\pi$
$631$	15.0213	+	8.67253i	0.597987	+	0.345248i	−0.170262	+	0.985399i	$0.554461\pi$
$632$	0.597489	−	0.344960i	0.0237668	−	0.0137218i
$633$	31.9191	−	55.2856i	1.26867	−	2.19740i
$634$	−0.128035	−	0.221763i	−0.00508491	−	0.00880732i
$635$			0.442069i			0.0175430i
$636$	27.6558			1.09663
$637$	8.82137	+	28.0298i	0.349515	+	1.11058i
$638$	0.937213	−	1.62330i	0.0371046	−	0.0642671i
$639$	−5.85965	+	3.38307i	−0.231804	+	0.133832i
$640$	−1.05976	+	1.83556i	−0.0418906	+	0.0725567i
$641$	21.7575	−	37.6851i	0.859369	−	1.48847i	−0.0131618	−	0.999913i	$-0.504190\pi$
$641$	21.7575	−	37.6851i	0.859369	−	1.48847i	0.872531	−	0.488558i	$-0.162477\pi$
$642$	−1.24389	−	0.718157i	−0.0490922	−	0.0283434i
$643$			19.8059i			0.781068i	0.920589	+	0.390534i	$0.127710\pi$
$643$			19.8059i			0.781068i	−0.920589	+	0.390534i	$0.872290\pi$
$644$	2.88654	−	1.66654i	0.113746	−	0.0656710i
$645$	−32.7648	+	18.9168i	−1.29011	+	0.744848i
$646$	−0.0183906	+	0.0318534i	−0.000723567	+	0.00125325i
$647$	−30.5580			−1.20136			−0.600679	−	0.799491i	$-0.705103\pi$
$647$	−30.5580			−1.20136			−0.600679	+	0.799491i	$0.705103\pi$
$648$	−0.141392	+	0.0816325i	−0.00555439	+	0.00320683i
$649$	−74.4497			−2.92240
$650$	−0.103145	+	0.464087i	−0.00404566	+	0.0182030i
$651$	46.4524	+	38.3010i	1.82061	+	1.50113i
$652$			30.6092i			1.19875i
$653$	−27.9507			−1.09379			−0.546897	−	0.837200i	$-0.684191\pi$
$653$	−27.9507			−1.09379			−0.546897	+	0.837200i	$0.684191\pi$
$654$	0.222561	+	0.385487i	0.00870284	+	0.0150738i
$655$		−	6.36144i		−	0.248562i
$656$	6.36692	+	3.67594i	0.248586	+	0.143521i
$657$	56.0594	−	32.3659i	2.18708	−	1.26271i
$658$	−0.537074	+	0.310080i	−0.0209373	+	0.0120882i
$659$	−36.8074			−1.43381			−0.716906	−	0.697170i	$-0.754442\pi$
$659$	−36.8074			−1.43381			−0.716906	+	0.697170i	$0.754442\pi$
$660$	21.4990	−	37.2374i	0.836847	−	1.44946i
$661$	−22.6262	−	13.0633i	−0.880059	−	0.508102i	−0.00938107	−	0.999956i	$-0.502986\pi$
$661$	−22.6262	−	13.0633i	−0.880059	−	0.508102i	−0.870678	+	0.491854i	$0.836319\pi$
$662$	−0.424637	+	0.735494i	−0.0165040	+	0.0285858i
$663$	−1.08838	−	3.45833i	−0.0422694	−	0.134310i
$664$	−1.08754	+	1.88368i	−0.0422049	+	0.0731010i
$665$	−10.9016	+	6.29404i	−0.422746	+	0.244072i
$666$	−1.28573			−0.0498210
$667$	−3.30059			−0.127799
$668$	34.3823	−	19.8506i	1.33029	−	0.768043i
$669$	−1.87672	−	1.08353i	−0.0725583	−	0.0418915i
$670$	−0.602926	+	0.348100i	−0.0232931	+	0.0134483i
$671$	−52.3563	−	30.2279i	−2.02119	−	1.16694i
$672$	2.95957	−	5.12613i	0.114168	−	0.197745i
$673$	20.8683	−	36.1449i	0.804413	−	1.39328i	−0.112274	−	0.993677i	$-0.535814\pi$
$673$	20.8683	−	36.1449i	0.804413	−	1.39328i	0.916687	−	0.399606i	$-0.130853\pi$
$674$		−	0.0733636i		−	0.00282586i
$675$	−6.88877	−	11.9317i	−0.265149	−	0.459251i
$676$	−2.23616	−	25.8764i	−0.0860060	−	0.995247i
$677$	−19.4456	+	33.6807i	−0.747354	+	1.29445i	0.201733	+	0.979441i	$0.435343\pi$
$677$	−19.4456	+	33.6807i	−0.747354	+	1.29445i	−0.949087	+	0.315014i	$0.897991\pi$
$678$		−	1.65525i		−	0.0635695i
$679$	−27.9000	−	48.3243i	−1.07071	−	1.85452i
$680$	0.0960952			0.00368508
$681$		−	10.4506i		−	0.400468i
$682$	0.862164	−	1.04565i	0.0330140	−	0.0400402i
$683$		−	2.48961i		−	0.0952622i	−0.998865	−	0.0476311i	$-0.984833\pi$
$683$		−	2.48961i		−	0.0952622i	0.998865	−	0.0476311i	$-0.0151672\pi$
$684$		−	20.9699i		−	0.801804i
$685$	−4.62484	−	8.01045i	−0.176706	−	0.306064i
$686$	0.204462			0.00780640
$687$	7.06040	+	4.07632i	0.269371	+	0.155521i
$688$	−18.6764	−	32.3485i	−0.712031	−	1.23327i
$689$	−5.39307	−	17.1364i	−0.205460	−	0.652845i
$690$	0.0790750			0.00301033
$691$	33.3797	+	19.2718i	1.26982	+	0.733132i	0.974954	−	0.222406i	$-0.0713909\pi$
$691$	33.3797	+	19.2718i	1.26982	+	0.733132i	0.294868	+	0.955538i	$0.404724\pi$
$692$	−3.81746	+	6.61204i	−0.145118	+	0.251352i
$693$	−48.9282	+	84.7461i	−1.85863	+	3.21924i
$694$	−0.0744452	+	0.0429810i	−0.00282590	+	0.00163154i
$695$	6.52742	+	3.76861i	0.247599	+	0.142951i
$696$	−3.38351	+	1.95347i	−0.128252	+	0.0740462i
$697$		−	0.667341i		−	0.0252773i
$698$	−1.07921			−0.0408486
$699$	12.8111	+	22.1895i	0.484561	+	0.839284i
$700$	−19.4397	−	11.2235i	−0.734750	−	0.424208i
$701$	5.20190	+	9.00995i	0.196473	+	0.340301i	0.947382	−	0.320104i	$-0.103718\pi$
$701$	5.20190	+	9.00995i	0.196473	+	0.340301i	−0.750909	+	0.660405i	$0.770385\pi$
$702$	−0.579307	−	0.531405i	−0.0218645	−	0.0200566i
$703$	−6.63571	+	11.4934i	−0.250271	+	0.433482i
$704$	36.6872	+	21.1814i	1.38270	+	0.798302i
$705$	14.0873			0.530560
$706$	−0.449103	−	0.777868i	−0.0169022	−	0.0292755i
$707$	42.2563	−	24.3967i	1.58921	−	0.917531i
$708$	67.1593	+	38.7744i	2.52400	+	1.45723i
$709$			26.4554i			0.993555i	0.867878	+	0.496778i	$0.165484\pi$
$709$			26.4554i			0.993555i	−0.867878	+	0.496778i	$0.834516\pi$
$710$	−0.0824760	+	0.0476175i	−0.00309527	+	0.00178705i
$711$	17.8241			0.668457
$712$	−3.01763			−0.113090
$713$	−2.35364	−	0.394130i	−0.0881445	−	0.0147603i
$714$	−0.178785			−0.00669085
$715$	−27.2658	−	6.05991i	−1.01968	−	0.226628i
$716$	6.05630	+	10.4898i	0.226334	+	0.392023i
$717$			16.7533i			0.625664i
$718$	−0.160179	+	0.277439i	−0.00597784	+	0.0103539i
$719$	20.5868	+	35.6573i	0.767757	+	1.32979i	0.938777	+	0.344526i	$0.111960\pi$
$719$	20.5868	+	35.6573i	0.767757	+	1.32979i	−0.171020	+	0.985268i	$0.554706\pi$
$720$	−23.6861	+	13.6752i	−0.882728	+	0.509643i
$721$			20.8514i			0.776546i
$722$	−0.555856	−	0.320924i	−0.0206868	−	0.0119435i
$723$	19.6555	+	11.3481i	0.730996	+	0.422041i
$724$	7.10381	−	12.3042i	0.264011	−	0.457281i
$725$	11.1141	+	19.2501i	0.412766	+	0.714932i
$726$	1.91172	+	1.10373i	0.0709505	+	0.0409633i
$727$	−8.85220	−	15.3325i	−0.328310	−	0.568650i	0.653867	−	0.756610i	$-0.273146\pi$
$727$	−8.85220	−	15.3325i	−0.328310	−	0.568650i	−0.982177	+	0.187960i	$0.939812\pi$
$728$	−2.50186	−	0.556046i	−0.0927251	−	0.0206084i
$729$	−43.9986			−1.62958
$730$	0.789049	−	0.455558i	0.0292040	−	0.0168609i
$731$	−1.69528	+	2.93632i	−0.0627023	+	0.108604i
$732$	31.4862	+	54.5358i	1.16376	+	2.01570i
$733$	−18.9721	−	10.9536i	−0.700751	−	0.404579i	0.106876	−	0.994272i	$-0.465915\pi$
$733$	−18.9721	−	10.9536i	−0.700751	−	0.404579i	−0.807627	+	0.589693i	$0.799249\pi$
$734$	1.03997	+	0.600425i	0.0383859	+	0.0221621i
$735$	−28.5062	−	16.4581i	−1.05147	−	0.607065i
$736$			0.234619i			0.00864817i
$737$	27.9320	+	48.3796i	1.02889	+	1.78209i
$738$	−0.198681	−	0.344126i	−0.00731355	−	0.0126674i
$739$	31.9225	+	18.4305i	1.17429	+	0.677977i	0.954687	−	0.297613i	$-0.0961904\pi$
$739$	31.9225	+	18.4305i	1.17429	+	0.677977i	0.219603	+	0.975589i	$0.429524\pi$
$740$	17.3276			0.636974
$741$	−21.2556	+	6.68944i	−0.780844	+	0.245743i
$742$	−0.885898			−0.0325223
$743$		−	5.05507i		−	0.185452i	−0.995692	−	0.0927262i	$-0.970442\pi$
$743$		−	5.05507i		−	0.185452i	0.995692	−	0.0927262i	$-0.0295581\pi$
$744$	−2.64604	+	0.988981i	−0.0970085	+	0.0362578i
$745$	22.3265			0.817980
$746$		−	0.0407138i		−	0.00149064i
$747$	−48.6650	+	28.0967i	−1.78056	+	1.02801i
$748$		−	3.85339i		−	0.140894i
$749$	−38.1513	−	22.0267i	−1.39402	−	0.804837i
$750$	−0.727496	−	1.26006i	−0.0265644	−	0.0460109i
$751$	9.58618	+	16.6037i	0.349804	+	0.605879i	0.986215	−	0.165472i	$-0.0529147\pi$
$751$	9.58618	+	16.6037i	0.349804	+	0.605879i	−0.636410	+	0.771351i	$0.719581\pi$
$752$			13.9083i			0.507184i
$753$	38.5534	−	66.7764i	1.40496	−	2.43347i
$754$	0.934631	+	0.857347i	0.0340373	+	0.0312227i
$755$	−0.304495	+	0.527401i	−0.0110817	+	0.0191941i
$756$	32.1447	−	18.5588i	1.16909	−	0.674975i
$757$	−13.6298	+	23.6075i	−0.495383	+	0.858029i	−0.999986	−	0.00532260i	$-0.998306\pi$
$757$	−13.6298	+	23.6075i	−0.495383	+	0.858029i	0.504602	+	0.863352i	$0.331639\pi$
$758$	−0.158334	−	0.274243i	−0.00575096	−	0.00996096i
$759$		−	6.34508i		−	0.230312i
$760$		−	0.590621i		−	0.0214241i
$761$	35.2717	−	20.3641i	1.27860	−	0.738198i	0.302006	−	0.953306i	$-0.402344\pi$
$761$	35.2717	−	20.3641i	1.27860	−	0.738198i	0.976590	+	0.215108i	$0.0690103\pi$
$762$	0.0334194	+	0.0192947i	0.00121066	+	0.000698973i
$763$	6.82620	+	11.8233i	0.247125	+	0.428033i
$764$	−10.0409	+	17.3913i	−0.363266	+	0.629195i
$765$	2.15002	+	1.24131i	0.0777340	+	0.0448798i
$766$	0.0335920	−	0.0581831i	0.00121373	−	0.00210224i
$767$	10.9293	−	49.1752i	0.394635	−	1.77561i
$768$	−21.9936	−	38.0941i	−0.793626	−	1.37460i
$769$	−21.6531	+	12.5014i	−0.780832	+	0.450814i	−0.836725	−	0.547623i	$-0.815533\pi$
$769$	−21.6531	+	12.5014i	−0.780832	+	0.450814i	0.0558929	+	0.998437i	$0.482199\pi$
$770$	−0.688676	+	1.19282i	−0.0248182	+	0.0429863i
$771$	22.2673			0.801936
$772$	1.24047	−	0.716185i	0.0446455	−	0.0257761i
$773$		−	29.0375i		−	1.04441i	−0.852821	−	0.522204i	$-0.825110\pi$
$773$		−	29.0375i		−	1.04441i	0.852821	−	0.522204i	$-0.174890\pi$
$774$			2.01888i			0.0725672i
$775$	5.62670	+	15.0543i	0.202117	+	0.540768i
$776$	2.61809			0.0939839
$777$	−64.5094			−2.31426
$778$	1.22498	−	0.707241i	0.0439176	−	0.0253558i
$779$	−4.10161			−0.146956
$780$	21.4398	+	19.6669i	0.767667	+	0.704189i
$781$	3.82089	+	6.61798i	0.136722	+	0.236810i
$782$	0.00613712	−	0.00354327i	0.000219463	−	0.000126707i
$783$	−36.7556			−1.31354
$784$	16.2489	−	28.1440i	0.580319	−	1.00514i
$785$	2.71819	+	1.56935i	0.0970163	+	0.0560124i
$786$	−0.480910	−	0.277654i	−0.0171535	−	0.00990358i
$787$	−27.9699	+	16.1484i	−0.997018	+	0.575629i	−0.907365	−	0.420344i	$-0.861909\pi$
$787$	−27.9699	+	16.1484i	−0.997018	+	0.575629i	−0.0896536	+	0.995973i	$0.528576\pi$
$788$	−9.51261	−	5.49211i	−0.338873	−	0.195648i
$789$	−2.78593	−	4.82537i	−0.0991817	−	0.171788i
$790$	0.250879			0.00892588
$791$		−	50.7684i		−	1.80512i
$792$	−2.29567	−	3.97621i	−0.0815729	−	0.141288i
$793$	27.6520	−	30.1447i	0.981951	−	1.07047i
$794$	−0.311560	−	0.539638i	−0.0110569	−	0.0191511i
$795$	17.4277	+	10.0619i	0.618096	+	0.356858i
$796$	15.1764	−	26.2863i	0.537912	−	0.931691i
$797$	23.0278	−	39.8854i	0.815688	−	1.41281i	−0.0931455	−	0.995653i	$-0.529692\pi$
$797$	23.0278	−	39.8854i	0.815688	−	1.41281i	0.908833	−	0.417160i	$-0.136974\pi$
$798$			1.09885i			0.0388988i
$799$	1.09334	−	0.631239i	0.0386795	−	0.0223316i
$800$	1.36837	−	0.790031i	0.0483793	−	0.0279318i
$801$	−67.5158	−	38.9803i	−2.38555	−	1.37730i
$802$	−0.864637			−0.0305314
$803$	−36.5545	−	63.3143i	−1.28998	−	2.23431i
$804$		−	58.1895i		−	2.05218i
$805$	2.42532			0.0854812
$806$	0.564104	+	0.722977i	0.0198697	+	0.0254658i
$807$	34.0583			1.19891
$808$			2.28934i			0.0805387i
$809$	13.5584	+	23.4838i	0.476687	+	0.825646i	0.999643	−	0.0267135i	$-0.00850417\pi$
$809$	13.5584	+	23.4838i	0.476687	+	0.825646i	−0.522956	+	0.852360i	$0.675171\pi$
$810$	−0.0593688			−0.00208601
$811$	18.4126	+	10.6305i	0.646552	+	0.373287i	0.787134	−	0.616782i	$-0.211564\pi$
$811$	18.4126	+	10.6305i	0.646552	+	0.373287i	−0.140582	+	0.990069i	$0.544897\pi$
$812$	−51.8610	+	29.9419i	−1.81996	+	1.05076i
$813$	−36.6846	+	21.1799i	−1.28658	+	0.742810i
$814$			1.45212i			0.0508968i
$815$	−11.1364	+	19.2888i	−0.390090	+	0.675656i
$816$	−2.00480	+	3.47242i	−0.0701821	+	0.121559i
$817$	18.0472	+	10.4196i	0.631392	+	0.364534i
$818$	0.623596	+	1.08010i	0.0218035	+	0.0377648i
$819$	−48.7934	−	44.7587i	−1.70498	−	1.56400i
$820$	2.67760	+	4.63773i	0.0935057	+	0.161957i
$821$			4.27210i			0.149097i	0.997217	+	0.0745486i	$0.0237516\pi$
$821$			4.27210i			0.149097i	−0.997217	+	0.0745486i	$0.976248\pi$
$822$	−0.807429			−0.0281623
$823$	−10.1826	−	17.6367i	−0.354942	−	0.614778i	0.632166	−	0.774833i	$-0.282166\pi$
$823$	−10.1826	−	17.6367i	−0.354942	−	0.614778i	−0.987108	+	0.160055i	$0.948833\pi$
$824$	−0.847257	−	0.489164i	−0.0295156	−	0.0170408i
$825$	−37.0066	+	21.3658i	−1.28840	+	0.743860i
$826$	−2.15131	−	1.24206i	−0.0748536	−	0.0432167i
$827$	−27.5966	−	15.9329i	−0.959626	−	0.554040i	−0.0635682	−	0.997977i	$-0.520248\pi$
$827$	−27.5966	−	15.9329i	−0.959626	−	0.554040i	−0.896058	+	0.443937i	$0.853581\pi$
$828$	−2.02011	+	3.49894i	−0.0702038	+	0.121597i
$829$	32.3558			1.12376			0.561882	−	0.827217i	$-0.310077\pi$
$829$	32.3558			1.12376			0.561882	+	0.827217i	$0.310077\pi$
$830$	−0.684971	+	0.395468i	−0.0237757	+	0.0137269i
$831$	7.98257	+	13.8262i	0.276912	+	0.479626i
$832$	−19.3764	+	21.1230i	−0.671754	+	0.732309i
$833$	−2.94988			−0.102207
$834$	0.569796	−	0.328972i	0.0197304	−	0.0113914i
$835$	28.8886			0.999730
$836$	−23.6837			−0.819119
$837$	−26.2103	−	4.38906i	−0.905960	−	0.151708i
$838$		−	0.350554i		−	0.0121097i
$839$		−	44.5019i		−	1.53638i	−0.640224	−	0.768189i	$-0.721158\pi$
$839$		−	44.5019i		−	1.53638i	0.640224	−	0.768189i	$-0.278842\pi$
$840$	2.48625	−	1.43544i	0.0857838	−	0.0495273i
$841$	30.3001			1.04483
$842$	0.257749	−	0.446434i	0.00888262	−	0.0153851i
$843$	−56.5572	+	32.6533i	−1.94793	+	1.12464i
$844$	22.9548	+	39.7589i	0.790136	+	1.36856i
$845$	8.00534	−	17.1199i	0.275392	−	0.588943i
$846$	0.375866	−	0.651018i	0.0129225	−	0.0223825i
$847$	58.6345	+	33.8526i	2.01470	+	1.16319i
$848$	−9.93402	+	17.2062i	−0.341136	+	0.590864i
$849$	9.64718	+	16.7094i	0.331090	+	0.573465i
$850$	−0.0413310	−	0.0238625i	−0.00141764	−	0.000818476i
$851$	2.21441	−	1.27849i	0.0759089	−	0.0438260i
$852$		−	7.95990i		−	0.272702i
$853$		−	11.2789i		−	0.386183i	−0.981181	−	0.193091i	$-0.938149\pi$
$853$		−	11.2789i		−	0.386183i	0.981181	−	0.193091i	$-0.0618514\pi$
$854$	−1.00860	−	1.74694i	−0.0345135	−	0.0597791i
$855$	7.62937	−	13.2144i	0.260919	−	0.451925i
$856$	1.79003	−	1.03347i	0.0611818	−	0.0353233i
$857$	−12.6143	+	21.8487i	−0.430898	+	0.746337i	−0.996951	−	0.0780321i	$-0.975136\pi$
$857$	−12.6143	+	21.8487i	−0.430898	+	0.746337i	0.566053	+	0.824369i	$0.308470\pi$
$858$	−1.64817	+	1.79674i	−0.0562676	+	0.0613398i
$859$	2.10975	−	3.65420i	0.0719838	−	0.124680i	−0.827787	−	0.561043i	$-0.810400\pi$
$859$	2.10975	−	3.65420i	0.0719838	−	0.124680i	0.899771	+	0.436363i	$0.143734\pi$
$860$		−	27.2082i		−	0.927791i
$861$	−9.96851	−	17.2660i	−0.339726	−	0.588422i
$862$	0.257244	+	0.445560i	0.00876178	+	0.0151758i
$863$	−15.3488	−	8.86161i	−0.522478	−	0.301653i	0.215470	−	0.976510i	$-0.430872\pi$
$863$	−15.3488	−	8.86161i	−0.522478	−	0.301653i	−0.737948	+	0.674858i	$0.764205\pi$
$864$			2.61273i			0.0888870i
$865$	−4.81124	+	2.77777i	−0.163587	+	0.0944471i
$866$			0.110312i			0.00374856i
$867$	−46.8645			−1.59160
$868$	−40.5573	+	15.1587i	−1.37660	+	0.514518i
$869$		−	20.1309i		−	0.682893i
$870$	−1.42070			−0.0481663
$871$	−36.0560	+	11.3473i	−1.22171	+	0.384489i
$872$	−0.640558			−0.0216920
$873$	58.5766	+	33.8192i	1.98252	+	1.14461i
$874$	−0.0217777	−	0.0377200i	−0.000736640	−	0.00127590i
$875$	−22.3131	−	38.6474i	−0.754321	−	1.30652i
$876$			76.1525i			2.57295i
$877$	−35.3362	−	20.4014i	−1.19322	−	0.688906i	−0.234185	−	0.972192i	$-0.575242\pi$
$877$	−35.3362	−	20.4014i	−1.19322	−	0.688906i	−0.959035	+	0.283286i	$0.908575\pi$
$878$	0.618038	+	0.356824i	0.0208578	+	0.0120422i
$879$	31.2314	+	18.0314i	1.05341	+	0.608185i
$880$	15.4449	+	26.7514i	0.520649	+	0.901790i
$881$	2.03185	−	3.51927i	0.0684549	−	0.118567i	−0.829766	−	0.558111i	$-0.811526\pi$
$881$	2.03185	−	3.51927i	0.0684549	−	0.118567i	0.898221	+	0.439543i	$0.144860\pi$
$882$	−1.52115	+	0.878239i	−0.0512199	+	0.0295718i
$883$	−29.7726			−1.00193			−0.500963	−	0.865468i	$-0.667021\pi$
$883$	−29.7726			−1.00193			−0.500963	+	0.865468i	$0.667021\pi$
$884$	2.54523	+	0.565684i	0.0856052	+	0.0190260i
$885$	28.2142	+	48.8684i	0.948409	+	1.64269i
$886$	−0.437590	−	0.252643i	−0.0147011	−	0.00848770i
$887$	−16.9824	−	29.4143i	−0.570212	−	0.987636i	−0.996544	−	0.0830692i	$-0.973528\pi$
$887$	−16.9824	−	29.4143i	−0.570212	−	0.987636i	0.426332	−	0.904567i	$-0.359806\pi$
$888$	1.51336	−	2.62122i	0.0507851	−	0.0879623i
$889$	1.02501	+	0.591790i	0.0343777	+	0.0198480i
$890$	−0.950301	−	0.548656i	−0.0318542	−	0.0183910i
$891$			4.76383i			0.159594i
$892$	1.34965	−	0.779223i	0.0451897	−	0.0260903i
$893$	−3.87972	−	6.71988i	−0.129830	−	0.224872i
$894$	0.974470	−	1.68783i	0.0325912	−	0.0564495i
$895$			8.81372i			0.294610i
$896$	2.83736	+	4.91445i	0.0947895	+	0.164180i
$897$	4.19103	+	0.931468i	0.139934	+	0.0311008i
$898$	−0.489087			−0.0163210
$899$	42.2866	+	7.08114i	1.41034	+	0.236169i
$900$	27.2093			0.906975
$901$	1.80345			0.0600816
$902$	−0.388661	+	0.224393i	−0.0129410	+	0.00747149i
$903$			101.294i			3.37086i
$904$	2.06288	+	1.19100i	0.0686103	+	0.0396122i
$905$	8.95311	−	5.16908i	0.297612	−	0.171826i
$906$	0.0265802	+	0.0460383i	0.000883068	+	0.00152952i
$907$	37.9946			1.26159			0.630795	−	0.775949i	$-0.282729\pi$
$907$	37.9946			1.26159			0.630795	+	0.775949i	$0.282729\pi$
$908$	6.50870	+	3.75780i	0.215999	+	0.124707i
$909$	−29.5726	+	51.2212i	−0.980861	+	1.69890i
$910$	−0.686779	−	0.629990i	−0.0227665	−	0.0208840i
$911$	21.4030	+	37.0710i	0.709112	+	1.22822i	0.965187	+	0.261561i	$0.0842373\pi$
$911$	21.4030	+	37.0710i	0.709112	+	1.22822i	−0.256075	+	0.966657i	$0.582429\pi$
$912$	21.3422	+	12.3219i	0.706711	+	0.408020i
$913$	31.7329	+	54.9630i	1.05021	+	1.81901i
$914$	−0.930283			−0.0307710
$915$			45.8219i			1.51482i
$916$	−5.07752	+	2.93151i	−0.167766	+	0.0968597i
$917$	−14.7501	−	8.51595i	−0.487090	−	0.281221i
$918$	0.0683434	−	0.0394581i	0.00225567	−	0.00130231i
$919$	−6.72087	+	11.6409i	−0.221701	+	0.383997i	−0.955325	−	0.295559i	$-0.904494\pi$
$919$	−6.72087	+	11.6409i	−0.221701	+	0.383997i	0.733624	+	0.679556i	$0.237828\pi$
$920$	−0.0568968	+	0.0985482i	−0.00187583	+	0.00324904i
$921$	−38.1160	−	22.0063i	−1.25597	−	0.725132i
$922$	0.889774			0.0293031
$923$	−4.93220	+	1.55223i	−0.162345	+	0.0510923i
$924$	−57.5606	−	99.6979i	−1.89361	−	3.27982i
$925$	−14.9131	−	8.61009i	−0.490340	−	0.283098i
$926$	−0.175296			−0.00576059
$927$	−12.6376	−	21.8889i	−0.415072	−	0.718927i
$928$		−	4.21528i		−	0.138373i
$929$			7.05767i			0.231555i	0.993275	+	0.115777i	$0.0369359\pi$
$929$			7.05767i			0.231555i	−0.993275	+	0.115777i	$0.963064\pi$
$930$	−1.01310	−	0.169649i	−0.0332207	−	0.00556300i
$931$			18.1305i			0.594205i
$932$	−18.4263			−0.603575
$933$	28.0055	+	48.5070i	0.916860	+	1.58805i
$934$			0.951418i			0.0311314i
$935$	1.40196	−	2.42826i	0.0458489	−	0.0794127i
$936$	2.96336	−	0.932610i	0.0968604	−	0.0304833i
$937$	−20.9806	−	36.3395i	−0.685406	−	1.18716i	−0.973309	−	0.229499i	$-0.926291\pi$
$937$	−20.9806	−	36.3395i	−0.685406	−	1.18716i	0.287903	−	0.957660i	$-0.407042\pi$
$938$			1.86398i			0.0608611i
$939$	21.1193	−	36.5797i	0.689202	−	1.19373i
$940$	−5.06548	+	8.77368i	−0.165218	+	0.286166i
$941$	42.4463	+	24.5064i	1.38371	+	0.798885i	0.992597	−	0.121458i	$-0.0387571\pi$
$941$	42.4463	+	24.5064i	1.38371	+	0.798885i	0.391112	+	0.920343i	$0.372090\pi$
$942$	0.237278	−	0.136992i	0.00773093	−	0.00446346i
$943$	0.684376	+	0.395125i	0.0222863	+	0.0128670i
$944$	−48.2474	+	27.8556i	−1.57032	+	0.906624i
$945$	27.0085			0.878587
$946$	2.28016			0.0741343
$947$	−26.7651	+	15.4528i	−0.869750	+	0.502150i	−0.867265	−	0.497847i	$-0.834124\pi$
$947$	−26.7651	+	15.4528i	−0.869750	+	0.502150i	−0.00248455	+	0.999997i	$0.500791\pi$
$948$	−10.4844	+	18.1596i	−0.340519	+	0.589795i
$949$	47.1864	−	14.8502i	1.53174	−	0.482059i
$950$	−0.146664	+	0.254029i	−0.00475840	+	0.00824178i
$951$	13.4872	+	7.78682i	0.437352	+	0.252505i
$952$	0.128641	−	0.222813i	0.00416928	−	0.00722140i
$953$	−40.7189			−1.31901			−0.659507	−	0.751699i	$-0.729235\pi$
$953$	−40.7189			−1.31901			−0.659507	+	0.751699i	$0.729235\pi$
$954$	0.929979	−	0.536924i	0.0301092	−	0.0173835i
$955$	−12.6548	+	7.30623i	−0.409499	+	0.236424i
$956$	−10.4341	−	6.02411i	−0.337462	−	0.194834i
$957$			113.999i			3.68506i
$958$	0.287342	+	0.497691i	0.00928360	+	0.0160797i
$959$	−24.7647			−0.799695
$960$		−	32.1084i		−	1.03629i
$961$	29.3089	+	10.0991i	0.945447	+	0.325776i
$962$	−0.959150	−	0.213174i	−0.0309242	−	0.00687300i
$963$	53.3996			1.72078
$964$	−14.1353	+	8.16104i	−0.455269	+	0.262850i
$965$	1.04226			0.0335516
$966$	0.105856	−	0.183348i	0.00340587	−	0.00589914i
$967$	−17.5975	+	10.1599i	−0.565897	+	0.326721i	−0.755509	−	0.655138i	$-0.772610\pi$
$967$	−17.5975	+	10.1599i	−0.565897	+	0.326721i	0.189612	+	0.981859i	$0.439277\pi$
$968$	−2.75108	+	1.58833i	−0.0884229	+	0.0510510i
$969$		−	2.23696i		−	0.0718614i
$970$	0.824480	+	0.476014i	0.0264725	+	0.0152839i
$971$	25.5597	−	44.2707i	0.820250	−	1.42071i	−0.0852468	−	0.996360i	$-0.527168\pi$
$971$	25.5597	−	44.2707i	0.820250	−	1.42071i	0.905496	−	0.424354i	$-0.139499\pi$
$972$	16.7853	−	29.0730i	0.538388	−	0.932516i
$973$	17.4763	−	10.0899i	0.560264	−	0.323468i
$974$	−0.556910	+	0.964597i	−0.0178446	+	0.0309077i
$975$	−8.67980	−	27.5800i	−0.277976	−	0.883266i
$976$	−45.2396			−1.44808
$977$			23.0780i			0.738330i	0.929364	+	0.369165i	$0.120356\pi$
$977$			23.0780i			0.738330i	−0.929364	+	0.369165i	$0.879644\pi$
$978$	0.972124	+	1.68377i	0.0310851	+	0.0538410i
$979$	−44.0249	+	76.2534i	−1.40704	+	2.43707i
$980$	20.5004	−	11.8359i	0.654860	−	0.378084i
$981$	−14.3317	−	8.27443i	−0.457577	−	0.264182i
$982$	0.591553	+	0.341534i	0.0188772	+	0.0108988i
$983$	−16.5523	−	9.55649i	−0.527937	−	0.304805i	0.212239	−	0.977218i	$-0.431925\pi$
$983$	−16.5523	−	9.55649i	−0.527937	−	0.304805i	−0.740176	+	0.672413i	$0.765258\pi$
$984$	0.935426			0.0298203
$985$	−3.99633	−	6.92184i	−0.127334	−	0.220548i
$986$	−0.110263	+	0.0636601i	−0.00351148	+	0.00202735i
$987$	18.8585	−	32.6638i	0.600271	−	1.03970i
$988$	3.47681	−	15.6435i	0.110612	−	0.497686i
$989$	−2.00751	−	3.47712i	−0.0638352	−	0.110566i
$990$		−	1.66957i		−	0.0530623i
$991$	−3.32877			−0.105742			−0.0528709	−	0.998601i	$-0.516837\pi$
$991$	−3.32877			−0.105742			−0.0528709	+	0.998601i	$0.516837\pi$
$992$	0.503355	−	3.00590i	0.0159815	−	0.0954374i
$993$		−	51.6512i		−	1.63910i
$994$			0.254979i			0.00808744i
$995$	19.1272	−	11.0431i	0.606372	−	0.350089i
$996$		−	66.1077i		−	2.09470i
$997$	14.4702	−	25.0632i	0.458277	−	0.793760i	−0.540593	−	0.841284i	$-0.681800\pi$
$997$	14.4702	−	25.0632i	0.458277	−	0.793760i	0.998870	+	0.0475248i	$0.0151333\pi$
$998$	0.964269	+	1.67016i	0.0305234	+	0.0528681i
$999$	24.6598	−	14.2373i	0.780201	−	0.450450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.18	yes	68
13.12	even	2	inner	403.2.l.c.25.17	✓	68
31.5	even	3	inner	403.2.l.c.129.18	yes	68
403.129	even	6	inner	403.2.l.c.129.17	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.17	✓	68	13.12	even	2	inner
403.2.l.c.25.18	yes	68	1.1	even	1	trivial
403.2.l.c.129.17	yes	68	403.129	even	6	inner
403.2.l.c.129.18	yes	68	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.0456796i q^{2} +(-1.38907 - 2.40594i) q^{3} +1.99791 q^{4} +(1.25901 + 0.726890i) q^{5} +(0.109902 - 0.0634522i) q^{6} +(3.37083 - 1.94615i) q^{7} +0.182623i q^{8} +(-2.35904 + 4.08597i) q^{9} +O(q^{10})\)	\(q+0.0456796i q^{2} +(-1.38907 - 2.40594i) q^{3} +1.99791 q^{4} +(1.25901 + 0.726890i) q^{5} +(0.109902 - 0.0634522i) q^{6} +(3.37083 - 1.94615i) q^{7} +0.182623i q^{8} +(-2.35904 + 4.08597i) q^{9} +(-0.0332040 + 0.0575110i) q^{10} +(4.61476 + 2.66433i) q^{11} +(-2.77524 - 4.80686i) q^{12} +(-2.43729 + 2.65700i) q^{13} +(0.0888992 + 0.153978i) q^{14} -4.03881i q^{15} +3.98748 q^{16} +(-0.180975 - 0.313457i) q^{17} +(-0.186645 - 0.107760i) q^{18} +(-1.92657 + 1.11231i) q^{19} +(2.51539 + 1.45226i) q^{20} +(-9.36464 - 5.40668i) q^{21} +(-0.121706 + 0.210800i) q^{22} +0.428612 q^{23} +(0.439380 - 0.253676i) q^{24} +(-1.44326 - 2.49980i) q^{25} +(-0.121370 - 0.111334i) q^{26} +4.77305 q^{27} +(6.73462 - 3.88823i) q^{28} -7.70065 q^{29} +0.184491 q^{30} +(-5.49130 - 0.919550i) q^{31} +0.547392i q^{32} -14.8038i q^{33} +(0.0143186 - 0.00826685i) q^{34} +5.65854 q^{35} +(-4.71315 + 8.16342i) q^{36} +(5.16646 - 2.98286i) q^{37} +(-0.0508098 - 0.0880051i) q^{38} +(9.77814 + 2.17322i) q^{39} +(-0.132747 + 0.229924i) q^{40} +(1.59673 + 0.921870i) q^{41} +(0.246975 - 0.427773i) q^{42} +(-4.68376 - 8.11250i) q^{43} +(9.21989 + 5.32311i) q^{44} +(-5.94010 + 3.42952i) q^{45} +0.0195788i q^{46} +3.48799i q^{47} +(-5.53890 - 9.59366i) q^{48} +(4.07498 - 7.05808i) q^{49} +(0.114190 - 0.0659276i) q^{50} +(-0.502774 + 0.870829i) q^{51} +(-4.86949 + 5.30845i) q^{52} +(-2.49130 + 4.31506i) q^{53} +0.218031i q^{54} +(3.87335 + 6.70884i) q^{55} +(0.355411 + 0.615590i) q^{56} +(5.35230 + 3.09015i) q^{57} -0.351763i q^{58} +(-12.0997 + 6.98577i) q^{59} -8.06918i q^{60} -11.3454 q^{61} +(0.0420047 - 0.250840i) q^{62} +18.3641i q^{63} +7.94996 q^{64} +(-4.99991 + 1.57354i) q^{65} +0.676231 q^{66} +(9.07912 + 5.24183i) q^{67} +(-0.361572 - 0.626261i) q^{68} +(-0.595372 - 1.03122i) q^{69} +0.258480i q^{70} +(1.24196 + 0.717045i) q^{71} +(-0.746192 - 0.430814i) q^{72} +(-11.8818 - 6.85998i) q^{73} +(0.136256 + 0.236002i) q^{74} +(-4.00959 + 6.94481i) q^{75} +(-3.84913 + 2.22230i) q^{76} +20.7407 q^{77} +(-0.0992717 + 0.446661i) q^{78} +(-1.88892 - 3.27171i) q^{79} +(5.02028 + 2.89846i) q^{80} +(0.447000 + 0.774227i) q^{81} +(-0.0421106 + 0.0729377i) q^{82} +(10.3146 + 5.95513i) q^{83} +(-18.7097 - 10.8021i) q^{84} -0.526195i q^{85} +(0.370576 - 0.213952i) q^{86} +(10.6968 + 18.5273i) q^{87} +(-0.486568 + 0.842761i) q^{88} +16.5238i q^{89} +(-0.156659 - 0.271341i) q^{90} +(-3.04477 + 13.6996i) q^{91} +0.856329 q^{92} +(5.41543 + 14.4891i) q^{93} -0.159330 q^{94} -3.23410 q^{95} +(1.31699 - 0.760367i) q^{96} -14.3360i q^{97} +(0.322410 + 0.186143i) q^{98} +(-21.7728 + 12.5705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more