LMFDB - Embedded newform 25.6.e.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,6,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	25.e (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:	$4.00959549532$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	25.9
Dual form			25.6.e.a.14.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.123616 - 0.170142i) q^{2} +(28.0358 - 9.10938i) q^{3} +(9.87488 + 30.3917i) q^{4} +(-30.6717 - 46.7359i) q^{5} +(1.91577 - 5.89614i) q^{6} +86.5992i q^{7} +(12.7921 + 4.15640i) q^{8} +(506.434 - 367.946i) q^{9} +O(q^{10})$	\(q+(0.123616 - 0.170142i) q^{2} +(28.0358 - 9.10938i) q^{3} +(9.87488 + 30.3917i) q^{4} +(-30.6717 - 46.7359i) q^{5} +(1.91577 - 5.89614i) q^{6} +86.5992i q^{7} +(12.7921 + 4.15640i) q^{8} +(506.434 - 367.946i) q^{9} +(-11.7433 - 0.558733i) q^{10} +(-256.136 - 186.094i) q^{11} +(553.700 + 762.103i) q^{12} +(287.902 + 396.263i) q^{13} +(14.7342 + 10.7050i) q^{14} +(-1285.64 - 1030.88i) q^{15} +(-825.000 + 599.398i) q^{16} +(-1757.39 - 571.010i) q^{17} -131.650i q^{18} +(-28.6352 + 88.1301i) q^{19} +(1117.51 - 1393.68i) q^{20} +(788.865 + 2427.88i) q^{21} +(-63.3249 + 20.5755i) q^{22} +(-1157.59 + 1593.29i) q^{23} +396.498 q^{24} +(-1243.49 + 2866.94i) q^{25} +103.010 q^{26} +(6636.04 - 9133.72i) q^{27} +(-2631.90 + 855.156i) q^{28} +(894.853 + 2754.07i) q^{29} +(-334.322 + 91.3094i) q^{30} +(971.004 - 2988.44i) q^{31} +644.875i q^{32} +(-8876.19 - 2884.05i) q^{33} +(-314.394 + 228.420i) q^{34} +(4047.29 - 2656.15i) q^{35} +(16183.5 + 11758.0i) q^{36} +(-3545.37 - 4879.78i) q^{37} +(11.4549 + 15.7663i) q^{38} +(11681.3 + 8486.95i) q^{39} +(-198.102 - 725.333i) q^{40} +(-1900.93 + 1381.11i) q^{41} +(510.601 + 165.904i) q^{42} -4745.01i q^{43} +(3126.40 - 9622.08i) q^{44} +(-32729.5 - 12383.1i) q^{45} +(127.989 + 393.911i) q^{46} +(13248.9 - 4304.81i) q^{47} +(-17669.4 + 24319.8i) q^{48} +9307.58 q^{49} +(334.073 + 565.970i) q^{50} -54471.3 q^{51} +(-9200.14 + 12662.9i) q^{52} +(17319.9 - 5627.57i) q^{53} +(-733.715 - 2258.14i) q^{54} +(-841.129 + 17678.6i) q^{55} +(-359.941 + 1107.78i) q^{56} +2731.65i q^{57} +(579.203 + 188.194i) q^{58} +(25391.4 - 18447.9i) q^{59} +(18634.6 - 49252.7i) q^{60} +(41014.0 + 29798.4i) q^{61} +(-388.430 - 534.628i) q^{62} +(31863.8 + 43856.8i) q^{63} +(-26290.3 - 19101.0i) q^{64} +(9689.28 - 25609.5i) q^{65} +(-1587.93 + 1153.70i) q^{66} +(-16856.9 - 5477.15i) q^{67} -59048.7i q^{68} +(-17940.1 + 55214.0i) q^{69} +(48.3858 - 1016.96i) q^{70} +(1223.17 + 3764.52i) q^{71} +(8007.67 - 2601.85i) q^{72} +(672.063 - 925.016i) q^{73} -1268.52 q^{74} +(-8746.21 + 91704.4i) q^{75} -2961.20 q^{76} +(16115.6 - 22181.2i) q^{77} +(2887.98 - 938.362i) q^{78} +(-12929.4 - 39792.8i) q^{79} +(53317.6 + 20172.6i) q^{80} +(55838.0 - 171852. i) q^{81} +494.156i q^{82} +(-65263.3 - 21205.3i) q^{83} +(-65997.5 + 47950.0i) q^{84} +(27215.4 + 99647.0i) q^{85} +(-807.327 - 586.557i) q^{86} +(50175.8 + 69061.1i) q^{87} +(-2503.04 - 3445.13i) q^{88} +(29151.1 + 21179.5i) q^{89} +(-6152.77 + 4037.92i) q^{90} +(-34316.1 + 24932.1i) q^{91} +(-59853.9 - 19447.7i) q^{92} -92628.6i q^{93} +(905.335 - 2786.33i) q^{94} +(4997.13 - 1364.81i) q^{95} +(5874.41 + 18079.6i) q^{96} +(-130039. + 42252.3i) q^{97} +(1150.56 - 1583.61i) q^{98} -198189. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 5 q^{3} + 189 q^{4} - 60 q^{5} - 139 q^{6} + 610 q^{8} + 1031 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 5 * q^3 + 189 * q^4 - 60 * q^5 - 139 * q^6 + 610 * q^8 + 1031 * q^9	\( 48 q - 5 q^{2} - 5 q^{3} + 189 q^{4} - 60 q^{5} - 139 q^{6} + 610 q^{8} + 1031 q^{9} + 435 q^{10} - 724 q^{11} + 315 q^{12} - 5 q^{13} - 497 q^{14} - 105 q^{15} - 6967 q^{16} - 960 q^{17} + 4075 q^{19} + 9155 q^{20} + 2016 q^{21} - 5450 q^{22} - 10995 q^{23} - 20720 q^{24} - 16610 q^{25} + 21666 q^{26} - 13805 q^{27} + 14235 q^{28} + 17195 q^{29} + 39595 q^{30} + 8631 q^{31} + 28460 q^{33} - 24067 q^{34} - 4145 q^{35} - 43827 q^{36} + 19980 q^{37} - 77385 q^{38} + 6037 q^{39} + 93210 q^{40} - 26514 q^{41} + 182885 q^{42} + 26748 q^{44} - 94185 q^{45} - 14559 q^{46} - 7700 q^{47} - 127830 q^{48} - 130126 q^{49} - 231115 q^{50} + 121116 q^{51} - 189260 q^{52} + 45840 q^{53} + 19985 q^{54} + 79370 q^{55} - 43280 q^{56} + 337370 q^{58} + 47640 q^{59} + 71480 q^{60} + 7791 q^{61} + 135320 q^{62} - 35790 q^{63} + 68204 q^{64} + 197485 q^{65} - 14798 q^{66} - 66180 q^{67} + 17957 q^{69} - 129930 q^{70} - 46694 q^{71} - 50545 q^{72} - 18985 q^{73} - 183292 q^{74} - 202210 q^{75} + 273360 q^{76} - 132990 q^{77} - 665225 q^{78} - 54065 q^{79} + 362810 q^{80} - 382452 q^{81} + 161155 q^{83} + 474258 q^{84} - 83075 q^{85} + 74691 q^{86} + 897680 q^{87} + 578430 q^{88} + 436475 q^{89} + 775655 q^{90} + 181046 q^{91} - 1412870 q^{92} - 336327 q^{94} - 362785 q^{95} - 766024 q^{96} - 475210 q^{97} - 361660 q^{98} - 451848 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 5 * q^3 + 189 * q^4 - 60 * q^5 - 139 * q^6 + 610 * q^8 + 1031 * q^9 + 435 * q^10 - 724 * q^11 + 315 * q^12 - 5 * q^13 - 497 * q^14 - 105 * q^15 - 6967 * q^16 - 960 * q^17 + 4075 * q^19 + 9155 * q^20 + 2016 * q^21 - 5450 * q^22 - 10995 * q^23 - 20720 * q^24 - 16610 * q^25 + 21666 * q^26 - 13805 * q^27 + 14235 * q^28 + 17195 * q^29 + 39595 * q^30 + 8631 * q^31 + 28460 * q^33 - 24067 * q^34 - 4145 * q^35 - 43827 * q^36 + 19980 * q^37 - 77385 * q^38 + 6037 * q^39 + 93210 * q^40 - 26514 * q^41 + 182885 * q^42 + 26748 * q^44 - 94185 * q^45 - 14559 * q^46 - 7700 * q^47 - 127830 * q^48 - 130126 * q^49 - 231115 * q^50 + 121116 * q^51 - 189260 * q^52 + 45840 * q^53 + 19985 * q^54 + 79370 * q^55 - 43280 * q^56 + 337370 * q^58 + 47640 * q^59 + 71480 * q^60 + 7791 * q^61 + 135320 * q^62 - 35790 * q^63 + 68204 * q^64 + 197485 * q^65 - 14798 * q^66 - 66180 * q^67 + 17957 * q^69 - 129930 * q^70 - 46694 * q^71 - 50545 * q^72 - 18985 * q^73 - 183292 * q^74 - 202210 * q^75 + 273360 * q^76 - 132990 * q^77 - 665225 * q^78 - 54065 * q^79 + 362810 * q^80 - 382452 * q^81 + 161155 * q^83 + 474258 * q^84 - 83075 * q^85 + 74691 * q^86 + 897680 * q^87 + 578430 * q^88 + 436475 * q^89 + 775655 * q^90 + 181046 * q^91 - 1412870 * q^92 - 336327 * q^94 - 362785 * q^95 - 766024 * q^96 - 475210 * q^97 - 361660 * q^98 - 451848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.123616	−	0.170142i	0.0218524	−	0.0300772i	−0.797951	−	0.602722i	$-0.794083\pi$
$2$	0.123616	−	0.170142i	0.0218524	−	0.0300772i	0.819803	+	0.572645i	$0.194083\pi$
$3$	28.0358	−	9.10938i	1.79850	−	0.584367i	0.798649	−	0.601797i	$-0.205548\pi$
$3$	28.0358	−	9.10938i	1.79850	−	0.584367i	0.999848	+	0.0174300i	$0.00554843\pi$
$4$	9.87488	+	30.3917i	0.308590	+	0.949742i
$5$	−30.6717	−	46.7359i	−0.548672	−	0.836037i
$5$	−30.6717	−	46.7359i	−0.548672	−	0.836037i
$6$	1.91577	−	5.89614i	0.0217253	−	0.0668636i
$7$			86.5992i			0.667988i	0.942575	+	0.333994i	$0.108397\pi$
$7$			86.5992i			0.667988i	−0.942575	+	0.333994i	$0.891603\pi$
$8$	12.7921	+	4.15640i	0.0706669	+	0.0229611i
$9$	506.434	−	367.946i	2.08409	−	1.51418i
$10$	−11.7433	−	0.558733i	−0.0371355	−	0.00176687i
$11$	−256.136	−	186.094i	−0.638248	−	0.463714i	0.221000	−	0.975274i	$-0.429068\pi$
$11$	−256.136	−	186.094i	−0.638248	−	0.463714i	−0.859248	+	0.511559i	$0.829068\pi$
$12$	553.700	+	762.103i	1.11000	+	1.52778i
$13$	287.902	+	396.263i	0.472483	+	0.650318i	0.977039	−	0.213062i	$-0.0683435\pi$
$13$	287.902	+	396.263i	0.472483	+	0.650318i	−0.504555	+	0.863379i	$0.668344\pi$
$14$	14.7342	+	10.7050i	0.0200912	+	0.0145971i
$15$	−1285.64	−	1030.88i	−1.47534	−	1.18298i
$16$	−825.000	+	599.398i	−0.805664	+	0.585349i
$17$	−1757.39	−	571.010i	−1.47484	−	0.479205i	−0.542274	−	0.840202i	$-0.682437\pi$
$17$	−1757.39	−	571.010i	−1.47484	−	0.479205i	−0.932567	+	0.360997i	$0.882437\pi$
$18$		−	131.650i		−	0.0957720i
$19$	−28.6352	+	88.1301i	−0.0181977	+	0.0560068i	−0.959743	−	0.280880i	$-0.909374\pi$
$19$	−28.6352	+	88.1301i	−0.0181977	+	0.0560068i	0.941545	+	0.336886i	$0.109374\pi$
$20$	1117.51	−	1393.68i	0.624705	−	0.779090i
$21$	788.865	+	2427.88i	0.390350	+	1.20137i
$22$	−63.3249	+	20.5755i	−0.0278945	+	0.00906346i
$23$	−1157.59	+	1593.29i	−0.456284	+	0.628022i	−0.973733	−	0.227693i	$-0.926882\pi$
$23$	−1157.59	+	1593.29i	−0.456284	+	0.628022i	0.517449	+	0.855714i	$0.326882\pi$
$24$	396.498			0.140512
$25$	−1243.49	+	2866.94i	−0.397917	+	0.917421i
$26$	103.010			0.0298846
$27$	6636.04	−	9133.72i	1.75186	−	2.41123i
$28$	−2631.90	+	855.156i	−0.634416	+	0.206134i
$29$	894.853	+	2754.07i	0.197586	+	0.608108i	0.999937	+	0.0112547i	$0.00358257\pi$
$29$	894.853	+	2754.07i	0.197586	+	0.608108i	−0.802350	+	0.596853i	$0.796417\pi$
$30$	−334.322	+	91.3094i	−0.0678205	+	0.0185230i
$31$	971.004	−	2988.44i	0.181475	−	0.558523i	−0.818395	−	0.574656i	$-0.805136\pi$
$31$	971.004	−	2988.44i	0.181475	−	0.558523i	0.999870	+	0.0161337i	$0.00513572\pi$
$32$			644.875i			0.111327i
$33$	−8876.19	−	2884.05i	−1.41887	−	0.461018i
$34$	−314.394	+	228.420i	−0.0466419	+	0.0338874i
$35$	4047.29	−	2656.15i	0.558463	−	0.366507i
$36$	16183.5	+	11758.0i	2.08121	+	1.51209i
$37$	−3545.37	−	4879.78i	−0.425753	−	0.585998i	0.541219	−	0.840882i	$-0.317963\pi$
$37$	−3545.37	−	4879.78i	−0.425753	−	0.585998i	−0.966972	+	0.254883i	$0.917963\pi$
$38$	11.4549	+	15.7663i	0.00128686	+	0.00177122i
$39$	11681.3	+	8486.95i	1.22978	+	0.893491i
$40$	−198.102	−	725.333i	−0.0195767	−	0.0716783i
$41$	−1900.93	+	1381.11i	−0.176607	+	0.128312i	−0.672577	−	0.740027i	$-0.734813\pi$
$41$	−1900.93	+	1381.11i	−0.176607	+	0.128312i	0.495970	+	0.868340i	$0.334813\pi$
$42$	510.601	+	165.904i	0.0446641	+	0.0145122i
$43$		−	4745.01i		−	0.391350i	−0.980669	−	0.195675i	$-0.937310\pi$
$43$		−	4745.01i		−	0.391350i	0.980669	−	0.195675i	$-0.0626898\pi$
$44$	3126.40	−	9622.08i	0.243452	−	0.749269i
$45$	−32729.5	−	12383.1i	−2.40939	−	0.911588i
$46$	127.989	+	393.911i	0.00891824	+	0.0274475i
$47$	13248.9	−	4304.81i	0.874850	−	0.284256i	0.163033	−	0.986621i	$-0.447872\pi$
$47$	13248.9	−	4304.81i	0.874850	−	0.284256i	0.711817	+	0.702365i	$0.247872\pi$
$48$	−17669.4	+	24319.8i	−1.10693	+	1.52355i
$49$	9307.58			0.553792
$50$	334.073	+	565.970i	0.0188980	+	0.0320161i
$51$	−54471.3			−2.93253
$52$	−9200.14	+	12662.9i	−0.471830	+	0.649419i
$53$	17319.9	−	5627.57i	0.846944	−	0.275189i	0.146779	−	0.989169i	$-0.453109\pi$
$53$	17319.9	−	5627.57i	0.846944	−	0.275189i	0.700166	+	0.713980i	$0.253109\pi$
$54$	−733.715	−	2258.14i	−0.0342407	−	0.105382i
$55$	−841.129	+	17678.6i	−0.0374935	+	0.788027i
$56$	−359.941	+	1107.78i	−0.0153377	+	0.0472047i
$57$			2731.65i			0.111362i
$58$	579.203	+	188.194i	0.0226079	+	0.00734576i
$59$	25391.4	−	18447.9i	0.949633	−	0.689949i	−0.00108688	−	0.999999i	$-0.500346\pi$
$59$	25391.4	−	18447.9i	0.949633	−	0.689949i	0.950720	+	0.310050i	$0.100346\pi$
$60$	18634.6	−	49252.7i	0.668256	−	1.76625i
$61$	41014.0	+	29798.4i	1.41126	+	1.02534i	0.993138	+	0.116950i	$0.0373117\pi$
$61$	41014.0	+	29798.4i	1.41126	+	1.02534i	0.418123	+	0.908391i	$0.362688\pi$
$62$	−388.430	−	534.628i	−0.0128331	−	0.0176633i
$63$	31863.8	+	43856.8i	1.01145	+	1.39215i
$64$	−26290.3	−	19101.0i	−0.802316	−	0.582916i
$65$	9689.28	−	25609.5i	0.284451	−	0.751825i
$66$	−1587.93	+	1153.70i	−0.0448717	+	0.0326012i
$67$	−16856.9	−	5477.15i	−0.458766	−	0.149062i	0.0705113	−	0.997511i	$-0.477537\pi$
$67$	−16856.9	−	5477.15i	−0.458766	−	0.149062i	−0.529277	+	0.848449i	$0.677537\pi$
$68$		−	59048.7i		−	1.54860i
$69$	−17940.1	+	55214.0i	−0.453631	+	1.39613i
$70$	48.3858	−	1016.96i	0.00118025	−	0.0248061i
$71$	1223.17	+	3764.52i	0.0287965	+	0.0886264i	0.964422	−	0.264368i	$-0.0851634\pi$
$71$	1223.17	+	3764.52i	0.0287965	+	0.0886264i	−0.935625	+	0.352995i	$0.885163\pi$
$72$	8007.67	−	2601.85i	0.182043	−	0.0591495i
$73$	672.063	−	925.016i	0.0147606	−	0.0203162i	−0.801573	−	0.597897i	$-0.796003\pi$
$73$	672.063	−	925.016i	0.0147606	−	0.0203162i	0.816334	+	0.577581i	$0.196003\pi$
$74$	−1268.52			−0.0269289
$75$	−8746.21	+	91704.4i	−0.179542	+	1.88251i
$76$	−2961.20			−0.0588076
$77$	16115.6	−	22181.2i	0.309756	−	0.426342i
$78$	2887.98	−	938.362i	0.0537474	−	0.0174636i
$79$	−12929.4	−	39792.8i	−0.233084	−	0.717358i	−0.997370	−	0.0724809i	$-0.976908\pi$
$79$	−12929.4	−	39792.8i	−0.233084	−	0.717358i	0.764286	−	0.644878i	$-0.223092\pi$
$80$	53317.6	+	20172.6i	0.931419	+	0.352400i
$81$	55838.0	−	171852.i	0.945621	−	2.91032i
$82$			494.156i			0.00811577i
$83$	−65263.3	−	21205.3i	−1.03986	−	0.337870i	−0.261177	−	0.965291i	$-0.584111\pi$
$83$	−65263.3	−	21205.3i	−1.03986	−	0.337870i	−0.778680	+	0.627421i	$0.784111\pi$
$84$	−65997.5	+	47950.0i	−1.02054	+	0.741464i
$85$	27215.4	+	99647.0i	0.408571	+	1.49595i
$86$	−807.327	−	586.557i	−0.0117707	−	0.00855193i
$87$	50175.8	+	69061.1i	0.710717	+	0.978218i
$88$	−2503.04	−	3445.13i	−0.0344556	−	0.0474241i
$89$	29151.1	+	21179.5i	0.390104	+	0.283427i	0.765498	−	0.643438i	$-0.222493\pi$
$89$	29151.1	+	21179.5i	0.390104	+	0.283427i	−0.375394	+	0.926865i	$0.622493\pi$
$90$	−6152.77	+	4037.92i	−0.0800690	+	0.0525475i
$91$	−34316.1	+	24932.1i	−0.434405	+	0.315613i
$92$	−59853.9	−	19447.7i	−0.737263	−	0.239551i
$93$		−	92628.6i		−	1.11055i
$94$	905.335	−	2786.33i	0.0105679	−	0.0325247i
$95$	4997.13	−	1364.81i	0.0568083	−	0.0155154i
$96$	5874.41	+	18079.6i	0.0650558	+	0.200221i
$97$	−130039.	+	42252.3i	−1.40328	+	0.455954i	−0.910251	−	0.414058i	$-0.864111\pi$
$97$	−130039.	+	42252.3i	−1.40328	+	0.455954i	−0.493031	+	0.870012i	$0.664111\pi$
$98$	1150.56	−	1583.61i	0.0121017	−	0.0166565i
$99$	−198189.			−2.03231
$100$	−99410.7	−	9481.18i	−0.994107	−	0.0948118i
$101$	29561.5			0.288352			0.144176	−	0.989552i	$-0.453947\pi$
$101$	29561.5			0.288352			0.144176	+	0.989552i	$0.453947\pi$
$102$	−6733.51	+	9267.88i	−0.0640827	+	0.0882023i
$103$	5162.41	−	1677.37i	0.0479468	−	0.0155788i	−0.284945	−	0.958544i	$-0.591975\pi$
$103$	5162.41	−	1677.37i	0.0479468	−	0.0155788i	0.332892	+	0.942965i	$0.391975\pi$
$104$	2035.84	+	6265.67i	0.0184570	+	0.0568047i
$105$	89273.2	−	111336.i	0.790220	−	0.985509i
$106$	1183.52	−	3642.50i	0.0102308	−	0.0314873i
$107$			129720.i			1.09533i	0.836697	+	0.547667i	$0.184484\pi$
$107$			129720.i			1.09533i	−0.836697	+	0.547667i	$0.815516\pi$
$108$	343120.	+	111486.i	2.83065	+	0.919734i
$109$	110833.	−	80525.2i	0.893521	−	0.649181i	−0.0432728	−	0.999063i	$-0.513778\pi$
$109$	110833.	−	80525.2i	0.893521	−	0.649181i	0.936794	+	0.349882i	$0.113778\pi$
$110$	2903.90	+	2328.46i	0.0228823	+	0.0183480i
$111$	−143849.	−	104512.i	−1.10815	−	0.805120i
$112$	−51907.3	−	71444.3i	−0.391006	−	0.538174i
$113$	6390.40	+	8795.64i	0.0470795	+	0.0647994i	0.831908	−	0.554914i	$-0.187249\pi$
$113$	6390.40	+	8795.64i	0.0470795	+	0.0647994i	−0.784828	+	0.619713i	$0.787249\pi$
$114$	464.769	+	337.674i	0.00334946	+	0.00243353i
$115$	109969.	+	5232.22i	0.775400	+	0.0368928i
$116$	−74864.6	+	54392.3i	−0.516573	+	0.375312i
$117$	291607.	+	94748.8i	1.96940	+	0.639896i
$118$		−	6600.60i		−	0.0436393i
$119$	49449.0	−	152188.i	0.320103	−	0.985177i
$120$	−12161.3	−	18530.7i	−0.0770950	−	0.117473i
$121$	−18792.6	−	57837.8i	−0.116687	−	0.359127i
$122$	10139.9	−	3294.67i	0.0616788	−	0.0200407i
$123$	−40713.1	+	56036.8i	−0.242645	+	0.333973i
$124$	100413.			0.586454
$125$	172129.	−	29818.3i	0.985325	−	0.170690i
$126$	11400.8			0.0639746
$127$	−172454.	+	237363.i	−0.948777	+	1.30588i	0.00329089	+	0.999995i	$0.498952\pi$
$127$	−172454.	+	237363.i	−0.948777	+	1.30588i	−0.952068	+	0.305886i	$0.901048\pi$
$128$	−26125.8	+	8488.78i	−0.140943	+	0.0457952i
$129$	−43224.1	−	133030.i	−0.228692	−	0.703842i
$130$	−3159.51	−	4814.29i	−0.0163969	−	0.0249847i
$131$	−104644.	+	322062.i	−0.532767	+	1.63969i	0.215658	+	0.976469i	$0.430810\pi$
$131$	−104644.	+	322062.i	−0.532767	+	1.63969i	−0.748425	+	0.663220i	$0.769190\pi$
$132$		−	298242.i		−	1.48982i
$133$	−7632.00	−	2479.79i	−0.0374119	−	0.0121558i
$134$	−3015.68	+	2191.02i	−0.0145085	+	0.0105410i
$135$	−630412.	−	29994.3i	−2.97707	−	0.141646i
$136$	−20107.3	−	14608.8i	−0.0932194	−	0.0677279i
$137$	−129536.	−	178291.i	−0.589642	−	0.811572i	0.405069	−	0.914286i	$-0.367247\pi$
$137$	−129536.	−	178291.i	−0.589642	−	0.811572i	−0.994711	+	0.102714i	$0.967247\pi$
$138$	7176.57	+	9877.70i	0.0320789	+	0.0441528i
$139$	194700.	+	141458.i	0.854729	+	0.620997i	0.926446	−	0.376428i	$-0.122848\pi$
$139$	194700.	+	141458.i	0.854729	+	0.620997i	−0.0717166	+	0.997425i	$0.522848\pi$
$140$	120691.	+	96775.2i	0.520423	+	0.417296i
$141$	332228.	−	241378.i	1.40731	−	1.02247i
$142$	791.706	+	257.241i	0.00329491	+	0.00107058i
$143$		−	155074.i		−	0.634161i
$144$	−197262.	+	607110.i	−0.792752	+	2.43984i
$145$	101268.	−	126294.i	0.399991	−	0.498842i
$146$	−74.3069	−	228.693i	−0.000288501	−	0.000887914i
$147$	260945.	−	84786.3i	0.995993	−	0.323618i
$148$	113295.	−	155937.i	0.425164	−	0.585188i
$149$	−132357.			−0.488406			−0.244203	−	0.969724i	$-0.578526\pi$
$149$	−132357.			−0.488406			−0.244203	+	0.969724i	$0.578526\pi$
$150$	14521.6	+	12824.2i	0.0526972	+	0.0465374i
$151$	432968.			1.54530			0.772651	−	0.634831i	$-0.218930\pi$
$151$	432968.			1.54530			0.772651	+	0.634831i	$0.218930\pi$
$152$	−732.608	+	1008.35i	−0.00257195	+	0.00353999i
$153$	−1.10010e6	+	357445.i	−3.79930	+	1.23447i
$154$	−1781.82	−	5483.89i	−0.00605429	−	0.0186332i
$155$	−169450.	+	46279.9i	−0.566516	+	0.154726i
$156$	−142582.	+	438822.i	−0.469087	+	1.44370i
$157$		−	178593.i		−	0.578248i	−0.957292	−	0.289124i	$-0.906636\pi$
$157$		−	178593.i		−	0.578248i	0.957292	−	0.289124i	$-0.0933641\pi$
$158$	−8368.72	−	2719.16i	−0.0266696	−	0.00866547i
$159$	434313.	−	315547.i	1.36242	−	0.989853i
$160$	30138.8	−	19779.4i	0.0930735	−	0.0610820i
$161$	−137977.	−	100246.i	−0.419511	−	0.304793i
$162$	−22336.8	−	30744.0i	−0.0668703	−	0.0920391i
$163$	−258817.	−	356231.i	−0.762999	−	1.05018i	−0.996959	−	0.0779312i	$-0.975169\pi$
$163$	−258817.	−	356231.i	−0.762999	−	1.05018i	0.233960	−	0.972246i	$-0.424831\pi$
$164$	−60745.8	−	44134.4i	−0.176363	−	0.128135i
$165$	137459.	+	503295.i	0.393065	+	1.43917i
$166$	−11675.5	+	8482.75i	−0.0328856	+	0.0238928i
$167$	−49597.3	−	16115.1i	−0.137615	−	0.0447139i	0.239400	−	0.970921i	$-0.423049\pi$
$167$	−49597.3	−	16115.1i	−0.137615	−	0.0447139i	−0.377015	+	0.926207i	$0.623049\pi$
$168$			34336.4i			0.0938603i
$169$	40598.8	−	124950.i	0.109344	−	0.336528i
$170$	20318.4	+	7687.43i	0.0539222	+	0.0204014i
$171$	17925.3	+	55168.3i	0.0468787	+	0.144278i
$172$	144209.	−	46856.4i	0.371682	−	0.120767i
$173$	−219468.	+	302071.i	−0.557514	+	0.767352i	−0.991008	−	0.133805i	$-0.957281\pi$
$173$	−219468.	+	302071.i	−0.557514	+	0.767352i	0.433494	+	0.901156i	$0.357281\pi$
$174$	17952.7			0.0449529
$175$	−248275.	−	107685.i	−0.612827	−	0.265804i
$176$	322857.			0.785648
$177$	543818.	−	748501.i	1.30473	−	1.79581i
$178$	7207.07	−	2341.72i	0.0170494	−	0.00553968i
$179$	37179.5	+	114427.i	0.0867304	+	0.266929i	0.985010	−	0.172495i	$-0.0551828\pi$
$179$	37179.5	+	114427.i	0.0867304	+	0.266929i	−0.898280	+	0.439423i	$0.855183\pi$
$180$	53145.1	−	1.11699e6i	0.122259	−	2.56961i
$181$	−78480.9	+	241539.i	−0.178061	+	0.548014i	−0.999760	−	0.0219071i	$-0.993026\pi$
$181$	−78480.9	+	241539.i	−0.178061	+	0.548014i	0.821700	+	0.569921i	$0.193026\pi$
$182$			8920.62i			0.0199626i
$183$	1.42130e6	+	461810.i	3.13732	+	1.01938i
$184$	−21430.3	+	15570.0i	−0.0466642	+	0.0339036i
$185$	−119319.	+	315367.i	−0.256318	+	0.677466i
$186$	−15760.1	−	11450.4i	−0.0334022	−	0.0242681i
$187$	343869.	+	473296.i	0.719100	+	0.989757i
$188$	261662.	+	360146.i	0.539940	+	0.743163i
$189$	790973.	+	574676.i	1.61067	+	1.17022i
$190$	385.512	−	1018.94i	0.000774737	−	0.00204768i
$191$	−405468.	+	294590.i	−0.804217	+	0.584298i	−0.912148	−	0.409861i	$-0.865577\pi$
$191$	−405468.	+	294590.i	−0.804217	+	0.584298i	0.107931	+	0.994158i	$0.465577\pi$
$192$	−911067.	−	296024.i	−1.78360	−	0.579527i
$193$		−	564208.i		−	1.09030i	−0.838339	−	0.545150i	$-0.816473\pi$
$193$		−	564208.i		−	1.09030i	0.838339	−	0.545150i	$-0.183527\pi$
$194$	−8885.98	+	27348.2i	−0.0169512	+	0.0521705i
$195$	38360.3	−	806245.i	0.0722430	−	1.51838i
$196$	91911.2	+	282874.i	0.170895	+	0.525959i
$197$	−447117.	+	145277.i	−0.820835	+	0.266705i	−0.689180	−	0.724590i	$-0.742029\pi$
$197$	−447117.	+	145277.i	−0.820835	+	0.266705i	−0.131655	+	0.991296i	$0.542029\pi$
$198$	−24499.2	+	33720.3i	−0.0444109	+	0.0611263i
$199$	−148255.			−0.265385			−0.132692	−	0.991157i	$-0.542362\pi$
$199$	−148255.			−0.265385			−0.132692	+	0.991157i	$0.542362\pi$
$200$	−27823.0	+	31505.7i	−0.0491846	+	0.0556947i
$201$	−522491.			−0.912196
$202$	3654.26	−	5029.66i	0.00630117	−	0.00867281i
$203$	−238501.	+	77493.6i	−0.406209	+	0.131985i
$204$	−537897.	−	1.65548e6i	−0.904949	−	2.78515i
$205$	122852.	+	46480.9i	0.204173	+	0.0772484i
$206$	352.763	−	1085.69i	0.000579182	−	0.00178254i
$207$			1.23283e6i			1.99975i
$208$	−475039.	−	154349.i	−0.761326	−	0.247370i
$209$	23735.0	−	17244.5i	0.0375858	−	0.0273077i
$210$	−7907.32	−	28952.0i	−0.0123732	−	0.0453033i
$211$	−454981.	−	330563.i	−0.703537	−	0.511150i	0.177545	−	0.984113i	$-0.443184\pi$
$211$	−454981.	−	330563.i	−0.703537	−	0.511150i	−0.881082	+	0.472963i	$0.843184\pi$
$212$	342063.	+	470809.i	0.522717	+	0.719458i
$213$	68584.8	+	94398.9i	0.103581	+	0.142567i
$214$	22070.8	+	16035.4i	0.0329446	+	0.0239356i
$215$	−221762.	+	145538.i	−0.327184	+	0.214723i
$216$	122852.	−	89257.3i	0.179163	−	0.130169i
$217$	258797.	+	84088.2i	0.373087	+	0.121223i
$218$		−	28811.7i		−	0.0410608i
$219$	10415.5	−	32055.6i	0.0146747	−	0.0451642i
$220$	−545589.	+	149010.i	−0.759992	+	0.207568i
$221$	−279686.	−	860784.i	−0.385203	−	1.18553i
$222$	−35564.0	+	11555.4i	−0.0484315	+	0.0157364i
$223$	−103678.	+	142700.i	−0.139612	+	0.192160i	−0.873097	−	0.487546i	$-0.837892\pi$
$223$	−103678.	+	142700.i	−0.139612	+	0.192160i	0.733485	+	0.679705i	$0.237892\pi$
$224$	−55845.6			−0.0743651
$225$	425133.	+	1.90945e6i	0.559846	+	2.51451i
$226$	2286.46			0.00297779
$227$	141738.	−	195086.i	0.182567	−	0.251282i	−0.707918	−	0.706295i	$-0.750365\pi$
$227$	141738.	−	195086.i	0.182567	−	0.251282i	0.890485	+	0.455013i	$0.150365\pi$
$228$	−83019.5	+	26974.7i	−0.105765	+	0.0343652i
$229$	432964.	+	1.33252e6i	0.545585	+	1.67914i	0.719594	+	0.694395i	$0.244328\pi$
$229$	432964.	+	1.33252e6i	0.545585	+	1.67914i	−0.174009	+	0.984744i	$0.555672\pi$
$230$	14484.1	−	18063.6i	0.0180540	−	0.0225157i
$231$	249756.	−	768671.i	0.307954	−	0.947786i
$232$			38949.7i			0.0475099i
$233$	447519.	+	145408.i	0.540035	+	0.175468i	0.566318	−	0.824187i	$-0.308367\pi$
$233$	447519.	+	145408.i	0.540035	+	0.175468i	−0.0262837	+	0.999655i	$0.508367\pi$
$234$	52168.0	−	37902.3i	0.0622823	−	0.0452507i
$235$	−607554.	−	487161.i	−0.717655	−	0.575444i
$236$	811400.	+	589517.i	0.948321	+	0.688995i
$237$	−724975.	−	997842.i	−0.838401	−	1.15396i
$238$	−19781.0	−	27226.2i	−0.0226364	−	0.0311563i
$239$	−851766.	−	618844.i	−0.964552	−	0.700788i	−0.0103483	−	0.999946i	$-0.503294\pi$
$239$	−851766.	−	618844.i	−0.964552	−	0.700788i	−0.954203	+	0.299159i	$0.903294\pi$
$240$	1.67856e6	+	79864.2i	1.88109	+	0.0895002i
$241$	1.06311e6	−	772396.i	1.17906	−	0.856638i	0.186995	−	0.982361i	$-0.440125\pi$
$241$	1.06311e6	−	772396.i	1.17906	−	0.856638i	0.992065	+	0.125723i	$0.0401251\pi$
$242$	−12163.7	−	3952.23i	−0.0133514	−	0.00433814i
$243$		−	2.58320e6i		−	2.80635i
$244$	−500617.	+	1.54074e6i	−0.538308	+	1.65674i
$245$	−285479.	−	434998.i	−0.303850	−	0.462991i
$246$	4501.46	+	13854.1i	0.00474259	+	0.0145962i
$247$	−43166.9	+	14025.8i	−0.0450203	+	0.0146280i
$248$	24842.3	−	34192.5i	0.0256486	−	0.0353022i
$249$	−2.02288e6			−2.06762
$250$	16204.5	−	32972.5i	0.0163978	−	0.0333658i
$251$	−985338.			−0.987190			−0.493595	−	0.869692i	$-0.664317\pi$
$251$	−985338.			−0.987190			−0.493595	+	0.869692i	$0.664317\pi$
$252$	−1.01823e6	+	1.40148e6i	−1.01006	+	1.39022i
$253$	593002.	−	192678.i	0.582445	−	0.189248i
$254$	19067.4	+	58683.5i	0.0185442	+	0.0570732i
$255$	1.67073e6	+	2.54577e6i	1.60900	+	2.45170i
$256$	319558.	−	983500.i	0.304755	−	0.937939i
$257$		−	1.41234e6i		−	1.33384i	−0.745127	−	0.666922i	$-0.767611\pi$
$257$		−	1.41234e6i		−	1.33384i	0.745127	−	0.666922i	$-0.232389\pi$
$258$	−27977.2	−	9090.35i	−0.0261671	−	0.00850220i
$259$	422585.	−	307026.i	0.391440	−	0.284398i
$260$	873996.	+	41583.9i	0.801819	+	0.0381497i
$261$	1.46653e6	+	1.06550e6i	1.33257	+	0.968171i
$262$	41860.7	+	57616.4i	0.0376750	+	0.0518552i
$263$	994445.	+	1.36874e6i	0.886526	+	1.22020i	0.974570	+	0.224081i	$0.0719381\pi$
$263$	994445.	+	1.36874e6i	0.886526	+	1.22020i	−0.0880448	+	0.996117i	$0.528062\pi$
$264$	−101558.	−	73785.9i	−0.0896814	−	0.0651574i
$265$	−794239.	−	636853.i	−0.694763	−	0.557089i
$266$	−1365.35	+	991.986i	−0.00118315	+	0.000859610i
$267$	1.01021e6	+	328236.i	0.867226	+	0.281779i
$268$		−	566397.i		−	0.481708i
$269$	206961.	−	636962.i	0.174385	−	0.536701i	−0.825220	−	0.564811i	$-0.808949\pi$
$269$	206961.	−	636962.i	0.174385	−	0.536701i	0.999605	+	0.0281101i	$0.00894891\pi$
$270$	−83032.1	+	103552.i	−0.0693165	+	0.0864468i
$271$	−37590.1	−	115690.i	−0.0310921	−	0.0956917i	0.934306	−	0.356472i	$-0.116020\pi$
$271$	−37590.1	−	115690.i	−0.0310921	−	0.0956917i	−0.965398	+	0.260780i	$0.916020\pi$
$272$	1.79211e6	−	582291.i	1.46873	−	0.477219i
$273$	−734963.	+	1.01159e6i	−0.596841	+	0.821482i
$274$	−46347.4			−0.0372949
$275$	852024.	−	502922.i	0.679391	−	0.401022i
$276$	−1.85521e6			−1.46595
$277$	−780429.	+	1.07417e6i	−0.611131	+	0.841149i	−0.996670	−	0.0815423i	$-0.974015\pi$
$277$	−780429.	+	1.07417e6i	−0.611131	+	0.841149i	0.385539	+	0.922691i	$0.374015\pi$
$278$	48135.9	−	15640.3i	0.0373557	−	0.0121376i
$279$	−607836.	−	1.87073e6i	−0.467494	−	1.43880i
$280$	62813.3	−	17155.5i	0.0478802	−	0.0130770i
$281$	605149.	−	1.86246e6i	0.457190	−	1.40709i	−0.411355	−	0.911475i	$-0.634944\pi$
$281$	605149.	−	1.86246e6i	0.457190	−	1.40709i	0.868545	−	0.495610i	$-0.165056\pi$
$282$		−	86364.1i		−	0.0646712i
$283$	−19936.3	−	6477.69i	−0.0147971	−	0.00480788i	0.301609	−	0.953432i	$-0.402476\pi$
$283$	−19936.3	−	6477.69i	−0.0147971	−	0.00480788i	−0.316406	+	0.948624i	$0.602476\pi$
$284$	−102332.	+	74348.2i	−0.0752859	+	0.0546984i
$285$	127666.	−	83784.3i	0.0931029	−	0.0611013i
$286$	−26384.7	−	19169.6i	−0.0190738	−	0.0138579i
$287$	−119603.	−	164619.i	−0.0857111	−	0.117971i
$288$	237279.	+	326586.i	0.168569	+	0.232015i
$289$	1.61367e6	+	1.17240e6i	1.13650	+	0.825718i
$290$	−8969.71	−	32841.8i	−0.00626301	−	0.0229315i
$291$	−3.26086e6	+	2.36915e6i	−2.25735	+	1.64006i
$292$	34749.4	+	11290.8i	0.0238501	+	0.00774936i
$293$			318825.i			0.216962i	0.994099	+	0.108481i	$0.0345986\pi$
$293$			318825.i			0.216962i	−0.994099	+	0.108481i	$0.965401\pi$
$294$	17831.2	−	54878.8i	0.0120313	−	0.0370285i
$295$	−1.64098e6	−	620860.i	−1.09786	−	0.415373i
$296$	−25070.3	−	77158.5i	−0.0166315	−	0.0511864i
$297$	−3.39946e6	+	1.10455e6i	−2.23624	+	0.726599i
$298$	−16361.4	+	22519.5i	−0.0106728	+	0.0146899i
$299$	−964635.			−0.624000
$300$	−2.87343e6	+	639757.i	−1.84330	+	0.410405i
$301$	410914.			0.261417
$302$	53521.6	−	73666.2i	0.0337685	−	0.0464784i
$303$	828779.	−	269287.i	0.518599	−	0.168503i
$304$	−29200.9	−	89871.2i	−0.0181223	−	0.0557746i
$305$	134686.	−	2.83079e6i	0.0829036	−	1.74244i
$306$	−75173.3	+	231360.i	−0.0458944	+	0.141249i
$307$			2.61211e6i			1.58178i	0.611958	+	0.790890i	$0.290382\pi$
$307$			2.61211e6i			1.58178i	−0.611958	+	0.790890i	$0.709618\pi$
$308$	833265.	+	270744.i	0.500503	+	0.162623i
$309$	129452.	−	94052.7i	0.0771284	−	0.0560370i
$310$	−13072.5	+	34551.6i	−0.00772600	+	0.0204204i
$311$	−195055.	−	141716.i	−0.114355	−	0.0830841i	0.529138	−	0.848536i	$-0.322515\pi$
$311$	−195055.	−	141716.i	−0.114355	−	0.0830841i	−0.643493	+	0.765452i	$0.722515\pi$
$312$	114153.	+	157118.i	0.0663896	+	0.0913774i
$313$	−166760.	−	229525.i	−0.0962124	−	0.132425i	0.758197	−	0.652026i	$-0.226081\pi$
$313$	−166760.	−	229525.i	−0.0962124	−	0.132425i	−0.854409	+	0.519601i	$0.826081\pi$
$314$	−30386.2	−	22076.9i	−0.0173921	−	0.0126361i
$315$	1.07237e6	−	2.83435e6i	0.608930	−	1.60945i
$316$	1.08169e6	−	785897.i	0.609378	−	0.442739i
$317$	943150.	+	306448.i	0.527148	+	0.171281i	0.560487	−	0.828163i	$-0.310614\pi$
$317$	943150.	+	306448.i	0.527148	+	0.171281i	−0.0333388	+	0.999444i	$0.510614\pi$
$318$		−	112901.i		−	0.0626083i
$319$	283312.	−	871945.i	0.155879	−	0.479747i
$320$	−86335.0	+	1.81456e6i	−0.0471315	+	0.990596i
$321$	1.18167e6	+	3.63679e6i	0.640077	+	1.96995i
$322$	−34112.4	+	11083.8i	−0.0183346	+	0.00595728i
$323$	100646.	−	138528.i	0.0536774	−	0.0738807i
$324$	5.77426e6			3.05586
$325$	−1.49407e6	+	332649.i	−0.784625	+	0.174694i
$326$	−92603.8			−0.0482597
$327$	2.37377e6	−	3.26721e6i	1.22763	−	1.68969i
$328$	−30057.3	+	9766.22i	−0.0154264	+	0.00501235i
$329$	372793.	+	1.14734e6i	0.189880	+	0.584390i
$330$	102624.	+	38827.6i	0.0518757	+	0.0196271i
$331$	537567.	−	1.65446e6i	0.269689	−	0.830016i	−0.720887	−	0.693052i	$-0.756266\pi$
$331$	537567.	−	1.65446e6i	0.269689	−	0.830016i	0.990576	−	0.136964i	$-0.0437345\pi$
$332$		−	2.19287e6i		−	1.09186i
$333$	−3.59099e6	−	1.16678e6i	−1.77461	−	0.576607i
$334$	−8872.87	+	6446.52i	−0.00435209	+	0.00316198i
$335$	261051.	+	955817.i	0.127091	+	0.465332i
$336$	−2.10608e6	−	1.53015e6i	−1.01771	−	0.739413i
$337$	755151.	+	1.03938e6i	0.362209	+	0.498538i	0.950763	−	0.309920i	$-0.100302\pi$
$337$	755151.	+	1.03938e6i	0.362209	+	0.498538i	−0.588554	+	0.808458i	$0.700302\pi$
$338$	−16240.7	−	22353.4i	−0.00773238	−	0.0106427i
$339$	259283.	+	188380.i	0.122539	+	0.0890298i
$340$	−2.75970e6	+	1.81113e6i	−1.29468	+	0.849672i
$341$	−804841.	+	584751.i	−0.374821	+	0.272323i
$342$	11602.3	+	3769.82i	0.00536388	+	0.00174283i
$343$			2.26150e6i			1.03791i
$344$	19722.1	−	60698.5i	0.00898582	−	0.0276555i
$345$	3.13073e6	−	855061.i	1.41611	−	0.386767i
$346$	24265.5	+	74681.6i	0.0108968	+	0.0335369i
$347$	2.26736e6	−	736711.i	1.01087	−	0.328453i	0.243672	−	0.969858i	$-0.421648\pi$
$347$	2.26736e6	−	736711.i	1.01087	−	0.328453i	0.767203	+	0.641405i	$0.221648\pi$
$348$	−1.60341e6	+	2.20690e6i	−0.709734	+	0.976866i
$349$	−1.40507e6			−0.617495			−0.308748	−	0.951144i	$-0.599910\pi$
$349$	−1.40507e6			−0.617495			−0.308748	+	0.951144i	$0.599910\pi$
$350$	−49012.5	+	28930.5i	−0.0213864	+	0.0126237i
$351$	5.52989e6			2.39579
$352$	120007.	−	165176.i	0.0516239	−	0.0710542i
$353$	−2.36957e6	+	769919.i	−1.01212	+	0.328858i	−0.767699	−	0.640811i	$-0.778598\pi$
$353$	−2.36957e6	+	769919.i	−1.01212	+	0.328858i	−0.244422	+	0.969669i	$0.578598\pi$
$354$	−60127.4	−	185053.i	−0.0255014	−	0.0784852i
$355$	138421.	−	172630.i	0.0582952	−	0.0727018i
$356$	−355819.	+	1.09510e6i	−0.148800	+	0.457961i
$357$		−	4.71717e6i		−	1.95890i
$358$	24064.8	+	7819.13i	0.00992373	+	0.00322442i
$359$	−1.08009e6	+	784731.i	−0.442307	+	0.321355i	−0.786551	−	0.617525i	$-0.788135\pi$
$359$	−1.08009e6	+	784731.i	−0.442307	+	0.321355i	0.344244	+	0.938880i	$0.388135\pi$
$360$	−367209.	−	294443.i	−0.149333	−	0.119741i
$361$	1.99626e6	+	1.45037e6i	0.806211	+	0.585747i
$362$	31394.6	+	43211.0i	0.0125917	+	0.0173310i
$363$	−1.05373e6	−	1.45034e6i	−0.419724	−	0.577700i
$364$	−1.09660e6	−	796725.i	−0.433804	−	0.315177i
$365$	−63844.8	−	3037.67i	−0.0250838	−	0.00119346i
$366$	254269.	−	184737.i	0.0992180	−	0.0720861i
$367$	−3.88564e6	−	1.26252e6i	−1.50590	−	0.489297i	−0.564170	−	0.825659i	$-0.690804\pi$
$367$	−3.88564e6	−	1.26252e6i	−1.50590	−	0.489297i	−0.941733	+	0.336361i	$0.890804\pi$
$368$		−	2.00832e6i		−	0.773060i
$369$	−454524.	+	1.39888e6i	−0.173776	+	0.534829i
$370$	38907.7	+	59285.5i	0.0147751	+	0.0225136i
$371$	487343.	+	1.49989e6i	0.183823	+	0.565749i
$372$	2.81515e6	−	914696.i	1.05474	−	0.342704i
$373$	1.81057e6	−	2.49204e6i	0.673819	−	0.927432i	−0.326020	−	0.945363i	$-0.605708\pi$
$373$	1.81057e6	−	2.49204e6i	0.673819	−	0.927432i	0.999839	+	0.0179305i	$0.00570776\pi$
$374$	123035.			0.0454832
$375$	4.55415e6	−	2.40397e6i	1.67236	−	0.882777i
$376$	187373.			0.0683498
$377$	−833709.	+	1.14750e6i	−0.302107	+	0.415815i
$378$	195553.	−	63539.1i	0.0703940	−	0.0228724i
$379$	1.40217e6	+	4.31544e6i	0.501422	+	1.54322i	0.806703	+	0.590957i	$0.201250\pi$
$379$	1.40217e6	+	4.31544e6i	0.501422	+	1.54322i	−0.305281	+	0.952262i	$0.598750\pi$
$380$	90825.0	+	138394.i	0.0322661	+	0.0491653i
$381$	−2.67266e6	+	8.22560e6i	−0.943260	+	2.90306i
$382$			105403.i			0.0369569i
$383$	699532.	+	227292.i	0.243675	+	0.0791748i	0.428308	−	0.903633i	$-0.359110\pi$
$383$	699532.	+	227292.i	0.243675	+	0.0791748i	−0.184633	+	0.982807i	$0.559110\pi$
$384$	−655129.	+	475979.i	−0.226725	+	0.164725i
$385$	−1.53095e6	−	72841.1i	−0.526392	−	0.0250452i
$386$	−95995.7	−	69745.0i	−0.0327932	−	0.0238256i
$387$	−1.74590e6	−	2.40303e6i	−0.592575	−	0.815609i
$388$	−2.56824e6	−	3.53488e6i	−0.866077	−	1.19205i
$389$	−2.66011e6	−	1.93268e6i	−0.891304	−	0.647571i	0.0449134	−	0.998991i	$-0.485699\pi$
$389$	−2.66011e6	−	1.93268e6i	−0.891304	−	0.647571i	−0.936218	+	0.351420i	$0.885699\pi$
$390$	−132434.	−	106191.i	−0.0440899	−	0.0353531i
$391$	2.94412e6	−	2.13903e6i	0.973898	−	0.707578i
$392$	119063.	+	38686.0i	0.0391347	+	0.0127157i
$393$			9.98251e6i			3.26031i
$394$	−30552.9	+	94032.2i	−0.00991544	+	0.0305166i
$395$	−1.46318e6	+	1.82478e6i	−0.471852	+	0.588462i
$396$	−1.95709e6	−	6.02330e6i	−0.627151	−	1.93017i
$397$	−1.85803e6	+	603711.i	−0.591666	+	0.192244i	−0.589520	−	0.807754i	$-0.700683\pi$
$397$	−1.85803e6	+	603711.i	−0.591666	+	0.192244i	−0.00214594	+	0.999998i	$0.500683\pi$
$398$	−18326.6	+	25224.4i	−0.00579929	+	0.00798203i
$399$	−236558.			−0.0743886
$400$	−692557.	−	3.11057e6i	−0.216424	−	0.972054i
$401$	−2.93721e6			−0.912166			−0.456083	−	0.889937i	$-0.650748\pi$
$401$	−2.93721e6			−0.912166			−0.456083	+	0.889937i	$0.650748\pi$
$402$	−64588.0	+	88897.8i	−0.0199337	+	0.0274363i
$403$	1.46377e6	−	475606.i	0.448961	−	0.145876i
$404$	291916.	+	898424.i	0.0889824	+	0.273860i
$405$	−9.74429e6	+	2.66135e6i	−2.95197	+	0.806239i
$406$	−16297.5	+	50158.5i	−0.00490688	+	0.0151018i
$407$			1.90966e6i			0.571440i
$408$	−696801.	−	226404.i	−0.207233	−	0.0673340i
$409$	4.77161e6	−	3.46678e6i	1.41045	−	1.02475i	0.417188	−	0.908820i	$-0.363015\pi$
$409$	4.77161e6	−	3.46678e6i	1.41045	−	1.02475i	0.993258	−	0.115929i	$-0.0369845\pi$
$410$	23094.8	−	15156.6i	0.00678509	−	0.00445290i
$411$	−5.25575e6	−	3.81853e6i	−1.53472	−	1.11504i
$412$	101956.	+	140331.i	0.0295918	+	0.0407296i
$413$	1.59757e6	+	2.19887e6i	0.460878	+	0.634344i
$414$	209756.	+	152397.i	0.0601469	+	0.0436993i
$415$	1.01069e6	+	3.70054e6i	0.288069	+	1.05474i
$416$	−255540.	+	185661.i	−0.0723979	+	0.0526002i
$417$	6.74716e6	+	2.19228e6i	1.90012	+	0.617386i
$418$		−	6170.02i		−	0.00172721i
$419$	1.05363e6	−	3.24273e6i	0.293191	−	0.902350i	−0.690632	−	0.723207i	$-0.742667\pi$
$419$	1.05363e6	−	3.24273e6i	0.293191	−	0.902350i	0.983823	−	0.179144i	$-0.0573327\pi$
$420$	4.26524e6	+	1.61374e6i	1.17983	+	0.446387i
$421$	−871749.	−	2.68297e6i	−0.239710	−	0.737752i	−0.996462	−	0.0840492i	$-0.973215\pi$
$421$	−871749.	−	2.68297e6i	−0.239710	−	0.737752i	0.756752	−	0.653703i	$-0.226785\pi$
$422$	−112486.	+	36548.8i	−0.0307479	+	0.00999060i
$423$	5.12573e6	−	7.05496e6i	1.39285	−	1.91710i
$424$	244947.			0.0661696
$425$	3.82235e6	−	4.32828e6i	1.02650	−	1.16237i
$426$	24539.4			0.00655149
$427$	−2.58052e6	+	3.55178e6i	−0.684915	+	0.942705i
$428$	−3.94241e6	+	1.28097e6i	−1.04028	+	0.338009i
$429$	−1.41263e6	−	4.34763e6i	−0.370583	−	1.14054i
$430$	−2651.19	+	55721.9i	−0.000691464	+	0.0145330i
$431$	−1.20303e6	+	3.70255e6i	−0.311949	+	0.960081i	0.665043	+	0.746805i	$0.268413\pi$
$431$	−1.20303e6	+	3.70255e6i	−0.311949	+	0.960081i	−0.976992	+	0.213276i	$0.931587\pi$
$432$			1.15129e7i			2.96809i
$433$	2.33193e6	+	757689.i	0.597716	+	0.194210i	0.592222	−	0.805775i	$-0.298251\pi$
$433$	2.33193e6	+	757689.i	0.597716	+	0.194210i	0.00549462	+	0.999985i	$0.498251\pi$
$434$	46298.3	−	33637.7i	0.0117989	−	0.00857239i
$435$	1.68866e6	−	4.46324e6i	0.427876	−	1.13091i
$436$	3.54177e6	+	2.57325e6i	0.892286	+	0.648284i
$437$	−107269.	−	147643.i	−0.0268701	−	0.0369836i
$438$	−4166.50	−	5734.70i	−0.00103774	−	0.00142832i
$439$	3.47822e6	+	2.52707e6i	0.861381	+	0.625830i	0.928260	−	0.371931i	$-0.121304\pi$
$439$	3.47822e6	+	2.52707e6i	0.861381	+	0.625830i	−0.0668794	+	0.997761i	$0.521304\pi$
$440$	−84239.0	+	222650.i	−0.0207435	+	0.0548265i
$441$	4.71367e6	−	3.42468e6i	1.15415	−	0.838540i
$442$	−181029.	−	58820.0i	−0.0440751	−	0.0143209i
$443$			366480.i			0.0887239i	0.999016	+	0.0443620i	$0.0141255\pi$
$443$			366480.i			0.0887239i	−0.999016	+	0.0443620i	$0.985875\pi$
$444$	1.75582e6	−	5.40387e6i	0.422692	−	1.30091i
$445$	95729.7	−	2.01202e6i	0.0229164	−	0.481650i
$446$	11463.1	+	35279.9i	0.00272877	+	0.00839828i
$447$	−3.71073e6	+	1.20569e6i	−0.878397	+	0.285409i
$448$	1.65413e6	−	2.27672e6i	0.389381	−	0.535937i
$449$	2.55779e6			0.598756			0.299378	−	0.954135i	$-0.403221\pi$
$449$	2.55779e6			0.598756			0.299378	+	0.954135i	$0.403221\pi$
$450$	377432.	+	163705.i	0.0878633	+	0.0381093i
$451$	743914.			0.172219
$452$	−204210.	+	281071.i	−0.0470145	+	0.0647099i
$453$	1.21386e7	−	3.94407e6i	2.77922	−	0.903023i
$454$	−15671.3	−	48231.3i	−0.00356833	−	0.0109822i
$455$	2.21776e6	+	839084.i	0.502210	+	0.190010i
$456$	−11353.8	+	34943.4i	−0.00255699	+	0.00786962i
$457$		−	2.51846e6i		−	0.564085i	−0.959402	−	0.282043i	$-0.908988\pi$
$457$		−	2.51846e6i		−	0.564085i	0.959402	−	0.282043i	$-0.0910120\pi$
$458$	280240.	+	91055.5i	0.0624261	+	0.0202835i
$459$	−1.68775e7	+	1.22622e7i	−3.73919	+	2.71668i
$460$	926915.	+	3.39382e6i	0.204242	+	0.747815i
$461$	−5.16943e6	−	3.75581e6i	−1.13290	−	0.823097i	−0.146782	−	0.989169i	$-0.546892\pi$
$461$	−5.16943e6	−	3.75581e6i	−1.13290	−	0.823097i	−0.986114	+	0.166072i	$0.946892\pi$
$462$	−99909.7	−	137514.i	−0.0217772	−	0.0299738i
$463$	−3.51261e6	−	4.83469e6i	−0.761514	−	1.04813i	−0.997087	−	0.0762768i	$-0.975697\pi$
$463$	−3.51261e6	−	4.83469e6i	−0.761514	−	1.04813i	0.235573	−	0.971857i	$-0.424303\pi$
$464$	−2.38904e6	−	1.73574e6i	−0.515144	−	0.374274i
$465$	−4.32908e6	+	2.84108e6i	−0.928461	+	0.609328i
$466$	80060.4	−	58167.3i	0.0170786	−	0.0124083i
$467$	−7.92182e6	−	2.57395e6i	−1.68086	−	0.546146i	−0.695785	−	0.718250i	$-0.744943\pi$
$467$	−7.92182e6	−	2.57395e6i	−1.68086	−	0.546146i	−0.985079	+	0.172104i	$0.944943\pi$
$468$			9.79807e6i			2.06788i
$469$	474316.	−	1.45980e6i	0.0995717	−	0.306450i
$470$	−157990.	+	43150.0i	−0.0329902	+	0.00901024i
$471$	−1.62687e6	−	5.00699e6i	−0.337909	−	1.03998i
$472$	401485.	−	130450.i	0.0829496	−	0.0269520i
$473$	−883017.	+	1.21537e6i	−0.181475	+	0.249779i
$474$	−259394.			−0.0530290
$475$	−217056.	−	191685.i	−0.0441406	−	0.0389810i
$476$	5.11357e6			1.03444
$477$	6.70073e6	−	9.22276e6i	1.34842	−	1.85594i
$478$	−210583.	+	68422.7i	−0.0421555	+	0.0136971i
$479$	2.34414e6	+	7.21451e6i	0.466815	+	1.43671i	0.856686	+	0.515838i	$0.172519\pi$
$479$	2.34414e6	+	7.21451e6i	0.466815	+	1.43671i	−0.389872	+	0.920869i	$0.627481\pi$
$480$	664787.	−	829078.i	0.131698	−	0.164245i
$481$	912960.	−	2.80980e6i	0.179924	−	0.553749i
$482$		−	276361.i		−	0.0541824i
$483$	−4.78149e6	−	1.55360e6i	−0.932600	−	0.303020i
$484$	1.57222e6	−	1.14228e6i	0.305069	−	0.221646i
$485$	5.96322e6	+	4.78155e6i	1.15114	+	0.923027i
$486$	−439512.	−	319324.i	−0.0844073	−	0.0613255i
$487$	4.29998e6	+	5.91841e6i	0.821568	+	1.13079i	0.989434	+	0.144982i	$0.0463124\pi$
$487$	4.29998e6	+	5.91841e6i	0.821568	+	1.13079i	−0.167866	+	0.985810i	$0.553688\pi$
$488$	400800.	+	551654.i	0.0761865	+	0.104862i
$489$	−1.05012e7	−	7.62956e6i	−1.98594	−	1.44287i
$490$	−109301.	−	5200.45i	−0.0205653	−	0.000978477i
$491$	−3.66777e6	+	2.66479e6i	−0.686591	+	0.498838i	−0.875538	−	0.483150i	$-0.839493\pi$
$491$	−3.66777e6	+	2.66479e6i	−0.686591	+	0.498838i	0.188947	+	0.981987i	$0.439493\pi$
$492$	−2.10509e6	−	683986.i	−0.392066	−	0.127390i
$493$		−	5.35095e6i		−	0.991547i
$494$	−2949.73	+	9078.32i	−0.000543831	+	0.00167374i
$495$	6.07878e6	+	9.26252e6i	1.11507	+	1.69909i
$496$	990187.	+	3.04748e6i	0.180723	+	0.556208i
$497$	−326004.	+	105925.i	−0.0592014	+	0.0192357i
$498$	−250059.	+	344177.i	−0.0451824	+	0.0621883i
$499$	−2.53511e6			−0.455769			−0.227885	−	0.973688i	$-0.573181\pi$
$499$	−2.53511e6			−0.455769			−0.227885	+	0.973688i	$0.573181\pi$
$500$	2.60598e6	+	4.93685e6i	0.466173	+	0.883131i
$501$	−1.53730e6			−0.273630
$502$	−121803.	+	167648.i	−0.0215724	+	0.0296919i
$503$	−613539.	+	199351.i	−0.108124	+	0.0351316i	−0.362579	−	0.931953i	$-0.618104\pi$
$503$	−613539.	+	199351.i	−0.108124	+	0.0351316i	0.254455	+	0.967085i	$0.418104\pi$
$504$	225318.	+	693458.i	0.0395111	+	0.121603i
$505$	−906701.	−	1.38158e6i	−0.158211	−	0.241073i
$506$	40521.7	−	124713.i	0.00703576	−	0.0216538i
$507$		−	3.87291e6i		−	0.669141i
$508$	−8.91683e6	−	2.89725e6i	−1.53303	−	0.498112i
$509$	6.18451e6	−	4.49331e6i	1.05806	−	0.768727i	0.0843331	−	0.996438i	$-0.473124\pi$
$509$	6.18451e6	−	4.49331e6i	1.05806	−	0.768727i	0.973729	+	0.227711i	$0.0731240\pi$
$510$	639671.	+	30434.9i	0.108901	+	0.00518139i
$511$	80105.6	+	58200.2i	0.0135710	+	0.00985989i
$512$	−644524.	−	887112.i	−0.108659	−	0.149556i
$513$	614932.	+	846381.i	0.103165	+	0.141995i
$514$	−240298.	−	174587.i	−0.0401183	−	0.0291477i
$515$	−236733.	−	189822.i	−0.0393316	−	0.0315376i
$516$	3.61618e6	−	2.62731e6i	0.597897	−	0.434397i
$517$	−4.19461e6	−	1.36291e6i	−0.690185	−	0.224255i
$518$		−	109853.i		−	0.0179882i
$519$	−3.40127e6	+	1.04680e7i	−0.554272	+	1.70587i
$520$	230389.	−	287326.i	0.0373640	−	0.0465979i
$521$	3.43357e6	+	1.05674e7i	0.554181	+	1.70559i	0.698096	+	0.716004i	$0.254031\pi$
$521$	3.43357e6	+	1.05674e7i	0.554181	+	1.70559i	−0.143915	+	0.989590i	$0.545969\pi$
$522$	362573.	−	117807.i	0.0582397	−	0.0189232i
$523$	−2.00369e6	+	2.75784e6i	−0.320314	+	0.440874i	−0.938563	−	0.345108i	$-0.887842\pi$
$523$	−2.00369e6	+	2.75784e6i	−0.320314	+	0.440874i	0.618249	+	0.785982i	$0.287842\pi$
$524$	−1.08214e7			−1.72169
$525$	−7.94153e6	−	757414.i	−1.25749	−	0.119932i
$526$	355809.			0.0560728
$527$	−3.41286e6	+	4.69740e6i	−0.535294	+	0.736769i
$528$	9.05154e6	−	2.94103e6i	1.41299	−	0.459107i
$529$	790391.	+	2.43257e6i	0.122801	+	0.377944i
$530$	−206536.	+	56408.8i	−0.0319379	+	0.00872283i
$531$	6.07122e6	−	1.86853e7i	0.934414	−	2.87583i
$532$		−	256437.i		−	0.0392828i
$533$	−1.09457e6	−	355646.i	−0.166888	−	0.0542251i
$534$	180724.	−	131304.i	0.0274261	−	0.0199262i
$535$	6.06257e6	−	3.97872e6i	0.915740	−	0.600979i
$536$	−192870.	−	140128.i	−0.0289969	−	0.0210675i
$537$	2.08471e6	+	2.86936e6i	0.311969	+	0.429388i
$538$	−82790.5	−	113951.i	−0.0123318	−	0.0169732i
$539$	−2.38401e6	−	1.73208e6i	−0.353457	−	0.256801i
$540$	−5.31366e6	−	1.94555e7i	−0.784168	−	2.87116i
$541$	−8.66152e6	+	6.29296e6i	−1.27233	+	0.924405i	−0.999293	−	0.0375979i	$-0.988029\pi$
$541$	−8.66152e6	+	6.29296e6i	−1.27233	+	0.924405i	−0.273041	+	0.962002i	$0.588029\pi$
$542$	−24330.6	−	7905.49i	−0.00355758	−	0.00115593i
$543$			7.48666e6i			1.08965i
$544$	368230.	−	1.13330e6i	0.0533484	−	0.164190i
$545$	−7.16287e6	−	2.71006e6i	−1.03299	−	0.390829i
$546$	81261.4	+	250097.i	0.0116655	+	0.0359026i
$547$	1.91679e6	−	622802.i	0.273909	−	0.0889984i	−0.168842	−	0.985643i	$-0.554003\pi$
$547$	1.91679e6	−	622802.i	0.273909	−	0.0889984i	0.442751	+	0.896645i	$0.354003\pi$
$548$	4.13941e6	−	5.69741e6i	0.588827	−	0.810450i
$549$	3.17350e7			4.49374
$550$	19755.2	−	207134.i	0.00278468	−	0.0291975i
$551$	−268341.			−0.0376538
$552$	−458983.	+	631736.i	−0.0641134	+	0.0882445i
$553$	3.44602e6	−	1.11968e6i	0.479187	−	0.155697i
$554$	86288.3	+	265568.i	0.0119448	+	0.0367622i
$555$	−472388.	+	9.92849e6i	−0.0650978	+	1.36820i
$556$	−2.37651e6	+	7.31415e6i	−0.326026	+	1.00341i
$557$		−	5.06926e6i		−	0.692320i	−0.938176	−	0.346160i	$-0.887485\pi$
$557$		−	5.06926e6i		−	0.692320i	0.938176	−	0.346160i	$-0.112515\pi$
$558$	−393428.	−	127832.i	−0.0534909	−	0.0173802i
$559$	1.88027e6	−	1.36610e6i	0.254502	−	0.184907i
$560$	−1.74693e6	+	4.61726e6i	−0.235399	+	0.622177i
$561$	1.39521e7	+	1.01368e7i	1.87168	+	1.35986i
$562$	−242077.	−	333190.i	−0.0323305	−	0.0444992i
$563$	596362.	+	820822.i	0.0792938	+	0.109139i	0.846821	−	0.531877i	$-0.178513\pi$
$563$	596362.	+	820822.i	0.0792938	+	0.109139i	−0.767528	+	0.641016i	$0.778513\pi$
$564$	1.06166e7	+	7.71341e6i	1.40536	+	1.02105i
$565$	215067.	−	568439.i	0.0283435	−	0.0749139i
$566$	−3566.57	+	2591.26i	−0.000467960	+	0.000339993i
$567$	1.48822e7	+	4.83552e6i	1.94406	+	0.631664i
$568$			53239.9i			0.00692415i
$569$	4.48028e6	−	1.37889e7i	0.580129	−	1.78545i	−0.0378817	−	0.999282i	$-0.512061\pi$
$569$	4.48028e6	−	1.37889e7i	0.580129	−	1.78545i	0.618010	−	0.786170i	$-0.287939\pi$
$570$	1526.26	−	32078.5i	0.000196762	−	0.00413548i
$571$	−1.04018e6	−	3.20134e6i	−0.133511	−	0.410906i	0.861844	−	0.507173i	$-0.169310\pi$
$571$	−1.04018e6	−	3.20134e6i	−0.133511	−	0.410906i	−0.995355	+	0.0962676i	$0.969310\pi$
$572$	4.71298e6	−	1.53134e6i	0.602290	−	0.195696i
$573$	−8.68409e6	+	1.19526e7i	−1.10494	+	1.52082i
$574$	−42793.5			−0.00542124
$575$	−3.12841e6	−	5.29999e6i	−0.394597	−	0.668506i
$576$	−2.03424e7			−2.55474
$577$	−6.41346e6	+	8.82738e6i	−0.801961	+	1.10380i	0.190554	+	0.981677i	$0.438972\pi$
$577$	−6.41346e6	+	8.82738e6i	−0.801961	+	1.10380i	−0.992514	+	0.122128i	$0.961028\pi$
$578$	398950.	−	129627.i	0.0496706	−	0.0161389i
$579$	−5.13959e6	−	1.58180e7i	−0.637135	−	1.96090i
$580$	4.83830e6	+	1.83056e6i	0.597204	+	0.225951i
$581$	1.83637e6	−	5.65175e6i	0.225693	−	0.694613i
$582$			847675.i			0.103734i
$583$	−5.48350e6	−	1.78170e6i	−0.668170	−	0.217101i
$584$	12441.8	−	9039.51i	0.00150956	−	0.00109676i
$585$	−4.51591e6	−	1.65346e7i	−0.545577	−	1.99758i
$586$	54245.6	+	39411.8i	0.00652560	+	0.00474113i
$587$	619112.	+	852135.i	0.0741608	+	0.102074i	0.844486	−	0.535578i	$-0.179906\pi$
$587$	619112.	+	852135.i	0.0741608	+	0.102074i	−0.770325	+	0.637651i	$0.779906\pi$
$588$	5.15361e6	+	7.09333e6i	0.614707	+	0.846071i
$589$	235567.	+	171149.i	0.0279786	+	0.0203277i
$590$	−308485.	+	202452.i	−0.0364841	+	0.0239437i
$591$	−1.12119e7	+	8.14592e6i	−1.32042	+	0.959338i
$592$	5.84986e6	+	1.90073e6i	0.686027	+	0.222904i
$593$		−	8.65234e6i		−	1.01041i	−0.863000	−	0.505204i	$-0.831417\pi$
$593$		−	8.65234e6i		−	1.01041i	0.863000	−	0.505204i	$-0.168583\pi$
$594$	−232296.	+	714932.i	−0.0270131	+	0.0831379i
$595$	−8.62935e6	+	2.35683e6i	−0.999276	+	0.272921i
$596$	−1.30701e6	−	4.02256e6i	−0.150717	−	0.463860i
$597$	−4.15644e6	+	1.35051e6i	−0.477294	+	0.155082i
$598$	−119244.	+	164125.i	−0.0136359	+	0.0187682i
$599$	646446.			0.0736148			0.0368074	−	0.999322i	$-0.488281\pi$
$599$	646446.			0.0736148			0.0368074	+	0.999322i	$0.488281\pi$
$600$	−493042.	+	1.13674e6i	−0.0559121	+	0.128909i
$601$	−712942.			−0.0805134			−0.0402567	−	0.999189i	$-0.512818\pi$
$601$	−712942.			−0.0805134			−0.0402567	+	0.999189i	$0.512818\pi$
$602$	50795.4	−	69913.9i	0.00571259	−	0.00786271i
$603$	−1.05522e7	+	3.42862e6i	−1.18182	+	0.383995i
$604$	4.27550e6	+	1.31586e7i	0.476864	+	1.46764i
$605$	−2.12670e6	+	2.65227e6i	−0.236220	+	0.294598i
$606$	56633.0	−	174298.i	0.00626452	−	0.0192802i
$607$		−	9.01221e6i		−	0.992795i	−0.868095	−	0.496397i	$-0.834656\pi$
$607$		−	9.01221e6i		−	0.992795i	0.868095	−	0.496397i	$-0.165344\pi$
$608$	−56832.9	−	18466.1i	−0.00623506	−	0.00202589i
$609$	−5.98064e6	+	4.34519e6i	−0.653438	+	0.474750i
$610$	−464989.	−	372846.i	−0.0505962	−	0.0405700i
$611$	5.52021e6	+	4.01067e6i	0.598209	+	0.434624i
$612$	−2.17267e7	−	2.99043e7i	−2.34485	−	3.22741i
$613$	6.77341e6	+	9.32280e6i	0.728042	+	1.00206i	0.999218	+	0.0395337i	$0.0125872\pi$
$613$	6.77341e6	+	9.32280e6i	0.728042	+	1.00206i	−0.271177	+	0.962530i	$0.587413\pi$
$614$	444431.	+	322898.i	0.0475756	+	0.0345657i
$615$	3.86767e6	+	184020.i	0.412346	+	0.0196190i
$616$	298346.	−	216761.i	0.0316787	−	0.0230160i
$617$	6.95524e6	+	2.25989e6i	0.735528	+	0.238987i	0.652742	−	0.757580i	$-0.273618\pi$
$617$	6.95524e6	+	2.25989e6i	0.735528	+	0.238987i	0.0827853	+	0.996567i	$0.473618\pi$
$618$		−	33651.7i		−	0.00354435i
$619$	−782884.	+	2.40947e6i	−0.0821241	+	0.252752i	−0.983685	−	0.179901i	$-0.942422\pi$
$619$	−782884.	+	2.40947e6i	−0.0821241	+	0.252752i	0.901561	+	0.432653i	$0.142422\pi$
$620$	−3.07983e6	−	4.69287e6i	−0.321771	−	0.490297i
$621$	6.87083e6	+	2.11462e7i	0.714957	+	2.20041i
$622$	−48223.8	+	15668.9i	−0.00499787	+	0.00162391i
$623$	−1.83413e6	+	2.52446e6i	−0.189326	+	0.260585i
$624$	−1.47241e7			−1.51380
$625$	−6.67308e6	−	7.13003e6i	−0.683324	−	0.730116i
$626$	−59666.2			−0.00608544
$627$	508343.	−	699674.i	0.0516402	−	0.0710767i
$628$	5.42774e6	−	1.76358e6i	0.549187	−	0.178442i
$629$	3.44419e6	+	1.06001e7i	0.347104	+	1.06828i
$630$	−349681.	−	532825.i	−0.0351011	−	0.0534852i
$631$	−972146.	+	2.99196e6i	−0.0971982	+	0.299145i	−0.987820	−	0.155599i	$-0.950269\pi$
$631$	−972146.	+	2.99196e6i	−0.0971982	+	0.299145i	0.890622	+	0.454744i	$0.150269\pi$
$632$		−	562772.i		−	0.0560454i
$633$	−1.57670e7	−	5.12300e6i	−1.56401	−	0.508177i
$634$	168728.	−	122588.i	0.0166711	−	0.0121123i
$635$	1.63828e7	+	779478.i	1.61233	+	0.0767131i
$636$	1.38788e7	+	1.00835e7i	1.36053	+	0.988485i
$637$	2.67967e6	+	3.68825e6i	0.261657	+	0.360141i
$638$	−113333.	−	155990.i	−0.0110231	−	0.0151720i
$639$	2.00459e6	+	1.45642e6i	0.194211	+	0.141102i
$640$	1.19805e6	+	960647.i	0.115618	+	0.0927072i
$641$	1.25840e7	−	9.14278e6i	1.20968	−	0.878887i	0.214482	−	0.976728i	$-0.431194\pi$
$641$	1.25840e7	−	9.14278e6i	1.20968	−	0.878887i	0.995202	+	0.0978411i	$0.0311937\pi$
$642$	764845.	+	248513.i	0.0732379	+	0.0237964i
$643$			1.61928e6i			0.154452i	0.997014	+	0.0772262i	$0.0246064\pi$
$643$			1.61928e6i			0.154452i	−0.997014	+	0.0772262i	$0.975394\pi$
$644$	1.68416e6	−	5.18330e6i	0.160017	−	0.492483i
$645$	−4.89152e6	+	6.10038e6i	−0.462961	+	0.577374i
$646$	−11128.0	−	34248.4i	−0.00104914	−	0.00322894i
$647$	3.53009e6	−	1.14700e6i	0.331532	−	0.107721i	−0.138521	−	0.990359i	$-0.544235\pi$
$647$	3.53009e6	−	1.14700e6i	0.331532	−	0.107721i	0.470053	+	0.882638i	$0.344235\pi$
$648$	1.42857e6	−	1.96625e6i	0.133648	−	0.183951i
$649$	−9.93669e6			−0.926041
$650$	−128093.	+	295325.i	−0.0118916	+	0.0274168i
$651$	8.02157e6			0.741834
$652$	8.27070e6	−	1.13836e7i	0.761944	−	1.04873i
$653$	−2.76408e6	+	898105.i	−0.253669	+	0.0824222i	−0.433091	−	0.901350i	$-0.642577\pi$
$653$	−2.76408e6	+	898105.i	−0.253669	+	0.0824222i	0.179422	+	0.983772i	$0.442577\pi$
$654$	−262456.	−	807758.i	−0.0239946	−	0.0738477i
$655$	1.82615e7	−	4.98755e6i	1.66316	−	0.454239i
$656$	740437.	−	2.27883e6i	0.0671782	−	0.206753i
$657$		−	715742.i		−	0.0646909i
$658$	241294.	+	78401.3i	0.0217261	+	0.00705925i
$659$	5.06846e6	−	3.68245e6i	0.454634	−	0.330311i	−0.336789	−	0.941580i	$-0.609341\pi$
$659$	5.06846e6	−	3.68245e6i	0.454634	−	0.330311i	0.791423	+	0.611269i	$0.209341\pi$
$660$	−1.39386e7	+	9.14761e6i	−1.24555	+	0.817425i
$661$	−1.47001e7	−	1.06802e7i	−1.30863	−	0.950774i	−0.308629	−	0.951183i	$-0.599870\pi$
$661$	−1.47001e7	−	1.06802e7i	−1.30863	−	0.950774i	−1.00000		0.000408091i	$0.999870\pi$
$662$	−215042.	−	295980.i	−0.0190712	−	0.0262493i
$663$	−1.56824e7	−	2.15850e7i	−1.38557	−	1.90708i
$664$	−746715.	−	542521.i	−0.0657257	−	0.0477525i
$665$	118191.	+	432748.i	0.0103641	+	0.0379473i
$666$	−642422.	+	466747.i	−0.0561222	+	0.0407752i
$667$	−5.42391e6	−	1.76233e6i	−0.472061	−	0.153382i
$668$		−	1.66648e6i		−	0.144497i
$669$	−1.60678e6	+	4.94515e6i	−0.138800	+	0.427183i
$670$	194895.	+	73738.1i	0.0167731	+	0.00634607i
$671$	−4.95987e6	−	1.52649e7i	−0.425269	−	1.30884i
$672$	−1.56568e6	+	508719.i	−0.133745	+	0.0434565i
$673$	−8.70036e6	+	1.19750e7i	−0.740457	+	1.01915i	0.258135	+	0.966109i	$0.416892\pi$
$673$	−8.70036e6	+	1.19750e7i	−0.740457	+	1.01915i	−0.998592	+	0.0530428i	$0.983108\pi$
$674$	270191.			0.0229098
$675$	1.79340e7	+	3.03828e7i	1.51502	+	2.56666i
$676$	4.19837e6			0.353357
$677$	1.32046e6	−	1.81746e6i	0.110727	−	0.152403i	−0.750057	−	0.661374i	$-0.769974\pi$
$677$	1.32046e6	−	1.81746e6i	0.110727	−	0.152403i	0.860784	+	0.508970i	$0.169974\pi$
$678$	64102.9	−	20828.3i	0.00535554	−	0.00174012i
$679$	−3.65901e6	−	1.12613e7i	−0.304572	−	0.937376i
$680$	−66030.6	+	1.38781e6i	−0.00547612	+	0.115095i
$681$	2.19663e6	−	6.76053e6i	0.181505	−	0.558615i
$682$			209222.i			0.0172245i
$683$	1.06229e7	+	3.45159e6i	0.871347	+	0.283118i	0.710360	−	0.703839i	$-0.248532\pi$
$683$	1.06229e7	+	3.45159e6i	0.871347	+	0.283118i	0.160987	+	0.986956i	$0.448532\pi$
$684$	−1.49965e6	+	1.08956e6i	−0.122560	+	0.0890453i
$685$	−4.35949e6	+	1.15225e7i	−0.354985	+	0.938250i
$686$	384777.	+	279557.i	0.0312176	+	0.0226809i
$687$	2.42770e7	+	3.34144e7i	1.96247	+	2.70110i
$688$	2.84415e6	+	3.91463e6i	0.229077	+	0.315297i
$689$	7.21643e6	+	5.24304e6i	0.579127	+	0.420761i
$690$	241526.	−	638369.i	0.0193126	−	0.0510445i
$691$	3.08772e6	−	2.24336e6i	0.246004	−	0.178733i	−0.457950	−	0.888978i	$-0.651416\pi$
$691$	3.08772e6	−	2.24336e6i	0.246004	−	0.178733i	0.703954	+	0.710245i	$0.251416\pi$
$692$	−1.13477e7	−	3.68709e6i	−0.900829	−	0.292697i
$693$		−	1.71630e7i		−	1.35756i
$694$	154936.	−	476844.i	0.0122111	−	0.0375818i
$695$	639377.	−	1.34382e7i	0.0502106	−	1.05531i
$696$	354808.	+	1.09199e6i	0.0277632	+	0.0854464i
$697$	4.12930e6	−	1.34169e6i	0.321955	−	0.104609i
$698$	−173688.	+	239062.i	−0.0134937	+	0.0185725i
$699$	1.38711e7			1.07379
$700$	821063.	−	8.60889e6i	0.0633332	−	0.664052i
$701$	7.28848e6			0.560199			0.280099	−	0.959971i	$-0.409633\pi$
$701$	7.28848e6			0.560199			0.280099	+	0.959971i	$0.409633\pi$
$702$	683581.	−	940869.i	0.0523537	−	0.0720587i
$703$	531578.	−	172720.i	0.0405676	−	0.0131812i
$704$	3.17931e6	+	9.78492e6i	0.241770	+	0.744090i
$705$	−2.14710e7	−	8.12351e6i	−1.62697	−	0.615561i
$706$	−161920.	+	498338.i	−0.0122261	+	0.0376281i
$707$			2.56000e6i			0.192615i
$708$	2.81184e7	+	9.13622e6i	2.10818	+	0.684989i
$709$	6.21987e6	−	4.51900e6i	0.464693	−	0.337619i	−0.330677	−	0.943744i	$-0.607277\pi$
$709$	6.21987e6	−	4.51900e6i	0.464693	−	0.337619i	0.795369	+	0.606125i	$0.207277\pi$
$710$	−12260.6	−	44891.1i	−0.000912779	−	0.00334206i
$711$	−2.11895e7	−	1.53951e7i	−1.57198	−	1.14211i
$712$	284873.	+	392094.i	0.0210596	+	0.0289861i
$713$	3.63742e6	+	5.00648e6i	0.267960	+	0.368815i
$714$	−802591.	−	583117.i	−0.0589181	−	0.0428065i
$715$	−7.24754e6	+	4.75640e6i	−0.530183	+	0.347947i
$716$	−3.11049e6	+	2.25990e6i	−0.226749	+	0.164743i
$717$	−2.95172e7	−	9.59073e6i	−2.14426	−	0.696713i
$718$			280774.i			0.0203257i
$719$	−6.80494e6	+	2.09435e7i	−0.490910	+	1.51087i	0.332325	+	0.943165i	$0.392167\pi$
$719$	−6.80494e6	+	2.09435e7i	−0.490910	+	1.51087i	−0.823235	+	0.567701i	$0.807833\pi$
$720$	3.44242e7	−	9.40189e6i	2.47476	−	0.675902i
$721$	145259.	+	447060.i	0.0104065	+	0.0320279i
$722$	493538.	−	160360.i	0.0352353	−	0.0114486i
$723$	2.27691e7	−	3.13390e7i	1.61995	−	2.22966i
$724$	−8.11579e6			−0.575419
$725$	−9.00851e6	−	859177.i	−0.636514	−	0.0607068i
$726$	−377022.			−0.0265476
$727$	1.20985e6	−	1.66521e6i	0.0848973	−	0.116851i	−0.764456	−	0.644676i	$-0.776992\pi$
$727$	1.20985e6	−	1.66521e6i	0.0848973	−	0.116851i	0.849353	+	0.527825i	$0.176992\pi$
$728$	−542602.	+	176302.i	−0.0379448	+	0.0123290i
$729$	−9.96273e6	−	3.06621e7i	−0.694320	−	2.13690i
$730$	−8409.06	+	10487.2i	−0.000584037	+	0.000728371i
$731$	−2.70945e6	+	8.33882e6i	−0.187537	+	0.577180i
$732$			4.77562e7i			3.29422i
$733$	1.78247e7	+	5.79160e6i	1.22536	+	0.398143i	0.849030	−	0.528344i	$-0.177187\pi$
$733$	1.78247e7	+	5.79160e6i	1.22536	+	0.398143i	0.376327	+	0.926487i	$0.377187\pi$
$734$	−695134.	+	505044.i	−0.0476243	+	0.0346010i
$735$	−1.19662e7	−	9.59498e6i	−0.817030	−	0.655127i
$736$	−1.02747e6	−	746501.i	−0.0699157	−	0.0507968i
$737$	3.29841e6	+	4.53987e6i	0.223684	+	0.307875i
$738$	181823.	+	250257.i	0.0122887	+	0.0169140i
$739$	−2.06974e7	−	1.50375e7i	−1.39413	−	1.01290i	−0.995398	−	0.0958297i	$-0.969450\pi$
$739$	−2.06974e7	−	1.50375e7i	−1.39413	−	1.01290i	−0.398734	−	0.917067i	$-0.630550\pi$
$740$	−1.07628e7	−	512084.i	−0.722515	−	0.0343765i
$741$	−1.08245e6	+	786447.i	−0.0724208	+	0.0526168i
$742$	315438.	+	102492.i	0.0210331	+	0.00683407i
$743$			1.34959e7i			0.896870i	0.893815	+	0.448435i	$0.148018\pi$
$743$			1.34959e7i			0.896870i	−0.893815	+	0.448435i	$0.851982\pi$
$744$	385001.	−	1.18491e6i	0.0254994	−	0.0784791i
$745$	4.05962e6	+	6.18582e6i	0.267975	+	0.408326i
$746$	−200186.	−	616110.i	−0.0131700	−	0.0405332i
$747$	−4.08540e7	+	1.32743e7i	−2.67875	+	0.870380i
$748$	−1.09886e7	+	1.51245e7i	−0.718107	+	0.988389i
$749$	−1.12336e7			−0.731670
$750$	153947.	−	1.07202e6i	0.00999353	−	0.0695906i
$751$	−2.34069e6			−0.151441			−0.0757206	−	0.997129i	$-0.524126\pi$
$751$	−2.34069e6			−0.151441			−0.0757206	+	0.997129i	$0.524126\pi$
$752$	−8.35001e6	+	1.14928e7i	−0.538446	+	0.741108i
$753$	−2.76247e7	+	8.97582e6i	−1.77546	+	0.576881i
$754$	92179.2	+	283698.i	0.00590479	+	0.0181731i
$755$	−1.32799e7	−	2.02351e7i	−0.847864	−	1.29193i
$756$	−9.65463e6	+	2.97139e7i	−0.614372	+	1.89084i
$757$		−	9.93995e6i		−	0.630441i	−0.949018	−	0.315220i	$-0.897922\pi$
$757$		−	9.93995e6i		−	0.630441i	0.949018	−	0.315220i	$-0.102078\pi$
$758$	907571.	+	294888.i	0.0573730	+	0.0186416i
$759$	1.48701e7	−	1.08038e7i	0.936936	−	0.680724i
$760$	69596.4	+	3311.33i	0.00437072	+	0.000207954i
$761$	−1.76709e7	−	1.28386e7i	−1.10610	−	0.803632i	−0.124059	−	0.992275i	$-0.539591\pi$
$761$	−1.76709e7	−	1.28386e7i	−1.10610	−	0.803632i	−0.982046	+	0.188643i	$0.939591\pi$
$762$	1.06914e6	+	1.47155e6i	0.0667034	+	0.0918093i
$763$	6.97342e6	+	9.59809e6i	0.433645	+	0.596861i
$764$	−1.29570e7	−	9.41384e6i	−0.803105	−	0.583490i
$765$	5.04475e7	+	4.04508e7i	3.11664	+	2.49904i
$766$	125145.	−	90923.3i	0.00770623	−	0.00559890i
$767$	1.46205e7	+	4.75047e6i	0.897372	+	0.291574i
$768$		−	3.04842e7i		−	1.86497i
$769$	−19321.4	+	59465.1i	−0.00117821	+	0.00362616i	−0.951644	−	0.307203i	$-0.900607\pi$
$769$	−19321.4	+	59465.1i	−0.00117821	+	0.00362616i	0.950466	+	0.310830i	$0.100607\pi$
$770$	−201643.	+	251475.i	−0.0122562	+	0.0152851i
$771$	−1.28655e7	−	3.95960e7i	−0.779455	−	2.39892i
$772$	1.71473e7	−	5.57148e6i	1.03550	−	0.336455i
$773$	9.00488e6	−	1.23942e7i	0.542037	−	0.746050i	−0.446868	−	0.894600i	$-0.647461\pi$
$773$	9.00488e6	−	1.23942e7i	0.542037	−	0.746050i	0.988905	+	0.148550i	$0.0474605\pi$
$774$	−624679.			−0.0374804
$775$	7.36026e6	+	6.49992e6i	0.440189	+	0.388735i
$776$	−1.83909e6			−0.109635
$777$	9.05070e6	−	1.24572e7i	0.537811	−	0.740233i
$778$	−657663.	+	213688.i	−0.0389542	+	0.0126570i
$779$	−67283.7	−	207078.i	−0.00397252	−	0.0122262i
$780$	2.48820e7	−	6.79573e6i	1.46436	−	0.399944i
$781$	387256.	−	1.19185e6i	0.0227181	−	0.0699190i
$782$		−	765337.i		−	0.0447544i
$783$	3.10932e7	+	1.01028e7i	1.81243	+	0.588895i
$784$	−7.67875e6	+	5.57894e6i	−0.446170	+	0.324162i
$785$	−8.34669e6	+	5.47774e6i	−0.483437	+	0.317269i
$786$	1.69845e6	+	1.23400e6i	0.0980609	+	0.0712454i
$787$	−4.68059e6	−	6.44228e6i	−0.269379	−	0.370768i	0.652801	−	0.757529i	$-0.273594\pi$
$787$	−4.68059e6	−	6.44228e6i	−0.269379	−	0.370768i	−0.922180	+	0.386761i	$0.873594\pi$
$788$	−8.83046e6	−	1.21541e7i	−0.506603	−	0.697279i
$789$	4.03484e7	+	2.93148e7i	2.30746	+	1.67647i
$790$	129600.	+	474521.i	0.00738820	+	0.0270513i
$791$	−761695.	+	553404.i	−0.0432852	+	0.0314486i
$792$	−2.53524e6	−	823750.i	−0.143617	−	0.0466641i
$793$			2.48314e7i			1.40222i
$794$	−126965.	+	390758.i	−0.00714714	+	0.0219966i
$795$	−2.80685e7	−	1.06196e7i	−1.57507	−	0.595926i
$796$	−1.46400e6	−	4.50572e6i	−0.0818950	−	0.252047i
$797$	2.88625e7	−	9.37798e6i	1.60949	−	0.522954i	0.640058	−	0.768327i	$-0.278910\pi$
$797$	2.88625e7	−	9.37798e6i	1.60949	−	0.522954i	0.969429	+	0.245373i	$0.0789103\pi$
$798$	−29242.3	+	40248.6i	−0.00162557	+	0.00223740i
$799$	−2.57415e7			−1.42648
$800$	−1.84882e6	−	801896.i	−0.102134	−	0.0442989i
$801$	2.25560e7			1.24217
$802$	−363085.	+	499744.i	−0.0199330	+	0.0274354i
$803$	−344280.	+	111863.i	−0.0188418	+	0.00612207i
$804$	−5.15953e6	−	1.58794e7i	−0.281495	−	0.866351i
$805$	−453106.	+	9.52323e6i	−0.0246439	+	0.517958i
$806$	100024.	−	307841.i	0.00542331	−	0.0166912i
$807$		−	1.97430e7i		−	1.06716i
$808$	378152.	+	122869.i	0.0203769	+	0.00662086i
$809$	−1.37149e7	+	9.96446e6i	−0.736752	+	0.535282i	−0.891692	−	0.452642i	$-0.850482\pi$
$809$	−1.37149e7	+	9.96446e6i	−0.736752	+	0.535282i	0.154940	+	0.987924i	$0.450482\pi$
$810$	−751739.	+	1.98690e6i	−0.0402582	+	0.106405i
$811$	1.26546e7	+	9.19409e6i	0.675609	+	0.490859i	0.871898	−	0.489687i	$-0.162889\pi$
$811$	1.26546e7	+	9.19409e6i	0.675609	+	0.490859i	−0.196289	+	0.980546i	$0.562889\pi$
$812$	−4.71033e6	−	6.48321e6i	−0.250704	−	0.345064i
$813$	−2.10774e6	−	2.90105e6i	−0.111838	−	0.153932i
$814$	324914.	+	236064.i	0.0171873	+	0.0124873i
$815$	−8.71042e6	+	2.30223e7i	−0.459351	+	1.21410i
$816$	4.49388e7	−	3.26500e7i	2.36263	−	1.71655i
$817$	418178.	+	135874.i	0.0219183	+	0.00712167i
$818$		−	1.24040e6i		−	0.0648155i
$819$	−8.20517e6	+	2.52529e7i	−0.427443	+	1.31553i
$820$	−199484.	+	4.19269e6i	−0.0103603	+	0.217750i
$821$	7.48310e6	+	2.30306e7i	0.387457	+	1.19247i	0.934682	+	0.355485i	$0.115684\pi$
$821$	7.48310e6	+	2.30306e7i	0.387457	+	1.19247i	−0.547225	+	0.836986i	$0.684316\pi$
$822$	−1.29939e6	+	422197.i	−0.0670748	+	0.0217939i
$823$	1.97630e7	−	2.72015e7i	1.01708	−	1.39989i	0.102843	−	0.994698i	$-0.467206\pi$
$823$	1.97630e7	−	2.72015e7i	1.01708	−	1.39989i	0.914233	−	0.405188i	$-0.132794\pi$
$824$	73009.7			0.00374596
$825$	1.93059e7	−	2.18612e7i	0.987539	−	1.11825i
$826$	571606.			0.0291506
$827$	−2.01152e7	+	2.76863e7i	−1.02273	+	1.40767i	−0.112460	+	0.993656i	$0.535873\pi$
$827$	−2.01152e7	+	2.76863e7i	−1.02273	+	1.40767i	−0.910271	+	0.414013i	$0.864127\pi$
$828$	−3.74677e7	+	1.21740e7i	−1.89925	+	0.617103i
$829$	700418.	+	2.15566e6i	0.0353973	+	0.108942i	0.967194	−	0.254039i	$-0.0817591\pi$
$829$	700418.	+	2.15566e6i	0.0353973	+	0.108942i	−0.931797	+	0.362981i	$0.881759\pi$
$830$	754556.	+	285485.i	0.0380186	+	0.0143843i
$831$	−1.20949e7	+	3.72244e7i	−0.607577	+	1.86993i
$832$		−	1.59171e7i		−	0.797178i
$833$	−1.63570e7	−	5.31472e6i	−0.816755	−	0.265380i
$834$	1.20706e6	−	876977.i	0.0600914	−	0.0436589i
$835$	768078.	+	2.81225e6i	0.0381232	+	0.139585i
$836$	758470.	+	551061.i	0.0375338	+	0.0272699i
$837$	−2.08520e7	−	2.87003e7i	−1.02881	−	1.41603i
$838$	−421481.	−	580118.i	−0.0207333	−	0.0285369i
$839$	2.17778e7	+	1.58225e7i	1.06809	+	0.776016i	0.975569	−	0.219695i	$-0.0705062\pi$
$839$	2.17778e7	+	1.58225e7i	1.06809	+	0.776016i	0.0925251	+	0.995710i	$0.470506\pi$
$840$	1.60474e6	−	1.05316e6i	0.0784707	−	0.0514985i
$841$	9.80970e6	−	7.12717e6i	0.478262	−	0.347478i
$842$	−564249.	−	183335.i	−0.0274278	−	0.00891182i
$843$		−	5.77280e7i		−	2.79781i
$844$	5.55351e6	−	1.70919e7i	0.268356	−	0.825914i
$845$	−7.08491e6	+	1.93502e6i	−0.341344	+	0.0932274i
$846$	−566728.	−	1.74421e6i	−0.0272238	−	0.0837862i
$847$	5.00870e6	−	1.62743e6i	0.239893	−	0.0779458i
$848$	−1.09157e7	+	1.50242e7i	−0.521271	+	0.717468i
$849$	−617937.			−0.0294222
$850$	−263922.	−	1.18539e6i	−0.0125293	−	0.0562747i
$851$	1.18790e7			0.562284
$852$	−2.19168e6	+	3.01659e6i	−0.103438	+	0.142370i
$853$	−1.51751e7	+	4.93068e6i	−0.714099	+	0.232025i	−0.643463	−	0.765477i	$-0.722503\pi$
$853$	−1.51751e7	+	4.93068e6i	−0.714099	+	0.232025i	−0.0706363	+	0.997502i	$0.522503\pi$
$854$	285315.	+	878111.i	0.0133869	+	0.0412007i
$855$	2.02854e6	−	2.52986e6i	0.0949005	−	0.118353i
$856$	−539166.	+	1.65938e6i	−0.0251500	+	0.0774038i
$857$			1.12735e7i			0.524331i	0.965023	+	0.262165i	$0.0844366\pi$
$857$			1.12735e7i			0.524331i	−0.965023	+	0.262165i	$0.915563\pi$
$858$	−914340.	−	297087.i	−0.0424023	−	0.0137773i
$859$	1.37454e7	−	9.98658e6i	0.635584	−	0.461779i	−0.222746	−	0.974876i	$-0.571502\pi$
$859$	1.37454e7	−	9.98658e6i	0.635584	−	0.461779i	0.858330	+	0.513098i	$0.171502\pi$
$860$	−6.61301e6	−	5.30258e6i	−0.304897	−	0.244479i
$861$	−4.85274e6	−	3.52573e6i	−0.223090	−	0.162084i
$862$	481247.	+	662380.i	0.0220597	+	0.0303626i
$863$	−7.04607e6	−	9.69808e6i	−0.322047	−	0.443260i	0.617043	−	0.786929i	$-0.288330\pi$
$863$	−7.04607e6	−	9.69808e6i	−0.322047	−	0.443260i	−0.939091	+	0.343669i	$0.888330\pi$
$864$	5.89011e6	+	4.27941e6i	0.268435	+	0.195029i
$865$	2.08490e7	+	991976.i	0.947427	+	0.0450776i
$866$	417178.	−	303097.i	0.0189028	−	0.0137337i
$867$	5.59204e7	+	1.81696e7i	2.52652	+	0.820916i
$868$			8.69565e6i			0.391744i
$869$	−4.09349e6	+	1.25985e7i	−0.183884	+	0.565937i
$870$	−550642.	−	839038.i	−0.0246644	−	0.0375823i
$871$	−2.68275e6	−	8.25666e6i	−0.119822	−	0.368773i
$872$	1.75248e6	−	569417.i	0.0780482	−	0.0253594i
$873$	−5.03097e7	+	6.92453e7i	−2.23417	+	3.07507i
$874$	−38380.4			−0.00169954
$875$	2.58224e6	+	1.49062e7i	0.114019	+	0.658185i
$876$	1.07708e6			0.0474228
$877$	1.77973e7	−	2.44958e7i	0.781365	−	1.07546i	−0.213765	−	0.976885i	$-0.568573\pi$
$877$	1.77973e7	−	2.44958e7i	0.781365	−	1.07546i	0.995130	−	0.0985719i	$-0.0314275\pi$
$878$	859924.	−	279406.i	0.0376464	−	0.0122321i
$879$	2.90430e6	+	8.93851e6i	0.126785	+	0.390205i
$880$	−9.90257e6	−	1.50890e7i	−0.431063	−	0.656831i
$881$	8.36922e6	−	2.57578e7i	0.363283	−	1.11807i	−0.587766	−	0.809031i	$-0.699992\pi$
$881$	8.36922e6	−	2.57578e7i	0.363283	−	1.11807i	0.951049	−	0.309040i	$-0.100008\pi$
$882$		−	1.22534e6i		−	0.0530378i
$883$	2.57838e7	+	8.37766e6i	1.11287	+	0.361594i	0.807043	−	0.590493i	$-0.201066\pi$
$883$	2.57838e7	+	8.37766e6i	1.11287	+	0.361594i	0.305829	+	0.952087i	$0.401066\pi$
$884$	2.33989e7	−	1.70003e7i	1.00708	−	0.731686i
$885$	−5.16617e7	−	2.45801e6i	−2.21723	−	0.105494i
$886$	62353.8	+	45302.7i	0.00266857	+	0.00193883i
$887$	4.90915e6	+	6.75687e6i	0.209506	+	0.288361i	0.900819	−	0.434195i	$-0.142967\pi$
$887$	4.90915e6	+	6.75687e6i	0.209506	+	0.288361i	−0.691312	+	0.722556i	$0.742967\pi$
$888$	−1.40573e6	−	1.93483e6i	−0.0598233	−	0.0823397i
$889$	−2.05554e7	−	1.49344e7i	−0.872312	−	0.633772i
$890$	−330496.	−	265005.i	−0.0139859	−	0.0112145i
$891$	−4.62827e7	+	3.36263e7i	−1.95310	+	1.41901i
$892$	−5.36071e6	−	1.74180e6i	−0.225585	−	0.0732970i
$893$			1.29089e6i			0.0541703i
$894$	−253566.	+	780395.i	−0.0106108	+	0.0326566i
$895$	4.20748e6	−	5.24728e6i	0.175576	−	0.218966i
$896$	−735121.	−	2.26247e6i	−0.0305907	−	0.0941484i
$897$	−2.70443e7	+	8.78723e6i	−1.12226	+	0.364645i
$898$	316183.	−	435189.i	0.0130842	−	0.0180089i
$899$	9.09930e6			0.375499
$900$	−5.38335e7	+	3.17761e7i	−2.21537	+	1.30766i
$901$	−3.36511e7			−1.38098
$902$	91959.5	−	126571.i	0.00376340	−	0.00517987i
$903$	1.15203e7	−	3.74317e6i	0.470158	−	0.152764i
$904$	45188.4	+	139075.i	0.00183910	+	0.00566017i
$905$	1.36957e7	−	3.74055e6i	0.555857	−	0.151815i
$906$	829468.	−	2.55284e6i	0.0335721	−	0.103324i
$907$		−	2.20199e7i		−	0.888787i	−0.895832	−	0.444393i	$-0.853419\pi$
$907$		−	2.20199e7i		−	0.888787i	0.895832	−	0.444393i	$-0.146581\pi$
$908$	7.32864e6	+	2.38122e6i	0.294991	+	0.0958484i
$909$	1.49709e7	−	1.08770e7i	0.600951	−	0.436616i
$910$	416913.	−	273611.i	0.0166895	−	0.0109529i
$911$	5.27401e6	+	3.83179e6i	0.210545	+	0.152970i	0.688060	−	0.725654i	$-0.258462\pi$
$911$	5.27401e6	+	3.83179e6i	0.210545	+	0.152970i	−0.477515	+	0.878623i	$0.658462\pi$
$912$	−1.63734e6	−	2.25361e6i	−0.0651857	−	0.0897204i
$913$	1.27701e7	+	1.75766e7i	0.507012	+	0.697842i
$914$	−428497.	−	311321.i	−0.0169661	−	0.0123266i
$915$	−2.20107e7	−	8.05904e7i	−0.869124	−	3.18222i
$916$	−3.62223e7	+	2.63170e7i	−1.42639	+	1.03633i
$917$	−2.78903e7	−	9.06211e6i	−1.09529	−	0.355882i
$918$			4.38739e6i			0.171830i
$919$	8.17414e6	−	2.51574e7i	0.319266	−	0.982601i	−0.654696	−	0.755892i	$-0.727203\pi$
$919$	8.17414e6	−	2.51574e7i	0.319266	−	0.982601i	0.973963	−	0.226709i	$-0.0727966\pi$
$920$	1.38499e6	+	524006.i	0.0539480	+	0.0204111i
$921$	2.37947e7	+	7.32327e7i	0.924341	+	2.84483i
$922$	−1.27804e6	+	415262.i	−0.0495129	+	0.0160877i
$923$	−1.13959e6	+	1.56851e6i	−0.0440295	+	0.0606014i
$924$	2.58276e7			0.995184
$925$	1.83987e7	−	4.09640e6i	0.707021	−	0.157416i
$926$	−1.25680e6			−0.0481658
$927$	1.99724e6	−	2.74896e6i	0.0763362	−	0.105068i
$928$	−1.77603e6	+	577068.i	−0.0676988	+	0.0219967i
$929$	1.91972e6	+	5.90830e6i	0.0729792	+	0.224607i	0.980892	−	0.194552i	$-0.0623252\pi$
$929$	1.91972e6	+	5.90830e6i	0.0729792	+	0.224607i	−0.907913	+	0.419158i	$0.862325\pi$
$930$	−51754.7	+	1.08776e6i	−0.00196219	+	0.0412408i
$931$	−266524.	+	820278.i	−0.0100777	+	0.0310161i
$932$			1.50368e7i			0.567041i
$933$	−6.75947e6	−	2.19629e6i	−0.254219	−	0.0826009i
$934$	−1.41720e6	+	1.02966e6i	−0.0531574	+	0.0386211i
$935$	1.15728e7	−	3.05878e7i	0.432923	−	1.14425i
$936$	3.33644e6	+	2.42407e6i	0.124478	+	0.0904389i
$937$	1.17191e7	+	1.61299e7i	0.436057	+	0.600181i	0.969330	−	0.245762i	$-0.0790381\pi$
$937$	1.17191e7	+	1.61299e7i	0.436057	+	0.600181i	−0.533273	+	0.845943i	$0.679038\pi$
$938$	−189740.	−	261155.i	−0.00704129	−	0.00969151i
$939$	−6.76608e6	−	4.91585e6i	−0.250422	−	0.181943i
$940$	8.80616e6	−	2.32753e7i	0.325062	−	0.859163i
$941$	−1.27540e7	+	9.26634e6i	−0.469541	+	0.341141i	−0.797262	−	0.603633i	$-0.793719\pi$
$941$	−1.27540e7	+	9.26634e6i	−0.469541	+	0.341141i	0.327722	+	0.944774i	$0.393719\pi$
$942$	−1.05301e6	−	342143.i	−0.0386638	−	0.0125626i
$943$		−	4.62749e6i		−	0.169460i
$944$	−9.89024e6	+	3.04390e7i	−0.361224	+	1.11173i
$945$	2.59749e6	−	5.45931e7i	0.0946180	−	1.98865i
$946$	97631.0	+	300477.i	0.00354699	+	0.0109165i
$947$	−1.81687e7	+	5.90336e6i	−0.658337	+	0.213907i	−0.619087	−	0.785323i	$-0.712497\pi$
$947$	−1.81687e7	+	5.90336e6i	−0.658337	+	0.213907i	−0.0392507	+	0.999229i	$0.512497\pi$
$948$	2.31671e7	−	3.18868e7i	0.837243	−	1.15237i
$949$	560039.			0.0201861
$950$	−59445.2	+	13235.3i	−0.00213702	+	0.000475799i
$951$	2.92335e7			1.04817
$952$	1.26511e6	−	1.74128e6i	0.0452414	−	0.0622695i
$953$	2.05433e7	−	6.67492e6i	0.732719	−	0.238075i	0.0811902	−	0.996699i	$-0.474128\pi$
$953$	2.05433e7	−	6.67492e6i	0.732719	−	0.238075i	0.651529	+	0.758624i	$0.274128\pi$
$954$	−740868.	−	2.28016e6i	−0.0263554	−	0.0811136i
$955$	2.62043e7	+	9.91434e6i	0.929746	+	0.351767i
$956$	1.03967e7	−	3.19977e7i	0.367917	−	1.13233i
$957$		−	2.70265e7i		−	0.953915i
$958$	1.51727e6	+	492990.i	0.0534132	+	0.0173550i
$959$	1.54398e7	−	1.12177e7i	0.542121	−	0.393874i
$960$	1.41091e7	+	5.16591e7i	0.494106	+	1.80913i
$961$	1.51735e7	+	1.10242e7i	0.530003	+	0.385069i
$962$	−365210.	−	502669.i	−0.0127235	−	0.0175123i
$963$	4.77298e7	+	6.56944e7i	1.65853	+	2.28277i
$964$	3.39725e7	+	2.46825e7i	1.17743	+	0.855454i
$965$	−2.63688e7	+	1.73052e7i	−0.911531	+	0.598217i
$966$	−855401.	+	621485.i	−0.0294935	+	0.0214283i
$967$	−9.11881e6	−	2.96288e6i	−0.313597	−	0.101894i	0.147990	−	0.988989i	$-0.452720\pi$
$967$	−9.11881e6	−	2.96288e6i	−0.313597	−	0.101894i	−0.461587	+	0.887095i	$0.652720\pi$
$968$		−	817975.i		−	0.0280577i
$969$	1.55980e6	−	4.80056e6i	0.0533653	−	0.164241i
$970$	1.55069e6	−	423523.i	0.0529171	−	0.0144526i
$971$	1.16599e7	+	3.58855e7i	0.396869	+	1.22144i	0.927497	+	0.373832i	$0.121956\pi$
$971$	1.16599e7	+	3.58855e7i	0.396869	+	1.22144i	−0.530628	+	0.847605i	$0.678044\pi$
$972$	7.85080e7	−	2.55088e7i	2.66531	−	0.866012i
$973$	−1.22501e7	+	1.68609e7i	−0.414819	+	0.570949i
$974$	1.53852e6			0.0519643
$975$	−3.88572e7	+	2.29361e7i	−1.30906	+	0.772695i
$976$	−5.16976e7			−1.73718
$977$	8.73299e6	−	1.20199e7i	0.292702	−	0.402870i	−0.637187	−	0.770709i	$-0.719902\pi$
$977$	8.73299e6	−	1.20199e7i	0.292702	−	0.402870i	0.929890	+	0.367839i	$0.119902\pi$
$978$	−2.59622e6	+	843564.i	−0.0867950	+	0.0282014i
$979$	−3.52528e6	−	1.08497e7i	−0.117554	−	0.361794i
$980$	1.04013e7	−	1.29718e7i	0.345957	−	0.431454i
$981$	2.65009e7	−	8.15614e7i	0.879201	−	2.70590i
$982$			953453.i			0.0315515i
$983$	−3.10759e7	−	1.00972e7i	−1.02575	−	0.333285i	−0.252639	−	0.967560i	$-0.581299\pi$
$983$	−3.10759e7	−	1.00972e7i	−1.02575	−	0.333285i	−0.773107	+	0.634275i	$0.781299\pi$
$984$	−753717.	+	547607.i	−0.0248154	+	0.0180294i
$985$	2.05035e7	+	1.64405e7i	0.673345	+	0.539915i
$986$	−910423.	−	661461.i	−0.0298230	−	0.0216677i
$987$	2.09031e7	+	2.87707e7i	0.682996	+	0.940063i
$988$	−852535.	−	1.17341e6i	−0.0277856	−	0.0382436i
$989$	7.56016e6	+	5.49278e6i	0.245776	+	0.178567i
$990$	2.32738e6	+	110734.i	0.0754709	+	0.00359083i
$991$	−315560.	+	229268.i	−0.0102070	+	0.00741581i	−0.592877	−	0.805293i	$-0.702008\pi$
$991$	−315560.	+	229268.i	−0.0102070	+	0.00741581i	0.582670	+	0.812709i	$0.302008\pi$
$992$	1.92717e6	+	626176.i	0.0621786	+	0.0202031i
$993$		−	5.12810e7i		−	1.65038i
$994$	−22276.9	+	68561.1i	−0.000715135	+	0.00220096i
$995$	4.54723e6	+	6.92882e6i	0.145609	+	0.221872i
$996$	−1.99757e7	−	6.14787e7i	−0.638047	−	1.96371i
$997$	−5.40862e7	+	1.75737e7i	−1.72325	+	0.559918i	−0.992447	−	0.122671i	$-0.960854\pi$
$997$	−5.40862e7	+	1.75737e7i	−1.72325	+	0.559918i	−0.730803	+	0.682589i	$0.760854\pi$
$998$	−313379.	+	431329.i	−0.00995964	+	0.0137083i
$999$	−6.80978e7			−2.15883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.6.e.a.9.6	✓	48
25.8	odd	20		625.6.a.g.1.25		48
25.14	even	10	inner	25.6.e.a.14.6	yes	48
25.17	odd	20		625.6.a.g.1.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.6.e.a.9.6	✓	48	1.1	even	1	trivial
25.6.e.a.14.6	yes	48	25.14	even	10	inner
625.6.a.g.1.24		48	25.17	odd	20
625.6.a.g.1.25		48	25.8	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.123616 - 0.170142i) q^{2} +(28.0358 - 9.10938i) q^{3} +(9.87488 + 30.3917i) q^{4} +(-30.6717 - 46.7359i) q^{5} +(1.91577 - 5.89614i) q^{6} +86.5992i q^{7} +(12.7921 + 4.15640i) q^{8} +(506.434 - 367.946i) q^{9} +O(q^{10})\)	\(q+(0.123616 - 0.170142i) q^{2} +(28.0358 - 9.10938i) q^{3} +(9.87488 + 30.3917i) q^{4} +(-30.6717 - 46.7359i) q^{5} +(1.91577 - 5.89614i) q^{6} +86.5992i q^{7} +(12.7921 + 4.15640i) q^{8} +(506.434 - 367.946i) q^{9} +(-11.7433 - 0.558733i) q^{10} +(-256.136 - 186.094i) q^{11} +(553.700 + 762.103i) q^{12} +(287.902 + 396.263i) q^{13} +(14.7342 + 10.7050i) q^{14} +(-1285.64 - 1030.88i) q^{15} +(-825.000 + 599.398i) q^{16} +(-1757.39 - 571.010i) q^{17} -131.650i q^{18} +(-28.6352 + 88.1301i) q^{19} +(1117.51 - 1393.68i) q^{20} +(788.865 + 2427.88i) q^{21} +(-63.3249 + 20.5755i) q^{22} +(-1157.59 + 1593.29i) q^{23} +396.498 q^{24} +(-1243.49 + 2866.94i) q^{25} +103.010 q^{26} +(6636.04 - 9133.72i) q^{27} +(-2631.90 + 855.156i) q^{28} +(894.853 + 2754.07i) q^{29} +(-334.322 + 91.3094i) q^{30} +(971.004 - 2988.44i) q^{31} +644.875i q^{32} +(-8876.19 - 2884.05i) q^{33} +(-314.394 + 228.420i) q^{34} +(4047.29 - 2656.15i) q^{35} +(16183.5 + 11758.0i) q^{36} +(-3545.37 - 4879.78i) q^{37} +(11.4549 + 15.7663i) q^{38} +(11681.3 + 8486.95i) q^{39} +(-198.102 - 725.333i) q^{40} +(-1900.93 + 1381.11i) q^{41} +(510.601 + 165.904i) q^{42} -4745.01i q^{43} +(3126.40 - 9622.08i) q^{44} +(-32729.5 - 12383.1i) q^{45} +(127.989 + 393.911i) q^{46} +(13248.9 - 4304.81i) q^{47} +(-17669.4 + 24319.8i) q^{48} +9307.58 q^{49} +(334.073 + 565.970i) q^{50} -54471.3 q^{51} +(-9200.14 + 12662.9i) q^{52} +(17319.9 - 5627.57i) q^{53} +(-733.715 - 2258.14i) q^{54} +(-841.129 + 17678.6i) q^{55} +(-359.941 + 1107.78i) q^{56} +2731.65i q^{57} +(579.203 + 188.194i) q^{58} +(25391.4 - 18447.9i) q^{59} +(18634.6 - 49252.7i) q^{60} +(41014.0 + 29798.4i) q^{61} +(-388.430 - 534.628i) q^{62} +(31863.8 + 43856.8i) q^{63} +(-26290.3 - 19101.0i) q^{64} +(9689.28 - 25609.5i) q^{65} +(-1587.93 + 1153.70i) q^{66} +(-16856.9 - 5477.15i) q^{67} -59048.7i q^{68} +(-17940.1 + 55214.0i) q^{69} +(48.3858 - 1016.96i) q^{70} +(1223.17 + 3764.52i) q^{71} +(8007.67 - 2601.85i) q^{72} +(672.063 - 925.016i) q^{73} -1268.52 q^{74} +(-8746.21 + 91704.4i) q^{75} -2961.20 q^{76} +(16115.6 - 22181.2i) q^{77} +(2887.98 - 938.362i) q^{78} +(-12929.4 - 39792.8i) q^{79} +(53317.6 + 20172.6i) q^{80} +(55838.0 - 171852. i) q^{81} +494.156i q^{82} +(-65263.3 - 21205.3i) q^{83} +(-65997.5 + 47950.0i) q^{84} +(27215.4 + 99647.0i) q^{85} +(-807.327 - 586.557i) q^{86} +(50175.8 + 69061.1i) q^{87} +(-2503.04 - 3445.13i) q^{88} +(29151.1 + 21179.5i) q^{89} +(-6152.77 + 4037.92i) q^{90} +(-34316.1 + 24932.1i) q^{91} +(-59853.9 - 19447.7i) q^{92} -92628.6i q^{93} +(905.335 - 2786.33i) q^{94} +(4997.13 - 1364.81i) q^{95} +(5874.41 + 18079.6i) q^{96} +(-130039. + 42252.3i) q^{97} +(1150.56 - 1583.61i) q^{98} -198189. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 5 q^{3} + 189 q^{4} - 60 q^{5} - 139 q^{6} + 610 q^{8} + 1031 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 5 * q^3 + 189 * q^4 - 60 * q^5 - 139 * q^6 + 610 * q^8 + 1031 * q^9	\( 48 q - 5 q^{2} - 5 q^{3} + 189 q^{4} - 60 q^{5} - 139 q^{6} + 610 q^{8} + 1031 q^{9} + 435 q^{10} - 724 q^{11} + 315 q^{12} - 5 q^{13} - 497 q^{14} - 105 q^{15} - 6967 q^{16} - 960 q^{17} + 4075 q^{19} + 9155 q^{20} + 2016 q^{21} - 5450 q^{22} - 10995 q^{23} - 20720 q^{24} - 16610 q^{25} + 21666 q^{26} - 13805 q^{27} + 14235 q^{28} + 17195 q^{29} + 39595 q^{30} + 8631 q^{31} + 28460 q^{33} - 24067 q^{34} - 4145 q^{35} - 43827 q^{36} + 19980 q^{37} - 77385 q^{38} + 6037 q^{39} + 93210 q^{40} - 26514 q^{41} + 182885 q^{42} + 26748 q^{44} - 94185 q^{45} - 14559 q^{46} - 7700 q^{47} - 127830 q^{48} - 130126 q^{49} - 231115 q^{50} + 121116 q^{51} - 189260 q^{52} + 45840 q^{53} + 19985 q^{54} + 79370 q^{55} - 43280 q^{56} + 337370 q^{58} + 47640 q^{59} + 71480 q^{60} + 7791 q^{61} + 135320 q^{62} - 35790 q^{63} + 68204 q^{64} + 197485 q^{65} - 14798 q^{66} - 66180 q^{67} + 17957 q^{69} - 129930 q^{70} - 46694 q^{71} - 50545 q^{72} - 18985 q^{73} - 183292 q^{74} - 202210 q^{75} + 273360 q^{76} - 132990 q^{77} - 665225 q^{78} - 54065 q^{79} + 362810 q^{80} - 382452 q^{81} + 161155 q^{83} + 474258 q^{84} - 83075 q^{85} + 74691 q^{86} + 897680 q^{87} + 578430 q^{88} + 436475 q^{89} + 775655 q^{90} + 181046 q^{91} - 1412870 q^{92} - 336327 q^{94} - 362785 q^{95} - 766024 q^{96} - 475210 q^{97} - 361660 q^{98} - 451848 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 5 * q^3 + 189 * q^4 - 60 * q^5 - 139 * q^6 + 610 * q^8 + 1031 * q^9 + 435 * q^10 - 724 * q^11 + 315 * q^12 - 5 * q^13 - 497 * q^14 - 105 * q^15 - 6967 * q^16 - 960 * q^17 + 4075 * q^19 + 9155 * q^20 + 2016 * q^21 - 5450 * q^22 - 10995 * q^23 - 20720 * q^24 - 16610 * q^25 + 21666 * q^26 - 13805 * q^27 + 14235 * q^28 + 17195 * q^29 + 39595 * q^30 + 8631 * q^31 + 28460 * q^33 - 24067 * q^34 - 4145 * q^35 - 43827 * q^36 + 19980 * q^37 - 77385 * q^38 + 6037 * q^39 + 93210 * q^40 - 26514 * q^41 + 182885 * q^42 + 26748 * q^44 - 94185 * q^45 - 14559 * q^46 - 7700 * q^47 - 127830 * q^48 - 130126 * q^49 - 231115 * q^50 + 121116 * q^51 - 189260 * q^52 + 45840 * q^53 + 19985 * q^54 + 79370 * q^55 - 43280 * q^56 + 337370 * q^58 + 47640 * q^59 + 71480 * q^60 + 7791 * q^61 + 135320 * q^62 - 35790 * q^63 + 68204 * q^64 + 197485 * q^65 - 14798 * q^66 - 66180 * q^67 + 17957 * q^69 - 129930 * q^70 - 46694 * q^71 - 50545 * q^72 - 18985 * q^73 - 183292 * q^74 - 202210 * q^75 + 273360 * q^76 - 132990 * q^77 - 665225 * q^78 - 54065 * q^79 + 362810 * q^80 - 382452 * q^81 + 161155 * q^83 + 474258 * q^84 - 83075 * q^85 + 74691 * q^86 + 897680 * q^87 + 578430 * q^88 + 436475 * q^89 + 775655 * q^90 + 181046 * q^91 - 1412870 * q^92 - 336327 * q^94 - 362785 * q^95 - 766024 * q^96 - 475210 * q^97 - 361660 * q^98 - 451848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more