LMFDB - Embedded newform 13.7.d.a.8.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,7,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99070308706$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + \cdots + 56070144 $ x^12 - 6x^11 + 18x^10 + 488x^9 + 36205x^8 - 155430x^7 + 399962x^6 + 9502784x^5 + 275595012x^4 - 541321656x^3 + 523196552x^2 - 242221824*x + 56070144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5^{2}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.5
Root			$-6.57888 + 6.57888i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.7.d.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.57888 + 7.57888i) q^{2} +26.7789 q^{3} +50.8787i q^{4} +(-59.0322 - 59.0322i) q^{5} +(202.954 + 202.954i) q^{6} +(-226.950 + 226.950i) q^{7} +(99.4446 - 99.4446i) q^{8} -11.8881 q^{9} +O(q^{10})$	\(q+(7.57888 + 7.57888i) q^{2} +26.7789 q^{3} +50.8787i q^{4} +(-59.0322 - 59.0322i) q^{5} +(202.954 + 202.954i) q^{6} +(-226.950 + 226.950i) q^{7} +(99.4446 - 99.4446i) q^{8} -11.8881 q^{9} -894.795i q^{10} +(1078.96 - 1078.96i) q^{11} +1362.48i q^{12} +(-2073.19 - 727.102i) q^{13} -3440.04 q^{14} +(-1580.82 - 1580.82i) q^{15} +4763.59 q^{16} +1506.86i q^{17} +(-90.0981 - 90.0981i) q^{18} +(4280.27 + 4280.27i) q^{19} +(3003.48 - 3003.48i) q^{20} +(-6077.47 + 6077.47i) q^{21} +16354.6 q^{22} +19283.9i q^{23} +(2663.02 - 2663.02i) q^{24} -8655.40i q^{25} +(-10201.9 - 21223.1i) q^{26} -19840.2 q^{27} +(-11546.9 - 11546.9i) q^{28} -34618.4 q^{29} -23961.7i q^{30} +(14488.1 + 14488.1i) q^{31} +(29738.2 + 29738.2i) q^{32} +(28893.4 - 28893.4i) q^{33} +(-11420.3 + 11420.3i) q^{34} +26794.7 q^{35} -604.849i q^{36} +(17906.3 - 17906.3i) q^{37} +64879.3i q^{38} +(-55517.9 - 19471.0i) q^{39} -11740.9 q^{40} +(72322.6 + 72322.6i) q^{41} -92120.8 q^{42} -122834. i q^{43} +(54896.1 + 54896.1i) q^{44} +(701.778 + 701.778i) q^{45} +(-146150. + 146150. i) q^{46} +(78678.8 - 78678.8i) q^{47} +127564. q^{48} +14636.8i q^{49} +(65598.2 - 65598.2i) q^{50} +40352.0i q^{51} +(36994.0 - 105481. i) q^{52} -31278.0 q^{53} +(-150366. - 150366. i) q^{54} -127387. q^{55} +45137.8i q^{56} +(114621. + 114621. i) q^{57} +(-262368. - 262368. i) q^{58} +(-26291.3 + 26291.3i) q^{59} +(80430.1 - 80430.1i) q^{60} -2955.68 q^{61} +219608. i q^{62} +(2697.99 - 2697.99i) q^{63} +145895. i q^{64} +(79462.8 + 165308. i) q^{65} +437959. q^{66} +(-229598. - 229598. i) q^{67} -76667.0 q^{68} +516403. i q^{69} +(203073. + 203073. i) q^{70} +(-58881.7 - 58881.7i) q^{71} +(-1182.20 + 1182.20i) q^{72} +(497137. - 497137. i) q^{73} +271419. q^{74} -231782. i q^{75} +(-217775. + 217775. i) q^{76} +489739. i q^{77} +(-273195. - 568332. i) q^{78} +48045.8 q^{79} +(-281205. - 281205. i) q^{80} -522633. q^{81} +1.09625e6i q^{82} +(-411022. - 411022. i) q^{83} +(-309214. - 309214. i) q^{84} +(88953.1 - 88953.1i) q^{85} +(930945. - 930945. i) q^{86} -927044. q^{87} -214594. i q^{88} +(-244331. + 244331. i) q^{89} +10637.4i q^{90} +(635526. - 305495. i) q^{91} -981141. q^{92} +(387977. + 387977. i) q^{93} +1.19259e6 q^{94} -505348. i q^{95} +(796359. + 796359. i) q^{96} +(417275. + 417275. i) q^{97} +(-110931. + 110931. i) q^{98} +(-12826.7 + 12826.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9 + 1686 * q^11 - 3926 * q^13 + 5484 * q^14 - 15268 * q^15 + 2132 * q^16 + 15254 * q^18 + 1766 * q^19 - 19044 * q^20 + 3428 * q^21 + 28832 * q^22 + 31608 * q^24 - 58266 * q^26 - 20464 * q^27 + 4092 * q^28 - 90108 * q^29 + 61014 * q^31 - 64932 * q^32 - 44452 * q^33 + 259896 * q^34 + 158772 * q^35 - 40212 * q^37 + 137852 * q^39 - 104196 * q^40 - 190416 * q^41 - 959204 * q^42 + 489372 * q^44 - 151444 * q^45 - 44412 * q^46 + 562446 * q^47 + 930308 * q^48 + 82422 * q^50 - 578500 * q^52 + 509136 * q^53 - 871432 * q^54 - 1264036 * q^55 + 939908 * q^57 - 1019980 * q^58 - 994458 * q^59 + 2407804 * q^60 + 1013696 * q^61 + 865778 * q^63 - 1130064 * q^65 - 418352 * q^66 - 1442386 * q^67 - 2313132 * q^68 + 2958968 * q^70 - 655866 * q^71 - 1706508 * q^72 + 2588228 * q^73 + 3373752 * q^74 + 246984 * q^76 + 77480 * q^78 - 75316 * q^79 - 2685408 * q^80 - 4016140 * q^81 + 894966 * q^83 - 3220504 * q^84 + 105396 * q^85 + 3704832 * q^86 + 2109064 * q^87 - 977376 * q^89 + 1088750 * q^91 + 3682872 * q^92 - 216268 * q^93 - 6238300 * q^94 + 896384 * q^96 + 983388 * q^97 + 1039302 * q^98 + 2894714 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	7.57888	+	7.57888i	0.947359	+	0.947359i	0.998682	−	0.0513227i	$-0.0163437\pi$
$2$	7.57888	+	7.57888i	0.947359	+	0.947359i	−0.0513227	+	0.998682i	$0.516344\pi$
$3$	26.7789			0.991813			0.495906	−	0.868376i	$-0.334836\pi$
$3$	26.7789			0.991813			0.495906	+	0.868376i	$0.334836\pi$
$4$			50.8787i			0.794980i
$5$	−59.0322	−	59.0322i	−0.472258	−	0.472258i	0.430387	−	0.902645i	$-0.358377\pi$
$5$	−59.0322	−	59.0322i	−0.472258	−	0.472258i	−0.902645	+	0.430387i	$0.858377\pi$
$6$	202.954	+	202.954i	0.939603	+	0.939603i
$7$	−226.950	+	226.950i	−0.661660	+	0.661660i	−0.955771	−	0.294111i	$-0.904976\pi$
$7$	−226.950	+	226.950i	−0.661660	+	0.661660i	0.294111	+	0.955771i	$0.404976\pi$
$8$	99.4446	−	99.4446i	0.194228	−	0.194228i
$9$	−11.8881			−0.0163074
$10$		−	894.795i		−	0.894795i
$11$	1078.96	−	1078.96i	0.810639	−	0.810639i	−0.174091	−	0.984730i	$-0.555699\pi$
$11$	1078.96	−	1078.96i	0.810639	−	0.810639i	0.984730	+	0.174091i	$0.0556986\pi$
$12$			1362.48i			0.788471i
$13$	−2073.19	−	727.102i	−0.943648	−	0.330952i
$13$	−2073.19	−	727.102i	−0.943648	−	0.330952i
$14$	−3440.04			−1.25366
$15$	−1580.82	−	1580.82i	−0.468391	−	0.468391i
$16$	4763.59			1.16299
$17$			1506.86i			0.306708i	0.988171	+	0.153354i	$0.0490075\pi$
$17$			1506.86i			0.306708i	−0.988171	+	0.153354i	$0.950992\pi$
$18$	−90.0981	−	90.0981i	−0.0154489	−	0.0154489i
$19$	4280.27	+	4280.27i	0.624038	+	0.624038i	0.946561	−	0.322524i	$-0.104531\pi$
$19$	4280.27	+	4280.27i	0.624038	+	0.624038i	−0.322524	+	0.946561i	$0.604531\pi$
$20$	3003.48	−	3003.48i	0.375435	−	0.375435i
$21$	−6077.47	+	6077.47i	−0.656243	+	0.656243i
$22$	16354.6			1.53593
$23$			19283.9i			1.58494i	0.609914	+	0.792468i	$0.291204\pi$
$23$			19283.9i			1.58494i	−0.609914	+	0.792468i	$0.708796\pi$
$24$	2663.02	−	2663.02i	0.192638	−	0.192638i
$25$		−	8655.40i		−	0.553945i
$26$	−10201.9	−	21223.1i	−0.580443	−	1.20750i
$27$	−19840.2			−1.00799
$28$	−11546.9	−	11546.9i	−0.526007	−	0.526007i
$29$	−34618.4			−1.41943			−0.709713	−	0.704491i	$-0.751175\pi$
$29$	−34618.4			−1.41943			−0.709713	+	0.704491i	$0.751175\pi$
$30$		−	23961.7i		−	0.887470i
$31$	14488.1	+	14488.1i	0.486326	+	0.486326i	0.907145	−	0.420819i	$-0.138257\pi$
$31$	14488.1	+	14488.1i	0.486326	+	0.486326i	−0.420819	+	0.907145i	$0.638257\pi$
$32$	29738.2	+	29738.2i	0.907539	+	0.907539i
$33$	28893.4	−	28893.4i	0.804002	−	0.804002i
$34$	−11420.3	+	11420.3i	−0.290563	+	0.290563i
$35$	26794.7			0.624948
$36$		−	604.849i		−	0.0129640i
$37$	17906.3	−	17906.3i	0.353509	−	0.353509i	−0.507904	−	0.861414i	$-0.669580\pi$
$37$	17906.3	−	17906.3i	0.353509	−	0.353509i	0.861414	+	0.507904i	$0.169580\pi$
$38$			64879.3i			1.18238i
$39$	−55517.9	−	19471.0i	−0.935922	−	0.328242i
$40$	−11740.9			−0.183451
$41$	72322.6	+	72322.6i	1.04936	+	1.04936i	0.998717	+	0.0506380i	$0.0161255\pi$
$41$	72322.6	+	72322.6i	1.04936	+	1.04936i	0.0506380	+	0.998717i	$0.483875\pi$
$42$	−92120.8			−1.24340
$43$		−	122834.i		−	1.54495i	−0.635046	−	0.772474i	$-0.719019\pi$
$43$		−	122834.i		−	1.54495i	0.635046	−	0.772474i	$-0.280981\pi$
$44$	54896.1	+	54896.1i	0.644442	+	0.644442i
$45$	701.778	+	701.778i	0.00770127	+	0.00770127i
$46$	−146150.	+	146150.i	−1.50150	+	1.50150i
$47$	78678.8	−	78678.8i	0.757817	−	0.757817i	−0.218108	−	0.975925i	$-0.569989\pi$
$47$	78678.8	−	78678.8i	0.757817	−	0.757817i	0.975925	+	0.218108i	$0.0699885\pi$
$48$	127564.			1.15347
$49$			14636.8i			0.124411i
$50$	65598.2	−	65598.2i	0.524786	−	0.524786i
$51$			40352.0i			0.304197i
$52$	36994.0	−	105481.i	0.263100	−	0.750181i
$53$	−31278.0			−0.210093			−0.105046	−	0.994467i	$-0.533499\pi$
$53$	−31278.0			−0.210093			−0.105046	+	0.994467i	$0.533499\pi$
$54$	−150366.	−	150366.i	−0.954926	−	0.954926i
$55$	−127387.			−0.765661
$56$			45137.8i			0.257026i
$57$	114621.	+	114621.i	0.618928	+	0.618928i
$58$	−262368.	−	262368.i	−1.34471	−	1.34471i
$59$	−26291.3	+	26291.3i	−0.128014	+	0.128014i	−0.768211	−	0.640197i	$-0.778853\pi$
$59$	−26291.3	+	26291.3i	−0.128014	+	0.128014i	0.640197	+	0.768211i	$0.278853\pi$
$60$	80430.1	−	80430.1i	0.372362	−	0.372362i
$61$	−2955.68			−0.0130217			−0.00651086	−	0.999979i	$-0.502072\pi$
$61$	−2955.68			−0.0130217			−0.00651086	+	0.999979i	$0.502072\pi$
$62$			219608.i			0.921451i
$63$	2697.99	−	2697.99i	0.0107899	−	0.0107899i
$64$			145895.i			0.556544i
$65$	79462.8	+	165308.i	0.289350	+	0.601939i
$66$	437959.			1.52336
$67$	−229598.	−	229598.i	−0.763385	−	0.763385i	0.213548	−	0.976933i	$-0.431498\pi$
$67$	−229598.	−	229598.i	−0.763385	−	0.763385i	−0.976933	+	0.213548i	$0.931498\pi$
$68$	−76667.0			−0.243827
$69$			516403.i			1.57196i
$70$	203073.	+	203073.i	0.592051	+	0.592051i
$71$	−58881.7	−	58881.7i	−0.164515	−	0.164515i	0.620049	−	0.784563i	$-0.287113\pi$
$71$	−58881.7	−	58881.7i	−0.164515	−	0.164515i	−0.784563	+	0.620049i	$0.787113\pi$
$72$	−1182.20	+	1182.20i	−0.00316734	+	0.00316734i
$73$	497137.	−	497137.i	1.27793	−	1.27793i	0.336107	−	0.941824i	$-0.390890\pi$
$73$	497137.	−	497137.i	1.27793	−	1.27793i	0.941824	−	0.336107i	$-0.109110\pi$
$74$	271419.			0.669801
$75$		−	231782.i		−	0.549410i
$76$	−217775.	+	217775.i	−0.496097	+	0.496097i
$77$			489739.i			1.07274i
$78$	−273195.	−	568332.i	−0.575691	−	1.19762i
$79$	48045.8			0.0974482			0.0487241	−	0.998812i	$-0.484484\pi$
$79$	48045.8			0.0974482			0.0487241	+	0.998812i	$0.484484\pi$
$80$	−281205.	−	281205.i	−0.549229	−	0.549229i
$81$	−522633.			−0.983427
$82$			1.09625e6i			1.98823i
$83$	−411022.	−	411022.i	−0.718837	−	0.718837i	0.249530	−	0.968367i	$-0.419724\pi$
$83$	−411022.	−	411022.i	−0.718837	−	0.718837i	−0.968367	+	0.249530i	$0.919724\pi$
$84$	−309214.	−	309214.i	−0.521700	−	0.521700i
$85$	88953.1	−	88953.1i	0.144845	−	0.144845i
$86$	930945.	−	930945.i	1.46362	−	1.46362i
$87$	−927044.			−1.40781
$88$		−	214594.i		−	0.314897i
$89$	−244331.	+	244331.i	−0.346584	+	0.346584i	−0.858835	−	0.512252i	$-0.828812\pi$
$89$	−244331.	+	244331.i	−0.346584	+	0.346584i	0.512252	+	0.858835i	$0.328812\pi$
$90$			10637.4i			0.0145917i
$91$	635526.	−	305495.i	0.843352	−	0.405396i
$92$	−981141.			−1.25999
$93$	387977.	+	387977.i	0.482345	+	0.482345i
$94$	1.19259e6			1.43585
$95$		−	505348.i		−	0.589413i
$96$	796359.	+	796359.i	0.900109	+	0.900109i
$97$	417275.	+	417275.i	0.457201	+	0.457201i	0.897736	−	0.440535i	$-0.145211\pi$
$97$	417275.	+	417275.i	0.457201	+	0.457201i	−0.440535	+	0.897736i	$0.645211\pi$
$98$	−110931.	+	110931.i	−0.117862	+	0.117862i
$99$	−12826.7	+	12826.7i	−0.0132194	+	0.0132194i
$100$	440376.			0.440376
$101$			386382.i			0.375019i	0.982263	+	0.187509i	$0.0600415\pi$
$101$			386382.i			0.375019i	−0.982263	+	0.187509i	$0.939958\pi$
$102$	−305823.	+	305823.i	−0.288184	+	0.288184i
$103$			1.72164e6i			1.57554i	0.615968	+	0.787771i	$0.288765\pi$
$103$			1.72164e6i			1.57554i	−0.615968	+	0.787771i	$0.711235\pi$
$104$	−278474.	+	133862.i	−0.247563	+	0.119002i
$105$	717533.			0.619832
$106$	−237052.	−	237052.i	−0.199034	−	0.199034i
$107$	−1.34071e6			−1.09442			−0.547209	−	0.836996i	$-0.684310\pi$
$107$	−1.34071e6			−1.09442			−0.547209	+	0.836996i	$0.684310\pi$
$108$		−	1.00944e6i		−	0.801329i
$109$	−830199.	−	830199.i	−0.641066	−	0.641066i	0.309751	−	0.950818i	$-0.399754\pi$
$109$	−830199.	−	830199.i	−0.641066	−	0.641066i	−0.950818	+	0.309751i	$0.899754\pi$
$110$	−965449.	−	965449.i	−0.725356	−	0.725356i
$111$	479512.	−	479512.i	0.350615	−	0.350615i
$112$	−1.08110e6	+	1.08110e6i	−0.769502	+	0.769502i
$113$	1.71627e6			1.18946			0.594731	−	0.803925i	$-0.297258\pi$
$113$	1.71627e6			1.18946			0.594731	+	0.803925i	$0.297258\pi$
$114$			1.73740e6i			1.17270i
$115$	1.13837e6	−	1.13837e6i	0.748498	−	0.748498i
$116$		−	1.76134e6i		−	1.12842i
$117$	24646.3	+	8643.83i	0.0153884	+	0.00539695i
$118$	−398518.			−0.242550
$119$	−341981.	−	341981.i	−0.202937	−	0.202937i
$120$	−314408.			−0.181949
$121$		−	556751.i		−	0.314271i
$122$	−22400.7	−	22400.7i	−0.0123362	−	0.0123362i
$123$	1.93672e6	+	1.93672e6i	1.04076	+	1.04076i
$124$	−737138.	+	737138.i	−0.386620	+	0.386620i
$125$	−1.43333e6	+	1.43333e6i	−0.733863	+	0.733863i
$126$	40895.5			0.0204439
$127$		−	2.98167e6i		−	1.45562i	−0.685778	−	0.727811i	$-0.740538\pi$
$127$		−	2.98167e6i		−	1.45562i	0.685778	−	0.727811i	$-0.259462\pi$
$128$	797529.	−	797529.i	0.380291	−	0.380291i
$129$		−	3.28937e6i		−	1.53230i
$130$	−650607.	+	1.85508e6i	−0.296134	+	0.844372i
$131$	673122.			0.299419			0.149710	−	0.988730i	$-0.452166\pi$
$131$	673122.			0.299419			0.149710	+	0.988730i	$0.452166\pi$
$132$	1.47006e6	+	1.47006e6i	0.639166	+	0.639166i
$133$	−1.94281e6			−0.825802
$134$		−	3.48019e6i		−	1.44640i
$135$	1.17121e6	+	1.17121e6i	0.476029	+	0.476029i
$136$	149849.	+	149849.i	0.0595712	+	0.0595712i
$137$	−1.01973e6	+	1.01973e6i	−0.396574	+	0.396574i	−0.877023	−	0.480448i	$-0.840474\pi$
$137$	−1.01973e6	+	1.01973e6i	−0.396574	+	0.396574i	0.480448	+	0.877023i	$0.340474\pi$
$138$	−3.91375e6	+	3.91375e6i	−1.48921	+	1.48921i
$139$	−2.05635e6			−0.765689			−0.382845	−	0.923813i	$-0.625056\pi$
$139$	−2.05635e6			−0.765689			−0.382845	+	0.923813i	$0.625056\pi$
$140$			1.36328e6i			0.496821i
$141$	2.10694e6	−	2.10694e6i	0.751612	−	0.751612i
$142$		−	892514.i		−	0.311709i
$143$	−3.02141e6	+	1.45238e6i	−1.03324	+	0.496675i
$144$	−56629.9			−0.0189652
$145$	2.04360e6	+	2.04360e6i	0.670335	+	0.670335i
$146$	7.53547e6			2.42132
$147$			391959.i			0.123393i
$148$	911050.	+	911050.i	0.281033	+	0.281033i
$149$	3.58897e6	+	3.58897e6i	1.08495	+	1.08495i	0.996039	+	0.0889147i	$0.0283399\pi$
$149$	3.58897e6	+	3.58897e6i	1.08495	+	1.08495i	0.0889147	+	0.996039i	$0.471660\pi$
$150$	1.75665e6	−	1.75665e6i	0.520489	−	0.520489i
$151$	1.86528e6	−	1.86528e6i	0.541767	−	0.541767i	−0.382280	−	0.924047i	$-0.624861\pi$
$151$	1.86528e6	−	1.86528e6i	0.541767	−	0.541767i	0.924047	+	0.382280i	$0.124861\pi$
$152$	851300.			0.242411
$153$		−	17913.6i		−	0.00500160i
$154$	−3.71167e6	+	3.71167e6i	−1.01627	+	1.01627i
$155$		−	1.71053e6i		−	0.459343i
$156$	990660.	−	2.82468e6i	0.260946	−	0.744039i
$157$	−3.55477e6			−0.918570			−0.459285	−	0.888289i	$-0.651894\pi$
$157$	−3.55477e6			−0.918570			−0.459285	+	0.888289i	$0.651894\pi$
$158$	364133.	+	364133.i	0.0923185	+	0.0923185i
$159$	−837592.			−0.208373
$160$		−	3.51103e6i		−	0.857184i
$161$	−4.37647e6	−	4.37647e6i	−1.04869	−	1.04869i
$162$	−3.96097e6	−	3.96097e6i	−0.931659	−	0.931659i
$163$	−367883.	+	367883.i	−0.0849467	+	0.0849467i	−0.748303	−	0.663357i	$-0.769131\pi$
$163$	−367883.	+	367883.i	−0.0849467	+	0.0849467i	0.663357	+	0.748303i	$0.269131\pi$
$164$	−3.67968e6	+	3.67968e6i	−0.834216	+	0.834216i
$165$	−3.41129e6			−0.759392
$166$		−	6.23016e6i		−	1.36199i
$167$	−1.91720e6	+	1.91720e6i	−0.411641	+	0.411641i	−0.882310	−	0.470669i	$-0.844013\pi$
$167$	−1.91720e6	+	1.91720e6i	−0.411641	+	0.411641i	0.470669	+	0.882310i	$0.344013\pi$
$168$			1.20874e6i			0.254921i
$169$	3.76946e6	+	3.01485e6i	0.780941	+	0.624604i
$170$	1.34833e6			0.274441
$171$	−50884.2	−	50884.2i	−0.0101764	−	0.0101764i
$172$	6.24965e6			1.22820
$173$			5.74042e6i			1.10868i	0.832291	+	0.554339i	$0.187029\pi$
$173$			5.74042e6i			1.10868i	−0.832291	+	0.554339i	$0.812971\pi$
$174$	−7.02595e6	−	7.02595e6i	−1.33370	−	1.33370i
$175$	1.96434e6	+	1.96434e6i	0.366524	+	0.366524i
$176$	5.13973e6	−	5.13973e6i	0.942763	−	0.942763i
$177$	−704054.	+	704054.i	−0.126966	+	0.126966i
$178$	−3.70351e6			−0.656679
$179$			5.25653e6i			0.916516i	0.888819	+	0.458258i	$0.151527\pi$
$179$			5.25653e6i			0.916516i	−0.888819	+	0.458258i	$0.848473\pi$
$180$	−35705.6	+	35705.6i	−0.00612236	+	0.00612236i
$181$		−	2.92299e6i		−	0.492937i	−0.969151	−	0.246469i	$-0.920730\pi$
$181$		−	2.92299e6i		−	0.492937i	0.969151	−	0.246469i	$-0.0792702\pi$
$182$	7.13188e6	+	2.50126e6i	1.18301	+	0.414901i
$183$	−79150.0			−0.0129151
$184$	1.91768e6	+	1.91768e6i	0.307838	+	0.307838i
$185$	−2.11410e6			−0.333895
$186$			5.88086e6i			0.913907i
$187$	1.62584e6	+	1.62584e6i	0.248630	+	0.248630i
$188$	4.00308e6	+	4.00308e6i	0.602449	+	0.602449i
$189$	4.50272e6	−	4.50272e6i	0.666945	−	0.666945i
$190$	3.82997e6	−	3.82997e6i	0.558386	−	0.558386i
$191$	−2.82697e6			−0.405716			−0.202858	−	0.979208i	$-0.565023\pi$
$191$	−2.82697e6			−0.405716			−0.202858	+	0.979208i	$0.565023\pi$
$192$			3.90691e6i			0.551988i
$193$	2.02485e6	−	2.02485e6i	0.281657	−	0.281657i	−0.552113	−	0.833770i	$-0.686178\pi$
$193$	2.02485e6	−	2.02485e6i	0.281657	−	0.281657i	0.833770	+	0.552113i	$0.186178\pi$
$194$			6.32495e6i			0.866267i
$195$	2.12793e6	+	4.42676e6i	0.286981	+	0.597011i
$196$	−744704.			−0.0989043
$197$	−8.90467e6	−	8.90467e6i	−1.16471	−	1.16471i	−0.983431	−	0.181283i	$-0.941975\pi$
$197$	−8.90467e6	−	8.90467e6i	−1.16471	−	1.16471i	−0.181283	−	0.983431i	$-0.558025\pi$
$198$	−194425.			−0.0250470
$199$			7.50433e6i			0.952253i	0.879377	+	0.476127i	$0.157960\pi$
$199$			7.50433e6i			0.952253i	−0.879377	+	0.476127i	$0.842040\pi$
$200$	−860732.	−	860732.i	−0.107592	−	0.107592i
$201$	−6.14839e6	−	6.14839e6i	−0.757135	−	0.757135i
$202$	−2.92834e6	+	2.92834e6i	−0.355278	+	0.355278i
$203$	7.85663e6	−	7.85663e6i	0.939178	−	0.939178i
$204$	−2.05306e6			−0.241831
$205$		−	8.53872e6i		−	0.991132i
$206$	−1.30481e7	+	1.30481e7i	−1.49260	+	1.49260i
$207$		−	229248.i		−	0.0258461i
$208$	−9.87585e6	−	3.46362e6i	−1.09745	−	0.384893i
$209$	9.23649e6			1.01174
$210$	5.43809e6	+	5.43809e6i	0.587203	+	0.587203i
$211$	1.20767e7			1.28559			0.642795	−	0.766039i	$-0.277775\pi$
$211$	1.20767e7			1.28559			0.642795	+	0.766039i	$0.277775\pi$
$212$		−	1.59139e6i		−	0.167020i
$213$	−1.57679e6	−	1.57679e6i	−0.163168	−	0.163168i
$214$	−1.01611e7	−	1.01611e7i	−1.03681	−	1.03681i
$215$	−7.25117e6	+	7.25117e6i	−0.729613	+	0.729613i
$216$	−1.97300e6	+	1.97300e6i	−0.195779	+	0.195779i
$217$	−6.57615e6			−0.643566
$218$		−	1.25840e7i		−	1.21464i
$219$	1.33128e7	−	1.33128e7i	1.26747	−	1.26747i
$220$		−	6.48128e6i		−	0.608685i
$221$	1.09564e6	−	3.12401e6i	0.101506	−	0.289424i
$222$	7.26833e6			0.664317
$223$	1.39585e6	+	1.39585e6i	0.125871	+	0.125871i	0.767236	−	0.641365i	$-0.221632\pi$
$223$	1.39585e6	+	1.39585e6i	0.125871	+	0.125871i	−0.641365	+	0.767236i	$0.721632\pi$
$224$	−1.34982e7			−1.20097
$225$			102896.i			0.00903339i
$226$	1.30074e7	+	1.30074e7i	1.12685	+	1.12685i
$227$	3.97620e6	+	3.97620e6i	0.339931	+	0.339931i	0.856341	−	0.516410i	$-0.172732\pi$
$227$	3.97620e6	+	3.97620e6i	0.339931	+	0.339931i	−0.516410	+	0.856341i	$0.672732\pi$
$228$	−5.83178e6	+	5.83178e6i	−0.492036	+	0.492036i
$229$	−1.50029e6	+	1.50029e6i	−0.124931	+	0.124931i	−0.766808	−	0.641877i	$-0.778156\pi$
$229$	−1.50029e6	+	1.50029e6i	−0.124931	+	0.124931i	0.641877	+	0.766808i	$0.278156\pi$
$230$	1.72552e7			1.41819
$231$			1.31147e7i			1.06395i
$232$	−3.44261e6	+	3.44261e6i	−0.275692	+	0.275692i
$233$		−	1.00047e7i		−	0.790925i	−0.918482	−	0.395462i	$-0.870584\pi$
$233$		−	1.00047e7i		−	0.790925i	0.918482	−	0.395462i	$-0.129416\pi$
$234$	121280.	+	252301.i	0.00946549	+	0.0196912i
$235$	−9.28916e6			−0.715769
$236$	−1.33767e6	−	1.33767e6i	−0.101768	−	0.101768i
$237$	1.28662e6			0.0966504
$238$		−	5.18366e6i		−	0.384508i
$239$	1.28236e7	+	1.28236e7i	0.939328	+	0.939328i	0.998262	−	0.0589339i	$-0.0187701\pi$
$239$	1.28236e7	+	1.28236e7i	0.939328	+	0.939328i	−0.0589339	+	0.998262i	$0.518770\pi$
$240$	−7.53039e6	−	7.53039e6i	−0.544733	−	0.544733i
$241$	−1.66353e7	+	1.66353e7i	−1.18844	+	1.18844i	−0.210946	+	0.977498i	$0.567655\pi$
$241$	−1.66353e7	+	1.66353e7i	−1.18844	+	1.18844i	−0.977498	+	0.210946i	$0.932345\pi$
$242$	4.21954e6	−	4.21954e6i	0.297728	−	0.297728i
$243$	467938.			0.0326114
$244$		−	150381.i		−	0.0103520i
$245$	864045.	−	864045.i	0.0587541	−	0.0587541i
$246$			2.93564e7i			1.97195i
$247$	−5.76164e6	−	1.19860e7i	−0.382345	−	0.795398i
$248$	2.88153e6			0.188916
$249$	−1.10067e7	−	1.10067e7i	−0.712952	−	0.712952i
$250$	−2.17260e7			−1.39046
$251$		−	1.39680e7i		−	0.883310i	−0.897185	−	0.441655i	$-0.854392\pi$
$251$		−	1.39680e7i		−	0.883310i	0.897185	−	0.441655i	$-0.145608\pi$
$252$	137270.	+	137270.i	0.00857778	+	0.00857778i
$253$	2.08066e7	+	2.08066e7i	1.28481	+	1.28481i
$254$	2.25977e7	−	2.25977e7i	1.37900	−	1.37900i
$255$	2.38207e6	−	2.38207e6i	0.143659	−	0.143659i
$256$	2.14260e7			1.27709
$257$			2.30963e7i			1.36064i	0.732916	+	0.680319i	$0.238159\pi$
$257$			2.30963e7i			1.36064i	−0.732916	+	0.680319i	$0.761841\pi$
$258$	2.49297e7	−	2.49297e7i	1.45164	−	1.45164i
$259$			8.12766e6i			0.467806i
$260$	−8.41064e6	+	4.04296e6i	−0.478530	+	0.230028i
$261$	411546.			0.0231471
$262$	5.10151e6	+	5.10151e6i	0.283658	+	0.283658i
$263$	−3.02571e7			−1.66326			−0.831630	−	0.555329i	$-0.812592\pi$
$263$	−3.02571e7			−1.66326			−0.831630	+	0.555329i	$0.812592\pi$
$264$		−	5.74659e6i		−	0.312319i
$265$	1.84641e6	+	1.84641e6i	0.0992180	+	0.0992180i
$266$	−1.47243e7	−	1.47243e7i	−0.782331	−	0.782331i
$267$	−6.54292e6	+	6.54292e6i	−0.343746	+	0.343746i
$268$	1.16816e7	−	1.16816e7i	0.606876	−	0.606876i
$269$	5.40474e6			0.277663			0.138832	−	0.990316i	$-0.455665\pi$
$269$	5.40474e6			0.277663			0.138832	+	0.990316i	$0.455665\pi$
$270$			1.77529e7i			0.901942i
$271$	−7.80124e6	+	7.80124e6i	−0.391973	+	0.391973i	−0.875390	−	0.483417i	$-0.839395\pi$
$271$	−7.80124e6	+	7.80124e6i	−0.391973	+	0.391973i	0.483417	+	0.875390i	$0.339395\pi$
$272$			7.17806e6i			0.356698i
$273$	1.70187e7	−	8.18083e6i	0.836447	−	0.402077i
$274$	−1.54569e7			−0.751397
$275$	−9.33883e6	−	9.33883e6i	−0.449050	−	0.449050i
$276$	−2.62739e7			−1.24968
$277$		−	2.88491e7i		−	1.35735i	−0.734438	−	0.678676i	$-0.762554\pi$
$277$		−	2.88491e7i		−	1.35735i	0.734438	−	0.678676i	$-0.237446\pi$
$278$	−1.55848e7	−	1.55848e7i	−0.725383	−	0.725383i
$279$	−172236.	−	172236.i	−0.00793069	−	0.00793069i
$280$	2.66458e6	−	2.66458e6i	0.121382	−	0.121382i
$281$	−1.77577e7	+	1.77577e7i	−0.800328	+	0.800328i	−0.983147	−	0.182819i	$-0.941478\pi$
$281$	−1.77577e7	+	1.77577e7i	−0.800328	+	0.800328i	0.182819	+	0.983147i	$0.441478\pi$
$282$	3.19364e7			1.42409
$283$		−	2.27638e7i		−	1.00435i	−0.864766	−	0.502175i	$-0.832533\pi$
$283$		−	2.27638e7i		−	1.00435i	0.864766	−	0.502175i	$-0.167467\pi$
$284$	2.99582e6	−	2.99582e6i	0.130786	−	0.130786i
$285$		−	1.35327e7i		−	0.584587i
$286$	−3.39063e7	−	1.18915e7i	−1.44938	−	0.508320i
$287$	−3.28272e7			−1.38863
$288$	−353530.	−	353530.i	−0.0147996	−	0.0147996i
$289$	2.18670e7			0.905930
$290$			3.09764e7i			1.27010i
$291$	1.11742e7	+	1.11742e7i	0.453458	+	0.453458i
$292$	2.52937e7	+	2.52937e7i	1.01593	+	1.01593i
$293$	1.38173e7	−	1.38173e7i	0.549314	−	0.549314i	−0.376928	−	0.926242i	$-0.623020\pi$
$293$	1.38173e7	−	1.38173e7i	0.549314	−	0.549314i	0.926242	+	0.376928i	$0.123020\pi$
$294$	−2.97061e6	+	2.97061e6i	−0.116897	+	0.116897i
$295$	3.10407e6			0.120911
$296$		−	3.56137e6i		−	0.137323i
$297$	−2.14068e7	+	2.14068e7i	−0.817113	+	0.817113i
$298$			5.44008e7i			2.05568i
$299$	1.40214e7	−	3.99793e7i	0.524538	−	1.49562i
$300$	1.17928e7			0.436770
$301$	2.78772e7	+	2.78772e7i	1.02223	+	1.02223i
$302$	2.82734e7			1.02650
$303$			1.03469e7i			0.371949i
$304$	2.03895e7	+	2.03895e7i	0.725747	+	0.725747i
$305$	174480.	+	174480.i	0.00614960	+	0.00614960i
$306$	135765.	−	135765.i	0.00473831	−	0.00473831i
$307$	3.53325e7	−	3.53325e7i	1.22112	−	1.22112i	0.253890	−	0.967233i	$-0.418290\pi$
$307$	3.53325e7	−	3.53325e7i	1.22112	−	1.22112i	0.967233	−	0.253890i	$-0.0817101\pi$
$308$	−2.49173e7			−0.852803
$309$			4.61036e7i			1.56264i
$310$	1.29639e7	−	1.29639e7i	0.435162	−	0.435162i
$311$		−	2.33450e7i		−	0.776091i	−0.921640	−	0.388045i	$-0.873150\pi$
$311$		−	2.33450e7i		−	0.776091i	0.921640	−	0.388045i	$-0.126850\pi$
$312$	−7.45725e6	+	3.58467e6i	−0.245536	+	0.118028i
$313$	4.68746e6			0.152864			0.0764320	−	0.997075i	$-0.475647\pi$
$313$	4.68746e6			0.152864			0.0764320	+	0.997075i	$0.475647\pi$
$314$	−2.69412e7	−	2.69412e7i	−0.870216	−	0.870216i
$315$	−318537.			−0.0101913
$316$			2.44451e6i			0.0774694i
$317$	1.08194e7	+	1.08194e7i	0.339646	+	0.339646i	0.856234	−	0.516588i	$-0.172798\pi$
$317$	1.08194e7	+	1.08194e7i	0.339646	+	0.339646i	−0.516588	+	0.856234i	$0.672798\pi$
$318$	−6.34801e6	−	6.34801e6i	−0.197404	−	0.197404i
$319$	−3.73519e7	+	3.73519e7i	−1.15064	+	1.15064i
$320$	8.61249e6	−	8.61249e6i	0.262832	−	0.262832i
$321$	−3.59028e7			−1.08546
$322$		−	6.63375e7i		−	1.98697i
$323$	−6.44976e6	+	6.44976e6i	−0.191397	+	0.191397i
$324$		−	2.65909e7i		−	0.781805i
$325$	−6.29335e6	+	1.79443e7i	−0.183329	+	0.522729i
$326$	−5.57628e6			−0.160950
$327$	−2.22319e7	−	2.22319e7i	−0.635818	−	0.635818i
$328$	1.43842e7			0.407628
$329$			3.57122e7i			1.00283i
$330$	−2.58537e7	−	2.58537e7i	−0.719417	−	0.719417i
$331$	−2.31847e7	−	2.31847e7i	−0.639319	−	0.639319i	0.311068	−	0.950388i	$-0.399313\pi$
$331$	−2.31847e7	−	2.31847e7i	−0.639319	−	0.639319i	−0.950388	+	0.311068i	$0.899313\pi$
$332$	2.09122e7	−	2.09122e7i	0.571461	−	0.571461i
$333$	−212871.	+	212871.i	−0.00576480	+	0.00576480i
$334$	−2.90605e7			−0.779944
$335$			2.71073e7i			0.721029i
$336$	−2.89506e7	+	2.89506e7i	−0.763202	+	0.763202i
$337$		−	4.41611e7i		−	1.15385i	−0.816796	−	0.576926i	$-0.804252\pi$
$337$		−	4.41611e7i		−	1.15385i	0.816796	−	0.576926i	$-0.195748\pi$
$338$	5.71910e6	+	5.14174e7i	0.148108	+	1.33156i
$339$	4.59600e7			1.17972
$340$	4.52582e6	+	4.52582e6i	0.115149	+	0.115149i
$341$	3.12643e7			0.788470
$342$		−	771289.i		−	0.0192814i
$343$	−3.00222e7	−	3.00222e7i	−0.743978	−	0.743978i
$344$	−1.22152e7	−	1.22152e7i	−0.300072	−	0.300072i
$345$	3.04844e7	−	3.04844e7i	0.742370	−	0.742370i
$346$	−4.35060e7	+	4.35060e7i	−1.05032	+	1.05032i
$347$	3.10492e7			0.743125			0.371563	−	0.928408i	$-0.378822\pi$
$347$	3.10492e7			0.743125			0.371563	+	0.928408i	$0.378822\pi$
$348$		−	4.71668e7i		−	1.11918i
$349$	2.34300e7	−	2.34300e7i	0.551182	−	0.551182i	−0.375600	−	0.926782i	$-0.622563\pi$
$349$	2.34300e7	−	2.34300e7i	0.551182	−	0.551182i	0.926782	+	0.375600i	$0.122563\pi$
$350$			2.97750e7i			0.694460i
$351$	4.11326e7	+	1.44258e7i	0.951184	+	0.333595i
$352$	6.41728e7			1.47137
$353$	2.38002e7	+	2.38002e7i	0.541073	+	0.541073i	0.923843	−	0.382771i	$-0.125030\pi$
$353$	2.38002e7	+	2.38002e7i	0.541073	+	0.541073i	−0.382771	+	0.923843i	$0.625030\pi$
$354$	−1.06719e7			−0.240564
$355$			6.95183e6i			0.155387i
$356$	−1.24312e7	−	1.24312e7i	−0.275527	−	0.275527i
$357$	−9.15788e6	−	9.15788e6i	−0.201275	−	0.201275i
$358$	−3.98386e7	+	3.98386e7i	−0.868271	+	0.868271i
$359$	8.33411e6	−	8.33411e6i	0.180126	−	0.180126i	−0.611285	−	0.791411i	$-0.709347\pi$
$359$	8.33411e6	−	8.33411e6i	0.180126	−	0.180126i	0.791411	+	0.611285i	$0.209347\pi$
$360$	139576.			0.00299160
$361$		−	1.04044e7i		−	0.221154i
$362$	2.21530e7	−	2.21530e7i	0.466989	−	0.466989i
$363$		−	1.49092e7i		−	0.311698i
$364$	1.55432e7	+	3.23347e7i	0.322282	+	0.670448i
$365$	−5.86941e7			−1.20702
$366$	−599868.	−	599868.i	−0.0122352	−	0.0122352i
$367$	−6.65880e6			−0.134709			−0.0673547	−	0.997729i	$-0.521456\pi$
$367$	−6.65880e6			−0.134709			−0.0673547	+	0.997729i	$0.521456\pi$
$368$			9.18607e7i			1.84326i
$369$	−859775.	−	859775.i	−0.0171122	−	0.0171122i
$370$	−1.60225e7	−	1.60225e7i	−0.316319	−	0.316319i
$371$	7.09853e6	−	7.09853e6i	0.139010	−	0.139010i
$372$	−1.97398e7	+	1.97398e7i	−0.383454	+	0.383454i
$373$	−8.65202e7			−1.66721			−0.833606	−	0.552359i	$-0.813728\pi$
$373$	−8.65202e7			−1.66721			−0.833606	+	0.552359i	$0.813728\pi$
$374$			2.46441e7i			0.471083i
$375$	−3.83829e7	+	3.83829e7i	−0.727854	+	0.727854i
$376$		−	1.56484e7i		−	0.294378i
$377$	7.17706e7	+	2.51711e7i	1.33944	+	0.469762i
$378$	6.82512e7			1.26367
$379$	2.61552e7	+	2.61552e7i	0.480441	+	0.480441i	0.905272	−	0.424831i	$-0.139667\pi$
$379$	2.61552e7	+	2.61552e7i	0.480441	+	0.480441i	−0.424831	+	0.905272i	$0.639667\pi$
$380$	2.57115e7			0.468571
$381$		−	7.98460e7i		−	1.44370i
$382$	−2.14253e7	−	2.14253e7i	−0.384359	−	0.384359i
$383$	1.10676e7	+	1.10676e7i	0.196996	+	0.196996i	0.798711	−	0.601715i	$-0.205516\pi$
$383$	1.10676e7	+	1.10676e7i	0.196996	+	0.196996i	−0.601715	+	0.798711i	$0.705516\pi$
$384$	2.13570e7	−	2.13570e7i	0.377178	−	0.377178i
$385$	2.89104e7	−	2.89104e7i	0.506607	−	0.506607i
$386$	3.06921e7			0.533661
$387$			1.46026e6i			0.0251940i
$388$	−2.12304e7	+	2.12304e7i	−0.363466	+	0.363466i
$389$			8.76405e6i			0.148887i	0.997225	+	0.0744434i	$0.0237180\pi$
$389$			8.76405e6i			0.148887i	−0.997225	+	0.0744434i	$0.976282\pi$
$390$	−1.74226e7	+	4.96772e7i	−0.293710	+	0.837459i
$391$	−2.90581e7			−0.486113
$392$	1.45555e6	+	1.45555e6i	0.0241641	+	0.0241641i
$393$	1.80255e7			0.296968
$394$		−	1.34975e8i		−	2.20681i
$395$	−2.83625e6	−	2.83625e6i	−0.0460207	−	0.0460207i
$396$	−652609.	−	652609.i	−0.0105091	−	0.0105091i
$397$	−5.90667e7	+	5.90667e7i	−0.943998	+	0.943998i	−0.998513	−	0.0545150i	$-0.982639\pi$
$397$	−5.90667e7	+	5.90667e7i	−0.943998	+	0.943998i	0.0545150	+	0.998513i	$0.482639\pi$
$398$	−5.68744e7	+	5.68744e7i	−0.902126	+	0.902126i
$399$	−5.20265e7			−0.819041
$400$		−	4.12308e7i		−	0.644231i
$401$	8.06645e6	−	8.06645e6i	0.125098	−	0.125098i	−0.641786	−	0.766884i	$-0.721806\pi$
$401$	8.06645e6	−	8.06645e6i	0.125098	−	0.125098i	0.766884	+	0.641786i	$0.221806\pi$
$402$		−	9.31958e7i		−	1.43456i
$403$	−1.95024e7	−	4.05711e7i	−0.297970	−	0.619871i
$404$	−1.96586e7			−0.298133
$405$	3.08522e7	+	3.08522e7i	0.464431	+	0.464431i
$406$	1.19089e8			1.77948
$407$		−	3.86404e7i		−	0.573137i
$408$	4.01279e6	+	4.01279e6i	0.0590835	+	0.0590835i
$409$	2.51714e7	+	2.51714e7i	0.367907	+	0.367907i	0.866713	−	0.498807i	$-0.166228\pi$
$409$	2.51714e7	+	2.51714e7i	0.367907	+	0.367907i	−0.498807	+	0.866713i	$0.666228\pi$
$410$	6.47139e7	−	6.47139e7i	0.938958	−	0.938958i
$411$	−2.73074e7	+	2.73074e7i	−0.393328	+	0.393328i
$412$	−8.75947e7			−1.25252
$413$		−	1.19336e7i		−	0.169403i
$414$	1.73744e6	−	1.73744e6i	0.0244856	−	0.0244856i
$415$			4.85270e7i			0.678952i
$416$	−4.00304e7	−	8.32758e7i	−0.556045	−	1.15675i
$417$	−5.50669e7			−0.759421
$418$	7.00022e7	+	7.00022e7i	0.958480	+	0.958480i
$419$	−9.44795e6			−0.128439			−0.0642193	−	0.997936i	$-0.520456\pi$
$419$	−9.44795e6			−0.128439			−0.0642193	+	0.997936i	$0.520456\pi$
$420$			3.65071e7i			0.492754i
$421$	−2.21073e7	−	2.21073e7i	−0.296272	−	0.296272i	0.543280	−	0.839552i	$-0.317182\pi$
$421$	−2.21073e7	−	2.21073e7i	−0.296272	−	0.296272i	−0.839552	+	0.543280i	$0.817182\pi$
$422$	9.15281e7	+	9.15281e7i	1.21792	+	1.21792i
$423$	−935338.	+	935338.i	−0.0123580	+	0.0123580i
$424$	−3.11043e6	+	3.11043e6i	−0.0408059	+	0.0408059i
$425$	1.30424e7			0.169900
$426$		−	2.39006e7i		−	0.309157i
$427$	670790.	−	670790.i	0.00861595	−	0.00861595i
$428$		−	6.82135e7i		−	0.870040i
$429$	−8.09101e7	+	3.88932e7i	−1.02478	+	0.492609i
$430$	−1.09911e8			−1.38241
$431$	−2.99941e7	−	2.99941e7i	−0.374631	−	0.374631i	0.494530	−	0.869161i	$-0.335340\pi$
$431$	−2.99941e7	−	2.99941e7i	−0.374631	−	0.374631i	−0.869161	+	0.494530i	$0.835340\pi$
$432$	−9.45107e7			−1.17228
$433$			4.58030e7i			0.564196i	0.959386	+	0.282098i	$0.0910304\pi$
$433$			4.58030e7i			0.564196i	−0.959386	+	0.282098i	$0.908970\pi$
$434$	−4.98399e7	−	4.98399e7i	−0.609688	−	0.609688i
$435$	5.47254e7	+	5.47254e7i	0.664847	+	0.664847i
$436$	4.22395e7	−	4.22395e7i	0.509635	−	0.509635i
$437$	−8.25404e7	+	8.25404e7i	−0.989059	+	0.989059i
$438$	2.01792e8			2.40150
$439$			3.19412e7i			0.377536i	0.982022	+	0.188768i	$0.0604494\pi$
$439$			3.19412e7i			0.377536i	−0.982022	+	0.188768i	$0.939551\pi$
$440$	−1.26679e7	+	1.26679e7i	−0.148713	+	0.148713i
$441$		−	174004.i		−	0.00202882i
$442$	3.19802e7	−	1.53728e7i	0.370351	−	0.178027i
$443$	3.61373e7			0.415666			0.207833	−	0.978164i	$-0.433359\pi$
$443$	3.61373e7			0.415666			0.207833	+	0.978164i	$0.433359\pi$
$444$	2.43970e7	+	2.43970e7i	0.278732	+	0.278732i
$445$	2.88468e7			0.327354
$446$			2.11580e7i			0.238490i
$447$	9.61089e7	+	9.61089e7i	1.07607	+	1.07607i
$448$	−3.31107e7	−	3.31107e7i	−0.368243	−	0.368243i
$449$	8.98341e7	−	8.98341e7i	0.992436	−	0.992436i	−0.00753584	−	0.999972i	$-0.502399\pi$
$449$	8.98341e7	−	8.98341e7i	0.992436	−	0.992436i	0.999972	+	0.00753584i	$0.00239876\pi$
$450$	−779835.	+	779835.i	−0.00855786	+	0.00855786i
$451$	1.56066e8			1.70130
$452$			8.73217e7i			0.945599i
$453$	4.99502e7	−	4.99502e7i	0.537331	−	0.537331i
$454$			6.02703e7i			0.644074i
$455$	−5.55505e7	−	1.94824e7i	−0.589731	−	0.206828i
$456$	2.27969e7			0.240426
$457$	−7.00089e7	−	7.00089e7i	−0.733507	−	0.733507i	0.237806	−	0.971313i	$-0.423572\pi$
$457$	−7.00089e7	−	7.00089e7i	−0.733507	−	0.733507i	−0.971313	+	0.237806i	$0.923572\pi$
$458$	−2.27410e7			−0.236708
$459$		−	2.98964e7i		−	0.309158i
$460$	5.79189e7	+	5.79189e7i	0.595041	+	0.595041i
$461$	3.59349e7	+	3.59349e7i	0.366787	+	0.366787i	0.866304	−	0.499517i	$-0.166489\pi$
$461$	3.59349e7	+	3.59349e7i	0.366787	+	0.366787i	−0.499517	+	0.866304i	$0.666489\pi$
$462$	−9.93947e7	+	9.93947e7i	−1.00795	+	1.00795i
$463$	−1.69301e7	+	1.69301e7i	−0.170576	+	0.170576i	−0.787232	−	0.616657i	$-0.788487\pi$
$463$	−1.69301e7	+	1.69301e7i	−0.170576	+	0.170576i	0.616657	+	0.787232i	$0.288487\pi$
$464$	−1.64908e8			−1.65077
$465$		−	4.58063e7i		−	0.455582i
$466$	7.58242e7	−	7.58242e7i	0.749290	−	0.749290i
$467$			1.42553e7i			0.139967i	0.997548	+	0.0699835i	$0.0222947\pi$
$467$			1.42553e7i			0.139967i	−0.997548	+	0.0699835i	$0.977705\pi$
$468$	−439787.	+	1.25397e6i	−0.00429047	+	0.0122335i
$469$	1.04214e8			1.01020
$470$	−7.04014e7	−	7.04014e7i	−0.678091	−	0.678091i
$471$	−9.51930e7			−0.911050
$472$			5.22906e6i			0.0497276i
$473$	−1.32533e8	−	1.32533e8i	−1.25240	−	1.25240i
$474$	9.75110e6	+	9.75110e6i	0.0915627	+	0.0915627i
$475$	3.70475e7	−	3.70475e7i	0.345683	−	0.345683i
$476$	1.73995e7	−	1.73995e7i	0.161331	−	0.161331i
$477$	371835.			0.00342606
$478$			1.94377e8i			1.77976i
$479$	6.01971e7	−	6.01971e7i	0.547733	−	0.547733i	−0.378051	−	0.925785i	$-0.623406\pi$
$479$	6.01971e7	−	6.01971e7i	0.547733	−	0.547733i	0.925785	+	0.378051i	$0.123406\pi$
$480$		−	9.40216e7i		−	0.850166i
$481$	−5.01430e7	+	2.41036e7i	−0.450583	+	0.216594i
$482$	−2.52153e8			−2.25177
$483$	−1.17197e8	−	1.17197e8i	−1.04010	−	1.04010i
$484$	2.83268e7			0.249839
$485$		−	4.92653e7i		−	0.431833i
$486$	3.54645e6	+	3.54645e6i	0.0308948	+	0.0308948i
$487$	477050.	+	477050.i	0.00413026	+	0.00413026i	0.709169	−	0.705039i	$-0.249070\pi$
$487$	477050.	+	477050.i	0.00413026	+	0.00413026i	−0.705039	+	0.709169i	$0.749070\pi$
$488$	−293926.	+	293926.i	−0.00252918	+	0.00252918i
$489$	−9.85151e6	+	9.85151e6i	−0.0842512	+	0.0842512i
$490$	1.30970e7			0.111322
$491$		−	4.45000e7i		−	0.375937i	−0.982175	−	0.187969i	$-0.939810\pi$
$491$		−	4.45000e7i		−	0.375937i	0.982175	−	0.187969i	$-0.0601904\pi$
$492$	−9.85380e7	+	9.85380e7i	−0.827386	+	0.827386i
$493$		−	5.21650e7i		−	0.435350i
$494$	4.71739e7	−	1.34507e8i	0.391310	−	1.11575i
$495$	1.51438e6			0.0124859
$496$	6.90156e7	+	6.90156e7i	0.565591	+	0.565591i
$497$	2.67263e7			0.217706
$498$		−	1.66837e8i		−	1.35084i
$499$	9.09143e7	+	9.09143e7i	0.731695	+	0.731695i	0.970956	−	0.239260i	$-0.0769048\pi$
$499$	9.09143e7	+	9.09143e7i	0.731695	+	0.731695i	−0.239260	+	0.970956i	$0.576905\pi$
$500$	−7.29258e7	−	7.29258e7i	−0.583406	−	0.583406i
$501$	−5.13407e7	+	5.13407e7i	−0.408271	+	0.408271i
$502$	1.05862e8	−	1.05862e8i	0.836812	−	0.836812i
$503$	1.02124e8			0.802462			0.401231	−	0.915977i	$-0.368583\pi$
$503$	1.02124e8			0.802462			0.401231	+	0.915977i	$0.368583\pi$
$504$		−	536601.i		−	0.00419141i
$505$	2.28090e7	−	2.28090e7i	0.177106	−	0.177106i
$506$			3.15381e8i			2.43436i
$507$	1.00942e8	+	8.07344e7i	0.774548	+	0.619490i
$508$	1.51704e8			1.15719
$509$	6.78573e7	+	6.78573e7i	0.514569	+	0.514569i	0.915923	−	0.401354i	$-0.131460\pi$
$509$	6.78573e7	+	6.78573e7i	0.514569	+	0.514569i	−0.401354	+	0.915923i	$0.631460\pi$
$510$	3.61068e7			0.272194
$511$			2.25650e8i			1.69111i
$512$	1.11343e8	+	1.11343e8i	0.829572	+	0.829572i
$513$	−8.49215e7	−	8.49215e7i	−0.629022	−	0.629022i
$514$	−1.75044e8	+	1.75044e8i	−1.28901	+	1.28901i
$515$	1.01632e8	−	1.01632e8i	0.744062	−	0.744062i
$516$	1.67359e8			1.21815
$517$		−	1.69783e8i		−	1.22863i
$518$	−6.15985e7	+	6.15985e7i	−0.443181	+	0.443181i
$519$			1.53722e8i			1.09960i
$520$	2.43411e7	+	8.53680e6i	0.173113	+	0.0607135i
$521$	2.12858e8			1.50514			0.752570	−	0.658512i	$-0.228814\pi$
$521$	2.12858e8			1.50514			0.752570	+	0.658512i	$0.228814\pi$
$522$	3.11905e6	+	3.11905e6i	0.0219286	+	0.0219286i
$523$	−2.19853e8			−1.53684			−0.768419	−	0.639947i	$-0.778956\pi$
$523$	−2.19853e8			−1.53684			−0.768419	+	0.639947i	$0.778956\pi$
$524$			3.42476e7i			0.238032i
$525$	5.26029e7	+	5.26029e7i	0.363523	+	0.363523i
$526$	−2.29315e8	−	2.29315e8i	−1.57571	−	1.57571i
$527$	−2.18316e7	+	2.18316e7i	−0.149160	+	0.149160i
$528$	1.37637e8	−	1.37637e8i	0.935044	−	0.935044i
$529$	−2.23833e8			−1.51202
$530$			2.79874e7i			0.187990i
$531$	312553.	−	312553.i	0.00208757	−	0.00208757i
$532$		−	9.88478e7i		−	0.656496i
$533$	−9.73529e7	−	2.02525e8i	−0.642935	−	1.33751i
$534$	−9.91760e7			−0.651303
$535$	7.91450e7	+	7.91450e7i	0.516847	+	0.516847i
$536$	−4.56645e7			−0.296541
$537$			1.40764e8i			0.909013i
$538$	4.09619e7	+	4.09619e7i	0.263047	+	0.263047i
$539$	1.57926e7	+	1.57926e7i	0.100852	+	0.100852i
$540$	−5.95897e7	+	5.95897e7i	−0.378434	+	0.378434i
$541$	2.90497e7	−	2.90497e7i	0.183464	−	0.183464i	−0.609400	−	0.792863i	$-0.708589\pi$
$541$	2.90497e7	−	2.90497e7i	0.183464	−	0.183464i	0.792863	+	0.609400i	$0.208589\pi$
$542$	−1.18249e8			−0.742678
$543$		−	7.82746e7i		−	0.488901i
$544$	−4.48113e7	+	4.48113e7i	−0.278350	+	0.278350i
$545$			9.80170e7i			0.605497i
$546$	1.90984e8	+	6.69812e7i	1.17333	+	0.411505i
$547$	7.53180e7			0.460189			0.230095	−	0.973168i	$-0.426096\pi$
$547$	7.53180e7			0.460189			0.230095	+	0.973168i	$0.426096\pi$
$548$	−5.18827e7	−	5.18827e7i	−0.315269	−	0.315269i
$549$	35137.3			0.000212350
$550$		−	1.41556e8i		−	0.850823i
$551$	−1.48176e8	−	1.48176e8i	−0.885775	−	0.885775i
$552$	5.13535e7	+	5.13535e7i	0.305318	+	0.305318i
$553$	−1.09040e7	+	1.09040e7i	−0.0644776	+	0.0644776i
$554$	2.18644e8	−	2.18644e8i	1.28590	−	1.28590i
$555$	−5.66133e7			−0.331161
$556$		−	1.04624e8i		−	0.608708i
$557$	−8.76993e7	+	8.76993e7i	−0.507493	+	0.507493i	−0.913756	−	0.406263i	$-0.866832\pi$
$557$	−8.76993e7	+	8.76993e7i	−0.507493	+	0.507493i	0.406263	+	0.913756i	$0.366832\pi$
$558$		−	2.61071e6i		−	0.0150264i
$559$	−8.93129e7	+	2.54659e8i	−0.511304	+	1.45789i
$560$	1.27639e8			0.726807
$561$	4.35383e7	+	4.35383e7i	0.246594	+	0.246594i
$562$	−2.69167e8			−1.51640
$563$			1.67475e8i			0.938479i	0.883071	+	0.469240i	$0.155472\pi$
$563$			1.67475e8i			0.938479i	−0.883071	+	0.469240i	$0.844528\pi$
$564$	1.07198e8	+	1.07198e8i	0.597517	+	0.597517i
$565$	−1.01315e8	−	1.01315e8i	−0.561733	−	0.561733i
$566$	1.72524e8	−	1.72524e8i	0.951480	−	0.951480i
$567$	1.18611e8	−	1.18611e8i	0.650694	−	0.650694i
$568$	−1.17109e7			−0.0639067
$569$			1.19766e8i			0.650123i	0.945693	+	0.325061i	$0.105385\pi$
$569$			1.19766e8i			0.650123i	−0.945693	+	0.325061i	$0.894615\pi$
$570$	1.02563e8	−	1.02563e8i	0.553814	−	0.553814i
$571$		−	2.90574e7i		−	0.156081i	−0.996950	−	0.0780403i	$-0.975134\pi$
$571$		−	2.90574e7i		−	0.156081i	0.996950	−	0.0780403i	$-0.0248663\pi$
$572$	−7.38952e7	−	1.53725e8i	−0.394847	−	0.821405i
$573$	−7.57034e7			−0.402394
$574$	−2.48793e8	−	2.48793e8i	−1.31553	−	1.31553i
$575$	1.66910e8			0.877968
$576$		−	1.73441e6i		−	0.00907576i
$577$	−6.36575e7	−	6.36575e7i	−0.331377	−	0.331377i	0.521732	−	0.853109i	$-0.325286\pi$
$577$	−6.36575e7	−	6.36575e7i	−0.331377	−	0.331377i	−0.853109	+	0.521732i	$0.825286\pi$
$578$	1.65727e8	+	1.65727e8i	0.858241	+	0.858241i
$579$	5.42233e7	−	5.42233e7i	0.279351	−	0.279351i
$580$	−1.03976e8	+	1.03976e8i	−0.532903	+	0.532903i
$581$	1.86562e8			0.951252
$582$			1.69376e8i			0.859175i
$583$	−3.37477e7	+	3.37477e7i	−0.170310	+	0.170310i
$584$		−	9.88751e7i		−	0.496419i
$585$	−944658.	−	1.96519e6i	−0.00471854	−	0.00981604i
$586$	2.09439e8			1.04080
$587$	−1.47686e8	−	1.47686e8i	−0.730172	−	0.730172i	0.240482	−	0.970654i	$-0.422695\pi$
$587$	−1.47686e8	−	1.47686e8i	−0.730172	−	0.730172i	−0.970654	+	0.240482i	$0.922695\pi$
$588$	−1.99424e7			−0.0980946
$589$			1.24026e8i			0.606972i
$590$	2.35254e7	+	2.35254e7i	0.114546	+	0.114546i
$591$	−2.38458e8	−	2.38458e8i	−1.15518	−	1.15518i
$592$	8.52984e7	−	8.52984e7i	0.411127	−	0.411127i
$593$	−4.33390e7	+	4.33390e7i	−0.207833	+	0.207833i	−0.803346	−	0.595513i	$-0.796949\pi$
$593$	−4.33390e7	+	4.33390e7i	−0.207833	+	0.207833i	0.595513	+	0.803346i	$0.296949\pi$
$594$	−3.24479e8			−1.54820
$595$			4.03757e7i			0.191677i
$596$	−1.82602e8	+	1.82602e8i	−0.862517	+	0.862517i
$597$			2.00958e8i			0.944457i
$598$	4.09264e8	−	1.96732e8i	1.91382	−	0.919965i
$599$	−2.22396e8			−1.03477			−0.517387	−	0.855751i	$-0.673095\pi$
$599$	−2.22396e8			−1.03477			−0.517387	+	0.855751i	$0.673095\pi$
$600$	−2.30495e7	−	2.30495e7i	−0.106711	−	0.106711i
$601$	−2.60139e8			−1.19835			−0.599173	−	0.800620i	$-0.704504\pi$
$601$	−2.60139e8			−1.19835			−0.599173	+	0.800620i	$0.704504\pi$
$602$			4.22555e8i			1.93684i
$603$	2.72947e6	+	2.72947e6i	0.0124488	+	0.0124488i
$604$	9.49029e7	+	9.49029e7i	0.430694	+	0.430694i
$605$	−3.28662e7	+	3.28662e7i	−0.148417	+	0.148417i
$606$	−7.84180e7	+	7.84180e7i	−0.352369	+	0.352369i
$607$	4.04305e8			1.80777			0.903884	−	0.427778i	$-0.140704\pi$
$607$	4.04305e8			1.80777			0.903884	+	0.427778i	$0.140704\pi$
$608$			2.54576e8i			1.13268i
$609$	2.10392e8	−	2.10392e8i	0.931489	−	0.931489i
$610$			2.64473e6i			0.0116518i
$611$	−2.20324e8	+	1.05909e8i	−0.965913	+	0.464311i
$612$	911422.			0.00397617
$613$	1.29644e8	+	1.29644e8i	0.562820	+	0.562820i	0.930107	−	0.367288i	$-0.119714\pi$
$613$	1.29644e8	+	1.29644e8i	0.562820	+	0.562820i	−0.367288	+	0.930107i	$0.619714\pi$
$614$	5.35562e8			2.31369
$615$		−	2.28658e8i		−	0.983017i
$616$	4.87019e7	+	4.87019e7i	0.208355	+	0.208355i
$617$	1.27030e8	+	1.27030e8i	0.540818	+	0.540818i	0.923769	−	0.382951i	$-0.125092\pi$
$617$	1.27030e8	+	1.27030e8i	0.540818	+	0.540818i	−0.382951	+	0.923769i	$0.625092\pi$
$618$	−3.49414e8	+	3.49414e8i	−1.48038	+	1.48038i
$619$	−1.21031e8	+	1.21031e8i	−0.510300	+	0.510300i	−0.914618	−	0.404318i	$-0.867509\pi$
$619$	−1.21031e8	+	1.21031e8i	−0.510300	+	0.510300i	0.404318	+	0.914618i	$0.367509\pi$
$620$	8.70298e7			0.365168
$621$		−	3.82597e8i		−	1.59759i
$622$	1.76929e8	−	1.76929e8i	0.735237	−	0.735237i
$623$		−	1.10902e8i		−	0.458642i
$624$	−2.64465e8	−	9.27520e7i	−1.08846	−	0.381742i
$625$	3.39841e7			0.139199
$626$	3.55257e7	+	3.55257e7i	0.144817	+	0.144817i
$627$	2.47344e8			1.00346
$628$		−	1.80862e8i		−	0.730245i
$629$	2.69823e7	+	2.69823e7i	0.108424	+	0.108424i
$630$	−2.41415e6	−	2.41415e6i	−0.00965478	−	0.00965478i
$631$	2.73690e8	−	2.73690e8i	1.08936	−	1.08936i	0.0937662	−	0.995594i	$-0.470109\pi$
$631$	2.73690e8	−	2.73690e8i	1.08936	−	1.08936i	0.995594	−	0.0937662i	$-0.0298906\pi$
$632$	4.77789e6	−	4.77789e6i	0.0189271	−	0.0189271i
$633$	3.23402e8			1.27506
$634$			1.63998e8i			0.643534i
$635$	−1.76015e8	+	1.76015e8i	−0.687428	+	0.687428i
$636$		−	4.26156e7i		−	0.165652i
$637$	1.06425e7	−	3.03450e7i	0.0411741	−	0.117400i
$638$	−5.66170e8			−2.18014
$639$	699989.	+	699989.i	0.00268280	+	0.00268280i
$640$	−9.41598e7			−0.359191
$641$			5.16969e7i			0.196286i	0.995172	+	0.0981432i	$0.0312903\pi$
$641$			5.16969e7i			0.196286i	−0.995172	+	0.0981432i	$0.968710\pi$
$642$	−2.72103e8	−	2.72103e8i	−1.02832	−	1.02832i
$643$	3.00222e7	+	3.00222e7i	0.112930	+	0.112930i	0.761314	−	0.648384i	$-0.224555\pi$
$643$	3.00222e7	+	3.00222e7i	0.112930	+	0.112930i	−0.648384	+	0.761314i	$0.724555\pi$
$644$	2.22669e8	−	2.22669e8i	0.833687	−	0.833687i
$645$	−1.94179e8	+	1.94179e8i	−0.723640	+	0.723640i
$646$	−9.77639e7			−0.362644
$647$		−	1.57925e8i		−	0.583094i	−0.956557	−	0.291547i	$-0.905830\pi$
$647$		−	1.57925e8i		−	0.583094i	0.956557	−	0.291547i	$-0.0941699\pi$
$648$	−5.19730e7	+	5.19730e7i	−0.191009	+	0.191009i
$649$			5.67346e7i			0.207546i
$650$	−1.83694e8	+	8.83012e7i	−0.668891	+	0.321534i
$651$	−1.76102e8			−0.638297
$652$	−1.87174e7	−	1.87174e7i	−0.0675309	−	0.0675309i
$653$	2.73657e8			0.982804			0.491402	−	0.870933i	$-0.336485\pi$
$653$	2.73657e8			0.982804			0.491402	+	0.870933i	$0.336485\pi$
$654$		−	3.36985e8i		−	1.20470i
$655$	−3.97359e7	−	3.97359e7i	−0.141403	−	0.141403i
$656$	3.44516e8	+	3.44516e8i	1.22039	+	1.22039i
$657$	−5.90999e6	+	5.90999e6i	−0.0208397	+	0.0208397i
$658$	−2.70659e8	+	2.70659e8i	−0.950045	+	0.950045i
$659$	−4.27581e8			−1.49404			−0.747019	−	0.664803i	$-0.768516\pi$
$659$	−4.27581e8			−1.49404			−0.747019	+	0.664803i	$0.768516\pi$
$660$		−	1.73562e8i		−	0.603702i
$661$	1.22478e8	−	1.22478e8i	0.424086	−	0.424086i	−0.462522	−	0.886608i	$-0.653055\pi$
$661$	1.22478e8	−	1.22478e8i	0.424086	−	0.424086i	0.886608	+	0.462522i	$0.153055\pi$
$662$		−	3.51428e8i		−	1.21133i
$663$	2.93400e7	−	8.36576e7i	0.100675	−	0.287055i
$664$	−8.17477e7			−0.279236
$665$	1.14688e8	+	1.14688e8i	0.389991	+	0.389991i
$666$	−3.22665e6			−0.0109227
$667$		−	6.67578e8i		−	2.24970i
$668$	−9.75448e7	−	9.75448e7i	−0.327246	−	0.327246i
$669$	3.73795e7	+	3.73795e7i	0.124840	+	0.124840i
$670$	−2.05443e8	+	2.05443e8i	−0.683073	+	0.683073i
$671$	−3.18906e6	+	3.18906e6i	−0.0105559	+	0.0105559i
$672$	−3.61466e8			−1.19113
$673$			5.75888e8i			1.88926i	0.328132	+	0.944632i	$0.393581\pi$
$673$			5.75888e8i			1.88926i	−0.328132	+	0.944632i	$0.606419\pi$
$674$	3.34692e8	−	3.34692e8i	1.09311	−	1.09311i
$675$			1.71725e8i			0.558370i
$676$	−1.53391e8	+	1.91785e8i	−0.496548	+	0.620833i
$677$	6.47353e7			0.208629			0.104315	−	0.994544i	$-0.466735\pi$
$677$	6.47353e7			0.208629			0.104315	+	0.994544i	$0.466735\pi$
$678$	3.48325e8	+	3.48325e8i	1.11762	+	1.11762i
$679$	−1.89401e8			−0.605024
$680$		−	1.76918e7i		−	0.0562659i
$681$	1.06478e8	+	1.06478e8i	0.337148	+	0.337148i
$682$	2.36948e8	+	2.36948e8i	0.746965	+	0.746965i
$683$	−4.03051e7	+	4.03051e7i	−0.126502	+	0.126502i	−0.767523	−	0.641021i	$-0.778511\pi$
$683$	−4.03051e7	+	4.03051e7i	−0.126502	+	0.126502i	0.641021	+	0.767523i	$0.278511\pi$
$684$	2.58892e6	−	2.58892e6i	0.00809003	−	0.00809003i
$685$	1.20394e8			0.374571
$686$		−	4.55069e8i		−	1.40963i
$687$	−4.01762e7	+	4.01762e7i	−0.123908	+	0.123908i
$688$		−	5.85132e8i		−	1.79675i
$689$	6.48454e7	+	2.27423e7i	0.198254	+	0.0695307i
$690$	4.62075e8			1.40658
$691$	5.72778e7	+	5.72778e7i	0.173601	+	0.173601i	0.788559	−	0.614958i	$-0.210827\pi$
$691$	5.72778e7	+	5.72778e7i	0.173601	+	0.173601i	−0.614958	+	0.788559i	$0.710827\pi$
$692$	−2.92065e8			−0.881377
$693$		−	5.82205e6i		−	0.0174935i
$694$	2.35318e8	+	2.35318e8i	0.704007	+	0.704007i
$695$	1.21391e8	+	1.21391e8i	0.361603	+	0.361603i
$696$	−9.21895e7	+	9.21895e7i	−0.273435	+	0.273435i
$697$	−1.08980e8	+	1.08980e8i	−0.321846	+	0.321846i
$698$	3.55146e8			1.04434
$699$		−	2.67915e8i		−	0.784449i
$700$	−9.99430e7	+	9.99430e7i	−0.291379	+	0.291379i
$701$			3.34829e8i			0.972005i	0.873958	+	0.486002i	$0.161545\pi$
$701$			3.34829e8i			0.972005i	−0.873958	+	0.486002i	$0.838455\pi$
$702$	2.02407e8	+	4.21070e8i	0.585079	+	1.21715i
$703$	1.53288e8			0.441206
$704$	1.57415e8	+	1.57415e8i	0.451157	+	0.451157i
$705$	−2.48754e8			−0.709909
$706$			3.60757e8i			1.02518i
$707$	−8.76893e7	−	8.76893e7i	−0.248135	−	0.248135i
$708$	−3.58214e7	−	3.58214e7i	−0.100935	−	0.100935i
$709$	3.70614e8	−	3.70614e8i	1.03988	−	1.03988i	0.0407092	−	0.999171i	$-0.487038\pi$
$709$	3.70614e8	−	3.70614e8i	1.03988	−	1.03988i	0.999171	−	0.0407092i	$-0.0129617\pi$
$710$	−5.26870e7	+	5.26870e7i	−0.147207	+	0.147207i
$711$	−571171.			−0.00158912
$712$			4.85948e7i			0.134632i
$713$	−2.79388e8	+	2.79388e8i	−0.770796	+	0.770796i
$714$		−	1.38813e8i		−	0.381360i
$715$	2.64098e8	+	9.26232e7i	0.722514	+	0.253397i
$716$	−2.67446e8			−0.728612
$717$	3.43403e8	+	3.43403e8i	0.931638	+	0.931638i
$718$	1.26326e8			0.341288
$719$		−	4.72918e8i		−	1.27233i	−0.771554	−	0.636164i	$-0.780520\pi$
$719$		−	4.72918e8i		−	1.27233i	0.771554	−	0.636164i	$-0.219480\pi$
$720$	3.34299e6	+	3.34299e6i	0.00895648	+	0.00895648i
$721$	−3.90725e8	−	3.90725e8i	−1.04247	−	1.04247i
$722$	7.88537e7	−	7.88537e7i	0.209513	−	0.209513i
$723$	−4.45475e8	+	4.45475e8i	−1.17871	+	1.17871i
$724$	1.48718e8			0.391875
$725$			2.99636e8i			0.786285i
$726$	1.12995e8	−	1.12995e8i	0.295290	−	0.295290i
$727$		−	4.64054e8i		−	1.20772i	−0.797091	−	0.603859i	$-0.793629\pi$
$727$		−	4.64054e8i		−	1.20772i	0.797091	−	0.603859i	$-0.206371\pi$
$728$	3.28198e7	−	9.35794e7i	0.0850631	−	0.242542i
$729$	3.93531e8			1.01577
$730$	−4.44836e8	−	4.44836e8i	−1.14349	−	1.14349i
$731$	1.85094e8			0.473848
$732$		−	4.02705e6i		−	0.0102672i
$733$	−2.99117e8	−	2.99117e8i	−0.759503	−	0.759503i	0.216729	−	0.976232i	$-0.430461\pi$
$733$	−2.99117e8	−	2.99117e8i	−0.759503	−	0.759503i	−0.976232	+	0.216729i	$0.930461\pi$
$734$	−5.04662e7	−	5.04662e7i	−0.127618	−	0.127618i
$735$	2.31382e7	−	2.31382e7i	0.0582731	−	0.0582731i
$736$	−5.73470e8	+	5.73470e8i	−1.43839	+	1.43839i
$737$	−4.95454e8			−1.23766
$738$		−	1.30323e7i		−	0.0324228i
$739$	−4.58741e8	+	4.58741e8i	−1.13667	+	1.13667i	−0.147626	+	0.989043i	$0.547163\pi$
$739$	−4.58741e8	+	4.58741e8i	−1.13667	+	1.13667i	−0.989043	+	0.147626i	$0.952837\pi$
$740$		−	1.07563e8i		−	0.265440i
$741$	−1.54291e8	−	3.20973e8i	−0.379215	−	0.788886i
$742$	1.07598e8			0.263385
$743$	−1.06908e7	−	1.06908e7i	−0.0260643	−	0.0260643i	0.693955	−	0.720019i	$-0.255867\pi$
$743$	−1.06908e7	−	1.06908e7i	−0.0260643	−	0.0260643i	−0.720019	+	0.693955i	$0.755867\pi$
$744$	7.71645e7			0.187369
$745$		−	4.23730e8i		−	1.02476i
$746$	−6.55726e8	−	6.55726e8i	−1.57945	−	1.57945i
$747$	4.88625e6	+	4.88625e6i	0.0117223	+	0.0117223i
$748$	−8.27206e7	+	8.27206e7i	−0.197656	+	0.197656i
$749$	3.04273e8	−	3.04273e8i	0.724133	−	0.724133i
$750$	−5.81799e8			−1.37908
$751$		−	1.10624e8i		−	0.261174i	−0.991437	−	0.130587i	$-0.958314\pi$
$751$		−	1.10624e8i		−	0.261174i	0.991437	−	0.130587i	$-0.0416862\pi$
$752$	3.74794e8	−	3.74794e8i	0.881331	−	0.881331i
$753$		−	3.74048e8i		−	0.876078i
$754$	3.53172e8	+	7.34709e8i	0.823896	+	1.71396i
$755$	−2.20223e8			−0.511707
$756$	2.29093e8	+	2.29093e8i	0.530208	+	0.530208i
$757$	3.71077e8			0.855413			0.427707	−	0.903918i	$-0.359322\pi$
$757$	3.71077e8			0.855413			0.427707	+	0.903918i	$0.359322\pi$
$758$			3.96454e8i			0.910301i
$759$	5.57178e8	+	5.57178e8i	1.27429	+	1.27429i
$760$	−5.02541e7	−	5.02541e7i	−0.114480	−	0.114480i
$761$	−1.01154e8	+	1.01154e8i	−0.229525	+	0.229525i	−0.812494	−	0.582969i	$-0.801891\pi$
$761$	−1.01154e8	+	1.01154e8i	−0.229525	+	0.229525i	0.582969	+	0.812494i	$0.301891\pi$
$762$	6.05143e8	−	6.05143e8i	1.36771	−	1.36771i
$763$	3.76827e8			0.848336
$764$		−	1.43833e8i		−	0.322536i
$765$	−1.05748e6	+	1.05748e6i	−0.00236204	+	0.00236204i
$766$			1.67760e8i			0.373251i
$767$	7.36235e7	−	3.53906e7i	0.163166	−	0.0784335i
$768$	5.73766e8			1.26663
$769$	−3.84131e8	−	3.84131e8i	−0.844697	−	0.844697i	0.144769	−	0.989466i	$-0.453756\pi$
$769$	−3.84131e8	−	3.84131e8i	−0.844697	−	0.844697i	−0.989466	+	0.144769i	$0.953756\pi$
$770$	4.38216e8			0.959879
$771$			6.18494e8i			1.34950i
$772$	1.03022e8	+	1.03022e8i	0.223912	+	0.223912i
$773$	−5.38813e8	−	5.38813e8i	−1.16654	−	1.16654i	−0.983015	−	0.183525i	$-0.941249\pi$
$773$	−5.38813e8	−	5.38813e8i	−1.16654	−	1.16654i	−0.183525	−	0.983015i	$-0.558751\pi$
$774$	−1.10671e7	+	1.10671e7i	−0.0238678	+	0.0238678i
$775$	1.25401e8	−	1.25401e8i	0.269398	−	0.269398i
$776$	8.29915e7			0.177602
$777$			2.17650e8i			0.463976i
$778$	−6.64217e7	+	6.64217e7i	−0.141049	+	0.141049i
$779$			6.19121e8i			1.30967i
$780$	−2.25228e8	+	1.08266e8i	−0.474612	+	0.228144i
$781$	−1.27062e8			−0.266724
$782$	−2.20228e8	−	2.20228e8i	−0.460524	−	0.460524i
$783$	6.86836e8			1.43076
$784$			6.97240e7i			0.144688i
$785$	2.09846e8	+	2.09846e8i	0.433802	+	0.433802i
$786$	1.36613e8	+	1.36613e8i	0.281335	+	0.281335i
$787$	−4.57567e8	+	4.57567e8i	−0.938708	+	0.938708i	−0.998227	−	0.0595191i	$-0.981043\pi$
$787$	−4.57567e8	+	4.57567e8i	−0.938708	+	0.938708i	0.0595191	+	0.998227i	$0.481043\pi$
$788$	4.53058e8	−	4.53058e8i	0.925924	−	0.925924i
$789$	−8.10254e8			−1.64964
$790$		−	4.29911e7i		−	0.0871962i
$791$	−3.89507e8	+	3.89507e8i	−0.787020	+	0.787020i
$792$			2.55110e6i			0.00513514i
$793$	6.12770e6	+	2.14908e6i	0.0122879	+	0.00430956i
$794$	−8.95318e8			−1.78861
$795$	4.94449e7	+	4.94449e7i	0.0984057	+	0.0984057i
$796$	−3.81811e8			−0.757022
$797$			8.44943e8i			1.66899i	0.551019	+	0.834493i	$0.314239\pi$
$797$			8.44943e8i			1.66899i	−0.551019	+	0.834493i	$0.685761\pi$
$798$	−3.94302e8	−	3.94302e8i	−0.775926	−	0.775926i
$799$	1.18558e8	+	1.18558e8i	0.232429	+	0.232429i
$800$	2.57396e8	−	2.57396e8i	0.502727	−	0.502727i
$801$	2.90462e6	−	2.90462e6i	0.00565186	−	0.00565186i
$802$	1.22269e8			0.237025
$803$		−	1.07278e9i		−	2.07188i
$804$	3.12822e8	−	3.12822e8i	0.601907	−	0.601907i
$805$			5.16706e8i			0.990503i
$806$	1.59677e8	−	4.55289e8i	0.304956	−	0.869525i
$807$	1.44733e8			0.275390
$808$	3.84236e7	+	3.84236e7i	0.0728391	+	0.0728391i
$809$	2.45542e8			0.463745			0.231873	−	0.972746i	$-0.425515\pi$
$809$	2.45542e8			0.463745			0.231873	+	0.972746i	$0.425515\pi$
$810$			4.67650e8i			0.879966i
$811$	−1.09257e8	−	1.09257e8i	−0.204827	−	0.204827i	0.597238	−	0.802064i	$-0.296265\pi$
$811$	−1.09257e8	−	1.09257e8i	−0.204827	−	0.204827i	−0.802064	+	0.597238i	$0.796265\pi$
$812$	3.99735e8	+	3.99735e8i	0.746628	+	0.746628i
$813$	−2.08909e8	+	2.08909e8i	−0.388764	+	0.388764i
$814$	2.92851e8	−	2.92851e8i	0.542967	−	0.542967i
$815$	4.34339e7			0.0802335
$816$			1.92221e8i			0.353777i
$817$	5.25764e8	−	5.25764e8i	0.964106	−	0.964106i
$818$			3.81542e8i			0.697079i
$819$	−7.55517e6	+	3.63174e6i	−0.0137528	+	0.00661094i
$820$	4.34439e8			0.787930
$821$	1.25745e7	+	1.25745e7i	0.0227228	+	0.0227228i	0.718377	−	0.695654i	$-0.244885\pi$
$821$	1.25745e7	+	1.25745e7i	0.0227228	+	0.0227228i	−0.695654	+	0.718377i	$0.744885\pi$
$822$	−4.13918e8			−0.745245
$823$			4.10647e8i			0.736664i	0.929694	+	0.368332i	$0.120071\pi$
$823$			4.10647e8i			0.736664i	−0.929694	+	0.368332i	$0.879929\pi$
$824$	1.71208e8	+	1.71208e8i	0.306014	+	0.306014i
$825$	−2.50084e8	−	2.50084e8i	−0.445373	−	0.445373i
$826$	9.04434e7	−	9.04434e7i	0.160486	−	0.160486i
$827$	−2.06338e8	+	2.06338e8i	−0.364807	+	0.364807i	−0.865579	−	0.500772i	$-0.833049\pi$
$827$	−2.06338e8	+	2.06338e8i	−0.364807	+	0.364807i	0.500772	+	0.865579i	$0.333049\pi$
$828$	1.16639e7			0.0205471
$829$			7.12094e8i			1.24990i	0.780667	+	0.624948i	$0.214880\pi$
$829$			7.12094e8i			1.24990i	−0.780667	+	0.624948i	$0.785120\pi$
$830$	−3.67780e8	+	3.67780e8i	−0.643212	+	0.643212i
$831$		−	7.72548e8i		−	1.34624i
$832$	1.06080e8	−	3.02468e8i	0.184189	−	0.525182i
$833$	−2.20556e7			−0.0381579
$834$	−4.17345e8	−	4.17345e8i	−0.719444	−	0.719444i
$835$	2.26353e8			0.388801
$836$			4.69941e8i			0.804312i
$837$	−2.87448e8	−	2.87448e8i	−0.490210	−	0.490210i
$838$	−7.16048e7	−	7.16048e7i	−0.121678	−	0.121678i
$839$	5.24119e8	−	5.24119e8i	0.887450	−	0.887450i	−0.106828	−	0.994278i	$-0.534069\pi$
$839$	5.24119e8	−	5.24119e8i	0.887450	−	0.887450i	0.994278	+	0.106828i	$0.0340693\pi$
$840$	7.13547e7	−	7.13547e7i	0.120388	−	0.120388i
$841$	6.03610e8			1.01477
$842$		−	3.35097e8i		−	0.561351i
$843$	−4.75533e8	+	4.75533e8i	−0.793775	+	0.793775i
$844$			6.14449e8i			1.02202i
$845$	−4.45463e7	−	4.00492e8i	−0.0738315	−	0.663780i
$846$	−1.41776e7			−0.0234149
$847$	1.26354e8	+	1.26354e8i	0.207941	+	0.207941i
$848$	−1.48996e8			−0.244335
$849$		−	6.09590e8i		−	0.996127i
$850$	9.88471e7	+	9.88471e7i	0.160956	+	0.160956i
$851$	3.45304e8	+	3.45304e8i	0.560290	+	0.560290i
$852$	8.02250e7	−	8.02250e7i	0.129715	−	0.129715i
$853$	6.79176e8	−	6.79176e8i	1.09430	−	1.09430i	0.0992327	−	0.995064i	$-0.468361\pi$
$853$	6.79176e8	−	6.79176e8i	1.09430	−	1.09430i	0.995064	−	0.0992327i	$-0.0316388\pi$
$854$	1.01677e7			0.0163248
$855$			6.00761e6i			0.00961177i
$856$	−1.33326e8	+	1.33326e8i	−0.212566	+	0.212566i
$857$			5.61022e7i			0.0891329i	0.999006	+	0.0445664i	$0.0141906\pi$
$857$			5.61022e7i			0.0891329i	−0.999006	+	0.0445664i	$0.985809\pi$
$858$	−9.07975e8	−	3.18441e8i	−1.43751	−	0.504158i
$859$	−1.73672e8			−0.273999			−0.137000	−	0.990571i	$-0.543746\pi$
$859$	−1.73672e8			−0.273999			−0.137000	+	0.990571i	$0.543746\pi$
$860$	−3.68930e8	−	3.68930e8i	−0.580028	−	0.580028i
$861$	−8.79077e8			−1.37726
$862$		−	4.54643e8i		−	0.709821i
$863$	−2.66613e8	−	2.66613e8i	−0.414809	−	0.414809i	0.468601	−	0.883410i	$-0.344758\pi$
$863$	−2.66613e8	−	2.66613e8i	−0.414809	−	0.414809i	−0.883410	+	0.468601i	$0.844758\pi$
$864$	−5.90013e8	−	5.90013e8i	−0.914787	−	0.914787i
$865$	3.38870e8	−	3.38870e8i	0.523582	−	0.523582i
$866$	−3.47135e8	+	3.47135e8i	−0.534497	+	0.534497i
$867$	5.85574e8			0.898513
$868$		−	3.34586e8i		−	0.511622i
$869$	5.18395e7	−	5.18395e7i	0.0789953	−	0.0789953i
$870$			8.29515e8i			1.25970i
$871$	3.09060e8	+	6.42942e8i	0.467722	+	0.973010i
$872$	−1.65118e8			−0.249026
$873$	−4.96059e6	−	4.96059e6i	−0.00745574	−	0.00745574i
$874$	−1.25113e9			−1.87399
$875$		−	6.50585e8i		−	0.971136i
$876$	6.77338e8	+	6.77338e8i	1.00761	+	1.00761i
$877$	−6.40494e8	−	6.40494e8i	−0.949547	−	0.949547i	0.0492402	−	0.998787i	$-0.484320\pi$
$877$	−6.40494e8	−	6.40494e8i	−0.949547	−	0.949547i	−0.998787	+	0.0492402i	$0.984320\pi$
$878$	−2.42079e8	+	2.42079e8i	−0.357662	+	0.357662i
$879$	3.70013e8	−	3.70013e8i	0.544817	−	0.544817i
$880$	−6.06819e8			−0.890454
$881$			1.00220e9i			1.46564i	0.680424	+	0.732819i	$0.261796\pi$
$881$			1.00220e9i			1.46564i	−0.680424	+	0.732819i	$0.738204\pi$
$882$	1.31875e6	−	1.31875e6i	0.00192202	−	0.00192202i
$883$		−	8.07443e8i		−	1.17282i	−0.810016	−	0.586408i	$-0.800542\pi$
$883$		−	8.07443e8i		−	1.17282i	0.810016	−	0.586408i	$-0.199458\pi$
$884$	1.58945e8	+	5.57447e7i	0.230087	+	0.0806950i
$885$	8.31237e7			0.119921
$886$	2.73880e8	+	2.73880e8i	0.393785	+	0.393785i
$887$	−1.06089e8			−0.152019			−0.0760097	−	0.997107i	$-0.524218\pi$
$887$	−1.06089e8			−0.152019			−0.0760097	+	0.997107i	$0.524218\pi$
$888$		−	9.53698e7i		−	0.136198i
$889$	6.76688e8	+	6.76688e8i	0.963127	+	0.963127i
$890$	2.18626e8	+	2.18626e8i	0.310122	+	0.310122i
$891$	−5.63901e8	+	5.63901e8i	−0.797204	+	0.797204i
$892$	−7.10192e7	+	7.10192e7i	−0.100065	+	0.100065i
$893$	6.73533e8			0.945812
$894$			1.45679e9i			2.03885i
$895$	3.10305e8	−	3.10305e8i	0.432832	−	0.432832i
$896$			3.61998e8i			0.503247i
$897$	3.75477e8	−	1.07060e9i	0.520243	−	1.48338i
$898$	1.36168e9			1.88039
$899$	−5.01556e8	−	5.01556e8i	−0.690304	−	0.690304i
$900$	−5.23521e6			−0.00718136
$901$		−	4.71315e7i		−	0.0644372i
$902$	1.18281e9	+	1.18281e9i	1.61174	+	1.61174i
$903$	7.46521e8	+	7.46521e8i	1.01386	+	1.01386i
$904$	1.70674e8	−	1.70674e8i	0.231027	−	0.231027i
$905$	−1.72550e8	+	1.72550e8i	−0.232793	+	0.232793i
$906$	7.57132e8			1.01809
$907$			8.30405e8i			1.11293i	0.830871	+	0.556465i	$0.187843\pi$
$907$			8.30405e8i			1.11293i	−0.830871	+	0.556465i	$0.812157\pi$
$908$	−2.02304e8	+	2.02304e8i	−0.270238	+	0.270238i
$909$		−	4.59334e6i		−	0.00611557i
$910$	−2.73355e8	−	5.68665e8i	−0.362747	−	0.754628i
$911$	−8.82985e8			−1.16788			−0.583940	−	0.811797i	$-0.698490\pi$
$911$	−8.82985e8			−1.16788			−0.583940	+	0.811797i	$0.698490\pi$
$912$	5.46009e8	+	5.46009e8i	0.719806	+	0.719806i
$913$	−8.86952e8			−1.16543
$914$		−	1.06118e9i		−	1.38979i
$915$	4.67240e6	+	4.67240e6i	0.00609925	+	0.00609925i
$916$	−7.63328e7	−	7.63328e7i	−0.0993173	−	0.0993173i
$917$	−1.52765e8	+	1.52765e8i	−0.198114	+	0.198114i
$918$	2.26581e8	−	2.26581e8i	0.292884	−	0.292884i
$919$	3.41065e8			0.439431			0.219715	−	0.975564i	$-0.429487\pi$
$919$	3.41065e8			0.439431			0.219715	+	0.975564i	$0.429487\pi$
$920$		−	2.26410e8i		−	0.290758i
$921$	9.46168e8	−	9.46168e8i	1.21113	−	1.21113i
$922$			5.44693e8i			0.694958i
$923$	7.92601e7	+	1.64886e8i	0.100798	+	0.209691i
$924$	−6.67259e8			−0.845821
$925$	−1.54986e8	−	1.54986e8i	−0.195825	−	0.195825i
$926$	−2.56622e8			−0.323193
$927$		−	2.04669e7i		−	0.0256929i
$928$	−1.02949e9	−	1.02949e9i	−1.28818	−	1.28818i
$929$	4.85048e8	+	4.85048e8i	0.604976	+	0.604976i	0.941629	−	0.336653i	$-0.109295\pi$
$929$	4.85048e8	+	4.85048e8i	0.604976	+	0.604976i	−0.336653	+	0.941629i	$0.609295\pi$
$930$	3.47160e8	−	3.47160e8i	0.431600	−	0.431600i
$931$	−6.26497e7	+	6.26497e7i	−0.0776372	+	0.0776372i
$932$	5.09025e8			0.628769
$933$		−	6.25154e8i		−	0.769737i
$934$	−1.08039e8	+	1.08039e8i	−0.132599	+	0.132599i
$935$		−	1.91954e8i		−	0.234834i
$936$	3.31052e6	−	1.59135e6i	0.00403709	−	0.00194061i
$937$	−1.08617e9			−1.32032			−0.660162	−	0.751123i	$-0.729512\pi$
$937$	−1.08617e9			−1.32032			−0.660162	+	0.751123i	$0.729512\pi$
$938$	7.89827e8	+	7.89827e8i	0.957025	+	0.957025i
$939$	1.25525e8			0.151612
$940$		−	4.72621e8i		−	0.569022i
$941$	6.01251e8	+	6.01251e8i	0.721584	+	0.721584i	0.968928	−	0.247344i	$-0.0795578\pi$
$941$	6.01251e8	+	6.01251e8i	0.721584	+	0.721584i	−0.247344	+	0.968928i	$0.579558\pi$
$942$	−7.21456e8	−	7.21456e8i	−0.863092	−	0.863092i
$943$	−1.39466e9	+	1.39466e9i	−1.66316	+	1.66316i
$944$	−1.25241e8	+	1.25241e8i	−0.148878	+	0.148878i
$945$	−5.31611e8			−0.629940
$946$		−	2.00891e9i		−	2.37294i
$947$	4.43941e8	−	4.43941e8i	0.522727	−	0.522727i	−0.395667	−	0.918394i	$-0.629487\pi$
$947$	4.43941e8	−	4.43941e8i	0.522727	−	0.522727i	0.918394	+	0.395667i	$0.129487\pi$
$948$			6.54613e7i			0.0768351i
$949$	−1.39213e9	+	6.69192e8i	−1.62885	+	0.782982i
$950$	5.61556e8			0.654972
$951$	2.89733e8	+	2.89733e8i	0.336865	+	0.336865i
$952$	−6.80162e7			−0.0788318
$953$			4.31464e8i			0.498501i	0.968439	+	0.249250i	$0.0801842\pi$
$953$			4.31464e8i			0.498501i	−0.968439	+	0.249250i	$0.919816\pi$
$954$	2.81809e6	+	2.81809e6i	0.00324571	+	0.00324571i
$955$	1.66883e8	+	1.66883e8i	0.191602	+	0.191602i
$956$	−6.52450e8	+	6.52450e8i	−0.746747	+	0.746747i
$957$	−1.00024e9	+	1.00024e9i	−1.14122	+	1.14122i
$958$	9.12453e8			1.03780
$959$		−	4.62856e8i		−	0.524795i
$960$	2.30633e8	−	2.30633e8i	0.260680	−	0.260680i
$961$		−	4.67691e8i		−	0.526974i
$962$	−5.62705e8	−	1.97350e8i	−0.632056	−	0.221672i
$963$	1.59384e7			0.0178471
$964$	−8.46381e8	−	8.46381e8i	−0.944789	−	0.944789i
$965$	−2.39062e8			−0.266029
$966$		−	1.77645e9i		−	1.97070i
$967$	−1.87564e8	−	1.87564e8i	−0.207429	−	0.207429i	0.595745	−	0.803174i	$-0.296857\pi$
$967$	−1.87564e8	−	1.87564e8i	−0.207429	−	0.207429i	−0.803174	+	0.595745i	$0.796857\pi$
$968$	−5.53658e7	−	5.53658e7i	−0.0610402	−	0.0610402i
$969$	−1.72718e8	+	1.72718e8i	−0.189830	+	0.189830i
$970$	3.73376e8	−	3.73376e8i	0.409101	−	0.409101i
$971$	−2.27350e7			−0.0248334			−0.0124167	−	0.999923i	$-0.503952\pi$
$971$	−2.27350e7			−0.0248334			−0.0124167	+	0.999923i	$0.503952\pi$
$972$			2.38081e7i			0.0259254i
$973$	4.66688e8	−	4.66688e8i	0.506626	−	0.506626i
$974$			7.23100e6i			0.00782567i
$975$	−1.68529e8	+	4.80530e8i	−0.181828	+	0.518450i
$976$	−1.40797e7			−0.0151441
$977$	−2.59001e8	−	2.59001e8i	−0.277727	−	0.277727i	0.554474	−	0.832201i	$-0.312919\pi$
$977$	−2.59001e8	−	2.59001e8i	−0.277727	−	0.277727i	−0.832201	+	0.554474i	$0.812919\pi$
$978$	−1.49327e8			−0.159632
$979$			5.27247e8i			0.561909i
$980$	4.39615e7	+	4.39615e7i	0.0467083	+	0.0467083i
$981$	9.86946e6	+	9.86946e6i	0.0104541	+	0.0104541i
$982$	3.37260e8	−	3.37260e8i	0.356148	−	0.356148i
$983$	4.20575e8	−	4.20575e8i	0.442775	−	0.442775i	−0.450169	−	0.892944i	$-0.648636\pi$
$983$	4.20575e8	−	4.20575e8i	0.442775	−	0.442775i	0.892944	+	0.450169i	$0.148636\pi$
$984$	3.85193e8			0.404290
$985$			1.05132e9i			1.10009i
$986$	3.95352e8	−	3.95352e8i	0.412433	−	0.412433i
$987$			9.56336e8i			0.994624i
$988$	6.09834e8	−	2.93145e8i	0.632325	−	0.303957i
$989$	2.36872e9			2.44864
$990$	1.14773e7	+	1.14773e7i	0.0118286	+	0.0118286i
$991$	1.02287e9			1.05099			0.525497	−	0.850795i	$-0.323879\pi$
$991$	1.02287e9			1.05099			0.525497	+	0.850795i	$0.323879\pi$
$992$			8.61704e8i			0.882720i
$993$	−6.20862e8	−	6.20862e8i	−0.634085	−	0.634085i
$994$	2.02556e8	+	2.02556e8i	0.206246	+	0.206246i
$995$	4.42997e8	−	4.42997e8i	0.449709	−	0.449709i
$996$	5.60008e8	−	5.60008e8i	0.566782	−	0.566782i
$997$	−1.93138e9			−1.94887			−0.974434	−	0.224675i	$-0.927868\pi$
$997$	−1.93138e9			−1.94887			−0.974434	+	0.224675i	$0.927868\pi$
$998$			1.37806e9i			1.38636i
$999$	−3.55265e8	+	3.55265e8i	−0.356333	+	0.356333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.d.a.8.5	yes	12
3.2	odd	2		117.7.j.b.73.2		12
4.3	odd	2		208.7.t.c.177.2		12
13.5	odd	4	inner	13.7.d.a.5.5	✓	12
39.5	even	4		117.7.j.b.109.2		12
52.31	even	4		208.7.t.c.161.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.d.a.5.5	✓	12	13.5	odd	4	inner
13.7.d.a.8.5	yes	12	1.1	even	1	trivial
117.7.j.b.73.2		12	3.2	odd	2
117.7.j.b.109.2		12	39.5	even	4
208.7.t.c.161.2		12	52.31	even	4
208.7.t.c.177.2		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.57888 + 7.57888i) q^{2} +26.7789 q^{3} +50.8787i q^{4} +(-59.0322 - 59.0322i) q^{5} +(202.954 + 202.954i) q^{6} +(-226.950 + 226.950i) q^{7} +(99.4446 - 99.4446i) q^{8} -11.8881 q^{9} +O(q^{10})\)	\(q+(7.57888 + 7.57888i) q^{2} +26.7789 q^{3} +50.8787i q^{4} +(-59.0322 - 59.0322i) q^{5} +(202.954 + 202.954i) q^{6} +(-226.950 + 226.950i) q^{7} +(99.4446 - 99.4446i) q^{8} -11.8881 q^{9} -894.795i q^{10} +(1078.96 - 1078.96i) q^{11} +1362.48i q^{12} +(-2073.19 - 727.102i) q^{13} -3440.04 q^{14} +(-1580.82 - 1580.82i) q^{15} +4763.59 q^{16} +1506.86i q^{17} +(-90.0981 - 90.0981i) q^{18} +(4280.27 + 4280.27i) q^{19} +(3003.48 - 3003.48i) q^{20} +(-6077.47 + 6077.47i) q^{21} +16354.6 q^{22} +19283.9i q^{23} +(2663.02 - 2663.02i) q^{24} -8655.40i q^{25} +(-10201.9 - 21223.1i) q^{26} -19840.2 q^{27} +(-11546.9 - 11546.9i) q^{28} -34618.4 q^{29} -23961.7i q^{30} +(14488.1 + 14488.1i) q^{31} +(29738.2 + 29738.2i) q^{32} +(28893.4 - 28893.4i) q^{33} +(-11420.3 + 11420.3i) q^{34} +26794.7 q^{35} -604.849i q^{36} +(17906.3 - 17906.3i) q^{37} +64879.3i q^{38} +(-55517.9 - 19471.0i) q^{39} -11740.9 q^{40} +(72322.6 + 72322.6i) q^{41} -92120.8 q^{42} -122834. i q^{43} +(54896.1 + 54896.1i) q^{44} +(701.778 + 701.778i) q^{45} +(-146150. + 146150. i) q^{46} +(78678.8 - 78678.8i) q^{47} +127564. q^{48} +14636.8i q^{49} +(65598.2 - 65598.2i) q^{50} +40352.0i q^{51} +(36994.0 - 105481. i) q^{52} -31278.0 q^{53} +(-150366. - 150366. i) q^{54} -127387. q^{55} +45137.8i q^{56} +(114621. + 114621. i) q^{57} +(-262368. - 262368. i) q^{58} +(-26291.3 + 26291.3i) q^{59} +(80430.1 - 80430.1i) q^{60} -2955.68 q^{61} +219608. i q^{62} +(2697.99 - 2697.99i) q^{63} +145895. i q^{64} +(79462.8 + 165308. i) q^{65} +437959. q^{66} +(-229598. - 229598. i) q^{67} -76667.0 q^{68} +516403. i q^{69} +(203073. + 203073. i) q^{70} +(-58881.7 - 58881.7i) q^{71} +(-1182.20 + 1182.20i) q^{72} +(497137. - 497137. i) q^{73} +271419. q^{74} -231782. i q^{75} +(-217775. + 217775. i) q^{76} +489739. i q^{77} +(-273195. - 568332. i) q^{78} +48045.8 q^{79} +(-281205. - 281205. i) q^{80} -522633. q^{81} +1.09625e6i q^{82} +(-411022. - 411022. i) q^{83} +(-309214. - 309214. i) q^{84} +(88953.1 - 88953.1i) q^{85} +(930945. - 930945. i) q^{86} -927044. q^{87} -214594. i q^{88} +(-244331. + 244331. i) q^{89} +10637.4i q^{90} +(635526. - 305495. i) q^{91} -981141. q^{92} +(387977. + 387977. i) q^{93} +1.19259e6 q^{94} -505348. i q^{95} +(796359. + 796359. i) q^{96} +(417275. + 417275. i) q^{97} +(-110931. + 110931. i) q^{98} +(-12826.7 + 12826.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9 + 1686 * q^11 - 3926 * q^13 + 5484 * q^14 - 15268 * q^15 + 2132 * q^16 + 15254 * q^18 + 1766 * q^19 - 19044 * q^20 + 3428 * q^21 + 28832 * q^22 + 31608 * q^24 - 58266 * q^26 - 20464 * q^27 + 4092 * q^28 - 90108 * q^29 + 61014 * q^31 - 64932 * q^32 - 44452 * q^33 + 259896 * q^34 + 158772 * q^35 - 40212 * q^37 + 137852 * q^39 - 104196 * q^40 - 190416 * q^41 - 959204 * q^42 + 489372 * q^44 - 151444 * q^45 - 44412 * q^46 + 562446 * q^47 + 930308 * q^48 + 82422 * q^50 - 578500 * q^52 + 509136 * q^53 - 871432 * q^54 - 1264036 * q^55 + 939908 * q^57 - 1019980 * q^58 - 994458 * q^59 + 2407804 * q^60 + 1013696 * q^61 + 865778 * q^63 - 1130064 * q^65 - 418352 * q^66 - 1442386 * q^67 - 2313132 * q^68 + 2958968 * q^70 - 655866 * q^71 - 1706508 * q^72 + 2588228 * q^73 + 3373752 * q^74 + 246984 * q^76 + 77480 * q^78 - 75316 * q^79 - 2685408 * q^80 - 4016140 * q^81 + 894966 * q^83 - 3220504 * q^84 + 105396 * q^85 + 3704832 * q^86 + 2109064 * q^87 - 977376 * q^89 + 1088750 * q^91 + 3682872 * q^92 - 216268 * q^93 - 6238300 * q^94 + 896384 * q^96 + 983388 * q^97 + 1039302 * q^98 + 2894714 * q^99

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