LMFDB - Embedded newform 55.6.e.b.32.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,6,Mod(32,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("55.32");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	55.e (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:	$8.82111008971$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.12
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37494 + 1.37494i) q^{2} +(16.5868 - 16.5868i) q^{3} +28.2191i q^{4} +(-55.3028 - 8.16074i) q^{5} +45.6116i q^{6} +(-178.839 + 178.839i) q^{7} +(-82.7976 - 82.7976i) q^{8} -307.243i q^{9} +(87.2585 - 64.8175i) q^{10} +(110.636 + 385.760i) q^{11} +(468.064 + 468.064i) q^{12} +(265.957 + 265.957i) q^{13} -491.786i q^{14} +(-1052.66 + 781.936i) q^{15} -675.328 q^{16} +(651.396 - 651.396i) q^{17} +(422.440 + 422.440i) q^{18} -2026.11 q^{19} +(230.289 - 1560.60i) q^{20} +5932.74i q^{21} +(-682.514 - 378.278i) q^{22} +(-936.058 + 936.058i) q^{23} -2746.69 q^{24} +(2991.80 + 902.624i) q^{25} -731.350 q^{26} +(-1065.59 - 1065.59i) q^{27} +(-5046.68 - 5046.68i) q^{28} -1446.61 q^{29} +(372.225 - 2522.45i) q^{30} -4538.68 q^{31} +(3578.06 - 3578.06i) q^{32} +(8233.62 + 4563.42i) q^{33} +1791.26i q^{34} +(11349.8 - 8430.85i) q^{35} +8670.12 q^{36} +(6600.11 + 6600.11i) q^{37} +(2785.77 - 2785.77i) q^{38} +8822.76 q^{39} +(3903.25 + 5254.63i) q^{40} -8625.28i q^{41} +(-8157.15 - 8157.15i) q^{42} +(-6936.88 - 6936.88i) q^{43} +(-10885.8 + 3122.05i) q^{44} +(-2507.33 + 16991.4i) q^{45} -2574.05i q^{46} +(8517.97 + 8517.97i) q^{47} +(-11201.5 + 11201.5i) q^{48} -47159.9i q^{49} +(-5354.60 + 2872.50i) q^{50} -21609.1i q^{51} +(-7505.08 + 7505.08i) q^{52} +(-6584.20 + 6584.20i) q^{53} +2930.24 q^{54} +(-2970.41 - 22236.5i) q^{55} +29614.9 q^{56} +(-33606.6 + 33606.6i) q^{57} +(1989.00 - 1989.00i) q^{58} +39318.2i q^{59} +(-22065.5 - 29705.0i) q^{60} -1429.55i q^{61} +(6240.41 - 6240.41i) q^{62} +(54947.1 + 54947.1i) q^{63} -11771.3i q^{64} +(-12537.8 - 16878.6i) q^{65} +(-17595.1 + 5046.30i) q^{66} +(1066.66 + 1066.66i) q^{67} +(18381.8 + 18381.8i) q^{68} +31052.4i q^{69} +(-4013.34 + 27197.1i) q^{70} -17330.1 q^{71} +(-25439.0 + 25439.0i) q^{72} +(29974.4 + 29974.4i) q^{73} -18149.5 q^{74} +(64596.1 - 34652.8i) q^{75} -57174.9i q^{76} +(-88775.1 - 49202.9i) q^{77} +(-12130.8 + 12130.8i) q^{78} +33647.5 q^{79} +(37347.5 + 5511.17i) q^{80} +39310.7 q^{81} +(11859.2 + 11859.2i) q^{82} +(29267.3 + 29267.3i) q^{83} -167416. q^{84} +(-41339.9 + 30708.2i) q^{85} +19075.6 q^{86} +(-23994.6 + 23994.6i) q^{87} +(22779.6 - 41100.4i) q^{88} -19729.5i q^{89} +(-19914.7 - 26809.6i) q^{90} -95127.2 q^{91} +(-26414.7 - 26414.7i) q^{92} +(-75282.1 + 75282.1i) q^{93} -23423.4 q^{94} +(112049. + 16534.5i) q^{95} -118697. i q^{96} +(43636.6 + 43636.6i) q^{97} +(64842.0 + 64842.0i) q^{98} +(118522. - 33992.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) $ 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.37494	+	1.37494i	−0.243057	+	0.243057i	−0.818114	−	0.575057i	$-0.804980\pi$
$2$	−1.37494	+	1.37494i	−0.243057	+	0.243057i	0.575057	+	0.818114i	$0.304980\pi$
$3$	16.5868	−	16.5868i	1.06404	−	1.06404i	0.0662393	−	0.997804i	$-0.478900\pi$
$3$	16.5868	−	16.5868i	1.06404	−	1.06404i	0.997804	−	0.0662393i	$-0.0211001\pi$
$4$			28.2191i			0.881846i
$5$	−55.3028	−	8.16074i	−0.989287	−	0.145984i
$5$	−55.3028	−	8.16074i	−0.989287	−	0.145984i
$6$			45.6116i			0.517246i
$7$	−178.839	+	178.839i	−1.37949	+	1.37949i	−0.534006	+	0.845480i	$0.679314\pi$
$7$	−178.839	+	178.839i	−1.37949	+	1.37949i	−0.845480	+	0.534006i	$0.820686\pi$
$8$	−82.7976	−	82.7976i	−0.457396	−	0.457396i
$9$		−	307.243i		−	1.26438i
$10$	87.2585	−	64.8175i	0.275936	−	0.204971i
$11$	110.636	+	385.760i	0.275687	+	0.961248i
$11$	110.636	+	385.760i	0.275687	+	0.961248i
$12$	468.064	+	468.064i	0.938323	+	0.938323i
$13$	265.957	+	265.957i	0.436469	+	0.436469i	0.890822	−	0.454353i	$-0.150129\pi$
$13$	265.957	+	265.957i	0.436469	+	0.436469i	−0.454353	+	0.890822i	$0.650129\pi$
$14$		−	491.786i		−	0.670588i
$15$	−1052.66	+	781.936i	−1.20798	+	0.897311i
$16$	−675.328			−0.659500
$17$	651.396	−	651.396i	0.546667	−	0.546667i	−0.378808	−	0.925475i	$-0.623666\pi$
$17$	651.396	−	651.396i	0.546667	−	0.546667i	0.925475	+	0.378808i	$0.123666\pi$
$18$	422.440	+	422.440i	0.307315	+	0.307315i
$19$	−2026.11			−1.28759			−0.643796	−	0.765197i	$-0.722642\pi$
$19$	−2026.11			−1.28759			−0.643796	+	0.765197i	$0.722642\pi$
$20$	230.289	−	1560.60i	0.128735	−	0.872399i
$21$			5932.74i			2.93567i
$22$	−682.514	−	378.278i	−0.300646	−	0.166630i
$23$	−936.058	+	936.058i	−0.368963	+	0.368963i	−0.867099	−	0.498136i	$-0.834018\pi$
$23$	−936.058	+	936.058i	−0.368963	+	0.368963i	0.498136	+	0.867099i	$0.334018\pi$
$24$	−2746.69			−0.973378
$25$	2991.80	+	902.624i	0.957378	+	0.288840i
$26$	−731.350			−0.212174
$27$	−1065.59	−	1065.59i	−0.281307	−	0.281307i
$28$	−5046.68	−	5046.68i	−1.21650	−	1.21650i
$29$	−1446.61			−0.319416			−0.159708	−	0.987164i	$-0.551055\pi$
$29$	−1446.61			−0.319416			−0.159708	+	0.987164i	$0.551055\pi$
$30$	372.225	−	2522.45i	0.0755096	−	0.511705i
$31$	−4538.68			−0.848253			−0.424126	−	0.905603i	$-0.639419\pi$
$31$	−4538.68			−0.848253			−0.424126	+	0.905603i	$0.639419\pi$
$32$	3578.06	−	3578.06i	0.617692	−	0.617692i
$33$	8233.62	+	4563.42i	1.31615	+	0.729466i
$34$			1791.26i			0.265742i
$35$	11349.8	−	8430.85i	1.56609	−	1.16333i
$36$	8670.12			1.11498
$37$	6600.11	+	6600.11i	0.792587	+	0.792587i	0.981914	−	0.189327i	$-0.0606305\pi$
$37$	6600.11	+	6600.11i	0.792587	+	0.792587i	−0.189327	+	0.981914i	$0.560631\pi$
$38$	2785.77	−	2785.77i	0.312959	−	0.312959i
$39$	8822.76			0.928844
$40$	3903.25	+	5254.63i	0.385724	+	0.519268i
$41$		−	8625.28i		−	0.801334i	−0.916224	−	0.400667i	$-0.868778\pi$
$41$		−	8625.28i		−	0.801334i	0.916224	−	0.400667i	$-0.131222\pi$
$42$	−8157.15	−	8157.15i	−0.713535	−	0.713535i
$43$	−6936.88	−	6936.88i	−0.572128	−	0.572128i	0.360595	−	0.932723i	$-0.382574\pi$
$43$	−6936.88	−	6936.88i	−0.572128	−	0.572128i	−0.932723	+	0.360595i	$0.882574\pi$
$44$	−10885.8	+	3122.05i	−0.847673	+	0.243113i
$45$	−2507.33	+	16991.4i	−0.184578	+	1.25083i
$46$		−	2574.05i		−	0.179358i
$47$	8517.97	+	8517.97i	0.562460	+	0.562460i	0.930006	−	0.367545i	$-0.119802\pi$
$47$	8517.97	+	8517.97i	0.562460	+	0.562460i	−0.367545	+	0.930006i	$0.619802\pi$
$48$	−11201.5	+	11201.5i	−0.701736	+	0.701736i
$49$		−	47159.9i		−	2.80597i
$50$	−5354.60	+	2872.50i	−0.302902	+	0.162493i
$51$		−	21609.1i		−	1.16335i
$52$	−7505.08	+	7505.08i	−0.384899	+	0.384899i
$53$	−6584.20	+	6584.20i	−0.321968	+	0.321968i	−0.849522	−	0.527553i	$-0.823109\pi$
$53$	−6584.20	+	6584.20i	−0.321968	+	0.321968i	0.527553	+	0.849522i	$0.323109\pi$
$54$	2930.24			0.136747
$55$	−2970.41	−	22236.5i	−0.132407	−	0.991195i
$56$	29614.9			1.26194
$57$	−33606.6	+	33606.6i	−1.37005	+	1.37005i
$58$	1989.00	−	1989.00i	0.0776363	−	0.0776363i
$59$			39318.2i			1.47050i	0.677798	+	0.735248i	$0.262934\pi$
$59$			39318.2i			1.47050i	−0.677798	+	0.735248i	$0.737066\pi$
$60$	−22065.5	−	29705.0i	−0.791291	−	1.06525i
$61$		−	1429.55i		−	0.0491899i	−0.999697	−	0.0245950i	$-0.992170\pi$
$61$		−	1429.55i		−	0.0491899i	0.999697	−	0.0245950i	$-0.00782961\pi$
$62$	6240.41	−	6240.41i	0.206174	−	0.206174i
$63$	54947.1	+	54947.1i	1.74419	+	1.74419i
$64$		−	11771.3i		−	0.359231i
$65$	−12537.8	−	16878.6i	−0.368076	−	0.495511i
$66$	−17595.1	+	5046.30i	−0.497202	+	0.142598i
$67$	1066.66	+	1066.66i	0.0290296	+	0.0290296i	0.721473	−	0.692443i	$-0.243466\pi$
$67$	1066.66	+	1066.66i	0.0290296	+	0.0290296i	−0.692443	+	0.721473i	$0.743466\pi$
$68$	18381.8	+	18381.8i	0.482076	+	0.482076i
$69$			31052.4i			0.785186i
$70$	−4013.34	+	27197.1i	−0.0978950	+	0.663404i
$71$	−17330.1			−0.407995			−0.203997	−	0.978971i	$-0.565393\pi$
$71$	−17330.1			−0.407995			−0.203997	+	0.978971i	$0.565393\pi$
$72$	−25439.0	+	25439.0i	−0.578320	+	0.578320i
$73$	29974.4	+	29974.4i	0.658329	+	0.658329i	0.954984	−	0.296656i	$-0.0958714\pi$
$73$	29974.4	+	29974.4i	0.658329	+	0.658329i	−0.296656	+	0.954984i	$0.595871\pi$
$74$	−18149.5			−0.385288
$75$	64596.1	−	34652.8i	1.32603	−	0.711353i
$76$		−	57174.9i		−	1.13546i
$77$	−88775.1	−	49202.9i	−1.70633	−	0.945722i
$78$	−12130.8	+	12130.8i	−0.225762	+	0.225762i
$79$	33647.5			0.606576			0.303288	−	0.952899i	$-0.401916\pi$
$79$	33647.5			0.606576			0.303288	+	0.952899i	$0.401916\pi$
$80$	37347.5	+	5511.17i	0.652434	+	0.0962762i
$81$	39310.7			0.665731
$82$	11859.2	+	11859.2i	0.194770	+	0.194770i
$83$	29267.3	+	29267.3i	0.466323	+	0.466323i	0.900721	−	0.434398i	$-0.143039\pi$
$83$	29267.3	+	29267.3i	0.466323	+	0.466323i	−0.434398	+	0.900721i	$0.643039\pi$
$84$	−167416.			−2.58881
$85$	−41339.9	+	30708.2i	−0.620615	+	0.461006i
$86$	19075.6			0.278120
$87$	−23994.6	+	23994.6i	−0.339872	+	0.339872i
$88$	22779.6	−	41100.4i	0.313573	−	0.565769i
$89$		−	19729.5i		−	0.264022i	−0.991248	−	0.132011i	$-0.957857\pi$
$89$		−	19729.5i		−	0.264022i	0.991248	−	0.132011i	$-0.0421435\pi$
$90$	−19914.7	−	26809.6i	−0.259160	−	0.348886i
$91$	−95127.2			−1.20421
$92$	−26414.7	−	26414.7i	−0.325369	−	0.325369i
$93$	−75282.1	+	75282.1i	−0.902577	+	0.902577i
$94$	−23423.4			−0.273420
$95$	112049.	+	16534.5i	1.27380	+	0.187968i
$96$		−	118697.i		−	1.31450i
$97$	43636.6	+	43636.6i	0.470893	+	0.470893i	0.902203	−	0.431311i	$-0.141949\pi$
$97$	43636.6	+	43636.6i	0.470893	+	0.470893i	−0.431311	+	0.902203i	$0.641949\pi$
$98$	64842.0	+	64842.0i	0.682010	+	0.682010i
$99$	118522.	−	33992.2i	1.21538	−	0.348571i
$100$	−25471.2	+	84426.0i	−0.254712	+	0.844260i
$101$			146144.i			1.42553i	0.701401	+	0.712767i	$0.252558\pi$
$101$			146144.i			1.42553i	−0.701401	+	0.712767i	$0.747442\pi$
$102$	29711.2	+	29711.2i	0.282761	+	0.282761i
$103$	16396.3	−	16396.3i	0.152283	−	0.152283i	−0.626854	−	0.779137i	$-0.715658\pi$
$103$	16396.3	−	16396.3i	0.152283	−	0.152283i	0.779137	+	0.626854i	$0.215658\pi$
$104$		−	44041.2i		−	0.399279i
$105$	48415.5	−	328097.i	0.428560	−	2.90422i
$106$		−	18105.7i		−	0.156513i
$107$	63590.8	−	63590.8i	0.536951	−	0.536951i	−0.385681	−	0.922632i	$-0.626033\pi$
$107$	63590.8	−	63590.8i	0.536951	−	0.536951i	0.922632	+	0.385681i	$0.126033\pi$
$108$	30069.9	−	30069.9i	0.248069	−	0.248069i
$109$	−108461.			−0.874392			−0.437196	−	0.899366i	$-0.644028\pi$
$109$	−108461.			−0.874392			−0.437196	+	0.899366i	$0.644028\pi$
$110$	34657.9	+	26489.7i	0.273100	+	0.208735i
$111$	218949.			1.68669
$112$	120775.	−	120775.i	0.909771	−	0.909771i
$113$	−81929.2	+	81929.2i	−0.603591	+	0.603591i	−0.941264	−	0.337673i	$-0.890360\pi$
$113$	−81929.2	+	81929.2i	−0.603591	+	0.603591i	0.337673	+	0.941264i	$0.390360\pi$
$114$		−	92414.1i		−	0.666003i
$115$	59405.6	−	44127.7i	0.418873	−	0.311148i
$116$		−	40822.0i		−	0.281676i
$117$	81713.6	−	81713.6i	0.551861	−	0.551861i
$118$	−54060.1	−	54060.1i	−0.357415	−	0.357415i
$119$			232990.i			1.50824i
$120$	151900.	+	22415.0i	0.962951	+	0.142097i
$121$	−136570.	+	85358.0i	−0.847994	+	0.530006i
$122$	1965.55	+	1965.55i	0.0119560	+	0.0119560i
$123$	−143066.	−	143066.i	−0.852654	−	0.852654i
$124$		−	128077.i		−	0.748029i
$125$	−158089.	−	74333.0i	−0.904955	−	0.425507i
$126$	−151098.			−0.847875
$127$	−193336.	+	193336.i	−1.06366	+	1.06366i	−0.0658316	+	0.997831i	$0.520970\pi$
$127$	−193336.	+	193336.i	−1.06366	+	1.06366i	−0.997831	+	0.0658316i	$0.979030\pi$
$128$	130683.	+	130683.i	0.705006	+	0.705006i
$129$	−230121.			−1.21754
$130$	40445.7	+	5968.36i	0.209901	+	0.0309739i
$131$			37263.4i			0.189716i	0.995491	+	0.0948580i	$0.0302397\pi$
$131$			37263.4i			0.189716i	−0.995491	+	0.0948580i	$0.969760\pi$
$132$	−128775.	+	232345.i	−0.643277	+	1.16064i
$133$	362347.	−	362347.i	1.77622	−	1.77622i
$134$	−2933.19			−0.0141117
$135$	50234.0	+	67626.0i	0.237227	+	0.319359i
$136$	−107868.			−0.500086
$137$	178171.	+	178171.i	0.811028	+	0.811028i	0.984788	−	0.173760i	$-0.0555917\pi$
$137$	178171.	+	178171.i	0.811028	+	0.811028i	−0.173760	+	0.984788i	$0.555592\pi$
$138$	−42695.2	−	42695.2i	−0.190845	−	0.190845i
$139$	−235275.			−1.03285			−0.516426	−	0.856332i	$-0.672738\pi$
$139$	−235275.			−1.03285			−0.516426	+	0.856332i	$0.672738\pi$
$140$	237911.	+	320280.i	1.02587	+	1.38105i
$141$	282572.			1.19696
$142$	23827.8	−	23827.8i	0.0991660	−	0.0991660i
$143$	−73171.1	+	132020.i	−0.299226	+	0.539884i
$144$			207490.i			0.833855i
$145$	80001.7	+	11805.4i	0.315994	+	0.0466295i
$146$	−82425.8			−0.320023
$147$	−782231.	−	782231.i	−2.98567	−	2.98567i
$148$	−186249.	+	186249.i	−0.698940	+	0.698940i
$149$	364978.			1.34679			0.673397	−	0.739281i	$-0.264835\pi$
$149$	364978.			1.34679			0.673397	+	0.739281i	$0.264835\pi$
$150$	−41170.1	+	136461.i	−0.149401	+	0.495200i
$151$		−	84828.5i		−	0.302760i	−0.988476	−	0.151380i	$-0.951628\pi$
$151$		−	84828.5i		−	0.302760i	0.988476	−	0.151380i	$-0.0483718\pi$
$152$	167757.	+	167757.i	0.588940	+	0.588940i
$153$	−200137.	−	200137.i	−0.691192	−	0.691192i
$154$	189711.	−	54409.3i	0.644601	−	0.184872i
$155$	251002.	+	37039.0i	0.839165	+	0.123831i
$156$			248970.i			0.819098i
$157$	81829.3	+	81829.3i	0.264947	+	0.264947i	0.827060	−	0.562113i	$-0.190011\pi$
$157$	81829.3	+	81829.3i	0.264947	+	0.264947i	−0.562113	+	0.827060i	$0.690011\pi$
$158$	−46263.3	+	46263.3i	−0.147433	+	0.147433i
$159$			218421.i			0.685177i
$160$	−227076.	+	168677.i	−0.701248	+	0.520902i
$161$		−	334808.i		−	1.01796i
$162$	−54049.8	+	54049.8i	−0.161811	+	0.161811i
$163$	−340495.	+	340495.i	−1.00379	+	1.00379i	−0.00379509	+	0.999993i	$0.501208\pi$
$163$	−340495.	+	340495.i	−1.00379	+	1.00379i	−0.999993	+	0.00379509i	$0.998792\pi$
$164$	243398.			0.706654
$165$	−418101.	−	319562.i	−1.19556	−	0.913788i
$166$	−80481.5			−0.226686
$167$	−185857.	+	185857.i	−0.515688	+	0.515688i	−0.916264	−	0.400576i	$-0.868810\pi$
$167$	−185857.	+	185857.i	−0.515688	+	0.515688i	0.400576	+	0.916264i	$0.368810\pi$
$168$	491216.	−	491216.i	1.34276	−	1.34276i
$169$		−	229826.i		−	0.618989i
$170$	14618.0	−	99061.6i	0.0387941	−	0.262896i
$171$			622508.i			1.62800i
$172$	195752.	−	195752.i	0.504529	−	0.504529i
$173$	354156.	+	354156.i	0.899661	+	0.899661i	0.995406	−	0.0957446i	$-0.0305232\pi$
$173$	354156.	+	354156.i	0.899661	+	0.899661i	−0.0957446	+	0.995406i	$0.530523\pi$
$174$		−	65982.3i		−	0.165217i
$175$	−696476.	+	373627.i	−1.71914	+	0.922239i
$176$	−74715.7	−	260514.i	−0.181815	−	0.633942i
$177$	652163.	+	652163.i	1.56467	+	1.56467i
$178$	27126.8	+	27126.8i	0.0641725	+	0.0641725i
$179$		−	446387.i		−	1.04131i	−0.853768	−	0.520654i	$-0.825688\pi$
$179$		−	446387.i		−	1.04131i	0.853768	−	0.520654i	$-0.174312\pi$
$180$	−479482.	−	70754.6i	−1.10304	−	0.162770i
$181$	−244156.			−0.553950			−0.276975	−	0.960877i	$-0.589332\pi$
$181$	−244156.			−0.553950			−0.276975	+	0.960877i	$0.589332\pi$
$182$	130794.	−	130794.i	0.292691	−	0.292691i
$183$	−23711.7	−	23711.7i	−0.0523402	−	0.0523402i
$184$	155007.			0.337525
$185$	−311143.	−	418867.i	−0.668392	−	0.899801i
$186$		−	207017.i		−	0.438756i
$187$	323350.	+	179214.i	0.676191	+	0.374773i
$188$	−240369.	+	240369.i	−0.496003	+	0.496003i
$189$	381138.			0.776117
$190$	−176795.	+	131327.i	−0.355293	+	0.263919i
$191$	67541.6			0.133964			0.0669820	−	0.997754i	$-0.478663\pi$
$191$	67541.6			0.133964			0.0669820	+	0.997754i	$0.478663\pi$
$192$	−195248.	−	195248.i	−0.382237	−	0.382237i
$193$	−500498.	−	500498.i	−0.967184	−	0.967184i	0.0322946	−	0.999478i	$-0.489719\pi$
$193$	−500498.	−	500498.i	−0.967184	−	0.967184i	−0.999478	+	0.0322946i	$0.989719\pi$
$194$	−119995.			−0.228908
$195$	−487924.	−	72000.2i	−0.918894	−	0.135596i
$196$	1.33081e6			2.47443
$197$	631845.	−	631845.i	1.15996	−	1.15996i	0.175482	−	0.984483i	$-0.443852\pi$
$197$	631845.	−	631845.i	1.15996	−	1.15996i	0.984483	−	0.175482i	$-0.0561484\pi$
$198$	−116223.	+	209698.i	−0.210683	+	0.380129i
$199$			390693.i			0.699364i	0.936869	+	0.349682i	$0.113710\pi$
$199$			390693.i			0.699364i	−0.936869	+	0.349682i	$0.886290\pi$
$200$	−172979.	−	322449.i	−0.305787	−	0.570015i
$201$	35385.0			0.0617774
$202$	−200939.	−	200939.i	−0.346486	−	0.346486i
$203$	258711.	−	258711.i	0.440630	−	0.440630i
$204$	609790.			1.02590
$205$	−70388.7	+	477003.i	−0.116982	+	0.792750i
$206$			45087.7i			0.0740270i
$207$	287598.	+	287598.i	0.466508	+	0.466508i
$208$	−179608.	−	179608.i	−0.287851	−	0.287851i
$209$	−224161.	−	781591.i	−0.354972	−	1.23770i
$210$	384545.	+	517682.i	0.601726	+	0.810055i
$211$		−	879221.i		−	1.35954i	−0.733426	−	0.679770i	$-0.762080\pi$
$211$		−	879221.i		−	1.35954i	0.733426	−	0.679770i	$-0.237920\pi$
$212$	−185800.	−	185800.i	−0.283927	−	0.283927i
$213$	−287450.	+	287450.i	−0.434124	+	0.434124i
$214$			174867.i			0.261020i
$215$	327019.	+	440239.i	0.482477	+	0.649520i
$216$			176456.i			0.257337i
$217$	811694.	−	811694.i	1.17015	−	1.17015i
$218$	149127.	−	149127.i	0.212527	−	0.212527i
$219$	994357.			1.40098
$220$	627493.	−	83822.3i	0.874082	−	0.116762i
$221$	346487.			0.477206
$222$	−301042.	+	301042.i	−0.409963	+	0.409963i
$223$	485149.	−	485149.i	0.653301	−	0.653301i	−0.300486	−	0.953786i	$-0.597149\pi$
$223$	485149.	−	485149.i	0.653301	−	0.653301i	0.953786	+	0.300486i	$0.0971488\pi$
$224$			1.27979e6i			1.70420i
$225$	277325.	−	919212.i	0.365202	−	1.21048i
$226$		−	225295.i		−	0.293414i
$227$	−348678.	+	348678.i	−0.449117	+	0.449117i	−0.895061	−	0.445944i	$-0.852868\pi$
$227$	−348678.	+	348678.i	−0.449117	+	0.449117i	0.445944	+	0.895061i	$0.352868\pi$
$228$	−948348.	−	948348.i	−1.20818	−	1.20818i
$229$			771211.i			0.971817i	0.874010	+	0.485908i	$0.161511\pi$
$229$			771211.i			0.971817i	−0.874010	+	0.485908i	$0.838489\pi$
$230$	−21006.1	+	142352.i	−0.0261834	+	0.177437i
$231$	−2.28861e6	+	656376.i	−2.82190	+	0.809324i
$232$	119776.	+	119776.i	0.146100	+	0.146100i
$233$	−294969.	−	294969.i	−0.355948	−	0.355948i	0.506369	−	0.862317i	$-0.330987\pi$
$233$	−294969.	−	294969.i	−0.355948	−	0.355948i	−0.862317	+	0.506369i	$0.830987\pi$
$234$			224702.i			0.268267i
$235$	−401555.	−	540581.i	−0.474324	−	0.638544i
$236$	−1.10952e6			−1.29675
$237$	558105.	−	558105.i	0.645423	−	0.645423i
$238$	−320347.	−	320347.i	−0.366588	−	0.366588i
$239$	−877875.			−0.994118			−0.497059	−	0.867717i	$-0.665587\pi$
$239$	−877875.			−0.994118			−0.497059	+	0.867717i	$0.665587\pi$
$240$	710888.	−	528063.i	0.796660	−	0.591776i
$241$			1.67928e6i			1.86244i	0.364464	+	0.931218i	$0.381252\pi$
$241$			1.67928e6i			1.86244i	−0.364464	+	0.931218i	$0.618748\pi$
$242$	70413.6	−	305138.i	0.0772891	−	0.334933i
$243$	910977.	−	910977.i	0.989673	−	0.989673i
$244$	40340.7			0.0433780
$245$	−384860.	+	2.60808e6i	−0.409626	+	2.77591i
$246$	393413.			0.414487
$247$	−538858.	−	538858.i	−0.561995	−	0.561995i
$248$	375792.	+	375792.i	0.387988	+	0.387988i
$249$	970901.			0.992376
$250$	319566.	−	115160.i	0.323378	−	0.116533i
$251$	810607.			0.812131			0.406066	−	0.913844i	$-0.366900\pi$
$251$	810607.			0.812131			0.406066	+	0.913844i	$0.366900\pi$
$252$	−1.55056e6	+	1.55056e6i	−1.53811	+	1.53811i
$253$	−464656.	−	257532.i	−0.456384	−	0.252947i
$254$		−	531651.i		−	0.517061i
$255$	−176346.	+	1.19505e6i	−0.169831	+	1.15089i
$256$	17319.7			0.0165173
$257$	118700.	+	118700.i	0.112103	+	0.112103i	0.760933	−	0.648830i	$-0.224741\pi$
$257$	118700.	+	118700.i	0.112103	+	0.112103i	−0.648830	+	0.760933i	$0.724741\pi$
$258$	316403.	−	316403.i	0.295931	−	0.295931i
$259$	−2.36072e6			−2.18673
$260$	476299.	−	353805.i	0.436965	−	0.324587i
$261$			444461.i			0.403862i
$262$	−51234.9	−	51234.9i	−0.0461118	−	0.0461118i
$263$	153212.	+	153212.i	0.136585	+	0.136585i	0.772094	−	0.635509i	$-0.219210\pi$
$263$	153212.	+	153212.i	0.136585	+	0.136585i	−0.635509	+	0.772094i	$0.719210\pi$
$264$	−303884.	−	1.05956e6i	−0.268347	−	0.935658i
$265$	417857.	−	310393.i	0.365521	−	0.271517i
$266$			996411.i			0.863444i
$267$	−327249.	−	327249.i	−0.280931	−	0.280931i
$268$	−30100.3	+	30100.3i	−0.0255996	+	0.0255996i
$269$		−	1.41784e6i		−	1.19466i	−0.801994	−	0.597332i	$-0.796227\pi$
$269$		−	1.41784e6i		−	1.19466i	0.801994	−	0.597332i	$-0.203773\pi$
$270$	−162050.	−	23912.9i	−0.135282	−	0.0199628i
$271$			744148.i			0.615512i	0.951465	+	0.307756i	$0.0995780\pi$
$271$			744148.i			0.615512i	−0.951465	+	0.307756i	$0.900422\pi$
$272$	−439906.	+	439906.i	−0.360526	+	0.360526i
$273$	−1.57786e6	+	1.57786e6i	−1.28133	+	1.28133i
$274$	−489949.			−0.394252
$275$	−17193.8	+	1.25398e6i	−0.0137101	+	0.999906i
$276$	−876271.			−0.692414
$277$	1.76281e6	−	1.76281e6i	1.38040	−	1.38040i	0.536510	−	0.843894i	$-0.319742\pi$
$277$	1.76281e6	−	1.76281e6i	1.38040	−	1.38040i	0.843894	−	0.536510i	$-0.180258\pi$
$278$	323488.	−	323488.i	0.251042	−	0.251042i
$279$			1.39448e6i			1.07251i
$280$	−1.63779e6	−	241679.i	−1.24842	−	0.184223i
$281$		−	575563.i		−	0.434838i	−0.976078	−	0.217419i	$-0.930236\pi$
$281$		−	575563.i		−	0.434838i	0.976078	−	0.217419i	$-0.0697638\pi$
$282$	−388519.	+	388519.i	−0.290930	+	0.290930i
$283$	250700.	+	250700.i	0.186075	+	0.186075i	0.793997	−	0.607922i	$-0.207997\pi$
$283$	250700.	+	250700.i	0.186075	+	0.186075i	−0.607922	+	0.793997i	$0.707997\pi$
$284$		−	489039.i		−	0.359789i
$285$	2.13280e6	−	1.58429e6i	1.55538	−	1.15537i
$286$	−80913.9	−	282126.i	−0.0584935	−	0.203952i
$287$	1.54254e6	+	1.54254e6i	1.10543	+	1.10543i
$288$	−1.09933e6	−	1.09933e6i	−0.780995	−	0.780995i
$289$			571224.i			0.402311i
$290$	−126229.	+	93765.7i	−0.0881383	+	0.0654710i
$291$	1.44758e6			1.00210
$292$	−845849.	+	845849.i	−0.580545	+	0.580545i
$293$	252156.	+	252156.i	0.171593	+	0.171593i	0.787679	−	0.616086i	$-0.211283\pi$
$293$	252156.	+	252156.i	0.171593	+	0.171593i	−0.616086	+	0.787679i	$0.711283\pi$
$294$	2.15104e6			1.45138
$295$	320866.	−	2.17441e6i	0.214668	−	1.45474i
$296$		−	1.09295e6i		−	0.725053i
$297$	293168.	−	528954.i	0.192853	−	0.347958i
$298$	−501822.	+	501822.i	−0.327348	+	0.327348i
$299$	−497903.			−0.322083
$300$	977871.	+	1.82284e6i	0.627304	+	1.16935i
$301$	2.48117e6			1.57849
$302$	116634.	+	116634.i	0.0735881	+	0.0735881i
$303$	2.42406e6	+	2.42406e6i	1.51683	+	1.51683i
$304$	1.36829e6			0.849167
$305$	−11666.2	+	79058.4i	−0.00718093	+	0.0486630i
$306$	550352.			0.335998
$307$	680836.	−	680836.i	0.412284	−	0.412284i	−0.470249	−	0.882534i	$-0.655836\pi$
$307$	680836.	−	680836.i	0.412284	−	0.412284i	0.882534	+	0.470249i	$0.155836\pi$
$308$	1.38846e6	−	2.50515e6i	0.833982	−	1.50473i
$309$		−	543923.i		−	0.324072i
$310$	−396038.	+	294186.i	−0.234063	+	0.173867i
$311$	−2.01610e6			−1.18198			−0.590992	−	0.806677i	$-0.701264\pi$
$311$	−2.01610e6			−1.18198			−0.590992	+	0.806677i	$0.701264\pi$
$312$	−730503.	−	730503.i	−0.424850	−	0.424850i
$313$	−1.59317e6	+	1.59317e6i	−0.919180	+	0.919180i	−0.996970	−	0.0777898i	$-0.975214\pi$
$313$	−1.59317e6	+	1.59317e6i	−0.919180	+	0.919180i	0.0777898	+	0.996970i	$0.475214\pi$
$314$	−225020.			−0.128795
$315$	−2.59032e6	−	3.48714e6i	−1.47088	−	1.98013i
$316$			949503.i			0.534907i
$317$	−1.91917e6	−	1.91917e6i	−1.07267	−	1.07267i	−0.997144	−	0.0755230i	$-0.975937\pi$
$317$	−1.91917e6	−	1.91917e6i	−1.07267	−	1.07267i	−0.0755230	−	0.997144i	$-0.524063\pi$
$318$	−300316.	−	300316.i	−0.166537	−	0.166537i
$319$	−160048.	−	558044.i	−0.0880587	−	0.307038i
$320$	−96062.3	+	650985.i	−0.0524418	+	0.355382i
$321$		−	2.10953e6i		−	1.14268i
$322$	460340.	+	460340.i	0.247423	+	0.247423i
$323$	−1.31980e6	+	1.31980e6i	−0.703884	+	0.703884i
$324$			1.10931e6i			0.587072i
$325$	555633.	+	1.03575e6i	0.291796	+	0.543936i
$326$		−	936320.i		−	0.487956i
$327$	−1.79901e6	+	1.79901e6i	−0.930391	+	0.930391i
$328$	−714152.	+	714152.i	−0.366527	+	0.366527i
$329$	−3.04669e6			−1.55181
$330$	1.01424e6	−	135485.i	0.512692	−	0.0684869i
$331$	−1.20783e6			−0.605951			−0.302975	−	0.952998i	$-0.597980\pi$
$331$	−1.20783e6			−0.605951			−0.302975	+	0.952998i	$0.597980\pi$
$332$	−825896.	+	825896.i	−0.411226	+	0.411226i
$333$	2.02784e6	−	2.02784e6i	1.00213	−	1.00213i
$334$		−	511083.i		−	0.250683i
$335$	−50284.7	−	67694.2i	−0.0244807	−	0.0329564i
$336$		−	4.00654e6i		−	1.93607i
$337$	−450946.	+	450946.i	−0.216296	+	0.216296i	−0.806936	−	0.590639i	$-0.798876\pi$
$337$	−450946.	+	450946.i	−0.216296	+	0.216296i	0.590639	+	0.806936i	$0.298876\pi$
$338$	315997.	+	315997.i	0.150450	+	0.150450i
$339$			2.71789e6i			1.28449i
$340$	−866556.	−	1.16657e6i	−0.406536	−	0.547287i
$341$	−502143.	−	1.75084e6i	−0.233852	−	0.815381i
$342$	−855910.	−	855910.i	−0.395697	−	0.395697i
$343$	5.42829e6	+	5.42829e6i	2.49131	+	2.49131i
$344$			1.14871e6i			0.523378i
$345$	253411.	−	1.71729e6i	0.114624	−	0.776774i
$346$	−973885.			−0.437338
$347$	2.07257e6	−	2.07257e6i	0.924028	−	0.924028i	−0.0732829	−	0.997311i	$-0.523348\pi$
$347$	2.07257e6	−	2.07257e6i	0.924028	−	0.924028i	0.997311	+	0.0732829i	$0.0233476\pi$
$348$	−677107.	−	677107.i	−0.299715	−	0.299715i
$349$	144729.			0.0636053			0.0318026	−	0.999494i	$-0.489875\pi$
$349$	144729.			0.0636053			0.0318026	+	0.999494i	$0.489875\pi$
$350$	443898.	−	1.47133e6i	0.193692	−	0.642006i
$351$		−	566802.i		−	0.245563i
$352$	1.77613e6	+	984407.i	0.764045	+	0.423466i
$353$	2.34964e6	−	2.34964e6i	1.00361	−	1.00361i	0.00361526	−	0.999993i	$-0.498849\pi$
$353$	2.34964e6	−	2.34964e6i	1.00361	−	1.00361i	0.999993	−	0.00361526i	$-0.00115077\pi$
$354$	−1.79337e6			−0.760609
$355$	958402.	+	141426.i	0.403624	+	0.0595606i
$356$	556748.			0.232827
$357$	3.86456e6	+	3.86456e6i	1.60483	+	1.60483i
$358$	613755.	+	613755.i	0.253097	+	0.253097i
$359$	2.60785e6			1.06794			0.533969	−	0.845504i	$-0.320700\pi$
$359$	2.60785e6			1.06794			0.533969	+	0.845504i	$0.320700\pi$
$360$	1.61445e6	−	1.19925e6i	0.656550	−	0.487699i
$361$	1.62901e6			0.657895
$362$	335699.	−	335699.i	0.134641	−	0.134641i
$363$	−849446.	+	3.68108e6i	−0.338352	+	1.46625i
$364$		−	2.68440e6i		−	1.06193i
$365$	−1.41305e6	−	1.90228e6i	−0.555171	−	0.747381i
$366$	65204.3			0.0254433
$367$	−1.68111e6	−	1.68111e6i	−0.651526	−	0.651526i	0.301834	−	0.953360i	$-0.402401\pi$
$367$	−1.68111e6	−	1.68111e6i	−0.651526	−	0.651526i	−0.953360	+	0.301834i	$0.902401\pi$
$368$	632146.	−	632146.i	0.243331	−	0.243331i
$369$	−2.65006e6			−1.01319
$370$	1.00372e6	+	148113.i	0.381160	+	0.0562458i
$371$		−	2.35503e6i		−	0.888303i
$372$	−2.12439e6	−	2.12439e6i	−0.795935	−	0.795935i
$373$	1.05581e6	+	1.05581e6i	0.392929	+	0.392929i	0.875730	−	0.482801i	$-0.160381\pi$
$373$	1.05581e6	+	1.05581e6i	0.392929	+	0.392929i	−0.482801	+	0.875730i	$0.660381\pi$
$374$	−690995.	+	198178.i	−0.255444	+	0.0732616i
$375$	−3.85514e6	+	1.38925e6i	−1.41567	+	0.510154i
$376$		−	1.41053e6i		−	0.514534i
$377$	−384737.	−	384737.i	−0.139415	−	0.139415i
$378$	−524041.	+	524041.i	−0.188641	+	0.188641i
$379$			411768.i			0.147250i	0.997286	+	0.0736249i	$0.0234568\pi$
$379$			411768.i			0.147250i	−0.997286	+	0.0736249i	$0.976543\pi$
$380$	−466589.	+	3.16193e6i	−0.165759	+	1.12329i
$381$			6.41365e6i			2.26357i
$382$	−92865.6	+	92865.6i	−0.0325609	+	0.0325609i
$383$	−3.05644e6	+	3.05644e6i	−1.06468	+	1.06468i	−0.0669222	+	0.997758i	$0.521318\pi$
$383$	−3.05644e6	+	3.05644e6i	−1.06468	+	1.06468i	−0.997758	+	0.0669222i	$0.978682\pi$
$384$	4.33521e6			1.50031
$385$	4.50798e6	+	3.44553e6i	1.54999	+	1.18469i
$386$	1.37631e6			0.470162
$387$	−2.13131e6	+	2.13131e6i	−0.723384	+	0.723384i
$388$	−1.23139e6	+	1.23139e6i	−0.415255	+	0.415255i
$389$		−	2.04636e6i		−	0.685658i	−0.939398	−	0.342829i	$-0.888615\pi$
$389$		−	2.04636e6i		−	0.685658i	0.939398	−	0.342829i	$-0.111385\pi$
$390$	769861.	−	571869.i	0.256301	−	0.190386i
$391$			1.21949e6i			0.403400i
$392$	−3.90472e6	+	3.90472e6i	−1.28344	+	1.28344i
$393$	618080.	+	618080.i	0.201866	+	0.201866i
$394$			1.73750e6i			0.563875i
$395$	−1.86080e6	−	274589.i	−0.600078	−	0.0885503i
$396$	959230.	+	3.34458e6i	0.307386	+	1.07178i
$397$	−1.54130e6	−	1.54130e6i	−0.490807	−	0.490807i	0.417754	−	0.908560i	$-0.362817\pi$
$397$	−1.54130e6	−	1.54130e6i	−0.490807	−	0.490807i	−0.908560	+	0.417754i	$0.862817\pi$
$398$	−537179.	−	537179.i	−0.169985	−	0.169985i
$399$		−	1.20204e7i		−	3.77994i
$400$	−2.02045e6	−	609567.i	−0.631390	−	0.190490i
$401$	1.55074e6			0.481591			0.240795	−	0.970576i	$-0.422592\pi$
$401$	1.55074e6			0.481591			0.240795	+	0.970576i	$0.422592\pi$
$402$	−48652.3	+	48652.3i	−0.0150154	+	0.0150154i
$403$	−1.20710e6	−	1.20710e6i	−0.370236	−	0.370236i
$404$	−4.12405e6			−1.25710
$405$	−2.17399e6	−	320805.i	−0.658599	−	0.0971858i
$406$			711423.i			0.214197i
$407$	−1.81585e6	+	3.27627e6i	−0.543367	+	0.980379i
$408$	−1.78918e6	+	1.78918e6i	−0.532114	+	0.532114i
$409$	−3.51395e6			−1.03869			−0.519347	−	0.854564i	$-0.673825\pi$
$409$	−3.51395e6			−1.03869			−0.519347	+	0.854564i	$0.673825\pi$
$410$	−559069.	−	752629.i	−0.164250	−	0.221117i
$411$	5.91057e6			1.72594
$412$	462688.	+	462688.i	0.134290	+	0.134290i
$413$	−7.03164e6	−	7.03164e6i	−2.02853	−	2.02853i
$414$	−790858.			−0.226776
$415$	−1.37972e6	−	1.85741e6i	−0.393252	−	0.529403i
$416$	1.90322e6			0.539207
$417$	−3.90245e6	+	3.90245e6i	−1.09900	+	1.09900i
$418$	1.38285e6	+	766432.i	0.387109	+	0.214552i
$419$			2.19519e6i			0.610853i	0.952216	+	0.305426i	$0.0987990\pi$
$419$			2.19519e6i			0.610853i	−0.952216	+	0.305426i	$0.901201\pi$
$420$	9.25860e6	+	1.36624e6i	2.56107	+	0.377924i
$421$	−6.73434e6			−1.85178			−0.925890	−	0.377793i	$-0.876683\pi$
$421$	−6.73434e6			−1.85178			−0.925890	+	0.377793i	$0.876683\pi$
$422$	1.20887e6	+	1.20887e6i	0.330446	+	0.330446i
$423$	2.61709e6	−	2.61709e6i	0.711160	−	0.711160i
$424$	1.09031e6			0.294534
$425$	2.53681e6	−	1.36088e6i	0.681265	−	0.365467i
$426$		−	790453.i		−	0.211034i
$427$	255660.	+	255660.i	0.0678568	+	0.0678568i
$428$	1.79447e6	+	1.79447e6i	0.473509	+	0.473509i
$429$	976117.	+	3.40347e6i	0.256070	+	0.892849i
$430$	−1.05493e6	−	155671.i	−0.275140	−	0.0406009i
$431$			1.11200e6i			0.288343i	0.989553	+	0.144172i	$0.0460517\pi$
$431$			1.11200e6i			0.288343i	−0.989553	+	0.144172i	$0.953948\pi$
$432$	719621.	+	719621.i	0.185522	+	0.185522i
$433$	3.87318e6	−	3.87318e6i	0.992768	−	0.992768i	−0.00720560	−	0.999974i	$-0.502294\pi$
$433$	3.87318e6	−	3.87318e6i	0.992768	−	0.992768i	0.999974	+	0.00720560i	$0.00229363\pi$
$434$			2.23206e6i			0.568828i
$435$	1.52278e6	−	1.13116e6i	0.385847	−	0.286616i
$436$		−	3.06066e6i		−	0.771079i
$437$	1.89656e6	−	1.89656e6i	0.475075	−	0.475075i
$438$	−1.36718e6	+	1.36718e6i	−0.340518	+	0.340518i
$439$	292135.			0.0723474			0.0361737	−	0.999346i	$-0.488483\pi$
$439$	292135.			0.0723474			0.0361737	+	0.999346i	$0.488483\pi$
$440$	−1.59518e6	+	2.08707e6i	−0.392807	+	0.513931i
$441$	−1.44896e7			−3.54780
$442$	−476398.	+	476398.i	−0.115988	+	0.115988i
$443$	−907357.	+	907357.i	−0.219669	+	0.219669i	−0.808359	−	0.588690i	$-0.799644\pi$
$443$	−907357.	+	907357.i	−0.219669	+	0.219669i	0.588690	+	0.808359i	$0.299644\pi$
$444$			6.17855e6i			1.48741i
$445$	−161007.	+	1.09110e6i	−0.0385430	+	0.261194i
$446$			1.33410e6i			0.317579i
$447$	6.05381e6	−	6.05381e6i	1.43305	−	1.43305i
$448$	2.10516e6	+	2.10516e6i	0.495554	+	0.495554i
$449$		−	3.38050e6i		−	0.791343i	−0.918392	−	0.395672i	$-0.870512\pi$
$449$		−	3.38050e6i		−	0.791343i	0.918392	−	0.395672i	$-0.129488\pi$
$450$	882555.	+	1.64516e6i	0.205452	+	0.382982i
$451$	3.32729e6	−	954269.i	0.770281	−	0.220917i
$452$	−2.31197e6	−	2.31197e6i	−0.532275	−	0.532275i
$453$	−1.40703e6	−	1.40703e6i	−0.322150	−	0.322150i
$454$		−	958822.i		−	0.218322i
$455$	5.26080e6	+	776308.i	1.19131	+	0.175795i
$456$	5.56509e6			1.25332
$457$	3.57737e6	−	3.57737e6i	0.801259	−	0.801259i	−0.182033	−	0.983292i	$-0.558268\pi$
$457$	3.57737e6	−	3.57737e6i	0.801259	−	0.801259i	0.983292	+	0.182033i	$0.0582679\pi$
$458$	−1.06037e6	−	1.06037e6i	−0.236207	−	0.236207i
$459$	−1.38824e6			−0.307562
$460$	1.24524e6	+	1.67637e6i	0.274385	+	0.369382i
$461$			1.22154e6i			0.267705i	0.991001	+	0.133853i	$0.0427349\pi$
$461$			1.22154e6i			0.267705i	−0.991001	+	0.133853i	$0.957265\pi$
$462$	2.24422e6	−	4.04918e6i	0.489171	−	0.882595i
$463$	1.61799e6	−	1.61799e6i	0.350771	−	0.350771i	−0.509625	−	0.860396i	$-0.670216\pi$
$463$	1.61799e6	−	1.61799e6i	0.350771	−	0.350771i	0.860396	+	0.509625i	$0.170216\pi$
$464$	976936.			0.210655
$465$	4.77767e6	−	3.54896e6i	1.02467	−	0.761147i
$466$	811129.			0.173031
$467$	1.19220e6	+	1.19220e6i	0.252964	+	0.252964i	0.822185	−	0.569221i	$-0.192755\pi$
$467$	1.19220e6	+	1.19220e6i	0.252964	+	0.252964i	−0.569221	+	0.822185i	$0.692755\pi$
$468$	2.30588e6	+	2.30588e6i	0.486657	+	0.486657i
$469$	−381522.			−0.0800918
$470$	1.29538e6	+	191152.i	0.270491	+	0.0399148i
$471$	2.71457e6			0.563831
$472$	3.25545e6	−	3.25545e6i	0.672599	−	0.672599i
$473$	1.90850e6	−	3.44344e6i	0.392228	−	0.707685i
$474$			1.53472e6i			0.313750i
$475$	−6.06172e6	−	1.82881e6i	−1.23271	−	0.371908i
$476$	−6.57477e6			−1.33004
$477$	2.02295e6	+	2.02295e6i	0.407089	+	0.407089i
$478$	1.20702e6	−	1.20702e6i	0.241627	−	0.241627i
$479$	−139147.			−0.0277100			−0.0138550	−	0.999904i	$-0.504410\pi$
$479$	−139147.			−0.0277100			−0.0138550	+	0.999904i	$0.504410\pi$
$480$	−968654.	+	6.56427e6i	−0.191896	+	1.30042i
$481$			3.51070e6i			0.691880i
$482$	−2.30891e6	−	2.30891e6i	−0.452678	−	0.452678i
$483$	−5.55339e6	−	5.55339e6i	−1.08315	−	1.08315i
$484$	−2.40873e6	−	3.85389e6i	−0.467384	−	0.747800i
$485$	−2.05712e6	−	2.76934e6i	−0.397105	−	0.534591i
$486$			2.50507e6i			0.481094i
$487$	3.74252e6	+	3.74252e6i	0.715058	+	0.715058i	0.967589	−	0.252531i	$-0.0812629\pi$
$487$	3.74252e6	+	3.74252e6i	0.715058	+	0.715058i	−0.252531	+	0.967589i	$0.581263\pi$
$488$	−118364.	+	118364.i	−0.0224993	+	0.0224993i
$489$			1.12954e7i			2.13615i
$490$	−3.05679e6	−	4.11510e6i	−0.575142	−	0.774266i
$491$		−	5.83574e6i		−	1.09243i	−0.837646	−	0.546213i	$-0.816069\pi$
$491$		−	5.83574e6i		−	1.09243i	0.837646	−	0.546213i	$-0.183931\pi$
$492$	4.03719e6	−	4.03719e6i	0.751910	−	0.751910i
$493$	−942316.	+	942316.i	−0.174614	+	0.174614i
$494$	1.48179e6			0.273194
$495$	−6.83201e6	+	912639.i	−1.25324	+	0.167412i
$496$	3.06510e6			0.559422
$497$	3.09929e6	−	3.09929e6i	0.562823	−	0.562823i
$498$	−1.33493e6	+	1.33493e6i	−0.241204	+	0.241204i
$499$			1.31028e6i			0.235566i	0.993039	+	0.117783i	$0.0375787\pi$
$499$			1.31028e6i			0.235566i	−0.993039	+	0.117783i	$0.962421\pi$
$500$	2.09761e6	−	4.46113e6i	0.375232	−	0.798032i
$501$			6.16553e6i			1.09743i
$502$	−1.11454e6	+	1.11454e6i	−0.197394	+	0.197394i
$503$	588357.	+	588357.i	0.103686	+	0.103686i	0.757047	−	0.653361i	$-0.226641\pi$
$503$	588357.	+	588357.i	0.103686	+	0.103686i	−0.653361	+	0.757047i	$0.726641\pi$
$504$		−	9.09897e6i		−	1.59557i
$505$	1.19264e6	−	8.08218e6i	0.208105	−	1.41026i
$506$	992963.	−	284783.i	0.172408	−	0.0494467i
$507$	−3.81208e6	−	3.81208e6i	−0.658631	−	0.658631i
$508$	−5.45577e6	−	5.45577e6i	−0.937987	−	0.937987i
$509$			2.21278e6i			0.378568i	0.981922	+	0.189284i	$0.0606167\pi$
$509$			2.21278e6i			0.378568i	−0.981922	+	0.189284i	$0.939383\pi$
$510$	−1.40065e6	−	1.88558e6i	−0.238454	−	0.321011i
$511$	−1.07212e7			−1.81631
$512$	−4.20566e6	+	4.20566e6i	−0.709020	+	0.709020i
$513$	2.15900e6	+	2.15900e6i	0.362208	+	0.362208i
$514$	−326410.			−0.0544949
$515$	−1.04057e6	+	772954.i	−0.172883	+	0.128421i
$516$		−	6.49381e6i		−	1.07368i
$517$	−2.34350e6	+	4.22829e6i	−0.385601	+	0.695726i
$518$	3.24584e6	−	3.24584e6i	0.531500	−	0.531500i
$519$	1.17486e7			1.91456
$520$	−359409.	+	2.43561e6i	−0.0582882	+	0.395001i
$521$	−155069.			−0.0250282			−0.0125141	−	0.999922i	$-0.503983\pi$
$521$	−155069.			−0.0250282			−0.0125141	+	0.999922i	$0.503983\pi$
$522$	−611107.	−	611107.i	−0.0981615	−	0.0981615i
$523$	6.42262e6	+	6.42262e6i	1.02673	+	1.02673i	0.999633	+	0.0271015i	$0.00862772\pi$
$523$	6.42262e6	+	6.42262e6i	1.02673	+	1.02673i	0.0271015	+	0.999633i	$0.491372\pi$
$524$	−1.05154e6			−0.167300
$525$	−5.35503e6	+	1.77496e7i	−0.847937	+	2.81054i
$526$	−421315.			−0.0663961
$527$	−2.95648e6	+	2.95648e6i	−0.463711	+	0.463711i
$528$	−5.56039e6	−	3.08180e6i	−0.868001	−	0.481083i
$529$			4.68393e6i			0.727732i
$530$	−147756.	+	1.00130e6i	−0.0228484	+	0.154837i
$531$	1.20803e7			1.85926
$532$	1.02251e7	+	1.02251e7i	1.56635	+	1.56635i
$533$	2.29396e6	−	2.29396e6i	0.349758	−	0.349758i
$534$	899894.			0.136565
$535$	−4.03570e6	+	2.99780e6i	−0.609585	+	0.452813i
$536$		−	176634.i		−	0.0265560i
$537$	−7.40413e6	−	7.40413e6i	−1.10800	−	1.10800i
$538$	1.94944e6	+	1.94944e6i	0.290372	+	0.290372i
$539$	1.81924e7	−	5.21760e6i	2.69723	−	0.773568i
$540$	−1.90834e6	+	1.41756e6i	−0.281626	+	0.209198i
$541$			6.73739e6i			0.989689i	0.868982	+	0.494845i	$0.164775\pi$
$541$			6.73739e6i			0.989689i	−0.868982	+	0.494845i	$0.835225\pi$
$542$	−1.02316e6	−	1.02316e6i	−0.149604	−	0.149604i
$543$	−4.04976e6	+	4.04976e6i	−0.589426	+	0.589426i
$544$		−	4.66146e6i		−	0.675344i
$545$	5.99818e6	+	885119.i	0.865025	+	0.127647i
$546$		−	4.33891e6i		−	0.622872i
$547$	1.40660e6	−	1.40660e6i	0.201002	−	0.201002i	−0.599427	−	0.800429i	$-0.704605\pi$
$547$	1.40660e6	−	1.40660e6i	0.201002	−	0.201002i	0.800429	+	0.599427i	$0.204605\pi$
$548$	−5.02783e6	+	5.02783e6i	−0.715202	+	0.715202i
$549$	−439221.			−0.0621945
$550$	−1.70051e6	−	1.74779e6i	−0.239702	−	0.246367i
$551$	2.93099e6			0.411278
$552$	2.57106e6	−	2.57106e6i	0.359141	−	0.359141i
$553$	−6.01750e6	+	6.01750e6i	−0.836764	+	0.836764i
$554$			4.84751e6i			0.671034i
$555$	−1.21085e7	−	1.78679e6i	−1.66862	−	0.246230i
$556$		−	6.63924e6i		−	0.910817i
$557$	2.53188e6	−	2.53188e6i	0.345784	−	0.345784i	−0.512753	−	0.858536i	$-0.671374\pi$
$557$	2.53188e6	−	2.53188e6i	0.345784	−	0.345784i	0.858536	+	0.512753i	$0.171374\pi$
$558$	−1.91732e6	−	1.91732e6i	−0.260681	−	0.260681i
$559$		−	3.68983e6i		−	0.499433i
$560$	−7.66481e6	+	5.69359e6i	−1.03284	+	0.767213i
$561$	8.33593e6	−	2.39075e6i	1.11827	−	0.320721i
$562$	791364.	+	791364.i	0.105690	+	0.105690i
$563$	−5.27520e6	−	5.27520e6i	−0.701404	−	0.701404i	0.263308	−	0.964712i	$-0.415186\pi$
$563$	−5.27520e6	−	5.27520e6i	−0.701404	−	0.701404i	−0.964712	+	0.263308i	$0.915186\pi$
$564$			7.97392e6i			1.05554i
$565$	5.19952e6	−	3.86231e6i	0.685239	−	0.509010i
$566$	−689394.			−0.0904538
$567$	−7.03030e6	+	7.03030e6i	−0.918367	+	0.918367i
$568$	1.43489e6	+	1.43489e6i	0.186615	+	0.186615i
$569$	2.35153e6			0.304487			0.152244	−	0.988343i	$-0.451350\pi$
$569$	2.35153e6			0.304487			0.152244	+	0.988343i	$0.451350\pi$
$570$	−754167.	+	5.11076e6i	−0.0972256	+	0.658868i
$571$			1.10913e7i			1.42362i	0.702374	+	0.711808i	$0.252123\pi$
$571$			1.10913e7i			1.42362i	−0.702374	+	0.711808i	$0.747877\pi$
$572$	−3.72549e6	−	2.06482e6i	−0.476095	−	0.263872i
$573$	1.12030e6	−	1.12030e6i	0.142543	−	0.142543i
$574$	−4.24179e6			−0.537365
$575$	−3.64541e6	+	1.95560e6i	−0.459809	+	0.246666i
$576$	−3.61664e6			−0.454202
$577$	−5.03936e6	−	5.03936e6i	−0.630139	−	0.630139i	0.317964	−	0.948103i	$-0.397001\pi$
$577$	−5.03936e6	−	5.03936e6i	−0.630139	−	0.630139i	−0.948103	+	0.317964i	$0.897001\pi$
$578$	−785398.	−	785398.i	−0.0977846	−	0.0977846i
$579$	−1.66033e7			−2.05825
$580$	−333138.	+	2.25757e6i	−0.0411201	+	0.278658i
$581$	−1.04683e7			−1.28657
$582$	−1.99034e6	+	1.99034e6i	−0.243568	+	0.243568i
$583$	−3.26837e6	−	1.81147e6i	−0.398254	−	0.220729i
$584$		−	4.96361e6i		−	0.602234i
$585$	−5.18584e6	+	3.85215e6i	−0.626512	+	0.465386i
$586$	−693398.			−0.0834139
$587$	6.47666e6	+	6.47666e6i	0.775811	+	0.775811i	0.979116	−	0.203304i	$-0.0651681\pi$
$587$	6.47666e6	+	6.47666e6i	0.775811	+	0.775811i	−0.203304	+	0.979116i	$0.565168\pi$
$588$	2.20739e7	−	2.20739e7i	2.63290	−	2.63290i
$589$	9.19585e6			1.09220
$590$	2.54851e6	+	3.43085e6i	0.301409	+	0.405762i
$591$		−	2.09606e7i		−	2.46850i
$592$	−4.45724e6	−	4.45724e6i	−0.522711	−	0.522711i
$593$	3.54180e6	+	3.54180e6i	0.413606	+	0.413606i	0.882993	−	0.469386i	$-0.155525\pi$
$593$	3.54180e6	+	3.54180e6i	0.413606	+	0.413606i	−0.469386	+	0.882993i	$0.655525\pi$
$594$	324190.	+	1.13037e6i	0.0376994	+	0.131448i
$595$	1.90137e6	−	1.28850e7i	0.220178	−	1.49208i
$596$			1.02993e7i			1.18766i
$597$	6.48034e6	+	6.48034e6i	0.744153	+	0.744153i
$598$	684587.	−	684587.i	0.0782844	−	0.0782844i
$599$			1.04560e7i			1.19069i	0.803469	+	0.595346i	$0.202985\pi$
$599$			1.04560e7i			1.19069i	−0.803469	+	0.595346i	$0.797015\pi$
$600$	−8.21756e6	−	2.47923e6i	−0.931891	−	0.281150i
$601$			1.04706e7i			1.18246i	0.806502	+	0.591231i	$0.201358\pi$
$601$			1.04706e7i			1.18246i	−0.806502	+	0.591231i	$0.798642\pi$
$602$	−3.41146e6	+	3.41146e6i	−0.383662	+	0.383662i
$603$	327725.	−	327725.i	0.0367042	−	0.0367042i
$604$	2.39378e6			0.266988
$605$	8.24930e6	−	3.60603e6i	0.916281	−	0.400535i
$606$	−6.66587e6			−0.737352
$607$	−1.44278e6	+	1.44278e6i	−0.158939	+	0.158939i	−0.782096	−	0.623158i	$-0.785850\pi$
$607$	−1.44278e6	+	1.44278e6i	−0.158939	+	0.158939i	0.623158	+	0.782096i	$0.285850\pi$
$608$	−7.24953e6	+	7.24953e6i	−0.795336	+	0.795336i
$609$		−	8.58236e6i		−	0.937699i
$610$	−92660.1	−	124741.i	−0.0100825	−	0.0135733i
$611$			4.53084e6i			0.490993i
$612$	5.64768e6	−	5.64768e6i	0.609525	−	0.609525i
$613$	−3.73091e6	−	3.73091e6i	−0.401017	−	0.401017i	0.477574	−	0.878591i	$-0.341516\pi$
$613$	−3.73091e6	−	3.73091e6i	−0.401017	−	0.401017i	−0.878591	+	0.477574i	$0.841516\pi$
$614$			1.87222e6i			0.200417i
$615$	6.74442e6	+	9.07946e6i	0.719046	+	0.967993i
$616$	3.27648e6	+	1.14242e7i	0.347901	+	1.21304i
$617$	4.22583e6	+	4.22583e6i	0.446888	+	0.446888i	0.894319	−	0.447431i	$-0.147661\pi$
$617$	4.22583e6	+	4.22583e6i	0.446888	+	0.446888i	−0.447431	+	0.894319i	$0.647661\pi$
$618$	747861.	+	747861.i	0.0787679	+	0.0787679i
$619$			3.91460e6i			0.410640i	0.978695	+	0.205320i	$0.0658235\pi$
$619$			3.91460e6i			0.410640i	−0.978695	+	0.205320i	$0.934177\pi$
$620$	−1.04521e6	+	7.08304e6i	−0.109200	+	0.740015i
$621$	1.99490e6			0.207584
$622$	2.77202e6	−	2.77202e6i	0.287290	−	0.287290i
$623$	3.52840e6	+	3.52840e6i	0.364215	+	0.364215i
$624$	−5.95825e6			−0.612573
$625$	8.13617e6	+	5.40095e6i	0.833143	+	0.553057i
$626$		−	4.38101e6i		−	0.446826i
$627$	−1.66822e7	−	9.24597e6i	−1.69467	−	0.939255i
$628$	−2.30915e6	+	2.30915e6i	−0.233643	+	0.233643i
$629$	8.59857e6			0.866562
$630$	8.35614e6	+	1.23307e6i	0.838792	+	0.123776i
$631$	−1.41483e7			−1.41459			−0.707293	−	0.706920i	$-0.750084\pi$
$631$	−1.41483e7			−1.41459			−0.707293	+	0.706920i	$0.750084\pi$
$632$	−2.78593e6	−	2.78593e6i	−0.277446	−	0.277446i
$633$	−1.45834e7	−	1.45834e7i	−1.44661	−	1.44661i
$634$	5.27748e6			0.521439
$635$	1.22698e7	−	9.11427e6i	1.20754	−	0.896990i
$636$	−6.16366e6			−0.604221
$637$	1.25425e7	−	1.25425e7i	1.22472	−	1.22472i
$638$	987332.	+	547221.i	0.0960310	+	0.0532244i
$639$			5.32454e6i			0.515858i
$640$	−6.16065e6	−	8.29358e6i	−0.594534	−	0.800372i
$641$	1.85985e7			1.78786			0.893930	−	0.448206i	$-0.147937\pi$
$641$	1.85985e7			1.78786			0.893930	+	0.448206i	$0.147937\pi$
$642$	2.90048e6	+	2.90048e6i	0.277736	+	0.277736i
$643$	−7.18707e6	+	7.18707e6i	−0.685526	+	0.685526i	−0.961240	−	0.275713i	$-0.911086\pi$
$643$	−7.18707e6	+	7.18707e6i	−0.685526	+	0.685526i	0.275713	+	0.961240i	$0.411086\pi$
$644$	9.44797e6			0.897685
$645$	1.27264e7	+	1.87796e6i	1.20449	+	0.177741i
$646$		−	3.62928e6i		−	0.342168i
$647$	1.05762e7	+	1.05762e7i	0.993272	+	0.993272i	0.999978	−	0.00670504i	$-0.00213430\pi$
$647$	1.05762e7	+	1.05762e7i	0.993272	+	0.993272i	−0.00670504	+	0.999978i	$0.502134\pi$
$648$	−3.25483e6	−	3.25483e6i	−0.304503	−	0.304503i
$649$	−1.51674e7	+	4.35002e6i	−1.41351	+	0.405396i
$650$	−2.18806e6	−	660134.i	−0.203131	−	0.0612842i
$651$		−	2.69268e7i		−	2.49019i
$652$	−9.60846e6	−	9.60846e6i	−0.885187	−	0.885187i
$653$	8.94915e6	−	8.94915e6i	0.821294	−	0.821294i	−0.164999	−	0.986294i	$-0.552762\pi$
$653$	8.94915e6	−	8.94915e6i	0.821294	−	0.821294i	0.986294	+	0.164999i	$0.0527622\pi$
$654$		−	4.94707e6i		−	0.452276i
$655$	304097.	−	2.06077e6i	0.0276954	−	0.187684i
$656$			5.82489e6i			0.528480i
$657$	9.20942e6	−	9.20942e6i	0.832374	−	0.832374i
$658$	4.18902e6	−	4.18902e6i	0.377179	−	0.377179i
$659$	1.11146e7			0.996969			0.498484	−	0.866899i	$-0.333890\pi$
$659$	1.11146e7			0.996969			0.498484	+	0.866899i	$0.333890\pi$
$660$	9.01775e6	−	1.17984e7i	0.805821	−	1.05430i
$661$	2.25071e6			0.200362			0.100181	−	0.994969i	$-0.468058\pi$
$661$	2.25071e6			0.200362			0.100181	+	0.994969i	$0.468058\pi$
$662$	1.66070e6	−	1.66070e6i	0.147281	−	0.147281i
$663$	5.74711e6	−	5.74711e6i	0.507768	−	0.507768i
$664$		−	4.84652e6i		−	0.426589i
$665$	−2.29959e7	+	1.70818e7i	−2.01649	+	1.49789i
$666$			5.57631e6i			0.487149i
$667$	1.35411e6	−	1.35411e6i	0.117853	−	0.117853i
$668$	−5.24471e6	−	5.24471e6i	−0.454758	−	0.454758i
$669$		−	1.60941e7i		−	1.39028i
$670$	162214.	+	23937.0i	0.0139605	+	0.00206008i
$671$	551465.	−	158161.i	0.0472837	−	0.0135610i
$672$	2.12277e7	+	2.12277e7i	1.81334	+	1.81334i
$673$	7.82446e6	+	7.82446e6i	0.665912	+	0.665912i	0.956767	−	0.290855i	$-0.0939397\pi$
$673$	7.82446e6	+	7.82446e6i	0.665912	+	0.665912i	−0.290855	+	0.956767i	$0.593940\pi$
$674$		−	1.24005e6i		−	0.105145i
$675$	−2.22621e6	−	4.14985e6i	−0.188064	−	0.350569i
$676$	6.48549e6			0.545853
$677$	2.07789e6	−	2.07789e6i	0.174241	−	0.174241i	−0.614599	−	0.788840i	$-0.710682\pi$
$677$	2.07789e6	−	2.07789e6i	0.174241	−	0.174241i	0.788840	+	0.614599i	$0.210682\pi$
$678$	−3.73693e6	−	3.73693e6i	−0.312205	−	0.312205i
$679$	−1.56079e7			−1.29918
$680$	5.96540e6	+	880282.i	0.494729	+	0.0730045i
$681$			1.15669e7i			0.955761i
$682$	3.09771e6	+	1.71688e6i	0.255024	+	0.141345i
$683$	3.71347e6	−	3.71347e6i	0.304599	−	0.304599i	−0.538211	−	0.842810i	$-0.680900\pi$
$683$	3.71347e6	−	3.71347e6i	0.304599	−	0.304599i	0.842810	+	0.538211i	$0.180900\pi$
$684$	−1.75666e7			−1.43565
$685$	−8.39936e6	−	1.13074e7i	−0.683942	−	0.920736i
$686$	−1.49271e7			−1.21106
$687$	1.27919e7	+	1.27919e7i	1.03405	+	1.03405i
$688$	4.68467e6	+	4.68467e6i	0.377318	+	0.377318i
$689$	−3.50223e6			−0.281059
$690$	2.01274e6	+	2.70959e6i	0.160940	+	0.216661i
$691$	1.84166e7			1.46728			0.733641	−	0.679537i	$-0.237819\pi$
$691$	1.84166e7			1.46728			0.733641	+	0.679537i	$0.237819\pi$
$692$	−9.99395e6	+	9.99395e6i	−0.793363	+	0.793363i
$693$	−1.51172e7	+	2.72755e7i	−1.19575	+	2.15745i
$694$			5.69931e6i			0.449183i
$695$	1.30114e7	+	1.92002e6i	1.02179	+	0.150780i
$696$	3.97339e6			0.310913
$697$	−5.61847e6	−	5.61847e6i	−0.438063	−	0.438063i
$698$	−198994.	+	198994.i	−0.0154597	+	0.0154597i
$699$	−9.78518e6			−0.757488
$700$	−1.05434e7	−	1.96539e7i	−0.813273	−	1.51602i
$701$			1.83007e7i			1.40661i	0.710890	+	0.703304i	$0.248293\pi$
$701$			1.83007e7i			1.40661i	−0.710890	+	0.703304i	$0.751707\pi$
$702$	779318.	+	779318.i	0.0596859	+	0.0596859i
$703$	−1.33725e7	−	1.33725e7i	−1.02053	−	1.02053i
$704$	4.54088e6	−	1.30233e6i	0.345310	−	0.0990351i
$705$	−1.56270e7	−	2.30599e6i	−1.18414	−	0.174737i
$706$			6.46122e6i			0.487868i
$707$	−2.61363e7	−	2.61363e7i	−1.96651	−	1.96651i
$708$	−1.84034e7	+	1.84034e7i	−1.37980	+	1.37980i
$709$			5.27902e6i			0.394401i	0.980363	+	0.197200i	$0.0631850\pi$
$709$			5.27902e6i			0.394401i	−0.980363	+	0.197200i	$0.936815\pi$
$710$	−1.51220e6	+	1.12329e6i	−0.112580	+	0.0836270i
$711$		−	1.03380e7i		−	0.766940i
$712$	−1.63355e6	+	1.63355e6i	−0.120763	+	0.120763i
$713$	4.24847e6	−	4.24847e6i	0.312974	−	0.312974i
$714$	−1.06271e7			−0.780131
$715$	5.12395e6	−	6.70396e6i	0.374835	−	0.490418i
$716$	1.25966e7			0.918273
$717$	−1.45611e7	+	1.45611e7i	−1.05778	+	1.05778i
$718$	−3.58563e6	+	3.58563e6i	−0.259570	+	0.259570i
$719$		−	2.29002e7i		−	1.65203i	−0.563648	−	0.826015i	$-0.690603\pi$
$719$		−	2.29002e7i		−	1.65203i	0.563648	−	0.826015i	$-0.309397\pi$
$720$	1.69327e6	−	1.14748e7i	0.121729	−	0.824922i
$721$			5.86459e6i			0.420145i
$722$	−2.23979e6	+	2.23979e6i	−0.159906	+	0.159906i
$723$	2.78539e7	+	2.78539e7i	1.98171	+	1.98171i
$724$		−	6.88985e6i		−	0.488499i
$725$	−4.32798e6	−	1.30575e6i	−0.305802	−	0.0922600i
$726$	−3.89332e6	−	6.22919e6i	−0.274144	−	0.438622i
$727$	7.77308e6	+	7.77308e6i	0.545453	+	0.545453i	0.925122	−	0.379669i	$-0.123962\pi$
$727$	7.77308e6	+	7.77308e6i	0.545453	+	0.545453i	−0.379669	+	0.925122i	$0.623962\pi$
$728$	7.87630e6	+	7.87630e6i	0.550800	+	0.550800i
$729$		−	2.06678e7i		−	1.44038i
$730$	4.55838e6	+	672655.i	0.316594	+	0.0467181i
$731$	−9.03731e6			−0.625526
$732$	669123.	−	669123.i	0.0461560	−	0.0461560i
$733$	−2.34666e6	−	2.34666e6i	−0.161321	−	0.161321i	0.621831	−	0.783152i	$-0.286389\pi$
$733$	−2.34666e6	−	2.34666e6i	−0.161321	−	0.161321i	−0.783152	+	0.621831i	$0.786389\pi$
$734$	4.62285e6			0.316716
$735$	3.68760e7	+	4.96432e7i	2.51783	+	3.38954i
$736$			6.69854e6i			0.455812i
$737$	−293464.	+	529487.i	−0.0199015	+	0.0359076i
$738$	3.64367e6	−	3.64367e6i	0.246262	−	0.246262i
$739$	848860.			0.0571775			0.0285887	−	0.999591i	$-0.490899\pi$
$739$	848860.			0.0571775			0.0285887	+	0.999591i	$0.490899\pi$
$740$	1.18200e7	−	8.78018e6i	0.793487	−	0.589419i
$741$	−1.78759e7			−1.19597
$742$	3.23802e6	+	3.23802e6i	0.215908	+	0.215908i
$743$	1.02746e7	+	1.02746e7i	0.682802	+	0.682802i	0.960631	−	0.277829i	$-0.0896148\pi$
$743$	1.02746e7	+	1.02746e7i	0.682802	+	0.682802i	−0.277829	+	0.960631i	$0.589615\pi$
$744$	1.24664e7			0.825671
$745$	−2.01843e7	−	2.97849e6i	−1.33237	−	0.196610i
$746$	−2.90335e6			−0.191008
$747$	8.99217e6	−	8.99217e6i	0.589608	−	0.589608i
$748$	−5.05726e6	+	9.12465e6i	−0.330492	+	0.596296i
$749$			2.27451e7i			1.48143i
$750$	3.39045e6	−	7.21071e6i	0.220092	−	0.468085i
$751$	6.59990e6			0.427009			0.213505	−	0.976942i	$-0.431512\pi$
$751$	6.59990e6			0.427009			0.213505	+	0.976942i	$0.431512\pi$
$752$	−5.75242e6	−	5.75242e6i	−0.370942	−	0.370942i
$753$	1.34454e7	−	1.34454e7i	0.864143	−	0.864143i
$754$	1.05798e6			0.0677718
$755$	−692263.	+	4.69125e6i	−0.0441981	+	0.299517i
$756$			1.07554e7i			0.684416i
$757$	−5.40678e6	−	5.40678e6i	−0.342925	−	0.342925i	0.514541	−	0.857466i	$-0.327962\pi$
$757$	−5.40678e6	−	5.40678e6i	−0.342925	−	0.342925i	−0.857466	+	0.514541i	$0.827962\pi$
$758$	−566156.	−	566156.i	−0.0357901	−	0.0357901i
$759$	−1.19788e7	+	3.43552e6i	−0.754758	+	0.216465i
$760$	−7.90840e6	−	1.06464e7i	−0.496655	−	0.668606i
$761$		−	1.70462e7i		−	1.06701i	−0.845798	−	0.533503i	$-0.820875\pi$
$761$		−	1.70462e7i		−	1.06701i	0.845798	−	0.533503i	$-0.179125\pi$
$762$	−8.81838e6	−	8.81838e6i	−0.550176	−	0.550176i
$763$	1.93970e7	−	1.93970e7i	1.20621	−	1.20621i
$764$			1.90596e6i			0.118136i
$765$	9.43487e6	+	1.27014e7i	0.582884	+	0.784690i
$766$		−	8.40484e6i		−	0.517556i
$767$	−1.04570e7	+	1.04570e7i	−0.641827	+	0.641827i
$768$	287278.	−	287278.i	0.0175752	−	0.0175752i
$769$	−7.53116e6			−0.459247			−0.229623	−	0.973280i	$-0.573749\pi$
$769$	−7.53116e6			−0.459247			−0.229623	+	0.973280i	$0.573749\pi$
$770$	−1.09356e7	+	1.46081e6i	−0.664684	+	0.0887904i
$771$	3.93770e6			0.238565
$772$	1.41236e7	−	1.41236e7i	0.852908	−	0.852908i
$773$	−1.25058e7	+	1.25058e7i	−0.752773	+	0.752773i	−0.974996	−	0.222223i	$-0.928669\pi$
$773$	−1.25058e7	+	1.25058e7i	−0.752773	+	0.752773i	0.222223	+	0.974996i	$0.428669\pi$
$774$		−	5.86084e6i		−	0.351647i
$775$	−1.35788e7	−	4.09672e6i	−0.812098	−	0.245009i
$776$		−	7.22601e6i		−	0.430769i
$777$	−3.91567e7	+	3.91567e7i	−2.32677	+	2.32677i
$778$	2.81362e6	+	2.81362e6i	0.166654	+	0.166654i
$779$			1.74758e7i			1.03179i
$780$	2.03178e6	−	1.37688e7i	0.119575	−	0.810323i
$781$	−1.91733e6	−	6.68524e6i	−0.112479	−	0.392184i
$782$	−1.67672e6	−	1.67672e6i	−0.0980493	−	0.0980493i
$783$	1.54149e6	+	1.54149e6i	0.0898538	+	0.0898538i
$784$			3.18484e7i			1.85053i
$785$	−3.85760e6	−	5.19318e6i	−0.223431	−	0.300787i
$786$	−1.69964e6			−0.0981299
$787$	−170854.	+	170854.i	−0.00983307	+	0.00983307i	−0.712006	−	0.702173i	$-0.752213\pi$
$787$	−170854.	+	170854.i	−0.00983307	+	0.00983307i	0.702173	+	0.712006i	$0.252213\pi$
$788$	1.78301e7	+	1.78301e7i	1.02291	+	1.02291i
$789$	5.08260e6			0.290665
$790$	2.93603e6	−	2.18095e6i	0.167376	−	0.124330i
$791$		−	2.93043e7i		−	1.66529i
$792$	−1.26278e7	−	6.99886e6i	−0.715344	−	0.396474i
$793$	380201.	−	380201.i	0.0214699	−	0.0214699i
$794$	4.23838e6			0.238588
$795$	1.78248e6	−	1.20793e7i	0.100025	−	0.677836i
$796$	−1.10250e7			−0.616731
$797$	9.76898e6	+	9.76898e6i	0.544758	+	0.544758i	0.924920	−	0.380162i	$-0.124132\pi$
$797$	9.76898e6	+	9.76898e6i	0.544758	+	0.544758i	−0.380162	+	0.924920i	$0.624132\pi$
$798$	1.65273e7	+	1.65273e7i	0.918742	+	0.918742i
$799$	1.10971e7			0.614956
$800$	1.39345e7	−	7.47521e6i	0.769779	−	0.412951i
$801$	−6.06175e6			−0.333823
$802$	−2.13217e6	+	2.13217e6i	−0.117054	+	0.117054i
$803$	−8.24665e6	+	1.48792e7i	−0.451324	+	0.814309i
$804$			998533.i			0.0544782i
$805$	−2.73228e6	+	1.85158e7i	−0.148606	+	1.00706i
$806$	3.31936e6			0.179977
$807$	−2.35174e7	−	2.35174e7i	−1.27117	−	1.27117i
$808$	1.21004e7	−	1.21004e7i	0.652034	−	0.652034i
$809$	−3.56702e7			−1.91617			−0.958085	−	0.286483i	$-0.907514\pi$
$809$	−3.56702e7			−1.91617			−0.958085	+	0.286483i	$0.907514\pi$
$810$	3.43020e6	−	2.54802e6i	0.183699	−	0.136455i
$811$			6.56552e6i			0.350523i	0.984522	+	0.175262i	$0.0560772\pi$
$811$			6.56552e6i			0.350523i	−0.984522	+	0.175262i	$0.943923\pi$
$812$	7.30058e6	+	7.30058e6i	0.388568	+	0.388568i
$813$	1.23430e7	+	1.23430e7i	0.654931	+	0.654931i
$814$	−2.00799e6	−	7.00135e6i	−0.106219	−	0.370357i
$815$	2.16090e7	−	1.60517e7i	1.13957	−	0.846498i
$816$			1.45932e7i			0.767231i
$817$	1.40549e7	+	1.40549e7i	0.736668	+	0.736668i
$818$	4.83147e6	−	4.83147e6i	0.252462	−	0.252462i
$819$			2.92272e7i			1.52257i
$820$	−1.34606e7	−	1.98630e6i	−0.699084	−	0.103160i
$821$		−	3.51579e7i		−	1.82039i	−0.414179	−	0.910195i	$-0.635931\pi$
$821$		−	3.51579e7i		−	1.82039i	0.414179	−	0.910195i	$-0.364069\pi$
$822$	−8.12667e6	+	8.12667e6i	−0.419501	+	0.419501i
$823$	−8.87336e6	+	8.87336e6i	−0.456655	+	0.456655i	−0.897556	−	0.440901i	$-0.854659\pi$
$823$	−8.87336e6	+	8.87336e6i	−0.456655	+	0.456655i	0.440901	+	0.897556i	$0.354659\pi$
$824$	−2.71514e6			−0.139308
$825$	2.05143e7	+	2.10847e7i	1.04935	+	1.07853i
$826$	1.93361e7			0.986097
$827$	−1.90006e7	+	1.90006e7i	−0.966061	+	0.966061i	−0.999443	−	0.0333814i	$-0.989372\pi$
$827$	−1.90006e7	+	1.90006e7i	−0.966061	+	0.966061i	0.0333814	+	0.999443i	$0.489372\pi$
$828$	−8.11574e6	+	8.11574e6i	−0.411389	+	0.411389i
$829$		−	1.60445e7i		−	0.810848i	−0.914129	−	0.405424i	$-0.867124\pi$
$829$		−	1.60445e7i		−	0.810848i	0.914129	−	0.405424i	$-0.132876\pi$
$830$	4.45085e6	+	656788.i	0.224258	+	0.0330925i
$831$		−	5.84787e7i		−	2.93762i
$832$	3.13066e6	−	3.13066e6i	0.156793	−	0.156793i
$833$	−3.07198e7	−	3.07198e7i	−1.53393	−	1.53393i
$834$		−	1.07313e7i		−	0.534239i
$835$	1.17951e7	−	8.76167e6i	0.585446	−	0.434881i
$836$	2.20558e7	−	6.32562e6i	1.09146	−	0.313031i
$837$	4.83636e6	+	4.83636e6i	0.238619	+	0.238619i
$838$	−3.01825e6	−	3.01825e6i	−0.148472	−	0.148472i
$839$		−	2.90331e7i		−	1.42393i	−0.702216	−	0.711964i	$-0.747806\pi$
$839$		−	2.90331e7i		−	1.42393i	0.702216	−	0.711964i	$-0.252194\pi$
$840$	−3.11743e7	+	2.31569e7i	−1.52440	+	1.13236i
$841$	−1.84185e7			−0.897973
$842$	9.25930e6	−	9.25930e6i	0.450088	−	0.450088i
$843$	−9.54675e6	−	9.54675e6i	−0.462686	−	0.462686i
$844$	2.48108e7			1.19890
$845$	−1.87555e6	+	1.27100e7i	−0.0903623	+	0.612358i
$846$			7.19667e6i			0.345705i
$847$	9.15875e6	−	3.96895e7i	0.438659	−	1.90093i
$848$	4.44649e6	−	4.44649e6i	0.212338	−	0.212338i
$849$	8.31662e6			0.395984
$850$	−1.61683e6	+	5.35909e6i	−0.0767569	+	0.254416i
$851$	−1.23562e7			−0.584872
$852$	−8.11158e6	−	8.11158e6i	−0.382830	−	0.382830i
$853$	−104892.	−	104892.i	−0.00493592	−	0.00493592i	0.704635	−	0.709570i	$-0.251111\pi$
$853$	−104892.	−	104892.i	−0.00493592	−	0.00493592i	−0.709570	+	0.704635i	$0.751111\pi$
$854$	−703035.			−0.0329862
$855$	5.08012e6	−	3.44264e7i	0.237662	−	1.61056i
$856$	−1.05303e7			−0.491199
$857$	−2.79009e7	+	2.79009e7i	−1.29767	+	1.29767i	−0.367749	+	0.929925i	$0.619871\pi$
$857$	−2.79009e7	+	2.79009e7i	−1.29767	+	1.29767i	−0.929925	+	0.367749i	$0.880129\pi$
$858$	−6.02166e6	−	3.33746e6i	−0.279253	−	0.154774i
$859$			1.96442e7i			0.908348i	0.890913	+	0.454174i	$0.150066\pi$
$859$			1.96442e7i			0.908348i	−0.890913	+	0.454174i	$0.849934\pi$
$860$	−1.24231e7	+	9.22818e6i	−0.572777	+	0.425471i
$861$	5.11715e7			2.35245
$862$	−1.52893e6	−	1.52893e6i	−0.0700839	−	0.0700839i
$863$	−2.72078e6	+	2.72078e6i	−0.124356	+	0.124356i	−0.766546	−	0.642190i	$-0.778026\pi$
$863$	−2.72078e6	+	2.72078e6i	−0.124356	+	0.124356i	0.642190	+	0.766546i	$0.278026\pi$
$864$	−7.62546e6			−0.347522
$865$	−1.66956e7	−	2.24760e7i	−0.758687	−	1.02136i
$866$			1.06508e7i			0.482599i
$867$	9.47478e6	+	9.47478e6i	0.428076	+	0.428076i
$868$	2.29053e7	+	2.29053e7i	1.03190	+	1.03190i
$869$	3.72264e6	+	1.29799e7i	0.167225	+	0.583070i
$870$	−538464.	+	3.64901e6i	−0.0241190	+	0.163447i
$871$			567374.i			0.0253410i
$872$	8.98028e6	+	8.98028e6i	0.399944	+	0.399944i
$873$	1.34071e7	−	1.34071e7i	0.595385	−	0.595385i
$874$			5.21529e6i			0.230941i
$875$	4.15662e7	−	1.49789e7i	1.83535	−	0.661393i
$876$			2.80598e7i			1.23545i
$877$	9.63891e6	−	9.63891e6i	0.423184	−	0.423184i	−0.463115	−	0.886298i	$-0.653268\pi$
$877$	9.63891e6	−	9.63891e6i	0.423184	−	0.423184i	0.886298	+	0.463115i	$0.153268\pi$
$878$	−401668.	+	401668.i	−0.0175845	+	0.0175845i
$879$	8.36491e6			0.365165
$880$	2.00600e6	+	1.50169e7i	0.0873222	+	0.653693i
$881$	2.88944e7			1.25422			0.627111	−	0.778930i	$-0.284237\pi$
$881$	2.88944e7			1.25422			0.627111	+	0.778930i	$0.284237\pi$
$882$	1.99223e7	−	1.99223e7i	0.862317	−	0.862317i
$883$	−2.53593e7	+	2.53593e7i	−1.09455	+	1.09455i	−0.0995127	+	0.995036i	$0.531728\pi$
$883$	−2.53593e7	+	2.53593e7i	−1.09455	+	1.09455i	−0.995036	+	0.0995127i	$0.968272\pi$
$884$			9.77755e6i			0.420823i
$885$	−3.07443e7	−	4.13886e7i	−1.31949	−	1.77633i
$886$		−	2.49512e6i		−	0.106784i
$887$	2.20913e7	−	2.20913e7i	0.942783	−	0.942783i	−0.0556666	−	0.998449i	$-0.517728\pi$
$887$	2.20913e7	−	2.20913e7i	0.942783	−	0.942783i	0.998449	+	0.0556666i	$0.0177284\pi$
$888$	−1.81285e7	−	1.81285e7i	−0.771488	−	0.771488i
$889$		−	6.91522e7i		−	2.93462i
$890$	−1.27881e6	−	1.72156e6i	−0.0541169	−	0.0728532i
$891$	4.34919e6	+	1.51645e7i	0.183533	+	0.639932i
$892$	1.36905e7	+	1.36905e7i	0.576111	+	0.576111i
$893$	−1.72583e7	−	1.72583e7i	−0.724219	−	0.724219i
$894$			1.66472e7i			0.696624i
$895$	−3.64285e6	+	2.46865e7i	−0.152014	+	1.03015i
$896$	−4.67423e7			−1.94509
$897$	−8.25862e6	+	8.25862e6i	−0.342710	+	0.342710i
$898$	4.64798e6	+	4.64798e6i	0.192342	+	0.192342i
$899$	6.56570e6			0.270946
$900$	2.59393e7	+	7.82586e6i	1.06746	+	0.322052i
$901$			8.57784e6i			0.352019i
$902$	−3.26276e6	+	5.88688e6i	−0.133527	+	0.240918i
$903$	4.11547e7	−	4.11547e7i	1.67958	−	1.67958i
$904$	1.35671e7			0.552160
$905$	1.35025e7	+	1.99249e6i	0.548015	+	0.0808676i
$906$	3.86916e6			0.156602
$907$	3.09100e7	+	3.09100e7i	1.24762	+	1.24762i	0.956770	+	0.290847i	$0.0939369\pi$
$907$	3.09100e7	+	3.09100e7i	1.24762	+	1.24762i	0.290847	+	0.956770i	$0.406063\pi$
$908$	−9.83938e6	−	9.83938e6i	−0.396053	−	0.396053i
$909$	4.49017e7			1.80241
$910$	−8.30066e6	+	6.16591e6i	−0.332284	+	0.246827i
$911$	1.18111e7			0.471515			0.235758	−	0.971812i	$-0.424243\pi$
$911$	1.18111e7			0.471515			0.235758	+	0.971812i	$0.424243\pi$
$912$	2.26955e7	−	2.26955e7i	0.903550	−	0.903550i
$913$	−8.05212e6	+	1.45282e7i	−0.319693	+	0.576811i
$914$			9.83732e6i			0.389503i
$915$	1.11782e6	+	1.50483e6i	0.0441387	+	0.0594203i
$916$	−2.17629e7			−0.856993
$917$	−6.66415e6	−	6.66415e6i	−0.261711	−	0.261711i
$918$	1.90874e6	−	1.90874e6i	0.0747551	−	0.0747551i
$919$	−4.12478e7			−1.61106			−0.805531	−	0.592553i	$-0.798120\pi$
$919$	−4.12478e7			−1.61106			−0.805531	+	0.592553i	$0.798120\pi$
$920$	−8.57231e6	−	1.26497e6i	−0.333909	−	0.0492732i
$921$		−	2.25858e7i		−	0.877376i
$922$	−1.67955e6	−	1.67955e6i	−0.0650677	−	0.0650677i
$923$	−4.60906e6	−	4.60906e6i	−0.178077	−	0.178077i
$924$	−1.85223e7	−	6.45825e7i	−0.713700	−	2.48848i
$925$	1.37888e7	+	2.57037e7i	0.529875	+	0.987736i
$926$			4.44928e6i			0.170515i
$927$	−5.03764e6	−	5.03764e6i	−0.192543	−	0.192543i
$928$	−5.17605e6	+	5.17605e6i	−0.197301	+	0.197301i
$929$		−	6.47011e6i		−	0.245965i	−0.992409	−	0.122982i	$-0.960754\pi$
$929$		−	6.47011e6i		−	0.245965i	0.992409	−	0.122982i	$-0.0392458\pi$
$930$	−1.68941e6	+	1.14486e7i	−0.0640512	+	0.434055i
$931$			9.55510e7i			3.61294i
$932$	8.32376e6	−	8.32376e6i	0.313892	−	0.313892i
$933$	−3.34407e7	+	3.34407e7i	−1.25768	+	1.25768i
$934$	−3.27841e6			−0.122969
$935$	−1.64197e7	−	1.25498e7i	−0.614236	−	0.469471i
$936$	−1.35314e7			−0.504838
$937$	1.86812e7	−	1.86812e7i	0.695113	−	0.695113i	−0.268239	−	0.963352i	$-0.586442\pi$
$937$	1.86812e7	−	1.86812e7i	0.695113	−	0.695113i	0.963352	+	0.268239i	$0.0864418\pi$
$938$	524570.	−	524570.i	0.0194669	−	0.0194669i
$939$			5.28511e7i			1.95609i
$940$	1.52547e7	−	1.13315e7i	0.563098	−	0.418281i
$941$			4.54439e7i			1.67302i	0.547952	+	0.836510i	$0.315408\pi$
$941$			4.54439e7i			1.67302i	−0.547952	+	0.836510i	$0.684592\pi$
$942$	−3.73237e6	+	3.73237e6i	−0.137043	+	0.137043i
$943$	8.07377e6	+	8.07377e6i	0.295663	+	0.295663i
$944$		−	2.65527e7i		−	0.969792i
$945$	−2.10780e7	−	3.11036e6i	−0.767803	−	0.113300i
$946$	2.11045e6	+	7.35859e6i	0.0766738	+	0.267342i
$947$	−2.21494e7	−	2.21494e7i	−0.802578	−	0.802578i	0.180920	−	0.983498i	$-0.442093\pi$
$947$	−2.21494e7	−	2.21494e7i	−0.802578	−	0.802578i	−0.983498	+	0.180920i	$0.942093\pi$
$948$	1.57492e7	+	1.57492e7i	0.569164	+	0.569164i
$949$			1.59438e7i			0.574681i
$950$	1.08490e7	−	5.81999e6i	0.390014	−	0.209225i
$951$	−6.36657e7			−2.28273
$952$	1.92910e7	−	1.92910e7i	0.689863	−	0.689863i
$953$	−2.20281e7	−	2.20281e7i	−0.785679	−	0.785679i	0.195104	−	0.980783i	$-0.437496\pi$
$953$	−2.20281e7	−	2.20281e7i	−0.785679	−	0.785679i	−0.980783	+	0.195104i	$0.937496\pi$
$954$	−5.56287e6			−0.197892
$955$	−3.73524e6	−	551189.i	−0.132529	−	0.0195566i
$956$		−	2.47728e7i		−	0.876659i
$957$	−1.19108e7	−	6.60149e6i	−0.420400	−	0.233003i
$958$	191319.	−	191319.i	0.00673510	−	0.00673510i
$959$	−6.37279e7			−2.23760
$960$	9.20438e6	+	1.23911e7i	0.322342	+	0.433942i
$961$	−8.02954e6			−0.280467
$962$	−4.82700e6	−	4.82700e6i	−0.168166	−	0.168166i
$963$	−1.95378e7	−	1.95378e7i	−0.678908	−	0.678908i
$964$	−4.73878e7			−1.64238
$965$	2.35945e7	+	3.17634e7i	0.815629	+	1.09802i
$966$	1.52711e7			0.526536
$967$	−1.66247e7	+	1.66247e7i	−0.571726	+	0.571726i	−0.932611	−	0.360884i	$-0.882475\pi$
$967$	−1.66247e7	+	1.66247e7i	−0.571726	+	0.571726i	0.360884	+	0.932611i	$0.382475\pi$
$968$	1.83751e7	+	4.24024e6i	0.630292	+	0.145446i
$969$			4.37824e7i			1.49793i
$970$	6.63608e6	+	979251.i	0.226455	+	0.0334168i
$971$	2.33982e7			0.796405			0.398203	−	0.917297i	$-0.369634\pi$
$971$	2.33982e7			0.796405			0.398203	+	0.917297i	$0.369634\pi$
$972$	2.57069e7	+	2.57069e7i	0.872739	+	0.872739i
$973$	4.20763e7	−	4.20763e7i	1.42481	−	1.42481i
$974$	−1.02915e7			−0.347600
$975$	2.63960e7	+	7.96363e6i	0.889255	+	0.268287i
$976$			965418.i			0.0324407i
$977$	−2.76182e7	−	2.76182e7i	−0.925674	−	0.925674i	0.0717484	−	0.997423i	$-0.477142\pi$
$977$	−2.76182e7	−	2.76182e7i	−0.925674	−	0.925674i	−0.997423	+	0.0717484i	$0.977142\pi$
$978$	−1.55305e7	−	1.55305e7i	−0.519206	−	0.519206i
$979$	7.61084e6	−	2.18280e6i	0.253791	−	0.0727874i
$980$	−7.35975e7	−	1.08604e7i	−2.44792	−	0.361227i
$981$			3.33238e7i			1.10556i
$982$	8.02378e6	+	8.02378e6i	0.265522	+	0.265522i
$983$	2.34349e7	−	2.34349e7i	0.773532	−	0.773532i	−0.205190	−	0.978722i	$-0.565781\pi$
$983$	2.34349e7	−	2.34349e7i	0.773532	−	0.773532i	0.978722	+	0.205190i	$0.0657812\pi$
$984$			2.36910e7i			0.780002i
$985$	−4.00991e7	+	2.97865e7i	−1.31687	+	0.978202i
$986$		−	2.59125e6i		−	0.0848824i
$987$	−5.05349e7	+	5.05349e7i	−1.65120	+	1.65120i
$988$	1.52061e7	−	1.52061e7i	0.495593	−	0.495593i
$989$	1.29867e7			0.422189
$990$	8.13877e6	−	1.06484e7i	0.263919	−	0.345300i
$991$	−1.35920e7			−0.439642			−0.219821	−	0.975540i	$-0.570547\pi$
$991$	−1.35920e7			−0.439642			−0.219821	+	0.975540i	$0.570547\pi$
$992$	−1.62396e7	+	1.62396e7i	−0.523959	+	0.523959i
$993$	−2.00341e7	+	2.00341e7i	−0.644757	+	0.644757i
$994$			8.52268e6i			0.273596i
$995$	3.18834e6	−	2.16064e7i	0.102096	−	0.691871i
$996$			2.73979e7i			0.875124i
$997$	2.25346e7	−	2.25346e7i	0.717979	−	0.717979i	−0.250212	−	0.968191i	$-0.580500\pi$
$997$	2.25346e7	−	2.25346e7i	0.717979	−	0.717979i	0.968191	+	0.250212i	$0.0805002\pi$
$998$	−1.80155e6	−	1.80155e6i	−0.0572559	−	0.0572559i
$999$		−	1.40660e7i		−	0.445920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.12	✓	52
5.3	odd	4	inner	55.6.e.b.43.15	yes	52
11.10	odd	2	inner	55.6.e.b.32.15	yes	52
55.43	even	4	inner	55.6.e.b.43.12	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.12	✓	52	1.1	even	1	trivial
55.6.e.b.32.15	yes	52	11.10	odd	2	inner
55.6.e.b.43.12	yes	52	55.43	even	4	inner
55.6.e.b.43.15	yes	52	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37494 + 1.37494i) q^{2} +(16.5868 - 16.5868i) q^{3} +28.2191i q^{4} +(-55.3028 - 8.16074i) q^{5} +45.6116i q^{6} +(-178.839 + 178.839i) q^{7} +(-82.7976 - 82.7976i) q^{8} -307.243i q^{9} +(87.2585 - 64.8175i) q^{10} +(110.636 + 385.760i) q^{11} +(468.064 + 468.064i) q^{12} +(265.957 + 265.957i) q^{13} -491.786i q^{14} +(-1052.66 + 781.936i) q^{15} -675.328 q^{16} +(651.396 - 651.396i) q^{17} +(422.440 + 422.440i) q^{18} -2026.11 q^{19} +(230.289 - 1560.60i) q^{20} +5932.74i q^{21} +(-682.514 - 378.278i) q^{22} +(-936.058 + 936.058i) q^{23} -2746.69 q^{24} +(2991.80 + 902.624i) q^{25} -731.350 q^{26} +(-1065.59 - 1065.59i) q^{27} +(-5046.68 - 5046.68i) q^{28} -1446.61 q^{29} +(372.225 - 2522.45i) q^{30} -4538.68 q^{31} +(3578.06 - 3578.06i) q^{32} +(8233.62 + 4563.42i) q^{33} +1791.26i q^{34} +(11349.8 - 8430.85i) q^{35} +8670.12 q^{36} +(6600.11 + 6600.11i) q^{37} +(2785.77 - 2785.77i) q^{38} +8822.76 q^{39} +(3903.25 + 5254.63i) q^{40} -8625.28i q^{41} +(-8157.15 - 8157.15i) q^{42} +(-6936.88 - 6936.88i) q^{43} +(-10885.8 + 3122.05i) q^{44} +(-2507.33 + 16991.4i) q^{45} -2574.05i q^{46} +(8517.97 + 8517.97i) q^{47} +(-11201.5 + 11201.5i) q^{48} -47159.9i q^{49} +(-5354.60 + 2872.50i) q^{50} -21609.1i q^{51} +(-7505.08 + 7505.08i) q^{52} +(-6584.20 + 6584.20i) q^{53} +2930.24 q^{54} +(-2970.41 - 22236.5i) q^{55} +29614.9 q^{56} +(-33606.6 + 33606.6i) q^{57} +(1989.00 - 1989.00i) q^{58} +39318.2i q^{59} +(-22065.5 - 29705.0i) q^{60} -1429.55i q^{61} +(6240.41 - 6240.41i) q^{62} +(54947.1 + 54947.1i) q^{63} -11771.3i q^{64} +(-12537.8 - 16878.6i) q^{65} +(-17595.1 + 5046.30i) q^{66} +(1066.66 + 1066.66i) q^{67} +(18381.8 + 18381.8i) q^{68} +31052.4i q^{69} +(-4013.34 + 27197.1i) q^{70} -17330.1 q^{71} +(-25439.0 + 25439.0i) q^{72} +(29974.4 + 29974.4i) q^{73} -18149.5 q^{74} +(64596.1 - 34652.8i) q^{75} -57174.9i q^{76} +(-88775.1 - 49202.9i) q^{77} +(-12130.8 + 12130.8i) q^{78} +33647.5 q^{79} +(37347.5 + 5511.17i) q^{80} +39310.7 q^{81} +(11859.2 + 11859.2i) q^{82} +(29267.3 + 29267.3i) q^{83} -167416. q^{84} +(-41339.9 + 30708.2i) q^{85} +19075.6 q^{86} +(-23994.6 + 23994.6i) q^{87} +(22779.6 - 41100.4i) q^{88} -19729.5i q^{89} +(-19914.7 - 26809.6i) q^{90} -95127.2 q^{91} +(-26414.7 - 26414.7i) q^{92} +(-75282.1 + 75282.1i) q^{93} -23423.4 q^{94} +(112049. + 16534.5i) q^{95} -118697. i q^{96} +(43636.6 + 43636.6i) q^{97} +(64842.0 + 64842.0i) q^{98} +(118522. - 33992.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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