LMFDB - Embedded newform 76.7.b.a.39.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, 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("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.1
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.98783 - 0.441092i) q^{2} -34.6865i q^{3} +(63.6109 + 7.04673i) q^{4} +112.076 q^{5} +(-15.2999 + 277.070i) q^{6} +328.667i q^{7} +(-505.005 - 84.3464i) q^{8} -474.152 q^{9} +O(q^{10})$	\(q+(-7.98783 - 0.441092i) q^{2} -34.6865i q^{3} +(63.6109 + 7.04673i) q^{4} +112.076 q^{5} +(-15.2999 + 277.070i) q^{6} +328.667i q^{7} +(-505.005 - 84.3464i) q^{8} -474.152 q^{9} +(-895.242 - 49.4357i) q^{10} +1250.56i q^{11} +(244.426 - 2206.44i) q^{12} -2823.18 q^{13} +(144.972 - 2625.33i) q^{14} -3887.51i q^{15} +(3996.69 + 896.498i) q^{16} -6938.39 q^{17} +(3787.44 + 209.145i) q^{18} +1573.56i q^{19} +(7129.23 + 789.768i) q^{20} +11400.3 q^{21} +(551.610 - 9989.23i) q^{22} +19738.1i q^{23} +(-2925.68 + 17516.8i) q^{24} -3064.03 q^{25} +(22551.1 + 1245.28i) q^{26} -8839.78i q^{27} +(-2316.03 + 20906.8i) q^{28} -41769.4 q^{29} +(-1714.75 + 31052.8i) q^{30} +41134.3i q^{31} +(-31529.4 - 8923.98i) q^{32} +43377.4 q^{33} +(55422.7 + 3060.47i) q^{34} +36835.5i q^{35} +(-30161.2 - 3341.22i) q^{36} +24225.1 q^{37} +(694.086 - 12569.4i) q^{38} +97926.2i q^{39} +(-56598.8 - 9453.18i) q^{40} +58313.3 q^{41} +(-91063.6 - 5028.57i) q^{42} +45439.8i q^{43} +(-8812.34 + 79549.0i) q^{44} -53140.9 q^{45} +(8706.30 - 157664. i) q^{46} -81318.7i q^{47} +(31096.4 - 138631. i) q^{48} +9627.25 q^{49} +(24475.0 + 1351.52i) q^{50} +240668. i q^{51} +(-179585. - 19894.2i) q^{52} +67048.8 q^{53} +(-3899.16 + 70610.7i) q^{54} +140157. i q^{55} +(27721.8 - 165978. i) q^{56} +54581.3 q^{57} +(333647. + 18424.1i) q^{58} -291353. i q^{59} +(27394.3 - 247288. i) q^{60} +140476. q^{61} +(18144.0 - 328574. i) q^{62} -155838. i q^{63} +(247915. + 85190.6i) q^{64} -316410. q^{65} +(-346491. - 19133.4i) q^{66} +62465.5i q^{67} +(-441357. - 48893.0i) q^{68} +684644. q^{69} +(16247.9 - 294236. i) q^{70} -81342.8i q^{71} +(239449. + 39993.0i) q^{72} -526053. q^{73} +(-193506. - 10685.5i) q^{74} +106281. i q^{75} +(-11088.5 + 100096. i) q^{76} -411016. q^{77} +(43194.4 - 782218. i) q^{78} +369245. i q^{79} +(447932. + 100476. i) q^{80} -652278. q^{81} +(-465796. - 25721.5i) q^{82} -117459. i q^{83} +(725182. + 80334.8i) q^{84} -777625. q^{85} +(20043.1 - 362966. i) q^{86} +1.44883e6i q^{87} +(105480. - 631537. i) q^{88} -75878.6 q^{89} +(424481. + 23440.0i) q^{90} -927885. i q^{91} +(-139089. + 1.25556e6i) q^{92} +1.42680e6 q^{93} +(-35869.0 + 649560. i) q^{94} +176358. i q^{95} +(-309541. + 1.09364e6i) q^{96} -1.03909e6 q^{97} +(-76900.8 - 4246.50i) q^{98} -592954. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−7.98783	−	0.441092i	−0.998479	−	0.0551365i
$2$	−7.98783	−	0.441092i	−0.998479	−	0.0551365i
$3$		−	34.6865i		−	1.28468i	−0.766418	−	0.642342i	$-0.777963\pi$
$3$		−	34.6865i		−	1.28468i	0.766418	−	0.642342i	$-0.222037\pi$
$4$	63.6109	+	7.04673i	0.993920	+	0.110105i
$5$	112.076			0.896606			0.448303	−	0.893882i	$-0.352029\pi$
$5$	112.076			0.896606			0.448303	+	0.893882i	$0.352029\pi$
$6$	−15.2999	+	277.070i	−0.0708330	+	1.28273i
$7$			328.667i			0.958212i	0.877757	+	0.479106i	$0.159039\pi$
$7$			328.667i			0.958212i	−0.877757	+	0.479106i	$0.840961\pi$
$8$	−505.005	−	84.3464i	−0.986337	−	0.164739i
$9$	−474.152			−0.650414
$10$	−895.242	−	49.4357i	−0.895242	−	0.0494357i
$11$			1250.56i			0.939561i	0.882783	+	0.469781i	$0.155667\pi$
$11$			1250.56i			0.939561i	−0.882783	+	0.469781i	$0.844333\pi$
$12$	244.426	−	2206.44i	0.141450	−	1.27687i
$13$	−2823.18			−1.28502			−0.642508	−	0.766279i	$-0.722106\pi$
$13$	−2823.18			−1.28502			−0.642508	+	0.766279i	$0.722106\pi$
$14$	144.972	−	2625.33i	0.0528324	−	0.956754i
$15$		−	3887.51i		−	1.15186i
$16$	3996.69	+	896.498i	0.975754	+	0.218872i
$17$	−6938.39			−1.41225			−0.706125	−	0.708087i	$-0.749558\pi$
$17$	−6938.39			−1.41225			−0.706125	+	0.708087i	$0.749558\pi$
$18$	3787.44	+	209.145i	0.649425	+	0.0358615i
$19$			1573.56i			0.229416i
$19$			1573.56i			0.229416i
$20$	7129.23	+	789.768i	0.891154	+	0.0987210i
$21$	11400.3			1.23100
$22$	551.610	−	9989.23i	0.0518041	−	0.938132i
$23$			19738.1i			1.62226i	0.584864	+	0.811131i	$0.301148\pi$
$23$			19738.1i			1.62226i	−0.584864	+	0.811131i	$0.698852\pi$
$24$	−2925.68	+	17516.8i	−0.211638	+	1.26713i
$25$	−3064.03			−0.196098
$26$	22551.1	+	1245.28i	1.28306	+	0.0708513i
$27$		−	8839.78i		−	0.449108i
$28$	−2316.03	+	20906.8i	−0.105504	+	0.952386i
$29$	−41769.4			−1.71263			−0.856317	−	0.516451i	$-0.827253\pi$
$29$	−41769.4			−1.71263			−0.856317	+	0.516451i	$0.827253\pi$
$30$	−1714.75	+	31052.8i	−0.0635093	+	1.15010i
$31$			41134.3i			1.38076i	0.723446	+	0.690381i	$0.242557\pi$
$31$			41134.3i			1.38076i	−0.723446	+	0.690381i	$0.757443\pi$
$32$	−31529.4	−	8923.98i	−0.962202	−	0.272338i
$33$	43377.4			1.20704
$34$	55422.7	+	3060.47i	1.41010	+	0.0778665i
$35$			36835.5i			0.859138i
$36$	−30161.2	−	3341.22i	−0.646460	−	0.0716140i
$37$	24225.1			0.478257			0.239128	−	0.970988i	$-0.423138\pi$
$37$	24225.1			0.478257			0.239128	+	0.970988i	$0.423138\pi$
$38$	694.086	−	12569.4i	0.0126492	−	0.229067i
$39$			97926.2i			1.65084i
$40$	−56598.8	−	9453.18i	−0.884356	−	0.147706i
$41$	58313.3			0.846088			0.423044	−	0.906109i	$-0.360962\pi$
$41$	58313.3			0.846088			0.423044	+	0.906109i	$0.360962\pi$
$42$	−91063.6	−	5028.57i	−1.22913	−	0.0678730i
$43$			45439.8i			0.571520i	0.958301	+	0.285760i	$0.0922460\pi$
$43$			45439.8i			0.571520i	−0.958301	+	0.285760i	$0.907754\pi$
$44$	−8812.34	+	79549.0i	−0.103451	+	0.933849i
$45$	−53140.9			−0.583165
$46$	8706.30	−	157664.i	0.0894458	−	1.61979i
$47$		−	81318.7i		−	0.783243i	−0.920126	−	0.391622i	$-0.871914\pi$
$47$		−	81318.7i		−	0.783243i	0.920126	−	0.391622i	$-0.128086\pi$
$48$	31096.4	−	138631.i	0.281181	−	1.25354i
$49$	9627.25			0.0818302
$50$	24475.0	+	1351.52i	0.195800	+	0.0108122i
$51$			240668.i			1.81430i
$52$	−179585.	−	19894.2i	−1.27720	−	0.141487i
$53$	67048.8			0.450364			0.225182	−	0.974317i	$-0.427702\pi$
$53$	67048.8			0.450364			0.225182	+	0.974317i	$0.427702\pi$
$54$	−3899.16	+	70610.7i	−0.0247622	+	0.448424i
$55$			140157.i			0.842416i
$56$	27721.8	−	165978.i	0.157855	−	0.945120i
$57$	54581.3			0.294727
$58$	333647.	+	18424.1i	1.71003	+	0.0944286i
$59$		−	291353.i		−	1.41861i	−0.704901	−	0.709306i	$-0.749008\pi$
$59$		−	291353.i		−	1.41861i	0.704901	−	0.709306i	$-0.250992\pi$
$60$	27394.3	−	247288.i	0.126825	−	1.14485i
$61$	140476.			0.618890			0.309445	−	0.950917i	$-0.399857\pi$
$61$	140476.			0.618890			0.309445	+	0.950917i	$0.399857\pi$
$62$	18144.0	−	328574.i	0.0761304	−	1.37866i
$63$		−	155838.i		−	0.623234i
$64$	247915.	+	85190.6i	0.945722	+	0.324976i
$65$	−316410.			−1.15215
$66$	−346491.	−	19133.4i	−1.20520	−	0.0665519i
$67$			62465.5i			0.207690i	0.994593	+	0.103845i	$0.0331146\pi$
$67$			62465.5i			0.207690i	−0.994593	+	0.103845i	$0.966885\pi$
$68$	−441357.	−	48893.0i	−1.40366	−	0.155496i
$69$	684644.			2.08410
$70$	16247.9	−	294236.i	0.0473699	−	0.857831i
$71$		−	81342.8i		−	0.227271i	−0.993523	−	0.113636i	$-0.963750\pi$
$71$		−	81342.8i		−	0.227271i	0.993523	−	0.113636i	$-0.0362496\pi$
$72$	239449.	+	39993.0i	0.641528	+	0.107149i
$73$	−526053.			−1.35226			−0.676131	−	0.736782i	$-0.736345\pi$
$73$	−526053.			−1.35226			−0.676131	+	0.736782i	$0.736345\pi$
$74$	−193506.	−	10685.5i	−0.477529	−	0.0263694i
$75$			106281.i			0.251924i
$76$	−11088.5	+	100096.i	−0.0252599	+	0.228021i
$77$	−411016.			−0.900299
$78$	43194.4	−	782218.i	0.0910215	−	1.64833i
$79$			369245.i			0.748916i	0.927244	+	0.374458i	$0.122171\pi$
$79$			369245.i			0.748916i	−0.927244	+	0.374458i	$0.877829\pi$
$80$	447932.	+	100476.i	0.874866	+	0.196241i
$81$	−652278.			−1.22738
$82$	−465796.	−	25721.5i	−0.844801	−	0.0466503i
$83$		−	117459.i		−	0.205424i	−0.994711	−	0.102712i	$-0.967248\pi$
$83$		−	117459.i		−	0.205424i	0.994711	−	0.102712i	$-0.0327520\pi$
$84$	725182.	+	80334.8i	1.22352	+	0.135539i
$85$	−777625.			−1.26623
$86$	20043.1	−	362966.i	0.0315116	−	0.570650i
$87$			1.44883e6i			2.20019i
$88$	105480.	−	631537.i	0.154782	−	0.926724i
$89$	−75878.6			−0.107634			−0.0538170	−	0.998551i	$-0.517139\pi$
$89$	−75878.6			−0.107634			−0.0538170	+	0.998551i	$0.517139\pi$
$90$	424481.	+	23440.0i	0.582278	+	0.0321537i
$91$		−	927885.i		−	1.23132i
$92$	−139089.	+	1.25556e6i	−0.178620	+	1.61240i
$93$	1.42680e6			1.77384
$94$	−35869.0	+	649560.i	−0.0431853	+	0.782052i
$95$			176358.i			0.205695i
$96$	−309541.	+	1.09364e6i	−0.349869	+	1.23613i
$97$	−1.03909e6			−1.13851			−0.569257	−	0.822159i	$-0.692769\pi$
$97$	−1.03909e6			−1.13851			−0.569257	+	0.822159i	$0.692769\pi$
$98$	−76900.8	−	4246.50i	−0.0817058	−	0.00451183i
$99$		−	592954.i		−	0.611104i
$100$	−194906.	−	21591.4i	−0.194906	−	0.0215914i
$101$	1.38349e6			1.34280			0.671399	−	0.741096i	$-0.265694\pi$
$101$	1.38349e6			1.34280			0.671399	+	0.741096i	$0.265694\pi$
$102$	106157.	−	1.92242e6i	0.100034	−	1.81154i
$103$			2.18136e6i			1.99625i	0.0611856	+	0.998126i	$0.480512\pi$
$103$			2.18136e6i			1.99625i	−0.0611856	+	0.998126i	$0.519488\pi$
$104$	1.42572e6	+	238125.i	1.26746	+	0.211692i
$105$	1.27770e6			1.10372
$106$	−535575.	−	29574.7i	−0.449679	−	0.0248315i
$107$		−	334925.i		−	0.273399i	−0.990613	−	0.136699i	$-0.956351\pi$
$107$		−	334925.i		−	0.273399i	0.990613	−	0.136699i	$-0.0436495\pi$
$108$	62291.6	−	562306.i	0.0494491	−	0.446377i
$109$	688853.			0.531921			0.265961	−	0.963984i	$-0.414311\pi$
$109$	688853.			0.531921			0.265961	+	0.963984i	$0.414311\pi$
$110$	61822.1	−	1.11955e6i	0.0464479	−	0.841135i
$111$		−	840285.i		−	0.614409i
$112$	−294649.	+	1.31358e6i	−0.209725	+	0.934979i
$113$	−243501.			−0.168758			−0.0843790	−	0.996434i	$-0.526891\pi$
$113$	−243501.			−0.168758			−0.0843790	+	0.996434i	$0.526891\pi$
$114$	−435987.	−	24075.4i	−0.294278	−	0.0162502i
$115$			2.21216e6i			1.45453i
$116$	−2.65699e6	−	294338.i	−1.70222	−	0.188570i
$117$	1.33862e6			0.835793
$118$	−128513.	+	2.32728e6i	−0.0782173	+	1.41645i
$119$		−	2.28042e6i		−	1.35324i
$120$	−327897.	+	1.96321e6i	−0.189755	+	1.13612i
$121$	207670.			0.117224
$122$	−1.12210e6	−	61963.0i	−0.617949	−	0.0341234i
$123$		−	2.02268e6i		−	1.08696i
$124$	−289862.	+	2.61659e6i	−0.152029	+	1.37237i
$125$	−2.09459e6			−1.07243
$126$	−68738.8	+	1.24481e6i	−0.0343630	+	0.622286i
$127$		−	2.49511e6i		−	1.21809i	−0.793136	−	0.609045i	$-0.791553\pi$
$127$		−	2.49511e6i		−	1.21809i	0.793136	−	0.609045i	$-0.208447\pi$
$128$	−1.94273e6	−	789842.i	−0.926365	−	0.376626i
$129$	1.57615e6			0.734223
$130$	2.52743e6	+	139566.i	1.15040	+	0.0635257i
$131$		−	1.68536e6i		−	0.749685i	−0.927088	−	0.374843i	$-0.877697\pi$
$131$		−	1.68536e6i		−	0.749685i	0.927088	−	0.374843i	$-0.122303\pi$
$132$	2.75927e6	+	305669.i	1.19970	+	0.132901i
$133$	−517177.			−0.219829
$134$	27553.0	−	498964.i	0.0114513	−	0.207374i
$135$		−	990725.i		−	0.402672i
$136$	3.50392e6	+	585228.i	1.39296	+	0.232653i
$137$	−1.21465e6			−0.472378			−0.236189	−	0.971707i	$-0.575898\pi$
$137$	−1.21465e6			−0.472378			−0.236189	+	0.971707i	$0.575898\pi$
$138$	−5.46882e6	−	301991.i	−2.08093	−	0.114910i
$139$			2.30910e6i			0.859803i	0.902876	+	0.429901i	$0.141452\pi$
$139$			2.30910e6i			0.859803i	−0.902876	+	0.429901i	$0.858548\pi$
$140$	−259570.	+	2.34314e6i	−0.0945956	+	0.853915i
$141$	−2.82066e6			−1.00622
$142$	−35879.7	+	649753.i	−0.0125309	+	0.226925i
$143$		−	3.53055e6i		−	1.20735i
$144$	−1.89504e6	−	425076.i	−0.634644	−	0.142357i
$145$	−4.68134e6			−1.53556
$146$	4.20202e6	+	232038.i	1.35020	+	0.0745589i
$147$		−	333935.i		−	0.105126i
$148$	1.54098e6	+	170708.i	0.475349	+	0.0526586i
$149$	1.34982e6			0.408054			0.204027	−	0.978965i	$-0.434597\pi$
$149$	1.34982e6			0.408054			0.204027	+	0.978965i	$0.434597\pi$
$150$	46879.5	−	848951.i	0.0138902	−	0.251541i
$151$			3.96177e6i			1.15069i	0.817911	+	0.575344i	$0.195132\pi$
$151$			3.96177e6i			1.15069i	−0.817911	+	0.575344i	$0.804868\pi$
$152$	132724.	−	794656.i	0.0377937	−	0.226281i
$153$	3.28985e6			0.918548
$154$	3.28313e6	+	181296.i	0.898929	+	0.0496393i
$155$			4.61015e6i			1.23800i
$156$	−690060.	+	6.22917e6i	−0.181766	+	1.64080i
$157$	3.80647e6			0.983611			0.491806	−	0.870705i	$-0.336337\pi$
$157$	3.80647e6			0.983611			0.491806	+	0.870705i	$0.336337\pi$
$158$	162871.	−	2.94946e6i	0.0412926	−	0.747777i
$159$		−	2.32569e6i		−	0.578576i
$160$	−3.53368e6	−	1.00016e6i	−0.862715	−	0.244180i
$161$	−6.48724e6			−1.55447
$162$	5.21028e6	+	287714.i	1.22551	+	0.0676732i
$163$			35100.4i			0.00810492i	0.999992	+	0.00405246i	$0.00128994\pi$
$163$			35100.4i			0.00810492i	−0.999992	+	0.00405246i	$0.998710\pi$
$164$	3.70936e6	+	410918.i	0.840944	+	0.0931587i
$165$	4.86155e6			1.08224
$166$	−51810.1	+	938241.i	−0.0113264	+	0.205112i
$167$		−	5.21572e6i		−	1.11986i	−0.828539	−	0.559931i	$-0.810828\pi$
$167$		−	5.21572e6i		−	1.11986i	0.828539	−	0.559931i	$-0.189172\pi$
$168$	−5.75720e6	−	961573.i	−1.21418	−	0.202794i
$169$	3.14354e6			0.651267
$170$	6.21153e6	+	343004.i	1.26431	+	0.0698156i
$171$		−	746108.i		−	0.149215i
$172$	−320202.	+	2.89047e6i	−0.0629273	+	0.568045i
$173$	−2.19845e6			−0.424598			−0.212299	−	0.977205i	$-0.568095\pi$
$173$	−2.19845e6			−0.424598			−0.212299	+	0.977205i	$0.568095\pi$
$174$	639069.	−	1.15730e7i	0.121311	−	2.19685i
$175$		−	1.00705e6i		−	0.187904i
$176$	−1.12112e6	+	4.99808e6i	−0.205643	+	0.916781i
$177$	−1.01060e7			−1.82247
$178$	606106.	+	33469.4i	0.107470	+	0.00593456i
$179$		−	9.98166e6i		−	1.74038i	−0.492718	−	0.870189i	$-0.663997\pi$
$179$		−	9.98166e6i		−	1.74038i	0.492718	−	0.870189i	$-0.336003\pi$
$180$	−3.38034e6	−	374470.i	−0.579619	−	0.0642095i
$181$	−1.21465e6			−0.204840			−0.102420	−	0.994741i	$-0.532659\pi$
$181$	−1.21465e6			−0.204840			−0.102420	+	0.994741i	$0.532659\pi$
$182$	−409283.	+	7.41179e6i	−0.0678905	+	1.22944i
$183$		−	4.87263e6i		−	0.795079i
$184$	1.66483e6	−	9.96782e6i	0.267250	−	1.60010i
$185$	2.71505e6			0.428808
$186$	−1.13971e7	−	629351.i	−1.77115	−	0.0978035i
$187$		−	8.67684e6i		−	1.32690i
$188$	573031.	−	5.17275e6i	0.0862392	−	0.778481i
$189$	2.90534e6			0.430340
$190$	77790.1	−	1.40872e6i	0.0113413	−	0.205383i
$191$			1.02093e7i			1.46519i	0.680662	+	0.732597i	$0.261692\pi$
$191$			1.02093e7i			1.46519i	−0.680662	+	0.732597i	$0.738308\pi$
$192$	2.95496e6	−	8.59931e6i	0.417492	−	1.21495i
$193$	7.78687e6			1.08316			0.541578	−	0.840651i	$-0.317827\pi$
$193$	7.78687e6			1.08316			0.541578	+	0.840651i	$0.317827\pi$
$194$	8.30009e6	+	458335.i	1.13678	+	0.0627737i
$195$			1.09751e7i			1.48015i
$196$	612397.	+	67840.6i	0.0813327	+	0.00900994i
$197$	−9.39219e6			−1.22848			−0.614240	−	0.789119i	$-0.710537\pi$
$197$	−9.39219e6			−1.22848			−0.614240	+	0.789119i	$0.710537\pi$
$198$	−261547.	+	4.73641e6i	−0.0336941	+	0.610174i
$199$		−	707925.i		−	0.0898314i	−0.998991	−	0.0449157i	$-0.985698\pi$
$199$		−	707925.i		−	0.0898314i	0.998991	−	0.0449157i	$-0.0143019\pi$
$200$	1.54735e6	+	258440.i	0.193419	+	0.0323050i
$201$	2.16671e6			0.266816
$202$	−1.10511e7	−	610244.i	−1.34076	−	0.0740371i
$203$		−	1.37282e7i		−	1.64107i
$204$	−1.69592e6	+	1.53091e7i	−0.199764	+	1.80327i
$205$	6.53550e6			0.758608
$206$	962180.	−	1.74243e7i	0.110066	−	1.99322i
$207$		−	9.35884e6i		−	1.05514i
$208$	−1.12834e7	−	2.53098e6i	−1.25386	−	0.281253i
$209$	−1.96783e6			−0.215550
$210$	−1.02060e7	−	563581.i	−1.10204	−	0.0608553i
$211$			1.59320e7i			1.69598i	0.530009	+	0.847992i	$0.322188\pi$
$211$			1.59320e7i			1.69598i	−0.530009	+	0.847992i	$0.677812\pi$
$212$	4.26504e6	+	472475.i	0.447626	+	0.0495874i
$213$	−2.82150e6			−0.291972
$214$	−147733.	+	2.67533e6i	−0.0150743	+	0.272983i
$215$			5.09270e6i			0.512428i
$216$	−745604.	+	4.46413e6i	−0.0739855	+	0.442971i
$217$	−1.35195e7			−1.32306
$218$	−5.50244e6	−	303848.i	−0.531112	−	0.0293283i
$219$			1.82469e7i			1.73723i
$220$	−987649.	+	8.91551e6i	−0.0927544	+	0.837294i
$221$	1.95883e7			1.81477
$222$	−370643.	+	6.71205e6i	−0.0338763	+	0.613474i
$223$			455089.i			0.0410376i	0.999789	+	0.0205188i	$0.00653179\pi$
$223$			455089.i			0.0410376i	−0.999789	+	0.0205188i	$0.993468\pi$
$224$	2.93301e6	−	1.03627e7i	0.260958	−	0.921993i
$225$	1.45282e6			0.127545
$226$	1.94504e6	+	107406.i	0.168501	+	0.00930473i
$227$			1.52497e7i			1.30372i	0.758340	+	0.651860i	$0.226011\pi$
$227$			1.52497e7i			1.30372i	−0.758340	+	0.651860i	$0.773989\pi$
$228$	3.47197e6	+	384620.i	0.292935	+	0.0324510i
$229$	8.95602e6			0.745776			0.372888	−	0.927876i	$-0.378368\pi$
$229$	8.95602e6			0.745776			0.372888	+	0.927876i	$0.378368\pi$
$230$	975765.	−	1.76703e7i	0.0801977	−	1.45232i
$231$			1.42567e7i			1.15660i
$232$	2.10937e7	+	3.52310e6i	1.68923	+	0.282137i
$233$	7.84350e6			0.620072			0.310036	−	0.950725i	$-0.399659\pi$
$233$	7.84350e6			0.620072			0.310036	+	0.950725i	$0.399659\pi$
$234$	−1.06926e7	−	590453.i	−0.834521	−	0.0460827i
$235$		−	9.11385e6i		−	0.702260i
$236$	2.05309e6	−	1.85332e7i	0.156197	−	1.40999i
$237$	1.28078e7			0.962121
$238$	−1.00587e6	+	1.82156e7i	−0.0746126	+	1.35118i
$239$			1.22469e7i			0.897083i	0.893762	+	0.448541i	$0.148056\pi$
$239$			1.22469e7i			0.897083i	−0.893762	+	0.448541i	$0.851944\pi$
$240$	3.48515e6	−	1.55372e7i	0.252108	−	1.12393i
$241$	−3.46065e6			−0.247233			−0.123616	−	0.992330i	$-0.539449\pi$
$241$	−3.46065e6			−0.247233			−0.123616	+	0.992330i	$0.539449\pi$
$242$	−1.65883e6	−	91601.5i	−0.117046	−	0.00646333i
$243$			1.61810e7i			1.12768i
$244$	8.93583e6	+	989900.i	0.615128	+	0.0681431i
$245$	1.07898e6			0.0733695
$246$	−892188.	+	1.61568e7i	−0.0599310	+	1.08530i
$247$		−	4.44245e6i		−	0.294803i
$248$	3.46953e6	−	2.07730e7i	0.227465	−	1.36190i
$249$	−4.07423e6			−0.263905
$250$	1.67312e7	+	923905.i	1.07080	+	0.0591299i
$251$			9.42839e6i			0.596233i	0.954529	+	0.298117i	$0.0963585\pi$
$251$			9.42839e6i			0.596233i	−0.954529	+	0.298117i	$0.903642\pi$
$252$	1.09815e6	−	9.91299e6i	0.0686214	−	0.619445i
$253$	−2.46836e7			−1.52422
$254$	−1.10057e6	+	1.99306e7i	−0.0671612	+	1.21624i
$255$			2.69731e7i			1.62671i
$256$	1.51698e7	+	7.16604e6i	0.904190	+	0.427129i
$257$	−3.99391e6			−0.235287			−0.117644	−	0.993056i	$-0.537534\pi$
$257$	−3.99391e6			−0.235287			−0.117644	+	0.993056i	$0.537534\pi$
$258$	−1.25900e7	−	695226.i	−0.733106	−	0.0404825i
$259$			7.96199e6i			0.458271i
$260$	−2.01271e7	−	2.22966e6i	−1.14515	−	0.126858i
$261$	1.98050e7			1.11392
$262$	−743399.	+	1.34624e7i	−0.0413350	+	0.748545i
$263$		−	8.08518e6i		−	0.444450i	−0.974995	−	0.222225i	$-0.928668\pi$
$263$		−	8.08518e6i		−	0.444450i	0.974995	−	0.222225i	$-0.0713319\pi$
$264$	−2.19058e7	−	3.65873e6i	−1.19055	−	0.198847i
$265$	7.51455e6			0.403799
$266$	4.13113e6	+	228123.i	0.219494	+	0.0121206i
$267$			2.63196e6i			0.138276i
$268$	−440178.	+	3.97349e6i	−0.0228678	+	0.206427i
$269$	−7.63248e6			−0.392111			−0.196055	−	0.980593i	$-0.562813\pi$
$269$	−7.63248e6			−0.392111			−0.196055	+	0.980593i	$0.562813\pi$
$270$	−437001.	+	7.91374e6i	−0.0222019	+	0.402060i
$271$		−	2.85661e7i		−	1.43530i	−0.696404	−	0.717650i	$-0.745218\pi$
$271$		−	2.85661e7i		−	1.43530i	0.696404	−	0.717650i	$-0.254782\pi$
$272$	−2.77306e7	−	6.22025e6i	−1.37801	−	0.309101i
$273$	−3.21851e7			−1.58185
$274$	9.70242e6	+	535772.i	0.471659	+	0.0260453i
$275$		−	3.83175e6i		−	0.184246i
$276$	4.35508e7	+	4.82450e6i	2.07142	+	0.229470i
$277$	−3.25814e7			−1.53296			−0.766479	−	0.642269i	$-0.777993\pi$
$277$	−3.25814e7			−1.53296			−0.766479	+	0.642269i	$0.777993\pi$
$278$	1.01853e6	−	1.84447e7i	0.0474065	−	0.858495i
$279$		−	1.95039e7i		−	0.898067i
$280$	3.10694e6	−	1.86021e7i	0.141534	−	0.847400i
$281$	−3.56444e7			−1.60647			−0.803236	−	0.595662i	$-0.796890\pi$
$281$	−3.56444e7			−1.60647			−0.803236	+	0.595662i	$0.796890\pi$
$282$	2.25309e7	+	1.24417e6i	1.00469	+	0.0554794i
$283$			3.13423e7i			1.38284i	0.722454	+	0.691419i	$0.243014\pi$
$283$			3.13423e7i			1.38284i	−0.722454	+	0.691419i	$0.756986\pi$
$284$	573201.	−	5.17429e6i	0.0250237	−	0.225889i
$285$	6.11724e6			0.264254
$286$	−1.55730e6	+	2.82014e7i	−0.0665691	+	1.20552i
$287$			1.91656e7i			0.810732i
$288$	1.49497e7	+	4.23132e6i	0.625829	+	0.177133i
$289$	2.40036e7			0.994452
$290$	3.73937e7	+	2.06490e6i	1.53322	+	0.0846652i
$291$			3.60424e7i			1.46263i
$292$	−3.34627e7	−	3.70695e6i	−1.34404	−	0.148891i
$293$	−2.42492e7			−0.964041			−0.482020	−	0.876160i	$-0.660097\pi$
$293$	−2.42492e7			−0.964041			−0.482020	+	0.876160i	$0.660097\pi$
$294$	−147296.	+	2.66742e6i	−0.00579628	+	0.104966i
$295$		−	3.26536e7i		−	1.27194i
$296$	−1.22338e7	−	2.04330e6i	−0.471722	−	0.0787875i
$297$	1.10546e7			0.421964
$298$	−1.07821e7	−	595395.i	−0.407433	−	0.0224986i
$299$		−	5.57241e7i		−	2.08463i
$300$	−748931.	+	6.76060e6i	−0.0277382	+	0.250393i
$301$	−1.49346e7			−0.547637
$302$	1.74750e6	−	3.16459e7i	0.0634449	−	1.14894i
$303$		−	4.79883e7i		−	1.72507i
$304$	−1.41070e6	+	6.28904e6i	−0.0502126	+	0.223853i
$305$	1.57440e7			0.554901
$306$	−2.62788e7	−	1.45113e6i	−0.917150	−	0.0506455i
$307$			51556.3i			0.00178183i	1.00000		0.000890916i	$0.000283587\pi$
$307$			51556.3i			0.00178183i	−1.00000		0.000890916i	$0.999716\pi$
$308$	−2.61451e7	−	2.89632e6i	−0.894825	−	0.0991276i
$309$	7.56637e7			2.56455
$310$	2.03350e6	−	3.68251e7i	0.0682589	−	1.23612i
$311$		−	5.04088e7i		−	1.67581i	−0.545815	−	0.837906i	$-0.683780\pi$
$311$		−	5.04088e7i		−	1.67581i	0.545815	−	0.837906i	$-0.316220\pi$
$312$	8.25972e6	−	4.94532e7i	0.271958	−	1.62829i
$313$	2.21077e7			0.720960			0.360480	−	0.932767i	$-0.382613\pi$
$313$	2.21077e7			0.720960			0.360480	+	0.932767i	$0.382613\pi$
$314$	−3.04054e7	−	1.67900e6i	−0.982115	−	0.0542329i
$315$		−	1.74656e7i		−	0.558796i
$316$	−2.60197e6	+	2.34880e7i	−0.0824595	+	0.744362i
$317$	3.59506e7			1.12857			0.564286	−	0.825580i	$-0.309152\pi$
$317$	3.59506e7			1.12857			0.564286	+	0.825580i	$0.309152\pi$
$318$	−1.02584e6	+	1.85772e7i	−0.0319006	+	0.577696i
$319$		−	5.22350e7i		−	1.60912i
$320$	2.77853e7	+	9.54780e6i	0.847940	+	0.291376i
$321$	−1.16174e7			−0.351231
$322$	5.18190e7	+	2.86147e6i	1.55211	+	0.0857081i
$323$		−	1.09180e7i		−	0.323993i
$324$	−4.14920e7	−	4.59643e6i	−1.21991	−	0.135140i
$325$	8.65032e6			0.251989
$326$	15482.5	−	280376.i	0.000446877	−	0.00809259i
$327$		−	2.38939e7i		−	0.683351i
$328$	−2.94485e7	−	4.91851e6i	−0.834528	−	0.139384i
$329$	2.67267e7			0.750513
$330$	−3.88333e7	−	2.14439e6i	−1.08059	−	0.0596708i
$331$			6.00753e7i			1.65658i	0.560302	+	0.828289i	$0.310685\pi$
$331$			6.00753e7i			1.65658i	−0.560302	+	0.828289i	$0.689315\pi$
$332$	827701.	−	7.47166e6i	0.0226183	−	0.204175i
$333$	−1.14864e7			−0.311065
$334$	−2.30061e6	+	4.16623e7i	−0.0617453	+	1.11816i
$335$			7.00087e6i			0.186216i
$336$	4.55634e7	+	1.02203e7i	1.20115	+	0.269431i
$337$	−4.59397e7			−1.20032			−0.600162	−	0.799878i	$-0.704897\pi$
$337$	−4.59397e7			−1.20032			−0.600162	+	0.799878i	$0.704897\pi$
$338$	−2.51101e7	−	1.38659e6i	−0.650276	−	0.0359086i
$339$			8.44618e6i			0.216801i
$340$	−4.94654e7	−	5.47971e6i	−1.25853	−	0.139419i
$341$	−5.14407e7			−1.29731
$342$	−329102.	+	5.95978e6i	−0.00822720	+	0.148988i
$343$			4.18315e7i			1.03662i
$344$	3.83268e6	−	2.29473e7i	0.0941516	−	0.563711i
$345$	7.67320e7			1.86861
$346$	1.75608e7	+	969717.i	0.423952	+	0.0234108i
$347$		−	5.66050e7i		−	1.35477i	−0.735628	−	0.677386i	$-0.763113\pi$
$347$		−	5.66050e7i		−	1.35477i	0.735628	−	0.677386i	$-0.236887\pi$
$348$	−1.02095e7	+	9.21616e7i	−0.242253	+	2.18682i
$349$	−2.90361e7			−0.683064			−0.341532	−	0.939870i	$-0.610946\pi$
$349$	−2.90361e7			−0.683064			−0.341532	+	0.939870i	$0.610946\pi$
$350$	−444200.	+	8.04411e6i	−0.0103603	+	0.187618i
$351$			2.49563e7i			0.577110i
$352$	1.11599e7	−	3.94293e7i	0.255879	−	0.904048i
$353$	7.38312e7			1.67848			0.839239	−	0.543763i	$-0.183001\pi$
$353$	7.38312e7			1.67848			0.839239	+	0.543763i	$0.183001\pi$
$354$	8.07251e7	+	4.45768e6i	1.81970	+	0.100485i
$355$		−	9.11656e6i		−	0.203773i
$356$	−4.82671e6	−	534697.i	−0.106980	−	0.0118511i
$357$	−7.90996e7			−1.73848
$358$	−4.40283e6	+	7.97318e7i	−0.0959583	+	1.73773i
$359$			7.31230e7i			1.58041i	0.612840	+	0.790207i	$0.290027\pi$
$359$			7.31230e7i			1.58041i	−0.612840	+	0.790207i	$0.709973\pi$
$360$	2.68364e7	+	4.48224e6i	0.575197	+	0.0960700i
$361$	−2.47610e6			−0.0526316
$362$	9.70240e6	+	535771.i	0.204528	+	0.0112941i
$363$		−	7.20334e6i		−	0.150596i
$364$	6.53856e6	−	5.90236e7i	0.135574	−	1.22383i
$365$	−5.89577e7			−1.21245
$366$	−2.14928e6	+	3.89217e7i	−0.0438379	+	0.793869i
$367$		−	9.34190e7i		−	1.88989i	−0.327225	−	0.944947i	$-0.606113\pi$
$367$		−	9.34190e7i		−	1.88989i	0.327225	−	0.944947i	$-0.393887\pi$
$368$	−1.76951e7	+	7.88869e7i	−0.355067	+	1.58293i
$369$	−2.76493e7			−0.550308
$370$	−2.16874e7	−	1.19759e6i	−0.428155	−	0.0236429i
$371$			2.20367e7i			0.431544i
$372$	9.07602e7	+	1.00543e7i	1.76306	+	0.195309i
$373$	7.49085e7			1.44346			0.721730	−	0.692175i	$-0.243347\pi$
$373$	7.49085e7			1.44346			0.721730	+	0.692175i	$0.243347\pi$
$374$	−3.82729e6	+	6.93092e7i	−0.0731604	+	1.32488i
$375$			7.26538e7i			1.37773i
$376$	−6.85893e6	+	4.10663e7i	−0.129031	+	0.772542i
$377$	1.17923e8			2.20076
$378$	−2.32074e7	−	1.28152e6i	−0.429686	−	0.0237274i
$379$		−	2.27784e7i		−	0.418414i	−0.977871	−	0.209207i	$-0.932912\pi$
$379$		−	2.27784e7i		−	0.418414i	0.977871	−	0.209207i	$-0.0670883\pi$
$380$	−1.24275e6	+	1.12183e7i	−0.0226481	+	0.204445i
$381$	−8.65467e7			−1.56486
$382$	4.50323e6	−	8.15501e7i	0.0807857	−	1.46297i
$383$			1.30351e7i			0.232016i	0.993248	+	0.116008i	$0.0370099\pi$
$383$			1.30351e7i			0.232016i	−0.993248	+	0.116008i	$0.962990\pi$
$384$	−2.73968e7	+	6.73864e7i	−0.483845	+	1.19009i
$385$	−4.60649e7			−0.807213
$386$	−6.22002e7	−	3.43472e6i	−1.08151	−	0.0597214i
$387$		−	2.15454e7i		−	0.371725i
$388$	−6.60975e7	−	7.32220e6i	−1.13159	−	0.125356i
$389$	−7.59231e7			−1.28981			−0.644904	−	0.764264i	$-0.723103\pi$
$389$	−7.59231e7			−1.28981			−0.644904	+	0.764264i	$0.723103\pi$
$390$	4.84105e6	−	8.76676e7i	0.0816104	−	1.47790i
$391$		−	1.36950e8i		−	2.29104i
$392$	−4.86180e6	−	812023.i	−0.0807122	−	0.0134806i
$393$	−5.84592e7			−0.963109
$394$	7.50232e7	+	4.14282e6i	1.22661	+	0.0677341i
$395$			4.13834e7i			0.671482i
$396$	4.17839e6	−	3.77183e7i	0.0672857	−	0.607389i
$397$	1.51688e7			0.242426			0.121213	−	0.992627i	$-0.461322\pi$
$397$	1.51688e7			0.242426			0.121213	+	0.992627i	$0.461322\pi$
$398$	−312260.	+	5.65479e6i	−0.00495299	+	0.0896948i
$399$			1.79391e7i			0.282411i
$400$	−1.22460e7	−	2.74690e6i	−0.191343	−	0.0429203i
$401$	−7.30606e7			−1.13305			−0.566527	−	0.824043i	$-0.691713\pi$
$401$	−7.30606e7			−1.13305			−0.566527	+	0.824043i	$0.691713\pi$
$402$	−1.73073e7	−	955718.i	−0.266410	−	0.0147113i
$403$		−	1.16130e8i		−	1.77430i
$404$	8.80047e7	+	9.74906e6i	1.33463	+	0.147849i
$405$	−7.31045e7			−1.10047
$406$	−6.05540e6	+	1.09659e8i	−0.0904826	+	1.63857i
$407$			3.02949e7i			0.449352i
$408$	2.02995e7	−	1.21539e8i	0.298885	−	1.78951i
$409$	9.19469e7			1.34390			0.671951	−	0.740596i	$-0.265457\pi$
$409$	9.19469e7			1.34390			0.671951	+	0.740596i	$0.265457\pi$
$410$	−5.22045e7	−	2.88276e6i	−0.757454	−	0.0418270i
$411$			4.21319e7i			0.606857i
$412$	−1.53715e7	+	1.38758e8i	−0.219798	+	1.98412i
$413$	9.57580e7			1.35933
$414$	−4.12811e6	+	7.47569e7i	−0.0581768	+	1.05354i
$415$		−	1.31643e7i		−	0.184184i
$416$	8.90133e7	+	2.51940e7i	1.23644	+	0.349959i
$417$	8.00947e7			1.10458
$418$	1.57187e7	+	867993.i	0.215222	+	0.0118847i
$419$		−	2.11000e7i		−	0.286840i	−0.989662	−	0.143420i	$-0.954190\pi$
$419$		−	2.11000e7i		−	0.286840i	0.989662	−	0.143420i	$-0.0458100\pi$
$420$	8.12753e7	+	9.00358e6i	1.09701	+	0.121525i
$421$	8.91846e7			1.19521			0.597604	−	0.801791i	$-0.296119\pi$
$421$	8.91846e7			1.19521			0.597604	+	0.801791i	$0.296119\pi$
$422$	7.02745e6	−	1.27262e8i	0.0935106	−	1.69340i
$423$			3.85574e7i			0.509432i
$424$	−3.38600e7	−	5.65533e6i	−0.444211	−	0.0741925i
$425$	2.12595e7			0.276940
$426$	2.25376e7	+	1.24454e6i	0.291528	+	0.0160983i
$427$			4.61699e7i			0.593028i
$428$	2.36013e6	−	2.13049e7i	0.0301026	−	0.271737i
$429$	−1.22462e8			−1.55107
$430$	2.24635e6	−	4.06796e7i	0.0282535	−	0.511648i
$431$			2.91434e7i			0.364006i	0.983298	+	0.182003i	$0.0582581\pi$
$431$			2.91434e7i			0.364006i	−0.983298	+	0.182003i	$0.941742\pi$
$432$	7.92485e6	−	3.53298e7i	0.0982969	−	0.438218i
$433$	2.55057e7			0.314177			0.157088	−	0.987585i	$-0.449789\pi$
$433$	2.55057e7			0.314177			0.157088	+	0.987585i	$0.449789\pi$
$434$	1.07991e8	+	5.96333e6i	1.32105	+	0.0729490i
$435$			1.62379e8i			1.97271i
$436$	4.38186e7	+	4.85417e6i	0.528687	+	0.0585673i
$437$	−3.10591e7			−0.372173
$438$	8.04857e6	−	1.45753e8i	0.0957847	−	1.73459i
$439$			1.30118e8i			1.53796i	0.639274	+	0.768979i	$0.279235\pi$
$439$			1.30118e8i			1.53796i	−0.639274	+	0.768979i	$0.720765\pi$
$440$	1.18217e7	−	7.07799e7i	0.138779	−	0.830906i
$441$	−4.56478e6			−0.0532235
$442$	−1.56468e8	−	8.64025e6i	−1.81200	−	0.100060i
$443$			1.18650e8i			1.36477i	0.730995	+	0.682383i	$0.239056\pi$
$443$			1.18650e8i			1.36477i	−0.730995	+	0.682383i	$0.760944\pi$
$444$	5.92126e6	−	5.34512e7i	0.0676496	−	0.610673i
$445$	−8.50415e6			−0.0965053
$446$	200736.	−	3.63517e6i	0.00226267	−	0.0409751i
$447$		−	4.68205e7i		−	0.524220i
$448$	−2.79993e7	+	8.14815e7i	−0.311396	+	0.906202i
$449$	1.18514e7			0.130927			0.0654635	−	0.997855i	$-0.479147\pi$
$449$	1.18514e7			0.130927			0.0654635	+	0.997855i	$0.479147\pi$
$450$	−1.16049e7	−	640826.i	−0.127351	−	0.00703238i
$451$			7.29240e7i			0.794952i
$452$	−1.54893e7	−	1.71588e6i	−0.167732	−	0.0185811i
$453$	1.37420e8			1.47827
$454$	6.72653e6	−	1.21812e8i	0.0718825	−	1.30174i
$455$		−	1.03993e8i		−	1.10401i
$456$	−2.75638e7	−	4.60374e6i	−0.290700	−	0.0485530i
$457$	−1.71583e8			−1.79774			−0.898869	−	0.438218i	$-0.855610\pi$
$457$	−1.71583e8			−1.79774			−0.898869	+	0.438218i	$0.855610\pi$
$458$	−7.15392e7	−	3.95043e6i	−0.744642	−	0.0411195i
$459$			6.13338e7i			0.634252i
$460$	−1.55885e7	+	1.40717e8i	−0.160151	+	1.44569i
$461$	626355.			0.00639319			0.00319660	−	0.999995i	$-0.498982\pi$
$461$	626355.			0.00639319			0.00319660	+	0.999995i	$0.498982\pi$
$462$	6.28852e6	−	1.13880e8i	0.0637708	−	1.15484i
$463$		−	2.70189e7i		−	0.272223i	−0.990694	−	0.136112i	$-0.956539\pi$
$463$		−	2.70189e7i		−	0.272223i	0.990694	−	0.136112i	$-0.0434606\pi$
$464$	−1.66939e8	−	3.74462e7i	−1.67111	−	0.374847i
$465$	1.59910e8			1.59044
$466$	−6.26526e7	−	3.45970e6i	−0.619129	−	0.0341886i
$467$		−	1.19504e8i		−	1.17336i	−0.809818	−	0.586681i	$-0.800434\pi$
$467$		−	1.19504e8i		−	1.17336i	0.809818	−	0.586681i	$-0.199566\pi$
$468$	8.51506e7	+	9.43287e6i	0.830711	+	0.0920251i
$469$	−2.05303e7			−0.199011
$470$	−4.02004e6	+	7.27999e7i	−0.0387202	+	0.701192i
$471$		−	1.32033e8i		−	1.26363i
$472$	−2.45746e7	+	1.47135e8i	−0.233701	+	1.39923i
$473$	−5.68251e7			−0.536978
$474$	−1.02307e8	−	5.64942e6i	−0.960657	−	0.0530479i
$475$		−	4.82145e6i		−	0.0449880i
$476$	1.60695e7	−	1.45059e8i	0.148998	−	1.34501i
$477$	−3.17913e7			−0.292923
$478$	5.40201e6	−	9.78262e7i	0.0494620	−	0.895718i
$479$		−	4.76303e7i		−	0.433388i	−0.976240	−	0.216694i	$-0.930473\pi$
$479$		−	4.76303e7i		−	0.433388i	0.976240	−	0.216694i	$-0.0695273\pi$
$480$	−3.46921e7	+	1.22571e8i	−0.313694	+	1.10832i
$481$	−6.83919e7			−0.614568
$482$	2.76431e7	+	1.52646e6i	0.246857	+	0.0136315i
$483$			2.25020e8i			1.99700i
$484$	1.32101e7	+	1.46339e6i	0.116511	+	0.0129070i
$485$	−1.16457e8			−1.02080
$486$	7.13731e6	−	1.29251e8i	0.0621765	−	1.12597i
$487$		−	5.21033e7i		−	0.451105i	−0.974231	−	0.225553i	$-0.927581\pi$
$487$		−	5.21033e7i		−	0.451105i	0.974231	−	0.225553i	$-0.0724188\pi$
$488$	−7.09412e7	−	1.18487e7i	−0.610435	−	0.101955i
$489$	1.21751e6			0.0104123
$490$	−8.61871e6	−	475929.i	−0.0732578	−	0.00404533i
$491$			1.07458e8i			0.907805i	0.891051	+	0.453902i	$0.149969\pi$
$491$			1.07458e8i			0.907805i	−0.891051	+	0.453902i	$0.850031\pi$
$492$	1.42533e7	−	1.28665e8i	0.119680	−	1.08035i
$493$	2.89812e8			2.41867
$494$	−1.95953e6	+	3.54855e7i	−0.0162544	+	0.294354i
$495$		−	6.64557e7i		−	0.547919i
$496$	−3.68768e7	+	1.64401e8i	−0.302210	+	1.34728i
$497$	2.67347e7			0.217774
$498$	3.25443e7	+	1.79711e6i	0.263504	+	0.0145508i
$499$		−	2.75270e7i		−	0.221542i	−0.993846	−	0.110771i	$-0.964668\pi$
$499$		−	2.75270e7i		−	0.221542i	0.993846	−	0.110771i	$-0.0353321\pi$
$500$	−1.33239e8	−	1.47600e7i	−1.06591	−	0.118080i
$501$	−1.80915e8			−1.43867
$502$	4.15879e6	−	7.53124e7i	0.0328742	−	0.595327i
$503$			1.33396e8i			1.04819i	0.851661	+	0.524094i	$0.175596\pi$
$503$			1.33396e8i			1.04819i	−0.851661	+	0.524094i	$0.824404\pi$
$504$	−1.31444e7	+	7.86989e7i	−0.102671	+	0.614719i
$505$	1.55055e8			1.20396
$506$	1.97168e8	+	1.08877e7i	1.52190	+	0.0840399i
$507$		−	1.09038e8i		−	0.836672i
$508$	1.75824e7	−	1.58716e8i	0.134118	−	1.21068i
$509$	1.61029e8			1.22110			0.610549	−	0.791978i	$-0.290949\pi$
$509$	1.61029e8			1.22110			0.610549	+	0.791978i	$0.290949\pi$
$510$	1.18976e7	−	2.15456e8i	0.0896910	−	1.62423i
$511$		−	1.72896e8i		−	1.29575i
$512$	−1.18013e8	−	6.39324e7i	−0.879265	−	0.476334i
$513$	1.39100e7			0.103032
$514$	3.19027e7	+	1.76168e6i	0.234930	+	0.0129729i
$515$			2.44477e8i			1.78985i
$516$	1.00260e8	+	1.11067e7i	0.729759	+	0.0808417i
$517$	1.01694e8			0.735905
$518$	3.51197e6	−	6.35991e7i	0.0252675	−	0.457574i
$519$			7.62564e7i			0.545474i
$520$	1.59789e8	+	2.66880e7i	1.13641	+	0.189804i
$521$	2.68149e8			1.89611			0.948055	−	0.318106i	$-0.103047\pi$
$521$	2.68149e8			1.89611			0.948055	+	0.318106i	$0.103047\pi$
$522$	−1.58199e8	−	8.73584e6i	−1.11223	−	0.0614177i
$523$		−	4.59288e7i		−	0.321055i	−0.987031	−	0.160528i	$-0.948680\pi$
$523$		−	4.59288e7i		−	0.321055i	0.987031	−	0.160528i	$-0.0513196\pi$
$524$	1.18763e7	−	1.07207e8i	0.0825442	−	0.745127i
$525$	−3.49309e7			−0.241397
$526$	−3.56631e6	+	6.45830e7i	−0.0245054	+	0.443773i
$527$		−	2.85406e8i		−	1.94998i
$528$	1.73366e8	+	3.88877e7i	1.17777	+	0.264187i
$529$	−2.41555e8			−1.63174
$530$	−6.00249e7	−	3.31461e6i	−0.403185	−	0.0222641i
$531$			1.38146e8i			0.922685i
$532$	−3.28981e7	−	3.64441e6i	−0.218492	−	0.0242043i
$533$	−1.64629e8			−1.08724
$534$	1.16094e6	−	2.10237e7i	0.00762404	−	0.138065i
$535$		−	3.75370e7i		−	0.245131i
$536$	5.26874e6	−	3.15454e7i	0.0342147	−	0.204853i
$537$	−3.46229e8			−2.23584
$538$	6.09669e7	+	3.36662e6i	0.391514	+	0.0216196i
$539$			1.20394e7i			0.0768845i
$540$	6.98138e6	−	6.30209e7i	0.0443363	−	0.400224i
$541$	8.36670e7			0.528399			0.264200	−	0.964468i	$-0.414892\pi$
$541$	8.36670e7			0.528399			0.264200	+	0.964468i	$0.414892\pi$
$542$	−1.26003e7	+	2.28181e8i	−0.0791374	+	1.43312i
$543$			4.21318e7i			0.263155i
$544$	2.18763e8	+	6.19180e7i	1.35887	+	0.384610i
$545$	7.72037e7			0.476924
$546$	2.57089e8	+	1.41966e7i	1.57945	+	0.0872179i
$547$			2.59002e8i			1.58249i	0.611499	+	0.791246i	$0.290567\pi$
$547$			2.59002e8i			1.58249i	−0.611499	+	0.791246i	$0.709433\pi$
$548$	−7.72650e7	−	8.55932e6i	−0.469506	−	0.0520113i
$549$	−6.66071e7			−0.402535
$550$	−1.69015e6	+	3.06073e7i	−0.0101587	+	0.183966i
$551$		−	6.57268e7i		−	0.392905i
$552$	−3.45748e8	−	5.77472e7i	−2.05562	−	0.343332i
$553$	−1.21358e8			−0.717620
$554$	2.60255e8	+	1.43714e7i	1.53063	+	0.0845219i
$555$		−	9.41755e7i		−	0.550883i
$556$	−1.62716e7	+	1.46884e8i	−0.0946688	+	0.854575i
$557$	6.95588e7			0.402519			0.201260	−	0.979538i	$-0.435496\pi$
$557$	6.95588e7			0.402519			0.201260	+	0.979538i	$0.435496\pi$
$558$	−8.60301e6	+	1.55794e8i	−0.0495163	+	0.896701i
$559$		−	1.28285e8i		−	0.734412i
$560$	−3.30230e7	+	1.47220e8i	−0.188041	+	0.838307i
$561$	−3.00969e8			−1.70464
$562$	2.84722e8	+	1.57225e7i	1.60403	+	0.0885752i
$563$			1.44106e8i			0.807525i	0.914864	+	0.403763i	$0.132298\pi$
$563$			1.44106e8i			0.807525i	−0.914864	+	0.403763i	$0.867702\pi$
$564$	−1.79425e8	−	1.98764e7i	−1.00010	−	0.110790i
$565$	−2.72905e7			−0.151309
$566$	1.38248e7	−	2.50357e8i	0.0762449	−	1.38074i
$567$		−	2.14382e8i		−	1.17609i
$568$	−6.86097e6	+	4.10785e7i	−0.0374404	+	0.224166i
$569$	−2.05217e8			−1.11398			−0.556989	−	0.830520i	$-0.688043\pi$
$569$	−2.05217e8			−1.11398			−0.556989	+	0.830520i	$0.688043\pi$
$570$	−4.88635e7	−	2.69827e6i	−0.263852	−	0.0145700i
$571$			4.57561e7i			0.245777i	0.992420	+	0.122888i	$0.0392157\pi$
$571$			4.57561e7i			0.245777i	−0.992420	+	0.122888i	$0.960784\pi$
$572$	2.48788e7	−	2.24581e8i	0.132936	−	1.20001i
$573$	3.54124e8			1.88231
$574$	8.45380e6	−	1.53092e8i	0.0447009	−	0.809498i
$575$		−	6.04781e7i		−	0.318123i
$576$	−1.17550e8	−	4.03933e7i	−0.615111	−	0.211369i
$577$	−1.03992e8			−0.541341			−0.270670	−	0.962672i	$-0.587245\pi$
$577$	−1.03992e8			−0.541341			−0.270670	+	0.962672i	$0.587245\pi$
$578$	−1.91737e8	−	1.05878e7i	−0.992939	−	0.0548306i
$579$		−	2.70099e8i		−	1.39151i
$580$	−2.97784e8	−	3.29881e7i	−1.52622	−	0.169073i
$581$	3.86048e7			0.196840
$582$	1.58980e7	−	2.87901e8i	0.0806444	−	1.46041i
$583$			8.38484e7i			0.423145i
$584$	2.65659e8	+	4.43706e7i	1.33379	+	0.222770i
$585$	1.50026e8			0.749377
$586$	1.93699e8	+	1.06961e7i	0.962574	+	0.0531538i
$587$			2.59742e8i			1.28419i	0.766627	+	0.642093i	$0.221934\pi$
$587$			2.59742e8i			1.28419i	−0.766627	+	0.642093i	$0.778066\pi$
$588$	2.35315e6	−	2.12419e7i	0.0115749	−	0.104487i
$589$	−6.47274e7			−0.316769
$590$	−1.44032e7	+	2.60831e8i	−0.0701300	+	1.27000i
$591$			3.25782e8i			1.57821i
$592$	9.68203e7	+	2.17178e7i	0.466661	+	0.104677i
$593$	2.96852e7			0.142356			0.0711781	−	0.997464i	$-0.477324\pi$
$593$	2.96852e7			0.142356			0.0711781	+	0.997464i	$0.477324\pi$
$594$	−8.83027e7	−	4.87611e6i	−0.421322	−	0.0232656i
$595$		−	2.55579e8i		−	1.21332i
$596$	8.58633e7	+	9.51183e6i	0.405573	+	0.0449288i
$597$	−2.45554e7			−0.115405
$598$	−2.45795e7	+	4.45115e8i	−0.114939	+	2.08146i
$599$			1.71858e8i			0.799632i	0.916595	+	0.399816i	$0.130926\pi$
$599$			1.71858e8i			0.799632i	−0.916595	+	0.399816i	$0.869074\pi$
$600$	8.96438e6	−	5.36722e7i	0.0415017	−	0.248482i
$601$	−2.11842e6			−0.00975862			−0.00487931	−	0.999988i	$-0.501553\pi$
$601$	−2.11842e6			−0.00975862			−0.00487931	+	0.999988i	$0.501553\pi$
$602$	1.19295e8	+	6.58751e6i	0.546804	+	0.0301948i
$603$		−	2.96181e7i		−	0.135085i
$604$	−2.79175e7	+	2.52011e8i	−0.126697	+	1.14369i
$605$	2.32747e7			0.105104
$606$	−2.11672e7	+	3.83322e8i	−0.0951144	+	1.72245i
$607$		−	3.42476e8i		−	1.53131i	−0.643249	−	0.765657i	$-0.722414\pi$
$607$		−	3.42476e8i		−	1.53131i	0.643249	−	0.765657i	$-0.277586\pi$
$608$	1.40424e7	−	4.96135e7i	0.0624787	−	0.220744i
$609$	−4.76183e8			−2.10825
$610$	−1.25760e8	−	6.94455e6i	−0.554057	−	0.0305953i
$611$			2.29577e8i			1.00648i
$612$	2.09270e8	+	2.31827e7i	0.912963	+	0.101137i
$613$	2.58643e8			1.12284			0.561422	−	0.827530i	$-0.310255\pi$
$613$	2.58643e8			1.12284			0.561422	+	0.827530i	$0.310255\pi$
$614$	22741.1	−	411823.i	9.82439e−5	−	0.00177912i
$615$		−	2.26693e8i		−	0.974571i
$616$	2.07565e8	+	3.46677e7i	0.887998	+	0.148314i
$617$	2.01314e8			0.857075			0.428537	−	0.903524i	$-0.359029\pi$
$617$	2.01314e8			0.857075			0.428537	+	0.903524i	$0.359029\pi$
$618$	−6.04389e8	−	3.33746e7i	−2.56065	−	0.141401i
$619$			1.84702e8i			0.778751i	0.921079	+	0.389375i	$0.127309\pi$
$619$			1.84702e8i			0.778751i	−0.921079	+	0.389375i	$0.872691\pi$
$620$	−3.24865e7	+	2.93256e8i	−0.136310	+	1.23047i
$621$	1.74480e8			0.728570
$622$	−2.22349e7	+	4.02657e8i	−0.0923983	+	1.67326i
$623$		−	2.49388e7i		−	0.103136i
$624$	−8.77906e7	+	3.91380e8i	−0.361322	+	1.61081i
$625$	−1.86877e8			−0.765447
$626$	−1.76593e8	−	9.75154e6i	−0.719863	−	0.0397512i
$627$			6.82570e7i			0.276914i
$628$	2.42133e8	+	2.68232e7i	0.977631	+	0.108301i
$629$	−1.68083e8			−0.675418
$630$	−7.70395e6	+	1.39513e8i	−0.0308100	+	0.557946i
$631$		−	2.96805e7i		−	0.118136i	−0.998254	−	0.0590681i	$-0.981187\pi$
$631$		−	2.96805e7i		−	0.118136i	0.998254	−	0.0590681i	$-0.0188129\pi$
$632$	3.11444e7	−	1.86470e8i	0.123376	−	0.738684i
$633$	5.52623e8			2.17880
$634$	−2.87168e8	−	1.58575e7i	−1.12685	−	0.0622254i
$635$		−	2.79642e8i		−	1.09215i
$636$	1.63885e7	−	1.47939e8i	0.0637042	−	0.575058i
$637$	−2.71795e7			−0.105153
$638$	−2.30404e7	+	4.17244e8i	−0.0887214	+	1.60668i
$639$			3.85689e7i			0.147820i
$640$	−2.17733e8	−	8.85221e7i	−0.830585	−	0.337685i
$641$	1.18576e8			0.450217			0.225108	−	0.974334i	$-0.427726\pi$
$641$	1.18576e8			0.450217			0.225108	+	0.974334i	$0.427726\pi$
$642$	9.27977e7	+	5.12433e6i	0.350697	+	0.0193657i
$643$		−	2.05671e8i		−	0.773641i	−0.922155	−	0.386820i	$-0.873573\pi$
$643$		−	2.05671e8i		−	0.773641i	0.922155	−	0.386820i	$-0.126427\pi$
$644$	−4.12659e8	−	4.57139e7i	−1.54502	−	0.171155i
$645$	1.76648e8			0.658308
$646$	−4.81583e6	+	8.72110e7i	−0.0178638	+	0.323500i
$647$			2.69627e8i			0.995521i	0.867315	+	0.497760i	$0.165844\pi$
$647$			2.69627e8i			0.995521i	−0.867315	+	0.497760i	$0.834156\pi$
$648$	3.29403e8	+	5.50172e7i	1.21061	+	0.202197i
$649$	3.64353e8			1.33287
$650$	−6.90973e7	−	3.81559e6i	−0.251606	−	0.0138938i
$651$			4.68943e8i			1.69972i
$652$	−247343.	+	2.23277e6i	−0.000892394	+	0.00805565i
$653$	2.08486e8			0.748749			0.374375	−	0.927278i	$-0.377857\pi$
$653$	2.08486e8			0.748749			0.374375	+	0.927278i	$0.377857\pi$
$654$	−1.05394e7	+	1.90860e8i	−0.0376776	+	0.682311i
$655$		−	1.88888e8i		−	0.672172i
$656$	2.33060e8	+	5.22777e7i	0.825574	+	0.185185i
$657$	2.49429e8			0.879530
$658$	−2.13489e8	−	1.17889e7i	−0.749371	−	0.0413806i
$659$			1.59433e7i			0.0557086i	0.999612	+	0.0278543i	$0.00886745\pi$
$659$			1.59433e7i			0.0557086i	−0.999612	+	0.0278543i	$0.991133\pi$
$660$	3.09248e8	+	3.42581e7i	1.07566	+	0.119160i
$661$	−4.69057e8			−1.62413			−0.812066	−	0.583566i	$-0.801657\pi$
$661$	−4.69057e8			−1.62413			−0.812066	+	0.583566i	$0.801657\pi$
$662$	2.64987e7	−	4.79871e8i	0.0913378	−	1.65406i
$663$		−	6.79450e8i		−	2.33140i
$664$	−9.90722e6	+	5.93172e7i	−0.0338413	+	0.202617i
$665$	−5.79630e7			−0.197100
$666$	9.17514e7	+	5.06655e6i	0.310592	+	0.0171510i
$667$		−	8.24447e8i		−	2.77834i
$668$	3.67538e7	−	3.31776e8i	0.123303	−	1.11305i
$669$	1.57854e7			0.0527203
$670$	3.08803e6	−	5.59218e7i	0.0102673	−	0.185933i
$671$			1.75674e8i			0.581486i
$672$	−3.59445e8	−	1.01736e8i	−1.18447	−	0.335248i
$673$	−3.12147e7			−0.102403			−0.0512016	−	0.998688i	$-0.516305\pi$
$673$	−3.12147e7			−0.102403			−0.0512016	+	0.998688i	$0.516305\pi$
$674$	3.66959e8	+	2.02636e7i	1.19850	+	0.0661816i
$675$			2.70854e7i			0.0880692i
$676$	1.99963e8	+	2.21517e7i	0.647307	+	0.0717079i
$677$	−2.37101e8			−0.764131			−0.382065	−	0.924135i	$-0.624787\pi$
$677$	−2.37101e8			−0.764131			−0.382065	+	0.924135i	$0.624787\pi$
$678$	3.72554e6	−	6.74666e7i	0.0119536	−	0.216471i
$679$		−	3.41515e8i		−	1.09094i
$680$	3.92704e8	+	6.55898e7i	1.24893	+	0.208598i
$681$	5.28959e8			1.67487
$682$	4.10900e8	+	2.26901e7i	1.29534	+	0.0715292i
$683$			4.90665e8i			1.54001i	0.638039	+	0.770004i	$0.279746\pi$
$683$			4.90665e8i			1.54001i	−0.638039	+	0.770004i	$0.720254\pi$
$684$	5.25762e6	−	4.74606e7i	0.0164294	−	0.148308i
$685$	−1.36133e8			−0.423537
$686$	1.84515e7	−	3.34143e8i	0.0571557	−	1.03505i
$687$		−	3.10653e8i		−	0.958087i
$688$	−4.07367e7	+	1.81609e8i	−0.125089	+	0.557663i
$689$	−1.89291e8			−0.578725
$690$	−6.12922e8	−	3.38459e7i	−1.86577	−	0.103029i
$691$		−	1.98355e8i		−	0.601185i	−0.953753	−	0.300592i	$-0.902816\pi$
$691$		−	1.98355e8i		−	0.601185i	0.953753	−	0.300592i	$-0.0971844\pi$
$692$	−1.39845e8	−	1.54919e7i	−0.422016	−	0.0467504i
$693$	1.94884e8			0.585567
$694$	−2.49680e7	+	4.52151e8i	−0.0746974	+	1.35271i
$695$			2.58794e8i			0.770904i
$696$	1.22204e8	−	7.31668e8i	0.362458	−	2.17013i
$697$	−4.04600e8			−1.19489
$698$	2.31935e8	+	1.28076e7i	0.682025	+	0.0376618i
$699$		−	2.72063e8i		−	0.796597i
$700$	7.09638e6	−	6.40591e7i	0.0206892	−	0.186761i
$701$	−6.08251e7			−0.176575			−0.0882874	−	0.996095i	$-0.528139\pi$
$701$	−6.08251e7			−0.176575			−0.0882874	+	0.996095i	$0.528139\pi$
$702$	1.10080e7	−	1.99347e8i	0.0318198	−	0.576233i
$703$			3.81198e7i			0.109720i
$704$	−1.06536e8	+	3.10032e8i	−0.305335	+	0.888564i
$705$	−3.16127e8			−0.902183
$706$	−5.89751e8	−	3.25663e7i	−1.67592	−	0.0925454i
$707$			4.54706e8i			1.28668i
$708$	−6.42852e8	−	7.12144e7i	−1.81139	−	0.200663i
$709$	−3.42159e8			−0.960041			−0.480021	−	0.877257i	$-0.659371\pi$
$709$	−3.42159e8			−0.960041			−0.480021	+	0.877257i	$0.659371\pi$
$710$	−4.02124e6	+	7.28215e7i	−0.0112353	+	0.203463i
$711$		−	1.75078e8i		−	0.487105i
$712$	3.83191e7	+	6.40009e6i	0.106163	+	0.0177315i
$713$	−8.11911e8			−2.23996
$714$	6.31834e8	+	3.48902e7i	1.73584	+	0.0958537i
$715$		−	3.95689e8i		−	1.08252i
$716$	7.03381e7	−	6.34942e8i	0.191625	−	1.72980i
$717$	4.24802e8			1.15247
$718$	3.22540e7	−	5.84094e8i	0.0871385	−	1.57801i
$719$			5.63200e8i			1.51522i	0.652707	+	0.757610i	$0.273633\pi$
$719$			5.63200e8i			1.51522i	−0.652707	+	0.757610i	$0.726367\pi$
$720$	−2.12388e8	−	4.76407e7i	−0.569025	−	0.127638i
$721$	−7.16940e8			−1.91283
$722$	1.97787e7	+	1.09219e6i	0.0525515	+	0.00290192i
$723$			1.20038e8i			0.317616i
$724$	−7.72648e7	−	8.55929e6i	−0.203594	−	0.0225539i
$725$	1.27983e8			0.335844
$726$	−3.17733e6	+	5.75390e7i	−0.00830334	+	0.150367i
$727$		−	3.14510e8i		−	0.818525i	−0.912417	−	0.409262i	$-0.865786\pi$
$727$		−	3.14510e8i		−	0.818525i	0.912417	−	0.409262i	$-0.134214\pi$
$728$	−7.82637e7	+	4.68586e8i	−0.202846	+	1.21449i
$729$	8.57520e7			0.221341
$730$	4.70944e8	+	2.60058e7i	1.21060	+	0.0668500i
$731$		−	3.15279e8i		−	0.807129i
$732$	3.43361e7	−	3.09952e8i	0.0875423	−	0.790245i
$733$	4.78695e8			1.21548			0.607738	−	0.794137i	$-0.292077\pi$
$733$	4.78695e8			1.21548			0.607738	+	0.794137i	$0.292077\pi$
$734$	−4.12064e7	+	7.46215e8i	−0.104202	+	1.88702i
$735$		−	3.74260e7i		−	0.0942566i
$736$	1.76142e8	−	6.22330e8i	0.441804	−	1.56094i
$737$	−7.81167e7			−0.195138
$738$	2.20858e8	+	1.21959e7i	0.549471	+	0.0303420i
$739$			1.28596e8i			0.318635i	0.987227	+	0.159318i	$0.0509294\pi$
$739$			1.28596e8i			0.318635i	−0.987227	+	0.159318i	$0.949071\pi$
$740$	1.72707e8	+	1.91322e7i	0.426201	+	0.0472140i
$741$	−1.54093e8			−0.378729
$742$	9.72022e6	−	1.76026e8i	0.0237938	−	0.430888i
$743$		−	6.17538e8i		−	1.50556i	−0.658273	−	0.752779i	$-0.728713\pi$
$743$		−	6.17538e8i		−	1.50556i	0.658273	−	0.752779i	$-0.271287\pi$
$744$	−7.20542e8	−	1.20346e8i	−1.74961	−	0.292221i
$745$	1.51282e8			0.365863
$746$	−5.98356e8	−	3.30415e7i	−1.44126	−	0.0795873i
$747$			5.56933e7i			0.133611i
$748$	6.11434e7	−	5.51942e8i	0.146098	−	1.31883i
$749$	1.10079e8			0.261974
$750$	3.20470e7	−	5.80347e8i	0.0759633	−	1.37564i
$751$		−	2.20707e8i		−	0.521071i	−0.965464	−	0.260535i	$-0.916101\pi$
$751$		−	2.20707e8i		−	0.521071i	0.965464	−	0.260535i	$-0.0838990\pi$
$752$	7.29020e7	−	3.25005e8i	0.171430	−	0.764252i
$753$	3.27038e8			0.765972
$754$	−9.41946e8	−	5.20147e7i	−2.19741	−	0.121342i
$755$			4.44018e8i			1.03171i
$756$	1.84811e8	+	2.04732e7i	0.427724	+	0.0473827i
$757$	−3.94192e7			−0.0908699			−0.0454350	−	0.998967i	$-0.514467\pi$
$757$	−3.94192e7			−0.0908699			−0.0454350	+	0.998967i	$0.514467\pi$
$758$	−1.00474e7	+	1.81950e8i	−0.0230699	+	0.417778i
$759$			8.56186e8i			1.95814i
$760$	1.48752e7	−	8.90617e7i	0.0338861	−	0.202885i
$761$	−7.73380e8			−1.75485			−0.877423	−	0.479718i	$-0.840739\pi$
$761$	−7.73380e8			−1.75485			−0.877423	+	0.479718i	$0.840739\pi$
$762$	6.91321e8	+	3.81751e7i	1.56248	+	0.0862809i
$763$			2.26403e8i			0.509693i
$764$	−7.19421e7	+	6.49422e8i	−0.161326	+	1.45629i
$765$	3.68712e8			0.823575
$766$	5.74968e6	−	1.04122e8i	0.0127926	−	0.231663i
$767$			8.22542e8i			1.82294i
$768$	2.48565e8	−	5.26187e8i	0.548727	−	1.16160i
$769$	5.71513e8			1.25674			0.628372	−	0.777913i	$-0.283722\pi$
$769$	5.71513e8			1.25674			0.628372	+	0.777913i	$0.283722\pi$
$770$	3.67959e8	+	2.03189e7i	0.805985	+	0.0445069i
$771$			1.38535e8i			0.302270i
$772$	4.95330e8	+	5.48720e7i	1.07657	+	0.119261i
$773$	−1.81166e8			−0.392227			−0.196113	−	0.980581i	$-0.562832\pi$
$773$	−1.81166e8			−0.392227			−0.196113	+	0.980581i	$0.562832\pi$
$774$	−9.50349e6	+	1.72101e8i	−0.0204956	+	0.371159i
$775$		−	1.26037e8i		−	0.270765i
$776$	5.24746e8	+	8.76436e7i	1.12296	+	0.187558i
$777$	2.76174e8			0.588734
$778$	6.06461e8	+	3.34891e7i	1.28785	+	0.0711155i
$779$			9.17595e7i			0.194106i
$780$	−7.73390e7	+	6.98139e8i	−0.162973	+	1.47115i
$781$	1.01724e8			0.213535
$782$	−6.04077e7	+	1.09394e9i	−0.126320	+	2.28756i
$783$			3.69233e8i			0.769156i
$784$	3.84771e7	+	8.63080e6i	0.0798462	+	0.0179103i
$785$	4.26613e8			0.881911
$786$	4.66962e8	+	2.57859e7i	0.961644	+	0.0531024i
$787$			1.78283e7i			0.0365752i	0.999833	+	0.0182876i	$0.00582145\pi$
$787$			1.78283e7i			0.0365752i	−0.999833	+	0.0182876i	$0.994179\pi$
$788$	−5.97445e8	−	6.61843e7i	−1.22101	−	0.135262i
$789$	−2.80446e8			−0.570977
$790$	1.82539e7	−	3.30563e8i	0.0370232	−	0.670461i
$791$		−	8.00305e7i		−	0.161706i
$792$	−5.00135e7	+	2.99444e8i	−0.100673	+	0.602755i
$793$	−3.96590e8			−0.795284
$794$	−1.21165e8	−	6.69081e6i	−0.242057	−	0.0133665i
$795$		−	2.60653e8i		−	0.518754i
$796$	4.98856e6	−	4.50317e7i	0.00989091	−	0.0892852i
$797$	5.40171e8			1.06698			0.533490	−	0.845807i	$-0.320880\pi$
$797$	5.40171e8			1.06698			0.533490	+	0.845807i	$0.320880\pi$
$798$	7.91278e6	−	1.43294e8i	0.0155711	−	0.281981i
$799$			5.64220e8i			1.10614i
$800$	9.66072e7	+	2.73434e7i	0.188686	+	0.0534050i
$801$	3.59780e7			0.0700067
$802$	5.83596e8	+	3.22265e7i	1.13133	+	0.0624726i
$803$		−	6.57858e8i		−	1.27053i
$804$	1.37826e8	+	1.52682e7i	0.265194	+	0.0293779i
$805$	−7.27063e8			−1.39375
$806$	−5.12238e7	+	9.27623e8i	−0.0978288	+	1.77160i
$807$			2.64744e8i			0.503739i
$808$	−6.98667e8	−	1.16692e8i	−1.32445	−	0.221211i
$809$	9.94825e8			1.87889			0.939445	−	0.342701i	$-0.111342\pi$
$809$	9.94825e8			1.87889			0.939445	+	0.342701i	$0.111342\pi$
$810$	5.83946e8	+	3.22458e7i	1.09880	+	0.0606762i
$811$		−	1.35764e8i		−	0.254519i	−0.991869	−	0.127260i	$-0.959382\pi$
$811$		−	1.35764e8i		−	0.254519i	0.991869	−	0.127260i	$-0.0406182\pi$
$812$	9.67390e7	−	8.73264e8i	0.180690	−	1.63109i
$813$	−9.90857e8			−1.84391
$814$	1.33628e7	−	2.41991e8i	0.0247757	−	0.448668i
$815$			3.93390e6i			0.00726692i
$816$	−2.15759e8	+	9.61876e8i	−0.397098	+	1.77031i
$817$	−7.15024e7			−0.131116
$818$	−7.34457e8	−	4.05570e7i	−1.34186	−	0.0740980i
$819$			4.39959e8i			0.800866i
$820$	4.15729e8	+	4.60539e7i	0.753995	+	0.0835267i
$821$	−3.18712e8			−0.575928			−0.287964	−	0.957641i	$-0.592978\pi$
$821$	−3.18712e8			−0.575928			−0.287964	+	0.957641i	$0.592978\pi$
$822$	1.85841e7	−	3.36543e8i	0.0334599	−	0.605933i
$823$			6.10138e8i			1.09453i	0.836959	+	0.547266i	$0.184331\pi$
$823$			6.10138e8i			1.09453i	−0.836959	+	0.547266i	$0.815669\pi$
$824$	1.83990e8	−	1.10160e9i	0.328861	−	1.96898i
$825$	−1.32910e8			−0.236698
$826$	−7.64899e8	−	4.22381e7i	−1.35726	−	0.0749487i
$827$			3.29266e8i			0.582145i	0.956701	+	0.291072i	$0.0940120\pi$
$827$			3.29266e8i			0.582145i	−0.956701	+	0.291072i	$0.905988\pi$
$828$	6.59493e7	−	5.95324e8i	0.116177	−	1.04873i
$829$	2.91994e8			0.512519			0.256259	−	0.966608i	$-0.417510\pi$
$829$	2.91994e8			0.512519			0.256259	+	0.966608i	$0.417510\pi$
$830$	−5.80666e6	+	1.05154e8i	−0.0101553	+	0.183904i
$831$			1.13013e9i			1.96937i
$832$	−6.99910e8	−	2.40508e8i	−1.21527	−	0.417600i
$833$	−6.67976e7			−0.115565
$834$	−6.39783e8	−	3.53291e7i	−1.10290	−	0.0609024i
$835$		−	5.84555e8i		−	1.00407i
$836$	−1.25175e8	−	1.38668e7i	−0.214240	−	0.0237332i
$837$	3.63618e8			0.620111
$838$	−9.30702e6	+	1.68543e8i	−0.0158153	+	0.286404i
$839$		−	4.72233e8i		−	0.799596i	−0.916603	−	0.399798i	$-0.869080\pi$
$839$		−	4.72233e8i		−	0.799596i	0.916603	−	0.399798i	$-0.130920\pi$
$840$	−6.45242e8	−	1.07769e8i	−1.08864	−	0.181826i
$841$	1.14986e9			1.93311
$842$	−7.12391e8	−	3.93386e7i	−1.19339	−	0.0658996i
$843$			1.23638e9i			2.06381i
$844$	−1.12268e8	+	1.01345e9i	−0.186737	+	1.68567i
$845$	3.52315e8			0.583930
$846$	1.70074e7	−	3.07990e8i	0.0280883	−	0.508657i
$847$			6.82542e7i			0.112326i
$848$	2.67973e8	+	6.01091e7i	0.439444	+	0.0985719i
$849$	1.08715e9			1.77651
$850$	−1.69817e8	−	9.37737e6i	−0.276518	−	0.0152695i
$851$			4.78157e8i			0.775858i
$852$	−1.79478e8	−	1.98823e7i	−0.290196	−	0.0321476i
$853$	1.91410e7			0.0308403			0.0154201	−	0.999881i	$-0.495091\pi$
$853$	1.91410e7			0.0308403			0.0154201	+	0.999881i	$0.495091\pi$
$854$	2.03652e7	−	3.68797e8i	0.0326975	−	0.592126i
$855$		−	8.36205e7i		−	0.133787i
$856$	−2.82497e7	+	1.69139e8i	−0.0450395	+	0.269664i
$857$	−1.01306e9			−1.60950			−0.804752	−	0.593612i	$-0.797702\pi$
$857$	−1.01306e9			−1.60950			−0.804752	+	0.593612i	$0.797702\pi$
$858$	9.78208e8	+	5.40171e7i	1.54871	+	0.0855203i
$859$			8.40311e8i			1.32575i	0.748732	+	0.662873i	$0.230663\pi$
$859$			8.40311e8i			1.32575i	−0.748732	+	0.662873i	$0.769337\pi$
$860$	−3.58869e7	+	3.23951e8i	−0.0564210	+	0.509312i
$861$	6.64788e8			1.04153
$862$	1.28549e7	−	2.32793e8i	0.0200700	−	0.363453i
$863$		−	9.11746e7i		−	0.141854i	−0.997482	−	0.0709269i	$-0.977404\pi$
$863$		−	9.11746e7i		−	0.141854i	0.997482	−	0.0709269i	$-0.0225957\pi$
$864$	−7.88860e7	+	2.78713e8i	−0.122309	+	0.432132i
$865$	−2.46393e8			−0.380697
$866$	−2.03735e8	−	1.12504e7i	−0.313699	−	0.0173226i
$867$		−	8.32602e8i		−	1.27756i
$868$	−8.59985e8	−	9.52681e7i	−1.31502	−	0.145676i
$869$	−4.61761e8			−0.703652
$870$	7.16241e7	−	1.29706e9i	0.108768	−	1.96970i
$871$		−	1.76351e8i		−	0.266885i
$872$	−3.47874e8	−	5.81023e7i	−0.524654	−	0.0876281i
$873$	4.92687e8			0.740506
$874$	2.48095e8	+	1.36999e7i	0.371606	+	0.0205203i
$875$		−	6.88421e8i		−	1.02761i
$876$	−1.28581e8	+	1.16070e9i	−0.191278	+	1.72667i
$877$	889860.			0.00131924			0.000659618	−	1.00000i	$-0.499790\pi$
$877$	889860.			0.00131924			0.000659618		1.00000i	$0.499790\pi$
$878$	5.73941e7	−	1.03936e9i	0.0847976	−	1.53562i
$879$			8.41121e8i			1.23849i
$880$	−1.25650e8	+	5.60164e8i	−0.184381	+	0.821991i
$881$	6.27469e8			0.917624			0.458812	−	0.888533i	$-0.348275\pi$
$881$	6.27469e8			0.917624			0.458812	+	0.888533i	$0.348275\pi$
$882$	3.64627e7	+	2.01349e6i	0.0531426	+	0.00293456i
$883$			7.55755e8i			1.09774i	0.835908	+	0.548869i	$0.184941\pi$
$883$			7.55755e8i			1.09774i	−0.835908	+	0.548869i	$0.815059\pi$
$884$	1.24603e9	+	1.38034e8i	1.80373	+	0.199815i
$885$	−1.13264e9			−1.63404
$886$	5.23357e7	−	9.47759e8i	0.0752484	−	1.36269i
$887$			3.36782e8i			0.482590i	0.970452	+	0.241295i	$0.0775722\pi$
$887$			3.36782e8i			0.482590i	−0.970452	+	0.241295i	$0.922428\pi$
$888$	−7.08750e7	+	4.24348e8i	−0.101217	+	0.606014i
$889$	8.20061e8			1.16719
$890$	6.79297e7	+	3.75111e6i	0.0963585	+	0.00532096i
$891$		−	8.15710e8i		−	1.15319i
$892$	−3.20689e6	+	2.89486e7i	−0.00451845	+	0.0407881i
$893$	1.27960e8			0.179688
$894$	−2.06522e7	+	3.73994e8i	−0.0289037	+	0.523423i
$895$		−	1.11870e9i		−	1.56043i
$896$	2.59595e8	−	6.38510e8i	0.360887	−	0.887654i
$897$	−1.93287e9			−2.67810
$898$	−9.46666e7	−	5.22754e6i	−0.130728	−	0.00721885i
$899$		−	1.71815e9i		−	2.36474i
$900$	9.24150e7	+	1.02376e7i	0.126770	+	0.0140434i
$901$	−4.65211e8			−0.636027
$902$	3.21662e7	−	5.82505e8i	0.0438309	−	0.793743i
$903$			5.18027e8i			0.703541i
$904$	1.22969e8	+	2.05384e7i	0.166452	+	0.0278010i
$905$	−1.36132e8			−0.183661
$906$	−1.09769e9	−	6.06147e7i	−1.47602	−	0.0815067i
$907$			3.70230e8i			0.496192i	0.968735	+	0.248096i	$0.0798048\pi$
$907$			3.70230e8i			0.496192i	−0.968735	+	0.248096i	$0.920195\pi$
$908$	−1.07461e8	+	9.70048e8i	−0.143546	+	1.29579i
$909$	−6.55982e8			−0.873375
$910$	−4.58706e7	+	8.30682e8i	−0.0608710	+	1.10233i
$911$			2.23211e8i			0.295230i	0.989045	+	0.147615i	$0.0471597\pi$
$911$			2.23211e8i			0.295230i	−0.989045	+	0.147615i	$0.952840\pi$
$912$	2.18145e8	+	4.89321e7i	0.287581	+	0.0645073i
$913$	1.46889e8			0.193009
$914$	1.37058e9	+	7.56840e7i	1.79500	+	0.0991209i
$915$		−	5.46104e8i		−	0.712872i
$916$	5.69700e8	+	6.31107e7i	0.741242	+	0.0821139i
$917$	5.53922e8			0.718357
$918$	2.70539e7	−	4.89924e8i	0.0349704	−	0.633288i
$919$		−	4.28094e8i		−	0.551560i	−0.961221	−	0.275780i	$-0.911064\pi$
$919$		−	4.28094e8i		−	0.551560i	0.961221	−	0.275780i	$-0.0889362\pi$
$920$	1.86587e8	−	1.11715e9i	0.239618	−	1.43466i
$921$	1.78831e6			0.00228909
$922$	−5.00322e6	−	276280.i	−0.00638347	−	0.000352498i
$923$			2.29646e8i			0.292047i
$924$	−1.00463e8	+	9.06881e8i	−0.127348	+	1.14957i
$925$	−7.42266e7			−0.0937853
$926$	−1.19178e7	+	2.15823e8i	−0.0150094	+	0.271809i
$927$		−	1.03430e9i		−	1.29839i
$928$	1.31697e9	+	3.72749e8i	1.64790	+	0.466415i
$929$	3.74337e8			0.466891			0.233445	−	0.972370i	$-0.425000\pi$
$929$	3.74337e8			0.466891			0.233445	+	0.972370i	$0.425000\pi$
$930$	−1.27733e9	−	7.05350e7i	−1.58802	−	0.0876912i
$931$			1.51491e7i			0.0187731i
$932$	4.98932e8	+	5.52711e7i	0.616302	+	0.0682732i
$933$	−1.74850e9			−2.15289
$934$	−5.27123e7	+	9.54578e8i	−0.0646951	+	1.17158i
$935$		−	9.72464e8i		−	1.18970i
$936$	−6.76008e8	−	1.12907e8i	−0.824373	−	0.137688i
$937$	1.23459e9			1.50073			0.750366	−	0.661023i	$-0.229877\pi$
$937$	1.23459e9			1.50073			0.750366	+	0.661023i	$0.229877\pi$
$938$	1.63993e8	+	9.05576e6i	0.198708	+	0.0109728i
$939$		−	7.66839e8i		−	0.926206i
$940$	6.42228e7	−	5.79740e8i	0.0773225	−	0.697990i
$941$	7.29026e8			0.874932			0.437466	−	0.899235i	$-0.355876\pi$
$941$	7.29026e8			0.874932			0.437466	+	0.899235i	$0.355876\pi$
$942$	−5.82387e7	+	1.05466e9i	−0.0696721	+	1.26171i
$943$			1.15099e9i			1.37258i
$944$	2.61197e8	−	1.16445e9i	0.310494	−	1.38422i
$945$	3.25618e8			0.385845
$946$	4.53909e8	+	2.50651e7i	0.536161	+	0.0296071i
$947$		−	8.15727e8i		−	0.960494i	−0.877133	−	0.480247i	$-0.840547\pi$
$947$		−	8.15727e8i		−	0.960494i	0.877133	−	0.480247i	$-0.159453\pi$
$948$	8.14715e8	+	9.02532e7i	0.956271	+	0.105934i
$949$	1.48514e9			1.73768
$950$	−2.12670e6	+	3.85129e7i	−0.00248048	+	0.0449196i
$951$		−	1.24700e9i		−	1.44986i
$952$	−1.92345e8	+	1.15162e9i	−0.222931	+	1.33475i
$953$	−8.77645e8			−1.01401			−0.507003	−	0.861944i	$-0.669247\pi$
$953$	−8.77645e8			−1.01401			−0.507003	+	0.861944i	$0.669247\pi$
$954$	2.53944e8	+	1.40229e7i	0.292478	+	0.0161508i
$955$			1.14421e9i			1.31370i
$956$	−8.63007e7	+	7.79036e8i	−0.0987735	+	0.891629i
$957$	−1.81185e9			−2.06722
$958$	−2.10093e7	+	3.80463e8i	−0.0238955	+	0.432729i
$959$		−	3.99215e8i		−	0.452638i
$960$	3.31179e8	−	9.63774e8i	0.374326	−	1.08934i
$961$	−8.04526e8			−0.906504
$962$	5.46303e8	+	3.01671e7i	0.613633	+	0.0338851i
$963$			1.58806e8i			0.177823i
$964$	−2.20135e8	−	2.43863e7i	−0.245730	−	0.0272216i
$965$	8.72719e8			0.971164
$966$	9.92543e7	−	1.79742e9i	0.110108	−	1.99397i
$967$			4.37721e8i			0.484081i	0.970266	+	0.242040i	$0.0778167\pi$
$967$			4.37721e8i			0.484081i	−0.970266	+	0.242040i	$0.922183\pi$
$968$	−1.04874e8	−	1.75162e7i	−0.115623	−	0.0193114i
$969$	−3.78707e8			−0.416228
$970$	9.30238e8	+	5.13682e7i	1.01925	+	0.0562832i
$971$		−	9.69728e8i		−	1.05923i	−0.848237	−	0.529617i	$-0.822336\pi$
$971$		−	9.69728e8i		−	1.05923i	0.848237	−	0.529617i	$-0.177664\pi$
$972$	−1.14023e8	+	1.02929e9i	−0.124164	+	1.12083i
$973$	−7.58925e8			−0.823873
$974$	−2.29823e7	+	4.16192e8i	−0.0248724	+	0.450419i
$975$		−	3.00049e8i		−	0.323727i
$976$	5.61440e8	+	1.25937e8i	0.603885	+	0.135458i
$977$	−5.88511e8			−0.631060			−0.315530	−	0.948916i	$-0.602182\pi$
$977$	−5.88511e8			−0.631060			−0.315530	+	0.948916i	$0.602182\pi$
$978$	−9.72525e6	−	537033.i	−0.0103964	−	0.000574096i
$979$		−	9.48905e7i		−	0.101129i
$980$	6.86349e7	+	7.60329e6i	0.0729234	+	0.00807836i
$981$	−3.26621e8			−0.345969
$982$	4.73987e7	−	8.58353e8i	0.0500532	−	0.906424i
$983$		−	2.95890e8i		−	0.311508i	−0.987796	−	0.155754i	$-0.950219\pi$
$983$		−	2.95890e8i		−	0.311508i	0.987796	−	0.155754i	$-0.0497807\pi$
$984$	−1.70606e8	+	1.02146e9i	−0.179064	+	1.07211i
$985$	−1.05264e9			−1.10146
$986$	−2.31497e9	−	1.27834e8i	−2.41499	−	0.133357i
$987$		−	9.27056e8i		−	0.964172i
$988$	3.13048e7	−	2.82588e8i	0.0324593	−	0.293011i
$989$	−8.96894e8			−0.927155
$990$	−2.93131e7	+	5.30837e8i	−0.0302103	+	0.547086i
$991$		−	1.54599e9i		−	1.58849i	−0.607596	−	0.794246i	$-0.707866\pi$
$991$		−	1.54599e9i		−	1.58849i	0.607596	−	0.794246i	$-0.292134\pi$
$992$	3.67081e8	−	1.29694e9i	0.376034	−	1.32857i
$993$	2.08380e9			2.12818
$994$	−2.13552e8	−	1.17924e7i	−0.217443	−	0.0120073i
$995$		−	7.93412e7i		−	0.0805434i
$996$	−2.59165e8	−	2.87100e7i	−0.262300	−	0.0290573i
$997$	1.43106e9			1.44402			0.722010	−	0.691882i	$-0.243218\pi$
$997$	1.43106e9			1.44402			0.722010	+	0.691882i	$0.243218\pi$
$998$	−1.21419e7	+	2.19881e8i	−0.0122151	+	0.221205i
$999$		−	2.14145e8i		−	0.214789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.1	✓	54
4.3	odd	2	inner	76.7.b.a.39.2	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.1	✓	54	1.1	even	1	trivial
76.7.b.a.39.2	yes	54	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.98783 - 0.441092i) q^{2} -34.6865i q^{3} +(63.6109 + 7.04673i) q^{4} +112.076 q^{5} +(-15.2999 + 277.070i) q^{6} +328.667i q^{7} +(-505.005 - 84.3464i) q^{8} -474.152 q^{9} +O(q^{10})\)	\(q+(-7.98783 - 0.441092i) q^{2} -34.6865i q^{3} +(63.6109 + 7.04673i) q^{4} +112.076 q^{5} +(-15.2999 + 277.070i) q^{6} +328.667i q^{7} +(-505.005 - 84.3464i) q^{8} -474.152 q^{9} +(-895.242 - 49.4357i) q^{10} +1250.56i q^{11} +(244.426 - 2206.44i) q^{12} -2823.18 q^{13} +(144.972 - 2625.33i) q^{14} -3887.51i q^{15} +(3996.69 + 896.498i) q^{16} -6938.39 q^{17} +(3787.44 + 209.145i) q^{18} +1573.56i q^{19} +(7129.23 + 789.768i) q^{20} +11400.3 q^{21} +(551.610 - 9989.23i) q^{22} +19738.1i q^{23} +(-2925.68 + 17516.8i) q^{24} -3064.03 q^{25} +(22551.1 + 1245.28i) q^{26} -8839.78i q^{27} +(-2316.03 + 20906.8i) q^{28} -41769.4 q^{29} +(-1714.75 + 31052.8i) q^{30} +41134.3i q^{31} +(-31529.4 - 8923.98i) q^{32} +43377.4 q^{33} +(55422.7 + 3060.47i) q^{34} +36835.5i q^{35} +(-30161.2 - 3341.22i) q^{36} +24225.1 q^{37} +(694.086 - 12569.4i) q^{38} +97926.2i q^{39} +(-56598.8 - 9453.18i) q^{40} +58313.3 q^{41} +(-91063.6 - 5028.57i) q^{42} +45439.8i q^{43} +(-8812.34 + 79549.0i) q^{44} -53140.9 q^{45} +(8706.30 - 157664. i) q^{46} -81318.7i q^{47} +(31096.4 - 138631. i) q^{48} +9627.25 q^{49} +(24475.0 + 1351.52i) q^{50} +240668. i q^{51} +(-179585. - 19894.2i) q^{52} +67048.8 q^{53} +(-3899.16 + 70610.7i) q^{54} +140157. i q^{55} +(27721.8 - 165978. i) q^{56} +54581.3 q^{57} +(333647. + 18424.1i) q^{58} -291353. i q^{59} +(27394.3 - 247288. i) q^{60} +140476. q^{61} +(18144.0 - 328574. i) q^{62} -155838. i q^{63} +(247915. + 85190.6i) q^{64} -316410. q^{65} +(-346491. - 19133.4i) q^{66} +62465.5i q^{67} +(-441357. - 48893.0i) q^{68} +684644. q^{69} +(16247.9 - 294236. i) q^{70} -81342.8i q^{71} +(239449. + 39993.0i) q^{72} -526053. q^{73} +(-193506. - 10685.5i) q^{74} +106281. i q^{75} +(-11088.5 + 100096. i) q^{76} -411016. q^{77} +(43194.4 - 782218. i) q^{78} +369245. i q^{79} +(447932. + 100476. i) q^{80} -652278. q^{81} +(-465796. - 25721.5i) q^{82} -117459. i q^{83} +(725182. + 80334.8i) q^{84} -777625. q^{85} +(20043.1 - 362966. i) q^{86} +1.44883e6i q^{87} +(105480. - 631537. i) q^{88} -75878.6 q^{89} +(424481. + 23440.0i) q^{90} -927885. i q^{91} +(-139089. + 1.25556e6i) q^{92} +1.42680e6 q^{93} +(-35869.0 + 649560. i) q^{94} +176358. i q^{95} +(-309541. + 1.09364e6i) q^{96} -1.03909e6 q^{97} +(-76900.8 - 4246.50i) q^{98} -592954. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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