LMFDB - Embedded newform 74.7.d.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 $ x^18 + 8470x^16 + 28007049x^14 + 45282701078x^12 + 36580026955844x^10 + 13599755691108102x^8 + 2140498199687229457x^6 + 117348928221103362406x^4 + 1596692663909213634249x^2 + 657611720884512028944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$-8.36225i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.7.d.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 - 4.00000i) q^{2} -12.3623i q^{3} -32.0000i q^{4} +(-142.025 - 142.025i) q^{5} +(-49.4490 - 49.4490i) q^{6} -327.411 q^{7} +(-128.000 - 128.000i) q^{8} +576.175 q^{9} +O(q^{10})$	\(q+(4.00000 - 4.00000i) q^{2} -12.3623i q^{3} -32.0000i q^{4} +(-142.025 - 142.025i) q^{5} +(-49.4490 - 49.4490i) q^{6} -327.411 q^{7} +(-128.000 - 128.000i) q^{8} +576.175 q^{9} -1136.20 q^{10} +1873.92i q^{11} -395.592 q^{12} +(471.226 + 471.226i) q^{13} +(-1309.65 + 1309.65i) q^{14} +(-1755.75 + 1755.75i) q^{15} -1024.00 q^{16} +(1653.75 + 1653.75i) q^{17} +(2304.70 - 2304.70i) q^{18} +(-331.819 - 331.819i) q^{19} +(-4544.81 + 4544.81i) q^{20} +4047.54i q^{21} +(7495.68 + 7495.68i) q^{22} +(-16501.6 - 16501.6i) q^{23} +(-1582.37 + 1582.37i) q^{24} +24717.5i q^{25} +3769.81 q^{26} -16134.9i q^{27} +10477.2i q^{28} +(-4645.17 + 4645.17i) q^{29} +14046.0i q^{30} +(-28352.1 + 28352.1i) q^{31} +(-4096.00 + 4096.00i) q^{32} +23165.9 q^{33} +13230.0 q^{34} +(46500.8 + 46500.8i) q^{35} -18437.6i q^{36} +(-23447.0 - 44899.5i) q^{37} -2654.55 q^{38} +(5825.41 - 5825.41i) q^{39} +36358.5i q^{40} +70914.8i q^{41} +(16190.2 + 16190.2i) q^{42} +(-28595.9 - 28595.9i) q^{43} +59965.5 q^{44} +(-81831.5 - 81831.5i) q^{45} -132013. q^{46} -47680.7 q^{47} +12658.9i q^{48} -10450.8 q^{49} +(98869.9 + 98869.9i) q^{50} +(20444.1 - 20444.1i) q^{51} +(15079.2 - 15079.2i) q^{52} +16731.9 q^{53} +(-64539.6 - 64539.6i) q^{54} +(266144. - 266144. i) q^{55} +(41908.7 + 41908.7i) q^{56} +(-4102.03 + 4102.03i) q^{57} +37161.4i q^{58} +(-160196. - 160196. i) q^{59} +(56184.1 + 56184.1i) q^{60} +(-123654. + 123654. i) q^{61} +226817. i q^{62} -188646. q^{63} +32768.0i q^{64} -133852. i q^{65} +(92663.5 - 92663.5i) q^{66} -13293.2i q^{67} +(52920.0 - 52920.0i) q^{68} +(-203997. + 203997. i) q^{69} +372006. q^{70} +332247. q^{71} +(-73750.4 - 73750.4i) q^{72} -656085. i q^{73} +(-273386. - 85810.0i) q^{74} +305564. q^{75} +(-10618.2 + 10618.2i) q^{76} -613543. i q^{77} -46603.3i q^{78} +(-570724. - 570724. i) q^{79} +(145434. + 145434. i) q^{80} +220568. q^{81} +(283659. + 283659. i) q^{82} +717191. q^{83} +129521. q^{84} -469750. i q^{85} -228767. q^{86} +(57424.8 + 57424.8i) q^{87} +(239862. - 239862. i) q^{88} +(-176723. + 176723. i) q^{89} -654652. q^{90} +(-154285. - 154285. i) q^{91} +(-528051. + 528051. i) q^{92} +(350496. + 350496. i) q^{93} +(-190723. + 190723. i) q^{94} +94253.4i q^{95} +(50635.8 + 50635.8i) q^{96} +(1.15438e6 + 1.15438e6i) q^{97} +(-41803.0 + 41803.0i) q^{98} +1.07971e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) $ 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9 + 2352 * q^10 - 2048 * q^12 - 6766 * q^13 - 416 * q^14 - 2136 * q^15 - 18432 * q^16 - 9134 * q^17 - 16168 * q^18 + 7578 * q^19 + 9408 * q^20 + 8928 * q^22 - 50578 * q^23 - 8192 * q^24 - 54128 * q^26 - 42950 * q^29 - 17358 * q^31 - 73728 * q^32 - 11056 * q^33 - 73072 * q^34 + 62152 * q^35 - 238242 * q^37 + 60624 * q^38 + 31572 * q^39 + 229024 * q^42 - 65470 * q^43 + 71424 * q^44 - 482358 * q^45 - 404624 * q^46 + 232192 * q^47 + 791686 * q^49 + 93752 * q^50 - 386848 * q^51 - 216512 * q^52 + 49972 * q^53 - 144560 * q^54 + 160168 * q^55 + 13312 * q^56 + 488476 * q^57 - 181570 * q^59 + 68352 * q^60 + 508802 * q^61 + 404788 * q^63 - 44224 * q^66 - 292288 * q^68 + 604532 * q^69 + 497216 * q^70 - 202632 * q^71 + 517376 * q^72 - 1191224 * q^74 + 2476628 * q^75 + 242496 * q^76 + 1752858 * q^79 - 301056 * q^80 + 2760658 * q^81 - 145808 * q^82 + 2371616 * q^83 + 1832192 * q^84 - 523760 * q^86 - 4188080 * q^87 + 285696 * q^88 + 1148346 * q^89 - 3858864 * q^90 + 433120 * q^91 - 1618496 * q^92 + 1589664 * q^93 + 928768 * q^94 + 262144 * q^96 - 1670270 * q^97 + 3166744 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	4.00000	−	4.00000i	0.500000	−	0.500000i
$2$	4.00000	−	4.00000i	0.500000	−	0.500000i
$3$		−	12.3623i		−	0.457861i	−0.973443	−	0.228931i	$-0.926477\pi$
$3$		−	12.3623i		−	0.457861i	0.973443	−	0.228931i	$-0.0735229\pi$
$4$		−	32.0000i		−	0.500000i
$5$	−142.025	−	142.025i	−1.13620	−	1.13620i	−0.989125	−	0.147079i	$-0.953013\pi$
$5$	−142.025	−	142.025i	−1.13620	−	1.13620i	−0.147079	−	0.989125i	$-0.546987\pi$
$6$	−49.4490	−	49.4490i	−0.228931	−	0.228931i
$7$	−327.411			−0.954552			−0.477276	−	0.878753i	$-0.658376\pi$
$7$	−327.411			−0.954552			−0.477276	+	0.878753i	$0.658376\pi$
$8$	−128.000	−	128.000i	−0.250000	−	0.250000i
$9$	576.175			0.790363
$10$	−1136.20			−1.13620
$11$			1873.92i			1.40790i	0.710247	+	0.703952i	$0.248583\pi$
$11$			1873.92i			1.40790i	−0.710247	+	0.703952i	$0.751417\pi$
$12$	−395.592			−0.228931
$13$	471.226	+	471.226i	0.214486	+	0.214486i	0.806170	−	0.591684i	$-0.201537\pi$
$13$	471.226	+	471.226i	0.214486	+	0.214486i	−0.591684	+	0.806170i	$0.701537\pi$
$14$	−1309.65	+	1309.65i	−0.477276	+	0.477276i
$15$	−1755.75	+	1755.75i	−0.520224	+	0.520224i
$16$	−1024.00			−0.250000
$17$	1653.75	+	1653.75i	0.336607	+	0.336607i	0.855089	−	0.518482i	$-0.173503\pi$
$17$	1653.75	+	1653.75i	0.336607	+	0.336607i	−0.518482	+	0.855089i	$0.673503\pi$
$18$	2304.70	−	2304.70i	0.395182	−	0.395182i
$19$	−331.819	−	331.819i	−0.0483771	−	0.0483771i	0.682504	−	0.730881i	$-0.260891\pi$
$19$	−331.819	−	331.819i	−0.0483771	−	0.0483771i	−0.730881	+	0.682504i	$0.760891\pi$
$20$	−4544.81	+	4544.81i	−0.568102	+	0.568102i
$21$			4047.54i			0.437052i
$22$	7495.68	+	7495.68i	0.703952	+	0.703952i
$23$	−16501.6	−	16501.6i	−1.35626	−	1.35626i	−0.878481	−	0.477778i	$-0.841442\pi$
$23$	−16501.6	−	16501.6i	−1.35626	−	1.35626i	−0.477778	−	0.878481i	$-0.658558\pi$
$24$	−1582.37	+	1582.37i	−0.114465	+	0.114465i
$25$			24717.5i			1.58192i
$26$	3769.81			0.214486
$27$		−	16134.9i		−	0.819738i
$28$			10477.2i			0.477276i
$29$	−4645.17	+	4645.17i	−0.190462	+	0.190462i	−0.795896	−	0.605434i	$-0.793000\pi$
$29$	−4645.17	+	4645.17i	−0.190462	+	0.190462i	0.605434	+	0.795896i	$0.293000\pi$
$30$			14046.0i			0.520224i
$31$	−28352.1	+	28352.1i	−0.951700	+	0.951700i	−0.998886	−	0.0471866i	$-0.984974\pi$
$31$	−28352.1	+	28352.1i	−0.951700	+	0.951700i	0.0471866	+	0.998886i	$0.484974\pi$
$32$	−4096.00	+	4096.00i	−0.125000	+	0.125000i
$33$	23165.9			0.644625
$34$	13230.0			0.336607
$35$	46500.8	+	46500.8i	1.08457	+	1.08457i
$36$		−	18437.6i		−	0.395182i
$37$	−23447.0	−	44899.5i	−0.462894	−	0.886413i
$37$	−23447.0	−	44899.5i	−0.462894	−	0.886413i
$38$	−2654.55			−0.0483771
$39$	5825.41	−	5825.41i	0.0982048	−	0.0982048i
$40$			36358.5i			0.568102i
$41$			70914.8i			1.02893i	0.857512	+	0.514464i	$0.172009\pi$
$41$			70914.8i			1.02893i	−0.857512	+	0.514464i	$0.827991\pi$
$42$	16190.2	+	16190.2i	0.218526	+	0.218526i
$43$	−28595.9	−	28595.9i	−0.359665	−	0.359665i	0.504024	−	0.863690i	$-0.331852\pi$
$43$	−28595.9	−	28595.9i	−0.359665	−	0.359665i	−0.863690	+	0.504024i	$0.831852\pi$
$44$	59965.5			0.703952
$45$	−81831.5	−	81831.5i	−0.898014	−	0.898014i
$46$	−132013.			−1.35626
$47$	−47680.7			−0.459250			−0.229625	−	0.973279i	$-0.573750\pi$
$47$	−47680.7			−0.459250			−0.229625	+	0.973279i	$0.573750\pi$
$48$			12658.9i			0.114465i
$49$	−10450.8			−0.0888300
$50$	98869.9	+	98869.9i	0.790959	+	0.790959i
$51$	20444.1	−	20444.1i	0.154119	−	0.154119i
$52$	15079.2	−	15079.2i	0.107243	−	0.107243i
$53$	16731.9			0.112387			0.0561937	−	0.998420i	$-0.482104\pi$
$53$	16731.9			0.112387			0.0561937	+	0.998420i	$0.482104\pi$
$54$	−64539.6	−	64539.6i	−0.409869	−	0.409869i
$55$	266144.	−	266144.i	1.59967	−	1.59967i
$56$	41908.7	+	41908.7i	0.238638	+	0.238638i
$57$	−4102.03	+	4102.03i	−0.0221500	+	0.0221500i
$58$			37161.4i			0.190462i
$59$	−160196.	−	160196.i	−0.780001	−	0.780001i	0.199829	−	0.979831i	$-0.435961\pi$
$59$	−160196.	−	160196.i	−0.780001	−	0.780001i	−0.979831	+	0.199829i	$0.935961\pi$
$60$	56184.1	+	56184.1i	0.260112	+	0.260112i
$61$	−123654.	+	123654.i	−0.544776	+	0.544776i	−0.924925	−	0.380149i	$-0.875873\pi$
$61$	−123654.	+	123654.i	−0.544776	+	0.544776i	0.380149	+	0.924925i	$0.375873\pi$
$62$			226817.i			0.951700i
$63$	−188646.			−0.754443
$64$			32768.0i			0.125000i
$65$		−	133852.i		−	0.487400i
$66$	92663.5	−	92663.5i	0.322312	−	0.322312i
$67$		−	13293.2i		−	0.0441984i	−0.999756	−	0.0220992i	$-0.992965\pi$
$67$		−	13293.2i		−	0.0441984i	0.999756	−	0.0220992i	$-0.00703496\pi$
$68$	52920.0	−	52920.0i	0.168304	−	0.168304i
$69$	−203997.	+	203997.i	−0.620978	+	0.620978i
$70$	372006.			1.08457
$71$	332247.			0.928294			0.464147	−	0.885758i	$-0.346361\pi$
$71$	332247.			0.928294			0.464147	+	0.885758i	$0.346361\pi$
$72$	−73750.4	−	73750.4i	−0.197591	−	0.197591i
$73$		−	656085.i		−	1.68652i	−0.537506	−	0.843260i	$-0.680634\pi$
$73$		−	656085.i		−	1.68652i	0.537506	−	0.843260i	$-0.319366\pi$
$74$	−273386.	−	85810.0i	−0.674654	−	0.211760i
$75$	305564.			0.724299
$76$	−10618.2	+	10618.2i	−0.0241886	+	0.0241886i
$77$		−	613543.i		−	1.34392i
$78$		−	46603.3i		−	0.0982048i
$79$	−570724.	−	570724.i	−1.15756	−	1.15756i	−0.984998	−	0.172567i	$-0.944794\pi$
$79$	−570724.	−	570724.i	−1.15756	−	1.15756i	−0.172567	−	0.984998i	$-0.555206\pi$
$80$	145434.	+	145434.i	0.284051	+	0.284051i
$81$	220568.			0.415037
$82$	283659.	+	283659.i	0.514464	+	0.514464i
$83$	717191.			1.25430			0.627149	−	0.778900i	$-0.284222\pi$
$83$	717191.			1.25430			0.627149	+	0.778900i	$0.284222\pi$
$84$	129521.			0.218526
$85$		−	469750.i		−	0.764909i
$86$	−228767.			−0.359665
$87$	57424.8	+	57424.8i	0.0872051	+	0.0872051i
$88$	239862.	−	239862.i	0.351976	−	0.351976i
$89$	−176723.	+	176723.i	−0.250682	+	0.250682i	−0.821250	−	0.570568i	$-0.806723\pi$
$89$	−176723.	+	176723.i	−0.250682	+	0.250682i	0.570568	+	0.821250i	$0.306723\pi$
$90$	−654652.			−0.898014
$91$	−154285.	−	154285.i	−0.204738	−	0.204738i
$92$	−528051.	+	528051.i	−0.678129	+	0.678129i
$93$	350496.	+	350496.i	0.435746	+	0.435746i
$94$	−190723.	+	190723.i	−0.229625	+	0.229625i
$95$			94253.4i			0.109933i
$96$	50635.8	+	50635.8i	0.0572327	+	0.0572327i
$97$	1.15438e6	+	1.15438e6i	1.26484	+	1.26484i	0.948719	+	0.316120i	$0.102380\pi$
$97$	1.15438e6	+	1.15438e6i	1.26484	+	1.26484i	0.316120	+	0.948719i	$0.397620\pi$
$98$	−41803.0	+	41803.0i	−0.0444150	+	0.0444150i
$99$			1.07971e6i			1.11276i
$100$	790959.			0.790959
$101$			469134.i			0.455337i	0.973739	+	0.227668i	$0.0731102\pi$
$101$			469134.i			0.455337i	−0.973739	+	0.227668i	$0.926890\pi$
$102$		−	163553.i		−	0.154119i
$103$	−964602.	+	964602.i	−0.882748	+	0.882748i	−0.993813	−	0.111065i	$-0.964574\pi$
$103$	−964602.	+	964602.i	−0.882748	+	0.882748i	0.111065	+	0.993813i	$0.464574\pi$
$104$		−	120634.i		−	0.107243i
$105$	574854.	−	574854.i	0.496581	−	0.496581i
$106$	66927.6	−	66927.6i	0.0561937	−	0.0561937i
$107$	−1.14372e6			−0.933615			−0.466807	−	0.884359i	$-0.654596\pi$
$107$	−1.14372e6			−0.933615			−0.466807	+	0.884359i	$0.654596\pi$
$108$	−516317.			−0.409869
$109$	−1.35097e6	−	1.35097e6i	−1.04320	−	1.04320i	−0.999024	−	0.0441719i	$-0.985935\pi$
$109$	−1.35097e6	−	1.35097e6i	−1.04320	−	1.04320i	−0.0441719	−	0.999024i	$-0.514065\pi$
$110$		−	2.12916e6i		−	1.59967i
$111$	−555059.	+	289858.i	−0.405854	+	0.211941i
$112$	335269.			0.238638
$113$	215916.	−	215916.i	0.149641	−	0.149641i	−0.628317	−	0.777957i	$-0.716256\pi$
$113$	215916.	−	215916.i	0.149641	−	0.149641i	0.777957	+	0.628317i	$0.216256\pi$
$114$			32816.2i			0.0221500i
$115$			4.68729e6i			3.08197i
$116$	148646.	+	148646.i	0.0952309	+	0.0952309i
$117$	271508.	+	271508.i	0.169522	+	0.169522i
$118$	−1.28157e6			−0.780001
$119$	−541457.	−	541457.i	−0.321309	−	0.321309i
$120$	449473.			0.260112
$121$	−1.74002e6			−0.982194
$122$			989231.i			0.544776i
$123$	876666.			0.471106
$124$	907267.	+	907267.i	0.475850	+	0.475850i
$125$	1.29136e6	−	1.29136e6i	0.661177	−	0.661177i
$126$	−754585.	+	754585.i	−0.377221	+	0.377221i
$127$	−693878.			−0.338744			−0.169372	−	0.985552i	$-0.554174\pi$
$127$	−693878.			−0.338744			−0.169372	+	0.985552i	$0.554174\pi$
$128$	131072.	+	131072.i	0.0625000	+	0.0625000i
$129$	−353510.	+	353510.i	−0.164677	+	0.164677i
$130$	−535408.	−	535408.i	−0.243700	−	0.243700i
$131$	−1.56710e6	+	1.56710e6i	−0.697081	+	0.697081i	−0.963780	−	0.266699i	$-0.914067\pi$
$131$	−1.56710e6	+	1.56710e6i	−0.697081	+	0.697081i	0.266699	+	0.963780i	$0.414067\pi$
$132$		−	741308.i		−	0.322312i
$133$	108641.	+	108641.i	0.0461785	+	0.0461785i
$134$	−53172.9	−	53172.9i	−0.0220992	−	0.0220992i
$135$	−2.29157e6	+	2.29157e6i	−0.931389	+	0.931389i
$136$		−	423360.i		−	0.168304i
$137$	2.79547e6			1.08716			0.543579	−	0.839358i	$-0.317069\pi$
$137$	2.79547e6			1.08716			0.543579	+	0.839358i	$0.317069\pi$
$138$			1.63198e6i			0.620978i
$139$		−	2.03481e6i		−	0.757669i	−0.925464	−	0.378834i	$-0.876325\pi$
$139$		−	2.03481e6i		−	0.757669i	0.925464	−	0.378834i	$-0.123675\pi$
$140$	1.48802e6	−	1.48802e6i	0.542283	−	0.542283i
$141$			589441.i			0.210273i
$142$	1.32899e6	−	1.32899e6i	0.464147	−	0.464147i
$143$	−883040.	+	883040.i	−0.301976	+	0.301976i
$144$	−590003.			−0.197591
$145$	1.31947e6			0.432807
$146$	−2.62434e6	−	2.62434e6i	−0.843260	−	0.843260i
$147$			129195.i			0.0406718i
$148$	−1.43678e6	+	750304.i	−0.443207	+	0.231447i
$149$	4.38790e6			1.32647			0.663236	−	0.748410i	$-0.269183\pi$
$149$	4.38790e6			1.32647			0.663236	+	0.748410i	$0.269183\pi$
$150$	1.22225e6	−	1.22225e6i	0.362149	−	0.362149i
$151$		−	2.00914e6i		−	0.583551i	−0.956487	−	0.291775i	$-0.905754\pi$
$151$		−	2.00914e6i		−	0.583551i	0.956487	−	0.291775i	$-0.0942459\pi$
$152$			84945.6i			0.0241886i
$153$	952850.	+	952850.i	0.266042	+	0.266042i
$154$	−2.45417e6	−	2.45417e6i	−0.671959	−	0.671959i
$155$	8.05343e6			2.16265
$156$	−186413.	−	186413.i	−0.0491024	−	0.0491024i
$157$	−2.11078e6			−0.545437			−0.272719	−	0.962094i	$-0.587923\pi$
$157$	−2.11078e6			−0.545437			−0.272719	+	0.962094i	$0.587923\pi$
$158$	−4.56580e6			−1.15756
$159$		−	206844.i		−	0.0514578i
$160$	1.16347e6			0.284051
$161$	5.40281e6	+	5.40281e6i	1.29462	+	1.29462i
$162$	882271.	−	882271.i	0.207518	−	0.207518i
$163$	3.52676e6	−	3.52676e6i	0.814353	−	0.814353i	−0.170930	−	0.985283i	$-0.554677\pi$
$163$	3.52676e6	−	3.52676e6i	0.814353	−	0.814353i	0.985283	+	0.170930i	$0.0546773\pi$
$164$	2.26927e6			0.514464
$165$	−3.29014e6	−	3.29014e6i	−0.732425	−	0.732425i
$166$	2.86876e6	−	2.86876e6i	0.627149	−	0.627149i
$167$	−3.93036e6	−	3.93036e6i	−0.843884	−	0.843884i	0.145477	−	0.989362i	$-0.453528\pi$
$167$	−3.93036e6	−	3.93036e6i	−0.843884	−	0.843884i	−0.989362	+	0.145477i	$0.953528\pi$
$168$	518085.	−	518085.i	0.109263	−	0.109263i
$169$		−	4.38270e6i		−	0.907992i
$170$	−1.87900e6	−	1.87900e6i	−0.382454	−	0.382454i
$171$	−191185.	−	191185.i	−0.0382355	−	0.0382355i
$172$	−915069.	+	915069.i	−0.179833	+	0.179833i
$173$			924554.i			0.178564i	0.996006	+	0.0892820i	$0.0284572\pi$
$173$			924554.i			0.178564i	−0.996006	+	0.0892820i	$0.971543\pi$
$174$	459398.			0.0872051
$175$		−	8.09278e6i		−	1.51002i
$176$		−	1.91889e6i		−	0.351976i
$177$	−1.98038e6	+	1.98038e6i	−0.357132	+	0.357132i
$178$			1.41378e6i			0.250682i
$179$	1.10687e6	−	1.10687e6i	0.192991	−	0.192991i	−0.603996	−	0.796987i	$-0.706426\pi$
$179$	1.10687e6	−	1.10687e6i	0.192991	−	0.192991i	0.796987	+	0.603996i	$0.206426\pi$
$180$	−2.61861e6	+	2.61861e6i	−0.449007	+	0.449007i
$181$	1.06572e7			1.79725			0.898624	−	0.438720i	$-0.144568\pi$
$181$	1.06572e7			1.79725			0.898624	+	0.438720i	$0.144568\pi$
$182$	−1.23428e6			−0.204738
$183$	1.52864e6	+	1.52864e6i	0.249432	+	0.249432i
$184$			4.22441e6i			0.678129i
$185$	−3.04680e6	+	9.70694e6i	−0.481204	+	1.53309i
$186$	2.80396e6			0.435746
$187$	−3.09900e6	+	3.09900e6i	−0.473911	+	0.473911i
$188$			1.52578e6i			0.229625i
$189$			5.28275e6i			0.782483i
$190$	377014.	+	377014.i	0.0549663	+	0.0549663i
$191$	−6.84260e6	−	6.84260e6i	−0.982021	−	0.982021i	0.0178203	−	0.999841i	$-0.494327\pi$
$191$	−6.84260e6	−	6.84260e6i	−0.982021	−	0.982021i	−0.999841	+	0.0178203i	$0.994327\pi$
$192$	405086.			0.0572327
$193$	−8.04844e6	−	8.04844e6i	−1.11954	−	1.11954i	−0.991809	−	0.127732i	$-0.959230\pi$
$193$	−8.04844e6	−	8.04844e6i	−1.11954	−	1.11954i	−0.127732	−	0.991809i	$-0.540770\pi$
$194$	9.23508e6			1.26484
$195$	−1.65471e6			−0.223161
$196$			334424.i			0.0444150i
$197$	−9.33067e6			−1.22043			−0.610217	−	0.792234i	$-0.708918\pi$
$197$	−9.33067e6			−1.22043			−0.610217	+	0.792234i	$0.708918\pi$
$198$	4.31882e6	+	4.31882e6i	0.556378	+	0.556378i
$199$	−9.03343e6	+	9.03343e6i	−1.14629	+	1.14629i	−0.159010	+	0.987277i	$0.550830\pi$
$199$	−9.03343e6	+	9.03343e6i	−1.14629	+	1.14629i	−0.987277	+	0.159010i	$0.949170\pi$
$200$	3.16384e6	−	3.16384e6i	0.395479	−	0.395479i
$201$	−164334.			−0.0202367
$202$	1.87654e6	+	1.87654e6i	0.227668	+	0.227668i
$203$	1.52088e6	−	1.52088e6i	0.181806	−	0.181806i
$204$	−654211.	−	654211.i	−0.0770597	−	0.0770597i
$205$	1.00717e7	−	1.00717e7i	1.16907	−	1.16907i
$206$			7.71682e6i			0.882748i
$207$	−9.50780e6	−	9.50780e6i	−1.07194	−	1.07194i
$208$	−482535.	−	482535.i	−0.0536215	−	0.0536215i
$209$	621802.	−	621802.i	0.0681103	−	0.0681103i
$210$		−	4.59883e6i		−	0.496581i
$211$	−5.29331e6			−0.563482			−0.281741	−	0.959491i	$-0.590912\pi$
$211$	−5.29331e6			−0.563482			−0.281741	+	0.959491i	$0.590912\pi$
$212$		−	535421.i		−	0.0561937i
$213$		−	4.10732e6i		−	0.425030i
$214$	−4.57487e6	+	4.57487e6i	−0.466807	+	0.466807i
$215$			8.12269e6i			0.817306i
$216$	−2.06527e6	+	2.06527e6i	−0.204934	+	0.204934i
$217$	9.28280e6	−	9.28280e6i	0.908447	−	0.908447i
$218$	−1.08078e7			−1.04320
$219$	−8.11069e6			−0.772192
$220$	−8.51662e6	−	8.51662e6i	−0.799833	−	0.799833i
$221$			1.55858e6i			0.144395i
$222$	−1.06081e6	+	3.37967e6i	−0.0969565	+	0.308898i
$223$	1.62356e6			0.146404			0.0732022	−	0.997317i	$-0.476678\pi$
$223$	1.62356e6			0.146404			0.0732022	+	0.997317i	$0.476678\pi$
$224$	1.34108e6	−	1.34108e6i	0.119319	−	0.119319i
$225$			1.42416e7i			1.25029i
$226$		−	1.72733e6i		−	0.149641i
$227$	1.09499e7	+	1.09499e7i	0.936126	+	0.936126i	0.998079	−	0.0619531i	$-0.0197329\pi$
$227$	1.09499e7	+	1.09499e7i	0.936126	+	0.936126i	−0.0619531	+	0.998079i	$0.519733\pi$
$228$	131265.	+	131265.i	0.0110750	+	0.0110750i
$229$	1.86754e7			1.55512			0.777559	−	0.628810i	$-0.216458\pi$
$229$	1.86754e7			1.55512			0.777559	+	0.628810i	$0.216458\pi$
$230$	1.87492e7	+	1.87492e7i	1.54099	+	1.54099i
$231$	−7.58477e6			−0.615328
$232$	1.18916e6			0.0952309
$233$			1.10713e7i			0.875247i	0.899158	+	0.437624i	$0.144180\pi$
$233$			1.10713e7i			0.875247i	−0.899158	+	0.437624i	$0.855820\pi$
$234$	2.17207e6			0.169522
$235$	6.77187e6	+	6.77187e6i	0.521801	+	0.521801i
$236$	−5.12627e6	+	5.12627e6i	−0.390001	+	0.390001i
$237$	−7.05544e6	+	7.05544e6i	−0.530004	+	0.530004i
$238$	−4.33166e6			−0.321309
$239$	8.90181e6	+	8.90181e6i	0.652055	+	0.652055i	0.953488	−	0.301432i	$-0.0974647\pi$
$239$	8.90181e6	+	8.90181e6i	0.652055	+	0.652055i	−0.301432	+	0.953488i	$0.597465\pi$
$240$	1.79789e6	−	1.79789e6i	0.130056	−	0.130056i
$241$	−6.87750e6	−	6.87750e6i	−0.491337	−	0.491337i	0.417390	−	0.908727i	$-0.362945\pi$
$241$	−6.87750e6	−	6.87750e6i	−0.491337	−	0.491337i	−0.908727	+	0.417390i	$0.862945\pi$
$242$	−6.96007e6	+	6.96007e6i	−0.491097	+	0.491097i
$243$		−	1.44891e7i		−	1.00977i
$244$	3.95693e6	+	3.95693e6i	0.272388	+	0.272388i
$245$	1.48427e6	+	1.48427e6i	0.100929	+	0.100929i
$246$	3.50666e6	−	3.50666e6i	0.235553	−	0.235553i
$247$		−	312723.i		−	0.0207524i
$248$	7.25813e6			0.475850
$249$		−	8.86609e6i		−	0.574294i
$250$		−	1.03309e7i		−	0.661177i
$251$	−1.69595e7	+	1.69595e7i	−1.07248	+	1.07248i	−0.0753248	+	0.997159i	$0.523999\pi$
$251$	−1.69595e7	+	1.69595e7i	−1.07248	+	1.07248i	−0.997159	+	0.0753248i	$0.976001\pi$
$252$			6.03668e6i			0.377221i
$253$	3.09227e7	−	3.09227e7i	1.90948	−	1.90948i
$254$	−2.77551e6	+	2.77551e6i	−0.169372	+	0.169372i
$255$	−5.80716e6			−0.350222
$256$	1.04858e6			0.0625000
$257$	−1.19740e7	−	1.19740e7i	−0.705409	−	0.705409i	0.260157	−	0.965566i	$-0.416226\pi$
$257$	−1.19740e7	−	1.19740e7i	−0.705409	−	0.705409i	−0.965566	+	0.260157i	$0.916226\pi$
$258$			2.82808e6i			0.164677i
$259$	7.67681e6	+	1.47006e7i	0.441857	+	0.846128i
$260$	−4.28327e6			−0.243700
$261$	−2.67643e6	+	2.67643e6i	−0.150534	+	0.150534i
$262$			1.25368e7i			0.697081i
$263$		−	534794.i		−	0.0293981i	−0.999892	−	0.0146990i	$-0.995321\pi$
$263$		−	534794.i		−	0.0293981i	0.999892	−	0.0146990i	$-0.00467902\pi$
$264$	−2.96523e6	−	2.96523e6i	−0.161156	−	0.161156i
$265$	−2.37636e6	−	2.37636e6i	−0.127695	−	0.127695i
$266$	869130.			0.0461785
$267$	2.18469e6	+	2.18469e6i	0.114777	+	0.114777i
$268$	−425383.			−0.0220992
$269$	1.01521e7			0.521553			0.260776	−	0.965399i	$-0.416021\pi$
$269$	1.01521e7			0.521553			0.260776	+	0.965399i	$0.416021\pi$
$270$			1.83325e7i			0.931389i
$271$	−3.64203e7			−1.82994			−0.914968	−	0.403526i	$-0.867784\pi$
$271$	−3.64203e7			−1.82994			−0.914968	+	0.403526i	$0.867784\pi$
$272$	−1.69344e6	−	1.69344e6i	−0.0841518	−	0.0841518i
$273$	−1.90731e6	+	1.90731e6i	−0.0937416	+	0.0937416i
$274$	1.11819e7	−	1.11819e7i	0.543579	−	0.543579i
$275$	−4.63186e7			−2.22719
$276$	6.52790e6	+	6.52790e6i	0.310489	+	0.310489i
$277$	2.52880e7	−	2.52880e7i	1.18980	−	1.18980i	0.212682	−	0.977122i	$-0.431780\pi$
$277$	2.52880e7	−	2.52880e7i	1.18980	−	1.18980i	0.977122	−	0.212682i	$-0.0682197\pi$
$278$	−8.13924e6	−	8.13924e6i	−0.378834	−	0.378834i
$279$	−1.63358e7	+	1.63358e7i	−0.752188	+	0.752188i
$280$		−	1.19042e7i		−	0.542283i
$281$	−1.00784e7	−	1.00784e7i	−0.454225	−	0.454225i	0.442529	−	0.896754i	$-0.354081\pi$
$281$	−1.00784e7	−	1.00784e7i	−0.454225	−	0.454225i	−0.896754	+	0.442529i	$0.854081\pi$
$282$	2.35776e6	+	2.35776e6i	0.105136	+	0.105136i
$283$	8.22079e6	−	8.22079e6i	0.362706	−	0.362706i	−0.502102	−	0.864808i	$-0.667440\pi$
$283$	8.22079e6	−	8.22079e6i	0.362706	−	0.362706i	0.864808	+	0.502102i	$0.167440\pi$
$284$		−	1.06319e7i		−	0.464147i
$285$	1.16518e6			0.0503338
$286$			7.06432e6i			0.301976i
$287$		−	2.32183e7i		−	0.982166i
$288$	−2.36001e6	+	2.36001e6i	−0.0987954	+	0.0987954i
$289$		−	1.86678e7i		−	0.773391i
$290$	5.27786e6	−	5.27786e6i	0.216403	−	0.216403i
$291$	1.42708e7	−	1.42708e7i	0.579121	−	0.579121i
$292$	−2.09947e7			−0.843260
$293$	−2.01103e7			−0.799496			−0.399748	−	0.916625i	$-0.630902\pi$
$293$	−2.01103e7			−0.799496			−0.399748	+	0.916625i	$0.630902\pi$
$294$	516780.	+	516780.i	0.0203359	+	0.0203359i
$295$			4.55038e7i			1.77248i
$296$	−2.74592e6	+	8.74835e6i	−0.105880	+	0.337327i
$297$	3.02355e7			1.15411
$298$	1.75516e7	−	1.75516e7i	0.663236	−	0.663236i
$299$		−	1.55520e7i		−	0.581797i
$300$		−	9.77803e6i		−	0.362149i
$301$	9.36263e6	+	9.36263e6i	0.343319	+	0.343319i
$302$	−8.03654e6	−	8.03654e6i	−0.291775	−	0.291775i
$303$	5.79955e6			0.208481
$304$	339782.	+	339782.i	0.0120943	+	0.0120943i
$305$	3.51240e7			1.23795
$306$	7.62280e6			0.266042
$307$		−	8.98342e6i		−	0.310475i	−0.987877	−	0.155238i	$-0.950386\pi$
$307$		−	8.98342e6i		−	0.310475i	0.987877	−	0.155238i	$-0.0496143\pi$
$308$	−1.96334e7			−0.671959
$309$	1.19247e7	+	1.19247e7i	0.404176	+	0.404176i
$310$	3.22137e7	−	3.22137e7i	1.08132	−	1.08132i
$311$	1.58018e7	−	1.58018e7i	0.525320	−	0.525320i	−0.393853	−	0.919173i	$-0.628858\pi$
$311$	1.58018e7	−	1.58018e7i	0.525320	−	0.525320i	0.919173	+	0.393853i	$0.128858\pi$
$312$	−1.49131e6			−0.0491024
$313$	−1.28316e7	−	1.28316e7i	−0.418454	−	0.418454i	0.466217	−	0.884671i	$-0.345617\pi$
$313$	−1.28316e7	−	1.28316e7i	−0.418454	−	0.418454i	−0.884671	+	0.466217i	$0.845617\pi$
$314$	−8.44314e6	+	8.44314e6i	−0.272719	+	0.272719i
$315$	2.67926e7	+	2.67926e7i	0.857201	+	0.857201i
$316$	−1.82632e7	+	1.82632e7i	−0.578782	+	0.578782i
$317$			5.99898e7i			1.88321i	0.336714	+	0.941607i	$0.390684\pi$
$317$			5.99898e7i			1.88321i	−0.336714	+	0.941607i	$0.609316\pi$
$318$	−827376.	−	827376.i	−0.0257289	−	0.0257289i
$319$	−8.70469e6	−	8.70469e6i	−0.268152	−	0.268152i
$320$	4.65389e6	−	4.65389e6i	0.142025	−	0.142025i
$321$			1.41389e7i			0.427466i
$322$	4.32225e7			1.29462
$323$		−	1.09749e6i		−	0.0325682i
$324$		−	7.05817e6i		−	0.207518i
$325$	−1.16475e7	+	1.16475e7i	−0.339299	+	0.339299i
$326$		−	2.82140e7i		−	0.814353i
$327$	−1.67010e7	+	1.67010e7i	−0.477639	+	0.477639i
$328$	9.07709e6	−	9.07709e6i	0.257232	−	0.257232i
$329$	1.56112e7			0.438378
$330$	−2.63212e7			−0.732425
$331$	3.01418e7	+	3.01418e7i	0.831162	+	0.831162i	0.987676	−	0.156514i	$-0.0500257\pi$
$331$	3.01418e7	+	3.01418e7i	0.831162	+	0.831162i	−0.156514	+	0.987676i	$0.550026\pi$
$332$		−	2.29501e7i		−	0.627149i
$333$	−1.35096e7	−	2.58700e7i	−0.365855	−	0.700588i
$334$	−3.14429e7			−0.843884
$335$	−1.88798e6	+	1.88798e6i	−0.0502183	+	0.0502183i
$336$		−	4.14468e6i		−	0.109263i
$337$		−	4.33177e7i		−	1.13182i	−0.824468	−	0.565908i	$-0.808526\pi$
$337$		−	4.33177e7i		−	1.13182i	0.824468	−	0.565908i	$-0.191474\pi$
$338$	−1.75308e7	−	1.75308e7i	−0.453996	−	0.453996i
$339$	−2.66921e6	−	2.66921e6i	−0.0685146	−	0.0685146i
$340$	−1.50320e7			−0.382454
$341$	−5.31295e7	−	5.31295e7i	−1.33990	−	1.33990i
$342$	−1.52948e6			−0.0382355
$343$	4.19413e7			1.03935
$344$			7.32055e6i			0.179833i
$345$	5.79455e7			1.41112
$346$	3.69822e6	+	3.69822e6i	0.0892820	+	0.0892820i
$347$	−2.05380e7	+	2.05380e7i	−0.491553	+	0.491553i	−0.908795	−	0.417242i	$-0.862997\pi$
$347$	−2.05380e7	+	2.05380e7i	−0.491553	+	0.491553i	0.417242	+	0.908795i	$0.362997\pi$
$348$	1.83759e6	−	1.83759e6i	0.0436025	−	0.0436025i
$349$	4.37394e7			1.02895			0.514477	−	0.857504i	$-0.327986\pi$
$349$	4.37394e7			1.02895			0.514477	+	0.857504i	$0.327986\pi$
$350$	−3.23711e7	−	3.23711e7i	−0.755012	−	0.755012i
$351$	7.60318e6	−	7.60318e6i	0.175822	−	0.175822i
$352$	−7.67558e6	−	7.67558e6i	−0.175988	−	0.175988i
$353$	1.13326e7	−	1.13326e7i	0.257636	−	0.257636i	−0.566456	−	0.824092i	$-0.691686\pi$
$353$	1.13326e7	−	1.13326e7i	0.257636	−	0.257636i	0.824092	+	0.566456i	$0.191686\pi$
$354$			1.58431e7i			0.357132i
$355$	−4.71875e7	−	4.71875e7i	−1.05473	−	1.05473i
$356$	5.65513e6	+	5.65513e6i	0.125341	+	0.125341i
$357$	−6.69363e6	+	6.69363e6i	−0.147115	+	0.147115i
$358$		−	8.85493e6i		−	0.192991i
$359$	8.54266e6			0.184633			0.0923166	−	0.995730i	$-0.470573\pi$
$359$	8.54266e6			0.184633			0.0923166	+	0.995730i	$0.470573\pi$
$360$			2.09489e7i			0.449007i
$361$		−	4.68257e7i		−	0.995319i
$362$	4.26289e7	−	4.26289e7i	0.898624	−	0.898624i
$363$			2.15105e7i			0.449709i
$364$	−4.93711e6	+	4.93711e6i	−0.102369	+	0.102369i
$365$	−9.31807e7	+	9.31807e7i	−1.91623	+	1.91623i
$366$	1.22291e7			0.249432
$367$	4.25372e7			0.860539			0.430270	−	0.902700i	$-0.358419\pi$
$367$	4.25372e7			0.860539			0.430270	+	0.902700i	$0.358419\pi$
$368$	1.68976e7	+	1.68976e7i	0.339065	+	0.339065i
$369$			4.08593e7i			0.813227i
$370$	2.66406e7	+	5.10150e7i	0.525942	+	1.00715i
$371$	−5.47822e6			−0.107280
$372$	1.12159e7	−	1.12159e7i	0.217873	−	0.217873i
$373$			3.73534e7i			0.719787i	0.932993	+	0.359894i	$0.117187\pi$
$373$			3.73534e7i			0.719787i	−0.932993	+	0.359894i	$0.882813\pi$
$374$			2.47920e7i			0.473911i
$375$	−1.59641e7	−	1.59641e7i	−0.302727	−	0.302727i
$376$	6.10313e6	+	6.10313e6i	0.114812	+	0.114812i
$377$	−4.37785e6			−0.0817028
$378$	2.11310e7	+	2.11310e7i	0.391241	+	0.391241i
$379$	−4.44387e7			−0.816288			−0.408144	−	0.912918i	$-0.633824\pi$
$379$	−4.44387e7			−0.816288			−0.408144	+	0.912918i	$0.633824\pi$
$380$	3.01611e6			0.0549663
$381$			8.57790e6i			0.155098i
$382$	−5.47408e7			−0.982021
$383$	5.52203e7	+	5.52203e7i	0.982885	+	0.982885i	0.999856	−	0.0169713i	$-0.00540239\pi$
$383$	5.52203e7	+	5.52203e7i	0.982885	+	0.982885i	−0.0169713	+	0.999856i	$0.505402\pi$
$384$	1.62035e6	−	1.62035e6i	0.0286163	−	0.0286163i
$385$	−8.71387e7	+	8.71387e7i	−1.52696	+	1.52696i
$386$	−6.43875e7			−1.11954
$387$	−1.64762e7	−	1.64762e7i	−0.284266	−	0.284266i
$388$	3.69403e7	−	3.69403e7i	0.632420	−	0.632420i
$389$	5.95371e7	+	5.95371e7i	1.01144	+	1.01144i	0.999934	+	0.0115037i	$0.00366183\pi$
$389$	5.95371e7	+	5.95371e7i	1.01144	+	1.01144i	0.0115037	+	0.999934i	$0.496338\pi$
$390$	−6.61885e6	+	6.61885e6i	−0.111581	+	0.111581i
$391$		−	5.45791e7i		−	0.913053i
$392$	1.33770e6	+	1.33770e6i	0.0222075	+	0.0222075i
$393$	1.93729e7	+	1.93729e7i	0.319166	+	0.319166i
$394$	−3.73227e7	+	3.73227e7i	−0.610217	+	0.610217i
$395$			1.62115e8i			2.63046i
$396$	3.45506e7			0.556378
$397$		−	7.15452e7i		−	1.14343i	−0.820453	−	0.571714i	$-0.806279\pi$
$397$		−	7.15452e7i		−	1.14343i	0.820453	−	0.571714i	$-0.193721\pi$
$398$			7.22674e7i			1.14629i
$399$	1.34305e6	−	1.34305e6i	0.0211433	−	0.0211433i
$400$		−	2.53107e7i		−	0.395479i
$401$	−4.66890e7	+	4.66890e7i	−0.724072	+	0.724072i	−0.969432	−	0.245360i	$-0.921094\pi$
$401$	−4.66890e7	+	4.66890e7i	−0.724072	+	0.724072i	0.245360	+	0.969432i	$0.421094\pi$
$402$	−657337.	+	657337.i	−0.0101184	+	0.0101184i
$403$	−2.67205e7			−0.408252
$404$	1.50123e7			0.227668
$405$	−3.13262e7	−	3.13262e7i	−0.471567	−	0.471567i
$406$		−	1.21671e7i		−	0.181806i
$407$	8.41381e7	−	4.39378e7i	1.24799	−	0.651711i
$408$	−5.23369e6			−0.0770597
$409$	−1.42406e7	+	1.42406e7i	−0.208142	+	0.208142i	−0.803477	−	0.595336i	$-0.797019\pi$
$409$	−1.42406e7	+	1.42406e7i	−0.208142	+	0.208142i	0.595336	+	0.803477i	$0.297019\pi$
$410$		−	8.05736e7i		−	1.16907i
$411$		−	3.45583e7i		−	0.497768i
$412$	3.08673e7	+	3.08673e7i	0.441374	+	0.441374i
$413$	5.24500e7	+	5.24500e7i	0.744552	+	0.744552i
$414$	−7.60624e7			−1.07194
$415$	−1.01859e8	−	1.01859e8i	−1.42514	−	1.42514i
$416$	−3.86028e6			−0.0536215
$417$	−2.51548e7			−0.346907
$418$		−	4.97441e6i		−	0.0681103i
$419$	4.45066e7			0.605037			0.302519	−	0.953144i	$-0.402173\pi$
$419$	4.45066e7			0.605037			0.302519	+	0.953144i	$0.402173\pi$
$420$	−1.83953e7	−	1.83953e7i	−0.248290	−	0.248290i
$421$	9.01397e7	−	9.01397e7i	1.20801	−	1.20801i	0.236336	−	0.971671i	$-0.424053\pi$
$421$	9.01397e7	−	9.01397e7i	1.20801	−	1.20801i	0.971671	−	0.236336i	$-0.0759466\pi$
$422$	−2.11732e7	+	2.11732e7i	−0.281741	+	0.281741i
$423$	−2.74724e7			−0.362974
$424$	−2.14168e6	−	2.14168e6i	−0.0280969	−	0.0280969i
$425$	−4.08765e7	+	4.08765e7i	−0.532485	+	0.532485i
$426$	−1.64293e7	−	1.64293e7i	−0.212515	−	0.212515i
$427$	4.04857e7	−	4.04857e7i	0.520018	−	0.520018i
$428$			3.65990e7i			0.466807i
$429$	1.09164e7	+	1.09164e7i	0.138263	+	0.138263i
$430$	3.24908e7	+	3.24908e7i	0.408653	+	0.408653i
$431$	5.00465e6	−	5.00465e6i	0.0625089	−	0.0625089i	−0.675161	−	0.737670i	$-0.735926\pi$
$431$	5.00465e6	−	5.00465e6i	0.0625089	−	0.0625089i	0.737670	+	0.675161i	$0.235926\pi$
$432$			1.65221e7i			0.204934i
$433$	−7.38688e7			−0.909908			−0.454954	−	0.890515i	$-0.650344\pi$
$433$	−7.38688e7			−0.909908			−0.454954	+	0.890515i	$0.650344\pi$
$434$		−	7.42624e7i		−	0.908447i
$435$		−	1.63116e7i		−	0.198165i
$436$	−4.32310e7	+	4.32310e7i	−0.521598	+	0.521598i
$437$			1.09511e7i			0.131224i
$438$	−3.24427e7	+	3.24427e7i	−0.386096	+	0.386096i
$439$	4.68662e6	−	4.68662e6i	0.0553944	−	0.0553944i	−0.678867	−	0.734261i	$-0.737529\pi$
$439$	4.68662e6	−	4.68662e6i	0.0553944	−	0.0553944i	0.734261	+	0.678867i	$0.237529\pi$
$440$	−6.81330e7			−0.799833
$441$	−6.02146e6			−0.0702079
$442$	6.23432e6	+	6.23432e6i	0.0721975	+	0.0721975i
$443$		−	1.06999e8i		−	1.23075i	−0.788235	−	0.615374i	$-0.789005\pi$
$443$		−	1.06999e8i		−	1.23075i	0.788235	−	0.615374i	$-0.210995\pi$
$444$	9.27544e6	+	1.77619e7i	0.105971	+	0.202927i
$445$	5.01983e7			0.569651
$446$	6.49424e6	−	6.49424e6i	0.0732022	−	0.0732022i
$447$		−	5.42444e7i		−	0.607340i
$448$		−	1.07286e7i		−	0.119319i
$449$	4.37631e7	+	4.37631e7i	0.483469	+	0.483469i	0.906238	−	0.422769i	$-0.138942\pi$
$449$	4.37631e7	+	4.37631e7i	0.483469	+	0.483469i	−0.422769	+	0.906238i	$0.638942\pi$
$450$	5.69663e7	+	5.69663e7i	0.625145	+	0.625145i
$451$	−1.32889e8			−1.44863
$452$	−6.90931e6	−	6.90931e6i	−0.0748203	−	0.0748203i
$453$	−2.48374e7			−0.267185
$454$	8.75995e7			0.936126
$455$			4.38247e7i			0.465248i
$456$	1.05012e6			0.0110750
$457$	−7.65822e7	−	7.65822e7i	−0.802378	−	0.802378i	0.181088	−	0.983467i	$-0.442038\pi$
$457$	−7.65822e7	−	7.65822e7i	−0.802378	−	0.802378i	−0.983467	+	0.181088i	$0.942038\pi$
$458$	7.47016e7	−	7.47016e7i	0.777559	−	0.777559i
$459$	2.66831e7	−	2.66831e7i	0.275930	−	0.275930i
$460$	1.49993e8			1.54099
$461$	6.56687e7	+	6.56687e7i	0.670279	+	0.670279i	0.957780	−	0.287501i	$-0.0928245\pi$
$461$	6.56687e7	+	6.56687e7i	0.670279	+	0.670279i	−0.287501	+	0.957780i	$0.592825\pi$
$462$	−3.03391e7	+	3.03391e7i	−0.307664	+	0.307664i
$463$	7.49580e7	+	7.49580e7i	0.755222	+	0.755222i	0.975449	−	0.220226i	$-0.0706796\pi$
$463$	7.49580e7	+	7.49580e7i	0.755222	+	0.755222i	−0.220226	+	0.975449i	$0.570680\pi$
$464$	4.75666e6	−	4.75666e6i	0.0476154	−	0.0476154i
$465$		−	9.95586e7i		−	0.990193i
$466$	4.42852e7	+	4.42852e7i	0.437624	+	0.437624i
$467$	4.15210e7	+	4.15210e7i	0.407678	+	0.407678i	0.880928	−	0.473250i	$-0.156919\pi$
$467$	4.15210e7	+	4.15210e7i	0.407678	+	0.407678i	−0.473250	+	0.880928i	$0.656919\pi$
$468$	8.68827e6	−	8.68827e6i	0.0847609	−	0.0847609i
$469$			4.35236e6i			0.0421896i
$470$	5.41750e7			0.521801
$471$			2.60941e7i			0.249735i
$472$			4.10101e7i			0.390001i
$473$	5.35865e7	−	5.35865e7i	0.506374	−	0.506374i
$474$			5.64435e7i			0.530004i
$475$	8.20171e6	−	8.20171e6i	0.0765286	−	0.0765286i
$476$	−1.73266e7	+	1.73266e7i	−0.160655	+	0.160655i
$477$	9.64050e6			0.0888269
$478$	7.12145e7			0.652055
$479$	−4.03691e7	−	4.03691e7i	−0.367318	−	0.367318i	0.499180	−	0.866498i	$-0.333635\pi$
$479$	−4.03691e7	−	4.03691e7i	−0.367318	−	0.367318i	−0.866498	+	0.499180i	$0.833635\pi$
$480$		−	1.43831e7i		−	0.130056i
$481$	1.01090e7	−	3.22066e7i	0.0908389	−	0.289408i
$482$	−5.50200e7			−0.491337
$483$	6.67909e7	−	6.67909e7i	0.592756	−	0.592756i
$484$			5.56806e7i			0.491097i
$485$		−	3.27904e8i		−	2.87423i
$486$	−5.79562e7	−	5.79562e7i	−0.504884	−	0.504884i
$487$	−7.17600e7	−	7.17600e7i	−0.621292	−	0.621292i	0.324570	−	0.945862i	$-0.394780\pi$
$487$	−7.17600e7	−	7.17600e7i	−0.621292	−	0.621292i	−0.945862	+	0.324570i	$0.894780\pi$
$488$	3.16554e7			0.272388
$489$	−4.35986e7	−	4.35986e7i	−0.372861	−	0.372861i
$490$	1.18742e7			0.100929
$491$	4.14336e7			0.350032			0.175016	−	0.984566i	$-0.444002\pi$
$491$	4.14336e7			0.350032			0.175016	+	0.984566i	$0.444002\pi$
$492$		−	2.80533e7i		−	0.235553i
$493$	−1.53639e7			−0.128222
$494$	−1.25089e6	−	1.25089e6i	−0.0103762	−	0.0103762i
$495$	1.53346e8	−	1.53346e8i	1.26432	−	1.26432i
$496$	2.90325e7	−	2.90325e7i	0.237925	−	0.237925i
$497$	−1.08781e8			−0.886105
$498$	−3.54644e7	−	3.54644e7i	−0.287147	−	0.287147i
$499$	−1.30951e8	+	1.30951e8i	−1.05392	+	1.05392i	−0.0554603	+	0.998461i	$0.517663\pi$
$499$	−1.30951e8	+	1.30951e8i	−1.05392	+	1.05392i	−0.998461	+	0.0554603i	$0.982337\pi$
$500$	−4.13236e7	−	4.13236e7i	−0.330589	−	0.330589i
$501$	−4.85881e7	+	4.85881e7i	−0.386382	+	0.386382i
$502$			1.35676e8i			1.07248i
$503$	2.07372e6	+	2.07372e6i	0.0162947	+	0.0162947i	0.715207	−	0.698913i	$-0.246332\pi$
$503$	2.07372e6	+	2.07372e6i	0.0162947	+	0.0162947i	−0.698913	+	0.715207i	$0.746332\pi$
$504$	2.41467e7	+	2.41467e7i	0.188611	+	0.188611i
$505$	6.66290e7	−	6.66290e7i	0.517355	−	0.517355i
$506$		−	2.47381e8i		−	1.90948i
$507$	−5.41801e7			−0.415734
$508$			2.22041e7i			0.169372i
$509$		−	1.23587e8i		−	0.937175i	−0.883417	−	0.468588i	$-0.844763\pi$
$509$		−	1.23587e8i		−	0.937175i	0.883417	−	0.468588i	$-0.155237\pi$
$510$	−2.32287e7	+	2.32287e7i	−0.175111	+	0.175111i
$511$			2.14810e8i			1.60987i
$512$	4.19430e6	−	4.19430e6i	0.0312500	−	0.0312500i
$513$	−5.35386e6	+	5.35386e6i	−0.0396565	+	0.0396565i
$514$	−9.57923e7			−0.705409
$515$	2.73996e8			2.00596
$516$	1.13123e7	+	1.13123e7i	0.0823384	+	0.0823384i
$517$		−	8.93498e7i		−	0.646580i
$518$	8.95097e7	+	2.80952e7i	0.643992	+	0.202136i
$519$	1.14296e7			0.0817576
$520$	−1.71331e7	+	1.71331e7i	−0.121850	+	0.121850i
$521$		−	1.40526e8i		−	0.993673i	−0.867844	−	0.496836i	$-0.834495\pi$
$521$		−	1.40526e8i		−	0.993673i	0.867844	−	0.496836i	$-0.165505\pi$
$522$			2.14114e7i			0.150534i
$523$	−1.82286e6	−	1.82286e6i	−0.0127423	−	0.0127423i	0.700707	−	0.713449i	$-0.252868\pi$
$523$	−1.82286e6	−	1.82286e6i	−0.0127423	−	0.0127423i	−0.713449	+	0.700707i	$0.752868\pi$
$524$	5.01472e7	+	5.01472e7i	0.348540	+	0.348540i
$525$	−1.00045e8			−0.691381
$526$	−2.13918e6	−	2.13918e6i	−0.0146990	−	0.0146990i
$527$	−9.37746e7			−0.640698
$528$	−2.37219e7			−0.161156
$529$			3.96570e8i			2.67887i
$530$	−1.90109e7			−0.127695
$531$	−9.23008e7	−	9.23008e7i	−0.616484	−	0.616484i
$532$	3.47652e6	−	3.47652e6i	0.0230892	−	0.0230892i
$533$	−3.34169e7	+	3.34169e7i	−0.220691	+	0.220691i
$534$	1.74775e7			0.114777
$535$	1.62437e8	+	1.62437e8i	1.06078	+	1.06078i
$536$	−1.70153e6	+	1.70153e6i	−0.0110496	+	0.0110496i
$537$	−1.36834e7	−	1.36834e7i	−0.0883629	−	0.0883629i
$538$	4.06083e7	−	4.06083e7i	0.260776	−	0.260776i
$539$		−	1.95839e7i		−	0.125064i
$540$	7.33301e7	+	7.33301e7i	0.465695	+	0.465695i
$541$	−1.79190e8	−	1.79190e8i	−1.13168	−	1.13168i	−0.989898	−	0.141780i	$-0.954717\pi$
$541$	−1.79190e8	−	1.79190e8i	−1.13168	−	1.13168i	−0.141780	−	0.989898i	$-0.545283\pi$
$542$	−1.45681e8	+	1.45681e8i	−0.914968	+	0.914968i
$543$		−	1.31747e8i		−	0.822890i
$544$	−1.35475e7			−0.0841518
$545$			3.83744e8i			2.37057i
$546$			1.52585e7i			0.0937416i
$547$	−1.12148e8	+	1.12148e8i	−0.685216	+	0.685216i	−0.961171	−	0.275954i	$-0.911006\pi$
$547$	−1.12148e8	+	1.12148e8i	−0.685216	+	0.685216i	0.275954	+	0.961171i	$0.411006\pi$
$548$		−	8.94550e7i		−	0.543579i
$549$	−7.12463e7	+	7.12463e7i	−0.430571	+	0.430571i
$550$	−1.85274e8	+	1.85274e8i	−1.11359	+	1.11359i
$551$	3.08271e6			0.0184280
$552$	5.22232e7			0.310489
$553$	1.86862e8	+	1.86862e8i	1.10496	+	1.10496i
$554$		−	2.02304e8i		−	1.18980i
$555$	1.20000e8	+	3.76653e7i	0.701942	+	0.220325i
$556$	−6.51139e7			−0.378834
$557$	−4.61077e7	+	4.61077e7i	−0.266814	+	0.266814i	−0.827815	−	0.561001i	$-0.810416\pi$
$557$	−4.61077e7	+	4.61077e7i	−0.266814	+	0.266814i	0.561001	+	0.827815i	$0.310416\pi$
$558$			1.30686e8i			0.752188i
$559$		−	2.69503e7i		−	0.154286i
$560$	−4.76168e7	−	4.76168e7i	−0.271141	−	0.271141i
$561$	3.83106e7	+	3.83106e7i	0.216985	+	0.216985i
$562$	−8.06269e7			−0.454225
$563$	−8.28031e6	−	8.28031e6i	−0.0464003	−	0.0464003i	0.683526	−	0.729926i	$-0.260446\pi$
$563$	−8.28031e6	−	8.28031e6i	−0.0464003	−	0.0464003i	−0.729926	+	0.683526i	$0.760446\pi$
$564$	1.88621e7			0.105136
$565$	−6.13311e7			−0.340044
$566$		−	6.57663e7i		−	0.362706i
$567$	−7.22164e7			−0.396174
$568$	−4.25276e7	−	4.25276e7i	−0.232074	−	0.232074i
$569$	−4.71454e7	+	4.71454e7i	−0.255919	+	0.255919i	−0.823392	−	0.567473i	$-0.807921\pi$
$569$	−4.71454e7	+	4.71454e7i	−0.255919	+	0.255919i	0.567473	+	0.823392i	$0.307921\pi$
$570$	4.66074e6	−	4.66074e6i	0.0251669	−	0.0251669i
$571$	2.39611e8			1.28706			0.643529	−	0.765422i	$-0.277470\pi$
$571$	2.39611e8			1.28706			0.643529	+	0.765422i	$0.277470\pi$
$572$	2.82573e7	+	2.82573e7i	0.150988	+	0.150988i
$573$	−8.45899e7	+	8.45899e7i	−0.449629	+	0.449629i
$574$	−9.28732e7	−	9.28732e7i	−0.491083	−	0.491083i
$575$	4.07878e8	−	4.07878e8i	2.14549	−	2.14549i
$576$			1.88801e7i			0.0987954i
$577$	8.40950e6	+	8.40950e6i	0.0437767	+	0.0437767i	0.728656	−	0.684880i	$-0.240145\pi$
$577$	8.40950e6	+	8.40950e6i	0.0437767	+	0.0437767i	−0.684880	+	0.728656i	$0.740145\pi$
$578$	−7.46711e7	−	7.46711e7i	−0.386696	−	0.386696i
$579$	−9.94969e7	+	9.94969e7i	−0.512594	+	0.512594i
$580$		−	4.22229e7i		−	0.216403i
$581$	−2.34816e8			−1.19729
$582$		−	1.14166e8i		−	0.579121i
$583$			3.13543e7i			0.158231i
$584$	−8.39789e7	+	8.39789e7i	−0.421630	+	0.421630i
$585$		−	7.71222e7i		−	0.385223i
$586$	−8.04414e7	+	8.04414e7i	−0.399748	+	0.399748i
$587$	3.25252e7	−	3.25252e7i	0.160807	−	0.160807i	−0.622117	−	0.782924i	$-0.713727\pi$
$587$	3.25252e7	−	3.25252e7i	0.160807	−	0.160807i	0.782924	+	0.622117i	$0.213727\pi$
$588$	4.13424e6			0.0203359
$589$	1.88155e7			0.0920809
$590$	1.82015e8	+	1.82015e8i	0.886240	+	0.886240i
$591$			1.15348e8i			0.558789i
$592$	2.40097e7	+	4.59771e7i	0.115724	+	0.221603i
$593$	−4.91588e7			−0.235742			−0.117871	−	0.993029i	$-0.537607\pi$
$593$	−4.91588e7			−0.235742			−0.117871	+	0.993029i	$0.537607\pi$
$594$	1.20942e8	−	1.20942e8i	0.577056	−	0.577056i
$595$			1.53801e8i			0.730145i
$596$		−	1.40413e8i		−	0.663236i
$597$	1.11674e8	+	1.11674e8i	0.524840	+	0.524840i
$598$	−6.22078e7	−	6.22078e7i	−0.290898	−	0.290898i
$599$	9.79457e6			0.0455727			0.0227864	−	0.999740i	$-0.492746\pi$
$599$	9.79457e6			0.0455727			0.0227864	+	0.999740i	$0.492746\pi$
$600$	−3.91121e7	−	3.91121e7i	−0.181075	−	0.181075i
$601$	−3.08738e8			−1.42222			−0.711111	−	0.703080i	$-0.751808\pi$
$601$	−3.08738e8			−1.42222			−0.711111	+	0.703080i	$0.751808\pi$
$602$	7.49010e7			0.343319
$603$		−	7.65922e6i		−	0.0349328i
$604$	−6.42924e7			−0.291775
$605$	2.47127e8	+	2.47127e8i	1.11597	+	1.11597i
$606$	2.31982e7	−	2.31982e7i	0.104241	−	0.104241i
$607$	−5.43133e7	+	5.43133e7i	−0.242851	+	0.242851i	−0.818029	−	0.575178i	$-0.804933\pi$
$607$	−5.43133e7	+	5.43133e7i	−0.242851	+	0.242851i	0.575178	+	0.818029i	$0.304933\pi$
$608$	2.71826e6			0.0120943
$609$	−1.88015e7	−	1.88015e7i	−0.0832418	−	0.0832418i
$610$	1.40496e8	−	1.40496e8i	0.618977	−	0.618977i
$611$	−2.24684e7	−	2.24684e7i	−0.0985027	−	0.0985027i
$612$	3.04912e7	−	3.04912e7i	0.133021	−	0.133021i
$613$			3.61934e8i			1.57126i	0.618697	+	0.785630i	$0.287661\pi$
$613$			3.61934e8i			1.57126i	−0.618697	+	0.785630i	$0.712339\pi$
$614$	−3.59337e7	−	3.59337e7i	−0.155238	−	0.155238i
$615$	−1.24509e8	−	1.24509e8i	−0.535273	−	0.535273i
$616$	−7.85335e7	+	7.85335e7i	−0.335980	+	0.335980i
$617$			3.23628e7i			0.137781i	0.997624	+	0.0688907i	$0.0219460\pi$
$617$			3.23628e7i			0.137781i	−0.997624	+	0.0688907i	$0.978054\pi$
$618$	9.53973e7			0.404176
$619$			2.42596e7i			0.102285i	0.998691	+	0.0511425i	$0.0162863\pi$
$619$			2.42596e7i			0.102285i	−0.998691	+	0.0511425i	$0.983714\pi$
$620$		−	2.57710e8i		−	1.08132i
$621$	−2.66252e8	+	2.66252e8i	−1.11178	+	1.11178i
$622$		−	1.26414e8i		−	0.525320i
$623$	5.78611e7	−	5.78611e7i	0.239289	−	0.239289i
$624$	−5.96522e6	+	5.96522e6i	−0.0245512	+	0.0245512i
$625$	1.93979e7			0.0794538
$626$	−1.02653e8			−0.418454
$627$	−7.68687e6	−	7.68687e6i	−0.0311851	−	0.0311851i
$628$			6.75451e7i			0.272719i
$629$	3.54771e7	−	1.13028e8i	0.142560	−	0.454187i
$630$	2.14340e8			0.857201
$631$	9.57666e7	−	9.57666e7i	0.381177	−	0.381177i	−0.490349	−	0.871526i	$-0.663131\pi$
$631$	9.57666e7	−	9.57666e7i	0.381177	−	0.381177i	0.871526	+	0.490349i	$0.163131\pi$
$632$			1.46105e8i			0.578782i
$633$			6.54372e7i			0.257996i
$634$	2.39959e8	+	2.39959e8i	0.941607	+	0.941607i
$635$	9.85484e7	+	9.85484e7i	0.384883	+	0.384883i
$636$	−6.61901e6			−0.0257289
$637$	−4.92467e6	−	4.92467e6i	−0.0190528	−	0.0190528i
$638$	−6.96375e7			−0.268152
$639$	1.91432e8			0.733689
$640$		−	3.72311e7i		−	0.142025i
$641$	−2.72419e8			−1.03434			−0.517169	−	0.855883i	$-0.673014\pi$
$641$	−2.72419e8			−1.03434			−0.517169	+	0.855883i	$0.673014\pi$
$642$	5.65557e7	+	5.65557e7i	0.213733	+	0.213733i
$643$	6.05275e7	−	6.05275e7i	0.227677	−	0.227677i	−0.584044	−	0.811722i	$-0.698531\pi$
$643$	6.05275e7	−	6.05275e7i	0.227677	−	0.227677i	0.811722	+	0.584044i	$0.198531\pi$
$644$	1.72890e8	−	1.72890e8i	0.647310	−	0.647310i
$645$	1.00415e8			0.374213
$646$	−4.38996e6	−	4.38996e6i	−0.0162841	−	0.0162841i
$647$	−2.01584e8	+	2.01584e8i	−0.744291	+	0.744291i	−0.973401	−	0.229109i	$-0.926419\pi$
$647$	−2.01584e8	+	2.01584e8i	−0.744291	+	0.744291i	0.229109	+	0.973401i	$0.426419\pi$
$648$	−2.82327e7	−	2.82327e7i	−0.103759	−	0.103759i
$649$	3.00194e8	−	3.00194e8i	1.09817	−	1.09817i
$650$			9.31801e7i			0.339299i
$651$	−1.14756e8	−	1.14756e8i	−0.415943	−	0.415943i
$652$	−1.12856e8	−	1.12856e8i	−0.407176	−	0.407176i
$653$	1.22917e7	−	1.22917e7i	0.0441439	−	0.0441439i	−0.684690	−	0.728834i	$-0.740063\pi$
$653$	1.22917e7	−	1.22917e7i	0.0441439	−	0.0441439i	0.728834	+	0.684690i	$0.240063\pi$
$654$			1.33608e8i			0.477639i
$655$	4.45137e8			1.58405
$656$		−	7.26167e7i		−	0.257232i
$657$		−	3.78019e8i		−	1.33296i
$658$	6.24448e7	−	6.24448e7i	0.219189	−	0.219189i
$659$			1.12317e8i			0.392456i	0.980558	+	0.196228i	$0.0628693\pi$
$659$			1.12317e8i			0.392456i	−0.980558	+	0.196228i	$0.937131\pi$
$660$	−1.05285e8	+	1.05285e8i	−0.366213	+	0.366213i
$661$	−9.92510e6	+	9.92510e6i	−0.0343661	+	0.0343661i	−0.724081	−	0.689715i	$-0.757736\pi$
$661$	−9.92510e6	+	9.92510e6i	−0.0343661	+	0.0343661i	0.689715	+	0.724081i	$0.257736\pi$
$662$	2.41135e8			0.831162
$663$	1.92676e7			0.0661129
$664$	−9.18004e7	−	9.18004e7i	−0.313574	−	0.313574i
$665$		−	3.08596e7i		−	0.104936i
$666$	−1.57518e8	−	4.94416e7i	−0.533222	−	0.167367i
$667$	1.53306e8			0.516631
$668$	−1.25772e8	+	1.25772e8i	−0.421942	+	0.421942i
$669$		−	2.00709e7i		−	0.0670329i
$670$			1.51038e7i			0.0502183i
$671$	−2.31718e8	−	2.31718e8i	−0.766993	−	0.766993i
$672$	−1.65787e7	−	1.65787e7i	−0.0546316	−	0.0546316i
$673$	−1.62562e8			−0.533301			−0.266651	−	0.963793i	$-0.585917\pi$
$673$	−1.62562e8			−0.533301			−0.266651	+	0.963793i	$0.585917\pi$
$674$	−1.73271e8	−	1.73271e8i	−0.565908	−	0.565908i
$675$	3.98814e8			1.29676
$676$	−1.40246e8			−0.453996
$677$			3.93482e8i			1.26811i	0.773286	+	0.634057i	$0.218612\pi$
$677$			3.93482e8i			1.26811i	−0.773286	+	0.634057i	$0.781388\pi$
$678$	−2.13537e7			−0.0685146
$679$	−3.77959e8	−	3.77959e8i	−1.20736	−	1.20736i
$680$	−6.01280e7	+	6.01280e7i	−0.191227	+	0.191227i
$681$	1.35366e8	−	1.35366e8i	0.428616	−	0.428616i
$682$	−4.25036e8			−1.33990
$683$	3.93184e8	+	3.93184e8i	1.23405	+	1.23405i	0.962393	+	0.271660i	$0.0875726\pi$
$683$	3.93184e8	+	3.93184e8i	1.23405	+	1.23405i	0.271660	+	0.962393i	$0.412427\pi$
$684$	−6.11794e6	+	6.11794e6i	−0.0191177	+	0.0191177i
$685$	−3.97028e8	−	3.97028e8i	−1.23523	−	1.23523i
$686$	1.67765e8	−	1.67765e8i	0.519673	−	0.519673i
$687$		−	2.30870e8i		−	0.712028i
$688$	2.92822e7	+	2.92822e7i	0.0899163	+	0.0899163i
$689$	7.88450e6	+	7.88450e6i	0.0241055	+	0.0241055i
$690$	2.31782e8	−	2.31782e8i	0.705558	−	0.705558i
$691$			2.50617e8i			0.759585i	0.925072	+	0.379792i	$0.124005\pi$
$691$			2.50617e8i			0.759585i	−0.925072	+	0.379792i	$0.875995\pi$
$692$	2.95857e7			0.0892820
$693$		−	3.53508e8i		−	1.06218i
$694$			1.64304e8i			0.491553i
$695$	−2.88995e8	+	2.88995e8i	−0.860866	+	0.860866i
$696$		−	1.47007e7i		−	0.0436025i
$697$	−1.17275e8	+	1.17275e8i	−0.346345	+	0.346345i
$698$	1.74957e8	−	1.74957e8i	0.514477	−	0.514477i
$699$	1.36866e8			0.400742
$700$	−2.58969e8			−0.755012
$701$	−1.54838e8	−	1.54838e8i	−0.449495	−	0.449495i	0.445692	−	0.895187i	$-0.352958\pi$
$701$	−1.54838e8	−	1.54838e8i	−0.449495	−	0.449495i	−0.895187	+	0.445692i	$0.852958\pi$
$702$		−	6.08254e7i		−	0.175822i
$703$	−7.11834e6	+	2.26786e7i	−0.0204886	+	0.0652756i
$704$	−6.14046e7			−0.175988
$705$	8.37156e7	−	8.37156e7i	0.238913	−	0.238913i
$706$		−	9.06609e7i		−	0.257636i
$707$		−	1.53600e8i		−	0.434643i
$708$	6.33722e7	+	6.33722e7i	0.178566	+	0.178566i
$709$	1.16587e8	+	1.16587e8i	0.327123	+	0.327123i	0.851492	−	0.524368i	$-0.175698\pi$
$709$	1.16587e8	+	1.16587e8i	0.327123	+	0.327123i	−0.524368	+	0.851492i	$0.675698\pi$
$710$	−3.77500e8			−1.05473
$711$	−3.28837e8	−	3.28837e8i	−0.914896	−	0.914896i
$712$	4.52411e7			0.125341
$713$	9.35709e8			2.58150
$714$			5.35490e7i			0.147115i
$715$	2.50828e8			0.686212
$716$	−3.54197e7	−	3.54197e7i	−0.0964953	−	0.0964953i
$717$	1.10046e8	−	1.10046e8i	0.298551	−	0.298551i
$718$	3.41706e7	−	3.41706e7i	0.0923166	−	0.0923166i
$719$	−5.20524e8			−1.40041			−0.700203	−	0.713944i	$-0.746907\pi$
$719$	−5.20524e8			−1.40041			−0.700203	+	0.713944i	$0.746907\pi$
$720$	8.37954e7	+	8.37954e7i	0.224503	+	0.224503i
$721$	3.15822e8	−	3.15822e8i	0.842629	−	0.842629i
$722$	−1.87303e8	−	1.87303e8i	−0.497660	−	0.497660i
$723$	−8.50214e7	+	8.50214e7i	−0.224964	+	0.224964i
$724$		−	3.41031e8i		−	0.898624i
$725$	−1.14817e8	−	1.14817e8i	−0.301295	−	0.301295i
$726$	8.60421e7	+	8.60421e7i	0.224854	+	0.224854i
$727$	−3.16206e8	+	3.16206e8i	−0.822938	+	0.822938i	−0.986528	−	0.163590i	$-0.947693\pi$
$727$	−3.16206e8	+	3.16206e8i	−0.822938	+	0.822938i	0.163590	+	0.986528i	$0.447693\pi$
$728$			3.94969e7i			0.102369i
$729$	−1.83235e7			−0.0472962
$730$			7.45446e8i			1.91623i
$731$		−	9.45811e7i		−	0.242132i
$732$	4.89165e7	−	4.89165e7i	0.124716	−	0.124716i
$733$			5.78289e8i			1.46836i	0.678954	+	0.734181i	$0.262434\pi$
$733$			5.78289e8i			1.46836i	−0.678954	+	0.734181i	$0.737566\pi$
$734$	1.70149e8	−	1.70149e8i	0.430270	−	0.430270i
$735$	1.83490e7	−	1.83490e7i	0.0462115	−	0.0462115i
$736$	1.35181e8			0.339065
$737$	2.49105e7			0.0622271
$738$	1.63437e8	+	1.63437e8i	0.406613	+	0.406613i
$739$			3.00683e8i			0.745033i	0.928026	+	0.372516i	$0.121505\pi$
$739$			3.00683e8i			0.745033i	−0.928026	+	0.372516i	$0.878495\pi$
$740$	3.10622e8	+	9.74977e7i	0.766544	+	0.240602i
$741$	−3.86596e6			−0.00950173
$742$	−2.19129e7	+	2.19129e7i	−0.0536398	+	0.0536398i
$743$		−	3.28721e8i		−	0.801422i	−0.916204	−	0.400711i	$-0.868763\pi$
$743$		−	3.28721e8i		−	0.801422i	0.916204	−	0.400711i	$-0.131237\pi$
$744$		−	8.97269e7i		−	0.217873i
$745$	−6.23194e8	−	6.23194e8i	−1.50714	−	1.50714i
$746$	1.49414e8	+	1.49414e8i	0.359894	+	0.359894i
$747$	4.13227e8			0.991350
$748$	9.91680e7	+	9.91680e7i	0.236955	+	0.236955i
$749$	3.74466e8			0.891184
$750$	−1.27713e8			−0.302727
$751$		−	1.89712e8i		−	0.447893i	−0.974601	−	0.223946i	$-0.928106\pi$
$751$		−	1.89712e8i		−	0.447893i	0.974601	−	0.223946i	$-0.0718940\pi$
$752$	4.88250e7			0.114812
$753$	2.09657e8	+	2.09657e8i	0.491049	+	0.491049i
$754$	−1.75114e7	+	1.75114e7i	−0.0408514	+	0.0408514i
$755$	−2.85348e8	+	2.85348e8i	−0.663032	+	0.663032i
$756$	1.69048e8			0.391241
$757$	−1.29795e8	−	1.29795e8i	−0.299206	−	0.299206i	0.541497	−	0.840703i	$-0.317858\pi$
$757$	−1.29795e8	−	1.29795e8i	−0.299206	−	0.299206i	−0.840703	+	0.541497i	$0.817858\pi$
$758$	−1.77755e8	+	1.77755e8i	−0.408144	+	0.408144i
$759$	−3.82274e8	−	3.82274e8i	−0.874278	−	0.874278i
$760$	1.20644e7	−	1.20644e7i	0.0274831	−	0.0274831i
$761$		−	4.83738e8i		−	1.09763i	−0.835944	−	0.548815i	$-0.815079\pi$
$761$		−	4.83738e8i		−	1.09763i	0.835944	−	0.548815i	$-0.184921\pi$
$762$	3.43116e7	+	3.43116e7i	0.0775489	+	0.0775489i
$763$	4.42323e8	+	4.42323e8i	0.995785	+	0.995785i
$764$	−2.18963e8	+	2.18963e8i	−0.491010	+	0.491010i
$765$		−	2.70658e8i		−	0.604556i
$766$	4.41763e8			0.982885
$767$		−	1.50977e8i		−	0.334599i
$768$		−	1.29628e7i		−	0.0286163i
$769$	−3.16871e8	+	3.16871e8i	−0.696793	+	0.696793i	−0.963718	−	0.266924i	$-0.913993\pi$
$769$	−3.16871e8	+	3.16871e8i	−0.696793	+	0.696793i	0.266924	+	0.963718i	$0.413993\pi$
$770$			6.97110e8i			1.52696i
$771$	−1.48026e8	+	1.48026e8i	−0.322979	+	0.322979i
$772$	−2.57550e8	+	2.57550e8i	−0.559770	+	0.559770i
$773$	4.67507e8			1.01216			0.506081	−	0.862486i	$-0.331094\pi$
$773$	4.67507e8			1.01216			0.506081	+	0.862486i	$0.331094\pi$
$774$	−1.31810e8			−0.284266
$775$	−7.00792e8	−	7.00792e8i	−1.50551	−	1.50551i
$776$		−	2.95522e8i		−	0.632420i
$777$	1.81733e8	−	9.49027e7i	0.387409	−	0.202309i
$778$	4.76297e8			1.01144
$779$	2.35308e7	−	2.35308e7i	0.0497766	−	0.0497766i
$780$			5.29508e7i			0.111581i
$781$			6.22604e8i			1.30695i
$782$	−2.18316e8	−	2.18316e8i	−0.456526	−	0.456526i
$783$	7.49494e7	+	7.49494e7i	0.156129	+	0.156129i
$784$	1.07016e7			0.0222075
$785$	2.99785e8	+	2.99785e8i	0.619728	+	0.619728i
$786$	1.54983e8			0.319166
$787$	−2.54351e8			−0.521807			−0.260904	−	0.965365i	$-0.584020\pi$
$787$	−2.54351e8			−0.521807			−0.260904	+	0.965365i	$0.584020\pi$
$788$			2.98581e8i			0.610217i
$789$	−6.61126e6			−0.0134602
$790$	6.48459e8	+	6.48459e8i	1.31523	+	1.31523i
$791$	−7.06933e7	+	7.06933e7i	−0.142840	+	0.142840i
$792$	1.38202e8	−	1.38202e8i	0.278189	−	0.278189i
$793$	−1.16538e8			−0.233694
$794$	−2.86181e8	−	2.86181e8i	−0.571714	−	0.571714i
$795$	−2.93771e7	+	2.93771e7i	−0.0584666	+	0.0584666i
$796$	2.89070e8	+	2.89070e8i	0.573144	+	0.573144i
$797$	−5.94983e8	+	5.94983e8i	−1.17525	+	1.17525i	−0.194309	+	0.980940i	$0.562246\pi$
$797$	−5.94983e8	+	5.94983e8i	−1.17525	+	1.17525i	−0.980940	+	0.194309i	$0.937754\pi$
$798$		−	1.07444e7i		−	0.0211433i
$799$	−7.88520e7	−	7.88520e7i	−0.154587	−	0.154587i
$800$	−1.01243e8	−	1.01243e8i	−0.197740	−	0.197740i
$801$	−1.01823e8	+	1.01823e8i	−0.198130	+	0.198130i
$802$			3.73512e8i			0.724072i
$803$	1.22945e9			2.37446
$804$			5.25870e6i			0.0101184i
$805$		−	1.53467e9i		−	2.94190i
$806$	−1.06882e8	+	1.06882e8i	−0.204126	+	0.204126i
$807$		−	1.25503e8i		−	0.238799i
$808$	6.00491e7	−	6.00491e7i	0.113834	−	0.113834i
$809$	5.05939e8	−	5.05939e8i	0.955548	−	0.955548i	−0.0435048	−	0.999053i	$-0.513852\pi$
$809$	5.05939e8	−	5.05939e8i	0.955548	−	0.955548i	0.999053	+	0.0435048i	$0.0138524\pi$
$810$	−2.50610e8			−0.471567
$811$	−4.34474e8			−0.814519			−0.407260	−	0.913312i	$-0.633516\pi$
$811$	−4.34474e8			−0.814519			−0.407260	+	0.913312i	$0.633516\pi$
$812$	−4.86682e7	−	4.86682e7i	−0.0909029	−	0.0909029i
$813$			4.50237e8i			0.837857i
$814$	1.60801e8	−	5.12304e8i	0.298137	−	0.949848i
$815$	−1.00178e9			−1.85054
$816$	−2.09348e7	+	2.09348e7i	−0.0385299	+	0.0385299i
$817$			1.89773e7i			0.0347991i
$818$			1.13925e8i			0.208142i
$819$	−8.88949e7	−	8.88949e7i	−0.161817	−	0.161817i
$820$	−3.22294e8	−	3.22294e8i	−0.584536	−	0.584536i
$821$	−8.19559e8			−1.48098			−0.740492	−	0.672065i	$-0.765408\pi$
$821$	−8.19559e8			−1.48098			−0.740492	+	0.672065i	$0.765408\pi$
$822$	−1.38233e8	−	1.38233e8i	−0.248884	−	0.248884i
$823$	5.56599e8			0.998488			0.499244	−	0.866462i	$-0.333611\pi$
$823$	5.56599e8			0.998488			0.499244	+	0.866462i	$0.333611\pi$
$824$	2.46938e8			0.441374
$825$			5.72602e8i			1.01974i
$826$	4.19600e8			0.744552
$827$	5.01860e8	+	5.01860e8i	0.887292	+	0.887292i	0.994262	−	0.106970i	$-0.0341150\pi$
$827$	5.01860e8	+	5.01860e8i	0.887292	+	0.887292i	−0.106970	+	0.994262i	$0.534115\pi$
$828$	−3.04250e8	+	3.04250e8i	−0.535968	+	0.535968i
$829$	−2.61267e8	+	2.61267e8i	−0.458587	+	0.458587i	−0.898191	−	0.439605i	$-0.855119\pi$
$829$	−2.61267e8	+	2.61267e8i	−0.458587	+	0.458587i	0.439605	+	0.898191i	$0.355119\pi$
$830$	−8.14875e8			−1.42514
$831$	−3.12617e8	−	3.12617e8i	−0.544765	−	0.544765i
$832$	−1.54411e7	+	1.54411e7i	−0.0268108	+	0.0268108i
$833$	−1.72830e7	−	1.72830e7i	−0.0299008	−	0.0299008i
$834$	−1.00619e8	+	1.00619e8i	−0.173454	+	0.173454i
$835$			1.11642e9i			1.91765i
$836$	−1.98977e7	−	1.98977e7i	−0.0340552	−	0.0340552i
$837$	4.57458e8	+	4.57458e8i	0.780144	+	0.780144i
$838$	1.78026e8	−	1.78026e8i	0.302519	−	0.302519i
$839$			7.62696e7i			0.129141i	0.997913	+	0.0645707i	$0.0205678\pi$
$839$			7.62696e7i			0.129141i	−0.997913	+	0.0645707i	$0.979432\pi$
$840$	−1.47163e8			−0.248290
$841$			5.51668e8i			0.927449i
$842$		−	7.21117e8i		−	1.20801i
$843$	−1.24591e8	+	1.24591e8i	−0.207972	+	0.207972i
$844$			1.69386e8i			0.281741i
$845$	−6.22455e8	+	6.22455e8i	−1.03166	+	1.03166i
$846$	−1.09890e8	+	1.09890e8i	−0.181487	+	0.181487i
$847$	5.69702e8			0.937556
$848$	−1.71335e7			−0.0280969
$849$	−1.01628e8	−	1.01628e8i	−0.166069	−	0.166069i
$850$			3.27012e8i			0.532485i
$851$	−3.54001e8	+	1.12783e9i	−0.574401	+	1.83001i
$852$	−1.31434e8			−0.212515
$853$	6.88104e8	−	6.88104e8i	1.10868	−	1.10868i	0.115358	−	0.993324i	$-0.463199\pi$
$853$	6.88104e8	−	6.88104e8i	1.10868	−	1.10868i	0.993324	−	0.115358i	$-0.0368014\pi$
$854$		−	3.23886e8i		−	0.520018i
$855$			5.43064e7i			0.0868866i
$856$	1.46396e8	+	1.46396e8i	0.233404	+	0.233404i
$857$	−6.01650e8	−	6.01650e8i	−0.955875	−	0.955875i	0.0431914	−	0.999067i	$-0.486247\pi$
$857$	−6.01650e8	−	6.01650e8i	−0.955875	−	0.955875i	−0.999067	+	0.0431914i	$0.986247\pi$
$858$	8.73309e7			0.138263
$859$	−6.15477e8	−	6.15477e8i	−0.971029	−	0.971029i	0.0285627	−	0.999592i	$-0.490907\pi$
$859$	−6.15477e8	−	6.15477e8i	−0.971029	−	0.971029i	−0.999592	+	0.0285627i	$0.990907\pi$
$860$	2.59926e8			0.408653
$861$	−2.87030e8			−0.449696
$862$		−	4.00372e7i		−	0.0625089i
$863$	−6.18583e8			−0.962422			−0.481211	−	0.876605i	$-0.659803\pi$
$863$	−6.18583e8			−0.962422			−0.481211	+	0.876605i	$0.659803\pi$
$864$	6.60885e7	+	6.60885e7i	0.102467	+	0.102467i
$865$	1.31310e8	−	1.31310e8i	0.202885	−	0.202885i
$866$	−2.95475e8	+	2.95475e8i	−0.454954	+	0.454954i
$867$	−2.30776e8			−0.354106
$868$	−2.97049e8	−	2.97049e8i	−0.454223	−	0.454223i
$869$	1.06949e9	−	1.06949e9i	1.62974	−	1.62974i
$870$	−6.52463e7	−	6.52463e7i	−0.0990827	−	0.0990827i
$871$	6.26411e6	−	6.26411e6i	0.00947993	−	0.00947993i
$872$			3.45848e8i			0.521598i
$873$	6.65127e8	+	6.65127e8i	0.999682	+	0.999682i
$874$	4.38043e7	+	4.38043e7i	0.0656119	+	0.0656119i
$875$	−4.22807e8	+	4.22807e8i	−0.631128	+	0.631128i
$876$			2.59542e8i			0.386096i
$877$	6.14901e8			0.911605			0.455802	−	0.890081i	$-0.349352\pi$
$877$	6.14901e8			0.911605			0.455802	+	0.890081i	$0.349352\pi$
$878$		−	3.74929e7i		−	0.0553944i
$879$			2.48609e8i			0.366058i
$880$	−2.72532e8	+	2.72532e8i	−0.399917	+	0.399917i
$881$			6.13106e8i			0.896618i	0.893879	+	0.448309i	$0.147974\pi$
$881$			6.13106e8i			0.896618i	−0.893879	+	0.448309i	$0.852026\pi$
$882$	−2.40859e7	+	2.40859e7i	−0.0351040	+	0.0351040i
$883$	3.62294e8	−	3.62294e8i	0.526235	−	0.526235i	−0.393213	−	0.919448i	$-0.628636\pi$
$883$	3.62294e8	−	3.62294e8i	0.526235	−	0.526235i	0.919448	+	0.393213i	$0.128636\pi$
$884$	4.98746e7			0.0721975
$885$	5.62529e8			0.811550
$886$	−4.27997e8	−	4.27997e8i	−0.615374	−	0.615374i
$887$		−	7.06145e8i		−	1.01187i	−0.862573	−	0.505933i	$-0.831148\pi$
$887$		−	7.06145e8i		−	1.01187i	0.862573	−	0.505933i	$-0.168852\pi$
$888$	1.08149e8	+	3.39458e7i	0.154449	+	0.0484782i
$889$	2.27184e8			0.323349
$890$	2.00793e8	−	2.00793e8i	0.284826	−	0.284826i
$891$			4.13326e8i			0.584332i
$892$		−	5.19539e7i		−	0.0732022i
$893$	1.58213e7	+	1.58213e7i	0.0222172	+	0.0222172i
$894$	−2.16977e8	−	2.16977e8i	−0.303670	−	0.303670i
$895$	−3.14406e8			−0.438553
$896$	−4.29145e7	−	4.29145e7i	−0.0596595	−	0.0596595i
$897$	−1.92257e8			−0.266382
$898$	3.50105e8			0.483469
$899$		−	2.63401e8i		−	0.362525i
$900$	4.55731e8			0.625145
$901$	2.76704e7	+	2.76704e7i	0.0378304	+	0.0378304i
$902$	−5.31554e8	+	5.31554e8i	−0.724316	+	0.724316i
$903$	1.15743e8	−	1.15743e8i	0.157193	−	0.157193i
$904$	−5.52745e7			−0.0748203
$905$	−1.51360e9	−	1.51360e9i	−2.04204	−	2.04204i
$906$	−9.93498e7	+	9.93498e7i	−0.133593	+	0.133593i
$907$	−8.81378e8	−	8.81378e8i	−1.18125	−	1.18125i	−0.979422	−	0.201825i	$-0.935313\pi$
$907$	−8.81378e8	−	8.81378e8i	−1.18125	−	1.18125i	−0.201825	−	0.979422i	$-0.564687\pi$
$908$	3.50398e8	−	3.50398e8i	0.468063	−	0.468063i
$909$			2.70303e8i			0.359881i
$910$	1.75299e8	+	1.75299e8i	0.232624	+	0.232624i
$911$	−4.90534e8	−	4.90534e8i	−0.648805	−	0.648805i	0.303899	−	0.952704i	$-0.401711\pi$
$911$	−4.90534e8	−	4.90534e8i	−0.648805	−	0.648805i	−0.952704	+	0.303899i	$0.901711\pi$
$912$	4.20047e6	−	4.20047e6i	0.00553750	−	0.00553750i
$913$			1.34396e9i			1.76593i
$914$	−6.12658e8			−0.802378
$915$		−	4.34212e8i		−	0.566811i
$916$		−	5.97613e8i		−	0.777559i
$917$	5.13087e8	−	5.13087e8i	0.665400	−	0.665400i
$918$		−	2.13465e8i		−	0.275930i
$919$	9.68659e8	−	9.68659e8i	1.24803	−	1.24803i	0.291439	−	0.956590i	$-0.405866\pi$
$919$	9.68659e8	−	9.68659e8i	1.24803	−	1.24803i	0.956590	−	0.291439i	$-0.0941339\pi$
$920$	5.99974e8	−	5.99974e8i	0.770493	−	0.770493i
$921$	−1.11055e8			−0.142154
$922$	5.25350e8			0.670279
$923$	1.56563e8	+	1.56563e8i	0.199106	+	0.199106i
$924$			2.42713e8i			0.307664i
$925$	1.10980e9	−	5.79550e8i	1.40223	−	0.732261i
$926$	5.99664e8			0.755222
$927$	−5.55779e8	+	5.55779e8i	−0.697691	+	0.697691i
$928$		−	3.80533e7i		−	0.0476154i
$929$			1.16565e8i			0.145385i	0.997354	+	0.0726925i	$0.0231592\pi$
$929$			1.16565e8i			0.145385i	−0.997354	+	0.0726925i	$0.976841\pi$
$930$	−3.98234e8	−	3.98234e8i	−0.495097	−	0.495097i
$931$	3.46776e6	+	3.46776e6i	0.00429734	+	0.00429734i
$932$	3.54282e8			0.437624
$933$	−1.95345e8	−	1.95345e8i	−0.240524	−	0.240524i
$934$	3.32168e8			0.407678
$935$	8.80274e8			1.07692
$936$		−	6.95061e7i		−	0.0847609i
$937$	1.71816e8			0.208855			0.104427	−	0.994533i	$-0.466699\pi$
$937$	1.71816e8			0.208855			0.104427	+	0.994533i	$0.466699\pi$
$938$	1.74094e7	+	1.74094e7i	0.0210948	+	0.0210948i
$939$	−1.58627e8	+	1.58627e8i	−0.191594	+	0.191594i
$940$	2.16700e8	−	2.16700e8i	0.260901	−	0.260901i
$941$	7.56964e8			0.908461			0.454230	−	0.890884i	$-0.349914\pi$
$941$	7.56964e8			0.908461			0.454230	+	0.890884i	$0.349914\pi$
$942$	1.04376e8	+	1.04376e8i	0.124867	+	0.124867i
$943$	1.17021e9	−	1.17021e9i	1.39549	−	1.39549i
$944$	1.64041e8	+	1.64041e8i	0.195000	+	0.195000i
$945$	7.50285e8	−	7.50285e8i	0.889060	−	0.889060i
$946$		−	4.28692e8i		−	0.506374i
$947$	8.54941e8	+	8.54941e8i	1.00667	+	1.00667i	0.999978	+	0.00669012i	$0.00212955\pi$
$947$	8.54941e8	+	8.54941e8i	1.00667	+	1.00667i	0.00669012	+	0.999978i	$0.497870\pi$
$948$	2.25774e8	+	2.25774e8i	0.265002	+	0.265002i
$949$	3.09164e8	−	3.09164e8i	0.361735	−	0.361735i
$950$		−	6.56137e7i		−	0.0765286i
$951$	7.41609e8			0.862251
$952$			1.38613e8i			0.160655i
$953$			4.48598e8i			0.518297i	0.965838	+	0.259148i	$0.0834418\pi$
$953$			4.48598e8i			0.518297i	−0.965838	+	0.259148i	$0.916558\pi$
$954$	3.85620e7	−	3.85620e7i	0.0444134	−	0.0444134i
$955$			1.94365e9i			2.23155i
$956$	2.84858e8	−	2.84858e8i	0.326028	−	0.326028i
$957$	−1.07610e8	+	1.07610e8i	−0.122776	+	0.122776i
$958$	−3.22953e8			−0.367318
$959$	−9.15268e8			−1.03775
$960$	−5.75326e7	−	5.75326e7i	−0.0650280	−	0.0650280i
$961$		−	7.20177e8i		−	0.811464i
$962$	−8.83906e7	−	1.69262e8i	−0.0992844	−	0.190123i
$963$	−6.58982e8			−0.737895
$964$	−2.20080e8	+	2.20080e8i	−0.245668	+	0.245668i
$965$			2.28617e9i			2.54405i
$966$		−	5.34327e8i		−	0.592756i
$967$	−5.61351e8	−	5.61351e8i	−0.620805	−	0.620805i	0.324933	−	0.945737i	$-0.394658\pi$
$967$	−5.61351e8	−	5.61351e8i	−0.620805	−	0.620805i	−0.945737	+	0.324933i	$0.894658\pi$
$968$	2.22722e8	+	2.22722e8i	0.245549	+	0.245549i
$969$	−1.35675e7			−0.0149117
$970$	−1.31162e9	−	1.31162e9i	−1.43711	−	1.43711i
$971$	−1.47808e9			−1.61451			−0.807254	−	0.590204i	$-0.799047\pi$
$971$	−1.47808e9			−1.61451			−0.807254	+	0.590204i	$0.799047\pi$
$972$	−4.63650e8			−0.504884
$973$			6.66220e8i			0.723235i
$974$	−5.74080e8			−0.621292
$975$	1.43989e8	+	1.43989e8i	0.155352	+	0.155352i
$976$	1.26622e8	−	1.26622e8i	0.136194	−	0.136194i
$977$	1.14059e9	−	1.14059e9i	1.22306	−	1.22306i	0.256521	−	0.966539i	$-0.417424\pi$
$977$	1.14059e9	−	1.14059e9i	1.22306	−	1.22306i	0.966539	−	0.256521i	$-0.0825763\pi$
$978$	−3.48789e8			−0.372861
$979$	−3.31165e8	−	3.31165e8i	−0.352936	−	0.352936i
$980$	4.74968e7	−	4.74968e7i	0.0504645	−	0.0504645i
$981$	−7.78394e8	−	7.78394e8i	−0.824504	−	0.824504i
$982$	1.65734e8	−	1.65734e8i	0.175016	−	0.175016i
$983$			1.93485e8i			0.203698i	0.994800	+	0.101849i	$0.0324758\pi$
$983$			1.93485e8i			0.203698i	−0.994800	+	0.101849i	$0.967524\pi$
$984$	−1.12213e8	−	1.12213e8i	−0.117777	−	0.117777i
$985$	1.32519e9	+	1.32519e9i	1.38666	+	1.38666i
$986$	−6.14557e7	+	6.14557e7i	−0.0641108	+	0.0641108i
$987$		−	1.92990e8i		−	0.200716i
$988$	−1.00071e7			−0.0103762
$989$			9.43756e8i			0.975598i
$990$		−	1.22677e9i		−	1.26432i
$991$	−9.22441e8	+	9.22441e8i	−0.947802	+	0.947802i	−0.998704	−	0.0509016i	$-0.983791\pi$
$991$	−9.22441e8	+	9.22441e8i	−0.947802	+	0.947802i	0.0509016	+	0.998704i	$0.483791\pi$
$992$		−	2.32260e8i		−	0.237925i
$993$	3.72621e8	−	3.72621e8i	0.380557	−	0.380557i
$994$	−4.35125e8	+	4.35125e8i	−0.443053	+	0.443053i
$995$	2.56595e9			2.60483
$996$	−2.83715e8			−0.287147
$997$	−5.04009e8	−	5.04009e8i	−0.508573	−	0.508573i	0.405515	−	0.914088i	$-0.367092\pi$
$997$	−5.04009e8	−	5.04009e8i	−0.508573	−	0.508573i	−0.914088	+	0.405515i	$0.867092\pi$
$998$			1.04761e9i			1.05392i
$999$	−7.24449e8	+	3.78315e8i	−0.726627	+	0.379452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.a.43.4	yes	18
37.31	odd	4	inner	74.7.d.a.31.6	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.a.31.6	✓	18	37.31	odd	4	inner
74.7.d.a.43.4	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.00000 - 4.00000i) q^{2} -12.3623i q^{3} -32.0000i q^{4} +(-142.025 - 142.025i) q^{5} +(-49.4490 - 49.4490i) q^{6} -327.411 q^{7} +(-128.000 - 128.000i) q^{8} +576.175 q^{9} +O(q^{10})\)	\(q+(4.00000 - 4.00000i) q^{2} -12.3623i q^{3} -32.0000i q^{4} +(-142.025 - 142.025i) q^{5} +(-49.4490 - 49.4490i) q^{6} -327.411 q^{7} +(-128.000 - 128.000i) q^{8} +576.175 q^{9} -1136.20 q^{10} +1873.92i q^{11} -395.592 q^{12} +(471.226 + 471.226i) q^{13} +(-1309.65 + 1309.65i) q^{14} +(-1755.75 + 1755.75i) q^{15} -1024.00 q^{16} +(1653.75 + 1653.75i) q^{17} +(2304.70 - 2304.70i) q^{18} +(-331.819 - 331.819i) q^{19} +(-4544.81 + 4544.81i) q^{20} +4047.54i q^{21} +(7495.68 + 7495.68i) q^{22} +(-16501.6 - 16501.6i) q^{23} +(-1582.37 + 1582.37i) q^{24} +24717.5i q^{25} +3769.81 q^{26} -16134.9i q^{27} +10477.2i q^{28} +(-4645.17 + 4645.17i) q^{29} +14046.0i q^{30} +(-28352.1 + 28352.1i) q^{31} +(-4096.00 + 4096.00i) q^{32} +23165.9 q^{33} +13230.0 q^{34} +(46500.8 + 46500.8i) q^{35} -18437.6i q^{36} +(-23447.0 - 44899.5i) q^{37} -2654.55 q^{38} +(5825.41 - 5825.41i) q^{39} +36358.5i q^{40} +70914.8i q^{41} +(16190.2 + 16190.2i) q^{42} +(-28595.9 - 28595.9i) q^{43} +59965.5 q^{44} +(-81831.5 - 81831.5i) q^{45} -132013. q^{46} -47680.7 q^{47} +12658.9i q^{48} -10450.8 q^{49} +(98869.9 + 98869.9i) q^{50} +(20444.1 - 20444.1i) q^{51} +(15079.2 - 15079.2i) q^{52} +16731.9 q^{53} +(-64539.6 - 64539.6i) q^{54} +(266144. - 266144. i) q^{55} +(41908.7 + 41908.7i) q^{56} +(-4102.03 + 4102.03i) q^{57} +37161.4i q^{58} +(-160196. - 160196. i) q^{59} +(56184.1 + 56184.1i) q^{60} +(-123654. + 123654. i) q^{61} +226817. i q^{62} -188646. q^{63} +32768.0i q^{64} -133852. i q^{65} +(92663.5 - 92663.5i) q^{66} -13293.2i q^{67} +(52920.0 - 52920.0i) q^{68} +(-203997. + 203997. i) q^{69} +372006. q^{70} +332247. q^{71} +(-73750.4 - 73750.4i) q^{72} -656085. i q^{73} +(-273386. - 85810.0i) q^{74} +305564. q^{75} +(-10618.2 + 10618.2i) q^{76} -613543. i q^{77} -46603.3i q^{78} +(-570724. - 570724. i) q^{79} +(145434. + 145434. i) q^{80} +220568. q^{81} +(283659. + 283659. i) q^{82} +717191. q^{83} +129521. q^{84} -469750. i q^{85} -228767. q^{86} +(57424.8 + 57424.8i) q^{87} +(239862. - 239862. i) q^{88} +(-176723. + 176723. i) q^{89} -654652. q^{90} +(-154285. - 154285. i) q^{91} +(-528051. + 528051. i) q^{92} +(350496. + 350496. i) q^{93} +(-190723. + 190723. i) q^{94} +94253.4i q^{95} +(50635.8 + 50635.8i) q^{96} +(1.15438e6 + 1.15438e6i) q^{97} +(-41803.0 + 41803.0i) q^{98} +1.07971e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9}+O(q^{10}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9	\( 18 q + 72 q^{2} + 294 q^{5} - 256 q^{6} - 104 q^{7} - 2304 q^{8} - 4042 q^{9} + 2352 q^{10} - 2048 q^{12} - 6766 q^{13} - 416 q^{14} - 2136 q^{15} - 18432 q^{16} - 9134 q^{17} - 16168 q^{18} + 7578 q^{19} + 9408 q^{20} + 8928 q^{22} - 50578 q^{23} - 8192 q^{24} - 54128 q^{26} - 42950 q^{29} - 17358 q^{31} - 73728 q^{32} - 11056 q^{33} - 73072 q^{34} + 62152 q^{35} - 238242 q^{37} + 60624 q^{38} + 31572 q^{39} + 229024 q^{42} - 65470 q^{43} + 71424 q^{44} - 482358 q^{45} - 404624 q^{46} + 232192 q^{47} + 791686 q^{49} + 93752 q^{50} - 386848 q^{51} - 216512 q^{52} + 49972 q^{53} - 144560 q^{54} + 160168 q^{55} + 13312 q^{56} + 488476 q^{57} - 181570 q^{59} + 68352 q^{60} + 508802 q^{61} + 404788 q^{63} - 44224 q^{66} - 292288 q^{68} + 604532 q^{69} + 497216 q^{70} - 202632 q^{71} + 517376 q^{72} - 1191224 q^{74} + 2476628 q^{75} + 242496 q^{76} + 1752858 q^{79} - 301056 q^{80} + 2760658 q^{81} - 145808 q^{82} + 2371616 q^{83} + 1832192 q^{84} - 523760 q^{86} - 4188080 q^{87} + 285696 q^{88} + 1148346 q^{89} - 3858864 q^{90} + 433120 q^{91} - 1618496 q^{92} + 1589664 q^{93} + 928768 q^{94} + 262144 q^{96} - 1670270 q^{97} + 3166744 q^{98}+O(q^{100}) \) 18 * q + 72 * q^2 + 294 * q^5 - 256 * q^6 - 104 * q^7 - 2304 * q^8 - 4042 * q^9 + 2352 * q^10 - 2048 * q^12 - 6766 * q^13 - 416 * q^14 - 2136 * q^15 - 18432 * q^16 - 9134 * q^17 - 16168 * q^18 + 7578 * q^19 + 9408 * q^20 + 8928 * q^22 - 50578 * q^23 - 8192 * q^24 - 54128 * q^26 - 42950 * q^29 - 17358 * q^31 - 73728 * q^32 - 11056 * q^33 - 73072 * q^34 + 62152 * q^35 - 238242 * q^37 + 60624 * q^38 + 31572 * q^39 + 229024 * q^42 - 65470 * q^43 + 71424 * q^44 - 482358 * q^45 - 404624 * q^46 + 232192 * q^47 + 791686 * q^49 + 93752 * q^50 - 386848 * q^51 - 216512 * q^52 + 49972 * q^53 - 144560 * q^54 + 160168 * q^55 + 13312 * q^56 + 488476 * q^57 - 181570 * q^59 + 68352 * q^60 + 508802 * q^61 + 404788 * q^63 - 44224 * q^66 - 292288 * q^68 + 604532 * q^69 + 497216 * q^70 - 202632 * q^71 + 517376 * q^72 - 1191224 * q^74 + 2476628 * q^75 + 242496 * q^76 + 1752858 * q^79 - 301056 * q^80 + 2760658 * q^81 - 145808 * q^82 + 2371616 * q^83 + 1832192 * q^84 - 523760 * q^86 - 4188080 * q^87 + 285696 * q^88 + 1148346 * q^89 - 3858864 * q^90 + 433120 * q^91 - 1618496 * q^92 + 1589664 * q^93 + 928768 * q^94 + 262144 * q^96 - 1670270 * q^97 + 3166744 * q^98

Introduction

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