LMFDB - Embedded newform 74.7.d.a.31.7

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			31.7
Root			$19.7872i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 4.00000i) q^{2} +23.7872i q^{3} +32.0000i q^{4} +(114.190 - 114.190i) q^{5} +(-95.1488 + 95.1488i) q^{6} +375.130 q^{7} +(-128.000 + 128.000i) q^{8} +163.169 q^{9} +O(q^{10})$	\(q+(4.00000 + 4.00000i) q^{2} +23.7872i q^{3} +32.0000i q^{4} +(114.190 - 114.190i) q^{5} +(-95.1488 + 95.1488i) q^{6} +375.130 q^{7} +(-128.000 + 128.000i) q^{8} +163.169 q^{9} +913.518 q^{10} +159.466i q^{11} -761.191 q^{12} +(2822.42 - 2822.42i) q^{13} +(1500.52 + 1500.52i) q^{14} +(2716.26 + 2716.26i) q^{15} -1024.00 q^{16} +(-2322.15 + 2322.15i) q^{17} +(652.675 + 652.675i) q^{18} +(205.346 - 205.346i) q^{19} +(3654.07 + 3654.07i) q^{20} +8923.29i q^{21} +(-637.864 + 637.864i) q^{22} +(-14151.5 + 14151.5i) q^{23} +(-3044.76 - 3044.76i) q^{24} -10453.6i q^{25} +22579.3 q^{26} +21222.2i q^{27} +12004.2i q^{28} +(5408.08 + 5408.08i) q^{29} +21730.1i q^{30} +(-9201.74 - 9201.74i) q^{31} +(-4096.00 - 4096.00i) q^{32} -3793.25 q^{33} -18577.2 q^{34} +(42836.0 - 42836.0i) q^{35} +5221.40i q^{36} +(25291.5 - 43887.0i) q^{37} +1642.76 q^{38} +(67137.4 + 67137.4i) q^{39} +29232.6i q^{40} +7137.50i q^{41} +(-35693.2 + 35693.2i) q^{42} +(-32954.9 + 32954.9i) q^{43} -5102.91 q^{44} +(18632.2 - 18632.2i) q^{45} -113212. q^{46} -49758.4 q^{47} -24358.1i q^{48} +23073.4 q^{49} +(41814.5 - 41814.5i) q^{50} +(-55237.5 - 55237.5i) q^{51} +(90317.3 + 90317.3i) q^{52} +149694. q^{53} +(-84888.8 + 84888.8i) q^{54} +(18209.4 + 18209.4i) q^{55} +(-48016.6 + 48016.6i) q^{56} +(4884.60 + 4884.60i) q^{57} +43264.6i q^{58} +(199829. - 199829. i) q^{59} +(-86920.2 + 86920.2i) q^{60} +(-121939. - 121939. i) q^{61} -73613.9i q^{62} +61209.5 q^{63} -32768.0i q^{64} -644582. i q^{65} +(-15173.0 - 15173.0i) q^{66} +349031. i q^{67} +(-74308.8 - 74308.8i) q^{68} +(-336625. - 336625. i) q^{69} +342688. q^{70} -478158. q^{71} +(-20885.6 + 20885.6i) q^{72} -711656. i q^{73} +(276714. - 74382.1i) q^{74} +248663. q^{75} +(6571.06 + 6571.06i) q^{76} +59820.4i q^{77} +537099. i q^{78} +(-385903. + 385903. i) q^{79} +(-116930. + 116930. i) q^{80} -385867. q^{81} +(-28550.0 + 28550.0i) q^{82} +458417. q^{83} -285545. q^{84} +530332. i q^{85} -263639. q^{86} +(-128643. + 128643. i) q^{87} +(-20411.6 - 20411.6i) q^{88} +(-411592. - 411592. i) q^{89} +149058. q^{90} +(1.05877e6 - 1.05877e6i) q^{91} +(-452849. - 452849. i) q^{92} +(218884. - 218884. i) q^{93} +(-199033. - 199033. i) q^{94} -46896.8i q^{95} +(97432.4 - 97432.4i) q^{96} +(214684. - 214684. i) q^{97} +(92293.5 + 92293.5i) q^{98} +26019.9i 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
$3$			23.7872i			0.881008i	0.897751	+	0.440504i	$0.145200\pi$
$3$			23.7872i			0.881008i	−0.897751	+	0.440504i	$0.854800\pi$
$4$			32.0000i			0.500000i
$5$	114.190	−	114.190i	0.913518	−	0.913518i	−0.0830287	−	0.996547i	$-0.526459\pi$
$5$	114.190	−	114.190i	0.913518	−	0.913518i	0.996547	+	0.0830287i	$0.0264593\pi$
$6$	−95.1488	+	95.1488i	−0.440504	+	0.440504i
$7$	375.130			1.09367			0.546836	−	0.837239i	$-0.315832\pi$
$7$	375.130			1.09367			0.546836	+	0.837239i	$0.315832\pi$
$8$	−128.000	+	128.000i	−0.250000	+	0.250000i
$9$	163.169			0.223826
$10$	913.518			0.913518
$11$			159.466i			0.119809i	0.998204	+	0.0599046i	$0.0190796\pi$
$11$			159.466i			0.119809i	−0.998204	+	0.0599046i	$0.980920\pi$
$12$	−761.191			−0.440504
$13$	2822.42	−	2822.42i	1.28467	−	1.28467i	0.346688	−	0.937981i	$-0.387306\pi$
$13$	2822.42	−	2822.42i	1.28467	−	1.28467i	0.937981	−	0.346688i	$-0.112694\pi$
$14$	1500.52	+	1500.52i	0.546836	+	0.546836i
$15$	2716.26	+	2716.26i	0.804817	+	0.804817i
$16$	−1024.00			−0.250000
$17$	−2322.15	+	2322.15i	−0.472654	+	0.472654i	−0.902772	−	0.430118i	$-0.858472\pi$
$17$	−2322.15	+	2322.15i	−0.472654	+	0.472654i	0.430118	+	0.902772i	$0.358472\pi$
$18$	652.675	+	652.675i	0.111913	+	0.111913i
$19$	205.346	−	205.346i	0.0299381	−	0.0299381i	−0.691979	−	0.721917i	$-0.743261\pi$
$19$	205.346	−	205.346i	0.0299381	−	0.0299381i	0.721917	+	0.691979i	$0.243261\pi$
$20$	3654.07	+	3654.07i	0.456759	+	0.456759i
$21$			8923.29i			0.963534i
$22$	−637.864	+	637.864i	−0.0599046	+	0.0599046i
$23$	−14151.5	+	14151.5i	−1.16311	+	1.16311i	−0.179317	+	0.983791i	$0.557389\pi$
$23$	−14151.5	+	14151.5i	−1.16311	+	1.16311i	−0.983791	+	0.179317i	$0.942611\pi$
$24$	−3044.76	−	3044.76i	−0.220252	−	0.220252i
$25$		−	10453.6i		−	0.669032i
$26$	22579.3			1.28467
$27$			21222.2i			1.07820i
$28$			12004.2i			0.546836i
$29$	5408.08	+	5408.08i	0.221742	+	0.221742i	0.809232	−	0.587489i	$-0.199884\pi$
$29$	5408.08	+	5408.08i	0.221742	+	0.221742i	−0.587489	+	0.809232i	$0.699884\pi$
$30$			21730.1i			0.804817i
$31$	−9201.74	−	9201.74i	−0.308877	−	0.308877i	0.535597	−	0.844474i	$-0.320087\pi$
$31$	−9201.74	−	9201.74i	−0.308877	−	0.308877i	−0.844474	+	0.535597i	$0.820087\pi$
$32$	−4096.00	−	4096.00i	−0.125000	−	0.125000i
$33$	−3793.25			−0.105553
$34$	−18577.2			−0.472654
$35$	42836.0	−	42836.0i	0.999090	−	0.999090i
$36$			5221.40i			0.111913i
$37$	25291.5	−	43887.0i	0.499308	−	0.866424i
$37$	25291.5	−	43887.0i	0.499308	−	0.866424i
$38$	1642.76			0.0299381
$39$	67137.4	+	67137.4i	1.13180	+	1.13180i
$40$			29232.6i			0.456759i
$41$			7137.50i			0.103561i	0.998659	+	0.0517803i	$0.0164896\pi$
$41$			7137.50i			0.103561i	−0.998659	+	0.0517803i	$0.983510\pi$
$42$	−35693.2	+	35693.2i	−0.481767	+	0.481767i
$43$	−32954.9	+	32954.9i	−0.414490	+	0.414490i	−0.883299	−	0.468809i	$-0.844683\pi$
$43$	−32954.9	+	32954.9i	−0.414490	+	0.414490i	0.468809	+	0.883299i	$0.344683\pi$
$44$	−5102.91			−0.0599046
$45$	18632.2	−	18632.2i	0.204469	−	0.204469i
$46$	−113212.			−1.16311
$47$	−49758.4			−0.479262			−0.239631	−	0.970864i	$-0.577026\pi$
$47$	−49758.4			−0.479262			−0.239631	+	0.970864i	$0.577026\pi$
$48$		−	24358.1i		−	0.220252i
$49$	23073.4			0.196120
$50$	41814.5	−	41814.5i	0.334516	−	0.334516i
$51$	−55237.5	−	55237.5i	−0.416412	−	0.416412i
$52$	90317.3	+	90317.3i	0.642334	+	0.642334i
$53$	149694.			1.00548			0.502742	−	0.864436i	$-0.332324\pi$
$53$	149694.			1.00548			0.502742	+	0.864436i	$0.332324\pi$
$54$	−84888.8	+	84888.8i	−0.539100	+	0.539100i
$55$	18209.4	+	18209.4i	0.109448	+	0.109448i
$56$	−48016.6	+	48016.6i	−0.273418	+	0.273418i
$57$	4884.60	+	4884.60i	0.0263757	+	0.0263757i
$58$			43264.6i			0.221742i
$59$	199829.	−	199829.i	0.972975	−	0.972975i	−0.0266695	−	0.999644i	$-0.508490\pi$
$59$	199829.	−	199829.i	0.972975	−	0.972975i	0.999644	+	0.0266695i	$0.00849019\pi$
$60$	−86920.2	+	86920.2i	−0.402408	+	0.402408i
$61$	−121939.	−	121939.i	−0.537221	−	0.537221i	0.385491	−	0.922712i	$-0.374032\pi$
$61$	−121939.	−	121939.i	−0.537221	−	0.537221i	−0.922712	+	0.385491i	$0.874032\pi$
$62$		−	73613.9i		−	0.308877i
$63$	61209.5			0.244792
$64$		−	32768.0i		−	0.125000i
$65$		−	644582.i		−	2.34714i
$66$	−15173.0	−	15173.0i	−0.0527764	−	0.0527764i
$67$			349031.i			1.16049i	0.814444	+	0.580243i	$0.197042\pi$
$67$			349031.i			1.16049i	−0.814444	+	0.580243i	$0.802958\pi$
$68$	−74308.8	−	74308.8i	−0.236327	−	0.236327i
$69$	−336625.	−	336625.i	−1.02471	−	1.02471i
$70$	342688.			0.999090
$71$	−478158.			−1.33597			−0.667985	−	0.744175i	$-0.732843\pi$
$71$	−478158.			−1.33597			−0.667985	+	0.744175i	$0.732843\pi$
$72$	−20885.6	+	20885.6i	−0.0559564	+	0.0559564i
$73$		−	711656.i		−	1.82937i	−0.404167	−	0.914685i	$-0.632439\pi$
$73$		−	711656.i		−	1.82937i	0.404167	−	0.914685i	$-0.367561\pi$
$74$	276714.	−	74382.1i	0.682866	−	0.183558i
$75$	248663.			0.589422
$76$	6571.06	+	6571.06i	0.0149691	+	0.0149691i
$77$			59820.4i			0.131032i
$78$			537099.i			1.13180i
$79$	−385903.	+	385903.i	−0.782703	+	0.782703i	−0.980286	−	0.197584i	$-0.936691\pi$
$79$	−385903.	+	385903.i	−0.782703	+	0.782703i	0.197584	+	0.980286i	$0.436691\pi$
$80$	−116930.	+	116930.i	−0.228380	+	0.228380i
$81$	−385867.			−0.726077
$82$	−28550.0	+	28550.0i	−0.0517803	+	0.0517803i
$83$	458417.			0.801726			0.400863	−	0.916138i	$-0.368710\pi$
$83$	458417.			0.801726			0.400863	+	0.916138i	$0.368710\pi$
$84$	−285545.			−0.481767
$85$			530332.i			0.863557i
$86$	−263639.			−0.414490
$87$	−128643.	+	128643.i	−0.195357	+	0.195357i
$88$	−20411.6	−	20411.6i	−0.0299523	−	0.0299523i
$89$	−411592.	−	411592.i	−0.583844	−	0.583844i	0.352113	−	0.935957i	$-0.385463\pi$
$89$	−411592.	−	411592.i	−0.583844	−	0.583844i	−0.935957	+	0.352113i	$0.885463\pi$
$90$	149058.			0.204469
$91$	1.05877e6	−	1.05877e6i	1.40501	−	1.40501i
$92$	−452849.	−	452849.i	−0.581554	−	0.581554i
$93$	218884.	−	218884.i	0.272123	−	0.272123i
$94$	−199033.	−	199033.i	−0.239631	−	0.239631i
$95$		−	46896.8i		−	0.0546981i
$96$	97432.4	−	97432.4i	0.110126	−	0.110126i
$97$	214684.	−	214684.i	0.235226	−	0.235226i	−0.579644	−	0.814870i	$-0.696808\pi$
$97$	214684.	−	214684.i	0.235226	−	0.235226i	0.814870	+	0.579644i	$0.196808\pi$
$98$	92293.5	+	92293.5i	0.0980602	+	0.0980602i
$99$			26019.9i			0.0268163i
$100$	334516.			0.334516
$101$			1.13382e6i			1.10047i	0.835009	+	0.550237i	$0.185463\pi$
$101$			1.13382e6i			1.10047i	−0.835009	+	0.550237i	$0.814537\pi$
$102$		−	441900.i		−	0.416412i
$103$	−1.06434e6	−	1.06434e6i	−0.974021	−	0.974021i	0.0256502	−	0.999671i	$-0.491834\pi$
$103$	−1.06434e6	−	1.06434e6i	−0.974021	−	0.974021i	−0.999671	+	0.0256502i	$0.991834\pi$
$104$			722539.i			0.642334i
$105$	1.01895e6	+	1.01895e6i	0.880206	+	0.880206i
$106$	598774.	+	598774.i	0.502742	+	0.502742i
$107$	−183165.			−0.149517			−0.0747587	−	0.997202i	$-0.523819\pi$
$107$	−183165.			−0.149517			−0.0747587	+	0.997202i	$0.523819\pi$
$108$	−679111.			−0.539100
$109$	−1.26383e6	+	1.26383e6i	−0.975912	+	0.975912i	−0.999717	−	0.0238045i	$-0.992422\pi$
$109$	−1.26383e6	+	1.26383e6i	−0.975912	+	0.975912i	0.0238045	+	0.999717i	$0.492422\pi$
$110$			145675.i			0.109448i
$111$	1.04395e6	+	601613.i	0.763326	+	0.439894i
$112$	−384133.			−0.273418
$113$	1.66481e6	+	1.66481e6i	1.15380	+	1.15380i	0.985785	+	0.168013i	$0.0537352\pi$
$113$	1.66481e6	+	1.66481e6i	1.15380	+	1.15380i	0.168013	+	0.985785i	$0.446265\pi$
$114$			39076.8i			0.0263757i
$115$			3.23192e6i			2.12504i
$116$	−173058.	+	173058.i	−0.110871	+	0.110871i
$117$	460530.	−	460530.i	0.287542	−	0.287542i
$118$	1.59863e6			0.972975
$119$	−871108.	+	871108.i	−0.516929	+	0.516929i
$120$	−695362.			−0.402408
$121$	1.74613e6			0.985646
$122$		−	975512.i		−	0.537221i
$123$	−169781.			−0.0912377
$124$	294456.	−	294456.i	0.154438	−	0.154438i
$125$	590518.	+	590518.i	0.302345	+	0.302345i
$126$	244838.	+	244838.i	0.122396	+	0.122396i
$127$	−954513.			−0.465984			−0.232992	−	0.972479i	$-0.574852\pi$
$127$	−954513.			−0.465984			−0.232992	+	0.972479i	$0.574852\pi$
$128$	131072.	−	131072.i	0.0625000	−	0.0625000i
$129$	−783905.	−	783905.i	−0.365169	−	0.365169i
$130$	2.57833e6	−	2.57833e6i	1.17357	−	1.17357i
$131$	373603.	+	373603.i	0.166187	+	0.166187i	0.785301	−	0.619114i	$-0.212508\pi$
$131$	373603.	+	373603.i	0.166187	+	0.166187i	−0.619114	+	0.785301i	$0.712508\pi$
$132$		−	121384.i		−	0.0527764i
$133$	77031.3	−	77031.3i	0.0327425	−	0.0327425i
$134$	−1.39612e6	+	1.39612e6i	−0.580243	+	0.580243i
$135$	2.42336e6	+	2.42336e6i	0.984955	+	0.984955i
$136$		−	594470.i		−	0.236327i
$137$	−2.36366e6			−0.919227			−0.459614	−	0.888119i	$-0.652012\pi$
$137$	−2.36366e6			−0.919227			−0.459614	+	0.888119i	$0.652012\pi$
$138$		−	2.69300e6i		−	1.02471i
$139$		−	3.80698e6i		−	1.41754i	−0.705439	−	0.708771i	$-0.749250\pi$
$139$		−	3.80698e6i		−	1.41754i	0.705439	−	0.708771i	$-0.250750\pi$
$140$	1.37075e6	+	1.37075e6i	0.499545	+	0.499545i
$141$		−	1.18361e6i		−	0.422233i
$142$	−1.91263e6	−	1.91263e6i	−0.667985	−	0.667985i
$143$	450079.	+	450079.i	0.153915	+	0.153915i
$144$	−167085.			−0.0559564
$145$	1.23509e6			0.405132
$146$	2.84662e6	−	2.84662e6i	0.914685	−	0.914685i
$147$			548851.i			0.172784i
$148$	1.40438e6	+	809327.i	0.433212	+	0.249654i
$149$	−5.08630e6			−1.53760			−0.768800	−	0.639489i	$-0.779146\pi$
$149$	−5.08630e6			−1.53760			−0.768800	+	0.639489i	$0.779146\pi$
$150$	994650.	+	994650.i	0.294711	+	0.294711i
$151$		−	2.89959e6i		−	0.842182i	−0.907018	−	0.421091i	$-0.861647\pi$
$151$		−	2.89959e6i		−	0.842182i	0.907018	−	0.421091i	$-0.138353\pi$
$152$			52568.5i			0.0149691i
$153$	−378902.	+	378902.i	−0.105792	+	0.105792i
$154$	−239282.	+	239282.i	−0.0655160	+	0.0655160i
$155$	−2.10149e6			−0.564329
$156$	−2.14840e6	+	2.14840e6i	−0.565901	+	0.565901i
$157$	−4.54973e6			−1.17567			−0.587837	−	0.808980i	$-0.700020\pi$
$157$	−4.54973e6			−1.17567			−0.587837	+	0.808980i	$0.700020\pi$
$158$	−3.08722e6			−0.782703
$159$			3.56079e6i			0.885840i
$160$	−935443.			−0.228380
$161$	−5.30866e6	+	5.30866e6i	−1.27206	+	1.27206i
$162$	−1.54347e6	−	1.54347e6i	−0.363038	−	0.363038i
$163$	2.27370e6	+	2.27370e6i	0.525014	+	0.525014i	0.919082	−	0.394067i	$-0.128932\pi$
$163$	2.27370e6	+	2.27370e6i	0.525014	+	0.525014i	−0.394067	+	0.919082i	$0.628932\pi$
$164$	−228400.			−0.0517803
$165$	−433150.	+	433150.i	−0.0964244	+	0.0964244i
$166$	1.83367e6	+	1.83367e6i	0.400863	+	0.400863i
$167$	2.31522e6	−	2.31522e6i	0.497098	−	0.497098i	−0.413435	−	0.910533i	$-0.635671\pi$
$167$	2.31522e6	−	2.31522e6i	0.497098	−	0.497098i	0.910533	+	0.413435i	$0.135671\pi$
$168$	−1.14218e6	−	1.14218e6i	−0.240884	−	0.240884i
$169$		−	1.11053e7i		−	2.30075i
$170$	−2.12133e6	+	2.12133e6i	−0.431778	+	0.431778i
$171$	33506.0	−	33506.0i	0.00670092	−	0.00670092i
$172$	−1.05456e6	−	1.05456e6i	−0.207245	−	0.207245i
$173$		−	5.73692e6i		−	1.10800i	−0.832516	−	0.554001i	$-0.813100\pi$
$173$		−	5.73692e6i		−	1.10800i	0.832516	−	0.554001i	$-0.186900\pi$
$174$	−1.02914e6			−0.195357
$175$		−	3.92147e6i		−	0.731702i
$176$		−	163293.i		−	0.0299523i
$177$	4.75336e6	+	4.75336e6i	0.857198	+	0.857198i
$178$		−	3.29274e6i		−	0.583844i
$179$	−2.61195e6	−	2.61195e6i	−0.455413	−	0.455413i	0.441733	−	0.897146i	$-0.354364\pi$
$179$	−2.61195e6	−	2.61195e6i	−0.455413	−	0.455413i	−0.897146	+	0.441733i	$0.854364\pi$
$180$	596231.	+	596231.i	0.102234	+	0.102234i
$181$	−8.07247e6			−1.36135			−0.680676	−	0.732585i	$-0.738314\pi$
$181$	−8.07247e6			−1.36135			−0.680676	+	0.732585i	$0.738314\pi$
$182$	8.47018e6			1.40501
$183$	2.90059e6	−	2.90059e6i	0.473296	−	0.473296i
$184$		−	3.62279e6i		−	0.581554i
$185$	−2.12342e6	−	7.89948e6i	−0.335367	−	1.24762i
$186$	1.75107e6			0.272123
$187$	−370304.	−	370304.i	−0.0566283	−	0.0566283i
$188$		−	1.59227e6i		−	0.239631i
$189$			7.96108e6i			1.17920i
$190$	187587.	−	187587.i	0.0273490	−	0.0273490i
$191$	471125.	−	471125.i	0.0676138	−	0.0676138i	−0.672491	−	0.740105i	$-0.734776\pi$
$191$	471125.	−	471125.i	0.0676138	−	0.0676138i	0.740105	+	0.672491i	$0.234776\pi$
$192$	779459.			0.110126
$193$	−1.41057e6	+	1.41057e6i	−0.196210	+	0.196210i	−0.798373	−	0.602163i	$-0.794306\pi$
$193$	−1.41057e6	+	1.41057e6i	−0.196210	+	0.196210i	0.602163	+	0.798373i	$0.294306\pi$
$194$	1.71747e6			0.235226
$195$	1.53328e7			2.06785
$196$			738348.i			0.0980602i
$197$	6.61097e6			0.864702			0.432351	−	0.901705i	$-0.357684\pi$
$197$	6.61097e6			0.864702			0.432351	+	0.901705i	$0.357684\pi$
$198$	−104079.	+	104079.i	−0.0134082	+	0.0134082i
$199$	8.87709e6	+	8.87709e6i	1.12645	+	1.12645i	0.990750	+	0.135698i	$0.0433278\pi$
$199$	8.87709e6	+	8.87709e6i	1.12645	+	1.12645i	0.135698	+	0.990750i	$0.456672\pi$
$200$	1.33806e6	+	1.33806e6i	0.167258	+	0.167258i
$201$	−8.30247e6			−1.02240
$202$	−4.53528e6	+	4.53528e6i	−0.550237	+	0.550237i
$203$	2.02873e6	+	2.02873e6i	0.242514	+	0.242514i
$204$	1.76760e6	−	1.76760e6i	0.208206	−	0.208206i
$205$	815030.	+	815030.i	0.0946045	+	0.0946045i
$206$		−	8.51471e6i		−	0.974021i
$207$	−2.30909e6	+	2.30909e6i	−0.260333	+	0.260333i
$208$	−2.89015e6	+	2.89015e6i	−0.321167	+	0.321167i
$209$	32745.6	+	32745.6i	0.00358686	+	0.00358686i
$210$			8.15159e6i			0.880206i
$211$	5.66375e6			0.602916			0.301458	−	0.953479i	$-0.402527\pi$
$211$	5.66375e6			0.602916			0.301458	+	0.953479i	$0.402527\pi$
$212$			4.79019e6i			0.502742i
$213$		−	1.13740e7i		−	1.17700i
$214$	−732661.	−	732661.i	−0.0747587	−	0.0747587i
$215$			7.52622e6i			0.757289i
$216$	−2.71644e6	−	2.71644e6i	−0.269550	−	0.269550i
$217$	−3.45185e6	−	3.45185e6i	−0.337810	−	0.337810i
$218$	−1.01107e7			−0.975912
$219$	1.69283e7			1.61169
$220$	−582700.	+	582700.i	−0.0547239	+	0.0547239i
$221$			1.31081e7i			1.21441i
$222$	1.76934e6	+	6.58225e6i	0.161716	+	0.601610i
$223$	−1.43710e7			−1.29591			−0.647953	−	0.761680i	$-0.724375\pi$
$223$	−1.43710e7			−1.29591			−0.647953	+	0.761680i	$0.724375\pi$
$224$	−1.53653e6	−	1.53653e6i	−0.136709	−	0.136709i
$225$		−	1.70571e6i		−	0.149746i
$226$			1.33185e7i			1.15380i
$227$	1.20043e7	−	1.20043e7i	1.02626	−	1.02626i	0.0266171	−	0.999646i	$-0.491527\pi$
$227$	1.20043e7	−	1.20043e7i	1.02626	−	1.02626i	0.999646	−	0.0266171i	$-0.00847347\pi$
$228$	−156307.	+	156307.i	−0.0131879	+	0.0131879i
$229$	−1.38447e7			−1.15286			−0.576430	−	0.817147i	$-0.695554\pi$
$229$	−1.38447e7			−1.15286			−0.576430	+	0.817147i	$0.695554\pi$
$230$	−1.29277e7	+	1.29277e7i	−1.06252	+	1.06252i
$231$	−1.42296e6			−0.115440
$232$	−1.38447e6			−0.110871
$233$			4.13786e6i			0.327121i	0.986533	+	0.163560i	$0.0522979\pi$
$233$			4.13786e6i			0.327121i	−0.986533	+	0.163560i	$0.947702\pi$
$234$	3.68424e6			0.287542
$235$	−5.68190e6	+	5.68190e6i	−0.437814	+	0.437814i
$236$	6.39451e6	+	6.39451e6i	0.486487	+	0.486487i
$237$	−9.17955e6	−	9.17955e6i	−0.689567	−	0.689567i
$238$	−6.96886e6			−0.516929
$239$	5.04966e6	−	5.04966e6i	0.369887	−	0.369887i	−0.497549	−	0.867436i	$-0.665767\pi$
$239$	5.04966e6	−	5.04966e6i	0.369887	−	0.369887i	0.867436	+	0.497549i	$0.165767\pi$
$240$	−2.78145e6	−	2.78145e6i	−0.201204	−	0.201204i
$241$	1.15903e7	−	1.15903e7i	0.828022	−	0.828022i	−0.159221	−	0.987243i	$-0.550898\pi$
$241$	1.15903e7	−	1.15903e7i	0.828022	−	0.828022i	0.987243	+	0.159221i	$0.0508983\pi$
$242$	6.98453e6	+	6.98453e6i	0.492823	+	0.492823i
$243$			6.29229e6i			0.438521i
$244$	3.90205e6	−	3.90205e6i	0.268610	−	0.268610i
$245$	2.63474e6	−	2.63474e6i	0.179160	−	0.179160i
$246$	−679125.	−	679125.i	−0.0456188	−	0.0456188i
$247$		−	1.15914e6i		−	0.0769211i
$248$	2.35565e6			0.154438
$249$			1.09045e7i			0.706327i
$250$			4.72415e6i			0.302345i
$251$	5.81562e6	+	5.81562e6i	0.367769	+	0.367769i	0.866663	−	0.498894i	$-0.166260\pi$
$251$	5.81562e6	+	5.81562e6i	0.367769	+	0.367769i	−0.498894	+	0.866663i	$0.666260\pi$
$252$			1.95870e6i			0.122396i
$253$	−2.25669e6	−	2.25669e6i	−0.139351	−	0.139351i
$254$	−3.81805e6	−	3.81805e6i	−0.232992	−	0.232992i
$255$	−1.26151e7			−0.760800
$256$	1.04858e6			0.0625000
$257$	−1.13668e7	+	1.13668e7i	−0.669637	+	0.669637i	−0.957632	−	0.287995i	$-0.907011\pi$
$257$	−1.13668e7	+	1.13668e7i	−0.669637	+	0.669637i	0.287995	+	0.957632i	$0.407011\pi$
$258$		−	6.27124e6i		−	0.365169i
$259$	9.48758e6	−	1.64633e7i	0.546080	−	0.947585i
$260$	2.06266e7			1.17357
$261$	882429.	+	882429.i	0.0496316	+	0.0496316i
$262$			2.98882e6i			0.166187i
$263$			2.15709e7i			1.18577i	0.805286	+	0.592887i	$0.202012\pi$
$263$			2.15709e7i			1.18577i	−0.805286	+	0.592887i	$0.797988\pi$
$264$	485536.	−	485536.i	0.0263882	−	0.0263882i
$265$	1.70935e7	−	1.70935e7i	0.918529	−	0.918529i
$266$	616250.			0.0327425
$267$	9.79063e6	−	9.79063e6i	0.514371	−	0.514371i
$268$	−1.11690e7			−0.580243
$269$	−2.24930e7			−1.15555			−0.577777	−	0.816195i	$-0.696079\pi$
$269$	−2.24930e7			−1.15555			−0.577777	+	0.816195i	$0.696079\pi$
$270$			1.93869e7i			0.984955i
$271$	−1.95216e6			−0.0980860			−0.0490430	−	0.998797i	$-0.515617\pi$
$271$	−1.95216e6			−0.0980860			−0.0490430	+	0.998797i	$0.515617\pi$
$272$	2.37788e6	−	2.37788e6i	0.118164	−	0.118164i
$273$	2.51852e7	+	2.51852e7i	1.23782	+	1.23782i
$274$	−9.45463e6	−	9.45463e6i	−0.459614	−	0.459614i
$275$	1.66700e6			0.0801561
$276$	1.07720e7	−	1.07720e7i	0.512354	−	0.512354i
$277$	−1.87494e7	−	1.87494e7i	−0.882163	−	0.882163i	0.111591	−	0.993754i	$-0.464405\pi$
$277$	−1.87494e7	−	1.87494e7i	−0.882163	−	0.882163i	−0.993754	+	0.111591i	$0.964405\pi$
$278$	1.52279e7	−	1.52279e7i	0.708771	−	0.708771i
$279$	−1.50144e6	−	1.50144e6i	−0.0691345	−	0.0691345i
$280$			1.09660e7i			0.499545i
$281$	8.45717e6	−	8.45717e6i	0.381159	−	0.381159i	−0.490361	−	0.871520i	$-0.663135\pi$
$281$	8.45717e6	−	8.45717e6i	0.381159	−	0.381159i	0.871520	+	0.490361i	$0.163135\pi$
$282$	4.73445e6	−	4.73445e6i	0.211117	−	0.211117i
$283$	−2.17892e7	−	2.17892e7i	−0.961351	−	0.961351i	0.0379291	−	0.999280i	$-0.487924\pi$
$283$	−2.17892e7	−	2.17892e7i	−0.961351	−	0.961351i	−0.999280	+	0.0379291i	$0.987924\pi$
$284$		−	1.53011e7i		−	0.667985i
$285$	1.11554e6			0.0481894
$286$			3.60063e6i			0.153915i
$287$			2.67749e6i			0.113261i
$288$	−668339.	−	668339.i	−0.0279782	−	0.0279782i
$289$			1.33528e7i			0.553196i
$290$	4.94038e6	+	4.94038e6i	0.202566	+	0.202566i
$291$	5.10674e6	+	5.10674e6i	0.207236	+	0.207236i
$292$	2.27730e7			0.914685
$293$	7.91765e6			0.314770			0.157385	−	0.987537i	$-0.449694\pi$
$293$	7.91765e6			0.314770			0.157385	+	0.987537i	$0.449694\pi$
$294$	−2.19540e6	+	2.19540e6i	−0.0863918	+	0.0863918i
$295$		−	4.56368e7i		−	1.77766i
$296$	2.38023e6	+	8.85484e6i	0.0917790	+	0.341433i
$297$	−3.38422e6			−0.129178
$298$	−2.03452e7	−	2.03452e7i	−0.768800	−	0.768800i
$299$			7.98831e7i			2.98842i
$300$			7.95720e6i			0.294711i
$301$	−1.23624e7	+	1.23624e7i	−0.453317	+	0.453317i
$302$	1.15984e7	−	1.15984e7i	0.421091	−	0.421091i
$303$	−2.69704e7			−0.969526
$304$	−210274.	+	210274.i	−0.00748453	+	0.00748453i
$305$	−2.78484e7			−0.981523
$306$	−3.03122e6			−0.105792
$307$		−	5.04973e7i		−	1.74523i	−0.488408	−	0.872616i	$-0.662422\pi$
$307$		−	5.04973e7i		−	1.74523i	0.488408	−	0.872616i	$-0.337578\pi$
$308$	−1.91425e6			−0.0655160
$309$	2.53176e7	−	2.53176e7i	0.858120	−	0.858120i
$310$	−8.40596e6	−	8.40596e6i	−0.282164	−	0.282164i
$311$	3.43244e7	+	3.43244e7i	1.14109	+	1.14109i	0.988250	+	0.152845i	$0.0488434\pi$
$311$	3.43244e7	+	3.43244e7i	1.14109	+	1.14109i	0.152845	+	0.988250i	$0.451157\pi$
$312$	−1.71872e7			−0.565901
$313$	1.46708e7	−	1.46708e7i	0.478434	−	0.478434i	−0.426196	−	0.904631i	$-0.640147\pi$
$313$	1.46708e7	−	1.46708e7i	0.478434	−	0.478434i	0.904631	+	0.426196i	$0.140147\pi$
$314$	−1.81989e7	−	1.81989e7i	−0.587837	−	0.587837i
$315$	6.98950e6	−	6.98950e6i	0.223622	−	0.223622i
$316$	−1.23489e7	−	1.23489e7i	−0.391351	−	0.391351i
$317$		−	3.11854e6i		−	0.0978979i	−0.998801	−	0.0489490i	$-0.984413\pi$
$317$		−	3.11854e6i		−	0.0978979i	0.998801	−	0.0489490i	$-0.0155872\pi$
$318$	−1.42432e7	+	1.42432e7i	−0.442920	+	0.442920i
$319$	−862404.	+	862404.i	−0.0265668	+	0.0265668i
$320$	−3.74177e6	−	3.74177e6i	−0.114190	−	0.114190i
$321$		−	4.35699e6i		−	0.131726i
$322$	−4.24693e7			−1.27206
$323$			953686.i			0.0283008i
$324$		−	1.23477e7i		−	0.363038i
$325$	−2.95045e7	−	2.95045e7i	−0.859484	−	0.859484i
$326$			1.81896e7i			0.525014i
$327$	−3.00631e7	−	3.00631e7i	−0.859786	−	0.859786i
$328$	−913600.	−	913600.i	−0.0258901	−	0.0258901i
$329$	−1.86658e7			−0.524155
$330$	−3.46520e6			−0.0964244
$331$	2.86539e7	−	2.86539e7i	0.790133	−	0.790133i	−0.191382	−	0.981516i	$-0.561297\pi$
$331$	2.86539e7	−	2.86539e7i	0.790133	−	0.790133i	0.981516	+	0.191382i	$0.0612970\pi$
$332$			1.46693e7i			0.400863i
$333$	4.12678e6	−	7.16099e6i	0.111758	−	0.193928i
$334$	1.85217e7			0.497098
$335$	3.98558e7	+	3.98558e7i	1.06012	+	1.06012i
$336$		−	9.13745e6i		−	0.240884i
$337$			2.11192e7i			0.551808i	0.961185	+	0.275904i	$0.0889771\pi$
$337$			2.11192e7i			0.551808i	−0.961185	+	0.275904i	$0.911023\pi$
$338$	4.44210e7	−	4.44210e7i	1.15037	−	1.15037i
$339$	−3.96012e7	+	3.96012e7i	−1.01651	+	1.01651i
$340$	−1.69706e7			−0.431778
$341$	1.46736e6	−	1.46736e6i	0.0370062	−	0.0370062i
$342$	268048.			0.00670092
$343$	−3.54781e7			−0.879181
$344$		−	8.43645e6i		−	0.207245i
$345$	−7.68784e7			−1.87218
$346$	2.29477e7	−	2.29477e7i	0.554001	−	0.554001i
$347$	3.34142e7	+	3.34142e7i	0.799730	+	0.799730i	0.983053	−	0.183323i	$-0.0586855\pi$
$347$	3.34142e7	+	3.34142e7i	0.799730	+	0.799730i	−0.183323	+	0.983053i	$0.558685\pi$
$348$	−4.11658e6	−	4.11658e6i	−0.0976784	−	0.0976784i
$349$	4.82665e7			1.13545			0.567727	−	0.823217i	$-0.307823\pi$
$349$	4.82665e7			1.13545			0.567727	+	0.823217i	$0.307823\pi$
$350$	1.56859e7	−	1.56859e7i	0.365851	−	0.365851i
$351$	5.98979e7	+	5.98979e7i	1.38513	+	1.38513i
$352$	653173.	−	653173.i	0.0149761	−	0.0149761i
$353$	1.24667e6	+	1.24667e6i	0.0283419	+	0.0283419i	0.721136	−	0.692794i	$-0.243620\pi$
$353$	1.24667e6	+	1.24667e6i	0.0283419	+	0.0283419i	−0.692794	+	0.721136i	$0.743620\pi$
$354$			3.80269e7i			0.857198i
$355$	−5.46008e7	+	5.46008e7i	−1.22043	+	1.22043i
$356$	1.31709e7	−	1.31709e7i	0.291922	−	0.291922i
$357$	−2.07212e7	−	2.07212e7i	−0.455418	−	0.455418i
$358$		−	2.08956e7i		−	0.455413i
$359$	1.93392e7			0.417980			0.208990	−	0.977918i	$-0.432982\pi$
$359$	1.93392e7			0.417980			0.208990	+	0.977918i	$0.432982\pi$
$360$			4.76985e6i			0.102234i
$361$			4.69615e7i			0.998207i
$362$	−3.22899e7	−	3.22899e7i	−0.680676	−	0.680676i
$363$			4.15356e7i			0.868361i
$364$	3.38807e7	+	3.38807e7i	0.702504	+	0.702504i
$365$	−8.12639e7	−	8.12639e7i	−1.67116	−	1.67116i
$366$	2.32047e7			0.473296
$367$	7.58354e7			1.53417			0.767085	−	0.641545i	$-0.221706\pi$
$367$	7.58354e7			1.53417			0.767085	+	0.641545i	$0.221706\pi$
$368$	1.44912e7	−	1.44912e7i	0.290777	−	0.290777i
$369$			1.16462e6i			0.0231795i
$370$	2.31042e7	−	4.00916e7i	0.456127	−	0.791495i
$371$	5.61545e7			1.09967
$372$	7.00428e6	+	7.00428e6i	0.136061	+	0.136061i
$373$		−	4.18187e7i		−	0.805831i	−0.915237	−	0.402915i	$-0.867997\pi$
$373$		−	4.18187e7i		−	0.805831i	0.915237	−	0.402915i	$-0.132003\pi$
$374$		−	2.96243e6i		−	0.0566283i
$375$	−1.40468e7	+	1.40468e7i	−0.266369	+	0.266369i
$376$	6.36907e6	−	6.36907e6i	0.119815	−	0.119815i
$377$	3.05277e7			0.569731
$378$	−3.18443e7	+	3.18443e7i	−0.589599	+	0.589599i
$379$	−5.09654e7			−0.936177			−0.468088	−	0.883682i	$-0.655057\pi$
$379$	−5.09654e7			−0.936177			−0.468088	+	0.883682i	$0.655057\pi$
$380$	1.50070e6			0.0273490
$381$		−	2.27052e7i		−	0.410535i
$382$	3.76900e6			0.0676138
$383$	4.04126e7	−	4.04126e7i	0.719317	−	0.719317i	−0.249148	−	0.968465i	$-0.580151\pi$
$383$	4.04126e7	−	4.04126e7i	0.719317	−	0.719317i	0.968465	+	0.249148i	$0.0801507\pi$
$384$	3.11784e6	+	3.11784e6i	0.0550630	+	0.0550630i
$385$	6.83088e6	+	6.83088e6i	0.119700	+	0.119700i
$386$	−1.12845e7			−0.196210
$387$	−5.37721e6	+	5.37721e6i	−0.0927735	+	0.0927735i
$388$	6.86989e6	+	6.86989e6i	0.117613	+	0.117613i
$389$	−6.95935e7	+	6.95935e7i	−1.18228	+	1.18228i	−0.203126	+	0.979153i	$0.565110\pi$
$389$	−6.95935e7	+	6.95935e7i	−1.18228	+	1.18228i	−0.979153	+	0.203126i	$0.934890\pi$
$390$	6.13313e7	+	6.13313e7i	1.03392	+	1.03392i
$391$		−	6.57240e7i		−	1.09950i
$392$	−2.95339e6	+	2.95339e6i	−0.0490301	+	0.0490301i
$393$	−8.88697e6	+	8.88697e6i	−0.146412	+	0.146412i
$394$	2.64439e7	+	2.64439e7i	0.432351	+	0.432351i
$395$			8.81324e7i			1.43003i
$396$	−832636.			−0.0134082
$397$			8.03536e7i			1.28420i	0.766619	+	0.642102i	$0.221937\pi$
$397$			8.03536e7i			1.28420i	−0.766619	+	0.642102i	$0.778063\pi$
$398$			7.10167e7i			1.12645i
$399$	1.83236e6	+	1.83236e6i	0.0288464	+	0.0288464i
$400$			1.07045e7i			0.167258i
$401$	2.23419e7	+	2.23419e7i	0.346486	+	0.346486i	0.858799	−	0.512313i	$-0.171211\pi$
$401$	2.23419e7	+	2.23419e7i	0.346486	+	0.346486i	−0.512313	+	0.858799i	$0.671211\pi$
$402$	−3.32099e7	−	3.32099e7i	−0.511198	−	0.511198i
$403$	−5.19423e7			−0.793608
$404$	−3.62822e7			−0.550237
$405$	−4.40621e7	+	4.40621e7i	−0.663284	+	0.663284i
$406$			1.62298e7i			0.242514i
$407$	6.99848e6	+	4.03313e6i	0.103806	+	0.0598217i
$408$	1.41408e7			0.208206
$409$	6.34935e7	+	6.34935e7i	0.928025	+	0.928025i	0.997578	−	0.0695532i	$-0.0221574\pi$
$409$	6.34935e7	+	6.34935e7i	0.928025	+	0.928025i	−0.0695532	+	0.997578i	$0.522157\pi$
$410$			6.52024e6i			0.0946045i
$411$		−	5.62248e7i		−	0.809846i
$412$	3.40588e7	−	3.40588e7i	0.487010	−	0.487010i
$413$	7.49617e7	−	7.49617e7i	1.06412	−	1.06412i
$414$	−1.84727e7			−0.260333
$415$	5.23465e7	−	5.23465e7i	0.732392	−	0.732392i
$416$	−2.31212e7			−0.321167
$417$	9.05574e7			1.24887
$418$			261965.i			0.00358686i
$419$	−1.22523e8			−1.66562			−0.832810	−	0.553559i	$-0.813269\pi$
$419$	−1.22523e8			−1.66562			−0.832810	+	0.553559i	$0.813269\pi$
$420$	−3.26064e7	+	3.26064e7i	−0.440103	+	0.440103i
$421$	4.30498e7	+	4.30498e7i	0.576932	+	0.576932i	0.934057	−	0.357125i	$-0.116243\pi$
$421$	4.30498e7	+	4.30498e7i	0.576932	+	0.576932i	−0.357125	+	0.934057i	$0.616243\pi$
$422$	2.26550e7	+	2.26550e7i	0.301458	+	0.301458i
$423$	−8.11901e6			−0.107271
$424$	−1.91608e7	+	1.91608e7i	−0.251371	+	0.251371i
$425$	2.42749e7	+	2.42749e7i	0.316221	+	0.316221i
$426$	4.54962e7	−	4.54962e7i	0.588500	−	0.588500i
$427$	−4.57429e7	−	4.57429e7i	−0.587544	−	0.587544i
$428$		−	5.86129e6i		−	0.0747587i
$429$	−1.07061e7	+	1.07061e7i	−0.135600	+	0.135600i
$430$	−3.01049e7	+	3.01049e7i	−0.378645	+	0.378645i
$431$	1.80249e7	+	1.80249e7i	0.225134	+	0.225134i	0.810656	−	0.585522i	$-0.199110\pi$
$431$	1.80249e7	+	1.80249e7i	0.225134	+	0.225134i	−0.585522	+	0.810656i	$0.699110\pi$
$432$		−	2.17315e7i		−	0.269550i
$433$	6.19185e7			0.762706			0.381353	−	0.924430i	$-0.375458\pi$
$433$	6.19185e7			0.762706			0.381353	+	0.924430i	$0.375458\pi$
$434$		−	2.76148e7i		−	0.337810i
$435$			2.93794e7i			0.356924i
$436$	−4.04427e7	−	4.04427e7i	−0.487956	−	0.487956i
$437$			5.81191e6i			0.0696425i
$438$	6.77133e7	+	6.77133e7i	0.805845	+	0.805845i
$439$	−373723.	−	373723.i	−0.00441729	−	0.00441729i	0.704895	−	0.709312i	$-0.250994\pi$
$439$	−373723.	−	373723.i	−0.00441729	−	0.00441729i	−0.709312	+	0.704895i	$0.750994\pi$
$440$	−4.66160e6			−0.0547239
$441$	3.76485e6			0.0438967
$442$	−5.24326e7	+	5.24326e7i	−0.607204	+	0.607204i
$443$			7.38901e7i			0.849914i	0.905214	+	0.424957i	$0.139711\pi$
$443$			7.38901e7i			0.849914i	−0.905214	+	0.424957i	$0.860289\pi$
$444$	−1.92516e7	+	3.34064e7i	−0.219947	+	0.381663i
$445$	−9.39993e7			−1.06671
$446$	−5.74842e7	−	5.74842e7i	−0.647953	−	0.647953i
$447$		−	1.20989e8i		−	1.35464i
$448$		−	1.22923e7i		−	0.136709i
$449$	1.00229e8	−	1.00229e8i	1.10728	−	1.10728i	0.113769	−	0.993507i	$-0.463708\pi$
$449$	1.00229e8	−	1.00229e8i	1.10728	−	1.10728i	0.993507	−	0.113769i	$-0.0362924\pi$
$450$	6.82282e6	−	6.82282e6i	0.0748732	−	0.0748732i
$451$	−1.13819e6			−0.0124075
$452$	−5.32740e7	+	5.32740e7i	−0.576899	+	0.576899i
$453$	6.89732e7			0.741969
$454$	9.60342e7			1.02626
$455$		−	2.41802e8i		−	2.56700i
$456$	−1.25046e6			−0.0131879
$457$	1.82344e7	−	1.82344e7i	0.191048	−	0.191048i	−0.605101	−	0.796149i	$-0.706867\pi$
$457$	1.82344e7	−	1.82344e7i	0.191048	−	0.191048i	0.796149	+	0.605101i	$0.206867\pi$
$458$	−5.53787e7	−	5.53787e7i	−0.576430	−	0.576430i
$459$	−4.92811e7	−	4.92811e7i	−0.509616	−	0.509616i
$460$	−1.03422e8			−1.06252
$461$	−3.84071e6	+	3.84071e6i	−0.0392020	+	0.0392020i	−0.726436	−	0.687234i	$-0.758825\pi$
$461$	−3.84071e6	+	3.84071e6i	−0.0392020	+	0.0392020i	0.687234	+	0.726436i	$0.258825\pi$
$462$	−5.69184e6	−	5.69184e6i	−0.0577201	−	0.0577201i
$463$	−3.47530e7	+	3.47530e7i	−0.350146	+	0.350146i	−0.860164	−	0.510018i	$-0.829639\pi$
$463$	−3.47530e7	+	3.47530e7i	−0.350146	+	0.350146i	0.510018	+	0.860164i	$0.329639\pi$
$464$	−5.53787e6	−	5.53787e6i	−0.0554356	−	0.0554356i
$465$		−	4.99886e7i		−	0.497178i
$466$	−1.65514e7	+	1.65514e7i	−0.163560	+	0.163560i
$467$	8.03908e7	−	8.03908e7i	0.789325	−	0.789325i	−0.192059	−	0.981383i	$-0.561516\pi$
$467$	8.03908e7	−	8.03908e7i	0.789325	−	0.789325i	0.981383	+	0.192059i	$0.0615164\pi$
$468$	1.47370e7	+	1.47370e7i	0.143771	+	0.143771i
$469$			1.30932e8i			1.26919i
$470$	−4.54552e7			−0.437814
$471$		−	1.08225e8i		−	1.03578i
$472$			5.11561e7i			0.486487i
$473$	−5.25518e6	−	5.25518e6i	−0.0496597	−	0.0496597i
$474$		−	7.34364e7i		−	0.689567i
$475$	−2.14661e6	−	2.14661e6i	−0.0200296	−	0.0200296i
$476$	−2.78754e7	−	2.78754e7i	−0.258464	−	0.258464i
$477$	2.44253e7			0.225053
$478$	4.03973e7			0.369887
$479$	−7.68431e6	+	7.68431e6i	−0.0699195	+	0.0699195i	−0.741202	−	0.671282i	$-0.765744\pi$
$479$	−7.68431e6	+	7.68431e6i	−0.0699195	+	0.0699195i	0.671282	+	0.741202i	$0.265744\pi$
$480$		−	2.22516e7i		−	0.201204i
$481$	−5.24843e7	−	1.95250e8i	−0.471622	−	1.75451i
$482$	9.27220e7			0.828022
$483$	−1.26278e8	−	1.26278e8i	−1.12069	−	1.12069i
$484$			5.58762e7i			0.492823i
$485$		−	4.90295e7i		−	0.429766i
$486$	−2.51692e7	+	2.51692e7i	−0.219260	+	0.219260i
$487$	−2.73566e7	+	2.73566e7i	−0.236851	+	0.236851i	−0.815545	−	0.578694i	$-0.803563\pi$
$487$	−2.73566e7	+	2.73566e7i	−0.236851	+	0.236851i	0.578694	+	0.815545i	$0.303563\pi$
$488$	3.12164e7			0.268610
$489$	−5.40851e7	+	5.40851e7i	−0.462542	+	0.462542i
$490$	2.10779e7			0.179160
$491$	−1.57212e8			−1.32813			−0.664066	−	0.747674i	$-0.731170\pi$
$491$	−1.57212e8			−1.32813			−0.664066	+	0.747674i	$0.731170\pi$
$492$		−	5.43300e6i		−	0.0456188i
$493$	−2.51167e7			−0.209615
$494$	4.63657e6	−	4.63657e6i	0.0384606	−	0.0384606i
$495$	2.97120e6	+	2.97120e6i	0.0244972	+	0.0244972i
$496$	9.42258e6	+	9.42258e6i	0.0772191	+	0.0772191i
$497$	−1.79371e8			−1.46111
$498$	−4.36178e7	+	4.36178e7i	−0.353164	+	0.353164i
$499$	5.44685e7	+	5.44685e7i	0.438373	+	0.438373i	0.891464	−	0.453091i	$-0.149679\pi$
$499$	5.44685e7	+	5.44685e7i	0.438373	+	0.438373i	−0.453091	+	0.891464i	$0.649679\pi$
$500$	−1.88966e7	+	1.88966e7i	−0.151173	+	0.151173i
$501$	5.50725e7	+	5.50725e7i	0.437947	+	0.437947i
$502$			4.65249e7i			0.367769i
$503$	−1.23973e8	+	1.23973e8i	−0.974146	+	0.974146i	−0.999674	−	0.0255279i	$-0.991873\pi$
$503$	−1.23973e8	+	1.23973e8i	−0.974146	+	0.974146i	0.0255279	+	0.999674i	$0.491873\pi$
$504$	−7.83481e6	+	7.83481e6i	−0.0611980	+	0.0611980i
$505$	1.29471e8	+	1.29471e8i	1.00530	+	1.00530i
$506$		−	1.80535e7i		−	0.139351i
$507$	2.64163e8			2.02697
$508$		−	3.05444e7i		−	0.232992i
$509$			1.75652e8i			1.33199i	0.745956	+	0.665995i	$0.231993\pi$
$509$			1.75652e8i			1.33199i	−0.745956	+	0.665995i	$0.768007\pi$
$510$	−5.04604e7	−	5.04604e7i	−0.380400	−	0.380400i
$511$		−	2.66963e8i		−	2.00073i
$512$	4.19430e6	+	4.19430e6i	0.0312500	+	0.0312500i
$513$	4.35789e6	+	4.35789e6i	0.0322793	+	0.0322793i
$514$	−9.09345e7			−0.669637
$515$	−2.43073e8			−1.77957
$516$	2.50849e7	−	2.50849e7i	0.182585	−	0.182585i
$517$		−	7.93477e6i		−	0.0574199i
$518$	1.03804e8	−	2.79029e7i	0.746832	−	0.200752i
$519$	1.36465e8			0.976158
$520$	8.25066e7	+	8.25066e7i	0.586784	+	0.586784i
$521$		−	6.42810e7i		−	0.454537i	−0.973832	−	0.227269i	$-0.927020\pi$
$521$		−	6.42810e7i		−	0.454537i	0.973832	−	0.227269i	$-0.0729795\pi$
$522$			7.05944e6i			0.0496316i
$523$	−1.11639e8	+	1.11639e8i	−0.780389	+	0.780389i	−0.979896	−	0.199507i	$-0.936066\pi$
$523$	−1.11639e8	+	1.11639e8i	−0.780389	+	0.780389i	0.199507	+	0.979896i	$0.436066\pi$
$524$	−1.19553e7	+	1.19553e7i	−0.0830934	+	0.0830934i
$525$	9.32807e7			0.644635
$526$	−8.62838e7	+	8.62838e7i	−0.592887	+	0.592887i
$527$	4.27356e7			0.291984
$528$	3.88429e6			0.0263882
$529$		−	2.52496e8i		−	1.70564i
$530$	1.36748e8			0.918529
$531$	3.26058e7	−	3.26058e7i	0.217777	−	0.217777i
$532$	2.46500e6	+	2.46500e6i	0.0163713	+	0.0163713i
$533$	2.01450e7	+	2.01450e7i	0.133041	+	0.133041i
$534$	7.83250e7			0.514371
$535$	−2.09156e7	+	2.09156e7i	−0.136587	+	0.136587i
$536$	−4.46760e7	−	4.46760e7i	−0.290121	−	0.290121i
$537$	6.21310e7	−	6.21310e7i	0.401222	−	0.401222i
$538$	−8.99719e7	−	8.99719e7i	−0.577777	−	0.577777i
$539$			3.67942e6i			0.0234970i
$540$	−7.75475e7	+	7.75475e7i	−0.492478	+	0.492478i
$541$	2.40852e7	−	2.40852e7i	0.152110	−	0.152110i	−0.626950	−	0.779060i	$-0.715697\pi$
$541$	2.40852e7	−	2.40852e7i	0.152110	−	0.152110i	0.779060	+	0.626950i	$0.215697\pi$
$542$	−7.80863e6	−	7.80863e6i	−0.0490430	−	0.0490430i
$543$		−	1.92021e8i		−	1.19936i
$544$	1.90231e7			0.118164
$545$			2.88634e8i			1.78303i
$546$			2.01482e8i			1.23782i
$547$	−1.58846e7	−	1.58846e7i	−0.0970540	−	0.0970540i	0.656913	−	0.753967i	$-0.271862\pi$
$547$	−1.58846e7	−	1.58846e7i	−0.0970540	−	0.0970540i	−0.753967	+	0.656913i	$0.771862\pi$
$548$		−	7.56371e7i		−	0.459614i
$549$	−1.98966e7	−	1.98966e7i	−0.120244	−	0.120244i
$550$	6.66799e6	+	6.66799e6i	0.0400781	+	0.0400781i
$551$	2.22105e6			0.0132771
$552$	8.61761e7			0.512354
$553$	−1.44764e8	+	1.44764e8i	−0.856021	+	0.856021i
$554$		−	1.49995e8i		−	0.882163i
$555$	1.87906e8	−	5.05102e7i	1.09916	−	0.295461i
$556$	1.21823e8			0.708771
$557$	1.93274e7	+	1.93274e7i	0.111843	+	0.111843i	0.760813	−	0.648971i	$-0.224800\pi$
$557$	1.93274e7	+	1.93274e7i	0.111843	+	0.111843i	−0.648971	+	0.760813i	$0.724800\pi$
$558$		−	1.20115e7i		−	0.0691345i
$559$			1.86025e8i			1.06497i
$560$	−4.38641e7	+	4.38641e7i	−0.249773	+	0.249773i
$561$	8.80849e6	−	8.80849e6i	0.0498899	−	0.0498899i
$562$	6.76573e7			0.381159
$563$	−2.42482e8	+	2.42482e8i	−1.35879	+	1.35879i	−0.483389	+	0.875405i	$0.660594\pi$
$563$	−2.42482e8	+	2.42482e8i	−1.35879	+	1.35879i	−0.875405	+	0.483389i	$0.839406\pi$
$564$	3.78756e7			0.211117
$565$	3.80209e8			2.10803
$566$		−	1.74314e8i		−	0.961351i
$567$	−1.44750e8			−0.794090
$568$	6.12042e7	−	6.12042e7i	0.333992	−	0.333992i
$569$	1.53778e8	+	1.53778e8i	0.834751	+	0.834751i	0.988162	−	0.153412i	$-0.0490261\pi$
$569$	1.53778e8	+	1.53778e8i	0.834751	+	0.834751i	−0.153412	+	0.988162i	$0.549026\pi$
$570$	4.46217e6	+	4.46217e6i	0.0240947	+	0.0240947i
$571$	1.74045e8			0.934872			0.467436	−	0.884027i	$-0.345178\pi$
$571$	1.74045e8			0.934872			0.467436	+	0.884027i	$0.345178\pi$
$572$	−1.44025e7	+	1.44025e7i	−0.0769575	+	0.0769575i
$573$	1.12067e7	+	1.12067e7i	0.0595683	+	0.0595683i
$574$	−1.07100e7	+	1.07100e7i	−0.0566307	+	0.0566307i
$575$	1.47935e8	+	1.47935e8i	0.778157	+	0.778157i
$576$		−	5.34672e6i		−	0.0279782i
$577$	3.97416e7	−	3.97416e7i	0.206879	−	0.206879i	−0.596060	−	0.802940i	$-0.703268\pi$
$577$	3.97416e7	−	3.97416e7i	0.206879	−	0.206879i	0.802940	+	0.596060i	$0.203268\pi$
$578$	−5.34112e7	+	5.34112e7i	−0.276598	+	0.276598i
$579$	−3.35534e7	−	3.35534e7i	−0.172863	−	0.172863i
$580$			3.95230e7i			0.202566i
$581$	1.71966e8			0.876826
$582$			4.08539e7i			0.207236i
$583$			2.38710e7i			0.120466i
$584$	9.10920e7	+	9.10920e7i	0.457343	+	0.457343i
$585$		−	1.05176e8i		−	0.525349i
$586$	3.16706e7	+	3.16706e7i	0.157385	+	0.157385i
$587$	−3.90049e7	−	3.90049e7i	−0.192844	−	0.192844i	0.604080	−	0.796924i	$-0.293541\pi$
$587$	−3.90049e7	−	3.90049e7i	−0.192844	−	0.192844i	−0.796924	+	0.604080i	$0.793541\pi$
$588$	−1.75632e7			−0.0863918
$589$	−3.77907e6			−0.0184944
$590$	1.82547e8	−	1.82547e8i	0.888830	−	0.888830i
$591$			1.57257e8i			0.761809i
$592$	−2.58985e7	+	4.49403e7i	−0.124827	+	0.216606i
$593$	−4.12462e8			−1.97797			−0.988986	−	0.148010i	$-0.952713\pi$
$593$	−4.12462e8			−1.97797			−0.988986	+	0.148010i	$0.952713\pi$
$594$	−1.35369e7	−	1.35369e7i	−0.0645891	−	0.0645891i
$595$			1.98943e8i			0.944448i
$596$		−	1.62762e8i		−	0.768800i
$597$	−2.11161e8	+	2.11161e8i	−0.992410	+	0.992410i
$598$	−3.19532e8	+	3.19532e8i	−1.49421	+	1.49421i
$599$	−3.75973e8			−1.74935			−0.874673	−	0.484714i	$-0.838924\pi$
$599$	−3.75973e8			−1.74935			−0.874673	+	0.484714i	$0.838924\pi$
$600$	−3.18288e7	+	3.18288e7i	−0.147356	+	0.147356i
$601$	2.93106e8			1.35021			0.675106	−	0.737721i	$-0.264098\pi$
$601$	2.93106e8			1.35021			0.675106	+	0.737721i	$0.264098\pi$
$602$	−9.88989e7			−0.453317
$603$			5.69510e7i			0.259746i
$604$	9.27870e7			0.421091
$605$	1.99390e8	−	1.99390e8i	0.900406	−	0.900406i
$606$	−1.07882e8	−	1.07882e8i	−0.484763	−	0.484763i
$607$	−5.94093e7	−	5.94093e7i	−0.265637	−	0.265637i	0.561703	−	0.827339i	$-0.310147\pi$
$607$	−5.94093e7	−	5.94093e7i	−0.265637	−	0.265637i	−0.827339	+	0.561703i	$0.810147\pi$
$608$	−1.68219e6			−0.00748453
$609$	−4.82578e7	+	4.82578e7i	−0.213656	+	0.213656i
$610$	−1.11393e8	−	1.11393e8i	−0.490761	−	0.490761i
$611$	−1.40439e8	+	1.40439e8i	−0.615692	+	0.615692i
$612$	−1.21249e7	−	1.21249e7i	−0.0528960	−	0.0528960i
$613$			2.12829e8i			0.923951i	0.886893	+	0.461976i	$0.152859\pi$
$613$			2.12829e8i			0.923951i	−0.886893	+	0.461976i	$0.847141\pi$
$614$	2.01989e8	−	2.01989e8i	0.872616	−	0.872616i
$615$	−1.93873e7	+	1.93873e7i	−0.0833473	+	0.0833473i
$616$	−7.65702e6	−	7.65702e6i	−0.0327580	−	0.0327580i
$617$		−	2.84978e8i		−	1.21327i	−0.794981	−	0.606634i	$-0.792519\pi$
$617$		−	2.84978e8i		−	1.21327i	0.794981	−	0.606634i	$-0.207481\pi$
$618$	2.02541e8			0.858120
$619$			3.01436e8i			1.27093i	0.772129	+	0.635466i	$0.219192\pi$
$619$			3.01436e8i			1.27093i	−0.772129	+	0.635466i	$0.780808\pi$
$620$		−	6.72477e7i		−	0.282164i
$621$	−3.00327e8	−	3.00327e8i	−1.25406	−	1.25406i
$622$			2.74595e8i			1.14109i
$623$	−1.54400e8	−	1.54400e8i	−0.638535	−	0.638535i
$624$	−6.87487e7	−	6.87487e7i	−0.282951	−	0.282951i
$625$	2.98200e8			1.22143
$626$	1.17367e8			0.478434
$627$	−778927.	+	778927.i	−0.00316005	+	0.00316005i
$628$		−	1.45591e8i		−	0.587837i
$629$	4.31816e7	+	1.60643e8i	0.173519	+	0.645519i
$630$	5.59160e7			0.223622
$631$	1.59966e8	+	1.59966e8i	0.636705	+	0.636705i	0.949741	−	0.313036i	$-0.101346\pi$
$631$	1.59966e8	+	1.59966e8i	0.636705	+	0.636705i	−0.313036	+	0.949741i	$0.601346\pi$
$632$		−	9.87911e7i		−	0.391351i
$633$			1.34725e8i			0.531174i
$634$	1.24742e7	−	1.24742e7i	0.0489490	−	0.0489490i
$635$	−1.08996e8	+	1.08996e8i	−0.425685	+	0.425685i
$636$	−1.13945e8			−0.442920
$637$	6.51227e7	−	6.51227e7i	0.251950	−	0.251950i
$638$	−6.89923e6			−0.0265668
$639$	−7.80205e7			−0.299024
$640$		−	2.99342e7i		−	0.114190i
$641$	7.41128e7			0.281397			0.140698	−	0.990053i	$-0.455065\pi$
$641$	7.41128e7			0.281397			0.140698	+	0.990053i	$0.455065\pi$
$642$	1.74280e7	−	1.74280e7i	0.0658630	−	0.0658630i
$643$	9.80231e6	+	9.80231e6i	0.0368719	+	0.0368719i	0.725302	−	0.688430i	$-0.241700\pi$
$643$	9.80231e6	+	9.80231e6i	0.0368719	+	0.0368719i	−0.688430	+	0.725302i	$0.741700\pi$
$644$	−1.69877e8	−	1.69877e8i	−0.636030	−	0.636030i
$645$	−1.79028e8			−0.667178
$646$	−3.81475e6	+	3.81475e6i	−0.0141504	+	0.0141504i
$647$	2.00222e8	+	2.00222e8i	0.739264	+	0.739264i	0.972436	−	0.233172i	$-0.0749104\pi$
$647$	2.00222e8	+	2.00222e8i	0.739264	+	0.739264i	−0.233172	+	0.972436i	$0.574910\pi$
$648$	4.93910e7	−	4.93910e7i	0.181519	−	0.181519i
$649$	3.18659e7	+	3.18659e7i	0.116571	+	0.116571i
$650$		−	2.36036e8i		−	0.859484i
$651$	8.21098e7	−	8.21098e7i	0.297613	−	0.297613i
$652$	−7.27585e7	+	7.27585e7i	−0.262507	+	0.262507i
$653$	−1.61043e8	−	1.61043e8i	−0.578365	−	0.578365i	0.356087	−	0.934453i	$-0.384111\pi$
$653$	−1.61043e8	−	1.61043e8i	−0.578365	−	0.578365i	−0.934453	+	0.356087i	$0.884111\pi$
$654$		−	2.40505e8i		−	0.859786i
$655$	8.53233e7			0.303629
$656$		−	7.30880e6i		−	0.0258901i
$657$		−	1.16120e8i		−	0.409460i
$658$	−7.46634e7	−	7.46634e7i	−0.262078	−	0.262078i
$659$		−	2.52079e8i		−	0.880807i	−0.897800	−	0.440403i	$-0.854835\pi$
$659$		−	2.52079e8i		−	0.880807i	0.897800	−	0.440403i	$-0.145165\pi$
$660$	−1.38608e7	−	1.38608e7i	−0.0482122	−	0.0482122i
$661$	1.09334e8	+	1.09334e8i	0.378573	+	0.378573i	0.870587	−	0.492014i	$-0.163739\pi$
$661$	1.09334e8	+	1.09334e8i	0.378573	+	0.378573i	−0.492014	+	0.870587i	$0.663739\pi$
$662$	2.29231e8			0.790133
$663$	−3.11806e8			−1.06990
$664$	−5.86773e7	+	5.86773e7i	−0.200432	+	0.200432i
$665$		−	1.75924e7i		−	0.0598218i
$666$	4.51511e7	−	1.21368e7i	0.152843	−	0.0410850i
$667$	−1.53065e8			−0.515821
$668$	7.40869e7	+	7.40869e7i	0.248549	+	0.248549i
$669$		−	3.41847e8i		−	1.14170i
$670$			3.18846e8i			1.06012i
$671$	1.94451e7	−	1.94451e7i	0.0643640	−	0.0643640i
$672$	3.65498e7	−	3.65498e7i	0.120442	−	0.120442i
$673$	−3.71214e8			−1.21781			−0.608905	−	0.793244i	$-0.708391\pi$
$673$	−3.71214e8			−1.21781			−0.608905	+	0.793244i	$0.708391\pi$
$674$	−8.44768e7	+	8.44768e7i	−0.275904	+	0.275904i
$675$	2.21849e8			0.721350
$676$	3.55368e8			1.15037
$677$			4.96652e8i			1.60061i	0.599591	+	0.800306i	$0.295330\pi$
$677$			4.96652e8i			1.60061i	−0.599591	+	0.800306i	$0.704670\pi$
$678$	−3.16810e8			−1.01651
$679$	8.05344e7	−	8.05344e7i	0.257260	−	0.257260i
$680$	−6.78825e7	−	6.78825e7i	−0.215889	−	0.215889i
$681$	2.85548e8	+	2.85548e8i	0.904145	+	0.904145i
$682$	1.17389e7			0.0370062
$683$	3.58446e7	−	3.58446e7i	0.112502	−	0.112502i	−0.648615	−	0.761117i	$-0.724651\pi$
$683$	3.58446e7	−	3.58446e7i	0.112502	−	0.112502i	0.761117	+	0.648615i	$0.224651\pi$
$684$	1.07219e6	+	1.07219e6i	0.00335046	+	0.00335046i
$685$	−2.69906e8	+	2.69906e8i	−0.839731	+	0.839731i
$686$	−1.41913e8	−	1.41913e8i	−0.439591	−	0.439591i
$687$		−	3.29326e8i		−	1.01568i
$688$	3.37458e7	−	3.37458e7i	0.103623	−	0.103623i
$689$	4.22498e8	−	4.22498e8i	1.29171	−	1.29171i
$690$	−3.07514e8	−	3.07514e8i	−0.936089	−	0.936089i
$691$		−	2.28599e8i		−	0.692850i	−0.938078	−	0.346425i	$-0.887395\pi$
$691$		−	2.28599e8i		−	0.692850i	0.938078	−	0.346425i	$-0.112605\pi$
$692$	1.83581e8			0.554001
$693$			9.76083e6i			0.0293283i
$694$			2.67314e8i			0.799730i
$695$	−4.34718e8	−	4.34718e8i	−1.29495	−	1.29495i
$696$		−	3.29326e7i		−	0.0976784i
$697$	−1.65743e7	−	1.65743e7i	−0.0489483	−	0.0489483i
$698$	1.93066e8	+	1.93066e8i	0.567727	+	0.567727i
$699$	−9.84282e7			−0.288196
$700$	1.25487e8			0.365851
$701$	3.21185e8	−	3.21185e8i	0.932397	−	0.932397i	−0.0654579	−	0.997855i	$-0.520851\pi$
$701$	3.21185e8	−	3.21185e8i	0.932397	−	0.932397i	0.997855	+	0.0654579i	$0.0208508\pi$
$702$			4.79183e8i			1.38513i
$703$	−3.81851e6	−	1.42055e7i	−0.0109908	−	0.0408875i
$704$	5.22538e6			0.0149761
$705$	−1.35157e8	−	1.35157e8i	−0.385718	−	0.385718i
$706$			9.97338e6i			0.0283419i
$707$			4.25329e8i			1.20356i
$708$	−1.52108e8	+	1.52108e8i	−0.428599	+	0.428599i
$709$	4.55553e8	−	4.55553e8i	1.27820	−	1.27820i	0.336531	−	0.941672i	$-0.390746\pi$
$709$	4.55553e8	−	4.55553e8i	1.27820	−	1.27820i	0.941672	−	0.336531i	$-0.109254\pi$
$710$	−4.36806e8			−1.22043
$711$	−6.29673e7	+	6.29673e7i	−0.175189	+	0.175189i
$712$	1.05368e8			0.291922
$713$	2.60438e8			0.718514
$714$		−	1.65770e8i		−	0.455418i
$715$	1.02789e8			0.281208
$716$	8.35824e7	−	8.35824e7i	0.227707	−	0.227707i
$717$	1.20117e8	+	1.20117e8i	0.325873	+	0.325873i
$718$	7.73568e7	+	7.73568e7i	0.208990	+	0.208990i
$719$	2.09525e8			0.563702			0.281851	−	0.959458i	$-0.409052\pi$
$719$	2.09525e8			0.563702			0.281851	+	0.959458i	$0.409052\pi$
$720$	−1.90794e7	+	1.90794e7i	−0.0511172	+	0.0511172i
$721$	−3.99265e8	−	3.99265e8i	−1.06526	−	1.06526i
$722$	−1.87846e8	+	1.87846e8i	−0.499104	+	0.499104i
$723$	2.75700e8	+	2.75700e8i	0.729494	+	0.729494i
$724$		−	2.58319e8i		−	0.680676i
$725$	5.65340e7	−	5.65340e7i	0.148353	−	0.148353i
$726$	−1.66142e8	+	1.66142e8i	−0.434181	+	0.434181i
$727$	−5.92905e7	−	5.92905e7i	−0.154306	−	0.154306i	0.625732	−	0.780038i	$-0.284800\pi$
$727$	−5.92905e7	−	5.92905e7i	−0.154306	−	0.154306i	−0.780038	+	0.625732i	$0.784800\pi$
$728$			2.71046e8i			0.702504i
$729$	−4.30973e8			−1.11242
$730$		−	6.50111e8i		−	1.67116i
$731$		−	1.53052e8i		−	0.391821i
$732$	9.28188e7	+	9.28188e7i	0.236648	+	0.236648i
$733$		−	2.62501e8i		−	0.666528i	−0.942834	−	0.333264i	$-0.891850\pi$
$733$		−	2.62501e8i		−	0.666528i	0.942834	−	0.333264i	$-0.108150\pi$
$734$	3.03342e8	+	3.03342e8i	0.767085	+	0.767085i
$735$	6.26732e7	+	6.26732e7i	0.157841	+	0.157841i
$736$	1.15929e8			0.290777
$737$	−5.56586e7			−0.139037
$738$	−4.65847e6	+	4.65847e6i	−0.0115898	+	0.0115898i
$739$			9.61496e7i			0.238240i	0.992880	+	0.119120i	$0.0380073\pi$
$739$			9.61496e7i			0.238240i	−0.992880	+	0.119120i	$0.961993\pi$
$740$	2.52783e8	−	6.79494e7i	0.623811	−	0.167684i
$741$	2.75727e7			0.0677681
$742$	2.24618e8	+	2.24618e8i	0.549836	+	0.549836i
$743$		−	1.43390e8i		−	0.349585i	−0.984605	−	0.174793i	$-0.944074\pi$
$743$		−	1.43390e8i		−	0.349585i	0.984605	−	0.174793i	$-0.0559255\pi$
$744$			5.60342e7i			0.136061i
$745$	−5.80804e8	+	5.80804e8i	−1.40463	+	1.40463i
$746$	1.67275e8	−	1.67275e8i	0.402915	−	0.402915i
$747$	7.47993e7			0.179447
$748$	1.18497e7	−	1.18497e7i	0.0283141	−	0.0283141i
$749$	−6.87107e7			−0.163523
$750$	−1.12374e8			−0.266369
$751$		−	4.57909e8i		−	1.08108i	−0.841317	−	0.540542i	$-0.818219\pi$
$751$		−	4.57909e8i		−	1.08108i	0.841317	−	0.540542i	$-0.181781\pi$
$752$	5.09526e7			0.119815
$753$	−1.38337e8	+	1.38337e8i	−0.324007	+	0.324007i
$754$	1.22111e8	+	1.22111e8i	0.284866	+	0.284866i
$755$	−3.31104e8	−	3.31104e8i	−0.769349	−	0.769349i
$756$	−2.54755e8			−0.589599
$757$	5.49795e8	−	5.49795e8i	1.26740	−	1.26740i	0.319970	−	0.947428i	$-0.396327\pi$
$757$	5.49795e8	−	5.49795e8i	1.26740	−	1.26740i	0.947428	−	0.319970i	$-0.103673\pi$
$758$	−2.03862e8	−	2.03862e8i	−0.468088	−	0.468088i
$759$	5.36803e7	−	5.36803e7i	0.122769	−	0.122769i
$760$	6.00278e6	+	6.00278e6i	0.0136745	+	0.0136745i
$761$			6.51324e8i			1.47789i	0.673764	+	0.738947i	$0.264677\pi$
$761$			6.51324e8i			1.47789i	−0.673764	+	0.738947i	$0.735323\pi$
$762$	9.08208e7	−	9.08208e7i	0.205268	−	0.205268i
$763$	−4.74102e8	+	4.74102e8i	−1.06733	+	1.06733i
$764$	1.50760e7	+	1.50760e7i	0.0338069	+	0.0338069i
$765$			8.65336e7i			0.193286i
$766$	3.23301e8			0.719317
$767$		−	1.12800e9i		−	2.49990i
$768$			2.49427e7i			0.0550630i
$769$	−1.36883e8	−	1.36883e8i	−0.301003	−	0.301003i	0.540403	−	0.841406i	$-0.318272\pi$
$769$	−1.36883e8	−	1.36883e8i	−0.301003	−	0.301003i	−0.841406	+	0.540403i	$0.818272\pi$
$770$			5.46471e7i			0.119700i
$771$	−2.70385e8	−	2.70385e8i	−0.589955	−	0.589955i
$772$	−4.51381e7	−	4.51381e7i	−0.0981051	−	0.0981051i
$773$	−2.17539e8			−0.470975			−0.235487	−	0.971877i	$-0.575669\pi$
$773$	−2.17539e8			−0.470975			−0.235487	+	0.971877i	$0.575669\pi$
$774$	−4.30177e7			−0.0927735
$775$	−9.61916e7	+	9.61916e7i	−0.206648	+	0.206648i
$776$			5.49591e7i			0.117613i
$777$	3.91616e8	+	2.25683e8i	0.834829	+	0.481101i
$778$	−5.56748e8			−1.18228
$779$	1.46565e6	+	1.46565e6i	0.00310041	+	0.00310041i
$780$			4.90650e8i			1.03392i
$781$		−	7.62499e7i		−	0.160061i
$782$	2.62896e8	−	2.62896e8i	0.549748	−	0.549748i
$783$	−1.14771e8	+	1.14771e8i	−0.239083	+	0.239083i
$784$	−2.36271e7			−0.0490301
$785$	−5.19533e8	+	5.19533e8i	−1.07400	+	1.07400i
$786$	−7.10958e7			−0.146412
$787$	1.82945e8			0.375315			0.187658	−	0.982234i	$-0.439910\pi$
$787$	1.82945e8			0.375315			0.187658	+	0.982234i	$0.439910\pi$
$788$			2.11551e8i			0.432351i
$789$	−5.13112e8			−1.04468
$790$	−3.52529e8	+	3.52529e8i	−0.715013	+	0.715013i
$791$	6.24521e8	+	6.24521e8i	1.26188	+	1.26188i
$792$	−3.33054e6	−	3.33054e6i	−0.00670409	−	0.00670409i
$793$	−6.88325e8			−1.38030
$794$	−3.21415e8	+	3.21415e8i	−0.642102	+	0.642102i
$795$	4.06606e8	+	4.06606e8i	0.809231	+	0.809231i
$796$	−2.84067e8	+	2.84067e8i	−0.563224	+	0.563224i
$797$	6.45687e8	+	6.45687e8i	1.27540	+	1.27540i	0.943213	+	0.332188i	$0.107787\pi$
$797$	6.45687e8	+	6.45687e8i	1.27540	+	1.27540i	0.332188	+	0.943213i	$0.392213\pi$
$798$			1.46589e7i			0.0288464i
$799$	1.15546e8	−	1.15546e8i	0.226525	−	0.226525i
$800$	−4.28181e7	+	4.28181e7i	−0.0836290	+	0.0836290i
$801$	−6.71590e7	−	6.71590e7i	−0.130679	−	0.130679i
$802$			1.78735e8i			0.346486i
$803$	1.13485e8			0.219175
$804$		−	2.65679e8i		−	0.511198i
$805$			1.21239e9i			2.32410i
$806$	−2.07769e8	−	2.07769e8i	−0.396804	−	0.396804i
$807$		−	5.35045e8i		−	1.01805i
$808$	−1.45129e8	−	1.45129e8i	−0.275118	−	0.275118i
$809$	2.50022e8	+	2.50022e8i	0.472208	+	0.472208i	0.902628	−	0.430421i	$-0.141635\pi$
$809$	2.50022e8	+	2.50022e8i	0.472208	+	0.472208i	−0.430421	+	0.902628i	$0.641635\pi$
$810$	−3.52497e8			−0.663284
$811$	9.30182e8			1.74384			0.871918	−	0.489652i	$-0.162876\pi$
$811$	9.30182e8			1.74384			0.871918	+	0.489652i	$0.162876\pi$
$812$	−6.49194e7	+	6.49194e7i	−0.121257	+	0.121257i
$813$		−	4.64364e7i		−	0.0864145i
$814$	1.18614e7	+	4.41264e7i	0.0219919	+	0.0818136i
$815$	5.19268e8			0.959220
$816$	5.65632e7	+	5.65632e7i	0.104103	+	0.104103i
$817$			1.35343e7i			0.0248181i
$818$			5.07948e8i			0.928025i
$819$	1.72759e8	−	1.72759e8i	0.314476	−	0.314476i
$820$	−2.60810e7	+	2.60810e7i	−0.0473023	+	0.0473023i
$821$	5.73016e8			1.03547			0.517735	−	0.855541i	$-0.326776\pi$
$821$	5.73016e8			1.03547			0.517735	+	0.855541i	$0.326776\pi$
$822$	2.24899e8	−	2.24899e8i	0.404923	−	0.404923i
$823$	−3.92246e8			−0.703654			−0.351827	−	0.936065i	$-0.614439\pi$
$823$	−3.92246e8			−0.703654			−0.351827	+	0.936065i	$0.614439\pi$
$824$	2.72471e8			0.487010
$825$			3.96532e7i			0.0706182i
$826$	5.99693e8			1.06412
$827$	−4.33121e8	+	4.33121e8i	−0.765760	+	0.765760i	−0.977357	−	0.211597i	$-0.932134\pi$
$827$	−4.33121e8	+	4.33121e8i	−0.765760	+	0.765760i	0.211597	+	0.977357i	$0.432134\pi$
$828$	−7.38908e7	−	7.38908e7i	−0.130167	−	0.130167i
$829$	5.80085e7	+	5.80085e7i	0.101819	+	0.101819i	0.756181	−	0.654362i	$-0.227063\pi$
$829$	5.80085e7	+	5.80085e7i	0.101819	+	0.101819i	−0.654362	+	0.756181i	$0.727063\pi$
$830$	4.18772e8			0.732392
$831$	4.45997e8	−	4.45997e8i	0.777193	−	0.777193i
$832$	−9.24849e7	−	9.24849e7i	−0.160584	−	0.160584i
$833$	−5.35798e7	+	5.35798e7i	−0.0926971	+	0.0926971i
$834$	3.62229e8	+	3.62229e8i	0.624433	+	0.624433i
$835$		−	5.28748e8i		−	0.908217i
$836$	−1.04786e6	+	1.04786e6i	−0.00179343	+	0.00179343i
$837$	1.95281e8	−	1.95281e8i	0.333031	−	0.333031i
$838$	−4.90092e8	−	4.90092e8i	−0.832810	−	0.832810i
$839$		−	3.58253e7i		−	0.0606602i	−0.999540	−	0.0303301i	$-0.990344\pi$
$839$		−	3.58253e7i		−	0.0606602i	0.999540	−	0.0303301i	$-0.00965586\pi$
$840$	−2.60851e8			−0.440103
$841$		−	5.36329e8i		−	0.901661i
$842$			3.44398e8i			0.576932i
$843$	2.01172e8	+	2.01172e8i	0.335804	+	0.335804i
$844$			1.81240e8i			0.301458i
$845$	−1.26811e9	−	1.26811e9i	−2.10177	−	2.10177i
$846$	−3.24761e7	−	3.24761e7i	−0.0536355	−	0.0536355i
$847$	6.55026e8			1.07797
$848$	−1.53286e8			−0.251371
$849$	5.18304e8	−	5.18304e8i	0.846958	−	0.846958i
$850$			1.94199e8i			0.316221i
$851$	2.63155e8	+	9.78981e8i	0.426996	+	1.58849i
$852$	3.63969e8			0.588500
$853$	6.45613e8	+	6.45613e8i	1.04022	+	1.04022i	0.999157	+	0.0410631i	$0.0130745\pi$
$853$	6.45613e8	+	6.45613e8i	1.04022	+	1.04022i	0.0410631	+	0.999157i	$0.486926\pi$
$854$		−	3.65943e8i		−	0.587544i
$855$		−	7.65209e6i		−	0.0122428i
$856$	2.34451e7	−	2.34451e7i	0.0373793	−	0.0373793i
$857$	3.03404e8	−	3.03404e8i	0.482036	−	0.482036i	−0.423745	−	0.905781i	$-0.639285\pi$
$857$	3.03404e8	−	3.03404e8i	0.482036	−	0.482036i	0.905781	+	0.423745i	$0.139285\pi$
$858$	−8.56490e7			−0.135600
$859$	5.37639e7	−	5.37639e7i	0.0848226	−	0.0848226i	−0.663422	−	0.748245i	$-0.730897\pi$
$859$	5.37639e7	−	5.37639e7i	0.0848226	−	0.0848226i	0.748245	+	0.663422i	$0.230897\pi$
$860$	−2.40839e8			−0.378645
$861$	−6.36900e7			−0.0997842
$862$			1.44199e8i			0.225134i
$863$	1.02644e9			1.59698			0.798490	−	0.602009i	$-0.205633\pi$
$863$	1.02644e9			1.59698			0.798490	+	0.602009i	$0.205633\pi$
$864$	8.69261e7	−	8.69261e7i	0.134775	−	0.134775i
$865$	−6.55098e8	−	6.55098e8i	−1.01218	−	1.01218i
$866$	2.47674e8	+	2.47674e8i	0.381353	+	0.381353i
$867$	−3.17626e8			−0.487370
$868$	1.10459e8	−	1.10459e8i	0.168905	−	0.168905i
$869$	−6.15384e7	−	6.15384e7i	−0.0937749	−	0.0937749i
$870$	−1.17518e8	+	1.17518e8i	−0.178462	+	0.178462i
$871$	9.85111e8	+	9.85111e8i	1.49084	+	1.49084i
$872$		−	3.23542e8i		−	0.487956i
$873$	3.50298e7	−	3.50298e7i	0.0526495	−	0.0526495i
$874$	−2.32476e7	+	2.32476e7i	−0.0348213	+	0.0348213i
$875$	2.21521e8	+	2.21521e8i	0.330667	+	0.330667i
$876$			5.41706e8i			0.805845i
$877$	−5.85194e8			−0.867563			−0.433782	−	0.901018i	$-0.642821\pi$
$877$	−5.85194e8			−0.867563			−0.433782	+	0.901018i	$0.642821\pi$
$878$		−	2.98978e6i		−	0.00441729i
$879$			1.88339e8i			0.277315i
$880$	−1.86464e7	−	1.86464e7i	−0.0273620	−	0.0273620i
$881$		−	9.63449e8i		−	1.40897i	−0.709720	−	0.704484i	$-0.751178\pi$
$881$		−	9.63449e8i		−	1.40897i	0.709720	−	0.704484i	$-0.248822\pi$
$882$	1.50594e7	+	1.50594e7i	0.0219484	+	0.0219484i
$883$	3.93246e8	+	3.93246e8i	0.571192	+	0.571192i	0.932461	−	0.361270i	$-0.117657\pi$
$883$	3.93246e8	+	3.93246e8i	0.571192	+	0.571192i	−0.361270	+	0.932461i	$0.617657\pi$
$884$	−4.19461e8			−0.607204
$885$	1.08557e9			1.56613
$886$	−2.95560e8	+	2.95560e8i	−0.424957	+	0.424957i
$887$		−	7.85455e8i		−	1.12551i	−0.826623	−	0.562756i	$-0.809741\pi$
$887$		−	7.85455e8i		−	1.12551i	0.826623	−	0.562756i	$-0.190259\pi$
$888$	−2.10632e8	+	5.66190e7i	−0.300805	+	0.0808580i
$889$	−3.58066e8			−0.509634
$890$	−3.75997e8	−	3.75997e8i	−0.533353	−	0.533353i
$891$		−	6.15326e7i		−	0.0869906i
$892$		−	4.59873e8i		−	0.647953i
$893$	−1.02177e7	+	1.02177e7i	−0.0143482	+	0.0143482i
$894$	4.83956e8	−	4.83956e8i	0.677319	−	0.677319i
$895$	−5.96516e8			−0.832057
$896$	4.91690e7	−	4.91690e7i	0.0683546	−	0.0683546i
$897$	−1.90019e9			−2.63282
$898$	8.01835e8			1.10728
$899$		−	9.95275e7i		−	0.136982i
$900$	5.45826e7			0.0748732
$901$	−3.47611e8	+	3.47611e8i	−0.475247	+	0.475247i
$902$	−4.55275e6	−	4.55275e6i	−0.00620375	−	0.00620375i
$903$	−2.94066e8	−	2.94066e8i	−0.399376	−	0.399376i
$904$	−4.26192e8			−0.576899
$905$	−9.21793e8	+	9.21793e8i	−1.24362	+	1.24362i
$906$	2.75893e8	+	2.75893e8i	0.370985	+	0.370985i
$907$	−8.94156e8	+	8.94156e8i	−1.19837	+	1.19837i	−0.223718	+	0.974654i	$0.571819\pi$
$907$	−8.94156e8	+	8.94156e8i	−1.19837	+	1.19837i	−0.974654	+	0.223718i	$0.928181\pi$
$908$	3.84137e8	+	3.84137e8i	0.513131	+	0.513131i
$909$			1.85004e8i			0.246314i
$910$	9.67208e8	−	9.67208e8i	1.28350	−	1.28350i
$911$	−7.47424e8	+	7.47424e8i	−0.988580	+	0.988580i	−0.999936	−	0.0113557i	$-0.996385\pi$
$911$	−7.47424e8	+	7.47424e8i	−0.988580	+	0.988580i	0.0113557	+	0.999936i	$0.496385\pi$
$912$	−5.00183e6	−	5.00183e6i	−0.00659393	−	0.00659393i
$913$			7.31019e7i			0.0960541i
$914$	1.45875e8			0.191048
$915$		−	6.62435e8i		−	0.864729i
$916$		−	4.43030e8i		−	0.576430i
$917$	1.40150e8	+	1.40150e8i	0.181754	+	0.181754i
$918$		−	3.94249e8i		−	0.509616i
$919$	−8.72827e8	−	8.72827e8i	−1.12456	−	1.12456i	−0.991047	−	0.133510i	$-0.957375\pi$
$919$	−8.72827e8	−	8.72827e8i	−1.12456	−	1.12456i	−0.133510	−	0.991047i	$-0.542625\pi$
$920$	−4.13686e8	−	4.13686e8i	−0.531260	−	0.531260i
$921$	1.20119e9			1.53756
$922$	−3.07256e7			−0.0392020
$923$	−1.34956e9	+	1.34956e9i	−1.71628	+	1.71628i
$924$		−	4.55347e7i		−	0.0577201i
$925$	−4.58778e8	−	2.64388e8i	−0.579666	−	0.334053i
$926$	−2.78024e8			−0.350146
$927$	−1.73667e8	−	1.73667e8i	−0.218011	−	0.218011i
$928$		−	4.43030e7i		−	0.0554356i
$929$			2.73949e8i			0.341682i	0.985299	+	0.170841i	$0.0546485\pi$
$929$			2.73949e8i			0.341682i	−0.985299	+	0.170841i	$0.945351\pi$
$930$	1.99954e8	−	1.99954e8i	0.248589	−	0.248589i
$931$	4.73801e6	−	4.73801e6i	0.00587148	−	0.00587148i
$932$	−1.32412e8			−0.163560
$933$	−8.16482e8	+	8.16482e8i	−1.00531	+	1.00531i
$934$	6.43126e8			0.789325
$935$	−8.45698e7			−0.103462
$936$			1.17896e8i			0.143771i
$937$	−4.92993e8			−0.599269			−0.299634	−	0.954054i	$-0.596865\pi$
$937$	−4.92993e8			−0.599269			−0.299634	+	0.954054i	$0.596865\pi$
$938$	−5.23728e8	+	5.23728e8i	−0.634596	+	0.634596i
$939$	3.48978e8	+	3.48978e8i	0.421504	+	0.421504i
$940$	−1.81821e8	−	1.81821e8i	−0.218907	−	0.218907i
$941$	7.84616e8			0.941648			0.470824	−	0.882227i	$-0.343957\pi$
$941$	7.84616e8			0.941648			0.470824	+	0.882227i	$0.343957\pi$
$942$	4.32901e8	−	4.32901e8i	0.517889	−	0.517889i
$943$	−1.01007e8	−	1.01007e8i	−0.120452	−	0.120452i
$944$	−2.04624e8	+	2.04624e8i	−0.243244	+	0.243244i
$945$	9.09074e8	+	9.09074e8i	1.07722	+	1.07722i
$946$		−	4.20415e7i		−	0.0496597i
$947$	2.25182e8	−	2.25182e8i	0.265145	−	0.265145i	−0.561996	−	0.827140i	$-0.689966\pi$
$947$	2.25182e8	−	2.25182e8i	0.265145	−	0.265145i	0.827140	+	0.561996i	$0.189966\pi$
$948$	2.93746e8	−	2.93746e8i	0.344783	−	0.344783i
$949$	−2.00859e9	−	2.00859e9i	−2.35013	−	2.35013i
$950$		−	1.71728e7i		−	0.0200296i
$951$	7.41814e7			0.0862488
$952$		−	2.23004e8i		−	0.258464i
$953$		−	5.12366e8i		−	0.591973i	−0.955192	−	0.295986i	$-0.904352\pi$
$953$		−	5.12366e8i		−	0.591973i	0.955192	−	0.295986i	$-0.0956483\pi$
$954$	9.77013e7	+	9.77013e7i	0.112527	+	0.112527i
$955$		−	1.07595e8i		−	0.123533i
$956$	1.61589e8	+	1.61589e8i	0.184943	+	0.184943i
$957$	−2.05142e7	−	2.05142e7i	−0.0234055	−	0.0234055i
$958$	−6.14745e7			−0.0699195
$959$	−8.86679e8			−1.00533
$960$	8.90063e7	−	8.90063e7i	0.100602	−	0.100602i
$961$		−	7.18160e8i		−	0.809191i
$962$	5.71064e8	−	9.90939e8i	0.641446	−	1.11307i
$963$	−2.98868e7			−0.0334658
$964$	3.70888e8	+	3.70888e8i	0.414011	+	0.414011i
$965$			3.22144e8i			0.358483i
$966$		−	1.01023e9i		−	1.12069i
$967$	1.13675e9	−	1.13675e9i	1.25714	−	1.25714i	0.304695	−	0.952450i	$-0.401446\pi$
$967$	1.13675e9	−	1.13675e9i	1.25714	−	1.25714i	0.952450	−	0.304695i	$-0.0985545\pi$
$968$	−2.23505e8	+	2.23505e8i	−0.246411	+	0.246411i
$969$	−2.26855e7			−0.0249332
$970$	1.96118e8	−	1.96118e8i	0.214883	−	0.214883i
$971$	−2.01449e8			−0.220043			−0.110021	−	0.993929i	$-0.535092\pi$
$971$	−2.01449e8			−0.220043			−0.110021	+	0.993929i	$0.535092\pi$
$972$	−2.01353e8			−0.219260
$973$		−	1.42811e9i		−	1.55033i
$974$	−2.18853e8			−0.236851
$975$	7.01829e8	−	7.01829e8i	0.757212	−	0.757212i
$976$	1.24865e8	+	1.24865e8i	0.134305	+	0.134305i
$977$	−5.47206e8	−	5.47206e8i	−0.586769	−	0.586769i	0.349986	−	0.936755i	$-0.386186\pi$
$977$	−5.47206e8	−	5.47206e8i	−0.586769	−	0.586769i	−0.936755	+	0.349986i	$0.886186\pi$
$978$	−4.32681e8			−0.462542
$979$	6.56349e7	−	6.56349e7i	0.0699499	−	0.0699499i
$980$	8.43118e7	+	8.43118e7i	0.0895798	+	0.0895798i
$981$	−2.06218e8	+	2.06218e8i	−0.218434	+	0.218434i
$982$	−6.28848e8	−	6.28848e8i	−0.664066	−	0.664066i
$983$		−	3.44110e8i		−	0.362274i	−0.983458	−	0.181137i	$-0.942022\pi$
$983$		−	3.44110e8i		−	0.362274i	0.983458	−	0.181137i	$-0.0579777\pi$
$984$	2.17320e7	−	2.17320e7i	0.0228094	−	0.0228094i
$985$	7.54906e8	−	7.54906e8i	0.789922	−	0.789922i
$986$	−1.00467e8	−	1.00467e8i	−0.104807	−	0.104807i
$987$		−	4.44008e8i		−	0.461785i
$988$	3.70925e7			0.0384606
$989$		−	9.32724e8i		−	0.964194i
$990$			2.37696e7i			0.0244972i
$991$	1.66125e8	+	1.66125e8i	0.170693	+	0.170693i	0.787284	−	0.616591i	$-0.211487\pi$
$991$	1.66125e8	+	1.66125e8i	0.170693	+	0.170693i	−0.616591	+	0.787284i	$0.711487\pi$
$992$			7.53807e7i			0.0772191i
$993$	6.81597e8	+	6.81597e8i	0.696113	+	0.696113i
$994$	−7.17485e8	−	7.17485e8i	−0.730557	−	0.730557i
$995$	2.02735e9			2.05806
$996$	−3.48942e8			−0.353164
$997$	−1.06050e9	+	1.06050e9i	−1.07010	+	1.07010i	−0.0727544	+	0.997350i	$0.523179\pi$
$997$	−1.06050e9	+	1.06050e9i	−1.07010	+	1.07010i	−0.997350	+	0.0727544i	$0.976821\pi$
$998$			4.35748e8i			0.438373i
$999$	9.31379e8	+	5.36741e8i	0.934178	+	0.538354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.a.31.7	✓	18
37.6	odd	4	inner	74.7.d.a.43.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.a.31.7	✓	18	1.1	even	1	trivial
74.7.d.a.43.3	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)

\(f(q)\)	\(=\)	\(q+(4.00000 + 4.00000i) q^{2} +23.7872i q^{3} +32.0000i q^{4} +(114.190 - 114.190i) q^{5} +(-95.1488 + 95.1488i) q^{6} +375.130 q^{7} +(-128.000 + 128.000i) q^{8} +163.169 q^{9} +O(q^{10})\)	\(q+(4.00000 + 4.00000i) q^{2} +23.7872i q^{3} +32.0000i q^{4} +(114.190 - 114.190i) q^{5} +(-95.1488 + 95.1488i) q^{6} +375.130 q^{7} +(-128.000 + 128.000i) q^{8} +163.169 q^{9} +913.518 q^{10} +159.466i q^{11} -761.191 q^{12} +(2822.42 - 2822.42i) q^{13} +(1500.52 + 1500.52i) q^{14} +(2716.26 + 2716.26i) q^{15} -1024.00 q^{16} +(-2322.15 + 2322.15i) q^{17} +(652.675 + 652.675i) q^{18} +(205.346 - 205.346i) q^{19} +(3654.07 + 3654.07i) q^{20} +8923.29i q^{21} +(-637.864 + 637.864i) q^{22} +(-14151.5 + 14151.5i) q^{23} +(-3044.76 - 3044.76i) q^{24} -10453.6i q^{25} +22579.3 q^{26} +21222.2i q^{27} +12004.2i q^{28} +(5408.08 + 5408.08i) q^{29} +21730.1i q^{30} +(-9201.74 - 9201.74i) q^{31} +(-4096.00 - 4096.00i) q^{32} -3793.25 q^{33} -18577.2 q^{34} +(42836.0 - 42836.0i) q^{35} +5221.40i q^{36} +(25291.5 - 43887.0i) q^{37} +1642.76 q^{38} +(67137.4 + 67137.4i) q^{39} +29232.6i q^{40} +7137.50i q^{41} +(-35693.2 + 35693.2i) q^{42} +(-32954.9 + 32954.9i) q^{43} -5102.91 q^{44} +(18632.2 - 18632.2i) q^{45} -113212. q^{46} -49758.4 q^{47} -24358.1i q^{48} +23073.4 q^{49} +(41814.5 - 41814.5i) q^{50} +(-55237.5 - 55237.5i) q^{51} +(90317.3 + 90317.3i) q^{52} +149694. q^{53} +(-84888.8 + 84888.8i) q^{54} +(18209.4 + 18209.4i) q^{55} +(-48016.6 + 48016.6i) q^{56} +(4884.60 + 4884.60i) q^{57} +43264.6i q^{58} +(199829. - 199829. i) q^{59} +(-86920.2 + 86920.2i) q^{60} +(-121939. - 121939. i) q^{61} -73613.9i q^{62} +61209.5 q^{63} -32768.0i q^{64} -644582. i q^{65} +(-15173.0 - 15173.0i) q^{66} +349031. i q^{67} +(-74308.8 - 74308.8i) q^{68} +(-336625. - 336625. i) q^{69} +342688. q^{70} -478158. q^{71} +(-20885.6 + 20885.6i) q^{72} -711656. i q^{73} +(276714. - 74382.1i) q^{74} +248663. q^{75} +(6571.06 + 6571.06i) q^{76} +59820.4i q^{77} +537099. i q^{78} +(-385903. + 385903. i) q^{79} +(-116930. + 116930. i) q^{80} -385867. q^{81} +(-28550.0 + 28550.0i) q^{82} +458417. q^{83} -285545. q^{84} +530332. i q^{85} -263639. q^{86} +(-128643. + 128643. i) q^{87} +(-20411.6 - 20411.6i) q^{88} +(-411592. - 411592. i) q^{89} +149058. q^{90} +(1.05877e6 - 1.05877e6i) q^{91} +(-452849. - 452849. i) q^{92} +(218884. - 218884. i) q^{93} +(-199033. - 199033. i) q^{94} -46896.8i q^{95} +(97432.4 - 97432.4i) q^{96} +(214684. - 214684. i) q^{97} +(92293.5 + 92293.5i) q^{98} +26019.9i 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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