LMFDB - Embedded newform 74.7.d.b.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$20$
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			43.7
Root			$-21.6219i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.7.d.b.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 4.00000i) q^{2} +18.6219i q^{3} -32.0000i q^{4} +(-151.370 - 151.370i) q^{5} +(-74.4876 - 74.4876i) q^{6} -414.903 q^{7} +(128.000 + 128.000i) q^{8} +382.225 q^{9} +O(q^{10})$	\(q+(-4.00000 + 4.00000i) q^{2} +18.6219i q^{3} -32.0000i q^{4} +(-151.370 - 151.370i) q^{5} +(-74.4876 - 74.4876i) q^{6} -414.903 q^{7} +(128.000 + 128.000i) q^{8} +382.225 q^{9} +1210.96 q^{10} -20.0436i q^{11} +595.901 q^{12} +(1177.78 + 1177.78i) q^{13} +(1659.61 - 1659.61i) q^{14} +(2818.80 - 2818.80i) q^{15} -1024.00 q^{16} +(1848.12 + 1848.12i) q^{17} +(-1528.90 + 1528.90i) q^{18} +(-4079.55 - 4079.55i) q^{19} +(-4843.85 + 4843.85i) q^{20} -7726.29i q^{21} +(80.1744 + 80.1744i) q^{22} +(8631.54 + 8631.54i) q^{23} +(-2383.60 + 2383.60i) q^{24} +30201.0i q^{25} -9422.26 q^{26} +20693.1i q^{27} +13276.9i q^{28} +(8617.96 - 8617.96i) q^{29} +22550.4i q^{30} +(35684.4 - 35684.4i) q^{31} +(4096.00 - 4096.00i) q^{32} +373.250 q^{33} -14785.0 q^{34} +(62804.0 + 62804.0i) q^{35} -12231.2i q^{36} +(-23166.7 + 45044.7i) q^{37} +32636.4 q^{38} +(-21932.5 + 21932.5i) q^{39} -38750.8i q^{40} +25121.4i q^{41} +(30905.1 + 30905.1i) q^{42} +(37607.1 + 37607.1i) q^{43} -641.395 q^{44} +(-57857.5 - 57857.5i) q^{45} -69052.3 q^{46} +125968. q^{47} -19068.8i q^{48} +54495.6 q^{49} +(-120804. - 120804. i) q^{50} +(-34415.5 + 34415.5i) q^{51} +(37689.0 - 37689.0i) q^{52} -210515. q^{53} +(-82772.5 - 82772.5i) q^{54} +(-3034.01 + 3034.01i) q^{55} +(-53107.6 - 53107.6i) q^{56} +(75969.0 - 75969.0i) q^{57} +68943.7i q^{58} +(115685. + 115685. i) q^{59} +(-90201.7 - 90201.7i) q^{60} +(257354. - 257354. i) q^{61} +285476. i q^{62} -158586. q^{63} +32768.0i q^{64} -356563. i q^{65} +(-1493.00 + 1493.00i) q^{66} -221990. i q^{67} +(59139.8 - 59139.8i) q^{68} +(-160736. + 160736. i) q^{69} -502432. q^{70} +639306. q^{71} +(48924.8 + 48924.8i) q^{72} -276091. i q^{73} +(-87512.1 - 272846. i) q^{74} -562400. q^{75} +(-130546. + 130546. i) q^{76} +8316.15i q^{77} -175460. i q^{78} +(-59670.7 - 59670.7i) q^{79} +(155003. + 155003. i) q^{80} -106703. q^{81} +(-100486. - 100486. i) q^{82} +858002. q^{83} -247241. q^{84} -559501. i q^{85} -300857. q^{86} +(160483. + 160483. i) q^{87} +(2565.58 - 2565.58i) q^{88} +(-724017. + 724017. i) q^{89} +462860. q^{90} +(-488666. - 488666. i) q^{91} +(276209. - 276209. i) q^{92} +(664512. + 664512. i) q^{93} +(-503871. + 503871. i) q^{94} +1.23505e6i q^{95} +(76275.3 + 76275.3i) q^{96} +(119162. + 119162. i) q^{97} +(-217982. + 217982. i) q^{98} -7661.16i 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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

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

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
$3$			18.6219i			0.689700i	0.938658	+	0.344850i	$0.112070\pi$
$3$			18.6219i			0.689700i	−0.938658	+	0.344850i	$0.887930\pi$
$4$		−	32.0000i		−	0.500000i
$5$	−151.370	−	151.370i	−1.21096	−	1.21096i	−0.970710	−	0.240252i	$-0.922770\pi$
$5$	−151.370	−	151.370i	−1.21096	−	1.21096i	−0.240252	−	0.970710i	$-0.577230\pi$
$6$	−74.4876	−	74.4876i	−0.344850	−	0.344850i
$7$	−414.903			−1.20963			−0.604815	−	0.796366i	$-0.706753\pi$
$7$	−414.903			−1.20963			−0.604815	+	0.796366i	$0.706753\pi$
$8$	128.000	+	128.000i	0.250000	+	0.250000i
$9$	382.225			0.524314
$10$	1210.96			1.21096
$11$		−	20.0436i		−	0.0150591i	−0.999972	−	0.00752953i	$-0.997603\pi$
$11$		−	20.0436i		−	0.0150591i	0.999972	−	0.00752953i	$-0.00239675\pi$
$12$	595.901			0.344850
$13$	1177.78	+	1177.78i	0.536087	+	0.536087i	0.922377	−	0.386291i	$-0.126244\pi$
$13$	1177.78	+	1177.78i	0.536087	+	0.536087i	−0.386291	+	0.922377i	$0.626244\pi$
$14$	1659.61	−	1659.61i	0.604815	−	0.604815i
$15$	2818.80	−	2818.80i	0.835201	−	0.835201i
$16$	−1024.00			−0.250000
$17$	1848.12	+	1848.12i	0.376169	+	0.376169i	0.869718	−	0.493549i	$-0.164301\pi$
$17$	1848.12	+	1848.12i	0.376169	+	0.376169i	−0.493549	+	0.869718i	$0.664301\pi$
$18$	−1528.90	+	1528.90i	−0.262157	+	0.262157i
$19$	−4079.55	−	4079.55i	−0.594773	−	0.594773i	0.344144	−	0.938917i	$-0.388169\pi$
$19$	−4079.55	−	4079.55i	−0.594773	−	0.594773i	−0.938917	+	0.344144i	$0.888169\pi$
$20$	−4843.85	+	4843.85i	−0.605481	+	0.605481i
$21$		−	7726.29i		−	0.834282i
$22$	80.1744	+	80.1744i	0.00752953	+	0.00752953i
$23$	8631.54	+	8631.54i	0.709422	+	0.709422i	0.966414	−	0.256991i	$-0.0827312\pi$
$23$	8631.54	+	8631.54i	0.709422	+	0.709422i	−0.256991	+	0.966414i	$0.582731\pi$
$24$	−2383.60	+	2383.60i	−0.172425	+	0.172425i
$25$			30201.0i			1.93286i
$26$	−9422.26			−0.536087
$27$			20693.1i			1.05132i
$28$			13276.9i			0.604815i
$29$	8617.96	−	8617.96i	0.353355	−	0.353355i	−0.508002	−	0.861356i	$-0.669616\pi$
$29$	8617.96	−	8617.96i	0.353355	−	0.353355i	0.861356	+	0.508002i	$0.169616\pi$
$30$			22550.4i			0.835201i
$31$	35684.4	−	35684.4i	1.19783	−	1.19783i	0.223010	−	0.974816i	$-0.428412\pi$
$31$	35684.4	−	35684.4i	1.19783	−	1.19783i	0.974816	−	0.223010i	$-0.0715883\pi$
$32$	4096.00	−	4096.00i	0.125000	−	0.125000i
$33$	373.250			0.0103862
$34$	−14785.0			−0.376169
$35$	62804.0	+	62804.0i	1.46482	+	1.46482i
$36$		−	12231.2i		−	0.262157i
$37$	−23166.7	+	45044.7i	−0.457361	+	0.889281i
$37$	−23166.7	+	45044.7i	−0.457361	+	0.889281i
$38$	32636.4			0.594773
$39$	−21932.5	+	21932.5i	−0.369739	+	0.369739i
$40$		−	38750.8i		−	0.605481i
$41$			25121.4i			0.364496i	0.983253	+	0.182248i	$0.0583374\pi$
$41$			25121.4i			0.364496i	−0.983253	+	0.182248i	$0.941663\pi$
$42$	30905.1	+	30905.1i	0.417141	+	0.417141i
$43$	37607.1	+	37607.1i	0.473004	+	0.473004i	0.902885	−	0.429882i	$-0.141445\pi$
$43$	37607.1	+	37607.1i	0.473004	+	0.473004i	−0.429882	+	0.902885i	$0.641445\pi$
$44$	−641.395			−0.00752953
$45$	−57857.5	−	57857.5i	−0.634924	−	0.634924i
$46$	−69052.3			−0.709422
$47$	125968.			1.21329			0.606646	−	0.794972i	$-0.292514\pi$
$47$	125968.			1.21329			0.606646	+	0.794972i	$0.292514\pi$
$48$		−	19068.8i		−	0.172425i
$49$	54495.6			0.463205
$50$	−120804.	−	120804.i	−0.966431	−	0.966431i
$51$	−34415.5	+	34415.5i	−0.259444	+	0.259444i
$52$	37689.0	−	37689.0i	0.268043	−	0.268043i
$53$	−210515.			−1.41402			−0.707011	−	0.707203i	$-0.749957\pi$
$53$	−210515.			−1.41402			−0.707011	+	0.707203i	$0.749957\pi$
$54$	−82772.5	−	82772.5i	−0.525660	−	0.525660i
$55$	−3034.01	+	3034.01i	−0.0182360	+	0.0182360i
$56$	−53107.6	−	53107.6i	−0.302408	−	0.302408i
$57$	75969.0	−	75969.0i	0.410215	−	0.410215i
$58$			68943.7i			0.353355i
$59$	115685.	+	115685.i	0.563277	+	0.563277i	0.930237	−	0.366960i	$-0.119601\pi$
$59$	115685.	+	115685.i	0.563277	+	0.563277i	−0.366960	+	0.930237i	$0.619601\pi$
$60$	−90201.7	−	90201.7i	−0.417601	−	0.417601i
$61$	257354.	−	257354.i	1.13382	−	1.13382i	0.144278	−	0.989537i	$-0.453914\pi$
$61$	257354.	−	257354.i	1.13382	−	1.13382i	0.989537	−	0.144278i	$-0.0460859\pi$
$62$			285476.i			1.19783i
$63$	−158586.			−0.634226
$64$			32768.0i			0.125000i
$65$		−	356563.i		−	1.29836i
$66$	−1493.00	+	1493.00i	−0.00519312	+	0.00519312i
$67$		−	221990.i		−	0.738090i	−0.929412	−	0.369045i	$-0.879685\pi$
$67$		−	221990.i		−	0.738090i	0.929412	−	0.369045i	$-0.120315\pi$
$68$	59139.8	−	59139.8i	0.188085	−	0.188085i
$69$	−160736.	+	160736.i	−0.489289	+	0.489289i
$70$	−502432.			−1.46482
$71$	639306.			1.78621			0.893107	−	0.449843i	$-0.148520\pi$
$71$	639306.			1.78621			0.893107	+	0.449843i	$0.148520\pi$
$72$	48924.8	+	48924.8i	0.131078	+	0.131078i
$73$		−	276091.i		−	0.709714i	−0.934921	−	0.354857i	$-0.884530\pi$
$73$		−	276091.i		−	0.709714i	0.934921	−	0.354857i	$-0.115470\pi$
$74$	−87512.1	−	272846.i	−0.215960	−	0.673321i
$75$	−562400.			−1.33310
$76$	−130546.	+	130546.i	−0.297387	+	0.297387i
$77$			8316.15i			0.0182159i
$78$		−	175460.i		−	0.369739i
$79$	−59670.7	−	59670.7i	−0.121026	−	0.121026i	0.644000	−	0.765026i	$-0.277274\pi$
$79$	−59670.7	−	59670.7i	−0.121026	−	0.121026i	−0.765026	+	0.644000i	$0.777274\pi$
$80$	155003.	+	155003.i	0.302741	+	0.302741i
$81$	−106703.			−0.200781
$82$	−100486.	−	100486.i	−0.182248	−	0.182248i
$83$	858002.			1.50056			0.750281	−	0.661119i	$-0.229918\pi$
$83$	858002.			1.50056			0.750281	+	0.661119i	$0.229918\pi$
$84$	−247241.			−0.417141
$85$		−	559501.i		−	0.911054i
$86$	−300857.			−0.473004
$87$	160483.	+	160483.i	0.243709	+	0.243709i
$88$	2565.58	−	2565.58i	0.00376476	−	0.00376476i
$89$	−724017.	+	724017.i	−1.02702	+	1.02702i	−0.0273951	+	0.999625i	$0.508721\pi$
$89$	−724017.	+	724017.i	−1.02702	+	1.02702i	−0.999625	+	0.0273951i	$0.991279\pi$
$90$	462860.			0.634924
$91$	−488666.	−	488666.i	−0.648466	−	0.648466i
$92$	276209.	−	276209.i	0.354711	−	0.354711i
$93$	664512.	+	664512.i	0.826141	+	0.826141i
$94$	−503871.	+	503871.i	−0.606646	+	0.606646i
$95$			1.23505e6i			1.44050i
$96$	76275.3	+	76275.3i	0.0862125	+	0.0862125i
$97$	119162.	+	119162.i	0.130563	+	0.130563i	0.769368	−	0.638805i	$-0.220571\pi$
$97$	119162.	+	119162.i	0.130563	+	0.130563i	−0.638805	+	0.769368i	$0.720571\pi$
$98$	−217982.	+	217982.i	−0.231602	+	0.231602i
$99$		−	7661.16i		−	0.00789567i
$100$	966431.			0.966431
$101$			443261.i			0.430225i	0.976589	+	0.215113i	$0.0690119\pi$
$101$			443261.i			0.430225i	−0.976589	+	0.215113i	$0.930988\pi$
$102$		−	275324.i		−	0.259444i
$103$	671150.	−	671150.i	0.614197	−	0.614197i	−0.329840	−	0.944037i	$-0.606995\pi$
$103$	671150.	−	671150.i	0.614197	−	0.614197i	0.944037	+	0.329840i	$0.106995\pi$
$104$			301512.i			0.268043i
$105$	−1.16953e6	+	1.16953e6i	−1.01028	+	1.01028i
$106$	842061.	−	842061.i	0.707011	−	0.707011i
$107$	−236329.			−0.192915			−0.0964575	−	0.995337i	$-0.530751\pi$
$107$	−236329.			−0.192915			−0.0964575	+	0.995337i	$0.530751\pi$
$108$	662180.			0.525660
$109$	729013.	+	729013.i	0.562932	+	0.562932i	0.930139	−	0.367207i	$-0.119686\pi$
$109$	729013.	+	729013.i	0.562932	+	0.562932i	−0.367207	+	0.930139i	$0.619686\pi$
$110$		−	24272.1i		−	0.0182360i
$111$	−838819.	−	431408.i	−0.613337	−	0.315442i
$112$	424861.			0.302408
$113$	−1.41245e6	+	1.41245e6i	−0.978900	+	0.978900i	−0.999782	−	0.0208820i	$-0.993353\pi$
$113$	−1.41245e6	+	1.41245e6i	−0.978900	+	0.978900i	0.0208820	+	0.999782i	$0.493353\pi$
$114$			607752.i			0.410215i
$115$		−	2.61312e6i		−	1.71817i
$116$	−275775.	−	275775.i	−0.176677	−	0.176677i
$117$	450178.	+	450178.i	0.281078	+	0.281078i
$118$	−925482.			−0.563277
$119$	−766791.	−	766791.i	−0.455026	−	0.455026i
$120$	721614.			0.417601
$121$	1.77116e6			0.999773
$122$			2.05884e6i			1.13382i
$123$	−467809.			−0.251393
$124$	−1.14190e6	−	1.14190e6i	−0.598913	−	0.598913i
$125$	2.20637e6	−	2.20637e6i	1.12966	−	1.12966i
$126$	634345.	−	634345.i	0.317113	−	0.317113i
$127$	935876.			0.456885			0.228443	−	0.973557i	$-0.426637\pi$
$127$	935876.			0.456885			0.228443	+	0.973557i	$0.426637\pi$
$128$	−131072.	−	131072.i	−0.0625000	−	0.0625000i
$129$	−700316.	+	700316.i	−0.326231	+	0.326231i
$130$	1.42625e6	+	1.42625e6i	0.649181	+	0.649181i
$131$	−1.01105e6	+	1.01105e6i	−0.449739	+	0.449739i	−0.895268	−	0.445529i	$-0.853016\pi$
$131$	−1.01105e6	+	1.01105e6i	−0.449739	+	0.449739i	0.445529	+	0.895268i	$0.353016\pi$
$132$		−	11944.0i		−	0.00519312i
$133$	1.69262e6	+	1.69262e6i	0.719455	+	0.719455i
$134$	887961.	+	887961.i	0.369045	+	0.369045i
$135$	3.13232e6	−	3.13232e6i	1.27311	−	1.27311i
$136$			473119.i			0.188085i
$137$	−989148.			−0.384680			−0.192340	−	0.981328i	$-0.561608\pi$
$137$	−989148.			−0.384680			−0.192340	+	0.981328i	$0.561608\pi$
$138$		−	1.28589e6i		−	0.489289i
$139$			3.49862e6i			1.30273i	0.758767	+	0.651363i	$0.225802\pi$
$139$			3.49862e6i			1.30273i	−0.758767	+	0.651363i	$0.774198\pi$
$140$	2.00973e6	−	2.00973e6i	0.732409	−	0.732409i
$141$			2.34576e6i			0.836808i
$142$	−2.55722e6	+	2.55722e6i	−0.893107	+	0.893107i
$143$	23607.0	−	23607.0i	0.00807296	−	0.00807296i
$144$	−391398.			−0.131078
$145$	−2.60901e6			−0.855799
$146$	1.10436e6	+	1.10436e6i	0.354857	+	0.354857i
$147$			1.01481e6i			0.319472i
$148$	1.44143e6	+	741335.i	0.444640	+	0.228681i
$149$	−3.26998e6			−0.988523			−0.494261	−	0.869313i	$-0.664561\pi$
$149$	−3.26998e6			−0.988523			−0.494261	+	0.869313i	$0.664561\pi$
$150$	2.24960e6	−	2.24960e6i	0.666548	−	0.666548i
$151$		−	4.95772e6i		−	1.43996i	−0.693993	−	0.719981i	$-0.744150\pi$
$151$		−	4.95772e6i		−	1.43996i	0.693993	−	0.719981i	$-0.255850\pi$
$152$		−	1.04436e6i		−	0.297387i
$153$	706397.	+	706397.i	0.197231	+	0.197231i
$154$	−33264.6	−	33264.6i	−0.00910794	−	0.00910794i
$155$	−1.08031e7			−2.90105
$156$	701842.	+	701842.i	0.184869	+	0.184869i
$157$	−4.26724e6			−1.10268			−0.551338	−	0.834282i	$-0.685883\pi$
$157$	−4.26724e6			−1.10268			−0.551338	+	0.834282i	$0.685883\pi$
$158$	477366.			0.121026
$159$		−	3.92020e6i		−	0.975251i
$160$	−1.24003e6			−0.302741
$161$	−3.58125e6	−	3.58125e6i	−0.858139	−	0.858139i
$162$	426814.	−	426814.i	0.100391	−	0.100391i
$163$	−547663.	+	547663.i	−0.126459	+	0.126459i	−0.767504	−	0.641044i	$-0.778501\pi$
$163$	−547663.	+	547663.i	−0.126459	+	0.126459i	0.641044	+	0.767504i	$0.278501\pi$
$164$	803886.			0.182248
$165$	−56499.0	−	56499.0i	−0.0125773	−	0.0125773i
$166$	−3.43201e6	+	3.43201e6i	−0.750281	+	0.750281i
$167$	4.39572e6	+	4.39572e6i	0.943802	+	0.943802i	0.998503	−	0.0547006i	$-0.0174204\pi$
$167$	4.39572e6	+	4.39572e6i	0.943802	+	0.943802i	−0.0547006	+	0.998503i	$0.517420\pi$
$168$	988965.	−	988965.i	0.208571	−	0.208571i
$169$		−	2.05247e6i		−	0.425222i
$170$	2.23800e6	+	2.23800e6i	0.455527	+	0.455527i
$171$	−1.55930e6	−	1.55930e6i	−0.311848	−	0.311848i
$172$	1.20343e6	−	1.20343e6i	0.236502	−	0.236502i
$173$			5.60952e6i			1.08340i	0.840573	+	0.541698i	$0.182218\pi$
$173$			5.60952e6i			1.08340i	−0.840573	+	0.541698i	$0.817782\pi$
$174$	−1.28386e6			−0.243709
$175$		−	1.25305e7i		−	2.33805i
$176$			20524.6i			0.00376476i
$177$	−2.15428e6	+	2.15428e6i	−0.388492	+	0.388492i
$178$		−	5.79214e6i		−	1.02702i
$179$	−520477.	+	520477.i	−0.0907492	+	0.0907492i	−0.751024	−	0.660275i	$-0.770440\pi$
$179$	−520477.	+	520477.i	−0.0907492	+	0.0907492i	0.660275	+	0.751024i	$0.270440\pi$
$180$	−1.85144e6	+	1.85144e6i	−0.317462	+	0.317462i
$181$	714343.			0.120468			0.0602340	−	0.998184i	$-0.480815\pi$
$181$	714343.			0.120468			0.0602340	+	0.998184i	$0.480815\pi$
$182$	3.90932e6			0.648466
$183$	4.79243e6	+	4.79243e6i	0.781992	+	0.781992i
$184$			2.20967e6i			0.354711i
$185$	1.03252e7	−	3.31169e6i	1.63073	−	0.523039i
$186$	−5.31610e6			−0.826141
$187$	37043.0	−	37043.0i	0.00566475	−	0.00566475i
$188$		−	4.03097e6i		−	0.606646i
$189$		−	8.58564e6i		−	1.27171i
$190$	−4.94018e6	−	4.94018e6i	−0.720248	−	0.720248i
$191$	2.76440e6	+	2.76440e6i	0.396735	+	0.396735i	0.877080	−	0.480345i	$-0.159488\pi$
$191$	2.76440e6	+	2.76440e6i	0.396735	+	0.396735i	−0.480345	+	0.877080i	$0.659488\pi$
$192$	−610203.			−0.0862125
$193$	−8.28995e6	−	8.28995e6i	−1.15313	−	1.15313i	−0.985921	−	0.167213i	$-0.946523\pi$
$193$	−8.28995e6	−	8.28995e6i	−1.15313	−	1.15313i	−0.167213	−	0.985921i	$-0.553477\pi$
$194$	−953292.			−0.130563
$195$	6.63988e6			0.895480
$196$		−	1.74386e6i		−	0.231602i
$197$	1.26161e7			1.65016			0.825078	−	0.565019i	$-0.191131\pi$
$197$	1.26161e7			1.65016			0.825078	+	0.565019i	$0.191131\pi$
$198$	30644.6	+	30644.6i	0.00394783	+	0.00394783i
$199$	−1.57404e6	+	1.57404e6i	−0.199736	+	0.199736i	−0.799887	−	0.600151i	$-0.795107\pi$
$199$	−1.57404e6	+	1.57404e6i	−0.199736	+	0.199736i	0.600151	+	0.799887i	$0.295107\pi$
$200$	−3.86572e6	+	3.86572e6i	−0.483216	+	0.483216i
$201$	4.13388e6			0.509061
$202$	−1.77305e6	−	1.77305e6i	−0.215113	−	0.215113i
$203$	−3.57562e6	+	3.57562e6i	−0.427428	+	0.427428i
$204$	1.10130e6	+	1.10130e6i	0.129722	+	0.129722i
$205$	3.80264e6	−	3.80264e6i	0.441391	−	0.441391i
$206$			5.36920e6i			0.614197i
$207$	3.29919e6	+	3.29919e6i	0.371960	+	0.371960i
$208$	−1.20605e6	−	1.20605e6i	−0.134022	−	0.134022i
$209$	−81768.8	+	81768.8i	−0.00895672	+	0.00895672i
$210$		−	9.35625e6i		−	1.01028i
$211$	−9.66224e6			−1.02856			−0.514281	−	0.857622i	$-0.671941\pi$
$211$	−9.66224e6			−1.02856			−0.514281	+	0.857622i	$0.671941\pi$
$212$			6.73649e6i			0.707011i
$213$			1.19051e7i			1.23195i
$214$	945317.	−	945317.i	0.0964575	−	0.0964575i
$215$		−	1.13852e7i		−	1.14558i
$216$	−2.64872e6	+	2.64872e6i	−0.262830	+	0.262830i
$217$	−1.48056e7	+	1.48056e7i	−1.44893	+	1.44893i
$218$	−5.83211e6			−0.562932
$219$	5.14133e6			0.489490
$220$	97088.2	+	97088.2i	0.00911798	+	0.00911798i
$221$			4.35337e6i			0.403319i
$222$	5.08091e6	−	1.62964e6i	0.464390	−	0.148948i
$223$	8.42383e6			0.759618			0.379809	−	0.925065i	$-0.375990\pi$
$223$	8.42383e6			0.759618			0.379809	+	0.925065i	$0.375990\pi$
$224$	−1.69944e6	+	1.69944e6i	−0.151204	+	0.151204i
$225$			1.15436e7i			1.01343i
$226$		−	1.12996e7i		−	0.978900i
$227$	9.89401e6	+	9.89401e6i	0.845853	+	0.845853i	0.989613	−	0.143760i	$-0.0459192\pi$
$227$	9.89401e6	+	9.89401e6i	0.845853	+	0.845853i	−0.143760	+	0.989613i	$0.545919\pi$
$228$	−2.43101e6	−	2.43101e6i	−0.205108	−	0.205108i
$229$	−945298.			−0.0787159			−0.0393580	−	0.999225i	$-0.512531\pi$
$229$	−945298.			−0.0787159			−0.0393580	+	0.999225i	$0.512531\pi$
$230$	1.04525e7	+	1.04525e7i	0.859084	+	0.859084i
$231$	−154863.			−0.0125635
$232$	2.20620e6			0.176677
$233$			1.87339e7i			1.48101i	0.672048	+	0.740507i	$0.265415\pi$
$233$			1.87339e7i			1.48101i	−0.672048	+	0.740507i	$0.734585\pi$
$234$	−3.60142e6			−0.281078
$235$	−1.90678e7	−	1.90678e7i	−1.46925	−	1.46925i
$236$	3.70193e6	−	3.70193e6i	0.281638	−	0.281638i
$237$	1.11118e6	−	1.11118e6i	0.0834719	−	0.0834719i
$238$	6.13433e6			0.455026
$239$	1.23652e7	+	1.23652e7i	0.905745	+	0.905745i	0.995925	−	0.0901805i	$-0.0287444\pi$
$239$	1.23652e7	+	1.23652e7i	0.905745	+	0.905745i	−0.0901805	+	0.995925i	$0.528744\pi$
$240$	−2.88646e6	+	2.88646e6i	−0.208800	+	0.208800i
$241$	1.22480e7	+	1.22480e7i	0.875013	+	0.875013i	0.993014	−	0.118000i	$-0.0376483\pi$
$241$	1.22480e7	+	1.22480e7i	0.875013	+	0.875013i	−0.118000	+	0.993014i	$0.537648\pi$
$242$	−7.08464e6	+	7.08464e6i	−0.499887	+	0.499887i
$243$			1.30983e7i			0.912840i
$244$	−8.23534e6	−	8.23534e6i	−0.566908	−	0.566908i
$245$	−8.24902e6	−	8.24902e6i	−0.560924	−	0.560924i
$246$	1.87124e6	−	1.87124e6i	0.125697	−	0.125697i
$247$		−	9.60964e6i		−	0.637700i
$248$	9.13522e6			0.598913
$249$			1.59776e7i			1.03494i
$250$			1.76510e7i			1.12966i
$251$	1.28944e7	−	1.28944e7i	0.815419	−	0.815419i	−0.170021	−	0.985440i	$-0.554384\pi$
$251$	1.28944e7	−	1.28944e7i	0.815419	−	0.815419i	0.985440	+	0.170021i	$0.0543836\pi$
$252$			5.07476e6i			0.317113i
$253$	173007.	−	173007.i	0.0106832	−	0.0106832i
$254$	−3.74350e6	+	3.74350e6i	−0.228443	+	0.228443i
$255$	1.04190e7			0.628354
$256$	1.04858e6			0.0625000
$257$	1.99093e7	+	1.99093e7i	1.17289	+	1.17289i	0.981519	+	0.191367i	$0.0612920\pi$
$257$	1.99093e7	+	1.99093e7i	1.17289	+	1.17289i	0.191367	+	0.981519i	$0.438708\pi$
$258$		−	5.60252e6i		−	0.326231i
$259$	9.61194e6	−	1.86892e7i	0.553238	−	1.07570i
$260$	−1.14100e7			−0.649181
$261$	3.29400e6	−	3.29400e6i	0.185269	−	0.185269i
$262$		−	8.08843e6i		−	0.449739i
$263$		−	2.97882e7i		−	1.63749i	−0.574160	−	0.818743i	$-0.694671\pi$
$263$		−	2.97882e7i		−	1.63749i	0.574160	−	0.818743i	$-0.305329\pi$
$264$	47776.0	+	47776.0i	0.00259656	+	0.00259656i
$265$	3.18658e7	+	3.18658e7i	1.71233	+	1.71233i
$266$	−1.35409e7			−0.719455
$267$	−1.34826e7	−	1.34826e7i	−0.708336	−	0.708336i
$268$	−7.10369e6			−0.369045
$269$	−1.94653e7			−1.00001			−0.500004	−	0.866023i	$-0.666668\pi$
$269$	−1.94653e7			−1.00001			−0.500004	+	0.866023i	$0.666668\pi$
$270$			2.50586e7i			1.27311i
$271$	−2.61100e7			−1.31189			−0.655946	−	0.754808i	$-0.727730\pi$
$271$	−2.61100e7			−1.31189			−0.655946	+	0.754808i	$0.727730\pi$
$272$	−1.89247e6	−	1.89247e6i	−0.0940423	−	0.0940423i
$273$	9.09988e6	−	9.09988e6i	0.447247	−	0.447247i
$274$	3.95659e6	−	3.95659e6i	0.192340	−	0.192340i
$275$	605336.			0.0291071
$276$	5.14354e6	+	5.14354e6i	0.244644	+	0.244644i
$277$	−1.07647e7	+	1.07647e7i	−0.506482	+	0.506482i	−0.913445	−	0.406963i	$-0.866588\pi$
$277$	−1.07647e7	+	1.07647e7i	−0.506482	+	0.506482i	0.406963	+	0.913445i	$0.366588\pi$
$278$	−1.39945e7	−	1.39945e7i	−0.651363	−	0.651363i
$279$	1.36395e7	−	1.36395e7i	0.628037	−	0.628037i
$280$			1.60778e7i			0.732409i
$281$	−1.77208e7	−	1.77208e7i	−0.798664	−	0.798664i	0.184221	−	0.982885i	$-0.441024\pi$
$281$	−1.77208e7	−	1.77208e7i	−0.798664	−	0.798664i	−0.982885	+	0.184221i	$0.941024\pi$
$282$	−9.38303e6	−	9.38303e6i	−0.418404	−	0.418404i
$283$	5.87503e6	−	5.87503e6i	0.259209	−	0.259209i	−0.565523	−	0.824732i	$-0.691326\pi$
$283$	5.87503e6	−	5.87503e6i	0.259209	−	0.259209i	0.824732	+	0.565523i	$0.191326\pi$
$284$		−	2.04578e7i		−	0.893107i
$285$	−2.29989e7			−0.993510
$286$			188856.i			0.00807296i
$287$		−	1.04230e7i		−	0.440906i
$288$	1.56559e6	−	1.56559e6i	0.0655392	−	0.0655392i
$289$		−	1.73065e7i		−	0.716993i
$290$	1.04360e7	−	1.04360e7i	0.427899	−	0.427899i
$291$	−2.21901e6	+	2.21901e6i	−0.0900494	+	0.0900494i
$292$	−8.83490e6			−0.354857
$293$	3.83081e7			1.52296			0.761479	−	0.648190i	$-0.224474\pi$
$293$	3.83081e7			1.52296			0.761479	+	0.648190i	$0.224474\pi$
$294$	−4.05925e6	−	4.05925e6i	−0.159736	−	0.159736i
$295$		−	3.50226e7i		−	1.36421i
$296$	−8.73107e6	+	2.80039e6i	−0.336661	+	0.107980i
$297$	414765.			0.0158319
$298$	1.30799e7	−	1.30799e7i	0.494261	−	0.494261i
$299$			2.03322e7i			0.760624i
$300$			1.79968e7i			0.666548i
$301$	−1.56033e7	−	1.56033e7i	−0.572159	−	0.572159i
$302$	1.98309e7	+	1.98309e7i	0.719981	+	0.719981i
$303$	−8.25437e6			−0.296726
$304$	4.17746e6	+	4.17746e6i	0.148693	+	0.148693i
$305$	−7.79117e7			−2.74602
$306$	−5.65118e6			−0.197231
$307$		−	1.58499e7i		−	0.547786i	−0.961760	−	0.273893i	$-0.911689\pi$
$307$		−	1.58499e7i		−	0.547786i	0.961760	−	0.273893i	$-0.0883113\pi$
$308$	266117.			0.00910794
$309$	1.24981e7	+	1.24981e7i	0.423612	+	0.423612i
$310$	4.32125e7	−	4.32125e7i	1.45052	−	1.45052i
$311$	1.50089e6	−	1.50089e6i	0.0498963	−	0.0498963i	−0.681718	−	0.731615i	$-0.738767\pi$
$311$	1.50089e6	−	1.50089e6i	0.0498963	−	0.0498963i	0.731615	+	0.681718i	$0.238767\pi$
$312$	−5.61473e6			−0.184869
$313$	674832.	+	674832.i	0.0220071	+	0.0220071i	0.718025	−	0.696018i	$-0.245046\pi$
$313$	674832.	+	674832.i	0.0220071	+	0.0220071i	−0.696018	+	0.718025i	$0.745046\pi$
$314$	1.70690e7	−	1.70690e7i	0.551338	−	0.551338i
$315$	2.40053e7	+	2.40053e7i	0.768024	+	0.768024i
$316$	−1.90946e6	+	1.90946e6i	−0.0605132	+	0.0605132i
$317$		−	5.24114e7i		−	1.64531i	−0.568541	−	0.822655i	$-0.692492\pi$
$317$		−	5.24114e7i		−	1.64531i	0.568541	−	0.822655i	$-0.307508\pi$
$318$	1.56808e7	+	1.56808e7i	0.487625	+	0.487625i
$319$	−172735.	−	172735.i	−0.00532119	−	0.00532119i
$320$	4.96010e6	−	4.96010e6i	0.151370	−	0.151370i
$321$		−	4.40090e6i		−	0.133054i
$322$	2.86500e7			0.858139
$323$		−	1.50790e7i		−	0.447471i
$324$			3.41451e6i			0.100391i
$325$	−3.55702e7	+	3.55702e7i	−1.03618	+	1.03618i
$326$		−	4.38130e6i		−	0.126459i
$327$	−1.35756e7	+	1.35756e7i	−0.388254	+	0.388254i
$328$	−3.21555e6	+	3.21555e6i	−0.0911241	+	0.0911241i
$329$	−5.22644e7			−1.46764
$330$	451992.			0.0125773
$331$	1.20361e7	+	1.20361e7i	0.331895	+	0.331895i	0.853306	−	0.521411i	$-0.174594\pi$
$331$	1.20361e7	+	1.20361e7i	0.331895	+	0.331895i	−0.521411	+	0.853306i	$0.674594\pi$
$332$		−	2.74561e7i		−	0.750281i
$333$	−8.85489e6	+	1.72172e7i	−0.239801	+	0.466262i
$334$	−3.51658e7			−0.943802
$335$	−3.36027e7	+	3.36027e7i	−0.893800	+	0.893800i
$336$			7.91172e6i			0.208571i
$337$			6.11887e7i			1.59875i	0.600830	+	0.799377i	$0.294837\pi$
$337$			6.11887e7i			1.59875i	−0.600830	+	0.799377i	$0.705163\pi$
$338$	8.20987e6	+	8.20987e6i	0.212611	+	0.212611i
$339$	−2.63025e7	−	2.63025e7i	−0.675147	−	0.675147i
$340$	−1.79040e7			−0.455527
$341$	−715245.	−	715245.i	−0.0180381	−	0.0180381i
$342$	1.24744e7			0.311848
$343$	2.62025e7			0.649323
$344$			9.62742e6i			0.236502i
$345$	4.86613e7			1.18502
$346$	−2.24381e7	−	2.24381e7i	−0.541698	−	0.541698i
$347$	−2.27799e7	+	2.27799e7i	−0.545211	+	0.545211i	−0.925052	−	0.379841i	$-0.875979\pi$
$347$	−2.27799e7	+	2.27799e7i	−0.545211	+	0.545211i	0.379841	+	0.925052i	$0.375979\pi$
$348$	5.13545e6	−	5.13545e6i	0.121854	−	0.121854i
$349$	−1.48992e7			−0.350499			−0.175250	−	0.984524i	$-0.556073\pi$
$349$	−1.48992e7			−0.350499			−0.175250	+	0.984524i	$0.556073\pi$
$350$	5.01219e7	+	5.01219e7i	1.16902	+	1.16902i
$351$	−2.43720e7	+	2.43720e7i	−0.563598	+	0.563598i
$352$	−82098.6	−	82098.6i	−0.00188238	−	0.00188238i
$353$	5.28963e7	−	5.28963e7i	1.20255	−	1.20255i	0.229155	−	0.973390i	$-0.426404\pi$
$353$	5.28963e7	−	5.28963e7i	1.20255	−	1.20255i	0.973390	−	0.229155i	$-0.0735963\pi$
$354$		−	1.72342e7i		−	0.388492i
$355$	−9.67720e7	−	9.67720e7i	−2.16304	−	2.16304i
$356$	2.31685e7	+	2.31685e7i	0.513510	+	0.513510i
$357$	1.42791e7	−	1.42791e7i	0.313831	−	0.313831i
$358$		−	4.16382e6i		−	0.0907492i
$359$	−7.74500e6			−0.167393			−0.0836966	−	0.996491i	$-0.526673\pi$
$359$	−7.74500e6			−0.167393			−0.0836966	+	0.996491i	$0.526673\pi$
$360$		−	1.48115e7i		−	0.317462i
$361$		−	1.37604e7i		−	0.292490i
$362$	−2.85737e6	+	2.85737e6i	−0.0602340	+	0.0602340i
$363$			3.29824e7i			0.689544i
$364$	−1.56373e7	+	1.56373e7i	−0.324233	+	0.324233i
$365$	−4.17919e7	+	4.17919e7i	−0.859437	+	0.859437i
$366$	−3.83394e7			−0.781992
$367$	5.37574e7			1.08753			0.543763	−	0.839239i	$-0.316999\pi$
$367$	5.37574e7			1.08753			0.543763	+	0.839239i	$0.316999\pi$
$368$	−8.83870e6	−	8.83870e6i	−0.177356	−	0.177356i
$369$			9.60204e6i			0.191110i
$370$	−2.80540e7	+	5.45475e7i	−0.553848	+	1.07689i
$371$	8.73434e7			1.71044
$372$	2.12644e7	−	2.12644e7i	0.413070	−	0.413070i
$373$		−	7.40224e7i		−	1.42638i	−0.700969	−	0.713192i	$-0.747249\pi$
$373$		−	7.40224e7i		−	1.42638i	0.700969	−	0.713192i	$-0.252751\pi$
$374$			296344.i			0.00566475i
$375$	4.10868e7	+	4.10868e7i	0.779128	+	0.779128i
$376$	1.61239e7	+	1.61239e7i	0.303323	+	0.303323i
$377$	2.03002e7			0.378857
$378$	3.43426e7	+	3.43426e7i	0.635854	+	0.635854i
$379$	6.35402e7			1.16716			0.583581	−	0.812055i	$-0.301651\pi$
$379$	6.35402e7			1.16716			0.583581	+	0.812055i	$0.301651\pi$
$380$	3.95215e7			0.720248
$381$			1.74278e7i			0.315114i
$382$	−2.21152e7			−0.396735
$383$	6.27012e7	+	6.27012e7i	1.11604	+	1.11604i	0.992317	+	0.123722i	$0.0394832\pi$
$383$	6.27012e7	+	6.27012e7i	1.11604	+	1.11604i	0.123722	+	0.992317i	$0.460517\pi$
$384$	2.44081e6	−	2.44081e6i	0.0431063	−	0.0431063i
$385$	1.25882e6	−	1.25882e6i	0.0220588	−	0.0220588i
$386$	6.63196e7			1.15313
$387$	1.43744e7	+	1.43744e7i	0.248002	+	0.248002i
$388$	3.81317e6	−	3.81317e6i	0.0652816	−	0.0652816i
$389$	8.95095e6	+	8.95095e6i	0.152062	+	0.152062i	0.779038	−	0.626976i	$-0.215708\pi$
$389$	8.95095e6	+	8.95095e6i	0.152062	+	0.152062i	−0.626976	+	0.779038i	$0.715708\pi$
$390$	−2.65595e7	+	2.65595e7i	−0.447740	+	0.447740i
$391$			3.19042e7i			0.533726i
$392$	6.97544e6	+	6.97544e6i	0.115801	+	0.115801i
$393$	−1.88277e7	−	1.88277e7i	−0.310185	−	0.310185i
$394$	−5.04642e7	+	5.04642e7i	−0.825078	+	0.825078i
$395$			1.80648e7i			0.293117i
$396$	−245157.			−0.00394783
$397$		−	4.29229e7i		−	0.685990i	−0.939337	−	0.342995i	$-0.888559\pi$
$397$		−	4.29229e7i		−	0.685990i	0.939337	−	0.342995i	$-0.111441\pi$
$398$		−	1.25923e7i		−	0.199736i
$399$	−3.15198e7	+	3.15198e7i	−0.496208	+	0.496208i
$400$		−	3.09258e7i		−	0.483216i
$401$	5.88451e7	−	5.88451e7i	0.912593	−	0.912593i	−0.0838825	−	0.996476i	$-0.526732\pi$
$401$	5.88451e7	−	5.88451e7i	0.912593	−	0.912593i	0.996476	+	0.0838825i	$0.0267320\pi$
$402$	−1.65355e7	+	1.65355e7i	−0.254530	+	0.254530i
$403$	8.40570e7			1.28428
$404$	1.41844e7			0.215113
$405$	1.61517e7	+	1.61517e7i	0.243139	+	0.243139i
$406$		−	2.86050e7i		−	0.427428i
$407$	902859.	+	464345.i	0.0133917	+	0.00688743i
$408$	−8.81037e6			−0.129722
$409$	−8.41344e7	+	8.41344e7i	−1.22971	+	1.22971i	−0.265640	+	0.964072i	$0.585583\pi$
$409$	−8.41344e7	+	8.41344e7i	−1.22971	+	1.22971i	−0.964072	+	0.265640i	$0.914417\pi$
$410$			3.04211e7i			0.441391i
$411$		−	1.84198e7i		−	0.265314i
$412$	−2.14768e7	−	2.14768e7i	−0.307099	−	0.307099i
$413$	−4.79982e7	−	4.79982e7i	−0.681357	−	0.681357i
$414$	−2.63935e7			−0.371960
$415$	−1.29876e8	−	1.29876e8i	−1.81713	−	1.81713i
$416$	9.64839e6			0.134022
$417$	−6.51510e7			−0.898490
$418$		−	654151.i		−	0.00895672i
$419$	−5.24025e7			−0.712377			−0.356188	−	0.934414i	$-0.615924\pi$
$419$	−5.24025e7			−0.712377			−0.356188	+	0.934414i	$0.615924\pi$
$420$	3.74250e7	+	3.74250e7i	0.505142	+	0.505142i
$421$	−1.12700e6	+	1.12700e6i	−0.0151036	+	0.0151036i	−0.714618	−	0.699515i	$-0.753400\pi$
$421$	−1.12700e6	+	1.12700e6i	−0.0151036	+	0.0151036i	0.699515	+	0.714618i	$0.253400\pi$
$422$	3.86490e7	−	3.86490e7i	0.514281	−	0.514281i
$423$	4.81480e7			0.636146
$424$	−2.69460e7	−	2.69460e7i	−0.353505	−	0.353505i
$425$	−5.58150e7	+	5.58150e7i	−0.727083	+	0.727083i
$426$	−4.76204e7	−	4.76204e7i	−0.615976	−	0.615976i
$427$	−1.06777e8	+	1.06777e8i	−1.37150	+	1.37150i
$428$			7.56254e6i			0.0964575i
$429$	439607.	+	439607.i	0.00556792	+	0.00556792i
$430$	4.55408e7	+	4.55408e7i	0.572790	+	0.572790i
$431$	−6.74983e7	+	6.74983e7i	−0.843065	+	0.843065i	−0.989256	−	0.146191i	$-0.953298\pi$
$431$	−6.74983e7	+	6.74983e7i	−0.843065	+	0.843065i	0.146191	+	0.989256i	$0.453298\pi$
$432$		−	2.11898e7i		−	0.262830i
$433$	9.65572e7			1.18938			0.594691	−	0.803955i	$-0.297275\pi$
$433$	9.65572e7			1.18938			0.594691	+	0.803955i	$0.297275\pi$
$434$		−	1.18445e8i		−	1.44893i
$435$		−	4.85847e7i		−	0.590244i
$436$	2.33284e7	−	2.33284e7i	0.281466	−	0.281466i
$437$		−	7.04256e7i		−	0.843891i
$438$	−2.05653e7	+	2.05653e7i	−0.244745	+	0.244745i
$439$	1.39303e7	−	1.39303e7i	0.164652	−	0.164652i	−0.619972	−	0.784624i	$-0.712856\pi$
$439$	1.39303e7	−	1.39303e7i	0.164652	−	0.164652i	0.784624	+	0.619972i	$0.212856\pi$
$440$	−776706.			−0.00911798
$441$	2.08296e7			0.242865
$442$	−1.74135e7	−	1.74135e7i	−0.201659	−	0.201659i
$443$		−	6.19606e6i		−	0.0712696i	−0.999365	−	0.0356348i	$-0.988655\pi$
$443$		−	6.19606e6i		−	0.0712696i	0.999365	−	0.0356348i	$-0.0113453\pi$
$444$	−1.38051e7	+	2.68422e7i	−0.157721	+	0.306669i
$445$	2.19189e8			2.48737
$446$	−3.36953e7	+	3.36953e7i	−0.379809	+	0.379809i
$447$		−	6.08933e7i		−	0.681784i
$448$		−	1.35955e7i		−	0.151204i
$449$	7.50116e7	+	7.50116e7i	0.828685	+	0.828685i	0.987335	−	0.158650i	$-0.0507142\pi$
$449$	7.50116e7	+	7.50116e7i	0.828685	+	0.828685i	−0.158650	+	0.987335i	$0.550714\pi$
$450$	−4.61742e7	−	4.61742e7i	−0.506713	−	0.506713i
$451$	503524.			0.00548897
$452$	4.51985e7	+	4.51985e7i	0.489450	+	0.489450i
$453$	9.23222e7			0.993143
$454$	−7.91521e7			−0.845853
$455$			1.47939e8i			1.57054i
$456$	1.94481e7			0.205108
$457$	1.16248e8	+	1.16248e8i	1.21797	+	1.21797i	0.968341	+	0.249631i	$0.0803094\pi$
$457$	1.16248e8	+	1.16248e8i	1.21797	+	1.21797i	0.249631	+	0.968341i	$0.419691\pi$
$458$	3.78119e6	−	3.78119e6i	0.0393580	−	0.0393580i
$459$	−3.82434e7	+	3.82434e7i	−0.395474	+	0.395474i
$460$	−8.36198e7			−0.859084
$461$	1.76231e7	+	1.76231e7i	0.179878	+	0.179878i	0.791303	−	0.611425i	$-0.209403\pi$
$461$	1.76231e7	+	1.76231e7i	0.179878	+	0.179878i	−0.611425	+	0.791303i	$0.709403\pi$
$462$	619450.	−	619450.i	0.00628175	−	0.00628175i
$463$	7.55467e7	+	7.55467e7i	0.761154	+	0.761154i	0.976531	−	0.215377i	$-0.0690980\pi$
$463$	7.55467e7	+	7.55467e7i	0.761154	+	0.761154i	−0.215377	+	0.976531i	$0.569098\pi$
$464$	−8.82480e6	+	8.82480e6i	−0.0883386	+	0.0883386i
$465$		−	2.01175e8i		−	2.00085i
$466$	−7.49354e7	−	7.49354e7i	−0.740507	−	0.740507i
$467$	−8.99714e7	−	8.99714e7i	−0.883393	−	0.883393i	0.110485	−	0.993878i	$-0.464760\pi$
$467$	−8.99714e7	−	8.99714e7i	−0.883393	−	0.883393i	−0.993878	+	0.110485i	$0.964760\pi$
$468$	1.44057e7	−	1.44057e7i	0.140539	−	0.140539i
$469$			9.21044e7i			0.892816i
$470$	1.52542e8			1.46925
$471$		−	7.94641e7i		−	0.760516i
$472$			2.96154e7i			0.281638i
$473$	753782.	−	753782.i	0.00712299	−	0.00712299i
$474$			8.88946e6i			0.0834719i
$475$	1.23206e8	−	1.23206e8i	1.14961	−	1.14961i
$476$	−2.45373e7	+	2.45373e7i	−0.227513	+	0.227513i
$477$	−8.04641e7			−0.741391
$478$	−9.89213e7			−0.905745
$479$	−1.02673e7	−	1.02673e7i	−0.0934226	−	0.0934226i	0.658851	−	0.752274i	$-0.271043\pi$
$479$	−1.02673e7	−	1.02673e7i	−0.0934226	−	0.0934226i	−0.752274	+	0.658851i	$0.771043\pi$
$480$		−	2.30916e7i		−	0.208800i
$481$	−8.03383e7	+	2.57676e7i	−0.721917	+	0.231546i
$482$	−9.79842e7			−0.875013
$483$	6.66898e7	−	6.66898e7i	0.591858	−	0.591858i
$484$		−	5.66771e7i		−	0.499887i
$485$		−	3.60750e7i		−	0.316214i
$486$	−5.23931e7	−	5.23931e7i	−0.456420	−	0.456420i
$487$	−6.94071e7	−	6.94071e7i	−0.600921	−	0.600921i	0.339636	−	0.940557i	$-0.389696\pi$
$487$	−6.94071e7	−	6.94071e7i	−0.600921	−	0.600921i	−0.940557	+	0.339636i	$0.889696\pi$
$488$	6.58828e7			0.566908
$489$	−1.01985e7	−	1.01985e7i	−0.0872190	−	0.0872190i
$490$	6.59921e7			0.560924
$491$	−7.80687e7			−0.659526			−0.329763	−	0.944064i	$-0.606969\pi$
$491$	−7.80687e7			−0.659526			−0.329763	+	0.944064i	$0.606969\pi$
$492$			1.49699e7i			0.125697i
$493$	3.18541e7			0.265842
$494$	3.84386e7	+	3.84386e7i	0.318850	+	0.318850i
$495$	−1.15967e6	+	1.15967e6i	−0.00956136	+	0.00956136i
$496$	−3.65409e7	+	3.65409e7i	−0.299457	+	0.299457i
$497$	−2.65250e8			−2.16066
$498$	−6.39105e7	−	6.39105e7i	−0.517469	−	0.517469i
$499$	3.41622e7	−	3.41622e7i	0.274944	−	0.274944i	−0.556143	−	0.831087i	$-0.687719\pi$
$499$	3.41622e7	−	3.41622e7i	0.274944	−	0.274944i	0.831087	+	0.556143i	$0.187719\pi$
$500$	−7.06039e7	−	7.06039e7i	−0.564831	−	0.564831i
$501$	−8.18567e7	+	8.18567e7i	−0.650940	+	0.650940i
$502$			1.03155e8i			0.815419i
$503$	−5.14709e6	−	5.14709e6i	−0.0404444	−	0.0404444i	0.686595	−	0.727040i	$-0.259104\pi$
$503$	−5.14709e6	−	5.14709e6i	−0.0404444	−	0.0404444i	−0.727040	+	0.686595i	$0.759104\pi$
$504$	−2.02990e7	−	2.02990e7i	−0.158556	−	0.158556i
$505$	6.70967e7	−	6.70967e7i	0.520987	−	0.520987i
$506$			1.38406e6i			0.0106832i
$507$	3.82208e7			0.293276
$508$		−	2.99480e7i		−	0.228443i
$509$		−	2.16216e8i		−	1.63958i	−0.572661	−	0.819792i	$-0.694089\pi$
$509$		−	2.16216e8i		−	1.63958i	0.572661	−	0.819792i	$-0.305911\pi$
$510$	−4.16759e7	+	4.16759e7i	−0.314177	+	0.314177i
$511$			1.14551e8i			0.858491i
$512$	−4.19430e6	+	4.19430e6i	−0.0312500	+	0.0312500i
$513$	8.44186e7	−	8.44186e7i	0.625296	−	0.625296i
$514$	−1.59274e8			−1.17289
$515$	−2.03184e8			−1.48754
$516$	2.24101e7	+	2.24101e7i	0.163115	+	0.163115i
$517$		−	2.52485e6i		−	0.0182710i
$518$	3.63090e7	+	1.13205e8i	0.261232	+	0.814469i
$519$	−1.04460e8			−0.747219
$520$	4.56400e7	−	4.56400e7i	0.324590	−	0.324590i
$521$			2.05146e8i			1.45061i	0.688428	+	0.725305i	$0.258301\pi$
$521$			2.05146e8i			1.45061i	−0.688428	+	0.725305i	$0.741699\pi$
$522$			2.63520e7i			0.185269i
$523$	−6.07258e6	−	6.07258e6i	−0.0424490	−	0.0424490i	0.685564	−	0.728013i	$-0.259556\pi$
$523$	−6.07258e6	−	6.07258e6i	−0.0424490	−	0.0424490i	−0.728013	+	0.685564i	$0.759556\pi$
$524$	3.23537e7	+	3.23537e7i	0.224869	+	0.224869i
$525$	2.33341e8			1.61255
$526$	1.19153e8	+	1.19153e8i	0.818743	+	0.818743i
$527$	1.31898e8			0.901171
$528$	−382208.			−0.00259656
$529$			971123.i			0.00656005i
$530$	−2.54926e8			−1.71233
$531$	4.42178e7	+	4.42178e7i	0.295334	+	0.295334i
$532$	5.41638e7	−	5.41638e7i	0.359728	−	0.359728i
$533$	−2.95876e7	+	2.95876e7i	−0.195402	+	0.195402i
$534$	1.07861e8			0.708336
$535$	3.57732e7	+	3.57732e7i	0.233613	+	0.233613i
$536$	2.84147e7	−	2.84147e7i	0.184522	−	0.184522i
$537$	−9.69228e6	−	9.69228e6i	−0.0625897	−	0.0625897i
$538$	7.78611e7	−	7.78611e7i	0.500004	−	0.500004i
$539$		−	1.09229e6i		−	0.00697543i
$540$	−1.00234e8	−	1.00234e8i	−0.636554	−	0.636554i
$541$	1.82106e7	+	1.82106e7i	0.115009	+	0.115009i	0.762269	−	0.647260i	$-0.224085\pi$
$541$	1.82106e7	+	1.82106e7i	0.115009	+	0.115009i	−0.647260	+	0.762269i	$0.724085\pi$
$542$	1.04440e8	−	1.04440e8i	0.655946	−	0.655946i
$543$			1.33024e7i			0.0830867i
$544$	1.51398e7			0.0940423
$545$		−	2.20702e8i		−	1.36338i
$546$			7.27991e7i			0.447247i
$547$	−9.97837e7	+	9.97837e7i	−0.609674	+	0.609674i	−0.942861	−	0.333187i	$-0.891876\pi$
$547$	−9.97837e7	+	9.97837e7i	−0.609674	+	0.609674i	0.333187	+	0.942861i	$0.391876\pi$
$548$			3.16527e7i			0.192340i
$549$	9.83673e7	−	9.83673e7i	0.594475	−	0.594475i
$550$	−2.42135e6	+	2.42135e6i	−0.0145535	+	0.0145535i
$551$	−7.03148e7			−0.420332
$552$	−4.11483e7			−0.244644
$553$	2.47576e7	+	2.47576e7i	0.146397	+	0.146397i
$554$		−	8.61179e7i		−	0.506482i
$555$	6.16699e7	+	1.92275e8i	0.360740	+	1.12472i
$556$	1.11956e8			0.651363
$557$	9.15949e7	−	9.15949e7i	0.530036	−	0.530036i	−0.390547	−	0.920583i	$-0.627714\pi$
$557$	9.15949e7	−	9.15949e7i	0.530036	−	0.530036i	0.920583	+	0.390547i	$0.127714\pi$
$558$			1.09116e8i			0.628037i
$559$			8.85859e7i			0.507142i
$560$	−6.43113e7	−	6.43113e7i	−0.366204	−	0.366204i
$561$	689811.	+	689811.i	0.00390698	+	0.00390698i
$562$	1.41766e8			0.798664
$563$	−2.20673e7	−	2.20673e7i	−0.123658	−	0.123658i	0.642569	−	0.766228i	$-0.277868\pi$
$563$	−2.20673e7	−	2.20673e7i	−0.123658	−	0.123658i	−0.766228	+	0.642569i	$0.777868\pi$
$564$	7.50643e7			0.418404
$565$	4.27607e8			2.37082
$566$			4.70002e7i			0.259209i
$567$	4.42716e7			0.242871
$568$	8.18312e7	+	8.18312e7i	0.446554	+	0.446554i
$569$	2.47801e7	−	2.47801e7i	0.134514	−	0.134514i	−0.636644	−	0.771158i	$-0.719678\pi$
$569$	2.47801e7	−	2.47801e7i	0.134514	−	0.134514i	0.771158	+	0.636644i	$0.219678\pi$
$570$	9.19956e7	−	9.19956e7i	0.496755	−	0.496755i
$571$	1.50637e8			0.809138			0.404569	−	0.914507i	$-0.367421\pi$
$571$	1.50637e8			0.809138			0.404569	+	0.914507i	$0.367421\pi$
$572$	−755424.	−	755424.i	−0.00403648	−	0.00403648i
$573$	−5.14784e7	+	5.14784e7i	−0.273628	+	0.273628i
$574$	4.16919e7	+	4.16919e7i	0.220453	+	0.220453i
$575$	−2.60681e8	+	2.60681e8i	−1.37122	+	1.37122i
$576$			1.25247e7i			0.0655392i
$577$	−2.65749e8	−	2.65749e8i	−1.38339	−	1.38339i	−0.838528	−	0.544858i	$-0.816583\pi$
$577$	−2.65749e8	−	2.65749e8i	−1.38339	−	1.38339i	−0.544858	−	0.838528i	$-0.683417\pi$
$578$	6.92259e7	+	6.92259e7i	0.358497	+	0.358497i
$579$	1.54375e8	−	1.54375e8i	0.795317	−	0.795317i
$580$			8.34883e7i			0.427899i
$581$	−3.55988e8			−1.81513
$582$		−	1.77521e7i		−	0.0900494i
$583$			4.21948e6i			0.0212938i
$584$	3.53396e7	−	3.53396e7i	0.177428	−	0.177428i
$585$		−	1.36287e8i		−	0.680749i
$586$	−1.53232e8	+	1.53232e8i	−0.761479	+	0.761479i
$587$	−2.28460e8	+	2.28460e8i	−1.12952	+	1.12952i	−0.139268	+	0.990255i	$0.544475\pi$
$587$	−2.28460e8	+	2.28460e8i	−1.12952	+	1.12952i	−0.990255	+	0.139268i	$0.955525\pi$
$588$	3.24740e7			0.159736
$589$	−2.91153e8			−1.42487
$590$	1.40091e8	+	1.40091e8i	0.682107	+	0.682107i
$591$			2.34935e8i			1.13811i
$592$	2.37227e7	−	4.61258e7i	0.114340	−	0.222320i
$593$	7.71277e7			0.369867			0.184934	−	0.982751i	$-0.440793\pi$
$593$	7.71277e7			0.369867			0.184934	+	0.982751i	$0.440793\pi$
$594$	−1.65906e6	+	1.65906e6i	−0.00791594	+	0.00791594i
$595$			2.32139e8i			1.10204i
$596$			1.04639e8i			0.494261i
$597$	−2.93116e7	−	2.93116e7i	−0.137758	−	0.137758i
$598$	−8.13286e7	−	8.13286e7i	−0.380312	−	0.380312i
$599$	3.74127e8			1.74076			0.870380	−	0.492380i	$-0.163873\pi$
$599$	3.74127e8			1.74076			0.870380	+	0.492380i	$0.163873\pi$
$600$	−7.19871e7	−	7.19871e7i	−0.333274	−	0.333274i
$601$	2.72144e8			1.25365			0.626824	−	0.779161i	$-0.284355\pi$
$601$	2.72144e8			1.25365			0.626824	+	0.779161i	$0.284355\pi$
$602$	1.24826e8			0.572159
$603$		−	8.48501e7i		−	0.386991i
$604$	−1.58647e8			−0.719981
$605$	−2.68101e8	−	2.68101e8i	−1.21069	−	1.21069i
$606$	3.30175e7	−	3.30175e7i	0.148363	−	0.148363i
$607$	−1.44904e8	+	1.44904e8i	−0.647909	+	0.647909i	−0.952487	−	0.304579i	$-0.901484\pi$
$607$	−1.44904e8	+	1.44904e8i	−0.647909	+	0.647909i	0.304579	+	0.952487i	$0.401484\pi$
$608$	−3.34197e7			−0.148693
$609$	−6.65849e7	−	6.65849e7i	−0.294797	−	0.294797i
$610$	3.11647e8	−	3.11647e8i	1.37301	−	1.37301i
$611$	1.48363e8	+	1.48363e8i	0.650430	+	0.650430i
$612$	2.26047e7	−	2.26047e7i	0.0986154	−	0.0986154i
$613$			7.64514e7i			0.331898i	0.986134	+	0.165949i	$0.0530687\pi$
$613$			7.64514e7i			0.331898i	−0.986134	+	0.165949i	$0.946931\pi$
$614$	6.33995e7	+	6.33995e7i	0.273893	+	0.273893i
$615$	7.08124e7	+	7.08124e7i	0.304428	+	0.304428i
$616$	−1.06447e6	+	1.06447e6i	−0.00455397	+	0.00455397i
$617$			1.79672e8i			0.764936i	0.923969	+	0.382468i	$0.124926\pi$
$617$			1.79672e8i			0.764936i	−0.923969	+	0.382468i	$0.875074\pi$
$618$	−9.99847e7			−0.423612
$619$			3.12870e8i			1.31914i	0.751641	+	0.659572i	$0.229262\pi$
$619$			3.12870e8i			1.31914i	−0.751641	+	0.659572i	$0.770738\pi$
$620$			3.45700e8i			1.45052i
$621$	−1.78614e8	+	1.78614e8i	−0.745829	+	0.745829i
$622$			1.20071e7i			0.0498963i
$623$	3.00397e8	−	3.00397e8i	1.24231	−	1.24231i
$624$	2.24589e7	−	2.24589e7i	0.0924347	−	0.0924347i
$625$	−1.96068e8			−0.803094
$626$	−5.39865e6			−0.0220071
$627$	−1.52269e6	−	1.52269e6i	−0.00617745	−	0.00617745i
$628$			1.36552e8i			0.551338i
$629$	−1.26063e8	+	4.04332e7i	−0.506566	+	0.162475i
$630$	−1.92042e8			−0.768024
$631$	−1.70402e8	+	1.70402e8i	−0.678244	+	0.678244i	−0.959603	−	0.281358i	$-0.909215\pi$
$631$	−1.70402e8	+	1.70402e8i	−0.678244	+	0.678244i	0.281358	+	0.959603i	$0.409215\pi$
$632$		−	1.52757e7i		−	0.0605132i
$633$		−	1.79929e8i		−	0.709400i
$634$	2.09646e8	+	2.09646e8i	0.822655	+	0.822655i
$635$	−1.41664e8	−	1.41664e8i	−0.553271	−	0.553271i
$636$	−1.25446e8			−0.487625
$637$	6.41839e7	+	6.41839e7i	0.248318	+	0.248318i
$638$	1.38188e6			0.00532119
$639$	2.44359e8			0.936537
$640$			3.96808e7i			0.151370i
$641$	−5.70227e7			−0.216508			−0.108254	−	0.994123i	$-0.534526\pi$
$641$	−5.70227e7			−0.216508			−0.108254	+	0.994123i	$0.534526\pi$
$642$	1.76036e7	+	1.76036e7i	0.0665268	+	0.0665268i
$643$	−7.15316e7	+	7.15316e7i	−0.269070	+	0.269070i	−0.828725	−	0.559656i	$-0.810933\pi$
$643$	−7.15316e7	+	7.15316e7i	−0.269070	+	0.269070i	0.559656	+	0.828725i	$0.310933\pi$
$644$	−1.14600e8	+	1.14600e8i	−0.429069	+	0.429069i
$645$	2.12014e8			0.790106
$646$	6.03160e7	+	6.03160e7i	0.223735	+	0.223735i
$647$	−1.84334e7	+	1.84334e7i	−0.0680600	+	0.0680600i	−0.740317	−	0.672257i	$-0.765325\pi$
$647$	−1.84334e7	+	1.84334e7i	−0.0680600	+	0.0680600i	0.672257	+	0.740317i	$0.265325\pi$
$648$	−1.36580e7	−	1.36580e7i	−0.0501953	−	0.0501953i
$649$	2.31875e6	−	2.31875e6i	0.00848242	−	0.00848242i
$650$		−	2.84561e8i		−	1.03618i
$651$	−2.75708e8	−	2.75708e8i	−0.999325	−	0.999325i
$652$	1.75252e7	+	1.75252e7i	0.0632296	+	0.0632296i
$653$	7.35542e7	−	7.35542e7i	0.264160	−	0.264160i	−0.562581	−	0.826742i	$-0.690192\pi$
$653$	7.35542e7	−	7.35542e7i	0.264160	−	0.264160i	0.826742	+	0.562581i	$0.190192\pi$
$654$		−	1.08605e8i		−	0.388254i
$655$	3.06087e8			1.08923
$656$		−	2.57244e7i		−	0.0911241i
$657$		−	1.05529e8i		−	0.372113i
$658$	2.09058e8	−	2.09058e8i	0.733818	−	0.733818i
$659$		−	3.72303e6i		−	0.0130089i	−0.999979	−	0.00650445i	$-0.997930\pi$
$659$		−	3.72303e6i		−	0.0130089i	0.999979	−	0.00650445i	$-0.00207044\pi$
$660$	−1.80797e6	+	1.80797e6i	−0.00628867	+	0.00628867i
$661$	−2.12084e7	+	2.12084e7i	−0.0734350	+	0.0734350i	−0.742870	−	0.669435i	$-0.766536\pi$
$661$	−2.12084e7	+	2.12084e7i	−0.0734350	+	0.0734350i	0.669435	+	0.742870i	$0.266536\pi$
$662$	−9.62887e7			−0.331895
$663$	−8.10680e7			−0.278169
$664$	1.09824e8	+	1.09824e8i	0.375141	+	0.375141i
$665$		−	5.12424e8i		−	1.74247i
$666$	−3.34493e7	−	1.04288e8i	−0.113231	−	0.353032i
$667$	1.48773e8			0.501355
$668$	1.40663e8	−	1.40663e8i	0.471901	−	0.471901i
$669$			1.56868e8i			0.523909i
$670$		−	2.68822e8i		−	0.893800i
$671$	−5.15831e6	−	5.15831e6i	−0.0170742	−	0.0170742i
$672$	−3.16469e7	−	3.16469e7i	−0.104285	−	0.104285i
$673$	−2.42618e8			−0.795935			−0.397967	−	0.917400i	$-0.630284\pi$
$673$	−2.42618e8			−0.795935			−0.397967	+	0.917400i	$0.630284\pi$
$674$	−2.44755e8	−	2.44755e8i	−0.799377	−	0.799377i
$675$	−6.24952e8			−2.03206
$676$	−6.56789e7			−0.212611
$677$			1.38797e8i			0.447315i	0.974668	+	0.223657i	$0.0717997\pi$
$677$			1.38797e8i			0.447315i	−0.974668	+	0.223657i	$0.928200\pi$
$678$	2.10420e8			0.675147
$679$	−4.94405e7	−	4.94405e7i	−0.157933	−	0.157933i
$680$	7.16161e7	−	7.16161e7i	0.227764	−	0.227764i
$681$	−1.84245e8	+	1.84245e8i	−0.583385	+	0.583385i
$682$	5.72196e6			0.0180381
$683$	−1.63511e8	−	1.63511e8i	−0.513198	−	0.513198i	0.402307	−	0.915505i	$-0.368209\pi$
$683$	−1.63511e8	−	1.63511e8i	−0.513198	−	0.513198i	−0.915505	+	0.402307i	$0.868209\pi$
$684$	−4.98977e7	+	4.98977e7i	−0.155924	+	0.155924i
$685$	1.49728e8	+	1.49728e8i	0.465833	+	0.465833i
$686$	−1.04810e8	+	1.04810e8i	−0.324662	+	0.324662i
$687$		−	1.76033e7i		−	0.0542904i
$688$	−3.85097e7	−	3.85097e7i	−0.118251	−	0.118251i
$689$	−2.47941e8	−	2.47941e8i	−0.758038	−	0.758038i
$690$	−1.94645e8	+	1.94645e8i	−0.592510	+	0.592510i
$691$		−	3.68514e8i		−	1.11692i	−0.829533	−	0.558458i	$-0.811393\pi$
$691$		−	3.68514e8i		−	1.11692i	0.829533	−	0.558458i	$-0.188607\pi$
$692$	1.79505e8			0.541698
$693$			3.17864e6i			0.00955084i
$694$		−	1.82240e8i		−	0.545211i
$695$	5.29588e8	−	5.29588e8i	1.57755	−	1.57755i
$696$			4.10836e7i			0.121854i
$697$	−4.64274e7	+	4.64274e7i	−0.137112	+	0.137112i
$698$	5.95969e7	−	5.95969e7i	0.175250	−	0.175250i
$699$	−3.48860e8			−1.02146
$700$	−4.00975e8			−1.16902
$701$	−1.89533e8	−	1.89533e8i	−0.550213	−	0.550213i	0.376289	−	0.926502i	$-0.377200\pi$
$701$	−1.89533e8	−	1.89533e8i	−0.550213	−	0.550213i	−0.926502	+	0.376289i	$0.877200\pi$
$702$		−	1.94976e8i		−	0.563598i
$703$	2.78272e8	−	8.92525e7i	0.800947	−	0.256894i
$704$	656789.			0.00188238
$705$	3.55078e8	−	3.55078e8i	1.01334	−	1.01334i
$706$			4.23171e8i			1.20255i
$707$		−	1.83911e8i		−	0.520413i
$708$	6.89369e7	+	6.89369e7i	0.194246	+	0.194246i
$709$	−2.73384e8	−	2.73384e8i	−0.767069	−	0.767069i	0.210521	−	0.977589i	$-0.432484\pi$
$709$	−2.73384e8	−	2.73384e8i	−0.767069	−	0.767069i	−0.977589	+	0.210521i	$0.932484\pi$
$710$	7.74176e8			2.16304
$711$	−2.28076e7	−	2.28076e7i	−0.0634558	−	0.0634558i
$712$	−1.85348e8			−0.513510
$713$	6.16024e8			1.69953
$714$			1.14233e8i			0.313831i
$715$	−7.14680e6			−0.0195521
$716$	1.66553e7	+	1.66553e7i	0.0453746	+	0.0453746i
$717$	−2.30263e8	+	2.30263e8i	−0.624692	+	0.624692i
$718$	3.09800e7	−	3.09800e7i	0.0836966	−	0.0836966i
$719$	3.51324e8			0.945194			0.472597	−	0.881279i	$-0.343317\pi$
$719$	3.51324e8			0.945194			0.472597	+	0.881279i	$0.343317\pi$
$720$	5.92461e7	+	5.92461e7i	0.158731	+	0.158731i
$721$	−2.78462e8	+	2.78462e8i	−0.742952	+	0.742952i
$722$	5.50418e7	+	5.50418e7i	0.146245	+	0.146245i
$723$	−2.28081e8	+	2.28081e8i	−0.603497	+	0.603497i
$724$		−	2.28590e7i		−	0.0602340i
$725$	2.60271e8	+	2.60271e8i	0.682986	+	0.682986i
$726$	−1.31929e8	−	1.31929e8i	−0.344772	−	0.344772i
$727$	−2.08458e8	+	2.08458e8i	−0.542521	+	0.542521i	−0.924267	−	0.381747i	$-0.875323\pi$
$727$	−2.08458e8	+	2.08458e8i	−0.542521	+	0.542521i	0.381747	+	0.924267i	$0.375323\pi$
$728$		−	1.25098e8i		−	0.324233i
$729$	−3.21701e8			−0.830368
$730$		−	3.34336e8i		−	0.859437i
$731$			1.39005e8i			0.355859i
$732$	1.53358e8	−	1.53358e8i	0.390996	−	0.390996i
$733$		−	3.00557e8i		−	0.763159i	−0.924336	−	0.381580i	$-0.875380\pi$
$733$		−	3.00557e8i		−	0.763159i	0.924336	−	0.381580i	$-0.124620\pi$
$734$	−2.15030e8	+	2.15030e8i	−0.543763	+	0.543763i
$735$	1.53612e8	−	1.53612e8i	0.386869	−	0.386869i
$736$	7.07096e7			0.177356
$737$	−4.44948e6			−0.0111149
$738$	−3.84082e7	−	3.84082e7i	−0.0955552	−	0.0955552i
$739$			3.19609e7i			0.0791928i	0.999216	+	0.0395964i	$0.0126072\pi$
$739$			3.19609e7i			0.0791928i	−0.999216	+	0.0395964i	$0.987393\pi$
$740$	−1.05974e8	−	3.30406e8i	−0.261519	−	0.815367i
$741$	1.78950e8			0.439822
$742$	−3.49374e8	+	3.49374e8i	−0.855221	+	0.855221i
$743$		−	6.93198e8i		−	1.69002i	−0.534753	−	0.845008i	$-0.679595\pi$
$743$		−	6.93198e8i		−	1.69002i	0.534753	−	0.845008i	$-0.320405\pi$
$744$			1.70115e8i			0.413070i
$745$	4.94978e8	+	4.94978e8i	1.19706	+	1.19706i
$746$	2.96090e8	+	2.96090e8i	0.713192	+	0.713192i
$747$	3.27950e8			0.786765
$748$	−1.18538e6	−	1.18538e6i	−0.00283238	−	0.00283238i
$749$	9.80537e7			0.233356
$750$	−3.28695e8			−0.779128
$751$		−	6.57218e8i		−	1.55163i	−0.630958	−	0.775817i	$-0.717338\pi$
$751$		−	6.57218e8i		−	1.55163i	0.630958	−	0.775817i	$-0.282662\pi$
$752$	−1.28991e8			−0.303323
$753$	2.40119e8	+	2.40119e8i	0.562395	+	0.562395i
$754$	−8.12007e7	+	8.12007e7i	−0.189429	+	0.189429i
$755$	−7.50452e8	+	7.50452e8i	−1.74374	+	1.74374i
$756$	−2.74740e8			−0.635854
$757$	4.31373e8	+	4.31373e8i	0.994409	+	0.994409i	0.999984	−	0.00557498i	$-0.00177458\pi$
$757$	4.31373e8	+	4.31373e8i	0.994409	+	0.994409i	−0.00557498	+	0.999984i	$0.501775\pi$
$758$	−2.54161e8	+	2.54161e8i	−0.583581	+	0.583581i
$759$	3.22172e6	+	3.22172e6i	0.00736822	+	0.00736822i
$760$	−1.58086e8	+	1.58086e8i	−0.360124	+	0.360124i
$761$		−	3.30524e8i		−	0.749978i	−0.927029	−	0.374989i	$-0.877647\pi$
$761$		−	3.30524e8i		−	0.749978i	0.927029	−	0.374989i	$-0.122353\pi$
$762$	−6.97112e7	−	6.97112e7i	−0.157557	−	0.157557i
$763$	−3.02470e8	−	3.02470e8i	−0.680939	−	0.680939i
$764$	8.84608e7	−	8.84608e7i	0.198368	−	0.198368i
$765$		−	2.13855e8i		−	0.477678i
$766$	−5.01610e8			−1.11604
$767$			2.72504e8i			0.603930i
$768$			1.95265e7i			0.0431063i
$769$	2.69795e8	−	2.69795e8i	0.593273	−	0.593273i	−0.345241	−	0.938514i	$-0.612203\pi$
$769$	2.69795e8	−	2.69795e8i	0.593273	−	0.593273i	0.938514	+	0.345241i	$0.112203\pi$
$770$			1.00706e7i			0.0220588i
$771$	−3.70748e8	+	3.70748e8i	−0.808939	+	0.808939i
$772$	−2.65278e8	+	2.65278e8i	−0.576567	+	0.576567i
$773$	−6.46441e8			−1.39956			−0.699778	−	0.714360i	$-0.746718\pi$
$773$	−6.46441e8			−1.39956			−0.699778	+	0.714360i	$0.746718\pi$
$774$	−1.14995e8			−0.248002
$775$	1.07770e9	+	1.07770e9i	2.31523	+	2.31523i
$776$			3.05053e7i			0.0652816i
$777$	3.48029e8	+	1.78993e8i	0.741911	+	0.381568i
$778$	−7.16076e7			−0.152062
$779$	1.02484e8	−	1.02484e8i	0.216793	−	0.216793i
$780$		−	2.12476e8i		−	0.447740i
$781$		−	1.28140e7i		−	0.0268987i
$782$	−1.27617e8	−	1.27617e8i	−0.266863	−	0.266863i
$783$	1.78333e8	+	1.78333e8i	0.371489	+	0.371489i
$784$	−5.58035e7			−0.115801
$785$	6.45934e8	+	6.45934e8i	1.33530	+	1.33530i
$786$	1.50622e8			0.310185
$787$	−5.15082e8			−1.05670			−0.528350	−	0.849027i	$-0.677189\pi$
$787$	−5.15082e8			−1.05670			−0.528350	+	0.849027i	$0.677189\pi$
$788$		−	4.03714e8i		−	0.825078i
$789$	5.54714e8			1.12937
$790$	−7.22590e7	−	7.22590e7i	−0.146558	−	0.146558i
$791$	5.86031e8	−	5.86031e8i	1.18411	−	1.18411i
$792$	980628.	−	980628.i	0.00197392	−	0.00197392i
$793$	6.06215e8			1.21565
$794$	1.71692e8	+	1.71692e8i	0.342995	+	0.342995i
$795$	−5.93401e8	+	5.93401e8i	−1.18099	+	1.18099i
$796$	5.03692e7	+	5.03692e7i	0.0998679	+	0.0998679i
$797$	−1.56421e8	+	1.56421e8i	−0.308973	+	0.308973i	−0.844511	−	0.535538i	$-0.820109\pi$
$797$	−1.56421e8	+	1.56421e8i	−0.308973	+	0.308973i	0.535538	+	0.844511i	$0.320109\pi$
$798$		−	2.52158e8i		−	0.496208i
$799$	2.32803e8	+	2.32803e8i	0.456404	+	0.456404i
$800$	1.23703e8	+	1.23703e8i	0.241608	+	0.241608i
$801$	−2.76737e8	+	2.76737e8i	−0.538481	+	0.538481i
$802$			4.70761e8i			0.912593i
$803$	−5.53385e6			−0.0106876
$804$		−	1.32284e8i		−	0.254530i
$805$			1.08419e9i			2.07835i
$806$	−3.36228e8	+	3.36228e8i	−0.642139	+	0.642139i
$807$		−	3.62480e8i		−	0.689706i
$808$	−5.67375e7	+	5.67375e7i	−0.107556	+	0.107556i
$809$	−4.55634e8	+	4.55634e8i	−0.860538	+	0.860538i	−0.991401	−	0.130862i	$-0.958225\pi$
$809$	−4.55634e8	+	4.55634e8i	−0.860538	+	0.860538i	0.130862	+	0.991401i	$0.458225\pi$
$810$	−1.29214e8			−0.243139
$811$	8.38103e7			0.157121			0.0785606	−	0.996909i	$-0.474968\pi$
$811$	8.38103e7			0.157121			0.0785606	+	0.996909i	$0.474968\pi$
$812$	1.14420e8	+	1.14420e8i	0.213714	+	0.213714i
$813$		−	4.86217e8i		−	0.904813i
$814$	−5.46881e6	+	1.75406e6i	−0.0101396	+	0.00325215i
$815$	1.65800e8			0.306275
$816$	3.52415e7	−	3.52415e7i	0.0648610	−	0.0648610i
$817$		−	3.06840e8i		−	0.562660i
$818$		−	6.73075e8i		−	1.22971i
$819$	−1.86780e8	−	1.86780e8i	−0.340000	−	0.340000i
$820$	−1.21685e8	−	1.21685e8i	−0.220696	−	0.220696i
$821$	−7.50345e8			−1.35591			−0.677956	−	0.735102i	$-0.737134\pi$
$821$	−7.50345e8			−1.35591			−0.677956	+	0.735102i	$0.737134\pi$
$822$	7.36793e7	+	7.36793e7i	0.132657	+	0.132657i
$823$	8.59004e8			1.54098			0.770488	−	0.637455i	$-0.220013\pi$
$823$	8.59004e8			1.54098			0.770488	+	0.637455i	$0.220013\pi$
$824$	1.71814e8			0.307099
$825$			1.12725e7i			0.0200752i
$826$	3.83985e8			0.681357
$827$	−5.84669e8	−	5.84669e8i	−1.03370	−	1.03370i	−0.999412	−	0.0342856i	$-0.989084\pi$
$827$	−5.84669e8	−	5.84669e8i	−1.03370	−	1.03370i	−0.0342856	−	0.999412i	$-0.510916\pi$
$828$	1.05574e8	−	1.05574e8i	0.185980	−	0.185980i
$829$	2.90808e8	−	2.90808e8i	0.510437	−	0.510437i	−0.404223	−	0.914660i	$-0.632458\pi$
$829$	2.90808e8	−	2.90808e8i	0.510437	−	0.510437i	0.914660	+	0.404223i	$0.132458\pi$
$830$	1.03901e9			1.81713
$831$	−2.00460e8	−	2.00460e8i	−0.349321	−	0.349321i
$832$	−3.85936e7	+	3.85936e7i	−0.0670108	+	0.0670108i
$833$	1.00714e8	+	1.00714e8i	0.174243	+	0.174243i
$834$	2.60604e8	−	2.60604e8i	0.449245	−	0.449245i
$835$		−	1.33076e9i		−	2.28582i
$836$	2.61660e6	+	2.61660e6i	0.00447836	+	0.00447836i
$837$	7.38422e8	+	7.38422e8i	1.25930	+	1.25930i
$838$	2.09610e8	−	2.09610e8i	0.356188	−	0.356188i
$839$		−	7.78085e7i		−	0.131747i	−0.997828	−	0.0658736i	$-0.979017\pi$
$839$		−	7.78085e7i		−	0.131747i	0.997828	−	0.0658736i	$-0.0209834\pi$
$840$	−2.99400e8			−0.505142
$841$			4.46285e8i			0.750281i
$842$		−	9.01603e6i		−	0.0151036i
$843$	3.29995e8	−	3.29995e8i	0.550839	−	0.550839i
$844$			3.09192e8i			0.514281i
$845$	−3.10683e8	+	3.10683e8i	−0.514928	+	0.514928i
$846$	−1.92592e8	+	1.92592e8i	−0.318073	+	0.318073i
$847$	−7.34859e8			−1.20936
$848$	2.15568e8			0.353505
$849$	1.09404e8	+	1.09404e8i	0.178777	+	0.178777i
$850$		−	4.46520e8i		−	0.727083i
$851$	−5.88770e8	+	1.88841e8i	−0.955338	+	0.306413i
$852$	3.80963e8			0.615976
$853$	−3.75972e8	+	3.75972e8i	−0.605771	+	0.605771i	−0.941838	−	0.336067i	$-0.890903\pi$
$853$	−3.75972e8	+	3.75972e8i	−0.605771	+	0.605771i	0.336067	+	0.941838i	$0.390903\pi$
$854$		−	8.54217e8i		−	1.37150i
$855$			4.72065e8i			0.755272i
$856$	−3.02501e7	−	3.02501e7i	−0.0482288	−	0.0482288i
$857$	2.78609e8	+	2.78609e8i	0.442643	+	0.442643i	0.892899	−	0.450257i	$-0.148667\pi$
$857$	2.78609e8	+	2.78609e8i	0.442643	+	0.442643i	−0.450257	+	0.892899i	$0.648667\pi$
$858$	−3.51686e6			−0.00556792
$859$	7.56934e8	+	7.56934e8i	1.19420	+	1.19420i	0.975875	+	0.218329i	$0.0700605\pi$
$859$	7.56934e8	+	7.56934e8i	1.19420	+	1.19420i	0.218329	+	0.975875i	$0.429939\pi$
$860$	−3.64326e8			−0.572790
$861$	1.94095e8			0.304093
$862$		−	5.39986e8i		−	0.843065i
$863$	4.53709e8			0.705903			0.352951	−	0.935642i	$-0.385178\pi$
$863$	4.53709e8			0.705903			0.352951	+	0.935642i	$0.385178\pi$
$864$	8.47590e7	+	8.47590e7i	0.131415	+	0.131415i
$865$	8.49115e8	−	8.49115e8i	1.31195	−	1.31195i
$866$	−3.86229e8	+	3.86229e8i	−0.594691	+	0.594691i
$867$	3.22279e8			0.494510
$868$	4.73779e8	+	4.73779e8i	0.724463	+	0.724463i
$869$	−1.19602e6	+	1.19602e6i	−0.00182254	+	0.00182254i
$870$	1.94339e8	+	1.94339e8i	0.295122	+	0.295122i
$871$	2.61456e8	−	2.61456e8i	0.395680	−	0.395680i
$872$			1.86627e8i			0.281466i
$873$	4.55465e7	+	4.55465e7i	0.0684561	+	0.0684561i
$874$	2.81702e8	+	2.81702e8i	0.421945	+	0.421945i
$875$	−9.15430e8	+	9.15430e8i	−1.36647	+	1.36647i
$876$		−	1.64523e8i		−	0.244745i
$877$	−1.30428e9			−1.93362			−0.966811	−	0.255492i	$-0.917763\pi$
$877$	−1.30428e9			−1.93362			−0.966811	+	0.255492i	$0.917763\pi$
$878$			1.11442e8i			0.164652i
$879$			7.13370e8i			1.05038i
$880$	3.10682e6	−	3.10682e6i	0.00455899	−	0.00455899i
$881$		−	7.09567e8i		−	1.03769i	−0.854870	−	0.518843i	$-0.826363\pi$
$881$		−	7.09567e8i		−	1.03769i	0.854870	−	0.518843i	$-0.173637\pi$
$882$	−8.33183e7	+	8.33183e7i	−0.121432	+	0.121432i
$883$	4.86509e8	−	4.86509e8i	0.706657	−	0.706657i	−0.259174	−	0.965831i	$-0.583450\pi$
$883$	4.86509e8	−	4.86509e8i	0.706657	−	0.706657i	0.965831	+	0.259174i	$0.0834502\pi$
$884$	1.39308e8			0.201659
$885$	6.52188e8			0.940899
$886$	2.47842e7	+	2.47842e7i	0.0356348	+	0.0356348i
$887$		−	1.73258e8i		−	0.248269i	−0.992265	−	0.124134i	$-0.960385\pi$
$887$		−	1.73258e8i		−	0.248269i	0.992265	−	0.124134i	$-0.0396154\pi$
$888$	−5.21485e7	−	1.62589e8i	−0.0744738	−	0.232195i
$889$	−3.88298e8			−0.552662
$890$	−8.76758e8	+	8.76758e8i	−1.24368	+	1.24368i
$891$			2.13872e6i			0.00302358i
$892$		−	2.69563e8i		−	0.379809i
$893$	−5.13891e8	−	5.13891e8i	−0.721634	−	0.721634i
$894$	2.43573e8	+	2.43573e8i	0.340892	+	0.340892i
$895$	1.57570e8			0.219788
$896$	5.43822e7	+	5.43822e7i	0.0756019	+	0.0756019i
$897$	−3.78623e8			−0.524602
$898$	−6.00093e8			−0.828685
$899$		−	6.15055e8i		−	0.846515i
$900$	3.69394e8			0.506713
$901$	−3.89057e8	−	3.89057e8i	−0.531912	−	0.531912i
$902$	−2.01410e6	+	2.01410e6i	−0.00274448	+	0.00274448i
$903$	2.90563e8	−	2.90563e8i	0.394618	−	0.394618i
$904$	−3.61588e8			−0.489450
$905$	−1.08130e8	−	1.08130e8i	−0.145882	−	0.145882i
$906$	−3.69289e8	+	3.69289e8i	−0.496571	+	0.496571i
$907$	−6.16723e8	−	6.16723e8i	−0.826548	−	0.826548i	0.160490	−	0.987038i	$-0.448693\pi$
$907$	−6.16723e8	−	6.16723e8i	−0.826548	−	0.826548i	−0.987038	+	0.160490i	$0.948693\pi$
$908$	3.16608e8	−	3.16608e8i	0.422926	−	0.422926i
$909$			1.69426e8i			0.225573i
$910$	−5.91756e8	−	5.91756e8i	−0.785269	−	0.785269i
$911$	−9.74968e8	−	9.74968e8i	−1.28954	−	1.28954i	−0.935065	−	0.354476i	$-0.884659\pi$
$911$	−9.74968e8	−	9.74968e8i	−1.28954	−	1.28954i	−0.354476	−	0.935065i	$-0.615341\pi$
$912$	−7.77922e7	+	7.77922e7i	−0.102554	+	0.102554i
$913$		−	1.71974e7i		−	0.0225970i
$914$	−9.29985e8			−1.21797
$915$		−	1.45086e9i		−	1.89393i
$916$			3.02496e7i			0.0393580i
$917$	4.19489e8	−	4.19489e8i	0.544018	−	0.544018i
$918$		−	3.05947e8i		−	0.395474i
$919$	−3.36177e8	+	3.36177e8i	−0.433133	+	0.433133i	−0.889693	−	0.456560i	$-0.849082\pi$
$919$	−3.36177e8	+	3.36177e8i	−0.433133	+	0.433133i	0.456560	+	0.889693i	$0.349082\pi$
$920$	3.34479e8	−	3.34479e8i	0.429542	−	0.429542i
$921$	2.95155e8			0.377808
$922$	−1.40984e8			−0.179878
$923$	7.52963e8	+	7.52963e8i	0.957566	+	0.957566i
$924$			4.95560e6i			0.00628175i
$925$	−1.36040e9	−	6.99658e8i	−1.71886	−	0.884016i
$926$	−6.04374e8			−0.761154
$927$	2.56530e8	−	2.56530e8i	0.322032	−	0.322032i
$928$		−	7.05984e7i		−	0.0883386i
$929$			5.58886e8i			0.697070i	0.937296	+	0.348535i	$0.113321\pi$
$929$			5.58886e8i			0.697070i	−0.937296	+	0.348535i	$0.886679\pi$
$930$	8.04700e8	+	8.04700e8i	1.00043	+	1.00043i
$931$	−2.22317e8	−	2.22317e8i	−0.275502	−	0.275502i
$932$	5.99483e8			0.740507
$933$	2.79495e7	+	2.79495e7i	0.0344135	+	0.0344135i
$934$	7.19771e8			0.883393
$935$	−1.12144e7			−0.0137196
$936$			1.15245e8i			0.140539i
$937$	−9.95845e8			−1.21052			−0.605262	−	0.796027i	$-0.706931\pi$
$937$	−9.95845e8			−1.21052			−0.605262	+	0.796027i	$0.706931\pi$
$938$	−3.68418e8	−	3.68418e8i	−0.446408	−	0.446408i
$939$	−1.25666e7	+	1.25666e7i	−0.0151783	+	0.0151783i
$940$	−6.10169e8	+	6.10169e8i	−0.734626	+	0.734626i
$941$	5.63902e8			0.676760			0.338380	−	0.941010i	$-0.390121\pi$
$941$	5.63902e8			0.676760			0.338380	+	0.941010i	$0.390121\pi$
$942$	3.17857e8	+	3.17857e8i	0.380258	+	0.380258i
$943$	−2.16837e8	+	2.16837e8i	−0.258582	+	0.258582i
$944$	−1.18462e8	−	1.18462e8i	−0.140819	−	0.140819i
$945$	−1.29961e9	+	1.29961e9i	−1.53999	+	1.53999i
$946$			6.03025e6i			0.00712299i
$947$	−3.19244e8	−	3.19244e8i	−0.375901	−	0.375901i	0.493720	−	0.869621i	$-0.335637\pi$
$947$	−3.19244e8	−	3.19244e8i	−0.375901	−	0.375901i	−0.869621	+	0.493720i	$0.835637\pi$
$948$	−3.55578e7	−	3.55578e7i	−0.0417360	−	0.0417360i
$949$	3.25175e8	−	3.25175e8i	0.380468	−	0.380468i
$950$			9.85651e8i			1.14961i
$951$	9.76000e8			1.13477
$952$		−	1.96298e8i		−	0.227513i
$953$			1.30393e9i			1.50653i	0.657720	+	0.753263i	$0.271521\pi$
$953$			1.30393e9i			1.50653i	−0.657720	+	0.753263i	$0.728479\pi$
$954$	3.21857e8	−	3.21857e8i	0.370695	−	0.370695i
$955$		−	8.36897e8i		−	0.960864i
$956$	3.95685e8	−	3.95685e8i	0.452872	−	0.452872i
$957$	3.21666e6	−	3.21666e6i	0.00367002	−	0.00367002i
$958$	8.21388e7			0.0934226
$959$	4.10401e8			0.465321
$960$	9.23666e7	+	9.23666e7i	0.104400	+	0.104400i
$961$		−	1.65926e9i		−	1.86958i
$962$	2.18283e8	−	4.24423e8i	0.245185	−	0.476732i
$963$	−9.03309e7			−0.101148
$964$	3.91937e8	−	3.91937e8i	0.437507	−	0.437507i
$965$			2.50970e9i			2.79280i
$966$			5.33518e8i			0.591858i
$967$	1.21416e9	+	1.21416e9i	1.34276	+	1.34276i	0.893304	+	0.449453i	$0.148381\pi$
$967$	1.21416e9	+	1.21416e9i	1.34276	+	1.34276i	0.449453	+	0.893304i	$0.351619\pi$
$968$	2.26708e8	+	2.26708e8i	0.249943	+	0.249943i
$969$	2.80799e8			0.308621
$970$	1.44300e8	+	1.44300e8i	0.158107	+	0.158107i
$971$	−3.26302e8			−0.356420			−0.178210	−	0.983993i	$-0.557031\pi$
$971$	−3.26302e8			−0.356420			−0.178210	+	0.983993i	$0.557031\pi$
$972$	4.19144e8			0.456420
$973$		−	1.45159e9i		−	1.57582i
$974$	5.55257e8			0.600921
$975$	−6.62384e8	−	6.62384e8i	−0.714655	−	0.714655i
$976$	−2.63531e8	+	2.63531e8i	−0.283454	+	0.283454i
$977$	1.63889e8	−	1.63889e8i	0.175739	−	0.175739i	−0.613757	−	0.789495i	$-0.710342\pi$
$977$	1.63889e8	−	1.63889e8i	0.175739	−	0.175739i	0.789495	+	0.613757i	$0.210342\pi$
$978$	8.15882e7			0.0872190
$979$	1.45119e7	+	1.45119e7i	0.0154659	+	0.0154659i
$980$	−2.63969e8	+	2.63969e8i	−0.280462	+	0.280462i
$981$	2.78647e8	+	2.78647e8i	0.295153	+	0.295153i
$982$	3.12275e8	−	3.12275e8i	0.329763	−	0.329763i
$983$		−	5.27082e8i		−	0.554903i	−0.960740	−	0.277452i	$-0.910510\pi$
$983$		−	5.27082e8i		−	0.554903i	0.960740	−	0.277452i	$-0.0894899\pi$
$984$	−5.98796e7	−	5.98796e7i	−0.0628483	−	0.0628483i
$985$	−1.90970e9	−	1.90970e9i	−1.99828	−	1.99828i
$986$	−1.27416e8	+	1.27416e8i	−0.132921	+	0.132921i
$987$		−	9.73263e8i		−	1.01223i
$988$	−3.07508e8			−0.318850
$989$			6.49214e8i			0.671119i
$990$		−	9.27738e6i		−	0.00956136i
$991$	−1.04153e9	+	1.04153e9i	−1.07016	+	1.07016i	−0.0728185	+	0.997345i	$0.523199\pi$
$991$	−1.04153e9	+	1.04153e9i	−1.07016	+	1.07016i	−0.997345	+	0.0728185i	$0.976801\pi$
$992$		−	2.92327e8i		−	0.299457i
$993$	−2.24135e8	+	2.24135e8i	−0.228908	+	0.228908i
$994$	1.06100e9	−	1.06100e9i	1.08033	−	1.08033i
$995$	4.76525e8			0.483745
$996$	5.11284e8			0.517469
$997$	1.04450e9	+	1.04450e9i	1.05396	+	1.05396i	0.998459	+	0.0554996i	$0.0176752\pi$
$997$	1.04450e9	+	1.04450e9i	1.05396	+	1.05396i	0.0554996	+	0.998459i	$0.482325\pi$
$998$			2.73297e8i			0.274944i
$999$	−9.32116e8	−	4.79392e8i	−0.934918	−	0.480833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.43.7	yes	20
37.31	odd	4	inner	74.7.d.b.31.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.4	✓	20	37.31	odd	4	inner
74.7.d.b.43.7	yes	20	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)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 4.00000i) q^{2} +18.6219i q^{3} -32.0000i q^{4} +(-151.370 - 151.370i) q^{5} +(-74.4876 - 74.4876i) q^{6} -414.903 q^{7} +(128.000 + 128.000i) q^{8} +382.225 q^{9} +O(q^{10})\)	\(q+(-4.00000 + 4.00000i) q^{2} +18.6219i q^{3} -32.0000i q^{4} +(-151.370 - 151.370i) q^{5} +(-74.4876 - 74.4876i) q^{6} -414.903 q^{7} +(128.000 + 128.000i) q^{8} +382.225 q^{9} +1210.96 q^{10} -20.0436i q^{11} +595.901 q^{12} +(1177.78 + 1177.78i) q^{13} +(1659.61 - 1659.61i) q^{14} +(2818.80 - 2818.80i) q^{15} -1024.00 q^{16} +(1848.12 + 1848.12i) q^{17} +(-1528.90 + 1528.90i) q^{18} +(-4079.55 - 4079.55i) q^{19} +(-4843.85 + 4843.85i) q^{20} -7726.29i q^{21} +(80.1744 + 80.1744i) q^{22} +(8631.54 + 8631.54i) q^{23} +(-2383.60 + 2383.60i) q^{24} +30201.0i q^{25} -9422.26 q^{26} +20693.1i q^{27} +13276.9i q^{28} +(8617.96 - 8617.96i) q^{29} +22550.4i q^{30} +(35684.4 - 35684.4i) q^{31} +(4096.00 - 4096.00i) q^{32} +373.250 q^{33} -14785.0 q^{34} +(62804.0 + 62804.0i) q^{35} -12231.2i q^{36} +(-23166.7 + 45044.7i) q^{37} +32636.4 q^{38} +(-21932.5 + 21932.5i) q^{39} -38750.8i q^{40} +25121.4i q^{41} +(30905.1 + 30905.1i) q^{42} +(37607.1 + 37607.1i) q^{43} -641.395 q^{44} +(-57857.5 - 57857.5i) q^{45} -69052.3 q^{46} +125968. q^{47} -19068.8i q^{48} +54495.6 q^{49} +(-120804. - 120804. i) q^{50} +(-34415.5 + 34415.5i) q^{51} +(37689.0 - 37689.0i) q^{52} -210515. q^{53} +(-82772.5 - 82772.5i) q^{54} +(-3034.01 + 3034.01i) q^{55} +(-53107.6 - 53107.6i) q^{56} +(75969.0 - 75969.0i) q^{57} +68943.7i q^{58} +(115685. + 115685. i) q^{59} +(-90201.7 - 90201.7i) q^{60} +(257354. - 257354. i) q^{61} +285476. i q^{62} -158586. q^{63} +32768.0i q^{64} -356563. i q^{65} +(-1493.00 + 1493.00i) q^{66} -221990. i q^{67} +(59139.8 - 59139.8i) q^{68} +(-160736. + 160736. i) q^{69} -502432. q^{70} +639306. q^{71} +(48924.8 + 48924.8i) q^{72} -276091. i q^{73} +(-87512.1 - 272846. i) q^{74} -562400. q^{75} +(-130546. + 130546. i) q^{76} +8316.15i q^{77} -175460. i q^{78} +(-59670.7 - 59670.7i) q^{79} +(155003. + 155003. i) q^{80} -106703. q^{81} +(-100486. - 100486. i) q^{82} +858002. q^{83} -247241. q^{84} -559501. i q^{85} -300857. q^{86} +(160483. + 160483. i) q^{87} +(2565.58 - 2565.58i) q^{88} +(-724017. + 724017. i) q^{89} +462860. q^{90} +(-488666. - 488666. i) q^{91} +(276209. - 276209. i) q^{92} +(664512. + 664512. i) q^{93} +(-503871. + 503871. i) q^{94} +1.23505e6i q^{95} +(76275.3 + 76275.3i) q^{96} +(119162. + 119162. i) q^{97} +(-217982. + 217982. i) q^{98} -7661.16i 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

Introduction

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