LMFDB - Embedded newform 20.7.b.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,7,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, 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:	$4.60108167240$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 18 x^{10} - 30 x^{9} + 174 x^{8} + 1853 x^{7} + 10388 x^{6} - 17262 x^{5} + \cdots + 7603655 $ x^12 - x^11 - 18x^10 - 30x^9 + 174x^8 + 1853x^7 + 10388x^6 - 17262x^5 - 88626x^4 - 240665x^3 - 173034x^2 + 3703420x + 7603655
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{33}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.9
Root			$4.83379 + 2.37885i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.7.b.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.43150 - 4.75771i) q^{2} -20.5795i q^{3} +(18.7284 - 61.1984i) q^{4} -55.9017 q^{5} +(-97.9113 - 132.357i) q^{6} -24.2619i q^{7} +(-170.712 - 482.702i) q^{8} +305.483 q^{9} +O(q^{10})$	\(q+(6.43150 - 4.75771i) q^{2} -20.5795i q^{3} +(18.7284 - 61.1984i) q^{4} -55.9017 q^{5} +(-97.9113 - 132.357i) q^{6} -24.2619i q^{7} +(-170.712 - 482.702i) q^{8} +305.483 q^{9} +(-359.532 + 265.964i) q^{10} -40.6577i q^{11} +(-1259.43 - 385.422i) q^{12} +1938.91 q^{13} +(-115.431 - 156.041i) q^{14} +1150.43i q^{15} +(-3394.49 - 2292.30i) q^{16} +5830.75 q^{17} +(1964.72 - 1453.40i) q^{18} +12002.0i q^{19} +(-1046.95 + 3421.10i) q^{20} -499.299 q^{21} +(-193.437 - 261.490i) q^{22} +8569.95i q^{23} +(-9933.78 + 3513.17i) q^{24} +3125.00 q^{25} +(12470.1 - 9224.76i) q^{26} -21289.2i q^{27} +(-1484.79 - 454.388i) q^{28} -19067.7 q^{29} +(5473.41 + 7398.99i) q^{30} -48329.0i q^{31} +(-32737.8 + 1407.05i) q^{32} -836.716 q^{33} +(37500.5 - 27741.0i) q^{34} +1356.28i q^{35} +(5721.23 - 18695.1i) q^{36} -9465.63 q^{37} +(57101.9 + 77190.7i) q^{38} -39901.8i q^{39} +(9543.10 + 26983.9i) q^{40} -100314. q^{41} +(-3211.24 + 2375.52i) q^{42} +137824. i q^{43} +(-2488.19 - 761.455i) q^{44} -17077.0 q^{45} +(40773.3 + 55117.7i) q^{46} +35806.2i q^{47} +(-47174.5 + 69857.0i) q^{48} +117060. q^{49} +(20098.4 - 14867.8i) q^{50} -119994. i q^{51} +(36312.7 - 118658. i) q^{52} +60878.2 q^{53} +(-101288. - 136921. i) q^{54} +2272.83i q^{55} +(-11711.3 + 4141.80i) q^{56} +246995. q^{57} +(-122634. + 90718.4i) q^{58} -5727.78i q^{59} +(70404.5 + 21545.8i) q^{60} -189058. q^{61} +(-229935. - 310828. i) q^{62} -7411.61i q^{63} +(-203859. + 164806. i) q^{64} -108388. q^{65} +(-5381.34 + 3980.85i) q^{66} +435857. i q^{67} +(109201. - 356833. i) q^{68} +176366. q^{69} +(6452.80 + 8722.94i) q^{70} -281476. i q^{71} +(-52149.7 - 147457. i) q^{72} +246850. q^{73} +(-60878.2 + 45034.7i) q^{74} -64311.0i q^{75} +(734502. + 224778. i) q^{76} -986.434 q^{77} +(-189841. - 256629. i) q^{78} +568574. i q^{79} +(189758. + 128144. i) q^{80} -215424. q^{81} +(-645168. + 477264. i) q^{82} -877394. i q^{83} +(-9351.09 + 30556.3i) q^{84} -325949. q^{85} +(655728. + 886418. i) q^{86} +392403. i q^{87} +(-19625.6 + 6940.76i) q^{88} -49386.0 q^{89} +(-109831. + 81247.6i) q^{90} -47041.7i q^{91} +(524468. + 160502. i) q^{92} -994587. q^{93} +(170355. + 230288. i) q^{94} -670931. i q^{95} +(28956.4 + 673728. i) q^{96} +1.50441e6 q^{97} +(752874. - 556939. i) q^{98} -12420.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9}+O(q^{10}) $ 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + 750 q^{10} - 440 q^{12} - 5040 q^{13} + 6248 q^{14} + 3312 q^{16} + 6840 q^{17} + 15790 q^{18} - 3500 q^{20} - 27464 q^{21} - 26160 q^{22} + 28528 q^{24} + 37500 q^{25} - 18684 q^{26} + 19320 q^{28} - 74968 q^{29} - 13000 q^{30} - 60800 q^{32} + 112880 q^{33} + 48204 q^{34} - 128580 q^{36} + 62640 q^{37} + 74800 q^{38} + 57000 q^{40} - 16976 q^{41} - 138360 q^{42} - 222160 q^{44} + 77000 q^{45} - 144792 q^{46} + 297600 q^{48} + 72564 q^{49} - 31250 q^{50} + 548280 q^{52} + 322160 q^{53} + 150416 q^{54} - 246512 q^{56} - 1213440 q^{57} + 350700 q^{58} + 157000 q^{60} + 46464 q^{61} - 7120 q^{62} - 542784 q^{64} - 133000 q^{65} - 65200 q^{66} - 1678280 q^{68} + 41256 q^{69} - 360000 q^{70} + 2317560 q^{72} - 415080 q^{73} + 1581924 q^{74} + 208320 q^{76} + 75600 q^{77} + 473200 q^{78} + 734000 q^{80} + 2287428 q^{81} - 3169500 q^{82} - 2256224 q^{84} + 372000 q^{85} - 62512 q^{86} - 278880 q^{88} + 278392 q^{89} - 2162250 q^{90} + 4095720 q^{92} - 3646000 q^{93} + 4706568 q^{94} - 2641152 q^{96} + 2344680 q^{97} + 1050270 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9 + 750 * q^10 - 440 * q^12 - 5040 * q^13 + 6248 * q^14 + 3312 * q^16 + 6840 * q^17 + 15790 * q^18 - 3500 * q^20 - 27464 * q^21 - 26160 * q^22 + 28528 * q^24 + 37500 * q^25 - 18684 * q^26 + 19320 * q^28 - 74968 * q^29 - 13000 * q^30 - 60800 * q^32 + 112880 * q^33 + 48204 * q^34 - 128580 * q^36 + 62640 * q^37 + 74800 * q^38 + 57000 * q^40 - 16976 * q^41 - 138360 * q^42 - 222160 * q^44 + 77000 * q^45 - 144792 * q^46 + 297600 * q^48 + 72564 * q^49 - 31250 * q^50 + 548280 * q^52 + 322160 * q^53 + 150416 * q^54 - 246512 * q^56 - 1213440 * q^57 + 350700 * q^58 + 157000 * q^60 + 46464 * q^61 - 7120 * q^62 - 542784 * q^64 - 133000 * q^65 - 65200 * q^66 - 1678280 * q^68 + 41256 * q^69 - 360000 * q^70 + 2317560 * q^72 - 415080 * q^73 + 1581924 * q^74 + 208320 * q^76 + 75600 * q^77 + 473200 * q^78 + 734000 * q^80 + 2287428 * q^81 - 3169500 * q^82 - 2256224 * q^84 + 372000 * q^85 - 62512 * q^86 - 278880 * q^88 + 278392 * q^89 - 2162250 * q^90 + 4095720 * q^92 - 3646000 * q^93 + 4706568 * q^94 - 2641152 * q^96 + 2344680 * q^97 + 1050270 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	6.43150	−	4.75771i	0.803938	−	0.594713i
$2$	6.43150	−	4.75771i	0.803938	−	0.594713i
$3$		−	20.5795i		−	0.762204i	−0.924533	−	0.381102i	$-0.875545\pi$
$3$		−	20.5795i		−	0.762204i	0.924533	−	0.381102i	$-0.124455\pi$
$4$	18.7284	−	61.1984i	0.292632	−	0.956225i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	−97.9113	−	132.357i	−0.453293	−	0.612765i
$7$		−	24.2619i		−	0.0707345i	−0.999374	−	0.0353672i	$-0.988740\pi$
$7$		−	24.2619i		−	0.0707345i	0.999374	−	0.0353672i	$-0.0112601\pi$
$8$	−170.712	−	482.702i	−0.333422	−	0.942778i
$9$	305.483			0.419044
$10$	−359.532	+	265.964i	−0.359532	+	0.265964i
$11$		−	40.6577i		−	0.0305467i	−0.999883	−	0.0152734i	$-0.995138\pi$
$11$		−	40.6577i		−	0.0305467i	0.999883	−	0.0152734i	$-0.00486185\pi$
$12$	−1259.43	−	385.422i	−0.728839	−	0.223045i
$13$	1938.91			0.882525			0.441263	−	0.897378i	$-0.354531\pi$
$13$	1938.91			0.882525			0.441263	+	0.897378i	$0.354531\pi$
$14$	−115.431	−	156.041i	−0.0420667	−	0.0568661i
$15$			1150.43i			0.340868i
$16$	−3394.49	−	2292.30i	−0.828733	−	0.559644i
$17$	5830.75			1.18680			0.593401	−	0.804907i	$-0.297785\pi$
$17$	5830.75			1.18680			0.593401	+	0.804907i	$0.297785\pi$
$18$	1964.72	−	1453.40i	0.336886	−	0.249211i
$19$			12002.0i			1.74981i	0.484291	+	0.874907i	$0.339078\pi$
$19$			12002.0i			1.74981i	−0.484291	+	0.874907i	$0.660922\pi$
$20$	−1046.95	+	3421.10i	−0.130869	+	0.427637i
$21$	−499.299			−0.0539141
$22$	−193.437	−	261.490i	−0.0181665	−	0.0245577i
$23$			8569.95i			0.704361i	0.935932	+	0.352180i	$0.114560\pi$
$23$			8569.95i			0.704361i	−0.935932	+	0.352180i	$0.885440\pi$
$24$	−9933.78	+	3513.17i	−0.718589	+	0.254136i
$25$	3125.00			0.200000
$26$	12470.1	−	9224.76i	0.709496	−	0.524850i
$27$		−	21289.2i		−	1.08160i
$28$	−1484.79	−	454.388i	−0.0676381	−	0.0206992i
$29$	−19067.7			−0.781814			−0.390907	−	0.920430i	$-0.627839\pi$
$29$	−19067.7			−0.781814			−0.390907	+	0.920430i	$0.627839\pi$
$30$	5473.41	+	7398.99i	0.202719	+	0.274037i
$31$		−	48329.0i		−	1.62227i	−0.584861	−	0.811134i	$-0.698851\pi$
$31$		−	48329.0i		−	1.62227i	0.584861	−	0.811134i	$-0.301149\pi$
$32$	−32737.8	+	1407.05i	−0.999078	+	0.0429397i
$33$	−836.716			−0.0232828
$34$	37500.5	−	27741.0i	0.954114	−	0.705807i
$35$			1356.28i			0.0316334i
$36$	5721.23	−	18695.1i	0.122626	−	0.400701i
$37$	−9465.63			−0.186872			−0.0934360	−	0.995625i	$-0.529785\pi$
$37$	−9465.63			−0.186872			−0.0934360	+	0.995625i	$0.529785\pi$
$38$	57101.9	+	77190.7i	1.04064	+	1.40674i
$39$		−	39901.8i		−	0.672665i
$40$	9543.10	+	26983.9i	0.149111	+	0.421623i
$41$	−100314.			−1.45549			−0.727745	−	0.685848i	$-0.759431\pi$
$41$	−100314.			−1.45549			−0.727745	+	0.685848i	$0.759431\pi$
$42$	−3211.24	+	2375.52i	−0.0433436	+	0.0320635i
$43$			137824.i			1.73349i	0.498754	+	0.866744i	$0.333791\pi$
$43$			137824.i			1.73349i	−0.498754	+	0.866744i	$0.666209\pi$
$44$	−2488.19	−	761.455i	−0.0292095	−	0.00893895i
$45$	−17077.0			−0.187402
$46$	40773.3	+	55117.7i	0.418893	+	0.566262i
$47$			35806.2i			0.344877i	0.985020	+	0.172439i	$0.0551647\pi$
$47$			35806.2i			0.344877i	−0.985020	+	0.172439i	$0.944835\pi$
$48$	−47174.5	+	69857.0i	−0.426563	+	0.631664i
$49$	117060.			0.994997
$50$	20098.4	−	14867.8i	0.160788	−	0.118943i
$51$		−	119994.i		−	0.904585i
$52$	36312.7	−	118658.i	0.258255	−	0.843893i
$53$	60878.2			0.408916			0.204458	−	0.978875i	$-0.434457\pi$
$53$	60878.2			0.408916			0.204458	+	0.978875i	$0.434457\pi$
$54$	−101288.	−	136921.i	−0.643243	−	0.869541i
$55$			2272.83i			0.0136609i
$56$	−11711.3	+	4141.80i	−0.0666869	+	0.0235844i
$57$	246995.			1.33372
$58$	−122634.	+	90718.4i	−0.628530	+	0.464955i
$59$		−	5727.78i		−	0.0278888i	−0.999903	−	0.0139444i	$-0.995561\pi$
$59$		−	5727.78i		−	0.0278888i	0.999903	−	0.0139444i	$-0.00443879\pi$
$60$	70404.5	+	21545.8i	0.325947	+	0.0997489i
$61$	−189058.			−0.832924			−0.416462	−	0.909153i	$-0.636730\pi$
$61$	−189058.			−0.832924			−0.416462	+	0.909153i	$0.636730\pi$
$62$	−229935.	−	310828.i	−0.964784	−	1.30420i
$63$		−	7411.61i		−	0.0296409i
$64$	−203859.	+	164806.i	−0.777659	+	0.628686i
$65$	−108388.			−0.394677
$66$	−5381.34	+	3980.85i	−0.0187180	+	0.0138466i
$67$			435857.i			1.44917i	0.689185	+	0.724585i	$0.257969\pi$
$67$			435857.i			1.44917i	−0.689185	+	0.724585i	$0.742031\pi$
$68$	109201.	−	356833.i	0.347296	−	1.13485i
$69$	176366.			0.536867
$70$	6452.80	+	8722.94i	0.0188128	+	0.0254313i
$71$		−	281476.i		−	0.786441i	−0.919444	−	0.393221i	$-0.871361\pi$
$71$		−	281476.i		−	0.786441i	0.919444	−	0.393221i	$-0.128639\pi$
$72$	−52149.7	−	147457.i	−0.139719	−	0.395066i
$73$	246850.			0.634548			0.317274	−	0.948334i	$-0.397232\pi$
$73$	246850.			0.634548			0.317274	+	0.948334i	$0.397232\pi$
$74$	−60878.2	+	45034.7i	−0.150234	+	0.111135i
$75$		−	64311.0i		−	0.152441i
$76$	734502.	+	224778.i	1.67322	+	0.512052i
$77$	−986.434			−0.00216071
$78$	−189841.	−	256629.i	−0.400043	−	0.540781i
$79$			568574.i			1.15320i	0.817026	+	0.576601i	$0.195621\pi$
$79$			568574.i			1.15320i	−0.817026	+	0.576601i	$0.804379\pi$
$80$	189758.	+	128144.i	0.370621	+	0.250280i
$81$	−215424.			−0.405357
$82$	−645168.	+	477264.i	−1.17012	+	0.865599i
$83$		−	877394.i		−	1.53448i	−0.641362	−	0.767238i	$-0.721630\pi$
$83$		−	877394.i		−	1.53448i	0.641362	−	0.767238i	$-0.278370\pi$
$84$	−9351.09	+	30556.3i	−0.0157770	+	0.0515540i
$85$	−325949.			−0.530754
$86$	655728.	+	886418.i	1.03093	+	1.39362i
$87$			392403.i			0.595902i
$88$	−19625.6	+	6940.76i	−0.0287988	+	0.0101850i
$89$	−49386.0			−0.0700541			−0.0350271	−	0.999386i	$-0.511152\pi$
$89$	−49386.0			−0.0700541			−0.0350271	+	0.999386i	$0.511152\pi$
$90$	−109831.	+	81247.6i	−0.150660	+	0.111451i
$91$		−	47041.7i		−	0.0624250i
$92$	524468.	+	160502.i	0.673527	+	0.206118i
$93$	−994587.			−1.23650
$94$	170355.	+	230288.i	0.205103	+	0.277260i
$95$		−	670931.i		−	0.782541i
$96$	28956.4	+	673728.i	0.0327288	+	0.761501i
$97$	1.50441e6			1.64835			0.824176	−	0.566334i	$-0.191639\pi$
$97$	1.50441e6			1.64835			0.824176	+	0.566334i	$0.191639\pi$
$98$	752874.	−	556939.i	0.799915	−	0.591738i
$99$		−	12420.2i		−	0.0128004i
$100$	58526.4	−	191245.i	0.0585264	−	0.191245i
$101$	−1.94071e6			−1.88363			−0.941815	−	0.336132i	$-0.890881\pi$
$101$	−1.94071e6			−1.88363			−0.941815	+	0.336132i	$0.890881\pi$
$102$	−570897.	−	771742.i	−0.537969	−	0.727230i
$103$		−	41692.0i		−	0.0381541i	−0.999818	−	0.0190770i	$-0.993927\pi$
$103$		−	41692.0i		−	0.0381541i	0.999818	−	0.0190770i	$-0.00607278\pi$
$104$	−330995.	−	935915.i	−0.294253	−	0.832025i
$105$	27911.6			0.0241111
$106$	391539.	−	289641.i	0.328743	−	0.243188i
$107$		−	721600.i		−	0.589040i	−0.955645	−	0.294520i	$-0.904840\pi$
$107$		−	721600.i		−	0.589040i	0.955645	−	0.294520i	$-0.0951598\pi$
$108$	−1.30286e6	−	398713.i	−1.03425	−	0.316511i
$109$	−221610.			−0.171123			−0.0855617	−	0.996333i	$-0.527268\pi$
$109$	−221610.			−0.171123			−0.0855617	+	0.996333i	$0.527268\pi$
$110$	10813.5	+	14617.7i	0.00812433	+	0.0109825i
$111$			194798.i			0.142435i
$112$	−55615.7	+	82356.9i	−0.0395861	+	0.0586200i
$113$	742683.			0.514717			0.257358	−	0.966316i	$-0.417148\pi$
$113$	742683.			0.514717			0.257358	+	0.966316i	$0.417148\pi$
$114$	1.58855e6	−	1.17513e6i	1.07222	−	0.793179i
$115$		−	479075.i		−	0.315000i
$116$	−357108.	+	1.16691e6i	−0.228784	+	0.747591i
$117$	592304.			0.369817
$118$	−27251.1	−	36838.2i	−0.0165858	−	0.0224209i
$119$		−	141465.i		−	0.0839478i
$120$	555315.	−	196392.i	0.321363	−	0.113653i
$121$	1.76991e6			0.999067
$122$	−1.21593e6	+	899482.i	−0.669619	+	0.495351i
$123$			2.06441e6i			1.10938i
$124$	−2.95766e6	−	905126.i	−1.55125	−	0.474727i
$125$	−174693.			−0.0894427
$126$	−35262.3	−	47667.8i	−0.0176278	−	0.0238294i
$127$			2.45824e6i			1.20009i	0.799967	+	0.600044i	$0.204850\pi$
$127$			2.45824e6i			1.20009i	−0.799967	+	0.600044i	$0.795150\pi$
$128$	−527018.	+	2.02985e6i	−0.251302	+	0.967909i
$129$	2.83636e6			1.32127
$130$	−697099.	+	515680.i	−0.317296	+	0.234720i
$131$			875075.i			0.389252i	0.980877	+	0.194626i	$0.0623494\pi$
$131$			875075.i			0.389252i	−0.980877	+	0.194626i	$0.937651\pi$
$132$	−15670.4	+	51205.7i	−0.00681330	+	0.0222636i
$133$	291191.			0.123772
$134$	2.07368e6	+	2.80321e6i	0.861841	+	1.16504i
$135$			1.19010e6i			0.483707i
$136$	−995380.	−	2.81452e6i	−0.395706	−	1.11889i
$137$	−1.79826e6			−0.699345			−0.349673	−	0.936872i	$-0.613707\pi$
$137$	−1.79826e6			−0.699345			−0.349673	+	0.936872i	$0.613707\pi$
$138$	1.13430e6	−	839096.i	0.431607	−	0.319282i
$139$		−	130543.i		−	0.0486083i	−0.999705	−	0.0243042i	$-0.992263\pi$
$139$		−	130543.i		−	0.0486083i	0.999705	−	0.0243042i	$-0.00773702\pi$
$140$	83002.4	+	25401.1i	0.0302487	+	0.00925695i
$141$	736875.			0.262867
$142$	−1.33918e6	−	1.81031e6i	−0.467707	−	0.632250i
$143$		−	78831.5i		−	0.0269583i
$144$	−1.03696e6	−	700260.i	−0.347276	−	0.234516i
$145$	1.06592e6			0.349638
$146$	1.58762e6	−	1.17444e6i	0.510137	−	0.377374i
$147$		−	2.40905e6i		−	0.758391i
$148$	−177277.	+	579282.i	−0.0546847	+	0.178692i
$149$	−4.46107e6			−1.34859			−0.674296	−	0.738461i	$-0.735553\pi$
$149$	−4.46107e6			−1.34859			−0.674296	+	0.738461i	$0.735553\pi$
$150$	−305973.	−	413616.i	−0.0906586	−	0.122553i
$151$		−	5.31949e6i		−	1.54504i	−0.634992	−	0.772519i	$-0.718996\pi$
$151$		−	5.31949e6i		−	1.54504i	0.634992	−	0.772519i	$-0.281004\pi$
$152$	5.79338e6	−	2.04888e6i	1.64969	−	0.583427i
$153$	1.78120e6			0.497322
$154$	−6344.25	+	4693.16i	−0.00173707	+	0.00128500i
$155$			2.70167e6i			0.725500i
$156$	−2.44193e6	−	747299.i	−0.643219	−	0.196843i
$157$	−5.17889e6			−1.33825			−0.669125	−	0.743149i	$-0.733331\pi$
$157$	−5.17889e6			−1.33825			−0.669125	+	0.743149i	$0.733331\pi$
$158$	2.70511e6	+	3.65678e6i	0.685825	+	0.927103i
$159$		−	1.25285e6i		−	0.311678i
$160$	1.83010e6	−	78656.4i	0.446801	−	0.0192032i
$161$	207924.			0.0498226
$162$	−1.38550e6	+	1.02492e6i	−0.325882	+	0.241071i
$163$		−	1.67288e6i		−	0.386279i	−0.981171	−	0.193139i	$-0.938133\pi$
$163$		−	1.67288e6i		−	0.386279i	0.981171	−	0.193139i	$-0.0618670\pi$
$164$	−1.87872e6	+	6.13904e6i	−0.425923	+	1.39178i
$165$	46773.8			0.0104124
$166$	−4.17438e6	−	5.64296e6i	−0.912574	−	1.23362i
$167$		−	5.82015e6i		−	1.24964i	−0.780769	−	0.624820i	$-0.785172\pi$
$167$		−	5.82015e6i		−	1.24964i	0.780769	−	0.624820i	$-0.214828\pi$
$168$	85236.3	+	241013.i	0.0179762	+	0.0508290i
$169$	−1.06744e6			−0.221149
$170$	−2.09634e6	+	1.55077e6i	−0.426693	+	0.315646i
$171$			3.66640e6i			0.733250i
$172$	8.43463e6	+	2.58124e6i	1.65760	+	0.507274i
$173$	−3.31004e6			−0.639285			−0.319642	−	0.947538i	$-0.603563\pi$
$173$	−3.31004e6			−0.639285			−0.319642	+	0.947538i	$0.603563\pi$
$174$	1.86694e6	+	2.52374e6i	0.354391	+	0.479068i
$175$		−	75818.5i		−	0.0141469i
$176$	−93199.7	+	138012.i	−0.0170953	+	0.0253151i
$177$	−117875.			−0.0212570
$178$	−317626.	+	234964.i	−0.0563192	+	0.0416621i
$179$		−	2.57688e6i		−	0.449299i	−0.974440	−	0.224650i	$-0.927876\pi$
$179$		−	2.57688e6i		−	0.449299i	0.974440	−	0.224650i	$-0.0721238\pi$
$180$	−319826.	+	1.04509e6i	−0.0548399	+	0.179199i
$181$	3.49422e6			0.589270			0.294635	−	0.955610i	$-0.404802\pi$
$181$	3.49422e6			0.589270			0.294635	+	0.955610i	$0.404802\pi$
$182$	−223810.	−	302548.i	−0.0371250	−	0.0501858i
$183$			3.89072e6i			0.634858i
$184$	4.13674e6	−	1.46299e6i	0.664055	−	0.234849i
$185$	529145.			0.0835717
$186$	−6.39669e6	+	4.73195e6i	−0.994069	+	0.735363i
$187$		−	237065.i		−	0.0362529i
$188$	2.19128e6	+	670594.i	0.329780	+	0.100922i
$189$	−516516.			−0.0765065
$190$	−3.19209e6	−	4.31509e6i	−0.465387	−	0.629114i
$191$			6.14107e6i			0.881341i	0.897669	+	0.440670i	$0.145259\pi$
$191$			6.14107e6i			0.881341i	−0.897669	+	0.440670i	$0.854741\pi$
$192$	3.39163e6	+	4.19532e6i	0.479187	+	0.592735i
$193$	2.81628e6			0.391746			0.195873	−	0.980629i	$-0.437246\pi$
$193$	2.81628e6			0.391746			0.195873	+	0.980629i	$0.437246\pi$
$194$	9.67559e6	−	7.15752e6i	1.32517	−	0.980297i
$195$			2.23058e6i			0.300825i
$196$	2.19236e6	−	7.16391e6i	0.291168	−	0.951441i
$197$	−4.26385e6			−0.557703			−0.278851	−	0.960334i	$-0.589954\pi$
$197$	−4.26385e6			−0.557703			−0.278851	+	0.960334i	$0.589954\pi$
$198$	−59091.9	−	79880.9i	−0.00761259	−	0.0102908i
$199$			1.52923e6i			0.194049i	0.995282	+	0.0970247i	$0.0309326\pi$
$199$			1.52923e6i			0.194049i	−0.995282	+	0.0970247i	$0.969067\pi$
$200$	−533475.	−	1.50844e6i	−0.0666844	−	0.188556i
$201$	8.96972e6			1.10456
$202$	−1.24817e7	+	9.23331e6i	−1.51432	+	1.12022i
$203$			462618.i			0.0553012i
$204$	−7.34345e6	−	2.24730e6i	−0.864987	−	0.264710i
$205$	5.60771e6			0.650914
$206$	−198358.	−	268142.i	−0.0226907	−	0.0306735i
$207$			2.61798e6i			0.295158i
$208$	−6.58161e6	−	4.44456e6i	−0.731378	−	0.493900i
$209$	487973.			0.0534511
$210$	179514.	−	132795.i	0.0193839	−	0.0143392i
$211$			1.29980e7i			1.38366i	0.722058	+	0.691832i	$0.243196\pi$
$211$			1.29980e7i			1.38366i	−0.722058	+	0.691832i	$0.756804\pi$
$212$	1.14015e6	−	3.72565e6i	0.119662	−	0.391016i
$213$	−5.79264e6			−0.599429
$214$	−3.43316e6	−	4.64097e6i	−0.350310	−	0.473552i
$215$		−	7.70462e6i		−	0.775239i
$216$	−1.02763e7	+	3.63432e6i	−1.01971	+	0.360630i
$217$	−1.17255e6			−0.114750
$218$	−1.42528e6	+	1.05435e6i	−0.137573	+	0.101769i
$219$		−	5.08006e6i		−	0.483656i
$220$	139094.	+	42566.6i	0.0130629	+	0.00399762i
$221$	1.13053e7			1.04738
$222$	926793.	+	1.25284e6i	0.0847078	+	0.114509i
$223$		−	6.60113e6i		−	0.595256i	−0.954682	−	0.297628i	$-0.903804\pi$
$223$		−	6.60113e6i		−	0.595256i	0.954682	−	0.297628i	$-0.0961955\pi$
$224$	34137.7	+	794281.i	0.00303732	+	0.0706692i
$225$	954636.			0.0838089
$226$	4.77657e6	−	3.53347e6i	0.413800	−	0.306109i
$227$		−	1.56180e7i		−	1.33521i	−0.744517	−	0.667604i	$-0.767320\pi$
$227$		−	1.56180e7i		−	1.33521i	0.744517	−	0.667604i	$-0.232680\pi$
$228$	4.62583e6	−	1.51157e7i	0.390288	−	1.27533i
$229$	552000.			0.0459656			0.0229828	−	0.999736i	$-0.492684\pi$
$229$	552000.			0.0459656			0.0229828	+	0.999736i	$0.492684\pi$
$230$	−2.27930e6	−	3.08117e6i	−0.187334	−	0.253240i
$231$			20300.3i			0.00164690i
$232$	3.25508e6	+	9.20401e6i	0.260674	+	0.737077i
$233$	−2.63489e6			−0.208302			−0.104151	−	0.994561i	$-0.533213\pi$
$233$	−2.63489e6			−0.208302			−0.104151	+	0.994561i	$0.533213\pi$
$234$	3.80941e6	−	2.81801e6i	0.297310	−	0.219935i
$235$		−	2.00163e6i		−	0.154234i
$236$	−350531.	−	107272.i	−0.0266680	−	0.00816116i
$237$	1.17010e7			0.878976
$238$	−673051.	−	909834.i	−0.0499249	−	0.0674888i
$239$			1.22694e7i			0.898734i	0.893347	+	0.449367i	$0.148350\pi$
$239$			1.22694e7i			0.898734i	−0.893347	+	0.449367i	$0.851650\pi$
$240$	2.63713e6	−	3.90512e6i	0.190765	−	0.282489i
$241$	−1.12114e7			−0.800959			−0.400480	−	0.916306i	$-0.631156\pi$
$241$	−1.12114e7			−0.800959			−0.400480	+	0.916306i	$0.631156\pi$
$242$	1.13832e7	−	8.42070e6i	0.803188	−	0.594158i
$243$		−	1.10865e7i		−	0.772637i
$244$	−3.54076e6	+	1.15700e7i	−0.243740	+	0.796462i
$245$	−6.54387e6			−0.444976
$246$	9.82185e6	+	1.32773e7i	0.659763	+	0.891873i
$247$			2.32707e7i			1.54426i
$248$	−2.33285e7	+	8.25034e6i	−1.52944	+	0.540900i
$249$	−1.80563e7			−1.16958
$250$	−1.12354e6	+	831137.i	−0.0719064	+	0.0531928i
$251$			7.65449e6i			0.484055i	0.970269	+	0.242028i	$0.0778125\pi$
$251$			7.65449e6i			0.484055i	−0.970269	+	0.242028i	$0.922188\pi$
$252$	−453579.	−	138808.i	−0.0283434	−	0.00867387i
$253$	348435.			0.0215159
$254$	1.16956e7	+	1.58102e7i	0.713708	+	0.964796i
$255$			6.70787e6i			0.404543i
$256$	6.26792e6	+	1.55624e7i	0.373597	+	0.927591i
$257$	−1.09187e7			−0.643236			−0.321618	−	0.946870i	$-0.604227\pi$
$257$	−1.09187e7			−0.643236			−0.321618	+	0.946870i	$0.604227\pi$
$258$	1.82421e7	−	1.34946e7i	1.06222	−	0.785778i
$259$			229654.i			0.0132183i
$260$	−2.02994e6	+	6.63319e6i	−0.115495	+	0.377400i
$261$	−5.82486e6			−0.327615
$262$	4.16335e6	+	5.62805e6i	0.231494	+	0.312935i
$263$		−	8.91372e6i		−	0.489995i	−0.969524	−	0.244998i	$-0.921213\pi$
$263$		−	8.91372e6i		−	0.489995i	0.969524	−	0.244998i	$-0.0787872\pi$
$264$	142837.	+	403884.i	0.00776301	+	0.0219505i
$265$	−3.40320e6			−0.182873
$266$	1.87280e6	−	1.38540e6i	0.0995051	−	0.0736090i
$267$			1.01634e6i			0.0533956i
$268$	2.66737e7	+	8.16292e6i	1.38573	+	0.424073i
$269$	2.68537e7			1.37958			0.689792	−	0.724008i	$-0.257702\pi$
$269$	2.68537e7			1.37958			0.689792	+	0.724008i	$0.257702\pi$
$270$	5.66215e6	+	7.65414e6i	0.287667	+	0.388870i
$271$		−	2.83005e7i		−	1.42196i	−0.703215	−	0.710978i	$-0.748253\pi$
$271$		−	2.83005e7i		−	1.42196i	0.703215	−	0.710978i	$-0.251747\pi$
$272$	−1.97924e7	−	1.33658e7i	−0.983541	−	0.664186i
$273$	−968095.			−0.0475806
$274$	−1.15655e7	+	8.55561e6i	−0.562230	+	0.415910i
$275$		−	127055.i		−	0.00610934i
$276$	3.30305e6	−	1.07933e7i	0.157104	−	0.513365i
$277$	6.22973e6			0.293109			0.146555	−	0.989203i	$-0.453182\pi$
$277$	6.22973e6			0.293109			0.146555	+	0.989203i	$0.453182\pi$
$278$	−621087.	−	839590.i	−0.0289080	−	0.0390781i
$279$		−	1.47637e7i		−	0.679802i
$280$	654681.	−	231534.i	0.0298233	−	0.0105473i
$281$	−3.17788e7			−1.43225			−0.716124	−	0.697973i	$-0.754085\pi$
$281$	−3.17788e7			−1.43225			−0.716124	+	0.697973i	$0.754085\pi$
$282$	4.73921e6	−	3.50583e6i	0.211329	−	0.156331i
$283$		−	6.72478e6i		−	0.296701i	−0.988935	−	0.148350i	$-0.952604\pi$
$283$		−	6.72478e6i		−	0.296701i	0.988935	−	0.148350i	$-0.0473964\pi$
$284$	−1.72259e7	−	5.27161e6i	−0.752015	−	0.230138i
$285$	−1.38074e7			−0.596456
$286$	−375057.	−	507005.i	−0.0160324	−	0.0216728i
$287$			2.43380e6i			0.102953i
$288$	−1.00008e7	+	429830.i	−0.418658	+	0.0179936i
$289$	9.86012e6			0.408497
$290$	6.85544e6	−	5.07131e6i	0.281087	−	0.207934i
$291$		−	3.09600e7i		−	1.25638i
$292$	4.62312e6	−	1.51068e7i	0.185689	−	0.606771i
$293$	2.92187e7			1.16161			0.580803	−	0.814044i	$-0.302739\pi$
$293$	2.92187e7			1.16161			0.580803	+	0.814044i	$0.302739\pi$
$294$	−1.14615e7	−	1.54938e7i	−0.451025	−	0.609699i
$295$			320192.i			0.0124723i
$296$	1.61590e6	+	4.56908e6i	0.0623073	+	0.176179i
$297$	−865568.			−0.0330394
$298$	−2.86914e7	+	2.12245e7i	−1.08418	+	0.802025i
$299$			1.66164e7i			0.621616i
$300$	−3.93573e6	−	1.20444e6i	−0.145768	−	0.0446091i
$301$	3.34388e6			0.122617
$302$	−2.53086e7	−	3.42123e7i	−0.918855	−	1.24211i
$303$			3.99388e7i			1.43571i
$304$	2.75122e7	−	4.07406e7i	0.979273	−	1.45013i
$305$	1.05687e7			0.372495
$306$	1.14558e7	−	8.47442e6i	0.399816	−	0.295764i
$307$			2.28641e7i			0.790205i	0.918637	+	0.395103i	$0.129291\pi$
$307$			2.28641e7i			0.790205i	−0.918637	+	0.395103i	$0.870709\pi$
$308$	−18474.4	+	60368.2i	−0.000632292	+	0.00206612i
$309$	−858001.			−0.0290812
$310$	1.28538e7	+	1.73758e7i	0.431465	+	0.583257i
$311$		−	5.60021e6i		−	0.186176i	−0.995658	−	0.0930879i	$-0.970326\pi$
$311$		−	5.60021e6i		−	0.186176i	0.995658	−	0.0930879i	$-0.0296738\pi$
$312$	−1.92607e7	+	6.81172e6i	−0.634173	+	0.224281i
$313$	−1.38055e7			−0.450213			−0.225107	−	0.974334i	$-0.572273\pi$
$313$	−1.38055e7			−0.450213			−0.225107	+	0.974334i	$0.572273\pi$
$314$	−3.33080e7	+	2.46396e7i	−1.07587	+	0.795876i
$315$			414322.i			0.0132558i
$316$	3.47958e7	+	1.06485e7i	1.10272	+	0.337464i
$317$	5.24913e7			1.64782			0.823910	−	0.566721i	$-0.191788\pi$
$317$	5.24913e7			1.64782			0.823910	+	0.566721i	$0.191788\pi$
$318$	−5.96067e6	−	8.05768e6i	−0.185359	−	0.250570i
$319$			775247.i			0.0238819i
$320$	1.13961e7	−	9.21295e6i	0.347780	−	0.281157i
$321$	−1.48502e7			−0.448969
$322$	1.33726e6	−	989240.i	0.0400542	−	0.0296302i
$323$			6.99806e7i			2.07668i
$324$	−4.03455e6	+	1.31836e7i	−0.118621	+	0.387613i
$325$	6.05909e6			0.176505
$326$	−7.95906e6	−	1.07591e7i	−0.229725	−	0.310544i
$327$			4.56062e6i			0.130431i
$328$	1.71248e7	+	4.84217e7i	0.485292	+	1.37220i
$329$	868727.			0.0243947
$330$	300826.	−	222536.i	0.00837093	−	0.00619240i
$331$			1.16408e6i			0.0320996i	0.999871	+	0.0160498i	$0.00510903\pi$
$331$			1.16408e6i			0.0320996i	−0.999871	+	0.0160498i	$0.994891\pi$
$332$	−5.36951e7	−	1.64322e7i	−1.46730	−	0.449037i
$333$	−2.89159e6			−0.0783077
$334$	−2.76906e7	−	3.74323e7i	−0.743178	−	1.00463i
$335$		−	2.43651e7i		−	0.648089i
$336$	1.69487e6	+	1.14454e6i	0.0446804	+	0.0301727i
$337$	1.47881e7			0.386387			0.193194	−	0.981161i	$-0.438115\pi$
$337$	1.47881e7			0.386387			0.193194	+	0.981161i	$0.438115\pi$
$338$	−6.86526e6	+	5.07858e6i	−0.177790	+	0.131520i
$339$		−	1.52841e7i		−	0.392319i
$340$	−6.10452e6	+	1.99476e7i	−0.155315	+	0.507520i
$341$	−1.96494e6			−0.0495550
$342$	1.74437e7	+	2.35805e7i	0.436074	+	0.589487i
$343$		−	5.69450e6i		−	0.141115i
$344$	6.65281e7	−	2.35283e7i	1.63429	−	0.577983i
$345$	−9.85913e6			−0.240094
$346$	−2.12885e7	+	1.57482e7i	−0.513945	+	0.380191i
$347$		−	1.67575e7i		−	0.401072i	−0.979686	−	0.200536i	$-0.935732\pi$
$347$		−	1.67575e7i		−	0.401072i	0.979686	−	0.200536i	$-0.0642683\pi$
$348$	2.40145e7	+	7.34911e6i	0.569817	+	0.174380i
$349$	2.65359e7			0.624248			0.312124	−	0.950041i	$-0.398959\pi$
$349$	2.65359e7			0.624248			0.312124	+	0.950041i	$0.398959\pi$
$350$	−360722.	−	487627.i	−0.00841335	−	0.0113732i
$351$		−	4.12778e7i		−	0.954541i
$352$	57207.3	+	1.33104e6i	0.00131167	+	0.0305185i
$353$	5.51050e7			1.25276			0.626379	−	0.779519i	$-0.284536\pi$
$353$	5.51050e7			1.25276			0.626379	+	0.779519i	$0.284536\pi$
$354$	−758112.	+	560814.i	−0.0170893	+	0.0126418i
$355$			1.57350e7i			0.351707i
$356$	−924923.	+	3.02234e6i	−0.0205001	+	0.0669875i
$357$	−2.91129e6			−0.0639853
$358$	−1.22601e7	−	1.65732e7i	−0.267204	−	0.361209i
$359$			4.29022e7i			0.927249i	0.886032	+	0.463625i	$0.153451\pi$
$359$			4.29022e7i			0.927249i	−0.886032	+	0.463625i	$0.846549\pi$
$360$	2.91526e6	+	8.24312e6i	0.0624841	+	0.176679i
$361$	−9.70016e7			−2.06185
$362$	2.24731e7	−	1.66245e7i	0.473737	−	0.350447i
$363$		−	3.64239e7i		−	0.761493i
$364$	−2.87887e6	−	881017.i	−0.0596923	−	0.0182675i
$365$	−1.37993e7			−0.283779
$366$	1.85109e7	+	2.50232e7i	0.377559	+	0.510386i
$367$		−	4.92753e7i		−	0.996853i	−0.866932	−	0.498427i	$-0.833911\pi$
$367$		−	4.92753e7i		−	0.996853i	0.866932	−	0.498427i	$-0.166089\pi$
$368$	1.96449e7	−	2.90906e7i	0.394191	−	0.583727i
$369$	−3.06442e7			−0.609915
$370$	3.40320e6	−	2.51752e6i	0.0671865	−	0.0497012i
$371$		−	1.47702e6i		−	0.0289245i
$372$	−1.86271e7	+	6.08671e7i	−0.361839	+	1.18237i
$373$	−1.02492e8			−1.97498			−0.987489	−	0.157685i	$-0.949597\pi$
$373$	−1.02492e8			−1.97498			−0.987489	+	0.157685i	$0.949597\pi$
$374$	−1.12789e6	−	1.52468e6i	−0.0215601	−	0.0291451i
$375$			3.59509e6i			0.0681736i
$376$	1.72837e7	−	6.11255e6i	0.325143	−	0.114990i
$377$	−3.69705e7			−0.689971
$378$	−3.32198e6	+	2.45743e6i	−0.0615065	+	0.0454995i
$379$		−	2.40144e7i		−	0.441117i	−0.975374	−	0.220559i	$-0.929212\pi$
$379$		−	2.40144e7i		−	0.441117i	0.975374	−	0.220559i	$-0.0707881\pi$
$380$	−4.10599e7	−	1.25655e7i	−0.748285	−	0.228996i
$381$	5.05894e7			0.914712
$382$	2.92174e7	+	3.94963e7i	0.524145	+	0.708543i
$383$		−	5.08955e7i		−	0.905906i	−0.891534	−	0.452953i	$-0.850371\pi$
$383$		−	5.08955e7i		−	0.905906i	0.891534	−	0.452953i	$-0.149629\pi$
$384$	4.17734e7	+	1.08458e7i	0.737744	+	0.191543i
$385$	55143.3			0.000966297
$386$	1.81129e7	−	1.33990e7i	0.314939	−	0.232976i
$387$			4.21031e7i			0.726408i
$388$	2.81752e7	−	9.20673e7i	0.482360	−	1.57620i
$389$	−3.54629e7			−0.602457			−0.301228	−	0.953552i	$-0.597397\pi$
$389$	−3.54629e7			−0.602457			−0.301228	+	0.953552i	$0.597397\pi$
$390$	1.06124e7	+	1.43460e7i	0.178905	+	0.241844i
$391$			4.99693e7i			0.835936i
$392$	−1.99836e7	−	5.65053e7i	−0.331754	−	0.938061i
$393$	1.80086e7			0.296690
$394$	−2.74229e7	+	2.02861e7i	−0.448358	+	0.331673i
$395$		−	3.17842e7i		−	0.515728i
$396$	−760099.	−	232612.i	−0.0122401	−	0.00374582i
$397$	1.41021e7			0.225379			0.112690	−	0.993630i	$-0.464053\pi$
$397$	1.41021e7			0.225379			0.112690	+	0.993630i	$0.464053\pi$
$398$	7.27561e6	+	9.83522e6i	0.115404	+	0.156004i
$399$		−	5.99257e6i		−	0.0943397i
$400$	−1.06078e7	−	7.16344e6i	−0.165747	−	0.111929i
$401$	7.63677e7			1.18434			0.592170	−	0.805813i	$-0.298271\pi$
$401$	7.63677e7			1.18434			0.592170	+	0.805813i	$0.298271\pi$
$402$	5.76888e7	−	4.26753e7i	0.888001	−	0.656899i
$403$		−	9.37054e7i		−	1.43169i
$404$	−3.63464e7	+	1.18768e8i	−0.551210	+	1.80117i
$405$	1.20425e7			0.181281
$406$	2.20100e6	+	2.97533e6i	0.0328884	+	0.0444587i
$407$			384851.i			0.00570833i
$408$	−5.79214e7	+	2.04844e7i	−0.852823	+	0.301609i
$409$	−4.76292e6			−0.0696150			−0.0348075	−	0.999394i	$-0.511082\pi$
$409$	−4.76292e6			−0.0696150			−0.0348075	+	0.999394i	$0.511082\pi$
$410$	3.60660e7	−	2.66798e7i	0.523295	−	0.387108i
$411$			3.70074e7i			0.533044i
$412$	−2.55148e6	−	780826.i	−0.0364839	−	0.0111651i
$413$	−138967.			−0.00197270
$414$	1.24556e7	+	1.68375e7i	0.175535	+	0.237289i
$415$			4.90478e7i			0.686239i
$416$	−6.34756e7	+	2.72814e6i	−0.881711	+	0.0378954i
$417$	−2.68652e6			−0.0370495
$418$	3.13840e6	−	2.32163e6i	0.0429714	−	0.0317881i
$419$			9.51171e7i			1.29305i	0.762891	+	0.646527i	$0.223779\pi$
$419$			9.51171e7i			1.29305i	−0.762891	+	0.646527i	$0.776221\pi$
$420$	522742.	−	1.70815e6i	0.00705569	−	0.0230557i
$421$	7.92057e7			1.06148			0.530738	−	0.847536i	$-0.321915\pi$
$421$	7.92057e7			1.06148			0.530738	+	0.847536i	$0.321915\pi$
$422$	6.18409e7	+	8.35970e7i	0.822884	+	1.11238i
$423$			1.09382e7i			0.144519i
$424$	−1.03927e7	−	2.93861e7i	−0.136342	−	0.385517i
$425$	1.82211e7			0.237360
$426$	−3.72554e7	+	2.75597e7i	−0.481904	+	0.356489i
$427$			4.58691e6i			0.0589164i
$428$	−4.41608e7	−	1.35144e7i	−0.563255	−	0.172372i
$429$	−1.62232e6			−0.0205477
$430$	−3.66563e7	−	4.95523e7i	−0.461045	−	0.623244i
$431$			1.24667e8i			1.55711i	0.627576	+	0.778555i	$0.284047\pi$
$431$			1.24667e8i			1.55711i	−0.627576	+	0.778555i	$0.715953\pi$
$432$	−4.88012e7	+	7.22659e7i	−0.605312	+	0.896359i
$433$	9.68564e7			1.19307			0.596533	−	0.802588i	$-0.296544\pi$
$433$	9.68564e7			1.19307			0.596533	+	0.802588i	$0.296544\pi$
$434$	−7.54128e6	+	5.57867e6i	−0.0922520	+	0.0682435i
$435$		−	2.19360e7i		−	0.266496i
$436$	−4.15041e6	+	1.35622e7i	−0.0500762	+	0.163633i
$437$	−1.02856e8			−1.23250
$438$	−2.41694e7	−	3.26724e7i	−0.287636	−	0.388829i
$439$		−	8.52847e7i		−	1.00804i	−0.863692	−	0.504020i	$-0.831854\pi$
$439$		−	8.52847e7i		−	1.00804i	0.863692	−	0.504020i	$-0.168146\pi$
$440$	1.09710e6	−	388000.i	0.0128792	−	0.00455485i
$441$	3.57600e7			0.416948
$442$	7.27100e7	−	5.37873e7i	0.842030	−	0.622892i
$443$			6.98986e7i			0.804002i	0.915639	+	0.402001i	$0.131685\pi$
$443$			6.98986e7i			0.804002i	−0.915639	+	0.402001i	$0.868315\pi$
$444$	1.19213e7	+	3.64827e6i	0.136200	+	0.0416810i
$445$	2.76076e6			0.0313292
$446$	−3.14063e7	−	4.24552e7i	−0.354007	−	0.478549i
$447$			9.18067e7i			1.02790i
$448$	3.99852e6	+	4.94601e6i	0.0444698	+	0.0550073i
$449$	7.16693e7			0.791762			0.395881	−	0.918302i	$-0.370439\pi$
$449$	7.16693e7			0.791762			0.395881	+	0.918302i	$0.370439\pi$
$450$	6.13974e6	−	4.54188e6i	0.0673771	−	0.0498423i
$451$			4.07853e6i			0.0444604i
$452$	1.39093e7	−	4.54510e7i	0.150623	−	0.492185i
$453$	−1.09473e8			−1.17763
$454$	−7.43060e7	−	1.00447e8i	−0.794066	−	1.07342i
$455$			2.62971e6i			0.0279173i
$456$	−4.21650e7	−	1.19225e8i	−0.444690	−	1.25740i
$457$	−8.06623e7			−0.845127			−0.422563	−	0.906333i	$-0.638870\pi$
$457$	−8.06623e7			−0.845127			−0.422563	+	0.906333i	$0.638870\pi$
$458$	3.55019e6	−	2.62626e6i	0.0369535	−	0.0273364i
$459$		−	1.24132e8i		−	1.28365i
$460$	−2.93186e7	−	8.97233e6i	−0.301211	−	0.0921789i
$461$	1.09917e8			1.12192			0.560961	−	0.827843i	$-0.310432\pi$
$461$	1.09917e8			1.12192			0.560961	+	0.827843i	$0.310432\pi$
$462$	96583.0	+	130562.i	0.000979434	+	0.00132401i
$463$		−	7.14847e7i		−	0.720229i	−0.932908	−	0.360114i	$-0.882738\pi$
$463$		−	7.14847e7i		−	0.720229i	0.932908	−	0.360114i	$-0.117262\pi$
$464$	6.47250e7	+	4.37089e7i	0.647915	+	0.437538i
$465$	5.55991e7			0.552979
$466$	−1.69463e7	+	1.25360e7i	−0.167462	+	0.123880i
$467$		−	1.00414e8i		−	0.985929i	−0.870050	−	0.492964i	$-0.835913\pi$
$467$		−	1.00414e8i		−	0.985929i	0.870050	−	0.492964i	$-0.164087\pi$
$468$	1.10929e7	−	3.62481e7i	0.108220	−	0.353629i
$469$	1.05747e7			0.102506
$470$	−9.52316e6	−	1.28735e7i	−0.0917249	−	0.123994i
$471$			1.06579e8i			1.02002i
$472$	−2.76481e6	+	977800.i	−0.0262929	+	0.00929874i
$473$	5.60362e6			0.0529524
$474$	7.52549e7	−	5.56698e7i	0.706642	−	0.522739i
$475$			3.75062e7i			0.349963i
$476$	−8.65745e6	−	2.64943e6i	−0.0802730	−	0.0245658i
$477$	1.85973e7			0.171354
$478$	5.83744e7	+	7.89109e7i	0.534489	+	0.722526i
$479$		−	9.67106e7i		−	0.879969i	−0.898005	−	0.439984i	$-0.854984\pi$
$479$		−	9.67106e7i		−	0.879969i	0.898005	−	0.439984i	$-0.145016\pi$
$480$	−1.61871e6	−	3.76625e7i	−0.0146368	−	0.340554i
$481$	−1.83530e7			−0.164919
$482$	−7.21064e7	+	5.33408e7i	−0.643921	+	0.476341i
$483$		−	4.27897e6i		−	0.0379750i
$484$	3.31476e7	−	1.08316e8i	0.292359	−	0.955333i
$485$	−8.40989e7			−0.737165
$486$	−5.27463e7	−	7.13028e7i	−0.459497	−	0.621152i
$487$		−	1.33542e8i		−	1.15619i	−0.815969	−	0.578096i	$-0.803796\pi$
$487$		−	1.33542e8i		−	1.15619i	0.815969	−	0.578096i	$-0.196204\pi$
$488$	3.22745e7	+	9.12586e7i	0.277715	+	0.785262i
$489$	−3.44270e7			−0.294423
$490$	−4.20869e7	+	3.11338e7i	−0.357733	+	0.264633i
$491$		−	1.33885e8i		−	1.13107i	−0.824725	−	0.565534i	$-0.808670\pi$
$491$		−	1.33885e8i		−	1.13107i	0.824725	−	0.565534i	$-0.191330\pi$
$492$	1.26339e8	+	3.86632e7i	1.06082	+	0.324640i
$493$	−1.11179e8			−0.927858
$494$	1.10715e8	+	1.49666e8i	0.918390	+	1.24149i
$495$			694313.i			0.00572453i
$496$	−1.10785e8	+	1.64052e8i	−0.907892	+	1.34443i
$497$	−6.82915e6			−0.0556285
$498$	−1.16129e8	+	8.59068e7i	−0.940273	+	0.695568i
$499$			1.04600e8i			0.841842i	0.907097	+	0.420921i	$0.138293\pi$
$499$			1.04600e8i			0.841842i	−0.907097	+	0.420921i	$0.861707\pi$
$500$	−3.27172e6	+	1.06909e7i	−0.0261738	+	0.0855274i
$501$	−1.19776e8			−0.952481
$502$	3.64178e7	+	4.92299e7i	0.287874	+	0.389150i
$503$			1.83299e8i			1.44031i	0.693813	+	0.720155i	$0.255930\pi$
$503$			1.83299e8i			1.44031i	−0.693813	+	0.720155i	$0.744070\pi$
$504$	−3.57760e6	+	1.26525e6i	−0.0279448	+	0.00988293i
$505$	1.08489e8			0.842385
$506$	2.24096e6	−	1.65775e6i	0.0172975	−	0.0127958i
$507$			2.19675e7i			0.168561i
$508$	1.50440e8	+	4.60390e7i	1.14755	+	0.351184i
$509$	−2.27028e8			−1.72158			−0.860789	−	0.508961i	$-0.830030\pi$
$509$	−2.27028e8			−1.72158			−0.860789	+	0.508961i	$0.830030\pi$
$510$	3.19141e7	+	4.31417e7i	0.240587	+	0.325227i
$511$		−	5.98906e6i		−	0.0448845i
$512$	1.14353e8	+	7.02687e7i	0.852000	+	0.523542i
$513$	2.55512e8			1.89260
$514$	−7.02234e7	+	5.19478e7i	−0.517122	+	0.382541i
$515$			2.33065e6i			0.0170630i
$516$	5.31206e7	−	1.73581e8i	0.386646	−	1.26343i
$517$	1.45580e6			0.0105349
$518$	1.09263e6	+	1.47702e6i	0.00786110	+	0.0106267i
$519$			6.81190e7i			0.487266i
$520$	1.85032e7	+	5.23193e7i	0.131594	+	0.372093i
$521$	−3.90610e7			−0.276204			−0.138102	−	0.990418i	$-0.544100\pi$
$521$	−3.90610e7			−0.276204			−0.138102	+	0.990418i	$0.544100\pi$
$522$	−3.74626e7	+	2.77130e7i	−0.263382	+	0.194837i
$523$			1.21695e8i			0.850686i	0.905032	+	0.425343i	$0.139846\pi$
$523$			1.21695e8i			0.850686i	−0.905032	+	0.425343i	$0.860154\pi$
$524$	5.35532e7	+	1.63888e7i	0.372213	+	0.113908i
$525$	−1.56031e6			−0.0107828
$526$	−4.24089e7	−	5.73286e7i	−0.291407	−	0.393926i
$527$		−	2.81794e8i		−	1.92531i
$528$	2.84022e6	+	1.91800e6i	0.0192953	+	0.0130301i
$529$	7.45918e7			0.503876
$530$	−2.18877e7	+	1.61914e7i	−0.147018	+	0.108757i
$531$		−	1.74974e6i		−	0.0116866i
$532$	5.45356e6	−	1.78204e7i	0.0362197	−	0.118354i
$533$	−1.94499e8			−1.28451
$534$	4.83545e6	+	6.53659e6i	0.0317551	+	0.0429267i
$535$			4.03387e7i			0.263427i
$536$	2.10389e8	−	7.44060e7i	1.36625	−	0.483185i
$537$	−5.30310e7			−0.342458
$538$	1.72710e8	−	1.27762e8i	1.10910	−	0.820457i
$539$		−	4.75940e6i		−	0.0303939i
$540$	7.28323e7	+	2.22887e7i	0.462533	+	0.141548i
$541$	1.30798e8			0.826053			0.413027	−	0.910719i	$-0.364472\pi$
$541$	1.30798e8			0.826053			0.413027	+	0.910719i	$0.364472\pi$
$542$	−1.34645e8	−	1.82015e8i	−0.845656	−	1.14316i
$543$		−	7.19094e7i		−	0.449145i
$544$	−1.90886e8	+	8.20415e6i	−1.18571	+	0.0509609i
$545$	1.23884e7			0.0765287
$546$	−6.22630e6	+	4.60591e6i	−0.0382518	+	0.0282968i
$547$			1.53703e8i			0.939120i	0.882901	+	0.469560i	$0.155587\pi$
$547$			1.53703e8i			0.939120i	−0.882901	+	0.469560i	$0.844413\pi$
$548$	−3.36787e7	+	1.10051e8i	−0.204651	+	0.668731i
$549$	−5.77540e7			−0.349032
$550$	−604492.	−	817156.i	−0.00363331	−	0.00491153i
$551$		−	2.28850e8i		−	1.36803i
$552$	−3.01077e7	−	8.51320e7i	−0.179003	−	0.506146i
$553$	1.37947e7			0.0815712
$554$	4.00665e7	−	2.96392e7i	0.235642	−	0.174316i
$555$		−	1.08895e7i		−	0.0636988i
$556$	−7.98905e6	−	2.44488e6i	−0.0464805	−	0.0142243i
$557$	6.91251e7			0.400009			0.200005	−	0.979795i	$-0.435904\pi$
$557$	6.91251e7			0.400009			0.200005	+	0.979795i	$0.435904\pi$
$558$	−7.02413e7	−	9.49527e7i	−0.404287	−	0.546519i
$559$			2.67229e8i			1.52985i
$560$	3.10901e6	−	4.60389e6i	0.0177035	−	0.0262157i
$561$	−4.87868e6			−0.0276321
$562$	−2.04385e8	+	1.51194e8i	−1.15144	+	0.851777i
$563$		−	1.01350e8i		−	0.567937i	−0.958834	−	0.283969i	$-0.908349\pi$
$563$		−	1.01350e8i		−	0.567937i	0.958834	−	0.283969i	$-0.0916512\pi$
$564$	1.38005e7	−	4.50955e7i	0.0769233	−	0.251360i
$565$	−4.15173e7			−0.230188
$566$	−3.19945e7	−	4.32505e7i	−0.176452	−	0.238529i
$567$			5.22659e6i			0.0286727i
$568$	−1.35869e8	+	4.80514e7i	−0.741439	+	0.262217i
$569$	−1.24684e8			−0.676820			−0.338410	−	0.940999i	$-0.609889\pi$
$569$	−1.24684e8			−0.676820			−0.338410	+	0.940999i	$0.609889\pi$
$570$	−8.88026e7	+	6.56917e7i	−0.479514	+	0.354720i
$571$		−	1.02626e8i		−	0.551252i	−0.961265	−	0.275626i	$-0.911115\pi$
$571$		−	1.02626e8i		−	0.551252i	0.961265	−	0.275626i	$-0.0888851\pi$
$572$	−4.82436e6	−	1.47639e6i	−0.0257782	−	0.00788885i
$573$	1.26380e8			0.671762
$574$	1.15793e7	+	1.56530e7i	0.0612277	+	0.0827680i
$575$			2.67811e7i			0.140872i
$576$	−6.22755e7	+	5.03456e7i	−0.325874	+	0.263447i
$577$	1.73246e8			0.901853			0.450926	−	0.892561i	$-0.351094\pi$
$577$	1.73246e8			0.901853			0.450926	+	0.892561i	$0.351094\pi$
$578$	6.34154e7	−	4.69116e7i	0.328406	−	0.242939i
$579$		−	5.79577e7i		−	0.298590i
$580$	1.99629e7	−	6.52323e7i	0.102315	−	0.334333i
$581$	−2.12873e7			−0.108540
$582$	−1.47298e8	−	1.99119e8i	−0.747187	−	1.01005i
$583$		−	2.47517e6i		−	0.0124911i
$584$	−4.21403e7	−	1.19155e8i	−0.211572	−	0.598238i
$585$	−3.31108e7			−0.165387
$586$	1.87920e8	−	1.39014e8i	0.933859	−	0.690822i
$587$			1.99472e8i			0.986204i	0.869971	+	0.493102i	$0.164137\pi$
$587$			1.99472e8i			0.986204i	−0.869971	+	0.493102i	$0.835863\pi$
$588$	−1.47430e8	−	4.51177e7i	−0.725192	−	0.221929i
$589$	5.80043e8			2.83867
$590$	1.52338e6	+	2.05932e6i	0.00741742	+	0.0100269i
$591$			8.77479e7i			0.425084i
$592$	3.21310e7	+	2.16981e7i	0.154867	+	0.104582i
$593$	2.74305e8			1.31543			0.657717	−	0.753265i	$-0.271522\pi$
$593$	2.74305e8			1.31543			0.657717	+	0.753265i	$0.271522\pi$
$594$	−5.56691e6	+	4.11812e6i	−0.0265616	+	0.0196490i
$595$			7.90815e6i			0.0375426i
$596$	−8.35489e7	+	2.73011e8i	−0.394641	+	1.28956i
$597$	3.14707e7			0.147905
$598$	7.90558e7	+	1.06868e8i	0.369683	+	0.499741i
$599$		−	3.19919e8i		−	1.48854i	−0.667881	−	0.744268i	$-0.732798\pi$
$599$		−	3.19919e8i		−	1.48854i	0.667881	−	0.744268i	$-0.267202\pi$
$600$	−3.10431e7	+	1.09787e7i	−0.143718	+	0.0508272i
$601$	−3.87120e8			−1.78329			−0.891646	−	0.452733i	$-0.850449\pi$
$601$	−3.87120e8			−1.78329			−0.891646	+	0.452733i	$0.850449\pi$
$602$	2.15062e7	−	1.59092e7i	0.0985767	−	0.0729222i
$603$			1.33147e8i			0.607267i
$604$	−3.25544e8	−	9.96258e7i	−1.47740	−	0.452128i
$605$	−9.89409e7			−0.446796
$606$	1.90017e8	+	2.56866e8i	0.853836	+	1.15422i
$607$			3.02210e8i			1.35127i	0.737236	+	0.675635i	$0.236131\pi$
$607$			3.02210e8i			1.35127i	−0.737236	+	0.675635i	$0.763869\pi$
$608$	−1.68874e7	−	3.92918e8i	−0.0751365	−	1.74820i
$609$	9.52046e6			0.0421508
$610$	6.79723e7	−	5.02826e7i	0.299463	−	0.221528i
$611$			6.94250e7i			0.304363i
$612$	3.33591e7	−	1.09007e8i	0.145532	−	0.475552i
$613$	−4.00237e8			−1.73754			−0.868771	−	0.495213i	$-0.835090\pi$
$613$	−4.00237e8			−1.73754			−0.868771	+	0.495213i	$0.835090\pi$
$614$	1.08781e8	+	1.47051e8i	0.469946	+	0.635276i
$615$		−	1.15404e8i		−	0.496130i
$616$	168396.	+	476154.i	0.000720427	+	0.00203707i
$617$	−6.04515e6			−0.0257366			−0.0128683	−	0.999917i	$-0.504096\pi$
$617$	−6.04515e6			−0.0257366			−0.0128683	+	0.999917i	$0.504096\pi$
$618$	−5.51823e6	+	4.08212e6i	−0.0233795	+	0.0172950i
$619$			2.61775e8i			1.10371i	0.833939	+	0.551857i	$0.186081\pi$
$619$			2.61775e8i			1.10371i	−0.833939	+	0.551857i	$0.813919\pi$
$620$	1.65338e8	+	5.05981e7i	0.693741	+	0.212304i
$621$	1.82447e8			0.761838
$622$	−2.66442e7	−	3.60178e7i	−0.110721	−	0.149674i
$623$			1.19820e6i			0.00495524i
$624$	−9.14670e7	+	1.35446e8i	−0.376453	+	0.557460i
$625$	9.76562e6			0.0400000
$626$	−8.87900e7	+	6.56824e7i	−0.361944	+	0.267748i
$627$		−	1.00422e7i		−	0.0407407i
$628$	−9.69925e7	+	3.16940e8i	−0.391615	+	1.27967i
$629$	−5.51918e7			−0.221780
$630$	1.97122e6	+	2.66471e6i	0.00788341	+	0.0106568i
$631$			6.02284e7i			0.239725i	0.992791	+	0.119862i	$0.0382454\pi$
$631$			6.02284e7i			0.239725i	−0.992791	+	0.119862i	$0.961755\pi$
$632$	2.74452e8	−	9.70624e7i	1.08721	−	0.384503i
$633$	2.67494e8			1.05464
$634$	3.37598e8	−	2.49738e8i	1.32474	−	0.979981i
$635$		−	1.37420e8i		−	0.536696i
$636$	−7.66721e7	−	2.34638e7i	−0.298034	−	0.0912069i
$637$	2.26969e8			0.878110
$638$	3.68840e6	+	4.98601e6i	0.0142029	+	0.0191995i
$639$		−	8.59862e7i		−	0.329554i
$640$	2.94612e7	−	1.13472e8i	0.112386	−	0.432862i
$641$	−4.36896e8			−1.65884			−0.829419	−	0.558627i	$-0.811328\pi$
$641$	−4.36896e8			−1.65884			−0.829419	+	0.558627i	$0.811328\pi$
$642$	−9.55089e7	+	7.06528e7i	−0.360943	+	0.267008i
$643$		−	2.07486e8i		−	0.780468i	−0.920716	−	0.390234i	$-0.872394\pi$
$643$		−	2.07486e8i		−	0.780468i	0.920716	−	0.390234i	$-0.127606\pi$
$644$	3.89409e6	−	1.27246e7i	0.0145797	−	0.0476416i
$645$	−1.58557e8			−0.590891
$646$	3.32947e8	+	4.50080e8i	1.23503	+	1.66952i
$647$			2.85482e8i			1.05406i	0.849847	+	0.527030i	$0.176694\pi$
$647$			2.85482e8i			1.05406i	−0.849847	+	0.527030i	$0.823306\pi$
$648$	3.67754e7	+	1.03985e8i	0.135155	+	0.382162i
$649$	−232878.			−0.000851912
$650$	3.89690e7	−	2.88274e7i	0.141899	−	0.104970i
$651$			2.41306e7i			0.0874631i
$652$	−1.02377e8	−	3.13304e7i	−0.369370	−	0.113038i
$653$	−2.64397e8			−0.949550			−0.474775	−	0.880107i	$-0.657470\pi$
$653$	−2.64397e8			−0.949550			−0.474775	+	0.880107i	$0.657470\pi$
$654$	2.16981e7	+	2.93317e7i	0.0775691	+	0.104858i
$655$		−	4.89182e7i		−	0.174079i
$656$	3.40514e8	+	2.29949e8i	1.20621	+	0.814556i
$657$	7.54086e7			0.265904
$658$	5.58722e6	−	4.13315e6i	0.0196118	−	0.0145079i
$659$		−	2.24450e8i		−	0.784267i	−0.919908	−	0.392133i	$-0.871737\pi$
$659$		−	2.24450e8i		−	0.784267i	0.919908	−	0.392133i	$-0.128263\pi$
$660$	876001.	−	2.86248e6i	0.00304700	−	0.00995660i
$661$	5.36714e7			0.185840			0.0929199	−	0.995674i	$-0.470380\pi$
$661$	5.36714e7			0.185840			0.0929199	+	0.995674i	$0.470380\pi$
$662$	5.53836e6	+	7.48679e6i	0.0190901	+	0.0258061i
$663$		−	2.32658e8i		−	0.798319i
$664$	−4.23520e8	+	1.49782e8i	−1.44667	+	0.511628i
$665$	−1.62781e7			−0.0553526
$666$	−1.85973e7	+	1.37574e7i	−0.0629545	+	0.0465706i
$667$		−	1.63409e8i		−	0.550679i
$668$	−3.56184e8	−	1.09002e8i	−1.19494	−	0.365685i
$669$	−1.35848e8			−0.453707
$670$	−1.15922e8	−	1.56704e8i	−0.385427	−	0.521023i
$671$			7.68665e6i			0.0254431i
$672$	1.63459e7	−	702538.i	0.0538644	−	0.00231506i
$673$	−2.66858e8			−0.875457			−0.437729	−	0.899107i	$-0.644217\pi$
$673$	−2.66858e8			−0.875457			−0.437729	+	0.899107i	$0.644217\pi$
$674$	9.51098e7	−	7.03575e7i	0.310631	−	0.229790i
$675$		−	6.65287e7i		−	0.216320i
$676$	−1.99916e7	+	6.53258e7i	−0.0647152	+	0.211468i
$677$	1.94003e8			0.625234			0.312617	−	0.949879i	$-0.398794\pi$
$677$	1.94003e8			0.625234			0.312617	+	0.949879i	$0.398794\pi$
$678$	−7.27171e7	−	9.82995e7i	−0.233318	−	0.315400i
$679$		−	3.64998e7i		−	0.116595i
$680$	5.56434e7	+	1.57336e8i	0.176965	+	0.500383i
$681$	−3.21412e8			−1.01770
$682$	−1.26375e7	+	9.34863e6i	−0.0398391	+	0.0294710i
$683$		−	1.59493e8i		−	0.500586i	−0.968170	−	0.250293i	$-0.919473\pi$
$683$		−	1.59493e8i		−	0.500586i	0.968170	−	0.250293i	$-0.0805270\pi$
$684$	2.24378e8	+	6.86660e7i	0.701152	+	0.214572i
$685$	1.00526e8			0.312757
$686$	−2.70928e7	−	3.66242e7i	−0.0839230	−	0.113448i
$687$		−	1.13599e7i		−	0.0350352i
$688$	3.15935e8	−	4.67844e8i	0.970136	−	1.43660i
$689$	1.18037e8			0.360879
$690$	−6.34090e7	+	4.69069e7i	−0.193021	+	0.142787i
$691$		−	6.04045e8i		−	1.83078i	−0.402573	−	0.915388i	$-0.631884\pi$
$691$		−	6.04045e8i		−	1.83078i	0.402573	−	0.915388i	$-0.368116\pi$
$692$	−6.19918e7	+	2.02569e8i	−0.187075	+	0.611300i
$693$	−301339.			−0.000905432
$694$	−7.97275e7	−	1.07776e8i	−0.238523	−	0.322437i
$695$			7.29760e6i			0.0217383i
$696$	1.89414e8	−	6.69880e7i	0.561803	−	0.198687i
$697$	−5.84905e8			−1.72738
$698$	1.70666e8	−	1.26250e8i	0.501857	−	0.371249i
$699$			5.42247e7i			0.158769i
$700$	−4.63997e6	−	1.41996e6i	−0.0135276	−	0.00413983i
$701$	3.93380e8			1.14198			0.570990	−	0.820957i	$-0.306559\pi$
$701$	3.93380e8			1.14198			0.570990	+	0.820957i	$0.306559\pi$
$702$	−1.96387e8	−	2.65478e8i	−0.567678	−	0.767392i
$703$		−	1.13606e8i		−	0.326991i
$704$	6.70064e6	+	8.28843e6i	0.0192043	+	0.0237549i
$705$	−4.11925e7			−0.117558
$706$	3.54408e8	−	2.62174e8i	1.00714	−	0.745032i
$707$			4.70852e7i			0.133238i
$708$	−2.20761e6	+	7.21375e6i	−0.00622047	+	0.0203265i
$709$	1.36855e8			0.383992			0.191996	−	0.981396i	$-0.438504\pi$
$709$	1.36855e8			0.383992			0.191996	+	0.981396i	$0.438504\pi$
$710$	7.48625e7	+	1.01200e8i	0.209165	+	0.282751i
$711$			1.73690e8i			0.483243i
$712$	8.43079e6	+	2.38387e7i	0.0233576	+	0.0660455i
$713$	4.14177e8			1.14266
$714$	−1.87240e7	+	1.38511e7i	−0.0514402	+	0.0380529i
$715$			4.40682e6i			0.0120561i
$716$	−1.57701e8	−	4.82610e7i	−0.429631	−	0.131479i
$717$	2.52499e8			0.685019
$718$	2.04116e8	+	2.75926e8i	0.551448	+	0.745451i
$719$			6.36997e8i			1.71376i	0.515513	+	0.856881i	$0.327601\pi$
$719$			6.36997e8i			1.71376i	−0.515513	+	0.856881i	$0.672399\pi$
$720$	5.79679e7	+	3.91457e7i	0.155307	+	0.104879i
$721$	−1.01153e6			−0.00269881
$722$	−6.23866e8	+	4.61505e8i	−1.65760	+	1.22621i
$723$			2.30726e8i			0.610495i
$724$	6.54413e7	−	2.13841e8i	0.172439	−	0.563475i
$725$	−5.95865e7			−0.156363
$726$	−1.73294e8	−	2.34260e8i	−0.452870	−	0.612193i
$727$		−	5.89955e7i		−	0.153538i	−0.997049	−	0.0767689i	$-0.975540\pi$
$727$		−	5.89955e7i		−	0.153538i	0.997049	−	0.0767689i	$-0.0244604\pi$
$728$	−2.27071e7	+	8.03058e6i	−0.0588529	+	0.0208139i
$729$	−3.85198e8			−0.994265
$730$	−8.87505e7	+	6.56532e7i	−0.228140	+	0.168767i
$731$			8.03620e8i			2.05730i
$732$	2.38106e8	+	7.28671e7i	0.607067	+	0.185780i
$733$	1.27557e7			0.0323886			0.0161943	−	0.999869i	$-0.494845\pi$
$733$	1.27557e7			0.0323886			0.0161943	+	0.999869i	$0.494845\pi$
$734$	−2.34438e8	−	3.16914e8i	−0.592842	−	0.801408i
$735$			1.34670e8i			0.339163i
$736$	−1.20583e7	−	2.80561e8i	−0.0302450	−	0.703711i
$737$	1.77209e7			0.0442674
$738$	−1.97088e8	+	1.45796e8i	−0.490333	+	0.362724i
$739$			5.13652e8i			1.27273i	0.771389	+	0.636364i	$0.219562\pi$
$739$			5.13652e8i			1.27273i	−0.771389	+	0.636364i	$0.780438\pi$
$740$	9.91006e6	−	3.23828e7i	0.0244558	−	0.0799134i
$741$	4.78901e8			1.17704
$742$	−7.02725e6	−	9.49948e6i	−0.0172018	−	0.0232535i
$743$			4.82260e8i			1.17575i	0.808952	+	0.587874i	$0.200035\pi$
$743$			4.82260e8i			1.17575i	−0.808952	+	0.587874i	$0.799965\pi$
$744$	1.69788e8	+	4.80089e8i	0.412276	+	1.16574i
$745$	2.49381e8			0.603108
$746$	−6.59176e8	+	4.87626e8i	−1.58776	+	1.17455i
$747$		−	2.68029e8i		−	0.643014i
$748$	−1.45080e7	−	4.43986e6i	−0.0346659	−	0.0106088i
$749$	−1.75074e7			−0.0416655
$750$	1.71044e7	+	2.31219e7i	0.0405438	+	0.0548074i
$751$		−	8.05235e8i		−	1.90109i	−0.310585	−	0.950546i	$-0.600525\pi$
$751$		−	8.05235e8i		−	1.90109i	0.310585	−	0.950546i	$-0.399475\pi$
$752$	8.20786e7	−	1.21544e8i	0.193009	−	0.285811i
$753$	1.57526e8			0.368949
$754$	−2.37776e8	+	1.75895e8i	−0.554694	+	0.410335i
$755$			2.97369e8i			0.690962i
$756$	−9.67355e6	+	3.16100e7i	−0.0223883	+	0.0731575i
$757$	4.01651e8			0.925894			0.462947	−	0.886386i	$-0.346792\pi$
$757$	4.01651e8			0.925894			0.462947	+	0.886386i	$0.346792\pi$
$758$	−1.14253e8	−	1.54449e8i	−0.262338	−	0.354631i
$759$		−	7.17062e6i		−	0.0163995i
$760$	−3.23860e8	+	1.14536e8i	−0.737762	+	0.260916i
$761$	−2.41523e8			−0.548029			−0.274015	−	0.961726i	$-0.588352\pi$
$761$	−2.41523e8			−0.548029			−0.274015	+	0.961726i	$0.588352\pi$
$762$	3.25366e8	−	2.40690e8i	0.735372	−	0.543992i
$763$			5.37668e6i			0.0121043i
$764$	3.75824e8	+	1.15013e8i	0.842760	+	0.257908i
$765$	−9.95720e7			−0.222409
$766$	−2.42146e8	−	3.27335e8i	−0.538754	−	0.728292i
$767$		−	1.11056e7i		−	0.0246126i
$768$	3.20267e8	−	1.28991e8i	0.707014	−	0.284757i
$769$	2.03639e8			0.447799			0.223899	−	0.974612i	$-0.428121\pi$
$769$	2.03639e8			0.447799			0.223899	+	0.974612i	$0.428121\pi$
$770$	354654.	−	262356.i	0.000776843	−	0.000574670i
$771$			2.24701e8i			0.490277i
$772$	5.27446e7	−	1.72352e8i	0.114637	−	0.374597i
$773$	2.34074e8			0.506774			0.253387	−	0.967365i	$-0.418455\pi$
$773$	2.34074e8			0.506774			0.253387	+	0.967365i	$0.418455\pi$
$774$	2.00314e8	+	2.70786e8i	0.432005	+	0.583987i
$775$		−	1.51028e8i		−	0.324453i
$776$	−2.56820e8	−	7.26180e8i	−0.549597	−	1.55403i
$777$	4.72618e6			0.0100750
$778$	−2.28080e8	+	1.68722e8i	−0.484338	+	0.358289i
$779$		−	1.20396e9i		−	2.54684i
$780$	1.36508e8	+	4.17753e7i	0.287656	+	0.0880310i
$781$	−1.14442e7			−0.0240232
$782$	2.37739e8	+	3.21378e8i	0.497142	+	0.672040i
$783$			4.05935e8i			0.845612i
$784$	−3.97360e8	−	2.68338e8i	−0.824587	−	0.556844i
$785$	2.89509e8			0.598484
$786$	1.15822e8	−	8.56798e7i	0.238520	−	0.176445i
$787$		−	6.41938e8i		−	1.31695i	−0.752603	−	0.658474i	$-0.771202\pi$
$787$		−	6.41938e8i		−	1.31695i	0.752603	−	0.658474i	$-0.228798\pi$
$788$	−7.98552e7	+	2.60941e8i	−0.163202	+	0.533290i
$789$	−1.83440e8			−0.373476
$790$	−1.51220e8	−	2.04420e8i	−0.306710	−	0.414613i
$791$		−	1.80189e7i		−	0.0364082i
$792$	−5.99528e6	+	2.12029e6i	−0.0120680	+	0.00426795i
$793$	−3.66566e8			−0.735076
$794$	9.06979e7	−	6.70938e7i	0.181191	−	0.134036i
$795$			7.00362e7i			0.139387i
$796$	9.35862e7	+	2.86400e7i	0.185555	+	0.0567851i
$797$	1.82268e8			0.360027			0.180013	−	0.983664i	$-0.442386\pi$
$797$	1.82268e8			0.360027			0.180013	+	0.983664i	$0.442386\pi$
$798$	−2.85109e7	−	3.85412e7i	−0.0561051	−	0.0758433i
$799$			2.08777e8i			0.409301i
$800$	−1.02306e8	+	4.39703e6i	−0.199816	+	0.00858794i
$801$	−1.50866e7			−0.0293558
$802$	4.91159e8	−	3.63335e8i	0.952136	−	0.704343i
$803$		−	1.00364e7i		−	0.0193834i
$804$	1.67989e8	−	5.48933e8i	0.323231	−	1.05621i
$805$	−1.16233e7			−0.0222813
$806$	−4.45823e8	−	6.02667e8i	−0.851447	−	1.15099i
$807$		−	5.52637e8i		−	1.05152i
$808$	3.31302e8	+	9.36783e8i	0.628044	+	1.77584i
$809$	−6.12560e8			−1.15692			−0.578460	−	0.815711i	$-0.696346\pi$
$809$	−6.12560e8			−1.15692			−0.578460	+	0.815711i	$0.696346\pi$
$810$	7.74516e7	−	5.72949e7i	0.145739	−	0.107810i
$811$			2.59393e8i			0.486291i	0.969990	+	0.243146i	$0.0781793\pi$
$811$			2.59393e8i			0.486291i	−0.969990	+	0.243146i	$0.921821\pi$
$812$	2.83115e7	+	8.66412e6i	0.0528804	+	0.0161829i
$813$	−5.82410e8			−1.08382
$814$	1.83101e6	+	2.47517e6i	0.00339482	+	0.00458914i
$815$			9.35166e7i			0.172749i
$816$	−2.75063e8	+	4.07319e8i	−0.506246	+	0.749660i
$817$	−1.65416e9			−3.03328
$818$	−3.06327e7	+	2.26606e7i	−0.0559662	+	0.0414010i
$819$		−	1.43704e7i		−	0.0261588i
$820$	1.05024e8	−	3.43183e8i	0.190478	−	0.622421i
$821$	7.94760e8			1.43617			0.718086	−	0.695954i	$-0.245018\pi$
$821$	7.94760e8			1.43617			0.718086	+	0.695954i	$0.245018\pi$
$822$	1.76070e8	+	2.38013e8i	0.317008	+	0.428534i
$823$		−	2.70019e8i		−	0.484390i	−0.970228	−	0.242195i	$-0.922133\pi$
$823$		−	2.70019e8i		−	0.484390i	0.970228	−	0.242195i	$-0.0778674\pi$
$824$	−2.01248e7	+	7.11732e6i	−0.0359708	+	0.0127214i
$825$	−2.61474e6			−0.00465657
$826$	−893766.	+	661164.i	−0.00158593	+	0.00117319i
$827$			6.56468e8i			1.16064i	0.814389	+	0.580320i	$0.197072\pi$
$827$			6.56468e8i			1.16064i	−0.814389	+	0.580320i	$0.802928\pi$
$828$	1.60216e8	+	4.90307e7i	0.282238	+	0.0863728i
$829$	6.40196e8			1.12370			0.561849	−	0.827240i	$-0.310090\pi$
$829$	6.40196e8			1.12370			0.561849	+	0.827240i	$0.310090\pi$
$830$	2.33355e8	+	3.15451e8i	0.408115	+	0.551693i
$831$		−	1.28205e8i		−	0.223409i
$832$	−3.95263e8	+	3.19544e8i	−0.686304	+	0.554831i
$833$	6.82550e8			1.18086
$834$	−1.72784e7	+	1.27817e7i	−0.0297855	+	0.0220338i
$835$			3.25356e8i			0.558856i
$836$	9.13897e6	−	2.98631e7i	0.0156415	−	0.0511113i
$837$	−1.02888e9			−1.75465
$838$	4.52540e8	+	6.11746e8i	0.768997	+	1.03954i
$839$		−	9.87826e8i		−	1.67261i	−0.548265	−	0.836305i	$-0.684711\pi$
$839$		−	9.87826e8i		−	1.67261i	0.548265	−	0.836305i	$-0.315289\pi$
$840$	−4.76486e6	−	1.34730e7i	−0.00803918	−	0.0227314i
$841$	−2.31247e8			−0.388766
$842$	5.09412e8	−	3.76838e8i	0.853361	−	0.631274i
$843$			6.53992e8i			1.09167i
$844$	7.95460e8	+	2.43433e8i	1.32309	+	0.404904i
$845$	5.96719e7			0.0989008
$846$	5.20408e7	+	7.03491e7i	0.0859474	+	0.116184i
$847$		−	4.29414e7i		−	0.0706685i
$848$	−2.06651e8	−	1.39551e8i	−0.338883	−	0.228848i
$849$	−1.38393e8			−0.226147
$850$	1.17189e8	−	8.66907e7i	0.190823	−	0.141161i
$851$		−	8.11200e7i		−	0.131625i
$852$	−1.08487e8	+	3.54500e8i	−0.175412	+	0.573189i
$853$	−4.88523e8			−0.787114			−0.393557	−	0.919300i	$-0.628756\pi$
$853$	−4.88523e8			−0.787114			−0.393557	+	0.919300i	$0.628756\pi$
$854$	2.18232e7	+	2.95007e7i	0.0350384	+	0.0473651i
$855$		−	2.04958e8i		−	0.327919i
$856$	−3.48318e8	+	1.23186e8i	−0.555334	+	0.196399i
$857$	1.42078e8			0.225728			0.112864	−	0.993610i	$-0.463998\pi$
$857$	1.42078e8			0.225728			0.112864	+	0.993610i	$0.463998\pi$
$858$	−1.04339e7	+	7.71850e6i	−0.0165191	+	0.0122200i
$859$		−	1.67240e8i		−	0.263852i	−0.991260	−	0.131926i	$-0.957884\pi$
$859$		−	1.67240e8i		−	0.263852i	0.991260	−	0.131926i	$-0.0421161\pi$
$860$	−4.71510e8	−	1.44295e8i	−0.741303	−	0.226860i
$861$	5.00865e7			0.0784714
$862$	5.93129e8	+	8.01796e8i	0.926035	+	1.25182i
$863$		−	3.61010e8i		−	0.561678i	−0.959755	−	0.280839i	$-0.909387\pi$
$863$		−	3.61010e8i		−	0.561678i	0.959755	−	0.280839i	$-0.0906127\pi$
$864$	2.99549e7	+	6.96960e8i	0.0464437	+	1.08060i
$865$	1.85037e8			0.285897
$866$	6.22932e8	−	4.60814e8i	0.959151	−	0.709533i
$867$		−	2.02917e8i		−	0.311358i
$868$	−2.19601e7	+	7.17584e7i	−0.0335796	+	0.109727i
$869$	2.31169e7			0.0352266
$870$	−1.04365e8	−	1.41082e8i	−0.158489	−	0.214246i
$871$			8.45086e8i			1.27893i
$872$	3.78315e7	+	1.06972e8i	0.0570563	+	0.161331i
$873$	4.59571e8			0.690733
$874$	−6.61521e8	+	4.89361e8i	−0.990853	+	0.732984i
$875$			4.23838e6i			0.00632668i
$876$	−3.10891e8	−	9.51416e7i	−0.462484	−	0.141533i
$877$	1.29370e8			0.191794			0.0958970	−	0.995391i	$-0.469428\pi$
$877$	1.29370e8			0.191794			0.0958970	+	0.995391i	$0.469428\pi$
$878$	−4.05760e8	−	5.48509e8i	−0.599495	−	0.810401i
$879$		−	6.01308e8i		−	0.885381i
$880$	5.21002e6	−	7.71511e6i	0.00764525	−	0.0113212i
$881$	8.24185e8			1.20531			0.602653	−	0.798004i	$-0.294111\pi$
$881$	8.24185e8			1.20531			0.602653	+	0.798004i	$0.294111\pi$
$882$	2.29990e8	−	1.70136e8i	0.335200	−	0.247964i
$883$		−	6.17488e8i		−	0.896906i	−0.893807	−	0.448453i	$-0.851975\pi$
$883$		−	6.17488e8i		−	0.896906i	0.893807	−	0.448453i	$-0.148025\pi$
$884$	2.11731e8	−	6.91866e8i	0.306497	−	1.00153i
$885$	6.58941e6			0.00950641
$886$	3.32557e8	+	4.49553e8i	0.478151	+	0.646367i
$887$			9.48736e8i			1.35948i	0.733451	+	0.679742i	$0.237908\pi$
$887$			9.48736e8i			1.35948i	−0.733451	+	0.679742i	$0.762092\pi$
$888$	9.40295e7	−	3.32544e7i	0.134284	−	0.0474909i
$889$	5.96416e7			0.0848876
$890$	1.77558e7	−	1.31349e7i	0.0251867	−	0.0186319i
$891$			8.75862e6i			0.0123823i
$892$	−4.03979e8	−	1.23629e8i	−0.569199	−	0.174191i
$893$	−4.29745e8			−0.603471
$894$	4.36789e8	+	5.90455e8i	0.611307	+	0.826370i
$895$			1.44052e8i			0.200933i
$896$	4.92481e7	+	1.27865e7i	0.0684645	+	0.0177757i
$897$	3.41957e8			0.473799
$898$	4.60942e8	−	3.40982e8i	0.636527	−	0.470871i
$899$			9.21521e8i			1.26831i
$900$	1.78788e7	−	5.84222e7i	0.0245252	−	0.0801402i
$901$	3.54966e8			0.485302
$902$	1.94044e7	+	2.62310e7i	0.0264412	+	0.0357434i
$903$		−	6.88155e7i		−	0.0934595i
$904$	−1.26785e8	−	3.58495e8i	−0.171618	−	0.485263i
$905$	−1.95333e8			−0.263530
$906$	−7.04073e8	+	5.20838e8i	−0.946745	+	0.700355i
$907$		−	6.41528e8i		−	0.859793i	−0.902878	−	0.429896i	$-0.858550\pi$
$907$		−	6.41528e8i		−	0.859793i	0.902878	−	0.429896i	$-0.141450\pi$
$908$	−9.55799e8	−	2.92501e8i	−1.27676	−	0.390724i
$909$	−5.92853e8			−0.789324
$910$	1.25114e7	+	1.69130e7i	0.0166028	+	0.0224438i
$911$			1.42626e8i			0.188645i	0.995542	+	0.0943223i	$0.0300684\pi$
$911$			1.42626e8i			0.188645i	−0.995542	+	0.0943223i	$0.969932\pi$
$912$	−8.38422e8	−	5.66187e8i	−1.10529	−	0.746406i
$913$	−3.56728e7			−0.0468732
$914$	−5.18780e8	+	3.83768e8i	−0.679429	+	0.502608i
$915$		−	2.17498e8i		−	0.283917i
$916$	1.03381e7	−	3.37816e7i	0.0134510	−	0.0439535i
$917$	2.12310e7			0.0275336
$918$	−5.90583e8	−	7.98355e8i	−0.763402	−	1.03197i
$919$			1.37495e9i			1.77149i	0.464171	+	0.885745i	$0.346352\pi$
$919$			1.37495e9i			1.77149i	−0.464171	+	0.885745i	$0.653648\pi$
$920$	−2.31251e8	+	8.17839e7i	−0.296975	+	0.105028i
$921$	4.70533e8			0.602298
$922$	7.06932e8	−	5.22953e8i	0.901955	−	0.667222i
$923$		−	5.45756e8i		−	0.694055i
$924$	1.24235e6	+	380194.i	0.00157481	+	0.000481936i
$925$	−2.95801e7			−0.0373744
$926$	−3.40103e8	−	4.59754e8i	−0.428330	−	0.579019i
$927$		−	1.27362e7i		−	0.0159882i
$928$	6.24233e8	−	2.68291e7i	0.781093	−	0.0335709i
$929$	−3.34030e8			−0.416618			−0.208309	−	0.978063i	$-0.566796\pi$
$929$	−3.34030e8			−0.416618			−0.208309	+	0.978063i	$0.566796\pi$
$930$	3.57586e8	−	2.64524e8i	0.444561	−	0.328864i
$931$			1.40496e9i			1.74106i
$932$	−4.93473e7	+	1.61251e8i	−0.0609559	+	0.199184i
$933$	−1.15250e8			−0.141904
$934$	−4.77742e8	−	6.45816e8i	−0.586345	−	0.792625i
$935$			1.32523e7i			0.0162128i
$936$	−1.01114e8	−	2.85907e8i	−0.123305	−	0.348656i
$937$	1.21360e9			1.47522			0.737608	−	0.675229i	$-0.235955\pi$
$937$	1.21360e9			1.47522			0.737608	+	0.675229i	$0.235955\pi$
$938$	6.80114e7	−	5.03114e7i	0.0824087	−	0.0609619i
$939$			2.84110e8i			0.343155i
$940$	−1.22496e8	−	3.74874e7i	−0.147482	−	0.0451338i
$941$	−4.33889e8			−0.520727			−0.260364	−	0.965511i	$-0.583842\pi$
$941$	−4.33889e8			−0.520727			−0.260364	+	0.965511i	$0.583842\pi$
$942$	5.07072e8	+	6.85463e8i	0.606620	+	0.820033i
$943$		−	8.59684e8i		−	1.02519i
$944$	−1.31298e7	+	1.94429e7i	−0.0156078	+	0.0231124i
$945$	2.88741e7			0.0342148
$946$	3.60397e7	−	2.66604e7i	0.0425704	−	0.0314915i
$947$		−	3.55184e8i		−	0.418218i	−0.977892	−	0.209109i	$-0.932944\pi$
$947$		−	3.55184e8i		−	0.418218i	0.977892	−	0.209109i	$-0.0670564\pi$
$948$	2.19141e8	−	7.16081e8i	0.257216	−	0.840499i
$949$	4.78620e8			0.560005
$950$	1.78443e8	+	2.41221e8i	0.208128	+	0.281348i
$951$		−	1.08025e9i		−	1.25598i
$952$	−6.82856e7	+	2.41498e7i	−0.0791441	+	0.0279900i
$953$	5.71323e8			0.660089			0.330045	−	0.943965i	$-0.392936\pi$
$953$	5.71323e8			0.660089			0.330045	+	0.943965i	$0.392936\pi$
$954$	1.19609e8	−	8.84805e7i	0.137758	−	0.101907i
$955$		−	3.43296e8i		−	0.394148i
$956$	7.50870e8	+	2.29787e8i	0.859392	+	0.262998i
$957$	1.59542e7			0.0182029
$958$	−4.60120e8	−	6.21994e8i	−0.523329	−	0.707440i
$959$			4.36293e7i			0.0494678i
$960$	−1.89598e8	−	2.34525e8i	−0.214299	−	0.265079i
$961$	−1.44819e9			−1.63175
$962$	−1.18037e8	+	8.73182e7i	−0.132585	+	0.0980798i
$963$		−	2.20437e8i		−	0.246834i
$964$	−2.09973e8	+	6.86123e8i	−0.234386	+	0.765897i
$965$	−1.57435e8			−0.175194
$966$	−2.03581e7	−	2.75202e7i	−0.0225842	−	0.0305295i
$967$			2.99131e8i			0.330812i	0.986226	+	0.165406i	$0.0528935\pi$
$967$			2.99131e8i			0.330812i	−0.986226	+	0.165406i	$0.947107\pi$
$968$	−3.02145e8	−	8.54338e8i	−0.333111	−	0.941898i
$969$	1.44017e9			1.58286
$970$	−5.40882e8	+	4.00118e8i	−0.592635	+	0.438402i
$971$		−	1.83579e8i		−	0.200524i	−0.994961	−	0.100262i	$-0.968032\pi$
$971$		−	1.83579e8i		−	0.200524i	0.994961	−	0.100262i	$-0.0319680\pi$
$972$	−6.78476e8	−	2.07633e8i	−0.738815	−	0.226098i
$973$	−3.16724e6			−0.00343828
$974$	−6.35352e8	−	8.58873e8i	−0.687602	−	0.929506i
$975$		−	1.24693e8i		−	0.134533i
$976$	6.41755e8	+	4.33378e8i	0.690271	+	0.466141i
$977$	7.32043e8			0.784970			0.392485	−	0.919758i	$-0.371615\pi$
$977$	7.32043e8			0.784970			0.392485	+	0.919758i	$0.371615\pi$
$978$	−2.21417e8	+	1.63794e8i	−0.236698	+	0.175098i
$979$			2.00792e6i			0.00213992i
$980$	−1.22557e8	+	4.00475e8i	−0.130214	+	0.425497i
$981$	−6.76981e7			−0.0717083
$982$	−6.36987e8	−	8.61084e8i	−0.672661	−	0.909308i
$983$			9.20691e8i			0.969289i	0.874711	+	0.484644i	$0.161051\pi$
$983$			9.20691e8i			0.969289i	−0.874711	+	0.484644i	$0.838949\pi$
$984$	9.96495e8	−	3.52420e8i	1.04590	−	0.369892i
$985$	2.38356e8			0.249412
$986$	−7.15047e8	+	5.28957e8i	−0.745940	+	0.551810i
$987$		−	1.78780e7i		−	0.0185938i
$988$	1.42413e9	+	4.35825e8i	1.47666	+	0.451899i
$989$	−1.18115e9			−1.22100
$990$	3.30334e6	+	4.46548e6i	0.00340445	+	0.00460216i
$991$			1.09773e8i			0.112792i	0.998408	+	0.0563958i	$0.0179609\pi$
$991$			1.09773e8i			0.112792i	−0.998408	+	0.0563958i	$0.982039\pi$
$992$	6.80012e7	+	1.58218e9i	0.0696597	+	1.62077i
$993$	2.39562e7			0.0244664
$994$	−4.39217e7	+	3.24911e7i	−0.0447219	+	0.0330830i
$995$		−	8.54863e7i		−	0.0867816i
$996$	−3.38167e8	+	1.10502e9i	−0.342258	+	1.11839i
$997$	9.84752e7			0.0993668			0.0496834	−	0.998765i	$-0.484179\pi$
$997$	9.84752e7			0.0993668			0.0496834	+	0.998765i	$0.484179\pi$
$998$	4.97657e8	+	6.72736e8i	0.500655	+	0.676789i
$999$			2.01515e8i			0.202121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.7.b.a.11.9	✓	12
3.2	odd	2		180.7.c.a.91.4		12
4.3	odd	2	inner	20.7.b.a.11.10	yes	12
5.2	odd	4		100.7.d.b.99.20		24
5.3	odd	4		100.7.d.b.99.5		24
5.4	even	2		100.7.b.h.51.4		12
8.3	odd	2		320.7.b.d.191.4		12
8.5	even	2		320.7.b.d.191.9		12
12.11	even	2		180.7.c.a.91.3		12
20.3	even	4		100.7.d.b.99.19		24
20.7	even	4		100.7.d.b.99.6		24
20.19	odd	2		100.7.b.h.51.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.b.a.11.9	✓	12	1.1	even	1	trivial
20.7.b.a.11.10	yes	12	4.3	odd	2	inner
100.7.b.h.51.3		12	20.19	odd	2
100.7.b.h.51.4		12	5.4	even	2
100.7.d.b.99.5		24	5.3	odd	4
100.7.d.b.99.6		24	20.7	even	4
100.7.d.b.99.19		24	20.3	even	4
100.7.d.b.99.20		24	5.2	odd	4
180.7.c.a.91.3		12	12.11	even	2
180.7.c.a.91.4		12	3.2	odd	2
320.7.b.d.191.4		12	8.3	odd	2
320.7.b.d.191.9		12	8.5	even	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(6.43150 - 4.75771i) q^{2} -20.5795i q^{3} +(18.7284 - 61.1984i) q^{4} -55.9017 q^{5} +(-97.9113 - 132.357i) q^{6} -24.2619i q^{7} +(-170.712 - 482.702i) q^{8} +305.483 q^{9} +O(q^{10})\)	\(q+(6.43150 - 4.75771i) q^{2} -20.5795i q^{3} +(18.7284 - 61.1984i) q^{4} -55.9017 q^{5} +(-97.9113 - 132.357i) q^{6} -24.2619i q^{7} +(-170.712 - 482.702i) q^{8} +305.483 q^{9} +(-359.532 + 265.964i) q^{10} -40.6577i q^{11} +(-1259.43 - 385.422i) q^{12} +1938.91 q^{13} +(-115.431 - 156.041i) q^{14} +1150.43i q^{15} +(-3394.49 - 2292.30i) q^{16} +5830.75 q^{17} +(1964.72 - 1453.40i) q^{18} +12002.0i q^{19} +(-1046.95 + 3421.10i) q^{20} -499.299 q^{21} +(-193.437 - 261.490i) q^{22} +8569.95i q^{23} +(-9933.78 + 3513.17i) q^{24} +3125.00 q^{25} +(12470.1 - 9224.76i) q^{26} -21289.2i q^{27} +(-1484.79 - 454.388i) q^{28} -19067.7 q^{29} +(5473.41 + 7398.99i) q^{30} -48329.0i q^{31} +(-32737.8 + 1407.05i) q^{32} -836.716 q^{33} +(37500.5 - 27741.0i) q^{34} +1356.28i q^{35} +(5721.23 - 18695.1i) q^{36} -9465.63 q^{37} +(57101.9 + 77190.7i) q^{38} -39901.8i q^{39} +(9543.10 + 26983.9i) q^{40} -100314. q^{41} +(-3211.24 + 2375.52i) q^{42} +137824. i q^{43} +(-2488.19 - 761.455i) q^{44} -17077.0 q^{45} +(40773.3 + 55117.7i) q^{46} +35806.2i q^{47} +(-47174.5 + 69857.0i) q^{48} +117060. q^{49} +(20098.4 - 14867.8i) q^{50} -119994. i q^{51} +(36312.7 - 118658. i) q^{52} +60878.2 q^{53} +(-101288. - 136921. i) q^{54} +2272.83i q^{55} +(-11711.3 + 4141.80i) q^{56} +246995. q^{57} +(-122634. + 90718.4i) q^{58} -5727.78i q^{59} +(70404.5 + 21545.8i) q^{60} -189058. q^{61} +(-229935. - 310828. i) q^{62} -7411.61i q^{63} +(-203859. + 164806. i) q^{64} -108388. q^{65} +(-5381.34 + 3980.85i) q^{66} +435857. i q^{67} +(109201. - 356833. i) q^{68} +176366. q^{69} +(6452.80 + 8722.94i) q^{70} -281476. i q^{71} +(-52149.7 - 147457. i) q^{72} +246850. q^{73} +(-60878.2 + 45034.7i) q^{74} -64311.0i q^{75} +(734502. + 224778. i) q^{76} -986.434 q^{77} +(-189841. - 256629. i) q^{78} +568574. i q^{79} +(189758. + 128144. i) q^{80} -215424. q^{81} +(-645168. + 477264. i) q^{82} -877394. i q^{83} +(-9351.09 + 30556.3i) q^{84} -325949. q^{85} +(655728. + 886418. i) q^{86} +392403. i q^{87} +(-19625.6 + 6940.76i) q^{88} -49386.0 q^{89} +(-109831. + 81247.6i) q^{90} -47041.7i q^{91} +(524468. + 160502. i) q^{92} -994587. q^{93} +(170355. + 230288. i) q^{94} -670931. i q^{95} +(28956.4 + 673728. i) q^{96} +1.50441e6 q^{97} +(752874. - 556939. i) q^{98} -12420.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9}+O(q^{10}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9	\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + 750 q^{10} - 440 q^{12} - 5040 q^{13} + 6248 q^{14} + 3312 q^{16} + 6840 q^{17} + 15790 q^{18} - 3500 q^{20} - 27464 q^{21} - 26160 q^{22} + 28528 q^{24} + 37500 q^{25} - 18684 q^{26} + 19320 q^{28} - 74968 q^{29} - 13000 q^{30} - 60800 q^{32} + 112880 q^{33} + 48204 q^{34} - 128580 q^{36} + 62640 q^{37} + 74800 q^{38} + 57000 q^{40} - 16976 q^{41} - 138360 q^{42} - 222160 q^{44} + 77000 q^{45} - 144792 q^{46} + 297600 q^{48} + 72564 q^{49} - 31250 q^{50} + 548280 q^{52} + 322160 q^{53} + 150416 q^{54} - 246512 q^{56} - 1213440 q^{57} + 350700 q^{58} + 157000 q^{60} + 46464 q^{61} - 7120 q^{62} - 542784 q^{64} - 133000 q^{65} - 65200 q^{66} - 1678280 q^{68} + 41256 q^{69} - 360000 q^{70} + 2317560 q^{72} - 415080 q^{73} + 1581924 q^{74} + 208320 q^{76} + 75600 q^{77} + 473200 q^{78} + 734000 q^{80} + 2287428 q^{81} - 3169500 q^{82} - 2256224 q^{84} + 372000 q^{85} - 62512 q^{86} - 278880 q^{88} + 278392 q^{89} - 2162250 q^{90} + 4095720 q^{92} - 3646000 q^{93} + 4706568 q^{94} - 2641152 q^{96} + 2344680 q^{97} + 1050270 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 156 * q^4 - 672 * q^6 + 440 * q^8 - 1996 * q^9 + 750 * q^10 - 440 * q^12 - 5040 * q^13 + 6248 * q^14 + 3312 * q^16 + 6840 * q^17 + 15790 * q^18 - 3500 * q^20 - 27464 * q^21 - 26160 * q^22 + 28528 * q^24 + 37500 * q^25 - 18684 * q^26 + 19320 * q^28 - 74968 * q^29 - 13000 * q^30 - 60800 * q^32 + 112880 * q^33 + 48204 * q^34 - 128580 * q^36 + 62640 * q^37 + 74800 * q^38 + 57000 * q^40 - 16976 * q^41 - 138360 * q^42 - 222160 * q^44 + 77000 * q^45 - 144792 * q^46 + 297600 * q^48 + 72564 * q^49 - 31250 * q^50 + 548280 * q^52 + 322160 * q^53 + 150416 * q^54 - 246512 * q^56 - 1213440 * q^57 + 350700 * q^58 + 157000 * q^60 + 46464 * q^61 - 7120 * q^62 - 542784 * q^64 - 133000 * q^65 - 65200 * q^66 - 1678280 * q^68 + 41256 * q^69 - 360000 * q^70 + 2317560 * q^72 - 415080 * q^73 + 1581924 * q^74 + 208320 * q^76 + 75600 * q^77 + 473200 * q^78 + 734000 * q^80 + 2287428 * q^81 - 3169500 * q^82 - 2256224 * q^84 + 372000 * q^85 - 62512 * q^86 - 278880 * q^88 + 278392 * q^89 - 2162250 * q^90 + 4095720 * q^92 - 3646000 * q^93 + 4706568 * q^94 - 2641152 * q^96 + 2344680 * q^97 + 1050270 * q^98

Introduction

L-functions

Modular forms

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