LMFDB - Embedded newform 12.7.d.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,7,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, 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("12.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	12.d (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:	$2.76064900344$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.50898483.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} - 10x^{3} + 64x^{2} - 40x + 25 $ x^6 + 8x^4 - 10x^3 + 64x^2 - 40x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.2
Root			$-1.55022 + 2.68505i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.7.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.12493 + 3.63805i) q^{2} -15.5885i q^{3} +(37.5291 - 51.8417i) q^{4} +172.232 q^{5} +(56.7117 + 111.067i) q^{6} -545.623i q^{7} +(-78.7890 + 505.901i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(-7.12493 + 3.63805i) q^{2} -15.5885i q^{3} +(37.5291 - 51.8417i) q^{4} +172.232 q^{5} +(56.7117 + 111.067i) q^{6} -545.623i q^{7} +(-78.7890 + 505.901i) q^{8} -243.000 q^{9} +(-1227.14 + 626.588i) q^{10} +147.793i q^{11} +(-808.133 - 585.021i) q^{12} +1198.44 q^{13} +(1985.01 + 3887.52i) q^{14} -2684.83i q^{15} +(-1279.13 - 3891.15i) q^{16} +319.429 q^{17} +(1731.36 - 884.047i) q^{18} +5768.21i q^{19} +(6463.70 - 8928.79i) q^{20} -8505.42 q^{21} +(-537.679 - 1053.01i) q^{22} +8044.99i q^{23} +(7886.22 + 1228.20i) q^{24} +14038.8 q^{25} +(-8538.83 + 4360.01i) q^{26} +3788.00i q^{27} +(-28286.0 - 20476.7i) q^{28} -34198.9 q^{29} +(9767.55 + 19129.2i) q^{30} +19886.7i q^{31} +(23269.9 + 23070.6i) q^{32} +2303.86 q^{33} +(-2275.90 + 1162.10i) q^{34} -93973.5i q^{35} +(-9119.57 + 12597.5i) q^{36} +92346.8 q^{37} +(-20985.1 - 41098.1i) q^{38} -18681.9i q^{39} +(-13570.0 + 87132.3i) q^{40} +19729.1 q^{41} +(60600.5 - 30943.2i) q^{42} -10650.3i q^{43} +(7661.84 + 5546.54i) q^{44} -41852.3 q^{45} +(-29268.1 - 57320.0i) q^{46} +145079. i q^{47} +(-60657.0 + 19939.7i) q^{48} -180055. q^{49} +(-100025. + 51073.8i) q^{50} -4979.40i q^{51} +(44976.5 - 62129.4i) q^{52} +20665.9 q^{53} +(-13780.9 - 26989.2i) q^{54} +25454.6i q^{55} +(276031. + 42989.1i) q^{56} +89917.5 q^{57} +(243665. - 124418. i) q^{58} +148313. i q^{59} +(-139186. - 100759. i) q^{60} -97811.2 q^{61} +(-72348.8 - 141691. i) q^{62} +132586. i q^{63} +(-249729. - 79719.0i) q^{64} +206410. q^{65} +(-16414.9 + 8381.58i) q^{66} -478892. i q^{67} +(11987.9 - 16559.7i) q^{68} +125409. q^{69} +(341881. + 669554. i) q^{70} -137300. i q^{71} +(19145.7 - 122934. i) q^{72} -251405. q^{73} +(-657964. + 335963. i) q^{74} -218843. i q^{75} +(299034. + 216476. i) q^{76} +80639.2 q^{77} +(67965.8 + 133107. i) q^{78} +616099. i q^{79} +(-220307. - 670179. i) q^{80} +59049.0 q^{81} +(-140569. + 71775.7i) q^{82} -746788. i q^{83} +(-319201. + 440936. i) q^{84} +55015.7 q^{85} +(38746.3 + 75882.5i) q^{86} +533109. i q^{87} +(-74768.7 - 11644.5i) q^{88} -406308. q^{89} +(298195. - 152261. i) q^{90} -653899. i q^{91} +(417066. + 301922. i) q^{92} +310003. q^{93} +(-527806. - 1.03368e6i) q^{94} +993469. i q^{95} +(359635. - 362742. i) q^{96} +1.11574e6 q^{97} +(1.28288e6 - 655051. i) q^{98} -35913.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9}+O(q^{10}) $ 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9} + 84 q^{10} - 972 q^{12} - 3348 q^{13} + 4776 q^{14} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 17608 q^{20} - 9720 q^{21} - 13512 q^{22} - 7776 q^{24} + 56418 q^{25} - 59252 q^{26} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} + 61280 q^{32} + 4536 q^{33} + 109404 q^{34} - 37908 q^{36} + 20796 q^{37} - 128088 q^{38} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 445008 q^{44} + 10692 q^{45} + 81120 q^{46} - 276048 q^{48} - 111546 q^{49} - 743118 q^{50} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 793728 q^{56} - 204120 q^{57} + 529860 q^{58} - 723816 q^{60} + 12924 q^{61} - 513384 q^{62} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} + 690328 q^{68} + 541728 q^{69} + 938928 q^{70} - 276048 q^{72} - 1283412 q^{73} - 1522916 q^{74} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} + 1272352 q^{80} + 354294 q^{81} + 240444 q^{82} - 143856 q^{84} + 814920 q^{85} - 1154568 q^{86} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} - 1338816 q^{92} - 83592 q^{93} - 390288 q^{94} + 624672 q^{96} + 3249420 q^{97} + 1604918 q^{98}+O(q^{100}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−7.12493	+	3.63805i	−0.890616	+	0.454757i
$2$	−7.12493	+	3.63805i	−0.890616	+	0.454757i
$3$		−	15.5885i		−	0.577350i
$3$		−	15.5885i		−	0.577350i
$4$	37.5291	−	51.8417i	0.586392	−	0.810027i
$5$	172.232			1.37785			0.688927	−	0.724831i	$-0.258082\pi$
$5$	172.232			1.37785			0.688927	+	0.724831i	$0.258082\pi$
$6$	56.7117	+	111.067i	0.262554	+	0.514197i
$7$		−	545.623i		−	1.59074i	−0.606126	−	0.795369i	$-0.707277\pi$
$7$		−	545.623i		−	1.59074i	0.606126	−	0.795369i	$-0.292723\pi$
$8$	−78.7890	+	505.901i	−0.153885	+	0.988089i
$9$	−243.000			−0.333333
$10$	−1227.14	+	626.588i	−1.22714	+	0.626588i
$11$			147.793i			0.111039i	0.998458	+	0.0555195i	$0.0176815\pi$
$11$			147.793i			0.111039i	−0.998458	+	0.0555195i	$0.982318\pi$
$12$	−808.133	−	585.021i	−0.467669	−	0.338554i
$13$	1198.44			0.545491			0.272746	−	0.962086i	$-0.412068\pi$
$13$	1198.44			0.545491			0.272746	+	0.962086i	$0.412068\pi$
$14$	1985.01	+	3887.52i	0.723399	+	1.41674i
$15$		−	2684.83i		−	0.795504i
$16$	−1279.13	−	3891.15i	−0.312288	−	0.949987i
$17$	319.429			0.0650170			0.0325085	−	0.999471i	$-0.489650\pi$
$17$	319.429			0.0650170			0.0325085	+	0.999471i	$0.489650\pi$
$18$	1731.36	−	884.047i	0.296872	−	0.151586i
$19$			5768.21i			0.840970i	0.907300	+	0.420485i	$0.138140\pi$
$19$			5768.21i			0.840970i	−0.907300	+	0.420485i	$0.861860\pi$
$20$	6463.70	−	8928.79i	0.807963	−	1.11610i
$21$	−8505.42			−0.918412
$22$	−537.679	−	1053.01i	−0.0504958	−	0.0988931i
$23$			8044.99i			0.661214i	0.943768	+	0.330607i	$0.107254\pi$
$23$			8044.99i			0.661214i	−0.943768	+	0.330607i	$0.892746\pi$
$24$	7886.22	+	1228.20i	0.570473	+	0.0888454i
$25$	14038.8			0.898481
$26$	−8538.83	+	4360.01i	−0.485823	+	0.248066i
$27$			3788.00i			0.192450i
$28$	−28286.0	−	20476.7i	−1.28854	−	0.932796i
$29$	−34198.9			−1.40223			−0.701114	−	0.713049i	$-0.747314\pi$
$29$	−34198.9			−1.40223			−0.701114	+	0.713049i	$0.747314\pi$
$30$	9767.55	+	19129.2i	0.361761	+	0.708488i
$31$			19886.7i			0.667540i	0.942655	+	0.333770i	$0.108321\pi$
$31$			19886.7i			0.667540i	−0.942655	+	0.333770i	$0.891679\pi$
$32$	23269.9	+	23070.6i	0.710142	+	0.704059i
$33$	2303.86			0.0641084
$34$	−2275.90	+	1162.10i	−0.0579052	+	0.0295669i
$35$		−	93973.5i		−	2.19180i
$36$	−9119.57	+	12597.5i	−0.195464	+	0.270009i
$37$	92346.8			1.82313			0.911563	−	0.411161i	$-0.134877\pi$
$37$	92346.8			1.82313			0.911563	+	0.411161i	$0.134877\pi$
$38$	−20985.1	−	41098.1i	−0.382437	−	0.748981i
$39$		−	18681.9i		−	0.314940i
$40$	−13570.0	+	87132.3i	−0.212031	+	1.36144i
$41$	19729.1			0.286257			0.143129	−	0.989704i	$-0.454284\pi$
$41$	19729.1			0.286257			0.143129	+	0.989704i	$0.454284\pi$
$42$	60600.5	−	30943.2i	0.817953	−	0.417654i
$43$		−	10650.3i		−	0.133954i	−0.997755	−	0.0669770i	$-0.978665\pi$
$43$		−	10650.3i		−	0.133954i	0.997755	−	0.0669770i	$-0.0213354\pi$
$44$	7661.84	+	5546.54i	0.0899446	+	0.0651124i
$45$	−41852.3			−0.459285
$46$	−29268.1	−	57320.0i	−0.300692	−	0.588888i
$47$			145079.i			1.39737i	0.715429	+	0.698686i	$0.246231\pi$
$47$			145079.i			1.39737i	−0.715429	+	0.698686i	$0.753769\pi$
$48$	−60657.0	+	19939.7i	−0.548476	+	0.180300i
$49$	−180055.			−1.53044
$50$	−100025.	+	51073.8i	−0.800201	+	0.408590i
$51$		−	4979.40i		−	0.0375376i
$52$	44976.5	−	62129.4i	0.319872	−	0.441863i
$53$	20665.9			0.138812			0.0694059	−	0.997589i	$-0.477890\pi$
$53$	20665.9			0.138812			0.0694059	+	0.997589i	$0.477890\pi$
$54$	−13780.9	−	26989.2i	−0.0875180	−	0.171399i
$55$			25454.6i			0.152996i
$56$	276031.	+	42989.1i	1.57179	+	0.244790i
$57$	89917.5			0.485534
$58$	243665.	−	124418.i	1.24885	−	0.637673i
$59$			148313.i			0.722142i	0.932538	+	0.361071i	$0.117589\pi$
$59$			148313.i			0.722142i	−0.932538	+	0.361071i	$0.882411\pi$
$60$	−139186.	−	100759.i	−0.644380	−	0.466478i
$61$	−97811.2			−0.430922			−0.215461	−	0.976512i	$-0.569125\pi$
$61$	−97811.2			−0.430922			−0.215461	+	0.976512i	$0.569125\pi$
$62$	−72348.8	−	141691.i	−0.303568	−	0.594521i
$63$			132586.i			0.530246i
$64$	−249729.	−	79719.0i	−0.952639	−	0.304104i
$65$	206410.			0.751607
$66$	−16414.9	+	8381.58i	−0.0570960	+	0.0291537i
$67$		−	478892.i		−	1.59226i	−0.605127	−	0.796129i	$-0.706878\pi$
$67$		−	478892.i		−	1.59226i	0.605127	−	0.796129i	$-0.293122\pi$
$68$	11987.9	−	16559.7i	0.0381255	−	0.0526655i
$69$	125409.			0.381752
$70$	341881.	+	669554.i	0.996737	+	1.95205i
$71$		−	137300.i		−	0.383615i	−0.981433	−	0.191807i	$-0.938565\pi$
$71$		−	137300.i		−	0.383615i	0.981433	−	0.191807i	$-0.0614349\pi$
$72$	19145.7	−	122934.i	0.0512949	−	0.329363i
$73$	−251405.			−0.646258			−0.323129	−	0.946355i	$-0.604735\pi$
$73$	−251405.			−0.646258			−0.323129	+	0.946355i	$0.604735\pi$
$74$	−657964.	+	335963.i	−1.62370	+	0.829079i
$75$		−	218843.i		−	0.518738i
$76$	299034.	+	216476.i	0.681208	+	0.493138i
$77$	80639.2			0.176634
$78$	67965.8	+	133107.i	0.143221	+	0.280490i
$79$			616099.i			1.24959i	0.780787	+	0.624797i	$0.214818\pi$
$79$			616099.i			1.24959i	−0.780787	+	0.624797i	$0.785182\pi$
$80$	−220307.	−	670179.i	−0.430287	−	1.30894i
$81$	59049.0			0.111111
$82$	−140569.	+	71775.7i	−0.254945	+	0.130177i
$83$		−	746788.i		−	1.30606i	−0.757333	−	0.653029i	$-0.773498\pi$
$83$		−	746788.i		−	1.30606i	0.757333	−	0.653029i	$-0.226502\pi$
$84$	−319201.	+	440936.i	−0.538550	+	0.743939i
$85$	55015.7			0.0895839
$86$	38746.3	+	75882.5i	0.0609165	+	0.119302i
$87$			533109.i			0.809577i
$88$	−74768.7	−	11644.5i	−0.109716	−	0.0170872i
$89$	−406308.			−0.576348			−0.288174	−	0.957578i	$-0.593048\pi$
$89$	−406308.			−0.576348			−0.288174	+	0.957578i	$0.593048\pi$
$90$	298195.	−	152261.i	0.409046	−	0.208863i
$91$		−	653899.i		−	0.867733i
$92$	417066.	+	301922.i	0.535602	+	0.387731i
$93$	310003.			0.385404
$94$	−527806.	−	1.03368e6i	−0.635464	−	1.24452i
$95$			993469.i			1.15873i
$96$	359635.	−	362742.i	0.406488	−	0.410001i
$97$	1.11574e6			1.22250			0.611250	−	0.791438i	$-0.290667\pi$
$97$	1.11574e6			1.22250			0.611250	+	0.791438i	$0.290667\pi$
$98$	1.28288e6	−	655051.i	1.36304	−	0.695980i
$99$		−	35913.7i		−	0.0370130i
$100$	526862.	−	727794.i	0.526862	−	0.727794i
$101$	−853307.			−0.828211			−0.414106	−	0.910229i	$-0.635906\pi$
$101$	−853307.			−0.828211			−0.414106	+	0.910229i	$0.635906\pi$
$102$	18115.3	+	35477.8i	0.0170705	+	0.0334316i
$103$			1.08151e6i			0.989738i	0.868968	+	0.494869i	$0.164784\pi$
$103$			1.08151e6i			0.989738i	−0.868968	+	0.494869i	$0.835216\pi$
$104$	−94424.3	+	606295.i	−0.0839428	+	0.538994i
$105$	−1.46490e6			−1.26544
$106$	−147243.	+	75183.6i	−0.123628	+	0.0631256i
$107$			219304.i			0.179017i	0.995986	+	0.0895087i	$0.0285297\pi$
$107$			219304.i			0.179017i	−0.995986	+	0.0895087i	$0.971470\pi$
$108$	196376.	+	142160.i	0.155890	+	0.112851i
$109$	−913974.			−0.705756			−0.352878	−	0.935669i	$-0.614797\pi$
$109$	−913974.			−0.705756			−0.352878	+	0.935669i	$0.614797\pi$
$110$	−92605.3	−	181362.i	−0.0695758	−	0.136260i
$111$		−	1.43954e6i		−	1.05258i
$112$	−2.12310e6	+	697923.i	−1.51118	+	0.496768i
$113$	1.37579e6			0.953490			0.476745	−	0.879042i	$-0.341816\pi$
$113$	1.37579e6			0.953490			0.476745	+	0.879042i	$0.341816\pi$
$114$	−640656.	+	327125.i	−0.432424	+	0.220800i
$115$			1.38560e6i			0.911057i
$116$	−1.28346e6	+	1.77293e6i	−0.822256	+	1.13584i
$117$	−291222.			−0.181830
$118$	−539570.	−	1.05672e6i	−0.328399	−	0.643151i
$119$		−	174288.i		−	0.103425i
$120$	1.35826e6	+	211535.i	0.786029	+	0.122416i
$121$	1.74972e6			0.987670
$122$	696898.	−	355843.i	0.383786	−	0.195965i
$123$		−	307547.i		−	0.165271i
$124$	1.03096e6	+	746329.i	0.540725	+	0.391440i
$125$	−273201.			−0.139879
$126$	−482356.	−	944668.i	−0.241133	−	0.472245i
$127$		−	3.46516e6i		−	1.69166i	−0.533456	−	0.845828i	$-0.679107\pi$
$127$		−	3.46516e6i		−	1.69166i	0.533456	−	0.845828i	$-0.320893\pi$
$128$	2.06932e6	−	340535.i	0.986728	−	0.162380i
$129$	−166022.			−0.0773384
$130$	−1.47066e6	+	750931.i	−0.669393	+	0.341798i
$131$		−	2.11232e6i		−	0.939608i	−0.882771	−	0.469804i	$-0.844325\pi$
$131$		−	2.11232e6i		−	0.939608i	0.882771	−	0.469804i	$-0.155675\pi$
$132$	86462.0	−	119436.i	0.0375927	−	0.0519296i
$133$	3.14727e6			1.33776
$134$	1.74224e6	+	3.41207e6i	0.724090	+	1.41809i
$135$			652413.i			0.265168i
$136$	−25167.5	+	161599.i	−0.0100051	+	0.0642426i
$137$	−1.39131e6			−0.541081			−0.270541	−	0.962709i	$-0.587202\pi$
$137$	−1.39131e6			−0.541081			−0.270541	+	0.962709i	$0.587202\pi$
$138$	−893530.	+	456245.i	−0.339995	+	0.173604i
$139$			647825.i			0.241220i	0.992700	+	0.120610i	$0.0384850\pi$
$139$			647825.i			0.241220i	−0.992700	+	0.120610i	$0.961515\pi$
$140$	−4.87175e6	−	3.52674e6i	−1.77542	−	1.28526i
$141$	2.26156e6			0.806773
$142$	499505.	+	978252.i	0.174452	+	0.341653i
$143$			177122.i			0.0605708i
$144$	310829.	+	945549.i	0.104096	+	0.316662i
$145$	−5.89014e6			−1.93207
$146$	1.79124e6	−	914626.i	0.575567	−	0.293890i
$147$			2.80678e6i			0.883603i
$148$	3.46569e6	−	4.78742e6i	1.06907	−	1.47678i
$149$	−617756.			−0.186749			−0.0933744	−	0.995631i	$-0.529765\pi$
$149$	−617756.			−0.186749			−0.0933744	+	0.995631i	$0.529765\pi$
$150$	796161.	+	1.55924e6i	0.235900	+	0.461996i
$151$			3.16384e6i			0.918931i	0.888196	+	0.459466i	$0.151959\pi$
$151$			3.16384e6i			0.918931i	−0.888196	+	0.459466i	$0.848041\pi$
$152$	−2.91815e6	−	454472.i	−0.830953	−	0.129412i
$153$	−77621.2			−0.0216723
$154$	−574548.	+	293370.i	−0.157313	+	0.0803255i
$155$			3.42512e6i			0.919772i
$156$	−968502.	−	701115.i	−0.255110	−	0.184678i
$157$	−2.09075e6			−0.540261			−0.270131	−	0.962824i	$-0.587067\pi$
$157$	−2.09075e6			−0.540261			−0.270131	+	0.962824i	$0.587067\pi$
$158$	−2.24140e6	−	4.38966e6i	−0.568261	−	1.11291i
$159$		−	322149.i		−	0.0801430i
$160$	4.00782e6	+	3.97349e6i	0.978472	+	0.970090i
$161$	4.38953e6			1.05182
$162$	−420720.	+	214824.i	−0.0989573	+	0.0505285i
$163$			449351.i			0.103758i	0.998653	+	0.0518792i	$0.0165211\pi$
$163$			449351.i			0.103758i	−0.998653	+	0.0518792i	$0.983479\pi$
$164$	740417.	−	1.02279e6i	0.167859	−	0.231876i
$165$	396798.			0.0883320
$166$	2.71685e6	+	5.32081e6i	0.593939	+	1.16320i
$167$		−	1.79059e6i		−	0.384456i	−0.981350	−	0.192228i	$-0.938429\pi$
$167$		−	1.79059e6i		−	0.384456i	0.981350	−	0.192228i	$-0.0615713\pi$
$168$	670134.	−	4.30290e6i	0.141330	−	0.907473i
$169$	−3.39054e6			−0.702439
$170$	−391983.	+	200150.i	−0.0797849	+	0.0407389i
$171$		−	1.40168e6i		−	0.280323i
$172$	−552129.	−	399696.i	−0.108506	−	0.0785496i
$173$	−6.06946e6			−1.17223			−0.586114	−	0.810229i	$-0.699343\pi$
$173$	−6.06946e6			−1.17223			−0.586114	+	0.810229i	$0.699343\pi$
$174$	−1.93948e6	−	3.79836e6i	−0.368161	−	0.721022i
$175$		−	7.65987e6i		−	1.42925i
$176$	575084.	−	189047.i	0.105486	−	0.0346761i
$177$	2.31197e6			0.416929
$178$	2.89491e6	−	1.47817e6i	0.513305	−	0.262098i
$179$			4.05372e6i			0.706797i	0.935473	+	0.353398i	$0.114974\pi$
$179$			4.05372e6i			0.706797i	−0.935473	+	0.353398i	$0.885026\pi$
$180$	−1.57068e6	+	2.16970e6i	−0.269321	+	0.372033i
$181$	6.32630e6			1.06688			0.533438	−	0.845839i	$-0.320900\pi$
$181$	6.32630e6			1.06688			0.533438	+	0.845839i	$0.320900\pi$
$182$	2.37892e6	+	4.65898e6i	0.394608	+	0.772817i
$183$			1.52473e6i			0.248793i
$184$	−4.06997e6	−	633857.i	−0.653338	−	0.101751i
$185$	1.59050e7			2.51200
$186$	−2.20874e6	+	1.12781e6i	−0.343247	+	0.175265i
$187$			47209.3i			0.00721943i
$188$	7.52116e6	+	5.44470e6i	1.13191	+	0.819408i
$189$	2.06682e6			0.306137
$190$	−3.61429e6	−	7.07839e6i	−0.526942	−	1.03199i
$191$		−	1.15014e7i		−	1.65063i	−0.564674	−	0.825314i	$-0.690998\pi$
$191$		−	1.15014e7i		−	1.65063i	0.564674	−	0.825314i	$-0.309002\pi$
$192$	−1.24270e6	+	3.89288e6i	−0.175574	+	0.550006i
$193$	−8.78066e6			−1.22139			−0.610696	−	0.791865i	$-0.709110\pi$
$193$	−8.78066e6			−1.22139			−0.610696	+	0.791865i	$0.709110\pi$
$194$	−7.94958e6	+	4.05913e6i	−1.08878	+	0.555940i
$195$		−	3.21761e6i		−	0.433941i
$196$	−6.75731e6	+	9.33438e6i	−0.897441	+	1.23970i
$197$	−9.77747e6			−1.27887			−0.639437	−	0.768843i	$-0.720833\pi$
$197$	−9.77747e6			−1.27887			−0.639437	+	0.768843i	$0.720833\pi$
$198$	130656.	+	255882.i	0.0168319	+	0.0329644i
$199$		−	3.78391e6i		−	0.480156i	−0.970754	−	0.240078i	$-0.922827\pi$
$199$		−	3.78391e6i		−	0.480156i	0.970754	−	0.240078i	$-0.0771730\pi$
$200$	−1.10610e6	+	7.10223e6i	−0.138263	+	0.887779i
$201$	−7.46519e6			−0.919291
$202$	6.07975e6	−	3.10438e6i	0.737618	−	0.376635i
$203$			1.86597e7i			2.23058i
$204$	−258141.	−	186872.i	−0.0304065	−	0.0220118i
$205$	3.39798e6			0.394421
$206$	−3.93461e6	−	7.70570e6i	−0.450090	−	0.881476i
$207$		−	1.95493e6i		−	0.220405i
$208$	−1.53297e6	−	4.66332e6i	−0.170350	−	0.518210i
$209$	−852501.			−0.0933805
$210$	1.04373e7	−	5.32940e6i	1.12702	−	0.575467i
$211$			2.78490e6i			0.296458i	0.988953	+	0.148229i	$0.0473572\pi$
$211$			2.78490e6i			0.296458i	−0.988953	+	0.148229i	$0.952643\pi$
$212$	775572.	−	1.07135e6i	0.0813982	−	0.112441i
$213$	−2.14030e6			−0.221480
$214$	−797840.	−	1.56253e6i	−0.0814094	−	0.159436i
$215$		−	1.83432e6i		−	0.184569i
$216$	−1.91635e6	−	298452.i	−0.190158	−	0.0296151i
$217$	1.08506e7			1.06188
$218$	6.51200e6	−	3.32509e6i	0.628557	−	0.320947i
$219$			3.91902e6i			0.373117i
$220$	1.31961e6	+	955290.i	0.123931	+	0.0897154i
$221$	382817.			0.0354662
$222$	5.23714e6	+	1.02566e7i	0.478669	+	0.937446i
$223$			9.97883e6i			0.899839i	0.893069	+	0.449920i	$0.148547\pi$
$223$			9.97883e6i			0.899839i	−0.893069	+	0.449920i	$0.851453\pi$
$224$	1.25878e7	−	1.26966e7i	1.11997	−	1.12965i
$225$	−3.41142e6			−0.299494
$226$	−9.80239e6	+	5.00519e6i	−0.849193	+	0.433606i
$227$		−	2.19292e7i		−	1.87476i	−0.348313	−	0.937378i	$-0.613245\pi$
$227$		−	2.19292e7i		−	1.87476i	0.348313	−	0.937378i	$-0.386755\pi$
$228$	3.37452e6	−	4.66148e6i	0.284714	−	0.393296i
$229$	1.11307e7			0.926865			0.463432	−	0.886132i	$-0.346618\pi$
$229$	1.11307e7			0.926865			0.463432	+	0.886132i	$0.346618\pi$
$230$	−5.04090e6	−	9.87232e6i	−0.414309	−	0.811401i
$231$		−	1.25704e6i		−	0.101980i
$232$	2.69450e6	−	1.73013e7i	0.215782	−	1.38553i
$233$	−1.19630e7			−0.945744			−0.472872	−	0.881131i	$-0.656783\pi$
$233$	−1.19630e7			−0.945744			−0.472872	+	0.881131i	$0.656783\pi$
$234$	2.07493e6	−	1.05948e6i	0.161941	−	0.0826886i
$235$			2.49872e7i			1.92537i
$236$	7.68879e6	+	5.56604e6i	0.584954	+	0.423458i
$237$	9.60403e6			0.721453
$238$	634068.	+	1.24179e6i	0.0470332	+	0.0921119i
$239$			7.26061e6i			0.531838i	0.963995	+	0.265919i	$0.0856754\pi$
$239$			7.26061e6i			0.531838i	−0.963995	+	0.265919i	$0.914325\pi$
$240$	−1.04471e7	+	3.43425e6i	−0.755719	+	0.248426i
$241$	649330.			0.0463889			0.0231945	−	0.999731i	$-0.492616\pi$
$241$	649330.			0.0463889			0.0231945	+	0.999731i	$0.492616\pi$
$242$	−1.24666e7	+	6.36557e6i	−0.879635	+	0.449150i
$243$		−	920483.i		−	0.0641500i
$244$	−3.67077e6	+	5.07070e6i	−0.252690	+	0.349059i
$245$	−3.10112e7			−2.10873
$246$	1.11887e6	+	2.19125e6i	0.0751580	+	0.147193i
$247$			6.91288e6i			0.458742i
$248$	−1.00607e7	−	1.56685e6i	−0.659588	−	0.102724i
$249$	−1.16413e7			−0.754053
$250$	1.94654e6	−	993920.i	0.124578	−	0.0636109i
$251$		−	2.13158e7i		−	1.34797i	−0.738744	−	0.673986i	$-0.764581\pi$
$251$		−	2.13158e7i		−	1.34797i	0.738744	−	0.673986i	$-0.235419\pi$
$252$	6.87351e6	+	4.97585e6i	0.429513	+	0.310932i
$253$	−1.18899e6			−0.0734206
$254$	1.26064e7	+	2.46890e7i	0.769292	+	1.50661i
$255$		−	857610.i		−	0.0517213i
$256$	−1.35049e7	+	9.95458e6i	−0.804952	+	0.593339i
$257$	3.34616e7			1.97128			0.985638	−	0.168872i	$-0.0540126\pi$
$257$	3.34616e7			1.97128			0.985638	+	0.168872i	$0.0540126\pi$
$258$	1.18289e6	−	603995.i	0.0688788	−	0.0351702i
$259$		−	5.03865e7i		−	2.90011i
$260$	7.74639e6	−	1.07007e7i	0.440737	−	0.608822i
$261$	8.31034e6			0.467409
$262$	7.68475e6	+	1.50501e7i	0.427293	+	0.836829i
$263$			3.12778e7i			1.71937i	0.510825	+	0.859685i	$0.329340\pi$
$263$			3.12778e7i			1.71937i	−0.510825	+	0.859685i	$0.670660\pi$
$264$	−181519.	+	1.16553e6i	−0.00986531	+	0.0633448i
$265$	3.55932e6			0.191262
$266$	−2.24240e7	+	1.14499e7i	−1.19143	+	0.608356i
$267$			6.33371e6i			0.332755i
$268$	−2.48266e7	−	1.79724e7i	−1.28977	−	0.933688i
$269$	2.30534e7			1.18435			0.592174	−	0.805810i	$-0.298270\pi$
$269$	2.30534e7			1.18435			0.592174	+	0.805810i	$0.298270\pi$
$270$	−2.37351e6	−	4.64839e6i	−0.120587	−	0.236163i
$271$		−	1.74540e7i		−	0.876974i	−0.898738	−	0.438487i	$-0.855515\pi$
$271$		−	1.74540e7i		−	0.876974i	0.898738	−	0.438487i	$-0.144485\pi$
$272$	−408591.	−	1.24294e6i	−0.0203040	−	0.0617654i
$273$	−1.01933e7			−0.500986
$274$	9.91299e6	−	5.06167e6i	0.481896	−	0.246060i
$275$			2.07483e6i			0.0997664i
$276$	4.70649e6	−	6.50142e6i	0.223857	−	0.309230i
$277$	−1.60256e7			−0.754007			−0.377003	−	0.926212i	$-0.623046\pi$
$277$	−1.60256e7			−0.754007			−0.377003	+	0.926212i	$0.623046\pi$
$278$	−2.35682e6	−	4.61570e6i	−0.109696	−	0.214834i
$279$		−	4.83246e6i		−	0.222513i
$280$	4.75414e7	+	7.40408e6i	2.16570	+	0.337285i
$281$	4.55471e6			0.205278			0.102639	−	0.994719i	$-0.467271\pi$
$281$	4.55471e6			0.205278			0.102639	+	0.994719i	$0.467271\pi$
$282$	−1.61135e7	+	8.22769e6i	−0.718524	+	0.366885i
$283$			1.40790e7i			0.621171i	0.950545	+	0.310586i	$0.100525\pi$
$283$			1.40790e7i			0.621171i	−0.950545	+	0.310586i	$0.899475\pi$
$284$	−7.11787e6	−	5.15275e6i	−0.310739	−	0.224949i
$285$	1.54866e7			0.668995
$286$	−644378.	−	1.26198e6i	−0.0275450	−	0.0539453i
$287$		−	1.07647e7i		−	0.455360i
$288$	−5.65459e6	−	5.60615e6i	−0.236714	−	0.234686i
$289$	−2.40355e7			−0.995773
$290$	4.19668e7	−	2.14287e7i	1.72073	−	0.878620i
$291$		−	1.73927e7i		−	0.705810i
$292$	−9.43502e6	+	1.30333e7i	−0.378961	+	0.523486i
$293$	7.00361e6			0.278432			0.139216	−	0.990262i	$-0.455542\pi$
$293$	7.00361e6			0.278432			0.139216	+	0.990262i	$0.455542\pi$
$294$	−1.02112e7	−	1.99981e7i	−0.401824	−	0.786950i
$295$			2.55442e7i			0.995005i
$296$	−7.27591e6	+	4.67184e7i	−0.280551	+	1.80141i
$297$	−559839.			−0.0213695
$298$	4.40146e6	−	2.24743e6i	0.166321	−	0.0849253i
$299$			9.64148e6i			0.360687i
$300$	−1.13452e7	−	8.21297e6i	−0.420192	−	0.304184i
$301$	−5.81104e6			−0.213086
$302$	−1.15102e7	−	2.25421e7i	−0.417890	−	0.818415i
$303$			1.33017e7i			0.478168i
$304$	2.24450e7	−	7.37830e6i	0.798911	−	0.262625i
$305$	−1.68462e7			−0.593748
$306$	553045.	−	282390.i	0.0193017	−	0.00985565i
$307$			318209.i			0.0109976i	0.999985	+	0.00549879i	$0.00175033\pi$
$307$			318209.i			0.0109976i	−0.999985	+	0.00549879i	$0.998250\pi$
$308$	3.02632e6	−	4.18048e6i	0.103577	−	0.143078i
$309$	1.68591e7			0.571425
$310$	−1.24608e7	−	2.44037e7i	−0.418273	−	0.819163i
$311$			4.67977e7i			1.55576i	0.628412	+	0.777881i	$0.283705\pi$
$311$			4.67977e7i			1.55576i	−0.628412	+	0.777881i	$0.716295\pi$
$312$	9.45120e6	+	1.47193e6i	0.311188	+	0.0484644i
$313$	−3.64905e7			−1.19000			−0.595000	−	0.803726i	$-0.702848\pi$
$313$	−3.64905e7			−1.19000			−0.595000	+	0.803726i	$0.702848\pi$
$314$	1.48965e7	−	7.60627e6i	0.481165	−	0.245687i
$315$			2.28356e7i			0.730601i
$316$	3.19396e7	+	2.31216e7i	1.01220	+	0.732752i
$317$	−4.96927e7			−1.55996			−0.779982	−	0.625801i	$-0.784772\pi$
$317$	−4.96927e7			−1.55996			−0.779982	+	0.625801i	$0.784772\pi$
$318$	1.17200e6	+	2.29529e6i	0.0364456	+	0.0713766i
$319$		−	5.05436e6i		−	0.155702i
$320$	−4.30112e7	−	1.37301e7i	−1.31260	−	0.419010i
$321$	3.41861e6			0.103356
$322$	−3.12751e7	+	1.59694e7i	−0.936766	+	0.478322i
$323$			1.84253e6i			0.0546773i
$324$	2.21606e6	−	3.06120e6i	0.0651547	−	0.0900030i
$325$	1.68247e7			0.490113
$326$	−1.63476e6	−	3.20159e6i	−0.0471848	−	0.0924088i
$327$			1.42474e7i			0.407468i
$328$	−1.55444e6	+	9.98100e6i	−0.0440506	+	0.282848i
$329$	7.91585e7			2.22285
$330$	−2.82716e6	+	1.44357e6i	−0.0786699	+	0.0401696i
$331$		−	4.59328e7i		−	1.26660i	−0.773907	−	0.633299i	$-0.781700\pi$
$331$		−	4.59328e7i		−	1.26660i	0.773907	−	0.633299i	$-0.218300\pi$
$332$	−3.87148e7	−	2.80263e7i	−1.05794	−	0.765863i
$333$	−2.24403e7			−0.607709
$334$	6.51427e6	+	1.27578e7i	0.174834	+	0.342403i
$335$		−	8.24804e7i		−	2.19390i
$336$	1.08795e7	+	3.30958e7i	0.286809	+	0.872480i
$337$	2.96501e7			0.774706			0.387353	−	0.921931i	$-0.373389\pi$
$337$	2.96501e7			0.774706			0.387353	+	0.921931i	$0.373389\pi$
$338$	2.41573e7	−	1.23350e7i	0.625603	−	0.319439i
$339$		−	2.14464e7i		−	0.550498i
$340$	2.06469e6	−	2.85211e6i	0.0525313	−	0.0725654i
$341$	−2.93911e6			−0.0741229
$342$	5.09937e6	+	9.98683e6i	0.127479	+	0.249660i
$343$			3.40503e7i			0.843798i
$344$	5.38799e6	+	839126.i	0.132359	+	0.0206135i
$345$	2.15994e7			0.525999
$346$	4.32445e7	−	2.20810e7i	1.04400	−	0.533078i
$347$		−	3.19623e7i		−	0.764980i	−0.923960	−	0.382490i	$-0.875067\pi$
$347$		−	3.19623e7i		−	0.764980i	0.923960	−	0.382490i	$-0.124933\pi$
$348$	2.76373e7	+	2.00071e7i	0.655779	+	0.474730i
$349$	2.02402e7			0.476145			0.238073	−	0.971247i	$-0.423484\pi$
$349$	2.02402e7			0.476145			0.238073	+	0.971247i	$0.423484\pi$
$350$	2.78670e7	+	5.45760e7i	0.649960	+	1.27291i
$351$			4.53970e6i			0.104980i
$352$	−3.40967e6	+	3.43913e6i	−0.0781780	+	0.0788535i
$353$	−2.37115e7			−0.539058			−0.269529	−	0.962992i	$-0.586868\pi$
$353$	−2.37115e7			−0.539058			−0.269529	+	0.962992i	$0.586868\pi$
$354$	−1.64726e7	+	8.41106e6i	−0.371323	+	0.189601i
$355$		−	2.36474e7i		−	0.528565i
$356$	−1.52484e7	+	2.10637e7i	−0.337966	+	0.466858i
$357$	−2.71687e6			−0.0597124
$358$	−1.47477e7	−	2.88825e7i	−0.321421	−	0.629484i
$359$			3.50832e7i			0.758255i	0.925344	+	0.379128i	$0.123776\pi$
$359$			3.50832e7i			0.758255i	−0.925344	+	0.379128i	$0.876224\pi$
$360$	3.29750e6	−	2.11731e7i	0.0706769	−	0.453814i
$361$	1.37736e7			0.292770
$362$	−4.50744e7	+	2.30154e7i	−0.950177	+	0.485169i
$363$		−	2.72754e7i		−	0.570232i
$364$	−3.38992e7	−	2.45402e7i	−0.702887	−	0.508832i
$365$	−4.33000e7			−0.890449
$366$	−5.54704e6	−	1.08636e7i	−0.113140	−	0.221579i
$367$			1.82217e7i			0.368630i	0.982867	+	0.184315i	$0.0590067\pi$
$367$			1.82217e7i			0.368630i	−0.982867	+	0.184315i	$0.940993\pi$
$368$	3.13043e7	−	1.02906e7i	0.628145	−	0.206489i
$369$	−4.79418e6			−0.0954191
$370$	−1.13322e8	+	5.78634e7i	−2.23723	+	1.14235i
$371$		−	1.12758e7i		−	0.220813i
$372$	1.16341e7	−	1.60711e7i	0.225998	−	0.312188i
$373$	3.69902e7			0.712788			0.356394	−	0.934336i	$-0.384006\pi$
$373$	3.69902e7			0.712788			0.356394	+	0.934336i	$0.384006\pi$
$374$	−171750.	−	336363.i	−0.00328308	−	0.00642973i
$375$			4.25878e6i			0.0807591i
$376$	−7.33958e7	−	1.14307e7i	−1.38073	−	0.215034i
$377$	−4.09855e7			−0.764903
$378$	−1.47259e7	+	7.51919e6i	−0.272651	+	0.139218i
$379$			8.07965e7i			1.48414i	0.670322	+	0.742070i	$0.266156\pi$
$379$			8.07965e7i			1.48414i	−0.670322	+	0.742070i	$0.733844\pi$
$380$	5.15032e7	+	3.72840e7i	0.938605	+	0.679472i
$381$	−5.40165e7			−0.976678
$382$	4.18426e7	+	8.19463e7i	0.750634	+	1.47007i
$383$		−	1.84048e7i		−	0.327594i	−0.986494	−	0.163797i	$-0.947626\pi$
$383$		−	1.84048e7i		−	0.327594i	0.986494	−	0.163797i	$-0.0523741\pi$
$384$	−5.30841e6	−	3.22575e7i	−0.0937499	−	0.569688i
$385$	1.38886e7			0.243376
$386$	6.25616e7	−	3.19445e7i	1.08779	−	0.555437i
$387$			2.58802e6i			0.0446514i
$388$	4.18728e7	−	5.78420e7i	0.716864	−	0.990258i
$389$	3.06205e7			0.520191			0.260096	−	0.965583i	$-0.416246\pi$
$389$	3.06205e7			0.520191			0.260096	+	0.965583i	$0.416246\pi$
$390$	1.17059e7	+	2.29253e7i	0.197337	+	0.386474i
$391$			2.56980e6i			0.0429902i
$392$	1.41864e7	−	9.10902e7i	0.235512	−	1.51221i
$393$	−3.29279e7			−0.542483
$394$	6.96638e7	−	3.55710e7i	1.13899	−	0.581577i
$395$			1.06112e8i			1.72176i
$396$	−1.86183e6	−	1.34781e6i	−0.0299815	−	0.0217041i
$397$	4.82333e7			0.770860			0.385430	−	0.922737i	$-0.374053\pi$
$397$	4.82333e7			0.770860			0.385430	+	0.922737i	$0.374053\pi$
$398$	1.37661e7	+	2.69601e7i	0.218354	+	0.427634i
$399$		−	4.90611e7i		−	0.772357i
$400$	−1.79574e7	−	5.46269e7i	−0.280585	−	0.853545i
$401$	2.62250e6			0.0406708			0.0203354	−	0.999793i	$-0.493527\pi$
$401$	2.62250e6			0.0406708			0.0203354	+	0.999793i	$0.493527\pi$
$402$	5.31889e7	−	2.71588e7i	0.818735	−	0.418054i
$403$			2.38331e7i			0.364137i
$404$	−3.20238e7	+	4.42369e7i	−0.485657	+	0.670873i
$405$	1.01701e7			0.153095
$406$	−6.78851e7	−	1.32949e8i	−1.01437	−	1.98659i
$407$			1.36482e7i			0.202438i
$408$	2.51909e6	+	392322.i	0.0370905	+	0.00577647i
$409$	−1.29865e8			−1.89812			−0.949059	−	0.315098i	$-0.897963\pi$
$409$	−1.29865e8			−1.89812			−0.949059	+	0.315098i	$0.897963\pi$
$410$	−2.42104e7	+	1.23620e7i	−0.351277	+	0.179365i
$411$			2.16884e7i			0.312393i
$412$	5.60675e7	+	4.05882e7i	0.801715	+	0.580375i
$413$	8.09228e7			1.14874
$414$	7.11216e6	+	1.39288e7i	0.100231	+	0.196296i
$415$		−	1.28620e8i		−	1.79956i
$416$	2.78877e7	+	2.76488e7i	0.387376	+	0.384058i
$417$	1.00986e7			0.139268
$418$	6.07401e6	−	3.10145e6i	0.0831661	−	0.0424654i
$419$			5.61116e6i			0.0762799i	0.999272	+	0.0381400i	$0.0121433\pi$
$419$			5.61116e6i			0.0762799i	−0.999272	+	0.0381400i	$0.987857\pi$
$420$	−5.49765e7	+	7.59431e7i	−0.742043	+	1.02504i
$421$	−1.62466e7			−0.217729			−0.108865	−	0.994057i	$-0.534721\pi$
$421$	−1.62466e7			−0.217729			−0.108865	+	0.994057i	$0.534721\pi$
$422$	−1.01316e7	−	1.98422e7i	−0.134816	−	0.264030i
$423$		−	3.52543e7i		−	0.465790i
$424$	−1.62824e6	+	1.04549e7i	−0.0213610	+	0.137158i
$425$	4.48438e6			0.0584165
$426$	1.52494e7	−	7.78651e6i	0.197254	−	0.100720i
$427$			5.33680e7i			0.685484i
$428$	1.13691e7	+	8.23029e6i	0.145009	+	0.104974i
$429$	2.76105e6			0.0349706
$430$	6.67335e6	+	1.30694e7i	0.0839341	+	0.164380i
$431$		−	2.83367e7i		−	0.353931i	−0.984217	−	0.176965i	$-0.943372\pi$
$431$		−	2.83367e7i		−	0.353931i	0.984217	−	0.176965i	$-0.0566280\pi$
$432$	1.47397e7	−	4.84534e6i	0.182825	−	0.0600998i
$433$	1.20593e8			1.48545			0.742727	−	0.669595i	$-0.233532\pi$
$433$	1.20593e8			1.48545			0.742727	+	0.669595i	$0.233532\pi$
$434$	−7.73099e7	+	3.94752e7i	−0.945727	+	0.482897i
$435$			9.18182e7i			1.11548i
$436$	−3.43006e7	+	4.73820e7i	−0.413850	+	0.571681i
$437$	−4.64052e7			−0.556061
$438$	−1.42576e7	−	2.79227e7i	−0.169678	−	0.332304i
$439$		−	4.16793e7i		−	0.492637i	−0.969189	−	0.246318i	$-0.920779\pi$
$439$		−	4.16793e7i		−	0.492637i	0.969189	−	0.246318i	$-0.0792209\pi$
$440$	−1.28775e7	−	2.00555e6i	−0.151173	−	0.0235437i
$441$	4.37534e7			0.510148
$442$	−2.72755e6	+	1.39271e6i	−0.0315868	+	0.0161285i
$443$		−	2.51566e7i		−	0.289362i	−0.989478	−	0.144681i	$-0.953784\pi$
$443$		−	2.51566e7i		−	0.289362i	0.989478	−	0.144681i	$-0.0462155\pi$
$444$	−7.46284e7	−	5.40248e7i	−0.852620	−	0.617226i
$445$	−6.99790e7			−0.794123
$446$	−3.63035e7	−	7.10984e7i	−0.409208	−	0.801411i
$447$			9.62986e6i			0.107820i
$448$	−4.34965e7	+	1.36258e8i	−0.483749	+	1.51540i
$449$	−1.15867e8			−1.28003			−0.640014	−	0.768363i	$-0.721071\pi$
$449$	−1.15867e8			−1.28003			−0.640014	+	0.768363i	$0.721071\pi$
$450$	2.43061e7	−	1.24109e7i	0.266734	−	0.136197i
$451$			2.91583e6i			0.0317857i
$452$	5.16321e7	−	7.13232e7i	0.559119	−	0.772353i
$453$	4.93193e7			0.530545
$454$	7.97796e7	+	1.56244e8i	0.852558	+	1.66969i
$455$		−	1.12622e8i		−	1.19561i
$456$	−7.08451e6	+	4.54894e7i	−0.0747163	+	0.479751i
$457$	6.14718e7			0.644061			0.322031	−	0.946729i	$-0.395635\pi$
$457$	6.14718e7			0.644061			0.322031	+	0.946729i	$0.395635\pi$
$458$	−7.93054e7	+	4.04941e7i	−0.825480	+	0.421498i
$459$			1.20999e6i			0.0125125i
$460$	7.18321e7	+	5.20005e7i	0.737981	+	0.534237i
$461$	9.60847e7			0.980734			0.490367	−	0.871516i	$-0.336863\pi$
$461$	9.60847e7			0.980734			0.490367	+	0.871516i	$0.336863\pi$
$462$	4.57318e6	+	8.95632e6i	0.0463759	+	0.0908247i
$463$		−	5.41563e7i		−	0.545639i	−0.962065	−	0.272820i	$-0.912044\pi$
$463$		−	5.41563e7i		−	0.545639i	0.962065	−	0.272820i	$-0.0879562\pi$
$464$	4.37449e7	+	1.33073e8i	0.437899	+	1.33210i
$465$	5.33923e7			0.531031
$466$	8.52357e7	−	4.35222e7i	0.842294	−	0.430083i
$467$		−	1.65365e8i		−	1.62365i	−0.583902	−	0.811824i	$-0.698475\pi$
$467$		−	1.65365e8i		−	1.62365i	0.583902	−	0.811824i	$-0.301525\pi$
$468$	−1.09293e7	+	1.50975e7i	−0.106624	+	0.147288i
$469$	−2.61295e8			−2.53286
$470$	−9.09050e7	−	1.78032e8i	−0.875576	−	1.71477i
$471$			3.25916e7i			0.311920i
$472$	−7.50316e7	−	1.16854e7i	−0.713540	−	0.111127i
$473$	1.57404e6			0.0148741
$474$	−6.84280e7	+	3.49400e7i	−0.642538	+	0.328086i
$475$			8.09785e7i			0.755595i
$476$	−9.03537e6	−	6.54086e6i	−0.0837770	−	0.0606476i
$477$	−5.02181e6			−0.0462706
$478$	−2.64145e7	−	5.17313e7i	−0.241857	−	0.473663i
$479$			1.68599e8i			1.53408i	0.641601	+	0.767039i	$0.278271\pi$
$479$			1.68599e8i			1.53408i	−0.641601	+	0.767039i	$0.721729\pi$
$480$	6.19405e7	−	6.24757e7i	0.560082	−	0.564921i
$481$	1.10672e8			0.994499
$482$	−4.62643e6	+	2.36230e6i	−0.0413147	+	0.0210957i
$483$		−	6.84260e7i		−	0.607267i
$484$	6.56654e7	−	9.07084e7i	0.579162	−	0.800040i
$485$	1.92166e8			1.68443
$486$	3.34877e6	+	6.55837e6i	0.0291727	+	0.0571330i
$487$		−	3.13794e6i		−	0.0271680i	−0.999908	−	0.0135840i	$-0.995676\pi$
$487$		−	3.13794e6i		−	0.0271680i	0.999908	−	0.0135840i	$-0.00432405\pi$
$488$	7.70645e6	−	4.94828e7i	0.0663124	−	0.425790i
$489$	7.00469e6			0.0599049
$490$	2.20953e8	−	1.12821e8i	1.87807	−	0.958959i
$491$			2.16648e8i			1.83025i	0.403175	+	0.915123i	$0.367907\pi$
$491$			2.16648e8i			1.83025i	−0.403175	+	0.915123i	$0.632093\pi$
$492$	−1.59438e7	−	1.15420e7i	−0.133874	−	0.0969135i
$493$	−1.09241e7			−0.0911687
$494$	−2.51494e7	−	4.92538e7i	−0.208616	−	0.408562i
$495$		−	6.18548e6i		−	0.0509985i
$496$	7.73820e7	−	2.54377e7i	0.634154	−	0.208465i
$497$	−7.49140e7			−0.610231
$498$	8.29431e7	−	4.23516e7i	0.671572	−	0.342911i
$499$		−	8.66193e7i		−	0.697129i	−0.937285	−	0.348564i	$-0.886669\pi$
$499$		−	8.66193e7i		−	0.697129i	0.937285	−	0.348564i	$-0.113331\pi$
$500$	−1.02530e7	+	1.41632e7i	−0.0820239	+	0.113306i
$501$	−2.79125e7			−0.221966
$502$	7.75481e7	+	1.51874e8i	0.612999	+	1.20052i
$503$		−	8.57535e7i		−	0.673826i	−0.941536	−	0.336913i	$-0.890617\pi$
$503$		−	8.57535e7i		−	0.673826i	0.941536	−	0.336913i	$-0.109383\pi$
$504$	−6.70756e7	−	1.04463e7i	−0.523930	−	0.0815968i
$505$	−1.46966e8			−1.14115
$506$	8.47149e6	−	4.32562e6i	0.0653895	−	0.0333885i
$507$			5.28533e7i			0.405554i
$508$	−1.79640e8	−	1.30044e8i	−1.37029	−	0.991974i
$509$	−428408.			−0.00324866			−0.00162433	−	0.999999i	$-0.500517\pi$
$509$	−428408.			−0.00324866			−0.00162433	+	0.999999i	$0.500517\pi$
$510$	3.12003e6	+	6.11041e6i	0.0235206	+	0.0460638i
$511$			1.37172e8i			1.02803i
$512$	6.00058e7	−	1.20057e8i	0.447078	−	0.894495i
$513$	−2.18500e7			−0.161845
$514$	−2.38411e8	+	1.21735e8i	−1.75565	+	0.896451i
$515$			1.86271e8i			1.36371i
$516$	−6.23064e6	+	8.60684e6i	−0.0453507	+	0.0626462i
$517$	−2.14417e7			−0.155163
$518$	1.83309e8	+	3.59000e8i	1.31885	+	2.58289i
$519$			9.46135e7i			0.676786i
$520$	−1.62629e7	+	1.04423e8i	−0.115661	+	0.742655i
$521$	−1.15523e8			−0.816872			−0.408436	−	0.912787i	$-0.633926\pi$
$521$	−1.15523e8			−0.816872			−0.408436	+	0.912787i	$0.633926\pi$
$522$	−5.92106e7	+	3.02335e7i	−0.416282	+	0.212558i
$523$		−	2.33392e8i		−	1.63147i	−0.578423	−	0.815737i	$-0.696332\pi$
$523$		−	2.33392e8i		−	1.63147i	0.578423	−	0.815737i	$-0.303668\pi$
$524$	−1.09507e8	−	7.92736e7i	−0.761108	−	0.550979i
$525$	−1.19406e8			−0.825176
$526$	−1.13790e8	−	2.22852e8i	−0.781895	−	1.53130i
$527$			6.35237e6i			0.0434014i
$528$	−2.94694e6	−	8.96468e6i	−0.0200203	−	0.0609022i
$529$	8.33140e7			0.562796
$530$	−2.53599e7	+	1.29490e7i	−0.170341	+	0.0869778i
$531$		−	3.60400e7i		−	0.240714i
$532$	1.18114e8	−	1.63160e8i	0.784453	−	1.08362i
$533$	2.36443e7			0.156151
$534$	−2.30424e7	−	4.51272e7i	−0.151323	−	0.296357i
$535$			3.77711e7i			0.246660i
$536$	2.42272e8	+	3.77315e7i	1.57329	+	0.245024i
$537$	6.31912e7			0.408069
$538$	−1.64254e8	+	8.38697e7i	−1.05480	+	0.538590i
$539$		−	2.66109e7i		−	0.169939i
$540$	3.38222e7	+	2.44845e7i	0.214793	+	0.155493i
$541$	7.23945e6			0.0457208			0.0228604	−	0.999739i	$-0.492723\pi$
$541$	7.23945e6			0.0457208			0.0228604	+	0.999739i	$0.492723\pi$
$542$	6.34985e7	+	1.24358e8i	0.398810	+	0.781046i
$543$		−	9.86173e7i		−	0.615961i
$544$	7.43308e6	+	7.36941e6i	0.0461713	+	0.0457758i
$545$	−1.57415e8			−0.972428
$546$	7.26263e7	−	3.70837e7i	0.446186	−	0.227827i
$547$			2.10222e8i			1.28444i	0.766518	+	0.642222i	$0.221987\pi$
$547$			2.10222e8i			1.28444i	−0.766518	+	0.642222i	$0.778013\pi$
$548$	−5.22147e7	+	7.21280e7i	−0.317286	+	0.438291i
$549$	2.37681e7			0.143641
$550$	−7.54834e6	−	1.47830e7i	−0.0453695	−	0.0888535i
$551$		−	1.97267e8i		−	1.17923i
$552$	−9.88086e6	+	6.34446e7i	−0.0587459	+	0.377205i
$553$	3.36157e8			1.98778
$554$	1.14181e8	−	5.83021e7i	0.671530	−	0.342890i
$555$		−	2.47935e8i		−	1.45030i
$556$	3.35844e7	+	2.43123e7i	0.195395	+	0.141450i
$557$	2.09356e8			1.21149			0.605745	−	0.795659i	$-0.292875\pi$
$557$	2.09356e8			1.21149			0.605745	+	0.795659i	$0.292875\pi$
$558$	1.75808e7	+	3.44309e7i	0.101189	+	0.198174i
$559$		−	1.27638e7i		−	0.0730708i
$560$	−3.65665e8	+	1.20205e8i	−2.08219	+	0.684474i
$561$	735920.			0.00416814
$562$	−3.24520e7	+	1.65703e7i	−0.182823	+	0.0933514i
$563$		−	2.84648e8i		−	1.59508i	−0.603266	−	0.797540i	$-0.706134\pi$
$563$		−	2.84648e8i		−	1.59508i	0.603266	−	0.797540i	$-0.293866\pi$
$564$	8.48744e7	−	1.17243e8i	0.473085	−	0.653508i
$565$	2.36954e8			1.31377
$566$	−5.12200e7	−	1.00312e8i	−0.282482	−	0.553225i
$567$		−	3.22185e7i		−	0.176749i
$568$	6.94603e7	+	1.08177e7i	0.379046	+	0.0590325i
$569$	3.14469e8			1.70703			0.853516	−	0.521067i	$-0.174466\pi$
$569$	3.14469e8			1.70703			0.853516	+	0.521067i	$0.174466\pi$
$570$	−1.10341e8	+	5.63413e7i	−0.595817	+	0.304230i
$571$		−	6.34099e6i		−	0.0340603i	−0.999855	−	0.0170302i	$-0.994579\pi$
$571$		−	6.34099e6i		−	0.0340603i	0.999855	−	0.0170302i	$-0.00542113\pi$
$572$	9.18229e6	+	6.64722e6i	0.0490640	+	0.0355183i
$573$	−1.79288e8			−0.952990
$574$	3.91624e7	+	7.66974e7i	0.207078	+	0.405551i
$575$			1.12942e8i			0.594088i
$576$	6.06840e7	+	1.93717e7i	0.317546	+	0.101368i
$577$	−1.02190e8			−0.531964			−0.265982	−	0.963978i	$-0.585696\pi$
$577$	−1.02190e8			−0.531964			−0.265982	+	0.963978i	$0.585696\pi$
$578$	1.71251e8	−	8.74426e7i	0.886851	−	0.452835i
$579$			1.36877e8i			0.705171i
$580$	−2.21052e8	+	3.05355e8i	−1.13295	+	1.56503i
$581$	−4.07464e8			−2.07760
$582$	6.32756e7	+	1.23922e8i	0.320972	+	0.628606i
$583$			3.05427e6i			0.0154135i
$584$	1.98080e7	−	1.27186e8i	0.0994493	−	0.638560i
$585$	−5.01577e7			−0.250536
$586$	−4.99002e7	+	2.54795e7i	−0.247976	+	0.126619i
$587$		−	1.05154e8i		−	0.519889i	−0.965624	−	0.259945i	$-0.916296\pi$
$587$		−	1.05154e8i		−	0.519889i	0.965624	−	0.259945i	$-0.0837043\pi$
$588$	1.45509e8	+	1.05336e8i	0.715742	+	0.518138i
$589$	−1.14711e8			−0.561381
$590$	−9.29310e7	−	1.82000e8i	−0.452486	−	0.886167i
$591$			1.52416e8i			0.738359i
$592$	−1.18124e8	−	3.59335e8i	−0.569340	−	1.73195i
$593$	−3.73401e8			−1.79065			−0.895326	−	0.445412i	$-0.853057\pi$
$593$	−3.73401e8			−1.79065			−0.895326	+	0.445412i	$0.853057\pi$
$594$	3.98881e6	−	2.03672e6i	0.0190320	−	0.00971791i
$595$		−	3.00178e7i		−	0.142504i
$596$	−2.31838e7	+	3.20255e7i	−0.109508	+	0.151272i
$597$	−5.89854e7			−0.277218
$598$	−3.50762e7	−	6.86948e7i	−0.164025	−	0.321233i
$599$			9.24133e7i			0.429986i	0.976616	+	0.214993i	$0.0689729\pi$
$599$			9.24133e7i			0.429986i	−0.976616	+	0.214993i	$0.931027\pi$
$600$	1.10713e8	+	1.72424e7i	0.512559	+	0.0798259i
$601$	−8.65606e7			−0.398747			−0.199373	−	0.979924i	$-0.563891\pi$
$601$	−8.65606e7			−0.398747			−0.199373	+	0.979924i	$0.563891\pi$
$602$	4.14032e7	−	2.11409e7i	0.189777	−	0.0969022i
$603$			1.16371e8i			0.530753i
$604$	1.64019e8	+	1.18736e8i	0.744359	+	0.538854i
$605$	3.01357e8			1.36087
$606$	−4.83924e7	−	9.47739e7i	−0.217450	−	0.425864i
$607$			2.82004e8i			1.26093i	0.776219	+	0.630463i	$0.217135\pi$
$607$			2.82004e8i			1.26093i	−0.776219	+	0.630463i	$0.782865\pi$
$608$	−1.33076e8	+	1.34226e8i	−0.592092	+	0.597208i
$609$	2.90876e8			1.28782
$610$	1.20028e8	−	6.12874e7i	0.528801	−	0.270011i
$611$			1.73869e8i			0.762254i
$612$	−2.91305e6	+	4.02402e6i	−0.0127085	+	0.0175552i
$613$	3.77812e8			1.64019			0.820095	−	0.572228i	$-0.193921\pi$
$613$	3.77812e8			1.64019			0.820095	+	0.572228i	$0.193921\pi$
$614$	−1.15766e6	−	2.26721e6i	−0.00500122	−	0.00979462i
$615$		−	5.29693e7i		−	0.227719i
$616$	−6.35348e6	+	4.07955e7i	−0.0271813	+	0.174530i
$617$	−3.24962e8			−1.38349			−0.691747	−	0.722140i	$-0.743159\pi$
$617$	−3.24962e8			−1.38349			−0.691747	+	0.722140i	$0.743159\pi$
$618$	−1.20120e8	+	6.13344e7i	−0.508920	+	0.259860i
$619$		−	2.43629e8i		−	1.02721i	−0.858028	−	0.513603i	$-0.828311\pi$
$619$		−	2.43629e8i		−	1.02721i	0.858028	−	0.513603i	$-0.171689\pi$
$620$	1.77564e8	+	1.28542e8i	0.745040	+	0.539347i
$621$	−3.04744e7			−0.127251
$622$	−1.70253e8	−	3.33430e8i	−0.707493	−	1.38559i
$623$			2.21691e8i			0.916818i
$624$	−7.26940e7	+	2.38966e7i	−0.299189	+	0.0983518i
$625$	−2.66409e8			−1.09121
$626$	2.59992e8	−	1.32755e8i	1.05983	−	0.541161i
$627$			1.32892e7i			0.0539132i
$628$	−7.84641e7	+	1.08388e8i	−0.316805	+	0.437626i
$629$	2.94982e7			0.118534
$630$	−8.30771e7	−	1.62702e8i	−0.332246	−	0.650685i
$631$			3.50492e8i			1.39505i	0.716560	+	0.697526i	$0.245716\pi$
$631$			3.50492e8i			1.39505i	−0.716560	+	0.697526i	$0.754284\pi$
$632$	−3.11685e8	−	4.85418e7i	−1.23471	−	0.192294i
$633$	4.34124e7			0.171160
$634$	3.54057e8	−	1.80785e8i	1.38933	−	0.709405i
$635$		−	5.96810e8i		−	2.33085i
$636$	−1.67008e7	−	1.20900e7i	−0.0649180	−	0.0469952i
$637$	−2.15786e8			−0.834844
$638$	1.83881e7	+	3.60120e7i	0.0708066	+	0.138671i
$639$			3.33639e7i			0.127872i
$640$	3.56402e8	−	5.86509e7i	1.35957	−	0.223735i
$641$	9.43200e7			0.358121			0.179061	−	0.983838i	$-0.442694\pi$
$641$	9.43200e7			0.358121			0.179061	+	0.983838i	$0.442694\pi$
$642$	−2.43574e7	+	1.24371e7i	−0.0920503	+	0.0470017i
$643$			2.45499e7i			0.0923459i	0.998933	+	0.0461730i	$0.0147025\pi$
$643$			2.45499e7i			0.0923459i	−0.998933	+	0.0461730i	$0.985297\pi$
$644$	1.64735e8	−	2.27561e8i	0.616778	−	0.852001i
$645$	−2.85942e7			−0.106561
$646$	−6.70323e6	−	1.31279e7i	−0.0248649	−	0.0486965i
$647$			4.28314e8i			1.58143i	0.612186	+	0.790713i	$0.290290\pi$
$647$			4.28314e8i			1.58143i	−0.612186	+	0.790713i	$0.709710\pi$
$648$	−4.65241e6	+	2.98730e7i	−0.0170983	+	0.109788i
$649$	−2.19196e7			−0.0801859
$650$	−1.19875e8	+	6.12091e7i	−0.436503	+	0.222882i
$651$		−	1.69144e8i		−	0.613077i
$652$	2.32952e7	+	1.68638e7i	0.0840471	+	0.0608431i
$653$	2.33639e8			0.839084			0.419542	−	0.907736i	$-0.362191\pi$
$653$	2.33639e8			0.839084			0.419542	+	0.907736i	$0.362191\pi$
$654$	−5.18330e7	−	1.01512e8i	−0.185299	−	0.362898i
$655$		−	3.63809e8i		−	1.29464i
$656$	−2.52362e7	−	7.67690e7i	−0.0893947	−	0.271941i
$657$	6.10915e7			0.215419
$658$	−5.63999e8	+	2.87983e8i	−1.97970	+	1.01086i
$659$			1.05674e8i			0.369244i	0.982810	+	0.184622i	$0.0591061\pi$
$659$			1.05674e8i			0.369244i	−0.982810	+	0.184622i	$0.940894\pi$
$660$	1.48915e7	−	2.05707e7i	0.0517972	−	0.0715513i
$661$	−1.65729e8			−0.573846			−0.286923	−	0.957954i	$-0.592632\pi$
$661$	−1.65729e8			−0.573846			−0.286923	+	0.957954i	$0.592632\pi$
$662$	1.67106e8	+	3.27268e8i	0.575994	+	1.12805i
$663$		−	5.96753e6i		−	0.0204764i
$664$	3.77801e8	+	5.88387e7i	1.29050	+	0.200983i
$665$	5.42059e8			1.84324
$666$	1.59885e8	−	8.16389e7i	0.541235	−	0.276360i
$667$		−	2.75130e8i		−	0.927173i
$668$	−9.28273e7	−	6.71993e7i	−0.311420	−	0.225442i
$669$	1.55554e8			0.519522
$670$	3.00068e8	+	5.87667e8i	0.997690	+	1.95392i
$671$		−	1.44558e7i		−	0.0478492i
$672$	−1.97920e8	−	1.96225e8i	−0.652203	−	0.646616i
$673$	−5.75722e7			−0.188872			−0.0944359	−	0.995531i	$-0.530105\pi$
$673$	−5.75722e7			−0.188872			−0.0944359	+	0.995531i	$0.530105\pi$
$674$	−2.11255e8	+	1.07869e8i	−0.689966	+	0.352303i
$675$			5.31788e7i			0.172913i
$676$	−1.27244e8	+	1.75772e8i	−0.411905	+	0.568995i
$677$	6.12762e7			0.197481			0.0987407	−	0.995113i	$-0.468519\pi$
$677$	6.12762e7			0.197481			0.0987407	+	0.995113i	$0.468519\pi$
$678$	7.80232e7	+	1.52804e8i	0.250343	+	0.490282i
$679$		−	6.08774e8i		−	1.94468i
$680$	−4.33464e6	+	2.78325e7i	−0.0137856	+	0.0885169i
$681$	−3.41842e8			−1.08239
$682$	2.09409e7	−	1.06926e7i	0.0660151	−	0.0337079i
$683$		−	1.02941e8i		−	0.323092i	−0.986865	−	0.161546i	$-0.948352\pi$
$683$		−	1.02941e8i		−	0.323092i	0.986865	−	0.161546i	$-0.0516479\pi$
$684$	−7.26653e7	−	5.26036e7i	−0.227069	−	0.164379i
$685$	−2.39628e8			−0.745531
$686$	−1.23877e8	−	2.42606e8i	−0.383723	−	0.751499i
$687$		−	1.73511e8i		−	0.535125i
$688$	−4.14418e7	+	1.36231e7i	−0.127255	+	0.0418322i
$689$	2.47669e7			0.0757206
$690$	−1.53894e8	+	7.85799e7i	−0.468463	+	0.239202i
$691$			1.95567e8i			0.592736i	0.955074	+	0.296368i	$0.0957755\pi$
$691$			1.95567e8i			0.592736i	−0.955074	+	0.296368i	$0.904225\pi$
$692$	−2.27781e8	+	3.14651e8i	−0.687385	+	0.949536i
$693$	−1.95953e7			−0.0588780
$694$	1.16281e8	+	2.27729e8i	0.347880	+	0.681303i
$695$			1.11576e8i			0.332366i
$696$	−2.69701e8	−	4.20031e7i	−0.799934	−	0.124582i
$697$	6.30205e6			0.0186116
$698$	−1.44210e8	+	7.36351e7i	−0.424062	+	0.216530i
$699$			1.86485e8i			0.546025i
$700$	−3.97101e8	−	2.87468e8i	−1.15773	−	0.838099i
$701$	9.70844e6			0.0281835			0.0140918	−	0.999901i	$-0.495514\pi$
$701$	9.70844e6			0.0281835			0.0140918	+	0.999901i	$0.495514\pi$
$702$	−1.65157e7	−	3.23450e7i	−0.0477403	−	0.0934967i
$703$			5.32676e8i			1.53319i
$704$	1.17819e7	−	3.69081e7i	0.0337674	−	0.105780i
$705$	3.89513e8			1.11161
$706$	1.68943e8	−	8.62639e7i	0.480094	−	0.245140i
$707$			4.65584e8i			1.31747i
$708$	8.67661e7	−	1.19856e8i	0.244484	−	0.337724i
$709$	−3.85467e8			−1.08155			−0.540777	−	0.841166i	$-0.681870\pi$
$709$	−3.85467e8			−1.08155			−0.540777	+	0.841166i	$0.681870\pi$
$710$	8.60306e7	+	1.68486e8i	0.240369	+	0.470748i
$711$		−	1.49712e8i		−	0.416531i
$712$	3.20126e7	−	2.05552e8i	0.0886912	−	0.569483i
$713$	−1.59988e8			−0.441387
$714$	1.93575e7	−	9.88414e6i	0.0531808	−	0.0271546i
$715$			3.05060e7i			0.0834577i
$716$	2.10152e8	+	1.52133e8i	0.572525	+	0.414460i
$717$	1.13182e8			0.307057
$718$	−1.27634e8	−	2.49965e8i	−0.344822	−	0.675314i
$719$		−	4.77343e8i		−	1.28423i	−0.766607	−	0.642116i	$-0.778057\pi$
$719$		−	4.77343e8i		−	1.28423i	0.766607	−	0.642116i	$-0.221943\pi$
$720$	5.35346e7	+	1.62854e8i	0.143429	+	0.436315i
$721$	5.90098e8			1.57441
$722$	−9.81360e7	+	5.01092e7i	−0.260745	+	0.133139i
$723$		−	1.01220e7i		−	0.0267826i
$724$	2.37420e8	−	3.27966e8i	0.625608	−	0.864199i
$725$	−4.80111e8			−1.25987
$726$	9.92294e7	+	1.94335e8i	0.259317	+	0.507857i
$727$		−	7.19080e8i		−	1.87143i	−0.352753	−	0.935716i	$-0.614754\pi$
$727$		−	7.19080e8i		−	1.87143i	0.352753	−	0.935716i	$-0.385246\pi$
$728$	3.30808e8	+	5.15200e7i	0.857397	+	0.133531i
$729$	−1.43489e7			−0.0370370
$730$	3.08509e8	−	1.57528e8i	0.793047	−	0.404938i
$731$		−	3.40201e6i		−	0.00870929i
$732$	7.90444e7	+	5.72216e7i	0.201529	+	0.145890i
$733$	−6.05981e7			−0.153867			−0.0769337	−	0.997036i	$-0.524513\pi$
$733$	−6.05981e7			−0.153867			−0.0769337	+	0.997036i	$0.524513\pi$
$734$	−6.62915e7	−	1.29828e8i	−0.167637	−	0.328308i
$735$			4.83417e8i			1.21747i
$736$	−1.85603e8	+	1.87206e8i	−0.465534	+	0.469556i
$737$	7.07769e7			0.176803
$738$	3.41582e7	−	1.74415e7i	0.0849817	−	0.0433925i
$739$			2.69944e8i			0.668868i	0.942419	+	0.334434i	$0.108545\pi$
$739$			2.69944e8i			0.668868i	−0.942419	+	0.334434i	$0.891455\pi$
$740$	5.96902e8	−	8.24545e8i	1.47302	−	2.03479i
$741$	1.07761e8			0.264855
$742$	4.10219e7	+	8.03390e7i	0.100416	+	0.196660i
$743$		−	6.61552e8i		−	1.61286i	−0.591327	−	0.806432i	$-0.701396\pi$
$743$		−	6.61552e8i		−	1.61286i	0.591327	−	0.806432i	$-0.298604\pi$
$744$	−2.44248e7	+	1.56831e8i	−0.0593078	+	0.380814i
$745$	−1.06397e8			−0.257313
$746$	−2.63553e8	+	1.34572e8i	−0.634820	+	0.324145i
$747$			1.81469e8i			0.435353i
$748$	2.44741e6	+	1.77172e6i	0.00584793	+	0.00423342i
$749$	1.19657e8			0.284770
$750$	−1.54937e7	−	3.03435e7i	−0.0367258	−	0.0719253i
$751$			5.41405e8i			1.27821i	0.769119	+	0.639105i	$0.220695\pi$
$751$			5.41405e8i			1.27821i	−0.769119	+	0.639105i	$0.779305\pi$
$752$	5.64525e8	−	1.85575e8i	1.32748	−	0.436382i
$753$	−3.32281e8			−0.778252
$754$	2.92019e8	−	1.49108e8i	0.681235	−	0.347845i
$755$			5.44913e8i			1.26615i
$756$	7.75658e7	−	1.07147e8i	0.179517	−	0.247980i
$757$	6.06873e8			1.39898			0.699488	−	0.714644i	$-0.253411\pi$
$757$	6.06873e8			1.39898			0.699488	+	0.714644i	$0.253411\pi$
$758$	−2.93942e8	−	5.75669e8i	−0.674923	−	1.32180i
$759$			1.85346e7i			0.0423894i
$760$	−5.02597e8	−	7.82745e7i	−1.14493	−	0.178311i
$761$	−1.34482e8			−0.305147			−0.152574	−	0.988292i	$-0.548756\pi$
$761$	−1.34482e8			−0.305147			−0.152574	+	0.988292i	$0.548756\pi$
$762$	3.84863e8	−	1.96515e8i	0.869844	−	0.444151i
$763$			4.98685e8i			1.12267i
$764$	−5.96251e8	−	4.31636e8i	−1.33705	−	0.967916i
$765$	−1.33688e7			−0.0298613
$766$	6.69578e7	+	1.31133e8i	0.148975	+	0.291760i
$767$			1.77745e8i			0.393922i
$768$	1.55177e8	+	2.10520e8i	0.342565	+	0.464740i
$769$	8.02045e7			0.176368			0.0881839	−	0.996104i	$-0.471894\pi$
$769$	8.02045e7			0.176368			0.0881839	+	0.996104i	$0.471894\pi$
$770$	−9.89554e7	+	5.05276e7i	−0.216754	+	0.110677i
$771$		−	5.21615e8i		−	1.13812i
$772$	−3.29530e8	+	4.55205e8i	−0.716215	+	0.989361i
$773$	−6.19810e8			−1.34190			−0.670950	−	0.741503i	$-0.734114\pi$
$773$	−6.19810e8			−1.34190			−0.670950	+	0.741503i	$0.734114\pi$
$774$	−9.41536e6	−	1.84394e7i	−0.0203055	−	0.0397672i
$775$			2.79184e8i			0.599771i
$776$	−8.79082e7	+	5.64456e8i	−0.188124	+	1.20794i
$777$	−7.85448e8			−1.67438
$778$	−2.18169e8	+	1.11399e8i	−0.463291	+	0.236561i
$779$			1.13802e8i			0.240734i
$780$	−1.66807e8	−	1.20754e8i	−0.351504	−	0.254459i
$781$	2.02920e7			0.0425962
$782$	−9.34908e6	−	1.83096e7i	−0.0195501	−	0.0382877i
$783$		−	1.29545e8i		−	0.269859i
$784$	2.30314e8	+	7.00622e8i	0.477939	+	1.45390i
$785$	−3.60094e8			−0.744401
$786$	2.34609e8	−	1.19793e8i	0.483144	−	0.246698i
$787$		−	1.14696e8i		−	0.235301i	−0.993055	−	0.117651i	$-0.962464\pi$
$787$		−	1.14696e8i		−	0.235301i	0.993055	−	0.117651i	$-0.0375363\pi$
$788$	−3.66940e8	+	5.06881e8i	−0.749922	+	1.03592i
$789$	4.87573e8			0.992678
$790$	−3.86040e8	−	7.56038e8i	−0.782981	−	1.53342i
$791$		−	7.50661e8i		−	1.51675i
$792$	1.81688e7	+	2.82960e6i	0.0365721	+	0.00569574i
$793$	−1.17221e8			−0.235064
$794$	−3.43659e8	+	1.75475e8i	−0.686540	+	0.350554i
$795$		−	5.54843e7i		−	0.110425i
$796$	−1.96165e8	−	1.42007e8i	−0.388939	−	0.281560i
$797$	6.07041e8			1.19907			0.599533	−	0.800350i	$-0.295353\pi$
$797$	6.07041e8			1.19907			0.599533	+	0.800350i	$0.295353\pi$
$798$	1.78487e8	+	3.49556e8i	0.351235	+	0.687873i
$799$			4.63425e7i			0.0908529i
$800$	3.26681e8	+	3.23883e8i	0.638049	+	0.632583i
$801$	9.87327e7			0.192116
$802$	−1.86851e7	+	9.54080e6i	−0.0362220	+	0.0184953i
$803$		−	3.71559e7i		−	0.0717598i
$804$	−2.80162e8	+	3.87009e8i	−0.539065	+	0.744650i
$805$	7.56017e8			1.44925
$806$	−8.67060e7	−	1.69809e8i	−0.165594	−	0.324306i
$807$		−	3.59368e8i		−	0.683783i
$808$	6.72312e7	−	4.31689e8i	0.127449	−	0.818346i
$809$	4.94530e8			0.934001			0.467000	−	0.884257i	$-0.345335\pi$
$809$	4.94530e8			0.934001			0.467000	+	0.884257i	$0.345335\pi$
$810$	−7.24613e7	+	3.69994e7i	−0.136349	+	0.0696209i
$811$		−	2.71672e8i		−	0.509310i	−0.967032	−	0.254655i	$-0.918038\pi$
$811$		−	2.71672e8i		−	0.509310i	0.967032	−	0.254655i	$-0.0819620\pi$
$812$	9.67353e8	+	7.00283e8i	1.80683	+	1.30799i
$813$	−2.72081e8			−0.506321
$814$	−4.96529e7	−	9.72424e7i	−0.0920601	−	0.180295i
$815$			7.73925e7i			0.142964i
$816$	−1.93756e7	+	6.36931e6i	−0.0356602	+	0.0117225i
$817$	6.14331e7			0.112651
$818$	9.25281e8	−	4.72457e8i	1.69049	−	0.863182i
$819$			1.58897e8i			0.289244i
$820$	1.27523e8	−	1.76157e8i	0.231285	−	0.319491i
$821$	−1.98822e8			−0.359281			−0.179640	−	0.983732i	$-0.557493\pi$
$821$	−1.98822e8			−0.359281			−0.179640	+	0.983732i	$0.557493\pi$
$822$	−7.89036e7	−	1.54528e8i	−0.142063	−	0.278223i
$823$		−	1.86806e8i		−	0.335114i	−0.985862	−	0.167557i	$-0.946412\pi$
$823$		−	1.86806e8i		−	0.335114i	0.985862	−	0.167557i	$-0.0535878\pi$
$824$	−5.47139e8	−	8.52114e7i	−0.977949	−	0.152306i
$825$	3.23434e7			0.0576002
$826$	−5.76569e8	+	2.94402e8i	−1.02308	+	0.522396i
$827$		−	3.36726e8i		−	0.595332i	−0.954670	−	0.297666i	$-0.903792\pi$
$827$		−	3.36726e8i		−	0.595332i	0.954670	−	0.297666i	$-0.0962082\pi$
$828$	−1.01347e8	−	7.33669e7i	−0.178534	−	0.129244i
$829$	−5.87046e8			−1.03041			−0.515204	−	0.857068i	$-0.672284\pi$
$829$	−5.87046e8			−1.03041			−0.515204	+	0.857068i	$0.672284\pi$
$830$	4.67928e8	+	9.16411e8i	0.818361	+	1.60271i
$831$			2.49815e8i			0.435326i
$832$	−2.99286e8	−	9.55387e7i	−0.519656	−	0.165886i
$833$	−5.75148e7			−0.0995049
$834$	−7.19517e7	+	3.67392e7i	−0.124035	+	0.0633333i
$835$		−	3.08396e8i		−	0.529724i
$836$	−3.19936e7	+	4.41951e7i	−0.0547576	+	0.0756407i
$837$	−7.53306e7			−0.128468
$838$	−2.04137e7	−	3.99791e7i	−0.0346888	−	0.0679361i
$839$		−	2.50547e8i		−	0.424231i	−0.977245	−	0.212116i	$-0.931965\pi$
$839$		−	2.50547e8i		−	0.424231i	0.977245	−	0.212116i	$-0.0680354\pi$
$840$	1.15418e8	−	7.41096e8i	0.194732	−	1.25037i
$841$	5.74745e8			0.966244
$842$	1.15756e8	−	5.91061e7i	0.193913	−	0.0990138i
$843$		−	7.10009e7i		−	0.118517i
$844$	1.44374e8	+	1.04515e8i	0.240139	+	0.173841i
$845$	−5.83959e8			−0.967859
$846$	1.28257e8	+	2.51184e8i	0.211821	+	0.414840i
$847$		−	9.54686e8i		−	1.57112i
$848$	−2.64344e7	−	8.04140e7i	−0.0433492	−	0.131869i
$849$	2.19469e8			0.358633
$850$	−3.19509e7	+	1.63144e7i	−0.0520267	+	0.0265653i
$851$			7.42929e8i			1.20548i
$852$	−8.03234e7	+	1.10957e8i	−0.129874	+	0.179405i
$853$	9.93388e8			1.60056			0.800280	−	0.599627i	$-0.204684\pi$
$853$	9.93388e8			1.60056			0.800280	+	0.599627i	$0.204684\pi$
$854$	−1.94156e8	−	3.80243e8i	−0.311729	−	0.610503i
$855$		−	2.41413e8i		−	0.386244i
$856$	−1.10946e8	−	1.72788e7i	−0.176885	−	0.0275481i
$857$	1.08596e9			1.72532			0.862662	−	0.505781i	$-0.168796\pi$
$857$	1.08596e9			1.72532			0.862662	+	0.505781i	$0.168796\pi$
$858$	−1.96723e7	+	1.00449e7i	−0.0311453	+	0.0159031i
$859$			4.90420e8i			0.773729i	0.922137	+	0.386865i	$0.126442\pi$
$859$			4.90420e8i			0.773729i	−0.922137	+	0.386865i	$0.873558\pi$
$860$	−9.50942e7	−	6.88403e7i	−0.149506	−	0.108230i
$861$	−1.67805e8			−0.262902
$862$	1.03091e8	+	2.01897e8i	0.160952	+	0.315216i
$863$			9.42173e8i			1.46588i	0.680293	+	0.732940i	$0.261852\pi$
$863$			9.42173e8i			1.46588i	−0.680293	+	0.732940i	$0.738148\pi$
$864$	−8.73913e7	+	8.81464e7i	−0.135496	+	0.136667i
$865$	−1.04535e9			−1.61516
$866$	−8.59217e8	+	4.38724e8i	−1.32297	+	0.675520i
$867$			3.74677e8i			0.574910i
$868$	4.07214e8	−	5.62515e8i	0.622678	−	0.860152i
$869$	−9.10550e7			−0.138754
$870$	−3.34040e8	−	6.54198e8i	−0.507271	−	0.993463i
$871$		−	5.73926e8i		−	0.868563i
$872$	7.20111e7	−	4.62381e8i	0.108605	−	0.697349i
$873$	−2.71125e8			−0.407500
$874$	3.30634e8	−	1.68825e8i	0.495237	−	0.252873i
$875$			1.49065e8i			0.222510i
$876$	2.03169e8	+	1.47077e8i	0.302235	+	0.218793i
$877$	−7.83937e8			−1.16220			−0.581102	−	0.813831i	$-0.697378\pi$
$877$	−7.83937e8			−1.16220			−0.581102	+	0.813831i	$0.697378\pi$
$878$	1.51632e8	+	2.96962e8i	0.224030	+	0.438750i
$879$		−	1.09175e8i		−	0.160753i
$880$	9.90478e7	−	3.25598e7i	0.145344	−	0.0477787i
$881$	3.53897e8			0.517546			0.258773	−	0.965938i	$-0.416682\pi$
$881$	3.53897e8			0.517546			0.258773	+	0.965938i	$0.416682\pi$
$882$	−3.11740e8	+	1.59177e8i	−0.454346	+	0.231993i
$883$			1.09742e9i			1.59401i	0.603974	+	0.797004i	$0.293583\pi$
$883$			1.09742e9i			1.59401i	−0.603974	+	0.797004i	$0.706417\pi$
$884$	1.43668e7	−	1.98459e7i	0.0207971	−	0.0287286i
$885$	3.98194e8			0.574467
$886$	9.15211e7	+	1.79239e8i	0.131589	+	0.257710i
$887$			9.70332e8i			1.39043i	0.718801	+	0.695216i	$0.244691\pi$
$887$			9.70332e8i			1.39043i	−0.718801	+	0.695216i	$0.755309\pi$
$888$	7.28267e8	+	1.13420e8i	1.04004	+	0.161976i
$889$	−1.89067e9			−2.69098
$890$	4.98595e8	−	2.54588e8i	0.707259	−	0.361133i
$891$			8.72703e6i			0.0123377i
$892$	5.17320e8	+	3.74496e8i	0.728894	+	0.527659i
$893$	−8.36848e8			−1.17515
$894$	−3.50340e7	−	6.86120e7i	−0.0490317	−	0.0960257i
$895$			6.98179e8i			0.973863i
$896$	−1.85803e8	−	1.12907e9i	−0.258303	−	1.56963i
$897$	1.50296e8			0.208243
$898$	8.25541e8	−	4.21529e8i	1.14001	−	0.582101i
$899$		−	6.80103e8i		−	0.936043i
$900$	−1.28028e8	+	1.76854e8i	−0.175621	+	0.242598i
$901$	6.60127e6			0.00902513
$902$	−1.06079e7	−	2.07750e7i	−0.0144548	−	0.0283089i
$903$			9.05851e7i			0.123025i
$904$	−1.08397e8	+	6.96013e8i	−0.146728	+	0.942133i
$905$	1.08959e9			1.47000
$906$	−3.51396e8	+	1.79426e8i	−0.472512	+	0.241269i
$907$			4.60206e8i			0.616780i	0.951260	+	0.308390i	$0.0997902\pi$
$907$			4.60206e8i			0.616780i	−0.951260	+	0.308390i	$0.900210\pi$
$908$	−1.13685e9	−	8.22983e8i	−1.51860	−	1.09934i
$909$	2.07354e8			0.276070
$910$	4.09725e8	+	8.02424e8i	0.543711	+	1.06483i
$911$		−	1.30765e9i		−	1.72956i	−0.502148	−	0.864782i	$-0.667457\pi$
$911$		−	1.30765e9i		−	1.72956i	0.502148	−	0.864782i	$-0.332543\pi$
$912$	−1.15016e8	−	3.49882e8i	−0.151626	−	0.461251i
$913$	1.10370e8			0.145024
$914$	−4.37982e8	+	2.23638e8i	−0.573611	+	0.292891i
$915$			2.62606e8i			0.342801i
$916$	4.17726e8	−	5.77035e8i	0.543506	−	0.750785i
$917$	−1.15253e9			−1.49467
$918$	−4.40202e6	−	8.62112e6i	−0.00569016	−	0.0111439i
$919$		−	4.64060e7i		−	0.0597898i	−0.999553	−	0.0298949i	$-0.990483\pi$
$919$		−	4.64060e7i		−	0.0597898i	0.999553	−	0.0298949i	$-0.00951727\pi$
$920$	−7.00979e8	−	1.09170e8i	−0.900205	−	0.140198i
$921$	4.96038e6			0.00634946
$922$	−6.84596e8	+	3.49561e8i	−0.873457	+	0.445996i
$923$		−	1.64546e8i		−	0.209259i
$924$	−6.51672e7	−	4.71756e7i	−0.0826063	−	0.0598001i
$925$	1.29643e9			1.63804
$926$	1.97023e8	+	3.85859e8i	0.248133	+	0.485955i
$927$		−	2.62808e8i		−	0.329913i
$928$	−7.95807e8	−	7.88990e8i	−0.995781	−	0.987251i
$929$	−7.13241e8			−0.889588			−0.444794	−	0.895633i	$-0.646723\pi$
$929$	−7.13241e8			−0.889588			−0.444794	+	0.895633i	$0.646723\pi$
$930$	−3.80416e8	+	1.94244e8i	−0.472944	+	0.241490i
$931$		−	1.03860e9i		−	1.28706i
$932$	−4.48962e8	+	6.20184e8i	−0.554577	+	0.766078i
$933$	7.29504e8			0.898220
$934$	6.01605e8	+	1.17821e9i	0.738365	+	1.44605i
$935$			8.13094e6i			0.00994731i
$936$	2.29451e7	−	1.47330e8i	0.0279809	−	0.179665i
$937$	8.74097e7			0.106253			0.0531265	−	0.998588i	$-0.483081\pi$
$937$	8.74097e7			0.106253			0.0531265	+	0.998588i	$0.483081\pi$
$938$	1.86170e9	−	9.50604e8i	2.25581	−	1.15184i
$939$			5.68831e8i			0.687047i
$940$	1.29538e9	+	9.37749e8i	1.55960	+	1.12902i
$941$	1.35628e9			1.62773			0.813863	−	0.581057i	$-0.197361\pi$
$941$	1.35628e9			1.62773			0.813863	+	0.581057i	$0.197361\pi$
$942$	−1.18570e8	−	2.32213e8i	−0.141848	−	0.277801i
$943$			1.58721e8i			0.189277i
$944$	5.77107e8	−	1.89711e8i	0.686026	−	0.225516i
$945$	3.55971e8			0.421813
$946$	−1.12149e7	+	5.72643e6i	−0.0132471	+	0.00676411i
$947$		−	9.31247e8i		−	1.09652i	−0.836309	−	0.548258i	$-0.815291\pi$
$947$		−	9.31247e8i		−	1.09652i	0.836309	−	0.548258i	$-0.184709\pi$
$948$	3.60431e8	−	4.97889e8i	0.423055	−	0.584397i
$949$	−3.01295e8			−0.352528
$950$	−2.94604e8	−	5.76966e8i	−0.343612	−	0.672945i
$951$			7.74633e8i			0.900646i
$952$	8.81723e7	+	1.37319e7i	0.102193	+	0.0159155i
$953$	9.78401e8			1.13042			0.565208	−	0.824949i	$-0.308796\pi$
$953$	9.78401e8			1.13042			0.565208	+	0.824949i	$0.308796\pi$
$954$	3.57800e7	−	1.82696e7i	0.0412093	−	0.0210419i
$955$		−	1.98090e9i		−	2.27432i
$956$	3.76403e8	+	2.72484e8i	0.430803	+	0.311866i
$957$	−7.87897e7			−0.0898946
$958$	−6.13371e8	−	1.20125e9i	−0.697632	−	1.36627i
$959$			7.59131e8i			0.860718i
$960$	−2.14032e8	+	6.70478e8i	−0.241916	+	0.757828i
$961$	4.92024e8			0.554391
$962$	−7.88533e8	+	4.02632e8i	−0.885716	+	0.452255i
$963$		−	5.32909e7i		−	0.0596725i
$964$	2.43688e7	−	3.36624e7i	0.0272021	−	0.0375763i
$965$	−1.51231e9			−1.68290
$966$	2.48938e8	+	4.87530e8i	0.276159	+	0.540842i
$967$			848332.i			0.000938180i	1.00000		0.000469090i	$0.000149316\pi$
$967$			848332.i			0.000938180i	−1.00000		0.000469090i	$0.999851\pi$
$968$	−1.37859e8	+	8.85185e8i	−0.151987	+	0.975906i
$969$	2.87222e7			0.0315680
$970$	−1.36917e9	+	6.99111e8i	−1.50018	+	0.766004i
$971$		−	2.01864e8i		−	0.220496i	−0.993904	−	0.110248i	$-0.964835\pi$
$971$		−	2.01864e8i		−	0.220496i	0.993904	−	0.110248i	$-0.0351645\pi$
$972$	−4.77194e7	−	3.45449e7i	−0.0519633	−	0.0376171i
$973$	3.53468e8			0.383718
$974$	1.14160e7	+	2.23576e7i	0.0123548	+	0.0241962i
$975$		−	2.62271e8i		−	0.282967i
$976$	1.25113e8	+	3.80598e8i	0.134572	+	0.409371i
$977$	3.23896e8			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$977$	3.23896e8			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$978$	−4.99079e7	+	2.54835e7i	−0.0533523	+	0.0272422i
$979$		−	6.00494e7i		−	0.0639971i
$980$	−1.16382e9	+	1.60768e9i	−1.23654	+	1.70813i
$981$	2.22096e8			0.235252
$982$	−7.88176e8	−	1.54360e9i	−0.832317	−	1.63005i
$983$			9.70682e8i			1.02192i	0.859605	+	0.510960i	$0.170710\pi$
$983$			9.70682e8i			1.02192i	−0.859605	+	0.510960i	$0.829290\pi$
$984$	1.55588e8	+	2.42313e7i	0.163302	+	0.0254327i
$985$	−1.68399e9			−1.76210
$986$	7.78335e7	−	3.97426e7i	0.0811963	−	0.0414596i
$987$		−	1.23396e9i		−	1.28336i
$988$	3.58376e8	+	2.59434e8i	0.371593	+	0.269003i
$989$	8.56815e7			0.0885723
$990$	2.25031e7	+	4.40710e7i	0.0231919	+	0.0454201i
$991$		−	2.58231e7i		−	0.0265330i	−0.999912	−	0.0132665i	$-0.995777\pi$
$991$		−	2.58231e7i		−	0.0265330i	0.999912	−	0.0132665i	$-0.00422299\pi$
$992$	−4.58797e8	+	4.62761e8i	−0.469987	+	0.474048i
$993$	−7.16021e8			−0.731270
$994$	5.33757e8	−	2.72541e8i	0.543481	−	0.277507i
$995$		−	6.51710e8i		−	0.661584i
$996$	−4.36886e8	+	6.03503e8i	−0.442171	+	0.610804i
$997$	−7.49027e8			−0.755809			−0.377904	−	0.925845i	$-0.623355\pi$
$997$	−7.49027e8			−0.755809			−0.377904	+	0.925845i	$0.623355\pi$
$998$	3.15126e8	+	6.17156e8i	0.317024	+	0.620874i
$999$			3.49809e8i			0.350861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.7.d.a.7.2	yes	6
3.2	odd	2		36.7.d.e.19.5		6
4.3	odd	2	inner	12.7.d.a.7.1	✓	6
8.3	odd	2		192.7.g.e.127.1		6
8.5	even	2		192.7.g.e.127.4		6
12.11	even	2		36.7.d.e.19.6		6
16.3	odd	4		768.7.b.h.127.2		12
16.5	even	4		768.7.b.h.127.5		12
16.11	odd	4		768.7.b.h.127.11		12
16.13	even	4		768.7.b.h.127.8		12
24.5	odd	2		576.7.g.p.127.5		6
24.11	even	2		576.7.g.p.127.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.7.d.a.7.1	✓	6	4.3	odd	2	inner
12.7.d.a.7.2	yes	6	1.1	even	1	trivial
36.7.d.e.19.5		6	3.2	odd	2
36.7.d.e.19.6		6	12.11	even	2
192.7.g.e.127.1		6	8.3	odd	2
192.7.g.e.127.4		6	8.5	even	2
576.7.g.p.127.5		6	24.5	odd	2
576.7.g.p.127.6		6	24.11	even	2
768.7.b.h.127.2		12	16.3	odd	4
768.7.b.h.127.5		12	16.5	even	4
768.7.b.h.127.8		12	16.13	even	4
768.7.b.h.127.11		12	16.11	odd	4

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.12493 + 3.63805i) q^{2} -15.5885i q^{3} +(37.5291 - 51.8417i) q^{4} +172.232 q^{5} +(56.7117 + 111.067i) q^{6} -545.623i q^{7} +(-78.7890 + 505.901i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(-7.12493 + 3.63805i) q^{2} -15.5885i q^{3} +(37.5291 - 51.8417i) q^{4} +172.232 q^{5} +(56.7117 + 111.067i) q^{6} -545.623i q^{7} +(-78.7890 + 505.901i) q^{8} -243.000 q^{9} +(-1227.14 + 626.588i) q^{10} +147.793i q^{11} +(-808.133 - 585.021i) q^{12} +1198.44 q^{13} +(1985.01 + 3887.52i) q^{14} -2684.83i q^{15} +(-1279.13 - 3891.15i) q^{16} +319.429 q^{17} +(1731.36 - 884.047i) q^{18} +5768.21i q^{19} +(6463.70 - 8928.79i) q^{20} -8505.42 q^{21} +(-537.679 - 1053.01i) q^{22} +8044.99i q^{23} +(7886.22 + 1228.20i) q^{24} +14038.8 q^{25} +(-8538.83 + 4360.01i) q^{26} +3788.00i q^{27} +(-28286.0 - 20476.7i) q^{28} -34198.9 q^{29} +(9767.55 + 19129.2i) q^{30} +19886.7i q^{31} +(23269.9 + 23070.6i) q^{32} +2303.86 q^{33} +(-2275.90 + 1162.10i) q^{34} -93973.5i q^{35} +(-9119.57 + 12597.5i) q^{36} +92346.8 q^{37} +(-20985.1 - 41098.1i) q^{38} -18681.9i q^{39} +(-13570.0 + 87132.3i) q^{40} +19729.1 q^{41} +(60600.5 - 30943.2i) q^{42} -10650.3i q^{43} +(7661.84 + 5546.54i) q^{44} -41852.3 q^{45} +(-29268.1 - 57320.0i) q^{46} +145079. i q^{47} +(-60657.0 + 19939.7i) q^{48} -180055. q^{49} +(-100025. + 51073.8i) q^{50} -4979.40i q^{51} +(44976.5 - 62129.4i) q^{52} +20665.9 q^{53} +(-13780.9 - 26989.2i) q^{54} +25454.6i q^{55} +(276031. + 42989.1i) q^{56} +89917.5 q^{57} +(243665. - 124418. i) q^{58} +148313. i q^{59} +(-139186. - 100759. i) q^{60} -97811.2 q^{61} +(-72348.8 - 141691. i) q^{62} +132586. i q^{63} +(-249729. - 79719.0i) q^{64} +206410. q^{65} +(-16414.9 + 8381.58i) q^{66} -478892. i q^{67} +(11987.9 - 16559.7i) q^{68} +125409. q^{69} +(341881. + 669554. i) q^{70} -137300. i q^{71} +(19145.7 - 122934. i) q^{72} -251405. q^{73} +(-657964. + 335963. i) q^{74} -218843. i q^{75} +(299034. + 216476. i) q^{76} +80639.2 q^{77} +(67965.8 + 133107. i) q^{78} +616099. i q^{79} +(-220307. - 670179. i) q^{80} +59049.0 q^{81} +(-140569. + 71775.7i) q^{82} -746788. i q^{83} +(-319201. + 440936. i) q^{84} +55015.7 q^{85} +(38746.3 + 75882.5i) q^{86} +533109. i q^{87} +(-74768.7 - 11644.5i) q^{88} -406308. q^{89} +(298195. - 152261. i) q^{90} -653899. i q^{91} +(417066. + 301922. i) q^{92} +310003. q^{93} +(-527806. - 1.03368e6i) q^{94} +993469. i q^{95} +(359635. - 362742. i) q^{96} +1.11574e6 q^{97} +(1.28288e6 - 655051. i) q^{98} -35913.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9}+O(q^{10}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9	\( 6 q - 10 q^{2} + 156 q^{4} - 44 q^{5} - 162 q^{6} + 1136 q^{8} - 1458 q^{9} + 84 q^{10} - 972 q^{12} - 3348 q^{13} + 4776 q^{14} - 9744 q^{16} + 12220 q^{17} + 2430 q^{18} + 17608 q^{20} - 9720 q^{21} - 13512 q^{22} - 7776 q^{24} + 56418 q^{25} - 59252 q^{26} - 17808 q^{28} - 84860 q^{29} + 57348 q^{30} + 61280 q^{32} + 4536 q^{33} + 109404 q^{34} - 37908 q^{36} + 20796 q^{37} - 128088 q^{38} - 195552 q^{40} - 65252 q^{41} + 210600 q^{42} + 445008 q^{44} + 10692 q^{45} + 81120 q^{46} - 276048 q^{48} - 111546 q^{49} - 743118 q^{50} - 179592 q^{52} + 470308 q^{53} + 39366 q^{54} + 793728 q^{56} - 204120 q^{57} + 529860 q^{58} - 723816 q^{60} + 12924 q^{61} - 513384 q^{62} - 642432 q^{64} + 321512 q^{65} + 771768 q^{66} + 690328 q^{68} + 541728 q^{69} + 938928 q^{70} - 276048 q^{72} - 1283412 q^{73} - 1522916 q^{74} + 67824 q^{76} - 1487328 q^{77} + 396252 q^{78} + 1272352 q^{80} + 354294 q^{81} + 240444 q^{82} - 143856 q^{84} + 814920 q^{85} - 1154568 q^{86} + 489600 q^{88} + 730924 q^{89} - 20412 q^{90} - 1338816 q^{92} - 83592 q^{93} - 390288 q^{94} + 624672 q^{96} + 3249420 q^{97} + 1604918 q^{98}+O(q^{100}) \) 6 * q - 10 * q^2 + 156 * q^4 - 44 * q^5 - 162 * q^6 + 1136 * q^8 - 1458 * q^9 + 84 * q^10 - 972 * q^12 - 3348 * q^13 + 4776 * q^14 - 9744 * q^16 + 12220 * q^17 + 2430 * q^18 + 17608 * q^20 - 9720 * q^21 - 13512 * q^22 - 7776 * q^24 + 56418 * q^25 - 59252 * q^26 - 17808 * q^28 - 84860 * q^29 + 57348 * q^30 + 61280 * q^32 + 4536 * q^33 + 109404 * q^34 - 37908 * q^36 + 20796 * q^37 - 128088 * q^38 - 195552 * q^40 - 65252 * q^41 + 210600 * q^42 + 445008 * q^44 + 10692 * q^45 + 81120 * q^46 - 276048 * q^48 - 111546 * q^49 - 743118 * q^50 - 179592 * q^52 + 470308 * q^53 + 39366 * q^54 + 793728 * q^56 - 204120 * q^57 + 529860 * q^58 - 723816 * q^60 + 12924 * q^61 - 513384 * q^62 - 642432 * q^64 + 321512 * q^65 + 771768 * q^66 + 690328 * q^68 + 541728 * q^69 + 938928 * q^70 - 276048 * q^72 - 1283412 * q^73 - 1522916 * q^74 + 67824 * q^76 - 1487328 * q^77 + 396252 * q^78 + 1272352 * q^80 + 354294 * q^81 + 240444 * q^82 - 143856 * q^84 + 814920 * q^85 - 1154568 * q^86 + 489600 * q^88 + 730924 * q^89 - 20412 * q^90 - 1338816 * q^92 - 83592 * q^93 - 390288 * q^94 + 624672 * q^96 + 3249420 * q^97 + 1604918 * q^98

Introduction

L-functions

Modular forms

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Database

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