LMFDB - Embedded newform 74.7.d.b.31.10

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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 $ x^20 + 10424x^18 + 44844916x^16 + 103219343022x^14 + 138101513095620x^12 + 109787124347520192x^10 + 51172837440825906441x^8 + 13199761586736849750156x^6 + 1629475196758519705300656x^4 + 65381450766316829487245376*x^2 + 736627437450607950694158336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.10
Root			$-44.9453i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 4.00000i) q^{2} +47.9453i q^{3} +32.0000i q^{4} +(-25.3958 + 25.3958i) q^{5} +(191.781 - 191.781i) q^{6} -536.323 q^{7} +(128.000 - 128.000i) q^{8} -1569.75 q^{9} +O(q^{10})$	\(q+(-4.00000 - 4.00000i) q^{2} +47.9453i q^{3} +32.0000i q^{4} +(-25.3958 + 25.3958i) q^{5} +(191.781 - 191.781i) q^{6} -536.323 q^{7} +(128.000 - 128.000i) q^{8} -1569.75 q^{9} +203.167 q^{10} +1614.60i q^{11} -1534.25 q^{12} +(729.774 - 729.774i) q^{13} +(2145.29 + 2145.29i) q^{14} +(-1217.61 - 1217.61i) q^{15} -1024.00 q^{16} +(5904.88 - 5904.88i) q^{17} +(6279.01 + 6279.01i) q^{18} +(815.702 - 815.702i) q^{19} +(-812.666 - 812.666i) q^{20} -25714.2i q^{21} +(6458.40 - 6458.40i) q^{22} +(-6384.70 + 6384.70i) q^{23} +(6137.00 + 6137.00i) q^{24} +14335.1i q^{25} -5838.19 q^{26} -40310.1i q^{27} -17162.3i q^{28} +(23048.9 + 23048.9i) q^{29} +9740.88i q^{30} +(-30254.5 - 30254.5i) q^{31} +(4096.00 + 4096.00i) q^{32} -77412.4 q^{33} -47239.0 q^{34} +(13620.4 - 13620.4i) q^{35} -50232.0i q^{36} +(14127.7 - 48642.9i) q^{37} -6525.62 q^{38} +(34989.2 + 34989.2i) q^{39} +6501.33i q^{40} -116545. i q^{41} +(-102857. + 102857. i) q^{42} +(10100.8 - 10100.8i) q^{43} -51667.2 q^{44} +(39865.1 - 39865.1i) q^{45} +51077.6 q^{46} -174029. q^{47} -49096.0i q^{48} +169993. q^{49} +(57340.4 - 57340.4i) q^{50} +(283111. + 283111. i) q^{51} +(23352.8 + 23352.8i) q^{52} +34416.1 q^{53} +(-161240. + 161240. i) q^{54} +(-41004.1 - 41004.1i) q^{55} +(-68649.3 + 68649.3i) q^{56} +(39109.1 + 39109.1i) q^{57} -184392. i q^{58} +(-24678.8 + 24678.8i) q^{59} +(38963.5 - 38963.5i) q^{60} +(-40824.4 - 40824.4i) q^{61} +242036. i q^{62} +841894. q^{63} -32768.0i q^{64} +37066.4i q^{65} +(309650. + 309650. i) q^{66} -8020.34i q^{67} +(188956. + 188956. i) q^{68} +(-306116. - 306116. i) q^{69} -108963. q^{70} -507051. q^{71} +(-200928. + 200928. i) q^{72} +450770. i q^{73} +(-251082. + 138061. i) q^{74} -687301. q^{75} +(26102.5 + 26102.5i) q^{76} -865946. i q^{77} -279914. i q^{78} +(-382638. + 382638. i) q^{79} +(26005.3 - 26005.3i) q^{80} +788330. q^{81} +(-466178. + 466178. i) q^{82} -189327. q^{83} +822853. q^{84} +299918. i q^{85} -80806.5 q^{86} +(-1.10509e6 + 1.10509e6i) q^{87} +(206669. + 206669. i) q^{88} +(-10969.2 - 10969.2i) q^{89} -318921. q^{90} +(-391395. + 391395. i) q^{91} +(-204310. - 204310. i) q^{92} +(1.45056e6 - 1.45056e6i) q^{93} +(696116. + 696116. i) q^{94} +41430.9i q^{95} +(-196384. + 196384. i) q^{96} +(508457. - 508457. i) q^{97} +(-679973. - 679973. i) q^{98} -2.53452e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) $ 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * 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
$3$			47.9453i			1.77575i	0.460083	+	0.887876i	$0.347820\pi$
$3$			47.9453i			1.77575i	−0.460083	+	0.887876i	$0.652180\pi$
$4$			32.0000i			0.500000i
$5$	−25.3958	+	25.3958i	−0.203167	+	0.203167i	−0.801355	−	0.598189i	$-0.795887\pi$
$5$	−25.3958	+	25.3958i	−0.203167	+	0.203167i	0.598189	+	0.801355i	$0.295887\pi$
$6$	191.781	−	191.781i	0.887876	−	0.887876i
$7$	−536.323			−1.56362			−0.781812	−	0.623514i	$-0.785704\pi$
$7$	−536.323			−1.56362			−0.781812	+	0.623514i	$0.785704\pi$
$8$	128.000	−	128.000i	0.250000	−	0.250000i
$9$	−1569.75			−2.15329
$10$	203.167			0.203167
$11$			1614.60i			1.21307i	0.795056	+	0.606536i	$0.207441\pi$
$11$			1614.60i			1.21307i	−0.795056	+	0.606536i	$0.792559\pi$
$12$	−1534.25			−0.887876
$13$	729.774	−	729.774i	0.332169	−	0.332169i	−0.521241	−	0.853410i	$-0.674531\pi$
$13$	729.774	−	729.774i	0.332169	−	0.332169i	0.853410	+	0.521241i	$0.174531\pi$
$14$	2145.29	+	2145.29i	0.781812	+	0.781812i
$15$	−1217.61	−	1217.61i	−0.360773	−	0.360773i
$16$	−1024.00			−0.250000
$17$	5904.88	−	5904.88i	1.20189	−	1.20189i	0.228297	−	0.973592i	$-0.426684\pi$
$17$	5904.88	−	5904.88i	1.20189	−	1.20189i	0.973592	−	0.228297i	$-0.0733156\pi$
$18$	6279.01	+	6279.01i	1.07665	+	1.07665i
$19$	815.702	−	815.702i	0.118924	−	0.118924i	−0.645140	−	0.764064i	$-0.723201\pi$
$19$	815.702	−	815.702i	0.118924	−	0.118924i	0.764064	+	0.645140i	$0.223201\pi$
$20$	−812.666	−	812.666i	−0.101583	−	0.101583i
$21$		−	25714.2i		−	2.77661i
$22$	6458.40	−	6458.40i	0.606536	−	0.606536i
$23$	−6384.70	+	6384.70i	−0.524755	+	0.524755i	−0.919004	−	0.394249i	$-0.871005\pi$
$23$	−6384.70	+	6384.70i	−0.524755	+	0.524755i	0.394249	+	0.919004i	$0.371005\pi$
$24$	6137.00	+	6137.00i	0.443938	+	0.443938i
$25$			14335.1i			0.917447i
$26$	−5838.19			−0.332169
$27$		−	40310.1i		−	2.04796i
$28$		−	17162.3i		−	0.781812i
$29$	23048.9	+	23048.9i	0.945055	+	0.945055i	0.998567	−	0.0535122i	$-0.0170416\pi$
$29$	23048.9	+	23048.9i	0.945055	+	0.945055i	−0.0535122	+	0.998567i	$0.517042\pi$
$30$			9740.88i			0.360773i
$31$	−30254.5	−	30254.5i	−1.01556	−	1.01556i	−0.999877	−	0.0156820i	$-0.995008\pi$
$31$	−30254.5	−	30254.5i	−1.01556	−	1.01556i	−0.0156820	−	0.999877i	$-0.504992\pi$
$32$	4096.00	+	4096.00i	0.125000	+	0.125000i
$33$	−77412.4			−2.15411
$34$	−47239.0			−1.20189
$35$	13620.4	−	13620.4i	0.317676	−	0.317676i
$36$		−	50232.0i		−	1.07665i
$37$	14127.7	−	48642.9i	0.278911	−	0.960317i
$37$	14127.7	−	48642.9i	0.278911	−	0.960317i
$38$	−6525.62			−0.118924
$39$	34989.2	+	34989.2i	0.589849	+	0.589849i
$40$			6501.33i			0.101583i
$41$		−	116545.i		−	1.69099i	−0.533985	−	0.845494i	$-0.679306\pi$
$41$		−	116545.i		−	1.69099i	0.533985	−	0.845494i	$-0.320694\pi$
$42$	−102857.	+	102857.i	−1.38830	+	1.38830i
$43$	10100.8	−	10100.8i	0.127043	−	0.127043i	−0.640726	−	0.767769i	$-0.721367\pi$
$43$	10100.8	−	10100.8i	0.127043	−	0.127043i	0.767769	+	0.640726i	$0.221367\pi$
$44$	−51667.2			−0.606536
$45$	39865.1	−	39865.1i	0.437477	−	0.437477i
$46$	51077.6			0.524755
$47$	−174029.			−1.67621			−0.838104	−	0.545511i	$-0.816336\pi$
$47$	−174029.			−1.67621			−0.838104	+	0.545511i	$0.816336\pi$
$48$		−	49096.0i		−	0.443938i
$49$	169993.			1.44492
$50$	57340.4	−	57340.4i	0.458723	−	0.458723i
$51$	283111.	+	283111.i	2.13426	+	2.13426i
$52$	23352.8	+	23352.8i	0.166084	+	0.166084i
$53$	34416.1			0.231171			0.115586	−	0.993298i	$-0.463126\pi$
$53$	34416.1			0.231171			0.115586	+	0.993298i	$0.463126\pi$
$54$	−161240.	+	161240.i	−1.02398	+	1.02398i
$55$	−41004.1	−	41004.1i	−0.246456	−	0.246456i
$56$	−68649.3	+	68649.3i	−0.390906	+	0.390906i
$57$	39109.1	+	39109.1i	0.211180	+	0.211180i
$58$		−	184392.i		−	0.945055i
$59$	−24678.8	+	24678.8i	−0.120162	+	0.120162i	−0.764631	−	0.644468i	$-0.777079\pi$
$59$	−24678.8	+	24678.8i	−0.120162	+	0.120162i	0.644468	+	0.764631i	$0.277079\pi$
$60$	38963.5	−	38963.5i	0.180387	−	0.180387i
$61$	−40824.4	−	40824.4i	−0.179858	−	0.179858i	0.611436	−	0.791294i	$-0.290592\pi$
$61$	−40824.4	−	40824.4i	−0.179858	−	0.179858i	−0.791294	+	0.611436i	$0.790592\pi$
$62$			242036.i			1.01556i
$63$	841894.			3.36694
$64$		−	32768.0i		−	0.125000i
$65$			37066.4i			0.134971i
$66$	309650.	+	309650.i	1.07706	+	1.07706i
$67$		−	8020.34i		−	0.0266666i	−0.999911	−	0.0133333i	$-0.995756\pi$
$67$		−	8020.34i		−	0.0266666i	0.999911	−	0.0133333i	$-0.00424425\pi$
$68$	188956.	+	188956.i	0.600944	+	0.600944i
$69$	−306116.	−	306116.i	−0.931835	−	0.931835i
$70$	−108963.			−0.317676
$71$	−507051.			−1.41670			−0.708348	−	0.705863i	$-0.750559\pi$
$71$	−507051.			−1.41670			−0.708348	+	0.705863i	$0.750559\pi$
$72$	−200928.	+	200928.i	−0.538324	+	0.538324i
$73$			450770.i			1.15874i	0.815064	+	0.579371i	$0.196702\pi$
$73$			450770.i			1.15874i	−0.815064	+	0.579371i	$0.803298\pi$
$74$	−251082.	+	138061.i	−0.619614	+	0.340703i
$75$	−687301.			−1.62916
$76$	26102.5	+	26102.5i	0.0594622	+	0.0594622i
$77$		−	865946.i		−	1.89679i
$78$		−	279914.i		−	0.589849i
$79$	−382638.	+	382638.i	−0.776081	+	0.776081i	−0.979162	−	0.203081i	$-0.934905\pi$
$79$	−382638.	+	382638.i	−0.776081	+	0.776081i	0.203081	+	0.979162i	$0.434905\pi$
$80$	26005.3	−	26005.3i	0.0507916	−	0.0507916i
$81$	788330.			1.48338
$82$	−466178.	+	466178.i	−0.845494	+	0.845494i
$83$	−189327.			−0.331115			−0.165557	−	0.986200i	$-0.552942\pi$
$83$	−189327.			−0.331115			−0.165557	+	0.986200i	$0.552942\pi$
$84$	822853.			1.38830
$85$			299918.i			0.488367i
$86$	−80806.5			−0.127043
$87$	−1.10509e6	+	1.10509e6i	−1.67818	+	1.67818i
$88$	206669.	+	206669.i	0.303268	+	0.303268i
$89$	−10969.2	−	10969.2i	−0.0155598	−	0.0155598i	0.699284	−	0.714844i	$-0.253502\pi$
$89$	−10969.2	−	10969.2i	−0.0155598	−	0.0155598i	−0.714844	+	0.699284i	$0.753502\pi$
$90$	−318921.			−0.437477
$91$	−391395.	+	391395.i	−0.519387	+	0.519387i
$92$	−204310.	−	204310.i	−0.262378	−	0.262378i
$93$	1.45056e6	−	1.45056e6i	1.80338	−	1.80338i
$94$	696116.	+	696116.i	0.838104	+	0.838104i
$95$			41430.9i			0.0483229i
$96$	−196384.	+	196384.i	−0.221969	+	0.221969i
$97$	508457.	−	508457.i	0.557108	−	0.557108i	−0.371375	−	0.928483i	$-0.621114\pi$
$97$	508457.	−	508457.i	0.557108	−	0.557108i	0.928483	+	0.371375i	$0.121114\pi$
$98$	−679973.	−	679973.i	−0.722460	−	0.722460i
$99$		−	2.53452e6i		−	2.61210i
$100$	−458723.			−0.458723
$101$		−	1.07256e6i		−	1.04102i	−0.853856	−	0.520509i	$-0.825742\pi$
$101$		−	1.07256e6i		−	1.04102i	0.853856	−	0.520509i	$-0.174258\pi$
$102$		−	2.26489e6i		−	2.13426i
$103$	505187.	+	505187.i	0.462318	+	0.462318i	0.899415	−	0.437097i	$-0.143993\pi$
$103$	505187.	+	505187.i	0.462318	+	0.462318i	−0.437097	+	0.899415i	$0.643993\pi$
$104$		−	186822.i		−	0.166084i
$105$	653032.	+	653032.i	0.564114	+	0.564114i
$106$	−137664.	−	137664.i	−0.115586	−	0.115586i
$107$	660703.			0.539330			0.269665	−	0.962954i	$-0.413087\pi$
$107$	660703.			0.539330			0.269665	+	0.962954i	$0.413087\pi$
$108$	1.28992e6			1.02398
$109$	−1.19239e6	+	1.19239e6i	−0.920747	+	0.920747i	−0.997082	−	0.0763356i	$-0.975678\pi$
$109$	−1.19239e6	+	1.19239e6i	−0.920747	+	0.920747i	0.0763356	+	0.997082i	$0.475678\pi$
$110$			328032.i			0.246456i
$111$	2.33220e6	+	677356.i	1.70528	+	0.495277i
$112$	549195.			0.390906
$113$	−199299.	−	199299.i	−0.138124	−	0.138124i	0.634664	−	0.772788i	$-0.281138\pi$
$113$	−199299.	−	199299.i	−0.138124	−	0.138124i	−0.772788	+	0.634664i	$0.781138\pi$
$114$		−	312873.i		−	0.211180i
$115$		−	324289.i		−	0.213225i
$116$	−737566.	+	737566.i	−0.472527	+	0.472527i
$117$	−1.14556e6	+	1.14556e6i	−0.715257	+	0.715257i
$118$	197431.			0.120162
$119$	−3.16692e6	+	3.16692e6i	−1.87930	+	1.87930i
$120$	−311708.			−0.180387
$121$	−835368.			−0.471544
$122$			326596.i			0.179858i
$123$	5.58777e6			3.00278
$124$	968145.	−	968145.i	0.507779	−	0.507779i
$125$	−760861.	−	760861.i	−0.389561	−	0.389561i
$126$	−3.36758e6	−	3.36758e6i	−1.68347	−	1.68347i
$127$	−1.43014e6			−0.698182			−0.349091	−	0.937089i	$-0.613510\pi$
$127$	−1.43014e6			−0.698182			−0.349091	+	0.937089i	$0.613510\pi$
$128$	−131072.	+	131072.i	−0.0625000	+	0.0625000i
$129$	484286.	+	484286.i	0.225597	+	0.225597i
$130$	148266.	−	148266.i	0.0674855	−	0.0674855i
$131$	−2.22387e6	−	2.22387e6i	−0.989225	−	0.989225i	0.0107173	−	0.999943i	$-0.496589\pi$
$131$	−2.22387e6	−	2.22387e6i	−0.989225	−	0.989225i	−0.999943	+	0.0107173i	$0.996589\pi$
$132$		−	2.47720e6i		−	1.07706i
$133$	−437480.	+	437480.i	−0.185953	+	0.185953i
$134$	−32081.4	+	32081.4i	−0.0133333	+	0.0133333i
$135$	1.02371e6	+	1.02371e6i	0.416078	+	0.416078i
$136$		−	1.51165e6i		−	0.600944i
$137$	−3.93267e6			−1.52942			−0.764708	−	0.644377i	$-0.777117\pi$
$137$	−3.93267e6			−1.52942			−0.764708	+	0.644377i	$0.777117\pi$
$138$			2.44893e6i			0.931835i
$139$		−	3.21169e6i		−	1.19589i	−0.801539	−	0.597943i	$-0.795985\pi$
$139$		−	3.21169e6i		−	1.19589i	0.801539	−	0.597943i	$-0.204015\pi$
$140$	435852.	+	435852.i	0.158838	+	0.158838i
$141$		−	8.34387e6i		−	2.97653i
$142$	2.02820e6	+	2.02820e6i	0.708348	+	0.708348i
$143$	1.17829e6	+	1.17829e6i	0.402944	+	0.402944i
$144$	1.60743e6			0.538324
$145$	−1.17069e6			−0.384007
$146$	1.80308e6	−	1.80308e6i	0.579371	−	0.579371i
$147$			8.15038e6i			2.56582i
$148$	1.55657e6	+	452086.i	0.480158	+	0.139456i
$149$	−2.35873e6			−0.713050			−0.356525	−	0.934286i	$-0.616039\pi$
$149$	−2.35873e6			−0.713050			−0.356525	+	0.934286i	$0.616039\pi$
$150$	2.74920e6	+	2.74920e6i	0.814579	+	0.814579i
$151$		−	1.84942e6i		−	0.537162i	−0.963257	−	0.268581i	$-0.913445\pi$
$151$		−	1.84942e6i		−	0.537162i	0.963257	−	0.268581i	$-0.0865547\pi$
$152$		−	208820.i		−	0.0594622i
$153$	−9.26919e6	+	9.26919e6i	−2.58802	+	2.58802i
$154$	−3.46379e6	+	3.46379e6i	−0.948394	+	0.948394i
$155$	1.53668e6			0.412655
$156$	−1.11966e6	+	1.11966e6i	−0.294924	+	0.294924i
$157$	2.80622e6			0.725142			0.362571	−	0.931956i	$-0.381899\pi$
$157$	2.80622e6			0.725142			0.362571	+	0.931956i	$0.381899\pi$
$158$	3.06111e6			0.776081
$159$			1.65009e6i			0.410502i
$160$	−208043.			−0.0507916
$161$	3.42426e6	−	3.42426e6i	0.820520	−	0.820520i
$162$	−3.15332e6	−	3.15332e6i	−0.741691	−	0.741691i
$163$	4.67999e6	+	4.67999e6i	1.08064	+	1.08064i	0.996449	+	0.0841930i	$0.0268312\pi$
$163$	4.67999e6	+	4.67999e6i	1.08064	+	1.08064i	0.0841930	+	0.996449i	$0.473169\pi$
$164$	3.72943e6			0.845494
$165$	1.96595e6	−	1.96595e6i	0.437644	−	0.437644i
$166$	757309.	+	757309.i	0.165557	+	0.165557i
$167$	2.94208e6	−	2.94208e6i	0.631692	−	0.631692i	−0.316801	−	0.948492i	$-0.602609\pi$
$167$	2.94208e6	−	2.94208e6i	0.631692	−	0.631692i	0.948492	+	0.316801i	$0.102609\pi$
$168$	−3.29141e6	−	3.29141e6i	−0.694152	−	0.694152i
$169$			3.76167e6i			0.779328i
$170$	1.19967e6	−	1.19967e6i	0.244184	−	0.244184i
$171$	−1.28045e6	+	1.28045e6i	−0.256079	+	0.256079i
$172$	323226.	+	323226.i	0.0635215	+	0.0635215i
$173$			3.20741e6i			0.619465i	0.950824	+	0.309732i	$0.100239\pi$
$173$			3.20741e6i			0.619465i	−0.950824	+	0.309732i	$0.899761\pi$
$174$	8.84071e6			1.67818
$175$		−	7.68825e6i		−	1.43454i
$176$		−	1.65335e6i		−	0.303268i
$177$	−1.18323e6	−	1.18323e6i	−0.213379	−	0.213379i
$178$			87753.3i			0.0155598i
$179$	−3.19484e6	−	3.19484e6i	−0.557045	−	0.557045i	0.371420	−	0.928465i	$-0.378871\pi$
$179$	−3.19484e6	−	3.19484e6i	−0.557045	−	0.557045i	−0.928465	+	0.371420i	$0.878871\pi$
$180$	1.27568e6	+	1.27568e6i	0.218739	+	0.218739i
$181$	−9.72848e6			−1.64062			−0.820312	−	0.571916i	$-0.806200\pi$
$181$	−9.72848e6			−1.64062			−0.820312	+	0.571916i	$0.806200\pi$
$182$	3.13116e6			0.519387
$183$	1.95734e6	−	1.95734e6i	0.319384	−	0.319384i
$184$			1.63448e6i			0.262378i
$185$	876543.	+	1.59411e6i	0.138439	+	0.251770i
$186$	−1.16045e7			−1.80338
$187$	9.53401e6	+	9.53401e6i	1.45798	+	1.45798i
$188$		−	5.56893e6i		−	0.838104i
$189$			2.16192e7i			3.20225i
$190$	165723.	−	165723.i	0.0241615	−	0.0241615i
$191$	75781.5	−	75781.5i	0.0108759	−	0.0108759i	−0.701648	−	0.712524i	$-0.747552\pi$
$191$	75781.5	−	75781.5i	0.0108759	−	0.0108759i	0.712524	+	0.701648i	$0.247552\pi$
$192$	1.57107e6			0.221969
$193$	2.27459e6	−	2.27459e6i	0.316396	−	0.316396i	−0.530985	−	0.847381i	$-0.678178\pi$
$193$	2.27459e6	−	2.27459e6i	0.316396	−	0.316396i	0.847381	+	0.530985i	$0.178178\pi$
$194$	−4.06766e6			−0.557108
$195$	−1.77716e6			−0.239675
$196$			5.43979e6i			0.722460i
$197$	585662.			0.0766035			0.0383017	−	0.999266i	$-0.487805\pi$
$197$	585662.			0.0766035			0.0383017	+	0.999266i	$0.487805\pi$
$198$	−1.01381e7	+	1.01381e7i	−1.30605	+	1.30605i
$199$	1.73029e6	+	1.73029e6i	0.219563	+	0.219563i	0.808314	−	0.588751i	$-0.200380\pi$
$199$	1.73029e6	+	1.73029e6i	0.219563	+	0.219563i	−0.588751	+	0.808314i	$0.700380\pi$
$200$	1.83489e6	+	1.83489e6i	0.229362	+	0.229362i
$201$	384537.			0.0473533
$202$	−4.29025e6	+	4.29025e6i	−0.520509	+	0.520509i
$203$	−1.23617e7	−	1.23617e7i	−1.47771	−	1.47771i
$204$	−9.05956e6	+	9.05956e6i	−1.06713	+	1.06713i
$205$	2.95975e6	+	2.95975e6i	0.343552	+	0.343552i
$206$		−	4.04150e6i		−	0.462318i
$207$	1.00224e7	−	1.00224e7i	1.12995	−	1.12995i
$208$	−747289.	+	747289.i	−0.0830421	+	0.0830421i
$209$	1.31703e6	+	1.31703e6i	0.144264	+	0.144264i
$210$		−	5.22426e6i		−	0.564114i
$211$	1.39180e7			1.48160			0.740799	−	0.671726i	$-0.234447\pi$
$211$	1.39180e7			1.48160			0.740799	+	0.671726i	$0.234447\pi$
$212$			1.10131e6i			0.115586i
$213$		−	2.43107e7i		−	2.51570i
$214$	−2.64281e6	−	2.64281e6i	−0.269665	−	0.269665i
$215$			513037.i			0.0516218i
$216$	−5.15969e6	−	5.15969e6i	−0.511991	−	0.511991i
$217$	1.62262e7	+	1.62262e7i	1.58795	+	1.58795i
$218$	9.53915e6			0.920747
$219$	−2.16123e7			−2.05764
$220$	1.31213e6	−	1.31213e6i	0.123228	−	0.123228i
$221$		−	8.61846e6i		−	0.798459i
$222$	−6.61938e6	−	1.20382e7i	−0.605004	−	1.10028i
$223$	−6.69064e6			−0.603328			−0.301664	−	0.953414i	$-0.597542\pi$
$223$	−6.69064e6			−0.603328			−0.301664	+	0.953414i	$0.597542\pi$
$224$	−2.19678e6	−	2.19678e6i	−0.195453	−	0.195453i
$225$		−	2.25026e7i		−	1.97553i
$226$			1.59439e6i			0.138124i
$227$	4.05671e6	−	4.05671e6i	0.346814	−	0.346814i	−0.512107	−	0.858922i	$-0.671135\pi$
$227$	4.05671e6	−	4.05671e6i	0.346814	−	0.346814i	0.858922	+	0.512107i	$0.171135\pi$
$228$	−1.25149e6	+	1.25149e6i	−0.105590	+	0.105590i
$229$	−1.12311e7			−0.935224			−0.467612	−	0.883934i	$-0.654885\pi$
$229$	−1.12311e7			−0.935224			−0.467612	+	0.883934i	$0.654885\pi$
$230$	−1.29716e6	+	1.29716e6i	−0.106613	+	0.106613i
$231$	4.15181e7			3.36823
$232$	5.90053e6			0.472527
$233$			1.39360e7i			1.10172i	0.834598	+	0.550859i	$0.185700\pi$
$233$			1.39360e7i			1.10172i	−0.834598	+	0.550859i	$0.814300\pi$
$234$	9.16451e6			0.715257
$235$	4.41961e6	−	4.41961e6i	0.340549	−	0.340549i
$236$	−789723.	−	789723.i	−0.0600812	−	0.0600812i
$237$	−1.83457e7	−	1.83457e7i	−1.37813	−	1.37813i
$238$	2.53354e7			1.87930
$239$	1.19738e7	−	1.19738e7i	0.877075	−	0.877075i	−0.116156	−	0.993231i	$-0.537057\pi$
$239$	1.19738e7	−	1.19738e7i	0.877075	−	0.877075i	0.993231	+	0.116156i	$0.0370573\pi$
$240$	1.24683e6	+	1.24683e6i	0.0901933	+	0.0901933i
$241$	−1.36819e7	+	1.36819e7i	−0.977455	+	0.977455i	−0.999751	−	0.0222963i	$-0.992902\pi$
$241$	−1.36819e7	+	1.36819e7i	−0.977455	+	0.977455i	0.0222963	+	0.999751i	$0.492902\pi$
$242$	3.34147e6	+	3.34147e6i	0.235772	+	0.235772i
$243$			8.41066e6i			0.586153i
$244$	1.30638e6	−	1.30638e6i	0.0899292	−	0.0899292i
$245$	−4.31712e6	+	4.31712e6i	−0.293559	+	0.293559i
$246$	−2.23511e7	−	2.23511e7i	−1.50139	−	1.50139i
$247$		−	1.19056e6i		−	0.0790059i
$248$	−7.74516e6			−0.507779
$249$		−	9.07735e6i		−	0.587978i
$250$			6.08689e6i			0.389561i
$251$	−6.66311e6	−	6.66311e6i	−0.421362	−	0.421362i	0.464310	−	0.885673i	$-0.346302\pi$
$251$	−6.66311e6	−	6.66311e6i	−0.421362	−	0.421362i	−0.885673	+	0.464310i	$0.846302\pi$
$252$			2.69406e7i			1.68347i
$253$	−1.03087e7	−	1.03087e7i	−0.636566	−	0.636566i
$254$	5.72058e6	+	5.72058e6i	0.349091	+	0.349091i
$255$	−1.43797e7			−0.867219
$256$	1.04858e6			0.0625000
$257$	1.43242e7	−	1.43242e7i	0.843863	−	0.843863i	−0.145495	−	0.989359i	$-0.546478\pi$
$257$	1.43242e7	−	1.43242e7i	0.843863	−	0.843863i	0.989359	+	0.145495i	$0.0464776\pi$
$258$		−	3.87429e6i		−	0.225597i
$259$	−7.57700e6	+	2.60883e7i	−0.436112	+	1.50157i
$260$	−1.18613e6			−0.0674855
$261$	−3.61811e7	−	3.61811e7i	−2.03498	−	2.03498i
$262$			1.77909e7i			0.989225i
$263$		−	1.71223e7i		−	0.941226i	−0.882340	−	0.470613i	$-0.844033\pi$
$263$		−	1.71223e7i		−	0.941226i	0.882340	−	0.470613i	$-0.155967\pi$
$264$	−9.90879e6	+	9.90879e6i	−0.538529	+	0.538529i
$265$	−874024.	+	874024.i	−0.0469662	+	0.0469662i
$266$	3.49984e6			0.185953
$267$	525920.	−	525920.i	0.0276303	−	0.0276303i
$268$	256651.			0.0133333
$269$	2.49702e7			1.28282			0.641409	−	0.767199i	$-0.278350\pi$
$269$	2.49702e7			1.28282			0.641409	+	0.767199i	$0.278350\pi$
$270$		−	8.18966e6i		−	0.416078i
$271$	−7.37324e6			−0.370468			−0.185234	−	0.982694i	$-0.559304\pi$
$271$	−7.37324e6			−0.370468			−0.185234	+	0.982694i	$0.559304\pi$
$272$	−6.04659e6	+	6.04659e6i	−0.300472	+	0.300472i
$273$	−1.87655e7	−	1.87655e7i	−0.922302	−	0.922302i
$274$	1.57307e7	+	1.57307e7i	0.764708	+	0.764708i
$275$	−2.31454e7			−1.11293
$276$	9.79572e6	−	9.79572e6i	0.465918	−	0.465918i
$277$	−1.54655e7	−	1.54655e7i	−0.727656	−	0.727656i	0.242496	−	0.970152i	$-0.422034\pi$
$277$	−1.54655e7	−	1.54655e7i	−0.727656	−	0.727656i	−0.970152	+	0.242496i	$0.922034\pi$
$278$	−1.28468e7	+	1.28468e7i	−0.597943	+	0.597943i
$279$	4.74921e7	+	4.74921e7i	2.18680	+	2.18680i
$280$		−	3.48681e6i		−	0.158838i
$281$	−1.37634e7	+	1.37634e7i	−0.620307	+	0.620307i	−0.945610	−	0.325303i	$-0.894534\pi$
$281$	−1.37634e7	+	1.37634e7i	−0.620307	+	0.620307i	0.325303	+	0.945610i	$0.394534\pi$
$282$	−3.33755e7	+	3.33755e7i	−1.48826	+	1.48826i
$283$	2.51677e7	+	2.51677e7i	1.11041	+	1.11041i	0.993095	+	0.117317i	$0.0374294\pi$
$283$	2.51677e7	+	2.51677e7i	1.11041	+	1.11041i	0.117317	+	0.993095i	$0.462571\pi$
$284$		−	1.62256e7i		−	0.708348i
$285$	−1.98641e6			−0.0858095
$286$		−	9.42634e6i		−	0.402944i
$287$			6.25056e7i			2.64407i
$288$	−6.42970e6	−	6.42970e6i	−0.269162	−	0.269162i
$289$		−	4.55976e7i		−	1.88907i
$290$	4.68277e6	+	4.68277e6i	0.192004	+	0.192004i
$291$	2.43781e7	+	2.43781e7i	0.989285	+	0.989285i
$292$	−1.44247e7			−0.579371
$293$	−2.30610e7			−0.916800			−0.458400	−	0.888746i	$-0.651577\pi$
$293$	−2.30610e7			−0.916800			−0.458400	+	0.888746i	$0.651577\pi$
$294$	3.26015e7	−	3.26015e7i	1.28291	−	1.28291i
$295$		−	1.25348e6i		−	0.0488260i
$296$	−4.41795e6	−	8.03464e6i	−0.170351	−	0.309807i
$297$	6.50846e7			2.48433
$298$	9.43494e6	+	9.43494e6i	0.356525	+	0.356525i
$299$			9.31878e6i			0.348614i
$300$		−	2.19936e7i		−	0.814579i
$301$	−5.41730e6	+	5.41730e6i	−0.198648	+	0.198648i
$302$	−7.39769e6	+	7.39769e6i	−0.268581	+	0.268581i
$303$	5.14243e7			1.84859
$304$	−835279.	+	835279.i	−0.0297311	+	0.0297311i
$305$	2.07354e6			0.0730824
$306$	7.41535e7			2.58802
$307$			4.61207e7i			1.59397i	0.603998	+	0.796986i	$0.293574\pi$
$307$			4.61207e7i			1.59397i	−0.603998	+	0.796986i	$0.706426\pi$
$308$	2.77103e7			0.948394
$309$	−2.42214e7	+	2.42214e7i	−0.820962	+	0.820962i
$310$	−6.14671e6	−	6.14671e6i	−0.206328	−	0.206328i
$311$	−3.02071e7	−	3.02071e7i	−1.00422	−	1.00422i	−0.999991	−	0.00422761i	$-0.998654\pi$
$311$	−3.02071e7	−	3.02071e7i	−1.00422	−	1.00422i	−0.00422761	−	0.999991i	$-0.501346\pi$
$312$	8.95725e6			0.294924
$313$	3.49597e7	−	3.49597e7i	1.14008	−	1.14008i	0.151644	−	0.988435i	$-0.451543\pi$
$313$	3.49597e7	−	3.49597e7i	1.14008	−	1.14008i	0.988435	−	0.151644i	$-0.0484566\pi$
$314$	−1.12249e7	−	1.12249e7i	−0.362571	−	0.362571i
$315$	−2.13806e7	+	2.13806e7i	−0.684050	+	0.684050i
$316$	−1.22444e7	−	1.22444e7i	−0.388040	−	0.388040i
$317$			5.30770e7i			1.66621i	0.553118	+	0.833103i	$0.313438\pi$
$317$			5.30770e7i			1.66621i	−0.553118	+	0.833103i	$0.686562\pi$
$318$	6.60035e6	−	6.60035e6i	0.205251	−	0.205251i
$319$	−3.72148e7	+	3.72148e7i	−1.14642	+	1.14642i
$320$	832170.	+	832170.i	0.0253958	+	0.0253958i
$321$			3.16776e7i			0.957716i
$322$	−2.73941e7			−0.820520
$323$		−	9.63324e6i		−	0.285868i
$324$			2.52266e7i			0.741691i
$325$	1.04614e7	+	1.04614e7i	0.304747	+	0.304747i
$326$		−	3.74399e7i		−	1.08064i
$327$	−5.71697e7	−	5.71697e7i	−1.63502	−	1.63502i
$328$	−1.49177e7	−	1.49177e7i	−0.422747	−	0.422747i
$329$	9.33357e7			2.62096
$330$	−1.57276e7			−0.437644
$331$	2.31492e7	−	2.31492e7i	0.638341	−	0.638341i	−0.311805	−	0.950146i	$-0.600934\pi$
$331$	2.31492e7	−	2.31492e7i	0.638341	−	0.638341i	0.950146	+	0.311805i	$0.100934\pi$
$332$		−	6.05847e6i		−	0.165557i
$333$	−2.21769e7	+	7.63573e7i	−0.600577	+	2.06784i
$334$	−2.35366e7			−0.631692
$335$	203683.	+	203683.i	0.00541777	+	0.00541777i
$336$			2.63313e7i			0.694152i
$337$			4.65158e7i			1.21538i	0.794176	+	0.607688i	$0.207903\pi$
$337$			4.65158e7i			1.21538i	−0.794176	+	0.607688i	$0.792097\pi$
$338$	1.50467e7	−	1.50467e7i	0.389664	−	0.389664i
$339$	9.55545e6	−	9.55545e6i	0.245274	−	0.245274i
$340$	−9.59739e6			−0.244184
$341$	4.88489e7	−	4.88489e7i	1.23195	−	1.23195i
$342$	1.02436e7			0.256079
$343$	−2.80735e7			−0.695687
$344$		−	2.58581e6i		−	0.0635215i
$345$	1.55481e7			0.378636
$346$	1.28297e7	−	1.28297e7i	0.309732	−	0.309732i
$347$	2.63524e7	+	2.63524e7i	0.630712	+	0.630712i	0.948247	−	0.317535i	$-0.102855\pi$
$347$	2.63524e7	+	2.63524e7i	0.630712	+	0.630712i	−0.317535	+	0.948247i	$0.602855\pi$
$348$	−3.53628e7	−	3.53628e7i	−0.839091	−	0.839091i
$349$	−5.06841e6			−0.119233			−0.0596163	−	0.998221i	$-0.518988\pi$
$349$	−5.06841e6			−0.119233			−0.0596163	+	0.998221i	$0.518988\pi$
$350$	−3.07530e7	+	3.07530e7i	−0.717271	+	0.717271i
$351$	−2.94173e7	−	2.94173e7i	−0.680269	−	0.680269i
$352$	−6.61340e6	+	6.61340e6i	−0.151634	+	0.151634i
$353$	−4.65738e7	−	4.65738e7i	−1.05881	−	1.05881i	−0.998159	−	0.0606499i	$-0.980683\pi$
$353$	−4.65738e7	−	4.65738e7i	−1.05881	−	1.05881i	−0.0606499	−	0.998159i	$-0.519317\pi$
$354$			9.46587e6i			0.213379i
$355$	1.28770e7	−	1.28770e7i	0.287825	−	0.287825i
$356$	351013.	−	351013.i	0.00777989	−	0.00777989i
$357$	−1.51839e8	−	1.51839e8i	−3.33717	−	3.33717i
$358$			2.55587e7i			0.557045i
$359$	−7.26860e7			−1.57097			−0.785485	−	0.618881i	$-0.787586\pi$
$359$	−7.26860e7			−1.57097			−0.785485	+	0.618881i	$0.787586\pi$
$360$		−	1.02055e7i		−	0.218739i
$361$			4.57151e7i			0.971714i
$362$	3.89139e7	+	3.89139e7i	0.820312	+	0.820312i
$363$		−	4.00520e7i		−	0.837344i
$364$	−1.25246e7	−	1.25246e7i	−0.259693	−	0.259693i
$365$	−1.14477e7	−	1.14477e7i	−0.235418	−	0.235418i
$366$	−1.56587e7			−0.319384
$367$	−4.37075e7			−0.884214			−0.442107	−	0.896962i	$-0.645769\pi$
$367$	−4.37075e7			−0.884214			−0.442107	+	0.896962i	$0.645769\pi$
$368$	6.53793e6	−	6.53793e6i	0.131189	−	0.131189i
$369$			1.82946e8i			3.64120i
$370$	2.87027e6	−	9.88262e6i	0.0566654	−	0.195104i
$371$	−1.84581e7			−0.361465
$372$	4.64180e7	+	4.64180e7i	0.901690	+	0.901690i
$373$		−	1.34191e6i		−	0.0258582i	−0.999916	−	0.0129291i	$-0.995884\pi$
$373$		−	1.34191e6i		−	0.0258582i	0.999916	−	0.0129291i	$-0.00411557\pi$
$374$		−	7.62721e7i		−	1.45798i
$375$	3.64797e7	−	3.64797e7i	0.691764	−	0.691764i
$376$	−2.22757e7	+	2.22757e7i	−0.419052	+	0.419052i
$377$	3.36411e7			0.627835
$378$	8.64769e7	−	8.64769e7i	1.60112	−	1.60112i
$379$	6.56507e7			1.20593			0.602965	−	0.797768i	$-0.293986\pi$
$379$	6.56507e7			1.20593			0.602965	+	0.797768i	$0.293986\pi$
$380$	−1.32579e6			−0.0241615
$381$		−	6.85687e7i		−	1.23980i
$382$	−606252.			−0.0108759
$383$	−3.28569e7	+	3.28569e7i	−0.584831	+	0.584831i	−0.936227	−	0.351396i	$-0.885707\pi$
$383$	−3.28569e7	+	3.28569e7i	−0.584831	+	0.584831i	0.351396	+	0.936227i	$0.385707\pi$
$384$	−6.28429e6	−	6.28429e6i	−0.110984	−	0.110984i
$385$	2.19914e7	+	2.19914e7i	0.385364	+	0.385364i
$386$	−1.81967e7			−0.316396
$387$	−1.58558e7	+	1.58558e7i	−0.273561	+	0.273561i
$388$	1.62706e7	+	1.62706e7i	0.278554	+	0.278554i
$389$	−5.23441e7	+	5.23441e7i	−0.889240	+	0.889240i	−0.994450	−	0.105210i	$-0.966449\pi$
$389$	−5.23441e7	+	5.23441e7i	−0.889240	+	0.889240i	0.105210	+	0.994450i	$0.466449\pi$
$390$	7.10864e6	+	7.10864e6i	0.119838	+	0.119838i
$391$			7.54017e7i			1.26139i
$392$	2.17592e7	−	2.17592e7i	0.361230	−	0.361230i
$393$	1.06624e8	−	1.06624e8i	1.75662	−	1.75662i
$394$	−2.34265e6	−	2.34265e6i	−0.0383017	−	0.0383017i
$395$		−	1.94348e7i		−	0.315347i
$396$	8.11046e7			1.30605
$397$		−	6.62347e7i		−	1.05856i	−0.848448	−	0.529279i	$-0.822463\pi$
$397$		−	6.62347e7i		−	1.05856i	0.848448	−	0.529279i	$-0.177537\pi$
$398$		−	1.38423e7i		−	0.219563i
$399$	−2.09751e7	−	2.09751e7i	−0.330206	−	0.330206i
$400$		−	1.46791e7i		−	0.229362i
$401$	−8.05854e7	−	8.05854e7i	−1.24975	−	1.24975i	−0.955830	−	0.293921i	$-0.905040\pi$
$401$	−8.05854e7	−	8.05854e7i	−1.24975	−	1.24975i	−0.293921	−	0.955830i	$-0.594960\pi$
$402$	−1.53815e6	−	1.53815e6i	−0.0236767	−	0.0236767i
$403$	−4.41579e7			−0.674674
$404$	3.43220e7			0.520509
$405$	−2.00203e7	+	2.00203e7i	−0.301374	+	0.301374i
$406$			9.88934e7i			1.47771i
$407$	7.85388e7	+	2.28105e7i	1.16493	+	0.338339i
$408$	7.24764e7			1.06713
$409$	−3.32660e7	−	3.32660e7i	−0.486217	−	0.486217i	0.420893	−	0.907110i	$-0.361717\pi$
$409$	−3.32660e7	−	3.32660e7i	−0.486217	−	0.486217i	−0.907110	+	0.420893i	$0.861717\pi$
$410$		−	2.36780e7i		−	0.343552i
$411$		−	1.88553e8i		−	2.71586i
$412$	−1.61660e7	+	1.61660e7i	−0.231159	+	0.231159i
$413$	1.32358e7	−	1.32358e7i	0.187889	−	0.187889i
$414$	−8.01791e7			−1.12995
$415$	4.80812e6	−	4.80812e6i	0.0672715	−	0.0672715i
$416$	5.97831e6			0.0830421
$417$	1.53986e8			2.12360
$418$		−	1.05363e7i		−	0.144264i
$419$	−7.07684e7			−0.962049			−0.481025	−	0.876707i	$-0.659735\pi$
$419$	−7.07684e7			−0.962049			−0.481025	+	0.876707i	$0.659735\pi$
$420$	−2.08970e7	+	2.08970e7i	−0.282057	+	0.282057i
$421$	2.97249e7	+	2.97249e7i	0.398359	+	0.398359i	0.877654	−	0.479295i	$-0.159108\pi$
$421$	2.97249e7	+	2.97249e7i	0.398359	+	0.398359i	−0.479295	+	0.877654i	$0.659108\pi$
$422$	−5.56721e7	−	5.56721e7i	−0.740799	−	0.740799i
$423$	2.73182e8			3.60937
$424$	4.40526e6	−	4.40526e6i	0.0577928	−	0.0577928i
$425$	8.46470e7	+	8.46470e7i	1.10267	+	1.10267i
$426$	−9.72429e7	+	9.72429e7i	−1.25785	+	1.25785i
$427$	2.18951e7	+	2.18951e7i	0.281231	+	0.281231i
$428$			2.11425e7i			0.269665i
$429$	−5.64936e7	+	5.64936e7i	−0.715529	+	0.715529i
$430$	2.05215e6	−	2.05215e6i	0.0258109	−	0.0258109i
$431$	3.03868e7	+	3.03868e7i	0.379536	+	0.379536i	0.870935	−	0.491399i	$-0.163514\pi$
$431$	3.03868e7	+	3.03868e7i	0.379536	+	0.379536i	−0.491399	+	0.870935i	$0.663514\pi$
$432$			4.12775e7i			0.511991i
$433$	−6.15738e7			−0.758459			−0.379230	−	0.925303i	$-0.623811\pi$
$433$	−6.15738e7			−0.758459			−0.379230	+	0.925303i	$0.623811\pi$
$434$		−	1.29810e8i		−	1.58795i
$435$		−	5.61293e7i		−	0.681901i
$436$	−3.81566e7	−	3.81566e7i	−0.460373	−	0.460373i
$437$			1.04160e7i			0.124812i
$438$	8.64493e7	+	8.64493e7i	1.02882	+	1.02882i
$439$	−3.85795e6	−	3.85795e6i	−0.0455998	−	0.0455998i	0.683939	−	0.729539i	$-0.260265\pi$
$439$	−3.85795e6	−	3.85795e6i	−0.0455998	−	0.0455998i	−0.729539	+	0.683939i	$0.760265\pi$
$440$	−1.04970e7			−0.123228
$441$	−2.66847e8			−3.11134
$442$	−3.44738e7	+	3.44738e7i	−0.399230	+	0.399230i
$443$			1.25764e8i			1.44659i	0.690540	+	0.723294i	$0.257373\pi$
$443$			1.25764e8i			1.44659i	−0.690540	+	0.723294i	$0.742627\pi$
$444$	−2.16754e7	+	7.46304e7i	−0.247638	+	0.852642i
$445$	557142.			0.00632246
$446$	2.67626e7	+	2.67626e7i	0.301664	+	0.301664i
$447$		−	1.13090e8i		−	1.26620i
$448$			1.75742e7i			0.195453i
$449$	−7.61525e7	+	7.61525e7i	−0.841289	+	0.841289i	−0.989027	−	0.147738i	$-0.952801\pi$
$449$	−7.61525e7	+	7.61525e7i	−0.841289	+	0.841289i	0.147738	+	0.989027i	$0.452801\pi$
$450$	−9.00102e7	+	9.00102e7i	−0.987766	+	0.987766i
$451$	1.88173e8			2.05129
$452$	6.37757e6	−	6.37757e6i	0.0690621	−	0.0690621i
$453$	8.86711e7			0.953866
$454$	−3.24537e7			−0.346814
$455$		−	1.98796e7i		−	0.211044i
$456$	1.00119e7			0.105590
$457$	9.65895e7	−	9.65895e7i	1.01200	−	1.01200i	0.0120753	−	0.999927i	$-0.496156\pi$
$457$	9.65895e7	−	9.65895e7i	1.01200	−	1.01200i	0.999927	−	0.0120753i	$-0.00384377\pi$
$458$	4.49244e7	+	4.49244e7i	0.467612	+	0.467612i
$459$	−2.38026e8	−	2.38026e8i	−2.46142	−	2.46142i
$460$	1.03773e7			0.106613
$461$	−9.69727e7	+	9.69727e7i	−0.989798	+	0.989798i	−0.999948	−	0.0101503i	$-0.996769\pi$
$461$	−9.69727e7	+	9.69727e7i	−0.989798	+	0.989798i	0.0101503	+	0.999948i	$0.496769\pi$
$462$	−1.66072e8	−	1.66072e8i	−1.68411	−	1.68411i
$463$	−9.79275e7	+	9.79275e7i	−0.986647	+	0.986647i	−0.999912	−	0.0132652i	$-0.995777\pi$
$463$	−9.79275e7	+	9.79275e7i	−0.986647	+	0.986647i	0.0132652	+	0.999912i	$0.495777\pi$
$464$	−2.36021e7	−	2.36021e7i	−0.236264	−	0.236264i
$465$			7.36764e7i			0.732773i
$466$	5.57440e7	−	5.57440e7i	0.550859	−	0.550859i
$467$	−1.87796e7	+	1.87796e7i	−0.184389	+	0.184389i	−0.793265	−	0.608876i	$-0.791621\pi$
$467$	−1.87796e7	+	1.87796e7i	−0.184389	+	0.184389i	0.608876	+	0.793265i	$0.291621\pi$
$468$	−3.66581e7	−	3.66581e7i	−0.357628	−	0.357628i
$469$			4.30149e6i			0.0416966i
$470$	−3.53569e7			−0.340549
$471$			1.34545e8i			1.28767i
$472$			6.31778e6i			0.0600812i
$473$	1.63088e7	+	1.63088e7i	0.154112	+	0.154112i
$474$			1.46766e8i			1.37813i
$475$	1.16932e7	+	1.16932e7i	0.109107	+	0.109107i
$476$	−1.01341e8	−	1.01341e8i	−0.939651	−	0.939651i
$477$	−5.40247e7			−0.497779
$478$	−9.57900e7			−0.877075
$479$	1.23867e8	−	1.23867e8i	1.12707	−	1.12707i	0.136416	−	0.990652i	$-0.456442\pi$
$479$	1.23867e8	−	1.23867e8i	1.12707	−	1.12707i	0.990652	−	0.136416i	$-0.0435583\pi$
$480$		−	9.97466e6i		−	0.0901933i
$481$	−2.51883e7	−	4.58084e7i	−0.226342	−	0.411633i
$482$	1.09456e8			0.977455
$483$	1.64177e8	+	1.64177e8i	1.45704	+	1.45704i
$484$		−	2.67318e7i		−	0.235772i
$485$			2.58254e7i			0.226371i
$486$	3.36426e7	−	3.36426e7i	0.293077	−	0.293077i
$487$	7.87511e7	−	7.87511e7i	0.681820	−	0.681820i	−0.278590	−	0.960410i	$-0.589867\pi$
$487$	7.87511e7	−	7.87511e7i	0.681820	−	0.681820i	0.960410	+	0.278590i	$0.0898672\pi$
$488$	−1.04511e7			−0.0899292
$489$	−2.24383e8	+	2.24383e8i	−1.91895	+	1.91895i
$490$	3.45370e7			0.293559
$491$	−6.40332e7			−0.540954			−0.270477	−	0.962726i	$-0.587181\pi$
$491$	−6.40332e7			−0.540954			−0.270477	+	0.962726i	$0.587181\pi$
$492$			1.78809e8i			1.50139i
$493$	2.72202e8			2.27170
$494$	−4.76223e6	+	4.76223e6i	−0.0395029	+	0.0395029i
$495$	6.43662e7	+	6.43662e7i	0.530692	+	0.530692i
$496$	3.09806e7	+	3.09806e7i	0.253890	+	0.253890i
$497$	2.71943e8			2.21518
$498$	−3.63094e7	+	3.63094e7i	−0.293989	+	0.293989i
$499$	−5.36911e7	−	5.36911e7i	−0.432116	−	0.432116i	0.457232	−	0.889348i	$-0.348841\pi$
$499$	−5.36911e7	−	5.36911e7i	−0.432116	−	0.432116i	−0.889348	+	0.457232i	$0.848841\pi$
$500$	2.43476e7	−	2.43476e7i	0.194781	−	0.194781i
$501$	1.41059e8	+	1.41059e8i	1.12173	+	1.12173i
$502$			5.33049e7i			0.421362i
$503$	6.28814e7	−	6.28814e7i	0.494104	−	0.494104i	−0.415493	−	0.909597i	$-0.636391\pi$
$503$	6.28814e7	−	6.28814e7i	0.494104	−	0.494104i	0.909597	+	0.415493i	$0.136391\pi$
$504$	1.07762e8	−	1.07762e8i	0.841736	−	0.841736i
$505$	2.72386e7	+	2.72386e7i	0.211500	+	0.211500i
$506$			8.24698e7i			0.636566i
$507$	−1.80354e8			−1.38389
$508$		−	4.57646e7i		−	0.349091i
$509$		−	1.94762e7i		−	0.147690i	−0.997270	−	0.0738450i	$-0.976473\pi$
$509$		−	1.94762e7i		−	0.147690i	0.997270	−	0.0738450i	$-0.0235270\pi$
$510$	5.75187e7	+	5.75187e7i	0.433609	+	0.433609i
$511$		−	2.41759e8i		−	1.81184i
$512$	−4.19430e6	−	4.19430e6i	−0.0312500	−	0.0312500i
$513$	−3.28810e7	−	3.28810e7i	−0.243553	−	0.243553i
$514$	−1.14594e8			−0.843863
$515$	−2.56593e7			−0.187855
$516$	−1.54972e7	+	1.54972e7i	−0.112798	+	0.112798i
$517$		−	2.80987e8i		−	2.03336i
$518$	1.34661e8	−	7.40453e7i	0.968843	−	0.532731i
$519$	−1.53780e8			−1.10002
$520$	4.74450e6	+	4.74450e6i	0.0337428	+	0.0337428i
$521$			2.36152e8i			1.66985i	0.550361	+	0.834926i	$0.314490\pi$
$521$			2.36152e8i			1.66985i	−0.550361	+	0.834926i	$0.685510\pi$
$522$			2.89449e8i			2.03498i
$523$	−1.57326e7	+	1.57326e7i	−0.109976	+	0.109976i	−0.759953	−	0.649978i	$-0.774778\pi$
$523$	−1.57326e7	+	1.57326e7i	−0.109976	+	0.109976i	0.649978	+	0.759953i	$0.274778\pi$
$524$	7.11638e7	−	7.11638e7i	0.494613	−	0.494613i
$525$	3.68615e8			2.54739
$526$	−6.84891e7	+	6.84891e7i	−0.470613	+	0.470613i
$527$	−3.57298e8			−2.44118
$528$	7.92703e7			0.538529
$529$			6.65071e7i			0.449264i
$530$	6.99219e6			0.0469662
$531$	3.87396e7	−	3.87396e7i	0.258745	−	0.258745i
$532$	−1.39994e7	−	1.39994e7i	−0.0929765	−	0.0929765i
$533$	−8.50513e7	−	8.50513e7i	−0.561693	−	0.561693i
$534$	−4.20736e6			−0.0276303
$535$	−1.67791e7	+	1.67791e7i	−0.109574	+	0.109574i
$536$	−1.02660e6	−	1.02660e6i	−0.00666666	−	0.00666666i
$537$	1.53178e8	−	1.53178e8i	0.989173	−	0.989173i
$538$	−9.98808e7	−	9.98808e7i	−0.641409	−	0.641409i
$539$			2.74471e8i			1.75279i
$540$	−3.27586e7	+	3.27586e7i	−0.208039	+	0.208039i
$541$	−4.47245e7	+	4.47245e7i	−0.282458	+	0.282458i	−0.834089	−	0.551631i	$-0.814006\pi$
$541$	−4.47245e7	+	4.47245e7i	−0.282458	+	0.282458i	0.551631	+	0.834089i	$0.314006\pi$
$542$	2.94930e7	+	2.94930e7i	0.185234	+	0.185234i
$543$		−	4.66435e8i		−	2.91334i
$544$	4.83728e7			0.300472
$545$		−	6.05636e7i		−	0.374130i
$546$			1.50124e8i			0.922302i
$547$	−1.12602e7	−	1.12602e7i	−0.0687994	−	0.0687994i	0.671870	−	0.740669i	$-0.265491\pi$
$547$	−1.12602e7	−	1.12602e7i	−0.0687994	−	0.0687994i	−0.740669	+	0.671870i	$0.765491\pi$
$548$		−	1.25845e8i		−	0.764708i
$549$	6.40842e7	+	6.40842e7i	0.387288	+	0.387288i
$550$	9.25818e7	+	9.25818e7i	0.556464	+	0.556464i
$551$	3.76022e7			0.224780
$552$	−7.83658e7			−0.465918
$553$	2.05218e8	−	2.05218e8i	1.21350	−	1.21350i
$554$			1.23724e8i			0.727656i
$555$	−7.64301e7	+	4.20261e7i	−0.447080	+	0.245833i
$556$	1.02774e8			0.597943
$557$	−666709.	−	666709.i	−0.00385807	−	0.00385807i	0.705175	−	0.709033i	$-0.250868\pi$
$557$	−666709.	−	666709.i	−0.00385807	−	0.00385807i	−0.709033	+	0.705175i	$0.750868\pi$
$558$		−	3.79937e8i		−	2.18680i
$559$		−	1.47426e7i		−	0.0843994i
$560$	−1.39473e7	+	1.39473e7i	−0.0794190	+	0.0794190i
$561$	−4.57111e8	+	4.57111e8i	−2.58901	+	2.58901i
$562$	1.10107e8			0.620307
$563$	3.84697e7	−	3.84697e7i	0.215572	−	0.215572i	−0.591057	−	0.806630i	$-0.701289\pi$
$563$	3.84697e7	−	3.84697e7i	0.215572	−	0.215572i	0.806630	+	0.591057i	$0.201289\pi$
$564$	2.67004e8			1.48826
$565$	1.01227e7			0.0561244
$566$		−	2.01341e8i		−	1.11041i
$567$	−4.22799e8			−2.31945
$568$	−6.49026e7	+	6.49026e7i	−0.354174	+	0.354174i
$569$	−4.73069e7	−	4.73069e7i	−0.256796	−	0.256796i	0.566954	−	0.823750i	$-0.308122\pi$
$569$	−4.73069e7	−	4.73069e7i	−0.256796	−	0.256796i	−0.823750	+	0.566954i	$0.808122\pi$
$570$	7.94566e6	+	7.94566e6i	0.0429047	+	0.0429047i
$571$	−1.28755e8			−0.691603			−0.345801	−	0.938308i	$-0.612393\pi$
$571$	−1.28755e8			−0.691603			−0.345801	+	0.938308i	$0.612393\pi$
$572$	−3.77054e7	+	3.77054e7i	−0.201472	+	0.201472i
$573$	3.63337e6	+	3.63337e6i	0.0193128	+	0.0193128i
$574$	2.50022e8	−	2.50022e8i	1.32203	−	1.32203i
$575$	−9.15253e7	−	9.15253e7i	−0.481435	−	0.481435i
$576$			5.14376e7i			0.269162i
$577$	−2.34994e7	+	2.34994e7i	−0.122329	+	0.122329i	−0.765621	−	0.643292i	$-0.777568\pi$
$577$	−2.34994e7	+	2.34994e7i	−0.122329	+	0.122329i	0.643292	+	0.765621i	$0.277568\pi$
$578$	−1.82390e8	+	1.82390e8i	−0.944536	+	0.944536i
$579$	1.09056e8	+	1.09056e8i	0.561841	+	0.561841i
$580$		−	3.74622e7i		−	0.192004i
$581$	1.01541e8			0.517739
$582$		−	1.95025e8i		−	0.989285i
$583$			5.55681e7i			0.280427i
$584$	5.76986e7	+	5.76986e7i	0.289686	+	0.289686i
$585$		−	5.81851e7i		−	0.290632i
$586$	9.22439e7	+	9.22439e7i	0.458400	+	0.458400i
$587$	916543.	+	916543.i	0.00453146	+	0.00453146i	0.709369	−	0.704837i	$-0.248980\pi$
$587$	916543.	+	916543.i	0.00453146	+	0.00453146i	−0.704837	+	0.709369i	$0.748980\pi$
$588$	−2.60812e8			−1.28291
$589$	−4.93574e7			−0.241549
$590$	−5.01391e6	+	5.01391e6i	−0.0244130	+	0.0244130i
$591$			2.80798e7i			0.136029i
$592$	−1.44667e7	+	4.98104e7i	−0.0697278	+	0.240079i
$593$	−1.48033e8			−0.709893			−0.354947	−	0.934887i	$-0.615501\pi$
$593$	−1.48033e8			−0.709893			−0.354947	+	0.934887i	$0.615501\pi$
$594$	−2.60338e8	−	2.60338e8i	−1.24216	−	1.24216i
$595$		−	1.60853e8i		−	0.763622i
$596$		−	7.54795e7i		−	0.356525i
$597$	−8.29591e7	+	8.29591e7i	−0.389889	+	0.389889i
$598$	3.72751e7	−	3.72751e7i	0.174307	−	0.174307i
$599$	3.44674e7			0.160372			0.0801860	−	0.996780i	$-0.474449\pi$
$599$	3.44674e7			0.160372			0.0801860	+	0.996780i	$0.474449\pi$
$600$	−8.79745e7	+	8.79745e7i	−0.407289	+	0.407289i
$601$	7.48082e7			0.344608			0.172304	−	0.985044i	$-0.444879\pi$
$601$	7.48082e7			0.344608			0.172304	+	0.985044i	$0.444879\pi$
$602$	4.33384e7			0.198648
$603$			1.25899e7i			0.0574211i
$604$	5.91815e7			0.268581
$605$	2.12149e7	−	2.12149e7i	0.0958019	−	0.0958019i
$606$	−2.05697e8	−	2.05697e8i	−0.924295	−	0.924295i
$607$	−1.30480e8	−	1.30480e8i	−0.583417	−	0.583417i	0.352424	−	0.935841i	$-0.385358\pi$
$607$	−1.30480e8	−	1.30480e8i	−0.583417	−	0.583417i	−0.935841	+	0.352424i	$0.885358\pi$
$608$	6.68223e6			0.0297311
$609$	5.92684e8	−	5.92684e8i	2.62405	−	2.62405i
$610$	−8.29416e6	−	8.29416e6i	−0.0365412	−	0.0365412i
$611$	−1.27002e8	+	1.27002e8i	−0.556784	+	0.556784i
$612$	−2.96614e8	−	2.96614e8i	−1.29401	−	1.29401i
$613$		−	2.50188e8i		−	1.08614i	−0.839687	−	0.543070i	$-0.817262\pi$
$613$		−	2.50188e8i		−	1.08614i	0.839687	−	0.543070i	$-0.182738\pi$
$614$	1.84483e8	−	1.84483e8i	0.796986	−	0.796986i
$615$	−1.41906e8	+	1.41906e8i	−0.610064	+	0.610064i
$616$	−1.10841e8	−	1.10841e8i	−0.474197	−	0.474197i
$617$			3.52798e6i			0.0150200i	0.999972	+	0.00751001i	$0.00239053\pi$
$617$			3.52798e6i			0.0150200i	−0.999972	+	0.00751001i	$0.997609\pi$
$618$	1.93771e8			0.820962
$619$			2.69767e8i			1.13741i	0.822542	+	0.568704i	$0.192555\pi$
$619$			2.69767e8i			1.13741i	−0.822542	+	0.568704i	$0.807445\pi$
$620$			4.91737e7i			0.206328i
$621$	2.57368e8	+	2.57368e8i	1.07468	+	1.07468i
$622$			2.41657e8i			1.00422i
$623$	5.88302e6	+	5.88302e6i	0.0243297	+	0.0243297i
$624$	−3.58290e7	−	3.58290e7i	−0.147462	−	0.147462i
$625$	−1.85341e8			−0.759155
$626$	−2.79678e8			−1.14008
$627$	−6.31455e7	+	6.31455e7i	−0.256177	+	0.256177i
$628$			8.97991e7i			0.362571i
$629$	−2.03808e8	−	3.70653e8i	−0.818974	−	1.48941i
$630$	1.71045e8			0.684050
$631$	−1.29882e8	−	1.29882e8i	−0.516965	−	0.516965i	0.399687	−	0.916652i	$-0.369119\pi$
$631$	−1.29882e8	−	1.29882e8i	−0.516965	−	0.516965i	−0.916652	+	0.399687i	$0.869119\pi$
$632$			9.79554e7i			0.388040i
$633$			6.67304e8i			2.63095i
$634$	2.12308e8	−	2.12308e8i	0.833103	−	0.833103i
$635$	3.63197e7	−	3.63197e7i	0.141847	−	0.141847i
$636$	−5.28028e7			−0.205251
$637$	1.24057e8	−	1.24057e8i	0.479957	−	0.479957i
$638$	2.97718e8			1.14642
$639$	7.95944e8			3.05056
$640$		−	6.65736e6i		−	0.0253958i
$641$	−2.27258e8			−0.862868			−0.431434	−	0.902145i	$-0.641992\pi$
$641$	−2.27258e8			−0.862868			−0.431434	+	0.902145i	$0.641992\pi$
$642$	1.26710e8	−	1.26710e8i	0.478858	−	0.478858i
$643$	9.27143e7	+	9.27143e7i	0.348750	+	0.348750i	0.859644	−	0.510894i	$-0.170686\pi$
$643$	9.27143e7	+	9.27143e7i	0.348750	+	0.348750i	−0.510894	+	0.859644i	$0.670686\pi$
$644$	1.09576e8	+	1.09576e8i	0.410260	+	0.410260i
$645$	−2.45977e7			−0.0916675
$646$	−3.85330e7	+	3.85330e7i	−0.142934	+	0.142934i
$647$	3.30009e8	+	3.30009e8i	1.21847	+	1.21847i	0.968169	+	0.250297i	$0.0805283\pi$
$647$	3.30009e8	+	3.30009e8i	1.21847	+	1.21847i	0.250297	+	0.968169i	$0.419472\pi$
$648$	1.00906e8	−	1.00906e8i	0.370845	−	0.370845i
$649$	−3.98464e7	−	3.98464e7i	−0.145766	−	0.145766i
$650$		−	8.36911e7i		−	0.304747i
$651$	−7.77970e8	+	7.77970e8i	−2.81981	+	2.81981i
$652$	−1.49760e8	+	1.49760e8i	−0.540321	+	0.540321i
$653$	2.35670e8	+	2.35670e8i	0.846379	+	0.846379i	0.989679	−	0.143301i	$-0.0457716\pi$
$653$	2.35670e8	+	2.35670e8i	0.846379	+	0.846379i	−0.143301	+	0.989679i	$0.545772\pi$
$654$			4.57357e8i			1.63502i
$655$	1.12954e8			0.401955
$656$			1.19342e8i			0.422747i
$657$		−	7.07598e8i		−	2.49511i
$658$	−3.73343e8	−	3.73343e8i	−1.31048	−	1.31048i
$659$			1.36427e8i			0.476697i	0.971180	+	0.238349i	$0.0766061\pi$
$659$			1.36427e8i			0.476697i	−0.971180	+	0.238349i	$0.923394\pi$
$660$	6.29105e7	+	6.29105e7i	0.218822	+	0.218822i
$661$	2.96985e8	+	2.96985e8i	1.02832	+	1.02832i	0.999587	+	0.0287375i	$0.00914869\pi$
$661$	2.96985e8	+	2.96985e8i	1.02832	+	1.02832i	0.0287375	+	0.999587i	$0.490851\pi$
$662$	−1.85194e8			−0.638341
$663$	4.13214e8			1.41786
$664$	−2.42339e7	+	2.42339e7i	−0.0827787	+	0.0827787i
$665$		−	2.22203e7i		−	0.0755589i
$666$	3.94137e8	−	2.16721e8i	1.33421	−	0.733634i
$667$	−2.94321e8			−0.991845
$668$	9.41466e7	+	9.41466e7i	0.315846	+	0.315846i
$669$		−	3.20785e8i		−	1.07136i
$670$		−	1.62946e6i		−	0.00541777i
$671$	6.59151e7	−	6.59151e7i	0.218181	−	0.218181i
$672$	1.05325e8	−	1.05325e8i	0.347076	−	0.347076i
$673$	−2.17070e8			−0.712122			−0.356061	−	0.934463i	$-0.615881\pi$
$673$	−2.17070e8			−0.712122			−0.356061	+	0.934463i	$0.615881\pi$
$674$	1.86063e8	−	1.86063e8i	0.607688	−	0.607688i
$675$	5.77849e8			1.87890
$676$	−1.20373e8			−0.389664
$677$		−	3.95391e8i		−	1.27427i	−0.770753	−	0.637134i	$-0.780120\pi$
$677$		−	3.95391e8i		−	1.27427i	0.770753	−	0.637134i	$-0.219880\pi$
$678$	−7.64436e7			−0.245274
$679$	−2.72697e8	+	2.72697e8i	−0.871107	+	0.871107i
$680$	3.83896e7	+	3.83896e7i	0.122092	+	0.122092i
$681$	1.94500e8	+	1.94500e8i	0.615856	+	0.615856i
$682$	−3.90791e8			−1.23195
$683$	−2.52678e8	+	2.52678e8i	−0.793060	+	0.793060i	−0.981990	−	0.188930i	$-0.939498\pi$
$683$	−2.52678e8	+	2.52678e8i	−0.793060	+	0.793060i	0.188930	+	0.981990i	$0.439498\pi$
$684$	−4.09744e7	−	4.09744e7i	−0.128040	−	0.128040i
$685$	9.98734e7	−	9.98734e7i	0.310726	−	0.310726i
$686$	1.12294e8	+	1.12294e8i	0.347844	+	0.347844i
$687$		−	5.38478e8i		−	1.66072i
$688$	−1.03432e7	+	1.03432e7i	−0.0317608	+	0.0317608i
$689$	2.51160e7	−	2.51160e7i	0.0767878	−	0.0767878i
$690$	−6.21926e7	−	6.21926e7i	−0.189318	−	0.189318i
$691$		−	1.06180e8i		−	0.321817i	−0.986969	−	0.160909i	$-0.948558\pi$
$691$		−	1.06180e8i		−	0.321817i	0.986969	−	0.160909i	$-0.0514425\pi$
$692$	−1.02637e8			−0.309732
$693$			1.35932e9i			4.08434i
$694$		−	2.10819e8i		−	0.630712i
$695$	8.15636e7	+	8.15636e7i	0.242964	+	0.242964i
$696$			2.82903e8i			0.839091i
$697$	−6.88182e8	−	6.88182e8i	−2.03238	−	2.03238i
$698$	2.02736e7	+	2.02736e7i	0.0596163	+	0.0596163i
$699$	−6.68166e8			−1.95638
$700$	2.46024e8			0.717271
$701$	−1.62231e8	+	1.62231e8i	−0.470954	+	0.470954i	−0.902223	−	0.431269i	$-0.858066\pi$
$701$	−1.62231e8	+	1.62231e8i	−0.470954	+	0.470954i	0.431269	+	0.902223i	$0.358066\pi$
$702$			2.35338e8i			0.680269i
$703$	−2.81542e7	−	5.12021e7i	−0.0810358	−	0.147374i
$704$	5.29072e7			0.151634
$705$	2.11899e8	+	2.11899e8i	0.604731	+	0.604731i
$706$			3.72590e8i			1.05881i
$707$			5.75240e8i			1.62776i
$708$	3.78635e7	−	3.78635e7i	0.106689	−	0.106689i
$709$	−4.17151e8	+	4.17151e8i	−1.17045	+	1.17045i	−0.188354	+	0.982101i	$0.560315\pi$
$709$	−4.17151e8	+	4.17151e8i	−1.17045	+	1.17045i	−0.982101	+	0.188354i	$0.939685\pi$
$710$	−1.03016e8			−0.287825
$711$	6.00647e8	−	6.00647e8i	1.67113	−	1.67113i
$712$	−2.80811e6			−0.00777989
$713$	3.86332e8			1.06584
$714$			1.21471e9i			3.33717i
$715$	−5.98474e7			−0.163730
$716$	1.02235e8	−	1.02235e8i	0.278522	−	0.278522i
$717$	5.74085e8	+	5.74085e8i	1.55747	+	1.55747i
$718$	2.90744e8	+	2.90744e8i	0.785485	+	0.785485i
$719$	−3.99121e8			−1.07379			−0.536893	−	0.843650i	$-0.680402\pi$
$719$	−3.99121e8			−1.07379			−0.536893	+	0.843650i	$0.680402\pi$
$720$	−4.08219e7	+	4.08219e7i	−0.109369	+	0.109369i
$721$	−2.70944e8	−	2.70944e8i	−0.722891	−	0.722891i
$722$	1.82861e8	−	1.82861e8i	0.485857	−	0.485857i
$723$	−6.55985e8	−	6.55985e8i	−1.73572	−	1.73572i
$724$		−	3.11311e8i		−	0.820312i
$725$	−3.30409e8	+	3.30409e8i	−0.867038	+	0.867038i
$726$	−1.60208e8	+	1.60208e8i	−0.418672	+	0.418672i
$727$	−1.25783e8	−	1.25783e8i	−0.327354	−	0.327354i	0.524226	−	0.851579i	$-0.324355\pi$
$727$	−1.25783e8	−	1.25783e8i	−0.327354	−	0.327354i	−0.851579	+	0.524226i	$0.824355\pi$
$728$			1.00197e8i			0.259693i
$729$	1.71441e8			0.442519
$730$			9.15815e7i			0.235418i
$731$		−	1.19288e8i		−	0.305383i
$732$	6.26349e7	+	6.26349e7i	0.159692	+	0.159692i
$733$			2.52560e8i			0.641288i	0.947200	+	0.320644i	$0.103899\pi$
$733$			2.52560e8i			0.641288i	−0.947200	+	0.320644i	$0.896101\pi$
$734$	1.74830e8	+	1.74830e8i	0.442107	+	0.442107i
$735$	−2.06986e8	−	2.06986e8i	−0.521289	−	0.521289i
$736$	−5.23035e7			−0.131189
$737$	1.29496e7			0.0323486
$738$	7.31784e8	−	7.31784e8i	1.82060	−	1.82060i
$739$		−	3.21313e8i		−	0.796151i	−0.917353	−	0.398075i	$-0.869678\pi$
$739$		−	3.21313e8i		−	0.796151i	0.917353	−	0.398075i	$-0.130322\pi$
$740$	−5.10116e7	+	2.80494e7i	−0.125885	+	0.0692195i
$741$	5.70816e7			0.140295
$742$	7.38325e7	+	7.38325e7i	0.180732	+	0.180732i
$743$			3.85535e8i			0.939933i	0.882684	+	0.469966i	$0.155734\pi$
$743$			3.85535e8i			0.939933i	−0.882684	+	0.469966i	$0.844266\pi$
$744$		−	3.71344e8i		−	0.901690i
$745$	5.99020e7	−	5.99020e7i	0.144868	−	0.144868i
$746$	−5.36766e6	+	5.36766e6i	−0.0129291	+	0.0129291i
$747$	2.97197e8			0.712988
$748$	−3.05088e8	+	3.05088e8i	−0.728989	+	0.728989i
$749$	−3.54350e8			−0.843309
$750$	−2.91838e8			−0.691764
$751$		−	8.28947e7i		−	0.195707i	−0.995201	−	0.0978536i	$-0.968802\pi$
$751$		−	8.28947e7i		−	0.195707i	0.995201	−	0.0978536i	$-0.0311977\pi$
$752$	1.78206e8			0.419052
$753$	3.19465e8	−	3.19465e8i	0.748235	−	0.748235i
$754$	−1.34564e8	−	1.34564e8i	−0.313918	−	0.313918i
$755$	4.69676e7	+	4.69676e7i	0.109133	+	0.109133i
$756$	−6.91815e8			−1.60112
$757$	5.76800e8	−	5.76800e8i	1.32965	−	1.32965i	0.423977	−	0.905673i	$-0.360634\pi$
$757$	5.76800e8	−	5.76800e8i	1.32965	−	1.32965i	0.905673	−	0.423977i	$-0.139366\pi$
$758$	−2.62603e8	−	2.62603e8i	−0.602965	−	0.602965i
$759$	4.94255e8	−	4.94255e8i	1.13038	−	1.13038i
$760$	5.30315e6	+	5.30315e6i	0.0120807	+	0.0120807i
$761$			5.00582e8i			1.13585i	0.823080	+	0.567925i	$0.192254\pi$
$761$			5.00582e8i			1.13585i	−0.823080	+	0.567925i	$0.807746\pi$
$762$	−2.74275e8	+	2.74275e8i	−0.619899	+	0.619899i
$763$	6.39508e8	−	6.39508e8i	1.43970	−	1.43970i
$764$	2.42501e6	+	2.42501e6i	0.00543793	+	0.00543793i
$765$		−	4.70797e8i		−	1.05160i
$766$	2.62855e8			0.584831
$767$			3.60200e7i			0.0798283i
$768$			5.02743e7i			0.110984i
$769$	−2.60637e7	−	2.60637e7i	−0.0573136	−	0.0573136i	0.677869	−	0.735183i	$-0.262904\pi$
$769$	−2.60637e7	−	2.60637e7i	−0.0573136	−	0.0573136i	−0.735183	+	0.677869i	$0.762904\pi$
$770$		−	1.75931e8i		−	0.385364i
$771$	6.86780e8	+	6.86780e8i	1.49849	+	1.49849i
$772$	7.27869e7	+	7.27869e7i	0.158198	+	0.158198i
$773$	4.14243e7			0.0896843			0.0448421	−	0.998994i	$-0.485722\pi$
$773$	4.14243e7			0.0896843			0.0448421	+	0.998994i	$0.485722\pi$
$774$	1.26846e8			0.273561
$775$	4.33702e8	−	4.33702e8i	0.931721	−	0.931721i
$776$		−	1.30165e8i		−	0.278554i
$777$	−1.25081e9	−	3.63281e8i	−2.66642	−	0.774427i
$778$	4.18753e8			0.889240
$779$	−9.50657e7	−	9.50657e7i	−0.201100	−	0.201100i
$780$		−	5.68692e7i		−	0.119838i
$781$		−	8.18684e8i		−	1.71855i
$782$	3.01607e8	−	3.01607e8i	0.630697	−	0.630697i
$783$	9.29105e8	−	9.29105e8i	1.93544	−	1.93544i
$784$	−1.74073e8			−0.361230
$785$	−7.12663e7	+	7.12663e7i	−0.147325	+	0.147325i
$786$	−8.52992e8			−1.75662
$787$	−8.44946e8			−1.73342			−0.866712	−	0.498808i	$-0.833771\pi$
$787$	−8.44946e8			−1.73342			−0.866712	+	0.498808i	$0.833771\pi$
$788$			1.87412e7i			0.0383017i
$789$	8.20932e8			1.67138
$790$	−7.77393e7	+	7.77393e7i	−0.157674	+	0.157674i
$791$	1.06889e8	+	1.06889e8i	0.215974	+	0.215974i
$792$	−3.24418e8	−	3.24418e8i	−0.653025	−	0.653025i
$793$	−5.95853e7			−0.119487
$794$	−2.64939e8	+	2.64939e8i	−0.529279	+	0.529279i
$795$	−4.19053e7	−	4.19053e7i	−0.0834004	−	0.0834004i
$796$	−5.53692e7	+	5.53692e7i	−0.109781	+	0.109781i
$797$	2.86356e8	+	2.86356e8i	0.565628	+	0.565628i	0.930901	−	0.365273i	$-0.119024\pi$
$797$	2.86356e8	+	2.86356e8i	0.565628	+	0.565628i	−0.365273	+	0.930901i	$0.619024\pi$
$798$			1.67801e8i			0.330206i
$799$	−1.02762e9	+	1.02762e9i	−2.01461	+	2.01461i
$800$	−5.87166e7	+	5.87166e7i	−0.114681	+	0.114681i
$801$	1.72189e7	+	1.72189e7i	0.0335048	+	0.0335048i
$802$			6.44683e8i			1.24975i
$803$	−7.27813e8			−1.40564
$804$			1.23052e7i			0.0236767i
$805$			1.73924e8i			0.333404i
$806$	1.76632e8	+	1.76632e8i	0.337337	+	0.337337i
$807$			1.19720e9i			2.27797i
$808$	−1.37288e8	−	1.37288e8i	−0.260255	−	0.260255i
$809$	−3.25438e8	−	3.25438e8i	−0.614642	−	0.614642i	0.329510	−	0.944152i	$-0.393117\pi$
$809$	−3.25438e8	−	3.25438e8i	−0.614642	−	0.614642i	−0.944152	+	0.329510i	$0.893117\pi$
$810$	1.60162e8			0.301374
$811$	3.04862e8			0.571533			0.285766	−	0.958299i	$-0.407752\pi$
$811$	3.04862e8			0.571533			0.285766	+	0.958299i	$0.407752\pi$
$812$	3.95574e8	−	3.95574e8i	0.738855	−	0.738855i
$813$		−	3.53512e8i		−	0.657859i
$814$	−2.22913e8	−	4.05397e8i	−0.413297	−	0.751636i
$815$	−2.37704e8			−0.439101
$816$	−2.89906e8	−	2.89906e8i	−0.533564	−	0.533564i
$817$		−	1.64785e7i		−	0.0302170i
$818$			2.66128e8i			0.486217i
$819$	6.14392e8	−	6.14392e8i	1.11839	−	1.11839i
$820$	−9.47119e7	+	9.47119e7i	−0.171776	+	0.171776i
$821$	2.85667e8			0.516215			0.258107	−	0.966116i	$-0.416901\pi$
$821$	2.85667e8			0.516215			0.258107	+	0.966116i	$0.416901\pi$
$822$	−7.54212e8	+	7.54212e8i	−1.35793	+	1.35793i
$823$	1.98288e8			0.355711			0.177856	−	0.984057i	$-0.443084\pi$
$823$	1.98288e8			0.355711			0.177856	+	0.984057i	$0.443084\pi$
$824$	1.29328e8			0.231159
$825$		−	1.10972e9i		−	1.97629i
$826$	−1.05887e8			−0.187889
$827$	2.05501e8	−	2.05501e8i	0.363326	−	0.363326i	−0.501710	−	0.865036i	$-0.667295\pi$
$827$	2.05501e8	−	2.05501e8i	0.363326	−	0.363326i	0.865036	+	0.501710i	$0.167295\pi$
$828$	3.20716e8	+	3.20716e8i	0.564976	+	0.564976i
$829$	2.08470e8	+	2.08470e8i	0.365915	+	0.365915i	0.865985	−	0.500070i	$-0.166692\pi$
$829$	2.08470e8	+	2.08470e8i	0.365915	+	0.365915i	−0.500070	+	0.865985i	$0.666692\pi$
$830$	−3.84650e7			−0.0672715
$831$	7.41500e8	−	7.41500e8i	1.29214	−	1.29214i
$832$	−2.39132e7	−	2.39132e7i	−0.0415211	−	0.0415211i
$833$	1.00379e9	−	1.00379e9i	1.73663	−	1.73663i
$834$	−6.15942e8	−	6.15942e8i	−1.06180	−	1.06180i
$835$			1.49433e8i			0.256677i
$836$	−4.21450e7	+	4.21450e7i	−0.0721319	+	0.0721319i
$837$	−1.21956e9	+	1.21956e9i	−2.07983	+	2.07983i
$838$	2.83074e8	+	2.83074e8i	0.481025	+	0.481025i
$839$			6.21484e6i			0.0105231i	0.999986	+	0.00526156i	$0.00167481\pi$
$839$			6.21484e6i			0.0105231i	−0.999986	+	0.00526156i	$0.998325\pi$
$840$	1.67176e8			0.282057
$841$			4.67684e8i			0.786258i
$842$		−	2.37800e8i		−	0.398359i
$843$	−6.59890e8	−	6.59890e8i	−1.10151	−	1.10151i
$844$			4.45377e8i			0.740799i
$845$	−9.55306e7	−	9.55306e7i	−0.158333	−	0.158333i
$846$	−1.09273e9	−	1.09273e9i	−1.80468	−	1.80468i
$847$	4.48027e8			0.737317
$848$	−3.52420e7			−0.0577928
$849$	−1.20667e9	+	1.20667e9i	−1.97182	+	1.97182i
$850$		−	6.77176e8i		−	1.10267i
$851$	2.20369e8	+	4.00771e8i	0.357571	+	0.650292i
$852$	7.77943e8			1.25785
$853$	4.62405e7	+	4.62405e7i	0.0745033	+	0.0745033i	0.743377	−	0.668873i	$-0.233223\pi$
$853$	4.62405e7	+	4.62405e7i	0.0745033	+	0.0745033i	−0.668873	+	0.743377i	$0.733223\pi$
$854$		−	1.75161e8i		−	0.281231i
$855$		−	6.50362e7i		−	0.104053i
$856$	8.45699e7	−	8.45699e7i	0.134833	−	0.134833i
$857$	4.53174e8	−	4.53174e8i	0.719983	−	0.719983i	−0.248619	−	0.968601i	$-0.579977\pi$
$857$	4.53174e8	−	4.53174e8i	0.719983	−	0.719983i	0.968601	+	0.248619i	$0.0799766\pi$
$858$	4.51949e8			0.715529
$859$	−2.61191e8	+	2.61191e8i	−0.412077	+	0.412077i	−0.882462	−	0.470384i	$-0.844115\pi$
$859$	−2.61191e8	+	2.61191e8i	−0.412077	+	0.412077i	0.470384	+	0.882462i	$0.344115\pi$
$860$	−1.64172e7			−0.0258109
$861$	−2.99685e9			−4.69521
$862$		−	2.43095e8i		−	0.379536i
$863$	−3.63141e6			−0.00564993			−0.00282496	−	0.999996i	$-0.500899\pi$
$863$	−3.63141e6			−0.00564993			−0.00282496	+	0.999996i	$0.500899\pi$
$864$	1.65110e8	−	1.65110e8i	0.255996	−	0.255996i
$865$	−8.14549e7	−	8.14549e7i	−0.125855	−	0.125855i
$866$	2.46295e8	+	2.46295e8i	0.379230	+	0.379230i
$867$	2.18619e9			3.35452
$868$	−5.19238e8	+	5.19238e8i	−0.793976	+	0.793976i
$869$	−6.17807e8	−	6.17807e8i	−0.941442	−	0.941442i
$870$	−2.24517e8	+	2.24517e8i	−0.340951	+	0.340951i
$871$	−5.85304e6	−	5.85304e6i	−0.00885782	−	0.00885782i
$872$			3.05253e8i			0.460373i
$873$	−7.98151e8	+	7.98151e8i	−1.19962	+	1.19962i
$874$	4.16641e7	−	4.16641e7i	0.0624062	−	0.0624062i
$875$	4.08067e8	+	4.08067e8i	0.609127	+	0.609127i
$876$		−	6.91594e8i		−	1.02882i
$877$	1.06195e9			1.57436			0.787182	−	0.616720i	$-0.211539\pi$
$877$	1.06195e9			1.57436			0.787182	+	0.616720i	$0.211539\pi$
$878$			3.08636e7i			0.0455998i
$879$		−	1.10566e9i		−	1.62801i
$880$	4.19882e7	+	4.19882e7i	0.0616139	+	0.0616139i
$881$			1.98143e8i			0.289768i	0.989449	+	0.144884i	$0.0462809\pi$
$881$			1.98143e8i			0.289768i	−0.989449	+	0.144884i	$0.953719\pi$
$882$	1.06739e9	+	1.06739e9i	1.55567	+	1.55567i
$883$	4.28057e8	+	4.28057e8i	0.621755	+	0.621755i	0.945980	−	0.324225i	$-0.105103\pi$
$883$	4.28057e8	+	4.28057e8i	0.621755	+	0.621755i	−0.324225	+	0.945980i	$0.605103\pi$
$884$	2.75791e8			0.399230
$885$	6.00984e7			0.0867028
$886$	5.03056e8	−	5.03056e8i	0.723294	−	0.723294i
$887$			1.05971e9i			1.51851i	0.650794	+	0.759254i	$0.274436\pi$
$887$			1.05971e9i			1.51851i	−0.650794	+	0.759254i	$0.725564\pi$
$888$	3.85223e8	−	2.11820e8i	0.550140	−	0.302502i
$889$	7.67019e8			1.09169
$890$	−2.22857e6	−	2.22857e6i	−0.00316123	−	0.00316123i
$891$			1.27284e9i			1.79945i
$892$		−	2.14101e8i		−	0.301664i
$893$	−1.41956e8	+	1.41956e8i	−0.199342	+	0.199342i
$894$	−4.52361e8	+	4.52361e8i	−0.633100	+	0.633100i
$895$	1.62271e8			0.226346
$896$	7.02969e7	−	7.02969e7i	0.0977265	−	0.0977265i
$897$	−4.46792e8			−0.619053
$898$	6.09220e8			0.841289
$899$		−	1.39467e9i		−	1.91952i
$900$	7.20082e8			0.987766
$901$	2.03223e8	−	2.03223e8i	0.277842	−	0.277842i
$902$	−7.52691e8	−	7.52691e8i	−1.02565	−	1.02565i
$903$	−2.59734e8	−	2.59734e8i	−0.352749	−	0.352749i
$904$	−5.10205e7			−0.0690621
$905$	2.47063e8	−	2.47063e8i	0.333320	−	0.333320i
$906$	−3.54684e8	−	3.54684e8i	−0.476933	−	0.476933i
$907$	−9.30457e7	+	9.30457e7i	−0.124702	+	0.124702i	−0.766704	−	0.642001i	$-0.778104\pi$
$907$	−9.30457e7	+	9.30457e7i	−0.124702	+	0.124702i	0.642001	+	0.766704i	$0.278104\pi$
$908$	1.29815e8	+	1.29815e8i	0.173407	+	0.173407i
$909$			1.68366e9i			2.24162i
$910$	−7.95183e7	+	7.95183e7i	−0.105522	+	0.105522i
$911$	7.90763e8	−	7.90763e8i	1.04590	−	1.04590i	0.0470081	−	0.998895i	$-0.485031\pi$
$911$	7.90763e8	−	7.90763e8i	1.04590	−	1.04590i	0.998895	−	0.0470081i	$-0.0149687\pi$
$912$	−4.00477e7	−	4.00477e7i	−0.0527950	−	0.0527950i
$913$		−	3.05687e8i		−	0.401666i
$914$	−7.72716e8			−1.01200
$915$			9.94165e7i			0.129776i
$916$		−	3.59395e8i		−	0.467612i
$917$	1.19271e9	+	1.19271e9i	1.54678	+	1.54678i
$918$			1.90421e9i			2.46142i
$919$	−5.09751e7	−	5.09751e7i	−0.0656768	−	0.0656768i	0.673505	−	0.739182i	$-0.264788\pi$
$919$	−5.09751e7	−	5.09751e7i	−0.0656768	−	0.0656768i	−0.739182	+	0.673505i	$0.764788\pi$
$920$	−4.15090e7	−	4.15090e7i	−0.0533064	−	0.0533064i
$921$	−2.21127e9			−2.83050
$922$	7.75781e8			0.989798
$923$	−3.70033e8	+	3.70033e8i	−0.470582	+	0.470582i
$924$			1.32858e9i			1.68411i
$925$	6.97302e8	+	2.02522e8i	0.881040	+	0.255886i
$926$	7.83420e8			0.986647
$927$	−7.93018e8	−	7.93018e8i	−0.995506	−	0.995506i
$928$			1.88817e8i			0.236264i
$929$			2.02690e8i			0.252805i	0.991979	+	0.126402i	$0.0403431\pi$
$929$			2.02690e8i			0.252805i	−0.991979	+	0.126402i	$0.959657\pi$
$930$	2.94706e8	−	2.94706e8i	0.366387	−	0.366387i
$931$	1.38664e8	−	1.38664e8i	0.171836	−	0.171836i
$932$	−4.45952e8			−0.550859
$933$	1.44829e9	−	1.44829e9i	1.78324	−	1.78324i
$934$	1.50237e8			0.184389
$935$	−4.84248e8			−0.592424
$936$			2.93264e8i			0.357628i
$937$	−8.66135e8			−1.05285			−0.526425	−	0.850221i	$-0.676468\pi$
$937$	−8.66135e8			−1.05285			−0.526425	+	0.850221i	$0.676468\pi$
$938$	1.72060e7	−	1.72060e7i	0.0208483	−	0.0208483i
$939$	1.67615e9	+	1.67615e9i	2.02450	+	2.02450i
$940$	1.41427e8	+	1.41427e8i	0.170275	+	0.170275i
$941$	−1.09171e7			−0.0131020			−0.00655101	−	0.999979i	$-0.502085\pi$
$941$	−1.09171e7			−0.0131020			−0.00655101	+	0.999979i	$0.502085\pi$
$942$	5.38181e8	−	5.38181e8i	0.643836	−	0.643836i
$943$	7.44102e8	+	7.44102e8i	0.887355	+	0.887355i
$944$	2.52711e7	−	2.52711e7i	0.0300406	−	0.0300406i
$945$	−5.49038e8	−	5.49038e8i	−0.650589	−	0.650589i
$946$		−	1.30470e8i		−	0.154112i
$947$	−7.08191e7	+	7.08191e7i	−0.0833874	+	0.0833874i	−0.747570	−	0.664183i	$-0.768780\pi$
$947$	−7.08191e7	+	7.08191e7i	−0.0833874	+	0.0833874i	0.664183	+	0.747570i	$0.268780\pi$
$948$	5.87062e8	−	5.87062e8i	0.689064	−	0.689064i
$949$	3.28961e8	+	3.28961e8i	0.384898	+	0.384898i
$950$		−	9.35454e7i		−	0.109107i
$951$	−2.54479e9			−2.95877
$952$			8.10732e8i			0.939651i
$953$		−	1.00792e9i		−	1.16452i	−0.813004	−	0.582258i	$-0.802169\pi$
$953$		−	1.00792e9i		−	1.16452i	0.813004	−	0.582258i	$-0.197831\pi$
$954$	2.16099e8	+	2.16099e8i	0.248890	+	0.248890i
$955$			3.84907e6i			0.00441922i
$956$	3.83160e8	+	3.83160e8i	0.438537	+	0.438537i
$957$	−1.78427e9	−	1.78427e9i	−2.03576	−	2.03576i
$958$	−9.90938e8			−1.12707
$959$	2.10918e9			2.39143
$960$	−3.98986e7	+	3.98986e7i	−0.0450967	+	0.0450967i
$961$			9.43168e8i			1.06272i
$962$	−8.24801e7	+	2.83987e8i	−0.0926455	+	0.318987i
$963$	−1.03714e9			−1.16134
$964$	−4.37822e8	−	4.37822e8i	−0.488728	−	0.488728i
$965$			1.15530e8i			0.128562i
$966$		−	1.31342e9i		−	1.45704i
$967$	−3.23114e8	+	3.23114e8i	−0.357336	+	0.357336i	−0.862830	−	0.505494i	$-0.831310\pi$
$967$	−3.23114e8	+	3.23114e8i	−0.357336	+	0.357336i	0.505494	+	0.862830i	$0.331310\pi$
$968$	−1.06927e8	+	1.06927e8i	−0.117886	+	0.117886i
$969$	4.61869e8			0.507630
$970$	1.03301e8	−	1.03301e8i	0.113186	−	0.113186i
$971$	−1.81592e9			−1.98354			−0.991768	−	0.128051i	$-0.959128\pi$
$971$	−1.81592e9			−1.98354			−0.991768	+	0.128051i	$0.959128\pi$
$972$	−2.69141e8			−0.293077
$973$			1.72250e9i			1.86992i
$974$	−6.30008e8			−0.681820
$975$	−5.01574e8	+	5.01574e8i	−0.541155	+	0.541155i
$976$	4.18042e7	+	4.18042e7i	0.0449646	+	0.0449646i
$977$	−1.02769e9	−	1.02769e9i	−1.10200	−	1.10200i	−0.994170	−	0.107826i	$-0.965611\pi$
$977$	−1.02769e9	−	1.02769e9i	−1.10200	−	1.10200i	−0.107826	−	0.994170i	$-0.534389\pi$
$978$	1.79507e9			1.91895
$979$	1.77108e7	−	1.77108e7i	0.0188751	−	0.0188751i
$980$	−1.38148e8	−	1.38148e8i	−0.146780	−	0.146780i
$981$	1.87176e9	−	1.87176e9i	1.98264	−	1.98264i
$982$	2.56133e8	+	2.56133e8i	0.270477	+	0.270477i
$983$		−	5.85007e8i		−	0.615886i	−0.951405	−	0.307943i	$-0.900359\pi$
$983$		−	5.85007e8i		−	0.615886i	0.951405	−	0.307943i	$-0.0996407\pi$
$984$	7.15234e8	−	7.15234e8i	0.750694	−	0.750694i
$985$	−1.48734e7	+	1.48734e7i	−0.0155633	+	0.0155633i
$986$	−1.08881e9	−	1.08881e9i	−1.13585	−	1.13585i
$987$			4.47501e9i			4.65417i
$988$	3.80978e7			0.0395029
$989$			1.28981e8i			0.133333i
$990$		−	5.14929e8i		−	0.530692i
$991$	6.53824e8	+	6.53824e8i	0.671799	+	0.671799i	0.958131	−	0.286331i	$-0.0924358\pi$
$991$	6.53824e8	+	6.53824e8i	0.671799	+	0.671799i	−0.286331	+	0.958131i	$0.592436\pi$
$992$		−	2.47845e8i		−	0.253890i
$993$	1.10990e9	+	1.10990e9i	1.13353	+	1.13353i
$994$	−1.08777e9	−	1.08777e9i	−1.10759	−	1.10759i
$995$	−8.78841e7			−0.0892157
$996$	2.90475e8			0.293989
$997$	−1.22387e9	+	1.22387e9i	−1.23495	+	1.23495i	−0.272917	+	0.962038i	$0.587988\pi$
$997$	−1.22387e9	+	1.22387e9i	−1.23495	+	1.23495i	−0.962038	+	0.272917i	$0.912012\pi$
$998$			4.29529e8i			0.432116i
$999$	−1.96080e9	−	5.69488e8i	−1.96669	−	0.571200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.31.10	✓	20
37.6	odd	4	inner	74.7.d.b.43.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.10	✓	20	1.1	even	1	trivial
74.7.d.b.43.1	yes	20	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)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 4.00000i) q^{2} +47.9453i q^{3} +32.0000i q^{4} +(-25.3958 + 25.3958i) q^{5} +(191.781 - 191.781i) q^{6} -536.323 q^{7} +(128.000 - 128.000i) q^{8} -1569.75 q^{9} +O(q^{10})\)	\(q+(-4.00000 - 4.00000i) q^{2} +47.9453i q^{3} +32.0000i q^{4} +(-25.3958 + 25.3958i) q^{5} +(191.781 - 191.781i) q^{6} -536.323 q^{7} +(128.000 - 128.000i) q^{8} -1569.75 q^{9} +203.167 q^{10} +1614.60i q^{11} -1534.25 q^{12} +(729.774 - 729.774i) q^{13} +(2145.29 + 2145.29i) q^{14} +(-1217.61 - 1217.61i) q^{15} -1024.00 q^{16} +(5904.88 - 5904.88i) q^{17} +(6279.01 + 6279.01i) q^{18} +(815.702 - 815.702i) q^{19} +(-812.666 - 812.666i) q^{20} -25714.2i q^{21} +(6458.40 - 6458.40i) q^{22} +(-6384.70 + 6384.70i) q^{23} +(6137.00 + 6137.00i) q^{24} +14335.1i q^{25} -5838.19 q^{26} -40310.1i q^{27} -17162.3i q^{28} +(23048.9 + 23048.9i) q^{29} +9740.88i q^{30} +(-30254.5 - 30254.5i) q^{31} +(4096.00 + 4096.00i) q^{32} -77412.4 q^{33} -47239.0 q^{34} +(13620.4 - 13620.4i) q^{35} -50232.0i q^{36} +(14127.7 - 48642.9i) q^{37} -6525.62 q^{38} +(34989.2 + 34989.2i) q^{39} +6501.33i q^{40} -116545. i q^{41} +(-102857. + 102857. i) q^{42} +(10100.8 - 10100.8i) q^{43} -51667.2 q^{44} +(39865.1 - 39865.1i) q^{45} +51077.6 q^{46} -174029. q^{47} -49096.0i q^{48} +169993. q^{49} +(57340.4 - 57340.4i) q^{50} +(283111. + 283111. i) q^{51} +(23352.8 + 23352.8i) q^{52} +34416.1 q^{53} +(-161240. + 161240. i) q^{54} +(-41004.1 - 41004.1i) q^{55} +(-68649.3 + 68649.3i) q^{56} +(39109.1 + 39109.1i) q^{57} -184392. i q^{58} +(-24678.8 + 24678.8i) q^{59} +(38963.5 - 38963.5i) q^{60} +(-40824.4 - 40824.4i) q^{61} +242036. i q^{62} +841894. q^{63} -32768.0i q^{64} +37066.4i q^{65} +(309650. + 309650. i) q^{66} -8020.34i q^{67} +(188956. + 188956. i) q^{68} +(-306116. - 306116. i) q^{69} -108963. q^{70} -507051. q^{71} +(-200928. + 200928. i) q^{72} +450770. i q^{73} +(-251082. + 138061. i) q^{74} -687301. q^{75} +(26102.5 + 26102.5i) q^{76} -865946. i q^{77} -279914. i q^{78} +(-382638. + 382638. i) q^{79} +(26005.3 - 26005.3i) q^{80} +788330. q^{81} +(-466178. + 466178. i) q^{82} -189327. q^{83} +822853. q^{84} +299918. i q^{85} -80806.5 q^{86} +(-1.10509e6 + 1.10509e6i) q^{87} +(206669. + 206669. i) q^{88} +(-10969.2 - 10969.2i) q^{89} -318921. q^{90} +(-391395. + 391395. i) q^{91} +(-204310. - 204310. i) q^{92} +(1.45056e6 - 1.45056e6i) q^{93} +(696116. + 696116. i) q^{94} +41430.9i q^{95} +(-196384. + 196384. i) q^{96} +(508457. - 508457. i) q^{97} +(-679973. - 679973. i) q^{98} -2.53452e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

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