LMFDB - Embedded newform 15.10.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,10,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	15.a (trivial)

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:	yes
Analytic conductor:	$7.72553754246$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{4729}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1182 $ x^2 - x - 1182
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-33.8839$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+43.8839 q^{2} +81.0000 q^{3} +1413.79 q^{4} -625.000 q^{5} +3554.59 q^{6} -7861.50 q^{7} +39574.2 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+43.8839 q^{2} +81.0000 q^{3} +1413.79 q^{4} -625.000 q^{5} +3554.59 q^{6} -7861.50 q^{7} +39574.2 q^{8} +6561.00 q^{9} -27427.4 q^{10} -49373.3 q^{11} +114517. q^{12} +24250.7 q^{13} -344993. q^{14} -50625.0 q^{15} +1.01281e6 q^{16} +268222. q^{17} +287922. q^{18} -168364. q^{19} -883621. q^{20} -636781. q^{21} -2.16669e6 q^{22} -2.12200e6 q^{23} +3.20551e6 q^{24} +390625. q^{25} +1.06422e6 q^{26} +531441. q^{27} -1.11145e7 q^{28} +389624. q^{29} -2.22162e6 q^{30} +90532.2 q^{31} +2.41838e7 q^{32} -3.99924e6 q^{33} +1.17706e7 q^{34} +4.91344e6 q^{35} +9.27590e6 q^{36} -3.31991e6 q^{37} -7.38848e6 q^{38} +1.96431e6 q^{39} -2.47339e7 q^{40} +2.32694e7 q^{41} -2.79444e7 q^{42} +1.91140e7 q^{43} -6.98036e7 q^{44} -4.10062e6 q^{45} -9.31215e7 q^{46} +6.28153e7 q^{47} +8.20372e7 q^{48} +2.14495e7 q^{49} +1.71421e7 q^{50} +2.17260e7 q^{51} +3.42855e7 q^{52} -180207. q^{53} +2.33217e7 q^{54} +3.08583e7 q^{55} -3.11112e8 q^{56} -1.36375e7 q^{57} +1.70982e7 q^{58} +3.84564e7 q^{59} -7.15733e7 q^{60} -553620. q^{61} +3.97290e6 q^{62} -5.15793e7 q^{63} +5.42724e8 q^{64} -1.51567e7 q^{65} -1.75502e8 q^{66} -2.39163e8 q^{67} +3.79211e8 q^{68} -1.71882e8 q^{69} +2.15621e8 q^{70} +1.28653e8 q^{71} +2.59646e8 q^{72} -2.39376e8 q^{73} -1.45690e8 q^{74} +3.16406e7 q^{75} -2.38033e8 q^{76} +3.88148e8 q^{77} +8.62015e7 q^{78} -5.28027e8 q^{79} -6.33003e8 q^{80} +4.30467e7 q^{81} +1.02115e9 q^{82} +2.12210e8 q^{83} -9.00277e8 q^{84} -1.67639e8 q^{85} +8.38797e8 q^{86} +3.15595e7 q^{87} -1.95391e9 q^{88} -2.07724e8 q^{89} -1.79951e8 q^{90} -1.90647e8 q^{91} -3.00007e9 q^{92} +7.33311e6 q^{93} +2.75658e9 q^{94} +1.05228e8 q^{95} +1.95889e9 q^{96} +1.70780e9 q^{97} +9.41288e8 q^{98} -3.23938e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9	\( 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9} - 11875 q^{10} + 35488 q^{11} + 123201 q^{12} + 143676 q^{13} - 245196 q^{14} - 101250 q^{15} + 707265 q^{16} + 385156 q^{17} + 124659 q^{18} - 403296 q^{19} - 950625 q^{20} - 961632 q^{21} - 4278368 q^{22} + 223704 q^{23} + 4021407 q^{24} + 781250 q^{25} - 1907546 q^{26} + 1062882 q^{27} - 11544484 q^{28} - 74572 q^{29} - 961875 q^{30} - 5027128 q^{31} + 26629583 q^{32} + 2874528 q^{33} + 8860882 q^{34} + 7420000 q^{35} + 9979281 q^{36} + 5373628 q^{37} - 1542476 q^{38} + 11637756 q^{39} - 31029375 q^{40} + 14211332 q^{41} - 19860876 q^{42} + 27748920 q^{43} - 60705952 q^{44} - 8201250 q^{45} - 151491648 q^{46} + 95966440 q^{47} + 57288465 q^{48} - 2819950 q^{49} + 7421875 q^{50} + 31197636 q^{51} + 47088706 q^{52} - 64305596 q^{53} + 10097379 q^{54} - 22180000 q^{55} - 351509340 q^{56} - 32666976 q^{57} + 28649198 q^{58} + 187863136 q^{59} - 77000625 q^{60} + 154080060 q^{61} + 131320056 q^{62} - 77892192 q^{63} + 638301089 q^{64} - 89797500 q^{65} - 346547808 q^{66} + 33592376 q^{67} + 391747238 q^{68} + 18120024 q^{69} + 153247500 q^{70} - 228270976 q^{71} + 325733967 q^{72} - 33122316 q^{73} - 362019226 q^{74} + 63281250 q^{75} - 263218724 q^{76} + 47811456 q^{77} - 154511226 q^{78} - 932406760 q^{79} - 442040625 q^{80} + 86093442 q^{81} + 1246549646 q^{82} + 207040152 q^{83} - 935103204 q^{84} - 240722500 q^{85} + 623926708 q^{86} - 6040332 q^{87} - 1099114848 q^{88} + 224518164 q^{89} - 77911875 q^{90} - 669602528 q^{91} - 2748592992 q^{92} - 407197368 q^{93} + 1931650816 q^{94} + 252060000 q^{95} + 2156996223 q^{96} + 387134596 q^{97} + 1545205739 q^{98} + 232836768 q^{99}+O(q^{100}) \) 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9 - 11875 * q^10 + 35488 * q^11 + 123201 * q^12 + 143676 * q^13 - 245196 * q^14 - 101250 * q^15 + 707265 * q^16 + 385156 * q^17 + 124659 * q^18 - 403296 * q^19 - 950625 * q^20 - 961632 * q^21 - 4278368 * q^22 + 223704 * q^23 + 4021407 * q^24 + 781250 * q^25 - 1907546 * q^26 + 1062882 * q^27 - 11544484 * q^28 - 74572 * q^29 - 961875 * q^30 - 5027128 * q^31 + 26629583 * q^32 + 2874528 * q^33 + 8860882 * q^34 + 7420000 * q^35 + 9979281 * q^36 + 5373628 * q^37 - 1542476 * q^38 + 11637756 * q^39 - 31029375 * q^40 + 14211332 * q^41 - 19860876 * q^42 + 27748920 * q^43 - 60705952 * q^44 - 8201250 * q^45 - 151491648 * q^46 + 95966440 * q^47 + 57288465 * q^48 - 2819950 * q^49 + 7421875 * q^50 + 31197636 * q^51 + 47088706 * q^52 - 64305596 * q^53 + 10097379 * q^54 - 22180000 * q^55 - 351509340 * q^56 - 32666976 * q^57 + 28649198 * q^58 + 187863136 * q^59 - 77000625 * q^60 + 154080060 * q^61 + 131320056 * q^62 - 77892192 * q^63 + 638301089 * q^64 - 89797500 * q^65 - 346547808 * q^66 + 33592376 * q^67 + 391747238 * q^68 + 18120024 * q^69 + 153247500 * q^70 - 228270976 * q^71 + 325733967 * q^72 - 33122316 * q^73 - 362019226 * q^74 + 63281250 * q^75 - 263218724 * q^76 + 47811456 * q^77 - 154511226 * q^78 - 932406760 * q^79 - 442040625 * q^80 + 86093442 * q^81 + 1246549646 * q^82 + 207040152 * q^83 - 935103204 * q^84 - 240722500 * q^85 + 623926708 * q^86 - 6040332 * q^87 - 1099114848 * q^88 + 224518164 * q^89 - 77911875 * q^90 - 669602528 * q^91 - 2748592992 * q^92 - 407197368 * q^93 + 1931650816 * q^94 + 252060000 * q^95 + 2156996223 * q^96 + 387134596 * q^97 + 1545205739 * q^98 + 232836768 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	43.8839	1.93941	0.969706	−	0.244277i	$-0.0785506\pi$
$2$	43.8839	1.93941	0.969706	+	0.244277i	$0.0785506\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	1413.79	2.76132
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	3554.59	1.11972
$7$	−7861.50	−1.23755	−0.618777	−	0.785567i	$-0.712371\pi$
$7$	−7861.50	−1.23755	−0.618777	+	0.785567i	$0.712371\pi$
$8$	39574.2	3.41591
$9$	6561.00	0.333333
$10$	−27427.4	−0.867331
$11$	−49373.3	−1.01678	−0.508388	−	0.861128i	$-0.669758\pi$
$11$	−49373.3	−1.01678	−0.508388	+	0.861128i	$0.669758\pi$
$12$	114517.	1.59425
$13$	24250.7	0.235494	0.117747	−	0.993044i	$-0.462433\pi$
$13$	24250.7	0.235494	0.117747	+	0.993044i	$0.462433\pi$
$14$	−344993.	−2.40013
$15$	−50625.0	−0.258199
$16$	1.01281e6	3.86355
$17$	268222.	0.778888	0.389444	−	0.921050i	$-0.372667\pi$
$17$	268222.	0.778888	0.389444	+	0.921050i	$0.372667\pi$
$18$	287922.	0.646470
$19$	−168364.	−0.296387	−0.148193	−	0.988958i	$-0.547346\pi$
$19$	−168364.	−0.296387	−0.148193	+	0.988958i	$0.547346\pi$
$20$	−883621.	−1.23490
$21$	−636781.	−0.714502
$22$	−2.16669e6	−1.97195
$23$	−2.12200e6	−1.58114	−0.790569	−	0.612373i	$-0.790215\pi$
$23$	−2.12200e6	−1.58114	−0.790569	+	0.612373i	$0.790215\pi$
$24$	3.20551e6	1.97218
$25$	390625.	0.200000
$26$	1.06422e6	0.456720
$27$	531441.	0.192450
$28$	−1.11145e7	−3.41728
$29$	389624.	0.102295	0.0511475	−	0.998691i	$-0.483712\pi$
$29$	389624.	0.102295	0.0511475	+	0.998691i	$0.483712\pi$
$30$	−2.22162e6	−0.500754
$31$	90532.2	0.0176066	0.00880330	−	0.999961i	$-0.497198\pi$
$31$	90532.2	0.0176066	0.00880330	+	0.999961i	$0.497198\pi$
$32$	2.41838e7	4.07709
$33$	−3.99924e6	−0.587036
$34$	1.17706e7	1.51058
$35$	4.91344e6	0.553451
$36$	9.27590e6	0.920438
$37$	−3.31991e6	−0.291218	−0.145609	−	0.989342i	$-0.546514\pi$
$37$	−3.31991e6	−0.291218	−0.145609	+	0.989342i	$0.546514\pi$
$38$	−7.38848e6	−0.574816
$39$	1.96431e6	0.135963
$40$	−2.47339e7	−1.52764
$41$	2.32694e7	1.28605	0.643024	−	0.765846i	$-0.277679\pi$
$41$	2.32694e7	1.28605	0.643024	+	0.765846i	$0.277679\pi$
$42$	−2.79444e7	−1.38571
$43$	1.91140e7	0.852597	0.426298	−	0.904583i	$-0.359817\pi$
$43$	1.91140e7	0.852597	0.426298	+	0.904583i	$0.359817\pi$
$44$	−6.98036e7	−2.80764
$45$	−4.10062e6	−0.149071
$46$	−9.31215e7	−3.06648
$47$	6.28153e7	1.87770	0.938848	−	0.344332i	$-0.111895\pi$
$47$	6.28153e7	1.87770	0.938848	+	0.344332i	$0.111895\pi$
$48$	8.20372e7	2.23062
$49$	2.14495e7	0.531539
$50$	1.71421e7	0.387882
$51$	2.17260e7	0.449691
$52$	3.42855e7	0.650273
$53$	−180207.	−0.00313711	−0.00156856	−	0.999999i	$-0.500499\pi$
$53$	−180207.	−0.00313711	−0.00156856	+	0.999999i	$0.500499\pi$
$54$	2.33217e7	0.373240
$55$	3.08583e7	0.454716
$56$	−3.11112e8	−4.22738
$57$	−1.36375e7	−0.171119
$58$	1.70982e7	0.198392
$59$	3.84564e7	0.413175	0.206588	−	0.978428i	$-0.433764\pi$
$59$	3.84564e7	0.413175	0.206588	+	0.978428i	$0.433764\pi$
$60$	−7.15733e7	−0.712969
$61$	−553620.	−0.00511950	−0.00255975	−	0.999997i	$-0.500815\pi$
$61$	−553620.	−0.00511950	−0.00255975	+	0.999997i	$0.500815\pi$
$62$	3.97290e6	0.0341464
$63$	−5.15793e7	−0.412518
$64$	5.42724e8	4.04361
$65$	−1.51567e7	−0.105316
$66$	−1.75502e8	−1.13850
$67$	−2.39163e8	−1.44996	−0.724982	−	0.688768i	$-0.758152\pi$
$67$	−2.39163e8	−1.44996	−0.724982	+	0.688768i	$0.758152\pi$
$68$	3.79211e8	2.15076
$69$	−1.71882e8	−0.912871
$70$	2.15621e8	1.07337
$71$	1.28653e8	0.600838	0.300419	−	0.953807i	$-0.402873\pi$
$71$	1.28653e8	0.600838	0.300419	+	0.953807i	$0.402873\pi$
$72$	2.59646e8	1.13864
$73$	−2.39376e8	−0.986569	−0.493284	−	0.869868i	$-0.664204\pi$
$73$	−2.39376e8	−0.986569	−0.493284	+	0.869868i	$0.664204\pi$
$74$	−1.45690e8	−0.564792
$75$	3.16406e7	0.115470
$76$	−2.38033e8	−0.818418
$77$	3.88148e8	1.25831
$78$	8.62015e7	0.263687
$79$	−5.28027e8	−1.52523	−0.762613	−	0.646855i	$-0.776084\pi$
$79$	−5.28027e8	−1.52523	−0.762613	+	0.646855i	$0.776084\pi$
$80$	−6.33003e8	−1.72783
$81$	4.30467e7	0.111111
$82$	1.02115e9	2.49418
$83$	2.12210e8	0.490812	0.245406	−	0.969420i	$-0.421079\pi$
$83$	2.12210e8	0.490812	0.245406	+	0.969420i	$0.421079\pi$
$84$	−9.00277e8	−1.97297
$85$	−1.67639e8	−0.348329
$86$	8.38797e8	1.65354
$87$	3.15595e7	0.0590601
$88$	−1.95391e9	−3.47322
$89$	−2.07724e8	−0.350939	−0.175469	−	0.984485i	$-0.556144\pi$
$89$	−2.07724e8	−0.350939	−0.175469	+	0.984485i	$0.556144\pi$
$90$	−1.79951e8	−0.289110
$91$	−1.90647e8	−0.291436
$92$	−3.00007e9	−4.36602
$93$	7.33311e6	0.0101652
$94$	2.75658e9	3.64162
$95$	1.05228e8	0.132548
$96$	1.95889e9	2.35391
$97$	1.70780e9	1.95868	0.979341	−	0.202214i	$-0.0648136\pi$
$97$	1.70780e9	1.95868	0.979341	+	0.202214i	$0.0648136\pi$
$98$	9.41288e8	1.03087
$99$	−3.23938e8	−0.338925
$100$	5.52263e8	0.552263
$101$	−1.81384e8	−0.173441	−0.0867206	−	0.996233i	$-0.527639\pi$
$101$	−1.81384e8	−0.173441	−0.0867206	+	0.996233i	$0.527639\pi$
$102$	9.53422e8	0.872136
$103$	−1.70453e9	−1.49223	−0.746116	−	0.665816i	$-0.768083\pi$
$103$	−1.70453e9	−1.49223	−0.746116	+	0.665816i	$0.768083\pi$
$104$	9.59703e8	0.804427
$105$	3.97988e8	0.319535
$106$	−7.90818e6	−0.00608415
$107$	1.73298e9	1.27811	0.639053	−	0.769163i	$-0.279326\pi$
$107$	1.73298e9	1.27811	0.639053	+	0.769163i	$0.279326\pi$
$108$	7.51348e8	0.531415
$109$	−1.17238e9	−0.795515	−0.397757	−	0.917491i	$-0.630211\pi$
$109$	−1.17238e9	−0.795515	−0.397757	+	0.917491i	$0.630211\pi$
$110$	1.35418e9	0.881881
$111$	−2.68913e8	−0.168135
$112$	−7.96217e9	−4.78135
$113$	−1.22180e9	−0.704935	−0.352467	−	0.935824i	$-0.614657\pi$
$113$	−1.22180e9	−0.704935	−0.352467	+	0.935824i	$0.614657\pi$
$114$	−5.98467e8	−0.331870
$115$	1.32625e9	0.707107
$116$	5.50848e8	0.282469
$117$	1.59109e8	0.0784980
$118$	1.68761e9	0.801317
$119$	−2.10863e9	−0.963916
$120$	−2.00344e9	−0.881985
$121$	7.97750e7	0.0338324
$122$	−2.42950e7	−0.00992881
$123$	1.88482e9	0.742501
$124$	1.27994e8	0.0486174
$125$	−2.44141e8	−0.0894427
$126$	−2.26350e9	−0.800042
$127$	−9.50324e8	−0.324157	−0.162078	−	0.986778i	$-0.551820\pi$
$127$	−9.50324e8	−0.324157	−0.162078	+	0.986778i	$0.551820\pi$
$128$	1.14347e10	3.76513
$129$	1.54823e9	0.492247
$130$	−6.65135e8	−0.204251
$131$	−4.03050e9	−1.19574	−0.597872	−	0.801592i	$-0.703987\pi$
$131$	−4.03050e9	−1.19574	−0.597872	+	0.801592i	$0.703987\pi$
$132$	−5.65410e9	−1.62099
$133$	1.32360e9	0.366795
$134$	−1.04954e10	−2.81207
$135$	−3.32151e8	−0.0860663
$136$	1.06147e10	2.66061
$137$	5.51871e9	1.33843	0.669214	−	0.743070i	$-0.266631\pi$
$137$	5.51871e9	1.33843	0.669214	+	0.743070i	$0.266631\pi$
$138$	−7.54284e9	−1.77043
$139$	−3.97776e9	−0.903798	−0.451899	−	0.892069i	$-0.649253\pi$
$139$	−3.97776e9	−0.903798	−0.451899	+	0.892069i	$0.649253\pi$
$140$	6.94658e9	1.52825
$141$	5.08804e9	1.08409
$142$	5.64579e9	1.16527
$143$	−1.19734e9	−0.239445
$144$	6.64502e9	1.28785
$145$	−2.43515e8	−0.0457478
$146$	−1.05047e10	−1.91336
$147$	1.73741e9	0.306884
$148$	−4.69367e9	−0.804145
$149$	−2.26538e9	−0.376533	−0.188266	−	0.982118i	$-0.560287\pi$
$149$	−2.26538e9	−0.376533	−0.188266	+	0.982118i	$0.560287\pi$
$150$	1.38851e9	0.223944
$151$	−8.49158e9	−1.32921	−0.664603	−	0.747197i	$-0.731399\pi$
$151$	−8.49158e9	−1.32921	−0.664603	+	0.747197i	$0.731399\pi$
$152$	−6.66288e9	−1.01243
$153$	1.75981e9	0.259629
$154$	1.70334e10	2.44039
$155$	−5.65826e7	−0.00787391
$156$	2.77713e9	0.375435
$157$	7.28379e9	0.956774	0.478387	−	0.878149i	$-0.341222\pi$
$157$	7.28379e9	0.956774	0.478387	+	0.878149i	$0.341222\pi$
$158$	−2.31719e10	−2.95804
$159$	−1.45968e7	−0.00181121
$160$	−1.51149e10	−1.82333
$161$	1.66821e10	1.95674
$162$	1.88906e9	0.215490
$163$	1.38419e10	1.53586	0.767929	−	0.640535i	$-0.221288\pi$
$163$	1.38419e10	1.53586	0.767929	+	0.640535i	$0.221288\pi$
$164$	3.28981e10	3.55119
$165$	2.49952e9	0.262530
$166$	9.31262e9	0.951887
$167$	−6.92038e9	−0.688503	−0.344252	−	0.938877i	$-0.611867\pi$
$167$	−6.92038e9	−0.688503	−0.344252	+	0.938877i	$0.611867\pi$
$168$	−2.52001e10	−2.44068
$169$	−1.00164e10	−0.944543
$170$	−7.35665e9	−0.675554
$171$	−1.10464e9	−0.0987957
$172$	2.70233e10	2.35429
$173$	3.26987e9	0.277539	0.138769	−	0.990325i	$-0.455685\pi$
$173$	3.26987e9	0.277539	0.138769	+	0.990325i	$0.455685\pi$
$174$	1.38495e9	0.114542
$175$	−3.07090e9	−0.247511
$176$	−5.00056e10	−3.92836
$177$	3.11497e9	0.238547
$178$	−9.11572e9	−0.680614
$179$	−1.12431e10	−0.818556	−0.409278	−	0.912410i	$-0.634219\pi$
$179$	−1.12431e10	−0.818556	−0.409278	+	0.912410i	$0.634219\pi$
$180$	−5.79744e9	−0.411633
$181$	3.75039e9	0.259731	0.129865	−	0.991532i	$-0.458546\pi$
$181$	3.75039e9	0.259731	0.129865	+	0.991532i	$0.458546\pi$
$182$	−8.36633e9	−0.565215
$183$	−4.48432e7	−0.00295574
$184$	−8.39764e10	−5.40103
$185$	2.07494e9	0.130237
$186$	3.21805e8	0.0197145
$187$	−1.32430e10	−0.791954
$188$	8.88079e10	5.18491
$189$	−4.17792e9	−0.238167
$190$	4.61780e9	0.257066
$191$	1.72426e10	0.937460	0.468730	−	0.883342i	$-0.344712\pi$
$191$	1.72426e10	0.937460	0.468730	+	0.883342i	$0.344712\pi$
$192$	4.39606e10	2.33458
$193$	−6.01060e9	−0.311824	−0.155912	−	0.987771i	$-0.549832\pi$
$193$	−6.01060e9	−0.311824	−0.155912	+	0.987771i	$0.549832\pi$
$194$	7.49448e10	3.79869
$195$	−1.22769e9	−0.0608043
$196$	3.03252e10	1.46775
$197$	−1.19077e10	−0.563289	−0.281645	−	0.959519i	$-0.590880\pi$
$197$	−1.19077e10	−0.563289	−0.281645	+	0.959519i	$0.590880\pi$
$198$	−1.42157e10	−0.657315
$199$	−6.10946e9	−0.276162	−0.138081	−	0.990421i	$-0.544093\pi$
$199$	−6.10946e9	−0.276162	−0.138081	+	0.990421i	$0.544093\pi$
$200$	1.54587e10	0.683183
$201$	−1.93722e10	−0.837137
$202$	−7.95982e9	−0.336374
$203$	−3.06303e9	−0.126596
$204$	3.07161e10	1.24174
$205$	−1.45434e10	−0.575139
$206$	−7.48012e10	−2.89405
$207$	−1.39224e10	−0.527046
$208$	2.45613e10	0.909842
$209$	8.31271e9	0.301359
$210$	1.74653e10	0.619710
$211$	−3.67892e10	−1.27776	−0.638881	−	0.769306i	$-0.720602\pi$
$211$	−3.67892e10	−1.27776	−0.638881	+	0.769306i	$0.720602\pi$
$212$	−2.54775e8	−0.00866256
$213$	1.04209e10	0.346894
$214$	7.60499e10	2.47877
$215$	−1.19463e10	−0.381293
$216$	2.10313e10	0.657393
$217$	−7.11719e8	−0.0217891
$218$	−5.14485e10	−1.54283
$219$	−1.93894e10	−0.569596
$220$	4.36273e10	1.25561
$221$	6.50459e9	0.183423
$222$	−1.18009e10	−0.326083
$223$	−5.01307e9	−0.135747	−0.0678737	−	0.997694i	$-0.521621\pi$
$223$	−5.01307e9	−0.135747	−0.0678737	+	0.997694i	$0.521621\pi$
$224$	−1.90121e11	−5.04562
$225$	2.56289e9	0.0666667
$226$	−5.36175e10	−1.36716
$227$	−2.73858e10	−0.684555	−0.342278	−	0.939599i	$-0.611198\pi$
$227$	−2.73858e10	−0.684555	−0.342278	+	0.939599i	$0.611198\pi$
$228$	−1.92806e10	−0.472514
$229$	5.36868e10	1.29005	0.645027	−	0.764159i	$-0.276846\pi$
$229$	5.36868e10	1.29005	0.645027	+	0.764159i	$0.276846\pi$
$230$	5.82009e10	1.37137
$231$	3.14400e10	0.726488
$232$	1.54191e10	0.349431
$233$	7.25874e10	1.61347	0.806733	−	0.590916i	$-0.201234\pi$
$233$	7.25874e10	1.61347	0.806733	+	0.590916i	$0.201234\pi$
$234$	6.98232e9	0.152240
$235$	−3.92596e10	−0.839731
$236$	5.43694e10	1.14091
$237$	−4.27702e10	−0.880590
$238$	−9.25348e10	−1.86943
$239$	1.73313e10	0.343589	0.171795	−	0.985133i	$-0.445043\pi$
$239$	1.73313e10	0.343589	0.171795	+	0.985133i	$0.445043\pi$
$240$	−5.12733e10	−0.997563
$241$	4.06448e10	0.776119	0.388059	−	0.921634i	$-0.373146\pi$
$241$	4.06448e10	0.776119	0.388059	+	0.921634i	$0.373146\pi$
$242$	3.50084e9	0.0656149
$243$	3.48678e9	0.0641500
$244$	−7.82704e8	−0.0141365
$245$	−1.34059e10	−0.237711
$246$	8.27132e10	1.44001
$247$	−4.08296e9	−0.0697973
$248$	3.58274e9	0.0601426
$249$	1.71890e10	0.283371
$250$	−1.07138e10	−0.173466
$251$	1.00920e11	1.60490	0.802448	−	0.596723i	$-0.203531\pi$
$251$	1.00920e11	1.60490	0.802448	+	0.596723i	$0.203531\pi$
$252$	−7.29224e10	−1.13909
$253$	1.04770e11	1.60766
$254$	−4.17039e10	−0.628673
$255$	−1.35788e10	−0.201108
$256$	2.23924e11	3.25852
$257$	5.03660e10	0.720176	0.360088	−	0.932918i	$-0.382747\pi$
$257$	5.03660e10	0.720176	0.360088	+	0.932918i	$0.382747\pi$
$258$	6.79425e10	0.954669
$259$	2.60995e10	0.360398
$260$	−2.14285e10	−0.290811
$261$	2.55632e9	0.0340984
$262$	−1.76874e11	−2.31904
$263$	−5.58677e10	−0.720046	−0.360023	−	0.932943i	$-0.617231\pi$
$263$	−5.58677e10	−0.720046	−0.360023	+	0.932943i	$0.617231\pi$
$264$	−1.58267e11	−2.00526
$265$	1.12629e8	0.00140296
$266$	5.80845e10	0.711366
$267$	−1.68256e10	−0.202614
$268$	−3.38127e11	−4.00381
$269$	−1.05175e11	−1.22469	−0.612345	−	0.790590i	$-0.709774\pi$
$269$	−1.05175e11	−1.22469	−0.612345	+	0.790590i	$0.709774\pi$
$270$	−1.45761e10	−0.166918
$271$	−5.44180e10	−0.612887	−0.306444	−	0.951889i	$-0.599139\pi$
$271$	−5.44180e10	−0.612887	−0.306444	+	0.951889i	$0.599139\pi$
$272$	2.71657e11	3.00927
$273$	−1.54424e10	−0.168261
$274$	2.42182e11	2.59576
$275$	−1.92864e10	−0.203355
$276$	−2.43005e11	−2.52072
$277$	1.64528e11	1.67912	0.839560	−	0.543268i	$-0.182813\pi$
$277$	1.64528e11	1.67912	0.839560	+	0.543268i	$0.182813\pi$
$278$	−1.74559e11	−1.75284
$279$	5.93982e8	0.00586887
$280$	1.94445e11	1.89054
$281$	−6.74255e10	−0.645128	−0.322564	−	0.946548i	$-0.604545\pi$
$281$	−6.74255e10	−0.645128	−0.322564	+	0.946548i	$0.604545\pi$
$282$	2.23283e11	2.10249
$283$	1.41917e11	1.31521	0.657603	−	0.753364i	$-0.271570\pi$
$283$	1.41917e11	1.31521	0.657603	+	0.753364i	$0.271570\pi$
$284$	1.81889e11	1.65910
$285$	8.52345e9	0.0765268
$286$	−5.25438e10	−0.464381
$287$	−1.82932e11	−1.59155
$288$	1.58670e11	1.35903
$289$	−4.66446e10	−0.393333
$290$	−1.06864e10	−0.0887237
$291$	1.38332e11	1.13085
$292$	−3.38428e11	−2.72423
$293$	2.79097e10	0.221233	0.110617	−	0.993863i	$-0.464717\pi$
$293$	2.79097e10	0.221233	0.110617	+	0.993863i	$0.464717\pi$
$294$	7.62443e10	0.595175
$295$	−2.40352e10	−0.184778
$296$	−1.31383e11	−0.994776
$297$	−2.62390e10	−0.195679
$298$	−9.94136e10	−0.730252
$299$	−5.14600e10	−0.372349
$300$	4.47333e10	0.318849
$301$	−1.50265e11	−1.05513
$302$	−3.72643e11	−2.57788
$303$	−1.46921e10	−0.100136
$304$	−1.70520e11	−1.14510
$305$	3.46012e8	0.00228951
$306$	7.72272e10	0.503528
$307$	1.59767e11	1.02651	0.513257	−	0.858235i	$-0.328439\pi$
$307$	1.59767e11	1.02651	0.513257	+	0.858235i	$0.328439\pi$
$308$	5.48761e11	3.47460
$309$	−1.38067e11	−0.861540
$310$	−2.48306e9	−0.0152707
$311$	−7.84292e10	−0.475396	−0.237698	−	0.971339i	$-0.576393\pi$
$311$	−7.84292e10	−0.475396	−0.237698	+	0.971339i	$0.576393\pi$
$312$	7.77359e10	0.464436
$313$	−1.26229e11	−0.743378	−0.371689	−	0.928357i	$-0.621221\pi$
$313$	−1.26229e11	−0.743378	−0.371689	+	0.928357i	$0.621221\pi$
$314$	3.19641e11	1.85558
$315$	3.22370e10	0.184484
$316$	−7.46521e11	−4.21163
$317$	−9.59499e10	−0.533676	−0.266838	−	0.963741i	$-0.585979\pi$
$317$	−9.59499e10	−0.533676	−0.266838	+	0.963741i	$0.585979\pi$
$318$	−6.40563e8	−0.00351269
$319$	−1.92370e10	−0.104011
$320$	−3.39202e11	−1.80836
$321$	1.40372e11	0.737915
$322$	7.32074e11	3.79493
$323$	−4.51591e10	−0.230852
$324$	6.08592e10	0.306813
$325$	9.47294e9	0.0470988
$326$	6.07435e11	2.97866
$327$	−9.49626e10	−0.459291
$328$	9.20867e11	4.39303
$329$	−4.93822e11	−2.32375
$330$	1.09689e11	0.509154
$331$	7.73728e10	0.354293	0.177146	−	0.984185i	$-0.443313\pi$
$331$	7.73728e10	0.354293	0.177146	+	0.984185i	$0.443313\pi$
$332$	3.00022e11	1.35529
$333$	−2.17819e10	−0.0970727
$334$	−3.03693e11	−1.33529
$335$	1.49477e11	0.648443
$336$	−6.44936e11	−2.76051
$337$	1.73809e11	0.734071	0.367035	−	0.930207i	$-0.380373\pi$
$337$	1.73809e11	0.734071	0.367035	+	0.930207i	$0.380373\pi$
$338$	−4.39558e11	−1.83186
$339$	−9.89662e10	−0.406994
$340$	−2.37007e11	−0.961847
$341$	−4.46987e9	−0.0179020
$342$	−4.84758e10	−0.191605
$343$	1.48614e11	0.579746
$344$	7.56421e11	2.91240
$345$	1.07426e11	0.408248
$346$	1.43495e11	0.538262
$347$	4.11335e11	1.52305	0.761523	−	0.648138i	$-0.224452\pi$
$347$	4.11335e11	1.52305	0.761523	+	0.648138i	$0.224452\pi$
$348$	4.46187e10	0.163084
$349$	2.97923e11	1.07495	0.537477	−	0.843278i	$-0.319377\pi$
$349$	2.97923e11	1.07495	0.537477	+	0.843278i	$0.319377\pi$
$350$	−1.34763e11	−0.480025
$351$	1.28878e10	0.0453208
$352$	−1.19404e12	−4.14549
$353$	5.69499e9	0.0195212	0.00976061	−	0.999952i	$-0.496893\pi$
$353$	5.69499e9	0.0195212	0.00976061	+	0.999952i	$0.496893\pi$
$354$	1.36697e11	0.462640
$355$	−8.04082e10	−0.268703
$356$	−2.93678e11	−0.969052
$357$	−1.70799e11	−0.556517
$358$	−4.93392e11	−1.58752
$359$	6.19565e11	1.96862	0.984310	−	0.176446i	$-0.0564602\pi$
$359$	6.19565e11	1.96862	0.984310	+	0.176446i	$0.0564602\pi$
$360$	−1.62279e11	−0.509214
$361$	−2.94341e11	−0.912155
$362$	1.64582e11	0.503724
$363$	6.46178e9	0.0195331
$364$	−2.69536e11	−0.804748
$365$	1.49610e11	0.441207
$366$	−1.96789e9	−0.00573240
$367$	−4.06833e9	−0.0117063	−0.00585314	−	0.999983i	$-0.501863\pi$
$367$	−4.06833e9	−0.0117063	−0.00585314	+	0.999983i	$0.501863\pi$
$368$	−2.14917e12	−6.10880
$369$	1.52670e11	0.428683
$370$	9.10565e10	0.252583
$371$	1.41670e9	0.00388235
$372$	1.03675e10	0.0280693
$373$	−6.75397e11	−1.80663	−0.903315	−	0.428978i	$-0.858874\pi$
$373$	−6.75397e11	−1.80663	−0.903315	+	0.428978i	$0.858874\pi$
$374$	−5.81155e11	−1.53592
$375$	−1.97754e10	−0.0516398
$376$	2.48586e12	6.41405
$377$	9.44867e9	0.0240899
$378$	−1.83343e11	−0.461904
$379$	−3.67146e11	−0.914033	−0.457017	−	0.889458i	$-0.651082\pi$
$379$	−3.67146e11	−0.914033	−0.457017	+	0.889458i	$0.651082\pi$
$380$	1.48770e11	0.366008
$381$	−7.69763e10	−0.187152
$382$	7.56672e11	1.81812
$383$	2.22057e11	0.527314	0.263657	−	0.964616i	$-0.415071\pi$
$383$	2.22057e11	0.527314	0.263657	+	0.964616i	$0.415071\pi$
$384$	9.26210e11	2.17380
$385$	−2.42593e11	−0.562735
$386$	−2.63768e11	−0.604756
$387$	1.25407e11	0.284199
$388$	2.41448e12	5.40854
$389$	−7.23043e11	−1.60100	−0.800499	−	0.599334i	$-0.795432\pi$
$389$	−7.23043e11	−1.60100	−0.800499	+	0.599334i	$0.795432\pi$
$390$	−5.38759e10	−0.117925
$391$	−5.69168e11	−1.23153
$392$	8.48847e11	1.81569
$393$	−3.26470e11	−0.690363
$394$	−5.22558e11	−1.09245
$395$	3.30017e11	0.682102
$396$	−4.57982e11	−0.935879
$397$	6.06161e11	1.22470	0.612352	−	0.790585i	$-0.290224\pi$
$397$	6.06161e11	1.22470	0.612352	+	0.790585i	$0.290224\pi$
$398$	−2.68107e11	−0.535592
$399$	1.07211e11	0.211769
$400$	3.95627e11	0.772709
$401$	6.72510e11	1.29882	0.649411	−	0.760438i	$-0.275016\pi$
$401$	6.72510e11	1.29882	0.649411	+	0.760438i	$0.275016\pi$
$402$	−8.50126e11	−1.62355
$403$	2.19547e9	0.00414625
$404$	−2.56439e11	−0.478926
$405$	−2.69042e10	−0.0496904
$406$	−1.34417e11	−0.245521
$407$	1.63915e11	0.296103
$408$	8.59789e11	1.53611
$409$	−3.02482e10	−0.0534497	−0.0267248	−	0.999643i	$-0.508508\pi$
$409$	−3.02482e10	−0.0534497	−0.0267248	+	0.999643i	$0.508508\pi$
$410$	−6.38219e11	−1.11543
$411$	4.47015e11	0.772742
$412$	−2.40985e12	−4.12052
$413$	−3.02325e11	−0.511326
$414$	−6.10970e11	−1.02216
$415$	−1.32632e11	−0.219498
$416$	5.86476e11	0.960130
$417$	−3.22198e11	−0.521808
$418$	3.64794e11	0.584459
$419$	−1.61938e11	−0.256676	−0.128338	−	0.991731i	$-0.540964\pi$
$419$	−1.61938e11	−0.256676	−0.128338	+	0.991731i	$0.540964\pi$
$420$	5.62673e11	0.882337
$421$	−8.06547e11	−1.25130	−0.625648	−	0.780105i	$-0.715165\pi$
$421$	−8.06547e11	−1.25130	−0.625648	+	0.780105i	$0.715165\pi$
$422$	−1.61445e12	−2.47810
$423$	4.12131e11	0.625899
$424$	−7.13154e9	−0.0107161
$425$	1.04774e11	0.155778
$426$	4.57309e11	0.672770
$427$	4.35228e9	0.00633565
$428$	2.45008e12	3.52925
$429$	−9.69844e10	−0.138243
$430$	−5.24248e11	−0.739484
$431$	8.54653e11	1.19300	0.596502	−	0.802611i	$-0.296557\pi$
$431$	8.54653e11	1.19300	0.596502	+	0.802611i	$0.296557\pi$
$432$	5.38246e11	0.743540
$433$	8.21884e11	1.12361	0.561804	−	0.827270i	$-0.310107\pi$
$433$	8.21884e11	1.12361	0.561804	+	0.827270i	$0.310107\pi$
$434$	−3.12330e10	−0.0422580
$435$	−1.97247e10	−0.0264125
$436$	−1.65750e12	−2.19667
$437$	3.57269e11	0.468629
$438$	−8.50883e11	−1.10468
$439$	9.97807e11	1.28220	0.641100	−	0.767457i	$-0.278478\pi$
$439$	9.97807e11	1.28220	0.641100	+	0.767457i	$0.278478\pi$
$440$	1.22119e12	1.55327
$441$	1.40730e11	0.177180
$442$	2.85447e11	0.355733
$443$	−2.22586e11	−0.274588	−0.137294	−	0.990530i	$-0.543840\pi$
$443$	−2.22586e11	−0.274588	−0.137294	+	0.990530i	$0.543840\pi$
$444$	−3.80187e11	−0.464273
$445$	1.29827e11	0.156945
$446$	−2.19993e11	−0.263270
$447$	−1.83496e11	−0.217391
$448$	−4.26662e12	−5.00418
$449$	1.28886e12	1.49657	0.748287	−	0.663375i	$-0.230877\pi$
$449$	1.28886e12	1.49657	0.748287	+	0.663375i	$0.230877\pi$
$450$	1.12470e11	0.129294
$451$	−1.14889e12	−1.30762
$452$	−1.72738e12	−1.94655
$453$	−6.87818e11	−0.767417
$454$	−1.20179e12	−1.32763
$455$	1.19154e11	0.130334
$456$	−5.39694e11	−0.584528
$457$	8.77644e11	0.941230	0.470615	−	0.882339i	$-0.344032\pi$
$457$	8.77644e11	0.941230	0.470615	+	0.882339i	$0.344032\pi$
$458$	2.35599e12	2.50195
$459$	1.42544e11	0.149897
$460$	1.87504e12	1.95254
$461$	−3.31142e11	−0.341476	−0.170738	−	0.985316i	$-0.554615\pi$
$461$	−3.31142e11	−0.341476	−0.170738	+	0.985316i	$0.554615\pi$
$462$	1.37971e12	1.40896
$463$	−1.05840e12	−1.07037	−0.535186	−	0.844735i	$-0.679758\pi$
$463$	−1.05840e12	−1.07037	−0.535186	+	0.844735i	$0.679758\pi$
$464$	3.94613e11	0.395222
$465$	−4.58319e9	−0.00454600
$466$	3.18542e12	3.12917
$467$	−1.49420e12	−1.45373	−0.726864	−	0.686782i	$-0.759023\pi$
$467$	−1.49420e12	−1.45373	−0.726864	+	0.686782i	$0.759023\pi$
$468$	2.24947e11	0.216758
$469$	1.88018e12	1.79441
$470$	−1.72286e12	−1.62858
$471$	5.89987e11	0.552394
$472$	1.52188e12	1.41137
$473$	−9.43722e11	−0.866900
$474$	−1.87692e12	−1.70783
$475$	−6.57674e10	−0.0592774
$476$	−2.98117e12	−2.66168
$477$	−1.18234e9	−0.00104570
$478$	7.60563e11	0.666361
$479$	1.04497e12	0.906970	0.453485	−	0.891264i	$-0.350181\pi$
$479$	1.04497e12	0.906970	0.453485	+	0.891264i	$0.350181\pi$
$480$	−1.22431e12	−1.05270
$481$	−8.05102e10	−0.0685801
$482$	1.78365e12	1.50521
$483$	1.35125e12	1.12973
$484$	1.12785e11	0.0934219
$485$	−1.06737e12	−0.875950
$486$	1.53014e11	0.124413
$487$	−2.30343e12	−1.85564	−0.927820	−	0.373027i	$-0.878320\pi$
$487$	−2.30343e12	−1.85564	−0.927820	+	0.373027i	$0.878320\pi$
$488$	−2.19091e10	−0.0174878
$489$	1.12119e12	0.886728
$490$	−5.88305e11	−0.461020
$491$	−5.37950e11	−0.417711	−0.208855	−	0.977947i	$-0.566974\pi$
$491$	−5.37950e11	−0.417711	−0.208855	+	0.977947i	$0.566974\pi$
$492$	2.66475e12	2.05028
$493$	1.04506e11	0.0796764
$494$	−1.79176e11	−0.135366
$495$	2.02461e11	0.151572
$496$	9.16915e10	0.0680239
$497$	−1.01141e12	−0.743570
$498$	7.54322e11	0.549572
$499$	−1.01572e12	−0.733364	−0.366682	−	0.930346i	$-0.619506\pi$
$499$	−1.01572e12	−0.733364	−0.366682	+	0.930346i	$0.619506\pi$
$500$	−3.45164e11	−0.246980
$501$	−5.60551e11	−0.397508
$502$	4.42877e12	3.11255
$503$	−1.07349e12	−0.747723	−0.373861	−	0.927485i	$-0.621966\pi$
$503$	−1.07349e12	−0.747723	−0.373861	+	0.927485i	$0.621966\pi$
$504$	−2.04121e12	−1.40913
$505$	1.13365e11	0.0775653
$506$	4.59772e12	3.11792
$507$	−8.11329e11	−0.545332
$508$	−1.34356e12	−0.895099
$509$	−1.48831e12	−0.982799	−0.491400	−	0.870934i	$-0.663515\pi$
$509$	−1.48831e12	−0.982799	−0.491400	+	0.870934i	$0.663515\pi$
$510$	−5.95889e11	−0.390031
$511$	1.88185e12	1.22093
$512$	3.97208e12	2.55449
$513$	−8.94758e10	−0.0570397
$514$	2.21026e12	1.39672
$515$	1.06533e12	0.667346
$516$	2.18888e12	1.35925
$517$	−3.10140e12	−1.90919
$518$	1.14534e12	0.698960
$519$	2.64860e11	0.160237
$520$	−5.99814e11	−0.359751
$521$	−9.98544e11	−0.593742	−0.296871	−	0.954918i	$-0.595943\pi$
$521$	−9.98544e11	−0.593742	−0.296871	+	0.954918i	$0.595943\pi$
$522$	1.12181e11	0.0661307
$523$	−1.59973e12	−0.934954	−0.467477	−	0.884005i	$-0.654837\pi$
$523$	−1.59973e12	−0.934954	−0.467477	+	0.884005i	$0.654837\pi$
$524$	−5.69829e12	−3.30182
$525$	−2.48743e11	−0.142900
$526$	−2.45169e12	−1.39646
$527$	2.42828e10	0.0137136
$528$	−4.05045e12	−2.26804
$529$	2.70173e12	1.50000
$530$	4.94261e9	0.00272092
$531$	2.52312e11	0.137725
$532$	1.87129e12	1.01284
$533$	5.64300e11	0.302857
$534$	−7.38373e11	−0.392953
$535$	−1.08311e12	−0.571586
$536$	−9.46467e12	−4.95295
$537$	−9.10693e11	−0.472593
$538$	−4.61548e12	−2.37518
$539$	−1.05903e12	−0.540456
$540$	−4.69592e11	−0.237656
$541$	5.11810e11	0.256875	0.128437	−	0.991718i	$-0.459004\pi$
$541$	5.11810e11	0.256875	0.128437	+	0.991718i	$0.459004\pi$
$542$	−2.38807e12	−1.18864
$543$	3.03782e11	0.149956
$544$	6.48665e12	3.17560
$545$	7.32736e11	0.355765
$546$	−6.77673e11	−0.326327
$547$	1.40910e12	0.672977	0.336489	−	0.941688i	$-0.390761\pi$
$547$	1.40910e12	0.672977	0.336489	+	0.941688i	$0.390761\pi$
$548$	7.80231e12	3.69582
$549$	−3.63230e9	−0.00170650
$550$	−8.46364e11	−0.394389
$551$	−6.55988e10	−0.0303189
$552$	−6.80208e12	−3.11829
$553$	4.15108e12	1.88755
$554$	7.22013e12	3.25650
$555$	1.68070e11	0.0751922
$556$	−5.62372e12	−2.49567
$557$	2.36835e12	1.04255	0.521276	−	0.853388i	$-0.325456\pi$
$557$	2.36835e12	1.04255	0.521276	+	0.853388i	$0.325456\pi$
$558$	2.60662e10	0.0113821
$559$	4.63529e11	0.200781
$560$	4.97635e12	2.13828
$561$	−1.07269e12	−0.457235
$562$	−2.95889e12	−1.25117
$563$	−2.36245e12	−0.991005	−0.495502	−	0.868607i	$-0.665016\pi$
$563$	−2.36245e12	−0.991005	−0.495502	+	0.868607i	$0.665016\pi$
$564$	7.19344e12	2.99351
$565$	7.63628e11	0.315256
$566$	6.22784e12	2.55073
$567$	−3.38412e11	−0.137506
$568$	5.09134e12	2.05241
$569$	2.25679e11	0.0902582	0.0451291	−	0.998981i	$-0.485630\pi$
$569$	2.25679e11	0.0902582	0.0451291	+	0.998981i	$0.485630\pi$
$570$	3.74042e11	0.148417
$571$	−9.15389e11	−0.360366	−0.180183	−	0.983633i	$-0.557669\pi$
$571$	−9.15389e11	−0.360366	−0.180183	+	0.983633i	$0.557669\pi$
$572$	−1.69279e12	−0.661182
$573$	1.39665e12	0.541243
$574$	−8.02777e12	−3.08668
$575$	−8.28906e11	−0.316228
$576$	3.56081e12	1.34787
$577$	2.22404e12	0.835318	0.417659	−	0.908604i	$-0.362851\pi$
$577$	2.22404e12	0.835318	0.417659	+	0.908604i	$0.362851\pi$
$578$	−2.04694e12	−0.762835
$579$	−4.86859e11	−0.180032
$580$	−3.44280e11	−0.126324
$581$	−1.66829e12	−0.607407
$582$	6.07053e12	2.19318
$583$	8.89741e9	0.00318974
$584$	−9.47310e12	−3.37003
$585$	−9.94432e10	−0.0351054
$586$	1.22478e12	0.429062
$587$	5.60186e12	1.94742	0.973712	−	0.227783i	$-0.0731477\pi$
$587$	5.60186e12	1.94742	0.973712	+	0.227783i	$0.0731477\pi$
$588$	2.45634e12	0.847404
$589$	−1.52424e10	−0.00521837
$590$	−1.05476e12	−0.358360
$591$	−9.64527e11	−0.325215
$592$	−3.36242e12	−1.12513
$593$	2.78326e12	0.924289	0.462145	−	0.886805i	$-0.347080\pi$
$593$	2.78326e12	0.924289	0.462145	+	0.886805i	$0.347080\pi$
$594$	−1.15147e12	−0.379501
$595$	1.31789e12	0.431076
$596$	−3.20278e12	−1.03973
$597$	−4.94867e11	−0.159442
$598$	−2.25826e12	−0.722137
$599$	−1.36720e12	−0.433922	−0.216961	−	0.976180i	$-0.569614\pi$
$599$	−1.36720e12	−0.433922	−0.216961	+	0.976180i	$0.569614\pi$
$600$	1.25215e12	0.394436
$601$	4.74171e12	1.48252	0.741259	−	0.671219i	$-0.234229\pi$
$601$	4.74171e12	1.48252	0.741259	+	0.671219i	$0.234229\pi$
$602$	−6.59420e12	−2.04634
$603$	−1.56915e12	−0.483321
$604$	−1.20053e13	−3.67036
$605$	−4.98594e10	−0.0151303
$606$	−6.44746e11	−0.194206
$607$	−5.74836e12	−1.71868	−0.859339	−	0.511406i	$-0.829125\pi$
$607$	−5.74836e12	−1.71868	−0.859339	+	0.511406i	$0.829125\pi$
$608$	−4.07170e12	−1.20840
$609$	−2.48105e11	−0.0730900
$610$	1.51844e10	0.00444030
$611$	1.52332e12	0.442186
$612$	2.48800e12	0.716918
$613$	2.99054e12	0.855416	0.427708	−	0.903917i	$-0.359321\pi$
$613$	2.99054e12	0.855416	0.427708	+	0.903917i	$0.359321\pi$
$614$	7.01120e12	1.99083
$615$	−1.17801e12	−0.332056
$616$	1.53606e13	4.29829
$617$	6.27174e12	1.74223	0.871114	−	0.491081i	$-0.163398\pi$
$617$	6.27174e12	1.74223	0.871114	+	0.491081i	$0.163398\pi$
$618$	−6.05890e12	−1.67088
$619$	−2.67240e12	−0.731632	−0.365816	−	0.930687i	$-0.619210\pi$
$619$	−2.67240e12	−0.731632	−0.365816	+	0.930687i	$0.619210\pi$
$620$	−7.99961e10	−0.0217423
$621$	−1.12772e12	−0.304290
$622$	−3.44177e12	−0.921989
$623$	1.63302e12	0.434305
$624$	1.98946e12	0.525297
$625$	1.52588e11	0.0400000
$626$	−5.53942e12	−1.44172
$627$	6.73329e11	0.173990
$628$	1.02978e13	2.64195
$629$	−8.90474e11	−0.226826
$630$	1.41469e12	0.357790
$631$	2.73608e12	0.687064	0.343532	−	0.939141i	$-0.388377\pi$
$631$	2.73608e12	0.687064	0.343532	+	0.939141i	$0.388377\pi$
$632$	−2.08962e13	−5.21004
$633$	−2.97993e12	−0.737716
$634$	−4.21065e12	−1.03502
$635$	5.93953e11	0.144967
$636$	−2.06368e10	−0.00500133
$637$	5.20167e11	0.125174
$638$	−8.44195e11	−0.201720
$639$	8.44093e11	0.200279
$640$	−7.14668e12	−1.68382
$641$	−2.58542e12	−0.604882	−0.302441	−	0.953168i	$-0.597802\pi$
$641$	−2.58542e12	−0.604882	−0.302441	+	0.953168i	$0.597802\pi$
$642$	6.16004e12	1.43112
$643$	−4.53865e12	−1.04707	−0.523537	−	0.852003i	$-0.675388\pi$
$643$	−4.53865e12	−1.04707	−0.523537	+	0.852003i	$0.675388\pi$
$644$	2.35850e13	5.40319
$645$	−9.67647e11	−0.220140
$646$	−1.98176e12	−0.447717
$647$	2.68597e12	0.602604	0.301302	−	0.953529i	$-0.402579\pi$
$647$	2.68597e12	0.602604	0.301302	+	0.953529i	$0.402579\pi$
$648$	1.70354e12	0.379546
$649$	−1.89872e12	−0.420106
$650$	4.15709e11	0.0913439
$651$	−5.76492e10	−0.0125799
$652$	1.95696e13	4.24099
$653$	−6.39120e12	−1.37554	−0.687770	−	0.725929i	$-0.741410\pi$
$653$	−6.39120e12	−1.37554	−0.687770	+	0.725929i	$0.741410\pi$
$654$	−4.16732e12	−0.890753
$655$	2.51906e12	0.534753
$656$	2.35674e13	4.96871
$657$	−1.57054e12	−0.328856
$658$	−2.16708e13	−4.50670
$659$	−4.23105e12	−0.873904	−0.436952	−	0.899485i	$-0.643942\pi$
$659$	−4.23105e12	−0.873904	−0.436952	+	0.899485i	$0.643942\pi$
$660$	3.53381e12	0.724929
$661$	−3.77872e12	−0.769907	−0.384953	−	0.922936i	$-0.625782\pi$
$661$	−3.77872e12	−0.769907	−0.384953	+	0.922936i	$0.625782\pi$
$662$	3.39542e12	0.687120
$663$	5.26872e11	0.105900
$664$	8.39806e12	1.67657
$665$	−8.27248e11	−0.164036
$666$	−9.55875e11	−0.188264
$667$	−8.26782e11	−0.161743
$668$	−9.78399e12	−1.90117
$669$	−4.06058e11	−0.0783738
$670$	6.55962e12	1.25760
$671$	2.73340e10	0.00520538
$672$	−1.53998e13	−2.91309
$673$	2.75736e12	0.518114	0.259057	−	0.965862i	$-0.416588\pi$
$673$	2.75736e12	0.518114	0.259057	+	0.965862i	$0.416588\pi$
$674$	7.62742e12	1.42367
$675$	2.07594e11	0.0384900
$676$	−1.41611e13	−2.60818
$677$	−2.40567e12	−0.440136	−0.220068	−	0.975485i	$-0.570628\pi$
$677$	−2.40567e12	−0.440136	−0.220068	+	0.975485i	$0.570628\pi$
$678$	−4.34302e12	−0.789329
$679$	−1.34259e13	−2.42397
$680$	−6.63418e12	−1.18986
$681$	−2.21825e12	−0.395228
$682$	−1.96155e11	−0.0347193
$683$	−7.88192e11	−0.138592	−0.0692961	−	0.997596i	$-0.522075\pi$
$683$	−7.88192e11	−0.138592	−0.0692961	+	0.997596i	$0.522075\pi$
$684$	−1.56173e12	−0.272806
$685$	−3.44919e12	−0.598563
$686$	6.52178e12	1.12436
$687$	4.34863e12	0.744813
$688$	1.93588e13	3.29405
$689$	−4.37015e9	−0.000738771 0
$690$	4.71428e12	0.791761
$691$	3.54288e12	0.591161	0.295580	−	0.955318i	$-0.404487\pi$
$691$	3.54288e12	0.591161	0.295580	+	0.955318i	$0.404487\pi$
$692$	4.62293e12	0.766372
$693$	2.54664e12	0.419438
$694$	1.80510e13	2.95381
$695$	2.48610e12	0.404191
$696$	1.24894e12	0.201744
$697$	6.24137e12	1.00169
$698$	1.30740e13	2.08478
$699$	5.87958e12	0.931535
$700$	−4.34161e12	−0.683455
$701$	−3.66998e12	−0.574027	−0.287014	−	0.957926i	$-0.592663\pi$
$701$	−3.66998e12	−0.574027	−0.287014	+	0.957926i	$0.592663\pi$
$702$	5.65568e11	0.0878957
$703$	5.58955e11	0.0863133
$704$	−2.67961e13	−4.11144
$705$	−3.18003e12	−0.484819
$706$	2.49918e11	0.0378597
$707$	1.42595e12	0.214643
$708$	4.40392e12	0.658703
$709$	6.68373e12	0.993369	0.496685	−	0.867931i	$-0.334551\pi$
$709$	6.68373e12	0.993369	0.496685	+	0.867931i	$0.334551\pi$
$710$	−3.52862e12	−0.521126
$711$	−3.46438e12	−0.508409
$712$	−8.22050e12	−1.19878
$713$	−1.92109e11	−0.0278385
$714$	−7.49532e12	−1.07932
$715$	7.48337e11	0.107083
$716$	−1.58954e13	−2.26029
$717$	1.40383e12	0.198371
$718$	2.71889e13	3.81796
$719$	−1.23056e13	−1.71721	−0.858604	−	0.512640i	$-0.828668\pi$
$719$	−1.23056e13	−1.71721	−0.858604	+	0.512640i	$0.828668\pi$
$720$	−4.15314e12	−0.575944
$721$	1.34001e13	1.84672
$722$	−1.29168e13	−1.76904
$723$	3.29223e12	0.448092
$724$	5.30228e12	0.717198
$725$	1.52197e11	0.0204590
$726$	2.83568e11	0.0378828
$727$	−1.07672e13	−1.42954	−0.714770	−	0.699360i	$-0.753469\pi$
$727$	−1.07672e13	−1.42954	−0.714770	+	0.699360i	$0.753469\pi$
$728$	−7.54470e12	−0.995522
$729$	2.82430e11	0.0370370
$730$	6.56546e12	0.855681
$731$	5.12681e12	0.664078
$732$	−6.33990e10	−0.00816174
$733$	−1.06410e13	−1.36149	−0.680744	−	0.732521i	$-0.738343\pi$
$733$	−1.06410e13	−1.36149	−0.680744	+	0.732521i	$0.738343\pi$
$734$	−1.78534e11	−0.0227033
$735$	−1.08588e12	−0.137243
$736$	−5.13181e13	−6.44644
$737$	1.18083e13	1.47429
$738$	6.69977e12	0.831393
$739$	−4.24704e12	−0.523825	−0.261912	−	0.965092i	$-0.584353\pi$
$739$	−4.24704e12	−0.523825	−0.261912	+	0.965092i	$0.584353\pi$
$740$	2.93354e12	0.359625
$741$	−3.30720e11	−0.0402975
$742$	6.21701e10	0.00752947
$743$	1.10732e13	1.33298	0.666488	−	0.745516i	$-0.267797\pi$
$743$	1.10732e13	1.33298	0.666488	+	0.745516i	$0.267797\pi$
$744$	2.90202e11	0.0347234
$745$	1.41586e12	0.168391
$746$	−2.96390e13	−3.50380
$747$	1.39231e12	0.163604
$748$	−1.87229e13	−2.18684
$749$	−1.36238e13	−1.58172
$750$	−8.67821e11	−0.100151
$751$	1.45365e13	1.66755	0.833777	−	0.552102i	$-0.186174\pi$
$751$	1.45365e13	1.66755	0.833777	+	0.552102i	$0.186174\pi$
$752$	6.36197e13	7.25456
$753$	8.17454e12	0.926587
$754$	4.14644e11	0.0467202
$755$	5.30724e12	0.594439
$756$	−5.90672e12	−0.657655
$757$	−5.75556e12	−0.637025	−0.318512	−	0.947919i	$-0.603183\pi$
$757$	−5.75556e12	−0.637025	−0.318512	+	0.947919i	$0.603183\pi$
$758$	−1.61118e13	−1.77269
$759$	8.48638e12	0.928184
$760$	4.16430e12	0.452774
$761$	−1.44303e13	−1.55971	−0.779854	−	0.625961i	$-0.784707\pi$
$761$	−1.44303e13	−1.55971	−0.779854	+	0.625961i	$0.784707\pi$
$762$	−3.37802e12	−0.362965
$763$	9.21664e12	0.984492
$764$	2.43775e13	2.58862
$765$	−1.09988e12	−0.116110
$766$	9.74471e12	1.02268
$767$	9.32595e11	0.0973003
$768$	1.81378e13	1.88131
$769$	2.65690e12	0.273973	0.136986	−	0.990573i	$-0.456258\pi$
$769$	2.65690e12	0.273973	0.136986	+	0.990573i	$0.456258\pi$
$770$	−1.06459e13	−1.09137
$771$	4.07965e12	0.415794
$772$	−8.49775e12	−0.861046
$773$	−4.35569e12	−0.438783	−0.219391	−	0.975637i	$-0.570407\pi$
$773$	−4.35569e12	−0.438783	−0.219391	+	0.975637i	$0.570407\pi$
$774$	5.50334e12	0.551179
$775$	3.53641e10	0.00352132
$776$	6.75848e13	6.69069
$777$	2.11406e12	0.208076
$778$	−3.17299e13	−3.10499
$779$	−3.91774e12	−0.381168
$780$	−1.73570e12	−0.167900
$781$	−6.35203e12	−0.610918
$782$	−2.49773e13	−2.38844
$783$	2.07062e11	0.0196867
$784$	2.17242e13	2.05363
$785$	−4.55237e12	−0.427882
$786$	−1.43268e13	−1.33890
$787$	−2.02013e13	−1.87713	−0.938564	−	0.345106i	$-0.887843\pi$
$787$	−2.02013e13	−1.87713	−0.938564	+	0.345106i	$0.887843\pi$
$788$	−1.68351e13	−1.55542
$789$	−4.52529e12	−0.415719
$790$	1.44824e13	1.32288
$791$	9.60521e12	0.872394
$792$	−1.28196e13	−1.15774
$793$	−1.34257e10	−0.00120561
$794$	2.66007e13	2.37520
$795$	9.12298e9	0.000809999 0
$796$	−8.63752e12	−0.762571
$797$	−2.07284e12	−0.181971	−0.0909857	−	0.995852i	$-0.529002\pi$
$797$	−2.07284e12	−0.181971	−0.0909857	+	0.995852i	$0.529002\pi$
$798$	4.70485e12	0.410707
$799$	1.68485e13	1.46251
$800$	9.44681e12	0.815418
$801$	−1.36288e12	−0.116980
$802$	2.95124e13	2.51895
$803$	1.18188e13	1.00312
$804$	−2.73883e13	−2.31160
$805$	−1.04263e13	−0.875082
$806$	9.63458e10	0.00804128
$807$	−8.51916e12	−0.707075
$808$	−7.17812e12	−0.592460
$809$	1.41673e13	1.16284	0.581418	−	0.813605i	$-0.302498\pi$
$809$	1.41673e13	1.16284	0.581418	+	0.813605i	$0.302498\pi$
$810$	−1.18066e12	−0.0963701
$811$	2.04580e12	0.166062	0.0830310	−	0.996547i	$-0.473540\pi$
$811$	2.04580e12	0.166062	0.0830310	+	0.996547i	$0.473540\pi$
$812$	−4.33049e12	−0.349570
$813$	−4.40786e12	−0.353851
$814$	7.19322e12	0.574266
$815$	−8.65117e12	−0.686856
$816$	2.20042e13	1.73740
$817$	−3.21812e12	−0.252699
$818$	−1.32741e12	−0.103661
$819$	−1.25084e12	−0.0971455
$820$	−2.05613e13	−1.58814
$821$	−1.27265e13	−0.977607	−0.488804	−	0.872394i	$-0.662567\pi$
$821$	−1.27265e13	−0.977607	−0.488804	+	0.872394i	$0.662567\pi$
$822$	1.96168e13	1.49866
$823$	6.94698e12	0.527833	0.263917	−	0.964546i	$-0.414986\pi$
$823$	6.94698e12	0.527833	0.263917	+	0.964546i	$0.414986\pi$
$824$	−6.74552e13	−5.09733
$825$	−1.56220e12	−0.117407
$826$	−1.32672e13	−0.991672
$827$	5.09129e11	0.0378489	0.0189244	−	0.999821i	$-0.493976\pi$
$827$	5.09129e11	0.0378489	0.0189244	+	0.999821i	$0.493976\pi$
$828$	−1.96834e13	−1.45534
$829$	−1.87663e13	−1.38001	−0.690006	−	0.723804i	$-0.742392\pi$
$829$	−1.87663e13	−1.38001	−0.690006	+	0.723804i	$0.742392\pi$
$830$	−5.82039e12	−0.425697
$831$	1.33268e13	0.969440
$832$	1.31615e13	0.952245
$833$	5.75324e12	0.414009
$834$	−1.41393e13	−1.01200
$835$	4.32524e12	0.307908
$836$	1.17525e13	0.832147
$837$	4.81125e10	0.00338839
$838$	−7.10645e12	−0.497800
$839$	6.68721e12	0.465925	0.232962	−	0.972486i	$-0.425158\pi$
$839$	6.68721e12	0.465925	0.232962	+	0.972486i	$0.425158\pi$
$840$	1.57501e13	1.09150
$841$	−1.43553e13	−0.989536
$842$	−3.53944e13	−2.42678
$843$	−5.46147e12	−0.372465
$844$	−5.20124e13	−3.52830
$845$	6.26025e12	0.422412
$846$	1.80859e13	1.21387
$847$	−6.27151e11	−0.0418694
$848$	−1.82515e11	−0.0121204
$849$	1.14952e13	0.759335
$850$	4.59791e12	0.302117
$851$	7.04484e12	0.460456
$852$	1.47330e13	0.957884
$853$	9.37029e12	0.606014	0.303007	−	0.952988i	$-0.402009\pi$
$853$	9.37029e12	0.606014	0.303007	+	0.952988i	$0.402009\pi$
$854$	1.90995e11	0.0122874
$855$	6.90399e11	0.0441828
$856$	6.85813e13	4.36590
$857$	8.81996e12	0.558538	0.279269	−	0.960213i	$-0.409908\pi$
$857$	8.81996e12	0.558538	0.279269	+	0.960213i	$0.409908\pi$
$858$	−4.25605e12	−0.268111
$859$	1.98932e13	1.24663	0.623313	−	0.781973i	$-0.285786\pi$
$859$	1.98932e13	1.24663	0.623313	+	0.781973i	$0.285786\pi$
$860$	−1.68895e13	−1.05287
$861$	−1.48175e13	−0.918884
$862$	3.75055e13	2.31373
$863$	−1.20953e13	−0.742278	−0.371139	−	0.928577i	$-0.621033\pi$
$863$	−1.20953e13	−0.742278	−0.371139	+	0.928577i	$0.621033\pi$
$864$	1.28523e13	0.784636
$865$	−2.04367e12	−0.124119
$866$	3.60674e13	2.17914
$867$	−3.77821e12	−0.227091
$868$	−1.00622e12	−0.0601666
$869$	2.60704e13	1.55081
$870$	−8.65597e11	−0.0512246
$871$	−5.79987e12	−0.341458
$872$	−4.63959e13	−2.71741
$873$	1.12049e13	0.652894
$874$	1.56783e13	0.908864
$875$	1.91931e12	0.110690
$876$	−2.74127e13	−1.57283
$877$	−2.52693e13	−1.44243	−0.721216	−	0.692710i	$-0.756416\pi$
$877$	−2.52693e13	−1.44243	−0.721216	+	0.692710i	$0.756416\pi$
$878$	4.37876e13	2.48671
$879$	2.26068e12	0.127729
$880$	3.12535e13	1.75682
$881$	4.23113e12	0.236628	0.118314	−	0.992976i	$-0.462251\pi$
$881$	4.23113e12	0.236628	0.118314	+	0.992976i	$0.462251\pi$
$882$	6.17579e12	0.343624
$883$	5.41348e12	0.299677	0.149839	−	0.988710i	$-0.452125\pi$
$883$	5.41348e12	0.299677	0.149839	+	0.988710i	$0.452125\pi$
$884$	9.19615e12	0.506490
$885$	−1.94685e12	−0.106681
$886$	−9.76794e12	−0.532539
$887$	−6.28957e12	−0.341165	−0.170583	−	0.985343i	$-0.554565\pi$
$887$	−6.28957e12	−0.341165	−0.170583	+	0.985343i	$0.554565\pi$
$888$	−1.06420e13	−0.574334
$889$	7.47097e12	0.401161
$890$	5.69733e12	0.304380
$891$	−2.12536e12	−0.112975
$892$	−7.08744e12	−0.374841
$893$	−1.05759e13	−0.556525
$894$	−8.05250e12	−0.421611
$895$	7.02695e12	0.366069
$896$	−8.98938e13	−4.65955
$897$	−4.16826e12	−0.214976
$898$	5.65603e13	2.90247
$899$	3.52735e10	0.00180107
$900$	3.62340e12	0.184088
$901$	−4.83356e10	−0.00244346
$902$	−5.04176e13	−2.53602
$903$	−1.21714e13	−0.609182
$904$	−4.83519e13	−2.40800
$905$	−2.34400e12	−0.116155
$906$	−3.01841e13	−1.48834
$907$	−1.27094e13	−0.623580	−0.311790	−	0.950151i	$-0.600928\pi$
$907$	−1.27094e13	−0.623580	−0.311790	+	0.950151i	$0.600928\pi$
$908$	−3.87178e13	−1.89027
$909$	−1.19006e12	−0.0578138
$910$	5.22896e12	0.252772
$911$	9.10912e12	0.438171	0.219086	−	0.975706i	$-0.429693\pi$
$911$	9.10912e12	0.438171	0.219086	+	0.975706i	$0.429693\pi$
$912$	−1.38122e13	−0.661127
$913$	−1.04775e13	−0.499046
$914$	3.85144e13	1.82543
$915$	2.80270e10	0.00132185
$916$	7.59021e13	3.56225
$917$	3.16858e13	1.47980
$918$	6.25540e12	0.290712
$919$	−6.78526e12	−0.313795	−0.156898	−	0.987615i	$-0.550149\pi$
$919$	−6.78526e12	−0.313795	−0.156898	+	0.987615i	$0.550149\pi$
$920$	5.24852e13	2.41542
$921$	1.29411e13	0.592658
$922$	−1.45318e13	−0.662263
$923$	3.11993e12	0.141494
$924$	4.44496e13	2.00606
$925$	−1.29684e12	−0.0582436
$926$	−4.64466e13	−2.07589
$927$	−1.11834e13	−0.497410
$928$	9.42261e12	0.417066
$929$	3.16131e12	0.139250	0.0696252	−	0.997573i	$-0.477820\pi$
$929$	3.16131e12	0.139250	0.0696252	+	0.997573i	$0.477820\pi$
$930$	−2.01128e11	−0.00881657
$931$	−3.61134e12	−0.157541
$932$	1.02624e14	4.45529
$933$	−6.35276e12	−0.274470
$934$	−6.55713e13	−2.81938
$935$	8.27689e12	0.354173
$936$	6.29661e12	0.268142
$937$	3.75670e13	1.59213	0.796065	−	0.605211i	$-0.206911\pi$
$937$	3.75670e13	1.59213	0.796065	+	0.605211i	$0.206911\pi$
$938$	8.25094e13	3.48009
$939$	−1.02246e13	−0.429190
$940$	−5.55049e13	−2.31876
$941$	−3.13713e13	−1.30431	−0.652153	−	0.758087i	$-0.726134\pi$
$941$	−3.13713e13	−1.30431	−0.652153	+	0.758087i	$0.726134\pi$
$942$	2.58909e13	1.07132
$943$	−4.93776e13	−2.03342
$944$	3.89488e13	1.59632
$945$	2.61120e12	0.106512
$946$	−4.14142e13	−1.68127
$947$	−1.78574e13	−0.721513	−0.360757	−	0.932660i	$-0.617481\pi$
$947$	−1.78574e13	−0.721513	−0.360757	+	0.932660i	$0.617481\pi$
$948$	−6.04682e13	−2.43159
$949$	−5.80504e12	−0.232331
$950$	−2.88613e12	−0.114963
$951$	−7.77194e12	−0.308118
$952$	−8.34473e13	−3.29265
$953$	8.76602e12	0.344258	0.172129	−	0.985074i	$-0.444935\pi$
$953$	8.76602e12	0.344258	0.172129	+	0.985074i	$0.444935\pi$
$954$	−5.18856e10	−0.00202805
$955$	−1.07766e13	−0.419245
$956$	2.45028e13	0.948758
$957$	−1.55820e12	−0.0600509
$958$	4.58572e13	1.75899
$959$	−4.33853e13	−1.65638
$960$	−2.74754e13	−1.04406
$961$	−2.64314e13	−0.999690
$962$	−3.53310e12	−0.133005
$963$	1.13701e13	0.426035
$964$	5.74633e13	2.14311
$965$	3.75663e12	0.139452
$966$	5.92980e13	2.19100
$967$	2.92145e13	1.07443	0.537217	−	0.843444i	$-0.319476\pi$
$967$	2.92145e13	1.07443	0.537217	+	0.843444i	$0.319476\pi$
$968$	3.15703e12	0.115569
$969$	−3.65789e12	−0.133283
$970$	−4.68405e13	−1.69883
$971$	1.10119e13	0.397536	0.198768	−	0.980047i	$-0.436306\pi$
$971$	1.10119e13	0.397536	0.198768	+	0.980047i	$0.436306\pi$
$972$	4.92959e12	0.177138
$973$	3.12711e13	1.11850
$974$	−1.01083e14	−3.59885
$975$	7.67308e11	0.0271925
$976$	−5.60709e11	−0.0197794
$977$	8.77989e12	0.308293	0.154146	−	0.988048i	$-0.450737\pi$
$977$	8.77989e12	0.308293	0.154146	+	0.988048i	$0.450737\pi$
$978$	4.92022e13	1.71973
$979$	1.02560e13	0.356826
$980$	−1.89532e13	−0.656396
$981$	−7.69197e12	−0.265172
$982$	−2.36073e13	−0.810113
$983$	−5.68473e13	−1.94186	−0.970932	−	0.239355i	$-0.923064\pi$
$983$	−5.68473e13	−1.94186	−0.970932	+	0.239355i	$0.923064\pi$
$984$	7.45902e13	2.53632
$985$	7.44234e12	0.251911
$986$	4.58612e12	0.154525
$987$	−3.99996e13	−1.34162
$988$	−5.77246e12	−0.192732
$989$	−4.05599e13	−1.34807
$990$	8.88479e12	0.293960
$991$	4.32479e13	1.42440	0.712202	−	0.701974i	$-0.247698\pi$
$991$	4.32479e13	1.42440	0.712202	+	0.701974i	$0.247698\pi$
$992$	2.18942e12	0.0717837
$993$	6.26720e12	0.204551
$994$	−4.43844e13	−1.44209
$995$	3.81841e12	0.123503
$996$	2.43018e13	0.782476
$997$	5.30139e13	1.69927	0.849633	−	0.527374i	$-0.176823\pi$
$997$	5.30139e13	1.69927	0.849633	+	0.527374i	$0.176823\pi$
$998$	−4.45735e13	−1.42229
$999$	−1.76434e12	−0.0560450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.10.a.c.1.2	✓	2
3.2	odd	2		45.10.a.e.1.1		2
4.3	odd	2		240.10.a.m.1.2		2
5.2	odd	4		75.10.b.e.49.4		4
5.3	odd	4		75.10.b.e.49.1		4
5.4	even	2		75.10.a.g.1.1		2
15.2	even	4		225.10.b.g.199.1		4
15.8	even	4		225.10.b.g.199.4		4
15.14	odd	2		225.10.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.c.1.2	✓	2	1.1	even	1	trivial
45.10.a.e.1.1		2	3.2	odd	2
75.10.a.g.1.1		2	5.4	even	2
75.10.b.e.49.1		4	5.3	odd	4
75.10.b.e.49.4		4	5.2	odd	4
225.10.a.j.1.2		2	15.14	odd	2
225.10.b.g.199.1		4	15.2	even	4
225.10.b.g.199.4		4	15.8	even	4
240.10.a.m.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q+43.8839 q^{2} +81.0000 q^{3} +1413.79 q^{4} -625.000 q^{5} +3554.59 q^{6} -7861.50 q^{7} +39574.2 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+43.8839 q^{2} +81.0000 q^{3} +1413.79 q^{4} -625.000 q^{5} +3554.59 q^{6} -7861.50 q^{7} +39574.2 q^{8} +6561.00 q^{9} -27427.4 q^{10} -49373.3 q^{11} +114517. q^{12} +24250.7 q^{13} -344993. q^{14} -50625.0 q^{15} +1.01281e6 q^{16} +268222. q^{17} +287922. q^{18} -168364. q^{19} -883621. q^{20} -636781. q^{21} -2.16669e6 q^{22} -2.12200e6 q^{23} +3.20551e6 q^{24} +390625. q^{25} +1.06422e6 q^{26} +531441. q^{27} -1.11145e7 q^{28} +389624. q^{29} -2.22162e6 q^{30} +90532.2 q^{31} +2.41838e7 q^{32} -3.99924e6 q^{33} +1.17706e7 q^{34} +4.91344e6 q^{35} +9.27590e6 q^{36} -3.31991e6 q^{37} -7.38848e6 q^{38} +1.96431e6 q^{39} -2.47339e7 q^{40} +2.32694e7 q^{41} -2.79444e7 q^{42} +1.91140e7 q^{43} -6.98036e7 q^{44} -4.10062e6 q^{45} -9.31215e7 q^{46} +6.28153e7 q^{47} +8.20372e7 q^{48} +2.14495e7 q^{49} +1.71421e7 q^{50} +2.17260e7 q^{51} +3.42855e7 q^{52} -180207. q^{53} +2.33217e7 q^{54} +3.08583e7 q^{55} -3.11112e8 q^{56} -1.36375e7 q^{57} +1.70982e7 q^{58} +3.84564e7 q^{59} -7.15733e7 q^{60} -553620. q^{61} +3.97290e6 q^{62} -5.15793e7 q^{63} +5.42724e8 q^{64} -1.51567e7 q^{65} -1.75502e8 q^{66} -2.39163e8 q^{67} +3.79211e8 q^{68} -1.71882e8 q^{69} +2.15621e8 q^{70} +1.28653e8 q^{71} +2.59646e8 q^{72} -2.39376e8 q^{73} -1.45690e8 q^{74} +3.16406e7 q^{75} -2.38033e8 q^{76} +3.88148e8 q^{77} +8.62015e7 q^{78} -5.28027e8 q^{79} -6.33003e8 q^{80} +4.30467e7 q^{81} +1.02115e9 q^{82} +2.12210e8 q^{83} -9.00277e8 q^{84} -1.67639e8 q^{85} +8.38797e8 q^{86} +3.15595e7 q^{87} -1.95391e9 q^{88} -2.07724e8 q^{89} -1.79951e8 q^{90} -1.90647e8 q^{91} -3.00007e9 q^{92} +7.33311e6 q^{93} +2.75658e9 q^{94} +1.05228e8 q^{95} +1.95889e9 q^{96} +1.70780e9 q^{97} +9.41288e8 q^{98} -3.23938e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9	\( 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9} - 11875 q^{10} + 35488 q^{11} + 123201 q^{12} + 143676 q^{13} - 245196 q^{14} - 101250 q^{15} + 707265 q^{16} + 385156 q^{17} + 124659 q^{18} - 403296 q^{19} - 950625 q^{20} - 961632 q^{21} - 4278368 q^{22} + 223704 q^{23} + 4021407 q^{24} + 781250 q^{25} - 1907546 q^{26} + 1062882 q^{27} - 11544484 q^{28} - 74572 q^{29} - 961875 q^{30} - 5027128 q^{31} + 26629583 q^{32} + 2874528 q^{33} + 8860882 q^{34} + 7420000 q^{35} + 9979281 q^{36} + 5373628 q^{37} - 1542476 q^{38} + 11637756 q^{39} - 31029375 q^{40} + 14211332 q^{41} - 19860876 q^{42} + 27748920 q^{43} - 60705952 q^{44} - 8201250 q^{45} - 151491648 q^{46} + 95966440 q^{47} + 57288465 q^{48} - 2819950 q^{49} + 7421875 q^{50} + 31197636 q^{51} + 47088706 q^{52} - 64305596 q^{53} + 10097379 q^{54} - 22180000 q^{55} - 351509340 q^{56} - 32666976 q^{57} + 28649198 q^{58} + 187863136 q^{59} - 77000625 q^{60} + 154080060 q^{61} + 131320056 q^{62} - 77892192 q^{63} + 638301089 q^{64} - 89797500 q^{65} - 346547808 q^{66} + 33592376 q^{67} + 391747238 q^{68} + 18120024 q^{69} + 153247500 q^{70} - 228270976 q^{71} + 325733967 q^{72} - 33122316 q^{73} - 362019226 q^{74} + 63281250 q^{75} - 263218724 q^{76} + 47811456 q^{77} - 154511226 q^{78} - 932406760 q^{79} - 442040625 q^{80} + 86093442 q^{81} + 1246549646 q^{82} + 207040152 q^{83} - 935103204 q^{84} - 240722500 q^{85} + 623926708 q^{86} - 6040332 q^{87} - 1099114848 q^{88} + 224518164 q^{89} - 77911875 q^{90} - 669602528 q^{91} - 2748592992 q^{92} - 407197368 q^{93} + 1931650816 q^{94} + 252060000 q^{95} + 2156996223 q^{96} + 387134596 q^{97} + 1545205739 q^{98} + 232836768 q^{99}+O(q^{100}) \) 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9 - 11875 * q^10 + 35488 * q^11 + 123201 * q^12 + 143676 * q^13 - 245196 * q^14 - 101250 * q^15 + 707265 * q^16 + 385156 * q^17 + 124659 * q^18 - 403296 * q^19 - 950625 * q^20 - 961632 * q^21 - 4278368 * q^22 + 223704 * q^23 + 4021407 * q^24 + 781250 * q^25 - 1907546 * q^26 + 1062882 * q^27 - 11544484 * q^28 - 74572 * q^29 - 961875 * q^30 - 5027128 * q^31 + 26629583 * q^32 + 2874528 * q^33 + 8860882 * q^34 + 7420000 * q^35 + 9979281 * q^36 + 5373628 * q^37 - 1542476 * q^38 + 11637756 * q^39 - 31029375 * q^40 + 14211332 * q^41 - 19860876 * q^42 + 27748920 * q^43 - 60705952 * q^44 - 8201250 * q^45 - 151491648 * q^46 + 95966440 * q^47 + 57288465 * q^48 - 2819950 * q^49 + 7421875 * q^50 + 31197636 * q^51 + 47088706 * q^52 - 64305596 * q^53 + 10097379 * q^54 - 22180000 * q^55 - 351509340 * q^56 - 32666976 * q^57 + 28649198 * q^58 + 187863136 * q^59 - 77000625 * q^60 + 154080060 * q^61 + 131320056 * q^62 - 77892192 * q^63 + 638301089 * q^64 - 89797500 * q^65 - 346547808 * q^66 + 33592376 * q^67 + 391747238 * q^68 + 18120024 * q^69 + 153247500 * q^70 - 228270976 * q^71 + 325733967 * q^72 - 33122316 * q^73 - 362019226 * q^74 + 63281250 * q^75 - 263218724 * q^76 + 47811456 * q^77 - 154511226 * q^78 - 932406760 * q^79 - 442040625 * q^80 + 86093442 * q^81 + 1246549646 * q^82 + 207040152 * q^83 - 935103204 * q^84 - 240722500 * q^85 + 623926708 * q^86 - 6040332 * q^87 - 1099114848 * q^88 + 224518164 * q^89 - 77911875 * q^90 - 669602528 * q^91 - 2748592992 * q^92 - 407197368 * q^93 + 1931650816 * q^94 + 252060000 * q^95 + 2156996223 * q^96 + 387134596 * q^97 + 1545205739 * q^98 + 232836768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more