LMFDB - Embedded newform 74.7.d.a.31.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,7,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, 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:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 $ x^18 + 8470x^16 + 28007049x^14 + 45282701078x^12 + 36580026955844x^10 + 13599755691108102x^8 + 2140498199687229457x^6 + 117348928221103362406x^4 + 1596692663909213634249x^2 + 657611720884512028944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.8
Root			$38.5266i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 4.00000i) q^{2} +42.5266i q^{3} +32.0000i q^{4} +(-72.1936 + 72.1936i) q^{5} +(-170.107 + 170.107i) q^{6} +66.7198 q^{7} +(-128.000 + 128.000i) q^{8} -1079.52 q^{9} +O(q^{10})$	\(q+(4.00000 + 4.00000i) q^{2} +42.5266i q^{3} +32.0000i q^{4} +(-72.1936 + 72.1936i) q^{5} +(-170.107 + 170.107i) q^{6} +66.7198 q^{7} +(-128.000 + 128.000i) q^{8} -1079.52 q^{9} -577.548 q^{10} +1344.94i q^{11} -1360.85 q^{12} +(906.141 - 906.141i) q^{13} +(266.879 + 266.879i) q^{14} +(-3070.15 - 3070.15i) q^{15} -1024.00 q^{16} +(939.258 - 939.258i) q^{17} +(-4318.06 - 4318.06i) q^{18} +(-203.830 + 203.830i) q^{19} +(-2310.19 - 2310.19i) q^{20} +2837.37i q^{21} +(-5379.78 + 5379.78i) q^{22} +(14205.2 - 14205.2i) q^{23} +(-5443.41 - 5443.41i) q^{24} +5201.18i q^{25} +7249.12 q^{26} -14906.3i q^{27} +2135.03i q^{28} +(-17034.8 - 17034.8i) q^{29} -24561.2i q^{30} +(4668.52 + 4668.52i) q^{31} +(-4096.00 - 4096.00i) q^{32} -57196.0 q^{33} +7514.07 q^{34} +(-4816.74 + 4816.74i) q^{35} -34544.5i q^{36} +(-40231.9 + 30775.3i) q^{37} -1630.64 q^{38} +(38535.1 + 38535.1i) q^{39} -18481.5i q^{40} +56227.9i q^{41} +(-11349.5 + 11349.5i) q^{42} +(-20675.8 + 20675.8i) q^{43} -43038.2 q^{44} +(77934.1 - 77934.1i) q^{45} +113641. q^{46} -62008.1 q^{47} -43547.3i q^{48} -113197. q^{49} +(-20804.7 + 20804.7i) q^{50} +(39943.5 + 39943.5i) q^{51} +(28996.5 + 28996.5i) q^{52} -17422.4 q^{53} +(59625.1 - 59625.1i) q^{54} +(-97096.3 - 97096.3i) q^{55} +(-8540.13 + 8540.13i) q^{56} +(-8668.21 - 8668.21i) q^{57} -136278. i q^{58} +(69920.0 - 69920.0i) q^{59} +(98244.8 - 98244.8i) q^{60} +(296679. + 296679. i) q^{61} +37348.2i q^{62} -72025.1 q^{63} -32768.0i q^{64} +130835. i q^{65} +(-228784. - 228784. i) q^{66} +423093. i q^{67} +(30056.3 + 30056.3i) q^{68} +(604097. + 604097. i) q^{69} -38533.9 q^{70} +55080.3 q^{71} +(138178. - 138178. i) q^{72} +143666. i q^{73} +(-284029. - 37826.4i) q^{74} -221189. q^{75} +(-6522.56 - 6522.56i) q^{76} +89734.4i q^{77} +308281. i q^{78} +(171921. - 171921. i) q^{79} +(73926.2 - 73926.2i) q^{80} -153054. q^{81} +(-224912. + 224912. i) q^{82} +276226. q^{83} -90795.8 q^{84} +135617. i q^{85} -165406. q^{86} +(724433. - 724433. i) q^{87} +(-172153. - 172153. i) q^{88} +(507572. + 507572. i) q^{89} +623473. q^{90} +(60457.5 - 60457.5i) q^{91} +(454565. + 454565. i) q^{92} +(-198537. + 198537. i) q^{93} +(-248032. - 248032. i) q^{94} -29430.4i q^{95} +(174189. - 174189. i) q^{96} +(-643511. + 643511. i) q^{97} +(-452790. - 452790. i) q^{98} -1.45189e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) $ 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9 + 2352 * q^10 - 2048 * q^12 - 6766 * q^13 - 416 * q^14 - 2136 * q^15 - 18432 * q^16 - 9134 * q^17 - 16168 * q^18 + 7578 * q^19 + 9408 * q^20 + 8928 * q^22 - 50578 * q^23 - 8192 * q^24 - 54128 * q^26 - 42950 * q^29 - 17358 * q^31 - 73728 * q^32 - 11056 * q^33 - 73072 * q^34 + 62152 * q^35 - 238242 * q^37 + 60624 * q^38 + 31572 * q^39 + 229024 * q^42 - 65470 * q^43 + 71424 * q^44 - 482358 * q^45 - 404624 * q^46 + 232192 * q^47 + 791686 * q^49 + 93752 * q^50 - 386848 * q^51 - 216512 * q^52 + 49972 * q^53 - 144560 * q^54 + 160168 * q^55 + 13312 * q^56 + 488476 * q^57 - 181570 * q^59 + 68352 * q^60 + 508802 * q^61 + 404788 * q^63 - 44224 * q^66 - 292288 * q^68 + 604532 * q^69 + 497216 * q^70 - 202632 * q^71 + 517376 * q^72 - 1191224 * q^74 + 2476628 * q^75 + 242496 * q^76 + 1752858 * q^79 - 301056 * q^80 + 2760658 * q^81 - 145808 * q^82 + 2371616 * q^83 + 1832192 * q^84 - 523760 * q^86 - 4188080 * q^87 + 285696 * q^88 + 1148346 * q^89 - 3858864 * q^90 + 433120 * q^91 - 1618496 * q^92 + 1589664 * q^93 + 928768 * q^94 + 262144 * q^96 - 1670270 * q^97 + 3166744 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	4.00000	+	4.00000i	0.500000	+	0.500000i
$2$	4.00000	+	4.00000i	0.500000	+	0.500000i
$3$			42.5266i			1.57506i	0.616276	+	0.787531i	$0.288641\pi$
$3$			42.5266i			1.57506i	−0.616276	+	0.787531i	$0.711359\pi$
$4$			32.0000i			0.500000i
$5$	−72.1936	+	72.1936i	−0.577548	+	0.577548i	−0.934227	−	0.356679i	$-0.883909\pi$
$5$	−72.1936	+	72.1936i	−0.577548	+	0.577548i	0.356679	+	0.934227i	$0.383909\pi$
$6$	−170.107	+	170.107i	−0.787531	+	0.787531i
$7$	66.7198			0.194518			0.0972592	−	0.995259i	$-0.468992\pi$
$7$	66.7198			0.194518			0.0972592	+	0.995259i	$0.468992\pi$
$8$	−128.000	+	128.000i	−0.250000	+	0.250000i
$9$	−1079.52			−1.48082
$10$	−577.548			−0.577548
$11$			1344.94i			1.01048i	0.862980	+	0.505238i	$0.168595\pi$
$11$			1344.94i			1.01048i	−0.862980	+	0.505238i	$0.831405\pi$
$12$	−1360.85			−0.787531
$13$	906.141	−	906.141i	0.412444	−	0.412444i	−0.470145	−	0.882589i	$-0.655798\pi$
$13$	906.141	−	906.141i	0.412444	−	0.412444i	0.882589	+	0.470145i	$0.155798\pi$
$14$	266.879	+	266.879i	0.0972592	+	0.0972592i
$15$	−3070.15	−	3070.15i	−0.909674	−	0.909674i
$16$	−1024.00			−0.250000
$17$	939.258	−	939.258i	0.191178	−	0.191178i	−0.605027	−	0.796205i	$-0.706838\pi$
$17$	939.258	−	939.258i	0.191178	−	0.191178i	0.796205	+	0.605027i	$0.206838\pi$
$18$	−4318.06	−	4318.06i	−0.740409	−	0.740409i
$19$	−203.830	+	203.830i	−0.0297172	+	0.0297172i	−0.721809	−	0.692092i	$-0.756689\pi$
$19$	−203.830	+	203.830i	−0.0297172	+	0.0297172i	0.692092	+	0.721809i	$0.256689\pi$
$20$	−2310.19	−	2310.19i	−0.288774	−	0.288774i
$21$			2837.37i			0.306378i
$22$	−5379.78	+	5379.78i	−0.505238	+	0.505238i
$23$	14205.2	−	14205.2i	1.16751	−	1.16751i	0.184724	−	0.982790i	$-0.440861\pi$
$23$	14205.2	−	14205.2i	1.16751	−	1.16751i	0.982790	−	0.184724i	$-0.0591392\pi$
$24$	−5443.41	−	5443.41i	−0.393765	−	0.393765i
$25$			5201.18i			0.332876i
$26$	7249.12			0.412444
$27$		−	14906.3i		−	0.757317i
$28$			2135.03i			0.0972592i
$29$	−17034.8	−	17034.8i	−0.698462	−	0.698462i	0.265617	−	0.964079i	$-0.414424\pi$
$29$	−17034.8	−	17034.8i	−0.698462	−	0.698462i	−0.964079	+	0.265617i	$0.914424\pi$
$30$		−	24561.2i		−	0.909674i
$31$	4668.52	+	4668.52i	0.156709	+	0.156709i	0.781107	−	0.624398i	$-0.214655\pi$
$31$	4668.52	+	4668.52i	0.156709	+	0.156709i	−0.624398	+	0.781107i	$0.714655\pi$
$32$	−4096.00	−	4096.00i	−0.125000	−	0.125000i
$33$	−57196.0			−1.59156
$34$	7514.07			0.191178
$35$	−4816.74	+	4816.74i	−0.112344	+	0.112344i
$36$		−	34544.5i		−	0.740409i
$37$	−40231.9	+	30775.3i	−0.794265	+	0.607571i
$37$	−40231.9	+	30775.3i	−0.794265	+	0.607571i
$38$	−1630.64			−0.0297172
$39$	38535.1	+	38535.1i	0.649625	+	0.649625i
$40$		−	18481.5i		−	0.288774i
$41$			56227.9i			0.815831i	0.913020	+	0.407916i	$0.133744\pi$
$41$			56227.9i			0.815831i	−0.913020	+	0.407916i	$0.866256\pi$
$42$	−11349.5	+	11349.5i	−0.153189	+	0.153189i
$43$	−20675.8	+	20675.8i	−0.260050	+	0.260050i	−0.825074	−	0.565024i	$-0.808867\pi$
$43$	−20675.8	+	20675.8i	−0.260050	+	0.260050i	0.565024	+	0.825074i	$0.308867\pi$
$44$	−43038.2			−0.505238
$45$	77934.1	−	77934.1i	0.855244	−	0.855244i
$46$	113641.			1.16751
$47$	−62008.1			−0.597248			−0.298624	−	0.954371i	$-0.596528\pi$
$47$	−62008.1			−0.597248			−0.298624	+	0.954371i	$0.596528\pi$
$48$		−	43547.3i		−	0.393765i
$49$	−113197.			−0.962163
$50$	−20804.7	+	20804.7i	−0.166438	+	0.166438i
$51$	39943.5	+	39943.5i	0.301117	+	0.301117i
$52$	28996.5	+	28996.5i	0.206222	+	0.206222i
$53$	−17422.4			−0.117025			−0.0585127	−	0.998287i	$-0.518636\pi$
$53$	−17422.4			−0.117025			−0.0585127	+	0.998287i	$0.518636\pi$
$54$	59625.1	−	59625.1i	0.378658	−	0.378658i
$55$	−97096.3	−	97096.3i	−0.583599	−	0.583599i
$56$	−8540.13	+	8540.13i	−0.0486296	+	0.0486296i
$57$	−8668.21	−	8668.21i	−0.0468063	−	0.0468063i
$58$		−	136278.i		−	0.698462i
$59$	69920.0	−	69920.0i	0.340444	−	0.340444i	−0.516090	−	0.856534i	$-0.672613\pi$
$59$	69920.0	−	69920.0i	0.340444	−	0.340444i	0.856534	+	0.516090i	$0.172613\pi$
$60$	98244.8	−	98244.8i	0.454837	−	0.454837i
$61$	296679.	+	296679.i	1.30706	+	1.30706i	0.923524	+	0.383541i	$0.125295\pi$
$61$	296679.	+	296679.i	1.30706	+	1.30706i	0.383541	+	0.923524i	$0.374705\pi$
$62$			37348.2i			0.156709i
$63$	−72025.1			−0.288046
$64$		−	32768.0i		−	0.125000i
$65$			130835.i			0.476413i
$66$	−228784.	−	228784.i	−0.795781	−	0.795781i
$67$			423093.i			1.40673i	0.710828	+	0.703366i	$0.248320\pi$
$67$			423093.i			1.40673i	−0.710828	+	0.703366i	$0.751680\pi$
$68$	30056.3	+	30056.3i	0.0955891	+	0.0955891i
$69$	604097.	+	604097.i	1.83891	+	1.83891i
$70$	−38533.9			−0.112344
$71$	55080.3			0.153894			0.0769469	−	0.997035i	$-0.475483\pi$
$71$	55080.3			0.153894			0.0769469	+	0.997035i	$0.475483\pi$
$72$	138178.	−	138178.i	0.370204	−	0.370204i
$73$			143666.i			0.369305i	0.982804	+	0.184652i	$0.0591159\pi$
$73$			143666.i			0.369305i	−0.982804	+	0.184652i	$0.940884\pi$
$74$	−284029.	−	37826.4i	−0.700918	−	0.0933470i
$75$	−221189.			−0.524299
$76$	−6522.56	−	6522.56i	−0.0148586	−	0.0148586i
$77$			89734.4i			0.196556i
$78$			308281.i			0.649625i
$79$	171921.	−	171921.i	0.348696	−	0.348696i	−0.510927	−	0.859624i	$-0.670698\pi$
$79$	171921.	−	171921.i	0.348696	−	0.348696i	0.859624	+	0.510927i	$0.170698\pi$
$80$	73926.2	−	73926.2i	0.144387	−	0.144387i
$81$	−153054.			−0.287997
$82$	−224912.	+	224912.i	−0.407916	+	0.407916i
$83$	276226.			0.483092			0.241546	−	0.970389i	$-0.422346\pi$
$83$	276226.			0.483092			0.241546	+	0.970389i	$0.422346\pi$
$84$	−90795.8			−0.153189
$85$			135617.i			0.220829i
$86$	−165406.			−0.260050
$87$	724433.	−	724433.i	1.10012	−	1.10012i
$88$	−172153.	−	172153.i	−0.252619	−	0.252619i
$89$	507572.	+	507572.i	0.719992	+	0.719992i	0.968603	−	0.248611i	$-0.0799741\pi$
$89$	507572.	+	507572.i	0.719992	+	0.719992i	−0.248611	+	0.968603i	$0.579974\pi$
$90$	623473.			0.855244
$91$	60457.5	−	60457.5i	0.0802280	−	0.0802280i
$92$	454565.	+	454565.i	0.583757	+	0.583757i
$93$	−198537.	+	198537.i	−0.246827	+	0.246827i
$94$	−248032.	−	248032.i	−0.298624	−	0.298624i
$95$		−	29430.4i		−	0.0343262i
$96$	174189.	−	174189.i	0.196883	−	0.196883i
$97$	−643511.	+	643511.i	−0.705084	+	0.705084i	−0.965497	−	0.260413i	$-0.916141\pi$
$97$	−643511.	+	643511.i	−0.705084	+	0.705084i	0.260413	+	0.965497i	$0.416141\pi$
$98$	−452790.	−	452790.i	−0.481081	−	0.481081i
$99$		−	1.45189e6i		−	1.49633i
$100$	−166438.			−0.166438
$101$			280355.i			0.272110i	0.990701	+	0.136055i	$0.0434424\pi$
$101$			280355.i			0.272110i	−0.990701	+	0.136055i	$0.956558\pi$
$102$			319548.i			0.301117i
$103$	−1.15576e6	−	1.15576e6i	−1.05768	−	1.05768i	−0.998231	−	0.0594525i	$-0.981065\pi$
$103$	−1.15576e6	−	1.15576e6i	−1.05768	−	1.05768i	−0.0594525	−	0.998231i	$-0.518935\pi$
$104$			231972.i			0.206222i
$105$	−204840.	−	204840.i	−0.176948	−	0.176948i
$106$	−69689.5	−	69689.5i	−0.0585127	−	0.0585127i
$107$	−263375.			−0.214993			−0.107496	−	0.994205i	$-0.534283\pi$
$107$	−263375.			−0.214993			−0.107496	+	0.994205i	$0.534283\pi$
$108$	477001.			0.378658
$109$	1.21825e6	−	1.21825e6i	0.940710	−	0.940710i	−0.0576282	−	0.998338i	$-0.518354\pi$
$109$	1.21825e6	−	1.21825e6i	0.940710	−	0.940710i	0.998338	+	0.0576282i	$0.0183538\pi$
$110$		−	776770.i		−	0.583599i
$111$	−1.30877e6	−	1.71093e6i	−0.956962	−	1.25102i
$112$	−68321.1			−0.0486296
$113$	−872186.	−	872186.i	−0.604469	−	0.604469i	0.337026	−	0.941495i	$-0.390579\pi$
$113$	−872186.	−	872186.i	−0.604469	−	0.604469i	−0.941495	+	0.337026i	$0.890579\pi$
$114$		−	69345.7i		−	0.0468063i
$115$			2.05104e6i			1.34859i
$116$	545113.	−	545113.i	0.349231	−	0.349231i
$117$	−978193.	+	978193.i	−0.610755	+	0.610755i
$118$	559360.			0.340444
$119$	62667.1	−	62667.1i	0.0371877	−	0.0371877i
$120$	785958.			0.454837
$121$	−37314.2			−0.0210629
$122$			2.37343e6i			1.30706i
$123$	−2.39118e6			−1.28498
$124$	−149393.	+	149393.i	−0.0783546	+	0.0783546i
$125$	−1.50352e6	−	1.50352e6i	−0.769800	−	0.769800i
$126$	−288100.	−	288100.i	−0.144023	−	0.144023i
$127$	−3.41037e6			−1.66491			−0.832455	−	0.554093i	$-0.813065\pi$
$127$	−3.41037e6			−1.66491			−0.832455	+	0.554093i	$0.813065\pi$
$128$	131072.	−	131072.i	0.0625000	−	0.0625000i
$129$	−879271.	−	879271.i	−0.409594	−	0.409594i
$130$	−523340.	+	523340.i	−0.238207	+	0.238207i
$131$	157660.	+	157660.i	0.0701307	+	0.0701307i	0.741302	−	0.671171i	$-0.234209\pi$
$131$	157660.	+	157660.i	0.0701307	+	0.0701307i	−0.671171	+	0.741302i	$0.734209\pi$
$132$		−	1.83027e6i		−	0.795781i
$133$	−13599.5	+	13599.5i	−0.00578053	+	0.00578053i
$134$	−1.69237e6	+	1.69237e6i	−0.703366	+	0.703366i
$135$	1.07614e6	+	1.07614e6i	0.437387	+	0.437387i
$136$			240450.i			0.0955891i
$137$	2.90771e6			1.13081			0.565405	−	0.824813i	$-0.308720\pi$
$137$	2.90771e6			1.13081			0.565405	+	0.824813i	$0.308720\pi$
$138$			4.83278e6i			1.83891i
$139$			52103.0i			0.0194007i	0.999953	+	0.00970036i	$0.00308777\pi$
$139$			52103.0i			0.0194007i	−0.999953	+	0.00970036i	$0.996912\pi$
$140$	−154136.	−	154136.i	−0.0561719	−	0.0561719i
$141$		−	2.63700e6i		−	0.940702i
$142$	220321.	+	220321.i	0.0769469	+	0.0769469i
$143$	1.21871e6	+	1.21871e6i	0.416765	+	0.416765i
$144$	1.10542e6			0.370204
$145$	2.45960e6			0.806791
$146$	−574663.	+	574663.i	−0.184652	+	0.184652i
$147$		−	4.81391e6i		−	1.51546i
$148$	−984810.	−	1.28742e6i	−0.303786	−	0.397133i
$149$	4.15510e6			1.25610			0.628048	−	0.778175i	$-0.283854\pi$
$149$	4.15510e6			1.25610			0.628048	+	0.778175i	$0.283854\pi$
$150$	−884755.	−	884755.i	−0.262150	−	0.262150i
$151$			1.94508e6i			0.564946i	0.959275	+	0.282473i	$0.0911548\pi$
$151$			1.94508e6i			0.564946i	−0.959275	+	0.282473i	$0.908845\pi$
$152$		−	52180.5i		−	0.0148586i
$153$	−1.01394e6	+	1.01394e6i	−0.283100	+	0.283100i
$154$	−358938.	+	358938.i	−0.0982781	+	0.0982781i
$155$	−674075.			−0.181014
$156$	−1.23312e6	+	1.23312e6i	−0.324813	+	0.324813i
$157$	7.10847e6			1.83687			0.918433	−	0.395577i	$-0.129455\pi$
$157$	7.10847e6			1.83687			0.918433	+	0.395577i	$0.129455\pi$
$158$	1.37537e6			0.348696
$159$		−	740915.i		−	0.184322i
$160$	591410.			0.144387
$161$	947765.	−	947765.i	0.227103	−	0.227103i
$162$	−612214.	−	612214.i	−0.143999	−	0.143999i
$163$	4.71540e6	+	4.71540e6i	1.08882	+	1.08882i	0.995650	+	0.0931682i	$0.0296994\pi$
$163$	4.71540e6	+	4.71540e6i	1.08882	+	1.08882i	0.0931682	+	0.995650i	$0.470301\pi$
$164$	−1.79929e6			−0.407916
$165$	4.12918e6	−	4.12918e6i	0.919204	−	0.919204i
$166$	1.10490e6	+	1.10490e6i	0.241546	+	0.241546i
$167$	3.71671e6	−	3.71671e6i	0.798012	−	0.798012i	−0.184770	−	0.982782i	$-0.559154\pi$
$167$	3.71671e6	−	3.71671e6i	0.798012	−	0.798012i	0.982782	+	0.184770i	$0.0591541\pi$
$168$	−363183.	−	363183.i	−0.0765946	−	0.0765946i
$169$			3.18463e6i			0.659779i
$170$	−542467.	+	542467.i	−0.110415	+	0.110415i
$171$	220038.	−	220038.i	0.0440057	−	0.0440057i
$172$	−661625.	−	661625.i	−0.130025	−	0.130025i
$173$		−	1.60808e6i		−	0.310577i	−0.987869	−	0.155288i	$-0.950369\pi$
$173$		−	1.60808e6i		−	0.310577i	0.987869	−	0.155288i	$-0.0496307\pi$
$174$	5.79546e6			1.10012
$175$			347022.i			0.0647504i
$176$		−	1.37722e6i		−	0.252619i
$177$	2.97346e6	+	2.97346e6i	0.536220	+	0.536220i
$178$			4.06058e6i			0.719992i
$179$	828341.	+	828341.i	0.144428	+	0.144428i	0.775623	−	0.631196i	$-0.217436\pi$
$179$	828341.	+	828341.i	0.144428	+	0.144428i	−0.631196	+	0.775623i	$0.717436\pi$
$180$	2.49389e6	+	2.49389e6i	0.427622	+	0.427622i
$181$	−8.87560e6			−1.49679			−0.748397	−	0.663251i	$-0.769176\pi$
$181$	−8.87560e6			−1.49679			−0.748397	+	0.663251i	$0.769176\pi$
$182$	483660.			0.0802280
$183$	−1.26168e7	+	1.26168e7i	−2.05871	+	2.05871i
$184$			3.63652e6i			0.583757i
$185$	682706.	−	5.12626e6i	0.107825	−	0.809628i
$186$	−1.58829e6			−0.246827
$187$	1.26325e6	+	1.26325e6i	0.193181	+	0.193181i
$188$		−	1.98426e6i		−	0.298624i
$189$		−	994543.i		−	0.147312i
$190$	117722.	−	117722.i	0.0171631	−	0.0171631i
$191$	−3.57220e6	+	3.57220e6i	−0.512668	+	0.512668i	−0.915343	−	0.402675i	$-0.868080\pi$
$191$	−3.57220e6	+	3.57220e6i	−0.512668	+	0.512668i	0.402675	+	0.915343i	$0.368080\pi$
$192$	1.39351e6			0.196883
$193$	2.14576e6	−	2.14576e6i	0.298476	−	0.298476i	−0.541941	−	0.840417i	$-0.682310\pi$
$193$	2.14576e6	−	2.14576e6i	0.298476	−	0.298476i	0.840417	+	0.541941i	$0.182310\pi$
$194$	−5.14809e6			−0.705084
$195$	−5.56397e6			−0.750380
$196$		−	3.62232e6i		−	0.481081i
$197$	6.77573e6			0.886252			0.443126	−	0.896459i	$-0.353869\pi$
$197$	6.77573e6			0.886252			0.443126	+	0.896459i	$0.353869\pi$
$198$	5.80755e6	−	5.80755e6i	0.748166	−	0.748166i
$199$	6.60913e6	+	6.60913e6i	0.838658	+	0.838658i	0.988682	−	0.150025i	$-0.0479353\pi$
$199$	6.60913e6	+	6.60913e6i	0.838658	+	0.838658i	−0.150025	+	0.988682i	$0.547935\pi$
$200$	−665751.	−	665751.i	−0.0832189	−	0.0832189i
$201$	−1.79927e7			−2.21569
$202$	−1.12142e6	+	1.12142e6i	−0.136055	+	0.136055i
$203$	−1.13656e6	−	1.13656e6i	−0.135864	−	0.135864i
$204$	−1.27819e6	+	1.27819e6i	−0.150559	+	0.150559i
$205$	−4.05929e6	−	4.05929e6i	−0.471182	−	0.471182i
$206$		−	9.24608e6i		−	1.05768i
$207$	−1.53347e7	+	1.53347e7i	−1.72888	+	1.72888i
$208$	−927888.	+	927888.i	−0.103111	+	0.103111i
$209$	−274140.	−	274140.i	−0.0300285	−	0.0300285i
$210$		−	1.63872e6i		−	0.176948i
$211$	8.76614e6			0.933170			0.466585	−	0.884476i	$-0.345484\pi$
$211$	8.76614e6			0.933170			0.466585	+	0.884476i	$0.345484\pi$
$212$		−	557516.i		−	0.0585127i
$213$			2.34238e6i			0.242392i
$214$	−1.05350e6	−	1.05350e6i	−0.107496	−	0.107496i
$215$		−	2.98531e6i		−	0.300383i
$216$	1.90800e6	+	1.90800e6i	0.189329	+	0.189329i
$217$	311483.	+	311483.i	0.0304828	+	0.0304828i
$218$	9.74597e6			0.940710
$219$	−6.10962e6			−0.581677
$220$	3.10708e6	−	3.10708e6i	0.291800	−	0.291800i
$221$		−	1.70220e6i		−	0.157701i
$222$	1.60863e6	−	1.20788e7i	0.147027	−	1.10399i
$223$	−3.11776e6			−0.281143			−0.140572	−	0.990071i	$-0.544894\pi$
$223$	−3.11776e6			−0.281143			−0.140572	+	0.990071i	$0.544894\pi$
$224$	−273284.	−	273284.i	−0.0243148	−	0.0243148i
$225$		−	5.61476e6i		−	0.492928i
$226$		−	6.97749e6i		−	0.604469i
$227$	772331.	−	772331.i	0.0660277	−	0.0660277i	−0.673322	−	0.739350i	$-0.735133\pi$
$227$	772331.	−	772331.i	0.0660277	−	0.0660277i	0.739350	+	0.673322i	$0.235133\pi$
$228$	277383.	−	277383.i	0.0234032	−	0.0234032i
$229$	1.53636e7			1.27934			0.639670	−	0.768649i	$-0.279071\pi$
$229$	1.53636e7			1.27934			0.639670	+	0.768649i	$0.279071\pi$
$230$	−8.20416e6	+	8.20416e6i	−0.674296	+	0.674296i
$231$	−3.81610e6			−0.309588
$232$	4.36091e6			0.349231
$233$		−	1.18815e7i		−	0.939301i	−0.882852	−	0.469650i	$-0.844380\pi$
$233$		−	1.18815e7i		−	0.939301i	0.882852	−	0.469650i	$-0.155620\pi$
$234$	−7.82554e6			−0.610755
$235$	4.47658e6	−	4.47658e6i	0.344940	−	0.344940i
$236$	2.23744e6	+	2.23744e6i	0.170222	+	0.170222i
$237$	7.31122e6	+	7.31122e6i	0.549218	+	0.549218i
$238$	501337.			0.0371877
$239$	1.07691e6	−	1.07691e6i	0.0788832	−	0.0788832i	−0.666564	−	0.745448i	$-0.732236\pi$
$239$	1.07691e6	−	1.07691e6i	0.0788832	−	0.0788832i	0.745448	+	0.666564i	$0.232236\pi$
$240$	3.14383e6	+	3.14383e6i	0.227419	+	0.227419i
$241$	1.69072e7	−	1.69072e7i	1.20787	−	1.20787i	0.236160	−	0.971714i	$-0.424111\pi$
$241$	1.69072e7	−	1.69072e7i	1.20787	−	1.20787i	0.971714	−	0.236160i	$-0.0758889\pi$
$242$	−149257.	−	149257.i	−0.0105314	−	0.0105314i
$243$		−	1.73755e7i		−	1.21093i
$244$	−9.49372e6	+	9.49372e6i	−0.653532	+	0.653532i
$245$	8.17213e6	−	8.17213e6i	0.555696	−	0.555696i
$246$	−9.56474e6	−	9.56474e6i	−0.642492	−	0.642492i
$247$			369397.i			0.0245134i
$248$	−1.19514e6			−0.0783546
$249$			1.17469e7i			0.760899i
$250$		−	1.20281e7i		−	0.769800i
$251$	−2.12070e7	−	2.12070e7i	−1.34109	−	1.34109i	−0.894973	−	0.446121i	$-0.852805\pi$
$251$	−2.12070e7	−	2.12070e7i	−1.34109	−	1.34109i	−0.446121	−	0.894973i	$-0.647195\pi$
$252$		−	2.30480e6i		−	0.144023i
$253$	1.91051e7	+	1.91051e7i	1.17975	+	1.17975i
$254$	−1.36415e7	−	1.36415e7i	−0.832455	−	0.832455i
$255$	−5.76733e6			−0.347820
$256$	1.04858e6			0.0625000
$257$	−1.11251e7	+	1.11251e7i	−0.655396	+	0.655396i	−0.954287	−	0.298891i	$-0.903383\pi$
$257$	−1.11251e7	+	1.11251e7i	−0.655396	+	0.655396i	0.298891	+	0.954287i	$0.403383\pi$
$258$		−	7.03417e6i		−	0.409594i
$259$	−2.68426e6	+	2.05332e6i	−0.154499	+	0.118184i
$260$	−4.18672e6			−0.238207
$261$	1.83893e7	+	1.83893e7i	1.03429	+	1.03429i
$262$			1.26128e6i			0.0701307i
$263$			386610.i			0.0212523i	0.999944	+	0.0106261i	$0.00338247\pi$
$263$			386610.i			0.0212523i	−0.999944	+	0.0106261i	$0.996618\pi$
$264$	7.32108e6	−	7.32108e6i	0.397891	−	0.397891i
$265$	1.25778e6	−	1.25778e6i	0.0675878	−	0.0675878i
$266$	−108796.			−0.00578053
$267$	−2.15853e7	+	2.15853e7i	−1.13403	+	1.13403i
$268$	−1.35390e7			−0.703366
$269$	−2.54284e7			−1.30636			−0.653179	−	0.757204i	$-0.726565\pi$
$269$	−2.54284e7			−1.30636			−0.653179	+	0.757204i	$0.726565\pi$
$270$			8.60909e6i			0.437387i
$271$	2.55672e6			0.128462			0.0642310	−	0.997935i	$-0.479541\pi$
$271$	2.55672e6			0.128462			0.0642310	+	0.997935i	$0.479541\pi$
$272$	−961800.	+	961800.i	−0.0477945	+	0.0477945i
$273$	2.57106e6	+	2.57106e6i	0.126364	+	0.126364i
$274$	1.16309e7	+	1.16309e7i	0.565405	+	0.565405i
$275$	−6.99530e6			−0.336363
$276$	−1.93311e7	+	1.93311e7i	−0.919453	+	0.919453i
$277$	2.07800e7	+	2.07800e7i	0.977700	+	0.977700i	0.999757	−	0.0220570i	$-0.00702154\pi$
$277$	2.07800e7	+	2.07800e7i	0.977700	+	0.977700i	−0.0220570	+	0.999757i	$0.507022\pi$
$278$	−208412.	+	208412.i	−0.00970036	+	0.00970036i
$279$	−5.03975e6	−	5.03975e6i	−0.232058	−	0.232058i
$280$		−	1.23309e6i		−	0.0561719i
$281$	−2.45963e7	+	2.45963e7i	−1.10854	+	1.10854i	−0.115198	+	0.993343i	$0.536750\pi$
$281$	−2.45963e7	+	2.45963e7i	−1.10854	+	1.10854i	−0.993343	+	0.115198i	$0.963250\pi$
$282$	1.05480e7	−	1.05480e7i	0.470351	−	0.470351i
$283$	1.65887e7	+	1.65887e7i	0.731904	+	0.731904i	0.970997	−	0.239093i	$-0.0768501\pi$
$283$	1.65887e7	+	1.65887e7i	0.731904	+	0.731904i	−0.239093	+	0.970997i	$0.576850\pi$
$284$			1.76257e6i			0.0769469i
$285$	1.25158e6			0.0540659
$286$			9.74967e6i			0.416765i
$287$			3.75151e6i			0.158694i
$288$	4.42170e6	+	4.42170e6i	0.185102	+	0.185102i
$289$			2.23732e7i			0.926902i
$290$	9.83842e6	+	9.83842e6i	0.403396	+	0.403396i
$291$	−2.73664e7	−	2.73664e7i	−1.11055	−	1.11055i
$292$	−4.59730e6			−0.184652
$293$	4.85028e7			1.92825			0.964126	−	0.265446i	$-0.0855192\pi$
$293$	4.85028e7			1.92825			0.964126	+	0.265446i	$0.0855192\pi$
$294$	1.92556e7	−	1.92556e7i	0.757732	−	0.757732i
$295$			1.00955e7i			0.393245i
$296$	1.21045e6	−	9.08892e6i	0.0466735	−	0.350459i
$297$	2.00481e7			0.765251
$298$	1.66204e7	+	1.66204e7i	0.628048	+	0.628048i
$299$		−	2.57437e7i		−	0.963070i
$300$		−	7.07804e6i		−	0.262150i
$301$	−1.37948e6	+	1.37948e6i	−0.0505844	+	0.0505844i
$302$	−7.78033e6	+	7.78033e6i	−0.282473	+	0.282473i
$303$	−1.19226e7			−0.428590
$304$	208722.	−	208722.i	0.00742929	−	0.00742929i
$305$	−4.28366e7			−1.50979
$306$	−8.11155e6			−0.283100
$307$		−	3.89483e7i		−	1.34609i	−0.739603	−	0.673044i	$-0.764987\pi$
$307$		−	3.89483e7i		−	1.34609i	0.739603	−	0.673044i	$-0.235013\pi$
$308$	−2.87150e6			−0.0982781
$309$	4.91506e7	−	4.91506e7i	1.66592	−	1.66592i
$310$	−2.69630e6	−	2.69630e6i	−0.0905072	−	0.0905072i
$311$	−2.08905e7	−	2.08905e7i	−0.694493	−	0.694493i	0.268724	−	0.963217i	$-0.413398\pi$
$311$	−2.08905e7	−	2.08905e7i	−0.694493	−	0.694493i	−0.963217	+	0.268724i	$0.913398\pi$
$312$	−9.86499e6			−0.324813
$313$	1.92458e7	−	1.92458e7i	0.627630	−	0.627630i	−0.319841	−	0.947471i	$-0.603630\pi$
$313$	1.92458e7	−	1.92458e7i	0.627630	−	0.627630i	0.947471	+	0.319841i	$0.103630\pi$
$314$	2.84339e7	+	2.84339e7i	0.918433	+	0.918433i
$315$	5.19975e6	−	5.19975e6i	0.166361	−	0.166361i
$316$	5.50147e6	+	5.50147e6i	0.174348	+	0.174348i
$317$			2.19865e7i			0.690204i	0.938565	+	0.345102i	$0.112156\pi$
$317$			2.19865e7i			0.690204i	−0.938565	+	0.345102i	$0.887844\pi$
$318$	2.96366e6	−	2.96366e6i	0.0921610	−	0.0921610i
$319$	2.29108e7	−	2.29108e7i	0.705780	−	0.705780i
$320$	2.36564e6	+	2.36564e6i	0.0721936	+	0.0721936i
$321$		−	1.12005e7i		−	0.338627i
$322$	7.58212e6			0.227103
$323$			382898.i			0.0113625i
$324$		−	4.89771e6i		−	0.143999i
$325$	4.71300e6	+	4.71300e6i	0.137293	+	0.137293i
$326$			3.77232e7i			1.08882i
$327$	5.18079e7	+	5.18079e7i	1.48168	+	1.48168i
$328$	−7.19717e6	−	7.19717e6i	−0.203958	−	0.203958i
$329$	−4.13717e6			−0.116176
$330$	3.30334e7			0.919204
$331$	−3.95230e7	+	3.95230e7i	−1.08985	+	1.08985i	−0.0943032	+	0.995544i	$0.530062\pi$
$331$	−3.95230e7	+	3.95230e7i	−1.08985	+	1.08985i	−0.995544	+	0.0943032i	$0.969938\pi$
$332$			8.83922e6i			0.241546i
$333$	4.34310e7	−	3.32224e7i	1.17616	−	0.899702i
$334$	2.97337e7			0.798012
$335$	−3.05446e7	−	3.05446e7i	−0.812455	−	0.812455i
$336$		−	2.90547e6i		−	0.0765946i
$337$			6.00590e7i			1.56924i	0.619979	+	0.784618i	$0.287141\pi$
$337$			6.00590e7i			1.56924i	−0.619979	+	0.784618i	$0.712859\pi$
$338$	−1.27385e7	+	1.27385e7i	−0.329890	+	0.329890i
$339$	3.70912e7	−	3.70912e7i	0.952075	−	0.952075i
$340$	−4.33974e6			−0.110415
$341$	−6.27891e6	+	6.27891e6i	−0.158351	+	0.158351i
$342$	1.76030e6			0.0440057
$343$	−1.54020e7			−0.381677
$344$		−	5.29300e6i		−	0.130025i
$345$	−8.72239e7			−2.12412
$346$	6.43232e6	−	6.43232e6i	0.155288	−	0.155288i
$347$	4.75971e7	+	4.75971e7i	1.13918	+	1.13918i	0.988598	+	0.150581i	$0.0481143\pi$
$347$	4.75971e7	+	4.75971e7i	1.13918	+	1.13918i	0.150581	+	0.988598i	$0.451886\pi$
$348$	2.31818e7	+	2.31818e7i	0.550060	+	0.550060i
$349$	−1.41946e7			−0.333923			−0.166962	−	0.985963i	$-0.553396\pi$
$349$	−1.41946e7			−0.333923			−0.166962	+	0.985963i	$0.553396\pi$
$350$	−1.38809e6	+	1.38809e6i	−0.0323752	+	0.0323752i
$351$	−1.35072e7	−	1.35072e7i	−0.312351	−	0.312351i
$352$	5.50889e6	−	5.50889e6i	0.126310	−	0.126310i
$353$	−1.62504e7	−	1.62504e7i	−0.369437	−	0.369437i	0.497835	−	0.867272i	$-0.334129\pi$
$353$	−1.62504e7	−	1.62504e7i	−0.369437	−	0.369437i	−0.867272	+	0.497835i	$0.834129\pi$
$354$			2.37877e7i			0.536220i
$355$	−3.97644e6	+	3.97644e6i	−0.0888812	+	0.0888812i
$356$	−1.62423e7	+	1.62423e7i	−0.359996	+	0.359996i
$357$	2.66502e6	+	2.66502e6i	0.0585728	+	0.0585728i
$358$			6.62673e6i			0.144428i
$359$	−3.53945e7			−0.764985			−0.382492	−	0.923959i	$-0.624934\pi$
$359$	−3.53945e7			−0.764985			−0.382492	+	0.923959i	$0.624934\pi$
$360$			1.99511e7i			0.427622i
$361$			4.69628e7i			0.998234i
$362$	−3.55024e7	−	3.55024e7i	−0.748397	−	0.748397i
$363$		−	1.58685e6i		−	0.0331753i
$364$	1.93464e6	+	1.93464e6i	0.0401140	+	0.0401140i
$365$	−1.03717e7	−	1.03717e7i	−0.213291	−	0.213291i
$366$	−1.00934e8			−2.05871
$367$	−8.86044e6			−0.179249			−0.0896246	−	0.995976i	$-0.528567\pi$
$367$	−8.86044e6			−0.179249			−0.0896246	+	0.995976i	$0.528567\pi$
$368$	−1.45461e7	+	1.45461e7i	−0.291879	+	0.291879i
$369$		−	6.06989e7i		−	1.20810i
$370$	2.32359e7	−	1.77742e7i	0.458727	−	0.350902i
$371$	−1.16242e6			−0.0227636
$372$	−6.35317e6	−	6.35317e6i	−0.123413	−	0.123413i
$373$			9.19160e7i			1.77119i	0.464460	+	0.885594i	$0.346248\pi$
$373$			9.19160e7i			1.77119i	−0.464460	+	0.885594i	$0.653752\pi$
$374$			1.01060e7i			0.193181i
$375$	6.39395e7	−	6.39395e7i	1.21248	−	1.21248i
$376$	7.93704e6	−	7.93704e6i	0.149312	−	0.149312i
$377$	−3.08718e7			−0.576154
$378$	3.97817e6	−	3.97817e6i	0.0736560	−	0.0736560i
$379$	−2.74691e7			−0.504576			−0.252288	−	0.967652i	$-0.581183\pi$
$379$	−2.74691e7			−0.504576			−0.252288	+	0.967652i	$0.581183\pi$
$380$	941774.			0.0171631
$381$		−	1.45032e8i		−	2.62233i
$382$	−2.85776e7			−0.512668
$383$	6.62807e6	−	6.62807e6i	0.117975	−	0.117975i	−0.645654	−	0.763630i	$-0.723415\pi$
$383$	6.62807e6	−	6.62807e6i	0.117975	−	0.117975i	0.763630	+	0.645654i	$0.223415\pi$
$384$	5.57405e6	+	5.57405e6i	0.0984413	+	0.0984413i
$385$	−6.47825e6	−	6.47825e6i	−0.113521	−	0.113521i
$386$	1.71661e7			0.298476
$387$	2.23198e7	−	2.23198e7i	0.385086	−	0.385086i
$388$	−2.05923e7	−	2.05923e7i	−0.352542	−	0.352542i
$389$	7.56160e7	−	7.56160e7i	1.28459	−	1.28459i	0.346566	−	0.938025i	$-0.387348\pi$
$389$	7.56160e7	−	7.56160e7i	1.28459	−	1.28459i	0.938025	−	0.346566i	$-0.112652\pi$
$390$	−2.22559e7	−	2.22559e7i	−0.375190	−	0.375190i
$391$		−	2.66846e7i		−	0.446407i
$392$	1.44893e7	−	1.44893e7i	0.240541	−	0.240541i
$393$	−6.70476e6	+	6.70476e6i	−0.110460	+	0.110460i
$394$	2.71029e7	+	2.71029e7i	0.443126	+	0.443126i
$395$			2.48232e7i			0.402778i
$396$	4.64604e7			0.748166
$397$			5.30952e7i			0.848562i	0.905531	+	0.424281i	$0.139473\pi$
$397$			5.30952e7i			0.848562i	−0.905531	+	0.424281i	$0.860527\pi$
$398$			5.28730e7i			0.838658i
$399$	−578341.	−	578341.i	−0.00910469	−	0.00910469i
$400$		−	5.32601e6i		−	0.0832189i
$401$	−5.99114e7	−	5.99114e7i	−0.929129	−	0.929129i	0.0685203	−	0.997650i	$-0.478172\pi$
$401$	−5.99114e7	−	5.99114e7i	−0.929129	−	0.929129i	−0.997650	+	0.0685203i	$0.978172\pi$
$402$	−7.19709e7	−	7.19709e7i	−1.10784	−	1.10784i
$403$	8.46068e6			0.129268
$404$	−8.97137e6			−0.136055
$405$	1.10495e7	−	1.10495e7i	0.166332	−	0.166332i
$406$		−	9.09246e6i		−	0.135864i
$407$	−4.13911e7	−	5.41097e7i	−0.613937	−	0.802586i
$408$	−1.02255e7			−0.150559
$409$	−5.43195e7	−	5.43195e7i	−0.793937	−	0.793937i	0.188195	−	0.982132i	$-0.439736\pi$
$409$	−5.43195e7	−	5.43195e7i	−0.793937	−	0.793937i	−0.982132	+	0.188195i	$0.939736\pi$
$410$		−	3.24743e7i		−	0.471182i
$411$			1.23655e8i			1.78110i
$412$	3.69843e7	−	3.69843e7i	0.528842	−	0.528842i
$413$	4.66505e6	−	4.66505e6i	0.0662225	−	0.0662225i
$414$	−1.22677e8			−1.72888
$415$	−1.99417e7	+	1.99417e7i	−0.279009	+	0.279009i
$416$	−7.42310e6			−0.103111
$417$	−2.21576e6			−0.0305573
$418$		−	2.19312e6i		−	0.0300285i
$419$	−9.11771e7			−1.23949			−0.619746	−	0.784803i	$-0.712764\pi$
$419$	−9.11771e7			−1.23949			−0.619746	+	0.784803i	$0.712764\pi$
$420$	6.55487e6	−	6.55487e6i	0.0884741	−	0.0884741i
$421$	3.18658e7	+	3.18658e7i	0.427050	+	0.427050i	0.887622	−	0.460572i	$-0.152356\pi$
$421$	3.18658e7	+	3.18658e7i	0.427050	+	0.427050i	−0.460572	+	0.887622i	$0.652356\pi$
$422$	3.50645e7	+	3.50645e7i	0.466585	+	0.466585i
$423$	6.69387e7			0.884415
$424$	2.23006e6	−	2.23006e6i	0.0292563	−	0.0292563i
$425$	4.88525e6	+	4.88525e6i	0.0636385	+	0.0636385i
$426$	−9.36952e6	+	9.36952e6i	−0.121196	+	0.121196i
$427$	1.97943e7	+	1.97943e7i	0.254248	+	0.254248i
$428$		−	8.42801e6i		−	0.107496i
$429$	−5.18276e7	+	5.18276e7i	−0.656431	+	0.656431i
$430$	1.19413e7	−	1.19413e7i	0.150191	−	0.150191i
$431$	7.05020e7	+	7.05020e7i	0.880582	+	0.880582i	0.993594	−	0.113012i	$-0.0360498\pi$
$431$	7.05020e7	+	7.05020e7i	0.880582	+	0.880582i	−0.113012	+	0.993594i	$0.536050\pi$
$432$			1.52640e7i			0.189329i
$433$	8.05803e7			0.992579			0.496290	−	0.868157i	$-0.334695\pi$
$433$	8.05803e7			0.992579			0.496290	+	0.868157i	$0.334695\pi$
$434$			2.49186e6i			0.0304828i
$435$			1.04599e8i			1.27075i
$436$	3.89839e7	+	3.89839e7i	0.470355	+	0.470355i
$437$			5.79087e6i			0.0693904i
$438$	−2.44385e7	−	2.44385e7i	−0.290839	−	0.290839i
$439$	−5.74342e7	−	5.74342e7i	−0.678855	−	0.678855i	0.280886	−	0.959741i	$-0.409372\pi$
$439$	−5.74342e7	−	5.74342e7i	−0.678855	−	0.678855i	−0.959741	+	0.280886i	$0.909372\pi$
$440$	2.48567e7			0.291800
$441$	1.22198e8			1.42479
$442$	6.80880e6	−	6.80880e6i	0.0788504	−	0.0788504i
$443$		−	1.14049e8i		−	1.31183i	−0.754833	−	0.655917i	$-0.772282\pi$
$443$		−	1.14049e8i		−	1.31183i	0.754833	−	0.655917i	$-0.227718\pi$
$444$	5.47497e7	−	4.18807e7i	0.625508	−	0.478481i
$445$	−7.32869e7			−0.831661
$446$	−1.24710e7	−	1.24710e7i	−0.140572	−	0.140572i
$447$			1.76702e8i			1.97843i
$448$		−	2.18627e6i		−	0.0243148i
$449$	1.25328e7	−	1.25328e7i	0.138455	−	0.138455i	−0.634483	−	0.772937i	$-0.718787\pi$
$449$	1.25328e7	−	1.25328e7i	0.138455	−	0.138455i	0.772937	+	0.634483i	$0.218787\pi$
$450$	2.24590e7	−	2.24590e7i	0.246464	−	0.246464i
$451$	−7.56234e7			−0.824378
$452$	2.79100e7	−	2.79100e7i	0.302234	−	0.302234i
$453$	−8.27179e7			−0.889825
$454$	6.17865e6			0.0660277
$455$			8.72928e6i			0.0926711i
$456$	2.21906e6			0.0234032
$457$	−1.59514e7	+	1.59514e7i	−0.167128	+	0.167128i	−0.785716	−	0.618587i	$-0.787705\pi$
$457$	−1.59514e7	+	1.59514e7i	−0.167128	+	0.167128i	0.618587	+	0.785716i	$0.287705\pi$
$458$	6.14543e7	+	6.14543e7i	0.639670	+	0.639670i
$459$	−1.40008e7	−	1.40008e7i	−0.144782	−	0.144782i
$460$	−6.56333e7			−0.674296
$461$	1.10412e7	−	1.10412e7i	0.112697	−	0.112697i	−0.648509	−	0.761207i	$-0.724607\pi$
$461$	1.10412e7	−	1.10412e7i	0.112697	−	0.112697i	0.761207	+	0.648509i	$0.224607\pi$
$462$	−1.52644e7	−	1.52644e7i	−0.154794	−	0.154794i
$463$	2.29394e7	−	2.29394e7i	0.231121	−	0.231121i	−0.582039	−	0.813161i	$-0.697745\pi$
$463$	2.29394e7	−	2.29394e7i	0.231121	−	0.231121i	0.813161	+	0.582039i	$0.197745\pi$
$464$	1.74436e7	+	1.74436e7i	0.174616	+	0.174616i
$465$		−	2.86661e7i		−	0.285109i
$466$	4.75261e7	−	4.75261e7i	0.469650	−	0.469650i
$467$	2.03450e7	−	2.03450e7i	0.199759	−	0.199759i	−0.600138	−	0.799897i	$-0.704888\pi$
$467$	2.03450e7	−	2.03450e7i	0.199759	−	0.199759i	0.799897	+	0.600138i	$0.204888\pi$
$468$	−3.13022e7	−	3.13022e7i	−0.305377	−	0.305377i
$469$			2.82287e7i			0.273635i
$470$	3.58127e7			0.344940
$471$			3.02300e8i			2.89318i
$472$			1.78995e7i			0.170222i
$473$	−2.78078e7	−	2.78078e7i	−0.262774	−	0.262774i
$474$			5.84898e7i			0.549218i
$475$	−1.06016e6	−	1.06016e6i	−0.00989212	−	0.00989212i
$476$	2.00535e6	+	2.00535e6i	0.0185938	+	0.0185938i
$477$	1.88077e7			0.173293
$478$	8.61526e6			0.0788832
$479$	1.27647e8	−	1.27647e8i	1.16146	−	1.16146i	0.177304	−	0.984156i	$-0.443263\pi$
$479$	1.27647e8	−	1.27647e8i	1.16146	−	1.16146i	0.984156	−	0.177304i	$-0.0567374\pi$
$480$			2.51507e7i			0.227419i
$481$	−8.56901e6	+	6.43425e7i	−0.0770009	+	0.578180i
$482$	1.35258e8			1.20787
$483$	4.03053e7	+	4.03053e7i	0.357701	+	0.357701i
$484$		−	1.19405e6i		−	0.0105314i
$485$		−	9.29147e7i		−	0.814440i
$486$	6.95021e7	−	6.95021e7i	0.605465	−	0.605465i
$487$	7.42768e7	−	7.42768e7i	0.643082	−	0.643082i	−0.308230	−	0.951312i	$-0.599737\pi$
$487$	7.42768e7	−	7.42768e7i	0.643082	−	0.643082i	0.951312	+	0.308230i	$0.0997367\pi$
$488$	−7.59498e7			−0.653532
$489$	−2.00530e8	+	2.00530e8i	−1.71496	+	1.71496i
$490$	6.53770e7			0.555696
$491$	1.65127e8			1.39500			0.697501	−	0.716584i	$-0.254295\pi$
$491$	1.65127e8			1.39500			0.697501	+	0.716584i	$0.254295\pi$
$492$		−	7.65179e7i		−	0.642492i
$493$	−3.20001e7			−0.267061
$494$	−1.47759e6	+	1.47759e6i	−0.0122567	+	0.0122567i
$495$	1.04817e8	+	1.04817e8i	0.864204	+	0.864204i
$496$	−4.78057e6	−	4.78057e6i	−0.0391773	−	0.0391773i
$497$	3.67495e6			0.0299352
$498$	−4.69878e7	+	4.69878e7i	−0.380449	+	0.380449i
$499$	8.04086e7	+	8.04086e7i	0.647144	+	0.647144i	0.952302	−	0.305158i	$-0.0987093\pi$
$499$	8.04086e7	+	8.04086e7i	0.647144	+	0.647144i	−0.305158	+	0.952302i	$0.598709\pi$
$500$	4.81125e7	−	4.81125e7i	0.384900	−	0.384900i
$501$	1.58059e8	+	1.58059e8i	1.25692	+	1.25692i
$502$		−	1.69656e8i		−	1.34109i
$503$	−1.18681e8	+	1.18681e8i	−0.932562	+	0.932562i	−0.997865	−	0.0653032i	$-0.979199\pi$
$503$	−1.18681e8	+	1.18681e8i	−0.932562	+	0.932562i	0.0653032	+	0.997865i	$0.479199\pi$
$504$	9.21921e6	−	9.21921e6i	0.0720115	−	0.0720115i
$505$	−2.02398e7	−	2.02398e7i	−0.157157	−	0.157157i
$506$			1.52841e8i			1.17975i
$507$	−1.35432e8			−1.03919
$508$		−	1.09132e8i		−	0.832455i
$509$			6.58216e7i			0.499132i	0.968358	+	0.249566i	$0.0802879\pi$
$509$			6.58216e7i			0.499132i	−0.968358	+	0.249566i	$0.919712\pi$
$510$	−2.30693e7	−	2.30693e7i	−0.173910	−	0.173910i
$511$			9.58535e6i			0.0718365i
$512$	4.19430e6	+	4.19430e6i	0.0312500	+	0.0312500i
$513$	3.03834e6	+	3.03834e6i	0.0225053	+	0.0225053i
$514$	−8.90007e7			−0.655396
$515$	1.66877e8			1.22173
$516$	2.81367e7	−	2.81367e7i	0.204797	−	0.204797i
$517$		−	8.33974e7i		−	0.603505i
$518$	−1.89503e7	−	2.52377e6i	−0.136341	−	0.0181577i
$519$	6.83862e7			0.489178
$520$	−1.67469e7	−	1.67469e7i	−0.119103	−	0.119103i
$521$		−	1.15116e8i		−	0.813995i	−0.913429	−	0.406997i	$-0.866576\pi$
$521$		−	1.15116e8i		−	0.813995i	0.913429	−	0.406997i	$-0.133424\pi$
$522$			1.47115e8i			1.03429i
$523$	9.67558e7	−	9.67558e7i	0.676350	−	0.676350i	−0.282822	−	0.959172i	$-0.591271\pi$
$523$	9.67558e7	−	9.67558e7i	0.676350	−	0.676350i	0.959172	+	0.282822i	$0.0912706\pi$
$524$	−5.04513e6	+	5.04513e6i	−0.0350654	+	0.0350654i
$525$	−1.47577e7			−0.101986
$526$	−1.54644e6	+	1.54644e6i	−0.0106261	+	0.0106261i
$527$	8.76990e6			0.0599188
$528$	5.85687e7			0.397891
$529$		−	2.55537e8i		−	1.72618i
$530$	1.00623e7			0.0675878
$531$	−7.54797e7	+	7.54797e7i	−0.504135	+	0.504135i
$532$	−435184.	−	435184.i	−0.00289027	−	0.00289027i
$533$	5.09504e7	+	5.09504e7i	0.336485	+	0.336485i
$534$	−1.72683e8			−1.13403
$535$	1.90140e7	−	1.90140e7i	0.124169	−	0.124169i
$536$	−5.41559e7	−	5.41559e7i	−0.351683	−	0.351683i
$537$	−3.52266e7	+	3.52266e7i	−0.227482	+	0.227482i
$538$	−1.01714e8	−	1.01714e8i	−0.653179	−	0.653179i
$539$		−	1.52244e8i		−	0.972243i
$540$	−3.44364e7	+	3.44364e7i	−0.218694	+	0.218694i
$541$	−1.05034e8	+	1.05034e8i	−0.663344	+	0.663344i	−0.956167	−	0.292822i	$-0.905406\pi$
$541$	−1.05034e8	+	1.05034e8i	−0.663344	+	0.663344i	0.292822	+	0.956167i	$0.405406\pi$
$542$	1.02269e7	+	1.02269e7i	0.0642310	+	0.0642310i
$543$		−	3.77449e8i		−	2.35754i
$544$	−7.69440e6			−0.0477945
$545$			1.75899e8i			1.08661i
$546$			2.05684e7i			0.126364i
$547$	−1.47253e8	−	1.47253e8i	−0.899708	−	0.899708i	0.0957017	−	0.995410i	$-0.469491\pi$
$547$	−1.47253e8	−	1.47253e8i	−0.899708	−	0.899708i	−0.995410	+	0.0957017i	$0.969491\pi$
$548$			9.30468e7i			0.565405i
$549$	−3.20270e8	−	3.20270e8i	−1.93552	−	1.93552i
$550$	−2.79812e7	−	2.79812e7i	−0.168181	−	0.168181i
$551$	6.94440e6			0.0415126
$552$	−1.54649e8			−0.919453
$553$	1.14705e7	−	1.14705e7i	0.0678278	−	0.0678278i
$554$			1.66240e8i			0.977700i
$555$	2.18003e8	+	2.90332e7i	1.27521	+	0.169831i
$556$	−1.66729e6			−0.00970036
$557$	6.50761e7	+	6.50761e7i	0.376579	+	0.376579i	0.869866	−	0.493287i	$-0.164205\pi$
$557$	6.50761e7	+	6.50761e7i	0.376579	+	0.376579i	−0.493287	+	0.869866i	$0.664205\pi$
$558$		−	4.03180e7i		−	0.232058i
$559$			3.74703e7i			0.214512i
$560$	4.93234e6	−	4.93234e6i	0.0280859	−	0.0280859i
$561$	−5.37218e7	+	5.37218e7i	−0.304272	+	0.304272i
$562$	−1.96771e8			−1.10854
$563$	7.79281e6	−	7.79281e6i	0.0436685	−	0.0436685i	−0.684935	−	0.728604i	$-0.740170\pi$
$563$	7.79281e6	−	7.79281e6i	0.0436685	−	0.0436685i	0.728604	+	0.684935i	$0.240170\pi$
$564$	8.43839e7			0.470351
$565$	1.25932e8			0.698220
$566$			1.32710e8i			0.731904i
$567$	−1.02117e7			−0.0560207
$568$	−7.05028e6	+	7.05028e6i	−0.0384735	+	0.0384735i
$569$	7.74222e7	+	7.74222e7i	0.420270	+	0.420270i	0.885297	−	0.465027i	$-0.153955\pi$
$569$	7.74222e7	+	7.74222e7i	0.420270	+	0.420270i	−0.465027	+	0.885297i	$0.653955\pi$
$570$	5.00631e6	+	5.00631e6i	0.0270329	+	0.0270329i
$571$	−2.12222e8			−1.13994			−0.569970	−	0.821665i	$-0.693045\pi$
$571$	−2.12222e8			−1.13994			−0.569970	+	0.821665i	$0.693045\pi$
$572$	−3.89987e7	+	3.89987e7i	−0.208383	+	0.208383i
$573$	−1.51914e8	−	1.51914e8i	−0.807483	−	0.807483i
$574$	−1.50061e7	+	1.50061e7i	−0.0793471	+	0.0793471i
$575$	7.38836e7	+	7.38836e7i	0.388637	+	0.388637i
$576$			3.53736e7i			0.185102i
$577$	−1.20826e8	+	1.20826e8i	−0.628972	+	0.628972i	−0.947809	−	0.318837i	$-0.896708\pi$
$577$	−1.20826e8	+	1.20826e8i	−0.628972	+	0.628972i	0.318837	+	0.947809i	$0.396708\pi$
$578$	−8.94926e7	+	8.94926e7i	−0.463451	+	0.463451i
$579$	9.12521e7	+	9.12521e7i	0.470118	+	0.470118i
$580$			7.87074e7i			0.403396i
$581$	1.84297e7			0.0939702
$582$		−	2.18931e8i		−	1.11055i
$583$		−	2.34321e7i		−	0.118251i
$584$	−1.83892e7	−	1.83892e7i	−0.0923261	−	0.0923261i
$585$		−	1.41238e8i		−	0.705481i
$586$	1.94011e8	+	1.94011e8i	0.964126	+	0.964126i
$587$	−1.16055e8	−	1.16055e8i	−0.573783	−	0.573783i	0.359400	−	0.933183i	$-0.382981\pi$
$587$	−1.16055e8	−	1.16055e8i	−0.573783	−	0.573783i	−0.933183	+	0.359400i	$0.882981\pi$
$588$	1.54045e8			0.757732
$589$	−1.90317e6			−0.00931391
$590$	−4.03822e7	+	4.03822e7i	−0.196623	+	0.196623i
$591$			2.88149e8i			1.39590i
$592$	4.11975e7	−	3.15139e7i	0.198566	−	0.151893i
$593$	−3.94395e7			−0.189133			−0.0945666	−	0.995519i	$-0.530147\pi$
$593$	−3.94395e7			−0.189133			−0.0945666	+	0.995519i	$0.530147\pi$
$594$	8.01924e7	+	8.01924e7i	0.382625	+	0.382625i
$595$			9.04832e6i			0.0429553i
$596$			1.32963e8i			0.628048i
$597$	−2.81064e8	+	2.81064e8i	−1.32094	+	1.32094i
$598$	1.02975e8	−	1.02975e8i	0.481535	−	0.481535i
$599$	−4.85761e7			−0.226017			−0.113009	−	0.993594i	$-0.536049\pi$
$599$	−4.85761e7			−0.226017			−0.113009	+	0.993594i	$0.536049\pi$
$600$	2.83122e7	−	2.83122e7i	0.131075	−	0.131075i
$601$	−1.05388e8			−0.485478			−0.242739	−	0.970092i	$-0.578046\pi$
$601$	−1.05388e8			−0.485478			−0.242739	+	0.970092i	$0.578046\pi$
$602$	−1.10359e7			−0.0505844
$603$		−	4.56735e8i		−	2.08311i
$604$	−6.22426e7			−0.282473
$605$	2.69384e6	−	2.69384e6i	0.0121648	−	0.0121648i
$606$	−4.76903e7	−	4.76903e7i	−0.214295	−	0.214295i
$607$	−1.21281e8	−	1.21281e8i	−0.542285	−	0.542285i	0.381913	−	0.924198i	$-0.375265\pi$
$607$	−1.21281e8	−	1.21281e8i	−0.542285	−	0.542285i	−0.924198	+	0.381913i	$0.875265\pi$
$608$	1.66978e6			0.00742929
$609$	4.83340e7	−	4.83340e7i	0.213994	−	0.213994i
$610$	−1.71346e8	−	1.71346e8i	−0.754893	−	0.754893i
$611$	−5.61880e7	+	5.61880e7i	−0.246332	+	0.246332i
$612$	−3.24462e7	−	3.24462e7i	−0.141550	−	0.141550i
$613$		−	4.36891e7i		−	0.189667i	−0.995493	−	0.0948335i	$-0.969768\pi$
$613$		−	4.36891e7i		−	0.189667i	0.995493	−	0.0948335i	$-0.0302319\pi$
$614$	1.55793e8	−	1.55793e8i	0.673044	−	0.673044i
$615$	1.72628e8	−	1.72628e8i	0.742140	−	0.742140i
$616$	−1.14860e7	−	1.14860e7i	−0.0491391	−	0.0491391i
$617$		−	1.61699e8i		−	0.688416i	−0.938893	−	0.344208i	$-0.888147\pi$
$617$		−	1.61699e8i		−	0.688416i	0.938893	−	0.344208i	$-0.111853\pi$
$618$	3.93205e8			1.66592
$619$		−	4.70392e8i		−	1.98330i	−0.128966	−	0.991649i	$-0.541166\pi$
$619$		−	4.70392e8i		−	1.98330i	0.128966	−	0.991649i	$-0.458834\pi$
$620$		−	2.15704e7i		−	0.0905072i
$621$	−2.11746e8	−	2.11746e8i	−0.884178	−	0.884178i
$622$		−	1.67124e8i		−	0.694493i
$623$	3.38651e7	+	3.38651e7i	0.140052	+	0.140052i
$624$	−3.94600e7	−	3.94600e7i	−0.162406	−	0.162406i
$625$	1.35820e8			0.556318
$626$	1.53967e8			0.627630
$627$	1.16583e7	−	1.16583e7i	0.0472967	−	0.0472967i
$628$			2.27471e8i			0.918433i
$629$	−8.88219e6	+	6.66941e7i	−0.0356918	+	0.268000i
$630$	4.15980e7			0.166361
$631$	1.21236e8	+	1.21236e8i	0.482551	+	0.482551i	0.905946	−	0.423394i	$-0.139161\pi$
$631$	1.21236e8	+	1.21236e8i	0.482551	+	0.482551i	−0.423394	+	0.905946i	$0.639161\pi$
$632$			4.40117e7i			0.174348i
$633$			3.72794e8i			1.46980i
$634$	−8.79458e7	+	8.79458e7i	−0.345102	+	0.345102i
$635$	2.46207e8	−	2.46207e8i	0.961566	−	0.961566i
$636$	2.37093e7			0.0921610
$637$	−1.02573e8	+	1.02573e8i	−0.396839	+	0.396839i
$638$	1.83287e8			0.705780
$639$	−5.94601e7			−0.227889
$640$			1.89251e7i			0.0721936i
$641$	1.84365e8			0.700011			0.350006	−	0.936748i	$-0.386180\pi$
$641$	1.84365e8			0.700011			0.350006	+	0.936748i	$0.386180\pi$
$642$	4.48019e7	−	4.48019e7i	0.169313	−	0.169313i
$643$	7.42644e7	+	7.42644e7i	0.279350	+	0.279350i	0.832849	−	0.553500i	$-0.186708\pi$
$643$	7.42644e7	+	7.42644e7i	0.279350	+	0.279350i	−0.553500	+	0.832849i	$0.686708\pi$
$644$	3.03285e7	+	3.03285e7i	0.113552	+	0.113552i
$645$	1.26955e8			0.473121
$646$	−1.53159e6	+	1.53159e6i	−0.00568127	+	0.00568127i
$647$	2.75499e8	+	2.75499e8i	1.01720	+	1.01720i	0.999849	+	0.0173516i	$0.00552346\pi$
$647$	2.75499e8	+	2.75499e8i	1.01720	+	1.01720i	0.0173516	+	0.999849i	$0.494477\pi$
$648$	1.95909e7	−	1.95909e7i	0.0719993	−	0.0719993i
$649$	9.40385e7	+	9.40385e7i	0.344010	+	0.344010i
$650$			3.77040e7i			0.137293i
$651$	−1.32463e7	+	1.32463e7i	−0.0480123	+	0.0480123i
$652$	−1.50893e8	+	1.50893e8i	−0.544409	+	0.544409i
$653$	−3.05026e8	−	3.05026e8i	−1.09546	−	1.09546i	−0.994934	−	0.100528i	$-0.967947\pi$
$653$	−3.05026e8	−	3.05026e8i	−1.09546	−	1.09546i	−0.100528	−	0.994934i	$-0.532053\pi$
$654$			4.14464e8i			1.48168i
$655$	−2.27641e7			−0.0810078
$656$		−	5.75774e7i		−	0.203958i
$657$		−	1.55089e8i		−	0.546873i
$658$	−1.65487e7	−	1.65487e7i	−0.0580879	−	0.0580879i
$659$		−	5.11104e8i		−	1.78588i	−0.450173	−	0.892941i	$-0.648638\pi$
$659$		−	5.11104e8i		−	1.78588i	0.450173	−	0.892941i	$-0.351362\pi$
$660$	1.32134e8	+	1.32134e8i	0.459602	+	0.459602i
$661$	8.51465e7	+	8.51465e7i	0.294824	+	0.294824i	0.838982	−	0.544159i	$-0.183151\pi$
$661$	8.51465e7	+	8.51465e7i	0.294824	+	0.294824i	−0.544159	+	0.838982i	$0.683151\pi$
$662$	−3.16184e8			−1.08985
$663$	7.23889e7			0.248388
$664$	−3.53569e7	+	3.53569e7i	−0.120773	+	0.120773i
$665$		−	1.96359e6i		−	0.00667708i
$666$	3.06614e8	+	4.08342e7i	1.03793	+	0.138230i
$667$	−4.83964e8			−1.63093
$668$	1.18935e8	+	1.18935e8i	0.399006	+	0.399006i
$669$		−	1.32588e8i		−	0.442818i
$670$		−	2.44357e8i		−	0.812455i
$671$	−3.99016e8	+	3.99016e8i	−1.32076	+	1.32076i
$672$	1.16219e7	−	1.16219e7i	0.0382973	−	0.0382973i
$673$	3.42020e8			1.12204			0.561018	−	0.827803i	$-0.310410\pi$
$673$	3.42020e8			1.12204			0.561018	+	0.827803i	$0.310410\pi$
$674$	−2.40236e8	+	2.40236e8i	−0.784618	+	0.784618i
$675$	7.75302e7			0.252092
$676$	−1.01908e8			−0.329890
$677$			3.34079e8i			1.07667i	0.842730	+	0.538336i	$0.180947\pi$
$677$			3.34079e8i			1.07667i	−0.842730	+	0.538336i	$0.819053\pi$
$678$	2.96729e8			0.952075
$679$	−4.29349e7	+	4.29349e7i	−0.137152	+	0.137152i
$680$	−1.73589e7	−	1.73589e7i	−0.0552073	−	0.0552073i
$681$	3.28447e7	+	3.28447e7i	0.103998	+	0.103998i
$682$	−5.02312e7			−0.158351
$683$	3.88510e8	−	3.88510e8i	1.21938	−	1.21938i	0.251536	−	0.967848i	$-0.419064\pi$
$683$	3.88510e8	−	3.88510e8i	1.21938	−	1.21938i	0.967848	−	0.251536i	$-0.0809358\pi$
$684$	7.04121e6	+	7.04121e6i	0.0220028	+	0.0220028i
$685$	−2.09918e8	+	2.09918e8i	−0.653098	+	0.653098i
$686$	−6.16081e7	−	6.16081e7i	−0.190838	−	0.190838i
$687$			6.53362e8i			2.01504i
$688$	2.11720e7	−	2.11720e7i	0.0650124	−	0.0650124i
$689$	−1.57871e7	+	1.57871e7i	−0.0482664	+	0.0482664i
$690$	−3.48896e8	−	3.48896e8i	−1.06206	−	1.06206i
$691$		−	2.96784e8i		−	0.899510i	−0.893152	−	0.449755i	$-0.851511\pi$
$691$		−	2.96784e8i		−	0.899510i	0.893152	−	0.449755i	$-0.148489\pi$
$692$	5.14585e7			0.155288
$693$		−	9.68697e7i		−	0.291064i
$694$			3.80776e8i			1.13918i
$695$	−3.76150e6	−	3.76150e6i	−0.0112049	−	0.0112049i
$696$			1.85455e8i			0.550060i
$697$	5.28125e7	+	5.28125e7i	0.155969	+	0.155969i
$698$	−5.67784e7	−	5.67784e7i	−0.166962	−	0.166962i
$699$	5.05282e8			1.47946
$700$	−1.11047e7			−0.0323752
$701$	−3.26601e8	+	3.26601e8i	−0.948120	+	0.948120i	−0.998719	−	0.0505994i	$-0.983887\pi$
$701$	−3.26601e8	+	3.26601e8i	−0.948120	+	0.948120i	0.0505994	+	0.998719i	$0.483887\pi$
$702$		−	1.08057e8i		−	0.312351i
$703$	1.92754e6	−	1.44734e7i	0.00554801	−	0.0416586i
$704$	4.40711e7			0.126310
$705$	1.90374e8	+	1.90374e8i	0.543301	+	0.543301i
$706$		−	1.30003e8i		−	0.369437i
$707$			1.87052e7i			0.0529304i
$708$	−9.51508e7	+	9.51508e7i	−0.268110	+	0.268110i
$709$	−4.56590e8	+	4.56590e8i	−1.28112	+	1.28112i	−0.341081	+	0.940034i	$0.610793\pi$
$709$	−4.56590e8	+	4.56590e8i	−1.28112	+	1.28112i	−0.940034	+	0.341081i	$0.889207\pi$
$710$	−3.18115e7			−0.0888812
$711$	−1.85591e8	+	1.85591e8i	−0.516356	+	0.516356i
$712$	−1.29938e8			−0.359996
$713$	1.32634e8			0.365921
$714$			2.13202e7i			0.0585728i
$715$	−1.75966e8			−0.481405
$716$	−2.65069e7	+	2.65069e7i	−0.0722138	+	0.0722138i
$717$	4.57972e7	+	4.57972e7i	0.124246	+	0.124246i
$718$	−1.41578e8	−	1.41578e8i	−0.382492	−	0.382492i
$719$	3.73741e8			1.00550			0.502752	−	0.864431i	$-0.332321\pi$
$719$	3.73741e8			1.00550			0.502752	+	0.864431i	$0.332321\pi$
$720$	−7.98045e7	+	7.98045e7i	−0.213811	+	0.213811i
$721$	−7.71120e7	−	7.71120e7i	−0.205739	−	0.205739i
$722$	−1.87851e8	+	1.87851e8i	−0.499117	+	0.499117i
$723$	7.19008e8	+	7.19008e8i	1.90248	+	1.90248i
$724$		−	2.84019e8i		−	0.748397i
$725$	8.86011e7	−	8.86011e7i	0.232501	−	0.232501i
$726$	6.34738e6	−	6.34738e6i	0.0165877	−	0.0165877i
$727$	6.52644e7	+	6.52644e7i	0.169853	+	0.169853i	0.786915	−	0.617062i	$-0.211677\pi$
$727$	6.52644e7	+	6.52644e7i	0.169853	+	0.169853i	−0.617062	+	0.786915i	$0.711677\pi$
$728$			1.54771e7i			0.0401140i
$729$	6.27347e8			1.61929
$730$		−	8.29739e7i		−	0.213291i
$731$			3.88398e7i			0.0994316i
$732$	−4.03736e8	−	4.03736e8i	−1.02935	−	1.02935i
$733$		−	4.64967e8i		−	1.18062i	−0.807176	−	0.590311i	$-0.799005\pi$
$733$		−	4.64967e8i		−	1.18062i	0.807176	−	0.590311i	$-0.200995\pi$
$734$	−3.54418e7	−	3.54418e7i	−0.0896246	−	0.0896246i
$735$	3.47533e8	+	3.47533e8i	0.875254	+	0.875254i
$736$	−1.16369e8			−0.291879
$737$	−5.69036e8			−1.42147
$738$	2.42796e8	−	2.42796e8i	0.604048	−	0.604048i
$739$			1.70327e8i			0.422037i	0.977482	+	0.211018i	$0.0676780\pi$
$739$			1.70327e8i			0.422037i	−0.977482	+	0.211018i	$0.932322\pi$
$740$	1.64040e8	+	2.18466e7i	0.404814	+	0.0539124i
$741$	−1.57092e7			−0.0386100
$742$	−4.64967e6	−	4.64967e6i	−0.0113818	−	0.0113818i
$743$		−	5.76274e8i		−	1.40496i	−0.711705	−	0.702478i	$-0.752077\pi$
$743$		−	5.76274e8i		−	1.40496i	0.711705	−	0.702478i	$-0.247923\pi$
$744$		−	5.08254e7i		−	0.123413i
$745$	−2.99971e8	+	2.99971e8i	−0.725456	+	0.725456i
$746$	−3.67664e8	+	3.67664e8i	−0.885594	+	0.885594i
$747$	−2.98190e8			−0.715371
$748$	−4.04240e7	+	4.04240e7i	−0.0965905	+	0.0965905i
$749$	−1.75723e7			−0.0418200
$750$	5.11516e8			1.21248
$751$			2.28343e7i			0.0539099i	0.999637	+	0.0269549i	$0.00858106\pi$
$751$			2.28343e7i			0.0539099i	−0.999637	+	0.0269549i	$0.991419\pi$
$752$	6.34963e7			0.149312
$753$	9.01865e8	−	9.01865e8i	2.11230	−	2.11230i
$754$	−1.23487e8	−	1.23487e8i	−0.288077	−	0.288077i
$755$	−1.40422e8	−	1.40422e8i	−0.326284	−	0.326284i
$756$	3.18254e7			0.0736560
$757$	3.89293e8	−	3.89293e8i	0.897406	−	0.897406i	−0.0978003	−	0.995206i	$-0.531181\pi$
$757$	3.89293e8	−	3.89293e8i	0.897406	−	0.897406i	0.995206	+	0.0978003i	$0.0311806\pi$
$758$	−1.09876e8	−	1.09876e8i	−0.252288	−	0.252288i
$759$	−8.12477e8	+	8.12477e8i	−1.85817	+	1.85817i
$760$	3.76709e6	+	3.76709e6i	0.00858155	+	0.00858155i
$761$		−	2.94909e8i		−	0.669166i	−0.942366	−	0.334583i	$-0.891405\pi$
$761$		−	2.94909e8i		−	0.669166i	0.942366	−	0.334583i	$-0.108595\pi$
$762$	5.80127e8	−	5.80127e8i	1.31117	−	1.31117i
$763$	8.12812e7	−	8.12812e7i	0.182985	−	0.182985i
$764$	−1.14310e8	−	1.14310e8i	−0.256334	−	0.256334i
$765$		−	1.46400e8i		−	0.327008i
$766$	5.30246e7			0.117975
$767$		−	1.26715e8i		−	0.280828i
$768$			4.45924e7i			0.0984413i
$769$	3.23518e8	+	3.23518e8i	0.711409	+	0.711409i	0.966830	−	0.255421i	$-0.0822140\pi$
$769$	3.23518e8	+	3.23518e8i	0.711409	+	0.711409i	−0.255421	+	0.966830i	$0.582214\pi$
$770$		−	5.18260e7i		−	0.113521i
$771$	−4.73113e8	−	4.73113e8i	−1.03229	−	1.03229i
$772$	6.86644e7	+	6.86644e7i	0.149238	+	0.149238i
$773$	2.66357e7			0.0576668			0.0288334	−	0.999584i	$-0.490821\pi$
$773$	2.66357e7			0.0576668			0.0288334	+	0.999584i	$0.490821\pi$
$774$	1.78559e8			0.385086
$775$	−2.42818e7	+	2.42818e7i	−0.0521647	+	0.0521647i
$776$		−	1.64739e8i		−	0.352542i
$777$	−8.73209e7	−	1.14153e8i	−0.186147	−	0.243346i
$778$	6.04928e8			1.28459
$779$	−1.14609e7	−	1.14609e7i	−0.0242442	−	0.0242442i
$780$		−	1.78047e8i		−	0.375190i
$781$			7.40799e7i			0.155506i
$782$	1.06738e8	−	1.06738e8i	0.223203	−	0.223203i
$783$	−2.53925e8	+	2.53925e8i	−0.528957	+	0.528957i
$784$	1.15914e8			0.240541
$785$	−5.13186e8	+	5.13186e8i	−1.06088	+	1.06088i
$786$	−5.36381e7			−0.110460
$787$	4.30446e8			0.883069			0.441535	−	0.897244i	$-0.354434\pi$
$787$	4.30446e8			0.883069			0.441535	+	0.897244i	$0.354434\pi$
$788$			2.16823e8i			0.443126i
$789$	−1.64412e7			−0.0334736
$790$	−9.92926e7	+	9.92926e7i	−0.201389	+	0.201389i
$791$	−5.81921e7	−	5.81921e7i	−0.117580	−	0.117580i
$792$	1.85842e8	+	1.85842e8i	0.374083	+	0.374083i
$793$	5.37665e8			1.07818
$794$	−2.12381e8	+	2.12381e8i	−0.424281	+	0.424281i
$795$	5.34893e7	+	5.34893e7i	0.106455	+	0.106455i
$796$	−2.11492e8	+	2.11492e8i	−0.419329	+	0.419329i
$797$	5.39929e8	+	5.39929e8i	1.06650	+	1.06650i	0.997625	+	0.0688768i	$0.0219415\pi$
$797$	5.39929e8	+	5.39929e8i	1.06650	+	1.06650i	0.0688768	+	0.997625i	$0.478058\pi$
$798$		−	4.62673e6i		−	0.00910469i
$799$	−5.82416e7	+	5.82416e7i	−0.114181	+	0.114181i
$800$	2.13040e7	−	2.13040e7i	0.0416095	−	0.0416095i
$801$	−5.47932e8	−	5.47932e8i	−1.06618	−	1.06618i
$802$		−	4.79291e8i		−	0.929129i
$803$	−1.93222e8			−0.373174
$804$		−	5.75767e8i		−	1.10784i
$805$			1.36845e8i			0.262326i
$806$	3.38427e7	+	3.38427e7i	0.0646339	+	0.0646339i
$807$		−	1.08138e9i		−	2.05759i
$808$	−3.58855e7	−	3.58855e7i	−0.0680275	−	0.0680275i
$809$	3.67732e8	+	3.67732e8i	0.694523	+	0.694523i	0.963224	−	0.268701i	$-0.0865944\pi$
$809$	3.67732e8	+	3.67732e8i	0.694523	+	0.694523i	−0.268701	+	0.963224i	$0.586594\pi$
$810$	8.83958e7			0.166332
$811$	−5.38213e8			−1.00900			−0.504501	−	0.863411i	$-0.668323\pi$
$811$	−5.38213e8			−1.00900			−0.504501	+	0.863411i	$0.668323\pi$
$812$	3.63699e7	−	3.63699e7i	0.0679319	−	0.0679319i
$813$			1.08729e8i			0.202335i
$814$	5.08744e7	−	3.82003e8i	0.0943249	−	0.708261i
$815$	−6.80843e8			−1.25769
$816$	−4.09021e7	−	4.09021e7i	−0.0752793	−	0.0752793i
$817$		−	8.42868e6i		−	0.0154559i
$818$		−	4.34556e8i		−	0.793937i
$819$	−6.52648e7	+	6.52648e7i	−0.118803	+	0.118803i
$820$	1.29897e8	−	1.29897e8i	0.235591	−	0.235591i
$821$	5.15529e7			0.0931588			0.0465794	−	0.998915i	$-0.485168\pi$
$821$	5.15529e7			0.0931588			0.0465794	+	0.998915i	$0.485168\pi$
$822$	−4.94621e8	+	4.94621e8i	−0.890548	+	0.890548i
$823$	1.75584e8			0.314982			0.157491	−	0.987520i	$-0.449660\pi$
$823$	1.75584e8			0.314982			0.157491	+	0.987520i	$0.449660\pi$
$824$	2.95874e8			0.528842
$825$		−	2.97487e8i		−	0.529792i
$826$	3.73204e7			0.0662225
$827$	−2.21813e8	+	2.21813e8i	−0.392167	+	0.392167i	−0.875459	−	0.483292i	$-0.839441\pi$
$827$	−2.21813e8	+	2.21813e8i	−0.392167	+	0.392167i	0.483292	+	0.875459i	$0.339441\pi$
$828$	−4.90710e8	−	4.90710e8i	−0.864438	−	0.864438i
$829$	−3.28545e8	−	3.28545e8i	−0.576676	−	0.576676i	0.357310	−	0.933986i	$-0.383694\pi$
$829$	−3.28545e8	−	3.28545e8i	−0.576676	−	0.576676i	−0.933986	+	0.357310i	$0.883694\pi$
$830$	−1.59534e8			−0.279009
$831$	−8.83702e8	+	8.83702e8i	−1.53994	+	1.53994i
$832$	−2.96924e7	−	2.96924e7i	−0.0515556	−	0.0515556i
$833$	−1.06322e8	+	1.06322e8i	−0.183944	+	0.183944i
$834$	−8.86306e6	−	8.86306e6i	−0.0152787	−	0.0152787i
$835$			5.36645e8i			0.921781i
$836$	8.77248e6	−	8.77248e6i	0.0150142	−	0.0150142i
$837$	6.95903e7	−	6.95903e7i	0.118679	−	0.118679i
$838$	−3.64708e8	−	3.64708e8i	−0.619746	−	0.619746i
$839$			3.42334e7i			0.0579648i	0.999580	+	0.0289824i	$0.00922668\pi$
$839$			3.42334e7i			0.0579648i	−0.999580	+	0.0289824i	$0.990773\pi$
$840$	5.24390e7			0.0884741
$841$		−	1.44549e7i		−	0.0243011i
$842$			2.54927e8i			0.427050i
$843$	−1.04600e9	−	1.04600e9i	−1.74602	−	1.74602i
$844$			2.80516e8i			0.466585i
$845$	−2.29910e8	−	2.29910e8i	−0.381054	−	0.381054i
$846$	2.67755e8	+	2.67755e8i	0.442208	+	0.442208i
$847$	−2.48959e6			−0.00409711
$848$	1.78405e7			0.0292563
$849$	−7.05463e8	+	7.05463e8i	−1.15279	+	1.15279i
$850$			3.90820e7i			0.0636385i
$851$	−1.34333e8	+	1.00867e9i	−0.217968	+	1.63666i
$852$	−7.49562e7			−0.121196
$853$	−5.91914e8	−	5.91914e8i	−0.953699	−	0.953699i	0.0452754	−	0.998975i	$-0.485583\pi$
$853$	−5.91914e8	−	5.91914e8i	−0.953699	−	0.953699i	−0.998975	+	0.0452754i	$0.985583\pi$
$854$			1.58355e8i			0.254248i
$855$			3.17706e7i			0.0508308i
$856$	3.37120e7	−	3.37120e7i	0.0537482	−	0.0537482i
$857$	3.55449e8	−	3.55449e8i	0.564723	−	0.564723i	−0.365923	−	0.930645i	$-0.619246\pi$
$857$	3.55449e8	−	3.55449e8i	0.564723	−	0.564723i	0.930645	+	0.365923i	$0.119246\pi$
$858$	−4.14621e8			−0.656431
$859$	7.66151e8	−	7.66151e8i	1.20875	−	1.20875i	0.237312	−	0.971433i	$-0.423734\pi$
$859$	7.66151e8	−	7.66151e8i	1.20875	−	1.20875i	0.971433	−	0.237312i	$-0.0762664\pi$
$860$	9.55301e7			0.150191
$861$	−1.59539e8			−0.249953
$862$			5.64016e8i			0.880582i
$863$	1.85885e7			0.0289209			0.0144604	−	0.999895i	$-0.495397\pi$
$863$	1.85885e7			0.0289209			0.0144604	+	0.999895i	$0.495397\pi$
$864$	−6.10561e7	+	6.10561e7i	−0.0946646	+	0.0946646i
$865$	1.16093e8	+	1.16093e8i	0.179373	+	0.179373i
$866$	3.22321e8	+	3.22321e8i	0.496290	+	0.496290i
$867$	−9.51455e8			−1.45993
$868$	−9.96746e6	+	9.96746e6i	−0.0152414	+	0.0152414i
$869$	2.31224e8	+	2.31224e8i	0.352349	+	0.352349i
$870$	−4.18395e8	+	4.18395e8i	−0.635373	+	0.635373i
$871$	3.83381e8	+	3.83381e8i	0.580198	+	0.580198i
$872$			3.11871e8i			0.470355i
$873$	6.94680e8	−	6.94680e8i	1.04410	−	1.04410i
$874$	−2.31635e7	+	2.31635e7i	−0.0346952	+	0.0346952i
$875$	−1.00314e8	−	1.00314e8i	−0.149740	−	0.149740i
$876$		−	1.95508e8i		−	0.290839i
$877$	6.84929e8			1.01542			0.507711	−	0.861527i	$-0.330492\pi$
$877$	6.84929e8			1.01542			0.507711	+	0.861527i	$0.330492\pi$
$878$		−	4.59474e8i		−	0.678855i
$879$			2.06266e9i			3.03711i
$880$	9.94266e7	+	9.94266e7i	0.145900	+	0.145900i
$881$		−	1.22419e9i		−	1.79028i	−0.445785	−	0.895140i	$-0.647076\pi$
$881$		−	1.22419e9i		−	1.79028i	0.445785	−	0.895140i	$-0.352924\pi$
$882$	4.88794e8	+	4.88794e8i	0.712394	+	0.712394i
$883$	6.77183e8	+	6.77183e8i	0.983612	+	0.983612i	0.999868	−	0.0162561i	$-0.00517471\pi$
$883$	6.77183e8	+	6.77183e8i	0.983612	+	0.983612i	−0.0162561	+	0.999868i	$0.505175\pi$
$884$	5.44704e7			0.0788504
$885$	−4.29330e8			−0.619386
$886$	4.56195e8	−	4.56195e8i	0.655917	−	0.655917i
$887$			3.01417e6i			0.00431914i	0.999998	+	0.00215957i	$0.000687413\pi$
$887$			3.01417e6i			0.00431914i	−0.999998	+	0.00215957i	$0.999313\pi$
$888$	3.86521e8	+	5.14762e7i	0.551995	+	0.0735136i
$889$	−2.27539e8			−0.323856
$890$	−2.93148e8	−	2.93148e8i	−0.415830	−	0.415830i
$891$		−	2.05848e8i		−	0.291014i
$892$		−	9.97683e7i		−	0.140572i
$893$	1.26391e7	−	1.26391e7i	0.0177485	−	0.0177485i
$894$	−7.06810e8	+	7.06810e8i	−0.989214	+	0.989214i
$895$	−1.19602e8			−0.166828
$896$	8.74510e6	−	8.74510e6i	0.0121574	−	0.0121574i
$897$	1.09479e9			1.51689
$898$	1.00262e8			0.138455
$899$		−	1.59055e8i		−	0.218911i
$900$	1.79672e8			0.246464
$901$	−1.63641e7	+	1.63641e7i	−0.0223727	+	0.0223727i
$902$	−3.02494e8	−	3.02494e8i	−0.412189	−	0.412189i
$903$	−5.86648e7	−	5.86648e7i	−0.0796736	−	0.0796736i
$904$	2.23280e8			0.302234
$905$	6.40761e8	−	6.40761e8i	0.864471	−	0.864471i
$906$	−3.30871e8	−	3.30871e8i	−0.444913	−	0.444913i
$907$	−2.14418e8	+	2.14418e8i	−0.287369	+	0.287369i	−0.836039	−	0.548670i	$-0.815134\pi$
$907$	−2.14418e8	+	2.14418e8i	−0.287369	+	0.287369i	0.548670	+	0.836039i	$0.315134\pi$
$908$	2.47146e7	+	2.47146e7i	0.0330138	+	0.0330138i
$909$		−	3.02648e8i		−	0.402945i
$910$	−3.49171e7	+	3.49171e7i	−0.0463356	+	0.0463356i
$911$	6.31700e8	−	6.31700e8i	0.835518	−	0.835518i	−0.152747	−	0.988265i	$-0.548812\pi$
$911$	6.31700e8	−	6.31700e8i	0.835518	−	0.835518i	0.988265	+	0.152747i	$0.0488121\pi$
$912$	8.87624e6	+	8.87624e6i	0.0117016	+	0.0117016i
$913$			3.71508e8i			0.488153i
$914$	−1.27611e8			−0.167128
$915$		−	1.82170e9i		−	2.37801i
$916$			4.91635e8i			0.639670i
$917$	1.05191e7	+	1.05191e7i	0.0136417	+	0.0136417i
$918$		−	1.12007e8i		−	0.144782i
$919$	−6.85747e8	−	6.85747e8i	−0.883523	−	0.883523i	0.110368	−	0.993891i	$-0.464797\pi$
$919$	−6.85747e8	−	6.85747e8i	−0.883523	−	0.883523i	−0.993891	+	0.110368i	$0.964797\pi$
$920$	−2.62533e8	−	2.62533e8i	−0.337148	−	0.337148i
$921$	1.65634e9			2.12017
$922$	8.83295e7			0.112697
$923$	4.99105e7	−	4.99105e7i	0.0634727	−	0.0634727i
$924$		−	1.22115e8i		−	0.154794i
$925$	−1.60068e8	−	2.09253e8i	−0.202246	−	0.264391i
$926$	1.83516e8			0.231121
$927$	1.24766e9	+	1.24766e9i	1.56624	+	1.56624i
$928$			1.39549e8i			0.174616i
$929$			4.55218e8i			0.567770i	0.958858	+	0.283885i	$0.0916234\pi$
$929$			4.55218e8i			0.567770i	−0.958858	+	0.283885i	$0.908377\pi$
$930$	1.14665e8	−	1.14665e8i	0.142554	−	0.142554i
$931$	2.30730e7	−	2.30730e7i	0.0285927	−	0.0285927i
$932$	3.80209e8			0.469650
$933$	8.88404e8	−	8.88404e8i	1.09387	−	1.09387i
$934$	1.62760e8			0.199759
$935$	−1.82397e8			−0.223143
$936$		−	2.50417e8i		−	0.305377i
$937$	3.82466e8			0.464916			0.232458	−	0.972606i	$-0.425323\pi$
$937$	3.82466e8			0.464916			0.232458	+	0.972606i	$0.425323\pi$
$938$	−1.12915e8	+	1.12915e8i	−0.136818	+	0.136818i
$939$	8.18461e8	+	8.18461e8i	0.988555	+	0.988555i
$940$	1.43251e8	+	1.43251e8i	0.172470	+	0.172470i
$941$	−1.25788e9			−1.50963			−0.754817	−	0.655935i	$-0.772274\pi$
$941$	−1.25788e9			−1.50963			−0.754817	+	0.655935i	$0.772274\pi$
$942$	−1.20920e9	+	1.20920e9i	−1.44659	+	1.44659i
$943$	7.98726e8	+	7.98726e8i	0.952495	+	0.952495i
$944$	−7.15981e7	+	7.15981e7i	−0.0851109	+	0.0851109i
$945$	7.17996e7	+	7.17996e7i	0.0850798	+	0.0850798i
$946$		−	2.22462e8i		−	0.262774i
$947$	6.65338e8	−	6.65338e8i	0.783415	−	0.783415i	−0.196990	−	0.980405i	$-0.563117\pi$
$947$	6.65338e8	−	6.65338e8i	0.783415	−	0.783415i	0.980405	+	0.196990i	$0.0631167\pi$
$948$	−2.33959e8	+	2.33959e8i	−0.274609	+	0.274609i
$949$	1.30181e8	+	1.30181e8i	0.152318	+	0.152318i
$950$		−	8.48125e6i		−	0.00989212i
$951$	−9.35010e8			−1.08711
$952$			1.60428e7i			0.0185938i
$953$			1.54824e9i			1.78879i	0.447281	+	0.894394i	$0.352392\pi$
$953$			1.54824e9i			1.78879i	−0.447281	+	0.894394i	$0.647608\pi$
$954$	7.52309e7	+	7.52309e7i	0.0866466	+	0.0866466i
$955$		−	5.15780e8i		−	0.592181i
$956$	3.44610e7	+	3.44610e7i	0.0394416	+	0.0394416i
$957$	9.74322e8	+	9.74322e8i	1.11165	+	1.11165i
$958$	1.02118e9			1.16146
$959$	1.94002e8			0.219963
$960$	−1.00603e8	+	1.00603e8i	−0.113709	+	0.113709i
$961$		−	8.43913e8i		−	0.950884i
$962$	−2.91646e8	+	2.23094e8i	−0.327590	+	0.250589i
$963$	2.84318e8			0.318365
$964$	5.41032e8	+	5.41032e8i	0.603937	+	0.603937i
$965$			3.09820e8i			0.344769i
$966$			3.22442e8i			0.357701i
$967$	3.27867e8	−	3.27867e8i	0.362592	−	0.362592i	−0.502175	−	0.864766i	$-0.667467\pi$
$967$	3.27867e8	−	3.27867e8i	0.362592	−	0.362592i	0.864766	+	0.502175i	$0.167467\pi$
$968$	4.77621e6	−	4.77621e6i	0.00526572	−	0.00526572i
$969$	−1.62834e7			−0.0178967
$970$	3.71659e8	−	3.71659e8i	0.407220	−	0.407220i
$971$	1.14949e9			1.25559			0.627795	−	0.778379i	$-0.283958\pi$
$971$	1.14949e9			1.25559			0.627795	+	0.778379i	$0.283958\pi$
$972$	5.56017e8			0.605465
$973$			3.47630e6i			0.00377380i
$974$	5.94214e8			0.643082
$975$	−2.00428e8	+	2.00428e8i	−0.216244	+	0.216244i
$976$	−3.03799e8	−	3.03799e8i	−0.326766	−	0.326766i
$977$	−1.91579e8	−	1.91579e8i	−0.205431	−	0.205431i	0.596891	−	0.802322i	$-0.296402\pi$
$977$	−1.91579e8	−	1.91579e8i	−0.205431	−	0.205431i	−0.802322	+	0.596891i	$0.796402\pi$
$978$	−1.60424e9			−1.71496
$979$	−6.82656e8	+	6.82656e8i	−0.727535	+	0.727535i
$980$	2.61508e8	+	2.61508e8i	0.277848	+	0.277848i
$981$	−1.31512e9	+	1.31512e9i	−1.39302	+	1.39302i
$982$	6.60510e8	+	6.60510e8i	0.697501	+	0.697501i
$983$		−	1.44455e9i		−	1.52080i	−0.649458	−	0.760398i	$-0.725004\pi$
$983$		−	1.44455e9i		−	1.52080i	0.649458	−	0.760398i	$-0.274996\pi$
$984$	3.06072e8	−	3.06072e8i	0.321246	−	0.321246i
$985$	−4.89164e8	+	4.89164e8i	−0.511854	+	0.511854i
$986$	−1.28001e8	−	1.28001e8i	−0.133531	−	0.133531i
$987$		−	1.75940e8i		−	0.182984i
$988$	−1.18207e7			−0.0122567
$989$			5.87405e8i			0.607224i
$990$			8.38536e8i			0.864204i
$991$	−3.81182e8	−	3.81182e8i	−0.391661	−	0.391661i	0.483618	−	0.875279i	$-0.339322\pi$
$991$	−3.81182e8	−	3.81182e8i	−0.391661	−	0.391661i	−0.875279	+	0.483618i	$0.839322\pi$
$992$		−	3.82446e7i		−	0.0391773i
$993$	−1.68078e9	−	1.68078e9i	−1.71658	−	1.71658i
$994$	1.46998e7	+	1.46998e7i	0.0149676	+	0.0149676i
$995$	−9.54273e8			−0.968731
$996$	−3.75902e8			−0.380449
$997$	−1.31424e9	+	1.31424e9i	−1.32613	+	1.32613i	−0.417422	+	0.908713i	$0.637066\pi$
$997$	−1.31424e9	+	1.31424e9i	−1.32613	+	1.32613i	−0.908713	+	0.417422i	$0.862934\pi$
$998$			6.43268e8i			0.647144i
$999$	4.58745e8	+	5.99708e8i	0.460124	+	0.601510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.a.31.8	✓	18
37.6	odd	4	inner	74.7.d.a.43.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.a.31.8	✓	18	1.1	even	1	trivial
74.7.d.a.43.2	yes	18	37.6	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 4.00000i) q^{2} +42.5266i q^{3} +32.0000i q^{4} +(-72.1936 + 72.1936i) q^{5} +(-170.107 + 170.107i) q^{6} +66.7198 q^{7} +(-128.000 + 128.000i) q^{8} -1079.52 q^{9} +O(q^{10})\)	\(q+(4.00000 + 4.00000i) q^{2} +42.5266i q^{3} +32.0000i q^{4} +(-72.1936 + 72.1936i) q^{5} +(-170.107 + 170.107i) q^{6} +66.7198 q^{7} +(-128.000 + 128.000i) q^{8} -1079.52 q^{9} -577.548 q^{10} +1344.94i q^{11} -1360.85 q^{12} +(906.141 - 906.141i) q^{13} +(266.879 + 266.879i) q^{14} +(-3070.15 - 3070.15i) q^{15} -1024.00 q^{16} +(939.258 - 939.258i) q^{17} +(-4318.06 - 4318.06i) q^{18} +(-203.830 + 203.830i) q^{19} +(-2310.19 - 2310.19i) q^{20} +2837.37i q^{21} +(-5379.78 + 5379.78i) q^{22} +(14205.2 - 14205.2i) q^{23} +(-5443.41 - 5443.41i) q^{24} +5201.18i q^{25} +7249.12 q^{26} -14906.3i q^{27} +2135.03i q^{28} +(-17034.8 - 17034.8i) q^{29} -24561.2i q^{30} +(4668.52 + 4668.52i) q^{31} +(-4096.00 - 4096.00i) q^{32} -57196.0 q^{33} +7514.07 q^{34} +(-4816.74 + 4816.74i) q^{35} -34544.5i q^{36} +(-40231.9 + 30775.3i) q^{37} -1630.64 q^{38} +(38535.1 + 38535.1i) q^{39} -18481.5i q^{40} +56227.9i q^{41} +(-11349.5 + 11349.5i) q^{42} +(-20675.8 + 20675.8i) q^{43} -43038.2 q^{44} +(77934.1 - 77934.1i) q^{45} +113641. q^{46} -62008.1 q^{47} -43547.3i q^{48} -113197. q^{49} +(-20804.7 + 20804.7i) q^{50} +(39943.5 + 39943.5i) q^{51} +(28996.5 + 28996.5i) q^{52} -17422.4 q^{53} +(59625.1 - 59625.1i) q^{54} +(-97096.3 - 97096.3i) q^{55} +(-8540.13 + 8540.13i) q^{56} +(-8668.21 - 8668.21i) q^{57} -136278. i q^{58} +(69920.0 - 69920.0i) q^{59} +(98244.8 - 98244.8i) q^{60} +(296679. + 296679. i) q^{61} +37348.2i q^{62} -72025.1 q^{63} -32768.0i q^{64} +130835. i q^{65} +(-228784. - 228784. i) q^{66} +423093. i q^{67} +(30056.3 + 30056.3i) q^{68} +(604097. + 604097. i) q^{69} -38533.9 q^{70} +55080.3 q^{71} +(138178. - 138178. i) q^{72} +143666. i q^{73} +(-284029. - 37826.4i) q^{74} -221189. q^{75} +(-6522.56 - 6522.56i) q^{76} +89734.4i q^{77} +308281. i q^{78} +(171921. - 171921. i) q^{79} +(73926.2 - 73926.2i) q^{80} -153054. q^{81} +(-224912. + 224912. i) q^{82} +276226. q^{83} -90795.8 q^{84} +135617. i q^{85} -165406. q^{86} +(724433. - 724433. i) q^{87} +(-172153. - 172153. i) q^{88} +(507572. + 507572. i) q^{89} +623473. q^{90} +(60457.5 - 60457.5i) q^{91} +(454565. + 454565. i) q^{92} +(-198537. + 198537. i) q^{93} +(-248032. - 248032. i) q^{94} -29430.4i q^{95} +(174189. - 174189. i) q^{96} +(-643511. + 643511. i) q^{97} +(-452790. - 452790. i) q^{98} -1.45189e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9 + 2352 * q^10 - 2048 * q^12 - 6766 * q^13 - 416 * q^14 - 2136 * q^15 - 18432 * q^16 - 9134 * q^17 - 16168 * q^18 + 7578 * q^19 + 9408 * q^20 + 8928 * q^22 - 50578 * q^23 - 8192 * q^24 - 54128 * q^26 - 42950 * q^29 - 17358 * q^31 - 73728 * q^32 - 11056 * q^33 - 73072 * q^34 + 62152 * q^35 - 238242 * q^37 + 60624 * q^38 + 31572 * q^39 + 229024 * q^42 - 65470 * q^43 + 71424 * q^44 - 482358 * q^45 - 404624 * q^46 + 232192 * q^47 + 791686 * q^49 + 93752 * q^50 - 386848 * q^51 - 216512 * q^52 + 49972 * q^53 - 144560 * q^54 + 160168 * q^55 + 13312 * q^56 + 488476 * q^57 - 181570 * q^59 + 68352 * q^60 + 508802 * q^61 + 404788 * q^63 - 44224 * q^66 - 292288 * q^68 + 604532 * q^69 + 497216 * q^70 - 202632 * q^71 + 517376 * q^72 - 1191224 * q^74 + 2476628 * q^75 + 242496 * q^76 + 1752858 * q^79 - 301056 * q^80 + 2760658 * q^81 - 145808 * q^82 + 2371616 * q^83 + 1832192 * q^84 - 523760 * q^86 - 4188080 * q^87 + 285696 * q^88 + 1148346 * q^89 - 3858864 * q^90 + 433120 * q^91 - 1618496 * q^92 + 1589664 * q^93 + 928768 * q^94 + 262144 * q^96 - 1670270 * q^97 + 3166744 * q^98

Introduction

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