LMFDB - Embedded newform 74.7.d.a.31.4

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			31.4
Root			$-4.39870i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 + 4.00000i) q^{2} -0.398699i q^{3} +32.0000i q^{4} +(44.3245 - 44.3245i) q^{5} +(1.59480 - 1.59480i) q^{6} -329.540 q^{7} +(-128.000 + 128.000i) q^{8} +728.841 q^{9} +O(q^{10})$	\(q+(4.00000 + 4.00000i) q^{2} -0.398699i q^{3} +32.0000i q^{4} +(44.3245 - 44.3245i) q^{5} +(1.59480 - 1.59480i) q^{6} -329.540 q^{7} +(-128.000 + 128.000i) q^{8} +728.841 q^{9} +354.596 q^{10} +2537.69i q^{11} +12.7584 q^{12} +(-1647.00 + 1647.00i) q^{13} +(-1318.16 - 1318.16i) q^{14} +(-17.6721 - 17.6721i) q^{15} -1024.00 q^{16} +(4015.98 - 4015.98i) q^{17} +(2915.36 + 2915.36i) q^{18} +(-4525.10 + 4525.10i) q^{19} +(1418.38 + 1418.38i) q^{20} +131.387i q^{21} +(-10150.8 + 10150.8i) q^{22} +(-10138.1 + 10138.1i) q^{23} +(51.0335 + 51.0335i) q^{24} +11695.7i q^{25} -13176.0 q^{26} -581.240i q^{27} -10545.3i q^{28} +(-5128.37 - 5128.37i) q^{29} -141.377i q^{30} +(15877.5 + 15877.5i) q^{31} +(-4096.00 - 4096.00i) q^{32} +1011.77 q^{33} +32127.9 q^{34} +(-14606.7 + 14606.7i) q^{35} +23322.9i q^{36} +(-27748.5 - 42376.2i) q^{37} -36200.8 q^{38} +(656.659 + 656.659i) q^{39} +11347.1i q^{40} -22593.6i q^{41} +(-525.549 + 525.549i) q^{42} +(-88945.6 + 88945.6i) q^{43} -81206.0 q^{44} +(32305.5 - 32305.5i) q^{45} -81104.7 q^{46} +175406. q^{47} +408.268i q^{48} -9052.69 q^{49} +(-46782.7 + 46782.7i) q^{50} +(-1601.17 - 1601.17i) q^{51} +(-52704.1 - 52704.1i) q^{52} +210044. q^{53} +(2324.96 - 2324.96i) q^{54} +(112482. + 112482. i) q^{55} +(42181.1 - 42181.1i) q^{56} +(1804.15 + 1804.15i) q^{57} -41027.0i q^{58} +(181842. - 181842. i) q^{59} +(565.508 - 565.508i) q^{60} +(29932.7 + 29932.7i) q^{61} +127020. i q^{62} -240182. q^{63} -32768.0i q^{64} +146005. i q^{65} +(4047.10 + 4047.10i) q^{66} -538365. i q^{67} +(128511. + 128511. i) q^{68} +(4042.05 + 4042.05i) q^{69} -116853. q^{70} +527545. q^{71} +(-93291.7 + 93291.7i) q^{72} +292602. i q^{73} +(58510.9 - 280499. i) q^{74} +4663.06 q^{75} +(-144803. - 144803. i) q^{76} -836269. i q^{77} +5253.27i q^{78} +(296286. - 296286. i) q^{79} +(-45388.2 + 45388.2i) q^{80} +531093. q^{81} +(90374.5 - 90374.5i) q^{82} -973921. q^{83} -4204.39 q^{84} -356013. i q^{85} -711565. q^{86} +(-2044.68 + 2044.68i) q^{87} +(-324824. - 324824. i) q^{88} +(630289. + 630289. i) q^{89} +258444. q^{90} +(542753. - 542753. i) q^{91} +(-324419. - 324419. i) q^{92} +(6330.34 - 6330.34i) q^{93} +(701623. + 701623. i) q^{94} +401145. i q^{95} +(-1633.07 + 1633.07i) q^{96} +(-524592. + 524592. i) q^{97} +(-36210.8 - 36210.8i) q^{98} +1.84957e6i 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
$3$		−	0.398699i		−	0.0147666i	−0.999973	−	0.00738332i	$-0.997650\pi$
$3$		−	0.398699i		−	0.0147666i	0.999973	−	0.00738332i	$-0.00235021\pi$
$4$			32.0000i			0.500000i
$5$	44.3245	−	44.3245i	0.354596	−	0.354596i	−0.507221	−	0.861816i	$-0.669327\pi$
$5$	44.3245	−	44.3245i	0.354596	−	0.354596i	0.861816	+	0.507221i	$0.169327\pi$
$6$	1.59480	−	1.59480i	0.00738332	−	0.00738332i
$7$	−329.540			−0.960757			−0.480378	−	0.877061i	$-0.659501\pi$
$7$	−329.540			−0.960757			−0.480378	+	0.877061i	$0.659501\pi$
$8$	−128.000	+	128.000i	−0.250000	+	0.250000i
$9$	728.841			0.999782
$10$	354.596			0.354596
$11$			2537.69i			1.90660i	0.302020	+	0.953301i	$0.402339\pi$
$11$			2537.69i			1.90660i	−0.302020	+	0.953301i	$0.597661\pi$
$12$	12.7584			0.00738332
$13$	−1647.00	+	1647.00i	−0.749660	+	0.749660i	−0.974415	−	0.224755i	$-0.927842\pi$
$13$	−1647.00	+	1647.00i	−0.749660	+	0.749660i	0.224755	+	0.974415i	$0.427842\pi$
$14$	−1318.16	−	1318.16i	−0.480378	−	0.480378i
$15$	−17.6721	−	17.6721i	−0.00523619	−	0.00523619i
$16$	−1024.00			−0.250000
$17$	4015.98	−	4015.98i	0.817420	−	0.817420i	−0.168314	−	0.985734i	$-0.553832\pi$
$17$	4015.98	−	4015.98i	0.817420	−	0.817420i	0.985734	+	0.168314i	$0.0538321\pi$
$18$	2915.36	+	2915.36i	0.499891	+	0.499891i
$19$	−4525.10	+	4525.10i	−0.659731	+	0.659731i	−0.955316	−	0.295585i	$-0.904485\pi$
$19$	−4525.10	+	4525.10i	−0.659731	+	0.659731i	0.295585	+	0.955316i	$0.404485\pi$
$20$	1418.38	+	1418.38i	0.177298	+	0.177298i
$21$			131.387i			0.0141871i
$22$	−10150.8	+	10150.8i	−0.953301	+	0.953301i
$23$	−10138.1	+	10138.1i	−0.833245	+	0.833245i	−0.987959	−	0.154714i	$-0.950554\pi$
$23$	−10138.1	+	10138.1i	−0.833245	+	0.833245i	0.154714	+	0.987959i	$0.450554\pi$
$24$	51.0335	+	51.0335i	0.00369166	+	0.00369166i
$25$			11695.7i			0.748524i
$26$	−13176.0			−0.749660
$27$		−	581.240i		−	0.0295301i
$28$		−	10545.3i		−	0.480378i
$29$	−5128.37	−	5128.37i	−0.210274	−	0.210274i	0.594110	−	0.804384i	$-0.297504\pi$
$29$	−5128.37	−	5128.37i	−0.210274	−	0.210274i	−0.804384	+	0.594110i	$0.797504\pi$
$30$		−	141.377i		−	0.00523619i
$31$	15877.5	+	15877.5i	0.532962	+	0.532962i	0.921453	−	0.388490i	$-0.127003\pi$
$31$	15877.5	+	15877.5i	0.532962	+	0.532962i	−0.388490	+	0.921453i	$0.627003\pi$
$32$	−4096.00	−	4096.00i	−0.125000	−	0.125000i
$33$	1011.77			0.0281541
$34$	32127.9			0.817420
$35$	−14606.7	+	14606.7i	−0.340680	+	0.340680i
$36$			23322.9i			0.499891i
$37$	−27748.5	−	42376.2i	−0.547816	−	0.836599i
$37$	−27748.5	−	42376.2i	−0.547816	−	0.836599i
$38$	−36200.8			−0.659731
$39$	656.659	+	656.659i	0.0110700	+	0.0110700i
$40$			11347.1i			0.177298i
$41$		−	22593.6i		−	0.327819i	−0.986475	−	0.163910i	$-0.947589\pi$
$41$		−	22593.6i		−	0.327819i	0.986475	−	0.163910i	$-0.0524105\pi$
$42$	−525.549	+	525.549i	−0.00709357	+	0.00709357i
$43$	−88945.6	+	88945.6i	−1.11871	+	1.11871i	−0.126783	+	0.991930i	$0.540465\pi$
$43$	−88945.6	+	88945.6i	−1.11871	+	1.11871i	−0.991930	+	0.126783i	$0.959535\pi$
$44$	−81206.0			−0.953301
$45$	32305.5	−	32305.5i	0.354518	−	0.354518i
$46$	−81104.7			−0.833245
$47$	175406.			1.68947			0.844735	−	0.535186i	$-0.179758\pi$
$47$	175406.			1.68947			0.844735	+	0.535186i	$0.179758\pi$
$48$			408.268i			0.00369166i
$49$	−9052.69			−0.0769466
$50$	−46782.7	+	46782.7i	−0.374262	+	0.374262i
$51$	−1601.17	−	1601.17i	−0.0120705	−	0.0120705i
$52$	−52704.1	−	52704.1i	−0.374830	−	0.374830i
$53$	210044.			1.41086			0.705430	−	0.708780i	$-0.250754\pi$
$53$	210044.			1.41086			0.705430	+	0.708780i	$0.250754\pi$
$54$	2324.96	−	2324.96i	0.0147650	−	0.0147650i
$55$	112482.	+	112482.i	0.676073	+	0.676073i
$56$	42181.1	−	42181.1i	0.240189	−	0.240189i
$57$	1804.15	+	1804.15i	0.00974202	+	0.00974202i
$58$		−	41027.0i		−	0.210274i
$59$	181842.	−	181842.i	0.885395	−	0.885395i	−0.108681	−	0.994077i	$-0.534663\pi$
$59$	181842.	−	181842.i	0.885395	−	0.885395i	0.994077	+	0.108681i	$0.0346628\pi$
$60$	565.508	−	565.508i	0.00261809	−	0.00261809i
$61$	29932.7	+	29932.7i	0.131873	+	0.131873i	0.769962	−	0.638089i	$-0.220275\pi$
$61$	29932.7	+	29932.7i	0.131873	+	0.131873i	−0.638089	+	0.769962i	$0.720275\pi$
$62$			127020.i			0.532962i
$63$	−240182.			−0.960547
$64$		−	32768.0i		−	0.125000i
$65$			146005.i			0.531653i
$66$	4047.10	+	4047.10i	0.0140771	+	0.0140771i
$67$		−	538365.i		−	1.79000i	−0.446070	−	0.894998i	$-0.647177\pi$
$67$		−	538365.i		−	1.79000i	0.446070	−	0.894998i	$-0.352823\pi$
$68$	128511.	+	128511.i	0.408710	+	0.408710i
$69$	4042.05	+	4042.05i	0.0123042	+	0.0123042i
$70$	−116853.			−0.340680
$71$	527545.			1.47396			0.736978	−	0.675917i	$-0.236252\pi$
$71$	527545.			1.47396			0.736978	+	0.675917i	$0.236252\pi$
$72$	−93291.7	+	93291.7i	−0.249945	+	0.249945i
$73$			292602.i			0.752158i	0.926588	+	0.376079i	$0.122728\pi$
$73$			292602.i			0.752158i	−0.926588	+	0.376079i	$0.877272\pi$
$74$	58510.9	−	280499.i	0.144392	−	0.692207i
$75$	4663.06			0.0110532
$76$	−144803.	−	144803.i	−0.329866	−	0.329866i
$77$		−	836269.i		−	1.83178i
$78$			5253.27i			0.0110700i
$79$	296286.	−	296286.i	0.600938	−	0.600938i	−0.339623	−	0.940562i	$-0.610300\pi$
$79$	296286.	−	296286.i	0.600938	−	0.600938i	0.940562	+	0.339623i	$0.110300\pi$
$80$	−45388.2	+	45388.2i	−0.0886489	+	0.0886489i
$81$	531093.			0.999346
$82$	90374.5	−	90374.5i	0.163910	−	0.163910i
$83$	−973921.			−1.70329			−0.851647	−	0.524116i	$-0.824396\pi$
$83$	−973921.			−1.70329			−0.851647	+	0.524116i	$0.824396\pi$
$84$	−4204.39			−0.00709357
$85$		−	356013.i		−	0.579707i
$86$	−711565.			−1.11871
$87$	−2044.68	+	2044.68i	−0.00310504	+	0.00310504i
$88$	−324824.	−	324824.i	−0.476651	−	0.476651i
$89$	630289.	+	630289.i	0.894067	+	0.894067i	0.994903	−	0.100836i	$-0.0321518\pi$
$89$	630289.	+	630289.i	0.894067	+	0.894067i	−0.100836	+	0.994903i	$0.532152\pi$
$90$	258444.			0.354518
$91$	542753.	−	542753.i	0.720241	−	0.720241i
$92$	−324419.	−	324419.i	−0.416623	−	0.416623i
$93$	6330.34	−	6330.34i	0.00787006	−	0.00787006i
$94$	701623.	+	701623.i	0.844735	+	0.844735i
$95$			401145.i			0.467876i
$96$	−1633.07	+	1633.07i	−0.00184583	+	0.00184583i
$97$	−524592.	+	524592.i	−0.574786	+	0.574786i	−0.933462	−	0.358676i	$-0.883228\pi$
$97$	−524592.	+	524592.i	−0.574786	+	0.574786i	0.358676	+	0.933462i	$0.383228\pi$
$98$	−36210.8	−	36210.8i	−0.0384733	−	0.0384733i
$99$			1.84957e6i			1.90619i
$100$	−374262.			−0.374262
$101$		−	1.13486e6i		−	1.10149i	−0.834675	−	0.550743i	$-0.814344\pi$
$101$		−	1.13486e6i		−	1.10149i	0.834675	−	0.550743i	$-0.185656\pi$
$102$		−	12809.4i		−	0.0120705i
$103$	299158.	+	299158.i	0.273772	+	0.273772i	0.830617	−	0.556845i	$-0.187988\pi$
$103$	299158.	+	299158.i	0.273772	+	0.273772i	−0.556845	+	0.830617i	$0.687988\pi$
$104$		−	421633.i		−	0.374830i
$105$	5823.67	+	5823.67i	0.00503070	+	0.00503070i
$106$	840178.	+	840178.i	0.705430	+	0.705430i
$107$	−1.79159e6			−1.46247			−0.731237	−	0.682123i	$-0.761057\pi$
$107$	−1.79159e6			−1.46247			−0.731237	+	0.682123i	$0.761057\pi$
$108$	18599.7			0.0147650
$109$	912.777	−	912.777i	0.000704831	−	0.000704831i	−0.706754	−	0.707459i	$-0.749841\pi$
$109$	912.777	−	912.777i	0.000704831	−	0.000704831i	0.707459	+	0.706754i	$0.249841\pi$
$110$			899853.i			0.676073i
$111$	−16895.4	+	11063.3i	−0.0123538	+	0.00808940i
$112$	337448.			0.240189
$113$	−680797.	−	680797.i	−0.471827	−	0.471827i	0.430679	−	0.902505i	$-0.358274\pi$
$113$	−680797.	−	680797.i	−0.471827	−	0.471827i	−0.902505	+	0.430679i	$0.858274\pi$
$114$			14433.2i			0.00974202i
$115$			898731.i			0.590930i
$116$	164108.	−	164108.i	0.105137	−	0.105137i
$117$	−1.20040e6	+	1.20040e6i	−0.749497	+	0.749497i
$118$	1.45473e6			0.885395
$119$	−1.32343e6	+	1.32343e6i	−0.785342	+	0.785342i
$120$	4524.07			0.00261809
$121$	−4.66830e6			−2.63513
$122$			239461.i			0.131873i
$123$	−9008.06			−0.00484079
$124$	−508079.	+	508079.i	−0.266481	+	0.266481i
$125$	1.21097e6	+	1.21097e6i	0.620019	+	0.620019i
$126$	−960728.	−	960728.i	−0.480274	−	0.480274i
$127$	2.18198e6			1.06522			0.532611	−	0.846360i	$-0.321211\pi$
$127$	2.18198e6			1.06522			0.532611	+	0.846360i	$0.321211\pi$
$128$	131072.	−	131072.i	0.0625000	−	0.0625000i
$129$	35462.5	+	35462.5i	0.0165196	+	0.0165196i
$130$	−584020.	+	584020.i	−0.265826	+	0.265826i
$131$	2.79242e6	+	2.79242e6i	1.24213	+	1.24213i	0.959116	+	0.283013i	$0.0913339\pi$
$131$	2.79242e6	+	2.79242e6i	1.24213	+	1.24213i	0.283013	+	0.959116i	$0.408666\pi$
$132$			32376.8i			0.0140771i
$133$	1.49120e6	−	1.49120e6i	0.633841	−	0.633841i
$134$	2.15346e6	−	2.15346e6i	0.894998	−	0.894998i
$135$	−25763.2	−	25763.2i	−0.0104712	−	0.0104712i
$136$			1.02809e6i			0.408710i
$137$	−2.83585e6			−1.10286			−0.551432	−	0.834220i	$-0.685918\pi$
$137$	−2.83585e6			−1.10286			−0.551432	+	0.834220i	$0.685918\pi$
$138$			32336.4i			0.0123042i
$139$		−	706492.i		−	0.263065i	−0.991312	−	0.131532i	$-0.958010\pi$
$139$		−	706492.i		−	0.263065i	0.991312	−	0.131532i	$-0.0419898\pi$
$140$	−467413.	−	467413.i	−0.170340	−	0.170340i
$141$		−	69934.1i		−	0.0249478i
$142$	2.11018e6	+	2.11018e6i	0.736978	+	0.736978i
$143$	−4.17958e6	−	4.17958e6i	−1.42930	−	1.42930i
$144$	−746333.			−0.249945
$145$	−454625.			−0.149125
$146$	−1.17041e6	+	1.17041e6i	−0.376079	+	0.376079i
$147$			3609.30i			0.00113624i
$148$	1.35604e6	−	887953.i	0.418299	−	0.273908i
$149$	387420.			0.117118			0.0585589	−	0.998284i	$-0.481349\pi$
$149$	387420.			0.117118			0.0585589	+	0.998284i	$0.481349\pi$
$150$	18652.2	+	18652.2i	0.00552659	+	0.00552659i
$151$			68436.3i			0.0198772i	0.999951	+	0.00993861i	$0.00316361\pi$
$151$			68436.3i			0.0198772i	−0.999951	+	0.00993861i	$0.996836\pi$
$152$		−	1.15842e6i		−	0.329866i
$153$	2.92701e6	−	2.92701e6i	0.817242	−	0.817242i
$154$	3.34507e6	−	3.34507e6i	0.915891	−	0.915891i
$155$	1.40752e6			0.377972
$156$	−21013.1	+	21013.1i	−0.00553498	+	0.00553498i
$157$	−1.79549e6			−0.463965			−0.231982	−	0.972720i	$-0.574521\pi$
$157$	−1.79549e6			−0.463965			−0.231982	+	0.972720i	$0.574521\pi$
$158$	2.37029e6			0.600938
$159$		−	83744.6i		−	0.0208336i
$160$	−363106.			−0.0886489
$161$	3.34090e6	−	3.34090e6i	0.800546	−	0.800546i
$162$	2.12437e6	+	2.12437e6i	0.499673	+	0.499673i
$163$	366699.	+	366699.i	0.0846733	+	0.0846733i	0.748175	−	0.663502i	$-0.230930\pi$
$163$	366699.	+	366699.i	0.0846733	+	0.0846733i	−0.663502	+	0.748175i	$0.730930\pi$
$164$	722996.			0.163910
$165$	44846.4	−	44846.4i	0.00998333	−	0.00998333i
$166$	−3.89568e6	−	3.89568e6i	−0.851647	−	0.851647i
$167$	−2.88212e6	+	2.88212e6i	−0.618817	+	0.618817i	−0.945228	−	0.326411i	$-0.894161\pi$
$167$	−2.88212e6	+	2.88212e6i	−0.618817	+	0.618817i	0.326411	+	0.945228i	$0.394161\pi$
$168$	−16817.6	−	16817.6i	−0.00354679	−	0.00354679i
$169$		−	598432.i		−	0.123981i
$170$	1.42405e6	−	1.42405e6i	0.289854	−	0.289854i
$171$	−3.29808e6	+	3.29808e6i	−0.659587	+	0.659587i
$172$	−2.84626e6	−	2.84626e6i	−0.559357	−	0.559357i
$173$		−	5.86963e6i		−	1.13363i	−0.823844	−	0.566816i	$-0.808175\pi$
$173$		−	5.86963e6i		−	1.13363i	0.823844	−	0.566816i	$-0.191825\pi$
$174$	−16357.4			−0.00310504
$175$		−	3.85419e6i		−	0.719149i
$176$		−	2.59859e6i		−	0.476651i
$177$	−72500.1	−	72500.1i	−0.0130743	−	0.0130743i
$178$			5.04232e6i			0.894067i
$179$	−3.58544e6	−	3.58544e6i	−0.625149	−	0.625149i	0.321695	−	0.946843i	$-0.395748\pi$
$179$	−3.58544e6	−	3.58544e6i	−0.625149	−	0.625149i	−0.946843	+	0.321695i	$0.895748\pi$
$180$	1.03378e6	+	1.03378e6i	0.177259	+	0.177259i
$181$	7.24894e6			1.22247			0.611236	−	0.791448i	$-0.290673\pi$
$181$	7.24894e6			1.22247			0.611236	+	0.791448i	$0.290673\pi$
$182$	4.34202e6			0.720241
$183$	11934.1	−	11934.1i	0.00194732	−	0.00194732i
$184$		−	2.59535e6i		−	0.416623i
$185$	−3.10824e6	−	648366.i	−0.490908	−	0.102401i
$186$	50642.7			0.00787006
$187$	1.01913e7	+	1.01913e7i	1.55850	+	1.55850i
$188$			5.61298e6i			0.844735i
$189$			191542.i			0.0283712i
$190$	−1.60458e6	+	1.60458e6i	−0.233938	+	0.233938i
$191$	−933155.	+	933155.i	−0.133922	+	0.133922i	−0.770890	−	0.636968i	$-0.780188\pi$
$191$	−933155.	+	933155.i	−0.133922	+	0.133922i	0.636968	+	0.770890i	$0.280188\pi$
$192$	−13064.6			−0.00184583
$193$	6.20490e6	−	6.20490e6i	0.863103	−	0.863103i	−0.128594	−	0.991697i	$-0.541047\pi$
$193$	6.20490e6	−	6.20490e6i	0.863103	−	0.863103i	0.991697	+	0.128594i	$0.0410466\pi$
$194$	−4.19673e6			−0.574786
$195$	58212.1			0.00785072
$196$		−	289686.i		−	0.0384733i
$197$	6.82774e6			0.893056			0.446528	−	0.894770i	$-0.352660\pi$
$197$	6.82774e6			0.893056			0.446528	+	0.894770i	$0.352660\pi$
$198$	−7.39829e6	+	7.39829e6i	−0.953094	+	0.953094i
$199$	4.25761e6	+	4.25761e6i	0.540265	+	0.540265i	0.923607	−	0.383341i	$-0.125227\pi$
$199$	4.25761e6	+	4.25761e6i	0.540265	+	0.540265i	−0.383341	+	0.923607i	$0.625227\pi$
$200$	−1.49705e6	−	1.49705e6i	−0.187131	−	0.187131i
$201$	−214646.			−0.0264322
$202$	4.53945e6	−	4.53945e6i	0.550743	−	0.550743i
$203$	1.69000e6	+	1.69000e6i	0.202022	+	0.202022i
$204$	51237.4	−	51237.4i	0.00603527	−	0.00603527i
$205$	−1.00145e6	−	1.00145e6i	−0.116243	−	0.116243i
$206$			2.39326e6i			0.273772i
$207$	−7.38906e6	+	7.38906e6i	−0.833063	+	0.833063i
$208$	1.68653e6	−	1.68653e6i	0.187415	−	0.187415i
$209$	−1.14833e7	−	1.14833e7i	−1.25785	−	1.25785i
$210$			46589.3i			0.00503070i
$211$	−788070.			−0.0838914			−0.0419457	−	0.999120i	$-0.513356\pi$
$211$	−788070.			−0.0838914			−0.0419457	+	0.999120i	$0.513356\pi$
$212$			6.72142e6i			0.705430i
$213$		−	210332.i		−	0.0217654i
$214$	−7.16638e6	−	7.16638e6i	−0.731237	−	0.731237i
$215$			7.88493e6i			0.793382i
$216$	74398.7	+	74398.7i	0.00738251	+	0.00738251i
$217$	−5.23226e6	−	5.23226e6i	−0.512047	−	0.512047i
$218$	7302.22			0.000704831
$219$	116660.			0.0111068
$220$	−3.59941e6	+	3.59941e6i	−0.338037	+	0.338037i
$221$			1.32287e7i			1.22557i
$222$	−111835.	−	23328.3i	−0.0102216	−	0.00213218i
$223$	1.83768e7			1.65713			0.828563	−	0.559896i	$-0.189159\pi$
$223$	1.83768e7			1.65713			0.828563	+	0.559896i	$0.189159\pi$
$224$	1.34979e6	+	1.34979e6i	0.120095	+	0.120095i
$225$			8.52429e6i			0.748361i
$226$		−	5.44638e6i		−	0.471827i
$227$	−1.86139e6	+	1.86139e6i	−0.159133	+	0.159133i	−0.782182	−	0.623050i	$-0.785893\pi$
$227$	−1.86139e6	+	1.86139e6i	−0.159133	+	0.159133i	0.623050	+	0.782182i	$0.285893\pi$
$228$	−57732.9	+	57732.9i	−0.00487101	+	0.00487101i
$229$	−1.68999e7			−1.40727			−0.703634	−	0.710563i	$-0.748440\pi$
$229$	−1.68999e7			−1.40727			−0.703634	+	0.710563i	$0.748440\pi$
$230$	−3.59492e6	+	3.59492e6i	−0.295465	+	0.295465i
$231$	−333420.			−0.0270493
$232$	1.31286e6			0.105137
$233$			1.14429e7i			0.904625i	0.891859	+	0.452313i	$0.149401\pi$
$233$			1.14429e7i			0.904625i	−0.891859	+	0.452313i	$0.850599\pi$
$234$	−9.60323e6			−0.749497
$235$	7.77476e6	−	7.77476e6i	0.599078	−	0.599078i
$236$	5.81893e6	+	5.81893e6i	0.442698	+	0.442698i
$237$	−118129.	−	118129.i	−0.00887384	−	0.00887384i
$238$	−1.05874e7			−0.785342
$239$	−8.47509e6	+	8.47509e6i	−0.620798	+	0.620798i	−0.945736	−	0.324937i	$-0.894657\pi$
$239$	−8.47509e6	+	8.47509e6i	−0.620798	+	0.620798i	0.324937	+	0.945736i	$0.394657\pi$
$240$	18096.3	+	18096.3i	0.00130905	+	0.00130905i
$241$	1.64320e7	−	1.64320e7i	1.17392	−	1.17392i	0.192656	−	0.981266i	$-0.438290\pi$
$241$	1.64320e7	−	1.64320e7i	1.17392	−	1.17392i	0.981266	−	0.192656i	$-0.0617103\pi$
$242$	−1.86732e7	−	1.86732e7i	−1.31757	−	1.31757i
$243$		−	635471.i		−	0.0442870i
$244$	−957845.	+	957845.i	−0.0659365	+	0.0659365i
$245$	−401256.	+	401256.i	−0.0272849	+	0.0272849i
$246$	−36032.2	−	36032.2i	−0.00242039	−	0.00242039i
$247$		−	1.49057e7i		−	0.989149i
$248$	−4.06463e6			−0.266481
$249$			388302.i			0.0251519i
$250$			9.68780e6i			0.620019i
$251$	1.42638e7	+	1.42638e7i	0.902016	+	0.902016i	0.995610	−	0.0935943i	$-0.0298357\pi$
$251$	1.42638e7	+	1.42638e7i	0.902016	+	0.902016i	−0.0935943	+	0.995610i	$0.529836\pi$
$252$		−	7.68582e6i		−	0.480274i
$253$	−2.57273e7	−	2.57273e7i	−1.58867	−	1.58867i
$254$	8.72793e6	+	8.72793e6i	0.532611	+	0.532611i
$255$	−141942.			−0.00856033
$256$	1.04858e6			0.0625000
$257$	8.40818e6	−	8.40818e6i	0.495339	−	0.495339i	−0.414644	−	0.909983i	$-0.636094\pi$
$257$	8.40818e6	−	8.40818e6i	0.495339	−	0.495339i	0.909983	+	0.414644i	$0.136094\pi$
$258$			283700.i			0.0165196i
$259$	9.14423e6	+	1.39646e7i	0.526318	+	0.803768i
$260$	−4.67216e6			−0.265826
$261$	−3.73777e6	−	3.73777e6i	−0.210228	−	0.210228i
$262$			2.23394e7i			1.24213i
$263$			2.24275e7i			1.23286i	0.787410	+	0.616429i	$0.211421\pi$
$263$			2.24275e7i			1.23286i	−0.787410	+	0.616429i	$0.788579\pi$
$264$	−129507.	+	129507.i	−0.00703853	+	0.00703853i
$265$	9.31011e6	−	9.31011e6i	0.500285	−	0.500285i
$266$	1.19296e7			0.633841
$267$	251296.	−	251296.i	0.0132024	−	0.0132024i
$268$	1.72277e7			0.894998
$269$	1.80193e7			0.925725			0.462862	−	0.886430i	$-0.346822\pi$
$269$	1.80193e7			0.925725			0.462862	+	0.886430i	$0.346822\pi$
$270$		−	206105.i		−	0.0104712i
$271$	−1.97205e7			−0.990853			−0.495427	−	0.868650i	$-0.664988\pi$
$271$	−1.97205e7			−0.990853			−0.495427	+	0.868650i	$0.664988\pi$
$272$	−4.11237e6	+	4.11237e6i	−0.204355	+	0.204355i
$273$	−216395.	−	216395.i	−0.0106355	−	0.0106355i
$274$	−1.13434e7	−	1.13434e7i	−0.551432	−	0.551432i
$275$	−2.96800e7			−1.42714
$276$	−129346.	+	129346.i	−0.00615212	+	0.00615212i
$277$	1.44579e7	+	1.44579e7i	0.680246	+	0.680246i	0.960056	−	0.279809i	$-0.0902712\pi$
$277$	1.44579e7	+	1.44579e7i	0.680246	+	0.680246i	−0.279809	+	0.960056i	$0.590271\pi$
$278$	2.82597e6	−	2.82597e6i	0.131532	−	0.131532i
$279$	1.15722e7	+	1.15722e7i	0.532846	+	0.532846i
$280$		−	3.73931e6i		−	0.170340i
$281$	−8.17246e6	+	8.17246e6i	−0.368327	+	0.368327i	−0.866867	−	0.498540i	$-0.833870\pi$
$281$	−8.17246e6	+	8.17246e6i	−0.368327	+	0.368327i	0.498540	+	0.866867i	$0.333870\pi$
$282$	279737.	−	279737.i	0.0124739	−	0.0124739i
$283$	4.21299e6	+	4.21299e6i	0.185879	+	0.185879i	0.793912	−	0.608033i	$-0.208041\pi$
$283$	4.21299e6	+	4.21299e6i	0.185879	+	0.185879i	−0.608033	+	0.793912i	$0.708041\pi$
$284$			1.68814e7i			0.736978i
$285$	159936.			0.00690895
$286$		−	3.34367e7i		−	1.42930i
$287$			7.44549e6i			0.314954i
$288$	−2.98533e6	−	2.98533e6i	−0.124973	−	0.124973i
$289$		−	8.11869e6i		−	0.336351i
$290$	−1.81850e6	−	1.81850e6i	−0.0745623	−	0.0745623i
$291$	209154.	+	209154.i	0.00848766	+	0.00848766i
$292$	−9.36327e6			−0.376079
$293$	−6.75868e6			−0.268695			−0.134347	−	0.990934i	$-0.542894\pi$
$293$	−6.75868e6			−0.268695			−0.134347	+	0.990934i	$0.542894\pi$
$294$	−14437.2	+	14437.2i	−0.000568121	+	0.000568121i
$295$		−	1.61201e7i		−	0.627915i
$296$	8.97597e6	+	1.87235e6i	0.346104	+	0.0721958i
$297$	1.47501e6			0.0563021
$298$	1.54968e6	+	1.54968e6i	0.0585589	+	0.0585589i
$299$		−	3.33950e7i		−	1.24930i
$300$			149218.i			0.00552659i
$301$	2.93111e7	−	2.93111e7i	1.07481	−	1.07481i
$302$	−273745.	+	273745.i	−0.00993861	+	0.00993861i
$303$	−452469.			−0.0162652
$304$	4.63370e6	−	4.63370e6i	0.164933	−	0.164933i
$305$	2.65350e6			0.0935232
$306$	2.34161e7			0.817242
$307$			1.39739e7i			0.482951i	0.970407	+	0.241476i	$0.0776314\pi$
$307$			1.39739e7i			0.482951i	−0.970407	+	0.241476i	$0.922369\pi$
$308$	2.67606e7			0.915891
$309$	119274.	−	119274.i	0.00404269	−	0.00404269i
$310$	5.63009e6	+	5.63009e6i	0.188986	+	0.188986i
$311$	9.37002e6	+	9.37002e6i	0.311501	+	0.311501i	0.845491	−	0.533990i	$-0.179308\pi$
$311$	9.37002e6	+	9.37002e6i	0.311501	+	0.311501i	−0.533990	+	0.845491i	$0.679308\pi$
$312$	−168105.			−0.00553498
$313$	1.72455e7	−	1.72455e7i	0.562397	−	0.562397i	−0.367590	−	0.929988i	$-0.619817\pi$
$313$	1.72455e7	−	1.72455e7i	0.562397	−	0.562397i	0.929988	+	0.367590i	$0.119817\pi$
$314$	−7.18198e6	−	7.18198e6i	−0.231982	−	0.231982i
$315$	−1.06459e7	+	1.06459e7i	−0.340606	+	0.340606i
$316$	9.48115e6	+	9.48115e6i	0.300469	+	0.300469i
$317$		−	3.19171e7i		−	1.00195i	−0.865462	−	0.500974i	$-0.832975\pi$
$317$		−	3.19171e7i		−	1.00195i	0.865462	−	0.500974i	$-0.167025\pi$
$318$	334978.	−	334978.i	0.0104168	−	0.0104168i
$319$	1.30142e7	−	1.30142e7i	0.400909	−	0.400909i
$320$	−1.45242e6	−	1.45242e6i	−0.0443245	−	0.0443245i
$321$			714307.i			0.0215958i
$322$	2.67272e7			0.800546
$323$			3.63454e7i			1.07856i
$324$			1.69950e7i			0.499673i
$325$	−1.92628e7	−	1.92628e7i	−0.561139	−	0.561139i
$326$			2.93359e6i			0.0846733i
$327$	−363.924	−	363.924i	−1.04080e−5	−	1.04080e-5i
$328$	2.89198e6	+	2.89198e6i	0.0819548	+	0.0819548i
$329$	−5.78031e7			−1.62317
$330$	358771.			0.00998333
$331$	8.86970e6	−	8.86970e6i	0.244582	−	0.244582i	−0.574161	−	0.818743i	$-0.694671\pi$
$331$	8.86970e6	−	8.86970e6i	0.244582	−	0.244582i	0.818743	+	0.574161i	$0.194671\pi$
$332$		−	3.11655e7i		−	0.851647i
$333$	−2.02243e7	−	3.08855e7i	−0.547696	−	0.836416i
$334$	−2.30569e7			−0.618817
$335$	−2.38627e7	−	2.38627e7i	−0.634725	−	0.634725i
$336$		−	134540.i		−	0.00354679i
$337$			4.04959e7i			1.05809i	0.848595	+	0.529043i	$0.177449\pi$
$337$			4.04959e7i			1.05809i	−0.848595	+	0.529043i	$0.822551\pi$
$338$	2.39373e6	−	2.39373e6i	0.0619904	−	0.0619904i
$339$	−271433.	+	271433.i	−0.00696729	+	0.00696729i
$340$	1.13924e7			0.289854
$341$	−4.02921e7	+	4.02921e7i	−1.01615	+	1.01615i
$342$	−2.63846e7			−0.659587
$343$	4.17532e7			1.03468
$344$		−	2.27701e7i		−	0.559357i
$345$	358323.			0.00872605
$346$	2.34785e7	−	2.34785e7i	0.566816	−	0.566816i
$347$	5.34384e6	+	5.34384e6i	0.127898	+	0.127898i	0.768158	−	0.640260i	$-0.221173\pi$
$347$	5.34384e6	+	5.34384e6i	0.127898	+	0.127898i	−0.640260	+	0.768158i	$0.721173\pi$
$348$	−65429.7	−	65429.7i	−0.00155252	−	0.00155252i
$349$	−1.23160e7			−0.289731			−0.144865	−	0.989451i	$-0.546275\pi$
$349$	−1.23160e7			−0.289731			−0.144865	+	0.989451i	$0.546275\pi$
$350$	1.54168e7	−	1.54168e7i	0.359575	−	0.359575i
$351$	957305.	+	957305.i	0.0221375	+	0.0221375i
$352$	1.03944e7	−	1.03944e7i	0.238325	−	0.238325i
$353$	2.12473e7	+	2.12473e7i	0.483036	+	0.483036i	0.906100	−	0.423064i	$-0.139045\pi$
$353$	2.12473e7	+	2.12473e7i	0.483036	+	0.483036i	−0.423064	+	0.906100i	$0.639045\pi$
$354$		−	580001.i		−	0.0130743i
$355$	2.33832e7	−	2.33832e7i	0.522659	−	0.522659i
$356$	−2.01693e7	+	2.01693e7i	−0.447033	+	0.447033i
$357$	527649.	+	527649.i	0.0115969	+	0.0115969i
$358$		−	2.86835e7i		−	0.625149i
$359$	1.70049e7			0.367529			0.183765	−	0.982970i	$-0.441172\pi$
$359$	1.70049e7			0.367529			0.183765	+	0.982970i	$0.441172\pi$
$360$			8.27020e6i			0.177259i
$361$			6.09287e6i			0.129509i
$362$	2.89958e7	+	2.89958e7i	0.611236	+	0.611236i
$363$			1.86125e6i			0.0389121i
$364$	1.73681e7	+	1.73681e7i	0.360121	+	0.360121i
$365$	1.29694e7	+	1.29694e7i	0.266712	+	0.266712i
$366$	95473.1			0.00194732
$367$	−3.94656e7			−0.798400			−0.399200	−	0.916864i	$-0.630712\pi$
$367$	−3.94656e7			−0.798400			−0.399200	+	0.916864i	$0.630712\pi$
$368$	1.03814e7	−	1.03814e7i	0.208311	−	0.208311i
$369$		−	1.64672e7i		−	0.327748i
$370$	−9.83950e6	−	1.50264e7i	−0.194253	−	0.296654i
$371$	−6.92180e7			−1.35549
$372$	202571.	+	202571.i	0.00393503	+	0.00393503i
$373$		−	6.35107e7i		−	1.22383i	−0.790924	−	0.611914i	$-0.790400\pi$
$373$		−	6.35107e7i		−	1.22383i	0.790924	−	0.611914i	$-0.209600\pi$
$374$			8.15305e7i			1.55850i
$375$	482815.	−	482815.i	0.00915560	−	0.00915560i
$376$	−2.24519e7	+	2.24519e7i	−0.422367	+	0.422367i
$377$	1.68929e7			0.315268
$378$	−766166.	+	766166.i	−0.0141856	+	0.0141856i
$379$	1.07272e7			0.197046			0.0985232	−	0.995135i	$-0.468588\pi$
$379$	1.07272e7			0.197046			0.0985232	+	0.995135i	$0.468588\pi$
$380$	−1.28366e7			−0.233938
$381$		−	869955.i		−	0.0157298i
$382$	−7.46524e6			−0.133922
$383$	−4.34273e7	+	4.34273e7i	−0.772977	+	0.772977i	−0.978626	−	0.205649i	$-0.934069\pi$
$383$	−4.34273e7	+	4.34273e7i	−0.772977	+	0.772977i	0.205649	+	0.978626i	$0.434069\pi$
$384$	−52258.3	−	52258.3i	−0.000922915	−	0.000922915i
$385$	−3.70672e7	−	3.70672e7i	−0.649542	−	0.649542i
$386$	4.96392e7			0.863103
$387$	−6.48272e7	+	6.48272e7i	−1.11847	+	1.11847i
$388$	−1.67869e7	−	1.67869e7i	−0.287393	−	0.287393i
$389$	−7.15119e7	+	7.15119e7i	−1.21487	+	1.21487i	−0.245464	+	0.969406i	$0.578940\pi$
$389$	−7.15119e7	+	7.15119e7i	−1.21487	+	1.21487i	−0.969406	+	0.245464i	$0.921060\pi$
$390$	232848.	+	232848.i	0.00392536	+	0.00392536i
$391$			8.14288e7i			1.36222i
$392$	1.15874e6	−	1.15874e6i	0.0192367	−	0.0192367i
$393$	1.11334e6	−	1.11334e6i	0.0183421	−	0.0183421i
$394$	2.73110e7	+	2.73110e7i	0.446528	+	0.446528i
$395$		−	2.62654e7i		−	0.426180i
$396$	−5.91863e7			−0.953094
$397$		−	1.02606e7i		−	0.163984i	−0.996633	−	0.0819918i	$-0.973872\pi$
$397$		−	1.02606e7i		−	0.163984i	0.996633	−	0.0819918i	$-0.0261281\pi$
$398$			3.40609e7i			0.540265i
$399$	−594540.	−	594540.i	−0.00935971	−	0.00935971i
$400$		−	1.19764e7i		−	0.187131i
$401$	6.02764e7	+	6.02764e7i	0.934790	+	0.934790i	0.998000	−	0.0632100i	$-0.0201338\pi$
$401$	6.02764e7	+	6.02764e7i	0.934790	+	0.934790i	−0.0632100	+	0.998000i	$0.520134\pi$
$402$	−858582.	−	858582.i	−0.0132161	−	0.0132161i
$403$	−5.23005e7			−0.799081
$404$	3.63156e7			0.550743
$405$	2.35404e7	−	2.35404e7i	0.354364	−	0.354364i
$406$			1.35200e7i			0.202022i
$407$	1.07538e8	−	7.04171e7i	1.59506	−	1.04447i
$408$	409900.			0.00603527
$409$	3.74599e7	+	3.74599e7i	0.547516	+	0.547516i	0.925722	−	0.378206i	$-0.123459\pi$
$409$	3.74599e7	+	3.74599e7i	0.547516	+	0.547516i	−0.378206	+	0.925722i	$0.623459\pi$
$410$		−	8.01160e6i		−	0.116243i
$411$			1.13065e6i			0.0162856i
$412$	−9.57306e6	+	9.57306e6i	−0.136886	+	0.136886i
$413$	−5.99240e7	+	5.99240e7i	−0.850649	+	0.850649i
$414$	−5.91125e7			−0.833063
$415$	−4.31685e7	+	4.31685e7i	−0.603980	+	0.603980i
$416$	1.34923e7			0.187415
$417$	−281678.			−0.00388459
$418$		−	9.18663e7i		−	1.25785i
$419$	−7.82646e7			−1.06395			−0.531977	−	0.846759i	$-0.678551\pi$
$419$	−7.82646e7			−1.06395			−0.531977	+	0.846759i	$0.678551\pi$
$420$	−186357.	+	186357.i	−0.00251535	+	0.00251535i
$421$	4.65107e7	+	4.65107e7i	0.623313	+	0.623313i	0.946377	−	0.323064i	$-0.104713\pi$
$421$	4.65107e7	+	4.65107e7i	0.623313	+	0.623313i	−0.323064	+	0.946377i	$0.604713\pi$
$422$	−3.15228e6	−	3.15228e6i	−0.0419457	−	0.0419457i
$423$	1.27843e8			1.68910
$424$	−2.68857e7	+	2.68857e7i	−0.352715	+	0.352715i
$425$	4.69697e7	+	4.69697e7i	0.611858	+	0.611858i
$426$	841327.	−	841327.i	0.0108827	−	0.0108827i
$427$	−9.86400e6	−	9.86400e6i	−0.126698	−	0.126698i
$428$		−	5.73310e7i		−	0.731237i
$429$	−1.66640e6	+	1.66640e6i	−0.0211060	+	0.0211060i
$430$	−3.15397e7	+	3.15397e7i	−0.396691	+	0.396691i
$431$	−1.42059e7	−	1.42059e7i	−0.177434	−	0.177434i	0.612802	−	0.790236i	$-0.290042\pi$
$431$	−1.42059e7	−	1.42059e7i	−0.177434	−	0.177434i	−0.790236	+	0.612802i	$0.790042\pi$
$432$			595190.i			0.00738251i
$433$	3.41255e7			0.420355			0.210177	−	0.977663i	$-0.432596\pi$
$433$	3.41255e7			0.420355			0.210177	+	0.977663i	$0.432596\pi$
$434$		−	4.18581e7i		−	0.512047i
$435$			181259.i			0.00220207i
$436$	29208.9	+	29208.9i	0.000352416	+	0.000352416i
$437$		−	9.17517e7i		−	1.09944i
$438$	466641.	+	466641.i	0.00555342	+	0.00555342i
$439$	−7.99192e6	−	7.99192e6i	−0.0944620	−	0.0944620i	0.658297	−	0.752759i	$-0.271277\pi$
$439$	−7.99192e6	−	7.99192e6i	−0.0944620	−	0.0944620i	−0.752759	+	0.658297i	$0.771277\pi$
$440$	−2.87953e7			−0.338037
$441$	−6.59797e6			−0.0769298
$442$	−5.29147e7	+	5.29147e7i	−0.612787	+	0.612787i
$443$		−	7.19674e7i		−	0.827798i	−0.910323	−	0.413899i	$-0.864167\pi$
$443$		−	7.19674e7i		−	0.827798i	0.910323	−	0.413899i	$-0.135833\pi$
$444$	−354026.	−	540652.i	−0.00404470	−	0.00617688i
$445$	5.58745e7			0.634064
$446$	7.35073e7	+	7.35073e7i	0.828563	+	0.828563i
$447$		−	154464.i		−	0.00172944i
$448$			1.07984e7i			0.120095i
$449$	−6.13226e7	+	6.13226e7i	−0.677457	+	0.677457i	−0.959424	−	0.281967i	$-0.909013\pi$
$449$	−6.13226e7	+	6.13226e7i	−0.677457	+	0.677457i	0.281967	+	0.959424i	$0.409013\pi$
$450$	−3.40972e7	+	3.40972e7i	−0.374180	+	0.374180i
$451$	5.73356e7			0.625021
$452$	2.17855e7	−	2.17855e7i	0.235913	−	0.235913i
$453$	27285.5			0.000293520
$454$	−1.48911e7			−0.159133
$455$		−	4.81144e7i		−	0.510789i
$456$	−461863.			−0.00487101
$457$	1.00464e8	−	1.00464e8i	1.05259	−	1.05259i	0.0540558	−	0.998538i	$-0.482785\pi$
$457$	1.00464e8	−	1.00464e8i	1.05259	−	1.05259i	0.998538	−	0.0540558i	$-0.0172149\pi$
$458$	−6.75995e7	−	6.75995e7i	−0.703634	−	0.703634i
$459$	−2.33425e6	−	2.33425e6i	−0.0241385	−	0.0241385i
$460$	−2.87594e7			−0.295465
$461$	1.05510e8	−	1.05510e8i	1.07694	−	1.07694i	0.0801571	−	0.996782i	$-0.474458\pi$
$461$	1.05510e8	−	1.05510e8i	1.07694	−	1.07694i	0.996782	−	0.0801571i	$-0.0255422\pi$
$462$	−1.33368e6	−	1.33368e6i	−0.0135246	−	0.0135246i
$463$	7.35576e7	−	7.35576e7i	0.741114	−	0.741114i	−0.231679	−	0.972792i	$-0.574422\pi$
$463$	7.35576e7	−	7.35576e7i	0.741114	−	0.741114i	0.972792	+	0.231679i	$0.0744218\pi$
$464$	5.25146e6	+	5.25146e6i	0.0525685	+	0.0525685i
$465$		−	561178.i		−	0.00558138i
$466$	−4.57717e7	+	4.57717e7i	−0.452313	+	0.452313i
$467$	3.48307e7	−	3.48307e7i	0.341988	−	0.341988i	−0.515126	−	0.857114i	$-0.672255\pi$
$467$	3.48307e7	−	3.48307e7i	0.341988	−	0.341988i	0.857114	+	0.515126i	$0.172255\pi$
$468$	−3.84129e7	−	3.84129e7i	−0.374748	−	0.374748i
$469$			1.77412e8i			1.71975i
$470$	6.21981e7			0.599078
$471$			715862.i			0.00685120i
$472$			4.65514e7i			0.442698i
$473$	−2.25716e8	−	2.25716e8i	−2.13294	−	2.13294i
$474$		−	945032.i		−	0.00887384i
$475$	−5.29241e7	−	5.29241e7i	−0.493825	−	0.493825i
$476$	−4.23496e7	−	4.23496e7i	−0.392671	−	0.392671i
$477$	1.53089e8			1.41055
$478$	−6.78007e7			−0.620798
$479$	8.08420e6	−	8.08420e6i	0.0735581	−	0.0735581i	−0.669371	−	0.742929i	$-0.733436\pi$
$479$	8.08420e6	−	8.08420e6i	0.0735581	−	0.0735581i	0.742929	+	0.669371i	$0.233436\pi$
$480$			144770.i			0.00130905i
$481$	1.15496e8	+	2.40919e7i	1.03784	+	0.216489i
$482$	1.31456e8			1.17392
$483$	−1.33202e6	−	1.33202e6i	−0.0118214	−	0.0118214i
$484$		−	1.49386e8i		−	1.31757i
$485$			4.65045e7i			0.407633i
$486$	2.54188e6	−	2.54188e6i	0.0221435	−	0.0221435i
$487$	1.25224e8	−	1.25224e8i	1.08418	−	1.08418i	0.0880617	−	0.996115i	$-0.471933\pi$
$487$	1.25224e8	−	1.25224e8i	1.08418	−	1.08418i	0.996115	−	0.0880617i	$-0.0280673\pi$
$488$	−7.66276e6			−0.0659365
$489$	146203.	−	146203.i	0.00125034	−	0.00125034i
$490$	−3.21005e6			−0.0272849
$491$	7.47575e7			0.631554			0.315777	−	0.948834i	$-0.397735\pi$
$491$	7.47575e7			0.631554			0.315777	+	0.948834i	$0.397735\pi$
$492$		−	288258.i		−	0.00242039i
$493$	−4.11909e7			−0.343764
$494$	5.96228e7	−	5.96228e7i	0.494574	−	0.494574i
$495$	8.19813e7	+	8.19813e7i	0.675926	+	0.675926i
$496$	−1.62585e7	−	1.62585e7i	−0.133241	−	0.133241i
$497$	−1.73847e8			−1.41611
$498$	−1.55321e6	+	1.55321e6i	−0.0125760	+	0.0125760i
$499$	−1.04219e8	−	1.04219e8i	−0.838773	−	0.838773i	0.149924	−	0.988697i	$-0.452097\pi$
$499$	−1.04219e8	−	1.04219e8i	−0.838773	−	0.838773i	−0.988697	+	0.149924i	$0.952097\pi$
$500$	−3.87512e7	+	3.87512e7i	−0.310009	+	0.310009i
$501$	1.14910e6	+	1.14910e6i	0.00913785	+	0.00913785i
$502$			1.14110e8i			0.902016i
$503$	3.59368e7	−	3.59368e7i	0.282381	−	0.282381i	−0.551677	−	0.834058i	$-0.686012\pi$
$503$	3.59368e7	−	3.59368e7i	0.282381	−	0.282381i	0.834058	+	0.551677i	$0.186012\pi$
$504$	3.07433e7	−	3.07433e7i	0.240137	−	0.240137i
$505$	−5.03021e7	−	5.03021e7i	−0.390582	−	0.390582i
$506$		−	2.05819e8i		−	1.58867i
$507$	−238594.			−0.00183078
$508$			6.98235e7i			0.532611i
$509$		−	5.79550e7i		−	0.439478i	−0.975559	−	0.219739i	$-0.929479\pi$
$509$		−	5.79550e7i		−	0.439478i	0.975559	−	0.219739i	$-0.0705206\pi$
$510$	−567768.	−	567768.i	−0.00428016	−	0.00428016i
$511$		−	9.64240e7i		−	0.722640i
$512$	4.19430e6	+	4.19430e6i	0.0312500	+	0.0312500i
$513$	2.63017e6	+	2.63017e6i	0.0194819	+	0.0194819i
$514$	6.72654e7			0.495339
$515$	2.65200e7			0.194157
$516$	−1.13480e6	+	1.13480e6i	−0.00825982	+	0.00825982i
$517$			4.45125e8i			3.22115i
$518$	−1.92817e7	+	9.24355e7i	−0.138725	+	0.665043i
$519$	−2.34022e6			−0.0167399
$520$	−1.86887e7	−	1.86887e7i	−0.132913	−	0.132913i
$521$			1.32627e8i			0.937817i	0.883247	+	0.468908i	$0.155353\pi$
$521$			1.32627e8i			0.937817i	−0.883247	+	0.468908i	$0.844647\pi$
$522$		−	2.99022e7i		−	0.210228i
$523$	−8.39040e7	+	8.39040e7i	−0.586513	+	0.586513i	−0.936685	−	0.350172i	$-0.886123\pi$
$523$	−8.39040e7	+	8.39040e7i	−0.586513	+	0.586513i	0.350172	+	0.936685i	$0.386123\pi$
$524$	−8.93574e7	+	8.93574e7i	−0.621065	+	0.621065i
$525$	−1.53666e6			−0.0106194
$526$	−8.97099e7	+	8.97099e7i	−0.616429	+	0.616429i
$527$	1.27527e8			0.871308
$528$	−1.03606e6			−0.00703853
$529$		−	5.75260e7i		−	0.388595i
$530$	7.44809e7			0.500285
$531$	1.32534e8	−	1.32534e8i	0.885202	−	0.885202i
$532$	4.77184e7	+	4.77184e7i	0.316921	+	0.316921i
$533$	3.72118e7	+	3.72118e7i	0.245753	+	0.245753i
$534$	2.01037e6			0.0132024
$535$	−7.94114e7	+	7.94114e7i	−0.518587	+	0.518587i
$536$	6.89107e7	+	6.89107e7i	0.447499	+	0.447499i
$537$	−1.42951e6	+	1.42951e6i	−0.00923135	+	0.00923135i
$538$	7.20774e7	+	7.20774e7i	0.462862	+	0.462862i
$539$		−	2.29729e7i		−	0.146707i
$540$	824421.	−	824421.i	0.00523562	−	0.00523562i
$541$	3.12497e7	−	3.12497e7i	0.197358	−	0.197358i	−0.601509	−	0.798866i	$-0.705433\pi$
$541$	3.12497e7	−	3.12497e7i	0.197358	−	0.197358i	0.798866	+	0.601509i	$0.205433\pi$
$542$	−7.88819e7	−	7.88819e7i	−0.495427	−	0.495427i
$543$		−	2.89015e6i		−	0.0180518i
$544$	−3.28989e7			−0.204355
$545$		−	80916.7i		−	0.000499860i
$546$		−	1.73116e6i		−	0.0106355i
$547$	1.58581e7	+	1.58581e7i	0.0968923	+	0.0968923i	0.753891	−	0.656999i	$-0.228174\pi$
$547$	1.58581e7	+	1.58581e7i	0.0968923	+	0.0968923i	−0.656999	+	0.753891i	$0.728174\pi$
$548$		−	9.07472e7i		−	0.551432i
$549$	2.18162e7	+	2.18162e7i	0.131844	+	0.131844i
$550$	−1.18720e8	−	1.18720e8i	−0.713569	−	0.713569i
$551$	4.64128e7			0.277449
$552$	−1.03476e6			−0.00615212
$553$	−9.76380e7	+	9.76380e7i	−0.577356	+	0.577356i
$554$			1.15663e8i			0.680246i
$555$	−258503.	+	1.23925e6i	−0.00151212	+	0.00724905i
$556$	2.26078e7			0.131532
$557$	8.41596e7	+	8.41596e7i	0.487010	+	0.487010i	0.907362	−	0.420351i	$-0.138093\pi$
$557$	8.41596e7	+	8.41596e7i	0.487010	+	0.487010i	−0.420351	+	0.907362i	$0.638093\pi$
$558$			9.25773e7i			0.532846i
$559$		−	2.92987e8i		−	1.67731i
$560$	1.49572e7	−	1.49572e7i	0.0851700	−	0.0851700i
$561$	4.06327e6	−	4.06327e6i	0.0230137	−	0.0230137i
$562$	−6.53797e7			−0.368327
$563$	−1.64916e8	+	1.64916e8i	−0.924141	+	0.924141i	−0.997319	−	0.0731776i	$-0.976686\pi$
$563$	−1.64916e8	+	1.64916e8i	−0.924141	+	0.924141i	0.0731776	+	0.997319i	$0.476686\pi$
$564$	2.23789e6			0.0124739
$565$	−6.03519e7			−0.334615
$566$			3.37039e7i			0.185879i
$567$	−1.75016e8			−0.960128
$568$	−6.75258e7	+	6.75258e7i	−0.368489	+	0.368489i
$569$	9.22101e7	+	9.22101e7i	0.500544	+	0.500544i	0.911607	−	0.411063i	$-0.134842\pi$
$569$	9.22101e7	+	9.22101e7i	0.500544	+	0.500544i	−0.411063	+	0.911607i	$0.634842\pi$
$570$	639745.	+	639745.i	0.00345448	+	0.00345448i
$571$	−1.31445e8			−0.706050			−0.353025	−	0.935614i	$-0.614847\pi$
$571$	−1.31445e8			−0.706050			−0.353025	+	0.935614i	$0.614847\pi$
$572$	1.33747e8	−	1.33747e8i	0.714652	−	0.714652i
$573$	372048.	+	372048.i	0.00197759	+	0.00197759i
$574$	−2.97820e7	+	2.97820e7i	−0.157477	+	0.157477i
$575$	−1.18572e8	−	1.18572e8i	−0.623704	−	0.623704i
$576$		−	2.38827e7i		−	0.124973i
$577$	−2.13242e8	+	2.13242e8i	−1.11006	+	1.11006i	−0.116913	+	0.993142i	$0.537300\pi$
$577$	−2.13242e8	+	2.13242e8i	−1.11006	+	1.11006i	−0.993142	+	0.116913i	$0.962700\pi$
$578$	3.24748e7	−	3.24748e7i	0.168175	−	0.168175i
$579$	−2.47389e6	−	2.47389e6i	−0.0127451	−	0.0127451i
$580$		−	1.45480e7i		−	0.0745623i
$581$	3.20945e8			1.63645
$582$			1.67323e6i			0.00848766i
$583$			5.33027e8i			2.68995i
$584$	−3.74531e7	−	3.74531e7i	−0.188039	−	0.188039i
$585$			1.06414e8i			0.531537i
$586$	−2.70347e7	−	2.70347e7i	−0.134347	−	0.134347i
$587$	−2.15910e8	−	2.15910e8i	−1.06748	−	1.06748i	−0.997552	−	0.0699234i	$-0.977725\pi$
$587$	−2.15910e8	−	2.15910e8i	−1.06748	−	1.06748i	−0.0699234	−	0.997552i	$-0.522275\pi$
$588$	−115498.			−0.000568121
$589$	−1.43694e8			−0.703224
$590$	6.44802e7	−	6.44802e7i	0.313957	−	0.313957i
$591$		−	2.72222e6i		−	0.0131874i
$592$	2.84145e7	+	4.33933e7i	0.136954	+	0.209150i
$593$	1.07467e8			0.515358			0.257679	−	0.966231i	$-0.417042\pi$
$593$	1.07467e8			0.515358			0.257679	+	0.966231i	$0.417042\pi$
$594$	5.90003e6	+	5.90003e6i	0.0281510	+	0.0281510i
$595$			1.17320e8i			0.556958i
$596$			1.23974e7i			0.0585589i
$597$	1.69751e6	−	1.69751e6i	0.00797790	−	0.00797790i
$598$	1.33580e8	−	1.33580e8i	0.624651	−	0.624651i
$599$	−1.51009e8			−0.702621			−0.351310	−	0.936259i	$-0.614264\pi$
$599$	−1.51009e8			−0.702621			−0.351310	+	0.936259i	$0.614264\pi$
$600$	−596872.	+	596872.i	−0.00276330	+	0.00276330i
$601$	−6.32464e7			−0.291348			−0.145674	−	0.989333i	$-0.546535\pi$
$601$	−6.32464e7			−0.291348			−0.145674	+	0.989333i	$0.546535\pi$
$602$	2.34489e8			1.07481
$603$		−	3.92382e8i		−	1.78961i
$604$	−2.18996e6			−0.00993861
$605$	−2.06920e8	+	2.06920e8i	−0.934407	+	0.934407i
$606$	−1.80987e6	−	1.80987e6i	−0.00813262	−	0.00813262i
$607$	−1.08736e8	−	1.08736e8i	−0.486191	−	0.486191i	0.420911	−	0.907102i	$-0.361710\pi$
$607$	−1.08736e8	−	1.08736e8i	−0.486191	−	0.486191i	−0.907102	+	0.420911i	$0.861710\pi$
$608$	3.70696e7			0.164933
$609$	673803.	−	673803.i	0.00298319	−	0.00298319i
$610$	1.06140e7	+	1.06140e7i	0.0467616	+	0.0467616i
$611$	−2.88894e8	+	2.88894e8i	−1.26653	+	1.26653i
$612$	9.36645e7	+	9.36645e7i	0.408621	+	0.408621i
$613$		−	2.19823e8i		−	0.954317i	−0.878817	−	0.477158i	$-0.841667\pi$
$613$		−	2.19823e8i		−	0.954317i	0.878817	−	0.477158i	$-0.158333\pi$
$614$	−5.58957e7	+	5.58957e7i	−0.241476	+	0.241476i
$615$	−399277.	+	399277.i	−0.00171652	+	0.00171652i
$616$	1.07042e8	+	1.07042e8i	0.457945	+	0.457945i
$617$		−	2.31665e8i		−	0.986290i	−0.869947	−	0.493145i	$-0.835847\pi$
$617$		−	2.31665e8i		−	0.986290i	0.869947	−	0.493145i	$-0.164153\pi$
$618$	954193.			0.00404269
$619$		−	5.93916e7i		−	0.250411i	−0.992131	−	0.125205i	$-0.960041\pi$
$619$		−	5.93916e7i		−	0.250411i	0.992131	−	0.125205i	$-0.0399590\pi$
$620$			4.50407e7i			0.188986i
$621$	5.89267e6	+	5.89267e6i	0.0246058	+	0.0246058i
$622$			7.49602e7i			0.311501i
$623$	−2.07705e8	−	2.07705e8i	−0.858981	−	0.858981i
$624$	−672419.	−	672419.i	−0.00276749	−	0.00276749i
$625$	−7.53935e7			−0.308812
$626$	1.37964e8			0.562397
$627$	−4.57838e6	+	4.57838e6i	−0.0185742	+	0.0185742i
$628$		−	5.74558e7i		−	0.231982i
$629$	−2.81620e8	−	5.87447e7i	−1.13165	−	0.236057i
$630$	−8.51675e7			−0.340606
$631$	4.15558e7	+	4.15558e7i	0.165403	+	0.165403i	0.784955	−	0.619552i	$-0.212686\pi$
$631$	4.15558e7	+	4.15558e7i	0.165403	+	0.165403i	−0.619552	+	0.784955i	$0.712686\pi$
$632$			7.58492e7i			0.300469i
$633$			314203.i			0.00123879i
$634$	1.27668e8	−	1.27668e8i	0.500974	−	0.500974i
$635$	9.67152e7	−	9.67152e7i	0.377723	−	0.377723i
$636$	2.67983e6			0.0104168
$637$	1.49098e7	−	1.49098e7i	0.0576838	−	0.0576838i
$638$	1.04114e8			0.400909
$639$	3.84497e8			1.47363
$640$		−	1.16194e7i		−	0.0443245i
$641$	3.31857e8			1.26002			0.630009	−	0.776588i	$-0.283051\pi$
$641$	3.31857e8			1.26002			0.630009	+	0.776588i	$0.283051\pi$
$642$	−2.85723e6	+	2.85723e6i	−0.0107979	+	0.0107979i
$643$	4.61640e7	+	4.61640e7i	0.173648	+	0.173648i	0.788580	−	0.614932i	$-0.210816\pi$
$643$	4.61640e7	+	4.61640e7i	0.173648	+	0.173648i	−0.614932	+	0.788580i	$0.710816\pi$
$644$	1.06909e8	+	1.06909e8i	0.400273	+	0.400273i
$645$	3.14372e6			0.0117156
$646$	−1.45382e8	+	1.45382e8i	−0.539278	+	0.539278i
$647$	−3.83214e7	−	3.83214e7i	−0.141491	−	0.141491i	0.632813	−	0.774304i	$-0.281900\pi$
$647$	−3.83214e7	−	3.83214e7i	−0.141491	−	0.141491i	−0.774304	+	0.632813i	$0.781900\pi$
$648$	−6.79800e7	+	6.79800e7i	−0.249836	+	0.249836i
$649$	4.61457e8	+	4.61457e8i	1.68810	+	1.68810i
$650$		−	1.54103e8i		−	0.561139i
$651$	−2.08610e6	+	2.08610e6i	−0.00756121	+	0.00756121i
$652$	−1.17344e7	+	1.17344e7i	−0.0423367	+	0.0423367i
$653$	−3.38554e8	−	3.38554e8i	−1.21587	−	1.21587i	−0.969064	−	0.246809i	$-0.920618\pi$
$653$	−3.38554e8	−	3.38554e8i	−1.21587	−	1.21587i	−0.246809	−	0.969064i	$-0.579382\pi$
$654$		−	2911.39i		−	1.04080e-5i
$655$	2.47545e8			0.880907
$656$			2.31359e7i			0.0819548i
$657$			2.13260e8i			0.751994i
$658$	−2.31213e8	−	2.31213e8i	−0.811584	−	0.811584i
$659$		−	1.47384e8i		−	0.514984i	−0.966280	−	0.257492i	$-0.917104\pi$
$659$		−	1.47384e8i		−	0.514984i	0.966280	−	0.257492i	$-0.0828960\pi$
$660$	1.43508e6	+	1.43508e6i	0.00499166	+	0.00499166i
$661$	2.64401e8	+	2.64401e8i	0.915499	+	0.915499i	0.996698	−	0.0811987i	$-0.0258748\pi$
$661$	2.64401e8	+	2.64401e8i	0.915499	+	0.915499i	−0.0811987	+	0.996698i	$0.525875\pi$
$662$	7.09576e7			0.244582
$663$	5.27427e6			0.0180976
$664$	1.24662e8	−	1.24662e8i	0.425823	−	0.425823i
$665$		−	1.32193e8i		−	0.449515i
$666$	4.26451e7	−	2.04439e8i	0.144360	−	0.692056i
$667$	1.03984e8			0.350420
$668$	−9.22278e7	−	9.22278e7i	−0.309409	−	0.309409i
$669$		−	7.32682e6i		−	0.0244702i
$670$		−	1.90902e8i		−	0.634725i
$671$	−7.59598e7	+	7.59598e7i	−0.251429	+	0.251429i
$672$	538162.	−	538162.i	0.00177339	−	0.00177339i
$673$	−2.75216e8			−0.902876			−0.451438	−	0.892303i	$-0.649089\pi$
$673$	−2.75216e8			−0.902876			−0.451438	+	0.892303i	$0.649089\pi$
$674$	−1.61983e8	+	1.61983e8i	−0.529043	+	0.529043i
$675$	6.79800e6			0.0221040
$676$	1.91498e7			0.0619904
$677$		−	3.11020e8i		−	1.00236i	−0.865344	−	0.501178i	$-0.832900\pi$
$677$		−	3.11020e8i		−	1.00236i	0.865344	−	0.501178i	$-0.167100\pi$
$678$	−2.17147e6			−0.00696729
$679$	1.72874e8	−	1.72874e8i	0.552230	−	0.552230i
$680$	4.55696e7	+	4.55696e7i	0.144927	+	0.144927i
$681$	742134.	+	742134.i	0.00234985	+	0.00234985i
$682$	−3.22337e8			−1.01615
$683$	2.32431e8	−	2.32431e8i	0.729512	−	0.729512i	−0.241011	−	0.970522i	$-0.577479\pi$
$683$	2.32431e8	−	2.32431e8i	0.729512	−	0.729512i	0.970522	+	0.241011i	$0.0774789\pi$
$684$	−1.05538e8	−	1.05538e8i	−0.329794	−	0.329794i
$685$	−1.25698e8	+	1.25698e8i	−0.391071	+	0.391071i
$686$	1.67013e8	+	1.67013e8i	0.517342	+	0.517342i
$687$			6.73796e6i			0.0207806i
$688$	9.10803e7	−	9.10803e7i	0.279678	−	0.279678i
$689$	−3.45944e8	+	3.45944e8i	−1.05766	+	1.05766i
$690$	1.43329e6	+	1.43329e6i	0.00436303	+	0.00436303i
$691$			3.00078e8i			0.909493i	0.890621	+	0.454747i	$0.150270\pi$
$691$			3.00078e8i			0.909493i	−0.890621	+	0.454747i	$0.849730\pi$
$692$	1.87828e8			0.566816
$693$		−	6.09507e8i		−	1.83138i
$694$			4.27507e7i			0.127898i
$695$	−3.13149e7	−	3.13149e7i	−0.0932817	−	0.0932817i
$696$		−	523438.i		−	0.00155252i
$697$	−9.07356e7	−	9.07356e7i	−0.267966	−	0.267966i
$698$	−4.92641e7	−	4.92641e7i	−0.144865	−	0.144865i
$699$	4.56228e6			0.0133583
$700$	1.23334e8			0.359575
$701$	3.06710e7	−	3.06710e7i	0.0890377	−	0.0890377i	−0.661185	−	0.750223i	$-0.729946\pi$
$701$	3.06710e7	−	3.06710e7i	0.0890377	−	0.0890377i	0.750223	+	0.661185i	$0.229946\pi$
$702$			7.65844e6i			0.0221375i
$703$	3.17321e8	+	6.61919e7i	0.913342	+	0.190519i
$704$	8.31550e7			0.238325
$705$	−3.09979e6	−	3.09979e6i	−0.00884638	−	0.00884638i
$706$			1.69978e8i			0.483036i
$707$			3.73982e8i			1.05826i
$708$	2.32000e6	−	2.32000e6i	0.00653716	−	0.00653716i
$709$	−1.14964e8	+	1.14964e8i	−0.322568	+	0.322568i	−0.849752	−	0.527183i	$-0.823248\pi$
$709$	−1.14964e8	+	1.14964e8i	−0.322568	+	0.322568i	0.527183	+	0.849752i	$0.323248\pi$
$710$	1.87065e8			0.522659
$711$	2.15945e8	−	2.15945e8i	0.600807	−	0.600807i
$712$	−1.61354e8			−0.447033
$713$	−3.21935e8			−0.888176
$714$			4.22119e6i			0.0115969i
$715$	−3.70515e8			−1.01365
$716$	1.14734e8	−	1.14734e8i	0.312574	−	0.312574i
$717$	3.37901e6	+	3.37901e6i	0.00916710	+	0.00916710i
$718$	6.80197e7	+	6.80197e7i	0.183765	+	0.183765i
$719$	3.32290e8			0.893986			0.446993	−	0.894538i	$-0.352495\pi$
$719$	3.32290e8			0.893986			0.446993	+	0.894538i	$0.352495\pi$
$720$	−3.30808e7	+	3.30808e7i	−0.0886296	+	0.0886296i
$721$	−9.85844e7	−	9.85844e7i	−0.263028	−	0.263028i
$722$	−2.43715e7	+	2.43715e7i	−0.0647545	+	0.0647545i
$723$	−6.55143e6	−	6.55143e6i	−0.0173349	−	0.0173349i
$724$			2.31966e8i			0.611236i
$725$	5.99798e7	−	5.99798e7i	0.157395	−	0.157395i
$726$	−7.44499e6	+	7.44499e6i	−0.0194560	+	0.0194560i
$727$	9.48717e7	+	9.48717e7i	0.246907	+	0.246907i	0.819700	−	0.572793i	$-0.194140\pi$
$727$	9.48717e7	+	9.48717e7i	0.246907	+	0.246907i	−0.572793	+	0.819700i	$0.694140\pi$
$728$			1.38945e8i			0.360121i
$729$	3.86914e8			0.998692
$730$			1.03755e8i			0.266712i
$731$			7.14408e8i			1.82892i
$732$	381892.	+	381892.i	0.000973661	+	0.000973661i
$733$		−	5.37610e8i		−	1.36507i	−0.730852	−	0.682535i	$-0.760877\pi$
$733$		−	5.37610e8i		−	1.36507i	0.730852	−	0.682535i	$-0.239123\pi$
$734$	−1.57862e8	−	1.57862e8i	−0.399200	−	0.399200i
$735$	159980.	+	159980.i	0.000402907	+	0.000402907i
$736$	8.30513e7			0.208311
$737$	1.36620e9			3.41281
$738$	6.58686e7	−	6.58686e7i	0.163874	−	0.163874i
$739$		−	4.26369e8i		−	1.05646i	−0.849102	−	0.528229i	$-0.822856\pi$
$739$		−	4.26369e8i		−	1.05646i	0.849102	−	0.528229i	$-0.177144\pi$
$740$	2.07477e7	−	9.94638e7i	0.0512006	−	0.245454i
$741$	−5.94289e6			−0.0146064
$742$	−2.76872e8	−	2.76872e8i	−0.677746	−	0.677746i
$743$		−	5.61236e8i		−	1.36829i	−0.729345	−	0.684146i	$-0.760175\pi$
$743$		−	5.61236e8i		−	1.36829i	0.729345	−	0.684146i	$-0.239825\pi$
$744$			1.62057e6i			0.00393503i
$745$	1.71722e7	−	1.71722e7i	0.0415295	−	0.0415295i
$746$	2.54043e8	−	2.54043e8i	0.611914	−	0.611914i
$747$	−7.09834e8			−1.70292
$748$	−3.26122e8	+	3.26122e8i	−0.779248	+	0.779248i
$749$	5.90401e8			1.40508
$750$	3.86252e6			0.00915560
$751$		−	2.92516e8i		−	0.690604i	−0.938492	−	0.345302i	$-0.887776\pi$
$751$		−	2.92516e8i		−	0.690604i	0.938492	−	0.345302i	$-0.112224\pi$
$752$	−1.79615e8			−0.422367
$753$	5.68697e6	−	5.68697e6i	0.0133197	−	0.0133197i
$754$	6.75716e7	+	6.75716e7i	0.157634	+	0.157634i
$755$	3.03340e6	+	3.03340e6i	0.00704838	+	0.00704838i
$756$	−6.12933e6			−0.0141856
$757$	−1.27678e8	+	1.27678e8i	−0.294326	+	0.294326i	−0.838786	−	0.544461i	$-0.816734\pi$
$757$	−1.27678e8	+	1.27678e8i	−0.294326	+	0.294326i	0.544461	+	0.838786i	$0.316734\pi$
$758$	4.29088e7	+	4.29088e7i	0.0985232	+	0.0985232i
$759$	−1.02575e7	+	1.02575e7i	−0.0234593	+	0.0234593i
$760$	−5.13466e7	−	5.13466e7i	−0.116969	−	0.116969i
$761$		−	4.08627e7i		−	0.0927200i	−0.998925	−	0.0463600i	$-0.985238\pi$
$761$		−	4.08627e7i		−	0.0927200i	0.998925	−	0.0463600i	$-0.0147621\pi$
$762$	3.47982e6	−	3.47982e6i	0.00786488	−	0.00786488i
$763$	−300796.	+	300796.i	−0.000677171	+	0.000677171i
$764$	−2.98610e7	−	2.98610e7i	−0.0669612	−	0.0669612i
$765$		−	2.59477e8i		−	0.579581i
$766$	−3.47418e8			−0.772977
$767$			5.98987e8i			1.32749i
$768$		−	418066.i		−	0.000922915i
$769$	−4.59023e8	−	4.59023e8i	−1.00938	−	1.00938i	−0.999956	−	0.00942668i	$-0.996999\pi$
$769$	−4.59023e8	−	4.59023e8i	−1.00938	−	1.00938i	−0.00942668	−	0.999956i	$-0.503001\pi$
$770$		−	2.96537e8i		−	0.649542i
$771$	−3.35233e6	−	3.35233e6i	−0.00731449	−	0.00731449i
$772$	1.98557e8	+	1.98557e8i	0.431551	+	0.431551i
$773$	−4.77565e8			−1.03394			−0.516969	−	0.856004i	$-0.672940\pi$
$773$	−4.77565e8			−1.03394			−0.516969	+	0.856004i	$0.672940\pi$
$774$	−5.18618e8			−1.11847
$775$	−1.85698e8	+	1.85698e8i	−0.398935	+	0.398935i
$776$		−	1.34295e8i		−	0.287393i
$777$	5.56770e6	−	3.64580e6i	0.0118690	−	0.00777194i
$778$	−5.72096e8			−1.21487
$779$	1.02238e8	+	1.02238e8i	0.216272	+	0.216272i
$780$			1.86279e6i			0.00392536i
$781$			1.33875e9i			2.81025i
$782$	−3.25715e8	+	3.25715e8i	−0.681111	+	0.681111i
$783$	−2.98082e6	+	2.98082e6i	−0.00620941	+	0.00620941i
$784$	9.26996e6			0.0192367
$785$	−7.95843e7	+	7.95843e7i	−0.164520	+	0.164520i
$786$	8.90668e6			0.0183421
$787$	5.39957e8			1.10773			0.553866	−	0.832606i	$-0.313152\pi$
$787$	5.39957e8			1.10773			0.553866	+	0.832606i	$0.313152\pi$
$788$			2.18488e8i			0.446528i
$789$	8.94182e6			0.0182052
$790$	1.05062e8	−	1.05062e8i	0.213090	−	0.213090i
$791$	2.24350e8	+	2.24350e8i	0.453311	+	0.453311i
$792$	−2.36745e8	−	2.36745e8i	−0.476547	−	0.476547i
$793$	−9.85984e7			−0.197720
$794$	4.10423e7	−	4.10423e7i	0.0819918	−	0.0819918i
$795$	−3.71193e6	−	3.71193e6i	−0.00738752	−	0.00738752i
$796$	−1.36244e8	+	1.36244e8i	−0.270133	+	0.270133i
$797$	1.28815e8	+	1.28815e8i	0.254444	+	0.254444i	0.822790	−	0.568346i	$-0.192416\pi$
$797$	1.28815e8	+	1.28815e8i	0.254444	+	0.254444i	−0.568346	+	0.822790i	$0.692416\pi$
$798$		−	4.75632e6i		−	0.00935971i
$799$	7.04427e8	−	7.04427e8i	1.38101	−	1.38101i
$800$	4.79055e7	−	4.79055e7i	0.0935655	−	0.0935655i
$801$	4.59381e8	+	4.59381e8i	0.893872	+	0.893872i
$802$			4.82211e8i			0.934790i
$803$	−7.42533e8			−1.43407
$804$		−	6.86866e6i		−	0.0132161i
$805$		−	2.96167e8i		−	0.567740i
$806$	−2.09202e8	−	2.09202e8i	−0.399541	−	0.399541i
$807$		−	7.18430e6i		−	0.0136698i
$808$	1.45262e8	+	1.45262e8i	0.275371	+	0.275371i
$809$	4.95891e7	+	4.95891e7i	0.0936572	+	0.0936572i	0.752383	−	0.658726i	$-0.228904\pi$
$809$	4.95891e7	+	4.95891e7i	0.0936572	+	0.0936572i	−0.658726	+	0.752383i	$0.728904\pi$
$810$	1.88323e8			0.354364
$811$	−8.06538e8			−1.51204			−0.756018	−	0.654550i	$-0.772858\pi$
$811$	−8.06538e8			−1.51204			−0.756018	+	0.654550i	$0.772858\pi$
$812$	−5.40801e7	+	5.40801e7i	−0.101011	+	0.101011i
$813$			7.86254e6i			0.0146316i
$814$	7.11819e8	+	1.48482e8i	1.31976	+	0.275297i
$815$	3.25074e7			0.0600496
$816$	1.63960e6	+	1.63960e6i	0.00301764	+	0.00301764i
$817$		−	8.04975e8i		−	1.47610i
$818$			2.99679e8i			0.547516i
$819$	3.95580e8	−	3.95580e8i	0.720084	−	0.720084i
$820$	3.20464e7	−	3.20464e7i	0.0581216	−	0.0581216i
$821$	−9.22112e8			−1.66630			−0.833152	−	0.553044i	$-0.813466\pi$
$821$	−9.22112e8			−1.66630			−0.833152	+	0.553044i	$0.813466\pi$
$822$	−4.52261e6	+	4.52261e6i	−0.00814279	+	0.00814279i
$823$	−9.72462e8			−1.74451			−0.872255	−	0.489052i	$-0.837343\pi$
$823$	−9.72462e8			−1.74451			−0.872255	+	0.489052i	$0.837343\pi$
$824$	−7.65845e7			−0.136886
$825$			1.18334e7i			0.0210740i
$826$	−4.79392e8			−0.850649
$827$	−3.59527e8	+	3.59527e8i	−0.635646	+	0.635646i	−0.949478	−	0.313832i	$-0.898387\pi$
$827$	−3.59527e8	+	3.59527e8i	−0.635646	+	0.635646i	0.313832	+	0.949478i	$0.398387\pi$
$828$	−2.36450e8	−	2.36450e8i	−0.416532	−	0.416532i
$829$	3.95255e8	+	3.95255e8i	0.693767	+	0.693767i	0.963059	−	0.269292i	$-0.0867897\pi$
$829$	3.95255e8	+	3.95255e8i	0.693767	+	0.693767i	−0.269292	+	0.963059i	$0.586790\pi$
$830$	−3.45348e8			−0.603980
$831$	5.76436e6	−	5.76436e6i	0.0100450	−	0.0100450i
$832$	5.39690e7	+	5.39690e7i	0.0937075	+	0.0937075i
$833$	−3.63555e7	+	3.63555e7i	−0.0628977	+	0.0628977i
$834$	−1.12671e6	−	1.12671e6i	−0.00194229	−	0.00194229i
$835$			2.55497e8i			0.438860i
$836$	3.67465e8	−	3.67465e8i	0.628923	−	0.628923i
$837$	9.22863e6	−	9.22863e6i	0.0157384	−	0.0157384i
$838$	−3.13058e8	−	3.13058e8i	−0.531977	−	0.531977i
$839$			5.95433e8i			1.00820i	0.863645	+	0.504101i	$0.168176\pi$
$839$			5.95433e8i			1.00820i	−0.863645	+	0.504101i	$0.831824\pi$
$840$	−1.49086e6			−0.00251535
$841$		−	5.42223e8i		−	0.911570i
$842$			3.72085e8i			0.623313i
$843$	3.25835e6	+	3.25835e6i	0.00543896	+	0.00543896i
$844$		−	2.52182e7i		−	0.0419457i
$845$	−2.65252e7	−	2.65252e7i	−0.0439631	−	0.0439631i
$846$	5.11372e8	+	5.11372e8i	0.844550	+	0.844550i
$847$	1.53839e9			2.53172
$848$	−2.15086e8			−0.352715
$849$	1.67972e6	−	1.67972e6i	0.00274481	−	0.00274481i
$850$			3.75757e8i			0.611858i
$851$	7.10931e8	+	1.48297e8i	1.15356	+	0.240627i
$852$	6.73062e6			0.0108827
$853$	3.10053e8	+	3.10053e8i	0.499561	+	0.499561i	0.911301	−	0.411741i	$-0.135079\pi$
$853$	3.10053e8	+	3.10053e8i	0.499561	+	0.499561i	−0.411741	+	0.911301i	$0.635079\pi$
$854$		−	7.89120e7i		−	0.126698i
$855$			2.92371e8i			0.467774i
$856$	2.29324e8	−	2.29324e8i	0.365619	−	0.365619i
$857$	−4.35211e8	+	4.35211e8i	−0.691445	+	0.691445i	−0.962550	−	0.271105i	$-0.912611\pi$
$857$	−4.35211e8	+	4.35211e8i	−0.691445	+	0.691445i	0.271105	+	0.962550i	$0.412611\pi$
$858$	−1.33312e7			−0.0211060
$859$	−5.85174e8	+	5.85174e8i	−0.923221	+	0.923221i	−0.997256	−	0.0740348i	$-0.976412\pi$
$859$	−5.85174e8	+	5.85174e8i	−0.923221	+	0.923221i	0.0740348	+	0.997256i	$0.476412\pi$
$860$	−2.52318e8			−0.396691
$861$	2.96851e6			0.00465082
$862$		−	1.13647e8i		−	0.177434i
$863$	−2.34869e7			−0.0365421			−0.0182711	−	0.999833i	$-0.505816\pi$
$863$	−2.34869e7			−0.0365421			−0.0182711	+	0.999833i	$0.505816\pi$
$864$	−2.38076e6	+	2.38076e6i	−0.00369126	+	0.00369126i
$865$	−2.60168e8	−	2.60168e8i	−0.401981	−	0.401981i
$866$	1.36502e8	+	1.36502e8i	0.210177	+	0.210177i
$867$	−3.23692e6			−0.00496677
$868$	1.67432e8	−	1.67432e8i	0.256024	−	0.256024i
$869$	7.51882e8	+	7.51882e8i	1.14575	+	1.14575i
$870$	−725034.	+	725034.i	−0.00110103	+	0.00110103i
$871$	8.86688e8	+	8.86688e8i	1.34189	+	1.34189i
$872$			233671.i			0.000352416i
$873$	−3.82344e8	+	3.82344e8i	−0.574661	+	0.574661i
$874$	3.67007e8	−	3.67007e8i	0.549718	−	0.549718i
$875$	−3.99064e8	−	3.99064e8i	−0.595687	−	0.595687i
$876$			3.73313e6i			0.00555342i
$877$	1.19252e8			0.176793			0.0883965	−	0.996085i	$-0.471826\pi$
$877$	1.19252e8			0.176793			0.0883965	+	0.996085i	$0.471826\pi$
$878$		−	6.39353e7i		−	0.0944620i
$879$			2.69468e6i			0.00396772i
$880$	−1.15181e8	−	1.15181e8i	−0.169018	−	0.169018i
$881$		−	5.24033e8i		−	0.766357i	−0.923674	−	0.383178i	$-0.874829\pi$
$881$		−	5.24033e8i		−	0.766357i	0.923674	−	0.383178i	$-0.125171\pi$
$882$	−2.63919e7	−	2.63919e7i	−0.0384649	−	0.0384649i
$883$	−4.33954e8	−	4.33954e8i	−0.630320	−	0.630320i	0.317828	−	0.948148i	$-0.397047\pi$
$883$	−4.33954e8	−	4.33954e8i	−0.630320	−	0.630320i	−0.948148	+	0.317828i	$0.897047\pi$
$884$	−4.23318e8			−0.612787
$885$	−6.42706e6			−0.00927219
$886$	2.87869e8	−	2.87869e8i	0.413899	−	0.413899i
$887$		−	8.15356e8i		−	1.16836i	−0.811624	−	0.584180i	$-0.801416\pi$
$887$		−	8.15356e8i		−	1.16836i	0.811624	−	0.584180i	$-0.198584\pi$
$888$	746504.	−	3.57871e6i	0.00106609	−	0.00511079i
$889$	−7.19050e8			−1.02342
$890$	2.23498e8	+	2.23498e8i	0.317032	+	0.317032i
$891$			1.34775e9i			1.90536i
$892$			5.88058e8i			0.828563i
$893$	−7.93728e8	+	7.93728e8i	−1.11460	+	1.11460i
$894$	617856.	−	617856.i	0.000864719	−	0.000864719i
$895$	−3.17845e8			−0.443350
$896$	−4.31934e7	+	4.31934e7i	−0.0600473	+	0.0600473i
$897$	−1.33145e7			−0.0184480
$898$	−4.90581e8			−0.677457
$899$		−	1.62851e8i		−	0.224136i
$900$	−2.72777e8			−0.374180
$901$	8.43535e8	−	8.43535e8i	1.15326	−	1.15326i
$902$	2.29342e8	+	2.29342e8i	0.312510	+	0.312510i
$903$	−1.16863e7	−	1.16863e7i	−0.0158714	−	0.0158714i
$904$	1.74284e8			0.235913
$905$	3.21306e8	−	3.21306e8i	0.433483	−	0.433483i
$906$	109142.	+	109142.i	0.000146760	+	0.000146760i
$907$	−3.19834e6	+	3.19834e6i	−0.00428650	+	0.00428650i	−0.709247	−	0.704960i	$-0.750965\pi$
$907$	−3.19834e6	+	3.19834e6i	−0.00428650	+	0.00428650i	0.704960	+	0.709247i	$0.250965\pi$
$908$	−5.95644e7	−	5.95644e7i	−0.0795663	−	0.0795663i
$909$		−	8.27134e8i		−	1.10125i
$910$	1.92458e8	−	1.92458e8i	0.255394	−	0.255394i
$911$	4.57608e8	−	4.57608e8i	0.605256	−	0.605256i	−0.336447	−	0.941702i	$-0.609225\pi$
$911$	4.57608e8	−	4.57608e8i	0.605256	−	0.605256i	0.941702	+	0.336447i	$0.109225\pi$
$912$	−1.84745e6	−	1.84745e6i	−0.00243550	−	0.00243550i
$913$		−	2.47151e9i		−	3.24750i
$914$	8.03710e8			1.05259
$915$		−	1.05795e6i		−	0.00138102i
$916$		−	5.40796e8i		−	0.703634i
$917$	−9.20213e8	−	9.20213e8i	−1.19338	−	1.19338i
$918$		−	1.86740e7i		−	0.0241385i
$919$	2.60369e8	+	2.60369e8i	0.335462	+	0.335462i	0.854656	−	0.519194i	$-0.173768\pi$
$919$	2.60369e8	+	2.60369e8i	0.335462	+	0.335462i	−0.519194	+	0.854656i	$0.673768\pi$
$920$	−1.15038e8	−	1.15038e8i	−0.147733	−	0.147733i
$921$	5.57140e6			0.00713157
$922$	8.44081e8			1.07694
$923$	−8.68869e8	+	8.68869e8i	−1.10497	+	1.10497i
$924$		−	1.06694e7i		−	0.0135246i
$925$	4.95619e8	−	3.24538e8i	0.626214	−	0.410053i
$926$	5.88461e8			0.741114
$927$	2.18039e8	+	2.18039e8i	0.273712	+	0.273712i
$928$			4.20116e7i			0.0525685i
$929$		−	2.98270e8i		−	0.372016i	−0.982548	−	0.186008i	$-0.940445\pi$
$929$		−	2.98270e8i		−	0.372016i	0.982548	−	0.186008i	$-0.0595551\pi$
$930$	2.24471e6	−	2.24471e6i	0.00279069	−	0.00279069i
$931$	4.09643e7	−	4.09643e7i	0.0507641	−	0.0507641i
$932$	−3.66173e8			−0.452313
$933$	3.73582e6	−	3.73582e6i	0.00459982	−	0.00459982i
$934$	2.78645e8			0.341988
$935$	9.03449e8			1.10527
$936$		−	3.07303e8i		−	0.374748i
$937$	6.41762e8			0.780109			0.390055	−	0.920792i	$-0.372456\pi$
$937$	6.41762e8			0.780109			0.390055	+	0.920792i	$0.372456\pi$
$938$	−7.09650e8	+	7.09650e8i	−0.859875	+	0.859875i
$939$	−6.87578e6	−	6.87578e6i	−0.00830472	−	0.00830472i
$940$	2.48792e8	+	2.48792e8i	0.299539	+	0.299539i
$941$	−9.35285e8			−1.12247			−0.561236	−	0.827656i	$-0.689674\pi$
$941$	−9.35285e8			−1.12247			−0.561236	+	0.827656i	$0.689674\pi$
$942$	−2.86345e6	+	2.86345e6i	−0.00342560	+	0.00342560i
$943$	2.29056e8	+	2.29056e8i	0.273154	+	0.273154i
$944$	−1.86206e8	+	1.86206e8i	−0.221349	+	0.221349i
$945$	8.48998e6	+	8.48998e6i	0.0100603	+	0.0100603i
$946$		−	1.80573e9i		−	2.13294i
$947$	8.52429e8	−	8.52429e8i	1.00371	−	1.00371i	0.00371719	−	0.999993i	$-0.498817\pi$
$947$	8.52429e8	−	8.52429e8i	1.00371	−	1.00371i	0.999993	−	0.00371719i	$-0.00118322\pi$
$948$	3.78013e6	−	3.78013e6i	0.00443692	−	0.00443692i
$949$	−4.81917e8	−	4.81917e8i	−0.563863	−	0.563863i
$950$		−	4.23393e8i		−	0.493825i
$951$	−1.27253e7			−0.0147954
$952$		−	3.38797e8i		−	0.392671i
$953$			2.98606e8i			0.345001i	0.985009	+	0.172501i	$0.0551847\pi$
$953$			2.98606e8i			0.345001i	−0.985009	+	0.172501i	$0.944815\pi$
$954$	6.12356e8	+	6.12356e8i	0.705276	+	0.705276i
$955$			8.27232e7i			0.0949767i
$956$	−2.71203e8	−	2.71203e8i	−0.310399	−	0.310399i
$957$	−5.18876e6	−	5.18876e6i	−0.00592008	−	0.00592008i
$958$	6.46736e7			0.0735581
$959$	9.34525e8			1.05958
$960$	−579080.	+	579080.i	−0.000654523	+	0.000654523i
$961$		−	3.83315e8i		−	0.431902i
$962$	3.65615e8	+	5.58351e8i	0.410676	+	0.627165i
$963$	−1.30579e9			−1.46216
$964$	5.25824e8	+	5.25824e8i	0.586961	+	0.586961i
$965$		−	5.50057e8i		−	0.612105i
$966$		−	1.06561e7i		−	0.0118214i
$967$	−8.13649e8	+	8.13649e8i	−0.899824	+	0.899824i	−0.995420	−	0.0955961i	$-0.969524\pi$
$967$	−8.13649e8	+	8.13649e8i	−0.899824	+	0.899824i	0.0955961	+	0.995420i	$0.469524\pi$
$968$	5.97543e8	−	5.97543e8i	0.658784	−	0.658784i
$969$	1.44909e7			0.0159266
$970$	−1.86018e8	+	1.86018e8i	−0.203817	+	0.203817i
$971$	−1.06942e9			−1.16813			−0.584065	−	0.811707i	$-0.698539\pi$
$971$	−1.06942e9			−1.16813			−0.584065	+	0.811707i	$0.698539\pi$
$972$	2.03351e7			0.0221435
$973$			2.32817e8i			0.252741i
$974$	1.00179e9			1.08418
$975$	−7.68008e6	+	7.68008e6i	−0.00828613	+	0.00828613i
$976$	−3.06510e7	−	3.06510e7i	−0.0329682	−	0.0329682i
$977$	−8.24682e7	−	8.24682e7i	−0.0884306	−	0.0884306i	0.661508	−	0.749938i	$-0.269917\pi$
$977$	−8.24682e7	−	8.24682e7i	−0.0884306	−	0.0884306i	−0.749938	+	0.661508i	$0.769917\pi$
$978$	1.16962e6			0.00125034
$979$	−1.59948e9	+	1.59948e9i	−1.70463	+	1.70463i
$980$	−1.28402e7	−	1.28402e7i	−0.0136425	−	0.0136425i
$981$	665269.	−	665269.i	0.000704678	−	0.000704678i
$982$	2.99030e8	+	2.99030e8i	0.315777	+	0.315777i
$983$		−	7.55663e8i		−	0.795550i	−0.917483	−	0.397775i	$-0.869782\pi$
$983$		−	7.55663e8i		−	0.795550i	0.917483	−	0.397775i	$-0.130218\pi$
$984$	1.15303e6	−	1.15303e6i	0.00121020	−	0.00121020i
$985$	3.02636e8	−	3.02636e8i	0.316674	−	0.316674i
$986$	−1.64764e8	−	1.64764e8i	−0.171882	−	0.171882i
$987$			2.30461e7i			0.0239687i
$988$	4.76982e8			0.494574
$989$		−	1.80348e9i		−	1.86433i
$990$			6.55850e8i			0.675926i
$991$	5.64218e8	+	5.64218e8i	0.579730	+	0.579730i	0.934829	−	0.355099i	$-0.115553\pi$
$991$	5.64218e8	+	5.64218e8i	0.579730	+	0.579730i	−0.355099	+	0.934829i	$0.615553\pi$
$992$		−	1.30068e8i		−	0.133241i
$993$	−3.53634e6	−	3.53634e6i	−0.00361166	−	0.00361166i
$994$	−6.95388e8	−	6.95388e8i	−0.708057	−	0.708057i
$995$	3.77433e8			0.383151
$996$	−1.24257e7			−0.0125760
$997$	−4.36173e7	+	4.36173e7i	−0.0440122	+	0.0440122i	−0.728770	−	0.684758i	$-0.759908\pi$
$997$	−4.36173e7	+	4.36173e7i	−0.0440122	+	0.0440122i	0.684758	+	0.728770i	$0.259908\pi$
$998$		−	8.33751e8i		−	0.838773i
$999$	−2.46308e7	+	1.61286e7i	−0.0247048	+	0.0161770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.a.31.4	✓	18
37.6	odd	4	inner	74.7.d.a.43.6	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.a.31.4	✓	18	1.1	even	1	trivial
74.7.d.a.43.6	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)

\(f(q)\)	\(=\)	\(q+(4.00000 + 4.00000i) q^{2} -0.398699i q^{3} +32.0000i q^{4} +(44.3245 - 44.3245i) q^{5} +(1.59480 - 1.59480i) q^{6} -329.540 q^{7} +(-128.000 + 128.000i) q^{8} +728.841 q^{9} +O(q^{10})\)	\(q+(4.00000 + 4.00000i) q^{2} -0.398699i q^{3} +32.0000i q^{4} +(44.3245 - 44.3245i) q^{5} +(1.59480 - 1.59480i) q^{6} -329.540 q^{7} +(-128.000 + 128.000i) q^{8} +728.841 q^{9} +354.596 q^{10} +2537.69i q^{11} +12.7584 q^{12} +(-1647.00 + 1647.00i) q^{13} +(-1318.16 - 1318.16i) q^{14} +(-17.6721 - 17.6721i) q^{15} -1024.00 q^{16} +(4015.98 - 4015.98i) q^{17} +(2915.36 + 2915.36i) q^{18} +(-4525.10 + 4525.10i) q^{19} +(1418.38 + 1418.38i) q^{20} +131.387i q^{21} +(-10150.8 + 10150.8i) q^{22} +(-10138.1 + 10138.1i) q^{23} +(51.0335 + 51.0335i) q^{24} +11695.7i q^{25} -13176.0 q^{26} -581.240i q^{27} -10545.3i q^{28} +(-5128.37 - 5128.37i) q^{29} -141.377i q^{30} +(15877.5 + 15877.5i) q^{31} +(-4096.00 - 4096.00i) q^{32} +1011.77 q^{33} +32127.9 q^{34} +(-14606.7 + 14606.7i) q^{35} +23322.9i q^{36} +(-27748.5 - 42376.2i) q^{37} -36200.8 q^{38} +(656.659 + 656.659i) q^{39} +11347.1i q^{40} -22593.6i q^{41} +(-525.549 + 525.549i) q^{42} +(-88945.6 + 88945.6i) q^{43} -81206.0 q^{44} +(32305.5 - 32305.5i) q^{45} -81104.7 q^{46} +175406. q^{47} +408.268i q^{48} -9052.69 q^{49} +(-46782.7 + 46782.7i) q^{50} +(-1601.17 - 1601.17i) q^{51} +(-52704.1 - 52704.1i) q^{52} +210044. q^{53} +(2324.96 - 2324.96i) q^{54} +(112482. + 112482. i) q^{55} +(42181.1 - 42181.1i) q^{56} +(1804.15 + 1804.15i) q^{57} -41027.0i q^{58} +(181842. - 181842. i) q^{59} +(565.508 - 565.508i) q^{60} +(29932.7 + 29932.7i) q^{61} +127020. i q^{62} -240182. q^{63} -32768.0i q^{64} +146005. i q^{65} +(4047.10 + 4047.10i) q^{66} -538365. i q^{67} +(128511. + 128511. i) q^{68} +(4042.05 + 4042.05i) q^{69} -116853. q^{70} +527545. q^{71} +(-93291.7 + 93291.7i) q^{72} +292602. i q^{73} +(58510.9 - 280499. i) q^{74} +4663.06 q^{75} +(-144803. - 144803. i) q^{76} -836269. i q^{77} +5253.27i q^{78} +(296286. - 296286. i) q^{79} +(-45388.2 + 45388.2i) q^{80} +531093. q^{81} +(90374.5 - 90374.5i) q^{82} -973921. q^{83} -4204.39 q^{84} -356013. i q^{85} -711565. q^{86} +(-2044.68 + 2044.68i) q^{87} +(-324824. - 324824. i) q^{88} +(630289. + 630289. i) q^{89} +258444. q^{90} +(542753. - 542753. i) q^{91} +(-324419. - 324419. i) q^{92} +(6330.34 - 6330.34i) q^{93} +(701623. + 701623. i) q^{94} +401145. i q^{95} +(-1633.07 + 1633.07i) q^{96} +(-524592. + 524592. i) q^{97} +(-36210.8 - 36210.8i) q^{98} +1.84957e6i 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

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