LMFDB - Embedded newform 312.2.bt.c.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(19,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 0, 5]))

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

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

chi := DirichletCharacter("312.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.1
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39432 + 0.236374i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.88825 - 0.659163i) q^{4} +(1.86647 - 1.86647i) q^{5} +(0.901866 + 1.08933i) q^{6} +(4.71214 - 1.26261i) q^{7} +(-2.47702 + 1.36542i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.16128 + 3.04365i) q^{10} +(-1.99964 - 0.535801i) q^{11} +(-1.51498 - 1.30569i) q^{12} +(-3.15234 + 1.75007i) q^{13} +(-6.27177 + 2.87431i) q^{14} +(-2.54965 - 0.683177i) q^{15} +(3.13101 - 2.48933i) q^{16} +(3.84928 + 2.22238i) q^{17} +(0.492454 - 1.32570i) q^{18} +(2.62661 - 0.703799i) q^{19} +(2.29407 - 4.75469i) q^{20} +(-3.44952 - 3.44952i) q^{21} +(2.91478 + 0.274415i) q^{22} +(-3.41537 - 5.91559i) q^{23} +(2.42100 + 1.46245i) q^{24} -1.96745i q^{25} +(3.98170 - 3.18529i) q^{26} +1.00000 q^{27} +(8.06544 - 5.49020i) q^{28} +(-0.143621 + 0.0829197i) q^{29} +(3.71651 + 0.349895i) q^{30} +(3.77330 - 3.77330i) q^{31} +(-3.77721 + 4.21102i) q^{32} +(0.535801 + 1.99964i) q^{33} +(-5.89244 - 2.18884i) q^{34} +(6.43844 - 11.1517i) q^{35} +(-0.373276 + 1.96486i) q^{36} +(-1.19716 + 4.46786i) q^{37} +(-3.49598 + 1.60218i) q^{38} +(3.09177 + 1.85498i) q^{39} +(-2.07478 + 7.17181i) q^{40} +(-2.06622 + 7.71126i) q^{41} +(5.62512 + 3.99436i) q^{42} +(-7.03012 - 4.05884i) q^{43} +(-4.12900 + 0.306357i) q^{44} +(0.683177 + 2.54965i) q^{45} +(6.16041 + 7.44092i) q^{46} +(-1.87036 - 1.87036i) q^{47} +(-3.72133 - 1.46687i) q^{48} +(14.5479 - 8.39921i) q^{49} +(0.465055 + 2.74326i) q^{50} -4.44476i q^{51} +(-4.79885 + 5.38248i) q^{52} -8.22085i q^{53} +(-1.39432 + 0.236374i) q^{54} +(-4.73233 + 2.73221i) q^{55} +(-9.94806 + 9.56155i) q^{56} +(-1.92281 - 1.92281i) q^{57} +(0.180654 - 0.149565i) q^{58} +(0.352439 + 1.31532i) q^{59} +(-5.26471 + 0.390623i) q^{60} +(0.601045 + 0.347013i) q^{61} +(-4.36928 + 6.15310i) q^{62} +(-1.26261 + 4.71214i) q^{63} +(4.27127 - 6.76434i) q^{64} +(-2.61731 + 9.15022i) q^{65} +(-1.21974 - 2.66148i) q^{66} +(1.26441 - 4.71883i) q^{67} +(8.73333 + 1.65912i) q^{68} +(-3.41537 + 5.91559i) q^{69} +(-6.34127 + 17.0709i) q^{70} +(2.46409 + 9.19612i) q^{71} +(0.0560238 - 2.82787i) q^{72} +(-11.2670 + 11.2670i) q^{73} +(0.613136 - 6.51261i) q^{74} +(-1.70386 + 0.983726i) q^{75} +(4.49579 - 3.06032i) q^{76} -10.0991 q^{77} +(-4.74939 - 1.85561i) q^{78} +9.91660i q^{79} +(1.19767 - 10.4902i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.05824 - 11.2404i) q^{82} +(3.88441 + 3.88441i) q^{83} +(-8.78737 - 4.23978i) q^{84} +(11.3326 - 3.03656i) q^{85} +(10.7616 + 3.99758i) q^{86} +(0.143621 + 0.0829197i) q^{87} +(5.68474 - 1.40315i) q^{88} +(13.1559 + 3.52510i) q^{89} +(-1.55524 - 3.39354i) q^{90} +(-12.6446 + 12.2267i) q^{91} +(-10.3484 - 8.91886i) q^{92} +(-5.15443 - 1.38112i) q^{93} +(3.04998 + 2.16577i) q^{94} +(3.58888 - 6.21613i) q^{95} +(5.53545 + 1.16565i) q^{96} +(-1.52421 + 0.408410i) q^{97} +(-18.2990 + 15.1499i) q^{98} +(1.46384 - 1.46384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	−1.39432	+	0.236374i	−0.985933	+	0.167142i
$2$	−1.39432	+	0.236374i	−0.985933	+	0.167142i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.88825	−	0.659163i	0.944127	−	0.329581i
$5$	1.86647	−	1.86647i	0.834713	−	0.834713i	−0.153445	−	0.988157i	$-0.549037\pi$
$5$	1.86647	−	1.86647i	0.834713	−	0.834713i	0.988157	+	0.153445i	$0.0490367\pi$
$6$	0.901866	+	1.08933i	0.368185	+	0.444717i
$7$	4.71214	−	1.26261i	1.78102	−	0.477223i	0.790251	−	0.612784i	$-0.209950\pi$
$7$	4.71214	−	1.26261i	1.78102	−	0.477223i	0.990769	+	0.135561i	$0.0432836\pi$
$8$	−2.47702	+	1.36542i	−0.875759	+	0.482748i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.16128	+	3.04365i	−0.683455	+	0.962486i
$11$	−1.99964	−	0.535801i	−0.602913	−	0.161550i	−0.0555651	−	0.998455i	$-0.517696\pi$
$11$	−1.99964	−	0.535801i	−0.602913	−	0.161550i	−0.547348	+	0.836905i	$0.684363\pi$
$12$	−1.51498	−	1.30569i	−0.437337	−	0.376922i
$13$	−3.15234	+	1.75007i	−0.874303	+	0.485381i
$13$	−3.15234	+	1.75007i	−0.874303	+	0.485381i
$14$	−6.27177	+	2.87431i	−1.67620	+	0.768193i
$15$	−2.54965	−	0.683177i	−0.658317	−	0.176396i
$16$	3.13101	−	2.48933i	0.782752	−	0.622333i
$17$	3.84928	+	2.22238i	0.933587	+	0.539007i	0.887944	−	0.459951i	$-0.152133\pi$
$17$	3.84928	+	2.22238i	0.933587	+	0.539007i	0.0456428	+	0.998958i	$0.485466\pi$
$18$	0.492454	−	1.32570i	0.116072	−	0.312471i
$19$	2.62661	−	0.703799i	0.602586	−	0.161462i	0.0553871	−	0.998465i	$-0.482361\pi$
$19$	2.62661	−	0.703799i	0.602586	−	0.161462i	0.547199	+	0.837002i	$0.315694\pi$
$20$	2.29407	−	4.75469i	0.512969	−	1.06318i
$21$	−3.44952	−	3.44952i	−0.752748	−	0.752748i
$22$	2.91478	+	0.274415i	0.621434	+	0.0585055i
$23$	−3.41537	−	5.91559i	−0.712154	−	1.23349i	−0.964047	−	0.265732i	$-0.914386\pi$
$23$	−3.41537	−	5.91559i	−0.712154	−	1.23349i	0.251893	−	0.967755i	$-0.418947\pi$
$24$	2.42100	+	1.46245i	0.494184	+	0.298522i
$25$		−	1.96745i		−	0.393490i
$26$	3.98170	−	3.18529i	0.780876	−	0.624686i
$27$	1.00000			0.192450
$28$	8.06544	−	5.49020i	1.52423	−	1.03755i
$29$	−0.143621	+	0.0829197i	−0.0266698	+	0.0153978i	−0.513276	−	0.858224i	$-0.671568\pi$
$29$	−0.143621	+	0.0829197i	−0.0266698	+	0.0153978i	0.486606	+	0.873622i	$0.338235\pi$
$30$	3.71651	+	0.349895i	0.678540	+	0.0638818i
$31$	3.77330	−	3.77330i	0.677705	−	0.677705i	−0.281775	−	0.959480i	$-0.590923\pi$
$31$	3.77330	−	3.77330i	0.677705	−	0.677705i	0.959480	+	0.281775i	$0.0909233\pi$
$32$	−3.77721	+	4.21102i	−0.667723	+	0.744410i
$33$	0.535801	+	1.99964i	0.0932710	+	0.348092i
$34$	−5.89244	−	2.18884i	−1.01054	−	0.375383i
$35$	6.43844	−	11.1517i	1.08830	−	1.88498i
$36$	−0.373276	+	1.96486i	−0.0622126	+	0.327476i
$37$	−1.19716	+	4.46786i	−0.196812	+	0.734512i	0.794978	+	0.606638i	$0.207482\pi$
$37$	−1.19716	+	4.46786i	−0.196812	+	0.734512i	−0.991790	+	0.127874i	$0.959185\pi$
$38$	−3.49598	+	1.60218i	−0.567122	+	0.259909i
$39$	3.09177	+	1.85498i	0.495080	+	0.297034i
$40$	−2.07478	+	7.17181i	−0.328051	+	1.13396i
$41$	−2.06622	+	7.71126i	−0.322690	+	1.20430i	0.593924	+	0.804521i	$0.297578\pi$
$41$	−2.06622	+	7.71126i	−0.322690	+	1.20430i	−0.916614	+	0.399774i	$0.869089\pi$
$42$	5.62512	+	3.99436i	0.867974	+	0.616343i
$43$	−7.03012	−	4.05884i	−1.07208	−	0.618968i	−0.143334	−	0.989674i	$-0.545782\pi$
$43$	−7.03012	−	4.05884i	−1.07208	−	0.618968i	−0.928750	+	0.370707i	$0.879116\pi$
$44$	−4.12900	+	0.306357i	−0.622471	+	0.0461851i
$45$	0.683177	+	2.54965i	0.101842	+	0.380080i
$46$	6.16041	+	7.44092i	0.908303	+	1.09710i
$47$	−1.87036	−	1.87036i	−0.272820	−	0.272820i	0.557415	−	0.830234i	$-0.311793\pi$
$47$	−1.87036	−	1.87036i	−0.272820	−	0.272820i	−0.830234	+	0.557415i	$0.811793\pi$
$48$	−3.72133	−	1.46687i	−0.537128	−	0.211724i
$49$	14.5479	−	8.39921i	2.07826	−	1.19989i
$50$	0.465055	+	2.74326i	0.0657687	+	0.387955i
$51$		−	4.44476i		−	0.622391i
$52$	−4.79885	+	5.38248i	−0.665480	+	0.746415i
$53$		−	8.22085i		−	1.12922i	−0.825358	−	0.564610i	$-0.809026\pi$
$53$		−	8.22085i		−	1.12922i	0.825358	−	0.564610i	$-0.190974\pi$
$54$	−1.39432	+	0.236374i	−0.189743	+	0.0321665i
$55$	−4.73233	+	2.73221i	−0.638107	+	0.368411i
$56$	−9.94806	+	9.56155i	−1.32937	+	1.27772i
$57$	−1.92281	−	1.92281i	−0.254683	−	0.254683i
$58$	0.180654	−	0.149565i	0.0237210	−	0.0196388i
$59$	0.352439	+	1.31532i	0.0458837	+	0.171240i	0.985065	−	0.172180i	$-0.0550811\pi$
$59$	0.352439	+	1.31532i	0.0458837	+	0.171240i	−0.939182	+	0.343420i	$0.888414\pi$
$60$	−5.26471	+	0.390623i	−0.679672	+	0.0504292i
$61$	0.601045	+	0.347013i	0.0769559	+	0.0444305i	0.537984	−	0.842955i	$-0.319186\pi$
$61$	0.601045	+	0.347013i	0.0769559	+	0.0444305i	−0.461028	+	0.887385i	$0.652519\pi$
$62$	−4.36928	+	6.15310i	−0.554899	+	0.781445i
$63$	−1.26261	+	4.71214i	−0.159074	+	0.593673i
$64$	4.27127	−	6.76434i	0.533908	−	0.845542i
$65$	−2.61731	+	9.15022i	−0.324638	+	1.13495i
$66$	−1.21974	−	2.66148i	−0.150140	−	0.327606i
$67$	1.26441	−	4.71883i	0.154472	−	0.576497i	−0.844678	−	0.535275i	$-0.820208\pi$
$67$	1.26441	−	4.71883i	0.154472	−	0.576497i	0.999150	−	0.0412224i	$-0.0131252\pi$
$68$	8.73333	+	1.65912i	1.05907	+	0.201198i
$69$	−3.41537	+	5.91559i	−0.411162	+	0.712154i
$70$	−6.34127	+	17.0709i	−0.757927	+	2.04037i
$71$	2.46409	+	9.19612i	0.292434	+	1.09138i	0.943234	+	0.332129i	$0.107767\pi$
$71$	2.46409	+	9.19612i	0.292434	+	1.09138i	−0.650800	+	0.759249i	$0.725566\pi$
$72$	0.0560238	−	2.82787i	0.00660246	−	0.333268i
$73$	−11.2670	+	11.2670i	−1.31870	+	1.31870i	−0.403895	+	0.914805i	$0.632344\pi$
$73$	−11.2670	+	11.2670i	−1.31870	+	1.31870i	−0.914805	+	0.403895i	$0.867656\pi$
$74$	0.613136	−	6.51261i	0.0712756	−	0.757075i
$75$	−1.70386	+	0.983726i	−0.196745	+	0.113591i
$76$	4.49579	−	3.06032i	0.515703	−	0.351042i
$77$	−10.0991			−1.15090
$78$	−4.74939	−	1.85561i	−0.537762	−	0.210107i
$79$			9.91660i			1.11570i	0.829940	+	0.557852i	$0.188374\pi$
$79$			9.91660i			1.11570i	−0.829940	+	0.557852i	$0.811626\pi$
$80$	1.19767	−	10.4902i	0.133904	−	1.17284i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.05824	−	11.2404i	0.116863	−	1.24129i
$83$	3.88441	+	3.88441i	0.426369	+	0.426369i	0.887390	−	0.461020i	$-0.152517\pi$
$83$	3.88441	+	3.88441i	0.426369	+	0.426369i	−0.461020	+	0.887390i	$0.652517\pi$
$84$	−8.78737	−	4.23978i	−0.958781	−	0.462598i
$85$	11.3326	−	3.03656i	1.22919	−	0.329361i
$86$	10.7616	+	3.99758i	1.16046	+	0.431071i
$87$	0.143621	+	0.0829197i	0.0153978	+	0.00888992i
$88$	5.68474	−	1.40315i	0.605995	−	0.149576i
$89$	13.1559	+	3.52510i	1.39452	+	0.373660i	0.876373	−	0.481632i	$-0.159956\pi$
$89$	13.1559	+	3.52510i	1.39452	+	0.373660i	0.518145	+	0.855293i	$0.326623\pi$
$90$	−1.55524	−	3.39354i	−0.163937	−	0.357711i
$91$	−12.6446	+	12.2267i	−1.32552	+	1.28171i
$92$	−10.3484	−	8.91886i	−1.07890	−	0.929856i
$93$	−5.15443	−	1.38112i	−0.534489	−	0.143216i
$94$	3.04998	+	2.16577i	0.314581	+	0.223382i
$95$	3.58888	−	6.21613i	0.368212	−	0.637761i
$96$	5.53545	+	1.16565i	0.564960	+	0.118969i
$97$	−1.52421	+	0.408410i	−0.154760	+	0.0414678i	−0.335367	−	0.942088i	$-0.608860\pi$
$97$	−1.52421	+	0.408410i	−0.154760	+	0.0414678i	0.180607	+	0.983555i	$0.442194\pi$
$98$	−18.2990	+	15.1499i	−1.84848	+	1.53037i
$99$	1.46384	−	1.46384i	0.147121	−	0.147121i
$100$	−1.29687	−	3.71505i	−0.129687	−	0.371505i
$101$	−1.42809	−	2.47353i	−0.142101	−	0.246126i	0.786187	−	0.617989i	$-0.212052\pi$
$101$	−1.42809	−	2.47353i	−0.142101	−	0.246126i	−0.928287	+	0.371863i	$0.878719\pi$
$102$	1.05063	+	6.19742i	0.104028	+	0.613636i
$103$	−10.1257			−0.997716			−0.498858	−	0.866684i	$-0.666247\pi$
$103$	−10.1257			−0.997716			−0.498858	+	0.866684i	$0.666247\pi$
$104$	5.41885	−	8.63922i	0.531362	−	0.847145i
$105$	−12.8769			−1.25666
$106$	1.94320	+	11.4625i	0.188740	+	1.11334i
$107$	5.08478	+	8.80709i	0.491564	+	0.851414i	0.999953	−	0.00971375i	$-0.00309203\pi$
$107$	5.08478	+	8.80709i	0.491564	+	0.851414i	−0.508389	+	0.861128i	$0.669759\pi$
$108$	1.88825	−	0.659163i	0.181697	−	0.0634280i
$109$	−5.06478	+	5.06478i	−0.485118	+	0.485118i	−0.906761	−	0.421644i	$-0.861453\pi$
$109$	−5.06478	+	5.06478i	−0.485118	+	0.485118i	0.421644	+	0.906761i	$0.361453\pi$
$110$	5.95256	−	4.92818i	0.567554	−	0.469883i
$111$	4.46786	−	1.19716i	0.424071	−	0.113629i
$112$	11.6107	−	15.6833i	1.09711	−	1.48194i
$113$	−0.373640	+	0.647164i	−0.0351491	+	0.0608801i	−0.883065	−	0.469251i	$-0.844524\pi$
$113$	−0.373640	+	0.647164i	−0.0351491	+	0.0608801i	0.847916	+	0.530131i	$0.177857\pi$
$114$	3.13552	+	2.22651i	0.293668	+	0.208532i
$115$	−17.4160	−	4.66660i	−1.62405	−	0.435163i
$116$	−0.216536	+	0.251243i	−0.0201048	+	0.0233273i
$117$	0.0605692	−	3.60504i	0.00559963	−	0.333286i
$118$	−0.802321	−	1.75067i	−0.0738596	−	0.161162i
$119$	20.9443	+	5.61202i	1.91996	+	0.514453i
$120$	7.24836	−	1.78910i	0.661682	−	0.163321i
$121$	−5.81481	−	3.35718i	−0.528619	−	0.305198i
$122$	−0.920073	−	0.341776i	−0.0832995	−	0.0309429i
$123$	7.71126	−	2.06622i	0.695300	−	0.186305i
$124$	4.63773	−	9.61217i	0.416481	−	0.863199i
$125$	5.66017	+	5.66017i	0.506261	+	0.506261i
$126$	0.646658	−	6.86867i	0.0576089	−	0.611910i
$127$	−8.06962	−	13.9770i	−0.716063	−	1.24026i	−0.962548	−	0.271111i	$-0.912609\pi$
$127$	−8.06962	−	13.9770i	−0.716063	−	1.24026i	0.246485	−	0.969147i	$-0.420724\pi$
$128$	−4.35660	+	10.4413i	−0.385072	+	0.922886i
$129$			8.11769i			0.714722i
$130$	1.48649	−	13.3770i	0.130374	−	1.17324i
$131$	16.6579			1.45540			0.727702	−	0.685894i	$-0.240588\pi$
$131$	16.6579			1.45540			0.727702	+	0.685894i	$0.240588\pi$
$132$	2.32982	+	3.42264i	0.202784	+	0.297903i
$133$	11.4883	−	6.63279i	0.996164	−	0.575136i
$134$	−0.647577	+	6.87843i	−0.0559421	+	0.594206i
$135$	1.86647	−	1.86647i	0.160641	−	0.160641i
$136$	−12.5692	−	0.249012i	−1.07780	−	0.0213526i
$137$	−0.760062	−	2.83659i	−0.0649365	−	0.242346i	0.925827	−	0.377948i	$-0.123370\pi$
$137$	−0.760062	−	2.83659i	−0.0649365	−	0.242346i	−0.990763	+	0.135601i	$0.956703\pi$
$138$	3.36382	−	9.05554i	0.286348	−	0.770858i
$139$	1.89159	−	3.27634i	0.160443	−	0.277895i	−0.774585	−	0.632470i	$-0.782041\pi$
$139$	1.89159	−	3.27634i	0.160443	−	0.277895i	0.935028	+	0.354575i	$0.115374\pi$
$140$	4.80663	−	25.3013i	0.406234	−	2.13835i
$141$	−0.684598	+	2.55495i	−0.0576536	+	0.215166i
$142$	−5.60946	−	12.2399i	−0.470735	−	1.02715i
$143$	7.24123	−	1.81047i	0.605542	−	0.151399i
$144$	0.590321	+	3.95620i	0.0491934	+	0.329683i
$145$	−0.113298	+	0.422832i	−0.00940885	+	0.0351143i
$146$	13.0465	−	18.3730i	1.07974	−	1.52056i
$147$	−14.5479	−	8.39921i	−1.19989	−	0.692755i
$148$	0.684505	+	9.22558i	0.0562660	+	0.758338i
$149$	4.90868	+	18.3194i	0.402134	+	1.50079i	0.809280	+	0.587423i	$0.199857\pi$
$149$	4.90868	+	18.3194i	0.402134	+	1.50079i	−0.407146	+	0.913363i	$0.633476\pi$
$150$	2.14320	−	1.77438i	0.174992	−	0.144877i
$151$	7.95676	+	7.95676i	0.647512	+	0.647512i	0.952391	−	0.304879i	$-0.0986160\pi$
$151$	7.95676	+	7.95676i	0.647512	+	0.647512i	−0.304879	+	0.952391i	$0.598616\pi$
$152$	−5.54520	+	5.32975i	−0.449775	+	0.432300i
$153$	−3.84928	+	2.22238i	−0.311196	+	0.179669i
$154$	14.0813	−	2.38716i	1.13471	−	0.192363i
$155$		−	14.0855i		−	1.13138i
$156$	7.06079	+	1.46468i	0.565315	+	0.117269i
$157$			9.73082i			0.776604i	0.921532	+	0.388302i	$0.126938\pi$
$157$			9.73082i			0.776604i	−0.921532	+	0.388302i	$0.873062\pi$
$158$	−2.34403	−	13.8269i	−0.186481	−	1.10001i
$159$	−7.11947	+	4.11043i	−0.564610	+	0.325978i
$160$	0.809682	+	14.9098i	0.0640110	+	1.17873i
$161$	−23.5628	−	23.5628i	−1.85701	−	1.85701i
$162$	0.901866	+	1.08933i	0.0708573	+	0.0855858i
$163$	6.44596	+	24.0567i	0.504887	+	1.88426i	0.465520	+	0.885038i	$0.345867\pi$
$163$	6.44596	+	24.0567i	0.504887	+	1.88426i	0.0393670	+	0.999225i	$0.487466\pi$
$164$	1.18141	+	15.9228i	0.0922529	+	1.24336i
$165$	4.73233	+	2.73221i	0.368411	+	0.212702i
$166$	−6.33428	−	4.49793i	−0.491635	−	0.349107i
$167$	2.58274	−	9.63891i	0.199858	−	0.745881i	−0.791097	−	0.611690i	$-0.790490\pi$
$167$	2.58274	−	9.63891i	0.199858	−	0.745881i	0.990956	−	0.134191i	$-0.0428435\pi$
$168$	13.2546	+	3.83450i	1.02261	+	0.295838i
$169$	6.87453	−	11.0336i	0.528810	−	0.848740i
$170$	−15.0835	+	6.91267i	−1.15685	+	0.530178i
$171$	−0.703799	+	2.62661i	−0.0538208	+	0.200862i
$172$	−15.9501	−	3.03013i	−1.21618	−	0.231046i
$173$	5.29984	−	9.17959i	0.402939	−	0.697911i	−0.591140	−	0.806569i	$-0.701322\pi$
$173$	5.29984	−	9.17959i	0.402939	−	0.697911i	0.994079	+	0.108658i	$0.0346553\pi$
$174$	−0.219854	−	0.0816682i	−0.0166671	−	0.00619125i
$175$	−2.48413	−	9.27090i	−0.187783	−	0.700814i
$176$	−7.59467	+	3.30017i	−0.572470	+	0.248759i
$177$	0.962881	−	0.962881i	0.0723746	−	0.0723746i
$178$	−19.1767	−	1.80541i	−1.43736	−	0.135321i
$179$	−13.8149	+	7.97602i	−1.03257	+	0.596156i	−0.917720	−	0.397227i	$-0.869973\pi$
$179$	−13.8149	+	7.97602i	−1.03257	+	0.596156i	−0.114851	+	0.993383i	$0.536639\pi$
$180$	2.97065	+	4.36407i	0.221419	+	0.325278i
$181$	−7.36580			−0.547496			−0.273748	−	0.961801i	$-0.588263\pi$
$181$	−7.36580			−0.547496			−0.273748	+	0.961801i	$0.588263\pi$
$182$	14.7405	−	20.0368i	1.09264	−	1.48523i
$183$		−	0.694026i		−	0.0513039i
$184$	16.5372	+	9.98964i	1.21914	+	0.736446i
$185$	6.10468	+	10.5736i	0.448825	+	0.777388i
$186$	7.51338	+	0.707355i	0.550908	+	0.0518658i
$187$	−6.50641	−	6.50641i	−0.475796	−	0.475796i
$188$	−4.76458	−	2.29884i	−0.347493	−	0.167660i
$189$	4.71214	−	1.26261i	0.342757	−	0.0918416i
$190$	−3.53472	+	9.51559i	−0.256435	+	0.690333i
$191$	5.05273	+	2.91720i	0.365603	+	0.211081i	0.671536	−	0.740972i	$-0.265635\pi$
$191$	5.05273	+	2.91720i	0.365603	+	0.211081i	−0.305933	+	0.952053i	$0.598968\pi$
$192$	−7.99372	−	0.316856i	−0.576897	−	0.0228671i
$193$	17.5387	+	4.69948i	1.26246	+	0.338276i	0.827139	−	0.561998i	$-0.189967\pi$
$193$	17.5387	+	4.69948i	1.26246	+	0.338276i	0.435324	+	0.900274i	$0.356634\pi$
$194$	2.02869	−	0.929738i	0.145652	−	0.0667513i
$195$	9.23298	−	2.30845i	0.661187	−	0.165312i
$196$	21.9336	−	25.4492i	1.56669	−	1.81780i
$197$	−7.77095	−	2.08222i	−0.553657	−	0.148352i	−0.0288665	−	0.999583i	$-0.509190\pi$
$197$	−7.77095	−	2.08222i	−0.553657	−	0.148352i	−0.524791	+	0.851231i	$0.675856\pi$
$198$	−1.69504	+	2.38707i	−0.120461	+	0.169642i
$199$	−1.64080	+	2.84194i	−0.116313	+	0.201460i	−0.918304	−	0.395876i	$-0.870441\pi$
$199$	−1.64080	+	2.84194i	−0.116313	+	0.201460i	0.801991	+	0.597336i	$0.203774\pi$
$200$	2.68639	+	4.87342i	0.189957	+	0.344603i
$201$	−4.71883	+	1.26441i	−0.332841	+	0.0891844i
$202$	2.57590	+	3.11133i	0.181240	+	0.218912i
$203$	−0.572067	+	0.572067i	−0.0401512	+	0.0401512i
$204$	−2.92982	−	8.39284i	−0.205129	−	0.587617i
$205$	10.5363	+	18.2494i	0.735887	+	1.27459i
$206$	14.1185	−	2.39346i	0.983681	−	0.166760i
$207$	6.83074			0.474769
$208$	−5.51352	+	13.3267i	−0.382294	+	0.924041i
$209$	−5.62937			−0.389392
$210$	17.9545	−	3.04377i	1.23898	−	0.210040i
$211$	6.16814	+	10.6835i	0.424632	+	0.735484i	0.996386	−	0.0849408i	$-0.0270701\pi$
$211$	6.16814	+	10.6835i	0.424632	+	0.735484i	−0.571754	+	0.820425i	$0.693737\pi$
$212$	−5.41888	−	15.5231i	−0.372170	−	1.06613i
$213$	6.73203	−	6.73203i	0.461271	−	0.461271i
$214$	−9.17158	−	11.0780i	−0.626956	−	0.757276i
$215$	−20.6973	+	5.54582i	−1.41154	+	0.378221i
$216$	−2.47702	+	1.36542i	−0.168540	+	0.0929049i
$217$	13.0161	−	22.5445i	0.883590	−	1.53042i
$218$	5.86473	−	8.25910i	0.397210	−	0.559377i
$219$	15.3910	+	4.12400i	1.04003	+	0.278674i
$220$	−7.13487	+	8.27849i	−0.481033	+	0.558136i
$221$	−16.0236	−	0.269216i	−1.07786	−	0.0181094i
$222$	−5.94665	+	2.72531i	−0.399113	+	0.182911i
$223$	−24.4285	−	6.54560i	−1.63585	−	0.438326i	−0.680250	−	0.732980i	$-0.738129\pi$
$223$	−24.4285	−	6.54560i	−1.63585	−	0.438326i	−0.955604	+	0.294655i	$0.904795\pi$
$224$	−12.4819	+	24.6120i	−0.833979	+	1.64446i
$225$	1.70386	+	0.983726i	0.113591	+	0.0655817i
$226$	0.368001	−	0.990673i	0.0244791	−	0.0658986i
$227$	−21.3233	+	5.71357i	−1.41528	+	0.379223i	−0.883807	−	0.467852i	$-0.845028\pi$
$227$	−21.3233	+	5.71357i	−1.41528	+	0.379223i	−0.531473	+	0.847075i	$0.678361\pi$
$228$	−4.89821	−	2.36331i	−0.324392	−	0.156514i
$229$	−11.7201	−	11.7201i	−0.774485	−	0.774485i	0.204402	−	0.978887i	$-0.434475\pi$
$229$	−11.7201	−	11.7201i	−0.774485	−	0.774485i	−0.978887	+	0.204402i	$0.934475\pi$
$230$	25.3865	+	2.39004i	1.67394	+	0.157595i
$231$	5.04954	+	8.74605i	0.332235	+	0.575448i
$232$	0.242532	−	0.401497i	0.0159230	−	0.0263595i
$233$			4.91123i			0.321746i	0.986975	+	0.160873i	$0.0514309\pi$
$233$			4.91123i			0.321746i	−0.986975	+	0.160873i	$0.948569\pi$
$234$	0.767686	+	5.04090i	0.0501852	+	0.329534i
$235$	−6.98195			−0.455452
$236$	1.53250	+	2.25135i	0.0997576	+	0.146550i
$237$	8.58803	−	4.95830i	0.557852	−	0.322076i
$238$	−30.5296	−	2.87424i	−1.97894	−	0.186310i
$239$	10.2089	−	10.2089i	0.660358	−	0.660358i	−0.295106	−	0.955465i	$-0.595355\pi$
$239$	10.2089	−	10.2089i	0.660358	−	0.660358i	0.955465	+	0.295106i	$0.0953550\pi$
$240$	−9.68364	+	4.20790i	−0.625076	+	0.271619i
$241$	0.695205	+	2.59454i	0.0447821	+	0.167129i	0.984695	−	0.174284i	$-0.0557611\pi$
$241$	0.695205	+	2.59454i	0.0447821	+	0.167129i	−0.939913	+	0.341413i	$0.889094\pi$
$242$	8.90126	+	3.30651i	0.572195	+	0.212551i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.36366	+	0.259063i	0.0872996	+	0.0165848i
$245$	11.4763	−	42.8301i	0.733193	−	2.73631i
$246$	−10.2636	+	4.70372i	−0.654380	+	0.299898i
$247$	−7.04829	+	6.81536i	−0.448472	+	0.433651i
$248$	−4.19441	+	14.4987i	−0.266346	+	0.920667i
$249$	1.42179	−	5.30620i	0.0901024	−	0.336267i
$250$	−9.23001	−	6.55417i	−0.583757	−	0.414522i
$251$	−2.76530	−	1.59655i	−0.174544	−	0.100773i	0.410183	−	0.912003i	$-0.365465\pi$
$251$	−2.76530	−	1.59655i	−0.174544	−	0.100773i	−0.584727	+	0.811230i	$0.698798\pi$
$252$	0.721929	+	9.72998i	0.0454773	+	0.612931i
$253$	3.65992	+	13.6590i	0.230097	+	0.858734i
$254$	14.5554	+	17.5809i	0.913289	+	1.10313i
$255$	−8.29604	−	8.29604i	−0.519518	−	0.519518i
$256$	3.60644	−	15.5883i	0.225402	−	0.974266i
$257$	−11.7430	+	6.77983i	−0.732509	+	0.422914i	−0.819339	−	0.573309i	$-0.805660\pi$
$257$	−11.7430	+	6.77983i	−0.732509	+	0.422914i	0.0868303	+	0.996223i	$0.472326\pi$
$258$	−1.91881	−	11.3186i	−0.119460	−	0.704668i
$259$			22.5647i			1.40210i
$260$	1.08933	+	19.0032i	0.0675575	+	1.17853i
$261$		−	0.165839i		−	0.0102652i
$262$	−23.2264	+	3.93749i	−1.43493	+	0.243259i
$263$	−15.4394	+	8.91391i	−0.952031	+	0.549655i	−0.893711	−	0.448642i	$-0.851908\pi$
$263$	−15.4394	+	8.91391i	−0.952031	+	0.549655i	−0.0583199	+	0.998298i	$0.518574\pi$
$264$	−4.05753	−	4.22155i	−0.249724	−	0.259819i
$265$	−15.3440	−	15.3440i	−0.942575	−	0.942575i
$266$	−14.4506	+	11.9638i	−0.886022	+	0.733546i
$267$	−3.52510	−	13.1559i	−0.215733	−	0.805126i
$268$	−0.722955	−	9.74380i	−0.0441615	−	0.595198i
$269$	15.1420	+	8.74224i	0.923225	+	0.533024i	0.884662	−	0.466232i	$-0.154389\pi$
$269$	15.1420	+	8.74224i	0.923225	+	0.533024i	0.0385623	+	0.999256i	$0.487722\pi$
$270$	−2.16128	+	3.04365i	−0.131531	+	0.185231i
$271$	−0.868914	+	3.24283i	−0.0527828	+	0.196988i	−0.987282	−	0.158976i	$-0.949181\pi$
$271$	−0.868914	+	3.24283i	−0.0527828	+	0.196988i	0.934500	+	0.355964i	$0.115847\pi$
$272$	17.5844	−	2.62384i	1.06621	−	0.159094i
$273$	16.9110	+	4.83718i	1.02350	+	0.292760i
$274$	1.73027	+	3.77545i	0.104529	+	0.228083i
$275$	−1.05416	+	3.93419i	−0.0635684	+	0.237241i
$276$	−2.54975	+	13.4214i	−0.153477	+	0.807875i
$277$	12.8269	−	22.2168i	0.770694	−	1.33488i	−0.166490	−	0.986043i	$-0.553243\pi$
$277$	12.8269	−	22.2168i	0.770694	−	1.33488i	0.937183	−	0.348837i	$-0.113423\pi$
$278$	−1.86304	+	5.01538i	−0.111738	+	0.300803i
$279$	1.38112	+	5.15443i	0.0826858	+	0.308587i
$280$	−0.721412	+	36.4142i	−0.0431126	+	2.17616i
$281$	13.6396	−	13.6396i	0.813669	−	0.813669i	−0.171513	−	0.985182i	$-0.554865\pi$
$281$	13.6396	−	13.6396i	0.813669	−	0.813669i	0.985182	+	0.171513i	$0.0548654\pi$
$282$	0.350623	−	3.72425i	0.0208793	−	0.221776i
$283$	4.91655	−	2.83857i	0.292258	−	0.168736i	−0.346701	−	0.937976i	$-0.612698\pi$
$283$	4.91655	−	2.83857i	0.292258	−	0.168736i	0.638960	+	0.769240i	$0.279365\pi$
$284$	10.7146	+	15.7404i	0.635793	+	0.934020i
$285$	−7.17776			−0.425174
$286$	−9.66864	+	4.23601i	−0.571719	+	0.250481i
$287$			38.9453i			2.29887i
$288$	−1.75824	−	5.37667i	−0.103605	−	0.316823i
$289$	1.37796	+	2.38670i	0.0810565	+	0.140394i
$290$	0.0580264	−	0.616344i	0.00340743	−	0.0361930i
$291$	1.11580	+	1.11580i	0.0654092	+	0.0654092i
$292$	−13.8482	+	28.7017i	−0.810402	+	1.67964i
$293$	5.74107	−	1.53832i	0.335397	−	0.0898693i	−0.0871901	−	0.996192i	$-0.527789\pi$
$293$	5.74107	−	1.53832i	0.335397	−	0.0898693i	0.422587	+	0.906322i	$0.361122\pi$
$294$	22.2697	+	8.27244i	1.29880	+	0.482459i
$295$	3.11283	+	1.79719i	0.181236	+	0.104637i
$296$	−3.13511	−	12.7016i	−0.182225	−	0.738266i
$297$	−1.99964	−	0.535801i	−0.116031	−	0.0310903i
$298$	−11.1745	−	24.3828i	−0.647322	−	1.41246i
$299$	21.1191	+	12.6709i	1.22135	+	0.732775i
$300$	−2.56889	+	2.98065i	−0.148315	+	0.172088i
$301$	−38.2516	−	10.2495i	−2.20479	−	0.590771i
$302$	−12.9750	−	9.21350i	−0.746630	−	0.530177i
$303$	−1.42809	+	2.47353i	−0.0820418	+	0.142101i
$304$	6.47196	−	8.74211i	0.371192	−	0.501395i
$305$	1.76953	−	0.474143i	0.101323	−	0.0271493i
$306$	4.84181	−	4.00858i	0.276788	−	0.229155i
$307$	−4.23600	+	4.23600i	−0.241761	+	0.241761i	−0.817578	−	0.575817i	$-0.804684\pi$
$307$	−4.23600	+	4.23600i	−0.241761	+	0.241761i	0.575817	+	0.817578i	$0.304684\pi$
$308$	−19.0696	+	6.65693i	−1.08659	+	0.379314i
$309$	5.06286	+	8.76912i	0.288016	+	0.498858i
$310$	3.32946	+	19.6397i	0.189101	+	1.11546i
$311$	−23.2153			−1.31642			−0.658209	−	0.752836i	$-0.728685\pi$
$311$	−23.2153			−1.31642			−0.658209	+	0.752836i	$0.728685\pi$
$312$	−10.1912	−	0.373250i	−0.576963	−	0.0211311i
$313$	23.0016			1.30013			0.650064	−	0.759880i	$-0.274742\pi$
$313$	23.0016			1.30013			0.650064	+	0.759880i	$0.274742\pi$
$314$	−2.30012	−	13.5679i	−0.129803	−	0.765680i
$315$	6.43844	+	11.1517i	0.362765	+	0.628328i
$316$	6.53665	+	18.7251i	0.367715	+	1.05337i
$317$	−13.3702	+	13.3702i	−0.750944	+	0.750944i	−0.974655	−	0.223711i	$-0.928183\pi$
$317$	−13.3702	+	13.3702i	−0.750944	+	0.750944i	0.223711	+	0.974655i	$0.428183\pi$
$318$	8.95521	−	7.41411i	0.502183	−	0.415762i
$319$	0.331619	−	0.0888569i	0.0185671	−	0.00497503i
$320$	−4.65325	−	20.5977i	−0.260125	−	1.15144i
$321$	5.08478	−	8.80709i	0.283805	−	0.491564i
$322$	38.4237	+	27.2844i	2.14127	+	1.52050i
$323$	11.6747	+	3.12822i	0.649596	+	0.174059i
$324$	−1.51498	−	1.30569i	−0.0841655	−	0.0725386i
$325$	3.44317	+	6.20208i	0.190993	+	0.344030i
$326$	−14.6741	−	32.0190i	−0.812723	−	1.77337i
$327$	6.91861	+	1.85384i	0.382600	+	0.102517i
$328$	−5.41101	−	21.9222i	−0.298773	−	1.21045i
$329$	−11.1749	−	6.45184i	−0.616093	−	0.355701i
$330$	−7.24421	−	2.69098i	−0.398780	−	0.148133i
$331$	15.9030	−	4.26121i	0.874110	−	0.234217i	0.206246	−	0.978500i	$-0.433875\pi$
$331$	15.9030	−	4.26121i	0.874110	−	0.234217i	0.667864	+	0.744283i	$0.267209\pi$
$332$	9.89520	+	4.77429i	0.543070	+	0.262023i
$333$	−3.27070	−	3.27070i	−0.179233	−	0.179233i
$334$	−1.32277	+	14.0502i	−0.0723788	+	0.768793i
$335$	−6.44759	−	11.1676i	−0.352270	−	0.610149i
$336$	−19.3875	−	2.21348i	−1.05767	−	0.120755i
$337$		−	27.5380i		−	1.50009i	−0.661386	−	0.750046i	$-0.730031\pi$
$337$		−	27.5380i		−	1.50009i	0.661386	−	0.750046i	$-0.269969\pi$
$338$	−6.97723	+	17.0094i	−0.379511	+	0.925187i
$339$	0.747281			0.0405867
$340$	19.3972	−	13.2038i	1.05196	−	0.716078i
$341$	−9.56698	+	5.52350i	−0.518081	+	0.299114i
$342$	0.360457	−	3.82870i	0.0194913	−	0.207032i
$343$	33.7998	−	33.7998i	1.82502	−	1.82502i
$344$	22.9558	+	0.454783i	1.23769	+	0.0245203i
$345$	4.66660	+	17.4160i	0.251242	+	0.937646i
$346$	−5.21985	+	14.0520i	−0.280621	+	0.755442i
$347$	9.78651	−	16.9507i	0.525367	−	0.909963i	−0.474196	−	0.880419i	$-0.657261\pi$
$347$	9.78651	−	16.9507i	0.525367	−	0.909963i	0.999563	−	0.0295437i	$-0.00940541\pi$
$348$	0.325851	+	0.0619038i	0.0174674	+	0.00331839i
$349$	1.58449	−	5.91341i	0.0848160	−	0.316538i	−0.910463	−	0.413590i	$-0.864275\pi$
$349$	1.58449	−	5.91341i	0.0848160	−	0.316538i	0.995279	+	0.0970522i	$0.0309414\pi$
$350$	5.65507	+	12.3394i	0.302276	+	0.659569i
$351$	−3.15234	+	1.75007i	−0.168260	+	0.0934117i
$352$	9.80933	−	6.39667i	0.522839	−	0.340944i
$353$	3.59259	−	13.4077i	0.191214	−	0.713621i	−0.802000	−	0.597324i	$-0.796231\pi$
$353$	3.59259	−	13.4077i	0.191214	−	0.713621i	0.993214	−	0.116297i	$-0.0371026\pi$
$354$	−1.11496	+	1.57016i	−0.0592597	+	0.0834533i
$355$	21.7635	+	12.5652i	1.15509	+	0.666889i
$356$	27.1652	−	2.01556i	1.43975	−	0.106825i
$357$	−5.61202	−	20.9443i	−0.297019	−	1.10849i
$358$	17.3770	−	14.3866i	0.918404	−	0.760355i
$359$	−12.7715	−	12.7715i	−0.674055	−	0.674055i	0.284593	−	0.958648i	$-0.408141\pi$
$359$	−12.7715	−	12.7715i	−0.674055	−	0.674055i	−0.958648	+	0.284593i	$0.908141\pi$
$360$	−5.17358	−	5.38272i	−0.272672	−	0.283694i
$361$	−10.0507	+	5.80279i	−0.528985	+	0.305410i
$362$	10.2703	−	1.74109i	0.539794	−	0.0915094i
$363$			6.71437i			0.352413i
$364$	−15.8168	+	31.4221i	−0.829027	+	1.64696i
$365$			42.0591i			2.20147i
$366$	0.164050	+	0.967695i	0.00857503	+	0.0505822i
$367$	−1.71553	+	0.990463i	−0.0895500	+	0.0517017i	−0.544106	−	0.839016i	$-0.683131\pi$
$367$	−1.71553	+	0.990463i	−0.0895500	+	0.0517017i	0.454556	+	0.890718i	$0.349798\pi$
$368$	−25.4194	−	10.0198i	−1.32508	−	0.522318i
$369$	−5.64503	−	5.64503i	−0.293869	−	0.293869i
$370$	−11.0112	−	13.3000i	−0.572445	−	0.691435i
$371$	−10.3798	−	38.7378i	−0.538890	−	2.01116i
$372$	−10.6433	+	0.789691i	−0.551827	+	0.0409436i
$373$	17.8013	+	10.2776i	0.921715	+	0.532152i	0.884182	−	0.467143i	$-0.154717\pi$
$373$	17.8013	+	10.2776i	0.921715	+	0.532152i	0.0375332	+	0.999295i	$0.488050\pi$
$374$	10.6100	+	7.53406i	0.548628	+	0.389577i
$375$	2.07177	−	7.73194i	0.106986	−	0.399276i
$376$	7.18673	+	2.07909i	0.370627	+	0.107221i
$377$	0.307628	−	0.512738i	0.0158436	−	0.0264073i
$378$	−6.27177	+	2.87431i	−0.322585	+	0.147839i
$379$	−1.58993	+	5.93369i	−0.0816691	+	0.304793i	−0.994663	−	0.103181i	$-0.967098\pi$
$379$	−1.58993	+	5.93369i	−0.0816691	+	0.304793i	0.912993	+	0.407974i	$0.133765\pi$
$380$	2.67928	−	14.1033i	0.137444	−	0.723483i
$381$	−8.06962	+	13.9770i	−0.413419	+	0.716063i
$382$	−7.73468	−	2.87317i	−0.395741	−	0.147004i
$383$	−3.16308	−	11.8048i	−0.161626	−	0.603196i	−0.998446	−	0.0557191i	$-0.982255\pi$
$383$	−3.16308	−	11.8048i	−0.161626	−	0.603196i	0.836820	−	0.547477i	$-0.184412\pi$
$384$	11.2207	−	1.44771i	0.572604	−	0.0738782i
$385$	−18.8497	+	18.8497i	−0.960668	+	0.960668i
$386$	−25.5654	−	2.40688i	−1.30124	−	0.122507i
$387$	7.03012	−	4.05884i	0.357361	−	0.206323i
$388$	−2.60888	+	1.77588i	−0.132446	+	0.0901568i
$389$	29.9634			1.51920			0.759601	−	0.650389i	$-0.225394\pi$
$389$	29.9634			1.51920			0.759601	+	0.650389i	$0.225394\pi$
$390$	−12.3281	+	5.40116i	−0.624256	+	0.273498i
$391$		−	30.3610i		−	1.53542i
$392$	−24.5669	+	40.6689i	−1.24082	+	2.05409i
$393$	−8.32893	−	14.4261i	−0.420139	−	0.727702i
$394$	11.3274	+	1.06643i	0.570665	+	0.0537258i
$395$	18.5091	+	18.5091i	0.931293	+	0.931293i
$396$	1.79919	−	3.72900i	0.0904127	−	0.187389i
$397$	−11.2356	+	3.01057i	−0.563899	+	0.151096i	−0.529497	−	0.848312i	$-0.677619\pi$
$397$	−11.2356	+	3.01057i	−0.563899	+	0.151096i	−0.0344019	+	0.999408i	$0.510953\pi$
$398$	1.61603	−	4.35042i	0.0810044	−	0.218067i
$399$	−11.4883	−	6.63279i	−0.575136	−	0.332055i
$400$	−4.89764	−	6.16011i	−0.244882	−	0.308005i
$401$	−24.4339	−	6.54704i	−1.22017	−	0.326943i	−0.409425	−	0.912344i	$-0.634271\pi$
$401$	−24.4339	−	6.54704i	−1.22017	−	0.326943i	−0.810744	+	0.585400i	$0.800937\pi$
$402$	6.28069	−	2.87840i	0.313252	−	0.143561i
$403$	−5.29121	+	18.4983i	−0.263574	+	0.921465i
$404$	−4.32706	−	3.72931i	−0.215279	−	0.185540i
$405$	−2.54965	−	0.683177i	−0.126693	−	0.0339473i
$406$	0.662422	−	0.932865i	0.0328754	−	0.0462973i
$407$	4.78777	−	8.29267i	0.237321	−	0.411052i
$408$	6.06896	+	11.0098i	0.300458	+	0.545065i
$409$	20.0336	−	5.36799i	0.990599	−	0.265430i	0.273097	−	0.961987i	$-0.411952\pi$
$409$	20.0336	−	5.36799i	0.990599	−	0.265430i	0.717502	+	0.696556i	$0.245285\pi$
$410$	−19.0047	−	22.9550i	−0.938574	−	1.13367i
$411$	−2.07653	+	2.07653i	−0.102428	+	0.102428i
$412$	−19.1199	+	6.67449i	−0.941971	+	0.328829i
$413$	3.32148	+	5.75297i	0.163439	+	0.283085i
$414$	−9.52424	+	1.61461i	−0.468091	+	0.0793538i
$415$	14.5003			0.711791
$416$	4.53751	−	19.8849i	0.222470	−	0.974940i
$417$	−3.78319			−0.185263
$418$	7.84914	−	1.33064i	0.383914	−	0.0650836i
$419$	−15.5683	−	26.9651i	−0.760560	−	1.31733i	−0.942562	−	0.334031i	$-0.891591\pi$
$419$	−15.5683	−	26.9651i	−0.760560	−	1.31733i	0.182002	−	0.983298i	$-0.441742\pi$
$420$	−24.3148	+	8.48796i	−1.18644	+	0.414170i
$421$	0.590979	−	0.590979i	0.0288026	−	0.0288026i	−0.692559	−	0.721361i	$-0.743517\pi$
$421$	0.590979	−	0.590979i	0.0288026	−	0.0288026i	0.721361	+	0.692559i	$0.243517\pi$
$422$	−11.1257	−	13.4383i	−0.541589	−	0.654164i
$423$	2.55495	−	0.684598i	0.124226	−	0.0332863i
$424$	11.2249	+	20.3632i	0.545129	+	0.988926i
$425$	4.37243	−	7.57327i	0.212094	−	0.367357i
$426$	−7.79532	+	10.9779i	−0.377685	+	0.531880i
$427$	3.27035	+	0.876287i	0.158263	+	0.0424065i
$428$	15.4067	+	13.2783i	0.744709	+	0.641833i
$429$	−5.18853	−	5.36586i	−0.250505	−	0.259066i
$430$	27.5477	−	12.6249i	1.32847	−	0.608829i
$431$	8.41002	+	2.25346i	0.405096	+	0.108545i	0.455613	−	0.890178i	$-0.349420\pi$
$431$	8.41002	+	2.25346i	0.405096	+	0.108545i	−0.0505166	+	0.998723i	$0.516087\pi$
$432$	3.13101	−	2.48933i	0.150641	−	0.119768i
$433$	−8.71099	−	5.02929i	−0.418624	−	0.241692i	0.275865	−	0.961196i	$-0.411036\pi$
$433$	−8.71099	−	5.02929i	−0.418624	−	0.241692i	−0.694488	+	0.719504i	$0.744369\pi$
$434$	−12.8196	+	34.5109i	−0.615363	+	1.65658i
$435$	0.422832	−	0.113298i	0.0202733	−	0.00543220i
$436$	−6.22507	+	12.9021i	−0.298127	+	0.617898i
$437$	−13.1342	−	13.1342i	−0.628296	−	0.628296i
$438$	−22.4348	−	2.11214i	−1.07197	−	0.100922i
$439$	3.83901	+	6.64936i	0.183226	+	0.317357i	0.942977	−	0.332857i	$-0.108013\pi$
$439$	3.83901	+	6.64936i	0.183226	+	0.317357i	−0.759751	+	0.650214i	$0.774679\pi$
$440$	7.99147	−	13.2294i	0.380978	−	0.630685i
$441$			16.7984i			0.799924i
$442$	22.4056	−	3.41218i	1.06573	−	0.162301i
$443$	−6.09878			−0.289762			−0.144881	−	0.989449i	$-0.546280\pi$
$443$	−6.09878			−0.289762			−0.144881	+	0.989449i	$0.546280\pi$
$444$	7.64734	−	5.20559i	0.362927	−	0.247046i
$445$	31.1346	−	17.9756i	1.47592	−	0.852123i
$446$	35.6084	+	3.35239i	1.68610	+	0.158740i
$447$	13.4107	−	13.4107i	0.634307	−	0.634307i
$448$	11.5860	−	37.2674i	0.547389	−	1.76072i
$449$	−6.24854	−	23.3199i	−0.294887	−	1.10053i	−0.941307	−	0.337551i	$-0.890401\pi$
$449$	−6.24854	−	23.3199i	−0.294887	−	1.10053i	0.646421	−	0.762981i	$-0.276265\pi$
$450$	−2.60826	−	0.968879i	−0.122954	−	0.0456734i
$451$	8.26340	−	14.3126i	0.389108	−	0.673955i
$452$	−0.278942	+	1.46830i	−0.0131203	+	0.0690630i
$453$	2.91238	−	10.8691i	0.136835	−	0.510677i
$454$	28.3810	−	13.0068i	1.33199	−	0.610441i
$455$	−0.779944	+	46.4217i	−0.0365643	+	2.17628i
$456$	7.38830	+	2.13741i	0.345989	+	0.100093i
$457$	−5.14536	+	19.2027i	−0.240690	+	0.898266i	0.734811	+	0.678272i	$0.237271\pi$
$457$	−5.14536	+	19.2027i	−0.240690	+	0.898266i	−0.975501	+	0.219995i	$0.929396\pi$
$458$	19.1119	+	13.5712i	0.893040	+	0.634142i
$459$	3.84928	+	2.22238i	0.179669	+	0.103732i
$460$	−35.9619	+	2.66824i	−1.67673	+	0.124407i
$461$	−3.19035	−	11.9065i	−0.148589	−	0.554543i	−0.999569	−	0.0293448i	$-0.990658\pi$
$461$	−3.19035	−	11.9065i	−0.148589	−	0.554543i	0.850980	−	0.525198i	$-0.176009\pi$
$462$	−9.10801	−	11.0012i	−0.423743	−	0.511823i
$463$	−5.89215	−	5.89215i	−0.273832	−	0.273832i	0.556809	−	0.830641i	$-0.312026\pi$
$463$	−5.89215	−	5.89215i	−0.273832	−	0.273832i	−0.830641	+	0.556809i	$0.812026\pi$
$464$	−0.243264	+	0.617143i	−0.0112933	+	0.0286501i
$465$	−12.1984	+	7.04277i	−0.565689	+	0.326601i
$466$	−1.16089	−	6.84783i	−0.0537771	−	0.317220i
$467$			23.5141i			1.08810i	0.839051	+	0.544052i	$0.183111\pi$
$467$			23.5141i			1.08810i	−0.839051	+	0.544052i	$0.816889\pi$
$468$	−2.26194	−	6.84716i	−0.104558	−	0.316510i
$469$		−	23.8322i		−	1.10047i
$470$	9.73506	−	1.65035i	0.449045	−	0.0761251i
$471$	8.42714	−	4.86541i	0.388302	−	0.224186i
$472$	−2.66896	−	2.77685i	−0.122849	−	0.127815i
$473$	11.8830	+	11.8830i	0.546379	+	0.546379i
$474$	−10.8024	+	8.94344i	−0.496172	+	0.410786i
$475$	−1.38469	−	5.16773i	−0.0635339	−	0.237112i
$476$	43.2474	−	3.20880i	1.98224	−	0.147075i
$477$	7.11947	+	4.11043i	0.325978	+	0.188203i
$478$	−11.8213	+	16.6476i	−0.540696	+	0.761443i
$479$	−0.824761	+	3.07805i	−0.0376843	+	0.140640i	−0.982205	−	0.187812i	$-0.939860\pi$
$479$	−0.824761	+	3.07805i	−0.0376843	+	0.140640i	0.944521	+	0.328452i	$0.106527\pi$
$480$	12.5074	−	8.15612i	0.570884	−	0.372274i
$481$	−4.04520	−	16.1793i	−0.184445	−	0.737715i
$482$	−1.58262	−	3.45329i	−0.0720864	−	0.157293i
$483$	−8.62458	+	32.1874i	−0.392432	+	1.46458i
$484$	−13.1928	−	2.50631i	−0.599672	−	0.113923i
$485$	−2.08261	+	3.60718i	−0.0945663	+	0.163794i
$486$	0.492454	−	1.32570i	0.0223382	−	0.0601351i
$487$	4.40943	+	16.4562i	0.199810	+	0.745702i	0.990969	+	0.134091i	$0.0428115\pi$
$487$	4.40943	+	16.4562i	0.199810	+	0.745702i	−0.791159	+	0.611611i	$0.790522\pi$
$488$	−1.96262	−	0.0388820i	−0.0888435	−	0.00176010i
$489$	17.6107	−	17.6107i	0.796383	−	0.796383i
$490$	−5.87768	+	62.4315i	−0.265527	+	2.82037i
$491$	10.5370	−	6.08352i	0.475527	−	0.274546i	−0.243024	−	0.970020i	$-0.578139\pi$
$491$	10.5370	−	6.08352i	0.475527	−	0.274546i	0.718551	+	0.695475i	$0.244806\pi$
$492$	13.1988	−	8.98453i	0.595049	−	0.405054i
$493$	−0.737117			−0.0331981
$494$	8.21659	−	11.1688i	0.369682	−	0.502509i
$495$		−	5.46443i		−	0.245608i
$496$	2.42124	−	21.2073i	0.108717	−	0.952234i
$497$	23.2223	+	40.2222i	1.04166	+	1.80421i
$498$	−0.728183	+	7.73461i	−0.0326307	+	0.346596i
$499$	−28.9374	−	28.9374i	−1.29542	−	1.29542i	−0.931389	−	0.364027i	$-0.881402\pi$
$499$	−28.9374	−	28.9374i	−1.29542	−	1.29542i	−0.364027	−	0.931389i	$-0.618598\pi$
$500$	14.4188	+	6.95687i	0.644829	+	0.311121i
$501$	−9.63891	+	2.58274i	−0.430635	+	0.115388i
$502$	4.23309	+	1.57245i	0.188932	+	0.0701818i
$503$	−21.8800	−	12.6324i	−0.975580	−	0.563252i	−0.0746475	−	0.997210i	$-0.523783\pi$
$503$	−21.8800	−	12.6324i	−0.975580	−	0.563252i	−0.900933	+	0.433958i	$0.857116\pi$
$504$	−3.30652	−	13.3961i	−0.147284	−	0.596708i
$505$	−7.28228	−	1.95128i	−0.324057	−	0.0868309i
$506$	−8.33174	−	18.1799i	−0.370391	−	0.808196i
$507$	−12.9927	−	0.436709i	−0.577024	−	0.0193949i
$508$	−24.4506	−	21.0729i	−1.08482	−	0.934960i
$509$	−18.9678	−	5.08241i	−0.840734	−	0.225274i	−0.187343	−	0.982295i	$-0.559988\pi$
$509$	−18.9678	−	5.08241i	−0.840734	−	0.225274i	−0.653391	+	0.757021i	$0.726654\pi$
$510$	13.5283	+	9.60636i	0.599043	+	0.425377i
$511$	−38.8657	+	67.3174i	−1.71932	+	2.97795i
$512$	−1.34387	+	22.5875i	−0.0593911	+	0.998235i
$513$	2.62661	−	0.703799i	0.115968	−	0.0310735i
$514$	14.7709	−	12.2290i	0.651518	−	0.539398i
$515$	−18.8994	+	18.8994i	−0.832806	+	0.832806i
$516$	5.35087	+	15.3283i	0.235559	+	0.674789i
$517$	2.73790	+	4.74218i	0.120413	+	0.208561i
$518$	−5.33372	−	31.4624i	−0.234350	−	1.38238i
$519$	−10.5997			−0.465274
$520$	−6.01074	−	26.2390i	−0.263588	−	1.15066i
$521$	−8.50132			−0.372450			−0.186225	−	0.982507i	$-0.559625\pi$
$521$	−8.50132			−0.372450			−0.186225	+	0.982507i	$0.559625\pi$
$522$	0.0392002	+	0.231233i	0.00171574	+	0.0101208i
$523$	−22.1486	−	38.3625i	−0.968490	−	1.67747i	−0.699932	−	0.714209i	$-0.746786\pi$
$523$	−22.1486	−	38.3625i	−0.968490	−	1.67747i	−0.268558	−	0.963264i	$-0.586547\pi$
$524$	31.4543	−	10.9802i	1.37409	−	0.479674i
$525$	−6.78677	+	6.78677i	−0.296199	+	0.296199i
$526$	19.4204	−	16.0783i	0.846768	−	0.701048i
$527$	22.9102	−	6.13877i	0.997984	−	0.267409i
$528$	6.65536	+	4.92710i	0.289638	+	0.214424i
$529$	−11.8295	+	20.4893i	−0.514326	+	0.890839i
$530$	25.0214	+	17.7675i	1.08686	+	0.771772i
$531$	−1.31532	−	0.352439i	−0.0570800	−	0.0152946i
$532$	17.3208	−	20.0971i	0.750952	−	0.871319i
$533$	−6.98176	−	27.9246i	−0.302414	−	1.20955i
$534$	8.02483	+	17.5102i	0.347268	+	0.757742i
$535$	25.9288	+	6.94761i	1.12100	+	0.300371i
$536$	3.31121	+	13.4151i	0.143023	+	0.579444i
$537$	13.8149	+	7.97602i	0.596156	+	0.344191i
$538$	−23.1792	−	8.61030i	−0.999328	−	0.371216i
$539$	−33.5907	+	9.00061i	−1.44686	+	0.387684i
$540$	2.29407	−	4.75469i	0.0987210	−	0.204609i
$541$	12.5837	+	12.5837i	0.541018	+	0.541018i	0.923827	−	0.382810i	$-0.125044\pi$
$541$	12.5837	+	12.5837i	0.541018	+	0.541018i	−0.382810	+	0.923827i	$0.625044\pi$
$542$	0.445022	−	4.72693i	0.0191153	−	0.203039i
$543$	3.68290	+	6.37897i	0.158048	+	0.273748i
$544$	−23.8980	+	7.81496i	−1.02462	+	0.335064i
$545$			18.9065i			0.809867i
$546$	−24.7227	−	2.74726i	−1.05803	−	0.117572i
$547$	−2.39098			−0.102231			−0.0511154	−	0.998693i	$-0.516278\pi$
$547$	−2.39098			−0.102231			−0.0511154	+	0.998693i	$0.516278\pi$
$548$	−3.30496	−	4.85520i	−0.141181	−	0.207404i
$549$	−0.601045	+	0.347013i	−0.0256520	+	0.0148102i
$550$	0.539899	−	5.73470i	0.0230214	−	0.244528i
$551$	−0.318878	+	0.318878i	−0.0135847	+	0.0135847i
$552$	0.382684	−	19.3165i	0.0162881	−	0.822163i
$553$	12.5208	+	46.7284i	0.532440	+	1.98709i
$554$	−12.6333	+	34.0093i	−0.536738	+	1.44492i
$555$	6.10468	−	10.5736i	0.259129	−	0.448825i
$556$	1.41217	−	7.43342i	0.0598894	−	0.315247i
$557$	−3.10542	+	11.5896i	−0.131581	+	0.491067i	−0.999989	−	0.00478427i	$-0.998477\pi$
$557$	−3.10542	+	11.5896i	−0.131581	+	0.491067i	0.868408	+	0.495851i	$0.165144\pi$
$558$	−3.14410	−	6.86046i	−0.133100	−	0.290426i
$559$	29.2646	+	0.491682i	1.23776	+	0.0207959i
$560$	−7.60150	−	50.9436i	−0.321222	−	2.15276i
$561$	−2.38151	+	8.88792i	−0.100547	+	0.375248i
$562$	−15.7939	+	22.2420i	−0.666225	+	0.938222i
$563$	−20.5535	−	11.8665i	−0.866225	−	0.500115i	−0.000133111	−	1.00000i	$-0.500042\pi$
$563$	−20.5535	−	11.8665i	−0.866225	−	0.500115i	−0.866092	+	0.499885i	$0.833376\pi$
$564$	0.391435	+	5.27567i	0.0164824	+	0.222146i
$565$	0.510525	+	1.90531i	0.0214779	+	0.0801568i
$566$	−6.18428	+	5.12002i	−0.259944	+	0.215211i
$567$	−3.44952	−	3.44952i	−0.144866	−	0.144866i
$568$	−18.6602	−	19.4145i	−0.782963	−	0.814613i
$569$	−26.9109	+	15.5370i	−1.12816	+	0.651346i	−0.943473	−	0.331450i	$-0.892462\pi$
$569$	−26.9109	+	15.5370i	−1.12816	+	0.651346i	−0.184692	+	0.982796i	$0.559129\pi$
$570$	10.0081	−	1.69664i	0.419193	−	0.0710644i
$571$		−	10.8606i		−	0.454500i	−0.973836	−	0.227250i	$-0.927027\pi$
$571$		−	10.8606i		−	0.454500i	0.973836	−	0.227250i	$-0.0729735\pi$
$572$	12.4799	−	8.19178i	0.521811	−	0.342515i
$573$		−	5.83440i		−	0.243735i
$574$	−9.20567	−	54.3022i	−0.384237	−	2.26653i
$575$	−11.6386	+	6.71958i	−0.485365	+	0.280226i
$576$	3.72246	+	7.08119i	0.155102	+	0.295050i
$577$	24.2438	+	24.2438i	1.00928	+	1.00928i	0.999956	+	0.00932743i	$0.00296906\pi$
$577$	24.2438	+	24.2438i	1.00928	+	1.00928i	0.00932743	+	0.999956i	$0.497031\pi$
$578$	−2.48547	−	3.00211i	−0.103382	−	0.124871i
$579$	−4.69948	−	17.5387i	−0.195304	−	0.728883i
$580$	0.0647806	+	0.873097i	0.00268987	+	0.0362534i
$581$	23.2084	+	13.3993i	0.962845	+	0.555899i
$582$	−1.81952	−	1.29203i	−0.0754217	−	0.0535565i
$583$	−4.40474	+	16.4387i	−0.182426	+	0.680822i
$584$	12.5244	−	43.2927i	0.518264	−	1.79146i
$585$	−6.61567	−	6.84177i	−0.273524	−	0.282872i
$586$	−7.64127	+	3.50194i	−0.315658	+	0.144664i
$587$	0.397645	−	1.48403i	0.0164125	−	0.0612525i	−0.957234	−	0.289315i	$-0.906572\pi$
$587$	0.397645	−	1.48403i	0.0164125	−	0.0612525i	0.973646	+	0.228063i	$0.0732391\pi$
$588$	−33.0065	−	6.27044i	−1.36116	−	0.258589i
$589$	7.25536	−	12.5666i	0.298952	−	0.517800i
$590$	−4.76509	−	1.77007i	−0.196176	−	0.0728726i
$591$	2.08222	+	7.77095i	0.0856511	+	0.319654i
$592$	7.37368	+	16.9690i	0.303056	+	0.697424i
$593$	4.86193	−	4.86193i	0.199656	−	0.199656i	−0.600197	−	0.799852i	$-0.704911\pi$
$593$	4.86193	−	4.86193i	0.199656	−	0.199656i	0.799852	+	0.600197i	$0.204911\pi$
$594$	2.91478	+	0.274415i	0.119595	+	0.0112594i
$595$	49.5667	−	28.6174i	2.03204	−	1.17320i
$596$	21.3443	+	31.3561i	0.874297	+	1.28440i
$597$	3.28159			0.134307
$598$	−32.4418	−	12.6752i	−1.32665	−	0.518328i
$599$		−	4.73413i		−	0.193431i	−0.995312	−	0.0967156i	$-0.969166\pi$
$599$		−	4.73413i		−	0.193431i	0.995312	−	0.0967156i	$-0.0308337\pi$
$600$	2.87731	−	4.76319i	0.117466	−	0.194457i
$601$	−5.84939	−	10.1314i	−0.238602	−	0.413270i	0.721712	−	0.692194i	$-0.243356\pi$
$601$	−5.84939	−	10.1314i	−0.238602	−	0.413270i	−0.960313	+	0.278924i	$0.910022\pi$
$602$	55.7577	+	5.24937i	2.27252	+	0.213948i
$603$	3.45442	+	3.45442i	0.140675	+	0.140675i
$604$	20.2692	+	9.77959i	0.824742	+	0.397926i
$605$	−17.1193	+	4.58710i	−0.695998	+	0.186492i
$606$	1.40654	−	3.78646i	0.0571368	−	0.153814i
$607$	5.29055	+	3.05450i	0.214737	+	0.123978i	0.603511	−	0.797355i	$-0.293768\pi$
$607$	5.29055	+	3.05450i	0.214737	+	0.123978i	−0.388774	+	0.921333i	$0.627101\pi$
$608$	−6.95757	+	13.7191i	−0.282167	+	0.556383i
$609$	0.781457	+	0.209391i	0.0316663	+	0.00848495i
$610$	−2.35521	+	1.07938i	−0.0953596	+	0.0437027i
$611$	9.16926	+	2.62276i	0.370948	+	0.106105i
$612$	−5.80351	+	6.73372i	−0.234593	+	0.272195i
$613$	34.2679	+	9.18205i	1.38407	+	0.370860i	0.872597	−	0.488442i	$-0.162434\pi$
$613$	34.2679	+	9.18205i	1.38407	+	0.370860i	0.511470	+	0.859301i	$0.329101\pi$
$614$	4.90505	−	6.90762i	0.197952	−	0.278769i
$615$	10.5363	−	18.2494i	0.424865	−	0.735887i
$616$	25.0156	−	13.7895i	1.00791	−	0.555593i
$617$	24.2158	−	6.48861i	0.974892	−	0.261221i	0.264000	−	0.964523i	$-0.414958\pi$
$617$	24.2158	−	6.48861i	0.974892	−	0.261221i	0.710892	+	0.703301i	$0.248291\pi$
$618$	−9.13204	−	11.0302i	−0.367344	−	0.443701i
$619$	−10.1532	+	10.1532i	−0.408091	+	0.408091i	−0.881072	−	0.472982i	$-0.843178\pi$
$619$	−10.1532	+	10.1532i	−0.408091	+	0.408091i	0.472982	+	0.881072i	$0.343178\pi$
$620$	−9.28466	−	26.5971i	−0.372881	−	1.06816i
$621$	−3.41537	−	5.91559i	−0.137054	−	0.237385i
$622$	32.3695	−	5.48749i	1.29790	−	0.220028i
$623$	66.4430			2.66198
$624$	14.2980	−	1.88851i	0.572379	−	0.0756009i
$625$	30.9664			1.23866
$626$	−32.0716	+	5.43699i	−1.28184	+	0.217306i
$627$	2.81468	+	4.87518i	0.112408	+	0.194696i
$628$	6.41420	+	18.3743i	0.255954	+	0.733213i
$629$	−14.5375	+	14.5375i	−0.579648	+	0.579648i
$630$	−11.6132	−	14.0272i	−0.462682	−	0.558856i
$631$	−13.5488	+	3.63038i	−0.539368	+	0.144523i	−0.518211	−	0.855253i	$-0.673402\pi$
$631$	−13.5488	+	3.63038i	−0.539368	+	0.144523i	−0.0211573	+	0.999776i	$0.506735\pi$
$632$	−13.5403	−	24.5636i	−0.538604	−	0.977088i
$633$	6.16814	−	10.6835i	0.245161	−	0.424632i
$634$	15.4819	−	21.8027i	0.614866	−	0.865895i
$635$	−41.1494	−	11.0260i	−1.63297	−	0.437552i
$636$	−10.7339	+	12.4544i	−0.425628	+	0.493850i
$637$	−31.1606	+	51.9369i	−1.23463	+	2.05781i
$638$	−0.441379	+	0.202281i	−0.0174744	+	0.00800838i
$639$	−9.19612	−	2.46409i	−0.363793	−	0.0974780i
$640$	11.3569	+	27.6198i	0.448920	+	1.09177i
$641$	−16.2594	−	9.38735i	−0.642206	−	0.370778i	0.143258	−	0.989685i	$-0.454242\pi$
$641$	−16.2594	−	9.38735i	−0.642206	−	0.370778i	−0.785464	+	0.618908i	$0.787576\pi$
$642$	−5.00804	+	13.4818i	−0.197651	+	0.532085i
$643$	37.3113	−	9.99754i	1.47142	−	0.394265i	0.567999	−	0.823029i	$-0.307718\pi$
$643$	37.3113	−	9.99754i	1.47142	−	0.394265i	0.903416	+	0.428765i	$0.141051\pi$
$644$	−60.0243	−	28.9608i	−2.36529	−	1.14122i
$645$	15.1515	+	15.1515i	0.596588	+	0.596588i
$646$	−17.0177	−	1.60214i	−0.669551	−	0.0630355i
$647$	−22.8502	−	39.5777i	−0.898333	−	1.55596i	−0.829624	−	0.558322i	$-0.811445\pi$
$647$	−22.8502	−	39.5777i	−0.898333	−	1.55596i	−0.0687090	−	0.997637i	$-0.521888\pi$
$648$	2.42100	+	1.46245i	0.0951058	+	0.0574506i
$649$		−	2.81900i		−	0.110655i
$650$	−6.26689	−	7.83381i	−0.245808	−	0.307267i
$651$	−26.0322			−1.02028
$652$	28.0289	+	41.1761i	1.09769	+	1.61258i
$653$	−17.6262	+	10.1765i	−0.689767	+	0.398237i	−0.803525	−	0.595271i	$-0.797045\pi$
$653$	−17.6262	+	10.1765i	−0.689767	+	0.398237i	0.113758	+	0.993509i	$0.463711\pi$
$654$	−10.0850	−	0.949459i	−0.394353	−	0.0371268i
$655$	31.0915	−	31.0915i	1.21484	−	1.21484i
$656$	12.7265	+	29.2875i	0.496887	+	1.14349i
$657$	−4.12400	−	15.3910i	−0.160893	−	0.600459i
$658$	17.1064	+	6.35446i	0.666879	+	0.247723i
$659$	−2.92527	+	5.06672i	−0.113952	+	0.197371i	−0.917361	−	0.398057i	$-0.869684\pi$
$659$	−2.92527	+	5.06672i	−0.113952	+	0.197371i	0.803408	+	0.595429i	$0.203018\pi$
$660$	10.7368	+	2.03974i	0.417930	+	0.0793967i
$661$	9.08145	−	33.8924i	0.353227	−	1.31826i	−0.529473	−	0.848327i	$-0.677610\pi$
$661$	9.08145	−	33.8924i	0.353227	−	1.31826i	0.882701	−	0.469936i	$-0.155723\pi$
$662$	−21.1667	+	9.70056i	−0.822667	+	0.377023i
$663$	7.77863	+	14.0114i	0.302097	+	0.544158i
$664$	−14.9256	−	4.31792i	−0.579225	−	0.167568i
$665$	9.06274	−	33.8226i	0.351438	−	1.31158i
$666$	5.33351	+	3.78729i	0.206669	+	0.146755i
$667$	0.981038	+	0.566403i	0.0379860	+	0.0219312i
$668$	−1.47674	−	19.9032i	−0.0571369	−	0.770076i
$669$	6.54560	+	24.4285i	0.253067	+	0.944461i
$670$	11.6297	+	14.0471i	0.449296	+	0.542687i
$671$	−1.01594	−	1.01594i	−0.0392200	−	0.0392200i
$672$	27.5556	−	1.49641i	1.06298	−	0.0577254i
$673$	−36.8546	+	21.2780i	−1.42064	+	0.820207i	−0.996353	−	0.0853213i	$-0.972808\pi$
$673$	−36.8546	+	21.2780i	−1.42064	+	0.820207i	−0.424286	+	0.905528i	$0.639475\pi$
$674$	6.50928	+	38.3968i	0.250728	+	1.47899i
$675$		−	1.96745i		−	0.0757272i
$676$	5.70792	−	25.3657i	0.219535	−	0.975605i
$677$			28.9422i			1.11234i	0.831069	+	0.556169i	$0.187729\pi$
$677$			28.9422i			1.11234i	−0.831069	+	0.556169i	$0.812271\pi$
$678$	−1.04195	+	0.176638i	−0.0400158	+	0.00678374i
$679$	−6.66661	+	3.84897i	−0.255841	+	0.147710i
$680$	−23.9249	+	22.9954i	−0.917478	+	0.881832i
$681$	15.6098	+	15.6098i	0.598168	+	0.598168i
$682$	12.0338	−	9.96291i	0.460798	−	0.381499i
$683$	8.32432	+	31.0668i	0.318521	+	1.18874i	0.920666	+	0.390351i	$0.127646\pi$
$683$	8.32432	+	31.0668i	0.318521	+	1.18874i	−0.602145	+	0.798387i	$0.705687\pi$
$684$	0.402414	+	5.42363i	0.0153867	+	0.207378i
$685$	−6.71306	−	3.87578i	−0.256493	−	0.148086i
$686$	−39.1384	+	55.1172i	−1.49431	+	2.10438i
$687$	−4.28985	+	16.0099i	−0.163668	+	0.610817i
$688$	−32.1152	+	4.79204i	−1.22438	+	0.182695i
$689$	14.3870	+	25.9149i	0.548103	+	0.987281i
$690$	−10.6234	−	23.1804i	−0.404427	−	0.882463i
$691$	−0.974151	+	3.63558i	−0.0370584	+	0.138304i	−0.981977	−	0.189003i	$-0.939474\pi$
$691$	−0.974151	+	3.63558i	−0.0370584	+	0.138304i	0.944918	+	0.327307i	$0.106141\pi$
$692$	3.95660	−	20.8269i	0.150407	−	0.791718i
$693$	5.04954	−	8.74605i	0.191816	−	0.332235i
$694$	−9.63880	+	25.9480i	−0.365884	+	0.984973i
$695$	−2.58459	−	9.64581i	−0.0980389	−	0.365886i
$696$	−0.468972	−	0.00929094i	−0.0177764	−	0.000352172i
$697$	−25.0908	+	25.0908i	−0.950383	+	0.950383i
$698$	−0.811513	+	8.61972i	−0.0307162	+	0.326261i
$699$	4.25325	−	2.45562i	0.160873	−	0.0928799i
$700$	−10.8017	−	15.8684i	−0.408266	−	0.599768i
$701$	−26.5127			−1.00137			−0.500685	−	0.865630i	$-0.666918\pi$
$701$	−26.5127			−1.00137			−0.500685	+	0.865630i	$0.666918\pi$
$702$	3.98170	−	3.18529i	0.150280	−	0.120221i
$703$			12.5779i			0.474385i
$704$	−12.1653	+	11.2377i	−0.458498	+	0.423536i
$705$	3.49097	+	6.04654i	0.131478	+	0.227726i
$706$	−1.83998	+	19.5438i	−0.0692484	+	0.735542i
$707$	−9.85248	−	9.85248i	−0.370541	−	0.370541i
$708$	1.18347	−	2.45286i	0.0444775	−	0.0921841i
$709$	−5.29377	+	1.41846i	−0.198812	+	0.0532715i	−0.356851	−	0.934161i	$-0.616150\pi$
$709$	−5.29377	+	1.41846i	−0.198812	+	0.0532715i	0.158039	+	0.987433i	$0.449483\pi$
$710$	−33.3153	−	12.3755i	−1.25030	−	0.464445i
$711$	−8.58803	−	4.95830i	−0.322076	−	0.185951i
$712$	−37.4006	+	9.23150i	−1.40165	+	0.345965i
$713$	−35.2085	−	9.43410i	−1.31857	−	0.353310i
$714$	12.7756	+	27.8766i	0.478116	+	1.04325i
$715$	10.1364	−	16.8948i	0.379079	−	0.631828i
$716$	−20.8285	+	24.1670i	−0.778397	+	0.903163i
$717$	−13.9456	−	3.73671i	−0.520808	−	0.139550i
$718$	20.8264	+	14.7887i	0.777236	+	0.551910i
$719$	−10.1805	+	17.6332i	−0.379670	+	0.657608i	−0.991014	−	0.133757i	$-0.957296\pi$
$719$	−10.1805	+	17.6332i	−0.379670	+	0.657608i	0.611344	+	0.791365i	$0.290629\pi$
$720$	8.48596	+	6.28233i	0.316253	+	0.234128i
$721$	−47.7137	+	12.7849i	−1.77695	+	0.476133i
$722$	12.6423	−	10.4667i	0.470497	−	0.389529i
$723$	1.89934	−	1.89934i	0.0706371	−	0.0706371i
$724$	−13.9085	+	4.85526i	−0.516906	+	0.180444i
$725$	0.163140	+	0.282568i	0.00605888	+	0.0104943i
$726$	−1.58710	−	9.36197i	−0.0589029	−	0.347455i
$727$	16.4107			0.608639			0.304320	−	0.952570i	$-0.401571\pi$
$727$	16.4107			0.608639			0.304320	+	0.952570i	$0.401571\pi$
$728$	14.6264	−	47.5511i	0.542089	−	1.76236i
$729$	1.00000			0.0370370
$730$	−9.94168	−	58.6438i	−0.367958	−	2.17050i
$731$	−18.0406	−	31.2472i	−0.667256	−	1.15572i
$732$	−0.457476	−	1.31050i	−0.0169088	−	0.0484374i
$733$	−26.6302	+	26.6302i	−0.983610	+	0.983610i	−0.999868	−	0.0162577i	$-0.994825\pi$
$733$	−26.6302	+	26.6302i	−0.983610	+	0.983610i	0.0162577	+	0.999868i	$0.494825\pi$
$734$	2.15788	−	1.78653i	0.0796488	−	0.0659420i
$735$	−42.8301	+	11.4763i	−1.57981	+	0.423309i
$736$	37.8112	+	7.96228i	1.39374	+	0.293494i
$737$	−5.05671	+	8.75848i	−0.186266	+	0.322623i
$738$	9.20532	+	6.53664i	0.338852	+	0.240617i
$739$	−16.2372	−	4.35076i	−0.597296	−	0.160045i	−0.0525107	−	0.998620i	$-0.516722\pi$
$739$	−16.2372	−	4.35076i	−0.597296	−	0.160045i	−0.544786	+	0.838575i	$0.683389\pi$
$740$	18.4969	+	15.9417i	0.679960	+	0.586029i
$741$	9.42642	+	2.69632i	0.346288	+	0.0990517i
$742$	23.6293	+	51.5593i	0.867459	+	1.89280i
$743$	13.7938	+	3.69604i	0.506046	+	0.135594i	0.502804	−	0.864400i	$-0.332302\pi$
$743$	13.7938	+	3.69604i	0.506046	+	0.135594i	0.00324119	+	0.999995i	$0.498968\pi$
$744$	14.6534	−	3.61687i	0.537221	−	0.132601i
$745$	43.3546	+	25.0308i	1.58839	+	0.917058i
$746$	−27.2500	−	10.1225i	−0.997694	−	0.370609i
$747$	−5.30620	+	1.42179i	−0.194144	+	0.0520206i
$748$	−16.5745	−	7.99697i	−0.606025	−	0.292398i
$749$	35.0801	+	35.0801i	1.28180	+	1.28180i
$750$	−1.06107	+	11.2705i	−0.0387449	+	0.411541i
$751$	−20.9053	−	36.2090i	−0.762844	−	1.32129i	−0.941379	−	0.337351i	$-0.890469\pi$
$751$	−20.9053	−	36.2090i	−0.762844	−	1.32129i	0.178534	−	0.983934i	$-0.442864\pi$
$752$	−10.5120	−	1.20016i	−0.383335	−	0.0437654i
$753$			3.19309i			0.116363i
$754$	−0.307734	+	0.787636i	−0.0112070	+	0.0286840i
$755$	29.7022			1.08097
$756$	8.06544	−	5.49020i	0.293337	−	0.199677i
$757$	−33.0464	+	19.0794i	−1.20109	+	0.693451i	−0.960798	−	0.277249i	$-0.910577\pi$
$757$	−33.0464	+	19.0794i	−1.20109	+	0.693451i	−0.240294	+	0.970700i	$0.577244\pi$
$758$	0.814296	−	8.64928i	0.0295766	−	0.314156i
$759$	9.99909	−	9.99909i	0.362944	−	0.362944i
$760$	−0.402125	+	20.2978i	−0.0145866	+	0.736279i
$761$	−0.805403	−	3.00580i	−0.0291958	−	0.108960i	0.949790	−	0.312887i	$-0.101296\pi$
$761$	−0.805403	−	3.00580i	−0.0291958	−	0.108960i	−0.978986	+	0.203927i	$0.934630\pi$
$762$	7.94783	−	21.3959i	0.287920	−	0.775090i
$763$	−17.4711	+	30.2608i	−0.632495	+	1.09551i
$764$	11.4638	+	2.17784i	0.414744	+	0.0787914i
$765$	−3.03656	+	11.3326i	−0.109787	+	0.409731i
$766$	7.20070	+	15.7120i	0.260172	+	0.567697i
$767$	−3.41291	−	3.52955i	−0.123233	−	0.127445i
$768$	−15.3030	+	4.67086i	−0.552201	+	0.168545i
$769$	2.20764	−	8.23902i	0.0796094	−	0.297106i	−0.914629	−	0.404293i	$-0.867518\pi$
$769$	2.20764	−	8.23902i	0.0796094	−	0.297106i	0.994239	+	0.107187i	$0.0341842\pi$
$770$	21.8269	−	30.7380i	0.786586	−	1.10772i
$771$	11.7430	+	6.77983i	0.422914	+	0.244170i
$772$	36.2152	−	2.68704i	1.30341	−	0.0967086i
$773$	−7.00923	−	26.1588i	−0.252105	−	0.940867i	−0.969678	−	0.244385i	$-0.921414\pi$
$773$	−7.00923	−	26.1588i	−0.252105	−	0.940867i	0.717574	−	0.696483i	$-0.245253\pi$
$774$	−8.84283	+	7.32106i	−0.317849	+	0.263150i
$775$	−7.42379	−	7.42379i	−0.266670	−	0.266670i
$776$	3.21784	−	3.09282i	0.115514	−	0.111026i
$777$	19.5416	−	11.2824i	0.701052	−	0.404752i
$778$	−41.7785	+	7.08257i	−1.49783	+	0.253922i
$779$			21.7087i			0.777794i
$780$	15.9126	−	10.4450i	0.569761	−	0.373990i
$781$		−	19.7092i		−	0.705250i
$782$	7.17657	+	42.3330i	0.256633	+	1.51382i
$783$	−0.143621	+	0.0829197i	−0.00513260	+	0.00296331i
$784$	24.6410	−	62.5124i	0.880037	−	2.23259i
$785$	18.1623	+	18.1623i	0.648241	+	0.648241i
$786$	15.0232	+	18.1459i	0.535858	+	0.647242i
$787$	−2.25972	−	8.43338i	−0.0805502	−	0.300617i	0.913884	−	0.405975i	$-0.133068\pi$
$787$	−2.25972	−	8.43338i	−0.0805502	−	0.300617i	−0.994434	+	0.105357i	$0.966401\pi$
$788$	−16.0461	+	1.19056i	−0.571617	+	0.0424119i
$789$	15.4394	+	8.91391i	0.549655	+	0.317344i
$790$	−30.1826	−	21.4325i	−1.07385	−	0.762534i
$791$	−0.943526	+	3.52129i	−0.0335479	+	0.125203i
$792$	−1.62720	+	5.62470i	−0.0578202	+	0.199865i
$793$	−2.50199	−	0.0420367i	−0.0888484	−	0.00149277i
$794$	14.9544	−	6.85351i	0.530712	−	0.243222i
$795$	−5.61630	+	20.9603i	−0.199190	+	0.743385i
$796$	−1.22494	+	6.44786i	−0.0434168	+	0.228538i
$797$	15.5889	−	27.0008i	0.552188	−	0.956418i	−0.445928	−	0.895069i	$-0.647126\pi$
$797$	15.5889	−	27.0008i	0.552188	−	0.956418i	0.998116	−	0.0613490i	$-0.0195403\pi$
$798$	17.5862	+	6.53268i	0.622546	+	0.231254i
$799$	−3.04288	−	11.3562i	−0.107649	−	0.401752i
$800$	8.28497	+	7.43148i	0.292918	+	0.262743i
$801$	−9.63076	+	9.63076i	−0.340286	+	0.340286i
$802$	35.6162	+	3.35312i	1.25765	+	0.118403i
$803$	28.5667	−	16.4930i	1.00810	−	0.582026i
$804$	−8.07690	+	5.49800i	−0.284850	+	0.193899i
$805$	−87.9587			−3.10014
$806$	3.00512	−	27.0432i	0.105851	−	0.952556i
$807$		−	17.4845i		−	0.615483i
$808$	6.91482	+	4.17704i	0.243263	+	0.146948i
$809$	3.86999	+	6.70302i	0.136062	+	0.235666i	0.926003	−	0.377517i	$-0.123222\pi$
$809$	3.86999	+	6.70302i	0.136062	+	0.235666i	−0.789941	+	0.613183i	$0.789889\pi$
$810$	3.71651	+	0.349895i	0.130585	+	0.0122941i
$811$	7.65096	+	7.65096i	0.268661	+	0.268661i	0.828561	−	0.559899i	$-0.189160\pi$
$811$	7.65096	+	7.65096i	0.268661	+	0.268661i	−0.559899	+	0.828561i	$0.689160\pi$
$812$	−0.703122	+	1.45729i	−0.0246748	+	0.0511409i
$813$	3.24283	−	0.868914i	0.113731	−	0.0304741i
$814$	−4.71551	+	12.6943i	−0.165279	+	0.444936i
$815$	56.9323	+	32.8699i	1.99425	+	1.15138i
$816$	−11.0645	−	13.9166i	−0.387335	−	0.487178i
$817$	−21.3220	−	5.71322i	−0.745963	−	0.199880i
$818$	−26.6644	+	12.2201i	−0.932300	+	0.427267i
$819$	−4.26636	−	17.0639i	−0.149079	−	0.596262i
$820$	31.9246	+	27.5144i	1.11485	+	0.960844i
$821$	−2.11509	−	0.566738i	−0.0738173	−	0.0197793i	0.221721	−	0.975110i	$-0.428832\pi$
$821$	−2.11509	−	0.566738i	−0.0738173	−	0.0197793i	−0.295539	+	0.955331i	$0.595499\pi$
$822$	2.40451	−	3.38618i	0.0838667	−	0.118107i
$823$	22.8632	−	39.6002i	0.796960	−	1.38037i	−0.124627	−	0.992204i	$-0.539774\pi$
$823$	22.8632	−	39.6002i	0.796960	−	1.38037i	0.921587	−	0.388171i	$-0.126893\pi$
$824$	25.0816	−	13.8258i	0.873759	−	0.481646i
$825$	3.93419	−	1.05416i	0.136971	−	0.0367012i
$826$	−5.99106	−	7.23637i	−0.208456	−	0.251786i
$827$	1.50831	−	1.50831i	0.0524490	−	0.0524490i	−0.680396	−	0.732845i	$-0.738192\pi$
$827$	1.50831	−	1.50831i	0.0524490	−	0.0524490i	0.732845	+	0.680396i	$0.238192\pi$
$828$	12.8982	−	4.50257i	0.448243	−	0.156475i
$829$	−2.20284	−	3.81543i	−0.0765077	−	0.132515i	0.825233	−	0.564792i	$-0.191044\pi$
$829$	−2.20284	−	3.81543i	−0.0765077	−	0.132515i	−0.901741	+	0.432277i	$0.857710\pi$
$830$	−20.2180	+	3.42750i	−0.701778	+	0.118970i
$831$	−25.6538			−0.889920
$832$	−1.62645	+	28.7985i	−0.0563871	+	0.998409i
$833$	74.6650			2.58699
$834$	5.27497	−	0.894248i	0.182657	−	0.0309653i
$835$	−13.1702	−	22.8114i	−0.455772	−	0.789420i
$836$	−10.6297	+	3.71067i	−0.367635	+	0.128336i
$837$	3.77330	−	3.77330i	0.130424	−	0.130424i
$838$	28.0810	+	33.9180i	0.970042	+	1.17168i
$839$	−9.23752	+	2.47519i	−0.318915	+	0.0854529i	−0.414725	−	0.909947i	$-0.636122\pi$
$839$	−9.23752	+	2.47519i	−0.318915	+	0.0854529i	0.0958107	+	0.995400i	$0.469456\pi$
$840$	31.8963	−	17.5823i	1.10053	−	0.606648i
$841$	−14.4862	+	25.0909i	−0.499526	+	0.865204i
$842$	−0.684322	+	0.963707i	−0.0235833	+	0.0332115i
$843$	−18.6320	−	4.99243i	−0.641721	−	0.171949i
$844$	18.6892	+	16.1074i	0.643309	+	0.554440i
$845$	−7.76283	−	33.4251i	−0.267050	−	1.14986i
$846$	−3.40060	+	1.55847i	−0.116915	+	0.0535814i
$847$	−31.6390	−	8.47765i	−1.08713	−	0.291295i
$848$	−20.4644	−	25.7396i	−0.702752	−	0.883900i
$849$	−4.91655	−	2.83857i	−0.168736	−	0.0974195i
$850$	−4.30644	+	11.5931i	−0.147710	+	0.397640i
$851$	30.5188	−	8.17749i	1.04617	−	0.280321i
$852$	8.27428	−	17.1493i	0.283472	−	0.587525i
$853$	−28.6500	−	28.6500i	−0.980956	−	0.980956i	0.0188661	−	0.999822i	$-0.493994\pi$
$853$	−28.6500	−	28.6500i	−0.980956	−	0.980956i	−0.999822	+	0.0188661i	$0.993994\pi$
$854$	−4.76704	−	0.448798i	−0.163125	−	0.0153575i
$855$	3.58888	+	6.21613i	0.122737	+	0.212587i
$856$	−24.6205	−	14.8725i	−0.841510	−	0.508332i
$857$		−	11.6602i		−	0.398306i	−0.979968	−	0.199153i	$-0.936181\pi$
$857$		−	11.6602i		−	0.398306i	0.979968	−	0.199153i	$-0.0638191\pi$
$858$	8.50282	+	6.25528i	0.290281	+	0.213552i
$859$	29.0257			0.990343			0.495172	−	0.868795i	$-0.335105\pi$
$859$	29.0257			0.990343			0.495172	+	0.868795i	$0.335105\pi$
$860$	−35.4261	+	24.1148i	−1.20802	+	0.822307i
$861$	33.7276	−	19.4727i	1.14943	−	0.663627i
$862$	−12.2589	−	1.15413i	−0.417540	−	0.0393098i
$863$	8.05746	−	8.05746i	0.274279	−	0.274279i	−0.556541	−	0.830820i	$-0.687872\pi$
$863$	8.05746	−	8.05746i	0.274279	−	0.274279i	0.830820	+	0.556541i	$0.187872\pi$
$864$	−3.77721	+	4.21102i	−0.128503	+	0.143262i
$865$	−7.24145	−	27.0255i	−0.246217	−	0.918894i
$866$	13.3347	+	4.95339i	0.453132	+	0.168323i
$867$	1.37796	−	2.38670i	0.0467980	−	0.0810565i
$868$	9.71718	−	51.1495i	0.329823	−	1.73613i
$869$	5.31333	−	19.8296i	0.180242	−	0.672673i
$870$	−0.562783	+	0.257920i	−0.0190801	+	0.00874430i
$871$	4.27243	+	17.0882i	0.144766	+	0.579011i
$872$	5.63002	−	19.4611i	0.190657	−	0.659036i
$873$	0.408410	−	1.52421i	0.0138226	−	0.0515866i
$874$	21.4179	+	15.2087i	0.724472	+	0.514443i
$875$	33.8181	+	19.5249i	1.14326	+	0.660062i
$876$	31.7805	−	2.35800i	1.07376	−	0.0796693i
$877$	1.68176	+	6.27643i	0.0567891	+	0.211940i	0.988490	−	0.151287i	$-0.0483417\pi$
$877$	1.68176	+	6.27643i	0.0567891	+	0.211940i	−0.931701	+	0.363227i	$0.881675\pi$
$878$	−6.92454	−	8.36389i	−0.233692	−	0.282268i
$879$	−4.20276	−	4.20276i	−0.141755	−	0.141755i
$880$	−8.01559	+	20.3349i	−0.270205	+	0.685490i
$881$	16.3109	−	9.41711i	0.549528	−	0.317270i	−0.199403	−	0.979917i	$-0.563900\pi$
$881$	16.3109	−	9.41711i	0.549528	−	0.317270i	0.748932	+	0.662647i	$0.230567\pi$
$882$	−3.97071	−	23.4224i	−0.133701	−	0.788672i
$883$			7.15931i			0.240930i	0.992718	+	0.120465i	$0.0384385\pi$
$883$			7.15931i			0.240930i	−0.992718	+	0.120465i	$0.961561\pi$
$884$	−30.4340	+	10.0538i	−1.02361	+	0.338145i
$885$		−	3.59439i		−	0.120824i
$886$	8.50365	−	1.44160i	0.285686	−	0.0484314i
$887$	−5.21027	+	3.00815i	−0.174944	+	0.101004i	−0.584915	−	0.811095i	$-0.698872\pi$
$887$	−5.21027	+	3.00815i	−0.174944	+	0.101004i	0.409971	+	0.912098i	$0.365539\pi$
$888$	−9.43237	+	9.06589i	−0.316529	+	0.304231i
$889$	−55.6727	−	55.6727i	−1.86720	−	1.86720i
$890$	−39.1626	+	32.4231i	−1.31273	+	1.08682i
$891$	0.535801	+	1.99964i	0.0179500	+	0.0669904i
$892$	−50.4418	+	3.74260i	−1.68892	+	0.125312i
$893$	−6.22906	−	3.59635i	−0.208447	−	0.120347i
$894$	−15.5289	+	21.8688i	−0.519365	+	0.731403i
$895$	−10.8981	+	40.6721i	−0.364282	+	1.35952i
$896$	−7.34559	+	54.7014i	−0.245399	+	1.82744i
$897$	0.413733	−	24.6251i	0.0138141	−	0.822208i
$898$	14.2247	+	31.0383i	0.474684	+	1.03576i
$899$	−0.229045	+	0.854807i	−0.00763907	+	0.0285094i
$900$	3.86576	+	0.734402i	0.128859	+	0.0244801i
$901$	18.2699	−	31.6443i	0.608658	−	1.05423i
$902$	−8.13868	+	21.9096i	−0.270989	+	0.729511i
$903$	10.2495	+	38.2516i	0.341082	+	1.27293i
$904$	0.0418655	−	2.11321i	0.00139242	−	0.0702845i
$905$	−13.7481	+	13.7481i	−0.457002	+	0.457002i
$906$	−1.49160	+	15.8435i	−0.0495551	+	0.526364i
$907$	7.90224	−	4.56236i	0.262390	−	0.151491i	−0.363035	−	0.931776i	$-0.618259\pi$
$907$	7.90224	−	4.56236i	0.262390	−	0.151491i	0.625424	+	0.780285i	$0.284926\pi$
$908$	−36.4977	+	24.8442i	−1.21122	+	0.824485i
$909$	2.85619			0.0947338
$910$	−9.88541	−	64.9111i	−0.327698	−	2.15178i
$911$		−	33.8691i		−	1.12213i	−0.827770	−	0.561067i	$-0.810391\pi$
$911$		−	33.8691i		−	1.12213i	0.827770	−	0.561067i	$-0.189609\pi$
$912$	−10.8069	−	1.23382i	−0.357851	−	0.0408560i
$913$	−5.68614	−	9.84868i	−0.188184	−	0.325944i
$914$	2.63524	−	27.9910i	0.0871660	−	0.925860i
$915$	−1.29538	−	1.29538i	−0.0428240	−	0.0428240i
$916$	−29.8560	−	14.4051i	−0.986469	−	0.475957i
$917$	78.4941	−	21.0324i	2.59210	−	0.694552i
$918$	−5.89244	−	2.18884i	−0.194479	−	0.0722425i
$919$	15.7907	+	9.11677i	0.520887	+	0.300734i	0.737298	−	0.675568i	$-0.236102\pi$
$919$	15.7907	+	9.11677i	0.520887	+	0.300734i	−0.216410	+	0.976302i	$0.569435\pi$
$920$	49.5117	−	12.2209i	1.63235	−	0.402910i
$921$	5.78648	+	1.55048i	0.190671	+	0.0510901i
$922$	7.26276	+	15.8474i	0.239186	+	0.521907i
$923$	−23.8615	−	24.6770i	−0.785411	−	0.812253i
$924$	15.2999	+	13.1863i	0.503329	+	0.433798i
$925$	8.79030	+	2.35535i	0.289023	+	0.0774436i
$926$	9.60830	+	6.82279i	0.315748	+	0.224211i
$927$	5.06286	−	8.76912i	0.166286	−	0.288016i
$928$	0.193311	−	0.917996i	0.00634576	−	0.0301347i
$929$	41.6902	−	11.1709i	1.36781	−	0.366504i	0.501133	−	0.865370i	$-0.332917\pi$
$929$	41.6902	−	11.1709i	1.36781	−	0.366504i	0.866679	+	0.498866i	$0.166250\pi$
$930$	15.3438	−	12.7033i	0.503143	−	0.416557i
$931$	32.3002	−	32.3002i	1.05860	−	1.05860i
$932$	3.23730	+	9.27366i	0.106041	+	0.303769i
$933$	11.6076	+	20.1050i	0.380017	+	0.658209i
$934$	−5.55814	−	32.7862i	−0.181868	−	1.07280i
$935$	−24.2881			−0.794305
$936$	4.77236	+	9.01247i	0.155989	+	0.294582i
$937$	12.5702			0.410650			0.205325	−	0.978694i	$-0.434175\pi$
$937$	12.5702			0.410650			0.205325	+	0.978694i	$0.434175\pi$
$938$	5.63333	+	33.2297i	0.183935	+	1.08499i
$939$	−11.5008	−	19.9200i	−0.375315	−	0.650064i
$940$	−13.1837	+	4.60224i	−0.430005	+	0.150108i
$941$	19.4028	−	19.4028i	0.632512	−	0.632512i	−0.316185	−	0.948697i	$-0.602402\pi$
$941$	19.4028	−	19.4028i	0.632512	−	0.632512i	0.948697	+	0.316185i	$0.102402\pi$
$942$	−10.6001	+	8.77590i	−0.345369	+	0.285934i
$943$	52.6736	−	14.1138i	1.71529	−	0.459610i
$944$	4.37776	+	3.24094i	0.142484	+	0.105484i
$945$	6.43844	−	11.1517i	0.209443	−	0.362765i
$946$	−19.3775	−	13.7598i	−0.630016	−	0.447370i
$947$	−23.2132	−	6.21995i	−0.754327	−	0.202121i	−0.138890	−	0.990308i	$-0.544354\pi$
$947$	−23.2132	−	6.21995i	−0.754327	−	0.202121i	−0.615437	+	0.788186i	$0.711020\pi$
$948$	12.9481	−	15.0234i	0.420533	−	0.487938i
$949$	15.7994	−	55.2354i	0.512871	−	1.79302i
$950$	3.15222	+	6.87817i	0.102271	+	0.223157i
$951$	18.2640	+	4.89382i	0.592251	+	0.158693i
$952$	−59.5423	+	14.6967i	−1.92978	+	0.476322i
$953$	−7.54135	−	4.35400i	−0.244288	−	0.141040i	0.372858	−	0.927889i	$-0.378378\pi$
$953$	−7.54135	−	4.35400i	−0.244288	−	0.141040i	−0.617146	+	0.786849i	$0.711711\pi$
$954$	−10.8984	−	4.04839i	−0.352849	−	0.131071i
$955$	14.8757	−	3.98592i	0.481365	−	0.128981i
$956$	12.5477	−	26.0063i	0.405821	−	0.841104i
$957$	−0.242762	−	0.242762i	−0.00784737	−	0.00784737i
$958$	0.422409	−	4.48674i	0.0136474	−	0.144960i
$959$	−7.16303	−	12.4067i	−0.231306	−	0.400634i
$960$	−15.5115	+	14.3287i	−0.500631	+	0.462456i
$961$			2.52438i			0.0814317i
$962$	9.46468	+	21.6030i	0.305154	+	0.696509i
$963$	−10.1696			−0.327709
$964$	3.02295	+	4.44090i	0.0973626	+	0.143032i
$965$	41.5070	−	23.9641i	1.33616	−	0.771430i
$966$	4.41715	−	46.9181i	0.142120	−	1.50957i
$967$	−32.8150	+	32.8150i	−1.05526	+	1.05526i	−0.0568771	+	0.998381i	$0.518114\pi$
$967$	−32.8150	+	32.8150i	−1.05526	+	1.05526i	−0.998381	+	0.0568771i	$0.981886\pi$
$968$	18.9874	+	0.376164i	0.610277	+	0.0120904i
$969$	−3.12822	−	11.6747i	−0.100493	−	0.375044i
$970$	2.05118	−	5.52184i	0.0658593	−	0.177296i
$971$	0.777271	−	1.34627i	0.0249438	−	0.0432040i	−0.853284	−	0.521446i	$-0.825393\pi$
$971$	0.777271	−	1.34627i	0.0249438	−	0.0432040i	0.878228	+	0.478242i	$0.158726\pi$
$972$	−0.373276	+	1.96486i	−0.0119728	+	0.0630228i
$973$	4.77670	−	17.8269i	0.153134	−	0.571504i
$974$	−10.0380	−	21.9029i	−0.321638	−	0.701816i
$975$	3.64957	−	6.08291i	0.116880	−	0.194809i
$976$	2.74571	−	0.409699i	0.0878880	−	0.0131141i
$977$	10.8059	−	40.3282i	0.345712	−	1.29021i	−0.546067	−	0.837742i	$-0.683875\pi$
$977$	10.8059	−	40.3282i	0.345712	−	1.29021i	0.891778	−	0.452472i	$-0.149458\pi$
$978$	−20.3922	+	28.7176i	−0.652071	+	0.918289i
$979$	−24.4182	−	14.0979i	−0.780409	−	0.450569i
$980$	−6.56184	−	88.4388i	−0.209610	−	2.82508i
$981$	−1.85384	−	6.91861i	−0.0591884	−	0.220894i
$982$	−13.2539	+	10.9730i	−0.422950	+	0.350164i
$983$	−18.5465	−	18.5465i	−0.591540	−	0.591540i	0.346507	−	0.938047i	$-0.387368\pi$
$983$	−18.5465	−	18.5465i	−0.591540	−	0.591540i	−0.938047	+	0.346507i	$0.887368\pi$
$984$	−16.2797	+	15.6472i	−0.518977	+	0.498814i
$985$	−18.3907	+	10.6179i	−0.585976	+	0.338313i
$986$	1.02778	−	0.174235i	0.0327311	−	0.00554879i
$987$			12.9037i			0.410729i
$988$	−8.81653	+	17.5151i	−0.280491	+	0.557230i
$989$			55.4498i			1.76320i
$990$	1.29165	+	7.61916i	0.0410513	+	0.242153i
$991$	−38.3423	+	22.1369i	−1.21798	+	0.703203i	−0.964486	−	0.264133i	$-0.914914\pi$
$991$	−38.3423	+	22.1369i	−1.21798	+	0.703203i	−0.253497	+	0.967336i	$0.581581\pi$
$992$	1.63687	+	30.1420i	0.0519707	+	0.957010i
$993$	−11.6418	−	11.6418i	−0.369442	−	0.369442i
$994$	−41.8868	−	50.5934i	−1.32857	−	1.60473i
$995$	2.24191	+	8.36691i	0.0710733	+	0.265249i
$996$	−0.812943	−	10.9566i	−0.0257591	−	0.347175i
$997$	11.1621	+	6.44442i	0.353506	+	0.204097i	0.666228	−	0.745748i	$-0.267908\pi$
$997$	11.1621	+	6.44442i	0.353506	+	0.204097i	−0.312722	+	0.949845i	$0.601241\pi$
$998$	47.1880	+	33.5079i	1.49371	+	1.06067i
$999$	−1.19716	+	4.46786i	−0.0378765	+	0.141357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.c.115.1	yes	48
3.2	odd	2		936.2.ed.c.739.12		48
8.3	odd	2	inner	312.2.bt.c.115.10	yes	48
13.6	odd	12	inner	312.2.bt.c.19.10	yes	48
24.11	even	2		936.2.ed.c.739.3		48
39.32	even	12		936.2.ed.c.19.3		48
104.19	even	12	inner	312.2.bt.c.19.1	✓	48
312.227	odd	12		936.2.ed.c.19.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.c.19.1	✓	48	104.19	even	12	inner
312.2.bt.c.19.10	yes	48	13.6	odd	12	inner
312.2.bt.c.115.1	yes	48	1.1	even	1	trivial
312.2.bt.c.115.10	yes	48	8.3	odd	2	inner
936.2.ed.c.19.3		48	39.32	even	12
936.2.ed.c.19.12		48	312.227	odd	12
936.2.ed.c.739.3		48	24.11	even	2
936.2.ed.c.739.12		48	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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39432 + 0.236374i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.88825 - 0.659163i) q^{4} +(1.86647 - 1.86647i) q^{5} +(0.901866 + 1.08933i) q^{6} +(4.71214 - 1.26261i) q^{7} +(-2.47702 + 1.36542i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.16128 + 3.04365i) q^{10} +(-1.99964 - 0.535801i) q^{11} +(-1.51498 - 1.30569i) q^{12} +(-3.15234 + 1.75007i) q^{13} +(-6.27177 + 2.87431i) q^{14} +(-2.54965 - 0.683177i) q^{15} +(3.13101 - 2.48933i) q^{16} +(3.84928 + 2.22238i) q^{17} +(0.492454 - 1.32570i) q^{18} +(2.62661 - 0.703799i) q^{19} +(2.29407 - 4.75469i) q^{20} +(-3.44952 - 3.44952i) q^{21} +(2.91478 + 0.274415i) q^{22} +(-3.41537 - 5.91559i) q^{23} +(2.42100 + 1.46245i) q^{24} -1.96745i q^{25} +(3.98170 - 3.18529i) q^{26} +1.00000 q^{27} +(8.06544 - 5.49020i) q^{28} +(-0.143621 + 0.0829197i) q^{29} +(3.71651 + 0.349895i) q^{30} +(3.77330 - 3.77330i) q^{31} +(-3.77721 + 4.21102i) q^{32} +(0.535801 + 1.99964i) q^{33} +(-5.89244 - 2.18884i) q^{34} +(6.43844 - 11.1517i) q^{35} +(-0.373276 + 1.96486i) q^{36} +(-1.19716 + 4.46786i) q^{37} +(-3.49598 + 1.60218i) q^{38} +(3.09177 + 1.85498i) q^{39} +(-2.07478 + 7.17181i) q^{40} +(-2.06622 + 7.71126i) q^{41} +(5.62512 + 3.99436i) q^{42} +(-7.03012 - 4.05884i) q^{43} +(-4.12900 + 0.306357i) q^{44} +(0.683177 + 2.54965i) q^{45} +(6.16041 + 7.44092i) q^{46} +(-1.87036 - 1.87036i) q^{47} +(-3.72133 - 1.46687i) q^{48} +(14.5479 - 8.39921i) q^{49} +(0.465055 + 2.74326i) q^{50} -4.44476i q^{51} +(-4.79885 + 5.38248i) q^{52} -8.22085i q^{53} +(-1.39432 + 0.236374i) q^{54} +(-4.73233 + 2.73221i) q^{55} +(-9.94806 + 9.56155i) q^{56} +(-1.92281 - 1.92281i) q^{57} +(0.180654 - 0.149565i) q^{58} +(0.352439 + 1.31532i) q^{59} +(-5.26471 + 0.390623i) q^{60} +(0.601045 + 0.347013i) q^{61} +(-4.36928 + 6.15310i) q^{62} +(-1.26261 + 4.71214i) q^{63} +(4.27127 - 6.76434i) q^{64} +(-2.61731 + 9.15022i) q^{65} +(-1.21974 - 2.66148i) q^{66} +(1.26441 - 4.71883i) q^{67} +(8.73333 + 1.65912i) q^{68} +(-3.41537 + 5.91559i) q^{69} +(-6.34127 + 17.0709i) q^{70} +(2.46409 + 9.19612i) q^{71} +(0.0560238 - 2.82787i) q^{72} +(-11.2670 + 11.2670i) q^{73} +(0.613136 - 6.51261i) q^{74} +(-1.70386 + 0.983726i) q^{75} +(4.49579 - 3.06032i) q^{76} -10.0991 q^{77} +(-4.74939 - 1.85561i) q^{78} +9.91660i q^{79} +(1.19767 - 10.4902i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.05824 - 11.2404i) q^{82} +(3.88441 + 3.88441i) q^{83} +(-8.78737 - 4.23978i) q^{84} +(11.3326 - 3.03656i) q^{85} +(10.7616 + 3.99758i) q^{86} +(0.143621 + 0.0829197i) q^{87} +(5.68474 - 1.40315i) q^{88} +(13.1559 + 3.52510i) q^{89} +(-1.55524 - 3.39354i) q^{90} +(-12.6446 + 12.2267i) q^{91} +(-10.3484 - 8.91886i) q^{92} +(-5.15443 - 1.38112i) q^{93} +(3.04998 + 2.16577i) q^{94} +(3.58888 - 6.21613i) q^{95} +(5.53545 + 1.16565i) q^{96} +(-1.52421 + 0.408410i) q^{97} +(-18.2990 + 15.1499i) q^{98} +(1.46384 - 1.46384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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