LMFDB - Embedded newform 49.6.g.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(2,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("49.2");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.g (of order $21$, degree $12$, 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$22$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	49.2
Dual form			49.6.g.a.25.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52973 - 0.471861i) q^{2} +(10.3277 - 26.3145i) q^{3} +(-24.3222 - 16.5826i) q^{4} +(90.2851 - 13.6083i) q^{5} +(-28.2154 + 35.3810i) q^{6} +(124.488 - 36.1916i) q^{7} +(61.3216 + 76.8948i) q^{8} +(-407.661 - 378.255i) q^{9} +(-144.533 - 21.7849i) q^{10} +(-128.000 + 118.767i) q^{11} +(-687.555 + 468.767i) q^{12} +(67.7066 + 296.642i) q^{13} +(-207.510 - 3.37723i) q^{14} +(574.341 - 2516.35i) q^{15} +(286.626 + 730.312i) q^{16} +(-62.2963 - 831.286i) q^{17} +(445.130 + 770.988i) q^{18} +(-912.061 + 1579.74i) q^{19} +(-2421.59 - 1166.18i) q^{20} +(333.304 - 3649.61i) q^{21} +(251.847 - 121.283i) q^{22} +(-25.5846 + 341.403i) q^{23} +(2656.76 - 819.502i) q^{24} +(4980.05 - 1536.14i) q^{25} +(36.4006 - 485.732i) q^{26} +(-7974.78 + 3840.45i) q^{27} +(-3627.96 - 1184.07i) q^{28} +(3320.37 + 1599.00i) q^{29} +(-2065.96 + 3578.34i) q^{30} +(2765.27 + 4789.58i) q^{31} +(-329.053 - 4390.90i) q^{32} +(1803.34 + 4594.84i) q^{33} +(-296.954 + 1301.04i) q^{34} +(10746.9 - 4961.63i) q^{35} +(3642.78 + 15960.1i) q^{36} +(-10846.4 + 7394.94i) q^{37} +(2140.63 - 1986.21i) q^{38} +(8505.25 + 1281.96i) q^{39} +(6582.84 + 6107.98i) q^{40} +(4562.34 + 5720.99i) q^{41} +(-2231.97 + 5425.66i) q^{42} +(14556.7 - 18253.5i) q^{43} +(5082.70 - 766.094i) q^{44} +(-41953.2 - 28603.2i) q^{45} +(200.232 - 510.184i) q^{46} +(-19403.0 - 5985.03i) q^{47} +22178.0 q^{48} +(14187.3 - 9010.82i) q^{49} -8343.00 q^{50} +(-22518.3 - 6945.97i) q^{51} +(3272.32 - 8337.74i) q^{52} +(3224.03 + 2198.11i) q^{53} +(14011.5 - 2111.89i) q^{54} +(-9940.28 + 12464.7i) q^{55} +(10416.7 + 7353.13i) q^{56} +(32150.5 + 40315.5i) q^{57} +(-4324.77 - 4012.80i) q^{58} +(20427.5 + 3078.95i) q^{59} +(-55696.9 + 51679.2i) q^{60} +(14173.2 - 9663.10i) q^{61} +(-1970.11 - 8631.61i) q^{62} +(-64438.4 - 32334.1i) q^{63} +(4017.95 - 17603.8i) q^{64} +(10149.7 + 25861.0i) q^{65} +(-590.510 - 7879.81i) q^{66} +(-33771.4 - 58493.7i) q^{67} +(-12269.7 + 21251.8i) q^{68} +(8719.63 + 4199.15i) q^{69} +(-18781.1 + 2518.95i) q^{70} +(-20055.6 + 9658.28i) q^{71} +(4087.38 - 54542.2i) q^{72} +(41487.6 - 12797.2i) q^{73} +(20081.5 - 6194.32i) q^{74} +(11009.6 - 146913. i) q^{75} +(48379.4 - 23298.3i) q^{76} +(-11636.1 + 19417.5i) q^{77} +(-12405.9 - 5974.35i) q^{78} +(-3311.84 + 5736.27i) q^{79} +(35816.4 + 62035.8i) q^{80} +(8599.89 + 114757. i) q^{81} +(-4279.66 - 10904.4i) q^{82} +(-5683.78 + 24902.3i) q^{83} +(-68626.7 + 83239.5i) q^{84} +(-16936.8 - 74205.1i) q^{85} +(-30881.0 + 21054.3i) q^{86} +(76368.8 - 70859.9i) q^{87} +(-16981.7 - 2559.58i) q^{88} +(43309.6 + 40185.4i) q^{89} +(50680.5 + 63551.3i) q^{90} +(19164.6 + 34477.9i) q^{91} +(6283.63 - 7879.42i) q^{92} +(154594. - 23301.4i) q^{93} +(26857.3 + 18311.0i) q^{94} +(-60848.0 + 155038. i) q^{95} +(-118943. - 36689.0i) q^{96} -2530.79 q^{97} +(-25954.7 + 7089.71i) q^{98} +97104.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} - 792 q^{10} - 635 q^{11} + 3605 q^{12} + 1834 q^{13} - 875 q^{14} - 2572 q^{15} + 3735 q^{16} - 1023 q^{17}+ \cdots + 1090736 q^{99}+O(q^{100}) $ 264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9 - 792 * q^10 - 635 * q^11 + 3605 * q^12 + 1834 * q^13 - 875 * q^14 - 2572 * q^15 + 3735 * q^16 - 1023 * q^17 - 1336 * q^18 + 9741 * q^19 + 8330 * q^20 + 1512 * q^21 + 842 * q^22 - 1553 * q^23 + 1756 * q^24 + 13144 * q^25 - 1946 * q^26 - 19849 * q^27 - 31584 * q^28 - 30356 * q^29 + 6129 * q^30 + 43903 * q^31 + 27725 * q^32 - 3412 * q^33 - 73182 * q^34 - 17360 * q^35 - 102868 * q^36 - 22105 * q^37 + 19116 * q^38 + 109165 * q^39 + 77354 * q^40 + 47446 * q^41 + 157738 * q^42 + 6674 * q^43 + 15154 * q^44 - 130923 * q^45 - 136952 * q^46 - 195163 * q^47 - 151484 * q^48 - 131194 * q^49 + 263000 * q^50 - 84276 * q^51 - 58758 * q^52 - 110577 * q^53 + 170313 * q^54 + 290245 * q^55 + 79688 * q^56 + 47310 * q^57 + 252156 * q^58 + 127308 * q^59 + 86254 * q^60 + 166863 * q^61 - 63578 * q^62 - 243033 * q^63 - 293812 * q^64 - 16702 * q^65 - 661788 * q^66 + 46195 * q^67 + 393869 * q^68 + 321394 * q^69 - 64330 * q^70 - 61793 * q^71 + 333944 * q^72 + 21699 * q^73 + 133514 * q^74 - 431136 * q^75 + 3087 * q^76 - 48993 * q^77 - 450576 * q^78 - 181 * q^79 + 264228 * q^80 + 142090 * q^81 - 512442 * q^82 + 102424 * q^83 + 344932 * q^84 - 205502 * q^85 + 611991 * q^86 + 1427200 * q^87 + 685993 * q^88 + 145800 * q^89 + 677844 * q^90 + 732956 * q^91 + 10018 * q^92 - 1233536 * q^93 - 601938 * q^94 - 945265 * q^95 - 2372958 * q^96 - 1932952 * q^97 - 672973 * q^98 + 1090736 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{21}\right)$

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 $

$2$	−1.52973	−	0.471861i	−0.270421	−	0.0834140i	0.156579	−	0.987665i	$-0.449953\pi$
$2$	−1.52973	−	0.471861i	−0.270421	−	0.0834140i	−0.427000	+	0.904252i	$0.640430\pi$
$3$	10.3277	−	26.3145i	0.662522	−	1.68808i	−0.0613261	−	0.998118i	$-0.519533\pi$
$3$	10.3277	−	26.3145i	0.662522	−	1.68808i	0.723848	−	0.689960i	$-0.242372\pi$
$4$	−24.3222	−	16.5826i	−0.760069	−	0.518206i
$5$	90.2851	−	13.6083i	1.61507	−	0.243433i	0.721519	−	0.692395i	$-0.243444\pi$
$5$	90.2851	−	13.6083i	1.61507	−	0.243433i	0.893551	+	0.448962i	$0.148206\pi$
$6$	−28.2154	+	35.3810i	−0.319969	+	0.401229i
$7$	124.488	−	36.1916i	0.960243	−	0.279166i
$7$	124.488	−	36.1916i	0.960243	−	0.279166i
$8$	61.3216	+	76.8948i	0.338757	+	0.424788i
$9$	−407.661	−	378.255i	−1.67762	−	1.55660i
$10$	−144.533	−	21.7849i	−0.457055	−	0.0688900i
$11$	−128.000	+	118.767i	−0.318954	+	0.295946i	−0.823359	−	0.567521i	$-0.807902\pi$
$11$	−128.000	+	118.767i	−0.318954	+	0.295946i	0.504405	+	0.863467i	$0.331712\pi$
$12$	−687.555	+	468.767i	−1.37833	+	0.939732i
$13$	67.7066	+	296.642i	0.111115	+	0.486827i	0.999610	+	0.0279396i	$0.00889461\pi$
$13$	67.7066	+	296.642i	0.111115	+	0.486827i	−0.888495	+	0.458887i	$0.848248\pi$
$14$	−207.510	−	3.37723i	−0.282957	−	0.00460512i
$15$	574.341	−	2516.35i	0.659085	−	2.88764i
$16$	286.626	+	730.312i	0.279909	+	0.713195i
$17$	−62.2963	−	831.286i	−0.0522805	−	0.697635i	−0.960347	−	0.278809i	$-0.910061\pi$
$17$	−62.2963	−	831.286i	−0.0522805	−	0.697635i	0.908066	−	0.418827i	$-0.137559\pi$
$18$	445.130	+	770.988i	0.323822	+	0.560876i
$19$	−912.061	+	1579.74i	−0.579615	+	1.00392i	0.415908	+	0.909407i	$0.363464\pi$
$19$	−912.061	+	1579.74i	−0.579615	+	1.00392i	−0.995523	+	0.0945163i	$0.969870\pi$
$20$	−2421.59	−	1166.18i	−1.35371	−	0.651914i
$21$	333.304	−	3649.61i	0.164927	−	1.80592i
$22$	251.847	−	121.283i	0.110938	−	0.0534249i
$23$	−25.5846	+	341.403i	−0.0100846	+	0.134570i	−0.999974	−	0.00727484i	$-0.997684\pi$
$23$	−25.5846	+	341.403i	−0.0100846	+	0.134570i	0.989889	+	0.141845i	$0.0453034\pi$
$24$	2656.76	−	819.502i	0.941509	−	0.290417i
$25$	4980.05	−	1536.14i	1.59362	−	0.491566i
$26$	36.4006	−	485.732i	0.0105603	−	0.140917i
$27$	−7974.78	+	3840.45i	−2.10528	+	1.01385i
$28$	−3627.96	−	1184.07i	−0.874516	−	0.285418i
$29$	3320.37	+	1599.00i	0.733147	+	0.353065i	0.762921	−	0.646492i	$-0.223764\pi$
$29$	3320.37	+	1599.00i	0.733147	+	0.353065i	−0.0297740	+	0.999557i	$0.509479\pi$
$30$	−2065.96	+	3578.34i	−0.419100	+	0.725903i
$31$	2765.27	+	4789.58i	0.516812	+	0.895145i	0.999809	+	0.0195233i	$0.00621484\pi$
$31$	2765.27	+	4789.58i	0.516812	+	0.895145i	−0.482997	+	0.875622i	$0.660452\pi$
$32$	−329.053	−	4390.90i	−0.0568055	−	0.758017i
$33$	1803.34	+	4594.84i	0.288266	+	0.734490i
$34$	−296.954	+	1301.04i	−0.0440547	+	0.193016i
$35$	10746.9	−	4961.63i	1.48290	−	0.684627i
$36$	3642.78	+	15960.1i	0.468465	+	2.05248i
$37$	−10846.4	+	7394.94i	−1.30251	+	0.888036i	−0.997921	−	0.0644482i	$-0.979471\pi$
$37$	−10846.4	+	7394.94i	−1.30251	+	0.888036i	−0.304588	+	0.952484i	$0.598519\pi$
$38$	2140.63	−	1986.21i	0.240482	−	0.223134i
$39$	8505.25	+	1281.96i	0.895417	+	0.134962i
$40$	6582.84	+	6107.98i	0.650524	+	0.603598i
$41$	4562.34	+	5720.99i	0.423865	+	0.531510i	0.947211	−	0.320610i	$-0.103888\pi$
$41$	4562.34	+	5720.99i	0.423865	+	0.531510i	−0.523346	+	0.852120i	$0.675316\pi$
$42$	−2231.97	+	5425.66i	−0.195239	+	0.474602i
$43$	14556.7	−	18253.5i	1.20058	−	1.50548i	0.389005	−	0.921236i	$-0.372819\pi$
$43$	14556.7	−	18253.5i	1.20058	−	1.50548i	0.811577	−	0.584246i	$-0.198610\pi$
$44$	5082.70	−	766.094i	0.395788	−	0.0596555i
$45$	−41953.2	−	28603.2i	−3.08840	−	2.10563i
$46$	200.232	−	510.184i	0.0139521	−	0.0355494i
$47$	−19403.0	−	5985.03i	−1.28122	−	0.395204i	−0.421901	−	0.906642i	$-0.638637\pi$
$47$	−19403.0	−	5985.03i	−1.28122	−	0.395204i	−0.859320	+	0.511438i	$0.829113\pi$
$48$	22178.0			1.38937
$49$	14187.3	−	9010.82i	0.844132	−	0.536135i
$50$	−8343.00			−0.471952
$51$	−22518.3	−	6945.97i	−1.21230	−	0.373945i
$52$	3272.32	−	8337.74i	0.167822	−	0.427602i
$53$	3224.03	+	2198.11i	0.157656	+	0.107488i	0.639578	−	0.768726i	$-0.279109\pi$
$53$	3224.03	+	2198.11i	0.157656	+	0.107488i	−0.481923	+	0.876214i	$0.660061\pi$
$54$	14011.5	−	2111.89i	0.653881	−	0.0985568i
$55$	−9940.28	+	12464.7i	−0.443090	+	0.555617i
$56$	10416.7	+	7353.13i	0.443876	+	0.313330i
$57$	32150.5	+	40315.5i	1.31069	+	1.64356i
$58$	−4324.77	−	4012.80i	−0.168808	−	0.156631i
$59$	20427.5	+	3078.95i	0.763986	+	0.115152i	0.519465	−	0.854492i	$-0.326131\pi$
$59$	20427.5	+	3078.95i	0.763986	+	0.115152i	0.244521	+	0.969644i	$0.421369\pi$
$60$	−55696.9	+	51679.2i	−1.99734	+	1.85326i
$61$	14173.2	−	9663.10i	0.487688	−	0.332500i	−0.294385	−	0.955687i	$-0.595115\pi$
$61$	14173.2	−	9663.10i	0.487688	−	0.332500i	0.782073	+	0.623187i	$0.214162\pi$
$62$	−1970.11	−	8631.61i	−0.0650895	−	0.285176i
$63$	−64438.4	−	32334.1i	−2.04547	−	1.02638i
$64$	4017.95	−	17603.8i	0.122618	−	0.537225i
$65$	10149.7	+	25861.0i	0.297968	+	0.759210i
$66$	−590.510	−	7879.81i	−0.0166866	−	0.222667i
$67$	−33771.4	−	58493.7i	−0.919097	−	1.59192i	−0.800789	−	0.598946i	$-0.795586\pi$
$67$	−33771.4	−	58493.7i	−0.919097	−	1.59192i	−0.118308	−	0.992977i	$-0.537747\pi$
$68$	−12269.7	+	21251.8i	−0.321782	+	0.557343i
$69$	8719.63	+	4199.15i	0.220483	+	0.106179i
$70$	−18781.1	+	2518.95i	−0.458116	+	0.0614433i
$71$	−20055.6	+	9658.28i	−0.472161	+	0.227381i	−0.654804	−	0.755798i	$-0.727249\pi$
$71$	−20055.6	+	9658.28i	−0.472161	+	0.227381i	0.182643	+	0.983179i	$0.441535\pi$
$72$	4087.38	−	54542.2i	0.0929209	−	1.23994i
$73$	41487.6	−	12797.2i	0.911195	−	0.281066i	0.196501	−	0.980504i	$-0.437042\pi$
$73$	41487.6	−	12797.2i	0.911195	−	0.281066i	0.714694	+	0.699437i	$0.246566\pi$
$74$	20081.5	−	6194.32i	0.426301	−	0.131496i
$75$	11009.6	−	146913.i	0.226005	−	3.01582i
$76$	48379.4	−	23298.3i	0.960787	−	0.462690i
$77$	−11636.1	+	19417.5i	−0.223655	+	0.373221i
$78$	−12405.9	−	5974.35i	−0.230882	−	0.111187i
$79$	−3311.84	+	5736.27i	−0.0597037	+	0.103410i	−0.894332	−	0.447403i	$-0.852349\pi$
$79$	−3311.84	+	5736.27i	−0.0597037	+	0.103410i	0.834629	+	0.550813i	$0.185682\pi$
$80$	35816.4	+	62035.8i	0.625687	+	1.08372i
$81$	8599.89	+	114757.i	0.145640	+	1.94343i
$82$	−4279.66	−	10904.4i	−0.0702869	−	0.179088i
$83$	−5683.78	+	24902.3i	−0.0905612	+	0.396774i	−0.999810	−	0.0194779i	$-0.993800\pi$
$83$	−5683.78	+	24902.3i	−0.0905612	+	0.396774i	0.909249	+	0.416252i	$0.136657\pi$
$84$	−68626.7	+	83239.5i	−1.06119	+	1.28716i
$85$	−16936.8	−	74205.1i	−0.254264	−	1.11400i
$86$	−30881.0	+	21054.3i	−0.450241	+	0.306969i
$87$	76368.8	−	70859.9i	1.08173	−	1.00370i
$88$	−16981.7	−	2559.58i	−0.233762	−	0.0352340i
$89$	43309.6	+	40185.4i	0.579574	+	0.537766i	0.914556	−	0.404458i	$-0.132540\pi$
$89$	43309.6	+	40185.4i	0.579574	+	0.537766i	−0.334982	+	0.942224i	$0.608730\pi$
$90$	50680.5	+	63551.3i	0.659530	+	0.827024i
$91$	19164.6	+	34477.9i	0.242603	+	0.436452i
$92$	6283.63	−	7879.42i	0.0774000	−	0.0970565i
$93$	154594.	−	23301.4i	1.85347	−	0.279366i
$94$	26857.3	+	18311.0i	0.313504	+	0.213743i
$95$	−60848.0	+	155038.i	−0.691731	+	1.76250i
$96$	−118943.	−	36689.0i	−1.31723	−	0.406310i
$97$	−2530.79			−0.0273103			−0.0136551	−	0.999907i	$-0.504347\pi$
$97$	−2530.79			−0.0273103			−0.0136551	+	0.999907i	$0.504347\pi$
$98$	−25954.7	+	7089.71i	−0.272993	+	0.0745699i
$99$	97104.6			0.995754
$100$	−146599.	−	45219.8i	−1.46599	−	0.452198i
$101$	−40453.7	+	103074.i	−0.394598	+	1.00542i	0.586160	+	0.810195i	$0.300639\pi$
$101$	−40453.7	+	103074.i	−0.394598	+	1.00542i	−0.980759	+	0.195225i	$0.937456\pi$
$102$	31169.5	+	21251.0i	0.296639	+	0.202245i
$103$	−89979.5	+	13562.2i	−0.835700	+	0.125961i	−0.552931	−	0.833227i	$-0.686491\pi$
$103$	−89979.5	+	13562.2i	−0.835700	+	0.125961i	−0.282768	+	0.959188i	$0.591253\pi$
$104$	−18658.4	+	23396.9i	−0.169157	+	0.212116i
$105$	−19572.5	−	334041.i	−0.173250	−	2.95683i
$106$	−3894.71	−	4883.81i	−0.0336675	−	0.0422177i
$107$	−42736.5	−	39653.6i	−0.360860	−	0.334829i	0.478817	−	0.877915i	$-0.341066\pi$
$107$	−42736.5	−	39653.6i	−0.360860	−	0.334829i	−0.839678	+	0.543085i	$0.817256\pi$
$108$	257649.	+	38834.3i	2.12554	+	0.320374i
$109$	−114832.	+	106549.i	−0.925758	+	0.858978i	−0.990301	−	0.138937i	$-0.955631\pi$
$109$	−114832.	+	106549.i	−0.925758	+	0.858978i	0.0645433	+	0.997915i	$0.479441\pi$
$110$	21087.6	−	14377.3i	0.166167	−	0.113291i
$111$	82576.3	+	361790.i	0.636133	+	2.78708i
$112$	62112.6	+	80541.3i	0.467880	+	0.606700i
$113$	−7352.14	+	32211.8i	−0.0541648	+	0.237312i	−0.994763	−	0.102211i	$-0.967408\pi$
$113$	−7352.14	+	32211.8i	−0.0541648	+	0.237312i	0.940598	+	0.339523i	$0.110265\pi$
$114$	−30158.5	−	76842.5i	−0.217344	−	0.553783i
$115$	2336.00	+	31171.8i	0.0164713	+	0.219795i
$116$	−54243.0	−	93951.6i	−0.374282	−	0.648275i
$117$	84604.8	−	146540.i	0.571387	−	0.989672i
$118$	−29795.8	−	14348.9i	−0.196993	−	0.0948668i
$119$	−37840.7	−	101230.i	−0.244958	−	0.655304i
$120$	228714.	−	110143.i	1.44991	−	0.698238i
$121$	−9756.87	+	130196.i	−0.0605825	+	0.808418i
$122$	−26240.8	+	8094.22i	−0.159616	+	0.0492352i
$123$	197664.	−	60971.1i	1.17805	−	0.363380i
$124$	12166.3	−	162349.i	0.0710568	−	0.948187i
$125$	171649.	−	82661.8i	0.982576	−	0.473184i
$126$	83316.5	+	79868.5i	0.467525	+	0.448177i
$127$	−34455.1	−	16592.7i	−0.189559	−	0.0912867i	0.336697	−	0.941613i	$-0.390690\pi$
$127$	−34455.1	−	16592.7i	−0.189559	−	0.0912867i	−0.526256	+	0.850326i	$0.676405\pi$
$128$	−84904.4	+	147059.i	−0.458042	+	0.793352i
$129$	−329996.	−	571569.i	−1.74596	−	3.02409i
$130$	−3323.55	−	44349.7i	−0.0172482	−	0.230161i
$131$	−41593.6	−	105979.i	−0.211762	−	0.539561i	0.785042	−	0.619442i	$-0.212641\pi$
$131$	−41593.6	−	105979.i	−0.211762	−	0.539561i	−0.996804	+	0.0798810i	$0.974546\pi$
$132$	32333.1	−	141661.i	0.161515	−	0.707644i
$133$	−56367.1	+	229666.i	−0.276310	+	1.12582i
$134$	24060.3	+	105415.i	0.115755	+	0.507156i
$135$	−667742.	+	455259.i	−3.15337	+	2.14993i
$136$	60101.5	−	55766.1i	0.278637	−	0.258537i
$137$	144629.	+	21799.3i	0.658346	+	0.0992297i	0.469715	−	0.882818i	$-0.344357\pi$
$137$	144629.	+	21799.3i	0.658346	+	0.0992297i	0.188631	+	0.982048i	$0.439595\pi$
$138$	−11357.3	−	10538.0i	−0.0507665	−	0.0471045i
$139$	−132947.	−	166710.i	−0.583636	−	0.731856i	0.399092	−	0.916911i	$-0.369325\pi$
$139$	−132947.	−	166710.i	−0.583636	−	0.731856i	−0.982728	+	0.185054i	$0.940754\pi$
$140$	−343664.	−	57533.3i	−1.48188	−	0.248084i
$141$	−357881.	+	448769.i	−1.51597	+	1.90097i
$142$	35237.1	−	5311.14i	0.146649	−	0.0221038i
$143$	−43897.6	−	29928.9i	−0.179515	−	0.122391i
$144$	159397.	−	406138.i	0.640582	−	1.63218i
$145$	321539.	+	99181.8i	1.27003	+	0.391753i
$146$	−69503.6			−0.269852
$147$	−90593.0	−	466394.i	−0.345781	−	1.78016i
$148$	386435.			1.45018
$149$	315522.	+	97325.8i	1.16430	+	0.359139i	0.815892	−	0.578205i	$-0.196246\pi$
$149$	315522.	+	97325.8i	1.16430	+	0.359139i	0.348407	+	0.937343i	$0.386723\pi$
$150$	−86164.0	+	219542.i	−0.312678	+	0.796691i
$151$	−52565.3	−	35838.4i	−0.187610	−	0.127911i	0.465873	−	0.884852i	$-0.345741\pi$
$151$	−52565.3	−	35838.4i	−0.187610	−	0.127911i	−0.653483	+	0.756941i	$0.726693\pi$
$152$	−177403.	+	26739.1i	−0.622803	+	0.0938725i
$153$	−289042.	+	362447.i	−0.998234	+	1.25175i
$154$	26962.4	−	24213.0i	0.0916130	−	0.0822710i
$155$	314841.	+	394798.i	1.05260	+	1.31991i
$156$	−185608.	−	172219.i	−0.610640	−	0.566592i
$157$	−34058.0	−	5133.41i	−0.110273	−	0.0166210i	0.0936738	−	0.995603i	$-0.470139\pi$
$157$	−34058.0	−	5133.41i	−0.110273	−	0.0166210i	−0.203947	+	0.978982i	$0.565377\pi$
$158$	7772.95	−	7212.24i	0.0247710	−	0.0229841i
$159$	91138.9	−	62137.5i	0.285898	−	0.194922i
$160$	−89461.2	−	391955.i	−0.276271	−	1.21042i
$161$	9170.96	+	43426.4i	0.0278837	+	0.132035i
$162$	40994.0	−	179606.i	0.122725	−	0.537693i
$163$	−17245.2	−	43940.0i	−0.0508392	−	0.129536i	0.903198	−	0.429224i	$-0.141213\pi$
$163$	−17245.2	−	43940.0i	−0.0508392	−	0.129536i	−0.954037	+	0.299688i	$0.903118\pi$
$164$	−16097.2	−	214803.i	−0.0467349	−	0.623634i
$165$	225343.	+	390305.i	0.644368	+	1.11608i
$166$	20445.1	−	35411.9i	0.0575862	−	0.0997422i
$167$	−177694.	−	85572.9i	−0.493039	−	0.237435i	0.170807	−	0.985305i	$-0.445363\pi$
$167$	−177694.	−	85572.9i	−0.493039	−	0.237435i	−0.663846	+	0.747869i	$0.731077\pi$
$168$	301075.	−	198170.i	0.823003	−	0.541708i
$169$	251111.	−	120929.i	0.676315	−	0.325696i
$170$	−9105.60	+	121506.i	−0.0241650	+	0.322459i
$171$	969354.	−	299006.i	2.53508	−	0.781969i
$172$	−656742.	+	202578.i	−1.69267	+	0.522121i
$173$	−2373.92	+	31677.7i	−0.00603045	+	0.0804708i	−0.999407	−	0.0344338i	$-0.989037\pi$
$173$	−2373.92	+	31677.7i	−0.00603045	+	0.0804708i	0.993377	+	0.114905i	$0.0366563\pi$
$174$	−150260.	+	72361.3i	−0.376244	+	0.181190i
$175$	564360.	−	371467.i	1.39303	−	0.916907i
$176$	−123425.	−	59438.2i	−0.300345	−	0.144639i
$177$	291990.	−	505742.i	0.700544	−	1.21338i
$178$	−47290.2	−	81909.1i	−0.111872	−	0.193768i
$179$	52274.9	+	697560.i	0.121944	+	1.62723i	0.637553	+	0.770406i	$0.279947\pi$
$179$	52274.9	+	697560.i	0.121944	+	1.62723i	−0.515609	+	0.856824i	$0.672434\pi$
$180$	546078.	+	1.39138e6i	1.25624	+	3.20086i
$181$	−16841.8	+	73788.8i	−0.0382113	+	0.167415i	−0.990433	−	0.137992i	$-0.955935\pi$
$181$	−16841.8	+	73788.8i	−0.0382113	+	0.167415i	0.952222	+	0.305407i	$0.0987924\pi$
$182$	−13048.0	−	61785.0i	−0.0291988	−	0.138262i
$183$	−107904.	−	472758.i	−0.238182	−	1.04354i
$184$	−27821.0	+	18968.1i	−0.0605799	+	0.0413027i
$185$	−878635.	+	815254.i	−1.88747	+	1.75131i
$186$	−247483.	−	37302.1i	−0.524522	−	0.0790590i
$187$	106703.	+	99005.9i	0.223137	+	0.207041i
$188$	372676.	+	467321.i	0.769019	+	0.964319i
$189$	−853770.	+	766709.i	−1.73855	+	1.56126i
$190$	166238.	−	208455.i	0.334076	−	0.418918i
$191$	751194.	−	113224.i	1.48994	−	0.224572i	0.646963	−	0.762521i	$-0.276039\pi$
$191$	751194.	−	113224.i	1.48994	−	0.224572i	0.842977	+	0.537949i	$0.180801\pi$
$192$	−421740.	−	287537.i	−0.825641	−	0.562913i
$193$	203804.	−	519284.i	0.393840	−	1.00349i	−0.587159	−	0.809472i	$-0.699754\pi$
$193$	203804.	−	519284.i	0.393840	−	1.00349i	0.980999	−	0.194015i	$-0.0621511\pi$
$194$	3871.43	+	1194.18i	0.00738529	+	0.00227806i
$195$	785343.			1.47902
$196$	−494490.	−	16099.9i	−0.919427	−	0.0299353i
$197$	−708773.			−1.30119			−0.650597	−	0.759423i	$-0.725481\pi$
$197$	−708773.			−1.30119			−0.650597	+	0.759423i	$0.725481\pi$
$198$	−148544.	−	45819.8i	−0.269273	−	0.0830597i
$199$	57949.5	−	147653.i	0.103733	−	0.264307i	−0.869579	−	0.493794i	$-0.835610\pi$
$199$	57949.5	−	147653.i	0.103733	−	0.264307i	0.973312	+	0.229487i	$0.0737048\pi$
$200$	423506.	+	288742.i	0.748660	+	0.510428i
$201$	−1.88801e6	+	284572.i	−3.29621	+	0.496824i
$202$	110520.	−	138588.i	0.190574	−	0.238972i
$203$	471215.	+	78886.8i	0.802563	+	0.134358i
$204$	432512.	+	542353.i	0.727651	+	0.912445i
$205$	489764.	+	454435.i	0.813959	+	0.755243i
$206$	144044.	+	21711.2i	0.236498	+	0.0356463i
$207$	139567.	−	129499.i	0.226390	−	0.210059i
$208$	−197235.	+	134472.i	−0.316100	+	0.215514i
$209$	−70876.1	−	310528.i	−0.112236	−	0.491740i
$210$	−127680.	+	520230.i	−0.199790	+	0.814042i
$211$	107222.	−	469768.i	0.165797	−	0.726403i	−0.821850	−	0.569704i	$-0.807058\pi$
$211$	107222.	−	469768.i	0.165797	−	0.726403i	0.987646	−	0.156699i	$-0.0500852\pi$
$212$	−41965.2	−	106926.i	−0.0641283	−	0.163396i
$213$	47024.8	+	627502.i	0.0710195	+	0.947689i
$214$	46664.4	+	80825.2i	0.0696549	+	0.120646i
$215$	1.06585e6	−	1.84611e6i	1.57254	−	2.72372i
$216$	−784338.	−	377717.i	−1.14385	−	0.550849i
$217$	517584.	+	496164.i	0.746160	+	0.715280i
$218$	225939.	−	108806.i	0.321995	−	0.155065i
$219$	91718.1	−	1.22389e6i	0.129224	−	1.72438i
$220$	448467.	−	138334.i	0.624703	−	0.192695i
$221$	242377.	−	74763.3i	0.333818	−	0.102969i
$222$	44394.8	−	592407.i	0.0604574	−	0.806748i
$223$	−16828.6	+	8104.22i	−0.0226613	+	0.0109131i	−0.445180	−	0.895441i	$-0.646860\pi$
$223$	−16828.6	+	8104.22i	−0.0226613	+	0.0109131i	0.422519	+	0.906354i	$0.361146\pi$
$224$	−199877.	−	534704.i	−0.266160	−	0.712022i
$225$	−2.61123e6	−	1.25750e6i	−3.43866	−	1.65597i
$226$	26446.3	−	45806.3i	0.0344424	−	0.0596560i
$227$	613597.	+	1.06278e6i	0.790349	+	1.36892i	0.925751	+	0.378134i	$0.123434\pi$
$227$	613597.	+	1.06278e6i	0.790349	+	1.36892i	−0.135402	+	0.990791i	$0.543233\pi$
$228$	−113436.	−	1.51370e6i	−0.144515	−	1.92842i
$229$	−49296.8	−	125606.i	−0.0621199	−	0.158279i	0.896444	−	0.443158i	$-0.146142\pi$
$229$	−49296.8	−	125606.i	−0.0621199	−	0.158279i	−0.958564	+	0.284879i	$0.908047\pi$
$230$	11135.3	−	48786.8i	0.0138797	−	0.0608111i
$231$	390789.	+	506735.i	0.481850	+	0.624814i
$232$	80655.0	+	353373.i	0.0983810	+	0.431035i
$233$	−512752.	+	349589.i	−0.618754	+	0.421859i	−0.831716	−	0.555201i	$-0.812641\pi$
$233$	−512752.	+	349589.i	−0.618754	+	0.421859i	0.212962	+	0.977060i	$0.431689\pi$
$234$	−198569.	+	184245.i	−0.237068	+	0.219967i
$235$	−1.83325e6	−	276318.i	−2.16547	−	0.326392i
$236$	−445785.	−	413628.i	−0.521010	−	0.483426i
$237$	116744.	+	146392.i	0.135009	+	0.169296i
$238$	10119.7	+	172711.i	0.0115804	+	0.197641i
$239$	−1.04852e6	+	1.31480e6i	−1.18736	+	1.48890i	−0.354814	+	0.934937i	$0.615456\pi$
$239$	−1.04852e6	+	1.31480e6i	−1.18736	+	1.48890i	−0.832543	+	0.553961i	$0.813116\pi$
$240$	2.00234e6	−	301805.i	2.24394	−	0.338219i
$241$	593543.	+	404670.i	0.658278	+	0.448806i	0.845833	−	0.533448i	$-0.179104\pi$
$241$	593543.	+	404670.i	0.658278	+	0.448806i	−0.187555	+	0.982254i	$0.560056\pi$
$242$	76360.0	−	194562.i	0.0838161	−	0.213560i
$243$	1.05329e6	+	324896.i	1.14428	+	0.352963i
$244$	−504962.			−0.542980
$245$	1.15828e6	−	1.00661e6i	1.23282	−	1.07138i
$246$	−331143.			−0.348881
$247$	−530369.	−	163597.i	−0.553140	−	0.170621i
$248$	−198724.	+	506340.i	−0.205173	+	0.522773i
$249$	596591.	+	406749.i	0.609787	+	0.415746i
$250$	−301582.	+	45456.2i	−0.305180	+	0.0459984i
$251$	822874.	−	1.03185e6i	0.824421	−	1.03379i	−0.174372	−	0.984680i	$-0.555790\pi$
$251$	822874.	−	1.03185e6i	0.824421	−	1.03379i	0.998793	−	0.0491117i	$-0.0156390\pi$
$252$	1.03110e6	+	1.85499e6i	1.02282	+	1.84010i
$253$	−37272.4	−	46738.2i	−0.0366089	−	0.0459061i
$254$	44877.7	+	41640.4i	0.0436462	+	0.0404977i
$255$	−2.12759e6	−	320682.i	−2.04898	−	0.308834i
$256$	−224291.	+	208112.i	−0.213901	+	0.198471i
$257$	−1.38178e6	+	942083.i	−1.30499	+	0.889726i	−0.998075	−	0.0620111i	$-0.980249\pi$
$257$	−1.38178e6	+	942083.i	−1.30499	+	0.889726i	−0.306913	+	0.951737i	$0.599296\pi$
$258$	235105.	+	1.03006e6i	0.219893	+	0.963416i
$259$	−1.08261e6	+	1.31313e6i	−1.00282	+	1.21635i
$260$	181980.	−	797305.i	0.166951	−	0.731461i
$261$	−748755.	−	1.90780e6i	−0.680359	−	1.73353i
$262$	13620.0	+	181746.i	0.0122581	+	0.163573i
$263$	−791220.	−	1.37043e6i	−0.705355	−	1.22171i	−0.966563	−	0.256428i	$-0.917454\pi$
$263$	−791220.	−	1.37043e6i	−0.705355	−	1.22171i	0.261208	−	0.965282i	$-0.415879\pi$
$264$	−242736.	+	420431.i	−0.214350	+	0.371266i
$265$	320994.	+	154583.i	0.280791	+	0.135222i
$266$	194597.	−	324731.i	0.168629	−	0.281397i
$267$	1.50475e6	−	724649.i	1.29177	−	0.622084i
$268$	−148584.	+	1.98271e6i	−0.126367	+	1.68625i
$269$	−1.39224e6	+	429450.i	−1.17310	+	0.361853i	−0.819243	−	0.573447i	$-0.805606\pi$
$269$	−1.39224e6	+	429450.i	−1.17310	+	0.361853i	−0.353856	+	0.935300i	$0.615130\pi$
$270$	1.23629e6	−	381344.i	1.03207	−	0.318352i
$271$	−37237.1	+	496895.i	−0.0308002	+	0.411000i	0.960400	+	0.278626i	$0.0898790\pi$
$271$	−37237.1	+	496895.i	−0.0308002	+	0.411000i	−0.991200	+	0.132374i	$0.957740\pi$
$272$	589243.	−	283764.i	0.482916	−	0.232560i
$273$	1.10519e6	−	148231.i	0.897495	−	0.120374i
$274$	−210958.	−	101592.i	−0.169754	−	0.0817491i
$275$	−455004.	+	788090.i	−0.362814	+	0.628412i
$276$	−142448.	−	246727.i	−0.112560	−	0.194959i
$277$	38.5526	+	514.449i	3.01894e−5	+	0.000402850i	0.997219	−	0.0745287i	$-0.0237452\pi$
$277$	38.5526	+	514.449i	3.01894e−5	+	0.000402850i	−0.997189	+	0.0749315i	$0.976126\pi$
$278$	124710.	+	317755.i	0.0967806	+	0.246593i
$279$	684389.	−	2.99850e6i	0.526372	−	2.30618i
$280$	1.04054e6	+	522124.i	0.793165	+	0.397996i
$281$	−307294.	−	1.34634e6i	−0.232160	−	1.01716i	−0.947843	−	0.318736i	$-0.896742\pi$
$281$	−307294.	−	1.34634e6i	−0.232160	−	1.01716i	0.715683	−	0.698425i	$-0.246116\pi$
$282$	759220.	−	517627.i	0.568519	−	0.387609i
$283$	565644.	−	524841.i	0.419834	−	0.389549i	−0.441772	−	0.897128i	$-0.645650\pi$
$283$	565644.	−	524841.i	0.419834	−	0.389549i	0.861605	+	0.507579i	$0.169459\pi$
$284$	647956.	+	97663.7i	0.476705	+	0.0718518i
$285$	3.45134e6	+	3.20237e6i	2.51695	+	2.33539i
$286$	53029.4	+	66496.8i	0.0383356	+	0.0480713i
$287$	775007.	+	547074.i	0.555393	+	0.392050i
$288$	−1.52674e6	+	1.91447e6i	−1.08463	+	1.36009i
$289$	716842.	−	108047.i	0.504869	−	0.0760968i
$290$	−445070.	−	303444.i	−0.310766	−	0.211877i
$291$	−26137.2	+	66596.5i	−0.0180937	+	0.0461019i
$292$	−1.22128e6	−	376716.i	−0.838222	−	0.258557i
$293$	−824318.			−0.560952			−0.280476	−	0.959861i	$-0.590492\pi$
$293$	−824318.			−0.560952			−0.280476	+	0.959861i	$0.590492\pi$
$294$	−81489.7	+	756206.i	−0.0549837	+	0.510237i
$295$	1.88620e6			1.26192
$296$	−1.23375e6	−	380562.i	−0.818461	−	0.252462i
$297$	564654.	−	1.43872e6i	0.371442	−	0.946420i
$298$	−436741.	−	297765.i	−0.284894	−	0.194238i
$299$	−103007.	+	15525.8i	−0.0666328	+	0.0100433i
$300$	−2.70397e6	+	3.39067e6i	−1.73460	+	2.17512i
$301$	1.15150e6	−	2.79917e6i	0.732570	−	1.78079i
$302$	63500.2	+	79626.7i	0.0400643	+	0.0502391i
$303$	2.29456e6	+	2.12904e6i	1.43580	+	1.33222i
$304$	−1.41512e6	−	213295.i	−0.878232	−	0.132372i
$305$	1.14813e6	−	1.06531e6i	0.706709	−	0.655730i
$306$	613182.	−	418061.i	0.374357	−	0.255232i
$307$	−367812.	−	1.61149e6i	−0.222731	−	0.975848i	−0.955412	−	0.295276i	$-0.904588\pi$
$307$	−367812.	−	1.61149e6i	−0.222731	−	0.975848i	0.732681	−	0.680572i	$-0.238269\pi$
$308$	605007.	−	279320.i	0.363399	−	0.167774i
$309$	−572397.	+	2.50783e6i	−0.341036	+	1.49418i
$310$	−295333.	−	752496.i	−0.174545	−	0.444734i
$311$	39571.1	+	528039.i	0.0231994	+	0.309575i	0.996717	+	0.0809630i	$0.0257995\pi$
$311$	39571.1	+	528039.i	0.0231994	+	0.309575i	−0.973518	+	0.228612i	$0.926581\pi$
$312$	422979.	+	732622.i	0.245999	+	0.426082i
$313$	−26384.8	+	45699.8i	−0.0152227	+	0.0263666i	−0.873536	−	0.486759i	$-0.838179\pi$
$313$	−26384.8	+	45699.8i	−0.0152227	+	0.0263666i	0.858314	+	0.513125i	$0.171512\pi$
$314$	49677.4	+	23923.4i	0.0284338	+	0.0136930i
$315$	−6.25784e6	−	2.04239e6i	−3.55344	−	1.15974i
$316$	175673.	−	84599.8i	0.0989665	−	0.0476598i
$317$	−166299.	+	2.21910e6i	−0.0929482	+	1.24031i	0.734439	+	0.678675i	$0.237446\pi$
$317$	−166299.	+	2.21910e6i	−0.0929482	+	1.24031i	−0.827387	+	0.561632i	$0.810174\pi$
$318$	−168739.	+	52049.0i	−0.0935721	+	0.0288632i
$319$	−614915.	+	189676.i	−0.338328	+	0.104360i
$320$	123204.	−	1.64404e6i	0.0672588	−	0.897506i
$321$	−1.48484e6	+	715059.i	−0.804296	+	0.387328i
$322$	6462.07	−	70758.3i	0.00347322	−	0.0380310i
$323$	1.37003e6	+	659772.i	0.730675	+	0.351874i
$324$	1.69381e6	−	2.93376e6i	0.896400	−	1.55261i
$325$	792867.	+	1.37329e6i	0.416382	+	0.721195i
$326$	5646.99	+	75353.9i	0.00294288	+	0.0392701i
$327$	1.61783e6	+	4.12216e6i	0.836687	+	2.13184i
$328$	−160145.	+	701641.i	−0.0821918	+	0.360106i
$329$	−2.63204e6	−	42836.4i	−1.34061	−	0.0218184i
$330$	−160545.	−	703394.i	−0.0811544	−	0.355561i
$331$	−1.28357e6	+	875122.i	−0.643945	+	0.439034i	−0.840761	−	0.541406i	$-0.817892\pi$
$331$	−1.28357e6	+	875122.i	−0.643945	+	0.439034i	0.196816	+	0.980440i	$0.436940\pi$
$332$	551186.	−	511426.i	0.274444	−	0.254647i
$333$	7.21883e6	+	1.08806e6i	3.56743	+	0.537704i
$334$	231446.	+	214751.i	0.113523	+	0.105334i
$335$	−3.84505e6	−	4.82154e6i	−1.87193	−	2.34733i
$336$	2.76089e6	−	802658.i	1.33414	−	0.387866i
$337$	−1.18264e6	+	1.48299e6i	−0.567256	+	0.711317i	−0.979881	−	0.199584i	$-0.936041\pi$
$337$	−1.18264e6	+	1.48299e6i	−0.567256	+	0.711317i	0.412624	+	0.910901i	$0.364612\pi$
$338$	−441195.	+	66499.4i	−0.210058	+	0.0316611i
$339$	771708.	+	526142.i	0.364715	+	0.248659i
$340$	−818572.	+	2.08569e6i	−0.384025	+	0.978480i
$341$	−922796.	−	284645.i	−0.429754	−	0.132562i
$342$	−1.62394e6			−0.750768
$343$	1.44003e6	−	1.63520e6i	0.660901	−	0.750473i
$344$	2.29624e6			1.04622
$345$	844396.	+	260462.i	0.381943	+	0.117814i
$346$	18578.9	−	47338.3i	0.00834315	−	0.0212580i
$347$	−1.04509e6	−	712528.i	−0.465939	−	0.317672i	0.307494	−	0.951550i	$-0.400510\pi$
$347$	−1.04509e6	−	712528.i	−0.465939	−	0.317672i	−0.773433	+	0.633878i	$0.781462\pi$
$348$	−3.03250e6	+	457075.i	−1.34231	+	0.202320i
$349$	739261.	−	927004.i	0.324888	−	0.407397i	−0.592385	−	0.805655i	$-0.701814\pi$
$349$	739261.	−	927004.i	0.324888	−	0.407397i	0.917274	+	0.398258i	$0.130385\pi$
$350$	−1.03860e6	+	301947.i	−0.453188	+	0.131753i
$351$	−1.67919e6	−	2.10563e6i	−0.727497	−	0.912252i
$352$	563611.	+	522955.i	0.242450	+	0.224961i
$353$	1.92393e6	+	289986.i	0.821774	+	0.123863i	0.546453	−	0.837490i	$-0.315978\pi$
$353$	1.92393e6	+	289986.i	0.821774	+	0.123863i	0.275321	+	0.961352i	$0.411216\pi$
$354$	−685307.	+	635872.i	−0.290655	+	0.269688i
$355$	−1.67929e6	+	1.14492e6i	−0.707221	+	0.482175i
$356$	−387006.	−	1.69558e6i	−0.161842	−	0.709078i
$357$	−3.05463e6	−	49714.2i	−1.26849	−	0.0206447i
$358$	249184.	−	1.09175e6i	0.102757	−	0.450210i
$359$	121431.	+	309402.i	0.0497272	+	0.126703i	0.953579	−	0.301143i	$-0.0973680\pi$
$359$	121431.	+	309402.i	0.0497272	+	0.126703i	−0.903852	+	0.427845i	$0.859273\pi$
$360$	−373198.	−	4.97997e6i	−0.151769	−	2.02521i
$361$	−425660.	−	737264.i	−0.171907	−	0.297752i
$362$	60581.5	−	104930.i	0.0242979	−	0.0420852i
$363$	3.32529e6	+	1.60138e6i	1.32453	+	0.637862i
$364$	105607.	−	1.15638e6i	0.0417773	−	0.457452i
$365$	3.57157e6	−	1.71998e6i	1.40322	−	0.675756i
$366$	−58011.5	+	774109.i	−0.0226366	+	0.302064i
$367$	−3.07236e6	+	947698.i	−1.19071	+	0.367286i	−0.825912	−	0.563799i	$-0.809339\pi$
$367$	−3.07236e6	+	947698.i	−1.19071	+	0.367286i	−0.364801	+	0.931085i	$0.618863\pi$
$368$	−256664.	+	79170.4i	−0.0987974	+	0.0304750i
$369$	304102.	−	4.05795e6i	0.116266	−	1.55146i
$370$	1.72876e6	−	832529.i	0.656495	−	0.316151i
$371$	480905.	+	156954.i	0.181395	+	0.0592022i
$372$	−4.14647e6	−	1.99684e6i	−1.55354	−	0.748144i
$373$	319651.	−	553652.i	0.118961	−	0.206046i	−0.800395	−	0.599473i	$-0.795377\pi$
$373$	319651.	−	553652.i	0.118961	−	0.206046i	0.919356	+	0.393426i	$0.128710\pi$
$374$	−116510.	−	201802.i	−0.0430710	−	0.0746012i
$375$	−402468.	−	5.37057e6i	−0.147793	−	1.97216i
$376$	−729604.	−	1.85900e6i	−0.266145	−	0.678126i
$377$	−249521.	+	1.09322e6i	−0.0904178	+	0.396146i
$378$	1.66782e6	−	770001.i	0.600371	−	0.277180i
$379$	828811.	+	3.63126e6i	0.296386	+	1.29855i	0.875466	+	0.483280i	$0.160555\pi$
$379$	828811.	+	3.63126e6i	0.296386	+	1.29855i	−0.579080	+	0.815271i	$0.696588\pi$
$380$	4.05089e6	−	2.76185e6i	1.43910	−	0.981164i
$381$	−792470.	+	735305.i	−0.279686	+	0.259511i
$382$	−1.20255e6	−	181256.i	−0.421644	−	0.0635526i
$383$	765396.	+	710184.i	0.266618	+	0.247385i	0.802140	−	0.597136i	$-0.203695\pi$
$383$	765396.	+	710184.i	0.266618	+	0.247385i	−0.535522	+	0.844521i	$0.679885\pi$
$384$	2.99291e6	+	3.75299e6i	1.03578	+	1.29882i
$385$	−786323.	+	1.91146e6i	−0.270364	+	0.657223i
$386$	−556795.	+	698199.i	−0.190207	+	0.238513i
$387$	−1.28387e7	+	1.93512e6i	−4.35756	+	0.656796i
$388$	61554.3	+	41967.0i	0.0207577	+	0.0141524i
$389$	−1.94143e6	+	4.94668e6i	−0.650501	+	1.65745i	0.0987098	+	0.995116i	$0.468528\pi$
$389$	−1.94143e6	+	4.94668e6i	−0.650501	+	1.65745i	−0.749210	+	0.662332i	$0.769567\pi$
$390$	−1.20137e6	−	370572.i	−0.399957	−	0.123371i
$391$	285398.			0.0944079
$392$	1.56288e6	+	538375.i	0.513700	+	0.176958i
$393$	−3.21835e6			−1.05112
$394$	1.08423e6	+	334442.i	0.351870	+	0.108538i
$395$	−220949.	+	562968.i	−0.0712523	+	0.181548i
$396$	−2.36180e6	−	1.61025e6i	−0.756841	−	0.516006i
$397$	5.56186e6	−	838315.i	1.77110	−	0.266951i	0.819234	−	0.573459i	$-0.194399\pi$
$397$	5.56186e6	−	838315.i	1.77110	−	0.266951i	0.951868	+	0.306508i	$0.0991607\pi$
$398$	−158319.	+	198526.i	−0.0500985	+	0.0628216i
$399$	5.46142e6	+	3.85520e6i	1.71741	+	1.21231i
$400$	2.54928e6	+	3.19669e6i	0.796649	+	0.998967i
$401$	−2.44858e6	−	2.27195e6i	−0.760421	−	0.705568i	0.201321	−	0.979525i	$-0.435477\pi$
$401$	−2.44858e6	−	2.27195e6i	−0.760421	−	0.705568i	−0.961742	+	0.273958i	$0.911667\pi$
$402$	3.02244e6	+	455559.i	0.932808	+	0.140598i
$403$	−1.23357e6	+	1.14458e6i	−0.378355	+	0.351062i
$404$	2.69317e6	−	1.83617e6i	0.820936	−	0.559705i
$405$	2.33810e6	+	1.02439e7i	0.708312	+	3.10332i
$406$	−683610.	−	343024.i	−0.205823	−	0.103278i
$407$	510065.	−	2.23474e6i	0.152630	−	0.668715i
$408$	−846748.	−	2.15748e6i	−0.251828	−	0.641647i
$409$	−88327.3	−	1.17865e6i	−0.0261088	−	0.348397i	−0.994925	−	0.100618i	$-0.967918\pi$
$409$	−88327.3	−	1.17865e6i	−0.0261088	−	0.348397i	0.968816	−	0.247780i	$-0.0797009\pi$
$410$	−534779.	−	926265.i	−0.157114	−	0.272129i
$411$	2.06732e6	−	3.58071e6i	0.603676	−	1.04560i
$412$	2.41340e6	+	1.16223e6i	0.700463	+	0.337325i
$413$	2.65441e6	−	356014.i	0.765759	−	0.102705i
$414$	−274606.	+	132243.i	−0.0787426	+	0.0379204i
$415$	−174283.	+	2.32565e6i	−0.0496748	+	0.662864i
$416$	1.28025e6	−	394904.i	0.362711	−	0.111881i
$417$	−5.75994e6	+	1.77671e6i	−1.62210	+	0.500352i
$418$	−38104.5	+	508469.i	−0.0106668	+	0.142339i
$419$	3.82857e6	−	1.84374e6i	1.06537	−	0.513057i	0.182761	−	0.983157i	$-0.441497\pi$
$419$	3.82857e6	−	1.84374e6i	1.06537	−	0.513057i	0.882613	+	0.470100i	$0.155782\pi$
$420$	−5.06322e6	+	8.44918e6i	−1.40057	+	2.33718i
$421$	700850.	+	337512.i	0.192717	+	0.0928076i	0.527754	−	0.849397i	$-0.323034\pi$
$421$	700850.	+	337512.i	0.192717	+	0.0928076i	−0.335037	+	0.942205i	$0.608749\pi$
$422$	−385686.	+	668027.i	−0.105427	+	0.182605i
$423$	5.64599e6	+	9.77914e6i	1.53422	+	2.65735i
$424$	28679.6	+	382703.i	0.00774745	+	0.103382i
$425$	−1.58721e6	−	4.04416e6i	−0.426249	−	1.08606i
$426$	224158.	−	982100.i	0.0598453	−	0.262200i
$427$	1.41466e6	−	1.71589e6i	0.375476	−	0.455427i
$428$	381884.	+	1.67315e6i	0.100768	+	0.441493i
$429$	−1.24092e6	+	846048.i	−0.325538	+	0.221948i
$430$	−2.50158e6	+	2.32113e6i	−0.652444	+	0.605380i
$431$	1.25910e6	+	189779.i	0.326488	+	0.0492101i	0.310241	−	0.950658i	$-0.399590\pi$
$431$	1.25910e6	+	189779.i	0.326488	+	0.0492101i	0.0162466	+	0.999868i	$0.494828\pi$
$432$	−5.09051e6	−	4.72331e6i	−1.31236	−	1.21769i
$433$	728191.	+	913123.i	0.186649	+	0.234050i	0.866348	−	0.499441i	$-0.166461\pi$
$433$	728191.	+	913123.i	0.186649	+	0.234050i	−0.679699	+	0.733491i	$0.737890\pi$
$434$	−557646.	−	1.00323e6i	−0.142113	−	0.255667i
$435$	5.93068e6	−	7.43684e6i	1.50273	−	1.88437i
$436$	4.55983e6	−	687283.i	1.14877	−	0.173149i
$437$	−515992.	−	351797.i	−0.129253	−	0.0881229i
$438$	−717811.	+	1.82895e6i	−0.178782	+	0.455530i
$439$	−4.51040e6	−	1.39128e6i	−1.11700	−	0.344550i	−0.319332	−	0.947643i	$-0.603458\pi$
$439$	−4.51040e6	−	1.39128e6i	−1.11700	−	0.344550i	−0.797671	+	0.603093i	$0.793935\pi$
$440$	−1.56803e6			−0.386119
$441$	−9.19201e6	−	1.69306e6i	−2.25068	−	0.414549i
$442$	−406050.			−0.0988607
$443$	158733.	+	48962.5i	0.0384288	+	0.0118537i	0.313910	−	0.949453i	$-0.398361\pi$
$443$	158733.	+	48962.5i	0.0384288	+	0.0118537i	−0.275481	+	0.961306i	$0.588837\pi$
$444$	3.99099e6	−	1.01689e7i	0.960777	−	2.44802i
$445$	4.45707e6	+	3.03878e6i	1.06696	+	0.727443i
$446$	29567.3	−	4456.56i	0.00703842	−	0.00106087i
$447$	5.81970e6	−	7.29767e6i	1.37763	−	1.72749i
$448$	−136925.	−	2.33687e6i	−0.0322320	−	0.550098i
$449$	−1.86813e6	−	2.34256e6i	−0.437312	−	0.548373i	0.513520	−	0.858077i	$-0.328341\pi$
$449$	−1.86813e6	−	2.34256e6i	−0.437312	−	0.548373i	−0.950833	+	0.309705i	$0.899770\pi$
$450$	3.40112e6	+	3.15578e6i	0.791755	+	0.734641i
$451$	−1.26344e6	−	190433.i	−0.292492	−	0.0440861i
$452$	712976.	−	661545.i	0.164145	−	0.152305i
$453$	−1.48595e6	+	1.01310e6i	−0.340219	+	0.231957i
$454$	−437156.	−	1.91531e6i	−0.0995399	−	0.436113i
$455$	2.19946e6	+	2.85204e6i	0.498067	+	0.645843i
$456$	−1.12853e6	+	4.94442e6i	−0.254157	+	1.11353i
$457$	−353767.	−	901383.i	−0.0792367	−	0.201892i	0.885766	−	0.464132i	$-0.153634\pi$
$457$	−353767.	−	901383.i	−0.0792367	−	0.201892i	−0.965003	+	0.262241i	$0.915539\pi$
$458$	16142.4	+	215406.i	0.00359588	+	0.0479836i
$459$	3.68932e6	+	6.39008e6i	0.817362	+	1.41571i
$460$	460093.	−	796904.i	0.101380	−	0.175595i
$461$	373431.	+	179835.i	0.0818385	+	0.0394113i	0.474355	−	0.880334i	$-0.342681\pi$
$461$	373431.	+	179835.i	0.0818385	+	0.0394113i	−0.392517	+	0.919745i	$0.628396\pi$
$462$	−358694.	−	959568.i	−0.0781843	−	0.209156i
$463$	−2.09907e6	+	1.01086e6i	−0.455067	+	0.219149i	−0.647353	−	0.762190i	$-0.724124\pi$
$463$	−2.09907e6	+	1.01086e6i	−0.455067	+	0.219149i	0.192286	+	0.981339i	$0.438410\pi$
$464$	−216068.	+	2.88322e6i	−0.0465902	+	0.621703i
$465$	1.36405e7	−	4.20753e6i	2.92548	−	0.902392i
$466$	949332.	−	292830.i	0.202513	−	0.0624671i
$467$	−78935.9	+	1.05333e6i	−0.0167487	+	0.223496i	0.982548	+	0.186008i	$0.0595549\pi$
$467$	−78935.9	+	1.05333e6i	−0.0167487	+	0.223496i	−0.999297	+	0.0374888i	$0.988064\pi$
$468$	−4.48779e6	+	2.16120e6i	−0.947148	+	0.456122i
$469$	−6.32110e6	−	6.05950e6i	−1.32697	−	1.27205i
$470$	2.67400e6	+	1.28773e6i	0.558363	+	0.268893i
$471$	−486823.	+	843203.i	−0.101116	+	0.175138i
$472$	1.01589e6	+	1.75958e6i	0.209890	+	0.363541i
$473$	304652.	+	4.06530e6i	0.0626111	+	0.835487i
$474$	−109510.	−	279027.i	−0.0223876	−	0.0570428i
$475$	−2.11541e6	+	9.26822e6i	−0.430191	+	1.88479i
$476$	−758291.	+	3.08964e6i	−0.153398	+	0.625015i
$477$	−482869.	−	2.11559e6i	−0.0971703	−	0.425731i
$478$	2.22436e6	−	1.51654e6i	0.445281	−	0.303588i
$479$	−6.54399e6	+	6.07193e6i	−1.30318	+	1.20917i	−0.339963	+	0.940439i	$0.610415\pi$
$479$	−6.54399e6	+	6.07193e6i	−1.30318	+	1.20917i	−0.963215	+	0.268733i	$0.913395\pi$
$480$	−1.12380e7	−	1.69386e6i	−2.22632	−	0.335564i
$481$	−2.92802e6	−	2.71681e6i	−0.577048	−	0.535422i
$482$	−717014.	−	899108.i	−0.140576	−	0.176276i
$483$	1.23746e6	+	207165.i	0.241359	+	0.0404062i
$484$	2.39630e6	−	3.00487e6i	0.464974	−	0.583059i
$485$	−228492.	+	34439.7i	−0.0441080	+	0.00664821i
$486$	−1.45794e6	−	994009.i	−0.279995	−	0.190897i
$487$	2.57386e6	−	6.55808e6i	0.491770	−	1.25301i	−0.442605	−	0.896717i	$-0.645946\pi$
$487$	2.57386e6	−	6.55808e6i	0.491770	−	1.25301i	0.934375	−	0.356292i	$-0.115959\pi$
$488$	1.61216e6	+	497287.i	0.306450	+	0.0945273i
$489$	−1.33436e6			−0.252349
$490$	−2.24684e6	+	993295.i	−0.422749	+	0.186891i
$491$	927559.			0.173635			0.0868176	−	0.996224i	$-0.472330\pi$
$491$	927559.			0.173635			0.0868176	+	0.996224i	$0.472330\pi$
$492$	−5.81867e6	−	1.79482e6i	−1.08371	−	0.334279i
$493$	1.12238e6	−	2.85979e6i	0.207981	−	0.529928i
$494$	734128.	+	500520.i	0.135349	+	0.0922792i
$495$	8.76710e6	−	1.32143e6i	1.60821	−	0.242399i
$496$	−2.70529e6	+	3.39233e6i	−0.493753	+	0.619147i
$497$	−2.14713e6	+	1.92818e6i	−0.389912	+	0.350152i
$498$	−720697.	−	903726.i	−0.130221	−	0.163291i
$499$	−4.50667e6	−	4.18158e6i	−0.810223	−	0.751777i	0.161759	−	0.986830i	$-0.448283\pi$
$499$	−4.50667e6	−	4.18158e6i	−0.810223	−	0.751777i	−0.971983	+	0.235053i	$0.924474\pi$
$500$	−5.54563e6	−	835869.i	−0.992032	−	0.149525i
$501$	−4.08698e6	+	3.79216e6i	−0.727458	+	0.674983i
$502$	−1.74567e6	+	1.19018e6i	−0.309174	+	0.210791i
$503$	−505244.	−	2.21362e6i	−0.0890391	−	0.390106i	0.910697	−	0.413075i	$-0.135545\pi$
$503$	−505244.	−	2.21362e6i	−0.0890391	−	0.390106i	−0.999736	+	0.0229690i	$0.992688\pi$
$504$	−1.46514e6	−	6.93776e6i	−0.256924	−	1.21659i
$505$	−2.24970e6	+	9.85659e6i	−0.392552	+	1.71988i
$506$	34963.0	+	89084.4i	0.00607062	+	0.0154677i
$507$	−588785.	−	7.85678e6i	−0.101727	−	1.35745i
$508$	562874.	+	974926.i	0.0967724	+	0.167615i
$509$	−1.06511e6	+	1.84482e6i	−0.182221	+	0.315616i	−0.942637	−	0.333821i	$-0.891662\pi$
$509$	−1.06511e6	+	1.84482e6i	−0.182221	+	0.315616i	0.760416	+	0.649437i	$0.224995\pi$
$510$	3.10333e6	+	1.49448e6i	0.528326	+	0.254429i
$511$	4.70154e6	−	3.09460e6i	0.796504	−	0.524267i
$512$	5.33706e6	−	2.57019e6i	0.899761	−	0.433302i
$513$	1.20659e6	−	1.61008e7i	0.202425	−	2.70118i
$514$	2.55829e6	−	789128.i	0.427112	−	0.131747i
$515$	−7.93925e6	+	2.44893e6i	−1.31905	+	0.406873i
$516$	−1.45188e6	+	1.93740e7i	−0.240053	+	3.20328i
$517$	3.19440e6	−	1.53834e6i	0.525610	−	0.253120i
$518$	2.27571e6	−	1.49790e6i	0.372643	−	0.245277i
$519$	809067.	+	389626.i	0.131846	+	0.0634935i
$520$	−1.36618e6	+	2.36630e6i	−0.221564	+	0.383761i
$521$	−3.38091e6	−	5.85591e6i	−0.545682	−	0.945148i	−0.998564	−	0.0535779i	$-0.982937\pi$
$521$	−3.38091e6	−	5.85591e6i	−0.545682	−	0.945148i	0.452882	−	0.891570i	$-0.350396\pi$
$522$	245182.	+	3.27173e6i	0.0393834	+	0.525534i
$523$	−3.58174e6	−	9.12613e6i	−0.572585	−	1.45892i	−0.864576	−	0.502502i	$-0.832413\pi$
$523$	−3.58174e6	−	9.12613e6i	−0.572585	−	1.45892i	0.291991	−	0.956421i	$-0.405682\pi$
$524$	−745756.	+	3.26737e6i	−0.118650	+	0.519840i
$525$	−3.94645e6	−	1.86872e7i	−0.624897	−	2.95901i
$526$	563703.	+	2.46974e6i	0.0888354	+	0.389213i
$527$	3.80925e6	−	2.59710e6i	0.597466	−	0.407345i
$528$	−2.83878e6	+	2.63401e6i	−0.443146	+	0.411180i
$529$	6.24855e6	+	941818.i	0.970823	+	0.146328i
$530$	−418095.	−	387935.i	−0.0646525	−	0.0599887i
$531$	−7.16288e6	−	8.98197e6i	−1.10243	−	1.38241i
$532$	5.17944e6	−	4.65128e6i	0.793421	−	0.712514i
$533$	−1.38819e6	+	1.74073e6i	−0.211656	+	0.265408i
$534$	−2.64380e6	+	398488.i	−0.401213	+	0.0604731i
$535$	−4.39808e6	−	2.99856e6i	−0.664323	−	0.452928i
$536$	2.42695e6	−	6.18377e6i	0.364879	−	0.929697i
$537$	1.88958e7	+	5.82859e6i	2.82768	+	0.872224i
$538$	2.33240e6			0.347414
$539$	−745794.	+	2.83836e6i	−0.110572	+	0.420820i
$540$	2.37903e7			3.51088
$541$	−794687.	−	245129.i	−0.116736	−	0.0360081i	0.235837	−	0.971793i	$-0.424217\pi$
$541$	−794687.	−	245129.i	−0.116736	−	0.0360081i	−0.352573	+	0.935784i	$0.614693\pi$
$542$	291428.	−	742547.i	0.0426121	−	0.108574i
$543$	1.76778e6	+	1.20525e6i	0.257293	+	0.175420i
$544$	−3.62960e6	+	547074.i	−0.525849	+	0.0792590i
$545$	−8.91769e6	+	1.11824e7i	−1.28606	+	1.61267i
$546$	−1.76060e6	−	294744.i	−0.252743	−	0.0423120i
$547$	−6.74668e6	−	8.46007e6i	−0.964099	−	1.20894i	−0.977908	−	0.209037i	$-0.932967\pi$
$547$	−6.74668e6	−	8.46007e6i	−0.964099	−	1.20894i	0.0138085	−	0.999905i	$-0.495604\pi$
$548$	−3.15621e6	−	2.92853e6i	−0.448967	−	0.416581i
$549$	−9.43296e6	−	1.42179e6i	−1.33573	−	0.201328i
$550$	1.06790e6	−	990870.i	0.150531	−	0.139672i
$551$	−5.55438e6	+	3.78691e6i	−0.779393	+	0.531381i
$552$	211808.	+	927993.i	0.0295866	+	0.129628i
$553$	−204678.	+	833955.i	−0.0284615	+	0.115966i
$554$	183.773	−	805.162i	2.54394e−5	−	0.000111457i
$555$	1.23788e7	+	3.15406e7i	1.70586	+	4.34647i
$556$	469075.	+	6.25938e6i	0.0643510	+	0.858705i
$557$	728093.	+	1.26109e6i	0.0994371	+	0.172230i	0.911452	−	0.411407i	$-0.134962\pi$
$557$	728093.	+	1.26109e6i	0.0994371	+	0.172230i	−0.812015	+	0.583637i	$0.801629\pi$
$558$	−2.46181e6	+	4.26398e6i	−0.334710	+	0.579735i
$559$	6.40035e6	+	3.08224e6i	0.866311	+	0.417194i
$560$	6.70387e6	+	6.42644e6i	0.903350	+	0.865965i
$561$	3.70729e6	−	1.78534e6i	0.497335	−	0.239504i
$562$	−165208.	+	2.20455e6i	−0.0220643	+	0.294428i
$563$	3.59992e6	−	1.11043e6i	0.478654	−	0.147645i	−0.0460338	−	0.998940i	$-0.514658\pi$
$563$	3.59992e6	−	1.11043e6i	0.478654	−	0.147645i	0.524688	+	0.851295i	$0.324182\pi$
$564$	1.61462e7	−	4.98045e6i	2.13734	−	0.659281i
$565$	−225441.	+	3.00830e6i	−0.0297106	+	0.396460i
$566$	−1.11294e6	+	535962.i	−0.146026	+	0.0703223i
$567$	5.22384e6	+	1.39746e7i	0.682389	+	1.82551i
$568$	−1.97251e6	−	949913.i	−0.256537	−	0.123542i
$569$	−3.98342e6	+	6.89949e6i	−0.515793	+	0.893380i	0.484039	+	0.875046i	$0.339169\pi$
$569$	−3.98342e6	+	6.89949e6i	−0.515793	+	0.893380i	−0.999832	+	0.0183332i	$0.994164\pi$
$570$	−3.76856e6	−	6.52733e6i	−0.485834	−	0.841489i
$571$	884134.	+	1.17979e7i	0.113482	+	1.51431i	0.705685	+	0.708526i	$0.250639\pi$
$571$	884134.	+	1.17979e7i	0.113482	+	1.51431i	−0.592203	+	0.805789i	$0.701742\pi$
$572$	571388.	+	1.45587e6i	0.0730199	+	0.186052i
$573$	4.77866e6	−	2.09367e7i	0.608022	−	2.66392i
$574$	−927412.	−	1.20257e6i	−0.117488	−	0.152346i
$575$	397031.	+	1.73951e6i	0.0500789	+	0.219410i
$576$	−8.29668e6	+	5.65658e6i	−1.04195	+	0.710392i
$577$	1.06769e7	−	9.90676e6i	1.33508	−	1.23877i	0.386480	−	0.922298i	$-0.373691\pi$
$577$	1.06769e7	−	9.90676e6i	1.33508	−	1.23877i	0.948600	−	0.316476i	$-0.102500\pi$
$578$	−1.14756e6	−	172967.i	−0.142875	−	0.0215349i
$579$	−1.15599e7	−	1.07260e7i	−1.43304	−	1.32966i
$580$	−6.17586e6	−	7.74428e6i	−0.762302	−	0.955897i
$581$	193693.	+	3.30573e6i	0.0238053	+	0.406281i
$582$	71407.2	−	89541.8i	0.00873845	−	0.0109577i
$583$	−673737.	+	101550.i	−0.0820955	+	0.0123739i
$584$	3.52813e6	+	2.40544e6i	0.428068	+	0.291852i
$585$	5.64440e6	−	1.43817e7i	0.681912	−	1.73748i
$586$	1.26099e6	+	388963.i	0.151693	+	0.0467912i
$587$	−1.63591e7			−1.95959			−0.979796	−	0.200001i	$-0.935905\pi$
$587$	−1.63591e7			−1.95959			−0.979796	+	0.200001i	$0.935905\pi$
$588$	−5.53060e6	+	1.28460e7i	−0.659673	+	1.53223i
$589$	−1.00884e7			−1.19821
$590$	−2.88539e6	−	890024.i	−0.341251	−	0.105262i
$591$	−7.31999e6	+	1.86510e7i	−0.862069	+	2.19652i
$592$	−8.50948e6	−	5.80166e6i	−0.997927	−	0.680375i
$593$	5.37988e6	−	810886.i	0.628255	−	0.0946942i	0.172806	−	0.984956i	$-0.444717\pi$
$593$	5.37988e6	−	810886.i	0.628255	−	0.0946942i	0.455449	+	0.890262i	$0.349479\pi$
$594$	−1.54264e6	+	1.93441e6i	−0.179391	+	0.224949i
$595$	−4.79403e6	−	8.62464e6i	−0.555147	−	0.998731i
$596$	−6.06029e6	−	7.59936e6i	−0.698840	−	0.876317i
$597$	−3.28693e6	−	3.04983e6i	−0.377446	−	0.350219i
$598$	164899.	+	24854.5i	0.0188567	+	0.00284219i
$599$	4.21567e6	−	3.91157e6i	0.480064	−	0.445434i	−0.402644	−	0.915357i	$-0.631909\pi$
$599$	4.21567e6	−	3.91157e6i	0.480064	−	0.445434i	0.882708	+	0.469923i	$0.155718\pi$
$600$	1.19719e7	−	8.16233e6i	1.35765	−	0.925627i
$601$	2.04822e6	+	8.97383e6i	0.231308	+	1.01343i	0.948556	+	0.316608i	$0.102544\pi$
$601$	2.04822e6	+	8.97383e6i	0.231308	+	1.01343i	−0.717249	+	0.696817i	$0.754599\pi$
$602$	−3.08231e6	+	3.73863e6i	−0.346645	+	0.420457i
$603$	−8.35823e6	+	3.66198e7i	−0.936097	+	4.10131i
$604$	684210.	+	1.74334e6i	0.0763127	+	0.194442i
$605$	890851.	+	1.18876e7i	0.0989502	+	1.32040i
$606$	−2.50546e6	−	4.33958e6i	−0.277144	−	0.480027i
$607$	1.93820e6	−	3.35705e6i	0.213514	−	0.369817i	−0.739298	−	0.673378i	$-0.764842\pi$
$607$	1.93820e6	−	3.35705e6i	0.213514	−	0.369817i	0.952812	+	0.303562i	$0.0981758\pi$
$608$	7.23658e6	+	3.48495e6i	0.793916	+	0.382330i
$609$	6.94243e6	−	1.15851e7i	0.758522	−	1.26577i
$610$	−2.25901e6	+	1.08788e6i	−0.245806	+	0.118374i
$611$	461701.	−	6.16097e6i	0.0500331	−	0.667646i
$612$	1.30405e7	−	4.02245e6i	1.40739	−	0.434122i
$613$	1.40529e6	−	433473.i	0.151047	−	0.0465920i	−0.218309	−	0.975880i	$-0.570054\pi$
$613$	1.40529e6	−	433473.i	0.151047	−	0.0465920i	0.369357	+	0.929288i	$0.379578\pi$
$614$	−197744.	+	2.63871e6i	−0.0211681	+	0.282469i
$615$	1.70164e7	−	8.19465e6i	1.81417	−	0.873661i
$616$	−2.20665e6	+	295959.i	−0.234305	+	0.0314253i
$617$	1.09635e7	+	5.27973e6i	1.15941	+	0.558340i	0.911846	−	0.410532i	$-0.134657\pi$
$617$	1.09635e7	+	5.27973e6i	1.15941	+	0.558340i	0.247560	+	0.968873i	$0.420371\pi$
$618$	2.05896e6	−	3.56623e6i	0.216859	−	0.375611i
$619$	1.06378e6	+	1.84252e6i	0.111590	+	0.193280i	0.916412	−	0.400237i	$-0.131072\pi$
$619$	1.06378e6	+	1.84252e6i	0.111590	+	0.193280i	−0.804821	+	0.593517i	$0.797739\pi$
$620$	−1.11085e6	−	1.48232e7i	−0.116058	−	1.54869i
$621$	−1.10711e6	−	2.82087e6i	−0.115203	−	0.293531i
$622$	188628.	−	826432.i	0.0195492	−	0.0856507i
$623$	6.84588e6	+	3.43514e6i	0.706658	+	0.354589i
$624$	1.50160e6	+	6.57893e6i	0.154380	+	0.676385i
$625$	916156.	−	624625.i	0.0938144	−	0.0639616i
$626$	61925.6	−	57458.6i	0.00631589	−	0.00586029i
$627$	−8.90339e6	−	1.34197e6i	−0.904454	−	0.136325i
$628$	743240.	+	689626.i	0.0752021	+	0.0697773i
$629$	6.82301e6	+	8.55578e6i	0.687621	+	0.862249i
$630$	8.60912e6	+	6.07714e6i	0.864186	+	0.610026i
$631$	1.33986e6	−	1.68013e6i	0.133963	−	0.167984i	−0.710325	−	0.703874i	$-0.751452\pi$
$631$	1.33986e6	−	1.68013e6i	0.133963	−	0.167984i	0.844288	+	0.535889i	$0.180024\pi$
$632$	−644176.	+	97094.0i	−0.0641523	+	0.00966940i
$633$	−1.12544e7	−	7.67311e6i	−1.11638	−	0.761136i
$634$	1.30150e6	−	3.31617e6i	0.128594	−	0.327652i
$635$	−3.33658e6	−	1.02920e6i	−0.328373	−	0.101290i
$636$	−3.24710e6			−0.318312
$637$	3.63356e6	+	3.59847e6i	0.354800	+	0.351374i
$638$	1.03016e6			0.100196
$639$	1.18292e7	+	3.64882e6i	1.14605	+	0.353509i
$640$	−5.66438e6	+	1.44326e7i	−0.546642	+	1.39282i
$641$	1.41233e7	+	9.62910e6i	1.35766	+	0.925637i	0.999966	−	0.00820219i	$-0.00261087\pi$
$641$	1.41233e7	+	9.62910e6i	1.35766	+	0.925637i	0.357694	+	0.933839i	$0.383563\pi$
$642$	2.60881e6	−	393215.i	0.249807	−	0.0376524i
$643$	4.80145e6	−	6.02083e6i	0.457978	−	0.574287i	−0.498203	−	0.867060i	$-0.666007\pi$
$643$	4.80145e6	−	6.02083e6i	0.457978	−	0.574287i	0.956182	+	0.292773i	$0.0945782\pi$
$644$	497065.	−	1.20830e6i	0.0472279	−	0.114805i
$645$	−3.75718e7	−	4.71135e7i	−3.55601	−	4.45909i
$646$	−1.78446e6	−	1.65574e6i	−0.168239	−	0.156103i
$647$	−1.33507e6	−	201229.i	−0.125384	−	0.0188986i	0.0860503	−	0.996291i	$-0.472575\pi$
$647$	−1.33507e6	−	201229.i	−0.125384	−	0.0188986i	−0.211435	+	0.977392i	$0.567814\pi$
$648$	−8.29690e6	+	7.69840e6i	−0.776209	+	0.720216i
$649$	−2.98040e6	+	2.03200e6i	−0.277755	+	0.189370i
$650$	−564877.	−	2.47489e6i	−0.0524409	−	0.229759i
$651$	1.84018e7	−	8.49575e6i	1.70180	−	0.785687i
$652$	−309199.	+	1.35469e6i	−0.0284852	+	0.124802i
$653$	−3.90832e6	−	9.95823e6i	−0.358680	−	0.913901i	−0.990341	−	0.138656i	$-0.955722\pi$
$653$	−3.90832e6	−	9.95823e6i	−0.358680	−	0.913901i	0.631661	−	0.775245i	$-0.282374\pi$
$654$	−529763.	−	7.06919e6i	−0.0484325	−	0.646287i
$655$	−5.19748e6	−	9.00229e6i	−0.473357	−	0.819879i
$656$	−2.87042e6	+	4.97172e6i	−0.260427	+	0.451073i
$657$	−2.17535e7	−	1.04759e7i	−1.96615	−	0.946847i
$658$	4.00611e6	+	1.30748e6i	0.360710	+	0.117726i
$659$	1.38531e6	−	667129.i	0.124260	−	0.0598406i	−0.370721	−	0.928744i	$-0.620889\pi$
$659$	1.38531e6	−	667129.i	0.124260	−	0.0598406i	0.494981	+	0.868904i	$0.335175\pi$
$660$	991441.	−	1.32299e7i	0.0885946	−	1.18221i
$661$	1.00750e7	−	3.10772e6i	0.896894	−	0.276655i	0.188166	−	0.982137i	$-0.439746\pi$
$661$	1.00750e7	−	3.10772e6i	0.896894	−	0.276655i	0.708728	+	0.705482i	$0.249269\pi$
$662$	2.37645e6	−	733039.i	0.210758	−	0.0650103i
$663$	535830.	−	7.15016e6i	0.0473417	−	0.631731i
$664$	−2.26339e6	+	1.08999e6i	−0.199223	+	0.0959409i
$665$	−1.96374e6	+	2.15025e7i	−0.172199	+	1.88554i
$666$	−1.05295e7	−	5.07073e6i	−0.919858	−	0.442980i
$667$	−630855.	+	1.09267e6i	−0.0549054	+	0.0950990i
$668$	2.90289e6	+	5.02795e6i	0.251703	+	0.435963i
$669$	39458.3	+	526534.i	0.00340858	+	0.0454843i
$670$	3.60681e6	+	9.19000e6i	0.310410	+	0.790913i
$671$	−666511.	+	2.92017e6i	−0.0571480	+	0.250382i
$672$	−1.61347e7	−	262593.i	−1.37828	−	0.0224316i
$673$	−1.97907e6	−	8.67086e6i	−0.168431	−	0.737946i	−0.986625	−	0.163004i	$-0.947882\pi$
$673$	−1.97907e6	−	8.67086e6i	−0.168431	−	0.737946i	0.818194	−	0.574942i	$-0.194975\pi$
$674$	2.50890e6	−	1.71054e6i	0.212732	−	0.145038i
$675$	−3.38154e7	+	3.13761e7i	−2.85663	+	2.65057i
$676$	−8.11289e6	−	1.22282e6i	−0.682824	−	0.102919i
$677$	916331.	+	850231.i	0.0768388	+	0.0712960i	0.717657	−	0.696396i	$-0.245214\pi$
$677$	916331.	+	850231.i	0.0768388	+	0.0712960i	−0.640819	+	0.767692i	$0.721405\pi$
$678$	−932243.	−	1.16900e6i	−0.0778852	−	0.0976649i
$679$	−315052.	+	91593.3i	−0.0262245	+	0.00762411i
$680$	4.66739e6	−	5.85273e6i	0.387081	−	0.485385i
$681$	3.43036e7	−	5.17044e6i	2.83447	−	0.427228i
$682$	1.27732e6	+	870862.i	0.105157	+	0.0716950i
$683$	−7.26718e6	+	1.85165e7i	−0.596094	+	1.51882i	0.240304	+	0.970698i	$0.422753\pi$
$683$	−7.26718e6	+	1.85165e7i	−0.596094	+	1.51882i	−0.836397	+	0.548124i	$0.815342\pi$
$684$	−2.85351e7	−	8.80192e6i	−2.33206	−	0.719345i
$685$	1.33545e7			1.08743
$686$	−2.97445e6	+	1.82192e6i	−0.241322	+	0.147816i
$687$	−3.81439e6			−0.308343
$688$	1.75031e7	+	5.39899e6i	1.40976	+	0.434852i
$689$	−433763.	+	1.10521e6i	−0.0348100	+	0.0886945i
$690$	−1.16880e6	−	796875.i	−0.0934582	−	0.0637188i
$691$	1.38419e7	−	2.08633e6i	1.10281	−	0.166222i	0.427687	−	0.903927i	$-0.359329\pi$
$691$	1.38419e7	−	2.08633e6i	1.10281	−	0.166222i	0.675123	+	0.737705i	$0.264091\pi$
$692$	583038.	−	731106.i	0.0462840	−	0.0580384i
$693$	1.20883e7	−	3.51437e6i	0.956165	−	0.277981i
$694$	1.26249e6	+	1.58311e6i	0.0995016	+	0.124771i
$695$	−1.42718e7	−	1.32423e7i	−1.12077	−	1.03992i
$696$	1.01318e7	+	1.52712e6i	0.792801	+	0.119495i
$697$	4.47157e6	−	4.14901e6i	0.348640	−	0.323491i
$698$	−1.56829e6	+	1.06924e6i	−0.121839	+	0.0830687i
$699$	3.90371e6	+	1.71033e7i	0.302193	+	1.32400i
$700$	−1.98864e7	−	323650.i	−1.53395	−	0.0249650i
$701$	2.11941e6	−	9.28572e6i	0.162899	−	0.713708i	−0.825821	−	0.563933i	$-0.809288\pi$
$701$	2.11941e6	−	9.28572e6i	0.162899	−	0.713708i	0.988720	−	0.149776i	$-0.0478551\pi$
$702$	1.57514e6	+	4.01340e6i	0.120636	+	0.307376i
$703$	−1.78949e6	−	2.38791e7i	−0.136565	−	1.82234i
$704$	1.57645e6	+	2.73048e6i	0.119880	+	0.207639i
$705$	−2.62044e7	+	4.53873e7i	−1.98564	+	3.43923i
$706$	−2.80627e6	−	1.35143e6i	−0.211893	−	0.102043i
$707$	−1.30556e6	+	1.42956e7i	−0.0982308	+	1.07561i
$708$	−1.54884e7	+	7.45880e6i	−1.16124	+	0.559224i
$709$	534295.	−	7.12966e6i	0.0399177	−	0.532664i	−0.941021	−	0.338348i	$-0.890132\pi$
$709$	534295.	−	7.12966e6i	0.0399177	−	0.532664i	0.980939	−	0.194317i	$-0.0622489\pi$
$710$	3.10911e6	−	959035.i	0.231468	−	0.0713984i
$711$	3.51988e6	−	1.08574e6i	0.261128	−	0.0805473i
$712$	−434239.	+	5.79452e6i	−0.0321018	+	0.428368i
$713$	−1.70593e6	+	821531.i	−0.125671	+	0.0605202i
$714$	4.64932e6	+	1.51741e6i	0.341306	+	0.111393i
$715$	−4.37058e6	−	2.10476e6i	−0.319723	−	0.153971i
$716$	1.02959e7	−	1.78330e7i	0.750555	−	1.30000i
$717$	2.37696e7	+	4.11701e7i	1.72673	+	2.99078i
$718$	−39763.1	−	530601.i	−0.00287852	−	0.0384111i
$719$	−7.96130e6	−	2.02851e7i	−0.574330	−	1.46337i	−0.862633	−	0.505830i	$-0.831186\pi$
$719$	−7.96130e6	−	2.02851e7i	−0.574330	−	1.46337i	0.288303	−	0.957539i	$-0.406909\pi$
$720$	8.86437e6	−	3.88373e7i	0.637260	−	2.79202i
$721$	−1.07105e7	+	4.94483e6i	−0.767311	+	0.354253i
$722$	303260.	+	1.32867e6i	0.0216507	+	0.0948581i
$723$	1.67786e7	−	1.14395e7i	1.19374	−	0.813880i
$724$	1.63324e6	−	1.51543e6i	0.115799	−	0.107445i
$725$	1.89919e7	+	2.86257e6i	1.34191	+	0.202260i
$726$	−4.33119e6	−	4.01875e6i	−0.304976	−	0.282976i
$727$	−1.27997e7	−	1.60504e7i	−0.898183	−	1.12629i	−0.991430	−	0.130643i	$-0.958296\pi$
$727$	−1.27997e7	−	1.60504e7i	−0.898183	−	1.12629i	0.0932466	−	0.995643i	$-0.470276\pi$
$728$	−1.47597e6	+	3.58790e6i	−0.103216	+	0.250906i
$729$	1.99207e6	−	2.49798e6i	0.138831	−	0.174089i
$730$	−6.27514e6	+	945825.i	−0.435829	+	0.0656906i
$731$	−1.60807e7	−	1.09637e7i	−1.11304	−	0.758861i
$732$	−5.21509e6	+	1.32878e7i	−0.359736	+	0.916593i
$733$	2.11241e7	+	6.51593e6i	1.45217	+	0.447936i	0.917709	−	0.397254i	$-0.130037\pi$
$733$	2.11241e7	+	6.51593e6i	1.45217	+	0.447936i	0.534465	+	0.845191i	$0.320513\pi$
$734$	5.14708e6			0.352631
$735$	−1.45260e7	−	4.08756e7i	−0.991810	−	2.79091i
$736$	1.50749e6			0.102579
$737$	1.12698e7	+	3.47628e6i	0.764273	+	0.235747i
$738$	−2.37998e6	+	6.06410e6i	−0.160854	+	0.409850i
$739$	−6.82534e6	−	4.65344e6i	−0.459741	−	0.313446i	0.311209	−	0.950341i	$-0.399266\pi$
$739$	−6.82534e6	−	4.65344e6i	−0.459741	−	0.313446i	−0.770950	+	0.636895i	$0.780218\pi$
$740$	3.48894e7	−	5.25873e6i	2.34215	−	0.353022i
$741$	−9.78246e6	+	1.22668e7i	−0.654489	+	0.820704i
$742$	−661596.	−	467018.i	−0.0441147	−	0.0311404i
$743$	1.06720e7	+	1.33822e7i	0.709207	+	0.889317i	0.997674	−	0.0681730i	$-0.0217170\pi$
$743$	1.06720e7	+	1.33822e7i	0.709207	+	0.889317i	−0.288467	+	0.957490i	$0.593146\pi$
$744$	1.12717e7	+	1.04586e7i	0.746549	+	0.692696i
$745$	2.98114e7	+	4.49335e6i	1.96785	+	0.296606i
$746$	−750228.	+	696110.i	−0.0493567	+	0.0457963i
$747$	1.17365e7	−	8.00178e6i	0.769547	−	0.524669i
$748$	−953477.	−	4.17745e6i	−0.0623098	−	0.272997i
$749$	−6.75529e6	−	3.38968e6i	−0.439986	−	0.220777i
$750$	−1.91849e6	+	8.40545e6i	−0.124539	+	0.545642i
$751$	382456.	+	974482.i	0.0247447	+	0.0630484i	0.942712	−	0.333607i	$-0.108266\pi$
$751$	382456.	+	974482.i	0.0247447	+	0.0630484i	−0.917967	+	0.396656i	$0.870171\pi$
$752$	−1.19047e6	−	1.58857e7i	−0.0767668	−	1.02438i
$753$	−1.86543e7	−	3.23102e7i	−1.19892	−	2.07660i
$754$	897550.	−	1.55460e6i	0.0574950	−	0.0995843i
$755$	−5.23356e6	−	2.52035e6i	−0.334141	−	0.160914i
$756$	3.34796e7	−	4.49034e6i	2.13047	−	0.285743i
$757$	4.76714e6	−	2.29574e6i	0.302356	−	0.145607i	−0.276554	−	0.960998i	$-0.589192\pi$
$757$	4.76714e6	−	2.29574e6i	0.302356	−	0.145607i	0.578910	+	0.815391i	$0.303478\pi$
$758$	445587.	−	5.94594e6i	0.0281682	−	0.375879i
$759$	−1.61483e6	+	498109.i	−0.101747	+	0.0313849i
$760$	−1.56529e7	+	4.82829e6i	−0.983019	+	0.303221i
$761$	1.04395e6	−	1.39305e7i	0.0653458	−	0.871979i	−0.864171	−	0.503199i	$-0.832156\pi$
$761$	1.04395e6	−	1.39305e7i	0.0653458	−	0.871979i	0.929517	−	0.368781i	$-0.120225\pi$
$762$	1.55923e6	−	750886.i	0.0972798	−	0.0468475i
$763$	−1.04390e7	+	1.74200e7i	−0.649155	+	1.08327i
$764$	−2.01483e7	−	9.70289e6i	−1.24883	−	0.601406i
$765$	−2.11639e7	+	3.66570e7i	−1.30750	+	2.26466i
$766$	−835745.	−	1.44755e6i	−0.0514638	−	0.0891379i
$767$	469731.	+	6.26813e6i	0.0288311	+	0.384724i
$768$	3.15996e6	+	8.05144e6i	0.193321	+	0.492573i
$769$	−3.49293e6	+	1.53035e7i	−0.212997	+	0.933201i	0.749520	+	0.661981i	$0.230284\pi$
$769$	−3.49293e6	+	1.53035e7i	−0.212997	+	0.933201i	−0.962517	+	0.271220i	$0.912573\pi$
$770$	2.10481e6	−	2.55299e6i	0.127934	−	0.155175i
$771$	1.05199e7	+	4.60905e7i	0.637344	+	2.79239i
$772$	−1.35680e7	+	9.25053e6i	−0.819358	+	0.558629i
$773$	−1.67853e7	+	1.55745e7i	−1.01037	+	0.937488i	−0.998049	−	0.0624365i	$-0.980113\pi$
$773$	−1.67853e7	+	1.55745e7i	−1.01037	+	0.937488i	−0.0123224	+	0.999924i	$0.503922\pi$
$774$	2.05529e7	+	3.09785e6i	1.23316	+	0.185869i
$775$	2.11287e7	+	1.96045e7i	1.26362	+	1.17247i
$776$	−155192.	−	194604.i	−0.00925155	−	0.0116011i
$777$	2.33735e7	+	4.20498e7i	1.38890	+	2.49869i
$778$	5.30402e6	−	6.65103e6i	0.314164	−	0.393949i
$779$	−1.31988e7	+	1.98940e6i	−0.779274	+	0.117457i
$780$	−1.91013e7	−	1.30230e7i	−1.12415	−	0.766435i
$781$	1.42004e6	−	3.61820e6i	0.0833052	−	0.212258i
$782$	−436583.	−	134668.i	−0.0255299	−	0.00787494i
$783$	−3.26201e7			−1.90143
$784$	1.06472e7	+	7.77844e6i	0.618649	+	0.451963i
$785$	−3.14479e6			−0.182145
$786$	4.92322e6	+	1.51861e6i	0.284245	+	0.0876779i
$787$	8.86303e6	−	2.25826e7i	0.510088	−	1.29968i	−0.411463	−	0.911426i	$-0.634982\pi$
$787$	8.86303e6	−	2.25826e7i	0.510088	−	1.29968i	0.921551	−	0.388257i	$-0.126923\pi$
$788$	1.72389e7	+	1.17533e7i	0.988997	+	0.674286i
$789$	−4.42338e7	+	6.66717e6i	−2.52966	+	0.381284i
$790$	603635.	−	756935.i	0.0344118	−	0.0431510i
$791$	250548.	+	4.27606e6i	0.0142380	+	0.242998i
$792$	5.95461e6	+	7.46684e6i	0.337319	+	0.422984i
$793$	3.82610e6	+	3.55010e6i	0.216059	+	0.200474i
$794$	−8.90373e6	−	1.34202e6i	−0.501211	−	0.0755455i
$795$	7.38290e6	−	6.85033e6i	0.414295	−	0.384409i
$796$	−3.85793e6	+	2.63029e6i	−0.215810	+	0.147137i
$797$	−5.19392e6	−	2.27561e7i	−0.289634	−	1.26897i	−0.885029	−	0.465536i	$-0.845861\pi$
$797$	−5.19392e6	−	2.27561e7i	−0.289634	−	1.26897i	0.595395	−	0.803433i	$-0.296996\pi$
$798$	−6.53541e6	−	8.47446e6i	−0.363300	−	0.471091i
$799$	−3.76654e6	+	1.65023e7i	−0.208726	+	0.914486i
$800$	−8.38375e6	−	2.13615e7i	−0.463141	−	1.18006i
$801$	−2.45533e6	−	3.27641e7i	−0.135216	−	1.80433i
$802$	2.67364e6	+	4.63088e6i	0.146780	+	0.254230i
$803$	−3.79053e6	+	6.56539e6i	−0.207449	+	0.359312i
$804$	5.06396e7	+	2.43868e7i	2.76281	+	1.33050i
$805$	1.41896e6	+	3.79596e6i	0.0771757	+	0.206458i
$806$	2.42711e6	−	1.16883e6i	0.131599	−	0.0633746i
$807$	−3.07788e6	+	4.10714e7i	−0.166367	+	2.22002i
$808$	−1.04066e7	+	3.21000e6i	−0.560763	+	0.172973i
$809$	2.91908e7	−	9.00417e6i	1.56810	−	0.483696i	0.615557	−	0.788092i	$-0.288931\pi$
$809$	2.91908e7	−	9.00417e6i	1.56810	−	0.483696i	0.952545	+	0.304397i	$0.0984548\pi$
$810$	1.25701e6	−	1.67736e7i	0.0673173	−	0.898287i
$811$	2.82208e7	−	1.35904e7i	1.50667	−	0.725573i	0.515341	−	0.856985i	$-0.327665\pi$
$811$	2.82208e7	−	1.35904e7i	1.50667	−	0.725573i	0.991328	+	0.131412i	$0.0419510\pi$
$812$	−1.01528e7	−	9.73267e6i	−0.540378	−	0.518015i
$813$	1.26910e7	+	6.11166e6i	0.673394	+	0.324289i
$814$	−1.83475e6	+	3.17788e6i	−0.0970545	+	0.168103i
$815$	−2.15493e6	−	3.73245e6i	−0.113642	−	0.196834i
$816$	−1.38161e6	−	1.84363e7i	−0.0726372	−	0.969277i
$817$	1.55591e7	+	3.96440e7i	0.815512	+	2.07789i
$818$	−421039.	+	1.84469e6i	−0.0220008	+	0.0963920i
$819$	5.22874e6	−	2.13044e7i	0.272387	−	1.10984i
$820$	−4.37644e6	−	1.91744e7i	−0.227293	−	0.995836i
$821$	−8.13040e6	+	5.54321e6i	−0.420973	+	0.287014i	−0.755220	−	0.655471i	$-0.772470\pi$
$821$	−8.13040e6	+	5.54321e6i	−0.420973	+	0.287014i	0.334248	+	0.942485i	$0.391518\pi$
$822$	−4.85205e6	+	4.50205e6i	−0.250464	+	0.232397i
$823$	2.18542e6	+	329399.i	0.112470	+	0.0169521i	0.205036	−	0.978754i	$-0.434269\pi$
$823$	2.18542e6	+	329399.i	0.112470	+	0.0169521i	−0.0925663	+	0.995707i	$0.529507\pi$
$824$	−6.56055e6	−	6.08730e6i	−0.336606	−	0.312325i
$825$	1.60391e7	+	2.01124e7i	0.820436	+	1.02879i
$826$	−4.22852e6	−	707903.i	−0.215645	−	0.0361014i
$827$	1.08555e7	−	1.36123e7i	0.551932	−	0.692101i	−0.425112	−	0.905141i	$-0.639765\pi$
$827$	1.08555e7	−	1.36123e7i	0.551932	−	0.692101i	0.977043	+	0.213040i	$0.0683366\pi$
$828$	−5.54202e6	+	835325.i	−0.280926	+	0.0423428i
$829$	−1.82822e7	−	1.24646e7i	−0.923935	−	0.629928i	0.00507361	−	0.999987i	$-0.498385\pi$
$829$	−1.82822e7	−	1.24646e7i	−0.923935	−	0.629928i	−0.929008	+	0.370059i	$0.879337\pi$
$830$	1.36399e6	−	3.47539e6i	0.0687252	−	0.175109i
$831$	13935.7	+	4298.58i	0.000700043	+	0.000215935i
$832$	5.49407e6			0.275160
$833$	−8.37439e6	−	1.12324e7i	−0.418158	−	0.560867i
$834$	9.64954e6			0.480387
$835$	−1.72076e7	−	5.30785e6i	−0.854092	−	0.263453i
$836$	−3.42550e6	+	8.72804e6i	−0.169515	+	0.431918i
$837$	−4.04466e7	−	2.75760e7i	−1.99558	−	1.36056i
$838$	−6.72669e6	+	1.01389e6i	−0.330896	+	0.0498745i
$839$	−1.90893e7	+	2.39372e7i	−0.936234	+	1.17400i	0.0483042	+	0.998833i	$0.484618\pi$
$839$	−1.90893e7	+	2.39372e7i	−0.936234	+	1.17400i	−0.984539	+	0.175168i	$0.943953\pi$
$840$	2.44858e7	−	2.19890e7i	1.19734	−	1.07524i
$841$	−4.32047e6	−	5.41770e6i	−0.210640	−	0.264134i
$842$	−912856.	−	847007.i	−0.0443734	−	0.0411725i
$843$	−3.86020e7	−	5.81832e6i	−1.87086	−	0.281987i
$844$	−1.03978e7	+	9.64779e6i	−0.502444	+	0.466200i
$845$	2.10260e7	−	1.43353e7i	1.01301	−	0.690659i
$846$	−4.02247e6	−	1.76236e7i	−0.193227	−	0.846581i
$847$	3.49741e6	+	1.65610e7i	0.167509	+	0.793190i
$848$	−681212.	+	2.98458e6i	−0.0325306	+	0.142526i
$849$	−7.96915e6	−	2.03051e7i	−0.379440	−	0.966796i
$850$	519738.	+	6.93543e6i	0.0246739	+	0.329250i
$851$	−2.24716e6	−	3.89219e6i	−0.106368	−	0.184234i
$852$	9.26187e6	−	1.60420e7i	0.437119	−	0.757112i
$853$	−3.35442e7	−	1.61540e7i	−1.57850	−	0.760167i	−0.579986	−	0.814626i	$-0.696942\pi$
$853$	−3.35442e7	−	1.61540e7i	−1.57850	−	0.760167i	−0.998516	+	0.0544596i	$0.982656\pi$
$854$	−2.97371e6	+	1.95733e6i	−0.139526	+	0.0918372i
$855$	8.34493e7	−	4.01871e7i	3.90398	−	1.88006i
$856$	428493.	−	5.71784e6i	0.0199875	−	0.266715i
$857$	1.03955e7	−	3.20658e6i	0.483496	−	0.149139i	−0.0434188	−	0.999057i	$-0.513825\pi$
$857$	1.03955e7	−	3.20658e6i	0.483496	−	0.149139i	0.526915	+	0.849918i	$0.323349\pi$
$858$	2.29750e6	−	708686.i	0.106546	−	0.0328651i
$859$	−1.49387e6	+	1.99344e7i	−0.0690766	+	0.921763i	0.849771	+	0.527151i	$0.176740\pi$
$859$	−1.49387e6	+	1.99344e7i	−0.0690766	+	0.921763i	−0.918848	+	0.394612i	$0.870879\pi$
$860$	−5.65373e7	+	2.72269e7i	−2.60669	+	1.25531i
$861$	2.24000e7	−	1.47439e7i	1.02977	−	0.677805i
$862$	−1.83654e6	−	884430.i	−0.0841845	−	0.0405411i
$863$	1.69819e7	−	2.94135e7i	0.776175	−	1.34437i	−0.157957	−	0.987446i	$-0.550491\pi$
$863$	1.69819e7	−	2.94135e7i	0.776175	−	1.34437i	0.934132	−	0.356928i	$-0.116176\pi$
$864$	1.94872e7	+	3.37528e7i	0.888105	+	1.53824i
$865$	216750.	+	2.89233e6i	0.00984961	+	0.131434i
$866$	−683072.	−	1.74044e6i	−0.0309508	−	0.0788614i
$867$	4.56013e6	−	1.99792e7i	0.206029	−	0.902674i
$868$	−4.36110e6	−	2.06507e7i	−0.196470	−	0.930327i
$869$	−257362.	−	1.12758e6i	−0.0115610	−	0.0506520i
$870$	−1.25815e7	+	8.57793e6i	−0.563553	+	0.384224i
$871$	1.50651e7	−	1.39784e7i	0.672865	−	0.624328i
$872$	−1.52347e7	−	2.29627e6i	−0.678491	−	0.102266i
$873$	1.03170e6	+	957282.i	0.0458163	+	0.0425113i
$874$	623331.	+	781633.i	0.0276020	+	0.0346118i
$875$	1.83765e7	−	1.65026e7i	0.811415	−	0.728673i
$876$	−2.25261e7	+	2.82469e7i	−0.991804	+	1.24368i
$877$	−2.70914e7	+	4.08337e6i	−1.18941	+	0.179275i	−0.713780	−	0.700370i	$-0.753018\pi$
$877$	−2.70914e7	+	4.08337e6i	−1.18941	+	0.179275i	−0.475631	+	0.879645i	$0.657780\pi$
$878$	6.24323e6	+	4.25656e6i	0.273321	+	0.186347i
$879$	−8.51330e6	+	2.16915e7i	−0.371643	+	0.946931i
$880$	−1.19523e7	−	3.68679e6i	−0.520288	−	0.160488i
$881$	3.91056e6			0.169746			0.0848730	−	0.996392i	$-0.472952\pi$
$881$	3.91056e6			0.169746			0.0848730	+	0.996392i	$0.472952\pi$
$882$	1.32624e7	+	6.92728e6i	0.574053	+	0.299841i
$883$	−3.74336e6			−0.161570			−0.0807849	−	0.996732i	$-0.525743\pi$
$883$	−3.74336e6			−0.161570			−0.0807849	+	0.996732i	$0.525743\pi$
$884$	−7.13490e6	−	2.20083e6i	−0.307084	−	0.0947229i
$885$	1.94801e7	−	4.96345e7i	0.836051	−	2.13022i
$886$	−219715.	−	149799.i	−0.00940320	−	0.00641099i
$887$	−2.94680e7	+	4.44159e6i	−1.25760	+	0.189552i	−0.743825	−	0.668374i	$-0.766991\pi$
$887$	−2.94680e7	+	4.44159e6i	−1.25760	+	0.189552i	−0.513773	+	0.857926i	$0.671752\pi$
$888$	−2.27561e7	+	2.85352e7i	−0.968424	+	1.21436i
$889$	−4.88975e6	−	818600.i	−0.207507	−	0.0347390i
$890$	−5.38425e6	−	6.75163e6i	−0.227851	−	0.285716i
$891$	−1.47301e7	−	1.36676e7i	−0.621602	−	0.576763i
$892$	543698.	+	81949.2i	0.0228794	+	0.00344852i
$893$	2.71515e7	−	2.51929e7i	1.13937	−	1.05718i
$894$	−1.23461e7	+	8.41741e6i	−0.516637	+	0.352237i
$895$	1.42122e7	+	6.22679e7i	0.593069	+	2.59840i
$896$	−5.24725e6	+	2.13798e7i	−0.218354	+	0.889680i
$897$	−655269.	+	2.87092e6i	−0.0271918	+	0.119135i
$898$	1.75238e6	+	4.46500e6i	0.0725167	+	0.184770i
$899$	1.52314e6	+	2.03248e7i	0.0628550	+	0.838741i
$900$	4.26582e7	+	7.38862e7i	1.75548	+	3.04058i
$901$	1.62641e6	−	2.81703e6i	0.0667449	−	0.115606i
$902$	1.84287e6	+	887480.i	0.0754187	+	0.0363197i
$903$	−6.17664e7	−	5.92102e7i	−2.52077	−	2.41645i
$904$	−2.92777e6	+	1.40994e6i	−0.119156	+	0.0573824i
$905$	−516425.	+	6.89122e6i	−0.0209598	+	0.279688i
$906$	2.75115e6	−	848618.i	0.111351	−	0.0343472i
$907$	−1.43224e7	+	4.41787e6i	−0.578092	+	0.178318i	−0.569993	−	0.821650i	$-0.693054\pi$
$907$	−1.43224e7	+	4.41787e6i	−0.578092	+	0.178318i	−0.00809868	+	0.999967i	$0.502578\pi$
$908$	2.69964e6	−	3.60242e7i	0.108666	−	1.45004i
$909$	5.54798e7	−	2.67177e7i	2.22702	−	1.07248i
$910$	−2.01883e6	−	5.40070e6i	−0.0808157	−	0.216196i
$911$	−23749.8	−	11437.3i	−0.000948120	−	0.000456591i	0.433410	−	0.901197i	$-0.357310\pi$
$911$	−23749.8	−	11437.3i	−0.000948120	−	0.000456591i	−0.434358	+	0.900740i	$0.643025\pi$
$912$	−2.02277e7	+	3.50354e7i	−0.805302	+	1.39482i
$913$	−2.23003e6	−	3.86253e6i	−0.0885390	−	0.153354i
$914$	115842.	+	1.54580e6i	0.00458671	+	0.0612053i
$915$	−1.61755e7	−	4.12146e7i	−0.638713	−	1.62741i
$916$	−883871.	+	3.87249e6i	−0.0348057	+	0.152494i
$917$	−9.01344e6	−	1.16877e7i	−0.353970	−	0.458993i
$918$	−2.62845e6	−	1.15160e7i	−0.102942	−	0.451018i
$919$	1.01643e7	−	6.92988e6i	0.396997	−	0.270668i	−0.348323	−	0.937374i	$-0.613249\pi$
$919$	1.01643e7	−	6.92988e6i	0.396997	−	0.270668i	0.745321	+	0.666706i	$0.232296\pi$
$920$	−2.25370e6	+	2.09113e6i	−0.0877864	+	0.0814538i
$921$	−4.62043e7	−	6.96418e6i	−1.79487	−	0.270533i
$922$	−486393.	−	451306.i	−0.0188434	−	0.0174841i
$923$	−4.22295e6	−	5.29541e6i	−0.163159	−	0.204595i
$924$	−1.10186e6	−	1.88052e7i	−0.0424566	−	0.724600i
$925$	−4.26559e7	+	5.34888e7i	−1.63917	+	2.05546i
$926$	3.68801e6	−	555878.i	0.141340	−	0.0213036i
$927$	4.18111e7	+	2.85063e7i	1.59806	+	1.08954i
$928$	5.92849e6	−	1.51056e7i	0.225982	−	0.575794i
$929$	1.10857e7	+	3.41949e6i	0.421429	+	0.129994i	0.498214	−	0.867054i	$-0.333989\pi$
$929$	1.10857e7	+	3.41949e6i	0.421429	+	0.129994i	−0.0767853	+	0.997048i	$0.524466\pi$
$930$	−2.28517e7			−0.866385
$931$	1.29500e6	+	3.06306e7i	0.0489660	+	1.15820i
$932$	1.82684e7			0.688906
$933$	1.43038e7	+	4.41213e6i	0.537956	+	0.165937i
$934$	617774.	−	1.57406e6i	0.0231719	−	0.0590411i
$935$	1.09810e7	+	7.48671e6i	0.410783	+	0.280067i
$936$	1.64563e7	−	2.48038e6i	0.613962	−	0.0925399i
$937$	5.77818e6	−	7.24561e6i	0.215002	−	0.269604i	−0.662622	−	0.748954i	$-0.730556\pi$
$937$	5.77818e6	−	7.24561e6i	0.215002	−	0.269604i	0.877624	+	0.479350i	$0.159128\pi$
$938$	6.81036e6	+	1.22521e7i	0.252734	+	0.454678i
$939$	930074.	+	1.16628e6i	0.0344234	+	0.0431656i
$940$	4.00066e7	+	3.71207e7i	1.47677	+	1.37024i
$941$	−3.92176e6	−	591111.i	−0.144380	−	0.0217618i	0.0764545	−	0.997073i	$-0.475640\pi$
$941$	−3.92176e6	−	591111.i	−0.144380	−	0.0217618i	−0.220835	+	0.975311i	$0.570878\pi$
$942$	1.14258e6	−	1.06016e6i	0.0419528	−	0.0389265i
$943$	−2.06989e6	+	1.41123e6i	−0.0757998	+	0.0516794i
$944$	3.60647e6	+	1.58010e7i	0.131720	+	0.577104i
$945$	−6.66491e7	+	8.08408e7i	−2.42781	+	2.94477i
$946$	1.45222e6	−	6.36258e6i	0.0527599	−	0.231156i
$947$	−1.04116e7	−	2.65284e7i	−0.377262	−	0.961248i	−0.985830	−	0.167746i	$-0.946351\pi$
$947$	−1.04116e7	−	2.65284e7i	−0.377262	−	0.961248i	0.608568	−	0.793502i	$-0.291744\pi$
$948$	−411904.	−	5.49648e6i	−0.0148859	−	0.198639i
$949$	6.60519e6	+	1.14405e7i	0.238078	+	0.412363i
$950$	7.60933e6	−	1.31797e7i	0.273550	−	0.473803i
$951$	5.66772e7	+	2.72943e7i	2.03215	+	0.978634i
$952$	5.46363e6	−	9.11736e6i	0.195384	−	0.326044i
$953$	2.13130e7	−	1.02638e7i	0.760172	−	0.366080i	−0.0132984	−	0.999912i	$-0.504233\pi$
$953$	2.13130e7	−	1.02638e7i	0.760172	−	0.366080i	0.773471	+	0.633832i	$0.218519\pi$
$954$	−259601.	+	3.46413e6i	−0.00923497	+	0.123232i
$955$	6.62809e7	−	2.04449e7i	2.35169	−	0.725400i
$956$	4.73051e7	−	1.45917e7i	1.67403	−	0.516370i
$957$	−1.35941e6	+	1.81401e7i	−0.0479813	+	0.640265i
$958$	1.28757e7	−	6.20059e6i	0.453269	−	0.218283i
$959$	1.87935e7	−	2.52062e6i	0.659874	−	0.0885034i
$960$	−4.19897e7	−	2.02212e7i	−1.47050	−	0.708155i
$961$	−978831.	+	1.69538e6i	−0.0341900	+	0.0592188i
$962$	3.19714e6	+	5.53761e6i	0.111384	+	0.192923i
$963$	2.42284e6	+	3.23305e7i	0.0841896	+	1.12343i
$964$	−7.72578e6	−	1.96850e7i	−0.267762	−	0.682247i
$965$	1.13339e7	−	4.96570e7i	0.391797	−	1.71657i
$966$	−1.79523e6	−	900816.i	−0.0618982	−	0.0310594i
$967$	−8.74664e6	−	3.83215e7i	−0.300798	−	1.31788i	−0.868926	−	0.494942i	$-0.835189\pi$
$967$	−8.74664e6	−	3.83215e7i	−0.300798	−	1.31788i	0.568128	−	0.822940i	$-0.307668\pi$
$968$	−1.06097e7	+	7.23360e6i	−0.363929	+	0.248122i
$969$	3.15108e7	−	2.92378e7i	1.07808	−	1.00031i
$970$	365783.	+	55133.0i	0.0124823	+	0.00188140i
$971$	−1.93018e7	−	1.79095e7i	−0.656976	−	0.609585i	0.279571	−	0.960125i	$-0.409808\pi$
$971$	−1.93018e7	−	1.79095e7i	−0.656976	−	0.609585i	−0.936548	+	0.350540i	$0.885998\pi$
$972$	−2.02306e7	−	2.53684e7i	−0.686822	−	0.861247i
$973$	−2.25838e7	−	1.59418e7i	−0.764742	−	0.539828i
$974$	−7.03181e6	+	8.81762e6i	−0.237503	+	0.297820i
$975$	4.43259e7	−	6.68105e6i	1.49330	−	0.225078i
$976$	1.11195e7	+	7.58113e6i	0.373646	+	0.254747i
$977$	−1.05541e7	+	2.68914e7i	−0.353740	+	0.901315i	0.637644	+	0.770331i	$0.279909\pi$
$977$	−1.05541e7	+	2.68914e7i	−0.353740	+	0.901315i	−0.991384	+	0.130984i	$0.958186\pi$
$978$	2.04122e6	+	629633.i	0.0682406	+	0.0210494i
$979$	−1.03163e7			−0.344007
$980$	−4.48642e7	+	5.27558e6i	−1.49223	+	0.175471i
$981$	8.71152e7			2.89016
$982$	−1.41892e6	−	437678.i	−0.0469547	−	0.0144836i
$983$	−6.06089e6	+	1.54429e7i	−0.200057	+	0.509736i	−0.995332	−	0.0965128i	$-0.969231\pi$
$983$	−6.06089e6	+	1.54429e7i	−0.200057	+	0.509736i	0.795275	+	0.606249i	$0.207326\pi$
$984$	1.68094e7	+	1.14605e7i	0.553433	+	0.377324i
$985$	−6.39917e7	+	9.64520e6i	−2.10152	+	0.316753i
$986$	−3.06637e6	+	3.84511e6i	−0.100446	+	0.125955i
$987$	−2.83101e7	+	6.88185e7i	−0.925015	+	2.24860i
$988$	1.01869e7	+	1.27739e7i	0.332008	+	0.416325i
$989$	5.85938e6	+	5.43671e6i	0.190485	+	0.176744i
$990$	−1.40349e7	−	2.11542e6i	−0.455114	−	0.0685974i
$991$	−1.28308e7	+	1.19053e7i	−0.415021	+	0.385084i	−0.859862	−	0.510526i	$-0.829451\pi$
$991$	−1.28308e7	+	1.19053e7i	−0.415021	+	0.385084i	0.444841	+	0.895610i	$0.353260\pi$
$992$	2.01207e7	−	1.37180e7i	0.649177	−	0.442601i
$993$	9.77212e6	+	4.28145e7i	0.314497	+	1.37790i
$994$	4.19437e6	−	1.93646e6i	0.134648	−	0.0621645i
$995$	3.22267e6	−	1.41194e7i	0.103195	−	0.452127i
$996$	−7.76546e6	−	1.97861e7i	−0.248038	−	0.631991i
$997$	1.47900e6	+	1.97359e7i	0.0471227	+	0.628809i	0.969904	+	0.243486i	$0.0782910\pi$
$997$	1.47900e6	+	1.97359e7i	0.0471227	+	0.628809i	−0.922782	+	0.385323i	$0.874090\pi$
$998$	4.92089e6	+	8.52323e6i	0.156393	+	0.270881i
$999$	5.80977e7	−	1.00628e8i	1.84181	−	3.19011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.g.a.2.10	✓	264
49.25	even	21	inner	49.6.g.a.25.10	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.g.a.2.10	✓	264	1.1	even	1	trivial
49.6.g.a.25.10	yes	264	49.25	even	21	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52973 - 0.471861i) q^{2} +(10.3277 - 26.3145i) q^{3} +(-24.3222 - 16.5826i) q^{4} +(90.2851 - 13.6083i) q^{5} +(-28.2154 + 35.3810i) q^{6} +(124.488 - 36.1916i) q^{7} +(61.3216 + 76.8948i) q^{8} +(-407.661 - 378.255i) q^{9} +(-144.533 - 21.7849i) q^{10} +(-128.000 + 118.767i) q^{11} +(-687.555 + 468.767i) q^{12} +(67.7066 + 296.642i) q^{13} +(-207.510 - 3.37723i) q^{14} +(574.341 - 2516.35i) q^{15} +(286.626 + 730.312i) q^{16} +(-62.2963 - 831.286i) q^{17} +(445.130 + 770.988i) q^{18} +(-912.061 + 1579.74i) q^{19} +(-2421.59 - 1166.18i) q^{20} +(333.304 - 3649.61i) q^{21} +(251.847 - 121.283i) q^{22} +(-25.5846 + 341.403i) q^{23} +(2656.76 - 819.502i) q^{24} +(4980.05 - 1536.14i) q^{25} +(36.4006 - 485.732i) q^{26} +(-7974.78 + 3840.45i) q^{27} +(-3627.96 - 1184.07i) q^{28} +(3320.37 + 1599.00i) q^{29} +(-2065.96 + 3578.34i) q^{30} +(2765.27 + 4789.58i) q^{31} +(-329.053 - 4390.90i) q^{32} +(1803.34 + 4594.84i) q^{33} +(-296.954 + 1301.04i) q^{34} +(10746.9 - 4961.63i) q^{35} +(3642.78 + 15960.1i) q^{36} +(-10846.4 + 7394.94i) q^{37} +(2140.63 - 1986.21i) q^{38} +(8505.25 + 1281.96i) q^{39} +(6582.84 + 6107.98i) q^{40} +(4562.34 + 5720.99i) q^{41} +(-2231.97 + 5425.66i) q^{42} +(14556.7 - 18253.5i) q^{43} +(5082.70 - 766.094i) q^{44} +(-41953.2 - 28603.2i) q^{45} +(200.232 - 510.184i) q^{46} +(-19403.0 - 5985.03i) q^{47} +22178.0 q^{48} +(14187.3 - 9010.82i) q^{49} -8343.00 q^{50} +(-22518.3 - 6945.97i) q^{51} +(3272.32 - 8337.74i) q^{52} +(3224.03 + 2198.11i) q^{53} +(14011.5 - 2111.89i) q^{54} +(-9940.28 + 12464.7i) q^{55} +(10416.7 + 7353.13i) q^{56} +(32150.5 + 40315.5i) q^{57} +(-4324.77 - 4012.80i) q^{58} +(20427.5 + 3078.95i) q^{59} +(-55696.9 + 51679.2i) q^{60} +(14173.2 - 9663.10i) q^{61} +(-1970.11 - 8631.61i) q^{62} +(-64438.4 - 32334.1i) q^{63} +(4017.95 - 17603.8i) q^{64} +(10149.7 + 25861.0i) q^{65} +(-590.510 - 7879.81i) q^{66} +(-33771.4 - 58493.7i) q^{67} +(-12269.7 + 21251.8i) q^{68} +(8719.63 + 4199.15i) q^{69} +(-18781.1 + 2518.95i) q^{70} +(-20055.6 + 9658.28i) q^{71} +(4087.38 - 54542.2i) q^{72} +(41487.6 - 12797.2i) q^{73} +(20081.5 - 6194.32i) q^{74} +(11009.6 - 146913. i) q^{75} +(48379.4 - 23298.3i) q^{76} +(-11636.1 + 19417.5i) q^{77} +(-12405.9 - 5974.35i) q^{78} +(-3311.84 + 5736.27i) q^{79} +(35816.4 + 62035.8i) q^{80} +(8599.89 + 114757. i) q^{81} +(-4279.66 - 10904.4i) q^{82} +(-5683.78 + 24902.3i) q^{83} +(-68626.7 + 83239.5i) q^{84} +(-16936.8 - 74205.1i) q^{85} +(-30881.0 + 21054.3i) q^{86} +(76368.8 - 70859.9i) q^{87} +(-16981.7 - 2559.58i) q^{88} +(43309.6 + 40185.4i) q^{89} +(50680.5 + 63551.3i) q^{90} +(19164.6 + 34477.9i) q^{91} +(6283.63 - 7879.42i) q^{92} +(154594. - 23301.4i) q^{93} +(26857.3 + 18311.0i) q^{94} +(-60848.0 + 155038. i) q^{95} +(-118943. - 36689.0i) q^{96} -2530.79 q^{97} +(-25954.7 + 7089.71i) q^{98} +97104.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 13 q^{2} - 22 q^{3} + 307 q^{4} - 52 q^{5} - 130 q^{6} + 154 q^{7} - 320 q^{8} + 6 q^{9} - 792 q^{10} - 635 q^{11} + 3605 q^{12} + 1834 q^{13} - 875 q^{14} - 2572 q^{15} + 3735 q^{16} - 1023 q^{17}+ \cdots + 1090736 q^{99}+O(q^{100}) \) 264 * q - 13 * q^2 - 22 * q^3 + 307 * q^4 - 52 * q^5 - 130 * q^6 + 154 * q^7 - 320 * q^8 + 6 * q^9 - 792 * q^10 - 635 * q^11 + 3605 * q^12 + 1834 * q^13 - 875 * q^14 - 2572 * q^15 + 3735 * q^16 - 1023 * q^17 - 1336 * q^18 + 9741 * q^19 + 8330 * q^20 + 1512 * q^21 + 842 * q^22 - 1553 * q^23 + 1756 * q^24 + 13144 * q^25 - 1946 * q^26 - 19849 * q^27 - 31584 * q^28 - 30356 * q^29 + 6129 * q^30 + 43903 * q^31 + 27725 * q^32 - 3412 * q^33 - 73182 * q^34 - 17360 * q^35 - 102868 * q^36 - 22105 * q^37 + 19116 * q^38 + 109165 * q^39 + 77354 * q^40 + 47446 * q^41 + 157738 * q^42 + 6674 * q^43 + 15154 * q^44 - 130923 * q^45 - 136952 * q^46 - 195163 * q^47 - 151484 * q^48 - 131194 * q^49 + 263000 * q^50 - 84276 * q^51 - 58758 * q^52 - 110577 * q^53 + 170313 * q^54 + 290245 * q^55 + 79688 * q^56 + 47310 * q^57 + 252156 * q^58 + 127308 * q^59 + 86254 * q^60 + 166863 * q^61 - 63578 * q^62 - 243033 * q^63 - 293812 * q^64 - 16702 * q^65 - 661788 * q^66 + 46195 * q^67 + 393869 * q^68 + 321394 * q^69 - 64330 * q^70 - 61793 * q^71 + 333944 * q^72 + 21699 * q^73 + 133514 * q^74 - 431136 * q^75 + 3087 * q^76 - 48993 * q^77 - 450576 * q^78 - 181 * q^79 + 264228 * q^80 + 142090 * q^81 - 512442 * q^82 + 102424 * q^83 + 344932 * q^84 - 205502 * q^85 + 611991 * q^86 + 1427200 * q^87 + 685993 * q^88 + 145800 * q^89 + 677844 * q^90 + 732956 * q^91 + 10018 * q^92 - 1233536 * q^93 - 601938 * q^94 - 945265 * q^95 - 2372958 * q^96 - 1932952 * q^97 - 672973 * q^98 + 1090736 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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