LMFDB - Embedded newform 35.6.e.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,6,Mod(11,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("35.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	35.e (of order $3$, degree $2$, 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:	$5.61343369345$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 110 x^{10} + 27 x^{9} + 9714 x^{8} - 3257 x^{7} + 240269 x^{6} - 608504 x^{5} + \cdots + 313600 $ x^12 - x^11 + 110x^10 + 27x^9 + 9714x^8 - 3257x^7 + 240269x^6 - 608504x^5 + 5067668x^4 - 7120352x^3 + 9029136x^2 - 1794240x + 313600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.5
Root			$-3.11366 - 5.39303i$ of defining polynomial
Character	$\chi$	$=$	35.11
Dual form			35.6.e.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.61366 + 6.25905i) q^{2} +(7.96046 - 13.7879i) q^{3} +(-10.1171 + 17.5234i) q^{4} +(12.5000 + 21.6506i) q^{5} +115.066 q^{6} +(102.346 + 79.5760i) q^{7} +85.0347 q^{8} +(-5.23796 - 9.07242i) q^{9} +O(q^{10})$	\(q+(3.61366 + 6.25905i) q^{2} +(7.96046 - 13.7879i) q^{3} +(-10.1171 + 17.5234i) q^{4} +(12.5000 + 21.6506i) q^{5} +115.066 q^{6} +(102.346 + 79.5760i) q^{7} +85.0347 q^{8} +(-5.23796 - 9.07242i) q^{9} +(-90.3416 + 156.476i) q^{10} +(193.533 - 335.209i) q^{11} +(161.074 + 278.989i) q^{12} -920.823 q^{13} +(-128.227 + 928.148i) q^{14} +398.023 q^{15} +(631.035 + 1092.99i) q^{16} +(-339.236 + 587.575i) q^{17} +(37.8565 - 65.5694i) q^{18} +(-1382.09 - 2393.86i) q^{19} -505.857 q^{20} +(1911.91 - 777.675i) q^{21} +2797.46 q^{22} +(-1032.86 - 1788.97i) q^{23} +(676.916 - 1172.45i) q^{24} +(-312.500 + 541.266i) q^{25} +(-3327.54 - 5763.48i) q^{26} +3702.00 q^{27} +(-2429.89 + 988.365i) q^{28} -2921.75 q^{29} +(1438.32 + 2491.25i) q^{30} +(-2127.53 + 3684.99i) q^{31} +(-3200.15 + 5542.81i) q^{32} +(-3081.23 - 5336.84i) q^{33} -4903.55 q^{34} +(-443.548 + 3210.55i) q^{35} +211.973 q^{36} +(77.3106 + 133.906i) q^{37} +(9988.85 - 17301.2i) q^{38} +(-7330.18 + 12696.2i) q^{39} +(1062.93 + 1841.06i) q^{40} -7600.35 q^{41} +(11776.5 + 9156.47i) q^{42} +13533.2 q^{43} +(3916.01 + 6782.72i) q^{44} +(130.949 - 226.811i) q^{45} +(7464.84 - 12929.5i) q^{46} +(-7501.27 - 12992.6i) q^{47} +20093.3 q^{48} +(4142.32 + 16288.5i) q^{49} -4517.08 q^{50} +(5400.96 + 9354.74i) q^{51} +(9316.09 - 16135.9i) q^{52} +(-9039.43 + 15656.8i) q^{53} +(13377.8 + 23171.0i) q^{54} +9676.66 q^{55} +(8702.94 + 6766.72i) q^{56} -44008.4 q^{57} +(-10558.2 - 18287.4i) q^{58} +(-3239.84 + 5611.57i) q^{59} +(-4026.86 + 6974.72i) q^{60} +(-2003.16 - 3469.58i) q^{61} -30752.7 q^{62} +(185.863 - 1345.34i) q^{63} -5870.74 q^{64} +(-11510.3 - 19936.4i) q^{65} +(22269.1 - 38571.1i) q^{66} +(16810.1 - 29116.0i) q^{67} +(-6864.21 - 11889.2i) q^{68} -32888.3 q^{69} +(-21697.8 + 8825.66i) q^{70} -61404.3 q^{71} +(-445.409 - 771.471i) q^{72} +(21332.2 - 36948.4i) q^{73} +(-558.749 + 967.782i) q^{74} +(4975.29 + 8617.45i) q^{75} +55931.4 q^{76} +(46481.9 - 18906.7i) q^{77} -105955. q^{78} +(53946.3 + 93437.7i) q^{79} +(-15775.9 + 27324.6i) q^{80} +(30742.5 - 53247.5i) q^{81} +(-27465.1 - 47570.9i) q^{82} +99024.8 q^{83} +(-5715.54 + 41371.0i) q^{84} -16961.8 q^{85} +(48904.3 + 84704.8i) q^{86} +(-23258.5 + 40284.8i) q^{87} +(16457.0 - 28504.4i) q^{88} +(-3830.92 - 6635.35i) q^{89} +1892.82 q^{90} +(-94242.3 - 73275.4i) q^{91} +41798.5 q^{92} +(33872.2 + 58668.4i) q^{93} +(54214.2 - 93901.7i) q^{94} +(34552.4 - 59846.4i) q^{95} +(50949.3 + 88246.7i) q^{96} +87087.4 q^{97} +(-86981.8 + 84788.3i) q^{98} -4054.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{2} - 20 q^{3} - 31 q^{4} + 150 q^{5} + 192 q^{6} - 20 q^{7} - 270 q^{8} - 378 q^{9}+O(q^{10}) $ 12 * q + 5 * q^2 - 20 * q^3 - 31 * q^4 + 150 * q^5 + 192 * q^6 - 20 * q^7 - 270 * q^8 - 378 * q^9	\( 12 q + 5 q^{2} - 20 q^{3} - 31 q^{4} + 150 q^{5} + 192 q^{6} - 20 q^{7} - 270 q^{8} - 378 q^{9} - 125 q^{10} + 924 q^{11} - 370 q^{12} - 300 q^{13} + 3409 q^{14} - 1000 q^{15} - 435 q^{16} - 1540 q^{17} - 195 q^{18} - 92 q^{19} - 1550 q^{20} + 7288 q^{21} - 13710 q^{22} + 3920 q^{23} + 7200 q^{24} - 3750 q^{25} - 2635 q^{26} + 4120 q^{27} - 6015 q^{28} + 2528 q^{29} + 2400 q^{30} + 7160 q^{31} - 9105 q^{32} - 4460 q^{33} + 4332 q^{34} - 2500 q^{35} - 52750 q^{36} + 14170 q^{37} + 46215 q^{38} + 15376 q^{39} - 3375 q^{40} + 8196 q^{41} + 10500 q^{42} - 48920 q^{43} + 27873 q^{44} + 9450 q^{45} - 6815 q^{46} - 42940 q^{47} + 23220 q^{48} - 17856 q^{49} - 6250 q^{50} + 42008 q^{51} + 36115 q^{52} + 2450 q^{53} - 19566 q^{54} + 46200 q^{55} + 67998 q^{56} - 194200 q^{57} + 36110 q^{58} + 64600 q^{59} + 9250 q^{60} - 73620 q^{61} + 222880 q^{62} - 57780 q^{63} - 315994 q^{64} - 3750 q^{65} + 139138 q^{66} + 142620 q^{67} - 124330 q^{68} + 34688 q^{69} + 34475 q^{70} - 308512 q^{71} + 117495 q^{72} + 5120 q^{73} - 2785 q^{74} - 12500 q^{75} + 15550 q^{76} + 44230 q^{77} - 428180 q^{78} + 222504 q^{79} + 10875 q^{80} + 43986 q^{81} - 31665 q^{82} + 359160 q^{83} - 19966 q^{84} - 77000 q^{85} + 207160 q^{86} + 209300 q^{87} + 45145 q^{88} - 41648 q^{89} - 9750 q^{90} - 31376 q^{91} - 584370 q^{92} + 198520 q^{93} + 333699 q^{94} + 2300 q^{95} - 61824 q^{96} - 147960 q^{97} - 101815 q^{98} - 381544 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 - 20 * q^3 - 31 * q^4 + 150 * q^5 + 192 * q^6 - 20 * q^7 - 270 * q^8 - 378 * q^9 - 125 * q^10 + 924 * q^11 - 370 * q^12 - 300 * q^13 + 3409 * q^14 - 1000 * q^15 - 435 * q^16 - 1540 * q^17 - 195 * q^18 - 92 * q^19 - 1550 * q^20 + 7288 * q^21 - 13710 * q^22 + 3920 * q^23 + 7200 * q^24 - 3750 * q^25 - 2635 * q^26 + 4120 * q^27 - 6015 * q^28 + 2528 * q^29 + 2400 * q^30 + 7160 * q^31 - 9105 * q^32 - 4460 * q^33 + 4332 * q^34 - 2500 * q^35 - 52750 * q^36 + 14170 * q^37 + 46215 * q^38 + 15376 * q^39 - 3375 * q^40 + 8196 * q^41 + 10500 * q^42 - 48920 * q^43 + 27873 * q^44 + 9450 * q^45 - 6815 * q^46 - 42940 * q^47 + 23220 * q^48 - 17856 * q^49 - 6250 * q^50 + 42008 * q^51 + 36115 * q^52 + 2450 * q^53 - 19566 * q^54 + 46200 * q^55 + 67998 * q^56 - 194200 * q^57 + 36110 * q^58 + 64600 * q^59 + 9250 * q^60 - 73620 * q^61 + 222880 * q^62 - 57780 * q^63 - 315994 * q^64 - 3750 * q^65 + 139138 * q^66 + 142620 * q^67 - 124330 * q^68 + 34688 * q^69 + 34475 * q^70 - 308512 * q^71 + 117495 * q^72 + 5120 * q^73 - 2785 * q^74 - 12500 * q^75 + 15550 * q^76 + 44230 * q^77 - 428180 * q^78 + 222504 * q^79 + 10875 * q^80 + 43986 * q^81 - 31665 * q^82 + 359160 * q^83 - 19966 * q^84 - 77000 * q^85 + 207160 * q^86 + 209300 * q^87 + 45145 * q^88 - 41648 * q^89 - 9750 * q^90 - 31376 * q^91 - 584370 * q^92 + 198520 * q^93 + 333699 * q^94 + 2300 * q^95 - 61824 * q^96 - 147960 * q^97 - 101815 * q^98 - 381544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	3.61366	+	6.25905i	0.638812	+	1.10645i	0.985694	+	0.168546i	$0.0539070\pi$
$2$	3.61366	+	6.25905i	0.638812	+	1.10645i	−0.346882	+	0.937909i	$0.612760\pi$
$3$	7.96046	−	13.7879i	0.510664	−	0.884496i	−0.489260	−	0.872138i	$-0.662733\pi$
$3$	7.96046	−	13.7879i	0.510664	−	0.884496i	0.999924	−	0.0123578i	$-0.00393371\pi$
$4$	−10.1171	+	17.5234i	−0.316161	+	0.547606i
$5$	12.5000	+	21.6506i	0.223607	+	0.387298i
$5$	12.5000	+	21.6506i	0.223607	+	0.387298i
$6$	115.066			1.30487
$7$	102.346	+	79.5760i	0.789451	+	0.613814i
$7$	102.346	+	79.5760i	0.789451	+	0.613814i
$8$	85.0347			0.469755
$9$	−5.23796	−	9.07242i	−0.0215554	−	0.0373351i
$10$	−90.3416	+	156.476i	−0.285685	+	0.494821i
$11$	193.533	−	335.209i	0.482252	−	0.835285i	−0.517541	−	0.855659i	$-0.673152\pi$
$11$	193.533	−	335.209i	0.482252	−	0.835285i	0.999792	+	0.0203741i	$0.00648571\pi$
$12$	161.074	+	278.989i	0.322904	+	0.559286i
$13$	−920.823			−1.51118			−0.755592	−	0.655042i	$-0.772651\pi$
$13$	−920.823			−1.51118			−0.755592	+	0.655042i	$0.772651\pi$
$14$	−128.227	+	928.148i	−0.174847	+	1.26560i
$15$	398.023			0.456752
$16$	631.035	+	1092.99i	0.616246	+	1.06737i
$17$	−339.236	+	587.575i	−0.284695	+	0.493107i	−0.972535	−	0.232756i	$-0.925226\pi$
$17$	−339.236	+	587.575i	−0.284695	+	0.493107i	0.687840	+	0.725862i	$0.258559\pi$
$18$	37.8565	−	65.5694i	0.0275397	−	0.0477002i
$19$	−1382.09	−	2393.86i	−0.878322	−	1.52130i	−0.853182	−	0.521614i	$-0.825330\pi$
$19$	−1382.09	−	2393.86i	−0.878322	−	1.52130i	−0.0251403	−	0.999684i	$-0.508003\pi$
$20$	−505.857			−0.282783
$21$	1911.91	−	777.675i	0.946060	−	0.384813i
$22$	2797.46			1.23227
$23$	−1032.86	−	1788.97i	−0.407121	−	0.705154i	0.587445	−	0.809264i	$-0.300134\pi$
$23$	−1032.86	−	1788.97i	−0.407121	−	0.705154i	−0.994566	+	0.104110i	$0.966801\pi$
$24$	676.916	−	1172.45i	0.239887	−	0.415496i
$25$	−312.500	+	541.266i	−0.100000	+	0.173205i
$26$	−3327.54	−	5763.48i	−0.965363	−	1.67206i
$27$	3702.00			0.977298
$28$	−2429.89	+	988.365i	−0.585722	+	0.238244i
$29$	−2921.75			−0.645131			−0.322565	−	0.946547i	$-0.604545\pi$
$29$	−2921.75			−0.645131			−0.322565	+	0.946547i	$0.604545\pi$
$30$	1438.32	+	2491.25i	0.291778	+	0.505375i
$31$	−2127.53	+	3684.99i	−0.397623	+	0.688703i	−0.993432	−	0.114423i	$-0.963498\pi$
$31$	−2127.53	+	3684.99i	−0.397623	+	0.688703i	0.595809	+	0.803126i	$0.296831\pi$
$32$	−3200.15	+	5542.81i	−0.552452	+	0.956875i
$33$	−3081.23	−	5336.84i	−0.492537	−	0.853099i
$34$	−4903.55			−0.727467
$35$	−443.548	+	3210.55i	−0.0612027	+	0.443006i
$36$	211.973			0.0272599
$37$	77.3106	+	133.906i	0.00928399	+	0.0160803i	0.870630	−	0.491938i	$-0.163711\pi$
$37$	77.3106	+	133.906i	0.00928399	+	0.0160803i	−0.861346	+	0.508019i	$0.830378\pi$
$38$	9988.85	−	17301.2i	1.12216	−	1.94365i
$39$	−7330.18	+	12696.2i	−0.771708	+	1.33664i
$40$	1062.93	+	1841.06i	0.105040	+	0.181935i
$41$	−7600.35			−0.706112			−0.353056	−	0.935602i	$-0.614858\pi$
$41$	−7600.35			−0.706112			−0.353056	+	0.935602i	$0.614858\pi$
$42$	11776.5	+	9156.47i	1.03013	+	0.800949i
$43$	13533.2			1.11616			0.558082	−	0.829786i	$-0.311537\pi$
$43$	13533.2			1.11616			0.558082	+	0.829786i	$0.311537\pi$
$44$	3916.01	+	6782.72i	0.304938	+	0.528168i
$45$	130.949	−	226.811i	0.00963987	−	0.0166967i
$46$	7464.84	−	12929.5i	0.520147	−	0.900921i
$47$	−7501.27	−	12992.6i	−0.495325	−	0.857928i	0.504660	−	0.863318i	$-0.331618\pi$
$47$	−7501.27	−	12992.6i	−0.495325	−	0.857928i	−0.999985	+	0.00538960i	$0.998284\pi$
$48$	20093.3			1.25878
$49$	4142.32	+	16288.5i	0.246464	+	0.969152i
$50$	−4517.08			−0.255525
$51$	5400.96	+	9354.74i	0.290767	+	0.503624i
$52$	9316.09	−	16135.9i	0.477777	−	0.827535i
$53$	−9039.43	+	15656.8i	−0.442030	+	0.765618i	−0.997840	−	0.0656911i	$-0.979075\pi$
$53$	−9039.43	+	15656.8i	−0.442030	+	0.765618i	0.555810	+	0.831309i	$0.312408\pi$
$54$	13377.8	+	23171.0i	0.624309	+	1.08134i
$55$	9676.66			0.431339
$56$	8702.94	+	6766.72i	0.370848	+	0.288342i
$57$	−44008.4			−1.79411
$58$	−10558.2	−	18287.4i	−0.412117	−	0.713808i
$59$	−3239.84	+	5611.57i	−0.121170	+	0.209872i	−0.920229	−	0.391380i	$-0.871998\pi$
$59$	−3239.84	+	5611.57i	−0.121170	+	0.209872i	0.799060	+	0.601252i	$0.205331\pi$
$60$	−4026.86	+	6974.72i	−0.144407	+	0.250120i
$61$	−2003.16	−	3469.58i	−0.0689274	−	0.119386i	0.829502	−	0.558504i	$-0.188624\pi$
$61$	−2003.16	−	3469.58i	−0.0689274	−	0.119386i	−0.898429	+	0.439118i	$0.855291\pi$
$62$	−30752.7			−1.01602
$63$	185.863	−	1345.34i	0.00589986	−	0.0427052i
$64$	−5870.74			−0.179161
$65$	−11510.3	−	19936.4i	−0.337911	−	0.585279i
$66$	22269.1	−	38571.1i	0.629277	−	1.08994i
$67$	16810.1	−	29116.0i	0.457493	−	0.792401i	−0.541335	−	0.840807i	$-0.682081\pi$
$67$	16810.1	−	29116.0i	0.457493	−	0.792401i	0.998828	+	0.0484062i	$0.0154142\pi$
$68$	−6864.21	−	11889.2i	−0.180019	−	0.311802i
$69$	−32888.3			−0.831608
$70$	−21697.8	+	8825.66i	−0.529263	+	0.215279i
$71$	−61404.3			−1.44562			−0.722808	−	0.691049i	$-0.757149\pi$
$71$	−61404.3			−1.44562			−0.722808	+	0.691049i	$0.757149\pi$
$72$	−445.409	−	771.471i	−0.0101258	−	0.0175383i
$73$	21332.2	−	36948.4i	0.468520	−	0.811500i	−0.530833	−	0.847476i	$-0.678121\pi$
$73$	21332.2	−	36948.4i	0.468520	−	0.811500i	0.999353	+	0.0359766i	$0.0114542\pi$
$74$	−558.749	+	967.782i	−0.0118614	+	0.0205446i
$75$	4975.29	+	8617.45i	0.102133	+	0.176899i
$76$	55931.4			1.11076
$77$	46481.9	−	18906.7i	0.893423	−	0.363403i
$78$	−105955.			−1.97190
$79$	53946.3	+	93437.7i	0.972510	+	1.68444i	0.687920	+	0.725787i	$0.258524\pi$
$79$	53946.3	+	93437.7i	0.972510	+	1.68444i	0.284590	+	0.958649i	$0.408143\pi$
$80$	−15775.9	+	27324.6i	−0.275593	+	0.477342i
$81$	30742.5	−	53247.5i	0.520626	−	0.901751i
$82$	−27465.1	−	47570.9i	−0.451073	−	0.781281i
$83$	99024.8			1.57779			0.788894	−	0.614529i	$-0.210654\pi$
$83$	99024.8			1.57779			0.788894	+	0.614529i	$0.210654\pi$
$84$	−5715.54	+	41371.0i	−0.0883810	+	0.639731i
$85$	−16961.8			−0.254639
$86$	48904.3	+	84704.8i	0.713019	+	1.23499i
$87$	−23258.5	+	40284.8i	−0.329445	+	0.570615i
$88$	16457.0	−	28504.4i	0.226540	−	0.392379i
$89$	−3830.92	−	6635.35i	−0.0512659	−	0.0887951i	0.839254	−	0.543740i	$-0.182992\pi$
$89$	−3830.92	−	6635.35i	−0.0512659	−	0.0887951i	−0.890520	+	0.454945i	$0.849659\pi$
$90$	1892.82			0.0246323
$91$	−94242.3	−	73275.4i	−1.19301	−	0.927587i
$92$	41798.5			0.514862
$93$	33872.2	+	58668.4i	0.406103	+	0.703391i
$94$	54214.2	−	93901.7i	0.632839	−	1.09611i
$95$	34552.4	−	59846.4i	0.392797	−	0.680345i
$96$	50949.3	+	88246.7i	0.564235	+	0.977284i
$97$	87087.4			0.939779			0.469890	−	0.882725i	$-0.344294\pi$
$97$	87087.4			0.939779			0.469890	+	0.882725i	$0.344294\pi$
$98$	−86981.8	+	84788.3i	−0.914878	+	0.891807i
$99$	−4054.88			−0.0415805
$100$	−6323.21	−	10952.1i	−0.0632321	−	0.109521i
$101$	−36378.5	+	63009.5i	−0.354848	+	0.614614i	−0.987092	−	0.160155i	$-0.948801\pi$
$101$	−36378.5	+	63009.5i	−0.354848	+	0.614614i	0.632244	+	0.774769i	$0.282134\pi$
$102$	−39034.5	+	67609.8i	−0.371491	+	0.643441i
$103$	−24911.1	−	43147.2i	−0.231366	−	0.400738i	0.726844	−	0.686802i	$-0.240986\pi$
$103$	−24911.1	−	43147.2i	−0.231366	−	0.400738i	−0.958210	+	0.286065i	$0.907653\pi$
$104$	−78301.9			−0.709886
$105$	40736.0	+	31673.1i	0.360583	+	0.280361i
$106$	−130662.			−1.12950
$107$	39654.4	+	68683.4i	0.334836	+	0.579953i	0.983453	−	0.181162i	$-0.0579858\pi$
$107$	39654.4	+	68683.4i	0.334836	+	0.579953i	−0.648617	+	0.761115i	$0.724652\pi$
$108$	−37453.7	+	64871.6i	−0.308983	+	0.535174i
$109$	91553.5	−	158575.i	0.738089	−	1.27841i	−0.215265	−	0.976556i	$-0.569062\pi$
$109$	91553.5	−	158575.i	0.738089	−	1.27841i	0.953355	−	0.301852i	$-0.0976050\pi$
$110$	34968.2	+	60566.7i	0.275544	+	0.477257i
$111$	2461.71			0.0189640
$112$	−22391.6	+	162078.i	−0.168671	+	1.22089i
$113$	137042.			1.00962			0.504809	−	0.863231i	$-0.331563\pi$
$113$	137042.			1.00962			0.504809	+	0.863231i	$0.331563\pi$
$114$	−159032.	−	275451.i	−1.14610	−	1.98510i
$115$	25821.6	−	44724.3i	0.182070	−	0.315354i
$116$	29559.7	−	51199.0i	0.203965	−	0.353278i
$117$	4823.24	+	8354.09i	0.0325742	+	0.0564202i
$118$	−46830.8			−0.309618
$119$	−81476.3	+	33140.7i	−0.527429	+	0.214533i
$120$	33845.8			0.214561
$121$	5615.28	+	9725.95i	0.0348665	+	0.0603905i
$122$	14477.5	−	25075.8i	0.0880632	−	0.152530i
$123$	−60502.3	+	104793.i	−0.360586	+	0.624553i
$124$	−43049.0	−	74563.1i	−0.251425	−	0.435482i
$125$	−15625.0			−0.0894427
$126$	9092.20	−	3698.28i	0.0510203	−	0.0207527i
$127$	−43001.7			−0.236579			−0.118290	−	0.992979i	$-0.537741\pi$
$127$	−43001.7			−0.236579			−0.118290	+	0.992979i	$0.537741\pi$
$128$	81189.8	+	140625.i	0.438002	+	0.758642i
$129$	107730.	−	186594.i	0.569985	−	0.987243i
$130$	83188.6	−	144087.i	0.431723	−	0.747767i
$131$	10602.9	+	18364.7i	0.0539815	+	0.0934988i	0.891753	−	0.452522i	$-0.149475\pi$
$131$	10602.9	+	18364.7i	0.0539815	+	0.0934988i	−0.837772	+	0.546020i	$0.816142\pi$
$132$	124693.			0.622884
$133$	49042.0	−	354983.i	0.240403	−	1.74012i
$134$	242985.			1.16901
$135$	46275.0	+	80150.6i	0.218530	+	0.378506i
$136$	−28846.9	+	49964.2i	−0.133737	+	0.231639i
$137$	−142598.	+	246988.i	−0.649102	+	1.12428i	0.334235	+	0.942490i	$0.391522\pi$
$137$	−142598.	+	246988.i	−0.649102	+	1.12428i	−0.983338	+	0.181788i	$0.941811\pi$
$138$	−118847.	−	205849.i	−0.531241	−	0.920136i
$139$	−282350.			−1.23951			−0.619756	−	0.784794i	$-0.712769\pi$
$139$	−282350.			−1.23951			−0.619756	+	0.784794i	$0.712769\pi$
$140$	−51772.4	−	40254.1i	−0.223243	−	0.173576i
$141$	−238855.			−1.01178
$142$	−221895.	−	384333.i	−0.923476	−	1.59951i
$143$	−178210.	+	308668.i	−0.728772	+	1.26227i
$144$	6610.68	−	11450.0i	0.0265669	−	0.0460151i
$145$	−36521.8	−	63257.7i	−0.144256	−	0.249858i
$146$	308349.			1.19718
$147$	257560.	+	72550.2i	0.983071	+	0.276914i
$148$	−3128.65			−0.0117409
$149$	−34718.1	−	60133.4i	−0.128112	−	0.221896i	0.794833	−	0.606828i	$-0.207558\pi$
$149$	−34718.1	−	60133.4i	−0.128112	−	0.221896i	−0.922945	+	0.384932i	$0.874225\pi$
$150$	−35958.1	+	62281.2i	−0.130487	+	0.226011i
$151$	−129489.	+	224281.i	−0.462157	+	0.800480i	−0.999068	−	0.0431588i	$-0.986258\pi$
$151$	−129489.	+	224281.i	−0.462157	+	0.800480i	0.536911	+	0.843639i	$0.319591\pi$
$152$	−117526.	−	203561.i	−0.412596	−	0.714637i
$153$	7107.63			0.0245469
$154$	286308.	+	222610.i	0.972818	+	0.756386i
$155$	−106376.			−0.355645
$156$	−148321.	−	256899.i	−0.487967	−	0.845184i
$157$	51497.3	−	89196.0i	0.166738	−	0.288799i	−0.770533	−	0.637400i	$-0.780010\pi$
$157$	51497.3	−	89196.0i	0.166738	−	0.288799i	0.937271	+	0.348601i	$0.113343\pi$
$158$	−389888.	+	675305.i	−1.24250	+	2.15207i
$159$	143916.	+	249270.i	0.451457	+	0.781947i
$160$	−160007.			−0.494128
$161$	36650.0	−	265285.i	0.111432	−	0.806581i
$162$	444372.			1.33033
$163$	290712.	+	503528.i	0.857026	+	1.48441i	0.874752	+	0.484570i	$0.161024\pi$
$163$	290712.	+	503528.i	0.857026	+	1.48441i	−0.0177258	+	0.999843i	$0.505643\pi$
$164$	76893.8	−	133184.i	0.223245	−	0.386672i
$165$	77030.7	−	133421.i	0.220269	−	0.381518i
$166$	357842.	+	619801.i	1.00791	+	1.74575i
$167$	−475920.			−1.32051			−0.660257	−	0.751040i	$-0.729553\pi$
$167$	−475920.			−1.32051			−0.660257	+	0.751040i	$0.729553\pi$
$168$	162579.	−	66129.3i	0.444416	−	0.180768i
$169$	476621.			1.28368
$170$	−61294.3	−	106165.i	−0.162666	−	0.281747i
$171$	−14478.7	+	25077.9i	−0.0378652	+	0.0655844i
$172$	−136917.	+	237147.i	−0.352887	+	0.611219i
$173$	−142829.	−	247387.i	−0.362828	−	0.628437i	0.625597	−	0.780147i	$-0.284856\pi$
$173$	−142829.	−	247387.i	−0.362828	−	0.628437i	−0.988425	+	0.151709i	$0.951522\pi$
$174$	−336193.			−0.841813
$175$	−75054.8	+	30528.8i	−0.185261	+	0.0753554i
$176$	488505.			1.18874
$177$	51581.3	+	89341.5i	0.123754	+	0.214348i
$178$	27687.3	−	47955.9i	0.0654985	−	0.113447i
$179$	225446.	−	390484.i	0.525909	−	0.910901i	−0.473636	−	0.880721i	$-0.657059\pi$
$179$	225446.	−	390484.i	0.525909	−	0.910901i	0.999544	−	0.0301799i	$-0.00960801\pi$
$180$	2649.66	+	4589.35i	0.00609550	+	0.0105577i
$181$	151606.			0.343969			0.171985	−	0.985100i	$-0.444982\pi$
$181$	151606.			0.343969			0.171985	+	0.985100i	$0.444982\pi$
$182$	118074.	−	854660.i	0.264226	−	1.91256i
$183$	−63784.4			−0.140795
$184$	−87829.2	−	152125.i	−0.191247	−	0.331249i
$185$	−1932.76	+	3347.65i	−0.00415193	+	0.00719135i
$186$	−244806.	+	424016.i	−0.518847	+	0.898669i
$187$	131307.	+	227430.i	0.274590	+	0.475603i
$188$	303566.			0.626409
$189$	378884.	+	294590.i	0.771528	+	0.599879i
$190$	499443.			1.00369
$191$	−257493.	−	445991.i	−0.510719	−	0.884592i	−0.999923	−	0.0124221i	$-0.996046\pi$
$191$	−257493.	−	445991.i	−0.510719	−	0.884592i	0.489204	−	0.872170i	$-0.337288\pi$
$192$	−46733.8	+	80945.4i	−0.0914910	+	0.158467i
$193$	384984.	−	666811.i	0.743959	−	1.28858i	−0.206720	−	0.978400i	$-0.566279\pi$
$193$	384984.	−	666811.i	0.743959	−	1.28858i	0.950679	−	0.310175i	$-0.100388\pi$
$194$	314705.	+	545084.i	0.600342	+	1.03982i
$195$	−366509.			−0.690236
$196$	−327339.	−	92205.8i	−0.608636	−	0.171442i
$197$	−246901.			−0.453269			−0.226635	−	0.973980i	$-0.572772\pi$
$197$	−246901.			−0.453269			−0.226635	+	0.973980i	$0.572772\pi$
$198$	−14653.0	−	25379.7i	−0.0265621	−	0.0460070i
$199$	−445320.	+	771316.i	−0.797148	+	1.38070i	0.124318	+	0.992242i	$0.460326\pi$
$199$	−445320.	+	771316.i	−0.797148	+	1.38070i	−0.921466	+	0.388459i	$0.873007\pi$
$200$	−26573.3	+	46026.4i	−0.0469755	+	0.0813639i
$201$	−267633.	−	463554.i	−0.467250	−	0.809301i
$202$	−525839.			−0.906723
$203$	−299029.	−	232501.i	−0.509299	−	0.395990i
$204$	−218569.			−0.367717
$205$	−95004.3	−	164552.i	−0.157891	−	0.273476i
$206$	180041.	−	311839.i	0.295599	−	0.511992i
$207$	−10820.2	+	18741.1i	−0.0175513	+	0.0303998i
$208$	−581072.	−	1.00645e6i	−0.931261	−	1.61299i
$209$	−1.06992e6			−1.69429
$210$	−51037.2	+	369425.i	−0.0798617	+	0.578066i
$211$	−538746.			−0.833063			−0.416531	−	0.909121i	$-0.636754\pi$
$211$	−538746.			−0.833063			−0.416531	+	0.909121i	$0.636754\pi$
$212$	−182906.	−	316803.i	−0.279505	−	0.484117i
$213$	−488807.	+	846638.i	−0.738224	+	1.27864i
$214$	−286595.	+	496398.i	−0.427794	+	0.740961i
$215$	169165.	+	293002.i	0.249582	+	0.432289i
$216$	314798.			0.459090
$217$	−510980.	+	207843.i	−0.736639	+	0.299630i
$218$	1.32338e6			1.88600
$219$	−339628.	−	588253.i	−0.478512	−	0.828808i
$220$	−97900.2	+	169568.i	−0.136372	+	0.236204i
$221$	312377.	−	541052.i	0.430227	−	0.745175i
$222$	8895.80	+	15408.0i	0.0121144	+	0.0209828i
$223$	1.34117e6			1.80602			0.903011	−	0.429618i	$-0.141352\pi$
$223$	1.34117e6			1.80602			0.903011	+	0.429618i	$0.141352\pi$
$224$	−768596.	+	312629.i	−1.02348	+	0.416303i
$225$	6547.46			0.00862216
$226$	495223.	+	857752.i	0.644956	+	1.11710i
$227$	290513.	−	503183.i	0.374197	−	0.648128i	−0.616009	−	0.787739i	$-0.711252\pi$
$227$	290513.	−	503183.i	0.374197	−	0.648128i	0.990207	+	0.139610i	$0.0445850\pi$
$228$	445240.	−	771178.i	0.567227	−	0.982466i
$229$	499309.	+	864828.i	0.629188	+	1.08979i	0.987715	+	0.156266i	$0.0499459\pi$
$229$	499309.	+	864828.i	0.629188	+	1.08979i	−0.358527	+	0.933519i	$0.616721\pi$
$230$	373242.			0.465234
$231$	109334.	−	791395.i	0.134811	−	0.975806i
$232$	−248450.			−0.303053
$233$	−689895.	−	1.19493e6i	−0.832517	−	1.44196i	−0.896036	−	0.443981i	$-0.853566\pi$
$233$	−689895.	−	1.19493e6i	−0.832517	−	1.44196i	0.0635191	−	0.997981i	$-0.479768\pi$
$234$	−34859.1	+	60377.8i	−0.0416176	+	0.0720838i
$235$	187532.	−	324815.i	0.221516	−	0.383677i
$236$	−65555.9	−	113546.i	−0.0766182	−	0.132707i
$237$	1.71775e6			1.98650
$238$	−501857.	−	390205.i	−0.574299	−	0.446529i
$239$	508394.			0.575713			0.287856	−	0.957674i	$-0.407057\pi$
$239$	508394.			0.575713			0.287856	+	0.957674i	$0.407057\pi$
$240$	251167.	+	435034.i	0.281471	+	0.487522i
$241$	−92935.4	+	160969.i	−0.103072	+	0.178525i	−0.912949	−	0.408074i	$-0.866200\pi$
$241$	−92935.4	+	160969.i	−0.103072	+	0.178525i	0.809877	+	0.586600i	$0.199534\pi$
$242$	−40583.5	+	70292.6i	−0.0445462	+	0.0771563i
$243$	−39655.5	−	68685.3i	−0.0430812	−	0.0746188i
$244$	81065.1			0.0871685
$245$	−300878.	+	293291.i	−0.320240	+	0.312164i
$246$	−874540.			−0.921386
$247$	1.27266e6	+	2.20432e6i	1.32731	+	2.29896i
$248$	−180914.	+	313352.i	−0.186785	+	0.323521i
$249$	788284.	−	1.36535e6i	0.805720	−	1.39555i
$250$	−56463.5	−	97797.7i	−0.0571371	−	0.0989643i
$251$	−421837.			−0.422630			−0.211315	−	0.977418i	$-0.567775\pi$
$251$	−421837.			−0.422630			−0.211315	+	0.977418i	$0.567775\pi$
$252$	21694.5	+	16868.0i	0.0215203	+	0.0167325i
$253$	−799573.			−0.785339
$254$	−155394.	−	269150.i	−0.151130	−	0.261764i
$255$	−135024.	+	233868.i	−0.130035	+	0.225227i
$256$	−680717.	+	1.17904e6i	−0.649182	+	1.12442i
$257$	973360.	+	1.68591e6i	0.919265	+	1.59221i	0.800534	+	0.599287i	$0.204549\pi$
$257$	973360.	+	1.68591e6i	0.919265	+	1.59221i	0.118731	+	0.992926i	$0.462117\pi$
$258$	1.55720e6			1.45645
$259$	−2743.28	+	19856.8i	−0.00254109	+	0.0183933i
$260$	465805.			0.427337
$261$	15304.0	+	26507.3i	0.0139061	+	0.0240860i
$262$	−76630.4	+	132728.i	−0.0689681	+	0.119456i
$263$	−815156.	+	1.41189e6i	−0.726693	+	1.25867i	0.231580	+	0.972816i	$0.425611\pi$
$263$	−815156.	+	1.41189e6i	−0.726693	+	1.25867i	−0.958273	+	0.285854i	$0.907723\pi$
$264$	−262011.	−	453817.i	−0.231372	−	0.400748i
$265$	−451972.			−0.395363
$266$	2.39908e6	−	975832.i	2.07893	−	0.845612i
$267$	−121984.			−0.104719
$268$	340141.	+	589142.i	0.289283	+	0.501052i
$269$	−685723.	+	1.18771e6i	−0.577788	+	1.00076i	0.417945	+	0.908472i	$0.362750\pi$
$269$	−685723.	+	1.18771e6i	−0.577788	+	1.00076i	−0.995733	+	0.0922852i	$0.970583\pi$
$270$	−334445.	+	579275.i	−0.279200	+	0.483588i
$271$	380868.	+	659683.i	0.315030	+	0.545648i	0.979444	−	0.201717i	$-0.0646521\pi$
$271$	380868.	+	659683.i	0.315030	+	0.545648i	−0.664414	+	0.747365i	$0.731319\pi$
$272$	−856281.			−0.701769
$273$	−1.76053e6	+	716100.i	−1.42967	+	0.581524i
$274$	−2.06121e6			−1.65862
$275$	120958.	+	209506.i	0.0964504	+	0.167057i
$276$	332735.	−	576315.i	0.262922	−	0.455394i
$277$	1.03437e6	−	1.79159e6i	0.809987	−	1.40294i	−0.102885	−	0.994693i	$-0.532807\pi$
$277$	1.03437e6	−	1.79159e6i	0.809987	−	1.40294i	0.912872	−	0.408246i	$-0.133859\pi$
$278$	−1.02032e6	−	1.76724e6i	−0.791815	−	1.37146i
$279$	44575.7			0.0342837
$280$	−37717.0	+	273008.i	−0.0287503	+	0.208104i
$281$	431842.			0.326257			0.163128	−	0.986605i	$-0.447842\pi$
$281$	431842.			0.326257			0.163128	+	0.986605i	$0.447842\pi$
$282$	−863140.	−	1.49500e6i	−0.646336	−	1.11949i
$283$	716735.	−	1.24142e6i	0.531977	−	0.921411i	−0.467326	−	0.884085i	$-0.654783\pi$
$283$	716735.	−	1.24142e6i	0.531977	−	0.921411i	0.999303	−	0.0373260i	$-0.0118840\pi$
$284$	621236.	−	1.07601e6i	0.457047	−	0.791629i
$285$	−550106.	−	952811.i	−0.401175	−	0.694856i
$286$	−2.57596e6			−1.86219
$287$	−777863.	−	604805.i	−0.557441	−	0.433422i
$288$	67049.0			0.0476333
$289$	479766.	+	830979.i	0.337897	+	0.585255i
$290$	263955.	−	457184.i	0.184304	−	0.319224i
$291$	693256.	−	1.20075e6i	0.479912	−	0.831231i
$292$	431641.	+	747624.i	0.296255	+	0.513129i
$293$	−138921.			−0.0945363			−0.0472682	−	0.998882i	$-0.515052\pi$
$293$	−138921.			−0.0945363			−0.0472682	+	0.998882i	$0.515052\pi$
$294$	476640.	+	1.87425e6i	0.321604	+	1.26462i
$295$	−161992.			−0.108377
$296$	6574.08	+	11386.6i	0.00436120	+	0.00755382i
$297$	716460.	−	1.24094e6i	0.471304	−	0.816322i
$298$	250919.	−	434604.i	0.163679	−	0.283500i
$299$	951084.	+	1.64733e6i	0.615235	+	1.06562i
$300$	−201343.			−0.129162
$301$	1.38506e6	+	1.07692e6i	0.881157	+	0.685118i
$302$	−1.87172e6			−1.18093
$303$	579180.	+	1.00317e6i	0.362416	+	0.627723i
$304$	1.74430e6	−	3.02122e6i	1.08252	−	1.87499i
$305$	50079.1	−	86739.5i	0.0308252	−	0.0533909i
$306$	25684.6	+	44487.0i	0.0156808	+	0.0271600i
$307$	−631297.			−0.382285			−0.191143	−	0.981562i	$-0.561219\pi$
$307$	−631297.			−0.382285			−0.191143	+	0.981562i	$0.561219\pi$
$308$	−138955.	+	1.00580e6i	−0.0834637	+	0.604138i
$309$	−793215.			−0.472601
$310$	−384409.	−	665816.i	−0.227190	−	0.393505i
$311$	1.10222e6	−	1.90910e6i	0.646199	−	1.11925i	−0.337824	−	0.941209i	$-0.609691\pi$
$311$	1.10222e6	−	1.90910e6i	0.646199	−	1.11925i	0.984023	−	0.178040i	$-0.0569758\pi$
$312$	−623319.	+	1.07962e6i	−0.362513	+	0.627892i
$313$	−220967.	−	382726.i	−0.127487	−	0.220814i	0.795215	−	0.606327i	$-0.207358\pi$
$313$	−220967.	−	382726.i	−0.127487	−	0.220814i	−0.922702	+	0.385513i	$0.874025\pi$
$314$	744376.			0.426058
$315$	31450.8	−	12792.7i	0.0178589	−	0.00726417i
$316$	−2.18313e6			−1.22988
$317$	−665658.	−	1.15295e6i	−0.372052	−	0.644412i	0.617829	−	0.786312i	$-0.288012\pi$
$317$	−665658.	−	1.15295e6i	−0.372052	−	0.644412i	−0.989881	+	0.141900i	$0.954679\pi$
$318$	−1.04013e6	+	1.80156e6i	−0.576793	+	0.999034i
$319$	−565455.	+	979397.i	−0.311115	+	0.538868i
$320$	−73384.3	−	127105.i	−0.0400616	−	0.0693887i
$321$	1.26267e6			0.683954
$322$	1.79287e6	−	729256.i	0.963628	−	0.391959i
$323$	1.87543e6			1.00022
$324$	622052.	+	1.07742e6i	0.329203	+	0.570196i
$325$	287757.	−	498410.i	0.151118	−	0.261745i
$326$	−2.10107e6	+	3.63916e6i	−1.09496	+	1.89652i
$327$	−1.45762e6	−	2.52467e6i	−0.753831	−	1.30567i
$328$	−646293.			−0.331700
$329$	266174.	−	1.92666e6i	0.135574	−	0.981330i
$330$	1.11345e6			0.562843
$331$	−751401.	−	1.30146e6i	−0.376966	−	0.652924i	0.613653	−	0.789575i	$-0.289699\pi$
$331$	−751401.	−	1.30146e6i	−0.376966	−	0.652924i	−0.990619	+	0.136652i	$0.956366\pi$
$332$	−1.00185e6	+	1.73525e6i	−0.498835	+	0.864007i
$333$	809.900	−	1402.79i	0.000400240	−	0.000693237i
$334$	−1.71982e6	−	2.97881e6i	−0.843559	−	1.46109i
$335$	840507.			0.409194
$336$	2.05647e6	+	1.59895e6i	0.993743	+	0.772656i
$337$	−2.34434e6			−1.12447			−0.562233	−	0.826979i	$-0.690058\pi$
$337$	−2.34434e6			−1.12447			−0.562233	+	0.826979i	$0.690058\pi$
$338$	1.72235e6	+	2.98320e6i	0.820030	+	1.42033i
$339$	1.09092e6	−	1.88952e6i	0.515576	−	0.893003i
$340$	171605.	−	297229.i	0.0805069	−	0.139442i
$341$	823495.	+	1.42634e6i	0.383509	+	0.664256i
$342$	−209285.			−0.0967549
$343$	−872227.	+	1.99669e6i	−0.400308	+	0.916381i
$344$	1.15079e6			0.524324
$345$	−411104.	−	712052.i	−0.185953	−	0.322080i
$346$	1.03227e6	−	1.78795e6i	0.463558	−	0.802906i
$347$	−139967.	+	242431.i	−0.0624026	+	0.108085i	−0.895539	−	0.444983i	$-0.853210\pi$
$347$	−139967.	+	242431.i	−0.0624026	+	0.108085i	0.833136	+	0.553068i	$0.186543\pi$
$348$	−470618.	−	815135.i	−0.208315	−	0.360812i
$349$	1.16659e6			0.512691			0.256346	−	0.966585i	$-0.417481\pi$
$349$	1.16659e6			0.512691			0.256346	+	0.966585i	$0.417481\pi$
$350$	−462304.	−	359451.i	−0.201724	−	0.156845i
$351$	−3.40888e6			−1.47688
$352$	1.23867e6	+	2.14544e6i	0.532842	+	0.922910i
$353$	−777216.	+	1.34618e6i	−0.331975	+	0.574997i	−0.982899	−	0.184146i	$-0.941048\pi$
$353$	−777216.	+	1.34618e6i	−0.331975	+	0.574997i	0.650924	+	0.759143i	$0.274382\pi$
$354$	−372795.	+	645700.i	−0.158111	+	0.273856i
$355$	−767554.	−	1.32944e6i	−0.323250	−	0.559885i
$356$	155032.			0.0648330
$357$	−191647.	+	1.38720e6i	−0.0795850	+	0.576063i
$358$	3.25875e6			1.34383
$359$	−428247.	−	741746.i	−0.175371	−	0.303752i	0.764918	−	0.644127i	$-0.222779\pi$
$359$	−428247.	−	741746.i	−0.175371	−	0.303752i	−0.940290	+	0.340375i	$0.889446\pi$
$360$	11135.2	−	19286.8i	0.00452838	−	0.00784338i
$361$	−2.58232e6	+	4.47271e6i	−1.04290	+	1.80635i
$362$	547853.	+	948909.i	0.219732	+	0.380586i
$363$	178801.			0.0712202
$364$	2.23750e6	−	910109.i	0.885134	−	0.360031i
$365$	1.06661e6			0.419057
$366$	−230495.	−	399230.i	−0.0899414	−	0.155783i
$367$	454636.	−	787452.i	0.176197	−	0.305182i	−0.764378	−	0.644769i	$-0.776954\pi$
$367$	454636.	−	787452.i	0.176197	−	0.305182i	0.940575	+	0.339586i	$0.110287\pi$
$368$	1.30355e6	−	2.25781e6i	0.501773	−	0.869096i
$369$	39810.3	+	68953.5i	0.0152205	+	0.0263627i
$370$	−27937.5			−0.0106092
$371$	−2.17105e6	+	883082.i	−0.818908	+	0.333093i
$372$	−1.37076e6			−0.513576
$373$	66917.7	+	115905.i	0.0249040	+	0.0431350i	0.878209	−	0.478277i	$-0.158739\pi$
$373$	66917.7	+	115905.i	0.0249040	+	0.0431350i	−0.853305	+	0.521412i	$0.825405\pi$
$374$	−948999.	+	1.64371e6i	−0.350822	+	0.607642i
$375$	−124382.	+	215436.i	−0.0456752	+	0.0791117i
$376$	−637869.	−	1.10482e6i	−0.232681	−	0.403016i
$377$	2.69041e6			0.974912
$378$	−474695.	+	3.43600e6i	−0.170878	+	1.23687i
$379$	1.07715e6			0.385192			0.192596	−	0.981278i	$-0.438309\pi$
$379$	1.07715e6			0.385192			0.192596	+	0.981278i	$0.438309\pi$
$380$	699142.	+	1.21095e6i	0.248374	+	0.430197i
$381$	−342314.	+	592904.i	−0.120812	+	0.209253i
$382$	1.86099e6	−	3.22333e6i	0.652507	−	1.13018i
$383$	−230542.	−	399310.i	−0.0803069	−	0.139096i	0.823075	−	0.567933i	$-0.192257\pi$
$383$	−230542.	−	399310.i	−0.0803069	−	0.139096i	−0.903382	+	0.428837i	$0.858923\pi$
$384$	2.58523e6			0.894688
$385$	990366.	+	770030.i	0.340521	+	0.264762i
$386$	5.56481e6			1.90100
$387$	−70886.3	−	122779.i	−0.0240594	−	0.0416721i
$388$	−881076.	+	1.52607e6i	−0.297121	+	0.514629i
$389$	−117587.	+	203667.i	−0.0393992	+	0.0682413i	−0.885053	−	0.465491i	$-0.845878\pi$
$389$	−117587.	+	203667.i	−0.0393992	+	0.0682413i	0.845653	+	0.533732i	$0.179211\pi$
$390$	−1.32444e6	−	2.29400e6i	−0.440931	−	0.763715i
$391$	1.40154e6			0.463621
$392$	352241.	+	1.38509e6i	0.115778	+	0.455264i
$393$	337615.			0.110266
$394$	−892216.	−	1.54536e6i	−0.289554	−	0.501522i
$395$	−1.34866e6	+	2.33594e6i	−0.434920	+	0.753303i
$396$	41023.8	−	71055.3i	0.0131461	−	0.0227698i
$397$	1.80489e6	+	3.12616e6i	0.574744	+	0.995485i	0.996069	+	0.0885758i	$0.0282316\pi$
$397$	1.80489e6	+	3.12616e6i	0.574744	+	0.995485i	−0.421326	+	0.906909i	$0.638435\pi$
$398$	−6.43694e6			−2.03691
$399$	−4.50408e6	−	3.50202e6i	−1.41636	−	1.10125i
$400$	−788794.			−0.246498
$401$	−2.39032e6	−	4.14016e6i	−0.742327	−	1.28575i	−0.951433	−	0.307855i	$-0.900389\pi$
$401$	−2.39032e6	−	4.14016e6i	−0.742327	−	1.28575i	0.209106	−	0.977893i	$-0.432945\pi$
$402$	1.93427e6	−	3.35026e6i	0.596970	−	1.03398i
$403$	1.95908e6	−	3.39322e6i	0.600882	−	1.04076i
$404$	−736094.	−	1.27495e6i	−0.224378	−	0.388634i
$405$	1.53712e6			0.465662
$406$	374646.	−	2.71182e6i	0.112799	−	0.816479i
$407$	59848.7			0.0179089
$408$	459269.	+	795477.i	0.136589	+	0.236580i
$409$	−166239.	+	287935.i	−0.0491389	+	0.0851110i	−0.889549	−	0.456840i	$-0.848981\pi$
$409$	−166239.	+	287935.i	−0.0491389	+	0.0851110i	0.840410	+	0.541951i	$0.182314\pi$
$410$	686627.	−	1.18927e6i	0.201726	−	0.349399i
$411$	2.27030e6	+	3.93227e6i	0.662946	+	1.14826i
$412$	1.00812e6			0.292595
$413$	−778131.	+	316507.i	−0.224480	+	0.0913079i
$414$	−156402.			−0.0448479
$415$	1.23781e6	+	2.14395e6i	0.352804	+	0.611075i
$416$	2.94677e6	−	5.10395e6i	0.834858	−	1.44602i
$417$	−2.24764e6	+	3.89302e6i	−0.632975	+	1.09634i
$418$	−3.86635e6	−	6.69671e6i	−1.08233	−	1.87465i
$419$	−3.01019e6			−0.837643			−0.418822	−	0.908068i	$-0.637557\pi$
$419$	−3.01019e6			−0.837643			−0.418822	+	0.908068i	$0.637557\pi$
$420$	−967152.	+	393392.i	−0.267529	+	0.108818i
$421$	−2.57143e6			−0.707083			−0.353541	−	0.935419i	$-0.615023\pi$
$421$	−2.57143e6			−0.707083			−0.353541	+	0.935419i	$0.615023\pi$
$422$	−1.94685e6	−	3.37204e6i	−0.532170	−	0.921746i
$423$	−78582.8	+	136109.i	−0.0213539	+	0.0369860i
$424$	−768666.	+	1.33137e6i	−0.207646	+	0.359653i
$425$	−212023.	−	367234.i	−0.0569390	−	0.0986213i
$426$	−7.06554e6			−1.88634
$427$	71079.9	−	514500.i	0.0188659	−	0.136558i
$428$	−1.60476e6			−0.423448
$429$	2.83727e6	+	4.91429e6i	0.744315	+	1.28919i
$430$	−1.22261e6	+	2.11762e6i	−0.318872	+	0.552302i
$431$	2.88458e6	−	4.99623e6i	0.747978	−	1.29554i	−0.200812	−	0.979630i	$-0.564358\pi$
$431$	2.88458e6	−	4.99623e6i	0.747978	−	1.29554i	0.948790	−	0.315907i	$-0.102309\pi$
$432$	2.33609e6	+	4.04623e6i	0.602255	+	1.04314i
$433$	−1.93748e6			−0.496611			−0.248306	−	0.968682i	$-0.579874\pi$
$433$	−1.93748e6			−0.496611			−0.248306	+	0.968682i	$0.579874\pi$
$434$	−3.14741e6	−	2.44718e6i	−0.802101	−	0.623650i
$435$	−1.16292e6			−0.294665
$436$	1.85252e6	+	3.20866e6i	0.466710	+	0.808365i
$437$	−2.85503e6	+	4.94505e6i	−0.715166	+	1.23870i
$438$	2.45460e6	−	4.25150e6i	0.611358	−	1.05890i
$439$	−2.24013e6	−	3.88002e6i	−0.554769	−	0.960889i	−0.997921	−	0.0644421i	$-0.979473\pi$
$439$	−2.24013e6	−	3.88002e6i	−0.554769	−	0.960889i	0.443152	−	0.896446i	$-0.353860\pi$
$440$	822852.			0.202624
$441$	126079.	−	122900.i	0.0308707	−	0.0300922i
$442$	4.51530e6			1.09934
$443$	−1.31381e6	−	2.27558e6i	−0.318069	−	0.550912i	0.662016	−	0.749490i	$-0.269701\pi$
$443$	−1.31381e6	−	2.27558e6i	−0.318069	−	0.550912i	−0.980085	+	0.198577i	$0.936368\pi$
$444$	−24905.5	+	43137.6i	−0.00599567	+	0.0103848i
$445$	95773.1	−	165884.i	0.0229268	−	0.0397104i
$446$	4.84655e6	+	8.39447e6i	1.15371	+	1.99828i
$447$	−1.10549e6			−0.261689
$448$	−600846.	−	467170.i	−0.141439	−	0.109971i
$449$	−6.11083e6			−1.43049			−0.715244	−	0.698875i	$-0.753684\pi$
$449$	−6.11083e6			−1.43049			−0.715244	+	0.698875i	$0.753684\pi$
$450$	23660.3	+	40980.9i	0.00550794	+	0.00954003i
$451$	−1.47092e6	+	2.54771e6i	−0.340524	+	0.589805i
$452$	−1.38647e6	+	2.40144e6i	−0.319202	+	0.552873i
$453$	2.06158e6	+	3.57077e6i	0.472014	+	0.817553i
$454$	4.19926e6			0.956166
$455$	408429.	−	2.95635e6i	0.0924886	−	0.669464i
$456$	−3.74224e6			−0.842791
$457$	−1.96802e6	−	3.40871e6i	−0.440797	−	0.763483i	0.556951	−	0.830545i	$-0.311971\pi$
$457$	−1.96802e6	−	3.40871e6i	−0.440797	−	0.763483i	−0.997749	+	0.0670616i	$0.978638\pi$
$458$	−3.60867e6	+	6.25040e6i	−0.803866	+	1.39234i
$459$	−1.25585e6	+	2.17520e6i	−0.278232	+	0.481912i
$460$	522481.	+	904964.i	0.115127	+	0.199405i
$461$	3.61769e6			0.792827			0.396414	−	0.918072i	$-0.370255\pi$
$461$	3.61769e6			0.792827			0.396414	+	0.918072i	$0.370255\pi$
$462$	5.34848e6	−	2.17551e6i	1.16580	−	0.474194i
$463$	6.68308e6			1.44885			0.724426	−	0.689352i	$-0.242105\pi$
$463$	6.68308e6			1.44885			0.724426	+	0.689352i	$0.242105\pi$
$464$	−1.84373e6	−	3.19343e6i	−0.397559	−	0.688592i
$465$	−846806.	+	1.46671e6i	−0.181615	+	0.314566i
$466$	4.98610e6	−	8.63617e6i	1.06364	−	1.84228i
$467$	1.18415e6	+	2.05101e6i	0.251255	+	0.435187i	0.963872	−	0.266367i	$-0.0858234\pi$
$467$	1.18415e6	+	2.05101e6i	0.251255	+	0.435187i	−0.712617	+	0.701554i	$0.752490\pi$
$468$	−195189.			−0.0411947
$469$	4.03738e6	−	1.64222e6i	0.847555	−	0.344746i
$470$	2.71071e6			0.566028
$471$	−819885.	−	1.42008e6i	−0.170295	−	0.294959i
$472$	−275499.	+	477178.i	−0.0569200	+	0.0985884i
$473$	2.61912e6	−	4.53644e6i	0.538272	−	0.932315i
$474$	6.20737e6	+	1.07515e7i	1.26900	+	2.19797i
$475$	1.72762e6			0.351329
$476$	243569.	−	1.76303e6i	0.0492724	−	0.356650i
$477$	189393.			0.0381125
$478$	1.83717e6	+	3.18207e6i	0.367772	+	0.637000i
$479$	1.13488e6	−	1.96567e6i	0.226002	−	0.391447i	−0.730618	−	0.682787i	$-0.760768\pi$
$479$	1.13488e6	−	1.96567e6i	0.226002	−	0.391447i	0.956620	+	0.291340i	$0.0941012\pi$
$480$	−1.27373e6	+	2.20617e6i	−0.252334	+	0.437055i
$481$	−71189.3	−	123304.i	−0.0140298	−	0.0243004i
$482$	−1.34335e6			−0.263373
$483$	−3.36598e6	−	2.61712e6i	−0.656513	−	0.510453i
$484$	−227242.			−0.0440936
$485$	1.08859e6	+	1.88550e6i	0.210141	+	0.363975i
$486$	286603.	−	496412.i	0.0550415	−	0.0953347i
$487$	845017.	−	1.46361e6i	0.161452	−	0.279643i	−0.773938	−	0.633262i	$-0.781716\pi$
$487$	845017.	−	1.46361e6i	0.161452	−	0.279643i	0.935390	+	0.353619i	$0.115049\pi$
$488$	−170338.	−	295035.i	−0.0323790	−	0.0560820i
$489$	9.25681e6			1.75061
$490$	−2.92299e6	−	823357.i	−0.549968	−	0.154917i
$491$	3.12583e6			0.585143			0.292572	−	0.956244i	$-0.405489\pi$
$491$	3.12583e6			0.585143			0.292572	+	0.956244i	$0.405489\pi$
$492$	−1.22422e6	−	2.12041e6i	−0.228006	−	0.394918i
$493$	991163.	−	1.71675e6i	0.183666	−	0.318118i
$494$	−9.19796e6	+	1.59313e7i	−1.69580	+	2.93721i
$495$	−50686.0	−	87790.7i	−0.00929769	−	0.0161041i
$496$	−5.37018e6			−0.980133
$497$	−6.28447e6	−	4.88631e6i	−1.14124	−	0.887340i
$498$	1.13944e7			2.05881
$499$	4.70340e6	+	8.14652e6i	0.845591	+	1.46461i	0.885107	+	0.465388i	$0.154085\pi$
$499$	4.70340e6	+	8.14652e6i	0.845591	+	1.46461i	−0.0395159	+	0.999219i	$0.512582\pi$
$500$	158080.	−	273803.i	0.0282783	−	0.0489794i
$501$	−3.78854e6	+	6.56195e6i	−0.674339	+	1.16799i
$502$	−1.52438e6	−	2.64030e6i	−0.269981	−	0.467620i
$503$	7.23245e6			1.27458			0.637288	−	0.770626i	$-0.280056\pi$
$503$	7.23245e6			1.27458			0.637288	+	0.770626i	$0.280056\pi$
$504$	15804.8	−	114401.i	0.00277149	−	0.0200610i
$505$	−1.81893e6			−0.317385
$506$	−2.88939e6	−	5.00457e6i	−0.501684	−	0.868941i
$507$	3.79413e6	−	6.57162e6i	0.655529	−	1.13541i
$508$	435054.	−	753536.i	0.0747970	−	0.129552i
$509$	−2.05351e6	−	3.55678e6i	−0.351319	−	0.608502i	0.635162	−	0.772379i	$-0.280933\pi$
$509$	−2.05351e6	−	3.55678e6i	−0.351319	−	0.608502i	−0.986481	+	0.163877i	$0.947600\pi$
$510$	−1.95173e6			−0.332272
$511$	5.12346e6	−	2.08399e6i	0.867983	−	0.353055i
$512$	−4.64339e6			−0.782816
$513$	−5.11651e6	−	8.86206e6i	−0.858382	−	1.48676i
$514$	−7.03479e6	+	1.21846e7i	−1.17447	+	2.03425i
$515$	622777.	−	1.07868e6i	0.103470	−	0.179215i
$516$	2.17985e6	+	3.77560e6i	0.360414	+	0.624255i
$517$	−5.80698e6			−0.955486
$518$	−134198.	+	54585.4i	−0.0219746	+	0.00893824i
$519$	−4.54794e6			−0.741134
$520$	−978773.	−	1.69529e6i	−0.158735	−	0.274938i
$521$	−3.40062e6	+	5.89005e6i	−0.548863	+	0.950659i	0.449490	+	0.893286i	$0.351606\pi$
$521$	−3.40062e6	+	5.89005e6i	−0.548863	+	0.950659i	−0.998353	+	0.0573734i	$0.981727\pi$
$522$	−110607.	+	191577.i	−0.0177667	+	0.0307728i
$523$	1.65758e6	+	2.87101e6i	0.264984	+	0.458966i	0.967559	−	0.252644i	$-0.0813000\pi$
$523$	1.65758e6	+	2.87101e6i	0.264984	+	0.458966i	−0.702576	+	0.711609i	$0.747967\pi$
$524$	−429083.			−0.0682674
$525$	−176542.	+	1.27787e6i	−0.0279544	+	0.202344i
$526$	−1.17828e7			−1.85688
$527$	−1.44347e6	−	2.50016e6i	−0.226403	−	0.392141i
$528$	3.88873e6	−	6.73548e6i	0.607048	−	1.05144i
$529$	1.08456e6	−	1.87851e6i	0.168505	−	0.291860i
$530$	−1.63327e6	−	2.82891e6i	−0.252563	−	0.437452i
$531$	67880.7			0.0104475
$532$	5.72434e6	+	4.45079e6i	0.876893	+	0.681802i
$533$	6.99857e6			1.06707
$534$	−440808.	−	763502.i	−0.0668954	−	0.115866i
$535$	−991360.	+	1.71709e6i	−0.149743	+	0.259363i
$536$	1.42945e6	−	2.47587e6i	0.214909	−	0.372234i
$537$	−3.58931e6	−	6.21687e6i	−0.537125	−	0.930328i
$538$	−9.91190e6			−1.47639
$539$	6.26175e6	+	1.76383e6i	0.928375	+	0.261507i
$540$	−1.87268e6			−0.276363
$541$	−1.73978e6	−	3.01338e6i	−0.255564	−	0.442650i	0.709484	−	0.704721i	$-0.248928\pi$
$541$	−1.73978e6	−	3.01338e6i	−0.255564	−	0.442650i	−0.965049	+	0.262071i	$0.915595\pi$
$542$	−2.75266e6	+	4.76775e6i	−0.402490	+	0.697132i
$543$	1.20685e6	−	2.09033e6i	0.175653	−	0.304239i
$544$	−2.17121e6	−	3.76065e6i	−0.314561	−	0.544836i
$545$	4.57768e6			0.660167
$546$	−1.08441e7	−	8.43149e6i	−1.55672	−	1.21038i
$547$	2.55022e6			0.364426			0.182213	−	0.983259i	$-0.441674\pi$
$547$	2.55022e6			0.364426			0.182213	+	0.983259i	$0.441674\pi$
$548$	−2.88538e6	−	4.99762e6i	−0.410441	−	0.710905i
$549$	−20985.0	+	36347.1i	−0.00297151	+	0.00514681i
$550$	−874205.	+	1.51417e6i	−0.123227	+	0.213436i
$551$	4.03813e6	+	6.99425e6i	0.566632	+	0.981436i
$552$	−2.79664e6			−0.390652
$553$	−1.91422e6	+	1.38558e7i	−0.266183	+	1.92672i
$554$	1.49515e7			2.06972
$555$	30771.4	+	53297.6i	0.00424048	+	0.00734473i
$556$	2.85658e6	−	4.94774e6i	0.391885	−	0.678765i
$557$	−1.67113e6	+	2.89449e6i	−0.228230	+	0.395307i	−0.957284	−	0.289150i	$-0.906627\pi$
$557$	−1.67113e6	+	2.89449e6i	−0.228230	+	0.395307i	0.729053	+	0.684457i	$0.239961\pi$
$558$	161082.	+	279001.i	0.0219008	+	0.0379333i
$559$	−1.24616e7			−1.68673
$560$	−3.78898e6	+	1.54118e6i	−0.510566	+	0.207675i
$561$	4.18106e6			0.560892
$562$	1.56053e6	+	2.70292e6i	0.208416	+	0.360988i
$563$	3.15206e6	−	5.45953e6i	0.419106	−	0.725913i	−0.576744	−	0.816925i	$-0.695677\pi$
$563$	3.15206e6	−	5.45953e6i	0.419106	−	0.725913i	0.995850	+	0.0910124i	$0.0290103\pi$
$564$	2.41653e6	−	4.18554e6i	0.319885	−	0.554057i
$565$	1.71302e6	+	2.96704e6i	0.225758	+	0.391024i
$566$	1.03602e7			1.35933
$567$	7.38358e6	−	3.00330e6i	0.964516	−	0.392320i
$568$	−5.22150e6			−0.679085
$569$	−1.76028e6	−	3.04890e6i	−0.227930	−	0.394786i	0.729265	−	0.684232i	$-0.239862\pi$
$569$	−1.76028e6	−	3.04890e6i	−0.227930	−	0.394786i	−0.957194	+	0.289446i	$0.906529\pi$
$570$	3.97579e6	−	6.88628e6i	0.512551	−	0.887764i
$571$	3.75659e6	−	6.50661e6i	0.482174	−	0.835150i	−0.517617	−	0.855613i	$-0.673181\pi$
$571$	3.75659e6	−	6.50661e6i	0.482174	−	0.835150i	0.999791	+	0.0204629i	$0.00651400\pi$
$572$	−3.60595e6	−	6.24568e6i	−0.460818	−	0.798160i
$573$	−8.19906e6			−1.04322
$574$	974568.	−	7.05425e6i	0.123462	−	0.893657i
$575$	1.29108e6			0.162848
$576$	30750.7	+	53261.8i	0.00386189	+	0.00668898i
$577$	3.33747e6	−	5.78067e6i	0.417329	−	0.722835i	−0.578341	−	0.815795i	$-0.696300\pi$
$577$	3.33747e6	−	5.78067e6i	0.417329	−	0.722835i	0.995670	+	0.0929604i	$0.0296330\pi$
$578$	−3.46742e6	+	6.00576e6i	−0.431705	+	0.747736i
$579$	−6.12930e6	−	1.06163e7i	−0.759826	−	1.31606i
$580$	1.47799e6			0.182432
$581$	1.01348e7	+	7.88000e6i	1.24559	+	0.968469i
$582$	1.00208e7			1.22629
$583$	3.49886e6	+	6.06021e6i	0.426339	+	0.738441i
$584$	1.81397e6	−	3.14190e6i	0.220089	−	0.381206i
$585$	−120581.	+	208852.i	−0.0145676	+	0.0252319i
$586$	−502014.	−	869513.i	−0.0603909	−	0.104600i
$587$	−1.44246e7			−1.72785			−0.863927	−	0.503617i	$-0.832002\pi$
$587$	−1.44246e7			−1.72785			−0.863927	+	0.503617i	$0.832002\pi$
$588$	−3.87710e6	+	3.77933e6i	−0.462449	+	0.450787i
$589$	1.17618e7			1.39696
$590$	−585385.	−	1.01392e6i	−0.0692328	−	0.119915i
$591$	−1.96544e6	+	3.40425e6i	−0.231468	+	0.400915i
$592$	−97571.4	+	168999.i	−0.0114424	+	0.0198189i
$593$	−4.31646e6	−	7.47633e6i	−0.504070	−	0.873075i	−0.999989	−	0.00470622i	$-0.998502\pi$
$593$	−4.31646e6	−	7.47633e6i	−0.504070	−	0.873075i	0.495919	−	0.868369i	$-0.334831\pi$
$594$	1.03562e7			1.20430
$595$	−1.73597e6	−	1.34975e6i	−0.201025	−	0.156301i
$596$	1.40499e6			0.162016
$597$	7.08990e6	+	1.22801e7i	0.814150	+	1.41015i
$598$	−6.87380e6	+	1.19058e7i	−0.786038	+	1.36146i
$599$	−2.87998e6	+	4.98827e6i	−0.327961	+	0.568046i	−0.982107	−	0.188323i	$-0.939695\pi$
$599$	−2.87998e6	+	4.98827e6i	−0.327961	+	0.568046i	0.654146	+	0.756368i	$0.273028\pi$
$600$	423072.	+	732783.i	0.0479774	+	0.0830992i
$601$	−6.23001e6			−0.703562			−0.351781	−	0.936082i	$-0.614424\pi$
$601$	−6.23001e6			−0.703562			−0.351781	+	0.936082i	$0.614424\pi$
$602$	−1.73531e6	+	1.25608e7i	−0.195158	+	1.41262i
$603$	−352204.			−0.0394458
$604$	−2.62011e6	−	4.53817e6i	−0.292232	−	0.506161i
$605$	−140382.	+	243149.i	−0.0155928	+	0.0270074i
$606$	−4.18593e6	+	7.25024e6i	−0.463031	+	0.801993i
$607$	−1.39932e6	−	2.42369e6i	−0.154150	−	0.266996i	0.778599	−	0.627522i	$-0.215931\pi$
$607$	−1.39932e6	−	2.42369e6i	−0.154150	−	0.266996i	−0.932749	+	0.360526i	$0.882597\pi$
$608$	1.76916e7			1.94092
$609$	−5.58611e6	+	2.27217e6i	−0.610332	+	0.248255i
$610$	723876.			0.0787661
$611$	6.90734e6	+	1.19639e7i	0.748528	+	1.29649i
$612$	−71909.0	+	124550.i	−0.00776076	+	0.0134420i
$613$	−6.20958e6	+	1.07553e7i	−0.667438	+	1.15604i	0.311180	+	0.950351i	$0.399276\pi$
$613$	−6.20958e6	+	1.07553e7i	−0.667438	+	1.15604i	−0.978618	+	0.205686i	$0.934058\pi$
$614$	−2.28130e6	−	3.95132e6i	−0.244208	−	0.422981i
$615$	−3.02511e6			−0.322518
$616$	3.95258e6	−	1.60772e6i	0.419690	−	0.170710i
$617$	5.63980e6			0.596418			0.298209	−	0.954501i	$-0.403611\pi$
$617$	5.63980e6			0.596418			0.298209	+	0.954501i	$0.403611\pi$
$618$	−2.86641e6	−	4.96477e6i	−0.301903	−	0.522911i
$619$	−2.89857e6	+	5.02047e6i	−0.304059	+	0.526645i	−0.977051	−	0.213004i	$-0.931675\pi$
$619$	−2.89857e6	+	5.02047e6i	−0.304059	+	0.526645i	0.672993	+	0.739649i	$0.265009\pi$
$620$	1.07623e6	−	1.86408e6i	0.112441	−	0.194753i
$621$	−3.82366e6	−	6.62277e6i	−0.397878	−	0.689145i
$622$	1.59322e7			1.65120
$623$	135936.	−	983950.i	0.0140318	−	0.101567i
$624$	−1.85024e7			−1.90225
$625$	−195312.	−	338291.i	−0.0200000	−	0.0346410i
$626$	1.59700e6	−	2.76609e6i	0.162881	−	0.282118i
$627$	−8.51710e6	+	1.47520e7i	−0.865212	+	1.49859i
$628$	1.04201e6	+	1.80482e6i	0.105432	+	0.182614i
$629$	−104906.			−0.0105724
$630$	193723.	+	150623.i	0.0194459	+	0.0151196i
$631$	−3.41197e6			−0.341140			−0.170570	−	0.985346i	$-0.554561\pi$
$631$	−3.41197e6			−0.341140			−0.170570	+	0.985346i	$0.554561\pi$
$632$	4.58731e6	+	7.94545e6i	0.456841	+	0.791272i
$633$	−4.28867e6	+	7.42819e6i	−0.425415	+	0.736841i
$634$	4.81093e6	−	8.33278e6i	0.475342	−	0.823316i
$635$	−537521.	−	931014.i	−0.0529007	−	0.0916267i
$636$	−5.82408e6			−0.570932
$637$	−3.81435e6	−	1.49989e7i	−0.372453	−	1.46457i
$638$	−8.17346e6			−0.794977
$639$	321634.	+	557086.i	0.0311609	+	0.0539722i
$640$	−2.02974e6	+	3.51562e6i	−0.195881	+	0.339275i
$641$	5.92432e6	−	1.02612e7i	0.569499	−	0.986402i	−0.427116	−	0.904197i	$-0.640470\pi$
$641$	5.92432e6	−	1.02612e7i	0.569499	−	0.986402i	0.996615	−	0.0822049i	$-0.0261962\pi$
$642$	4.56286e6	+	7.90311e6i	0.436918	+	0.756764i
$643$	−6.05156e6			−0.577218			−0.288609	−	0.957447i	$-0.593193\pi$
$643$	−6.05156e6			−0.577218			−0.288609	+	0.957447i	$0.593193\pi$
$644$	4.27790e6	+	3.32616e6i	0.406458	+	0.316030i
$645$	5.38651e6			0.509810
$646$	6.77716e6	+	1.17384e7i	0.638950	+	1.10669i
$647$	4.91125e6	−	8.50654e6i	0.461245	−	0.798900i	−0.537778	−	0.843086i	$-0.680736\pi$
$647$	4.91125e6	−	8.50654e6i	0.461245	−	0.798900i	0.999023	+	0.0441865i	$0.0140696\pi$
$648$	2.61418e6	−	4.52788e6i	0.244567	−	0.423602i
$649$	1.25403e6	+	2.17205e6i	0.116869	+	0.202422i
$650$	4.15943e6			0.386145
$651$	−1.20192e6	+	8.69988e6i	−0.111153	+	0.804565i
$652$	−1.17647e7			−1.08383
$653$	478593.	+	828947.i	0.0439221	+	0.0760753i	0.887151	−	0.461480i	$-0.152681\pi$
$653$	478593.	+	828947.i	0.0439221	+	0.0760753i	−0.843229	+	0.537555i	$0.819348\pi$
$654$	1.05347e7	−	1.82466e7i	0.963112	−	1.66816i
$655$	−265072.	+	459118.i	−0.0241413	+	0.0418139i
$656$	−4.79609e6	−	8.30707e6i	−0.435138	−	0.753682i
$657$	−446949.			−0.0403965
$658$	1.30209e7	−	5.29630e6i	1.17240	−	0.476879i
$659$	−1.54679e7			−1.38745			−0.693725	−	0.720240i	$-0.744032\pi$
$659$	−1.54679e7			−1.38745			−0.693725	+	0.720240i	$0.744032\pi$
$660$	1.55866e6	+	2.69968e6i	0.139281	+	0.241242i
$661$	1.97518e6	−	3.42111e6i	0.175834	−	0.304554i	−0.764615	−	0.644487i	$-0.777071\pi$
$661$	1.97518e6	−	3.42111e6i	0.175834	−	0.304554i	0.940450	+	0.339933i	$0.110404\pi$
$662$	5.43062e6	−	9.40612e6i	0.481620	−	0.834191i
$663$	−4.97333e6	−	8.61405e6i	−0.439403	−	0.761068i
$664$	8.42055e6			0.741174
$665$	8.29863e6	−	3.37549e6i	0.727700	−	0.295994i
$666$	11706.8			0.00102271
$667$	3.01777e6	+	5.22692e6i	0.262646	+	0.454916i
$668$	4.81495e6	−	8.33974e6i	0.417494	−	0.723122i
$669$	1.06764e7	−	1.84920e7i	0.922270	−	1.59742i
$670$	3.03731e6	+	5.26078e6i	0.261398	+	0.452755i
$671$	−1.55071e6			−0.132961
$672$	−1.80788e6	+	1.30860e7i	−0.154435	+	1.11785i
$673$	−1.64772e7			−1.40231			−0.701157	−	0.713007i	$-0.747333\pi$
$673$	−1.64772e7			−1.40231			−0.701157	+	0.713007i	$0.747333\pi$
$674$	−8.47167e6	−	1.46734e7i	−0.718322	−	1.24417i
$675$	−1.15687e6	+	2.00377e6i	−0.0977298	+	0.169273i
$676$	−4.82205e6	+	8.35203e6i	−0.405849	+	0.702951i
$677$	4.50162e6	+	7.79704e6i	0.377483	+	0.653820i	0.990695	−	0.136099i	$-0.0434564\pi$
$677$	4.50162e6	+	7.79704e6i	0.377483	+	0.653820i	−0.613212	+	0.789918i	$0.710123\pi$
$678$	1.57688e7			1.31742
$679$	8.91303e6	+	6.93007e6i	0.741909	+	0.576850i
$680$	−1.44234e6			−0.119618
$681$	−4.62523e6	−	8.01113e6i	−0.382178	−	0.661952i
$682$	−5.95167e6	+	1.03086e7i	−0.489980	+	0.848669i
$683$	−4.69191e6	+	8.12662e6i	−0.384856	+	0.666589i	−0.991749	−	0.128194i	$-0.959082\pi$
$683$	−4.69191e6	+	8.12662e6i	−0.384856	+	0.666589i	0.606894	+	0.794783i	$0.292415\pi$
$684$	−292967.	−	507433.i	−0.0239430	−	0.0414704i
$685$	−7.12992e6			−0.580575
$686$	−1.56493e7	+	1.75607e6i	−1.26965	+	0.142472i
$687$	1.58989e7			1.28522
$688$	8.53991e6	+	1.47916e7i	0.687832	+	1.19136i
$689$	8.32372e6	−	1.44171e7i	0.667989	−	1.15699i
$690$	2.97118e6	−	5.14624e6i	0.237578	−	0.411497i
$691$	2.52902e6	+	4.38038e6i	0.201491	+	0.348993i	0.949009	−	0.315249i	$-0.102088\pi$
$691$	2.52902e6	+	4.38038e6i	0.201491	+	0.348993i	−0.747518	+	0.664242i	$0.768755\pi$
$692$	5.78009e6			0.458848
$693$	−415000.	−	322671.i	−0.0328258	−	0.0255227i
$694$	−2.02318e6			−0.159454
$695$	−3.52938e6	−	6.11306e6i	−0.277164	−	0.480061i
$696$	−1.97778e6	+	3.42561e6i	−0.154758	+	0.268049i
$697$	2.57831e6	−	4.46577e6i	0.201027	−	0.348189i
$698$	4.21568e6	+	7.30176e6i	0.327513	+	0.567269i
$699$	−2.19675e7			−1.70055
$700$	224372.	−	1.62408e6i	0.0173071	−	0.125274i
$701$	−2.25374e7			−1.73224			−0.866121	−	0.499835i	$-0.833394\pi$
$701$	−2.25374e7			−1.73224			−0.866121	+	0.499835i	$0.833394\pi$
$702$	−1.23186e7	−	2.13364e7i	−0.943447	−	1.63410i
$703$	213701.	−	370141.i	0.0163087	−	0.0282474i
$704$	−1.13618e6	+	1.96793e6i	−0.0864006	+	0.149650i
$705$	−2.98568e6	−	5.17135e6i	−0.226241	−	0.391860i
$706$	−1.12344e7			−0.848277
$707$	−8.73723e6	+	3.55390e6i	−0.657394	+	0.267397i
$708$	−2.08742e6			−0.156505
$709$	1.18519e6	+	2.05280e6i	0.0885463	+	0.153367i	0.906897	−	0.421353i	$-0.138445\pi$
$709$	1.18519e6	+	2.05280e6i	0.0885463	+	0.153367i	−0.818351	+	0.574719i	$0.805111\pi$
$710$	5.54736e6	−	9.60832e6i	0.412991	−	0.715322i
$711$	565138.	−	978847.i	0.0419257	−	0.0726174i
$712$	−325761.	−	564235.i	−0.0240824	−	0.0417119i
$713$	8.78979e6			0.647522
$714$	−9.37513e6	+	3.81336e6i	−0.688227	+	0.279939i
$715$	−8.91049e6			−0.651833
$716$	4.56174e6	+	7.90117e6i	0.332543	+	0.575982i
$717$	4.04706e6	−	7.00971e6i	0.293996	−	0.509216i
$718$	3.09508e6	−	5.36084e6i	0.224058	−	0.388080i
$719$	6.27304e6	+	1.08652e7i	0.452539	+	0.783820i	0.998543	−	0.0539625i	$-0.0171852\pi$
$719$	6.27304e6	+	1.08652e7i	0.452539	+	0.783820i	−0.546004	+	0.837782i	$0.683852\pi$
$720$	330534.			0.0237621
$721$	883941.	−	6.39826e6i	0.0633264	−	0.458378i
$722$	−3.73266e7			−2.66486
$723$	1.47962e6	+	2.56277e6i	0.105270	+	0.182333i
$724$	−1.53382e6	+	2.65665e6i	−0.108750	+	0.188360i
$725$	913046.	−	1.58144e6i	0.0645131	−	0.111740i
$726$	646127.	+	1.11912e6i	0.0454963	+	0.0788019i
$727$	5.18009e6			0.363498			0.181749	−	0.983345i	$-0.441824\pi$
$727$	5.18009e6			0.363498			0.181749	+	0.983345i	$0.441824\pi$
$728$	−8.01387e6	−	6.23095e6i	−0.560420	−	0.435738i
$729$	1.36781e7			0.953252
$730$	3.85436e6	+	6.67596e6i	0.267698	+	0.463667i
$731$	−4.59094e6	+	7.95175e6i	−0.317767	+	0.550388i
$732$	645316.	−	1.11772e6i	0.0445138	−	0.0771002i
$733$	7.71894e6	+	1.33696e7i	0.530637	+	0.919091i	0.999361	+	0.0357461i	$0.0113808\pi$
$733$	7.71894e6	+	1.33696e7i	0.530637	+	0.919091i	−0.468723	+	0.883345i	$0.655286\pi$
$734$	6.57161e6			0.450227
$735$	1.64874e6	+	6.48321e6i	0.112573	+	0.442662i
$736$	1.32213e7			0.899659
$737$	−6.50664e6	−	1.12698e7i	−0.441253	−	0.764273i
$738$	−287722.	+	498350.i	−0.0194461	+	0.0336817i
$739$	8.23661e6	−	1.42662e7i	0.554801	−	0.960944i	−0.443118	−	0.896463i	$-0.646128\pi$
$739$	8.23661e6	−	1.42662e7i	0.554801	−	0.960944i	0.997919	−	0.0644803i	$-0.0205390\pi$
$740$	−39108.1	−	67737.2i	−0.00262535	−	0.00454724i
$741$	4.05240e7			2.71123
$742$	−1.33727e7	−	1.03976e7i	−0.891681	−	0.693300i
$743$	−2.59403e7			−1.72386			−0.861931	−	0.507026i	$-0.830745\pi$
$743$	−2.59403e7			−1.72386			−0.861931	+	0.507026i	$0.830745\pi$
$744$	2.88032e6	+	4.98885e6i	0.190769	+	0.330421i
$745$	867951.	−	1.50334e6i	0.0572934	−	0.0992351i
$746$	−483636.	+	837683.i	−0.0318179	+	0.0551103i
$747$	−518689.	−	898395.i	−0.0340099	−	0.0589068i
$748$	−5.31381e6			−0.347258
$749$	−1.40709e6	+	1.01850e7i	−0.0916469	+	0.663371i
$750$	−1.79790e6			−0.116711
$751$	−5.93040e6	−	1.02718e7i	−0.383693	−	0.664576i	0.607894	−	0.794018i	$-0.292015\pi$
$751$	−5.93040e6	−	1.02718e7i	−0.383693	−	0.664576i	−0.991587	+	0.129442i	$0.958681\pi$
$752$	9.46714e6	−	1.63976e7i	0.610484	−	1.05739i
$753$	−3.35801e6	+	5.81625e6i	−0.215822	+	0.373814i
$754$	9.72224e6	+	1.68394e7i	0.622785	+	1.07870i
$755$	−6.47444e6			−0.413366
$756$	−8.99545e6	+	3.65893e6i	−0.572425	+	0.232836i
$757$	−6.25104e6			−0.396472			−0.198236	−	0.980154i	$-0.563521\pi$
$757$	−6.25104e6			−0.396472			−0.198236	+	0.980154i	$0.563521\pi$
$758$	3.89245e6	+	6.74193e6i	0.246065	+	0.426198i
$759$	−6.36498e6	+	1.10245e7i	−0.401044	+	0.694629i
$760$	2.93815e6	−	5.08902e6i	0.184518	−	0.319595i
$761$	−1.10266e7	−	1.90986e7i	−0.690206	−	1.19547i	−0.971770	−	0.235929i	$-0.924187\pi$
$761$	−1.10266e7	−	1.90986e7i	−0.690206	−	1.19547i	0.281565	−	0.959542i	$-0.409147\pi$
$762$	−4.94803e6			−0.308706
$763$	2.19889e7	−	8.94406e6i	1.36739	−	0.556190i
$764$	1.04204e7			0.645877
$765$	88845.4	+	153885.i	0.00548885	+	0.00950697i
$766$	1.66620e6	−	2.88595e6i	0.102602	−	0.177712i
$767$	2.98332e6	−	5.16726e6i	0.183110	−	0.317156i
$768$	1.08376e7	+	1.87714e7i	0.663028	+	1.14840i
$769$	−1.37289e7			−0.837181			−0.418591	−	0.908175i	$-0.637476\pi$
$769$	−1.37289e7			−0.837181			−0.418591	+	0.908175i	$0.637476\pi$
$770$	−1.24081e6	+	8.98138e6i	−0.0754184	+	0.545904i
$771$	3.09936e7			1.87774
$772$	7.78987e6	+	1.34925e7i	0.470421	+	0.814794i
$773$	7.53578e6	−	1.30523e7i	0.453606	−	0.785670i	−0.545000	−	0.838436i	$-0.683471\pi$
$773$	7.53578e6	−	1.30523e7i	0.453606	−	0.785670i	0.998607	+	0.0527663i	$0.0168038\pi$
$774$	512318.	−	887361.i	0.0307388	−	0.0532412i
$775$	−1.32971e6	−	2.30312e6i	−0.0795246	−	0.137741i
$776$	7.40545e6			0.441466
$777$	251946.	+	195893.i	0.0149711	+	0.0116404i
$778$	−1.69969e6			−0.100675
$779$	1.05044e7	+	1.81941e7i	0.620194	+	1.07421i
$780$	3.70802e6	−	6.42248e6i	0.218226	−	0.377978i
$781$	−1.18838e7	+	2.05833e7i	−0.697151	+	1.20750i
$782$	5.06469e6	+	8.77231e6i	0.296167	+	0.512976i
$783$	−1.08163e7			−0.630485
$784$	−1.51892e7	+	1.48061e7i	−0.882560	+	0.860304i
$785$	2.57487e6			0.149135
$786$	1.22003e6	+	2.11315e6i	0.0704390	+	0.122004i
$787$	−9.65279e6	+	1.67191e7i	−0.555541	+	0.962225i	0.442320	+	0.896857i	$0.354155\pi$
$787$	−9.65279e6	+	1.67191e7i	−0.555541	+	0.962225i	−0.997861	+	0.0653679i	$0.979178\pi$
$788$	2.49793e6	−	4.32654e6i	0.143306	−	0.248213i
$789$	1.29780e7	+	2.24786e7i	0.742192	+	1.28551i
$790$	−1.94944e7			−1.11133
$791$	1.40257e7	+	1.09052e7i	0.797044	+	0.619718i
$792$	−344806.			−0.0195327
$793$	1.84456e6	+	3.19487e6i	0.104162	+	0.180414i
$794$	−1.30445e7	+	2.25938e7i	−0.734306	+	1.27186i
$795$	−3.59790e6	+	6.23175e6i	−0.201898	+	0.349697i
$796$	−9.01073e6	−	1.56070e7i	−0.504054	−	0.873047i
$797$	2.05347e7			1.14510			0.572549	−	0.819871i	$-0.305955\pi$
$797$	2.05347e7			1.14510			0.572549	+	0.819871i	$0.305955\pi$
$798$	5.64306e6	−	4.08464e7i	0.313695	−	2.27063i
$799$	1.01788e7			0.564067
$800$	−2.00009e6	−	3.46426e6i	−0.110490	−	0.191375i
$801$	−40132.5	+	69511.5i	−0.00221011	+	0.00382803i
$802$	1.72756e7	−	2.99223e7i	0.948414	−	1.64270i
$803$	−8.25697e6	−	1.43015e7i	−0.451889	−	0.782695i
$804$	1.08307e7			0.590905
$805$	6.20171e6	−	2.52257e6i	0.337304	−	0.137200i
$806$	2.83178e7			1.53540
$807$	1.09174e7	+	1.89094e7i	0.590111	+	1.02210i
$808$	−3.09344e6	+	5.35799e6i	−0.166691	+	0.288718i
$809$	−3.67354e6	+	6.36276e6i	−0.197339	+	0.341801i	−0.947665	−	0.319267i	$-0.896563\pi$
$809$	−3.67354e6	+	6.36276e6i	−0.197339	+	0.341801i	0.750326	+	0.661068i	$0.229897\pi$
$810$	5.55465e6	+	9.62093e6i	0.297470	+	0.515234i
$811$	2.36201e7			1.26104			0.630522	−	0.776171i	$-0.282841\pi$
$811$	2.36201e7			1.26104			0.630522	+	0.776171i	$0.282841\pi$
$812$	7.09952e6	−	2.88775e6i	0.377867	−	0.153699i
$813$	1.21276e7			0.643498
$814$	216273.	+	374596.i	0.0114404	+	0.0198154i
$815$	−7.26780e6	+	1.25882e7i	−0.383274	+	0.663850i
$816$	−6.81639e6	+	1.18063e7i	−0.358368	+	0.620712i
$817$	−1.87041e7	−	3.23965e7i	−0.980352	−	1.69802i
$818$	−2.40293e6			−0.125562
$819$	−171147.	+	1.23882e6i	−0.00891579	+	0.0645355i
$820$	3.84469e6			0.199676
$821$	−9.22476e6	−	1.59777e7i	−0.477636	−	0.827290i	0.522035	−	0.852924i	$-0.325173\pi$
$821$	−9.22476e6	−	1.59777e7i	−0.477636	−	0.827290i	−0.999671	+	0.0256341i	$0.991840\pi$
$822$	−1.64082e7	+	2.84198e7i	−0.846996	+	1.46704i
$823$	5.06547e6	−	8.77364e6i	0.260687	−	0.451524i	−0.705738	−	0.708473i	$-0.749384\pi$
$823$	5.06547e6	−	8.77364e6i	0.260687	−	0.451524i	0.966425	+	0.256950i	$0.0827175\pi$
$824$	−2.11831e6	−	3.66901e6i	−0.108685	−	0.188248i
$825$	3.85154e6			0.197015
$826$	−4.79294e6	−	3.72661e6i	−0.244428	−	0.190048i
$827$	−9.10559e6			−0.462961			−0.231480	−	0.972840i	$-0.574357\pi$
$827$	−9.10559e6			−0.462961			−0.231480	+	0.972840i	$0.574357\pi$
$828$	−218939.	−	379214.i	−0.0110981	−	0.0192224i
$829$	1.20216e7	−	2.08220e7i	0.607540	−	1.05229i	−0.384104	−	0.923290i	$-0.625490\pi$
$829$	1.20216e7	−	2.08220e7i	0.607540	−	1.05229i	0.991644	−	0.129001i	$-0.0411771\pi$
$830$	−8.94606e6	+	1.54950e7i	−0.450751	+	0.780724i
$831$	−1.64682e7	−	2.85237e7i	−0.827262	−	1.43286i
$832$	5.40591e6			0.270745
$833$	−1.09760e7	−	3.09174e6i	−0.548062	−	0.154380i
$834$	−3.24888e7			−1.61741
$835$	−5.94900e6	−	1.03040e7i	−0.295276	−	0.511433i
$836$	1.08246e7	−	1.87487e7i	0.535668	−	0.927804i
$837$	−7.87611e6	+	1.36418e7i	−0.388596	+	0.673068i
$838$	−1.08778e7	−	1.88409e7i	−0.535096	−	0.926814i
$839$	−3.70147e7			−1.81539			−0.907694	−	0.419633i	$-0.862159\pi$
$839$	−3.70147e7			−1.81539			−0.907694	+	0.419633i	$0.862159\pi$
$840$	3.46397e6	+	2.69331e6i	0.169386	+	0.131701i
$841$	−1.19745e7			−0.583806
$842$	−9.29230e6	−	1.60947e7i	−0.451693	−	0.782355i
$843$	3.43766e6	−	5.95421e6i	0.166607	−	0.288573i
$844$	5.45057e6	−	9.44066e6i	0.263382	−	0.456190i
$845$	5.95777e6	+	1.03192e7i	0.287040	+	0.497167i
$846$	−1.13589e6			−0.0545644
$847$	−199252.	+	1.44225e6i	−0.00954319	+	0.0690768i
$848$	−2.28168e7			−1.08960
$849$	−1.14111e7	−	1.97646e7i	−0.543323	−	0.941063i
$850$	1.53236e6	−	2.65412e6i	0.0727467	−	0.126001i
$851$	159703.	−	276613.i	0.00755941	−	0.0130933i
$852$	−9.89066e6	−	1.71311e7i	−0.466795	−	0.808513i
$853$	−79427.6			−0.00373765			−0.00186883	−	0.999998i	$-0.500595\pi$
$853$	−79427.6			−0.00373765			−0.00186883	+	0.999998i	$0.500595\pi$
$854$	3.47714e6	−	1.41434e6i	0.163147	−	0.0663604i
$855$	−723936.			−0.0338676
$856$	3.37200e6	+	5.84047e6i	0.157291	+	0.272435i
$857$	−6.43794e6	+	1.11508e7i	−0.299430	+	0.518627i	−0.976006	−	0.217746i	$-0.930130\pi$
$857$	−6.43794e6	+	1.11508e7i	−0.299430	+	0.518627i	0.676576	+	0.736373i	$0.263463\pi$
$858$	−2.05058e7	+	3.55172e7i	−0.950954	+	1.64710i
$859$	−1.91448e6	−	3.31598e6i	−0.0885256	−	0.153331i	0.818362	−	0.574702i	$-0.194882\pi$
$859$	−1.91448e6	−	3.31598e6i	−0.0885256	−	0.153331i	−0.906888	+	0.421372i	$0.861549\pi$
$860$	−6.84585e6			−0.315632
$861$	−1.45312e7	+	5.91060e6i	−0.668025	+	0.271721i
$862$	4.16956e7			1.91127
$863$	6.35275e6	+	1.10033e7i	0.290359	+	0.502916i	0.973895	−	0.227001i	$-0.0728920\pi$
$863$	6.35275e6	+	1.10033e7i	0.290359	+	0.502916i	−0.683536	+	0.729917i	$0.739559\pi$
$864$	−1.18469e7	+	2.05195e7i	−0.539910	+	0.935152i
$865$	3.57073e6	−	6.18468e6i	0.162262	−	0.281046i
$866$	−7.00139e6	−	1.21268e7i	−0.317241	−	0.549478i
$867$	1.52766e7			0.690208
$868$	1.52755e6	−	1.10569e7i	0.0688169	−	0.498120i
$869$	4.17616e7			1.87598
$870$	−4.20241e6	−	7.27880e6i	−0.188235	−	0.326033i
$871$	−1.54792e7	+	2.68107e7i	−0.691356	+	1.19746i
$872$	7.78523e6	−	1.34844e7i	0.346721	−	0.600538i
$873$	−456161.	−	790094.i	−0.0202573	−	0.0350867i
$874$	−4.12685e7			−1.82743
$875$	−1.59915e6	−	1.24337e6i	−0.0706106	−	0.0549012i
$876$	1.37443e7			0.605147
$877$	9.42920e6	+	1.63318e7i	0.413977	+	0.717028i	0.995320	−	0.0966295i	$-0.0308062\pi$
$877$	9.42920e6	+	1.63318e7i	0.413977	+	0.717028i	−0.581344	+	0.813658i	$0.697473\pi$
$878$	1.61902e7	−	2.80422e7i	0.708786	−	1.22765i
$879$	−1.10588e6	+	1.91543e6i	−0.0482763	+	0.0836170i
$880$	6.10632e6	+	1.05764e7i	0.265811	+	0.460398i
$881$	−3.82921e7			−1.66215			−0.831073	−	0.556163i	$-0.812273\pi$
$881$	−3.82921e7			−1.66215			−0.831073	+	0.556163i	$0.812273\pi$
$882$	1.22484e6	+	345017.i	0.0530162	+	0.0149338i
$883$	3.02825e7			1.30704			0.653521	−	0.756909i	$-0.273291\pi$
$883$	3.02825e7			1.30704			0.653521	+	0.756909i	$0.273291\pi$
$884$	6.32072e6	+	1.09478e7i	0.272042	+	0.471190i
$885$	−1.28953e6	+	2.23354e6i	−0.0553445	+	0.0958594i
$886$	9.49531e6	−	1.64464e7i	0.406373	−	0.703859i
$887$	1.40441e7	+	2.43250e7i	0.599354	+	1.03811i	0.992917	+	0.118814i	$0.0379092\pi$
$887$	1.40441e7	+	2.43250e7i	0.599354	+	1.03811i	−0.393562	+	0.919298i	$0.628757\pi$
$888$	209331.			0.00890843
$889$	−4.40104e6	−	3.42190e6i	−0.186768	−	0.145216i
$890$	1.38437e6			0.0585836
$891$	−1.18994e7	−	2.06103e7i	−0.502146	−	0.869742i
$892$	−1.35688e7	+	2.35019e7i	−0.570993	+	0.988989i
$893$	−2.07349e7	+	3.59140e7i	−0.870110	+	1.50707i
$894$	−3.99486e6	−	6.91930e6i	−0.167170	−	0.289547i
$895$	1.12723e7			0.470387
$896$	−2.88093e6	+	2.08531e7i	−0.119884	+	0.867762i
$897$	3.02843e7			1.25671
$898$	−2.20825e7	−	3.82480e7i	−0.913812	−	1.58277i
$899$	6.21610e6	−	1.07666e7i	0.256519	−	0.444303i
$900$	−66241.5	+	114734.i	−0.00272599	+	0.00472155i
$901$	−6.13301e6	−	1.06227e7i	−0.251688	−	0.435936i
$902$	−2.12616e7			−0.870122
$903$	2.58742e7	−	1.05244e7i	1.05596	−	0.429515i
$904$	1.16533e7			0.474273
$905$	1.89507e6	+	3.28236e6i	0.0769138	+	0.133219i
$906$	−1.48997e7	+	2.58071e7i	−0.603057	+	1.04452i
$907$	−7.52080e6	+	1.30264e7i	−0.303561	+	0.525783i	−0.976940	−	0.213515i	$-0.931509\pi$
$907$	−7.52080e6	+	1.30264e7i	−0.303561	+	0.525783i	0.673379	+	0.739297i	$0.264842\pi$
$908$	5.87832e6	+	1.01815e7i	0.236613	+	0.409825i
$909$	762198.			0.0305955
$910$	1.99799e7	−	8.12687e6i	0.799814	−	0.325327i
$911$	1.53071e7			0.611078			0.305539	−	0.952179i	$-0.401163\pi$
$911$	1.53071e7			0.611078			0.305539	+	0.952179i	$0.401163\pi$
$912$	−2.77709e7	−	4.81006e7i	−1.10561	−	1.91498i
$913$	1.91646e7	−	3.31941e7i	0.760891	−	1.31790i
$914$	1.42235e7	−	2.46359e7i	0.563173	−	0.975444i
$915$	−797305.	−	1.38097e6i	−0.0314827	−	0.0545296i
$916$	−2.02063e7			−0.795698
$917$	−376231.	+	2.72329e6i	−0.0147751	+	0.106947i
$918$	−1.81529e7			−0.710951
$919$	−1.21207e7	−	2.09936e7i	−0.473410	−	0.819970i	0.526127	−	0.850406i	$-0.323644\pi$
$919$	−1.21207e7	−	2.09936e7i	−0.473410	−	0.819970i	−0.999537	+	0.0304359i	$0.990310\pi$
$920$	2.19573e6	−	3.80312e6i	0.0855282	−	0.148139i
$921$	−5.02542e6	+	8.70428e6i	−0.195219	+	0.338130i
$922$	1.30731e7	+	2.26433e7i	0.506467	+	0.877227i
$923$	5.65425e7			2.18459
$924$	1.27618e7	+	9.92256e6i	0.491736	+	0.382335i
$925$	−96638.2			−0.00371360
$926$	2.41504e7	+	4.18297e7i	0.925544	+	1.60309i
$927$	−260967.	+	452008.i	−0.00997438	+	0.0172761i
$928$	9.35002e6	−	1.61947e7i	0.356404	−	0.617310i
$929$	1.05281e7	+	1.82352e7i	0.400231	+	0.693220i	0.993754	−	0.111597i	$-0.0355967\pi$
$929$	1.05281e7	+	1.82352e7i	0.400231	+	0.693220i	−0.593523	+	0.804817i	$0.702263\pi$
$930$	−1.22403e7			−0.464071
$931$	3.32674e7	−	3.24284e7i	1.25789	−	1.22617i
$932$	2.79191e7			1.05284
$933$	−1.75483e7	−	3.03946e7i	−0.659981	−	1.14312i
$934$	−8.55825e6	+	1.48233e7i	−0.321009	+	0.556005i
$935$	−3.28268e6	+	5.68576e6i	−0.122800	+	0.212696i
$936$	410142.	+	710388.i	0.0153019	+	0.0265037i
$937$	−1.43242e7			−0.532993			−0.266497	−	0.963836i	$-0.585866\pi$
$937$	−1.43242e7			−0.532993			−0.266497	+	0.963836i	$0.585866\pi$
$938$	2.48685e7	+	1.93358e7i	0.922873	+	0.717553i
$939$	−7.03600e6			−0.260413
$940$	3.79457e6	+	6.57239e6i	0.140069	+	0.242607i
$941$	5.63611e6	−	9.76203e6i	0.207494	−	0.359390i	−0.743431	−	0.668813i	$-0.766803\pi$
$941$	5.63611e6	−	9.76203e6i	0.207494	−	0.359390i	0.950924	+	0.309423i	$0.100136\pi$
$942$	5.92558e6	−	1.02634e7i	0.217572	−	0.376846i
$943$	7.85012e6	+	1.35968e7i	0.287473	+	0.497918i
$944$	−8.17782e6			−0.298681
$945$	−1.64201e6	+	1.18855e7i	−0.0598133	+	0.432949i
$946$	3.78584e7			1.37542
$947$	1.43075e7	+	2.47812e7i	0.518427	+	0.897941i	0.999771	+	0.0214096i	$0.00681542\pi$
$947$	1.43075e7	+	2.47812e7i	0.518427	+	0.897941i	−0.481344	+	0.876532i	$0.659851\pi$
$948$	−1.73787e7	+	3.01008e7i	−0.628054	+	1.08782i
$949$	−1.96431e7	+	3.40229e7i	−0.708020	+	1.22633i
$950$	6.24303e6	+	1.08132e7i	0.224433	+	0.388729i
$951$	−2.11958e7			−0.759974
$952$	−6.92831e6	+	2.81811e6i	−0.247762	+	0.100778i
$953$	−2.67535e7			−0.954219			−0.477109	−	0.878844i	$-0.658315\pi$
$953$	−2.67535e7			−0.954219			−0.477109	+	0.878844i	$0.658315\pi$
$954$	684403.	+	1.18542e6i	0.0243467	+	0.0421698i
$955$	6.43733e6	−	1.11498e7i	0.228401	−	0.395601i
$956$	−5.14350e6	+	8.90880e6i	−0.182018	+	0.315264i
$957$	9.00257e6	+	1.55929e7i	0.317751	+	0.550361i
$958$	1.64043e7			0.577490
$959$	−3.42486e7	+	1.39307e7i	−1.20253	+	0.489134i
$960$	−2.33669e6			−0.0818320
$961$	5.26182e6	+	9.11373e6i	0.183792	+	0.318338i
$962$	514509.	−	891155.i	0.0179248	−	0.0310467i
$963$	415417.	−	719523.i	0.0144350	−	0.0250022i
$964$	−1.88048e6	−	3.25709e6i	−0.0651743	−	0.112885i
$965$	1.92492e7			0.665417
$966$	4.21716e6	−	3.05252e7i	0.145404	−	1.05248i
$967$	−1.79212e7			−0.616311			−0.308155	−	0.951336i	$-0.599712\pi$
$967$	−1.79212e7			−0.616311			−0.308155	+	0.951336i	$0.599712\pi$
$968$	477494.	+	827043.i	0.0163787	+	0.0283687i
$969$	1.49293e7	−	2.58583e7i	0.510774	−	0.884687i
$970$	−7.86762e6	+	1.36271e7i	−0.268481	+	0.465023i
$971$	−1.69129e7	−	2.92940e7i	−0.575666	−	0.997082i	−0.995969	−	0.0896984i	$-0.971410\pi$
$971$	−1.69129e7	−	2.92940e7i	−0.575666	−	0.997082i	0.420303	−	0.907384i	$-0.361924\pi$
$972$	1.60480e6			0.0544823
$973$	−2.88974e7	−	2.24683e7i	−0.978534	−	0.760831i
$974$	1.22144e7			0.412549
$975$	−4.58136e6	−	7.93515e6i	−0.154342	−	0.267327i
$976$	2.52813e6	−	4.37885e6i	0.0849523	−	0.147142i
$977$	−1.81082e7	+	3.13644e7i	−0.606931	+	1.05124i	0.384812	+	0.922995i	$0.374266\pi$
$977$	−1.81082e7	+	3.13644e7i	−0.606931	+	1.05124i	−0.991743	+	0.128241i	$0.959067\pi$
$978$	3.34510e7	+	5.79389e7i	1.11831	+	1.93697i
$979$	−2.96564e6			−0.0988922
$980$	−2.09542e6	−	8.23967e6i	−0.0696958	−	0.274059i
$981$	−1.91822e6			−0.0636393
$982$	1.12957e7	+	1.95648e7i	0.373796	+	0.647434i
$983$	−5.36928e6	+	9.29987e6i	−0.177228	+	0.306968i	−0.940930	−	0.338601i	$-0.890046\pi$
$983$	−5.36928e6	+	9.29987e6i	−0.177228	+	0.306968i	0.763702	+	0.645569i	$0.223380\pi$
$984$	−5.14479e6	+	8.91104e6i	−0.169387	+	0.293387i
$985$	−3.08626e6	−	5.34555e6i	−0.101354	−	0.175551i
$986$	1.43269e7			0.469311
$987$	−2.44458e7	−	1.90071e7i	−0.798749	−	0.621044i
$988$	−5.15029e7			−1.67857
$989$	−1.39779e7	−	2.42105e7i	−0.454414	−	0.787068i
$990$	366324.	−	634493.i	0.0118789	−	0.0205749i
$991$	−2.64503e6	+	4.58133e6i	−0.0855552	+	0.148186i	−0.905628	−	0.424074i	$-0.860600\pi$
$991$	−2.64503e6	+	4.58133e6i	−0.0855552	+	0.148186i	0.820072	+	0.572260i	$0.193933\pi$
$992$	−1.36168e7	−	2.35850e7i	−0.439335	−	0.760951i
$993$	−2.39260e7			−0.770011
$994$	7.87368e6	−	5.69923e7i	0.252762	−	1.82958i
$995$	−2.22660e7			−0.712991
$996$	1.59504e7	+	2.76268e7i	0.509474	+	0.882435i
$997$	8.50726e6	−	1.47350e7i	0.271051	−	0.469475i	−0.698080	−	0.716020i	$-0.745962\pi$
$997$	8.50726e6	−	1.47350e7i	0.271051	−	0.469475i	0.969131	+	0.246545i	$0.0792953\pi$
$998$	−3.39930e7	+	5.88776e7i	−1.08035	+	1.87122i
$999$	286204.	+	495719.i	0.00907322	+	0.0157153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.6.e.a.11.5	✓	12
7.2	even	3	inner	35.6.e.a.16.5	yes	12
7.3	odd	6		245.6.a.h.1.2		6
7.4	even	3		245.6.a.i.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.e.a.11.5	✓	12	1.1	even	1	trivial
35.6.e.a.16.5	yes	12	7.2	even	3	inner
245.6.a.h.1.2		6	7.3	odd	6
245.6.a.i.1.2		6	7.4	even	3

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.61366 + 6.25905i) q^{2} +(7.96046 - 13.7879i) q^{3} +(-10.1171 + 17.5234i) q^{4} +(12.5000 + 21.6506i) q^{5} +115.066 q^{6} +(102.346 + 79.5760i) q^{7} +85.0347 q^{8} +(-5.23796 - 9.07242i) q^{9} +O(q^{10})\)	\(q+(3.61366 + 6.25905i) q^{2} +(7.96046 - 13.7879i) q^{3} +(-10.1171 + 17.5234i) q^{4} +(12.5000 + 21.6506i) q^{5} +115.066 q^{6} +(102.346 + 79.5760i) q^{7} +85.0347 q^{8} +(-5.23796 - 9.07242i) q^{9} +(-90.3416 + 156.476i) q^{10} +(193.533 - 335.209i) q^{11} +(161.074 + 278.989i) q^{12} -920.823 q^{13} +(-128.227 + 928.148i) q^{14} +398.023 q^{15} +(631.035 + 1092.99i) q^{16} +(-339.236 + 587.575i) q^{17} +(37.8565 - 65.5694i) q^{18} +(-1382.09 - 2393.86i) q^{19} -505.857 q^{20} +(1911.91 - 777.675i) q^{21} +2797.46 q^{22} +(-1032.86 - 1788.97i) q^{23} +(676.916 - 1172.45i) q^{24} +(-312.500 + 541.266i) q^{25} +(-3327.54 - 5763.48i) q^{26} +3702.00 q^{27} +(-2429.89 + 988.365i) q^{28} -2921.75 q^{29} +(1438.32 + 2491.25i) q^{30} +(-2127.53 + 3684.99i) q^{31} +(-3200.15 + 5542.81i) q^{32} +(-3081.23 - 5336.84i) q^{33} -4903.55 q^{34} +(-443.548 + 3210.55i) q^{35} +211.973 q^{36} +(77.3106 + 133.906i) q^{37} +(9988.85 - 17301.2i) q^{38} +(-7330.18 + 12696.2i) q^{39} +(1062.93 + 1841.06i) q^{40} -7600.35 q^{41} +(11776.5 + 9156.47i) q^{42} +13533.2 q^{43} +(3916.01 + 6782.72i) q^{44} +(130.949 - 226.811i) q^{45} +(7464.84 - 12929.5i) q^{46} +(-7501.27 - 12992.6i) q^{47} +20093.3 q^{48} +(4142.32 + 16288.5i) q^{49} -4517.08 q^{50} +(5400.96 + 9354.74i) q^{51} +(9316.09 - 16135.9i) q^{52} +(-9039.43 + 15656.8i) q^{53} +(13377.8 + 23171.0i) q^{54} +9676.66 q^{55} +(8702.94 + 6766.72i) q^{56} -44008.4 q^{57} +(-10558.2 - 18287.4i) q^{58} +(-3239.84 + 5611.57i) q^{59} +(-4026.86 + 6974.72i) q^{60} +(-2003.16 - 3469.58i) q^{61} -30752.7 q^{62} +(185.863 - 1345.34i) q^{63} -5870.74 q^{64} +(-11510.3 - 19936.4i) q^{65} +(22269.1 - 38571.1i) q^{66} +(16810.1 - 29116.0i) q^{67} +(-6864.21 - 11889.2i) q^{68} -32888.3 q^{69} +(-21697.8 + 8825.66i) q^{70} -61404.3 q^{71} +(-445.409 - 771.471i) q^{72} +(21332.2 - 36948.4i) q^{73} +(-558.749 + 967.782i) q^{74} +(4975.29 + 8617.45i) q^{75} +55931.4 q^{76} +(46481.9 - 18906.7i) q^{77} -105955. q^{78} +(53946.3 + 93437.7i) q^{79} +(-15775.9 + 27324.6i) q^{80} +(30742.5 - 53247.5i) q^{81} +(-27465.1 - 47570.9i) q^{82} +99024.8 q^{83} +(-5715.54 + 41371.0i) q^{84} -16961.8 q^{85} +(48904.3 + 84704.8i) q^{86} +(-23258.5 + 40284.8i) q^{87} +(16457.0 - 28504.4i) q^{88} +(-3830.92 - 6635.35i) q^{89} +1892.82 q^{90} +(-94242.3 - 73275.4i) q^{91} +41798.5 q^{92} +(33872.2 + 58668.4i) q^{93} +(54214.2 - 93901.7i) q^{94} +(34552.4 - 59846.4i) q^{95} +(50949.3 + 88246.7i) q^{96} +87087.4 q^{97} +(-86981.8 + 84788.3i) q^{98} -4054.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} - 20 q^{3} - 31 q^{4} + 150 q^{5} + 192 q^{6} - 20 q^{7} - 270 q^{8} - 378 q^{9}+O(q^{10}) \) 12 * q + 5 * q^2 - 20 * q^3 - 31 * q^4 + 150 * q^5 + 192 * q^6 - 20 * q^7 - 270 * q^8 - 378 * q^9	\( 12 q + 5 q^{2} - 20 q^{3} - 31 q^{4} + 150 q^{5} + 192 q^{6} - 20 q^{7} - 270 q^{8} - 378 q^{9} - 125 q^{10} + 924 q^{11} - 370 q^{12} - 300 q^{13} + 3409 q^{14} - 1000 q^{15} - 435 q^{16} - 1540 q^{17} - 195 q^{18} - 92 q^{19} - 1550 q^{20} + 7288 q^{21} - 13710 q^{22} + 3920 q^{23} + 7200 q^{24} - 3750 q^{25} - 2635 q^{26} + 4120 q^{27} - 6015 q^{28} + 2528 q^{29} + 2400 q^{30} + 7160 q^{31} - 9105 q^{32} - 4460 q^{33} + 4332 q^{34} - 2500 q^{35} - 52750 q^{36} + 14170 q^{37} + 46215 q^{38} + 15376 q^{39} - 3375 q^{40} + 8196 q^{41} + 10500 q^{42} - 48920 q^{43} + 27873 q^{44} + 9450 q^{45} - 6815 q^{46} - 42940 q^{47} + 23220 q^{48} - 17856 q^{49} - 6250 q^{50} + 42008 q^{51} + 36115 q^{52} + 2450 q^{53} - 19566 q^{54} + 46200 q^{55} + 67998 q^{56} - 194200 q^{57} + 36110 q^{58} + 64600 q^{59} + 9250 q^{60} - 73620 q^{61} + 222880 q^{62} - 57780 q^{63} - 315994 q^{64} - 3750 q^{65} + 139138 q^{66} + 142620 q^{67} - 124330 q^{68} + 34688 q^{69} + 34475 q^{70} - 308512 q^{71} + 117495 q^{72} + 5120 q^{73} - 2785 q^{74} - 12500 q^{75} + 15550 q^{76} + 44230 q^{77} - 428180 q^{78} + 222504 q^{79} + 10875 q^{80} + 43986 q^{81} - 31665 q^{82} + 359160 q^{83} - 19966 q^{84} - 77000 q^{85} + 207160 q^{86} + 209300 q^{87} + 45145 q^{88} - 41648 q^{89} - 9750 q^{90} - 31376 q^{91} - 584370 q^{92} + 198520 q^{93} + 333699 q^{94} + 2300 q^{95} - 61824 q^{96} - 147960 q^{97} - 101815 q^{98} - 381544 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 - 20 * q^3 - 31 * q^4 + 150 * q^5 + 192 * q^6 - 20 * q^7 - 270 * q^8 - 378 * q^9 - 125 * q^10 + 924 * q^11 - 370 * q^12 - 300 * q^13 + 3409 * q^14 - 1000 * q^15 - 435 * q^16 - 1540 * q^17 - 195 * q^18 - 92 * q^19 - 1550 * q^20 + 7288 * q^21 - 13710 * q^22 + 3920 * q^23 + 7200 * q^24 - 3750 * q^25 - 2635 * q^26 + 4120 * q^27 - 6015 * q^28 + 2528 * q^29 + 2400 * q^30 + 7160 * q^31 - 9105 * q^32 - 4460 * q^33 + 4332 * q^34 - 2500 * q^35 - 52750 * q^36 + 14170 * q^37 + 46215 * q^38 + 15376 * q^39 - 3375 * q^40 + 8196 * q^41 + 10500 * q^42 - 48920 * q^43 + 27873 * q^44 + 9450 * q^45 - 6815 * q^46 - 42940 * q^47 + 23220 * q^48 - 17856 * q^49 - 6250 * q^50 + 42008 * q^51 + 36115 * q^52 + 2450 * q^53 - 19566 * q^54 + 46200 * q^55 + 67998 * q^56 - 194200 * q^57 + 36110 * q^58 + 64600 * q^59 + 9250 * q^60 - 73620 * q^61 + 222880 * q^62 - 57780 * q^63 - 315994 * q^64 - 3750 * q^65 + 139138 * q^66 + 142620 * q^67 - 124330 * q^68 + 34688 * q^69 + 34475 * q^70 - 308512 * q^71 + 117495 * q^72 + 5120 * q^73 - 2785 * q^74 - 12500 * q^75 + 15550 * q^76 + 44230 * q^77 - 428180 * q^78 + 222504 * q^79 + 10875 * q^80 + 43986 * q^81 - 31665 * q^82 + 359160 * q^83 - 19966 * q^84 - 77000 * q^85 + 207160 * q^86 + 209300 * q^87 + 45145 * q^88 - 41648 * q^89 - 9750 * q^90 - 31376 * q^91 - 584370 * q^92 + 198520 * q^93 + 333699 * q^94 + 2300 * q^95 - 61824 * q^96 - 147960 * q^97 - 101815 * q^98 - 381544 * q^99

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