LMFDB - Embedded newform 11.9.b.b.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,9,Mod(10,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("11.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	11.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.48116471067$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 1374x^{4} + 436560x^{2} + 40320000 $ x^6 + 1374x^4 + 436560x^2 + 40320000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.6
Root			$31.0620i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.9.b.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.0620i q^{2} -35.5230 q^{3} -708.845 q^{4} +583.097 q^{5} -1103.41i q^{6} +1704.90i q^{7} -14066.3i q^{8} -5299.12 q^{9} +O(q^{10})$	\(q+31.0620i q^{2} -35.5230 q^{3} -708.845 q^{4} +583.097 q^{5} -1103.41i q^{6} +1704.90i q^{7} -14066.3i q^{8} -5299.12 q^{9} +18112.1i q^{10} +(-10275.8 + 10429.1i) q^{11} +25180.3 q^{12} +463.679i q^{13} -52957.7 q^{14} -20713.3 q^{15} +255461. q^{16} +47002.3i q^{17} -164601. i q^{18} +193047. i q^{19} -413326. q^{20} -60563.3i q^{21} +(-323950. - 319186. i) q^{22} +328997. q^{23} +499676. i q^{24} -50623.1 q^{25} -14402.8 q^{26} +421307. q^{27} -1.20851e6i q^{28} -378601. i q^{29} -643397. i q^{30} +531409. q^{31} +4.33417e6i q^{32} +(365027. - 370474. i) q^{33} -1.45998e6 q^{34} +994124. i q^{35} +3.75626e6 q^{36} +149858. q^{37} -5.99642e6 q^{38} -16471.3i q^{39} -8.20200e6i q^{40} +3.07392e6i q^{41} +1.88121e6 q^{42} -356329. i q^{43} +(7.28395e6 - 7.39265e6i) q^{44} -3.08990e6 q^{45} +1.02193e7i q^{46} -3.12404e6 q^{47} -9.07475e6 q^{48} +2.85810e6 q^{49} -1.57245e6i q^{50} -1.66966e6i q^{51} -328677. i q^{52} -5.30402e6 q^{53} +1.30866e7i q^{54} +(-5.99178e6 + 6.08120e6i) q^{55} +2.39816e7 q^{56} -6.85760e6i q^{57} +1.17601e7 q^{58} +6.23485e6 q^{59} +1.46826e7 q^{60} -2.27014e7i q^{61} +1.65066e7i q^{62} -9.03449e6i q^{63} -6.92296e7 q^{64} +270370. i q^{65} +(1.15077e7 + 1.13384e7i) q^{66} +1.47048e7 q^{67} -3.33174e7i q^{68} -1.16870e7 q^{69} -3.08794e7 q^{70} +1.38102e7 q^{71} +7.45388e7i q^{72} +1.89424e7i q^{73} +4.65489e6i q^{74} +1.79828e6 q^{75} -1.36840e8i q^{76} +(-1.77807e7 - 1.75192e7i) q^{77} +511630. q^{78} +2.11732e7i q^{79} +1.48959e8 q^{80} +1.98014e7 q^{81} -9.54820e7 q^{82} +2.39639e7i q^{83} +4.29300e7i q^{84} +2.74069e7i q^{85} +1.10683e7 q^{86} +1.34490e7i q^{87} +(1.46699e8 + 1.44542e8i) q^{88} -6.54388e7 q^{89} -9.59783e7i q^{90} -790529. q^{91} -2.33208e8 q^{92} -1.88772e7 q^{93} -9.70389e7i q^{94} +1.12565e8i q^{95} -1.53963e8i q^{96} +5.14262e7 q^{97} +8.87783e7i q^{98} +(5.44526e7 - 5.52652e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9}+O(q^{10}) $ 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9	$ 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9} - 32318 q^{11} + 54564 q^{12} - 33768 q^{14} + 85824 q^{15} + 312264 q^{16} - 894868 q^{20} - 550440 q^{22} + 683084 q^{23} - 141498 q^{25} - 657432 q^{26} + 988848 q^{27} + 942684 q^{31} + 2992704 q^{33} - 1345128 q^{34} + 7401360 q^{36} - 3804816 q^{37} - 8900760 q^{38} - 8158920 q^{42} + 14210284 q^{44} - 2499684 q^{45} + 15828644 q^{47} - 19028376 q^{48} - 10066602 q^{49} - 35477956 q^{53} + 7335372 q^{55} + 68829936 q^{56} + 65482560 q^{58} - 29614804 q^{59} + 35069244 q^{60} - 212921520 q^{64} + 75167400 q^{66} + 39419484 q^{67} + 62859468 q^{69} - 168190680 q^{70} + 3219212 q^{71} - 110874276 q^{75} + 91605360 q^{77} + 111889320 q^{78} + 383392952 q^{80} - 103764906 q^{81} - 163977720 q^{82} - 261274512 q^{86} + 328724880 q^{88} + 38785664 q^{89} + 355260528 q^{91} - 456128956 q^{92} - 182572452 q^{93} - 222185616 q^{97} + 159125406 q^{99}+O(q^{100}) $ 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9 - 32318 * q^11 + 54564 * q^12 - 33768 * q^14 + 85824 * q^15 + 312264 * q^16 - 894868 * q^20 - 550440 * q^22 + 683084 * q^23 - 141498 * q^25 - 657432 * q^26 + 988848 * q^27 + 942684 * q^31 + 2992704 * q^33 - 1345128 * q^34 + 7401360 * q^36 - 3804816 * q^37 - 8900760 * q^38 - 8158920 * q^42 + 14210284 * q^44 - 2499684 * q^45 + 15828644 * q^47 - 19028376 * q^48 - 10066602 * q^49 - 35477956 * q^53 + 7335372 * q^55 + 68829936 * q^56 + 65482560 * q^58 - 29614804 * q^59 + 35069244 * q^60 - 212921520 * q^64 + 75167400 * q^66 + 39419484 * q^67 + 62859468 * q^69 - 168190680 * q^70 + 3219212 * q^71 - 110874276 * q^75 + 91605360 * q^77 + 111889320 * q^78 + 383392952 * q^80 - 103764906 * q^81 - 163977720 * q^82 - 261274512 * q^86 + 328724880 * q^88 + 38785664 * q^89 + 355260528 * q^91 - 456128956 * q^92 - 182572452 * q^93 - 222185616 * q^97 + 159125406 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			31.0620i			1.94137i	0.240350	+	0.970686i	$0.422738\pi$
$2$			31.0620i			1.94137i	−0.240350	+	0.970686i	$0.577262\pi$
$3$	−35.5230			−0.438555			−0.219278	−	0.975662i	$-0.570370\pi$
$3$	−35.5230			−0.438555			−0.219278	+	0.975662i	$0.570370\pi$
$4$	−708.845			−2.76893
$5$	583.097			0.932955			0.466477	−	0.884533i	$-0.345523\pi$
$5$	583.097			0.932955			0.466477	+	0.884533i	$0.345523\pi$
$6$		−	1103.41i		−	0.851399i
$7$			1704.90i			0.710081i	0.934851	+	0.355040i	$0.115533\pi$
$7$			1704.90i			0.710081i	−0.934851	+	0.355040i	$0.884467\pi$
$8$		−	14066.3i		−	3.43415i
$9$	−5299.12			−0.807669
$10$			18112.1i			1.81121i
$11$	−10275.8	+	10429.1i	−0.701850	+	0.712324i
$11$	−10275.8	+	10429.1i	−0.701850	+	0.712324i
$12$	25180.3			1.21433
$13$			463.679i			0.0162347i	0.999967	+	0.00811735i	$0.00258386\pi$
$13$			463.679i			0.0162347i	−0.999967	+	0.00811735i	$0.997416\pi$
$14$	−52957.7			−1.37853
$15$	−20713.3			−0.409152
$16$	255461.			3.89803
$17$			47002.3i			0.562761i	0.959596	+	0.281380i	$0.0907922\pi$
$17$			47002.3i			0.562761i	−0.959596	+	0.281380i	$0.909208\pi$
$18$		−	164601.i		−	1.56799i
$19$			193047.i			1.48132i	0.671881	+	0.740660i	$0.265487\pi$
$19$			193047.i			1.48132i	−0.671881	+	0.740660i	$0.734513\pi$
$20$	−413326.			−2.58328
$21$		−	60563.3i		−	0.311410i
$22$	−323950.	−	319186.i	−1.38289	−	1.36255i
$23$	328997.			1.17566			0.587828	−	0.808986i	$-0.299983\pi$
$23$	328997.			1.17566			0.587828	+	0.808986i	$0.299983\pi$
$24$			499676.i			1.50606i
$25$	−50623.1			−0.129595
$26$	−14402.8			−0.0315176
$27$	421307.			0.792763
$28$		−	1.20851e6i		−	1.96616i
$29$		−	378601.i		−	0.535291i	−0.963517	−	0.267646i	$-0.913754\pi$
$29$		−	378601.i		−	0.535291i	0.963517	−	0.267646i	$-0.0862456\pi$
$30$		−	643397.i		−	0.794317i
$31$	531409.			0.575417			0.287708	−	0.957718i	$-0.407107\pi$
$31$	531409.			0.575417			0.287708	+	0.957718i	$0.407107\pi$
$32$			4.33417e6i			4.13338i
$33$	365027.	−	370474.i	0.307800	−	0.312394i
$34$	−1.45998e6			−1.09253
$35$			994124.i			0.662473i
$36$	3.75626e6			2.23638
$37$	149858.			0.0799602			0.0399801	−	0.999200i	$-0.487271\pi$
$37$	149858.			0.0799602			0.0399801	+	0.999200i	$0.487271\pi$
$38$	−5.99642e6			−2.87579
$39$		−	16471.3i		−	0.00711982i
$40$		−	8.20200e6i		−	3.20390i
$41$			3.07392e6i			1.08782i	0.839143	+	0.543910i	$0.183057\pi$
$41$			3.07392e6i			1.08782i	−0.839143	+	0.543910i	$0.816943\pi$
$42$	1.88121e6			0.604562
$43$		−	356329.i		−	0.104226i	−0.998641	−	0.0521131i	$-0.983404\pi$
$43$		−	356329.i		−	0.104226i	0.998641	−	0.0521131i	$-0.0165956\pi$
$44$	7.28395e6	−	7.39265e6i	1.94337	−	1.97237i
$45$	−3.08990e6			−0.753519
$46$			1.02193e7i			2.28239i
$47$	−3.12404e6			−0.640214			−0.320107	−	0.947381i	$-0.603719\pi$
$47$	−3.12404e6			−0.640214			−0.320107	+	0.947381i	$0.603719\pi$
$48$	−9.07475e6			−1.70950
$49$	2.85810e6			0.495785
$50$		−	1.57245e6i		−	0.251592i
$51$		−	1.66966e6i		−	0.246802i
$52$		−	328677.i		−	0.0449527i
$53$	−5.30402e6			−0.672204			−0.336102	−	0.941826i	$-0.609109\pi$
$53$	−5.30402e6			−0.672204			−0.336102	+	0.941826i	$0.609109\pi$
$54$			1.30866e7i			1.53905i
$55$	−5.99178e6	+	6.08120e6i	−0.654795	+	0.664566i
$56$	2.39816e7			2.43852
$57$		−	6.85760e6i		−	0.649640i
$58$	1.17601e7			1.03920
$59$	6.23485e6			0.514538			0.257269	−	0.966340i	$-0.417177\pi$
$59$	6.23485e6			0.514538			0.257269	+	0.966340i	$0.417177\pi$
$60$	1.46826e7			1.13291
$61$		−	2.27014e7i		−	1.63958i	−0.572664	−	0.819790i	$-0.694090\pi$
$61$		−	2.27014e7i		−	1.63958i	0.572664	−	0.819790i	$-0.305910\pi$
$62$			1.65066e7i			1.11710i
$63$		−	9.03449e6i		−	0.573510i
$64$	−6.92296e7			−4.12641
$65$			270370.i			0.0151462i
$66$	1.15077e7	+	1.13384e7i	0.606472	+	0.597555i
$67$	1.47048e7			0.729724			0.364862	−	0.931062i	$-0.381116\pi$
$67$	1.47048e7			0.729724			0.364862	+	0.931062i	$0.381116\pi$
$68$		−	3.33174e7i		−	1.55824i
$69$	−1.16870e7			−0.515590
$70$	−3.08794e7			−1.28611
$71$	1.38102e7			0.543458			0.271729	−	0.962374i	$-0.412405\pi$
$71$	1.38102e7			0.543458			0.271729	+	0.962374i	$0.412405\pi$
$72$			7.45388e7i			2.77365i
$73$			1.89424e7i			0.667029i	0.942745	+	0.333514i	$0.108235\pi$
$73$			1.89424e7i			0.667029i	−0.942745	+	0.333514i	$0.891765\pi$
$74$			4.65489e6i			0.155232i
$75$	1.79828e6			0.0568346
$76$		−	1.36840e8i		−	4.10166i
$77$	−1.77807e7	−	1.75192e7i	−0.505808	−	0.498370i
$78$	511630.			0.0138222
$79$			2.11732e7i			0.543599i	0.962354	+	0.271800i	$0.0876188\pi$
$79$			2.11732e7i			0.543599i	−0.962354	+	0.271800i	$0.912381\pi$
$80$	1.48959e8			3.63669
$81$	1.98014e7			0.459999
$82$	−9.54820e7			−2.11187
$83$			2.39639e7i			0.504947i	0.967604	+	0.252474i	$0.0812441\pi$
$83$			2.39639e7i			0.504947i	−0.967604	+	0.252474i	$0.918756\pi$
$84$			4.29300e7i			0.862271i
$85$			2.74069e7i			0.525030i
$86$	1.10683e7			0.202342
$87$			1.34490e7i			0.234755i
$88$	1.46699e8	+	1.44542e8i	2.44623	+	2.41026i
$89$	−6.54388e7			−1.04298			−0.521489	−	0.853258i	$-0.674623\pi$
$89$	−6.54388e7			−1.04298			−0.521489	+	0.853258i	$0.674623\pi$
$90$		−	9.59783e7i		−	1.46286i
$91$	−790529.			−0.0115280
$92$	−2.33208e8			−3.25531
$93$	−1.88772e7			−0.252352
$94$		−	9.70389e7i		−	1.24289i
$95$			1.12565e8i			1.38200i
$96$		−	1.53963e8i		−	1.81272i
$97$	5.14262e7			0.580895			0.290447	−	0.956891i	$-0.406196\pi$
$97$	5.14262e7			0.580895			0.290447	+	0.956891i	$0.406196\pi$
$98$			8.87783e7i			0.962504i
$99$	5.44526e7	−	5.52652e7i	0.566863	−	0.575322i
$100$	3.58840e7			0.358840
$101$		−	9.17774e7i		−	0.881963i	−0.897516	−	0.440982i	$-0.854630\pi$
$101$		−	9.17774e7i		−	0.881963i	0.897516	−	0.440982i	$-0.145370\pi$
$102$	5.18630e7			0.479134
$103$	9.43156e7			0.837982			0.418991	−	0.907990i	$-0.362384\pi$
$103$	9.43156e7			0.837982			0.418991	+	0.907990i	$0.362384\pi$
$104$	6.52224e6			0.0557524
$105$		−	3.53142e7i		−	0.290531i
$106$		−	1.64753e8i		−	1.30500i
$107$			1.40386e8i			1.07100i	0.844537	+	0.535498i	$0.179876\pi$
$107$			1.40386e8i			1.07100i	−0.844537	+	0.535498i	$0.820124\pi$
$108$	−2.98641e8			−2.19510
$109$		−	8.32614e7i		−	0.589845i	−0.955521	−	0.294922i	$-0.904706\pi$
$109$		−	8.32614e7i		−	0.589845i	0.955521	−	0.294922i	$-0.0952938\pi$
$110$	−1.88894e8	−	1.86116e8i	−1.29017	−	1.27120i
$111$	−5.32341e6			−0.0350670
$112$			4.35537e8i			2.76792i
$113$	−4.41025e7			−0.270489			−0.135244	−	0.990812i	$-0.543182\pi$
$113$	−4.41025e7			−0.270489			−0.135244	+	0.990812i	$0.543182\pi$
$114$	2.13011e8			1.26119
$115$	1.91837e8			1.09683
$116$			2.68370e8i			1.48218i
$117$		−	2.45709e6i		−	0.0131123i
$118$			1.93667e8i			0.998911i
$119$	−8.01344e7			−0.399605
$120$			2.91359e8i			1.40509i
$121$	−3.17505e6	−	2.14335e8i	−0.0148119	−	0.999890i
$122$	7.05149e8			3.18304
$123$		−	1.09195e8i		−	0.477070i
$124$	−3.76687e8			−1.59329
$125$	−2.57290e8			−1.05386
$126$	2.80629e8			1.11340
$127$		−	3.99993e8i		−	1.53758i	−0.639503	−	0.768789i	$-0.720860\pi$
$127$		−	3.99993e8i		−	1.53758i	0.639503	−	0.768789i	$-0.279140\pi$
$128$		−	1.04086e9i		−	3.87751i
$129$			1.26579e7i			0.0457090i
$130$	−8.39822e6			−0.0294045
$131$			4.49423e8i			1.52606i	0.646365	+	0.763028i	$0.276288\pi$
$131$			4.49423e8i			1.52606i	−0.646365	+	0.763028i	$0.723712\pi$
$132$	−2.58748e8	+	2.62609e8i	−0.852277	+	0.864995i
$133$	−3.29127e8			−1.05186
$134$			4.56759e8i			1.41667i
$135$	2.45663e8			0.739612
$136$	6.61147e8			1.93260
$137$	−5.30276e8			−1.50529			−0.752644	−	0.658428i	$-0.771222\pi$
$137$	−5.30276e8			−1.50529			−0.752644	+	0.658428i	$0.771222\pi$
$138$		−	3.63020e8i		−	1.00095i
$139$			6.63878e8i			1.77840i	0.457521	+	0.889199i	$0.348737\pi$
$139$			6.63878e8i			1.77840i	−0.457521	+	0.889199i	$0.651263\pi$
$140$		−	7.04680e8i		−	1.83434i
$141$	1.10975e8			0.280769
$142$			4.28971e8i			1.05505i
$143$	−4.83578e6	−	4.76467e6i	−0.0115644	−	0.0113943i
$144$	−1.35372e9			−3.14832
$145$		−	2.20761e8i		−	0.499403i
$146$	−5.88389e8			−1.29495
$147$	−1.01528e8			−0.217429
$148$	−1.06226e8			−0.221404
$149$		−	5.39033e8i		−	1.09363i	−0.837254	−	0.546815i	$-0.815840\pi$
$149$		−	5.39033e8i		−	1.09363i	0.837254	−	0.546815i	$-0.184160\pi$
$150$			5.58582e7i			0.110337i
$151$			3.77170e8i			0.725487i	0.931889	+	0.362744i	$0.118160\pi$
$151$			3.77170e8i			0.725487i	−0.931889	+	0.362744i	$0.881840\pi$
$152$	2.71545e9			5.08707
$153$		−	2.49071e8i		−	0.454524i
$154$	5.44182e8	−	5.52303e8i	0.967523	−	0.981961i
$155$	3.09863e8			0.536838
$156$			1.16756e7i			0.0197143i
$157$	3.05322e8			0.502527			0.251264	−	0.967919i	$-0.419154\pi$
$157$	3.05322e8			0.502527			0.251264	+	0.967919i	$0.419154\pi$
$158$	−6.57682e8			−1.05533
$159$	1.88414e8			0.294799
$160$			2.52724e9i			3.85626i
$161$			5.60908e8i			0.834811i
$162$			6.15072e8i			0.893029i
$163$	−3.10944e8			−0.440486			−0.220243	−	0.975445i	$-0.570685\pi$
$163$	−3.10944e8			−0.440486			−0.220243	+	0.975445i	$0.570685\pi$
$164$		−	2.17894e9i		−	3.01210i
$165$	2.12846e8	−	2.16022e8i	0.287164	−	0.291449i
$166$	−7.44367e8			−0.980291
$167$		−	5.85703e8i		−	0.753029i	−0.926411	−	0.376515i	$-0.877122\pi$
$167$		−	5.85703e8i		−	0.753029i	0.926411	−	0.376515i	$-0.122878\pi$
$168$	−8.51899e8			−1.06943
$169$	8.15516e8			0.999736
$170$	−8.51312e8			−1.01928
$171$		−	1.02298e9i		−	1.19642i
$172$			2.52582e8i			0.288595i
$173$			1.48466e9i			1.65746i	0.559646	+	0.828732i	$0.310937\pi$
$173$			1.48466e9i			1.65746i	−0.559646	+	0.828732i	$0.689063\pi$
$174$	−4.17754e8			−0.455747
$175$		−	8.63075e7i		−	0.0920230i
$176$	−2.62507e9	+	2.66424e9i	−2.73584	+	2.77666i
$177$	−2.21480e8			−0.225654
$178$		−	2.03266e9i		−	2.02481i
$179$	8.73897e8			0.851232			0.425616	−	0.904904i	$-0.360057\pi$
$179$	8.73897e8			0.851232			0.425616	+	0.904904i	$0.360057\pi$
$180$	2.19026e9			2.08644
$181$	1.18831e9			1.10717			0.553584	−	0.832793i	$-0.313260\pi$
$181$	1.18831e9			1.10717			0.553584	+	0.832793i	$0.313260\pi$
$182$		−	2.45554e7i		−	0.0223800i
$183$			8.06420e8i			0.719047i
$184$		−	4.62776e9i		−	4.03738i
$185$	8.73818e7			0.0745992
$186$		−	5.86364e8i		−	0.489909i
$187$	−4.90194e8	−	4.82986e8i	−0.400868	−	0.394974i
$188$	2.21446e9			1.77271
$189$			7.18287e8i			0.562926i
$190$	−3.49649e9			−2.68298
$191$	−1.91638e9			−1.43995			−0.719977	−	0.693998i	$-0.755848\pi$
$191$	−1.91638e9			−1.43995			−0.719977	+	0.693998i	$0.755848\pi$
$192$	2.45924e9			1.80966
$193$		−	1.40845e6i		−	0.00101511i	−1.00000		0.000507554i	$-0.999838\pi$
$193$		−	1.40845e6i		−	0.00101511i	1.00000		0.000507554i	$-0.000161559\pi$
$194$			1.59740e9i			1.12773i
$195$		−	9.60435e6i		−	0.00664247i
$196$	−2.02595e9			−1.37279
$197$		−	1.53570e8i		−	0.101963i	−0.998700	−	0.0509813i	$-0.983765\pi$
$197$		−	1.53570e8i		−	0.101963i	0.998700	−	0.0509813i	$-0.0162349\pi$
$198$	1.71665e9	+	1.69141e9i	1.11692	+	1.10049i
$199$	6.91153e7			0.0440719			0.0220360	−	0.999757i	$-0.492985\pi$
$199$	6.91153e7			0.0440719			0.0220360	+	0.999757i	$0.492985\pi$
$200$			7.12078e8i			0.445049i
$201$	−5.22357e8			−0.320024
$202$	2.85079e9			1.71222
$203$	6.45479e8			0.380100
$204$			1.18353e9i			0.683376i
$205$			1.79239e9i			1.01489i
$206$			2.92963e9i			1.62684i
$207$	−1.74339e9			−0.949542
$208$			1.18452e8i			0.0632834i
$209$	−2.01331e9	−	1.98371e9i	−1.05518	−	1.03966i
$210$	1.09693e9			0.564029
$211$			2.80428e8i			0.141479i	0.997495	+	0.0707395i	$0.0225359\pi$
$211$			2.80428e8i			0.141479i	−0.997495	+	0.0707395i	$0.977464\pi$
$212$	3.75973e9			1.86129
$213$	−4.90579e8			−0.238336
$214$	−4.36065e9			−2.07920
$215$		−	2.07774e8i		−	0.0972383i
$216$		−	5.92621e9i		−	2.72246i
$217$			9.06002e8i			0.408592i
$218$	2.58626e9			1.14511
$219$		−	6.72892e8i		−	0.292529i
$220$	4.24725e9	−	4.31063e9i	1.81308	−	1.84014i
$221$	−2.17940e7			−0.00913625
$222$		−	1.65356e8i		−	0.0680780i
$223$	9.38967e8			0.379692			0.189846	−	0.981814i	$-0.439201\pi$
$223$	9.38967e8			0.379692			0.189846	+	0.981814i	$0.439201\pi$
$224$	−7.38934e9			−2.93504
$225$	2.68258e8			0.104670
$226$		−	1.36991e9i		−	0.525120i
$227$		−	1.34914e9i		−	0.508105i	−0.967190	−	0.254053i	$-0.918236\pi$
$227$		−	1.34914e9i		−	0.508105i	0.967190	−	0.254053i	$-0.0817636\pi$
$228$			4.86098e9i			1.79881i
$229$	4.94331e9			1.79753			0.898765	−	0.438430i	$-0.144465\pi$
$229$	4.94331e9			1.79753			0.898765	+	0.438430i	$0.144465\pi$
$230$			5.95883e9i			2.12936i
$231$	6.31623e8	+	6.22336e8i	0.221825	+	0.218563i
$232$	−5.32551e9			−1.83827
$233$		−	3.43364e9i		−	1.16501i	−0.812826	−	0.582507i	$-0.802072\pi$
$233$		−	3.43364e9i		−	1.16501i	0.812826	−	0.582507i	$-0.197928\pi$
$234$	7.63221e7			0.0254558
$235$	−1.82162e9			−0.597291
$236$	−4.41954e9			−1.42472
$237$		−	7.52136e8i		−	0.238398i
$238$		−	2.48913e9i		−	0.775783i
$239$		−	5.42983e9i		−	1.66416i	−0.554656	−	0.832080i	$-0.687150\pi$
$239$		−	5.42983e9i		−	1.66416i	0.554656	−	0.832080i	$-0.312850\pi$
$240$	−5.29146e9			−1.59489
$241$			2.74306e9i			0.813143i	0.913619	+	0.406572i	$0.133276\pi$
$241$			2.74306e9i			0.813143i	−0.913619	+	0.406572i	$0.866724\pi$
$242$	6.65768e9	−	9.86233e7i	1.94116	−	0.0287553i
$243$	−3.46760e9			−0.994498
$244$			1.60918e10i			4.53988i
$245$	1.66655e9			0.462545
$246$	3.39181e9			0.926170
$247$	−8.95119e7			−0.0240488
$248$		−	7.47495e9i		−	1.97607i
$249$		−	8.51271e8i		−	0.221447i
$250$		−	7.99194e9i		−	2.04594i
$251$	−4.79713e8			−0.120861			−0.0604306	−	0.998172i	$-0.519247\pi$
$251$	−4.79713e8			−0.120861			−0.0604306	+	0.998172i	$0.519247\pi$
$252$			6.40405e9i			1.58801i
$253$	−3.38070e9	+	3.43115e9i	−0.825135	+	0.837449i
$254$	1.24246e10			2.98501
$255$		−	9.73575e8i		−	0.230255i
$256$	1.46084e10			3.40128
$257$	4.14905e9			0.951079			0.475539	−	0.879694i	$-0.342253\pi$
$257$	4.14905e9			0.951079			0.475539	+	0.879694i	$0.342253\pi$
$258$	−3.93178e8			−0.0887381
$259$			2.55494e8i			0.0567782i
$260$		−	1.91651e8i		−	0.0419389i
$261$			2.00625e9i			0.432338i
$262$	−1.39600e10			−2.96264
$263$			3.14872e9i			0.658129i	0.944307	+	0.329065i	$0.106733\pi$
$263$			3.14872e9i			0.658129i	−0.944307	+	0.329065i	$0.893267\pi$
$264$	−5.21119e9	−	5.13456e9i	−1.07281	−	1.05703i
$265$	−3.09275e9			−0.627136
$266$		−	1.02233e10i		−	2.04204i
$267$	2.32458e9			0.457404
$268$	−1.04234e10			−2.02055
$269$	5.17645e9			0.988605			0.494303	−	0.869290i	$-0.335424\pi$
$269$	5.17645e9			0.988605			0.494303	+	0.869290i	$0.335424\pi$
$270$			7.63076e9i			1.43586i
$271$		−	2.11946e9i		−	0.392960i	−0.980508	−	0.196480i	$-0.937049\pi$
$271$		−	2.11946e9i		−	0.392960i	0.980508	−	0.196480i	$-0.0629511\pi$
$272$			1.20073e10i			2.19366i
$273$	2.80819e7			0.00505564
$274$		−	1.64714e10i		−	2.92232i
$275$	5.20192e8	−	5.27955e8i	0.0909564	−	0.0923138i
$276$	8.28424e9			1.42763
$277$			9.78952e9i			1.66281i	0.555667	+	0.831405i	$0.312463\pi$
$277$			9.78952e9i			1.66281i	−0.555667	+	0.831405i	$0.687537\pi$
$278$	−2.06213e10			−3.45253
$279$	−2.81600e9			−0.464746
$280$	1.39836e10			2.27503
$281$			1.07257e10i			1.72029i	0.510053	+	0.860143i	$0.329626\pi$
$281$			1.07257e10i			1.72029i	−0.510053	+	0.860143i	$0.670374\pi$
$282$			3.44711e9i			0.545078i
$283$			4.11267e9i			0.641177i	0.947219	+	0.320588i	$0.103881\pi$
$283$			4.11267e9i			0.641177i	−0.947219	+	0.320588i	$0.896119\pi$
$284$	−9.78928e9			−1.50480
$285$		−	3.99865e9i		−	0.606085i
$286$	1.48000e8	−	1.50209e8i	0.0221206	−	0.0224508i
$287$	−5.24074e9			−0.772441
$288$		−	2.29673e10i		−	3.33841i
$289$	4.76654e9			0.683300
$290$	6.85728e9			0.969526
$291$	−1.82681e9			−0.254754
$292$		−	1.34273e10i		−	1.84695i
$293$		−	8.73415e9i		−	1.18509i	−0.805538	−	0.592543i	$-0.798124\pi$
$293$		−	8.73415e9i		−	1.18509i	0.805538	−	0.592543i	$-0.201876\pi$
$294$		−	3.15367e9i		−	0.422111i
$295$	3.63552e9			0.480041
$296$		−	2.10795e9i		−	0.274595i
$297$	−4.32926e9	+	4.39387e9i	−0.556401	+	0.564704i
$298$	1.67434e10			2.12314
$299$			1.52549e8i			0.0190864i
$300$	−1.27471e9			−0.157371
$301$	6.07506e8			0.0740090
$302$	−1.17157e10			−1.40844
$303$			3.26021e9i			0.386790i
$304$			4.93161e10i			5.77423i
$305$		−	1.32371e10i		−	1.52965i
$306$	7.73663e9			0.882401
$307$		−	9.15602e9i		−	1.03075i	−0.856965	−	0.515375i	$-0.827653\pi$
$307$		−	9.15602e9i		−	1.03075i	0.856965	−	0.515375i	$-0.172347\pi$
$308$	1.26038e10	+	1.24184e10i	1.40054	+	1.37995i
$309$	−3.35037e9			−0.367501
$310$			9.62496e9i			1.04220i
$311$	1.28528e10			1.37390			0.686951	−	0.726704i	$-0.258949\pi$
$311$	1.28528e10			1.37390			0.686951	+	0.726704i	$0.258949\pi$
$312$	−2.31689e8			−0.0244505
$313$	1.48516e9			0.154738			0.0773690	−	0.997003i	$-0.475348\pi$
$313$	1.48516e9			0.154738			0.0773690	+	0.997003i	$0.475348\pi$
$314$			9.48390e9i			0.975593i
$315$		−	5.26798e9i		−	0.535059i
$316$		−	1.50085e10i		−	1.50519i
$317$	1.07401e9			0.106358			0.0531790	−	0.998585i	$-0.483065\pi$
$317$	1.07401e9			0.106358			0.0531790	+	0.998585i	$0.483065\pi$
$318$			5.85252e9i			0.572314i
$319$	3.94849e9	+	3.89043e9i	0.381301	+	0.375694i
$320$	−4.03676e10			−3.84975
$321$		−	4.98692e9i		−	0.469691i
$322$	−1.74229e10			−1.62068
$323$	−9.07366e9			−0.833628
$324$	−1.40362e10			−1.27370
$325$		−	2.34729e7i		−	0.00210394i
$326$		−	9.65853e9i		−	0.855147i
$327$			2.95769e9i			0.258680i
$328$	4.32386e10			3.73574
$329$		−	5.32619e9i		−	0.454604i
$330$	6.71008e9	+	6.61141e9i	0.565811	+	0.557492i
$331$	−4.39319e9			−0.365989			−0.182994	−	0.983114i	$-0.558579\pi$
$331$	−4.39319e9			−0.365989			−0.182994	+	0.983114i	$0.558579\pi$
$332$		−	1.69867e10i		−	1.39816i
$333$	−7.94116e8			−0.0645814
$334$	1.81931e10			1.46191
$335$	8.57430e9			0.680800
$336$		−	1.54716e10i		−	1.21388i
$337$		−	1.22221e10i		−	0.947602i	−0.880632	−	0.473801i	$-0.842882\pi$
$337$		−	1.22221e10i		−	0.947602i	0.880632	−	0.473801i	$-0.157118\pi$
$338$			2.53315e10i			1.94086i
$339$	1.56665e9			0.118624
$340$		−	1.94273e10i		−	1.45377i
$341$	−5.46065e9	+	5.54214e9i	−0.403856	+	0.409883i
$342$	3.17757e10			2.32269
$343$			1.47012e10i			1.06213i
$344$	−5.01221e9			−0.357928
$345$	−6.81462e9			−0.481023
$346$	−4.61166e10			−3.21775
$347$			1.69271e10i			1.16752i	0.811925	+	0.583762i	$0.198420\pi$
$347$			1.69271e10i			1.16752i	−0.811925	+	0.583762i	$0.801580\pi$
$348$		−	9.53329e9i		−	0.650019i
$349$		−	1.42847e10i		−	0.962876i	−0.876480	−	0.481438i	$-0.840115\pi$
$349$		−	1.42847e10i		−	0.962876i	0.876480	−	0.481438i	$-0.159885\pi$
$350$	2.68088e9			0.178651
$351$			1.95351e8i			0.0128703i
$352$	−4.52016e10	−	4.45370e10i	−2.94431	−	2.90102i
$353$	−2.54761e10			−1.64072			−0.820358	−	0.571851i	$-0.806226\pi$
$353$	−2.54761e10			−1.64072			−0.820358	+	0.571851i	$0.806226\pi$
$354$		−	6.87962e9i		−	0.438078i
$355$	8.05267e9			0.507022
$356$	4.63860e10			2.88793
$357$	2.84661e9			0.175249
$358$			2.71450e10i			1.65256i
$359$		−	1.08286e10i		−	0.651923i	−0.945383	−	0.325961i	$-0.894312\pi$
$359$		−	1.08286e10i		−	0.651923i	0.945383	−	0.325961i	$-0.105688\pi$
$360$			4.34633e10i			2.58770i
$361$	−2.02836e10			−1.19431
$362$			3.69111e10i			2.14943i
$363$	1.12787e8	+	7.61383e9i	0.00649582	+	0.438507i
$364$	5.60363e8			0.0319201
$365$			1.10453e10i			0.622308i
$366$	−2.50490e10			−1.39594
$367$	−9.48367e9			−0.522772			−0.261386	−	0.965234i	$-0.584180\pi$
$367$	−9.48367e9			−0.522772			−0.261386	+	0.965234i	$0.584180\pi$
$368$	8.40460e10			4.58275
$369$		−	1.62891e10i		−	0.878599i
$370$			2.71425e9i			0.144825i
$371$		−	9.04284e9i		−	0.477319i
$372$	1.33810e10			0.698745
$373$			2.04733e10i			1.05768i	0.848723	+	0.528838i	$0.177372\pi$
$373$			2.04733e10i			1.05768i	−0.848723	+	0.528838i	$0.822628\pi$
$374$	1.50025e10	−	1.52264e10i	0.766791	−	0.778234i
$375$	9.13972e9			0.462177
$376$			4.39436e10i			2.19859i
$377$	1.75550e8			0.00869029
$378$	−2.23114e10			−1.09285
$379$	3.52729e10			1.70956			0.854781	−	0.518989i	$-0.173692\pi$
$379$	3.52729e10			1.70956			0.854781	+	0.518989i	$0.173692\pi$
$380$		−	7.97912e10i		−	3.82667i
$381$			1.42089e10i			0.674313i
$382$		−	5.95266e10i		−	2.79549i
$383$	−1.92909e10			−0.896516			−0.448258	−	0.893904i	$-0.647955\pi$
$383$	−1.92909e10			−0.896516			−0.448258	+	0.893904i	$0.647955\pi$
$384$			3.69745e10i			1.70050i
$385$	−1.03679e10	−	1.02154e10i	−0.471896	−	0.464957i
$386$	4.37492e7			0.00197070
$387$			1.88823e9i			0.0841803i
$388$	−3.64532e10			−1.60846
$389$	2.24671e10			0.981179			0.490590	−	0.871391i	$-0.336781\pi$
$389$	2.24671e10			0.981179			0.490590	+	0.871391i	$0.336781\pi$
$390$	2.98330e8			0.0128955
$391$			1.54636e10i			0.661613i
$392$		−	4.02029e10i		−	1.70260i
$393$		−	1.59649e10i		−	0.669260i
$394$	4.77018e9			0.197947
$395$			1.23460e10i			0.507153i
$396$	−3.85985e10	+	3.91745e10i	−1.56960	+	1.59303i
$397$	2.80065e10			1.12745			0.563725	−	0.825963i	$-0.309368\pi$
$397$	2.80065e10			1.12745			0.563725	+	0.825963i	$0.309368\pi$
$398$			2.14686e9i			0.0855600i
$399$	1.16916e10			0.461297
$400$	−1.29322e10			−0.505166
$401$	−1.62704e10			−0.629245			−0.314622	−	0.949217i	$-0.601878\pi$
$401$	−1.62704e10			−0.629245			−0.314622	+	0.949217i	$0.601878\pi$
$402$		−	1.62254e10i		−	0.621287i
$403$			2.46404e8i			0.00934172i
$404$			6.50560e10i			2.44209i
$405$	1.15462e10			0.429158
$406$			2.00498e10i			0.737916i
$407$	−1.53991e9	+	1.56289e9i	−0.0561201	+	0.0569576i
$408$	−2.34859e10			−0.847553
$409$		−	2.94918e10i		−	1.05392i	−0.849890	−	0.526960i	$-0.823332\pi$
$409$		−	2.94918e10i		−	1.05392i	0.849890	−	0.526960i	$-0.176668\pi$
$410$	−5.56753e10			−1.97028
$411$	1.88370e10			0.660152
$412$	−6.68552e10			−2.32031
$413$			1.06298e10i			0.365364i
$414$		−	5.41532e10i		−	1.84341i
$415$			1.39733e10i			0.471093i
$416$	−2.00966e9			−0.0671043
$417$		−	2.35829e10i		−	0.779926i
$418$	6.16179e10	−	6.25375e10i	2.01838	−	2.04850i
$419$	−2.51888e10			−0.817243			−0.408621	−	0.912704i	$-0.633990\pi$
$419$	−2.51888e10			−0.817243			−0.408621	+	0.912704i	$0.633990\pi$
$420$			2.50323e10i			0.804460i
$421$	5.24677e10			1.67018			0.835090	−	0.550113i	$-0.185415\pi$
$421$	5.24677e10			1.67018			0.835090	+	0.550113i	$0.185415\pi$
$422$	−8.71065e9			−0.274663
$423$	1.65547e10			0.517081
$424$			7.46077e10i			2.30845i
$425$		−	2.37940e9i		−	0.0729310i
$426$		−	1.52383e10i		−	0.462700i
$427$	3.87037e10			1.16423
$428$		−	9.95117e10i		−	2.96551i
$429$	1.71781e8	+	1.69255e8i	0.00507162	+	0.00499705i
$430$	6.45387e9			0.188776
$431$		−	1.02895e10i		−	0.298186i	−0.988823	−	0.149093i	$-0.952365\pi$
$431$		−	1.02895e10i		−	0.298186i	0.988823	−	0.149093i	$-0.0476353\pi$
$432$	1.07628e11			3.09022
$433$	−6.09604e10			−1.73419			−0.867095	−	0.498143i	$-0.834015\pi$
$433$	−6.09604e10			−1.73419			−0.867095	+	0.498143i	$0.834015\pi$
$434$	−2.81422e10			−0.793230
$435$			7.84210e9i			0.219016i
$436$			5.90195e10i			1.63324i
$437$			6.35119e10i			1.74152i
$438$	2.09013e10			0.567908
$439$		−	1.25000e10i		−	0.336553i	−0.985740	−	0.168276i	$-0.946180\pi$
$439$		−	1.25000e10i		−	0.336553i	0.985740	−	0.168276i	$-0.0538201\pi$
$440$	8.55398e10	+	8.42820e10i	2.28222	+	2.24866i
$441$	−1.51454e10			−0.400431
$442$		−	6.76965e8i		−	0.0177369i
$443$	−3.95265e10			−1.02630			−0.513149	−	0.858300i	$-0.671521\pi$
$443$	−3.95265e10			−1.02630			−0.513149	+	0.858300i	$0.671521\pi$
$444$	3.77348e9			0.0970979
$445$	−3.81572e10			−0.973052
$446$			2.91662e10i			0.737123i
$447$			1.91480e10i			0.479617i
$448$		−	1.18030e11i		−	2.93008i
$449$	8.09845e9			0.199258			0.0996291	−	0.995025i	$-0.468234\pi$
$449$	8.09845e9			0.199258			0.0996291	+	0.995025i	$0.468234\pi$
$450$			8.33261e9i			0.203203i
$451$	−3.20584e10	−	3.15870e10i	−0.774881	−	0.763488i
$452$	3.12618e10			0.748964
$453$		−	1.33982e10i		−	0.318166i
$454$	4.19069e10			0.986421
$455$	−4.60955e8			−0.0107551
$456$	−9.64609e10			−2.23096
$457$		−	4.04315e10i		−	0.926947i	−0.886111	−	0.463474i	$-0.846603\pi$
$457$		−	4.04315e10i		−	0.926947i	0.886111	−	0.463474i	$-0.153397\pi$
$458$			1.53549e11i			3.48968i
$459$			1.98024e10i			0.446136i
$460$	−1.35983e11			−3.03706
$461$			4.04942e10i			0.896580i	0.893888	+	0.448290i	$0.147967\pi$
$461$			4.04942e10i			0.896580i	−0.893888	+	0.448290i	$0.852033\pi$
$462$	−1.93310e10	+	1.96194e10i	−0.424312	+	0.430644i
$463$	−1.32231e10			−0.287745			−0.143872	−	0.989596i	$-0.545956\pi$
$463$	−1.32231e10			−0.287745			−0.143872	+	0.989596i	$0.545956\pi$
$464$		−	9.67180e10i		−	2.08658i
$465$	−1.10073e10			−0.235433
$466$	1.06656e11			2.26173
$467$	2.48430e8			0.00522320			0.00261160	−	0.999997i	$-0.499169\pi$
$467$	2.48430e8			0.00522320			0.00261160	+	0.999997i	$0.499169\pi$
$468$			1.74170e9i			0.0363069i
$469$			2.50702e10i			0.518163i
$470$		−	5.65830e10i		−	1.15956i
$471$	−1.08460e10			−0.220386
$472$		−	8.77010e10i		−	1.76700i
$473$	3.71620e9	+	3.66156e9i	0.0742429	+	0.0731512i
$474$	2.33628e10			0.462820
$475$		−	9.77264e9i		−	0.191972i
$476$	5.68029e10			1.10648
$477$	2.81066e10			0.542919
$478$	1.68661e11			3.23075
$479$		−	9.15635e10i		−	1.73932i	−0.493648	−	0.869662i	$-0.664337\pi$
$479$		−	9.15635e10i		−	1.73932i	0.493648	−	0.869662i	$-0.335663\pi$
$480$		−	8.97751e10i		−	1.69118i
$481$			6.94862e7i			0.00129813i
$482$	−8.52048e10			−1.57861
$483$		−	1.99251e10i		−	0.366111i
$484$	2.25062e9	+	1.51931e11i	0.0410129	+	2.76862i
$485$	2.99864e10			0.541949
$486$		−	1.07710e11i		−	1.93069i
$487$	−8.23359e10			−1.46377			−0.731886	−	0.681427i	$-0.761360\pi$
$487$	−8.23359e10			−1.46377			−0.731886	+	0.681427i	$0.761360\pi$
$488$	−3.19324e11			−5.63056
$489$	1.10457e10			0.193177
$490$			5.17664e10i			0.897973i
$491$			3.35430e10i			0.577132i	0.957460	+	0.288566i	$0.0931785\pi$
$491$			3.35430e10i			0.577132i	−0.957460	+	0.288566i	$0.906821\pi$
$492$			7.74023e10i			1.32097i
$493$	1.77951e10			0.301241
$494$		−	2.78042e9i		−	0.0466876i
$495$	3.17512e10	−	3.22250e10i	0.528858	−	0.536750i
$496$	1.35755e11			2.24299
$497$			2.35450e10i			0.385899i
$498$	2.64421e10			0.429912
$499$	−1.51543e9			−0.0244418			−0.0122209	−	0.999925i	$-0.503890\pi$
$499$	−1.51543e9			−0.0244418			−0.0122209	+	0.999925i	$0.503890\pi$
$500$	1.82379e11			2.91807
$501$			2.08059e10i			0.330245i
$502$		−	1.49008e10i		−	0.234637i
$503$		−	1.62137e10i		−	0.253286i	−0.991948	−	0.126643i	$-0.959580\pi$
$503$		−	1.62137e10i		−	0.253286i	0.991948	−	0.126643i	$-0.0404203\pi$
$504$	−1.27081e11			−1.96952
$505$		−	5.35151e10i		−	0.822832i
$506$	−1.06578e11	−	1.05011e11i	−1.62580	−	1.60189i
$507$	−2.89695e10			−0.438440
$508$			2.83533e11i			4.25744i
$509$	7.86778e10			1.17214			0.586072	−	0.810259i	$-0.300673\pi$
$509$	7.86778e10			1.17214			0.586072	+	0.810259i	$0.300673\pi$
$510$	3.02412e10			0.447010
$511$	−3.22950e10			−0.473644
$512$			1.87305e11i			2.72565i
$513$			8.13320e10i			1.17433i
$514$			1.28878e11i			1.84640i
$515$	5.49951e10			0.781799
$516$		−	8.97246e9i		−	0.126565i
$517$	3.21020e10	−	3.25811e10i	0.449335	−	0.456040i
$518$	−7.93614e9			−0.110228
$519$		−	5.27397e10i		−	0.726890i
$520$	3.80310e9			0.0520144
$521$	4.06424e10			0.551606			0.275803	−	0.961214i	$-0.411056\pi$
$521$	4.06424e10			0.551606			0.275803	+	0.961214i	$0.411056\pi$
$522$	−6.23181e10			−0.839330
$523$		−	1.08696e11i		−	1.45280i	−0.687273	−	0.726399i	$-0.741193\pi$
$523$		−	1.08696e11i		−	1.45280i	0.687273	−	0.726399i	$-0.258807\pi$
$524$		−	3.18572e11i		−	4.22554i
$525$			3.06590e9i			0.0403572i
$526$	−9.78055e10			−1.27767
$527$			2.49775e10i			0.323822i
$528$	9.32503e10	−	9.46418e10i	1.19982	−	1.21772i
$529$	2.99280e10			0.382168
$530$		−	9.60670e10i		−	1.21751i
$531$	−3.30392e10			−0.415577
$532$	2.33300e11			2.91251
$533$	−1.42531e9			−0.0176605
$534$			7.22061e10i			0.887991i
$535$			8.18584e10i			0.999191i
$536$		−	2.06841e11i		−	2.50598i
$537$	−3.10434e10			−0.373312
$538$			1.60791e11i			1.91925i
$539$	−2.93693e10	+	2.98076e10i	−0.347967	+	0.353160i
$540$	−1.74137e11			−2.04793
$541$			3.23254e10i			0.377359i	0.982039	+	0.188679i	$0.0604207\pi$
$541$			3.23254e10i			0.377359i	−0.982039	+	0.188679i	$0.939579\pi$
$542$	6.58346e10			0.762882
$543$	−4.22122e10			−0.485555
$544$	−2.03716e11			−2.32611
$545$		−	4.85494e10i		−	0.550298i
$546$			8.72280e8i			0.00981489i
$547$			3.84072e10i			0.429006i	0.976723	+	0.214503i	$0.0688132\pi$
$547$			3.84072e10i			0.429006i	−0.976723	+	0.214503i	$0.931187\pi$
$548$	3.75883e11			4.16803
$549$			1.20297e11i			1.32424i
$550$	1.63993e10	+	1.61582e10i	0.179215	+	0.176580i
$551$	7.30878e10			0.792937
$552$			1.64392e11i			1.77061i
$553$	−3.60983e10			−0.385999
$554$	−3.04082e11			−3.22813
$555$	−3.10406e9			−0.0327159
$556$		−	4.70587e11i		−	4.92425i
$557$			4.74571e8i			0.00493038i	0.999997	+	0.00246519i	$0.000784695\pi$
$557$			4.74571e8i			0.00493038i	−0.999997	+	0.00246519i	$0.999215\pi$
$558$		−	8.74705e10i		−	0.902246i
$559$	1.65222e8			0.00169208
$560$			2.53960e11i			2.58234i
$561$	1.74131e10	+	1.71571e10i	0.175803	+	0.173218i
$562$	−3.33162e11			−3.33972
$563$			8.29165e9i			0.0825292i	0.999148	+	0.0412646i	$0.0131387\pi$
$563$			8.29165e9i			0.0825292i	−0.999148	+	0.0412646i	$0.986861\pi$
$564$	−7.86643e10			−0.777430
$565$	−2.57160e10			−0.252354
$566$	−1.27747e11			−1.24476
$567$			3.37595e10i			0.326636i
$568$		−	1.94258e11i		−	1.86631i
$569$			9.78873e10i			0.933850i	0.884297	+	0.466925i	$0.154638\pi$
$569$			9.78873e10i			0.933850i	−0.884297	+	0.466925i	$0.845362\pi$
$570$	1.24206e11			1.17664
$571$			7.06043e10i			0.664181i	0.943248	+	0.332091i	$0.107754\pi$
$571$			7.06043e10i			0.664181i	−0.943248	+	0.332091i	$0.892246\pi$
$572$	3.42782e9	+	3.37742e9i	0.0320209	+	0.0315501i
$573$	6.80756e10			0.631499
$574$		−	1.62788e11i		−	1.49960i
$575$	−1.66548e10			−0.152359
$576$	3.66856e11			3.33277
$577$	−1.13635e11			−1.02520			−0.512602	−	0.858626i	$-0.671318\pi$
$577$	−1.13635e11			−1.02520			−0.512602	+	0.858626i	$0.671318\pi$
$578$			1.48058e11i			1.32654i
$579$			5.00323e7i			0.000445181i
$580$			1.56486e11i			1.38281i
$581$	−4.08562e10			−0.358553
$582$		−	5.67443e10i		−	0.494573i
$583$	5.45030e10	−	5.53163e10i	0.471787	−	0.478828i
$584$	2.66449e11			2.29067
$585$		−	1.43272e9i		−	0.0122332i
$586$	2.71300e11			2.30070
$587$	1.36139e11			1.14665			0.573325	−	0.819328i	$-0.305653\pi$
$587$	1.36139e11			1.14665			0.573325	+	0.819328i	$0.305653\pi$
$588$	7.19679e10			0.602046
$589$			1.02587e11i			0.852376i
$590$			1.12926e11i			0.931939i
$591$			5.45526e9i			0.0447163i
$592$	3.82830e10			0.311687
$593$		−	1.80776e11i		−	1.46192i	−0.682423	−	0.730958i	$-0.739074\pi$
$593$		−	1.80776e11i		−	1.46192i	0.682423	−	0.730958i	$-0.260926\pi$
$594$	−1.36482e11	−	1.34475e11i	−1.09630	−	1.08018i
$595$	−4.67261e10			−0.372814
$596$			3.82091e11i			3.02818i
$597$	−2.45518e9			−0.0193280
$598$	−4.73847e9			−0.0370539
$599$	−4.64103e10			−0.360502			−0.180251	−	0.983621i	$-0.557691\pi$
$599$	−4.64103e10			−0.360502			−0.180251	+	0.983621i	$0.557691\pi$
$600$		−	2.52951e10i		−	0.195179i
$601$		−	8.81431e10i		−	0.675601i	−0.941218	−	0.337801i	$-0.890317\pi$
$601$		−	8.81431e10i		−	0.675601i	0.941218	−	0.337801i	$-0.109683\pi$
$602$			1.88703e10i			0.143679i
$603$	−7.79223e10			−0.589376
$604$		−	2.67356e11i		−	2.00882i
$605$	−1.85136e9	−	1.24978e11i	−0.0138188	−	0.932853i
$606$	−1.01268e11			−0.750903
$607$		−	5.89816e10i		−	0.434472i	−0.976119	−	0.217236i	$-0.930296\pi$
$607$		−	5.89816e10i		−	0.434472i	0.976119	−	0.217236i	$-0.0697041\pi$
$608$	−8.36698e11			−6.12286
$609$	−2.29293e10			−0.166695
$610$	4.11170e11			2.96963
$611$		−	1.44855e9i		−	0.0103937i
$612$			1.76553e11i			1.25855i
$613$			3.46609e10i			0.245470i	0.992439	+	0.122735i	$0.0391665\pi$
$613$			3.46609e10i			0.245470i	−0.992439	+	0.122735i	$0.960833\pi$
$614$	2.84404e11			2.00107
$615$		−	6.36712e10i		−	0.445084i
$616$	−2.46430e11	+	2.50108e11i	−1.71148	+	1.73702i
$617$	2.26109e11			1.56019			0.780093	−	0.625664i	$-0.215172\pi$
$617$	2.26109e11			1.56019			0.780093	+	0.625664i	$0.215172\pi$
$618$		−	1.04069e11i		−	0.713457i
$619$	−1.23452e11			−0.840886			−0.420443	−	0.907319i	$-0.638125\pi$
$619$	−1.23452e11			−0.840886			−0.420443	+	0.907319i	$0.638125\pi$
$620$	−2.19645e11			−1.48646
$621$	1.38609e11			0.932017
$622$			3.99233e11i			2.66725i
$623$		−	1.11567e11i		−	0.740599i
$624$		−	4.20777e9i		−	0.0277533i
$625$	−1.30251e11			−0.853610
$626$			4.61321e10i			0.300404i
$627$	7.15189e10	+	7.04673e10i	0.462755	+	0.455950i
$628$	−2.16426e11			−1.39146
$629$			7.04369e9i			0.0449984i
$630$	1.63634e11			1.03875
$631$	1.22545e11			0.772996			0.386498	−	0.922290i	$-0.373685\pi$
$631$	1.22545e11			0.772996			0.386498	+	0.922290i	$0.373685\pi$
$632$	2.97828e11			1.86680
$633$		−	9.96164e9i		−	0.0620463i
$634$			3.33608e10i			0.206481i
$635$		−	2.33234e11i		−	1.43449i
$636$	−1.33557e11			−0.816277
$637$			1.32524e9i			0.00804893i
$638$	−1.20844e11	+	1.22648e11i	−0.729363	+	0.740247i
$639$	−7.31818e10			−0.438934
$640$		−	6.06923e11i		−	3.61754i
$641$	−1.04910e11			−0.621417			−0.310709	−	0.950505i	$-0.600566\pi$
$641$	−1.04910e11			−0.621417			−0.310709	+	0.950505i	$0.600566\pi$
$642$	1.54903e11			0.911845
$643$	9.91264e10			0.579890			0.289945	−	0.957043i	$-0.406363\pi$
$643$	9.91264e10			0.579890			0.289945	+	0.957043i	$0.406363\pi$
$644$		−	3.97597e11i		−	2.31153i
$645$			7.38076e9i			0.0426444i
$646$		−	2.81846e11i		−	1.61838i
$647$	−1.88323e11			−1.07470			−0.537349	−	0.843360i	$-0.680574\pi$
$647$	−1.88323e11			−1.07470			−0.537349	+	0.843360i	$0.680574\pi$
$648$		−	2.78532e11i		−	1.57970i
$649$	−6.40680e10	+	6.50241e10i	−0.361129	+	0.366518i
$650$	7.29114e8			0.00408453
$651$		−	3.21839e10i		−	0.179190i
$652$	2.20411e11			1.21967
$653$	−4.63799e10			−0.255081			−0.127540	−	0.991833i	$-0.540708\pi$
$653$	−4.63799e10			−0.255081			−0.127540	+	0.991833i	$0.540708\pi$
$654$	−9.18717e10			−0.502193
$655$			2.62057e11i			1.42374i
$656$			7.85268e11i			4.24036i
$657$		−	1.00378e11i		−	0.538738i
$658$	1.65442e11			0.882555
$659$			8.09935e10i			0.429446i	0.976675	+	0.214723i	$0.0688848\pi$
$659$			8.09935e10i			0.429446i	−0.976675	+	0.214723i	$0.931115\pi$
$660$	−1.50875e11	+	1.53126e11i	−0.795136	+	0.807002i
$661$	1.14955e11			0.602172			0.301086	−	0.953597i	$-0.402651\pi$
$661$	1.14955e11			0.602172			0.301086	+	0.953597i	$0.402651\pi$
$662$		−	1.36461e11i		−	0.710521i
$663$	7.74188e8			0.00400675
$664$	3.37083e11			1.73406
$665$	−1.91913e11			−0.981334
$666$		−	2.46668e10i		−	0.125376i
$667$		−	1.24559e11i		−	0.629319i
$668$			4.15173e11i			2.08508i
$669$	−3.33549e10			−0.166516
$670$			2.66335e11i			1.32169i
$671$	2.36756e11	+	2.33275e11i	1.16791	+	1.15074i
$672$	2.62491e11			1.28718
$673$		−	2.07629e11i		−	1.01211i	−0.862502	−	0.506054i	$-0.831104\pi$
$673$		−	2.07629e11i		−	1.01211i	0.862502	−	0.506054i	$-0.168896\pi$
$674$	3.79642e11			1.83965
$675$	−2.13279e10			−0.102738
$676$	−5.78075e11			−2.76820
$677$		−	3.60776e10i		−	0.171745i	−0.996306	−	0.0858723i	$-0.972632\pi$
$677$		−	3.60776e10i		−	0.171745i	0.996306	−	0.0858723i	$-0.0273677\pi$
$678$			4.86633e10i			0.230294i
$679$			8.76767e10i			0.412482i
$680$	3.85513e11			1.80303
$681$			4.79255e10i			0.222832i
$682$	−1.72150e11	−	1.69619e11i	−0.795736	−	0.784036i
$683$	−1.84277e11			−0.846815			−0.423407	−	0.905939i	$-0.639166\pi$
$683$	−1.84277e11			−0.846815			−0.423407	+	0.905939i	$0.639166\pi$
$684$			7.25134e11i			3.31279i
$685$	−3.09202e11			−1.40437
$686$	−4.56649e11			−2.06199
$687$	−1.75601e11			−0.788317
$688$		−	9.10282e10i		−	0.406277i
$689$		−	2.45936e9i		−	0.0109130i
$690$		−	2.11676e11i		−	0.933844i
$691$	3.32702e11			1.45930			0.729648	−	0.683822i	$-0.239684\pi$
$691$	3.32702e11			1.45930			0.729648	+	0.683822i	$0.239684\pi$
$692$		−	1.05240e12i		−	4.58940i
$693$	9.42219e10	+	9.28365e10i	0.408525	+	0.402518i
$694$	−5.25790e11			−2.26660
$695$			3.87105e11i			1.65916i
$696$	1.89178e11			0.806183
$697$	−1.44481e11			−0.612183
$698$	4.43712e11			1.86930
$699$			1.21973e11i			0.510923i
$700$			6.11787e10i			0.254805i
$701$		−	1.55015e11i		−	0.641949i	−0.947088	−	0.320974i	$-0.895990\pi$
$701$		−	1.55015e11i		−	0.641949i	0.947088	−	0.320974i	$-0.104010\pi$
$702$	−6.06799e9			−0.0249860
$703$			2.89297e10i			0.118447i
$704$	7.11389e11	−	7.22006e11i	2.89612	−	2.93934i
$705$	6.47093e10			0.261945
$706$		−	7.91336e11i		−	3.18524i
$707$	1.56472e11			0.626265
$708$	1.56995e11			0.624818
$709$	−1.02052e11			−0.403866			−0.201933	−	0.979399i	$-0.564722\pi$
$709$	−1.02052e11			−0.403866			−0.201933	+	0.979399i	$0.564722\pi$
$710$			2.50132e11i			0.984318i
$711$		−	1.12199e11i		−	0.439048i
$712$			9.20480e11i			3.58174i
$713$	1.74832e11			0.676492
$714$			8.84214e10i			0.340224i
$715$	−2.81973e9	−	2.77827e9i	−0.0107890	−	0.0106304i
$716$	−6.19458e11			−2.35700
$717$			1.92884e11i			0.729826i
$718$	3.36359e11			1.26562
$719$	3.11981e11			1.16738			0.583690	−	0.811977i	$-0.301608\pi$
$719$	3.11981e11			1.16738			0.583690	+	0.811977i	$0.301608\pi$
$720$	−7.89350e11			−2.93724
$721$			1.60799e11i			0.595035i
$722$		−	6.30048e11i		−	2.31859i
$723$		−	9.74417e10i		−	0.356608i
$724$	−8.42325e11			−3.06567
$725$			1.91660e10i			0.0693711i
$726$	−2.36501e11	+	3.50340e9i	−0.851306	+	0.0126108i
$727$	4.96073e11			1.77586			0.887929	−	0.459981i	$-0.152144\pi$
$727$	4.96073e11			1.77586			0.887929	+	0.459981i	$0.152144\pi$
$728$			1.11198e10i			0.0395887i
$729$	−6.73777e9			−0.0238565
$730$	−3.43088e11			−1.20813
$731$	1.67483e10			0.0586544
$732$		−	5.71627e11i		−	1.99099i
$733$		−	5.63409e11i		−	1.95168i	−0.218494	−	0.975838i	$-0.570114\pi$
$733$		−	5.63409e11i		−	1.95168i	0.218494	−	0.975838i	$-0.429886\pi$
$734$		−	2.94581e11i		−	1.01490i
$735$	−5.92009e10			−0.202852
$736$			1.42593e12i			4.85944i
$737$	−1.51103e11	+	1.53358e11i	−0.512157	+	0.519800i
$738$	5.05971e11			1.70569
$739$			2.95872e11i			0.992034i	0.868313	+	0.496017i	$0.165205\pi$
$739$			2.95872e11i			0.992034i	−0.868313	+	0.496017i	$0.834795\pi$
$740$	−6.19402e10			−0.206560
$741$	3.17973e9			0.0105467
$742$	2.80888e11			0.926655
$743$		−	8.82230e10i		−	0.289485i	−0.989469	−	0.144743i	$-0.953765\pi$
$743$		−	8.82230e10i		−	0.289485i	0.989469	−	0.144743i	$-0.0462354\pi$
$744$			2.65532e11i			0.866614i
$745$		−	3.14308e11i		−	1.02031i
$746$	−6.35941e11			−2.05334
$747$		−	1.26988e11i		−	0.407830i
$748$	3.47472e11	+	3.42363e11i	1.10997	+	1.09365i
$749$	−2.39344e11			−0.760493
$750$			2.83898e11i			0.897257i
$751$	6.45601e10			0.202957			0.101479	−	0.994838i	$-0.467643\pi$
$751$	6.45601e10			0.202957			0.101479	+	0.994838i	$0.467643\pi$
$752$	−7.98072e11			−2.49558
$753$	1.70408e10			0.0530043
$754$			5.45292e9i			0.0168711i
$755$			2.19927e11i			0.676847i
$756$		−	5.09155e11i		−	1.55870i
$757$	4.64668e11			1.41501			0.707505	−	0.706708i	$-0.249821\pi$
$757$	4.64668e11			1.41501			0.707505	+	0.706708i	$0.249821\pi$
$758$			1.09565e12i			3.31890i
$759$	1.20093e11	−	1.21885e11i	0.361867	−	0.367268i
$760$	1.58337e12			4.74600
$761$			5.02323e10i			0.149777i	0.997192	+	0.0748884i	$0.0238601\pi$
$761$			5.02323e10i			0.149777i	−0.997192	+	0.0748884i	$0.976140\pi$
$762$	−4.41357e11			−1.30909
$763$	1.41953e11			0.418837
$764$	1.35842e12			3.98713
$765$		−	1.45232e11i		−	0.424051i
$766$		−	5.99214e11i		−	1.74047i
$767$			2.89097e9i			0.00835338i
$768$	−5.18934e11			−1.49165
$769$		−	2.84333e11i		−	0.813060i	−0.913637	−	0.406530i	$-0.866739\pi$
$769$		−	2.84333e11i		−	0.813060i	0.913637	−	0.406530i	$-0.133261\pi$
$770$	3.17311e11	−	3.22046e11i	0.902655	−	0.916126i
$771$	−1.47387e11			−0.417101
$772$			9.98373e8i			0.00281076i
$773$	−3.11741e11			−0.873123			−0.436561	−	0.899674i	$-0.643804\pi$
$773$	−3.11741e11			−0.873123			−0.436561	+	0.899674i	$0.643804\pi$
$774$	−5.86520e10			−0.163425
$775$	−2.69016e10			−0.0745712
$776$		−	7.23374e11i		−	1.99488i
$777$		−	9.07590e9i		−	0.0249004i
$778$			6.97872e11i			1.90483i
$779$	−5.93411e11			−1.61141
$780$			6.80800e9i			0.0183925i
$781$	−1.41911e11	+	1.44028e11i	−0.381426	+	0.387118i
$782$	−4.80330e11			−1.28444
$783$		−	1.59507e11i		−	0.424359i
$784$	7.30135e11			1.93259
$785$	1.78032e11			0.468835
$786$	4.95900e11			1.29928
$787$			3.88577e11i			1.01293i	0.862261	+	0.506463i	$0.169047\pi$
$787$			3.88577e11i			1.01293i	−0.862261	+	0.506463i	$0.830953\pi$
$788$			1.08857e11i			0.282327i
$789$		−	1.11852e11i		−	0.288626i
$790$	−3.83492e11			−0.984574
$791$		−	7.51905e10i		−	0.192069i
$792$	−7.77376e11	−	7.65945e11i	−1.97574	−	1.94669i
$793$	1.05262e10			0.0266181
$794$			8.69937e11i			2.18880i
$795$	1.09864e11			0.275034
$796$	−4.89921e10			−0.122032
$797$	−2.79043e11			−0.691572			−0.345786	−	0.938313i	$-0.612388\pi$
$797$	−2.79043e11			−0.691572			−0.345786	+	0.938313i	$0.612388\pi$
$798$			3.63163e11i			0.895549i
$799$		−	1.46837e11i		−	0.360287i
$800$		−	2.19409e11i		−	0.535667i
$801$	3.46768e11			0.842382
$802$		−	5.05389e11i		−	1.22160i
$803$	−1.97553e11	−	1.94649e11i	−0.475141	−	0.468154i
$804$	3.70270e11			0.886124
$805$			3.27064e11i			0.778841i
$806$	−7.65378e9			−0.0181358
$807$	−1.83883e11			−0.433558
$808$	−1.29097e12			−3.02879
$809$			7.04977e11i			1.64582i	0.568175	+	0.822908i	$0.307650\pi$
$809$			7.04977e11i			1.64582i	−0.568175	+	0.822908i	$0.692350\pi$
$810$			3.58646e11i			0.833156i
$811$			6.69327e11i			1.54723i	0.633656	+	0.773615i	$0.281553\pi$
$811$			6.69327e11i			1.54723i	−0.633656	+	0.773615i	$0.718447\pi$
$812$	−4.57545e11			−1.05247
$813$			7.52896e10i			0.172335i
$814$	−4.85465e10	−	4.78327e10i	−0.110576	−	0.108950i
$815$	−1.81311e11			−0.410953
$816$		−	4.26534e11i		−	0.962041i
$817$	6.87882e10			0.154392
$818$	9.16073e11			2.04605
$819$	4.18910e9			0.00931077
$820$		−	1.27053e12i		−	2.81015i
$821$		−	9.53006e10i		−	0.209760i	−0.994485	−	0.104880i	$-0.966554\pi$
$821$		−	9.53006e10i		−	0.209760i	0.994485	−	0.104880i	$-0.0334459\pi$
$822$			5.85113e11i			1.28160i
$823$	−5.32621e11			−1.16096			−0.580482	−	0.814273i	$-0.697136\pi$
$823$	−5.32621e11			−1.16096			−0.580482	+	0.814273i	$0.697136\pi$
$824$		−	1.32667e12i		−	2.87775i
$825$	−1.84788e10	+	1.87546e10i	−0.0398894	+	0.0404847i
$826$	−3.30183e11			−0.709307
$827$		−	7.56727e11i		−	1.61777i	−0.587965	−	0.808886i	$-0.700071\pi$
$827$		−	7.56727e11i		−	1.61777i	0.587965	−	0.808886i	$-0.299929\pi$
$828$	1.23580e12			2.62921
$829$	−4.86684e11			−1.03045			−0.515227	−	0.857054i	$-0.672293\pi$
$829$	−4.86684e11			−1.03045			−0.515227	+	0.857054i	$0.672293\pi$
$830$	−4.34038e11			−0.914567
$831$		−	3.47753e11i		−	0.729234i
$832$		−	3.21004e10i		−	0.0669910i
$833$			1.34338e11i			0.279009i
$834$	7.32532e11			1.51413
$835$		−	3.41522e11i		−	0.702542i
$836$	1.42713e12	+	1.40614e12i	2.92172	+	2.87876i
$837$	2.23886e11			0.456169
$838$		−	7.82413e11i		−	1.58657i
$839$	−5.28752e11			−1.06710			−0.533549	−	0.845769i	$-0.679142\pi$
$839$	−5.28752e11			−1.06710			−0.533549	+	0.845769i	$0.679142\pi$
$840$	−4.96740e11			−0.997727
$841$	3.56907e11			0.713463
$842$			1.62975e12i			3.24244i
$843$		−	3.81009e11i		−	0.754441i
$844$		−	1.98780e11i		−	0.391745i
$845$	4.75525e11			0.932709
$846$			5.14220e11i			1.00385i
$847$	3.65421e11	−	5.41316e9i	0.710003	−	0.0105176i
$848$	−1.35497e12			−2.62027
$849$		−	1.46094e11i		−	0.281191i
$850$	7.39089e10			0.141586
$851$	4.93029e10			0.0940057
$852$	3.47745e11			0.659936
$853$		−	7.42893e11i		−	1.40323i	−0.712554	−	0.701617i	$-0.752462\pi$
$853$		−	7.42893e11i		−	1.40323i	0.712554	−	0.701617i	$-0.247538\pi$
$854$			1.20221e12i			2.26021i
$855$		−	5.96496e11i		−	1.11620i
$856$	1.97470e12			3.67796
$857$			8.84654e11i			1.64002i	0.572347	+	0.820012i	$0.306033\pi$
$857$			8.84654e11i			1.64002i	−0.572347	+	0.820012i	$0.693967\pi$
$858$	−5.25740e9	+	5.33586e9i	−0.00970113	+	0.00984590i
$859$	−3.28645e11			−0.603608			−0.301804	−	0.953370i	$-0.597589\pi$
$859$	−3.28645e11			−0.603608			−0.301804	+	0.953370i	$0.597589\pi$
$860$			1.47280e11i			0.269246i
$861$	1.86167e11			0.338758
$862$	3.19613e11			0.578889
$863$	−1.20739e11			−0.217672			−0.108836	−	0.994060i	$-0.534712\pi$
$863$	−1.20739e11			−0.217672			−0.108836	+	0.994060i	$0.534712\pi$
$864$			1.82601e12i			3.27679i
$865$			8.65703e11i			1.54634i
$866$		−	1.89355e12i		−	3.36671i
$867$	−1.69322e11			−0.299665
$868$		−	6.42215e11i		−	1.13136i
$869$	−2.20819e11	−	2.17572e11i	−0.387219	−	0.381525i
$870$	−2.43591e11			−0.425191
$871$			6.81829e9i			0.0118469i
$872$	−1.17118e12			−2.02561
$873$	−2.72513e11			−0.469171
$874$	−1.97280e12			−3.38094
$875$		−	4.38655e11i		−	0.748327i
$876$			4.76976e11i			0.809991i
$877$			3.02352e11i			0.511111i	0.966794	+	0.255555i	$0.0822583\pi$
$877$			3.02352e11i			0.511111i	−0.966794	+	0.255555i	$0.917742\pi$
$878$	3.88275e11			0.653374
$879$			3.10263e11i			0.519726i
$880$	−1.53067e12	+	1.55351e12i	−2.55241	+	2.59050i
$881$	7.89008e11			1.30972			0.654859	−	0.755751i	$-0.272728\pi$
$881$	7.89008e11			1.30972			0.654859	+	0.755751i	$0.272728\pi$
$882$		−	4.70447e11i		−	0.777385i
$883$	9.24323e11			1.52048			0.760240	−	0.649642i	$-0.225081\pi$
$883$	9.24323e11			1.52048			0.760240	+	0.649642i	$0.225081\pi$
$884$	1.54486e10			0.0252976
$885$	−1.29145e11			−0.210525
$886$		−	1.22777e12i		−	1.99243i
$887$			2.64438e11i			0.427199i	0.976921	+	0.213599i	$0.0685187\pi$
$887$			2.64438e11i			0.427199i	−0.976921	+	0.213599i	$0.931481\pi$
$888$			7.48805e10i			0.120425i
$889$	6.81949e11			1.09180
$890$		−	1.18524e12i		−	1.88906i
$891$	−2.03475e11	+	2.06512e11i	−0.322850	+	0.327668i
$892$	−6.65583e11			−1.05134
$893$		−	6.03087e11i		−	0.948362i
$894$	−5.94776e11			−0.931115
$895$	5.09567e11			0.794161
$896$	1.77457e12			2.75335
$897$		−	5.41900e9i		−	0.00837046i
$898$			2.51554e11i			0.386835i
$899$		−	2.01192e11i		−	0.308015i
$900$	−1.90153e11			−0.289824
$901$		−	2.49301e11i		−	0.378290i
$902$	9.81154e11	−	9.95796e11i	1.48221	−	1.50433i
$903$	−2.15804e10			−0.0324570
$904$			6.20357e11i			0.928898i
$905$	6.92897e11			1.03294
$906$	4.16175e11			0.617680
$907$	1.06426e12			1.57260			0.786299	−	0.617847i	$-0.211995\pi$
$907$	1.06426e12			1.57260			0.786299	+	0.617847i	$0.211995\pi$
$908$			9.56332e11i			1.40691i
$909$			4.86340e11i			0.712335i
$910$		−	1.43182e10i		−	0.0208796i
$911$	−5.79630e11			−0.841545			−0.420773	−	0.907166i	$-0.638241\pi$
$911$	−5.79630e11			−0.841545			−0.420773	+	0.907166i	$0.638241\pi$
$912$		−	1.75185e12i		−	2.53232i
$913$	−2.49923e11	−	2.46249e11i	−0.359686	−	0.354397i
$914$	1.25588e12			1.79955
$915$			4.70221e11i			0.670838i
$916$	−3.50405e12			−4.97723
$917$	−7.66224e11			−1.08362
$918$	−6.15101e11			−0.866116
$919$			4.94274e11i			0.692956i	0.938058	+	0.346478i	$0.112622\pi$
$919$			4.94274e11i			0.692956i	−0.938058	+	0.346478i	$0.887378\pi$
$920$		−	2.69843e12i		−	3.76669i
$921$			3.25249e11i			0.452041i
$922$	−1.25783e12			−1.74060
$923$			6.40350e9i			0.00882288i
$924$	−4.47723e11	−	4.41140e11i	−0.614216	−	0.605185i
$925$	−7.58629e9			−0.0103624
$926$		−	4.10734e11i		−	0.558620i
$927$	−4.99789e11			−0.676812
$928$	1.64092e12			2.21256
$929$	1.05781e12			1.42018			0.710091	−	0.704110i	$-0.248654\pi$
$929$	1.05781e12			1.42018			0.710091	+	0.704110i	$0.248654\pi$
$930$		−	3.41907e11i		−	0.457063i
$931$			5.51748e11i			0.734416i
$932$			2.43392e12i			3.22584i
$933$	−4.56569e11			−0.602532
$934$			7.71672e9i			0.0101402i
$935$	−2.85830e11	−	2.81628e11i	−0.373992	−	0.368493i
$936$	−3.45621e10			−0.0450295
$937$			6.91745e10i			0.0897403i	0.998993	+	0.0448702i	$0.0142874\pi$
$937$			6.91745e10i			0.0897403i	−0.998993	+	0.0448702i	$0.985713\pi$
$938$	−7.78730e11			−1.00595
$939$	−5.27574e10			−0.0678612
$940$	1.29125e12			1.65386
$941$		−	7.18389e11i		−	0.916223i	−0.888895	−	0.458111i	$-0.848526\pi$
$941$		−	7.18389e11i		−	0.916223i	0.888895	−	0.458111i	$-0.151474\pi$
$942$		−	3.36897e11i		−	0.427851i
$943$			1.01131e12i			1.27890i
$944$	1.59276e12			2.00569
$945$			4.18831e11i			0.525184i
$946$	−1.13735e11	+	1.15433e11i	−0.142014	+	0.144133i
$947$	−1.34982e12			−1.67833			−0.839165	−	0.543877i	$-0.816956\pi$
$947$	−1.34982e12			−1.67833			−0.839165	+	0.543877i	$0.816956\pi$
$948$			5.33148e11i			0.660107i
$949$	−8.78322e9			−0.0108290
$950$	3.03557e11			0.372689
$951$	−3.81519e10			−0.0466439
$952$			1.12719e12i			1.37230i
$953$			1.45051e12i			1.75853i	0.476332	+	0.879266i	$0.341966\pi$
$953$			1.45051e12i			1.75853i	−0.476332	+	0.879266i	$0.658034\pi$
$954$			8.73046e11i			1.05401i
$955$	−1.11744e12			−1.34341
$956$			3.84891e12i			4.60794i
$957$	−1.40262e11	−	1.38200e11i	−0.167222	−	0.164763i
$958$	2.84414e12			3.37667
$959$		−	9.04069e11i		−	1.06888i
$960$	1.43398e12			1.68833
$961$	−5.70495e11			−0.668896
$962$	−2.15838e9			−0.00252015
$963$		−	7.43920e11i		−	0.865010i
$964$		−	1.94441e12i		−	2.25153i
$965$		−	8.21263e8i		−	0.000947050i
$966$	6.18913e11			0.710757
$967$		−	4.13713e11i		−	0.473144i	−0.971614	−	0.236572i	$-0.923976\pi$
$967$		−	4.13713e11i		−	0.473144i	0.971614	−	0.236572i	$-0.0760239\pi$
$968$	−3.01490e12	+	4.46611e10i	−3.43377	+	0.0508661i
$969$	3.22323e11			0.365592
$970$			9.31438e11i			1.05212i
$971$	9.91758e11			1.11565			0.557826	−	0.829958i	$-0.311636\pi$
$971$	9.91758e11			1.11565			0.557826	+	0.829958i	$0.311636\pi$
$972$	2.45799e12			2.75369
$973$	−1.13185e12			−1.26281
$974$		−	2.55751e12i		−	2.84173i
$975$			8.33827e8i			0.000922694i
$976$		−	5.79932e12i		−	6.39114i
$977$	8.96536e11			0.983987			0.491994	−	0.870599i	$-0.336268\pi$
$977$	8.96536e11			0.983987			0.491994	+	0.870599i	$0.336268\pi$
$978$			3.43100e11i			0.375029i
$979$	6.72436e11	−	6.82471e11i	0.732015	−	0.742939i
$980$	−1.18133e12			−1.28075
$981$			4.41212e11i			0.476399i
$982$	−1.04191e12			−1.12043
$983$	1.23720e12			1.32503			0.662516	−	0.749048i	$-0.269489\pi$
$983$	1.23720e12			1.32503			0.662516	+	0.749048i	$0.269489\pi$
$984$	−1.53596e12			−1.63833
$985$		−	8.95461e10i		−	0.0951265i
$986$			5.52752e11i			0.584821i
$987$			1.89202e11i			0.199369i
$988$	6.34501e10			0.0665893
$989$		−	1.17231e11i		−	0.122534i
$990$	1.00097e12	+	9.86253e11i	1.04203	+	1.02671i
$991$	−1.38793e12			−1.43904			−0.719519	−	0.694473i	$-0.755638\pi$
$991$	−1.38793e12			−1.43904			−0.719519	+	0.694473i	$0.755638\pi$
$992$			2.30322e12i			2.37842i
$993$	1.56059e11			0.160506
$994$	−7.31355e11			−0.749174
$995$	4.03009e10			0.0411171
$996$			6.03419e11i			0.613171i
$997$		−	1.06260e12i		−	1.07545i	−0.843120	−	0.537726i	$-0.819284\pi$
$997$		−	1.06260e12i		−	1.07545i	0.843120	−	0.537726i	$-0.180716\pi$
$998$		−	4.70721e10i		−	0.0474506i
$999$	6.31363e10			0.0633895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.9.b.b.10.6	yes	6
3.2	odd	2		99.9.c.b.10.1		6
4.3	odd	2		176.9.h.c.65.3		6
11.10	odd	2	inner	11.9.b.b.10.1	✓	6
33.32	even	2		99.9.c.b.10.6		6
44.43	even	2		176.9.h.c.65.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.9.b.b.10.1	✓	6	11.10	odd	2	inner
11.9.b.b.10.6	yes	6	1.1	even	1	trivial
99.9.c.b.10.1		6	3.2	odd	2
99.9.c.b.10.6		6	33.32	even	2
176.9.h.c.65.3		6	4.3	odd	2
176.9.h.c.65.4		6	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+31.0620i q^{2} -35.5230 q^{3} -708.845 q^{4} +583.097 q^{5} -1103.41i q^{6} +1704.90i q^{7} -14066.3i q^{8} -5299.12 q^{9} +O(q^{10})\)	\(q+31.0620i q^{2} -35.5230 q^{3} -708.845 q^{4} +583.097 q^{5} -1103.41i q^{6} +1704.90i q^{7} -14066.3i q^{8} -5299.12 q^{9} +18112.1i q^{10} +(-10275.8 + 10429.1i) q^{11} +25180.3 q^{12} +463.679i q^{13} -52957.7 q^{14} -20713.3 q^{15} +255461. q^{16} +47002.3i q^{17} -164601. i q^{18} +193047. i q^{19} -413326. q^{20} -60563.3i q^{21} +(-323950. - 319186. i) q^{22} +328997. q^{23} +499676. i q^{24} -50623.1 q^{25} -14402.8 q^{26} +421307. q^{27} -1.20851e6i q^{28} -378601. i q^{29} -643397. i q^{30} +531409. q^{31} +4.33417e6i q^{32} +(365027. - 370474. i) q^{33} -1.45998e6 q^{34} +994124. i q^{35} +3.75626e6 q^{36} +149858. q^{37} -5.99642e6 q^{38} -16471.3i q^{39} -8.20200e6i q^{40} +3.07392e6i q^{41} +1.88121e6 q^{42} -356329. i q^{43} +(7.28395e6 - 7.39265e6i) q^{44} -3.08990e6 q^{45} +1.02193e7i q^{46} -3.12404e6 q^{47} -9.07475e6 q^{48} +2.85810e6 q^{49} -1.57245e6i q^{50} -1.66966e6i q^{51} -328677. i q^{52} -5.30402e6 q^{53} +1.30866e7i q^{54} +(-5.99178e6 + 6.08120e6i) q^{55} +2.39816e7 q^{56} -6.85760e6i q^{57} +1.17601e7 q^{58} +6.23485e6 q^{59} +1.46826e7 q^{60} -2.27014e7i q^{61} +1.65066e7i q^{62} -9.03449e6i q^{63} -6.92296e7 q^{64} +270370. i q^{65} +(1.15077e7 + 1.13384e7i) q^{66} +1.47048e7 q^{67} -3.33174e7i q^{68} -1.16870e7 q^{69} -3.08794e7 q^{70} +1.38102e7 q^{71} +7.45388e7i q^{72} +1.89424e7i q^{73} +4.65489e6i q^{74} +1.79828e6 q^{75} -1.36840e8i q^{76} +(-1.77807e7 - 1.75192e7i) q^{77} +511630. q^{78} +2.11732e7i q^{79} +1.48959e8 q^{80} +1.98014e7 q^{81} -9.54820e7 q^{82} +2.39639e7i q^{83} +4.29300e7i q^{84} +2.74069e7i q^{85} +1.10683e7 q^{86} +1.34490e7i q^{87} +(1.46699e8 + 1.44542e8i) q^{88} -6.54388e7 q^{89} -9.59783e7i q^{90} -790529. q^{91} -2.33208e8 q^{92} -1.88772e7 q^{93} -9.70389e7i q^{94} +1.12565e8i q^{95} -1.53963e8i q^{96} +5.14262e7 q^{97} +8.87783e7i q^{98} +(5.44526e7 - 5.52652e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9}+O(q^{10}) \) 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9	\( 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9} - 32318 q^{11} + 54564 q^{12} - 33768 q^{14} + 85824 q^{15} + 312264 q^{16} - 894868 q^{20} - 550440 q^{22} + 683084 q^{23} - 141498 q^{25} - 657432 q^{26} + 988848 q^{27} + 942684 q^{31} + 2992704 q^{33} - 1345128 q^{34} + 7401360 q^{36} - 3804816 q^{37} - 8900760 q^{38} - 8158920 q^{42} + 14210284 q^{44} - 2499684 q^{45} + 15828644 q^{47} - 19028376 q^{48} - 10066602 q^{49} - 35477956 q^{53} + 7335372 q^{55} + 68829936 q^{56} + 65482560 q^{58} - 29614804 q^{59} + 35069244 q^{60} - 212921520 q^{64} + 75167400 q^{66} + 39419484 q^{67} + 62859468 q^{69} - 168190680 q^{70} + 3219212 q^{71} - 110874276 q^{75} + 91605360 q^{77} + 111889320 q^{78} + 383392952 q^{80} - 103764906 q^{81} - 163977720 q^{82} - 261274512 q^{86} + 328724880 q^{88} + 38785664 q^{89} + 355260528 q^{91} - 456128956 q^{92} - 182572452 q^{93} - 222185616 q^{97} + 159125406 q^{99}+O(q^{100}) \) 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9 - 32318 * q^11 + 54564 * q^12 - 33768 * q^14 + 85824 * q^15 + 312264 * q^16 - 894868 * q^20 - 550440 * q^22 + 683084 * q^23 - 141498 * q^25 - 657432 * q^26 + 988848 * q^27 + 942684 * q^31 + 2992704 * q^33 - 1345128 * q^34 + 7401360 * q^36 - 3804816 * q^37 - 8900760 * q^38 - 8158920 * q^42 + 14210284 * q^44 - 2499684 * q^45 + 15828644 * q^47 - 19028376 * q^48 - 10066602 * q^49 - 35477956 * q^53 + 7335372 * q^55 + 68829936 * q^56 + 65482560 * q^58 - 29614804 * q^59 + 35069244 * q^60 - 212921520 * q^64 + 75167400 * q^66 + 39419484 * q^67 + 62859468 * q^69 - 168190680 * q^70 + 3219212 * q^71 - 110874276 * q^75 + 91605360 * q^77 + 111889320 * q^78 + 383392952 * q^80 - 103764906 * q^81 - 163977720 * q^82 - 261274512 * q^86 + 328724880 * q^88 + 38785664 * q^89 + 355260528 * q^91 - 456128956 * q^92 - 182572452 * q^93 - 222185616 * q^97 + 159125406 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more