LMFDB - Embedded newform 27.4.e.a.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	27.25
Dual form			27.4.e.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.553775 - 3.14062i) q^{2} +(-0.697722 - 5.14910i) q^{3} +(-2.03925 - 0.742228i) q^{4} +(-10.9819 + 9.21490i) q^{5} +(-16.5577 - 0.660166i) q^{6} +(30.2596 - 11.0136i) q^{7} +(9.29592 - 16.1010i) q^{8} +(-26.0264 + 7.18527i) q^{9} +O(q^{10})$	\(q+(0.553775 - 3.14062i) q^{2} +(-0.697722 - 5.14910i) q^{3} +(-2.03925 - 0.742228i) q^{4} +(-10.9819 + 9.21490i) q^{5} +(-16.5577 - 0.660166i) q^{6} +(30.2596 - 11.0136i) q^{7} +(9.29592 - 16.1010i) q^{8} +(-26.0264 + 7.18527i) q^{9} +(22.8590 + 39.5929i) q^{10} +(15.6100 + 13.0984i) q^{11} +(-2.39897 + 11.0182i) q^{12} +(7.14749 + 40.5354i) q^{13} +(-17.8325 - 101.133i) q^{14} +(55.1107 + 50.1174i) q^{15} +(-58.7185 - 49.2707i) q^{16} +(14.6690 + 25.4075i) q^{17} +(8.15342 + 85.7178i) q^{18} +(-31.1332 + 53.9243i) q^{19} +(29.2344 - 10.6405i) q^{20} +(-77.8229 - 148.125i) q^{21} +(49.7814 - 41.7715i) q^{22} +(-97.4029 - 35.4518i) q^{23} +(-89.3915 - 36.6315i) q^{24} +(13.9815 - 79.2930i) q^{25} +131.264 q^{26} +(55.1568 + 128.999i) q^{27} -69.8817 q^{28} +(0.781803 - 4.43383i) q^{29} +(187.918 - 145.328i) q^{30} +(-47.4267 - 17.2619i) q^{31} +(-73.3198 + 61.5226i) q^{32} +(56.5533 - 89.5165i) q^{33} +(87.9184 - 31.9997i) q^{34} +(-230.819 + 399.790i) q^{35} +(58.4075 + 4.66490i) q^{36} +(-29.6947 - 51.4327i) q^{37} +(152.115 + 127.639i) q^{38} +(203.734 - 65.0855i) q^{39} +(46.2824 + 262.480i) q^{40} +(33.1564 + 188.039i) q^{41} +(-508.301 + 162.384i) q^{42} +(-270.590 - 227.052i) q^{43} +(-22.1108 - 38.2971i) q^{44} +(219.607 - 318.738i) q^{45} +(-165.280 + 286.273i) q^{46} +(282.646 - 102.875i) q^{47} +(-212.730 + 336.724i) q^{48} +(531.593 - 446.059i) q^{49} +(-241.286 - 87.8210i) q^{50} +(120.591 - 93.2594i) q^{51} +(15.5110 - 87.9671i) q^{52} -128.439 q^{53} +(435.680 - 101.790i) q^{54} -292.128 q^{55} +(103.961 - 589.592i) q^{56} +(299.384 + 122.684i) q^{57} +(-13.4920 - 4.91069i) q^{58} +(440.395 - 369.535i) q^{59} +(-75.1862 - 143.107i) q^{60} +(-633.299 + 230.502i) q^{61} +(-80.4767 + 139.390i) q^{62} +(-708.413 + 504.068i) q^{63} +(-153.990 - 266.719i) q^{64} +(-452.023 - 379.292i) q^{65} +(-249.819 - 227.184i) q^{66} +(127.040 + 720.481i) q^{67} +(-11.0557 - 62.7000i) q^{68} +(-114.584 + 526.272i) q^{69} +(1127.76 + 946.306i) q^{70} +(-223.375 - 386.897i) q^{71} +(-126.249 + 485.844i) q^{72} +(408.446 - 707.450i) q^{73} +(-177.974 + 64.7774i) q^{74} +(-418.042 - 16.6676i) q^{75} +(103.513 - 86.8575i) q^{76} +(616.614 + 224.429i) q^{77} +(-91.5859 - 675.892i) q^{78} +(13.9053 - 78.8610i) q^{79} +1098.86 q^{80} +(625.744 - 374.013i) q^{81} +608.920 q^{82} +(-177.693 + 1007.75i) q^{83} +(48.7580 + 359.828i) q^{84} +(-395.220 - 143.848i) q^{85} +(-862.928 + 724.083i) q^{86} +(-23.3757 - 0.932002i) q^{87} +(356.006 - 129.576i) q^{88} +(-241.246 + 417.851i) q^{89} +(-879.421 - 866.211i) q^{90} +(662.722 + 1147.87i) q^{91} +(172.316 + 144.590i) q^{92} +(-55.7926 + 256.249i) q^{93} +(-166.567 - 944.651i) q^{94} +(-155.006 - 879.080i) q^{95} +(367.942 + 334.605i) q^{96} +(-1013.02 - 850.025i) q^{97} +(-1106.52 - 1916.55i) q^{98} +(-500.387 - 228.741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.553775	−	3.14062i	0.195789	−	1.11038i	−0.715501	−	0.698611i	$-0.753802\pi$
$2$	0.553775	−	3.14062i	0.195789	−	1.11038i	0.911291	−	0.411764i	$-0.135087\pi$
$3$	−0.697722	−	5.14910i	−0.134277	−	0.990944i
$3$	−0.697722	−	5.14910i	−0.134277	−	0.990944i
$4$	−2.03925	−	0.742228i	−0.254907	−	0.0927785i
$5$	−10.9819	+	9.21490i	−0.982250	+	0.824206i	−0.984427	−	0.175792i	$-0.943751\pi$
$5$	−10.9819	+	9.21490i	−0.982250	+	0.824206i	0.00217737	+	0.999998i	$0.499307\pi$
$6$	−16.5577	−	0.660166i	−1.12661	−	0.0449186i
$7$	30.2596	−	11.0136i	1.63387	−	0.594679i	0.647916	−	0.761712i	$-0.275641\pi$
$7$	30.2596	−	11.0136i	1.63387	−	0.594679i	0.985951	+	0.167033i	$0.0534187\pi$
$8$	9.29592	−	16.1010i	0.410825	−	0.711570i
$9$	−26.0264	+	7.18527i	−0.963940	+	0.266121i
$10$	22.8590	+	39.5929i	0.722864	+	1.25204i
$11$	15.6100	+	13.0984i	0.427873	+	0.359028i	0.831148	−	0.556051i	$-0.187684\pi$
$11$	15.6100	+	13.0984i	0.427873	+	0.359028i	−0.403276	+	0.915079i	$0.632128\pi$
$12$	−2.39897	+	11.0182i	−0.0577103	+	0.265056i
$13$	7.14749	+	40.5354i	0.152489	+	0.864808i	0.961046	+	0.276390i	$0.0891380\pi$
$13$	7.14749	+	40.5354i	0.152489	+	0.864808i	−0.808557	+	0.588418i	$0.799751\pi$
$14$	−17.8325	−	101.133i	−0.340423	−	1.93064i
$15$	55.1107	+	50.1174i	0.948635	+	0.862683i
$16$	−58.7185	−	49.2707i	−0.917477	−	0.769854i
$17$	14.6690	+	25.4075i	0.209280	+	0.362483i	0.951488	−	0.307686i	$-0.0995548\pi$
$17$	14.6690	+	25.4075i	0.209280	+	0.362483i	−0.742208	+	0.670169i	$0.766221\pi$
$18$	8.15342	+	85.7178i	0.106766	+	1.12244i
$19$	−31.1332	+	53.9243i	−0.375918	+	0.651110i	−0.990464	−	0.137771i	$-0.956006\pi$
$19$	−31.1332	+	53.9243i	−0.375918	+	0.651110i	0.614546	+	0.788881i	$0.289339\pi$
$20$	29.2344	−	10.6405i	0.326851	−	0.118964i
$21$	−77.8229	−	148.125i	−0.808684	−	1.53922i
$22$	49.7814	−	41.7715i	0.482428	−	0.404805i
$23$	−97.4029	−	35.4518i	−0.883040	−	0.321400i	−0.139604	−	0.990207i	$-0.544583\pi$
$23$	−97.4029	−	35.4518i	−0.883040	−	0.321400i	−0.743436	+	0.668807i	$0.766805\pi$
$24$	−89.3915	−	36.6315i	−0.760290	−	0.311558i
$25$	13.9815	−	79.2930i	0.111852	−	0.634344i
$26$	131.264			0.990117
$27$	55.1568	+	128.999i	0.393146	+	0.919476i
$28$	−69.8817			−0.471657
$29$	0.781803	−	4.43383i	0.00500611	−	0.0283911i	−0.982202	−	0.187826i	$-0.939856\pi$
$29$	0.781803	−	4.43383i	0.00500611	−	0.0283911i	0.987208	+	0.159435i	$0.0509671\pi$
$30$	187.918	−	145.328i	1.14363	−	0.884436i
$31$	−47.4267	−	17.2619i	−0.274777	−	0.100011i	0.200956	−	0.979600i	$-0.435595\pi$
$31$	−47.4267	−	17.2619i	−0.274777	−	0.100011i	−0.475733	+	0.879590i	$0.657817\pi$
$32$	−73.3198	+	61.5226i	−0.405038	+	0.339867i
$33$	56.5533	−	89.5165i	0.298323	−	0.472207i
$34$	87.9184	−	31.9997i	0.443467	−	0.161409i
$35$	−230.819	+	399.790i	−1.11473	+	1.93077i
$36$	58.4075	+	4.66490i	0.270405	+	0.0215968i
$37$	−29.6947	−	51.4327i	−0.131940	−	0.228526i	0.792484	−	0.609892i	$-0.208787\pi$
$37$	−29.6947	−	51.4327i	−0.131940	−	0.228526i	−0.924424	+	0.381366i	$0.875454\pi$
$38$	152.115	+	127.639i	0.649375	+	0.544891i
$39$	203.734	−	65.0855i	0.836500	−	0.267231i
$40$	46.2824	+	262.480i	0.182947	+	1.03754i
$41$	33.1564	+	188.039i	0.126297	+	0.716263i	0.980529	+	0.196373i	$0.0629162\pi$
$41$	33.1564	+	188.039i	0.126297	+	0.716263i	−0.854233	+	0.519891i	$0.825973\pi$
$42$	−508.301	+	162.384i	−1.86744	+	0.596580i
$43$	−270.590	−	227.052i	−0.959641	−	0.805234i	0.0212539	−	0.999774i	$-0.493234\pi$
$43$	−270.590	−	227.052i	−0.959641	−	0.805234i	−0.980895	+	0.194540i	$0.937679\pi$
$44$	−22.1108	−	38.2971i	−0.0757576	−	0.131216i
$45$	219.607	−	318.738i	0.727491	−	1.05588i
$46$	−165.280	+	286.273i	−0.529764	+	0.917578i
$47$	282.646	−	102.875i	0.877194	−	0.319272i	0.136117	−	0.990693i	$-0.456538\pi$
$47$	282.646	−	102.875i	0.877194	−	0.319272i	0.741077	+	0.671420i	$0.234315\pi$
$48$	−212.730	+	336.724i	−0.639687	+	1.01254i
$49$	531.593	−	446.059i	1.54983	−	1.30046i
$50$	−241.286	−	87.8210i	−0.682460	−	0.248395i
$51$	120.591	−	93.2594i	0.331099	−	0.256057i
$52$	15.5110	−	87.9671i	0.0413651	−	0.234593i
$53$	−128.439			−0.332876			−0.166438	−	0.986052i	$-0.553227\pi$
$53$	−128.439			−0.332876			−0.166438	+	0.986052i	$0.553227\pi$
$54$	435.680	−	101.790i	1.09794	−	0.256516i
$55$	−292.128			−0.716191
$56$	103.961	−	589.592i	0.248078	−	1.40692i
$57$	299.384	+	122.684i	0.695690	+	0.285085i
$58$	−13.4920	−	4.91069i	−0.0305446	−	0.0111173i
$59$	440.395	−	369.535i	0.971771	−	0.815413i	−0.0110562	−	0.999939i	$-0.503519\pi$
$59$	440.395	−	369.535i	0.971771	−	0.815413i	0.982828	+	0.184526i	$0.0590749\pi$
$60$	−75.1862	−	143.107i	−0.161775	−	0.307917i
$61$	−633.299	+	230.502i	−1.32927	+	0.483816i	−0.906418	−	0.422382i	$-0.861194\pi$
$61$	−633.299	+	230.502i	−1.32927	+	0.483816i	−0.422855	+	0.906197i	$0.638972\pi$
$62$	−80.4767	+	139.390i	−0.164848	+	0.285525i
$63$	−708.413	+	504.068i	−1.41669	+	1.00804i
$64$	−153.990	−	266.719i	−0.300762	−	0.520935i
$65$	−452.023	−	379.292i	−0.862562	−	0.723775i
$66$	−249.819	−	227.184i	−0.465918	−	0.423703i
$67$	127.040	+	720.481i	0.231648	+	1.31374i	0.849559	+	0.527494i	$0.176868\pi$
$67$	127.040	+	720.481i	0.231648	+	1.31374i	−0.617910	+	0.786249i	$0.712021\pi$
$68$	−11.0557	−	62.7000i	−0.0197162	−	0.111816i
$69$	−114.584	+	526.272i	−0.199918	+	0.918199i
$70$	1127.76	+	946.306i	1.92562	+	1.61579i
$71$	−223.375	−	386.897i	−0.373377	−	0.646708i	0.616706	−	0.787194i	$-0.288467\pi$
$71$	−223.375	−	386.897i	−0.373377	−	0.646708i	−0.990083	+	0.140486i	$0.955134\pi$
$72$	−126.249	+	485.844i	−0.206647	+	0.795240i
$73$	408.446	−	707.450i	0.654863	−	1.13426i	−0.327065	−	0.945002i	$-0.606059\pi$
$73$	408.446	−	707.450i	0.654863	−	1.13426i	0.981928	−	0.189255i	$-0.0606072\pi$
$74$	−177.974	+	64.7774i	−0.279582	+	0.101760i
$75$	−418.042	−	16.6676i	−0.643618	−	0.0256614i
$76$	103.513	−	86.8575i	0.156233	−	0.131095i
$77$	616.614	+	224.429i	0.912593	+	0.332157i
$78$	−91.5859	−	675.892i	−0.132950	−	0.981150i
$79$	13.9053	−	78.8610i	0.0198034	−	0.112311i	−0.973304	−	0.229521i	$-0.926284\pi$
$79$	13.9053	−	78.8610i	0.0198034	−	0.112311i	0.993107	+	0.117210i	$0.0373951\pi$
$80$	1098.86			1.53571
$81$	625.744	−	374.013i	0.858359	−	0.513050i
$82$	608.920			0.820048
$83$	−177.693	+	1007.75i	−0.234992	+	1.33270i	0.607640	+	0.794213i	$0.292116\pi$
$83$	−177.693	+	1007.75i	−0.234992	+	1.33270i	−0.842631	+	0.538491i	$0.818995\pi$
$84$	48.7580	+	359.828i	0.0633326	+	0.467386i
$85$	−395.220	−	143.848i	−0.504326	−	0.183559i
$86$	−862.928	+	724.083i	−1.08200	+	0.907905i
$87$	−23.3757	−	0.932002i	−0.0288062	−	0.00114852i
$88$	356.006	−	129.576i	0.431254	−	0.156964i
$89$	−241.246	+	417.851i	−0.287327	+	0.497664i	−0.973171	−	0.230084i	$-0.926100\pi$
$89$	−241.246	+	417.851i	−0.287327	+	0.497664i	0.685844	+	0.727748i	$0.259433\pi$
$90$	−879.421	−	866.211i	−1.02999	−	1.01452i
$91$	662.722	+	1147.87i	0.763430	+	1.32230i
$92$	172.316	+	144.590i	0.195274	+	0.163854i
$93$	−55.7926	+	256.249i	−0.0622088	+	0.285718i
$94$	−166.567	−	944.651i	−0.182767	−	1.03652i
$95$	−155.006	−	879.080i	−0.167402	−	0.949387i
$96$	367.942	+	334.605i	0.391177	+	0.355734i
$97$	−1013.02	−	850.025i	−1.06038	−	0.889763i	−0.0662317	−	0.997804i	$-0.521098\pi$
$97$	−1013.02	−	850.025i	−1.06038	−	0.889763i	−0.994146	+	0.108041i	$0.965542\pi$
$98$	−1106.52	−	1916.55i	−1.14056	−	1.97551i
$99$	−500.387	−	228.741i	−0.507988	−	0.232215i
$100$	−87.3653	+	151.321i	−0.0873653	+	0.151321i
$101$	−478.256	+	174.071i	−0.471171	+	0.171492i	−0.566683	−	0.823936i	$-0.691773\pi$
$101$	−478.256	+	174.071i	−0.471171	+	0.171492i	0.0955119	+	0.995428i	$0.469551\pi$
$102$	−226.112	−	430.373i	−0.219494	−	0.417777i
$103$	−1004.20	+	842.621i	−0.960645	+	0.806077i	−0.981058	−	0.193715i	$-0.937946\pi$
$103$	−1004.20	+	842.621i	−0.960645	+	0.806077i	0.0204132	+	0.999792i	$0.493502\pi$
$104$	719.103	+	261.732i	0.678018	+	0.246778i
$105$	2219.60	+	909.566i	2.06296	+	0.845376i
$106$	−71.1262	+	403.376i	−0.0651734	+	0.369617i
$107$	1146.52			1.03587			0.517937	−	0.855419i	$-0.326700\pi$
$107$	1146.52			1.03587			0.517937	+	0.855419i	$0.326700\pi$
$108$	−16.7322	−	304.001i	−0.0149079	−	0.270856i
$109$	325.587			0.286106			0.143053	−	0.989715i	$-0.454308\pi$
$109$	325.587			0.286106			0.143053	+	0.989715i	$0.454308\pi$
$110$	−161.773	+	917.460i	−0.140222	+	0.795240i
$111$	−244.113	+	188.786i	−0.208740	+	0.161431i
$112$	−2319.45	−	844.210i	−1.95685	−	0.712236i
$113$	237.949	−	199.663i	0.198091	−	0.166218i	−0.538347	−	0.842724i	$-0.680951\pi$
$113$	237.949	−	199.663i	0.198091	−	0.166218i	0.736438	+	0.676505i	$0.236506\pi$
$114$	551.094	−	872.310i	0.452760	−	0.716661i
$115$	1396.35	−	508.231i	1.13227	−	0.412111i
$116$	−4.88521	+	8.46143i	−0.00391017	+	0.00677262i
$117$	−477.281	−	1003.63i	−0.377134	−	0.793042i
$118$	−916.688	−	1587.75i	−0.715152	−	1.23868i
$119$	723.706	+	607.262i	0.557496	+	0.467795i
$120$	1319.24	−	421.450i	1.00358	−	0.320608i
$121$	−159.020	−	901.848i	−0.119474	−	0.677571i
$122$	373.213	+	2116.59i	0.276960	+	1.57072i
$123$	945.098	−	301.925i	0.692818	−	0.221330i
$124$	83.9028	+	70.4028i	0.0607637	+	0.0509868i
$125$	−318.856	−	552.275i	−0.228155	−	0.395176i
$126$	1190.78	+	2503.99i	0.841931	+	1.77042i
$127$	6.15688	−	10.6640i	0.00430185	−	0.00745102i	−0.863866	−	0.503721i	$-0.831964\pi$
$127$	6.15688	−	10.6640i	0.00430185	−	0.00745102i	0.868168	+	0.496270i	$0.165297\pi$
$128$	−1642.46	+	597.806i	−1.13417	+	0.412805i
$129$	−980.315	+	1551.71i	−0.669085	+	1.05907i
$130$	−1441.53	+	1209.59i	−0.972542	+	0.816060i
$131$	−926.134	−	337.085i	−0.617684	−	0.224819i	0.0141778	−	0.999899i	$-0.495487\pi$
$131$	−926.134	−	337.085i	−0.617684	−	0.224819i	−0.631862	+	0.775081i	$0.717709\pi$
$132$	−181.768	+	140.572i	−0.119855	+	0.0926908i
$133$	−348.179	+	1974.62i	−0.226999	+	1.28738i
$134$	2333.11			1.50410
$135$	−1794.44	−	908.387i	−1.14400	−	0.579123i
$136$	545.447			0.343910
$137$	112.885	−	640.204i	0.0703973	−	0.399243i	−0.929165	−	0.369665i	$-0.879472\pi$
$137$	112.885	−	640.204i	0.0703973	−	0.399243i	0.999562	−	0.0295782i	$-0.00941640\pi$
$138$	1589.36	+	651.302i	0.980404	+	0.401757i
$139$	2677.52	+	974.536i	1.63384	+	0.594670i	0.985947	−	0.167060i	$-0.0534274\pi$
$139$	2677.52	+	974.536i	1.63384	+	0.594670i	0.647895	+	0.761730i	$0.275650\pi$
$140$	767.433	−	643.953i	0.463285	−	0.388743i
$141$	−726.919	−	1383.59i	−0.434168	−	0.826379i
$142$	−1338.79	+	487.281i	−0.791191	+	0.287970i
$143$	−419.375	+	726.379i	−0.245244	+	0.424775i
$144$	1882.25	+	860.428i	1.08927	+	0.497933i
$145$	32.2716	+	55.8960i	0.0184828	+	0.0320132i
$146$	−1995.64	−	1674.54i	−1.13124	−	0.949219i
$147$	−2667.71	−	2426.00i	−1.49679	−	1.36118i
$148$	22.3802	+	126.925i	0.0124300	+	0.0704941i
$149$	78.2788	+	443.941i	0.0430393	+	0.244088i	0.998736	−	0.0502657i	$-0.0160068\pi$
$149$	78.2788	+	443.941i	0.0430393	+	0.244088i	−0.955697	+	0.294353i	$0.904896\pi$
$150$	−283.848	+	1303.68i	−0.154507	+	0.709634i
$151$	278.120	+	233.370i	0.149888	+	0.125771i	0.714648	−	0.699484i	$-0.246587\pi$
$151$	278.120	+	233.370i	0.149888	+	0.125771i	−0.564760	+	0.825255i	$0.691031\pi$
$152$	578.823	+	1002.55i	0.308874	+	0.534985i
$153$	−564.340	−	555.863i	−0.298197	−	0.293718i
$154$	1046.31	−	1812.26i	0.547494	−	0.948288i
$155$	679.901	−	247.464i	0.352329	−	0.128237i
$156$	−463.773	−	18.4909i	−0.238023	−	0.00949012i
$157$	1691.02	−	1418.93i	0.859605	−	0.721294i	−0.102278	−	0.994756i	$-0.532613\pi$
$157$	1691.02	−	1418.93i	0.859605	−	0.721294i	0.961883	+	0.273462i	$0.0881688\pi$
$158$	−239.972	−	87.3425i	−0.120830	−	0.0439785i
$159$	89.6145	+	661.343i	0.0446974	+	0.329861i
$160$	238.265	−	1351.27i	0.117728	−	0.667670i
$161$	−3337.83			−1.63390
$162$	−828.110	−	2172.34i	−0.401620	−	1.05355i
$163$	−64.8931			−0.0311829			−0.0155915	−	0.999878i	$-0.504963\pi$
$163$	−64.8931			−0.0311829			−0.0155915	+	0.999878i	$0.504963\pi$
$164$	71.9537	−	408.070i	0.0342600	−	0.194298i
$165$	203.824	+	1504.19i	0.0961676	+	0.709705i
$166$	3066.54	+	1116.13i	1.43379	+	0.521858i
$167$	1807.26	−	1516.47i	0.837423	−	0.702681i	−0.119560	−	0.992827i	$-0.538148\pi$
$167$	1807.26	−	1516.47i	0.837423	−	0.702681i	0.956982	+	0.290146i	$0.0937038\pi$
$168$	−3108.40	−	123.934i	−1.42749	−	0.0569149i
$169$	472.471	−	171.965i	0.215053	−	0.0782728i
$170$	−670.636	+	1161.58i	−0.302561	+	0.524052i
$171$	422.824	−	1627.15i	0.189089	−	0.727670i
$172$	383.277	+	663.856i	0.169911	+	0.294294i
$173$	1913.17	+	1605.34i	0.840783	+	0.705501i	0.957740	−	0.287636i	$-0.0928694\pi$
$173$	1913.17	+	1605.34i	0.840783	+	0.705501i	−0.116957	+	0.993137i	$0.537314\pi$
$174$	−15.8719	+	72.8979i	−0.00691522	+	0.0317608i
$175$	−450.227	−	2553.36i	−0.194480	−	1.10295i
$176$	−271.232	−	1538.23i	−0.116164	−	0.658799i
$177$	−2210.04	−	2009.80i	−0.938515	−	0.853480i
$178$	1178.71	+	989.058i	0.496339	+	0.416478i
$179$	−1968.57	−	3409.66i	−0.821997	−	1.42374i	−0.904193	−	0.427125i	$-0.859526\pi$
$179$	−1968.57	−	3409.66i	−0.821997	−	1.42374i	0.0821954	−	0.996616i	$-0.473807\pi$
$180$	−684.411	+	486.990i	−0.283406	+	0.201656i
$181$	−2152.95	+	3729.01i	−0.884129	+	1.53136i	−0.0374198	+	0.999300i	$0.511914\pi$
$181$	−2152.95	+	3729.01i	−0.884129	+	1.53136i	−0.846709	+	0.532056i	$0.821419\pi$
$182$	3972.01	−	1445.69i	1.61772	−	0.588802i
$183$	1628.74	+	3100.09i	0.657924	+	1.25227i
$184$	−1476.26	+	1238.73i	−0.591474	+	0.496305i
$185$	800.050	+	291.195i	0.317951	+	0.115725i
$186$	773.882	+	317.127i	0.305074	+	0.125016i
$187$	−103.813	+	588.751i	−0.0405964	+	0.230234i
$188$	−652.743			−0.253224
$189$	3089.77	+	3295.99i	1.18914	+	1.26851i
$190$	−2846.69			−1.08695
$191$	696.054	−	3947.52i	0.263689	−	1.49546i	−0.509052	−	0.860736i	$-0.670004\pi$
$191$	696.054	−	3947.52i	0.263689	−	1.49546i	0.772741	−	0.634721i	$-0.218885\pi$
$192$	−1265.92	+	979.006i	−0.475832	+	0.367988i
$193$	1978.35	+	720.061i	0.737849	+	0.268555i	0.683483	−	0.729966i	$-0.260464\pi$
$193$	1978.35	+	720.061i	0.737849	+	0.268555i	0.0543656	+	0.998521i	$0.482686\pi$
$194$	−3230.59	+	2710.79i	−1.19558	+	1.00321i
$195$	−1637.62	+	2592.15i	−0.601399	+	0.951936i
$196$	−1415.13	+	515.066i	−0.515718	+	0.187706i
$197$	−437.504	+	757.779i	−0.158228	+	0.274059i	−0.934230	−	0.356672i	$-0.883911\pi$
$197$	−437.504	+	757.779i	−0.158228	+	0.274059i	0.776002	+	0.630731i	$0.217245\pi$
$198$	−995.488	+	1444.85i	−0.357304	+	0.518592i
$199$	477.760	+	827.505i	0.170188	+	0.294775i	0.938486	−	0.345318i	$-0.112229\pi$
$199$	477.760	+	827.505i	0.170188	+	0.294775i	−0.768297	+	0.640093i	$0.778896\pi$
$200$	−1146.73	−	962.217i	−0.405429	−	0.340195i
$201$	3621.19	−	1156.84i	1.27074	−	0.405955i
$202$	281.844	+	1598.41i	0.0981705	+	0.556753i
$203$	−25.1754	−	142.777i	−0.00870425	−	0.0493643i
$204$	−315.135	+	100.674i	−0.108156	+	0.0345519i
$205$	−2096.88	−	1759.49i	−0.714403	−	0.599455i
$206$	2090.25	+	3620.42i	0.706964	+	1.22450i
$207$	2789.77	+	222.814i	0.936728	+	0.0748147i
$208$	1577.52	−	2732.34i	0.525871	−	0.910835i
$209$	−1192.31	+	433.966i	−0.394612	+	0.143627i
$210$	4085.76	−	6467.22i	1.34259	−	2.12515i
$211$	−841.508	+	706.109i	−0.274558	+	0.230382i	−0.769661	−	0.638453i	$-0.779575\pi$
$211$	−841.508	+	706.109i	−0.274558	+	0.230382i	0.495103	+	0.868834i	$0.335130\pi$
$212$	261.919	+	95.3308i	0.0848523	+	0.0308837i
$213$	−1836.32	+	1420.13i	−0.590715	+	0.456833i
$214$	634.915	−	3600.78i	0.202813	−	1.15021i
$215$	5063.85			1.60629
$216$	2589.74	+	311.083i	0.815786	+	0.0979932i
$217$	−1625.23			−0.508423
$218$	180.302	−	1022.54i	0.0560165	−	0.317685i
$219$	−3927.71	−	1609.53i	−1.21192	−	0.496629i
$220$	595.723	+	216.825i	0.182562	+	0.0664471i
$221$	−925.055	+	776.214i	−0.281565	+	0.236261i
$222$	457.722	+	871.211i	0.138380	+	0.263387i
$223$	−190.606	+	69.3748i	−0.0572372	+	0.0208326i	−0.370480	−	0.928840i	$-0.620807\pi$
$223$	−190.606	+	69.3748i	−0.0572372	+	0.0208326i	0.313243	+	0.949673i	$0.398585\pi$
$224$	−1541.04	+	2669.17i	−0.459667	+	0.796166i
$225$	205.854	+	2164.17i	0.0609939	+	0.641235i
$226$	−495.293	−	857.873i	−0.145781	−	0.252499i
$227$	2286.32	+	1918.45i	0.668494	+	0.560933i	0.912619	−	0.408811i	$-0.134056\pi$
$227$	2286.32	+	1918.45i	0.668494	+	0.560933i	−0.244125	+	0.969744i	$0.578501\pi$
$228$	−519.460	−	472.394i	−0.150886	−	0.137215i
$229$	−198.375	−	1125.04i	−0.0572446	−	0.324650i	0.942715	−	0.333598i	$-0.108263\pi$
$229$	−198.375	−	1125.04i	−0.0572446	−	0.324650i	−0.999960	+	0.00894782i	$0.997152\pi$
$230$	−822.892	−	4666.85i	−0.235912	−	1.33793i
$231$	725.382	−	3331.59i	0.206609	−	0.948930i
$232$	−64.1215	−	53.8043i	−0.0181456	−	0.0152260i
$233$	2058.19	+	3564.89i	0.578698	+	1.00233i	0.995629	+	0.0933962i	$0.0297723\pi$
$233$	2058.19	+	3564.89i	0.578698	+	1.00233i	−0.416931	+	0.908938i	$0.636894\pi$
$234$	−3416.33	+	943.169i	−0.954413	+	0.263491i
$235$	−2156.00	+	3734.31i	−0.598477	+	1.03659i
$236$	−1172.36	+	426.703i	−0.323364	+	0.117695i
$237$	−415.765	−	16.5768i	−0.113953	−	0.00454337i
$238$	2307.95	−	1936.60i	0.628580	−	0.527441i
$239$	−5774.59	−	2101.78i	−1.56287	−	0.568840i	−0.591481	−	0.806319i	$-0.701457\pi$
$239$	−5774.59	−	2101.78i	−1.56287	−	0.568840i	−0.971393	+	0.237479i	$0.923679\pi$
$240$	−766.702	−	5658.16i	−0.206210	−	1.52180i
$241$	841.776	−	4773.95i	0.224994	−	1.27600i	−0.637702	−	0.770283i	$-0.720115\pi$
$241$	841.776	−	4773.95i	0.224994	−	1.27600i	0.862697	−	0.505722i	$-0.168774\pi$
$242$	−2920.42			−0.775750
$243$	−2362.42	−	2961.06i	−0.623661	−	0.781695i
$244$	1462.54			0.383728
$245$	−1727.50	+	9797.15i	−0.450474	+	2.55476i
$246$	−424.857	−	3135.39i	−0.110113	−	0.812622i
$247$	−2408.37	−	876.575i	−0.620408	−	0.225810i
$248$	−718.808	+	603.152i	−0.184050	+	0.154436i
$249$	5312.96	+	211.831i	1.35219	+	0.0539125i
$250$	−1911.06	+	695.568i	−0.483464	+	0.175966i
$251$	1093.63	−	1894.22i	0.275017	−	0.476343i	−0.695122	−	0.718891i	$-0.744650\pi$
$251$	1093.63	−	1894.22i	0.275017	−	0.476343i	0.970139	+	0.242548i	$0.0779832\pi$
$252$	1818.77	−	502.119i	0.454649	−	0.125518i
$253$	−1056.10	−	1829.22i	−0.262437	−	0.454554i
$254$	−30.0821	−	25.2419i	−0.00743118	−	0.00623550i
$255$	−464.936	+	2135.39i	−0.114178	+	0.524406i
$256$	540.083	+	3062.96i	0.131856	+	0.747794i
$257$	140.686	+	797.871i	0.0341469	+	0.193657i	0.997109	−	0.0759783i	$-0.0242080\pi$
$257$	140.686	+	797.871i	0.0341469	+	0.193657i	−0.962963	+	0.269635i	$0.913097\pi$
$258$	4330.45	+	3938.09i	1.04497	+	0.950290i
$259$	−1465.01	−	1229.29i	−0.351472	−	0.294920i
$260$	640.268	+	1108.98i	0.152722	+	0.264522i
$261$	11.5108	+	121.014i	0.00272988	+	0.0286995i
$262$	−1571.52	+	2721.96i	−0.370569	+	0.641844i
$263$	2743.81	−	998.665i	0.643310	−	0.234146i	0.000295868	−	1.00000i	$-0.499906\pi$
$263$	2743.81	−	998.665i	0.643310	−	0.234146i	0.643014	+	0.765854i	$0.277684\pi$
$264$	−915.591	−	1742.70i	−0.213450	−	0.406272i
$265$	1410.50	−	1183.55i	0.326967	−	0.274358i
$266$	6008.71	+	2186.99i	1.38503	+	0.504109i
$267$	2319.88	+	950.657i	0.531739	+	0.217900i
$268$	275.694	−	1563.54i	0.0628383	−	0.356374i
$269$	−6017.64			−1.36395			−0.681974	−	0.731377i	$-0.738878\pi$
$269$	−6017.64			−1.36395			−0.681974	+	0.731377i	$0.738878\pi$
$270$	−3846.61	+	5132.60i	−0.867027	+	1.15689i
$271$	2048.63			0.459208			0.229604	−	0.973284i	$-0.426257\pi$
$271$	2048.63			0.459208			0.229604	+	0.973284i	$0.426257\pi$
$272$	390.501	−	2214.64i	0.0870499	−	0.493685i
$273$	5448.08	−	4213.31i	1.20781	−	0.934070i
$274$	−1948.12	−	709.058i	−0.429527	−	0.156335i
$275$	1256.86	−	1054.63i	0.275606	−	0.231260i
$276$	624.281	−	988.156i	0.136150	−	0.215507i
$277$	3934.69	−	1432.11i	0.853474	−	0.310639i	0.122018	−	0.992528i	$-0.461063\pi$
$277$	3934.69	−	1432.11i	0.853474	−	0.310639i	0.731456	+	0.681889i	$0.238841\pi$
$278$	4543.38	−	7869.37i	0.980195	−	1.69775i
$279$	1358.38	+	108.491i	0.291483	+	0.0232802i
$280$	4291.34	+	7432.82i	0.915917	+	1.58641i
$281$	−84.4702	−	70.8789i	−0.0179326	−	0.0150473i	0.633777	−	0.773516i	$-0.281504\pi$
$281$	−84.4702	−	70.8789i	−0.0179326	−	0.0150473i	−0.651710	+	0.758468i	$0.725948\pi$
$282$	−4747.88	+	1516.77i	−1.00260	+	0.320293i
$283$	539.734	+	3060.98i	0.113370	+	0.642956i	0.987544	+	0.157342i	$0.0502926\pi$
$283$	539.734	+	3060.98i	0.113370	+	0.642956i	−0.874174	+	0.485613i	$0.838596\pi$
$284$	168.353	+	954.777i	0.0351758	+	0.199492i
$285$	−4418.32	+	1411.49i	−0.918311	+	0.293367i
$286$	2049.04	+	1719.35i	0.423644	+	0.355479i
$287$	3074.29	+	5324.83i	0.632298	+	1.09517i
$288$	1466.19	−	2128.03i	0.299986	−	0.435401i
$289$	2026.14	−	3509.38i	0.412404	−	0.714305i
$290$	193.419	−	70.3988i	0.0391654	−	0.0142550i
$291$	−3670.06	+	5809.22i	−0.739321	+	1.17025i
$292$	−1358.02	+	1139.51i	−0.272164	+	0.228373i
$293$	−9124.08	−	3320.89i	−1.81923	−	0.662145i	−0.995456	−	0.0952266i	$-0.969642\pi$
$293$	−9124.08	−	3320.89i	−1.81923	−	0.662145i	−0.823774	−	0.566919i	$-0.808135\pi$
$294$	−9096.43	+	7034.78i	−1.80447	+	1.39550i
$295$	−1431.14	+	8116.39i	−0.282454	+	1.60188i
$296$	−1104.16			−0.216817
$297$	−828.676	+	2736.14i	−0.161901	+	0.534569i
$298$	1437.60			0.279456
$299$	740.866	−	4201.66i	0.143296	−	0.812670i
$300$	840.124	+	344.272i	0.161682	+	0.0662552i
$301$	−10688.6	−	3890.34i	−2.04678	−	0.744967i
$302$	886.942	−	744.232i	0.168999	−	0.141807i
$303$	1230.00	+	2341.13i	0.233206	+	0.443876i
$304$	4484.98	−	1632.40i	0.846156	−	0.307976i
$305$	4830.77	−	8367.13i	0.906914	−	1.57082i
$306$	−2058.27	+	1464.55i	−0.384521	+	0.273604i
$307$	−1925.30	−	3334.72i	−0.357924	−	0.619942i	0.629690	−	0.776847i	$-0.283182\pi$
$307$	−1925.30	−	3334.72i	−0.357924	−	0.619942i	−0.987614	+	0.156904i	$0.949849\pi$
$308$	−1090.86	−	915.336i	−0.201809	−	0.169338i
$309$	5039.38	+	4582.79i	0.927769	+	0.843708i
$310$	−400.676	−	2272.35i	−0.0734093	−	0.416325i
$311$	1180.90	+	6697.21i	0.215314	+	1.22111i	0.880361	+	0.474304i	$0.157300\pi$
$311$	1180.90	+	6697.21i	0.215314	+	1.22111i	−0.665047	+	0.746801i	$0.731589\pi$
$312$	845.950	−	3885.35i	0.153502	−	0.705014i
$313$	−2544.69	−	2135.25i	−0.459535	−	0.385596i	0.383425	−	0.923572i	$-0.374745\pi$
$313$	−2544.69	−	2135.25i	−0.459535	−	0.385596i	−0.842960	+	0.537976i	$0.819189\pi$
$314$	−3519.88	−	6096.61i	−0.632606	−	1.09570i
$315$	3134.77	−	12063.6i	0.560713	−	2.15779i
$316$	−86.8893	+	150.497i	−0.0154681	+	0.0267915i
$317$	−2049.18	+	745.842i	−0.363071	+	0.132147i	−0.517113	−	0.855917i	$-0.672993\pi$
$317$	−2049.18	+	745.842i	−0.363071	+	0.132147i	0.154042	+	0.988064i	$0.450771\pi$
$318$	2126.65	+	84.7908i	0.375021	+	0.0149523i
$319$	70.2799	−	58.9718i	0.0123352	−	0.0103504i
$320$	4148.89	+	1510.07i	0.724781	+	0.263799i
$321$	−799.953	−	5903.55i	−0.139094	−	1.02649i
$322$	−1848.41	+	10482.8i	−0.319900	+	1.81424i
$323$	−1826.77			−0.314688
$324$	−1553.65	+	298.263i	−0.266402	+	0.0511426i
$325$	3314.11			0.565642
$326$	−35.9362	+	203.804i	−0.00610528	+	0.0346248i
$327$	−227.169	−	1676.48i	−0.0384174	−	0.283515i
$328$	3335.84	+	1214.15i	0.561558	+	0.204390i
$329$	7419.73	−	6225.90i	1.24335	−	1.04330i
$330$	4836.96	+	192.853i	0.806867	+	0.0321703i
$331$	4960.39	−	1805.43i	0.823709	−	0.299805i	0.104434	−	0.994532i	$-0.466697\pi$
$331$	4960.39	−	1805.43i	0.823709	−	0.299805i	0.719274	+	0.694726i	$0.244475\pi$
$332$	1110.34	−	1923.16i	0.183547	−	0.317913i
$333$	1142.40	+	1125.24i	0.187998	+	0.185174i
$334$	−3761.83	−	6515.68i	−0.616281	−	1.06743i
$335$	−8034.30	−	6741.58i	−1.31033	−	1.09950i
$336$	−2728.59	+	12532.1i	−0.443026	+	2.03477i
$337$	1421.64	+	8062.50i	0.229797	+	1.30324i	0.853300	+	0.521421i	$0.174598\pi$
$337$	1421.64	+	8062.50i	0.229797	+	1.30324i	−0.623503	+	0.781821i	$0.714291\pi$
$338$	−278.434	−	1579.08i	−0.0448072	−	0.254114i
$339$	−1194.10	−	1085.91i	−0.191312	−	0.173978i
$340$	699.187	+	586.687i	0.111526	+	0.0935811i
$341$	−514.229	−	890.671i	−0.0816629	−	0.141444i
$342$	−4876.12	−	2229.00i	−0.770966	−	0.352429i
$343$	5650.51	−	9786.97i	0.889501	−	1.54066i
$344$	−6171.14	+	2246.11i	−0.967225	+	0.352041i
$345$	−3591.19	−	6835.35i	−0.560416	−	1.06667i
$346$	6101.22	−	5119.53i	0.947987	−	0.795455i
$347$	9502.39	+	3458.59i	1.47007	+	0.535062i	0.948120	−	0.317913i	$-0.102982\pi$
$347$	9502.39	+	3458.59i	1.47007	+	0.535062i	0.521952	+	0.852975i	$0.325204\pi$
$348$	46.9772	+	19.2507i	0.00723633	+	0.00296536i
$349$	−621.019	+	3521.97i	−0.0952503	+	0.540191i	0.899420	+	0.437085i	$0.143989\pi$
$349$	−621.019	+	3521.97i	−0.0952503	+	0.540191i	−0.994670	+	0.103106i	$0.967122\pi$
$350$	−8268.46			−1.26276
$351$	−4834.79	+	3157.82i	−0.735220	+	0.480205i
$352$	−1950.37			−0.295327
$353$	−84.9764	+	481.925i	−0.0128126	+	0.0726637i	−0.990544	−	0.137198i	$-0.956190\pi$
$353$	−84.9764	+	481.925i	−0.0128126	+	0.0726637i	0.977731	+	0.209862i	$0.0673014\pi$
$354$	−7535.88	+	5827.92i	−1.13143	+	0.875001i
$355$	6018.30	+	2190.48i	0.899770	+	0.327489i
$356$	802.104	−	673.045i	0.119414	−	0.100200i
$357$	2621.90	−	4150.13i	0.388700	−	0.615261i
$358$	−11798.6	+	4294.32i	−1.74182	+	0.633972i
$359$	−6453.59	+	11177.9i	−0.948768	+	1.64331i	−0.200742	+	0.979644i	$0.564335\pi$
$359$	−6453.59	+	11177.9i	−0.948768	+	1.64331i	−0.748026	+	0.663669i	$0.768998\pi$
$360$	−3090.55	−	6498.86i	−0.452462	−	0.951444i
$361$	1490.95	+	2582.39i	0.217371	+	0.376497i
$362$	10519.1	+	8826.61i	1.52728	+	1.28154i
$363$	−4532.75	+	1448.05i	−0.655393	+	0.209374i
$364$	−499.479	−	2832.68i	−0.0719225	−	0.407893i
$365$	2033.57	+	11532.9i	0.291621	+	1.65387i
$366$	10638.2	−	3398.50i	1.51930	−	0.485362i
$367$	7475.79	+	6272.93i	1.06330	+	0.892219i	0.994429	−	0.105407i	$-0.0336144\pi$
$367$	7475.79	+	6272.93i	1.06330	+	0.892219i	0.0688757	+	0.997625i	$0.478059\pi$
$368$	3972.62	+	6880.78i	0.562737	+	0.974689i
$369$	−2214.05	−	4655.74i	−0.312355	−	0.656824i
$370$	1357.58	−	2351.39i	0.190749	−	0.330387i
$371$	−3886.51	+	1414.57i	−0.543875	+	0.197954i
$372$	303.970	−	481.145i	0.0423659	−	0.0670597i
$373$	6223.69	−	5222.30i	0.863943	−	0.724934i	−0.0988711	−	0.995100i	$-0.531523\pi$
$373$	6223.69	−	5222.30i	0.863943	−	0.724934i	0.962814	+	0.270166i	$0.0870787\pi$
$374$	1791.55	+	652.071i	0.247698	+	0.0901545i
$375$	−2621.24	+	2027.15i	−0.360961	+	0.279152i
$376$	971.066	−	5507.19i	0.133189	−	0.755350i
$377$	185.315			0.0253162
$378$	12062.5	−	7878.54i	1.64134	−	1.07203i
$379$	−7191.62			−0.974693			−0.487347	−	0.873209i	$-0.662035\pi$
$379$	−7191.62			−0.974693			−0.487347	+	0.873209i	$0.662035\pi$
$380$	−336.382	+	1907.72i	−0.0454106	+	0.257536i
$381$	−59.2059	−	24.2619i	−0.00796119	−	0.00326239i
$382$	−12012.2	−	4372.07i	−1.60889	−	0.585588i
$383$	−10052.1	+	8434.71i	−1.34109	+	1.12531i	−0.359748	+	0.933050i	$0.617137\pi$
$383$	−10052.1	+	8434.71i	−1.34109	+	1.12531i	−0.981344	+	0.192260i	$0.938418\pi$
$384$	4224.14	+	8040.07i	0.561359	+	1.06847i
$385$	−8839.68	+	3217.38i	−1.17016	+	0.425903i
$386$	3357.00	−	5814.49i	0.442660	−	0.766709i
$387$	8673.90	+	3965.07i	1.13933	+	0.520816i
$388$	1434.89	+	2485.31i	0.187747	+	0.325187i
$389$	−6136.99	−	5149.55i	−0.799892	−	0.671189i	0.148280	−	0.988945i	$-0.452626\pi$
$389$	−6136.99	−	5149.55i	−0.799892	−	0.671189i	−0.948172	+	0.317756i	$0.897071\pi$
$390$	7234.06	+	6578.62i	0.939259	+	0.854157i
$391$	−528.064	−	2994.80i	−0.0683002	−	0.387349i
$392$	−2240.36	−	12705.7i	−0.288661	−	1.63708i
$393$	−1089.50	+	5003.94i	−0.139842	+	0.642279i
$394$	2137.61	+	1793.67i	0.273328	+	0.229350i
$395$	573.989	+	994.179i	0.0731153	+	0.126639i
$396$	850.640	+	837.862i	0.107945	+	0.106324i
$397$	−1817.69	+	3148.34i	−0.229792	+	0.398011i	−0.957746	−	0.287614i	$-0.907138\pi$
$397$	−1817.69	+	3148.34i	−0.229792	+	0.398011i	0.727954	+	0.685626i	$0.240471\pi$
$398$	2863.45	−	1042.21i	0.360632	−	0.131259i
$399$	10410.4	+	415.070i	1.30620	+	0.0520789i
$400$	−4727.79	+	3967.09i	−0.590974	+	0.495886i
$401$	11370.4	+	4138.47i	1.41598	+	0.515375i	0.932880	−	0.360188i	$-0.117288\pi$
$401$	11370.4	+	4138.47i	1.41598	+	0.515375i	0.483103	+	0.875564i	$0.339510\pi$
$402$	−1627.86	−	12013.4i	−0.201966	−	1.49048i
$403$	360.737	−	2045.84i	0.0445895	−	0.252880i
$404$	1104.49			0.136015
$405$	−3425.35	+	9873.53i	−0.420265	+	1.21141i
$406$	−462.348			−0.0565171
$407$	210.149	−	1191.82i	0.0255939	−	0.145150i
$408$	−380.570	−	2808.56i	−0.0461790	−	0.340795i
$409$	−5572.83	−	2028.34i	−0.673737	−	0.245220i	−0.0175811	−	0.999845i	$-0.505597\pi$
$409$	−5572.83	−	2028.34i	−0.673737	−	0.245220i	−0.656156	+	0.754625i	$0.727819\pi$
$410$	−6687.09	+	5611.14i	−0.805493	+	0.675888i
$411$	−3375.23	−	134.573i	−0.405080	−	0.0161508i
$412$	2673.23	−	972.976i	0.319661	−	0.116347i
$413$	9256.27	−	16032.3i	1.10284	−	1.91017i
$414$	2244.68	−	8638.22i	0.266474	−	1.02547i
$415$	−7334.87	−	12704.4i	−0.867601	−	1.50273i
$416$	−3017.90	−	2532.31i	−0.355684	−	0.298454i
$417$	3149.82	−	14466.7i	0.369898	−	1.69890i
$418$	702.647	+	3984.91i	0.0822191	+	0.466288i
$419$	−185.116	−	1049.85i	−0.0215836	−	0.122407i	0.972112	−	0.234516i	$-0.0753505\pi$
$419$	−185.116	−	1049.85i	−0.0215836	−	0.122407i	−0.993696	+	0.112109i	$0.964239\pi$
$420$	−3851.23	−	3502.29i	−0.447430	−	0.406891i
$421$	−458.729	−	384.919i	−0.0531047	−	0.0445601i	0.615849	−	0.787864i	$-0.288813\pi$
$421$	−458.729	−	384.919i	−0.0531047	−	0.0445601i	−0.668954	+	0.743304i	$0.733258\pi$
$422$	1751.61	+	3033.88i	0.202055	+	0.349969i
$423$	−6617.06	+	4708.34i	−0.760597	+	0.541199i
$424$	−1193.96	+	2067.99i	−0.136754	+	0.236864i
$425$	2219.73	−	807.915i	0.253347	−	0.0922109i
$426$	3443.17	+	6553.60i	0.391601	+	0.745359i
$427$	−16624.7	+	13949.8i	−1.88414	+	1.58098i
$428$	−2338.05	−	850.980i	−0.264051	−	0.0961067i
$429$	4032.80	+	1652.59i	0.453859	+	0.185986i
$430$	2804.23	−	15903.6i	0.314493	−	1.78358i
$431$	−5699.28			−0.636948			−0.318474	−	0.947932i	$-0.603170\pi$
$431$	−5699.28			−0.636948			−0.318474	+	0.947932i	$0.603170\pi$
$432$	3117.14	−	10292.2i	0.347161	−	1.14626i
$433$	14318.4			1.58914			0.794570	−	0.607173i	$-0.207696\pi$
$433$	14318.4			1.58914			0.794570	+	0.607173i	$0.207696\pi$
$434$	−900.012	+	5104.22i	−0.0995437	+	0.564540i
$435$	265.297	−	205.169i	0.0292415	−	0.0226141i
$436$	−663.955	−	241.660i	−0.0729305	−	0.0265445i
$437$	4944.18	−	4148.66i	0.541218	−	0.454135i
$438$	−7229.97	+	11444.1i	−0.788724	+	1.24845i
$439$	1698.24	−	618.110i	0.184630	−	0.0671999i	−0.248051	−	0.968747i	$-0.579790\pi$
$439$	1698.24	−	618.110i	0.184630	−	0.0671999i	0.432681	+	0.901547i	$0.357568\pi$
$440$	−2715.59	+	4703.55i	−0.294229	+	0.509620i
$441$	−10630.4	+	15428.9i	−1.14786	+	1.66601i
$442$	1925.52	+	3335.09i	0.207211	+	0.358901i
$443$	7184.35	+	6028.38i	0.770516	+	0.646540i	0.940841	−	0.338848i	$-0.110037\pi$
$443$	7184.35	+	6028.38i	0.770516	+	0.646540i	−0.170325	+	0.985388i	$0.554482\pi$
$444$	637.931	−	203.796i	0.0681867	−	0.0217832i
$445$	−1201.11	−	6811.85i	−0.127951	−	0.725647i
$446$	112.327	+	637.037i	0.0119256	+	0.0676336i
$447$	2231.28	−	712.812i	0.236098	−	0.0754248i
$448$	−7597.23	−	6374.83i	−0.801195	−	0.672282i
$449$	82.8471	+	143.495i	0.00870779	+	0.0150823i	0.870346	−	0.492440i	$-0.163895\pi$
$449$	82.8471	+	143.495i	0.00870779	+	0.0150823i	−0.861639	+	0.507522i	$0.830562\pi$
$450$	6910.82	+	551.954i	0.723954	+	0.0578208i
$451$	−1945.43	+	3369.59i	−0.203120	+	0.351813i
$452$	−633.433	+	230.551i	−0.0659163	+	0.0239916i
$453$	1007.59	−	1594.89i	0.104505	−	0.165418i
$454$	7291.21	−	6118.05i	0.753730	−	0.632455i
$455$	−17855.4	−	6498.84i	−1.83973	−	0.669605i
$456$	4758.38	−	3679.92i	0.488665	−	0.377912i
$457$	−1225.72	+	6951.39i	−0.125463	+	0.711537i	0.855569	+	0.517689i	$0.173208\pi$
$457$	−1225.72	+	6951.39i	−0.125463	+	0.711537i	−0.981032	+	0.193847i	$0.937903\pi$
$458$	−3643.18			−0.371692
$459$	−2468.44	+	3293.68i	−0.251017	+	0.334936i
$460$	−3224.74			−0.326857
$461$	924.402	−	5242.54i	0.0933919	−	0.529652i	−0.901836	−	0.432078i	$-0.857781\pi$
$461$	924.402	−	5242.54i	0.0933919	−	0.529652i	0.995228	−	0.0975741i	$-0.0311083\pi$
$462$	−10061.6	−	4123.10i	−1.01322	−	0.415203i
$463$	8793.05	+	3200.41i	0.882609	+	0.321243i	0.743262	−	0.669000i	$-0.233278\pi$
$463$	8793.05	+	3200.41i	0.882609	+	0.321243i	0.139347	+	0.990244i	$0.455500\pi$
$464$	−264.364	+	221.828i	−0.0264500	+	0.0221942i
$465$	−1748.60	−	3328.22i	−0.174385	−	0.331919i
$466$	12335.7	−	4489.84i	1.22627	−	0.446326i
$467$	−917.123	+	1588.50i	−0.0908767	+	0.157403i	−0.907880	−	0.419230i	$-0.862300\pi$
$467$	−917.123	+	1588.50i	−0.0908767	+	0.157403i	0.817004	+	0.576633i	$0.195634\pi$
$468$	228.373	+	2400.92i	0.0225568	+	0.237142i
$469$	11779.3	+	20402.3i	1.15974	+	2.00872i
$470$	10534.1	+	8839.15i	1.03383	+	0.867488i
$471$	−8486.08	−	7717.19i	−0.830187	−	0.754967i
$472$	−1856.01	−	10526.0i	−0.180995	−	1.02648i
$473$	−1249.91	−	7088.57i	−0.121503	−	0.689075i
$474$	−282.302	+	1296.58i	−0.0273556	+	0.125641i
$475$	3840.53	+	3222.59i	0.370980	+	0.311289i
$476$	−1025.09	−	1775.52i	−0.0987083	−	0.170968i
$477$	3342.79	−	922.867i	0.320872	−	0.0885853i
$478$	−9798.69	+	16971.8i	−0.937619	+	1.62400i
$479$	11229.0	−	4087.03i	1.07112	−	0.389856i	0.254525	−	0.967066i	$-0.418081\pi$
$479$	11229.0	−	4087.03i	1.07112	−	0.389856i	0.816596	+	0.577210i	$0.195859\pi$
$480$	−7124.05	−	284.040i	−0.677431	−	0.0270096i
$481$	1872.60	−	1571.30i	0.177512	−	0.148950i
$482$	−14527.0	−	5287.39i	−1.37279	−	0.499656i
$483$	2328.88	+	17186.8i	0.219394	+	1.61910i
$484$	−345.094	+	1957.13i	−0.0324093	+	0.183802i
$485$	18957.8			1.77490
$486$	−10607.8	+	5779.71i	−0.990081	+	0.539450i
$487$	−2241.16			−0.208536			−0.104268	−	0.994549i	$-0.533250\pi$
$487$	−2241.16			−0.208536			−0.104268	+	0.994549i	$0.533250\pi$
$488$	−2175.78	+	12339.5i	−0.201830	+	1.14463i
$489$	45.2773	+	334.141i	0.00418714	+	0.0309005i
$490$	29812.4	+	10850.8i	2.74855	+	1.00039i
$491$	14180.0	−	11898.5i	1.30333	−	1.09363i	0.313774	−	0.949498i	$-0.398406\pi$
$491$	14180.0	−	11898.5i	1.30333	−	1.09363i	0.989559	−	0.144129i	$-0.0460380\pi$
$492$	−2151.39	−	85.7773i	−0.197139	−	0.00786004i
$493$	124.121	−	45.1762i	0.0113390	−	0.00412704i
$494$	−4086.68	+	7078.33i	−0.372203	+	0.644675i
$495$	7603.02	−	2099.02i	0.690364	−	0.190593i
$496$	1934.32	+	3350.34i	0.175108	+	0.303296i
$497$	−11020.4	−	9247.20i	−0.994632	−	0.834595i
$498$	3607.46	−	16568.6i	0.324607	−	1.49088i
$499$	2338.70	+	13263.4i	0.209809	+	1.18988i	0.889691	+	0.456563i	$0.150920\pi$
$499$	2338.70	+	13263.4i	0.209809	+	1.18988i	−0.679882	+	0.733321i	$0.737969\pi$
$500$	240.315	+	1362.89i	0.0214944	+	0.121901i
$501$	−9069.40	−	8247.66i	−0.808764	−	0.735485i
$502$	−5343.39	−	4483.64i	−0.475074	−	0.398635i
$503$	4772.18	+	8265.65i	0.423023	+	0.732698i	0.996234	−	0.0867103i	$-0.0276354\pi$
$503$	4772.18	+	8265.65i	0.423023	+	0.732698i	−0.573210	+	0.819408i	$0.694302\pi$
$504$	1530.65	+	16091.9i	0.135279	+	1.42221i
$505$	3648.11	−	6318.71i	0.321463	−	0.556790i
$506$	−6329.72	+	2303.83i	−0.556108	+	0.202407i
$507$	−1215.12	−	2312.81i	−0.106441	−	0.202595i
$508$	−20.4706	+	17.1769i	−0.00178787	+	0.00150020i
$509$	−8149.65	−	2966.23i	−0.709679	−	0.258302i	−0.0381413	−	0.999272i	$-0.512144\pi$
$509$	−8149.65	−	2966.23i	−0.709679	−	0.258302i	−0.671538	+	0.740970i	$0.734366\pi$
$510$	6448.98	+	2642.71i	0.559933	+	0.229453i
$511$	4567.86	−	25905.6i	0.395441	−	2.24266i
$512$	−4064.26			−0.350814
$513$	−8673.39	−	1041.86i	−0.746471	−	0.0896670i
$514$	2583.71			0.221717
$515$	3263.31	−	18507.1i	0.279220	−	1.58354i
$516$	3150.84	−	2436.72i	0.268814	−	0.207889i
$517$	5759.59	+	2096.32i	0.489955	+	0.178329i
$518$	−4672.01	+	3920.28i	−0.396286	+	0.332524i
$519$	6931.18	−	10971.2i	0.586214	−	0.927901i
$520$	−10308.9	+	3752.15i	−0.869379	+	0.316428i
$521$	−7793.09	+	13498.0i	−0.655320	+	1.13505i	0.326494	+	0.945199i	$0.394133\pi$
$521$	−7793.09	+	13498.0i	−0.655320	+	1.13505i	−0.981814	+	0.189848i	$0.939201\pi$
$522$	386.432	+	30.8636i	0.0324017	+	0.00258786i
$523$	−6350.65	−	10999.7i	−0.530965	−	0.919658i	−0.999347	−	0.0361324i	$-0.988496\pi$
$523$	−6350.65	−	10999.7i	−0.530965	−	0.919658i	0.468382	−	0.883526i	$-0.344837\pi$
$524$	1638.43	+	1374.80i	0.136594	+	0.114616i
$525$	−12833.4	+	4099.80i	−1.06685	+	0.340819i
$526$	−1616.97	−	9170.29i	−0.134036	−	0.760159i
$527$	−257.121	−	1458.21i	−0.0212531	−	0.120532i
$528$	−7731.26	+	2469.86i	−0.637235	+	0.203573i
$529$	−1089.96	−	914.588i	−0.0895836	−	0.0751696i
$530$	−2935.97	−	5085.26i	−0.240624	−	0.416772i
$531$	−8806.67	+	12782.0i	−0.719730	+	1.04462i
$532$	2175.64	−	3768.32i	0.177305	−	0.307101i
$533$	−7385.26	+	2688.02i	−0.600171	+	0.218444i
$534$	4270.34	−	6759.39i	0.346059	−	0.547767i
$535$	−12591.0	+	10565.1i	−1.01749	+	0.853772i
$536$	12781.4	+	4652.06i	1.02999	+	0.374885i
$537$	−16183.1	+	12515.3i	−1.30047	+	1.00573i
$538$	−3332.42	+	18899.1i	−0.267046	+	1.51449i
$539$	14140.8			1.13003
$540$	2985.09	+	3184.32i	0.237885	+	0.253761i
$541$	−15915.4			−1.26480			−0.632399	−	0.774643i	$-0.717930\pi$
$541$	−15915.4			−1.26480			−0.632399	+	0.774643i	$0.717930\pi$
$542$	1134.48	−	6433.96i	0.0899079	−	0.509893i
$543$	20703.2	+	8483.92i	1.63621	+	0.670497i
$544$	−2638.66	−	960.393i	−0.207962	−	0.0756922i
$545$	−3575.56	+	3000.25i	−0.281028	+	0.235810i
$546$	−10215.4	−	19443.6i	−0.800691	−	1.52401i
$547$	4290.07	−	1561.46i	0.335339	−	0.122053i	−0.168862	−	0.985640i	$-0.554009\pi$
$547$	4290.07	−	1561.46i	0.335339	−	0.122053i	0.504201	+	0.863586i	$0.331787\pi$
$548$	−705.379	+	1221.75i	−0.0549859	+	0.0952384i
$549$	14826.3	−	10549.6i	1.15258	−	0.820117i
$550$	−2616.17	−	4531.34i	−0.202825	−	0.351304i
$551$	214.751	+	180.198i	0.0166038	+	0.0139323i
$552$	7408.34	+	6737.11i	0.571232	+	0.519475i
$553$	−447.774	−	2539.45i	−0.0344327	−	0.195278i
$554$	−2318.77	−	13150.4i	−0.177825	−	1.00850i
$555$	941.176	−	4322.71i	0.0719832	−	0.330610i
$556$	−4736.81	−	3974.66i	−0.361305	−	0.303171i
$557$	−7631.87	−	13218.8i	−0.580562	−	1.00556i	−0.995413	−	0.0956732i	$-0.969500\pi$
$557$	−7631.87	−	13218.8i	−0.580562	−	1.00556i	0.414851	−	0.909889i	$-0.363834\pi$
$558$	1092.96	−	4206.06i	0.0829190	−	0.319098i
$559$	7269.60	−	12591.3i	0.550038	−	0.952694i
$560$	33251.2	−	12102.5i	2.50915	−	0.913254i
$561$	3103.97	+	123.757i	0.233600	+	0.00931377i
$562$	−269.381	+	226.037i	−0.0202191	+	0.0169658i
$563$	−18106.8	−	6590.34i	−1.35544	−	0.493339i	−0.440797	−	0.897607i	$-0.645304\pi$
$563$	−18106.8	−	6590.34i	−1.35544	−	0.493339i	−0.914641	+	0.404268i	$0.867526\pi$
$564$	455.433	+	3361.04i	0.0340021	+	0.250931i
$565$	−773.254	+	4385.34i	−0.0575771	+	0.326536i
$566$	9912.26			0.736119
$567$	14815.5	−	18209.2i	1.09734	−	1.34870i
$568$	−8305.91			−0.613571
$569$	−738.639	+	4189.03i	−0.0544206	+	0.308635i	−0.999852	−	0.0171857i	$-0.994529\pi$
$569$	−738.639	+	4189.03i	−0.0544206	+	0.308635i	0.945432	+	0.325820i	$0.105640\pi$
$570$	1986.20	+	14657.9i	0.145952	+	1.07711i
$571$	3973.16	+	1446.11i	0.291194	+	0.105986i	0.483487	−	0.875352i	$-0.339370\pi$
$571$	3973.16	+	1446.11i	0.291194	+	0.105986i	−0.192293	+	0.981338i	$0.561592\pi$
$572$	1394.35	−	1170.00i	0.101924	−	0.0855248i
$573$	−20811.8	−	829.778i	−1.51732	−	0.0604965i
$574$	18425.7	−	6706.41i	1.33985	−	0.487666i
$575$	−4172.91	+	7227.70i	−0.302648	+	0.524202i
$576$	5924.25	+	5835.26i	0.428548	+	0.422111i
$577$	1201.69	+	2081.38i	0.0867016	+	0.150172i	0.906115	−	0.423031i	$-0.139034\pi$
$577$	1201.69	+	2081.38i	0.0867016	+	0.150172i	−0.819413	+	0.573203i	$0.805701\pi$
$578$	−9899.58	−	8306.74i	−0.712402	−	0.597776i
$579$	2327.32	−	10689.1i	0.167047	−	0.767228i
$580$	−24.3224	−	137.939i	−0.00174126	−	0.00987519i
$581$	5721.99	+	32451.0i	0.408586	+	2.31720i
$582$	16212.1	+	14743.2i	1.15466	+	1.05005i
$583$	−2004.93	−	1682.34i	−0.142428	−	0.119512i
$584$	−7593.77	−	13152.8i	−0.538069	−	0.931963i
$585$	14489.8	+	6623.69i	1.02407	+	0.468130i
$586$	−15482.3	+	26816.2i	−1.09141	+	1.89039i
$587$	2410.61	−	877.389i	0.169500	−	0.0616929i	−0.255876	−	0.966710i	$-0.582364\pi$
$587$	2410.61	−	877.389i	0.169500	−	0.0616929i	0.425376	+	0.905017i	$0.360142\pi$
$588$	3639.49	+	6927.27i	0.255255	+	0.485843i
$589$	2407.38	−	2020.03i	0.168412	−	0.141314i
$590$	24697.9	+	8989.31i	1.72338	+	0.627261i
$591$	4207.13	+	1724.03i	0.292823	+	0.119995i
$592$	−790.496	+	4483.13i	−0.0548804	+	0.311242i
$593$	−11554.0			−0.800112			−0.400056	−	0.916491i	$-0.631009\pi$
$593$	−11554.0			−0.800112			−0.400056	+	0.916491i	$0.631009\pi$
$594$	8134.26	+	4117.76i	0.561874	+	0.284434i
$595$	−13543.5			−0.933160
$596$	169.875	−	963.410i	0.0116751	−	0.0662127i
$597$	3927.56	−	3037.40i	0.269253	−	0.208229i
$598$	−12785.5	−	4653.55i	−0.874312	−	0.318224i
$599$	−11775.6	+	9880.93i	−0.803237	+	0.673996i	−0.948983	−	0.315326i	$-0.897886\pi$
$599$	−11775.6	+	9880.93i	−0.803237	+	0.673996i	0.145746	+	0.989322i	$0.453442\pi$
$600$	−4154.45	+	6575.96i	−0.282675	+	0.447437i
$601$	−19439.9	+	7075.54i	−1.31942	+	0.480228i	−0.903271	−	0.429070i	$-0.858841\pi$
$601$	−19439.9	+	7075.54i	−1.31942	+	0.480228i	−0.416145	+	0.909298i	$0.636619\pi$
$602$	−18137.1	+	31414.4i	−1.22793	+	2.12684i
$603$	−8483.25	−	17838.7i	−0.572910	−	1.20472i
$604$	−393.943	−	682.329i	−0.0265386	−	0.0459662i
$605$	10056.8	+	8438.64i	0.675812	+	0.567073i
$606$	8033.74	−	2566.49i	0.538529	−	0.172040i
$607$	−2894.83	−	16417.4i	−0.193571	−	1.09779i	−0.914439	−	0.404723i	$-0.867368\pi$
$607$	−2894.83	−	16417.4i	−0.193571	−	1.09779i	0.720868	−	0.693072i	$-0.243743\pi$
$608$	−1034.88	−	5869.11i	−0.0690297	−	0.391487i
$609$	−717.605	+	229.249i	−0.0477484	+	0.0152539i
$610$	−23602.8	−	19805.1i	−1.56664	−	1.31457i
$611$	6190.27	+	10721.9i	0.409872	+	0.709919i
$612$	738.256	+	1552.42i	0.0487618	+	0.102537i
$613$	2046.39	−	3544.45i	0.134833	−	0.233538i	−0.790700	−	0.612203i	$-0.790283\pi$
$613$	2046.39	−	3544.45i	0.134833	−	0.233538i	0.925534	+	0.378665i	$0.123617\pi$
$614$	−11539.2	+	4199.94i	−0.758446	+	0.276052i
$615$	−7596.76	+	12024.7i	−0.498099	+	0.788426i
$616$	9345.52	−	7841.82i	0.611269	−	0.512916i
$617$	20423.4	+	7433.51i	1.33260	+	0.485027i	0.907475	−	0.420106i	$-0.138007\pi$
$617$	20423.4	+	7433.51i	1.33260	+	0.485027i	0.425127	+	0.905134i	$0.360229\pi$
$618$	17183.5	−	13288.9i	1.11848	−	0.864983i
$619$	−1735.43	+	9842.11i	−0.112686	+	0.639075i	0.875184	+	0.483791i	$0.160740\pi$
$619$	−1735.43	+	9842.11i	−0.112686	+	0.639075i	−0.987870	+	0.155284i	$0.950371\pi$
$620$	−1570.17			−0.101709
$621$	−799.195	−	14520.3i	−0.0516435	−	0.938291i
$622$	21687.3			1.39804
$623$	−2697.98	+	15301.0i	−0.173503	+	0.983984i
$624$	−15169.8	−	6216.38i	−0.973199	−	0.398805i
$625$	18048.4	+	6569.07i	1.15510	+	0.420420i
$626$	−8115.18	+	6809.45i	−0.518128	+	0.434761i
$627$	3066.43	+	5836.53i	0.195313	+	0.371752i
$628$	−4501.59	+	1638.44i	−0.286040	+	0.104110i
$629$	871.182	−	1508.93i	0.0552247	−	0.0956519i
$630$	−36151.1	−	16525.6i	−2.28618	−	1.04507i
$631$	1084.24	+	1877.97i	0.0684043	+	0.118480i	0.898199	−	0.439589i	$-0.144876\pi$
$631$	1084.24	+	1877.97i	0.0684043	+	0.118480i	−0.829795	+	0.558069i	$0.811543\pi$
$632$	−1140.48	−	956.975i	−0.0717813	−	0.0602316i
$633$	4222.96	+	3840.34i	0.265162	+	0.241137i
$634$	1207.61	+	6848.72i	0.0756475	+	0.429018i
$635$	30.6538	+	173.846i	0.00191568	+	0.0108644i
$636$	308.121	−	1415.16i	0.0192103	−	0.0882308i
$637$	21880.8	+	18360.1i	1.36098	+	1.14200i
$638$	−146.288	−	253.379i	−0.00907777	−	0.0157232i
$639$	8593.61	+	8464.52i	0.532015	+	0.524024i
$640$	12528.6	−	21700.1i	0.773805	−	1.34027i
$641$	−14042.1	+	5110.89i	−0.865254	+	0.314927i	−0.736244	−	0.676716i	$-0.763402\pi$
$641$	−14042.1	+	5110.89i	−0.865254	+	0.314927i	−0.129011	+	0.991643i	$0.541180\pi$
$642$	−18983.8	−	756.894i	−1.16702	−	0.0465299i
$643$	14505.7	−	12171.8i	0.889658	−	0.746512i	−0.0784835	−	0.996915i	$-0.525008\pi$
$643$	14505.7	−	12171.8i	0.889658	−	0.746512i	0.968142	+	0.250404i	$0.0805634\pi$
$644$	6806.68	+	2477.43i	0.416492	+	0.151591i
$645$	−3533.16	−	26074.2i	−0.215687	−	1.59174i
$646$	−1011.62	+	5737.19i	−0.0616125	+	0.349422i
$647$	−10983.5			−0.667400			−0.333700	−	0.942679i	$-0.608297\pi$
$647$	−10983.5			−0.667400			−0.333700	+	0.942679i	$0.608297\pi$
$648$	−205.124	−	13551.9i	−0.0124352	−	0.821556i
$649$	11714.9			0.708550
$650$	1835.27	−	10408.3i	0.110747	−	0.628075i
$651$	1133.96	+	8368.47i	0.0682694	+	0.503819i
$652$	132.334	+	48.1655i	0.00794875	+	0.00289311i
$653$	22030.2	−	18485.5i	1.32023	−	1.10780i	0.333970	−	0.942584i	$-0.391612\pi$
$653$	22030.2	−	18485.5i	1.32023	−	1.10780i	0.986257	−	0.165218i	$-0.0528329\pi$
$654$	−5390.98	−	214.941i	−0.322330	−	0.0128515i
$655$	13276.9	−	4832.40i	0.792017	−	0.288271i
$656$	7317.93	−	12675.0i	0.435544	−	0.754385i
$657$	−5547.16	+	21347.1i	−0.329399	+	1.26763i
$658$	−15444.3	−	26750.3i	−0.915016	−	1.58485i
$659$	12412.7	+	10415.5i	0.733736	+	0.615677i	0.931147	−	0.364643i	$-0.118809\pi$
$659$	12412.7	+	10415.5i	0.733736	+	0.615677i	−0.197412	+	0.980321i	$0.563254\pi$
$660$	700.805	−	3218.72i	0.0413315	−	0.189831i
$661$	−152.498	−	864.862i	−0.00897353	−	0.0508914i	0.979992	−	0.199036i	$-0.0637810\pi$
$661$	−152.498	−	864.862i	−0.00897353	−	0.0508914i	−0.988966	+	0.148144i	$0.952670\pi$
$662$	−2923.23	−	16578.5i	−0.171623	−	0.973324i
$663$	4642.23	+	4221.62i	0.271929	+	0.247291i
$664$	14573.9	+	12228.9i	0.851772	+	0.714721i
$665$	−14372.3	−	24893.5i	−0.838094	−	1.45162i
$666$	4166.58	−	2964.71i	0.242420	−	0.172493i
$667$	−233.337	+	404.151i	−0.0135455	+	0.0234615i
$668$	−4811.02	+	1751.07i	−0.278659	+	0.101423i
$669$	490.207	+	933.042i	0.0283296	+	0.0539215i
$670$	−25621.9	+	21499.3i	−1.47740	+	1.23969i
$671$	−12905.0	−	4697.04i	−0.742463	−	0.270234i
$672$	14819.0	+	6072.65i	0.850678	+	0.348597i
$673$	359.580	−	2039.28i	0.0205955	−	0.116803i	−0.972777	−	0.231744i	$-0.925557\pi$
$673$	359.580	−	2039.28i	0.0205955	−	0.116803i	0.993372	+	0.114941i	$0.0366679\pi$
$674$	26108.5			1.49208
$675$	10999.9	−	2569.95i	0.627238	−	0.146544i
$676$	−1091.13			−0.0620805
$677$	−1246.66	+	7070.17i	−0.0707727	+	0.401372i	0.928757	+	0.370690i	$0.120879\pi$
$677$	−1246.66	+	7070.17i	−0.0707727	+	0.401372i	−0.999529	+	0.0306815i	$0.990232\pi$
$678$	−4071.69	+	3148.87i	−0.230638	+	0.178365i
$679$	−40015.5	−	14564.4i	−2.26164	−	0.823170i
$680$	−5990.04	+	5026.24i	−0.337805	+	0.283452i
$681$	8283.06	−	13111.0i	0.466090	−	0.737760i
$682$	−3082.02	+	1121.76i	−0.173045	+	0.0629832i
$683$	6300.70	−	10913.1i	0.352986	−	0.611390i	−0.633785	−	0.773509i	$-0.718500\pi$
$683$	6300.70	−	10913.1i	0.352986	−	0.611390i	0.986771	+	0.162119i	$0.0518330\pi$
$684$	−2069.96	+	3004.35i	−0.115712	+	0.167945i
$685$	4659.72	+	8070.87i	0.259911	+	0.450178i
$686$	−27608.0	−	23165.8i	−1.53656	−	1.28932i
$687$	−5654.54	+	1806.42i	−0.314024	+	0.100319i
$688$	4701.63	+	26664.3i	0.260535	+	1.47757i
$689$	−918.014	−	5206.32i	−0.0507599	−	0.287873i
$690$	−23455.9	+	7493.31i	−1.29413	+	0.413428i
$691$	2525.98	+	2119.55i	0.139064	+	0.116688i	0.709666	−	0.704538i	$-0.248846\pi$
$691$	2525.98	+	2119.55i	0.139064	+	0.116688i	−0.570602	+	0.821226i	$0.693290\pi$
$692$	−2709.91	−	4693.70i	−0.148866	−	0.257844i
$693$	−17660.8	−	1410.54i	−0.968079	−	0.0773186i
$694$	16124.3	−	27928.1i	0.881944	−	1.52757i
$695$	−38384.4	+	13970.8i	−2.09497	+	0.762507i
$696$	−232.305	+	367.708i	−0.0126516	+	0.0200258i
$697$	−4291.23	+	3600.77i	−0.233202	+	0.195680i
$698$	10717.3	+	3900.76i	0.581166	+	0.211527i
$699$	16919.9	−	13085.1i	0.915552	−	0.708047i
$700$	−977.051	+	5541.13i	−0.0527558	+	0.299193i
$701$	29161.3			1.57119			0.785596	−	0.618739i	$-0.212356\pi$
$701$	29161.3			1.57119			0.785596	+	0.618739i	$0.212356\pi$
$702$	7240.12	+	16932.9i	0.389260	+	0.910389i
$703$	3697.96			0.198394
$704$	1089.79	−	6180.51i	0.0583424	−	0.330876i
$705$	20732.6	+	8495.96i	1.10757	+	0.453867i
$706$	1466.48	+	533.756i	0.0781754	+	0.0284535i
$707$	−12554.7	+	10534.6i	−0.667848	+	0.560391i
$708$	3015.11	+	5738.86i	0.160049	+	0.304632i
$709$	−30356.3	+	11048.8i	−1.60798	+	0.585256i	−0.981039	−	0.193812i	$-0.937915\pi$
$709$	−30356.3	+	11048.8i	−1.60798	+	0.585256i	−0.626939	+	0.779068i	$0.715693\pi$
$710$	10212.2	−	17688.1i	0.539801	−	0.934963i
$711$	204.733	+	2152.38i	0.0107990	+	0.113531i
$712$	4485.21	+	7768.61i	0.236082	+	0.408906i
$713$	4007.53	+	3362.72i	0.210496	+	0.176627i
$714$	−11582.0	−	10532.6i	−0.607068	−	0.552064i
$715$	−2087.98	−	11841.5i	−0.109211	−	0.619367i
$716$	1483.66	+	8414.28i	0.0774402	+	0.439185i
$717$	−6793.20	+	31200.3i	−0.353831	+	1.62510i
$718$	31531.8	+	26458.3i	1.63894	+	1.37523i
$719$	−2138.32	−	3703.67i	−0.110912	−	0.192105i	0.805226	−	0.592968i	$-0.202044\pi$
$719$	−2138.32	−	3703.67i	−0.110912	−	0.192105i	−0.916138	+	0.400862i	$0.868711\pi$
$720$	−28599.5	+	7895.64i	−1.48033	+	0.408685i
$721$	−21106.3	+	36557.2i	−1.09021	+	1.88830i
$722$	8935.95	−	3252.42i	0.460612	−	0.167649i
$723$	−25168.8	−	1003.50i	−1.29466	−	0.0516189i
$724$	7158.19	−	6006.43i	0.367447	−	0.308325i
$725$	−340.641	−	123.983i	−0.0174498	−	0.00635120i
$726$	2037.64	+	15037.5i	0.104165	+	0.768725i
$727$	6189.02	−	35099.7i	0.315733	−	1.79061i	−0.252344	−	0.967637i	$-0.581202\pi$
$727$	6189.02	−	35099.7i	0.315733	−	1.79061i	0.568078	−	0.822975i	$-0.307687\pi$
$728$	24642.4			1.25454
$729$	−13598.5	+	14230.3i	−0.690873	+	0.722976i
$730$	37346.6			1.89351
$731$	1799.53	−	10205.6i	0.0910504	−	0.516373i
$732$	−1020.45	−	7530.77i	−0.0515258	−	0.380253i
$733$	−16264.4	−	5919.75i	−0.819562	−	0.298296i	−0.101994	−	0.994785i	$-0.532522\pi$
$733$	−16264.4	−	5919.75i	−0.819562	−	0.298296i	−0.717568	+	0.696489i	$0.754745\pi$
$734$	23840.8	−	20004.8i	1.19888	−	1.00598i
$735$	51651.8	+	2059.39i	2.59212	+	0.103349i
$736$	9322.64	−	3393.16i	0.466898	−	0.169937i
$737$	−7454.02	+	12910.7i	−0.372554	+	0.645283i
$738$	−15848.0	+	4375.26i	−0.790477	+	0.218232i
$739$	5197.85	+	9002.94i	0.258736	+	0.448144i	0.965904	−	0.258902i	$-0.0833607\pi$
$739$	5197.85	+	9002.94i	0.258736	+	0.448144i	−0.707167	+	0.707046i	$0.750027\pi$
$740$	−1415.37	−	1187.64i	−0.0703111	−	0.0589980i
$741$	−2833.19	+	13012.5i	−0.140459	+	0.645111i
$742$	2290.38	+	12989.4i	0.113319	+	0.642662i
$743$	1060.37	+	6013.64i	0.0523568	+	0.296930i	0.999731	−	0.0231986i	$-0.00738500\pi$
$743$	1060.37	+	6013.64i	0.0523568	+	0.296930i	−0.947374	+	0.320129i	$0.896274\pi$
$744$	3607.21	+	3280.38i	0.177751	+	0.161646i
$745$	−4950.52	−	4153.98i	−0.243454	−	0.204282i
$746$	−12954.7	−	22438.2i	−0.635798	−	1.10123i
$747$	−2616.23	−	27504.7i	−0.128143	−	1.34718i
$748$	648.688	−	1123.56i	0.0317091	−	0.0549217i
$749$	34693.3	−	12627.3i	1.69248	−	0.616012i
$750$	4914.93	+	9354.90i	0.239291	+	0.455457i
$751$	12138.3	−	10185.2i	0.589791	−	0.494893i	−0.298355	−	0.954455i	$-0.596438\pi$
$751$	12138.3	−	10185.2i	0.589791	−	0.494893i	0.888146	+	0.459562i	$0.151993\pi$
$752$	−21665.2	−	7885.50i	−1.05060	−	0.382386i
$753$	−10516.6	−	4309.56i	−0.508958	−	0.208565i
$754$	102.623	−	582.003i	0.00495664	−	0.0281105i
$755$	−5204.76			−0.250888
$756$	−3854.45	−	9014.67i	−0.185430	−	0.433678i
$757$	2034.87			0.0976995			0.0488498	−	0.998806i	$-0.484444\pi$
$757$	2034.87			0.0976995			0.0488498	+	0.998806i	$0.484444\pi$
$758$	−3982.54	+	22586.1i	−0.190834	+	1.08228i
$759$	−8681.97	+	6714.26i	−0.415198	+	0.321096i
$760$	−15595.0	−	5676.11i	−0.744328	−	0.270913i
$761$	1158.85	−	972.389i	0.0552013	−	0.0463194i	−0.614770	−	0.788707i	$-0.710751\pi$
$761$	1158.85	−	972.389i	0.0552013	−	0.0463194i	0.669971	+	0.742387i	$0.266307\pi$
$762$	−108.984	+	172.507i	−0.00518119	+	0.00820116i
$763$	9852.15	−	3585.89i	0.467460	−	0.170141i
$764$	−4349.39	+	7533.36i	−0.205962	+	0.356738i
$765$	11319.7	+	904.087i	0.534988	+	0.0427285i
$766$	20923.6	+	36240.7i	0.986945	+	1.70944i
$767$	18127.0	+	15210.3i	0.853360	+	0.716054i
$768$	15394.7	−	4918.04i	0.723316	−	0.231073i
$769$	121.214	+	687.438i	0.00568411	+	0.0322362i	0.987518	−	0.157507i	$-0.0503456\pi$
$769$	121.214	+	687.438i	0.00568411	+	0.0322362i	−0.981834	+	0.189743i	$0.939235\pi$
$770$	5209.36	+	29543.7i	0.243808	+	1.38270i
$771$	4010.16	−	1281.10i	0.187318	−	0.0598413i
$772$	−3499.91	−	2936.78i	−0.163167	−	0.136913i
$773$	−19332.9	−	33485.6i	−0.899556	−	1.55808i	−0.828063	−	0.560635i	$-0.810557\pi$
$773$	−19332.9	−	33485.6i	−0.899556	−	1.55808i	−0.0714925	−	0.997441i	$-0.522776\pi$
$774$	17256.2	−	25045.6i	0.801369	−	1.16311i
$775$	−2031.84	+	3519.26i	−0.0941755	+	0.163117i
$776$	−23103.2	+	8408.88i	−1.06876	+	0.388996i
$777$	−5307.56	+	8401.17i	−0.245055	+	0.387890i
$778$	−19571.3	+	16422.2i	−0.901882	+	0.756769i
$779$	−11172.2	−	4066.33i	−0.513843	−	0.187024i
$780$	5263.50	−	4070.56i	0.241620	−	0.186858i
$781$	1580.83	−	8965.32i	0.0724283	−	0.410761i
$782$	−9697.95			−0.443476
$783$	615.081	−	143.704i	0.0280730	−	0.00655883i
$784$	−53192.0			−2.42311
$785$	−5495.25	+	31165.1i	−0.249852	+	1.41698i
$786$	15112.1	+	6192.76i	0.685791	+	0.281028i
$787$	−31799.3	−	11574.0i	−1.44031	−	0.524229i	−0.500441	−	0.865771i	$-0.666829\pi$
$787$	−31799.3	−	11574.0i	−1.44031	−	0.524229i	−0.939867	+	0.341542i	$0.889051\pi$
$788$	1454.63	−	1220.58i	0.0657601	−	0.0551793i
$789$	−7056.64	−	13431.3i	−0.318407	−	0.606044i
$790$	3440.19	−	1252.13i	0.154932	−	0.0563908i
$791$	5001.23	−	8662.39i	0.224808	−	0.389379i
$792$	−8334.51	+	5930.38i	−0.373932	+	0.266070i
$793$	−13870.0	−	24023.5i	−0.621107	−	1.07579i
$794$	8881.12	+	7452.14i	0.396951	+	0.333081i
$795$	−7078.35	−	6437.01i	−0.315777	−	0.287166i
$796$	−360.077	−	2042.10i	−0.0160334	−	0.0909300i
$797$	−3594.76	−	20386.9i	−0.159765	−	0.906073i	−0.954299	−	0.298853i	$-0.903396\pi$
$797$	−3594.76	−	20386.9i	−0.159765	−	0.906073i	0.794534	−	0.607220i	$-0.207715\pi$
$798$	7068.62	−	32465.3i	0.313567	−	1.44017i
$799$	6759.91	+	5672.24i	0.299310	+	0.251151i
$800$	3853.19	+	6673.92i	0.170289	+	0.294948i
$801$	3276.39	−	12608.6i	0.144526	−	0.556182i
$802$	19294.0	−	33418.2i	0.849494	−	1.47137i
$803$	15642.3	−	5693.33i	0.687428	−	0.250203i
$804$	−8243.16	−	328.660i	−0.361584	−	0.0144166i
$805$	36655.7	−	30757.8i	1.60490	−	1.34667i
$806$	−6225.43	−	2265.87i	−0.272061	−	0.0990222i
$807$	4198.64	+	30985.4i	0.183146	+	1.35160i
$808$	−1643.11	+	9318.55i	−0.0715402	+	0.405724i
$809$	−14765.9			−0.641708			−0.320854	−	0.947129i	$-0.603970\pi$
$809$	−14765.9			−0.641708			−0.320854	+	0.947129i	$0.603970\pi$
$810$	29112.1	+	16225.4i	1.26283	+	0.703832i
$811$	31275.1			1.35415			0.677076	−	0.735913i	$-0.263247\pi$
$811$	31275.1			1.35415			0.677076	+	0.735913i	$0.263247\pi$
$812$	−54.6338	+	309.844i	−0.00236117	+	0.0133909i
$813$	−1429.37	−	10548.6i	−0.0616609	−	0.455049i
$814$	−3626.66	−	1320.00i	−0.156160	−	0.0568377i
$815$	712.649	−	597.983i	0.0306294	−	0.0257012i
$816$	−11675.9	−	465.523i	−0.500903	−	0.0199713i
$817$	20667.9	−	7522.51i	0.885042	−	0.322129i
$818$	−9456.34	+	16378.9i	−0.404197	+	0.700090i
$819$	−25496.0	−	25113.0i	−1.08779	−	1.07145i
$820$	2970.13	+	5144.42i	0.126490	+	0.219086i
$821$	−20255.2	−	16996.2i	−0.861039	−	0.722497i	0.101153	−	0.994871i	$-0.467747\pi$
$821$	−20255.2	−	16996.2i	−0.861039	−	0.722497i	−0.962192	+	0.272373i	$0.912191\pi$
$822$	−2291.76	+	10525.8i	−0.0972437	+	0.446629i
$823$	6435.10	+	36495.3i	0.272556	+	1.54574i	0.746620	+	0.665251i	$0.231675\pi$
$823$	6435.10	+	36495.3i	0.272556	+	1.54574i	−0.474064	+	0.880490i	$0.657214\pi$
$824$	4232.11	+	24001.5i	0.178923	+	1.01472i
$825$	−6307.33	−	5735.85i	−0.266174	−	0.242057i
$826$	−45225.5	−	37948.7i	−1.90508	−	1.59855i
$827$	21061.9	+	36480.3i	0.885604	+	1.53391i	0.845020	+	0.534735i	$0.179589\pi$
$827$	21061.9	+	36480.3i	0.885604	+	1.53391i	0.0405844	+	0.999176i	$0.487078\pi$
$828$	−5523.68	−	2525.02i	−0.231837	−	0.105979i
$829$	−5648.47	+	9783.43i	−0.236646	+	0.409883i	−0.959750	−	0.280857i	$-0.909381\pi$
$829$	−5648.47	+	9783.43i	−0.236646	+	0.409883i	0.723104	+	0.690739i	$0.242715\pi$
$830$	−43961.4	+	16000.6i	−1.83846	+	0.669145i
$831$	−10119.4	−	19260.9i	−0.422428	−	0.804034i
$832$	9710.92	−	8148.43i	0.404646	−	0.339538i
$833$	19131.2	+	6963.18i	0.795745	+	0.289628i
$834$	−43690.2	−	17903.7i	−1.81399	−	0.743350i
$835$	−5872.98	+	33307.3i	−0.243405	+	1.38042i
$836$	2753.53			0.113915
$837$	−389.138	−	7070.11i	−0.0160700	−	0.291970i
$838$	−3399.68			−0.140143
$839$	1943.27	−	11020.8i	0.0799633	−	0.453494i	−0.918367	−	0.395730i	$-0.870492\pi$
$839$	1943.27	−	11020.8i	0.0799633	−	0.453494i	0.998330	−	0.0577644i	$-0.0183972\pi$
$840$	35278.2	−	27282.6i	1.44906	−	1.12064i
$841$	22899.1	+	8334.60i	0.938912	+	0.341736i
$842$	−1462.92	+	1227.53i	−0.0598758	+	0.0502417i
$843$	−306.025	+	484.399i	−0.0125031	+	0.0197907i
$844$	2240.14	−	815.346i	0.0913613	−	0.0332528i
$845$	−3603.98	+	6242.28i	−0.146723	+	0.254131i
$846$	11122.7	+	23389.0i	0.452018	+	0.950508i
$847$	−14744.5	−	25538.2i	−0.598142	−	1.03601i
$848$	7541.73	+	6328.26i	0.305406	+	0.256266i
$849$	15384.7	−	4914.85i	0.621910	−	0.198678i
$850$	−1308.12	−	7418.71i	−0.0527860	−	0.299364i
$851$	1068.97	+	6062.42i	0.0430596	+	0.244203i
$852$	4798.78	−	1533.03i	0.192962	−	0.0616443i
$853$	−21657.1	−	18172.5i	−0.869313	−	0.729441i	0.0946400	−	0.995512i	$-0.469830\pi$
$853$	−21657.1	−	18172.5i	−0.869313	−	0.729441i	−0.963953	+	0.266071i	$0.914274\pi$
$854$	34604.6	+	59937.0i	1.38659	+	2.40164i
$855$	10350.7	+	21765.5i	0.414018	+	0.870602i
$856$	10658.0	−	18460.1i	0.425563	−	0.737096i
$857$	36636.6	−	13334.6i	1.46031	−	0.531508i	0.514857	−	0.857276i	$-0.327845\pi$
$857$	36636.6	−	13334.6i	1.46031	−	0.531508i	0.945450	+	0.325768i	$0.105623\pi$
$858$	7423.42	−	11750.3i	0.295375	−	0.467540i
$859$	−13609.2	+	11419.5i	−0.540561	+	0.453584i	−0.871730	−	0.489987i	$-0.837001\pi$
$859$	−13609.2	+	11419.5i	−0.540561	+	0.453584i	0.331169	+	0.943571i	$0.392557\pi$
$860$	−10326.5	−	3758.53i	−0.409453	−	0.149029i
$861$	25273.0	−	19545.1i	1.00035	−	0.773628i
$862$	−3156.12	+	17899.2i	−0.124708	+	0.707252i
$863$	−7872.07			−0.310508			−0.155254	−	0.987875i	$-0.549620\pi$
$863$	−7872.07			−0.310508			−0.155254	+	0.987875i	$0.549620\pi$
$864$	−11980.4	−	6064.78i	−0.471739	−	0.238806i
$865$	−35803.2			−1.40734
$866$	7929.16	−	44968.5i	0.311136	−	1.76454i
$867$	−19483.8	−	7984.22i	−0.763212	−	0.312755i
$868$	3314.26	+	1206.29i	0.129601	+	0.0471707i
$869$	1250.01	−	1048.88i	0.0487960	−	0.0409447i
$870$	−497.443	−	946.815i	−0.0193849	−	0.0368966i
$871$	−28297.0	+	10299.3i	−1.10081	+	0.400663i
$872$	3026.63	−	5242.28i	0.117540	−	0.203585i
$873$	32472.9	+	14844.2i	1.25893	+	0.575489i
$874$	−10291.4	−	17825.2i	−0.398296	−	0.689869i
$875$	−15731.0	−	13199.9i	−0.607777	−	0.509986i
$876$	6814.96	+	6197.49i	0.262850	+	0.239034i
$877$	−3043.76	−	17262.0i	−0.117196	−	0.664650i	−0.985640	−	0.168862i	$-0.945991\pi$
$877$	−3043.76	−	17262.0i	−0.117196	−	0.664650i	0.868444	−	0.495787i	$-0.165120\pi$
$878$	−1000.80	−	5675.82i	−0.0384685	−	0.218166i
$879$	−10733.5	+	49297.8i	−0.411869	+	1.89166i
$880$	17153.3	+	14393.3i	0.657088	+	0.551362i
$881$	4803.61	+	8320.09i	0.183698	+	0.318174i	0.943137	−	0.332405i	$-0.107860\pi$
$881$	4803.61	+	8320.09i	0.183698	+	0.318174i	−0.759439	+	0.650578i	$0.774527\pi$
$882$	42569.6	+	41930.1i	1.62516	+	1.60075i
$883$	−10581.8	+	18328.2i	−0.403291	+	0.698521i	−0.994121	−	0.108275i	$-0.965467\pi$
$883$	−10581.8	+	18328.2i	−0.403291	+	0.698521i	0.590830	+	0.806796i	$0.298801\pi$
$884$	2462.55	−	896.295i	0.0936929	−	0.0341014i
$885$	42790.6	+	1706.09i	1.62530	+	0.0648016i
$886$	22911.3	−	19224.9i	0.868760	−	0.728977i
$887$	22199.9	+	8080.11i	0.840361	+	0.305866i	0.726104	−	0.687585i	$-0.241329\pi$
$887$	22199.9	+	8080.11i	0.840361	+	0.305866i	0.114257	+	0.993451i	$0.463551\pi$
$888$	770.394	+	5685.41i	0.0291134	+	0.214853i
$889$	68.8556	−	390.499i	0.00259768	−	0.0147322i
$890$	−22058.6			−0.830792
$891$	14666.8	+	2357.87i	0.551467	+	0.0886549i
$892$	440.185			0.0165230
$893$	−3252.23	+	18444.3i	−0.121872	+	0.691170i
$894$	−1003.04	−	7402.32i	−0.0375243	−	0.276925i
$895$	53038.2	+	19304.3i	1.98086	+	0.720975i
$896$	−43116.2	+	36178.8i	−1.60760	+	1.34894i
$897$	−22151.7	−	883.200i	−0.824551	−	0.0328753i
$898$	496.543	−	180.727i	0.0184519	−	0.00671596i
$899$	−113.615	+	196.786i	−0.00421497	+	0.00730055i
$900$	1186.52	−	4566.08i	0.0439451	−	0.169114i
$901$	−1884.07	−	3263.30i	−0.0696641	−	0.120662i
$902$	9505.26	+	7975.86i	0.350876	+	0.294420i
$903$	−12574.0	+	57751.0i	−0.463386	+	2.12828i
$904$	−1002.82	−	5687.25i	−0.0368951	−	0.209243i
$905$	−10719.1	−	60790.8i	−0.393717	−	2.23288i
$906$	−4450.96	−	4047.68i	−0.163216	−	0.148427i
$907$	−194.057	−	162.833i	−0.00710425	−	0.00596117i	0.639229	−	0.769017i	$-0.279254\pi$
$907$	−194.057	−	162.833i	−0.00710425	−	0.00596117i	−0.646333	+	0.763056i	$0.723698\pi$
$908$	−3238.46	−	5609.17i	−0.118361	−	0.205008i
$909$	11196.5	−	7966.83i	0.408542	−	0.290697i
$910$	−30298.2	+	52478.1i	−1.10371	+	1.91168i
$911$	11760.4	−	4280.42i	0.427704	−	0.155671i	−0.119194	−	0.992871i	$-0.538031\pi$
$911$	11760.4	−	4280.42i	0.427704	−	0.155671i	0.546897	+	0.837200i	$0.315809\pi$
$912$	−11534.7	−	21954.6i	−0.418806	−	0.797139i
$913$	−15973.6	+	13403.4i	−0.579024	+	0.485859i
$914$	21152.9	+	7699.01i	0.765508	+	0.278622i
$915$	−46453.7	−	19036.1i	−1.67837	−	0.687777i
$916$	−430.500	+	2441.49i	−0.0155285	+	0.0880667i
$917$	−31737.0			−1.14291
$918$	8977.22	+	9576.37i	0.322759	+	0.344300i
$919$	−30267.5			−1.08644			−0.543218	−	0.839592i	$-0.682794\pi$
$919$	−30267.5			−1.08644			−0.543218	+	0.839592i	$0.682794\pi$
$920$	4797.35	−	27207.1i	0.171917	−	0.974992i
$921$	−15827.4	+	12240.3i	−0.566267	+	0.437926i
$922$	−15952.9	−	5806.38i	−0.569827	−	0.207400i
$923$	14086.5	−	11820.0i	0.502342	−	0.421515i
$924$	−3952.04	+	6255.57i	−0.140706	+	0.222720i
$925$	−4493.43	+	1635.47i	−0.159722	+	0.0581341i
$926$	14920.6	−	25843.3i	0.529506	−	0.917131i
$927$	20081.1	−	29145.8i	0.711489	−	1.03266i
$928$	215.459	+	373.186i	0.00762153	+	0.0132009i
$929$	−3873.63	−	3250.36i	−0.136803	−	0.114791i	0.571819	−	0.820380i	$-0.306238\pi$
$929$	−3873.63	−	3250.36i	−0.136803	−	0.114791i	−0.708621	+	0.705589i	$0.750682\pi$
$930$	−11421.0	+	3648.59i	−0.402697	+	0.128647i
$931$	7503.25	+	42553.1i	0.264134	+	1.49798i
$932$	−1551.21	−	8797.37i	−0.0545190	−	0.309193i
$933$	33660.6	−	10753.3i	1.18113	−	0.377330i
$934$	4481.00	+	3760.00i	0.156984	+	0.131725i
$935$	−4285.22	−	7422.22i	−0.149884	−	0.259607i
$936$	−20596.3	−	1644.98i	−0.719241	−	0.0574445i
$937$	12701.0	−	21998.7i	0.442820	−	0.766987i	−0.555077	−	0.831799i	$-0.687311\pi$
$937$	12701.0	−	21998.7i	0.442820	−	0.766987i	0.997898	+	0.0648119i	$0.0206447\pi$
$938$	70598.9	−	25695.9i	2.45750	−	0.894457i
$939$	−9219.12	+	14592.7i	−0.320399	+	0.507150i
$940$	7168.35	−	6014.96i	0.248730	−	0.208709i
$941$	1241.48	+	451.861i	0.0430085	+	0.0156538i	0.363435	−	0.931620i	$-0.381604\pi$
$941$	1241.48	+	451.861i	0.0430085	+	0.0156538i	−0.320426	+	0.947273i	$0.603826\pi$
$942$	−28936.1	+	22377.9i	−1.00084	+	0.774004i
$943$	3436.79	−	19491.0i	0.118682	−	0.673081i
$944$	−44066.6			−1.51933
$945$	−64303.7	−	7724.24i	−2.21354	−	0.265894i
$946$	−22954.6			−0.788921
$947$	4471.82	−	25360.9i	0.153447	−	0.870242i	−0.806744	−	0.590900i	$-0.798773\pi$
$947$	4471.82	−	25360.9i	0.153447	−	0.870242i	0.960192	−	0.279342i	$-0.0901163\pi$
$948$	835.547	+	342.397i	0.0286258	+	0.0117305i
$949$	31596.1	+	11500.1i	1.08077	+	0.393369i
$950$	12247.7	−	10277.0i	0.418282	−	0.350980i
$951$	5270.17	+	10031.0i	0.179702	+	0.342039i
$952$	16505.0	−	6007.34i	0.561903	−	0.204516i
$953$	−19703.7	+	34127.9i	−0.669745	+	1.16003i	0.308231	+	0.951312i	$0.400263\pi$
$953$	−19703.7	+	34127.9i	−0.669745	+	1.16003i	−0.977975	+	0.208720i	$0.933070\pi$
$954$	−1047.21	−	11009.5i	−0.0355396	−	0.373632i
$955$	28732.0	+	49765.3i	0.973555	+	1.68625i
$956$	10215.9	+	8572.12i	0.345611	+	0.290002i
$957$	−352.687	−	320.732i	−0.0119130	−	0.0108336i
$958$	−6617.43	−	37529.3i	−0.223173	−	1.26568i
$959$	−3635.09	−	20615.6i	−0.122402	−	0.694174i
$960$	4880.74	−	22416.6i	0.164089	−	0.753640i
$961$	−20869.9	−	17511.9i	−0.700544	−	0.587826i
$962$	−3897.85	−	6751.27i	−0.130636	−	0.226268i
$963$	−29839.8	+	8238.07i	−0.998519	+	0.275668i
$964$	−5259.96	+	9110.51i	−0.175738	+	0.304388i
$965$	−28361.3	+	10322.7i	−0.946097	+	0.344351i
$966$	55266.8	+	2203.52i	1.84077	+	0.0733924i
$967$	24831.4	−	20836.0i	0.825775	−	0.692908i	−0.128542	−	0.991704i	$-0.541030\pi$
$967$	24831.4	−	20836.0i	0.825775	−	0.692908i	0.954317	+	0.298796i	$0.0965851\pi$
$968$	−15998.9	−	5823.12i	−0.531223	−	0.193349i
$969$	1274.58	+	9406.23i	0.0422553	+	0.311839i
$970$	10498.3	−	59539.1i	0.347507	−	1.97081i
$971$	−1324.42			−0.0437722			−0.0218861	−	0.999760i	$-0.506967\pi$
$971$	−1324.42			−0.0437722			−0.0218861	+	0.999760i	$0.506967\pi$
$972$	2619.81	+	7791.81i	0.0864509	+	0.257122i
$973$	91753.8			3.02312
$974$	−1241.10	+	7038.64i	−0.0408290	+	0.231553i
$975$	−2312.33	−	17064.7i	−0.0759525	−	0.560519i
$976$	48543.4	+	17668.3i	1.59204	+	0.579457i
$977$	−19239.2	+	16143.6i	−0.630005	+	0.528637i	−0.900931	−	0.433963i	$-0.857115\pi$
$977$	−19239.2	+	16143.6i	−0.630005	+	0.528637i	0.270925	+	0.962600i	$0.412670\pi$
$978$	1074.48	+	42.8402i	0.0351310	+	0.00140069i
$979$	−9239.03	+	3362.73i	−0.301614	+	0.109779i
$980$	10794.5	−	18696.7i	0.351856	−	0.609432i
$981$	−8473.85	+	2339.43i	−0.275789	+	0.0761390i
$982$	−29516.0	−	51123.2i	−0.959157	−	1.66131i
$983$	9426.29	+	7909.59i	0.305851	+	0.256640i	0.782775	−	0.622305i	$-0.213804\pi$
$983$	9426.29	+	7909.59i	0.305851	+	0.256640i	−0.476923	+	0.878945i	$0.658248\pi$
$984$	3924.27	−	18023.7i	0.127135	−	0.583917i
$985$	−2178.24	−	12353.4i	−0.0704613	−	0.399606i
$986$	−73.1461	−	414.832i	−0.00236252	−	0.0133985i
$987$	−37234.6	−	33861.0i	−1.20080	−	1.09200i
$988$	4260.66	+	3575.12i	0.137196	+	0.115121i
$989$	18306.8	+	31708.4i	0.588598	+	1.01948i
$990$	−2381.84	−	25040.5i	−0.0764644	−	0.803880i
$991$	−11532.2	+	19974.4i	−0.369660	+	0.640270i	−0.989512	−	0.144449i	$-0.953859\pi$
$991$	−11532.2	+	19974.4i	−0.369660	+	0.640270i	0.619852	+	0.784718i	$0.287192\pi$
$992$	4539.31	−	1652.17i	0.145286	−	0.0528796i
$993$	−12757.3	−	24281.8i	−0.407695	−	0.775992i
$994$	−35144.7	+	29489.9i	−1.12145	+	0.941010i
$995$	−12872.1	−	4685.05i	−0.410123	−	0.149273i
$996$	−10677.2	−	4375.40i	−0.339680	−	0.139197i
$997$	2993.18	−	16975.1i	0.0950801	−	0.539226i	−0.899643	−	0.436627i	$-0.856173\pi$
$997$	2993.18	−	16975.1i	0.0950801	−	0.539226i	0.994723	−	0.102599i	$-0.0327159\pi$
$998$	42950.4			1.36230
$999$	4996.90	−	6667.44i	0.158253	−	0.211160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.25.6	yes	48
3.2	odd	2		81.4.e.a.73.3		48
9.2	odd	6		243.4.e.a.55.6		48
9.4	even	3		243.4.e.c.136.6		48
9.5	odd	6		243.4.e.b.136.3		48
9.7	even	3		243.4.e.d.55.3		48
27.4	even	9		243.4.e.c.109.6		48
27.5	odd	18		243.4.e.a.190.6		48
27.11	odd	18		729.4.a.c.1.6		24
27.13	even	9	inner	27.4.e.a.13.6	✓	48
27.14	odd	18		81.4.e.a.10.3		48
27.16	even	9		729.4.a.d.1.19		24
27.22	even	9		243.4.e.d.190.3		48
27.23	odd	18		243.4.e.b.109.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.6	✓	48	27.13	even	9	inner
27.4.e.a.25.6	yes	48	1.1	even	1	trivial
81.4.e.a.10.3		48	27.14	odd	18
81.4.e.a.73.3		48	3.2	odd	2
243.4.e.a.55.6		48	9.2	odd	6
243.4.e.a.190.6		48	27.5	odd	18
243.4.e.b.109.3		48	27.23	odd	18
243.4.e.b.136.3		48	9.5	odd	6
243.4.e.c.109.6		48	27.4	even	9
243.4.e.c.136.6		48	9.4	even	3
243.4.e.d.55.3		48	9.7	even	3
243.4.e.d.190.3		48	27.22	even	9
729.4.a.c.1.6		24	27.11	odd	18
729.4.a.d.1.19		24	27.16	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.553775 - 3.14062i) q^{2} +(-0.697722 - 5.14910i) q^{3} +(-2.03925 - 0.742228i) q^{4} +(-10.9819 + 9.21490i) q^{5} +(-16.5577 - 0.660166i) q^{6} +(30.2596 - 11.0136i) q^{7} +(9.29592 - 16.1010i) q^{8} +(-26.0264 + 7.18527i) q^{9} +O(q^{10})\)	\(q+(0.553775 - 3.14062i) q^{2} +(-0.697722 - 5.14910i) q^{3} +(-2.03925 - 0.742228i) q^{4} +(-10.9819 + 9.21490i) q^{5} +(-16.5577 - 0.660166i) q^{6} +(30.2596 - 11.0136i) q^{7} +(9.29592 - 16.1010i) q^{8} +(-26.0264 + 7.18527i) q^{9} +(22.8590 + 39.5929i) q^{10} +(15.6100 + 13.0984i) q^{11} +(-2.39897 + 11.0182i) q^{12} +(7.14749 + 40.5354i) q^{13} +(-17.8325 - 101.133i) q^{14} +(55.1107 + 50.1174i) q^{15} +(-58.7185 - 49.2707i) q^{16} +(14.6690 + 25.4075i) q^{17} +(8.15342 + 85.7178i) q^{18} +(-31.1332 + 53.9243i) q^{19} +(29.2344 - 10.6405i) q^{20} +(-77.8229 - 148.125i) q^{21} +(49.7814 - 41.7715i) q^{22} +(-97.4029 - 35.4518i) q^{23} +(-89.3915 - 36.6315i) q^{24} +(13.9815 - 79.2930i) q^{25} +131.264 q^{26} +(55.1568 + 128.999i) q^{27} -69.8817 q^{28} +(0.781803 - 4.43383i) q^{29} +(187.918 - 145.328i) q^{30} +(-47.4267 - 17.2619i) q^{31} +(-73.3198 + 61.5226i) q^{32} +(56.5533 - 89.5165i) q^{33} +(87.9184 - 31.9997i) q^{34} +(-230.819 + 399.790i) q^{35} +(58.4075 + 4.66490i) q^{36} +(-29.6947 - 51.4327i) q^{37} +(152.115 + 127.639i) q^{38} +(203.734 - 65.0855i) q^{39} +(46.2824 + 262.480i) q^{40} +(33.1564 + 188.039i) q^{41} +(-508.301 + 162.384i) q^{42} +(-270.590 - 227.052i) q^{43} +(-22.1108 - 38.2971i) q^{44} +(219.607 - 318.738i) q^{45} +(-165.280 + 286.273i) q^{46} +(282.646 - 102.875i) q^{47} +(-212.730 + 336.724i) q^{48} +(531.593 - 446.059i) q^{49} +(-241.286 - 87.8210i) q^{50} +(120.591 - 93.2594i) q^{51} +(15.5110 - 87.9671i) q^{52} -128.439 q^{53} +(435.680 - 101.790i) q^{54} -292.128 q^{55} +(103.961 - 589.592i) q^{56} +(299.384 + 122.684i) q^{57} +(-13.4920 - 4.91069i) q^{58} +(440.395 - 369.535i) q^{59} +(-75.1862 - 143.107i) q^{60} +(-633.299 + 230.502i) q^{61} +(-80.4767 + 139.390i) q^{62} +(-708.413 + 504.068i) q^{63} +(-153.990 - 266.719i) q^{64} +(-452.023 - 379.292i) q^{65} +(-249.819 - 227.184i) q^{66} +(127.040 + 720.481i) q^{67} +(-11.0557 - 62.7000i) q^{68} +(-114.584 + 526.272i) q^{69} +(1127.76 + 946.306i) q^{70} +(-223.375 - 386.897i) q^{71} +(-126.249 + 485.844i) q^{72} +(408.446 - 707.450i) q^{73} +(-177.974 + 64.7774i) q^{74} +(-418.042 - 16.6676i) q^{75} +(103.513 - 86.8575i) q^{76} +(616.614 + 224.429i) q^{77} +(-91.5859 - 675.892i) q^{78} +(13.9053 - 78.8610i) q^{79} +1098.86 q^{80} +(625.744 - 374.013i) q^{81} +608.920 q^{82} +(-177.693 + 1007.75i) q^{83} +(48.7580 + 359.828i) q^{84} +(-395.220 - 143.848i) q^{85} +(-862.928 + 724.083i) q^{86} +(-23.3757 - 0.932002i) q^{87} +(356.006 - 129.576i) q^{88} +(-241.246 + 417.851i) q^{89} +(-879.421 - 866.211i) q^{90} +(662.722 + 1147.87i) q^{91} +(172.316 + 144.590i) q^{92} +(-55.7926 + 256.249i) q^{93} +(-166.567 - 944.651i) q^{94} +(-155.006 - 879.080i) q^{95} +(367.942 + 334.605i) q^{96} +(-1013.02 - 850.025i) q^{97} +(-1106.52 - 1916.55i) q^{98} +(-500.387 - 228.741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

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