LMFDB - Embedded newform 74.7.d.a.43.6

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			43.6
Root			$4.39870i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.7.d.a.31.4

$q$-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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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	$0.00235021\pi$
$3$			0.398699i			0.0147666i	−0.999973	+	0.00738332i	$0.997650\pi$
$4$		−	32.0000i		−	0.500000i
$5$	44.3245	+	44.3245i	0.354596	+	0.354596i	0.861816	−	0.507221i	$-0.169327\pi$
$5$	44.3245	+	44.3245i	0.354596	+	0.354596i	−0.507221	+	0.861816i	$0.669327\pi$
$6$	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	$-0.597661\pi$
$11$		−	2537.69i		−	1.90660i	0.302020	−	0.953301i	$-0.402339\pi$
$12$	12.7584			0.00738332
$13$	−1647.00	−	1647.00i	−0.749660	−	0.749660i	0.224755	−	0.974415i	$-0.427842\pi$
$13$	−1647.00	−	1647.00i	−0.749660	−	0.749660i	−0.974415	+	0.224755i	$0.927842\pi$
$14$	−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	0.985734	−	0.168314i	$-0.0538321\pi$
$17$	4015.98	+	4015.98i	0.817420	+	0.817420i	−0.168314	+	0.985734i	$0.553832\pi$
$18$	2915.36	−	2915.36i	0.499891	−	0.499891i
$19$	−4525.10	−	4525.10i	−0.659731	−	0.659731i	0.295585	−	0.955316i	$-0.404485\pi$
$19$	−4525.10	−	4525.10i	−0.659731	−	0.659731i	−0.955316	+	0.295585i	$0.904485\pi$
$20$	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	0.154714	−	0.987959i	$-0.450554\pi$
$23$	−10138.1	−	10138.1i	−0.833245	−	0.833245i	−0.987959	+	0.154714i	$0.950554\pi$
$24$	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	−0.804384	−	0.594110i	$-0.797504\pi$
$29$	−5128.37	+	5128.37i	−0.210274	+	0.210274i	0.594110	+	0.804384i	$0.297504\pi$
$30$			141.377i			0.00523619i
$31$	15877.5	−	15877.5i	0.532962	−	0.532962i	−0.388490	−	0.921453i	$-0.627003\pi$
$31$	15877.5	−	15877.5i	0.532962	−	0.532962i	0.921453	+	0.388490i	$0.127003\pi$
$32$	−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	$0.0524105\pi$
$41$			22593.6i			0.327819i	−0.986475	+	0.163910i	$0.947589\pi$
$42$	−525.549	−	525.549i	−0.00709357	−	0.00709357i
$43$	−88945.6	−	88945.6i	−1.11871	−	1.11871i	−0.991930	−	0.126783i	$-0.959535\pi$
$43$	−88945.6	−	88945.6i	−1.11871	−	1.11871i	−0.126783	−	0.991930i	$-0.540465\pi$
$44$	−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	0.994077	−	0.108681i	$-0.0346628\pi$
$59$	181842.	+	181842.i	0.885395	+	0.885395i	−0.108681	+	0.994077i	$0.534663\pi$
$60$	565.508	+	565.508i	0.00261809	+	0.00261809i
$61$	29932.7	−	29932.7i	0.131873	−	0.131873i	−0.638089	−	0.769962i	$-0.720275\pi$
$61$	29932.7	−	29932.7i	0.131873	−	0.131873i	0.769962	+	0.638089i	$0.220275\pi$
$62$		−	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	$0.352823\pi$
$67$			538365.i			1.79000i	−0.446070	+	0.894998i	$0.647177\pi$
$68$	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	$-0.877272\pi$
$73$		−	292602.i		−	0.752158i	0.926588	−	0.376079i	$-0.122728\pi$
$74$	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	0.940562	−	0.339623i	$-0.110300\pi$
$79$	296286.	+	296286.i	0.600938	+	0.600938i	−0.339623	+	0.940562i	$0.610300\pi$
$80$	−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	−0.100836	−	0.994903i	$-0.532152\pi$
$89$	630289.	−	630289.i	0.894067	−	0.894067i	0.994903	+	0.100836i	$0.0321518\pi$
$90$	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	0.358676	−	0.933462i	$-0.383228\pi$
$97$	−524592.	−	524592.i	−0.574786	−	0.574786i	−0.933462	+	0.358676i	$0.883228\pi$
$98$	−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	$0.185656\pi$
$101$			1.13486e6i			1.10149i	−0.834675	+	0.550743i	$0.814344\pi$
$102$			12809.4i			0.0120705i
$103$	299158.	−	299158.i	0.273772	−	0.273772i	−0.556845	−	0.830617i	$-0.687988\pi$
$103$	299158.	−	299158.i	0.273772	−	0.273772i	0.830617	+	0.556845i	$0.187988\pi$
$104$			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	0.707459	−	0.706754i	$-0.249841\pi$
$109$	912.777	+	912.777i	0.000704831	+	0.000704831i	−0.706754	+	0.707459i	$0.749841\pi$
$110$		−	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	−0.902505	−	0.430679i	$-0.858274\pi$
$113$	−680797.	+	680797.i	−0.471827	+	0.471827i	0.430679	+	0.902505i	$0.358274\pi$
$114$		−	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	0.283013	−	0.959116i	$-0.408666\pi$
$131$	2.79242e6	−	2.79242e6i	1.24213	−	1.24213i	0.959116	−	0.283013i	$-0.0913339\pi$
$132$		−	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	$0.0419898\pi$
$139$			706492.i			0.263065i	−0.991312	+	0.131532i	$0.958010\pi$
$140$	−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	$-0.996836\pi$
$151$		−	68436.3i		−	0.0198772i	0.999951	−	0.00993861i	$-0.00316361\pi$
$152$			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	−0.663502	−	0.748175i	$-0.730930\pi$
$163$	366699.	−	366699.i	0.0846733	−	0.0846733i	0.748175	+	0.663502i	$0.230930\pi$
$164$	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	0.326411	−	0.945228i	$-0.394161\pi$
$167$	−2.88212e6	−	2.88212e6i	−0.618817	−	0.618817i	−0.945228	+	0.326411i	$0.894161\pi$
$168$	−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	$0.191825\pi$
$173$			5.86963e6i			1.13363i	−0.823844	+	0.566816i	$0.808175\pi$
$174$	−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	−0.946843	−	0.321695i	$-0.895748\pi$
$179$	−3.58544e6	+	3.58544e6i	−0.625149	+	0.625149i	0.321695	+	0.946843i	$0.395748\pi$
$180$	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	0.636968	−	0.770890i	$-0.280188\pi$
$191$	−933155.	−	933155.i	−0.133922	−	0.133922i	−0.770890	+	0.636968i	$0.780188\pi$
$192$	−13064.6			−0.00184583
$193$	6.20490e6	+	6.20490e6i	0.863103	+	0.863103i	0.991697	−	0.128594i	$-0.0410466\pi$
$193$	6.20490e6	+	6.20490e6i	0.863103	+	0.863103i	−0.128594	+	0.991697i	$0.541047\pi$
$194$	−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	−0.383341	−	0.923607i	$-0.625227\pi$
$199$	4.25761e6	−	4.25761e6i	0.540265	−	0.540265i	0.923607	+	0.383341i	$0.125227\pi$
$200$	−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	0.623050	−	0.782182i	$-0.285893\pi$
$227$	−1.86139e6	−	1.86139e6i	−0.159133	−	0.159133i	−0.782182	+	0.623050i	$0.785893\pi$
$228$	−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	$-0.850599\pi$
$233$		−	1.14429e7i		−	0.904625i	0.891859	−	0.452313i	$-0.149401\pi$
$234$	−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	0.324937	−	0.945736i	$-0.394657\pi$
$239$	−8.47509e6	−	8.47509e6i	−0.620798	−	0.620798i	−0.945736	+	0.324937i	$0.894657\pi$
$240$	18096.3	−	18096.3i	0.00130905	−	0.00130905i
$241$	1.64320e7	+	1.64320e7i	1.17392	+	1.17392i	0.981266	+	0.192656i	$0.0617103\pi$
$241$	1.64320e7	+	1.64320e7i	1.17392	+	1.17392i	0.192656	+	0.981266i	$0.438290\pi$
$242$	−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	−0.0935943	−	0.995610i	$-0.529836\pi$
$251$	1.42638e7	−	1.42638e7i	0.902016	−	0.902016i	0.995610	+	0.0935943i	$0.0298357\pi$
$252$			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	0.909983	−	0.414644i	$-0.136094\pi$
$257$	8.40818e6	+	8.40818e6i	0.495339	+	0.495339i	−0.414644	+	0.909983i	$0.636094\pi$
$258$		−	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	$-0.788579\pi$
$263$		−	2.24275e7i		−	1.23286i	0.787410	−	0.616429i	$-0.211421\pi$
$264$	−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	−0.279809	−	0.960056i	$-0.590271\pi$
$277$	1.44579e7	−	1.44579e7i	0.680246	−	0.680246i	0.960056	+	0.279809i	$0.0902712\pi$
$278$	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	0.498540	−	0.866867i	$-0.333870\pi$
$281$	−8.17246e6	−	8.17246e6i	−0.368327	−	0.368327i	−0.866867	+	0.498540i	$0.833870\pi$
$282$	279737.	+	279737.i	0.0124739	+	0.0124739i
$283$	4.21299e6	−	4.21299e6i	0.185879	−	0.185879i	−0.608033	−	0.793912i	$-0.708041\pi$
$283$	4.21299e6	−	4.21299e6i	0.185879	−	0.185879i	0.793912	+	0.608033i	$0.208041\pi$
$284$		−	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	$-0.922369\pi$
$307$		−	1.39739e7i		−	0.482951i	0.970407	−	0.241476i	$-0.0776314\pi$
$308$	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	−0.533990	−	0.845491i	$-0.679308\pi$
$311$	9.37002e6	−	9.37002e6i	0.311501	−	0.311501i	0.845491	+	0.533990i	$0.179308\pi$
$312$	−168105.			−0.00553498
$313$	1.72455e7	+	1.72455e7i	0.562397	+	0.562397i	0.929988	−	0.367590i	$-0.119817\pi$
$313$	1.72455e7	+	1.72455e7i	0.562397	+	0.562397i	−0.367590	+	0.929988i	$0.619817\pi$
$314$	−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	$0.167025\pi$
$317$			3.19171e7i			1.00195i	−0.865462	+	0.500974i	$0.832975\pi$
$318$	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	0.818743	−	0.574161i	$-0.194671\pi$
$331$	8.86970e6	+	8.86970e6i	0.244582	+	0.244582i	−0.574161	+	0.818743i	$0.694671\pi$
$332$			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	$-0.822551\pi$
$337$		−	4.04959e7i		−	1.05809i	0.848595	−	0.529043i	$-0.177449\pi$
$338$	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	−0.640260	−	0.768158i	$-0.721173\pi$
$347$	5.34384e6	−	5.34384e6i	0.127898	−	0.127898i	0.768158	+	0.640260i	$0.221173\pi$
$348$	−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	−0.423064	−	0.906100i	$-0.639045\pi$
$353$	2.12473e7	−	2.12473e7i	0.483036	−	0.483036i	0.906100	+	0.423064i	$0.139045\pi$
$354$			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	$0.209600\pi$
$373$			6.35107e7i			1.22383i	−0.790924	+	0.611914i	$0.790400\pi$
$374$		−	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	0.205649	−	0.978626i	$-0.434069\pi$
$383$	−4.34273e7	−	4.34273e7i	−0.772977	−	0.772977i	−0.978626	+	0.205649i	$0.934069\pi$
$384$	−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	−0.969406	−	0.245464i	$-0.921060\pi$
$389$	−7.15119e7	−	7.15119e7i	−1.21487	−	1.21487i	−0.245464	−	0.969406i	$-0.578940\pi$
$390$	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	$0.0261281\pi$
$397$			1.02606e7i			0.163984i	−0.996633	+	0.0819918i	$0.973872\pi$
$398$		−	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	−0.0632100	−	0.998000i	$-0.520134\pi$
$401$	6.02764e7	−	6.02764e7i	0.934790	−	0.934790i	0.998000	+	0.0632100i	$0.0201338\pi$
$402$	−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	−0.378206	−	0.925722i	$-0.623459\pi$
$409$	3.74599e7	−	3.74599e7i	0.547516	−	0.547516i	0.925722	+	0.378206i	$0.123459\pi$
$410$			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	−0.323064	−	0.946377i	$-0.604713\pi$
$421$	4.65107e7	−	4.65107e7i	0.623313	−	0.623313i	0.946377	+	0.323064i	$0.104713\pi$
$422$	−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	−0.790236	−	0.612802i	$-0.790042\pi$
$431$	−1.42059e7	+	1.42059e7i	−0.177434	+	0.177434i	0.612802	+	0.790236i	$0.290042\pi$
$432$		−	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	−0.752759	−	0.658297i	$-0.771277\pi$
$439$	−7.99192e6	+	7.99192e6i	−0.0944620	+	0.0944620i	0.658297	+	0.752759i	$0.271277\pi$
$440$	−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	$0.135833\pi$
$443$			7.19674e7i			0.827798i	−0.910323	+	0.413899i	$0.864167\pi$
$444$	−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	0.281967	−	0.959424i	$-0.409013\pi$
$449$	−6.13226e7	−	6.13226e7i	−0.677457	−	0.677457i	−0.959424	+	0.281967i	$0.909013\pi$
$450$	−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	0.998538	+	0.0540558i	$0.0172149\pi$
$457$	1.00464e8	+	1.00464e8i	1.05259	+	1.05259i	0.0540558	+	0.998538i	$0.482785\pi$
$458$	−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	0.996782	+	0.0801571i	$0.0255422\pi$
$461$	1.05510e8	+	1.05510e8i	1.07694	+	1.07694i	0.0801571	+	0.996782i	$0.474458\pi$
$462$	−1.33368e6	+	1.33368e6i	−0.0135246	+	0.0135246i
$463$	7.35576e7	+	7.35576e7i	0.741114	+	0.741114i	0.972792	−	0.231679i	$-0.0744218\pi$
$463$	7.35576e7	+	7.35576e7i	0.741114	+	0.741114i	−0.231679	+	0.972792i	$0.574422\pi$
$464$	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	0.857114	−	0.515126i	$-0.172255\pi$
$467$	3.48307e7	+	3.48307e7i	0.341988	+	0.341988i	−0.515126	+	0.857114i	$0.672255\pi$
$468$	−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	0.742929	−	0.669371i	$-0.233436\pi$
$479$	8.08420e6	+	8.08420e6i	0.0735581	+	0.0735581i	−0.669371	+	0.742929i	$0.733436\pi$
$480$		−	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	0.996115	+	0.0880617i	$0.0280673\pi$
$487$	1.25224e8	+	1.25224e8i	1.08418	+	1.08418i	0.0880617	+	0.996115i	$0.471933\pi$
$488$	−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	−0.988697	−	0.149924i	$-0.952097\pi$
$499$	−1.04219e8	+	1.04219e8i	−0.838773	+	0.838773i	0.149924	+	0.988697i	$0.452097\pi$
$500$	−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	0.834058	−	0.551677i	$-0.186012\pi$
$503$	3.59368e7	+	3.59368e7i	0.282381	+	0.282381i	−0.551677	+	0.834058i	$0.686012\pi$
$504$	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	$0.0705206\pi$
$509$			5.79550e7i			0.439478i	−0.975559	+	0.219739i	$0.929479\pi$
$510$	−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	$-0.844647\pi$
$521$		−	1.32627e8i		−	0.937817i	0.883247	−	0.468908i	$-0.155353\pi$
$522$			2.99022e7i			0.210228i
$523$	−8.39040e7	−	8.39040e7i	−0.586513	−	0.586513i	0.350172	−	0.936685i	$-0.386123\pi$
$523$	−8.39040e7	−	8.39040e7i	−0.586513	−	0.586513i	−0.936685	+	0.350172i	$0.886123\pi$
$524$	−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	0.798866	−	0.601509i	$-0.205433\pi$
$541$	3.12497e7	+	3.12497e7i	0.197358	+	0.197358i	−0.601509	+	0.798866i	$0.705433\pi$
$542$	−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	−0.656999	−	0.753891i	$-0.728174\pi$
$547$	1.58581e7	−	1.58581e7i	0.0968923	−	0.0968923i	0.753891	+	0.656999i	$0.228174\pi$
$548$			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	−0.420351	−	0.907362i	$-0.638093\pi$
$557$	8.41596e7	−	8.41596e7i	0.487010	−	0.487010i	0.907362	+	0.420351i	$0.138093\pi$
$558$		−	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	0.0731776	−	0.997319i	$-0.476686\pi$
$563$	−1.64916e8	−	1.64916e8i	−0.924141	−	0.924141i	−0.997319	+	0.0731776i	$0.976686\pi$
$564$	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	−0.411063	−	0.911607i	$-0.634842\pi$
$569$	9.22101e7	−	9.22101e7i	0.500544	−	0.500544i	0.911607	+	0.411063i	$0.134842\pi$
$570$	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	−0.993142	−	0.116913i	$-0.962700\pi$
$577$	−2.13242e8	−	2.13242e8i	−1.11006	−	1.11006i	−0.116913	−	0.993142i	$-0.537300\pi$
$578$	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	−0.0699234	+	0.997552i	$0.522275\pi$
$587$	−2.15910e8	+	2.15910e8i	−1.06748	+	1.06748i	−0.997552	+	0.0699234i	$0.977725\pi$
$588$	−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	−0.907102	−	0.420911i	$-0.861710\pi$
$607$	−1.08736e8	+	1.08736e8i	−0.486191	+	0.486191i	0.420911	+	0.907102i	$0.361710\pi$
$608$	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	$0.158333\pi$
$613$			2.19823e8i			0.954317i	−0.878817	+	0.477158i	$0.841667\pi$
$614$	−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	$0.164153\pi$
$617$			2.31665e8i			0.986290i	−0.869947	+	0.493145i	$0.835847\pi$
$618$	954193.			0.00404269
$619$			5.93916e7i			0.250411i	0.992131	+	0.125205i	$0.0399590\pi$
$619$			5.93916e7i			0.250411i	−0.992131	+	0.125205i	$0.960041\pi$
$620$		−	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	−0.619552	−	0.784955i	$-0.712686\pi$
$631$	4.15558e7	−	4.15558e7i	0.165403	−	0.165403i	0.784955	+	0.619552i	$0.212686\pi$
$632$		−	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	−0.614932	−	0.788580i	$-0.710816\pi$
$643$	4.61640e7	−	4.61640e7i	0.173648	−	0.173648i	0.788580	+	0.614932i	$0.210816\pi$
$644$	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	−0.774304	−	0.632813i	$-0.781900\pi$
$647$	−3.83214e7	+	3.83214e7i	−0.141491	+	0.141491i	0.632813	+	0.774304i	$0.281900\pi$
$648$	−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	−0.246809	+	0.969064i	$0.579382\pi$
$653$	−3.38554e8	+	3.38554e8i	−1.21587	+	1.21587i	−0.969064	+	0.246809i	$0.920618\pi$
$654$			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	$0.0828960\pi$
$659$			1.47384e8i			0.514984i	−0.966280	+	0.257492i	$0.917104\pi$
$660$	1.43508e6	−	1.43508e6i	0.00499166	−	0.00499166i
$661$	2.64401e8	−	2.64401e8i	0.915499	−	0.915499i	−0.0811987	−	0.996698i	$-0.525875\pi$
$661$	2.64401e8	−	2.64401e8i	0.915499	−	0.915499i	0.996698	+	0.0811987i	$0.0258748\pi$
$662$	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	$0.167100\pi$
$677$			3.11020e8i			1.00236i	−0.865344	+	0.501178i	$0.832900\pi$
$678$	−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	0.970522	−	0.241011i	$-0.0774789\pi$
$683$	2.32431e8	+	2.32431e8i	0.729512	+	0.729512i	−0.241011	+	0.970522i	$0.577479\pi$
$684$	−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	$-0.849730\pi$
$691$		−	3.00078e8i		−	0.909493i	0.890621	−	0.454747i	$-0.150270\pi$
$692$	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	0.750223	−	0.661185i	$-0.229946\pi$
$701$	3.06710e7	+	3.06710e7i	0.0890377	+	0.0890377i	−0.661185	+	0.750223i	$0.729946\pi$
$702$		−	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	0.527183	−	0.849752i	$-0.323248\pi$
$709$	−1.14964e8	−	1.14964e8i	−0.322568	−	0.322568i	−0.849752	+	0.527183i	$0.823248\pi$
$710$	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	−0.572793	−	0.819700i	$-0.694140\pi$
$727$	9.48717e7	−	9.48717e7i	0.246907	−	0.246907i	0.819700	+	0.572793i	$0.194140\pi$
$728$		−	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	$0.239123\pi$
$733$			5.37610e8i			1.36507i	−0.730852	+	0.682535i	$0.760877\pi$
$734$	−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	$0.177144\pi$
$739$			4.26369e8i			1.05646i	−0.849102	+	0.528229i	$0.822856\pi$
$740$	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	$0.239825\pi$
$743$			5.61236e8i			1.36829i	−0.729345	+	0.684146i	$0.760175\pi$
$744$		−	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	$0.112224\pi$
$751$			2.92516e8i			0.690604i	−0.938492	+	0.345302i	$0.887776\pi$
$752$	−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	0.544461	−	0.838786i	$-0.316734\pi$
$757$	−1.27678e8	−	1.27678e8i	−0.294326	−	0.294326i	−0.838786	+	0.544461i	$0.816734\pi$
$758$	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	$0.0147621\pi$
$761$			4.08627e7i			0.0927200i	−0.998925	+	0.0463600i	$0.985238\pi$
$762$	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	−0.00942668	+	0.999956i	$0.503001\pi$
$769$	−4.59023e8	+	4.59023e8i	−1.00938	+	1.00938i	−0.999956	+	0.00942668i	$0.996999\pi$
$770$			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	−0.568346	−	0.822790i	$-0.692416\pi$
$797$	1.28815e8	−	1.28815e8i	0.254444	−	0.254444i	0.822790	+	0.568346i	$0.192416\pi$
$798$			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	−0.658726	−	0.752383i	$-0.728904\pi$
$809$	4.95891e7	−	4.95891e7i	0.0936572	−	0.0936572i	0.752383	+	0.658726i	$0.228904\pi$
$810$	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	0.313832	−	0.949478i	$-0.398387\pi$
$827$	−3.59527e8	−	3.59527e8i	−0.635646	−	0.635646i	−0.949478	+	0.313832i	$0.898387\pi$
$828$	−2.36450e8	+	2.36450e8i	−0.416532	+	0.416532i
$829$	3.95255e8	−	3.95255e8i	0.693767	−	0.693767i	−0.269292	−	0.963059i	$-0.586790\pi$
$829$	3.95255e8	−	3.95255e8i	0.693767	−	0.693767i	0.963059	+	0.269292i	$0.0867897\pi$
$830$	−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	$-0.831824\pi$
$839$		−	5.95433e8i		−	1.00820i	0.863645	−	0.504101i	$-0.168176\pi$
$840$	−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	−0.411741	−	0.911301i	$-0.635079\pi$
$853$	3.10053e8	−	3.10053e8i	0.499561	−	0.499561i	0.911301	+	0.411741i	$0.135079\pi$
$854$			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	0.271105	−	0.962550i	$-0.412611\pi$
$857$	−4.35211e8	−	4.35211e8i	−0.691445	−	0.691445i	−0.962550	+	0.271105i	$0.912611\pi$
$858$	−1.33312e7			−0.0211060
$859$	−5.85174e8	−	5.85174e8i	−0.923221	−	0.923221i	0.0740348	−	0.997256i	$-0.476412\pi$
$859$	−5.85174e8	−	5.85174e8i	−0.923221	−	0.923221i	−0.997256	+	0.0740348i	$0.976412\pi$
$860$	−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	$0.125171\pi$
$881$			5.24033e8i			0.766357i	−0.923674	+	0.383178i	$0.874829\pi$
$882$	−2.63919e7	+	2.63919e7i	−0.0384649	+	0.0384649i
$883$	−4.33954e8	+	4.33954e8i	−0.630320	+	0.630320i	−0.948148	−	0.317828i	$-0.897047\pi$
$883$	−4.33954e8	+	4.33954e8i	−0.630320	+	0.630320i	0.317828	+	0.948148i	$0.397047\pi$
$884$	−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	$0.198584\pi$
$887$			8.15356e8i			1.16836i	−0.811624	+	0.584180i	$0.801416\pi$
$888$	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	0.704960	−	0.709247i	$-0.250965\pi$
$907$	−3.19834e6	−	3.19834e6i	−0.00428650	−	0.00428650i	−0.709247	+	0.704960i	$0.750965\pi$
$908$	−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	0.941702	−	0.336447i	$-0.109225\pi$
$911$	4.57608e8	+	4.57608e8i	0.605256	+	0.605256i	−0.336447	+	0.941702i	$0.609225\pi$
$912$	−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	−0.519194	−	0.854656i	$-0.673768\pi$
$919$	2.60369e8	−	2.60369e8i	0.335462	−	0.335462i	0.854656	+	0.519194i	$0.173768\pi$
$920$	−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	$0.0595551\pi$
$929$			2.98270e8i			0.372016i	−0.982548	+	0.186008i	$0.940445\pi$
$930$	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	0.999993	+	0.00371719i	$0.00118322\pi$
$947$	8.52429e8	+	8.52429e8i	1.00371	+	1.00371i	0.00371719	+	0.999993i	$0.498817\pi$
$948$	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	$-0.944815\pi$
$953$		−	2.98606e8i		−	0.345001i	0.985009	−	0.172501i	$-0.0551847\pi$
$954$	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	0.0955961	−	0.995420i	$-0.469524\pi$
$967$	−8.13649e8	−	8.13649e8i	−0.899824	−	0.899824i	−0.995420	+	0.0955961i	$0.969524\pi$
$968$	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	−0.749938	−	0.661508i	$-0.769917\pi$
$977$	−8.24682e7	+	8.24682e7i	−0.0884306	+	0.0884306i	0.661508	+	0.749938i	$0.269917\pi$
$978$	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	$0.130218\pi$
$983$			7.55663e8i			0.795550i	−0.917483	+	0.397775i	$0.869782\pi$
$984$	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	−0.355099	−	0.934829i	$-0.615553\pi$
$991$	5.64218e8	−	5.64218e8i	0.579730	−	0.579730i	0.934829	+	0.355099i	$0.115553\pi$
$992$			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	0.684758	−	0.728770i	$-0.259908\pi$
$997$	−4.36173e7	−	4.36173e7i	−0.0440122	−	0.0440122i	−0.728770	+	0.684758i	$0.759908\pi$
$998$			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.43.6	yes	18
37.31	odd	4	inner	74.7.d.a.31.4	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.a.31.4	✓	18	37.31	odd	4	inner
74.7.d.a.43.6	yes	18	1.1	even	1	trivial

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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