LMFDB - Embedded newform 41.6.f.a.4.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,6,Mod(4,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("41.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	41.f (of order $10$, 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:	$6.57573661233$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	41.4
Dual form			41.6.f.a.31.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.81801 - 2.04741i) q^{2} +0.415051i q^{3} +(-6.13922 + 18.8946i) q^{4} +(17.2643 - 53.1340i) q^{5} +(0.849777 + 1.16962i) q^{6} +(122.097 - 168.052i) q^{7} +(55.8288 + 171.823i) q^{8} +242.828 q^{9} +O(q^{10})$	\(q+(2.81801 - 2.04741i) q^{2} +0.415051i q^{3} +(-6.13922 + 18.8946i) q^{4} +(17.2643 - 53.1340i) q^{5} +(0.849777 + 1.16962i) q^{6} +(122.097 - 168.052i) q^{7} +(55.8288 + 171.823i) q^{8} +242.828 q^{9} +(-60.1359 - 185.079i) q^{10} +(167.198 - 54.3260i) q^{11} +(-7.84221 - 2.54809i) q^{12} +(-180.969 - 249.083i) q^{13} -723.556i q^{14} +(22.0533 + 7.16555i) q^{15} +(-5.20817 - 3.78396i) q^{16} +(-298.457 + 96.9747i) q^{17} +(684.291 - 497.167i) q^{18} +(-390.378 + 537.309i) q^{19} +(897.955 + 652.403i) q^{20} +(69.7502 + 50.6765i) q^{21} +(359.939 - 495.414i) q^{22} +(-676.789 + 491.716i) q^{23} +(-71.3154 + 23.1718i) q^{24} +(3.01326 + 2.18926i) q^{25} +(-1019.95 - 331.401i) q^{26} +201.643i q^{27} +(2425.70 + 3338.69i) q^{28} +(-3550.05 - 1153.48i) q^{29} +(76.8172 - 24.9594i) q^{30} +(1850.08 + 5693.96i) q^{31} -5803.73 q^{32} +(22.5480 + 69.3957i) q^{33} +(-642.510 + 884.339i) q^{34} +(-6821.37 - 9388.81i) q^{35} +(-1490.77 + 4588.13i) q^{36} +(-625.563 + 1925.29i) q^{37} +2313.40i q^{38} +(103.382 - 75.1115i) q^{39} +10093.5 q^{40} +(2311.96 + 10512.4i) q^{41} +300.312 q^{42} +(-886.025 + 643.735i) q^{43} +3492.66i q^{44} +(4192.25 - 12902.4i) q^{45} +(-900.457 + 2771.32i) q^{46} +(-7311.19 - 10063.0i) q^{47} +(1.57053 - 2.16165i) q^{48} +(-8140.21 - 25053.0i) q^{49} +12.9737 q^{50} +(-40.2494 - 123.875i) q^{51} +(5817.33 - 1890.17i) q^{52} +(3187.63 + 1035.72i) q^{53} +(412.845 + 568.232i) q^{54} -9821.80i q^{55} +(35691.8 + 11597.0i) q^{56} +(-223.010 - 162.026i) q^{57} +(-12365.7 + 4017.87i) q^{58} +(30281.7 - 22000.9i) q^{59} +(-270.780 + 372.697i) q^{60} +(40950.8 + 29752.5i) q^{61} +(16871.4 + 12257.8i) q^{62} +(29648.6 - 40807.8i) q^{63} +(-16188.3 + 11761.5i) q^{64} +(-16359.1 + 5315.39i) q^{65} +(205.622 + 149.393i) q^{66} +(-57861.5 - 18800.3i) q^{67} -6234.58i q^{68} +(-204.087 - 280.902i) q^{69} +(-38445.4 - 12491.7i) q^{70} +(-46684.4 + 15168.7i) q^{71} +(13556.8 + 41723.5i) q^{72} -63097.3 q^{73} +(2179.00 + 6706.26i) q^{74} +(-0.908655 + 1.25066i) q^{75} +(-7755.61 - 10674.7i) q^{76} +(11284.8 - 34731.1i) q^{77} +(137.548 - 423.330i) q^{78} +96125.9i q^{79} +(-290.972 + 211.404i) q^{80} +58923.4 q^{81} +(28038.3 + 24890.6i) q^{82} -48732.5 q^{83} +(-1385.72 + 1006.79i) q^{84} +17532.4i q^{85} +(-1178.84 + 3628.11i) q^{86} +(478.753 - 1473.45i) q^{87} +(18668.9 + 25695.6i) q^{88} +(-25348.6 + 34889.3i) q^{89} +(-14602.7 - 44942.3i) q^{90} -63954.8 q^{91} +(-5135.81 - 15806.4i) q^{92} +(-2363.28 + 767.876i) q^{93} +(-41206.0 - 13388.7i) q^{94} +(21809.8 + 30018.6i) q^{95} -2408.84i q^{96} +(95091.9 + 30897.2i) q^{97} +(-74232.9 - 53933.3i) q^{98} +(40600.4 - 13191.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 11 q^{2} - 227 q^{4} - 37 q^{5} + 135 q^{6} - 5 q^{7} - 1208 q^{8} - 4342 q^{9}+O(q^{10}) $ 64 * q - 11 * q^2 - 227 * q^4 - 37 * q^5 + 135 * q^6 - 5 * q^7 - 1208 * q^8 - 4342 * q^9	\( 64 q - 11 q^{2} - 227 q^{4} - 37 q^{5} + 135 q^{6} - 5 q^{7} - 1208 q^{8} - 4342 q^{9} - 1688 q^{10} + 1140 q^{11} + 1210 q^{12} - 5 q^{13} + 2200 q^{15} + 53 q^{16} - 1810 q^{17} + 820 q^{18} - 2240 q^{19} + 720 q^{20} - 3785 q^{21} + 4715 q^{22} + 7191 q^{23} - 17510 q^{24} - 13567 q^{25} + 11935 q^{26} - 2570 q^{28} + 37395 q^{29} - 17790 q^{30} + 8354 q^{31} + 53228 q^{32} + 10733 q^{33} - 39935 q^{34} + 18590 q^{35} + 56822 q^{36} + 42392 q^{37} - 43324 q^{39} + 16462 q^{40} + 25547 q^{41} - 82584 q^{42} + 10871 q^{43} + 44293 q^{45} - 31176 q^{46} - 12920 q^{47} - 61525 q^{48} - 29425 q^{49} + 134100 q^{50} - 301 q^{51} - 56955 q^{52} - 123130 q^{53} - 128450 q^{54} - 219835 q^{56} - 72730 q^{57} - 16250 q^{58} + 101479 q^{59} - 349500 q^{60} - 125391 q^{61} + 27700 q^{62} + 46335 q^{63} + 405298 q^{64} - 209500 q^{65} - 223598 q^{66} - 16820 q^{67} + 318800 q^{69} + 701815 q^{70} - 14890 q^{71} + 554619 q^{72} + 31416 q^{73} - 140667 q^{74} + 88055 q^{75} + 332310 q^{76} - 15988 q^{77} - 241076 q^{78} + 12169 q^{80} - 177268 q^{81} + 159925 q^{82} - 119808 q^{83} - 371258 q^{84} + 380419 q^{86} - 552916 q^{87} - 370060 q^{88} + 160175 q^{89} + 138120 q^{90} + 997890 q^{91} + 146175 q^{92} + 363110 q^{93} - 316690 q^{94} - 418865 q^{95} + 22160 q^{97} + 630282 q^{98} - 339895 q^{99}+O(q^{100}) \) 64 * q - 11 * q^2 - 227 * q^4 - 37 * q^5 + 135 * q^6 - 5 * q^7 - 1208 * q^8 - 4342 * q^9 - 1688 * q^10 + 1140 * q^11 + 1210 * q^12 - 5 * q^13 + 2200 * q^15 + 53 * q^16 - 1810 * q^17 + 820 * q^18 - 2240 * q^19 + 720 * q^20 - 3785 * q^21 + 4715 * q^22 + 7191 * q^23 - 17510 * q^24 - 13567 * q^25 + 11935 * q^26 - 2570 * q^28 + 37395 * q^29 - 17790 * q^30 + 8354 * q^31 + 53228 * q^32 + 10733 * q^33 - 39935 * q^34 + 18590 * q^35 + 56822 * q^36 + 42392 * q^37 - 43324 * q^39 + 16462 * q^40 + 25547 * q^41 - 82584 * q^42 + 10871 * q^43 + 44293 * q^45 - 31176 * q^46 - 12920 * q^47 - 61525 * q^48 - 29425 * q^49 + 134100 * q^50 - 301 * q^51 - 56955 * q^52 - 123130 * q^53 - 128450 * q^54 - 219835 * q^56 - 72730 * q^57 - 16250 * q^58 + 101479 * q^59 - 349500 * q^60 - 125391 * q^61 + 27700 * q^62 + 46335 * q^63 + 405298 * q^64 - 209500 * q^65 - 223598 * q^66 - 16820 * q^67 + 318800 * q^69 + 701815 * q^70 - 14890 * q^71 + 554619 * q^72 + 31416 * q^73 - 140667 * q^74 + 88055 * q^75 + 332310 * q^76 - 15988 * q^77 - 241076 * q^78 + 12169 * q^80 - 177268 * q^81 + 159925 * q^82 - 119808 * q^83 - 371258 * q^84 + 380419 * q^86 - 552916 * q^87 - 370060 * q^88 + 160175 * q^89 + 138120 * q^90 + 997890 * q^91 + 146175 * q^92 + 363110 * q^93 - 316690 * q^94 - 418865 * q^95 + 22160 * q^97 + 630282 * q^98 - 339895 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	2.81801	−	2.04741i	0.498159	−	0.361934i	−0.310155	−	0.950686i	$-0.600381\pi$
$2$	2.81801	−	2.04741i	0.498159	−	0.361934i	0.808313	+	0.588753i	$0.200381\pi$
$3$			0.415051i			0.0266255i	0.999911	+	0.0133128i	$0.00423771\pi$
$3$			0.415051i			0.0266255i	−0.999911	+	0.0133128i	$0.995762\pi$
$4$	−6.13922	+	18.8946i	−0.191851	+	0.590456i
$5$	17.2643	−	53.1340i	0.308833	−	0.950490i	−0.669386	−	0.742915i	$-0.733443\pi$
$5$	17.2643	−	53.1340i	0.308833	−	0.950490i	0.978219	−	0.207575i	$-0.0665571\pi$
$6$	0.849777	+	1.16962i	0.00963666	+	0.0132637i
$7$	122.097	−	168.052i	0.941804	−	1.29628i	−0.0132696	−	0.999912i	$-0.504224\pi$
$7$	122.097	−	168.052i	0.941804	−	1.29628i	0.955073	−	0.296370i	$-0.0957760\pi$
$8$	55.8288	+	171.823i	0.308413	+	0.949199i
$9$	242.828			0.999291
$10$	−60.1359	−	185.079i	−0.190166	−	0.585272i
$11$	167.198	−	54.3260i	0.416629	−	0.135371i	−0.0931985	−	0.995648i	$-0.529709\pi$
$11$	167.198	−	54.3260i	0.416629	−	0.135371i	0.509828	+	0.860276i	$0.329709\pi$
$12$	−7.84221	−	2.54809i	−0.0157212	−	0.00510812i
$13$	−180.969	−	249.083i	−0.296993	−	0.408776i	0.634277	−	0.773106i	$-0.281298\pi$
$13$	−180.969	−	249.083i	−0.296993	−	0.408776i	−0.931270	+	0.364330i	$0.881298\pi$
$14$		−	723.556i		−	0.986624i
$15$	22.0533	+	7.16555i	0.0253073	+	0.00822283i
$16$	−5.20817	−	3.78396i	−0.00508611	−	0.00369527i
$17$	−298.457	+	96.9747i	−0.250472	+	0.0813834i	−0.431562	−	0.902083i	$-0.642038\pi$
$17$	−298.457	+	96.9747i	−0.250472	+	0.0813834i	0.181090	+	0.983467i	$0.442038\pi$
$18$	684.291	−	497.167i	0.497806	−	0.361677i
$19$	−390.378	+	537.309i	−0.248085	+	0.341460i	−0.914840	−	0.403818i	$-0.867683\pi$
$19$	−390.378	+	537.309i	−0.248085	+	0.341460i	0.666754	+	0.745278i	$0.267683\pi$
$20$	897.955	+	652.403i	0.501972	+	0.364704i
$21$	69.7502	+	50.6765i	0.0345141	+	0.0250760i
$22$	359.939	−	495.414i	0.158552	−	0.218228i
$23$	−676.789	+	491.716i	−0.266768	+	0.193818i	−0.713125	−	0.701036i	$-0.752721\pi$
$23$	−676.789	+	491.716i	−0.266768	+	0.193818i	0.446357	+	0.894855i	$0.352721\pi$
$24$	−71.3154	+	23.1718i	−0.0252729	+	0.00821166i
$25$	3.01326	+	2.18926i	0.000964244	+	0.000700564i
$26$	−1019.95	−	331.401i	−0.295900	−	0.0961437i
$27$			201.643i			0.0532321i
$28$	2425.70	+	3338.69i	0.584711	+	0.804786i
$29$	−3550.05	−	1153.48i	−0.783861	−	0.254692i	−0.110373	−	0.993890i	$-0.535205\pi$
$29$	−3550.05	−	1153.48i	−0.783861	−	0.254692i	−0.673488	+	0.739198i	$0.735205\pi$
$30$	76.8172	−	24.9594i	0.0155832	−	0.00506327i
$31$	1850.08	+	5693.96i	0.345769	+	1.06417i	0.961171	+	0.275954i	$0.0889938\pi$
$31$	1850.08	+	5693.96i	0.345769	+	1.06417i	−0.615402	+	0.788214i	$0.711006\pi$
$32$	−5803.73			−1.00192
$33$	22.5480	+	69.3957i	0.00360432	+	0.0110930i
$34$	−642.510	+	884.339i	−0.0953196	+	0.131196i
$35$	−6821.37	−	9388.81i	−0.941242	−	1.29551i
$36$	−1490.77	+	4588.13i	−0.191715	+	0.590037i
$37$	−625.563	+	1925.29i	−0.0751220	+	0.231202i	−0.981566	−	0.191125i	$-0.938786\pi$
$37$	−625.563	+	1925.29i	−0.0751220	+	0.231202i	0.906444	+	0.422327i	$0.138786\pi$
$38$			2313.40i			0.259892i
$39$	103.382	−	75.1115i	0.0108839	−	0.00790760i
$40$	10093.5			0.997452
$41$	2311.96	+	10512.4i	0.214793	+	0.976660i
$41$	2311.96	+	10512.4i	0.214793	+	0.976660i
$42$	300.312			0.0262694
$43$	−886.025	+	643.735i	−0.0730760	+	0.0530928i	−0.623723	−	0.781645i	$-0.714381\pi$
$43$	−886.025	+	643.735i	−0.0730760	+	0.0530928i	0.550647	+	0.834738i	$0.314381\pi$
$44$			3492.66i			0.271972i
$45$	4192.25	−	12902.4i	0.308614	−	0.949816i
$46$	−900.457	+	2771.32i	−0.0627435	+	0.193105i
$47$	−7311.19	−	10063.0i	−0.482773	−	0.664481i	0.496261	−	0.868173i	$-0.334706\pi$
$47$	−7311.19	−	10063.0i	−0.482773	−	0.664481i	−0.979035	+	0.203692i	$0.934706\pi$
$48$	1.57053	−	2.16165i	9.83885e−5	−	0.000135420i
$49$	−8140.21	−	25053.0i	−0.484335	−	1.49063i
$50$	12.9737			0.000733904
$51$	−40.2494	−	123.875i	−0.00216687	−	0.00666895i
$52$	5817.33	−	1890.17i	0.298343	−	0.0969375i
$53$	3187.63	+	1035.72i	0.155876	+	0.0506470i	0.385915	−	0.922534i	$-0.373886\pi$
$53$	3187.63	+	1035.72i	0.155876	+	0.0506470i	−0.230040	+	0.973181i	$0.573886\pi$
$54$	412.845	+	568.232i	0.0192665	+	0.0265181i
$55$		−	9821.80i		−	0.437809i
$56$	35691.8	+	11597.0i	1.52089	+	0.494168i
$57$	−223.010	−	162.026i	−0.00909154	−	0.00660539i
$58$	−12365.7	+	4017.87i	−0.482669	+	0.156829i
$59$	30281.7	−	22000.9i	1.13253	−	0.822831i	0.146469	−	0.989215i	$-0.453209\pi$
$59$	30281.7	−	22000.9i	1.13253	−	0.822831i	0.986061	+	0.166384i	$0.0532092\pi$
$60$	−270.780	+	372.697i	−0.00971043	+	0.0133653i
$61$	40950.8	+	29752.5i	1.40909	+	1.02376i	0.993455	+	0.114227i	$0.0364393\pi$
$61$	40950.8	+	29752.5i	1.40909	+	1.02376i	0.415631	+	0.909533i	$0.363561\pi$
$62$	16871.4	+	12257.8i	0.557406	+	0.404979i
$63$	29648.6	−	40807.8i	0.941136	−	1.29536i
$64$	−16188.3	+	11761.5i	−0.494028	+	0.358932i
$65$	−16359.1	+	5315.39i	−0.480259	+	0.156046i
$66$	205.622	+	149.393i	0.00581044	+	0.00422153i
$67$	−57861.5	−	18800.3i	−1.57472	−	0.511656i	−0.614028	−	0.789284i	$-0.710452\pi$
$67$	−57861.5	−	18800.3i	−1.57472	−	0.511656i	−0.960689	+	0.277628i	$0.910452\pi$
$68$		−	6234.58i		−	0.163506i
$69$	−204.087	−	280.902i	−0.00516051	−	0.00710283i
$70$	−38445.4	−	12491.7i	−0.937776	−	0.304702i
$71$	−46684.4	+	15168.7i	−1.09907	+	0.357110i	−0.801745	−	0.597666i	$-0.796095\pi$
$71$	−46684.4	+	15168.7i	−1.09907	+	0.357110i	−0.297326	+	0.954776i	$0.596095\pi$
$72$	13556.8	+	41723.5i	0.308195	+	0.948526i
$73$	−63097.3			−1.38581			−0.692905	−	0.721029i	$-0.743670\pi$
$73$	−63097.3			−1.38581			−0.692905	+	0.721029i	$0.743670\pi$
$74$	2179.00	+	6706.26i	0.0462570	+	0.142364i
$75$	−0.908655	+	1.25066i	−1.86529e−5	+	2.56735e-5i
$76$	−7755.61	−	10674.7i	−0.154022	−	0.211993i
$77$	11284.8	−	34731.1i	0.216904	−	0.667562i
$78$	137.548	−	423.330i	0.00255987	−	0.00787848i
$79$			96125.9i			1.73290i	0.499267	+	0.866448i	$0.333603\pi$
$79$			96125.9i			1.73290i	−0.499267	+	0.866448i	$0.666397\pi$
$80$	−290.972	+	211.404i	−0.00508307	+	0.00369307i
$81$	58923.4			0.997874
$82$	28038.3	+	24890.6i	0.460487	+	0.408791i
$83$	−48732.5			−0.776468			−0.388234	−	0.921561i	$-0.626915\pi$
$83$	−48732.5			−0.776468			−0.388234	+	0.921561i	$0.626915\pi$
$84$	−1385.72	+	1006.79i	−0.0214278	+	0.0155682i
$85$			17532.4i			0.263205i
$86$	−1178.84	+	3628.11i	−0.0171874	+	0.0528973i
$87$	478.753	−	1473.45i	0.00678130	−	0.0208707i
$88$	18668.9	+	25695.6i	0.256988	+	0.353714i
$89$	−25348.6	+	34889.3i	−0.339217	+	0.466893i	−0.944213	−	0.329336i	$-0.893175\pi$
$89$	−25348.6	+	34889.3i	−0.339217	+	0.466893i	0.604995	+	0.796229i	$0.293175\pi$
$90$	−14602.7	−	44942.3i	−0.190031	−	0.584857i
$91$	−63954.8			−0.809599
$92$	−5135.81	−	15806.4i	−0.0632615	−	0.194699i
$93$	−2363.28	+	767.876i	−0.0283340	+	0.00920627i
$94$	−41206.0	−	13388.7i	−0.480996	−	0.156285i
$95$	21809.8	+	30018.6i	0.247937	+	0.341256i
$96$		−	2408.84i		−	0.0266766i
$97$	95091.9	+	30897.2i	1.02616	+	0.333419i	0.773270	−	0.634077i	$-0.218620\pi$
$97$	95091.9	+	30897.2i	1.02616	+	0.333419i	0.252888	+	0.967496i	$0.418620\pi$
$98$	−74232.9	−	53933.3i	−0.780784	−	0.567273i
$99$	40600.4	−	13191.9i	0.416334	−	0.135275i
$100$	−59.8643	+	43.4940i	−0.000598643	+	0.000434940i
$101$	93848.1	−	129171.i	0.915423	−	1.25997i	−0.0498574	−	0.998756i	$-0.515877\pi$
$101$	93848.1	−	129171.i	0.915423	−	1.25997i	0.965281	−	0.261215i	$-0.0841233\pi$
$102$	−367.045	−	266.674i	−0.00349317	−	0.00253793i
$103$	83327.1	+	60540.7i	0.773915	+	0.562282i	0.903146	−	0.429333i	$-0.141251\pi$
$103$	83327.1	+	60540.7i	0.773915	+	0.562282i	−0.129232	+	0.991614i	$0.541251\pi$
$104$	32695.0	−	45000.8i	0.296413	−	0.407978i
$105$	3896.83	−	2831.21i	0.0344936	−	0.0250610i
$106$	11103.3	−	3607.69i	0.0959816	−	0.0311863i
$107$	2906.94	+	2112.02i	0.0245458	+	0.0178335i	0.599990	−	0.800007i	$-0.295171\pi$
$107$	2906.94	+	2112.02i	0.0245458	+	0.0178335i	−0.575445	+	0.817841i	$0.695171\pi$
$108$	−3809.96	−	1237.93i	−0.0314312	−	0.0102126i
$109$			21031.3i			0.169551i	0.996400	+	0.0847756i	$0.0270173\pi$
$109$			21031.3i			0.169551i	−0.996400	+	0.0847756i	$0.972983\pi$
$110$	−20109.2	−	27678.0i	−0.158458	−	0.218098i
$111$	−799.091	−	259.640i	−0.00615586	−	0.00200016i
$112$	−1271.81	+	413.235i	−0.00958023	+	0.00311280i
$113$	−11252.6	−	34632.1i	−0.0829007	−	0.255142i	0.901011	−	0.433795i	$-0.142826\pi$
$113$	−11252.6	−	34632.1i	−0.0829007	−	0.255142i	−0.983912	+	0.178653i	$0.942826\pi$
$114$	−960.179			−0.00691974
$115$	14442.6	+	44449.6i	0.101836	+	0.313418i
$116$	43589.1	−	59995.2i	0.300769	−	0.413973i
$117$	−43944.4	−	60484.3i	−0.296783	−	0.408487i
$118$	40289.3	−	123998.i	0.266369	−	0.819801i
$119$	−20144.0	+	61996.8i	−0.130400	+	0.401330i
$120$			4189.31i			0.0265577i
$121$	−105289.	+	76497.0i	−0.653762	+	0.474986i
$122$	176315.			1.07248
$123$	−4363.19	+	959.581i	−0.0260041	+	0.00571898i
$124$	−118943.			−0.694680
$125$	141414.	−	102743.i	0.809498	−	0.588135i
$126$		−	175699.i		−	0.985925i
$127$	−37685.5	+	115984.i	−0.207331	+	0.638100i	0.792278	+	0.610160i	$0.208895\pi$
$127$	−37685.5	+	115984.i	−0.207331	+	0.638100i	−0.999610	+	0.0279404i	$0.991105\pi$
$128$	35852.1	−	110341.i	0.193415	−	0.595270i
$129$	−267.183	−	367.745i	−0.00141362	−	0.00194569i
$130$	−35217.3	+	48472.5i	−0.182767	+	0.251557i
$131$	86826.4	+	267224.i	0.442052	+	1.36050i	0.885684	+	0.464288i	$0.153690\pi$
$131$	86826.4	+	267224.i	0.442052	+	1.36050i	−0.443632	+	0.896209i	$0.646310\pi$
$132$	−1449.63			−0.00724140
$133$	42632.0	+	131208.i	0.208981	+	0.643177i
$134$	−201546.	+	65486.3i	−0.969644	+	0.315057i
$135$	10714.1	+	3481.22i	0.0505966	+	0.0164398i
$136$	−33325.0	−	45867.9i	−0.154498	−	0.212648i
$137$		−	118997.i		−	0.541671i	−0.962626	−	0.270835i	$-0.912700\pi$
$137$		−	118997.i		−	0.541671i	0.962626	−	0.270835i	$-0.0872999\pi$
$138$	−1150.24	−	373.735i	−0.00514151	−	0.00167058i
$139$	−284986.	−	207055.i	−1.25109	−	0.908967i	−0.252801	−	0.967518i	$-0.581352\pi$
$139$	−284986.	−	207055.i	−1.25109	−	0.908967i	−0.998284	+	0.0585514i	$0.981352\pi$
$140$	219276.	−	71247.0i	0.945519	−	0.307218i
$141$	4176.65	−	3034.51i	0.0176921	−	0.0128541i
$142$	−100501.	+	138327.i	−0.418262	+	0.575688i
$143$	−43789.4	−	31814.9i	−0.179073	−	0.130104i
$144$	−1264.69	−	918.850i	−0.00508250	−	0.00369265i
$145$	−122578.	+	168714.i	−0.484164	+	0.666395i
$146$	−177809.	+	129186.i	−0.690354	+	0.501571i
$147$	10398.3	−	3378.60i	0.0396887	−	0.0128957i
$148$	−32537.0	−	23639.5i	−0.122102	−	0.0887124i
$149$	452531.	+	147036.i	1.66987	+	0.542574i	0.982904	−	0.184117i	$-0.0589425\pi$
$149$	452531.	+	147036.i	1.66987	+	0.542574i	0.686965	+	0.726690i	$0.258942\pi$
$150$			5.38475i			1.95406e-5i
$151$	52130.6	+	71751.6i	0.186059	+	0.256088i	0.891849	−	0.452333i	$-0.149408\pi$
$151$	52130.6	+	71751.6i	0.186059	+	0.256088i	−0.705790	+	0.708421i	$0.749408\pi$
$152$	−114116.	−	37078.7i	−0.400626	−	0.130171i
$153$	−72473.7	+	23548.1i	−0.250295	+	0.0813257i
$154$	−39307.9	−	120977.i	−0.133560	−	0.411057i
$155$	334483.			1.11827
$156$	784.514	+	2414.49i	0.00258101	+	0.00794353i
$157$	−71259.7	+	98080.6i	−0.230725	+	0.317566i	−0.908645	−	0.417570i	$-0.862882\pi$
$157$	−71259.7	+	98080.6i	−0.230725	+	0.317566i	0.677919	+	0.735136i	$0.262882\pi$
$158$	196809.	+	270884.i	0.627193	+	0.863257i
$159$	−429.878	+	1323.03i	−0.00134850	+	0.00415027i
$160$	−100197.	+	308375.i	−0.309425	+	0.952312i
$161$			173773.i			0.528345i
$162$	166047.	−	120640.i	0.497100	−	0.361164i
$163$	−634971.			−1.87191			−0.935955	−	0.352118i	$-0.885461\pi$
$163$	−634971.			−1.87191			−0.935955	+	0.352118i	$0.885461\pi$
$164$	−212822.	−	20854.6i	−0.617883	−	0.0605468i
$165$	4076.54			0.0116569
$166$	−137329.	+	99775.2i	−0.386804	+	0.281030i
$167$		−	620138.i		−	1.72067i	−0.509731	−	0.860334i	$-0.670255\pi$
$167$		−	620138.i		−	1.72067i	0.509731	−	0.860334i	$-0.329745\pi$
$168$	−4813.33	+	14813.9i	−0.0131575	+	0.0404946i
$169$	85443.4	−	262968.i	0.230124	−	0.708249i
$170$	35896.0	+	49406.6i	0.0952628	+	0.131118i
$171$	−94794.5	+	130473.i	−0.247909	+	0.341218i
$172$	−6723.60	−	20693.1i	−0.0173293	−	0.0533341i
$173$	49716.4			0.126294			0.0631472	−	0.998004i	$-0.479886\pi$
$173$	49716.4			0.126294			0.0631472	+	0.998004i	$0.479886\pi$
$174$	−1667.62	−	5132.40i	−0.00417564	−	0.0128513i
$175$	735.822	−	239.083i	0.00181626	−	0.000590138i
$176$	−1076.36	−	349.732i	−0.00261925	−	0.000851047i
$177$	9131.49	+	12568.4i	0.0219083	+	0.0301542i
$178$			150217.i			0.355361i
$179$	−666658.	−	216610.i	−1.55514	−	0.505297i	−0.599638	−	0.800271i	$-0.704689\pi$
$179$	−666658.	−	216610.i	−1.55514	−	0.505297i	−0.955505	+	0.294975i	$0.904689\pi$
$180$	218048.	+	158421.i	0.501616	+	0.364446i
$181$	716439.	−	232785.i	1.62548	−	0.528152i	0.652256	−	0.757998i	$-0.273823\pi$
$181$	716439.	−	232785.i	1.62548	−	0.528152i	0.973227	+	0.229847i	$0.0738225\pi$
$182$	−180225.	+	130941.i	−0.403309	+	0.293021i
$183$	−12348.8	+	16996.6i	−0.0272581	+	0.0375176i
$184$	−122273.	−	88836.2i	−0.266247	−	0.193440i
$185$	91498.2	+	66477.3i	0.196555	+	0.142805i
$186$	−5087.60	+	7002.48i	−0.0107828	+	0.0148412i
$187$	−44633.3	+	32428.0i	−0.0933372	+	0.0678134i
$188$	235021.	−	76363.0i	0.484967	−	0.157575i
$189$	33886.6	+	24620.0i	0.0690038	+	0.0501342i
$190$	122920.	+	39939.2i	0.247024	+	0.0802631i
$191$		−	155480.i		−	0.308383i	−0.988041	−	0.154192i	$-0.950723\pi$
$191$		−	155480.i		−	0.308383i	0.988041	−	0.154192i	$-0.0492773\pi$
$192$	−4881.61	−	6718.97i	−0.00955675	−	0.0131537i
$193$	587733.	+	190966.i	1.13576	+	0.369031i	0.815762	−	0.578387i	$-0.196318\pi$
$193$	587733.	+	190966.i	1.13576	+	0.369031i	0.319998	+	0.947418i	$0.396318\pi$
$194$	331229.	−	107623.i	0.631865	−	0.205305i
$195$	−2206.15	−	6789.84i	−0.00415479	−	0.0127871i
$196$	523341.			0.973071
$197$	−224984.	−	692428.i	−0.413033	−	1.27119i	−0.913998	−	0.405718i	$-0.867021\pi$
$197$	−224984.	−	692428.i	−0.413033	−	1.27119i	0.500965	−	0.865468i	$-0.332979\pi$
$198$	87403.2	−	120300.i	0.158440	−	0.218074i
$199$	−422848.	−	582001.i	−0.756923	−	1.04182i	−0.997464	−	0.0711766i	$-0.977325\pi$
$199$	−422848.	−	582001.i	−0.756923	−	1.04182i	0.240540	−	0.970639i	$-0.422675\pi$
$200$	−207.940	+	639.973i	−0.000367589	+	0.00113132i
$201$	7803.09	−	24015.4i	0.0136231	−	0.0419276i
$202$		−	556150.i		−	0.958988i
$203$	−627296.	+	455757.i	−1.06840	+	0.776235i
$204$	2587.66			0.00435344
$205$	598481.	+	58645.7i	0.994640	+	0.0974656i
$206$	358768.			0.589041
$207$	−164343.	+	119402.i	−0.266579	+	0.193681i
$208$			1982.05i			0.00317655i
$209$	−36080.6	+	111045.i	−0.0571358	+	0.175846i
$210$	5184.67	−	15956.8i	0.00811284	−	0.0249688i
$211$	−90886.4	−	125094.i	−0.140538	−	0.193434i	0.732946	−	0.680287i	$-0.238145\pi$
$211$	−90886.4	−	125094.i	−0.140538	−	0.193434i	−0.873484	+	0.486853i	$0.838145\pi$
$212$	−39139.1	+	53870.4i	−0.0598097	+	0.0823210i
$213$	−6295.77	−	19376.4i	−0.00950823	−	0.0292633i
$214$	12515.9			0.0186822
$215$	18907.6	+	58191.7i	0.0278959	+	0.0858548i
$216$	−34647.0	+	11257.5i	−0.0505279	+	0.0164175i
$217$	1.18277e6	+	384306.i	1.70511	+	0.554023i
$218$	43059.7	+	59266.6i	0.0613662	+	0.0844634i
$219$		−	26188.6i		−	0.0368979i
$220$	185579.	+	60298.3i	0.258507	+	0.0839940i
$221$	78166.4	+	56791.2i	0.107656	+	0.0782169i
$222$	−2783.44	+	904.393i	−0.00379052	+	0.00123161i
$223$	−150677.	+	109473.i	−0.202902	+	0.147417i	−0.684596	−	0.728922i	$-0.740021\pi$
$223$	−150677.	+	109473.i	−0.202902	+	0.147417i	0.481695	+	0.876339i	$0.340021\pi$
$224$	−708618.	+	975330.i	−0.943610	+	1.29877i
$225$	731.704	+	531.614i	0.000963561	+	0.000700068i
$226$	−102616.	−	74554.8i	−0.133642	−	0.0970967i
$227$	394139.	−	542486.i	0.507674	−	0.698753i	−0.475851	−	0.879526i	$-0.657860\pi$
$227$	394139.	−	542486.i	0.507674	−	0.698753i	0.983525	+	0.180773i	$0.0578598\pi$
$228$	4430.53	−	3218.97i	0.00564441	−	0.00410091i
$229$	−652570.	+	212033.i	−0.822316	+	0.267187i	−0.689805	−	0.723995i	$-0.742304\pi$
$229$	−652570.	+	212033.i	−0.822316	+	0.267187i	−0.132510	+	0.991182i	$0.542304\pi$
$230$	131706.	+	95689.8i	0.164167	+	0.119274i
$231$	14415.2	+	4683.77i	0.0177742	+	0.00577518i
$232$		−	674378.i		−	0.822591i
$233$	−691020.	−	951108.i	−0.833875	−	1.14773i	−0.987189	−	0.159553i	$-0.948995\pi$
$233$	−691020.	−	951108.i	−0.833875	−	1.14773i	0.153314	−	0.988177i	$-0.451005\pi$
$234$	−247672.	−	80473.4i	−0.295690	−	0.0960755i
$235$	−660909.	+	214742.i	−0.780678	+	0.253658i
$236$	229792.	+	707228.i	0.268569	+	0.826569i
$237$	−39897.1			−0.0461392
$238$	70166.6	+	215950.i	0.0802949	+	0.247122i
$239$	−398721.	+	548792.i	−0.451517	+	0.621460i	−0.972723	−	0.231972i	$-0.925482\pi$
$239$	−398721.	+	548792.i	−0.451517	+	0.621460i	0.521206	+	0.853431i	$0.325482\pi$
$240$	−87.7432	−	120.768i	−9.83298e−5	−	0.000135339i
$241$	120132.	−	369729.i	0.133235	−	0.410054i	−0.862077	−	0.506778i	$-0.830836\pi$
$241$	120132.	−	369729.i	0.133235	−	0.410054i	0.995311	+	0.0967238i	$0.0308364\pi$
$242$	−140085.	+	431139.i	−0.153764	+	0.473237i
$243$			73455.5i			0.0798010i
$244$	−813567.	+	591091.i	−0.874820	+	0.635594i
$245$	−1.47170e6			−1.56641
$246$	−10330.9	+	11637.3i	−0.0108843	+	0.0122607i
$247$	204481.			0.213260
$248$	−875067.	+	635773.i	−0.903467	+	0.656407i
$249$		−	20226.4i		−	0.0206738i
$250$	188149.	−	579062.i	0.190393	−	0.585969i
$251$	−295511.	+	909491.i	−0.296067	+	0.911200i	0.686794	+	0.726852i	$0.259017\pi$
$251$	−295511.	+	909491.i	−0.296067	+	0.911200i	−0.982861	+	0.184348i	$0.940983\pi$
$252$	589027.	+	810725.i	0.584297	+	0.804216i
$253$	−86444.9	+	118981.i	−0.0849060	+	0.116863i
$254$	131268.	+	404002.i	0.127666	+	0.392915i
$255$	−7276.84			−0.00700797
$256$	−322750.	−	993323.i	−0.307799	−	0.947307i
$257$	1.38499e6	−	450012.i	1.30802	−	0.425002i	0.429657	−	0.902992i	$-0.358634\pi$
$257$	1.38499e6	−	450012.i	1.30802	−	0.425002i	0.878365	+	0.477990i	$0.158634\pi$
$258$	−1505.85	−	489.279i	−0.00140842	−	0.000457623i
$259$	247169.	+	340199.i	0.228952	+	0.315126i
$260$		−	341730.i		−	0.313509i
$261$	−862050.	−	280097.i	−0.783306	−	0.254511i
$262$	791794.	+	575272.i	0.712622	+	0.517750i
$263$	−536693.	+	174382.i	−0.478450	+	0.155458i	−0.538306	−	0.842749i	$-0.680936\pi$
$263$	−536693.	+	174382.i	−0.478450	+	0.155458i	0.0598565	+	0.998207i	$0.480936\pi$
$264$	−10665.0	+	7748.55i	−0.00941781	+	0.00684244i
$265$	110064.	−	151490.i	0.0962790	−	0.132517i
$266$	388773.	+	282460.i	0.336893	+	0.244767i
$267$	−14480.8	−	10520.9i	−0.0124313	−	0.00903184i
$268$	710449.	−	977849.i	0.604221	−	0.831639i
$269$	865792.	−	629035.i	0.729513	−	0.530022i	−0.159896	−	0.987134i	$-0.551116\pi$
$269$	865792.	−	629035.i	0.729513	−	0.530022i	0.889409	+	0.457112i	$0.151116\pi$
$270$	37319.9	−	12126.0i	0.0311553	−	0.0101230i
$271$	749386.	+	544461.i	0.619844	+	0.450343i	0.852867	−	0.522128i	$-0.174862\pi$
$271$	749386.	+	544461.i	0.619844	+	0.450343i	−0.233023	+	0.972471i	$0.574862\pi$
$272$	1921.37	+	624.289i	0.00157466	+	0.000511639i
$273$		−	26544.5i		−	0.0215560i
$274$	−243636.	−	335336.i	−0.196049	−	0.269838i
$275$	622.746	+	202.342i	0.000496569	+	0.000161345i
$276$	6560.46	−	2131.62i	0.00518396	−	0.00168437i
$277$	450413.	+	1.38623e6i	0.352705	+	1.08551i	0.957328	+	0.289003i	$0.0933237\pi$
$277$	450413.	+	1.38623e6i	0.352705	+	1.08551i	−0.604623	+	0.796512i	$0.706676\pi$
$278$	−1.22702e6			−0.952225
$279$	449251.	+	1.38265e6i	0.345524	+	1.06341i
$280$	1.23239e6	−	1.69624e6i	0.939404	−	1.29298i
$281$	−1.23785e6	−	1.70375e6i	−0.935192	−	1.28718i	−0.957799	−	0.287438i	$-0.907197\pi$
$281$	−1.23785e6	−	1.70375e6i	−0.935192	−	1.28718i	0.0226069	−	0.999744i	$-0.492803\pi$
$282$	5556.97	−	17102.6i	0.00416117	−	0.0128068i
$283$	337329.	−	1.03819e6i	0.250373	−	0.770569i	−0.744333	−	0.667809i	$-0.767232\pi$
$283$	337329.	−	1.03819e6i	0.250373	−	0.770569i	0.994706	−	0.102761i	$-0.0327676\pi$
$284$		−	975206.i		−	0.717465i
$285$	−12459.2	+	9052.15i	−0.00908612	+	0.00660146i
$286$	−188537.			−0.136296
$287$	2.04892e6	+	895006.i	1.46832	+	0.641389i
$288$	−1.40931e6			−1.00121
$289$	−1.06902e6	+	776685.i	−0.752904	+	0.547017i
$290$			726405.i			0.507206i
$291$	−12823.9	+	39468.0i	−0.00887745	+	0.0273220i
$292$	387369.	−	1.19220e6i	0.265869	−	0.818260i
$293$	106509.	+	146597.i	0.0724800	+	0.0997602i	0.843718	−	0.536787i	$-0.180362\pi$
$293$	106509.	+	146597.i	0.0724800	+	0.0997602i	−0.771238	+	0.636547i	$0.780362\pi$
$294$	22385.1	−	30810.4i	0.0151039	−	0.0207888i
$295$	−646205.	−	1.98881e6i	−0.432330	−	1.33057i
$296$	−365733.			−0.242625
$297$	10954.5	+	33714.4i	0.00720609	+	0.0221781i
$298$	1.57628e6	−	512164.i	1.02824	−	0.334094i
$299$	244956.	+	79591.1i	0.158457	+	0.0514857i
$300$	−18.0522	−	24.8467i	−1.15805e−5	−	1.59392e-5i
$301$			227497.i			0.144730i
$302$	293809.	+	95464.4i	0.185374	+	0.0602316i
$303$	53612.4	+	38951.7i	0.0335474	+	0.0243736i
$304$	4066.31	−	1321.22i	0.00252358	−	0.000819959i
$305$	2.28785e6	−	1.66222e6i	1.40825	−	1.02315i
$306$	−156019.	+	214742.i	−0.0952521	+	0.131103i
$307$	1.52208e6	+	1.10585e6i	0.921702	+	0.669656i	0.943947	−	0.330097i	$-0.107081\pi$
$307$	1.52208e6	+	1.10585e6i	0.921702	+	0.669656i	−0.0222448	+	0.999753i	$0.507081\pi$
$308$	586950.	+	426444.i	0.352553	+	0.256144i
$309$	−25127.4	+	34584.9i	−0.0149710	+	0.0206059i
$310$	942577.	−	684822.i	0.557074	−	0.404738i
$311$	−953679.	+	309869.i	−0.559115	+	0.181668i	−0.574923	−	0.818208i	$-0.694968\pi$
$311$	−953679.	+	309869.i	−0.559115	+	0.181668i	0.0158079	+	0.999875i	$0.494968\pi$
$312$	18677.6	+	13570.1i	0.0108626	+	0.00789215i
$313$	2.64577e6	+	859663.i	1.52648	+	0.495984i	0.947608	−	0.319435i	$-0.103493\pi$
$313$	2.64577e6	+	859663.i	1.52648	+	0.495984i	0.578872	+	0.815418i	$0.303493\pi$
$314$			422290.i			0.241705i
$315$	−1.65642e6	−	2.27986e6i	−0.940575	−	1.29459i
$316$	−1.81626e6	−	590138.i	−1.02320	−	0.332457i
$317$	−404136.	+	131312.i	−0.225881	+	0.0733932i	−0.419771	−	0.907630i	$-0.637890\pi$
$317$	−404136.	+	131312.i	−0.225881	+	0.0733932i	0.193890	+	0.981023i	$0.437890\pi$
$318$	1497.37	+	4608.44i	0.000830352	+	0.00255556i
$319$	−656226.			−0.361058
$320$	345456.	+	1.06320e6i	0.188589	+	0.580418i
$321$	−876.593	+	1206.53i	−0.000474827	+	0.000653543i
$322$	355784.	+	489694.i	0.191226	+	0.263200i
$323$	64405.7	−	198220.i	0.0343493	−	0.105716i
$324$	−361744.	+	1.11333e6i	−0.191443	+	0.589200i
$325$		−	1146.74i		−	0.000602223i
$326$	−1.78936e6	+	1.30004e6i	−0.932509	+	0.677507i
$327$	−8729.07			−0.00451438
$328$	−1.67721e6	+	984145.i	−0.860799	+	0.505096i
$329$	−2.58378e6			−1.31603
$330$	11487.8	−	8346.34i	0.00580698	−	0.00421902i
$331$		−	1.16436e6i		−	0.584139i	−0.956397	−	0.292069i	$-0.905656\pi$
$331$		−	1.16436e6i		−	0.584139i	0.956397	−	0.292069i	$-0.0943438\pi$
$332$	299180.	−	920780.i	0.148966	−	0.458470i
$333$	−151904.	+	467513.i	−0.0750687	+	0.231038i
$334$	−1.26967e6	−	1.74756e6i	−0.622767	−	0.857166i
$335$	−1.99787e6	+	2.74984e6i	−0.972648	+	1.33874i
$336$	−171.513	−	527.864i	−8.28800e−5	−	0.000255078i
$337$	3.23099e6			1.54975			0.774873	−	0.632117i	$-0.217814\pi$
$337$	3.23099e6			1.54975			0.774873	+	0.632117i	$0.217814\pi$
$338$	−297621.	−	915984.i	−0.141701	−	0.436110i
$339$	14374.1	−	4670.41i	0.00679329	−	0.00220727i
$340$	−331268.	−	107635.i	−0.155411	−	0.0504961i
$341$	618660.	+	851512.i	0.288115	+	0.396556i
$342$			561758.i			0.259707i
$343$	−1.88377e6	−	612073.i	−0.864553	−	0.280910i
$344$	−160074.	−	116301.i	−0.0729333	−	0.0529891i
$345$	−18448.8	+	5994.39i	−0.00834490	+	0.00271142i
$346$	140101.	−	101790.i	0.0629147	−	0.0457102i
$347$	1.48748e6	−	2.04734e6i	0.663172	−	0.912778i	−0.336409	−	0.941716i	$-0.609212\pi$
$347$	1.48748e6	−	2.04734e6i	0.663172	−	0.912778i	0.999581	+	0.0289377i	$0.00921243\pi$
$348$	24901.0	+	18091.7i	0.0110222	+	0.00800812i
$349$	705720.	+	512736.i	0.310148	+	0.225336i	0.731960	−	0.681348i	$-0.238606\pi$
$349$	705720.	+	512736.i	0.310148	+	0.225336i	−0.421812	+	0.906683i	$0.638606\pi$
$350$	1584.05	−	2180.26i	0.000691194	−	0.000951347i
$351$	50225.9	−	36491.2i	0.0217600	−	0.0158096i
$352$	−970373.	+	315293.i	−0.417428	+	0.135631i
$353$	1.28538e6	+	933883.i	0.549028	+	0.398892i	0.827427	−	0.561573i	$-0.189804\pi$
$353$	1.28538e6	+	933883.i	0.549028	+	0.398892i	−0.278399	+	0.960466i	$0.589804\pi$
$354$	51465.3	+	16722.1i	0.0218276	+	0.00709222i
$355$			2.74240e6i			1.15494i
$356$	−503598.	−	693144.i	−0.210600	−	0.289867i
$357$	−25731.8	−	8360.77i	−0.0106856	−	0.00347197i
$358$	−2.32214e6	+	754508.i	−0.957592	+	0.311140i
$359$	−22211.8	−	68360.8i	−0.00909592	−	0.0279944i	0.946406	−	0.322981i	$-0.104685\pi$
$359$	−22211.8	−	68360.8i	−0.00909592	−	0.0279944i	−0.955501	+	0.294986i	$0.904685\pi$
$360$	2.45098e6			0.996744
$361$	628851.	+	1.93540e6i	0.253968	+	0.781634i
$362$	1.54233e6	−	2.12283e6i	0.618593	−	0.851420i
$363$	−31750.1	−	43700.3i	−0.0126467	−	0.0174068i
$364$	392633.	−	1.20840e6i	0.155322	−	0.478032i
$365$	−1.08933e6	+	3.35261e6i	−0.427984	+	1.31720i
$366$			73179.7i			0.0285554i
$367$	−2.41347e6	+	1.75349e6i	−0.935354	+	0.679574i	−0.947298	−	0.320354i	$-0.896198\pi$
$367$	−2.41347e6	+	1.75349e6i	−0.935354	+	0.679574i	0.0119439	+	0.999929i	$0.496198\pi$
$368$	5385.47			0.00207302
$369$	561408.	+	2.55271e6i	0.214641	+	0.975967i
$370$	393949.			0.149601
$371$	563256.	−	409229.i	0.212457	−	0.154359i
$372$		−	49367.4i		−	0.0184962i
$373$	−725809.	+	2.23381e6i	−0.270116	+	0.831332i	0.720354	+	0.693606i	$0.243979\pi$
$373$	−725809.	+	2.23381e6i	−0.270116	+	0.831332i	−0.990470	+	0.137726i	$0.956021\pi$
$374$	−59383.9	+	182765.i	−0.0219528	+	0.0675637i
$375$	42643.5	+	58693.8i	0.0156594	+	0.0215533i
$376$	1.32088e6	−	1.81804e6i	0.481830	−	0.663183i
$377$	355138.	+	1.09300e6i	0.128690	+	0.396066i
$378$	145900.			0.0525201
$379$	−1.47388e6	−	4.53615e6i	−0.527066	−	1.62214i	−0.760193	−	0.649697i	$-0.774896\pi$
$379$	−1.47388e6	−	4.53615e6i	−0.527066	−	1.62214i	0.233127	−	0.972446i	$-0.425104\pi$
$380$	−701083.	+	227796.i	−0.249064	+	0.0809257i
$381$	−48139.2	−	15641.4i	−0.0169897	−	0.00552030i
$382$	−318330.	−	438144.i	−0.111614	−	0.153624i
$383$		−	1.02893e6i		−	0.358417i	−0.983811	−	0.179208i	$-0.942646\pi$
$383$		−	1.02893e6i		−	0.358417i	0.983811	−	0.179208i	$-0.0573537\pi$
$384$	45797.3	+	14880.4i	0.0158494	+	0.00514977i
$385$	−1.65058e6	−	1.19921e6i	−0.567524	−	0.412330i
$386$	2.04722e6	−	665183.i	0.699354	−	0.227234i
$387$	−215152.	+	156317.i	−0.0730242	+	0.0530552i
$388$	−1.16758e6	+	1.60704e6i	−0.393738	+	0.541934i
$389$	−1.58994e6	−	1.15516e6i	−0.532729	−	0.387050i	0.288648	−	0.957435i	$-0.406794\pi$
$389$	−1.58994e6	−	1.15516e6i	−0.532729	−	0.387050i	−0.821378	+	0.570385i	$0.806794\pi$
$390$	−20118.5	−	14617.0i	−0.00669784	−	0.00486627i
$391$	154309.	−	212388.i	0.0510444	−	0.0702566i
$392$	3.85023e6	−	2.79736e6i	1.26553	−	0.919460i
$393$	−110912.	+	36037.3i	−0.0362239	+	0.0117699i
$394$	−2.05169e6	−	1.49064e6i	−0.665841	−	0.483762i
$395$	5.10755e6	+	1.65954e6i	1.64710	+	0.535175i
$396$			848115.i			0.271779i
$397$	367549.	+	505888.i	0.117041	+	0.161093i	0.863518	−	0.504318i	$-0.168256\pi$
$397$	367549.	+	505888.i	0.117041	+	0.161093i	−0.746477	+	0.665412i	$0.768256\pi$
$398$	−2.38318e6	−	774343.i	−0.754136	−	0.245034i
$399$	−54457.8	+	17694.4i	−0.0171249	+	0.00556422i
$400$	−7.40951	−	22.8041i	−2.31547e−6	−	7.12629e-6i
$401$	−4.96412e6			−1.54163			−0.770817	−	0.637056i	$-0.780152\pi$
$401$	−4.96412e6			−1.54163			−0.770817	+	0.637056i	$0.780152\pi$
$402$	−27180.1	−	83651.8i	−0.00838854	−	0.0258173i
$403$	1.08346e6	−	1.49126e6i	0.332315	−	0.457393i
$404$	1.86447e6	+	2.56623e6i	0.568333	+	0.782243i
$405$	1.01727e6	−	3.13084e6i	0.308176	−	0.948469i
$406$	−834607.	+	2.56866e6i	−0.251285	+	0.773377i
$407$			355889.i			0.106495i
$408$	19037.5	−	13831.6i	0.00566187	−	0.00411359i
$409$	−2.05338e6			−0.606962			−0.303481	−	0.952838i	$-0.598149\pi$
$409$	−2.05338e6			−0.606962			−0.303481	+	0.952838i	$0.598149\pi$
$410$	1.80660e6	−	1.06007e6i	0.530765	−	0.311440i
$411$	49389.9			0.0144223
$412$	−1.65545e6	+	1.20276e6i	−0.480479	+	0.349088i
$413$		−	7.77515e6i		−	2.24302i
$414$	−218656.	+	672954.i	−0.0626990	+	0.192968i
$415$	−841331.	+	2.58935e6i	−0.239799	+	0.738025i
$416$	1.05030e6	+	1.44561e6i	0.297563	+	0.409560i
$417$	85938.1	−	118284.i	0.0242017	−	0.0333108i
$418$	125678.	+	386797.i	0.0351818	+	0.108278i
$419$	−1.01164e6			−0.281509			−0.140754	−	0.990045i	$-0.544953\pi$
$419$	−1.01164e6			−0.281509			−0.140754	+	0.990045i	$0.544953\pi$
$420$	29571.1	+	91010.4i	0.00817982	+	0.0251749i
$421$	1.91517e6	−	622278.i	0.526627	−	0.171112i	−0.0336237	−	0.999435i	$-0.510705\pi$
$421$	1.91517e6	−	622278.i	0.526627	−	0.171112i	0.560251	+	0.828323i	$0.310705\pi$
$422$	−512238.	−	166436.i	−0.140020	−	0.0454953i
$423$	−1.77536e6	−	2.44357e6i	−0.482431	−	0.664010i
$424$			605532.i			0.163577i
$425$	−1111.63	−	361.192i	−0.000298531	−	9.69986e-5i
$426$	−57412.8	−	41712.9i	−0.0153280	−	0.0111364i
$427$	9.99994e6	−	3.24918e6i	2.65416	−	0.862390i
$428$	−57752.0	+	41959.3i	−0.0152390	+	0.0110718i
$429$	13204.8	−	18174.8i	0.00346408	−	0.00476790i
$430$	172424.	+	125273.i	0.0449703	+	0.0326729i
$431$	5.26390e6	+	3.82444e6i	1.36494	+	0.991688i	0.998113	+	0.0613999i	$0.0195565\pi$
$431$	5.26390e6	+	3.82444e6i	1.36494	+	0.991688i	0.366829	+	0.930288i	$0.380444\pi$
$432$	763.009	−	1050.19i	0.000196707	−	0.000270744i
$433$	−2.74070e6	+	1.99124e6i	−0.702493	+	0.510391i	−0.880743	−	0.473594i	$-0.842956\pi$
$433$	−2.74070e6	+	1.99124e6i	−0.702493	+	0.510391i	0.178250	+	0.983985i	$0.442956\pi$
$434$	4.11990e6	−	1.33864e6i	1.04993	−	0.341144i
$435$	−70024.9	−	50876.1i	−0.0177431	−	0.0128911i
$436$	−397378.	−	129116.i	−0.100112	−	0.0325285i
$437$		−	555599.i		−	0.139174i
$438$	−53618.6	−	73799.7i	−0.0133546	−	0.0183810i
$439$	1.76679e6	+	574066.i	0.437547	+	0.142168i	0.519504	−	0.854468i	$-0.326117\pi$
$439$	1.76679e6	+	574066.i	0.437547	+	0.142168i	−0.0819567	+	0.996636i	$0.526117\pi$
$440$	1.68762e6	−	548339.i	0.415568	−	0.135026i
$441$	−1.97667e6	−	6.08356e6i	−0.483991	−	1.48957i
$442$	336548.			0.0819392
$443$	−1.51662e6	−	4.66768e6i	−0.367170	−	1.13003i	−0.948611	−	0.316445i	$-0.897511\pi$
$443$	−1.51662e6	−	4.66768e6i	−0.367170	−	1.13003i	0.581441	−	0.813589i	$-0.302489\pi$
$444$	9811.60	−	13504.5i	0.00236201	−	0.00325103i
$445$	1.41618e6	+	1.94921e6i	0.339015	+	0.466614i
$446$	−200474.	+	616995.i	−0.0477222	+	0.146874i
$447$	−61027.4	+	187823.i	−0.0144463	+	0.0444611i
$448$			4.15653e6i			0.978443i
$449$	−3.33906e6	+	2.42597e6i	−0.781642	+	0.567896i	−0.905471	−	0.424407i	$-0.860482\pi$
$449$	−3.33906e6	+	2.42597e6i	−0.781642	+	0.567896i	0.123829	+	0.992304i	$0.460482\pi$
$450$	3150.38			0.000733384
$451$	957654.	+	1.63206e6i	0.221701	+	0.377828i
$452$	723441.			0.166555
$453$	−29780.5	+	21636.8i	−0.00681847	+	0.00495391i
$454$		−	2.33569e6i		−	0.531834i
$455$	−1.10413e6	+	3.39817e6i	−0.250031	+	0.769515i
$456$	15389.5	−	47364.1i	0.00346588	−	0.0106669i
$457$	−3.44950e6	−	4.74783e6i	−0.772619	−	1.06342i	−0.996058	−	0.0887011i	$-0.971728\pi$
$457$	−3.44950e6	−	4.74783e6i	−0.772619	−	1.06342i	0.223439	−	0.974718i	$-0.428272\pi$
$458$	−1.40483e6	+	1.93359e6i	−0.312940	+	0.430725i
$459$	−19554.3	−	60181.8i	−0.00433221	−	0.0133332i
$460$	−928523.			−0.204596
$461$	−1.67195e6	−	5.14573e6i	−0.366413	−	1.12770i	−0.949091	−	0.315001i	$-0.897995\pi$
$461$	−1.67195e6	−	5.14573e6i	−0.366413	−	1.12770i	0.582678	−	0.812703i	$-0.302005\pi$
$462$	50211.6	−	16314.8i	0.0109446	−	0.00355611i
$463$	6.88304e6	+	2.23644e6i	1.49220	+	0.484846i	0.937733	−	0.347357i	$-0.112921\pi$
$463$	6.88304e6	+	2.23644e6i	1.49220	+	0.484846i	0.554470	+	0.832203i	$0.312921\pi$
$464$	14124.5	+	19440.8i	0.00304565	+	0.00419197i
$465$			138827.i			0.0297744i
$466$	−3.89461e6	−	1.26543e6i	−0.830804	−	0.269945i
$467$	−1.97934e6	−	1.43807e6i	−0.419979	−	0.305133i	0.357650	−	0.933856i	$-0.383578\pi$
$467$	−1.97934e6	−	1.43807e6i	−0.419979	−	0.305133i	−0.777630	+	0.628723i	$0.783578\pi$
$468$	1.41261e6	−	458985.i	0.298131	−	0.0968687i
$469$	−1.02242e7	+	7.42828e6i	−2.14632	+	1.55940i
$470$	−1.42278e6	+	1.95830e6i	−0.297094	+	0.408915i
$471$	−40708.4	−	29576.4i	−0.00845535	−	0.00614317i
$472$	5.47086e6	+	3.97481e6i	1.13032	+	0.821224i
$473$	−113170.	+	155766.i	−0.0232584	+	0.0320124i
$474$	−112430.	+	81685.5i	−0.0229847	+	0.0166993i
$475$	−2352.62	+	764.413i	−0.000478429	+	0.000155451i
$476$	−1.04773e6	−	761224.i	−0.211950	−	0.153991i
$477$	774045.	+	251502.i	0.155765	+	0.0506111i
$478$			2.36284e6i			0.473005i
$479$	−867817.	−	1.19445e6i	−0.172818	−	0.237864i	0.713818	−	0.700331i	$-0.246964\pi$
$479$	−867817.	−	1.19445e6i	−0.172818	−	0.237864i	−0.886636	+	0.462467i	$0.846964\pi$
$480$	−127991.	−	41586.9i	−0.0253558	−	0.00823860i
$481$	592764.	−	192601.i	0.116821	−	0.0379573i
$482$	−418451.	−	1.28786e6i	−0.0820403	−	0.252494i
$483$	−72124.6			−0.0140675
$484$	−798986.	−	2.45903e6i	−0.155034	−	0.477144i
$485$	3.28339e6	−	4.51919e6i	0.633823	−	0.872382i
$486$	150393.	+	206998.i	0.0288827	+	0.0397536i
$487$	677948.	−	2.08651e6i	0.129531	−	0.398656i	−0.865168	−	0.501482i	$-0.832788\pi$
$487$	677948.	−	2.08651e6i	0.129531	−	0.398656i	0.994699	+	0.102826i	$0.0327885\pi$
$488$	−2.82594e6	+	8.69734e6i	−0.537171	+	1.65324i
$489$		−	263545.i		−	0.0498406i
$490$	−4.14727e6	+	3.01317e6i	−0.780319	+	0.566935i
$491$	−154919.			−0.0290003			−0.0145001	−	0.999895i	$-0.504616\pi$
$491$	−154919.			−0.0290003			−0.0145001	+	0.999895i	$0.504616\pi$
$492$	8655.69	−	88331.7i	0.00161209	−	0.0164514i
$493$	1.17140e6			0.217063
$494$	576229.	−	418655.i	0.106238	−	0.0771861i
$495$		−	2.38501e6i		−	0.437499i
$496$	11910.2	−	36655.7i	0.00217377	−	0.00669018i
$497$	−3.15090e6	+	9.69747e6i	−0.572194	+	1.76103i
$498$	−41411.7	−	56998.4i	−0.00748256	−	0.0102989i
$499$	−1.32806e6	+	1.82791e6i	−0.238762	+	0.328628i	−0.911536	−	0.411221i	$-0.865103\pi$
$499$	−1.32806e6	+	1.82791e6i	−0.238762	+	0.328628i	0.672774	+	0.739848i	$0.265103\pi$
$500$	1.07312e6	+	3.30271e6i	0.191965	+	0.590807i
$501$	257388.			0.0458136
$502$	1.02934e6	+	3.16799e6i	0.182306	+	0.561079i
$503$	−715374.	+	232439.i	−0.126070	+	0.0409628i	−0.371373	−	0.928484i	$-0.621113\pi$
$503$	−715374.	+	232439.i	−0.126070	+	0.0409628i	0.245302	+	0.969447i	$0.421113\pi$
$504$	8.66697e6	+	2.81607e6i	1.51982	+	0.493818i
$505$	−5.24314e6	−	7.21656e6i	−0.914877	−	1.25922i
$506$			512278.i			0.0889467i
$507$	109145.	+	35463.3i	0.0188575	+	0.00612717i
$508$	−1.96011e6	−	1.42410e6i	−0.336993	−	0.244840i
$509$	1.65192e6	−	536741.i	0.282614	−	0.0918270i	−0.164280	−	0.986414i	$-0.552530\pi$
$509$	1.65192e6	−	536741.i	0.282614	−	0.0918270i	0.446894	+	0.894587i	$0.352530\pi$
$510$	−20506.2	+	14898.6i	−0.00349108	+	0.00253642i
$511$	−7.70400e6	+	1.06037e7i	−1.30516	+	1.79640i
$512$	60336.8	+	43837.3i	0.0101720	+	0.00739041i
$513$	−108345.	−	78716.9i	−0.0181766	−	0.0132061i
$514$	2.98157e6	−	4.10378e6i	0.497780	−	0.685136i
$515$	4.65535e6	−	3.38231e6i	0.773453	−	0.561947i
$516$	8588.69	−	2790.63i	0.00142005	−	0.000461401i
$517$	−1.76910e6	−	1.28533e6i	−0.291089	−	0.211489i
$518$	1.39305e6	+	452630.i	0.228109	+	0.0741172i
$519$			20634.8i			0.00336265i
$520$	−1.82662e6	−	2.51412e6i	−0.296237	−	0.407735i
$521$	−6.77662e6	−	2.20186e6i	−1.09375	−	0.355381i	−0.294057	−	0.955788i	$-0.595005\pi$
$521$	−6.77662e6	−	2.20186e6i	−1.09375	−	0.355381i	−0.799695	+	0.600407i	$0.795005\pi$
$522$	−3.00274e6	+	975649.i	−0.482327	+	0.156717i
$523$	−778306.	−	2.39538e6i	−0.124422	−	0.382931i	0.869374	−	0.494156i	$-0.164523\pi$
$523$	−778306.	−	2.39538e6i	−0.124422	−	0.382931i	−0.993795	+	0.111225i	$0.964523\pi$
$524$	−5.58214e6			−0.888121
$525$	99.2315	+	305.403i	1.57127e−5	+	4.83588e-5i
$526$	−1.15538e6	+	1.59024e6i	−0.182079	+	0.250610i
$527$	−1.10434e6	−	1.51999e6i	−0.173211	−	0.238405i
$528$	145.156	−	446.746i	2.26596e−5	−	6.97390e-5i
$529$	−1.77268e6	+	5.45575e6i	−0.275417	+	0.847647i
$530$		−	652248.i		−	0.100861i
$531$	7.35323e6	−	5.34243e6i	1.13173	−	0.822248i
$532$	−2.74084e6			−0.419860
$533$	2.20007e6	−	2.47830e6i	0.335443	−	0.377864i
$534$	−62347.7			−0.00946166
$535$	162406.	−	117995.i	0.0245311	−	0.0178229i
$536$		−	1.09915e7i		−	1.65252i
$537$	89904.2	−	276697.i	0.0134538	−	0.0414065i
$538$	1.15192e6	−	3.54525e6i	0.171580	−	0.528070i
$539$	−2.72206e6	−	3.74659e6i	−0.403576	−	0.555475i
$540$	−131552.	+	181066.i	−0.0194140	+	0.0267211i
$541$	−2.50120e6	−	7.69791e6i	−0.367414	−	1.13078i	−0.948456	−	0.316910i	$-0.897355\pi$
$541$	−2.50120e6	−	7.69791e6i	−0.367414	−	1.13078i	0.581042	−	0.813874i	$-0.302645\pi$
$542$	3.22651e6			0.471775
$543$	96617.5	+	297358.i	0.0140623	+	0.0432793i
$544$	1.73216e6	−	562814.i	0.250953	−	0.0815395i
$545$	1.11748e6	+	363091.i	0.161157	+	0.0523630i
$546$	−54347.3	−	74802.7i	−0.00780183	−	0.0107383i
$547$			9.78139e6i			1.39776i	0.715240	+	0.698879i	$0.246318\pi$
$547$			9.78139e6i			1.39776i	−0.715240	+	0.698879i	$0.753682\pi$
$548$	2.24840e6	+	730551.i	0.319833	+	0.103920i
$549$	9.94398e6	+	7.22473e6i	1.40809	+	1.02303i
$550$	2169.18	−	704.810i	0.000305766	−	9.93494e-5i
$551$	2.00563e6	−	1.45718e6i	0.281432	−	0.204472i
$552$	36871.5	−	50749.3i	0.00515043	−	0.00708896i
$553$	1.61542e7	+	1.17367e7i	2.24632	+	1.63205i
$554$	4.10744e6	+	2.98423e6i	0.568587	+	0.413103i
$555$	−27591.5	+	37976.4i	−0.00380226	+	0.00523337i
$556$	5.66181e6	−	4.11354e6i	0.776726	−	0.564325i
$557$	4.62023e6	−	1.50120e6i	0.630994	−	0.205023i	0.0239789	−	0.999712i	$-0.492367\pi$
$557$	4.62023e6	−	1.50120e6i	0.630994	−	0.205023i	0.607016	+	0.794690i	$0.292367\pi$
$558$	4.09684e6	+	2.97653e6i	0.557011	+	0.404692i
$559$	320687.	+	104198.i	0.0434062	+	0.0141035i
$560$			74710.3i			0.0100672i
$561$	−13459.2	−	18525.1i	−0.00180557	−	0.00248515i
$562$	−6.97653e6	−	2.26681e6i	−0.931749	−	0.302743i
$563$	6.57921e6	−	2.13772e6i	0.874788	−	0.284236i	0.162997	−	0.986627i	$-0.447884\pi$
$563$	6.57921e6	−	2.13772e6i	0.874788	−	0.284236i	0.711792	+	0.702391i	$0.247884\pi$
$564$	31694.5	+	97545.6i	0.00419552	+	0.0129125i
$565$	−2.03441e6			−0.268112
$566$	−1.17500e6	−	3.61629e6i	−0.154169	−	0.474484i
$567$	7.19438e6	−	9.90222e6i	0.939801	−	1.29353i
$568$	−5.21266e6	−	7.17462e6i	−0.677936	−	0.933099i
$569$	450073.	−	1.38518e6i	0.0582776	−	0.179360i	−0.917680	−	0.397320i	$-0.869940\pi$
$569$	450073.	−	1.38518e6i	0.0582776	−	0.179360i	0.975958	+	0.217960i	$0.0699403\pi$
$570$	−16576.8	+	51018.1i	−0.00213704	+	0.00657715i
$571$		−	558741.i		−	0.0717167i	−0.999357	−	0.0358584i	$-0.988583\pi$
$571$		−	558741.i		−	0.0717167i	0.999357	−	0.0358584i	$-0.0114165\pi$
$572$	869962.	−	632065.i	0.111176	−	0.0807740i
$573$	64532.0			0.00821086
$574$	7.60632e6	−	1.67283e6i	0.963596	−	0.211920i
$575$	−3115.84			−0.000393012
$576$	−3.93097e6	+	2.85602e6i	−0.493678	+	0.358678i
$577$			1.10185e6i			0.137779i	0.997624	+	0.0688895i	$0.0219456\pi$
$577$			1.10185e6i			0.137779i	−0.997624	+	0.0688895i	$0.978054\pi$
$578$	−1.42231e6	+	4.37742e6i	−0.177082	+	0.545002i
$579$	−79260.5	+	243939.i	−0.00982563	+	0.0302402i
$580$	−2.43525e6	−	3.35184e6i	−0.300589	−	0.413726i
$581$	−5.95010e6	+	8.18961e6i	−0.731280	+	1.00652i
$582$	44668.9	+	137477.i	0.00546636	+	0.0168237i
$583$	589232.			0.0717985
$584$	−3.52265e6	−	1.08416e7i	−0.427402	−	1.31541i
$585$	−3.97244e6	+	1.29072e6i	−0.479919	+	0.155935i
$586$	600289.	+	195046.i	0.0722131	+	0.0234635i
$587$	−5.32131e6	−	7.32416e6i	−0.637417	−	0.877329i	0.361058	−	0.932543i	$-0.382416\pi$
$587$	−5.32131e6	−	7.32416e6i	−0.637417	−	0.877329i	−0.998475	+	0.0552145i	$0.982416\pi$
$588$			217213.i			0.0259085i
$589$	−3.78164e6	−	1.22873e6i	−0.449151	−	0.145938i
$590$	−5.89292e6	−	4.28146e6i	−0.696949	−	0.506363i
$591$	287393.	−	93379.5i	0.0338460	−	0.0109972i
$592$	10543.2	−	7660.12i	0.00123643	−	0.000898320i
$593$	2.30235e6	−	3.16891e6i	0.268865	−	0.370061i	−0.653141	−	0.757236i	$-0.726549\pi$
$593$	2.30235e6	−	3.16891e6i	0.268865	−	0.370061i	0.922006	+	0.387175i	$0.126549\pi$
$594$	99896.7	+	72579.2i	0.0116168	+	0.00844007i
$595$	2.94636e6	+	2.14066e6i	0.341188	+	0.247888i
$596$	−5.55638e6	+	7.64770e6i	−0.640731	+	0.881891i
$597$	241560.	−	175503.i	0.0277389	−	0.0201535i
$598$	853245.	−	277236.i	0.0975710	−	0.0317027i
$599$	4.25834e6	+	3.09387e6i	0.484924	+	0.352318i	0.803229	−	0.595671i	$-0.203114\pi$
$599$	4.25834e6	+	3.09387e6i	0.484924	+	0.352318i	−0.318305	+	0.947988i	$0.603114\pi$
$600$	−265.621	−	86.3055i	−3.01220e−5	−	9.78724e-6i
$601$			3.16847e6i			0.357819i	0.983866	+	0.178910i	$0.0572570\pi$
$601$			3.16847e6i			0.357819i	−0.983866	+	0.178910i	$0.942743\pi$
$602$	465778.	+	641089.i	0.0523827	+	0.0720986i
$603$	−1.40504e7	−	4.56524e6i	−1.57360	−	0.511294i
$604$	−1.67576e6	+	544487.i	−0.186904	+	0.0607289i
$605$	2.24685e6	+	6.91509e6i	0.249566	+	0.768086i
$606$	230830.			0.0255335
$607$	3.35399e6	+	1.03225e7i	0.369479	+	1.13714i	0.947128	+	0.320855i	$0.103970\pi$
$607$	3.35399e6	+	1.03225e7i	0.369479	+	1.13714i	−0.577649	+	0.816285i	$0.696030\pi$
$608$	2.26564e6	−	3.11839e6i	0.248561	−	0.342115i
$609$	−189162.	−	260359.i	−0.0206677	−	0.0284466i
$610$	3.04395e6	−	9.36832e6i	0.331218	−	1.01938i
$611$	−1.18342e6	+	3.64219e6i	−0.128243	+	0.394693i
$612$		−	1.51393e6i		−	0.163390i
$613$	−7.01335e6	+	5.09550e6i	−0.753831	+	0.547691i	−0.897012	−	0.442006i	$-0.854267\pi$
$613$	−7.01335e6	+	5.09550e6i	−0.753831	+	0.547691i	0.143181	+	0.989697i	$0.454267\pi$
$614$	6.55336e6			0.701525
$615$	−24340.9	+	248400.i	−0.00259507	+	0.0264828i
$616$	6.59763e6			0.700545
$617$	−7.14672e6	+	5.19240e6i	−0.755777	+	0.549104i	−0.897612	−	0.440786i	$-0.854700\pi$
$617$	−7.14672e6	+	5.19240e6i	−0.755777	+	0.549104i	0.141835	+	0.989890i	$0.454700\pi$
$618$			148907.i			0.0156835i
$619$	746329.	−	2.29696e6i	0.0782895	−	0.240950i	−0.904250	−	0.427003i	$-0.859569\pi$
$619$	746329.	−	2.29696e6i	0.0782895	−	0.240950i	0.982540	+	0.186052i	$0.0595695\pi$
$620$	−2.05347e6	+	6.31992e6i	−0.214540	+	0.660286i
$621$	−99151.1	−	136470.i	−0.0103174	−	0.0142006i
$622$	−2.05305e6	+	2.82578e6i	−0.212777	+	0.292862i
$623$	2.76824e6	+	8.51977e6i	0.285748	+	0.879443i
$624$	−822.650			−8.45773e−5
$625$	−3.01414e6	−	9.27658e6i	−0.308648	−	0.949922i
$626$	9.21589e6	−	2.99442e6i	0.939943	−	0.305406i
$627$	−46089.1	−	14975.3i	−0.00468198	−	0.00152127i
$628$	−1.41571e6	−	1.94856e6i	−0.143244	−	0.197158i
$629$		−	635280.i		−	0.0640233i
$630$	−9.33561e6	−	3.03332e6i	−0.937111	−	0.304486i
$631$	1.10447e7	+	8.02445e6i	1.10428	+	0.802309i	0.981754	−	0.190156i	$-0.0608993\pi$
$631$	1.10447e7	+	8.02445e6i	1.10428	+	0.802309i	0.122530	+	0.992465i	$0.460899\pi$
$632$	−1.65167e7	+	5.36659e6i	−1.64486	+	0.534448i
$633$	51920.5	−	37722.5i	0.00515027	−	0.00374189i
$634$	−870012.	+	1.19747e6i	−0.0859611	+	0.118315i
$635$	5.51208e6	+	4.00476e6i	0.542477	+	0.394133i
$636$	−22358.9	−	16244.7i	−0.00219184	−	0.00159246i
$637$	−4.76715e6	+	6.56142e6i	−0.465490	+	0.640692i
$638$	−1.84925e6	+	1.34356e6i	−0.179864	+	0.130679i
$639$	−1.13363e7	+	3.68338e6i	−1.09829	+	0.356857i
$640$	−5.24392e6	−	3.80993e6i	−0.506065	−	0.367678i
$641$	1.32221e7	+	4.29612e6i	1.27103	+	0.412982i	0.865412	−	0.501062i	$-0.167057\pi$
$641$	1.32221e7	+	4.29612e6i	1.27103	+	0.412982i	0.405616	+	0.914044i	$0.367057\pi$
$642$			5194.75i			0.000497424i
$643$	−8.86817e6	−	1.22060e7i	−0.845875	−	1.16425i	−0.984757	−	0.173939i	$-0.944351\pi$
$643$	−8.86817e6	−	1.22060e7i	−0.845875	−	1.16425i	0.138881	−	0.990309i	$-0.455649\pi$
$644$	−3.28337e6	−	1.06683e6i	−0.311964	−	0.101363i
$645$	−24152.5	+	7847.62i	−0.00228593	+	0.000742743i
$646$	−224341.	−	690452.i	−0.0211509	−	0.0650957i
$647$	−1.34130e7			−1.25969			−0.629846	−	0.776720i	$-0.716882\pi$
$647$	−1.34130e7			−1.25969			−0.629846	+	0.776720i	$0.716882\pi$
$648$	3.28962e6	+	1.01244e7i	0.307758	+	0.947180i
$649$	3.86782e6	−	5.32359e6i	0.360458	−	0.496127i
$650$	−2347.85	−	3231.53i	−0.000217965	−	0.000300003i
$651$	−159506.	+	490910.i	−0.0147511	+	0.0453993i
$652$	3.89823e6	−	1.19975e7i	0.359127	−	1.10528i
$653$		−	640462.i		−	0.0587774i	−0.999568	−	0.0293887i	$-0.990644\pi$
$653$		−	640462.i		−	0.0587774i	0.999568	−	0.0293887i	$-0.00935606\pi$
$654$	−24598.6	+	17871.9i	−0.00224888	+	0.00163391i
$655$	1.56977e7			1.42966
$656$	27737.5	−	63498.9i	0.00251656	−	0.00576111i
$657$	−1.53218e7			−1.38483
$658$	−7.28113e6	+	5.29005e6i	−0.655593	+	0.476316i
$659$			7.96843e6i			0.714758i	0.933959	+	0.357379i	$0.116330\pi$
$659$			7.96843e6i			0.714758i	−0.933959	+	0.357379i	$0.883670\pi$
$660$	−25026.8	+	77024.6i	−0.00223638	+	0.00688287i
$661$	−3.45622e6	+	1.06371e7i	−0.307679	+	0.946938i	0.670985	+	0.741471i	$0.265871\pi$
$661$	−3.45622e6	+	1.06371e7i	−0.307679	+	0.946938i	−0.978664	+	0.205467i	$0.934129\pi$
$662$	−2.38391e6	−	3.28117e6i	−0.211419	−	0.290994i
$663$	−23571.2	+	32443.0i	−0.00208256	+	0.00286640i
$664$	−2.72068e6	−	8.37338e6i	−0.239473	−	0.737022i
$665$	7.70760e6			0.675873
$666$	529121.	+	1.62847e6i	0.0462242	+	0.142263i
$667$	2.96982e6	−	964953.i	0.258473	−	0.0839830i
$668$	1.17172e7	+	3.80716e6i	1.01598	+	0.330111i
$669$	−45437.0	−	62538.7i	−0.00392504	−	0.00540236i
$670$			1.18395e7i			1.01894i
$671$	8.46323e6	+	2.74987e6i	0.725654	+	0.235779i
$672$	−404811.	−	294112.i	−0.0345803	−	0.0251241i
$673$	−4.84854e6	+	1.57539e6i	−0.412642	+	0.134075i	−0.507979	−	0.861370i	$-0.669607\pi$
$673$	−4.84854e6	+	1.57539e6i	−0.412642	+	0.134075i	0.0953369	+	0.995445i	$0.469607\pi$
$674$	9.10496e6	−	6.61514e6i	0.772020	−	0.560905i
$675$	−441.450	+	607.604i	−3.72925e−5	+	5.13288e-5i
$676$	4.44411e6	+	3.22884e6i	0.374040	+	0.271756i
$677$	7.24604e6	+	5.26455e6i	0.607615	+	0.441458i	0.848574	−	0.529077i	$-0.177462\pi$
$677$	7.24604e6	+	5.26455e6i	0.607615	+	0.441458i	−0.240958	+	0.970535i	$0.577462\pi$
$678$	30944.0	−	42590.8i	0.00258525	−	0.00355829i
$679$	1.68028e7	−	1.22080e7i	1.39864	−	1.01617i
$680$	−3.01248e6	+	978814.i	−0.249834	+	0.0811760i
$681$	225159.	+	163588.i	0.0186047	+	0.0135171i
$682$	3.48678e6	+	1.13292e6i	0.287054	+	0.0932695i
$683$		−	1.24276e7i		−	1.01938i	−0.860358	−	0.509691i	$-0.829760\pi$
$683$		−	1.24276e7i		−	1.01938i	0.860358	−	0.509691i	$-0.170240\pi$
$684$	−1.88328e6	−	2.59211e6i	−0.153913	−	0.211842i
$685$	−6.32280e6	−	2.05440e6i	−0.514852	−	0.167286i
$686$	−6.56163e6	+	2.13200e6i	−0.532355	+	0.172973i
$687$	−88004.4	−	270850.i	−0.00711398	−	0.0218946i
$688$	7050.44			0.000567865
$689$	−318882.	−	981419.i	−0.0255907	−	0.0787601i
$690$	−39716.1	+	54664.5i	−0.00317573	+	0.00437102i
$691$	5.11870e6	+	7.04528e6i	0.407816	+	0.561310i	0.962684	−	0.270628i	$-0.0872313\pi$
$691$	5.11870e6	+	7.04528e6i	0.407816	+	0.561310i	−0.554868	+	0.831938i	$0.687231\pi$
$692$	−305220.	+	939371.i	−0.0242297	+	0.0745713i
$693$	2.74027e6	−	8.43367e6i	0.216750	−	0.667089i
$694$		−	8.81488e6i		−	0.694733i
$695$	−1.59217e7	+	1.15678e7i	−1.25034	+	0.908425i
$696$	279901.			0.0219019
$697$	−1.70946e6	−	2.91331e6i	−0.133284	−	0.227146i
$698$	3.03851e6			0.236060
$699$	394758.	−	286808.i	0.0305589	−	0.0222023i
$700$			15370.8i			0.00118564i
$701$	3.67614e6	−	1.13140e7i	0.282551	−	0.869603i	−0.704571	−	0.709634i	$-0.748860\pi$
$701$	3.67614e6	−	1.13140e7i	0.282551	−	0.869603i	0.987122	−	0.159969i	$-0.0511396\pi$
$702$	66824.7	−	205665.i	0.00511793	−	0.0157514i
$703$	−790267.	−	1.08771e6i	−0.0603095	−	0.0830089i
$704$	−2.06770e6	+	2.84595e6i	−0.157237	+	0.216419i
$705$	−89128.9	−	274311.i	−0.00675376	−	0.0207859i
$706$	5.53425e6			0.417876
$707$	−1.02489e7	−	3.15428e7i	−0.771129	−	2.37329i
$708$	−293535.	+	95375.4i	−0.0220078	+	0.00715078i
$709$	−1.00698e7	−	3.27189e6i	−0.752327	−	0.244446i	−0.0923447	−	0.995727i	$-0.529436\pi$
$709$	−1.00698e7	−	3.27189e6i	−0.752327	−	0.244446i	−0.659982	+	0.751281i	$0.729436\pi$
$710$	5.61481e6	+	7.72812e6i	0.418013	+	0.575345i
$711$			2.33420e7i			1.73167i
$712$	−7.40997e6	−	2.40765e6i	−0.547793	−	0.177989i
$713$	−4.05192e6	−	2.94389e6i	−0.298495	−	0.216869i
$714$	−89630.3	+	29122.7i	−0.00657975	+	0.00213789i
$715$	−2.44645e6	+	1.77745e6i	−0.178966	+	0.130026i
$716$	8.18552e6	−	1.12664e7i	0.596711	−	0.821302i
$717$	−227776.	−	165489.i	−0.0165467	−	0.0120219i
$718$	−202555.	−	147165.i	−0.0146633	−	0.0106535i
$719$	−70313.1	+	96777.7i	−0.00507241	+	0.00698157i	−0.811546	−	0.584289i	$-0.801373\pi$
$719$	−70313.1	+	96777.7i	−0.00507241	+	0.00698157i	0.806473	+	0.591271i	$0.201373\pi$
$720$	−70656.1	+	51334.7i	−0.00507947	+	0.00369045i
$721$	2.03480e7	−	6.61146e6i	1.45775	−	0.473652i
$722$	5.73466e6	+	4.16648e6i	0.409416	+	0.297458i
$723$	153456.	+	49861.0i	0.0109179	+	0.00354744i
$724$			1.49659e7i			1.06110i
$725$	−8171.96	−	11247.7i	−0.000577406	−	0.000794731i
$726$	−178944.	−	58142.6i	−0.0126002	−	0.00409404i
$727$	−9.69080e6	+	3.14873e6i	−0.680023	+	0.220953i	−0.628605	−	0.777724i	$-0.716374\pi$
$727$	−9.69080e6	+	3.14873e6i	−0.680023	+	0.220953i	−0.0514176	+	0.998677i	$0.516374\pi$
$728$	−3.57052e6	−	1.09889e7i	−0.249691	−	0.768470i
$729$	1.42879e7			0.995749
$730$	3.79441e6	+	1.16780e7i	0.263534	+	0.811076i
$731$	202015.	−	278049.i	0.0139827	−	0.0192455i
$732$	−245332.	−	337671.i	−0.0169230	−	0.0232925i
$733$	8.71891e6	−	2.68340e7i	0.599380	−	1.84470i	0.0677910	−	0.997700i	$-0.478405\pi$
$733$	8.71891e6	−	2.68340e7i	0.599380	−	1.84470i	0.531589	−	0.847002i	$-0.321595\pi$
$734$	−3.21108e6	+	9.88268e6i	−0.219994	+	0.677072i
$735$		−	610830.i		−	0.0417063i
$736$	3.92790e6	−	2.85379e6i	0.267280	−	0.194190i
$737$	−1.06957e7			−0.725337
$738$	6.80848e6	+	6.04413e6i	0.460161	+	0.408501i
$739$	1.35035e7			0.909571			0.454786	−	0.890601i	$-0.349716\pi$
$739$	1.35035e7			0.909571			0.454786	+	0.890601i	$0.349716\pi$
$740$	−1.81779e6	+	1.32070e6i	−0.122029	+	0.0886595i
$741$			84869.9i			0.00567817i
$742$	749403.	−	2.30643e6i	0.0499696	−	0.153791i
$743$	−2.02129e6	+	6.22090e6i	−0.134325	+	0.413410i	−0.995484	−	0.0949251i	$-0.969739\pi$
$743$	−2.02129e6	+	6.22090e6i	−0.134325	+	0.413410i	0.861159	+	0.508335i	$0.169739\pi$
$744$	−263878.	−	363197.i	−0.0174772	−	0.0240553i
$745$	1.56252e7	−	2.15063e7i	1.03142	−	1.41963i
$746$	2.52818e6	+	7.78093e6i	0.166326	+	0.511899i
$747$	−1.18336e7			−0.775917
$748$	−338700.	−	1.04241e6i	−0.0221340	−	0.0681216i
$749$	709858.	−	230647.i	0.0462346	−	0.0150225i
$750$	240340.	+	78091.1i	0.0156017	+	0.00506931i
$751$	−1.24513e7	−	1.71378e7i	−0.805592	−	1.10880i	−0.991989	−	0.126328i	$-0.959681\pi$
$751$	−1.24513e7	−	1.71378e7i	−0.805592	−	1.10880i	0.186396	−	0.982475i	$-0.440319\pi$
$752$			80075.0i			0.00516360i
$753$	−377485.	−	122652.i	−0.0242612	−	0.00788293i
$754$	3.23860e6	+	2.35298e6i	0.207457	+	0.150727i
$755$	4.71245e6	−	1.53117e6i	0.300870	−	0.0977586i
$756$	−673223.	+	489125.i	−0.0428405	+	0.0311254i
$757$	−4.68332e6	+	6.44604e6i	−0.297039	+	0.408840i	−0.931285	−	0.364292i	$-0.881311\pi$
$757$	−4.68332e6	+	6.44604e6i	−0.297039	+	0.408840i	0.634245	+	0.773132i	$0.281311\pi$
$758$	−1.34408e7	−	9.76528e6i	−0.849671	−	0.617322i
$759$	−49383.2	−	35879.0i	−0.00311154	−	0.00226066i
$760$	−3.94028e6	+	5.42332e6i	−0.247453	+	0.340590i
$761$	1.12592e7	−	8.18028e6i	0.704767	−	0.512043i	−0.176714	−	0.984262i	$-0.556547\pi$
$761$	1.12592e7	−	8.18028e6i	0.704767	−	0.512043i	0.881481	+	0.472219i	$0.156547\pi$
$762$	−167681.	+	54482.9i	−0.0104616	+	0.00339917i
$763$	3.53437e6	+	2.56787e6i	0.219786	+	0.159684i
$764$	2.93773e6	+	954525.i	0.182087	+	0.0591635i
$765$			4.25736e6i			0.263019i
$766$	−2.10663e6	−	2.89953e6i	−0.129723	−	0.178549i
$767$	−1.09601e7	−	3.56116e6i	−0.672708	−	0.218576i
$768$	412279.	−	133958.i	0.0252225	−	0.00819529i
$769$	992708.	+	3.05524e6i	0.0605349	+	0.186307i	0.976751	−	0.214378i	$-0.0687723\pi$
$769$	992708.	+	3.05524e6i	0.0605349	+	0.186307i	−0.916216	+	0.400685i	$0.868772\pi$
$770$	−7.10662e6			−0.431953
$771$	186778.	+	574843.i	0.0113159	+	0.0348268i
$772$	−7.21645e6	+	9.93259e6i	−0.435793	+	0.599817i
$773$	1.13918e7	+	1.56795e7i	0.685717	+	0.943808i	0.999985	−	0.00552623i	$-0.00175906\pi$
$773$	1.13918e7	+	1.56795e7i	0.685717	+	0.943808i	−0.314268	+	0.949334i	$0.601759\pi$
$774$	−286256.	+	881005.i	−0.0171752	+	0.0528598i
$775$	−6890.80	+	21207.7i	−0.000412112	+	0.00126835i
$776$			1.80640e7i			1.07686i
$777$	−141200.	+	102588.i	−0.00839038	+	0.00609597i
$778$	−6.84554e6			−0.405470
$779$	−6.55095e6	−	2.86158e6i	−0.386777	−	0.168951i
$780$	141835.			0.00834734
$781$	−6.98149e6	+	5.07235e6i	−0.409563	+	0.297565i
$782$		−	914443.i		−	0.0534736i
$783$	232591.	−	715843.i	0.0135578	−	0.0417266i
$784$	−52403.9	+	161283.i	−0.00304490	+	0.00937125i
$785$	3.98117e6	+	5.47960e6i	0.230588	+	0.317377i
$786$	−238767.	+	328635.i	−0.0137854	+	0.0189739i
$787$	−4.83168e6	−	1.48704e7i	−0.278074	−	0.855825i	−0.988390	−	0.151941i	$-0.951448\pi$
$787$	−4.83168e6	−	1.48704e7i	−0.278074	−	0.855825i	0.710315	−	0.703884i	$-0.248552\pi$
$788$	1.44644e7			0.829820
$789$	−72377.4	−	222755.i	−0.00413914	−	0.0127390i
$790$	1.77909e7	−	5.78061e6i	1.01421	−	0.329538i
$791$	−7.19391e6	−	2.33744e6i	−0.408812	−	0.132831i
$792$	4.53334e6	+	6.23960e6i	0.256806	+	0.353463i
$793$		−	1.55844e7i		−	0.880051i
$794$	2.07151e6	+	673076.i	0.116610	+	0.0378890i
$795$	62876.2	+	45682.2i	0.00352832	+	0.00256348i
$796$	1.35926e7	−	4.41651e6i	0.760363	−	0.247057i
$797$	−1.80330e7	+	1.31018e7i	−1.00560	+	0.730608i	−0.963281	−	0.268497i	$-0.913473\pi$
$797$	−1.80330e7	+	1.31018e7i	−1.00560	+	0.730608i	−0.0423146	+	0.999104i	$0.513473\pi$
$798$	−117235.	+	161360.i	−0.00651704	+	0.00896994i
$799$	3.15793e6	+	2.29437e6i	0.174999	+	0.127144i
$800$	−17488.2	−	12705.9i	−0.000966093	−	0.000701908i
$801$	−6.15533e6	+	8.47209e6i	−0.338977	+	0.466562i
$802$	−1.39890e7	+	1.01636e7i	−0.767979	+	0.557969i
$803$	−1.05498e7	+	3.42782e6i	−0.577369	+	0.187599i
$804$	405857.	+	294872.i	0.0221428	+	0.0160877i
$805$	9.23325e6	+	3.00007e6i	0.502187	+	0.163170i
$806$		−	6.42066e6i		−	0.348130i
$807$	261081.	+	359348.i	0.0141121	+	0.0194236i
$808$	2.74340e7	+	8.91384e6i	1.47829	+	0.480326i
$809$	2.50579e7	−	8.14179e6i	1.34609	−	0.437370i	0.454712	−	0.890639i	$-0.349742\pi$
$809$	2.50579e7	−	8.14179e6i	1.34609	−	0.437370i	0.891374	+	0.453269i	$0.149742\pi$
$810$	−3.54341e6	−	1.09055e7i	−0.189762	−	0.584027i
$811$	−5.94388e6			−0.317335			−0.158667	−	0.987332i	$-0.550720\pi$
$811$	−5.94388e6			−0.317335			−0.158667	+	0.987332i	$0.550720\pi$
$812$	−4.76023e6	−	1.46505e7i	−0.253360	−	0.779762i
$813$	−225979.	+	311033.i	−0.0119906	+	0.0165037i
$814$	728648.	+	1.00290e6i	0.0385440	+	0.0530513i
$815$	−1.09623e7	+	3.37386e7i	−0.578107	+	1.77923i
$816$	−259.112	+	797.464i	−1.36226e−5	+	4.19262e-5i
$817$		−	727369.i		−	0.0381241i
$818$	−5.78645e6	+	4.20410e6i	−0.302363	+	0.219680i
$819$	−1.55300e7			−0.809025
$820$	−4.78230e6	+	1.09480e7i	−0.248372	+	0.568592i
$821$	−1.77802e7			−0.920617			−0.460308	−	0.887759i	$-0.652261\pi$
$821$	−1.77802e7			−0.920617			−0.460308	+	0.887759i	$0.652261\pi$
$822$	139181.	−	101121.i	0.00718457	−	0.00521990i
$823$			7.31593e6i			0.376504i	0.982121	+	0.188252i	$0.0602822\pi$
$823$			7.31593e6i			0.376504i	−0.982121	+	0.188252i	$0.939718\pi$
$824$	−5.75025e6	+	1.76974e7i	−0.295032	+	0.908014i
$825$	−83.9823	+	258.471i	−4.29589e−6	+	1.32214e-5i
$826$	−1.59189e7	−	2.19105e7i	−0.811825	−	1.11738i
$827$	−1.37453e6	+	1.89187e6i	−0.0698858	+	0.0961896i	−0.842529	−	0.538651i	$-0.818934\pi$
$827$	−1.37453e6	+	1.89187e6i	−0.0698858	+	0.0961896i	0.772643	+	0.634840i	$0.218934\pi$
$828$	−1.24712e6	−	3.83823e6i	−0.0632167	−	0.194561i
$829$	1.32414e7			0.669189			0.334594	−	0.942362i	$-0.391401\pi$
$829$	1.32414e7			0.669189			0.334594	+	0.942362i	$0.391401\pi$
$830$	2.93057e6	+	9.01937e6i	0.147658	+	0.454445i
$831$	−575355.	+	186944.i	−0.0289024	+	0.00939095i
$832$	5.85918e6	+	1.90376e6i	0.293446	+	0.0953464i
$833$	4.85901e6	+	6.68786e6i	0.242625	+	0.333945i
$834$		−	509275.i		−	0.0253535i
$835$	−3.29504e7	−	1.07062e7i	−1.63548	−	0.531399i
$836$	−1.87664e6	−	1.36346e6i	−0.0928676	−	0.0674723i
$837$	−1.14815e6	+	373056.i	−0.0566479	+	0.0184060i
$838$	−2.85082e6	+	2.07124e6i	−0.140236	+	0.101887i
$839$	−1.17522e7	+	1.61756e7i	−0.576389	+	0.793331i	−0.993294	−	0.115619i	$-0.963115\pi$
$839$	−1.17522e7	+	1.61756e7i	−0.576389	+	0.793331i	0.416905	+	0.908950i	$0.363115\pi$
$840$	704024.	+	511503.i	0.0344262	+	0.0250121i
$841$	−5.32154e6	−	3.86633e6i	−0.259446	−	0.188499i
$842$	4.12293e6	−	5.67473e6i	0.200413	−	0.275845i
$843$	707142.	−	513769.i	0.0342719	−	0.0249000i
$844$	2.92158e6	−	949279.i	0.141176	−	0.0458709i
$845$	−1.24974e7	−	9.07990e6i	−0.602113	−	0.437461i
$846$	−1.00060e7	−	3.25114e6i	−0.480655	−	0.156174i
$847$			2.70341e7i			1.29480i
$848$	−12682.6	−	17456.1i	−0.000605645	−	0.000833599i
$849$	430902.	+	140009.i	0.0205168	+	0.00666631i
$850$	−3872.10	+	1258.12i	−0.000183823	+	5.97277e-5i
$851$	−523320.	−	1.61061e6i	−0.0247710	−	0.0762372i
$852$	404760.			0.0191029
$853$	−9.45580e6	−	2.91020e7i	−0.444965	−	1.36946i	−0.882522	−	0.470271i	$-0.844156\pi$
$853$	−9.45580e6	−	2.91020e7i	−0.444965	−	1.36946i	0.437557	−	0.899190i	$-0.355844\pi$
$854$	2.15276e7	−	2.96302e7i	1.01007	−	1.39024i
$855$	5.29601e6	+	7.28934e6i	0.247762	+	0.341014i
$856$	−200603.	+	617391.i	−0.00935733	+	0.0287989i
$857$	−1.10717e7	+	3.40752e7i	−0.514947	+	1.58485i	0.268430	+	0.963299i	$0.413495\pi$
$857$	−1.10717e7	+	3.40752e7i	−0.514947	+	1.58485i	−0.783378	+	0.621546i	$0.786505\pi$
$858$		−	78252.4i		−	0.00362894i
$859$	1.42440e7	−	1.03489e7i	0.658643	−	0.478532i	−0.207561	−	0.978222i	$-0.566553\pi$
$859$	1.42440e7	−	1.03489e7i	0.658643	−	0.478532i	0.866205	+	0.499690i	$0.166553\pi$
$860$	−1.21559e6			−0.0560453
$861$	−371473.	+	850406.i	−0.0170773	+	0.0390947i
$862$	2.26639e7			1.03888
$863$	2.67110e7	−	1.94067e7i	1.22085	−	0.887003i	0.224684	−	0.974432i	$-0.427865\pi$
$863$	2.67110e7	−	1.94067e7i	1.22085	−	0.887003i	0.996171	+	0.0874291i	$0.0278651\pi$
$864$		−	1.17028e6i		−	0.0533342i
$865$	858318.	−	2.64163e6i	0.0390039	−	0.120042i
$866$	−3.64646e6	+	1.12227e7i	−0.165225	+	0.508511i
$867$	−322364.	−	443696.i	−0.0145646	−	0.0200464i
$868$	−1.45226e7	+	1.99886e7i	−0.654252	+	0.900501i
$869$	5.22213e6	+	1.60721e7i	0.234584	+	0.721975i
$870$	−301495.			−0.0135046
$871$	5.78831e6	+	1.78146e7i	0.258527	+	0.795665i
$872$	−3.61367e6	+	1.17415e6i	−0.160938	+	0.0522918i
$873$	2.30910e7	+	7.50271e6i	1.02543	+	0.333183i
$874$	−1.13754e6	−	1.56569e6i	−0.0503717	−	0.0693308i
$875$		−	3.63095e7i		−	1.60325i
$876$	494822.	+	160778.i	0.0217866	+	0.00707889i
$877$	3.88305e6	+	2.82120e6i	0.170480	+	0.123861i	0.669754	−	0.742583i	$-0.266400\pi$
$877$	3.88305e6	+	2.82120e6i	0.170480	+	0.123861i	−0.499273	+	0.866444i	$0.666400\pi$
$878$	6.15419e6	−	1.99962e6i	0.269423	−	0.0875409i
$879$	−60845.3	+	44206.7i	−0.00265617	+	0.00192982i
$880$	−37165.3	+	51153.7i	−0.00161782	+	0.00222674i
$881$	−1.08676e7	−	7.89576e6i	−0.471730	−	0.342732i	0.326385	−	0.945237i	$-0.394169\pi$
$881$	−1.08676e7	−	7.89576e6i	−0.471730	−	0.342732i	−0.798115	+	0.602505i	$0.794169\pi$
$882$	−1.80258e7	−	1.30965e7i	−0.780231	−	0.566871i
$883$	1.89984e7	−	2.61491e7i	0.820004	−	1.12864i	−0.169699	−	0.985496i	$-0.554279\pi$
$883$	1.89984e7	−	2.61491e7i	0.820004	−	1.12864i	0.989702	−	0.143142i	$-0.0457206\pi$
$884$	−1.55293e6	+	1.12827e6i	−0.0668375	+	0.0485603i
$885$	825459.	−	268208.i	0.0354272	−	0.0115110i
$886$	−1.38305e7	−	1.00484e7i	−0.591906	−	0.430045i
$887$	−2.09758e7	−	6.81546e6i	−0.895180	−	0.290862i	−0.174934	−	0.984580i	$-0.555971\pi$
$887$	−2.09758e7	−	6.81546e6i	−0.895180	−	0.290862i	−0.720246	+	0.693719i	$0.755971\pi$
$888$		−	151798.i		−	0.00646001i
$889$	1.48901e7	+	2.04945e7i	0.631892	+	0.869725i
$890$	7.98164e6	+	2.59339e6i	0.337767	+	0.109747i
$891$	9.85189e6	−	3.20107e6i	0.415743	−	0.135083i
$892$	−1.14341e6	−	3.51907e6i	−0.0481162	−	0.148086i
$893$	8.26105e6			0.346662
$894$	212574.	+	654236.i	0.00889542	+	0.0273773i
$895$	−2.30187e7	+	3.16826e7i	−0.960558	+	1.32209i
$896$	−1.41657e7	−	1.94974e7i	−0.589478	−	0.811347i
$897$	−33034.3	+	101669.i	−0.00137083	+	0.00421899i
$898$	−4.44256e6	+	1.36728e7i	−0.183841	+	0.565805i
$899$		−	2.23479e7i		−	0.922225i
$900$	−14536.7	+	10561.5i	−0.000598219	+	0.000434631i
$901$	−1.05181e6			−0.0431644
$902$	6.04016e6	+	2.63845e6i	0.247191	+	0.107978i
$903$	−94422.7			−0.00385351
$904$	5.32237e6	−	3.86693e6i	0.216613	−	0.157378i
$905$		−	4.20861e7i		−	1.70812i
$906$	−39622.6	+	121946.i	−0.00160370	+	0.00493567i
$907$	7.81590e6	−	2.40549e7i	0.315472	−	0.970922i	−0.660088	−	0.751188i	$-0.729481\pi$
$907$	7.81590e6	−	2.40549e7i	0.315472	−	0.970922i	0.975560	−	0.219734i	$-0.0705190\pi$
$908$	7.83034e6	+	1.07775e7i	0.315185	+	0.433815i
$909$	2.27889e7	−	3.13662e7i	0.914774	−	1.25908i
$910$	3.84598e6	+	1.18367e7i	0.153958	+	0.473835i
$911$	−2.78862e7			−1.11325			−0.556625	−	0.830764i	$-0.687904\pi$
$911$	−2.78862e7			−1.11325			−0.556625	+	0.830764i	$0.687904\pi$
$912$	548.374	+	1687.72i	2.18318e−5	+	6.71915e-5i
$913$	−8.14799e6	+	2.64744e6i	−0.323499	+	0.105111i
$914$	−1.94415e7	−	6.31691e6i	−0.769774	−	0.250115i
$915$	689906.	+	949574.i	0.0272419	+	0.0374953i
$916$		−	1.36318e7i		−	0.536801i
$917$	5.55089e7	+	1.80359e7i	2.17991	+	0.708297i
$918$	−178321.	−	129558.i	−0.00698385	−	0.00507407i
$919$	2.46660e7	−	8.01446e6i	0.963406	−	0.313030i	0.215255	−	0.976558i	$-0.430942\pi$
$919$	2.46660e7	−	8.01446e6i	0.963406	−	0.313030i	0.748151	+	0.663528i	$0.230942\pi$
$920$	−6.83117e6	+	4.96314e6i	−0.266088	+	0.193324i
$921$	−458985.	+	631739.i	−0.0178299	+	0.0245408i
$922$	−1.52470e7	−	1.10776e7i	−0.590686	−	0.429158i
$923$	1.22267e7	+	8.88322e6i	0.472395	+	0.343215i
$924$	−176996.	+	243614.i	−0.00681998	+	0.00938689i
$925$	−6099.95	+	4431.87i	−0.000234408	+	0.000170307i
$926$	2.39754e7	−	7.79007e6i	0.918836	−	0.298548i
$927$	2.02341e7	+	1.47010e7i	0.773366	+	0.561883i
$928$	2.06035e7	+	6.69449e6i	0.785365	+	0.255180i
$929$			5.38467e6i			0.204701i	0.994748	+	0.102350i	$0.0326363\pi$
$929$			5.38467e6i			0.204701i	−0.994748	+	0.102350i	$0.967364\pi$
$930$	284236.	+	391217.i	0.0107763	+	0.0148324i
$931$	1.66390e7	+	5.40632e6i	0.629146	+	0.204422i
$932$	2.22131e7	−	7.21748e6i	0.837664	−	0.272173i
$933$	−128611.	−	395825.i	−0.00483699	−	0.0148867i
$934$	−8.52212e6			−0.319654
$935$	952466.	+	2.93139e6i	0.0356304	+	0.109659i
$936$	7.93925e6	−	1.09274e7i	0.296203	−	0.407689i
$937$	−1.98043e6	−	2.72583e6i	−0.0736904	−	0.101426i	0.770581	−	0.637342i	$-0.219966\pi$
$937$	−1.98043e6	−	2.72583e6i	−0.0736904	−	0.101426i	−0.844271	+	0.535916i	$0.819966\pi$
$938$	−1.36031e7	+	4.18660e7i	−0.504813	+	1.55365i
$939$	−356803.	+	1.09813e6i	−0.0132058	+	0.0406433i
$940$		−	1.38060e7i		−	0.509620i
$941$	2.51259e7	−	1.82550e7i	0.925012	−	0.672061i	−0.0197541	−	0.999805i	$-0.506288\pi$
$941$	2.51259e7	−	1.82550e7i	0.925012	−	0.672061i	0.944767	+	0.327744i	$0.106288\pi$
$942$	−175272.			−0.00643553
$943$	−6.73384e6	−	5.97786e6i	−0.246594	−	0.218911i
$944$	−240963.			−0.00880075
$945$	1.89319e6	−	1.37548e6i	0.0689627	−	0.0501043i
$946$			670654.i			0.0243653i
$947$	−7.61491e6	+	2.34363e7i	−0.275924	+	0.849207i	0.713049	+	0.701114i	$0.247314\pi$
$947$	−7.61491e6	+	2.34363e7i	−0.275924	+	0.849207i	−0.988973	+	0.148093i	$0.952686\pi$
$948$	244937.	−	753839.i	0.00885184	−	0.0272432i
$949$	1.14187e7	+	1.57165e7i	0.411577	+	0.566487i
$950$	−5064.65	+	6970.89i	−0.000182071	+	0.000250599i
$951$	−54501.0	−	167737.i	−0.00195413	−	0.00601419i
$952$	−1.17771e7			−0.421159
$953$	9.89492e6	+	3.04534e7i	0.352923	+	1.08619i	0.957204	+	0.289414i	$0.0934605\pi$
$953$	9.89492e6	+	3.04534e7i	0.352923	+	1.08619i	−0.604281	+	0.796771i	$0.706539\pi$
$954$	2.69619e6	−	876047.i	0.0959136	−	0.0311642i
$955$	−8.26126e6	−	2.68425e6i	−0.293115	−	0.0952388i
$956$	−7.92136e6	−	1.09028e7i	−0.280321	−	0.385828i
$957$		−	272367.i		−	0.00961334i
$958$	−4.89104e6	−	1.58919e6i	−0.172182	−	0.0559452i
$959$	−1.99978e7	−	1.45292e7i	−0.702158	−	0.510148i
$960$	−441283.	+	143382.i	−0.0154539	+	0.00502129i
$961$	−5.83690e6	+	4.24075e6i	−0.203880	+	0.148127i
$962$	1.27608e6	−	1.75638e6i	0.0444571	−	0.0611900i
$963$	705886.	+	512856.i	0.0245284	+	0.0178209i
$964$	6.24836e6	+	4.53970e6i	0.216558	+	0.157338i
$965$	2.02936e7	−	2.79317e7i	0.701520	−	0.965559i
$966$	−203248.	+	147668.i	−0.00700783	+	0.00509148i
$967$	−3.31791e7	+	1.07806e7i	−1.14103	+	0.370745i	−0.817759	−	0.575560i	$-0.804784\pi$
$967$	−3.31791e7	+	1.07806e7i	−1.14103	+	0.370745i	−0.323275	+	0.946305i	$0.604784\pi$
$968$	−1.90221e7	−	1.38204e7i	−0.652485	−	0.474058i
$969$	82271.5	+	26731.6i	0.00281475	+	0.000914568i
$970$		−	1.94576e7i		−	0.663986i
$971$	1.18267e7	+	1.62780e7i	0.402545	+	0.554056i	0.961380	−	0.275223i	$-0.0887517\pi$
$971$	1.18267e7	+	1.62780e7i	0.402545	+	0.554056i	−0.558835	+	0.829279i	$0.688752\pi$
$972$	−1.38791e6	−	450960.i	−0.0471190	−	0.0153099i
$973$	−6.95920e7	+	2.26118e7i	−2.35655	+	0.765691i
$974$	−2.36146e6	−	7.26784e6i	−0.0797598	−	0.245475i
$975$	475.956			1.60345e−5
$976$	−100697.	−	309912.i	−0.00338368	−	0.0104139i
$977$	629914.	−	867002.i	0.0211127	−	0.0290592i	−0.798330	−	0.602220i	$-0.794283\pi$
$977$	629914.	−	867002.i	0.0211127	−	0.0290592i	0.819443	+	0.573161i	$0.194283\pi$
$978$	−539584.	−	742673.i	−0.0180390	−	0.0248285i
$979$	−2.34284e6	+	7.21051e6i	−0.0781242	+	0.240441i
$980$	9.03510e6	−	2.78072e7i	0.300516	−	0.924893i
$981$			5.10699e6i			0.169431i
$982$	−436565.	+	317183.i	−0.0144467	+	0.0104962i
$983$	−3.11167e7			−1.02709			−0.513546	−	0.858062i	$-0.671668\pi$
$983$	−3.11167e7			−1.02709			−0.513546	+	0.858062i	$0.671668\pi$
$984$	−408470.	−	696125.i	−0.0134484	−	0.0229192i
$985$	−4.06756e7			−1.33581
$986$	3.30101e6	−	2.39832e6i	0.108132	−	0.0785625i
$987$		−	1.07240e6i		−	0.0350400i
$988$	−1.25535e6	+	3.86358e6i	−0.0409142	+	0.125921i
$989$	283117.	−	871346.i	0.00920398	−	0.0283269i
$990$	−4.88307e6	−	6.72098e6i	−0.158345	−	0.217944i
$991$	−2.16016e7	+	2.97320e7i	−0.698718	+	0.961702i	0.301249	+	0.953546i	$0.402596\pi$
$991$	−2.16016e7	+	2.97320e7i	−0.698718	+	0.961702i	−0.999967	+	0.00815692i	$0.997404\pi$
$992$	−1.07374e7	−	3.30462e7i	−0.346432	−	1.06621i
$993$	483267.			0.0155530
$994$	1.09754e7	+	3.37788e7i	0.352333	+	1.08437i
$995$	−3.82242e7	+	1.24198e7i	−1.22400	+	0.397701i
$996$	382170.	+	124175.i	0.0122070	+	0.00396629i
$997$	2.05584e7	+	2.82963e7i	0.655016	+	0.901552i	0.999304	−	0.0373118i	$-0.0118795\pi$
$997$	2.05584e7	+	2.82963e7i	0.655016	+	0.901552i	−0.344287	+	0.938864i	$0.611879\pi$
$998$			7.87015e6i			0.250125i
$999$	−388221.	−	126141.i	−0.0123074	−	0.00399890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.6.f.a.4.12	✓	64
41.31	even	10	inner	41.6.f.a.31.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.6.f.a.4.12	✓	64	1.1	even	1	trivial
41.6.f.a.31.12	yes	64	41.31	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	41.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81801 - 2.04741i) q^{2} +0.415051i q^{3} +(-6.13922 + 18.8946i) q^{4} +(17.2643 - 53.1340i) q^{5} +(0.849777 + 1.16962i) q^{6} +(122.097 - 168.052i) q^{7} +(55.8288 + 171.823i) q^{8} +242.828 q^{9} +O(q^{10})\)	\(q+(2.81801 - 2.04741i) q^{2} +0.415051i q^{3} +(-6.13922 + 18.8946i) q^{4} +(17.2643 - 53.1340i) q^{5} +(0.849777 + 1.16962i) q^{6} +(122.097 - 168.052i) q^{7} +(55.8288 + 171.823i) q^{8} +242.828 q^{9} +(-60.1359 - 185.079i) q^{10} +(167.198 - 54.3260i) q^{11} +(-7.84221 - 2.54809i) q^{12} +(-180.969 - 249.083i) q^{13} -723.556i q^{14} +(22.0533 + 7.16555i) q^{15} +(-5.20817 - 3.78396i) q^{16} +(-298.457 + 96.9747i) q^{17} +(684.291 - 497.167i) q^{18} +(-390.378 + 537.309i) q^{19} +(897.955 + 652.403i) q^{20} +(69.7502 + 50.6765i) q^{21} +(359.939 - 495.414i) q^{22} +(-676.789 + 491.716i) q^{23} +(-71.3154 + 23.1718i) q^{24} +(3.01326 + 2.18926i) q^{25} +(-1019.95 - 331.401i) q^{26} +201.643i q^{27} +(2425.70 + 3338.69i) q^{28} +(-3550.05 - 1153.48i) q^{29} +(76.8172 - 24.9594i) q^{30} +(1850.08 + 5693.96i) q^{31} -5803.73 q^{32} +(22.5480 + 69.3957i) q^{33} +(-642.510 + 884.339i) q^{34} +(-6821.37 - 9388.81i) q^{35} +(-1490.77 + 4588.13i) q^{36} +(-625.563 + 1925.29i) q^{37} +2313.40i q^{38} +(103.382 - 75.1115i) q^{39} +10093.5 q^{40} +(2311.96 + 10512.4i) q^{41} +300.312 q^{42} +(-886.025 + 643.735i) q^{43} +3492.66i q^{44} +(4192.25 - 12902.4i) q^{45} +(-900.457 + 2771.32i) q^{46} +(-7311.19 - 10063.0i) q^{47} +(1.57053 - 2.16165i) q^{48} +(-8140.21 - 25053.0i) q^{49} +12.9737 q^{50} +(-40.2494 - 123.875i) q^{51} +(5817.33 - 1890.17i) q^{52} +(3187.63 + 1035.72i) q^{53} +(412.845 + 568.232i) q^{54} -9821.80i q^{55} +(35691.8 + 11597.0i) q^{56} +(-223.010 - 162.026i) q^{57} +(-12365.7 + 4017.87i) q^{58} +(30281.7 - 22000.9i) q^{59} +(-270.780 + 372.697i) q^{60} +(40950.8 + 29752.5i) q^{61} +(16871.4 + 12257.8i) q^{62} +(29648.6 - 40807.8i) q^{63} +(-16188.3 + 11761.5i) q^{64} +(-16359.1 + 5315.39i) q^{65} +(205.622 + 149.393i) q^{66} +(-57861.5 - 18800.3i) q^{67} -6234.58i q^{68} +(-204.087 - 280.902i) q^{69} +(-38445.4 - 12491.7i) q^{70} +(-46684.4 + 15168.7i) q^{71} +(13556.8 + 41723.5i) q^{72} -63097.3 q^{73} +(2179.00 + 6706.26i) q^{74} +(-0.908655 + 1.25066i) q^{75} +(-7755.61 - 10674.7i) q^{76} +(11284.8 - 34731.1i) q^{77} +(137.548 - 423.330i) q^{78} +96125.9i q^{79} +(-290.972 + 211.404i) q^{80} +58923.4 q^{81} +(28038.3 + 24890.6i) q^{82} -48732.5 q^{83} +(-1385.72 + 1006.79i) q^{84} +17532.4i q^{85} +(-1178.84 + 3628.11i) q^{86} +(478.753 - 1473.45i) q^{87} +(18668.9 + 25695.6i) q^{88} +(-25348.6 + 34889.3i) q^{89} +(-14602.7 - 44942.3i) q^{90} -63954.8 q^{91} +(-5135.81 - 15806.4i) q^{92} +(-2363.28 + 767.876i) q^{93} +(-41206.0 - 13388.7i) q^{94} +(21809.8 + 30018.6i) q^{95} -2408.84i q^{96} +(95091.9 + 30897.2i) q^{97} +(-74232.9 - 53933.3i) q^{98} +(40600.4 - 13191.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 11 q^{2} - 227 q^{4} - 37 q^{5} + 135 q^{6} - 5 q^{7} - 1208 q^{8} - 4342 q^{9}+O(q^{10}) \) 64 * q - 11 * q^2 - 227 * q^4 - 37 * q^5 + 135 * q^6 - 5 * q^7 - 1208 * q^8 - 4342 * q^9	\( 64 q - 11 q^{2} - 227 q^{4} - 37 q^{5} + 135 q^{6} - 5 q^{7} - 1208 q^{8} - 4342 q^{9} - 1688 q^{10} + 1140 q^{11} + 1210 q^{12} - 5 q^{13} + 2200 q^{15} + 53 q^{16} - 1810 q^{17} + 820 q^{18} - 2240 q^{19} + 720 q^{20} - 3785 q^{21} + 4715 q^{22} + 7191 q^{23} - 17510 q^{24} - 13567 q^{25} + 11935 q^{26} - 2570 q^{28} + 37395 q^{29} - 17790 q^{30} + 8354 q^{31} + 53228 q^{32} + 10733 q^{33} - 39935 q^{34} + 18590 q^{35} + 56822 q^{36} + 42392 q^{37} - 43324 q^{39} + 16462 q^{40} + 25547 q^{41} - 82584 q^{42} + 10871 q^{43} + 44293 q^{45} - 31176 q^{46} - 12920 q^{47} - 61525 q^{48} - 29425 q^{49} + 134100 q^{50} - 301 q^{51} - 56955 q^{52} - 123130 q^{53} - 128450 q^{54} - 219835 q^{56} - 72730 q^{57} - 16250 q^{58} + 101479 q^{59} - 349500 q^{60} - 125391 q^{61} + 27700 q^{62} + 46335 q^{63} + 405298 q^{64} - 209500 q^{65} - 223598 q^{66} - 16820 q^{67} + 318800 q^{69} + 701815 q^{70} - 14890 q^{71} + 554619 q^{72} + 31416 q^{73} - 140667 q^{74} + 88055 q^{75} + 332310 q^{76} - 15988 q^{77} - 241076 q^{78} + 12169 q^{80} - 177268 q^{81} + 159925 q^{82} - 119808 q^{83} - 371258 q^{84} + 380419 q^{86} - 552916 q^{87} - 370060 q^{88} + 160175 q^{89} + 138120 q^{90} + 997890 q^{91} + 146175 q^{92} + 363110 q^{93} - 316690 q^{94} - 418865 q^{95} + 22160 q^{97} + 630282 q^{98} - 339895 q^{99}+O(q^{100}) \) 64 * q - 11 * q^2 - 227 * q^4 - 37 * q^5 + 135 * q^6 - 5 * q^7 - 1208 * q^8 - 4342 * q^9 - 1688 * q^10 + 1140 * q^11 + 1210 * q^12 - 5 * q^13 + 2200 * q^15 + 53 * q^16 - 1810 * q^17 + 820 * q^18 - 2240 * q^19 + 720 * q^20 - 3785 * q^21 + 4715 * q^22 + 7191 * q^23 - 17510 * q^24 - 13567 * q^25 + 11935 * q^26 - 2570 * q^28 + 37395 * q^29 - 17790 * q^30 + 8354 * q^31 + 53228 * q^32 + 10733 * q^33 - 39935 * q^34 + 18590 * q^35 + 56822 * q^36 + 42392 * q^37 - 43324 * q^39 + 16462 * q^40 + 25547 * q^41 - 82584 * q^42 + 10871 * q^43 + 44293 * q^45 - 31176 * q^46 - 12920 * q^47 - 61525 * q^48 - 29425 * q^49 + 134100 * q^50 - 301 * q^51 - 56955 * q^52 - 123130 * q^53 - 128450 * q^54 - 219835 * q^56 - 72730 * q^57 - 16250 * q^58 + 101479 * q^59 - 349500 * q^60 - 125391 * q^61 + 27700 * q^62 + 46335 * q^63 + 405298 * q^64 - 209500 * q^65 - 223598 * q^66 - 16820 * q^67 + 318800 * q^69 + 701815 * q^70 - 14890 * q^71 + 554619 * q^72 + 31416 * q^73 - 140667 * q^74 + 88055 * q^75 + 332310 * q^76 - 15988 * q^77 - 241076 * q^78 + 12169 * q^80 - 177268 * q^81 + 159925 * q^82 - 119808 * q^83 - 371258 * q^84 + 380419 * q^86 - 552916 * q^87 - 370060 * q^88 + 160175 * q^89 + 138120 * q^90 + 997890 * q^91 + 146175 * q^92 + 363110 * q^93 - 316690 * q^94 - 418865 * q^95 + 22160 * q^97 + 630282 * q^98 - 339895 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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